From bdd8c21fcfff8041ea94a972903ce42e58c2a5c2 Mon Sep 17 00:00:00 2001 From: ozpv <39195175+ozpv@users.noreply.github.com> Date: Sat, 29 Aug 2026 23:04:49 -0500 Subject: add retain --- Core/Inc/Effects/retain.h | 34 + Core/Inc/Effects/ringmod.h | 9 +- Core/Inc/cs4272.h | 21 +- Core/Src/Effects/retain.c | 256 + Core/Src/Effects/ringmod.c | 31 +- Core/Src/cs4272.c | 45 +- Core/Src/main.c | 3 + Middlewares/ST/ARM/DSP/Inc/arm_math.h | 8970 ++++ .../Include/arm_common_tables.h | 318 + .../Include/arm_common_tables_f16.h | 95 + .../Include/arm_const_structs.h | 86 + .../Include/arm_const_structs_f16.h | 59 + .../Include/arm_helium_utils.h | 749 + .../ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math.h | 80 + .../ARM.CMSIS-DSP.1.17.1/Include/arm_math_f16.h | 59 + .../ARM.CMSIS-DSP.1.17.1/Include/arm_math_memory.h | 224 + .../ARM.CMSIS-DSP.1.17.1/Include/arm_math_types.h | 729 + .../Include/arm_math_types_f16.h | 163 + .../ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables.h | 193 + 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.../Include/dsp/interpolation_functions.h | 275 + .../Include/dsp/interpolation_functions_f16.h | 109 + .../Include/dsp/matrix_functions.h | 871 + .../Include/dsp/matrix_functions_f16.h | 260 + .../Include/dsp/matrix_utils.h | 649 + .../ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/none.h | 576 + .../Include/dsp/quaternion_math_functions.h | 153 + .../Include/dsp/statistics_functions.h | 988 + .../Include/dsp/statistics_functions_f16.h | 274 + .../Include/dsp/support_functions.h | 539 + .../Include/dsp/support_functions_f16.h | 204 + .../ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_defines.h | 46 + .../Include/dsp/svm_functions.h | 280 + .../Include/dsp/svm_functions_f16.h | 265 + .../Include/dsp/transform_functions.h | 1408 + .../Include/dsp/transform_functions_f16.h | 383 + .../ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/utils.h | 272 + .../Include/dsp/window_functions.h | 812 + .../Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/LICENSE | 201 + .../PrivateInclude/arm_compiler_specific.h | 20 + 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.../Source/TransformFunctions/arm_mfcc_f16.c | 181 + .../Source/TransformFunctions/arm_mfcc_f32.c | 181 + .../Source/TransformFunctions/arm_mfcc_init_f16.c | 419 + .../Source/TransformFunctions/arm_mfcc_init_f32.c | 418 + .../Source/TransformFunctions/arm_mfcc_init_q15.c | 432 + .../Source/TransformFunctions/arm_mfcc_init_q31.c | 435 + .../Source/TransformFunctions/arm_mfcc_q15.c | 234 + .../Source/TransformFunctions/arm_mfcc_q31.c | 233 + .../Source/TransformFunctions/arm_rfft_fast_f16.c | 556 + .../Source/TransformFunctions/arm_rfft_fast_f32.c | 706 + .../Source/TransformFunctions/arm_rfft_fast_f64.c | 236 + .../TransformFunctions/arm_rfft_fast_init_f16.c | 407 + .../TransformFunctions/arm_rfft_fast_init_f32.c | 386 + .../TransformFunctions/arm_rfft_fast_init_f64.c | 328 + .../Source/TransformFunctions/arm_rfft_init_q15.c | 487 + .../Source/TransformFunctions/arm_rfft_init_q31.c | 482 + .../Source/TransformFunctions/arm_rfft_q15.c | 585 + .../Source/TransformFunctions/arm_rfft_q31.c | 481 + .../arm_transform_buffer_sizes.c | 346 + .../Source/WindowFunctions/arm_bartlett_f32.c | 95 + .../Source/WindowFunctions/arm_bartlett_f64.c | 91 + .../WindowFunctions/arm_blackman_harris_92db_f32.c | 95 + .../WindowFunctions/arm_blackman_harris_92db_f64.c | 91 + .../Source/WindowFunctions/arm_hamming_f32.c | 92 + .../Source/WindowFunctions/arm_hamming_f64.c | 89 + .../Source/WindowFunctions/arm_hanning_f32.c | 94 + .../Source/WindowFunctions/arm_hanning_f64.c | 90 + .../Source/WindowFunctions/arm_hft116d_f32.c | 114 + .../Source/WindowFunctions/arm_hft116d_f64.c | 110 + .../Source/WindowFunctions/arm_hft144d_f32.c | 114 + .../Source/WindowFunctions/arm_hft144d_f64.c | 110 + .../Source/WindowFunctions/arm_hft169d_f32.c | 115 + .../Source/WindowFunctions/arm_hft169d_f64.c | 111 + .../Source/WindowFunctions/arm_hft196d_f32.c | 116 + .../Source/WindowFunctions/arm_hft196d_f64.c | 112 + .../Source/WindowFunctions/arm_hft223d_f32.c | 116 + .../Source/WindowFunctions/arm_hft223d_f64.c | 113 + .../Source/WindowFunctions/arm_hft248d_f32.c | 118 + .../Source/WindowFunctions/arm_hft248d_f64.c | 114 + .../Source/WindowFunctions/arm_hft90d_f32.c | 113 + .../Source/WindowFunctions/arm_hft90d_f64.c | 120 + .../Source/WindowFunctions/arm_hft95_f32.c | 113 + .../Source/WindowFunctions/arm_hft95_f64.c | 109 + .../Source/WindowFunctions/arm_nuttall3_f32.c | 93 + .../Source/WindowFunctions/arm_nuttall3_f64.c | 90 + .../Source/WindowFunctions/arm_nuttall3a_f32.c | 95 + .../Source/WindowFunctions/arm_nuttall3a_f64.c | 91 + .../Source/WindowFunctions/arm_nuttall3b_f32.c | 95 + .../Source/WindowFunctions/arm_nuttall3b_f64.c | 91 + .../Source/WindowFunctions/arm_nuttall4_f32.c | 95 + .../Source/WindowFunctions/arm_nuttall4_f64.c | 91 + .../Source/WindowFunctions/arm_nuttall4a_f32.c | 96 + .../Source/WindowFunctions/arm_nuttall4a_f64.c | 92 + .../Source/WindowFunctions/arm_nuttall4b_f32.c | 96 + .../Source/WindowFunctions/arm_nuttall4b_f64.c | 92 + .../Source/WindowFunctions/arm_nuttall4c_f32.c | 95 + .../Source/WindowFunctions/arm_nuttall4c_f64.c | 91 + .../Source/WindowFunctions/arm_welch_f32.c | 92 + .../Source/WindowFunctions/arm_welch_f64.c | 97 + Middlewares/Third_Party/ARM/DSP/LICENSE.txt | 201 + STM32H750ZBTX_FLASH.ld | 12 +- audio.ioc | 189 +- 215 files changed, 184118 insertions(+), 155 deletions(-) create mode 100755 Core/Inc/Effects/retain.h create mode 100755 Core/Src/Effects/retain.c create mode 100755 Middlewares/ST/ARM/DSP/Inc/arm_math.h create mode 100755 Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables.h create mode 100755 Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables_f16.h create mode 100755 Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs.h create mode 100755 Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs_f16.h create mode 100755 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retain.h + * + * Created on: Aug 23, 2026 + * Author: ozpv + */ + +#ifndef INC_EFFECTS_RETAIN_H_ +#define INC_EFFECTS_RETAIN_H_ + +#include +#include +#include "cs4272.h" + +/* must be a power of two + higher values give better frequency resolution + and must be paired with a higher BUFFER_SIZE */ +#define WINDOW_SIZE 4096 +/* change based on necessary overlap */ +#define HOP_SIZE (WINDOW_SIZE / 4) +#define OVERLAP_SIZE (WINDOW_SIZE - HOP_SIZE) +#define NUM_OVERLAPS (WINDOW_SIZE / HOP_SIZE) +#define COMPLEX_BIN_COUNT (WINDOW_SIZE / 2 - 1) + +void retain_init(void); +void retain( + const int32_t *samples_in, + int32_t *samples_out, + const size_t range_min, + const size_t range_max, + const enum Channel channel +); + +#endif /* INC_EFFECTS_RETAIN_H_ */ diff --git a/Core/Inc/Effects/ringmod.h b/Core/Inc/Effects/ringmod.h index 516ca6c..766fad4 100755 --- a/Core/Inc/Effects/ringmod.h +++ b/Core/Inc/Effects/ringmod.h @@ -20,6 +20,13 @@ typedef struct RingModParams { bool square_lfo; } RingModParams; -void ringmod(float *samples, const size_t range_min, const size_t range_max, const struct RingModParams *params); +void ringmod( + const struct RingModParams *params, + const int32_t *samples_in, + int32_t *samples_out, + const size_t range_min, + const size_t range_max, + const enum Channel channel +); #endif /* INC_EFFECTS_RINGMOD_H_ */ diff --git a/Core/Inc/cs4272.h b/Core/Inc/cs4272.h index 423b7c0..4e22263 100755 --- a/Core/Inc/cs4272.h +++ b/Core/Inc/cs4272.h @@ -26,16 +26,27 @@ #define CS4272_I2C_ADDR (0b0010000 << 1) #define SAMPLE_RATE 48000 -#define BUFFER_SIZE 512 +#define BUFFER_SIZE 1024 -extern volatile int32_t rx_buffer[BUFFER_SIZE]; -extern volatile int32_t tx_buffer[BUFFER_SIZE]; -extern volatile float samples[BUFFER_SIZE]; +typedef enum Channel { + LEFT = 0, + RIGHT = 1, + MONO = 0, +} Channel; + +extern int32_t rx_buffer[BUFFER_SIZE]; +extern int32_t tx_buffer[BUFFER_SIZE]; extern const uint8_t CS4272_CONFIG[7]; uint8_t CS4272_Init(void); -#define INT24_MAX 0x7FFFFF +static inline __attribute__((always_inline)) float int24_t_to_f32(const int32_t in) { + return ((float)(in << 8)) / ((float)INT32_MAX); +} + +static inline __attribute__((always_inline)) int32_t f32_to_int24_t(const float in) { + return ((int32_t)(in * ((float)INT32_MAX))) >> 8; +} #endif /* INC_CS4272_H_ */ diff --git a/Core/Src/Effects/retain.c b/Core/Src/Effects/retain.c new file mode 100755 index 0000000..9b3acbe --- /dev/null +++ b/Core/Src/Effects/retain.c @@ -0,0 +1,256 @@ +/* + * retain.c + * + * Created on: Aug 23, 2026 + * Author: ozpv + */ + +#include "retain.h" +#include "arm_math.h" + +__attribute__((section(".audio_buffers"))) static float input[WINDOW_SIZE]; +static size_t input_position; +static size_t samples_since_frame; + +__attribute__((section(".RAM_D2"))) static float window_function[WINDOW_SIZE]; +__attribute__((section(".RAM_D2"))) static float normalize[HOP_SIZE]; + +__attribute__((section(".audio_buffers"))) static float fft_input[WINDOW_SIZE]; + +__attribute__((section(".audio_buffers"))) static float spectral[WINDOW_SIZE]; + +__attribute__((section(".RAM_D2"))) static float output[WINDOW_SIZE]; + +__attribute__((section(".RAM_D2"))) static float output_history[OVERLAP_SIZE]; +static size_t output_position; + +__attribute__((section(".RAM_D2"))) static float retain_scratch[COMPLEX_BIN_COUNT]; + +static arm_rfft_fast_instance_f32 fft_instance; + +static inline void create_normalize_buffer(float *out, const float *function, const size_t window_size, const size_t hop_size) { + const size_t num_overlaps = window_size / hop_size; + + for (size_t i = 0; i < hop_size; ++i) { + float sum = 0.0f; + + for (size_t j = 0; j < num_overlaps; ++j) { + const float w = function[i + j * hop_size]; + + sum += w * w; + } + + out[i] = sum; + } +} + +void retain_init(void) { + arm_blackman_harris_92db_f32(window_function, WINDOW_SIZE); + + create_normalize_buffer(normalize, window_function, WINDOW_SIZE, HOP_SIZE); + + arm_rfft_fast_init_f32(&fft_instance, WINDOW_SIZE); + + for (size_t i = 0; i < WINDOW_SIZE; ++i) { + input[i] = 0.0f; + fft_input[i] = 0.0f; + output[i] = 0.0f; + spectral[i] = 0.0f; + } + + for (size_t i = 0; i < OVERLAP_SIZE; ++i) { + output_history[i] = 0.0f; + } + + input_position = 0; + samples_since_frame = 0; + output_position = 0; +} + +static inline float select_nth_largest(float *x, const size_t len, const size_t n) { + size_t left = 0; + size_t right = len - 1; + size_t target = n - 1; + + while (left < right) { + size_t mid = left + ((right - left) >> 1); + float a = x[left]; + float b = x[mid]; + float c = x[right]; + float pivot; + + if (a < b) { + if (b < c) { + pivot = b; + } else if (a < c) { + pivot = c; + } else { + pivot = a; + } + } else { + if (a < c) { + pivot = a; + } else if (b < c) { + pivot = c; + } else { + pivot = b; + } + } + + size_t i = left; + size_t j = right; + + while (i <= j) { + while (x[i] > pivot) { + ++i; + } + + while (x[j] < pivot) { + --j; + } + + if (i <= j) { + float t = x[i]; + x[i] = x[j]; + x[j] = t; + + ++i; + --j; + } + } + + if (target <= j) { + right = j; + } else if (target >= i) { + left = i; + } else { + break; + } + } + + return x[target]; +} + +static inline void process(float *spectral, const size_t n) { + if (n == 0) { + for (size_t bin = 1; bin < WINDOW_SIZE / 2; ++bin) { + const size_t i = 2 * bin; + + spectral[i] = 0.0f; + spectral[i + 1] = 0.0f; + } + + return; + } + + if (n >= COMPLEX_BIN_COUNT) { + return; + } + + for (size_t bin = 1; bin < WINDOW_SIZE / 2; ++bin) { + const size_t i = 2 * bin; + + const float re = spectral[i]; + const float im = spectral[i + 1]; + + retain_scratch[bin - 1] = re * re + im * im; + } + + const float threshold = select_nth_largest(retain_scratch, COMPLEX_BIN_COUNT, n); + + for (size_t bin = 1; bin < WINDOW_SIZE / 2; ++bin) { + const size_t i = 2 * bin; + + const float re = spectral[i]; + const float im = spectral[i + 1]; + + const float mag2 = re * re + im * im; + + if (mag2 < threshold) { + spectral[i] = 0.0f; + spectral[i + 1] = 0.0f; + } + } +} + +static inline void process_frame(void) { + /* build a contiguous FFT frame */ + size_t src = input_position; + for (size_t i = 0; i < WINDOW_SIZE; ++i) { + fft_input[i] = input[src]; + + ++src; + + if (src == WINDOW_SIZE) { + src = 0; + } + } + + /* apply window function */ + for (size_t i = 0; i < WINDOW_SIZE; ++i) { + fft_input[i] *= window_function[i]; + } + + /* forward FFT */ + arm_rfft_fast_f32(&fft_instance, fft_input, spectral, 0); + + process(spectral, 5); + + /* inverse FFT */ + arm_rfft_fast_f32(&fft_instance, spectral, output, 1); + + /* synthesis window because of heavy processing */ + for (size_t i = 0; i < WINDOW_SIZE; ++i) { + output[i] *= window_function[i]; + } + + /* overlap add */ + for (size_t i = 0; i < OVERLAP_SIZE; ++i) { + output[i] += output_history[i]; + } + + /* save future overlap */ + for (size_t i = 0; i < OVERLAP_SIZE; ++i) { + output_history[i] = output[i + HOP_SIZE]; + } + + /* normalize output samples */ + for (size_t i = 0; i < HOP_SIZE; ++i) { + output[i] /= normalize[i]; + } + + output_position = 0; + samples_since_frame = 0; +} + +inline void retain( + const int32_t *samples_in, + int32_t *samples_out, + const size_t range_min, + const size_t range_max, + const enum Channel channel +) { + for (size_t i = range_min + channel; i < range_max; i += 2) { + input[input_position] = int24_t_to_f32(samples_in[i]); + + ++input_position; + + if (input_position == WINDOW_SIZE) { + input_position = 0; + } + + ++samples_since_frame; + + if (samples_since_frame == HOP_SIZE) { + process_frame(); + } + + samples_out[i] = f32_to_int24_t(output[output_position]); + + ++output_position; + + if (output_position == HOP_SIZE) { + output_position = 0; + } + } +} diff --git a/Core/Src/Effects/ringmod.c b/Core/Src/Effects/ringmod.c index 1b411dc..be58c11 100755 --- a/Core/Src/Effects/ringmod.c +++ b/Core/Src/Effects/ringmod.c @@ -7,11 +7,17 @@ #include "cs4272.h" #include "ringmod.h" -#include -#include +#include "arm_math.h" /* MF-102S ring modulator */ -void ringmod(float *samples, const size_t range_min, const size_t range_max, const struct RingModParams *params) { +void ringmod( + const struct RingModParams *params, + const int32_t *samples_in, + int32_t *samples_out, + const size_t range_min, + const size_t range_max, + const enum Channel channel +) { static float lfo_phase = 0.0f; static float carrier_phase = 0.0f; @@ -19,23 +25,30 @@ void ringmod(float *samples, const size_t range_min, const size_t range_max, con const float inverse_sample_rate = 1.0f / sample_rate; /* samples are interleaved */ - for (size_t i = range_min; i < range_max; i += 2) { + for (size_t i = range_min + channel; i < range_max; i += 2) { + float sample = int24_t_to_f32(samples_in[i]); + float frequency_lfo = 0.0f; if (params->square_lfo) { frequency_lfo = (lfo_phase < 0.5f) ? params->lfo_amount : -params->lfo_amount; } else { - frequency_lfo = params->lfo_amount * sinf(M_TWOPI * lfo_phase); + frequency_lfo = params->lfo_amount * arm_sin_f32(M_TWOPI * lfo_phase); } - float carrier = sinf(M_TWOPI * carrier_phase); + float carrier = arm_sin_f32(M_TWOPI * carrier_phase); - samples[i] = (samples[i] * (1.0f - params->mix)) + (samples[i] * carrier * params->mix); + float output_sample = (sample * (1.0f - params->mix)) + (sample * carrier * params->mix); + samples_out[i] = f32_to_int24_t(output_sample); lfo_phase += params->lfo_rate * inverse_sample_rate; - lfo_phase = fmod(lfo_phase, 1.0f); + while (lfo_phase >= 1.0f) { + lfo_phase -= 1.0f; + } carrier_phase += (params->frequency + frequency_lfo) * inverse_sample_rate; - carrier_phase = fmod(carrier_phase, 1.0f); + while (carrier_phase >= 1.0f) { + carrier_phase -= 1.0f; + } } } diff --git a/Core/Src/cs4272.c b/Core/Src/cs4272.c index 9a7f0d1..8ba9885 100755 --- a/Core/Src/cs4272.c +++ b/Core/Src/cs4272.c @@ -8,18 +8,10 @@ #include "i2c.h" #include "cs4272.h" #include "ringmod.h" +#include "retain.h" -const struct RingModParams params = { - 0.40f, - 156.0f, - 6.90f, - 0.18f, - true, -}; - -volatile int32_t rx_buffer[BUFFER_SIZE] __attribute__((section(".audio_buffers"))); -volatile int32_t tx_buffer[BUFFER_SIZE] __attribute__((section(".audio_buffers"))); -volatile float samples[BUFFER_SIZE] __attribute__((section(".sdram"))); +__attribute__((section(".audio_buffers"))) int32_t rx_buffer[BUFFER_SIZE]; +__attribute__((section(".audio_buffers"))) int32_t tx_buffer[BUFFER_SIZE]; const uint8_t CS4272_CONFIG[7] = { /* MODE CONTROL 1 @@ -58,35 +50,22 @@ const uint8_t CS4272_CONFIG[7] = { 0b00000010, }; -inline void int32_t_to_float(int32_t *in, float *out, const size_t range_min, const size_t range_max) { - for (size_t i = range_min; i < range_max; ++i) { - out[i] = ((float)(in[i] << 8)) / ((float)INT32_MAX); - } -} - -inline void float_to_int32_t(float *in, int32_t *out, const size_t range_min, const size_t range_max) { - for (size_t i = range_min; i < range_max; ++i) { - out[i] = ((int32_t)(in[i] * ((float)INT32_MAX))) >> 8; - } -} +//const struct RingModParams params = { +// 0.40f, +// 156.0f, +// 16.90f, +// 0.18f, +// false, +//}; void HAL_SAI_RxHalfCpltCallback(SAI_HandleTypeDef *hsai) { - int32_t_to_float((int32_t *)rx_buffer, (float *)samples, 0, BUFFER_SIZE / 2); - - ringmod((float *)samples, 0, BUFFER_SIZE / 2, ¶ms); - - float_to_int32_t((float *)samples, (int32_t *)tx_buffer, 0, BUFFER_SIZE / 2); + retain(rx_buffer, tx_buffer, 0, BUFFER_SIZE / 2, MONO); } void HAL_SAI_RxCpltCallback(SAI_HandleTypeDef *hsai) { - int32_t_to_float((int32_t *)rx_buffer, (float *)samples, BUFFER_SIZE / 2, BUFFER_SIZE); - - ringmod((float *)samples, BUFFER_SIZE / 2, BUFFER_SIZE, ¶ms); - - float_to_int32_t((float *)samples, (int32_t *)tx_buffer, BUFFER_SIZE / 2, BUFFER_SIZE); + retain(rx_buffer, tx_buffer, BUFFER_SIZE / 2, BUFFER_SIZE, MONO); } - HAL_StatusTypeDef CS4272_ReadRegister(const uint8_t addr, uint8_t *data) { return HAL_I2C_Mem_Read(&hi2c4, CS4272_I2C_ADDR, addr, I2C_MEMADD_SIZE_8BIT, data, 1, HAL_MAX_DELAY); } diff --git a/Core/Src/main.c b/Core/Src/main.c index f7fdeac..1b3ef91 100755 --- a/Core/Src/main.c +++ b/Core/Src/main.c @@ -30,6 +30,7 @@ /* USER CODE BEGIN Includes */ #include "cs4272.h" #include "w9825g6kh6.h" +#include "retain.h" /* USER CODE END Includes */ /* Private typedef -----------------------------------------------------------*/ @@ -123,6 +124,8 @@ int main(void) FMC_Init(); //SDRAM_Test(); + retain_init(); + __HAL_RCC_SAI1_CLK_ENABLE(); __HAL_SAI_ENABLE(&hsai_BlockA1); diff --git a/Middlewares/ST/ARM/DSP/Inc/arm_math.h b/Middlewares/ST/ARM/DSP/Inc/arm_math.h new file mode 100755 index 0000000..8daa218 --- /dev/null +++ b/Middlewares/ST/ARM/DSP/Inc/arm_math.h @@ -0,0 +1,8970 @@ +/****************************************************************************** + * @file arm_math.h + * @brief Public header file for CMSIS DSP Library + * @version V1.7.0 + * @date 18. March 2019 + ******************************************************************************/ +/* + * Copyright (c) 2010-2019 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/** + \mainpage CMSIS DSP Software Library + * + * Introduction + * ------------ + * + * This user manual describes the CMSIS DSP software library, + * a suite of common signal processing functions for use on Cortex-M and Cortex-A processor + * based devices. + * + * The library is divided into a number of functions each covering a specific category: + * - Basic math functions + * - Fast math functions + * - Complex math functions + * - Filtering functions + * - Matrix functions + * - Transform functions + * - Motor control functions + * - Statistical functions + * - Support functions + * - Interpolation functions + * - Support Vector Machine functions (SVM) + * - Bayes classifier functions + * - Distance functions + * + * The library has generally separate functions for operating on 8-bit integers, 16-bit integers, + * 32-bit integer and 32-bit floating-point values. + * + * Using the Library + * ------------ + * + * The library installer contains prebuilt versions of the libraries in the Lib folder. + * + * Here is the list of pre-built libraries : + * - arm_cortexM7lfdp_math.lib (Cortex-M7, Little endian, Double Precision Floating Point Unit) + * - arm_cortexM7bfdp_math.lib (Cortex-M7, Big endian, Double Precision Floating Point Unit) + * - arm_cortexM7lfsp_math.lib (Cortex-M7, Little endian, Single Precision Floating Point Unit) + * - arm_cortexM7bfsp_math.lib (Cortex-M7, Big endian and Single Precision Floating Point Unit on) + * - arm_cortexM7l_math.lib (Cortex-M7, Little endian) + * - arm_cortexM7b_math.lib (Cortex-M7, Big endian) + * - arm_cortexM4lf_math.lib (Cortex-M4, Little endian, Floating Point Unit) + * - arm_cortexM4bf_math.lib (Cortex-M4, Big endian, Floating Point Unit) + * - arm_cortexM4l_math.lib (Cortex-M4, Little endian) + * - arm_cortexM4b_math.lib (Cortex-M4, Big endian) + * - arm_cortexM3l_math.lib (Cortex-M3, Little endian) + * - arm_cortexM3b_math.lib (Cortex-M3, Big endian) + * - arm_cortexM0l_math.lib (Cortex-M0 / Cortex-M0+, Little endian) + * - arm_cortexM0b_math.lib (Cortex-M0 / Cortex-M0+, Big endian) + * - arm_ARMv8MBLl_math.lib (Armv8-M Baseline, Little endian) + * - arm_ARMv8MMLl_math.lib (Armv8-M Mainline, Little endian) + * - arm_ARMv8MMLlfsp_math.lib (Armv8-M Mainline, Little endian, Single Precision Floating Point Unit) + * - arm_ARMv8MMLld_math.lib (Armv8-M Mainline, Little endian, DSP instructions) + * - arm_ARMv8MMLldfsp_math.lib (Armv8-M Mainline, Little endian, DSP instructions, Single Precision Floating Point Unit) + * + * The library functions are declared in the public file arm_math.h which is placed in the Include folder. + * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single + * public header file arm_math.h for Cortex-M cores with little endian and big endian. Same header file will be used for floating point unit(FPU) variants. + * + * + * Examples + * -------- + * + * The library ships with a number of examples which demonstrate how to use the library functions. + * + * Toolchain Support + * ------------ + * + * The library is now tested on Fast Models building with cmake. + * Core M0, M7, A5 are tested. + * + * + * + * Building the Library + * ------------ + * + * The library installer contains a project file to rebuild libraries on MDK toolchain in the CMSIS\\DSP\\Projects\\ARM folder. + * - arm_cortexM_math.uvprojx + * + * + * The libraries can be built by opening the arm_cortexM_math.uvprojx project in MDK-ARM, selecting a specific target, and defining the optional preprocessor macros detailed above. + * + * There is also a work in progress cmake build. The README file is giving more details. + * + * Preprocessor Macros + * ------------ + * + * Each library project have different preprocessor macros. + * + * - ARM_MATH_BIG_ENDIAN: + * + * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets. + * + * - ARM_MATH_MATRIX_CHECK: + * + * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices + * + * - ARM_MATH_ROUNDING: + * + * Define macro ARM_MATH_ROUNDING for rounding on support functions + * + * - ARM_MATH_LOOPUNROLL: + * + * Define macro ARM_MATH_LOOPUNROLL to enable manual loop unrolling in DSP functions + * + * - ARM_MATH_NEON: + * + * Define macro ARM_MATH_NEON to enable Neon versions of the DSP functions. + * It is not enabled by default when Neon is available because performances are + * dependent on the compiler and target architecture. + * + * - ARM_MATH_NEON_EXPERIMENTAL: + * + * Define macro ARM_MATH_NEON_EXPERIMENTAL to enable experimental Neon versions of + * of some DSP functions. Experimental Neon versions currently do not have better + * performances than the scalar versions. + * + * - ARM_MATH_HELIUM: + * + * It implies the flags ARM_MATH_MVEF and ARM_MATH_MVEI and ARM_MATH_FLOAT16. + * + * - ARM_MATH_MVEF: + * + * Select Helium versions of the f32 algorithms. + * It implies ARM_MATH_FLOAT16 and ARM_MATH_MVEI. + * + * - ARM_MATH_MVEI: + * + * Select Helium versions of the int and fixed point algorithms. + * + * - ARM_MATH_FLOAT16: + * + * Float16 implementations of some algorithms (Requires MVE extension). + * + *
+ * CMSIS-DSP in ARM::CMSIS Pack + * ----------------------------- + * + * The following files relevant to CMSIS-DSP are present in the ARM::CMSIS Pack directories: + * |File/Folder |Content | + * |---------------------------------|------------------------------------------------------------------------| + * |\b CMSIS\\Documentation\\DSP | This documentation | + * |\b CMSIS\\DSP\\DSP_Lib_TestSuite | DSP_Lib test suite | + * |\b CMSIS\\DSP\\Examples | Example projects demonstrating the usage of the library functions | + * |\b CMSIS\\DSP\\Include | DSP_Lib include files | + * |\b CMSIS\\DSP\\Lib | DSP_Lib binaries | + * |\b CMSIS\\DSP\\Projects | Projects to rebuild DSP_Lib binaries | + * |\b CMSIS\\DSP\\Source | DSP_Lib source files | + * + *
+ * Revision History of CMSIS-DSP + * ------------ + * Please refer to \ref ChangeLog_pg. + */ + + +/** + * @defgroup groupMath Basic Math Functions + */ + +/** + * @defgroup groupFastMath Fast Math Functions + * This set of functions provides a fast approximation to sine, cosine, and square root. + * As compared to most of the other functions in the CMSIS math library, the fast math functions + * operate on individual values and not arrays. + * There are separate functions for Q15, Q31, and floating-point data. + * + */ + +/** + * @defgroup groupCmplxMath Complex Math Functions + * This set of functions operates on complex data vectors. + * The data in the complex arrays is stored in an interleaved fashion + * (real, imag, real, imag, ...). + * In the API functions, the number of samples in a complex array refers + * to the number of complex values; the array contains twice this number of + * real values. + */ + +/** + * @defgroup groupFilters Filtering Functions + */ + +/** + * @defgroup groupMatrix Matrix Functions + * + * This set of functions provides basic matrix math operations. + * The functions operate on matrix data structures. For example, + * the type + * definition for the floating-point matrix structure is shown + * below: + * 
+ *     typedef struct
+ *     {
+ *       uint16_t numRows;     // number of rows of the matrix.
+ *       uint16_t numCols;     // number of columns of the matrix.
+ *       float32_t *pData;     // points to the data of the matrix.
+ *     } arm_matrix_instance_f32;
+ *
+ * There are similar definitions for Q15 and Q31 data types. + * + * The structure specifies the size of the matrix and then points to + * an array of data. The array is of size numRows X numCols + * and the values are arranged in row order. That is, the + * matrix element (i, j) is stored at: + * 
+ *     pData[i*numCols + j]
+ *
+ * + * \par Init Functions + * There is an associated initialization function for each type of matrix + * data structure. + * The initialization function sets the values of the internal structure fields. + * Refer to \ref arm_mat_init_f32(), \ref arm_mat_init_q31() and \ref arm_mat_init_q15() + * for floating-point, Q31 and Q15 types, respectively. + * + * \par + * Use of the initialization function is optional. However, if initialization function is used + * then the instance structure cannot be placed into a const data section. + * To place the instance structure in a const data + * section, manually initialize the data structure. For example: + * 
+ * arm_matrix_instance_f32 S = {nRows, nColumns, pData};
+ * arm_matrix_instance_q31 S = {nRows, nColumns, pData};
+ * arm_matrix_instance_q15 S = {nRows, nColumns, pData};
+ *
+ * where nRows specifies the number of rows, nColumns + * specifies the number of columns, and pData points to the + * data array. + * + * \par Size Checking + * By default all of the matrix functions perform size checking on the input and + * output matrices. For example, the matrix addition function verifies that the + * two input matrices and the output matrix all have the same number of rows and + * columns. If the size check fails the functions return: + * 
+ *     ARM_MATH_SIZE_MISMATCH
+ *
+ * Otherwise the functions return + * 
+ *     ARM_MATH_SUCCESS
+ *
+ * There is some overhead associated with this matrix size checking. + * The matrix size checking is enabled via the \#define + * 
+ *     ARM_MATH_MATRIX_CHECK
+ *
+ * within the library project settings. By default this macro is defined + * and size checking is enabled. By changing the project settings and + * undefining this macro size checking is eliminated and the functions + * run a bit faster. With size checking disabled the functions always + * return ARM_MATH_SUCCESS. + */ + +/** + * @defgroup groupTransforms Transform Functions + */ + +/** + * @defgroup groupController Controller Functions + */ + +/** + * @defgroup groupStats Statistics Functions + */ + +/** + * @defgroup groupSupport Support Functions + */ + +/** + * @defgroup groupInterpolation Interpolation Functions + * These functions perform 1- and 2-dimensional interpolation of data. + * Linear interpolation is used for 1-dimensional data and + * bilinear interpolation is used for 2-dimensional data. + */ + +/** + * @defgroup groupExamples Examples + */ + +/** + * @defgroup groupSVM SVM Functions + * This set of functions is implementing SVM classification on 2 classes. + * The training must be done from scikit-learn. The parameters can be easily + * generated from the scikit-learn object. Some examples are given in + * DSP/Testing/PatternGeneration/SVM.py + * + * If more than 2 classes are needed, the functions in this folder + * will have to be used, as building blocks, to do multi-class classification. + * + * No multi-class classification is provided in this SVM folder. + * + */ + + +/** + * @defgroup groupBayes Bayesian estimators + * + * Implement the naive gaussian Bayes estimator. + * The training must be done from scikit-learn. + * + * The parameters can be easily + * generated from the scikit-learn object. Some examples are given in + * DSP/Testing/PatternGeneration/Bayes.py + */ + +/** + * @defgroup groupDistance Distance functions + * + * Distance functions for use with clustering algorithms. + * There are distance functions for float vectors and boolean vectors. + * + */ + + +#ifndef _ARM_MATH_H +#define _ARM_MATH_H + +#ifdef __cplusplus +extern "C" +{ +#endif + +/* Compiler specific diagnostic adjustment */ +#if defined ( __CC_ARM ) + +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + +#elif defined ( __GNUC__ ) + #pragma GCC diagnostic push + #pragma GCC diagnostic ignored "-Wsign-conversion" + #pragma GCC diagnostic ignored "-Wconversion" + #pragma GCC diagnostic ignored "-Wunused-parameter" + +#elif defined ( __ICCARM__ ) + +#elif defined ( __TI_ARM__ ) + +#elif defined ( __CSMC__ ) + +#elif defined ( __TASKING__ ) + +#elif defined ( _MSC_VER ) + +#else + #error Unknown compiler +#endif + + +/* Included for instrinsics definitions */ +#if defined (_MSC_VER ) +#include +#define __STATIC_FORCEINLINE static __forceinline +#define __STATIC_INLINE static __inline +#define __ALIGNED(x) __declspec(align(x)) + +#elif defined (__GNUC_PYTHON__) +#include +#define __ALIGNED(x) __attribute__((aligned(x))) +#define __STATIC_FORCEINLINE static __attribute__((inline)) +#define __STATIC_INLINE static __attribute__((inline)) +#pragma GCC diagnostic ignored "-Wunused-function" +#pragma GCC diagnostic ignored "-Wattributes" + +#else +#include "cmsis_compiler.h" +#endif + + + +#include +#include +#include +#include + + +#define F64_MAX ((float64_t)DBL_MAX) +#define F32_MAX ((float32_t)FLT_MAX) + +#if defined(ARM_MATH_FLOAT16) +#define F16_MAX ((float16_t)FLT_MAX) +#endif + +#define F64_MIN (-DBL_MAX) +#define F32_MIN (-FLT_MAX) + +#if defined(ARM_MATH_FLOAT16) +#define F16_MIN (-(float16_t)FLT_MAX) +#endif + +#define F64_ABSMAX ((float64_t)DBL_MAX) +#define F32_ABSMAX ((float32_t)FLT_MAX) + +#if defined(ARM_MATH_FLOAT16) +#define F16_ABSMAX ((float16_t)FLT_MAX) +#endif + +#define F64_ABSMIN ((float64_t)0.0) +#define F32_ABSMIN ((float32_t)0.0) + +#if defined(ARM_MATH_FLOAT16) +#define F16_ABSMIN ((float16_t)0.0) +#endif + +#define Q31_MAX ((q31_t)(0x7FFFFFFFL)) +#define Q15_MAX ((q15_t)(0x7FFF)) +#define Q7_MAX ((q7_t)(0x7F)) +#define Q31_MIN ((q31_t)(0x80000000L)) +#define Q15_MIN ((q15_t)(0x8000)) +#define Q7_MIN ((q7_t)(0x80)) + +#define Q31_ABSMAX ((q31_t)(0x7FFFFFFFL)) +#define Q15_ABSMAX ((q15_t)(0x7FFF)) +#define Q7_ABSMAX ((q7_t)(0x7F)) +#define Q31_ABSMIN ((q31_t)0) +#define Q15_ABSMIN ((q15_t)0) +#define Q7_ABSMIN ((q7_t)0) + +/* evaluate ARM DSP feature */ +#if (defined (__ARM_FEATURE_DSP) && (__ARM_FEATURE_DSP == 1)) + #define ARM_MATH_DSP 1 +#endif + +#if defined(ARM_MATH_NEON) +#include +#endif + +#if defined (ARM_MATH_HELIUM) + #define ARM_MATH_MVEF + #define ARM_MATH_FLOAT16 +#endif + +#if defined (ARM_MATH_MVEF) + #define ARM_MATH_MVEI + #define ARM_MATH_FLOAT16 +#endif + +#if defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF) || defined(ARM_MATH_MVEI) +#include +#endif + + + /** + * @brief Macros required for reciprocal calculation in Normalized LMS + */ + +#define DELTA_Q31 ((q31_t)(0x100)) +#define DELTA_Q15 ((q15_t)0x5) +#define INDEX_MASK 0x0000003F +#ifndef PI + #define PI 3.14159265358979f +#endif + + /** + * @brief Macros required for SINE and COSINE Fast math approximations + */ + +#define FAST_MATH_TABLE_SIZE 512 +#define FAST_MATH_Q31_SHIFT (32 - 10) +#define FAST_MATH_Q15_SHIFT (16 - 10) +#define CONTROLLER_Q31_SHIFT (32 - 9) +#define TABLE_SPACING_Q31 0x400000 +#define TABLE_SPACING_Q15 0x80 + + /** + * @brief Macros required for SINE and COSINE Controller functions + */ + /* 1.31(q31) Fixed value of 2/360 */ + /* -1 to +1 is divided into 360 values so total spacing is (2/360) */ +#define INPUT_SPACING 0xB60B61 + + /** + * @brief Macros for complex numbers + */ + + /* Dimension C vector space */ + #define CMPLX_DIM 2 + + /** + * @brief Error status returned by some functions in the library. + */ + + typedef enum + { + ARM_MATH_SUCCESS = 0, /**< No error */ + ARM_MATH_ARGUMENT_ERROR = -1, /**< One or more arguments are incorrect */ + ARM_MATH_LENGTH_ERROR = -2, /**< Length of data buffer is incorrect */ + ARM_MATH_SIZE_MISMATCH = -3, /**< Size of matrices is not compatible with the operation */ + ARM_MATH_NANINF = -4, /**< Not-a-number (NaN) or infinity is generated */ + ARM_MATH_SINGULAR = -5, /**< Input matrix is singular and cannot be inverted */ + ARM_MATH_TEST_FAILURE = -6 /**< Test Failed */ + } arm_status; + + /** + * @brief 8-bit fractional data type in 1.7 format. + */ + typedef int8_t q7_t; + + /** + * @brief 16-bit fractional data type in 1.15 format. + */ + typedef int16_t q15_t; + + /** + * @brief 32-bit fractional data type in 1.31 format. + */ + typedef int32_t q31_t; + + /** + * @brief 64-bit fractional data type in 1.63 format. + */ + typedef int64_t q63_t; + + /** + * @brief 32-bit floating-point type definition. + */ + typedef float float32_t; + + /** + * @brief 64-bit floating-point type definition. + */ + typedef double float64_t; + + /** + * @brief vector types + */ +#if defined(ARM_MATH_NEON) || defined (ARM_MATH_MVEI) + /** + * @brief 64-bit fractional 128-bit vector data type in 1.63 format + */ + typedef int64x2_t q63x2_t; + + /** + * @brief 32-bit fractional 128-bit vector data type in 1.31 format. + */ + typedef int32x4_t q31x4_t; + + /** + * @brief 16-bit fractional 128-bit vector data type with 16-bit alignement in 1.15 format. + */ + typedef __ALIGNED(2) int16x8_t q15x8_t; + + /** + * @brief 8-bit fractional 128-bit vector data type with 8-bit alignement in 1.7 format. + */ + typedef __ALIGNED(1) int8x16_t q7x16_t; + + /** + * @brief 32-bit fractional 128-bit vector pair data type in 1.31 format. + */ + typedef int32x4x2_t q31x4x2_t; + + /** + * @brief 32-bit fractional 128-bit vector quadruplet data type in 1.31 format. + */ + typedef int32x4x4_t q31x4x4_t; + + /** + * @brief 16-bit fractional 128-bit vector pair data type in 1.15 format. + */ + typedef int16x8x2_t q15x8x2_t; + + /** + * @brief 16-bit fractional 128-bit vector quadruplet data type in 1.15 format. + */ + typedef int16x8x4_t q15x8x4_t; + + /** + * @brief 8-bit fractional 128-bit vector pair data type in 1.7 format. + */ + typedef int8x16x2_t q7x16x2_t; + + /** + * @brief 8-bit fractional 128-bit vector quadruplet data type in 1.7 format. + */ + typedef int8x16x4_t q7x16x4_t; + + /** + * @brief 32-bit fractional data type in 9.23 format. + */ + typedef int32_t q23_t; + + /** + * @brief 32-bit fractional 128-bit vector data type in 9.23 format. + */ + typedef int32x4_t q23x4_t; + + /** + * @brief 64-bit status 128-bit vector data type. + */ + typedef int64x2_t status64x2_t; + + /** + * @brief 32-bit status 128-bit vector data type. + */ + typedef int32x4_t status32x4_t; + + /** + * @brief 16-bit status 128-bit vector data type. + */ + typedef int16x8_t status16x8_t; + + /** + * @brief 8-bit status 128-bit vector data type. + */ + typedef int8x16_t status8x16_t; + + +#endif + +#if defined(ARM_MATH_NEON) || defined(ARM_MATH_MVEF) /* floating point vector*/ + /** + * @brief 32-bit floating-point 128-bit vector type + */ + typedef float32x4_t f32x4_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit floating-point 128-bit vector data type + */ + typedef __ALIGNED(2) float16x8_t f16x8_t; +#endif + + /** + * @brief 32-bit floating-point 128-bit vector pair data type + */ + typedef float32x4x2_t f32x4x2_t; + + /** + * @brief 32-bit floating-point 128-bit vector quadruplet data type + */ + typedef float32x4x4_t f32x4x4_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit floating-point 128-bit vector pair data type + */ + typedef float16x8x2_t f16x8x2_t; + + /** + * @brief 16-bit floating-point 128-bit vector quadruplet data type + */ + typedef float16x8x4_t f16x8x4_t; +#endif + + /** + * @brief 32-bit ubiquitous 128-bit vector data type + */ + typedef union _any32x4_t + { + float32x4_t f; + int32x4_t i; + } any32x4_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit ubiquitous 128-bit vector data type + */ + typedef union _any16x8_t + { + float16x8_t f; + int16x8_t i; + } any16x8_t; +#endif + +#endif + +#if defined(ARM_MATH_NEON) + /** + * @brief 32-bit fractional 64-bit vector data type in 1.31 format. + */ + typedef int32x2_t q31x2_t; + + /** + * @brief 16-bit fractional 64-bit vector data type in 1.15 format. + */ + typedef __ALIGNED(2) int16x4_t q15x4_t; + + /** + * @brief 8-bit fractional 64-bit vector data type in 1.7 format. + */ + typedef __ALIGNED(1) int8x8_t q7x8_t; + + /** + * @brief 32-bit float 64-bit vector data type. + */ + typedef float32x2_t f32x2_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit float 64-bit vector data type. + */ + typedef __ALIGNED(2) float16x4_t f16x4_t; +#endif + + /** + * @brief 32-bit floating-point 128-bit vector triplet data type + */ + typedef float32x4x3_t f32x4x3_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit floating-point 128-bit vector triplet data type + */ + typedef float16x8x3_t f16x8x3_t; +#endif + + /** + * @brief 32-bit fractional 128-bit vector triplet data type in 1.31 format + */ + typedef int32x4x3_t q31x4x3_t; + + /** + * @brief 16-bit fractional 128-bit vector triplet data type in 1.15 format + */ + typedef int16x8x3_t q15x8x3_t; + + /** + * @brief 8-bit fractional 128-bit vector triplet data type in 1.7 format + */ + typedef int8x16x3_t q7x16x3_t; + + /** + * @brief 32-bit floating-point 64-bit vector pair data type + */ + typedef float32x2x2_t f32x2x2_t; + + /** + * @brief 32-bit floating-point 64-bit vector triplet data type + */ + typedef float32x2x3_t f32x2x3_t; + + /** + * @brief 32-bit floating-point 64-bit vector quadruplet data type + */ + typedef float32x2x4_t f32x2x4_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit floating-point 64-bit vector pair data type + */ + typedef float16x4x2_t f16x4x2_t; + + /** + * @brief 16-bit floating-point 64-bit vector triplet data type + */ + typedef float16x4x3_t f16x4x3_t; + + /** + * @brief 16-bit floating-point 64-bit vector quadruplet data type + */ + typedef float16x4x4_t f16x4x4_t; +#endif + + /** + * @brief 32-bit fractional 64-bit vector pair data type in 1.31 format + */ + typedef int32x2x2_t q31x2x2_t; + + /** + * @brief 32-bit fractional 64-bit vector triplet data type in 1.31 format + */ + typedef int32x2x3_t q31x2x3_t; + + /** + * @brief 32-bit fractional 64-bit vector quadruplet data type in 1.31 format + */ + typedef int32x4x3_t q31x2x4_t; + + /** + * @brief 16-bit fractional 64-bit vector pair data type in 1.15 format + */ + typedef int16x4x2_t q15x4x2_t; + + /** + * @brief 16-bit fractional 64-bit vector triplet data type in 1.15 format + */ + typedef int16x4x2_t q15x4x3_t; + + /** + * @brief 16-bit fractional 64-bit vector quadruplet data type in 1.15 format + */ + typedef int16x4x3_t q15x4x4_t; + + /** + * @brief 8-bit fractional 64-bit vector pair data type in 1.7 format + */ + typedef int8x8x2_t q7x8x2_t; + + /** + * @brief 8-bit fractional 64-bit vector triplet data type in 1.7 format + */ + typedef int8x8x3_t q7x8x3_t; + + /** + * @brief 8-bit fractional 64-bit vector quadruplet data type in 1.7 format + */ + typedef int8x8x4_t q7x8x4_t; + + /** + * @brief 32-bit ubiquitous 64-bit vector data type + */ + typedef union _any32x2_t + { + float32x2_t f; + int32x2_t i; + } any32x2_t; + +#if defined(ARM_MATH_FLOAT16) + /** + * @brief 16-bit ubiquitous 64-bit vector data type + */ + typedef union _any16x4_t + { + float16x4_t f; + int16x4_t i; + } any16x4_t; +#endif + + /** + * @brief 32-bit status 64-bit vector data type. + */ + typedef int32x4_t status32x2_t; + + /** + * @brief 16-bit status 64-bit vector data type. + */ + typedef int16x8_t status16x4_t; + + /** + * @brief 8-bit status 64-bit vector data type. + */ + typedef int8x16_t status8x8_t; + +#endif + + + +/** + @brief definition to read/write two 16 bit values. + @deprecated + */ +#if defined ( __CC_ARM ) + #define __SIMD32_TYPE int32_t __packed +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + #define __SIMD32_TYPE int32_t +#elif defined ( __GNUC__ ) + #define __SIMD32_TYPE int32_t +#elif defined ( __ICCARM__ ) + #define __SIMD32_TYPE int32_t __packed +#elif defined ( __TI_ARM__ ) + #define __SIMD32_TYPE int32_t +#elif defined ( __CSMC__ ) + #define __SIMD32_TYPE int32_t +#elif defined ( __TASKING__ ) + #define __SIMD32_TYPE __un(aligned) int32_t +#elif defined(_MSC_VER ) + #define __SIMD32_TYPE int32_t +#else + #error Unknown compiler +#endif + +#define __SIMD32(addr) (*(__SIMD32_TYPE **) & (addr)) +#define __SIMD32_CONST(addr) ( (__SIMD32_TYPE * ) (addr)) +#define _SIMD32_OFFSET(addr) (*(__SIMD32_TYPE * ) (addr)) +#define __SIMD64(addr) (*( int64_t **) & (addr)) + +#define STEP(x) (x) <= 0 ? 0 : 1 +#define SQ(x) ((x) * (x)) + +/* SIMD replacement */ + + +/** + @brief Read 2 Q15 from Q15 pointer. + @param[in] pQ15 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q15x2 ( + q15_t * pQ15) +{ + q31_t val; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, pQ15, 4); +#else + val = (pQ15[1] << 16) | (pQ15[0] & 0x0FFFF) ; +#endif + + return (val); +} + +/** + @brief Read 2 Q15 from Q15 pointer and increment pointer afterwards. + @param[in] pQ15 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q15x2_ia ( + q15_t ** pQ15) +{ + q31_t val; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, *pQ15, 4); +#else + val = ((*pQ15)[1] << 16) | ((*pQ15)[0] & 0x0FFFF); +#endif + + *pQ15 += 2; + return (val); +} + +/** + @brief Read 2 Q15 from Q15 pointer and decrement pointer afterwards. + @param[in] pQ15 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q15x2_da ( + q15_t ** pQ15) +{ + q31_t val; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, *pQ15, 4); +#else + val = ((*pQ15)[1] << 16) | ((*pQ15)[0] & 0x0FFFF); +#endif + + *pQ15 -= 2; + return (val); +} + +/** + @brief Write 2 Q15 to Q15 pointer and increment pointer afterwards. + @param[in] pQ15 points to input value + @param[in] value Q31 value + @return none + */ +__STATIC_FORCEINLINE void write_q15x2_ia ( + q15_t ** pQ15, + q31_t value) +{ + q31_t val = value; +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (*pQ15, &val, 4); +#else + (*pQ15)[0] = (val & 0x0FFFF); + (*pQ15)[1] = (val >> 16) & 0x0FFFF; +#endif + + *pQ15 += 2; +} + +/** + @brief Write 2 Q15 to Q15 pointer. + @param[in] pQ15 points to input value + @param[in] value Q31 value + @return none + */ +__STATIC_FORCEINLINE void write_q15x2 ( + q15_t * pQ15, + q31_t value) +{ + q31_t val = value; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (pQ15, &val, 4); +#else + pQ15[0] = val & 0x0FFFF; + pQ15[1] = val >> 16; +#endif +} + + +/** + @brief Read 4 Q7 from Q7 pointer and increment pointer afterwards. + @param[in] pQ7 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q7x4_ia ( + q7_t ** pQ7) +{ + q31_t val; + + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, *pQ7, 4); +#else + val =(((*pQ7)[3] & 0x0FF) << 24) | (((*pQ7)[2] & 0x0FF) << 16) | (((*pQ7)[1] & 0x0FF) << 8) | ((*pQ7)[0] & 0x0FF); +#endif + + *pQ7 += 4; + + return (val); +} + +/** + @brief Read 4 Q7 from Q7 pointer and decrement pointer afterwards. + @param[in] pQ7 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q7x4_da ( + q7_t ** pQ7) +{ + q31_t val; +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, *pQ7, 4); +#else + val = ((((*pQ7)[3]) & 0x0FF) << 24) | ((((*pQ7)[2]) & 0x0FF) << 16) | ((((*pQ7)[1]) & 0x0FF) << 8) | ((*pQ7)[0] & 0x0FF); +#endif + *pQ7 -= 4; + + return (val); +} + +/** + @brief Write 4 Q7 to Q7 pointer and increment pointer afterwards. + @param[in] pQ7 points to input value + @param[in] value Q31 value + @return none + */ +__STATIC_FORCEINLINE void write_q7x4_ia ( + q7_t ** pQ7, + q31_t value) +{ + q31_t val = value; +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (*pQ7, &val, 4); +#else + (*pQ7)[0] = val & 0x0FF; + (*pQ7)[1] = (val >> 8) & 0x0FF; + (*pQ7)[2] = (val >> 16) & 0x0FF; + (*pQ7)[3] = (val >> 24) & 0x0FF; + +#endif + *pQ7 += 4; +} + +/* + +Normally those kind of definitions are in a compiler file +in Core or Core_A. + +But for MSVC compiler it is a bit special. The goal is very specific +to CMSIS-DSP and only to allow the use of this library from other +systems like Python or Matlab. + +MSVC is not going to be used to cross-compile to ARM. So, having a MSVC +compiler file in Core or Core_A would not make sense. + +*/ +#if defined ( _MSC_VER ) || defined(__GNUC_PYTHON__) + __STATIC_FORCEINLINE uint8_t __CLZ(uint32_t data) + { + if (data == 0U) { return 32U; } + + uint32_t count = 0U; + uint32_t mask = 0x80000000U; + + while ((data & mask) == 0U) + { + count += 1U; + mask = mask >> 1U; + } + return count; + } + + __STATIC_FORCEINLINE int32_t __SSAT(int32_t val, uint32_t sat) + { + if ((sat >= 1U) && (sat <= 32U)) + { + const int32_t max = (int32_t)((1U << (sat - 1U)) - 1U); + const int32_t min = -1 - max ; + if (val > max) + { + return max; + } + else if (val < min) + { + return min; + } + } + return val; + } + + __STATIC_FORCEINLINE uint32_t __USAT(int32_t val, uint32_t sat) + { + if (sat <= 31U) + { + const uint32_t max = ((1U << sat) - 1U); + if (val > (int32_t)max) + { + return max; + } + else if (val < 0) + { + return 0U; + } + } + return (uint32_t)val; + } +#endif + +#ifndef ARM_MATH_DSP + /** + * @brief definition to pack two 16 bit values. + */ + #define __PKHBT(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) << 0) & (int32_t)0x0000FFFF) | \ + (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000) ) + #define __PKHTB(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) << 0) & (int32_t)0xFFFF0000) | \ + (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF) ) +#endif + + /** + * @brief definition to pack four 8 bit values. + */ +#ifndef ARM_MATH_BIG_ENDIAN + #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) << 0) & (int32_t)0x000000FF) | \ + (((int32_t)(v1) << 8) & (int32_t)0x0000FF00) | \ + (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \ + (((int32_t)(v3) << 24) & (int32_t)0xFF000000) ) +#else + #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) << 0) & (int32_t)0x000000FF) | \ + (((int32_t)(v2) << 8) & (int32_t)0x0000FF00) | \ + (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \ + (((int32_t)(v0) << 24) & (int32_t)0xFF000000) ) +#endif + + + /** + * @brief Clips Q63 to Q31 values. + */ + __STATIC_FORCEINLINE q31_t clip_q63_to_q31( + q63_t x) + { + return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ? + ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x; + } + + /** + * @brief Clips Q63 to Q15 values. + */ + __STATIC_FORCEINLINE q15_t clip_q63_to_q15( + q63_t x) + { + return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ? + ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15); + } + + /** + * @brief Clips Q31 to Q7 values. + */ + __STATIC_FORCEINLINE q7_t clip_q31_to_q7( + q31_t x) + { + return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ? + ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x; + } + + /** + * @brief Clips Q31 to Q15 values. + */ + __STATIC_FORCEINLINE q15_t clip_q31_to_q15( + q31_t x) + { + return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ? + ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x; + } + + /** + * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format. + */ + __STATIC_FORCEINLINE q63_t mult32x64( + q63_t x, + q31_t y) + { + return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) + + (((q63_t) (x >> 32) * y) ) ); + } + + /** + * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type. + */ + __STATIC_FORCEINLINE uint32_t arm_recip_q31( + q31_t in, + q31_t * dst, + const q31_t * pRecipTable) + { + q31_t out; + uint32_t tempVal; + uint32_t index, i; + uint32_t signBits; + + if (in > 0) + { + signBits = ((uint32_t) (__CLZ( in) - 1)); + } + else + { + signBits = ((uint32_t) (__CLZ(-in) - 1)); + } + + /* Convert input sample to 1.31 format */ + in = (in << signBits); + + /* calculation of index for initial approximated Val */ + index = (uint32_t)(in >> 24); + index = (index & INDEX_MASK); + + /* 1.31 with exp 1 */ + out = pRecipTable[index]; + + /* calculation of reciprocal value */ + /* running approximation for two iterations */ + for (i = 0U; i < 2U; i++) + { + tempVal = (uint32_t) (((q63_t) in * out) >> 31); + tempVal = 0x7FFFFFFFu - tempVal; + /* 1.31 with exp 1 */ + /* out = (q31_t) (((q63_t) out * tempVal) >> 30); */ + out = clip_q63_to_q31(((q63_t) out * tempVal) >> 30); + } + + /* write output */ + *dst = out; + + /* return num of signbits of out = 1/in value */ + return (signBits + 1U); + } + + + /** + * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type. + */ + __STATIC_FORCEINLINE uint32_t arm_recip_q15( + q15_t in, + q15_t * dst, + const q15_t * pRecipTable) + { + q15_t out = 0; + uint32_t tempVal = 0; + uint32_t index = 0, i = 0; + uint32_t signBits = 0; + + if (in > 0) + { + signBits = ((uint32_t)(__CLZ( in) - 17)); + } + else + { + signBits = ((uint32_t)(__CLZ(-in) - 17)); + } + + /* Convert input sample to 1.15 format */ + in = (in << signBits); + + /* calculation of index for initial approximated Val */ + index = (uint32_t)(in >> 8); + index = (index & INDEX_MASK); + + /* 1.15 with exp 1 */ + out = pRecipTable[index]; + + /* calculation of reciprocal value */ + /* running approximation for two iterations */ + for (i = 0U; i < 2U; i++) + { + tempVal = (uint32_t) (((q31_t) in * out) >> 15); + tempVal = 0x7FFFu - tempVal; + /* 1.15 with exp 1 */ + out = (q15_t) (((q31_t) out * tempVal) >> 14); + /* out = clip_q31_to_q15(((q31_t) out * tempVal) >> 14); */ + } + + /* write output */ + *dst = out; + + /* return num of signbits of out = 1/in value */ + return (signBits + 1); + } + +/** + * @brief Integer exponentiation + * @param[in] x value + * @param[in] nb integer exponent >= 1 + * @return x^nb + * + */ +__STATIC_INLINE float32_t arm_exponent_f32(float32_t x, int32_t nb) +{ + float32_t r = x; + nb --; + while(nb > 0) + { + r = r * x; + nb--; + } + return(r); +} + +/** + * @brief 64-bit to 32-bit unsigned normalization + * @param[in] in is input unsigned long long value + * @param[out] normalized is the 32-bit normalized value + * @param[out] norm is norm scale + */ +__STATIC_INLINE void arm_norm_64_to_32u(uint64_t in, int32_t * normalized, int32_t *norm) +{ + int32_t n1; + int32_t hi = (int32_t) (in >> 32); + int32_t lo = (int32_t) ((in << 32) >> 32); + + n1 = __CLZ(hi) - 32; + if (!n1) + { + /* + * input fits in 32-bit + */ + n1 = __CLZ(lo); + if (!n1) + { + /* + * MSB set, need to scale down by 1 + */ + *norm = -1; + *normalized = (((uint32_t) lo) >> 1); + } else + { + if (n1 == 32) + { + /* + * input is zero + */ + *norm = 0; + *normalized = 0; + } else + { + /* + * 32-bit normalization + */ + *norm = n1 - 1; + *normalized = lo << *norm; + } + } + } else + { + /* + * input fits in 64-bit + */ + n1 = 1 - n1; + *norm = -n1; + /* + * 64 bit normalization + */ + *normalized = (((uint32_t) lo) >> n1) | (hi << (32 - n1)); + } +} + +__STATIC_INLINE q31_t arm_div_q63_to_q31(q63_t num, q31_t den) +{ + q31_t result; + uint64_t absNum; + int32_t normalized; + int32_t norm; + + /* + * if sum fits in 32bits + * avoid costly 64-bit division + */ + absNum = num > 0 ? num : -num; + arm_norm_64_to_32u(absNum, &normalized, &norm); + if (norm > 0) + /* + * 32-bit division + */ + result = (q31_t) num / den; + else + /* + * 64-bit division + */ + result = (q31_t) (num / den); + + return result; +} + + +/* + * @brief C custom defined intrinsic functions + */ +#if !defined (ARM_MATH_DSP) + + /* + * @brief C custom defined QADD8 + */ + __STATIC_FORCEINLINE uint32_t __QADD8( + uint32_t x, + uint32_t y) + { + q31_t r, s, t, u; + + r = __SSAT(((((q31_t)x << 24) >> 24) + (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF; + s = __SSAT(((((q31_t)x << 16) >> 24) + (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF; + t = __SSAT(((((q31_t)x << 8) >> 24) + (((q31_t)y << 8) >> 24)), 8) & (int32_t)0x000000FF; + u = __SSAT(((((q31_t)x ) >> 24) + (((q31_t)y ) >> 24)), 8) & (int32_t)0x000000FF; + + return ((uint32_t)((u << 24) | (t << 16) | (s << 8) | (r ))); + } + + + /* + * @brief C custom defined QSUB8 + */ + __STATIC_FORCEINLINE uint32_t __QSUB8( + uint32_t x, + uint32_t y) + { + q31_t r, s, t, u; + + r = __SSAT(((((q31_t)x << 24) >> 24) - (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF; + s = __SSAT(((((q31_t)x << 16) >> 24) - (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF; + t = __SSAT(((((q31_t)x << 8) >> 24) - (((q31_t)y << 8) >> 24)), 8) & (int32_t)0x000000FF; + u = __SSAT(((((q31_t)x ) >> 24) - (((q31_t)y ) >> 24)), 8) & (int32_t)0x000000FF; + + return ((uint32_t)((u << 24) | (t << 16) | (s << 8) | (r ))); + } + + + /* + * @brief C custom defined QADD16 + */ + __STATIC_FORCEINLINE uint32_t __QADD16( + uint32_t x, + uint32_t y) + { +/* q31_t r, s; without initialisation 'arm_offset_q15 test' fails but 'intrinsic' tests pass! for armCC */ + q31_t r = 0, s = 0; + + r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) + (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHADD16 + */ + __STATIC_FORCEINLINE uint32_t __SHADD16( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) + (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined QSUB16 + */ + __STATIC_FORCEINLINE uint32_t __QSUB16( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) - (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHSUB16 + */ + __STATIC_FORCEINLINE uint32_t __SHSUB16( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) - (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined QASX + */ + __STATIC_FORCEINLINE uint32_t __QASX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHASX + */ + __STATIC_FORCEINLINE uint32_t __SHASX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) - (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined QSAX + */ + __STATIC_FORCEINLINE uint32_t __QSAX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHSAX + */ + __STATIC_FORCEINLINE uint32_t __SHSAX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) + (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SMUSDX + */ + __STATIC_FORCEINLINE uint32_t __SMUSDX( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) - + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) )); + } + + /* + * @brief C custom defined SMUADX + */ + __STATIC_FORCEINLINE uint32_t __SMUADX( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) )); + } + + + /* + * @brief C custom defined QADD + */ + __STATIC_FORCEINLINE int32_t __QADD( + int32_t x, + int32_t y) + { + return ((int32_t)(clip_q63_to_q31((q63_t)x + (q31_t)y))); + } + + + /* + * @brief C custom defined QSUB + */ + __STATIC_FORCEINLINE int32_t __QSUB( + int32_t x, + int32_t y) + { + return ((int32_t)(clip_q63_to_q31((q63_t)x - (q31_t)y))); + } + + + /* + * @brief C custom defined SMLAD + */ + __STATIC_FORCEINLINE uint32_t __SMLAD( + uint32_t x, + uint32_t y, + uint32_t sum) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) + + ( ((q31_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLADX + */ + __STATIC_FORCEINLINE uint32_t __SMLADX( + uint32_t x, + uint32_t y, + uint32_t sum) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) + + ( ((q31_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLSDX + */ + __STATIC_FORCEINLINE uint32_t __SMLSDX( + uint32_t x, + uint32_t y, + uint32_t sum) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) - + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) + + ( ((q31_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLALD + */ + __STATIC_FORCEINLINE uint64_t __SMLALD( + uint32_t x, + uint32_t y, + uint64_t sum) + { +/* return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) + ((q15_t) x * (q15_t) y)); */ + return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) + + ( ((q63_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLALDX + */ + __STATIC_FORCEINLINE uint64_t __SMLALDX( + uint32_t x, + uint32_t y, + uint64_t sum) + { +/* return (sum + ((q15_t) (x >> 16) * (q15_t) y)) + ((q15_t) x * (q15_t) (y >> 16)); */ + return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) + + ( ((q63_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMUAD + */ + __STATIC_FORCEINLINE uint32_t __SMUAD( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) )); + } + + + /* + * @brief C custom defined SMUSD + */ + __STATIC_FORCEINLINE uint32_t __SMUSD( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) - + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) )); + } + + + /* + * @brief C custom defined SXTB16 + */ + __STATIC_FORCEINLINE uint32_t __SXTB16( + uint32_t x) + { + return ((uint32_t)(((((q31_t)x << 24) >> 24) & (q31_t)0x0000FFFF) | + ((((q31_t)x << 8) >> 8) & (q31_t)0xFFFF0000) )); + } + + /* + * @brief C custom defined SMMLA + */ + __STATIC_FORCEINLINE int32_t __SMMLA( + int32_t x, + int32_t y, + int32_t sum) + { + return (sum + (int32_t) (((int64_t) x * y) >> 32)); + } + +#endif /* !defined (ARM_MATH_DSP) */ + + + /** + * @brief Instance structure for the Q7 FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + q7_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const q7_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + } arm_fir_instance_q7; + + /** + * @brief Instance structure for the Q15 FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + } arm_fir_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + } arm_fir_instance_q31; + + /** + * @brief Instance structure for the floating-point FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + } arm_fir_instance_f32; + + /** + * @brief Processing function for the Q7 FIR filter. + * @param[in] S points to an instance of the Q7 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_q7( + const arm_fir_instance_q7 * S, + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q7 FIR filter. + * @param[in,out] S points to an instance of the Q7 FIR structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed. + */ + void arm_fir_init_q7( + arm_fir_instance_q7 * S, + uint16_t numTaps, + const q7_t * pCoeffs, + q7_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the Q15 FIR filter. + * @param[in] S points to an instance of the Q15 FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_q15( + const arm_fir_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the fast Q15 FIR filter (fast version). + * @param[in] S points to an instance of the Q15 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_fast_q15( + const arm_fir_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q15 FIR filter. + * @param[in,out] S points to an instance of the Q15 FIR filter structure. + * @param[in] numTaps Number of filter coefficients in the filter. Must be even and greater than or equal to 4. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + * @return The function returns either + * ARM_MATH_SUCCESS if initialization was successful or + * ARM_MATH_ARGUMENT_ERROR if numTaps is not a supported value. + */ + arm_status arm_fir_init_q15( + arm_fir_instance_q15 * S, + uint16_t numTaps, + const q15_t * pCoeffs, + q15_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the Q31 FIR filter. + * @param[in] S points to an instance of the Q31 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_q31( + const arm_fir_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the fast Q31 FIR filter (fast version). + * @param[in] S points to an instance of the Q31 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_fast_q31( + const arm_fir_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q31 FIR filter. + * @param[in,out] S points to an instance of the Q31 FIR structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + */ + void arm_fir_init_q31( + arm_fir_instance_q31 * S, + uint16_t numTaps, + const q31_t * pCoeffs, + q31_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the floating-point FIR filter. + * @param[in] S points to an instance of the floating-point FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_f32( + const arm_fir_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point FIR filter. + * @param[in,out] S points to an instance of the floating-point FIR filter structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + */ + void arm_fir_init_f32( + arm_fir_instance_f32 * S, + uint16_t numTaps, + const float32_t * pCoeffs, + float32_t * pState, + uint32_t blockSize); + + /** + * @brief Instance structure for the Q15 Biquad cascade filter. + */ + typedef struct + { + int8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + q15_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const q15_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + int8_t postShift; /**< Additional shift, in bits, applied to each output sample. */ + } arm_biquad_casd_df1_inst_q15; + + /** + * @brief Instance structure for the Q31 Biquad cascade filter. + */ + typedef struct + { + uint32_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + q31_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const q31_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + uint8_t postShift; /**< Additional shift, in bits, applied to each output sample. */ + } arm_biquad_casd_df1_inst_q31; + + /** + * @brief Instance structure for the floating-point Biquad cascade filter. + */ + typedef struct + { + uint32_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float32_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const float32_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_casd_df1_inst_f32; + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + /** + * @brief Instance structure for the modified Biquad coefs required by vectorized code. + */ + typedef struct + { + float32_t coeffs[8][4]; /**< Points to the array of modified coefficients. The array is of length 32. There is one per stage */ + } arm_biquad_mod_coef_f32; +#endif + + /** + * @brief Processing function for the Q15 Biquad cascade filter. + * @param[in] S points to an instance of the Q15 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_q15( + const arm_biquad_casd_df1_inst_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q15 Biquad cascade filter. + * @param[in,out] S points to an instance of the Q15 Biquad cascade structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] postShift Shift to be applied to the output. Varies according to the coefficients format + */ + void arm_biquad_cascade_df1_init_q15( + arm_biquad_casd_df1_inst_q15 * S, + uint8_t numStages, + const q15_t * pCoeffs, + q15_t * pState, + int8_t postShift); + + /** + * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q15 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_fast_q15( + const arm_biquad_casd_df1_inst_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the Q31 Biquad cascade filter + * @param[in] S points to an instance of the Q31 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_q31( + const arm_biquad_casd_df1_inst_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q31 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_fast_q31( + const arm_biquad_casd_df1_inst_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q31 Biquad cascade filter. + * @param[in,out] S points to an instance of the Q31 Biquad cascade structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] postShift Shift to be applied to the output. Varies according to the coefficients format + */ + void arm_biquad_cascade_df1_init_q31( + arm_biquad_casd_df1_inst_q31 * S, + uint8_t numStages, + const q31_t * pCoeffs, + q31_t * pState, + int8_t postShift); + + /** + * @brief Processing function for the floating-point Biquad cascade filter. + * @param[in] S points to an instance of the floating-point Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_f32( + const arm_biquad_casd_df1_inst_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point Biquad cascade filter. + * @param[in,out] S points to an instance of the floating-point Biquad cascade structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pCoeffsMod points to the modified filter coefficients (only MVE version). + * @param[in] pState points to the state buffer. + */ +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + void arm_biquad_cascade_df1_mve_init_f32( + arm_biquad_casd_df1_inst_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + arm_biquad_mod_coef_f32 * pCoeffsMod, + float32_t * pState); +#endif + + void arm_biquad_cascade_df1_init_f32( + arm_biquad_casd_df1_inst_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Compute the logical bitwise AND of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_and_u16( + const uint16_t * pSrcA, + const uint16_t * pSrcB, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise AND of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_and_u32( + const uint32_t * pSrcA, + const uint32_t * pSrcB, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise AND of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_and_u8( + const uint8_t * pSrcA, + const uint8_t * pSrcB, + uint8_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise OR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_or_u16( + const uint16_t * pSrcA, + const uint16_t * pSrcB, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise OR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_or_u32( + const uint32_t * pSrcA, + const uint32_t * pSrcB, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise OR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_or_u8( + const uint8_t * pSrcA, + const uint8_t * pSrcB, + uint8_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise NOT of a fixed-point vector. + * @param[in] pSrc points to input vector + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_not_u16( + const uint16_t * pSrc, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise NOT of a fixed-point vector. + * @param[in] pSrc points to input vector + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_not_u32( + const uint32_t * pSrc, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise NOT of a fixed-point vector. + * @param[in] pSrc points to input vector + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_not_u8( + const uint8_t * pSrc, + uint8_t * pDst, + uint32_t blockSize); + +/** + * @brief Compute the logical bitwise XOR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_xor_u16( + const uint16_t * pSrcA, + const uint16_t * pSrcB, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise XOR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_xor_u32( + const uint32_t * pSrcA, + const uint32_t * pSrcB, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise XOR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + * @return none + */ + void arm_xor_u8( + const uint8_t * pSrcA, + const uint8_t * pSrcB, + uint8_t * pDst, + uint32_t blockSize); + + /** + * @brief Struct for specifying sorting algorithm + */ + typedef enum + { + ARM_SORT_BITONIC = 0, + /**< Bitonic sort */ + ARM_SORT_BUBBLE = 1, + /**< Bubble sort */ + ARM_SORT_HEAP = 2, + /**< Heap sort */ + ARM_SORT_INSERTION = 3, + /**< Insertion sort */ + ARM_SORT_QUICK = 4, + /**< Quick sort */ + ARM_SORT_SELECTION = 5 + /**< Selection sort */ + } arm_sort_alg; + + /** + * @brief Struct for specifying sorting algorithm + */ + typedef enum + { + ARM_SORT_DESCENDING = 0, + /**< Descending order (9 to 0) */ + ARM_SORT_ASCENDING = 1 + /**< Ascending order (0 to 9) */ + } arm_sort_dir; + + /** + * @brief Instance structure for the sorting algorithms. + */ + typedef struct + { + arm_sort_alg alg; /**< Sorting algorithm selected */ + arm_sort_dir dir; /**< Sorting order (direction) */ + } arm_sort_instance_f32; + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @param[in,out] S points to an instance of the sorting structure. + * @param[in] alg Selected algorithm. + * @param[in] dir Sorting order. + */ + void arm_sort_init_f32( + arm_sort_instance_f32 * S, + arm_sort_alg alg, + arm_sort_dir dir); + + /** + * @brief Instance structure for the sorting algorithms. + */ + typedef struct + { + arm_sort_dir dir; /**< Sorting order (direction) */ + float32_t * buffer; /**< Working buffer */ + } arm_merge_sort_instance_f32; + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in,out] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_merge_sort_f32( + const arm_merge_sort_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + uint32_t blockSize); + + /** + * @param[in,out] S points to an instance of the sorting structure. + * @param[in] dir Sorting order. + * @param[in] buffer Working buffer. + */ + void arm_merge_sort_init_f32( + arm_merge_sort_instance_f32 * S, + arm_sort_dir dir, + float32_t * buffer); + + /** + * @brief Struct for specifying cubic spline type + */ + typedef enum + { + ARM_SPLINE_NATURAL = 0, /**< Natural spline */ + ARM_SPLINE_PARABOLIC_RUNOUT = 1 /**< Parabolic runout spline */ + } arm_spline_type; + + /** + * @brief Instance structure for the floating-point cubic spline interpolation. + */ + typedef struct + { + arm_spline_type type; /**< Type (boundary conditions) */ + const float32_t * x; /**< x values */ + const float32_t * y; /**< y values */ + uint32_t n_x; /**< Number of known data points */ + float32_t * coeffs; /**< Coefficients buffer (b,c, and d) */ + } arm_spline_instance_f32; + + /** + * @brief Processing function for the floating-point cubic spline interpolation. + * @param[in] S points to an instance of the floating-point spline structure. + * @param[in] xq points to the x values ot the interpolated data points. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples of output data. + */ + void arm_spline_f32( + arm_spline_instance_f32 * S, + const float32_t * xq, + float32_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point cubic spline interpolation. + * @param[in,out] S points to an instance of the floating-point spline structure. + * @param[in] type type of cubic spline interpolation (boundary conditions) + * @param[in] x points to the x values of the known data points. + * @param[in] y points to the y values of the known data points. + * @param[in] n number of known data points. + * @param[in] coeffs coefficients array for b, c, and d + * @param[in] tempBuffer buffer array for internal computations + */ + void arm_spline_init_f32( + arm_spline_instance_f32 * S, + arm_spline_type type, + const float32_t * x, + const float32_t * y, + uint32_t n, + float32_t * coeffs, + float32_t * tempBuffer); + + /** + * @brief Instance structure for the floating-point matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + float32_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_f32; + + /** + * @brief Instance structure for the floating-point matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + float64_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_f64; + + /** + * @brief Instance structure for the Q15 matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + q15_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_q15; + + /** + * @brief Instance structure for the Q31 matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + q31_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_q31; + + /** + * @brief Floating-point matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst, + q15_t * pScratch); + + /** + * @brief Q31, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_f32( + const arm_matrix_instance_f32 * pSrc, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_q15( + const arm_matrix_instance_q15 * pSrc, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_q31( + const arm_matrix_instance_q31 * pSrc, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @param[in] pState points to the array for storing intermediate results + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst, + q15_t * pState); + + /** + * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @param[in] pState points to the array for storing intermediate results + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_fast_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst, + q15_t * pState); + + /** + * @brief Q31 matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_fast_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix scaling. + * @param[in] pSrc points to the input matrix + * @param[in] scale scale factor + * @param[out] pDst points to the output matrix + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_f32( + const arm_matrix_instance_f32 * pSrc, + float32_t scale, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix scaling. + * @param[in] pSrc points to input matrix + * @param[in] scaleFract fractional portion of the scale factor + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to output matrix + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_q15( + const arm_matrix_instance_q15 * pSrc, + q15_t scaleFract, + int32_t shift, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix scaling. + * @param[in] pSrc points to input matrix + * @param[in] scaleFract fractional portion of the scale factor + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_q31( + const arm_matrix_instance_q31 * pSrc, + q31_t scaleFract, + int32_t shift, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Q31 matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_q31( + arm_matrix_instance_q31 * S, + uint16_t nRows, + uint16_t nColumns, + q31_t * pData); + + /** + * @brief Q15 matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_q15( + arm_matrix_instance_q15 * S, + uint16_t nRows, + uint16_t nColumns, + q15_t * pData); + + /** + * @brief Floating-point matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_f32( + arm_matrix_instance_f32 * S, + uint16_t nRows, + uint16_t nColumns, + float32_t * pData); + + + /** + * @brief Instance structure for the Q15 PID Control. + */ + typedef struct + { + q15_t A0; /**< The derived gain, A0 = Kp + Ki + Kd . */ +#if !defined (ARM_MATH_DSP) + q15_t A1; + q15_t A2; +#else + q31_t A1; /**< The derived gain A1 = -Kp - 2Kd | Kd.*/ +#endif + q15_t state[3]; /**< The state array of length 3. */ + q15_t Kp; /**< The proportional gain. */ + q15_t Ki; /**< The integral gain. */ + q15_t Kd; /**< The derivative gain. */ + } arm_pid_instance_q15; + + /** + * @brief Instance structure for the Q31 PID Control. + */ + typedef struct + { + q31_t A0; /**< The derived gain, A0 = Kp + Ki + Kd . */ + q31_t A1; /**< The derived gain, A1 = -Kp - 2Kd. */ + q31_t A2; /**< The derived gain, A2 = Kd . */ + q31_t state[3]; /**< The state array of length 3. */ + q31_t Kp; /**< The proportional gain. */ + q31_t Ki; /**< The integral gain. */ + q31_t Kd; /**< The derivative gain. */ + } arm_pid_instance_q31; + + /** + * @brief Instance structure for the floating-point PID Control. + */ + typedef struct + { + float32_t A0; /**< The derived gain, A0 = Kp + Ki + Kd . */ + float32_t A1; /**< The derived gain, A1 = -Kp - 2Kd. */ + float32_t A2; /**< The derived gain, A2 = Kd . */ + float32_t state[3]; /**< The state array of length 3. */ + float32_t Kp; /**< The proportional gain. */ + float32_t Ki; /**< The integral gain. */ + float32_t Kd; /**< The derivative gain. */ + } arm_pid_instance_f32; + + + + /** + * @brief Initialization function for the floating-point PID Control. + * @param[in,out] S points to an instance of the PID structure. + * @param[in] resetStateFlag flag to reset the state. 0 = no change in state 1 = reset the state. + */ + void arm_pid_init_f32( + arm_pid_instance_f32 * S, + int32_t resetStateFlag); + + + /** + * @brief Reset function for the floating-point PID Control. + * @param[in,out] S is an instance of the floating-point PID Control structure + */ + void arm_pid_reset_f32( + arm_pid_instance_f32 * S); + + + /** + * @brief Initialization function for the Q31 PID Control. + * @param[in,out] S points to an instance of the Q15 PID structure. + * @param[in] resetStateFlag flag to reset the state. 0 = no change in state 1 = reset the state. + */ + void arm_pid_init_q31( + arm_pid_instance_q31 * S, + int32_t resetStateFlag); + + + /** + * @brief Reset function for the Q31 PID Control. + * @param[in,out] S points to an instance of the Q31 PID Control structure + */ + + void arm_pid_reset_q31( + arm_pid_instance_q31 * S); + + + /** + * @brief Initialization function for the Q15 PID Control. + * @param[in,out] S points to an instance of the Q15 PID structure. + * @param[in] resetStateFlag flag to reset the state. 0 = no change in state 1 = reset the state. + */ + void arm_pid_init_q15( + arm_pid_instance_q15 * S, + int32_t resetStateFlag); + + + /** + * @brief Reset function for the Q15 PID Control. + * @param[in,out] S points to an instance of the q15 PID Control structure + */ + void arm_pid_reset_q15( + arm_pid_instance_q15 * S); + + + /** + * @brief Instance structure for the floating-point Linear Interpolate function. + */ + typedef struct + { + uint32_t nValues; /**< nValues */ + float32_t x1; /**< x1 */ + float32_t xSpacing; /**< xSpacing */ + float32_t *pYData; /**< pointer to the table of Y values */ + } arm_linear_interp_instance_f32; + + /** + * @brief Instance structure for the floating-point bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + float32_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_f32; + + /** + * @brief Instance structure for the Q31 bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + q31_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_q31; + + /** + * @brief Instance structure for the Q15 bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + q15_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_q15; + + /** + * @brief Instance structure for the Q15 bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + q7_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_q7; + + + /** + * @brief Q7 vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Floating-point vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q15_t *pTwiddle; /**< points to the Sin twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix2_instance_q15; + +/* Deprecated */ + arm_status arm_cfft_radix2_init_q15( + arm_cfft_radix2_instance_q15 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_q15( + const arm_cfft_radix2_instance_q15 * S, + q15_t * pSrc); + + + /** + * @brief Instance structure for the Q15 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q15_t *pTwiddle; /**< points to the twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix4_instance_q15; + +/* Deprecated */ + arm_status arm_cfft_radix4_init_q15( + arm_cfft_radix4_instance_q15 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix4_q15( + const arm_cfft_radix4_instance_q15 * S, + q15_t * pSrc); + + /** + * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q31_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix2_instance_q31; + +/* Deprecated */ + arm_status arm_cfft_radix2_init_q31( + arm_cfft_radix2_instance_q31 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_q31( + const arm_cfft_radix2_instance_q31 * S, + q31_t * pSrc); + + /** + * @brief Instance structure for the Q31 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q31_t *pTwiddle; /**< points to the twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix4_instance_q31; + +/* Deprecated */ + void arm_cfft_radix4_q31( + const arm_cfft_radix4_instance_q31 * S, + q31_t * pSrc); + +/* Deprecated */ + arm_status arm_cfft_radix4_init_q31( + arm_cfft_radix4_instance_q31 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + float32_t onebyfftLen; /**< value of 1/fftLen. */ + } arm_cfft_radix2_instance_f32; + +/* Deprecated */ + arm_status arm_cfft_radix2_init_f32( + arm_cfft_radix2_instance_f32 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_f32( + const arm_cfft_radix2_instance_f32 * S, + float32_t * pSrc); + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + float32_t onebyfftLen; /**< value of 1/fftLen. */ + } arm_cfft_radix4_instance_f32; + +/* Deprecated */ + arm_status arm_cfft_radix4_init_f32( + arm_cfft_radix4_instance_f32 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix4_f32( + const arm_cfft_radix4_instance_f32 * S, + float32_t * pSrc); + + /** + * @brief Instance structure for the fixed-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const q15_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEI) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const q15_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const q15_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const q15_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_q15; + +arm_status arm_cfft_init_q15( + arm_cfft_instance_q15 * S, + uint16_t fftLen); + +void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + q15_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + /** + * @brief Instance structure for the fixed-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const q31_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEI) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const q31_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const q31_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const q31_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_q31; + +arm_status arm_cfft_init_q31( + arm_cfft_instance_q31 * S, + uint16_t fftLen); + +void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + q31_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const float32_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const float32_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const float32_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_f32; + + + arm_status arm_cfft_init_f32( + arm_cfft_instance_f32 * S, + uint16_t fftLen); + + void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + float32_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + + /** + * @brief Instance structure for the Double Precision Floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const float64_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ + } arm_cfft_instance_f64; + + void arm_cfft_f64( + const arm_cfft_instance_f64 * S, + float64_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + /** + * @brief Instance structure for the Q15 RFFT/RIFFT function. + */ + typedef struct + { + uint32_t fftLenReal; /**< length of the real FFT. */ + uint8_t ifftFlagR; /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */ + uint8_t bitReverseFlagR; /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */ + uint32_t twidCoefRModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + const q15_t *pTwiddleAReal; /**< points to the real twiddle factor table. */ + const q15_t *pTwiddleBReal; /**< points to the imag twiddle factor table. */ +#if defined(ARM_MATH_MVEI) + arm_cfft_instance_q15 cfftInst; +#else + const arm_cfft_instance_q15 *pCfft; /**< points to the complex FFT instance. */ +#endif + } arm_rfft_instance_q15; + + arm_status arm_rfft_init_q15( + arm_rfft_instance_q15 * S, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + q15_t * pSrc, + q15_t * pDst); + + /** + * @brief Instance structure for the Q31 RFFT/RIFFT function. + */ + typedef struct + { + uint32_t fftLenReal; /**< length of the real FFT. */ + uint8_t ifftFlagR; /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */ + uint8_t bitReverseFlagR; /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */ + uint32_t twidCoefRModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + const q31_t *pTwiddleAReal; /**< points to the real twiddle factor table. */ + const q31_t *pTwiddleBReal; /**< points to the imag twiddle factor table. */ +#if defined(ARM_MATH_MVEI) + arm_cfft_instance_q31 cfftInst; +#else + const arm_cfft_instance_q31 *pCfft; /**< points to the complex FFT instance. */ +#endif + } arm_rfft_instance_q31; + + arm_status arm_rfft_init_q31( + arm_rfft_instance_q31 * S, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + q31_t * pSrc, + q31_t * pDst); + + /** + * @brief Instance structure for the floating-point RFFT/RIFFT function. + */ + typedef struct + { + uint32_t fftLenReal; /**< length of the real FFT. */ + uint16_t fftLenBy2; /**< length of the complex FFT. */ + uint8_t ifftFlagR; /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */ + uint8_t bitReverseFlagR; /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */ + uint32_t twidCoefRModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + const float32_t *pTwiddleAReal; /**< points to the real twiddle factor table. */ + const float32_t *pTwiddleBReal; /**< points to the imag twiddle factor table. */ + arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */ + } arm_rfft_instance_f32; + + arm_status arm_rfft_init_f32( + arm_rfft_instance_f32 * S, + arm_cfft_radix4_instance_f32 * S_CFFT, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + void arm_rfft_f32( + const arm_rfft_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst); + + /** + * @brief Instance structure for the Double Precision Floating-point RFFT/RIFFT function. + */ +typedef struct + { + arm_cfft_instance_f64 Sint; /**< Internal CFFT structure. */ + uint16_t fftLenRFFT; /**< length of the real sequence */ + const float64_t * pTwiddleRFFT; /**< Twiddle factors real stage */ + } arm_rfft_fast_instance_f64 ; + +arm_status arm_rfft_fast_init_f64 ( + arm_rfft_fast_instance_f64 * S, + uint16_t fftLen); + + +void arm_rfft_fast_f64( + arm_rfft_fast_instance_f64 * S, + float64_t * p, float64_t * pOut, + uint8_t ifftFlag); + + + /** + * @brief Instance structure for the floating-point RFFT/RIFFT function. + */ +typedef struct + { + arm_cfft_instance_f32 Sint; /**< Internal CFFT structure. */ + uint16_t fftLenRFFT; /**< length of the real sequence */ + const float32_t * pTwiddleRFFT; /**< Twiddle factors real stage */ + } arm_rfft_fast_instance_f32 ; + +arm_status arm_rfft_fast_init_f32 ( + arm_rfft_fast_instance_f32 * S, + uint16_t fftLen); + + + void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + float32_t * p, float32_t * pOut, + uint8_t ifftFlag); + + /** + * @brief Instance structure for the floating-point DCT4/IDCT4 function. + */ + typedef struct + { + uint16_t N; /**< length of the DCT4. */ + uint16_t Nby2; /**< half of the length of the DCT4. */ + float32_t normalize; /**< normalizing factor. */ + const float32_t *pTwiddle; /**< points to the twiddle factor table. */ + const float32_t *pCosFactor; /**< points to the cosFactor table. */ + arm_rfft_instance_f32 *pRfft; /**< points to the real FFT instance. */ + arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */ + } arm_dct4_instance_f32; + + + /** + * @brief Initialization function for the floating-point DCT4/IDCT4. + * @param[in,out] S points to an instance of floating-point DCT4/IDCT4 structure. + * @param[in] S_RFFT points to an instance of floating-point RFFT/RIFFT structure. + * @param[in] S_CFFT points to an instance of floating-point CFFT/CIFFT structure. + * @param[in] N length of the DCT4. + * @param[in] Nby2 half of the length of the DCT4. + * @param[in] normalize normalizing factor. + * @return arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if fftLenReal is not a supported transform length. + */ + arm_status arm_dct4_init_f32( + arm_dct4_instance_f32 * S, + arm_rfft_instance_f32 * S_RFFT, + arm_cfft_radix4_instance_f32 * S_CFFT, + uint16_t N, + uint16_t Nby2, + float32_t normalize); + + + /** + * @brief Processing function for the floating-point DCT4/IDCT4. + * @param[in] S points to an instance of the floating-point DCT4/IDCT4 structure. + * @param[in] pState points to state buffer. + * @param[in,out] pInlineBuffer points to the in-place input and output buffer. + */ + void arm_dct4_f32( + const arm_dct4_instance_f32 * S, + float32_t * pState, + float32_t * pInlineBuffer); + + + /** + * @brief Instance structure for the Q31 DCT4/IDCT4 function. + */ + typedef struct + { + uint16_t N; /**< length of the DCT4. */ + uint16_t Nby2; /**< half of the length of the DCT4. */ + q31_t normalize; /**< normalizing factor. */ + const q31_t *pTwiddle; /**< points to the twiddle factor table. */ + const q31_t *pCosFactor; /**< points to the cosFactor table. */ + arm_rfft_instance_q31 *pRfft; /**< points to the real FFT instance. */ + arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */ + } arm_dct4_instance_q31; + + + /** + * @brief Initialization function for the Q31 DCT4/IDCT4. + * @param[in,out] S points to an instance of Q31 DCT4/IDCT4 structure. + * @param[in] S_RFFT points to an instance of Q31 RFFT/RIFFT structure + * @param[in] S_CFFT points to an instance of Q31 CFFT/CIFFT structure + * @param[in] N length of the DCT4. + * @param[in] Nby2 half of the length of the DCT4. + * @param[in] normalize normalizing factor. + * @return arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if N is not a supported transform length. + */ + arm_status arm_dct4_init_q31( + arm_dct4_instance_q31 * S, + arm_rfft_instance_q31 * S_RFFT, + arm_cfft_radix4_instance_q31 * S_CFFT, + uint16_t N, + uint16_t Nby2, + q31_t normalize); + + + /** + * @brief Processing function for the Q31 DCT4/IDCT4. + * @param[in] S points to an instance of the Q31 DCT4 structure. + * @param[in] pState points to state buffer. + * @param[in,out] pInlineBuffer points to the in-place input and output buffer. + */ + void arm_dct4_q31( + const arm_dct4_instance_q31 * S, + q31_t * pState, + q31_t * pInlineBuffer); + + + /** + * @brief Instance structure for the Q15 DCT4/IDCT4 function. + */ + typedef struct + { + uint16_t N; /**< length of the DCT4. */ + uint16_t Nby2; /**< half of the length of the DCT4. */ + q15_t normalize; /**< normalizing factor. */ + const q15_t *pTwiddle; /**< points to the twiddle factor table. */ + const q15_t *pCosFactor; /**< points to the cosFactor table. */ + arm_rfft_instance_q15 *pRfft; /**< points to the real FFT instance. */ + arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */ + } arm_dct4_instance_q15; + + + /** + * @brief Initialization function for the Q15 DCT4/IDCT4. + * @param[in,out] S points to an instance of Q15 DCT4/IDCT4 structure. + * @param[in] S_RFFT points to an instance of Q15 RFFT/RIFFT structure. + * @param[in] S_CFFT points to an instance of Q15 CFFT/CIFFT structure. + * @param[in] N length of the DCT4. + * @param[in] Nby2 half of the length of the DCT4. + * @param[in] normalize normalizing factor. + * @return arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if N is not a supported transform length. + */ + arm_status arm_dct4_init_q15( + arm_dct4_instance_q15 * S, + arm_rfft_instance_q15 * S_RFFT, + arm_cfft_radix4_instance_q15 * S_CFFT, + uint16_t N, + uint16_t Nby2, + q15_t normalize); + + + /** + * @brief Processing function for the Q15 DCT4/IDCT4. + * @param[in] S points to an instance of the Q15 DCT4 structure. + * @param[in] pState points to state buffer. + * @param[in,out] pInlineBuffer points to the in-place input and output buffer. + */ + void arm_dct4_q15( + const arm_dct4_instance_q15 * S, + q15_t * pState, + q15_t * pInlineBuffer); + + + /** + * @brief Floating-point vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q7 vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Floating-point vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q7 vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a floating-point vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scale scale factor to be applied + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_f32( + const float32_t * pSrc, + float32_t scale, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a Q7 vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_q7( + const q7_t * pSrc, + q7_t scaleFract, + int8_t shift, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a Q15 vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_q15( + const q15_t * pSrc, + q15_t scaleFract, + int8_t shift, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a Q31 vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_q31( + const q31_t * pSrc, + q31_t scaleFract, + int8_t shift, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q7 vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_q7( + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Floating-point vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Dot product of floating-point vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t blockSize, + float32_t * result); + + + /** + * @brief Dot product of Q7 vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + uint32_t blockSize, + q31_t * result); + + + /** + * @brief Dot product of Q15 vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t blockSize, + q63_t * result); + + + /** + * @brief Dot product of Q31 vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t blockSize, + q63_t * result); + + + /** + * @brief Shifts the elements of a Q7 vector a specified number of bits. + * @param[in] pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_shift_q7( + const q7_t * pSrc, + int8_t shiftBits, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Shifts the elements of a Q15 vector a specified number of bits. + * @param[in] pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_shift_q15( + const q15_t * pSrc, + int8_t shiftBits, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Shifts the elements of a Q31 vector a specified number of bits. + * @param[in] pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_shift_q31( + const q31_t * pSrc, + int8_t shiftBits, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_f32( + const float32_t * pSrc, + float32_t offset, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a Q7 vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_q7( + const q7_t * pSrc, + q7_t offset, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a Q15 vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_q15( + const q15_t * pSrc, + q15_t offset, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a Q31 vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_q31( + const q31_t * pSrc, + q31_t offset, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a Q7 vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_q7( + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a Q15 vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a Q31 vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Copies the elements of a floating-point vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Copies the elements of a Q7 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_q7( + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Copies the elements of a Q15 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Copies the elements of a Q31 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a floating-point vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_f32( + float32_t value, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a Q7 vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_q7( + q7_t value, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a Q15 vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_q15( + q15_t value, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a Q31 vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_q31( + q31_t value, + q31_t * pDst, + uint32_t blockSize); + + +/** + * @brief Convolution of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the location where the output result is written. Length srcALen+srcBLen-1. + */ + void arm_conv_f32( + const float32_t * pSrcA, + uint32_t srcALen, + const float32_t * pSrcB, + uint32_t srcBLen, + float32_t * pDst); + + + /** + * @brief Convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + */ + void arm_conv_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + +/** + * @brief Convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the location where the output result is written. Length srcALen+srcBLen-1. + */ + void arm_conv_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + + /** + * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_fast_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + + /** + * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + */ + void arm_conv_fast_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Convolution of Q31 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + + /** + * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_fast_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + + /** + * @brief Convolution of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + * @param[in] pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen). + */ + void arm_conv_opt_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Convolution of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst); + + + /** + * @brief Partial convolution of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_f32( + const float32_t * pSrcA, + uint32_t srcALen, + const float32_t * pSrcB, + uint32_t srcBLen, + float32_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Partial convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_fast_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_fast_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Partial convolution of Q31 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_fast_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q7 sequences + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @param[in] pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen). + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_opt_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + uint32_t firstIndex, + uint32_t numPoints, + q15_t * pScratch1, + q15_t * pScratch2); + + +/** + * @brief Partial convolution of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Instance structure for the Q15 FIR decimator. + */ + typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR decimator. + */ + typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_q31; + +/** + @brief Instance structure for floating-point FIR decimator. + */ +typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_f32; + + +/** + @brief Processing function for floating-point FIR decimator. + @param[in] S points to an instance of the floating-point FIR decimator structure + @param[in] pSrc points to the block of input data + @param[out] pDst points to the block of output data + @param[in] blockSize number of samples to process + */ +void arm_fir_decimate_f32( + const arm_fir_decimate_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + +/** + @brief Initialization function for the floating-point FIR decimator. + @param[in,out] S points to an instance of the floating-point FIR decimator structure + @param[in] numTaps number of coefficients in the filter + @param[in] M decimation factor + @param[in] pCoeffs points to the filter coefficients + @param[in] pState points to the state buffer + @param[in] blockSize number of input samples to process per call + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_LENGTH_ERROR : blockSize is not a multiple of M + */ +arm_status arm_fir_decimate_init_f32( + arm_fir_decimate_instance_f32 * S, + uint16_t numTaps, + uint8_t M, + const float32_t * pCoeffs, + float32_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 FIR decimator. + * @param[in] S points to an instance of the Q15 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_q15( + const arm_fir_decimate_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q15 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_fast_q15( + const arm_fir_decimate_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q15 FIR decimator. + * @param[in,out] S points to an instance of the Q15 FIR decimator structure. + * @param[in] numTaps number of coefficients in the filter. + * @param[in] M decimation factor. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * blockSize is not a multiple of M. + */ + arm_status arm_fir_decimate_init_q15( + arm_fir_decimate_instance_q15 * S, + uint16_t numTaps, + uint8_t M, + const q15_t * pCoeffs, + q15_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 FIR decimator. + * @param[in] S points to an instance of the Q31 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_q31( + const arm_fir_decimate_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q31 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_fast_q31( + const arm_fir_decimate_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 FIR decimator. + * @param[in,out] S points to an instance of the Q31 FIR decimator structure. + * @param[in] numTaps number of coefficients in the filter. + * @param[in] M decimation factor. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * blockSize is not a multiple of M. + */ + arm_status arm_fir_decimate_init_q31( + arm_fir_decimate_instance_q31 * S, + uint16_t numTaps, + uint8_t M, + const q31_t * pCoeffs, + q31_t * pState, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 FIR interpolator. + */ + typedef struct + { + uint8_t L; /**< upsample factor. */ + uint16_t phaseLength; /**< length of each polyphase filter component. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length L*phaseLength. */ + q15_t *pState; /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */ + } arm_fir_interpolate_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR interpolator. + */ + typedef struct + { + uint8_t L; /**< upsample factor. */ + uint16_t phaseLength; /**< length of each polyphase filter component. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length L*phaseLength. */ + q31_t *pState; /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */ + } arm_fir_interpolate_instance_q31; + + /** + * @brief Instance structure for the floating-point FIR interpolator. + */ + typedef struct + { + uint8_t L; /**< upsample factor. */ + uint16_t phaseLength; /**< length of each polyphase filter component. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length L*phaseLength. */ + float32_t *pState; /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */ + } arm_fir_interpolate_instance_f32; + + + /** + * @brief Processing function for the Q15 FIR interpolator. + * @param[in] S points to an instance of the Q15 FIR interpolator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_interpolate_q15( + const arm_fir_interpolate_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q15 FIR interpolator. + * @param[in,out] S points to an instance of the Q15 FIR interpolator structure. + * @param[in] L upsample factor. + * @param[in] numTaps number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * the filter length numTaps is not a multiple of the interpolation factor L. + */ + arm_status arm_fir_interpolate_init_q15( + arm_fir_interpolate_instance_q15 * S, + uint8_t L, + uint16_t numTaps, + const q15_t * pCoeffs, + q15_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 FIR interpolator. + * @param[in] S points to an instance of the Q15 FIR interpolator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_interpolate_q31( + const arm_fir_interpolate_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 FIR interpolator. + * @param[in,out] S points to an instance of the Q31 FIR interpolator structure. + * @param[in] L upsample factor. + * @param[in] numTaps number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * the filter length numTaps is not a multiple of the interpolation factor L. + */ + arm_status arm_fir_interpolate_init_q31( + arm_fir_interpolate_instance_q31 * S, + uint8_t L, + uint16_t numTaps, + const q31_t * pCoeffs, + q31_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the floating-point FIR interpolator. + * @param[in] S points to an instance of the floating-point FIR interpolator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_interpolate_f32( + const arm_fir_interpolate_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the floating-point FIR interpolator. + * @param[in,out] S points to an instance of the floating-point FIR interpolator structure. + * @param[in] L upsample factor. + * @param[in] numTaps number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * the filter length numTaps is not a multiple of the interpolation factor L. + */ + arm_status arm_fir_interpolate_init_f32( + arm_fir_interpolate_instance_f32 * S, + uint8_t L, + uint16_t numTaps, + const float32_t * pCoeffs, + float32_t * pState, + uint32_t blockSize); + + + /** + * @brief Instance structure for the high precision Q31 Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + q63_t *pState; /**< points to the array of state coefficients. The array is of length 4*numStages. */ + const q31_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + uint8_t postShift; /**< additional shift, in bits, applied to each output sample. */ + } arm_biquad_cas_df1_32x64_ins_q31; + + + /** + * @param[in] S points to an instance of the high precision Q31 Biquad cascade filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cas_df1_32x64_q31( + const arm_biquad_cas_df1_32x64_ins_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @param[in,out] S points to an instance of the high precision Q31 Biquad cascade filter structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] postShift shift to be applied to the output. Varies according to the coefficients format + */ + void arm_biquad_cas_df1_32x64_init_q31( + arm_biquad_cas_df1_32x64_ins_q31 * S, + uint8_t numStages, + const q31_t * pCoeffs, + q63_t * pState, + uint8_t postShift); + + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float32_t *pState; /**< points to the array of state coefficients. The array is of length 2*numStages. */ + const float32_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_df2T_instance_f32; + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float32_t *pState; /**< points to the array of state coefficients. The array is of length 4*numStages. */ + const float32_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_stereo_df2T_instance_f32; + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float64_t *pState; /**< points to the array of state coefficients. The array is of length 2*numStages. */ + const float64_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_df2T_instance_f64; + + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df2T_f32( + const arm_biquad_cascade_df2T_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_stereo_df2T_f32( + const arm_biquad_cascade_stereo_df2T_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df2T_f64( + const arm_biquad_cascade_df2T_instance_f64 * S, + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + +#if defined(ARM_MATH_NEON) +void arm_biquad_cascade_df2T_compute_coefs_f32( + arm_biquad_cascade_df2T_instance_f32 * S, + uint8_t numStages, + float32_t * pCoeffs); +#endif + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_df2T_init_f32( + arm_biquad_cascade_df2T_instance_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_stereo_df2T_init_f32( + arm_biquad_cascade_stereo_df2T_instance_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_df2T_init_f64( + arm_biquad_cascade_df2T_instance_f64 * S, + uint8_t numStages, + const float64_t * pCoeffs, + float64_t * pState); + + + /** + * @brief Instance structure for the Q15 FIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of filter stages. */ + q15_t *pState; /**< points to the state variable array. The array is of length numStages. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numStages. */ + } arm_fir_lattice_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of filter stages. */ + q31_t *pState; /**< points to the state variable array. The array is of length numStages. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numStages. */ + } arm_fir_lattice_instance_q31; + + /** + * @brief Instance structure for the floating-point FIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of filter stages. */ + float32_t *pState; /**< points to the state variable array. The array is of length numStages. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numStages. */ + } arm_fir_lattice_instance_f32; + + + /** + * @brief Initialization function for the Q15 FIR lattice filter. + * @param[in] S points to an instance of the Q15 FIR lattice structure. + * @param[in] numStages number of filter stages. + * @param[in] pCoeffs points to the coefficient buffer. The array is of length numStages. + * @param[in] pState points to the state buffer. The array is of length numStages. + */ + void arm_fir_lattice_init_q15( + arm_fir_lattice_instance_q15 * S, + uint16_t numStages, + const q15_t * pCoeffs, + q15_t * pState); + + + /** + * @brief Processing function for the Q15 FIR lattice filter. + * @param[in] S points to an instance of the Q15 FIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_lattice_q15( + const arm_fir_lattice_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 FIR lattice filter. + * @param[in] S points to an instance of the Q31 FIR lattice structure. + * @param[in] numStages number of filter stages. + * @param[in] pCoeffs points to the coefficient buffer. The array is of length numStages. + * @param[in] pState points to the state buffer. The array is of length numStages. + */ + void arm_fir_lattice_init_q31( + arm_fir_lattice_instance_q31 * S, + uint16_t numStages, + const q31_t * pCoeffs, + q31_t * pState); + + + /** + * @brief Processing function for the Q31 FIR lattice filter. + * @param[in] S points to an instance of the Q31 FIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_fir_lattice_q31( + const arm_fir_lattice_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + +/** + * @brief Initialization function for the floating-point FIR lattice filter. + * @param[in] S points to an instance of the floating-point FIR lattice structure. + * @param[in] numStages number of filter stages. + * @param[in] pCoeffs points to the coefficient buffer. The array is of length numStages. + * @param[in] pState points to the state buffer. The array is of length numStages. + */ + void arm_fir_lattice_init_f32( + arm_fir_lattice_instance_f32 * S, + uint16_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Processing function for the floating-point FIR lattice filter. + * @param[in] S points to an instance of the floating-point FIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_fir_lattice_f32( + const arm_fir_lattice_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 IIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of stages in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numStages+blockSize. */ + q15_t *pkCoeffs; /**< points to the reflection coefficient array. The array is of length numStages. */ + q15_t *pvCoeffs; /**< points to the ladder coefficient array. The array is of length numStages+1. */ + } arm_iir_lattice_instance_q15; + + /** + * @brief Instance structure for the Q31 IIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of stages in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numStages+blockSize. */ + q31_t *pkCoeffs; /**< points to the reflection coefficient array. The array is of length numStages. */ + q31_t *pvCoeffs; /**< points to the ladder coefficient array. The array is of length numStages+1. */ + } arm_iir_lattice_instance_q31; + + /** + * @brief Instance structure for the floating-point IIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of stages in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numStages+blockSize. */ + float32_t *pkCoeffs; /**< points to the reflection coefficient array. The array is of length numStages. */ + float32_t *pvCoeffs; /**< points to the ladder coefficient array. The array is of length numStages+1. */ + } arm_iir_lattice_instance_f32; + + + /** + * @brief Processing function for the floating-point IIR lattice filter. + * @param[in] S points to an instance of the floating-point IIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_f32( + const arm_iir_lattice_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the floating-point IIR lattice filter. + * @param[in] S points to an instance of the floating-point IIR lattice structure. + * @param[in] numStages number of stages in the filter. + * @param[in] pkCoeffs points to the reflection coefficient buffer. The array is of length numStages. + * @param[in] pvCoeffs points to the ladder coefficient buffer. The array is of length numStages+1. + * @param[in] pState points to the state buffer. The array is of length numStages+blockSize-1. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_init_f32( + arm_iir_lattice_instance_f32 * S, + uint16_t numStages, + float32_t * pkCoeffs, + float32_t * pvCoeffs, + float32_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 IIR lattice filter. + * @param[in] S points to an instance of the Q31 IIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_q31( + const arm_iir_lattice_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 IIR lattice filter. + * @param[in] S points to an instance of the Q31 IIR lattice structure. + * @param[in] numStages number of stages in the filter. + * @param[in] pkCoeffs points to the reflection coefficient buffer. The array is of length numStages. + * @param[in] pvCoeffs points to the ladder coefficient buffer. The array is of length numStages+1. + * @param[in] pState points to the state buffer. The array is of length numStages+blockSize. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_init_q31( + arm_iir_lattice_instance_q31 * S, + uint16_t numStages, + q31_t * pkCoeffs, + q31_t * pvCoeffs, + q31_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 IIR lattice filter. + * @param[in] S points to an instance of the Q15 IIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_q15( + const arm_iir_lattice_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + +/** + * @brief Initialization function for the Q15 IIR lattice filter. + * @param[in] S points to an instance of the fixed-point Q15 IIR lattice structure. + * @param[in] numStages number of stages in the filter. + * @param[in] pkCoeffs points to reflection coefficient buffer. The array is of length numStages. + * @param[in] pvCoeffs points to ladder coefficient buffer. The array is of length numStages+1. + * @param[in] pState points to state buffer. The array is of length numStages+blockSize. + * @param[in] blockSize number of samples to process per call. + */ + void arm_iir_lattice_init_q15( + arm_iir_lattice_instance_q15 * S, + uint16_t numStages, + q15_t * pkCoeffs, + q15_t * pvCoeffs, + q15_t * pState, + uint32_t blockSize); + + + /** + * @brief Instance structure for the floating-point LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + float32_t mu; /**< step size that controls filter coefficient updates. */ + } arm_lms_instance_f32; + + + /** + * @brief Processing function for floating-point LMS filter. + * @param[in] S points to an instance of the floating-point LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_f32( + const arm_lms_instance_f32 * S, + const float32_t * pSrc, + float32_t * pRef, + float32_t * pOut, + float32_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for floating-point LMS filter. + * @param[in] S points to an instance of the floating-point LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to the coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_init_f32( + arm_lms_instance_f32 * S, + uint16_t numTaps, + float32_t * pCoeffs, + float32_t * pState, + float32_t mu, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q15_t mu; /**< step size that controls filter coefficient updates. */ + uint32_t postShift; /**< bit shift applied to coefficients. */ + } arm_lms_instance_q15; + + + /** + * @brief Initialization function for the Q15 LMS filter. + * @param[in] S points to an instance of the Q15 LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to the coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_init_q15( + arm_lms_instance_q15 * S, + uint16_t numTaps, + q15_t * pCoeffs, + q15_t * pState, + q15_t mu, + uint32_t blockSize, + uint32_t postShift); + + + /** + * @brief Processing function for Q15 LMS filter. + * @param[in] S points to an instance of the Q15 LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_q15( + const arm_lms_instance_q15 * S, + const q15_t * pSrc, + q15_t * pRef, + q15_t * pOut, + q15_t * pErr, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q31 LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q31_t mu; /**< step size that controls filter coefficient updates. */ + uint32_t postShift; /**< bit shift applied to coefficients. */ + } arm_lms_instance_q31; + + + /** + * @brief Processing function for Q31 LMS filter. + * @param[in] S points to an instance of the Q15 LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_q31( + const arm_lms_instance_q31 * S, + const q31_t * pSrc, + q31_t * pRef, + q31_t * pOut, + q31_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for Q31 LMS filter. + * @param[in] S points to an instance of the Q31 LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_init_q31( + arm_lms_instance_q31 * S, + uint16_t numTaps, + q31_t * pCoeffs, + q31_t * pState, + q31_t mu, + uint32_t blockSize, + uint32_t postShift); + + + /** + * @brief Instance structure for the floating-point normalized LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + float32_t mu; /**< step size that control filter coefficient updates. */ + float32_t energy; /**< saves previous frame energy. */ + float32_t x0; /**< saves previous input sample. */ + } arm_lms_norm_instance_f32; + + + /** + * @brief Processing function for floating-point normalized LMS filter. + * @param[in] S points to an instance of the floating-point normalized LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_f32( + arm_lms_norm_instance_f32 * S, + const float32_t * pSrc, + float32_t * pRef, + float32_t * pOut, + float32_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for floating-point normalized LMS filter. + * @param[in] S points to an instance of the floating-point LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_init_f32( + arm_lms_norm_instance_f32 * S, + uint16_t numTaps, + float32_t * pCoeffs, + float32_t * pState, + float32_t mu, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q31 normalized LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q31_t mu; /**< step size that controls filter coefficient updates. */ + uint8_t postShift; /**< bit shift applied to coefficients. */ + const q31_t *recipTable; /**< points to the reciprocal initial value table. */ + q31_t energy; /**< saves previous frame energy. */ + q31_t x0; /**< saves previous input sample. */ + } arm_lms_norm_instance_q31; + + + /** + * @brief Processing function for Q31 normalized LMS filter. + * @param[in] S points to an instance of the Q31 normalized LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_q31( + arm_lms_norm_instance_q31 * S, + const q31_t * pSrc, + q31_t * pRef, + q31_t * pOut, + q31_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for Q31 normalized LMS filter. + * @param[in] S points to an instance of the Q31 normalized LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_norm_init_q31( + arm_lms_norm_instance_q31 * S, + uint16_t numTaps, + q31_t * pCoeffs, + q31_t * pState, + q31_t mu, + uint32_t blockSize, + uint8_t postShift); + + + /** + * @brief Instance structure for the Q15 normalized LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< Number of coefficients in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q15_t mu; /**< step size that controls filter coefficient updates. */ + uint8_t postShift; /**< bit shift applied to coefficients. */ + const q15_t *recipTable; /**< Points to the reciprocal initial value table. */ + q15_t energy; /**< saves previous frame energy. */ + q15_t x0; /**< saves previous input sample. */ + } arm_lms_norm_instance_q15; + + + /** + * @brief Processing function for Q15 normalized LMS filter. + * @param[in] S points to an instance of the Q15 normalized LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_q15( + arm_lms_norm_instance_q15 * S, + const q15_t * pSrc, + q15_t * pRef, + q15_t * pOut, + q15_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for Q15 normalized LMS filter. + * @param[in] S points to an instance of the Q15 normalized LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_norm_init_q15( + arm_lms_norm_instance_q15 * S, + uint16_t numTaps, + q15_t * pCoeffs, + q15_t * pState, + q15_t mu, + uint32_t blockSize, + uint8_t postShift); + + + /** + * @brief Correlation of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_f32( + const float32_t * pSrcA, + uint32_t srcALen, + const float32_t * pSrcB, + uint32_t srcBLen, + float32_t * pDst); + + +/** + @brief Correlation of Q15 sequences + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + @param[in] pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. +*/ +void arm_correlate_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch); + + +/** + @brief Correlation of Q15 sequences. + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + +/** + @brief Correlation of Q15 sequences (fast version). + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1. + @return none + */ +void arm_correlate_fast_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + +/** + @brief Correlation of Q15 sequences (fast version). + @param[in] pSrcA points to the first input sequence. + @param[in] srcALen length of the first input sequence. + @param[in] pSrcB points to the second input sequence. + @param[in] srcBLen length of the second input sequence. + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + @param[in] pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + */ +void arm_correlate_fast_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch); + + + /** + * @brief Correlation of Q31 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + +/** + @brief Correlation of Q31 sequences (fast version). + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ +void arm_correlate_fast_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + + /** + * @brief Correlation of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + * @param[in] pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen). + */ + void arm_correlate_opt_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Correlation of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst); + + + /** + * @brief Instance structure for the floating-point sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + float32_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_f32; + + /** + * @brief Instance structure for the Q31 sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + q31_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_q31; + + /** + * @brief Instance structure for the Q15 sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + q15_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_q15; + + /** + * @brief Instance structure for the Q7 sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + q7_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const q7_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_q7; + + + /** + * @brief Processing function for the floating-point sparse FIR filter. + * @param[in] S points to an instance of the floating-point sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_f32( + arm_fir_sparse_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + float32_t * pScratchIn, + uint32_t blockSize); + + + /** + * @brief Initialization function for the floating-point sparse FIR filter. + * @param[in,out] S points to an instance of the floating-point sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_f32( + arm_fir_sparse_instance_f32 * S, + uint16_t numTaps, + const float32_t * pCoeffs, + float32_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 sparse FIR filter. + * @param[in] S points to an instance of the Q31 sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_q31( + arm_fir_sparse_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + q31_t * pScratchIn, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 sparse FIR filter. + * @param[in,out] S points to an instance of the Q31 sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_q31( + arm_fir_sparse_instance_q31 * S, + uint16_t numTaps, + const q31_t * pCoeffs, + q31_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 sparse FIR filter. + * @param[in] S points to an instance of the Q15 sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] pScratchOut points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_q15( + arm_fir_sparse_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + q15_t * pScratchIn, + q31_t * pScratchOut, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q15 sparse FIR filter. + * @param[in,out] S points to an instance of the Q15 sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_q15( + arm_fir_sparse_instance_q15 * S, + uint16_t numTaps, + const q15_t * pCoeffs, + q15_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q7 sparse FIR filter. + * @param[in] S points to an instance of the Q7 sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] pScratchOut points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_q7( + arm_fir_sparse_instance_q7 * S, + const q7_t * pSrc, + q7_t * pDst, + q7_t * pScratchIn, + q31_t * pScratchOut, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q7 sparse FIR filter. + * @param[in,out] S points to an instance of the Q7 sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_q7( + arm_fir_sparse_instance_q7 * S, + uint16_t numTaps, + const q7_t * pCoeffs, + q7_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Floating-point sin_cos function. + * @param[in] theta input value in degrees + * @param[out] pSinVal points to the processed sine output. + * @param[out] pCosVal points to the processed cos output. + */ + void arm_sin_cos_f32( + float32_t theta, + float32_t * pSinVal, + float32_t * pCosVal); + + + /** + * @brief Q31 sin_cos function. + * @param[in] theta scaled input value in degrees + * @param[out] pSinVal points to the processed sine output. + * @param[out] pCosVal points to the processed cosine output. + */ + void arm_sin_cos_q31( + q31_t theta, + q31_t * pSinVal, + q31_t * pCosVal); + + + /** + * @brief Floating-point complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples); + + /** + * @brief Q31 complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @ingroup groupController + */ + + /** + * @defgroup PID PID Motor Control + * + * A Proportional Integral Derivative (PID) controller is a generic feedback control + * loop mechanism widely used in industrial control systems. + * A PID controller is the most commonly used type of feedback controller. + * + * This set of functions implements (PID) controllers + * for Q15, Q31, and floating-point data types. The functions operate on a single sample + * of data and each call to the function returns a single processed value. + * S points to an instance of the PID control data structure. in + * is the input sample value. The functions return the output value. + * + * \par Algorithm: + * 
+   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
+   *    A0 = Kp + Ki + Kd
+   *    A1 = (-Kp ) - (2 * Kd )
+   *    A2 = Kd
+   *
+ * + * \par + * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant + * + * \par + * \image html PID.gif "Proportional Integral Derivative Controller" + * + * \par + * The PID controller calculates an "error" value as the difference between + * the measured output and the reference input. + * The controller attempts to minimize the error by adjusting the process control inputs. + * The proportional value determines the reaction to the current error, + * the integral value determines the reaction based on the sum of recent errors, + * and the derivative value determines the reaction based on the rate at which the error has been changing. + * + * \par Instance Structure + * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure. + * A separate instance structure must be defined for each PID Controller. + * There are separate instance structure declarations for each of the 3 supported data types. + * + * \par Reset Functions + * There is also an associated reset function for each data type which clears the state array. + * + * \par Initialization Functions + * There is also an associated initialization function for each data type. + * The initialization function performs the following operations: + * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains. + * - Zeros out the values in the state buffer. + * + * \par + * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function. + * + * \par Fixed-Point Behavior + * Care must be taken when using the fixed-point versions of the PID Controller functions. + * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + /** + * @addtogroup PID + * @{ + */ + + /** + * @brief Process function for the floating-point PID Control. + * @param[in,out] S is an instance of the floating-point PID Control structure + * @param[in] in input sample to process + * @return processed output sample. + */ + __STATIC_FORCEINLINE float32_t arm_pid_f32( + arm_pid_instance_f32 * S, + float32_t in) + { + float32_t out; + + /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2] */ + out = (S->A0 * in) + + (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]); + + /* Update state */ + S->state[1] = S->state[0]; + S->state[0] = in; + S->state[2] = out; + + /* return to application */ + return (out); + + } + +/** + @brief Process function for the Q31 PID Control. + @param[in,out] S points to an instance of the Q31 PID Control structure + @param[in] in input sample to process + @return processed output sample. + + \par Scaling and Overflow Behavior + The function is implemented using an internal 64-bit accumulator. + The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. + Thus, if the accumulator result overflows it wraps around rather than clip. + In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions. + After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format. + */ +__STATIC_FORCEINLINE q31_t arm_pid_q31( + arm_pid_instance_q31 * S, + q31_t in) + { + q63_t acc; + q31_t out; + + /* acc = A0 * x[n] */ + acc = (q63_t) S->A0 * in; + + /* acc += A1 * x[n-1] */ + acc += (q63_t) S->A1 * S->state[0]; + + /* acc += A2 * x[n-2] */ + acc += (q63_t) S->A2 * S->state[1]; + + /* convert output to 1.31 format to add y[n-1] */ + out = (q31_t) (acc >> 31U); + + /* out += y[n-1] */ + out += S->state[2]; + + /* Update state */ + S->state[1] = S->state[0]; + S->state[0] = in; + S->state[2] = out; + + /* return to application */ + return (out); + } + + +/** + @brief Process function for the Q15 PID Control. + @param[in,out] S points to an instance of the Q15 PID Control structure + @param[in] in input sample to process + @return processed output sample. + + \par Scaling and Overflow Behavior + The function is implemented using a 64-bit internal accumulator. + Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result. + The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. + There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved. + After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits. + Lastly, the accumulator is saturated to yield a result in 1.15 format. + */ +__STATIC_FORCEINLINE q15_t arm_pid_q15( + arm_pid_instance_q15 * S, + q15_t in) + { + q63_t acc; + q15_t out; + +#if defined (ARM_MATH_DSP) + /* Implementation of PID controller */ + + /* acc = A0 * x[n] */ + acc = (q31_t) __SMUAD((uint32_t)S->A0, (uint32_t)in); + + /* acc += A1 * x[n-1] + A2 * x[n-2] */ + acc = (q63_t)__SMLALD((uint32_t)S->A1, (uint32_t)read_q15x2 (S->state), (uint64_t)acc); +#else + /* acc = A0 * x[n] */ + acc = ((q31_t) S->A0) * in; + + /* acc += A1 * x[n-1] + A2 * x[n-2] */ + acc += (q31_t) S->A1 * S->state[0]; + acc += (q31_t) S->A2 * S->state[1]; +#endif + + /* acc += y[n-1] */ + acc += (q31_t) S->state[2] << 15; + + /* saturate the output */ + out = (q15_t) (__SSAT((q31_t)(acc >> 15), 16)); + + /* Update state */ + S->state[1] = S->state[0]; + S->state[0] = in; + S->state[2] = out; + + /* return to application */ + return (out); + } + + /** + * @} end of PID group + */ + + + /** + * @brief Floating-point matrix inverse. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR. + */ + arm_status arm_mat_inverse_f32( + const arm_matrix_instance_f32 * src, + arm_matrix_instance_f32 * dst); + + + /** + * @brief Floating-point matrix inverse. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR. + */ + arm_status arm_mat_inverse_f64( + const arm_matrix_instance_f64 * src, + arm_matrix_instance_f64 * dst); + + + + /** + * @ingroup groupController + */ + + /** + * @defgroup clarke Vector Clarke Transform + * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector. + * Generally the Clarke transform uses three-phase currents Ia, Ib and Ic to calculate currents + * in the two-phase orthogonal stator axis Ialpha and Ibeta. + * When Ialpha is superposed with Ia as shown in the figure below + * \image html clarke.gif Stator current space vector and its components in (a,b). + * and Ia + Ib + Ic = 0, in this condition Ialpha and Ibeta + * can be calculated using only Ia and Ib. + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html clarkeFormula.gif + * where Ia and Ib are the instantaneous stator phases and + * pIalpha and pIbeta are the two coordinates of time invariant vector. + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Clarke transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + /** + * @addtogroup clarke + * @{ + */ + + /** + * + * @brief Floating-point Clarke transform + * @param[in] Ia input three-phase coordinate a + * @param[in] Ib input three-phase coordinate b + * @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + * @param[out] pIbeta points to output two-phase orthogonal vector axis beta + * @return none + */ + __STATIC_FORCEINLINE void arm_clarke_f32( + float32_t Ia, + float32_t Ib, + float32_t * pIalpha, + float32_t * pIbeta) + { + /* Calculate pIalpha using the equation, pIalpha = Ia */ + *pIalpha = Ia; + + /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */ + *pIbeta = ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib); + } + + +/** + @brief Clarke transform for Q31 version + @param[in] Ia input three-phase coordinate a + @param[in] Ib input three-phase coordinate b + @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + @param[out] pIbeta points to output two-phase orthogonal vector axis beta + @return none + + \par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the addition, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_clarke_q31( + q31_t Ia, + q31_t Ib, + q31_t * pIalpha, + q31_t * pIbeta) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + + /* Calculating pIalpha from Ia by equation pIalpha = Ia */ + *pIalpha = Ia; + + /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */ + product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30); + + /* Intermediate product is calculated by (2/sqrt(3) * Ib) */ + product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30); + + /* pIbeta is calculated by adding the intermediate products */ + *pIbeta = __QADD(product1, product2); + } + + /** + * @} end of clarke group + */ + + + /** + * @ingroup groupController + */ + + /** + * @defgroup inv_clarke Vector Inverse Clarke Transform + * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases. + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html clarkeInvFormula.gif + * where pIa and pIb are the instantaneous stator phases and + * Ialpha and Ibeta are the two coordinates of time invariant vector. + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Clarke transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + /** + * @addtogroup inv_clarke + * @{ + */ + + /** + * @brief Floating-point Inverse Clarke transform + * @param[in] Ialpha input two-phase orthogonal vector axis alpha + * @param[in] Ibeta input two-phase orthogonal vector axis beta + * @param[out] pIa points to output three-phase coordinate a + * @param[out] pIb points to output three-phase coordinate b + * @return none + */ + __STATIC_FORCEINLINE void arm_inv_clarke_f32( + float32_t Ialpha, + float32_t Ibeta, + float32_t * pIa, + float32_t * pIb) + { + /* Calculating pIa from Ialpha by equation pIa = Ialpha */ + *pIa = Ialpha; + + /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */ + *pIb = -0.5f * Ialpha + 0.8660254039f * Ibeta; + } + + +/** + @brief Inverse Clarke transform for Q31 version + @param[in] Ialpha input two-phase orthogonal vector axis alpha + @param[in] Ibeta input two-phase orthogonal vector axis beta + @param[out] pIa points to output three-phase coordinate a + @param[out] pIb points to output three-phase coordinate b + @return none + + \par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the subtraction, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_inv_clarke_q31( + q31_t Ialpha, + q31_t Ibeta, + q31_t * pIa, + q31_t * pIb) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + + /* Calculating pIa from Ialpha by equation pIa = Ialpha */ + *pIa = Ialpha; + + /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */ + product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31); + + /* Intermediate product is calculated by (1/sqrt(3) * pIb) */ + product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31); + + /* pIb is calculated by subtracting the products */ + *pIb = __QSUB(product2, product1); + } + + /** + * @} end of inv_clarke group + */ + + + + /** + * @ingroup groupController + */ + + /** + * @defgroup park Vector Park Transform + * + * Forward Park transform converts the input two-coordinate vector to flux and torque components. + * The Park transform can be used to realize the transformation of the Ialpha and the Ibeta currents + * from the stationary to the moving reference frame and control the spatial relationship between + * the stator vector current and rotor flux vector. + * If we consider the d axis aligned with the rotor flux, the diagram below shows the + * current vector and the relationship from the two reference frames: + * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame" + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html parkFormula.gif + * where Ialpha and Ibeta are the stator vector components, + * pId and pIq are rotor vector components and cosVal and sinVal are the + * cosine and sine values of theta (rotor flux position). + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Park transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + /** + * @addtogroup park + * @{ + */ + + /** + * @brief Floating-point Park transform + * @param[in] Ialpha input two-phase vector coordinate alpha + * @param[in] Ibeta input two-phase vector coordinate beta + * @param[out] pId points to output rotor reference frame d + * @param[out] pIq points to output rotor reference frame q + * @param[in] sinVal sine value of rotation angle theta + * @param[in] cosVal cosine value of rotation angle theta + * @return none + * + * The function implements the forward Park transform. + * + */ + __STATIC_FORCEINLINE void arm_park_f32( + float32_t Ialpha, + float32_t Ibeta, + float32_t * pId, + float32_t * pIq, + float32_t sinVal, + float32_t cosVal) + { + /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */ + *pId = Ialpha * cosVal + Ibeta * sinVal; + + /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */ + *pIq = -Ialpha * sinVal + Ibeta * cosVal; + } + + +/** + @brief Park transform for Q31 version + @param[in] Ialpha input two-phase vector coordinate alpha + @param[in] Ibeta input two-phase vector coordinate beta + @param[out] pId points to output rotor reference frame d + @param[out] pIq points to output rotor reference frame q + @param[in] sinVal sine value of rotation angle theta + @param[in] cosVal cosine value of rotation angle theta + @return none + + \par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the addition and subtraction, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_park_q31( + q31_t Ialpha, + q31_t Ibeta, + q31_t * pId, + q31_t * pIq, + q31_t sinVal, + q31_t cosVal) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + q31_t product3, product4; /* Temporary variables used to store intermediate results */ + + /* Intermediate product is calculated by (Ialpha * cosVal) */ + product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31); + + /* Intermediate product is calculated by (Ibeta * sinVal) */ + product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31); + + + /* Intermediate product is calculated by (Ialpha * sinVal) */ + product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31); + + /* Intermediate product is calculated by (Ibeta * cosVal) */ + product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31); + + /* Calculate pId by adding the two intermediate products 1 and 2 */ + *pId = __QADD(product1, product2); + + /* Calculate pIq by subtracting the two intermediate products 3 from 4 */ + *pIq = __QSUB(product4, product3); + } + + /** + * @} end of park group + */ + + + /** + * @ingroup groupController + */ + + /** + * @defgroup inv_park Vector Inverse Park transform + * Inverse Park transform converts the input flux and torque components to two-coordinate vector. + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html parkInvFormula.gif + * where pIalpha and pIbeta are the stator vector components, + * Id and Iq are rotor vector components and cosVal and sinVal are the + * cosine and sine values of theta (rotor flux position). + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Park transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + /** + * @addtogroup inv_park + * @{ + */ + + /** + * @brief Floating-point Inverse Park transform + * @param[in] Id input coordinate of rotor reference frame d + * @param[in] Iq input coordinate of rotor reference frame q + * @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + * @param[out] pIbeta points to output two-phase orthogonal vector axis beta + * @param[in] sinVal sine value of rotation angle theta + * @param[in] cosVal cosine value of rotation angle theta + * @return none + */ + __STATIC_FORCEINLINE void arm_inv_park_f32( + float32_t Id, + float32_t Iq, + float32_t * pIalpha, + float32_t * pIbeta, + float32_t sinVal, + float32_t cosVal) + { + /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */ + *pIalpha = Id * cosVal - Iq * sinVal; + + /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */ + *pIbeta = Id * sinVal + Iq * cosVal; + } + + +/** + @brief Inverse Park transform for Q31 version + @param[in] Id input coordinate of rotor reference frame d + @param[in] Iq input coordinate of rotor reference frame q + @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + @param[out] pIbeta points to output two-phase orthogonal vector axis beta + @param[in] sinVal sine value of rotation angle theta + @param[in] cosVal cosine value of rotation angle theta + @return none + + @par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the addition, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_inv_park_q31( + q31_t Id, + q31_t Iq, + q31_t * pIalpha, + q31_t * pIbeta, + q31_t sinVal, + q31_t cosVal) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + q31_t product3, product4; /* Temporary variables used to store intermediate results */ + + /* Intermediate product is calculated by (Id * cosVal) */ + product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31); + + /* Intermediate product is calculated by (Iq * sinVal) */ + product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31); + + + /* Intermediate product is calculated by (Id * sinVal) */ + product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31); + + /* Intermediate product is calculated by (Iq * cosVal) */ + product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31); + + /* Calculate pIalpha by using the two intermediate products 1 and 2 */ + *pIalpha = __QSUB(product1, product2); + + /* Calculate pIbeta by using the two intermediate products 3 and 4 */ + *pIbeta = __QADD(product4, product3); + } + + /** + * @} end of Inverse park group + */ + + + /** + * @ingroup groupInterpolation + */ + + /** + * @defgroup LinearInterpolate Linear Interpolation + * + * Linear interpolation is a method of curve fitting using linear polynomials. + * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line + * + * \par + * \image html LinearInterp.gif "Linear interpolation" + * + * \par + * A Linear Interpolate function calculates an output value(y), for the input(x) + * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values) + * + * \par Algorithm: + * 
+   *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
+   *       where x0, x1 are nearest values of input x
+   *             y0, y1 are nearest values to output y
+   *
+ * + * \par + * This set of functions implements Linear interpolation process + * for Q7, Q15, Q31, and floating-point data types. The functions operate on a single + * sample of data and each call to the function returns a single processed value. + * S points to an instance of the Linear Interpolate function data structure. + * x is the input sample value. The functions returns the output value. + * + * \par + * if x is outside of the table boundary, Linear interpolation returns first value of the table + * if x is below input range and returns last value of table if x is above range. + */ + + /** + * @addtogroup LinearInterpolate + * @{ + */ + + /** + * @brief Process function for the floating-point Linear Interpolation Function. + * @param[in,out] S is an instance of the floating-point Linear Interpolation structure + * @param[in] x input sample to process + * @return y processed output sample. + * + */ + __STATIC_FORCEINLINE float32_t arm_linear_interp_f32( + arm_linear_interp_instance_f32 * S, + float32_t x) + { + float32_t y; + float32_t x0, x1; /* Nearest input values */ + float32_t y0, y1; /* Nearest output values */ + float32_t xSpacing = S->xSpacing; /* spacing between input values */ + int32_t i; /* Index variable */ + float32_t *pYData = S->pYData; /* pointer to output table */ + + /* Calculation of index */ + i = (int32_t) ((x - S->x1) / xSpacing); + + if (i < 0) + { + /* Iniatilize output for below specified range as least output value of table */ + y = pYData[0]; + } + else if ((uint32_t)i >= (S->nValues - 1)) + { + /* Iniatilize output for above specified range as last output value of table */ + y = pYData[S->nValues - 1]; + } + else + { + /* Calculation of nearest input values */ + x0 = S->x1 + i * xSpacing; + x1 = S->x1 + (i + 1) * xSpacing; + + /* Read of nearest output values */ + y0 = pYData[i]; + y1 = pYData[i + 1]; + + /* Calculation of output */ + y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0)); + + } + + /* returns output value */ + return (y); + } + + + /** + * + * @brief Process function for the Q31 Linear Interpolation Function. + * @param[in] pYData pointer to Q31 Linear Interpolation table + * @param[in] x input sample to process + * @param[in] nValues number of table values + * @return y processed output sample. + * + * \par + * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part. + * This function can support maximum of table size 2^12. + * + */ + __STATIC_FORCEINLINE q31_t arm_linear_interp_q31( + q31_t * pYData, + q31_t x, + uint32_t nValues) + { + q31_t y; /* output */ + q31_t y0, y1; /* Nearest output values */ + q31_t fract; /* fractional part */ + int32_t index; /* Index to read nearest output values */ + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + index = ((x & (q31_t)0xFFF00000) >> 20); + + if (index >= (int32_t)(nValues - 1)) + { + return (pYData[nValues - 1]); + } + else if (index < 0) + { + return (pYData[0]); + } + else + { + /* 20 bits for the fractional part */ + /* shift left by 11 to keep fract in 1.31 format */ + fract = (x & 0x000FFFFF) << 11; + + /* Read two nearest output values from the index in 1.31(q31) format */ + y0 = pYData[index]; + y1 = pYData[index + 1]; + + /* Calculation of y0 * (1-fract) and y is in 2.30 format */ + y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32)); + + /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */ + y += ((q31_t) (((q63_t) y1 * fract) >> 32)); + + /* Convert y to 1.31 format */ + return (y << 1U); + } + } + + + /** + * + * @brief Process function for the Q15 Linear Interpolation Function. + * @param[in] pYData pointer to Q15 Linear Interpolation table + * @param[in] x input sample to process + * @param[in] nValues number of table values + * @return y processed output sample. + * + * \par + * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part. + * This function can support maximum of table size 2^12. + * + */ + __STATIC_FORCEINLINE q15_t arm_linear_interp_q15( + q15_t * pYData, + q31_t x, + uint32_t nValues) + { + q63_t y; /* output */ + q15_t y0, y1; /* Nearest output values */ + q31_t fract; /* fractional part */ + int32_t index; /* Index to read nearest output values */ + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + index = ((x & (int32_t)0xFFF00000) >> 20); + + if (index >= (int32_t)(nValues - 1)) + { + return (pYData[nValues - 1]); + } + else if (index < 0) + { + return (pYData[0]); + } + else + { + /* 20 bits for the fractional part */ + /* fract is in 12.20 format */ + fract = (x & 0x000FFFFF); + + /* Read two nearest output values from the index */ + y0 = pYData[index]; + y1 = pYData[index + 1]; + + /* Calculation of y0 * (1-fract) and y is in 13.35 format */ + y = ((q63_t) y0 * (0xFFFFF - fract)); + + /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */ + y += ((q63_t) y1 * (fract)); + + /* convert y to 1.15 format */ + return (q15_t) (y >> 20); + } + } + + + /** + * + * @brief Process function for the Q7 Linear Interpolation Function. + * @param[in] pYData pointer to Q7 Linear Interpolation table + * @param[in] x input sample to process + * @param[in] nValues number of table values + * @return y processed output sample. + * + * \par + * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part. + * This function can support maximum of table size 2^12. + */ + __STATIC_FORCEINLINE q7_t arm_linear_interp_q7( + q7_t * pYData, + q31_t x, + uint32_t nValues) + { + q31_t y; /* output */ + q7_t y0, y1; /* Nearest output values */ + q31_t fract; /* fractional part */ + uint32_t index; /* Index to read nearest output values */ + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + if (x < 0) + { + return (pYData[0]); + } + index = (x >> 20) & 0xfff; + + if (index >= (nValues - 1)) + { + return (pYData[nValues - 1]); + } + else + { + /* 20 bits for the fractional part */ + /* fract is in 12.20 format */ + fract = (x & 0x000FFFFF); + + /* Read two nearest output values from the index and are in 1.7(q7) format */ + y0 = pYData[index]; + y1 = pYData[index + 1]; + + /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */ + y = ((y0 * (0xFFFFF - fract))); + + /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */ + y += (y1 * fract); + + /* convert y to 1.7(q7) format */ + return (q7_t) (y >> 20); + } + } + + /** + * @} end of LinearInterpolate group + */ + + /** + * @brief Fast approximation to the trigonometric sine function for floating-point data. + * @param[in] x input value in radians. + * @return sin(x). + */ + float32_t arm_sin_f32( + float32_t x); + + + /** + * @brief Fast approximation to the trigonometric sine function for Q31 data. + * @param[in] x Scaled input value in radians. + * @return sin(x). + */ + q31_t arm_sin_q31( + q31_t x); + + + /** + * @brief Fast approximation to the trigonometric sine function for Q15 data. + * @param[in] x Scaled input value in radians. + * @return sin(x). + */ + q15_t arm_sin_q15( + q15_t x); + + + /** + * @brief Fast approximation to the trigonometric cosine function for floating-point data. + * @param[in] x input value in radians. + * @return cos(x). + */ + float32_t arm_cos_f32( + float32_t x); + + + /** + * @brief Fast approximation to the trigonometric cosine function for Q31 data. + * @param[in] x Scaled input value in radians. + * @return cos(x). + */ + q31_t arm_cos_q31( + q31_t x); + + + /** + * @brief Fast approximation to the trigonometric cosine function for Q15 data. + * @param[in] x Scaled input value in radians. + * @return cos(x). + */ + q15_t arm_cos_q15( + q15_t x); + + +/** + @brief Floating-point vector of log values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + @return none + */ + void arm_vlog_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + +/** + @brief Floating-point vector of exp values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + @return none + */ + void arm_vexp_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @ingroup groupFastMath + */ + + + /** + * @defgroup SQRT Square Root + * + * Computes the square root of a number. + * There are separate functions for Q15, Q31, and floating-point data types. + * The square root function is computed using the Newton-Raphson algorithm. + * This is an iterative algorithm of the form: + * 
+   *      x1 = x0 - f(x0)/f'(x0)
+   *
+ * where x1 is the current estimate, + * x0 is the previous estimate, and + * f'(x0) is the derivative of f() evaluated at x0. + * For the square root function, the algorithm reduces to: + * 
+   *     x0 = in/2                         [initial guess]
+   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
+   *
+ */ + + + /** + * @addtogroup SQRT + * @{ + */ + +/** + @brief Floating-point square root function. + @param[in] in input value + @param[out] pOut square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +__STATIC_FORCEINLINE arm_status arm_sqrt_f32( + float32_t in, + float32_t * pOut) + { + if (in >= 0.0f) + { +#if defined ( __CC_ARM ) + #if defined __TARGET_FPU_VFP + *pOut = __sqrtf(in); + #else + *pOut = sqrtf(in); + #endif + +#elif defined ( __ICCARM__ ) + #if defined __ARMVFP__ + __ASM("VSQRT.F32 %0,%1" : "=t"(*pOut) : "t"(in)); + #else + *pOut = sqrtf(in); + #endif + +#else + *pOut = sqrtf(in); +#endif + + return (ARM_MATH_SUCCESS); + } + else + { + *pOut = 0.0f; + return (ARM_MATH_ARGUMENT_ERROR); + } + } + + +/** + @brief Q31 square root function. + @param[in] in input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF + @param[out] pOut points to square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +arm_status arm_sqrt_q31( + q31_t in, + q31_t * pOut); + + +/** + @brief Q15 square root function. + @param[in] in input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF + @param[out] pOut points to square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +arm_status arm_sqrt_q15( + q15_t in, + q15_t * pOut); + + /** + * @brief Vector Floating-point square root function. + * @param[in] pIn input vector. + * @param[out] pOut vector of square roots of input elements. + * @param[in] len length of input vector. + * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if + * in is negative value and returns zero output for negative values. + */ + void arm_vsqrt_f32( + float32_t * pIn, + float32_t * pOut, + uint16_t len); + + void arm_vsqrt_q31( + q31_t * pIn, + q31_t * pOut, + uint16_t len); + + void arm_vsqrt_q15( + q15_t * pIn, + q15_t * pOut, + uint16_t len); + + /** + * @} end of SQRT group + */ + + + /** + * @brief floating-point Circular write function. + */ + __STATIC_FORCEINLINE void arm_circularWrite_f32( + int32_t * circBuffer, + int32_t L, + uint16_t * writeOffset, + int32_t bufferInc, + const int32_t * src, + int32_t srcInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t wOffset; + + /* Copy the value of Index pointer that points + * to the current location where the input samples to be copied */ + wOffset = *writeOffset; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the input sample to the circular buffer */ + circBuffer[wOffset] = *src; + + /* Update the input pointer */ + src += srcInc; + + /* Circularly update wOffset. Watch out for positive and negative value */ + wOffset += bufferInc; + if (wOffset >= L) + wOffset -= L; + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *writeOffset = (uint16_t)wOffset; + } + + + + /** + * @brief floating-point Circular Read function. + */ + __STATIC_FORCEINLINE void arm_circularRead_f32( + int32_t * circBuffer, + int32_t L, + int32_t * readOffset, + int32_t bufferInc, + int32_t * dst, + int32_t * dst_base, + int32_t dst_length, + int32_t dstInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t rOffset; + int32_t* dst_end; + + /* Copy the value of Index pointer that points + * to the current location from where the input samples to be read */ + rOffset = *readOffset; + dst_end = dst_base + dst_length; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the sample from the circular buffer to the destination buffer */ + *dst = circBuffer[rOffset]; + + /* Update the input pointer */ + dst += dstInc; + + if (dst == dst_end) + { + dst = dst_base; + } + + /* Circularly update rOffset. Watch out for positive and negative value */ + rOffset += bufferInc; + + if (rOffset >= L) + { + rOffset -= L; + } + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *readOffset = rOffset; + } + + + /** + * @brief Q15 Circular write function. + */ + __STATIC_FORCEINLINE void arm_circularWrite_q15( + q15_t * circBuffer, + int32_t L, + uint16_t * writeOffset, + int32_t bufferInc, + const q15_t * src, + int32_t srcInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t wOffset; + + /* Copy the value of Index pointer that points + * to the current location where the input samples to be copied */ + wOffset = *writeOffset; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the input sample to the circular buffer */ + circBuffer[wOffset] = *src; + + /* Update the input pointer */ + src += srcInc; + + /* Circularly update wOffset. Watch out for positive and negative value */ + wOffset += bufferInc; + if (wOffset >= L) + wOffset -= L; + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *writeOffset = (uint16_t)wOffset; + } + + + /** + * @brief Q15 Circular Read function. + */ + __STATIC_FORCEINLINE void arm_circularRead_q15( + q15_t * circBuffer, + int32_t L, + int32_t * readOffset, + int32_t bufferInc, + q15_t * dst, + q15_t * dst_base, + int32_t dst_length, + int32_t dstInc, + uint32_t blockSize) + { + uint32_t i = 0; + int32_t rOffset; + q15_t* dst_end; + + /* Copy the value of Index pointer that points + * to the current location from where the input samples to be read */ + rOffset = *readOffset; + + dst_end = dst_base + dst_length; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the sample from the circular buffer to the destination buffer */ + *dst = circBuffer[rOffset]; + + /* Update the input pointer */ + dst += dstInc; + + if (dst == dst_end) + { + dst = dst_base; + } + + /* Circularly update wOffset. Watch out for positive and negative value */ + rOffset += bufferInc; + + if (rOffset >= L) + { + rOffset -= L; + } + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *readOffset = rOffset; + } + + + /** + * @brief Q7 Circular write function. + */ + __STATIC_FORCEINLINE void arm_circularWrite_q7( + q7_t * circBuffer, + int32_t L, + uint16_t * writeOffset, + int32_t bufferInc, + const q7_t * src, + int32_t srcInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t wOffset; + + /* Copy the value of Index pointer that points + * to the current location where the input samples to be copied */ + wOffset = *writeOffset; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the input sample to the circular buffer */ + circBuffer[wOffset] = *src; + + /* Update the input pointer */ + src += srcInc; + + /* Circularly update wOffset. Watch out for positive and negative value */ + wOffset += bufferInc; + if (wOffset >= L) + wOffset -= L; + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *writeOffset = (uint16_t)wOffset; + } + + + /** + * @brief Q7 Circular Read function. + */ + __STATIC_FORCEINLINE void arm_circularRead_q7( + q7_t * circBuffer, + int32_t L, + int32_t * readOffset, + int32_t bufferInc, + q7_t * dst, + q7_t * dst_base, + int32_t dst_length, + int32_t dstInc, + uint32_t blockSize) + { + uint32_t i = 0; + int32_t rOffset; + q7_t* dst_end; + + /* Copy the value of Index pointer that points + * to the current location from where the input samples to be read */ + rOffset = *readOffset; + + dst_end = dst_base + dst_length; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the sample from the circular buffer to the destination buffer */ + *dst = circBuffer[rOffset]; + + /* Update the input pointer */ + dst += dstInc; + + if (dst == dst_end) + { + dst = dst_base; + } + + /* Circularly update rOffset. Watch out for positive and negative value */ + rOffset += bufferInc; + + if (rOffset >= L) + { + rOffset -= L; + } + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *readOffset = rOffset; + } + + + /** + * @brief Sum of the squares of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_q31( + const q31_t * pSrc, + uint32_t blockSize, + q63_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_q15( + const q15_t * pSrc, + uint32_t blockSize, + q63_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_q7( + const q7_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Mean value of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult); + + + /** + * @brief Mean value of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Mean value of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Mean value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Variance of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Variance of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Variance of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Root Mean Square of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Root Mean Square of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Root Mean Square of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Standard deviation of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Standard deviation of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Standard deviation of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Floating-point complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t numSamples, + q31_t * realResult, + q31_t * imagResult); + + + /** + * @brief Q31 complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t numSamples, + q63_t * realResult, + q63_t * imagResult); + + + /** + * @brief Floating-point complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t numSamples, + float32_t * realResult, + float32_t * imagResult); + + + /** + * @brief Q15 complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_q15( + const q15_t * pSrcCmplx, + const q15_t * pSrcReal, + q15_t * pCmplxDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_q31( + const q31_t * pSrcCmplx, + const q31_t * pSrcReal, + q31_t * pCmplxDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_f32( + const float32_t * pSrcCmplx, + const float32_t * pSrcReal, + float32_t * pCmplxDst, + uint32_t numSamples); + + + /** + * @brief Minimum value of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] result is output pointer + * @param[in] index is the array index of the minimum value in the input buffer. + */ + void arm_min_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * result, + uint32_t * index); + + + /** + * @brief Minimum value of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[in] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult, + uint32_t * pIndex); + + + /** + * @brief Minimum value of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult, + uint32_t * pIndex); + + + /** + * @brief Minimum value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult, + uint32_t * pIndex); + + +/** + * @brief Maximum value of a Q7 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult, + uint32_t * pIndex); + + +/** + * @brief Maximum value of a Q15 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult, + uint32_t * pIndex); + + +/** + * @brief Maximum value of a Q31 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult, + uint32_t * pIndex); + + +/** + * @brief Maximum value of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult, + uint32_t * pIndex); + + /** + @brief Maximum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + @return none + */ + void arm_max_no_idx_f32( + const float32_t *pSrc, + uint32_t blockSize, + float32_t *pResult); + + /** + * @brief Q15 complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t numSamples); + + + /** + * @brief Converts the elements of the floating-point vector to Q31 vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the Q31 output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_q31( + const float32_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the floating-point vector to Q15 vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the Q15 output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_q15( + const float32_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the floating-point vector to Q7 vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the Q7 output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_q7( + const float32_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q31 vector to floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q31_to_float( + const q31_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q31 vector to Q15 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q31_to_q15( + const q31_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q31 vector to Q7 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q31_to_q7( + const q31_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q15 vector to floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q15_to_float( + const q15_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q15 vector to Q31 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q15_to_q31( + const q15_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q15 vector to Q7 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q15_to_q7( + const q15_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q7 vector to floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q7_to_float( + const q7_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q7 vector to Q31 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_q7_to_q31( + const q7_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q7 vector to Q15 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_q7_to_q15( + const q7_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + +/** + * @brief Struct for specifying SVM Kernel + */ +typedef enum +{ + ARM_ML_KERNEL_LINEAR = 0, + /**< Linear kernel */ + ARM_ML_KERNEL_POLYNOMIAL = 1, + /**< Polynomial kernel */ + ARM_ML_KERNEL_RBF = 2, + /**< Radial Basis Function kernel */ + ARM_ML_KERNEL_SIGMOID = 3 + /**< Sigmoid kernel */ +} arm_ml_kernel_type; + + +/** + * @brief Instance structure for linear SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ +} arm_svm_linear_instance_f32; + + +/** + * @brief Instance structure for polynomial SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + int32_t degree; /**< Polynomial degree */ + float32_t coef0; /**< Polynomial constant */ + float32_t gamma; /**< Gamma factor */ +} arm_svm_polynomial_instance_f32; + +/** + * @brief Instance structure for rbf SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + float32_t gamma; /**< Gamma factor */ +} arm_svm_rbf_instance_f32; + +/** + * @brief Instance structure for sigmoid SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + float32_t coef0; /**< Independant constant */ + float32_t gamma; /**< Gamma factor */ +} arm_svm_sigmoid_instance_f32; + +/** + * @brief SVM linear instance init function + * @param[in] S Parameters for SVM functions + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @return none. + * + */ + + +void arm_svm_linear_init_f32(arm_svm_linear_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes); + +/** + * @brief SVM linear prediction + * @param[in] S Pointer to an instance of the linear SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + * @return none. + * + */ + +void arm_svm_linear_predict_f32(const arm_svm_linear_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + +/** + * @brief SVM polynomial instance init function + * @param[in] S points to an instance of the polynomial SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] degree Polynomial degree + * @param[in] coef0 coeff0 (scikit-learn terminology) + * @param[in] gamma gamma (scikit-learn terminology) + * @return none. + * + */ + + +void arm_svm_polynomial_init_f32(arm_svm_polynomial_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes, + int32_t degree, + float32_t coef0, + float32_t gamma + ); + +/** + * @brief SVM polynomial prediction + * @param[in] S Pointer to an instance of the polynomial SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + * @return none. + * + */ +void arm_svm_polynomial_predict_f32(const arm_svm_polynomial_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + +/** + * @brief SVM radial basis function instance init function + * @param[in] S points to an instance of the polynomial SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] gamma gamma (scikit-learn terminology) + * @return none. + * + */ + +void arm_svm_rbf_init_f32(arm_svm_rbf_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes, + float32_t gamma + ); + +/** + * @brief SVM rbf prediction + * @param[in] S Pointer to an instance of the rbf SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult decision value + * @return none. + * + */ +void arm_svm_rbf_predict_f32(const arm_svm_rbf_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + +/** + * @brief SVM sigmoid instance init function + * @param[in] S points to an instance of the rbf SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] coef0 coeff0 (scikit-learn terminology) + * @param[in] gamma gamma (scikit-learn terminology) + * @return none. + * + */ + +void arm_svm_sigmoid_init_f32(arm_svm_sigmoid_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes, + float32_t coef0, + float32_t gamma + ); + +/** + * @brief SVM sigmoid prediction + * @param[in] S Pointer to an instance of the rbf SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + * @return none. + * + */ +void arm_svm_sigmoid_predict_f32(const arm_svm_sigmoid_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + + +/** + * @brief Instance structure for Naive Gaussian Bayesian estimator. + */ +typedef struct +{ + uint32_t vectorDimension; /**< Dimension of vector space */ + uint32_t numberOfClasses; /**< Number of different classes */ + const float32_t *theta; /**< Mean values for the Gaussians */ + const float32_t *sigma; /**< Variances for the Gaussians */ + const float32_t *classPriors; /**< Class prior probabilities */ + float32_t epsilon; /**< Additive value to variances */ +} arm_gaussian_naive_bayes_instance_f32; + +/** + * @brief Naive Gaussian Bayesian Estimator + * + * @param[in] S points to a naive bayes instance structure + * @param[in] in points to the elements of the input vector. + * @param[in] pBuffer points to a buffer of length numberOfClasses + * @return The predicted class + * + */ + + +uint32_t arm_gaussian_naive_bayes_predict_f32(const arm_gaussian_naive_bayes_instance_f32 *S, + const float32_t * in, + float32_t *pBuffer); + +/** + * @brief Computation of the LogSumExp + * + * In probabilistic computations, the dynamic of the probability values can be very + * wide because they come from gaussian functions. + * To avoid underflow and overflow issues, the values are represented by their log. + * In this representation, multiplying the original exp values is easy : their logs are added. + * But adding the original exp values is requiring some special handling and it is the + * goal of the LogSumExp function. + * + * If the values are x1...xn, the function is computing: + * + * ln(exp(x1) + ... + exp(xn)) and the computation is done in such a way that + * rounding issues are minimised. + * + * The max xm of the values is extracted and the function is computing: + * xm + ln(exp(x1 - xm) + ... + exp(xn - xm)) + * + * @param[in] *in Pointer to an array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return LogSumExp + * + */ + + +float32_t arm_logsumexp_f32(const float32_t *in, uint32_t blockSize); + +/** + * @brief Dot product with log arithmetic + * + * Vectors are containing the log of the samples + * + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[in] pTmpBuffer temporary buffer of length blockSize + * @return The log of the dot product . + * + */ + + +float32_t arm_logsumexp_dot_prod_f32(const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t blockSize, + float32_t *pTmpBuffer); + +/** + * @brief Entropy + * + * @param[in] pSrcA Array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return Entropy -Sum(p ln p) + * + */ + + +float32_t arm_entropy_f32(const float32_t * pSrcA,uint32_t blockSize); + + +/** + * @brief Entropy + * + * @param[in] pSrcA Array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return Entropy -Sum(p ln p) + * + */ + + +float64_t arm_entropy_f64(const float64_t * pSrcA, uint32_t blockSize); + + +/** + * @brief Kullback-Leibler + * + * @param[in] pSrcA Pointer to an array of input values for probability distribution A. + * @param[in] pSrcB Pointer to an array of input values for probability distribution B. + * @param[in] blockSize Number of samples in the input array. + * @return Kullback-Leibler Divergence D(A || B) + * + */ +float32_t arm_kullback_leibler_f32(const float32_t * pSrcA + ,const float32_t * pSrcB + ,uint32_t blockSize); + + +/** + * @brief Kullback-Leibler + * + * @param[in] pSrcA Pointer to an array of input values for probability distribution A. + * @param[in] pSrcB Pointer to an array of input values for probability distribution B. + * @param[in] blockSize Number of samples in the input array. + * @return Kullback-Leibler Divergence D(A || B) + * + */ +float64_t arm_kullback_leibler_f64(const float64_t * pSrcA, + const float64_t * pSrcB, + uint32_t blockSize); + + +/** + * @brief Weighted sum + * + * + * @param[in] *in Array of input values. + * @param[in] *weigths Weights + * @param[in] blockSize Number of samples in the input array. + * @return Weighted sum + * + */ +float32_t arm_weighted_sum_f32(const float32_t *in + , const float32_t *weigths + , uint32_t blockSize); + + +/** + * @brief Barycenter + * + * + * @param[in] in List of vectors + * @param[in] weights Weights of the vectors + * @param[out] out Barycenter + * @param[in] nbVectors Number of vectors + * @param[in] vecDim Dimension of space (vector dimension) + * @return None + * + */ +void arm_barycenter_f32(const float32_t *in + , const float32_t *weights + , float32_t *out + , uint32_t nbVectors + , uint32_t vecDim); + +/** + * @brief Euclidean distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float32_t arm_euclidean_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Bray-Curtis distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_braycurtis_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Canberra distance between two vectors + * + * This function may divide by zero when samples pA[i] and pB[i] are both zero. + * The result of the computation will be correct. So the division per zero may be + * ignored. + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_canberra_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + + +/** + * @brief Chebyshev distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_chebyshev_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + + +/** + * @brief Cityblock (Manhattan) distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_cityblock_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Correlation distance between two vectors + * + * The input vectors are modified in place ! + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_correlation_distance_f32(float32_t *pA,float32_t *pB, uint32_t blockSize); + +/** + * @brief Cosine distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float32_t arm_cosine_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Jensen-Shannon distance between two vectors + * + * This function is assuming that elements of second vector are > 0 + * and 0 only when the corresponding element of first vector is 0. + * Otherwise the result of the computation does not make sense + * and for speed reasons, the cases returning NaN or Infinity are not + * managed. + * + * When the function is computing x log (x / y) with x 0 and y 0, + * it will compute the right value (0) but a division per zero will occur + * and shoudl be ignored in client code. + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float32_t arm_jensenshannon_distance_f32(const float32_t *pA,const float32_t *pB,uint32_t blockSize); + +/** + * @brief Minkowski distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] n Norm order (>= 2) + * @param[in] blockSize vector length + * @return distance + * + */ + + + +float32_t arm_minkowski_distance_f32(const float32_t *pA,const float32_t *pB, int32_t order, uint32_t blockSize); + +/** + * @brief Dice distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] order Distance order + * @param[in] blockSize Number of samples + * @return distance + * + */ + + +float32_t arm_dice_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Hamming distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_hamming_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Jaccard distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_jaccard_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Kulsinski distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_kulsinski_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Roger Stanimoto distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_rogerstanimoto_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Russell-Rao distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_russellrao_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Sokal-Michener distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_sokalmichener_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Sokal-Sneath distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_sokalsneath_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Yule distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_yule_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + + + /** + * @ingroup groupInterpolation + */ + + /** + * @defgroup BilinearInterpolate Bilinear Interpolation + * + * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid. + * The underlying function f(x, y) is sampled on a regular grid and the interpolation process + * determines values between the grid points. + * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension. + * Bilinear interpolation is often used in image processing to rescale images. + * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types. + * + * Algorithm + * \par + * The instance structure used by the bilinear interpolation functions describes a two dimensional data table. + * For floating-point, the instance structure is defined as: + * 
+   *   typedef struct
+   *   {
+   *     uint16_t numRows;
+   *     uint16_t numCols;
+   *     float32_t *pData;
+   * } arm_bilinear_interp_instance_f32;
+   *
+ * + * \par + * where numRows specifies the number of rows in the table; + * numCols specifies the number of columns in the table; + * and pData points to an array of size numRows*numCols values. + * The data table pTable is organized in row order and the supplied data values fall on integer indexes. + * That is, table element (x,y) is located at pTable[x + y*numCols] where x and y are integers. + * + * \par + * Let (x, y) specify the desired interpolation point. Then define: + * 
+   *     XF = floor(x)
+   *     YF = floor(y)
+   *
+ * \par + * The interpolated output point is computed as: + * 
+   *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
+   *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
+   *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
+   *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
+   *
+ * Note that the coordinates (x, y) contain integer and fractional components. + * The integer components specify which portion of the table to use while the + * fractional components control the interpolation processor. + * + * \par + * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output. + */ + + + /** + * @addtogroup BilinearInterpolate + * @{ + */ + + /** + * @brief Floating-point bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate. + * @param[in] Y interpolation coordinate. + * @return out interpolated value. + */ + __STATIC_FORCEINLINE float32_t arm_bilinear_interp_f32( + const arm_bilinear_interp_instance_f32 * S, + float32_t X, + float32_t Y) + { + float32_t out; + float32_t f00, f01, f10, f11; + float32_t *pData = S->pData; + int32_t xIndex, yIndex, index; + float32_t xdiff, ydiff; + float32_t b1, b2, b3, b4; + + xIndex = (int32_t) X; + yIndex = (int32_t) Y; + + /* Care taken for table outside boundary */ + /* Returns zero output when values are outside table boundary */ + if (xIndex < 0 || xIndex > (S->numCols - 2) || yIndex < 0 || yIndex > (S->numRows - 2)) + { + return (0); + } + + /* Calculation of index for two nearest points in X-direction */ + index = (xIndex ) + (yIndex ) * S->numCols; + + + /* Read two nearest points in X-direction */ + f00 = pData[index]; + f01 = pData[index + 1]; + + /* Calculation of index for two nearest points in Y-direction */ + index = (xIndex ) + (yIndex+1) * S->numCols; + + + /* Read two nearest points in Y-direction */ + f10 = pData[index]; + f11 = pData[index + 1]; + + /* Calculation of intermediate values */ + b1 = f00; + b2 = f01 - f00; + b3 = f10 - f00; + b4 = f00 - f01 - f10 + f11; + + /* Calculation of fractional part in X */ + xdiff = X - xIndex; + + /* Calculation of fractional part in Y */ + ydiff = Y - yIndex; + + /* Calculation of bi-linear interpolated output */ + out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff; + + /* return to application */ + return (out); + } + + + /** + * @brief Q31 bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate in 12.20 format. + * @param[in] Y interpolation coordinate in 12.20 format. + * @return out interpolated value. + */ + __STATIC_FORCEINLINE q31_t arm_bilinear_interp_q31( + arm_bilinear_interp_instance_q31 * S, + q31_t X, + q31_t Y) + { + q31_t out; /* Temporary output */ + q31_t acc = 0; /* output */ + q31_t xfract, yfract; /* X, Y fractional parts */ + q31_t x1, x2, y1, y2; /* Nearest output values */ + int32_t rI, cI; /* Row and column indices */ + q31_t *pYData = S->pData; /* pointer to output table values */ + uint32_t nCols = S->numCols; /* num of rows */ + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + rI = ((X & (q31_t)0xFFF00000) >> 20); + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + cI = ((Y & (q31_t)0xFFF00000) >> 20); + + /* Care taken for table outside boundary */ + /* Returns zero output when values are outside table boundary */ + if (rI < 0 || rI > (S->numCols - 2) || cI < 0 || cI > (S->numRows - 2)) + { + return (0); + } + + /* 20 bits for the fractional part */ + /* shift left xfract by 11 to keep 1.31 format */ + xfract = (X & 0x000FFFFF) << 11U; + + /* Read two nearest output values from the index */ + x1 = pYData[(rI) + (int32_t)nCols * (cI) ]; + x2 = pYData[(rI) + (int32_t)nCols * (cI) + 1]; + + /* 20 bits for the fractional part */ + /* shift left yfract by 11 to keep 1.31 format */ + yfract = (Y & 0x000FFFFF) << 11U; + + /* Read two nearest output values from the index */ + y1 = pYData[(rI) + (int32_t)nCols * (cI + 1) ]; + y2 = pYData[(rI) + (int32_t)nCols * (cI + 1) + 1]; + + /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */ + out = ((q31_t) (((q63_t) x1 * (0x7FFFFFFF - xfract)) >> 32)); + acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32)); + + /* x2 * (xfract) * (1-yfract) in 3.29(q29) and adding to acc */ + out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32)); + acc += ((q31_t) ((q63_t) out * (xfract) >> 32)); + + /* y1 * (1 - xfract) * (yfract) in 3.29(q29) and adding to acc */ + out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32)); + acc += ((q31_t) ((q63_t) out * (yfract) >> 32)); + + /* y2 * (xfract) * (yfract) in 3.29(q29) and adding to acc */ + out = ((q31_t) ((q63_t) y2 * (xfract) >> 32)); + acc += ((q31_t) ((q63_t) out * (yfract) >> 32)); + + /* Convert acc to 1.31(q31) format */ + return ((q31_t)(acc << 2)); + } + + + /** + * @brief Q15 bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate in 12.20 format. + * @param[in] Y interpolation coordinate in 12.20 format. + * @return out interpolated value. + */ + __STATIC_FORCEINLINE q15_t arm_bilinear_interp_q15( + arm_bilinear_interp_instance_q15 * S, + q31_t X, + q31_t Y) + { + q63_t acc = 0; /* output */ + q31_t out; /* Temporary output */ + q15_t x1, x2, y1, y2; /* Nearest output values */ + q31_t xfract, yfract; /* X, Y fractional parts */ + int32_t rI, cI; /* Row and column indices */ + q15_t *pYData = S->pData; /* pointer to output table values */ + uint32_t nCols = S->numCols; /* num of rows */ + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + rI = ((X & (q31_t)0xFFF00000) >> 20); + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + cI = ((Y & (q31_t)0xFFF00000) >> 20); + + /* Care taken for table outside boundary */ + /* Returns zero output when values are outside table boundary */ + if (rI < 0 || rI > (S->numCols - 2) || cI < 0 || cI > (S->numRows - 2)) + { + return (0); + } + + /* 20 bits for the fractional part */ + /* xfract should be in 12.20 format */ + xfract = (X & 0x000FFFFF); + + /* Read two nearest output values from the index */ + x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) ]; + x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1]; + + /* 20 bits for the fractional part */ + /* yfract should be in 12.20 format */ + yfract = (Y & 0x000FFFFF); + + /* Read two nearest output values from the index */ + y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) ]; + y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1]; + + /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */ + + /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */ + /* convert 13.35 to 13.31 by right shifting and out is in 1.31 */ + out = (q31_t) (((q63_t) x1 * (0x0FFFFF - xfract)) >> 4U); + acc = ((q63_t) out * (0x0FFFFF - yfract)); + + /* x2 * (xfract) * (1-yfract) in 1.51 and adding to acc */ + out = (q31_t) (((q63_t) x2 * (0x0FFFFF - yfract)) >> 4U); + acc += ((q63_t) out * (xfract)); + + /* y1 * (1 - xfract) * (yfract) in 1.51 and adding to acc */ + out = (q31_t) (((q63_t) y1 * (0x0FFFFF - xfract)) >> 4U); + acc += ((q63_t) out * (yfract)); + + /* y2 * (xfract) * (yfract) in 1.51 and adding to acc */ + out = (q31_t) (((q63_t) y2 * (xfract)) >> 4U); + acc += ((q63_t) out * (yfract)); + + /* acc is in 13.51 format and down shift acc by 36 times */ + /* Convert out to 1.15 format */ + return ((q15_t)(acc >> 36)); + } + + + /** + * @brief Q7 bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate in 12.20 format. + * @param[in] Y interpolation coordinate in 12.20 format. + * @return out interpolated value. + */ + __STATIC_FORCEINLINE q7_t arm_bilinear_interp_q7( + arm_bilinear_interp_instance_q7 * S, + q31_t X, + q31_t Y) + { + q63_t acc = 0; /* output */ + q31_t out; /* Temporary output */ + q31_t xfract, yfract; /* X, Y fractional parts */ + q7_t x1, x2, y1, y2; /* Nearest output values */ + int32_t rI, cI; /* Row and column indices */ + q7_t *pYData = S->pData; /* pointer to output table values */ + uint32_t nCols = S->numCols; /* num of rows */ + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + rI = ((X & (q31_t)0xFFF00000) >> 20); + + /* Input is in 12.20 format */ + /* 12 bits for the table index */ + /* Index value calculation */ + cI = ((Y & (q31_t)0xFFF00000) >> 20); + + /* Care taken for table outside boundary */ + /* Returns zero output when values are outside table boundary */ + if (rI < 0 || rI > (S->numCols - 2) || cI < 0 || cI > (S->numRows - 2)) + { + return (0); + } + + /* 20 bits for the fractional part */ + /* xfract should be in 12.20 format */ + xfract = (X & (q31_t)0x000FFFFF); + + /* Read two nearest output values from the index */ + x1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) ]; + x2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI) + 1]; + + /* 20 bits for the fractional part */ + /* yfract should be in 12.20 format */ + yfract = (Y & (q31_t)0x000FFFFF); + + /* Read two nearest output values from the index */ + y1 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) ]; + y2 = pYData[((uint32_t)rI) + nCols * ((uint32_t)cI + 1) + 1]; + + /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */ + out = ((x1 * (0xFFFFF - xfract))); + acc = (((q63_t) out * (0xFFFFF - yfract))); + + /* x2 * (xfract) * (1-yfract) in 2.22 and adding to acc */ + out = ((x2 * (0xFFFFF - yfract))); + acc += (((q63_t) out * (xfract))); + + /* y1 * (1 - xfract) * (yfract) in 2.22 and adding to acc */ + out = ((y1 * (0xFFFFF - xfract))); + acc += (((q63_t) out * (yfract))); + + /* y2 * (xfract) * (yfract) in 2.22 and adding to acc */ + out = ((y2 * (yfract))); + acc += (((q63_t) out * (xfract))); + + /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */ + return ((q7_t)(acc >> 40)); + } + + /** + * @} end of BilinearInterpolate group + */ + + +/* SMMLAR */ +#define multAcc_32x32_keep32_R(a, x, y) \ + a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32) + +/* SMMLSR */ +#define multSub_32x32_keep32_R(a, x, y) \ + a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32) + +/* SMMULR */ +#define mult_32x32_keep32_R(a, x, y) \ + a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32) + +/* SMMLA */ +#define multAcc_32x32_keep32(a, x, y) \ + a += (q31_t) (((q63_t) x * y) >> 32) + +/* SMMLS */ +#define multSub_32x32_keep32(a, x, y) \ + a -= (q31_t) (((q63_t) x * y) >> 32) + +/* SMMUL */ +#define mult_32x32_keep32(a, x, y) \ + a = (q31_t) (((q63_t) x * y ) >> 32) + + +#if defined ( __CC_ARM ) + /* Enter low optimization region - place directly above function definition */ + #if defined( __ARM_ARCH_7EM__ ) + #define LOW_OPTIMIZATION_ENTER \ + _Pragma ("push") \ + _Pragma ("O1") + #else + #define LOW_OPTIMIZATION_ENTER + #endif + + /* Exit low optimization region - place directly after end of function definition */ + #if defined ( __ARM_ARCH_7EM__ ) + #define LOW_OPTIMIZATION_EXIT \ + _Pragma ("pop") + #else + #define LOW_OPTIMIZATION_EXIT + #endif + + /* Enter low optimization region - place directly above function definition */ + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + + /* Exit low optimization region - place directly after end of function definition */ + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined (__ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __GNUC__ ) + #define LOW_OPTIMIZATION_ENTER \ + __attribute__(( optimize("-O1") )) + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __ICCARM__ ) + /* Enter low optimization region - place directly above function definition */ + #if defined ( __ARM_ARCH_7EM__ ) + #define LOW_OPTIMIZATION_ENTER \ + _Pragma ("optimize=low") + #else + #define LOW_OPTIMIZATION_ENTER + #endif + + /* Exit low optimization region - place directly after end of function definition */ + #define LOW_OPTIMIZATION_EXIT + + /* Enter low optimization region - place directly above function definition */ + #if defined ( __ARM_ARCH_7EM__ ) + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \ + _Pragma ("optimize=low") + #else + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #endif + + /* Exit low optimization region - place directly after end of function definition */ + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __TI_ARM__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __CSMC__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __TASKING__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( _MSC_VER ) || defined(__GNUC_PYTHON__) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT +#endif + + + +/* Compiler specific diagnostic adjustment */ +#if defined ( __CC_ARM ) + +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + +#elif defined ( __GNUC__ ) +#pragma GCC diagnostic pop + +#elif defined ( __ICCARM__ ) + +#elif defined ( __TI_ARM__ ) + +#elif defined ( __CSMC__ ) + +#elif defined ( __TASKING__ ) + +#elif defined ( _MSC_VER ) + +#else + #error Unknown compiler +#endif + +#ifdef __cplusplus +} +#endif + + +#endif /* _ARM_MATH_H */ + +/** + * + * End of file. + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables.h new file mode 100755 index 0000000..6a92704 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables.h @@ -0,0 +1,318 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_common_tables.h + * Description: Extern declaration for common tables + * + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_COMMON_TABLES_H +#define ARM_COMMON_TABLES_H + +#include "arm_math_types.h" +#include "dsp/fast_math_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + /* Double Precision Float CFFT twiddles */ + extern const uint16_t armBitRevTable[1024]; + + extern const uint64_t twiddleCoefF64_16[32]; + + extern const uint64_t twiddleCoefF64_32[64]; + + extern const uint64_t twiddleCoefF64_64[128]; + + extern const uint64_t twiddleCoefF64_128[256]; + + extern const uint64_t twiddleCoefF64_256[512]; + + extern const uint64_t twiddleCoefF64_512[1024]; + + extern const uint64_t twiddleCoefF64_1024[2048]; + + extern const uint64_t twiddleCoefF64_2048[4096]; + + extern const uint64_t twiddleCoefF64_4096[8192]; + + extern const float32_t twiddleCoef_16[32]; + + extern const float32_t twiddleCoef_32[64]; + + extern const float32_t twiddleCoef_64[128]; + + extern const float32_t twiddleCoef_128[256]; + + extern const float32_t twiddleCoef_256[512]; + + extern const float32_t twiddleCoef_512[1024]; + + extern const float32_t twiddleCoef_1024[2048]; + + extern const float32_t twiddleCoef_2048[4096]; + + extern const float32_t twiddleCoef_4096[8192]; + #define twiddleCoef twiddleCoef_4096 + + /* Q31 */ + + extern const q31_t twiddleCoef_16_q31[24]; + + extern const q31_t twiddleCoef_32_q31[48]; + + extern const q31_t twiddleCoef_64_q31[96]; + + extern const q31_t twiddleCoef_128_q31[192]; + + extern const q31_t twiddleCoef_256_q31[384]; + + extern const q31_t twiddleCoef_512_q31[768]; + + extern const q31_t twiddleCoef_1024_q31[1536]; + + extern const q31_t twiddleCoef_2048_q31[3072]; + + extern const q31_t twiddleCoef_4096_q31[6144]; + + extern const q15_t twiddleCoef_16_q15[24]; + + extern const q15_t twiddleCoef_32_q15[48]; + + extern const q15_t twiddleCoef_64_q15[96]; + + extern const q15_t twiddleCoef_128_q15[192]; + + extern const q15_t twiddleCoef_256_q15[384]; + + extern const q15_t twiddleCoef_512_q15[768]; + + extern const q15_t twiddleCoef_1024_q15[1536]; + + extern const q15_t twiddleCoef_2048_q15[3072]; + + extern const q15_t twiddleCoef_4096_q15[6144]; + + /* Double Precision Float RFFT twiddles */ + extern const uint64_t twiddleCoefF64_rfft_32[32]; + + extern const uint64_t twiddleCoefF64_rfft_64[64]; + + extern const uint64_t twiddleCoefF64_rfft_128[128]; + + extern const uint64_t twiddleCoefF64_rfft_256[256]; + + extern const uint64_t twiddleCoefF64_rfft_512[512]; + + extern const uint64_t twiddleCoefF64_rfft_1024[1024]; + + extern const uint64_t twiddleCoefF64_rfft_2048[2048]; + + extern const uint64_t twiddleCoefF64_rfft_4096[4096]; + + extern const float32_t twiddleCoef_rfft_32[32]; + + extern const float32_t twiddleCoef_rfft_64[64]; + + extern const float32_t twiddleCoef_rfft_128[128]; + + extern const float32_t twiddleCoef_rfft_256[256]; + + extern const float32_t twiddleCoef_rfft_512[512]; + + extern const float32_t twiddleCoef_rfft_1024[1024]; + + extern const float32_t twiddleCoef_rfft_2048[2048]; + + extern const float32_t twiddleCoef_rfft_4096[4096]; + + /* Double precision floating-point bit reversal tables */ + + #define ARMBITREVINDEXTABLEF64_16_TABLE_LENGTH ((uint16_t)12) + extern const uint16_t armBitRevIndexTableF64_16[ARMBITREVINDEXTABLEF64_16_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_32_TABLE_LENGTH ((uint16_t)24) + extern const uint16_t armBitRevIndexTableF64_32[ARMBITREVINDEXTABLEF64_32_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_64_TABLE_LENGTH ((uint16_t)56) + extern const uint16_t armBitRevIndexTableF64_64[ARMBITREVINDEXTABLEF64_64_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_128_TABLE_LENGTH ((uint16_t)112) + extern const uint16_t armBitRevIndexTableF64_128[ARMBITREVINDEXTABLEF64_128_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_256_TABLE_LENGTH ((uint16_t)240) + extern const uint16_t armBitRevIndexTableF64_256[ARMBITREVINDEXTABLEF64_256_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_512_TABLE_LENGTH ((uint16_t)480) + extern const uint16_t armBitRevIndexTableF64_512[ARMBITREVINDEXTABLEF64_512_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_1024_TABLE_LENGTH ((uint16_t)992) + extern const uint16_t armBitRevIndexTableF64_1024[ARMBITREVINDEXTABLEF64_1024_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_2048_TABLE_LENGTH ((uint16_t)1984) + extern const uint16_t armBitRevIndexTableF64_2048[ARMBITREVINDEXTABLEF64_2048_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLEF64_4096_TABLE_LENGTH ((uint16_t)4032) + extern const uint16_t armBitRevIndexTableF64_4096[ARMBITREVINDEXTABLEF64_4096_TABLE_LENGTH]; + /* floating-point bit reversal tables */ + + #define ARMBITREVINDEXTABLE_16_TABLE_LENGTH ((uint16_t)20) + extern const uint16_t armBitRevIndexTable16[ARMBITREVINDEXTABLE_16_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_32_TABLE_LENGTH ((uint16_t)48) + extern const uint16_t armBitRevIndexTable32[ARMBITREVINDEXTABLE_32_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_64_TABLE_LENGTH ((uint16_t)56) + extern const uint16_t armBitRevIndexTable64[ARMBITREVINDEXTABLE_64_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_128_TABLE_LENGTH ((uint16_t)208) + extern const uint16_t armBitRevIndexTable128[ARMBITREVINDEXTABLE_128_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_256_TABLE_LENGTH ((uint16_t)440) + extern const uint16_t armBitRevIndexTable256[ARMBITREVINDEXTABLE_256_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_512_TABLE_LENGTH ((uint16_t)448) + extern const uint16_t armBitRevIndexTable512[ARMBITREVINDEXTABLE_512_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_1024_TABLE_LENGTH ((uint16_t)1800) + extern const uint16_t armBitRevIndexTable1024[ARMBITREVINDEXTABLE_1024_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_2048_TABLE_LENGTH ((uint16_t)3808) + extern const uint16_t armBitRevIndexTable2048[ARMBITREVINDEXTABLE_2048_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_4096_TABLE_LENGTH ((uint16_t)4032) + extern const uint16_t armBitRevIndexTable4096[ARMBITREVINDEXTABLE_4096_TABLE_LENGTH]; + + + /* fixed-point bit reversal tables */ + + #define ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH ((uint16_t)12) + extern const uint16_t armBitRevIndexTable_fixed_16[ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH ((uint16_t)24) + extern const uint16_t armBitRevIndexTable_fixed_32[ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH ((uint16_t)56) + extern const uint16_t armBitRevIndexTable_fixed_64[ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH ((uint16_t)112) + extern const uint16_t armBitRevIndexTable_fixed_128[ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH ((uint16_t)240) + extern const uint16_t armBitRevIndexTable_fixed_256[ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH ((uint16_t)480) + extern const uint16_t armBitRevIndexTable_fixed_512[ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH ((uint16_t)992) + extern const uint16_t armBitRevIndexTable_fixed_1024[ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH ((uint16_t)1984) + extern const uint16_t armBitRevIndexTable_fixed_2048[ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH]; + + #define ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH ((uint16_t)4032) + extern const uint16_t armBitRevIndexTable_fixed_4096[ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH]; + + extern const float32_t realCoefA[8192]; + extern const float32_t realCoefB[8192]; + + extern const q31_t realCoefAQ31[8192]; + extern const q31_t realCoefBQ31[8192]; + + extern const q15_t realCoefAQ15[8192]; + extern const q15_t realCoefBQ15[8192]; + + extern const float32_t Weights_128[256]; + extern const float32_t cos_factors_128[128]; + + extern const float32_t Weights_512[1024]; + extern const float32_t cos_factors_512[512]; + + extern const float32_t Weights_2048[4096]; + extern const float32_t cos_factors_2048[2048]; + + extern const float32_t Weights_8192[16384]; + extern const float32_t cos_factors_8192[8192]; + + extern const q15_t WeightsQ15_128[256]; + extern const q15_t cos_factorsQ15_128[128]; + + extern const q15_t WeightsQ15_512[1024]; + extern const q15_t cos_factorsQ15_512[512]; + + extern const q15_t WeightsQ15_2048[4096]; + extern const q15_t cos_factorsQ15_2048[2048]; + + extern const q15_t WeightsQ15_8192[16384]; + extern const q15_t cos_factorsQ15_8192[8192]; + + extern const q31_t WeightsQ31_128[256]; + extern const q31_t cos_factorsQ31_128[128]; + + extern const q31_t WeightsQ31_512[1024]; + extern const q31_t cos_factorsQ31_512[512]; + + extern const q31_t WeightsQ31_2048[4096]; + extern const q31_t cos_factorsQ31_2048[2048]; + + extern const q31_t WeightsQ31_8192[16384]; + extern const q31_t cos_factorsQ31_8192[8192]; + + + extern const q15_t armRecipTableQ15[64]; + + extern const q31_t armRecipTableQ31[64]; + + /* Tables for Fast Math Sine and Cosine */ + extern const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1]; + + extern const q31_t sinTable_q31[FAST_MATH_TABLE_SIZE + 1]; + + extern const q15_t sinTable_q15[FAST_MATH_TABLE_SIZE + 1]; + + + /* Accurate scalar sqrt */ + extern const q31_t sqrt_initial_lut_q31[32]; + + extern const q15_t sqrt_initial_lut_q15[16]; + +#if (defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + extern const q15_t sqrtTable_Q15[256]; + extern const q31_t sqrtTable_Q31[256]; + extern const unsigned char hwLUT[256]; +#endif + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + extern const float32_t exp_tab[8]; + extern const float32_t __logf_lut_f32[8]; +#endif + + +#ifdef __cplusplus +} +#endif + +#endif /* ARM_COMMON_TABLES_H */ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables_f16.h new file mode 100755 index 0000000..c84a766 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_common_tables_f16.h @@ -0,0 +1,95 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_common_tables_f16.h + * Description: Extern declaration for common tables + * + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_COMMON_TABLES_F16_H +#define ARM_COMMON_TABLES_F16_H + +#include "arm_math_types_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + /* F16 */ + #if !defined(__CC_ARM) && defined(ARM_FLOAT16_SUPPORTED) + extern const float16_t twiddleCoefF16_16[32]; + + extern const float16_t twiddleCoefF16_32[64]; + + extern const float16_t twiddleCoefF16_64[128]; + + extern const float16_t twiddleCoefF16_128[256]; + + extern const float16_t twiddleCoefF16_256[512]; + + extern const float16_t twiddleCoefF16_512[1024]; + + extern const float16_t twiddleCoefF16_1024[2048]; + + extern const float16_t twiddleCoefF16_2048[4096]; + + extern const float16_t twiddleCoefF16_4096[8192]; + #define twiddleCoefF16 twiddleCoefF16_4096 + + + extern const float16_t twiddleCoefF16_rfft_32[32]; + + extern const float16_t twiddleCoefF16_rfft_64[64]; + + extern const float16_t twiddleCoefF16_rfft_128[128]; + + extern const float16_t twiddleCoefF16_rfft_256[256]; + + extern const float16_t twiddleCoefF16_rfft_512[512]; + + extern const float16_t twiddleCoefF16_rfft_1024[1024]; + + extern const float16_t twiddleCoefF16_rfft_2048[2048]; + + extern const float16_t twiddleCoefF16_rfft_4096[4096]; + + #endif /* ARMAC5 */ + + +#if !defined(__CC_ARM) && defined(ARM_FLOAT16_SUPPORTED) +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + extern const float16_t exp_tab_f16[8]; + extern const float16_t __logf_lut_f16[8]; +#endif +#endif + + +#ifdef __cplusplus +} +#endif + +#endif /* _ARM_COMMON_TABLES_F16_H */ + + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs.h new file mode 100755 index 0000000..32c1a43 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs.h @@ -0,0 +1,86 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_const_structs.h + * Description: Constant structs that are initialized for user convenience. + * For example, some can be given as arguments to the arm_cfft_f32() function. + * + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_CONST_STRUCTS_H +#define ARM_CONST_STRUCTS_H + +#include "arm_math_types.h" +#include "arm_common_tables.h" +#include "dsp/transform_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len16; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len32; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len64; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len128; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len256; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len512; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len1024; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len2048; + extern const arm_cfft_instance_f64 arm_cfft_sR_f64_len4096; + + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len16; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len32; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len64; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len128; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len256; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len512; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len1024; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len2048; + extern const arm_cfft_instance_f32 arm_cfft_sR_f32_len4096; + + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len16; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len32; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len64; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len128; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len256; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len512; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len1024; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len2048; + extern const arm_cfft_instance_q31 arm_cfft_sR_q31_len4096; + + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len16; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len32; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len64; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len128; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len256; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len512; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len1024; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len2048; + extern const arm_cfft_instance_q15 arm_cfft_sR_q15_len4096; + +#ifdef __cplusplus +} +#endif + +#endif + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs_f16.h new file mode 100755 index 0000000..3a520b6 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_const_structs_f16.h @@ -0,0 +1,59 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_const_structs_f16.h + * Description: Constant structs that are initialized for user convenience. + * For example, some can be given as arguments to the arm_cfft_f16() function. + * + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_CONST_STRUCTS_F16_H +#define ARM_CONST_STRUCTS_F16_H + +#include "arm_math_types_f16.h" +#include "arm_common_tables.h" +#include "arm_common_tables_f16.h" +#include "dsp/transform_functions_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if !defined(__CC_ARM) && defined(ARM_FLOAT16_SUPPORTED) + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len16; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len32; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len64; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len128; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len256; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len512; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len1024; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len2048; + extern const arm_cfft_instance_f16 arm_cfft_sR_f16_len4096; +#endif + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_helium_utils.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_helium_utils.h new file mode 100755 index 0000000..7ef5210 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_helium_utils.h @@ -0,0 +1,749 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_helium_utils.h + * Description: Utility functions for Helium development + * + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_UTILS_HELIUM_H_ +#define ARM_UTILS_HELIUM_H_ + + +#ifdef __cplusplus +extern "C" +{ +#endif +/*************************************** + +Definitions available for MVEF and MVEI + +***************************************/ +#if (defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF) || defined(ARM_MATH_MVEI)) && !defined(ARM_MATH_AUTOVECTORIZE) + +#define INACTIVELANE 0 /* inactive lane content */ + + +#endif /* defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF) || defined(ARM_MATH_MVEI) */ + +/*************************************** + +Definitions available for MVEF only + +***************************************/ +#if (defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF)) && !defined(ARM_MATH_AUTOVECTORIZE) + +__STATIC_FORCEINLINE float32_t vecAddAcrossF32Mve(float32x4_t in) +{ + float32_t acc; + + acc = vgetq_lane(in, 0) + vgetq_lane(in, 1) + + vgetq_lane(in, 2) + vgetq_lane(in, 3); + + return acc; +} + + + + +/* newton initial guess */ +#define INVSQRT_MAGIC_F32 0x5f3759df +#define INV_NEWTON_INIT_F32 0x7EF127EA + + +#define INVSQRT_NEWTON_MVE_F32(invSqrt, xHalf, xStart)\ +{ \ + float32x4_t tmp; \ + \ + /* tmp = xhalf * x * x */ \ + tmp = vmulq(xStart, xStart); \ + tmp = vmulq(tmp, xHalf); \ + /* (1.5f - xhalf * x * x) */ \ + tmp = vsubq(vdupq_n_f32(1.5f), tmp); \ + /* x = x*(1.5f-xhalf*x*x); */ \ + invSqrt = vmulq(tmp, xStart); \ +} +#endif /* defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF) */ + + +/*************************************** + +Definitions available for f16 datatype with HW acceleration only + +***************************************/ +#if defined(ARM_FLOAT16_SUPPORTED) +#if defined (ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +__STATIC_FORCEINLINE float16_t vecAddAcrossF16Mve(float16x8_t in) +{ + float16x8_t tmpVec; + _Float16 acc; + + tmpVec = (float16x8_t) vrev32q_s16((int16x8_t) in); + in = vaddq_f16(tmpVec, in); + tmpVec = (float16x8_t) vrev64q_s32((int32x4_t) in); + in = vaddq_f16(tmpVec, in); + acc = (_Float16)vgetq_lane_f16(in, 0) + (_Float16)vgetq_lane_f16(in, 4); + + return (float16_t)acc; +} + +__STATIC_FORCEINLINE float16x8_t __mve_cmplx_sum_intra_vec_f16( + float16x8_t vecIn) +{ + float16x8_t vecTmp, vecOut; + uint32_t tmp = 0; + + vecTmp = (float16x8_t) vrev64q_s32((int32x4_t) vecIn); + // TO TRACK : using canonical addition leads to inefficient code generation for f16 + // vecTmp = vecTmp + vecAccCpx0; + /* + * Compute + * re0+re1 | im0+im1 | re0+re1 | im0+im1 + * re2+re3 | im2+im3 | re2+re3 | im2+im3 + */ + vecTmp = vaddq_f16(vecTmp, vecIn); + vecOut = vecTmp; + /* + * shift left, random tmp insertion in bottom + */ + vecOut = vreinterpretq_f16_s32(vshlcq_s32(vreinterpretq_s32_f16(vecOut) , &tmp, 32)); + /* + * Compute: + * DONTCARE | DONTCARE | re0+re1+re0+re1 |im0+im1+im0+im1 + * re0+re1+re2+re3 | im0+im1+im2+im3 | re2+re3+re2+re3 |im2+im3+im2+im3 + */ + vecOut = vaddq_f16(vecOut, vecTmp); + /* + * Cmplx sum is in 4th & 5th f16 elt + * return full vector + */ + return vecOut; +} + + +#define mve_cmplx_sum_intra_r_i_f16(vec, Re, Im) \ +{ \ + float16x8_t vecOut = __mve_cmplx_sum_intra_vec_f16(vec); \ + Re = vgetq_lane(vecOut, 4); \ + Im = vgetq_lane(vecOut, 5); \ +} + +__STATIC_FORCEINLINE void mve_cmplx_sum_intra_vec_f16( + float16x8_t vecIn, + float16_t *pOut) +{ + float16x8_t vecOut = __mve_cmplx_sum_intra_vec_f16(vecIn); + /* + * Cmplx sum is in 4th & 5th f16 elt + * use 32-bit extraction + */ + *(float32_t *) pOut = ((float32x4_t) vecOut)[2]; +} + + +#define INVSQRT_MAGIC_F16 0x59ba /* ( 0x1ba = 0x3759df >> 13) */ + +/* canonical version of INVSQRT_NEWTON_MVE_F16 leads to bad performance */ +#define INVSQRT_NEWTON_MVE_F16(invSqrt, xHalf, xStart) \ +{ \ + float16x8_t tmp; \ + \ + /* tmp = xhalf * x * x */ \ + tmp = vmulq(xStart, xStart); \ + tmp = vmulq(tmp, xHalf); \ + /* (1.5f - xhalf * x * x) */ \ + tmp = vsubq(vdupq_n_f16((float16_t)1.5), tmp); \ + /* x = x*(1.5f-xhalf*x*x); */ \ + invSqrt = vmulq(tmp, xStart); \ +} + +#endif +#endif + +/*************************************** + +Definitions available for MVEI and MVEF only + +***************************************/ +#if (defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEF) || defined(ARM_MATH_MVEI)) && !defined(ARM_MATH_AUTOVECTORIZE) +/* Following functions are used to transpose matrix in f32 and q31 cases */ +__STATIC_INLINE arm_status arm_mat_trans_32bit_2x2_mve( + uint32_t * pDataSrc, + uint32_t * pDataDest) +{ + static const uint32x4_t vecOffs = { 0, 2, 1, 3 }; + /* + * + * | 0 1 | => | 0 2 | + * | 2 3 | | 1 3 | + * + */ + uint32x4_t vecIn = vldrwq_u32((uint32_t const *)pDataSrc); + vstrwq_scatter_shifted_offset_u32(pDataDest, vecOffs, vecIn); + + return (ARM_MATH_SUCCESS); +} + +__STATIC_INLINE arm_status arm_mat_trans_32bit_3x3_mve( + uint32_t * pDataSrc, + uint32_t * pDataDest) +{ + const uint32x4_t vecOffs1 = { 0, 3, 6, 1}; + const uint32x4_t vecOffs2 = { 4, 7, 2, 5}; + /* + * + * | 0 1 2 | | 0 3 6 | 4 x 32 flattened version | 0 3 6 1 | + * | 3 4 5 | => | 1 4 7 | => | 4 7 2 5 | + * | 6 7 8 | | 2 5 8 | (row major) | 8 . . . | + * + */ + uint32x4_t vecIn1 = vldrwq_u32((uint32_t const *) pDataSrc); + uint32x4_t vecIn2 = vldrwq_u32((uint32_t const *) &pDataSrc[4]); + + vstrwq_scatter_shifted_offset_u32(pDataDest, vecOffs1, vecIn1); + vstrwq_scatter_shifted_offset_u32(pDataDest, vecOffs2, vecIn2); + + pDataDest[8] = pDataSrc[8]; + + return (ARM_MATH_SUCCESS); +} + +__STATIC_INLINE arm_status arm_mat_trans_32bit_4x4_mve(uint32_t * pDataSrc, uint32_t * pDataDest) +{ + /* + * 4x4 Matrix transposition + * is 4 x de-interleave operation + * + * 0 1 2 3 0 4 8 12 + * 4 5 6 7 1 5 9 13 + * 8 9 10 11 2 6 10 14 + * 12 13 14 15 3 7 11 15 + */ + + uint32x4x4_t vecIn; + + vecIn = vld4q((uint32_t const *) pDataSrc); + vstrwq(pDataDest, vecIn.val[0]); + pDataDest += 4; + vstrwq(pDataDest, vecIn.val[1]); + pDataDest += 4; + vstrwq(pDataDest, vecIn.val[2]); + pDataDest += 4; + vstrwq(pDataDest, vecIn.val[3]); + + return (ARM_MATH_SUCCESS); +} + + +__STATIC_INLINE arm_status arm_mat_trans_32bit_generic_mve( + uint16_t srcRows, + uint16_t srcCols, + uint32_t * pDataSrc, + uint32_t * pDataDest) +{ + uint32x4_t vecOffs; + uint32_t i; + uint32_t blkCnt; + uint32_t const *pDataC; + uint32_t *pDataDestR; + uint32x4_t vecIn; + + vecOffs = vidupq_u32((uint32_t)0, 1); + vecOffs = vecOffs * srcCols; + + i = srcCols; + do + { + pDataC = (uint32_t const *) pDataSrc; + pDataDestR = pDataDest; + + blkCnt = srcRows >> 2; + while (blkCnt > 0U) + { + vecIn = vldrwq_gather_shifted_offset_u32(pDataC, vecOffs); + vstrwq(pDataDestR, vecIn); + pDataDestR += 4; + pDataC = pDataC + srcCols * 4; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* + * tail + */ + blkCnt = srcRows & 3; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp32q(blkCnt); + vecIn = vldrwq_gather_shifted_offset_u32(pDataC, vecOffs); + vstrwq_p(pDataDestR, vecIn, p0); + } + + pDataSrc += 1; + pDataDest += srcRows; + } + while (--i); + + return (ARM_MATH_SUCCESS); +} + +__STATIC_INLINE arm_status arm_mat_cmplx_trans_32bit( + uint16_t srcRows, + uint16_t srcCols, + uint32_t *pDataSrc, + uint16_t dstRows, + uint16_t dstCols, + uint32_t *pDataDest) +{ + uint32_t i; + uint32_t const *pDataC; + uint32_t *pDataRow; + uint32_t *pDataDestR, *pDataDestRow; + uint32x4_t vecOffsRef, vecOffsCur; + uint32_t blkCnt; + uint32x4_t vecIn; + +#ifdef ARM_MATH_MATRIX_CHECK + /* + * Check for matrix mismatch condition + */ + if ((srcRows != dstCols) || (srcCols != dstRows)) + { + /* + * Set status as ARM_MATH_SIZE_MISMATCH + */ + return ARM_MATH_SIZE_MISMATCH; + } +#else + (void)dstRows; + (void)dstCols; +#endif + + /* 2x2, 3x3 and 4x4 specialization to be added */ + + vecOffsRef[0] = 0; + vecOffsRef[1] = 1; + vecOffsRef[2] = srcCols << 1; + vecOffsRef[3] = (srcCols << 1) + 1; + + pDataRow = pDataSrc; + pDataDestRow = pDataDest; + i = srcCols; + do + { + pDataC = (uint32_t const *) pDataRow; + pDataDestR = pDataDestRow; + vecOffsCur = vecOffsRef; + + blkCnt = (srcRows * CMPLX_DIM) >> 2; + while (blkCnt > 0U) + { + vecIn = vldrwq_gather_shifted_offset(pDataC, vecOffsCur); + vstrwq(pDataDestR, vecIn); + pDataDestR += 4; + vecOffsCur = vaddq_n_u32(vecOffsCur, (srcCols << 2)); + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + /* + * tail + * (will be merged thru tail predication) + */ + blkCnt = (srcRows * CMPLX_DIM) & 3; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp32q(blkCnt); + vecIn = vldrwq_gather_shifted_offset(pDataC, vecOffsCur); + vstrwq_p(pDataDestR, vecIn, p0); + } + + pDataRow += CMPLX_DIM; + pDataDestRow += (srcRows * CMPLX_DIM); + } + while (--i); + + return (ARM_MATH_SUCCESS); +} + +__STATIC_INLINE arm_status arm_mat_trans_16bit_2x2(uint16_t * pDataSrc, uint16_t * pDataDest) +{ + pDataDest[0] = pDataSrc[0]; + pDataDest[3] = pDataSrc[3]; + pDataDest[2] = pDataSrc[1]; + pDataDest[1] = pDataSrc[2]; + + return (ARM_MATH_SUCCESS); +} + +__STATIC_INLINE arm_status arm_mat_trans_16bit_3x3_mve(uint16_t * pDataSrc, uint16_t * pDataDest) +{ + static const uint16_t stridesTr33[8] = { 0, 3, 6, 1, 4, 7, 2, 5 }; + uint16x8_t vecOffs1; + uint16x8_t vecIn1; + /* + * + * | 0 1 2 | | 0 3 6 | 8 x 16 flattened version | 0 3 6 1 4 7 2 5 | + * | 3 4 5 | => | 1 4 7 | => | 8 . . . . . . . | + * | 6 7 8 | | 2 5 8 | (row major) + * + */ + vecOffs1 = vldrhq_u16((uint16_t const *) stridesTr33); + vecIn1 = vldrhq_u16((uint16_t const *) pDataSrc); + + vstrhq_scatter_shifted_offset_u16(pDataDest, vecOffs1, vecIn1); + + pDataDest[8] = pDataSrc[8]; + + return (ARM_MATH_SUCCESS); +} + + +__STATIC_INLINE arm_status arm_mat_trans_16bit_4x4_mve(uint16_t * pDataSrc, uint16_t * pDataDest) +{ + static const uint16_t stridesTr44_1[8] = { 0, 4, 8, 12, 1, 5, 9, 13 }; + static const uint16_t stridesTr44_2[8] = { 2, 6, 10, 14, 3, 7, 11, 15 }; + uint16x8_t vecOffs1, vecOffs2; + uint16x8_t vecIn1, vecIn2; + uint16_t const * pDataSrcVec = (uint16_t const *) pDataSrc; + + /* + * 4x4 Matrix transposition + * + * | 0 1 2 3 | | 0 4 8 12 | 8 x 16 flattened version + * | 4 5 6 7 | => | 1 5 9 13 | => [0 4 8 12 1 5 9 13] + * | 8 9 10 11 | | 2 6 10 14 | [2 6 10 14 3 7 11 15] + * | 12 13 14 15 | | 3 7 11 15 | + */ + + vecOffs1 = vldrhq_u16((uint16_t const *) stridesTr44_1); + vecOffs2 = vldrhq_u16((uint16_t const *) stridesTr44_2); + vecIn1 = vldrhq_u16(pDataSrcVec); + pDataSrcVec += 8; + vecIn2 = vldrhq_u16(pDataSrcVec); + + vstrhq_scatter_shifted_offset_u16(pDataDest, vecOffs1, vecIn1); + vstrhq_scatter_shifted_offset_u16(pDataDest, vecOffs2, vecIn2); + + + return (ARM_MATH_SUCCESS); +} + + + +__STATIC_INLINE arm_status arm_mat_trans_16bit_generic( + uint16_t srcRows, + uint16_t srcCols, + uint16_t * pDataSrc, + uint16_t * pDataDest) +{ + uint16x8_t vecOffs; + uint32_t i; + uint32_t blkCnt; + uint16_t const *pDataC; + uint16_t *pDataDestR; + uint16x8_t vecIn; + + vecOffs = vidupq_u16((uint32_t)0, 1); + vecOffs = vecOffs * srcCols; + + i = srcCols; + while(i > 0U) + { + pDataC = (uint16_t const *) pDataSrc; + pDataDestR = pDataDest; + + blkCnt = srcRows >> 3; + while (blkCnt > 0U) + { + vecIn = vldrhq_gather_shifted_offset_u16(pDataC, vecOffs); + vstrhq_u16(pDataDestR, vecIn); + pDataDestR += 8; + pDataC = pDataC + srcCols * 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* + * tail + */ + blkCnt = srcRows & 7; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp16q(blkCnt); + vecIn = vldrhq_gather_shifted_offset_u16(pDataC, vecOffs); + vstrhq_p_u16(pDataDestR, vecIn, p0); + } + pDataSrc += 1; + pDataDest += srcRows; + i--; + } + + return (ARM_MATH_SUCCESS); +} + + +__STATIC_INLINE arm_status arm_mat_cmplx_trans_16bit( + uint16_t srcRows, + uint16_t srcCols, + uint16_t *pDataSrc, + uint16_t dstRows, + uint16_t dstCols, + uint16_t *pDataDest) +{ + static const uint16_t loadCmplxCol[8] = { 0, 0, 1, 1, 2, 2, 3, 3 }; + int i; + uint16x8_t vecOffsRef, vecOffsCur; + uint16_t const *pDataC; + uint16_t *pDataRow; + uint16_t *pDataDestR, *pDataDestRow; + uint32_t blkCnt; + uint16x8_t vecIn; + +#ifdef ARM_MATH_MATRIX_CHECK + /* + * Check for matrix mismatch condition + */ + if ((srcRows != dstCols) || (srcCols != dstRows)) + { + /* + * Set status as ARM_MATH_SIZE_MISMATCH + */ + return ARM_MATH_SIZE_MISMATCH; + } +#else + (void)dstRows; + (void)dstCols; +#endif + + /* + * 2x2, 3x3 and 4x4 specialization to be added + */ + + + /* + * build [0, 1, 2xcol, 2xcol+1, 4xcol, 4xcol+1, 6xcol, 6xcol+1] + */ + vecOffsRef = vldrhq_u16((uint16_t const *) loadCmplxCol); + vecOffsRef = vmulq_n_u16(vecOffsRef, (uint16_t) (srcCols * CMPLX_DIM)) + + viwdupq_u16((uint32_t)0, (uint16_t) 2, 1); + + pDataRow = pDataSrc; + pDataDestRow = pDataDest; + i = srcCols; + do + { + pDataC = (uint16_t const *) pDataRow; + pDataDestR = pDataDestRow; + vecOffsCur = vecOffsRef; + + blkCnt = (srcRows * CMPLX_DIM) >> 3; + while (blkCnt > 0U) + { + vecIn = vldrhq_gather_shifted_offset(pDataC, vecOffsCur); + vstrhq(pDataDestR, vecIn); + pDataDestR+= 8; // VEC_LANES_U16 + vecOffsCur = vaddq_n_u16(vecOffsCur, (srcCols << 3)); + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + /* + * tail + * (will be merged thru tail predication) + */ + blkCnt = (srcRows * CMPLX_DIM) & 0x7; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp16q(blkCnt); + vecIn = vldrhq_gather_shifted_offset(pDataC, vecOffsCur); + vstrhq_p(pDataDestR, vecIn, p0); + } + + pDataRow += CMPLX_DIM; + pDataDestRow += (srcRows * CMPLX_DIM); + } + while (--i); + + return (ARM_MATH_SUCCESS); +} +#endif /* MVEF and MVEI */ + +/*************************************** + +Definitions available for MVEI only + +***************************************/ +#if (defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEI)) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_common_tables.h" + +#define MVE_ASRL_SAT16(acc, shift) ((sqrshrl_sat48(acc, -(32-shift)) >> 32) & 0xffffffff) +#define MVE_ASRL_SAT32(acc, shift) ((sqrshrl(acc, -(32-shift)) >> 32) & 0xffffffff) + + +__STATIC_INLINE q31x4_t FAST_VSQRT_Q31(q31x4_t vecIn) +{ + q63x2_t vecTmpLL; + q31x4_t vecTmp0, vecTmp1; + q31_t scale; + q63_t tmp64; + q31x4_t vecNrm, vecDst, vecIdx, vecSignBits; + + + vecSignBits = vclsq(vecIn); + vecSignBits = vbicq_n_s32(vecSignBits, 1); + /* + * in = in << no_of_sign_bits; + */ + vecNrm = vshlq(vecIn, vecSignBits); + /* + * index = in >> 24; + */ + vecIdx = vecNrm >> 24; + vecIdx = vecIdx << 1; + + vecTmp0 = vldrwq_gather_shifted_offset_s32(sqrtTable_Q31, (uint32x4_t)vecIdx); + + vecIdx = vecIdx + 1; + + vecTmp1 = vldrwq_gather_shifted_offset_s32(sqrtTable_Q31, (uint32x4_t)vecIdx); + + vecTmp1 = vqrdmulhq(vecTmp1, vecNrm); + vecTmp0 = vecTmp0 - vecTmp1; + vecTmp1 = vqrdmulhq(vecTmp0, vecTmp0); + vecTmp1 = vqrdmulhq(vecNrm, vecTmp1); + vecTmp1 = vdupq_n_s32(0x18000000) - vecTmp1; + vecTmp0 = vqrdmulhq(vecTmp0, vecTmp1); + vecTmpLL = vmullbq_int(vecNrm, vecTmp0); + + /* + * scale elements 0, 2 + */ + scale = 26 + (vecSignBits[0] >> 1); + tmp64 = asrl(vecTmpLL[0], scale); + vecDst[0] = (q31_t) tmp64; + + scale = 26 + (vecSignBits[2] >> 1); + tmp64 = asrl(vecTmpLL[1], scale); + vecDst[2] = (q31_t) tmp64; + + vecTmpLL = vmulltq_int(vecNrm, vecTmp0); + + /* + * scale elements 1, 3 + */ + scale = 26 + (vecSignBits[1] >> 1); + tmp64 = asrl(vecTmpLL[0], scale); + vecDst[1] = (q31_t) tmp64; + + scale = 26 + (vecSignBits[3] >> 1); + tmp64 = asrl(vecTmpLL[1], scale); + vecDst[3] = (q31_t) tmp64; + /* + * set negative values to 0 + */ + vecDst = vdupq_m(vecDst, 0, vcmpltq_n_s32(vecIn, 0)); + + return vecDst; +} + +__STATIC_INLINE q15x8_t FAST_VSQRT_Q15(q15x8_t vecIn) +{ + q31x4_t vecTmpLev, vecTmpLodd, vecSignL; + q15x8_t vecTmp0, vecTmp1; + q15x8_t vecNrm, vecDst, vecIdx, vecSignBits; + + vecDst = vuninitializedq_s16(); + + vecSignBits = vclsq(vecIn); + vecSignBits = vbicq_n_s16(vecSignBits, 1); + /* + * in = in << no_of_sign_bits; + */ + vecNrm = vshlq(vecIn, vecSignBits); + + vecIdx = vecNrm >> 8; + vecIdx = vecIdx << 1; + + vecTmp0 = vldrhq_gather_shifted_offset_s16(sqrtTable_Q15, (uint16x8_t)vecIdx); + + vecIdx = vecIdx + 1; + + vecTmp1 = vldrhq_gather_shifted_offset_s16(sqrtTable_Q15, (uint16x8_t)vecIdx); + + vecTmp1 = vqrdmulhq(vecTmp1, vecNrm); + vecTmp0 = vecTmp0 - vecTmp1; + vecTmp1 = vqrdmulhq(vecTmp0, vecTmp0); + vecTmp1 = vqrdmulhq(vecNrm, vecTmp1); + vecTmp1 = vdupq_n_s16(0x1800) - vecTmp1; + vecTmp0 = vqrdmulhq(vecTmp0, vecTmp1); + + vecSignBits = vecSignBits >> 1; + + vecTmpLev = vmullbq_int(vecNrm, vecTmp0); + vecTmpLodd = vmulltq_int(vecNrm, vecTmp0); + + vecTmp0 = vecSignBits + 10; + /* + * negate sign to apply register based vshl + */ + vecTmp0 = -vecTmp0; + + /* + * shift even elements + */ + vecSignL = vmovlbq(vecTmp0); + vecTmpLev = vshlq(vecTmpLev, vecSignL); + /* + * shift odd elements + */ + vecSignL = vmovltq(vecTmp0); + vecTmpLodd = vshlq(vecTmpLodd, vecSignL); + /* + * merge and narrow odd and even parts + */ + vecDst = vmovnbq_s32(vecDst, vecTmpLev); + vecDst = vmovntq_s32(vecDst, vecTmpLodd); + /* + * set negative values to 0 + */ + vecDst = vdupq_m(vecDst, 0, vcmpltq_n_s16(vecIn, 0)); + + return vecDst; +} + +#endif /* defined (ARM_MATH_HELIUM) || defined(ARM_MATH_MVEI) */ + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math.h new file mode 100755 index 0000000..0e9ca59 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math.h @@ -0,0 +1,80 @@ +/****************************************************************************** + * @file arm_math.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef ARM_MATH_H +#define ARM_MATH_H + + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/basic_math_functions.h" +#include "dsp/interpolation_functions.h" +#include "dsp/bayes_functions.h" +#include "dsp/matrix_functions.h" +#include "dsp/complex_math_functions.h" +#include "dsp/statistics_functions.h" +#include "dsp/controller_functions.h" +#include "dsp/support_functions.h" +#include "dsp/distance_functions.h" +#include "dsp/svm_functions.h" +#include "dsp/fast_math_functions.h" +#include "dsp/transform_functions.h" +#include "dsp/filtering_functions.h" +#include "dsp/quaternion_math_functions.h" +#include "dsp/window_functions.h" + + + +#ifdef __cplusplus +extern "C" +{ +#endif + + + + +//#define TABLE_SPACING_Q31 0x400000 +//#define TABLE_SPACING_Q15 0x80 + + + + + +#ifdef __cplusplus +} +#endif + + +#endif /* _ARM_MATH_H */ + +/** + * + * End of file. + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_f16.h new file mode 100755 index 0000000..34ca0e5 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_f16.h @@ -0,0 +1,59 @@ +/****************************************************************************** + * @file arm_math_f16.h + * @brief Public header file for f16 function of the CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_MATH_F16_H +#define ARM_MATH_F16_H + +#include "arm_math.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#include "arm_math_types_f16.h" +#include "dsp/none.h" +#include "dsp/utils.h" +#include "dsp/basic_math_functions_f16.h" +#include "dsp/interpolation_functions_f16.h" +#include "dsp/bayes_functions_f16.h" +#include "dsp/matrix_functions_f16.h" +#include "dsp/complex_math_functions_f16.h" +#include "dsp/statistics_functions_f16.h" +#include "dsp/controller_functions_f16.h" +#include "dsp/support_functions_f16.h" +#include "dsp/distance_functions_f16.h" +#include "dsp/svm_functions_f16.h" +#include "dsp/fast_math_functions_f16.h" +#include "dsp/transform_functions_f16.h" +#include "dsp/filtering_functions_f16.h" + +#ifdef __cplusplus +} +#endif + +#endif /* _ARM_MATH_F16_H */ + + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_memory.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_memory.h new file mode 100755 index 0000000..43dfcbd --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_memory.h @@ -0,0 +1,224 @@ +/****************************************************************************** + * @file arm_math_memory.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_MATH_MEMORY_H_ + +#define ARM_MATH_MEMORY_H_ + +#include "arm_math_types.h" + +/* Size are in bytes */ +#if !defined(ARM_MATH_L1_CACHE_SIZE) +#define ARM_MATH_L1_CACHE_SIZE (16*1024) +#endif + +#if !defined(ARM_MATH_L2_CACHE_SIZE) +#define ARM_MATH_L2_CACHE_SIZE (128*1024) +#endif + +#if !defined(ARM_MATH_L3_CACHE_SIZE) +#define ARM_MATH_L3_CACHE_SIZE (512*1024) +#endif + +#if defined(ARM_MATH_NEON) + + +extern char ARM_CACHE_PACKEDB[]; +extern char ARM_CACHE_PACKEDA[]; +// PACKEDC contains the accumulators +extern char ARM_CACHE_PACKEDC[]; +#endif + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + @brief definition to read/write two 16 bit values. + @deprecated + */ +#if defined ( __CC_ARM ) + #define __SIMD32_TYPE int32_t __packed +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + #define __SIMD32_TYPE int32_t +#elif defined ( __GNUC__ ) + #define __SIMD32_TYPE int32_t +#elif defined ( __ICCARM__ ) + #define __SIMD32_TYPE int32_t __packed +#elif defined ( __TI_ARM__ ) + #define __SIMD32_TYPE int32_t +#elif defined ( __CSMC__ ) + #define __SIMD32_TYPE int32_t +#elif defined ( __TASKING__ ) + #define __SIMD32_TYPE __un(aligned) int32_t +#elif defined(_MSC_VER ) + #define __SIMD32_TYPE int32_t +#else + #error Unknown compiler +#endif + +#define __SIMD32(addr) (*(__SIMD32_TYPE **) & (addr)) +#define __SIMD32_CONST(addr) ( (__SIMD32_TYPE * ) (addr)) +#define _SIMD32_OFFSET(addr) (*(__SIMD32_TYPE * ) (addr)) +#define __SIMD64(addr) (*( int64_t **) & (addr)) + + +/* SIMD replacement */ + + +/** + @brief Read 2 Q15 from Q15 pointer. + @param[in] pQ15 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q15x2 ( + q15_t const * pQ15) +{ + q31_t val; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, pQ15, 4); +#else + val = (pQ15[1] << 16) | (pQ15[0] & 0x0FFFF) ; +#endif + + return (val); +} + +/** + @brief Read 2 Q15 from Q15 pointer and increment pointer afterwards. + @param[in] pQ15 points to input value + @return Q31 value + */ +#define read_q15x2_ia(pQ15) read_q15x2((*(pQ15) += 2) - 2) + +/** + @brief Read 2 Q15 from Q15 pointer and decrement pointer afterwards. + @param[in] pQ15 points to input value + @return Q31 value + */ +#define read_q15x2_da(pQ15) read_q15x2((*(pQ15) -= 2) + 2) + +/** + @brief Write 2 Q15 to Q15 pointer and increment pointer afterwards. + @param[in] pQ15 points to input value + @param[in] value Q31 value + */ +__STATIC_FORCEINLINE void write_q15x2_ia ( + q15_t ** pQ15, + q31_t value) +{ + q31_t val = value; +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (*pQ15, &val, 4); +#else + (*pQ15)[0] = (q15_t)(val & 0x0FFFF); + (*pQ15)[1] = (q15_t)((val >> 16) & 0x0FFFF); +#endif + + *pQ15 += 2; +} + +/** + @brief Write 2 Q15 to Q15 pointer. + @param[in] pQ15 points to input value + @param[in] value Q31 value + */ +__STATIC_FORCEINLINE void write_q15x2 ( + q15_t * pQ15, + q31_t value) +{ + q31_t val = value; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (pQ15, &val, 4); +#else + pQ15[0] = (q15_t)(val & 0x0FFFF); + pQ15[1] = (q15_t)(val >> 16); +#endif +} + + +/** + @brief Read 4 Q7 from Q7 pointer + @param[in] pQ7 points to input value + @return Q31 value + */ +__STATIC_FORCEINLINE q31_t read_q7x4 ( + q7_t const * pQ7) +{ + q31_t val; + +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (&val, pQ7, 4); +#else + val =((pQ7[3] & 0x0FF) << 24) | ((pQ7[2] & 0x0FF) << 16) | ((pQ7[1] & 0x0FF) << 8) | (pQ7[0] & 0x0FF); +#endif + return (val); +} + +/** + @brief Read 4 Q7 from Q7 pointer and increment pointer afterwards. + @param[in] pQ7 points to input value + @return Q31 value + */ +#define read_q7x4_ia(pQ7) read_q7x4((*(pQ7) += 4) - 4) + +/** + @brief Read 4 Q7 from Q7 pointer and decrement pointer afterwards. + @param[in] pQ7 points to input value + @return Q31 value + */ +#define read_q7x4_da(pQ7) read_q7x4((*(pQ7) -= 4) + 4) + +/** + @brief Write 4 Q7 to Q7 pointer and increment pointer afterwards. + @param[in] pQ7 points to input value + @param[in] value Q31 value + */ +__STATIC_FORCEINLINE void write_q7x4_ia ( + q7_t ** pQ7, + q31_t value) +{ + q31_t val = value; +#ifdef __ARM_FEATURE_UNALIGNED + memcpy (*pQ7, &val, 4); +#else + (*pQ7)[0] = (q7_t)(val & 0x0FF); + (*pQ7)[1] = (q7_t)((val >> 8) & 0x0FF); + (*pQ7)[2] = (q7_t)((val >> 16) & 0x0FF); + (*pQ7)[3] = (q7_t)((val >> 24) & 0x0FF); + +#endif + *pQ7 += 4; +} + + +#ifdef __cplusplus +} +#endif + +#endif /*ifndef _ARM_MATH_MEMORY_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_types.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_types.h new file mode 100755 index 0000000..a7a0d21 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_types.h @@ -0,0 +1,729 @@ +/****************************************************************************** + * @file arm_math_types.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_MATH_TYPES_H_ + +#define ARM_MATH_TYPES_H_ + +#if defined(ARM_DSP_CUSTOM_CONFIG) +#include "arm_dsp_config.h" +#endif + +#ifndef ARM_DSP_ATTRIBUTE +#define ARM_DSP_ATTRIBUTE +#endif + +#ifndef ARM_DSP_TABLE_ATTRIBUTE +#define ARM_DSP_TABLE_ATTRIBUTE +#endif + +#ifdef __cplusplus +#include +#include +#include +#include +#include +extern "C" +{ +#else +#include +#include +#include +#include +#include +#endif + +/* Compiler specific diagnostic adjustment */ +#if defined ( __CC_ARM ) + +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + +#elif defined ( __APPLE_CC__ ) + #pragma GCC diagnostic ignored "-Wold-style-cast" + +#elif defined(__clang__) + #pragma GCC diagnostic push + #pragma GCC diagnostic ignored "-Wsign-conversion" + #pragma GCC diagnostic ignored "-Wconversion" + #pragma GCC diagnostic ignored "-Wunused-parameter" + +#elif defined ( __GNUC__ ) + #pragma GCC diagnostic push + #pragma GCC diagnostic ignored "-Wsign-conversion" + #pragma GCC diagnostic ignored "-Wconversion" + #pragma GCC diagnostic ignored "-Wunused-parameter" + // Disable some code having issue with GCC + #define ARM_DSP_BUILT_WITH_GCC + +#elif defined ( __ICCARM__ ) + +#elif defined ( __TI_ARM__ ) + +#elif defined ( __CSMC__ ) + +#elif defined ( __TASKING__ ) + +#elif defined ( _MSC_VER ) + +#else + #error Unknown compiler +#endif + + +/* Included for intrinsics definitions */ +#if defined (_MSC_VER ) +#define __STATIC_FORCEINLINE static __forceinline +#define __STATIC_INLINE static __inline +#define __ALIGNED(x) __declspec(align(x)) +#define __WEAK +#define SECTION_NOINIT +#define NO_INLINE __declspec(noinline) + + +#elif defined ( __APPLE_CC__ ) +#define __ALIGNED(x) __attribute__((aligned(x))) +#define __STATIC_FORCEINLINE static inline __attribute__((always_inline)) +#define __STATIC_INLINE static inline +#define __WEAK +#define SECTION_NOINIT +#define NO_INLINE __attribute__ ((noinline)) +#elif defined (__GNUC_PYTHON__) +#define __ALIGNED(x) __attribute__((aligned(x))) +#define __STATIC_FORCEINLINE static inline __attribute__((always_inline)) +#define __STATIC_INLINE static inline +#define __WEAK +#define SECTION_NOINIT __attribute__((section(".noinit"))) +#define NO_INLINE __attribute__ ((noinline)) + +#else +#define SECTION_NOINIT +#define NO_INLINE __attribute__ ((noinline)) + +#include "cmsis_compiler.h" +#endif + + + + + +/* evaluate ARM DSP feature */ +/* __GNUC_PYTHON__ is disabling dependency to CMSIS Core. + * As consequence, DSP intrinsics (defined in CMSIS Core) + * cannot be used anymore even if __ARM_FEATURE_DSP is defined. + * It is the only way to build on a target not supported + * by CMSIS Core. + * + * ARM_MATH_NEON is used to enable the Neon variants. + * When Neon variants are enabled, the DSP extension are disabled + * + */ +#if (!defined(__GNUC_PYTHON__) && !defined(ARM_MATH_NEON) && !defined(ARM_MATH_NEON_EXPERIMENTAL)) +#if (defined (__ARM_FEATURE_DSP) && (__ARM_FEATURE_DSP == 1)) + #define ARM_MATH_DSP 1 +#endif +#endif + +#if defined(ARM_MATH_NEON) + #if defined(_MSC_VER) && defined(_M_ARM64EC) + #include + #else + #include + #endif + #if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC) && __ARM_FEATURE_FP16_VECTOR_ARITHMETIC + #if !defined(ARM_MATH_NEON_FLOAT16) + #define ARM_MATH_NEON_FLOAT16 + #endif + #endif +#endif + +#if !defined(ARM_MATH_AUTOVECTORIZE) + + +#if defined(__ARM_FEATURE_MVE) +#if __ARM_FEATURE_MVE + #if !defined(ARM_MATH_MVEI) + #define ARM_MATH_MVEI + #endif +#endif + +#if defined(__ARM_FEATURE_MVE) && (__ARM_FEATURE_MVE & 2) + #if !defined(ARM_MATH_MVEF) + #define ARM_MATH_MVEF + #endif + #if !defined(ARM_MATH_MVE_FLOAT16) + #define ARM_MATH_MVE_FLOAT16 + #endif +#endif + +#endif /* defined (__ARM_FEATURE_MVE) */ +#endif /* !defined (ARM_MATH_AUTOVECTORIZE) */ + + +#if defined (ARM_MATH_HELIUM) + #if !defined(ARM_MATH_MVEF) + #define ARM_MATH_MVEF + #endif + + #if !defined(ARM_MATH_MVEI) + #define ARM_MATH_MVEI + #endif + + #if !defined(ARM_MATH_MVE_FLOAT16) + #define ARM_MATH_MVE_FLOAT16 + #endif +#endif + + + +#if defined ( __CC_ARM ) + /* Enter low optimization region - place directly above function definition */ + #if defined( __ARM_ARCH_7EM__ ) + #define LOW_OPTIMIZATION_ENTER \ + _Pragma ("push") \ + _Pragma ("O1") + #else + #define LOW_OPTIMIZATION_ENTER + #endif + + /* Exit low optimization region - place directly after end of function definition */ + #if defined ( __ARM_ARCH_7EM__ ) + #define LOW_OPTIMIZATION_EXIT \ + _Pragma ("pop") + #else + #define LOW_OPTIMIZATION_EXIT + #endif + + /* Enter low optimization region - place directly above function definition */ + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + + /* Exit low optimization region - place directly after end of function definition */ + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined (__ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __APPLE_CC__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __GNUC__ ) + #define LOW_OPTIMIZATION_ENTER \ + __attribute__(( optimize("-O1") )) + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __ICCARM__ ) + /* Enter low optimization region - place directly above function definition */ + #if defined ( __ARM_ARCH_7EM__ ) + #define LOW_OPTIMIZATION_ENTER \ + _Pragma ("optimize=low") + #else + #define LOW_OPTIMIZATION_ENTER + #endif + + /* Exit low optimization region - place directly after end of function definition */ + #define LOW_OPTIMIZATION_EXIT + + /* Enter low optimization region - place directly above function definition */ + #if defined ( __ARM_ARCH_7EM__ ) + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \ + _Pragma ("optimize=low") + #else + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #endif + + /* Exit low optimization region - place directly after end of function definition */ + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __TI_ARM__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __CSMC__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( __TASKING__ ) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT + +#elif defined ( _MSC_VER ) || defined(__GNUC_PYTHON__) + #define LOW_OPTIMIZATION_ENTER + #define LOW_OPTIMIZATION_EXIT + #define IAR_ONLY_LOW_OPTIMIZATION_ENTER + #define IAR_ONLY_LOW_OPTIMIZATION_EXIT +#endif + + + +/* Compiler specific diagnostic adjustment */ +#if defined ( __CC_ARM ) + +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + +#elif defined ( __APPLE_CC__ ) + +#elif defined ( __GNUC__ ) +#pragma GCC diagnostic pop + +#elif defined ( __ICCARM__ ) + +#elif defined ( __TI_ARM__ ) + +#elif defined ( __CSMC__ ) + +#elif defined ( __TASKING__ ) + +#elif defined ( _MSC_VER ) + +#else + #error Unknown compiler +#endif + +#ifdef __cplusplus +} +#endif + +#if defined(__ARM_FEATURE_MVE) && __ARM_FEATURE_MVE +#include +#endif + +#if defined(ARM_DSP_CONFIG_TABLES) +#error("-DARM_DSP_CONFIG_TABLES no more supported. Use the new initialization functions to let the linker optimize the code size.") +#endif + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup genericTypes Generic Types + * @{ +*/ + + /** + * @brief 8-bit fractional data type in 1.7 format. + */ + typedef int8_t q7_t; + + /** + * @brief 16-bit fractional data type in 1.15 format. + */ + typedef int16_t q15_t; + + /** + * @brief 32-bit fractional data type in 1.31 format. + */ + typedef int32_t q31_t; + + /** + * @brief 64-bit fractional data type in 1.63 format. + */ + typedef int64_t q63_t; + + /** + * @brief 32-bit floating-point type definition. + */ +#if !defined(__ICCARM__) || !defined(__ARM_FEATURE_MVE) || !(__ARM_FEATURE_MVE & 2) + typedef float float32_t; +#endif + + /** + * @brief 64-bit floating-point type definition. + */ + typedef double float64_t; + + /** + * @brief vector types + */ +#if defined(ARM_MATH_NEON) || (defined (ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE)) + + /** + * @brief 64-bit fractional 128-bit vector data type in 1.63 format + */ + typedef int64x2_t q63x2_t; + + /** + * @brief 32-bit fractional 128-bit vector data type in 1.31 format. + */ + typedef int32x4_t q31x4_t; + + /** + * @brief 16-bit fractional 128-bit vector data type with 16-bit alignment in 1.15 format. + */ + typedef __ALIGNED(2) int16x8_t q15x8_t; + + /** + * @brief 8-bit fractional 128-bit vector data type with 8-bit alignment in 1.7 format. + */ + typedef __ALIGNED(1) int8x16_t q7x16_t; + + /** + * @brief 32-bit fractional 128-bit vector pair data type in 1.31 format. + */ + typedef int32x4x2_t q31x4x2_t; + + /** + * @brief 32-bit fractional 128-bit vector quadruplet data type in 1.31 format. + */ + typedef int32x4x4_t q31x4x4_t; + + /** + * @brief 16-bit fractional 128-bit vector pair data type in 1.15 format. + */ + typedef int16x8x2_t q15x8x2_t; + + /** + * @brief 16-bit fractional 128-bit vector quadruplet data type in 1.15 format. + */ + typedef int16x8x4_t q15x8x4_t; + + /** + * @brief 8-bit fractional 128-bit vector pair data type in 1.7 format. + */ + typedef int8x16x2_t q7x16x2_t; + + /** + * @brief 8-bit fractional 128-bit vector quadruplet data type in 1.7 format. + */ + typedef int8x16x4_t q7x16x4_t; + + /** + * @brief 32-bit fractional data type in 9.23 format. + */ + typedef int32_t q23_t; + + /** + * @brief 32-bit fractional 128-bit vector data type in 9.23 format. + */ + typedef int32x4_t q23x4_t; + + /** + * @brief 64-bit status 128-bit vector data type. + */ + typedef int64x2_t status64x2_t; + + /** + * @brief 32-bit status 128-bit vector data type. + */ + typedef int32x4_t status32x4_t; + + /** + * @brief 16-bit status 128-bit vector data type. + */ + typedef int16x8_t status16x8_t; + + /** + * @brief 8-bit status 128-bit vector data type. + */ + typedef int8x16_t status8x16_t; + + +#endif + +#if defined(ARM_MATH_NEON) || (defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)) /* floating point vector*/ + + /** + * @brief 32-bit floating-point 128-bit vector type + */ + typedef float32x4_t f32x4_t; + + /** + * @brief 32-bit floating-point 128-bit vector pair data type + */ + typedef float32x4x2_t f32x4x2_t; + + /** + * @brief 32-bit floating-point 128-bit vector quadruplet data type + */ + typedef float32x4x4_t f32x4x4_t; + + /** + * @brief 32-bit ubiquitous 128-bit vector data type + */ + typedef union _any32x4_t + { + float32x4_t f; + int32x4_t i; + } any32x4_t; + +#endif + +#if defined(ARM_MATH_NEON) + /** + * @brief 32-bit fractional 64-bit vector data type in 1.31 format. + */ + typedef int32x2_t q31x2_t; + + /** + * @brief 16-bit fractional 64-bit vector data type in 1.15 format. + */ + typedef __ALIGNED(2) int16x4_t q15x4_t; + + /** + * @brief 8-bit fractional 64-bit vector data type in 1.7 format. + */ + typedef __ALIGNED(1) int8x8_t q7x8_t; + + /** + * @brief 32-bit float 64-bit vector data type. + */ + typedef float32x2_t f32x2_t; + + /** + * @brief 32-bit floating-point 128-bit vector triplet data type + */ + typedef float32x4x3_t f32x4x3_t; + + /** + * @brief 32-bit fractional 128-bit vector triplet data type in 1.31 format + */ + typedef int32x4x3_t q31x4x3_t; + + /** + * @brief 16-bit fractional 128-bit vector triplet data type in 1.15 format + */ + typedef int16x8x3_t q15x8x3_t; + + /** + * @brief 8-bit fractional 128-bit vector triplet data type in 1.7 format + */ + typedef int8x16x3_t q7x16x3_t; + + /** + * @brief 32-bit floating-point 64-bit vector pair data type + */ + typedef float32x2x2_t f32x2x2_t; + + /** + * @brief 32-bit floating-point 64-bit vector triplet data type + */ + typedef float32x2x3_t f32x2x3_t; + + /** + * @brief 32-bit floating-point 64-bit vector quadruplet data type + */ + typedef float32x2x4_t f32x2x4_t; + + /** + * @brief 32-bit fractional 64-bit vector pair data type in 1.31 format + */ + typedef int32x2x2_t q31x2x2_t; + + /** + * @brief 32-bit fractional 64-bit vector triplet data type in 1.31 format + */ + typedef int32x2x3_t q31x2x3_t; + + /** + * @brief 32-bit fractional 64-bit vector quadruplet data type in 1.31 format + */ + typedef int32x4x3_t q31x2x4_t; + + /** + * @brief 16-bit fractional 64-bit vector pair data type in 1.15 format + */ + typedef int16x4x2_t q15x4x2_t; + + /** + * @brief 16-bit fractional 64-bit vector triplet data type in 1.15 format + */ + typedef int16x4x2_t q15x4x3_t; + + /** + * @brief 16-bit fractional 64-bit vector quadruplet data type in 1.15 format + */ + typedef int16x4x3_t q15x4x4_t; + + /** + * @brief 8-bit fractional 64-bit vector pair data type in 1.7 format + */ + typedef int8x8x2_t q7x8x2_t; + + /** + * @brief 8-bit fractional 64-bit vector triplet data type in 1.7 format + */ + typedef int8x8x3_t q7x8x3_t; + + /** + * @brief 8-bit fractional 64-bit vector quadruplet data type in 1.7 format + */ + typedef int8x8x4_t q7x8x4_t; + + /** + * @brief 32-bit ubiquitous 64-bit vector data type + */ + typedef union _any32x2_t + { + float32x2_t f; + int32x2_t i; + } any32x2_t; + + /** + * @brief 32-bit status 64-bit vector data type. + */ + typedef int32x4_t status32x2_t; + + /** + * @brief 16-bit status 64-bit vector data type. + */ + typedef int16x8_t status16x4_t; + + /** + * @brief 8-bit status 64-bit vector data type. + */ + typedef int8x16_t status8x8_t; + +#endif + + /** + * @ingroup genericTypes + */ + + /** + * @brief Error status returned by some functions in the library. + */ + typedef enum + { + ARM_MATH_SUCCESS = 0, /**< No error */ + ARM_MATH_ARGUMENT_ERROR = -1, /**< One or more arguments are incorrect */ + ARM_MATH_LENGTH_ERROR = -2, /**< Length of data buffer is incorrect */ + ARM_MATH_SIZE_MISMATCH = -3, /**< Size of matrices is not compatible with the operation */ + ARM_MATH_NANINF = -4, /**< Not-a-number (NaN) or infinity is generated */ + ARM_MATH_SINGULAR = -5, /**< Input matrix is singular and cannot be inverted */ + ARM_MATH_TEST_FAILURE = -6, /**< Test Failed */ + ARM_MATH_DECOMPOSITION_FAILURE = -7 /**< Decomposition Failed */ + } arm_status; + +/** + * @} // endgroup generic +*/ + + +#define F64_MAX ((float64_t)DBL_MAX) +#define F32_MAX ((float32_t)FLT_MAX) + + + +#define F64_MIN (-DBL_MAX) +#define F32_MIN (-FLT_MAX) + + + +#define F64_ABSMAX ((float64_t)DBL_MAX) +#define F32_ABSMAX ((float32_t)FLT_MAX) + + + +#define F64_ABSMIN ((float64_t)0.0) +#define F32_ABSMIN ((float32_t)0.0) + + +#define Q31_MAX ((q31_t)(0x7FFFFFFFL)) +#define Q15_MAX ((q15_t)(0x7FFF)) +#define Q7_MAX ((q7_t)(0x7F)) +#define Q31_MIN ((q31_t)(0x80000000L)) +#define Q15_MIN ((q15_t)(0x8000)) +#define Q7_MIN ((q7_t)(0x80)) + +#define Q31_ABSMAX ((q31_t)(0x7FFFFFFFL)) +#define Q15_ABSMAX ((q15_t)(0x7FFF)) +#define Q7_ABSMAX ((q7_t)(0x7F)) +#define Q31_ABSMIN ((q31_t)0) +#define Q15_ABSMIN ((q15_t)0) +#define Q7_ABSMIN ((q7_t)0) + + /* Dimension C vector space */ + #define CMPLX_DIM 2 + + /** + * @ingroup genericTypes + */ + /** + * @defgroup bufferSizeTypes Enumerations for transform buffer size functions + * @{ +*/ + +/** + * @brief Datatype identifier + */ +typedef enum { + ARM_MATH_F16 = 16, /**< f16 datatype identifier */ + ARM_MATH_F32 = 32, /**< f32 datatype identifier */ + ARM_MATH_F64 = 64, /**< f64 datatype identifier */ + ARM_MATH_Q7 = 7, /**< Q7 datatype identifier */ + ARM_MATH_Q15 = 15, /**< Q15 datatype identifier */ + ARM_MATH_Q31 = 31 /**< Q31 datatype identifier */ +} arm_math_datatype; + +/** + * @brief Architecture target identifier + * + * @note In case the target supports both DSP extensions and Neon extensions, only Neon extensions + * should be used as identification in the corresponding buffer functions. + */ + typedef enum { + ARM_MATH_SCALAR_ARCH = 1, /**< Identifier for Scalar build mode */ + ARM_MATH_DSP_EXTENSIONS_ARCH = 2, /**< Identifier for build mode with dsp extensions */ + ARM_MATH_HELIUM_ARCH = 3, /**< Identifier for build mode with Helium extensions */ + ARM_MATH_NEON_ARCH = 4 /**< Identifier for build mode with Neon extensions */ +} arm_math_target_arch; + +#if !defined(ARM_MATH_AUTOVECTORIZE) + #if defined(ARM_MATH_MVEI) || defined(ARM_MATH_MVEF) + #define ARM_MATH_DEFAULT_TARGET_ARCH ARM_MATH_HELIUM_ARCH + #elif defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) + #define ARM_MATH_DEFAULT_TARGET_ARCH ARM_MATH_NEON_ARCH + #elif defined(ARM_MATH_DSP) + #define ARM_MATH_DEFAULT_TARGET_ARCH ARM_MATH_DSP_EXTENSIONS_ARCH + #else + #define ARM_MATH_DEFAULT_TARGET_ARCH ARM_MATH_SCALAR_ARCH + #endif +#else + #define ARM_MATH_DEFAULT_TARGET_ARCH ARM_MATH_SCALAR_ARCH +#endif + +/** + * @} // endgroup bufferSizeTypes +*/ + +#ifdef __cplusplus +} +#endif + +#endif /*ifndef _ARM_MATH_TYPES_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_types_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_types_f16.h new file mode 100755 index 0000000..26b8fee --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_math_types_f16.h @@ -0,0 +1,163 @@ +/****************************************************************************** + * @file arm_math_types_f16.h + * @brief Public header file for f16 function of the CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_MATH_TYPES_F16_H +#define ARM_MATH_TYPES_F16_H + +#include "arm_math_types.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if !defined( __CC_ARM ) + +/** + * @brief 16-bit floating-point type definition. + * This is already defined in arm_mve.h + * + * This is not fully supported on ARM AC5. + */ + +/* + +Check if the type __fp16 is available. +If it is not available, f16 version of the kernels +won't be built. + +*/ +#if defined(__ARM_FEATURE_MVE) && (__ARM_FEATURE_MVE & 2) +/* When Vector float16, this flag is always defined and can't be disabled */ + #define ARM_FLOAT16_SUPPORTED +#else + #if !defined(DISABLEFLOAT16) + #if defined(__ARM_FP16_FORMAT_IEEE) || defined(__ARM_FP16_FORMAT_ALTERNATIVE) + typedef __fp16 float16_t; + #define ARM_FLOAT16_SUPPORTED + #endif + #endif +#endif + +#if defined(ARM_MATH_NEON) || (defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)) /* floating point vector*/ + +#if defined(ARM_MATH_MVE_FLOAT16) || defined(ARM_MATH_NEON_FLOAT16) + + /** + * @brief 16-bit floating-point 128-bit vector data type + */ + typedef __ALIGNED(2) float16x8_t f16x8_t; + + /** + * @brief 16-bit floating-point 128-bit vector pair data type + */ + typedef float16x8x2_t f16x8x2_t; + + /** + * @brief 16-bit floating-point 128-bit vector quadruplet data type + */ + typedef float16x8x4_t f16x8x4_t; + + /** + * @brief 16-bit ubiquitous 128-bit vector data type + */ + typedef union _any16x8_t + { + float16x8_t f; + int16x8_t i; + } any16x8_t; +#endif + +#endif + +#if defined(ARM_MATH_NEON) + + +#if defined(ARM_MATH_NEON_FLOAT16) + /** + * @brief 16-bit float 64-bit vector data type. + */ + typedef __ALIGNED(2) float16x4_t f16x4_t; + + /** + * @brief 16-bit floating-point 128-bit vector triplet data type + */ + typedef float16x8x3_t f16x8x3_t; + + /** + * @brief 16-bit floating-point 64-bit vector pair data type + */ + typedef float16x4x2_t f16x4x2_t; + + /** + * @brief 16-bit floating-point 64-bit vector triplet data type + */ + typedef float16x4x3_t f16x4x3_t; + + /** + * @brief 16-bit floating-point 64-bit vector quadruplet data type + */ + typedef float16x4x4_t f16x4x4_t; + + /** + * @brief 16-bit ubiquitous 64-bit vector data type + */ + typedef union _any16x4_t + { + float16x4_t f; + int16x4_t i; + } any16x4_t; +#endif + +#endif + + + +#if defined(ARM_FLOAT16_SUPPORTED) + +#if defined(__ICCARM__) + +#define F16INFINITY ((float16_t) INFINITY) + +#else + +#define F16INFINITY ((float16_t)__builtin_inf()) + +#endif + +#define F16_MAX ((float16_t)__FLT16_MAX__) +#define F16_MIN (-(_Float16)__FLT16_MAX__) + +#define F16_ABSMAX ((float16_t)__FLT16_MAX__) +#define F16_ABSMIN ((float16_t)0.0f16) + +#endif /* ARM_FLOAT16_SUPPORTED*/ +#endif /* !defined( __CC_ARM ) */ + +#ifdef __cplusplus +} +#endif + +#endif /* _ARM_MATH_F16_H */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables.h new file mode 100755 index 0000000..aa58d7a --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables.h @@ -0,0 +1,193 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mve_tables.h + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for MVE implementation only + * + * @version V1.10.0 + * @date 04 October 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + #ifndef ARM_MVE_TABLES_H + #define ARM_MVE_TABLES_H + +#include "arm_math_types.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_16_f32[2]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_16_f32[2]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_16_f32[2]; +extern const float32_t rearranged_twiddle_stride1_16_f32[8]; +extern const float32_t rearranged_twiddle_stride2_16_f32[8]; +extern const float32_t rearranged_twiddle_stride3_16_f32[8]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_64_f32[3]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_64_f32[3]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_64_f32[3]; +extern const float32_t rearranged_twiddle_stride1_64_f32[40]; +extern const float32_t rearranged_twiddle_stride2_64_f32[40]; +extern const float32_t rearranged_twiddle_stride3_64_f32[40]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_256_f32[4]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_256_f32[4]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_256_f32[4]; +extern const float32_t rearranged_twiddle_stride1_256_f32[168]; +extern const float32_t rearranged_twiddle_stride2_256_f32[168]; +extern const float32_t rearranged_twiddle_stride3_256_f32[168]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_1024_f32[5]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_1024_f32[5]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_1024_f32[5]; +extern const float32_t rearranged_twiddle_stride1_1024_f32[680]; +extern const float32_t rearranged_twiddle_stride2_1024_f32[680]; +extern const float32_t rearranged_twiddle_stride3_1024_f32[680]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_4096_f32[6]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_4096_f32[6]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_4096_f32[6]; +extern const float32_t rearranged_twiddle_stride1_4096_f32[2728]; +extern const float32_t rearranged_twiddle_stride2_4096_f32[2728]; +extern const float32_t rearranged_twiddle_stride3_4096_f32[2728]; + + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_16_q31[2]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_16_q31[2]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_16_q31[2]; +extern const q31_t rearranged_twiddle_stride1_16_q31[8]; +extern const q31_t rearranged_twiddle_stride2_16_q31[8]; +extern const q31_t rearranged_twiddle_stride3_16_q31[8]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_64_q31[3]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_64_q31[3]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_64_q31[3]; +extern const q31_t rearranged_twiddle_stride1_64_q31[40]; +extern const q31_t rearranged_twiddle_stride2_64_q31[40]; +extern const q31_t rearranged_twiddle_stride3_64_q31[40]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_256_q31[4]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_256_q31[4]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_256_q31[4]; +extern const q31_t rearranged_twiddle_stride1_256_q31[168]; +extern const q31_t rearranged_twiddle_stride2_256_q31[168]; +extern const q31_t rearranged_twiddle_stride3_256_q31[168]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_1024_q31[5]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_1024_q31[5]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_1024_q31[5]; +extern const q31_t rearranged_twiddle_stride1_1024_q31[680]; +extern const q31_t rearranged_twiddle_stride2_1024_q31[680]; +extern const q31_t rearranged_twiddle_stride3_1024_q31[680]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_4096_q31[6]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_4096_q31[6]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_4096_q31[6]; +extern const q31_t rearranged_twiddle_stride1_4096_q31[2728]; +extern const q31_t rearranged_twiddle_stride2_4096_q31[2728]; +extern const q31_t rearranged_twiddle_stride3_4096_q31[2728]; + + + +#endif /* defined(ARM_MATH_MVEI) */ + + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_16_q15[2]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_16_q15[2]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_16_q15[2]; +extern const q15_t rearranged_twiddle_stride1_16_q15[8]; +extern const q15_t rearranged_twiddle_stride2_16_q15[8]; +extern const q15_t rearranged_twiddle_stride3_16_q15[8]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_64_q15[3]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_64_q15[3]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_64_q15[3]; +extern const q15_t rearranged_twiddle_stride1_64_q15[40]; +extern const q15_t rearranged_twiddle_stride2_64_q15[40]; +extern const q15_t rearranged_twiddle_stride3_64_q15[40]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_256_q15[4]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_256_q15[4]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_256_q15[4]; +extern const q15_t rearranged_twiddle_stride1_256_q15[168]; +extern const q15_t rearranged_twiddle_stride2_256_q15[168]; +extern const q15_t rearranged_twiddle_stride3_256_q15[168]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_1024_q15[5]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_1024_q15[5]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_1024_q15[5]; +extern const q15_t rearranged_twiddle_stride1_1024_q15[680]; +extern const q15_t rearranged_twiddle_stride2_1024_q15[680]; +extern const q15_t rearranged_twiddle_stride3_1024_q15[680]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_4096_q15[6]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_4096_q15[6]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_4096_q15[6]; +extern const q15_t rearranged_twiddle_stride1_4096_q15[2728]; +extern const q15_t rearranged_twiddle_stride2_4096_q15[2728]; +extern const q15_t rearranged_twiddle_stride3_4096_q15[2728]; + + +#endif /* defined(ARM_MATH_MVEI) */ + + + +#ifdef __cplusplus +} +#endif + +#endif /*_ARM_MVE_TABLES_H*/ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables_f16.h new file mode 100755 index 0000000..ae28245 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_mve_tables_f16.h @@ -0,0 +1,97 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mve_tables_f16.h + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for MVE implementation only + * + * @version V1.10.0 + * @date 04 October 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + #ifndef ARM_MVE_TABLES_F16_H + #define ARM_MVE_TABLES_F16_H + +#include "arm_math_types_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_16_f16[2]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_16_f16[2]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_16_f16[2]; +extern const float16_t rearranged_twiddle_stride1_16_f16[8]; +extern const float16_t rearranged_twiddle_stride2_16_f16[8]; +extern const float16_t rearranged_twiddle_stride3_16_f16[8]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_64_f16[3]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_64_f16[3]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_64_f16[3]; +extern const float16_t rearranged_twiddle_stride1_64_f16[40]; +extern const float16_t rearranged_twiddle_stride2_64_f16[40]; +extern const float16_t rearranged_twiddle_stride3_64_f16[40]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_256_f16[4]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_256_f16[4]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_256_f16[4]; +extern const float16_t rearranged_twiddle_stride1_256_f16[168]; +extern const float16_t rearranged_twiddle_stride2_256_f16[168]; +extern const float16_t rearranged_twiddle_stride3_256_f16[168]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_1024_f16[5]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_1024_f16[5]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_1024_f16[5]; +extern const float16_t rearranged_twiddle_stride1_1024_f16[680]; +extern const float16_t rearranged_twiddle_stride2_1024_f16[680]; +extern const float16_t rearranged_twiddle_stride3_1024_f16[680]; + + +extern const uint32_t rearranged_twiddle_tab_stride1_arr_4096_f16[6]; +extern const uint32_t rearranged_twiddle_tab_stride2_arr_4096_f16[6]; +extern const uint32_t rearranged_twiddle_tab_stride3_arr_4096_f16[6]; +extern const float16_t rearranged_twiddle_stride1_4096_f16[2728]; +extern const float16_t rearranged_twiddle_stride2_4096_f16[2728]; +extern const float16_t rearranged_twiddle_stride3_4096_f16[2728]; + + + +#endif /* defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) */ + + + +#ifdef __cplusplus +} +#endif + +#endif /*_ARM_MVE_TABLES_F16_H*/ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_neon_tables.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_neon_tables.h new file mode 100755 index 0000000..8fb50f2 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_neon_tables.h @@ -0,0 +1,472 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_neon_tables.h + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for NEON implementation only + * + * @date 02 October 2024 + * + * Target Processor: Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2024 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + #ifndef ARM_NEON_TABLES_H + #define ARM_NEON_TABLES_H + +#include "arm_math_types.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + + +#if defined(ARM_MATH_NEON) + + +#define ARM_NEON_RFFT_TWIDDLES_16_F32_LEN 24 +extern const float32_t arm_neon_rfft_twiddles_16_f32[ARM_NEON_RFFT_TWIDDLES_16_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_16_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_16_f32[ARM_NEON_RFFT_FACTORS_16_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_16_F32_LEN 0 +extern const float32_t *arm_neon_rfft_twiddles_neon_16_f32; + +#define ARM_NEON_RFFT_FACTORS_NEON_16_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_16_f32[ARM_NEON_RFFT_FACTORS_NEON_16_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_F32_LEN 24 +extern const float32_t arm_neon_rfft_super_twiddles_neon_16_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_16_F32 12 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_16_F32 0 + +#define ARM_NEON_RFFT_TWIDDLES_32_F32_LEN 48 +extern const float32_t arm_neon_rfft_twiddles_32_f32[ARM_NEON_RFFT_TWIDDLES_32_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_32_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_32_f32[ARM_NEON_RFFT_FACTORS_32_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_32_F32_LEN 0 +extern const float32_t *arm_neon_rfft_twiddles_neon_32_f32; + +#define ARM_NEON_RFFT_FACTORS_NEON_32_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_32_f32[ARM_NEON_RFFT_FACTORS_NEON_32_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_F32_LEN 24 +extern const float32_t arm_neon_rfft_super_twiddles_neon_32_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_32_F32 24 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_32_F32 0 + +#define ARM_NEON_RFFT_TWIDDLES_64_F32_LEN 120 +extern const float32_t arm_neon_rfft_twiddles_64_f32[ARM_NEON_RFFT_TWIDDLES_64_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_64_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_64_f32[ARM_NEON_RFFT_FACTORS_64_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_64_F32_LEN 24 +extern const float32_t arm_neon_rfft_twiddles_neon_64_f32[ARM_NEON_RFFT_TWIDDLES_NEON_64_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_64_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_64_f32[ARM_NEON_RFFT_FACTORS_NEON_64_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_F32_LEN 48 +extern const float32_t arm_neon_rfft_super_twiddles_neon_64_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_64_F32 60 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_64_F32 12 + +#define ARM_NEON_RFFT_TWIDDLES_128_F32_LEN 240 +extern const float32_t arm_neon_rfft_twiddles_128_f32[ARM_NEON_RFFT_TWIDDLES_128_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_128_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_128_f32[ARM_NEON_RFFT_FACTORS_128_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_128_F32_LEN 48 +extern const float32_t arm_neon_rfft_twiddles_neon_128_f32[ARM_NEON_RFFT_TWIDDLES_NEON_128_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_128_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_128_f32[ARM_NEON_RFFT_FACTORS_NEON_128_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_F32_LEN 96 +extern const float32_t arm_neon_rfft_super_twiddles_neon_128_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_128_F32 120 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_128_F32 24 + +#define ARM_NEON_RFFT_TWIDDLES_256_F32_LEN 504 +extern const float32_t arm_neon_rfft_twiddles_256_f32[ARM_NEON_RFFT_TWIDDLES_256_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_256_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_256_f32[ARM_NEON_RFFT_FACTORS_256_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_256_F32_LEN 120 +extern const float32_t arm_neon_rfft_twiddles_neon_256_f32[ARM_NEON_RFFT_TWIDDLES_NEON_256_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_256_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_256_f32[ARM_NEON_RFFT_FACTORS_NEON_256_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_F32_LEN 192 +extern const float32_t arm_neon_rfft_super_twiddles_neon_256_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_256_F32 252 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_256_F32 60 + +#define ARM_NEON_RFFT_TWIDDLES_512_F32_LEN 1008 +extern const float32_t arm_neon_rfft_twiddles_512_f32[ARM_NEON_RFFT_TWIDDLES_512_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_512_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_512_f32[ARM_NEON_RFFT_FACTORS_512_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_512_F32_LEN 240 +extern const float32_t arm_neon_rfft_twiddles_neon_512_f32[ARM_NEON_RFFT_TWIDDLES_NEON_512_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_512_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_512_f32[ARM_NEON_RFFT_FACTORS_NEON_512_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_F32_LEN 384 +extern const float32_t arm_neon_rfft_super_twiddles_neon_512_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_512_F32 504 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_512_F32 120 + +#define ARM_NEON_RFFT_TWIDDLES_1024_F32_LEN 2040 +extern const float32_t arm_neon_rfft_twiddles_1024_f32[ARM_NEON_RFFT_TWIDDLES_1024_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_1024_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_1024_f32[ARM_NEON_RFFT_FACTORS_1024_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_1024_F32_LEN 504 +extern const float32_t arm_neon_rfft_twiddles_neon_1024_f32[ARM_NEON_RFFT_TWIDDLES_NEON_1024_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_1024_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_1024_f32[ARM_NEON_RFFT_FACTORS_NEON_1024_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_F32_LEN 768 +extern const float32_t arm_neon_rfft_super_twiddles_neon_1024_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_1024_F32 1020 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_1024_F32 252 + +#define ARM_NEON_RFFT_TWIDDLES_2048_F32_LEN 4080 +extern const float32_t arm_neon_rfft_twiddles_2048_f32[ARM_NEON_RFFT_TWIDDLES_2048_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_2048_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_2048_f32[ARM_NEON_RFFT_FACTORS_2048_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_2048_F32_LEN 1008 +extern const float32_t arm_neon_rfft_twiddles_neon_2048_f32[ARM_NEON_RFFT_TWIDDLES_NEON_2048_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_2048_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_2048_f32[ARM_NEON_RFFT_FACTORS_NEON_2048_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_F32_LEN 1536 +extern const float32_t arm_neon_rfft_super_twiddles_neon_2048_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_2048_F32 2040 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_2048_F32 504 + +#define ARM_NEON_RFFT_TWIDDLES_4096_F32_LEN 8184 +extern const float32_t arm_neon_rfft_twiddles_4096_f32[ARM_NEON_RFFT_TWIDDLES_4096_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_4096_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_4096_f32[ARM_NEON_RFFT_FACTORS_4096_F32_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_4096_F32_LEN 2040 +extern const float32_t arm_neon_rfft_twiddles_neon_4096_f32[ARM_NEON_RFFT_TWIDDLES_NEON_4096_F32_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_4096_F32_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_4096_f32[ARM_NEON_RFFT_FACTORS_NEON_4096_F32_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_F32_LEN 3072 +extern const float32_t arm_neon_rfft_super_twiddles_neon_4096_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_4096_F32 4092 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_4096_F32 1020 + +#define ARM_NEON_RFFT_TWIDDLES_16_Q31_LEN 0 +extern const q31_t *arm_neon_rfft_twiddles_16_q31; + +#define ARM_NEON_RFFT_FACTORS_16_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_16_q31[ARM_NEON_RFFT_FACTORS_16_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_Q31_LEN 8 +extern const q31_t arm_neon_rfft_super_twiddles_neon_16_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_16_Q31 0 + +#define ARM_NEON_RFFT_TWIDDLES_32_Q31_LEN 24 +extern const q31_t arm_neon_rfft_twiddles_32_q31[ARM_NEON_RFFT_TWIDDLES_32_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_32_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_32_q31[ARM_NEON_RFFT_FACTORS_32_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_Q31_LEN 16 +extern const q31_t arm_neon_rfft_super_twiddles_neon_32_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_32_Q31 12 + +#define ARM_NEON_RFFT_TWIDDLES_64_Q31_LEN 48 +extern const q31_t arm_neon_rfft_twiddles_64_q31[ARM_NEON_RFFT_TWIDDLES_64_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_64_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_64_q31[ARM_NEON_RFFT_FACTORS_64_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_Q31_LEN 32 +extern const q31_t arm_neon_rfft_super_twiddles_neon_64_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_64_Q31 24 + +#define ARM_NEON_RFFT_TWIDDLES_128_Q31_LEN 120 +extern const q31_t arm_neon_rfft_twiddles_128_q31[ARM_NEON_RFFT_TWIDDLES_128_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_128_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_128_q31[ARM_NEON_RFFT_FACTORS_128_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_Q31_LEN 64 +extern const q31_t arm_neon_rfft_super_twiddles_neon_128_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_128_Q31 60 + +#define ARM_NEON_RFFT_TWIDDLES_256_Q31_LEN 240 +extern const q31_t arm_neon_rfft_twiddles_256_q31[ARM_NEON_RFFT_TWIDDLES_256_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_256_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_256_q31[ARM_NEON_RFFT_FACTORS_256_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_Q31_LEN 128 +extern const q31_t arm_neon_rfft_super_twiddles_neon_256_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_256_Q31 120 + +#define ARM_NEON_RFFT_TWIDDLES_512_Q31_LEN 504 +extern const q31_t arm_neon_rfft_twiddles_512_q31[ARM_NEON_RFFT_TWIDDLES_512_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_512_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_512_q31[ARM_NEON_RFFT_FACTORS_512_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_Q31_LEN 256 +extern const q31_t arm_neon_rfft_super_twiddles_neon_512_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_512_Q31 252 + +#define ARM_NEON_RFFT_TWIDDLES_1024_Q31_LEN 1008 +extern const q31_t arm_neon_rfft_twiddles_1024_q31[ARM_NEON_RFFT_TWIDDLES_1024_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_1024_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_1024_q31[ARM_NEON_RFFT_FACTORS_1024_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_Q31_LEN 512 +extern const q31_t arm_neon_rfft_super_twiddles_neon_1024_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_1024_Q31 504 + +#define ARM_NEON_RFFT_TWIDDLES_2048_Q31_LEN 2040 +extern const q31_t arm_neon_rfft_twiddles_2048_q31[ARM_NEON_RFFT_TWIDDLES_2048_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_2048_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_2048_q31[ARM_NEON_RFFT_FACTORS_2048_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_Q31_LEN 1024 +extern const q31_t arm_neon_rfft_super_twiddles_neon_2048_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_2048_Q31 1020 + +#define ARM_NEON_RFFT_TWIDDLES_4096_Q31_LEN 4080 +extern const q31_t arm_neon_rfft_twiddles_4096_q31[ARM_NEON_RFFT_TWIDDLES_4096_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_4096_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_4096_q31[ARM_NEON_RFFT_FACTORS_4096_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_Q31_LEN 2048 +extern const q31_t arm_neon_rfft_super_twiddles_neon_4096_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_4096_Q31 2040 + +#define ARM_NEON_RFFT_TWIDDLES_8192_Q31_LEN 8184 +extern const q31_t arm_neon_rfft_twiddles_8192_q31[ARM_NEON_RFFT_TWIDDLES_8192_Q31_LEN]; +#define ARM_NEON_RFFT_FACTORS_8192_Q31_LEN 4 +extern const uint32_t arm_neon_rfft_factors_8192_q31[ARM_NEON_RFFT_FACTORS_8192_Q31_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_8192_Q31_LEN 4096 +extern const q31_t arm_neon_rfft_super_twiddles_neon_8192_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_8192_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_8192_Q31 4092 + +#define ARM_NEON_RFFT_TWIDDLES_16_Q15_LEN 0 +extern const q15_t *arm_neon_rfft_twiddles_16_q15; + +#define ARM_NEON_RFFT_FACTORS_16_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_16_q15[ARM_NEON_RFFT_FACTORS_16_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_Q15_LEN 8 +extern const q15_t arm_neon_rfft_super_twiddles_neon_16_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_16_Q15 0 + +#define ARM_NEON_RFFT_TWIDDLES_32_Q15_LEN 24 +extern const q15_t arm_neon_rfft_twiddles_32_q15[ARM_NEON_RFFT_TWIDDLES_32_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_32_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_32_q15[ARM_NEON_RFFT_FACTORS_32_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_Q15_LEN 16 +extern const q15_t arm_neon_rfft_super_twiddles_neon_32_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_32_Q15 12 + +#define ARM_NEON_RFFT_TWIDDLES_64_Q15_LEN 48 +extern const q15_t arm_neon_rfft_twiddles_64_q15[ARM_NEON_RFFT_TWIDDLES_64_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_64_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_64_q15[ARM_NEON_RFFT_FACTORS_64_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_Q15_LEN 32 +extern const q15_t arm_neon_rfft_super_twiddles_neon_64_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_64_Q15 24 + +#define ARM_NEON_RFFT_TWIDDLES_128_Q15_LEN 120 +extern const q15_t arm_neon_rfft_twiddles_128_q15[ARM_NEON_RFFT_TWIDDLES_128_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_128_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_128_q15[ARM_NEON_RFFT_FACTORS_128_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_Q15_LEN 64 +extern const q15_t arm_neon_rfft_super_twiddles_neon_128_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_128_Q15 60 + +#define ARM_NEON_RFFT_TWIDDLES_256_Q15_LEN 240 +extern const q15_t arm_neon_rfft_twiddles_256_q15[ARM_NEON_RFFT_TWIDDLES_256_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_256_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_256_q15[ARM_NEON_RFFT_FACTORS_256_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_Q15_LEN 128 +extern const q15_t arm_neon_rfft_super_twiddles_neon_256_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_256_Q15 120 + +#define ARM_NEON_RFFT_TWIDDLES_512_Q15_LEN 504 +extern const q15_t arm_neon_rfft_twiddles_512_q15[ARM_NEON_RFFT_TWIDDLES_512_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_512_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_512_q15[ARM_NEON_RFFT_FACTORS_512_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_Q15_LEN 256 +extern const q15_t arm_neon_rfft_super_twiddles_neon_512_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_512_Q15 252 + +#define ARM_NEON_RFFT_TWIDDLES_1024_Q15_LEN 1008 +extern const q15_t arm_neon_rfft_twiddles_1024_q15[ARM_NEON_RFFT_TWIDDLES_1024_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_1024_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_1024_q15[ARM_NEON_RFFT_FACTORS_1024_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_Q15_LEN 512 +extern const q15_t arm_neon_rfft_super_twiddles_neon_1024_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_1024_Q15 504 + +#define ARM_NEON_RFFT_TWIDDLES_2048_Q15_LEN 2040 +extern const q15_t arm_neon_rfft_twiddles_2048_q15[ARM_NEON_RFFT_TWIDDLES_2048_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_2048_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_2048_q15[ARM_NEON_RFFT_FACTORS_2048_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_Q15_LEN 1024 +extern const q15_t arm_neon_rfft_super_twiddles_neon_2048_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_2048_Q15 1020 + +#define ARM_NEON_RFFT_TWIDDLES_4096_Q15_LEN 4080 +extern const q15_t arm_neon_rfft_twiddles_4096_q15[ARM_NEON_RFFT_TWIDDLES_4096_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_4096_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_4096_q15[ARM_NEON_RFFT_FACTORS_4096_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_Q15_LEN 2048 +extern const q15_t arm_neon_rfft_super_twiddles_neon_4096_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_4096_Q15 2040 + +#define ARM_NEON_RFFT_TWIDDLES_8192_Q15_LEN 8184 +extern const q15_t arm_neon_rfft_twiddles_8192_q15[ARM_NEON_RFFT_TWIDDLES_8192_Q15_LEN]; +#define ARM_NEON_RFFT_FACTORS_8192_Q15_LEN 4 +extern const uint32_t arm_neon_rfft_factors_8192_q15[ARM_NEON_RFFT_FACTORS_8192_Q15_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_8192_Q15_LEN 4096 +extern const q15_t arm_neon_rfft_super_twiddles_neon_8192_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_8192_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_8192_Q15 4092 + +#define ARM_NEON_TWIDDLES_16_F32_LEN 24 +extern const float32_t arm_neon_twiddles_16_f32[ARM_NEON_TWIDDLES_16_F32_LEN]; +#define ARM_NEON_FACTORS_16_F32_LEN 4 +extern const uint32_t arm_neon_factors_16_f32[ARM_NEON_FACTORS_16_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_16_F32 12 +#define ARM_NEON_TWIDDLES_32_F32_LEN 48 +extern const float32_t arm_neon_twiddles_32_f32[ARM_NEON_TWIDDLES_32_F32_LEN]; +#define ARM_NEON_FACTORS_32_F32_LEN 4 +extern const uint32_t arm_neon_factors_32_f32[ARM_NEON_FACTORS_32_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_32_F32 24 +#define ARM_NEON_TWIDDLES_64_F32_LEN 120 +extern const float32_t arm_neon_twiddles_64_f32[ARM_NEON_TWIDDLES_64_F32_LEN]; +#define ARM_NEON_FACTORS_64_F32_LEN 4 +extern const uint32_t arm_neon_factors_64_f32[ARM_NEON_FACTORS_64_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_64_F32 60 +#define ARM_NEON_TWIDDLES_128_F32_LEN 240 +extern const float32_t arm_neon_twiddles_128_f32[ARM_NEON_TWIDDLES_128_F32_LEN]; +#define ARM_NEON_FACTORS_128_F32_LEN 4 +extern const uint32_t arm_neon_factors_128_f32[ARM_NEON_FACTORS_128_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_128_F32 120 +#define ARM_NEON_TWIDDLES_256_F32_LEN 504 +extern const float32_t arm_neon_twiddles_256_f32[ARM_NEON_TWIDDLES_256_F32_LEN]; +#define ARM_NEON_FACTORS_256_F32_LEN 4 +extern const uint32_t arm_neon_factors_256_f32[ARM_NEON_FACTORS_256_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_256_F32 252 +#define ARM_NEON_TWIDDLES_512_F32_LEN 1008 +extern const float32_t arm_neon_twiddles_512_f32[ARM_NEON_TWIDDLES_512_F32_LEN]; +#define ARM_NEON_FACTORS_512_F32_LEN 4 +extern const uint32_t arm_neon_factors_512_f32[ARM_NEON_FACTORS_512_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_512_F32 504 +#define ARM_NEON_TWIDDLES_1024_F32_LEN 2040 +extern const float32_t arm_neon_twiddles_1024_f32[ARM_NEON_TWIDDLES_1024_F32_LEN]; +#define ARM_NEON_FACTORS_1024_F32_LEN 4 +extern const uint32_t arm_neon_factors_1024_f32[ARM_NEON_FACTORS_1024_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_1024_F32 1020 +#define ARM_NEON_TWIDDLES_2048_F32_LEN 4080 +extern const float32_t arm_neon_twiddles_2048_f32[ARM_NEON_TWIDDLES_2048_F32_LEN]; +#define ARM_NEON_FACTORS_2048_F32_LEN 4 +extern const uint32_t arm_neon_factors_2048_f32[ARM_NEON_FACTORS_2048_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_2048_F32 2040 +#define ARM_NEON_TWIDDLES_4096_F32_LEN 8184 +extern const float32_t arm_neon_twiddles_4096_f32[ARM_NEON_TWIDDLES_4096_F32_LEN]; +#define ARM_NEON_FACTORS_4096_F32_LEN 4 +extern const uint32_t arm_neon_factors_4096_f32[ARM_NEON_FACTORS_4096_F32_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_4096_F32 4092 +#define ARM_NEON_TWIDDLES_16_Q31_LEN 24 +extern const q31_t arm_neon_twiddles_16_q31[ARM_NEON_TWIDDLES_16_Q31_LEN]; +#define ARM_NEON_FACTORS_16_Q31_LEN 4 +extern const uint32_t arm_neon_factors_16_q31[ARM_NEON_FACTORS_16_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_16_Q31 12 +#define ARM_NEON_TWIDDLES_32_Q31_LEN 48 +extern const q31_t arm_neon_twiddles_32_q31[ARM_NEON_TWIDDLES_32_Q31_LEN]; +#define ARM_NEON_FACTORS_32_Q31_LEN 4 +extern const uint32_t arm_neon_factors_32_q31[ARM_NEON_FACTORS_32_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_32_Q31 24 +#define ARM_NEON_TWIDDLES_64_Q31_LEN 120 +extern const q31_t arm_neon_twiddles_64_q31[ARM_NEON_TWIDDLES_64_Q31_LEN]; +#define ARM_NEON_FACTORS_64_Q31_LEN 4 +extern const uint32_t arm_neon_factors_64_q31[ARM_NEON_FACTORS_64_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_64_Q31 60 +#define ARM_NEON_TWIDDLES_128_Q31_LEN 240 +extern const q31_t arm_neon_twiddles_128_q31[ARM_NEON_TWIDDLES_128_Q31_LEN]; +#define ARM_NEON_FACTORS_128_Q31_LEN 4 +extern const uint32_t arm_neon_factors_128_q31[ARM_NEON_FACTORS_128_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_128_Q31 120 +#define ARM_NEON_TWIDDLES_256_Q31_LEN 504 +extern const q31_t arm_neon_twiddles_256_q31[ARM_NEON_TWIDDLES_256_Q31_LEN]; +#define ARM_NEON_FACTORS_256_Q31_LEN 4 +extern const uint32_t arm_neon_factors_256_q31[ARM_NEON_FACTORS_256_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_256_Q31 252 +#define ARM_NEON_TWIDDLES_512_Q31_LEN 1008 +extern const q31_t arm_neon_twiddles_512_q31[ARM_NEON_TWIDDLES_512_Q31_LEN]; +#define ARM_NEON_FACTORS_512_Q31_LEN 4 +extern const uint32_t arm_neon_factors_512_q31[ARM_NEON_FACTORS_512_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_512_Q31 504 +#define ARM_NEON_TWIDDLES_1024_Q31_LEN 2040 +extern const q31_t arm_neon_twiddles_1024_q31[ARM_NEON_TWIDDLES_1024_Q31_LEN]; +#define ARM_NEON_FACTORS_1024_Q31_LEN 4 +extern const uint32_t arm_neon_factors_1024_q31[ARM_NEON_FACTORS_1024_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_1024_Q31 1020 +#define ARM_NEON_TWIDDLES_2048_Q31_LEN 4080 +extern const q31_t arm_neon_twiddles_2048_q31[ARM_NEON_TWIDDLES_2048_Q31_LEN]; +#define ARM_NEON_FACTORS_2048_Q31_LEN 4 +extern const uint32_t arm_neon_factors_2048_q31[ARM_NEON_FACTORS_2048_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_2048_Q31 2040 +#define ARM_NEON_TWIDDLES_4096_Q31_LEN 8184 +extern const q31_t arm_neon_twiddles_4096_q31[ARM_NEON_TWIDDLES_4096_Q31_LEN]; +#define ARM_NEON_FACTORS_4096_Q31_LEN 4 +extern const uint32_t arm_neon_factors_4096_q31[ARM_NEON_FACTORS_4096_Q31_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_4096_Q31 4092 +#define ARM_NEON_TWIDDLES_16_Q15_LEN 24 +extern const q15_t arm_neon_twiddles_16_q15[ARM_NEON_TWIDDLES_16_Q15_LEN]; +#define ARM_NEON_FACTORS_16_Q15_LEN 4 +extern const uint32_t arm_neon_factors_16_q15[ARM_NEON_FACTORS_16_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_16_Q15 12 +#define ARM_NEON_TWIDDLES_32_Q15_LEN 48 +extern const q15_t arm_neon_twiddles_32_q15[ARM_NEON_TWIDDLES_32_Q15_LEN]; +#define ARM_NEON_FACTORS_32_Q15_LEN 4 +extern const uint32_t arm_neon_factors_32_q15[ARM_NEON_FACTORS_32_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_32_Q15 24 +#define ARM_NEON_TWIDDLES_64_Q15_LEN 120 +extern const q15_t arm_neon_twiddles_64_q15[ARM_NEON_TWIDDLES_64_Q15_LEN]; +#define ARM_NEON_FACTORS_64_Q15_LEN 4 +extern const uint32_t arm_neon_factors_64_q15[ARM_NEON_FACTORS_64_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_64_Q15 60 +#define ARM_NEON_TWIDDLES_128_Q15_LEN 240 +extern const q15_t arm_neon_twiddles_128_q15[ARM_NEON_TWIDDLES_128_Q15_LEN]; +#define ARM_NEON_FACTORS_128_Q15_LEN 4 +extern const uint32_t arm_neon_factors_128_q15[ARM_NEON_FACTORS_128_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_128_Q15 120 +#define ARM_NEON_TWIDDLES_256_Q15_LEN 504 +extern const q15_t arm_neon_twiddles_256_q15[ARM_NEON_TWIDDLES_256_Q15_LEN]; +#define ARM_NEON_FACTORS_256_Q15_LEN 4 +extern const uint32_t arm_neon_factors_256_q15[ARM_NEON_FACTORS_256_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_256_Q15 252 +#define ARM_NEON_TWIDDLES_512_Q15_LEN 1008 +extern const q15_t arm_neon_twiddles_512_q15[ARM_NEON_TWIDDLES_512_Q15_LEN]; +#define ARM_NEON_FACTORS_512_Q15_LEN 4 +extern const uint32_t arm_neon_factors_512_q15[ARM_NEON_FACTORS_512_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_512_Q15 504 +#define ARM_NEON_TWIDDLES_1024_Q15_LEN 2040 +extern const q15_t arm_neon_twiddles_1024_q15[ARM_NEON_TWIDDLES_1024_Q15_LEN]; +#define ARM_NEON_FACTORS_1024_Q15_LEN 4 +extern const uint32_t arm_neon_factors_1024_q15[ARM_NEON_FACTORS_1024_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_1024_Q15 1020 +#define ARM_NEON_TWIDDLES_2048_Q15_LEN 4080 +extern const q15_t arm_neon_twiddles_2048_q15[ARM_NEON_TWIDDLES_2048_Q15_LEN]; +#define ARM_NEON_FACTORS_2048_Q15_LEN 4 +extern const uint32_t arm_neon_factors_2048_q15[ARM_NEON_FACTORS_2048_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_2048_Q15 2040 +#define ARM_NEON_TWIDDLES_4096_Q15_LEN 8184 +extern const q15_t arm_neon_twiddles_4096_q15[ARM_NEON_TWIDDLES_4096_Q15_LEN]; +#define ARM_NEON_FACTORS_4096_Q15_LEN 4 +extern const uint32_t arm_neon_factors_4096_q15[ARM_NEON_FACTORS_4096_Q15_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_4096_Q15 4092 + + +#endif /* defined(ARM_MATH_NEON) */ + + + +#ifdef __cplusplus +} +#endif + +#endif /*ARM_NEON_TABLES_H*/ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_neon_tables_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_neon_tables_f16.h new file mode 100755 index 0000000..6e4a00a --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_neon_tables_f16.h @@ -0,0 +1,220 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_neon_tables_f16.h + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for NEON implementation only + * + * @date 02 October 2024 + * + * Target Processor: Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2024 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + #ifndef ARM_NEON_TABLES_F16_H + #define ARM_NEON_TABLES_F16_H + +#include "arm_math_types_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + + +#if defined(ARM_MATH_NEON_FLOAT16) && defined(ARM_FLOAT16_SUPPORTED) + + +#define ARM_NEON_TWIDDLES_16_F16_LEN 24 +extern const float16_t arm_neon_twiddles_16_f16[ARM_NEON_TWIDDLES_16_F16_LEN]; +#define ARM_NEON_FACTORS_16_F16_LEN 4 +extern const uint32_t arm_neon_factors_16_f16[ARM_NEON_FACTORS_16_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_16_F16 12 +#define ARM_NEON_TWIDDLES_32_F16_LEN 48 +extern const float16_t arm_neon_twiddles_32_f16[ARM_NEON_TWIDDLES_32_F16_LEN]; +#define ARM_NEON_FACTORS_32_F16_LEN 4 +extern const uint32_t arm_neon_factors_32_f16[ARM_NEON_FACTORS_32_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_32_F16 24 +#define ARM_NEON_TWIDDLES_64_F16_LEN 120 +extern const float16_t arm_neon_twiddles_64_f16[ARM_NEON_TWIDDLES_64_F16_LEN]; +#define ARM_NEON_FACTORS_64_F16_LEN 4 +extern const uint32_t arm_neon_factors_64_f16[ARM_NEON_FACTORS_64_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_64_F16 60 +#define ARM_NEON_TWIDDLES_128_F16_LEN 240 +extern const float16_t arm_neon_twiddles_128_f16[ARM_NEON_TWIDDLES_128_F16_LEN]; +#define ARM_NEON_FACTORS_128_F16_LEN 4 +extern const uint32_t arm_neon_factors_128_f16[ARM_NEON_FACTORS_128_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_128_F16 120 +#define ARM_NEON_TWIDDLES_256_F16_LEN 504 +extern const float16_t arm_neon_twiddles_256_f16[ARM_NEON_TWIDDLES_256_F16_LEN]; +#define ARM_NEON_FACTORS_256_F16_LEN 4 +extern const uint32_t arm_neon_factors_256_f16[ARM_NEON_FACTORS_256_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_256_F16 252 +#define ARM_NEON_TWIDDLES_512_F16_LEN 1008 +extern const float16_t arm_neon_twiddles_512_f16[ARM_NEON_TWIDDLES_512_F16_LEN]; +#define ARM_NEON_FACTORS_512_F16_LEN 4 +extern const uint32_t arm_neon_factors_512_f16[ARM_NEON_FACTORS_512_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_512_F16 504 +#define ARM_NEON_TWIDDLES_1024_F16_LEN 2040 +extern const float16_t arm_neon_twiddles_1024_f16[ARM_NEON_TWIDDLES_1024_F16_LEN]; +#define ARM_NEON_FACTORS_1024_F16_LEN 4 +extern const uint32_t arm_neon_factors_1024_f16[ARM_NEON_FACTORS_1024_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_1024_F16 1020 +#define ARM_NEON_TWIDDLES_2048_F16_LEN 4080 +extern const float16_t arm_neon_twiddles_2048_f16[ARM_NEON_TWIDDLES_2048_F16_LEN]; +#define ARM_NEON_FACTORS_2048_F16_LEN 4 +extern const uint32_t arm_neon_factors_2048_f16[ARM_NEON_FACTORS_2048_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_2048_F16 2040 +#define ARM_NEON_TWIDDLES_4096_F16_LEN 8184 +extern const float16_t arm_neon_twiddles_4096_f16[ARM_NEON_TWIDDLES_4096_F16_LEN]; +#define ARM_NEON_FACTORS_4096_F16_LEN 4 +extern const uint32_t arm_neon_factors_4096_f16[ARM_NEON_FACTORS_4096_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_4096_F16 4092 +#define ARM_NEON_RFFT_TWIDDLES_16_F16_LEN 24 +extern const float16_t arm_neon_rfft_twiddles_16_f16[ARM_NEON_RFFT_TWIDDLES_16_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_16_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_16_f16[ARM_NEON_RFFT_FACTORS_16_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_16_F16_LEN 0 +extern const float16_t *arm_neon_rfft_twiddles_neon_16_f16; + +#define ARM_NEON_RFFT_FACTORS_NEON_16_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_16_f16[ARM_NEON_RFFT_FACTORS_NEON_16_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_F16_LEN 24 +extern const float16_t arm_neon_rfft_super_twiddles_neon_16_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_16_F16 12 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_16_F16 0 + +#define ARM_NEON_RFFT_TWIDDLES_32_F16_LEN 48 +extern const float16_t arm_neon_rfft_twiddles_32_f16[ARM_NEON_RFFT_TWIDDLES_32_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_32_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_32_f16[ARM_NEON_RFFT_FACTORS_32_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_32_F16_LEN 0 +extern const float16_t *arm_neon_rfft_twiddles_neon_32_f16; + +#define ARM_NEON_RFFT_FACTORS_NEON_32_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_32_f16[ARM_NEON_RFFT_FACTORS_NEON_32_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_F16_LEN 24 +extern const float16_t arm_neon_rfft_super_twiddles_neon_32_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_32_F16 24 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_32_F16 0 + +#define ARM_NEON_RFFT_TWIDDLES_64_F16_LEN 120 +extern const float16_t arm_neon_rfft_twiddles_64_f16[ARM_NEON_RFFT_TWIDDLES_64_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_64_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_64_f16[ARM_NEON_RFFT_FACTORS_64_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_64_F16_LEN 24 +extern const float16_t arm_neon_rfft_twiddles_neon_64_f16[ARM_NEON_RFFT_TWIDDLES_NEON_64_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_64_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_64_f16[ARM_NEON_RFFT_FACTORS_NEON_64_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_F16_LEN 48 +extern const float16_t arm_neon_rfft_super_twiddles_neon_64_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_64_F16 60 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_64_F16 12 + +#define ARM_NEON_RFFT_TWIDDLES_128_F16_LEN 240 +extern const float16_t arm_neon_rfft_twiddles_128_f16[ARM_NEON_RFFT_TWIDDLES_128_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_128_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_128_f16[ARM_NEON_RFFT_FACTORS_128_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_128_F16_LEN 48 +extern const float16_t arm_neon_rfft_twiddles_neon_128_f16[ARM_NEON_RFFT_TWIDDLES_NEON_128_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_128_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_128_f16[ARM_NEON_RFFT_FACTORS_NEON_128_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_F16_LEN 96 +extern const float16_t arm_neon_rfft_super_twiddles_neon_128_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_128_F16 120 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_128_F16 24 + +#define ARM_NEON_RFFT_TWIDDLES_256_F16_LEN 504 +extern const float16_t arm_neon_rfft_twiddles_256_f16[ARM_NEON_RFFT_TWIDDLES_256_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_256_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_256_f16[ARM_NEON_RFFT_FACTORS_256_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_256_F16_LEN 120 +extern const float16_t arm_neon_rfft_twiddles_neon_256_f16[ARM_NEON_RFFT_TWIDDLES_NEON_256_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_256_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_256_f16[ARM_NEON_RFFT_FACTORS_NEON_256_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_F16_LEN 192 +extern const float16_t arm_neon_rfft_super_twiddles_neon_256_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_256_F16 252 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_256_F16 60 + +#define ARM_NEON_RFFT_TWIDDLES_512_F16_LEN 1008 +extern const float16_t arm_neon_rfft_twiddles_512_f16[ARM_NEON_RFFT_TWIDDLES_512_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_512_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_512_f16[ARM_NEON_RFFT_FACTORS_512_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_512_F16_LEN 240 +extern const float16_t arm_neon_rfft_twiddles_neon_512_f16[ARM_NEON_RFFT_TWIDDLES_NEON_512_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_512_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_512_f16[ARM_NEON_RFFT_FACTORS_NEON_512_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_F16_LEN 384 +extern const float16_t arm_neon_rfft_super_twiddles_neon_512_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_512_F16 504 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_512_F16 120 + +#define ARM_NEON_RFFT_TWIDDLES_1024_F16_LEN 2040 +extern const float16_t arm_neon_rfft_twiddles_1024_f16[ARM_NEON_RFFT_TWIDDLES_1024_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_1024_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_1024_f16[ARM_NEON_RFFT_FACTORS_1024_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_1024_F16_LEN 504 +extern const float16_t arm_neon_rfft_twiddles_neon_1024_f16[ARM_NEON_RFFT_TWIDDLES_NEON_1024_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_1024_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_1024_f16[ARM_NEON_RFFT_FACTORS_NEON_1024_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_F16_LEN 768 +extern const float16_t arm_neon_rfft_super_twiddles_neon_1024_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_1024_F16 1020 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_1024_F16 252 + +#define ARM_NEON_RFFT_TWIDDLES_2048_F16_LEN 4080 +extern const float16_t arm_neon_rfft_twiddles_2048_f16[ARM_NEON_RFFT_TWIDDLES_2048_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_2048_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_2048_f16[ARM_NEON_RFFT_FACTORS_2048_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_2048_F16_LEN 1008 +extern const float16_t arm_neon_rfft_twiddles_neon_2048_f16[ARM_NEON_RFFT_TWIDDLES_NEON_2048_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_2048_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_2048_f16[ARM_NEON_RFFT_FACTORS_NEON_2048_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_F16_LEN 1536 +extern const float16_t arm_neon_rfft_super_twiddles_neon_2048_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_2048_F16 2040 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_2048_F16 504 + +#define ARM_NEON_RFFT_TWIDDLES_4096_F16_LEN 8184 +extern const float16_t arm_neon_rfft_twiddles_4096_f16[ARM_NEON_RFFT_TWIDDLES_4096_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_4096_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_4096_f16[ARM_NEON_RFFT_FACTORS_4096_F16_LEN]; +#define ARM_NEON_RFFT_TWIDDLES_NEON_4096_F16_LEN 2040 +extern const float16_t arm_neon_rfft_twiddles_neon_4096_f16[ARM_NEON_RFFT_TWIDDLES_NEON_4096_F16_LEN]; +#define ARM_NEON_RFFT_FACTORS_NEON_4096_F16_LEN 4 +extern const uint32_t arm_neon_rfft_factors_neon_4096_f16[ARM_NEON_RFFT_FACTORS_NEON_4096_F16_LEN]; +#define ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_F16_LEN 3072 +extern const float16_t arm_neon_rfft_super_twiddles_neon_4096_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_F16_LEN]; +#define ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_4096_F16 4092 +#define ARM_NE10_OFFSET_BACKWARD_TWID_NEON_4096_F16 1020 + + + +#endif /* defined(ARM_MATH_NEON_FLOAT16) && defined(ARM_FLOAT16_SUPPORTED) */ + + + +#ifdef __cplusplus +} +#endif + +#endif /*ARM_NEON_TABLES_F16_H*/ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_vec_math.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_vec_math.h new file mode 100755 index 0000000..3b65bf1 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_vec_math.h @@ -0,0 +1,373 @@ +/****************************************************************************** + * @file arm_vec_math.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_VEC_MATH_H +#define ARM_VEC_MATH_H + +#include "arm_math_types.h" +#include "arm_common_tables.h" +#include "arm_helium_utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + +#define INV_NEWTON_INIT_F32 0x7EF127EA + +static const float32_t __logf_rng_f32=0.693147180f; + + +/* fast inverse approximation (3x newton) */ +__STATIC_INLINE f32x4_t vrecip_medprec_f32( + f32x4_t x) +{ + q31x4_t m; + f32x4_t b; + any32x4_t xinv; + f32x4_t ax = vabsq(x); + + xinv.f = ax; + m = 0x3F800000 - (xinv.i & 0x7F800000); + xinv.i = xinv.i + m; + xinv.f = 1.41176471f - 0.47058824f * xinv.f; + xinv.i = xinv.i + m; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + xinv.f = vdupq_m_n_f32(xinv.f, F32_MAX, vcmpeqq_n_f32(x, 0.0f)); + /* + * restore sign + */ + xinv.f = vnegq_m_f32(xinv.f, xinv.f, vcmpltq_n_f32(x, 0.0f)); + + return xinv.f; +} + +/* fast inverse approximation (4x newton) */ +__STATIC_INLINE f32x4_t vrecip_hiprec_f32( + f32x4_t x) +{ + q31x4_t m; + f32x4_t b; + any32x4_t xinv; + f32x4_t ax = vabsq(x); + + xinv.f = ax; + + m = 0x3F800000 - (xinv.i & 0x7F800000); + xinv.i = xinv.i + m; + xinv.f = 1.41176471f - 0.47058824f * xinv.f; + xinv.i = xinv.i + m; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f - xinv.f * ax; + xinv.f = xinv.f * b; + + xinv.f = vdupq_m_n_f32(xinv.f, F32_MAX, vcmpeqq_n_f32(x, 0.0f)); + /* + * restore sign + */ + xinv.f = vnegq_m_f32(xinv.f, xinv.f, vcmpltq_n_f32(x, 0.0f)); + + return xinv.f; +} + +__STATIC_INLINE f32x4_t vdiv_f32( + f32x4_t num, f32x4_t den) +{ + return vmulq_f32(num, vrecip_hiprec_f32(den)); +} + +/** + @brief Single-precision taylor dev. + @param[in] x f32 quad vector input + @param[in] coeffs f32 quad vector coeffs + @return destination f32 quad vector + */ + +__STATIC_INLINE f32x4_t vtaylor_polyq_f32( + f32x4_t x, + const float32_t * coeffs) +{ + f32x4_t A = vfmasq_n_f32(vdupq_n_f32(coeffs[4]), x, coeffs[0]); + f32x4_t B = vfmasq_n_f32(vdupq_n_f32(coeffs[6]), x, coeffs[2]); + f32x4_t C = vfmasq_n_f32(vdupq_n_f32(coeffs[5]), x, coeffs[1]); + f32x4_t D = vfmasq_n_f32(vdupq_n_f32(coeffs[7]), x, coeffs[3]); + f32x4_t x2 = vmulq_f32(x, x); + f32x4_t x4 = vmulq_f32(x2, x2); + f32x4_t res = vfmaq_f32(vfmaq_f32(A, B, x2), vfmaq_f32(C, D, x2), x4); + + return res; +} + +__STATIC_INLINE f32x4_t vmant_exp_f32( + f32x4_t x, + int32x4_t * e) +{ + any32x4_t r; + int32x4_t n; + + r.f = x; + n = r.i >> 23; + n = n - 127; + r.i = r.i - (n << 23); + + *e = n; + return r.f; +} + + +__STATIC_INLINE f32x4_t vlogq_f32(f32x4_t vecIn) +{ + q31x4_t vecExpUnBiased; + f32x4_t vecTmpFlt0, vecTmpFlt1; + f32x4_t vecAcc0, vecAcc1, vecAcc2, vecAcc3; + f32x4_t vecExpUnBiasedFlt; + + /* + * extract exponent + */ + vecTmpFlt1 = vmant_exp_f32(vecIn, &vecExpUnBiased); + + vecTmpFlt0 = vecTmpFlt1 * vecTmpFlt1; + /* + * a = (__logf_lut_f32[4] * r.f) + (__logf_lut_f32[0]); + */ + vecAcc0 = vdupq_n_f32(__logf_lut_f32[0]); + vecAcc0 = vfmaq_n_f32(vecAcc0, vecTmpFlt1, __logf_lut_f32[4]); + /* + * b = (__logf_lut_f32[6] * r.f) + (__logf_lut_f32[2]); + */ + vecAcc1 = vdupq_n_f32(__logf_lut_f32[2]); + vecAcc1 = vfmaq_n_f32(vecAcc1, vecTmpFlt1, __logf_lut_f32[6]); + /* + * c = (__logf_lut_f32[5] * r.f) + (__logf_lut_f32[1]); + */ + vecAcc2 = vdupq_n_f32(__logf_lut_f32[1]); + vecAcc2 = vfmaq_n_f32(vecAcc2, vecTmpFlt1, __logf_lut_f32[5]); + /* + * d = (__logf_lut_f32[7] * r.f) + (__logf_lut_f32[3]); + */ + vecAcc3 = vdupq_n_f32(__logf_lut_f32[3]); + vecAcc3 = vfmaq_n_f32(vecAcc3, vecTmpFlt1, __logf_lut_f32[7]); + /* + * a = a + b * xx; + */ + vecAcc0 = vfmaq(vecAcc0, vecAcc1, vecTmpFlt0); + /* + * c = c + d * xx; + */ + vecAcc2 = vfmaq(vecAcc2, vecAcc3, vecTmpFlt0); + /* + * xx = xx * xx; + */ + vecTmpFlt0 = vecTmpFlt0 * vecTmpFlt0; + vecExpUnBiasedFlt = vcvtq_f32_s32(vecExpUnBiased); + /* + * r.f = a + c * xx; + */ + vecAcc0 = vfmaq_f32(vecAcc0, vecAcc2, vecTmpFlt0); + /* + * add exponent + * r.f = r.f + ((float32_t) m) * __logf_rng_f32; + */ + vecAcc0 = vfmaq_n_f32(vecAcc0, vecExpUnBiasedFlt, __logf_rng_f32); + // set log0 down to -inf + vecAcc0 = vdupq_m(vecAcc0, -F32_MAX, vcmpeqq(vecIn, 0.0f)); + return vecAcc0; +} + +__STATIC_INLINE f32x4_t vexpq_f32( + f32x4_t x) +{ + // Perform range reduction [-log(2),log(2)] + int32x4_t m = vcvtq_s32_f32(vmulq_n_f32(x, 1.4426950408f)); + f32x4_t val = vfmsq_f32(x, vcvtq_f32_s32(m), vdupq_n_f32(0.6931471805f)); + + // Polynomial Approximation + f32x4_t poly = vtaylor_polyq_f32(val, exp_tab); + + // Reconstruct + poly = (f32x4_t) (vqaddq_s32((q31x4_t) (poly), vqshlq_n_s32(m, 23))); + + poly = vdupq_m(poly, 0.0f, vcmpltq_n_s32(m, -126)); + return poly; +} + +__STATIC_INLINE f32x4_t arm_vec_exponent_f32(f32x4_t x, int32_t nb) +{ + f32x4_t r = x; + nb--; + while (nb > 0) { + r = vmulq(r, x); + nb--; + } + return (r); +} + +__STATIC_INLINE f32x4_t vrecip_f32(f32x4_t vecIn) +{ + f32x4_t vecSx, vecW, vecTmp; + any32x4_t v; + + vecSx = vabsq(vecIn); + + v.f = vecIn; + v.i = vsubq(vdupq_n_s32(INV_NEWTON_INIT_F32), v.i); + + vecW = vmulq(vecSx, v.f); + + // v.f = v.f * (8 + w * (-28 + w * (56 + w * (-70 + w *(56 + w * (-28 + w * (8 - w))))))); + vecTmp = vsubq(vdupq_n_f32(8.0f), vecW); + vecTmp = vfmasq(vecW, vecTmp, -28.0f); + vecTmp = vfmasq(vecW, vecTmp, 56.0f); + vecTmp = vfmasq(vecW, vecTmp, -70.0f); + vecTmp = vfmasq(vecW, vecTmp, 56.0f); + vecTmp = vfmasq(vecW, vecTmp, -28.0f); + vecTmp = vfmasq(vecW, vecTmp, 8.0f); + v.f = vmulq(v.f, vecTmp); + + v.f = vdupq_m(v.f, F32_MAX, vcmpeqq(vecIn, 0.0f)); + /* + * restore sign + */ + v.f = vnegq_m(v.f, v.f, vcmpltq(vecIn, 0.0f)); + return v.f; +} + +__STATIC_INLINE f32x4_t vtanhq_f32( + f32x4_t val) +{ + f32x4_t x = + vminnmq_f32(vmaxnmq_f32(val, vdupq_n_f32(-10.f)), vdupq_n_f32(10.0f)); + f32x4_t exp2x = vexpq_f32(vmulq_n_f32(x, 2.f)); + f32x4_t num = vsubq_n_f32(exp2x, 1.f); + f32x4_t den = vaddq_n_f32(exp2x, 1.f); + f32x4_t tanh = vmulq_f32(num, vrecip_f32(den)); + return tanh; +} + +__STATIC_INLINE f32x4_t vpowq_f32( + f32x4_t val, + f32x4_t n) +{ + return vexpq_f32(vmulq_f32(n, vlogq_f32(val))); +} + +#endif /* (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE)*/ + +#if (defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) +#endif /* (defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) */ + +#if defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) + +#include "NEMath.h" +/** + * @brief Vectorized integer exponentiation + * @param[in] x value + * @param[in] nb integer exponent >= 1 + * @return x^nb + * + */ +__STATIC_INLINE float32x4_t arm_vec_exponent_f32(float32x4_t x, int32_t nb) +{ + float32x4_t r = x; + nb --; + while(nb > 0) + { + r = vmulq_f32(r , x); + nb--; + } + return(r); +} + + +__STATIC_INLINE float32x4_t __arm_vec_sqrt_f32_neon(float32x4_t x) +{ + float32x4_t x1 = vmaxq_f32(x, vdupq_n_f32(FLT_MIN)); + float32x4_t e = vrsqrteq_f32(x1); + e = vmulq_f32(vrsqrtsq_f32(vmulq_f32(x1, e), e), e); + e = vmulq_f32(vrsqrtsq_f32(vmulq_f32(x1, e), e), e); + return vmulq_f32(x, e); +} + +__STATIC_INLINE int16x8_t __arm_vec_sqrt_q15_neon(int16x8_t vec) +{ + float32x4_t tempF; + int32x4_t tempHI,tempLO; + + tempLO = vmovl_s16(vget_low_s16(vec)); + tempF = vcvtq_n_f32_s32(tempLO,15); + tempF = __arm_vec_sqrt_f32_neon(tempF); + tempLO = vcvtq_n_s32_f32(tempF,15); + + tempHI = vmovl_s16(vget_high_s16(vec)); + tempF = vcvtq_n_f32_s32(tempHI,15); + tempF = __arm_vec_sqrt_f32_neon(tempF); + tempHI = vcvtq_n_s32_f32(tempF,15); + + return(vcombine_s16(vqmovn_s32(tempLO),vqmovn_s32(tempHI))); +} + +__STATIC_INLINE int32x4_t __arm_vec_sqrt_q31_neon(int32x4_t vec) +{ + float32x4_t temp; + + temp = vcvtq_n_f32_s32(vec,31); + temp = __arm_vec_sqrt_f32_neon(temp); + return(vcvtq_n_s32_f32(temp,31)); +} + +#endif /* defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL)*/ + +#ifdef __cplusplus +} +#endif + + +#endif /* _ARM_VEC_MATH_H */ + +/** + * + * End of file. + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_vec_math_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_vec_math_f16.h new file mode 100755 index 0000000..a44c63d --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/arm_vec_math_f16.h @@ -0,0 +1,312 @@ +/****************************************************************************** + * @file arm_vec_math_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_VEC_MATH_F16_H +#define ARM_VEC_MATH_F16_H + +#include "arm_math_types_f16.h" +#include "arm_common_tables_f16.h" +#include "arm_helium_utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + + +static const float16_t __logf_rng_f16=0.693147180f16; + +/* fast inverse approximation (3x newton) */ +__STATIC_INLINE f16x8_t vrecip_medprec_f16( + f16x8_t x) +{ + q15x8_t m; + f16x8_t b; + any16x8_t xinv; + f16x8_t ax = vabsq(x); + + xinv.f = ax; + + m = 0x03c00 - (xinv.i & 0x07c00); + xinv.i = xinv.i + m; + xinv.f = 1.41176471f16 - 0.47058824f16 * xinv.f; + xinv.i = xinv.i + m; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + xinv.f = vdupq_m_n_f16(xinv.f, F16_MAX, vcmpeqq_n_f16(x, 0.0f)); + /* + * restore sign + */ + xinv.f = vnegq_m(xinv.f, xinv.f, vcmpltq_n_f16(x, 0.0f)); + + return xinv.f; +} + +/* fast inverse approximation (4x newton) */ +__STATIC_INLINE f16x8_t vrecip_hiprec_f16( + f16x8_t x) +{ + q15x8_t m; + f16x8_t b; + any16x8_t xinv; + f16x8_t ax = vabsq(x); + + xinv.f = ax; + + m = 0x03c00 - (xinv.i & 0x07c00); + xinv.i = xinv.i + m; + xinv.f = 1.41176471f16 - 0.47058824f16 * xinv.f; + xinv.i = xinv.i + m; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + b = 2.0f16 - xinv.f * ax; + xinv.f = xinv.f * b; + + xinv.f = vdupq_m_n_f16(xinv.f, F16_MAX, vcmpeqq_n_f16(x, 0.0f)); + /* + * restore sign + */ + xinv.f = vnegq_m(xinv.f, xinv.f, vcmpltq_n_f16(x, 0.0f)); + + return xinv.f; +} + +__STATIC_INLINE f16x8_t vdiv_f16( + f16x8_t num, f16x8_t den) +{ + return vmulq(num, vrecip_hiprec_f16(den)); +} + + +/** + @brief Single-precision taylor dev. + @param[in] x f16 vector input + @param[in] coeffs f16 vector coeffs + @return destination f16 vector + */ + +__STATIC_INLINE float16x8_t vtaylor_polyq_f16( + float16x8_t x, + const float16_t * coeffs) +{ + float16x8_t A = vfmasq(vdupq_n_f16(coeffs[4]), x, coeffs[0]); + float16x8_t B = vfmasq(vdupq_n_f16(coeffs[6]), x, coeffs[2]); + float16x8_t C = vfmasq(vdupq_n_f16(coeffs[5]), x, coeffs[1]); + float16x8_t D = vfmasq(vdupq_n_f16(coeffs[7]), x, coeffs[3]); + float16x8_t x2 = vmulq(x, x); + float16x8_t x4 = vmulq(x2, x2); + float16x8_t res = vfmaq(vfmaq_f16(A, B, x2), vfmaq_f16(C, D, x2), x4); + + return res; +} + +#define VMANT_EXP_F16(x) \ + any16x8_t r; \ + int16x8_t n; \ + \ + r.f = x; \ + n = r.i >> 10; \ + n = n - 15; \ + r.i = r.i - (n << 10);\ + \ + vecExpUnBiased = n; \ + vecTmpFlt1 = r.f; + +__STATIC_INLINE float16x8_t vlogq_f16(float16x8_t vecIn) +{ + q15x8_t vecExpUnBiased; + float16x8_t vecTmpFlt0, vecTmpFlt1; + float16x8_t vecAcc0, vecAcc1, vecAcc2, vecAcc3; + float16x8_t vecExpUnBiasedFlt; + + /* + * extract exponent + */ + VMANT_EXP_F16(vecIn); + + vecTmpFlt0 = vecTmpFlt1 * vecTmpFlt1; + /* + * a = (__logf_lut_f16[4] * r.f) + (__logf_lut_f16[0]); + */ + vecAcc0 = vdupq_n_f16(__logf_lut_f16[0]); + vecAcc0 = vfmaq(vecAcc0, vecTmpFlt1, __logf_lut_f16[4]); + /* + * b = (__logf_lut_f16[6] * r.f) + (__logf_lut_f16[2]); + */ + vecAcc1 = vdupq_n_f16(__logf_lut_f16[2]); + vecAcc1 = vfmaq(vecAcc1, vecTmpFlt1, __logf_lut_f16[6]); + /* + * c = (__logf_lut_f16[5] * r.f) + (__logf_lut_f16[1]); + */ + vecAcc2 = vdupq_n_f16(__logf_lut_f16[1]); + vecAcc2 = vfmaq(vecAcc2, vecTmpFlt1, __logf_lut_f16[5]); + /* + * d = (__logf_lut_f16[7] * r.f) + (__logf_lut_f16[3]); + */ + vecAcc3 = vdupq_n_f16(__logf_lut_f16[3]); + vecAcc3 = vfmaq(vecAcc3, vecTmpFlt1, __logf_lut_f16[7]); + /* + * a = a + b * xx; + */ + vecAcc0 = vfmaq(vecAcc0, vecAcc1, vecTmpFlt0); + /* + * c = c + d * xx; + */ + vecAcc2 = vfmaq(vecAcc2, vecAcc3, vecTmpFlt0); + /* + * xx = xx * xx; + */ + vecTmpFlt0 = vecTmpFlt0 * vecTmpFlt0; + vecExpUnBiasedFlt = vcvtq_f16_s16(vecExpUnBiased); + /* + * r.f = a + c * xx; + */ + vecAcc0 = vfmaq(vecAcc0, vecAcc2, vecTmpFlt0); + /* + * add exponent + * r.f = r.f + ((float32_t) m) * __logf_rng_f16; + */ + vecAcc0 = vfmaq(vecAcc0, vecExpUnBiasedFlt, __logf_rng_f16); + // set log0 down to -inf + vecAcc0 = vdupq_m_n_f16(vecAcc0, F16_MIN, vcmpeqq_n_f16(vecIn, 0.0f)); + return vecAcc0; +} + +__STATIC_INLINE float16x8_t vexpq_f16( + float16x8_t x) +{ + // Perform range reduction [-log(2),log(2)] + int16x8_t m = vcvtq_s16_f16(vmulq_n_f16(x, 1.4426950408f16)); + float16x8_t val = vfmsq_f16(x, vcvtq_f16_s16(m), vdupq_n_f16(0.6931471805f16)); + + // Polynomial Approximation + float16x8_t poly = vtaylor_polyq_f16(val, exp_tab_f16); + + // Reconstruct + poly = (float16x8_t) (vqaddq_s16((int16x8_t) (poly), vqshlq_n_s16(m, 10))); + + poly = vdupq_m_n_f16(poly, 0.0f16, vcmpltq_n_s16(m, -14)); + return poly; +} + +__STATIC_INLINE float16x8_t arm_vec_exponent_f16(float16x8_t x, int16_t nb) +{ + float16x8_t r = x; + nb--; + while (nb > 0) { + r = vmulq(r, x); + nb--; + } + return (r); +} + +__STATIC_INLINE f16x8_t vpowq_f16( + f16x8_t val, + f16x8_t n) +{ + return vexpq_f16(vmulq_f16(n, vlogq_f16(val))); +} + +#define INV_NEWTON_INIT_F16 0x7773 + +__STATIC_INLINE f16x8_t vrecip_f16(f16x8_t vecIn) +{ + f16x8_t vecSx, vecW, vecTmp; + any16x8_t v; + + vecSx = vabsq(vecIn); + + v.f = vecIn; + v.i = vsubq(vdupq_n_s16(INV_NEWTON_INIT_F16), v.i); + + vecW = vmulq(vecSx, v.f); + + // v.f = v.f * (8 + w * (-28 + w * (56 + w * (-70 + w *(56 + w * (-28 + w * (8 - w))))))); + vecTmp = vsubq(vdupq_n_f16(8.0f16), vecW); + vecTmp = vfmasq_n_f16(vecW, vecTmp, -28.0f16); + vecTmp = vfmasq_n_f16(vecW, vecTmp, 56.0f16); + vecTmp = vfmasq_n_f16(vecW, vecTmp, -70.0f16); + vecTmp = vfmasq_n_f16(vecW, vecTmp, 56.0f16); + vecTmp = vfmasq_n_f16(vecW, vecTmp, -28.0f16); + vecTmp = vfmasq_n_f16(vecW, vecTmp, 8.0f16); + v.f = vmulq(v.f, vecTmp); + + v.f = vdupq_m_n_f16(v.f, F16_MAX, vcmpeqq_n_f16(vecIn, 0.0f)); + /* + * restore sign + */ + v.f = vnegq_m(v.f, v.f, vcmpltq_n_f16(vecIn, 0.0f)); + return v.f; +} + +__STATIC_INLINE f16x8_t vtanhq_f16( + f16x8_t val) +{ + f16x8_t x = + vminnmq_f16(vmaxnmq_f16(val, vdupq_n_f16(-10.f16)), vdupq_n_f16(10.0f16)); + f16x8_t exp2x = vexpq_f16(vmulq_n_f16(x, 2.f16)); + f16x8_t num = vsubq_n_f16(exp2x, 1.f16); + f16x8_t den = vaddq_n_f16(exp2x, 1.f16); + f16x8_t tanh = vmulq_f16(num, vrecip_f16(den)); + return tanh; +} + +#endif /* defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)*/ + + + +#ifdef __cplusplus +} +#endif + +#endif /* ARM FLOAT16 SUPPORTED */ + +#endif /* _ARM_VEC_MATH_F16_H */ + +/** + * + * End of file. + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/basic_math_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/basic_math_functions.h new file mode 100755 index 0000000..645afdc --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/basic_math_functions.h @@ -0,0 +1,864 @@ +/****************************************************************************** + * @file basic_math_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef BASIC_MATH_FUNCTIONS_H_ +#define BASIC_MATH_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup groupMath Basic Math Functions + */ + + /** + * @brief Q7 vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Floating-point vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize); + + + +/** + * @brief Floating-point vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ +void arm_mult_f64( +const float64_t * pSrcA, +const float64_t * pSrcB, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Floating-point vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize); + + + +/** + * @brief Floating-point vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_f64( + const float64_t * pSrcA, + const float64_t * pSrcB, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Q7 vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Floating-point vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Floating-point vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_f64( + const float64_t * pSrcA, + const float64_t * pSrcB, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Q7 vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q15 vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a floating-point vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scale scale factor to be applied + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_f32( + const float32_t * pSrc, + float32_t scale, + float32_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Multiplies a floating-point vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scale scale factor to be applied + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_f64( + const float64_t * pSrc, + float64_t scale, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Multiplies a Q7 vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_q7( + const q7_t * pSrc, + q7_t scaleFract, + int8_t shift, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a Q15 vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_q15( + const q15_t * pSrc, + q15_t scaleFract, + int8_t shift, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Multiplies a Q31 vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scaleFract fractional portion of the scale value + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_q31( + const q31_t * pSrc, + q31_t scaleFract, + int8_t shift, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q7 vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_q7( + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Floating-point vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + +/** + * @brief Floating-point vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ +void arm_abs_f64( +const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Q15 vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Q31 vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Dot product of floating-point vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t blockSize, + float32_t * result); + + + +/** + * @brief Dot product of floating-point vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ +void arm_dot_prod_f64( +const float64_t * pSrcA, +const float64_t * pSrcB, + uint32_t blockSize, + float64_t * result); + + + + /** + * @brief Dot product of Q7 vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + uint32_t blockSize, + q31_t * result); + + + /** + * @brief Dot product of Q15 vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t blockSize, + q63_t * result); + + + /** + * @brief Dot product of Q31 vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t blockSize, + q63_t * result); + + + /** + * @brief Shifts the elements of a Q7 vector a specified number of bits. + * @param[in] pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_shift_q7( + const q7_t * pSrc, + int8_t shiftBits, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Shifts the elements of a Q15 vector a specified number of bits. + * @param[in] pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_shift_q15( + const q15_t * pSrc, + int8_t shiftBits, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Shifts the elements of a Q31 vector a specified number of bits. + * @param[in] pSrc points to the input vector + * @param[in] shiftBits number of bits to shift. A positive value shifts left; a negative value shifts right. + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_shift_q31( + const q31_t * pSrc, + int8_t shiftBits, + q31_t * pDst, + uint32_t blockSize); + + +/** + * @brief Adds a constant offset to a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ +void arm_offset_f64( +const float64_t * pSrc, + float64_t offset, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Adds a constant offset to a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_f32( + const float32_t * pSrc, + float32_t offset, + float32_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Adds a constant offset to a Q7 vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_q7( + const q7_t * pSrc, + q7_t offset, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a Q15 vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_q15( + const q15_t * pSrc, + q15_t offset, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a Q31 vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_q31( + const q31_t * pSrc, + q31_t offset, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + +/** + * @brief Negates the elements of a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ +void arm_negate_f64( +const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Negates the elements of a Q7 vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_q7( + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a Q15 vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Negates the elements of a Q31 vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + +/** + * @brief Compute the logical bitwise AND of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_and_u16( + const uint16_t * pSrcA, + const uint16_t * pSrcB, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise AND of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_and_u32( + const uint32_t * pSrcA, + const uint32_t * pSrcB, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise AND of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_and_u8( + const uint8_t * pSrcA, + const uint8_t * pSrcB, + uint8_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise OR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_or_u16( + const uint16_t * pSrcA, + const uint16_t * pSrcB, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise OR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_or_u32( + const uint32_t * pSrcA, + const uint32_t * pSrcB, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise OR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_or_u8( + const uint8_t * pSrcA, + const uint8_t * pSrcB, + uint8_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise NOT of a fixed-point vector. + * @param[in] pSrc points to input vector + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_not_u16( + const uint16_t * pSrc, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise NOT of a fixed-point vector. + * @param[in] pSrc points to input vector + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_not_u32( + const uint32_t * pSrc, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise NOT of a fixed-point vector. + * @param[in] pSrc points to input vector + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_not_u8( + const uint8_t * pSrc, + uint8_t * pDst, + uint32_t blockSize); + +/** + * @brief Compute the logical bitwise XOR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_xor_u16( + const uint16_t * pSrcA, + const uint16_t * pSrcB, + uint16_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise XOR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_xor_u32( + const uint32_t * pSrcA, + const uint32_t * pSrcB, + uint32_t * pDst, + uint32_t blockSize); + + /** + * @brief Compute the logical bitwise XOR of two fixed-point vectors. + * @param[in] pSrcA points to input vector A + * @param[in] pSrcB points to input vector B + * @param[out] pDst points to output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_xor_u8( + const uint8_t * pSrcA, + const uint8_t * pSrcB, + uint8_t * pDst, + uint32_t blockSize); + + /** + @brief Elementwise floating-point clipping + @param[in] pSrc points to input values + @param[out] pDst points to output clipped values + @param[in] low lower bound + @param[in] high higher bound + @param[in] numSamples number of samples to clip + */ + +void arm_clip_f32(const float32_t * pSrc, + float32_t * pDst, + float32_t low, + float32_t high, + uint32_t numSamples); + + /** + @brief Elementwise fixed-point clipping + @param[in] pSrc points to input values + @param[out] pDst points to output clipped values + @param[in] low lower bound + @param[in] high higher bound + @param[in] numSamples number of samples to clip + */ + +void arm_clip_q31(const q31_t * pSrc, + q31_t * pDst, + q31_t low, + q31_t high, + uint32_t numSamples); + + /** + @brief Elementwise fixed-point clipping + @param[in] pSrc points to input values + @param[out] pDst points to output clipped values + @param[in] low lower bound + @param[in] high higher bound + @param[in] numSamples number of samples to clip + */ + +void arm_clip_q15(const q15_t * pSrc, + q15_t * pDst, + q15_t low, + q15_t high, + uint32_t numSamples); + + /** + @brief Elementwise fixed-point clipping + @param[in] pSrc points to input values + @param[out] pDst points to output clipped values + @param[in] low lower bound + @param[in] high higher bound + @param[in] numSamples number of samples to clip + */ + +void arm_clip_q7(const q7_t * pSrc, + q7_t * pDst, + q7_t low, + q7_t high, + uint32_t numSamples); + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _BASIC_MATH_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/basic_math_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/basic_math_functions_f16.h new file mode 100755 index 0000000..b3d5ecd --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/basic_math_functions_f16.h @@ -0,0 +1,165 @@ +/****************************************************************************** + * @file basic_math_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef BASIC_MATH_FUNCTIONS_F16_H_ +#define BASIC_MATH_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + + /** + * @brief Floating-point vector addition. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_add_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Floating-point vector subtraction. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_sub_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Multiplies a floating-point vector by a scalar. + * @param[in] pSrc points to the input vector + * @param[in] scale scale factor to be applied + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_scale_f16( + const float16_t * pSrc, + float16_t scale, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Floating-point vector absolute value. + * @param[in] pSrc points to the input buffer + * @param[out] pDst points to the output buffer + * @param[in] blockSize number of samples in each vector + */ + void arm_abs_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + + /** + * @brief Adds a constant offset to a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[in] offset is the offset to be added + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_offset_f16( + const float16_t * pSrc, + float16_t offset, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Dot product of floating-point vectors. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[out] result output result returned here + */ + void arm_dot_prod_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + uint32_t blockSize, + float16_t * result); + + /** + * @brief Floating-point vector multiplication. + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in each vector + */ + void arm_mult_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Negates the elements of a floating-point vector. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] blockSize number of samples in the vector + */ + void arm_negate_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + /** + @brief Elementwise floating-point clipping + @param[in] pSrc points to input values + @param[out] pDst points to output clipped values + @param[in] low lower bound + @param[in] high higher bound + @param[in] numSamples number of samples to clip + */ +void arm_clip_f16(const float16_t * pSrc, + float16_t * pDst, + float16_t low, + float16_t high, + uint32_t numSamples); + +#endif /* defined(ARM_FLOAT16_SUPPORTED)*/ + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _BASIC_MATH_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/bayes_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/bayes_functions.h new file mode 100755 index 0000000..7b3e0ef --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/bayes_functions.h @@ -0,0 +1,86 @@ +/****************************************************************************** + * @file bayes_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef BAYES_FUNCTIONS_H_ +#define BAYES_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/statistics_functions.h" + +/** + * @defgroup groupBayes Bayesian estimators + * + * Implement the naive gaussian Bayes estimator. + * The training must be done from scikit-learn. + * + * The parameters can be easily + * generated from the scikit-learn object. Some examples are given in + * DSP/Testing/PatternGeneration/Bayes.py + */ + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @brief Instance structure for Naive Gaussian Bayesian estimator. + */ +typedef struct +{ + uint32_t vectorDimension; /**< Dimension of vector space */ + uint32_t numberOfClasses; /**< Number of different classes */ + const float32_t *theta; /**< Mean values for the Gaussians */ + const float32_t *sigma; /**< Variances for the Gaussians */ + const float32_t *classPriors; /**< Class prior probabilities */ + float32_t epsilon; /**< Additive value to variances */ +} arm_gaussian_naive_bayes_instance_f32; + +/** + * @brief Naive Gaussian Bayesian Estimator + * + * @param[in] S points to a naive bayes instance structure + * @param[in] in points to the elements of the input vector. + * @param[out] *pOutputProbabilities points to a buffer of length numberOfClasses containing estimated probabilities + * @param[out] *pBufferB points to a temporary buffer of length numberOfClasses + * @return The predicted class + */ +uint32_t arm_gaussian_naive_bayes_predict_f32(const arm_gaussian_naive_bayes_instance_f32 *S, + const float32_t * in, + float32_t *pOutputProbabilities, + float32_t *pBufferB); + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _BAYES_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/bayes_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/bayes_functions_f16.h new file mode 100755 index 0000000..100162e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/bayes_functions_f16.h @@ -0,0 +1,77 @@ +/****************************************************************************** + * @file bayes_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef BAYES_FUNCTIONS_F16_H_ +#define BAYES_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/statistics_functions_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + * @brief Instance structure for Naive Gaussian Bayesian estimator. + */ +typedef struct +{ + uint32_t vectorDimension; /**< Dimension of vector space */ + uint32_t numberOfClasses; /**< Number of different classes */ + const float16_t *theta; /**< Mean values for the Gaussians */ + const float16_t *sigma; /**< Variances for the Gaussians */ + const float16_t *classPriors; /**< Class prior probabilities */ + float16_t epsilon; /**< Additive value to variances */ +} arm_gaussian_naive_bayes_instance_f16; + +/** + * @brief Naive Gaussian Bayesian Estimator + * + * @param[in] S points to a naive bayes instance structure + * @param[in] in points to the elements of the input vector. + * @param[out] *pOutputProbabilities points to a buffer of length numberOfClasses containing estimated probabilities + * @param[out] *pBufferB points to a temporary buffer of length numberOfClasses + * @return The predicted class + */ +uint32_t arm_gaussian_naive_bayes_predict_f16(const arm_gaussian_naive_bayes_instance_f16 *S, + const float16_t * in, + float16_t *pOutputProbabilities, + float16_t *pBufferB); + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _BAYES_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/complex_math_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/complex_math_functions.h new file mode 100755 index 0000000..bdbc2a4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/complex_math_functions.h @@ -0,0 +1,345 @@ +/****************************************************************************** + * @file complex_math_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef COMPLEX_MATH_FUNCTIONS_H_ +#define COMPLEX_MATH_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" +#include "dsp/fast_math_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup groupCmplxMath Complex Math Functions + * This set of functions operates on complex data vectors. + * The data in the complex arrays is stored in an interleaved fashion + * (real, imag, real, imag, ...). + * In the API functions, the number of samples in a complex array refers + * to the number of complex values; the array contains twice this number of + * real values. + */ + + /** + * @brief Floating-point complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples); + + /** + * @brief Q31 complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + +/** + * @brief Floating-point complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples); + + +/** + * @brief Floating-point complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + /** + * @brief Q15 complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_fast_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q15 complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t numSamples, + q31_t * realResult, + q31_t * imagResult); + + + /** + * @brief Q31 complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t numSamples, + q63_t * realResult, + q63_t * imagResult); + + + /** + * @brief Floating-point complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t numSamples, + float32_t * realResult, + float32_t * imagResult); + + + /** + * @brief Q15 complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_q15( + const q15_t * pSrcCmplx, + const q15_t * pSrcReal, + q15_t * pCmplxDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_q31( + const q31_t * pSrcCmplx, + const q31_t * pSrcReal, + q31_t * pCmplxDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_f32( + const float32_t * pSrcCmplx, + const float32_t * pSrcReal, + float32_t * pCmplxDst, + uint32_t numSamples); + + /** + * @brief Q15 complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t numSamples); + + + /** + * @brief Q31 complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t numSamples); + + + /** + * @brief Floating-point complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t numSamples); + + + +/** + * @brief Floating-point complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ +void arm_cmplx_mult_cmplx_f64( +const float64_t * pSrcA, +const float64_t * pSrcB, + float64_t * pDst, + uint32_t numSamples); + + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _COMPLEX_MATH_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/complex_math_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/complex_math_functions_f16.h new file mode 100755 index 0000000..bd14732 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/complex_math_functions_f16.h @@ -0,0 +1,123 @@ +/****************************************************************************** + * @file complex_math_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef COMPLEX_MATH_FUNCTIONS_F16_H_ +#define COMPLEX_MATH_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" +#include "dsp/fast_math_functions_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + /** + * @brief Floating-point complex conjugate. + * @param[in] pSrc points to the input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_conj_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples); + + /** + * @brief Floating-point complex magnitude squared + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_squared_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples); + + /** + * @brief Floating-point complex magnitude + * @param[in] pSrc points to the complex input vector + * @param[out] pDst points to the real output vector + * @param[in] numSamples number of complex samples in the input vector + */ + void arm_cmplx_mag_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples); + + /** + * @brief Floating-point complex dot product + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] numSamples number of complex samples in each vector + * @param[out] realResult real part of the result returned here + * @param[out] imagResult imaginary part of the result returned here + */ + void arm_cmplx_dot_prod_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + uint32_t numSamples, + float16_t * realResult, + float16_t * imagResult); + + /** + * @brief Floating-point complex-by-real multiplication + * @param[in] pSrcCmplx points to the complex input vector + * @param[in] pSrcReal points to the real input vector + * @param[out] pCmplxDst points to the complex output vector + * @param[in] numSamples number of samples in each vector + */ + void arm_cmplx_mult_real_f16( + const float16_t * pSrcCmplx, + const float16_t * pSrcReal, + float16_t * pCmplxDst, + uint32_t numSamples); + + /** + * @brief Floating-point complex-by-complex multiplication + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[out] pDst points to the output vector + * @param[in] numSamples number of complex samples in each vector + */ + void arm_cmplx_mult_cmplx_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + float16_t * pDst, + uint32_t numSamples); + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _COMPLEX_MATH_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/controller_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/controller_functions.h new file mode 100755 index 0000000..5d5de98 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/controller_functions.h @@ -0,0 +1,785 @@ +/****************************************************************************** + * @file controller_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef CONTROLLER_FUNCTIONS_H_ +#define CONTROLLER_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + /** + * @brief Macros required for SINE and COSINE Controller functions + */ + +#define CONTROLLER_Q31_SHIFT (32 - 9) + /* 1.31(q31) Fixed value of 2/360 */ + /* -1 to +1 is divided into 360 values so total spacing is (2/360) */ +#define INPUT_SPACING 0xB60B61 + +/** + * @defgroup groupController Controller Functions + */ + + +/** + @ingroup groupController + */ + +/** + @defgroup SinCos Sine Cosine + + Computes the trigonometric sine and cosine values using a combination of table lookup + and linear interpolation. + There are separate functions for Q31 and floating-point data types. + The input to the floating-point version is in degrees while the + fixed-point Q31 have a scaled input with the range + [-1 0.9999] mapping to [-180 +180] degrees. + + The floating point function also allows values that are out of the usual range. When this happens, the function will + take extra time to adjust the input value to the range of [-180 180]. + + The result is accurate to 5 digits after the decimal point. + + The implementation is based on table lookup using 360 values together with linear interpolation. + The steps used are: + -# Calculation of the nearest integer table index. + -# Compute the fractional portion (fract) of the input. + -# Fetch the value corresponding to \c index from sine table to \c y0 and also value from \c index+1 to \c y1. + -# Sine value is computed as *psinVal = y0 + (fract * (y1 - y0)). + -# Fetch the value corresponding to \c index from cosine table to \c y0 and also value from \c index+1 to \c y1. + -# Cosine value is computed as *pcosVal = y0 + (fract * (y1 - y0)). + */ + +/** + * @brief Floating-point sin_cos function. + * @param[in] theta input value in degrees + * @param[out] pSinVal points to the processed sine output. + * @param[out] pCosVal points to the processed cos output. + */ + void arm_sin_cos_f32( + float32_t theta, + float32_t * pSinVal, + float32_t * pCosVal); + + + /** + * @brief Q31 sin_cos function. + * @param[in] theta scaled input value in degrees + * @param[out] pSinVal points to the processed sine output. + * @param[out] pCosVal points to the processed cosine output. + */ + void arm_sin_cos_q31( + q31_t theta, + q31_t * pSinVal, + q31_t * pCosVal); + + +/** + @ingroup groupController + */ + +/** + * @defgroup PID PID Motor Control + * + * A Proportional Integral Derivative (PID) controller is a generic feedback control + * loop mechanism widely used in industrial control systems. + * A PID controller is the most commonly used type of feedback controller. + * + * This set of functions implements (PID) controllers + * for Q15, Q31, and floating-point data types. The functions operate on a single sample + * of data and each call to the function returns a single processed value. + * S points to an instance of the PID control data structure. in + * is the input sample value. The functions return the output value. + * + * \par Algorithm: + * 
+   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
+   *    A0 = Kp + Ki + Kd
+   *    A1 = (-Kp ) - (2 * Kd )
+   *    A2 = Kd
+   *
+ * + * \par + * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant + * + * \par + * \image html PID.gif "Proportional Integral Derivative Controller" + * + * \par + * The PID controller calculates an "error" value as the difference between + * the measured output and the reference input. + * The controller attempts to minimize the error by adjusting the process control inputs. + * The proportional value determines the reaction to the current error, + * the integral value determines the reaction based on the sum of recent errors, + * and the derivative value determines the reaction based on the rate at which the error has been changing. + * + * \par Instance Structure + * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure. + * A separate instance structure must be defined for each PID Controller. + * There are separate instance structure declarations for each of the 3 supported data types. + * + * \par Reset Functions + * There is also an associated reset function for each data type which clears the state array. + * + * \par Initialization Functions + * There is also an associated initialization function for each data type. + * The initialization function performs the following operations: + * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains. + * - Zeros out the values in the state buffer. + * + * \par + * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function. + * + * \par Fixed-Point Behavior + * Care must be taken when using the fixed-point versions of the PID Controller functions. + * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + + /** + * @ingroup PID + * @brief Instance structure for the Q15 PID Control. + */ + typedef struct + { + q15_t A0; /**< The derived gain, A0 = Kp + Ki + Kd . */ +#if !defined (ARM_MATH_DSP) + q15_t A1; /**< The derived gain A1 = -Kp - 2Kd */ + q15_t A2; /**< The derived gain A1 = Kd. */ +#else + q31_t A1; /**< The derived gain A1 = -Kp - 2Kd | Kd.*/ +#endif + q15_t state[3]; /**< The state array of length 3. */ + q15_t Kp; /**< The proportional gain. */ + q15_t Ki; /**< The integral gain. */ + q15_t Kd; /**< The derivative gain. */ + } arm_pid_instance_q15; + + /** + * @ingroup PID + * @brief Instance structure for the Q31 PID Control. + */ + typedef struct + { + q31_t A0; /**< The derived gain, A0 = Kp + Ki + Kd . */ + q31_t A1; /**< The derived gain, A1 = -Kp - 2Kd. */ + q31_t A2; /**< The derived gain, A2 = Kd . */ + q31_t state[3]; /**< The state array of length 3. */ + q31_t Kp; /**< The proportional gain. */ + q31_t Ki; /**< The integral gain. */ + q31_t Kd; /**< The derivative gain. */ + } arm_pid_instance_q31; + + /** + * @ingroup PID + * @brief Instance structure for the floating-point PID Control. + */ + typedef struct + { + float32_t A0; /**< The derived gain, A0 = Kp + Ki + Kd . */ + float32_t A1; /**< The derived gain, A1 = -Kp - 2Kd. */ + float32_t A2; /**< The derived gain, A2 = Kd . */ + float32_t state[3]; /**< The state array of length 3. */ + float32_t Kp; /**< The proportional gain. */ + float32_t Ki; /**< The integral gain. */ + float32_t Kd; /**< The derivative gain. */ + } arm_pid_instance_f32; + + + + /** + * @brief Initialization function for the floating-point PID Control. + * @param[in,out] S points to an instance of the PID structure. + * @param[in] resetStateFlag flag to reset the state. 0 = no change in state 1 = reset the state. + */ + void arm_pid_init_f32( + arm_pid_instance_f32 * S, + int32_t resetStateFlag); + + + /** + * @brief Reset function for the floating-point PID Control. + * @param[in,out] S is an instance of the floating-point PID Control structure + */ + void arm_pid_reset_f32( + arm_pid_instance_f32 * S); + + + /** + * @brief Initialization function for the Q31 PID Control. + * @param[in,out] S points to an instance of the Q15 PID structure. + * @param[in] resetStateFlag flag to reset the state. 0 = no change in state 1 = reset the state. + */ + void arm_pid_init_q31( + arm_pid_instance_q31 * S, + int32_t resetStateFlag); + + + /** + * @brief Reset function for the Q31 PID Control. + * @param[in,out] S points to an instance of the Q31 PID Control structure + */ + + void arm_pid_reset_q31( + arm_pid_instance_q31 * S); + + + /** + * @brief Initialization function for the Q15 PID Control. + * @param[in,out] S points to an instance of the Q15 PID structure. + * @param[in] resetStateFlag flag to reset the state. 0 = no change in state 1 = reset the state. + */ + void arm_pid_init_q15( + arm_pid_instance_q15 * S, + int32_t resetStateFlag); + + + /** + * @brief Reset function for the Q15 PID Control. + * @param[in,out] S points to an instance of the q15 PID Control structure + */ + void arm_pid_reset_q15( + arm_pid_instance_q15 * S); + + + + + + /** + * @ingroup PID + * @brief Process function for the floating-point PID Control. + * @param[in,out] S is an instance of the floating-point PID Control structure + * @param[in] in input sample to process + * @return processed output sample. + */ + __STATIC_FORCEINLINE float32_t arm_pid_f32( + arm_pid_instance_f32 * S, + float32_t in) + { + float32_t out; + + /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2] */ + out = (S->A0 * in) + + (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]); + + /* Update state */ + S->state[1] = S->state[0]; + S->state[0] = in; + S->state[2] = out; + + /* return to application */ + return (out); + + } + +/** + @ingroup PID + @brief Process function for the Q31 PID Control. + @param[in,out] S points to an instance of the Q31 PID Control structure + @param[in] in input sample to process + @return processed output sample. + + \par Scaling and Overflow Behavior + The function is implemented using an internal 64-bit accumulator. + The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. + Thus, if the accumulator result overflows it wraps around rather than clip. + In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions. + After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format. + */ +__STATIC_FORCEINLINE q31_t arm_pid_q31( + arm_pid_instance_q31 * S, + q31_t in) + { + q63_t acc; + q31_t out; + + /* acc = A0 * x[n] */ + acc = (q63_t) S->A0 * in; + + /* acc += A1 * x[n-1] */ + acc += (q63_t) S->A1 * S->state[0]; + + /* acc += A2 * x[n-2] */ + acc += (q63_t) S->A2 * S->state[1]; + + /* convert output to 1.31 format to add y[n-1] */ + out = (q31_t) (acc >> 31U); + + /* out += y[n-1] */ + out += S->state[2]; + + /* Update state */ + S->state[1] = S->state[0]; + S->state[0] = in; + S->state[2] = out; + + /* return to application */ + return (out); + } + + +/** + @ingroup PID + @brief Process function for the Q15 PID Control. + @param[in,out] S points to an instance of the Q15 PID Control structure + @param[in] in input sample to process + @return processed output sample. + + \par Scaling and Overflow Behavior + The function is implemented using a 64-bit internal accumulator. + Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result. + The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format. + There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved. + After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits. + Lastly, the accumulator is saturated to yield a result in 1.15 format. + */ +__STATIC_FORCEINLINE q15_t arm_pid_q15( + arm_pid_instance_q15 * S, + q15_t in) + { + q63_t acc; + q15_t out; + +#if defined (ARM_MATH_DSP) + /* Implementation of PID controller */ + + /* acc = A0 * x[n] */ + acc = (q31_t) __SMUAD((uint32_t)S->A0, (uint32_t)in); + + /* acc += A1 * x[n-1] + A2 * x[n-2] */ + acc = (q63_t)__SMLALD((uint32_t)S->A1, (uint32_t)read_q15x2 (S->state), (uint64_t)acc); +#else + /* acc = A0 * x[n] */ + acc = ((q31_t) S->A0) * in; + + /* acc += A1 * x[n-1] + A2 * x[n-2] */ + acc += (q31_t) S->A1 * S->state[0]; + acc += (q31_t) S->A2 * S->state[1]; +#endif + + /* acc += y[n-1] */ + acc += (q31_t) S->state[2] << 15; + + /* saturate the output */ + out = (q15_t) (__SSAT((q31_t)(acc >> 15), 16)); + + /* Update state */ + S->state[1] = S->state[0]; + S->state[0] = in; + S->state[2] = out; + + /* return to application */ + return (out); + } + + + + /** + * @ingroup groupController + */ + + /** + * @defgroup park Vector Park Transform + * + * Forward Park transform converts the input two-coordinate vector to flux and torque components. + * The Park transform can be used to realize the transformation of the Ialpha and the Ibeta currents + * from the stationary to the moving reference frame and control the spatial relationship between + * the stator vector current and rotor flux vector. + * If we consider the d axis aligned with the rotor flux, the diagram below shows the + * current vector and the relationship from the two reference frames: + * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame" + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html parkFormula.gif + * where Ialpha and Ibeta are the stator vector components, + * pId and pIq are rotor vector components and cosVal and sinVal are the + * cosine and sine values of theta (rotor flux position). + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Park transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + + + /** + * @ingroup park + * @brief Floating-point Park transform + * @param[in] Ialpha input two-phase vector coordinate alpha + * @param[in] Ibeta input two-phase vector coordinate beta + * @param[out] pId points to output rotor reference frame d + * @param[out] pIq points to output rotor reference frame q + * @param[in] sinVal sine value of rotation angle theta + * @param[in] cosVal cosine value of rotation angle theta + * + * The function implements the forward Park transform. + * + */ + __STATIC_FORCEINLINE void arm_park_f32( + float32_t Ialpha, + float32_t Ibeta, + float32_t * pId, + float32_t * pIq, + float32_t sinVal, + float32_t cosVal) + { + /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */ + *pId = Ialpha * cosVal + Ibeta * sinVal; + + /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */ + *pIq = -Ialpha * sinVal + Ibeta * cosVal; + } + + +/** + @ingroup park + @brief Park transform for Q31 version + @param[in] Ialpha input two-phase vector coordinate alpha + @param[in] Ibeta input two-phase vector coordinate beta + @param[out] pId points to output rotor reference frame d + @param[out] pIq points to output rotor reference frame q + @param[in] sinVal sine value of rotation angle theta + @param[in] cosVal cosine value of rotation angle theta + + \par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the addition and subtraction, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_park_q31( + q31_t Ialpha, + q31_t Ibeta, + q31_t * pId, + q31_t * pIq, + q31_t sinVal, + q31_t cosVal) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + q31_t product3, product4; /* Temporary variables used to store intermediate results */ + + /* Intermediate product is calculated by (Ialpha * cosVal) */ + product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31); + + /* Intermediate product is calculated by (Ibeta * sinVal) */ + product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31); + + + /* Intermediate product is calculated by (Ialpha * sinVal) */ + product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31); + + /* Intermediate product is calculated by (Ibeta * cosVal) */ + product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31); + + /* Calculate pId by adding the two intermediate products 1 and 2 */ + *pId = __QADD(product1, product2); + + /* Calculate pIq by subtracting the two intermediate products 3 from 4 */ + *pIq = __QSUB(product4, product3); + } + + + + /** + * @ingroup groupController + */ + + /** + * @defgroup inv_park Vector Inverse Park transform + * Inverse Park transform converts the input flux and torque components to two-coordinate vector. + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html parkInvFormula.gif + * where pIalpha and pIbeta are the stator vector components, + * Id and Iq are rotor vector components and cosVal and sinVal are the + * cosine and sine values of theta (rotor flux position). + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Park transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + + + /** + * @ingroup inv_park + * @brief Floating-point Inverse Park transform + * @param[in] Id input coordinate of rotor reference frame d + * @param[in] Iq input coordinate of rotor reference frame q + * @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + * @param[out] pIbeta points to output two-phase orthogonal vector axis beta + * @param[in] sinVal sine value of rotation angle theta + * @param[in] cosVal cosine value of rotation angle theta + */ + __STATIC_FORCEINLINE void arm_inv_park_f32( + float32_t Id, + float32_t Iq, + float32_t * pIalpha, + float32_t * pIbeta, + float32_t sinVal, + float32_t cosVal) + { + /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */ + *pIalpha = Id * cosVal - Iq * sinVal; + + /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */ + *pIbeta = Id * sinVal + Iq * cosVal; + } + + +/** + @ingroup inv_park + @brief Inverse Park transform for Q31 version + @param[in] Id input coordinate of rotor reference frame d + @param[in] Iq input coordinate of rotor reference frame q + @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + @param[out] pIbeta points to output two-phase orthogonal vector axis beta + @param[in] sinVal sine value of rotation angle theta + @param[in] cosVal cosine value of rotation angle theta + + @par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the addition, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_inv_park_q31( + q31_t Id, + q31_t Iq, + q31_t * pIalpha, + q31_t * pIbeta, + q31_t sinVal, + q31_t cosVal) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + q31_t product3, product4; /* Temporary variables used to store intermediate results */ + + /* Intermediate product is calculated by (Id * cosVal) */ + product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31); + + /* Intermediate product is calculated by (Iq * sinVal) */ + product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31); + + + /* Intermediate product is calculated by (Id * sinVal) */ + product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31); + + /* Intermediate product is calculated by (Iq * cosVal) */ + product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31); + + /* Calculate pIalpha by using the two intermediate products 1 and 2 */ + *pIalpha = __QSUB(product1, product2); + + /* Calculate pIbeta by using the two intermediate products 3 and 4 */ + *pIbeta = __QADD(product4, product3); + } + + +/** + * @ingroup groupController + */ + + /** + * @defgroup clarke Vector Clarke Transform + * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector. + * Generally the Clarke transform uses three-phase currents Ia, Ib and Ic to calculate currents + * in the two-phase orthogonal stator axis Ialpha and Ibeta. + * When Ialpha is superposed with Ia as shown in the figure below + * \image html clarke.gif Stator current space vector and its components in (a,b). + * and Ia + Ib + Ic = 0, in this condition Ialpha and Ibeta + * can be calculated using only Ia and Ib. + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html clarkeFormula.gif + * where Ia and Ib are the instantaneous stator phases and + * pIalpha and pIbeta are the two coordinates of time invariant vector. + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Clarke transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + + /** + * + * @ingroup clarke + * @brief Floating-point Clarke transform + * @param[in] Ia input three-phase coordinate a + * @param[in] Ib input three-phase coordinate b + * @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + * @param[out] pIbeta points to output two-phase orthogonal vector axis beta + */ + __STATIC_FORCEINLINE void arm_clarke_f32( + float32_t Ia, + float32_t Ib, + float32_t * pIalpha, + float32_t * pIbeta) + { + /* Calculate pIalpha using the equation, pIalpha = Ia */ + *pIalpha = Ia; + + /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */ + *pIbeta = (0.57735026919f * Ia + 1.15470053838f * Ib); + } + + +/** + @ingroup clarke + @brief Clarke transform for Q31 version + @param[in] Ia input three-phase coordinate a + @param[in] Ib input three-phase coordinate b + @param[out] pIalpha points to output two-phase orthogonal vector axis alpha + @param[out] pIbeta points to output two-phase orthogonal vector axis beta + + \par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the addition, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_clarke_q31( + q31_t Ia, + q31_t Ib, + q31_t * pIalpha, + q31_t * pIbeta) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + + /* Calculating pIalpha from Ia by equation pIalpha = Ia */ + *pIalpha = Ia; + + /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */ + product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30); + + /* Intermediate product is calculated by (2/sqrt(3) * Ib) */ + product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30); + + /* pIbeta is calculated by adding the intermediate products */ + *pIbeta = __QADD(product1, product2); + } + + + + /** + * @ingroup groupController + */ + + /** + * @defgroup inv_clarke Vector Inverse Clarke Transform + * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases. + * + * The function operates on a single sample of data and each call to the function returns the processed output. + * The library provides separate functions for Q31 and floating-point data types. + * \par Algorithm + * \image html clarkeInvFormula.gif + * where pIa and pIb are the instantaneous stator phases and + * Ialpha and Ibeta are the two coordinates of time invariant vector. + * \par Fixed-Point Behavior + * Care must be taken when using the Q31 version of the Clarke transform. + * In particular, the overflow and saturation behavior of the accumulator used must be considered. + * Refer to the function specific documentation below for usage guidelines. + */ + + + + /** + * @ingroup inv_clarke + * @brief Floating-point Inverse Clarke transform + * @param[in] Ialpha input two-phase orthogonal vector axis alpha + * @param[in] Ibeta input two-phase orthogonal vector axis beta + * @param[out] pIa points to output three-phase coordinate a + * @param[out] pIb points to output three-phase coordinate b + */ + __STATIC_FORCEINLINE void arm_inv_clarke_f32( + float32_t Ialpha, + float32_t Ibeta, + float32_t * pIa, + float32_t * pIb) + { + /* Calculating pIa from Ialpha by equation pIa = Ialpha */ + *pIa = Ialpha; + + /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */ + *pIb = -0.5f * Ialpha + 0.8660254039f * Ibeta; + } + + +/** + @ingroup inv_clarke + @brief Inverse Clarke transform for Q31 version + @param[in] Ialpha input two-phase orthogonal vector axis alpha + @param[in] Ibeta input two-phase orthogonal vector axis beta + @param[out] pIa points to output three-phase coordinate a + @param[out] pIb points to output three-phase coordinate b + + \par Scaling and Overflow Behavior + The function is implemented using an internal 32-bit accumulator. + The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. + There is saturation on the subtraction, hence there is no risk of overflow. + */ +__STATIC_FORCEINLINE void arm_inv_clarke_q31( + q31_t Ialpha, + q31_t Ibeta, + q31_t * pIa, + q31_t * pIb) + { + q31_t product1, product2; /* Temporary variables used to store intermediate results */ + + /* Calculating pIa from Ialpha by equation pIa = Ialpha */ + *pIa = Ialpha; + + /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */ + product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31); + + /* Intermediate product is calculated by (1/sqrt(3) * pIb) */ + product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31); + + /* pIb is calculated by subtracting the products */ + *pIb = __QSUB(product2, product1); + } + + + + + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _CONTROLLER_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/controller_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/controller_functions_f16.h new file mode 100755 index 0000000..a4622ec --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/controller_functions_f16.h @@ -0,0 +1,41 @@ +/****************************************************************************** + * @file controller_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef CONTROLLER_FUNCTIONS_F16_H_ +#define CONTROLLER_FUNCTIONS_F16_H_ + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _CONTROLLER_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/debug.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/debug.h new file mode 100755 index 0000000..587f8a7 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/debug.h @@ -0,0 +1,149 @@ +/****************************************************************************** + * @file basic_math_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef DEBUG_FUNCTIONS_H_ +#define DEBUG_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/matrix_functions.h" +#include "dsp/matrix_functions_f16.h" + + + +#ifdef __cplusplus +#include +extern "C" +{ +#else +#include +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) +#define PROW_f16(S,NB) \ +{ \ + printf("{%f",(double)(S)[0]); \ + for(unsigned int i=1;i<(NB) ;i++) \ + { \ + printf(",%f",(double)(S)[i]);\ + } \ + printf("}"); \ +}; + +#define PV_f16(S,V,NB)\ +{ \ + printf("%s=",(S)); \ + PROW_f16((V),(NB)); \ + printf(";\n"); \ +}; + +#define PM_f16(S,M) \ +{ \ + printf("%s={",(S)); \ + for(unsigned int row=0;row<(M)->numRows;row++) \ + { \ + if (row != 0) \ + { \ + printf("\n,"); \ + } \ + PROW_f16((M)->pData + row * (M)->numCols, (M)->numCols);\ + } \ + printf("};\n"); \ +} + +#endif + +#define PROW_f32(S,NB) \ +{ \ + printf("{%f",(double)(S)[0]); \ + for(unsigned int i=1;i<(NB) ;i++) \ + { \ + printf(",%f",(double)(S)[i]);\ + } \ + printf("}"); \ +}; + +#define PV_f32(S,V,NB)\ +{ \ + printf("%s=",(S)); \ + PROW_f32((V),(NB)); \ + printf(";\n"); \ +}; + +#define PM_f32(S,M) \ +{ \ + printf("%s={",(S)); \ + for(unsigned int row=0;row<(M)->numRows;row++) \ + { \ + if (row != 0) \ + { \ + printf("\n,"); \ + } \ + PROW_f32((M)->pData + row * (M)->numCols, (M)->numCols);\ + } \ + printf("};\n"); \ +} + +#define PROW_f64(S,NB) \ +{ \ + printf("{%.20g",(double)(S)[0]); \ + for(unsigned int i=1;i<(NB) ;i++) \ + { \ + printf(",%.20g",(double)(S)[i]);\ + } \ + printf("}"); \ +}; + +#define PV_f64(S,V,NB) \ +{ \ + printf("%s=",(S)); \ + PROW_f64((V),(NB));\ + printf(";\n"); \ +}; + +#define PM_f64(S,M) \ +{ \ + printf("%s={",(S)); \ + for(unsigned int row=0;row<(M)->numRows;row++) \ + { \ + if (row != 0) \ + { \ + printf("\n,"); \ + } \ + PROW_f64((M)->pData + row * (M)->numCols, (M)->numCols);\ + } \ + printf("};\n"); \ +} + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _DEBUG_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/distance_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/distance_functions.h new file mode 100755 index 0000000..dac4b62 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/distance_functions.h @@ -0,0 +1,386 @@ +/****************************************************************************** + * @file distance_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef DISTANCE_FUNCTIONS_H_ +#define DISTANCE_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/statistics_functions.h" +#include "dsp/basic_math_functions.h" +#include "dsp/fast_math_functions.h" +#include "dsp/matrix_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + +/** + * @defgroup groupDistance Distance Functions + * + * Distance functions for use with clustering algorithms. + * There are distance functions for float vectors and boolean vectors. + * + */ + +/* 6.14 bug */ +#if defined (__ARMCC_VERSION) && (__ARMCC_VERSION >= 6100100) && (__ARMCC_VERSION < 6150001) + +__attribute__((weak)) float __powisf2(float a, int b); + +#endif + +/** + * @brief Euclidean distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float32_t arm_euclidean_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Euclidean distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float64_t arm_euclidean_distance_f64(const float64_t *pA,const float64_t *pB, uint32_t blockSize); + +/** + * @brief Bray-Curtis distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_braycurtis_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Canberra distance between two vectors + * + * This function may divide by zero when samples pA[i] and pB[i] are both zero. + * The result of the computation will be correct. So the division per zero may be + * ignored. + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_canberra_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + + +/** + * @brief Chebyshev distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_chebyshev_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + + +/** + * @brief Chebyshev distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float64_t arm_chebyshev_distance_f64(const float64_t *pA,const float64_t *pB, uint32_t blockSize); + + +/** + * @brief Cityblock (Manhattan) distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_cityblock_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Cityblock (Manhattan) distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float64_t arm_cityblock_distance_f64(const float64_t *pA,const float64_t *pB, uint32_t blockSize); + +/** + * @brief Correlation distance between two vectors + * + * The input vectors are modified in place ! + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ +float32_t arm_correlation_distance_f32(float32_t *pA,float32_t *pB, uint32_t blockSize); + +/** + * @brief Cosine distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float32_t arm_cosine_distance_f32(const float32_t *pA,const float32_t *pB, uint32_t blockSize); + +/** + * @brief Cosine distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float64_t arm_cosine_distance_f64(const float64_t *pA,const float64_t *pB, uint32_t blockSize); + +/** + * @brief Jensen-Shannon distance between two vectors + * + * This function is assuming that elements of second vector are > 0 + * and 0 only when the corresponding element of first vector is 0. + * Otherwise the result of the computation does not make sense + * and for speed reasons, the cases returning NaN or Infinity are not + * managed. + * + * When the function is computing x log (x / y) with x 0 and y 0, + * it will compute the right value (0) but a division per zero will occur + * and should be ignored in client code. + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + * + */ + +float32_t arm_jensenshannon_distance_f32(const float32_t *pA,const float32_t *pB,uint32_t blockSize); + +/** + * @brief Minkowski distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] n Norm order (>= 2) + * @param[in] blockSize vector length + * @return distance + * + */ + + + +float32_t arm_minkowski_distance_f32(const float32_t *pA,const float32_t *pB, int32_t order, uint32_t blockSize); + +/** + * @brief Dice distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] order Distance order + * @param[in] blockSize Number of samples + * @return distance + * + */ + + +float32_t arm_dice_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Hamming distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_hamming_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Jaccard distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_jaccard_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Kulsinski distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_kulsinski_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Roger Stanimoto distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_rogerstanimoto_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Russell-Rao distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_russellrao_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Sokal-Michener distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_sokalmichener_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Sokal-Sneath distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_sokalsneath_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +/** + * @brief Yule distance between two vectors + * + * @param[in] pA First vector of packed booleans + * @param[in] pB Second vector of packed booleans + * @param[in] numberOfBools Number of booleans + * @return distance + * + */ + +float32_t arm_yule_distance(const uint32_t *pA, const uint32_t *pB, uint32_t numberOfBools); + +typedef enum + { + ARM_DTW_SAKOE_CHIBA_WINDOW = 1, + /*ARM_DTW_ITAKURA_WINDOW = 2,*/ + ARM_DTW_SLANTED_BAND_WINDOW = 3 + } arm_dtw_window; + +/** + * @brief Window for dynamic time warping computation + * @param[in] windowType Type of window + * @param[in] windowSize Window size + * @param[in,out] pWindow Window + * @return Error if window type not recognized + * + */ +arm_status arm_dtw_init_window_q7(const arm_dtw_window windowType, + const int32_t windowSize, + arm_matrix_instance_q7 *pWindow); + +/** + * @brief Dynamic Time Warping distance + * @param[in] pDistance Distance matrix (Query rows * Template columns) + * @param[in] pWindow Windowing (can be NULL if no windowing used) + * @param[out] pDTW Temporary cost buffer (same size) + * @param[out] distance Distance + * @return Error in case no path can be found with window constraint + * + */ + +arm_status arm_dtw_distance_f32(const arm_matrix_instance_f32 *pDistance, + const arm_matrix_instance_q7 *pWindow, + arm_matrix_instance_f32 *pDTW, + float32_t *distance); + + +/** + * @brief Mapping between query and template + * @param[in] pDTW Cost matrix (Query rows * Template columns) + * @param[out] pPath Warping path in cost matrix 2*(nb rows + nb columns) + * @param[out] pathLength Length of path in number of points + * + */ + +void arm_dtw_path_f32(const arm_matrix_instance_f32 *pDTW, + int16_t *pPath, + uint32_t *pathLength); +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _DISTANCE_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/distance_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/distance_functions_f16.h new file mode 100755 index 0000000..4a4e70f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/distance_functions_f16.h @@ -0,0 +1,170 @@ +/****************************************************************************** + * @file distance_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef DISTANCE_FUNCTIONS_F16_H_ +#define DISTANCE_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +/* 6.14 bug */ +#if defined (__ARMCC_VERSION) && (__ARMCC_VERSION >= 6100100) && (__ARMCC_VERSION < 6150001) +/* Defined in minkowski_f32 */ +__attribute__((weak)) float __powisf2(float a, int b); +#endif + +#include "dsp/statistics_functions_f16.h" +#include "dsp/basic_math_functions_f16.h" + +#include "dsp/fast_math_functions_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + * @brief Euclidean distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_euclidean_distance_f16(const float16_t *pA,const float16_t *pB, uint32_t blockSize); + + +/** + * @brief Bray-Curtis distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_braycurtis_distance_f16(const float16_t *pA,const float16_t *pB, uint32_t blockSize); + +/** + * @brief Canberra distance between two vectors + * + * This function may divide by zero when samples pA[i] and pB[i] are both zero. + * The result of the computation will be correct. So the division per zero may be + * ignored. + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_canberra_distance_f16(const float16_t *pA,const float16_t *pB, uint32_t blockSize); + + +/** + * @brief Chebyshev distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_chebyshev_distance_f16(const float16_t *pA,const float16_t *pB, uint32_t blockSize); + + +/** + * @brief Cityblock (Manhattan) distance between two vectors + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_cityblock_distance_f16(const float16_t *pA,const float16_t *pB, uint32_t blockSize); + + +/** + * @brief Correlation distance between two vectors + * + * The input vectors are modified in place ! + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_correlation_distance_f16(float16_t *pA,float16_t *pB, uint32_t blockSize); + + +/** + * @brief Cosine distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_cosine_distance_f16(const float16_t *pA,const float16_t *pB, uint32_t blockSize); + + +/** + * @brief Jensen-Shannon distance between two vectors + * + * This function is assuming that elements of second vector are > 0 + * and 0 only when the corresponding element of first vector is 0. + * Otherwise the result of the computation does not make sense + * and for speed reasons, the cases returning NaN or Infinity are not + * managed. + * + * When the function is computing x log (x / y) with x 0 and y 0, + * it will compute the right value (0) but a division per zero will occur + * and should be ignored in client code. + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_jensenshannon_distance_f16(const float16_t *pA,const float16_t *pB,uint32_t blockSize); + + +/** + * @brief Minkowski distance between two vectors + * + * @param[in] pA First vector + * @param[in] pB Second vector + * @param[in] n Norm order (>= 2) + * @param[in] blockSize vector length + * @return distance + */ +float16_t arm_minkowski_distance_f16(const float16_t *pA,const float16_t *pB, int32_t order, uint32_t blockSize); + + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _DISTANCE_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/fast_math_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/fast_math_functions.h new file mode 100755 index 0000000..0bd536b --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/fast_math_functions.h @@ -0,0 +1,379 @@ +/****************************************************************************** + * @file fast_math_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef FAST_MATH_FUNCTIONS_H_ +#define FAST_MATH_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/basic_math_functions.h" + + +#ifdef __cplusplus +#include +extern "C" +{ +#else +#include +#endif + + /** + * @brief Macros required for SINE and COSINE Fast math approximations + */ + +#define FAST_MATH_TABLE_SIZE 512 +#define FAST_MATH_Q31_SHIFT (32 - 10) +#define FAST_MATH_Q15_SHIFT (16 - 10) + +#ifndef PI + #define PI 3.14159265358979f +#endif + +#ifndef PI_F64 + #define PI_F64 3.14159265358979323846 +#endif + + + +/** + * @defgroup groupFastMath Fast Math Functions + * This set of functions provides a fast approximation to sine, cosine, and square root. + * As compared to most of the other functions in the CMSIS math library, the fast math functions + * operate on individual values and not arrays. + * There are separate functions for Q15, Q31, and floating-point data. + * + */ + + + /** + * @brief Fast approximation to the trigonometric sine function for floating-point data. + * @param[in] x input value in radians. + * @return sin(x). + */ + float32_t arm_sin_f32( + float32_t x); + + + /** + * @brief Fast approximation to the trigonometric sine function for Q31 data. + * @param[in] x Scaled input value in radians. + * @return sin(x). + */ + q31_t arm_sin_q31( + q31_t x); + + /** + * @brief Fast approximation to the trigonometric sine function for Q15 data. + * @param[in] x Scaled input value in radians. + * @return sin(x). + */ + q15_t arm_sin_q15( + q15_t x); + + + /** + * @brief Fast approximation to the trigonometric cosine function for floating-point data. + * @param[in] x input value in radians. + * @return cos(x). + */ + float32_t arm_cos_f32( + float32_t x); + + + /** + * @brief Fast approximation to the trigonometric cosine function for Q31 data. + * @param[in] x Scaled input value in radians. + * @return cos(x). + */ + q31_t arm_cos_q31( + q31_t x); + + + /** + * @brief Fast approximation to the trigonometric cosine function for Q15 data. + * @param[in] x Scaled input value in radians. + * @return cos(x). + */ + q15_t arm_cos_q15( + q15_t x); + + +/** + @brief Floating-point vector of log values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vlog_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + +/** + @brief Floating-point vector of log values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vlog_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief q31 vector of log values. + * @param[in] pSrc points to the input vector in q31 + * @param[out] pDst points to the output vector in q5.26 + * @param[in] blockSize number of samples in each vector + */ + void arm_vlog_q31(const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief q15 vector of log values. + * @param[in] pSrc points to the input vector in q15 + * @param[out] pDst points to the output vector in q4.11 + * @param[in] blockSize number of samples in each vector + */ + void arm_vlog_q15(const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + +/** + @brief Floating-point vector of exp values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vexp_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + +/** + @brief Floating-point vector of exp values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vexp_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @defgroup SQRT Square Root + * + * Computes the square root of a number. + * There are separate functions for Q15, Q31, and floating-point data types. + * The square root function is computed using the Newton-Raphson algorithm. + * This is an iterative algorithm of the form: + * 
+   *      x1 = x0 - f(x0)/f'(x0)
+   *
+ * where x1 is the current estimate, + * x0 is the previous estimate, and + * f'(x0) is the derivative of f() evaluated at x0. + * For the square root function, the algorithm reduces to: + * 
+   *     x0 = in/2                         [initial guess]
+   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
+   *
+ */ + + + /** + * @addtogroup SQRT + * @{ + */ + +/** + @brief Floating-point square root function. + @param[in] in input value + @param[out] pOut square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +__STATIC_FORCEINLINE arm_status arm_sqrt_f32( + const float32_t in, + float32_t * pOut) + { + if (in >= 0.0f) + { +#if defined ( __CC_ARM ) + #if defined __TARGET_FPU_VFP + *pOut = __sqrtf(in); + #else + *pOut = sqrtf(in); + #endif + +#elif defined ( __ICCARM__ ) + #if defined __ARMVFP__ + __ASM("VSQRT.F32 %0,%1" : "=t"(*pOut) : "t"(in)); + #else + *pOut = sqrtf(in); + #endif + +#elif defined ( __ARMCC_VERSION ) && ( __ARMCC_VERSION >= 6010050 ) + *pOut = _sqrtf(in); +#elif defined(__GNUC_PYTHON__) + *pOut = sqrtf(in); +#elif defined ( __GNUC__ ) + #if defined (__VFP_FP__) && !defined(__SOFTFP__) + __ASM("VSQRT.F32 %0,%1" : "=t"(*pOut) : "t"(in)); + #else + *pOut = sqrtf(in); + #endif +#else + *pOut = sqrtf(in); +#endif + + return (ARM_MATH_SUCCESS); + } + else + { + *pOut = 0.0f; + return (ARM_MATH_ARGUMENT_ERROR); + } + } + + +/** + @brief Q31 square root function. + @param[in] in input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF + @param[out] pOut points to square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +arm_status arm_sqrt_q31( + q31_t in, + q31_t * pOut); + + +/** + @brief Q15 square root function. + @param[in] in input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF + @param[out] pOut points to square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +arm_status arm_sqrt_q15( + q15_t in, + q15_t * pOut); + + + + /** + * @} end of SQRT group + */ + + /** + @brief Fixed point division + @param[in] numerator Numerator + @param[in] denominator Denominator + @param[out] quotient Quotient value normalized between -1.0 and 1.0 + @param[out] shift Shift left value to get the unnormalized quotient + @return error status + + When dividing by 0, an error ARM_MATH_NANINF is returned. And the quotient is forced + to the saturated negative or positive value. + */ + +arm_status arm_divide_q15(q15_t numerator, + q15_t denominator, + q15_t *quotient, + int16_t *shift); + + /** + @brief Fixed point division + @param[in] numerator Numerator + @param[in] denominator Denominator + @param[out] quotient Quotient value normalized between -1.0 and 1.0 + @param[out] shift Shift left value to get the unnormalized quotient + @return error status + + When dividing by 0, an error ARM_MATH_NANINF is returned. And the quotient is forced + to the saturated negative or positive value. + */ + +arm_status arm_divide_q31(q31_t numerator, + q31_t denominator, + q31_t *quotient, + int16_t *shift); + + + + /** + @brief Arc tangent in radian of y/x using sign of x and y to determine right quadrant. + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result + @return error status. + */ + arm_status arm_atan2_f32(float32_t y,float32_t x,float32_t *result); + + + /** + @brief Arc tangent in radian of y/x using sign of x and y to determine right quadrant. + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result in Q2.29 + @return error status. + */ + arm_status arm_atan2_q31(q31_t y,q31_t x,q31_t *result); + + /** + @brief Arc tangent in radian of y/x using sign of x and y to determine right quadrant. + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result in Q2.13 + @return error status. + */ + arm_status arm_atan2_q15(q15_t y,q15_t x,q15_t *result); + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _FAST_MATH_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/fast_math_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/fast_math_functions_f16.h new file mode 100755 index 0000000..1fa45a8 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/fast_math_functions_f16.h @@ -0,0 +1,122 @@ +/****************************************************************************** + * @file fast_math_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef FAST_MATH_FUNCTIONS_F16_H_ +#define FAST_MATH_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +/* For sqrt_f32 */ +#include "dsp/fast_math_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + /** + * @addtogroup SQRT + * @{ + */ + +/** + @brief Floating-point square root function. + @param[in] in input value + @param[out] pOut square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ +__STATIC_FORCEINLINE arm_status arm_sqrt_f16( + float16_t in, + float16_t * pOut) + { + float32_t r; + arm_status status; + status=arm_sqrt_f32((float32_t)in,&r); + *pOut=(float16_t)r; + return(status); + } + + +/** + @} end of SQRT group + */ + +/** + @brief Floating-point vector of log values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vlog_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + +/** + @brief Floating-point vector of exp values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vexp_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + /** + @brief Floating-point vector of inverse values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + void arm_vinverse_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + /** + @brief Arc tangent in radian of y/x using sign of x and y to determine right quadrant. + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result + @return error status. + */ + arm_status arm_atan2_f16(float16_t y,float16_t x,float16_t *result); + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _FAST_MATH_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/filtering_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/filtering_functions.h new file mode 100755 index 0000000..98b2168 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/filtering_functions.h @@ -0,0 +1,2570 @@ +/****************************************************************************** + * @file filtering_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef FILTERING_FUNCTIONS_H_ +#define FILTERING_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/support_functions.h" +#include "dsp/fast_math_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + +#define DELTA_Q31 ((q31_t)(0x100)) +#define DELTA_Q15 ((q15_t)0x5) + +/** + * @defgroup groupFilters Filtering Functions + */ + + /** + * @brief Instance structure for the Q7 FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + q7_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const q7_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + } arm_fir_instance_q7; + + /** + * @brief Instance structure for the Q15 FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + } arm_fir_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + } arm_fir_instance_q31; + + /** + * @brief Instance structure for the floating-point FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + } arm_fir_instance_f32; + + /** + * @brief Instance structure for the floating-point FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + float64_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const float64_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + } arm_fir_instance_f64; + + /** + * @brief Processing function for the Q7 FIR filter. + * @param[in] S points to an instance of the Q7 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_q7( + const arm_fir_instance_q7 * S, + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q7 FIR filter. + * @param[in,out] S points to an instance of the Q7 FIR structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed. + * + * For the MVE version, the coefficient length must be a multiple of 16. + * You can pad with zeros if you have less coefficients. + */ + void arm_fir_init_q7( + arm_fir_instance_q7 * S, + uint16_t numTaps, + const q7_t * pCoeffs, + q7_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the Q15 FIR filter. + * @param[in] S points to an instance of the Q15 FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_q15( + const arm_fir_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the fast Q15 FIR filter (fast version). + * @param[in] S points to an instance of the Q15 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_fast_q15( + const arm_fir_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q15 FIR filter. + * @param[in,out] S points to an instance of the Q15 FIR filter structure. + * @param[in] numTaps Number of filter coefficients in the filter. Must be even and greater than or equal to 4. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + * @return The function returns either + * ARM_MATH_SUCCESS if initialization was successful or + * ARM_MATH_ARGUMENT_ERROR if numTaps is not a supported value. + * + * For the MVE version, the coefficient length must be a multiple of 8. + * You can pad with zeros if you have less coefficients. + * + */ + arm_status arm_fir_init_q15( + arm_fir_instance_q15 * S, + uint16_t numTaps, + const q15_t * pCoeffs, + q15_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the Q31 FIR filter. + * @param[in] S points to an instance of the Q31 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_q31( + const arm_fir_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the fast Q31 FIR filter (fast version). + * @param[in] S points to an instance of the Q31 FIR filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_fast_q31( + const arm_fir_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q31 FIR filter. + * @param[in,out] S points to an instance of the Q31 FIR structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + * + * For the MVE version, the coefficient length must be a multiple of 4. + * You can pad with zeros if you have less coefficients. + */ + void arm_fir_init_q31( + arm_fir_instance_q31 * S, + uint16_t numTaps, + const q31_t * pCoeffs, + q31_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the floating-point FIR filter. + * @param[in] S points to an instance of the floating-point FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_f32( + const arm_fir_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the floating-point FIR filter. + * @param[in] S points to an instance of the floating-point FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_f64( + const arm_fir_instance_f64 * S, + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point FIR filter. + * @param[in,out] S points to an instance of the floating-point FIR filter structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + */ + void arm_fir_init_f32( + arm_fir_instance_f32 * S, + uint16_t numTaps, + const float32_t * pCoeffs, + float32_t * pState, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point FIR filter. + * @param[in,out] S points to an instance of the floating-point FIR filter structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + */ + void arm_fir_init_f64( + arm_fir_instance_f64 * S, + uint16_t numTaps, + const float64_t * pCoeffs, + float64_t * pState, + uint32_t blockSize); + + /** + * @brief Instance structure for the Q15 Biquad cascade filter. + */ + typedef struct + { + int8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + q15_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const q15_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + int8_t postShift; /**< Additional shift, in bits, applied to each output sample. */ + } arm_biquad_casd_df1_inst_q15; + + /** + * @brief Instance structure for the Q31 Biquad cascade filter. + */ + typedef struct + { + uint32_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + q31_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const q31_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + uint8_t postShift; /**< Additional shift, in bits, applied to each output sample. */ + } arm_biquad_casd_df1_inst_q31; + + /** + * @brief Instance structure for the floating-point Biquad cascade filter. + */ + typedef struct + { + uint32_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float32_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const float32_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_casd_df1_inst_f32; + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + /** + * @brief Instance structure for the modified Biquad coefs required by vectorized code. + */ + typedef struct + { + float32_t coeffs[8][4]; /**< Points to the array of modified coefficients. The array is of length 32. There is one per stage */ + } arm_biquad_mod_coef_f32; +#endif + + /** + * @brief Processing function for the Q15 Biquad cascade filter. + * @param[in] S points to an instance of the Q15 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_q15( + const arm_biquad_casd_df1_inst_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q15 Biquad cascade filter. + * @param[in,out] S points to an instance of the Q15 Biquad cascade structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] postShift Shift to be applied to the output. Varies according to the coefficients format + */ + void arm_biquad_cascade_df1_init_q15( + arm_biquad_casd_df1_inst_q15 * S, + uint8_t numStages, + const q15_t * pCoeffs, + q15_t * pState, + int8_t postShift); + + /** + * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q15 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_fast_q15( + const arm_biquad_casd_df1_inst_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the Q31 Biquad cascade filter + * @param[in] S points to an instance of the Q31 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_q31( + const arm_biquad_casd_df1_inst_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q31 Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_fast_q31( + const arm_biquad_casd_df1_inst_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the Q31 Biquad cascade filter. + * @param[in,out] S points to an instance of the Q31 Biquad cascade structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] postShift Shift to be applied to the output. Varies according to the coefficients format + */ + void arm_biquad_cascade_df1_init_q31( + arm_biquad_casd_df1_inst_q31 * S, + uint8_t numStages, + const q31_t * pCoeffs, + q31_t * pState, + int8_t postShift); + + /** + * @brief Processing function for the floating-point Biquad cascade filter. + * @param[in] S points to an instance of the floating-point Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_f32( + const arm_biquad_casd_df1_inst_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point Biquad cascade filter. + * @param[in,out] S points to an instance of the floating-point Biquad cascade structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pCoeffsMod points to the modified filter coefficients (only MVE version). + * @param[in] pState points to the state buffer. + */ +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + void arm_biquad_cascade_df1_mve_init_f32( + arm_biquad_casd_df1_inst_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + arm_biquad_mod_coef_f32 * pCoeffsMod, + float32_t * pState); +#endif + + void arm_biquad_cascade_df1_init_f32( + arm_biquad_casd_df1_inst_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + +/** + * @brief Convolution of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the location where the output result is written. Length srcALen+srcBLen-1. + */ + void arm_conv_f32( + const float32_t * pSrcA, + uint32_t srcALen, + const float32_t * pSrcB, + uint32_t srcBLen, + float32_t * pDst); + + + /** + * @brief Convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + */ + void arm_conv_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + +/** + * @brief Convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the location where the output result is written. Length srcALen+srcBLen-1. + */ + void arm_conv_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + + /** + * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_fast_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + + /** + * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + */ + void arm_conv_fast_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Convolution of Q31 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + + /** + * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_fast_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + + /** + * @brief Convolution of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + * @param[in] pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen). + */ + void arm_conv_opt_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Convolution of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length srcALen+srcBLen-1. + */ + void arm_conv_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst); + + + /** + * @brief Partial convolution of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_f32( + const float32_t * pSrcA, + uint32_t srcALen, + const float32_t * pSrcB, + uint32_t srcBLen, + float32_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Partial convolution of Q15 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_fast_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @param[in] pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer of size min(srcALen, srcBLen). + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_fast_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + uint32_t firstIndex, + uint32_t numPoints, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Partial convolution of Q31 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_fast_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Partial convolution of Q7 sequences + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @param[in] pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen). + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_opt_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + uint32_t firstIndex, + uint32_t numPoints, + q15_t * pScratch1, + q15_t * pScratch2); + + +/** + * @brief Partial convolution of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data + * @param[in] firstIndex is the first output sample to start with. + * @param[in] numPoints is the number of output points to be computed. + * @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2]. + */ + arm_status arm_conv_partial_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + uint32_t firstIndex, + uint32_t numPoints); + + + /** + * @brief Instance structure for the Q15 FIR decimator. + */ + typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR decimator. + */ + typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_q31; + +/** + @brief Instance structure for single precision floating-point FIR decimator. + */ +typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_f32; + + /** + @brief Instance structure for double precision floating-point FIR decimator. + */ + typedef struct + { + uint8_t M; /**< decimation factor. */ + uint16_t numTaps; /**< number of coefficients in the filter. */ + const float64_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + float64_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + } arm_fir_decimate_instance_f64; + + /** + @brief Processing function for floating-point FIR decimator. + @param[in] S points to an instance of the floating-point FIR decimator structure + @param[in] pSrc points to the block of input data + @param[out] pDst points to the block of output data + @param[in] blockSize number of samples to process + */ + void arm_fir_decimate_f64( + const arm_fir_decimate_instance_f64 * S, + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + + /** + @brief Initialization function for the floating-point FIR decimator. + @param[in,out] S points to an instance of the floating-point FIR decimator structure + @param[in] numTaps number of coefficients in the filter + @param[in] M decimation factor + @param[in] pCoeffs points to the filter coefficients + @param[in] pState points to the state buffer + @param[in] blockSize number of input samples to process per call + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_LENGTH_ERROR : blockSize is not a multiple of M + */ + arm_status arm_fir_decimate_init_f64( + arm_fir_decimate_instance_f64 * S, + uint16_t numTaps, + uint8_t M, + const float64_t * pCoeffs, + float64_t * pState, + uint32_t blockSize); + + + /** + @brief Processing function for floating-point FIR decimator. + @param[in] S points to an instance of the floating-point FIR decimator structure + @param[in] pSrc points to the block of input data + @param[out] pDst points to the block of output data + @param[in] blockSize number of samples to process + */ +void arm_fir_decimate_f32( + const arm_fir_decimate_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + +/** + @brief Initialization function for the floating-point FIR decimator. + @param[in,out] S points to an instance of the floating-point FIR decimator structure + @param[in] numTaps number of coefficients in the filter + @param[in] M decimation factor + @param[in] pCoeffs points to the filter coefficients + @param[in] pState points to the state buffer + @param[in] blockSize number of input samples to process per call + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_LENGTH_ERROR : blockSize is not a multiple of M + */ +arm_status arm_fir_decimate_init_f32( + arm_fir_decimate_instance_f32 * S, + uint16_t numTaps, + uint8_t M, + const float32_t * pCoeffs, + float32_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 FIR decimator. + * @param[in] S points to an instance of the Q15 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_q15( + const arm_fir_decimate_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q15 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_fast_q15( + const arm_fir_decimate_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q15 FIR decimator. + * @param[in,out] S points to an instance of the Q15 FIR decimator structure. + * @param[in] numTaps number of coefficients in the filter. + * @param[in] M decimation factor. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * blockSize is not a multiple of M. + */ + arm_status arm_fir_decimate_init_q15( + arm_fir_decimate_instance_q15 * S, + uint16_t numTaps, + uint8_t M, + const q15_t * pCoeffs, + q15_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 FIR decimator. + * @param[in] S points to an instance of the Q31 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_q31( + const arm_fir_decimate_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4. + * @param[in] S points to an instance of the Q31 FIR decimator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_decimate_fast_q31( + const arm_fir_decimate_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 FIR decimator. + * @param[in,out] S points to an instance of the Q31 FIR decimator structure. + * @param[in] numTaps number of coefficients in the filter. + * @param[in] M decimation factor. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * blockSize is not a multiple of M. + */ + arm_status arm_fir_decimate_init_q31( + arm_fir_decimate_instance_q31 * S, + uint16_t numTaps, + uint8_t M, + const q31_t * pCoeffs, + q31_t * pState, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 FIR interpolator. + */ + typedef struct + { + uint8_t L; /**< upsample factor. */ + uint16_t phaseLength; /**< length of each polyphase filter component. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length L*phaseLength. */ + q15_t *pState; /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */ + } arm_fir_interpolate_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR interpolator. + */ + typedef struct + { + uint8_t L; /**< upsample factor. */ + uint16_t phaseLength; /**< length of each polyphase filter component. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length L*phaseLength. */ + q31_t *pState; /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */ + } arm_fir_interpolate_instance_q31; + + /** + * @brief Instance structure for the floating-point FIR interpolator. + */ + typedef struct + { + uint8_t L; /**< upsample factor. */ + uint16_t phaseLength; /**< length of each polyphase filter component. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length L*phaseLength. */ + float32_t *pState; /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */ + } arm_fir_interpolate_instance_f32; + + + /** + * @brief Processing function for the Q15 FIR interpolator. + * @param[in] S points to an instance of the Q15 FIR interpolator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_interpolate_q15( + const arm_fir_interpolate_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q15 FIR interpolator. + * @param[in,out] S points to an instance of the Q15 FIR interpolator structure. + * @param[in] L upsample factor. + * @param[in] numTaps number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * the filter length numTaps is not a multiple of the interpolation factor L. + */ + arm_status arm_fir_interpolate_init_q15( + arm_fir_interpolate_instance_q15 * S, + uint8_t L, + uint16_t numTaps, + const q15_t * pCoeffs, + q15_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 FIR interpolator. + * @param[in] S points to an instance of the Q15 FIR interpolator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_interpolate_q31( + const arm_fir_interpolate_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 FIR interpolator. + * @param[in,out] S points to an instance of the Q31 FIR interpolator structure. + * @param[in] L upsample factor. + * @param[in] numTaps number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * the filter length numTaps is not a multiple of the interpolation factor L. + */ + arm_status arm_fir_interpolate_init_q31( + arm_fir_interpolate_instance_q31 * S, + uint8_t L, + uint16_t numTaps, + const q31_t * pCoeffs, + q31_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the floating-point FIR interpolator. + * @param[in] S points to an instance of the floating-point FIR interpolator structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_interpolate_f32( + const arm_fir_interpolate_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the floating-point FIR interpolator. + * @param[in,out] S points to an instance of the floating-point FIR interpolator structure. + * @param[in] L upsample factor. + * @param[in] numTaps number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of input samples to process per call. + * @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if + * the filter length numTaps is not a multiple of the interpolation factor L. + */ + arm_status arm_fir_interpolate_init_f32( + arm_fir_interpolate_instance_f32 * S, + uint8_t L, + uint16_t numTaps, + const float32_t * pCoeffs, + float32_t * pState, + uint32_t blockSize); + + + /** + * @brief Instance structure for the high precision Q31 Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + q63_t *pState; /**< points to the array of state coefficients. The array is of length 4*numStages. */ + const q31_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + uint8_t postShift; /**< additional shift, in bits, applied to each output sample. */ + } arm_biquad_cas_df1_32x64_ins_q31; + + + /** + * @param[in] S points to an instance of the high precision Q31 Biquad cascade filter structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cas_df1_32x64_q31( + const arm_biquad_cas_df1_32x64_ins_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @param[in,out] S points to an instance of the high precision Q31 Biquad cascade filter structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] postShift shift to be applied to the output. Varies according to the coefficients format + */ + void arm_biquad_cas_df1_32x64_init_q31( + arm_biquad_cas_df1_32x64_ins_q31 * S, + uint8_t numStages, + const q31_t * pCoeffs, + q63_t * pState, + uint8_t postShift); + + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float32_t *pState; /**< points to the array of state coefficients. The array is of length 2*numStages. */ + const float32_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_df2T_instance_f32; + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float32_t *pState; /**< points to the array of state coefficients. The array is of length 4*numStages. */ + const float32_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_stereo_df2T_instance_f32; + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float64_t *pState; /**< points to the array of state coefficients. The array is of length 2*numStages. */ + const float64_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_df2T_instance_f64; + + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df2T_f32( + const arm_biquad_cascade_df2T_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_stereo_df2T_f32( + const arm_biquad_cascade_stereo_df2T_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df2T_f64( + const arm_biquad_cascade_df2T_instance_f64 * S, + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + +#if (defined(ARM_MATH_NEON) || defined(DOXYGEN)) +/** + @brief Compute new coefficient arrays for use in vectorized filter (Neon only). + @param[in] numStages number of 2nd order stages in the filter. + @param[in] pCoeffs points to the original filter coefficients. + @param[in] pComputedCoeffs points to the new computed coefficients for the vectorized version. +*/ +void arm_biquad_cascade_df2T_compute_coefs_f32( + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pComputedCoeffs); +#endif + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_df2T_init_f32( + arm_biquad_cascade_df2T_instance_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_stereo_df2T_init_f32( + arm_biquad_cascade_stereo_df2T_instance_f32 * S, + uint8_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_df2T_init_f64( + arm_biquad_cascade_df2T_instance_f64 * S, + uint8_t numStages, + const float64_t * pCoeffs, + float64_t * pState); + + + /** + * @brief Instance structure for the Q15 FIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of filter stages. */ + q15_t *pState; /**< points to the state variable array. The array is of length numStages. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numStages. */ + } arm_fir_lattice_instance_q15; + + /** + * @brief Instance structure for the Q31 FIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of filter stages. */ + q31_t *pState; /**< points to the state variable array. The array is of length numStages. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numStages. */ + } arm_fir_lattice_instance_q31; + + /** + * @brief Instance structure for the floating-point FIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of filter stages. */ + float32_t *pState; /**< points to the state variable array. The array is of length numStages. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numStages. */ + } arm_fir_lattice_instance_f32; + + + /** + * @brief Initialization function for the Q15 FIR lattice filter. + * @param[in] S points to an instance of the Q15 FIR lattice structure. + * @param[in] numStages number of filter stages. + * @param[in] pCoeffs points to the coefficient buffer. The array is of length numStages. + * @param[in] pState points to the state buffer. The array is of length numStages. + */ + void arm_fir_lattice_init_q15( + arm_fir_lattice_instance_q15 * S, + uint16_t numStages, + const q15_t * pCoeffs, + q15_t * pState); + + + /** + * @brief Processing function for the Q15 FIR lattice filter. + * @param[in] S points to an instance of the Q15 FIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_lattice_q15( + const arm_fir_lattice_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 FIR lattice filter. + * @param[in] S points to an instance of the Q31 FIR lattice structure. + * @param[in] numStages number of filter stages. + * @param[in] pCoeffs points to the coefficient buffer. The array is of length numStages. + * @param[in] pState points to the state buffer. The array is of length numStages. + */ + void arm_fir_lattice_init_q31( + arm_fir_lattice_instance_q31 * S, + uint16_t numStages, + const q31_t * pCoeffs, + q31_t * pState); + + + /** + * @brief Processing function for the Q31 FIR lattice filter. + * @param[in] S points to an instance of the Q31 FIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_fir_lattice_q31( + const arm_fir_lattice_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + +/** + * @brief Initialization function for the floating-point FIR lattice filter. + * @param[in] S points to an instance of the floating-point FIR lattice structure. + * @param[in] numStages number of filter stages. + * @param[in] pCoeffs points to the coefficient buffer. The array is of length numStages. + * @param[in] pState points to the state buffer. The array is of length numStages. + */ + void arm_fir_lattice_init_f32( + arm_fir_lattice_instance_f32 * S, + uint16_t numStages, + const float32_t * pCoeffs, + float32_t * pState); + + + /** + * @brief Processing function for the floating-point FIR lattice filter. + * @param[in] S points to an instance of the floating-point FIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_fir_lattice_f32( + const arm_fir_lattice_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 IIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of stages in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numStages+blockSize. */ + q15_t *pkCoeffs; /**< points to the reflection coefficient array. The array is of length numStages. */ + q15_t *pvCoeffs; /**< points to the ladder coefficient array. The array is of length numStages+1. */ + } arm_iir_lattice_instance_q15; + + /** + * @brief Instance structure for the Q31 IIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of stages in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numStages+blockSize. */ + q31_t *pkCoeffs; /**< points to the reflection coefficient array. The array is of length numStages. */ + q31_t *pvCoeffs; /**< points to the ladder coefficient array. The array is of length numStages+1. */ + } arm_iir_lattice_instance_q31; + + /** + * @brief Instance structure for the floating-point IIR lattice filter. + */ + typedef struct + { + uint16_t numStages; /**< number of stages in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numStages+blockSize. */ + float32_t *pkCoeffs; /**< points to the reflection coefficient array. The array is of length numStages. */ + float32_t *pvCoeffs; /**< points to the ladder coefficient array. The array is of length numStages+1. */ + } arm_iir_lattice_instance_f32; + + + /** + * @brief Processing function for the floating-point IIR lattice filter. + * @param[in] S points to an instance of the floating-point IIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_f32( + const arm_iir_lattice_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the floating-point IIR lattice filter. + * @param[in] S points to an instance of the floating-point IIR lattice structure. + * @param[in] numStages number of stages in the filter. + * @param[in] pkCoeffs points to the reflection coefficient buffer. The array is of length numStages. + * @param[in] pvCoeffs points to the ladder coefficient buffer. The array is of length numStages+1. + * @param[in] pState points to the state buffer. The array is of length numStages+blockSize-1. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_init_f32( + arm_iir_lattice_instance_f32 * S, + uint16_t numStages, + float32_t * pkCoeffs, + float32_t * pvCoeffs, + float32_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 IIR lattice filter. + * @param[in] S points to an instance of the Q31 IIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_q31( + const arm_iir_lattice_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 IIR lattice filter. + * @param[in] S points to an instance of the Q31 IIR lattice structure. + * @param[in] numStages number of stages in the filter. + * @param[in] pkCoeffs points to the reflection coefficient buffer. The array is of length numStages. + * @param[in] pvCoeffs points to the ladder coefficient buffer. The array is of length numStages+1. + * @param[in] pState points to the state buffer. The array is of length numStages+blockSize. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_init_q31( + arm_iir_lattice_instance_q31 * S, + uint16_t numStages, + q31_t * pkCoeffs, + q31_t * pvCoeffs, + q31_t * pState, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 IIR lattice filter. + * @param[in] S points to an instance of the Q15 IIR lattice structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_iir_lattice_q15( + const arm_iir_lattice_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + +/** + * @brief Initialization function for the Q15 IIR lattice filter. + * @param[in] S points to an instance of the fixed-point Q15 IIR lattice structure. + * @param[in] numStages number of stages in the filter. + * @param[in] pkCoeffs points to reflection coefficient buffer. The array is of length numStages. + * @param[in] pvCoeffs points to ladder coefficient buffer. The array is of length numStages+1. + * @param[in] pState points to state buffer. The array is of length numStages+blockSize. + * @param[in] blockSize number of samples to process per call. + */ + void arm_iir_lattice_init_q15( + arm_iir_lattice_instance_q15 * S, + uint16_t numStages, + q15_t * pkCoeffs, + q15_t * pvCoeffs, + q15_t * pState, + uint32_t blockSize); + + + /** + * @brief Instance structure for the floating-point LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + float32_t mu; /**< step size that controls filter coefficient updates. */ + } arm_lms_instance_f32; + + + /** + * @brief Processing function for floating-point LMS filter. + * @param[in] S points to an instance of the floating-point LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_f32( + const arm_lms_instance_f32 * S, + const float32_t * pSrc, + float32_t * pRef, + float32_t * pOut, + float32_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for floating-point LMS filter. + * @param[in] S points to an instance of the floating-point LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to the coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_init_f32( + arm_lms_instance_f32 * S, + uint16_t numTaps, + float32_t * pCoeffs, + float32_t * pState, + float32_t mu, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q15 LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q15_t mu; /**< step size that controls filter coefficient updates. */ + uint32_t postShift; /**< bit shift applied to coefficients. */ + } arm_lms_instance_q15; + + + /** + * @brief Initialization function for the Q15 LMS filter. + * @param[in] S points to an instance of the Q15 LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to the coefficient buffer. + * @param[in] pState points to the state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_init_q15( + arm_lms_instance_q15 * S, + uint16_t numTaps, + q15_t * pCoeffs, + q15_t * pState, + q15_t mu, + uint32_t blockSize, + uint32_t postShift); + + + /** + * @brief Processing function for Q15 LMS filter. + * @param[in] S points to an instance of the Q15 LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_q15( + const arm_lms_instance_q15 * S, + const q15_t * pSrc, + q15_t * pRef, + q15_t * pOut, + q15_t * pErr, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q31 LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q31_t mu; /**< step size that controls filter coefficient updates. */ + uint32_t postShift; /**< bit shift applied to coefficients. */ + } arm_lms_instance_q31; + + + /** + * @brief Processing function for Q31 LMS filter. + * @param[in] S points to an instance of the Q15 LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_q31( + const arm_lms_instance_q31 * S, + const q31_t * pSrc, + q31_t * pRef, + q31_t * pOut, + q31_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for Q31 LMS filter. + * @param[in] S points to an instance of the Q31 LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_init_q31( + arm_lms_instance_q31 * S, + uint16_t numTaps, + q31_t * pCoeffs, + q31_t * pState, + q31_t mu, + uint32_t blockSize, + uint32_t postShift); + + + /** + * @brief Instance structure for the floating-point normalized LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + float32_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + float32_t mu; /**< step size that control filter coefficient updates. */ + float32_t energy; /**< saves previous frame energy. */ + float32_t x0; /**< saves previous input sample. */ + } arm_lms_norm_instance_f32; + + + /** + * @brief Processing function for floating-point normalized LMS filter. + * @param[in] S points to an instance of the floating-point normalized LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_f32( + arm_lms_norm_instance_f32 * S, + const float32_t * pSrc, + float32_t * pRef, + float32_t * pOut, + float32_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for floating-point normalized LMS filter. + * @param[in] S points to an instance of the floating-point LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_init_f32( + arm_lms_norm_instance_f32 * S, + uint16_t numTaps, + float32_t * pCoeffs, + float32_t * pState, + float32_t mu, + uint32_t blockSize); + + + /** + * @brief Instance structure for the Q31 normalized LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + q31_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q31_t mu; /**< step size that controls filter coefficient updates. */ + uint8_t postShift; /**< bit shift applied to coefficients. */ + const q31_t *recipTable; /**< points to the reciprocal initial value table. */ + q31_t energy; /**< saves previous frame energy. */ + q31_t x0; /**< saves previous input sample. */ + } arm_lms_norm_instance_q31; + + + /** + * @brief Processing function for Q31 normalized LMS filter. + * @param[in] S points to an instance of the Q31 normalized LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_q31( + arm_lms_norm_instance_q31 * S, + const q31_t * pSrc, + q31_t * pRef, + q31_t * pOut, + q31_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for Q31 normalized LMS filter. + * @param[in] S points to an instance of the Q31 normalized LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_norm_init_q31( + arm_lms_norm_instance_q31 * S, + uint16_t numTaps, + q31_t * pCoeffs, + q31_t * pState, + q31_t mu, + uint32_t blockSize, + uint8_t postShift); + + + /** + * @brief Instance structure for the Q15 normalized LMS filter. + */ + typedef struct + { + uint16_t numTaps; /**< Number of coefficients in the filter. */ + q15_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + q15_t mu; /**< step size that controls filter coefficient updates. */ + uint8_t postShift; /**< bit shift applied to coefficients. */ + const q15_t *recipTable; /**< Points to the reciprocal initial value table. */ + q15_t energy; /**< saves previous frame energy. */ + q15_t x0; /**< saves previous input sample. */ + } arm_lms_norm_instance_q15; + + + /** + * @brief Processing function for Q15 normalized LMS filter. + * @param[in] S points to an instance of the Q15 normalized LMS filter structure. + * @param[in] pSrc points to the block of input data. + * @param[in] pRef points to the block of reference data. + * @param[out] pOut points to the block of output data. + * @param[out] pErr points to the block of error data. + * @param[in] blockSize number of samples to process. + */ + void arm_lms_norm_q15( + arm_lms_norm_instance_q15 * S, + const q15_t * pSrc, + q15_t * pRef, + q15_t * pOut, + q15_t * pErr, + uint32_t blockSize); + + + /** + * @brief Initialization function for Q15 normalized LMS filter. + * @param[in] S points to an instance of the Q15 normalized LMS filter structure. + * @param[in] numTaps number of filter coefficients. + * @param[in] pCoeffs points to coefficient buffer. + * @param[in] pState points to state buffer. + * @param[in] mu step size that controls filter coefficient updates. + * @param[in] blockSize number of samples to process. + * @param[in] postShift bit shift applied to coefficients. + */ + void arm_lms_norm_init_q15( + arm_lms_norm_instance_q15 * S, + uint16_t numTaps, + q15_t * pCoeffs, + q15_t * pState, + q15_t mu, + uint32_t blockSize, + uint8_t postShift); + + + /** + * @brief Correlation of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_f32( + const float32_t * pSrcA, + uint32_t srcALen, + const float32_t * pSrcB, + uint32_t srcBLen, + float32_t * pDst); + + + /** + * @brief Correlation of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_f64( + const float64_t * pSrcA, + uint32_t srcALen, + const float64_t * pSrcB, + uint32_t srcBLen, + float64_t * pDst); + + +/** + @brief Correlation of Q15 sequences + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + @param[in] pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. +*/ +void arm_correlate_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch); + + +/** + @brief Correlation of Q15 sequences. + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + +/** + @brief Correlation of Q15 sequences (fast version). + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1. + */ +void arm_correlate_fast_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst); + + +/** + @brief Correlation of Q15 sequences (fast version). + @param[in] pSrcA points to the first input sequence. + @param[in] srcALen length of the first input sequence. + @param[in] pSrcB points to the second input sequence. + @param[in] srcBLen length of the second input sequence. + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + @param[in] pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + */ +void arm_correlate_fast_opt_q15( + const q15_t * pSrcA, + uint32_t srcALen, + const q15_t * pSrcB, + uint32_t srcBLen, + q15_t * pDst, + q15_t * pScratch); + + + /** + * @brief Correlation of Q31 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + +/** + @brief Correlation of Q31 sequences (fast version). + @param[in] pSrcA points to the first input sequence + @param[in] srcALen length of the first input sequence + @param[in] pSrcB points to the second input sequence + @param[in] srcBLen length of the second input sequence + @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ +void arm_correlate_fast_q31( + const q31_t * pSrcA, + uint32_t srcALen, + const q31_t * pSrcB, + uint32_t srcBLen, + q31_t * pDst); + + + /** + * @brief Correlation of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + * @param[in] pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2. + * @param[in] pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen). + */ + void arm_correlate_opt_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst, + q15_t * pScratch1, + q15_t * pScratch2); + + + /** + * @brief Correlation of Q7 sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_q7( + const q7_t * pSrcA, + uint32_t srcALen, + const q7_t * pSrcB, + uint32_t srcBLen, + q7_t * pDst); + + + /** + * @brief Instance structure for the floating-point sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + float32_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const float32_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_f32; + + /** + * @brief Instance structure for the Q31 sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + q31_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const q31_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_q31; + + /** + * @brief Instance structure for the Q15 sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + q15_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const q15_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_q15; + + /** + * @brief Instance structure for the Q7 sparse FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of coefficients in the filter. */ + uint16_t stateIndex; /**< state buffer index. Points to the oldest sample in the state buffer. */ + q7_t *pState; /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */ + const q7_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps.*/ + uint16_t maxDelay; /**< maximum offset specified by the pTapDelay array. */ + int32_t *pTapDelay; /**< points to the array of delay values. The array is of length numTaps. */ + } arm_fir_sparse_instance_q7; + + + /** + * @brief Processing function for the floating-point sparse FIR filter. + * @param[in] S points to an instance of the floating-point sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_f32( + arm_fir_sparse_instance_f32 * S, + const float32_t * pSrc, + float32_t * pDst, + float32_t * pScratchIn, + uint32_t blockSize); + + + /** + * @brief Initialization function for the floating-point sparse FIR filter. + * @param[in,out] S points to an instance of the floating-point sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_f32( + arm_fir_sparse_instance_f32 * S, + uint16_t numTaps, + const float32_t * pCoeffs, + float32_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q31 sparse FIR filter. + * @param[in] S points to an instance of the Q31 sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_q31( + arm_fir_sparse_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + q31_t * pScratchIn, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q31 sparse FIR filter. + * @param[in,out] S points to an instance of the Q31 sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_q31( + arm_fir_sparse_instance_q31 * S, + uint16_t numTaps, + const q31_t * pCoeffs, + q31_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q15 sparse FIR filter. + * @param[in] S points to an instance of the Q15 sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] pScratchOut points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_q15( + arm_fir_sparse_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + q15_t * pScratchIn, + q31_t * pScratchOut, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q15 sparse FIR filter. + * @param[in,out] S points to an instance of the Q15 sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_q15( + arm_fir_sparse_instance_q15 * S, + uint16_t numTaps, + const q15_t * pCoeffs, + q15_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + /** + * @brief Processing function for the Q7 sparse FIR filter. + * @param[in] S points to an instance of the Q7 sparse FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] pScratchIn points to a temporary buffer of size blockSize. + * @param[in] pScratchOut points to a temporary buffer of size blockSize. + * @param[in] blockSize number of input samples to process per call. + */ + void arm_fir_sparse_q7( + arm_fir_sparse_instance_q7 * S, + const q7_t * pSrc, + q7_t * pDst, + q7_t * pScratchIn, + q31_t * pScratchOut, + uint32_t blockSize); + + + /** + * @brief Initialization function for the Q7 sparse FIR filter. + * @param[in,out] S points to an instance of the Q7 sparse FIR structure. + * @param[in] numTaps number of nonzero coefficients in the filter. + * @param[in] pCoeffs points to the array of filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] pTapDelay points to the array of offset times. + * @param[in] maxDelay maximum offset time supported. + * @param[in] blockSize number of samples that will be processed per block. + */ + void arm_fir_sparse_init_q7( + arm_fir_sparse_instance_q7 * S, + uint16_t numTaps, + const q7_t * pCoeffs, + q7_t * pState, + int32_t * pTapDelay, + uint16_t maxDelay, + uint32_t blockSize); + + + + + + + /** + * @brief floating-point Circular write function. + */ + __STATIC_FORCEINLINE void arm_circularWrite_f32( + int32_t * circBuffer, + int32_t L, + uint16_t * writeOffset, + int32_t bufferInc, + const int32_t * src, + int32_t srcInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t wOffset; + + /* Copy the value of Index pointer that points + * to the current location where the input samples to be copied */ + wOffset = *writeOffset; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the input sample to the circular buffer */ + circBuffer[wOffset] = *src; + + /* Update the input pointer */ + src += srcInc; + + /* Circularly update wOffset. Watch out for positive and negative value */ + wOffset += bufferInc; + if (wOffset >= L) + wOffset -= L; + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *writeOffset = (uint16_t)wOffset; + } + + + + /** + * @brief floating-point Circular Read function. + */ + __STATIC_FORCEINLINE void arm_circularRead_f32( + int32_t * circBuffer, + int32_t L, + int32_t * readOffset, + int32_t bufferInc, + int32_t * dst, + int32_t * dst_base, + int32_t dst_length, + int32_t dstInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t rOffset; + int32_t* dst_end; + + /* Copy the value of Index pointer that points + * to the current location from where the input samples to be read */ + rOffset = *readOffset; + dst_end = dst_base + dst_length; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the sample from the circular buffer to the destination buffer */ + *dst = circBuffer[rOffset]; + + /* Update the input pointer */ + dst += dstInc; + + if (dst == dst_end) + { + dst = dst_base; + } + + /* Circularly update rOffset. Watch out for positive and negative value */ + rOffset += bufferInc; + + if (rOffset >= L) + { + rOffset -= L; + } + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *readOffset = rOffset; + } + + + /** + * @brief Q15 Circular write function. + */ + __STATIC_FORCEINLINE void arm_circularWrite_q15( + q15_t * circBuffer, + int32_t L, + uint16_t * writeOffset, + int32_t bufferInc, + const q15_t * src, + int32_t srcInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t wOffset; + + /* Copy the value of Index pointer that points + * to the current location where the input samples to be copied */ + wOffset = *writeOffset; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the input sample to the circular buffer */ + circBuffer[wOffset] = *src; + + /* Update the input pointer */ + src += srcInc; + + /* Circularly update wOffset. Watch out for positive and negative value */ + wOffset += bufferInc; + if (wOffset >= L) + wOffset -= L; + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *writeOffset = (uint16_t)wOffset; + } + + + /** + * @brief Q15 Circular Read function. + */ + __STATIC_FORCEINLINE void arm_circularRead_q15( + q15_t * circBuffer, + int32_t L, + int32_t * readOffset, + int32_t bufferInc, + q15_t * dst, + q15_t * dst_base, + int32_t dst_length, + int32_t dstInc, + uint32_t blockSize) + { + uint32_t i = 0; + int32_t rOffset; + q15_t* dst_end; + + /* Copy the value of Index pointer that points + * to the current location from where the input samples to be read */ + rOffset = *readOffset; + + dst_end = dst_base + dst_length; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the sample from the circular buffer to the destination buffer */ + *dst = circBuffer[rOffset]; + + /* Update the input pointer */ + dst += dstInc; + + if (dst == dst_end) + { + dst = dst_base; + } + + /* Circularly update wOffset. Watch out for positive and negative value */ + rOffset += bufferInc; + + if (rOffset >= L) + { + rOffset -= L; + } + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *readOffset = rOffset; + } + + + /** + * @brief Q7 Circular write function. + */ + __STATIC_FORCEINLINE void arm_circularWrite_q7( + q7_t * circBuffer, + int32_t L, + uint16_t * writeOffset, + int32_t bufferInc, + const q7_t * src, + int32_t srcInc, + uint32_t blockSize) + { + uint32_t i = 0U; + int32_t wOffset; + + /* Copy the value of Index pointer that points + * to the current location where the input samples to be copied */ + wOffset = *writeOffset; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the input sample to the circular buffer */ + circBuffer[wOffset] = *src; + + /* Update the input pointer */ + src += srcInc; + + /* Circularly update wOffset. Watch out for positive and negative value */ + wOffset += bufferInc; + if (wOffset >= L) + wOffset -= L; + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *writeOffset = (uint16_t)wOffset; + } + + + /** + * @brief Q7 Circular Read function. + */ + __STATIC_FORCEINLINE void arm_circularRead_q7( + q7_t * circBuffer, + int32_t L, + int32_t * readOffset, + int32_t bufferInc, + q7_t * dst, + q7_t * dst_base, + int32_t dst_length, + int32_t dstInc, + uint32_t blockSize) + { + uint32_t i = 0; + int32_t rOffset; + q7_t* dst_end; + + /* Copy the value of Index pointer that points + * to the current location from where the input samples to be read */ + rOffset = *readOffset; + + dst_end = dst_base + dst_length; + + /* Loop over the blockSize */ + i = blockSize; + + while (i > 0U) + { + /* copy the sample from the circular buffer to the destination buffer */ + *dst = circBuffer[rOffset]; + + /* Update the input pointer */ + dst += dstInc; + + if (dst == dst_end) + { + dst = dst_base; + } + + /* Circularly update rOffset. Watch out for positive and negative value */ + rOffset += bufferInc; + + if (rOffset >= L) + { + rOffset -= L; + } + + /* Decrement the loop counter */ + i--; + } + + /* Update the index pointer */ + *readOffset = rOffset; + } + + +/** + @brief Levinson Durbin + @param[in] phi autocovariance vector starting with lag 0 (length is nbCoefs + 1) + @param[out] a autoregressive coefficients + @param[out] err prediction error (variance) + @param[in] nbCoefs number of autoregressive coefficients + */ +void arm_levinson_durbin_f32(const float32_t *phi, + float32_t *a, + float32_t *err, + int nbCoefs); + + +/** + @brief Levinson Durbin + @param[in] phi autocovariance vector starting with lag 0 (length is nbCoefs + 1) + @param[out] a autoregressive coefficients + @param[out] err prediction error (variance) + @param[in] nbCoefs number of autoregressive coefficients + */ +void arm_levinson_durbin_q31(const q31_t *phi, + q31_t *a, + q31_t *err, + int nbCoefs); + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _FILTERING_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/filtering_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/filtering_functions_f16.h new file mode 100755 index 0000000..655cd7e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/filtering_functions_f16.h @@ -0,0 +1,236 @@ +/****************************************************************************** + * @file filtering_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef FILTERING_FUNCTIONS_F16_H_ +#define FILTERING_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + /** + * @brief Instance structure for the floating-point FIR filter. + */ + typedef struct + { + uint16_t numTaps; /**< number of filter coefficients in the filter. */ + float16_t *pState; /**< points to the state variable array. The array is of length numTaps+blockSize-1. */ + const float16_t *pCoeffs; /**< points to the coefficient array. The array is of length numTaps. */ + } arm_fir_instance_f16; + + /** + * @brief Initialization function for the floating-point FIR filter. + * @param[in,out] S points to an instance of the floating-point FIR filter structure. + * @param[in] numTaps Number of filter coefficients in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + * @param[in] blockSize number of samples that are processed at a time. + */ + void arm_fir_init_f16( + arm_fir_instance_f16 * S, + uint16_t numTaps, + const float16_t * pCoeffs, + float16_t * pState, + uint32_t blockSize); + + /** + * @brief Processing function for the floating-point FIR filter. + * @param[in] S points to an instance of the floating-point FIR structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_fir_f16( + const arm_fir_instance_f16 * S, + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + + /** + * @brief Instance structure for the floating-point Biquad cascade filter. + */ + typedef struct + { + uint32_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float16_t *pState; /**< Points to the array of state coefficients. The array is of length 4*numStages. */ + const float16_t *pCoeffs; /**< Points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_casd_df1_inst_f16; + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + /** + * @brief Instance structure for the modified Biquad coefs required by vectorized code. + */ + typedef struct + { + float16_t coeffs[12][8]; /**< Points to the array of modified coefficients. The array is of length 32. There is one per stage */ + } arm_biquad_mod_coef_f16; +#endif + + /** + * @brief Processing function for the floating-point Biquad cascade filter. + * @param[in] S points to an instance of the floating-point Biquad cascade structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df1_f16( + const arm_biquad_casd_df1_inst_f16 * S, + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + void arm_biquad_cascade_df1_mve_init_f16( + arm_biquad_casd_df1_inst_f16 * S, + uint8_t numStages, + const float16_t * pCoeffs, + arm_biquad_mod_coef_f16 * pCoeffsMod, + float16_t * pState); +#endif + + void arm_biquad_cascade_df1_init_f16( + arm_biquad_casd_df1_inst_f16 * S, + uint8_t numStages, + const float16_t * pCoeffs, + float16_t * pState); + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float16_t *pState; /**< points to the array of state coefficients. The array is of length 2*numStages. */ + const float16_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_df2T_instance_f16; + + /** + * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter. + */ + typedef struct + { + uint8_t numStages; /**< number of 2nd order stages in the filter. Overall order is 2*numStages. */ + float16_t *pState; /**< points to the array of state coefficients. The array is of length 4*numStages. */ + const float16_t *pCoeffs; /**< points to the array of coefficients. The array is of length 5*numStages. */ + } arm_biquad_cascade_stereo_df2T_instance_f16; + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_df2T_f16( + const arm_biquad_cascade_df2T_instance_f16 * S, + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels + * @param[in] S points to an instance of the filter data structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_biquad_cascade_stereo_df2T_f16( + const arm_biquad_cascade_stereo_df2T_instance_f16 * S, + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_df2T_init_f16( + arm_biquad_cascade_df2T_instance_f16 * S, + uint8_t numStages, + const float16_t * pCoeffs, + float16_t * pState); + + /** + * @brief Initialization function for the floating-point transposed direct form II Biquad cascade filter. + * @param[in,out] S points to an instance of the filter data structure. + * @param[in] numStages number of 2nd order stages in the filter. + * @param[in] pCoeffs points to the filter coefficients. + * @param[in] pState points to the state buffer. + */ + void arm_biquad_cascade_stereo_df2T_init_f16( + arm_biquad_cascade_stereo_df2T_instance_f16 * S, + uint8_t numStages, + const float16_t * pCoeffs, + float16_t * pState); + + /** + * @brief Correlation of floating-point sequences. + * @param[in] pSrcA points to the first input sequence. + * @param[in] srcALen length of the first input sequence. + * @param[in] pSrcB points to the second input sequence. + * @param[in] srcBLen length of the second input sequence. + * @param[out] pDst points to the block of output data Length 2 * max(srcALen, srcBLen) - 1. + */ + void arm_correlate_f16( + const float16_t * pSrcA, + uint32_t srcALen, + const float16_t * pSrcB, + uint32_t srcBLen, + float16_t * pDst); + + +/** + @brief Levinson Durbin + @param[in] phi autocovariance vector starting with lag 0 (length is nbCoefs + 1) + @param[out] a autoregressive coefficients + @param[out] err prediction error (variance) + @param[in] nbCoefs number of autoregressive coefficients + */ +void arm_levinson_durbin_f16(const float16_t *phi, + float16_t *a, + float16_t *err, + int nbCoefs); + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _FILTERING_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/interpolation_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/interpolation_functions.h new file mode 100755 index 0000000..66ef995 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/interpolation_functions.h @@ -0,0 +1,275 @@ +/****************************************************************************** + * @file interpolation_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef INTERPOLATION_FUNCTIONS_H_ +#define INTERPOLATION_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + +/** + * @defgroup groupInterpolation Interpolation Functions + * These functions perform 1- and 2-dimensional interpolation of data. + * Linear interpolation is used for 1-dimensional data and + * bilinear interpolation is used for 2-dimensional data. + */ + + + /** + * @brief Instance structure for the floating-point Linear Interpolate function. + */ + typedef struct + { + uint32_t nValues; /**< nValues */ + float32_t x1; /**< x1 */ + float32_t xSpacing; /**< xSpacing */ + const float32_t *pYData; /**< pointer to the table of Y values */ + } arm_linear_interp_instance_f32; + + /** + * @brief Instance structure for the floating-point bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + const float32_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_f32; + + /** + * @brief Instance structure for the Q31 bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + const q31_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_q31; + + /** + * @brief Instance structure for the Q15 bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + const q15_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_q15; + + /** + * @brief Instance structure for the Q15 bilinear interpolation function. + */ + typedef struct + { + uint16_t numRows; /**< number of rows in the data table. */ + uint16_t numCols; /**< number of columns in the data table. */ + const q7_t *pData; /**< points to the data table. */ + } arm_bilinear_interp_instance_q7; + + + /** + * @brief Struct for specifying cubic spline type + */ + typedef enum + { + ARM_SPLINE_NATURAL = 0, /**< Natural spline */ + ARM_SPLINE_PARABOLIC_RUNOUT = 1 /**< Parabolic runout spline */ + } arm_spline_type; + + /** + * @brief Instance structure for the floating-point cubic spline interpolation. + */ + typedef struct + { + arm_spline_type type; /**< Type (boundary conditions) */ + const float32_t * x; /**< x values */ + const float32_t * y; /**< y values */ + uint32_t n_x; /**< Number of known data points */ + float32_t * coeffs; /**< Coefficients buffer (b,c, and d) */ + } arm_spline_instance_f32; + + + /** + * @brief Processing function for the floating-point cubic spline interpolation. + * @param[in] S points to an instance of the floating-point spline structure. + * @param[in] xq points to the x values of the interpolated data points. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples of output data. + */ + void arm_spline_f32( + arm_spline_instance_f32 * S, + const float32_t * xq, + float32_t * pDst, + uint32_t blockSize); + + /** + * @brief Initialization function for the floating-point cubic spline interpolation. + * @param[in,out] S points to an instance of the floating-point spline structure. + * @param[in] type type of cubic spline interpolation (boundary conditions) + * @param[in] x points to the x values of the known data points. + * @param[in] y points to the y values of the known data points. + * @param[in] n number of known data points. + * @param[in] coeffs coefficients array for b, c, and d + * @param[in] tempBuffer buffer array for internal computations + */ + void arm_spline_init_f32( + arm_spline_instance_f32 * S, + arm_spline_type type, + const float32_t * x, + const float32_t * y, + uint32_t n, + float32_t * coeffs, + float32_t * tempBuffer); + + + /** + * @brief Process function for the floating-point Linear Interpolation Function. + * @param[in,out] S is an instance of the floating-point Linear Interpolation structure + * @param[in] x input sample to process + * @return y processed output sample. + * + */ + float32_t arm_linear_interp_f32( + const arm_linear_interp_instance_f32 * S, + float32_t x); + + /** + * + * @brief Process function for the Q31 Linear Interpolation Function. + * @param[in] pYData pointer to Q31 Linear Interpolation table + * @param[in] x input sample to process + * @param[in] nValues number of table values + * @return y processed output sample. + * + * \par + * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part. + * This function can support maximum of table size 2^12. + * + */ + q31_t arm_linear_interp_q31( + const q31_t * pYData, + q31_t x, + uint32_t nValues); + + /** + * + * @brief Process function for the Q15 Linear Interpolation Function. + * @param[in] pYData pointer to Q15 Linear Interpolation table + * @param[in] x input sample to process + * @param[in] nValues number of table values + * @return y processed output sample. + * + * \par + * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part. + * This function can support maximum of table size 2^12. + * + */ + q15_t arm_linear_interp_q15( + const q15_t * pYData, + q31_t x, + uint32_t nValues); + + /** + * + * @brief Process function for the Q7 Linear Interpolation Function. + * @param[in] pYData pointer to Q7 Linear Interpolation table + * @param[in] x input sample to process + * @param[in] nValues number of table values + * @return y processed output sample. + * + * \par + * Input sample x is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part. + * This function can support maximum of table size 2^12. + */ +q7_t arm_linear_interp_q7( + const q7_t * pYData, + q31_t x, + uint32_t nValues); + + /** + * @brief Floating-point bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate. + * @param[in] Y interpolation coordinate. + * @return out interpolated value. + */ + float32_t arm_bilinear_interp_f32( + const arm_bilinear_interp_instance_f32 * S, + float32_t X, + float32_t Y); + + /** + * @brief Q31 bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate in 12.20 format. + * @param[in] Y interpolation coordinate in 12.20 format. + * @return out interpolated value. + */ + q31_t arm_bilinear_interp_q31( + arm_bilinear_interp_instance_q31 * S, + q31_t X, + q31_t Y); + + + /** + * @brief Q15 bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate in 12.20 format. + * @param[in] Y interpolation coordinate in 12.20 format. + * @return out interpolated value. + */ + q15_t arm_bilinear_interp_q15( + arm_bilinear_interp_instance_q15 * S, + q31_t X, + q31_t Y); + + /** + * @brief Q7 bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate in 12.20 format. + * @param[in] Y interpolation coordinate in 12.20 format. + * @return out interpolated value. + */ + q7_t arm_bilinear_interp_q7( + arm_bilinear_interp_instance_q7 * S, + q31_t X, + q31_t Y); + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _INTERPOLATION_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/interpolation_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/interpolation_functions_f16.h new file mode 100755 index 0000000..e1f27c3 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/interpolation_functions_f16.h @@ -0,0 +1,109 @@ +/****************************************************************************** + * @file interpolation_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef INTERPOLATION_FUNCTIONS_F16_H_ +#define INTERPOLATION_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + * @brief Instance structure for the half floating-point Linear Interpolate function. + */ +typedef struct +{ + uint32_t nValues; /**< nValues */ + float16_t x1; /**< x1 */ + float16_t xSpacing; /**< xSpacing */ + const float16_t *pYData; /**< pointer to the table of Y values */ +} arm_linear_interp_instance_f16; + +/** + * @brief Instance structure for the floating-point bilinear interpolation function. + */ +typedef struct +{ + uint16_t numRows;/**< number of rows in the data table. */ + uint16_t numCols;/**< number of columns in the data table. */ + const float16_t *pData; /**< points to the data table. */ +} arm_bilinear_interp_instance_f16; + + /** + * @addtogroup LinearInterpolate + * @{ + */ + + /** + * @brief Process function for the floating-point Linear Interpolation Function. + * @param[in,out] S is an instance of the floating-point Linear Interpolation structure + * @param[in] x input sample to process + * @return y processed output sample. + */ + float16_t arm_linear_interp_f16( + const arm_linear_interp_instance_f16 * S, + float16_t x); + + /** + * @} end of LinearInterpolate group + */ + +/** + * @addtogroup BilinearInterpolate + * @{ + */ + + /** + * @brief Floating-point bilinear interpolation. + * @param[in,out] S points to an instance of the interpolation structure. + * @param[in] X interpolation coordinate. + * @param[in] Y interpolation coordinate. + * @return out interpolated value. + */ + float16_t arm_bilinear_interp_f16( + const arm_bilinear_interp_instance_f16 * S, + float16_t X, + float16_t Y); + + + /** + * @} end of BilinearInterpolate group + */ +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _INTERPOLATION_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_functions.h new file mode 100755 index 0000000..a19144b --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_functions.h @@ -0,0 +1,871 @@ +/****************************************************************************** + * @file matrix_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.1 + * @date 10 August 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef MATRIX_FUNCTIONS_H_ +#define MATRIX_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup groupMatrix Matrix Functions + * + * This set of functions provides basic matrix math operations. + * The functions operate on matrix data structures. For example, + * the type + * definition for the floating-point matrix structure is shown + * below: + * 
+ *     typedef struct
+ *     {
+ *       uint16_t numRows;     // number of rows of the matrix.
+ *       uint16_t numCols;     // number of columns of the matrix.
+ *       float32_t *pData;     // points to the data of the matrix.
+ *     } arm_matrix_instance_f32;
+ *
+ * There are similar definitions for Q15 and Q31 data types. + * + * The structure specifies the size of the matrix and then points to + * an array of data. The array is of size numRows X numCols + * and the values are arranged in row order. That is, the + * matrix element (i, j) is stored at: + * 
+ *     pData[i*numCols + j]
+ *
+ * + * \par Init Functions + * There is an associated initialization function for each type of matrix + * data structure. + * The initialization function sets the values of the internal structure fields. + * Refer to \ref arm_mat_init_f32(), \ref arm_mat_init_q31() and \ref arm_mat_init_q15() + * for floating-point, Q31 and Q15 types, respectively. + * + * \par + * Use of the initialization function is optional. However, if initialization function is used + * then the instance structure cannot be placed into a const data section. + * To place the instance structure in a const data + * section, manually initialize the data structure. For example: + * 
+ * arm_matrix_instance_f32 S = {nRows, nColumns, pData};
+ * arm_matrix_instance_q31 S = {nRows, nColumns, pData};
+ * arm_matrix_instance_q15 S = {nRows, nColumns, pData};
+ *
+ * where nRows specifies the number of rows, nColumns + * specifies the number of columns, and pData points to the + * data array. + * + * \par Size Checking + * By default all of the matrix functions perform size checking on the input and + * output matrices. For example, the matrix addition function verifies that the + * two input matrices and the output matrix all have the same number of rows and + * columns. If the size check fails the functions return: + * 
+ *     ARM_MATH_SIZE_MISMATCH
+ *
+ * Otherwise the functions return + * 
+ *     ARM_MATH_SUCCESS
+ *
+ * There is some overhead associated with this matrix size checking. + * The matrix size checking is enabled via the \#define + * 
+ *     ARM_MATH_MATRIX_CHECK
+ *
+ * within the library project settings. By default this macro is defined + * and size checking is enabled. By changing the project settings and + * undefining this macro size checking is eliminated and the functions + * run a bit faster. With size checking disabled the functions always + * return ARM_MATH_SUCCESS. + */ + + #define DEFAULT_HOUSEHOLDER_THRESHOLD_F64 (1.0e-16) + #define DEFAULT_HOUSEHOLDER_THRESHOLD_F32 (1.0e-12f) + + /** + * @brief Instance structure for the floating-point matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + float32_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_f32; + + /** + * @brief Instance structure for the floating-point matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + float64_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_f64; + + /** + * @brief Instance structure for the Q7 matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + q7_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_q7; + + /** + * @brief Instance structure for the Q15 matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + q15_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_q15; + + /** + * @brief Instance structure for the Q31 matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + q31_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_q31; + + /** + * @brief Floating-point matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst, + q15_t * pScratch); + + /** + * @brief Q31, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_f32( + const arm_matrix_instance_f32 * pSrc, + arm_matrix_instance_f32 * pDst); + +/** + * @brief Floating-point matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_f64( + const arm_matrix_instance_f64 * pSrc, + arm_matrix_instance_f64 * pDst); + + /** + * @brief Floating-point complex matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_trans_f32( + const arm_matrix_instance_f32 * pSrc, + arm_matrix_instance_f32 * pDst); + + + /** + * @brief Q15 matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_q15( + const arm_matrix_instance_q15 * pSrc, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q15 complex matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_trans_q15( + const arm_matrix_instance_q15 * pSrc, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q7 matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_q7( + const arm_matrix_instance_q7 * pSrc, + arm_matrix_instance_q7 * pDst); + + /** + * @brief Q31 matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_q31( + const arm_matrix_instance_q31 * pSrc, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Q31 complex matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_trans_q31( + const arm_matrix_instance_q31 * pSrc, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Floating-point matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_f64( + const arm_matrix_instance_f64 * pSrcA, + const arm_matrix_instance_f64 * pSrcB, + arm_matrix_instance_f64 * pDst); + + /** + * @brief Floating-point matrix and vector multiplication + * @param[in] pSrcMat points to the input matrix structure + * @param[in] pVec points to vector + * @param[out] pDst points to output vector + */ +void arm_mat_vec_mult_f32( + const arm_matrix_instance_f32 *pSrcMat, + const float32_t *pVec, + float32_t *pDst); + + /** + * @brief Q7 matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @param[in] pState points to the array for storing intermediate results + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_q7( + const arm_matrix_instance_q7 * pSrcA, + const arm_matrix_instance_q7 * pSrcB, + arm_matrix_instance_q7 * pDst, + q7_t * pState); + + /** + * @brief Q7 matrix and vector multiplication + * @param[in] pSrcMat points to the input matrix structure + * @param[in] pVec points to vector + * @param[out] pDst points to output vector + */ +void arm_mat_vec_mult_q7( + const arm_matrix_instance_q7 *pSrcMat, + const q7_t *pVec, + q7_t *pDst); + + /** + * @brief Q15 matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @param[in] pState points to the array for storing intermediate results + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst, + q15_t * pState); + + /** + * @brief Q15 matrix and vector multiplication + * @param[in] pSrcMat points to the input matrix structure + * @param[in] pVec points to vector + * @param[out] pDst points to output vector + */ +void arm_mat_vec_mult_q15( + const arm_matrix_instance_q15 *pSrcMat, + const q15_t *pVec, + q15_t *pDst); + + /** + * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @param[in] pState points to the array for storing intermediate results + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_fast_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst, + q15_t * pState); + + /** + * @brief Q31 matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Q31 matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @param[in] pState points to the array for storing intermediate results + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_opt_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst, + q31_t *pState); + + /** + * @brief Q31 matrix and vector multiplication + * @param[in] pSrcMat points to the input matrix structure + * @param[in] pVec points to vector + * @param[out] pDst points to output vector + */ +void arm_mat_vec_mult_q31( + const arm_matrix_instance_q31 *pSrcMat, + const q31_t *pVec, + q31_t *pDst); + + /** + * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4 + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_fast_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_f32( + const arm_matrix_instance_f32 * pSrcA, + const arm_matrix_instance_f32 * pSrcB, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Floating-point matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_f64( + const arm_matrix_instance_f64 * pSrcA, + const arm_matrix_instance_f64 * pSrcB, + arm_matrix_instance_f64 * pDst); + + /** + * @brief Q15 matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_q15( + const arm_matrix_instance_q15 * pSrcA, + const arm_matrix_instance_q15 * pSrcB, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_q31( + const arm_matrix_instance_q31 * pSrcA, + const arm_matrix_instance_q31 * pSrcB, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Floating-point matrix scaling. + * @param[in] pSrc points to the input matrix + * @param[in] scale scale factor + * @param[out] pDst points to the output matrix + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_f32( + const arm_matrix_instance_f32 * pSrc, + float32_t scale, + arm_matrix_instance_f32 * pDst); + + /** + * @brief Q15 matrix scaling. + * @param[in] pSrc points to input matrix + * @param[in] scaleFract fractional portion of the scale factor + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to output matrix + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_q15( + const arm_matrix_instance_q15 * pSrc, + q15_t scaleFract, + int32_t shift, + arm_matrix_instance_q15 * pDst); + + /** + * @brief Q31 matrix scaling. + * @param[in] pSrc points to input matrix + * @param[in] scaleFract fractional portion of the scale factor + * @param[in] shift number of bits to shift the result by + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_q31( + const arm_matrix_instance_q31 * pSrc, + q31_t scaleFract, + int32_t shift, + arm_matrix_instance_q31 * pDst); + + /** + * @brief Q31 matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_q31( + arm_matrix_instance_q31 * S, + uint16_t nRows, + uint16_t nColumns, + q31_t * pData); + + /** + * @brief Q15 matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_q15( + arm_matrix_instance_q15 * S, + uint16_t nRows, + uint16_t nColumns, + q15_t * pData); + + /** + * @brief Q7 matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_q7( + arm_matrix_instance_q7 * S, + uint16_t nRows, + uint16_t nColumns, + q7_t * pData); + + /** + * @brief Floating-point matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_f32( + arm_matrix_instance_f32 * S, + uint16_t nRows, + uint16_t nColumns, + float32_t * pData); + +/** + * @brief Floating-point matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_f64( + arm_matrix_instance_f64 * S, + uint16_t nRows, + uint16_t nColumns, + float64_t * pData); + + + + + /** + * @brief Floating-point matrix inverse. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR. + */ + arm_status arm_mat_inverse_f32( + const arm_matrix_instance_f32 * src, + arm_matrix_instance_f32 * dst); + + + /** + * @brief Floating-point matrix inverse. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR. + */ + arm_status arm_mat_inverse_f64( + const arm_matrix_instance_f64 * src, + arm_matrix_instance_f64 * dst); + + /** + * @brief Floating-point Cholesky decomposition of Symmetric Positive Definite Matrix. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix does not have a decomposition, then the algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE. + * If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition. + * The decomposition is returning a lower triangular matrix. + */ + arm_status arm_mat_cholesky_f64( + const arm_matrix_instance_f64 * src, + arm_matrix_instance_f64 * dst); + + /** + * @brief Floating-point Cholesky decomposition of Symmetric Positive Definite Matrix. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix does not have a decomposition, then the algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE. + * If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition. + * The decomposition is returning a lower triangular matrix. + */ + arm_status arm_mat_cholesky_f32( + const arm_matrix_instance_f32 * src, + arm_matrix_instance_f32 * dst); + + /** + * @brief Solve UT . X = A where UT is an upper triangular matrix + * @param[in] ut The upper triangular matrix + * @param[in] a The matrix a + * @param[out] dst The solution X of UT . X = A + * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved. + */ + arm_status arm_mat_solve_upper_triangular_f32( + const arm_matrix_instance_f32 * ut, + const arm_matrix_instance_f32 * a, + arm_matrix_instance_f32 * dst); + + /** + * @brief Solve LT . X = A where LT is a lower triangular matrix + * @param[in] lt The lower triangular matrix + * @param[in] a The matrix a + * @param[out] dst The solution X of LT . X = A + * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved. + */ + arm_status arm_mat_solve_lower_triangular_f32( + const arm_matrix_instance_f32 * lt, + const arm_matrix_instance_f32 * a, + arm_matrix_instance_f32 * dst); + + + /** + * @brief Solve UT . X = A where UT is an upper triangular matrix + * @param[in] ut The upper triangular matrix + * @param[in] a The matrix a + * @param[out] dst The solution X of UT . X = A + * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved. + */ + arm_status arm_mat_solve_upper_triangular_f64( + const arm_matrix_instance_f64 * ut, + const arm_matrix_instance_f64 * a, + arm_matrix_instance_f64 * dst); + + /** + * @brief Solve LT . X = A where LT is a lower triangular matrix + * @param[in] lt The lower triangular matrix + * @param[in] a The matrix a + * @param[out] dst The solution X of LT . X = A + * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved. + */ + arm_status arm_mat_solve_lower_triangular_f64( + const arm_matrix_instance_f64 * lt, + const arm_matrix_instance_f64 * a, + arm_matrix_instance_f64 * dst); + + + /** + * @brief Floating-point LDL decomposition of Symmetric Positive Semi-Definite Matrix. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] l points to the instance of the output floating-point triangular matrix structure. + * @param[out] d points to the instance of the output floating-point diagonal matrix structure. + * @param[out] p points to the instance of the output floating-point permutation vector. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix does not have a decomposition, then the algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE. + * The decomposition is returning a lower triangular matrix. + */ + arm_status arm_mat_ldlt_f32( + const arm_matrix_instance_f32 * src, + arm_matrix_instance_f32 * l, + arm_matrix_instance_f32 * d, + uint16_t * pp); + + /** + * @brief Floating-point LDL decomposition of Symmetric Positive Semi-Definite Matrix. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] l points to the instance of the output floating-point triangular matrix structure. + * @param[out] d points to the instance of the output floating-point diagonal matrix structure. + * @param[out] p points to the instance of the output floating-point permutation vector. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix does not have a decomposition, then the algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE. + * The decomposition is returning a lower triangular matrix. + */ + arm_status arm_mat_ldlt_f64( + const arm_matrix_instance_f64 * src, + arm_matrix_instance_f64 * l, + arm_matrix_instance_f64 * d, + uint16_t * pp); + +/** + @brief QR decomposition of a m x n floating point matrix with m >= n. + @param[in] pSrc points to input matrix structure. The source matrix is modified by the function. + @param[in] threshold norm2 threshold. + @param[out] pOutR points to output R matrix structure of dimension m x n + @param[out] pOutQ points to output Q matrix structure of dimension m x m + @param[out] pOutTau points to Householder scaling factors of dimension n + @param[inout] pTmpA points to a temporary vector of dimension m. + @param[inout] pTmpB points to a temporary vector of dimension n. + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed + - \ref ARM_MATH_SINGULAR : Input matrix is found to be singular (non-invertible) + */ + +arm_status arm_mat_qr_f32( + const arm_matrix_instance_f32 * pSrc, + const float32_t threshold, + arm_matrix_instance_f32 * pOutR, + arm_matrix_instance_f32 * pOutQ, + float32_t * pOutTau, + float32_t *pTmpA, + float32_t *pTmpB + ); + +/** + @brief QR decomposition of a m x n floating point matrix with m >= n. + @param[in] pSrc points to input matrix structure. The source matrix is modified by the function. + @param[in] threshold norm2 threshold. + @param[out] pOutR points to output R matrix structure of dimension m x n + @param[out] pOutQ points to output Q matrix structure of dimension m x m + @param[out] pOutTau points to Householder scaling factors of dimension n + @param[inout] pTmpA points to a temporary vector of dimension m. + @param[inout] pTmpB points to a temporary vector of dimension n. + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed + - \ref ARM_MATH_SINGULAR : Input matrix is found to be singular (non-invertible) + */ + +arm_status arm_mat_qr_f64( + const arm_matrix_instance_f64 * pSrc, + const float64_t threshold, + arm_matrix_instance_f64 * pOutR, + arm_matrix_instance_f64 * pOutQ, + float64_t * pOutTau, + float64_t *pTmpA, + float64_t *pTmpB + ); + +/** + @brief Householder transform of a floating point vector. + @param[in] pSrc points to the input vector. + @param[in] threshold norm2 threshold. + @param[in] blockSize dimension of the vector space. + @param[outQ] pOut points to the output vector. + @return beta return the scaling factor beta + */ + +float32_t arm_householder_f32( + const float32_t * pSrc, + const float32_t threshold, + uint32_t blockSize, + float32_t * pOut + ); + +/** + @brief Householder transform of a double floating point vector. + @param[in] pSrc points to the input vector. + @param[in] threshold norm2 threshold. + @param[in] blockSize dimension of the vector space. + @param[outQ] pOut points to the output vector. + @return beta return the scaling factor beta + */ + +float64_t arm_householder_f64( + const float64_t * pSrc, + const float64_t threshold, + uint32_t blockSize, + float64_t * pOut + ); + + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _MATRIX_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_functions_f16.h new file mode 100755 index 0000000..25f99ab --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_functions_f16.h @@ -0,0 +1,260 @@ +/****************************************************************************** + * @file matrix_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef MATRIX_FUNCTIONS_F16_H_ +#define MATRIX_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + #define DEFAULT_HOUSEHOLDER_THRESHOLD_F16 (1.0e-3f) + + /** + * @brief Instance structure for the floating-point matrix structure. + */ + typedef struct + { + uint16_t numRows; /**< number of rows of the matrix. */ + uint16_t numCols; /**< number of columns of the matrix. */ + float16_t *pData; /**< points to the data of the matrix. */ + } arm_matrix_instance_f16; + + /** + * @brief Floating-point matrix addition. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_add_f16( + const arm_matrix_instance_f16 * pSrcA, + const arm_matrix_instance_f16 * pSrcB, + arm_matrix_instance_f16 * pDst); + + /** + * @brief Floating-point, complex, matrix multiplication. + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_mult_f16( + const arm_matrix_instance_f16 * pSrcA, + const arm_matrix_instance_f16 * pSrcB, + arm_matrix_instance_f16 * pDst); + + /** + * @brief Floating-point matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_trans_f16( + const arm_matrix_instance_f16 * pSrc, + arm_matrix_instance_f16 * pDst); + + /** + * @brief Floating-point complex matrix transpose. + * @param[in] pSrc points to the input matrix + * @param[out] pDst points to the output matrix + * @return The function returns either ARM_MATH_SIZE_MISMATCH + * or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_cmplx_trans_f16( + const arm_matrix_instance_f16 * pSrc, + arm_matrix_instance_f16 * pDst); + + /** + * @brief Floating-point matrix multiplication + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_mult_f16( + const arm_matrix_instance_f16 * pSrcA, + const arm_matrix_instance_f16 * pSrcB, + arm_matrix_instance_f16 * pDst); + /** + * @brief Floating-point matrix and vector multiplication + * @param[in] pSrcMat points to the input matrix structure + * @param[in] pVec points to vector + * @param[out] pDst points to output vector + */ +void arm_mat_vec_mult_f16( + const arm_matrix_instance_f16 *pSrcMat, + const float16_t *pVec, + float16_t *pDst); + + /** + * @brief Floating-point matrix subtraction + * @param[in] pSrcA points to the first input matrix structure + * @param[in] pSrcB points to the second input matrix structure + * @param[out] pDst points to output matrix structure + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_sub_f16( + const arm_matrix_instance_f16 * pSrcA, + const arm_matrix_instance_f16 * pSrcB, + arm_matrix_instance_f16 * pDst); + + /** + * @brief Floating-point matrix scaling. + * @param[in] pSrc points to the input matrix + * @param[in] scale scale factor + * @param[out] pDst points to the output matrix + * @return The function returns either + * ARM_MATH_SIZE_MISMATCH or ARM_MATH_SUCCESS based on the outcome of size checking. + */ +arm_status arm_mat_scale_f16( + const arm_matrix_instance_f16 * pSrc, + float16_t scale, + arm_matrix_instance_f16 * pDst); + + /** + * @brief Floating-point matrix initialization. + * @param[in,out] S points to an instance of the floating-point matrix structure. + * @param[in] nRows number of rows in the matrix. + * @param[in] nColumns number of columns in the matrix. + * @param[in] pData points to the matrix data array. + */ +void arm_mat_init_f16( + arm_matrix_instance_f16 * S, + uint16_t nRows, + uint16_t nColumns, + float16_t * pData); + + + /** + * @brief Floating-point matrix inverse. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR. + */ + arm_status arm_mat_inverse_f16( + const arm_matrix_instance_f16 * src, + arm_matrix_instance_f16 * dst); + + + /** + * @brief Floating-point Cholesky decomposition of Symmetric Positive Definite Matrix. + * @param[in] src points to the instance of the input floating-point matrix structure. + * @param[out] dst points to the instance of the output floating-point matrix structure. + * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match. + * If the input matrix does not have a decomposition, then the algorithm terminates and returns error status ARM_MATH_DECOMPOSITION_FAILURE. + * If the matrix is ill conditioned or only semi-definite, then it is better using the LDL^t decomposition. + * The decomposition is returning a lower triangular matrix. + */ + arm_status arm_mat_cholesky_f16( + const arm_matrix_instance_f16 * src, + arm_matrix_instance_f16 * dst); + + /** + * @brief Solve UT . X = A where UT is an upper triangular matrix + * @param[in] ut The upper triangular matrix + * @param[in] a The matrix a + * @param[out] dst The solution X of UT . X = A + * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved. + */ + arm_status arm_mat_solve_upper_triangular_f16( + const arm_matrix_instance_f16 * ut, + const arm_matrix_instance_f16 * a, + arm_matrix_instance_f16 * dst); + + /** + * @brief Solve LT . X = A where LT is a lower triangular matrix + * @param[in] lt The lower triangular matrix + * @param[in] a The matrix a + * @param[out] dst The solution X of LT . X = A + * @return The function returns ARM_MATH_SINGULAR, if the system can't be solved. + */ + arm_status arm_mat_solve_lower_triangular_f16( + const arm_matrix_instance_f16 * lt, + const arm_matrix_instance_f16 * a, + arm_matrix_instance_f16 * dst); + + +/** + @brief QR decomposition of a m x n floating point matrix with m >= n. + @param[in] pSrc points to input matrix structure. The source matrix is modified by the function. + @param[in] threshold norm2 threshold. + @param[out] pOutR points to output R matrix structure of dimension m x n + @param[out] pOutQ points to output Q matrix structure of dimension m x m + @param[out] pOutTau points to Householder scaling factors of dimension n + @param[inout] pTmpA points to a temporary vector of dimension m. + @param[inout] pTmpB points to a temporary vector of dimension n. + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_SIZE_MISMATCH : Matrix size check failed + - \ref ARM_MATH_SINGULAR : Input matrix is found to be singular (non-invertible) + */ +arm_status arm_mat_qr_f16( + const arm_matrix_instance_f16 * pSrc, + const float16_t threshold, + arm_matrix_instance_f16 * pOutR, + arm_matrix_instance_f16 * pOutQ, + float16_t * pOutTau, + float16_t *pTmpA, + float16_t *pTmpB + ); + +/** + @brief Householder transform of a half floating point vector. + @param[in] pSrc points to the input vector. + @param[in] threshold norm2 threshold. + @param[in] blockSize dimension of the vector space. + @param[outQ] pOut points to the output vector. + @return beta return the scaling factor beta + */ +float16_t arm_householder_f16( + const float16_t * pSrc, + const float16_t threshold, + uint32_t blockSize, + float16_t * pOut + ); + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _MATRIX_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_utils.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_utils.h new file mode 100755 index 0000000..acb996f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/matrix_utils.h @@ -0,0 +1,649 @@ +/****************************************************************************** + * @file matrix_utils.h + * @brief Public header file for CMSIS DSP Library + * @version V1.11.0 + * @date 30 May 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2022 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef MATRIX_UTILS_H_ +#define MATRIX_UTILS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#define ELEM(A,ROW,COL) &((A)->pData[(A)->numCols* (ROW) + (COL)]) + +#define SCALE_COL_T(T,CAST,A,ROW,v,i) \ +{ \ + int32_t _w; \ + T *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + const int32_t nb = (A)->numRows - ROW;\ + \ + data += i + _numCols * (ROW); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *data = CAST *data * CAST v; \ + data += _numCols; \ + } \ +} + +#define COPY_COL_T(T,A,ROW,COL,DST) \ +{ \ + uint32_t _row; \ + T *_pb=DST; \ + T *_pa = (A)->pData + ROW * (A)->numCols + COL;\ + for(_row = ROW; _row < (A)->numRows; _row ++) \ + { \ + *_pb++ = *_pa; \ + _pa += (A)->numCols; \ + } \ +} + +#if defined(ARM_FLOAT16_SUPPORTED) +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +#define SWAP_ROWS_F16(A,COL,i,j) \ + { \ + int cnt = ((A)->numCols)-(COL); \ + int32_t _w; \ + float16_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + \ + for(_w=(COL);_w < _numCols; _w+=8) \ + { \ + f16x8_t tmpa,tmpb; \ + mve_pred16_t p0 = vctp16q(cnt); \ + \ + tmpa=vldrhq_z_f16(&data[i*_numCols + _w],p0);\ + tmpb=vldrhq_z_f16(&data[j*_numCols + _w],p0);\ + \ + vstrhq_p(&data[i*_numCols + _w], tmpb, p0); \ + vstrhq_p(&data[j*_numCols + _w], tmpa, p0); \ + \ + cnt -= 8; \ + } \ + } + +#define SCALE_ROW_F16(A,COL,v,i) \ +{ \ + int cnt = ((A)->numCols)-(COL); \ + int32_t _w; \ + float16_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + \ + for(_w=(COL);_w < _numCols; _w+=8) \ + { \ + f16x8_t tmpa; \ + mve_pred16_t p0 = vctp16q(cnt); \ + tmpa = vldrhq_z_f16(&data[i*_numCols + _w],p0);\ + tmpa = vmulq_n_f16(tmpa,(_Float16)v); \ + vstrhq_p(&data[i*_numCols + _w], tmpa, p0); \ + cnt -= 8; \ + } \ + \ +} + +#define MAC_ROW_F16(COL,A,i,v,B,j) \ +{ \ + int cnt = ((A)->numCols)-(COL); \ + int32_t _w; \ + float16_t *dataA = (A)->pData; \ + float16_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols; \ + \ + for(_w=(COL);_w < _numCols; _w+=8) \ + { \ + f16x8_t tmpa,tmpb; \ + mve_pred16_t p0 = vctp16q(cnt); \ + tmpa = vldrhq_z_f16(&dataA[i*_numCols + _w],p0);\ + tmpb = vldrhq_z_f16(&dataB[j*_numCols + _w],p0);\ + tmpa = vfmaq_n_f16(tmpa,tmpb,v); \ + vstrhq_p(&dataA[i*_numCols + _w], tmpa, p0); \ + cnt -= 8; \ + } \ + \ +} + +#define MAS_ROW_F16(COL,A,i,v,B,j) \ +{ \ + int cnt = ((A)->numCols)-(COL); \ + int32_t _w; \ + float16_t *dataA = (A)->pData; \ + float16_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols; \ + f16x8_t vec=vdupq_n_f16(v); \ + \ + for(_w=(COL);_w < _numCols; _w+=8) \ + { \ + f16x8_t tmpa,tmpb; \ + mve_pred16_t p0 = vctp16q(cnt); \ + tmpa = vldrhq_z_f16(&dataA[i*_numCols + _w],p0);\ + tmpb = vldrhq_z_f16(&dataB[j*_numCols + _w],p0);\ + tmpa = vfmsq_f16(tmpa,tmpb,vec); \ + vstrhq_p(&dataA[i*_numCols + _w], tmpa, p0); \ + cnt -= 8; \ + } \ + \ +} + +#else + + +#define SWAP_ROWS_F16(A,COL,i,j) \ +{ \ + int32_t _w; \ + float16_t *dataI = (A)->pData; \ + float16_t *dataJ = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + dataI += i*_numCols + (COL); \ + dataJ += j*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + float16_t tmp; \ + tmp = *dataI; \ + *dataI++ = *dataJ; \ + *dataJ++ = tmp; \ + } \ +} + +#define SCALE_ROW_F16(A,COL,v,i) \ +{ \ + int32_t _w; \ + float16_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + data += i*_numCols + (COL); \ + \ + _Float16 sum; \ + for(_w=0;_w < nb; _w++) \ + { \ + sum = *data; \ + sum *= (_Float16)v; \ + *data++ = sum; \ + } \ +} + + +#define MAC_ROW_F16(COL,A,i,v,B,j) \ +{ \ + int32_t _w; \ + float16_t *dataA = (A)->pData; \ + float16_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols; \ + const int32_t nb = _numCols-(COL); \ + \ + dataA += i*_numCols + (COL); \ + dataB += j*_numCols + (COL); \ + \ + _Float16 sum ; \ + for(_w=0;_w < nb; _w++) \ + { \ + sum = *dataA; \ + sum += (_Float16)v * (_Float16)*dataB++;\ + *dataA++ = sum; \ + } \ +} + +#define MAS_ROW_F16(COL,A,i,v,B,j) \ +{ \ + int32_t _w; \ + float16_t *dataA = (A)->pData; \ + float16_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols; \ + const int32_t nb = _numCols-(COL); \ + \ + dataA += i*_numCols + (COL); \ + dataB += j*_numCols + (COL); \ + \ + _Float16 sum ; \ + for(_w=0;_w < nb; _w++) \ + { \ + sum = *dataA; \ + sum -= (_Float16)v * (_Float16)*dataB++;\ + *dataA++ = sum; \ + } \ +} + +#endif /*defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)*/ + +/* Functions with only a scalar version */ +#define COPY_COL_F16(A,ROW,COL,DST) \ + COPY_COL_T(float16_t,A,ROW,COL,DST) + +#define SCALE_COL_F16(A,ROW,v,i) \ + SCALE_COL_T(float16_t,(_Float16),A,ROW,v,i) + +#endif /* defined(ARM_FLOAT16_SUPPORTED)*/ + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +#define SWAP_ROWS_F32(A,COL,i,j) \ + { \ + int cnt = ((A)->numCols)-(COL); \ + float32_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + int32_t _w; \ + \ + for(_w=(COL);_w < _numCols; _w+=4) \ + { \ + f32x4_t tmpa,tmpb; \ + mve_pred16_t p0 = vctp32q(cnt); \ + \ + tmpa=vldrwq_z_f32(&data[i*_numCols + _w],p0);\ + tmpb=vldrwq_z_f32(&data[j*_numCols + _w],p0);\ + \ + vstrwq_p(&data[i*_numCols + _w], tmpb, p0); \ + vstrwq_p(&data[j*_numCols + _w], tmpa, p0); \ + \ + cnt -= 4; \ + } \ + } + +#define MAC_ROW_F32(COL,A,i,v,B,j) \ +{ \ + int cnt = ((A)->numCols)-(COL); \ + float32_t *dataA = (A)->pData; \ + float32_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols; \ + int32_t _w; \ + \ + for(_w=(COL);_w < _numCols; _w+=4) \ + { \ + f32x4_t tmpa,tmpb; \ + mve_pred16_t p0 = vctp32q(cnt); \ + tmpa = vldrwq_z_f32(&dataA[i*_numCols + _w],p0);\ + tmpb = vldrwq_z_f32(&dataB[j*_numCols + _w],p0);\ + tmpa = vfmaq_n_f32(tmpa,tmpb,v); \ + vstrwq_p(&dataA[i*_numCols + _w], tmpa, p0); \ + cnt -= 4; \ + } \ + \ +} + +#define MAS_ROW_F32(COL,A,i,v,B,j) \ +{ \ + int cnt = ((A)->numCols)-(COL); \ + float32_t *dataA = (A)->pData; \ + float32_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols; \ + int32_t _w; \ + f32x4_t vec=vdupq_n_f32(v); \ + \ + for(_w=(COL);_w < _numCols; _w+=4) \ + { \ + f32x4_t tmpa,tmpb; \ + mve_pred16_t p0 = vctp32q(cnt); \ + tmpa = vldrwq_z_f32(&dataA[i*_numCols + _w],p0);\ + tmpb = vldrwq_z_f32(&dataB[j*_numCols + _w],p0);\ + tmpa = vfmsq_f32(tmpa,tmpb,vec); \ + vstrwq_p(&dataA[i*_numCols + _w], tmpa, p0); \ + cnt -= 4; \ + } \ + \ +} + +#define SCALE_ROW_F32(A,COL,v,i) \ +{ \ + int cnt = ((A)->numCols)-(COL); \ + float32_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + int32_t _w; \ + \ + for(_w=(COL);_w < _numCols; _w+=4) \ + { \ + f32x4_t tmpa; \ + mve_pred16_t p0 = vctp32q(cnt); \ + tmpa = vldrwq_z_f32(&data[i*_numCols + _w],p0);\ + tmpa = vmulq_n_f32(tmpa,v); \ + vstrwq_p(&data[i*_numCols + _w], tmpa, p0); \ + cnt -= 4; \ + } \ + \ +} + +#elif defined(ARM_MATH_NEON) + +#define SWAP_ROWS_F32(A,COL,i,j) \ +{ \ + int32_t _w; \ + float32_t *dataI = (A)->pData; \ + float32_t *dataJ = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols - COL; \ + \ + dataI += i*_numCols + (COL); \ + dataJ += j*_numCols + (COL); \ + \ + float32_t tmp; \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + tmp = *dataI; \ + *dataI++ = *dataJ; \ + *dataJ++ = tmp; \ + } \ +} + +#define MAC_ROW_F32(COL,A,i,v,B,j) \ +{ \ + float32_t *dataA = (A)->pData; \ + float32_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols - (COL); \ + int32_t nbElems; \ + f32x4_t vec = vdupq_n_f32(v); \ + \ + nbElems = nb >> 2; \ + \ + dataA += i*_numCols + (COL); \ + dataB += j*_numCols + (COL); \ + \ + while(nbElems>0) \ + { \ + f32x4_t tmpa,tmpb; \ + tmpa = vld1q_f32(dataA,p0); \ + tmpb = vld1q_f32(dataB,p0); \ + tmpa = vmlaq_f32(tmpa,tmpb,vec);\ + vst1q_f32(dataA, tmpa, p0); \ + nbElems--; \ + dataA += 4; \ + dataB += 4; \ + } \ + \ + nbElems = nb & 3; \ + while(nbElems > 0) \ + { \ + *dataA++ += v* *dataB++; \ + nbElems--; \ + } \ +} + +#define MAS_ROW_F32(COL,A,i,v,B,j) \ +{ \ + float32_t *dataA = (A)->pData; \ + float32_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols - (COL); \ + int32_t nbElems; \ + f32x4_t vec = vdupq_n_f32(v); \ + \ + nbElems = nb >> 2; \ + \ + dataA += i*_numCols + (COL); \ + dataB += j*_numCols + (COL); \ + \ + while(nbElems>0) \ + { \ + f32x4_t tmpa,tmpb; \ + tmpa = vld1q_f32(dataA); \ + tmpb = vld1q_f32(dataB); \ + tmpa = vmlsq_f32(tmpa,tmpb,vec);\ + vst1q_f32(dataA, tmpa); \ + nbElems--; \ + dataA += 4; \ + dataB += 4; \ + } \ + \ + nbElems = nb & 3; \ + while(nbElems > 0) \ + { \ + *dataA++ -= v* *dataB++; \ + nbElems--; \ + } \ +} + +#define SCALE_ROW_F32(A,COL,v,i) \ +{ \ + float32_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + const int32_t nb = _numCols - (COL); \ + int32_t nbElems; \ + f32x4_t vec = vdupq_n_f32(v); \ + \ + nbElems = nb >> 2; \ + \ + data += i*_numCols + (COL); \ + while(nbElems>0) \ + { \ + f32x4_t tmpa; \ + tmpa = vld1q_f32(data); \ + tmpa = vmulq_f32(tmpa,vec); \ + vst1q_f32(data, tmpa); \ + data += 4; \ + nbElems --; \ + } \ + \ + nbElems = nb & 3; \ + while(nbElems > 0) \ + { \ + *data++ *= v; \ + nbElems--; \ + } \ + \ +} + +#else + +#define SWAP_ROWS_F32(A,COL,i,j) \ +{ \ + int32_t _w; \ + float32_t tmp; \ + float32_t *dataI = (A)->pData; \ + float32_t *dataJ = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols - COL; \ + \ + dataI += i*_numCols + (COL); \ + dataJ += j*_numCols + (COL); \ + \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + tmp = *dataI; \ + *dataI++ = *dataJ; \ + *dataJ++ = tmp; \ + } \ +} + +#define SCALE_ROW_F32(A,COL,v,i) \ +{ \ + int32_t _w; \ + float32_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols - COL; \ + \ + data += i*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *data++ *= v; \ + } \ +} + + +#define MAC_ROW_F32(COL,A,i,v,B,j) \ +{ \ + int32_t _w; \ + float32_t *dataA = (A)->pData; \ + float32_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + dataA = dataA + i*_numCols + (COL); \ + dataB = dataB + j*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *dataA++ += v* *dataB++; \ + } \ +} + +#define MAS_ROW_F32(COL,A,i,v,B,j) \ +{ \ + int32_t _w; \ + float32_t *dataA = (A)->pData; \ + float32_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + dataA = dataA + i*_numCols + (COL); \ + dataB = dataB + j*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *dataA++ -= v* *dataB++; \ + } \ +} + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + + +/* Functions _with only a scalar version */ + +#define COPY_COL_F32(A,ROW,COL,DST) \ + COPY_COL_T(float32_t,A,ROW,COL,DST) + +#define COPY_COL_F64(A,ROW,COL,DST) \ + COPY_COL_T(float64_t,A,ROW,COL,DST) + +#define SWAP_COLS_F32(A,COL,i,j) \ +{ \ + int32_t _w; \ + float32_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + for(_w=(COL);_w < _numCols; _w++) \ + { \ + float32_t tmp; \ + tmp = data[_w*_numCols + i]; \ + data[_w*_numCols + i] = data[_w*_numCols + j];\ + data[_w*_numCols + j] = tmp; \ + } \ +} + +#define SCALE_COL_F32(A,ROW,v,i) \ + SCALE_COL_T(float32_t,,A,ROW,v,i) + +#define SWAP_ROWS_F64(A,COL,i,j) \ +{ \ + int32_t _w; \ + float64_t *dataI = (A)->pData; \ + float64_t *dataJ = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + dataI += i*_numCols + (COL); \ + dataJ += j*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + float64_t tmp; \ + tmp = *dataI; \ + *dataI++ = *dataJ; \ + *dataJ++ = tmp; \ + } \ +} + +#define SWAP_COLS_F64(A,COL,i,j) \ +{ \ + int32_t _w; \ + float64_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols; \ + for(_w=(COL);_w < _numCols; _w++) \ + { \ + float64_t tmp; \ + tmp = data[_w*_numCols + i]; \ + data[_w*_numCols + i] = data[_w*_numCols + j];\ + data[_w*_numCols + j] = tmp; \ + } \ +} + +#define SCALE_ROW_F64(A,COL,v,i) \ +{ \ + int32_t _w; \ + float64_t *data = (A)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + data += i*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *data++ *= v; \ + } \ +} + +#define SCALE_COL_F64(A,ROW,v,i) \ + SCALE_COL_T(float64_t,,A,ROW,v,i) + +#define MAC_ROW_F64(COL,A,i,v,B,j) \ +{ \ + int32_t _w; \ + float64_t *dataA = (A)->pData; \ + float64_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + dataA += i*_numCols + (COL); \ + dataB += j*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *dataA++ += v* *dataB++; \ + } \ +} + +#define MAS_ROW_F64(COL,A,i,v,B,j) \ +{ \ + int32_t _w; \ + float64_t *dataA = (A)->pData; \ + float64_t *dataB = (B)->pData; \ + const int32_t _numCols = (A)->numCols;\ + const int32_t nb = _numCols-(COL); \ + \ + dataA += i*_numCols + (COL); \ + dataB += j*_numCols + (COL); \ + \ + for(_w=0;_w < nb; _w++) \ + { \ + *dataA++ -= v* *dataB++; \ + } \ +} + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _MATRIX_UTILS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/none.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/none.h new file mode 100755 index 0000000..019c41f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/none.h @@ -0,0 +1,576 @@ +/****************************************************************************** + * @file none.h + * @brief Intrinsics when no DSP extension available + * @version V1.9.0 + * @date 20. July 2020 + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + +Definitions in this file are allowing to reuse some versions of the +CMSIS-DSP to build on a core (M0 for instance) or a host where +DSP extension are not available. + +Ideally a pure C version should have been used instead. +But those are not always available or use a restricted set +of intrinsics. + +*/ + +#ifndef NONE_H_ +#define NONE_H_ + +#include "arm_math_types.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + + +/* + +Normally those kind of definitions are in a compiler file +in Core or Core_A. + +But for MSVC compiler it is a bit special. The goal is very specific +to CMSIS-DSP and only to allow the use of this library from other +systems like Python or Matlab. + +MSVC is not going to be used to cross-compile to ARM. So, having a MSVC +compiler file in Core or Core_A would not make sense. + +*/ +#if defined ( _MSC_VER ) || defined(__GNUC_PYTHON__) || defined(__APPLE_CC__) + __STATIC_FORCEINLINE uint8_t __CLZ(uint32_t data) + { + if (data == 0U) { return 32U; } + + uint32_t count = 0U; + uint32_t mask = 0x80000000U; + + while ((data & mask) == 0U) + { + count += 1U; + mask = mask >> 1U; + } + return ((uint8_t)count); + } + + __STATIC_FORCEINLINE int32_t __SSAT(int32_t val, uint32_t sat) + { + if ((sat >= 1U) && (sat <= 32U)) + { + const int32_t max = (int32_t)((1U << (sat - 1U)) - 1U); + const int32_t min = -1 - max ; + if (val > max) + { + return max; + } + else if (val < min) + { + return min; + } + } + return val; + } + + __STATIC_FORCEINLINE uint32_t __USAT(int32_t val, uint32_t sat) + { + if (sat <= 31U) + { + const uint32_t max = ((1U << sat) - 1U); + if (val > (int32_t)max) + { + return max; + } + else if (val < 0) + { + return 0U; + } + } + return (uint32_t)val; + } + + /** + \brief Rotate Right in unsigned value (32 bit) + \details Rotate Right (immediate) provides the value of the contents of a register rotated by a variable number of bits. + \param [in] op1 Value to rotate + \param [in] op2 Number of Bits to rotate + \return Rotated value + */ +__STATIC_FORCEINLINE uint32_t __ROR(uint32_t op1, uint32_t op2) +{ + op2 %= 32U; + if (op2 == 0U) + { + return op1; + } + return (op1 >> op2) | (op1 << (32U - op2)); +} + + +#endif + +/** + * @brief Clips Q63 to Q31 values. + */ + __STATIC_FORCEINLINE q31_t clip_q63_to_q31( + q63_t x) + { + return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ? + ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x; + } + + /** + * @brief Clips Q63 to Q15 values. + */ + __STATIC_FORCEINLINE q15_t clip_q63_to_q15( + q63_t x) + { + return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ? + ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15); + } + + /** + * @brief Clips Q31 to Q7 values. + */ + __STATIC_FORCEINLINE q7_t clip_q31_to_q7( + q31_t x) + { + return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ? + ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x; + } + + /** + * @brief Clips Q31 to Q15 values. + */ + __STATIC_FORCEINLINE q15_t clip_q31_to_q15( + q31_t x) + { + return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ? + ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x; + } + + /** + * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format. + */ + __STATIC_FORCEINLINE q63_t mult32x64( + q63_t x, + q31_t y) + { + return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) + + (((q63_t) (x >> 32) * y) ) ); + } + +/* SMMLAR */ +#define multAcc_32x32_keep32_R(a, x, y) \ + a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32) + +/* SMMLSR */ +#define multSub_32x32_keep32_R(a, x, y) \ + a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32) + +/* SMMULR */ +#define mult_32x32_keep32_R(a, x, y) \ + a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32) + +/* SMMLA */ +#define multAcc_32x32_keep32(a, x, y) \ + a += (q31_t) (((q63_t) x * y) >> 32) + +/* SMMLS */ +#define multSub_32x32_keep32(a, x, y) \ + a -= (q31_t) (((q63_t) x * y) >> 32) + +/* SMMUL */ +#define mult_32x32_keep32(a, x, y) \ + a = (q31_t) (((q63_t) x * y ) >> 32) + +#ifndef ARM_MATH_DSP + /** + * @brief definition to pack two 16 bit values. + */ + #define __PKHBT(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) << 0) & (int32_t)0x0000FFFF) | \ + (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000) ) + #define __PKHTB(ARG1, ARG2, ARG3) ( (((int32_t)(ARG1) << 0) & (int32_t)0xFFFF0000) | \ + (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF) ) +#endif + + /** + * @brief definition to pack four 8 bit values. + */ +#ifndef ARM_MATH_BIG_ENDIAN + #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) << 0) & (int32_t)0x000000FF) | \ + (((int32_t)(v1) << 8) & (int32_t)0x0000FF00) | \ + (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \ + (((int32_t)(v3) << 24) & (int32_t)0xFF000000) ) +#else + #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) << 0) & (int32_t)0x000000FF) | \ + (((int32_t)(v2) << 8) & (int32_t)0x0000FF00) | \ + (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \ + (((int32_t)(v0) << 24) & (int32_t)0xFF000000) ) +#endif + + + + +/* + * @brief C custom defined intrinsic functions + */ +#if !defined (ARM_MATH_DSP) + + + /* + * @brief C custom defined QADD8 + */ + __STATIC_FORCEINLINE uint32_t __QADD8( + uint32_t x, + uint32_t y) + { + q31_t r, s, t, u; + + r = __SSAT(((((q31_t)x << 24) >> 24) + (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF; + s = __SSAT(((((q31_t)x << 16) >> 24) + (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF; + t = __SSAT(((((q31_t)x << 8) >> 24) + (((q31_t)y << 8) >> 24)), 8) & (int32_t)0x000000FF; + u = __SSAT(((((q31_t)x ) >> 24) + (((q31_t)y ) >> 24)), 8) & (int32_t)0x000000FF; + + return ((uint32_t)((u << 24) | (t << 16) | (s << 8) | (r ))); + } + + + /* + * @brief C custom defined QSUB8 + */ + __STATIC_FORCEINLINE uint32_t __QSUB8( + uint32_t x, + uint32_t y) + { + q31_t r, s, t, u; + + r = __SSAT(((((q31_t)x << 24) >> 24) - (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF; + s = __SSAT(((((q31_t)x << 16) >> 24) - (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF; + t = __SSAT(((((q31_t)x << 8) >> 24) - (((q31_t)y << 8) >> 24)), 8) & (int32_t)0x000000FF; + u = __SSAT(((((q31_t)x ) >> 24) - (((q31_t)y ) >> 24)), 8) & (int32_t)0x000000FF; + + return ((uint32_t)((u << 24) | (t << 16) | (s << 8) | (r ))); + } + + + /* + * @brief C custom defined QADD16 + */ + __STATIC_FORCEINLINE uint32_t __QADD16( + uint32_t x, + uint32_t y) + { +/* q31_t r, s; without initialisation 'arm_offset_q15 test' fails but 'intrinsic' tests pass! for armCC */ + q31_t r = 0, s = 0; + + r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) + (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHADD16 + */ + __STATIC_FORCEINLINE uint32_t __SHADD16( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) + (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined QSUB16 + */ + __STATIC_FORCEINLINE uint32_t __QSUB16( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) - (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHSUB16 + */ + __STATIC_FORCEINLINE uint32_t __SHSUB16( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) - (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined QASX + */ + __STATIC_FORCEINLINE uint32_t __QASX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHASX + */ + __STATIC_FORCEINLINE uint32_t __SHASX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) - (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined QSAX + */ + __STATIC_FORCEINLINE uint32_t __QSAX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y ) >> 16)), 16) & (int32_t)0x0000FFFF; + s = __SSAT(((((q31_t)x ) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SHSAX + */ + __STATIC_FORCEINLINE uint32_t __SHSAX( + uint32_t x, + uint32_t y) + { + q31_t r, s; + + r = (((((q31_t)x << 16) >> 16) + (((q31_t)y ) >> 16)) >> 1) & (int32_t)0x0000FFFF; + s = (((((q31_t)x ) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF; + + return ((uint32_t)((s << 16) | (r ))); + } + + + /* + * @brief C custom defined SMUSDX + */ + __STATIC_FORCEINLINE uint32_t __SMUSDX( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) - + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) )); + } + + /* + * @brief C custom defined SMUADX + */ + __STATIC_FORCEINLINE uint32_t __SMUADX( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) )); + } + + + /* + * @brief C custom defined QADD + */ + __STATIC_FORCEINLINE int32_t __QADD( + int32_t x, + int32_t y) + { + return ((int32_t)(clip_q63_to_q31((q63_t)x + (q31_t)y))); + } + + + /* + * @brief C custom defined QSUB + */ + __STATIC_FORCEINLINE int32_t __QSUB( + int32_t x, + int32_t y) + { + return ((int32_t)(clip_q63_to_q31((q63_t)x - (q31_t)y))); + } + + + /* + * @brief C custom defined SMLAD + */ + __STATIC_FORCEINLINE uint32_t __SMLAD( + uint32_t x, + uint32_t y, + uint32_t sum) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) + + ( ((q31_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLADX + */ + __STATIC_FORCEINLINE uint32_t __SMLADX( + uint32_t x, + uint32_t y, + uint32_t sum) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) + + ( ((q31_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLSDX + */ + __STATIC_FORCEINLINE uint32_t __SMLSDX( + uint32_t x, + uint32_t y, + uint32_t sum) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) - + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) + + ( ((q31_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLALD + */ + __STATIC_FORCEINLINE uint64_t __SMLALD( + uint32_t x, + uint32_t y, + uint64_t sum) + { +/* return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) + ((q15_t) x * (q15_t) y)); */ + return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) + + ( ((q63_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMLALDX + */ + __STATIC_FORCEINLINE uint64_t __SMLALDX( + uint32_t x, + uint32_t y, + uint64_t sum) + { +/* return (sum + ((q15_t) (x >> 16) * (q15_t) y)) + ((q15_t) x * (q15_t) (y >> 16)); */ + return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y ) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y << 16) >> 16)) + + ( ((q63_t)sum ) ) )); + } + + + /* + * @brief C custom defined SMUAD + */ + __STATIC_FORCEINLINE uint32_t __SMUAD( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) + + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) )); + } + + + /* + * @brief C custom defined SMUSD + */ + __STATIC_FORCEINLINE uint32_t __SMUSD( + uint32_t x, + uint32_t y) + { + return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) - + ((((q31_t)x ) >> 16) * (((q31_t)y ) >> 16)) )); + } + + + /* + * @brief C custom defined SXTB16 + */ + __STATIC_FORCEINLINE uint32_t __SXTB16( + uint32_t x) + { + return ((uint32_t)(((((q31_t)x << 24) >> 24) & (q31_t)0x0000FFFF) | + ((((q31_t)x << 8) >> 8) & (q31_t)0xFFFF0000) )); + } + + /* + * @brief C custom defined SMMLA + */ + __STATIC_FORCEINLINE int32_t __SMMLA( + int32_t x, + int32_t y, + int32_t sum) + { + return (sum + (int32_t) (((int64_t) x * y) >> 32)); + } + +#endif /* !defined (ARM_MATH_DSP) */ + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _TRANSFORM_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/quaternion_math_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/quaternion_math_functions.h new file mode 100755 index 0000000..6c823a3 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/quaternion_math_functions.h @@ -0,0 +1,153 @@ +/****************************************************************************** + * @file quaternion_math_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2021 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef QUATERNION_MATH_FUNCTIONS_H_ +#define QUATERNION_MATH_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup groupQuaternionMath Quaternion Math Functions + * Functions to operates on quaternions and convert between a + * rotation and quaternion representation. + */ + + +/** + @brief Floating-point quaternion Norm. + @param[in] pInputQuaternions points to the input vector of quaternions + @param[out] pNorms points to the output vector of norms + @param[in] nbQuaternions number of quaternions in each vector + */ +void arm_quaternion_norm_f32(const float32_t *pInputQuaternions, + float32_t *pNorms, + uint32_t nbQuaternions); + + +/** + @brief Floating-point quaternion inverse. + @param[in] pInputQuaternions points to the input vector of quaternions + @param[out] pInverseQuaternions points to the output vector of inverse quaternions + @param[in] nbQuaternions number of quaternions in each vector + */ +void arm_quaternion_inverse_f32(const float32_t *pInputQuaternions, + float32_t *pInverseQuaternions, + uint32_t nbQuaternions); + + +/** + @brief Floating-point quaternion conjugates. + @param[in] pInputQuaternions points to the input vector of quaternions + @param[out] pConjugateQuaternions points to the output vector of conjugate quaternions + @param[in] nbQuaternions number of quaternions in each vector + */ +void arm_quaternion_conjugate_f32(const float32_t *inputQuaternions, + float32_t *pConjugateQuaternions, + uint32_t nbQuaternions); + + +/** + @brief Floating-point normalization of quaternions. + @param[in] pInputQuaternions points to the input vector of quaternions + @param[out] pNormalizedQuaternions points to the output vector of normalized quaternions + @param[in] nbQuaternions number of quaternions in each vector + */ +void arm_quaternion_normalize_f32(const float32_t *inputQuaternions, + float32_t *pNormalizedQuaternions, + uint32_t nbQuaternions); + + +/** + @brief Floating-point product of two quaternions. + @param[in] qa First quaternion + @param[in] qb Second quaternion + @param[out] r Product of two quaternions + */ +void arm_quaternion_product_single_f32(const float32_t *qa, + const float32_t *qb, + float32_t *r); + + +/** + @brief Floating-point elementwise product two quaternions. + @param[in] qa First array of quaternions + @param[in] qb Second array of quaternions + @param[out] r Elementwise product of quaternions + @param[in] nbQuaternions Number of quaternions in the array + */ +void arm_quaternion_product_f32(const float32_t *qa, + const float32_t *qb, + float32_t *r, + uint32_t nbQuaternions); + + +/** + * @brief Conversion of quaternion to equivalent rotation matrix. + * @param[in] pInputQuaternions points to an array of normalized quaternions + * @param[out] pOutputRotations points to an array of 3x3 rotations (in row order) + * @param[in] nbQuaternions in the array + * + * Format of rotation matrix + * \par + * The quaternion a + ib + jc + kd is converted into rotation matrix: + * a^2 + b^2 - c^2 - d^2 2bc - 2ad 2bd + 2ac + * 2bc + 2ad a^2 - b^2 + c^2 - d^2 2cd - 2ab + * 2bd - 2ac 2cd + 2ab a^2 - b^2 - c^2 + d^2 + * + * Rotation matrix is saved in row order : R00 R01 R02 R10 R11 R12 R20 R21 R22 + */ +void arm_quaternion2rotation_f32(const float32_t *pInputQuaternions, + float32_t *pOutputRotations, + uint32_t nbQuaternions); + + +/** + * @brief Conversion of a rotation matrix to equivalent quaternion. + * @param[in] pInputRotations points to an array 3x3 rotation matrix (in row order) + * @param[out] pOutputQuaternions points to an array of quaternions + * @param[in] nbQuaternions in the array +*/ +void arm_rotation2quaternion_f32(const float32_t *pInputRotations, + float32_t *pOutputQuaternions, + uint32_t nbQuaternions); + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _QUATERNION_MATH_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/statistics_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/statistics_functions.h new file mode 100755 index 0000000..301aadd --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/statistics_functions.h @@ -0,0 +1,988 @@ +/****************************************************************************** + * @file statistics_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.1 + * @date 14 July 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef STATISTICS_FUNCTIONS_H_ +#define STATISTICS_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/basic_math_functions.h" +#include "dsp/fast_math_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + +/** + * @defgroup groupStats Statistics Functions + */ + +/** + * @brief Computation of the LogSumExp + * + * In probabilistic computations, the dynamic of the probability values can be very + * wide because they come from gaussian functions. + * To avoid underflow and overflow issues, the values are represented by their log. + * In this representation, multiplying the original exp values is easy : their logs are added. + * But adding the original exp values is requiring some special handling and it is the + * goal of the LogSumExp function. + * + * If the values are x1...xn, the function is computing: + * + * ln(exp(x1) + ... + exp(xn)) and the computation is done in such a way that + * rounding issues are minimised. + * + * The max xm of the values is extracted and the function is computing: + * xm + ln(exp(x1 - xm) + ... + exp(xn - xm)) + * + * @param[in] *in Pointer to an array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return LogSumExp + * + */ + + +float32_t arm_logsumexp_f32(const float32_t *in, uint32_t blockSize); + +/** + * @brief Dot product with log arithmetic + * + * Vectors are containing the log of the samples + * + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[in] pTmpBuffer temporary buffer of length blockSize + * @return The log of the dot product . + * + */ + + +float32_t arm_logsumexp_dot_prod_f32(const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t blockSize, + float32_t *pTmpBuffer); + +/** + * @brief Entropy + * + * @param[in] pSrcA Array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return Entropy -Sum(p ln p) + * + */ + + +float32_t arm_entropy_f32(const float32_t * pSrcA,uint32_t blockSize); + + +/** + * @brief Entropy + * + * @param[in] pSrcA Array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return Entropy -Sum(p ln p) + * + */ + + +float64_t arm_entropy_f64(const float64_t * pSrcA, uint32_t blockSize); + + +/** + * @brief Kullback-Leibler + * + * @param[in] pSrcA Pointer to an array of input values for probability distribution A. + * @param[in] pSrcB Pointer to an array of input values for probability distribution B. + * @param[in] blockSize Number of samples in the input array. + * @return Kullback-Leibler Divergence D(A || B) + * + */ +float32_t arm_kullback_leibler_f32(const float32_t * pSrcA + ,const float32_t * pSrcB + ,uint32_t blockSize); + + +/** + * @brief Kullback-Leibler + * + * @param[in] pSrcA Pointer to an array of input values for probability distribution A. + * @param[in] pSrcB Pointer to an array of input values for probability distribution B. + * @param[in] blockSize Number of samples in the input array. + * @return Kullback-Leibler Divergence D(A || B) + * + */ +float64_t arm_kullback_leibler_f64(const float64_t * pSrcA, + const float64_t * pSrcB, + uint32_t blockSize); + + + /** + * @brief Sum of the squares of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_q31( + const q31_t * pSrc, + uint32_t blockSize, + q63_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_q15( + const q15_t * pSrc, + uint32_t blockSize, + q63_t * pResult); + + + /** + * @brief Sum of the squares of the elements of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_q7( + const q7_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Mean value of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult); + + + /** + * @brief Mean value of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Mean value of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Mean value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Mean value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + + /** + * @brief Variance of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Variance of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + + /** + * @brief Variance of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Variance of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Root Mean Square of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Root Mean Square of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Root Mean Square of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Standard deviation of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Standard deviation of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + + /** + * @brief Standard deviation of the elements of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Standard deviation of the elements of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + + /** + * @brief Minimum value of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[in] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[in] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_absmin_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a Q7 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + */ + void arm_absmin_no_idx_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult); + + + /** + * @brief Minimum value of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[in] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult, + uint32_t * pIndex); + +/** + * @brief Minimum value of absolute values of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[in] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_absmin_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a Q15 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + */ + void arm_absmin_no_idx_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + + + /** + * @brief Minimum value of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_absmin_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a Q31 vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + */ + void arm_absmin_no_idx_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + + + /** + * @brief Minimum value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_absmin_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + */ + void arm_absmin_no_idx_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + + + /** + * @brief Minimum value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_absmin_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + */ + void arm_absmin_no_idx_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + +/** + * @brief Maximum value of a Q7 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a Q7 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_absmax_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a Q7 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + */ + void arm_absmax_no_idx_q7( + const q7_t * pSrc, + uint32_t blockSize, + q7_t * pResult); + + +/** + * @brief Maximum value of a Q15 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a Q15 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_absmax_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult, + uint32_t * pIndex); + + /** + * @brief Maximum value of absolute values of a Q15 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + */ + void arm_absmax_no_idx_q15( + const q15_t * pSrc, + uint32_t blockSize, + q15_t * pResult); + +/** + * @brief Maximum value of a Q31 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a Q31 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_absmax_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult, + uint32_t * pIndex); + + /** + * @brief Maximum value of absolute values of a Q31 vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + */ + void arm_absmax_no_idx_q31( + const q31_t * pSrc, + uint32_t blockSize, + q31_t * pResult); + +/** + * @brief Maximum value of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_absmax_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult, + uint32_t * pIndex); + + /** + * @brief Maximum value of absolute values of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + */ + void arm_absmax_no_idx_f32( + const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + +/** + * @brief Maximum value of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_absmax_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + */ + void arm_absmax_no_idx_f64( + const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + /** + @brief Maximum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + */ + void arm_max_no_idx_f32( + const float32_t *pSrc, + uint32_t blockSize, + float32_t *pResult); + + /** + @brief Minimum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult minimum value returned here + */ + void arm_min_no_idx_f32( + const float32_t *pSrc, + uint32_t blockSize, + float32_t *pResult); + + /** + @brief Maximum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + */ + void arm_max_no_idx_f64( + const float64_t *pSrc, + uint32_t blockSize, + float64_t *pResult); + + /** + @brief Maximum value of a q31 vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + */ + void arm_max_no_idx_q31( + const q31_t *pSrc, + uint32_t blockSize, + q31_t *pResult); + + /** + @brief Maximum value of a q15 vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + */ + void arm_max_no_idx_q15( + const q15_t *pSrc, + uint32_t blockSize, + q15_t *pResult); + + /** + @brief Maximum value of a q7 vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + */ + void arm_max_no_idx_q7( + const q7_t *pSrc, + uint32_t blockSize, + q7_t *pResult); + + /** + @brief Minimum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult minimum value returned here + */ + void arm_min_no_idx_f64( + const float64_t *pSrc, + uint32_t blockSize, + float64_t *pResult); + +/** + @brief Minimum value of a q31 vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult minimum value returned here + */ + void arm_min_no_idx_q31( + const q31_t *pSrc, + uint32_t blockSize, + q31_t *pResult); + + /** + @brief Minimum value of a q15 vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult minimum value returned here + */ + void arm_min_no_idx_q15( + const q15_t *pSrc, + uint32_t blockSize, + q15_t *pResult); + + /** + @brief Minimum value of a q7 vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult minimum value returned here + */ +void arm_min_no_idx_q7( + const q7_t *pSrc, + uint32_t blockSize, + q7_t *pResult); + +/** + @brief Mean square error between two Q7 vectors. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult mean square error +*/ + +void arm_mse_q7( + const q7_t * pSrcA, + const q7_t * pSrcB, + uint32_t blockSize, + q7_t * pResult); + +/** + @brief Mean square error between two Q15 vectors. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult mean square error +*/ + +void arm_mse_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t blockSize, + q15_t * pResult); + +/** + @brief Mean square error between two Q31 vectors. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult mean square error +*/ + +void arm_mse_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t blockSize, + q31_t * pResult); + +/** + @brief Mean square error between two single precision float vectors. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult mean square error +*/ + +void arm_mse_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t blockSize, + float32_t * pResult); + +/** + @brief Mean square error between two double precision float vectors. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult mean square error +*/ + +void arm_mse_f64( + const float64_t * pSrcA, + const float64_t * pSrcB, + uint32_t blockSize, + float64_t * pResult); + + +/** + * @brief Accumulation value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + +void arm_accumulate_f32( +const float32_t * pSrc, + uint32_t blockSize, + float32_t * pResult); + +/** + * @brief Accumulation value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + +void arm_accumulate_f64( +const float64_t * pSrc, + uint32_t blockSize, + float64_t * pResult); + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _STATISTICS_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/statistics_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/statistics_functions_f16.h new file mode 100755 index 0000000..746e8df --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/statistics_functions_f16.h @@ -0,0 +1,274 @@ +/****************************************************************************** + * @file statistics_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.1 + * @date 14 July 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef STATISTICS_FUNCTIONS_F16_H_ +#define STATISTICS_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/basic_math_functions_f16.h" +#include "dsp/fast_math_functions_f16.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + /** + * @brief Sum of the squares of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_power_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + /** + * @brief Mean value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_mean_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + /** + * @brief Variance of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_var_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + /** + * @brief Root Mean Square of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_rms_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + /** + * @brief Standard deviation of the elements of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_std_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + /** + * @brief Minimum value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_min_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + * @param[out] pIndex is the array index of the minimum value in the input buffer. + */ + void arm_absmin_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_max_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult, + uint32_t * pIndex); + +/** + * @brief Maximum value of absolute values of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + * @param[out] pIndex index of maximum value returned here + */ + void arm_absmax_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult, + uint32_t * pIndex); + + /** + * @brief Minimum value of absolute values of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output pointer + */ + void arm_absmin_no_idx_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + +/** + * @brief Maximum value of a floating-point vector. + * @param[in] pSrc points to the input buffer + * @param[in] blockSize length of the input vector + * @param[out] pResult maximum value returned here + */ + void arm_absmax_no_idx_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + +/** + * @brief Entropy + * + * @param[in] pSrcA Array of input values. + * @param[in] blockSize Number of samples in the input array. + * @return Entropy -Sum(p ln p) + */ +float16_t arm_entropy_f16(const float16_t * pSrcA,uint32_t blockSize); + + +float16_t arm_logsumexp_f16(const float16_t *in, uint32_t blockSize); + + +/** + * @brief Dot product with log arithmetic + * + * Vectors are containing the log of the samples + * + * @param[in] pSrcA points to the first input vector + * @param[in] pSrcB points to the second input vector + * @param[in] blockSize number of samples in each vector + * @param[in] pTmpBuffer temporary buffer of length blockSize + * @return The log of the dot product . + */ +float16_t arm_logsumexp_dot_prod_f16(const float16_t * pSrcA, + const float16_t * pSrcB, + uint32_t blockSize, + float16_t *pTmpBuffer); + + +/** + * @brief Kullback-Leibler + * + * @param[in] pSrcA Pointer to an array of input values for probability distribution A. + * @param[in] pSrcB Pointer to an array of input values for probability distribution B. + * @param[in] blockSize Number of samples in the input array. + * @return Kullback-Leibler Divergence D(A || B) + */ +float16_t arm_kullback_leibler_f16(const float16_t * pSrcA + ,const float16_t * pSrcB + ,uint32_t blockSize); + + +/** + @brief Maximum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult maximum value returned here + */ + void arm_max_no_idx_f16( + const float16_t *pSrc, + uint32_t blockSize, + float16_t *pResult); + + +/** + @brief Minimum value of a floating-point vector. + @param[in] pSrc points to the input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult minimum value returned here + */ + void arm_min_no_idx_f16( + const float16_t *pSrc, + uint32_t blockSize, + float16_t *pResult); + + +/** + @brief Mean square error between two half precision float vectors. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] blockSize number of samples in input vector + @param[out] pResult mean square error +*/ +void arm_mse_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + uint32_t blockSize, + float16_t * pResult); + + +/** + * @brief Sum value of a floating-point vector. + * @param[in] pSrc is input pointer + * @param[in] blockSize is the number of samples to process + * @param[out] pResult is output value. + */ + void arm_accumulate_f16( + const float16_t * pSrc, + uint32_t blockSize, + float16_t * pResult); + + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _STATISTICS_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/support_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/support_functions.h new file mode 100755 index 0000000..1f3ce8c --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/support_functions.h @@ -0,0 +1,539 @@ +/****************************************************************************** + * @file support_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.1 + * @date 18 August 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef SUPPORT_FUNCTIONS_H_ +#define SUPPORT_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup groupSupport Support Functions + */ + + +/** + * @brief Converts the elements of the 64 bit floating-point vector to floating-point vector. + * @param[in] pSrc points to the floating-point 64 input vector + * @param[out] pDst points to the floating-point output vector + * @param[in] blockSize length of the input vector + */ + void arm_f64_to_float( + const float64_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the 64 bit floating-point vector to Q31 vector. + * @param[in] pSrc points to the floating-point 64 input vector + * @param[out] pDst points to the Q31 output vector + * @param[in] blockSize length of the input vector + */ + void arm_f64_to_q31( + const float64_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the 64 bit floating-point vector to Q15 vector. + * @param[in] pSrc points to the floating-point 64 input vector + * @param[out] pDst points to the Q15 output vector + * @param[in] blockSize length of the input vector + */ + void arm_f64_to_q15( + const float64_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the 64 bit floating-point vector to Q7 vector. + * @param[in] pSrc points to the floating-point 64 input vector + * @param[out] pDst points to the Q7 output vector + * @param[in] blockSize length of the input vector + */ + void arm_f64_to_q7( + const float64_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + +/** + * @brief Converts the elements of the floating-point vector to 64 bit floating-point vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the 64 bit floating-point output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_f64( + const float32_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the floating-point vector to Q31 vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the Q31 output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_q31( + const float32_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the floating-point vector to Q15 vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the Q15 output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_q15( + const float32_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the floating-point vector to Q7 vector. + * @param[in] pSrc points to the floating-point input vector + * @param[out] pDst points to the Q7 output vector + * @param[in] blockSize length of the input vector + */ + void arm_float_to_q7( + const float32_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the Q31 vector to 64 bit floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ +void arm_q31_to_f64( +const q31_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Converts the elements of the Q31 vector to floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q31_to_float( + const q31_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q31 vector to Q15 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q31_to_q15( + const q31_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q31 vector to Q7 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q31_to_q7( + const q31_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the Q15 vector to 64 bit floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ +void arm_q15_to_f64( +const q15_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Converts the elements of the Q15 vector to floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q15_to_float( + const q15_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q15 vector to Q31 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q15_to_q31( + const q15_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q15 vector to Q7 vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q15_to_q7( + const q15_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + +/** + * @brief Converts the elements of the Q7 vector to 64 bit floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ +void arm_q7_to_f64( +const q7_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Converts the elements of the Q7 vector to floating-point vector. + * @param[in] pSrc is input pointer + * @param[out] pDst is output pointer + * @param[in] blockSize is the number of samples to process + */ + void arm_q7_to_float( + const q7_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q7 vector to Q31 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_q7_to_q31( + const q7_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Converts the elements of the Q7 vector to Q15 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_q7_to_q15( + const q7_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + + + + /** + * @brief Struct for specifying sorting algorithm + */ + typedef enum + { + ARM_SORT_BITONIC = 0, + /**< Bitonic sort */ + ARM_SORT_BUBBLE = 1, + /**< Bubble sort */ + ARM_SORT_HEAP = 2, + /**< Heap sort */ + ARM_SORT_INSERTION = 3, + /**< Insertion sort */ + ARM_SORT_QUICK = 4, + /**< Quick sort */ + ARM_SORT_SELECTION = 5 + /**< Selection sort */ + } arm_sort_alg; + + /** + * @brief Struct for specifying sorting algorithm + */ + typedef enum + { + ARM_SORT_DESCENDING = 0, + /**< Descending order (9 to 0) */ + ARM_SORT_ASCENDING = 1 + /**< Ascending order (0 to 9) */ + } arm_sort_dir; + + /** + * @brief Instance structure for the sorting algorithms. + */ + typedef struct + { + arm_sort_alg alg; /**< Sorting algorithm selected */ + arm_sort_dir dir; /**< Sorting order (direction) */ + } arm_sort_instance_f32; + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @param[in,out] S points to an instance of the sorting structure. + * @param[in] alg Selected algorithm. + * @param[in] dir Sorting order. + */ + void arm_sort_init_f32( + arm_sort_instance_f32 * S, + arm_sort_alg alg, + arm_sort_dir dir); + + /** + * @brief Instance structure for the sorting algorithms. + */ + typedef struct + { + arm_sort_dir dir; /**< Sorting order (direction) */ + float32_t * buffer; /**< Working buffer */ + } arm_merge_sort_instance_f32; + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in,out] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_merge_sort_f32( + const arm_merge_sort_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + uint32_t blockSize); + + /** + * @param[in,out] S points to an instance of the sorting structure. + * @param[in] dir Sorting order. + * @param[in] buffer Working buffer. + */ + void arm_merge_sort_init_f32( + arm_merge_sort_instance_f32 * S, + arm_sort_dir dir, + float32_t * buffer); + + + + /** + * @brief Copies the elements of a floating-point vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Copies the elements of a floating-point vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize); + + + + /** + * @brief Copies the elements of a Q7 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_q7( + const q7_t * pSrc, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Copies the elements of a Q15 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Copies the elements of a Q31 vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_copy_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a floating-point vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_f32( + float32_t value, + float32_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a floating-point vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_f64( + float64_t value, + float64_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a Q7 vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_q7( + q7_t value, + q7_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a Q15 vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_q15( + q15_t value, + q15_t * pDst, + uint32_t blockSize); + + + /** + * @brief Fills a constant value into a Q31 vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ + void arm_fill_q31( + q31_t value, + q31_t * pDst, + uint32_t blockSize); + + + + + + + +/** + * @brief Weighted average + * + * + * @param[in] *in Array of input values. + * @param[in] *weights Weights + * @param[in] blockSize Number of samples in the input array. + * @return Weighted average + * + */ +float32_t arm_weighted_average_f32(const float32_t *in + , const float32_t *weights + , uint32_t blockSize); + + +/** + * @brief Barycenter + * + * + * @param[in] in List of vectors + * @param[in] weights Weights of the vectors + * @param[out] out Barycenter + * @param[in] nbVectors Number of vectors + * @param[in] vecDim Dimension of space (vector dimension) + * + */ +void arm_barycenter_f32(const float32_t *in + , const float32_t *weights + , float32_t *out + , uint32_t nbVectors + , uint32_t vecDim); + + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _SUPPORT_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/support_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/support_functions_f16.h new file mode 100755 index 0000000..4786e59 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/support_functions_f16.h @@ -0,0 +1,204 @@ +/****************************************************************************** + * @file support_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.1 + * @date 18 August 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef SUPPORT_FUNCTIONS_F16_H_ +#define SUPPORT_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + + /** + * @brief Copies the elements of a floating-point vector. + * @param[in] pSrc input pointer + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ +void arm_copy_f16(const float16_t * pSrc, float16_t * pDst, uint32_t blockSize); + + + /** + * @brief Fills a constant value into a floating-point vector. + * @param[in] value input value to be filled + * @param[out] pDst output pointer + * @param[in] blockSize number of samples to process + */ +void arm_fill_f16(float16_t value, float16_t * pDst, uint32_t blockSize); + + +/** + * @brief Converts the elements of the floating-point vector to Q31 vector. + * @param[in] pSrc points to the f16 input vector + * @param[out] pDst points to the q15 output vector + * @param[in] blockSize length of the input vector + */ +void arm_f16_to_q15(const float16_t * pSrc, q15_t * pDst, uint32_t blockSize); + + +/** + * @brief Converts the elements of the floating-point vector to Q31 vector. + * @param[in] pSrc points to the q15 input vector + * @param[out] pDst points to the f16 output vector + * @param[in] blockSize length of the input vector + */ +void arm_q15_to_f16(const q15_t * pSrc, float16_t * pDst, uint32_t blockSize); + + +/** + * @brief Converts the elements of the 64 bit floating-point vector to 16 bit floating-point vector. + * @param[in] pSrc points to the f64 input vector + * @param[out] pDst points to the f16 output vector + * @param[in] blockSize length of the input vector + */ +void arm_f64_to_f16(const float64_t * pSrc, float16_t * pDst, uint32_t blockSize); + + +/** + * @brief Converts the elements of the 16 bit floating-point vector to 64 bit floating-point vector. + * @param[in] pSrc points to the f16 input vector + * @param[out] pDst points to the f64 output vector + * @param[in] blockSize length of the input vector + */ +void arm_f16_to_f64(const float16_t * pSrc, float64_t * pDst, uint32_t blockSize); + + +/** + * @brief Converts the elements of the floating-point vector to Q31 vector. + * @param[in] pSrc points to the f32 input vector + * @param[out] pDst points to the f16 output vector + * @param[in] blockSize length of the input vector + */ +void arm_float_to_f16(const float32_t * pSrc, float16_t * pDst, uint32_t blockSize); + + +/** + * @brief Converts the elements of the floating-point vector to Q31 vector. + * @param[in] pSrc points to the f16 input vector + * @param[out] pDst points to the f32 output vector + * @param[in] blockSize length of the input vector + */ +void arm_f16_to_float(const float16_t * pSrc, float32_t * pDst, uint32_t blockSize); + + +/** + * @brief Weighted average + * @param[in] *in Array of input values. + * @param[in] *weights Weights + * @param[in] blockSize Number of samples in the input array. + * @return Weighted average + */ +float16_t arm_weighted_average_f16(const float16_t *in + , const float16_t *weights + , uint32_t blockSize); + + +/** + * @brief Barycenter + * @param[in] in List of vectors + * @param[in] weights Weights of the vectors + * @param[out] out Barycenter + * @param[in] nbVectors Number of vectors + * @param[in] vecDim Dimension of space (vector dimension) + */ +void arm_barycenter_f16(const float16_t *in + , const float16_t *weights + , float16_t *out + , uint32_t nbVectors + , uint32_t vecDim); + + +/** + @ingroup groupSupport + */ + +/** + * @defgroup typecast Typecasting + */ + +/** + @addtogroup typecast + @{ + */ + +/** + * @brief Interpret a f16 as an s16 value + * @param[in] x input value. + * @return return value. + * + * @par Description + * It is a typecast. No conversion of the float to int is done. + * The memcpy will be optimized out by the compiler. + * memcpy is used to prevent type punning issues. + * With gcc, -fno-builtins MUST not be used or the + * memcpy will not be optimized out. + */ +__STATIC_INLINE int16_t arm_typecast_s16_f16(float16_t x) +{ + int16_t res; + res=*(int16_t*)memcpy((char*)&res,(char*)&x,sizeof(float16_t)); + return(res); +} + +/** + * @brief Interpret an s16 as an f16 value + * @param[in] x input value. + * @return return value. + * + * @par Description + * It is a typecast. No conversion of the int to float is done. + * The memcpy will be optimized out by the compiler. + * memcpy is used to prevent type punning issues. + * With gcc, -fno-builtins MUST not be used or the + * memcpy will not be optimized out. + */ +__STATIC_INLINE float16_t arm_typecast_f16_s16(int16_t x) +{ + float16_t res; + res=*(float16_t*)memcpy((char*)&res,(char*)&x,sizeof(int16_t)); + return(res); +} + + +/** + @} end of typecast group + */ + + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _SUPPORT_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_defines.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_defines.h new file mode 100755 index 0000000..185a8a9 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_defines.h @@ -0,0 +1,46 @@ +/****************************************************************************** + * @file svm_defines.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef SVM_DEFINES_H_ +#define SVM_DEFINES_H_ + +/** + * @brief Struct for specifying SVM Kernel + */ +typedef enum +{ + ARM_ML_KERNEL_LINEAR = 0, + /**< Linear kernel */ + ARM_ML_KERNEL_POLYNOMIAL = 1, + /**< Polynomial kernel */ + ARM_ML_KERNEL_RBF = 2, + /**< Radial Basis Function kernel */ + ARM_ML_KERNEL_SIGMOID = 3 + /**< Sigmoid kernel */ +} arm_ml_kernel_type; + +#endif diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_functions.h new file mode 100755 index 0000000..cb00cd4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_functions.h @@ -0,0 +1,280 @@ +/****************************************************************************** + * @file svm_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef SVM_FUNCTIONS_H_ +#define SVM_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" +#include "dsp/svm_defines.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#define STEP(x) (x) <= 0 ? 0 : 1 + +/** + * @defgroup groupSVM SVM Functions + * This set of functions is implementing SVM classification on 2 classes. + * The training must be done from scikit-learn. The parameters can be easily + * generated from the scikit-learn object. Some examples are given in + * DSP/Testing/PatternGeneration/SVM.py + * + * If more than 2 classes are needed, the functions in this folder + * will have to be used, as building blocks, to do multi-class classification. + * + * No multi-class classification is provided in this SVM folder. + * + */ + +/** + * @brief Integer exponentiation + * @param[in] x value + * @param[in] nb integer exponent >= 1 + * @return x^nb + */ +__STATIC_INLINE float32_t arm_exponent_f32(float32_t x, int32_t nb) +{ + float32_t r = x; + nb --; + while(nb > 0) + { + r = r * x; + nb--; + } + return(r); +} + + +/** + * @brief Instance structure for linear SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ +} arm_svm_linear_instance_f32; + + +/** + * @brief Instance structure for polynomial SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + int32_t degree; /**< Polynomial degree */ + float32_t coef0; /**< Polynomial constant */ + float32_t gamma; /**< Gamma factor */ +} arm_svm_polynomial_instance_f32; + + +/** + * @brief Instance structure for rbf SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + float32_t gamma; /**< Gamma factor */ +} arm_svm_rbf_instance_f32; + + +/** + * @brief Instance structure for sigmoid SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float32_t intercept; /**< Intercept */ + const float32_t *dualCoefficients; /**< Dual coefficients */ + const float32_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + float32_t coef0; /**< Independent constant */ + float32_t gamma; /**< Gamma factor */ +} arm_svm_sigmoid_instance_f32; + + +/** + * @brief SVM linear instance init function + * @param[in] S Parameters for SVM functions + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + */ +void arm_svm_linear_init_f32(arm_svm_linear_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes); + + +/** + * @brief SVM linear prediction + * @param[in] S Pointer to an instance of the linear SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + */ +void arm_svm_linear_predict_f32(const arm_svm_linear_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + +/** + * @brief SVM polynomial instance init function + * @param[in] S points to an instance of the polynomial SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] degree Polynomial degree + * @param[in] coef0 coeff0 (scikit-learn terminology) + * @param[in] gamma gamma (scikit-learn terminology) + */ +void arm_svm_polynomial_init_f32(arm_svm_polynomial_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes, + int32_t degree, + float32_t coef0, + float32_t gamma + ); + + +/** + * @brief SVM polynomial prediction + * @param[in] S Pointer to an instance of the polynomial SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + */ +void arm_svm_polynomial_predict_f32(const arm_svm_polynomial_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + +/** + * @brief SVM radial basis function instance init function + * @param[in] S points to an instance of the polynomial SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] gamma gamma (scikit-learn terminology) + */ +void arm_svm_rbf_init_f32(arm_svm_rbf_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes, + float32_t gamma + ); + + +/** + * @brief SVM rbf prediction + * @param[in] S Pointer to an instance of the rbf SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult decision value + */ +void arm_svm_rbf_predict_f32(const arm_svm_rbf_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + +/** + * @brief SVM sigmoid instance init function + * @param[in] S points to an instance of the rbf SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] coef0 coeff0 (scikit-learn terminology) + * @param[in] gamma gamma (scikit-learn terminology) + */ +void arm_svm_sigmoid_init_f32(arm_svm_sigmoid_instance_f32 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float32_t intercept, + const float32_t *dualCoefficients, + const float32_t *supportVectors, + const int32_t *classes, + float32_t coef0, + float32_t gamma + ); + + +/** + * @brief SVM sigmoid prediction + * @param[in] S Pointer to an instance of the rbf SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + */ +void arm_svm_sigmoid_predict_f32(const arm_svm_sigmoid_instance_f32 *S, + const float32_t * in, + int32_t * pResult); + + + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _SVM_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_functions_f16.h new file mode 100755 index 0000000..5f757a0 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/svm_functions_f16.h @@ -0,0 +1,265 @@ +/****************************************************************************** + * @file svm_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef SVM_FUNCTIONS_F16_H_ +#define SVM_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" +#include "dsp/svm_defines.h" + + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_FLOAT16_SUPPORTED) + +#define STEP(x) (x) <= 0 ? 0 : 1 + +/** + * @defgroup groupSVM SVM Functions + * This set of functions is implementing SVM classification on 2 classes. + * The training must be done from scikit-learn. The parameters can be easily + * generated from the scikit-learn object. Some examples are given in + * DSP/Testing/PatternGeneration/SVM.py + * + * If more than 2 classes are needed, the functions in this folder + * will have to be used, as building blocks, to do multi-class classification. + * + * No multi-class classification is provided in this SVM folder. + * + */ + + + +/** + * @brief Instance structure for linear SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float16_t intercept; /**< Intercept */ + const float16_t *dualCoefficients; /**< Dual coefficients */ + const float16_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ +} arm_svm_linear_instance_f16; + + +/** + * @brief Instance structure for polynomial SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float16_t intercept; /**< Intercept */ + const float16_t *dualCoefficients; /**< Dual coefficients */ + const float16_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + int32_t degree; /**< Polynomial degree */ + float16_t coef0; /**< Polynomial constant */ + float16_t gamma; /**< Gamma factor */ +} arm_svm_polynomial_instance_f16; + + +/** + * @brief Instance structure for rbf SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float16_t intercept; /**< Intercept */ + const float16_t *dualCoefficients; /**< Dual coefficients */ + const float16_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + float16_t gamma; /**< Gamma factor */ +} arm_svm_rbf_instance_f16; + + +/** + * @brief Instance structure for sigmoid SVM prediction function. + */ +typedef struct +{ + uint32_t nbOfSupportVectors; /**< Number of support vectors */ + uint32_t vectorDimension; /**< Dimension of vector space */ + float16_t intercept; /**< Intercept */ + const float16_t *dualCoefficients; /**< Dual coefficients */ + const float16_t *supportVectors; /**< Support vectors */ + const int32_t *classes; /**< The two SVM classes */ + float16_t coef0; /**< Independent constant */ + float16_t gamma; /**< Gamma factor */ +} arm_svm_sigmoid_instance_f16; + + +/** + * @brief SVM linear instance init function + * @param[in] S Parameters for SVM functions + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + */ +void arm_svm_linear_init_f16(arm_svm_linear_instance_f16 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float16_t intercept, + const float16_t *dualCoefficients, + const float16_t *supportVectors, + const int32_t *classes); + +/** + * @brief SVM linear prediction + * @param[in] S Pointer to an instance of the linear SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + */ +void arm_svm_linear_predict_f16(const arm_svm_linear_instance_f16 *S, + const float16_t * in, + int32_t * pResult); + + +/** + * @brief SVM polynomial instance init function + * @param[in] S points to an instance of the polynomial SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] degree Polynomial degree + * @param[in] coef0 coeff0 (scikit-learn terminology) + * @param[in] gamma gamma (scikit-learn terminology) + */ +void arm_svm_polynomial_init_f16(arm_svm_polynomial_instance_f16 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float16_t intercept, + const float16_t *dualCoefficients, + const float16_t *supportVectors, + const int32_t *classes, + int32_t degree, + float16_t coef0, + float16_t gamma + ); + + +/** + * @brief SVM polynomial prediction + * @param[in] S Pointer to an instance of the polynomial SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + */ +void arm_svm_polynomial_predict_f16(const arm_svm_polynomial_instance_f16 *S, + const float16_t * in, + int32_t * pResult); + + +/** + * @brief SVM radial basis function instance init function + * @param[in] S points to an instance of the polynomial SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] gamma gamma (scikit-learn terminology) + */ +void arm_svm_rbf_init_f16(arm_svm_rbf_instance_f16 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float16_t intercept, + const float16_t *dualCoefficients, + const float16_t *supportVectors, + const int32_t *classes, + float16_t gamma + ); + + +/** + * @brief SVM rbf prediction + * @param[in] S Pointer to an instance of the rbf SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult decision value + */ +void arm_svm_rbf_predict_f16(const arm_svm_rbf_instance_f16 *S, + const float16_t * in, + int32_t * pResult); + + +/** + * @brief SVM sigmoid instance init function + * @param[in] S points to an instance of the rbf SVM structure. + * @param[in] nbOfSupportVectors Number of support vectors + * @param[in] vectorDimension Dimension of vector space + * @param[in] intercept Intercept + * @param[in] dualCoefficients Array of dual coefficients + * @param[in] supportVectors Array of support vectors + * @param[in] classes Array of 2 classes ID + * @param[in] coef0 coeff0 (scikit-learn terminology) + * @param[in] gamma gamma (scikit-learn terminology) + */ +void arm_svm_sigmoid_init_f16(arm_svm_sigmoid_instance_f16 *S, + uint32_t nbOfSupportVectors, + uint32_t vectorDimension, + float16_t intercept, + const float16_t *dualCoefficients, + const float16_t *supportVectors, + const int32_t *classes, + float16_t coef0, + float16_t gamma + ); + + +/** + * @brief SVM sigmoid prediction + * @param[in] S Pointer to an instance of the rbf SVM structure. + * @param[in] in Pointer to input vector + * @param[out] pResult Decision value + */ +void arm_svm_sigmoid_predict_f16(const arm_svm_sigmoid_instance_f16 *S, + const float16_t * in, + int32_t * pResult); + + + +#endif /*defined(ARM_FLOAT16_SUPPORTED)*/ +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _SVM_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/transform_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/transform_functions.h new file mode 100755 index 0000000..27094e5 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/transform_functions.h @@ -0,0 +1,1408 @@ +/****************************************************************************** + * @file transform_functions.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef TRANSFORM_FUNCTIONS_H_ +#define TRANSFORM_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#include "dsp/basic_math_functions.h" +#include "dsp/complex_math_functions.h" + +// Only available for Neon versions of the FFTs +// otherwise only powers of 2 are supported + +#if !defined(ARM_MIXED_RADIX_FFT) +#define ARM_MIXED_RADIX_FFT 1 +#endif + +#if !defined(ARM_MATH_NEON) +#if defined(ARM_MFCC_CFFT_BASED) +#if !defined(ARM_MFCC_USE_CFFT) +#define ARM_MFCC_USE_CFFT +#endif +#endif +#endif + +#ifdef __cplusplus +extern "C" +{ +#endif + + +/** + * @defgroup groupTransforms Transform Functions + * + * CMSIS-DSP provides CFFT and RFFT for different architectures. + * The implementation of those transforms may be different for the + * different architectures : different algorithms, different capabilities + * of the instruction set. + * + * All those variants are not giving exactly the same results but they + * are passing the same tests with same SNR checks and same threshold for + * the sample errors. + * + * The APIs for the Neon variants are different : some additional + * temporary buffers are required. + * + * Float16 versions are provided but they are not very accurate and + * should only be used for small FFTs. + * + * @par Transform initializations + * + * There are several ways to initialize the transform functions. + * Below explanations are using q15 as example but the same explanations + * apply to other datatypes. + * + * Before Helium and Neon, you can just use a pre-initialized + * constant data structure and use it in the arm_cfft_... function. + * For instance, &arm_cfft_sR_q15_len256 for a 256 Q15 CFFT. + * + * On Helium and Neon, you *must* use an initialization function. If you know the size of your FFT (or other transform) you can use a specific initialization function for this size only : like arm_cfft_init_256_q15 for a 256 Q15 complex FFT. + * + * By using a specific initialization function, you give an hint to the linker and it will be able to remove all unused initialization tables (some compilation and link flags must be used for the linker to be able to do this optimization. It is compiler dependent). + * + * If you don't know the size you'll need at runtime, you need to use a function like arm_cfft_init_q15. If you use such a function, all the tables for all FFT sizes (up to the CMSIS-DSP maximum of 4096) will be included in the build ! + * + * On Neon, there is another possibility. You can use arm_cfft_init_dynamic_q15. This function will allocate a buffer at runtime and compute at runtime all the tables that are required for a specific FFT size. This initialization is also supported by RFFT. + * The computation to initialize all the tables can take lot of cycles + * (since several cos and sin must be computed) + * + * With this new Neon specific initialization you can use longer lengths. + * With CFFT, you can also use lengths containing radix 3 and/or 5 (but + * the length must still be a multiple of 4). + * + * @par Size of buffers according to the target architecture and datatype: + * They are described on the page \ref transformbuffers "transform buffers". + */ + + + /** + * @brief Instance structure for the Q15 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q15_t *pTwiddle; /**< points to the Sin twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix2_instance_q15; + +/* Deprecated */ + arm_status arm_cfft_radix2_init_q15( + arm_cfft_radix2_instance_q15 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_q15( + const arm_cfft_radix2_instance_q15 * S, + q15_t * pSrc); + + + /** + * @brief Instance structure for the Q15 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q15_t *pTwiddle; /**< points to the twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix4_instance_q15; + +/* Deprecated */ + arm_status arm_cfft_radix4_init_q15( + arm_cfft_radix4_instance_q15 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix4_q15( + const arm_cfft_radix4_instance_q15 * S, + q15_t * pSrc); + + /** + * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q31_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix2_instance_q31; + +/* Deprecated */ + arm_status arm_cfft_radix2_init_q31( + arm_cfft_radix2_instance_q31 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_q31( + const arm_cfft_radix2_instance_q31 * S, + q31_t * pSrc); + + /** + * @brief Instance structure for the Q31 CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const q31_t *pTwiddle; /**< points to the twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + } arm_cfft_radix4_instance_q31; + +/* Deprecated */ + void arm_cfft_radix4_q31( + const arm_cfft_radix4_instance_q31 * S, + q31_t * pSrc); + +/* Deprecated */ + arm_status arm_cfft_radix4_init_q31( + arm_cfft_radix4_instance_q31 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + float32_t onebyfftLen; /**< value of 1/fftLen. */ + } arm_cfft_radix2_instance_f32; + + +/* Deprecated */ + arm_status arm_cfft_radix2_init_f32( + arm_cfft_radix2_instance_f32 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_f32( + const arm_cfft_radix2_instance_f32 * S, + float32_t * pSrc); + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + float32_t onebyfftLen; /**< value of 1/fftLen. */ + } arm_cfft_radix4_instance_f32; + + + +/* Deprecated */ + arm_status arm_cfft_radix4_init_f32( + arm_cfft_radix4_instance_f32 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix4_f32( + const arm_cfft_radix4_instance_f32 * S, + float32_t * pSrc); + + /** + * @brief Instance structure for the fixed-point CFFT/CIFFT function. + */ +#if defined(ARM_MATH_NEON) +typedef struct +{ + uint32_t fftLen; /**< length of the FFT. */ + const q15_t *pTwiddle; /**< points to the Twiddle factor table. */ + const q15_t *last_twiddles; /**< last stage twiddle used for mixed radix */ + const uint32_t *factors; + int32_t algorithm_flag; +} arm_cfft_instance_q15; +#else + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const q15_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const q15_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const q15_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const q15_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_q15; +#endif + +arm_status arm_cfft_init_4096_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_2048_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_1024_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_512_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_256_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_128_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_64_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_32_q15(arm_cfft_instance_q15 * S); +arm_status arm_cfft_init_16_q15(arm_cfft_instance_q15 * S); + +arm_status arm_cfft_init_q15( + arm_cfft_instance_q15 * S, + uint16_t fftLen); + + + +#if defined(ARM_MATH_NEON) + +extern arm_cfft_instance_q15 *arm_cfft_init_dynamic_q15(uint32_t fftLen); + +void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + const q15_t * src, + q15_t * dst, + q15_t * buffer, + uint8_t ifftFlag + ); +#else +void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + q15_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); +#endif + + /** + * @brief Instance structure for the fixed-point CFFT/CIFFT function. + */ +#if defined(ARM_MATH_NEON) +typedef struct +{ + uint32_t fftLen; /**< length of the FFT. */ + const q31_t *pTwiddle; /**< points to the Twiddle factor table. */ + const q31_t *last_twiddles; /**< last stage twiddle used for mixed radix */ + const uint32_t *factors; + int32_t algorithm_flag; +} arm_cfft_instance_q31; +#else + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const q31_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const q31_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const q31_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const q31_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_q31; +#endif + +arm_status arm_cfft_init_4096_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_2048_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_1024_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_512_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_256_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_128_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_64_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_32_q31(arm_cfft_instance_q31 * S); +arm_status arm_cfft_init_16_q31(arm_cfft_instance_q31 * S); + +arm_status arm_cfft_init_q31( + arm_cfft_instance_q31 * S, + uint16_t fftLen); + +#if defined(ARM_MATH_NEON) + +extern arm_cfft_instance_q31 *arm_cfft_init_dynamic_q31(uint32_t fftLen); + +void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + const q31_t * src, + q31_t * dst, + q31_t * buffer, + uint8_t ifftFlag + ); +#else +void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + q31_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); +#endif + +#if defined(ARM_MATH_NEON) +typedef struct +{ + uint32_t fftLen; /**< length of the FFT. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const float32_t *last_twiddles; /**< last stage twiddle used for mixed radix */ + const uint32_t *factors; + int32_t algorithm_flag; +} arm_cfft_instance_f32; +#else + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const float32_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const float32_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const float32_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const float32_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_f32; +#endif + + +arm_status arm_cfft_init_4096_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_2048_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_1024_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_512_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_256_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_128_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_64_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_32_f32(arm_cfft_instance_f32 * S); +arm_status arm_cfft_init_16_f32(arm_cfft_instance_f32 * S); + + arm_status arm_cfft_init_f32( + arm_cfft_instance_f32 * S, + uint16_t fftLen); + +#if defined(ARM_MATH_NEON) + +extern arm_cfft_instance_f32 *arm_cfft_init_dynamic_f32(uint32_t fftLen); + +/* `pIn` content is modified by the function. + `pIn` array must be different from `pOut` one +*/ +void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + const float32_t * pIn, + float32_t * pOut, + float32_t * pBuffer, /* When used, `in` is not modified */ + uint8_t ifftFlag); +#else + void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + float32_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); +#endif + + + /** + * @brief Instance structure for the Double Precision Floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const float64_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ + } arm_cfft_instance_f64; + +arm_status arm_cfft_init_4096_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_2048_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_1024_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_512_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_256_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_128_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_64_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_32_f64(arm_cfft_instance_f64 * S); +arm_status arm_cfft_init_16_f64(arm_cfft_instance_f64 * S); + + arm_status arm_cfft_init_f64( + arm_cfft_instance_f64 * S, + uint16_t fftLen); + + void arm_cfft_f64( + const arm_cfft_instance_f64 * S, + float64_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + + /** + * @brief Instance structure for the Q15 RFFT/RIFFT function. + */ +#if defined(ARM_MATH_NEON) + typedef struct + { + uint32_t nfft; + uint32_t ncfft; + const uint32_t *factors; + const q15_t *twiddles; + const q15_t *super_twiddles; + } arm_rfft_instance_q15; +#else + typedef struct + { + uint32_t fftLenReal; /**< length of the real FFT. */ + uint8_t ifftFlagR; /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */ + uint8_t bitReverseFlagR; /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */ + uint32_t twidCoefRModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + const q15_t *pTwiddleAReal; /**< points to the real twiddle factor table. */ + const q15_t *pTwiddleBReal; /**< points to the imag twiddle factor table. */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + arm_cfft_instance_q15 cfftInst; +#else + const arm_cfft_instance_q15 *pCfft; /**< points to the complex FFT instance. */ +#endif + } arm_rfft_instance_q15; +#endif + +#if defined(ARM_MATH_NEON) + +extern arm_rfft_instance_q15 *arm_rfft_init_dynamic_q15(uint32_t fftLenReal); + +arm_status arm_rfft_init_32_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_64_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_128_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_256_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_512_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_1024_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_2048_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_4096_q15( + arm_rfft_instance_q15 * S); + +arm_status arm_rfft_init_8192_q15( + arm_rfft_instance_q15 * S); + + arm_status arm_rfft_init_q15( + arm_rfft_instance_q15 * S, + uint32_t fftLenReal); + +void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + q15_t * tmp, + uint8_t ifftFlag); +#else +arm_status arm_rfft_init_32_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_64_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_128_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_256_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_512_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_1024_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_2048_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_4096_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + +arm_status arm_rfft_init_8192_q15( + arm_rfft_instance_q15 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_q15( + arm_rfft_instance_q15 * S, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + q15_t * pSrc, + q15_t * pDst); +#endif + + /** + * @brief Instance structure for the Q31 RFFT/RIFFT function. + */ +#if defined(ARM_MATH_NEON) + typedef struct + { + uint32_t nfft; + uint32_t ncfft; + const uint32_t *factors; + const q31_t *twiddles; + const q31_t *super_twiddles; + } arm_rfft_instance_q31; +#else + typedef struct + { + uint32_t fftLenReal; /**< length of the real FFT. */ + uint8_t ifftFlagR; /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */ + uint8_t bitReverseFlagR; /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */ + uint32_t twidCoefRModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + const q31_t *pTwiddleAReal; /**< points to the real twiddle factor table. */ + const q31_t *pTwiddleBReal; /**< points to the imag twiddle factor table. */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + arm_cfft_instance_q31 cfftInst; +#else + const arm_cfft_instance_q31 *pCfft; /**< points to the complex FFT instance. */ +#endif + } arm_rfft_instance_q31; +#endif + + +#if defined(ARM_MATH_NEON) + +extern arm_rfft_instance_q31 *arm_rfft_init_dynamic_q31(uint32_t fftLenReal); + + arm_status arm_rfft_init_32_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_64_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_128_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_256_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_512_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_1024_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_2048_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_4096_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_8192_q31( + arm_rfft_instance_q31 * S); + + arm_status arm_rfft_init_q31( + arm_rfft_instance_q31 * S, + uint32_t fftLenReal); + + void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + q31_t * tmp, + uint8_t ifftFlag); +#else + arm_status arm_rfft_init_32_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_64_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_128_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_256_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_512_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_1024_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_2048_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_4096_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_8192_q31( + arm_rfft_instance_q31 * S, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + arm_status arm_rfft_init_q31( + arm_rfft_instance_q31 * S, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag); + + void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + q31_t * pSrc, + q31_t * pDst); +#endif + + /** + * @brief Instance structure for the floating-point RFFT/RIFFT function. + */ + typedef struct + { + uint32_t fftLenReal; /**< length of the real FFT. */ + uint16_t fftLenBy2; /**< length of the complex FFT. */ + uint8_t ifftFlagR; /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */ + uint8_t bitReverseFlagR; /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */ + uint32_t twidCoefRModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + const float32_t *pTwiddleAReal; /**< points to the real twiddle factor table. */ + const float32_t *pTwiddleBReal; /**< points to the imag twiddle factor table. */ + arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */ + } arm_rfft_instance_f32; + + /** + * @brief Instance structure for the Double Precision Floating-point RFFT/RIFFT function. + */ +typedef struct + { + arm_cfft_instance_f64 Sint; /**< Internal CFFT structure. */ + uint16_t fftLenRFFT; /**< length of the real sequence */ + const float64_t * pTwiddleRFFT; /**< Twiddle factors real stage */ + } arm_rfft_fast_instance_f64 ; + +arm_status arm_rfft_fast_init_32_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_64_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_128_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_256_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_512_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_1024_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_2048_f64( arm_rfft_fast_instance_f64 * S ); +arm_status arm_rfft_fast_init_4096_f64( arm_rfft_fast_instance_f64 * S ); + +arm_status arm_rfft_fast_init_f64 ( + arm_rfft_fast_instance_f64 * S, + uint16_t fftLen); + + +void arm_rfft_fast_f64( + arm_rfft_fast_instance_f64 * S, + float64_t * p, float64_t * pOut, + uint8_t ifftFlag); + + + /** + * @brief Instance structure for the floating-point RFFT/RIFFT function. + */ +#if defined(ARM_MATH_NEON) + typedef struct + { + uint32_t nfft; + const float32_t *r_twiddles; + const uint32_t *r_factors; + const float32_t *r_twiddles_backward; + const float32_t *r_twiddles_neon; + const float32_t *r_twiddles_neon_backward; + const uint32_t *r_factors_neon; + const float32_t *r_super_twiddles_neon; + } arm_rfft_fast_instance_f32 ; +#else +typedef struct + { + arm_cfft_instance_f32 Sint; /**< Internal CFFT structure. */ + uint16_t fftLenRFFT; /**< length of the real sequence */ + const float32_t * pTwiddleRFFT; /**< Twiddle factors real stage */ + } arm_rfft_fast_instance_f32 ; +#endif + +arm_status arm_rfft_fast_init_32_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_64_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_128_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_256_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_512_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_1024_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_2048_f32( arm_rfft_fast_instance_f32 * S ); +arm_status arm_rfft_fast_init_4096_f32( arm_rfft_fast_instance_f32 * S ); + + +arm_status arm_rfft_fast_init_f32 ( + arm_rfft_fast_instance_f32 * S, + uint16_t fftLen); + +#if defined(ARM_MATH_NEON) + +extern arm_rfft_fast_instance_f32 *arm_rfft_fast_init_dynamic_f32 (uint32_t fftLen); + +void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut, + float32_t *tmpbuf, + uint8_t ifftFlag); +#else + void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + float32_t * p, float32_t * pOut, + uint8_t ifftFlag); +#endif + + + /** + * @brief Instance structure for the Floating-point MFCC function. + */ +typedef struct + { + const float32_t *dctCoefs; /**< Internal DCT coefficients */ + const float32_t *filterCoefs; /**< Internal Mel filter coefficients */ + const float32_t *windowCoefs; /**< Windowing coefficients */ + const uint32_t *filterPos; /**< Internal Mel filter positions in spectrum */ + const uint32_t *filterLengths; /**< Internal Mel filter lengths */ + uint32_t fftLen; /**< FFT length */ + uint32_t nbMelFilters; /**< Number of Mel filters */ + uint32_t nbDctOutputs; /**< Number of DCT outputs */ +#if defined(ARM_MFCC_USE_CFFT) + /* Implementation of the MFCC is using a CFFT */ + arm_cfft_instance_f32 cfft; /**< Internal CFFT instance */ +#else + /* Implementation of the MFCC is using a RFFT (default) */ + arm_rfft_fast_instance_f32 rfft; +#endif + } arm_mfcc_instance_f32 ; + +arm_status arm_mfcc_init_32_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_64_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_128_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_256_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_512_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_1024_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_2048_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_4096_f32( + arm_mfcc_instance_f32 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + +arm_status arm_mfcc_init_f32( + arm_mfcc_instance_f32 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ); + + +/** + @brief MFCC F32 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples + @param[out] pDst points to the output MFCC values + @param[inout] pTmp points to a temporary buffer of complex + */ +#if defined(ARM_MATH_NEON) +void arm_mfcc_f32( + const arm_mfcc_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + float32_t *pTmp, + float32_t *pTmp2 + ); +#else + void arm_mfcc_f32( + const arm_mfcc_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + float32_t *pTmp + ); +#endif + + /** + * @brief Instance structure for the Q31 MFCC function. + */ +typedef struct + { + const q31_t *dctCoefs; /**< Internal DCT coefficients */ + const q31_t *filterCoefs; /**< Internal Mel filter coefficients */ + const q31_t *windowCoefs; /**< Windowing coefficients */ + const uint32_t *filterPos; /**< Internal Mel filter positions in spectrum */ + const uint32_t *filterLengths; /**< Internal Mel filter lengths */ + uint32_t fftLen; /**< FFT length */ + uint32_t nbMelFilters; /**< Number of Mel filters */ + uint32_t nbDctOutputs; /**< Number of DCT outputs */ +#if defined(ARM_MFCC_USE_CFFT) + /* Implementation of the MFCC is using a CFFT */ + arm_cfft_instance_q31 cfft; /**< Internal CFFT instance */ +#else + /* Implementation of the MFCC is using a RFFT (default) */ + arm_rfft_instance_q31 rfft; +#endif + } arm_mfcc_instance_q31 ; + +arm_status arm_mfcc_init_32_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_64_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_128_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_256_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_512_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_1024_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_2048_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_4096_q31( + arm_mfcc_instance_q31 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + +arm_status arm_mfcc_init_q31( + arm_mfcc_instance_q31 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ); + + +/** + @brief MFCC Q31 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples + @param[out] pDst points to the output MFCC values + @param[inout] pTmp points to a temporary buffer of complex + @return error status + */ +#if defined(ARM_MATH_NEON) + arm_status arm_mfcc_q31( + const arm_mfcc_instance_q31 * S, + q31_t *pSrc, + q31_t *pDst, + q31_t *pTmp, + q31_t *pTmp2 + ); +#else + arm_status arm_mfcc_q31( + const arm_mfcc_instance_q31 * S, + q31_t *pSrc, + q31_t *pDst, + q31_t *pTmp + ); +#endif + + /** + * @brief Instance structure for the Q15 MFCC function. + */ +typedef struct + { + const q15_t *dctCoefs; /**< Internal DCT coefficients */ + const q15_t *filterCoefs; /**< Internal Mel filter coefficients */ + const q15_t *windowCoefs; /**< Windowing coefficients */ + const uint32_t *filterPos; /**< Internal Mel filter positions in spectrum */ + const uint32_t *filterLengths; /**< Internal Mel filter lengths */ + uint32_t fftLen; /**< FFT length */ + uint32_t nbMelFilters; /**< Number of Mel filters */ + uint32_t nbDctOutputs; /**< Number of DCT outputs */ +#if defined(ARM_MFCC_USE_CFFT) + /* Implementation of the MFCC is using a CFFT */ + arm_cfft_instance_q15 cfft; /**< Internal CFFT instance */ +#else + /* Implementation of the MFCC is using a RFFT (default) */ + arm_rfft_instance_q15 rfft; +#endif + } arm_mfcc_instance_q15 ; + +arm_status arm_mfcc_init_32_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_64_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_128_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_256_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_512_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_1024_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_2048_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_4096_q15( + arm_mfcc_instance_q15 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + +arm_status arm_mfcc_init_q15( + arm_mfcc_instance_q15 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ); + + +/** + @brief MFCC Q15 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples + @param[out] pDst points to the output MFCC values in q8.7 format + @param[inout] pTmp points to a temporary buffer of complex + @return error status + */ +#if defined(ARM_MATH_NEON) + arm_status arm_mfcc_q15( + const arm_mfcc_instance_q15 * S, + q15_t *pSrc, + q15_t *pDst, + q31_t *pTmp, + q15_t *pTmp2 + ); +#else + arm_status arm_mfcc_q15( + const arm_mfcc_instance_q15 * S, + q15_t *pSrc, + q15_t *pDst, + q31_t *pTmp + ); +#endif + +/** + @brief Calculate required length for the temporary buffer + @param[in] arch Target architecture identification + @param[in] dt Data type of the input data + @param[in] nb_samples Number of samples in the input data + @param[in] buf_id Identification for the temporary buffer + @return Length in datatype elements (real numbers) for the temporary buffer + + @note 0 means not applicable (temporary buffer not needed) + @note -1 means error : configuration not supported +*/ +extern int32_t arm_cfft_tmp_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples, + uint32_t buf_id); + +/** + @brief Calculate required length for the output buffer + @param[in] arch Target architecture identification + @param[in] dt Data type of the input data + @param[in] nb_samples Number of samples in the input data + @return Length in datatype elements (real numbers) for the temporary buffer + + @note 0 means not applicable (temporary buffer not needed) + @note -1 means error : configuration not supported +*/ +extern int32_t arm_cfft_output_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples); + +/** + @brief Calculate required length for the output buffer + @param[in] arch Target architecture identification + @param[in] dt Data type of the input data + @param[in] nb_samples Number of samples in the input data + @return Length in datatype elements (real numbers) for the temporary buffer + + @note 0 means not applicable (temporary buffer not needed) + @note -1 means error : configuration not supported +*/ +extern int32_t arm_cifft_output_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples); + +/** + @brief Calculate required length for the temporary buffer for both RFFT and RIFFT + @param[in] arch Target architecture identification + @param[in] dt Data type of the input data + @param[in] nb_samples Number of samples in the input data + @param[in] buf_id Identification for the temporary buffer + @return Length in datatype elements (real numbers) for the temporary buffer + + @note 0 means not applicable (temporary buffer not needed) + @note -1 means error : configuration not supported +*/ +extern int32_t arm_rfft_tmp_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples, + uint32_t buf_id); + +/** + @brief Calculate required length for the output buffer + @param[in] arch Target architecture identification + @param[in] dt Data type of the input data + @param[in] nb_samples Number of samples in the input data + @return Length in datatype elements (real numbers) for the output buffer + + @note 0 means not applicable (temporary buffer not needed) + @note -1 means error : configuration not supported +*/ +extern int32_t arm_rfft_output_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples); + + +/** + * @brief Calculate required length for the input buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples RFFT length in samples + * @param[in] buf_id Identification for the temporary buffer + * @return Length in datatype elements (real numbers) for the input buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +extern int32_t arm_rifft_input_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples); + +/** + @brief Calculate required length for the temporary buffer + @param[in] arch Target architecture identification + @param[in] dt Data type of the input data + @param[in] nb_samples Number of samples in the input data + @param[in] buf_id Identification for the temporary buffer + @param[in] use_cfft 1 if implementastion uses CFFT, 0 if RFFT + @return Length in datatype elements (real numbers) for the temporary buffer + + @note 0 means not applicable (temporary buffer not needed) + @note -1 means error : configuration not supported +*/ +extern int32_t arm_mfcc_tmp_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples, + uint32_t buf_id, + uint32_t use_cfft); + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _TRANSFORM_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/transform_functions_f16.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/transform_functions_f16.h new file mode 100755 index 0000000..cad9321 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/transform_functions_f16.h @@ -0,0 +1,383 @@ +/****************************************************************************** + * @file transform_functions_f16.h + * @brief Public header file for CMSIS DSP Library + * @version V1.10.0 + * @date 08 July 2021 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef TRANSFORM_FUNCTIONS_F16_H_ +#define TRANSFORM_FUNCTIONS_F16_H_ + +#include "arm_math_types_f16.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + +#if !defined(ARM_MIXED_RADIX_FFT) +#define ARM_MIXED_RADIX_FFT 1 +#endif + +#if !defined(ARM_MATH_NEON) +#if defined(ARM_MFCC_CFFT_BASED) +#if !defined(ARM_MFCC_USE_CFFT) +#define ARM_MFCC_USE_CFFT +#endif +#endif +#endif + +#ifdef __cplusplus +extern "C" +{ +#endif + + + +#if defined(ARM_FLOAT16_SUPPORTED) + + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const float16_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + float16_t onebyfftLen; /**< value of 1/fftLen. */ + } arm_cfft_radix2_instance_f16; + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + uint8_t ifftFlag; /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */ + uint8_t bitReverseFlag; /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */ + const float16_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t twidCoefModifier; /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */ + uint16_t bitRevFactor; /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */ + float16_t onebyfftLen; /**< value of 1/fftLen. */ + } arm_cfft_radix4_instance_f16; + + /** + * @brief Instance structure for the floating-point CFFT/CIFFT function. + */ +#if defined(ARM_MATH_NEON_FLOAT16) +typedef struct +{ + uint32_t fftLen; /**< length of the FFT. */ + const float16_t *pTwiddle; /**< points to the Twiddle factor table. */ + const float16_t *last_twiddles; /**< last stage twiddle used for mixed radix */ + const uint32_t *factors; + int32_t algorithm_flag; +} arm_cfft_instance_f16; +#else + typedef struct + { + uint16_t fftLen; /**< length of the FFT. */ + const float16_t *pTwiddle; /**< points to the Twiddle factor table. */ + const uint16_t *pBitRevTable; /**< points to the bit reversal table. */ + uint16_t bitRevLength; /**< bit reversal table length. */ +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + const uint32_t *rearranged_twiddle_tab_stride1_arr; /**< Per stage reordered twiddle pointer (offset 1) */ \ + const uint32_t *rearranged_twiddle_tab_stride2_arr; /**< Per stage reordered twiddle pointer (offset 2) */ \ + const uint32_t *rearranged_twiddle_tab_stride3_arr; /**< Per stage reordered twiddle pointer (offset 3) */ \ + const float16_t *rearranged_twiddle_stride1; /**< reordered twiddle offset 1 storage */ \ + const float16_t *rearranged_twiddle_stride2; /**< reordered twiddle offset 2 storage */ \ + const float16_t *rearranged_twiddle_stride3; +#endif + } arm_cfft_instance_f16; +#endif + +arm_status arm_cfft_init_4096_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_2048_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_1024_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_512_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_256_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_128_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_64_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_32_f16(arm_cfft_instance_f16 * S); +arm_status arm_cfft_init_16_f16(arm_cfft_instance_f16 * S); + + + arm_status arm_cfft_init_f16( + arm_cfft_instance_f16 * S, + uint16_t fftLen); + +#if defined(ARM_MATH_NEON_FLOAT16) + +extern arm_cfft_instance_f16 *arm_cfft_init_dynamic_f16(uint32_t fftLen); + +void arm_cfft_f16( + const arm_cfft_instance_f16 * S, + const float16_t * pIn, + float16_t * pOut, + float16_t * pBuffer, /* When used, `in` is not modified */ + uint8_t ifftFlag); +#else + void arm_cfft_f16( + const arm_cfft_instance_f16 * S, + float16_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag); +#endif + /** + * @brief Instance structure for the floating-point RFFT/RIFFT function. + */ +#if defined(ARM_MATH_NEON_FLOAT16) + typedef struct + { + uint32_t nfft; + const float16_t *r_twiddles; + const uint32_t *r_factors; + const float16_t *r_twiddles_backward; + const float16_t *r_twiddles_neon; + const float16_t *r_twiddles_neon_backward; + const uint32_t *r_factors_neon; + const float16_t *r_super_twiddles_neon; + } arm_rfft_fast_instance_f16 ; +#else +typedef struct + { + arm_cfft_instance_f16 Sint; /**< Internal CFFT structure. */ + uint16_t fftLenRFFT; /**< length of the real sequence */ + const float16_t * pTwiddleRFFT; /**< Twiddle factors real stage */ + } arm_rfft_fast_instance_f16 ; +#endif + +arm_status arm_rfft_fast_init_32_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_64_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_128_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_256_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_512_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_1024_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_2048_f16( arm_rfft_fast_instance_f16 * S ); +arm_status arm_rfft_fast_init_4096_f16( arm_rfft_fast_instance_f16 * S ); + +arm_status arm_rfft_fast_init_f16 ( + arm_rfft_fast_instance_f16 * S, + uint16_t fftLen); + +#if defined(ARM_MATH_NEON_FLOAT16) + +extern arm_rfft_fast_instance_f16 *arm_rfft_fast_init_dynamic_f16 (uint32_t fftLen); + +void arm_rfft_fast_f16( + const arm_rfft_fast_instance_f16 * S, + const float16_t * p, + float16_t * pOut, + float16_t *tmpbuf, + uint8_t ifftFlag); +#else + void arm_rfft_fast_f16( + const arm_rfft_fast_instance_f16 * S, + float16_t * p, float16_t * pOut, + uint8_t ifftFlag); +#endif + +/* Deprecated */ + arm_status arm_cfft_radix4_init_f16( + arm_cfft_radix4_instance_f16 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix4_f16( + const arm_cfft_radix4_instance_f16 * S, + float16_t * pSrc); + + +/* Deprecated */ + arm_status arm_cfft_radix2_init_f16( + arm_cfft_radix2_instance_f16 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag); + +/* Deprecated */ + void arm_cfft_radix2_f16( + const arm_cfft_radix2_instance_f16 * S, + float16_t * pSrc); + + /** + * @brief Instance structure for the Floating-point MFCC function. + */ +typedef struct + { + const float16_t *dctCoefs; /**< Internal DCT coefficients */ + const float16_t *filterCoefs; /**< Internal Mel filter coefficients */ + const float16_t *windowCoefs; /**< Windowing coefficients */ + const uint32_t *filterPos; /**< Internal Mel filter positions in spectrum */ + const uint32_t *filterLengths; /**< Internal Mel filter lengths */ + uint32_t fftLen; /**< FFT length */ + uint32_t nbMelFilters; /**< Number of Mel filters */ + uint32_t nbDctOutputs; /**< Number of DCT outputs */ +#if defined(ARM_MFCC_USE_CFFT) + /* Implementation of the MFCC is using a CFFT */ + arm_cfft_instance_f16 cfft; /**< Internal CFFT instance */ +#else + /* Implementation of the MFCC is using a RFFT (default) */ + arm_rfft_fast_instance_f16 rfft; +#endif + } arm_mfcc_instance_f16 ; + +arm_status arm_mfcc_init_32_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_64_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_128_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_256_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_512_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_1024_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_2048_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_4096_f16( + arm_mfcc_instance_f16 * S, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + +arm_status arm_mfcc_init_f16( + arm_mfcc_instance_f16 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ); + + + +/** + @brief MFCC F16 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples + @param[out] pDst points to the output MFCC values + @param[inout] pTmp points to a temporary buffer of complex + */ +#if defined(ARM_MATH_NEON_FLOAT16) +void arm_mfcc_f16( + const arm_mfcc_instance_f16 * S, + float16_t *pSrc, + float16_t *pDst, + float16_t *pTmp, + float16_t *pTmp2 + ); +#else + void arm_mfcc_f16( + const arm_mfcc_instance_f16 * S, + float16_t *pSrc, + float16_t *pDst, + float16_t *pTmp + ); +#endif + +#endif /* defined(ARM_FLOAT16_SUPPORTED)*/ + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _TRANSFORM_FUNCTIONS_F16_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/utils.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/utils.h new file mode 100755 index 0000000..348e878 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/utils.h @@ -0,0 +1,272 @@ +/****************************************************************************** + * @file arm_math_utils.h + * @brief Public header file for CMSIS DSP Library + * @version V1.9.0 + * @date 20. July 2020 + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_MATH_UTILS_H_ + +#define ARM_MATH_UTILS_H_ + +#include "arm_math_types.h" + +#ifdef __cplusplus +#include +extern "C" +{ +#else +#include +#endif + + + /** + * @brief Macros required for reciprocal calculation in Normalized LMS + */ + +#define INDEX_MASK 0x0000003F + +#ifndef MIN + #define MIN(x,y) ((x) < (y) ? (x) : (y)) +#endif + +#ifndef MAX + #define MAX(x,y) ((x) > (y) ? (x) : (y)) +#endif + +#ifndef ARM_SQ +#define ARM_SQ(x) ((x) * (x)) +#endif + +#ifndef ARM_ROUND_UP + #define ARM_ROUND_UP(N, S) ((((N) + (S) - 1) / (S)) * (S)) +#endif + + + /** + * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type. + It should not be used with negative values. + */ + __STATIC_FORCEINLINE uint32_t arm_recip_q31( + q31_t in, + q31_t * dst, + const q31_t * pRecipTable) + { + q31_t out; + uint32_t tempVal; + uint32_t index, i; + uint32_t signBits; + + if (in > 0) + { + signBits = ((uint32_t) (__CLZ( (uint32_t)in) - 1)); + } + else + { + signBits = ((uint32_t) (__CLZ((uint32_t)(-in)) - 1)); + } + + /* Convert input sample to 1.31 format */ + in = (in << signBits); + + /* calculation of index for initial approximated Val */ + index = (uint32_t)(in >> 24); + index = (index & INDEX_MASK); + + /* 1.31 with exp 1 */ + out = pRecipTable[index]; + + /* calculation of reciprocal value */ + /* running approximation for two iterations */ + for (i = 0U; i < 2U; i++) + { + tempVal = (uint32_t) (((q63_t) in * out) >> 31); + tempVal = 0x7FFFFFFFu - tempVal; + /* 1.31 with exp 1 */ + /* out = (q31_t) (((q63_t) out * tempVal) >> 30); */ + out = clip_q63_to_q31(((q63_t) out * tempVal) >> 30); + } + + /* write output */ + *dst = out; + + /* return num of signbits of out = 1/in value */ + return (signBits + 1U); + } + + + /** + * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type. + It should not be used with negative values. + */ + __STATIC_FORCEINLINE uint32_t arm_recip_q15( + q15_t in, + q15_t * dst, + const q15_t * pRecipTable) + { + q15_t out = 0; + int32_t tempVal = 0; + uint32_t index = 0, i = 0; + uint32_t signBits = 0; + + if (in > 0) + { + signBits = ((uint32_t)(__CLZ( (uint32_t)in) - 17)); + } + else + { + signBits = ((uint32_t)(__CLZ((uint32_t)(-in)) - 17)); + } + + /* Convert input sample to 1.15 format */ + in = (q15_t)(in << signBits); + + /* calculation of index for initial approximated Val */ + index = (uint32_t)(in >> 8); + index = (index & INDEX_MASK); + + /* 1.15 with exp 1 */ + out = pRecipTable[index]; + + /* calculation of reciprocal value */ + /* running approximation for two iterations */ + for (i = 0U; i < 2U; i++) + { + tempVal = (((q31_t) in * out) >> 15); + tempVal = 0x7FFF - tempVal; + /* 1.15 with exp 1 */ + out = (q15_t) (((q31_t) out * tempVal) >> 14); + /* out = clip_q31_to_q15(((q31_t) out * tempVal) >> 14); */ + } + + /* write output */ + *dst = out; + + /* return num of signbits of out = 1/in value */ + return (signBits + 1); + } + + +/** + * @brief 64-bit to 32-bit unsigned normalization + * @param[in] in is input unsigned long long value + * @param[out] normalized is the 32-bit normalized value + * @param[out] norm is norm scale + */ +__STATIC_INLINE void arm_norm_64_to_32u(uint64_t in, int32_t * normalized, int32_t *norm) +{ + int32_t n1; + int32_t hi = (int32_t) (in >> 32); + int32_t lo = (int32_t) ((in << 32) >> 32); + + n1 = __CLZ((uint32_t)hi) - 32; + if (!n1) + { + /* + * input fits in 32-bit + */ + n1 = __CLZ((uint32_t)lo); + if (!n1) + { + /* + * MSB set, need to scale down by 1 + */ + *norm = -1; + *normalized = (((uint32_t) lo) >> 1); + } else + { + if (n1 == 32) + { + /* + * input is zero + */ + *norm = 0; + *normalized = 0; + } else + { + /* + * 32-bit normalization + */ + *norm = n1 - 1; + *normalized = lo << *norm; + } + } + } else + { + /* + * input fits in 64-bit + */ + n1 = 1 - n1; + *norm = -n1; + /* + * 64 bit normalization + */ + *normalized = (int32_t)(((uint32_t)lo) >> n1) | (hi << (32 - n1)); + } +} + +/** + * arm_div_int64_to_int32 function performs division of a 64-bit integer by a 32-bit integer + * and returns a 32-bit integer result. The function saturates the result to fit within the 32-bit integer range. + * @param num The 64-bit integer numerator. + * @param den The 32-bit integer denominator. + * @return The saturated 32-bit integer result of the division. + */ +__STATIC_INLINE int32_t arm_div_int64_to_int32(int64_t num, int32_t den) +{ + int32_t result; + uint64_t absNum; + int32_t normalized; + int32_t norm; + + /* + * if sum fits in 32bits + * avoid costly 64-bit division + */ + if (num == LLONG_MIN) + { + absNum = LLONG_MAX; + } + else + { + absNum = (uint64_t) (num > 0 ? num : -num); + } + arm_norm_64_to_32u(absNum, &normalized, &norm); + if (norm > 0) + /* + * 32-bit division + */ + result = (int32_t) num / den; + else + /* + * 64-bit division + */ + result = clip_q63_to_q31(num / den); + + return result; +} + +#undef INDEX_MASK + +#ifdef __cplusplus +} +#endif + +#endif /*ifndef _ARM_MATH_UTILS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/window_functions.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/window_functions.h new file mode 100755 index 0000000..27f05a7 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Include/dsp/window_functions.h @@ -0,0 +1,812 @@ +/****************************************************************************** + * @file window_functions.h + * @brief Public header file for CMSIS DSP Library + * @version v1.15.0 + * @date 15 December 2022 + * Target Processor: Cortex-M and Cortex-A cores + ******************************************************************************/ +/* + * Copyright (c) 2010-2022 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + +#ifndef WINDOW_FUNCTIONS_H_ +#define WINDOW_FUNCTIONS_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#include "dsp/none.h" +#include "dsp/utils.h" + + +#ifdef __cplusplus +extern "C" +{ +#endif + +/** + * @defgroup groupWindow Window Functions + */ + + /** + * @brief Welch window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 21.3 dB | + * | Normalized equivalent noise bandwidth | 1.2 bins | + * | Flatness | -2.2248 dB | + * | Recommended overlap | 29.3 % | + * + */ + void arm_welch_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Welch window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 21.3 dB | + * | Normalized equivalent noise bandwidth | 1.2 bins | + * | Flatness | -2.2248 dB | + * | Recommended overlap | 29.3 % | + * + * + */ + void arm_welch_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Bartlett window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 26.5 dB | + * | Normalized equivalent noise bandwidth | 1.3333 bins | + * | Flatness | -1.8242 dB | + * | Recommended overlap | 50.0 % | + * + */ + void arm_bartlett_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Bartlett window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 26.5 dB | + * | Normalized equivalent noise bandwidth | 1.3333 bins | + * | Flatness | -1.8242 dB | + * | Recommended overlap | 50.0 % | + * + * + */ + void arm_bartlett_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hamming window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 42.7 dB | + * | Normalized equivalent noise bandwidth | 1.3628 bins | + * | Flatness | -1.7514 dB | + * | Recommended overlap | 50 % | + * + */ + void arm_hamming_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hamming window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 42.7 dB | + * | Normalized equivalent noise bandwidth | 1.3628 bins | + * | Flatness | -1.7514 dB | + * | Recommended overlap | 50 % | + * + * + */ + void arm_hamming_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hanning window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 31.5 dB | + * | Normalized equivalent noise bandwidth | 1.5 bins | + * | Flatness | -1.4236 dB | + * | Recommended overlap | 50 % | + * + */ + void arm_hanning_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hanning window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 31.5 dB | + * | Normalized equivalent noise bandwidth | 1.5 bins | + * | Flatness | -1.4236 dB | + * | Recommended overlap | 50 % | + * + * + */ + void arm_hanning_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall3 window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 46.7 dB | + * | Normalized equivalent noise bandwidth | 1.9444 bins | + * | Flatness | -0.863 dB | + * | Recommended overlap | 64.7 % | + * + */ + void arm_nuttall3_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall3 window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 46.7 dB | + * | Normalized equivalent noise bandwidth | 1.9444 bins | + * | Flatness | -0.863 dB | + * | Recommended overlap | 64.7 % | + * + * + */ + void arm_nuttall3_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall4 window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 60.9 dB | + * | Normalized equivalent noise bandwidth | 2.31 bins | + * | Flatness | -0.6184 dB | + * | Recommended overlap | 70.5 % | + * + */ + void arm_nuttall4_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall4 window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 60.9 dB | + * | Normalized equivalent noise bandwidth | 2.31 bins | + * | Flatness | -0.6184 dB | + * | Recommended overlap | 70.5 % | + * + * + */ + void arm_nuttall4_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall3a window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 64.2 dB | + * | Normalized equivalent noise bandwidth | 1.7721 bins | + * | Flatness | -1.0453 dB | + * | Recommended overlap | 61.2 % | + * + */ + void arm_nuttall3a_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall3a window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 64.2 dB | + * | Normalized equivalent noise bandwidth | 1.7721 bins | + * | Flatness | -1.0453 dB | + * | Recommended overlap | 61.2 % | + * + * + */ + void arm_nuttall3a_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall3b window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 71.5 dB | + * | Normalized equivalent noise bandwidth | 1.7037 bins | + * | Flatness | -1.1352 dB | + * | Recommended overlap | 59.8 % | + * + */ + void arm_nuttall3b_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall3b window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 71.5 dB | + * | Normalized equivalent noise bandwidth | 1.7037 bins | + * | Flatness | -1.1352 dB | + * | Recommended overlap | 59.8 % | + * + * + */ + void arm_nuttall3b_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall4a window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 82.6 dB | + * | Normalized equivalent noise bandwidth | 2.1253 bins | + * | Flatness | -0.7321 dB | + * | Recommended overlap | 68.0 % | + * + */ + void arm_nuttall4a_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall4a window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 82.6 dB | + * | Normalized equivalent noise bandwidth | 2.1253 bins | + * | Flatness | -0.7321 dB | + * | Recommended overlap | 68.0 % | + * + * + */ + void arm_nuttall4a_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief 92 db blackman harris window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 92.0 dB | + * | Normalized equivalent noise bandwidth | 2.0044 bins | + * | Flatness | -0.8256 dB | + * | Recommended overlap | 66.1 % | + * + */ + void arm_blackman_harris_92db_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief 92 db blackman harris window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 92.0 dB | + * | Normalized equivalent noise bandwidth | 2.0044 bins | + * | Flatness | -0.8256 dB | + * | Recommended overlap | 66.1 % | + * + * + */ + void arm_blackman_harris_92db_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall4b window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 93.3 dB | + * | Normalized equivalent noise bandwidth | 2.0212 bins | + * | Flatness | -0.8118 dB | + * | Recommended overlap | 66.3 % | + * + */ + void arm_nuttall4b_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall4b window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 93.3 dB | + * | Normalized equivalent noise bandwidth | 2.0212 bins | + * | Flatness | -0.8118 dB | + * | Recommended overlap | 66.3 % | + * + * + */ + void arm_nuttall4b_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Nuttall4c window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 98.1 dB | + * | Normalized equivalent noise bandwidth | 1.9761 bins | + * | Flatness | -0.8506 dB | + * | Recommended overlap | 65.6 % | + * + */ + void arm_nuttall4c_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Nuttall4c window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 98.1 dB | + * | Normalized equivalent noise bandwidth | 1.9761 bins | + * | Flatness | -0.8506 dB | + * | Recommended overlap | 65.6 % | + * + * + */ + void arm_nuttall4c_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft90d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 90.2 dB | + * | Normalized equivalent noise bandwidth | 3.8832 bins | + * | Flatness | -0.0039 dB | + * | Recommended overlap | 76.0 % | + * + */ + void arm_hft90d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft90d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 90.2 dB | + * | Normalized equivalent noise bandwidth | 3.8832 bins | + * | Flatness | -0.0039 dB | + * | Recommended overlap | 76.0 % | + * + * + */ + void arm_hft90d_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft95 window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 95.0 dB | + * | Normalized equivalent noise bandwidth | 3.8112 bins | + * | Flatness | 0.0044 dB | + * | Recommended overlap | 75.6 % | + * + */ + void arm_hft95_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft95 window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 95.0 dB | + * | Normalized equivalent noise bandwidth | 3.8112 bins | + * | Flatness | 0.0044 dB | + * | Recommended overlap | 75.6 % | + * + * + */ + void arm_hft95_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft116d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 116.8 dB | + * | Normalized equivalent noise bandwidth | 4.2186 bins | + * | Flatness | -0.0028 dB | + * | Recommended overlap | 78.2 % | + * + */ + void arm_hft116d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft116d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 116.8 dB | + * | Normalized equivalent noise bandwidth | 4.2186 bins | + * | Flatness | -0.0028 dB | + * | Recommended overlap | 78.2 % | + * + * + */ + void arm_hft116d_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft144d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 144.1 dB | + * | Normalized equivalent noise bandwidth | 4.5386 bins | + * | Flatness | 0.0021 dB | + * | Recommended overlap | 79.9 % | + * + */ + void arm_hft144d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft144d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 144.1 dB | + * | Normalized equivalent noise bandwidth | 4.5386 bins | + * | Flatness | 0.0021 dB | + * | Recommended overlap | 79.9 % | + * + * + */ + void arm_hft144d_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft169d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 169.5 dB | + * | Normalized equivalent noise bandwidth | 4.8347 bins | + * | Flatness | 0.0017 dB | + * | Recommended overlap | 81.2 % | + * + */ + void arm_hft169d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft169d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 169.5 dB | + * | Normalized equivalent noise bandwidth | 4.8347 bins | + * | Flatness | 0.0017 dB | + * | Recommended overlap | 81.2 % | + * + * + */ + void arm_hft169d_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft196d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 196.2 dB | + * | Normalized equivalent noise bandwidth | 5.1134 bins | + * | Flatness | 0.0013 dB | + * | Recommended overlap | 82.3 % | + * + */ + void arm_hft196d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft196d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 196.2 dB | + * | Normalized equivalent noise bandwidth | 5.1134 bins | + * | Flatness | 0.0013 dB | + * | Recommended overlap | 82.3 % | + * + * + */ + void arm_hft196d_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft223d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 223.0 dB | + * | Normalized equivalent noise bandwidth | 5.3888 bins | + * | Flatness | 0.0011 dB | + * | Recommended overlap | 83.3 % | + * + */ + void arm_hft223d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft223d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 223.0 dB | + * | Normalized equivalent noise bandwidth | 5.3888 bins | + * | Flatness | 0.0011 dB | + * | Recommended overlap | 83.3 % | + * + * + */ + void arm_hft223d_f32( + float32_t * pDst, + uint32_t blockSize); + /** + * @brief Hft248d window (double). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 248.4 dB | + * | Normalized equivalent noise bandwidth | 5.6512 bins | + * | Flatness | 0.0009 dB | + * | Recommended overlap | 84.1 % | + * + */ + void arm_hft248d_f64( + float64_t * pDst, + uint32_t blockSize); + + /** + * @brief Hft248d window (float). + * @param[out] pDst points to the output generated window + * @param[in] blockSize number of samples in the window + * + * @par Parameters of the window + * + * | Parameter | Value | + * | ------------------------------------: | -----------------: | + * | Peak sidelobe level | 248.4 dB | + * | Normalized equivalent noise bandwidth | 5.6512 bins | + * | Flatness | 0.0009 dB | + * | Recommended overlap | 84.1 % | + * + * + */ + void arm_hft248d_f32( + float32_t * pDst, + uint32_t blockSize); + + +#ifdef __cplusplus +} +#endif + +#endif /* ifndef _BASIC_MATH_FUNCTIONS_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/LICENSE b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/LICENSE new file mode 100755 index 0000000..8dada3e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright {yyyy} {name of copyright owner} + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_compiler_specific.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_compiler_specific.h new file mode 100755 index 0000000..8278026 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_compiler_specific.h @@ -0,0 +1,20 @@ +#ifndef ARM_COMPILER_SPECIFIC_H_ +#define ARM_COMPILER_SPECIFIC_H_ + +/* CMSIS-DSP definitions for some specific compilers. + Those definitions should not interfere with client code + and as consequence are in a private header. +*/ + +#if defined (_MSC_VER ) +#pragma warning(push) +#pragma warning(disable:4127) +#pragma warning(disable:4244) +#pragma warning(disable:4456) +#pragma warning(disable:4701) +#pragma warning(disable:4703) +#pragma warning(disable:4310) + +#endif + +#endif \ No newline at end of file diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_neon_private.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_neon_private.h new file mode 100755 index 0000000..67f604a --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_neon_private.h @@ -0,0 +1,57 @@ +/****************************************************************************** + * @file arm_neon_private.h + * @brief Private header file for CMSIS DSP Library + ******************************************************************************/ +/* + * Copyright (c) 2025 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_NEON_PRIVATE_H_ +#define ARM_NEON_PRIVATE_H_ + +#include "arm_math_types.h" +#include "arm_math_memory.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) + +#define DCS 4 // Max number of vectors for columns (can't be changed) +#define MAXDC (8*DCS) // Must be multiple of lane + +#define DR 4 // Max number rows in kernels (can't be changed) +#define HDR 2 // Max number rows by half + +// INNER * DC < L1/2 +// INNER * ROWS < L2 +// INNER * COLS < L3 +#define INNER_BLOCK ((((ARM_MATH_L1_CACHE_SIZE>>2) >> 1)/MAXDC+MAXDC-1) & ~(MAXDC-1)) +#define ROWS_BLOCK ((((ARM_MATH_L2_CACHE_SIZE>>2) >> 0) / INNER_BLOCK + DR - 1) & ~(DR-1) ) +#define COLS_BLOCK (((ARM_MATH_L3_CACHE_SIZE>>2) / INNER_BLOCK + MAXDC - 1) & ~(MAXDC-1)) + + +#endif + +#ifdef __cplusplus +} +#endif + + +#endif /* _ARM_VEC_FILTERING_H_ */ \ No newline at end of file diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_sorting.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_sorting.h new file mode 100755 index 0000000..937b196 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_sorting.h @@ -0,0 +1,200 @@ +/****************************************************************************** + * @file arm_sorting.h + * @brief Private header file for CMSIS DSP Library + * @version V1.7.0 + * @date 2019 + ******************************************************************************/ +/* + * Copyright (c) 2010-2019 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_SORTING_H_ +#define ARM_SORTING_H_ + +#include "dsp/support_functions.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_bubble_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_heap_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data. + * @param[in] blockSize number of samples to process. + */ + void arm_insertion_sort_f32( + const arm_sort_instance_f32 * S, + float32_t *pSrc, + float32_t* pDst, + uint32_t blockSize); + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_quick_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_selection_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + + /** + * @param[in] S points to an instance of the sorting structure. + * @param[in] pSrc points to the block of input data. + * @param[out] pDst points to the block of output data + * @param[in] blockSize number of samples to process. + */ + void arm_bitonic_sort_f32( + const arm_sort_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize); + +#if defined(ARM_MATH_NEON) + +#define vtrn256_128q(a, b) \ +do { \ + float32x4_t vtrn128_temp = a.val[1]; \ + a.val[1] = b.val[0]; \ + b.val[0] = vtrn128_temp ; \ +} while (0) + +#define vtrn128_64q(a, b) \ +do { \ + float32x2_t ab, cd, ef, gh; \ + ab = vget_low_f32(a); \ + ef = vget_low_f32(b); \ + cd = vget_high_f32(a); \ + gh = vget_high_f32(b); \ + a = vcombine_f32(ab, ef); \ + b = vcombine_f32(cd, gh); \ +} while (0) + +#define vtrn256_64q(a, b) \ +do { \ + float32x2_t a_0, a_1, a_2, a_3; \ + float32x2_t b_0, b_1, b_2, b_3; \ + a_0 = vget_low_f32(a.val[0]); \ + a_1 = vget_high_f32(a.val[0]); \ + a_2 = vget_low_f32(a.val[1]); \ + a_3 = vget_high_f32(a.val[1]); \ + b_0 = vget_low_f32(b.val[0]); \ + b_1 = vget_high_f32(b.val[0]); \ + b_2 = vget_low_f32(b.val[1]); \ + b_3 = vget_high_f32(b.val[1]); \ + a.val[0] = vcombine_f32(a_0, b_0); \ + a.val[1] = vcombine_f32(a_2, b_2); \ + b.val[0] = vcombine_f32(a_1, b_1); \ + b.val[1] = vcombine_f32(a_3, b_3); \ +} while (0) + +#define vtrn128_32q(a, b) \ +do { \ + float32x4x2_t vtrn32_tmp = vtrnq_f32((a), (b)); \ + (a) = vtrn32_tmp.val[0]; \ + (b) = vtrn32_tmp.val[1]; \ +} while (0) + +#define vtrn256_32q(a, b) \ +do { \ + float32x4x2_t vtrn32_tmp_1 = vtrnq_f32((a.val[0]), (b.val[0])); \ + float32x4x2_t vtrn32_tmp_2 = vtrnq_f32((a.val[1]), (b.val[1])); \ + a.val[0] = vtrn32_tmp_1.val[0]; \ + a.val[1] = vtrn32_tmp_2.val[0]; \ + b.val[0] = vtrn32_tmp_1.val[1]; \ + b.val[1] = vtrn32_tmp_2.val[1]; \ +} while (0) + +#define vminmaxq(a, b) \ + do { \ + float32x4_t minmax_tmp = (a); \ + (a) = vminq_f32((a), (b)); \ + (b) = vmaxq_f32(minmax_tmp, (b)); \ +} while (0) + +#define vminmax256q(a, b) \ + do { \ + float32x4x2_t minmax256_tmp = (a); \ + a.val[0] = vminq_f32(a.val[0], b.val[0]); \ + a.val[1] = vminq_f32(a.val[1], b.val[1]); \ + b.val[0] = vmaxq_f32(minmax256_tmp.val[0], b.val[0]); \ + b.val[1] = vmaxq_f32(minmax256_tmp.val[1], b.val[1]); \ +} while (0) + +#define vrev128q_f32(a) \ + vcombine_f32(vrev64_f32(vget_high_f32(a)), vrev64_f32(vget_low_f32(a))) + +#define vrev256q_f32(a) \ + do { \ + float32x4_t rev_tmp = vcombine_f32(vrev64_f32(vget_high_f32(a.val[0])), vrev64_f32(vget_low_f32(a.val[0]))); \ + a.val[0] = vcombine_f32(vrev64_f32(vget_high_f32(a.val[1])), vrev64_f32(vget_low_f32(a.val[1]))); \ + a.val[1] = rev_tmp; \ +} while (0) + +#define vldrev128q_f32(a, p) \ + do { \ + a = vld1q_f32(p); \ + a = vrev128q_f32(a); \ +} while (0) + +#endif /* ARM_MATH_NEON */ + +#ifdef __cplusplus +} +#endif + +#endif /* _ARM_SORTING_H */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_vec_fft.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_vec_fft.h new file mode 100755 index 0000000..e316612 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_vec_fft.h @@ -0,0 +1,325 @@ +/****************************************************************************** + * @file arm_vec_fft.h + * @brief Private header file for CMSIS DSP Library + * @version V1.7.0 + * @date 07. January 2020 + ******************************************************************************/ +/* + * Copyright (c) 2010-2020 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_VEC_FFT_H_ +#define ARM_VEC_FFT_H_ + +#include "arm_math.h" +#include "arm_helium_utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + +#define MVE_CMPLX_ADD_A_ixB(A, B) vcaddq_rot90(A,B) +#define MVE_CMPLX_SUB_A_ixB(A,B) vcaddq_rot270(A,B) +#define MVE_CMPLX_MULT_FLT_AxB(A,B) vcmlaq_rot90(vcmulq(A, B), A, B) +#define MVE_CMPLX_MULT_FLT_Conj_AxB(A,B) vcmlaq_rot270(vcmulq(A, B), A, B) + +#define MVE_CMPLX_MULT_FX_AxB(A,B,TyA) vqdmladhxq(vqdmlsdhq((TyA)vuninitializedq_s32(), A, B), A, B) +#define MVE_CMPLX_MULT_FX_AxConjB(A,B,TyA) vqdmladhq(vqdmlsdhxq((TyA)vuninitializedq_s32(), A, B), A, B) + +#define MVE_CMPLX_ADD_FX_A_ixB(A, B) vhcaddq_rot90(A,B) +#define MVE_CMPLX_SUB_FX_A_ixB(A,B) vhcaddq_rot270(A,B) + + +/** + @brief In-place 32 bit reversal function for helium + @param[in,out] pSrc points to in-place buffer of unknown 32-bit data type + @param[in] bitRevLen bit reversal table length + @param[in] pBitRevTab points to bit reversal table + @return none +*/ + +__STATIC_INLINE void arm_bitreversal_32_inpl_mve( + uint32_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab) + +{ + uint64_t *src = (uint64_t *) pSrc; + int32_t blkCnt; /* loop counters */ + uint32x4_t bitRevTabOff; + uint32x4_t one = vdupq_n_u32(1); + uint64x2_t inLow, inHigh; + uint64x2_t bitRevOff1Low, bitRevOff0Low; + uint64x2_t bitRevOff1High, bitRevOff0High; + + /* load scheduling to increase gather load idx update / gather load distance */ + bitRevTabOff = vldrhq_u32(pBitRevTab); + pBitRevTab += 4; + + bitRevOff0Low = vmullbq_int_u32(bitRevTabOff, one); + bitRevOff0High = vmulltq_int_u32(bitRevTabOff, one); + + + blkCnt = bitRevLen / 8; + while (blkCnt > 0) { + bitRevTabOff = vldrhq_u32(pBitRevTab); + pBitRevTab += 4; + + /* 64-bit index expansion */ + bitRevOff1Low = vmullbq_int_u32(bitRevTabOff, one); + bitRevOff1High = vmulltq_int_u32(bitRevTabOff, one); + + inLow = vldrdq_gather_offset_u64(src, bitRevOff0Low); + inHigh = vldrdq_gather_offset_u64(src, bitRevOff0High); + + vstrdq_scatter_offset_u64(src, bitRevOff0Low, inHigh); + vstrdq_scatter_offset_u64(src, bitRevOff0High, inLow); + + + /* unrolled */ + bitRevTabOff = vldrhq_u32(pBitRevTab); + pBitRevTab += 4; + + bitRevOff0Low = vmullbq_int_u32(bitRevTabOff, one); + bitRevOff0High = vmulltq_int_u32(bitRevTabOff, one); + + inLow = vldrdq_gather_offset_u64(src, bitRevOff1Low); + inHigh = vldrdq_gather_offset_u64(src, bitRevOff1High); + + vstrdq_scatter_offset_u64(src, bitRevOff1Low, inHigh); + vstrdq_scatter_offset_u64(src, bitRevOff1High, inLow); + + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + if (bitRevLen & 7) { + /* FFT size = 16 */ + inLow = vldrdq_gather_offset_u64(src, bitRevOff0Low); + inHigh = vldrdq_gather_offset_u64(src, bitRevOff0High); + + vstrdq_scatter_offset_u64(src, bitRevOff0Low, inHigh); + vstrdq_scatter_offset_u64(src, bitRevOff0High, inLow); + } +} + + + +/** + @brief In-place 16 bit reversal function for helium + @param[in,out] pSrc points to in-place buffer of unknown 16-bit data type + @param[in] bitRevLen bit reversal table length + @param[in] pBitRevTab points to bit reversal table + @return none +*/ + +__STATIC_INLINE void arm_bitreversal_16_inpl_mve( + uint16_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab) + +{ + uint32_t *src = (uint32_t *) pSrc; + int32_t blkCnt; /* loop counters */ + uint16x8_t bitRevTabOff; + uint16x8_t one = vdupq_n_u16(1); + uint32x4_t bitRevOff1Low, bitRevOff0Low; + uint32x4_t bitRevOff1High, bitRevOff0High; + uint32x4_t inLow, inHigh; + + /* load scheduling to increase gather load idx update / gather load distance */ + bitRevTabOff = vldrhq_u16(pBitRevTab); + pBitRevTab += 8; + + bitRevOff0Low = vmullbq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff0High = vmulltq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff0Low = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff0Low, 3); + bitRevOff0High = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff0High, 3); + + blkCnt = (bitRevLen / 16); + while (blkCnt > 0) { + bitRevTabOff = vldrhq_u16(pBitRevTab); + pBitRevTab += 8; + + bitRevOff1Low = vmullbq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff1High = vmulltq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff1Low = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff1Low, 3); + bitRevOff1High = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff1High, 3); + + inLow = vldrwq_gather_shifted_offset_u32(src, bitRevOff0Low); + inHigh = vldrwq_gather_shifted_offset_u32(src, bitRevOff0High); + + vstrwq_scatter_shifted_offset_u32(src, bitRevOff0Low, inHigh); + vstrwq_scatter_shifted_offset_u32(src, bitRevOff0High, inLow); + + /* loop unrolling */ + bitRevTabOff = vldrhq_u16(pBitRevTab); + pBitRevTab += 8; + + bitRevOff0Low = vmullbq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff0High = vmulltq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff0Low = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff0Low, 3); + bitRevOff0High = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff0High, 3); + + inLow = vldrwq_gather_shifted_offset_u32(src, bitRevOff1Low); + inHigh = vldrwq_gather_shifted_offset_u32(src, bitRevOff1High); + + vstrwq_scatter_shifted_offset_u32(src, bitRevOff1Low, inHigh); + vstrwq_scatter_shifted_offset_u32(src, bitRevOff1High, inLow); + + blkCnt--; + } + + /* tail handling */ + blkCnt = bitRevLen & 0xf; + if (blkCnt == 8) { + inLow = vldrwq_gather_shifted_offset_u32(src, bitRevOff0Low); + inHigh = vldrwq_gather_shifted_offset_u32(src, bitRevOff0High); + + vstrwq_scatter_shifted_offset_u32(src, bitRevOff0Low, inHigh); + vstrwq_scatter_shifted_offset_u32(src, bitRevOff0High, inLow); + } else if (blkCnt == 12) { + /* FFT 16 special case */ + mve_pred16_t p = vctp16q(4); + + bitRevTabOff = vldrhq_z_u16(pBitRevTab, p); + + inLow = vldrwq_gather_shifted_offset_u32(src, bitRevOff0Low); + inHigh = vldrwq_gather_shifted_offset_u32(src, bitRevOff0High); + + vstrwq_scatter_shifted_offset_u32(src, bitRevOff0Low, inHigh); + vstrwq_scatter_shifted_offset_u32(src, bitRevOff0High, inLow); + + bitRevOff0Low = vmullbq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff0High = vmulltq_int_u16((uint16x8_t)bitRevTabOff, one); + bitRevOff0Low = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff0Low, 3); + bitRevOff0High = (uint32x4_t)vshrq_n_u16((uint16x8_t)bitRevOff0High, 3); + + inLow = vldrwq_gather_shifted_offset_z_u32(src, bitRevOff0Low, p); + inHigh = vldrwq_gather_shifted_offset_z_u32(src, bitRevOff0High, p); + + vstrwq_scatter_shifted_offset_p_u32(src, bitRevOff0Low, inHigh, p); + vstrwq_scatter_shifted_offset_p_u32(src, bitRevOff0High, inLow, p); + } +} + +/** + @brief Out-of-place 32 bit reversal function for helium + @param[out] pDst points to destination buffer of unknown 32-bit data type + @param[in] pSrc points to input buffer of unknown 32-bit data type + @param[in] fftLen FFT length + @return none +*/ +__STATIC_INLINE void arm_bitreversal_32_outpl_mve(void *pDst, void *pSrc, uint32_t fftLen) +{ + uint32x4_t idxOffs0, idxOffs1, bitRevOffs0, bitRevOffs1; + uint32_t bitRevPos, blkCnt; + uint32_t *pDst32 = (uint32_t *) pDst; + + /* fwd indexes */ + idxOffs0 = vdupq_n_u32(0); + idxOffs1 = vdupq_n_u32(0); + idxOffs0[0] = 0; idxOffs0[2] = 4; + idxOffs1[0] = 8; idxOffs1[2] = 12; + + bitRevPos = (31 - __CLZ(fftLen)) + 5; + blkCnt = fftLen >> 2; + + /* issued earlier to increase gather load idx update / gather load distance */ + /* bit-reverse fwd indexes */ + bitRevOffs0 = vbrsrq(idxOffs0, bitRevPos); + bitRevOffs1 = vbrsrq(idxOffs1, bitRevPos); + while (blkCnt > 0) { + uint64x2_t vecIn; + + vecIn = vldrdq_gather_offset_u64(pSrc, (uint64x2_t) bitRevOffs0); + idxOffs0 = idxOffs0 + 16; + vst1q(pDst32, (uint32x4_t) vecIn); + pDst32 += 4; + bitRevOffs0 = vbrsrq(idxOffs0, bitRevPos); + + vecIn = vldrdq_gather_offset_u64(pSrc, (uint64x2_t) bitRevOffs1); + idxOffs1 = idxOffs1 + 16; + vst1q(pDst32, (uint32x4_t) vecIn); + pDst32 += 4; + bitRevOffs1 = vbrsrq(idxOffs1, bitRevPos); + + blkCnt--; + } +} + + +/** + @brief Out-of-place 16 bit reversal function for helium + @param[out] pDst points to destination buffer of unknown 16-bit data type + @param[in] pSrc points to input buffer of unknown 16-bit data type + @param[in] fftLen FFT length + @return none +*/ + +__STATIC_INLINE void arm_bitreversal_16_outpl_mve(void *pDst, void *pSrc, uint32_t fftLen) +{ + uint32x4_t idxOffs0, idxOffs1, bitRevOffs0, bitRevOffs1; + uint32_t bitRevPos, blkCnt; + uint16_t *pDst16 = (uint16_t *) pDst; + uint32_t incrIdx = 0; + + /* fwd indexes */ + idxOffs0 = vidupq_wb_u32(&incrIdx, 4); // {0, 4, 8, 12} + idxOffs1 = vidupq_wb_u32(&incrIdx, 4); // {16, 20, 24, 28} + + bitRevPos = (31 - __CLZ(fftLen)) + 4; + blkCnt = fftLen >> 3; + + /* issued earlier to increase gather load idx update / gather load distance */ + /* bit-reverse fwd indexes */ + bitRevOffs0 = vbrsrq(idxOffs0, bitRevPos); + bitRevOffs1 = vbrsrq(idxOffs1, bitRevPos); + while (blkCnt > 0) { + uint32x4_t vecIn; + + vecIn = vldrwq_gather_offset_u32(pSrc, bitRevOffs0); + idxOffs0 = idxOffs0 + 32; + vst1q(pDst16, (uint16x8_t) vecIn); + pDst16 += 8; + bitRevOffs0 = vbrsrq(idxOffs0, bitRevPos); + + vecIn = vldrwq_gather_offset_u32(pSrc, bitRevOffs1); + idxOffs1 = idxOffs1 + 32; + vst1q(pDst16, (uint16x8_t) vecIn); + pDst16 += 8; + bitRevOffs1 = vbrsrq(idxOffs1, bitRevPos); + + blkCnt--; + } +} + + +#endif /* (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE)*/ + + +#ifdef __cplusplus +} +#endif + + +#endif /* _ARM_VEC_FFT_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_vec_filtering.h b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_vec_filtering.h new file mode 100755 index 0000000..998dc5c --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/PrivateInclude/arm_vec_filtering.h @@ -0,0 +1,1586 @@ +/****************************************************************************** + * @file arm_vec_filtering.h + * @brief Private header file for CMSIS DSP Library + * @version V1.7.0 + * @date 30. October 2019 + ******************************************************************************/ +/* + * Copyright (c) 2010-2019 Arm Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef ARM_VEC_FILTERING_H_ +#define ARM_VEC_FILTERING_H_ + +#include "arm_math.h" +#include "arm_helium_utils.h" + +#ifdef __cplusplus +extern "C" +{ +#endif + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + +#define MVE_INTR_CORR_QUAD_INC_X_FIXED_SIZE_F32(acc0, acc1, acc2, acc3, pX, pY, count)\ +{ \ + float32_t const *pSrcX, *pSrcY; \ + f32x4_t acc0Vec, acc1Vec, acc2Vec, acc3Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + acc2Vec = vdupq_n_f32(0.0f); \ + acc3Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + pSrcY = (float32_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + xVec = vldrwq_f32(&pSrcX[2]); \ + acc2Vec = vfmaq_f32(acc2Vec, xVec, yVec); \ + xVec = vldrwq_f32(&pSrcX[3]); \ + acc3Vec = vfmaq_f32(acc3Vec, xVec, yVec); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec, p0); \ + xVec = vldrwq_f32(&pSrcX[2]); \ + acc2Vec = vfmaq_m_f32(acc2Vec, xVec, yVec, p0); \ + xVec = vldrwq_f32(&pSrcX[3]); \ + acc3Vec = vfmaq_m_f32(acc3Vec, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec, p0); \ + } \ + \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ + acc2 = vecAddAcrossF32Mve(acc2Vec); \ + acc3 = vecAddAcrossF32Mve(acc3Vec); \ +} + +#define MVE_INTR_CORR_SINGLE_F32(acc, pX, pY, count) \ +{ \ + float32_t const *pSrcX, *pSrcY; \ + f32x4_t accVec, xVec, yVec; \ + uint32_t k; \ + \ + accVec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + pSrcY = (float32_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + accVec = vfmaq_f32(accVec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + accVec = vfmaq_m_f32(accVec, xVec, yVec, p0);\ + } \ + acc = vecAddAcrossF32Mve(accVec); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_DEC_SIZE_F32(acc0, acc1, pX, pY, count)\ +{ \ + float32_t const *pSrcX, *pSrcY; \ + f32x4_t acc0Vec, acc1Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + pSrcY = (float32_t const *) pY; \ + k = (count-1) >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + k = (count-1) % 0x4U; \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp32q(k+1); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec, p0); \ + \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_FIXED_SIZE_F32(acc0, acc1, pX, pY, count)\ +{ \ + float32_t const *pSrcX, *pSrcY; \ + f32x4_t acc0Vec, acc1Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + pSrcY = (float32_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec, p0); \ + } \ + \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ +} + +#define MVE_INTR_CORR_DUAL_DEC_Y_INC_SIZE_F32(acc0, acc1, pX, pY, count)\ +{ \ + float32_t const *pSrcX, *pSrcY; \ + f32x4_t acc0Vec, acc1Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + pSrcY = (float32_t const *) pY; \ + k = count >> 2; \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + yVec = vldrwq_f32(&pSrcY[-1]); \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x4U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + mve_pred16_t p0 = vctp32q(k+1); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + yVec = vldrwq_f32(&pSrcY[-1]); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec,p0); \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); \ + pSrcY += 4; \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec,p0); \ + \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ +} + +#define MVE_INTR_CONV_DUAL_INC_X_DEC_SIZE_F32(acc0, acc1, pX, pY, count) \ +{ \ + float32_t const *pSrcX; \ + f32x4_t acc0Vec, acc1Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + k = (count - 1) >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = (count - 1) % 0x4U; \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + p0 = vctp32q(k+1); \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec, p0); \ + \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ +} + +#define MVE_INTR_CONV_DUAL_INC_X_FIXED_SIZE_F32(acc0, acc1, pX, pY, count) \ +{ \ + float32_t const *pSrcX; \ + f32x4_t acc0Vec, acc1Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + xVec = vldrwq_f32(&pSrcX[1]); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec, p0); \ + } \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ +} + +#define MVE_INTR_CONV_DUAL_INC_Y_INC_SIZE_F32(acc0, acc1, pX, pY, count)\ +{ \ + float32_t const *pSrcX; \ + const float32_t *pY1 = pY + 1; \ + f32x4_t acc0Vec, acc1Vec, xVec, yVec; \ + uint32_t k; \ + \ + acc0Vec = vdupq_n_f32(0.0f); \ + acc1Vec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + pY-=4; \ + acc0Vec = vfmaq_f32(acc0Vec, xVec, yVec); \ + yVec = vldrwq_gather_shifted_offset_f32(pY1, decrIdxVec); \ + pY1-=4; \ + acc1Vec = vfmaq_f32(acc1Vec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x4U; \ + /* use predication to finalize MAC sum */ \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp32q(k); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + acc0Vec = vfmaq_m_f32(acc0Vec, xVec, yVec, p0); \ + yVec = vldrwq_gather_shifted_offset_f32(pY1, decrIdxVec); \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp32q(k+1); \ + acc1Vec = vfmaq_m_f32(acc1Vec, xVec, yVec, p0); \ + \ + acc0 = vecAddAcrossF32Mve(acc0Vec); \ + acc1 = vecAddAcrossF32Mve(acc1Vec); \ +} + +#define MVE_INTR_CONV_SINGLE_F32(acc, pX, pY, count) \ +{ \ + float32_t const *pSrcX; \ + f32x4_t accVec, xVec, yVec; \ + uint32_t k; \ + \ + accVec = vdupq_n_f32(0.0f); \ + pSrcX = (float32_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + accVec = vfmaq_f32(accVec, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_gather_shifted_offset_f32(pY, decrIdxVec); \ + accVec = vfmaq_m_f32(accVec, xVec, yVec, p0); \ + } \ + acc = vecAddAcrossF32Mve(accVec); \ +} + +#endif /* (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE)*/ + +#if (defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) + +#define MVE_INTR_CONV_SINGLE_Q31(acc, pX, pY, count) \ +{ \ + q31_t const *pSrcX; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc = vmlaldavaq(acc, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + acc = vmlaldavaq_p(acc, xVec, yVec, p0); \ + } \ + acc = asrl(acc, 31); \ +} + + + +#define MVE_INTR_CONV_DUAL_INC_Y_INC_SIZE_Q31(acc0, acc1, pX, pY, count)\ +{ \ + q31_t const *pSrcX; \ + const q31_t *pY1 = pY + 1; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + pY-=4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + yVec = vldrwq_gather_shifted_offset_s32(pY1, decrIdxVec); \ + pY1-=4; \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x4U; \ + /* use predication to finalize MAC sum */ \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp32q(k); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + yVec = vldrwq_gather_shifted_offset_s32(pY1, decrIdxVec); \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp32q(k+1); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ +} + + + + +#define MVE_INTR_CONV_DUAL_INC_X_DEC_SIZE_Q31(acc0, acc1, pX, pY, count) \ +{ \ + q31_t const *pSrcX; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + k = (count-1) >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = (count - 1) % 0x4U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp32q(k+1); \ + xVec = vld1q(pSrcX); \ + pSrcX += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ +} + + + +#define MVE_INTR_CONV_DUAL_INC_X_FIXED_SIZE_Q31(acc0, acc1, pX, pY, count) \ +{ \ + q31_t const *pSrcX; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ +} + + + +#define MVE_INTR_CONV_QUAD_INC_X_FIXED_SIZE_Q31(acc0, acc1, acc2, acc3, pX, pY, count) \ +{ \ + q31_t const *pSrcX; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + pY-=4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vldrwq_s32(&pSrcX[2]); \ + acc2 = vmlaldavaq(acc2, xVec, yVec); \ + xVec = vldrwq_s32(&pSrcX[3]); \ + acc3 = vmlaldavaq(acc3, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vldrwq_gather_shifted_offset_s32(pY, decrIdxVec); \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vldrwq_s32(&pSrcX[2]); \ + acc2 = vmlaldavaq_p(acc2, xVec, yVec, p0); \ + xVec = vldrwq_s32(&pSrcX[3]); \ + acc3 = vmlaldavaq_p(acc3, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ + acc2 = asrl(acc2, 31); \ + acc3 = asrl(acc3, 31); \ +} + +#define MVE_INTR_CORR_DUAL_DEC_Y_INC_SIZE_Q31(acc0, acc1, pX, pY, count)\ +{ \ + q31_t const *pSrcX, *pSrcY; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + pSrcY = (q31_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_s32(&pSrcY[-1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x4U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + mve_pred16_t p0 = vctp32q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vldrwq_s32(&pSrcY[-1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec,p0); \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec,p0); \ + \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ +} + +#define MVE_INTR_CORR_SINGLE_Q31(acc, pX, pY, count)\ +{ \ + q31_t const *pSrcX, *pSrcY; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + pSrcY = (q31_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + acc = vmlaldavaq(acc, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + acc = vmlaldavaq_p(acc, xVec, yVec, p0); \ + } \ + acc = asrl(acc, 31); \ +} + +#define MVE_INTR_CORR_QUAD_INC_X_FIXED_SIZE_Q31(acc0, acc1, acc2, acc3, pX, pY, count)\ +{ \ + q31_t const *pSrcX, *pSrcY; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + pSrcY = (q31_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vldrwq_s32(&pSrcX[2]); \ + acc2 = vmlaldavaq(acc2, xVec, yVec); \ + xVec = vldrwq_s32(&pSrcX[3]); \ + acc3 = vmlaldavaq(acc3, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vldrwq_s32(&pSrcX[2]); \ + acc2 = vmlaldavaq_p(acc2, xVec, yVec, p0); \ + xVec = vldrwq_s32(&pSrcX[3]); \ + acc3 = vmlaldavaq_p(acc3, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ + acc2 = asrl(acc2, 31); \ + acc3 = asrl(acc3, 31); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_FIXED_SIZE_Q31(acc0, acc1, pX, pY, count)\ +{ \ + q31_t const *pSrcX, *pSrcY; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + pSrcY = (q31_t const *) pY; \ + k = count >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x4U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_DEC_SIZE_Q31(acc0, acc1, pX, pY, count)\ +{ \ + q31_t const *pSrcX, *pSrcY; \ + q31x4_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q31_t const *) pX; \ + pSrcY = (q31_t const *) pY; \ + k = (count-1) >> 2; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + k = (count-1) % 0x4U; \ + mve_pred16_t p0 = vctp32q(k); \ + yVec = vld1q(pSrcY); pSrcY += 4; \ + xVec = vldrwq_s32(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp32q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 4; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + \ + acc0 = asrl(acc0, 31); \ + acc1 = asrl(acc1, 31); \ +} + +#define MVE_INTR_CORR_DUAL_DEC_Y_INC_SIZE_Q15(acc0, acc1, pX, pY, count)\ +{ \ + q15_t const *pSrcX, *pSrcY; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + pSrcY = (q15_t const *) pY; \ + k = count >> 3; \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vldrhq_s16(&pSrcY[-1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x8U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + mve_pred16_t p0 = vctp16q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vldrhq_s16(&pSrcY[-1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec,p0); \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + p0 = vctp16q(k); \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec,p0); \ + \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ +} + +#define MVE_INTR_CORR_SINGLE_Q15(acc, pX, pY, count)\ +{ \ + q15_t const *pSrcX, *pSrcY; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + pSrcY = (q15_t const *) pY; \ + k = count >> 3; \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + acc = vmlaldavaq(acc, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* tail predication expected here */ \ + k = count % 0x8U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp16q(k); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + acc = vmlaldavaq_p(acc, xVec, yVec, p0); \ + } \ + acc = asrl(acc, 15); \ + acc = __SSAT(acc, 16); \ +} + +#define MVE_INTR_CORR_QUAD_INC_X_FIXED_SIZE_Q15(acc0, acc1, acc2, acc3, pX, pY, count)\ +{ \ + q15_t const *pSrcX, *pSrcY; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + pSrcY = (q15_t const *) pY; \ + k = count >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vldrhq_s16(&pSrcX[2]); \ + acc2 = vmlaldavaq(acc2, xVec, yVec); \ + xVec = vldrhq_s16(&pSrcX[3]); \ + acc3 = vmlaldavaq(acc3, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x8U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp16q(k); \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vldrhq_s16(&pSrcX[2]); \ + acc2 = vmlaldavaq_p(acc2, xVec, yVec, p0); \ + xVec = vldrhq_s16(&pSrcX[3]); \ + acc3 = vmlaldavaq_p(acc3, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc2 = asrl(acc2, 15); \ + acc3 = asrl(acc3, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ + acc2 = __SSAT(acc2, 16); \ + acc3 = __SSAT(acc3, 16); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_FIXED_SIZE_Q15(acc0, acc1, pX, pY, count)\ +{ \ + q15_t const *pSrcX, *pSrcY; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + pSrcY = (q15_t const *) pY; \ + k = count >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x8U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp16q(k); \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_DEC_SIZE_Q15(acc0, acc1, pX, pY, count)\ +{ \ + q15_t const *pSrcX, *pSrcY; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + pSrcY = (q15_t const *) pY; \ + k = (count-1) >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + k = (count-1) % 0x8U; \ + mve_pred16_t p0 = vctp16q(k); \ + yVec = vld1q(pSrcY); pSrcY += 8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp16q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ +} + +#define MVE_INTR_CONV_DUAL_INC_Y_INC_SIZE_Q15(acc0, acc1, pX, pY, count)\ +{ \ + q15_t const *pSrcX; \ + const q15_t *pY1 = pY + 1; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + k = count >> 3; \ + \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + pY-=8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + yVec = vldrhq_gather_shifted_offset_s16(pY1, decrIdxVec); \ + pY1-=8; \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x8U; \ + /* use predication to finalize MAC sum */ \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp16q(k); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + yVec = vldrhq_gather_shifted_offset_s16(pY1, decrIdxVec); \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp16q(k+1); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ +} + +#define MVE_INTR_CONV_SINGLE_Q15(acc, pX, pY, count) \ +{ \ + q15_t const *pSrcX; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + k = count >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + pY-=8; \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc = vmlaldavaq(acc, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x8U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp16q(k); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + acc = vmlaldavaq_p(acc, xVec, yVec, p0); \ + } \ + acc = asrl(acc, 15); \ + acc = __SSAT(acc, 16); \ +} + +#define MVE_INTR_CONV_QUAD_INC_X_FIXED_SIZE_Q15(acc0, acc1, acc2, acc3, pX, pY, count) \ +{ \ + q15_t const *pSrcX; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + k = count >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + pY-=8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vldrhq_s16(&pSrcX[2]); \ + acc2 = vmlaldavaq(acc2, xVec, yVec); \ + xVec = vldrhq_s16(&pSrcX[3]); \ + acc3 = vmlaldavaq(acc3, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x8U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp16q(k); \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vldrhq_s16(&pSrcX[2]); \ + acc2 = vmlaldavaq_p(acc2, xVec, yVec, p0); \ + xVec = vldrhq_s16(&pSrcX[3]); \ + acc3 = vmlaldavaq_p(acc3, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc2 = asrl(acc2, 15); \ + acc3 = asrl(acc3, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ + acc2 = __SSAT(acc2, 16); \ + acc3 = __SSAT(acc3, 16); \ +} + +#define MVE_INTR_CONV_DUAL_INC_X_FIXED_SIZE_Q15(acc0, acc1, pX, pY, count) \ +{ \ + q15_t const *pSrcX; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + k = count >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + pY-=8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x8U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp16q(k); \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + } \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ +} + +#define MVE_INTR_CONV_DUAL_INC_X_DEC_SIZE_Q15(acc0, acc1, pX, pY, count) \ +{ \ + q15_t const *pSrcX; \ + q15x8_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q15_t const *) pX; \ + k = (count-1) >> 3; \ + \ + while (k > 0U) \ + { \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + pY-=8; \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = (count - 1) % 0x8U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp16q(k); \ + yVec = vldrhq_gather_shifted_offset_s16(pY, decrIdxVec); \ + xVec = vldrhq_s16(&pSrcX[1]); \ + acc1 = vmlaldavaq_p(acc1, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp16q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 8; \ + acc0 = vmlaldavaq_p(acc0, xVec, yVec, p0); \ + \ + acc0 = asrl(acc0, 15); \ + acc1 = asrl(acc1, 15); \ + acc0 = __SSAT(acc0, 16); \ + acc1 = __SSAT(acc1, 16); \ +} + +#define MVE_INTR_CORR_DUAL_DEC_Y_INC_SIZE_Q7(acc0, acc1, pX, pY, count)\ +{ \ + q7_t const *pSrcX, *pSrcY; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + pSrcY = (q7_t const *) pY; \ + k = count >> 4; \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vldrbq_s8(&pSrcY[-1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x10U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + mve_pred16_t p0 = vctp8q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vldrbq_s8(&pSrcY[-1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec,p0); \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + p0 = vctp8q(k); \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec,p0); \ + \ + acc0 = (acc0 >> 7); \ + acc1 = (acc1 >> 7); \ + acc0 = __SSAT(acc0, 8); \ + acc1 = __SSAT(acc1, 8); \ +} + +#define MVE_INTR_CORR_SINGLE_Q7(acc, pX, pY, count)\ +{ \ + q7_t const *pSrcX, *pSrcY; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + pSrcY = (q7_t const *) pY; \ + k = count >> 4; \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + acc = vmladavaq(acc, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* tail predication expected here */ \ + k = count % 0x10U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp8q(k); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + acc = vmladavaq_p(acc, xVec, yVec, p0); \ + } \ + acc =(acc >> 7); \ + acc = __SSAT(acc, 8); \ +} + +#define MVE_INTR_CORR_QUAD_INC_X_FIXED_SIZE_Q7(acc0, acc1, acc2, acc3, pX, pY, count)\ +{ \ + q7_t const *pSrcX, *pSrcY; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + pSrcY = (q7_t const *) pY; \ + k = count >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + xVec = vldrbq_s8(&pSrcX[2]); \ + acc2 = vmladavaq(acc2, xVec, yVec); \ + xVec = vldrbq_s8(&pSrcX[3]); \ + acc3 = vmladavaq(acc3, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x10U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp8q(k); \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + xVec = vldrbq_s8(&pSrcX[2]); \ + acc2 = vmladavaq_p(acc2, xVec, yVec, p0); \ + xVec = vldrbq_s8(&pSrcX[3]); \ + acc3 = vmladavaq_p(acc3, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + } \ + \ + acc0 = (acc0 >> 7); \ + acc1 = (acc1 >> 7); \ + acc2 = (acc2 >> 7); \ + acc3 = (acc3 >> 7); \ + acc0 = __SSAT(acc0, 8); \ + acc1 = __SSAT(acc1, 8); \ + acc2 = __SSAT(acc2, 8); \ + acc3 = __SSAT(acc3, 8); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_FIXED_SIZE_Q7(acc0, acc1, pX, pY, count)\ +{ \ + q7_t const *pSrcX, *pSrcY; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + pSrcY = (q7_t const *) pY; \ + k = count >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* loop + tail predication expected here */ \ + k = count % 0x10U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp8q(k); \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + } \ + \ + acc0 = (acc0 >> 7); \ + acc1 = (acc1 >> 7); \ + acc0 = __SSAT(acc0, 8); \ + acc1 = __SSAT(acc1, 8); \ +} + +#define MVE_INTR_CORR_DUAL_INC_X_DEC_SIZE_Q7(acc0, acc1, pX, pY, count)\ +{ \ + q7_t const *pSrcX, *pSrcY; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + pSrcY = (q7_t const *) pY; \ + k = (count-1) >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + k = (count-1) % 0x10U; \ + mve_pred16_t p0 = vctp8q(k); \ + yVec = vld1q(pSrcY); pSrcY += 16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp8q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + \ + acc0 = (acc0 >> 7); \ + acc1 = (acc1 >> 7); \ + acc0 = __SSAT(acc0, 8); \ + acc1 = __SSAT(acc1, 8); \ +} + +#define MVE_INTR_CONV_DUAL_INC_Y_INC_SIZE_Q7(acc0, acc1, pX, pY, count)\ +{ \ + q7_t const *pSrcX; \ + const q7_t *pY1 = pY + 1; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + k = count >> 4; \ + \ + while (k > 0U) \ + { \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + pY-=16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + yVec = vldrbq_gather_offset_s8(pY1, decrIdxVec); \ + pY1-=16; \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = count % 0x10U; \ + /* use predication to finalize MAC sum */ \ + /* acc0 requires exact number of sample */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp8q(k); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + yVec = vldrbq_gather_offset_s8(pY1, decrIdxVec); \ + /* acc1 requires 1 additional sample */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp8q(k+1); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + \ + acc0 = (acc0 >> 7); \ + acc1 = (acc1 >> 7); \ + acc0 = __SSAT(acc0, 8); \ + acc1 = __SSAT(acc1, 8); \ +} + +#define MVE_INTR_CONV_SINGLE_Q7(acc, pX, pY, count) \ +{ \ + q7_t const *pSrcX; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + k = count >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + pY-=16; \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc = vmladavaq(acc, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x10U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp8q(k); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + acc = vmladavaq_p(acc, xVec, yVec, p0); \ + } \ + acc = __SSAT(acc >> 7, 8); \ +} + +#define MVE_INTR_CONV_QUAD_INC_X_FIXED_SIZE_Q7(acc0, acc1, acc2, acc3, pX, pY, count) \ +{ \ + q7_t const *pSrcX; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + k = count >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + pY-=16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + xVec = vldrbq_s8(&pSrcX[2]); \ + acc2 = vmladavaq(acc2, xVec, yVec); \ + xVec = vldrbq_s8(&pSrcX[3]); \ + acc3 = vmladavaq(acc3, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x10U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp8q(k); \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + xVec = vldrbq_s8(&pSrcX[2]); \ + acc2 = vmladavaq_p(acc2, xVec, yVec, p0); \ + xVec = vldrbq_s8(&pSrcX[3]); \ + acc3 = vmladavaq_p(acc3, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + } \ + acc0 = __SSAT(acc0 >> 7, 8); \ + acc1 = __SSAT(acc1 >> 7, 8); \ + acc2 = __SSAT(acc2 >> 7, 8); \ + acc3 = __SSAT(acc3 >> 7, 8); \ +} + +#define MVE_INTR_CONV_DUAL_INC_X_FIXED_SIZE_Q7(acc0, acc1, pX, pY, count) \ +{ \ + q7_t const *pSrcX; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + k = count >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + pY-=16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + /* Loop with tail predication expected here */ \ + k = count % 0x10U; \ + if (k > 0U) \ + { \ + mve_pred16_t p0 = vctp8q(k); \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + } \ + acc0 = __SSAT(acc0 >> 7, 8); \ + acc1 = __SSAT(acc1 >> 7, 8); \ +} + + +#define MVE_INTR_CONV_DUAL_INC_X_DEC_SIZE_Q7(acc0, acc1, pX, pY, count) \ +{ \ + q7_t const *pSrcX; \ + q7x16_t xVec, yVec; \ + uint32_t k; \ + \ + pSrcX = (q7_t const *) pX; \ + k = (count-1) >> 4; \ + \ + while (k > 0U) \ + { \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + pY-=16; \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq(acc1, xVec, yVec); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq(acc0, xVec, yVec); \ + /* Decrement the loop counter */ \ + k--; \ + } \ + k = (count - 1) % 0x10U; \ + /* use predication to finalize MAC sum */ \ + /* acc1 requires exact number of sample (count-1) */ \ + /* disable extra lanes in final MAC computation */ \ + mve_pred16_t p0 = vctp8q(k); \ + yVec = vldrbq_gather_offset_s8(pY, decrIdxVec); \ + xVec = vldrbq_s8(&pSrcX[1]); \ + acc1 = vmladavaq_p(acc1, xVec, yVec, p0); \ + /* acc0 requires 1 additional sample (count) */ \ + /* so add 1 to unmask an extra lane in final MAC computation */ \ + p0 = vctp8q(k+1); \ + xVec = vld1q(pSrcX); pSrcX += 16; \ + acc0 = vmladavaq_p(acc0, xVec, yVec, p0); \ + \ + acc0 = (acc0 >> 7); \ + acc1 = (acc1 >> 7); \ + acc0 = __SSAT(acc0, 8); \ + acc1 = __SSAT(acc1, 8); \ +} + +#endif /* (defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) */ + +#ifdef __cplusplus +} +#endif + + +#endif /* _ARM_VEC_FILTERING_H_ */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_common_tables.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_common_tables.c new file mode 100755 index 0000000..5044075 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_common_tables.c @@ -0,0 +1,45787 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_common_tables.c + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include "arm_compiler_specific.h" +#include "arm_math_types.h" +#include "arm_common_tables.h" + +/** + @ingroup ComplexFFT + */ + +/** + @addtogroup CFFT_CIFFT Complex FFT Tables + @{ + */ + +/** + @par + Pseudo code for Generation of Bit reversal Table is + @par + 
for (l = 1; l <= N/4; l++)
+  {
+    for (i = 0; i< logN2; i++)
+    {
+      a[i] = l & (1 << i);
+    }
+    for (j = 0; j < logN2; j++)
+    {
+      if (a[j] != 0)
+      y[l] += (1 << ((logN2 - 1) - j));
+    }
+    y[l] = y[l] >> 1;
+   }
+ @par + where N = 4096, logN2 = 12 + @par + N is the maximum FFT Size supported +*/ + +/** + @brief Table for bit reversal process +*/ +const uint16_t armBitRevTable[1024] ARM_DSP_TABLE_ATTRIBUTE = { + 0x400, 0x200, 0x600, 0x100, 0x500, 0x300, 0x700, 0x080, 0x480, 0x280, + 0x680, 0x180, 0x580, 0x380, 0x780, 0x040, 0x440, 0x240, 0x640, 0x140, + 0x540, 0x340, 0x740, 0x0c0, 0x4c0, 0x2c0, 0x6c0, 0x1c0, 0x5c0, 0x3c0, + 0x7c0, 0x020, 0x420, 0x220, 0x620, 0x120, 0x520, 0x320, 0x720, 0x0a0, + 0x4a0, 0x2a0, 0x6a0, 0x1a0, 0x5a0, 0x3a0, 0x7a0, 0x060, 0x460, 0x260, + 0x660, 0x160, 0x560, 0x360, 0x760, 0x0e0, 0x4e0, 0x2e0, 0x6e0, 0x1e0, + 0x5e0, 0x3e0, 0x7e0, 0x010, 0x410, 0x210, 0x610, 0x110, 0x510, 0x310, + 0x710, 0x090, 0x490, 0x290, 0x690, 0x190, 0x590, 0x390, 0x790, 0x050, + 0x450, 0x250, 0x650, 0x150, 0x550, 0x350, 0x750, 0x0d0, 0x4d0, 0x2d0, + 0x6d0, 0x1d0, 0x5d0, 0x3d0, 0x7d0, 0x030, 0x430, 0x230, 0x630, 0x130, + 0x530, 0x330, 0x730, 0x0b0, 0x4b0, 0x2b0, 0x6b0, 0x1b0, 0x5b0, 0x3b0, + 0x7b0, 0x070, 0x470, 0x270, 0x670, 0x170, 0x570, 0x370, 0x770, 0x0f0, + 0x4f0, 0x2f0, 0x6f0, 0x1f0, 0x5f0, 0x3f0, 0x7f0, 0x008, 0x408, 0x208, + 0x608, 0x108, 0x508, 0x308, 0x708, 0x088, 0x488, 0x288, 0x688, 0x188, + 0x588, 0x388, 0x788, 0x048, 0x448, 0x248, 0x648, 0x148, 0x548, 0x348, + 0x748, 0x0c8, 0x4c8, 0x2c8, 0x6c8, 0x1c8, 0x5c8, 0x3c8, 0x7c8, 0x028, + 0x428, 0x228, 0x628, 0x128, 0x528, 0x328, 0x728, 0x0a8, 0x4a8, 0x2a8, + 0x6a8, 0x1a8, 0x5a8, 0x3a8, 0x7a8, 0x068, 0x468, 0x268, 0x668, 0x168, + 0x568, 0x368, 0x768, 0x0e8, 0x4e8, 0x2e8, 0x6e8, 0x1e8, 0x5e8, 0x3e8, + 0x7e8, 0x018, 0x418, 0x218, 0x618, 0x118, 0x518, 0x318, 0x718, 0x098, + 0x498, 0x298, 0x698, 0x198, 0x598, 0x398, 0x798, 0x058, 0x458, 0x258, + 0x658, 0x158, 0x558, 0x358, 0x758, 0x0d8, 0x4d8, 0x2d8, 0x6d8, 0x1d8, + 0x5d8, 0x3d8, 0x7d8, 0x038, 0x438, 0x238, 0x638, 0x138, 0x538, 0x338, + 0x738, 0x0b8, 0x4b8, 0x2b8, 0x6b8, 0x1b8, 0x5b8, 0x3b8, 0x7b8, 0x078, + 0x478, 0x278, 0x678, 0x178, 0x578, 0x378, 0x778, 0x0f8, 0x4f8, 0x2f8, + 0x6f8, 0x1f8, 0x5f8, 0x3f8, 0x7f8, 0x004, 0x404, 0x204, 0x604, 0x104, + 0x504, 0x304, 0x704, 0x084, 0x484, 0x284, 0x684, 0x184, 0x584, 0x384, + 0x784, 0x044, 0x444, 0x244, 0x644, 0x144, 0x544, 0x344, 0x744, 0x0c4, + 0x4c4, 0x2c4, 0x6c4, 0x1c4, 0x5c4, 0x3c4, 0x7c4, 0x024, 0x424, 0x224, + 0x624, 0x124, 0x524, 0x324, 0x724, 0x0a4, 0x4a4, 0x2a4, 0x6a4, 0x1a4, + 0x5a4, 0x3a4, 0x7a4, 0x064, 0x464, 0x264, 0x664, 0x164, 0x564, 0x364, + 0x764, 0x0e4, 0x4e4, 0x2e4, 0x6e4, 0x1e4, 0x5e4, 0x3e4, 0x7e4, 0x014, + 0x414, 0x214, 0x614, 0x114, 0x514, 0x314, 0x714, 0x094, 0x494, 0x294, + 0x694, 0x194, 0x594, 0x394, 0x794, 0x054, 0x454, 0x254, 0x654, 0x154, + 0x554, 0x354, 0x754, 0x0d4, 0x4d4, 0x2d4, 0x6d4, 0x1d4, 0x5d4, 0x3d4, + 0x7d4, 0x034, 0x434, 0x234, 0x634, 0x134, 0x534, 0x334, 0x734, 0x0b4, + 0x4b4, 0x2b4, 0x6b4, 0x1b4, 0x5b4, 0x3b4, 0x7b4, 0x074, 0x474, 0x274, + 0x674, 0x174, 0x574, 0x374, 0x774, 0x0f4, 0x4f4, 0x2f4, 0x6f4, 0x1f4, + 0x5f4, 0x3f4, 0x7f4, 0x00c, 0x40c, 0x20c, 0x60c, 0x10c, 0x50c, 0x30c, + 0x70c, 0x08c, 0x48c, 0x28c, 0x68c, 0x18c, 0x58c, 0x38c, 0x78c, 0x04c, + 0x44c, 0x24c, 0x64c, 0x14c, 0x54c, 0x34c, 0x74c, 0x0cc, 0x4cc, 0x2cc, + 0x6cc, 0x1cc, 0x5cc, 0x3cc, 0x7cc, 0x02c, 0x42c, 0x22c, 0x62c, 0x12c, + 0x52c, 0x32c, 0x72c, 0x0ac, 0x4ac, 0x2ac, 0x6ac, 0x1ac, 0x5ac, 0x3ac, + 0x7ac, 0x06c, 0x46c, 0x26c, 0x66c, 0x16c, 0x56c, 0x36c, 0x76c, 0x0ec, + 0x4ec, 0x2ec, 0x6ec, 0x1ec, 0x5ec, 0x3ec, 0x7ec, 0x01c, 0x41c, 0x21c, + 0x61c, 0x11c, 0x51c, 0x31c, 0x71c, 0x09c, 0x49c, 0x29c, 0x69c, 0x19c, + 0x59c, 0x39c, 0x79c, 0x05c, 0x45c, 0x25c, 0x65c, 0x15c, 0x55c, 0x35c, + 0x75c, 0x0dc, 0x4dc, 0x2dc, 0x6dc, 0x1dc, 0x5dc, 0x3dc, 0x7dc, 0x03c, + 0x43c, 0x23c, 0x63c, 0x13c, 0x53c, 0x33c, 0x73c, 0x0bc, 0x4bc, 0x2bc, + 0x6bc, 0x1bc, 0x5bc, 0x3bc, 0x7bc, 0x07c, 0x47c, 0x27c, 0x67c, 0x17c, + 0x57c, 0x37c, 0x77c, 0x0fc, 0x4fc, 0x2fc, 0x6fc, 0x1fc, 0x5fc, 0x3fc, + 0x7fc, 0x002, 0x402, 0x202, 0x602, 0x102, 0x502, 0x302, 0x702, 0x082, + 0x482, 0x282, 0x682, 0x182, 0x582, 0x382, 0x782, 0x042, 0x442, 0x242, + 0x642, 0x142, 0x542, 0x342, 0x742, 0x0c2, 0x4c2, 0x2c2, 0x6c2, 0x1c2, + 0x5c2, 0x3c2, 0x7c2, 0x022, 0x422, 0x222, 0x622, 0x122, 0x522, 0x322, + 0x722, 0x0a2, 0x4a2, 0x2a2, 0x6a2, 0x1a2, 0x5a2, 0x3a2, 0x7a2, 0x062, + 0x462, 0x262, 0x662, 0x162, 0x562, 0x362, 0x762, 0x0e2, 0x4e2, 0x2e2, + 0x6e2, 0x1e2, 0x5e2, 0x3e2, 0x7e2, 0x012, 0x412, 0x212, 0x612, 0x112, + 0x512, 0x312, 0x712, 0x092, 0x492, 0x292, 0x692, 0x192, 0x592, 0x392, + 0x792, 0x052, 0x452, 0x252, 0x652, 0x152, 0x552, 0x352, 0x752, 0x0d2, + 0x4d2, 0x2d2, 0x6d2, 0x1d2, 0x5d2, 0x3d2, 0x7d2, 0x032, 0x432, 0x232, + 0x632, 0x132, 0x532, 0x332, 0x732, 0x0b2, 0x4b2, 0x2b2, 0x6b2, 0x1b2, + 0x5b2, 0x3b2, 0x7b2, 0x072, 0x472, 0x272, 0x672, 0x172, 0x572, 0x372, + 0x772, 0x0f2, 0x4f2, 0x2f2, 0x6f2, 0x1f2, 0x5f2, 0x3f2, 0x7f2, 0x00a, + 0x40a, 0x20a, 0x60a, 0x10a, 0x50a, 0x30a, 0x70a, 0x08a, 0x48a, 0x28a, + 0x68a, 0x18a, 0x58a, 0x38a, 0x78a, 0x04a, 0x44a, 0x24a, 0x64a, 0x14a, + 0x54a, 0x34a, 0x74a, 0x0ca, 0x4ca, 0x2ca, 0x6ca, 0x1ca, 0x5ca, 0x3ca, + 0x7ca, 0x02a, 0x42a, 0x22a, 0x62a, 0x12a, 0x52a, 0x32a, 0x72a, 0x0aa, + 0x4aa, 0x2aa, 0x6aa, 0x1aa, 0x5aa, 0x3aa, 0x7aa, 0x06a, 0x46a, 0x26a, + 0x66a, 0x16a, 0x56a, 0x36a, 0x76a, 0x0ea, 0x4ea, 0x2ea, 0x6ea, 0x1ea, + 0x5ea, 0x3ea, 0x7ea, 0x01a, 0x41a, 0x21a, 0x61a, 0x11a, 0x51a, 0x31a, + 0x71a, 0x09a, 0x49a, 0x29a, 0x69a, 0x19a, 0x59a, 0x39a, 0x79a, 0x5a, + 0x45a, 0x25a, 0x65a, 0x15a, 0x55a, 0x35a, 0x75a, 0x0da, 0x4da, 0x2da, + 0x6da, 0x1da, 0x5da, 0x3da, 0x7da, 0x03a, 0x43a, 0x23a, 0x63a, 0x13a, + 0x53a, 0x33a, 0x73a, 0x0ba, 0x4ba, 0x2ba, 0x6ba, 0x1ba, 0x5ba, 0x3ba, + 0x7ba, 0x07a, 0x47a, 0x27a, 0x67a, 0x17a, 0x57a, 0x37a, 0x77a, 0x0fa, + 0x4fa, 0x2fa, 0x6fa, 0x1fa, 0x5fa, 0x3fa, 0x7fa, 0x006, 0x406, 0x206, + 0x606, 0x106, 0x506, 0x306, 0x706, 0x086, 0x486, 0x286, 0x686, 0x186, + 0x586, 0x386, 0x786, 0x046, 0x446, 0x246, 0x646, 0x146, 0x546, 0x346, + 0x746, 0x0c6, 0x4c6, 0x2c6, 0x6c6, 0x1c6, 0x5c6, 0x3c6, 0x7c6, 0x026, + 0x426, 0x226, 0x626, 0x126, 0x526, 0x326, 0x726, 0x0a6, 0x4a6, 0x2a6, + 0x6a6, 0x1a6, 0x5a6, 0x3a6, 0x7a6, 0x066, 0x466, 0x266, 0x666, 0x166, + 0x566, 0x366, 0x766, 0x0e6, 0x4e6, 0x2e6, 0x6e6, 0x1e6, 0x5e6, 0x3e6, + 0x7e6, 0x016, 0x416, 0x216, 0x616, 0x116, 0x516, 0x316, 0x716, 0x096, + 0x496, 0x296, 0x696, 0x196, 0x596, 0x396, 0x796, 0x056, 0x456, 0x256, + 0x656, 0x156, 0x556, 0x356, 0x756, 0x0d6, 0x4d6, 0x2d6, 0x6d6, 0x1d6, + 0x5d6, 0x3d6, 0x7d6, 0x036, 0x436, 0x236, 0x636, 0x136, 0x536, 0x336, + 0x736, 0x0b6, 0x4b6, 0x2b6, 0x6b6, 0x1b6, 0x5b6, 0x3b6, 0x7b6, 0x076, + 0x476, 0x276, 0x676, 0x176, 0x576, 0x376, 0x776, 0x0f6, 0x4f6, 0x2f6, + 0x6f6, 0x1f6, 0x5f6, 0x3f6, 0x7f6, 0x00e, 0x40e, 0x20e, 0x60e, 0x10e, + 0x50e, 0x30e, 0x70e, 0x08e, 0x48e, 0x28e, 0x68e, 0x18e, 0x58e, 0x38e, + 0x78e, 0x04e, 0x44e, 0x24e, 0x64e, 0x14e, 0x54e, 0x34e, 0x74e, 0x0ce, + 0x4ce, 0x2ce, 0x6ce, 0x1ce, 0x5ce, 0x3ce, 0x7ce, 0x02e, 0x42e, 0x22e, + 0x62e, 0x12e, 0x52e, 0x32e, 0x72e, 0x0ae, 0x4ae, 0x2ae, 0x6ae, 0x1ae, + 0x5ae, 0x3ae, 0x7ae, 0x06e, 0x46e, 0x26e, 0x66e, 0x16e, 0x56e, 0x36e, + 0x76e, 0x0ee, 0x4ee, 0x2ee, 0x6ee, 0x1ee, 0x5ee, 0x3ee, 0x7ee, 0x01e, + 0x41e, 0x21e, 0x61e, 0x11e, 0x51e, 0x31e, 0x71e, 0x09e, 0x49e, 0x29e, + 0x69e, 0x19e, 0x59e, 0x39e, 0x79e, 0x05e, 0x45e, 0x25e, 0x65e, 0x15e, + 0x55e, 0x35e, 0x75e, 0x0de, 0x4de, 0x2de, 0x6de, 0x1de, 0x5de, 0x3de, + 0x7de, 0x03e, 0x43e, 0x23e, 0x63e, 0x13e, 0x53e, 0x33e, 0x73e, 0x0be, + 0x4be, 0x2be, 0x6be, 0x1be, 0x5be, 0x3be, 0x7be, 0x07e, 0x47e, 0x27e, + 0x67e, 0x17e, 0x57e, 0x37e, 0x77e, 0x0fe, 0x4fe, 0x2fe, 0x6fe, 0x1fe, + 0x5fe, 0x3fe, 0x7fe, 0x001 +}; + +/** + @brief Double Precision Floating-point Twiddle factors Table Generation +*/ + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i < N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(double)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(double)N);
+  }
+ @par + where N = 16, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_16[32] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, //-0.38268, 0.92388' + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, //-0.70711, 0.70711' + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, //-0.92388, 0.38268' + 0xbff0000000000000, 0x0000000000000000, // -1, 0' + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, //-0.92388,-0.38268' + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, //-0.70711,-0.70711' + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, //-0.38268,-0.92388' + 0x0000000000000000, 0xbff0000000000000, // 0, -1' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268,-0.92388' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711,-0.70711' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388,-0.38268' +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/N);
+  }
+ @par + where N = 32, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_32[64] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, //-0.19509, 0.98079' + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, //-0.38268, 0.92388' + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, //-0.55557, 0.83147' + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, //-0.70711, 0.70711' + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, //-0.83147, 0.55557' + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, //-0.92388, 0.38268' + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, //-0.98079, 0.19509' + 0xbff0000000000000, 0x0000000000000000, // -1, 0' + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, //-0.98079,-0.19509' + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, //-0.92388,-0.38268' + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, //-0.83147,-0.55557' + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, //-0.70711,-0.70711' + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, //-0.55557,-0.83147' + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, //-0.38268,-0.92388' + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, //-0.19509,-0.98079' + 0x0000000000000000, 0xbff0000000000000, // 0, -1' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509,-0.98079' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268,-0.92388' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557,-0.83147' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711,-0.70711' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147,-0.55557' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388,-0.38268' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079,-0.19509' +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for(i = 0; i < N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 64, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_64[128] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518' + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, //-0.098017, 0.99518' + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079' + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694' + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388' + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192' + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147' + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301' + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711' + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439' + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557' + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714' + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268' + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028' + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509' + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017' + 0xbff0000000000000, 0x0000000000000000, // -1, 0' + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518,-0.098017' + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509' + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028' + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268' + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714' + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557' + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439' + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711' + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301' + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147' + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192' + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388' + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694' + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079' + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, //-0.098017, -0.99518' + 0x0000000000000000, 0xbff0000000000000, // 0, -1' + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079' + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388' + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147' + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711' + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557' + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268' + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509' + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017' + }; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 128, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_128[256] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068' + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017' + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298' + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028' + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756' + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714' + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957' + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439' + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095' + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301' + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773' + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192' + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154' + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694' + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918' + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518' + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988' + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0xbfa91f65f10dd814, 0x3feff621e3796d7e, //-0.049068, 0.9988' + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, //-0.098017, 0.99518' + 0xbfc2c8106e8e613a, 0x3fefa7557f08a517, // -0.14673, 0.98918' + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079' + 0xbfcf19f97b215f1a, 0x3fef0a7efb9230d7, // -0.24298, 0.97003' + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694' + 0xbfd58f9a75ab1fdd, 0x3fee212104f686e5, // -0.33689, 0.94154' + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388' + 0xbfdb5d1009e15cc0, 0x3feced7af43cc773, // -0.42756, 0.90399' + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192' + 0xbfe073879922ffed, 0x3feb728345196e3e, // -0.5141, 0.85773' + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147' + 0xbfe30ff7fce17035, 0x3fe9b3e047f38741, // -0.5957, 0.80321' + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301' + 0xbfe57d69348cec9f, 0x3fe7b5df226aafb0, // -0.67156, 0.74095' + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711' + 0xbfe7b5df226aafb0, 0x3fe57d69348cec9f, // -0.74095, 0.67156' + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439' + 0xbfe9b3e047f38741, 0x3fe30ff7fce17035, // -0.80321, 0.5957' + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557' + 0xbfeb728345196e3e, 0x3fe073879922ffed, // -0.85773, 0.5141' + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714' + 0xbfeced7af43cc773, 0x3fdb5d1009e15cc0, // -0.90399, 0.42756' + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268' + 0xbfee212104f686e5, 0x3fd58f9a75ab1fdd, // -0.94154, 0.33689' + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028' + 0xbfef0a7efb9230d7, 0x3fcf19f97b215f1a, // -0.97003, 0.24298' + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509' + 0xbfefa7557f08a517, 0x3fc2c8106e8e613a, // -0.98918, 0.14673' + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017' + 0xbfeff621e3796d7e, 0x3fa91f65f10dd814, // -0.9988, 0.049068' + 0xbff0000000000000, 0x0000000000000000, // -1, 0' + 0xbfeff621e3796d7e, 0xbfa91f65f10dd814, // -0.9988,-0.049068' + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518,-0.098017' + 0xbfefa7557f08a517, 0xbfc2c8106e8e613a, // -0.98918, -0.14673' + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509' + 0xbfef0a7efb9230d7, 0xbfcf19f97b215f1a, // -0.97003, -0.24298' + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028' + 0xbfee212104f686e5, 0xbfd58f9a75ab1fdd, // -0.94154, -0.33689' + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268' + 0xbfeced7af43cc773, 0xbfdb5d1009e15cc0, // -0.90399, -0.42756' + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714' + 0xbfeb728345196e3e, 0xbfe073879922ffed, // -0.85773, -0.5141' + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557' + 0xbfe9b3e047f38741, 0xbfe30ff7fce17035, // -0.80321, -0.5957' + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439' + 0xbfe7b5df226aafb0, 0xbfe57d69348cec9f, // -0.74095, -0.67156' + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711' + 0xbfe57d69348cec9f, 0xbfe7b5df226aafb0, // -0.67156, -0.74095' + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301' + 0xbfe30ff7fce17035, 0xbfe9b3e047f38741, // -0.5957, -0.80321' + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147' + 0xbfe073879922ffed, 0xbfeb728345196e3e, // -0.5141, -0.85773' + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192' + 0xbfdb5d1009e15cc0, 0xbfeced7af43cc773, // -0.42756, -0.90399' + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388' + 0xbfd58f9a75ab1fdd, 0xbfee212104f686e5, // -0.33689, -0.94154' + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694' + 0xbfcf19f97b215f1a, 0xbfef0a7efb9230d7, // -0.24298, -0.97003' + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079' + 0xbfc2c8106e8e613a, 0xbfefa7557f08a517, // -0.14673, -0.98918' + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, //-0.098017, -0.99518' + 0xbfa91f65f10dd814, 0xbfeff621e3796d7e, //-0.049068, -0.9988' + 0x0000000000000000, 0xbff0000000000000, // 0, -1' + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988' + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518' + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079' + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003' + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694' + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388' + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399' + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192' + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147' + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321' + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301' + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711' + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156' + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439' + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557' + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141' + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714' + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268' + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689' + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028' + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509' + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673' + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017' + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988,-0.049068' +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for(i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 256, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_256[512] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0xbf992155f7a3667e, 0x3feffd886084cd0d, //-0.024541, 0.9997 + 0xbfa91f65f10dd814, 0x3feff621e3796d7e, //-0.049068, 0.9988 + 0xbfb2d52092ce19f6, 0x3fefe9cdad01883a, //-0.073565, 0.99729 + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, //-0.098017, 0.99518 + 0xbfbf564e56a9730e, 0x3fefc26470e19fd3, // -0.12241, 0.99248 + 0xbfc2c8106e8e613a, 0x3fefa7557f08a517, // -0.14673, 0.98918 + 0xbfc5e214448b3fc6, 0x3fef8764fa714ba9, // -0.17096, 0.98528 + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079 + 0xbfcc0b826a7e4f63, 0x3fef38f3ac64e589, // -0.2191, 0.9757 + 0xbfcf19f97b215f1a, 0x3fef0a7efb9230d7, // -0.24298, 0.97003 + 0xbfd111d262b1f677, 0x3feed740e7684963, // -0.26671, 0.96378 + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694 + 0xbfd4135c94176602, 0x3fee6288ec48e112, // -0.31368, 0.94953 + 0xbfd58f9a75ab1fdd, 0x3fee212104f686e5, // -0.33689, 0.94154 + 0xbfd7088530fa459e, 0x3feddb13b6ccc23d, // -0.3599, 0.93299 + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388 + 0xbfd9ef7943a8ed8a, 0x3fed4134d14dc93a, // -0.40524, 0.91421 + 0xbfdb5d1009e15cc0, 0x3feced7af43cc773, // -0.42756, 0.90399 + 0xbfdcc66e9931c45d, 0x3fec954b213411f5, // -0.44961, 0.89322 + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192 + 0xbfdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // -0.4929, 0.87009 + 0xbfe073879922ffed, 0x3feb728345196e3e, // -0.5141, 0.85773 + 0xbfe11eb3541b4b22, 0x3feb090a58150200, // -0.535, 0.84485 + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147 + 0xbfe26d054cdd12df, 0x3fea29a7a0462782, // -0.57581, 0.81758 + 0xbfe30ff7fce17035, 0x3fe9b3e047f38741, // -0.5957, 0.80321 + 0xbfe3affa292050b9, 0x3fe93a22499263fc, // -0.61523, 0.78835 + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301 + 0xbfe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // -0.65317, 0.75721 + 0xbfe57d69348cec9f, 0x3fe7b5df226aafb0, // -0.67156, 0.74095 + 0xbfe610b7551d2cde, 0x3fe72d0837efff97, // -0.68954, 0.72425 + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711 + 0xbfe72d0837efff97, 0x3fe610b7551d2cde, // -0.72425, 0.68954 + 0xbfe7b5df226aafb0, 0x3fe57d69348cec9f, // -0.74095, 0.67156 + 0xbfe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // -0.75721, 0.65317 + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439 + 0xbfe93a22499263fc, 0x3fe3affa292050b9, // -0.78835, 0.61523 + 0xbfe9b3e047f38741, 0x3fe30ff7fce17035, // -0.80321, 0.5957 + 0xbfea29a7a0462782, 0x3fe26d054cdd12df, // -0.81758, 0.57581 + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557 + 0xbfeb090a58150200, 0x3fe11eb3541b4b22, // -0.84485, 0.535 + 0xbfeb728345196e3e, 0x3fe073879922ffed, // -0.85773, 0.5141 + 0xbfebd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // -0.87009, 0.4929 + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714 + 0xbfec954b213411f5, 0x3fdcc66e9931c45d, // -0.89322, 0.44961 + 0xbfeced7af43cc773, 0x3fdb5d1009e15cc0, // -0.90399, 0.42756 + 0xbfed4134d14dc93a, 0x3fd9ef7943a8ed8a, // -0.91421, 0.40524 + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268 + 0xbfeddb13b6ccc23d, 0x3fd7088530fa459e, // -0.93299, 0.3599 + 0xbfee212104f686e5, 0x3fd58f9a75ab1fdd, // -0.94154, 0.33689 + 0xbfee6288ec48e112, 0x3fd4135c94176602, // -0.94953, 0.31368 + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028 + 0xbfeed740e7684963, 0x3fd111d262b1f677, // -0.96378, 0.26671 + 0xbfef0a7efb9230d7, 0x3fcf19f97b215f1a, // -0.97003, 0.24298 + 0xbfef38f3ac64e589, 0x3fcc0b826a7e4f63, // -0.9757, 0.2191 + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509 + 0xbfef8764fa714ba9, 0x3fc5e214448b3fc6, // -0.98528, 0.17096 + 0xbfefa7557f08a517, 0x3fc2c8106e8e613a, // -0.98918, 0.14673 + 0xbfefc26470e19fd3, 0x3fbf564e56a9730e, // -0.99248, 0.12241 + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017 + 0xbfefe9cdad01883a, 0x3fb2d52092ce19f6, // -0.99729, 0.073565 + 0xbfeff621e3796d7e, 0x3fa91f65f10dd814, // -0.9988, 0.049068 + 0xbfeffd886084cd0d, 0x3f992155f7a3667e, // -0.9997, 0.024541 + 0xbff0000000000000, 0x0000000000000000, // -1, 0 + 0xbfeffd886084cd0d, 0xbf992155f7a3667e, // -0.9997,-0.024541 + 0xbfeff621e3796d7e, 0xbfa91f65f10dd814, // -0.9988,-0.049068 + 0xbfefe9cdad01883a, 0xbfb2d52092ce19f6, // -0.99729,-0.073565 + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518,-0.098017 + 0xbfefc26470e19fd3, 0xbfbf564e56a9730e, // -0.99248, -0.12241 + 0xbfefa7557f08a517, 0xbfc2c8106e8e613a, // -0.98918, -0.14673 + 0xbfef8764fa714ba9, 0xbfc5e214448b3fc6, // -0.98528, -0.17096 + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509 + 0xbfef38f3ac64e589, 0xbfcc0b826a7e4f63, // -0.9757, -0.2191 + 0xbfef0a7efb9230d7, 0xbfcf19f97b215f1a, // -0.97003, -0.24298 + 0xbfeed740e7684963, 0xbfd111d262b1f677, // -0.96378, -0.26671 + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028 + 0xbfee6288ec48e112, 0xbfd4135c94176602, // -0.94953, -0.31368 + 0xbfee212104f686e5, 0xbfd58f9a75ab1fdd, // -0.94154, -0.33689 + 0xbfeddb13b6ccc23d, 0xbfd7088530fa459e, // -0.93299, -0.3599 + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268 + 0xbfed4134d14dc93a, 0xbfd9ef7943a8ed8a, // -0.91421, -0.40524 + 0xbfeced7af43cc773, 0xbfdb5d1009e15cc0, // -0.90399, -0.42756 + 0xbfec954b213411f5, 0xbfdcc66e9931c45d, // -0.89322, -0.44961 + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714 + 0xbfebd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // -0.87009, -0.4929 + 0xbfeb728345196e3e, 0xbfe073879922ffed, // -0.85773, -0.5141 + 0xbfeb090a58150200, 0xbfe11eb3541b4b22, // -0.84485, -0.535 + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557 + 0xbfea29a7a0462782, 0xbfe26d054cdd12df, // -0.81758, -0.57581 + 0xbfe9b3e047f38741, 0xbfe30ff7fce17035, // -0.80321, -0.5957 + 0xbfe93a22499263fc, 0xbfe3affa292050b9, // -0.78835, -0.61523 + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439 + 0xbfe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // -0.75721, -0.65317 + 0xbfe7b5df226aafb0, 0xbfe57d69348cec9f, // -0.74095, -0.67156 + 0xbfe72d0837efff97, 0xbfe610b7551d2cde, // -0.72425, -0.68954 + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711 + 0xbfe610b7551d2cde, 0xbfe72d0837efff97, // -0.68954, -0.72425 + 0xbfe57d69348cec9f, 0xbfe7b5df226aafb0, // -0.67156, -0.74095 + 0xbfe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // -0.65317, -0.75721 + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301 + 0xbfe3affa292050b9, 0xbfe93a22499263fc, // -0.61523, -0.78835 + 0xbfe30ff7fce17035, 0xbfe9b3e047f38741, // -0.5957, -0.80321 + 0xbfe26d054cdd12df, 0xbfea29a7a0462782, // -0.57581, -0.81758 + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147 + 0xbfe11eb3541b4b22, 0xbfeb090a58150200, // -0.535, -0.84485 + 0xbfe073879922ffed, 0xbfeb728345196e3e, // -0.5141, -0.85773 + 0xbfdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // -0.4929, -0.87009 + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192 + 0xbfdcc66e9931c45d, 0xbfec954b213411f5, // -0.44961, -0.89322 + 0xbfdb5d1009e15cc0, 0xbfeced7af43cc773, // -0.42756, -0.90399 + 0xbfd9ef7943a8ed8a, 0xbfed4134d14dc93a, // -0.40524, -0.91421 + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388 + 0xbfd7088530fa459e, 0xbfeddb13b6ccc23d, // -0.3599, -0.93299 + 0xbfd58f9a75ab1fdd, 0xbfee212104f686e5, // -0.33689, -0.94154 + 0xbfd4135c94176602, 0xbfee6288ec48e112, // -0.31368, -0.94953 + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694 + 0xbfd111d262b1f677, 0xbfeed740e7684963, // -0.26671, -0.96378 + 0xbfcf19f97b215f1a, 0xbfef0a7efb9230d7, // -0.24298, -0.97003 + 0xbfcc0b826a7e4f63, 0xbfef38f3ac64e589, // -0.2191, -0.9757 + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079 + 0xbfc5e214448b3fc6, 0xbfef8764fa714ba9, // -0.17096, -0.98528 + 0xbfc2c8106e8e613a, 0xbfefa7557f08a517, // -0.14673, -0.98918 + 0xbfbf564e56a9730e, 0xbfefc26470e19fd3, // -0.12241, -0.99248 + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, //-0.098017, -0.99518 + 0xbfb2d52092ce19f6, 0xbfefe9cdad01883a, //-0.073565, -0.99729 + 0xbfa91f65f10dd814, 0xbfeff621e3796d7e, //-0.049068, -0.9988 + 0xbf992155f7a3667e, 0xbfeffd886084cd0d, //-0.024541, -0.9997 + 0x0000000000000000, 0xbff0000000000000, // 0, -1 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729,-0.073565 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988,-0.049068 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997,-0.024541 +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 512, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_512[1024] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992 + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0xbf8921d1fcdec784, 0x3fefff62169b92db, //-0.012272, 0.99992 + 0xbf992155f7a3667e, 0x3feffd886084cd0d, //-0.024541, 0.9997 + 0xbfa2d865759455cd, 0x3feffa72effef75d, //-0.036807, 0.99932 + 0xbfa91f65f10dd814, 0x3feff621e3796d7e, //-0.049068, 0.9988 + 0xbfaf656e79f820e0, 0x3feff095658e71ad, //-0.061321, 0.99812 + 0xbfb2d52092ce19f6, 0x3fefe9cdad01883a, //-0.073565, 0.99729 + 0xbfb5f6d00a9aa419, 0x3fefe1cafcbd5b09, //-0.085797, 0.99631 + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, //-0.098017, 0.99518 + 0xbfbc3785c79ec2d5, 0x3fefce15fd6da67b, // -0.11022, 0.99391 + 0xbfbf564e56a9730e, 0x3fefc26470e19fd3, // -0.12241, 0.99248 + 0xbfc139f0cedaf576, 0x3fefb5797195d741, // -0.13458, 0.9909 + 0xbfc2c8106e8e613a, 0x3fefa7557f08a517, // -0.14673, 0.98918 + 0xbfc45576b1293e5a, 0x3fef97f924c9099b, // -0.15886, 0.9873 + 0xbfc5e214448b3fc6, 0x3fef8764fa714ba9, // -0.17096, 0.98528 + 0xbfc76dd9de50bf31, 0x3fef7599a3a12077, // -0.18304, 0.98311 + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079 + 0xbfca82a025b00451, 0x3fef4e603b0b2f2d, // -0.20711, 0.97832 + 0xbfcc0b826a7e4f63, 0x3fef38f3ac64e589, // -0.2191, 0.9757 + 0xbfcd934fe5454311, 0x3fef2252f7763ada, // -0.23106, 0.97294 + 0xbfcf19f97b215f1a, 0x3fef0a7efb9230d7, // -0.24298, 0.97003 + 0xbfd04fb80e37fdae, 0x3feef178a3e473c2, // -0.25487, 0.96698 + 0xbfd111d262b1f677, 0x3feed740e7684963, // -0.26671, 0.96378 + 0xbfd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // -0.27852, 0.96043 + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694 + 0xbfd35410c2e18152, 0x3fee817bab4cd10d, // -0.30201, 0.95331 + 0xbfd4135c94176602, 0x3fee6288ec48e112, // -0.31368, 0.94953 + 0xbfd4d1e24278e76a, 0x3fee426a4b2bc17e, // -0.32531, 0.94561 + 0xbfd58f9a75ab1fdd, 0x3fee212104f686e5, // -0.33689, 0.94154 + 0xbfd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // -0.34842, 0.93734 + 0xbfd7088530fa459e, 0x3feddb13b6ccc23d, // -0.3599, 0.93299 + 0xbfd7c3a9311dcce7, 0x3fedb6526238a09b, // -0.37132, 0.92851 + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388 + 0xbfd9372a63bc93d7, 0x3fed696173c9e68b, // -0.39399, 0.91911 + 0xbfd9ef7943a8ed8a, 0x3fed4134d14dc93a, // -0.40524, 0.91421 + 0xbfdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // -0.41643, 0.90917 + 0xbfdb5d1009e15cc0, 0x3feced7af43cc773, // -0.42756, 0.90399 + 0xbfdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // -0.43862, 0.89867 + 0xbfdcc66e9931c45d, 0x3fec954b213411f5, // -0.44961, 0.89322 + 0xbfdd79775b86e389, 0x3fec678b3488739b, // -0.46054, 0.88764 + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192 + 0xbfdedc1952ef78d5, 0x3fec08c426725549, // -0.48218, 0.87607 + 0xbfdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // -0.4929, 0.87009 + 0xbfe01cfc874c3eb7, 0x3feba5aa673590d2, // -0.50354, 0.86397 + 0xbfe073879922ffed, 0x3feb728345196e3e, // -0.5141, 0.85773 + 0xbfe0c9704d5d898f, 0x3feb3e4d3ef55712, // -0.52459, 0.85136 + 0xbfe11eb3541b4b22, 0x3feb090a58150200, // -0.535, 0.84485 + 0xbfe1734d63dedb49, 0x3fead2bc9e21d511, // -0.54532, 0.83822 + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147 + 0xbfe21a799933eb58, 0x3fea63091b02fae2, // -0.56573, 0.82459 + 0xbfe26d054cdd12df, 0x3fea29a7a0462782, // -0.57581, 0.81758 + 0xbfe2bedb25faf3ea, 0x3fe9ef43ef29af94, // -0.5858, 0.81046 + 0xbfe30ff7fce17035, 0x3fe9b3e047f38741, // -0.5957, 0.80321 + 0xbfe36058b10659f3, 0x3fe9777ef4c7d742, // -0.60551, 0.79584 + 0xbfe3affa292050b9, 0x3fe93a22499263fc, // -0.61523, 0.78835 + 0xbfe3fed9534556d4, 0x3fe8fbcca3ef940d, // -0.62486, 0.78074 + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301 + 0xbfe49a449b9b0938, 0x3fe87c400fba2ebf, // -0.64383, 0.76517 + 0xbfe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // -0.65317, 0.75721 + 0xbfe5328292a35596, 0x3fe7f8ece3571771, // -0.66242, 0.74914 + 0xbfe57d69348cec9f, 0x3fe7b5df226aafb0, // -0.67156, 0.74095 + 0xbfe5c77bbe65018c, 0x3fe771e75f037261, // -0.6806, 0.73265 + 0xbfe610b7551d2cde, 0x3fe72d0837efff97, // -0.68954, 0.72425 + 0xbfe6591925f0783e, 0x3fe6e74454eaa8ae, // -0.69838, 0.71573 + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711 + 0xbfe6e74454eaa8ae, 0x3fe6591925f0783e, // -0.71573, 0.69838 + 0xbfe72d0837efff97, 0x3fe610b7551d2cde, // -0.72425, 0.68954 + 0xbfe771e75f037261, 0x3fe5c77bbe65018c, // -0.73265, 0.6806 + 0xbfe7b5df226aafb0, 0x3fe57d69348cec9f, // -0.74095, 0.67156 + 0xbfe7f8ece3571771, 0x3fe5328292a35596, // -0.74914, 0.66242 + 0xbfe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // -0.75721, 0.65317 + 0xbfe87c400fba2ebf, 0x3fe49a449b9b0938, // -0.76517, 0.64383 + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439 + 0xbfe8fbcca3ef940d, 0x3fe3fed9534556d4, // -0.78074, 0.62486 + 0xbfe93a22499263fc, 0x3fe3affa292050b9, // -0.78835, 0.61523 + 0xbfe9777ef4c7d742, 0x3fe36058b10659f3, // -0.79584, 0.60551 + 0xbfe9b3e047f38741, 0x3fe30ff7fce17035, // -0.80321, 0.5957 + 0xbfe9ef43ef29af94, 0x3fe2bedb25faf3ea, // -0.81046, 0.5858 + 0xbfea29a7a0462782, 0x3fe26d054cdd12df, // -0.81758, 0.57581 + 0xbfea63091b02fae2, 0x3fe21a799933eb58, // -0.82459, 0.56573 + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557 + 0xbfead2bc9e21d511, 0x3fe1734d63dedb49, // -0.83822, 0.54532 + 0xbfeb090a58150200, 0x3fe11eb3541b4b22, // -0.84485, 0.535 + 0xbfeb3e4d3ef55712, 0x3fe0c9704d5d898f, // -0.85136, 0.52459 + 0xbfeb728345196e3e, 0x3fe073879922ffed, // -0.85773, 0.5141 + 0xbfeba5aa673590d2, 0x3fe01cfc874c3eb7, // -0.86397, 0.50354 + 0xbfebd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // -0.87009, 0.4929 + 0xbfec08c426725549, 0x3fdedc1952ef78d5, // -0.87607, 0.48218 + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714 + 0xbfec678b3488739b, 0x3fdd79775b86e389, // -0.88764, 0.46054 + 0xbfec954b213411f5, 0x3fdcc66e9931c45d, // -0.89322, 0.44961 + 0xbfecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // -0.89867, 0.43862 + 0xbfeced7af43cc773, 0x3fdb5d1009e15cc0, // -0.90399, 0.42756 + 0xbfed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // -0.90917, 0.41643 + 0xbfed4134d14dc93a, 0x3fd9ef7943a8ed8a, // -0.91421, 0.40524 + 0xbfed696173c9e68b, 0x3fd9372a63bc93d7, // -0.91911, 0.39399 + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268 + 0xbfedb6526238a09b, 0x3fd7c3a9311dcce7, // -0.92851, 0.37132 + 0xbfeddb13b6ccc23d, 0x3fd7088530fa459e, // -0.93299, 0.3599 + 0xbfedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // -0.93734, 0.34842 + 0xbfee212104f686e5, 0x3fd58f9a75ab1fdd, // -0.94154, 0.33689 + 0xbfee426a4b2bc17e, 0x3fd4d1e24278e76a, // -0.94561, 0.32531 + 0xbfee6288ec48e112, 0x3fd4135c94176602, // -0.94953, 0.31368 + 0xbfee817bab4cd10d, 0x3fd35410c2e18152, // -0.95331, 0.30201 + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028 + 0xbfeebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // -0.96043, 0.27852 + 0xbfeed740e7684963, 0x3fd111d262b1f677, // -0.96378, 0.26671 + 0xbfeef178a3e473c2, 0x3fd04fb80e37fdae, // -0.96698, 0.25487 + 0xbfef0a7efb9230d7, 0x3fcf19f97b215f1a, // -0.97003, 0.24298 + 0xbfef2252f7763ada, 0x3fcd934fe5454311, // -0.97294, 0.23106 + 0xbfef38f3ac64e589, 0x3fcc0b826a7e4f63, // -0.9757, 0.2191 + 0xbfef4e603b0b2f2d, 0x3fca82a025b00451, // -0.97832, 0.20711 + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509 + 0xbfef7599a3a12077, 0x3fc76dd9de50bf31, // -0.98311, 0.18304 + 0xbfef8764fa714ba9, 0x3fc5e214448b3fc6, // -0.98528, 0.17096 + 0xbfef97f924c9099b, 0x3fc45576b1293e5a, // -0.9873, 0.15886 + 0xbfefa7557f08a517, 0x3fc2c8106e8e613a, // -0.98918, 0.14673 + 0xbfefb5797195d741, 0x3fc139f0cedaf576, // -0.9909, 0.13458 + 0xbfefc26470e19fd3, 0x3fbf564e56a9730e, // -0.99248, 0.12241 + 0xbfefce15fd6da67b, 0x3fbc3785c79ec2d5, // -0.99391, 0.11022 + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017 + 0xbfefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // -0.99631, 0.085797 + 0xbfefe9cdad01883a, 0x3fb2d52092ce19f6, // -0.99729, 0.073565 + 0xbfeff095658e71ad, 0x3faf656e79f820e0, // -0.99812, 0.061321 + 0xbfeff621e3796d7e, 0x3fa91f65f10dd814, // -0.9988, 0.049068 + 0xbfeffa72effef75d, 0x3fa2d865759455cd, // -0.99932, 0.036807 + 0xbfeffd886084cd0d, 0x3f992155f7a3667e, // -0.9997, 0.024541 + 0xbfefff62169b92db, 0x3f8921d1fcdec784, // -0.99992, 0.012272 + 0xbff0000000000000, 0x0000000000000000, // -1, 0 + 0xbfefff62169b92db, 0xbf8921d1fcdec784, // -0.99992,-0.012272 + 0xbfeffd886084cd0d, 0xbf992155f7a3667e, // -0.9997,-0.024541 + 0xbfeffa72effef75d, 0xbfa2d865759455cd, // -0.99932,-0.036807 + 0xbfeff621e3796d7e, 0xbfa91f65f10dd814, // -0.9988,-0.049068 + 0xbfeff095658e71ad, 0xbfaf656e79f820e0, // -0.99812,-0.061321 + 0xbfefe9cdad01883a, 0xbfb2d52092ce19f6, // -0.99729,-0.073565 + 0xbfefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // -0.99631,-0.085797 + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518,-0.098017 + 0xbfefce15fd6da67b, 0xbfbc3785c79ec2d5, // -0.99391, -0.11022 + 0xbfefc26470e19fd3, 0xbfbf564e56a9730e, // -0.99248, -0.12241 + 0xbfefb5797195d741, 0xbfc139f0cedaf576, // -0.9909, -0.13458 + 0xbfefa7557f08a517, 0xbfc2c8106e8e613a, // -0.98918, -0.14673 + 0xbfef97f924c9099b, 0xbfc45576b1293e5a, // -0.9873, -0.15886 + 0xbfef8764fa714ba9, 0xbfc5e214448b3fc6, // -0.98528, -0.17096 + 0xbfef7599a3a12077, 0xbfc76dd9de50bf31, // -0.98311, -0.18304 + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509 + 0xbfef4e603b0b2f2d, 0xbfca82a025b00451, // -0.97832, -0.20711 + 0xbfef38f3ac64e589, 0xbfcc0b826a7e4f63, // -0.9757, -0.2191 + 0xbfef2252f7763ada, 0xbfcd934fe5454311, // -0.97294, -0.23106 + 0xbfef0a7efb9230d7, 0xbfcf19f97b215f1a, // -0.97003, -0.24298 + 0xbfeef178a3e473c2, 0xbfd04fb80e37fdae, // -0.96698, -0.25487 + 0xbfeed740e7684963, 0xbfd111d262b1f677, // -0.96378, -0.26671 + 0xbfeebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // -0.96043, -0.27852 + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028 + 0xbfee817bab4cd10d, 0xbfd35410c2e18152, // -0.95331, -0.30201 + 0xbfee6288ec48e112, 0xbfd4135c94176602, // -0.94953, -0.31368 + 0xbfee426a4b2bc17e, 0xbfd4d1e24278e76a, // -0.94561, -0.32531 + 0xbfee212104f686e5, 0xbfd58f9a75ab1fdd, // -0.94154, -0.33689 + 0xbfedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // -0.93734, -0.34842 + 0xbfeddb13b6ccc23d, 0xbfd7088530fa459e, // -0.93299, -0.3599 + 0xbfedb6526238a09b, 0xbfd7c3a9311dcce7, // -0.92851, -0.37132 + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268 + 0xbfed696173c9e68b, 0xbfd9372a63bc93d7, // -0.91911, -0.39399 + 0xbfed4134d14dc93a, 0xbfd9ef7943a8ed8a, // -0.91421, -0.40524 + 0xbfed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // -0.90917, -0.41643 + 0xbfeced7af43cc773, 0xbfdb5d1009e15cc0, // -0.90399, -0.42756 + 0xbfecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // -0.89867, -0.43862 + 0xbfec954b213411f5, 0xbfdcc66e9931c45d, // -0.89322, -0.44961 + 0xbfec678b3488739b, 0xbfdd79775b86e389, // -0.88764, -0.46054 + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714 + 0xbfec08c426725549, 0xbfdedc1952ef78d5, // -0.87607, -0.48218 + 0xbfebd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // -0.87009, -0.4929 + 0xbfeba5aa673590d2, 0xbfe01cfc874c3eb7, // -0.86397, -0.50354 + 0xbfeb728345196e3e, 0xbfe073879922ffed, // -0.85773, -0.5141 + 0xbfeb3e4d3ef55712, 0xbfe0c9704d5d898f, // -0.85136, -0.52459 + 0xbfeb090a58150200, 0xbfe11eb3541b4b22, // -0.84485, -0.535 + 0xbfead2bc9e21d511, 0xbfe1734d63dedb49, // -0.83822, -0.54532 + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557 + 0xbfea63091b02fae2, 0xbfe21a799933eb58, // -0.82459, -0.56573 + 0xbfea29a7a0462782, 0xbfe26d054cdd12df, // -0.81758, -0.57581 + 0xbfe9ef43ef29af94, 0xbfe2bedb25faf3ea, // -0.81046, -0.5858 + 0xbfe9b3e047f38741, 0xbfe30ff7fce17035, // -0.80321, -0.5957 + 0xbfe9777ef4c7d742, 0xbfe36058b10659f3, // -0.79584, -0.60551 + 0xbfe93a22499263fc, 0xbfe3affa292050b9, // -0.78835, -0.61523 + 0xbfe8fbcca3ef940d, 0xbfe3fed9534556d4, // -0.78074, -0.62486 + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439 + 0xbfe87c400fba2ebf, 0xbfe49a449b9b0938, // -0.76517, -0.64383 + 0xbfe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // -0.75721, -0.65317 + 0xbfe7f8ece3571771, 0xbfe5328292a35596, // -0.74914, -0.66242 + 0xbfe7b5df226aafb0, 0xbfe57d69348cec9f, // -0.74095, -0.67156 + 0xbfe771e75f037261, 0xbfe5c77bbe65018c, // -0.73265, -0.6806 + 0xbfe72d0837efff97, 0xbfe610b7551d2cde, // -0.72425, -0.68954 + 0xbfe6e74454eaa8ae, 0xbfe6591925f0783e, // -0.71573, -0.69838 + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711 + 0xbfe6591925f0783e, 0xbfe6e74454eaa8ae, // -0.69838, -0.71573 + 0xbfe610b7551d2cde, 0xbfe72d0837efff97, // -0.68954, -0.72425 + 0xbfe5c77bbe65018c, 0xbfe771e75f037261, // -0.6806, -0.73265 + 0xbfe57d69348cec9f, 0xbfe7b5df226aafb0, // -0.67156, -0.74095 + 0xbfe5328292a35596, 0xbfe7f8ece3571771, // -0.66242, -0.74914 + 0xbfe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // -0.65317, -0.75721 + 0xbfe49a449b9b0938, 0xbfe87c400fba2ebf, // -0.64383, -0.76517 + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301 + 0xbfe3fed9534556d4, 0xbfe8fbcca3ef940d, // -0.62486, -0.78074 + 0xbfe3affa292050b9, 0xbfe93a22499263fc, // -0.61523, -0.78835 + 0xbfe36058b10659f3, 0xbfe9777ef4c7d742, // -0.60551, -0.79584 + 0xbfe30ff7fce17035, 0xbfe9b3e047f38741, // -0.5957, -0.80321 + 0xbfe2bedb25faf3ea, 0xbfe9ef43ef29af94, // -0.5858, -0.81046 + 0xbfe26d054cdd12df, 0xbfea29a7a0462782, // -0.57581, -0.81758 + 0xbfe21a799933eb58, 0xbfea63091b02fae2, // -0.56573, -0.82459 + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147 + 0xbfe1734d63dedb49, 0xbfead2bc9e21d511, // -0.54532, -0.83822 + 0xbfe11eb3541b4b22, 0xbfeb090a58150200, // -0.535, -0.84485 + 0xbfe0c9704d5d898f, 0xbfeb3e4d3ef55712, // -0.52459, -0.85136 + 0xbfe073879922ffed, 0xbfeb728345196e3e, // -0.5141, -0.85773 + 0xbfe01cfc874c3eb7, 0xbfeba5aa673590d2, // -0.50354, -0.86397 + 0xbfdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // -0.4929, -0.87009 + 0xbfdedc1952ef78d5, 0xbfec08c426725549, // -0.48218, -0.87607 + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192 + 0xbfdd79775b86e389, 0xbfec678b3488739b, // -0.46054, -0.88764 + 0xbfdcc66e9931c45d, 0xbfec954b213411f5, // -0.44961, -0.89322 + 0xbfdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // -0.43862, -0.89867 + 0xbfdb5d1009e15cc0, 0xbfeced7af43cc773, // -0.42756, -0.90399 + 0xbfdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // -0.41643, -0.90917 + 0xbfd9ef7943a8ed8a, 0xbfed4134d14dc93a, // -0.40524, -0.91421 + 0xbfd9372a63bc93d7, 0xbfed696173c9e68b, // -0.39399, -0.91911 + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388 + 0xbfd7c3a9311dcce7, 0xbfedb6526238a09b, // -0.37132, -0.92851 + 0xbfd7088530fa459e, 0xbfeddb13b6ccc23d, // -0.3599, -0.93299 + 0xbfd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // -0.34842, -0.93734 + 0xbfd58f9a75ab1fdd, 0xbfee212104f686e5, // -0.33689, -0.94154 + 0xbfd4d1e24278e76a, 0xbfee426a4b2bc17e, // -0.32531, -0.94561 + 0xbfd4135c94176602, 0xbfee6288ec48e112, // -0.31368, -0.94953 + 0xbfd35410c2e18152, 0xbfee817bab4cd10d, // -0.30201, -0.95331 + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694 + 0xbfd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // -0.27852, -0.96043 + 0xbfd111d262b1f677, 0xbfeed740e7684963, // -0.26671, -0.96378 + 0xbfd04fb80e37fdae, 0xbfeef178a3e473c2, // -0.25487, -0.96698 + 0xbfcf19f97b215f1a, 0xbfef0a7efb9230d7, // -0.24298, -0.97003 + 0xbfcd934fe5454311, 0xbfef2252f7763ada, // -0.23106, -0.97294 + 0xbfcc0b826a7e4f63, 0xbfef38f3ac64e589, // -0.2191, -0.9757 + 0xbfca82a025b00451, 0xbfef4e603b0b2f2d, // -0.20711, -0.97832 + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079 + 0xbfc76dd9de50bf31, 0xbfef7599a3a12077, // -0.18304, -0.98311 + 0xbfc5e214448b3fc6, 0xbfef8764fa714ba9, // -0.17096, -0.98528 + 0xbfc45576b1293e5a, 0xbfef97f924c9099b, // -0.15886, -0.9873 + 0xbfc2c8106e8e613a, 0xbfefa7557f08a517, // -0.14673, -0.98918 + 0xbfc139f0cedaf576, 0xbfefb5797195d741, // -0.13458, -0.9909 + 0xbfbf564e56a9730e, 0xbfefc26470e19fd3, // -0.12241, -0.99248 + 0xbfbc3785c79ec2d5, 0xbfefce15fd6da67b, // -0.11022, -0.99391 + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, //-0.098017, -0.99518 + 0xbfb5f6d00a9aa419, 0xbfefe1cafcbd5b09, //-0.085797, -0.99631 + 0xbfb2d52092ce19f6, 0xbfefe9cdad01883a, //-0.073565, -0.99729 + 0xbfaf656e79f820e0, 0xbfeff095658e71ad, //-0.061321, -0.99812 + 0xbfa91f65f10dd814, 0xbfeff621e3796d7e, //-0.049068, -0.9988 + 0xbfa2d865759455cd, 0xbfeffa72effef75d, //-0.036807, -0.99932 + 0xbf992155f7a3667e, 0xbfeffd886084cd0d, //-0.024541, -0.9997 + 0xbf8921d1fcdec784, 0xbfefff62169b92db, //-0.012272, -0.99992 + 0x0000000000000000, 0xbff0000000000000, // 0, -1 + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017 + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631,-0.085797 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729,-0.073565 + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812,-0.061321 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988,-0.049068 + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932,-0.036807 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997,-0.024541 + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992,-0.012272 +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 1024, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_1024[2048] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3fefffd8858e8a92, 0x3f7921f0fe670071, // 0.99998, 0.0061359 + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272 + 0x3feffe9cb44b51a1, 0x3f92d936bbe30efd, // 0.99983, 0.018407 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feffc251df1d3f8, 0x3f9f693731d1cf01, // 0.99953, 0.030675 + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807 + 0x3feff871dadb81df, 0x3fa5fc00d290cd43, // 0.99908, 0.042938 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feff3830f8d575c, 0x3fac428d12c0d7e3, // 0.99848, 0.055195 + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321 + 0x3fefed58ecb673c4, 0x3fb1440134d709b2, // 0.99772, 0.067444 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefe5f3af2e3940, 0x3fb4661179272096, // 0.99682, 0.079682 + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797 + 0x3fefdd539ff1f456, 0x3fb787586a5d5b21, // 0.99577, 0.091909 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefd37914220b84, 0x3fbaa7b724495c04, // 0.99456, 0.10412 + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022 + 0x3fefc8646cfeb721, 0x3fbdc70ecbae9fc8, // 0.99321, 0.11632 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefbc1617e44186, 0x3fc072a047ba831d, // 0.99171, 0.1285 + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458 + 0x3fefae8e8e46cfbb, 0x3fc20116d4ec7bce, // 0.99006, 0.14066 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fef9fce55adb2c8, 0x3fc38edbb0cd8d14, // 0.98826, 0.1528 + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886 + 0x3fef8fd5ffae41db, 0x3fc51bdf8597c5f2, // 0.98631, 0.16491 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef7ea629e63d6e, 0x3fc6a81304f64ab2, // 0.98421, 0.177 + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304 + 0x3fef6c3f7df5bbb7, 0x3fc83366e89c64c5, // 0.98196, 0.18907 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef58a2b1789e84, 0x3fc9bdcbf2dc4366, // 0.97957, 0.2011 + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711 + 0x3fef43d085ff92dd, 0x3fcb4732ef3d6722, // 0.97703, 0.21311 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef2dc9c9089a9d, 0x3fcccf8cb312b286, // 0.97434, 0.22508 + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106 + 0x3fef168f53f7205d, 0x3fce56ca1e101a1b, // 0.9715, 0.23702 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3feefe220c0b95ec, 0x3fcfdcdc1adfedf8, // 0.96852, 0.24893 + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487 + 0x3feee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // 0.96539, 0.26079 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3feec9b2d3c3bf84, 0x3fd172a0d7765177, // 0.96212, 0.27262 + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852 + 0x3feeadb2e8e7a88e, 0x3fd233bbabc3bb72, // 0.9587, 0.28441 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3fee9084361df7f3, 0x3fd2f422daec0386, // 0.95514, 0.29615 + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201 + 0x3fee7227db6a9744, 0x3fd3b3cefa0414b7, // 0.95144, 0.30785 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee529f04729ffc, 0x3fd472b8a5571054, // 0.94759, 0.3195 + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531 + 0x3fee31eae870ce25, 0x3fd530d880af3c24, // 0.94359, 0.33111 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fee100cca2980ac, 0x3fd5ee27379ea693, // 0.93946, 0.34266 + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842 + 0x3feded05f7de47da, 0x3fd6aa9d7dc77e16, // 0.93518, 0.35416 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fedc8d7cb410260, 0x3fd766340f2418f6, // 0.93077, 0.36561 + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132 + 0x3feda383a9668988, 0x3fd820e3b04eaac4, // 0.92621, 0.37701 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // 0.92151, 0.38835 + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399 + 0x3fed556f52e93eb1, 0x3fd993716141bdfe, // 0.91668, 0.39962 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed2cb220e0ef9f, 0x3fda4b4127dea1e4, // 0.91171, 0.41084 + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643 + 0x3fed02d4feb2bd92, 0x3fdb020d6c7f4009, // 0.9066, 0.422 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fecd7d9898b32f6, 0x3fdbb7cf2304bd01, // 0.90135, 0.43309 + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862 + 0x3fecabc169a0b901, 0x3fdc6c7f4997000a, // 0.89597, 0.44412 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3fec7e8e52233cf3, 0x3fdd2016e8e9db5b, // 0.89045, 0.45508 + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054 + 0x3fec5042012b6907, 0x3fddd28f1481cc58, // 0.8848, 0.46598 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec20de3fa971b0, 0x3fde83e0eaf85113, // 0.87901, 0.4768 + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218 + 0x3febf064e15377dd, 0x3fdf3405963fd068, // 0.87309, 0.48755 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3febbed7c49380ea, 0x3fdfe2f64be7120f, // 0.86705, 0.49823 + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354 + 0x3feb8c38d27504e9, 0x3fe0485626ae221a, // 0.86087, 0.50883 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb5889fe921405, 0x3fe09e907417c5e1, // 0.85456, 0.51936 + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459 + 0x3feb23cd470013b4, 0x3fe0f426bb2a8e7d, // 0.84812, 0.5298 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3feaee04b43c1474, 0x3fe14915af336ceb, // 0.84155, 0.54017 + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532 + 0x3feab7325916c0d4, 0x3fe19d5a09f2b9b8, // 0.83486, 0.55046 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3fea7f58529fe69d, 0x3fe1f0f08bbc861b, // 0.82805, 0.56066 + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573 + 0x3fea4678c8119ac8, 0x3fe243d5fb98ac1f, // 0.8211, 0.57078 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fea0c95eabaf937, 0x3fe2960727629ca8, // 0.81404, 0.58081 + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858 + 0x3fe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // 0.80685, 0.59076 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe995cf2ed80d22, 0x3fe338400d0c8e57, // 0.79954, 0.60062 + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551 + 0x3fe958efe48e6dd7, 0x3fe3884185dfeb22, // 0.79211, 0.61038 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe91b166fd49da2, 0x3fe3d78238c58343, // 0.78456, 0.62006 + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486 + 0x3fe8dc45331698cc, 0x3fe425ff178e6bb1, // 0.77689, 0.62964 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe89c7e9a4dd4ab, 0x3fe473b51b987347, // 0.7691, 0.63912 + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383 + 0x3fe85bc51ae958cc, 0x3fe4c0a145ec0004, // 0.7612, 0.64851 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe81a1b33b57acc, 0x3fe50cc09f59a09b, // 0.75319, 0.65781 + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242 + 0x3fe7d7836cc33db2, 0x3fe5581038975137, // 0.74506, 0.667 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe79400574f55e4, 0x3fe5a28d2a5d7250, // 0.73682, 0.67609 + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806 + 0x3fe74f948da8d28d, 0x3fe5ec3495837074, // 0.72846, 0.68508 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe70a42b3176d7a, 0x3fe63503a31c1be8, // 0.72, 0.69397 + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838 + 0x3fe6c40d73c18275, 0x3fe67cf78491af10, // 0.71143, 0.70275 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe67cf78491af10, 0x3fe6c40d73c18275, // 0.70275, 0.71143 + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573 + 0x3fe63503a31c1be8, 0x3fe70a42b3176d7a, // 0.69397, 0.72 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe5ec3495837074, 0x3fe74f948da8d28d, // 0.68508, 0.72846 + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265 + 0x3fe5a28d2a5d7250, 0x3fe79400574f55e4, // 0.67609, 0.73682 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe5581038975137, 0x3fe7d7836cc33db2, // 0.667, 0.74506 + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914 + 0x3fe50cc09f59a09b, 0x3fe81a1b33b57acc, // 0.65781, 0.75319 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe4c0a145ec0004, 0x3fe85bc51ae958cc, // 0.64851, 0.7612 + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517 + 0x3fe473b51b987347, 0x3fe89c7e9a4dd4ab, // 0.63912, 0.7691 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe425ff178e6bb1, 0x3fe8dc45331698cc, // 0.62964, 0.77689 + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074 + 0x3fe3d78238c58343, 0x3fe91b166fd49da2, // 0.62006, 0.78456 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe3884185dfeb22, 0x3fe958efe48e6dd7, // 0.61038, 0.79211 + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584 + 0x3fe338400d0c8e57, 0x3fe995cf2ed80d22, // 0.60062, 0.79954 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // 0.59076, 0.80685 + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046 + 0x3fe2960727629ca8, 0x3fea0c95eabaf937, // 0.58081, 0.81404 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe243d5fb98ac1f, 0x3fea4678c8119ac8, // 0.57078, 0.8211 + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459 + 0x3fe1f0f08bbc861b, 0x3fea7f58529fe69d, // 0.56066, 0.82805 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe19d5a09f2b9b8, 0x3feab7325916c0d4, // 0.55046, 0.83486 + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822 + 0x3fe14915af336ceb, 0x3feaee04b43c1474, // 0.54017, 0.84155 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe0f426bb2a8e7d, 0x3feb23cd470013b4, // 0.5298, 0.84812 + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136 + 0x3fe09e907417c5e1, 0x3feb5889fe921405, // 0.51936, 0.85456 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe0485626ae221a, 0x3feb8c38d27504e9, // 0.50883, 0.86087 + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397 + 0x3fdfe2f64be7120f, 0x3febbed7c49380ea, // 0.49823, 0.86705 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fdf3405963fd068, 0x3febf064e15377dd, // 0.48755, 0.87309 + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607 + 0x3fde83e0eaf85113, 0x3fec20de3fa971b0, // 0.4768, 0.87901 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fddd28f1481cc58, 0x3fec5042012b6907, // 0.46598, 0.8848 + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764 + 0x3fdd2016e8e9db5b, 0x3fec7e8e52233cf3, // 0.45508, 0.89045 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdc6c7f4997000a, 0x3fecabc169a0b901, // 0.44412, 0.89597 + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867 + 0x3fdbb7cf2304bd01, 0x3fecd7d9898b32f6, // 0.43309, 0.90135 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdb020d6c7f4009, 0x3fed02d4feb2bd92, // 0.422, 0.9066 + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917 + 0x3fda4b4127dea1e4, 0x3fed2cb220e0ef9f, // 0.41084, 0.91171 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fd993716141bdfe, 0x3fed556f52e93eb1, // 0.39962, 0.91668 + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911 + 0x3fd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // 0.38835, 0.92151 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd820e3b04eaac4, 0x3feda383a9668988, // 0.37701, 0.92621 + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851 + 0x3fd766340f2418f6, 0x3fedc8d7cb410260, // 0.36561, 0.93077 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd6aa9d7dc77e16, 0x3feded05f7de47da, // 0.35416, 0.93518 + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734 + 0x3fd5ee27379ea693, 0x3fee100cca2980ac, // 0.34266, 0.93946 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd530d880af3c24, 0x3fee31eae870ce25, // 0.33111, 0.94359 + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561 + 0x3fd472b8a5571054, 0x3fee529f04729ffc, // 0.3195, 0.94759 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd3b3cefa0414b7, 0x3fee7227db6a9744, // 0.30785, 0.95144 + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331 + 0x3fd2f422daec0386, 0x3fee9084361df7f3, // 0.29615, 0.95514 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd233bbabc3bb72, 0x3feeadb2e8e7a88e, // 0.28441, 0.9587 + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043 + 0x3fd172a0d7765177, 0x3feec9b2d3c3bf84, // 0.27262, 0.96212 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // 0.26079, 0.96539 + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698 + 0x3fcfdcdc1adfedf8, 0x3feefe220c0b95ec, // 0.24893, 0.96852 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fce56ca1e101a1b, 0x3fef168f53f7205d, // 0.23702, 0.9715 + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294 + 0x3fcccf8cb312b286, 0x3fef2dc9c9089a9d, // 0.22508, 0.97434 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fcb4732ef3d6722, 0x3fef43d085ff92dd, // 0.21311, 0.97703 + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832 + 0x3fc9bdcbf2dc4366, 0x3fef58a2b1789e84, // 0.2011, 0.97957 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc83366e89c64c5, 0x3fef6c3f7df5bbb7, // 0.18907, 0.98196 + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311 + 0x3fc6a81304f64ab2, 0x3fef7ea629e63d6e, // 0.177, 0.98421 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc51bdf8597c5f2, 0x3fef8fd5ffae41db, // 0.16491, 0.98631 + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873 + 0x3fc38edbb0cd8d14, 0x3fef9fce55adb2c8, // 0.1528, 0.98826 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc20116d4ec7bce, 0x3fefae8e8e46cfbb, // 0.14066, 0.99006 + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909 + 0x3fc072a047ba831d, 0x3fefbc1617e44186, // 0.1285, 0.99171 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fbdc70ecbae9fc8, 0x3fefc8646cfeb721, // 0.11632, 0.99321 + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391 + 0x3fbaa7b724495c04, 0x3fefd37914220b84, // 0.10412, 0.99456 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb787586a5d5b21, 0x3fefdd539ff1f456, // 0.091909, 0.99577 + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631 + 0x3fb4661179272096, 0x3fefe5f3af2e3940, // 0.079682, 0.99682 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3fb1440134d709b2, 0x3fefed58ecb673c4, // 0.067444, 0.99772 + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812 + 0x3fac428d12c0d7e3, 0x3feff3830f8d575c, // 0.055195, 0.99848 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3fa5fc00d290cd43, 0x3feff871dadb81df, // 0.042938, 0.99908 + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932 + 0x3f9f693731d1cf01, 0x3feffc251df1d3f8, // 0.030675, 0.99953 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x3f92d936bbe30efd, 0x3feffe9cb44b51a1, // 0.018407, 0.99983 + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992 + 0x3f7921f0fe670071, 0x3fefffd8858e8a92, // 0.0061359, 0.99998 + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0xbf7921f0fe670071, 0x3fefffd8858e8a92, //-0.0061359, 0.99998 + 0xbf8921d1fcdec784, 0x3fefff62169b92db, // -0.012272, 0.99992 + 0xbf92d936bbe30efd, 0x3feffe9cb44b51a1, // -0.018407, 0.99983 + 0xbf992155f7a3667e, 0x3feffd886084cd0d, // -0.024541, 0.9997 + 0xbf9f693731d1cf01, 0x3feffc251df1d3f8, // -0.030675, 0.99953 + 0xbfa2d865759455cd, 0x3feffa72effef75d, // -0.036807, 0.99932 + 0xbfa5fc00d290cd43, 0x3feff871dadb81df, // -0.042938, 0.99908 + 0xbfa91f65f10dd814, 0x3feff621e3796d7e, // -0.049068, 0.9988 + 0xbfac428d12c0d7e3, 0x3feff3830f8d575c, // -0.055195, 0.99848 + 0xbfaf656e79f820e0, 0x3feff095658e71ad, // -0.061321, 0.99812 + 0xbfb1440134d709b2, 0x3fefed58ecb673c4, // -0.067444, 0.99772 + 0xbfb2d52092ce19f6, 0x3fefe9cdad01883a, // -0.073565, 0.99729 + 0xbfb4661179272096, 0x3fefe5f3af2e3940, // -0.079682, 0.99682 + 0xbfb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // -0.085797, 0.99631 + 0xbfb787586a5d5b21, 0x3fefdd539ff1f456, // -0.091909, 0.99577 + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, // -0.098017, 0.99518 + 0xbfbaa7b724495c04, 0x3fefd37914220b84, // -0.10412, 0.99456 + 0xbfbc3785c79ec2d5, 0x3fefce15fd6da67b, // -0.11022, 0.99391 + 0xbfbdc70ecbae9fc8, 0x3fefc8646cfeb721, // -0.11632, 0.99321 + 0xbfbf564e56a9730e, 0x3fefc26470e19fd3, // -0.12241, 0.99248 + 0xbfc072a047ba831d, 0x3fefbc1617e44186, // -0.1285, 0.99171 + 0xbfc139f0cedaf576, 0x3fefb5797195d741, // -0.13458, 0.9909 + 0xbfc20116d4ec7bce, 0x3fefae8e8e46cfbb, // -0.14066, 0.99006 + 0xbfc2c8106e8e613a, 0x3fefa7557f08a517, // -0.14673, 0.98918 + 0xbfc38edbb0cd8d14, 0x3fef9fce55adb2c8, // -0.1528, 0.98826 + 0xbfc45576b1293e5a, 0x3fef97f924c9099b, // -0.15886, 0.9873 + 0xbfc51bdf8597c5f2, 0x3fef8fd5ffae41db, // -0.16491, 0.98631 + 0xbfc5e214448b3fc6, 0x3fef8764fa714ba9, // -0.17096, 0.98528 + 0xbfc6a81304f64ab2, 0x3fef7ea629e63d6e, // -0.177, 0.98421 + 0xbfc76dd9de50bf31, 0x3fef7599a3a12077, // -0.18304, 0.98311 + 0xbfc83366e89c64c5, 0x3fef6c3f7df5bbb7, // -0.18907, 0.98196 + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079 + 0xbfc9bdcbf2dc4366, 0x3fef58a2b1789e84, // -0.2011, 0.97957 + 0xbfca82a025b00451, 0x3fef4e603b0b2f2d, // -0.20711, 0.97832 + 0xbfcb4732ef3d6722, 0x3fef43d085ff92dd, // -0.21311, 0.97703 + 0xbfcc0b826a7e4f63, 0x3fef38f3ac64e589, // -0.2191, 0.9757 + 0xbfcccf8cb312b286, 0x3fef2dc9c9089a9d, // -0.22508, 0.97434 + 0xbfcd934fe5454311, 0x3fef2252f7763ada, // -0.23106, 0.97294 + 0xbfce56ca1e101a1b, 0x3fef168f53f7205d, // -0.23702, 0.9715 + 0xbfcf19f97b215f1a, 0x3fef0a7efb9230d7, // -0.24298, 0.97003 + 0xbfcfdcdc1adfedf8, 0x3feefe220c0b95ec, // -0.24893, 0.96852 + 0xbfd04fb80e37fdae, 0x3feef178a3e473c2, // -0.25487, 0.96698 + 0xbfd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // -0.26079, 0.96539 + 0xbfd111d262b1f677, 0x3feed740e7684963, // -0.26671, 0.96378 + 0xbfd172a0d7765177, 0x3feec9b2d3c3bf84, // -0.27262, 0.96212 + 0xbfd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // -0.27852, 0.96043 + 0xbfd233bbabc3bb72, 0x3feeadb2e8e7a88e, // -0.28441, 0.9587 + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694 + 0xbfd2f422daec0386, 0x3fee9084361df7f3, // -0.29615, 0.95514 + 0xbfd35410c2e18152, 0x3fee817bab4cd10d, // -0.30201, 0.95331 + 0xbfd3b3cefa0414b7, 0x3fee7227db6a9744, // -0.30785, 0.95144 + 0xbfd4135c94176602, 0x3fee6288ec48e112, // -0.31368, 0.94953 + 0xbfd472b8a5571054, 0x3fee529f04729ffc, // -0.3195, 0.94759 + 0xbfd4d1e24278e76a, 0x3fee426a4b2bc17e, // -0.32531, 0.94561 + 0xbfd530d880af3c24, 0x3fee31eae870ce25, // -0.33111, 0.94359 + 0xbfd58f9a75ab1fdd, 0x3fee212104f686e5, // -0.33689, 0.94154 + 0xbfd5ee27379ea693, 0x3fee100cca2980ac, // -0.34266, 0.93946 + 0xbfd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // -0.34842, 0.93734 + 0xbfd6aa9d7dc77e16, 0x3feded05f7de47da, // -0.35416, 0.93518 + 0xbfd7088530fa459e, 0x3feddb13b6ccc23d, // -0.3599, 0.93299 + 0xbfd766340f2418f6, 0x3fedc8d7cb410260, // -0.36561, 0.93077 + 0xbfd7c3a9311dcce7, 0x3fedb6526238a09b, // -0.37132, 0.92851 + 0xbfd820e3b04eaac4, 0x3feda383a9668988, // -0.37701, 0.92621 + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388 + 0xbfd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // -0.38835, 0.92151 + 0xbfd9372a63bc93d7, 0x3fed696173c9e68b, // -0.39399, 0.91911 + 0xbfd993716141bdfe, 0x3fed556f52e93eb1, // -0.39962, 0.91668 + 0xbfd9ef7943a8ed8a, 0x3fed4134d14dc93a, // -0.40524, 0.91421 + 0xbfda4b4127dea1e4, 0x3fed2cb220e0ef9f, // -0.41084, 0.91171 + 0xbfdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // -0.41643, 0.90917 + 0xbfdb020d6c7f4009, 0x3fed02d4feb2bd92, // -0.422, 0.9066 + 0xbfdb5d1009e15cc0, 0x3feced7af43cc773, // -0.42756, 0.90399 + 0xbfdbb7cf2304bd01, 0x3fecd7d9898b32f6, // -0.43309, 0.90135 + 0xbfdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // -0.43862, 0.89867 + 0xbfdc6c7f4997000a, 0x3fecabc169a0b901, // -0.44412, 0.89597 + 0xbfdcc66e9931c45d, 0x3fec954b213411f5, // -0.44961, 0.89322 + 0xbfdd2016e8e9db5b, 0x3fec7e8e52233cf3, // -0.45508, 0.89045 + 0xbfdd79775b86e389, 0x3fec678b3488739b, // -0.46054, 0.88764 + 0xbfddd28f1481cc58, 0x3fec5042012b6907, // -0.46598, 0.8848 + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192 + 0xbfde83e0eaf85113, 0x3fec20de3fa971b0, // -0.4768, 0.87901 + 0xbfdedc1952ef78d5, 0x3fec08c426725549, // -0.48218, 0.87607 + 0xbfdf3405963fd068, 0x3febf064e15377dd, // -0.48755, 0.87309 + 0xbfdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // -0.4929, 0.87009 + 0xbfdfe2f64be7120f, 0x3febbed7c49380ea, // -0.49823, 0.86705 + 0xbfe01cfc874c3eb7, 0x3feba5aa673590d2, // -0.50354, 0.86397 + 0xbfe0485626ae221a, 0x3feb8c38d27504e9, // -0.50883, 0.86087 + 0xbfe073879922ffed, 0x3feb728345196e3e, // -0.5141, 0.85773 + 0xbfe09e907417c5e1, 0x3feb5889fe921405, // -0.51936, 0.85456 + 0xbfe0c9704d5d898f, 0x3feb3e4d3ef55712, // -0.52459, 0.85136 + 0xbfe0f426bb2a8e7d, 0x3feb23cd470013b4, // -0.5298, 0.84812 + 0xbfe11eb3541b4b22, 0x3feb090a58150200, // -0.535, 0.84485 + 0xbfe14915af336ceb, 0x3feaee04b43c1474, // -0.54017, 0.84155 + 0xbfe1734d63dedb49, 0x3fead2bc9e21d511, // -0.54532, 0.83822 + 0xbfe19d5a09f2b9b8, 0x3feab7325916c0d4, // -0.55046, 0.83486 + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147 + 0xbfe1f0f08bbc861b, 0x3fea7f58529fe69d, // -0.56066, 0.82805 + 0xbfe21a799933eb58, 0x3fea63091b02fae2, // -0.56573, 0.82459 + 0xbfe243d5fb98ac1f, 0x3fea4678c8119ac8, // -0.57078, 0.8211 + 0xbfe26d054cdd12df, 0x3fea29a7a0462782, // -0.57581, 0.81758 + 0xbfe2960727629ca8, 0x3fea0c95eabaf937, // -0.58081, 0.81404 + 0xbfe2bedb25faf3ea, 0x3fe9ef43ef29af94, // -0.5858, 0.81046 + 0xbfe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // -0.59076, 0.80685 + 0xbfe30ff7fce17035, 0x3fe9b3e047f38741, // -0.5957, 0.80321 + 0xbfe338400d0c8e57, 0x3fe995cf2ed80d22, // -0.60062, 0.79954 + 0xbfe36058b10659f3, 0x3fe9777ef4c7d742, // -0.60551, 0.79584 + 0xbfe3884185dfeb22, 0x3fe958efe48e6dd7, // -0.61038, 0.79211 + 0xbfe3affa292050b9, 0x3fe93a22499263fc, // -0.61523, 0.78835 + 0xbfe3d78238c58343, 0x3fe91b166fd49da2, // -0.62006, 0.78456 + 0xbfe3fed9534556d4, 0x3fe8fbcca3ef940d, // -0.62486, 0.78074 + 0xbfe425ff178e6bb1, 0x3fe8dc45331698cc, // -0.62964, 0.77689 + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301 + 0xbfe473b51b987347, 0x3fe89c7e9a4dd4ab, // -0.63912, 0.7691 + 0xbfe49a449b9b0938, 0x3fe87c400fba2ebf, // -0.64383, 0.76517 + 0xbfe4c0a145ec0004, 0x3fe85bc51ae958cc, // -0.64851, 0.7612 + 0xbfe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // -0.65317, 0.75721 + 0xbfe50cc09f59a09b, 0x3fe81a1b33b57acc, // -0.65781, 0.75319 + 0xbfe5328292a35596, 0x3fe7f8ece3571771, // -0.66242, 0.74914 + 0xbfe5581038975137, 0x3fe7d7836cc33db2, // -0.667, 0.74506 + 0xbfe57d69348cec9f, 0x3fe7b5df226aafb0, // -0.67156, 0.74095 + 0xbfe5a28d2a5d7250, 0x3fe79400574f55e4, // -0.67609, 0.73682 + 0xbfe5c77bbe65018c, 0x3fe771e75f037261, // -0.6806, 0.73265 + 0xbfe5ec3495837074, 0x3fe74f948da8d28d, // -0.68508, 0.72846 + 0xbfe610b7551d2cde, 0x3fe72d0837efff97, // -0.68954, 0.72425 + 0xbfe63503a31c1be8, 0x3fe70a42b3176d7a, // -0.69397, 0.72 + 0xbfe6591925f0783e, 0x3fe6e74454eaa8ae, // -0.69838, 0.71573 + 0xbfe67cf78491af10, 0x3fe6c40d73c18275, // -0.70275, 0.71143 + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711 + 0xbfe6c40d73c18275, 0x3fe67cf78491af10, // -0.71143, 0.70275 + 0xbfe6e74454eaa8ae, 0x3fe6591925f0783e, // -0.71573, 0.69838 + 0xbfe70a42b3176d7a, 0x3fe63503a31c1be8, // -0.72, 0.69397 + 0xbfe72d0837efff97, 0x3fe610b7551d2cde, // -0.72425, 0.68954 + 0xbfe74f948da8d28d, 0x3fe5ec3495837074, // -0.72846, 0.68508 + 0xbfe771e75f037261, 0x3fe5c77bbe65018c, // -0.73265, 0.6806 + 0xbfe79400574f55e4, 0x3fe5a28d2a5d7250, // -0.73682, 0.67609 + 0xbfe7b5df226aafb0, 0x3fe57d69348cec9f, // -0.74095, 0.67156 + 0xbfe7d7836cc33db2, 0x3fe5581038975137, // -0.74506, 0.667 + 0xbfe7f8ece3571771, 0x3fe5328292a35596, // -0.74914, 0.66242 + 0xbfe81a1b33b57acc, 0x3fe50cc09f59a09b, // -0.75319, 0.65781 + 0xbfe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // -0.75721, 0.65317 + 0xbfe85bc51ae958cc, 0x3fe4c0a145ec0004, // -0.7612, 0.64851 + 0xbfe87c400fba2ebf, 0x3fe49a449b9b0938, // -0.76517, 0.64383 + 0xbfe89c7e9a4dd4ab, 0x3fe473b51b987347, // -0.7691, 0.63912 + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439 + 0xbfe8dc45331698cc, 0x3fe425ff178e6bb1, // -0.77689, 0.62964 + 0xbfe8fbcca3ef940d, 0x3fe3fed9534556d4, // -0.78074, 0.62486 + 0xbfe91b166fd49da2, 0x3fe3d78238c58343, // -0.78456, 0.62006 + 0xbfe93a22499263fc, 0x3fe3affa292050b9, // -0.78835, 0.61523 + 0xbfe958efe48e6dd7, 0x3fe3884185dfeb22, // -0.79211, 0.61038 + 0xbfe9777ef4c7d742, 0x3fe36058b10659f3, // -0.79584, 0.60551 + 0xbfe995cf2ed80d22, 0x3fe338400d0c8e57, // -0.79954, 0.60062 + 0xbfe9b3e047f38741, 0x3fe30ff7fce17035, // -0.80321, 0.5957 + 0xbfe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // -0.80685, 0.59076 + 0xbfe9ef43ef29af94, 0x3fe2bedb25faf3ea, // -0.81046, 0.5858 + 0xbfea0c95eabaf937, 0x3fe2960727629ca8, // -0.81404, 0.58081 + 0xbfea29a7a0462782, 0x3fe26d054cdd12df, // -0.81758, 0.57581 + 0xbfea4678c8119ac8, 0x3fe243d5fb98ac1f, // -0.8211, 0.57078 + 0xbfea63091b02fae2, 0x3fe21a799933eb58, // -0.82459, 0.56573 + 0xbfea7f58529fe69d, 0x3fe1f0f08bbc861b, // -0.82805, 0.56066 + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557 + 0xbfeab7325916c0d4, 0x3fe19d5a09f2b9b8, // -0.83486, 0.55046 + 0xbfead2bc9e21d511, 0x3fe1734d63dedb49, // -0.83822, 0.54532 + 0xbfeaee04b43c1474, 0x3fe14915af336ceb, // -0.84155, 0.54017 + 0xbfeb090a58150200, 0x3fe11eb3541b4b22, // -0.84485, 0.535 + 0xbfeb23cd470013b4, 0x3fe0f426bb2a8e7d, // -0.84812, 0.5298 + 0xbfeb3e4d3ef55712, 0x3fe0c9704d5d898f, // -0.85136, 0.52459 + 0xbfeb5889fe921405, 0x3fe09e907417c5e1, // -0.85456, 0.51936 + 0xbfeb728345196e3e, 0x3fe073879922ffed, // -0.85773, 0.5141 + 0xbfeb8c38d27504e9, 0x3fe0485626ae221a, // -0.86087, 0.50883 + 0xbfeba5aa673590d2, 0x3fe01cfc874c3eb7, // -0.86397, 0.50354 + 0xbfebbed7c49380ea, 0x3fdfe2f64be7120f, // -0.86705, 0.49823 + 0xbfebd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // -0.87009, 0.4929 + 0xbfebf064e15377dd, 0x3fdf3405963fd068, // -0.87309, 0.48755 + 0xbfec08c426725549, 0x3fdedc1952ef78d5, // -0.87607, 0.48218 + 0xbfec20de3fa971b0, 0x3fde83e0eaf85113, // -0.87901, 0.4768 + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714 + 0xbfec5042012b6907, 0x3fddd28f1481cc58, // -0.8848, 0.46598 + 0xbfec678b3488739b, 0x3fdd79775b86e389, // -0.88764, 0.46054 + 0xbfec7e8e52233cf3, 0x3fdd2016e8e9db5b, // -0.89045, 0.45508 + 0xbfec954b213411f5, 0x3fdcc66e9931c45d, // -0.89322, 0.44961 + 0xbfecabc169a0b901, 0x3fdc6c7f4997000a, // -0.89597, 0.44412 + 0xbfecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // -0.89867, 0.43862 + 0xbfecd7d9898b32f6, 0x3fdbb7cf2304bd01, // -0.90135, 0.43309 + 0xbfeced7af43cc773, 0x3fdb5d1009e15cc0, // -0.90399, 0.42756 + 0xbfed02d4feb2bd92, 0x3fdb020d6c7f4009, // -0.9066, 0.422 + 0xbfed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // -0.90917, 0.41643 + 0xbfed2cb220e0ef9f, 0x3fda4b4127dea1e4, // -0.91171, 0.41084 + 0xbfed4134d14dc93a, 0x3fd9ef7943a8ed8a, // -0.91421, 0.40524 + 0xbfed556f52e93eb1, 0x3fd993716141bdfe, // -0.91668, 0.39962 + 0xbfed696173c9e68b, 0x3fd9372a63bc93d7, // -0.91911, 0.39399 + 0xbfed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // -0.92151, 0.38835 + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268 + 0xbfeda383a9668988, 0x3fd820e3b04eaac4, // -0.92621, 0.37701 + 0xbfedb6526238a09b, 0x3fd7c3a9311dcce7, // -0.92851, 0.37132 + 0xbfedc8d7cb410260, 0x3fd766340f2418f6, // -0.93077, 0.36561 + 0xbfeddb13b6ccc23d, 0x3fd7088530fa459e, // -0.93299, 0.3599 + 0xbfeded05f7de47da, 0x3fd6aa9d7dc77e16, // -0.93518, 0.35416 + 0xbfedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // -0.93734, 0.34842 + 0xbfee100cca2980ac, 0x3fd5ee27379ea693, // -0.93946, 0.34266 + 0xbfee212104f686e5, 0x3fd58f9a75ab1fdd, // -0.94154, 0.33689 + 0xbfee31eae870ce25, 0x3fd530d880af3c24, // -0.94359, 0.33111 + 0xbfee426a4b2bc17e, 0x3fd4d1e24278e76a, // -0.94561, 0.32531 + 0xbfee529f04729ffc, 0x3fd472b8a5571054, // -0.94759, 0.3195 + 0xbfee6288ec48e112, 0x3fd4135c94176602, // -0.94953, 0.31368 + 0xbfee7227db6a9744, 0x3fd3b3cefa0414b7, // -0.95144, 0.30785 + 0xbfee817bab4cd10d, 0x3fd35410c2e18152, // -0.95331, 0.30201 + 0xbfee9084361df7f3, 0x3fd2f422daec0386, // -0.95514, 0.29615 + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028 + 0xbfeeadb2e8e7a88e, 0x3fd233bbabc3bb72, // -0.9587, 0.28441 + 0xbfeebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // -0.96043, 0.27852 + 0xbfeec9b2d3c3bf84, 0x3fd172a0d7765177, // -0.96212, 0.27262 + 0xbfeed740e7684963, 0x3fd111d262b1f677, // -0.96378, 0.26671 + 0xbfeee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // -0.96539, 0.26079 + 0xbfeef178a3e473c2, 0x3fd04fb80e37fdae, // -0.96698, 0.25487 + 0xbfeefe220c0b95ec, 0x3fcfdcdc1adfedf8, // -0.96852, 0.24893 + 0xbfef0a7efb9230d7, 0x3fcf19f97b215f1a, // -0.97003, 0.24298 + 0xbfef168f53f7205d, 0x3fce56ca1e101a1b, // -0.9715, 0.23702 + 0xbfef2252f7763ada, 0x3fcd934fe5454311, // -0.97294, 0.23106 + 0xbfef2dc9c9089a9d, 0x3fcccf8cb312b286, // -0.97434, 0.22508 + 0xbfef38f3ac64e589, 0x3fcc0b826a7e4f63, // -0.9757, 0.2191 + 0xbfef43d085ff92dd, 0x3fcb4732ef3d6722, // -0.97703, 0.21311 + 0xbfef4e603b0b2f2d, 0x3fca82a025b00451, // -0.97832, 0.20711 + 0xbfef58a2b1789e84, 0x3fc9bdcbf2dc4366, // -0.97957, 0.2011 + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509 + 0xbfef6c3f7df5bbb7, 0x3fc83366e89c64c5, // -0.98196, 0.18907 + 0xbfef7599a3a12077, 0x3fc76dd9de50bf31, // -0.98311, 0.18304 + 0xbfef7ea629e63d6e, 0x3fc6a81304f64ab2, // -0.98421, 0.177 + 0xbfef8764fa714ba9, 0x3fc5e214448b3fc6, // -0.98528, 0.17096 + 0xbfef8fd5ffae41db, 0x3fc51bdf8597c5f2, // -0.98631, 0.16491 + 0xbfef97f924c9099b, 0x3fc45576b1293e5a, // -0.9873, 0.15886 + 0xbfef9fce55adb2c8, 0x3fc38edbb0cd8d14, // -0.98826, 0.1528 + 0xbfefa7557f08a517, 0x3fc2c8106e8e613a, // -0.98918, 0.14673 + 0xbfefae8e8e46cfbb, 0x3fc20116d4ec7bce, // -0.99006, 0.14066 + 0xbfefb5797195d741, 0x3fc139f0cedaf576, // -0.9909, 0.13458 + 0xbfefbc1617e44186, 0x3fc072a047ba831d, // -0.99171, 0.1285 + 0xbfefc26470e19fd3, 0x3fbf564e56a9730e, // -0.99248, 0.12241 + 0xbfefc8646cfeb721, 0x3fbdc70ecbae9fc8, // -0.99321, 0.11632 + 0xbfefce15fd6da67b, 0x3fbc3785c79ec2d5, // -0.99391, 0.11022 + 0xbfefd37914220b84, 0x3fbaa7b724495c04, // -0.99456, 0.10412 + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017 + 0xbfefdd539ff1f456, 0x3fb787586a5d5b21, // -0.99577, 0.091909 + 0xbfefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // -0.99631, 0.085797 + 0xbfefe5f3af2e3940, 0x3fb4661179272096, // -0.99682, 0.079682 + 0xbfefe9cdad01883a, 0x3fb2d52092ce19f6, // -0.99729, 0.073565 + 0xbfefed58ecb673c4, 0x3fb1440134d709b2, // -0.99772, 0.067444 + 0xbfeff095658e71ad, 0x3faf656e79f820e0, // -0.99812, 0.061321 + 0xbfeff3830f8d575c, 0x3fac428d12c0d7e3, // -0.99848, 0.055195 + 0xbfeff621e3796d7e, 0x3fa91f65f10dd814, // -0.9988, 0.049068 + 0xbfeff871dadb81df, 0x3fa5fc00d290cd43, // -0.99908, 0.042938 + 0xbfeffa72effef75d, 0x3fa2d865759455cd, // -0.99932, 0.036807 + 0xbfeffc251df1d3f8, 0x3f9f693731d1cf01, // -0.99953, 0.030675 + 0xbfeffd886084cd0d, 0x3f992155f7a3667e, // -0.9997, 0.024541 + 0xbfeffe9cb44b51a1, 0x3f92d936bbe30efd, // -0.99983, 0.018407 + 0xbfefff62169b92db, 0x3f8921d1fcdec784, // -0.99992, 0.012272 + 0xbfefffd8858e8a92, 0x3f7921f0fe670071, // -0.99998, 0.0061359 + 0xbff0000000000000, 0x0000000000000000, // -1, 0 + 0xbfefffd8858e8a92, 0xbf7921f0fe670071, // -0.99998,-0.0061359 + 0xbfefff62169b92db, 0xbf8921d1fcdec784, // -0.99992, -0.012272 + 0xbfeffe9cb44b51a1, 0xbf92d936bbe30efd, // -0.99983, -0.018407 + 0xbfeffd886084cd0d, 0xbf992155f7a3667e, // -0.9997, -0.024541 + 0xbfeffc251df1d3f8, 0xbf9f693731d1cf01, // -0.99953, -0.030675 + 0xbfeffa72effef75d, 0xbfa2d865759455cd, // -0.99932, -0.036807 + 0xbfeff871dadb81df, 0xbfa5fc00d290cd43, // -0.99908, -0.042938 + 0xbfeff621e3796d7e, 0xbfa91f65f10dd814, // -0.9988, -0.049068 + 0xbfeff3830f8d575c, 0xbfac428d12c0d7e3, // -0.99848, -0.055195 + 0xbfeff095658e71ad, 0xbfaf656e79f820e0, // -0.99812, -0.061321 + 0xbfefed58ecb673c4, 0xbfb1440134d709b2, // -0.99772, -0.067444 + 0xbfefe9cdad01883a, 0xbfb2d52092ce19f6, // -0.99729, -0.073565 + 0xbfefe5f3af2e3940, 0xbfb4661179272096, // -0.99682, -0.079682 + 0xbfefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // -0.99631, -0.085797 + 0xbfefdd539ff1f456, 0xbfb787586a5d5b21, // -0.99577, -0.091909 + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518, -0.098017 + 0xbfefd37914220b84, 0xbfbaa7b724495c04, // -0.99456, -0.10412 + 0xbfefce15fd6da67b, 0xbfbc3785c79ec2d5, // -0.99391, -0.11022 + 0xbfefc8646cfeb721, 0xbfbdc70ecbae9fc8, // -0.99321, -0.11632 + 0xbfefc26470e19fd3, 0xbfbf564e56a9730e, // -0.99248, -0.12241 + 0xbfefbc1617e44186, 0xbfc072a047ba831d, // -0.99171, -0.1285 + 0xbfefb5797195d741, 0xbfc139f0cedaf576, // -0.9909, -0.13458 + 0xbfefae8e8e46cfbb, 0xbfc20116d4ec7bce, // -0.99006, -0.14066 + 0xbfefa7557f08a517, 0xbfc2c8106e8e613a, // -0.98918, -0.14673 + 0xbfef9fce55adb2c8, 0xbfc38edbb0cd8d14, // -0.98826, -0.1528 + 0xbfef97f924c9099b, 0xbfc45576b1293e5a, // -0.9873, -0.15886 + 0xbfef8fd5ffae41db, 0xbfc51bdf8597c5f2, // -0.98631, -0.16491 + 0xbfef8764fa714ba9, 0xbfc5e214448b3fc6, // -0.98528, -0.17096 + 0xbfef7ea629e63d6e, 0xbfc6a81304f64ab2, // -0.98421, -0.177 + 0xbfef7599a3a12077, 0xbfc76dd9de50bf31, // -0.98311, -0.18304 + 0xbfef6c3f7df5bbb7, 0xbfc83366e89c64c5, // -0.98196, -0.18907 + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509 + 0xbfef58a2b1789e84, 0xbfc9bdcbf2dc4366, // -0.97957, -0.2011 + 0xbfef4e603b0b2f2d, 0xbfca82a025b00451, // -0.97832, -0.20711 + 0xbfef43d085ff92dd, 0xbfcb4732ef3d6722, // -0.97703, -0.21311 + 0xbfef38f3ac64e589, 0xbfcc0b826a7e4f63, // -0.9757, -0.2191 + 0xbfef2dc9c9089a9d, 0xbfcccf8cb312b286, // -0.97434, -0.22508 + 0xbfef2252f7763ada, 0xbfcd934fe5454311, // -0.97294, -0.23106 + 0xbfef168f53f7205d, 0xbfce56ca1e101a1b, // -0.9715, -0.23702 + 0xbfef0a7efb9230d7, 0xbfcf19f97b215f1a, // -0.97003, -0.24298 + 0xbfeefe220c0b95ec, 0xbfcfdcdc1adfedf8, // -0.96852, -0.24893 + 0xbfeef178a3e473c2, 0xbfd04fb80e37fdae, // -0.96698, -0.25487 + 0xbfeee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // -0.96539, -0.26079 + 0xbfeed740e7684963, 0xbfd111d262b1f677, // -0.96378, -0.26671 + 0xbfeec9b2d3c3bf84, 0xbfd172a0d7765177, // -0.96212, -0.27262 + 0xbfeebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // -0.96043, -0.27852 + 0xbfeeadb2e8e7a88e, 0xbfd233bbabc3bb72, // -0.9587, -0.28441 + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028 + 0xbfee9084361df7f3, 0xbfd2f422daec0386, // -0.95514, -0.29615 + 0xbfee817bab4cd10d, 0xbfd35410c2e18152, // -0.95331, -0.30201 + 0xbfee7227db6a9744, 0xbfd3b3cefa0414b7, // -0.95144, -0.30785 + 0xbfee6288ec48e112, 0xbfd4135c94176602, // -0.94953, -0.31368 + 0xbfee529f04729ffc, 0xbfd472b8a5571054, // -0.94759, -0.3195 + 0xbfee426a4b2bc17e, 0xbfd4d1e24278e76a, // -0.94561, -0.32531 + 0xbfee31eae870ce25, 0xbfd530d880af3c24, // -0.94359, -0.33111 + 0xbfee212104f686e5, 0xbfd58f9a75ab1fdd, // -0.94154, -0.33689 + 0xbfee100cca2980ac, 0xbfd5ee27379ea693, // -0.93946, -0.34266 + 0xbfedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // -0.93734, -0.34842 + 0xbfeded05f7de47da, 0xbfd6aa9d7dc77e16, // -0.93518, -0.35416 + 0xbfeddb13b6ccc23d, 0xbfd7088530fa459e, // -0.93299, -0.3599 + 0xbfedc8d7cb410260, 0xbfd766340f2418f6, // -0.93077, -0.36561 + 0xbfedb6526238a09b, 0xbfd7c3a9311dcce7, // -0.92851, -0.37132 + 0xbfeda383a9668988, 0xbfd820e3b04eaac4, // -0.92621, -0.37701 + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268 + 0xbfed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // -0.92151, -0.38835 + 0xbfed696173c9e68b, 0xbfd9372a63bc93d7, // -0.91911, -0.39399 + 0xbfed556f52e93eb1, 0xbfd993716141bdfe, // -0.91668, -0.39962 + 0xbfed4134d14dc93a, 0xbfd9ef7943a8ed8a, // -0.91421, -0.40524 + 0xbfed2cb220e0ef9f, 0xbfda4b4127dea1e4, // -0.91171, -0.41084 + 0xbfed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // -0.90917, -0.41643 + 0xbfed02d4feb2bd92, 0xbfdb020d6c7f4009, // -0.9066, -0.422 + 0xbfeced7af43cc773, 0xbfdb5d1009e15cc0, // -0.90399, -0.42756 + 0xbfecd7d9898b32f6, 0xbfdbb7cf2304bd01, // -0.90135, -0.43309 + 0xbfecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // -0.89867, -0.43862 + 0xbfecabc169a0b901, 0xbfdc6c7f4997000a, // -0.89597, -0.44412 + 0xbfec954b213411f5, 0xbfdcc66e9931c45d, // -0.89322, -0.44961 + 0xbfec7e8e52233cf3, 0xbfdd2016e8e9db5b, // -0.89045, -0.45508 + 0xbfec678b3488739b, 0xbfdd79775b86e389, // -0.88764, -0.46054 + 0xbfec5042012b6907, 0xbfddd28f1481cc58, // -0.8848, -0.46598 + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714 + 0xbfec20de3fa971b0, 0xbfde83e0eaf85113, // -0.87901, -0.4768 + 0xbfec08c426725549, 0xbfdedc1952ef78d5, // -0.87607, -0.48218 + 0xbfebf064e15377dd, 0xbfdf3405963fd068, // -0.87309, -0.48755 + 0xbfebd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // -0.87009, -0.4929 + 0xbfebbed7c49380ea, 0xbfdfe2f64be7120f, // -0.86705, -0.49823 + 0xbfeba5aa673590d2, 0xbfe01cfc874c3eb7, // -0.86397, -0.50354 + 0xbfeb8c38d27504e9, 0xbfe0485626ae221a, // -0.86087, -0.50883 + 0xbfeb728345196e3e, 0xbfe073879922ffed, // -0.85773, -0.5141 + 0xbfeb5889fe921405, 0xbfe09e907417c5e1, // -0.85456, -0.51936 + 0xbfeb3e4d3ef55712, 0xbfe0c9704d5d898f, // -0.85136, -0.52459 + 0xbfeb23cd470013b4, 0xbfe0f426bb2a8e7d, // -0.84812, -0.5298 + 0xbfeb090a58150200, 0xbfe11eb3541b4b22, // -0.84485, -0.535 + 0xbfeaee04b43c1474, 0xbfe14915af336ceb, // -0.84155, -0.54017 + 0xbfead2bc9e21d511, 0xbfe1734d63dedb49, // -0.83822, -0.54532 + 0xbfeab7325916c0d4, 0xbfe19d5a09f2b9b8, // -0.83486, -0.55046 + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557 + 0xbfea7f58529fe69d, 0xbfe1f0f08bbc861b, // -0.82805, -0.56066 + 0xbfea63091b02fae2, 0xbfe21a799933eb58, // -0.82459, -0.56573 + 0xbfea4678c8119ac8, 0xbfe243d5fb98ac1f, // -0.8211, -0.57078 + 0xbfea29a7a0462782, 0xbfe26d054cdd12df, // -0.81758, -0.57581 + 0xbfea0c95eabaf937, 0xbfe2960727629ca8, // -0.81404, -0.58081 + 0xbfe9ef43ef29af94, 0xbfe2bedb25faf3ea, // -0.81046, -0.5858 + 0xbfe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // -0.80685, -0.59076 + 0xbfe9b3e047f38741, 0xbfe30ff7fce17035, // -0.80321, -0.5957 + 0xbfe995cf2ed80d22, 0xbfe338400d0c8e57, // -0.79954, -0.60062 + 0xbfe9777ef4c7d742, 0xbfe36058b10659f3, // -0.79584, -0.60551 + 0xbfe958efe48e6dd7, 0xbfe3884185dfeb22, // -0.79211, -0.61038 + 0xbfe93a22499263fc, 0xbfe3affa292050b9, // -0.78835, -0.61523 + 0xbfe91b166fd49da2, 0xbfe3d78238c58343, // -0.78456, -0.62006 + 0xbfe8fbcca3ef940d, 0xbfe3fed9534556d4, // -0.78074, -0.62486 + 0xbfe8dc45331698cc, 0xbfe425ff178e6bb1, // -0.77689, -0.62964 + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439 + 0xbfe89c7e9a4dd4ab, 0xbfe473b51b987347, // -0.7691, -0.63912 + 0xbfe87c400fba2ebf, 0xbfe49a449b9b0938, // -0.76517, -0.64383 + 0xbfe85bc51ae958cc, 0xbfe4c0a145ec0004, // -0.7612, -0.64851 + 0xbfe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // -0.75721, -0.65317 + 0xbfe81a1b33b57acc, 0xbfe50cc09f59a09b, // -0.75319, -0.65781 + 0xbfe7f8ece3571771, 0xbfe5328292a35596, // -0.74914, -0.66242 + 0xbfe7d7836cc33db2, 0xbfe5581038975137, // -0.74506, -0.667 + 0xbfe7b5df226aafb0, 0xbfe57d69348cec9f, // -0.74095, -0.67156 + 0xbfe79400574f55e4, 0xbfe5a28d2a5d7250, // -0.73682, -0.67609 + 0xbfe771e75f037261, 0xbfe5c77bbe65018c, // -0.73265, -0.6806 + 0xbfe74f948da8d28d, 0xbfe5ec3495837074, // -0.72846, -0.68508 + 0xbfe72d0837efff97, 0xbfe610b7551d2cde, // -0.72425, -0.68954 + 0xbfe70a42b3176d7a, 0xbfe63503a31c1be8, // -0.72, -0.69397 + 0xbfe6e74454eaa8ae, 0xbfe6591925f0783e, // -0.71573, -0.69838 + 0xbfe6c40d73c18275, 0xbfe67cf78491af10, // -0.71143, -0.70275 + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711 + 0xbfe67cf78491af10, 0xbfe6c40d73c18275, // -0.70275, -0.71143 + 0xbfe6591925f0783e, 0xbfe6e74454eaa8ae, // -0.69838, -0.71573 + 0xbfe63503a31c1be8, 0xbfe70a42b3176d7a, // -0.69397, -0.72 + 0xbfe610b7551d2cde, 0xbfe72d0837efff97, // -0.68954, -0.72425 + 0xbfe5ec3495837074, 0xbfe74f948da8d28d, // -0.68508, -0.72846 + 0xbfe5c77bbe65018c, 0xbfe771e75f037261, // -0.6806, -0.73265 + 0xbfe5a28d2a5d7250, 0xbfe79400574f55e4, // -0.67609, -0.73682 + 0xbfe57d69348cec9f, 0xbfe7b5df226aafb0, // -0.67156, -0.74095 + 0xbfe5581038975137, 0xbfe7d7836cc33db2, // -0.667, -0.74506 + 0xbfe5328292a35596, 0xbfe7f8ece3571771, // -0.66242, -0.74914 + 0xbfe50cc09f59a09b, 0xbfe81a1b33b57acc, // -0.65781, -0.75319 + 0xbfe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // -0.65317, -0.75721 + 0xbfe4c0a145ec0004, 0xbfe85bc51ae958cc, // -0.64851, -0.7612 + 0xbfe49a449b9b0938, 0xbfe87c400fba2ebf, // -0.64383, -0.76517 + 0xbfe473b51b987347, 0xbfe89c7e9a4dd4ab, // -0.63912, -0.7691 + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301 + 0xbfe425ff178e6bb1, 0xbfe8dc45331698cc, // -0.62964, -0.77689 + 0xbfe3fed9534556d4, 0xbfe8fbcca3ef940d, // -0.62486, -0.78074 + 0xbfe3d78238c58343, 0xbfe91b166fd49da2, // -0.62006, -0.78456 + 0xbfe3affa292050b9, 0xbfe93a22499263fc, // -0.61523, -0.78835 + 0xbfe3884185dfeb22, 0xbfe958efe48e6dd7, // -0.61038, -0.79211 + 0xbfe36058b10659f3, 0xbfe9777ef4c7d742, // -0.60551, -0.79584 + 0xbfe338400d0c8e57, 0xbfe995cf2ed80d22, // -0.60062, -0.79954 + 0xbfe30ff7fce17035, 0xbfe9b3e047f38741, // -0.5957, -0.80321 + 0xbfe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // -0.59076, -0.80685 + 0xbfe2bedb25faf3ea, 0xbfe9ef43ef29af94, // -0.5858, -0.81046 + 0xbfe2960727629ca8, 0xbfea0c95eabaf937, // -0.58081, -0.81404 + 0xbfe26d054cdd12df, 0xbfea29a7a0462782, // -0.57581, -0.81758 + 0xbfe243d5fb98ac1f, 0xbfea4678c8119ac8, // -0.57078, -0.8211 + 0xbfe21a799933eb58, 0xbfea63091b02fae2, // -0.56573, -0.82459 + 0xbfe1f0f08bbc861b, 0xbfea7f58529fe69d, // -0.56066, -0.82805 + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147 + 0xbfe19d5a09f2b9b8, 0xbfeab7325916c0d4, // -0.55046, -0.83486 + 0xbfe1734d63dedb49, 0xbfead2bc9e21d511, // -0.54532, -0.83822 + 0xbfe14915af336ceb, 0xbfeaee04b43c1474, // -0.54017, -0.84155 + 0xbfe11eb3541b4b22, 0xbfeb090a58150200, // -0.535, -0.84485 + 0xbfe0f426bb2a8e7d, 0xbfeb23cd470013b4, // -0.5298, -0.84812 + 0xbfe0c9704d5d898f, 0xbfeb3e4d3ef55712, // -0.52459, -0.85136 + 0xbfe09e907417c5e1, 0xbfeb5889fe921405, // -0.51936, -0.85456 + 0xbfe073879922ffed, 0xbfeb728345196e3e, // -0.5141, -0.85773 + 0xbfe0485626ae221a, 0xbfeb8c38d27504e9, // -0.50883, -0.86087 + 0xbfe01cfc874c3eb7, 0xbfeba5aa673590d2, // -0.50354, -0.86397 + 0xbfdfe2f64be7120f, 0xbfebbed7c49380ea, // -0.49823, -0.86705 + 0xbfdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // -0.4929, -0.87009 + 0xbfdf3405963fd068, 0xbfebf064e15377dd, // -0.48755, -0.87309 + 0xbfdedc1952ef78d5, 0xbfec08c426725549, // -0.48218, -0.87607 + 0xbfde83e0eaf85113, 0xbfec20de3fa971b0, // -0.4768, -0.87901 + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192 + 0xbfddd28f1481cc58, 0xbfec5042012b6907, // -0.46598, -0.8848 + 0xbfdd79775b86e389, 0xbfec678b3488739b, // -0.46054, -0.88764 + 0xbfdd2016e8e9db5b, 0xbfec7e8e52233cf3, // -0.45508, -0.89045 + 0xbfdcc66e9931c45d, 0xbfec954b213411f5, // -0.44961, -0.89322 + 0xbfdc6c7f4997000a, 0xbfecabc169a0b901, // -0.44412, -0.89597 + 0xbfdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // -0.43862, -0.89867 + 0xbfdbb7cf2304bd01, 0xbfecd7d9898b32f6, // -0.43309, -0.90135 + 0xbfdb5d1009e15cc0, 0xbfeced7af43cc773, // -0.42756, -0.90399 + 0xbfdb020d6c7f4009, 0xbfed02d4feb2bd92, // -0.422, -0.9066 + 0xbfdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // -0.41643, -0.90917 + 0xbfda4b4127dea1e4, 0xbfed2cb220e0ef9f, // -0.41084, -0.91171 + 0xbfd9ef7943a8ed8a, 0xbfed4134d14dc93a, // -0.40524, -0.91421 + 0xbfd993716141bdfe, 0xbfed556f52e93eb1, // -0.39962, -0.91668 + 0xbfd9372a63bc93d7, 0xbfed696173c9e68b, // -0.39399, -0.91911 + 0xbfd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // -0.38835, -0.92151 + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388 + 0xbfd820e3b04eaac4, 0xbfeda383a9668988, // -0.37701, -0.92621 + 0xbfd7c3a9311dcce7, 0xbfedb6526238a09b, // -0.37132, -0.92851 + 0xbfd766340f2418f6, 0xbfedc8d7cb410260, // -0.36561, -0.93077 + 0xbfd7088530fa459e, 0xbfeddb13b6ccc23d, // -0.3599, -0.93299 + 0xbfd6aa9d7dc77e16, 0xbfeded05f7de47da, // -0.35416, -0.93518 + 0xbfd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // -0.34842, -0.93734 + 0xbfd5ee27379ea693, 0xbfee100cca2980ac, // -0.34266, -0.93946 + 0xbfd58f9a75ab1fdd, 0xbfee212104f686e5, // -0.33689, -0.94154 + 0xbfd530d880af3c24, 0xbfee31eae870ce25, // -0.33111, -0.94359 + 0xbfd4d1e24278e76a, 0xbfee426a4b2bc17e, // -0.32531, -0.94561 + 0xbfd472b8a5571054, 0xbfee529f04729ffc, // -0.3195, -0.94759 + 0xbfd4135c94176602, 0xbfee6288ec48e112, // -0.31368, -0.94953 + 0xbfd3b3cefa0414b7, 0xbfee7227db6a9744, // -0.30785, -0.95144 + 0xbfd35410c2e18152, 0xbfee817bab4cd10d, // -0.30201, -0.95331 + 0xbfd2f422daec0386, 0xbfee9084361df7f3, // -0.29615, -0.95514 + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694 + 0xbfd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // -0.28441, -0.9587 + 0xbfd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // -0.27852, -0.96043 + 0xbfd172a0d7765177, 0xbfeec9b2d3c3bf84, // -0.27262, -0.96212 + 0xbfd111d262b1f677, 0xbfeed740e7684963, // -0.26671, -0.96378 + 0xbfd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // -0.26079, -0.96539 + 0xbfd04fb80e37fdae, 0xbfeef178a3e473c2, // -0.25487, -0.96698 + 0xbfcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // -0.24893, -0.96852 + 0xbfcf19f97b215f1a, 0xbfef0a7efb9230d7, // -0.24298, -0.97003 + 0xbfce56ca1e101a1b, 0xbfef168f53f7205d, // -0.23702, -0.9715 + 0xbfcd934fe5454311, 0xbfef2252f7763ada, // -0.23106, -0.97294 + 0xbfcccf8cb312b286, 0xbfef2dc9c9089a9d, // -0.22508, -0.97434 + 0xbfcc0b826a7e4f63, 0xbfef38f3ac64e589, // -0.2191, -0.9757 + 0xbfcb4732ef3d6722, 0xbfef43d085ff92dd, // -0.21311, -0.97703 + 0xbfca82a025b00451, 0xbfef4e603b0b2f2d, // -0.20711, -0.97832 + 0xbfc9bdcbf2dc4366, 0xbfef58a2b1789e84, // -0.2011, -0.97957 + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079 + 0xbfc83366e89c64c5, 0xbfef6c3f7df5bbb7, // -0.18907, -0.98196 + 0xbfc76dd9de50bf31, 0xbfef7599a3a12077, // -0.18304, -0.98311 + 0xbfc6a81304f64ab2, 0xbfef7ea629e63d6e, // -0.177, -0.98421 + 0xbfc5e214448b3fc6, 0xbfef8764fa714ba9, // -0.17096, -0.98528 + 0xbfc51bdf8597c5f2, 0xbfef8fd5ffae41db, // -0.16491, -0.98631 + 0xbfc45576b1293e5a, 0xbfef97f924c9099b, // -0.15886, -0.9873 + 0xbfc38edbb0cd8d14, 0xbfef9fce55adb2c8, // -0.1528, -0.98826 + 0xbfc2c8106e8e613a, 0xbfefa7557f08a517, // -0.14673, -0.98918 + 0xbfc20116d4ec7bce, 0xbfefae8e8e46cfbb, // -0.14066, -0.99006 + 0xbfc139f0cedaf576, 0xbfefb5797195d741, // -0.13458, -0.9909 + 0xbfc072a047ba831d, 0xbfefbc1617e44186, // -0.1285, -0.99171 + 0xbfbf564e56a9730e, 0xbfefc26470e19fd3, // -0.12241, -0.99248 + 0xbfbdc70ecbae9fc8, 0xbfefc8646cfeb721, // -0.11632, -0.99321 + 0xbfbc3785c79ec2d5, 0xbfefce15fd6da67b, // -0.11022, -0.99391 + 0xbfbaa7b724495c04, 0xbfefd37914220b84, // -0.10412, -0.99456 + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, // -0.098017, -0.99518 + 0xbfb787586a5d5b21, 0xbfefdd539ff1f456, // -0.091909, -0.99577 + 0xbfb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // -0.085797, -0.99631 + 0xbfb4661179272096, 0xbfefe5f3af2e3940, // -0.079682, -0.99682 + 0xbfb2d52092ce19f6, 0xbfefe9cdad01883a, // -0.073565, -0.99729 + 0xbfb1440134d709b2, 0xbfefed58ecb673c4, // -0.067444, -0.99772 + 0xbfaf656e79f820e0, 0xbfeff095658e71ad, // -0.061321, -0.99812 + 0xbfac428d12c0d7e3, 0xbfeff3830f8d575c, // -0.055195, -0.99848 + 0xbfa91f65f10dd814, 0xbfeff621e3796d7e, // -0.049068, -0.9988 + 0xbfa5fc00d290cd43, 0xbfeff871dadb81df, // -0.042938, -0.99908 + 0xbfa2d865759455cd, 0xbfeffa72effef75d, // -0.036807, -0.99932 + 0xbf9f693731d1cf01, 0xbfeffc251df1d3f8, // -0.030675, -0.99953 + 0xbf992155f7a3667e, 0xbfeffd886084cd0d, // -0.024541, -0.9997 + 0xbf92d936bbe30efd, 0xbfeffe9cb44b51a1, // -0.018407, -0.99983 + 0xbf8921d1fcdec784, 0xbfefff62169b92db, // -0.012272, -0.99992 + 0xbf7921f0fe670071, 0xbfefffd8858e8a92, //-0.0061359, -0.99998 + 0x0000000000000000, 0xbff0000000000000, // 0, -1 + 0x3f7921f0fe670071, 0xbfefffd8858e8a92, // 0.0061359, -0.99998 + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992 + 0x3f92d936bbe30efd, 0xbfeffe9cb44b51a1, // 0.018407, -0.99983 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3f9f693731d1cf01, 0xbfeffc251df1d3f8, // 0.030675, -0.99953 + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932 + 0x3fa5fc00d290cd43, 0xbfeff871dadb81df, // 0.042938, -0.99908 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3fac428d12c0d7e3, 0xbfeff3830f8d575c, // 0.055195, -0.99848 + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812 + 0x3fb1440134d709b2, 0xbfefed58ecb673c4, // 0.067444, -0.99772 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb4661179272096, 0xbfefe5f3af2e3940, // 0.079682, -0.99682 + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631 + 0x3fb787586a5d5b21, 0xbfefdd539ff1f456, // 0.091909, -0.99577 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fbaa7b724495c04, 0xbfefd37914220b84, // 0.10412, -0.99456 + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391 + 0x3fbdc70ecbae9fc8, 0xbfefc8646cfeb721, // 0.11632, -0.99321 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fc072a047ba831d, 0xbfefbc1617e44186, // 0.1285, -0.99171 + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909 + 0x3fc20116d4ec7bce, 0xbfefae8e8e46cfbb, // 0.14066, -0.99006 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc38edbb0cd8d14, 0xbfef9fce55adb2c8, // 0.1528, -0.98826 + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873 + 0x3fc51bdf8597c5f2, 0xbfef8fd5ffae41db, // 0.16491, -0.98631 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc6a81304f64ab2, 0xbfef7ea629e63d6e, // 0.177, -0.98421 + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311 + 0x3fc83366e89c64c5, 0xbfef6c3f7df5bbb7, // 0.18907, -0.98196 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fc9bdcbf2dc4366, 0xbfef58a2b1789e84, // 0.2011, -0.97957 + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832 + 0x3fcb4732ef3d6722, 0xbfef43d085ff92dd, // 0.21311, -0.97703 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcccf8cb312b286, 0xbfef2dc9c9089a9d, // 0.22508, -0.97434 + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294 + 0x3fce56ca1e101a1b, 0xbfef168f53f7205d, // 0.23702, -0.9715 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // 0.24893, -0.96852 + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698 + 0x3fd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // 0.26079, -0.96539 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd172a0d7765177, 0xbfeec9b2d3c3bf84, // 0.27262, -0.96212 + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043 + 0x3fd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // 0.28441, -0.9587 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd2f422daec0386, 0xbfee9084361df7f3, // 0.29615, -0.95514 + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331 + 0x3fd3b3cefa0414b7, 0xbfee7227db6a9744, // 0.30785, -0.95144 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd472b8a5571054, 0xbfee529f04729ffc, // 0.3195, -0.94759 + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561 + 0x3fd530d880af3c24, 0xbfee31eae870ce25, // 0.33111, -0.94359 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd5ee27379ea693, 0xbfee100cca2980ac, // 0.34266, -0.93946 + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734 + 0x3fd6aa9d7dc77e16, 0xbfeded05f7de47da, // 0.35416, -0.93518 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd766340f2418f6, 0xbfedc8d7cb410260, // 0.36561, -0.93077 + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851 + 0x3fd820e3b04eaac4, 0xbfeda383a9668988, // 0.37701, -0.92621 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // 0.38835, -0.92151 + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911 + 0x3fd993716141bdfe, 0xbfed556f52e93eb1, // 0.39962, -0.91668 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fda4b4127dea1e4, 0xbfed2cb220e0ef9f, // 0.41084, -0.91171 + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917 + 0x3fdb020d6c7f4009, 0xbfed02d4feb2bd92, // 0.422, -0.9066 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdbb7cf2304bd01, 0xbfecd7d9898b32f6, // 0.43309, -0.90135 + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867 + 0x3fdc6c7f4997000a, 0xbfecabc169a0b901, // 0.44412, -0.89597 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdd2016e8e9db5b, 0xbfec7e8e52233cf3, // 0.45508, -0.89045 + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764 + 0x3fddd28f1481cc58, 0xbfec5042012b6907, // 0.46598, -0.8848 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fde83e0eaf85113, 0xbfec20de3fa971b0, // 0.4768, -0.87901 + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607 + 0x3fdf3405963fd068, 0xbfebf064e15377dd, // 0.48755, -0.87309 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fdfe2f64be7120f, 0xbfebbed7c49380ea, // 0.49823, -0.86705 + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397 + 0x3fe0485626ae221a, 0xbfeb8c38d27504e9, // 0.50883, -0.86087 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe09e907417c5e1, 0xbfeb5889fe921405, // 0.51936, -0.85456 + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136 + 0x3fe0f426bb2a8e7d, 0xbfeb23cd470013b4, // 0.5298, -0.84812 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe14915af336ceb, 0xbfeaee04b43c1474, // 0.54017, -0.84155 + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822 + 0x3fe19d5a09f2b9b8, 0xbfeab7325916c0d4, // 0.55046, -0.83486 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe1f0f08bbc861b, 0xbfea7f58529fe69d, // 0.56066, -0.82805 + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459 + 0x3fe243d5fb98ac1f, 0xbfea4678c8119ac8, // 0.57078, -0.8211 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe2960727629ca8, 0xbfea0c95eabaf937, // 0.58081, -0.81404 + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046 + 0x3fe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // 0.59076, -0.80685 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe338400d0c8e57, 0xbfe995cf2ed80d22, // 0.60062, -0.79954 + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584 + 0x3fe3884185dfeb22, 0xbfe958efe48e6dd7, // 0.61038, -0.79211 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe3d78238c58343, 0xbfe91b166fd49da2, // 0.62006, -0.78456 + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074 + 0x3fe425ff178e6bb1, 0xbfe8dc45331698cc, // 0.62964, -0.77689 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe473b51b987347, 0xbfe89c7e9a4dd4ab, // 0.63912, -0.7691 + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517 + 0x3fe4c0a145ec0004, 0xbfe85bc51ae958cc, // 0.64851, -0.7612 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe50cc09f59a09b, 0xbfe81a1b33b57acc, // 0.65781, -0.75319 + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914 + 0x3fe5581038975137, 0xbfe7d7836cc33db2, // 0.667, -0.74506 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe5a28d2a5d7250, 0xbfe79400574f55e4, // 0.67609, -0.73682 + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265 + 0x3fe5ec3495837074, 0xbfe74f948da8d28d, // 0.68508, -0.72846 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe63503a31c1be8, 0xbfe70a42b3176d7a, // 0.69397, -0.72 + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573 + 0x3fe67cf78491af10, 0xbfe6c40d73c18275, // 0.70275, -0.71143 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe6c40d73c18275, 0xbfe67cf78491af10, // 0.71143, -0.70275 + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838 + 0x3fe70a42b3176d7a, 0xbfe63503a31c1be8, // 0.72, -0.69397 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe74f948da8d28d, 0xbfe5ec3495837074, // 0.72846, -0.68508 + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806 + 0x3fe79400574f55e4, 0xbfe5a28d2a5d7250, // 0.73682, -0.67609 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe7d7836cc33db2, 0xbfe5581038975137, // 0.74506, -0.667 + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242 + 0x3fe81a1b33b57acc, 0xbfe50cc09f59a09b, // 0.75319, -0.65781 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe85bc51ae958cc, 0xbfe4c0a145ec0004, // 0.7612, -0.64851 + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383 + 0x3fe89c7e9a4dd4ab, 0xbfe473b51b987347, // 0.7691, -0.63912 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe8dc45331698cc, 0xbfe425ff178e6bb1, // 0.77689, -0.62964 + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486 + 0x3fe91b166fd49da2, 0xbfe3d78238c58343, // 0.78456, -0.62006 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe958efe48e6dd7, 0xbfe3884185dfeb22, // 0.79211, -0.61038 + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551 + 0x3fe995cf2ed80d22, 0xbfe338400d0c8e57, // 0.79954, -0.60062 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // 0.80685, -0.59076 + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858 + 0x3fea0c95eabaf937, 0xbfe2960727629ca8, // 0.81404, -0.58081 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea4678c8119ac8, 0xbfe243d5fb98ac1f, // 0.8211, -0.57078 + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573 + 0x3fea7f58529fe69d, 0xbfe1f0f08bbc861b, // 0.82805, -0.56066 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3feab7325916c0d4, 0xbfe19d5a09f2b9b8, // 0.83486, -0.55046 + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532 + 0x3feaee04b43c1474, 0xbfe14915af336ceb, // 0.84155, -0.54017 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feb23cd470013b4, 0xbfe0f426bb2a8e7d, // 0.84812, -0.5298 + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459 + 0x3feb5889fe921405, 0xbfe09e907417c5e1, // 0.85456, -0.51936 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feb8c38d27504e9, 0xbfe0485626ae221a, // 0.86087, -0.50883 + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354 + 0x3febbed7c49380ea, 0xbfdfe2f64be7120f, // 0.86705, -0.49823 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3febf064e15377dd, 0xbfdf3405963fd068, // 0.87309, -0.48755 + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218 + 0x3fec20de3fa971b0, 0xbfde83e0eaf85113, // 0.87901, -0.4768 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec5042012b6907, 0xbfddd28f1481cc58, // 0.8848, -0.46598 + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054 + 0x3fec7e8e52233cf3, 0xbfdd2016e8e9db5b, // 0.89045, -0.45508 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3fecabc169a0b901, 0xbfdc6c7f4997000a, // 0.89597, -0.44412 + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862 + 0x3fecd7d9898b32f6, 0xbfdbb7cf2304bd01, // 0.90135, -0.43309 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fed02d4feb2bd92, 0xbfdb020d6c7f4009, // 0.9066, -0.422 + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643 + 0x3fed2cb220e0ef9f, 0xbfda4b4127dea1e4, // 0.91171, -0.41084 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed556f52e93eb1, 0xbfd993716141bdfe, // 0.91668, -0.39962 + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399 + 0x3fed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // 0.92151, -0.38835 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3feda383a9668988, 0xbfd820e3b04eaac4, // 0.92621, -0.37701 + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132 + 0x3fedc8d7cb410260, 0xbfd766340f2418f6, // 0.93077, -0.36561 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3feded05f7de47da, 0xbfd6aa9d7dc77e16, // 0.93518, -0.35416 + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842 + 0x3fee100cca2980ac, 0xbfd5ee27379ea693, // 0.93946, -0.34266 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee31eae870ce25, 0xbfd530d880af3c24, // 0.94359, -0.33111 + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531 + 0x3fee529f04729ffc, 0xbfd472b8a5571054, // 0.94759, -0.3195 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee7227db6a9744, 0xbfd3b3cefa0414b7, // 0.95144, -0.30785 + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201 + 0x3fee9084361df7f3, 0xbfd2f422daec0386, // 0.95514, -0.29615 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3feeadb2e8e7a88e, 0xbfd233bbabc3bb72, // 0.9587, -0.28441 + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852 + 0x3feec9b2d3c3bf84, 0xbfd172a0d7765177, // 0.96212, -0.27262 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3feee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // 0.96539, -0.26079 + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487 + 0x3feefe220c0b95ec, 0xbfcfdcdc1adfedf8, // 0.96852, -0.24893 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef168f53f7205d, 0xbfce56ca1e101a1b, // 0.9715, -0.23702 + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106 + 0x3fef2dc9c9089a9d, 0xbfcccf8cb312b286, // 0.97434, -0.22508 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef43d085ff92dd, 0xbfcb4732ef3d6722, // 0.97703, -0.21311 + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711 + 0x3fef58a2b1789e84, 0xbfc9bdcbf2dc4366, // 0.97957, -0.2011 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef6c3f7df5bbb7, 0xbfc83366e89c64c5, // 0.98196, -0.18907 + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304 + 0x3fef7ea629e63d6e, 0xbfc6a81304f64ab2, // 0.98421, -0.177 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef8fd5ffae41db, 0xbfc51bdf8597c5f2, // 0.98631, -0.16491 + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886 + 0x3fef9fce55adb2c8, 0xbfc38edbb0cd8d14, // 0.98826, -0.1528 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefae8e8e46cfbb, 0xbfc20116d4ec7bce, // 0.99006, -0.14066 + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458 + 0x3fefbc1617e44186, 0xbfc072a047ba831d, // 0.99171, -0.1285 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefc8646cfeb721, 0xbfbdc70ecbae9fc8, // 0.99321, -0.11632 + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022 + 0x3fefd37914220b84, 0xbfbaa7b724495c04, // 0.99456, -0.10412 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518, -0.098017 + 0x3fefdd539ff1f456, 0xbfb787586a5d5b21, // 0.99577, -0.091909 + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631, -0.085797 + 0x3fefe5f3af2e3940, 0xbfb4661179272096, // 0.99682, -0.079682 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729, -0.073565 + 0x3fefed58ecb673c4, 0xbfb1440134d709b2, // 0.99772, -0.067444 + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812, -0.061321 + 0x3feff3830f8d575c, 0xbfac428d12c0d7e3, // 0.99848, -0.055195 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988, -0.049068 + 0x3feff871dadb81df, 0xbfa5fc00d290cd43, // 0.99908, -0.042938 + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932, -0.036807 + 0x3feffc251df1d3f8, 0xbf9f693731d1cf01, // 0.99953, -0.030675 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997, -0.024541 + 0x3feffe9cb44b51a1, 0xbf92d936bbe30efd, // 0.99983, -0.018407 + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992, -0.012272 + 0x3fefffd8858e8a92, 0xbf7921f0fe670071, // 0.99998,-0.0061359 +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 2048, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_2048[4096] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3feffff621621d02, 0x3f6921f8becca4ba, // 1, 0.003068 + 0x3fefffd8858e8a92, 0x3f7921f0fe670071, // 0.99998, 0.0061359 + 0x3fefffa72c978c4f, 0x3f82d96b0e509703, // 0.99996, 0.0092038 + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272 + 0x3fefff0943c53bd1, 0x3f8f6a296ab997ca, // 0.99988, 0.015339 + 0x3feffe9cb44b51a1, 0x3f92d936bbe30efd, // 0.99983, 0.018407 + 0x3feffe1c6870cb77, 0x3f95fd4d21fab226, // 0.99977, 0.021474 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feffce09ce2a679, 0x3f9c454f4ce53b1c, // 0.99962, 0.027608 + 0x3feffc251df1d3f8, 0x3f9f693731d1cf01, // 0.99953, 0.030675 + 0x3feffb55e425fdae, 0x3fa14685db42c17e, // 0.99943, 0.033741 + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807 + 0x3feff97c4208c014, 0x3fa46a396ff86179, // 0.9992, 0.039873 + 0x3feff871dadb81df, 0x3fa5fc00d290cd43, // 0.99908, 0.042938 + 0x3feff753bb1b9164, 0x3fa78dbaa5874685, // 0.99894, 0.046003 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feff4dc54b1bed3, 0x3faab101bd5f8317, // 0.99864, 0.052132 + 0x3feff3830f8d575c, 0x3fac428d12c0d7e3, // 0.99848, 0.055195 + 0x3feff21614e131ed, 0x3fadd406f9808ec8, // 0.9983, 0.058258 + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321 + 0x3fefef0102826191, 0x3fb07b614e463064, // 0.99793, 0.064383 + 0x3fefed58ecb673c4, 0x3fb1440134d709b2, // 0.99772, 0.067444 + 0x3fefeb9d2530410f, 0x3fb20c9674ed444c, // 0.99751, 0.070505 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefe7ea85482d60, 0x3fb39d9f12c5a299, // 0.99706, 0.076624 + 0x3fefe5f3af2e3940, 0x3fb4661179272096, // 0.99682, 0.079682 + 0x3fefe3e92be9d886, 0x3fb52e774a4d4d0a, // 0.99657, 0.08274 + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797 + 0x3fefdf9922f73307, 0x3fb6bf1b3e79b129, // 0.99604, 0.088854 + 0x3fefdd539ff1f456, 0x3fb787586a5d5b21, // 0.99577, 0.091909 + 0x3fefdafa7514538c, 0x3fb84f8712c130a0, // 0.99548, 0.094963 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefd60d2da75c9e, 0x3fb9dfb6eb24a85c, // 0.99488, 0.10107 + 0x3fefd37914220b84, 0x3fbaa7b724495c04, // 0.99456, 0.10412 + 0x3fefd0d158d86087, 0x3fbb6fa6ec38f64c, // 0.99424, 0.10717 + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022 + 0x3fefcb4703914354, 0x3fbcff533b307dc1, // 0.99356, 0.11327 + 0x3fefc8646cfeb721, 0x3fbdc70ecbae9fc8, // 0.99321, 0.11632 + 0x3fefc56e3b7d9af6, 0x3fbe8eb7fde4aa3e, // 0.99285, 0.11937 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefbf470f0a8d88, 0x3fc00ee8ad6fb85b, // 0.9921, 0.12545 + 0x3fefbc1617e44186, 0x3fc072a047ba831d, // 0.99171, 0.1285 + 0x3fefb8d18d66adb7, 0x3fc0d64dbcb26786, // 0.99131, 0.13154 + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458 + 0x3fefb20dc681d54d, 0x3fc19d8940be24e7, // 0.99049, 0.13762 + 0x3fefae8e8e46cfbb, 0x3fc20116d4ec7bce, // 0.99006, 0.14066 + 0x3fefaafbcb0cfddc, 0x3fc264994dfd340a, // 0.98962, 0.1437 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fefa39bac7a1791, 0x3fc32b7bf94516a7, // 0.98872, 0.14976 + 0x3fef9fce55adb2c8, 0x3fc38edbb0cd8d14, // 0.98826, 0.1528 + 0x3fef9bed7cfbde29, 0x3fc3f22f57db4893, // 0.98778, 0.15583 + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886 + 0x3fef93f14f85ac08, 0x3fc4b8b17f79fa88, // 0.98681, 0.16189 + 0x3fef8fd5ffae41db, 0x3fc51bdf8597c5f2, // 0.98631, 0.16491 + 0x3fef8ba737cb4b78, 0x3fc57f008654cbde, // 0.9858, 0.16794 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef830f4a40c60c, 0x3fc6451a831d830d, // 0.98475, 0.17398 + 0x3fef7ea629e63d6e, 0x3fc6a81304f64ab2, // 0.98421, 0.177 + 0x3fef7a299c1a322a, 0x3fc70afd8d08c4ff, // 0.98366, 0.18002 + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304 + 0x3fef70f6434b7eb7, 0x3fc7d0a7bbd2cb1b, // 0.98254, 0.18606 + 0x3fef6c3f7df5bbb7, 0x3fc83366e89c64c5, // 0.98196, 0.18907 + 0x3fef677556883cee, 0x3fc8961727c41804, // 0.98138, 0.19208 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef5da6ed43685d, 0x3fc95b49e9b62af9, // 0.98018, 0.1981 + 0x3fef58a2b1789e84, 0x3fc9bdcbf2dc4366, // 0.97957, 0.2011 + 0x3fef538b1faf2d07, 0x3fca203e1b1831da, // 0.97895, 0.20411 + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711 + 0x3fef492206bcabb4, 0x3fcae4f1d5f3b9ab, // 0.97768, 0.21011 + 0x3fef43d085ff92dd, 0x3fcb4732ef3d6722, // 0.97703, 0.21311 + 0x3fef3e6bbc1bbc65, 0x3fcba96334f15dad, // 0.97637, 0.21611 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef33685a3aaef0, 0x3fcc6d90535d74dc, // 0.97503, 0.22209 + 0x3fef2dc9c9089a9d, 0x3fcccf8cb312b286, // 0.97434, 0.22508 + 0x3fef2817fc4609ce, 0x3fcd31774d2cbdee, // 0.97364, 0.22807 + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106 + 0x3fef1c7abe284708, 0x3fcdf5163f01099a, // 0.97223, 0.23404 + 0x3fef168f53f7205d, 0x3fce56ca1e101a1b, // 0.9715, 0.23702 + 0x3fef1090bc898f5f, 0x3fceb86b462de348, // 0.97077, 0.24 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3fef045a14cf738c, 0x3fcf7b7480bd3801, // 0.96928, 0.24596 + 0x3feefe220c0b95ec, 0x3fcfdcdc1adfedf8, // 0.96852, 0.24893 + 0x3feef7d6e51ca3c0, 0x3fd01f1806b9fdd2, // 0.96775, 0.2519 + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487 + 0x3feeeb074c50a544, 0x3fd0804e05eb661e, // 0.96619, 0.25783 + 0x3feee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // 0.96539, 0.26079 + 0x3feeddeb6a078651, 0x3fd0e15b4e1749cd, // 0.96459, 0.26375 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3feed0835e999009, 0x3fd1423eefc69378, // 0.96295, 0.26967 + 0x3feec9b2d3c3bf84, 0x3fd172a0d7765177, // 0.96212, 0.27262 + 0x3feec2cf4b1af6b2, 0x3fd1a2f7fbe8f243, // 0.96128, 0.27557 + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852 + 0x3feeb4cf515b8811, 0x3fd2038583d727bd, // 0.95957, 0.28146 + 0x3feeadb2e8e7a88e, 0x3fd233bbabc3bb72, // 0.9587, 0.28441 + 0x3feea68393e65800, 0x3fd263e6995554ba, // 0.95783, 0.28735 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3fee97ec36016b30, 0x3fd2c41a4e954520, // 0.95605, 0.29322 + 0x3fee9084361df7f3, 0x3fd2f422daec0386, // 0.95514, 0.29615 + 0x3fee89095bad6025, 0x3fd3241fb638baaf, // 0.95423, 0.29908 + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201 + 0x3fee79db29a5165a, 0x3fd383f5e353b6aa, // 0.95238, 0.30493 + 0x3fee7227db6a9744, 0x3fd3b3cefa0414b7, // 0.95144, 0.30785 + 0x3fee6a61c55d53a7, 0x3fd3e39be96ec271, // 0.95049, 0.31077 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee5a9d550467d3, 0x3fd44310dc8936f0, // 0.94856, 0.31659 + 0x3fee529f04729ffc, 0x3fd472b8a5571054, // 0.94759, 0.3195 + 0x3fee4a8dff81ce5e, 0x3fd4a253d11b82f3, // 0.9466, 0.32241 + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531 + 0x3fee3a33ec75ce85, 0x3fd50163dc197047, // 0.9446, 0.32821 + 0x3fee31eae870ce25, 0x3fd530d880af3c24, // 0.94359, 0.33111 + 0x3fee298f4439197a, 0x3fd5604012f467b4, // 0.94257, 0.334 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fee18a02fdc66d9, 0x3fd5bee78b9db3b6, // 0.94051, 0.33978 + 0x3fee100cca2980ac, 0x3fd5ee27379ea693, // 0.93946, 0.34266 + 0x3fee0766d9280f54, 0x3fd61d595c88c203, // 0.9384, 0.34554 + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842 + 0x3fedf5e36a9ba59c, 0x3fd67b949cad63ca, // 0.93627, 0.35129 + 0x3feded05f7de47da, 0x3fd6aa9d7dc77e16, // 0.93518, 0.35416 + 0x3fede4160f6d8d81, 0x3fd6d998638a0cb5, // 0.93409, 0.35703 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fedd1fef38a915a, 0x3fd73763c9261092, // 0.93188, 0.36276 + 0x3fedc8d7cb410260, 0x3fd766340f2418f6, // 0.93077, 0.36561 + 0x3fedbf9e4395759a, 0x3fd794f5e613dfae, // 0.92964, 0.36847 + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132 + 0x3fedacf42ce68ab9, 0x3fd7f24dd37341e3, // 0.92736, 0.37416 + 0x3feda383a9668988, 0x3fd820e3b04eaac4, // 0.92621, 0.37701 + 0x3fed9a00dd8b3d46, 0x3fd84f6aaaf3903f, // 0.92505, 0.37985 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed86c48445a450, 0x3fd8ac4b86d5ed44, // 0.9227, 0.38552 + 0x3fed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // 0.92151, 0.38835 + 0x3fed733f508c0dff, 0x3fd908ef81ef7bd1, // 0.92032, 0.39117 + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399 + 0x3fed5f7172888a7f, 0x3fd96555b7ab948f, // 0.9179, 0.39681 + 0x3fed556f52e93eb1, 0x3fd993716141bdfe, // 0.91668, 0.39962 + 0x3fed4b5b1b187524, 0x3fd9c17d440df9f2, // 0.91545, 0.40243 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed36fc7bcbfbdc, 0x3fda1d6543b50ac0, // 0.91296, 0.40804 + 0x3fed2cb220e0ef9f, 0x3fda4b4127dea1e4, // 0.91171, 0.41084 + 0x3fed2255c6e5a4e1, 0x3fda790cd3dbf31a, // 0.91044, 0.41364 + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643 + 0x3fed0d672f59d2b9, 0x3fdad473125cdc08, // 0.90789, 0.41922 + 0x3fed02d4feb2bd92, 0x3fdb020d6c7f4009, // 0.9066, 0.422 + 0x3fecf830e8ce467b, 0x3fdb2f971db31972, // 0.9053, 0.42478 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fece2b32799a060, 0x3fdb8a7814fd5693, // 0.90267, 0.43033 + 0x3fecd7d9898b32f6, 0x3fdbb7cf2304bd01, // 0.90135, 0.43309 + 0x3fecccee20c2de9f, 0x3fdbe51517ffc0d9, // 0.90002, 0.43586 + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862 + 0x3fecb6e20a00da99, 0x3fdc3f6d47263129, // 0.89732, 0.44137 + 0x3fecabc169a0b901, 0x3fdc6c7f4997000a, // 0.89597, 0.44412 + 0x3feca08f19b9c449, 0x3fdc997fc3865388, // 0.8946, 0.44687 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3fec89f587029c13, 0x3fdcf34baee1cd21, // 0.89184, 0.45235 + 0x3fec7e8e52233cf3, 0x3fdd2016e8e9db5b, // 0.89045, 0.45508 + 0x3fec7315899eaad7, 0x3fdd4cd02ba8609c, // 0.88905, 0.45781 + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054 + 0x3fec5bef59fef85a, 0x3fdda60c5cfa10d8, // 0.88622, 0.46326 + 0x3fec5042012b6907, 0x3fddd28f1481cc58, // 0.8848, 0.46598 + 0x3fec44833141c004, 0x3fddfeff66a941de, // 0.88336, 0.46869 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec2cd14931e3f1, 0x3fde57a86d3cd824, // 0.88047, 0.4741 + 0x3fec20de3fa971b0, 0x3fde83e0eaf85113, // 0.87901, 0.4768 + 0x3fec14d9dc465e58, 0x3fdeb00695f25620, // 0.87755, 0.47949 + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218 + 0x3febfc9d25a1b147, 0x3fdf081906bff7fd, // 0.87459, 0.48487 + 0x3febf064e15377dd, 0x3fdf3405963fd068, // 0.87309, 0.48755 + 0x3febe41b611154c1, 0x3fdf5fdee656cda3, // 0.8716, 0.49023 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3febcb54cb0d2327, 0x3fdfb7575c24d2de, // 0.86857, 0.49557 + 0x3febbed7c49380ea, 0x3fdfe2f64be7120f, // 0.86705, 0.49823 + 0x3febb249a0b6c40d, 0x3fe00740c82b82e0, // 0.86551, 0.50089 + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354 + 0x3feb98fa1fd9155e, 0x3fe032ae55edbd95, // 0.86242, 0.50619 + 0x3feb8c38d27504e9, 0x3fe0485626ae221a, // 0.86087, 0.50883 + 0x3feb7f6686e792ea, 0x3fe05df3ec31b8b6, // 0.8593, 0.51147 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb658f14fdbc47, 0x3fe089112032b08c, // 0.85615, 0.51673 + 0x3feb5889fe921405, 0x3fe09e907417c5e1, // 0.85456, 0.51936 + 0x3feb4b7409de7925, 0x3fe0b405878f85ec, // 0.85296, 0.52198 + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459 + 0x3feb3115a5f37bf4, 0x3fe0ded0b84bc4b5, // 0.84974, 0.5272 + 0x3feb23cd470013b4, 0x3fe0f426bb2a8e7d, // 0.84812, 0.5298 + 0x3feb16742a4ca2f5, 0x3fe1097248d0a956, // 0.84649, 0.5324 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3feafb8fd89f57b6, 0x3fe133e9cfee254e, // 0.84321, 0.53759 + 0x3feaee04b43c1474, 0x3fe14915af336ceb, // 0.84155, 0.54017 + 0x3feae068f345ecef, 0x3fe15e36e4dbe2bc, // 0.83989, 0.54275 + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532 + 0x3feac4ffbd3efac8, 0x3fe188591f3a46e5, // 0.83655, 0.54789 + 0x3feab7325916c0d4, 0x3fe19d5a09f2b9b8, // 0.83486, 0.55046 + 0x3feaa9547a2cb98e, 0x3fe1b250171373be, // 0.83317, 0.55302 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3fea8d676e545ad2, 0x3fe1dc1b64dc4872, // 0.82976, 0.55812 + 0x3fea7f58529fe69d, 0x3fe1f0f08bbc861b, // 0.82805, 0.56066 + 0x3fea7138de9d60f5, 0x3fe205baa17560d6, // 0.82632, 0.5632 + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573 + 0x3fea54c91090f524, 0x3fe22f2d662c13e1, // 0.82285, 0.56826 + 0x3fea4678c8119ac8, 0x3fe243d5fb98ac1f, // 0.8211, 0.57078 + 0x3fea38184a593bc6, 0x3fe258734cbb7110, // 0.81935, 0.5733 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fea1b26d2c0a75e, 0x3fe2818bef4d3cba, // 0.81581, 0.57831 + 0x3fea0c95eabaf937, 0x3fe2960727629ca8, // 0.81404, 0.58081 + 0x3fe9fdf4f13149de, 0x3fe2aa76e87aeb58, // 0.81225, 0.58331 + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858 + 0x3fe9e082edb42472, 0x3fe2d333d34e9bb7, // 0.80866, 0.58828 + 0x3fe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // 0.80685, 0.59076 + 0x3fe9c2d110f075c3, 0x3fe2fbc24b441015, // 0.80503, 0.59323 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe9a4dfa42b06b2, 0x3fe32421ec49a620, // 0.80138, 0.59816 + 0x3fe995cf2ed80d22, 0x3fe338400d0c8e57, // 0.79954, 0.60062 + 0x3fe986aef1457594, 0x3fe34c5252c14de1, // 0.79769, 0.60307 + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551 + 0x3fe9683f42bd7fe1, 0x3fe374531b817f8d, // 0.79398, 0.60795 + 0x3fe958efe48e6dd7, 0x3fe3884185dfeb22, // 0.79211, 0.61038 + 0x3fe94990e3ac4a6c, 0x3fe39c23e3d63029, // 0.79023, 0.61281 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe92aa41fc5a815, 0x3fe3c3c44981c517, // 0.78646, 0.61765 + 0x3fe91b166fd49da2, 0x3fe3d78238c58343, // 0.78456, 0.62006 + 0x3fe90b7943575efe, 0x3fe3eb33eabe0680, // 0.78265, 0.62246 + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486 + 0x3fe8ec109b486c49, 0x3fe41272663d108c, // 0.77882, 0.62725 + 0x3fe8dc45331698cc, 0x3fe425ff178e6bb1, // 0.77689, 0.62964 + 0x3fe8cc6a75184655, 0x3fe4397f5b2a4380, // 0.77495, 0.63202 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe8ac871ede1d88, 0x3fe4605a692b32a2, // 0.77106, 0.63676 + 0x3fe89c7e9a4dd4ab, 0x3fe473b51b987347, // 0.7691, 0.63912 + 0x3fe88c66e7481ba1, 0x3fe48703306091fe, // 0.76714, 0.64148 + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383 + 0x3fe86c0a1d9aa195, 0x3fe4ad79516722f0, // 0.76319, 0.64618 + 0x3fe85bc51ae958cc, 0x3fe4c0a145ec0004, // 0.7612, 0.64851 + 0x3fe84b7111af83f9, 0x3fe4d3bc6d589f80, // 0.75921, 0.65085 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe82a9c13f545ff, 0x3fe4f9cc25cca486, // 0.7552, 0.65549 + 0x3fe81a1b33b57acc, 0x3fe50cc09f59a09b, // 0.75319, 0.65781 + 0x3fe8098b756e52fa, 0x3fe51fa81cd99aa6, // 0.75117, 0.66011 + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242 + 0x3fe7e83f87b03686, 0x3fe5454ff5159dfb, // 0.7471, 0.66471 + 0x3fe7d7836cc33db2, 0x3fe5581038975137, // 0.74506, 0.667 + 0x3fe7c6b89ce2d333, 0x3fe56ac35197649e, // 0.74301, 0.66928 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe7a4f707bf97d2, 0x3fe59001d5f723df, // 0.73889, 0.67383 + 0x3fe79400574f55e4, 0x3fe5a28d2a5d7250, // 0.73682, 0.67609 + 0x3fe782fb1b90b35b, 0x3fe5b50b264f7448, // 0.73474, 0.67835 + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806 + 0x3fe760c52c304764, 0x3fe5d9dee73e345c, // 0.73056, 0.68285 + 0x3fe74f948da8d28d, 0x3fe5ec3495837074, // 0.72846, 0.68508 + 0x3fe73e558e079942, 0x3fe5fe7cbde56a0f, // 0.72636, 0.68732 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe71bac960e41bf, 0x3fe622e44fec22ff, // 0.72213, 0.69176 + 0x3fe70a42b3176d7a, 0x3fe63503a31c1be8, // 0.72, 0.69397 + 0x3fe6f8ca99c95b75, 0x3fe64715437f535b, // 0.71787, 0.69618 + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838 + 0x3fe6d5afef4aafcc, 0x3fe66b0f3f52b386, // 0.71358, 0.70057 + 0x3fe6c40d73c18275, 0x3fe67cf78491af10, // 0.71143, 0.70275 + 0x3fe6b25ced2fe29c, 0x3fe68ed1eaa19c71, // 0.70927, 0.70493 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe68ed1eaa19c71, 0x3fe6b25ced2fe29c, // 0.70493, 0.70927 + 0x3fe67cf78491af10, 0x3fe6c40d73c18275, // 0.70275, 0.71143 + 0x3fe66b0f3f52b386, 0x3fe6d5afef4aafcc, // 0.70057, 0.71358 + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573 + 0x3fe64715437f535b, 0x3fe6f8ca99c95b75, // 0.69618, 0.71787 + 0x3fe63503a31c1be8, 0x3fe70a42b3176d7a, // 0.69397, 0.72 + 0x3fe622e44fec22ff, 0x3fe71bac960e41bf, // 0.69176, 0.72213 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe5fe7cbde56a0f, 0x3fe73e558e079942, // 0.68732, 0.72636 + 0x3fe5ec3495837074, 0x3fe74f948da8d28d, // 0.68508, 0.72846 + 0x3fe5d9dee73e345c, 0x3fe760c52c304764, // 0.68285, 0.73056 + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265 + 0x3fe5b50b264f7448, 0x3fe782fb1b90b35b, // 0.67835, 0.73474 + 0x3fe5a28d2a5d7250, 0x3fe79400574f55e4, // 0.67609, 0.73682 + 0x3fe59001d5f723df, 0x3fe7a4f707bf97d2, // 0.67383, 0.73889 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe56ac35197649e, 0x3fe7c6b89ce2d333, // 0.66928, 0.74301 + 0x3fe5581038975137, 0x3fe7d7836cc33db2, // 0.667, 0.74506 + 0x3fe5454ff5159dfb, 0x3fe7e83f87b03686, // 0.66471, 0.7471 + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914 + 0x3fe51fa81cd99aa6, 0x3fe8098b756e52fa, // 0.66011, 0.75117 + 0x3fe50cc09f59a09b, 0x3fe81a1b33b57acc, // 0.65781, 0.75319 + 0x3fe4f9cc25cca486, 0x3fe82a9c13f545ff, // 0.65549, 0.7552 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe4d3bc6d589f80, 0x3fe84b7111af83f9, // 0.65085, 0.75921 + 0x3fe4c0a145ec0004, 0x3fe85bc51ae958cc, // 0.64851, 0.7612 + 0x3fe4ad79516722f0, 0x3fe86c0a1d9aa195, // 0.64618, 0.76319 + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517 + 0x3fe48703306091fe, 0x3fe88c66e7481ba1, // 0.64148, 0.76714 + 0x3fe473b51b987347, 0x3fe89c7e9a4dd4ab, // 0.63912, 0.7691 + 0x3fe4605a692b32a2, 0x3fe8ac871ede1d88, // 0.63676, 0.77106 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe4397f5b2a4380, 0x3fe8cc6a75184655, // 0.63202, 0.77495 + 0x3fe425ff178e6bb1, 0x3fe8dc45331698cc, // 0.62964, 0.77689 + 0x3fe41272663d108c, 0x3fe8ec109b486c49, // 0.62725, 0.77882 + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074 + 0x3fe3eb33eabe0680, 0x3fe90b7943575efe, // 0.62246, 0.78265 + 0x3fe3d78238c58343, 0x3fe91b166fd49da2, // 0.62006, 0.78456 + 0x3fe3c3c44981c517, 0x3fe92aa41fc5a815, // 0.61765, 0.78646 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe39c23e3d63029, 0x3fe94990e3ac4a6c, // 0.61281, 0.79023 + 0x3fe3884185dfeb22, 0x3fe958efe48e6dd7, // 0.61038, 0.79211 + 0x3fe374531b817f8d, 0x3fe9683f42bd7fe1, // 0.60795, 0.79398 + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584 + 0x3fe34c5252c14de1, 0x3fe986aef1457594, // 0.60307, 0.79769 + 0x3fe338400d0c8e57, 0x3fe995cf2ed80d22, // 0.60062, 0.79954 + 0x3fe32421ec49a620, 0x3fe9a4dfa42b06b2, // 0.59816, 0.80138 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe2fbc24b441015, 0x3fe9c2d110f075c3, // 0.59323, 0.80503 + 0x3fe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // 0.59076, 0.80685 + 0x3fe2d333d34e9bb7, 0x3fe9e082edb42472, // 0.58828, 0.80866 + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046 + 0x3fe2aa76e87aeb58, 0x3fe9fdf4f13149de, // 0.58331, 0.81225 + 0x3fe2960727629ca8, 0x3fea0c95eabaf937, // 0.58081, 0.81404 + 0x3fe2818bef4d3cba, 0x3fea1b26d2c0a75e, // 0.57831, 0.81581 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe258734cbb7110, 0x3fea38184a593bc6, // 0.5733, 0.81935 + 0x3fe243d5fb98ac1f, 0x3fea4678c8119ac8, // 0.57078, 0.8211 + 0x3fe22f2d662c13e1, 0x3fea54c91090f524, // 0.56826, 0.82285 + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459 + 0x3fe205baa17560d6, 0x3fea7138de9d60f5, // 0.5632, 0.82632 + 0x3fe1f0f08bbc861b, 0x3fea7f58529fe69d, // 0.56066, 0.82805 + 0x3fe1dc1b64dc4872, 0x3fea8d676e545ad2, // 0.55812, 0.82976 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe1b250171373be, 0x3feaa9547a2cb98e, // 0.55302, 0.83317 + 0x3fe19d5a09f2b9b8, 0x3feab7325916c0d4, // 0.55046, 0.83486 + 0x3fe188591f3a46e5, 0x3feac4ffbd3efac8, // 0.54789, 0.83655 + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822 + 0x3fe15e36e4dbe2bc, 0x3feae068f345ecef, // 0.54275, 0.83989 + 0x3fe14915af336ceb, 0x3feaee04b43c1474, // 0.54017, 0.84155 + 0x3fe133e9cfee254e, 0x3feafb8fd89f57b6, // 0.53759, 0.84321 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe1097248d0a956, 0x3feb16742a4ca2f5, // 0.5324, 0.84649 + 0x3fe0f426bb2a8e7d, 0x3feb23cd470013b4, // 0.5298, 0.84812 + 0x3fe0ded0b84bc4b5, 0x3feb3115a5f37bf4, // 0.5272, 0.84974 + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136 + 0x3fe0b405878f85ec, 0x3feb4b7409de7925, // 0.52198, 0.85296 + 0x3fe09e907417c5e1, 0x3feb5889fe921405, // 0.51936, 0.85456 + 0x3fe089112032b08c, 0x3feb658f14fdbc47, // 0.51673, 0.85615 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe05df3ec31b8b6, 0x3feb7f6686e792ea, // 0.51147, 0.8593 + 0x3fe0485626ae221a, 0x3feb8c38d27504e9, // 0.50883, 0.86087 + 0x3fe032ae55edbd95, 0x3feb98fa1fd9155e, // 0.50619, 0.86242 + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397 + 0x3fe00740c82b82e0, 0x3febb249a0b6c40d, // 0.50089, 0.86551 + 0x3fdfe2f64be7120f, 0x3febbed7c49380ea, // 0.49823, 0.86705 + 0x3fdfb7575c24d2de, 0x3febcb54cb0d2327, // 0.49557, 0.86857 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fdf5fdee656cda3, 0x3febe41b611154c1, // 0.49023, 0.8716 + 0x3fdf3405963fd068, 0x3febf064e15377dd, // 0.48755, 0.87309 + 0x3fdf081906bff7fd, 0x3febfc9d25a1b147, // 0.48487, 0.87459 + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607 + 0x3fdeb00695f25620, 0x3fec14d9dc465e58, // 0.47949, 0.87755 + 0x3fde83e0eaf85113, 0x3fec20de3fa971b0, // 0.4768, 0.87901 + 0x3fde57a86d3cd824, 0x3fec2cd14931e3f1, // 0.4741, 0.88047 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fddfeff66a941de, 0x3fec44833141c004, // 0.46869, 0.88336 + 0x3fddd28f1481cc58, 0x3fec5042012b6907, // 0.46598, 0.8848 + 0x3fdda60c5cfa10d8, 0x3fec5bef59fef85a, // 0.46326, 0.88622 + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764 + 0x3fdd4cd02ba8609c, 0x3fec7315899eaad7, // 0.45781, 0.88905 + 0x3fdd2016e8e9db5b, 0x3fec7e8e52233cf3, // 0.45508, 0.89045 + 0x3fdcf34baee1cd21, 0x3fec89f587029c13, // 0.45235, 0.89184 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdc997fc3865388, 0x3feca08f19b9c449, // 0.44687, 0.8946 + 0x3fdc6c7f4997000a, 0x3fecabc169a0b901, // 0.44412, 0.89597 + 0x3fdc3f6d47263129, 0x3fecb6e20a00da99, // 0.44137, 0.89732 + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867 + 0x3fdbe51517ffc0d9, 0x3fecccee20c2de9f, // 0.43586, 0.90002 + 0x3fdbb7cf2304bd01, 0x3fecd7d9898b32f6, // 0.43309, 0.90135 + 0x3fdb8a7814fd5693, 0x3fece2b32799a060, // 0.43033, 0.90267 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdb2f971db31972, 0x3fecf830e8ce467b, // 0.42478, 0.9053 + 0x3fdb020d6c7f4009, 0x3fed02d4feb2bd92, // 0.422, 0.9066 + 0x3fdad473125cdc08, 0x3fed0d672f59d2b9, // 0.41922, 0.90789 + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917 + 0x3fda790cd3dbf31a, 0x3fed2255c6e5a4e1, // 0.41364, 0.91044 + 0x3fda4b4127dea1e4, 0x3fed2cb220e0ef9f, // 0.41084, 0.91171 + 0x3fda1d6543b50ac0, 0x3fed36fc7bcbfbdc, // 0.40804, 0.91296 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fd9c17d440df9f2, 0x3fed4b5b1b187524, // 0.40243, 0.91545 + 0x3fd993716141bdfe, 0x3fed556f52e93eb1, // 0.39962, 0.91668 + 0x3fd96555b7ab948f, 0x3fed5f7172888a7f, // 0.39681, 0.9179 + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911 + 0x3fd908ef81ef7bd1, 0x3fed733f508c0dff, // 0.39117, 0.92032 + 0x3fd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // 0.38835, 0.92151 + 0x3fd8ac4b86d5ed44, 0x3fed86c48445a450, // 0.38552, 0.9227 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd84f6aaaf3903f, 0x3fed9a00dd8b3d46, // 0.37985, 0.92505 + 0x3fd820e3b04eaac4, 0x3feda383a9668988, // 0.37701, 0.92621 + 0x3fd7f24dd37341e3, 0x3fedacf42ce68ab9, // 0.37416, 0.92736 + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851 + 0x3fd794f5e613dfae, 0x3fedbf9e4395759a, // 0.36847, 0.92964 + 0x3fd766340f2418f6, 0x3fedc8d7cb410260, // 0.36561, 0.93077 + 0x3fd73763c9261092, 0x3fedd1fef38a915a, // 0.36276, 0.93188 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd6d998638a0cb5, 0x3fede4160f6d8d81, // 0.35703, 0.93409 + 0x3fd6aa9d7dc77e16, 0x3feded05f7de47da, // 0.35416, 0.93518 + 0x3fd67b949cad63ca, 0x3fedf5e36a9ba59c, // 0.35129, 0.93627 + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734 + 0x3fd61d595c88c203, 0x3fee0766d9280f54, // 0.34554, 0.9384 + 0x3fd5ee27379ea693, 0x3fee100cca2980ac, // 0.34266, 0.93946 + 0x3fd5bee78b9db3b6, 0x3fee18a02fdc66d9, // 0.33978, 0.94051 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd5604012f467b4, 0x3fee298f4439197a, // 0.334, 0.94257 + 0x3fd530d880af3c24, 0x3fee31eae870ce25, // 0.33111, 0.94359 + 0x3fd50163dc197047, 0x3fee3a33ec75ce85, // 0.32821, 0.9446 + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561 + 0x3fd4a253d11b82f3, 0x3fee4a8dff81ce5e, // 0.32241, 0.9466 + 0x3fd472b8a5571054, 0x3fee529f04729ffc, // 0.3195, 0.94759 + 0x3fd44310dc8936f0, 0x3fee5a9d550467d3, // 0.31659, 0.94856 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd3e39be96ec271, 0x3fee6a61c55d53a7, // 0.31077, 0.95049 + 0x3fd3b3cefa0414b7, 0x3fee7227db6a9744, // 0.30785, 0.95144 + 0x3fd383f5e353b6aa, 0x3fee79db29a5165a, // 0.30493, 0.95238 + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331 + 0x3fd3241fb638baaf, 0x3fee89095bad6025, // 0.29908, 0.95423 + 0x3fd2f422daec0386, 0x3fee9084361df7f3, // 0.29615, 0.95514 + 0x3fd2c41a4e954520, 0x3fee97ec36016b30, // 0.29322, 0.95605 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd263e6995554ba, 0x3feea68393e65800, // 0.28735, 0.95783 + 0x3fd233bbabc3bb72, 0x3feeadb2e8e7a88e, // 0.28441, 0.9587 + 0x3fd2038583d727bd, 0x3feeb4cf515b8811, // 0.28146, 0.95957 + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043 + 0x3fd1a2f7fbe8f243, 0x3feec2cf4b1af6b2, // 0.27557, 0.96128 + 0x3fd172a0d7765177, 0x3feec9b2d3c3bf84, // 0.27262, 0.96212 + 0x3fd1423eefc69378, 0x3feed0835e999009, // 0.26967, 0.96295 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd0e15b4e1749cd, 0x3feeddeb6a078651, // 0.26375, 0.96459 + 0x3fd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // 0.26079, 0.96539 + 0x3fd0804e05eb661e, 0x3feeeb074c50a544, // 0.25783, 0.96619 + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698 + 0x3fd01f1806b9fdd2, 0x3feef7d6e51ca3c0, // 0.2519, 0.96775 + 0x3fcfdcdc1adfedf8, 0x3feefe220c0b95ec, // 0.24893, 0.96852 + 0x3fcf7b7480bd3801, 0x3fef045a14cf738c, // 0.24596, 0.96928 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fceb86b462de348, 0x3fef1090bc898f5f, // 0.24, 0.97077 + 0x3fce56ca1e101a1b, 0x3fef168f53f7205d, // 0.23702, 0.9715 + 0x3fcdf5163f01099a, 0x3fef1c7abe284708, // 0.23404, 0.97223 + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294 + 0x3fcd31774d2cbdee, 0x3fef2817fc4609ce, // 0.22807, 0.97364 + 0x3fcccf8cb312b286, 0x3fef2dc9c9089a9d, // 0.22508, 0.97434 + 0x3fcc6d90535d74dc, 0x3fef33685a3aaef0, // 0.22209, 0.97503 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fcba96334f15dad, 0x3fef3e6bbc1bbc65, // 0.21611, 0.97637 + 0x3fcb4732ef3d6722, 0x3fef43d085ff92dd, // 0.21311, 0.97703 + 0x3fcae4f1d5f3b9ab, 0x3fef492206bcabb4, // 0.21011, 0.97768 + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832 + 0x3fca203e1b1831da, 0x3fef538b1faf2d07, // 0.20411, 0.97895 + 0x3fc9bdcbf2dc4366, 0x3fef58a2b1789e84, // 0.2011, 0.97957 + 0x3fc95b49e9b62af9, 0x3fef5da6ed43685d, // 0.1981, 0.98018 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc8961727c41804, 0x3fef677556883cee, // 0.19208, 0.98138 + 0x3fc83366e89c64c5, 0x3fef6c3f7df5bbb7, // 0.18907, 0.98196 + 0x3fc7d0a7bbd2cb1b, 0x3fef70f6434b7eb7, // 0.18606, 0.98254 + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311 + 0x3fc70afd8d08c4ff, 0x3fef7a299c1a322a, // 0.18002, 0.98366 + 0x3fc6a81304f64ab2, 0x3fef7ea629e63d6e, // 0.177, 0.98421 + 0x3fc6451a831d830d, 0x3fef830f4a40c60c, // 0.17398, 0.98475 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc57f008654cbde, 0x3fef8ba737cb4b78, // 0.16794, 0.9858 + 0x3fc51bdf8597c5f2, 0x3fef8fd5ffae41db, // 0.16491, 0.98631 + 0x3fc4b8b17f79fa88, 0x3fef93f14f85ac08, // 0.16189, 0.98681 + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873 + 0x3fc3f22f57db4893, 0x3fef9bed7cfbde29, // 0.15583, 0.98778 + 0x3fc38edbb0cd8d14, 0x3fef9fce55adb2c8, // 0.1528, 0.98826 + 0x3fc32b7bf94516a7, 0x3fefa39bac7a1791, // 0.14976, 0.98872 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc264994dfd340a, 0x3fefaafbcb0cfddc, // 0.1437, 0.98962 + 0x3fc20116d4ec7bce, 0x3fefae8e8e46cfbb, // 0.14066, 0.99006 + 0x3fc19d8940be24e7, 0x3fefb20dc681d54d, // 0.13762, 0.99049 + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909 + 0x3fc0d64dbcb26786, 0x3fefb8d18d66adb7, // 0.13154, 0.99131 + 0x3fc072a047ba831d, 0x3fefbc1617e44186, // 0.1285, 0.99171 + 0x3fc00ee8ad6fb85b, 0x3fefbf470f0a8d88, // 0.12545, 0.9921 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fbe8eb7fde4aa3e, 0x3fefc56e3b7d9af6, // 0.11937, 0.99285 + 0x3fbdc70ecbae9fc8, 0x3fefc8646cfeb721, // 0.11632, 0.99321 + 0x3fbcff533b307dc1, 0x3fefcb4703914354, // 0.11327, 0.99356 + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391 + 0x3fbb6fa6ec38f64c, 0x3fefd0d158d86087, // 0.10717, 0.99424 + 0x3fbaa7b724495c04, 0x3fefd37914220b84, // 0.10412, 0.99456 + 0x3fb9dfb6eb24a85c, 0x3fefd60d2da75c9e, // 0.10107, 0.99488 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb84f8712c130a0, 0x3fefdafa7514538c, // 0.094963, 0.99548 + 0x3fb787586a5d5b21, 0x3fefdd539ff1f456, // 0.091909, 0.99577 + 0x3fb6bf1b3e79b129, 0x3fefdf9922f73307, // 0.088854, 0.99604 + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631 + 0x3fb52e774a4d4d0a, 0x3fefe3e92be9d886, // 0.08274, 0.99657 + 0x3fb4661179272096, 0x3fefe5f3af2e3940, // 0.079682, 0.99682 + 0x3fb39d9f12c5a299, 0x3fefe7ea85482d60, // 0.076624, 0.99706 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3fb20c9674ed444c, 0x3fefeb9d2530410f, // 0.070505, 0.99751 + 0x3fb1440134d709b2, 0x3fefed58ecb673c4, // 0.067444, 0.99772 + 0x3fb07b614e463064, 0x3fefef0102826191, // 0.064383, 0.99793 + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812 + 0x3fadd406f9808ec8, 0x3feff21614e131ed, // 0.058258, 0.9983 + 0x3fac428d12c0d7e3, 0x3feff3830f8d575c, // 0.055195, 0.99848 + 0x3faab101bd5f8317, 0x3feff4dc54b1bed3, // 0.052132, 0.99864 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3fa78dbaa5874685, 0x3feff753bb1b9164, // 0.046003, 0.99894 + 0x3fa5fc00d290cd43, 0x3feff871dadb81df, // 0.042938, 0.99908 + 0x3fa46a396ff86179, 0x3feff97c4208c014, // 0.039873, 0.9992 + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932 + 0x3fa14685db42c17e, 0x3feffb55e425fdae, // 0.033741, 0.99943 + 0x3f9f693731d1cf01, 0x3feffc251df1d3f8, // 0.030675, 0.99953 + 0x3f9c454f4ce53b1c, 0x3feffce09ce2a679, // 0.027608, 0.99962 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x3f95fd4d21fab226, 0x3feffe1c6870cb77, // 0.021474, 0.99977 + 0x3f92d936bbe30efd, 0x3feffe9cb44b51a1, // 0.018407, 0.99983 + 0x3f8f6a296ab997ca, 0x3fefff0943c53bd1, // 0.015339, 0.99988 + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992 + 0x3f82d96b0e509703, 0x3fefffa72c978c4f, // 0.0092038, 0.99996 + 0x3f7921f0fe670071, 0x3fefffd8858e8a92, // 0.0061359, 0.99998 + 0x3f6921f8becca4ba, 0x3feffff621621d02, // 0.003068, 1 + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0xbf6921f8becca4ba, 0x3feffff621621d02, // -0.003068, 1 + 0xbf7921f0fe670071, 0x3fefffd8858e8a92, //-0.0061359, 0.99998 + 0xbf82d96b0e509703, 0x3fefffa72c978c4f, //-0.0092038, 0.99996 + 0xbf8921d1fcdec784, 0x3fefff62169b92db, // -0.012272, 0.99992 + 0xbf8f6a296ab997ca, 0x3fefff0943c53bd1, // -0.015339, 0.99988 + 0xbf92d936bbe30efd, 0x3feffe9cb44b51a1, // -0.018407, 0.99983 + 0xbf95fd4d21fab226, 0x3feffe1c6870cb77, // -0.021474, 0.99977 + 0xbf992155f7a3667e, 0x3feffd886084cd0d, // -0.024541, 0.9997 + 0xbf9c454f4ce53b1c, 0x3feffce09ce2a679, // -0.027608, 0.99962 + 0xbf9f693731d1cf01, 0x3feffc251df1d3f8, // -0.030675, 0.99953 + 0xbfa14685db42c17e, 0x3feffb55e425fdae, // -0.033741, 0.99943 + 0xbfa2d865759455cd, 0x3feffa72effef75d, // -0.036807, 0.99932 + 0xbfa46a396ff86179, 0x3feff97c4208c014, // -0.039873, 0.9992 + 0xbfa5fc00d290cd43, 0x3feff871dadb81df, // -0.042938, 0.99908 + 0xbfa78dbaa5874685, 0x3feff753bb1b9164, // -0.046003, 0.99894 + 0xbfa91f65f10dd814, 0x3feff621e3796d7e, // -0.049068, 0.9988 + 0xbfaab101bd5f8317, 0x3feff4dc54b1bed3, // -0.052132, 0.99864 + 0xbfac428d12c0d7e3, 0x3feff3830f8d575c, // -0.055195, 0.99848 + 0xbfadd406f9808ec8, 0x3feff21614e131ed, // -0.058258, 0.9983 + 0xbfaf656e79f820e0, 0x3feff095658e71ad, // -0.061321, 0.99812 + 0xbfb07b614e463064, 0x3fefef0102826191, // -0.064383, 0.99793 + 0xbfb1440134d709b2, 0x3fefed58ecb673c4, // -0.067444, 0.99772 + 0xbfb20c9674ed444c, 0x3fefeb9d2530410f, // -0.070505, 0.99751 + 0xbfb2d52092ce19f6, 0x3fefe9cdad01883a, // -0.073565, 0.99729 + 0xbfb39d9f12c5a299, 0x3fefe7ea85482d60, // -0.076624, 0.99706 + 0xbfb4661179272096, 0x3fefe5f3af2e3940, // -0.079682, 0.99682 + 0xbfb52e774a4d4d0a, 0x3fefe3e92be9d886, // -0.08274, 0.99657 + 0xbfb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // -0.085797, 0.99631 + 0xbfb6bf1b3e79b129, 0x3fefdf9922f73307, // -0.088854, 0.99604 + 0xbfb787586a5d5b21, 0x3fefdd539ff1f456, // -0.091909, 0.99577 + 0xbfb84f8712c130a0, 0x3fefdafa7514538c, // -0.094963, 0.99548 + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, // -0.098017, 0.99518 + 0xbfb9dfb6eb24a85c, 0x3fefd60d2da75c9e, // -0.10107, 0.99488 + 0xbfbaa7b724495c04, 0x3fefd37914220b84, // -0.10412, 0.99456 + 0xbfbb6fa6ec38f64c, 0x3fefd0d158d86087, // -0.10717, 0.99424 + 0xbfbc3785c79ec2d5, 0x3fefce15fd6da67b, // -0.11022, 0.99391 + 0xbfbcff533b307dc1, 0x3fefcb4703914354, // -0.11327, 0.99356 + 0xbfbdc70ecbae9fc8, 0x3fefc8646cfeb721, // -0.11632, 0.99321 + 0xbfbe8eb7fde4aa3e, 0x3fefc56e3b7d9af6, // -0.11937, 0.99285 + 0xbfbf564e56a9730e, 0x3fefc26470e19fd3, // -0.12241, 0.99248 + 0xbfc00ee8ad6fb85b, 0x3fefbf470f0a8d88, // -0.12545, 0.9921 + 0xbfc072a047ba831d, 0x3fefbc1617e44186, // -0.1285, 0.99171 + 0xbfc0d64dbcb26786, 0x3fefb8d18d66adb7, // -0.13154, 0.99131 + 0xbfc139f0cedaf576, 0x3fefb5797195d741, // -0.13458, 0.9909 + 0xbfc19d8940be24e7, 0x3fefb20dc681d54d, // -0.13762, 0.99049 + 0xbfc20116d4ec7bce, 0x3fefae8e8e46cfbb, // -0.14066, 0.99006 + 0xbfc264994dfd340a, 0x3fefaafbcb0cfddc, // -0.1437, 0.98962 + 0xbfc2c8106e8e613a, 0x3fefa7557f08a517, // -0.14673, 0.98918 + 0xbfc32b7bf94516a7, 0x3fefa39bac7a1791, // -0.14976, 0.98872 + 0xbfc38edbb0cd8d14, 0x3fef9fce55adb2c8, // -0.1528, 0.98826 + 0xbfc3f22f57db4893, 0x3fef9bed7cfbde29, // -0.15583, 0.98778 + 0xbfc45576b1293e5a, 0x3fef97f924c9099b, // -0.15886, 0.9873 + 0xbfc4b8b17f79fa88, 0x3fef93f14f85ac08, // -0.16189, 0.98681 + 0xbfc51bdf8597c5f2, 0x3fef8fd5ffae41db, // -0.16491, 0.98631 + 0xbfc57f008654cbde, 0x3fef8ba737cb4b78, // -0.16794, 0.9858 + 0xbfc5e214448b3fc6, 0x3fef8764fa714ba9, // -0.17096, 0.98528 + 0xbfc6451a831d830d, 0x3fef830f4a40c60c, // -0.17398, 0.98475 + 0xbfc6a81304f64ab2, 0x3fef7ea629e63d6e, // -0.177, 0.98421 + 0xbfc70afd8d08c4ff, 0x3fef7a299c1a322a, // -0.18002, 0.98366 + 0xbfc76dd9de50bf31, 0x3fef7599a3a12077, // -0.18304, 0.98311 + 0xbfc7d0a7bbd2cb1b, 0x3fef70f6434b7eb7, // -0.18606, 0.98254 + 0xbfc83366e89c64c5, 0x3fef6c3f7df5bbb7, // -0.18907, 0.98196 + 0xbfc8961727c41804, 0x3fef677556883cee, // -0.19208, 0.98138 + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079 + 0xbfc95b49e9b62af9, 0x3fef5da6ed43685d, // -0.1981, 0.98018 + 0xbfc9bdcbf2dc4366, 0x3fef58a2b1789e84, // -0.2011, 0.97957 + 0xbfca203e1b1831da, 0x3fef538b1faf2d07, // -0.20411, 0.97895 + 0xbfca82a025b00451, 0x3fef4e603b0b2f2d, // -0.20711, 0.97832 + 0xbfcae4f1d5f3b9ab, 0x3fef492206bcabb4, // -0.21011, 0.97768 + 0xbfcb4732ef3d6722, 0x3fef43d085ff92dd, // -0.21311, 0.97703 + 0xbfcba96334f15dad, 0x3fef3e6bbc1bbc65, // -0.21611, 0.97637 + 0xbfcc0b826a7e4f63, 0x3fef38f3ac64e589, // -0.2191, 0.9757 + 0xbfcc6d90535d74dc, 0x3fef33685a3aaef0, // -0.22209, 0.97503 + 0xbfcccf8cb312b286, 0x3fef2dc9c9089a9d, // -0.22508, 0.97434 + 0xbfcd31774d2cbdee, 0x3fef2817fc4609ce, // -0.22807, 0.97364 + 0xbfcd934fe5454311, 0x3fef2252f7763ada, // -0.23106, 0.97294 + 0xbfcdf5163f01099a, 0x3fef1c7abe284708, // -0.23404, 0.97223 + 0xbfce56ca1e101a1b, 0x3fef168f53f7205d, // -0.23702, 0.9715 + 0xbfceb86b462de348, 0x3fef1090bc898f5f, // -0.24, 0.97077 + 0xbfcf19f97b215f1a, 0x3fef0a7efb9230d7, // -0.24298, 0.97003 + 0xbfcf7b7480bd3801, 0x3fef045a14cf738c, // -0.24596, 0.96928 + 0xbfcfdcdc1adfedf8, 0x3feefe220c0b95ec, // -0.24893, 0.96852 + 0xbfd01f1806b9fdd2, 0x3feef7d6e51ca3c0, // -0.2519, 0.96775 + 0xbfd04fb80e37fdae, 0x3feef178a3e473c2, // -0.25487, 0.96698 + 0xbfd0804e05eb661e, 0x3feeeb074c50a544, // -0.25783, 0.96619 + 0xbfd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // -0.26079, 0.96539 + 0xbfd0e15b4e1749cd, 0x3feeddeb6a078651, // -0.26375, 0.96459 + 0xbfd111d262b1f677, 0x3feed740e7684963, // -0.26671, 0.96378 + 0xbfd1423eefc69378, 0x3feed0835e999009, // -0.26967, 0.96295 + 0xbfd172a0d7765177, 0x3feec9b2d3c3bf84, // -0.27262, 0.96212 + 0xbfd1a2f7fbe8f243, 0x3feec2cf4b1af6b2, // -0.27557, 0.96128 + 0xbfd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // -0.27852, 0.96043 + 0xbfd2038583d727bd, 0x3feeb4cf515b8811, // -0.28146, 0.95957 + 0xbfd233bbabc3bb72, 0x3feeadb2e8e7a88e, // -0.28441, 0.9587 + 0xbfd263e6995554ba, 0x3feea68393e65800, // -0.28735, 0.95783 + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694 + 0xbfd2c41a4e954520, 0x3fee97ec36016b30, // -0.29322, 0.95605 + 0xbfd2f422daec0386, 0x3fee9084361df7f3, // -0.29615, 0.95514 + 0xbfd3241fb638baaf, 0x3fee89095bad6025, // -0.29908, 0.95423 + 0xbfd35410c2e18152, 0x3fee817bab4cd10d, // -0.30201, 0.95331 + 0xbfd383f5e353b6aa, 0x3fee79db29a5165a, // -0.30493, 0.95238 + 0xbfd3b3cefa0414b7, 0x3fee7227db6a9744, // -0.30785, 0.95144 + 0xbfd3e39be96ec271, 0x3fee6a61c55d53a7, // -0.31077, 0.95049 + 0xbfd4135c94176602, 0x3fee6288ec48e112, // -0.31368, 0.94953 + 0xbfd44310dc8936f0, 0x3fee5a9d550467d3, // -0.31659, 0.94856 + 0xbfd472b8a5571054, 0x3fee529f04729ffc, // -0.3195, 0.94759 + 0xbfd4a253d11b82f3, 0x3fee4a8dff81ce5e, // -0.32241, 0.9466 + 0xbfd4d1e24278e76a, 0x3fee426a4b2bc17e, // -0.32531, 0.94561 + 0xbfd50163dc197047, 0x3fee3a33ec75ce85, // -0.32821, 0.9446 + 0xbfd530d880af3c24, 0x3fee31eae870ce25, // -0.33111, 0.94359 + 0xbfd5604012f467b4, 0x3fee298f4439197a, // -0.334, 0.94257 + 0xbfd58f9a75ab1fdd, 0x3fee212104f686e5, // -0.33689, 0.94154 + 0xbfd5bee78b9db3b6, 0x3fee18a02fdc66d9, // -0.33978, 0.94051 + 0xbfd5ee27379ea693, 0x3fee100cca2980ac, // -0.34266, 0.93946 + 0xbfd61d595c88c203, 0x3fee0766d9280f54, // -0.34554, 0.9384 + 0xbfd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // -0.34842, 0.93734 + 0xbfd67b949cad63ca, 0x3fedf5e36a9ba59c, // -0.35129, 0.93627 + 0xbfd6aa9d7dc77e16, 0x3feded05f7de47da, // -0.35416, 0.93518 + 0xbfd6d998638a0cb5, 0x3fede4160f6d8d81, // -0.35703, 0.93409 + 0xbfd7088530fa459e, 0x3feddb13b6ccc23d, // -0.3599, 0.93299 + 0xbfd73763c9261092, 0x3fedd1fef38a915a, // -0.36276, 0.93188 + 0xbfd766340f2418f6, 0x3fedc8d7cb410260, // -0.36561, 0.93077 + 0xbfd794f5e613dfae, 0x3fedbf9e4395759a, // -0.36847, 0.92964 + 0xbfd7c3a9311dcce7, 0x3fedb6526238a09b, // -0.37132, 0.92851 + 0xbfd7f24dd37341e3, 0x3fedacf42ce68ab9, // -0.37416, 0.92736 + 0xbfd820e3b04eaac4, 0x3feda383a9668988, // -0.37701, 0.92621 + 0xbfd84f6aaaf3903f, 0x3fed9a00dd8b3d46, // -0.37985, 0.92505 + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388 + 0xbfd8ac4b86d5ed44, 0x3fed86c48445a450, // -0.38552, 0.9227 + 0xbfd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // -0.38835, 0.92151 + 0xbfd908ef81ef7bd1, 0x3fed733f508c0dff, // -0.39117, 0.92032 + 0xbfd9372a63bc93d7, 0x3fed696173c9e68b, // -0.39399, 0.91911 + 0xbfd96555b7ab948f, 0x3fed5f7172888a7f, // -0.39681, 0.9179 + 0xbfd993716141bdfe, 0x3fed556f52e93eb1, // -0.39962, 0.91668 + 0xbfd9c17d440df9f2, 0x3fed4b5b1b187524, // -0.40243, 0.91545 + 0xbfd9ef7943a8ed8a, 0x3fed4134d14dc93a, // -0.40524, 0.91421 + 0xbfda1d6543b50ac0, 0x3fed36fc7bcbfbdc, // -0.40804, 0.91296 + 0xbfda4b4127dea1e4, 0x3fed2cb220e0ef9f, // -0.41084, 0.91171 + 0xbfda790cd3dbf31a, 0x3fed2255c6e5a4e1, // -0.41364, 0.91044 + 0xbfdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // -0.41643, 0.90917 + 0xbfdad473125cdc08, 0x3fed0d672f59d2b9, // -0.41922, 0.90789 + 0xbfdb020d6c7f4009, 0x3fed02d4feb2bd92, // -0.422, 0.9066 + 0xbfdb2f971db31972, 0x3fecf830e8ce467b, // -0.42478, 0.9053 + 0xbfdb5d1009e15cc0, 0x3feced7af43cc773, // -0.42756, 0.90399 + 0xbfdb8a7814fd5693, 0x3fece2b32799a060, // -0.43033, 0.90267 + 0xbfdbb7cf2304bd01, 0x3fecd7d9898b32f6, // -0.43309, 0.90135 + 0xbfdbe51517ffc0d9, 0x3fecccee20c2de9f, // -0.43586, 0.90002 + 0xbfdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // -0.43862, 0.89867 + 0xbfdc3f6d47263129, 0x3fecb6e20a00da99, // -0.44137, 0.89732 + 0xbfdc6c7f4997000a, 0x3fecabc169a0b901, // -0.44412, 0.89597 + 0xbfdc997fc3865388, 0x3feca08f19b9c449, // -0.44687, 0.8946 + 0xbfdcc66e9931c45d, 0x3fec954b213411f5, // -0.44961, 0.89322 + 0xbfdcf34baee1cd21, 0x3fec89f587029c13, // -0.45235, 0.89184 + 0xbfdd2016e8e9db5b, 0x3fec7e8e52233cf3, // -0.45508, 0.89045 + 0xbfdd4cd02ba8609c, 0x3fec7315899eaad7, // -0.45781, 0.88905 + 0xbfdd79775b86e389, 0x3fec678b3488739b, // -0.46054, 0.88764 + 0xbfdda60c5cfa10d8, 0x3fec5bef59fef85a, // -0.46326, 0.88622 + 0xbfddd28f1481cc58, 0x3fec5042012b6907, // -0.46598, 0.8848 + 0xbfddfeff66a941de, 0x3fec44833141c004, // -0.46869, 0.88336 + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192 + 0xbfde57a86d3cd824, 0x3fec2cd14931e3f1, // -0.4741, 0.88047 + 0xbfde83e0eaf85113, 0x3fec20de3fa971b0, // -0.4768, 0.87901 + 0xbfdeb00695f25620, 0x3fec14d9dc465e58, // -0.47949, 0.87755 + 0xbfdedc1952ef78d5, 0x3fec08c426725549, // -0.48218, 0.87607 + 0xbfdf081906bff7fd, 0x3febfc9d25a1b147, // -0.48487, 0.87459 + 0xbfdf3405963fd068, 0x3febf064e15377dd, // -0.48755, 0.87309 + 0xbfdf5fdee656cda3, 0x3febe41b611154c1, // -0.49023, 0.8716 + 0xbfdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // -0.4929, 0.87009 + 0xbfdfb7575c24d2de, 0x3febcb54cb0d2327, // -0.49557, 0.86857 + 0xbfdfe2f64be7120f, 0x3febbed7c49380ea, // -0.49823, 0.86705 + 0xbfe00740c82b82e0, 0x3febb249a0b6c40d, // -0.50089, 0.86551 + 0xbfe01cfc874c3eb7, 0x3feba5aa673590d2, // -0.50354, 0.86397 + 0xbfe032ae55edbd95, 0x3feb98fa1fd9155e, // -0.50619, 0.86242 + 0xbfe0485626ae221a, 0x3feb8c38d27504e9, // -0.50883, 0.86087 + 0xbfe05df3ec31b8b6, 0x3feb7f6686e792ea, // -0.51147, 0.8593 + 0xbfe073879922ffed, 0x3feb728345196e3e, // -0.5141, 0.85773 + 0xbfe089112032b08c, 0x3feb658f14fdbc47, // -0.51673, 0.85615 + 0xbfe09e907417c5e1, 0x3feb5889fe921405, // -0.51936, 0.85456 + 0xbfe0b405878f85ec, 0x3feb4b7409de7925, // -0.52198, 0.85296 + 0xbfe0c9704d5d898f, 0x3feb3e4d3ef55712, // -0.52459, 0.85136 + 0xbfe0ded0b84bc4b5, 0x3feb3115a5f37bf4, // -0.5272, 0.84974 + 0xbfe0f426bb2a8e7d, 0x3feb23cd470013b4, // -0.5298, 0.84812 + 0xbfe1097248d0a956, 0x3feb16742a4ca2f5, // -0.5324, 0.84649 + 0xbfe11eb3541b4b22, 0x3feb090a58150200, // -0.535, 0.84485 + 0xbfe133e9cfee254e, 0x3feafb8fd89f57b6, // -0.53759, 0.84321 + 0xbfe14915af336ceb, 0x3feaee04b43c1474, // -0.54017, 0.84155 + 0xbfe15e36e4dbe2bc, 0x3feae068f345ecef, // -0.54275, 0.83989 + 0xbfe1734d63dedb49, 0x3fead2bc9e21d511, // -0.54532, 0.83822 + 0xbfe188591f3a46e5, 0x3feac4ffbd3efac8, // -0.54789, 0.83655 + 0xbfe19d5a09f2b9b8, 0x3feab7325916c0d4, // -0.55046, 0.83486 + 0xbfe1b250171373be, 0x3feaa9547a2cb98e, // -0.55302, 0.83317 + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147 + 0xbfe1dc1b64dc4872, 0x3fea8d676e545ad2, // -0.55812, 0.82976 + 0xbfe1f0f08bbc861b, 0x3fea7f58529fe69d, // -0.56066, 0.82805 + 0xbfe205baa17560d6, 0x3fea7138de9d60f5, // -0.5632, 0.82632 + 0xbfe21a799933eb58, 0x3fea63091b02fae2, // -0.56573, 0.82459 + 0xbfe22f2d662c13e1, 0x3fea54c91090f524, // -0.56826, 0.82285 + 0xbfe243d5fb98ac1f, 0x3fea4678c8119ac8, // -0.57078, 0.8211 + 0xbfe258734cbb7110, 0x3fea38184a593bc6, // -0.5733, 0.81935 + 0xbfe26d054cdd12df, 0x3fea29a7a0462782, // -0.57581, 0.81758 + 0xbfe2818bef4d3cba, 0x3fea1b26d2c0a75e, // -0.57831, 0.81581 + 0xbfe2960727629ca8, 0x3fea0c95eabaf937, // -0.58081, 0.81404 + 0xbfe2aa76e87aeb58, 0x3fe9fdf4f13149de, // -0.58331, 0.81225 + 0xbfe2bedb25faf3ea, 0x3fe9ef43ef29af94, // -0.5858, 0.81046 + 0xbfe2d333d34e9bb7, 0x3fe9e082edb42472, // -0.58828, 0.80866 + 0xbfe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // -0.59076, 0.80685 + 0xbfe2fbc24b441015, 0x3fe9c2d110f075c3, // -0.59323, 0.80503 + 0xbfe30ff7fce17035, 0x3fe9b3e047f38741, // -0.5957, 0.80321 + 0xbfe32421ec49a620, 0x3fe9a4dfa42b06b2, // -0.59816, 0.80138 + 0xbfe338400d0c8e57, 0x3fe995cf2ed80d22, // -0.60062, 0.79954 + 0xbfe34c5252c14de1, 0x3fe986aef1457594, // -0.60307, 0.79769 + 0xbfe36058b10659f3, 0x3fe9777ef4c7d742, // -0.60551, 0.79584 + 0xbfe374531b817f8d, 0x3fe9683f42bd7fe1, // -0.60795, 0.79398 + 0xbfe3884185dfeb22, 0x3fe958efe48e6dd7, // -0.61038, 0.79211 + 0xbfe39c23e3d63029, 0x3fe94990e3ac4a6c, // -0.61281, 0.79023 + 0xbfe3affa292050b9, 0x3fe93a22499263fc, // -0.61523, 0.78835 + 0xbfe3c3c44981c517, 0x3fe92aa41fc5a815, // -0.61765, 0.78646 + 0xbfe3d78238c58343, 0x3fe91b166fd49da2, // -0.62006, 0.78456 + 0xbfe3eb33eabe0680, 0x3fe90b7943575efe, // -0.62246, 0.78265 + 0xbfe3fed9534556d4, 0x3fe8fbcca3ef940d, // -0.62486, 0.78074 + 0xbfe41272663d108c, 0x3fe8ec109b486c49, // -0.62725, 0.77882 + 0xbfe425ff178e6bb1, 0x3fe8dc45331698cc, // -0.62964, 0.77689 + 0xbfe4397f5b2a4380, 0x3fe8cc6a75184655, // -0.63202, 0.77495 + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301 + 0xbfe4605a692b32a2, 0x3fe8ac871ede1d88, // -0.63676, 0.77106 + 0xbfe473b51b987347, 0x3fe89c7e9a4dd4ab, // -0.63912, 0.7691 + 0xbfe48703306091fe, 0x3fe88c66e7481ba1, // -0.64148, 0.76714 + 0xbfe49a449b9b0938, 0x3fe87c400fba2ebf, // -0.64383, 0.76517 + 0xbfe4ad79516722f0, 0x3fe86c0a1d9aa195, // -0.64618, 0.76319 + 0xbfe4c0a145ec0004, 0x3fe85bc51ae958cc, // -0.64851, 0.7612 + 0xbfe4d3bc6d589f80, 0x3fe84b7111af83f9, // -0.65085, 0.75921 + 0xbfe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // -0.65317, 0.75721 + 0xbfe4f9cc25cca486, 0x3fe82a9c13f545ff, // -0.65549, 0.7552 + 0xbfe50cc09f59a09b, 0x3fe81a1b33b57acc, // -0.65781, 0.75319 + 0xbfe51fa81cd99aa6, 0x3fe8098b756e52fa, // -0.66011, 0.75117 + 0xbfe5328292a35596, 0x3fe7f8ece3571771, // -0.66242, 0.74914 + 0xbfe5454ff5159dfb, 0x3fe7e83f87b03686, // -0.66471, 0.7471 + 0xbfe5581038975137, 0x3fe7d7836cc33db2, // -0.667, 0.74506 + 0xbfe56ac35197649e, 0x3fe7c6b89ce2d333, // -0.66928, 0.74301 + 0xbfe57d69348cec9f, 0x3fe7b5df226aafb0, // -0.67156, 0.74095 + 0xbfe59001d5f723df, 0x3fe7a4f707bf97d2, // -0.67383, 0.73889 + 0xbfe5a28d2a5d7250, 0x3fe79400574f55e4, // -0.67609, 0.73682 + 0xbfe5b50b264f7448, 0x3fe782fb1b90b35b, // -0.67835, 0.73474 + 0xbfe5c77bbe65018c, 0x3fe771e75f037261, // -0.6806, 0.73265 + 0xbfe5d9dee73e345c, 0x3fe760c52c304764, // -0.68285, 0.73056 + 0xbfe5ec3495837074, 0x3fe74f948da8d28d, // -0.68508, 0.72846 + 0xbfe5fe7cbde56a0f, 0x3fe73e558e079942, // -0.68732, 0.72636 + 0xbfe610b7551d2cde, 0x3fe72d0837efff97, // -0.68954, 0.72425 + 0xbfe622e44fec22ff, 0x3fe71bac960e41bf, // -0.69176, 0.72213 + 0xbfe63503a31c1be8, 0x3fe70a42b3176d7a, // -0.69397, 0.72 + 0xbfe64715437f535b, 0x3fe6f8ca99c95b75, // -0.69618, 0.71787 + 0xbfe6591925f0783e, 0x3fe6e74454eaa8ae, // -0.69838, 0.71573 + 0xbfe66b0f3f52b386, 0x3fe6d5afef4aafcc, // -0.70057, 0.71358 + 0xbfe67cf78491af10, 0x3fe6c40d73c18275, // -0.70275, 0.71143 + 0xbfe68ed1eaa19c71, 0x3fe6b25ced2fe29c, // -0.70493, 0.70927 + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711 + 0xbfe6b25ced2fe29c, 0x3fe68ed1eaa19c71, // -0.70927, 0.70493 + 0xbfe6c40d73c18275, 0x3fe67cf78491af10, // -0.71143, 0.70275 + 0xbfe6d5afef4aafcc, 0x3fe66b0f3f52b386, // -0.71358, 0.70057 + 0xbfe6e74454eaa8ae, 0x3fe6591925f0783e, // -0.71573, 0.69838 + 0xbfe6f8ca99c95b75, 0x3fe64715437f535b, // -0.71787, 0.69618 + 0xbfe70a42b3176d7a, 0x3fe63503a31c1be8, // -0.72, 0.69397 + 0xbfe71bac960e41bf, 0x3fe622e44fec22ff, // -0.72213, 0.69176 + 0xbfe72d0837efff97, 0x3fe610b7551d2cde, // -0.72425, 0.68954 + 0xbfe73e558e079942, 0x3fe5fe7cbde56a0f, // -0.72636, 0.68732 + 0xbfe74f948da8d28d, 0x3fe5ec3495837074, // -0.72846, 0.68508 + 0xbfe760c52c304764, 0x3fe5d9dee73e345c, // -0.73056, 0.68285 + 0xbfe771e75f037261, 0x3fe5c77bbe65018c, // -0.73265, 0.6806 + 0xbfe782fb1b90b35b, 0x3fe5b50b264f7448, // -0.73474, 0.67835 + 0xbfe79400574f55e4, 0x3fe5a28d2a5d7250, // -0.73682, 0.67609 + 0xbfe7a4f707bf97d2, 0x3fe59001d5f723df, // -0.73889, 0.67383 + 0xbfe7b5df226aafb0, 0x3fe57d69348cec9f, // -0.74095, 0.67156 + 0xbfe7c6b89ce2d333, 0x3fe56ac35197649e, // -0.74301, 0.66928 + 0xbfe7d7836cc33db2, 0x3fe5581038975137, // -0.74506, 0.667 + 0xbfe7e83f87b03686, 0x3fe5454ff5159dfb, // -0.7471, 0.66471 + 0xbfe7f8ece3571771, 0x3fe5328292a35596, // -0.74914, 0.66242 + 0xbfe8098b756e52fa, 0x3fe51fa81cd99aa6, // -0.75117, 0.66011 + 0xbfe81a1b33b57acc, 0x3fe50cc09f59a09b, // -0.75319, 0.65781 + 0xbfe82a9c13f545ff, 0x3fe4f9cc25cca486, // -0.7552, 0.65549 + 0xbfe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // -0.75721, 0.65317 + 0xbfe84b7111af83f9, 0x3fe4d3bc6d589f80, // -0.75921, 0.65085 + 0xbfe85bc51ae958cc, 0x3fe4c0a145ec0004, // -0.7612, 0.64851 + 0xbfe86c0a1d9aa195, 0x3fe4ad79516722f0, // -0.76319, 0.64618 + 0xbfe87c400fba2ebf, 0x3fe49a449b9b0938, // -0.76517, 0.64383 + 0xbfe88c66e7481ba1, 0x3fe48703306091fe, // -0.76714, 0.64148 + 0xbfe89c7e9a4dd4ab, 0x3fe473b51b987347, // -0.7691, 0.63912 + 0xbfe8ac871ede1d88, 0x3fe4605a692b32a2, // -0.77106, 0.63676 + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439 + 0xbfe8cc6a75184655, 0x3fe4397f5b2a4380, // -0.77495, 0.63202 + 0xbfe8dc45331698cc, 0x3fe425ff178e6bb1, // -0.77689, 0.62964 + 0xbfe8ec109b486c49, 0x3fe41272663d108c, // -0.77882, 0.62725 + 0xbfe8fbcca3ef940d, 0x3fe3fed9534556d4, // -0.78074, 0.62486 + 0xbfe90b7943575efe, 0x3fe3eb33eabe0680, // -0.78265, 0.62246 + 0xbfe91b166fd49da2, 0x3fe3d78238c58343, // -0.78456, 0.62006 + 0xbfe92aa41fc5a815, 0x3fe3c3c44981c517, // -0.78646, 0.61765 + 0xbfe93a22499263fc, 0x3fe3affa292050b9, // -0.78835, 0.61523 + 0xbfe94990e3ac4a6c, 0x3fe39c23e3d63029, // -0.79023, 0.61281 + 0xbfe958efe48e6dd7, 0x3fe3884185dfeb22, // -0.79211, 0.61038 + 0xbfe9683f42bd7fe1, 0x3fe374531b817f8d, // -0.79398, 0.60795 + 0xbfe9777ef4c7d742, 0x3fe36058b10659f3, // -0.79584, 0.60551 + 0xbfe986aef1457594, 0x3fe34c5252c14de1, // -0.79769, 0.60307 + 0xbfe995cf2ed80d22, 0x3fe338400d0c8e57, // -0.79954, 0.60062 + 0xbfe9a4dfa42b06b2, 0x3fe32421ec49a620, // -0.80138, 0.59816 + 0xbfe9b3e047f38741, 0x3fe30ff7fce17035, // -0.80321, 0.5957 + 0xbfe9c2d110f075c3, 0x3fe2fbc24b441015, // -0.80503, 0.59323 + 0xbfe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // -0.80685, 0.59076 + 0xbfe9e082edb42472, 0x3fe2d333d34e9bb7, // -0.80866, 0.58828 + 0xbfe9ef43ef29af94, 0x3fe2bedb25faf3ea, // -0.81046, 0.5858 + 0xbfe9fdf4f13149de, 0x3fe2aa76e87aeb58, // -0.81225, 0.58331 + 0xbfea0c95eabaf937, 0x3fe2960727629ca8, // -0.81404, 0.58081 + 0xbfea1b26d2c0a75e, 0x3fe2818bef4d3cba, // -0.81581, 0.57831 + 0xbfea29a7a0462782, 0x3fe26d054cdd12df, // -0.81758, 0.57581 + 0xbfea38184a593bc6, 0x3fe258734cbb7110, // -0.81935, 0.5733 + 0xbfea4678c8119ac8, 0x3fe243d5fb98ac1f, // -0.8211, 0.57078 + 0xbfea54c91090f524, 0x3fe22f2d662c13e1, // -0.82285, 0.56826 + 0xbfea63091b02fae2, 0x3fe21a799933eb58, // -0.82459, 0.56573 + 0xbfea7138de9d60f5, 0x3fe205baa17560d6, // -0.82632, 0.5632 + 0xbfea7f58529fe69d, 0x3fe1f0f08bbc861b, // -0.82805, 0.56066 + 0xbfea8d676e545ad2, 0x3fe1dc1b64dc4872, // -0.82976, 0.55812 + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557 + 0xbfeaa9547a2cb98e, 0x3fe1b250171373be, // -0.83317, 0.55302 + 0xbfeab7325916c0d4, 0x3fe19d5a09f2b9b8, // -0.83486, 0.55046 + 0xbfeac4ffbd3efac8, 0x3fe188591f3a46e5, // -0.83655, 0.54789 + 0xbfead2bc9e21d511, 0x3fe1734d63dedb49, // -0.83822, 0.54532 + 0xbfeae068f345ecef, 0x3fe15e36e4dbe2bc, // -0.83989, 0.54275 + 0xbfeaee04b43c1474, 0x3fe14915af336ceb, // -0.84155, 0.54017 + 0xbfeafb8fd89f57b6, 0x3fe133e9cfee254e, // -0.84321, 0.53759 + 0xbfeb090a58150200, 0x3fe11eb3541b4b22, // -0.84485, 0.535 + 0xbfeb16742a4ca2f5, 0x3fe1097248d0a956, // -0.84649, 0.5324 + 0xbfeb23cd470013b4, 0x3fe0f426bb2a8e7d, // -0.84812, 0.5298 + 0xbfeb3115a5f37bf4, 0x3fe0ded0b84bc4b5, // -0.84974, 0.5272 + 0xbfeb3e4d3ef55712, 0x3fe0c9704d5d898f, // -0.85136, 0.52459 + 0xbfeb4b7409de7925, 0x3fe0b405878f85ec, // -0.85296, 0.52198 + 0xbfeb5889fe921405, 0x3fe09e907417c5e1, // -0.85456, 0.51936 + 0xbfeb658f14fdbc47, 0x3fe089112032b08c, // -0.85615, 0.51673 + 0xbfeb728345196e3e, 0x3fe073879922ffed, // -0.85773, 0.5141 + 0xbfeb7f6686e792ea, 0x3fe05df3ec31b8b6, // -0.8593, 0.51147 + 0xbfeb8c38d27504e9, 0x3fe0485626ae221a, // -0.86087, 0.50883 + 0xbfeb98fa1fd9155e, 0x3fe032ae55edbd95, // -0.86242, 0.50619 + 0xbfeba5aa673590d2, 0x3fe01cfc874c3eb7, // -0.86397, 0.50354 + 0xbfebb249a0b6c40d, 0x3fe00740c82b82e0, // -0.86551, 0.50089 + 0xbfebbed7c49380ea, 0x3fdfe2f64be7120f, // -0.86705, 0.49823 + 0xbfebcb54cb0d2327, 0x3fdfb7575c24d2de, // -0.86857, 0.49557 + 0xbfebd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // -0.87009, 0.4929 + 0xbfebe41b611154c1, 0x3fdf5fdee656cda3, // -0.8716, 0.49023 + 0xbfebf064e15377dd, 0x3fdf3405963fd068, // -0.87309, 0.48755 + 0xbfebfc9d25a1b147, 0x3fdf081906bff7fd, // -0.87459, 0.48487 + 0xbfec08c426725549, 0x3fdedc1952ef78d5, // -0.87607, 0.48218 + 0xbfec14d9dc465e58, 0x3fdeb00695f25620, // -0.87755, 0.47949 + 0xbfec20de3fa971b0, 0x3fde83e0eaf85113, // -0.87901, 0.4768 + 0xbfec2cd14931e3f1, 0x3fde57a86d3cd824, // -0.88047, 0.4741 + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714 + 0xbfec44833141c004, 0x3fddfeff66a941de, // -0.88336, 0.46869 + 0xbfec5042012b6907, 0x3fddd28f1481cc58, // -0.8848, 0.46598 + 0xbfec5bef59fef85a, 0x3fdda60c5cfa10d8, // -0.88622, 0.46326 + 0xbfec678b3488739b, 0x3fdd79775b86e389, // -0.88764, 0.46054 + 0xbfec7315899eaad7, 0x3fdd4cd02ba8609c, // -0.88905, 0.45781 + 0xbfec7e8e52233cf3, 0x3fdd2016e8e9db5b, // -0.89045, 0.45508 + 0xbfec89f587029c13, 0x3fdcf34baee1cd21, // -0.89184, 0.45235 + 0xbfec954b213411f5, 0x3fdcc66e9931c45d, // -0.89322, 0.44961 + 0xbfeca08f19b9c449, 0x3fdc997fc3865388, // -0.8946, 0.44687 + 0xbfecabc169a0b901, 0x3fdc6c7f4997000a, // -0.89597, 0.44412 + 0xbfecb6e20a00da99, 0x3fdc3f6d47263129, // -0.89732, 0.44137 + 0xbfecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // -0.89867, 0.43862 + 0xbfecccee20c2de9f, 0x3fdbe51517ffc0d9, // -0.90002, 0.43586 + 0xbfecd7d9898b32f6, 0x3fdbb7cf2304bd01, // -0.90135, 0.43309 + 0xbfece2b32799a060, 0x3fdb8a7814fd5693, // -0.90267, 0.43033 + 0xbfeced7af43cc773, 0x3fdb5d1009e15cc0, // -0.90399, 0.42756 + 0xbfecf830e8ce467b, 0x3fdb2f971db31972, // -0.9053, 0.42478 + 0xbfed02d4feb2bd92, 0x3fdb020d6c7f4009, // -0.9066, 0.422 + 0xbfed0d672f59d2b9, 0x3fdad473125cdc08, // -0.90789, 0.41922 + 0xbfed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // -0.90917, 0.41643 + 0xbfed2255c6e5a4e1, 0x3fda790cd3dbf31a, // -0.91044, 0.41364 + 0xbfed2cb220e0ef9f, 0x3fda4b4127dea1e4, // -0.91171, 0.41084 + 0xbfed36fc7bcbfbdc, 0x3fda1d6543b50ac0, // -0.91296, 0.40804 + 0xbfed4134d14dc93a, 0x3fd9ef7943a8ed8a, // -0.91421, 0.40524 + 0xbfed4b5b1b187524, 0x3fd9c17d440df9f2, // -0.91545, 0.40243 + 0xbfed556f52e93eb1, 0x3fd993716141bdfe, // -0.91668, 0.39962 + 0xbfed5f7172888a7f, 0x3fd96555b7ab948f, // -0.9179, 0.39681 + 0xbfed696173c9e68b, 0x3fd9372a63bc93d7, // -0.91911, 0.39399 + 0xbfed733f508c0dff, 0x3fd908ef81ef7bd1, // -0.92032, 0.39117 + 0xbfed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // -0.92151, 0.38835 + 0xbfed86c48445a450, 0x3fd8ac4b86d5ed44, // -0.9227, 0.38552 + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268 + 0xbfed9a00dd8b3d46, 0x3fd84f6aaaf3903f, // -0.92505, 0.37985 + 0xbfeda383a9668988, 0x3fd820e3b04eaac4, // -0.92621, 0.37701 + 0xbfedacf42ce68ab9, 0x3fd7f24dd37341e3, // -0.92736, 0.37416 + 0xbfedb6526238a09b, 0x3fd7c3a9311dcce7, // -0.92851, 0.37132 + 0xbfedbf9e4395759a, 0x3fd794f5e613dfae, // -0.92964, 0.36847 + 0xbfedc8d7cb410260, 0x3fd766340f2418f6, // -0.93077, 0.36561 + 0xbfedd1fef38a915a, 0x3fd73763c9261092, // -0.93188, 0.36276 + 0xbfeddb13b6ccc23d, 0x3fd7088530fa459e, // -0.93299, 0.3599 + 0xbfede4160f6d8d81, 0x3fd6d998638a0cb5, // -0.93409, 0.35703 + 0xbfeded05f7de47da, 0x3fd6aa9d7dc77e16, // -0.93518, 0.35416 + 0xbfedf5e36a9ba59c, 0x3fd67b949cad63ca, // -0.93627, 0.35129 + 0xbfedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // -0.93734, 0.34842 + 0xbfee0766d9280f54, 0x3fd61d595c88c203, // -0.9384, 0.34554 + 0xbfee100cca2980ac, 0x3fd5ee27379ea693, // -0.93946, 0.34266 + 0xbfee18a02fdc66d9, 0x3fd5bee78b9db3b6, // -0.94051, 0.33978 + 0xbfee212104f686e5, 0x3fd58f9a75ab1fdd, // -0.94154, 0.33689 + 0xbfee298f4439197a, 0x3fd5604012f467b4, // -0.94257, 0.334 + 0xbfee31eae870ce25, 0x3fd530d880af3c24, // -0.94359, 0.33111 + 0xbfee3a33ec75ce85, 0x3fd50163dc197047, // -0.9446, 0.32821 + 0xbfee426a4b2bc17e, 0x3fd4d1e24278e76a, // -0.94561, 0.32531 + 0xbfee4a8dff81ce5e, 0x3fd4a253d11b82f3, // -0.9466, 0.32241 + 0xbfee529f04729ffc, 0x3fd472b8a5571054, // -0.94759, 0.3195 + 0xbfee5a9d550467d3, 0x3fd44310dc8936f0, // -0.94856, 0.31659 + 0xbfee6288ec48e112, 0x3fd4135c94176602, // -0.94953, 0.31368 + 0xbfee6a61c55d53a7, 0x3fd3e39be96ec271, // -0.95049, 0.31077 + 0xbfee7227db6a9744, 0x3fd3b3cefa0414b7, // -0.95144, 0.30785 + 0xbfee79db29a5165a, 0x3fd383f5e353b6aa, // -0.95238, 0.30493 + 0xbfee817bab4cd10d, 0x3fd35410c2e18152, // -0.95331, 0.30201 + 0xbfee89095bad6025, 0x3fd3241fb638baaf, // -0.95423, 0.29908 + 0xbfee9084361df7f3, 0x3fd2f422daec0386, // -0.95514, 0.29615 + 0xbfee97ec36016b30, 0x3fd2c41a4e954520, // -0.95605, 0.29322 + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028 + 0xbfeea68393e65800, 0x3fd263e6995554ba, // -0.95783, 0.28735 + 0xbfeeadb2e8e7a88e, 0x3fd233bbabc3bb72, // -0.9587, 0.28441 + 0xbfeeb4cf515b8811, 0x3fd2038583d727bd, // -0.95957, 0.28146 + 0xbfeebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // -0.96043, 0.27852 + 0xbfeec2cf4b1af6b2, 0x3fd1a2f7fbe8f243, // -0.96128, 0.27557 + 0xbfeec9b2d3c3bf84, 0x3fd172a0d7765177, // -0.96212, 0.27262 + 0xbfeed0835e999009, 0x3fd1423eefc69378, // -0.96295, 0.26967 + 0xbfeed740e7684963, 0x3fd111d262b1f677, // -0.96378, 0.26671 + 0xbfeeddeb6a078651, 0x3fd0e15b4e1749cd, // -0.96459, 0.26375 + 0xbfeee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // -0.96539, 0.26079 + 0xbfeeeb074c50a544, 0x3fd0804e05eb661e, // -0.96619, 0.25783 + 0xbfeef178a3e473c2, 0x3fd04fb80e37fdae, // -0.96698, 0.25487 + 0xbfeef7d6e51ca3c0, 0x3fd01f1806b9fdd2, // -0.96775, 0.2519 + 0xbfeefe220c0b95ec, 0x3fcfdcdc1adfedf8, // -0.96852, 0.24893 + 0xbfef045a14cf738c, 0x3fcf7b7480bd3801, // -0.96928, 0.24596 + 0xbfef0a7efb9230d7, 0x3fcf19f97b215f1a, // -0.97003, 0.24298 + 0xbfef1090bc898f5f, 0x3fceb86b462de348, // -0.97077, 0.24 + 0xbfef168f53f7205d, 0x3fce56ca1e101a1b, // -0.9715, 0.23702 + 0xbfef1c7abe284708, 0x3fcdf5163f01099a, // -0.97223, 0.23404 + 0xbfef2252f7763ada, 0x3fcd934fe5454311, // -0.97294, 0.23106 + 0xbfef2817fc4609ce, 0x3fcd31774d2cbdee, // -0.97364, 0.22807 + 0xbfef2dc9c9089a9d, 0x3fcccf8cb312b286, // -0.97434, 0.22508 + 0xbfef33685a3aaef0, 0x3fcc6d90535d74dc, // -0.97503, 0.22209 + 0xbfef38f3ac64e589, 0x3fcc0b826a7e4f63, // -0.9757, 0.2191 + 0xbfef3e6bbc1bbc65, 0x3fcba96334f15dad, // -0.97637, 0.21611 + 0xbfef43d085ff92dd, 0x3fcb4732ef3d6722, // -0.97703, 0.21311 + 0xbfef492206bcabb4, 0x3fcae4f1d5f3b9ab, // -0.97768, 0.21011 + 0xbfef4e603b0b2f2d, 0x3fca82a025b00451, // -0.97832, 0.20711 + 0xbfef538b1faf2d07, 0x3fca203e1b1831da, // -0.97895, 0.20411 + 0xbfef58a2b1789e84, 0x3fc9bdcbf2dc4366, // -0.97957, 0.2011 + 0xbfef5da6ed43685d, 0x3fc95b49e9b62af9, // -0.98018, 0.1981 + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509 + 0xbfef677556883cee, 0x3fc8961727c41804, // -0.98138, 0.19208 + 0xbfef6c3f7df5bbb7, 0x3fc83366e89c64c5, // -0.98196, 0.18907 + 0xbfef70f6434b7eb7, 0x3fc7d0a7bbd2cb1b, // -0.98254, 0.18606 + 0xbfef7599a3a12077, 0x3fc76dd9de50bf31, // -0.98311, 0.18304 + 0xbfef7a299c1a322a, 0x3fc70afd8d08c4ff, // -0.98366, 0.18002 + 0xbfef7ea629e63d6e, 0x3fc6a81304f64ab2, // -0.98421, 0.177 + 0xbfef830f4a40c60c, 0x3fc6451a831d830d, // -0.98475, 0.17398 + 0xbfef8764fa714ba9, 0x3fc5e214448b3fc6, // -0.98528, 0.17096 + 0xbfef8ba737cb4b78, 0x3fc57f008654cbde, // -0.9858, 0.16794 + 0xbfef8fd5ffae41db, 0x3fc51bdf8597c5f2, // -0.98631, 0.16491 + 0xbfef93f14f85ac08, 0x3fc4b8b17f79fa88, // -0.98681, 0.16189 + 0xbfef97f924c9099b, 0x3fc45576b1293e5a, // -0.9873, 0.15886 + 0xbfef9bed7cfbde29, 0x3fc3f22f57db4893, // -0.98778, 0.15583 + 0xbfef9fce55adb2c8, 0x3fc38edbb0cd8d14, // -0.98826, 0.1528 + 0xbfefa39bac7a1791, 0x3fc32b7bf94516a7, // -0.98872, 0.14976 + 0xbfefa7557f08a517, 0x3fc2c8106e8e613a, // -0.98918, 0.14673 + 0xbfefaafbcb0cfddc, 0x3fc264994dfd340a, // -0.98962, 0.1437 + 0xbfefae8e8e46cfbb, 0x3fc20116d4ec7bce, // -0.99006, 0.14066 + 0xbfefb20dc681d54d, 0x3fc19d8940be24e7, // -0.99049, 0.13762 + 0xbfefb5797195d741, 0x3fc139f0cedaf576, // -0.9909, 0.13458 + 0xbfefb8d18d66adb7, 0x3fc0d64dbcb26786, // -0.99131, 0.13154 + 0xbfefbc1617e44186, 0x3fc072a047ba831d, // -0.99171, 0.1285 + 0xbfefbf470f0a8d88, 0x3fc00ee8ad6fb85b, // -0.9921, 0.12545 + 0xbfefc26470e19fd3, 0x3fbf564e56a9730e, // -0.99248, 0.12241 + 0xbfefc56e3b7d9af6, 0x3fbe8eb7fde4aa3e, // -0.99285, 0.11937 + 0xbfefc8646cfeb721, 0x3fbdc70ecbae9fc8, // -0.99321, 0.11632 + 0xbfefcb4703914354, 0x3fbcff533b307dc1, // -0.99356, 0.11327 + 0xbfefce15fd6da67b, 0x3fbc3785c79ec2d5, // -0.99391, 0.11022 + 0xbfefd0d158d86087, 0x3fbb6fa6ec38f64c, // -0.99424, 0.10717 + 0xbfefd37914220b84, 0x3fbaa7b724495c04, // -0.99456, 0.10412 + 0xbfefd60d2da75c9e, 0x3fb9dfb6eb24a85c, // -0.99488, 0.10107 + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017 + 0xbfefdafa7514538c, 0x3fb84f8712c130a0, // -0.99548, 0.094963 + 0xbfefdd539ff1f456, 0x3fb787586a5d5b21, // -0.99577, 0.091909 + 0xbfefdf9922f73307, 0x3fb6bf1b3e79b129, // -0.99604, 0.088854 + 0xbfefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // -0.99631, 0.085797 + 0xbfefe3e92be9d886, 0x3fb52e774a4d4d0a, // -0.99657, 0.08274 + 0xbfefe5f3af2e3940, 0x3fb4661179272096, // -0.99682, 0.079682 + 0xbfefe7ea85482d60, 0x3fb39d9f12c5a299, // -0.99706, 0.076624 + 0xbfefe9cdad01883a, 0x3fb2d52092ce19f6, // -0.99729, 0.073565 + 0xbfefeb9d2530410f, 0x3fb20c9674ed444c, // -0.99751, 0.070505 + 0xbfefed58ecb673c4, 0x3fb1440134d709b2, // -0.99772, 0.067444 + 0xbfefef0102826191, 0x3fb07b614e463064, // -0.99793, 0.064383 + 0xbfeff095658e71ad, 0x3faf656e79f820e0, // -0.99812, 0.061321 + 0xbfeff21614e131ed, 0x3fadd406f9808ec8, // -0.9983, 0.058258 + 0xbfeff3830f8d575c, 0x3fac428d12c0d7e3, // -0.99848, 0.055195 + 0xbfeff4dc54b1bed3, 0x3faab101bd5f8317, // -0.99864, 0.052132 + 0xbfeff621e3796d7e, 0x3fa91f65f10dd814, // -0.9988, 0.049068 + 0xbfeff753bb1b9164, 0x3fa78dbaa5874685, // -0.99894, 0.046003 + 0xbfeff871dadb81df, 0x3fa5fc00d290cd43, // -0.99908, 0.042938 + 0xbfeff97c4208c014, 0x3fa46a396ff86179, // -0.9992, 0.039873 + 0xbfeffa72effef75d, 0x3fa2d865759455cd, // -0.99932, 0.036807 + 0xbfeffb55e425fdae, 0x3fa14685db42c17e, // -0.99943, 0.033741 + 0xbfeffc251df1d3f8, 0x3f9f693731d1cf01, // -0.99953, 0.030675 + 0xbfeffce09ce2a679, 0x3f9c454f4ce53b1c, // -0.99962, 0.027608 + 0xbfeffd886084cd0d, 0x3f992155f7a3667e, // -0.9997, 0.024541 + 0xbfeffe1c6870cb77, 0x3f95fd4d21fab226, // -0.99977, 0.021474 + 0xbfeffe9cb44b51a1, 0x3f92d936bbe30efd, // -0.99983, 0.018407 + 0xbfefff0943c53bd1, 0x3f8f6a296ab997ca, // -0.99988, 0.015339 + 0xbfefff62169b92db, 0x3f8921d1fcdec784, // -0.99992, 0.012272 + 0xbfefffa72c978c4f, 0x3f82d96b0e509703, // -0.99996, 0.0092038 + 0xbfefffd8858e8a92, 0x3f7921f0fe670071, // -0.99998, 0.0061359 + 0xbfeffff621621d02, 0x3f6921f8becca4ba, // -1, 0.003068 + 0xbff0000000000000, 0x0000000000000000, // -1, 0 + 0xbfeffff621621d02, 0xbf6921f8becca4ba, // -1, -0.003068 + 0xbfefffd8858e8a92, 0xbf7921f0fe670071, // -0.99998,-0.0061359 + 0xbfefffa72c978c4f, 0xbf82d96b0e509703, // -0.99996,-0.0092038 + 0xbfefff62169b92db, 0xbf8921d1fcdec784, // -0.99992, -0.012272 + 0xbfefff0943c53bd1, 0xbf8f6a296ab997ca, // -0.99988, -0.015339 + 0xbfeffe9cb44b51a1, 0xbf92d936bbe30efd, // -0.99983, -0.018407 + 0xbfeffe1c6870cb77, 0xbf95fd4d21fab226, // -0.99977, -0.021474 + 0xbfeffd886084cd0d, 0xbf992155f7a3667e, // -0.9997, -0.024541 + 0xbfeffce09ce2a679, 0xbf9c454f4ce53b1c, // -0.99962, -0.027608 + 0xbfeffc251df1d3f8, 0xbf9f693731d1cf01, // -0.99953, -0.030675 + 0xbfeffb55e425fdae, 0xbfa14685db42c17e, // -0.99943, -0.033741 + 0xbfeffa72effef75d, 0xbfa2d865759455cd, // -0.99932, -0.036807 + 0xbfeff97c4208c014, 0xbfa46a396ff86179, // -0.9992, -0.039873 + 0xbfeff871dadb81df, 0xbfa5fc00d290cd43, // -0.99908, -0.042938 + 0xbfeff753bb1b9164, 0xbfa78dbaa5874685, // -0.99894, -0.046003 + 0xbfeff621e3796d7e, 0xbfa91f65f10dd814, // -0.9988, -0.049068 + 0xbfeff4dc54b1bed3, 0xbfaab101bd5f8317, // -0.99864, -0.052132 + 0xbfeff3830f8d575c, 0xbfac428d12c0d7e3, // -0.99848, -0.055195 + 0xbfeff21614e131ed, 0xbfadd406f9808ec8, // -0.9983, -0.058258 + 0xbfeff095658e71ad, 0xbfaf656e79f820e0, // -0.99812, -0.061321 + 0xbfefef0102826191, 0xbfb07b614e463064, // -0.99793, -0.064383 + 0xbfefed58ecb673c4, 0xbfb1440134d709b2, // -0.99772, -0.067444 + 0xbfefeb9d2530410f, 0xbfb20c9674ed444c, // -0.99751, -0.070505 + 0xbfefe9cdad01883a, 0xbfb2d52092ce19f6, // -0.99729, -0.073565 + 0xbfefe7ea85482d60, 0xbfb39d9f12c5a299, // -0.99706, -0.076624 + 0xbfefe5f3af2e3940, 0xbfb4661179272096, // -0.99682, -0.079682 + 0xbfefe3e92be9d886, 0xbfb52e774a4d4d0a, // -0.99657, -0.08274 + 0xbfefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // -0.99631, -0.085797 + 0xbfefdf9922f73307, 0xbfb6bf1b3e79b129, // -0.99604, -0.088854 + 0xbfefdd539ff1f456, 0xbfb787586a5d5b21, // -0.99577, -0.091909 + 0xbfefdafa7514538c, 0xbfb84f8712c130a0, // -0.99548, -0.094963 + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518, -0.098017 + 0xbfefd60d2da75c9e, 0xbfb9dfb6eb24a85c, // -0.99488, -0.10107 + 0xbfefd37914220b84, 0xbfbaa7b724495c04, // -0.99456, -0.10412 + 0xbfefd0d158d86087, 0xbfbb6fa6ec38f64c, // -0.99424, -0.10717 + 0xbfefce15fd6da67b, 0xbfbc3785c79ec2d5, // -0.99391, -0.11022 + 0xbfefcb4703914354, 0xbfbcff533b307dc1, // -0.99356, -0.11327 + 0xbfefc8646cfeb721, 0xbfbdc70ecbae9fc8, // -0.99321, -0.11632 + 0xbfefc56e3b7d9af6, 0xbfbe8eb7fde4aa3e, // -0.99285, -0.11937 + 0xbfefc26470e19fd3, 0xbfbf564e56a9730e, // -0.99248, -0.12241 + 0xbfefbf470f0a8d88, 0xbfc00ee8ad6fb85b, // -0.9921, -0.12545 + 0xbfefbc1617e44186, 0xbfc072a047ba831d, // -0.99171, -0.1285 + 0xbfefb8d18d66adb7, 0xbfc0d64dbcb26786, // -0.99131, -0.13154 + 0xbfefb5797195d741, 0xbfc139f0cedaf576, // -0.9909, -0.13458 + 0xbfefb20dc681d54d, 0xbfc19d8940be24e7, // -0.99049, -0.13762 + 0xbfefae8e8e46cfbb, 0xbfc20116d4ec7bce, // -0.99006, -0.14066 + 0xbfefaafbcb0cfddc, 0xbfc264994dfd340a, // -0.98962, -0.1437 + 0xbfefa7557f08a517, 0xbfc2c8106e8e613a, // -0.98918, -0.14673 + 0xbfefa39bac7a1791, 0xbfc32b7bf94516a7, // -0.98872, -0.14976 + 0xbfef9fce55adb2c8, 0xbfc38edbb0cd8d14, // -0.98826, -0.1528 + 0xbfef9bed7cfbde29, 0xbfc3f22f57db4893, // -0.98778, -0.15583 + 0xbfef97f924c9099b, 0xbfc45576b1293e5a, // -0.9873, -0.15886 + 0xbfef93f14f85ac08, 0xbfc4b8b17f79fa88, // -0.98681, -0.16189 + 0xbfef8fd5ffae41db, 0xbfc51bdf8597c5f2, // -0.98631, -0.16491 + 0xbfef8ba737cb4b78, 0xbfc57f008654cbde, // -0.9858, -0.16794 + 0xbfef8764fa714ba9, 0xbfc5e214448b3fc6, // -0.98528, -0.17096 + 0xbfef830f4a40c60c, 0xbfc6451a831d830d, // -0.98475, -0.17398 + 0xbfef7ea629e63d6e, 0xbfc6a81304f64ab2, // -0.98421, -0.177 + 0xbfef7a299c1a322a, 0xbfc70afd8d08c4ff, // -0.98366, -0.18002 + 0xbfef7599a3a12077, 0xbfc76dd9de50bf31, // -0.98311, -0.18304 + 0xbfef70f6434b7eb7, 0xbfc7d0a7bbd2cb1b, // -0.98254, -0.18606 + 0xbfef6c3f7df5bbb7, 0xbfc83366e89c64c5, // -0.98196, -0.18907 + 0xbfef677556883cee, 0xbfc8961727c41804, // -0.98138, -0.19208 + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509 + 0xbfef5da6ed43685d, 0xbfc95b49e9b62af9, // -0.98018, -0.1981 + 0xbfef58a2b1789e84, 0xbfc9bdcbf2dc4366, // -0.97957, -0.2011 + 0xbfef538b1faf2d07, 0xbfca203e1b1831da, // -0.97895, -0.20411 + 0xbfef4e603b0b2f2d, 0xbfca82a025b00451, // -0.97832, -0.20711 + 0xbfef492206bcabb4, 0xbfcae4f1d5f3b9ab, // -0.97768, -0.21011 + 0xbfef43d085ff92dd, 0xbfcb4732ef3d6722, // -0.97703, -0.21311 + 0xbfef3e6bbc1bbc65, 0xbfcba96334f15dad, // -0.97637, -0.21611 + 0xbfef38f3ac64e589, 0xbfcc0b826a7e4f63, // -0.9757, -0.2191 + 0xbfef33685a3aaef0, 0xbfcc6d90535d74dc, // -0.97503, -0.22209 + 0xbfef2dc9c9089a9d, 0xbfcccf8cb312b286, // -0.97434, -0.22508 + 0xbfef2817fc4609ce, 0xbfcd31774d2cbdee, // -0.97364, -0.22807 + 0xbfef2252f7763ada, 0xbfcd934fe5454311, // -0.97294, -0.23106 + 0xbfef1c7abe284708, 0xbfcdf5163f01099a, // -0.97223, -0.23404 + 0xbfef168f53f7205d, 0xbfce56ca1e101a1b, // -0.9715, -0.23702 + 0xbfef1090bc898f5f, 0xbfceb86b462de348, // -0.97077, -0.24 + 0xbfef0a7efb9230d7, 0xbfcf19f97b215f1a, // -0.97003, -0.24298 + 0xbfef045a14cf738c, 0xbfcf7b7480bd3801, // -0.96928, -0.24596 + 0xbfeefe220c0b95ec, 0xbfcfdcdc1adfedf8, // -0.96852, -0.24893 + 0xbfeef7d6e51ca3c0, 0xbfd01f1806b9fdd2, // -0.96775, -0.2519 + 0xbfeef178a3e473c2, 0xbfd04fb80e37fdae, // -0.96698, -0.25487 + 0xbfeeeb074c50a544, 0xbfd0804e05eb661e, // -0.96619, -0.25783 + 0xbfeee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // -0.96539, -0.26079 + 0xbfeeddeb6a078651, 0xbfd0e15b4e1749cd, // -0.96459, -0.26375 + 0xbfeed740e7684963, 0xbfd111d262b1f677, // -0.96378, -0.26671 + 0xbfeed0835e999009, 0xbfd1423eefc69378, // -0.96295, -0.26967 + 0xbfeec9b2d3c3bf84, 0xbfd172a0d7765177, // -0.96212, -0.27262 + 0xbfeec2cf4b1af6b2, 0xbfd1a2f7fbe8f243, // -0.96128, -0.27557 + 0xbfeebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // -0.96043, -0.27852 + 0xbfeeb4cf515b8811, 0xbfd2038583d727bd, // -0.95957, -0.28146 + 0xbfeeadb2e8e7a88e, 0xbfd233bbabc3bb72, // -0.9587, -0.28441 + 0xbfeea68393e65800, 0xbfd263e6995554ba, // -0.95783, -0.28735 + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028 + 0xbfee97ec36016b30, 0xbfd2c41a4e954520, // -0.95605, -0.29322 + 0xbfee9084361df7f3, 0xbfd2f422daec0386, // -0.95514, -0.29615 + 0xbfee89095bad6025, 0xbfd3241fb638baaf, // -0.95423, -0.29908 + 0xbfee817bab4cd10d, 0xbfd35410c2e18152, // -0.95331, -0.30201 + 0xbfee79db29a5165a, 0xbfd383f5e353b6aa, // -0.95238, -0.30493 + 0xbfee7227db6a9744, 0xbfd3b3cefa0414b7, // -0.95144, -0.30785 + 0xbfee6a61c55d53a7, 0xbfd3e39be96ec271, // -0.95049, -0.31077 + 0xbfee6288ec48e112, 0xbfd4135c94176602, // -0.94953, -0.31368 + 0xbfee5a9d550467d3, 0xbfd44310dc8936f0, // -0.94856, -0.31659 + 0xbfee529f04729ffc, 0xbfd472b8a5571054, // -0.94759, -0.3195 + 0xbfee4a8dff81ce5e, 0xbfd4a253d11b82f3, // -0.9466, -0.32241 + 0xbfee426a4b2bc17e, 0xbfd4d1e24278e76a, // -0.94561, -0.32531 + 0xbfee3a33ec75ce85, 0xbfd50163dc197047, // -0.9446, -0.32821 + 0xbfee31eae870ce25, 0xbfd530d880af3c24, // -0.94359, -0.33111 + 0xbfee298f4439197a, 0xbfd5604012f467b4, // -0.94257, -0.334 + 0xbfee212104f686e5, 0xbfd58f9a75ab1fdd, // -0.94154, -0.33689 + 0xbfee18a02fdc66d9, 0xbfd5bee78b9db3b6, // -0.94051, -0.33978 + 0xbfee100cca2980ac, 0xbfd5ee27379ea693, // -0.93946, -0.34266 + 0xbfee0766d9280f54, 0xbfd61d595c88c203, // -0.9384, -0.34554 + 0xbfedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // -0.93734, -0.34842 + 0xbfedf5e36a9ba59c, 0xbfd67b949cad63ca, // -0.93627, -0.35129 + 0xbfeded05f7de47da, 0xbfd6aa9d7dc77e16, // -0.93518, -0.35416 + 0xbfede4160f6d8d81, 0xbfd6d998638a0cb5, // -0.93409, -0.35703 + 0xbfeddb13b6ccc23d, 0xbfd7088530fa459e, // -0.93299, -0.3599 + 0xbfedd1fef38a915a, 0xbfd73763c9261092, // -0.93188, -0.36276 + 0xbfedc8d7cb410260, 0xbfd766340f2418f6, // -0.93077, -0.36561 + 0xbfedbf9e4395759a, 0xbfd794f5e613dfae, // -0.92964, -0.36847 + 0xbfedb6526238a09b, 0xbfd7c3a9311dcce7, // -0.92851, -0.37132 + 0xbfedacf42ce68ab9, 0xbfd7f24dd37341e3, // -0.92736, -0.37416 + 0xbfeda383a9668988, 0xbfd820e3b04eaac4, // -0.92621, -0.37701 + 0xbfed9a00dd8b3d46, 0xbfd84f6aaaf3903f, // -0.92505, -0.37985 + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268 + 0xbfed86c48445a450, 0xbfd8ac4b86d5ed44, // -0.9227, -0.38552 + 0xbfed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // -0.92151, -0.38835 + 0xbfed733f508c0dff, 0xbfd908ef81ef7bd1, // -0.92032, -0.39117 + 0xbfed696173c9e68b, 0xbfd9372a63bc93d7, // -0.91911, -0.39399 + 0xbfed5f7172888a7f, 0xbfd96555b7ab948f, // -0.9179, -0.39681 + 0xbfed556f52e93eb1, 0xbfd993716141bdfe, // -0.91668, -0.39962 + 0xbfed4b5b1b187524, 0xbfd9c17d440df9f2, // -0.91545, -0.40243 + 0xbfed4134d14dc93a, 0xbfd9ef7943a8ed8a, // -0.91421, -0.40524 + 0xbfed36fc7bcbfbdc, 0xbfda1d6543b50ac0, // -0.91296, -0.40804 + 0xbfed2cb220e0ef9f, 0xbfda4b4127dea1e4, // -0.91171, -0.41084 + 0xbfed2255c6e5a4e1, 0xbfda790cd3dbf31a, // -0.91044, -0.41364 + 0xbfed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // -0.90917, -0.41643 + 0xbfed0d672f59d2b9, 0xbfdad473125cdc08, // -0.90789, -0.41922 + 0xbfed02d4feb2bd92, 0xbfdb020d6c7f4009, // -0.9066, -0.422 + 0xbfecf830e8ce467b, 0xbfdb2f971db31972, // -0.9053, -0.42478 + 0xbfeced7af43cc773, 0xbfdb5d1009e15cc0, // -0.90399, -0.42756 + 0xbfece2b32799a060, 0xbfdb8a7814fd5693, // -0.90267, -0.43033 + 0xbfecd7d9898b32f6, 0xbfdbb7cf2304bd01, // -0.90135, -0.43309 + 0xbfecccee20c2de9f, 0xbfdbe51517ffc0d9, // -0.90002, -0.43586 + 0xbfecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // -0.89867, -0.43862 + 0xbfecb6e20a00da99, 0xbfdc3f6d47263129, // -0.89732, -0.44137 + 0xbfecabc169a0b901, 0xbfdc6c7f4997000a, // -0.89597, -0.44412 + 0xbfeca08f19b9c449, 0xbfdc997fc3865388, // -0.8946, -0.44687 + 0xbfec954b213411f5, 0xbfdcc66e9931c45d, // -0.89322, -0.44961 + 0xbfec89f587029c13, 0xbfdcf34baee1cd21, // -0.89184, -0.45235 + 0xbfec7e8e52233cf3, 0xbfdd2016e8e9db5b, // -0.89045, -0.45508 + 0xbfec7315899eaad7, 0xbfdd4cd02ba8609c, // -0.88905, -0.45781 + 0xbfec678b3488739b, 0xbfdd79775b86e389, // -0.88764, -0.46054 + 0xbfec5bef59fef85a, 0xbfdda60c5cfa10d8, // -0.88622, -0.46326 + 0xbfec5042012b6907, 0xbfddd28f1481cc58, // -0.8848, -0.46598 + 0xbfec44833141c004, 0xbfddfeff66a941de, // -0.88336, -0.46869 + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714 + 0xbfec2cd14931e3f1, 0xbfde57a86d3cd824, // -0.88047, -0.4741 + 0xbfec20de3fa971b0, 0xbfde83e0eaf85113, // -0.87901, -0.4768 + 0xbfec14d9dc465e58, 0xbfdeb00695f25620, // -0.87755, -0.47949 + 0xbfec08c426725549, 0xbfdedc1952ef78d5, // -0.87607, -0.48218 + 0xbfebfc9d25a1b147, 0xbfdf081906bff7fd, // -0.87459, -0.48487 + 0xbfebf064e15377dd, 0xbfdf3405963fd068, // -0.87309, -0.48755 + 0xbfebe41b611154c1, 0xbfdf5fdee656cda3, // -0.8716, -0.49023 + 0xbfebd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // -0.87009, -0.4929 + 0xbfebcb54cb0d2327, 0xbfdfb7575c24d2de, // -0.86857, -0.49557 + 0xbfebbed7c49380ea, 0xbfdfe2f64be7120f, // -0.86705, -0.49823 + 0xbfebb249a0b6c40d, 0xbfe00740c82b82e0, // -0.86551, -0.50089 + 0xbfeba5aa673590d2, 0xbfe01cfc874c3eb7, // -0.86397, -0.50354 + 0xbfeb98fa1fd9155e, 0xbfe032ae55edbd95, // -0.86242, -0.50619 + 0xbfeb8c38d27504e9, 0xbfe0485626ae221a, // -0.86087, -0.50883 + 0xbfeb7f6686e792ea, 0xbfe05df3ec31b8b6, // -0.8593, -0.51147 + 0xbfeb728345196e3e, 0xbfe073879922ffed, // -0.85773, -0.5141 + 0xbfeb658f14fdbc47, 0xbfe089112032b08c, // -0.85615, -0.51673 + 0xbfeb5889fe921405, 0xbfe09e907417c5e1, // -0.85456, -0.51936 + 0xbfeb4b7409de7925, 0xbfe0b405878f85ec, // -0.85296, -0.52198 + 0xbfeb3e4d3ef55712, 0xbfe0c9704d5d898f, // -0.85136, -0.52459 + 0xbfeb3115a5f37bf4, 0xbfe0ded0b84bc4b5, // -0.84974, -0.5272 + 0xbfeb23cd470013b4, 0xbfe0f426bb2a8e7d, // -0.84812, -0.5298 + 0xbfeb16742a4ca2f5, 0xbfe1097248d0a956, // -0.84649, -0.5324 + 0xbfeb090a58150200, 0xbfe11eb3541b4b22, // -0.84485, -0.535 + 0xbfeafb8fd89f57b6, 0xbfe133e9cfee254e, // -0.84321, -0.53759 + 0xbfeaee04b43c1474, 0xbfe14915af336ceb, // -0.84155, -0.54017 + 0xbfeae068f345ecef, 0xbfe15e36e4dbe2bc, // -0.83989, -0.54275 + 0xbfead2bc9e21d511, 0xbfe1734d63dedb49, // -0.83822, -0.54532 + 0xbfeac4ffbd3efac8, 0xbfe188591f3a46e5, // -0.83655, -0.54789 + 0xbfeab7325916c0d4, 0xbfe19d5a09f2b9b8, // -0.83486, -0.55046 + 0xbfeaa9547a2cb98e, 0xbfe1b250171373be, // -0.83317, -0.55302 + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557 + 0xbfea8d676e545ad2, 0xbfe1dc1b64dc4872, // -0.82976, -0.55812 + 0xbfea7f58529fe69d, 0xbfe1f0f08bbc861b, // -0.82805, -0.56066 + 0xbfea7138de9d60f5, 0xbfe205baa17560d6, // -0.82632, -0.5632 + 0xbfea63091b02fae2, 0xbfe21a799933eb58, // -0.82459, -0.56573 + 0xbfea54c91090f524, 0xbfe22f2d662c13e1, // -0.82285, -0.56826 + 0xbfea4678c8119ac8, 0xbfe243d5fb98ac1f, // -0.8211, -0.57078 + 0xbfea38184a593bc6, 0xbfe258734cbb7110, // -0.81935, -0.5733 + 0xbfea29a7a0462782, 0xbfe26d054cdd12df, // -0.81758, -0.57581 + 0xbfea1b26d2c0a75e, 0xbfe2818bef4d3cba, // -0.81581, -0.57831 + 0xbfea0c95eabaf937, 0xbfe2960727629ca8, // -0.81404, -0.58081 + 0xbfe9fdf4f13149de, 0xbfe2aa76e87aeb58, // -0.81225, -0.58331 + 0xbfe9ef43ef29af94, 0xbfe2bedb25faf3ea, // -0.81046, -0.5858 + 0xbfe9e082edb42472, 0xbfe2d333d34e9bb7, // -0.80866, -0.58828 + 0xbfe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // -0.80685, -0.59076 + 0xbfe9c2d110f075c3, 0xbfe2fbc24b441015, // -0.80503, -0.59323 + 0xbfe9b3e047f38741, 0xbfe30ff7fce17035, // -0.80321, -0.5957 + 0xbfe9a4dfa42b06b2, 0xbfe32421ec49a620, // -0.80138, -0.59816 + 0xbfe995cf2ed80d22, 0xbfe338400d0c8e57, // -0.79954, -0.60062 + 0xbfe986aef1457594, 0xbfe34c5252c14de1, // -0.79769, -0.60307 + 0xbfe9777ef4c7d742, 0xbfe36058b10659f3, // -0.79584, -0.60551 + 0xbfe9683f42bd7fe1, 0xbfe374531b817f8d, // -0.79398, -0.60795 + 0xbfe958efe48e6dd7, 0xbfe3884185dfeb22, // -0.79211, -0.61038 + 0xbfe94990e3ac4a6c, 0xbfe39c23e3d63029, // -0.79023, -0.61281 + 0xbfe93a22499263fc, 0xbfe3affa292050b9, // -0.78835, -0.61523 + 0xbfe92aa41fc5a815, 0xbfe3c3c44981c517, // -0.78646, -0.61765 + 0xbfe91b166fd49da2, 0xbfe3d78238c58343, // -0.78456, -0.62006 + 0xbfe90b7943575efe, 0xbfe3eb33eabe0680, // -0.78265, -0.62246 + 0xbfe8fbcca3ef940d, 0xbfe3fed9534556d4, // -0.78074, -0.62486 + 0xbfe8ec109b486c49, 0xbfe41272663d108c, // -0.77882, -0.62725 + 0xbfe8dc45331698cc, 0xbfe425ff178e6bb1, // -0.77689, -0.62964 + 0xbfe8cc6a75184655, 0xbfe4397f5b2a4380, // -0.77495, -0.63202 + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439 + 0xbfe8ac871ede1d88, 0xbfe4605a692b32a2, // -0.77106, -0.63676 + 0xbfe89c7e9a4dd4ab, 0xbfe473b51b987347, // -0.7691, -0.63912 + 0xbfe88c66e7481ba1, 0xbfe48703306091fe, // -0.76714, -0.64148 + 0xbfe87c400fba2ebf, 0xbfe49a449b9b0938, // -0.76517, -0.64383 + 0xbfe86c0a1d9aa195, 0xbfe4ad79516722f0, // -0.76319, -0.64618 + 0xbfe85bc51ae958cc, 0xbfe4c0a145ec0004, // -0.7612, -0.64851 + 0xbfe84b7111af83f9, 0xbfe4d3bc6d589f80, // -0.75921, -0.65085 + 0xbfe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // -0.75721, -0.65317 + 0xbfe82a9c13f545ff, 0xbfe4f9cc25cca486, // -0.7552, -0.65549 + 0xbfe81a1b33b57acc, 0xbfe50cc09f59a09b, // -0.75319, -0.65781 + 0xbfe8098b756e52fa, 0xbfe51fa81cd99aa6, // -0.75117, -0.66011 + 0xbfe7f8ece3571771, 0xbfe5328292a35596, // -0.74914, -0.66242 + 0xbfe7e83f87b03686, 0xbfe5454ff5159dfb, // -0.7471, -0.66471 + 0xbfe7d7836cc33db2, 0xbfe5581038975137, // -0.74506, -0.667 + 0xbfe7c6b89ce2d333, 0xbfe56ac35197649e, // -0.74301, -0.66928 + 0xbfe7b5df226aafb0, 0xbfe57d69348cec9f, // -0.74095, -0.67156 + 0xbfe7a4f707bf97d2, 0xbfe59001d5f723df, // -0.73889, -0.67383 + 0xbfe79400574f55e4, 0xbfe5a28d2a5d7250, // -0.73682, -0.67609 + 0xbfe782fb1b90b35b, 0xbfe5b50b264f7448, // -0.73474, -0.67835 + 0xbfe771e75f037261, 0xbfe5c77bbe65018c, // -0.73265, -0.6806 + 0xbfe760c52c304764, 0xbfe5d9dee73e345c, // -0.73056, -0.68285 + 0xbfe74f948da8d28d, 0xbfe5ec3495837074, // -0.72846, -0.68508 + 0xbfe73e558e079942, 0xbfe5fe7cbde56a0f, // -0.72636, -0.68732 + 0xbfe72d0837efff97, 0xbfe610b7551d2cde, // -0.72425, -0.68954 + 0xbfe71bac960e41bf, 0xbfe622e44fec22ff, // -0.72213, -0.69176 + 0xbfe70a42b3176d7a, 0xbfe63503a31c1be8, // -0.72, -0.69397 + 0xbfe6f8ca99c95b75, 0xbfe64715437f535b, // -0.71787, -0.69618 + 0xbfe6e74454eaa8ae, 0xbfe6591925f0783e, // -0.71573, -0.69838 + 0xbfe6d5afef4aafcc, 0xbfe66b0f3f52b386, // -0.71358, -0.70057 + 0xbfe6c40d73c18275, 0xbfe67cf78491af10, // -0.71143, -0.70275 + 0xbfe6b25ced2fe29c, 0xbfe68ed1eaa19c71, // -0.70927, -0.70493 + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711 + 0xbfe68ed1eaa19c71, 0xbfe6b25ced2fe29c, // -0.70493, -0.70927 + 0xbfe67cf78491af10, 0xbfe6c40d73c18275, // -0.70275, -0.71143 + 0xbfe66b0f3f52b386, 0xbfe6d5afef4aafcc, // -0.70057, -0.71358 + 0xbfe6591925f0783e, 0xbfe6e74454eaa8ae, // -0.69838, -0.71573 + 0xbfe64715437f535b, 0xbfe6f8ca99c95b75, // -0.69618, -0.71787 + 0xbfe63503a31c1be8, 0xbfe70a42b3176d7a, // -0.69397, -0.72 + 0xbfe622e44fec22ff, 0xbfe71bac960e41bf, // -0.69176, -0.72213 + 0xbfe610b7551d2cde, 0xbfe72d0837efff97, // -0.68954, -0.72425 + 0xbfe5fe7cbde56a0f, 0xbfe73e558e079942, // -0.68732, -0.72636 + 0xbfe5ec3495837074, 0xbfe74f948da8d28d, // -0.68508, -0.72846 + 0xbfe5d9dee73e345c, 0xbfe760c52c304764, // -0.68285, -0.73056 + 0xbfe5c77bbe65018c, 0xbfe771e75f037261, // -0.6806, -0.73265 + 0xbfe5b50b264f7448, 0xbfe782fb1b90b35b, // -0.67835, -0.73474 + 0xbfe5a28d2a5d7250, 0xbfe79400574f55e4, // -0.67609, -0.73682 + 0xbfe59001d5f723df, 0xbfe7a4f707bf97d2, // -0.67383, -0.73889 + 0xbfe57d69348cec9f, 0xbfe7b5df226aafb0, // -0.67156, -0.74095 + 0xbfe56ac35197649e, 0xbfe7c6b89ce2d333, // -0.66928, -0.74301 + 0xbfe5581038975137, 0xbfe7d7836cc33db2, // -0.667, -0.74506 + 0xbfe5454ff5159dfb, 0xbfe7e83f87b03686, // -0.66471, -0.7471 + 0xbfe5328292a35596, 0xbfe7f8ece3571771, // -0.66242, -0.74914 + 0xbfe51fa81cd99aa6, 0xbfe8098b756e52fa, // -0.66011, -0.75117 + 0xbfe50cc09f59a09b, 0xbfe81a1b33b57acc, // -0.65781, -0.75319 + 0xbfe4f9cc25cca486, 0xbfe82a9c13f545ff, // -0.65549, -0.7552 + 0xbfe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // -0.65317, -0.75721 + 0xbfe4d3bc6d589f80, 0xbfe84b7111af83f9, // -0.65085, -0.75921 + 0xbfe4c0a145ec0004, 0xbfe85bc51ae958cc, // -0.64851, -0.7612 + 0xbfe4ad79516722f0, 0xbfe86c0a1d9aa195, // -0.64618, -0.76319 + 0xbfe49a449b9b0938, 0xbfe87c400fba2ebf, // -0.64383, -0.76517 + 0xbfe48703306091fe, 0xbfe88c66e7481ba1, // -0.64148, -0.76714 + 0xbfe473b51b987347, 0xbfe89c7e9a4dd4ab, // -0.63912, -0.7691 + 0xbfe4605a692b32a2, 0xbfe8ac871ede1d88, // -0.63676, -0.77106 + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301 + 0xbfe4397f5b2a4380, 0xbfe8cc6a75184655, // -0.63202, -0.77495 + 0xbfe425ff178e6bb1, 0xbfe8dc45331698cc, // -0.62964, -0.77689 + 0xbfe41272663d108c, 0xbfe8ec109b486c49, // -0.62725, -0.77882 + 0xbfe3fed9534556d4, 0xbfe8fbcca3ef940d, // -0.62486, -0.78074 + 0xbfe3eb33eabe0680, 0xbfe90b7943575efe, // -0.62246, -0.78265 + 0xbfe3d78238c58343, 0xbfe91b166fd49da2, // -0.62006, -0.78456 + 0xbfe3c3c44981c517, 0xbfe92aa41fc5a815, // -0.61765, -0.78646 + 0xbfe3affa292050b9, 0xbfe93a22499263fc, // -0.61523, -0.78835 + 0xbfe39c23e3d63029, 0xbfe94990e3ac4a6c, // -0.61281, -0.79023 + 0xbfe3884185dfeb22, 0xbfe958efe48e6dd7, // -0.61038, -0.79211 + 0xbfe374531b817f8d, 0xbfe9683f42bd7fe1, // -0.60795, -0.79398 + 0xbfe36058b10659f3, 0xbfe9777ef4c7d742, // -0.60551, -0.79584 + 0xbfe34c5252c14de1, 0xbfe986aef1457594, // -0.60307, -0.79769 + 0xbfe338400d0c8e57, 0xbfe995cf2ed80d22, // -0.60062, -0.79954 + 0xbfe32421ec49a620, 0xbfe9a4dfa42b06b2, // -0.59816, -0.80138 + 0xbfe30ff7fce17035, 0xbfe9b3e047f38741, // -0.5957, -0.80321 + 0xbfe2fbc24b441015, 0xbfe9c2d110f075c3, // -0.59323, -0.80503 + 0xbfe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // -0.59076, -0.80685 + 0xbfe2d333d34e9bb7, 0xbfe9e082edb42472, // -0.58828, -0.80866 + 0xbfe2bedb25faf3ea, 0xbfe9ef43ef29af94, // -0.5858, -0.81046 + 0xbfe2aa76e87aeb58, 0xbfe9fdf4f13149de, // -0.58331, -0.81225 + 0xbfe2960727629ca8, 0xbfea0c95eabaf937, // -0.58081, -0.81404 + 0xbfe2818bef4d3cba, 0xbfea1b26d2c0a75e, // -0.57831, -0.81581 + 0xbfe26d054cdd12df, 0xbfea29a7a0462782, // -0.57581, -0.81758 + 0xbfe258734cbb7110, 0xbfea38184a593bc6, // -0.5733, -0.81935 + 0xbfe243d5fb98ac1f, 0xbfea4678c8119ac8, // -0.57078, -0.8211 + 0xbfe22f2d662c13e1, 0xbfea54c91090f524, // -0.56826, -0.82285 + 0xbfe21a799933eb58, 0xbfea63091b02fae2, // -0.56573, -0.82459 + 0xbfe205baa17560d6, 0xbfea7138de9d60f5, // -0.5632, -0.82632 + 0xbfe1f0f08bbc861b, 0xbfea7f58529fe69d, // -0.56066, -0.82805 + 0xbfe1dc1b64dc4872, 0xbfea8d676e545ad2, // -0.55812, -0.82976 + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147 + 0xbfe1b250171373be, 0xbfeaa9547a2cb98e, // -0.55302, -0.83317 + 0xbfe19d5a09f2b9b8, 0xbfeab7325916c0d4, // -0.55046, -0.83486 + 0xbfe188591f3a46e5, 0xbfeac4ffbd3efac8, // -0.54789, -0.83655 + 0xbfe1734d63dedb49, 0xbfead2bc9e21d511, // -0.54532, -0.83822 + 0xbfe15e36e4dbe2bc, 0xbfeae068f345ecef, // -0.54275, -0.83989 + 0xbfe14915af336ceb, 0xbfeaee04b43c1474, // -0.54017, -0.84155 + 0xbfe133e9cfee254e, 0xbfeafb8fd89f57b6, // -0.53759, -0.84321 + 0xbfe11eb3541b4b22, 0xbfeb090a58150200, // -0.535, -0.84485 + 0xbfe1097248d0a956, 0xbfeb16742a4ca2f5, // -0.5324, -0.84649 + 0xbfe0f426bb2a8e7d, 0xbfeb23cd470013b4, // -0.5298, -0.84812 + 0xbfe0ded0b84bc4b5, 0xbfeb3115a5f37bf4, // -0.5272, -0.84974 + 0xbfe0c9704d5d898f, 0xbfeb3e4d3ef55712, // -0.52459, -0.85136 + 0xbfe0b405878f85ec, 0xbfeb4b7409de7925, // -0.52198, -0.85296 + 0xbfe09e907417c5e1, 0xbfeb5889fe921405, // -0.51936, -0.85456 + 0xbfe089112032b08c, 0xbfeb658f14fdbc47, // -0.51673, -0.85615 + 0xbfe073879922ffed, 0xbfeb728345196e3e, // -0.5141, -0.85773 + 0xbfe05df3ec31b8b6, 0xbfeb7f6686e792ea, // -0.51147, -0.8593 + 0xbfe0485626ae221a, 0xbfeb8c38d27504e9, // -0.50883, -0.86087 + 0xbfe032ae55edbd95, 0xbfeb98fa1fd9155e, // -0.50619, -0.86242 + 0xbfe01cfc874c3eb7, 0xbfeba5aa673590d2, // -0.50354, -0.86397 + 0xbfe00740c82b82e0, 0xbfebb249a0b6c40d, // -0.50089, -0.86551 + 0xbfdfe2f64be7120f, 0xbfebbed7c49380ea, // -0.49823, -0.86705 + 0xbfdfb7575c24d2de, 0xbfebcb54cb0d2327, // -0.49557, -0.86857 + 0xbfdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // -0.4929, -0.87009 + 0xbfdf5fdee656cda3, 0xbfebe41b611154c1, // -0.49023, -0.8716 + 0xbfdf3405963fd068, 0xbfebf064e15377dd, // -0.48755, -0.87309 + 0xbfdf081906bff7fd, 0xbfebfc9d25a1b147, // -0.48487, -0.87459 + 0xbfdedc1952ef78d5, 0xbfec08c426725549, // -0.48218, -0.87607 + 0xbfdeb00695f25620, 0xbfec14d9dc465e58, // -0.47949, -0.87755 + 0xbfde83e0eaf85113, 0xbfec20de3fa971b0, // -0.4768, -0.87901 + 0xbfde57a86d3cd824, 0xbfec2cd14931e3f1, // -0.4741, -0.88047 + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192 + 0xbfddfeff66a941de, 0xbfec44833141c004, // -0.46869, -0.88336 + 0xbfddd28f1481cc58, 0xbfec5042012b6907, // -0.46598, -0.8848 + 0xbfdda60c5cfa10d8, 0xbfec5bef59fef85a, // -0.46326, -0.88622 + 0xbfdd79775b86e389, 0xbfec678b3488739b, // -0.46054, -0.88764 + 0xbfdd4cd02ba8609c, 0xbfec7315899eaad7, // -0.45781, -0.88905 + 0xbfdd2016e8e9db5b, 0xbfec7e8e52233cf3, // -0.45508, -0.89045 + 0xbfdcf34baee1cd21, 0xbfec89f587029c13, // -0.45235, -0.89184 + 0xbfdcc66e9931c45d, 0xbfec954b213411f5, // -0.44961, -0.89322 + 0xbfdc997fc3865388, 0xbfeca08f19b9c449, // -0.44687, -0.8946 + 0xbfdc6c7f4997000a, 0xbfecabc169a0b901, // -0.44412, -0.89597 + 0xbfdc3f6d47263129, 0xbfecb6e20a00da99, // -0.44137, -0.89732 + 0xbfdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // -0.43862, -0.89867 + 0xbfdbe51517ffc0d9, 0xbfecccee20c2de9f, // -0.43586, -0.90002 + 0xbfdbb7cf2304bd01, 0xbfecd7d9898b32f6, // -0.43309, -0.90135 + 0xbfdb8a7814fd5693, 0xbfece2b32799a060, // -0.43033, -0.90267 + 0xbfdb5d1009e15cc0, 0xbfeced7af43cc773, // -0.42756, -0.90399 + 0xbfdb2f971db31972, 0xbfecf830e8ce467b, // -0.42478, -0.9053 + 0xbfdb020d6c7f4009, 0xbfed02d4feb2bd92, // -0.422, -0.9066 + 0xbfdad473125cdc08, 0xbfed0d672f59d2b9, // -0.41922, -0.90789 + 0xbfdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // -0.41643, -0.90917 + 0xbfda790cd3dbf31a, 0xbfed2255c6e5a4e1, // -0.41364, -0.91044 + 0xbfda4b4127dea1e4, 0xbfed2cb220e0ef9f, // -0.41084, -0.91171 + 0xbfda1d6543b50ac0, 0xbfed36fc7bcbfbdc, // -0.40804, -0.91296 + 0xbfd9ef7943a8ed8a, 0xbfed4134d14dc93a, // -0.40524, -0.91421 + 0xbfd9c17d440df9f2, 0xbfed4b5b1b187524, // -0.40243, -0.91545 + 0xbfd993716141bdfe, 0xbfed556f52e93eb1, // -0.39962, -0.91668 + 0xbfd96555b7ab948f, 0xbfed5f7172888a7f, // -0.39681, -0.9179 + 0xbfd9372a63bc93d7, 0xbfed696173c9e68b, // -0.39399, -0.91911 + 0xbfd908ef81ef7bd1, 0xbfed733f508c0dff, // -0.39117, -0.92032 + 0xbfd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // -0.38835, -0.92151 + 0xbfd8ac4b86d5ed44, 0xbfed86c48445a450, // -0.38552, -0.9227 + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388 + 0xbfd84f6aaaf3903f, 0xbfed9a00dd8b3d46, // -0.37985, -0.92505 + 0xbfd820e3b04eaac4, 0xbfeda383a9668988, // -0.37701, -0.92621 + 0xbfd7f24dd37341e3, 0xbfedacf42ce68ab9, // -0.37416, -0.92736 + 0xbfd7c3a9311dcce7, 0xbfedb6526238a09b, // -0.37132, -0.92851 + 0xbfd794f5e613dfae, 0xbfedbf9e4395759a, // -0.36847, -0.92964 + 0xbfd766340f2418f6, 0xbfedc8d7cb410260, // -0.36561, -0.93077 + 0xbfd73763c9261092, 0xbfedd1fef38a915a, // -0.36276, -0.93188 + 0xbfd7088530fa459e, 0xbfeddb13b6ccc23d, // -0.3599, -0.93299 + 0xbfd6d998638a0cb5, 0xbfede4160f6d8d81, // -0.35703, -0.93409 + 0xbfd6aa9d7dc77e16, 0xbfeded05f7de47da, // -0.35416, -0.93518 + 0xbfd67b949cad63ca, 0xbfedf5e36a9ba59c, // -0.35129, -0.93627 + 0xbfd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // -0.34842, -0.93734 + 0xbfd61d595c88c203, 0xbfee0766d9280f54, // -0.34554, -0.9384 + 0xbfd5ee27379ea693, 0xbfee100cca2980ac, // -0.34266, -0.93946 + 0xbfd5bee78b9db3b6, 0xbfee18a02fdc66d9, // -0.33978, -0.94051 + 0xbfd58f9a75ab1fdd, 0xbfee212104f686e5, // -0.33689, -0.94154 + 0xbfd5604012f467b4, 0xbfee298f4439197a, // -0.334, -0.94257 + 0xbfd530d880af3c24, 0xbfee31eae870ce25, // -0.33111, -0.94359 + 0xbfd50163dc197047, 0xbfee3a33ec75ce85, // -0.32821, -0.9446 + 0xbfd4d1e24278e76a, 0xbfee426a4b2bc17e, // -0.32531, -0.94561 + 0xbfd4a253d11b82f3, 0xbfee4a8dff81ce5e, // -0.32241, -0.9466 + 0xbfd472b8a5571054, 0xbfee529f04729ffc, // -0.3195, -0.94759 + 0xbfd44310dc8936f0, 0xbfee5a9d550467d3, // -0.31659, -0.94856 + 0xbfd4135c94176602, 0xbfee6288ec48e112, // -0.31368, -0.94953 + 0xbfd3e39be96ec271, 0xbfee6a61c55d53a7, // -0.31077, -0.95049 + 0xbfd3b3cefa0414b7, 0xbfee7227db6a9744, // -0.30785, -0.95144 + 0xbfd383f5e353b6aa, 0xbfee79db29a5165a, // -0.30493, -0.95238 + 0xbfd35410c2e18152, 0xbfee817bab4cd10d, // -0.30201, -0.95331 + 0xbfd3241fb638baaf, 0xbfee89095bad6025, // -0.29908, -0.95423 + 0xbfd2f422daec0386, 0xbfee9084361df7f3, // -0.29615, -0.95514 + 0xbfd2c41a4e954520, 0xbfee97ec36016b30, // -0.29322, -0.95605 + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694 + 0xbfd263e6995554ba, 0xbfeea68393e65800, // -0.28735, -0.95783 + 0xbfd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // -0.28441, -0.9587 + 0xbfd2038583d727bd, 0xbfeeb4cf515b8811, // -0.28146, -0.95957 + 0xbfd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // -0.27852, -0.96043 + 0xbfd1a2f7fbe8f243, 0xbfeec2cf4b1af6b2, // -0.27557, -0.96128 + 0xbfd172a0d7765177, 0xbfeec9b2d3c3bf84, // -0.27262, -0.96212 + 0xbfd1423eefc69378, 0xbfeed0835e999009, // -0.26967, -0.96295 + 0xbfd111d262b1f677, 0xbfeed740e7684963, // -0.26671, -0.96378 + 0xbfd0e15b4e1749cd, 0xbfeeddeb6a078651, // -0.26375, -0.96459 + 0xbfd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // -0.26079, -0.96539 + 0xbfd0804e05eb661e, 0xbfeeeb074c50a544, // -0.25783, -0.96619 + 0xbfd04fb80e37fdae, 0xbfeef178a3e473c2, // -0.25487, -0.96698 + 0xbfd01f1806b9fdd2, 0xbfeef7d6e51ca3c0, // -0.2519, -0.96775 + 0xbfcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // -0.24893, -0.96852 + 0xbfcf7b7480bd3801, 0xbfef045a14cf738c, // -0.24596, -0.96928 + 0xbfcf19f97b215f1a, 0xbfef0a7efb9230d7, // -0.24298, -0.97003 + 0xbfceb86b462de348, 0xbfef1090bc898f5f, // -0.24, -0.97077 + 0xbfce56ca1e101a1b, 0xbfef168f53f7205d, // -0.23702, -0.9715 + 0xbfcdf5163f01099a, 0xbfef1c7abe284708, // -0.23404, -0.97223 + 0xbfcd934fe5454311, 0xbfef2252f7763ada, // -0.23106, -0.97294 + 0xbfcd31774d2cbdee, 0xbfef2817fc4609ce, // -0.22807, -0.97364 + 0xbfcccf8cb312b286, 0xbfef2dc9c9089a9d, // -0.22508, -0.97434 + 0xbfcc6d90535d74dc, 0xbfef33685a3aaef0, // -0.22209, -0.97503 + 0xbfcc0b826a7e4f63, 0xbfef38f3ac64e589, // -0.2191, -0.9757 + 0xbfcba96334f15dad, 0xbfef3e6bbc1bbc65, // -0.21611, -0.97637 + 0xbfcb4732ef3d6722, 0xbfef43d085ff92dd, // -0.21311, -0.97703 + 0xbfcae4f1d5f3b9ab, 0xbfef492206bcabb4, // -0.21011, -0.97768 + 0xbfca82a025b00451, 0xbfef4e603b0b2f2d, // -0.20711, -0.97832 + 0xbfca203e1b1831da, 0xbfef538b1faf2d07, // -0.20411, -0.97895 + 0xbfc9bdcbf2dc4366, 0xbfef58a2b1789e84, // -0.2011, -0.97957 + 0xbfc95b49e9b62af9, 0xbfef5da6ed43685d, // -0.1981, -0.98018 + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079 + 0xbfc8961727c41804, 0xbfef677556883cee, // -0.19208, -0.98138 + 0xbfc83366e89c64c5, 0xbfef6c3f7df5bbb7, // -0.18907, -0.98196 + 0xbfc7d0a7bbd2cb1b, 0xbfef70f6434b7eb7, // -0.18606, -0.98254 + 0xbfc76dd9de50bf31, 0xbfef7599a3a12077, // -0.18304, -0.98311 + 0xbfc70afd8d08c4ff, 0xbfef7a299c1a322a, // -0.18002, -0.98366 + 0xbfc6a81304f64ab2, 0xbfef7ea629e63d6e, // -0.177, -0.98421 + 0xbfc6451a831d830d, 0xbfef830f4a40c60c, // -0.17398, -0.98475 + 0xbfc5e214448b3fc6, 0xbfef8764fa714ba9, // -0.17096, -0.98528 + 0xbfc57f008654cbde, 0xbfef8ba737cb4b78, // -0.16794, -0.9858 + 0xbfc51bdf8597c5f2, 0xbfef8fd5ffae41db, // -0.16491, -0.98631 + 0xbfc4b8b17f79fa88, 0xbfef93f14f85ac08, // -0.16189, -0.98681 + 0xbfc45576b1293e5a, 0xbfef97f924c9099b, // -0.15886, -0.9873 + 0xbfc3f22f57db4893, 0xbfef9bed7cfbde29, // -0.15583, -0.98778 + 0xbfc38edbb0cd8d14, 0xbfef9fce55adb2c8, // -0.1528, -0.98826 + 0xbfc32b7bf94516a7, 0xbfefa39bac7a1791, // -0.14976, -0.98872 + 0xbfc2c8106e8e613a, 0xbfefa7557f08a517, // -0.14673, -0.98918 + 0xbfc264994dfd340a, 0xbfefaafbcb0cfddc, // -0.1437, -0.98962 + 0xbfc20116d4ec7bce, 0xbfefae8e8e46cfbb, // -0.14066, -0.99006 + 0xbfc19d8940be24e7, 0xbfefb20dc681d54d, // -0.13762, -0.99049 + 0xbfc139f0cedaf576, 0xbfefb5797195d741, // -0.13458, -0.9909 + 0xbfc0d64dbcb26786, 0xbfefb8d18d66adb7, // -0.13154, -0.99131 + 0xbfc072a047ba831d, 0xbfefbc1617e44186, // -0.1285, -0.99171 + 0xbfc00ee8ad6fb85b, 0xbfefbf470f0a8d88, // -0.12545, -0.9921 + 0xbfbf564e56a9730e, 0xbfefc26470e19fd3, // -0.12241, -0.99248 + 0xbfbe8eb7fde4aa3e, 0xbfefc56e3b7d9af6, // -0.11937, -0.99285 + 0xbfbdc70ecbae9fc8, 0xbfefc8646cfeb721, // -0.11632, -0.99321 + 0xbfbcff533b307dc1, 0xbfefcb4703914354, // -0.11327, -0.99356 + 0xbfbc3785c79ec2d5, 0xbfefce15fd6da67b, // -0.11022, -0.99391 + 0xbfbb6fa6ec38f64c, 0xbfefd0d158d86087, // -0.10717, -0.99424 + 0xbfbaa7b724495c04, 0xbfefd37914220b84, // -0.10412, -0.99456 + 0xbfb9dfb6eb24a85c, 0xbfefd60d2da75c9e, // -0.10107, -0.99488 + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, // -0.098017, -0.99518 + 0xbfb84f8712c130a0, 0xbfefdafa7514538c, // -0.094963, -0.99548 + 0xbfb787586a5d5b21, 0xbfefdd539ff1f456, // -0.091909, -0.99577 + 0xbfb6bf1b3e79b129, 0xbfefdf9922f73307, // -0.088854, -0.99604 + 0xbfb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // -0.085797, -0.99631 + 0xbfb52e774a4d4d0a, 0xbfefe3e92be9d886, // -0.08274, -0.99657 + 0xbfb4661179272096, 0xbfefe5f3af2e3940, // -0.079682, -0.99682 + 0xbfb39d9f12c5a299, 0xbfefe7ea85482d60, // -0.076624, -0.99706 + 0xbfb2d52092ce19f6, 0xbfefe9cdad01883a, // -0.073565, -0.99729 + 0xbfb20c9674ed444c, 0xbfefeb9d2530410f, // -0.070505, -0.99751 + 0xbfb1440134d709b2, 0xbfefed58ecb673c4, // -0.067444, -0.99772 + 0xbfb07b614e463064, 0xbfefef0102826191, // -0.064383, -0.99793 + 0xbfaf656e79f820e0, 0xbfeff095658e71ad, // -0.061321, -0.99812 + 0xbfadd406f9808ec8, 0xbfeff21614e131ed, // -0.058258, -0.9983 + 0xbfac428d12c0d7e3, 0xbfeff3830f8d575c, // -0.055195, -0.99848 + 0xbfaab101bd5f8317, 0xbfeff4dc54b1bed3, // -0.052132, -0.99864 + 0xbfa91f65f10dd814, 0xbfeff621e3796d7e, // -0.049068, -0.9988 + 0xbfa78dbaa5874685, 0xbfeff753bb1b9164, // -0.046003, -0.99894 + 0xbfa5fc00d290cd43, 0xbfeff871dadb81df, // -0.042938, -0.99908 + 0xbfa46a396ff86179, 0xbfeff97c4208c014, // -0.039873, -0.9992 + 0xbfa2d865759455cd, 0xbfeffa72effef75d, // -0.036807, -0.99932 + 0xbfa14685db42c17e, 0xbfeffb55e425fdae, // -0.033741, -0.99943 + 0xbf9f693731d1cf01, 0xbfeffc251df1d3f8, // -0.030675, -0.99953 + 0xbf9c454f4ce53b1c, 0xbfeffce09ce2a679, // -0.027608, -0.99962 + 0xbf992155f7a3667e, 0xbfeffd886084cd0d, // -0.024541, -0.9997 + 0xbf95fd4d21fab226, 0xbfeffe1c6870cb77, // -0.021474, -0.99977 + 0xbf92d936bbe30efd, 0xbfeffe9cb44b51a1, // -0.018407, -0.99983 + 0xbf8f6a296ab997ca, 0xbfefff0943c53bd1, // -0.015339, -0.99988 + 0xbf8921d1fcdec784, 0xbfefff62169b92db, // -0.012272, -0.99992 + 0xbf82d96b0e509703, 0xbfefffa72c978c4f, //-0.0092038, -0.99996 + 0xbf7921f0fe670071, 0xbfefffd8858e8a92, //-0.0061359, -0.99998 + 0xbf6921f8becca4ba, 0xbfeffff621621d02, // -0.003068, -1 + 0x0000000000000000, 0xbff0000000000000, // 0, -1 + 0x3f6921f8becca4ba, 0xbfeffff621621d02, // 0.003068, -1 + 0x3f7921f0fe670071, 0xbfefffd8858e8a92, // 0.0061359, -0.99998 + 0x3f82d96b0e509703, 0xbfefffa72c978c4f, // 0.0092038, -0.99996 + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992 + 0x3f8f6a296ab997ca, 0xbfefff0943c53bd1, // 0.015339, -0.99988 + 0x3f92d936bbe30efd, 0xbfeffe9cb44b51a1, // 0.018407, -0.99983 + 0x3f95fd4d21fab226, 0xbfeffe1c6870cb77, // 0.021474, -0.99977 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3f9c454f4ce53b1c, 0xbfeffce09ce2a679, // 0.027608, -0.99962 + 0x3f9f693731d1cf01, 0xbfeffc251df1d3f8, // 0.030675, -0.99953 + 0x3fa14685db42c17e, 0xbfeffb55e425fdae, // 0.033741, -0.99943 + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932 + 0x3fa46a396ff86179, 0xbfeff97c4208c014, // 0.039873, -0.9992 + 0x3fa5fc00d290cd43, 0xbfeff871dadb81df, // 0.042938, -0.99908 + 0x3fa78dbaa5874685, 0xbfeff753bb1b9164, // 0.046003, -0.99894 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3faab101bd5f8317, 0xbfeff4dc54b1bed3, // 0.052132, -0.99864 + 0x3fac428d12c0d7e3, 0xbfeff3830f8d575c, // 0.055195, -0.99848 + 0x3fadd406f9808ec8, 0xbfeff21614e131ed, // 0.058258, -0.9983 + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812 + 0x3fb07b614e463064, 0xbfefef0102826191, // 0.064383, -0.99793 + 0x3fb1440134d709b2, 0xbfefed58ecb673c4, // 0.067444, -0.99772 + 0x3fb20c9674ed444c, 0xbfefeb9d2530410f, // 0.070505, -0.99751 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb39d9f12c5a299, 0xbfefe7ea85482d60, // 0.076624, -0.99706 + 0x3fb4661179272096, 0xbfefe5f3af2e3940, // 0.079682, -0.99682 + 0x3fb52e774a4d4d0a, 0xbfefe3e92be9d886, // 0.08274, -0.99657 + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631 + 0x3fb6bf1b3e79b129, 0xbfefdf9922f73307, // 0.088854, -0.99604 + 0x3fb787586a5d5b21, 0xbfefdd539ff1f456, // 0.091909, -0.99577 + 0x3fb84f8712c130a0, 0xbfefdafa7514538c, // 0.094963, -0.99548 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fb9dfb6eb24a85c, 0xbfefd60d2da75c9e, // 0.10107, -0.99488 + 0x3fbaa7b724495c04, 0xbfefd37914220b84, // 0.10412, -0.99456 + 0x3fbb6fa6ec38f64c, 0xbfefd0d158d86087, // 0.10717, -0.99424 + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391 + 0x3fbcff533b307dc1, 0xbfefcb4703914354, // 0.11327, -0.99356 + 0x3fbdc70ecbae9fc8, 0xbfefc8646cfeb721, // 0.11632, -0.99321 + 0x3fbe8eb7fde4aa3e, 0xbfefc56e3b7d9af6, // 0.11937, -0.99285 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fc00ee8ad6fb85b, 0xbfefbf470f0a8d88, // 0.12545, -0.9921 + 0x3fc072a047ba831d, 0xbfefbc1617e44186, // 0.1285, -0.99171 + 0x3fc0d64dbcb26786, 0xbfefb8d18d66adb7, // 0.13154, -0.99131 + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909 + 0x3fc19d8940be24e7, 0xbfefb20dc681d54d, // 0.13762, -0.99049 + 0x3fc20116d4ec7bce, 0xbfefae8e8e46cfbb, // 0.14066, -0.99006 + 0x3fc264994dfd340a, 0xbfefaafbcb0cfddc, // 0.1437, -0.98962 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc32b7bf94516a7, 0xbfefa39bac7a1791, // 0.14976, -0.98872 + 0x3fc38edbb0cd8d14, 0xbfef9fce55adb2c8, // 0.1528, -0.98826 + 0x3fc3f22f57db4893, 0xbfef9bed7cfbde29, // 0.15583, -0.98778 + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873 + 0x3fc4b8b17f79fa88, 0xbfef93f14f85ac08, // 0.16189, -0.98681 + 0x3fc51bdf8597c5f2, 0xbfef8fd5ffae41db, // 0.16491, -0.98631 + 0x3fc57f008654cbde, 0xbfef8ba737cb4b78, // 0.16794, -0.9858 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc6451a831d830d, 0xbfef830f4a40c60c, // 0.17398, -0.98475 + 0x3fc6a81304f64ab2, 0xbfef7ea629e63d6e, // 0.177, -0.98421 + 0x3fc70afd8d08c4ff, 0xbfef7a299c1a322a, // 0.18002, -0.98366 + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311 + 0x3fc7d0a7bbd2cb1b, 0xbfef70f6434b7eb7, // 0.18606, -0.98254 + 0x3fc83366e89c64c5, 0xbfef6c3f7df5bbb7, // 0.18907, -0.98196 + 0x3fc8961727c41804, 0xbfef677556883cee, // 0.19208, -0.98138 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fc95b49e9b62af9, 0xbfef5da6ed43685d, // 0.1981, -0.98018 + 0x3fc9bdcbf2dc4366, 0xbfef58a2b1789e84, // 0.2011, -0.97957 + 0x3fca203e1b1831da, 0xbfef538b1faf2d07, // 0.20411, -0.97895 + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832 + 0x3fcae4f1d5f3b9ab, 0xbfef492206bcabb4, // 0.21011, -0.97768 + 0x3fcb4732ef3d6722, 0xbfef43d085ff92dd, // 0.21311, -0.97703 + 0x3fcba96334f15dad, 0xbfef3e6bbc1bbc65, // 0.21611, -0.97637 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcc6d90535d74dc, 0xbfef33685a3aaef0, // 0.22209, -0.97503 + 0x3fcccf8cb312b286, 0xbfef2dc9c9089a9d, // 0.22508, -0.97434 + 0x3fcd31774d2cbdee, 0xbfef2817fc4609ce, // 0.22807, -0.97364 + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294 + 0x3fcdf5163f01099a, 0xbfef1c7abe284708, // 0.23404, -0.97223 + 0x3fce56ca1e101a1b, 0xbfef168f53f7205d, // 0.23702, -0.9715 + 0x3fceb86b462de348, 0xbfef1090bc898f5f, // 0.24, -0.97077 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fcf7b7480bd3801, 0xbfef045a14cf738c, // 0.24596, -0.96928 + 0x3fcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // 0.24893, -0.96852 + 0x3fd01f1806b9fdd2, 0xbfeef7d6e51ca3c0, // 0.2519, -0.96775 + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698 + 0x3fd0804e05eb661e, 0xbfeeeb074c50a544, // 0.25783, -0.96619 + 0x3fd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // 0.26079, -0.96539 + 0x3fd0e15b4e1749cd, 0xbfeeddeb6a078651, // 0.26375, -0.96459 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd1423eefc69378, 0xbfeed0835e999009, // 0.26967, -0.96295 + 0x3fd172a0d7765177, 0xbfeec9b2d3c3bf84, // 0.27262, -0.96212 + 0x3fd1a2f7fbe8f243, 0xbfeec2cf4b1af6b2, // 0.27557, -0.96128 + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043 + 0x3fd2038583d727bd, 0xbfeeb4cf515b8811, // 0.28146, -0.95957 + 0x3fd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // 0.28441, -0.9587 + 0x3fd263e6995554ba, 0xbfeea68393e65800, // 0.28735, -0.95783 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd2c41a4e954520, 0xbfee97ec36016b30, // 0.29322, -0.95605 + 0x3fd2f422daec0386, 0xbfee9084361df7f3, // 0.29615, -0.95514 + 0x3fd3241fb638baaf, 0xbfee89095bad6025, // 0.29908, -0.95423 + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331 + 0x3fd383f5e353b6aa, 0xbfee79db29a5165a, // 0.30493, -0.95238 + 0x3fd3b3cefa0414b7, 0xbfee7227db6a9744, // 0.30785, -0.95144 + 0x3fd3e39be96ec271, 0xbfee6a61c55d53a7, // 0.31077, -0.95049 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd44310dc8936f0, 0xbfee5a9d550467d3, // 0.31659, -0.94856 + 0x3fd472b8a5571054, 0xbfee529f04729ffc, // 0.3195, -0.94759 + 0x3fd4a253d11b82f3, 0xbfee4a8dff81ce5e, // 0.32241, -0.9466 + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561 + 0x3fd50163dc197047, 0xbfee3a33ec75ce85, // 0.32821, -0.9446 + 0x3fd530d880af3c24, 0xbfee31eae870ce25, // 0.33111, -0.94359 + 0x3fd5604012f467b4, 0xbfee298f4439197a, // 0.334, -0.94257 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd5bee78b9db3b6, 0xbfee18a02fdc66d9, // 0.33978, -0.94051 + 0x3fd5ee27379ea693, 0xbfee100cca2980ac, // 0.34266, -0.93946 + 0x3fd61d595c88c203, 0xbfee0766d9280f54, // 0.34554, -0.9384 + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734 + 0x3fd67b949cad63ca, 0xbfedf5e36a9ba59c, // 0.35129, -0.93627 + 0x3fd6aa9d7dc77e16, 0xbfeded05f7de47da, // 0.35416, -0.93518 + 0x3fd6d998638a0cb5, 0xbfede4160f6d8d81, // 0.35703, -0.93409 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd73763c9261092, 0xbfedd1fef38a915a, // 0.36276, -0.93188 + 0x3fd766340f2418f6, 0xbfedc8d7cb410260, // 0.36561, -0.93077 + 0x3fd794f5e613dfae, 0xbfedbf9e4395759a, // 0.36847, -0.92964 + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851 + 0x3fd7f24dd37341e3, 0xbfedacf42ce68ab9, // 0.37416, -0.92736 + 0x3fd820e3b04eaac4, 0xbfeda383a9668988, // 0.37701, -0.92621 + 0x3fd84f6aaaf3903f, 0xbfed9a00dd8b3d46, // 0.37985, -0.92505 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd8ac4b86d5ed44, 0xbfed86c48445a450, // 0.38552, -0.9227 + 0x3fd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // 0.38835, -0.92151 + 0x3fd908ef81ef7bd1, 0xbfed733f508c0dff, // 0.39117, -0.92032 + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911 + 0x3fd96555b7ab948f, 0xbfed5f7172888a7f, // 0.39681, -0.9179 + 0x3fd993716141bdfe, 0xbfed556f52e93eb1, // 0.39962, -0.91668 + 0x3fd9c17d440df9f2, 0xbfed4b5b1b187524, // 0.40243, -0.91545 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fda1d6543b50ac0, 0xbfed36fc7bcbfbdc, // 0.40804, -0.91296 + 0x3fda4b4127dea1e4, 0xbfed2cb220e0ef9f, // 0.41084, -0.91171 + 0x3fda790cd3dbf31a, 0xbfed2255c6e5a4e1, // 0.41364, -0.91044 + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917 + 0x3fdad473125cdc08, 0xbfed0d672f59d2b9, // 0.41922, -0.90789 + 0x3fdb020d6c7f4009, 0xbfed02d4feb2bd92, // 0.422, -0.9066 + 0x3fdb2f971db31972, 0xbfecf830e8ce467b, // 0.42478, -0.9053 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdb8a7814fd5693, 0xbfece2b32799a060, // 0.43033, -0.90267 + 0x3fdbb7cf2304bd01, 0xbfecd7d9898b32f6, // 0.43309, -0.90135 + 0x3fdbe51517ffc0d9, 0xbfecccee20c2de9f, // 0.43586, -0.90002 + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867 + 0x3fdc3f6d47263129, 0xbfecb6e20a00da99, // 0.44137, -0.89732 + 0x3fdc6c7f4997000a, 0xbfecabc169a0b901, // 0.44412, -0.89597 + 0x3fdc997fc3865388, 0xbfeca08f19b9c449, // 0.44687, -0.8946 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdcf34baee1cd21, 0xbfec89f587029c13, // 0.45235, -0.89184 + 0x3fdd2016e8e9db5b, 0xbfec7e8e52233cf3, // 0.45508, -0.89045 + 0x3fdd4cd02ba8609c, 0xbfec7315899eaad7, // 0.45781, -0.88905 + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764 + 0x3fdda60c5cfa10d8, 0xbfec5bef59fef85a, // 0.46326, -0.88622 + 0x3fddd28f1481cc58, 0xbfec5042012b6907, // 0.46598, -0.8848 + 0x3fddfeff66a941de, 0xbfec44833141c004, // 0.46869, -0.88336 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fde57a86d3cd824, 0xbfec2cd14931e3f1, // 0.4741, -0.88047 + 0x3fde83e0eaf85113, 0xbfec20de3fa971b0, // 0.4768, -0.87901 + 0x3fdeb00695f25620, 0xbfec14d9dc465e58, // 0.47949, -0.87755 + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607 + 0x3fdf081906bff7fd, 0xbfebfc9d25a1b147, // 0.48487, -0.87459 + 0x3fdf3405963fd068, 0xbfebf064e15377dd, // 0.48755, -0.87309 + 0x3fdf5fdee656cda3, 0xbfebe41b611154c1, // 0.49023, -0.8716 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fdfb7575c24d2de, 0xbfebcb54cb0d2327, // 0.49557, -0.86857 + 0x3fdfe2f64be7120f, 0xbfebbed7c49380ea, // 0.49823, -0.86705 + 0x3fe00740c82b82e0, 0xbfebb249a0b6c40d, // 0.50089, -0.86551 + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397 + 0x3fe032ae55edbd95, 0xbfeb98fa1fd9155e, // 0.50619, -0.86242 + 0x3fe0485626ae221a, 0xbfeb8c38d27504e9, // 0.50883, -0.86087 + 0x3fe05df3ec31b8b6, 0xbfeb7f6686e792ea, // 0.51147, -0.8593 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe089112032b08c, 0xbfeb658f14fdbc47, // 0.51673, -0.85615 + 0x3fe09e907417c5e1, 0xbfeb5889fe921405, // 0.51936, -0.85456 + 0x3fe0b405878f85ec, 0xbfeb4b7409de7925, // 0.52198, -0.85296 + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136 + 0x3fe0ded0b84bc4b5, 0xbfeb3115a5f37bf4, // 0.5272, -0.84974 + 0x3fe0f426bb2a8e7d, 0xbfeb23cd470013b4, // 0.5298, -0.84812 + 0x3fe1097248d0a956, 0xbfeb16742a4ca2f5, // 0.5324, -0.84649 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe133e9cfee254e, 0xbfeafb8fd89f57b6, // 0.53759, -0.84321 + 0x3fe14915af336ceb, 0xbfeaee04b43c1474, // 0.54017, -0.84155 + 0x3fe15e36e4dbe2bc, 0xbfeae068f345ecef, // 0.54275, -0.83989 + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822 + 0x3fe188591f3a46e5, 0xbfeac4ffbd3efac8, // 0.54789, -0.83655 + 0x3fe19d5a09f2b9b8, 0xbfeab7325916c0d4, // 0.55046, -0.83486 + 0x3fe1b250171373be, 0xbfeaa9547a2cb98e, // 0.55302, -0.83317 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe1dc1b64dc4872, 0xbfea8d676e545ad2, // 0.55812, -0.82976 + 0x3fe1f0f08bbc861b, 0xbfea7f58529fe69d, // 0.56066, -0.82805 + 0x3fe205baa17560d6, 0xbfea7138de9d60f5, // 0.5632, -0.82632 + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459 + 0x3fe22f2d662c13e1, 0xbfea54c91090f524, // 0.56826, -0.82285 + 0x3fe243d5fb98ac1f, 0xbfea4678c8119ac8, // 0.57078, -0.8211 + 0x3fe258734cbb7110, 0xbfea38184a593bc6, // 0.5733, -0.81935 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe2818bef4d3cba, 0xbfea1b26d2c0a75e, // 0.57831, -0.81581 + 0x3fe2960727629ca8, 0xbfea0c95eabaf937, // 0.58081, -0.81404 + 0x3fe2aa76e87aeb58, 0xbfe9fdf4f13149de, // 0.58331, -0.81225 + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046 + 0x3fe2d333d34e9bb7, 0xbfe9e082edb42472, // 0.58828, -0.80866 + 0x3fe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // 0.59076, -0.80685 + 0x3fe2fbc24b441015, 0xbfe9c2d110f075c3, // 0.59323, -0.80503 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe32421ec49a620, 0xbfe9a4dfa42b06b2, // 0.59816, -0.80138 + 0x3fe338400d0c8e57, 0xbfe995cf2ed80d22, // 0.60062, -0.79954 + 0x3fe34c5252c14de1, 0xbfe986aef1457594, // 0.60307, -0.79769 + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584 + 0x3fe374531b817f8d, 0xbfe9683f42bd7fe1, // 0.60795, -0.79398 + 0x3fe3884185dfeb22, 0xbfe958efe48e6dd7, // 0.61038, -0.79211 + 0x3fe39c23e3d63029, 0xbfe94990e3ac4a6c, // 0.61281, -0.79023 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe3c3c44981c517, 0xbfe92aa41fc5a815, // 0.61765, -0.78646 + 0x3fe3d78238c58343, 0xbfe91b166fd49da2, // 0.62006, -0.78456 + 0x3fe3eb33eabe0680, 0xbfe90b7943575efe, // 0.62246, -0.78265 + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074 + 0x3fe41272663d108c, 0xbfe8ec109b486c49, // 0.62725, -0.77882 + 0x3fe425ff178e6bb1, 0xbfe8dc45331698cc, // 0.62964, -0.77689 + 0x3fe4397f5b2a4380, 0xbfe8cc6a75184655, // 0.63202, -0.77495 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe4605a692b32a2, 0xbfe8ac871ede1d88, // 0.63676, -0.77106 + 0x3fe473b51b987347, 0xbfe89c7e9a4dd4ab, // 0.63912, -0.7691 + 0x3fe48703306091fe, 0xbfe88c66e7481ba1, // 0.64148, -0.76714 + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517 + 0x3fe4ad79516722f0, 0xbfe86c0a1d9aa195, // 0.64618, -0.76319 + 0x3fe4c0a145ec0004, 0xbfe85bc51ae958cc, // 0.64851, -0.7612 + 0x3fe4d3bc6d589f80, 0xbfe84b7111af83f9, // 0.65085, -0.75921 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe4f9cc25cca486, 0xbfe82a9c13f545ff, // 0.65549, -0.7552 + 0x3fe50cc09f59a09b, 0xbfe81a1b33b57acc, // 0.65781, -0.75319 + 0x3fe51fa81cd99aa6, 0xbfe8098b756e52fa, // 0.66011, -0.75117 + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914 + 0x3fe5454ff5159dfb, 0xbfe7e83f87b03686, // 0.66471, -0.7471 + 0x3fe5581038975137, 0xbfe7d7836cc33db2, // 0.667, -0.74506 + 0x3fe56ac35197649e, 0xbfe7c6b89ce2d333, // 0.66928, -0.74301 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe59001d5f723df, 0xbfe7a4f707bf97d2, // 0.67383, -0.73889 + 0x3fe5a28d2a5d7250, 0xbfe79400574f55e4, // 0.67609, -0.73682 + 0x3fe5b50b264f7448, 0xbfe782fb1b90b35b, // 0.67835, -0.73474 + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265 + 0x3fe5d9dee73e345c, 0xbfe760c52c304764, // 0.68285, -0.73056 + 0x3fe5ec3495837074, 0xbfe74f948da8d28d, // 0.68508, -0.72846 + 0x3fe5fe7cbde56a0f, 0xbfe73e558e079942, // 0.68732, -0.72636 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe622e44fec22ff, 0xbfe71bac960e41bf, // 0.69176, -0.72213 + 0x3fe63503a31c1be8, 0xbfe70a42b3176d7a, // 0.69397, -0.72 + 0x3fe64715437f535b, 0xbfe6f8ca99c95b75, // 0.69618, -0.71787 + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573 + 0x3fe66b0f3f52b386, 0xbfe6d5afef4aafcc, // 0.70057, -0.71358 + 0x3fe67cf78491af10, 0xbfe6c40d73c18275, // 0.70275, -0.71143 + 0x3fe68ed1eaa19c71, 0xbfe6b25ced2fe29c, // 0.70493, -0.70927 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe6b25ced2fe29c, 0xbfe68ed1eaa19c71, // 0.70927, -0.70493 + 0x3fe6c40d73c18275, 0xbfe67cf78491af10, // 0.71143, -0.70275 + 0x3fe6d5afef4aafcc, 0xbfe66b0f3f52b386, // 0.71358, -0.70057 + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838 + 0x3fe6f8ca99c95b75, 0xbfe64715437f535b, // 0.71787, -0.69618 + 0x3fe70a42b3176d7a, 0xbfe63503a31c1be8, // 0.72, -0.69397 + 0x3fe71bac960e41bf, 0xbfe622e44fec22ff, // 0.72213, -0.69176 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe73e558e079942, 0xbfe5fe7cbde56a0f, // 0.72636, -0.68732 + 0x3fe74f948da8d28d, 0xbfe5ec3495837074, // 0.72846, -0.68508 + 0x3fe760c52c304764, 0xbfe5d9dee73e345c, // 0.73056, -0.68285 + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806 + 0x3fe782fb1b90b35b, 0xbfe5b50b264f7448, // 0.73474, -0.67835 + 0x3fe79400574f55e4, 0xbfe5a28d2a5d7250, // 0.73682, -0.67609 + 0x3fe7a4f707bf97d2, 0xbfe59001d5f723df, // 0.73889, -0.67383 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe7c6b89ce2d333, 0xbfe56ac35197649e, // 0.74301, -0.66928 + 0x3fe7d7836cc33db2, 0xbfe5581038975137, // 0.74506, -0.667 + 0x3fe7e83f87b03686, 0xbfe5454ff5159dfb, // 0.7471, -0.66471 + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242 + 0x3fe8098b756e52fa, 0xbfe51fa81cd99aa6, // 0.75117, -0.66011 + 0x3fe81a1b33b57acc, 0xbfe50cc09f59a09b, // 0.75319, -0.65781 + 0x3fe82a9c13f545ff, 0xbfe4f9cc25cca486, // 0.7552, -0.65549 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe84b7111af83f9, 0xbfe4d3bc6d589f80, // 0.75921, -0.65085 + 0x3fe85bc51ae958cc, 0xbfe4c0a145ec0004, // 0.7612, -0.64851 + 0x3fe86c0a1d9aa195, 0xbfe4ad79516722f0, // 0.76319, -0.64618 + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383 + 0x3fe88c66e7481ba1, 0xbfe48703306091fe, // 0.76714, -0.64148 + 0x3fe89c7e9a4dd4ab, 0xbfe473b51b987347, // 0.7691, -0.63912 + 0x3fe8ac871ede1d88, 0xbfe4605a692b32a2, // 0.77106, -0.63676 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe8cc6a75184655, 0xbfe4397f5b2a4380, // 0.77495, -0.63202 + 0x3fe8dc45331698cc, 0xbfe425ff178e6bb1, // 0.77689, -0.62964 + 0x3fe8ec109b486c49, 0xbfe41272663d108c, // 0.77882, -0.62725 + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486 + 0x3fe90b7943575efe, 0xbfe3eb33eabe0680, // 0.78265, -0.62246 + 0x3fe91b166fd49da2, 0xbfe3d78238c58343, // 0.78456, -0.62006 + 0x3fe92aa41fc5a815, 0xbfe3c3c44981c517, // 0.78646, -0.61765 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe94990e3ac4a6c, 0xbfe39c23e3d63029, // 0.79023, -0.61281 + 0x3fe958efe48e6dd7, 0xbfe3884185dfeb22, // 0.79211, -0.61038 + 0x3fe9683f42bd7fe1, 0xbfe374531b817f8d, // 0.79398, -0.60795 + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551 + 0x3fe986aef1457594, 0xbfe34c5252c14de1, // 0.79769, -0.60307 + 0x3fe995cf2ed80d22, 0xbfe338400d0c8e57, // 0.79954, -0.60062 + 0x3fe9a4dfa42b06b2, 0xbfe32421ec49a620, // 0.80138, -0.59816 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe9c2d110f075c3, 0xbfe2fbc24b441015, // 0.80503, -0.59323 + 0x3fe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // 0.80685, -0.59076 + 0x3fe9e082edb42472, 0xbfe2d333d34e9bb7, // 0.80866, -0.58828 + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858 + 0x3fe9fdf4f13149de, 0xbfe2aa76e87aeb58, // 0.81225, -0.58331 + 0x3fea0c95eabaf937, 0xbfe2960727629ca8, // 0.81404, -0.58081 + 0x3fea1b26d2c0a75e, 0xbfe2818bef4d3cba, // 0.81581, -0.57831 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea38184a593bc6, 0xbfe258734cbb7110, // 0.81935, -0.5733 + 0x3fea4678c8119ac8, 0xbfe243d5fb98ac1f, // 0.8211, -0.57078 + 0x3fea54c91090f524, 0xbfe22f2d662c13e1, // 0.82285, -0.56826 + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573 + 0x3fea7138de9d60f5, 0xbfe205baa17560d6, // 0.82632, -0.5632 + 0x3fea7f58529fe69d, 0xbfe1f0f08bbc861b, // 0.82805, -0.56066 + 0x3fea8d676e545ad2, 0xbfe1dc1b64dc4872, // 0.82976, -0.55812 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3feaa9547a2cb98e, 0xbfe1b250171373be, // 0.83317, -0.55302 + 0x3feab7325916c0d4, 0xbfe19d5a09f2b9b8, // 0.83486, -0.55046 + 0x3feac4ffbd3efac8, 0xbfe188591f3a46e5, // 0.83655, -0.54789 + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532 + 0x3feae068f345ecef, 0xbfe15e36e4dbe2bc, // 0.83989, -0.54275 + 0x3feaee04b43c1474, 0xbfe14915af336ceb, // 0.84155, -0.54017 + 0x3feafb8fd89f57b6, 0xbfe133e9cfee254e, // 0.84321, -0.53759 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feb16742a4ca2f5, 0xbfe1097248d0a956, // 0.84649, -0.5324 + 0x3feb23cd470013b4, 0xbfe0f426bb2a8e7d, // 0.84812, -0.5298 + 0x3feb3115a5f37bf4, 0xbfe0ded0b84bc4b5, // 0.84974, -0.5272 + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459 + 0x3feb4b7409de7925, 0xbfe0b405878f85ec, // 0.85296, -0.52198 + 0x3feb5889fe921405, 0xbfe09e907417c5e1, // 0.85456, -0.51936 + 0x3feb658f14fdbc47, 0xbfe089112032b08c, // 0.85615, -0.51673 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feb7f6686e792ea, 0xbfe05df3ec31b8b6, // 0.8593, -0.51147 + 0x3feb8c38d27504e9, 0xbfe0485626ae221a, // 0.86087, -0.50883 + 0x3feb98fa1fd9155e, 0xbfe032ae55edbd95, // 0.86242, -0.50619 + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354 + 0x3febb249a0b6c40d, 0xbfe00740c82b82e0, // 0.86551, -0.50089 + 0x3febbed7c49380ea, 0xbfdfe2f64be7120f, // 0.86705, -0.49823 + 0x3febcb54cb0d2327, 0xbfdfb7575c24d2de, // 0.86857, -0.49557 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3febe41b611154c1, 0xbfdf5fdee656cda3, // 0.8716, -0.49023 + 0x3febf064e15377dd, 0xbfdf3405963fd068, // 0.87309, -0.48755 + 0x3febfc9d25a1b147, 0xbfdf081906bff7fd, // 0.87459, -0.48487 + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218 + 0x3fec14d9dc465e58, 0xbfdeb00695f25620, // 0.87755, -0.47949 + 0x3fec20de3fa971b0, 0xbfde83e0eaf85113, // 0.87901, -0.4768 + 0x3fec2cd14931e3f1, 0xbfde57a86d3cd824, // 0.88047, -0.4741 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec44833141c004, 0xbfddfeff66a941de, // 0.88336, -0.46869 + 0x3fec5042012b6907, 0xbfddd28f1481cc58, // 0.8848, -0.46598 + 0x3fec5bef59fef85a, 0xbfdda60c5cfa10d8, // 0.88622, -0.46326 + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054 + 0x3fec7315899eaad7, 0xbfdd4cd02ba8609c, // 0.88905, -0.45781 + 0x3fec7e8e52233cf3, 0xbfdd2016e8e9db5b, // 0.89045, -0.45508 + 0x3fec89f587029c13, 0xbfdcf34baee1cd21, // 0.89184, -0.45235 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3feca08f19b9c449, 0xbfdc997fc3865388, // 0.8946, -0.44687 + 0x3fecabc169a0b901, 0xbfdc6c7f4997000a, // 0.89597, -0.44412 + 0x3fecb6e20a00da99, 0xbfdc3f6d47263129, // 0.89732, -0.44137 + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862 + 0x3fecccee20c2de9f, 0xbfdbe51517ffc0d9, // 0.90002, -0.43586 + 0x3fecd7d9898b32f6, 0xbfdbb7cf2304bd01, // 0.90135, -0.43309 + 0x3fece2b32799a060, 0xbfdb8a7814fd5693, // 0.90267, -0.43033 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fecf830e8ce467b, 0xbfdb2f971db31972, // 0.9053, -0.42478 + 0x3fed02d4feb2bd92, 0xbfdb020d6c7f4009, // 0.9066, -0.422 + 0x3fed0d672f59d2b9, 0xbfdad473125cdc08, // 0.90789, -0.41922 + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643 + 0x3fed2255c6e5a4e1, 0xbfda790cd3dbf31a, // 0.91044, -0.41364 + 0x3fed2cb220e0ef9f, 0xbfda4b4127dea1e4, // 0.91171, -0.41084 + 0x3fed36fc7bcbfbdc, 0xbfda1d6543b50ac0, // 0.91296, -0.40804 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed4b5b1b187524, 0xbfd9c17d440df9f2, // 0.91545, -0.40243 + 0x3fed556f52e93eb1, 0xbfd993716141bdfe, // 0.91668, -0.39962 + 0x3fed5f7172888a7f, 0xbfd96555b7ab948f, // 0.9179, -0.39681 + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399 + 0x3fed733f508c0dff, 0xbfd908ef81ef7bd1, // 0.92032, -0.39117 + 0x3fed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // 0.92151, -0.38835 + 0x3fed86c48445a450, 0xbfd8ac4b86d5ed44, // 0.9227, -0.38552 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3fed9a00dd8b3d46, 0xbfd84f6aaaf3903f, // 0.92505, -0.37985 + 0x3feda383a9668988, 0xbfd820e3b04eaac4, // 0.92621, -0.37701 + 0x3fedacf42ce68ab9, 0xbfd7f24dd37341e3, // 0.92736, -0.37416 + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132 + 0x3fedbf9e4395759a, 0xbfd794f5e613dfae, // 0.92964, -0.36847 + 0x3fedc8d7cb410260, 0xbfd766340f2418f6, // 0.93077, -0.36561 + 0x3fedd1fef38a915a, 0xbfd73763c9261092, // 0.93188, -0.36276 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3fede4160f6d8d81, 0xbfd6d998638a0cb5, // 0.93409, -0.35703 + 0x3feded05f7de47da, 0xbfd6aa9d7dc77e16, // 0.93518, -0.35416 + 0x3fedf5e36a9ba59c, 0xbfd67b949cad63ca, // 0.93627, -0.35129 + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842 + 0x3fee0766d9280f54, 0xbfd61d595c88c203, // 0.9384, -0.34554 + 0x3fee100cca2980ac, 0xbfd5ee27379ea693, // 0.93946, -0.34266 + 0x3fee18a02fdc66d9, 0xbfd5bee78b9db3b6, // 0.94051, -0.33978 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee298f4439197a, 0xbfd5604012f467b4, // 0.94257, -0.334 + 0x3fee31eae870ce25, 0xbfd530d880af3c24, // 0.94359, -0.33111 + 0x3fee3a33ec75ce85, 0xbfd50163dc197047, // 0.9446, -0.32821 + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531 + 0x3fee4a8dff81ce5e, 0xbfd4a253d11b82f3, // 0.9466, -0.32241 + 0x3fee529f04729ffc, 0xbfd472b8a5571054, // 0.94759, -0.3195 + 0x3fee5a9d550467d3, 0xbfd44310dc8936f0, // 0.94856, -0.31659 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee6a61c55d53a7, 0xbfd3e39be96ec271, // 0.95049, -0.31077 + 0x3fee7227db6a9744, 0xbfd3b3cefa0414b7, // 0.95144, -0.30785 + 0x3fee79db29a5165a, 0xbfd383f5e353b6aa, // 0.95238, -0.30493 + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201 + 0x3fee89095bad6025, 0xbfd3241fb638baaf, // 0.95423, -0.29908 + 0x3fee9084361df7f3, 0xbfd2f422daec0386, // 0.95514, -0.29615 + 0x3fee97ec36016b30, 0xbfd2c41a4e954520, // 0.95605, -0.29322 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3feea68393e65800, 0xbfd263e6995554ba, // 0.95783, -0.28735 + 0x3feeadb2e8e7a88e, 0xbfd233bbabc3bb72, // 0.9587, -0.28441 + 0x3feeb4cf515b8811, 0xbfd2038583d727bd, // 0.95957, -0.28146 + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852 + 0x3feec2cf4b1af6b2, 0xbfd1a2f7fbe8f243, // 0.96128, -0.27557 + 0x3feec9b2d3c3bf84, 0xbfd172a0d7765177, // 0.96212, -0.27262 + 0x3feed0835e999009, 0xbfd1423eefc69378, // 0.96295, -0.26967 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3feeddeb6a078651, 0xbfd0e15b4e1749cd, // 0.96459, -0.26375 + 0x3feee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // 0.96539, -0.26079 + 0x3feeeb074c50a544, 0xbfd0804e05eb661e, // 0.96619, -0.25783 + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487 + 0x3feef7d6e51ca3c0, 0xbfd01f1806b9fdd2, // 0.96775, -0.2519 + 0x3feefe220c0b95ec, 0xbfcfdcdc1adfedf8, // 0.96852, -0.24893 + 0x3fef045a14cf738c, 0xbfcf7b7480bd3801, // 0.96928, -0.24596 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef1090bc898f5f, 0xbfceb86b462de348, // 0.97077, -0.24 + 0x3fef168f53f7205d, 0xbfce56ca1e101a1b, // 0.9715, -0.23702 + 0x3fef1c7abe284708, 0xbfcdf5163f01099a, // 0.97223, -0.23404 + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106 + 0x3fef2817fc4609ce, 0xbfcd31774d2cbdee, // 0.97364, -0.22807 + 0x3fef2dc9c9089a9d, 0xbfcccf8cb312b286, // 0.97434, -0.22508 + 0x3fef33685a3aaef0, 0xbfcc6d90535d74dc, // 0.97503, -0.22209 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef3e6bbc1bbc65, 0xbfcba96334f15dad, // 0.97637, -0.21611 + 0x3fef43d085ff92dd, 0xbfcb4732ef3d6722, // 0.97703, -0.21311 + 0x3fef492206bcabb4, 0xbfcae4f1d5f3b9ab, // 0.97768, -0.21011 + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711 + 0x3fef538b1faf2d07, 0xbfca203e1b1831da, // 0.97895, -0.20411 + 0x3fef58a2b1789e84, 0xbfc9bdcbf2dc4366, // 0.97957, -0.2011 + 0x3fef5da6ed43685d, 0xbfc95b49e9b62af9, // 0.98018, -0.1981 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef677556883cee, 0xbfc8961727c41804, // 0.98138, -0.19208 + 0x3fef6c3f7df5bbb7, 0xbfc83366e89c64c5, // 0.98196, -0.18907 + 0x3fef70f6434b7eb7, 0xbfc7d0a7bbd2cb1b, // 0.98254, -0.18606 + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304 + 0x3fef7a299c1a322a, 0xbfc70afd8d08c4ff, // 0.98366, -0.18002 + 0x3fef7ea629e63d6e, 0xbfc6a81304f64ab2, // 0.98421, -0.177 + 0x3fef830f4a40c60c, 0xbfc6451a831d830d, // 0.98475, -0.17398 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef8ba737cb4b78, 0xbfc57f008654cbde, // 0.9858, -0.16794 + 0x3fef8fd5ffae41db, 0xbfc51bdf8597c5f2, // 0.98631, -0.16491 + 0x3fef93f14f85ac08, 0xbfc4b8b17f79fa88, // 0.98681, -0.16189 + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886 + 0x3fef9bed7cfbde29, 0xbfc3f22f57db4893, // 0.98778, -0.15583 + 0x3fef9fce55adb2c8, 0xbfc38edbb0cd8d14, // 0.98826, -0.1528 + 0x3fefa39bac7a1791, 0xbfc32b7bf94516a7, // 0.98872, -0.14976 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefaafbcb0cfddc, 0xbfc264994dfd340a, // 0.98962, -0.1437 + 0x3fefae8e8e46cfbb, 0xbfc20116d4ec7bce, // 0.99006, -0.14066 + 0x3fefb20dc681d54d, 0xbfc19d8940be24e7, // 0.99049, -0.13762 + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458 + 0x3fefb8d18d66adb7, 0xbfc0d64dbcb26786, // 0.99131, -0.13154 + 0x3fefbc1617e44186, 0xbfc072a047ba831d, // 0.99171, -0.1285 + 0x3fefbf470f0a8d88, 0xbfc00ee8ad6fb85b, // 0.9921, -0.12545 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefc56e3b7d9af6, 0xbfbe8eb7fde4aa3e, // 0.99285, -0.11937 + 0x3fefc8646cfeb721, 0xbfbdc70ecbae9fc8, // 0.99321, -0.11632 + 0x3fefcb4703914354, 0xbfbcff533b307dc1, // 0.99356, -0.11327 + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022 + 0x3fefd0d158d86087, 0xbfbb6fa6ec38f64c, // 0.99424, -0.10717 + 0x3fefd37914220b84, 0xbfbaa7b724495c04, // 0.99456, -0.10412 + 0x3fefd60d2da75c9e, 0xbfb9dfb6eb24a85c, // 0.99488, -0.10107 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518, -0.098017 + 0x3fefdafa7514538c, 0xbfb84f8712c130a0, // 0.99548, -0.094963 + 0x3fefdd539ff1f456, 0xbfb787586a5d5b21, // 0.99577, -0.091909 + 0x3fefdf9922f73307, 0xbfb6bf1b3e79b129, // 0.99604, -0.088854 + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631, -0.085797 + 0x3fefe3e92be9d886, 0xbfb52e774a4d4d0a, // 0.99657, -0.08274 + 0x3fefe5f3af2e3940, 0xbfb4661179272096, // 0.99682, -0.079682 + 0x3fefe7ea85482d60, 0xbfb39d9f12c5a299, // 0.99706, -0.076624 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729, -0.073565 + 0x3fefeb9d2530410f, 0xbfb20c9674ed444c, // 0.99751, -0.070505 + 0x3fefed58ecb673c4, 0xbfb1440134d709b2, // 0.99772, -0.067444 + 0x3fefef0102826191, 0xbfb07b614e463064, // 0.99793, -0.064383 + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812, -0.061321 + 0x3feff21614e131ed, 0xbfadd406f9808ec8, // 0.9983, -0.058258 + 0x3feff3830f8d575c, 0xbfac428d12c0d7e3, // 0.99848, -0.055195 + 0x3feff4dc54b1bed3, 0xbfaab101bd5f8317, // 0.99864, -0.052132 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988, -0.049068 + 0x3feff753bb1b9164, 0xbfa78dbaa5874685, // 0.99894, -0.046003 + 0x3feff871dadb81df, 0xbfa5fc00d290cd43, // 0.99908, -0.042938 + 0x3feff97c4208c014, 0xbfa46a396ff86179, // 0.9992, -0.039873 + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932, -0.036807 + 0x3feffb55e425fdae, 0xbfa14685db42c17e, // 0.99943, -0.033741 + 0x3feffc251df1d3f8, 0xbf9f693731d1cf01, // 0.99953, -0.030675 + 0x3feffce09ce2a679, 0xbf9c454f4ce53b1c, // 0.99962, -0.027608 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997, -0.024541 + 0x3feffe1c6870cb77, 0xbf95fd4d21fab226, // 0.99977, -0.021474 + 0x3feffe9cb44b51a1, 0xbf92d936bbe30efd, // 0.99983, -0.018407 + 0x3fefff0943c53bd1, 0xbf8f6a296ab997ca, // 0.99988, -0.015339 + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992, -0.012272 + 0x3fefffa72c978c4f, 0xbf82d96b0e509703, // 0.99996,-0.0092038 + 0x3fefffd8858e8a92, 0xbf7921f0fe670071, // 0.99998,-0.0061359 + 0x3feffff621621d02, 0xbf6921f8becca4ba, // 1, -0.003068 + +}; + +/** + @par + Example code for Double Precision Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 4096, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_4096[8192] ARM_DSP_TABLE_ATTRIBUTE = { + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3feffffd88586ee6, 0x3f5921faaee6472d, // 1, 0.001534 + 0x3feffff621621d02, 0x3f6921f8becca4ba, // 1, 0.003068 + 0x3fefffe9cb1e2e8d, 0x3f72d97822f996bc, // 0.99999, 0.0046019 + 0x3fefffd8858e8a92, 0x3f7921f0fe670071, // 0.99998, 0.0061359 + 0x3fefffc250b5daef, 0x3f7f6a65f9a2a3c5, // 0.99997, 0.0076698 + 0x3fefffa72c978c4f, 0x3f82d96b0e509703, // 0.99996, 0.0092038 + 0x3fefff871937ce2f, 0x3f85fda037ac05e0, // 0.99994, 0.010738 + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272 + 0x3fefff3824c88f6f, 0x3f8c45ffe1e48ad9, // 0.9999, 0.013805 + 0x3fefff0943c53bd1, 0x3f8f6a296ab997ca, // 0.99988, 0.015339 + 0x3feffed57398d2b7, 0x3f9147270dad7132, // 0.99986, 0.016873 + 0x3feffe9cb44b51a1, 0x3f92d936bbe30efd, // 0.99983, 0.018407 + 0x3feffe5f05e578db, 0x3f946b4381fce81c, // 0.9998, 0.01994 + 0x3feffe1c6870cb77, 0x3f95fd4d21fab226, // 0.99977, 0.021474 + 0x3feffdd4dbf78f52, 0x3f978f535ddc9f03, // 0.99974, 0.023008 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feffd36f624500c, 0x3f9ab354b1504fca, // 0.99966, 0.026075 + 0x3feffce09ce2a679, 0x3f9c454f4ce53b1c, // 0.99962, 0.027608 + 0x3feffc8554cd213a, 0x3f9dd7458c64ab39, // 0.99958, 0.029142 + 0x3feffc251df1d3f8, 0x3f9f693731d1cf01, // 0.99953, 0.030675 + 0x3feffbbff85f9515, 0x3fa07d91ff984580, // 0.99948, 0.032208 + 0x3feffb55e425fdae, 0x3fa14685db42c17e, // 0.99943, 0.033741 + 0x3feffae6e1556998, 0x3fa20f770ceb11c6, // 0.99938, 0.035274 + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807 + 0x3feff9fa10348837, 0x3fa3a150f6421afc, // 0.99926, 0.03834 + 0x3feff97c4208c014, 0x3fa46a396ff86179, // 0.9992, 0.039873 + 0x3feff8f9858f058b, 0x3fa5331ec3bba0eb, // 0.99914, 0.041406 + 0x3feff871dadb81df, 0x3fa5fc00d290cd43, // 0.99908, 0.042938 + 0x3feff7e5420320f9, 0x3fa6c4df7d7d5b84, // 0.99901, 0.044471 + 0x3feff753bb1b9164, 0x3fa78dbaa5874685, // 0.99894, 0.046003 + 0x3feff6bd463b444d, 0x3fa856922bb513c1, // 0.99887, 0.047535 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feff58192ee0358, 0x3fa9e835d6993c87, // 0.99872, 0.0506 + 0x3feff4dc54b1bed3, 0x3faab101bd5f8317, // 0.99864, 0.052132 + 0x3feff43228de1b77, 0x3fab79c986698b78, // 0.99856, 0.053664 + 0x3feff3830f8d575c, 0x3fac428d12c0d7e3, // 0.99848, 0.055195 + 0x3feff2cf08da7321, 0x3fad0b4c436f91d0, // 0.99839, 0.056727 + 0x3feff21614e131ed, 0x3fadd406f9808ec8, // 0.9983, 0.058258 + 0x3feff15833be1965, 0x3fae9cbd15ff5527, // 0.99821, 0.05979 + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321 + 0x3fefefcdaa704562, 0x3fb0170d833bf421, // 0.99802, 0.062852 + 0x3fefef0102826191, 0x3fb07b614e463064, // 0.99793, 0.064383 + 0x3fefee2f6de455ba, 0x3fb0dfb28ea201e6, // 0.99783, 0.065913 + 0x3fefed58ecb673c4, 0x3fb1440134d709b2, // 0.99772, 0.067444 + 0x3fefec7d7f19cffc, 0x3fb1a84d316d4f8a, // 0.99762, 0.068974 + 0x3fefeb9d2530410f, 0x3fb20c9674ed444c, // 0.99751, 0.070505 + 0x3fefeab7df1c6005, 0x3fb270dcefdfc45b, // 0.9974, 0.072035 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefe8de8f03d75c, 0x3fb339614e41ffa5, // 0.99718, 0.075094 + 0x3fefe7ea85482d60, 0x3fb39d9f12c5a299, // 0.99706, 0.076624 + 0x3fefe6f18ff42c84, 0x3fb401d9d0e3a507, // 0.99694, 0.078153 + 0x3fefe5f3af2e3940, 0x3fb4661179272096, // 0.99682, 0.079682 + 0x3fefe4f0e31d7a4a, 0x3fb4ca45fc1ba8b6, // 0.9967, 0.081211 + 0x3fefe3e92be9d886, 0x3fb52e774a4d4d0a, // 0.99657, 0.08274 + 0x3fefe2dc89bbff08, 0x3fb592a554489bc8, // 0.99644, 0.084269 + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797 + 0x3fefe0b485181be3, 0x3fb65af75dd0f87b, // 0.99618, 0.087326 + 0x3fefdf9922f73307, 0x3fb6bf1b3e79b129, // 0.99604, 0.088854 + 0x3fefde78d68653fd, 0x3fb7233b9d236e71, // 0.99591, 0.090381 + 0x3fefdd539ff1f456, 0x3fb787586a5d5b21, // 0.99577, 0.091909 + 0x3fefdc297f674ba9, 0x3fb7eb7196b72ee4, // 0.99563, 0.093436 + 0x3fefdafa7514538c, 0x3fb84f8712c130a0, // 0.99548, 0.094963 + 0x3fefd9c68127c78c, 0x3fb8b398cf0c38e0, // 0.99533, 0.09649 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefd74fdd40abbf, 0x3fb97bb0caaba56f, // 0.99503, 0.099544 + 0x3fefd60d2da75c9e, 0x3fb9dfb6eb24a85c, // 0.99488, 0.10107 + 0x3fefd4c59536fae4, 0x3fba43b90e27f3c4, // 0.99472, 0.1026 + 0x3fefd37914220b84, 0x3fbaa7b724495c04, // 0.99456, 0.10412 + 0x3fefd227aa9bd53b, 0x3fbb0bb11e1d5559, // 0.9944, 0.10565 + 0x3fefd0d158d86087, 0x3fbb6fa6ec38f64c, // 0.99424, 0.10717 + 0x3fefcf761f0c77a3, 0x3fbbd3987f31fa0e, // 0.99407, 0.1087 + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022 + 0x3fefccb0f4323aa3, 0x3fbc9b6eb6165c42, // 0.99374, 0.11175 + 0x3fefcb4703914354, 0x3fbcff533b307dc1, // 0.99356, 0.11327 + 0x3fefc9d82bc2915e, 0x3fbd633347858ce4, // 0.99339, 0.11479 + 0x3fefc8646cfeb721, 0x3fbdc70ecbae9fc8, // 0.99321, 0.11632 + 0x3fefc6ebc77f0887, 0x3fbe2ae5b8457f77, // 0.99303, 0.11784 + 0x3fefc56e3b7d9af6, 0x3fbe8eb7fde4aa3e, // 0.99285, 0.11937 + 0x3fefc3ebc935454c, 0x3fbef2858d27561b, // 0.99267, 0.12089 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefc0d832bf043a, 0x3fbfba124b07ad85, // 0.99229, 0.12393 + 0x3fefbf470f0a8d88, 0x3fc00ee8ad6fb85b, // 0.9921, 0.12545 + 0x3fefbdb106021816, 0x3fc040c5bb67747e, // 0.99191, 0.12698 + 0x3fefbc1617e44186, 0x3fc072a047ba831d, // 0.99171, 0.1285 + 0x3fefba7644f068b5, 0x3fc0a4784ab8bf1d, // 0.99151, 0.13002 + 0x3fefb8d18d66adb7, 0x3fc0d64dbcb26786, // 0.99131, 0.13154 + 0x3fefb727f187f1c7, 0x3fc1082095f820b0, // 0.99111, 0.13306 + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458 + 0x3fefb3c60dd2c199, 0x3fc16bbe5fac5865, // 0.9907, 0.1361 + 0x3fefb20dc681d54d, 0x3fc19d8940be24e7, // 0.99049, 0.13762 + 0x3fefb0509be6f7db, 0x3fc1cf516a62a077, // 0.99027, 0.13914 + 0x3fefae8e8e46cfbb, 0x3fc20116d4ec7bce, // 0.99006, 0.14066 + 0x3fefacc79de6c44f, 0x3fc232d978aed413, // 0.98984, 0.14218 + 0x3fefaafbcb0cfddc, 0x3fc264994dfd340a, // 0.98962, 0.1437 + 0x3fefa92b1600657c, 0x3fc296564d2b953e, // 0.9894, 0.14521 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fefa57b066e2754, 0x3fc2f9c7aa7a72af, // 0.98895, 0.14825 + 0x3fefa39bac7a1791, 0x3fc32b7bf94516a7, // 0.98872, 0.14976 + 0x3fefa1b7717661d5, 0x3fc35d2d53440db2, // 0.98849, 0.15128 + 0x3fef9fce55adb2c8, 0x3fc38edbb0cd8d14, // 0.98826, 0.1528 + 0x3fef9de0596b77a3, 0x3fc3c0870a383ff6, // 0.98802, 0.15431 + 0x3fef9bed7cfbde29, 0x3fc3f22f57db4893, // 0.98778, 0.15583 + 0x3fef99f5c0abd496, 0x3fc423d4920e4166, // 0.98754, 0.15734 + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886 + 0x3fef95f7a9a1ec47, 0x3fc48715ad84cdf5, // 0.98706, 0.16037 + 0x3fef93f14f85ac08, 0x3fc4b8b17f79fa88, // 0.98681, 0.16189 + 0x3fef91e616c43891, 0x3fc4ea4a1f624b61, // 0.98656, 0.1634 + 0x3fef8fd5ffae41db, 0x3fc51bdf8597c5f2, // 0.98631, 0.16491 + 0x3fef8dc10a95380d, 0x3fc54d71aa74ef02, // 0.98605, 0.16643 + 0x3fef8ba737cb4b78, 0x3fc57f008654cbde, // 0.9858, 0.16794 + 0x3fef898887a36c84, 0x3fc5b08c1192e381, // 0.98554, 0.16945 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef853c9089595e, 0x3fc61399179a6e94, // 0.98501, 0.17247 + 0x3fef830f4a40c60c, 0x3fc6451a831d830d, // 0.98475, 0.17398 + 0x3fef80dd27ed8204, 0x3fc676987f7216b8, // 0.98448, 0.17549 + 0x3fef7ea629e63d6e, 0x3fc6a81304f64ab2, // 0.98421, 0.177 + 0x3fef7c6a50826840, 0x3fc6d98a0c08c8da, // 0.98394, 0.17851 + 0x3fef7a299c1a322a, 0x3fc70afd8d08c4ff, // 0.98366, 0.18002 + 0x3fef77e40d068a90, 0x3fc73c6d8055fe0a, // 0.98339, 0.18153 + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304 + 0x3fef734a60446279, 0x3fc79f429f59e11d, // 0.98282, 0.18455 + 0x3fef70f6434b7eb7, 0x3fc7d0a7bbd2cb1b, // 0.98254, 0.18606 + 0x3fef6e9d4d1262ca, 0x3fc802092c1d744b, // 0.98225, 0.18756 + 0x3fef6c3f7df5bbb7, 0x3fc83366e89c64c5, // 0.98196, 0.18907 + 0x3fef69dcd652f5de, 0x3fc864c0e9b2b6cf, // 0.98167, 0.19057 + 0x3fef677556883cee, 0x3fc8961727c41804, // 0.98138, 0.19208 + 0x3fef6508fef47bd5, 0x3fc8c7699b34ca7e, // 0.98108, 0.19359 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef6021c9f148c2, 0x3fc92a0303c8194f, // 0.98048, 0.19659 + 0x3fef5da6ed43685d, 0x3fc95b49e9b62af9, // 0.98018, 0.1981 + 0x3fef5b273a4fa2d9, 0x3fc98c8ce69a7aec, // 0.97988, 0.1996 + 0x3fef58a2b1789e84, 0x3fc9bdcbf2dc4366, // 0.97957, 0.2011 + 0x3fef56195321c090, 0x3fc9ef0706e35a35, // 0.97926, 0.20261 + 0x3fef538b1faf2d07, 0x3fca203e1b1831da, // 0.97895, 0.20411 + 0x3fef50f81785c6b9, 0x3fca517127e3dabc, // 0.97863, 0.20561 + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711 + 0x3fef4bc38aa5c694, 0x3fcab3cb0ce6fe44, // 0.978, 0.20861 + 0x3fef492206bcabb4, 0x3fcae4f1d5f3b9ab, // 0.97768, 0.21011 + 0x3fef467bafb7bbe0, 0x3fcb16147941ca2a, // 0.97735, 0.21161 + 0x3fef43d085ff92dd, 0x3fcb4732ef3d6722, // 0.97703, 0.21311 + 0x3fef412089fd8adc, 0x3fcb784d30536cda, // 0.9767, 0.21461 + 0x3fef3e6bbc1bbc65, 0x3fcba96334f15dad, // 0.97637, 0.21611 + 0x3fef3bb21cc4fe47, 0x3fcbda74f5856330, // 0.97604, 0.2176 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef36306b67c556, 0x3fcc3c8b8c4b9dd7, // 0.97536, 0.2206 + 0x3fef33685a3aaef0, 0x3fcc6d90535d74dc, // 0.97503, 0.22209 + 0x3fef309b794b719f, 0x3fcc9e90b824a6a9, // 0.97468, 0.22359 + 0x3fef2dc9c9089a9d, 0x3fcccf8cb312b286, // 0.97434, 0.22508 + 0x3fef2af349e17507, 0x3fcd00843c99c5f9, // 0.97399, 0.22658 + 0x3fef2817fc4609ce, 0x3fcd31774d2cbdee, // 0.97364, 0.22807 + 0x3fef2537e0a71f9f, 0x3fcd6265dd3f27e3, // 0.97329, 0.22957 + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106 + 0x3fef1f6941259d7a, 0x3fcdc4355db40195, // 0.97258, 0.23255 + 0x3fef1c7abe284708, 0x3fcdf5163f01099a, // 0.97223, 0.23404 + 0x3fef19876ef1f486, 0x3fce25f281a2b684, // 0.97187, 0.23553 + 0x3fef168f53f7205d, 0x3fce56ca1e101a1b, // 0.9715, 0.23702 + 0x3fef13926dad024e, 0x3fce879d0cc0fdaf, // 0.97114, 0.23851 + 0x3fef1090bc898f5f, 0x3fceb86b462de348, // 0.97077, 0.24 + 0x3fef0d8a410379c5, 0x3fcee934c2d006c7, // 0.9704, 0.24149 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3fef076eecade0fa, 0x3fcf4ab9679c9f5c, // 0.96966, 0.24447 + 0x3fef045a14cf738c, 0x3fcf7b7480bd3801, // 0.96928, 0.24596 + 0x3fef014074708ed3, 0x3fcfac2abeff57ff, // 0.9689, 0.24744 + 0x3feefe220c0b95ec, 0x3fcfdcdc1adfedf8, // 0.96852, 0.24893 + 0x3feefafedc1ba8b7, 0x3fd006c4466e54af, // 0.96814, 0.25041 + 0x3feef7d6e51ca3c0, 0x3fd01f1806b9fdd2, // 0.96775, 0.2519 + 0x3feef4aa278b2032, 0x3fd037694a928cac, // 0.96737, 0.25338 + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487 + 0x3feeee425aa6b09a, 0x3fd068044deab002, // 0.96658, 0.25635 + 0x3feeeb074c50a544, 0x3fd0804e05eb661e, // 0.96619, 0.25783 + 0x3feee7c77961dc9e, 0x3fd09895327b465e, // 0.96579, 0.25931 + 0x3feee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // 0.96539, 0.26079 + 0x3feee13987bbebdc, 0x3fd0c91bda4f158d, // 0.96499, 0.26227 + 0x3feeddeb6a078651, 0x3fd0e15b4e1749cd, // 0.96459, 0.26375 + 0x3feeda9889bfe86a, 0x3fd0f998277733f7, // 0.96418, 0.26523 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3feed3e483849c51, 0x3fd12a09fc0b1b12, // 0.96337, 0.26819 + 0x3feed0835e999009, 0x3fd1423eefc69378, // 0.96295, 0.26967 + 0x3feecd1d792c8f10, 0x3fd15a713a28b9d9, // 0.96254, 0.27115 + 0x3feec9b2d3c3bf84, 0x3fd172a0d7765177, // 0.96212, 0.27262 + 0x3feec6436ee60309, 0x3fd18acdc3f4873a, // 0.9617, 0.2741 + 0x3feec2cf4b1af6b2, 0x3fd1a2f7fbe8f243, // 0.96128, 0.27557 + 0x3feebf5668eaf2ef, 0x3fd1bb1f7b999480, // 0.96086, 0.27705 + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852 + 0x3feeb8566b810f2a, 0x3fd1eb6643499fbb, // 0.96, 0.27999 + 0x3feeb4cf515b8811, 0x3fd2038583d727bd, // 0.95957, 0.28146 + 0x3feeb1437af9bb34, 0x3fd21ba1fd3d2623, // 0.95914, 0.28294 + 0x3feeadb2e8e7a88e, 0x3fd233bbabc3bb72, // 0.9587, 0.28441 + 0x3feeaa1d9bb20af3, 0x3fd24bd28bb37672, // 0.95827, 0.28588 + 0x3feea68393e65800, 0x3fd263e6995554ba, // 0.95783, 0.28735 + 0x3feea2e4d212c000, 0x3fd27bf7d0f2c346, // 0.95738, 0.28882 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3fee9b99229046f8, 0x3fd2ac11af483572, // 0.95649, 0.29175 + 0x3fee97ec36016b30, 0x3fd2c41a4e954520, // 0.95605, 0.29322 + 0x3fee943a91aab4b4, 0x3fd2dc200907fe51, // 0.95559, 0.29469 + 0x3fee9084361df7f3, 0x3fd2f422daec0386, // 0.95514, 0.29615 + 0x3fee8cc923edc388, 0x3fd30c22c08d6a13, // 0.95469, 0.29762 + 0x3fee89095bad6025, 0x3fd3241fb638baaf, // 0.95423, 0.29908 + 0x3fee8544ddf0d075, 0x3fd33c19b83af207, // 0.95377, 0.30054 + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201 + 0x3fee7dadc456d850, 0x3fd36c04d27a4edf, // 0.95284, 0.30347 + 0x3fee79db29a5165a, 0x3fd383f5e353b6aa, // 0.95238, 0.30493 + 0x3fee7603dbce74e9, 0x3fd39be3f1bc8aef, // 0.95191, 0.30639 + 0x3fee7227db6a9744, 0x3fd3b3cefa0414b7, // 0.95144, 0.30785 + 0x3fee6e472911da27, 0x3fd3cbb6f87a146e, // 0.95096, 0.30931 + 0x3fee6a61c55d53a7, 0x3fd3e39be96ec271, // 0.95049, 0.31077 + 0x3fee6677b0e6d31e, 0x3fd3fb7dc932cfa4, // 0.95001, 0.31222 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee5e95781ebf1c, 0x3fd42b38466e2928, // 0.94905, 0.31514 + 0x3fee5a9d550467d3, 0x3fd44310dc8936f0, // 0.94856, 0.31659 + 0x3fee56a083968eb1, 0x3fd45ae652bb2800, // 0.94807, 0.31805 + 0x3fee529f04729ffc, 0x3fd472b8a5571054, // 0.94759, 0.3195 + 0x3fee4e98d836c0af, 0x3fd48a87d0b07fd7, // 0.94709, 0.32096 + 0x3fee4a8dff81ce5e, 0x3fd4a253d11b82f3, // 0.9466, 0.32241 + 0x3fee467e7af35f23, 0x3fd4ba1ca2eca31c, // 0.94611, 0.32386 + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531 + 0x3fee3e5170cbfc46, 0x3fd4e9a4ac15d520, // 0.94511, 0.32676 + 0x3fee3a33ec75ce85, 0x3fd50163dc197047, // 0.9446, 0.32821 + 0x3fee3611becbaf69, 0x3fd5191fceda3c35, // 0.9441, 0.32966 + 0x3fee31eae870ce25, 0x3fd530d880af3c24, // 0.94359, 0.33111 + 0x3fee2dbf6a0911d9, 0x3fd5488dedeff3be, // 0.94308, 0.33255 + 0x3fee298f4439197a, 0x3fd5604012f467b4, // 0.94257, 0.334 + 0x3fee255a77a63bb8, 0x3fd577eeec151e47, // 0.94206, 0.33545 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fee1ce2ecd0c0d8, 0x3fd5a742ac0ff78d, // 0.94103, 0.33833 + 0x3fee18a02fdc66d9, 0x3fd5bee78b9db3b6, // 0.94051, 0.33978 + 0x3fee1458cec1ad83, 0x3fd5d68910aee686, // 0.93998, 0.34122 + 0x3fee100cca2980ac, 0x3fd5ee27379ea693, // 0.93946, 0.34266 + 0x3fee0bbc22bd8349, 0x3fd605c1fcc88f63, // 0.93893, 0.3441 + 0x3fee0766d9280f54, 0x3fd61d595c88c203, // 0.9384, 0.34554 + 0x3fee030cee1435b8, 0x3fd634ed533be58e, // 0.93787, 0.34698 + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842 + 0x3fedfa4b3621271d, 0x3fd6640af6f03d9e, // 0.9368, 0.34986 + 0x3fedf5e36a9ba59c, 0x3fd67b949cad63ca, // 0.93627, 0.35129 + 0x3fedf177004b2534, 0x3fd6931acad55f51, // 0.93573, 0.35273 + 0x3feded05f7de47da, 0x3fd6aa9d7dc77e16, // 0.93518, 0.35416 + 0x3fede890520465ce, 0x3fd6c21cb1e39771, // 0.93464, 0.3556 + 0x3fede4160f6d8d81, 0x3fd6d998638a0cb5, // 0.93409, 0.35703 + 0x3feddf9730ca837b, 0x3fd6f1108f1bc9c5, // 0.93354, 0.35846 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fedd68ba2267a25, 0x3fd71ff6458782ec, // 0.93244, 0.36133 + 0x3fedd1fef38a915a, 0x3fd73763c9261092, // 0.93188, 0.36276 + 0x3fedcd6dabaca3a5, 0x3fd74ecdb8390a3e, // 0.93133, 0.36418 + 0x3fedc8d7cb410260, 0x3fd766340f2418f6, // 0.93077, 0.36561 + 0x3fedc43d52fcb453, 0x3fd77d96ca4b73a6, // 0.93021, 0.36704 + 0x3fedbf9e4395759a, 0x3fd794f5e613dfae, // 0.92964, 0.36847 + 0x3fedbafa9dc1b78d, 0x3fd7ac515ee2b172, // 0.92907, 0.36989 + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132 + 0x3fedb1a591b20c38, 0x3fd7dafd592ba621, // 0.92794, 0.37274 + 0x3fedacf42ce68ab9, 0x3fd7f24dd37341e3, // 0.92736, 0.37416 + 0x3feda83e348f613b, 0x3fd8099a9c5c362d, // 0.92679, 0.37559 + 0x3feda383a9668988, 0x3fd820e3b04eaac4, // 0.92621, 0.37701 + 0x3fed9ec48c26b1f3, 0x3fd838290bb359c8, // 0.92563, 0.37843 + 0x3fed9a00dd8b3d46, 0x3fd84f6aaaf3903f, // 0.92505, 0.37985 + 0x3fed95389e50429b, 0x3fd866a88a792ea0, // 0.92447, 0.38127 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed8b9a70ef9cb4, 0x3fd89518fbff098e, // 0.92329, 0.3841 + 0x3fed86c48445a450, 0x3fd8ac4b86d5ed44, // 0.9227, 0.38552 + 0x3fed81ea09f38b63, 0x3fd8c37a439f884f, // 0.92211, 0.38693 + 0x3fed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // 0.92151, 0.38835 + 0x3fed78276f5617c6, 0x3fd8f1cc44bea329, // 0.92092, 0.38976 + 0x3fed733f508c0dff, 0x3fd908ef81ef7bd1, // 0.92032, 0.39117 + 0x3fed6e52a71c8547, 0x3fd9200ee2c9be97, // 0.91972, 0.39258 + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399 + 0x3fed646bb7574de5, 0x3fd94e420137bce3, // 0.91851, 0.3954 + 0x3fed5f7172888a7f, 0x3fd96555b7ab948f, // 0.9179, 0.39681 + 0x3fed5a72a6221e73, 0x3fd97c6583890fc2, // 0.91729, 0.39822 + 0x3fed556f52e93eb1, 0x3fd993716141bdfe, // 0.91668, 0.39962 + 0x3fed506779a3d2d9, 0x3fd9aa794d47c9ee, // 0.91606, 0.40103 + 0x3fed4b5b1b187524, 0x3fd9c17d440df9f2, // 0.91545, 0.40243 + 0x3fed464a380e7242, 0x3fd9d87d4207b0ab, // 0.91483, 0.40384 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed3c1ae79f2b4e, 0x3fda067145664d57, // 0.91359, 0.40664 + 0x3fed36fc7bcbfbdc, 0x3fda1d6543b50ac0, // 0.91296, 0.40804 + 0x3fed31d98e9e503a, 0x3fda34553b0afee5, // 0.91234, 0.40944 + 0x3fed2cb220e0ef9f, 0x3fda4b4127dea1e4, // 0.91171, 0.41084 + 0x3fed2786335f52fc, 0x3fda622906a70b63, // 0.91107, 0.41224 + 0x3fed2255c6e5a4e1, 0x3fda790cd3dbf31a, // 0.91044, 0.41364 + 0x3fed1d20dc40c15c, 0x3fda8fec8bf5b166, // 0.90981, 0.41503 + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643 + 0x3fed12a98fac410c, 0x3fdabd9faebc3980, // 0.90853, 0.41782 + 0x3fed0d672f59d2b9, 0x3fdad473125cdc08, // 0.90789, 0.41922 + 0x3fed082054168bac, 0x3fdaeb4252ca07ab, // 0.90724, 0.42061 + 0x3fed02d4feb2bd92, 0x3fdb020d6c7f4009, // 0.9066, 0.422 + 0x3fecfd852fff6ad4, 0x3fdb18d45bf8aca6, // 0.90595, 0.42339 + 0x3fecf830e8ce467b, 0x3fdb2f971db31972, // 0.9053, 0.42478 + 0x3fecf2d829f1b40e, 0x3fdb4655ae2bf757, // 0.90464, 0.42617 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fece819488344ce, 0x3fdb73c62d520624, // 0.90333, 0.42894 + 0x3fece2b32799a060, 0x3fdb8a7814fd5693, // 0.90267, 0.43033 + 0x3fecdd489254fe65, 0x3fdba125bd63583e, // 0.90201, 0.43171 + 0x3fecd7d9898b32f6, 0x3fdbb7cf2304bd01, // 0.90135, 0.43309 + 0x3fecd2660e12c1e6, 0x3fdbce744262deee, // 0.90068, 0.43448 + 0x3fecccee20c2de9f, 0x3fdbe51517ffc0d9, // 0.90002, 0.43586 + 0x3fecc771c2736c09, 0x3fdbfbb1a05e0edc, // 0.89935, 0.43724 + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862 + 0x3fecbc6bb638d10b, 0x3fdc28ddbb6cf145, // 0.898, 0.43999 + 0x3fecb6e20a00da99, 0x3fdc3f6d47263129, // 0.89732, 0.44137 + 0x3fecb153f02fb87d, 0x3fdc55f877b23537, // 0.89665, 0.44275 + 0x3fecabc169a0b901, 0x3fdc6c7f4997000a, // 0.89597, 0.44412 + 0x3feca62a772fd919, 0x3fdc8301b95b40c2, // 0.89528, 0.4455 + 0x3feca08f19b9c449, 0x3fdc997fc3865388, // 0.8946, 0.44687 + 0x3fec9aef521bd480, 0x3fdcaff964a0421d, // 0.89391, 0.44824 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3fec8fa287e13305, 0x3fdcdcdf5dc440ce, // 0.89253, 0.45098 + 0x3fec89f587029c13, 0x3fdcf34baee1cd21, // 0.89184, 0.45235 + 0x3fec84441f785f61, 0x3fdd09b389152ec1, // 0.89115, 0.45372 + 0x3fec7e8e52233cf3, 0x3fdd2016e8e9db5b, // 0.89045, 0.45508 + 0x3fec78d41fe4a267, 0x3fdd3675caebf962, // 0.88975, 0.45645 + 0x3fec7315899eaad7, 0x3fdd4cd02ba8609c, // 0.88905, 0.45781 + 0x3fec6d5290341eb2, 0x3fdd632607ac9aa9, // 0.88835, 0.45918 + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054 + 0x3fec61bf777fcc48, 0x3fdd8fc423c62a25, // 0.88693, 0.4619 + 0x3fec5bef59fef85a, 0x3fdda60c5cfa10d8, // 0.88622, 0.46326 + 0x3fec561adceb743e, 0x3fddbc5003b2edf8, // 0.88551, 0.46462 + 0x3fec5042012b6907, 0x3fddd28f1481cc58, // 0.8848, 0.46598 + 0x3fec4a64c7a5ac4c, 0x3fdde8c98bf86bd6, // 0.88408, 0.46733 + 0x3fec44833141c004, 0x3fddfeff66a941de, // 0.88336, 0.46869 + 0x3fec3e9d3ee7d262, 0x3fde1530a12779f4, // 0.88264, 0.47004 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec32c449f60831, 0x3fde418527dc4ffa, // 0.8812, 0.47275 + 0x3fec2cd14931e3f1, 0x3fde57a86d3cd824, // 0.88047, 0.4741 + 0x3fec26d9f01f2eaf, 0x3fde6dc704be97e2, // 0.87974, 0.47545 + 0x3fec20de3fa971b0, 0x3fde83e0eaf85113, // 0.87901, 0.4768 + 0x3fec1ade38bce19b, 0x3fde99f61c817eda, // 0.87828, 0.47815 + 0x3fec14d9dc465e58, 0x3fdeb00695f25620, // 0.87755, 0.47949 + 0x3fec0ed12b3372e9, 0x3fdec61253e3c61b, // 0.87681, 0.48084 + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218 + 0x3fec02b2cef1e641, 0x3fdef21b8fafd3b5, // 0.87533, 0.48353 + 0x3febfc9d25a1b147, 0x3fdf081906bff7fd, // 0.87459, 0.48487 + 0x3febf6832b71ec5b, 0x3fdf1e11b4bbc35c, // 0.87384, 0.48621 + 0x3febf064e15377dd, 0x3fdf3405963fd068, // 0.87309, 0.48755 + 0x3febea424837de6d, 0x3fdf49f4a7e97729, // 0.87235, 0.48889 + 0x3febe41b611154c1, 0x3fdf5fdee656cda3, // 0.8716, 0.49023 + 0x3febddf02cd2b983, 0x3fdf75c44e26a852, // 0.87084, 0.49156 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3febd18ce0dc19d6, 0x3fdfa1808c6cf7e0, // 0.86933, 0.49423 + 0x3febcb54cb0d2327, 0x3fdfb7575c24d2de, // 0.86857, 0.49557 + 0x3febc5186bf8361d, 0x3fdfcd2947c1ff57, // 0.86781, 0.4969 + 0x3febbed7c49380ea, 0x3fdfe2f64be7120f, // 0.86705, 0.49823 + 0x3febb892d5d5dad5, 0x3fdff8be6537615e, // 0.86628, 0.49956 + 0x3febb249a0b6c40d, 0x3fe00740c82b82e0, // 0.86551, 0.50089 + 0x3febabfc262e6586, 0x3fe0121fe4f56d2c, // 0.86474, 0.50221 + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354 + 0x3feb9f5464c5bffc, 0x3fe027d6ad83287e, // 0.8632, 0.50486 + 0x3feb98fa1fd9155e, 0x3fe032ae55edbd95, // 0.86242, 0.50619 + 0x3feb929b996a5b7f, 0x3fe03d837edff370, // 0.86165, 0.50751 + 0x3feb8c38d27504e9, 0x3fe0485626ae221a, // 0.86087, 0.50883 + 0x3feb85d1cbf52c02, 0x3fe053264bad0483, // 0.86009, 0.51015 + 0x3feb7f6686e792ea, 0x3fe05df3ec31b8b6, // 0.8593, 0.51147 + 0x3feb78f70449a34b, 0x3fe068bf0691c028, // 0.85852, 0.51279 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb6c0b4a55ac17, 0x3fe07e4da23bc102, // 0.85694, 0.51542 + 0x3feb658f14fdbc47, 0x3fe089112032b08c, // 0.85615, 0.51673 + 0x3feb5f0ea611a532, 0x3fe093d2115ee018, // 0.85535, 0.51804 + 0x3feb5889fe921405, 0x3fe09e907417c5e1, // 0.85456, 0.51936 + 0x3feb52011f805c92, 0x3fe0a94c46b53d0b, // 0.85376, 0.52067 + 0x3feb4b7409de7925, 0x3fe0b405878f85ec, // 0.85296, 0.52198 + 0x3feb44e2beaf0a61, 0x3fe0bebc34ff4646, // 0.85216, 0.52328 + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459 + 0x3feb37b38bb54c09, 0x3fe0d421cf03c12b, // 0.85055, 0.5259 + 0x3feb3115a5f37bf4, 0x3fe0ded0b84bc4b5, // 0.84974, 0.5272 + 0x3feb2a738eb51f33, 0x3fe0e97d078fd23b, // 0.84893, 0.5285 + 0x3feb23cd470013b4, 0x3fe0f426bb2a8e7d, // 0.84812, 0.5298 + 0x3feb1d22cfdadcc6, 0x3fe0fecdd1770537, // 0.84731, 0.5311 + 0x3feb16742a4ca2f5, 0x3fe1097248d0a956, // 0.84649, 0.5324 + 0x3feb0fc1575d33db, 0x3fe114141f935545, // 0.84567, 0.5337 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3feb024f2d7d24a9, 0x3fe1294fe4c5350a, // 0.84403, 0.53629 + 0x3feafb8fd89f57b6, 0x3fe133e9cfee254e, // 0.84321, 0.53759 + 0x3feaf4cc5a85fb73, 0x3fe13e8113f396c1, // 0.84238, 0.53888 + 0x3feaee04b43c1474, 0x3fe14915af336ceb, // 0.84155, 0.54017 + 0x3feae738e6cd4b67, 0x3fe153a7a00bf453, // 0.84073, 0.54146 + 0x3feae068f345ecef, 0x3fe15e36e4dbe2bc, // 0.83989, 0.54275 + 0x3fead994dab2e979, 0x3fe168c37c025764, // 0.83906, 0.54404 + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532 + 0x3feacbe03ea0e73b, 0x3fe17dd49ad16161, // 0.83739, 0.54661 + 0x3feac4ffbd3efac8, 0x3fe188591f3a46e5, // 0.83655, 0.54789 + 0x3feabe1b1b0b8dac, 0x3fe192daef7a5386, // 0.83571, 0.54918 + 0x3feab7325916c0d4, 0x3fe19d5a09f2b9b8, // 0.83486, 0.55046 + 0x3feab045787157ff, 0x3fe1a7d66d0516e6, // 0.83402, 0.55174 + 0x3feaa9547a2cb98e, 0x3fe1b250171373be, // 0.83317, 0.55302 + 0x3feaa25f5f5aee60, 0x3fe1bcc706804467, // 0.83232, 0.55429 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3fea9468d85b20ae, 0x3fe1d1acaf012cc2, // 0.83062, 0.55685 + 0x3fea8d676e545ad2, 0x3fe1dc1b64dc4872, // 0.82976, 0.55812 + 0x3fea8661ec0ee133, 0x3fe1e68759a3e074, // 0.8289, 0.55939 + 0x3fea7f58529fe69d, 0x3fe1f0f08bbc861b, // 0.82805, 0.56066 + 0x3fea784aa31d3f55, 0x3fe1fb56f98b37b8, // 0.82718, 0.56193 + 0x3fea7138de9d60f5, 0x3fe205baa17560d6, // 0.82632, 0.5632 + 0x3fea6a230637623b, 0x3fe2101b81e0da78, // 0.82546, 0.56447 + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573 + 0x3fea5beb1e188375, 0x3fe224d4e5d5482e, // 0.82372, 0.567 + 0x3fea54c91090f524, 0x3fe22f2d662c13e1, // 0.82285, 0.56826 + 0x3fea4da2f385e997, 0x3fe23983189fdfd5, // 0.82198, 0.56952 + 0x3fea4678c8119ac8, 0x3fe243d5fb98ac1f, // 0.8211, 0.57078 + 0x3fea3f4a8f4ee2d2, 0x3fe24e260d7ee7c9, // 0.82023, 0.57204 + 0x3fea38184a593bc6, 0x3fe258734cbb7110, // 0.81935, 0.5733 + 0x3fea30e1fa4cbf81, 0x3fe262bdb7b795a2, // 0.81847, 0.57455 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fea22693d62ccb9, 0x3fe2774a0a961612, // 0.8167, 0.57706 + 0x3fea1b26d2c0a75e, 0x3fe2818bef4d3cba, // 0.81581, 0.57831 + 0x3fea13e0617e4ec7, 0x3fe28bcaf96d94ba, // 0.81493, 0.57956 + 0x3fea0c95eabaf937, 0x3fe2960727629ca8, // 0.81404, 0.58081 + 0x3fea05476f967bb5, 0x3fe2a040779843fb, // 0.81314, 0.58206 + 0x3fe9fdf4f13149de, 0x3fe2aa76e87aeb58, // 0.81225, 0.58331 + 0x3fe9f69e70ac75bc, 0x3fe2b4aa787764c4, // 0.81135, 0.58455 + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858 + 0x3fe9e7e56dcb45bd, 0x3fe2c908ef734e57, // 0.80956, 0.58704 + 0x3fe9e082edb42472, 0x3fe2d333d34e9bb7, // 0.80866, 0.58828 + 0x3fe9d91c7007d5a6, 0x3fe2dd5bcffb7616, // 0.80775, 0.58952 + 0x3fe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // 0.80685, 0.59076 + 0x3fe9ca438080eadb, 0x3fe2f1a30d86773a, // 0.80594, 0.592 + 0x3fe9c2d110f075c3, 0x3fe2fbc24b441015, // 0.80503, 0.59323 + 0x3fe9bb5aa85f2098, 0x3fe305de9b921a94, // 0.80412, 0.59447 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe9ac61f0d4e247, 0x3fe31a0e6da35e44, // 0.80229, 0.59693 + 0x3fe9a4dfa42b06b2, 0x3fe32421ec49a620, // 0.80138, 0.59816 + 0x3fe99d59631e65d5, 0x3fe32e3277467d6b, // 0.80046, 0.59939 + 0x3fe995cf2ed80d22, 0x3fe338400d0c8e57, // 0.79954, 0.60062 + 0x3fe98e410881a600, 0x3fe3424aac0ef7d6, // 0.79861, 0.60184 + 0x3fe986aef1457594, 0x3fe34c5252c14de1, // 0.79769, 0.60307 + 0x3fe97f18ea4e5c9e, 0x3fe35656ff9799ae, // 0.79676, 0.60429 + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551 + 0x3fe96fe111ddfce0, 0x3fe36a576582831b, // 0.79491, 0.60673 + 0x3fe9683f42bd7fe1, 0x3fe374531b817f8d, // 0.79398, 0.60795 + 0x3fe960998893ad8c, 0x3fe37e4bd1792fe2, // 0.79304, 0.60917 + 0x3fe958efe48e6dd7, 0x3fe3884185dfeb22, // 0.79211, 0.61038 + 0x3fe9514257dc4335, 0x3fe39234372c7f04, // 0.79117, 0.6116 + 0x3fe94990e3ac4a6c, 0x3fe39c23e3d63029, // 0.79023, 0.61281 + 0x3fe941db892e3a65, 0x3fe3a6108a54ba58, // 0.78929, 0.61402 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe932652609b1cf, 0x3fe3b9e0beb19e18, // 0.7874, 0.61644 + 0x3fe92aa41fc5a815, 0x3fe3c3c44981c517, // 0.78646, 0.61765 + 0x3fe922df37f8646a, 0x3fe3cda4c80a6076, // 0.78551, 0.61885 + 0x3fe91b166fd49da2, 0x3fe3d78238c58343, // 0.78456, 0.62006 + 0x3fe91349c88da398, 0x3fe3e15c9a2db922, // 0.7836, 0.62126 + 0x3fe90b7943575efe, 0x3fe3eb33eabe0680, // 0.78265, 0.62246 + 0x3fe903a4e1665133, 0x3fe3f50828f1e8d2, // 0.78169, 0.62366 + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486 + 0x3fe8f3f08c28d9ac, 0x3fe408a76834c0c0, // 0.77978, 0.62606 + 0x3fe8ec109b486c49, 0x3fe41272663d108c, // 0.77882, 0.62725 + 0x3fe8e42cd2852e0a, 0x3fe41c3a4bdbaa26, // 0.77785, 0.62845 + 0x3fe8dc45331698cc, 0x3fe425ff178e6bb1, // 0.77689, 0.62964 + 0x3fe8d459be34bdfa, 0x3fe42fc0c7d3adbb, // 0.77592, 0.63083 + 0x3fe8cc6a75184655, 0x3fe4397f5b2a4380, // 0.77495, 0.63202 + 0x3fe8c47758fa71cb, 0x3fe4433ad0117b1d, // 0.77398, 0.63321 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe8b485aca2a468, 0x3fe456a858917046, // 0.77204, 0.63558 + 0x3fe8ac871ede1d88, 0x3fe4605a692b32a2, // 0.77106, 0.63676 + 0x3fe8a484c3031d50, 0x3fe46a095557a0f1, // 0.77008, 0.63794 + 0x3fe89c7e9a4dd4ab, 0x3fe473b51b987347, // 0.7691, 0.63912 + 0x3fe89474a5fb0a84, 0x3fe47d5dba6fde01, // 0.76812, 0.6403 + 0x3fe88c66e7481ba1, 0x3fe48703306091fe, // 0.76714, 0.64148 + 0x3fe884555f72fa6b, 0x3fe490a57bedbcdf, // 0.76615, 0.64266 + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383 + 0x3fe87426f95cd5bd, 0x3fe4a3e08dec9ed6, // 0.76418, 0.645 + 0x3fe86c0a1d9aa195, 0x3fe4ad79516722f0, // 0.76319, 0.64618 + 0x3fe863e97db3d95a, 0x3fe4b70ee48fb869, // 0.7622, 0.64735 + 0x3fe85bc51ae958cc, 0x3fe4c0a145ec0004, // 0.7612, 0.64851 + 0x3fe8539cf67c9029, 0x3fe4ca30740218a3, // 0.76021, 0.64968 + 0x3fe84b7111af83f9, 0x3fe4d3bc6d589f80, // 0.75921, 0.65085 + 0x3fe843416dc4cce2, 0x3fe4dd453076b064, // 0.75821, 0.65201 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe832d6eda3a3e0, 0x3fe4f04d0e2859aa, // 0.75621, 0.65433 + 0x3fe82a9c13f545ff, 0x3fe4f9cc25cca486, // 0.7552, 0.65549 + 0x3fe8225d803964e5, 0x3fe503480159ded2, // 0.75419, 0.65665 + 0x3fe81a1b33b57acc, 0x3fe50cc09f59a09b, // 0.75319, 0.65781 + 0x3fe811d52faf94dc, 0x3fe51635fe5601d7, // 0.75218, 0.65896 + 0x3fe8098b756e52fa, 0x3fe51fa81cd99aa6, // 0.75117, 0.66011 + 0x3fe8013e0638e795, 0x3fe52916f96f8388, // 0.75015, 0.66127 + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242 + 0x3fe7f0980e113978, 0x3fe53beae7012abe, // 0.74812, 0.66356 + 0x3fe7e83f87b03686, 0x3fe5454ff5159dfb, // 0.7471, 0.66471 + 0x3fe7dfe3517d8937, 0x3fe54eb1bb6dcb8f, // 0.74608, 0.66586 + 0x3fe7d7836cc33db2, 0x3fe5581038975137, // 0.74506, 0.667 + 0x3fe7cf1fdacbf179, 0x3fe5616b6b204e6e, // 0.74403, 0.66814 + 0x3fe7c6b89ce2d333, 0x3fe56ac35197649e, // 0.74301, 0.66928 + 0x3fe7be4db453a27c, 0x3fe57417ea8bb75c, // 0.74198, 0.67042 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe7ad6ce874dbb6, 0x3fe586b72e2b2cfd, // 0.73992, 0.67269 + 0x3fe7a4f707bf97d2, 0x3fe59001d5f723df, // 0.73889, 0.67383 + 0x3fe79c7d8198e56e, 0x3fe599492a81ffbc, // 0.73785, 0.67496 + 0x3fe79400574f55e4, 0x3fe5a28d2a5d7250, // 0.73682, 0.67609 + 0x3fe78b7f8a320a52, 0x3fe5abcdd41bb0d8, // 0.73578, 0.67722 + 0x3fe782fb1b90b35b, 0x3fe5b50b264f7448, // 0.73474, 0.67835 + 0x3fe77a730cbb9100, 0x3fe5be451f8bf980, // 0.7337, 0.67948 + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806 + 0x3fe7695813b9b594, 0x3fe5d0af016ed1d4, // 0.73161, 0.68172 + 0x3fe760c52c304764, 0x3fe5d9dee73e345c, // 0.73056, 0.68285 + 0x3fe7582ea9b9a329, 0x3fe5e30b6e6877f3, // 0.72951, 0.68397 + 0x3fe74f948da8d28d, 0x3fe5ec3495837074, // 0.72846, 0.68508 + 0x3fe746f6d9516d59, 0x3fe5f55a5b2576f8, // 0.72741, 0.6862 + 0x3fe73e558e079942, 0x3fe5fe7cbde56a0f, // 0.72636, 0.68732 + 0x3fe735b0ad2009b2, 0x3fe6079bbc5aadfa, // 0.7253, 0.68843 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe7245c2fcd492a, 0x3fe619cf86c55702, // 0.72319, 0.69065 + 0x3fe71bac960e41bf, 0x3fe622e44fec22ff, // 0.72213, 0.69176 + 0x3fe712f96c09d18d, 0x3fe62bf5af2b0dfd, // 0.72107, 0.69287 + 0x3fe70a42b3176d7a, 0x3fe63503a31c1be8, // 0.72, 0.69397 + 0x3fe701886c8f16e6, 0x3fe63e0e2a59d7aa, // 0.71894, 0.69508 + 0x3fe6f8ca99c95b75, 0x3fe64715437f535b, // 0.71787, 0.69618 + 0x3fe6f0093c1f54de, 0x3fe65018ed28287f, // 0.7168, 0.69728 + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838 + 0x3fe6de7be585881d, 0x3fe66215ec74eb91, // 0.71466, 0.69947 + 0x3fe6d5afef4aafcc, 0x3fe66b0f3f52b386, // 0.71358, 0.70057 + 0x3fe6cce07395679f, 0x3fe674051d27896c, // 0.71251, 0.70166 + 0x3fe6c40d73c18275, 0x3fe67cf78491af10, // 0.71143, 0.70275 + 0x3fe6bb36f12b5e06, 0x3fe685e6742feeef, // 0.71035, 0.70385 + 0x3fe6b25ced2fe29c, 0x3fe68ed1eaa19c71, // 0.70927, 0.70493 + 0x3fe6a97f692c82ea, 0x3fe697b9e686941c, // 0.70819, 0.70602 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe697b9e686941c, 0x3fe6a97f692c82ea, // 0.70602, 0.70819 + 0x3fe68ed1eaa19c71, 0x3fe6b25ced2fe29c, // 0.70493, 0.70927 + 0x3fe685e6742feeef, 0x3fe6bb36f12b5e06, // 0.70385, 0.71035 + 0x3fe67cf78491af10, 0x3fe6c40d73c18275, // 0.70275, 0.71143 + 0x3fe674051d27896c, 0x3fe6cce07395679f, // 0.70166, 0.71251 + 0x3fe66b0f3f52b386, 0x3fe6d5afef4aafcc, // 0.70057, 0.71358 + 0x3fe66215ec74eb91, 0x3fe6de7be585881d, // 0.69947, 0.71466 + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573 + 0x3fe65018ed28287f, 0x3fe6f0093c1f54de, // 0.69728, 0.7168 + 0x3fe64715437f535b, 0x3fe6f8ca99c95b75, // 0.69618, 0.71787 + 0x3fe63e0e2a59d7aa, 0x3fe701886c8f16e6, // 0.69508, 0.71894 + 0x3fe63503a31c1be8, 0x3fe70a42b3176d7a, // 0.69397, 0.72 + 0x3fe62bf5af2b0dfd, 0x3fe712f96c09d18d, // 0.69287, 0.72107 + 0x3fe622e44fec22ff, 0x3fe71bac960e41bf, // 0.69176, 0.72213 + 0x3fe619cf86c55702, 0x3fe7245c2fcd492a, // 0.69065, 0.72319 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe6079bbc5aadfa, 0x3fe735b0ad2009b2, // 0.68843, 0.7253 + 0x3fe5fe7cbde56a0f, 0x3fe73e558e079942, // 0.68732, 0.72636 + 0x3fe5f55a5b2576f8, 0x3fe746f6d9516d59, // 0.6862, 0.72741 + 0x3fe5ec3495837074, 0x3fe74f948da8d28d, // 0.68508, 0.72846 + 0x3fe5e30b6e6877f3, 0x3fe7582ea9b9a329, // 0.68397, 0.72951 + 0x3fe5d9dee73e345c, 0x3fe760c52c304764, // 0.68285, 0.73056 + 0x3fe5d0af016ed1d4, 0x3fe7695813b9b594, // 0.68172, 0.73161 + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265 + 0x3fe5be451f8bf980, 0x3fe77a730cbb9100, // 0.67948, 0.7337 + 0x3fe5b50b264f7448, 0x3fe782fb1b90b35b, // 0.67835, 0.73474 + 0x3fe5abcdd41bb0d8, 0x3fe78b7f8a320a52, // 0.67722, 0.73578 + 0x3fe5a28d2a5d7250, 0x3fe79400574f55e4, // 0.67609, 0.73682 + 0x3fe599492a81ffbc, 0x3fe79c7d8198e56e, // 0.67496, 0.73785 + 0x3fe59001d5f723df, 0x3fe7a4f707bf97d2, // 0.67383, 0.73889 + 0x3fe586b72e2b2cfd, 0x3fe7ad6ce874dbb6, // 0.67269, 0.73992 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe57417ea8bb75c, 0x3fe7be4db453a27c, // 0.67042, 0.74198 + 0x3fe56ac35197649e, 0x3fe7c6b89ce2d333, // 0.66928, 0.74301 + 0x3fe5616b6b204e6e, 0x3fe7cf1fdacbf179, // 0.66814, 0.74403 + 0x3fe5581038975137, 0x3fe7d7836cc33db2, // 0.667, 0.74506 + 0x3fe54eb1bb6dcb8f, 0x3fe7dfe3517d8937, // 0.66586, 0.74608 + 0x3fe5454ff5159dfb, 0x3fe7e83f87b03686, // 0.66471, 0.7471 + 0x3fe53beae7012abe, 0x3fe7f0980e113978, // 0.66356, 0.74812 + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914 + 0x3fe52916f96f8388, 0x3fe8013e0638e795, // 0.66127, 0.75015 + 0x3fe51fa81cd99aa6, 0x3fe8098b756e52fa, // 0.66011, 0.75117 + 0x3fe51635fe5601d7, 0x3fe811d52faf94dc, // 0.65896, 0.75218 + 0x3fe50cc09f59a09b, 0x3fe81a1b33b57acc, // 0.65781, 0.75319 + 0x3fe503480159ded2, 0x3fe8225d803964e5, // 0.65665, 0.75419 + 0x3fe4f9cc25cca486, 0x3fe82a9c13f545ff, // 0.65549, 0.7552 + 0x3fe4f04d0e2859aa, 0x3fe832d6eda3a3e0, // 0.65433, 0.75621 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe4dd453076b064, 0x3fe843416dc4cce2, // 0.65201, 0.75821 + 0x3fe4d3bc6d589f80, 0x3fe84b7111af83f9, // 0.65085, 0.75921 + 0x3fe4ca30740218a3, 0x3fe8539cf67c9029, // 0.64968, 0.76021 + 0x3fe4c0a145ec0004, 0x3fe85bc51ae958cc, // 0.64851, 0.7612 + 0x3fe4b70ee48fb869, 0x3fe863e97db3d95a, // 0.64735, 0.7622 + 0x3fe4ad79516722f0, 0x3fe86c0a1d9aa195, // 0.64618, 0.76319 + 0x3fe4a3e08dec9ed6, 0x3fe87426f95cd5bd, // 0.645, 0.76418 + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517 + 0x3fe490a57bedbcdf, 0x3fe884555f72fa6b, // 0.64266, 0.76615 + 0x3fe48703306091fe, 0x3fe88c66e7481ba1, // 0.64148, 0.76714 + 0x3fe47d5dba6fde01, 0x3fe89474a5fb0a84, // 0.6403, 0.76812 + 0x3fe473b51b987347, 0x3fe89c7e9a4dd4ab, // 0.63912, 0.7691 + 0x3fe46a095557a0f1, 0x3fe8a484c3031d50, // 0.63794, 0.77008 + 0x3fe4605a692b32a2, 0x3fe8ac871ede1d88, // 0.63676, 0.77106 + 0x3fe456a858917046, 0x3fe8b485aca2a468, // 0.63558, 0.77204 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe4433ad0117b1d, 0x3fe8c47758fa71cb, // 0.63321, 0.77398 + 0x3fe4397f5b2a4380, 0x3fe8cc6a75184655, // 0.63202, 0.77495 + 0x3fe42fc0c7d3adbb, 0x3fe8d459be34bdfa, // 0.63083, 0.77592 + 0x3fe425ff178e6bb1, 0x3fe8dc45331698cc, // 0.62964, 0.77689 + 0x3fe41c3a4bdbaa26, 0x3fe8e42cd2852e0a, // 0.62845, 0.77785 + 0x3fe41272663d108c, 0x3fe8ec109b486c49, // 0.62725, 0.77882 + 0x3fe408a76834c0c0, 0x3fe8f3f08c28d9ac, // 0.62606, 0.77978 + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074 + 0x3fe3f50828f1e8d2, 0x3fe903a4e1665133, // 0.62366, 0.78169 + 0x3fe3eb33eabe0680, 0x3fe90b7943575efe, // 0.62246, 0.78265 + 0x3fe3e15c9a2db922, 0x3fe91349c88da398, // 0.62126, 0.7836 + 0x3fe3d78238c58343, 0x3fe91b166fd49da2, // 0.62006, 0.78456 + 0x3fe3cda4c80a6076, 0x3fe922df37f8646a, // 0.61885, 0.78551 + 0x3fe3c3c44981c517, 0x3fe92aa41fc5a815, // 0.61765, 0.78646 + 0x3fe3b9e0beb19e18, 0x3fe932652609b1cf, // 0.61644, 0.7874 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe3a6108a54ba58, 0x3fe941db892e3a65, // 0.61402, 0.78929 + 0x3fe39c23e3d63029, 0x3fe94990e3ac4a6c, // 0.61281, 0.79023 + 0x3fe39234372c7f04, 0x3fe9514257dc4335, // 0.6116, 0.79117 + 0x3fe3884185dfeb22, 0x3fe958efe48e6dd7, // 0.61038, 0.79211 + 0x3fe37e4bd1792fe2, 0x3fe960998893ad8c, // 0.60917, 0.79304 + 0x3fe374531b817f8d, 0x3fe9683f42bd7fe1, // 0.60795, 0.79398 + 0x3fe36a576582831b, 0x3fe96fe111ddfce0, // 0.60673, 0.79491 + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584 + 0x3fe35656ff9799ae, 0x3fe97f18ea4e5c9e, // 0.60429, 0.79676 + 0x3fe34c5252c14de1, 0x3fe986aef1457594, // 0.60307, 0.79769 + 0x3fe3424aac0ef7d6, 0x3fe98e410881a600, // 0.60184, 0.79861 + 0x3fe338400d0c8e57, 0x3fe995cf2ed80d22, // 0.60062, 0.79954 + 0x3fe32e3277467d6b, 0x3fe99d59631e65d5, // 0.59939, 0.80046 + 0x3fe32421ec49a620, 0x3fe9a4dfa42b06b2, // 0.59816, 0.80138 + 0x3fe31a0e6da35e44, 0x3fe9ac61f0d4e247, // 0.59693, 0.80229 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe305de9b921a94, 0x3fe9bb5aa85f2098, // 0.59447, 0.80412 + 0x3fe2fbc24b441015, 0x3fe9c2d110f075c3, // 0.59323, 0.80503 + 0x3fe2f1a30d86773a, 0x3fe9ca438080eadb, // 0.592, 0.80594 + 0x3fe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // 0.59076, 0.80685 + 0x3fe2dd5bcffb7616, 0x3fe9d91c7007d5a6, // 0.58952, 0.80775 + 0x3fe2d333d34e9bb7, 0x3fe9e082edb42472, // 0.58828, 0.80866 + 0x3fe2c908ef734e57, 0x3fe9e7e56dcb45bd, // 0.58704, 0.80956 + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046 + 0x3fe2b4aa787764c4, 0x3fe9f69e70ac75bc, // 0.58455, 0.81135 + 0x3fe2aa76e87aeb58, 0x3fe9fdf4f13149de, // 0.58331, 0.81225 + 0x3fe2a040779843fb, 0x3fea05476f967bb5, // 0.58206, 0.81314 + 0x3fe2960727629ca8, 0x3fea0c95eabaf937, // 0.58081, 0.81404 + 0x3fe28bcaf96d94ba, 0x3fea13e0617e4ec7, // 0.57956, 0.81493 + 0x3fe2818bef4d3cba, 0x3fea1b26d2c0a75e, // 0.57831, 0.81581 + 0x3fe2774a0a961612, 0x3fea22693d62ccb9, // 0.57706, 0.8167 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe262bdb7b795a2, 0x3fea30e1fa4cbf81, // 0.57455, 0.81847 + 0x3fe258734cbb7110, 0x3fea38184a593bc6, // 0.5733, 0.81935 + 0x3fe24e260d7ee7c9, 0x3fea3f4a8f4ee2d2, // 0.57204, 0.82023 + 0x3fe243d5fb98ac1f, 0x3fea4678c8119ac8, // 0.57078, 0.8211 + 0x3fe23983189fdfd5, 0x3fea4da2f385e997, // 0.56952, 0.82198 + 0x3fe22f2d662c13e1, 0x3fea54c91090f524, // 0.56826, 0.82285 + 0x3fe224d4e5d5482e, 0x3fea5beb1e188375, // 0.567, 0.82372 + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459 + 0x3fe2101b81e0da78, 0x3fea6a230637623b, // 0.56447, 0.82546 + 0x3fe205baa17560d6, 0x3fea7138de9d60f5, // 0.5632, 0.82632 + 0x3fe1fb56f98b37b8, 0x3fea784aa31d3f55, // 0.56193, 0.82718 + 0x3fe1f0f08bbc861b, 0x3fea7f58529fe69d, // 0.56066, 0.82805 + 0x3fe1e68759a3e074, 0x3fea8661ec0ee133, // 0.55939, 0.8289 + 0x3fe1dc1b64dc4872, 0x3fea8d676e545ad2, // 0.55812, 0.82976 + 0x3fe1d1acaf012cc2, 0x3fea9468d85b20ae, // 0.55685, 0.83062 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe1bcc706804467, 0x3feaa25f5f5aee60, // 0.55429, 0.83232 + 0x3fe1b250171373be, 0x3feaa9547a2cb98e, // 0.55302, 0.83317 + 0x3fe1a7d66d0516e6, 0x3feab045787157ff, // 0.55174, 0.83402 + 0x3fe19d5a09f2b9b8, 0x3feab7325916c0d4, // 0.55046, 0.83486 + 0x3fe192daef7a5386, 0x3feabe1b1b0b8dac, // 0.54918, 0.83571 + 0x3fe188591f3a46e5, 0x3feac4ffbd3efac8, // 0.54789, 0.83655 + 0x3fe17dd49ad16161, 0x3feacbe03ea0e73b, // 0.54661, 0.83739 + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822 + 0x3fe168c37c025764, 0x3fead994dab2e979, // 0.54404, 0.83906 + 0x3fe15e36e4dbe2bc, 0x3feae068f345ecef, // 0.54275, 0.83989 + 0x3fe153a7a00bf453, 0x3feae738e6cd4b67, // 0.54146, 0.84073 + 0x3fe14915af336ceb, 0x3feaee04b43c1474, // 0.54017, 0.84155 + 0x3fe13e8113f396c1, 0x3feaf4cc5a85fb73, // 0.53888, 0.84238 + 0x3fe133e9cfee254e, 0x3feafb8fd89f57b6, // 0.53759, 0.84321 + 0x3fe1294fe4c5350a, 0x3feb024f2d7d24a9, // 0.53629, 0.84403 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe114141f935545, 0x3feb0fc1575d33db, // 0.5337, 0.84567 + 0x3fe1097248d0a956, 0x3feb16742a4ca2f5, // 0.5324, 0.84649 + 0x3fe0fecdd1770537, 0x3feb1d22cfdadcc6, // 0.5311, 0.84731 + 0x3fe0f426bb2a8e7d, 0x3feb23cd470013b4, // 0.5298, 0.84812 + 0x3fe0e97d078fd23b, 0x3feb2a738eb51f33, // 0.5285, 0.84893 + 0x3fe0ded0b84bc4b5, 0x3feb3115a5f37bf4, // 0.5272, 0.84974 + 0x3fe0d421cf03c12b, 0x3feb37b38bb54c09, // 0.5259, 0.85055 + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136 + 0x3fe0bebc34ff4646, 0x3feb44e2beaf0a61, // 0.52328, 0.85216 + 0x3fe0b405878f85ec, 0x3feb4b7409de7925, // 0.52198, 0.85296 + 0x3fe0a94c46b53d0b, 0x3feb52011f805c92, // 0.52067, 0.85376 + 0x3fe09e907417c5e1, 0x3feb5889fe921405, // 0.51936, 0.85456 + 0x3fe093d2115ee018, 0x3feb5f0ea611a532, // 0.51804, 0.85535 + 0x3fe089112032b08c, 0x3feb658f14fdbc47, // 0.51673, 0.85615 + 0x3fe07e4da23bc102, 0x3feb6c0b4a55ac17, // 0.51542, 0.85694 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe068bf0691c028, 0x3feb78f70449a34b, // 0.51279, 0.85852 + 0x3fe05df3ec31b8b6, 0x3feb7f6686e792ea, // 0.51147, 0.8593 + 0x3fe053264bad0483, 0x3feb85d1cbf52c02, // 0.51015, 0.86009 + 0x3fe0485626ae221a, 0x3feb8c38d27504e9, // 0.50883, 0.86087 + 0x3fe03d837edff370, 0x3feb929b996a5b7f, // 0.50751, 0.86165 + 0x3fe032ae55edbd95, 0x3feb98fa1fd9155e, // 0.50619, 0.86242 + 0x3fe027d6ad83287e, 0x3feb9f5464c5bffc, // 0.50486, 0.8632 + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397 + 0x3fe0121fe4f56d2c, 0x3febabfc262e6586, // 0.50221, 0.86474 + 0x3fe00740c82b82e0, 0x3febb249a0b6c40d, // 0.50089, 0.86551 + 0x3fdff8be6537615e, 0x3febb892d5d5dad5, // 0.49956, 0.86628 + 0x3fdfe2f64be7120f, 0x3febbed7c49380ea, // 0.49823, 0.86705 + 0x3fdfcd2947c1ff57, 0x3febc5186bf8361d, // 0.4969, 0.86781 + 0x3fdfb7575c24d2de, 0x3febcb54cb0d2327, // 0.49557, 0.86857 + 0x3fdfa1808c6cf7e0, 0x3febd18ce0dc19d6, // 0.49423, 0.86933 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fdf75c44e26a852, 0x3febddf02cd2b983, // 0.49156, 0.87084 + 0x3fdf5fdee656cda3, 0x3febe41b611154c1, // 0.49023, 0.8716 + 0x3fdf49f4a7e97729, 0x3febea424837de6d, // 0.48889, 0.87235 + 0x3fdf3405963fd068, 0x3febf064e15377dd, // 0.48755, 0.87309 + 0x3fdf1e11b4bbc35c, 0x3febf6832b71ec5b, // 0.48621, 0.87384 + 0x3fdf081906bff7fd, 0x3febfc9d25a1b147, // 0.48487, 0.87459 + 0x3fdef21b8fafd3b5, 0x3fec02b2cef1e641, // 0.48353, 0.87533 + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607 + 0x3fdec61253e3c61b, 0x3fec0ed12b3372e9, // 0.48084, 0.87681 + 0x3fdeb00695f25620, 0x3fec14d9dc465e58, // 0.47949, 0.87755 + 0x3fde99f61c817eda, 0x3fec1ade38bce19b, // 0.47815, 0.87828 + 0x3fde83e0eaf85113, 0x3fec20de3fa971b0, // 0.4768, 0.87901 + 0x3fde6dc704be97e2, 0x3fec26d9f01f2eaf, // 0.47545, 0.87974 + 0x3fde57a86d3cd824, 0x3fec2cd14931e3f1, // 0.4741, 0.88047 + 0x3fde418527dc4ffa, 0x3fec32c449f60831, // 0.47275, 0.8812 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fde1530a12779f4, 0x3fec3e9d3ee7d262, // 0.47004, 0.88264 + 0x3fddfeff66a941de, 0x3fec44833141c004, // 0.46869, 0.88336 + 0x3fdde8c98bf86bd6, 0x3fec4a64c7a5ac4c, // 0.46733, 0.88408 + 0x3fddd28f1481cc58, 0x3fec5042012b6907, // 0.46598, 0.8848 + 0x3fddbc5003b2edf8, 0x3fec561adceb743e, // 0.46462, 0.88551 + 0x3fdda60c5cfa10d8, 0x3fec5bef59fef85a, // 0.46326, 0.88622 + 0x3fdd8fc423c62a25, 0x3fec61bf777fcc48, // 0.4619, 0.88693 + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764 + 0x3fdd632607ac9aa9, 0x3fec6d5290341eb2, // 0.45918, 0.88835 + 0x3fdd4cd02ba8609c, 0x3fec7315899eaad7, // 0.45781, 0.88905 + 0x3fdd3675caebf962, 0x3fec78d41fe4a267, // 0.45645, 0.88975 + 0x3fdd2016e8e9db5b, 0x3fec7e8e52233cf3, // 0.45508, 0.89045 + 0x3fdd09b389152ec1, 0x3fec84441f785f61, // 0.45372, 0.89115 + 0x3fdcf34baee1cd21, 0x3fec89f587029c13, // 0.45235, 0.89184 + 0x3fdcdcdf5dc440ce, 0x3fec8fa287e13305, // 0.45098, 0.89253 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdcaff964a0421d, 0x3fec9aef521bd480, // 0.44824, 0.89391 + 0x3fdc997fc3865388, 0x3feca08f19b9c449, // 0.44687, 0.8946 + 0x3fdc8301b95b40c2, 0x3feca62a772fd919, // 0.4455, 0.89528 + 0x3fdc6c7f4997000a, 0x3fecabc169a0b901, // 0.44412, 0.89597 + 0x3fdc55f877b23537, 0x3fecb153f02fb87d, // 0.44275, 0.89665 + 0x3fdc3f6d47263129, 0x3fecb6e20a00da99, // 0.44137, 0.89732 + 0x3fdc28ddbb6cf145, 0x3fecbc6bb638d10b, // 0.43999, 0.898 + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867 + 0x3fdbfbb1a05e0edc, 0x3fecc771c2736c09, // 0.43724, 0.89935 + 0x3fdbe51517ffc0d9, 0x3fecccee20c2de9f, // 0.43586, 0.90002 + 0x3fdbce744262deee, 0x3fecd2660e12c1e6, // 0.43448, 0.90068 + 0x3fdbb7cf2304bd01, 0x3fecd7d9898b32f6, // 0.43309, 0.90135 + 0x3fdba125bd63583e, 0x3fecdd489254fe65, // 0.43171, 0.90201 + 0x3fdb8a7814fd5693, 0x3fece2b32799a060, // 0.43033, 0.90267 + 0x3fdb73c62d520624, 0x3fece819488344ce, // 0.42894, 0.90333 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdb4655ae2bf757, 0x3fecf2d829f1b40e, // 0.42617, 0.90464 + 0x3fdb2f971db31972, 0x3fecf830e8ce467b, // 0.42478, 0.9053 + 0x3fdb18d45bf8aca6, 0x3fecfd852fff6ad4, // 0.42339, 0.90595 + 0x3fdb020d6c7f4009, 0x3fed02d4feb2bd92, // 0.422, 0.9066 + 0x3fdaeb4252ca07ab, 0x3fed082054168bac, // 0.42061, 0.90724 + 0x3fdad473125cdc08, 0x3fed0d672f59d2b9, // 0.41922, 0.90789 + 0x3fdabd9faebc3980, 0x3fed12a98fac410c, // 0.41782, 0.90853 + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917 + 0x3fda8fec8bf5b166, 0x3fed1d20dc40c15c, // 0.41503, 0.90981 + 0x3fda790cd3dbf31a, 0x3fed2255c6e5a4e1, // 0.41364, 0.91044 + 0x3fda622906a70b63, 0x3fed2786335f52fc, // 0.41224, 0.91107 + 0x3fda4b4127dea1e4, 0x3fed2cb220e0ef9f, // 0.41084, 0.91171 + 0x3fda34553b0afee5, 0x3fed31d98e9e503a, // 0.40944, 0.91234 + 0x3fda1d6543b50ac0, 0x3fed36fc7bcbfbdc, // 0.40804, 0.91296 + 0x3fda067145664d57, 0x3fed3c1ae79f2b4e, // 0.40664, 0.91359 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fd9d87d4207b0ab, 0x3fed464a380e7242, // 0.40384, 0.91483 + 0x3fd9c17d440df9f2, 0x3fed4b5b1b187524, // 0.40243, 0.91545 + 0x3fd9aa794d47c9ee, 0x3fed506779a3d2d9, // 0.40103, 0.91606 + 0x3fd993716141bdfe, 0x3fed556f52e93eb1, // 0.39962, 0.91668 + 0x3fd97c6583890fc2, 0x3fed5a72a6221e73, // 0.39822, 0.91729 + 0x3fd96555b7ab948f, 0x3fed5f7172888a7f, // 0.39681, 0.9179 + 0x3fd94e420137bce3, 0x3fed646bb7574de5, // 0.3954, 0.91851 + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911 + 0x3fd9200ee2c9be97, 0x3fed6e52a71c8547, // 0.39258, 0.91972 + 0x3fd908ef81ef7bd1, 0x3fed733f508c0dff, // 0.39117, 0.92032 + 0x3fd8f1cc44bea329, 0x3fed78276f5617c6, // 0.38976, 0.92092 + 0x3fd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // 0.38835, 0.92151 + 0x3fd8c37a439f884f, 0x3fed81ea09f38b63, // 0.38693, 0.92211 + 0x3fd8ac4b86d5ed44, 0x3fed86c48445a450, // 0.38552, 0.9227 + 0x3fd89518fbff098e, 0x3fed8b9a70ef9cb4, // 0.3841, 0.92329 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd866a88a792ea0, 0x3fed95389e50429b, // 0.38127, 0.92447 + 0x3fd84f6aaaf3903f, 0x3fed9a00dd8b3d46, // 0.37985, 0.92505 + 0x3fd838290bb359c8, 0x3fed9ec48c26b1f3, // 0.37843, 0.92563 + 0x3fd820e3b04eaac4, 0x3feda383a9668988, // 0.37701, 0.92621 + 0x3fd8099a9c5c362d, 0x3feda83e348f613b, // 0.37559, 0.92679 + 0x3fd7f24dd37341e3, 0x3fedacf42ce68ab9, // 0.37416, 0.92736 + 0x3fd7dafd592ba621, 0x3fedb1a591b20c38, // 0.37274, 0.92794 + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851 + 0x3fd7ac515ee2b172, 0x3fedbafa9dc1b78d, // 0.36989, 0.92907 + 0x3fd794f5e613dfae, 0x3fedbf9e4395759a, // 0.36847, 0.92964 + 0x3fd77d96ca4b73a6, 0x3fedc43d52fcb453, // 0.36704, 0.93021 + 0x3fd766340f2418f6, 0x3fedc8d7cb410260, // 0.36561, 0.93077 + 0x3fd74ecdb8390a3e, 0x3fedcd6dabaca3a5, // 0.36418, 0.93133 + 0x3fd73763c9261092, 0x3fedd1fef38a915a, // 0.36276, 0.93188 + 0x3fd71ff6458782ec, 0x3fedd68ba2267a25, // 0.36133, 0.93244 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd6f1108f1bc9c5, 0x3feddf9730ca837b, // 0.35846, 0.93354 + 0x3fd6d998638a0cb5, 0x3fede4160f6d8d81, // 0.35703, 0.93409 + 0x3fd6c21cb1e39771, 0x3fede890520465ce, // 0.3556, 0.93464 + 0x3fd6aa9d7dc77e16, 0x3feded05f7de47da, // 0.35416, 0.93518 + 0x3fd6931acad55f51, 0x3fedf177004b2534, // 0.35273, 0.93573 + 0x3fd67b949cad63ca, 0x3fedf5e36a9ba59c, // 0.35129, 0.93627 + 0x3fd6640af6f03d9e, 0x3fedfa4b3621271d, // 0.34986, 0.9368 + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734 + 0x3fd634ed533be58e, 0x3fee030cee1435b8, // 0.34698, 0.93787 + 0x3fd61d595c88c203, 0x3fee0766d9280f54, // 0.34554, 0.9384 + 0x3fd605c1fcc88f63, 0x3fee0bbc22bd8349, // 0.3441, 0.93893 + 0x3fd5ee27379ea693, 0x3fee100cca2980ac, // 0.34266, 0.93946 + 0x3fd5d68910aee686, 0x3fee1458cec1ad83, // 0.34122, 0.93998 + 0x3fd5bee78b9db3b6, 0x3fee18a02fdc66d9, // 0.33978, 0.94051 + 0x3fd5a742ac0ff78d, 0x3fee1ce2ecd0c0d8, // 0.33833, 0.94103 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd577eeec151e47, 0x3fee255a77a63bb8, // 0.33545, 0.94206 + 0x3fd5604012f467b4, 0x3fee298f4439197a, // 0.334, 0.94257 + 0x3fd5488dedeff3be, 0x3fee2dbf6a0911d9, // 0.33255, 0.94308 + 0x3fd530d880af3c24, 0x3fee31eae870ce25, // 0.33111, 0.94359 + 0x3fd5191fceda3c35, 0x3fee3611becbaf69, // 0.32966, 0.9441 + 0x3fd50163dc197047, 0x3fee3a33ec75ce85, // 0.32821, 0.9446 + 0x3fd4e9a4ac15d520, 0x3fee3e5170cbfc46, // 0.32676, 0.94511 + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561 + 0x3fd4ba1ca2eca31c, 0x3fee467e7af35f23, // 0.32386, 0.94611 + 0x3fd4a253d11b82f3, 0x3fee4a8dff81ce5e, // 0.32241, 0.9466 + 0x3fd48a87d0b07fd7, 0x3fee4e98d836c0af, // 0.32096, 0.94709 + 0x3fd472b8a5571054, 0x3fee529f04729ffc, // 0.3195, 0.94759 + 0x3fd45ae652bb2800, 0x3fee56a083968eb1, // 0.31805, 0.94807 + 0x3fd44310dc8936f0, 0x3fee5a9d550467d3, // 0.31659, 0.94856 + 0x3fd42b38466e2928, 0x3fee5e95781ebf1c, // 0.31514, 0.94905 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd3fb7dc932cfa4, 0x3fee6677b0e6d31e, // 0.31222, 0.95001 + 0x3fd3e39be96ec271, 0x3fee6a61c55d53a7, // 0.31077, 0.95049 + 0x3fd3cbb6f87a146e, 0x3fee6e472911da27, // 0.30931, 0.95096 + 0x3fd3b3cefa0414b7, 0x3fee7227db6a9744, // 0.30785, 0.95144 + 0x3fd39be3f1bc8aef, 0x3fee7603dbce74e9, // 0.30639, 0.95191 + 0x3fd383f5e353b6aa, 0x3fee79db29a5165a, // 0.30493, 0.95238 + 0x3fd36c04d27a4edf, 0x3fee7dadc456d850, // 0.30347, 0.95284 + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331 + 0x3fd33c19b83af207, 0x3fee8544ddf0d075, // 0.30054, 0.95377 + 0x3fd3241fb638baaf, 0x3fee89095bad6025, // 0.29908, 0.95423 + 0x3fd30c22c08d6a13, 0x3fee8cc923edc388, // 0.29762, 0.95469 + 0x3fd2f422daec0386, 0x3fee9084361df7f3, // 0.29615, 0.95514 + 0x3fd2dc200907fe51, 0x3fee943a91aab4b4, // 0.29469, 0.95559 + 0x3fd2c41a4e954520, 0x3fee97ec36016b30, // 0.29322, 0.95605 + 0x3fd2ac11af483572, 0x3fee9b99229046f8, // 0.29175, 0.95649 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd27bf7d0f2c346, 0x3feea2e4d212c000, // 0.28882, 0.95738 + 0x3fd263e6995554ba, 0x3feea68393e65800, // 0.28735, 0.95783 + 0x3fd24bd28bb37672, 0x3feeaa1d9bb20af3, // 0.28588, 0.95827 + 0x3fd233bbabc3bb72, 0x3feeadb2e8e7a88e, // 0.28441, 0.9587 + 0x3fd21ba1fd3d2623, 0x3feeb1437af9bb34, // 0.28294, 0.95914 + 0x3fd2038583d727bd, 0x3feeb4cf515b8811, // 0.28146, 0.95957 + 0x3fd1eb6643499fbb, 0x3feeb8566b810f2a, // 0.27999, 0.96 + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043 + 0x3fd1bb1f7b999480, 0x3feebf5668eaf2ef, // 0.27705, 0.96086 + 0x3fd1a2f7fbe8f243, 0x3feec2cf4b1af6b2, // 0.27557, 0.96128 + 0x3fd18acdc3f4873a, 0x3feec6436ee60309, // 0.2741, 0.9617 + 0x3fd172a0d7765177, 0x3feec9b2d3c3bf84, // 0.27262, 0.96212 + 0x3fd15a713a28b9d9, 0x3feecd1d792c8f10, // 0.27115, 0.96254 + 0x3fd1423eefc69378, 0x3feed0835e999009, // 0.26967, 0.96295 + 0x3fd12a09fc0b1b12, 0x3feed3e483849c51, // 0.26819, 0.96337 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd0f998277733f7, 0x3feeda9889bfe86a, // 0.26523, 0.96418 + 0x3fd0e15b4e1749cd, 0x3feeddeb6a078651, // 0.26375, 0.96459 + 0x3fd0c91bda4f158d, 0x3feee13987bbebdc, // 0.26227, 0.96499 + 0x3fd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // 0.26079, 0.96539 + 0x3fd09895327b465e, 0x3feee7c77961dc9e, // 0.25931, 0.96579 + 0x3fd0804e05eb661e, 0x3feeeb074c50a544, // 0.25783, 0.96619 + 0x3fd068044deab002, 0x3feeee425aa6b09a, // 0.25635, 0.96658 + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698 + 0x3fd037694a928cac, 0x3feef4aa278b2032, // 0.25338, 0.96737 + 0x3fd01f1806b9fdd2, 0x3feef7d6e51ca3c0, // 0.2519, 0.96775 + 0x3fd006c4466e54af, 0x3feefafedc1ba8b7, // 0.25041, 0.96814 + 0x3fcfdcdc1adfedf8, 0x3feefe220c0b95ec, // 0.24893, 0.96852 + 0x3fcfac2abeff57ff, 0x3fef014074708ed3, // 0.24744, 0.9689 + 0x3fcf7b7480bd3801, 0x3fef045a14cf738c, // 0.24596, 0.96928 + 0x3fcf4ab9679c9f5c, 0x3fef076eecade0fa, // 0.24447, 0.96966 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fcee934c2d006c7, 0x3fef0d8a410379c5, // 0.24149, 0.9704 + 0x3fceb86b462de348, 0x3fef1090bc898f5f, // 0.24, 0.97077 + 0x3fce879d0cc0fdaf, 0x3fef13926dad024e, // 0.23851, 0.97114 + 0x3fce56ca1e101a1b, 0x3fef168f53f7205d, // 0.23702, 0.9715 + 0x3fce25f281a2b684, 0x3fef19876ef1f486, // 0.23553, 0.97187 + 0x3fcdf5163f01099a, 0x3fef1c7abe284708, // 0.23404, 0.97223 + 0x3fcdc4355db40195, 0x3fef1f6941259d7a, // 0.23255, 0.97258 + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294 + 0x3fcd6265dd3f27e3, 0x3fef2537e0a71f9f, // 0.22957, 0.97329 + 0x3fcd31774d2cbdee, 0x3fef2817fc4609ce, // 0.22807, 0.97364 + 0x3fcd00843c99c5f9, 0x3fef2af349e17507, // 0.22658, 0.97399 + 0x3fcccf8cb312b286, 0x3fef2dc9c9089a9d, // 0.22508, 0.97434 + 0x3fcc9e90b824a6a9, 0x3fef309b794b719f, // 0.22359, 0.97468 + 0x3fcc6d90535d74dc, 0x3fef33685a3aaef0, // 0.22209, 0.97503 + 0x3fcc3c8b8c4b9dd7, 0x3fef36306b67c556, // 0.2206, 0.97536 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fcbda74f5856330, 0x3fef3bb21cc4fe47, // 0.2176, 0.97604 + 0x3fcba96334f15dad, 0x3fef3e6bbc1bbc65, // 0.21611, 0.97637 + 0x3fcb784d30536cda, 0x3fef412089fd8adc, // 0.21461, 0.9767 + 0x3fcb4732ef3d6722, 0x3fef43d085ff92dd, // 0.21311, 0.97703 + 0x3fcb16147941ca2a, 0x3fef467bafb7bbe0, // 0.21161, 0.97735 + 0x3fcae4f1d5f3b9ab, 0x3fef492206bcabb4, // 0.21011, 0.97768 + 0x3fcab3cb0ce6fe44, 0x3fef4bc38aa5c694, // 0.20861, 0.978 + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832 + 0x3fca517127e3dabc, 0x3fef50f81785c6b9, // 0.20561, 0.97863 + 0x3fca203e1b1831da, 0x3fef538b1faf2d07, // 0.20411, 0.97895 + 0x3fc9ef0706e35a35, 0x3fef56195321c090, // 0.20261, 0.97926 + 0x3fc9bdcbf2dc4366, 0x3fef58a2b1789e84, // 0.2011, 0.97957 + 0x3fc98c8ce69a7aec, 0x3fef5b273a4fa2d9, // 0.1996, 0.97988 + 0x3fc95b49e9b62af9, 0x3fef5da6ed43685d, // 0.1981, 0.98018 + 0x3fc92a0303c8194f, 0x3fef6021c9f148c2, // 0.19659, 0.98048 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc8c7699b34ca7e, 0x3fef6508fef47bd5, // 0.19359, 0.98108 + 0x3fc8961727c41804, 0x3fef677556883cee, // 0.19208, 0.98138 + 0x3fc864c0e9b2b6cf, 0x3fef69dcd652f5de, // 0.19057, 0.98167 + 0x3fc83366e89c64c5, 0x3fef6c3f7df5bbb7, // 0.18907, 0.98196 + 0x3fc802092c1d744b, 0x3fef6e9d4d1262ca, // 0.18756, 0.98225 + 0x3fc7d0a7bbd2cb1b, 0x3fef70f6434b7eb7, // 0.18606, 0.98254 + 0x3fc79f429f59e11d, 0x3fef734a60446279, // 0.18455, 0.98282 + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311 + 0x3fc73c6d8055fe0a, 0x3fef77e40d068a90, // 0.18153, 0.98339 + 0x3fc70afd8d08c4ff, 0x3fef7a299c1a322a, // 0.18002, 0.98366 + 0x3fc6d98a0c08c8da, 0x3fef7c6a50826840, // 0.17851, 0.98394 + 0x3fc6a81304f64ab2, 0x3fef7ea629e63d6e, // 0.177, 0.98421 + 0x3fc676987f7216b8, 0x3fef80dd27ed8204, // 0.17549, 0.98448 + 0x3fc6451a831d830d, 0x3fef830f4a40c60c, // 0.17398, 0.98475 + 0x3fc61399179a6e94, 0x3fef853c9089595e, // 0.17247, 0.98501 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc5b08c1192e381, 0x3fef898887a36c84, // 0.16945, 0.98554 + 0x3fc57f008654cbde, 0x3fef8ba737cb4b78, // 0.16794, 0.9858 + 0x3fc54d71aa74ef02, 0x3fef8dc10a95380d, // 0.16643, 0.98605 + 0x3fc51bdf8597c5f2, 0x3fef8fd5ffae41db, // 0.16491, 0.98631 + 0x3fc4ea4a1f624b61, 0x3fef91e616c43891, // 0.1634, 0.98656 + 0x3fc4b8b17f79fa88, 0x3fef93f14f85ac08, // 0.16189, 0.98681 + 0x3fc48715ad84cdf5, 0x3fef95f7a9a1ec47, // 0.16037, 0.98706 + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873 + 0x3fc423d4920e4166, 0x3fef99f5c0abd496, // 0.15734, 0.98754 + 0x3fc3f22f57db4893, 0x3fef9bed7cfbde29, // 0.15583, 0.98778 + 0x3fc3c0870a383ff6, 0x3fef9de0596b77a3, // 0.15431, 0.98802 + 0x3fc38edbb0cd8d14, 0x3fef9fce55adb2c8, // 0.1528, 0.98826 + 0x3fc35d2d53440db2, 0x3fefa1b7717661d5, // 0.15128, 0.98849 + 0x3fc32b7bf94516a7, 0x3fefa39bac7a1791, // 0.14976, 0.98872 + 0x3fc2f9c7aa7a72af, 0x3fefa57b066e2754, // 0.14825, 0.98895 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc296564d2b953e, 0x3fefa92b1600657c, // 0.14521, 0.9894 + 0x3fc264994dfd340a, 0x3fefaafbcb0cfddc, // 0.1437, 0.98962 + 0x3fc232d978aed413, 0x3fefacc79de6c44f, // 0.14218, 0.98984 + 0x3fc20116d4ec7bce, 0x3fefae8e8e46cfbb, // 0.14066, 0.99006 + 0x3fc1cf516a62a077, 0x3fefb0509be6f7db, // 0.13914, 0.99027 + 0x3fc19d8940be24e7, 0x3fefb20dc681d54d, // 0.13762, 0.99049 + 0x3fc16bbe5fac5865, 0x3fefb3c60dd2c199, // 0.1361, 0.9907 + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909 + 0x3fc1082095f820b0, 0x3fefb727f187f1c7, // 0.13306, 0.99111 + 0x3fc0d64dbcb26786, 0x3fefb8d18d66adb7, // 0.13154, 0.99131 + 0x3fc0a4784ab8bf1d, 0x3fefba7644f068b5, // 0.13002, 0.99151 + 0x3fc072a047ba831d, 0x3fefbc1617e44186, // 0.1285, 0.99171 + 0x3fc040c5bb67747e, 0x3fefbdb106021816, // 0.12698, 0.99191 + 0x3fc00ee8ad6fb85b, 0x3fefbf470f0a8d88, // 0.12545, 0.9921 + 0x3fbfba124b07ad85, 0x3fefc0d832bf043a, // 0.12393, 0.99229 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fbef2858d27561b, 0x3fefc3ebc935454c, // 0.12089, 0.99267 + 0x3fbe8eb7fde4aa3e, 0x3fefc56e3b7d9af6, // 0.11937, 0.99285 + 0x3fbe2ae5b8457f77, 0x3fefc6ebc77f0887, // 0.11784, 0.99303 + 0x3fbdc70ecbae9fc8, 0x3fefc8646cfeb721, // 0.11632, 0.99321 + 0x3fbd633347858ce4, 0x3fefc9d82bc2915e, // 0.11479, 0.99339 + 0x3fbcff533b307dc1, 0x3fefcb4703914354, // 0.11327, 0.99356 + 0x3fbc9b6eb6165c42, 0x3fefccb0f4323aa3, // 0.11175, 0.99374 + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391 + 0x3fbbd3987f31fa0e, 0x3fefcf761f0c77a3, // 0.1087, 0.99407 + 0x3fbb6fa6ec38f64c, 0x3fefd0d158d86087, // 0.10717, 0.99424 + 0x3fbb0bb11e1d5559, 0x3fefd227aa9bd53b, // 0.10565, 0.9944 + 0x3fbaa7b724495c04, 0x3fefd37914220b84, // 0.10412, 0.99456 + 0x3fba43b90e27f3c4, 0x3fefd4c59536fae4, // 0.1026, 0.99472 + 0x3fb9dfb6eb24a85c, 0x3fefd60d2da75c9e, // 0.10107, 0.99488 + 0x3fb97bb0caaba56f, 0x3fefd74fdd40abbf, // 0.099544, 0.99503 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb8b398cf0c38e0, 0x3fefd9c68127c78c, // 0.09649, 0.99533 + 0x3fb84f8712c130a0, 0x3fefdafa7514538c, // 0.094963, 0.99548 + 0x3fb7eb7196b72ee4, 0x3fefdc297f674ba9, // 0.093436, 0.99563 + 0x3fb787586a5d5b21, 0x3fefdd539ff1f456, // 0.091909, 0.99577 + 0x3fb7233b9d236e71, 0x3fefde78d68653fd, // 0.090381, 0.99591 + 0x3fb6bf1b3e79b129, 0x3fefdf9922f73307, // 0.088854, 0.99604 + 0x3fb65af75dd0f87b, 0x3fefe0b485181be3, // 0.087326, 0.99618 + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631 + 0x3fb592a554489bc8, 0x3fefe2dc89bbff08, // 0.084269, 0.99644 + 0x3fb52e774a4d4d0a, 0x3fefe3e92be9d886, // 0.08274, 0.99657 + 0x3fb4ca45fc1ba8b6, 0x3fefe4f0e31d7a4a, // 0.081211, 0.9967 + 0x3fb4661179272096, 0x3fefe5f3af2e3940, // 0.079682, 0.99682 + 0x3fb401d9d0e3a507, 0x3fefe6f18ff42c84, // 0.078153, 0.99694 + 0x3fb39d9f12c5a299, 0x3fefe7ea85482d60, // 0.076624, 0.99706 + 0x3fb339614e41ffa5, 0x3fefe8de8f03d75c, // 0.075094, 0.99718 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3fb270dcefdfc45b, 0x3fefeab7df1c6005, // 0.072035, 0.9974 + 0x3fb20c9674ed444c, 0x3fefeb9d2530410f, // 0.070505, 0.99751 + 0x3fb1a84d316d4f8a, 0x3fefec7d7f19cffc, // 0.068974, 0.99762 + 0x3fb1440134d709b2, 0x3fefed58ecb673c4, // 0.067444, 0.99772 + 0x3fb0dfb28ea201e6, 0x3fefee2f6de455ba, // 0.065913, 0.99783 + 0x3fb07b614e463064, 0x3fefef0102826191, // 0.064383, 0.99793 + 0x3fb0170d833bf421, 0x3fefefcdaa704562, // 0.062852, 0.99802 + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812 + 0x3fae9cbd15ff5527, 0x3feff15833be1965, // 0.05979, 0.99821 + 0x3fadd406f9808ec8, 0x3feff21614e131ed, // 0.058258, 0.9983 + 0x3fad0b4c436f91d0, 0x3feff2cf08da7321, // 0.056727, 0.99839 + 0x3fac428d12c0d7e3, 0x3feff3830f8d575c, // 0.055195, 0.99848 + 0x3fab79c986698b78, 0x3feff43228de1b77, // 0.053664, 0.99856 + 0x3faab101bd5f8317, 0x3feff4dc54b1bed3, // 0.052132, 0.99864 + 0x3fa9e835d6993c87, 0x3feff58192ee0358, // 0.0506, 0.99872 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3fa856922bb513c1, 0x3feff6bd463b444d, // 0.047535, 0.99887 + 0x3fa78dbaa5874685, 0x3feff753bb1b9164, // 0.046003, 0.99894 + 0x3fa6c4df7d7d5b84, 0x3feff7e5420320f9, // 0.044471, 0.99901 + 0x3fa5fc00d290cd43, 0x3feff871dadb81df, // 0.042938, 0.99908 + 0x3fa5331ec3bba0eb, 0x3feff8f9858f058b, // 0.041406, 0.99914 + 0x3fa46a396ff86179, 0x3feff97c4208c014, // 0.039873, 0.9992 + 0x3fa3a150f6421afc, 0x3feff9fa10348837, // 0.03834, 0.99926 + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932 + 0x3fa20f770ceb11c6, 0x3feffae6e1556998, // 0.035274, 0.99938 + 0x3fa14685db42c17e, 0x3feffb55e425fdae, // 0.033741, 0.99943 + 0x3fa07d91ff984580, 0x3feffbbff85f9515, // 0.032208, 0.99948 + 0x3f9f693731d1cf01, 0x3feffc251df1d3f8, // 0.030675, 0.99953 + 0x3f9dd7458c64ab39, 0x3feffc8554cd213a, // 0.029142, 0.99958 + 0x3f9c454f4ce53b1c, 0x3feffce09ce2a679, // 0.027608, 0.99962 + 0x3f9ab354b1504fca, 0x3feffd36f624500c, // 0.026075, 0.99966 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x3f978f535ddc9f03, 0x3feffdd4dbf78f52, // 0.023008, 0.99974 + 0x3f95fd4d21fab226, 0x3feffe1c6870cb77, // 0.021474, 0.99977 + 0x3f946b4381fce81c, 0x3feffe5f05e578db, // 0.01994, 0.9998 + 0x3f92d936bbe30efd, 0x3feffe9cb44b51a1, // 0.018407, 0.99983 + 0x3f9147270dad7132, 0x3feffed57398d2b7, // 0.016873, 0.99986 + 0x3f8f6a296ab997ca, 0x3fefff0943c53bd1, // 0.015339, 0.99988 + 0x3f8c45ffe1e48ad9, 0x3fefff3824c88f6f, // 0.013805, 0.9999 + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992 + 0x3f85fda037ac05e0, 0x3fefff871937ce2f, // 0.010738, 0.99994 + 0x3f82d96b0e509703, 0x3fefffa72c978c4f, // 0.0092038, 0.99996 + 0x3f7f6a65f9a2a3c5, 0x3fefffc250b5daef, // 0.0076698, 0.99997 + 0x3f7921f0fe670071, 0x3fefffd8858e8a92, // 0.0061359, 0.99998 + 0x3f72d97822f996bc, 0x3fefffe9cb1e2e8d, // 0.0046019, 0.99999 + 0x3f6921f8becca4ba, 0x3feffff621621d02, // 0.003068, 1 + 0x3f5921faaee6472d, 0x3feffffd88586ee6, // 0.001534, 1 + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0xbf5921faaee6472d, 0x3feffffd88586ee6, // -0.001534, 1 + 0xbf6921f8becca4ba, 0x3feffff621621d02, // -0.003068, 1 + 0xbf72d97822f996bc, 0x3fefffe9cb1e2e8d, //-0.0046019, 0.99999 + 0xbf7921f0fe670071, 0x3fefffd8858e8a92, //-0.0061359, 0.99998 + 0xbf7f6a65f9a2a3c5, 0x3fefffc250b5daef, //-0.0076698, 0.99997 + 0xbf82d96b0e509703, 0x3fefffa72c978c4f, //-0.0092038, 0.99996 + 0xbf85fda037ac05e0, 0x3fefff871937ce2f, // -0.010738, 0.99994 + 0xbf8921d1fcdec784, 0x3fefff62169b92db, // -0.012272, 0.99992 + 0xbf8c45ffe1e48ad9, 0x3fefff3824c88f6f, // -0.013805, 0.9999 + 0xbf8f6a296ab997ca, 0x3fefff0943c53bd1, // -0.015339, 0.99988 + 0xbf9147270dad7132, 0x3feffed57398d2b7, // -0.016873, 0.99986 + 0xbf92d936bbe30efd, 0x3feffe9cb44b51a1, // -0.018407, 0.99983 + 0xbf946b4381fce81c, 0x3feffe5f05e578db, // -0.01994, 0.9998 + 0xbf95fd4d21fab226, 0x3feffe1c6870cb77, // -0.021474, 0.99977 + 0xbf978f535ddc9f03, 0x3feffdd4dbf78f52, // -0.023008, 0.99974 + 0xbf992155f7a3667e, 0x3feffd886084cd0d, // -0.024541, 0.9997 + 0xbf9ab354b1504fca, 0x3feffd36f624500c, // -0.026075, 0.99966 + 0xbf9c454f4ce53b1c, 0x3feffce09ce2a679, // -0.027608, 0.99962 + 0xbf9dd7458c64ab39, 0x3feffc8554cd213a, // -0.029142, 0.99958 + 0xbf9f693731d1cf01, 0x3feffc251df1d3f8, // -0.030675, 0.99953 + 0xbfa07d91ff984580, 0x3feffbbff85f9515, // -0.032208, 0.99948 + 0xbfa14685db42c17e, 0x3feffb55e425fdae, // -0.033741, 0.99943 + 0xbfa20f770ceb11c6, 0x3feffae6e1556998, // -0.035274, 0.99938 + 0xbfa2d865759455cd, 0x3feffa72effef75d, // -0.036807, 0.99932 + 0xbfa3a150f6421afc, 0x3feff9fa10348837, // -0.03834, 0.99926 + 0xbfa46a396ff86179, 0x3feff97c4208c014, // -0.039873, 0.9992 + 0xbfa5331ec3bba0eb, 0x3feff8f9858f058b, // -0.041406, 0.99914 + 0xbfa5fc00d290cd43, 0x3feff871dadb81df, // -0.042938, 0.99908 + 0xbfa6c4df7d7d5b84, 0x3feff7e5420320f9, // -0.044471, 0.99901 + 0xbfa78dbaa5874685, 0x3feff753bb1b9164, // -0.046003, 0.99894 + 0xbfa856922bb513c1, 0x3feff6bd463b444d, // -0.047535, 0.99887 + 0xbfa91f65f10dd814, 0x3feff621e3796d7e, // -0.049068, 0.9988 + 0xbfa9e835d6993c87, 0x3feff58192ee0358, // -0.0506, 0.99872 + 0xbfaab101bd5f8317, 0x3feff4dc54b1bed3, // -0.052132, 0.99864 + 0xbfab79c986698b78, 0x3feff43228de1b77, // -0.053664, 0.99856 + 0xbfac428d12c0d7e3, 0x3feff3830f8d575c, // -0.055195, 0.99848 + 0xbfad0b4c436f91d0, 0x3feff2cf08da7321, // -0.056727, 0.99839 + 0xbfadd406f9808ec8, 0x3feff21614e131ed, // -0.058258, 0.9983 + 0xbfae9cbd15ff5527, 0x3feff15833be1965, // -0.05979, 0.99821 + 0xbfaf656e79f820e0, 0x3feff095658e71ad, // -0.061321, 0.99812 + 0xbfb0170d833bf421, 0x3fefefcdaa704562, // -0.062852, 0.99802 + 0xbfb07b614e463064, 0x3fefef0102826191, // -0.064383, 0.99793 + 0xbfb0dfb28ea201e6, 0x3fefee2f6de455ba, // -0.065913, 0.99783 + 0xbfb1440134d709b2, 0x3fefed58ecb673c4, // -0.067444, 0.99772 + 0xbfb1a84d316d4f8a, 0x3fefec7d7f19cffc, // -0.068974, 0.99762 + 0xbfb20c9674ed444c, 0x3fefeb9d2530410f, // -0.070505, 0.99751 + 0xbfb270dcefdfc45b, 0x3fefeab7df1c6005, // -0.072035, 0.9974 + 0xbfb2d52092ce19f6, 0x3fefe9cdad01883a, // -0.073565, 0.99729 + 0xbfb339614e41ffa5, 0x3fefe8de8f03d75c, // -0.075094, 0.99718 + 0xbfb39d9f12c5a299, 0x3fefe7ea85482d60, // -0.076624, 0.99706 + 0xbfb401d9d0e3a507, 0x3fefe6f18ff42c84, // -0.078153, 0.99694 + 0xbfb4661179272096, 0x3fefe5f3af2e3940, // -0.079682, 0.99682 + 0xbfb4ca45fc1ba8b6, 0x3fefe4f0e31d7a4a, // -0.081211, 0.9967 + 0xbfb52e774a4d4d0a, 0x3fefe3e92be9d886, // -0.08274, 0.99657 + 0xbfb592a554489bc8, 0x3fefe2dc89bbff08, // -0.084269, 0.99644 + 0xbfb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // -0.085797, 0.99631 + 0xbfb65af75dd0f87b, 0x3fefe0b485181be3, // -0.087326, 0.99618 + 0xbfb6bf1b3e79b129, 0x3fefdf9922f73307, // -0.088854, 0.99604 + 0xbfb7233b9d236e71, 0x3fefde78d68653fd, // -0.090381, 0.99591 + 0xbfb787586a5d5b21, 0x3fefdd539ff1f456, // -0.091909, 0.99577 + 0xbfb7eb7196b72ee4, 0x3fefdc297f674ba9, // -0.093436, 0.99563 + 0xbfb84f8712c130a0, 0x3fefdafa7514538c, // -0.094963, 0.99548 + 0xbfb8b398cf0c38e0, 0x3fefd9c68127c78c, // -0.09649, 0.99533 + 0xbfb917a6bc29b42c, 0x3fefd88da3d12526, // -0.098017, 0.99518 + 0xbfb97bb0caaba56f, 0x3fefd74fdd40abbf, // -0.099544, 0.99503 + 0xbfb9dfb6eb24a85c, 0x3fefd60d2da75c9e, // -0.10107, 0.99488 + 0xbfba43b90e27f3c4, 0x3fefd4c59536fae4, // -0.1026, 0.99472 + 0xbfbaa7b724495c04, 0x3fefd37914220b84, // -0.10412, 0.99456 + 0xbfbb0bb11e1d5559, 0x3fefd227aa9bd53b, // -0.10565, 0.9944 + 0xbfbb6fa6ec38f64c, 0x3fefd0d158d86087, // -0.10717, 0.99424 + 0xbfbbd3987f31fa0e, 0x3fefcf761f0c77a3, // -0.1087, 0.99407 + 0xbfbc3785c79ec2d5, 0x3fefce15fd6da67b, // -0.11022, 0.99391 + 0xbfbc9b6eb6165c42, 0x3fefccb0f4323aa3, // -0.11175, 0.99374 + 0xbfbcff533b307dc1, 0x3fefcb4703914354, // -0.11327, 0.99356 + 0xbfbd633347858ce4, 0x3fefc9d82bc2915e, // -0.11479, 0.99339 + 0xbfbdc70ecbae9fc8, 0x3fefc8646cfeb721, // -0.11632, 0.99321 + 0xbfbe2ae5b8457f77, 0x3fefc6ebc77f0887, // -0.11784, 0.99303 + 0xbfbe8eb7fde4aa3e, 0x3fefc56e3b7d9af6, // -0.11937, 0.99285 + 0xbfbef2858d27561b, 0x3fefc3ebc935454c, // -0.12089, 0.99267 + 0xbfbf564e56a9730e, 0x3fefc26470e19fd3, // -0.12241, 0.99248 + 0xbfbfba124b07ad85, 0x3fefc0d832bf043a, // -0.12393, 0.99229 + 0xbfc00ee8ad6fb85b, 0x3fefbf470f0a8d88, // -0.12545, 0.9921 + 0xbfc040c5bb67747e, 0x3fefbdb106021816, // -0.12698, 0.99191 + 0xbfc072a047ba831d, 0x3fefbc1617e44186, // -0.1285, 0.99171 + 0xbfc0a4784ab8bf1d, 0x3fefba7644f068b5, // -0.13002, 0.99151 + 0xbfc0d64dbcb26786, 0x3fefb8d18d66adb7, // -0.13154, 0.99131 + 0xbfc1082095f820b0, 0x3fefb727f187f1c7, // -0.13306, 0.99111 + 0xbfc139f0cedaf576, 0x3fefb5797195d741, // -0.13458, 0.9909 + 0xbfc16bbe5fac5865, 0x3fefb3c60dd2c199, // -0.1361, 0.9907 + 0xbfc19d8940be24e7, 0x3fefb20dc681d54d, // -0.13762, 0.99049 + 0xbfc1cf516a62a077, 0x3fefb0509be6f7db, // -0.13914, 0.99027 + 0xbfc20116d4ec7bce, 0x3fefae8e8e46cfbb, // -0.14066, 0.99006 + 0xbfc232d978aed413, 0x3fefacc79de6c44f, // -0.14218, 0.98984 + 0xbfc264994dfd340a, 0x3fefaafbcb0cfddc, // -0.1437, 0.98962 + 0xbfc296564d2b953e, 0x3fefa92b1600657c, // -0.14521, 0.9894 + 0xbfc2c8106e8e613a, 0x3fefa7557f08a517, // -0.14673, 0.98918 + 0xbfc2f9c7aa7a72af, 0x3fefa57b066e2754, // -0.14825, 0.98895 + 0xbfc32b7bf94516a7, 0x3fefa39bac7a1791, // -0.14976, 0.98872 + 0xbfc35d2d53440db2, 0x3fefa1b7717661d5, // -0.15128, 0.98849 + 0xbfc38edbb0cd8d14, 0x3fef9fce55adb2c8, // -0.1528, 0.98826 + 0xbfc3c0870a383ff6, 0x3fef9de0596b77a3, // -0.15431, 0.98802 + 0xbfc3f22f57db4893, 0x3fef9bed7cfbde29, // -0.15583, 0.98778 + 0xbfc423d4920e4166, 0x3fef99f5c0abd496, // -0.15734, 0.98754 + 0xbfc45576b1293e5a, 0x3fef97f924c9099b, // -0.15886, 0.9873 + 0xbfc48715ad84cdf5, 0x3fef95f7a9a1ec47, // -0.16037, 0.98706 + 0xbfc4b8b17f79fa88, 0x3fef93f14f85ac08, // -0.16189, 0.98681 + 0xbfc4ea4a1f624b61, 0x3fef91e616c43891, // -0.1634, 0.98656 + 0xbfc51bdf8597c5f2, 0x3fef8fd5ffae41db, // -0.16491, 0.98631 + 0xbfc54d71aa74ef02, 0x3fef8dc10a95380d, // -0.16643, 0.98605 + 0xbfc57f008654cbde, 0x3fef8ba737cb4b78, // -0.16794, 0.9858 + 0xbfc5b08c1192e381, 0x3fef898887a36c84, // -0.16945, 0.98554 + 0xbfc5e214448b3fc6, 0x3fef8764fa714ba9, // -0.17096, 0.98528 + 0xbfc61399179a6e94, 0x3fef853c9089595e, // -0.17247, 0.98501 + 0xbfc6451a831d830d, 0x3fef830f4a40c60c, // -0.17398, 0.98475 + 0xbfc676987f7216b8, 0x3fef80dd27ed8204, // -0.17549, 0.98448 + 0xbfc6a81304f64ab2, 0x3fef7ea629e63d6e, // -0.177, 0.98421 + 0xbfc6d98a0c08c8da, 0x3fef7c6a50826840, // -0.17851, 0.98394 + 0xbfc70afd8d08c4ff, 0x3fef7a299c1a322a, // -0.18002, 0.98366 + 0xbfc73c6d8055fe0a, 0x3fef77e40d068a90, // -0.18153, 0.98339 + 0xbfc76dd9de50bf31, 0x3fef7599a3a12077, // -0.18304, 0.98311 + 0xbfc79f429f59e11d, 0x3fef734a60446279, // -0.18455, 0.98282 + 0xbfc7d0a7bbd2cb1b, 0x3fef70f6434b7eb7, // -0.18606, 0.98254 + 0xbfc802092c1d744b, 0x3fef6e9d4d1262ca, // -0.18756, 0.98225 + 0xbfc83366e89c64c5, 0x3fef6c3f7df5bbb7, // -0.18907, 0.98196 + 0xbfc864c0e9b2b6cf, 0x3fef69dcd652f5de, // -0.19057, 0.98167 + 0xbfc8961727c41804, 0x3fef677556883cee, // -0.19208, 0.98138 + 0xbfc8c7699b34ca7e, 0x3fef6508fef47bd5, // -0.19359, 0.98108 + 0xbfc8f8b83c69a60a, 0x3fef6297cff75cb0, // -0.19509, 0.98079 + 0xbfc92a0303c8194f, 0x3fef6021c9f148c2, // -0.19659, 0.98048 + 0xbfc95b49e9b62af9, 0x3fef5da6ed43685d, // -0.1981, 0.98018 + 0xbfc98c8ce69a7aec, 0x3fef5b273a4fa2d9, // -0.1996, 0.97988 + 0xbfc9bdcbf2dc4366, 0x3fef58a2b1789e84, // -0.2011, 0.97957 + 0xbfc9ef0706e35a35, 0x3fef56195321c090, // -0.20261, 0.97926 + 0xbfca203e1b1831da, 0x3fef538b1faf2d07, // -0.20411, 0.97895 + 0xbfca517127e3dabc, 0x3fef50f81785c6b9, // -0.20561, 0.97863 + 0xbfca82a025b00451, 0x3fef4e603b0b2f2d, // -0.20711, 0.97832 + 0xbfcab3cb0ce6fe44, 0x3fef4bc38aa5c694, // -0.20861, 0.978 + 0xbfcae4f1d5f3b9ab, 0x3fef492206bcabb4, // -0.21011, 0.97768 + 0xbfcb16147941ca2a, 0x3fef467bafb7bbe0, // -0.21161, 0.97735 + 0xbfcb4732ef3d6722, 0x3fef43d085ff92dd, // -0.21311, 0.97703 + 0xbfcb784d30536cda, 0x3fef412089fd8adc, // -0.21461, 0.9767 + 0xbfcba96334f15dad, 0x3fef3e6bbc1bbc65, // -0.21611, 0.97637 + 0xbfcbda74f5856330, 0x3fef3bb21cc4fe47, // -0.2176, 0.97604 + 0xbfcc0b826a7e4f63, 0x3fef38f3ac64e589, // -0.2191, 0.9757 + 0xbfcc3c8b8c4b9dd7, 0x3fef36306b67c556, // -0.2206, 0.97536 + 0xbfcc6d90535d74dc, 0x3fef33685a3aaef0, // -0.22209, 0.97503 + 0xbfcc9e90b824a6a9, 0x3fef309b794b719f, // -0.22359, 0.97468 + 0xbfcccf8cb312b286, 0x3fef2dc9c9089a9d, // -0.22508, 0.97434 + 0xbfcd00843c99c5f9, 0x3fef2af349e17507, // -0.22658, 0.97399 + 0xbfcd31774d2cbdee, 0x3fef2817fc4609ce, // -0.22807, 0.97364 + 0xbfcd6265dd3f27e3, 0x3fef2537e0a71f9f, // -0.22957, 0.97329 + 0xbfcd934fe5454311, 0x3fef2252f7763ada, // -0.23106, 0.97294 + 0xbfcdc4355db40195, 0x3fef1f6941259d7a, // -0.23255, 0.97258 + 0xbfcdf5163f01099a, 0x3fef1c7abe284708, // -0.23404, 0.97223 + 0xbfce25f281a2b684, 0x3fef19876ef1f486, // -0.23553, 0.97187 + 0xbfce56ca1e101a1b, 0x3fef168f53f7205d, // -0.23702, 0.9715 + 0xbfce879d0cc0fdaf, 0x3fef13926dad024e, // -0.23851, 0.97114 + 0xbfceb86b462de348, 0x3fef1090bc898f5f, // -0.24, 0.97077 + 0xbfcee934c2d006c7, 0x3fef0d8a410379c5, // -0.24149, 0.9704 + 0xbfcf19f97b215f1a, 0x3fef0a7efb9230d7, // -0.24298, 0.97003 + 0xbfcf4ab9679c9f5c, 0x3fef076eecade0fa, // -0.24447, 0.96966 + 0xbfcf7b7480bd3801, 0x3fef045a14cf738c, // -0.24596, 0.96928 + 0xbfcfac2abeff57ff, 0x3fef014074708ed3, // -0.24744, 0.9689 + 0xbfcfdcdc1adfedf8, 0x3feefe220c0b95ec, // -0.24893, 0.96852 + 0xbfd006c4466e54af, 0x3feefafedc1ba8b7, // -0.25041, 0.96814 + 0xbfd01f1806b9fdd2, 0x3feef7d6e51ca3c0, // -0.2519, 0.96775 + 0xbfd037694a928cac, 0x3feef4aa278b2032, // -0.25338, 0.96737 + 0xbfd04fb80e37fdae, 0x3feef178a3e473c2, // -0.25487, 0.96698 + 0xbfd068044deab002, 0x3feeee425aa6b09a, // -0.25635, 0.96658 + 0xbfd0804e05eb661e, 0x3feeeb074c50a544, // -0.25783, 0.96619 + 0xbfd09895327b465e, 0x3feee7c77961dc9e, // -0.25931, 0.96579 + 0xbfd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // -0.26079, 0.96539 + 0xbfd0c91bda4f158d, 0x3feee13987bbebdc, // -0.26227, 0.96499 + 0xbfd0e15b4e1749cd, 0x3feeddeb6a078651, // -0.26375, 0.96459 + 0xbfd0f998277733f7, 0x3feeda9889bfe86a, // -0.26523, 0.96418 + 0xbfd111d262b1f677, 0x3feed740e7684963, // -0.26671, 0.96378 + 0xbfd12a09fc0b1b12, 0x3feed3e483849c51, // -0.26819, 0.96337 + 0xbfd1423eefc69378, 0x3feed0835e999009, // -0.26967, 0.96295 + 0xbfd15a713a28b9d9, 0x3feecd1d792c8f10, // -0.27115, 0.96254 + 0xbfd172a0d7765177, 0x3feec9b2d3c3bf84, // -0.27262, 0.96212 + 0xbfd18acdc3f4873a, 0x3feec6436ee60309, // -0.2741, 0.9617 + 0xbfd1a2f7fbe8f243, 0x3feec2cf4b1af6b2, // -0.27557, 0.96128 + 0xbfd1bb1f7b999480, 0x3feebf5668eaf2ef, // -0.27705, 0.96086 + 0xbfd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // -0.27852, 0.96043 + 0xbfd1eb6643499fbb, 0x3feeb8566b810f2a, // -0.27999, 0.96 + 0xbfd2038583d727bd, 0x3feeb4cf515b8811, // -0.28146, 0.95957 + 0xbfd21ba1fd3d2623, 0x3feeb1437af9bb34, // -0.28294, 0.95914 + 0xbfd233bbabc3bb72, 0x3feeadb2e8e7a88e, // -0.28441, 0.9587 + 0xbfd24bd28bb37672, 0x3feeaa1d9bb20af3, // -0.28588, 0.95827 + 0xbfd263e6995554ba, 0x3feea68393e65800, // -0.28735, 0.95783 + 0xbfd27bf7d0f2c346, 0x3feea2e4d212c000, // -0.28882, 0.95738 + 0xbfd294062ed59f05, 0x3fee9f4156c62dda, // -0.29028, 0.95694 + 0xbfd2ac11af483572, 0x3fee9b99229046f8, // -0.29175, 0.95649 + 0xbfd2c41a4e954520, 0x3fee97ec36016b30, // -0.29322, 0.95605 + 0xbfd2dc200907fe51, 0x3fee943a91aab4b4, // -0.29469, 0.95559 + 0xbfd2f422daec0386, 0x3fee9084361df7f3, // -0.29615, 0.95514 + 0xbfd30c22c08d6a13, 0x3fee8cc923edc388, // -0.29762, 0.95469 + 0xbfd3241fb638baaf, 0x3fee89095bad6025, // -0.29908, 0.95423 + 0xbfd33c19b83af207, 0x3fee8544ddf0d075, // -0.30054, 0.95377 + 0xbfd35410c2e18152, 0x3fee817bab4cd10d, // -0.30201, 0.95331 + 0xbfd36c04d27a4edf, 0x3fee7dadc456d850, // -0.30347, 0.95284 + 0xbfd383f5e353b6aa, 0x3fee79db29a5165a, // -0.30493, 0.95238 + 0xbfd39be3f1bc8aef, 0x3fee7603dbce74e9, // -0.30639, 0.95191 + 0xbfd3b3cefa0414b7, 0x3fee7227db6a9744, // -0.30785, 0.95144 + 0xbfd3cbb6f87a146e, 0x3fee6e472911da27, // -0.30931, 0.95096 + 0xbfd3e39be96ec271, 0x3fee6a61c55d53a7, // -0.31077, 0.95049 + 0xbfd3fb7dc932cfa4, 0x3fee6677b0e6d31e, // -0.31222, 0.95001 + 0xbfd4135c94176602, 0x3fee6288ec48e112, // -0.31368, 0.94953 + 0xbfd42b38466e2928, 0x3fee5e95781ebf1c, // -0.31514, 0.94905 + 0xbfd44310dc8936f0, 0x3fee5a9d550467d3, // -0.31659, 0.94856 + 0xbfd45ae652bb2800, 0x3fee56a083968eb1, // -0.31805, 0.94807 + 0xbfd472b8a5571054, 0x3fee529f04729ffc, // -0.3195, 0.94759 + 0xbfd48a87d0b07fd7, 0x3fee4e98d836c0af, // -0.32096, 0.94709 + 0xbfd4a253d11b82f3, 0x3fee4a8dff81ce5e, // -0.32241, 0.9466 + 0xbfd4ba1ca2eca31c, 0x3fee467e7af35f23, // -0.32386, 0.94611 + 0xbfd4d1e24278e76a, 0x3fee426a4b2bc17e, // -0.32531, 0.94561 + 0xbfd4e9a4ac15d520, 0x3fee3e5170cbfc46, // -0.32676, 0.94511 + 0xbfd50163dc197047, 0x3fee3a33ec75ce85, // -0.32821, 0.9446 + 0xbfd5191fceda3c35, 0x3fee3611becbaf69, // -0.32966, 0.9441 + 0xbfd530d880af3c24, 0x3fee31eae870ce25, // -0.33111, 0.94359 + 0xbfd5488dedeff3be, 0x3fee2dbf6a0911d9, // -0.33255, 0.94308 + 0xbfd5604012f467b4, 0x3fee298f4439197a, // -0.334, 0.94257 + 0xbfd577eeec151e47, 0x3fee255a77a63bb8, // -0.33545, 0.94206 + 0xbfd58f9a75ab1fdd, 0x3fee212104f686e5, // -0.33689, 0.94154 + 0xbfd5a742ac0ff78d, 0x3fee1ce2ecd0c0d8, // -0.33833, 0.94103 + 0xbfd5bee78b9db3b6, 0x3fee18a02fdc66d9, // -0.33978, 0.94051 + 0xbfd5d68910aee686, 0x3fee1458cec1ad83, // -0.34122, 0.93998 + 0xbfd5ee27379ea693, 0x3fee100cca2980ac, // -0.34266, 0.93946 + 0xbfd605c1fcc88f63, 0x3fee0bbc22bd8349, // -0.3441, 0.93893 + 0xbfd61d595c88c203, 0x3fee0766d9280f54, // -0.34554, 0.9384 + 0xbfd634ed533be58e, 0x3fee030cee1435b8, // -0.34698, 0.93787 + 0xbfd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // -0.34842, 0.93734 + 0xbfd6640af6f03d9e, 0x3fedfa4b3621271d, // -0.34986, 0.9368 + 0xbfd67b949cad63ca, 0x3fedf5e36a9ba59c, // -0.35129, 0.93627 + 0xbfd6931acad55f51, 0x3fedf177004b2534, // -0.35273, 0.93573 + 0xbfd6aa9d7dc77e16, 0x3feded05f7de47da, // -0.35416, 0.93518 + 0xbfd6c21cb1e39771, 0x3fede890520465ce, // -0.3556, 0.93464 + 0xbfd6d998638a0cb5, 0x3fede4160f6d8d81, // -0.35703, 0.93409 + 0xbfd6f1108f1bc9c5, 0x3feddf9730ca837b, // -0.35846, 0.93354 + 0xbfd7088530fa459e, 0x3feddb13b6ccc23d, // -0.3599, 0.93299 + 0xbfd71ff6458782ec, 0x3fedd68ba2267a25, // -0.36133, 0.93244 + 0xbfd73763c9261092, 0x3fedd1fef38a915a, // -0.36276, 0.93188 + 0xbfd74ecdb8390a3e, 0x3fedcd6dabaca3a5, // -0.36418, 0.93133 + 0xbfd766340f2418f6, 0x3fedc8d7cb410260, // -0.36561, 0.93077 + 0xbfd77d96ca4b73a6, 0x3fedc43d52fcb453, // -0.36704, 0.93021 + 0xbfd794f5e613dfae, 0x3fedbf9e4395759a, // -0.36847, 0.92964 + 0xbfd7ac515ee2b172, 0x3fedbafa9dc1b78d, // -0.36989, 0.92907 + 0xbfd7c3a9311dcce7, 0x3fedb6526238a09b, // -0.37132, 0.92851 + 0xbfd7dafd592ba621, 0x3fedb1a591b20c38, // -0.37274, 0.92794 + 0xbfd7f24dd37341e3, 0x3fedacf42ce68ab9, // -0.37416, 0.92736 + 0xbfd8099a9c5c362d, 0x3feda83e348f613b, // -0.37559, 0.92679 + 0xbfd820e3b04eaac4, 0x3feda383a9668988, // -0.37701, 0.92621 + 0xbfd838290bb359c8, 0x3fed9ec48c26b1f3, // -0.37843, 0.92563 + 0xbfd84f6aaaf3903f, 0x3fed9a00dd8b3d46, // -0.37985, 0.92505 + 0xbfd866a88a792ea0, 0x3fed95389e50429b, // -0.38127, 0.92447 + 0xbfd87de2a6aea963, 0x3fed906bcf328d46, // -0.38268, 0.92388 + 0xbfd89518fbff098e, 0x3fed8b9a70ef9cb4, // -0.3841, 0.92329 + 0xbfd8ac4b86d5ed44, 0x3fed86c48445a450, // -0.38552, 0.9227 + 0xbfd8c37a439f884f, 0x3fed81ea09f38b63, // -0.38693, 0.92211 + 0xbfd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // -0.38835, 0.92151 + 0xbfd8f1cc44bea329, 0x3fed78276f5617c6, // -0.38976, 0.92092 + 0xbfd908ef81ef7bd1, 0x3fed733f508c0dff, // -0.39117, 0.92032 + 0xbfd9200ee2c9be97, 0x3fed6e52a71c8547, // -0.39258, 0.91972 + 0xbfd9372a63bc93d7, 0x3fed696173c9e68b, // -0.39399, 0.91911 + 0xbfd94e420137bce3, 0x3fed646bb7574de5, // -0.3954, 0.91851 + 0xbfd96555b7ab948f, 0x3fed5f7172888a7f, // -0.39681, 0.9179 + 0xbfd97c6583890fc2, 0x3fed5a72a6221e73, // -0.39822, 0.91729 + 0xbfd993716141bdfe, 0x3fed556f52e93eb1, // -0.39962, 0.91668 + 0xbfd9aa794d47c9ee, 0x3fed506779a3d2d9, // -0.40103, 0.91606 + 0xbfd9c17d440df9f2, 0x3fed4b5b1b187524, // -0.40243, 0.91545 + 0xbfd9d87d4207b0ab, 0x3fed464a380e7242, // -0.40384, 0.91483 + 0xbfd9ef7943a8ed8a, 0x3fed4134d14dc93a, // -0.40524, 0.91421 + 0xbfda067145664d57, 0x3fed3c1ae79f2b4e, // -0.40664, 0.91359 + 0xbfda1d6543b50ac0, 0x3fed36fc7bcbfbdc, // -0.40804, 0.91296 + 0xbfda34553b0afee5, 0x3fed31d98e9e503a, // -0.40944, 0.91234 + 0xbfda4b4127dea1e4, 0x3fed2cb220e0ef9f, // -0.41084, 0.91171 + 0xbfda622906a70b63, 0x3fed2786335f52fc, // -0.41224, 0.91107 + 0xbfda790cd3dbf31a, 0x3fed2255c6e5a4e1, // -0.41364, 0.91044 + 0xbfda8fec8bf5b166, 0x3fed1d20dc40c15c, // -0.41503, 0.90981 + 0xbfdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // -0.41643, 0.90917 + 0xbfdabd9faebc3980, 0x3fed12a98fac410c, // -0.41782, 0.90853 + 0xbfdad473125cdc08, 0x3fed0d672f59d2b9, // -0.41922, 0.90789 + 0xbfdaeb4252ca07ab, 0x3fed082054168bac, // -0.42061, 0.90724 + 0xbfdb020d6c7f4009, 0x3fed02d4feb2bd92, // -0.422, 0.9066 + 0xbfdb18d45bf8aca6, 0x3fecfd852fff6ad4, // -0.42339, 0.90595 + 0xbfdb2f971db31972, 0x3fecf830e8ce467b, // -0.42478, 0.9053 + 0xbfdb4655ae2bf757, 0x3fecf2d829f1b40e, // -0.42617, 0.90464 + 0xbfdb5d1009e15cc0, 0x3feced7af43cc773, // -0.42756, 0.90399 + 0xbfdb73c62d520624, 0x3fece819488344ce, // -0.42894, 0.90333 + 0xbfdb8a7814fd5693, 0x3fece2b32799a060, // -0.43033, 0.90267 + 0xbfdba125bd63583e, 0x3fecdd489254fe65, // -0.43171, 0.90201 + 0xbfdbb7cf2304bd01, 0x3fecd7d9898b32f6, // -0.43309, 0.90135 + 0xbfdbce744262deee, 0x3fecd2660e12c1e6, // -0.43448, 0.90068 + 0xbfdbe51517ffc0d9, 0x3fecccee20c2de9f, // -0.43586, 0.90002 + 0xbfdbfbb1a05e0edc, 0x3fecc771c2736c09, // -0.43724, 0.89935 + 0xbfdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // -0.43862, 0.89867 + 0xbfdc28ddbb6cf145, 0x3fecbc6bb638d10b, // -0.43999, 0.898 + 0xbfdc3f6d47263129, 0x3fecb6e20a00da99, // -0.44137, 0.89732 + 0xbfdc55f877b23537, 0x3fecb153f02fb87d, // -0.44275, 0.89665 + 0xbfdc6c7f4997000a, 0x3fecabc169a0b901, // -0.44412, 0.89597 + 0xbfdc8301b95b40c2, 0x3feca62a772fd919, // -0.4455, 0.89528 + 0xbfdc997fc3865388, 0x3feca08f19b9c449, // -0.44687, 0.8946 + 0xbfdcaff964a0421d, 0x3fec9aef521bd480, // -0.44824, 0.89391 + 0xbfdcc66e9931c45d, 0x3fec954b213411f5, // -0.44961, 0.89322 + 0xbfdcdcdf5dc440ce, 0x3fec8fa287e13305, // -0.45098, 0.89253 + 0xbfdcf34baee1cd21, 0x3fec89f587029c13, // -0.45235, 0.89184 + 0xbfdd09b389152ec1, 0x3fec84441f785f61, // -0.45372, 0.89115 + 0xbfdd2016e8e9db5b, 0x3fec7e8e52233cf3, // -0.45508, 0.89045 + 0xbfdd3675caebf962, 0x3fec78d41fe4a267, // -0.45645, 0.88975 + 0xbfdd4cd02ba8609c, 0x3fec7315899eaad7, // -0.45781, 0.88905 + 0xbfdd632607ac9aa9, 0x3fec6d5290341eb2, // -0.45918, 0.88835 + 0xbfdd79775b86e389, 0x3fec678b3488739b, // -0.46054, 0.88764 + 0xbfdd8fc423c62a25, 0x3fec61bf777fcc48, // -0.4619, 0.88693 + 0xbfdda60c5cfa10d8, 0x3fec5bef59fef85a, // -0.46326, 0.88622 + 0xbfddbc5003b2edf8, 0x3fec561adceb743e, // -0.46462, 0.88551 + 0xbfddd28f1481cc58, 0x3fec5042012b6907, // -0.46598, 0.8848 + 0xbfdde8c98bf86bd6, 0x3fec4a64c7a5ac4c, // -0.46733, 0.88408 + 0xbfddfeff66a941de, 0x3fec44833141c004, // -0.46869, 0.88336 + 0xbfde1530a12779f4, 0x3fec3e9d3ee7d262, // -0.47004, 0.88264 + 0xbfde2b5d3806f63b, 0x3fec38b2f180bdb1, // -0.4714, 0.88192 + 0xbfde418527dc4ffa, 0x3fec32c449f60831, // -0.47275, 0.8812 + 0xbfde57a86d3cd824, 0x3fec2cd14931e3f1, // -0.4741, 0.88047 + 0xbfde6dc704be97e2, 0x3fec26d9f01f2eaf, // -0.47545, 0.87974 + 0xbfde83e0eaf85113, 0x3fec20de3fa971b0, // -0.4768, 0.87901 + 0xbfde99f61c817eda, 0x3fec1ade38bce19b, // -0.47815, 0.87828 + 0xbfdeb00695f25620, 0x3fec14d9dc465e58, // -0.47949, 0.87755 + 0xbfdec61253e3c61b, 0x3fec0ed12b3372e9, // -0.48084, 0.87681 + 0xbfdedc1952ef78d5, 0x3fec08c426725549, // -0.48218, 0.87607 + 0xbfdef21b8fafd3b5, 0x3fec02b2cef1e641, // -0.48353, 0.87533 + 0xbfdf081906bff7fd, 0x3febfc9d25a1b147, // -0.48487, 0.87459 + 0xbfdf1e11b4bbc35c, 0x3febf6832b71ec5b, // -0.48621, 0.87384 + 0xbfdf3405963fd068, 0x3febf064e15377dd, // -0.48755, 0.87309 + 0xbfdf49f4a7e97729, 0x3febea424837de6d, // -0.48889, 0.87235 + 0xbfdf5fdee656cda3, 0x3febe41b611154c1, // -0.49023, 0.8716 + 0xbfdf75c44e26a852, 0x3febddf02cd2b983, // -0.49156, 0.87084 + 0xbfdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // -0.4929, 0.87009 + 0xbfdfa1808c6cf7e0, 0x3febd18ce0dc19d6, // -0.49423, 0.86933 + 0xbfdfb7575c24d2de, 0x3febcb54cb0d2327, // -0.49557, 0.86857 + 0xbfdfcd2947c1ff57, 0x3febc5186bf8361d, // -0.4969, 0.86781 + 0xbfdfe2f64be7120f, 0x3febbed7c49380ea, // -0.49823, 0.86705 + 0xbfdff8be6537615e, 0x3febb892d5d5dad5, // -0.49956, 0.86628 + 0xbfe00740c82b82e0, 0x3febb249a0b6c40d, // -0.50089, 0.86551 + 0xbfe0121fe4f56d2c, 0x3febabfc262e6586, // -0.50221, 0.86474 + 0xbfe01cfc874c3eb7, 0x3feba5aa673590d2, // -0.50354, 0.86397 + 0xbfe027d6ad83287e, 0x3feb9f5464c5bffc, // -0.50486, 0.8632 + 0xbfe032ae55edbd95, 0x3feb98fa1fd9155e, // -0.50619, 0.86242 + 0xbfe03d837edff370, 0x3feb929b996a5b7f, // -0.50751, 0.86165 + 0xbfe0485626ae221a, 0x3feb8c38d27504e9, // -0.50883, 0.86087 + 0xbfe053264bad0483, 0x3feb85d1cbf52c02, // -0.51015, 0.86009 + 0xbfe05df3ec31b8b6, 0x3feb7f6686e792ea, // -0.51147, 0.8593 + 0xbfe068bf0691c028, 0x3feb78f70449a34b, // -0.51279, 0.85852 + 0xbfe073879922ffed, 0x3feb728345196e3e, // -0.5141, 0.85773 + 0xbfe07e4da23bc102, 0x3feb6c0b4a55ac17, // -0.51542, 0.85694 + 0xbfe089112032b08c, 0x3feb658f14fdbc47, // -0.51673, 0.85615 + 0xbfe093d2115ee018, 0x3feb5f0ea611a532, // -0.51804, 0.85535 + 0xbfe09e907417c5e1, 0x3feb5889fe921405, // -0.51936, 0.85456 + 0xbfe0a94c46b53d0b, 0x3feb52011f805c92, // -0.52067, 0.85376 + 0xbfe0b405878f85ec, 0x3feb4b7409de7925, // -0.52198, 0.85296 + 0xbfe0bebc34ff4646, 0x3feb44e2beaf0a61, // -0.52328, 0.85216 + 0xbfe0c9704d5d898f, 0x3feb3e4d3ef55712, // -0.52459, 0.85136 + 0xbfe0d421cf03c12b, 0x3feb37b38bb54c09, // -0.5259, 0.85055 + 0xbfe0ded0b84bc4b5, 0x3feb3115a5f37bf4, // -0.5272, 0.84974 + 0xbfe0e97d078fd23b, 0x3feb2a738eb51f33, // -0.5285, 0.84893 + 0xbfe0f426bb2a8e7d, 0x3feb23cd470013b4, // -0.5298, 0.84812 + 0xbfe0fecdd1770537, 0x3feb1d22cfdadcc6, // -0.5311, 0.84731 + 0xbfe1097248d0a956, 0x3feb16742a4ca2f5, // -0.5324, 0.84649 + 0xbfe114141f935545, 0x3feb0fc1575d33db, // -0.5337, 0.84567 + 0xbfe11eb3541b4b22, 0x3feb090a58150200, // -0.535, 0.84485 + 0xbfe1294fe4c5350a, 0x3feb024f2d7d24a9, // -0.53629, 0.84403 + 0xbfe133e9cfee254e, 0x3feafb8fd89f57b6, // -0.53759, 0.84321 + 0xbfe13e8113f396c1, 0x3feaf4cc5a85fb73, // -0.53888, 0.84238 + 0xbfe14915af336ceb, 0x3feaee04b43c1474, // -0.54017, 0.84155 + 0xbfe153a7a00bf453, 0x3feae738e6cd4b67, // -0.54146, 0.84073 + 0xbfe15e36e4dbe2bc, 0x3feae068f345ecef, // -0.54275, 0.83989 + 0xbfe168c37c025764, 0x3fead994dab2e979, // -0.54404, 0.83906 + 0xbfe1734d63dedb49, 0x3fead2bc9e21d511, // -0.54532, 0.83822 + 0xbfe17dd49ad16161, 0x3feacbe03ea0e73b, // -0.54661, 0.83739 + 0xbfe188591f3a46e5, 0x3feac4ffbd3efac8, // -0.54789, 0.83655 + 0xbfe192daef7a5386, 0x3feabe1b1b0b8dac, // -0.54918, 0.83571 + 0xbfe19d5a09f2b9b8, 0x3feab7325916c0d4, // -0.55046, 0.83486 + 0xbfe1a7d66d0516e6, 0x3feab045787157ff, // -0.55174, 0.83402 + 0xbfe1b250171373be, 0x3feaa9547a2cb98e, // -0.55302, 0.83317 + 0xbfe1bcc706804467, 0x3feaa25f5f5aee60, // -0.55429, 0.83232 + 0xbfe1c73b39ae68c8, 0x3fea9b66290ea1a3, // -0.55557, 0.83147 + 0xbfe1d1acaf012cc2, 0x3fea9468d85b20ae, // -0.55685, 0.83062 + 0xbfe1dc1b64dc4872, 0x3fea8d676e545ad2, // -0.55812, 0.82976 + 0xbfe1e68759a3e074, 0x3fea8661ec0ee133, // -0.55939, 0.8289 + 0xbfe1f0f08bbc861b, 0x3fea7f58529fe69d, // -0.56066, 0.82805 + 0xbfe1fb56f98b37b8, 0x3fea784aa31d3f55, // -0.56193, 0.82718 + 0xbfe205baa17560d6, 0x3fea7138de9d60f5, // -0.5632, 0.82632 + 0xbfe2101b81e0da78, 0x3fea6a230637623b, // -0.56447, 0.82546 + 0xbfe21a799933eb58, 0x3fea63091b02fae2, // -0.56573, 0.82459 + 0xbfe224d4e5d5482e, 0x3fea5beb1e188375, // -0.567, 0.82372 + 0xbfe22f2d662c13e1, 0x3fea54c91090f524, // -0.56826, 0.82285 + 0xbfe23983189fdfd5, 0x3fea4da2f385e997, // -0.56952, 0.82198 + 0xbfe243d5fb98ac1f, 0x3fea4678c8119ac8, // -0.57078, 0.8211 + 0xbfe24e260d7ee7c9, 0x3fea3f4a8f4ee2d2, // -0.57204, 0.82023 + 0xbfe258734cbb7110, 0x3fea38184a593bc6, // -0.5733, 0.81935 + 0xbfe262bdb7b795a2, 0x3fea30e1fa4cbf81, // -0.57455, 0.81847 + 0xbfe26d054cdd12df, 0x3fea29a7a0462782, // -0.57581, 0.81758 + 0xbfe2774a0a961612, 0x3fea22693d62ccb9, // -0.57706, 0.8167 + 0xbfe2818bef4d3cba, 0x3fea1b26d2c0a75e, // -0.57831, 0.81581 + 0xbfe28bcaf96d94ba, 0x3fea13e0617e4ec7, // -0.57956, 0.81493 + 0xbfe2960727629ca8, 0x3fea0c95eabaf937, // -0.58081, 0.81404 + 0xbfe2a040779843fb, 0x3fea05476f967bb5, // -0.58206, 0.81314 + 0xbfe2aa76e87aeb58, 0x3fe9fdf4f13149de, // -0.58331, 0.81225 + 0xbfe2b4aa787764c4, 0x3fe9f69e70ac75bc, // -0.58455, 0.81135 + 0xbfe2bedb25faf3ea, 0x3fe9ef43ef29af94, // -0.5858, 0.81046 + 0xbfe2c908ef734e57, 0x3fe9e7e56dcb45bd, // -0.58704, 0.80956 + 0xbfe2d333d34e9bb7, 0x3fe9e082edb42472, // -0.58828, 0.80866 + 0xbfe2dd5bcffb7616, 0x3fe9d91c7007d5a6, // -0.58952, 0.80775 + 0xbfe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // -0.59076, 0.80685 + 0xbfe2f1a30d86773a, 0x3fe9ca438080eadb, // -0.592, 0.80594 + 0xbfe2fbc24b441015, 0x3fe9c2d110f075c3, // -0.59323, 0.80503 + 0xbfe305de9b921a94, 0x3fe9bb5aa85f2098, // -0.59447, 0.80412 + 0xbfe30ff7fce17035, 0x3fe9b3e047f38741, // -0.5957, 0.80321 + 0xbfe31a0e6da35e44, 0x3fe9ac61f0d4e247, // -0.59693, 0.80229 + 0xbfe32421ec49a620, 0x3fe9a4dfa42b06b2, // -0.59816, 0.80138 + 0xbfe32e3277467d6b, 0x3fe99d59631e65d5, // -0.59939, 0.80046 + 0xbfe338400d0c8e57, 0x3fe995cf2ed80d22, // -0.60062, 0.79954 + 0xbfe3424aac0ef7d6, 0x3fe98e410881a600, // -0.60184, 0.79861 + 0xbfe34c5252c14de1, 0x3fe986aef1457594, // -0.60307, 0.79769 + 0xbfe35656ff9799ae, 0x3fe97f18ea4e5c9e, // -0.60429, 0.79676 + 0xbfe36058b10659f3, 0x3fe9777ef4c7d742, // -0.60551, 0.79584 + 0xbfe36a576582831b, 0x3fe96fe111ddfce0, // -0.60673, 0.79491 + 0xbfe374531b817f8d, 0x3fe9683f42bd7fe1, // -0.60795, 0.79398 + 0xbfe37e4bd1792fe2, 0x3fe960998893ad8c, // -0.60917, 0.79304 + 0xbfe3884185dfeb22, 0x3fe958efe48e6dd7, // -0.61038, 0.79211 + 0xbfe39234372c7f04, 0x3fe9514257dc4335, // -0.6116, 0.79117 + 0xbfe39c23e3d63029, 0x3fe94990e3ac4a6c, // -0.61281, 0.79023 + 0xbfe3a6108a54ba58, 0x3fe941db892e3a65, // -0.61402, 0.78929 + 0xbfe3affa292050b9, 0x3fe93a22499263fc, // -0.61523, 0.78835 + 0xbfe3b9e0beb19e18, 0x3fe932652609b1cf, // -0.61644, 0.7874 + 0xbfe3c3c44981c517, 0x3fe92aa41fc5a815, // -0.61765, 0.78646 + 0xbfe3cda4c80a6076, 0x3fe922df37f8646a, // -0.61885, 0.78551 + 0xbfe3d78238c58343, 0x3fe91b166fd49da2, // -0.62006, 0.78456 + 0xbfe3e15c9a2db922, 0x3fe91349c88da398, // -0.62126, 0.7836 + 0xbfe3eb33eabe0680, 0x3fe90b7943575efe, // -0.62246, 0.78265 + 0xbfe3f50828f1e8d2, 0x3fe903a4e1665133, // -0.62366, 0.78169 + 0xbfe3fed9534556d4, 0x3fe8fbcca3ef940d, // -0.62486, 0.78074 + 0xbfe408a76834c0c0, 0x3fe8f3f08c28d9ac, // -0.62606, 0.77978 + 0xbfe41272663d108c, 0x3fe8ec109b486c49, // -0.62725, 0.77882 + 0xbfe41c3a4bdbaa26, 0x3fe8e42cd2852e0a, // -0.62845, 0.77785 + 0xbfe425ff178e6bb1, 0x3fe8dc45331698cc, // -0.62964, 0.77689 + 0xbfe42fc0c7d3adbb, 0x3fe8d459be34bdfa, // -0.63083, 0.77592 + 0xbfe4397f5b2a4380, 0x3fe8cc6a75184655, // -0.63202, 0.77495 + 0xbfe4433ad0117b1d, 0x3fe8c47758fa71cb, // -0.63321, 0.77398 + 0xbfe44cf325091dd6, 0x3fe8bc806b151741, // -0.63439, 0.77301 + 0xbfe456a858917046, 0x3fe8b485aca2a468, // -0.63558, 0.77204 + 0xbfe4605a692b32a2, 0x3fe8ac871ede1d88, // -0.63676, 0.77106 + 0xbfe46a095557a0f1, 0x3fe8a484c3031d50, // -0.63794, 0.77008 + 0xbfe473b51b987347, 0x3fe89c7e9a4dd4ab, // -0.63912, 0.7691 + 0xbfe47d5dba6fde01, 0x3fe89474a5fb0a84, // -0.6403, 0.76812 + 0xbfe48703306091fe, 0x3fe88c66e7481ba1, // -0.64148, 0.76714 + 0xbfe490a57bedbcdf, 0x3fe884555f72fa6b, // -0.64266, 0.76615 + 0xbfe49a449b9b0938, 0x3fe87c400fba2ebf, // -0.64383, 0.76517 + 0xbfe4a3e08dec9ed6, 0x3fe87426f95cd5bd, // -0.645, 0.76418 + 0xbfe4ad79516722f0, 0x3fe86c0a1d9aa195, // -0.64618, 0.76319 + 0xbfe4b70ee48fb869, 0x3fe863e97db3d95a, // -0.64735, 0.7622 + 0xbfe4c0a145ec0004, 0x3fe85bc51ae958cc, // -0.64851, 0.7612 + 0xbfe4ca30740218a3, 0x3fe8539cf67c9029, // -0.64968, 0.76021 + 0xbfe4d3bc6d589f80, 0x3fe84b7111af83f9, // -0.65085, 0.75921 + 0xbfe4dd453076b064, 0x3fe843416dc4cce2, // -0.65201, 0.75821 + 0xbfe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // -0.65317, 0.75721 + 0xbfe4f04d0e2859aa, 0x3fe832d6eda3a3e0, // -0.65433, 0.75621 + 0xbfe4f9cc25cca486, 0x3fe82a9c13f545ff, // -0.65549, 0.7552 + 0xbfe503480159ded2, 0x3fe8225d803964e5, // -0.65665, 0.75419 + 0xbfe50cc09f59a09b, 0x3fe81a1b33b57acc, // -0.65781, 0.75319 + 0xbfe51635fe5601d7, 0x3fe811d52faf94dc, // -0.65896, 0.75218 + 0xbfe51fa81cd99aa6, 0x3fe8098b756e52fa, // -0.66011, 0.75117 + 0xbfe52916f96f8388, 0x3fe8013e0638e795, // -0.66127, 0.75015 + 0xbfe5328292a35596, 0x3fe7f8ece3571771, // -0.66242, 0.74914 + 0xbfe53beae7012abe, 0x3fe7f0980e113978, // -0.66356, 0.74812 + 0xbfe5454ff5159dfb, 0x3fe7e83f87b03686, // -0.66471, 0.7471 + 0xbfe54eb1bb6dcb8f, 0x3fe7dfe3517d8937, // -0.66586, 0.74608 + 0xbfe5581038975137, 0x3fe7d7836cc33db2, // -0.667, 0.74506 + 0xbfe5616b6b204e6e, 0x3fe7cf1fdacbf179, // -0.66814, 0.74403 + 0xbfe56ac35197649e, 0x3fe7c6b89ce2d333, // -0.66928, 0.74301 + 0xbfe57417ea8bb75c, 0x3fe7be4db453a27c, // -0.67042, 0.74198 + 0xbfe57d69348cec9f, 0x3fe7b5df226aafb0, // -0.67156, 0.74095 + 0xbfe586b72e2b2cfd, 0x3fe7ad6ce874dbb6, // -0.67269, 0.73992 + 0xbfe59001d5f723df, 0x3fe7a4f707bf97d2, // -0.67383, 0.73889 + 0xbfe599492a81ffbc, 0x3fe79c7d8198e56e, // -0.67496, 0.73785 + 0xbfe5a28d2a5d7250, 0x3fe79400574f55e4, // -0.67609, 0.73682 + 0xbfe5abcdd41bb0d8, 0x3fe78b7f8a320a52, // -0.67722, 0.73578 + 0xbfe5b50b264f7448, 0x3fe782fb1b90b35b, // -0.67835, 0.73474 + 0xbfe5be451f8bf980, 0x3fe77a730cbb9100, // -0.67948, 0.7337 + 0xbfe5c77bbe65018c, 0x3fe771e75f037261, // -0.6806, 0.73265 + 0xbfe5d0af016ed1d4, 0x3fe7695813b9b594, // -0.68172, 0.73161 + 0xbfe5d9dee73e345c, 0x3fe760c52c304764, // -0.68285, 0.73056 + 0xbfe5e30b6e6877f3, 0x3fe7582ea9b9a329, // -0.68397, 0.72951 + 0xbfe5ec3495837074, 0x3fe74f948da8d28d, // -0.68508, 0.72846 + 0xbfe5f55a5b2576f8, 0x3fe746f6d9516d59, // -0.6862, 0.72741 + 0xbfe5fe7cbde56a0f, 0x3fe73e558e079942, // -0.68732, 0.72636 + 0xbfe6079bbc5aadfa, 0x3fe735b0ad2009b2, // -0.68843, 0.7253 + 0xbfe610b7551d2cde, 0x3fe72d0837efff97, // -0.68954, 0.72425 + 0xbfe619cf86c55702, 0x3fe7245c2fcd492a, // -0.69065, 0.72319 + 0xbfe622e44fec22ff, 0x3fe71bac960e41bf, // -0.69176, 0.72213 + 0xbfe62bf5af2b0dfd, 0x3fe712f96c09d18d, // -0.69287, 0.72107 + 0xbfe63503a31c1be8, 0x3fe70a42b3176d7a, // -0.69397, 0.72 + 0xbfe63e0e2a59d7aa, 0x3fe701886c8f16e6, // -0.69508, 0.71894 + 0xbfe64715437f535b, 0x3fe6f8ca99c95b75, // -0.69618, 0.71787 + 0xbfe65018ed28287f, 0x3fe6f0093c1f54de, // -0.69728, 0.7168 + 0xbfe6591925f0783e, 0x3fe6e74454eaa8ae, // -0.69838, 0.71573 + 0xbfe66215ec74eb91, 0x3fe6de7be585881d, // -0.69947, 0.71466 + 0xbfe66b0f3f52b386, 0x3fe6d5afef4aafcc, // -0.70057, 0.71358 + 0xbfe674051d27896c, 0x3fe6cce07395679f, // -0.70166, 0.71251 + 0xbfe67cf78491af10, 0x3fe6c40d73c18275, // -0.70275, 0.71143 + 0xbfe685e6742feeef, 0x3fe6bb36f12b5e06, // -0.70385, 0.71035 + 0xbfe68ed1eaa19c71, 0x3fe6b25ced2fe29c, // -0.70493, 0.70927 + 0xbfe697b9e686941c, 0x3fe6a97f692c82ea, // -0.70602, 0.70819 + 0xbfe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // -0.70711, 0.70711 + 0xbfe6a97f692c82ea, 0x3fe697b9e686941c, // -0.70819, 0.70602 + 0xbfe6b25ced2fe29c, 0x3fe68ed1eaa19c71, // -0.70927, 0.70493 + 0xbfe6bb36f12b5e06, 0x3fe685e6742feeef, // -0.71035, 0.70385 + 0xbfe6c40d73c18275, 0x3fe67cf78491af10, // -0.71143, 0.70275 + 0xbfe6cce07395679f, 0x3fe674051d27896c, // -0.71251, 0.70166 + 0xbfe6d5afef4aafcc, 0x3fe66b0f3f52b386, // -0.71358, 0.70057 + 0xbfe6de7be585881d, 0x3fe66215ec74eb91, // -0.71466, 0.69947 + 0xbfe6e74454eaa8ae, 0x3fe6591925f0783e, // -0.71573, 0.69838 + 0xbfe6f0093c1f54de, 0x3fe65018ed28287f, // -0.7168, 0.69728 + 0xbfe6f8ca99c95b75, 0x3fe64715437f535b, // -0.71787, 0.69618 + 0xbfe701886c8f16e6, 0x3fe63e0e2a59d7aa, // -0.71894, 0.69508 + 0xbfe70a42b3176d7a, 0x3fe63503a31c1be8, // -0.72, 0.69397 + 0xbfe712f96c09d18d, 0x3fe62bf5af2b0dfd, // -0.72107, 0.69287 + 0xbfe71bac960e41bf, 0x3fe622e44fec22ff, // -0.72213, 0.69176 + 0xbfe7245c2fcd492a, 0x3fe619cf86c55702, // -0.72319, 0.69065 + 0xbfe72d0837efff97, 0x3fe610b7551d2cde, // -0.72425, 0.68954 + 0xbfe735b0ad2009b2, 0x3fe6079bbc5aadfa, // -0.7253, 0.68843 + 0xbfe73e558e079942, 0x3fe5fe7cbde56a0f, // -0.72636, 0.68732 + 0xbfe746f6d9516d59, 0x3fe5f55a5b2576f8, // -0.72741, 0.6862 + 0xbfe74f948da8d28d, 0x3fe5ec3495837074, // -0.72846, 0.68508 + 0xbfe7582ea9b9a329, 0x3fe5e30b6e6877f3, // -0.72951, 0.68397 + 0xbfe760c52c304764, 0x3fe5d9dee73e345c, // -0.73056, 0.68285 + 0xbfe7695813b9b594, 0x3fe5d0af016ed1d4, // -0.73161, 0.68172 + 0xbfe771e75f037261, 0x3fe5c77bbe65018c, // -0.73265, 0.6806 + 0xbfe77a730cbb9100, 0x3fe5be451f8bf980, // -0.7337, 0.67948 + 0xbfe782fb1b90b35b, 0x3fe5b50b264f7448, // -0.73474, 0.67835 + 0xbfe78b7f8a320a52, 0x3fe5abcdd41bb0d8, // -0.73578, 0.67722 + 0xbfe79400574f55e4, 0x3fe5a28d2a5d7250, // -0.73682, 0.67609 + 0xbfe79c7d8198e56e, 0x3fe599492a81ffbc, // -0.73785, 0.67496 + 0xbfe7a4f707bf97d2, 0x3fe59001d5f723df, // -0.73889, 0.67383 + 0xbfe7ad6ce874dbb6, 0x3fe586b72e2b2cfd, // -0.73992, 0.67269 + 0xbfe7b5df226aafb0, 0x3fe57d69348cec9f, // -0.74095, 0.67156 + 0xbfe7be4db453a27c, 0x3fe57417ea8bb75c, // -0.74198, 0.67042 + 0xbfe7c6b89ce2d333, 0x3fe56ac35197649e, // -0.74301, 0.66928 + 0xbfe7cf1fdacbf179, 0x3fe5616b6b204e6e, // -0.74403, 0.66814 + 0xbfe7d7836cc33db2, 0x3fe5581038975137, // -0.74506, 0.667 + 0xbfe7dfe3517d8937, 0x3fe54eb1bb6dcb8f, // -0.74608, 0.66586 + 0xbfe7e83f87b03686, 0x3fe5454ff5159dfb, // -0.7471, 0.66471 + 0xbfe7f0980e113978, 0x3fe53beae7012abe, // -0.74812, 0.66356 + 0xbfe7f8ece3571771, 0x3fe5328292a35596, // -0.74914, 0.66242 + 0xbfe8013e0638e795, 0x3fe52916f96f8388, // -0.75015, 0.66127 + 0xbfe8098b756e52fa, 0x3fe51fa81cd99aa6, // -0.75117, 0.66011 + 0xbfe811d52faf94dc, 0x3fe51635fe5601d7, // -0.75218, 0.65896 + 0xbfe81a1b33b57acc, 0x3fe50cc09f59a09b, // -0.75319, 0.65781 + 0xbfe8225d803964e5, 0x3fe503480159ded2, // -0.75419, 0.65665 + 0xbfe82a9c13f545ff, 0x3fe4f9cc25cca486, // -0.7552, 0.65549 + 0xbfe832d6eda3a3e0, 0x3fe4f04d0e2859aa, // -0.75621, 0.65433 + 0xbfe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // -0.75721, 0.65317 + 0xbfe843416dc4cce2, 0x3fe4dd453076b064, // -0.75821, 0.65201 + 0xbfe84b7111af83f9, 0x3fe4d3bc6d589f80, // -0.75921, 0.65085 + 0xbfe8539cf67c9029, 0x3fe4ca30740218a3, // -0.76021, 0.64968 + 0xbfe85bc51ae958cc, 0x3fe4c0a145ec0004, // -0.7612, 0.64851 + 0xbfe863e97db3d95a, 0x3fe4b70ee48fb869, // -0.7622, 0.64735 + 0xbfe86c0a1d9aa195, 0x3fe4ad79516722f0, // -0.76319, 0.64618 + 0xbfe87426f95cd5bd, 0x3fe4a3e08dec9ed6, // -0.76418, 0.645 + 0xbfe87c400fba2ebf, 0x3fe49a449b9b0938, // -0.76517, 0.64383 + 0xbfe884555f72fa6b, 0x3fe490a57bedbcdf, // -0.76615, 0.64266 + 0xbfe88c66e7481ba1, 0x3fe48703306091fe, // -0.76714, 0.64148 + 0xbfe89474a5fb0a84, 0x3fe47d5dba6fde01, // -0.76812, 0.6403 + 0xbfe89c7e9a4dd4ab, 0x3fe473b51b987347, // -0.7691, 0.63912 + 0xbfe8a484c3031d50, 0x3fe46a095557a0f1, // -0.77008, 0.63794 + 0xbfe8ac871ede1d88, 0x3fe4605a692b32a2, // -0.77106, 0.63676 + 0xbfe8b485aca2a468, 0x3fe456a858917046, // -0.77204, 0.63558 + 0xbfe8bc806b151741, 0x3fe44cf325091dd6, // -0.77301, 0.63439 + 0xbfe8c47758fa71cb, 0x3fe4433ad0117b1d, // -0.77398, 0.63321 + 0xbfe8cc6a75184655, 0x3fe4397f5b2a4380, // -0.77495, 0.63202 + 0xbfe8d459be34bdfa, 0x3fe42fc0c7d3adbb, // -0.77592, 0.63083 + 0xbfe8dc45331698cc, 0x3fe425ff178e6bb1, // -0.77689, 0.62964 + 0xbfe8e42cd2852e0a, 0x3fe41c3a4bdbaa26, // -0.77785, 0.62845 + 0xbfe8ec109b486c49, 0x3fe41272663d108c, // -0.77882, 0.62725 + 0xbfe8f3f08c28d9ac, 0x3fe408a76834c0c0, // -0.77978, 0.62606 + 0xbfe8fbcca3ef940d, 0x3fe3fed9534556d4, // -0.78074, 0.62486 + 0xbfe903a4e1665133, 0x3fe3f50828f1e8d2, // -0.78169, 0.62366 + 0xbfe90b7943575efe, 0x3fe3eb33eabe0680, // -0.78265, 0.62246 + 0xbfe91349c88da398, 0x3fe3e15c9a2db922, // -0.7836, 0.62126 + 0xbfe91b166fd49da2, 0x3fe3d78238c58343, // -0.78456, 0.62006 + 0xbfe922df37f8646a, 0x3fe3cda4c80a6076, // -0.78551, 0.61885 + 0xbfe92aa41fc5a815, 0x3fe3c3c44981c517, // -0.78646, 0.61765 + 0xbfe932652609b1cf, 0x3fe3b9e0beb19e18, // -0.7874, 0.61644 + 0xbfe93a22499263fc, 0x3fe3affa292050b9, // -0.78835, 0.61523 + 0xbfe941db892e3a65, 0x3fe3a6108a54ba58, // -0.78929, 0.61402 + 0xbfe94990e3ac4a6c, 0x3fe39c23e3d63029, // -0.79023, 0.61281 + 0xbfe9514257dc4335, 0x3fe39234372c7f04, // -0.79117, 0.6116 + 0xbfe958efe48e6dd7, 0x3fe3884185dfeb22, // -0.79211, 0.61038 + 0xbfe960998893ad8c, 0x3fe37e4bd1792fe2, // -0.79304, 0.60917 + 0xbfe9683f42bd7fe1, 0x3fe374531b817f8d, // -0.79398, 0.60795 + 0xbfe96fe111ddfce0, 0x3fe36a576582831b, // -0.79491, 0.60673 + 0xbfe9777ef4c7d742, 0x3fe36058b10659f3, // -0.79584, 0.60551 + 0xbfe97f18ea4e5c9e, 0x3fe35656ff9799ae, // -0.79676, 0.60429 + 0xbfe986aef1457594, 0x3fe34c5252c14de1, // -0.79769, 0.60307 + 0xbfe98e410881a600, 0x3fe3424aac0ef7d6, // -0.79861, 0.60184 + 0xbfe995cf2ed80d22, 0x3fe338400d0c8e57, // -0.79954, 0.60062 + 0xbfe99d59631e65d5, 0x3fe32e3277467d6b, // -0.80046, 0.59939 + 0xbfe9a4dfa42b06b2, 0x3fe32421ec49a620, // -0.80138, 0.59816 + 0xbfe9ac61f0d4e247, 0x3fe31a0e6da35e44, // -0.80229, 0.59693 + 0xbfe9b3e047f38741, 0x3fe30ff7fce17035, // -0.80321, 0.5957 + 0xbfe9bb5aa85f2098, 0x3fe305de9b921a94, // -0.80412, 0.59447 + 0xbfe9c2d110f075c3, 0x3fe2fbc24b441015, // -0.80503, 0.59323 + 0xbfe9ca438080eadb, 0x3fe2f1a30d86773a, // -0.80594, 0.592 + 0xbfe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // -0.80685, 0.59076 + 0xbfe9d91c7007d5a6, 0x3fe2dd5bcffb7616, // -0.80775, 0.58952 + 0xbfe9e082edb42472, 0x3fe2d333d34e9bb7, // -0.80866, 0.58828 + 0xbfe9e7e56dcb45bd, 0x3fe2c908ef734e57, // -0.80956, 0.58704 + 0xbfe9ef43ef29af94, 0x3fe2bedb25faf3ea, // -0.81046, 0.5858 + 0xbfe9f69e70ac75bc, 0x3fe2b4aa787764c4, // -0.81135, 0.58455 + 0xbfe9fdf4f13149de, 0x3fe2aa76e87aeb58, // -0.81225, 0.58331 + 0xbfea05476f967bb5, 0x3fe2a040779843fb, // -0.81314, 0.58206 + 0xbfea0c95eabaf937, 0x3fe2960727629ca8, // -0.81404, 0.58081 + 0xbfea13e0617e4ec7, 0x3fe28bcaf96d94ba, // -0.81493, 0.57956 + 0xbfea1b26d2c0a75e, 0x3fe2818bef4d3cba, // -0.81581, 0.57831 + 0xbfea22693d62ccb9, 0x3fe2774a0a961612, // -0.8167, 0.57706 + 0xbfea29a7a0462782, 0x3fe26d054cdd12df, // -0.81758, 0.57581 + 0xbfea30e1fa4cbf81, 0x3fe262bdb7b795a2, // -0.81847, 0.57455 + 0xbfea38184a593bc6, 0x3fe258734cbb7110, // -0.81935, 0.5733 + 0xbfea3f4a8f4ee2d2, 0x3fe24e260d7ee7c9, // -0.82023, 0.57204 + 0xbfea4678c8119ac8, 0x3fe243d5fb98ac1f, // -0.8211, 0.57078 + 0xbfea4da2f385e997, 0x3fe23983189fdfd5, // -0.82198, 0.56952 + 0xbfea54c91090f524, 0x3fe22f2d662c13e1, // -0.82285, 0.56826 + 0xbfea5beb1e188375, 0x3fe224d4e5d5482e, // -0.82372, 0.567 + 0xbfea63091b02fae2, 0x3fe21a799933eb58, // -0.82459, 0.56573 + 0xbfea6a230637623b, 0x3fe2101b81e0da78, // -0.82546, 0.56447 + 0xbfea7138de9d60f5, 0x3fe205baa17560d6, // -0.82632, 0.5632 + 0xbfea784aa31d3f55, 0x3fe1fb56f98b37b8, // -0.82718, 0.56193 + 0xbfea7f58529fe69d, 0x3fe1f0f08bbc861b, // -0.82805, 0.56066 + 0xbfea8661ec0ee133, 0x3fe1e68759a3e074, // -0.8289, 0.55939 + 0xbfea8d676e545ad2, 0x3fe1dc1b64dc4872, // -0.82976, 0.55812 + 0xbfea9468d85b20ae, 0x3fe1d1acaf012cc2, // -0.83062, 0.55685 + 0xbfea9b66290ea1a3, 0x3fe1c73b39ae68c8, // -0.83147, 0.55557 + 0xbfeaa25f5f5aee60, 0x3fe1bcc706804467, // -0.83232, 0.55429 + 0xbfeaa9547a2cb98e, 0x3fe1b250171373be, // -0.83317, 0.55302 + 0xbfeab045787157ff, 0x3fe1a7d66d0516e6, // -0.83402, 0.55174 + 0xbfeab7325916c0d4, 0x3fe19d5a09f2b9b8, // -0.83486, 0.55046 + 0xbfeabe1b1b0b8dac, 0x3fe192daef7a5386, // -0.83571, 0.54918 + 0xbfeac4ffbd3efac8, 0x3fe188591f3a46e5, // -0.83655, 0.54789 + 0xbfeacbe03ea0e73b, 0x3fe17dd49ad16161, // -0.83739, 0.54661 + 0xbfead2bc9e21d511, 0x3fe1734d63dedb49, // -0.83822, 0.54532 + 0xbfead994dab2e979, 0x3fe168c37c025764, // -0.83906, 0.54404 + 0xbfeae068f345ecef, 0x3fe15e36e4dbe2bc, // -0.83989, 0.54275 + 0xbfeae738e6cd4b67, 0x3fe153a7a00bf453, // -0.84073, 0.54146 + 0xbfeaee04b43c1474, 0x3fe14915af336ceb, // -0.84155, 0.54017 + 0xbfeaf4cc5a85fb73, 0x3fe13e8113f396c1, // -0.84238, 0.53888 + 0xbfeafb8fd89f57b6, 0x3fe133e9cfee254e, // -0.84321, 0.53759 + 0xbfeb024f2d7d24a9, 0x3fe1294fe4c5350a, // -0.84403, 0.53629 + 0xbfeb090a58150200, 0x3fe11eb3541b4b22, // -0.84485, 0.535 + 0xbfeb0fc1575d33db, 0x3fe114141f935545, // -0.84567, 0.5337 + 0xbfeb16742a4ca2f5, 0x3fe1097248d0a956, // -0.84649, 0.5324 + 0xbfeb1d22cfdadcc6, 0x3fe0fecdd1770537, // -0.84731, 0.5311 + 0xbfeb23cd470013b4, 0x3fe0f426bb2a8e7d, // -0.84812, 0.5298 + 0xbfeb2a738eb51f33, 0x3fe0e97d078fd23b, // -0.84893, 0.5285 + 0xbfeb3115a5f37bf4, 0x3fe0ded0b84bc4b5, // -0.84974, 0.5272 + 0xbfeb37b38bb54c09, 0x3fe0d421cf03c12b, // -0.85055, 0.5259 + 0xbfeb3e4d3ef55712, 0x3fe0c9704d5d898f, // -0.85136, 0.52459 + 0xbfeb44e2beaf0a61, 0x3fe0bebc34ff4646, // -0.85216, 0.52328 + 0xbfeb4b7409de7925, 0x3fe0b405878f85ec, // -0.85296, 0.52198 + 0xbfeb52011f805c92, 0x3fe0a94c46b53d0b, // -0.85376, 0.52067 + 0xbfeb5889fe921405, 0x3fe09e907417c5e1, // -0.85456, 0.51936 + 0xbfeb5f0ea611a532, 0x3fe093d2115ee018, // -0.85535, 0.51804 + 0xbfeb658f14fdbc47, 0x3fe089112032b08c, // -0.85615, 0.51673 + 0xbfeb6c0b4a55ac17, 0x3fe07e4da23bc102, // -0.85694, 0.51542 + 0xbfeb728345196e3e, 0x3fe073879922ffed, // -0.85773, 0.5141 + 0xbfeb78f70449a34b, 0x3fe068bf0691c028, // -0.85852, 0.51279 + 0xbfeb7f6686e792ea, 0x3fe05df3ec31b8b6, // -0.8593, 0.51147 + 0xbfeb85d1cbf52c02, 0x3fe053264bad0483, // -0.86009, 0.51015 + 0xbfeb8c38d27504e9, 0x3fe0485626ae221a, // -0.86087, 0.50883 + 0xbfeb929b996a5b7f, 0x3fe03d837edff370, // -0.86165, 0.50751 + 0xbfeb98fa1fd9155e, 0x3fe032ae55edbd95, // -0.86242, 0.50619 + 0xbfeb9f5464c5bffc, 0x3fe027d6ad83287e, // -0.8632, 0.50486 + 0xbfeba5aa673590d2, 0x3fe01cfc874c3eb7, // -0.86397, 0.50354 + 0xbfebabfc262e6586, 0x3fe0121fe4f56d2c, // -0.86474, 0.50221 + 0xbfebb249a0b6c40d, 0x3fe00740c82b82e0, // -0.86551, 0.50089 + 0xbfebb892d5d5dad5, 0x3fdff8be6537615e, // -0.86628, 0.49956 + 0xbfebbed7c49380ea, 0x3fdfe2f64be7120f, // -0.86705, 0.49823 + 0xbfebc5186bf8361d, 0x3fdfcd2947c1ff57, // -0.86781, 0.4969 + 0xbfebcb54cb0d2327, 0x3fdfb7575c24d2de, // -0.86857, 0.49557 + 0xbfebd18ce0dc19d6, 0x3fdfa1808c6cf7e0, // -0.86933, 0.49423 + 0xbfebd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // -0.87009, 0.4929 + 0xbfebddf02cd2b983, 0x3fdf75c44e26a852, // -0.87084, 0.49156 + 0xbfebe41b611154c1, 0x3fdf5fdee656cda3, // -0.8716, 0.49023 + 0xbfebea424837de6d, 0x3fdf49f4a7e97729, // -0.87235, 0.48889 + 0xbfebf064e15377dd, 0x3fdf3405963fd068, // -0.87309, 0.48755 + 0xbfebf6832b71ec5b, 0x3fdf1e11b4bbc35c, // -0.87384, 0.48621 + 0xbfebfc9d25a1b147, 0x3fdf081906bff7fd, // -0.87459, 0.48487 + 0xbfec02b2cef1e641, 0x3fdef21b8fafd3b5, // -0.87533, 0.48353 + 0xbfec08c426725549, 0x3fdedc1952ef78d5, // -0.87607, 0.48218 + 0xbfec0ed12b3372e9, 0x3fdec61253e3c61b, // -0.87681, 0.48084 + 0xbfec14d9dc465e58, 0x3fdeb00695f25620, // -0.87755, 0.47949 + 0xbfec1ade38bce19b, 0x3fde99f61c817eda, // -0.87828, 0.47815 + 0xbfec20de3fa971b0, 0x3fde83e0eaf85113, // -0.87901, 0.4768 + 0xbfec26d9f01f2eaf, 0x3fde6dc704be97e2, // -0.87974, 0.47545 + 0xbfec2cd14931e3f1, 0x3fde57a86d3cd824, // -0.88047, 0.4741 + 0xbfec32c449f60831, 0x3fde418527dc4ffa, // -0.8812, 0.47275 + 0xbfec38b2f180bdb1, 0x3fde2b5d3806f63b, // -0.88192, 0.4714 + 0xbfec3e9d3ee7d262, 0x3fde1530a12779f4, // -0.88264, 0.47004 + 0xbfec44833141c004, 0x3fddfeff66a941de, // -0.88336, 0.46869 + 0xbfec4a64c7a5ac4c, 0x3fdde8c98bf86bd6, // -0.88408, 0.46733 + 0xbfec5042012b6907, 0x3fddd28f1481cc58, // -0.8848, 0.46598 + 0xbfec561adceb743e, 0x3fddbc5003b2edf8, // -0.88551, 0.46462 + 0xbfec5bef59fef85a, 0x3fdda60c5cfa10d8, // -0.88622, 0.46326 + 0xbfec61bf777fcc48, 0x3fdd8fc423c62a25, // -0.88693, 0.4619 + 0xbfec678b3488739b, 0x3fdd79775b86e389, // -0.88764, 0.46054 + 0xbfec6d5290341eb2, 0x3fdd632607ac9aa9, // -0.88835, 0.45918 + 0xbfec7315899eaad7, 0x3fdd4cd02ba8609c, // -0.88905, 0.45781 + 0xbfec78d41fe4a267, 0x3fdd3675caebf962, // -0.88975, 0.45645 + 0xbfec7e8e52233cf3, 0x3fdd2016e8e9db5b, // -0.89045, 0.45508 + 0xbfec84441f785f61, 0x3fdd09b389152ec1, // -0.89115, 0.45372 + 0xbfec89f587029c13, 0x3fdcf34baee1cd21, // -0.89184, 0.45235 + 0xbfec8fa287e13305, 0x3fdcdcdf5dc440ce, // -0.89253, 0.45098 + 0xbfec954b213411f5, 0x3fdcc66e9931c45d, // -0.89322, 0.44961 + 0xbfec9aef521bd480, 0x3fdcaff964a0421d, // -0.89391, 0.44824 + 0xbfeca08f19b9c449, 0x3fdc997fc3865388, // -0.8946, 0.44687 + 0xbfeca62a772fd919, 0x3fdc8301b95b40c2, // -0.89528, 0.4455 + 0xbfecabc169a0b901, 0x3fdc6c7f4997000a, // -0.89597, 0.44412 + 0xbfecb153f02fb87d, 0x3fdc55f877b23537, // -0.89665, 0.44275 + 0xbfecb6e20a00da99, 0x3fdc3f6d47263129, // -0.89732, 0.44137 + 0xbfecbc6bb638d10b, 0x3fdc28ddbb6cf145, // -0.898, 0.43999 + 0xbfecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // -0.89867, 0.43862 + 0xbfecc771c2736c09, 0x3fdbfbb1a05e0edc, // -0.89935, 0.43724 + 0xbfecccee20c2de9f, 0x3fdbe51517ffc0d9, // -0.90002, 0.43586 + 0xbfecd2660e12c1e6, 0x3fdbce744262deee, // -0.90068, 0.43448 + 0xbfecd7d9898b32f6, 0x3fdbb7cf2304bd01, // -0.90135, 0.43309 + 0xbfecdd489254fe65, 0x3fdba125bd63583e, // -0.90201, 0.43171 + 0xbfece2b32799a060, 0x3fdb8a7814fd5693, // -0.90267, 0.43033 + 0xbfece819488344ce, 0x3fdb73c62d520624, // -0.90333, 0.42894 + 0xbfeced7af43cc773, 0x3fdb5d1009e15cc0, // -0.90399, 0.42756 + 0xbfecf2d829f1b40e, 0x3fdb4655ae2bf757, // -0.90464, 0.42617 + 0xbfecf830e8ce467b, 0x3fdb2f971db31972, // -0.9053, 0.42478 + 0xbfecfd852fff6ad4, 0x3fdb18d45bf8aca6, // -0.90595, 0.42339 + 0xbfed02d4feb2bd92, 0x3fdb020d6c7f4009, // -0.9066, 0.422 + 0xbfed082054168bac, 0x3fdaeb4252ca07ab, // -0.90724, 0.42061 + 0xbfed0d672f59d2b9, 0x3fdad473125cdc08, // -0.90789, 0.41922 + 0xbfed12a98fac410c, 0x3fdabd9faebc3980, // -0.90853, 0.41782 + 0xbfed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // -0.90917, 0.41643 + 0xbfed1d20dc40c15c, 0x3fda8fec8bf5b166, // -0.90981, 0.41503 + 0xbfed2255c6e5a4e1, 0x3fda790cd3dbf31a, // -0.91044, 0.41364 + 0xbfed2786335f52fc, 0x3fda622906a70b63, // -0.91107, 0.41224 + 0xbfed2cb220e0ef9f, 0x3fda4b4127dea1e4, // -0.91171, 0.41084 + 0xbfed31d98e9e503a, 0x3fda34553b0afee5, // -0.91234, 0.40944 + 0xbfed36fc7bcbfbdc, 0x3fda1d6543b50ac0, // -0.91296, 0.40804 + 0xbfed3c1ae79f2b4e, 0x3fda067145664d57, // -0.91359, 0.40664 + 0xbfed4134d14dc93a, 0x3fd9ef7943a8ed8a, // -0.91421, 0.40524 + 0xbfed464a380e7242, 0x3fd9d87d4207b0ab, // -0.91483, 0.40384 + 0xbfed4b5b1b187524, 0x3fd9c17d440df9f2, // -0.91545, 0.40243 + 0xbfed506779a3d2d9, 0x3fd9aa794d47c9ee, // -0.91606, 0.40103 + 0xbfed556f52e93eb1, 0x3fd993716141bdfe, // -0.91668, 0.39962 + 0xbfed5a72a6221e73, 0x3fd97c6583890fc2, // -0.91729, 0.39822 + 0xbfed5f7172888a7f, 0x3fd96555b7ab948f, // -0.9179, 0.39681 + 0xbfed646bb7574de5, 0x3fd94e420137bce3, // -0.91851, 0.3954 + 0xbfed696173c9e68b, 0x3fd9372a63bc93d7, // -0.91911, 0.39399 + 0xbfed6e52a71c8547, 0x3fd9200ee2c9be97, // -0.91972, 0.39258 + 0xbfed733f508c0dff, 0x3fd908ef81ef7bd1, // -0.92032, 0.39117 + 0xbfed78276f5617c6, 0x3fd8f1cc44bea329, // -0.92092, 0.38976 + 0xbfed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // -0.92151, 0.38835 + 0xbfed81ea09f38b63, 0x3fd8c37a439f884f, // -0.92211, 0.38693 + 0xbfed86c48445a450, 0x3fd8ac4b86d5ed44, // -0.9227, 0.38552 + 0xbfed8b9a70ef9cb4, 0x3fd89518fbff098e, // -0.92329, 0.3841 + 0xbfed906bcf328d46, 0x3fd87de2a6aea963, // -0.92388, 0.38268 + 0xbfed95389e50429b, 0x3fd866a88a792ea0, // -0.92447, 0.38127 + 0xbfed9a00dd8b3d46, 0x3fd84f6aaaf3903f, // -0.92505, 0.37985 + 0xbfed9ec48c26b1f3, 0x3fd838290bb359c8, // -0.92563, 0.37843 + 0xbfeda383a9668988, 0x3fd820e3b04eaac4, // -0.92621, 0.37701 + 0xbfeda83e348f613b, 0x3fd8099a9c5c362d, // -0.92679, 0.37559 + 0xbfedacf42ce68ab9, 0x3fd7f24dd37341e3, // -0.92736, 0.37416 + 0xbfedb1a591b20c38, 0x3fd7dafd592ba621, // -0.92794, 0.37274 + 0xbfedb6526238a09b, 0x3fd7c3a9311dcce7, // -0.92851, 0.37132 + 0xbfedbafa9dc1b78d, 0x3fd7ac515ee2b172, // -0.92907, 0.36989 + 0xbfedbf9e4395759a, 0x3fd794f5e613dfae, // -0.92964, 0.36847 + 0xbfedc43d52fcb453, 0x3fd77d96ca4b73a6, // -0.93021, 0.36704 + 0xbfedc8d7cb410260, 0x3fd766340f2418f6, // -0.93077, 0.36561 + 0xbfedcd6dabaca3a5, 0x3fd74ecdb8390a3e, // -0.93133, 0.36418 + 0xbfedd1fef38a915a, 0x3fd73763c9261092, // -0.93188, 0.36276 + 0xbfedd68ba2267a25, 0x3fd71ff6458782ec, // -0.93244, 0.36133 + 0xbfeddb13b6ccc23d, 0x3fd7088530fa459e, // -0.93299, 0.3599 + 0xbfeddf9730ca837b, 0x3fd6f1108f1bc9c5, // -0.93354, 0.35846 + 0xbfede4160f6d8d81, 0x3fd6d998638a0cb5, // -0.93409, 0.35703 + 0xbfede890520465ce, 0x3fd6c21cb1e39771, // -0.93464, 0.3556 + 0xbfeded05f7de47da, 0x3fd6aa9d7dc77e16, // -0.93518, 0.35416 + 0xbfedf177004b2534, 0x3fd6931acad55f51, // -0.93573, 0.35273 + 0xbfedf5e36a9ba59c, 0x3fd67b949cad63ca, // -0.93627, 0.35129 + 0xbfedfa4b3621271d, 0x3fd6640af6f03d9e, // -0.9368, 0.34986 + 0xbfedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // -0.93734, 0.34842 + 0xbfee030cee1435b8, 0x3fd634ed533be58e, // -0.93787, 0.34698 + 0xbfee0766d9280f54, 0x3fd61d595c88c203, // -0.9384, 0.34554 + 0xbfee0bbc22bd8349, 0x3fd605c1fcc88f63, // -0.93893, 0.3441 + 0xbfee100cca2980ac, 0x3fd5ee27379ea693, // -0.93946, 0.34266 + 0xbfee1458cec1ad83, 0x3fd5d68910aee686, // -0.93998, 0.34122 + 0xbfee18a02fdc66d9, 0x3fd5bee78b9db3b6, // -0.94051, 0.33978 + 0xbfee1ce2ecd0c0d8, 0x3fd5a742ac0ff78d, // -0.94103, 0.33833 + 0xbfee212104f686e5, 0x3fd58f9a75ab1fdd, // -0.94154, 0.33689 + 0xbfee255a77a63bb8, 0x3fd577eeec151e47, // -0.94206, 0.33545 + 0xbfee298f4439197a, 0x3fd5604012f467b4, // -0.94257, 0.334 + 0xbfee2dbf6a0911d9, 0x3fd5488dedeff3be, // -0.94308, 0.33255 + 0xbfee31eae870ce25, 0x3fd530d880af3c24, // -0.94359, 0.33111 + 0xbfee3611becbaf69, 0x3fd5191fceda3c35, // -0.9441, 0.32966 + 0xbfee3a33ec75ce85, 0x3fd50163dc197047, // -0.9446, 0.32821 + 0xbfee3e5170cbfc46, 0x3fd4e9a4ac15d520, // -0.94511, 0.32676 + 0xbfee426a4b2bc17e, 0x3fd4d1e24278e76a, // -0.94561, 0.32531 + 0xbfee467e7af35f23, 0x3fd4ba1ca2eca31c, // -0.94611, 0.32386 + 0xbfee4a8dff81ce5e, 0x3fd4a253d11b82f3, // -0.9466, 0.32241 + 0xbfee4e98d836c0af, 0x3fd48a87d0b07fd7, // -0.94709, 0.32096 + 0xbfee529f04729ffc, 0x3fd472b8a5571054, // -0.94759, 0.3195 + 0xbfee56a083968eb1, 0x3fd45ae652bb2800, // -0.94807, 0.31805 + 0xbfee5a9d550467d3, 0x3fd44310dc8936f0, // -0.94856, 0.31659 + 0xbfee5e95781ebf1c, 0x3fd42b38466e2928, // -0.94905, 0.31514 + 0xbfee6288ec48e112, 0x3fd4135c94176602, // -0.94953, 0.31368 + 0xbfee6677b0e6d31e, 0x3fd3fb7dc932cfa4, // -0.95001, 0.31222 + 0xbfee6a61c55d53a7, 0x3fd3e39be96ec271, // -0.95049, 0.31077 + 0xbfee6e472911da27, 0x3fd3cbb6f87a146e, // -0.95096, 0.30931 + 0xbfee7227db6a9744, 0x3fd3b3cefa0414b7, // -0.95144, 0.30785 + 0xbfee7603dbce74e9, 0x3fd39be3f1bc8aef, // -0.95191, 0.30639 + 0xbfee79db29a5165a, 0x3fd383f5e353b6aa, // -0.95238, 0.30493 + 0xbfee7dadc456d850, 0x3fd36c04d27a4edf, // -0.95284, 0.30347 + 0xbfee817bab4cd10d, 0x3fd35410c2e18152, // -0.95331, 0.30201 + 0xbfee8544ddf0d075, 0x3fd33c19b83af207, // -0.95377, 0.30054 + 0xbfee89095bad6025, 0x3fd3241fb638baaf, // -0.95423, 0.29908 + 0xbfee8cc923edc388, 0x3fd30c22c08d6a13, // -0.95469, 0.29762 + 0xbfee9084361df7f3, 0x3fd2f422daec0386, // -0.95514, 0.29615 + 0xbfee943a91aab4b4, 0x3fd2dc200907fe51, // -0.95559, 0.29469 + 0xbfee97ec36016b30, 0x3fd2c41a4e954520, // -0.95605, 0.29322 + 0xbfee9b99229046f8, 0x3fd2ac11af483572, // -0.95649, 0.29175 + 0xbfee9f4156c62dda, 0x3fd294062ed59f05, // -0.95694, 0.29028 + 0xbfeea2e4d212c000, 0x3fd27bf7d0f2c346, // -0.95738, 0.28882 + 0xbfeea68393e65800, 0x3fd263e6995554ba, // -0.95783, 0.28735 + 0xbfeeaa1d9bb20af3, 0x3fd24bd28bb37672, // -0.95827, 0.28588 + 0xbfeeadb2e8e7a88e, 0x3fd233bbabc3bb72, // -0.9587, 0.28441 + 0xbfeeb1437af9bb34, 0x3fd21ba1fd3d2623, // -0.95914, 0.28294 + 0xbfeeb4cf515b8811, 0x3fd2038583d727bd, // -0.95957, 0.28146 + 0xbfeeb8566b810f2a, 0x3fd1eb6643499fbb, // -0.96, 0.27999 + 0xbfeebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // -0.96043, 0.27852 + 0xbfeebf5668eaf2ef, 0x3fd1bb1f7b999480, // -0.96086, 0.27705 + 0xbfeec2cf4b1af6b2, 0x3fd1a2f7fbe8f243, // -0.96128, 0.27557 + 0xbfeec6436ee60309, 0x3fd18acdc3f4873a, // -0.9617, 0.2741 + 0xbfeec9b2d3c3bf84, 0x3fd172a0d7765177, // -0.96212, 0.27262 + 0xbfeecd1d792c8f10, 0x3fd15a713a28b9d9, // -0.96254, 0.27115 + 0xbfeed0835e999009, 0x3fd1423eefc69378, // -0.96295, 0.26967 + 0xbfeed3e483849c51, 0x3fd12a09fc0b1b12, // -0.96337, 0.26819 + 0xbfeed740e7684963, 0x3fd111d262b1f677, // -0.96378, 0.26671 + 0xbfeeda9889bfe86a, 0x3fd0f998277733f7, // -0.96418, 0.26523 + 0xbfeeddeb6a078651, 0x3fd0e15b4e1749cd, // -0.96459, 0.26375 + 0xbfeee13987bbebdc, 0x3fd0c91bda4f158d, // -0.96499, 0.26227 + 0xbfeee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // -0.96539, 0.26079 + 0xbfeee7c77961dc9e, 0x3fd09895327b465e, // -0.96579, 0.25931 + 0xbfeeeb074c50a544, 0x3fd0804e05eb661e, // -0.96619, 0.25783 + 0xbfeeee425aa6b09a, 0x3fd068044deab002, // -0.96658, 0.25635 + 0xbfeef178a3e473c2, 0x3fd04fb80e37fdae, // -0.96698, 0.25487 + 0xbfeef4aa278b2032, 0x3fd037694a928cac, // -0.96737, 0.25338 + 0xbfeef7d6e51ca3c0, 0x3fd01f1806b9fdd2, // -0.96775, 0.2519 + 0xbfeefafedc1ba8b7, 0x3fd006c4466e54af, // -0.96814, 0.25041 + 0xbfeefe220c0b95ec, 0x3fcfdcdc1adfedf8, // -0.96852, 0.24893 + 0xbfef014074708ed3, 0x3fcfac2abeff57ff, // -0.9689, 0.24744 + 0xbfef045a14cf738c, 0x3fcf7b7480bd3801, // -0.96928, 0.24596 + 0xbfef076eecade0fa, 0x3fcf4ab9679c9f5c, // -0.96966, 0.24447 + 0xbfef0a7efb9230d7, 0x3fcf19f97b215f1a, // -0.97003, 0.24298 + 0xbfef0d8a410379c5, 0x3fcee934c2d006c7, // -0.9704, 0.24149 + 0xbfef1090bc898f5f, 0x3fceb86b462de348, // -0.97077, 0.24 + 0xbfef13926dad024e, 0x3fce879d0cc0fdaf, // -0.97114, 0.23851 + 0xbfef168f53f7205d, 0x3fce56ca1e101a1b, // -0.9715, 0.23702 + 0xbfef19876ef1f486, 0x3fce25f281a2b684, // -0.97187, 0.23553 + 0xbfef1c7abe284708, 0x3fcdf5163f01099a, // -0.97223, 0.23404 + 0xbfef1f6941259d7a, 0x3fcdc4355db40195, // -0.97258, 0.23255 + 0xbfef2252f7763ada, 0x3fcd934fe5454311, // -0.97294, 0.23106 + 0xbfef2537e0a71f9f, 0x3fcd6265dd3f27e3, // -0.97329, 0.22957 + 0xbfef2817fc4609ce, 0x3fcd31774d2cbdee, // -0.97364, 0.22807 + 0xbfef2af349e17507, 0x3fcd00843c99c5f9, // -0.97399, 0.22658 + 0xbfef2dc9c9089a9d, 0x3fcccf8cb312b286, // -0.97434, 0.22508 + 0xbfef309b794b719f, 0x3fcc9e90b824a6a9, // -0.97468, 0.22359 + 0xbfef33685a3aaef0, 0x3fcc6d90535d74dc, // -0.97503, 0.22209 + 0xbfef36306b67c556, 0x3fcc3c8b8c4b9dd7, // -0.97536, 0.2206 + 0xbfef38f3ac64e589, 0x3fcc0b826a7e4f63, // -0.9757, 0.2191 + 0xbfef3bb21cc4fe47, 0x3fcbda74f5856330, // -0.97604, 0.2176 + 0xbfef3e6bbc1bbc65, 0x3fcba96334f15dad, // -0.97637, 0.21611 + 0xbfef412089fd8adc, 0x3fcb784d30536cda, // -0.9767, 0.21461 + 0xbfef43d085ff92dd, 0x3fcb4732ef3d6722, // -0.97703, 0.21311 + 0xbfef467bafb7bbe0, 0x3fcb16147941ca2a, // -0.97735, 0.21161 + 0xbfef492206bcabb4, 0x3fcae4f1d5f3b9ab, // -0.97768, 0.21011 + 0xbfef4bc38aa5c694, 0x3fcab3cb0ce6fe44, // -0.978, 0.20861 + 0xbfef4e603b0b2f2d, 0x3fca82a025b00451, // -0.97832, 0.20711 + 0xbfef50f81785c6b9, 0x3fca517127e3dabc, // -0.97863, 0.20561 + 0xbfef538b1faf2d07, 0x3fca203e1b1831da, // -0.97895, 0.20411 + 0xbfef56195321c090, 0x3fc9ef0706e35a35, // -0.97926, 0.20261 + 0xbfef58a2b1789e84, 0x3fc9bdcbf2dc4366, // -0.97957, 0.2011 + 0xbfef5b273a4fa2d9, 0x3fc98c8ce69a7aec, // -0.97988, 0.1996 + 0xbfef5da6ed43685d, 0x3fc95b49e9b62af9, // -0.98018, 0.1981 + 0xbfef6021c9f148c2, 0x3fc92a0303c8194f, // -0.98048, 0.19659 + 0xbfef6297cff75cb0, 0x3fc8f8b83c69a60a, // -0.98079, 0.19509 + 0xbfef6508fef47bd5, 0x3fc8c7699b34ca7e, // -0.98108, 0.19359 + 0xbfef677556883cee, 0x3fc8961727c41804, // -0.98138, 0.19208 + 0xbfef69dcd652f5de, 0x3fc864c0e9b2b6cf, // -0.98167, 0.19057 + 0xbfef6c3f7df5bbb7, 0x3fc83366e89c64c5, // -0.98196, 0.18907 + 0xbfef6e9d4d1262ca, 0x3fc802092c1d744b, // -0.98225, 0.18756 + 0xbfef70f6434b7eb7, 0x3fc7d0a7bbd2cb1b, // -0.98254, 0.18606 + 0xbfef734a60446279, 0x3fc79f429f59e11d, // -0.98282, 0.18455 + 0xbfef7599a3a12077, 0x3fc76dd9de50bf31, // -0.98311, 0.18304 + 0xbfef77e40d068a90, 0x3fc73c6d8055fe0a, // -0.98339, 0.18153 + 0xbfef7a299c1a322a, 0x3fc70afd8d08c4ff, // -0.98366, 0.18002 + 0xbfef7c6a50826840, 0x3fc6d98a0c08c8da, // -0.98394, 0.17851 + 0xbfef7ea629e63d6e, 0x3fc6a81304f64ab2, // -0.98421, 0.177 + 0xbfef80dd27ed8204, 0x3fc676987f7216b8, // -0.98448, 0.17549 + 0xbfef830f4a40c60c, 0x3fc6451a831d830d, // -0.98475, 0.17398 + 0xbfef853c9089595e, 0x3fc61399179a6e94, // -0.98501, 0.17247 + 0xbfef8764fa714ba9, 0x3fc5e214448b3fc6, // -0.98528, 0.17096 + 0xbfef898887a36c84, 0x3fc5b08c1192e381, // -0.98554, 0.16945 + 0xbfef8ba737cb4b78, 0x3fc57f008654cbde, // -0.9858, 0.16794 + 0xbfef8dc10a95380d, 0x3fc54d71aa74ef02, // -0.98605, 0.16643 + 0xbfef8fd5ffae41db, 0x3fc51bdf8597c5f2, // -0.98631, 0.16491 + 0xbfef91e616c43891, 0x3fc4ea4a1f624b61, // -0.98656, 0.1634 + 0xbfef93f14f85ac08, 0x3fc4b8b17f79fa88, // -0.98681, 0.16189 + 0xbfef95f7a9a1ec47, 0x3fc48715ad84cdf5, // -0.98706, 0.16037 + 0xbfef97f924c9099b, 0x3fc45576b1293e5a, // -0.9873, 0.15886 + 0xbfef99f5c0abd496, 0x3fc423d4920e4166, // -0.98754, 0.15734 + 0xbfef9bed7cfbde29, 0x3fc3f22f57db4893, // -0.98778, 0.15583 + 0xbfef9de0596b77a3, 0x3fc3c0870a383ff6, // -0.98802, 0.15431 + 0xbfef9fce55adb2c8, 0x3fc38edbb0cd8d14, // -0.98826, 0.1528 + 0xbfefa1b7717661d5, 0x3fc35d2d53440db2, // -0.98849, 0.15128 + 0xbfefa39bac7a1791, 0x3fc32b7bf94516a7, // -0.98872, 0.14976 + 0xbfefa57b066e2754, 0x3fc2f9c7aa7a72af, // -0.98895, 0.14825 + 0xbfefa7557f08a517, 0x3fc2c8106e8e613a, // -0.98918, 0.14673 + 0xbfefa92b1600657c, 0x3fc296564d2b953e, // -0.9894, 0.14521 + 0xbfefaafbcb0cfddc, 0x3fc264994dfd340a, // -0.98962, 0.1437 + 0xbfefacc79de6c44f, 0x3fc232d978aed413, // -0.98984, 0.14218 + 0xbfefae8e8e46cfbb, 0x3fc20116d4ec7bce, // -0.99006, 0.14066 + 0xbfefb0509be6f7db, 0x3fc1cf516a62a077, // -0.99027, 0.13914 + 0xbfefb20dc681d54d, 0x3fc19d8940be24e7, // -0.99049, 0.13762 + 0xbfefb3c60dd2c199, 0x3fc16bbe5fac5865, // -0.9907, 0.1361 + 0xbfefb5797195d741, 0x3fc139f0cedaf576, // -0.9909, 0.13458 + 0xbfefb727f187f1c7, 0x3fc1082095f820b0, // -0.99111, 0.13306 + 0xbfefb8d18d66adb7, 0x3fc0d64dbcb26786, // -0.99131, 0.13154 + 0xbfefba7644f068b5, 0x3fc0a4784ab8bf1d, // -0.99151, 0.13002 + 0xbfefbc1617e44186, 0x3fc072a047ba831d, // -0.99171, 0.1285 + 0xbfefbdb106021816, 0x3fc040c5bb67747e, // -0.99191, 0.12698 + 0xbfefbf470f0a8d88, 0x3fc00ee8ad6fb85b, // -0.9921, 0.12545 + 0xbfefc0d832bf043a, 0x3fbfba124b07ad85, // -0.99229, 0.12393 + 0xbfefc26470e19fd3, 0x3fbf564e56a9730e, // -0.99248, 0.12241 + 0xbfefc3ebc935454c, 0x3fbef2858d27561b, // -0.99267, 0.12089 + 0xbfefc56e3b7d9af6, 0x3fbe8eb7fde4aa3e, // -0.99285, 0.11937 + 0xbfefc6ebc77f0887, 0x3fbe2ae5b8457f77, // -0.99303, 0.11784 + 0xbfefc8646cfeb721, 0x3fbdc70ecbae9fc8, // -0.99321, 0.11632 + 0xbfefc9d82bc2915e, 0x3fbd633347858ce4, // -0.99339, 0.11479 + 0xbfefcb4703914354, 0x3fbcff533b307dc1, // -0.99356, 0.11327 + 0xbfefccb0f4323aa3, 0x3fbc9b6eb6165c42, // -0.99374, 0.11175 + 0xbfefce15fd6da67b, 0x3fbc3785c79ec2d5, // -0.99391, 0.11022 + 0xbfefcf761f0c77a3, 0x3fbbd3987f31fa0e, // -0.99407, 0.1087 + 0xbfefd0d158d86087, 0x3fbb6fa6ec38f64c, // -0.99424, 0.10717 + 0xbfefd227aa9bd53b, 0x3fbb0bb11e1d5559, // -0.9944, 0.10565 + 0xbfefd37914220b84, 0x3fbaa7b724495c04, // -0.99456, 0.10412 + 0xbfefd4c59536fae4, 0x3fba43b90e27f3c4, // -0.99472, 0.1026 + 0xbfefd60d2da75c9e, 0x3fb9dfb6eb24a85c, // -0.99488, 0.10107 + 0xbfefd74fdd40abbf, 0x3fb97bb0caaba56f, // -0.99503, 0.099544 + 0xbfefd88da3d12526, 0x3fb917a6bc29b42c, // -0.99518, 0.098017 + 0xbfefd9c68127c78c, 0x3fb8b398cf0c38e0, // -0.99533, 0.09649 + 0xbfefdafa7514538c, 0x3fb84f8712c130a0, // -0.99548, 0.094963 + 0xbfefdc297f674ba9, 0x3fb7eb7196b72ee4, // -0.99563, 0.093436 + 0xbfefdd539ff1f456, 0x3fb787586a5d5b21, // -0.99577, 0.091909 + 0xbfefde78d68653fd, 0x3fb7233b9d236e71, // -0.99591, 0.090381 + 0xbfefdf9922f73307, 0x3fb6bf1b3e79b129, // -0.99604, 0.088854 + 0xbfefe0b485181be3, 0x3fb65af75dd0f87b, // -0.99618, 0.087326 + 0xbfefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // -0.99631, 0.085797 + 0xbfefe2dc89bbff08, 0x3fb592a554489bc8, // -0.99644, 0.084269 + 0xbfefe3e92be9d886, 0x3fb52e774a4d4d0a, // -0.99657, 0.08274 + 0xbfefe4f0e31d7a4a, 0x3fb4ca45fc1ba8b6, // -0.9967, 0.081211 + 0xbfefe5f3af2e3940, 0x3fb4661179272096, // -0.99682, 0.079682 + 0xbfefe6f18ff42c84, 0x3fb401d9d0e3a507, // -0.99694, 0.078153 + 0xbfefe7ea85482d60, 0x3fb39d9f12c5a299, // -0.99706, 0.076624 + 0xbfefe8de8f03d75c, 0x3fb339614e41ffa5, // -0.99718, 0.075094 + 0xbfefe9cdad01883a, 0x3fb2d52092ce19f6, // -0.99729, 0.073565 + 0xbfefeab7df1c6005, 0x3fb270dcefdfc45b, // -0.9974, 0.072035 + 0xbfefeb9d2530410f, 0x3fb20c9674ed444c, // -0.99751, 0.070505 + 0xbfefec7d7f19cffc, 0x3fb1a84d316d4f8a, // -0.99762, 0.068974 + 0xbfefed58ecb673c4, 0x3fb1440134d709b2, // -0.99772, 0.067444 + 0xbfefee2f6de455ba, 0x3fb0dfb28ea201e6, // -0.99783, 0.065913 + 0xbfefef0102826191, 0x3fb07b614e463064, // -0.99793, 0.064383 + 0xbfefefcdaa704562, 0x3fb0170d833bf421, // -0.99802, 0.062852 + 0xbfeff095658e71ad, 0x3faf656e79f820e0, // -0.99812, 0.061321 + 0xbfeff15833be1965, 0x3fae9cbd15ff5527, // -0.99821, 0.05979 + 0xbfeff21614e131ed, 0x3fadd406f9808ec8, // -0.9983, 0.058258 + 0xbfeff2cf08da7321, 0x3fad0b4c436f91d0, // -0.99839, 0.056727 + 0xbfeff3830f8d575c, 0x3fac428d12c0d7e3, // -0.99848, 0.055195 + 0xbfeff43228de1b77, 0x3fab79c986698b78, // -0.99856, 0.053664 + 0xbfeff4dc54b1bed3, 0x3faab101bd5f8317, // -0.99864, 0.052132 + 0xbfeff58192ee0358, 0x3fa9e835d6993c87, // -0.99872, 0.0506 + 0xbfeff621e3796d7e, 0x3fa91f65f10dd814, // -0.9988, 0.049068 + 0xbfeff6bd463b444d, 0x3fa856922bb513c1, // -0.99887, 0.047535 + 0xbfeff753bb1b9164, 0x3fa78dbaa5874685, // -0.99894, 0.046003 + 0xbfeff7e5420320f9, 0x3fa6c4df7d7d5b84, // -0.99901, 0.044471 + 0xbfeff871dadb81df, 0x3fa5fc00d290cd43, // -0.99908, 0.042938 + 0xbfeff8f9858f058b, 0x3fa5331ec3bba0eb, // -0.99914, 0.041406 + 0xbfeff97c4208c014, 0x3fa46a396ff86179, // -0.9992, 0.039873 + 0xbfeff9fa10348837, 0x3fa3a150f6421afc, // -0.99926, 0.03834 + 0xbfeffa72effef75d, 0x3fa2d865759455cd, // -0.99932, 0.036807 + 0xbfeffae6e1556998, 0x3fa20f770ceb11c6, // -0.99938, 0.035274 + 0xbfeffb55e425fdae, 0x3fa14685db42c17e, // -0.99943, 0.033741 + 0xbfeffbbff85f9515, 0x3fa07d91ff984580, // -0.99948, 0.032208 + 0xbfeffc251df1d3f8, 0x3f9f693731d1cf01, // -0.99953, 0.030675 + 0xbfeffc8554cd213a, 0x3f9dd7458c64ab39, // -0.99958, 0.029142 + 0xbfeffce09ce2a679, 0x3f9c454f4ce53b1c, // -0.99962, 0.027608 + 0xbfeffd36f624500c, 0x3f9ab354b1504fca, // -0.99966, 0.026075 + 0xbfeffd886084cd0d, 0x3f992155f7a3667e, // -0.9997, 0.024541 + 0xbfeffdd4dbf78f52, 0x3f978f535ddc9f03, // -0.99974, 0.023008 + 0xbfeffe1c6870cb77, 0x3f95fd4d21fab226, // -0.99977, 0.021474 + 0xbfeffe5f05e578db, 0x3f946b4381fce81c, // -0.9998, 0.01994 + 0xbfeffe9cb44b51a1, 0x3f92d936bbe30efd, // -0.99983, 0.018407 + 0xbfeffed57398d2b7, 0x3f9147270dad7132, // -0.99986, 0.016873 + 0xbfefff0943c53bd1, 0x3f8f6a296ab997ca, // -0.99988, 0.015339 + 0xbfefff3824c88f6f, 0x3f8c45ffe1e48ad9, // -0.9999, 0.013805 + 0xbfefff62169b92db, 0x3f8921d1fcdec784, // -0.99992, 0.012272 + 0xbfefff871937ce2f, 0x3f85fda037ac05e0, // -0.99994, 0.010738 + 0xbfefffa72c978c4f, 0x3f82d96b0e509703, // -0.99996, 0.0092038 + 0xbfefffc250b5daef, 0x3f7f6a65f9a2a3c5, // -0.99997, 0.0076698 + 0xbfefffd8858e8a92, 0x3f7921f0fe670071, // -0.99998, 0.0061359 + 0xbfefffe9cb1e2e8d, 0x3f72d97822f996bc, // -0.99999, 0.0046019 + 0xbfeffff621621d02, 0x3f6921f8becca4ba, // -1, 0.003068 + 0xbfeffffd88586ee6, 0x3f5921faaee6472d, // -1, 0.001534 + 0xbff0000000000000, 0x0000000000000000, // -1, 0 + 0xbfeffffd88586ee6, 0xbf5921faaee6472d, // -1, -0.001534 + 0xbfeffff621621d02, 0xbf6921f8becca4ba, // -1, -0.003068 + 0xbfefffe9cb1e2e8d, 0xbf72d97822f996bc, // -0.99999,-0.0046019 + 0xbfefffd8858e8a92, 0xbf7921f0fe670071, // -0.99998,-0.0061359 + 0xbfefffc250b5daef, 0xbf7f6a65f9a2a3c5, // -0.99997,-0.0076698 + 0xbfefffa72c978c4f, 0xbf82d96b0e509703, // -0.99996,-0.0092038 + 0xbfefff871937ce2f, 0xbf85fda037ac05e0, // -0.99994, -0.010738 + 0xbfefff62169b92db, 0xbf8921d1fcdec784, // -0.99992, -0.012272 + 0xbfefff3824c88f6f, 0xbf8c45ffe1e48ad9, // -0.9999, -0.013805 + 0xbfefff0943c53bd1, 0xbf8f6a296ab997ca, // -0.99988, -0.015339 + 0xbfeffed57398d2b7, 0xbf9147270dad7132, // -0.99986, -0.016873 + 0xbfeffe9cb44b51a1, 0xbf92d936bbe30efd, // -0.99983, -0.018407 + 0xbfeffe5f05e578db, 0xbf946b4381fce81c, // -0.9998, -0.01994 + 0xbfeffe1c6870cb77, 0xbf95fd4d21fab226, // -0.99977, -0.021474 + 0xbfeffdd4dbf78f52, 0xbf978f535ddc9f03, // -0.99974, -0.023008 + 0xbfeffd886084cd0d, 0xbf992155f7a3667e, // -0.9997, -0.024541 + 0xbfeffd36f624500c, 0xbf9ab354b1504fca, // -0.99966, -0.026075 + 0xbfeffce09ce2a679, 0xbf9c454f4ce53b1c, // -0.99962, -0.027608 + 0xbfeffc8554cd213a, 0xbf9dd7458c64ab39, // -0.99958, -0.029142 + 0xbfeffc251df1d3f8, 0xbf9f693731d1cf01, // -0.99953, -0.030675 + 0xbfeffbbff85f9515, 0xbfa07d91ff984580, // -0.99948, -0.032208 + 0xbfeffb55e425fdae, 0xbfa14685db42c17e, // -0.99943, -0.033741 + 0xbfeffae6e1556998, 0xbfa20f770ceb11c6, // -0.99938, -0.035274 + 0xbfeffa72effef75d, 0xbfa2d865759455cd, // -0.99932, -0.036807 + 0xbfeff9fa10348837, 0xbfa3a150f6421afc, // -0.99926, -0.03834 + 0xbfeff97c4208c014, 0xbfa46a396ff86179, // -0.9992, -0.039873 + 0xbfeff8f9858f058b, 0xbfa5331ec3bba0eb, // -0.99914, -0.041406 + 0xbfeff871dadb81df, 0xbfa5fc00d290cd43, // -0.99908, -0.042938 + 0xbfeff7e5420320f9, 0xbfa6c4df7d7d5b84, // -0.99901, -0.044471 + 0xbfeff753bb1b9164, 0xbfa78dbaa5874685, // -0.99894, -0.046003 + 0xbfeff6bd463b444d, 0xbfa856922bb513c1, // -0.99887, -0.047535 + 0xbfeff621e3796d7e, 0xbfa91f65f10dd814, // -0.9988, -0.049068 + 0xbfeff58192ee0358, 0xbfa9e835d6993c87, // -0.99872, -0.0506 + 0xbfeff4dc54b1bed3, 0xbfaab101bd5f8317, // -0.99864, -0.052132 + 0xbfeff43228de1b77, 0xbfab79c986698b78, // -0.99856, -0.053664 + 0xbfeff3830f8d575c, 0xbfac428d12c0d7e3, // -0.99848, -0.055195 + 0xbfeff2cf08da7321, 0xbfad0b4c436f91d0, // -0.99839, -0.056727 + 0xbfeff21614e131ed, 0xbfadd406f9808ec8, // -0.9983, -0.058258 + 0xbfeff15833be1965, 0xbfae9cbd15ff5527, // -0.99821, -0.05979 + 0xbfeff095658e71ad, 0xbfaf656e79f820e0, // -0.99812, -0.061321 + 0xbfefefcdaa704562, 0xbfb0170d833bf421, // -0.99802, -0.062852 + 0xbfefef0102826191, 0xbfb07b614e463064, // -0.99793, -0.064383 + 0xbfefee2f6de455ba, 0xbfb0dfb28ea201e6, // -0.99783, -0.065913 + 0xbfefed58ecb673c4, 0xbfb1440134d709b2, // -0.99772, -0.067444 + 0xbfefec7d7f19cffc, 0xbfb1a84d316d4f8a, // -0.99762, -0.068974 + 0xbfefeb9d2530410f, 0xbfb20c9674ed444c, // -0.99751, -0.070505 + 0xbfefeab7df1c6005, 0xbfb270dcefdfc45b, // -0.9974, -0.072035 + 0xbfefe9cdad01883a, 0xbfb2d52092ce19f6, // -0.99729, -0.073565 + 0xbfefe8de8f03d75c, 0xbfb339614e41ffa5, // -0.99718, -0.075094 + 0xbfefe7ea85482d60, 0xbfb39d9f12c5a299, // -0.99706, -0.076624 + 0xbfefe6f18ff42c84, 0xbfb401d9d0e3a507, // -0.99694, -0.078153 + 0xbfefe5f3af2e3940, 0xbfb4661179272096, // -0.99682, -0.079682 + 0xbfefe4f0e31d7a4a, 0xbfb4ca45fc1ba8b6, // -0.9967, -0.081211 + 0xbfefe3e92be9d886, 0xbfb52e774a4d4d0a, // -0.99657, -0.08274 + 0xbfefe2dc89bbff08, 0xbfb592a554489bc8, // -0.99644, -0.084269 + 0xbfefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // -0.99631, -0.085797 + 0xbfefe0b485181be3, 0xbfb65af75dd0f87b, // -0.99618, -0.087326 + 0xbfefdf9922f73307, 0xbfb6bf1b3e79b129, // -0.99604, -0.088854 + 0xbfefde78d68653fd, 0xbfb7233b9d236e71, // -0.99591, -0.090381 + 0xbfefdd539ff1f456, 0xbfb787586a5d5b21, // -0.99577, -0.091909 + 0xbfefdc297f674ba9, 0xbfb7eb7196b72ee4, // -0.99563, -0.093436 + 0xbfefdafa7514538c, 0xbfb84f8712c130a0, // -0.99548, -0.094963 + 0xbfefd9c68127c78c, 0xbfb8b398cf0c38e0, // -0.99533, -0.09649 + 0xbfefd88da3d12526, 0xbfb917a6bc29b42c, // -0.99518, -0.098017 + 0xbfefd74fdd40abbf, 0xbfb97bb0caaba56f, // -0.99503, -0.099544 + 0xbfefd60d2da75c9e, 0xbfb9dfb6eb24a85c, // -0.99488, -0.10107 + 0xbfefd4c59536fae4, 0xbfba43b90e27f3c4, // -0.99472, -0.1026 + 0xbfefd37914220b84, 0xbfbaa7b724495c04, // -0.99456, -0.10412 + 0xbfefd227aa9bd53b, 0xbfbb0bb11e1d5559, // -0.9944, -0.10565 + 0xbfefd0d158d86087, 0xbfbb6fa6ec38f64c, // -0.99424, -0.10717 + 0xbfefcf761f0c77a3, 0xbfbbd3987f31fa0e, // -0.99407, -0.1087 + 0xbfefce15fd6da67b, 0xbfbc3785c79ec2d5, // -0.99391, -0.11022 + 0xbfefccb0f4323aa3, 0xbfbc9b6eb6165c42, // -0.99374, -0.11175 + 0xbfefcb4703914354, 0xbfbcff533b307dc1, // -0.99356, -0.11327 + 0xbfefc9d82bc2915e, 0xbfbd633347858ce4, // -0.99339, -0.11479 + 0xbfefc8646cfeb721, 0xbfbdc70ecbae9fc8, // -0.99321, -0.11632 + 0xbfefc6ebc77f0887, 0xbfbe2ae5b8457f77, // -0.99303, -0.11784 + 0xbfefc56e3b7d9af6, 0xbfbe8eb7fde4aa3e, // -0.99285, -0.11937 + 0xbfefc3ebc935454c, 0xbfbef2858d27561b, // -0.99267, -0.12089 + 0xbfefc26470e19fd3, 0xbfbf564e56a9730e, // -0.99248, -0.12241 + 0xbfefc0d832bf043a, 0xbfbfba124b07ad85, // -0.99229, -0.12393 + 0xbfefbf470f0a8d88, 0xbfc00ee8ad6fb85b, // -0.9921, -0.12545 + 0xbfefbdb106021816, 0xbfc040c5bb67747e, // -0.99191, -0.12698 + 0xbfefbc1617e44186, 0xbfc072a047ba831d, // -0.99171, -0.1285 + 0xbfefba7644f068b5, 0xbfc0a4784ab8bf1d, // -0.99151, -0.13002 + 0xbfefb8d18d66adb7, 0xbfc0d64dbcb26786, // -0.99131, -0.13154 + 0xbfefb727f187f1c7, 0xbfc1082095f820b0, // -0.99111, -0.13306 + 0xbfefb5797195d741, 0xbfc139f0cedaf576, // -0.9909, -0.13458 + 0xbfefb3c60dd2c199, 0xbfc16bbe5fac5865, // -0.9907, -0.1361 + 0xbfefb20dc681d54d, 0xbfc19d8940be24e7, // -0.99049, -0.13762 + 0xbfefb0509be6f7db, 0xbfc1cf516a62a077, // -0.99027, -0.13914 + 0xbfefae8e8e46cfbb, 0xbfc20116d4ec7bce, // -0.99006, -0.14066 + 0xbfefacc79de6c44f, 0xbfc232d978aed413, // -0.98984, -0.14218 + 0xbfefaafbcb0cfddc, 0xbfc264994dfd340a, // -0.98962, -0.1437 + 0xbfefa92b1600657c, 0xbfc296564d2b953e, // -0.9894, -0.14521 + 0xbfefa7557f08a517, 0xbfc2c8106e8e613a, // -0.98918, -0.14673 + 0xbfefa57b066e2754, 0xbfc2f9c7aa7a72af, // -0.98895, -0.14825 + 0xbfefa39bac7a1791, 0xbfc32b7bf94516a7, // -0.98872, -0.14976 + 0xbfefa1b7717661d5, 0xbfc35d2d53440db2, // -0.98849, -0.15128 + 0xbfef9fce55adb2c8, 0xbfc38edbb0cd8d14, // -0.98826, -0.1528 + 0xbfef9de0596b77a3, 0xbfc3c0870a383ff6, // -0.98802, -0.15431 + 0xbfef9bed7cfbde29, 0xbfc3f22f57db4893, // -0.98778, -0.15583 + 0xbfef99f5c0abd496, 0xbfc423d4920e4166, // -0.98754, -0.15734 + 0xbfef97f924c9099b, 0xbfc45576b1293e5a, // -0.9873, -0.15886 + 0xbfef95f7a9a1ec47, 0xbfc48715ad84cdf5, // -0.98706, -0.16037 + 0xbfef93f14f85ac08, 0xbfc4b8b17f79fa88, // -0.98681, -0.16189 + 0xbfef91e616c43891, 0xbfc4ea4a1f624b61, // -0.98656, -0.1634 + 0xbfef8fd5ffae41db, 0xbfc51bdf8597c5f2, // -0.98631, -0.16491 + 0xbfef8dc10a95380d, 0xbfc54d71aa74ef02, // -0.98605, -0.16643 + 0xbfef8ba737cb4b78, 0xbfc57f008654cbde, // -0.9858, -0.16794 + 0xbfef898887a36c84, 0xbfc5b08c1192e381, // -0.98554, -0.16945 + 0xbfef8764fa714ba9, 0xbfc5e214448b3fc6, // -0.98528, -0.17096 + 0xbfef853c9089595e, 0xbfc61399179a6e94, // -0.98501, -0.17247 + 0xbfef830f4a40c60c, 0xbfc6451a831d830d, // -0.98475, -0.17398 + 0xbfef80dd27ed8204, 0xbfc676987f7216b8, // -0.98448, -0.17549 + 0xbfef7ea629e63d6e, 0xbfc6a81304f64ab2, // -0.98421, -0.177 + 0xbfef7c6a50826840, 0xbfc6d98a0c08c8da, // -0.98394, -0.17851 + 0xbfef7a299c1a322a, 0xbfc70afd8d08c4ff, // -0.98366, -0.18002 + 0xbfef77e40d068a90, 0xbfc73c6d8055fe0a, // -0.98339, -0.18153 + 0xbfef7599a3a12077, 0xbfc76dd9de50bf31, // -0.98311, -0.18304 + 0xbfef734a60446279, 0xbfc79f429f59e11d, // -0.98282, -0.18455 + 0xbfef70f6434b7eb7, 0xbfc7d0a7bbd2cb1b, // -0.98254, -0.18606 + 0xbfef6e9d4d1262ca, 0xbfc802092c1d744b, // -0.98225, -0.18756 + 0xbfef6c3f7df5bbb7, 0xbfc83366e89c64c5, // -0.98196, -0.18907 + 0xbfef69dcd652f5de, 0xbfc864c0e9b2b6cf, // -0.98167, -0.19057 + 0xbfef677556883cee, 0xbfc8961727c41804, // -0.98138, -0.19208 + 0xbfef6508fef47bd5, 0xbfc8c7699b34ca7e, // -0.98108, -0.19359 + 0xbfef6297cff75cb0, 0xbfc8f8b83c69a60a, // -0.98079, -0.19509 + 0xbfef6021c9f148c2, 0xbfc92a0303c8194f, // -0.98048, -0.19659 + 0xbfef5da6ed43685d, 0xbfc95b49e9b62af9, // -0.98018, -0.1981 + 0xbfef5b273a4fa2d9, 0xbfc98c8ce69a7aec, // -0.97988, -0.1996 + 0xbfef58a2b1789e84, 0xbfc9bdcbf2dc4366, // -0.97957, -0.2011 + 0xbfef56195321c090, 0xbfc9ef0706e35a35, // -0.97926, -0.20261 + 0xbfef538b1faf2d07, 0xbfca203e1b1831da, // -0.97895, -0.20411 + 0xbfef50f81785c6b9, 0xbfca517127e3dabc, // -0.97863, -0.20561 + 0xbfef4e603b0b2f2d, 0xbfca82a025b00451, // -0.97832, -0.20711 + 0xbfef4bc38aa5c694, 0xbfcab3cb0ce6fe44, // -0.978, -0.20861 + 0xbfef492206bcabb4, 0xbfcae4f1d5f3b9ab, // -0.97768, -0.21011 + 0xbfef467bafb7bbe0, 0xbfcb16147941ca2a, // -0.97735, -0.21161 + 0xbfef43d085ff92dd, 0xbfcb4732ef3d6722, // -0.97703, -0.21311 + 0xbfef412089fd8adc, 0xbfcb784d30536cda, // -0.9767, -0.21461 + 0xbfef3e6bbc1bbc65, 0xbfcba96334f15dad, // -0.97637, -0.21611 + 0xbfef3bb21cc4fe47, 0xbfcbda74f5856330, // -0.97604, -0.2176 + 0xbfef38f3ac64e589, 0xbfcc0b826a7e4f63, // -0.9757, -0.2191 + 0xbfef36306b67c556, 0xbfcc3c8b8c4b9dd7, // -0.97536, -0.2206 + 0xbfef33685a3aaef0, 0xbfcc6d90535d74dc, // -0.97503, -0.22209 + 0xbfef309b794b719f, 0xbfcc9e90b824a6a9, // -0.97468, -0.22359 + 0xbfef2dc9c9089a9d, 0xbfcccf8cb312b286, // -0.97434, -0.22508 + 0xbfef2af349e17507, 0xbfcd00843c99c5f9, // -0.97399, -0.22658 + 0xbfef2817fc4609ce, 0xbfcd31774d2cbdee, // -0.97364, -0.22807 + 0xbfef2537e0a71f9f, 0xbfcd6265dd3f27e3, // -0.97329, -0.22957 + 0xbfef2252f7763ada, 0xbfcd934fe5454311, // -0.97294, -0.23106 + 0xbfef1f6941259d7a, 0xbfcdc4355db40195, // -0.97258, -0.23255 + 0xbfef1c7abe284708, 0xbfcdf5163f01099a, // -0.97223, -0.23404 + 0xbfef19876ef1f486, 0xbfce25f281a2b684, // -0.97187, -0.23553 + 0xbfef168f53f7205d, 0xbfce56ca1e101a1b, // -0.9715, -0.23702 + 0xbfef13926dad024e, 0xbfce879d0cc0fdaf, // -0.97114, -0.23851 + 0xbfef1090bc898f5f, 0xbfceb86b462de348, // -0.97077, -0.24 + 0xbfef0d8a410379c5, 0xbfcee934c2d006c7, // -0.9704, -0.24149 + 0xbfef0a7efb9230d7, 0xbfcf19f97b215f1a, // -0.97003, -0.24298 + 0xbfef076eecade0fa, 0xbfcf4ab9679c9f5c, // -0.96966, -0.24447 + 0xbfef045a14cf738c, 0xbfcf7b7480bd3801, // -0.96928, -0.24596 + 0xbfef014074708ed3, 0xbfcfac2abeff57ff, // -0.9689, -0.24744 + 0xbfeefe220c0b95ec, 0xbfcfdcdc1adfedf8, // -0.96852, -0.24893 + 0xbfeefafedc1ba8b7, 0xbfd006c4466e54af, // -0.96814, -0.25041 + 0xbfeef7d6e51ca3c0, 0xbfd01f1806b9fdd2, // -0.96775, -0.2519 + 0xbfeef4aa278b2032, 0xbfd037694a928cac, // -0.96737, -0.25338 + 0xbfeef178a3e473c2, 0xbfd04fb80e37fdae, // -0.96698, -0.25487 + 0xbfeeee425aa6b09a, 0xbfd068044deab002, // -0.96658, -0.25635 + 0xbfeeeb074c50a544, 0xbfd0804e05eb661e, // -0.96619, -0.25783 + 0xbfeee7c77961dc9e, 0xbfd09895327b465e, // -0.96579, -0.25931 + 0xbfeee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // -0.96539, -0.26079 + 0xbfeee13987bbebdc, 0xbfd0c91bda4f158d, // -0.96499, -0.26227 + 0xbfeeddeb6a078651, 0xbfd0e15b4e1749cd, // -0.96459, -0.26375 + 0xbfeeda9889bfe86a, 0xbfd0f998277733f7, // -0.96418, -0.26523 + 0xbfeed740e7684963, 0xbfd111d262b1f677, // -0.96378, -0.26671 + 0xbfeed3e483849c51, 0xbfd12a09fc0b1b12, // -0.96337, -0.26819 + 0xbfeed0835e999009, 0xbfd1423eefc69378, // -0.96295, -0.26967 + 0xbfeecd1d792c8f10, 0xbfd15a713a28b9d9, // -0.96254, -0.27115 + 0xbfeec9b2d3c3bf84, 0xbfd172a0d7765177, // -0.96212, -0.27262 + 0xbfeec6436ee60309, 0xbfd18acdc3f4873a, // -0.9617, -0.2741 + 0xbfeec2cf4b1af6b2, 0xbfd1a2f7fbe8f243, // -0.96128, -0.27557 + 0xbfeebf5668eaf2ef, 0xbfd1bb1f7b999480, // -0.96086, -0.27705 + 0xbfeebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // -0.96043, -0.27852 + 0xbfeeb8566b810f2a, 0xbfd1eb6643499fbb, // -0.96, -0.27999 + 0xbfeeb4cf515b8811, 0xbfd2038583d727bd, // -0.95957, -0.28146 + 0xbfeeb1437af9bb34, 0xbfd21ba1fd3d2623, // -0.95914, -0.28294 + 0xbfeeadb2e8e7a88e, 0xbfd233bbabc3bb72, // -0.9587, -0.28441 + 0xbfeeaa1d9bb20af3, 0xbfd24bd28bb37672, // -0.95827, -0.28588 + 0xbfeea68393e65800, 0xbfd263e6995554ba, // -0.95783, -0.28735 + 0xbfeea2e4d212c000, 0xbfd27bf7d0f2c346, // -0.95738, -0.28882 + 0xbfee9f4156c62dda, 0xbfd294062ed59f05, // -0.95694, -0.29028 + 0xbfee9b99229046f8, 0xbfd2ac11af483572, // -0.95649, -0.29175 + 0xbfee97ec36016b30, 0xbfd2c41a4e954520, // -0.95605, -0.29322 + 0xbfee943a91aab4b4, 0xbfd2dc200907fe51, // -0.95559, -0.29469 + 0xbfee9084361df7f3, 0xbfd2f422daec0386, // -0.95514, -0.29615 + 0xbfee8cc923edc388, 0xbfd30c22c08d6a13, // -0.95469, -0.29762 + 0xbfee89095bad6025, 0xbfd3241fb638baaf, // -0.95423, -0.29908 + 0xbfee8544ddf0d075, 0xbfd33c19b83af207, // -0.95377, -0.30054 + 0xbfee817bab4cd10d, 0xbfd35410c2e18152, // -0.95331, -0.30201 + 0xbfee7dadc456d850, 0xbfd36c04d27a4edf, // -0.95284, -0.30347 + 0xbfee79db29a5165a, 0xbfd383f5e353b6aa, // -0.95238, -0.30493 + 0xbfee7603dbce74e9, 0xbfd39be3f1bc8aef, // -0.95191, -0.30639 + 0xbfee7227db6a9744, 0xbfd3b3cefa0414b7, // -0.95144, -0.30785 + 0xbfee6e472911da27, 0xbfd3cbb6f87a146e, // -0.95096, -0.30931 + 0xbfee6a61c55d53a7, 0xbfd3e39be96ec271, // -0.95049, -0.31077 + 0xbfee6677b0e6d31e, 0xbfd3fb7dc932cfa4, // -0.95001, -0.31222 + 0xbfee6288ec48e112, 0xbfd4135c94176602, // -0.94953, -0.31368 + 0xbfee5e95781ebf1c, 0xbfd42b38466e2928, // -0.94905, -0.31514 + 0xbfee5a9d550467d3, 0xbfd44310dc8936f0, // -0.94856, -0.31659 + 0xbfee56a083968eb1, 0xbfd45ae652bb2800, // -0.94807, -0.31805 + 0xbfee529f04729ffc, 0xbfd472b8a5571054, // -0.94759, -0.3195 + 0xbfee4e98d836c0af, 0xbfd48a87d0b07fd7, // -0.94709, -0.32096 + 0xbfee4a8dff81ce5e, 0xbfd4a253d11b82f3, // -0.9466, -0.32241 + 0xbfee467e7af35f23, 0xbfd4ba1ca2eca31c, // -0.94611, -0.32386 + 0xbfee426a4b2bc17e, 0xbfd4d1e24278e76a, // -0.94561, -0.32531 + 0xbfee3e5170cbfc46, 0xbfd4e9a4ac15d520, // -0.94511, -0.32676 + 0xbfee3a33ec75ce85, 0xbfd50163dc197047, // -0.9446, -0.32821 + 0xbfee3611becbaf69, 0xbfd5191fceda3c35, // -0.9441, -0.32966 + 0xbfee31eae870ce25, 0xbfd530d880af3c24, // -0.94359, -0.33111 + 0xbfee2dbf6a0911d9, 0xbfd5488dedeff3be, // -0.94308, -0.33255 + 0xbfee298f4439197a, 0xbfd5604012f467b4, // -0.94257, -0.334 + 0xbfee255a77a63bb8, 0xbfd577eeec151e47, // -0.94206, -0.33545 + 0xbfee212104f686e5, 0xbfd58f9a75ab1fdd, // -0.94154, -0.33689 + 0xbfee1ce2ecd0c0d8, 0xbfd5a742ac0ff78d, // -0.94103, -0.33833 + 0xbfee18a02fdc66d9, 0xbfd5bee78b9db3b6, // -0.94051, -0.33978 + 0xbfee1458cec1ad83, 0xbfd5d68910aee686, // -0.93998, -0.34122 + 0xbfee100cca2980ac, 0xbfd5ee27379ea693, // -0.93946, -0.34266 + 0xbfee0bbc22bd8349, 0xbfd605c1fcc88f63, // -0.93893, -0.3441 + 0xbfee0766d9280f54, 0xbfd61d595c88c203, // -0.9384, -0.34554 + 0xbfee030cee1435b8, 0xbfd634ed533be58e, // -0.93787, -0.34698 + 0xbfedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // -0.93734, -0.34842 + 0xbfedfa4b3621271d, 0xbfd6640af6f03d9e, // -0.9368, -0.34986 + 0xbfedf5e36a9ba59c, 0xbfd67b949cad63ca, // -0.93627, -0.35129 + 0xbfedf177004b2534, 0xbfd6931acad55f51, // -0.93573, -0.35273 + 0xbfeded05f7de47da, 0xbfd6aa9d7dc77e16, // -0.93518, -0.35416 + 0xbfede890520465ce, 0xbfd6c21cb1e39771, // -0.93464, -0.3556 + 0xbfede4160f6d8d81, 0xbfd6d998638a0cb5, // -0.93409, -0.35703 + 0xbfeddf9730ca837b, 0xbfd6f1108f1bc9c5, // -0.93354, -0.35846 + 0xbfeddb13b6ccc23d, 0xbfd7088530fa459e, // -0.93299, -0.3599 + 0xbfedd68ba2267a25, 0xbfd71ff6458782ec, // -0.93244, -0.36133 + 0xbfedd1fef38a915a, 0xbfd73763c9261092, // -0.93188, -0.36276 + 0xbfedcd6dabaca3a5, 0xbfd74ecdb8390a3e, // -0.93133, -0.36418 + 0xbfedc8d7cb410260, 0xbfd766340f2418f6, // -0.93077, -0.36561 + 0xbfedc43d52fcb453, 0xbfd77d96ca4b73a6, // -0.93021, -0.36704 + 0xbfedbf9e4395759a, 0xbfd794f5e613dfae, // -0.92964, -0.36847 + 0xbfedbafa9dc1b78d, 0xbfd7ac515ee2b172, // -0.92907, -0.36989 + 0xbfedb6526238a09b, 0xbfd7c3a9311dcce7, // -0.92851, -0.37132 + 0xbfedb1a591b20c38, 0xbfd7dafd592ba621, // -0.92794, -0.37274 + 0xbfedacf42ce68ab9, 0xbfd7f24dd37341e3, // -0.92736, -0.37416 + 0xbfeda83e348f613b, 0xbfd8099a9c5c362d, // -0.92679, -0.37559 + 0xbfeda383a9668988, 0xbfd820e3b04eaac4, // -0.92621, -0.37701 + 0xbfed9ec48c26b1f3, 0xbfd838290bb359c8, // -0.92563, -0.37843 + 0xbfed9a00dd8b3d46, 0xbfd84f6aaaf3903f, // -0.92505, -0.37985 + 0xbfed95389e50429b, 0xbfd866a88a792ea0, // -0.92447, -0.38127 + 0xbfed906bcf328d46, 0xbfd87de2a6aea963, // -0.92388, -0.38268 + 0xbfed8b9a70ef9cb4, 0xbfd89518fbff098e, // -0.92329, -0.3841 + 0xbfed86c48445a450, 0xbfd8ac4b86d5ed44, // -0.9227, -0.38552 + 0xbfed81ea09f38b63, 0xbfd8c37a439f884f, // -0.92211, -0.38693 + 0xbfed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // -0.92151, -0.38835 + 0xbfed78276f5617c6, 0xbfd8f1cc44bea329, // -0.92092, -0.38976 + 0xbfed733f508c0dff, 0xbfd908ef81ef7bd1, // -0.92032, -0.39117 + 0xbfed6e52a71c8547, 0xbfd9200ee2c9be97, // -0.91972, -0.39258 + 0xbfed696173c9e68b, 0xbfd9372a63bc93d7, // -0.91911, -0.39399 + 0xbfed646bb7574de5, 0xbfd94e420137bce3, // -0.91851, -0.3954 + 0xbfed5f7172888a7f, 0xbfd96555b7ab948f, // -0.9179, -0.39681 + 0xbfed5a72a6221e73, 0xbfd97c6583890fc2, // -0.91729, -0.39822 + 0xbfed556f52e93eb1, 0xbfd993716141bdfe, // -0.91668, -0.39962 + 0xbfed506779a3d2d9, 0xbfd9aa794d47c9ee, // -0.91606, -0.40103 + 0xbfed4b5b1b187524, 0xbfd9c17d440df9f2, // -0.91545, -0.40243 + 0xbfed464a380e7242, 0xbfd9d87d4207b0ab, // -0.91483, -0.40384 + 0xbfed4134d14dc93a, 0xbfd9ef7943a8ed8a, // -0.91421, -0.40524 + 0xbfed3c1ae79f2b4e, 0xbfda067145664d57, // -0.91359, -0.40664 + 0xbfed36fc7bcbfbdc, 0xbfda1d6543b50ac0, // -0.91296, -0.40804 + 0xbfed31d98e9e503a, 0xbfda34553b0afee5, // -0.91234, -0.40944 + 0xbfed2cb220e0ef9f, 0xbfda4b4127dea1e4, // -0.91171, -0.41084 + 0xbfed2786335f52fc, 0xbfda622906a70b63, // -0.91107, -0.41224 + 0xbfed2255c6e5a4e1, 0xbfda790cd3dbf31a, // -0.91044, -0.41364 + 0xbfed1d20dc40c15c, 0xbfda8fec8bf5b166, // -0.90981, -0.41503 + 0xbfed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // -0.90917, -0.41643 + 0xbfed12a98fac410c, 0xbfdabd9faebc3980, // -0.90853, -0.41782 + 0xbfed0d672f59d2b9, 0xbfdad473125cdc08, // -0.90789, -0.41922 + 0xbfed082054168bac, 0xbfdaeb4252ca07ab, // -0.90724, -0.42061 + 0xbfed02d4feb2bd92, 0xbfdb020d6c7f4009, // -0.9066, -0.422 + 0xbfecfd852fff6ad4, 0xbfdb18d45bf8aca6, // -0.90595, -0.42339 + 0xbfecf830e8ce467b, 0xbfdb2f971db31972, // -0.9053, -0.42478 + 0xbfecf2d829f1b40e, 0xbfdb4655ae2bf757, // -0.90464, -0.42617 + 0xbfeced7af43cc773, 0xbfdb5d1009e15cc0, // -0.90399, -0.42756 + 0xbfece819488344ce, 0xbfdb73c62d520624, // -0.90333, -0.42894 + 0xbfece2b32799a060, 0xbfdb8a7814fd5693, // -0.90267, -0.43033 + 0xbfecdd489254fe65, 0xbfdba125bd63583e, // -0.90201, -0.43171 + 0xbfecd7d9898b32f6, 0xbfdbb7cf2304bd01, // -0.90135, -0.43309 + 0xbfecd2660e12c1e6, 0xbfdbce744262deee, // -0.90068, -0.43448 + 0xbfecccee20c2de9f, 0xbfdbe51517ffc0d9, // -0.90002, -0.43586 + 0xbfecc771c2736c09, 0xbfdbfbb1a05e0edc, // -0.89935, -0.43724 + 0xbfecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // -0.89867, -0.43862 + 0xbfecbc6bb638d10b, 0xbfdc28ddbb6cf145, // -0.898, -0.43999 + 0xbfecb6e20a00da99, 0xbfdc3f6d47263129, // -0.89732, -0.44137 + 0xbfecb153f02fb87d, 0xbfdc55f877b23537, // -0.89665, -0.44275 + 0xbfecabc169a0b901, 0xbfdc6c7f4997000a, // -0.89597, -0.44412 + 0xbfeca62a772fd919, 0xbfdc8301b95b40c2, // -0.89528, -0.4455 + 0xbfeca08f19b9c449, 0xbfdc997fc3865388, // -0.8946, -0.44687 + 0xbfec9aef521bd480, 0xbfdcaff964a0421d, // -0.89391, -0.44824 + 0xbfec954b213411f5, 0xbfdcc66e9931c45d, // -0.89322, -0.44961 + 0xbfec8fa287e13305, 0xbfdcdcdf5dc440ce, // -0.89253, -0.45098 + 0xbfec89f587029c13, 0xbfdcf34baee1cd21, // -0.89184, -0.45235 + 0xbfec84441f785f61, 0xbfdd09b389152ec1, // -0.89115, -0.45372 + 0xbfec7e8e52233cf3, 0xbfdd2016e8e9db5b, // -0.89045, -0.45508 + 0xbfec78d41fe4a267, 0xbfdd3675caebf962, // -0.88975, -0.45645 + 0xbfec7315899eaad7, 0xbfdd4cd02ba8609c, // -0.88905, -0.45781 + 0xbfec6d5290341eb2, 0xbfdd632607ac9aa9, // -0.88835, -0.45918 + 0xbfec678b3488739b, 0xbfdd79775b86e389, // -0.88764, -0.46054 + 0xbfec61bf777fcc48, 0xbfdd8fc423c62a25, // -0.88693, -0.4619 + 0xbfec5bef59fef85a, 0xbfdda60c5cfa10d8, // -0.88622, -0.46326 + 0xbfec561adceb743e, 0xbfddbc5003b2edf8, // -0.88551, -0.46462 + 0xbfec5042012b6907, 0xbfddd28f1481cc58, // -0.8848, -0.46598 + 0xbfec4a64c7a5ac4c, 0xbfdde8c98bf86bd6, // -0.88408, -0.46733 + 0xbfec44833141c004, 0xbfddfeff66a941de, // -0.88336, -0.46869 + 0xbfec3e9d3ee7d262, 0xbfde1530a12779f4, // -0.88264, -0.47004 + 0xbfec38b2f180bdb1, 0xbfde2b5d3806f63b, // -0.88192, -0.4714 + 0xbfec32c449f60831, 0xbfde418527dc4ffa, // -0.8812, -0.47275 + 0xbfec2cd14931e3f1, 0xbfde57a86d3cd824, // -0.88047, -0.4741 + 0xbfec26d9f01f2eaf, 0xbfde6dc704be97e2, // -0.87974, -0.47545 + 0xbfec20de3fa971b0, 0xbfde83e0eaf85113, // -0.87901, -0.4768 + 0xbfec1ade38bce19b, 0xbfde99f61c817eda, // -0.87828, -0.47815 + 0xbfec14d9dc465e58, 0xbfdeb00695f25620, // -0.87755, -0.47949 + 0xbfec0ed12b3372e9, 0xbfdec61253e3c61b, // -0.87681, -0.48084 + 0xbfec08c426725549, 0xbfdedc1952ef78d5, // -0.87607, -0.48218 + 0xbfec02b2cef1e641, 0xbfdef21b8fafd3b5, // -0.87533, -0.48353 + 0xbfebfc9d25a1b147, 0xbfdf081906bff7fd, // -0.87459, -0.48487 + 0xbfebf6832b71ec5b, 0xbfdf1e11b4bbc35c, // -0.87384, -0.48621 + 0xbfebf064e15377dd, 0xbfdf3405963fd068, // -0.87309, -0.48755 + 0xbfebea424837de6d, 0xbfdf49f4a7e97729, // -0.87235, -0.48889 + 0xbfebe41b611154c1, 0xbfdf5fdee656cda3, // -0.8716, -0.49023 + 0xbfebddf02cd2b983, 0xbfdf75c44e26a852, // -0.87084, -0.49156 + 0xbfebd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // -0.87009, -0.4929 + 0xbfebd18ce0dc19d6, 0xbfdfa1808c6cf7e0, // -0.86933, -0.49423 + 0xbfebcb54cb0d2327, 0xbfdfb7575c24d2de, // -0.86857, -0.49557 + 0xbfebc5186bf8361d, 0xbfdfcd2947c1ff57, // -0.86781, -0.4969 + 0xbfebbed7c49380ea, 0xbfdfe2f64be7120f, // -0.86705, -0.49823 + 0xbfebb892d5d5dad5, 0xbfdff8be6537615e, // -0.86628, -0.49956 + 0xbfebb249a0b6c40d, 0xbfe00740c82b82e0, // -0.86551, -0.50089 + 0xbfebabfc262e6586, 0xbfe0121fe4f56d2c, // -0.86474, -0.50221 + 0xbfeba5aa673590d2, 0xbfe01cfc874c3eb7, // -0.86397, -0.50354 + 0xbfeb9f5464c5bffc, 0xbfe027d6ad83287e, // -0.8632, -0.50486 + 0xbfeb98fa1fd9155e, 0xbfe032ae55edbd95, // -0.86242, -0.50619 + 0xbfeb929b996a5b7f, 0xbfe03d837edff370, // -0.86165, -0.50751 + 0xbfeb8c38d27504e9, 0xbfe0485626ae221a, // -0.86087, -0.50883 + 0xbfeb85d1cbf52c02, 0xbfe053264bad0483, // -0.86009, -0.51015 + 0xbfeb7f6686e792ea, 0xbfe05df3ec31b8b6, // -0.8593, -0.51147 + 0xbfeb78f70449a34b, 0xbfe068bf0691c028, // -0.85852, -0.51279 + 0xbfeb728345196e3e, 0xbfe073879922ffed, // -0.85773, -0.5141 + 0xbfeb6c0b4a55ac17, 0xbfe07e4da23bc102, // -0.85694, -0.51542 + 0xbfeb658f14fdbc47, 0xbfe089112032b08c, // -0.85615, -0.51673 + 0xbfeb5f0ea611a532, 0xbfe093d2115ee018, // -0.85535, -0.51804 + 0xbfeb5889fe921405, 0xbfe09e907417c5e1, // -0.85456, -0.51936 + 0xbfeb52011f805c92, 0xbfe0a94c46b53d0b, // -0.85376, -0.52067 + 0xbfeb4b7409de7925, 0xbfe0b405878f85ec, // -0.85296, -0.52198 + 0xbfeb44e2beaf0a61, 0xbfe0bebc34ff4646, // -0.85216, -0.52328 + 0xbfeb3e4d3ef55712, 0xbfe0c9704d5d898f, // -0.85136, -0.52459 + 0xbfeb37b38bb54c09, 0xbfe0d421cf03c12b, // -0.85055, -0.5259 + 0xbfeb3115a5f37bf4, 0xbfe0ded0b84bc4b5, // -0.84974, -0.5272 + 0xbfeb2a738eb51f33, 0xbfe0e97d078fd23b, // -0.84893, -0.5285 + 0xbfeb23cd470013b4, 0xbfe0f426bb2a8e7d, // -0.84812, -0.5298 + 0xbfeb1d22cfdadcc6, 0xbfe0fecdd1770537, // -0.84731, -0.5311 + 0xbfeb16742a4ca2f5, 0xbfe1097248d0a956, // -0.84649, -0.5324 + 0xbfeb0fc1575d33db, 0xbfe114141f935545, // -0.84567, -0.5337 + 0xbfeb090a58150200, 0xbfe11eb3541b4b22, // -0.84485, -0.535 + 0xbfeb024f2d7d24a9, 0xbfe1294fe4c5350a, // -0.84403, -0.53629 + 0xbfeafb8fd89f57b6, 0xbfe133e9cfee254e, // -0.84321, -0.53759 + 0xbfeaf4cc5a85fb73, 0xbfe13e8113f396c1, // -0.84238, -0.53888 + 0xbfeaee04b43c1474, 0xbfe14915af336ceb, // -0.84155, -0.54017 + 0xbfeae738e6cd4b67, 0xbfe153a7a00bf453, // -0.84073, -0.54146 + 0xbfeae068f345ecef, 0xbfe15e36e4dbe2bc, // -0.83989, -0.54275 + 0xbfead994dab2e979, 0xbfe168c37c025764, // -0.83906, -0.54404 + 0xbfead2bc9e21d511, 0xbfe1734d63dedb49, // -0.83822, -0.54532 + 0xbfeacbe03ea0e73b, 0xbfe17dd49ad16161, // -0.83739, -0.54661 + 0xbfeac4ffbd3efac8, 0xbfe188591f3a46e5, // -0.83655, -0.54789 + 0xbfeabe1b1b0b8dac, 0xbfe192daef7a5386, // -0.83571, -0.54918 + 0xbfeab7325916c0d4, 0xbfe19d5a09f2b9b8, // -0.83486, -0.55046 + 0xbfeab045787157ff, 0xbfe1a7d66d0516e6, // -0.83402, -0.55174 + 0xbfeaa9547a2cb98e, 0xbfe1b250171373be, // -0.83317, -0.55302 + 0xbfeaa25f5f5aee60, 0xbfe1bcc706804467, // -0.83232, -0.55429 + 0xbfea9b66290ea1a3, 0xbfe1c73b39ae68c8, // -0.83147, -0.55557 + 0xbfea9468d85b20ae, 0xbfe1d1acaf012cc2, // -0.83062, -0.55685 + 0xbfea8d676e545ad2, 0xbfe1dc1b64dc4872, // -0.82976, -0.55812 + 0xbfea8661ec0ee133, 0xbfe1e68759a3e074, // -0.8289, -0.55939 + 0xbfea7f58529fe69d, 0xbfe1f0f08bbc861b, // -0.82805, -0.56066 + 0xbfea784aa31d3f55, 0xbfe1fb56f98b37b8, // -0.82718, -0.56193 + 0xbfea7138de9d60f5, 0xbfe205baa17560d6, // -0.82632, -0.5632 + 0xbfea6a230637623b, 0xbfe2101b81e0da78, // -0.82546, -0.56447 + 0xbfea63091b02fae2, 0xbfe21a799933eb58, // -0.82459, -0.56573 + 0xbfea5beb1e188375, 0xbfe224d4e5d5482e, // -0.82372, -0.567 + 0xbfea54c91090f524, 0xbfe22f2d662c13e1, // -0.82285, -0.56826 + 0xbfea4da2f385e997, 0xbfe23983189fdfd5, // -0.82198, -0.56952 + 0xbfea4678c8119ac8, 0xbfe243d5fb98ac1f, // -0.8211, -0.57078 + 0xbfea3f4a8f4ee2d2, 0xbfe24e260d7ee7c9, // -0.82023, -0.57204 + 0xbfea38184a593bc6, 0xbfe258734cbb7110, // -0.81935, -0.5733 + 0xbfea30e1fa4cbf81, 0xbfe262bdb7b795a2, // -0.81847, -0.57455 + 0xbfea29a7a0462782, 0xbfe26d054cdd12df, // -0.81758, -0.57581 + 0xbfea22693d62ccb9, 0xbfe2774a0a961612, // -0.8167, -0.57706 + 0xbfea1b26d2c0a75e, 0xbfe2818bef4d3cba, // -0.81581, -0.57831 + 0xbfea13e0617e4ec7, 0xbfe28bcaf96d94ba, // -0.81493, -0.57956 + 0xbfea0c95eabaf937, 0xbfe2960727629ca8, // -0.81404, -0.58081 + 0xbfea05476f967bb5, 0xbfe2a040779843fb, // -0.81314, -0.58206 + 0xbfe9fdf4f13149de, 0xbfe2aa76e87aeb58, // -0.81225, -0.58331 + 0xbfe9f69e70ac75bc, 0xbfe2b4aa787764c4, // -0.81135, -0.58455 + 0xbfe9ef43ef29af94, 0xbfe2bedb25faf3ea, // -0.81046, -0.5858 + 0xbfe9e7e56dcb45bd, 0xbfe2c908ef734e57, // -0.80956, -0.58704 + 0xbfe9e082edb42472, 0xbfe2d333d34e9bb7, // -0.80866, -0.58828 + 0xbfe9d91c7007d5a6, 0xbfe2dd5bcffb7616, // -0.80775, -0.58952 + 0xbfe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // -0.80685, -0.59076 + 0xbfe9ca438080eadb, 0xbfe2f1a30d86773a, // -0.80594, -0.592 + 0xbfe9c2d110f075c3, 0xbfe2fbc24b441015, // -0.80503, -0.59323 + 0xbfe9bb5aa85f2098, 0xbfe305de9b921a94, // -0.80412, -0.59447 + 0xbfe9b3e047f38741, 0xbfe30ff7fce17035, // -0.80321, -0.5957 + 0xbfe9ac61f0d4e247, 0xbfe31a0e6da35e44, // -0.80229, -0.59693 + 0xbfe9a4dfa42b06b2, 0xbfe32421ec49a620, // -0.80138, -0.59816 + 0xbfe99d59631e65d5, 0xbfe32e3277467d6b, // -0.80046, -0.59939 + 0xbfe995cf2ed80d22, 0xbfe338400d0c8e57, // -0.79954, -0.60062 + 0xbfe98e410881a600, 0xbfe3424aac0ef7d6, // -0.79861, -0.60184 + 0xbfe986aef1457594, 0xbfe34c5252c14de1, // -0.79769, -0.60307 + 0xbfe97f18ea4e5c9e, 0xbfe35656ff9799ae, // -0.79676, -0.60429 + 0xbfe9777ef4c7d742, 0xbfe36058b10659f3, // -0.79584, -0.60551 + 0xbfe96fe111ddfce0, 0xbfe36a576582831b, // -0.79491, -0.60673 + 0xbfe9683f42bd7fe1, 0xbfe374531b817f8d, // -0.79398, -0.60795 + 0xbfe960998893ad8c, 0xbfe37e4bd1792fe2, // -0.79304, -0.60917 + 0xbfe958efe48e6dd7, 0xbfe3884185dfeb22, // -0.79211, -0.61038 + 0xbfe9514257dc4335, 0xbfe39234372c7f04, // -0.79117, -0.6116 + 0xbfe94990e3ac4a6c, 0xbfe39c23e3d63029, // -0.79023, -0.61281 + 0xbfe941db892e3a65, 0xbfe3a6108a54ba58, // -0.78929, -0.61402 + 0xbfe93a22499263fc, 0xbfe3affa292050b9, // -0.78835, -0.61523 + 0xbfe932652609b1cf, 0xbfe3b9e0beb19e18, // -0.7874, -0.61644 + 0xbfe92aa41fc5a815, 0xbfe3c3c44981c517, // -0.78646, -0.61765 + 0xbfe922df37f8646a, 0xbfe3cda4c80a6076, // -0.78551, -0.61885 + 0xbfe91b166fd49da2, 0xbfe3d78238c58343, // -0.78456, -0.62006 + 0xbfe91349c88da398, 0xbfe3e15c9a2db922, // -0.7836, -0.62126 + 0xbfe90b7943575efe, 0xbfe3eb33eabe0680, // -0.78265, -0.62246 + 0xbfe903a4e1665133, 0xbfe3f50828f1e8d2, // -0.78169, -0.62366 + 0xbfe8fbcca3ef940d, 0xbfe3fed9534556d4, // -0.78074, -0.62486 + 0xbfe8f3f08c28d9ac, 0xbfe408a76834c0c0, // -0.77978, -0.62606 + 0xbfe8ec109b486c49, 0xbfe41272663d108c, // -0.77882, -0.62725 + 0xbfe8e42cd2852e0a, 0xbfe41c3a4bdbaa26, // -0.77785, -0.62845 + 0xbfe8dc45331698cc, 0xbfe425ff178e6bb1, // -0.77689, -0.62964 + 0xbfe8d459be34bdfa, 0xbfe42fc0c7d3adbb, // -0.77592, -0.63083 + 0xbfe8cc6a75184655, 0xbfe4397f5b2a4380, // -0.77495, -0.63202 + 0xbfe8c47758fa71cb, 0xbfe4433ad0117b1d, // -0.77398, -0.63321 + 0xbfe8bc806b151741, 0xbfe44cf325091dd6, // -0.77301, -0.63439 + 0xbfe8b485aca2a468, 0xbfe456a858917046, // -0.77204, -0.63558 + 0xbfe8ac871ede1d88, 0xbfe4605a692b32a2, // -0.77106, -0.63676 + 0xbfe8a484c3031d50, 0xbfe46a095557a0f1, // -0.77008, -0.63794 + 0xbfe89c7e9a4dd4ab, 0xbfe473b51b987347, // -0.7691, -0.63912 + 0xbfe89474a5fb0a84, 0xbfe47d5dba6fde01, // -0.76812, -0.6403 + 0xbfe88c66e7481ba1, 0xbfe48703306091fe, // -0.76714, -0.64148 + 0xbfe884555f72fa6b, 0xbfe490a57bedbcdf, // -0.76615, -0.64266 + 0xbfe87c400fba2ebf, 0xbfe49a449b9b0938, // -0.76517, -0.64383 + 0xbfe87426f95cd5bd, 0xbfe4a3e08dec9ed6, // -0.76418, -0.645 + 0xbfe86c0a1d9aa195, 0xbfe4ad79516722f0, // -0.76319, -0.64618 + 0xbfe863e97db3d95a, 0xbfe4b70ee48fb869, // -0.7622, -0.64735 + 0xbfe85bc51ae958cc, 0xbfe4c0a145ec0004, // -0.7612, -0.64851 + 0xbfe8539cf67c9029, 0xbfe4ca30740218a3, // -0.76021, -0.64968 + 0xbfe84b7111af83f9, 0xbfe4d3bc6d589f80, // -0.75921, -0.65085 + 0xbfe843416dc4cce2, 0xbfe4dd453076b064, // -0.75821, -0.65201 + 0xbfe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // -0.75721, -0.65317 + 0xbfe832d6eda3a3e0, 0xbfe4f04d0e2859aa, // -0.75621, -0.65433 + 0xbfe82a9c13f545ff, 0xbfe4f9cc25cca486, // -0.7552, -0.65549 + 0xbfe8225d803964e5, 0xbfe503480159ded2, // -0.75419, -0.65665 + 0xbfe81a1b33b57acc, 0xbfe50cc09f59a09b, // -0.75319, -0.65781 + 0xbfe811d52faf94dc, 0xbfe51635fe5601d7, // -0.75218, -0.65896 + 0xbfe8098b756e52fa, 0xbfe51fa81cd99aa6, // -0.75117, -0.66011 + 0xbfe8013e0638e795, 0xbfe52916f96f8388, // -0.75015, -0.66127 + 0xbfe7f8ece3571771, 0xbfe5328292a35596, // -0.74914, -0.66242 + 0xbfe7f0980e113978, 0xbfe53beae7012abe, // -0.74812, -0.66356 + 0xbfe7e83f87b03686, 0xbfe5454ff5159dfb, // -0.7471, -0.66471 + 0xbfe7dfe3517d8937, 0xbfe54eb1bb6dcb8f, // -0.74608, -0.66586 + 0xbfe7d7836cc33db2, 0xbfe5581038975137, // -0.74506, -0.667 + 0xbfe7cf1fdacbf179, 0xbfe5616b6b204e6e, // -0.74403, -0.66814 + 0xbfe7c6b89ce2d333, 0xbfe56ac35197649e, // -0.74301, -0.66928 + 0xbfe7be4db453a27c, 0xbfe57417ea8bb75c, // -0.74198, -0.67042 + 0xbfe7b5df226aafb0, 0xbfe57d69348cec9f, // -0.74095, -0.67156 + 0xbfe7ad6ce874dbb6, 0xbfe586b72e2b2cfd, // -0.73992, -0.67269 + 0xbfe7a4f707bf97d2, 0xbfe59001d5f723df, // -0.73889, -0.67383 + 0xbfe79c7d8198e56e, 0xbfe599492a81ffbc, // -0.73785, -0.67496 + 0xbfe79400574f55e4, 0xbfe5a28d2a5d7250, // -0.73682, -0.67609 + 0xbfe78b7f8a320a52, 0xbfe5abcdd41bb0d8, // -0.73578, -0.67722 + 0xbfe782fb1b90b35b, 0xbfe5b50b264f7448, // -0.73474, -0.67835 + 0xbfe77a730cbb9100, 0xbfe5be451f8bf980, // -0.7337, -0.67948 + 0xbfe771e75f037261, 0xbfe5c77bbe65018c, // -0.73265, -0.6806 + 0xbfe7695813b9b594, 0xbfe5d0af016ed1d4, // -0.73161, -0.68172 + 0xbfe760c52c304764, 0xbfe5d9dee73e345c, // -0.73056, -0.68285 + 0xbfe7582ea9b9a329, 0xbfe5e30b6e6877f3, // -0.72951, -0.68397 + 0xbfe74f948da8d28d, 0xbfe5ec3495837074, // -0.72846, -0.68508 + 0xbfe746f6d9516d59, 0xbfe5f55a5b2576f8, // -0.72741, -0.6862 + 0xbfe73e558e079942, 0xbfe5fe7cbde56a0f, // -0.72636, -0.68732 + 0xbfe735b0ad2009b2, 0xbfe6079bbc5aadfa, // -0.7253, -0.68843 + 0xbfe72d0837efff97, 0xbfe610b7551d2cde, // -0.72425, -0.68954 + 0xbfe7245c2fcd492a, 0xbfe619cf86c55702, // -0.72319, -0.69065 + 0xbfe71bac960e41bf, 0xbfe622e44fec22ff, // -0.72213, -0.69176 + 0xbfe712f96c09d18d, 0xbfe62bf5af2b0dfd, // -0.72107, -0.69287 + 0xbfe70a42b3176d7a, 0xbfe63503a31c1be8, // -0.72, -0.69397 + 0xbfe701886c8f16e6, 0xbfe63e0e2a59d7aa, // -0.71894, -0.69508 + 0xbfe6f8ca99c95b75, 0xbfe64715437f535b, // -0.71787, -0.69618 + 0xbfe6f0093c1f54de, 0xbfe65018ed28287f, // -0.7168, -0.69728 + 0xbfe6e74454eaa8ae, 0xbfe6591925f0783e, // -0.71573, -0.69838 + 0xbfe6de7be585881d, 0xbfe66215ec74eb91, // -0.71466, -0.69947 + 0xbfe6d5afef4aafcc, 0xbfe66b0f3f52b386, // -0.71358, -0.70057 + 0xbfe6cce07395679f, 0xbfe674051d27896c, // -0.71251, -0.70166 + 0xbfe6c40d73c18275, 0xbfe67cf78491af10, // -0.71143, -0.70275 + 0xbfe6bb36f12b5e06, 0xbfe685e6742feeef, // -0.71035, -0.70385 + 0xbfe6b25ced2fe29c, 0xbfe68ed1eaa19c71, // -0.70927, -0.70493 + 0xbfe6a97f692c82ea, 0xbfe697b9e686941c, // -0.70819, -0.70602 + 0xbfe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // -0.70711, -0.70711 + 0xbfe697b9e686941c, 0xbfe6a97f692c82ea, // -0.70602, -0.70819 + 0xbfe68ed1eaa19c71, 0xbfe6b25ced2fe29c, // -0.70493, -0.70927 + 0xbfe685e6742feeef, 0xbfe6bb36f12b5e06, // -0.70385, -0.71035 + 0xbfe67cf78491af10, 0xbfe6c40d73c18275, // -0.70275, -0.71143 + 0xbfe674051d27896c, 0xbfe6cce07395679f, // -0.70166, -0.71251 + 0xbfe66b0f3f52b386, 0xbfe6d5afef4aafcc, // -0.70057, -0.71358 + 0xbfe66215ec74eb91, 0xbfe6de7be585881d, // -0.69947, -0.71466 + 0xbfe6591925f0783e, 0xbfe6e74454eaa8ae, // -0.69838, -0.71573 + 0xbfe65018ed28287f, 0xbfe6f0093c1f54de, // -0.69728, -0.7168 + 0xbfe64715437f535b, 0xbfe6f8ca99c95b75, // -0.69618, -0.71787 + 0xbfe63e0e2a59d7aa, 0xbfe701886c8f16e6, // -0.69508, -0.71894 + 0xbfe63503a31c1be8, 0xbfe70a42b3176d7a, // -0.69397, -0.72 + 0xbfe62bf5af2b0dfd, 0xbfe712f96c09d18d, // -0.69287, -0.72107 + 0xbfe622e44fec22ff, 0xbfe71bac960e41bf, // -0.69176, -0.72213 + 0xbfe619cf86c55702, 0xbfe7245c2fcd492a, // -0.69065, -0.72319 + 0xbfe610b7551d2cde, 0xbfe72d0837efff97, // -0.68954, -0.72425 + 0xbfe6079bbc5aadfa, 0xbfe735b0ad2009b2, // -0.68843, -0.7253 + 0xbfe5fe7cbde56a0f, 0xbfe73e558e079942, // -0.68732, -0.72636 + 0xbfe5f55a5b2576f8, 0xbfe746f6d9516d59, // -0.6862, -0.72741 + 0xbfe5ec3495837074, 0xbfe74f948da8d28d, // -0.68508, -0.72846 + 0xbfe5e30b6e6877f3, 0xbfe7582ea9b9a329, // -0.68397, -0.72951 + 0xbfe5d9dee73e345c, 0xbfe760c52c304764, // -0.68285, -0.73056 + 0xbfe5d0af016ed1d4, 0xbfe7695813b9b594, // -0.68172, -0.73161 + 0xbfe5c77bbe65018c, 0xbfe771e75f037261, // -0.6806, -0.73265 + 0xbfe5be451f8bf980, 0xbfe77a730cbb9100, // -0.67948, -0.7337 + 0xbfe5b50b264f7448, 0xbfe782fb1b90b35b, // -0.67835, -0.73474 + 0xbfe5abcdd41bb0d8, 0xbfe78b7f8a320a52, // -0.67722, -0.73578 + 0xbfe5a28d2a5d7250, 0xbfe79400574f55e4, // -0.67609, -0.73682 + 0xbfe599492a81ffbc, 0xbfe79c7d8198e56e, // -0.67496, -0.73785 + 0xbfe59001d5f723df, 0xbfe7a4f707bf97d2, // -0.67383, -0.73889 + 0xbfe586b72e2b2cfd, 0xbfe7ad6ce874dbb6, // -0.67269, -0.73992 + 0xbfe57d69348cec9f, 0xbfe7b5df226aafb0, // -0.67156, -0.74095 + 0xbfe57417ea8bb75c, 0xbfe7be4db453a27c, // -0.67042, -0.74198 + 0xbfe56ac35197649e, 0xbfe7c6b89ce2d333, // -0.66928, -0.74301 + 0xbfe5616b6b204e6e, 0xbfe7cf1fdacbf179, // -0.66814, -0.74403 + 0xbfe5581038975137, 0xbfe7d7836cc33db2, // -0.667, -0.74506 + 0xbfe54eb1bb6dcb8f, 0xbfe7dfe3517d8937, // -0.66586, -0.74608 + 0xbfe5454ff5159dfb, 0xbfe7e83f87b03686, // -0.66471, -0.7471 + 0xbfe53beae7012abe, 0xbfe7f0980e113978, // -0.66356, -0.74812 + 0xbfe5328292a35596, 0xbfe7f8ece3571771, // -0.66242, -0.74914 + 0xbfe52916f96f8388, 0xbfe8013e0638e795, // -0.66127, -0.75015 + 0xbfe51fa81cd99aa6, 0xbfe8098b756e52fa, // -0.66011, -0.75117 + 0xbfe51635fe5601d7, 0xbfe811d52faf94dc, // -0.65896, -0.75218 + 0xbfe50cc09f59a09b, 0xbfe81a1b33b57acc, // -0.65781, -0.75319 + 0xbfe503480159ded2, 0xbfe8225d803964e5, // -0.65665, -0.75419 + 0xbfe4f9cc25cca486, 0xbfe82a9c13f545ff, // -0.65549, -0.7552 + 0xbfe4f04d0e2859aa, 0xbfe832d6eda3a3e0, // -0.65433, -0.75621 + 0xbfe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // -0.65317, -0.75721 + 0xbfe4dd453076b064, 0xbfe843416dc4cce2, // -0.65201, -0.75821 + 0xbfe4d3bc6d589f80, 0xbfe84b7111af83f9, // -0.65085, -0.75921 + 0xbfe4ca30740218a3, 0xbfe8539cf67c9029, // -0.64968, -0.76021 + 0xbfe4c0a145ec0004, 0xbfe85bc51ae958cc, // -0.64851, -0.7612 + 0xbfe4b70ee48fb869, 0xbfe863e97db3d95a, // -0.64735, -0.7622 + 0xbfe4ad79516722f0, 0xbfe86c0a1d9aa195, // -0.64618, -0.76319 + 0xbfe4a3e08dec9ed6, 0xbfe87426f95cd5bd, // -0.645, -0.76418 + 0xbfe49a449b9b0938, 0xbfe87c400fba2ebf, // -0.64383, -0.76517 + 0xbfe490a57bedbcdf, 0xbfe884555f72fa6b, // -0.64266, -0.76615 + 0xbfe48703306091fe, 0xbfe88c66e7481ba1, // -0.64148, -0.76714 + 0xbfe47d5dba6fde01, 0xbfe89474a5fb0a84, // -0.6403, -0.76812 + 0xbfe473b51b987347, 0xbfe89c7e9a4dd4ab, // -0.63912, -0.7691 + 0xbfe46a095557a0f1, 0xbfe8a484c3031d50, // -0.63794, -0.77008 + 0xbfe4605a692b32a2, 0xbfe8ac871ede1d88, // -0.63676, -0.77106 + 0xbfe456a858917046, 0xbfe8b485aca2a468, // -0.63558, -0.77204 + 0xbfe44cf325091dd6, 0xbfe8bc806b151741, // -0.63439, -0.77301 + 0xbfe4433ad0117b1d, 0xbfe8c47758fa71cb, // -0.63321, -0.77398 + 0xbfe4397f5b2a4380, 0xbfe8cc6a75184655, // -0.63202, -0.77495 + 0xbfe42fc0c7d3adbb, 0xbfe8d459be34bdfa, // -0.63083, -0.77592 + 0xbfe425ff178e6bb1, 0xbfe8dc45331698cc, // -0.62964, -0.77689 + 0xbfe41c3a4bdbaa26, 0xbfe8e42cd2852e0a, // -0.62845, -0.77785 + 0xbfe41272663d108c, 0xbfe8ec109b486c49, // -0.62725, -0.77882 + 0xbfe408a76834c0c0, 0xbfe8f3f08c28d9ac, // -0.62606, -0.77978 + 0xbfe3fed9534556d4, 0xbfe8fbcca3ef940d, // -0.62486, -0.78074 + 0xbfe3f50828f1e8d2, 0xbfe903a4e1665133, // -0.62366, -0.78169 + 0xbfe3eb33eabe0680, 0xbfe90b7943575efe, // -0.62246, -0.78265 + 0xbfe3e15c9a2db922, 0xbfe91349c88da398, // -0.62126, -0.7836 + 0xbfe3d78238c58343, 0xbfe91b166fd49da2, // -0.62006, -0.78456 + 0xbfe3cda4c80a6076, 0xbfe922df37f8646a, // -0.61885, -0.78551 + 0xbfe3c3c44981c517, 0xbfe92aa41fc5a815, // -0.61765, -0.78646 + 0xbfe3b9e0beb19e18, 0xbfe932652609b1cf, // -0.61644, -0.7874 + 0xbfe3affa292050b9, 0xbfe93a22499263fc, // -0.61523, -0.78835 + 0xbfe3a6108a54ba58, 0xbfe941db892e3a65, // -0.61402, -0.78929 + 0xbfe39c23e3d63029, 0xbfe94990e3ac4a6c, // -0.61281, -0.79023 + 0xbfe39234372c7f04, 0xbfe9514257dc4335, // -0.6116, -0.79117 + 0xbfe3884185dfeb22, 0xbfe958efe48e6dd7, // -0.61038, -0.79211 + 0xbfe37e4bd1792fe2, 0xbfe960998893ad8c, // -0.60917, -0.79304 + 0xbfe374531b817f8d, 0xbfe9683f42bd7fe1, // -0.60795, -0.79398 + 0xbfe36a576582831b, 0xbfe96fe111ddfce0, // -0.60673, -0.79491 + 0xbfe36058b10659f3, 0xbfe9777ef4c7d742, // -0.60551, -0.79584 + 0xbfe35656ff9799ae, 0xbfe97f18ea4e5c9e, // -0.60429, -0.79676 + 0xbfe34c5252c14de1, 0xbfe986aef1457594, // -0.60307, -0.79769 + 0xbfe3424aac0ef7d6, 0xbfe98e410881a600, // -0.60184, -0.79861 + 0xbfe338400d0c8e57, 0xbfe995cf2ed80d22, // -0.60062, -0.79954 + 0xbfe32e3277467d6b, 0xbfe99d59631e65d5, // -0.59939, -0.80046 + 0xbfe32421ec49a620, 0xbfe9a4dfa42b06b2, // -0.59816, -0.80138 + 0xbfe31a0e6da35e44, 0xbfe9ac61f0d4e247, // -0.59693, -0.80229 + 0xbfe30ff7fce17035, 0xbfe9b3e047f38741, // -0.5957, -0.80321 + 0xbfe305de9b921a94, 0xbfe9bb5aa85f2098, // -0.59447, -0.80412 + 0xbfe2fbc24b441015, 0xbfe9c2d110f075c3, // -0.59323, -0.80503 + 0xbfe2f1a30d86773a, 0xbfe9ca438080eadb, // -0.592, -0.80594 + 0xbfe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // -0.59076, -0.80685 + 0xbfe2dd5bcffb7616, 0xbfe9d91c7007d5a6, // -0.58952, -0.80775 + 0xbfe2d333d34e9bb7, 0xbfe9e082edb42472, // -0.58828, -0.80866 + 0xbfe2c908ef734e57, 0xbfe9e7e56dcb45bd, // -0.58704, -0.80956 + 0xbfe2bedb25faf3ea, 0xbfe9ef43ef29af94, // -0.5858, -0.81046 + 0xbfe2b4aa787764c4, 0xbfe9f69e70ac75bc, // -0.58455, -0.81135 + 0xbfe2aa76e87aeb58, 0xbfe9fdf4f13149de, // -0.58331, -0.81225 + 0xbfe2a040779843fb, 0xbfea05476f967bb5, // -0.58206, -0.81314 + 0xbfe2960727629ca8, 0xbfea0c95eabaf937, // -0.58081, -0.81404 + 0xbfe28bcaf96d94ba, 0xbfea13e0617e4ec7, // -0.57956, -0.81493 + 0xbfe2818bef4d3cba, 0xbfea1b26d2c0a75e, // -0.57831, -0.81581 + 0xbfe2774a0a961612, 0xbfea22693d62ccb9, // -0.57706, -0.8167 + 0xbfe26d054cdd12df, 0xbfea29a7a0462782, // -0.57581, -0.81758 + 0xbfe262bdb7b795a2, 0xbfea30e1fa4cbf81, // -0.57455, -0.81847 + 0xbfe258734cbb7110, 0xbfea38184a593bc6, // -0.5733, -0.81935 + 0xbfe24e260d7ee7c9, 0xbfea3f4a8f4ee2d2, // -0.57204, -0.82023 + 0xbfe243d5fb98ac1f, 0xbfea4678c8119ac8, // -0.57078, -0.8211 + 0xbfe23983189fdfd5, 0xbfea4da2f385e997, // -0.56952, -0.82198 + 0xbfe22f2d662c13e1, 0xbfea54c91090f524, // -0.56826, -0.82285 + 0xbfe224d4e5d5482e, 0xbfea5beb1e188375, // -0.567, -0.82372 + 0xbfe21a799933eb58, 0xbfea63091b02fae2, // -0.56573, -0.82459 + 0xbfe2101b81e0da78, 0xbfea6a230637623b, // -0.56447, -0.82546 + 0xbfe205baa17560d6, 0xbfea7138de9d60f5, // -0.5632, -0.82632 + 0xbfe1fb56f98b37b8, 0xbfea784aa31d3f55, // -0.56193, -0.82718 + 0xbfe1f0f08bbc861b, 0xbfea7f58529fe69d, // -0.56066, -0.82805 + 0xbfe1e68759a3e074, 0xbfea8661ec0ee133, // -0.55939, -0.8289 + 0xbfe1dc1b64dc4872, 0xbfea8d676e545ad2, // -0.55812, -0.82976 + 0xbfe1d1acaf012cc2, 0xbfea9468d85b20ae, // -0.55685, -0.83062 + 0xbfe1c73b39ae68c8, 0xbfea9b66290ea1a3, // -0.55557, -0.83147 + 0xbfe1bcc706804467, 0xbfeaa25f5f5aee60, // -0.55429, -0.83232 + 0xbfe1b250171373be, 0xbfeaa9547a2cb98e, // -0.55302, -0.83317 + 0xbfe1a7d66d0516e6, 0xbfeab045787157ff, // -0.55174, -0.83402 + 0xbfe19d5a09f2b9b8, 0xbfeab7325916c0d4, // -0.55046, -0.83486 + 0xbfe192daef7a5386, 0xbfeabe1b1b0b8dac, // -0.54918, -0.83571 + 0xbfe188591f3a46e5, 0xbfeac4ffbd3efac8, // -0.54789, -0.83655 + 0xbfe17dd49ad16161, 0xbfeacbe03ea0e73b, // -0.54661, -0.83739 + 0xbfe1734d63dedb49, 0xbfead2bc9e21d511, // -0.54532, -0.83822 + 0xbfe168c37c025764, 0xbfead994dab2e979, // -0.54404, -0.83906 + 0xbfe15e36e4dbe2bc, 0xbfeae068f345ecef, // -0.54275, -0.83989 + 0xbfe153a7a00bf453, 0xbfeae738e6cd4b67, // -0.54146, -0.84073 + 0xbfe14915af336ceb, 0xbfeaee04b43c1474, // -0.54017, -0.84155 + 0xbfe13e8113f396c1, 0xbfeaf4cc5a85fb73, // -0.53888, -0.84238 + 0xbfe133e9cfee254e, 0xbfeafb8fd89f57b6, // -0.53759, -0.84321 + 0xbfe1294fe4c5350a, 0xbfeb024f2d7d24a9, // -0.53629, -0.84403 + 0xbfe11eb3541b4b22, 0xbfeb090a58150200, // -0.535, -0.84485 + 0xbfe114141f935545, 0xbfeb0fc1575d33db, // -0.5337, -0.84567 + 0xbfe1097248d0a956, 0xbfeb16742a4ca2f5, // -0.5324, -0.84649 + 0xbfe0fecdd1770537, 0xbfeb1d22cfdadcc6, // -0.5311, -0.84731 + 0xbfe0f426bb2a8e7d, 0xbfeb23cd470013b4, // -0.5298, -0.84812 + 0xbfe0e97d078fd23b, 0xbfeb2a738eb51f33, // -0.5285, -0.84893 + 0xbfe0ded0b84bc4b5, 0xbfeb3115a5f37bf4, // -0.5272, -0.84974 + 0xbfe0d421cf03c12b, 0xbfeb37b38bb54c09, // -0.5259, -0.85055 + 0xbfe0c9704d5d898f, 0xbfeb3e4d3ef55712, // -0.52459, -0.85136 + 0xbfe0bebc34ff4646, 0xbfeb44e2beaf0a61, // -0.52328, -0.85216 + 0xbfe0b405878f85ec, 0xbfeb4b7409de7925, // -0.52198, -0.85296 + 0xbfe0a94c46b53d0b, 0xbfeb52011f805c92, // -0.52067, -0.85376 + 0xbfe09e907417c5e1, 0xbfeb5889fe921405, // -0.51936, -0.85456 + 0xbfe093d2115ee018, 0xbfeb5f0ea611a532, // -0.51804, -0.85535 + 0xbfe089112032b08c, 0xbfeb658f14fdbc47, // -0.51673, -0.85615 + 0xbfe07e4da23bc102, 0xbfeb6c0b4a55ac17, // -0.51542, -0.85694 + 0xbfe073879922ffed, 0xbfeb728345196e3e, // -0.5141, -0.85773 + 0xbfe068bf0691c028, 0xbfeb78f70449a34b, // -0.51279, -0.85852 + 0xbfe05df3ec31b8b6, 0xbfeb7f6686e792ea, // -0.51147, -0.8593 + 0xbfe053264bad0483, 0xbfeb85d1cbf52c02, // -0.51015, -0.86009 + 0xbfe0485626ae221a, 0xbfeb8c38d27504e9, // -0.50883, -0.86087 + 0xbfe03d837edff370, 0xbfeb929b996a5b7f, // -0.50751, -0.86165 + 0xbfe032ae55edbd95, 0xbfeb98fa1fd9155e, // -0.50619, -0.86242 + 0xbfe027d6ad83287e, 0xbfeb9f5464c5bffc, // -0.50486, -0.8632 + 0xbfe01cfc874c3eb7, 0xbfeba5aa673590d2, // -0.50354, -0.86397 + 0xbfe0121fe4f56d2c, 0xbfebabfc262e6586, // -0.50221, -0.86474 + 0xbfe00740c82b82e0, 0xbfebb249a0b6c40d, // -0.50089, -0.86551 + 0xbfdff8be6537615e, 0xbfebb892d5d5dad5, // -0.49956, -0.86628 + 0xbfdfe2f64be7120f, 0xbfebbed7c49380ea, // -0.49823, -0.86705 + 0xbfdfcd2947c1ff57, 0xbfebc5186bf8361d, // -0.4969, -0.86781 + 0xbfdfb7575c24d2de, 0xbfebcb54cb0d2327, // -0.49557, -0.86857 + 0xbfdfa1808c6cf7e0, 0xbfebd18ce0dc19d6, // -0.49423, -0.86933 + 0xbfdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // -0.4929, -0.87009 + 0xbfdf75c44e26a852, 0xbfebddf02cd2b983, // -0.49156, -0.87084 + 0xbfdf5fdee656cda3, 0xbfebe41b611154c1, // -0.49023, -0.8716 + 0xbfdf49f4a7e97729, 0xbfebea424837de6d, // -0.48889, -0.87235 + 0xbfdf3405963fd068, 0xbfebf064e15377dd, // -0.48755, -0.87309 + 0xbfdf1e11b4bbc35c, 0xbfebf6832b71ec5b, // -0.48621, -0.87384 + 0xbfdf081906bff7fd, 0xbfebfc9d25a1b147, // -0.48487, -0.87459 + 0xbfdef21b8fafd3b5, 0xbfec02b2cef1e641, // -0.48353, -0.87533 + 0xbfdedc1952ef78d5, 0xbfec08c426725549, // -0.48218, -0.87607 + 0xbfdec61253e3c61b, 0xbfec0ed12b3372e9, // -0.48084, -0.87681 + 0xbfdeb00695f25620, 0xbfec14d9dc465e58, // -0.47949, -0.87755 + 0xbfde99f61c817eda, 0xbfec1ade38bce19b, // -0.47815, -0.87828 + 0xbfde83e0eaf85113, 0xbfec20de3fa971b0, // -0.4768, -0.87901 + 0xbfde6dc704be97e2, 0xbfec26d9f01f2eaf, // -0.47545, -0.87974 + 0xbfde57a86d3cd824, 0xbfec2cd14931e3f1, // -0.4741, -0.88047 + 0xbfde418527dc4ffa, 0xbfec32c449f60831, // -0.47275, -0.8812 + 0xbfde2b5d3806f63b, 0xbfec38b2f180bdb1, // -0.4714, -0.88192 + 0xbfde1530a12779f4, 0xbfec3e9d3ee7d262, // -0.47004, -0.88264 + 0xbfddfeff66a941de, 0xbfec44833141c004, // -0.46869, -0.88336 + 0xbfdde8c98bf86bd6, 0xbfec4a64c7a5ac4c, // -0.46733, -0.88408 + 0xbfddd28f1481cc58, 0xbfec5042012b6907, // -0.46598, -0.8848 + 0xbfddbc5003b2edf8, 0xbfec561adceb743e, // -0.46462, -0.88551 + 0xbfdda60c5cfa10d8, 0xbfec5bef59fef85a, // -0.46326, -0.88622 + 0xbfdd8fc423c62a25, 0xbfec61bf777fcc48, // -0.4619, -0.88693 + 0xbfdd79775b86e389, 0xbfec678b3488739b, // -0.46054, -0.88764 + 0xbfdd632607ac9aa9, 0xbfec6d5290341eb2, // -0.45918, -0.88835 + 0xbfdd4cd02ba8609c, 0xbfec7315899eaad7, // -0.45781, -0.88905 + 0xbfdd3675caebf962, 0xbfec78d41fe4a267, // -0.45645, -0.88975 + 0xbfdd2016e8e9db5b, 0xbfec7e8e52233cf3, // -0.45508, -0.89045 + 0xbfdd09b389152ec1, 0xbfec84441f785f61, // -0.45372, -0.89115 + 0xbfdcf34baee1cd21, 0xbfec89f587029c13, // -0.45235, -0.89184 + 0xbfdcdcdf5dc440ce, 0xbfec8fa287e13305, // -0.45098, -0.89253 + 0xbfdcc66e9931c45d, 0xbfec954b213411f5, // -0.44961, -0.89322 + 0xbfdcaff964a0421d, 0xbfec9aef521bd480, // -0.44824, -0.89391 + 0xbfdc997fc3865388, 0xbfeca08f19b9c449, // -0.44687, -0.8946 + 0xbfdc8301b95b40c2, 0xbfeca62a772fd919, // -0.4455, -0.89528 + 0xbfdc6c7f4997000a, 0xbfecabc169a0b901, // -0.44412, -0.89597 + 0xbfdc55f877b23537, 0xbfecb153f02fb87d, // -0.44275, -0.89665 + 0xbfdc3f6d47263129, 0xbfecb6e20a00da99, // -0.44137, -0.89732 + 0xbfdc28ddbb6cf145, 0xbfecbc6bb638d10b, // -0.43999, -0.898 + 0xbfdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // -0.43862, -0.89867 + 0xbfdbfbb1a05e0edc, 0xbfecc771c2736c09, // -0.43724, -0.89935 + 0xbfdbe51517ffc0d9, 0xbfecccee20c2de9f, // -0.43586, -0.90002 + 0xbfdbce744262deee, 0xbfecd2660e12c1e6, // -0.43448, -0.90068 + 0xbfdbb7cf2304bd01, 0xbfecd7d9898b32f6, // -0.43309, -0.90135 + 0xbfdba125bd63583e, 0xbfecdd489254fe65, // -0.43171, -0.90201 + 0xbfdb8a7814fd5693, 0xbfece2b32799a060, // -0.43033, -0.90267 + 0xbfdb73c62d520624, 0xbfece819488344ce, // -0.42894, -0.90333 + 0xbfdb5d1009e15cc0, 0xbfeced7af43cc773, // -0.42756, -0.90399 + 0xbfdb4655ae2bf757, 0xbfecf2d829f1b40e, // -0.42617, -0.90464 + 0xbfdb2f971db31972, 0xbfecf830e8ce467b, // -0.42478, -0.9053 + 0xbfdb18d45bf8aca6, 0xbfecfd852fff6ad4, // -0.42339, -0.90595 + 0xbfdb020d6c7f4009, 0xbfed02d4feb2bd92, // -0.422, -0.9066 + 0xbfdaeb4252ca07ab, 0xbfed082054168bac, // -0.42061, -0.90724 + 0xbfdad473125cdc08, 0xbfed0d672f59d2b9, // -0.41922, -0.90789 + 0xbfdabd9faebc3980, 0xbfed12a98fac410c, // -0.41782, -0.90853 + 0xbfdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // -0.41643, -0.90917 + 0xbfda8fec8bf5b166, 0xbfed1d20dc40c15c, // -0.41503, -0.90981 + 0xbfda790cd3dbf31a, 0xbfed2255c6e5a4e1, // -0.41364, -0.91044 + 0xbfda622906a70b63, 0xbfed2786335f52fc, // -0.41224, -0.91107 + 0xbfda4b4127dea1e4, 0xbfed2cb220e0ef9f, // -0.41084, -0.91171 + 0xbfda34553b0afee5, 0xbfed31d98e9e503a, // -0.40944, -0.91234 + 0xbfda1d6543b50ac0, 0xbfed36fc7bcbfbdc, // -0.40804, -0.91296 + 0xbfda067145664d57, 0xbfed3c1ae79f2b4e, // -0.40664, -0.91359 + 0xbfd9ef7943a8ed8a, 0xbfed4134d14dc93a, // -0.40524, -0.91421 + 0xbfd9d87d4207b0ab, 0xbfed464a380e7242, // -0.40384, -0.91483 + 0xbfd9c17d440df9f2, 0xbfed4b5b1b187524, // -0.40243, -0.91545 + 0xbfd9aa794d47c9ee, 0xbfed506779a3d2d9, // -0.40103, -0.91606 + 0xbfd993716141bdfe, 0xbfed556f52e93eb1, // -0.39962, -0.91668 + 0xbfd97c6583890fc2, 0xbfed5a72a6221e73, // -0.39822, -0.91729 + 0xbfd96555b7ab948f, 0xbfed5f7172888a7f, // -0.39681, -0.9179 + 0xbfd94e420137bce3, 0xbfed646bb7574de5, // -0.3954, -0.91851 + 0xbfd9372a63bc93d7, 0xbfed696173c9e68b, // -0.39399, -0.91911 + 0xbfd9200ee2c9be97, 0xbfed6e52a71c8547, // -0.39258, -0.91972 + 0xbfd908ef81ef7bd1, 0xbfed733f508c0dff, // -0.39117, -0.92032 + 0xbfd8f1cc44bea329, 0xbfed78276f5617c6, // -0.38976, -0.92092 + 0xbfd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // -0.38835, -0.92151 + 0xbfd8c37a439f884f, 0xbfed81ea09f38b63, // -0.38693, -0.92211 + 0xbfd8ac4b86d5ed44, 0xbfed86c48445a450, // -0.38552, -0.9227 + 0xbfd89518fbff098e, 0xbfed8b9a70ef9cb4, // -0.3841, -0.92329 + 0xbfd87de2a6aea963, 0xbfed906bcf328d46, // -0.38268, -0.92388 + 0xbfd866a88a792ea0, 0xbfed95389e50429b, // -0.38127, -0.92447 + 0xbfd84f6aaaf3903f, 0xbfed9a00dd8b3d46, // -0.37985, -0.92505 + 0xbfd838290bb359c8, 0xbfed9ec48c26b1f3, // -0.37843, -0.92563 + 0xbfd820e3b04eaac4, 0xbfeda383a9668988, // -0.37701, -0.92621 + 0xbfd8099a9c5c362d, 0xbfeda83e348f613b, // -0.37559, -0.92679 + 0xbfd7f24dd37341e3, 0xbfedacf42ce68ab9, // -0.37416, -0.92736 + 0xbfd7dafd592ba621, 0xbfedb1a591b20c38, // -0.37274, -0.92794 + 0xbfd7c3a9311dcce7, 0xbfedb6526238a09b, // -0.37132, -0.92851 + 0xbfd7ac515ee2b172, 0xbfedbafa9dc1b78d, // -0.36989, -0.92907 + 0xbfd794f5e613dfae, 0xbfedbf9e4395759a, // -0.36847, -0.92964 + 0xbfd77d96ca4b73a6, 0xbfedc43d52fcb453, // -0.36704, -0.93021 + 0xbfd766340f2418f6, 0xbfedc8d7cb410260, // -0.36561, -0.93077 + 0xbfd74ecdb8390a3e, 0xbfedcd6dabaca3a5, // -0.36418, -0.93133 + 0xbfd73763c9261092, 0xbfedd1fef38a915a, // -0.36276, -0.93188 + 0xbfd71ff6458782ec, 0xbfedd68ba2267a25, // -0.36133, -0.93244 + 0xbfd7088530fa459e, 0xbfeddb13b6ccc23d, // -0.3599, -0.93299 + 0xbfd6f1108f1bc9c5, 0xbfeddf9730ca837b, // -0.35846, -0.93354 + 0xbfd6d998638a0cb5, 0xbfede4160f6d8d81, // -0.35703, -0.93409 + 0xbfd6c21cb1e39771, 0xbfede890520465ce, // -0.3556, -0.93464 + 0xbfd6aa9d7dc77e16, 0xbfeded05f7de47da, // -0.35416, -0.93518 + 0xbfd6931acad55f51, 0xbfedf177004b2534, // -0.35273, -0.93573 + 0xbfd67b949cad63ca, 0xbfedf5e36a9ba59c, // -0.35129, -0.93627 + 0xbfd6640af6f03d9e, 0xbfedfa4b3621271d, // -0.34986, -0.9368 + 0xbfd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // -0.34842, -0.93734 + 0xbfd634ed533be58e, 0xbfee030cee1435b8, // -0.34698, -0.93787 + 0xbfd61d595c88c203, 0xbfee0766d9280f54, // -0.34554, -0.9384 + 0xbfd605c1fcc88f63, 0xbfee0bbc22bd8349, // -0.3441, -0.93893 + 0xbfd5ee27379ea693, 0xbfee100cca2980ac, // -0.34266, -0.93946 + 0xbfd5d68910aee686, 0xbfee1458cec1ad83, // -0.34122, -0.93998 + 0xbfd5bee78b9db3b6, 0xbfee18a02fdc66d9, // -0.33978, -0.94051 + 0xbfd5a742ac0ff78d, 0xbfee1ce2ecd0c0d8, // -0.33833, -0.94103 + 0xbfd58f9a75ab1fdd, 0xbfee212104f686e5, // -0.33689, -0.94154 + 0xbfd577eeec151e47, 0xbfee255a77a63bb8, // -0.33545, -0.94206 + 0xbfd5604012f467b4, 0xbfee298f4439197a, // -0.334, -0.94257 + 0xbfd5488dedeff3be, 0xbfee2dbf6a0911d9, // -0.33255, -0.94308 + 0xbfd530d880af3c24, 0xbfee31eae870ce25, // -0.33111, -0.94359 + 0xbfd5191fceda3c35, 0xbfee3611becbaf69, // -0.32966, -0.9441 + 0xbfd50163dc197047, 0xbfee3a33ec75ce85, // -0.32821, -0.9446 + 0xbfd4e9a4ac15d520, 0xbfee3e5170cbfc46, // -0.32676, -0.94511 + 0xbfd4d1e24278e76a, 0xbfee426a4b2bc17e, // -0.32531, -0.94561 + 0xbfd4ba1ca2eca31c, 0xbfee467e7af35f23, // -0.32386, -0.94611 + 0xbfd4a253d11b82f3, 0xbfee4a8dff81ce5e, // -0.32241, -0.9466 + 0xbfd48a87d0b07fd7, 0xbfee4e98d836c0af, // -0.32096, -0.94709 + 0xbfd472b8a5571054, 0xbfee529f04729ffc, // -0.3195, -0.94759 + 0xbfd45ae652bb2800, 0xbfee56a083968eb1, // -0.31805, -0.94807 + 0xbfd44310dc8936f0, 0xbfee5a9d550467d3, // -0.31659, -0.94856 + 0xbfd42b38466e2928, 0xbfee5e95781ebf1c, // -0.31514, -0.94905 + 0xbfd4135c94176602, 0xbfee6288ec48e112, // -0.31368, -0.94953 + 0xbfd3fb7dc932cfa4, 0xbfee6677b0e6d31e, // -0.31222, -0.95001 + 0xbfd3e39be96ec271, 0xbfee6a61c55d53a7, // -0.31077, -0.95049 + 0xbfd3cbb6f87a146e, 0xbfee6e472911da27, // -0.30931, -0.95096 + 0xbfd3b3cefa0414b7, 0xbfee7227db6a9744, // -0.30785, -0.95144 + 0xbfd39be3f1bc8aef, 0xbfee7603dbce74e9, // -0.30639, -0.95191 + 0xbfd383f5e353b6aa, 0xbfee79db29a5165a, // -0.30493, -0.95238 + 0xbfd36c04d27a4edf, 0xbfee7dadc456d850, // -0.30347, -0.95284 + 0xbfd35410c2e18152, 0xbfee817bab4cd10d, // -0.30201, -0.95331 + 0xbfd33c19b83af207, 0xbfee8544ddf0d075, // -0.30054, -0.95377 + 0xbfd3241fb638baaf, 0xbfee89095bad6025, // -0.29908, -0.95423 + 0xbfd30c22c08d6a13, 0xbfee8cc923edc388, // -0.29762, -0.95469 + 0xbfd2f422daec0386, 0xbfee9084361df7f3, // -0.29615, -0.95514 + 0xbfd2dc200907fe51, 0xbfee943a91aab4b4, // -0.29469, -0.95559 + 0xbfd2c41a4e954520, 0xbfee97ec36016b30, // -0.29322, -0.95605 + 0xbfd2ac11af483572, 0xbfee9b99229046f8, // -0.29175, -0.95649 + 0xbfd294062ed59f05, 0xbfee9f4156c62dda, // -0.29028, -0.95694 + 0xbfd27bf7d0f2c346, 0xbfeea2e4d212c000, // -0.28882, -0.95738 + 0xbfd263e6995554ba, 0xbfeea68393e65800, // -0.28735, -0.95783 + 0xbfd24bd28bb37672, 0xbfeeaa1d9bb20af3, // -0.28588, -0.95827 + 0xbfd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // -0.28441, -0.9587 + 0xbfd21ba1fd3d2623, 0xbfeeb1437af9bb34, // -0.28294, -0.95914 + 0xbfd2038583d727bd, 0xbfeeb4cf515b8811, // -0.28146, -0.95957 + 0xbfd1eb6643499fbb, 0xbfeeb8566b810f2a, // -0.27999, -0.96 + 0xbfd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // -0.27852, -0.96043 + 0xbfd1bb1f7b999480, 0xbfeebf5668eaf2ef, // -0.27705, -0.96086 + 0xbfd1a2f7fbe8f243, 0xbfeec2cf4b1af6b2, // -0.27557, -0.96128 + 0xbfd18acdc3f4873a, 0xbfeec6436ee60309, // -0.2741, -0.9617 + 0xbfd172a0d7765177, 0xbfeec9b2d3c3bf84, // -0.27262, -0.96212 + 0xbfd15a713a28b9d9, 0xbfeecd1d792c8f10, // -0.27115, -0.96254 + 0xbfd1423eefc69378, 0xbfeed0835e999009, // -0.26967, -0.96295 + 0xbfd12a09fc0b1b12, 0xbfeed3e483849c51, // -0.26819, -0.96337 + 0xbfd111d262b1f677, 0xbfeed740e7684963, // -0.26671, -0.96378 + 0xbfd0f998277733f7, 0xbfeeda9889bfe86a, // -0.26523, -0.96418 + 0xbfd0e15b4e1749cd, 0xbfeeddeb6a078651, // -0.26375, -0.96459 + 0xbfd0c91bda4f158d, 0xbfeee13987bbebdc, // -0.26227, -0.96499 + 0xbfd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // -0.26079, -0.96539 + 0xbfd09895327b465e, 0xbfeee7c77961dc9e, // -0.25931, -0.96579 + 0xbfd0804e05eb661e, 0xbfeeeb074c50a544, // -0.25783, -0.96619 + 0xbfd068044deab002, 0xbfeeee425aa6b09a, // -0.25635, -0.96658 + 0xbfd04fb80e37fdae, 0xbfeef178a3e473c2, // -0.25487, -0.96698 + 0xbfd037694a928cac, 0xbfeef4aa278b2032, // -0.25338, -0.96737 + 0xbfd01f1806b9fdd2, 0xbfeef7d6e51ca3c0, // -0.2519, -0.96775 + 0xbfd006c4466e54af, 0xbfeefafedc1ba8b7, // -0.25041, -0.96814 + 0xbfcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // -0.24893, -0.96852 + 0xbfcfac2abeff57ff, 0xbfef014074708ed3, // -0.24744, -0.9689 + 0xbfcf7b7480bd3801, 0xbfef045a14cf738c, // -0.24596, -0.96928 + 0xbfcf4ab9679c9f5c, 0xbfef076eecade0fa, // -0.24447, -0.96966 + 0xbfcf19f97b215f1a, 0xbfef0a7efb9230d7, // -0.24298, -0.97003 + 0xbfcee934c2d006c7, 0xbfef0d8a410379c5, // -0.24149, -0.9704 + 0xbfceb86b462de348, 0xbfef1090bc898f5f, // -0.24, -0.97077 + 0xbfce879d0cc0fdaf, 0xbfef13926dad024e, // -0.23851, -0.97114 + 0xbfce56ca1e101a1b, 0xbfef168f53f7205d, // -0.23702, -0.9715 + 0xbfce25f281a2b684, 0xbfef19876ef1f486, // -0.23553, -0.97187 + 0xbfcdf5163f01099a, 0xbfef1c7abe284708, // -0.23404, -0.97223 + 0xbfcdc4355db40195, 0xbfef1f6941259d7a, // -0.23255, -0.97258 + 0xbfcd934fe5454311, 0xbfef2252f7763ada, // -0.23106, -0.97294 + 0xbfcd6265dd3f27e3, 0xbfef2537e0a71f9f, // -0.22957, -0.97329 + 0xbfcd31774d2cbdee, 0xbfef2817fc4609ce, // -0.22807, -0.97364 + 0xbfcd00843c99c5f9, 0xbfef2af349e17507, // -0.22658, -0.97399 + 0xbfcccf8cb312b286, 0xbfef2dc9c9089a9d, // -0.22508, -0.97434 + 0xbfcc9e90b824a6a9, 0xbfef309b794b719f, // -0.22359, -0.97468 + 0xbfcc6d90535d74dc, 0xbfef33685a3aaef0, // -0.22209, -0.97503 + 0xbfcc3c8b8c4b9dd7, 0xbfef36306b67c556, // -0.2206, -0.97536 + 0xbfcc0b826a7e4f63, 0xbfef38f3ac64e589, // -0.2191, -0.9757 + 0xbfcbda74f5856330, 0xbfef3bb21cc4fe47, // -0.2176, -0.97604 + 0xbfcba96334f15dad, 0xbfef3e6bbc1bbc65, // -0.21611, -0.97637 + 0xbfcb784d30536cda, 0xbfef412089fd8adc, // -0.21461, -0.9767 + 0xbfcb4732ef3d6722, 0xbfef43d085ff92dd, // -0.21311, -0.97703 + 0xbfcb16147941ca2a, 0xbfef467bafb7bbe0, // -0.21161, -0.97735 + 0xbfcae4f1d5f3b9ab, 0xbfef492206bcabb4, // -0.21011, -0.97768 + 0xbfcab3cb0ce6fe44, 0xbfef4bc38aa5c694, // -0.20861, -0.978 + 0xbfca82a025b00451, 0xbfef4e603b0b2f2d, // -0.20711, -0.97832 + 0xbfca517127e3dabc, 0xbfef50f81785c6b9, // -0.20561, -0.97863 + 0xbfca203e1b1831da, 0xbfef538b1faf2d07, // -0.20411, -0.97895 + 0xbfc9ef0706e35a35, 0xbfef56195321c090, // -0.20261, -0.97926 + 0xbfc9bdcbf2dc4366, 0xbfef58a2b1789e84, // -0.2011, -0.97957 + 0xbfc98c8ce69a7aec, 0xbfef5b273a4fa2d9, // -0.1996, -0.97988 + 0xbfc95b49e9b62af9, 0xbfef5da6ed43685d, // -0.1981, -0.98018 + 0xbfc92a0303c8194f, 0xbfef6021c9f148c2, // -0.19659, -0.98048 + 0xbfc8f8b83c69a60a, 0xbfef6297cff75cb0, // -0.19509, -0.98079 + 0xbfc8c7699b34ca7e, 0xbfef6508fef47bd5, // -0.19359, -0.98108 + 0xbfc8961727c41804, 0xbfef677556883cee, // -0.19208, -0.98138 + 0xbfc864c0e9b2b6cf, 0xbfef69dcd652f5de, // -0.19057, -0.98167 + 0xbfc83366e89c64c5, 0xbfef6c3f7df5bbb7, // -0.18907, -0.98196 + 0xbfc802092c1d744b, 0xbfef6e9d4d1262ca, // -0.18756, -0.98225 + 0xbfc7d0a7bbd2cb1b, 0xbfef70f6434b7eb7, // -0.18606, -0.98254 + 0xbfc79f429f59e11d, 0xbfef734a60446279, // -0.18455, -0.98282 + 0xbfc76dd9de50bf31, 0xbfef7599a3a12077, // -0.18304, -0.98311 + 0xbfc73c6d8055fe0a, 0xbfef77e40d068a90, // -0.18153, -0.98339 + 0xbfc70afd8d08c4ff, 0xbfef7a299c1a322a, // -0.18002, -0.98366 + 0xbfc6d98a0c08c8da, 0xbfef7c6a50826840, // -0.17851, -0.98394 + 0xbfc6a81304f64ab2, 0xbfef7ea629e63d6e, // -0.177, -0.98421 + 0xbfc676987f7216b8, 0xbfef80dd27ed8204, // -0.17549, -0.98448 + 0xbfc6451a831d830d, 0xbfef830f4a40c60c, // -0.17398, -0.98475 + 0xbfc61399179a6e94, 0xbfef853c9089595e, // -0.17247, -0.98501 + 0xbfc5e214448b3fc6, 0xbfef8764fa714ba9, // -0.17096, -0.98528 + 0xbfc5b08c1192e381, 0xbfef898887a36c84, // -0.16945, -0.98554 + 0xbfc57f008654cbde, 0xbfef8ba737cb4b78, // -0.16794, -0.9858 + 0xbfc54d71aa74ef02, 0xbfef8dc10a95380d, // -0.16643, -0.98605 + 0xbfc51bdf8597c5f2, 0xbfef8fd5ffae41db, // -0.16491, -0.98631 + 0xbfc4ea4a1f624b61, 0xbfef91e616c43891, // -0.1634, -0.98656 + 0xbfc4b8b17f79fa88, 0xbfef93f14f85ac08, // -0.16189, -0.98681 + 0xbfc48715ad84cdf5, 0xbfef95f7a9a1ec47, // -0.16037, -0.98706 + 0xbfc45576b1293e5a, 0xbfef97f924c9099b, // -0.15886, -0.9873 + 0xbfc423d4920e4166, 0xbfef99f5c0abd496, // -0.15734, -0.98754 + 0xbfc3f22f57db4893, 0xbfef9bed7cfbde29, // -0.15583, -0.98778 + 0xbfc3c0870a383ff6, 0xbfef9de0596b77a3, // -0.15431, -0.98802 + 0xbfc38edbb0cd8d14, 0xbfef9fce55adb2c8, // -0.1528, -0.98826 + 0xbfc35d2d53440db2, 0xbfefa1b7717661d5, // -0.15128, -0.98849 + 0xbfc32b7bf94516a7, 0xbfefa39bac7a1791, // -0.14976, -0.98872 + 0xbfc2f9c7aa7a72af, 0xbfefa57b066e2754, // -0.14825, -0.98895 + 0xbfc2c8106e8e613a, 0xbfefa7557f08a517, // -0.14673, -0.98918 + 0xbfc296564d2b953e, 0xbfefa92b1600657c, // -0.14521, -0.9894 + 0xbfc264994dfd340a, 0xbfefaafbcb0cfddc, // -0.1437, -0.98962 + 0xbfc232d978aed413, 0xbfefacc79de6c44f, // -0.14218, -0.98984 + 0xbfc20116d4ec7bce, 0xbfefae8e8e46cfbb, // -0.14066, -0.99006 + 0xbfc1cf516a62a077, 0xbfefb0509be6f7db, // -0.13914, -0.99027 + 0xbfc19d8940be24e7, 0xbfefb20dc681d54d, // -0.13762, -0.99049 + 0xbfc16bbe5fac5865, 0xbfefb3c60dd2c199, // -0.1361, -0.9907 + 0xbfc139f0cedaf576, 0xbfefb5797195d741, // -0.13458, -0.9909 + 0xbfc1082095f820b0, 0xbfefb727f187f1c7, // -0.13306, -0.99111 + 0xbfc0d64dbcb26786, 0xbfefb8d18d66adb7, // -0.13154, -0.99131 + 0xbfc0a4784ab8bf1d, 0xbfefba7644f068b5, // -0.13002, -0.99151 + 0xbfc072a047ba831d, 0xbfefbc1617e44186, // -0.1285, -0.99171 + 0xbfc040c5bb67747e, 0xbfefbdb106021816, // -0.12698, -0.99191 + 0xbfc00ee8ad6fb85b, 0xbfefbf470f0a8d88, // -0.12545, -0.9921 + 0xbfbfba124b07ad85, 0xbfefc0d832bf043a, // -0.12393, -0.99229 + 0xbfbf564e56a9730e, 0xbfefc26470e19fd3, // -0.12241, -0.99248 + 0xbfbef2858d27561b, 0xbfefc3ebc935454c, // -0.12089, -0.99267 + 0xbfbe8eb7fde4aa3e, 0xbfefc56e3b7d9af6, // -0.11937, -0.99285 + 0xbfbe2ae5b8457f77, 0xbfefc6ebc77f0887, // -0.11784, -0.99303 + 0xbfbdc70ecbae9fc8, 0xbfefc8646cfeb721, // -0.11632, -0.99321 + 0xbfbd633347858ce4, 0xbfefc9d82bc2915e, // -0.11479, -0.99339 + 0xbfbcff533b307dc1, 0xbfefcb4703914354, // -0.11327, -0.99356 + 0xbfbc9b6eb6165c42, 0xbfefccb0f4323aa3, // -0.11175, -0.99374 + 0xbfbc3785c79ec2d5, 0xbfefce15fd6da67b, // -0.11022, -0.99391 + 0xbfbbd3987f31fa0e, 0xbfefcf761f0c77a3, // -0.1087, -0.99407 + 0xbfbb6fa6ec38f64c, 0xbfefd0d158d86087, // -0.10717, -0.99424 + 0xbfbb0bb11e1d5559, 0xbfefd227aa9bd53b, // -0.10565, -0.9944 + 0xbfbaa7b724495c04, 0xbfefd37914220b84, // -0.10412, -0.99456 + 0xbfba43b90e27f3c4, 0xbfefd4c59536fae4, // -0.1026, -0.99472 + 0xbfb9dfb6eb24a85c, 0xbfefd60d2da75c9e, // -0.10107, -0.99488 + 0xbfb97bb0caaba56f, 0xbfefd74fdd40abbf, // -0.099544, -0.99503 + 0xbfb917a6bc29b42c, 0xbfefd88da3d12526, // -0.098017, -0.99518 + 0xbfb8b398cf0c38e0, 0xbfefd9c68127c78c, // -0.09649, -0.99533 + 0xbfb84f8712c130a0, 0xbfefdafa7514538c, // -0.094963, -0.99548 + 0xbfb7eb7196b72ee4, 0xbfefdc297f674ba9, // -0.093436, -0.99563 + 0xbfb787586a5d5b21, 0xbfefdd539ff1f456, // -0.091909, -0.99577 + 0xbfb7233b9d236e71, 0xbfefde78d68653fd, // -0.090381, -0.99591 + 0xbfb6bf1b3e79b129, 0xbfefdf9922f73307, // -0.088854, -0.99604 + 0xbfb65af75dd0f87b, 0xbfefe0b485181be3, // -0.087326, -0.99618 + 0xbfb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // -0.085797, -0.99631 + 0xbfb592a554489bc8, 0xbfefe2dc89bbff08, // -0.084269, -0.99644 + 0xbfb52e774a4d4d0a, 0xbfefe3e92be9d886, // -0.08274, -0.99657 + 0xbfb4ca45fc1ba8b6, 0xbfefe4f0e31d7a4a, // -0.081211, -0.9967 + 0xbfb4661179272096, 0xbfefe5f3af2e3940, // -0.079682, -0.99682 + 0xbfb401d9d0e3a507, 0xbfefe6f18ff42c84, // -0.078153, -0.99694 + 0xbfb39d9f12c5a299, 0xbfefe7ea85482d60, // -0.076624, -0.99706 + 0xbfb339614e41ffa5, 0xbfefe8de8f03d75c, // -0.075094, -0.99718 + 0xbfb2d52092ce19f6, 0xbfefe9cdad01883a, // -0.073565, -0.99729 + 0xbfb270dcefdfc45b, 0xbfefeab7df1c6005, // -0.072035, -0.9974 + 0xbfb20c9674ed444c, 0xbfefeb9d2530410f, // -0.070505, -0.99751 + 0xbfb1a84d316d4f8a, 0xbfefec7d7f19cffc, // -0.068974, -0.99762 + 0xbfb1440134d709b2, 0xbfefed58ecb673c4, // -0.067444, -0.99772 + 0xbfb0dfb28ea201e6, 0xbfefee2f6de455ba, // -0.065913, -0.99783 + 0xbfb07b614e463064, 0xbfefef0102826191, // -0.064383, -0.99793 + 0xbfb0170d833bf421, 0xbfefefcdaa704562, // -0.062852, -0.99802 + 0xbfaf656e79f820e0, 0xbfeff095658e71ad, // -0.061321, -0.99812 + 0xbfae9cbd15ff5527, 0xbfeff15833be1965, // -0.05979, -0.99821 + 0xbfadd406f9808ec8, 0xbfeff21614e131ed, // -0.058258, -0.9983 + 0xbfad0b4c436f91d0, 0xbfeff2cf08da7321, // -0.056727, -0.99839 + 0xbfac428d12c0d7e3, 0xbfeff3830f8d575c, // -0.055195, -0.99848 + 0xbfab79c986698b78, 0xbfeff43228de1b77, // -0.053664, -0.99856 + 0xbfaab101bd5f8317, 0xbfeff4dc54b1bed3, // -0.052132, -0.99864 + 0xbfa9e835d6993c87, 0xbfeff58192ee0358, // -0.0506, -0.99872 + 0xbfa91f65f10dd814, 0xbfeff621e3796d7e, // -0.049068, -0.9988 + 0xbfa856922bb513c1, 0xbfeff6bd463b444d, // -0.047535, -0.99887 + 0xbfa78dbaa5874685, 0xbfeff753bb1b9164, // -0.046003, -0.99894 + 0xbfa6c4df7d7d5b84, 0xbfeff7e5420320f9, // -0.044471, -0.99901 + 0xbfa5fc00d290cd43, 0xbfeff871dadb81df, // -0.042938, -0.99908 + 0xbfa5331ec3bba0eb, 0xbfeff8f9858f058b, // -0.041406, -0.99914 + 0xbfa46a396ff86179, 0xbfeff97c4208c014, // -0.039873, -0.9992 + 0xbfa3a150f6421afc, 0xbfeff9fa10348837, // -0.03834, -0.99926 + 0xbfa2d865759455cd, 0xbfeffa72effef75d, // -0.036807, -0.99932 + 0xbfa20f770ceb11c6, 0xbfeffae6e1556998, // -0.035274, -0.99938 + 0xbfa14685db42c17e, 0xbfeffb55e425fdae, // -0.033741, -0.99943 + 0xbfa07d91ff984580, 0xbfeffbbff85f9515, // -0.032208, -0.99948 + 0xbf9f693731d1cf01, 0xbfeffc251df1d3f8, // -0.030675, -0.99953 + 0xbf9dd7458c64ab39, 0xbfeffc8554cd213a, // -0.029142, -0.99958 + 0xbf9c454f4ce53b1c, 0xbfeffce09ce2a679, // -0.027608, -0.99962 + 0xbf9ab354b1504fca, 0xbfeffd36f624500c, // -0.026075, -0.99966 + 0xbf992155f7a3667e, 0xbfeffd886084cd0d, // -0.024541, -0.9997 + 0xbf978f535ddc9f03, 0xbfeffdd4dbf78f52, // -0.023008, -0.99974 + 0xbf95fd4d21fab226, 0xbfeffe1c6870cb77, // -0.021474, -0.99977 + 0xbf946b4381fce81c, 0xbfeffe5f05e578db, // -0.01994, -0.9998 + 0xbf92d936bbe30efd, 0xbfeffe9cb44b51a1, // -0.018407, -0.99983 + 0xbf9147270dad7132, 0xbfeffed57398d2b7, // -0.016873, -0.99986 + 0xbf8f6a296ab997ca, 0xbfefff0943c53bd1, // -0.015339, -0.99988 + 0xbf8c45ffe1e48ad9, 0xbfefff3824c88f6f, // -0.013805, -0.9999 + 0xbf8921d1fcdec784, 0xbfefff62169b92db, // -0.012272, -0.99992 + 0xbf85fda037ac05e0, 0xbfefff871937ce2f, // -0.010738, -0.99994 + 0xbf82d96b0e509703, 0xbfefffa72c978c4f, //-0.0092038, -0.99996 + 0xbf7f6a65f9a2a3c5, 0xbfefffc250b5daef, //-0.0076698, -0.99997 + 0xbf7921f0fe670071, 0xbfefffd8858e8a92, //-0.0061359, -0.99998 + 0xbf72d97822f996bc, 0xbfefffe9cb1e2e8d, //-0.0046019, -0.99999 + 0xbf6921f8becca4ba, 0xbfeffff621621d02, // -0.003068, -1 + 0xbf5921faaee6472d, 0xbfeffffd88586ee6, // -0.001534, -1 + 0x0000000000000000, 0xbff0000000000000, // 0, -1 + 0x3f5921faaee6472d, 0xbfeffffd88586ee6, // 0.001534, -1 + 0x3f6921f8becca4ba, 0xbfeffff621621d02, // 0.003068, -1 + 0x3f72d97822f996bc, 0xbfefffe9cb1e2e8d, // 0.0046019, -0.99999 + 0x3f7921f0fe670071, 0xbfefffd8858e8a92, // 0.0061359, -0.99998 + 0x3f7f6a65f9a2a3c5, 0xbfefffc250b5daef, // 0.0076698, -0.99997 + 0x3f82d96b0e509703, 0xbfefffa72c978c4f, // 0.0092038, -0.99996 + 0x3f85fda037ac05e0, 0xbfefff871937ce2f, // 0.010738, -0.99994 + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992 + 0x3f8c45ffe1e48ad9, 0xbfefff3824c88f6f, // 0.013805, -0.9999 + 0x3f8f6a296ab997ca, 0xbfefff0943c53bd1, // 0.015339, -0.99988 + 0x3f9147270dad7132, 0xbfeffed57398d2b7, // 0.016873, -0.99986 + 0x3f92d936bbe30efd, 0xbfeffe9cb44b51a1, // 0.018407, -0.99983 + 0x3f946b4381fce81c, 0xbfeffe5f05e578db, // 0.01994, -0.9998 + 0x3f95fd4d21fab226, 0xbfeffe1c6870cb77, // 0.021474, -0.99977 + 0x3f978f535ddc9f03, 0xbfeffdd4dbf78f52, // 0.023008, -0.99974 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3f9ab354b1504fca, 0xbfeffd36f624500c, // 0.026075, -0.99966 + 0x3f9c454f4ce53b1c, 0xbfeffce09ce2a679, // 0.027608, -0.99962 + 0x3f9dd7458c64ab39, 0xbfeffc8554cd213a, // 0.029142, -0.99958 + 0x3f9f693731d1cf01, 0xbfeffc251df1d3f8, // 0.030675, -0.99953 + 0x3fa07d91ff984580, 0xbfeffbbff85f9515, // 0.032208, -0.99948 + 0x3fa14685db42c17e, 0xbfeffb55e425fdae, // 0.033741, -0.99943 + 0x3fa20f770ceb11c6, 0xbfeffae6e1556998, // 0.035274, -0.99938 + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932 + 0x3fa3a150f6421afc, 0xbfeff9fa10348837, // 0.03834, -0.99926 + 0x3fa46a396ff86179, 0xbfeff97c4208c014, // 0.039873, -0.9992 + 0x3fa5331ec3bba0eb, 0xbfeff8f9858f058b, // 0.041406, -0.99914 + 0x3fa5fc00d290cd43, 0xbfeff871dadb81df, // 0.042938, -0.99908 + 0x3fa6c4df7d7d5b84, 0xbfeff7e5420320f9, // 0.044471, -0.99901 + 0x3fa78dbaa5874685, 0xbfeff753bb1b9164, // 0.046003, -0.99894 + 0x3fa856922bb513c1, 0xbfeff6bd463b444d, // 0.047535, -0.99887 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3fa9e835d6993c87, 0xbfeff58192ee0358, // 0.0506, -0.99872 + 0x3faab101bd5f8317, 0xbfeff4dc54b1bed3, // 0.052132, -0.99864 + 0x3fab79c986698b78, 0xbfeff43228de1b77, // 0.053664, -0.99856 + 0x3fac428d12c0d7e3, 0xbfeff3830f8d575c, // 0.055195, -0.99848 + 0x3fad0b4c436f91d0, 0xbfeff2cf08da7321, // 0.056727, -0.99839 + 0x3fadd406f9808ec8, 0xbfeff21614e131ed, // 0.058258, -0.9983 + 0x3fae9cbd15ff5527, 0xbfeff15833be1965, // 0.05979, -0.99821 + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812 + 0x3fb0170d833bf421, 0xbfefefcdaa704562, // 0.062852, -0.99802 + 0x3fb07b614e463064, 0xbfefef0102826191, // 0.064383, -0.99793 + 0x3fb0dfb28ea201e6, 0xbfefee2f6de455ba, // 0.065913, -0.99783 + 0x3fb1440134d709b2, 0xbfefed58ecb673c4, // 0.067444, -0.99772 + 0x3fb1a84d316d4f8a, 0xbfefec7d7f19cffc, // 0.068974, -0.99762 + 0x3fb20c9674ed444c, 0xbfefeb9d2530410f, // 0.070505, -0.99751 + 0x3fb270dcefdfc45b, 0xbfefeab7df1c6005, // 0.072035, -0.9974 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb339614e41ffa5, 0xbfefe8de8f03d75c, // 0.075094, -0.99718 + 0x3fb39d9f12c5a299, 0xbfefe7ea85482d60, // 0.076624, -0.99706 + 0x3fb401d9d0e3a507, 0xbfefe6f18ff42c84, // 0.078153, -0.99694 + 0x3fb4661179272096, 0xbfefe5f3af2e3940, // 0.079682, -0.99682 + 0x3fb4ca45fc1ba8b6, 0xbfefe4f0e31d7a4a, // 0.081211, -0.9967 + 0x3fb52e774a4d4d0a, 0xbfefe3e92be9d886, // 0.08274, -0.99657 + 0x3fb592a554489bc8, 0xbfefe2dc89bbff08, // 0.084269, -0.99644 + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631 + 0x3fb65af75dd0f87b, 0xbfefe0b485181be3, // 0.087326, -0.99618 + 0x3fb6bf1b3e79b129, 0xbfefdf9922f73307, // 0.088854, -0.99604 + 0x3fb7233b9d236e71, 0xbfefde78d68653fd, // 0.090381, -0.99591 + 0x3fb787586a5d5b21, 0xbfefdd539ff1f456, // 0.091909, -0.99577 + 0x3fb7eb7196b72ee4, 0xbfefdc297f674ba9, // 0.093436, -0.99563 + 0x3fb84f8712c130a0, 0xbfefdafa7514538c, // 0.094963, -0.99548 + 0x3fb8b398cf0c38e0, 0xbfefd9c68127c78c, // 0.09649, -0.99533 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fb97bb0caaba56f, 0xbfefd74fdd40abbf, // 0.099544, -0.99503 + 0x3fb9dfb6eb24a85c, 0xbfefd60d2da75c9e, // 0.10107, -0.99488 + 0x3fba43b90e27f3c4, 0xbfefd4c59536fae4, // 0.1026, -0.99472 + 0x3fbaa7b724495c04, 0xbfefd37914220b84, // 0.10412, -0.99456 + 0x3fbb0bb11e1d5559, 0xbfefd227aa9bd53b, // 0.10565, -0.9944 + 0x3fbb6fa6ec38f64c, 0xbfefd0d158d86087, // 0.10717, -0.99424 + 0x3fbbd3987f31fa0e, 0xbfefcf761f0c77a3, // 0.1087, -0.99407 + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391 + 0x3fbc9b6eb6165c42, 0xbfefccb0f4323aa3, // 0.11175, -0.99374 + 0x3fbcff533b307dc1, 0xbfefcb4703914354, // 0.11327, -0.99356 + 0x3fbd633347858ce4, 0xbfefc9d82bc2915e, // 0.11479, -0.99339 + 0x3fbdc70ecbae9fc8, 0xbfefc8646cfeb721, // 0.11632, -0.99321 + 0x3fbe2ae5b8457f77, 0xbfefc6ebc77f0887, // 0.11784, -0.99303 + 0x3fbe8eb7fde4aa3e, 0xbfefc56e3b7d9af6, // 0.11937, -0.99285 + 0x3fbef2858d27561b, 0xbfefc3ebc935454c, // 0.12089, -0.99267 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fbfba124b07ad85, 0xbfefc0d832bf043a, // 0.12393, -0.99229 + 0x3fc00ee8ad6fb85b, 0xbfefbf470f0a8d88, // 0.12545, -0.9921 + 0x3fc040c5bb67747e, 0xbfefbdb106021816, // 0.12698, -0.99191 + 0x3fc072a047ba831d, 0xbfefbc1617e44186, // 0.1285, -0.99171 + 0x3fc0a4784ab8bf1d, 0xbfefba7644f068b5, // 0.13002, -0.99151 + 0x3fc0d64dbcb26786, 0xbfefb8d18d66adb7, // 0.13154, -0.99131 + 0x3fc1082095f820b0, 0xbfefb727f187f1c7, // 0.13306, -0.99111 + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909 + 0x3fc16bbe5fac5865, 0xbfefb3c60dd2c199, // 0.1361, -0.9907 + 0x3fc19d8940be24e7, 0xbfefb20dc681d54d, // 0.13762, -0.99049 + 0x3fc1cf516a62a077, 0xbfefb0509be6f7db, // 0.13914, -0.99027 + 0x3fc20116d4ec7bce, 0xbfefae8e8e46cfbb, // 0.14066, -0.99006 + 0x3fc232d978aed413, 0xbfefacc79de6c44f, // 0.14218, -0.98984 + 0x3fc264994dfd340a, 0xbfefaafbcb0cfddc, // 0.1437, -0.98962 + 0x3fc296564d2b953e, 0xbfefa92b1600657c, // 0.14521, -0.9894 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc2f9c7aa7a72af, 0xbfefa57b066e2754, // 0.14825, -0.98895 + 0x3fc32b7bf94516a7, 0xbfefa39bac7a1791, // 0.14976, -0.98872 + 0x3fc35d2d53440db2, 0xbfefa1b7717661d5, // 0.15128, -0.98849 + 0x3fc38edbb0cd8d14, 0xbfef9fce55adb2c8, // 0.1528, -0.98826 + 0x3fc3c0870a383ff6, 0xbfef9de0596b77a3, // 0.15431, -0.98802 + 0x3fc3f22f57db4893, 0xbfef9bed7cfbde29, // 0.15583, -0.98778 + 0x3fc423d4920e4166, 0xbfef99f5c0abd496, // 0.15734, -0.98754 + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873 + 0x3fc48715ad84cdf5, 0xbfef95f7a9a1ec47, // 0.16037, -0.98706 + 0x3fc4b8b17f79fa88, 0xbfef93f14f85ac08, // 0.16189, -0.98681 + 0x3fc4ea4a1f624b61, 0xbfef91e616c43891, // 0.1634, -0.98656 + 0x3fc51bdf8597c5f2, 0xbfef8fd5ffae41db, // 0.16491, -0.98631 + 0x3fc54d71aa74ef02, 0xbfef8dc10a95380d, // 0.16643, -0.98605 + 0x3fc57f008654cbde, 0xbfef8ba737cb4b78, // 0.16794, -0.9858 + 0x3fc5b08c1192e381, 0xbfef898887a36c84, // 0.16945, -0.98554 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc61399179a6e94, 0xbfef853c9089595e, // 0.17247, -0.98501 + 0x3fc6451a831d830d, 0xbfef830f4a40c60c, // 0.17398, -0.98475 + 0x3fc676987f7216b8, 0xbfef80dd27ed8204, // 0.17549, -0.98448 + 0x3fc6a81304f64ab2, 0xbfef7ea629e63d6e, // 0.177, -0.98421 + 0x3fc6d98a0c08c8da, 0xbfef7c6a50826840, // 0.17851, -0.98394 + 0x3fc70afd8d08c4ff, 0xbfef7a299c1a322a, // 0.18002, -0.98366 + 0x3fc73c6d8055fe0a, 0xbfef77e40d068a90, // 0.18153, -0.98339 + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311 + 0x3fc79f429f59e11d, 0xbfef734a60446279, // 0.18455, -0.98282 + 0x3fc7d0a7bbd2cb1b, 0xbfef70f6434b7eb7, // 0.18606, -0.98254 + 0x3fc802092c1d744b, 0xbfef6e9d4d1262ca, // 0.18756, -0.98225 + 0x3fc83366e89c64c5, 0xbfef6c3f7df5bbb7, // 0.18907, -0.98196 + 0x3fc864c0e9b2b6cf, 0xbfef69dcd652f5de, // 0.19057, -0.98167 + 0x3fc8961727c41804, 0xbfef677556883cee, // 0.19208, -0.98138 + 0x3fc8c7699b34ca7e, 0xbfef6508fef47bd5, // 0.19359, -0.98108 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fc92a0303c8194f, 0xbfef6021c9f148c2, // 0.19659, -0.98048 + 0x3fc95b49e9b62af9, 0xbfef5da6ed43685d, // 0.1981, -0.98018 + 0x3fc98c8ce69a7aec, 0xbfef5b273a4fa2d9, // 0.1996, -0.97988 + 0x3fc9bdcbf2dc4366, 0xbfef58a2b1789e84, // 0.2011, -0.97957 + 0x3fc9ef0706e35a35, 0xbfef56195321c090, // 0.20261, -0.97926 + 0x3fca203e1b1831da, 0xbfef538b1faf2d07, // 0.20411, -0.97895 + 0x3fca517127e3dabc, 0xbfef50f81785c6b9, // 0.20561, -0.97863 + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832 + 0x3fcab3cb0ce6fe44, 0xbfef4bc38aa5c694, // 0.20861, -0.978 + 0x3fcae4f1d5f3b9ab, 0xbfef492206bcabb4, // 0.21011, -0.97768 + 0x3fcb16147941ca2a, 0xbfef467bafb7bbe0, // 0.21161, -0.97735 + 0x3fcb4732ef3d6722, 0xbfef43d085ff92dd, // 0.21311, -0.97703 + 0x3fcb784d30536cda, 0xbfef412089fd8adc, // 0.21461, -0.9767 + 0x3fcba96334f15dad, 0xbfef3e6bbc1bbc65, // 0.21611, -0.97637 + 0x3fcbda74f5856330, 0xbfef3bb21cc4fe47, // 0.2176, -0.97604 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcc3c8b8c4b9dd7, 0xbfef36306b67c556, // 0.2206, -0.97536 + 0x3fcc6d90535d74dc, 0xbfef33685a3aaef0, // 0.22209, -0.97503 + 0x3fcc9e90b824a6a9, 0xbfef309b794b719f, // 0.22359, -0.97468 + 0x3fcccf8cb312b286, 0xbfef2dc9c9089a9d, // 0.22508, -0.97434 + 0x3fcd00843c99c5f9, 0xbfef2af349e17507, // 0.22658, -0.97399 + 0x3fcd31774d2cbdee, 0xbfef2817fc4609ce, // 0.22807, -0.97364 + 0x3fcd6265dd3f27e3, 0xbfef2537e0a71f9f, // 0.22957, -0.97329 + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294 + 0x3fcdc4355db40195, 0xbfef1f6941259d7a, // 0.23255, -0.97258 + 0x3fcdf5163f01099a, 0xbfef1c7abe284708, // 0.23404, -0.97223 + 0x3fce25f281a2b684, 0xbfef19876ef1f486, // 0.23553, -0.97187 + 0x3fce56ca1e101a1b, 0xbfef168f53f7205d, // 0.23702, -0.9715 + 0x3fce879d0cc0fdaf, 0xbfef13926dad024e, // 0.23851, -0.97114 + 0x3fceb86b462de348, 0xbfef1090bc898f5f, // 0.24, -0.97077 + 0x3fcee934c2d006c7, 0xbfef0d8a410379c5, // 0.24149, -0.9704 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fcf4ab9679c9f5c, 0xbfef076eecade0fa, // 0.24447, -0.96966 + 0x3fcf7b7480bd3801, 0xbfef045a14cf738c, // 0.24596, -0.96928 + 0x3fcfac2abeff57ff, 0xbfef014074708ed3, // 0.24744, -0.9689 + 0x3fcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // 0.24893, -0.96852 + 0x3fd006c4466e54af, 0xbfeefafedc1ba8b7, // 0.25041, -0.96814 + 0x3fd01f1806b9fdd2, 0xbfeef7d6e51ca3c0, // 0.2519, -0.96775 + 0x3fd037694a928cac, 0xbfeef4aa278b2032, // 0.25338, -0.96737 + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698 + 0x3fd068044deab002, 0xbfeeee425aa6b09a, // 0.25635, -0.96658 + 0x3fd0804e05eb661e, 0xbfeeeb074c50a544, // 0.25783, -0.96619 + 0x3fd09895327b465e, 0xbfeee7c77961dc9e, // 0.25931, -0.96579 + 0x3fd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // 0.26079, -0.96539 + 0x3fd0c91bda4f158d, 0xbfeee13987bbebdc, // 0.26227, -0.96499 + 0x3fd0e15b4e1749cd, 0xbfeeddeb6a078651, // 0.26375, -0.96459 + 0x3fd0f998277733f7, 0xbfeeda9889bfe86a, // 0.26523, -0.96418 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd12a09fc0b1b12, 0xbfeed3e483849c51, // 0.26819, -0.96337 + 0x3fd1423eefc69378, 0xbfeed0835e999009, // 0.26967, -0.96295 + 0x3fd15a713a28b9d9, 0xbfeecd1d792c8f10, // 0.27115, -0.96254 + 0x3fd172a0d7765177, 0xbfeec9b2d3c3bf84, // 0.27262, -0.96212 + 0x3fd18acdc3f4873a, 0xbfeec6436ee60309, // 0.2741, -0.9617 + 0x3fd1a2f7fbe8f243, 0xbfeec2cf4b1af6b2, // 0.27557, -0.96128 + 0x3fd1bb1f7b999480, 0xbfeebf5668eaf2ef, // 0.27705, -0.96086 + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043 + 0x3fd1eb6643499fbb, 0xbfeeb8566b810f2a, // 0.27999, -0.96 + 0x3fd2038583d727bd, 0xbfeeb4cf515b8811, // 0.28146, -0.95957 + 0x3fd21ba1fd3d2623, 0xbfeeb1437af9bb34, // 0.28294, -0.95914 + 0x3fd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // 0.28441, -0.9587 + 0x3fd24bd28bb37672, 0xbfeeaa1d9bb20af3, // 0.28588, -0.95827 + 0x3fd263e6995554ba, 0xbfeea68393e65800, // 0.28735, -0.95783 + 0x3fd27bf7d0f2c346, 0xbfeea2e4d212c000, // 0.28882, -0.95738 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd2ac11af483572, 0xbfee9b99229046f8, // 0.29175, -0.95649 + 0x3fd2c41a4e954520, 0xbfee97ec36016b30, // 0.29322, -0.95605 + 0x3fd2dc200907fe51, 0xbfee943a91aab4b4, // 0.29469, -0.95559 + 0x3fd2f422daec0386, 0xbfee9084361df7f3, // 0.29615, -0.95514 + 0x3fd30c22c08d6a13, 0xbfee8cc923edc388, // 0.29762, -0.95469 + 0x3fd3241fb638baaf, 0xbfee89095bad6025, // 0.29908, -0.95423 + 0x3fd33c19b83af207, 0xbfee8544ddf0d075, // 0.30054, -0.95377 + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331 + 0x3fd36c04d27a4edf, 0xbfee7dadc456d850, // 0.30347, -0.95284 + 0x3fd383f5e353b6aa, 0xbfee79db29a5165a, // 0.30493, -0.95238 + 0x3fd39be3f1bc8aef, 0xbfee7603dbce74e9, // 0.30639, -0.95191 + 0x3fd3b3cefa0414b7, 0xbfee7227db6a9744, // 0.30785, -0.95144 + 0x3fd3cbb6f87a146e, 0xbfee6e472911da27, // 0.30931, -0.95096 + 0x3fd3e39be96ec271, 0xbfee6a61c55d53a7, // 0.31077, -0.95049 + 0x3fd3fb7dc932cfa4, 0xbfee6677b0e6d31e, // 0.31222, -0.95001 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd42b38466e2928, 0xbfee5e95781ebf1c, // 0.31514, -0.94905 + 0x3fd44310dc8936f0, 0xbfee5a9d550467d3, // 0.31659, -0.94856 + 0x3fd45ae652bb2800, 0xbfee56a083968eb1, // 0.31805, -0.94807 + 0x3fd472b8a5571054, 0xbfee529f04729ffc, // 0.3195, -0.94759 + 0x3fd48a87d0b07fd7, 0xbfee4e98d836c0af, // 0.32096, -0.94709 + 0x3fd4a253d11b82f3, 0xbfee4a8dff81ce5e, // 0.32241, -0.9466 + 0x3fd4ba1ca2eca31c, 0xbfee467e7af35f23, // 0.32386, -0.94611 + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561 + 0x3fd4e9a4ac15d520, 0xbfee3e5170cbfc46, // 0.32676, -0.94511 + 0x3fd50163dc197047, 0xbfee3a33ec75ce85, // 0.32821, -0.9446 + 0x3fd5191fceda3c35, 0xbfee3611becbaf69, // 0.32966, -0.9441 + 0x3fd530d880af3c24, 0xbfee31eae870ce25, // 0.33111, -0.94359 + 0x3fd5488dedeff3be, 0xbfee2dbf6a0911d9, // 0.33255, -0.94308 + 0x3fd5604012f467b4, 0xbfee298f4439197a, // 0.334, -0.94257 + 0x3fd577eeec151e47, 0xbfee255a77a63bb8, // 0.33545, -0.94206 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd5a742ac0ff78d, 0xbfee1ce2ecd0c0d8, // 0.33833, -0.94103 + 0x3fd5bee78b9db3b6, 0xbfee18a02fdc66d9, // 0.33978, -0.94051 + 0x3fd5d68910aee686, 0xbfee1458cec1ad83, // 0.34122, -0.93998 + 0x3fd5ee27379ea693, 0xbfee100cca2980ac, // 0.34266, -0.93946 + 0x3fd605c1fcc88f63, 0xbfee0bbc22bd8349, // 0.3441, -0.93893 + 0x3fd61d595c88c203, 0xbfee0766d9280f54, // 0.34554, -0.9384 + 0x3fd634ed533be58e, 0xbfee030cee1435b8, // 0.34698, -0.93787 + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734 + 0x3fd6640af6f03d9e, 0xbfedfa4b3621271d, // 0.34986, -0.9368 + 0x3fd67b949cad63ca, 0xbfedf5e36a9ba59c, // 0.35129, -0.93627 + 0x3fd6931acad55f51, 0xbfedf177004b2534, // 0.35273, -0.93573 + 0x3fd6aa9d7dc77e16, 0xbfeded05f7de47da, // 0.35416, -0.93518 + 0x3fd6c21cb1e39771, 0xbfede890520465ce, // 0.3556, -0.93464 + 0x3fd6d998638a0cb5, 0xbfede4160f6d8d81, // 0.35703, -0.93409 + 0x3fd6f1108f1bc9c5, 0xbfeddf9730ca837b, // 0.35846, -0.93354 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd71ff6458782ec, 0xbfedd68ba2267a25, // 0.36133, -0.93244 + 0x3fd73763c9261092, 0xbfedd1fef38a915a, // 0.36276, -0.93188 + 0x3fd74ecdb8390a3e, 0xbfedcd6dabaca3a5, // 0.36418, -0.93133 + 0x3fd766340f2418f6, 0xbfedc8d7cb410260, // 0.36561, -0.93077 + 0x3fd77d96ca4b73a6, 0xbfedc43d52fcb453, // 0.36704, -0.93021 + 0x3fd794f5e613dfae, 0xbfedbf9e4395759a, // 0.36847, -0.92964 + 0x3fd7ac515ee2b172, 0xbfedbafa9dc1b78d, // 0.36989, -0.92907 + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851 + 0x3fd7dafd592ba621, 0xbfedb1a591b20c38, // 0.37274, -0.92794 + 0x3fd7f24dd37341e3, 0xbfedacf42ce68ab9, // 0.37416, -0.92736 + 0x3fd8099a9c5c362d, 0xbfeda83e348f613b, // 0.37559, -0.92679 + 0x3fd820e3b04eaac4, 0xbfeda383a9668988, // 0.37701, -0.92621 + 0x3fd838290bb359c8, 0xbfed9ec48c26b1f3, // 0.37843, -0.92563 + 0x3fd84f6aaaf3903f, 0xbfed9a00dd8b3d46, // 0.37985, -0.92505 + 0x3fd866a88a792ea0, 0xbfed95389e50429b, // 0.38127, -0.92447 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd89518fbff098e, 0xbfed8b9a70ef9cb4, // 0.3841, -0.92329 + 0x3fd8ac4b86d5ed44, 0xbfed86c48445a450, // 0.38552, -0.9227 + 0x3fd8c37a439f884f, 0xbfed81ea09f38b63, // 0.38693, -0.92211 + 0x3fd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // 0.38835, -0.92151 + 0x3fd8f1cc44bea329, 0xbfed78276f5617c6, // 0.38976, -0.92092 + 0x3fd908ef81ef7bd1, 0xbfed733f508c0dff, // 0.39117, -0.92032 + 0x3fd9200ee2c9be97, 0xbfed6e52a71c8547, // 0.39258, -0.91972 + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911 + 0x3fd94e420137bce3, 0xbfed646bb7574de5, // 0.3954, -0.91851 + 0x3fd96555b7ab948f, 0xbfed5f7172888a7f, // 0.39681, -0.9179 + 0x3fd97c6583890fc2, 0xbfed5a72a6221e73, // 0.39822, -0.91729 + 0x3fd993716141bdfe, 0xbfed556f52e93eb1, // 0.39962, -0.91668 + 0x3fd9aa794d47c9ee, 0xbfed506779a3d2d9, // 0.40103, -0.91606 + 0x3fd9c17d440df9f2, 0xbfed4b5b1b187524, // 0.40243, -0.91545 + 0x3fd9d87d4207b0ab, 0xbfed464a380e7242, // 0.40384, -0.91483 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fda067145664d57, 0xbfed3c1ae79f2b4e, // 0.40664, -0.91359 + 0x3fda1d6543b50ac0, 0xbfed36fc7bcbfbdc, // 0.40804, -0.91296 + 0x3fda34553b0afee5, 0xbfed31d98e9e503a, // 0.40944, -0.91234 + 0x3fda4b4127dea1e4, 0xbfed2cb220e0ef9f, // 0.41084, -0.91171 + 0x3fda622906a70b63, 0xbfed2786335f52fc, // 0.41224, -0.91107 + 0x3fda790cd3dbf31a, 0xbfed2255c6e5a4e1, // 0.41364, -0.91044 + 0x3fda8fec8bf5b166, 0xbfed1d20dc40c15c, // 0.41503, -0.90981 + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917 + 0x3fdabd9faebc3980, 0xbfed12a98fac410c, // 0.41782, -0.90853 + 0x3fdad473125cdc08, 0xbfed0d672f59d2b9, // 0.41922, -0.90789 + 0x3fdaeb4252ca07ab, 0xbfed082054168bac, // 0.42061, -0.90724 + 0x3fdb020d6c7f4009, 0xbfed02d4feb2bd92, // 0.422, -0.9066 + 0x3fdb18d45bf8aca6, 0xbfecfd852fff6ad4, // 0.42339, -0.90595 + 0x3fdb2f971db31972, 0xbfecf830e8ce467b, // 0.42478, -0.9053 + 0x3fdb4655ae2bf757, 0xbfecf2d829f1b40e, // 0.42617, -0.90464 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdb73c62d520624, 0xbfece819488344ce, // 0.42894, -0.90333 + 0x3fdb8a7814fd5693, 0xbfece2b32799a060, // 0.43033, -0.90267 + 0x3fdba125bd63583e, 0xbfecdd489254fe65, // 0.43171, -0.90201 + 0x3fdbb7cf2304bd01, 0xbfecd7d9898b32f6, // 0.43309, -0.90135 + 0x3fdbce744262deee, 0xbfecd2660e12c1e6, // 0.43448, -0.90068 + 0x3fdbe51517ffc0d9, 0xbfecccee20c2de9f, // 0.43586, -0.90002 + 0x3fdbfbb1a05e0edc, 0xbfecc771c2736c09, // 0.43724, -0.89935 + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867 + 0x3fdc28ddbb6cf145, 0xbfecbc6bb638d10b, // 0.43999, -0.898 + 0x3fdc3f6d47263129, 0xbfecb6e20a00da99, // 0.44137, -0.89732 + 0x3fdc55f877b23537, 0xbfecb153f02fb87d, // 0.44275, -0.89665 + 0x3fdc6c7f4997000a, 0xbfecabc169a0b901, // 0.44412, -0.89597 + 0x3fdc8301b95b40c2, 0xbfeca62a772fd919, // 0.4455, -0.89528 + 0x3fdc997fc3865388, 0xbfeca08f19b9c449, // 0.44687, -0.8946 + 0x3fdcaff964a0421d, 0xbfec9aef521bd480, // 0.44824, -0.89391 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdcdcdf5dc440ce, 0xbfec8fa287e13305, // 0.45098, -0.89253 + 0x3fdcf34baee1cd21, 0xbfec89f587029c13, // 0.45235, -0.89184 + 0x3fdd09b389152ec1, 0xbfec84441f785f61, // 0.45372, -0.89115 + 0x3fdd2016e8e9db5b, 0xbfec7e8e52233cf3, // 0.45508, -0.89045 + 0x3fdd3675caebf962, 0xbfec78d41fe4a267, // 0.45645, -0.88975 + 0x3fdd4cd02ba8609c, 0xbfec7315899eaad7, // 0.45781, -0.88905 + 0x3fdd632607ac9aa9, 0xbfec6d5290341eb2, // 0.45918, -0.88835 + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764 + 0x3fdd8fc423c62a25, 0xbfec61bf777fcc48, // 0.4619, -0.88693 + 0x3fdda60c5cfa10d8, 0xbfec5bef59fef85a, // 0.46326, -0.88622 + 0x3fddbc5003b2edf8, 0xbfec561adceb743e, // 0.46462, -0.88551 + 0x3fddd28f1481cc58, 0xbfec5042012b6907, // 0.46598, -0.8848 + 0x3fdde8c98bf86bd6, 0xbfec4a64c7a5ac4c, // 0.46733, -0.88408 + 0x3fddfeff66a941de, 0xbfec44833141c004, // 0.46869, -0.88336 + 0x3fde1530a12779f4, 0xbfec3e9d3ee7d262, // 0.47004, -0.88264 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fde418527dc4ffa, 0xbfec32c449f60831, // 0.47275, -0.8812 + 0x3fde57a86d3cd824, 0xbfec2cd14931e3f1, // 0.4741, -0.88047 + 0x3fde6dc704be97e2, 0xbfec26d9f01f2eaf, // 0.47545, -0.87974 + 0x3fde83e0eaf85113, 0xbfec20de3fa971b0, // 0.4768, -0.87901 + 0x3fde99f61c817eda, 0xbfec1ade38bce19b, // 0.47815, -0.87828 + 0x3fdeb00695f25620, 0xbfec14d9dc465e58, // 0.47949, -0.87755 + 0x3fdec61253e3c61b, 0xbfec0ed12b3372e9, // 0.48084, -0.87681 + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607 + 0x3fdef21b8fafd3b5, 0xbfec02b2cef1e641, // 0.48353, -0.87533 + 0x3fdf081906bff7fd, 0xbfebfc9d25a1b147, // 0.48487, -0.87459 + 0x3fdf1e11b4bbc35c, 0xbfebf6832b71ec5b, // 0.48621, -0.87384 + 0x3fdf3405963fd068, 0xbfebf064e15377dd, // 0.48755, -0.87309 + 0x3fdf49f4a7e97729, 0xbfebea424837de6d, // 0.48889, -0.87235 + 0x3fdf5fdee656cda3, 0xbfebe41b611154c1, // 0.49023, -0.8716 + 0x3fdf75c44e26a852, 0xbfebddf02cd2b983, // 0.49156, -0.87084 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fdfa1808c6cf7e0, 0xbfebd18ce0dc19d6, // 0.49423, -0.86933 + 0x3fdfb7575c24d2de, 0xbfebcb54cb0d2327, // 0.49557, -0.86857 + 0x3fdfcd2947c1ff57, 0xbfebc5186bf8361d, // 0.4969, -0.86781 + 0x3fdfe2f64be7120f, 0xbfebbed7c49380ea, // 0.49823, -0.86705 + 0x3fdff8be6537615e, 0xbfebb892d5d5dad5, // 0.49956, -0.86628 + 0x3fe00740c82b82e0, 0xbfebb249a0b6c40d, // 0.50089, -0.86551 + 0x3fe0121fe4f56d2c, 0xbfebabfc262e6586, // 0.50221, -0.86474 + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397 + 0x3fe027d6ad83287e, 0xbfeb9f5464c5bffc, // 0.50486, -0.8632 + 0x3fe032ae55edbd95, 0xbfeb98fa1fd9155e, // 0.50619, -0.86242 + 0x3fe03d837edff370, 0xbfeb929b996a5b7f, // 0.50751, -0.86165 + 0x3fe0485626ae221a, 0xbfeb8c38d27504e9, // 0.50883, -0.86087 + 0x3fe053264bad0483, 0xbfeb85d1cbf52c02, // 0.51015, -0.86009 + 0x3fe05df3ec31b8b6, 0xbfeb7f6686e792ea, // 0.51147, -0.8593 + 0x3fe068bf0691c028, 0xbfeb78f70449a34b, // 0.51279, -0.85852 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe07e4da23bc102, 0xbfeb6c0b4a55ac17, // 0.51542, -0.85694 + 0x3fe089112032b08c, 0xbfeb658f14fdbc47, // 0.51673, -0.85615 + 0x3fe093d2115ee018, 0xbfeb5f0ea611a532, // 0.51804, -0.85535 + 0x3fe09e907417c5e1, 0xbfeb5889fe921405, // 0.51936, -0.85456 + 0x3fe0a94c46b53d0b, 0xbfeb52011f805c92, // 0.52067, -0.85376 + 0x3fe0b405878f85ec, 0xbfeb4b7409de7925, // 0.52198, -0.85296 + 0x3fe0bebc34ff4646, 0xbfeb44e2beaf0a61, // 0.52328, -0.85216 + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136 + 0x3fe0d421cf03c12b, 0xbfeb37b38bb54c09, // 0.5259, -0.85055 + 0x3fe0ded0b84bc4b5, 0xbfeb3115a5f37bf4, // 0.5272, -0.84974 + 0x3fe0e97d078fd23b, 0xbfeb2a738eb51f33, // 0.5285, -0.84893 + 0x3fe0f426bb2a8e7d, 0xbfeb23cd470013b4, // 0.5298, -0.84812 + 0x3fe0fecdd1770537, 0xbfeb1d22cfdadcc6, // 0.5311, -0.84731 + 0x3fe1097248d0a956, 0xbfeb16742a4ca2f5, // 0.5324, -0.84649 + 0x3fe114141f935545, 0xbfeb0fc1575d33db, // 0.5337, -0.84567 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe1294fe4c5350a, 0xbfeb024f2d7d24a9, // 0.53629, -0.84403 + 0x3fe133e9cfee254e, 0xbfeafb8fd89f57b6, // 0.53759, -0.84321 + 0x3fe13e8113f396c1, 0xbfeaf4cc5a85fb73, // 0.53888, -0.84238 + 0x3fe14915af336ceb, 0xbfeaee04b43c1474, // 0.54017, -0.84155 + 0x3fe153a7a00bf453, 0xbfeae738e6cd4b67, // 0.54146, -0.84073 + 0x3fe15e36e4dbe2bc, 0xbfeae068f345ecef, // 0.54275, -0.83989 + 0x3fe168c37c025764, 0xbfead994dab2e979, // 0.54404, -0.83906 + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822 + 0x3fe17dd49ad16161, 0xbfeacbe03ea0e73b, // 0.54661, -0.83739 + 0x3fe188591f3a46e5, 0xbfeac4ffbd3efac8, // 0.54789, -0.83655 + 0x3fe192daef7a5386, 0xbfeabe1b1b0b8dac, // 0.54918, -0.83571 + 0x3fe19d5a09f2b9b8, 0xbfeab7325916c0d4, // 0.55046, -0.83486 + 0x3fe1a7d66d0516e6, 0xbfeab045787157ff, // 0.55174, -0.83402 + 0x3fe1b250171373be, 0xbfeaa9547a2cb98e, // 0.55302, -0.83317 + 0x3fe1bcc706804467, 0xbfeaa25f5f5aee60, // 0.55429, -0.83232 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe1d1acaf012cc2, 0xbfea9468d85b20ae, // 0.55685, -0.83062 + 0x3fe1dc1b64dc4872, 0xbfea8d676e545ad2, // 0.55812, -0.82976 + 0x3fe1e68759a3e074, 0xbfea8661ec0ee133, // 0.55939, -0.8289 + 0x3fe1f0f08bbc861b, 0xbfea7f58529fe69d, // 0.56066, -0.82805 + 0x3fe1fb56f98b37b8, 0xbfea784aa31d3f55, // 0.56193, -0.82718 + 0x3fe205baa17560d6, 0xbfea7138de9d60f5, // 0.5632, -0.82632 + 0x3fe2101b81e0da78, 0xbfea6a230637623b, // 0.56447, -0.82546 + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459 + 0x3fe224d4e5d5482e, 0xbfea5beb1e188375, // 0.567, -0.82372 + 0x3fe22f2d662c13e1, 0xbfea54c91090f524, // 0.56826, -0.82285 + 0x3fe23983189fdfd5, 0xbfea4da2f385e997, // 0.56952, -0.82198 + 0x3fe243d5fb98ac1f, 0xbfea4678c8119ac8, // 0.57078, -0.8211 + 0x3fe24e260d7ee7c9, 0xbfea3f4a8f4ee2d2, // 0.57204, -0.82023 + 0x3fe258734cbb7110, 0xbfea38184a593bc6, // 0.5733, -0.81935 + 0x3fe262bdb7b795a2, 0xbfea30e1fa4cbf81, // 0.57455, -0.81847 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe2774a0a961612, 0xbfea22693d62ccb9, // 0.57706, -0.8167 + 0x3fe2818bef4d3cba, 0xbfea1b26d2c0a75e, // 0.57831, -0.81581 + 0x3fe28bcaf96d94ba, 0xbfea13e0617e4ec7, // 0.57956, -0.81493 + 0x3fe2960727629ca8, 0xbfea0c95eabaf937, // 0.58081, -0.81404 + 0x3fe2a040779843fb, 0xbfea05476f967bb5, // 0.58206, -0.81314 + 0x3fe2aa76e87aeb58, 0xbfe9fdf4f13149de, // 0.58331, -0.81225 + 0x3fe2b4aa787764c4, 0xbfe9f69e70ac75bc, // 0.58455, -0.81135 + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046 + 0x3fe2c908ef734e57, 0xbfe9e7e56dcb45bd, // 0.58704, -0.80956 + 0x3fe2d333d34e9bb7, 0xbfe9e082edb42472, // 0.58828, -0.80866 + 0x3fe2dd5bcffb7616, 0xbfe9d91c7007d5a6, // 0.58952, -0.80775 + 0x3fe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // 0.59076, -0.80685 + 0x3fe2f1a30d86773a, 0xbfe9ca438080eadb, // 0.592, -0.80594 + 0x3fe2fbc24b441015, 0xbfe9c2d110f075c3, // 0.59323, -0.80503 + 0x3fe305de9b921a94, 0xbfe9bb5aa85f2098, // 0.59447, -0.80412 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe31a0e6da35e44, 0xbfe9ac61f0d4e247, // 0.59693, -0.80229 + 0x3fe32421ec49a620, 0xbfe9a4dfa42b06b2, // 0.59816, -0.80138 + 0x3fe32e3277467d6b, 0xbfe99d59631e65d5, // 0.59939, -0.80046 + 0x3fe338400d0c8e57, 0xbfe995cf2ed80d22, // 0.60062, -0.79954 + 0x3fe3424aac0ef7d6, 0xbfe98e410881a600, // 0.60184, -0.79861 + 0x3fe34c5252c14de1, 0xbfe986aef1457594, // 0.60307, -0.79769 + 0x3fe35656ff9799ae, 0xbfe97f18ea4e5c9e, // 0.60429, -0.79676 + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584 + 0x3fe36a576582831b, 0xbfe96fe111ddfce0, // 0.60673, -0.79491 + 0x3fe374531b817f8d, 0xbfe9683f42bd7fe1, // 0.60795, -0.79398 + 0x3fe37e4bd1792fe2, 0xbfe960998893ad8c, // 0.60917, -0.79304 + 0x3fe3884185dfeb22, 0xbfe958efe48e6dd7, // 0.61038, -0.79211 + 0x3fe39234372c7f04, 0xbfe9514257dc4335, // 0.6116, -0.79117 + 0x3fe39c23e3d63029, 0xbfe94990e3ac4a6c, // 0.61281, -0.79023 + 0x3fe3a6108a54ba58, 0xbfe941db892e3a65, // 0.61402, -0.78929 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe3b9e0beb19e18, 0xbfe932652609b1cf, // 0.61644, -0.7874 + 0x3fe3c3c44981c517, 0xbfe92aa41fc5a815, // 0.61765, -0.78646 + 0x3fe3cda4c80a6076, 0xbfe922df37f8646a, // 0.61885, -0.78551 + 0x3fe3d78238c58343, 0xbfe91b166fd49da2, // 0.62006, -0.78456 + 0x3fe3e15c9a2db922, 0xbfe91349c88da398, // 0.62126, -0.7836 + 0x3fe3eb33eabe0680, 0xbfe90b7943575efe, // 0.62246, -0.78265 + 0x3fe3f50828f1e8d2, 0xbfe903a4e1665133, // 0.62366, -0.78169 + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074 + 0x3fe408a76834c0c0, 0xbfe8f3f08c28d9ac, // 0.62606, -0.77978 + 0x3fe41272663d108c, 0xbfe8ec109b486c49, // 0.62725, -0.77882 + 0x3fe41c3a4bdbaa26, 0xbfe8e42cd2852e0a, // 0.62845, -0.77785 + 0x3fe425ff178e6bb1, 0xbfe8dc45331698cc, // 0.62964, -0.77689 + 0x3fe42fc0c7d3adbb, 0xbfe8d459be34bdfa, // 0.63083, -0.77592 + 0x3fe4397f5b2a4380, 0xbfe8cc6a75184655, // 0.63202, -0.77495 + 0x3fe4433ad0117b1d, 0xbfe8c47758fa71cb, // 0.63321, -0.77398 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe456a858917046, 0xbfe8b485aca2a468, // 0.63558, -0.77204 + 0x3fe4605a692b32a2, 0xbfe8ac871ede1d88, // 0.63676, -0.77106 + 0x3fe46a095557a0f1, 0xbfe8a484c3031d50, // 0.63794, -0.77008 + 0x3fe473b51b987347, 0xbfe89c7e9a4dd4ab, // 0.63912, -0.7691 + 0x3fe47d5dba6fde01, 0xbfe89474a5fb0a84, // 0.6403, -0.76812 + 0x3fe48703306091fe, 0xbfe88c66e7481ba1, // 0.64148, -0.76714 + 0x3fe490a57bedbcdf, 0xbfe884555f72fa6b, // 0.64266, -0.76615 + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517 + 0x3fe4a3e08dec9ed6, 0xbfe87426f95cd5bd, // 0.645, -0.76418 + 0x3fe4ad79516722f0, 0xbfe86c0a1d9aa195, // 0.64618, -0.76319 + 0x3fe4b70ee48fb869, 0xbfe863e97db3d95a, // 0.64735, -0.7622 + 0x3fe4c0a145ec0004, 0xbfe85bc51ae958cc, // 0.64851, -0.7612 + 0x3fe4ca30740218a3, 0xbfe8539cf67c9029, // 0.64968, -0.76021 + 0x3fe4d3bc6d589f80, 0xbfe84b7111af83f9, // 0.65085, -0.75921 + 0x3fe4dd453076b064, 0xbfe843416dc4cce2, // 0.65201, -0.75821 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe4f04d0e2859aa, 0xbfe832d6eda3a3e0, // 0.65433, -0.75621 + 0x3fe4f9cc25cca486, 0xbfe82a9c13f545ff, // 0.65549, -0.7552 + 0x3fe503480159ded2, 0xbfe8225d803964e5, // 0.65665, -0.75419 + 0x3fe50cc09f59a09b, 0xbfe81a1b33b57acc, // 0.65781, -0.75319 + 0x3fe51635fe5601d7, 0xbfe811d52faf94dc, // 0.65896, -0.75218 + 0x3fe51fa81cd99aa6, 0xbfe8098b756e52fa, // 0.66011, -0.75117 + 0x3fe52916f96f8388, 0xbfe8013e0638e795, // 0.66127, -0.75015 + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914 + 0x3fe53beae7012abe, 0xbfe7f0980e113978, // 0.66356, -0.74812 + 0x3fe5454ff5159dfb, 0xbfe7e83f87b03686, // 0.66471, -0.7471 + 0x3fe54eb1bb6dcb8f, 0xbfe7dfe3517d8937, // 0.66586, -0.74608 + 0x3fe5581038975137, 0xbfe7d7836cc33db2, // 0.667, -0.74506 + 0x3fe5616b6b204e6e, 0xbfe7cf1fdacbf179, // 0.66814, -0.74403 + 0x3fe56ac35197649e, 0xbfe7c6b89ce2d333, // 0.66928, -0.74301 + 0x3fe57417ea8bb75c, 0xbfe7be4db453a27c, // 0.67042, -0.74198 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe586b72e2b2cfd, 0xbfe7ad6ce874dbb6, // 0.67269, -0.73992 + 0x3fe59001d5f723df, 0xbfe7a4f707bf97d2, // 0.67383, -0.73889 + 0x3fe599492a81ffbc, 0xbfe79c7d8198e56e, // 0.67496, -0.73785 + 0x3fe5a28d2a5d7250, 0xbfe79400574f55e4, // 0.67609, -0.73682 + 0x3fe5abcdd41bb0d8, 0xbfe78b7f8a320a52, // 0.67722, -0.73578 + 0x3fe5b50b264f7448, 0xbfe782fb1b90b35b, // 0.67835, -0.73474 + 0x3fe5be451f8bf980, 0xbfe77a730cbb9100, // 0.67948, -0.7337 + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265 + 0x3fe5d0af016ed1d4, 0xbfe7695813b9b594, // 0.68172, -0.73161 + 0x3fe5d9dee73e345c, 0xbfe760c52c304764, // 0.68285, -0.73056 + 0x3fe5e30b6e6877f3, 0xbfe7582ea9b9a329, // 0.68397, -0.72951 + 0x3fe5ec3495837074, 0xbfe74f948da8d28d, // 0.68508, -0.72846 + 0x3fe5f55a5b2576f8, 0xbfe746f6d9516d59, // 0.6862, -0.72741 + 0x3fe5fe7cbde56a0f, 0xbfe73e558e079942, // 0.68732, -0.72636 + 0x3fe6079bbc5aadfa, 0xbfe735b0ad2009b2, // 0.68843, -0.7253 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe619cf86c55702, 0xbfe7245c2fcd492a, // 0.69065, -0.72319 + 0x3fe622e44fec22ff, 0xbfe71bac960e41bf, // 0.69176, -0.72213 + 0x3fe62bf5af2b0dfd, 0xbfe712f96c09d18d, // 0.69287, -0.72107 + 0x3fe63503a31c1be8, 0xbfe70a42b3176d7a, // 0.69397, -0.72 + 0x3fe63e0e2a59d7aa, 0xbfe701886c8f16e6, // 0.69508, -0.71894 + 0x3fe64715437f535b, 0xbfe6f8ca99c95b75, // 0.69618, -0.71787 + 0x3fe65018ed28287f, 0xbfe6f0093c1f54de, // 0.69728, -0.7168 + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573 + 0x3fe66215ec74eb91, 0xbfe6de7be585881d, // 0.69947, -0.71466 + 0x3fe66b0f3f52b386, 0xbfe6d5afef4aafcc, // 0.70057, -0.71358 + 0x3fe674051d27896c, 0xbfe6cce07395679f, // 0.70166, -0.71251 + 0x3fe67cf78491af10, 0xbfe6c40d73c18275, // 0.70275, -0.71143 + 0x3fe685e6742feeef, 0xbfe6bb36f12b5e06, // 0.70385, -0.71035 + 0x3fe68ed1eaa19c71, 0xbfe6b25ced2fe29c, // 0.70493, -0.70927 + 0x3fe697b9e686941c, 0xbfe6a97f692c82ea, // 0.70602, -0.70819 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe6a97f692c82ea, 0xbfe697b9e686941c, // 0.70819, -0.70602 + 0x3fe6b25ced2fe29c, 0xbfe68ed1eaa19c71, // 0.70927, -0.70493 + 0x3fe6bb36f12b5e06, 0xbfe685e6742feeef, // 0.71035, -0.70385 + 0x3fe6c40d73c18275, 0xbfe67cf78491af10, // 0.71143, -0.70275 + 0x3fe6cce07395679f, 0xbfe674051d27896c, // 0.71251, -0.70166 + 0x3fe6d5afef4aafcc, 0xbfe66b0f3f52b386, // 0.71358, -0.70057 + 0x3fe6de7be585881d, 0xbfe66215ec74eb91, // 0.71466, -0.69947 + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838 + 0x3fe6f0093c1f54de, 0xbfe65018ed28287f, // 0.7168, -0.69728 + 0x3fe6f8ca99c95b75, 0xbfe64715437f535b, // 0.71787, -0.69618 + 0x3fe701886c8f16e6, 0xbfe63e0e2a59d7aa, // 0.71894, -0.69508 + 0x3fe70a42b3176d7a, 0xbfe63503a31c1be8, // 0.72, -0.69397 + 0x3fe712f96c09d18d, 0xbfe62bf5af2b0dfd, // 0.72107, -0.69287 + 0x3fe71bac960e41bf, 0xbfe622e44fec22ff, // 0.72213, -0.69176 + 0x3fe7245c2fcd492a, 0xbfe619cf86c55702, // 0.72319, -0.69065 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe735b0ad2009b2, 0xbfe6079bbc5aadfa, // 0.7253, -0.68843 + 0x3fe73e558e079942, 0xbfe5fe7cbde56a0f, // 0.72636, -0.68732 + 0x3fe746f6d9516d59, 0xbfe5f55a5b2576f8, // 0.72741, -0.6862 + 0x3fe74f948da8d28d, 0xbfe5ec3495837074, // 0.72846, -0.68508 + 0x3fe7582ea9b9a329, 0xbfe5e30b6e6877f3, // 0.72951, -0.68397 + 0x3fe760c52c304764, 0xbfe5d9dee73e345c, // 0.73056, -0.68285 + 0x3fe7695813b9b594, 0xbfe5d0af016ed1d4, // 0.73161, -0.68172 + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806 + 0x3fe77a730cbb9100, 0xbfe5be451f8bf980, // 0.7337, -0.67948 + 0x3fe782fb1b90b35b, 0xbfe5b50b264f7448, // 0.73474, -0.67835 + 0x3fe78b7f8a320a52, 0xbfe5abcdd41bb0d8, // 0.73578, -0.67722 + 0x3fe79400574f55e4, 0xbfe5a28d2a5d7250, // 0.73682, -0.67609 + 0x3fe79c7d8198e56e, 0xbfe599492a81ffbc, // 0.73785, -0.67496 + 0x3fe7a4f707bf97d2, 0xbfe59001d5f723df, // 0.73889, -0.67383 + 0x3fe7ad6ce874dbb6, 0xbfe586b72e2b2cfd, // 0.73992, -0.67269 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe7be4db453a27c, 0xbfe57417ea8bb75c, // 0.74198, -0.67042 + 0x3fe7c6b89ce2d333, 0xbfe56ac35197649e, // 0.74301, -0.66928 + 0x3fe7cf1fdacbf179, 0xbfe5616b6b204e6e, // 0.74403, -0.66814 + 0x3fe7d7836cc33db2, 0xbfe5581038975137, // 0.74506, -0.667 + 0x3fe7dfe3517d8937, 0xbfe54eb1bb6dcb8f, // 0.74608, -0.66586 + 0x3fe7e83f87b03686, 0xbfe5454ff5159dfb, // 0.7471, -0.66471 + 0x3fe7f0980e113978, 0xbfe53beae7012abe, // 0.74812, -0.66356 + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242 + 0x3fe8013e0638e795, 0xbfe52916f96f8388, // 0.75015, -0.66127 + 0x3fe8098b756e52fa, 0xbfe51fa81cd99aa6, // 0.75117, -0.66011 + 0x3fe811d52faf94dc, 0xbfe51635fe5601d7, // 0.75218, -0.65896 + 0x3fe81a1b33b57acc, 0xbfe50cc09f59a09b, // 0.75319, -0.65781 + 0x3fe8225d803964e5, 0xbfe503480159ded2, // 0.75419, -0.65665 + 0x3fe82a9c13f545ff, 0xbfe4f9cc25cca486, // 0.7552, -0.65549 + 0x3fe832d6eda3a3e0, 0xbfe4f04d0e2859aa, // 0.75621, -0.65433 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe843416dc4cce2, 0xbfe4dd453076b064, // 0.75821, -0.65201 + 0x3fe84b7111af83f9, 0xbfe4d3bc6d589f80, // 0.75921, -0.65085 + 0x3fe8539cf67c9029, 0xbfe4ca30740218a3, // 0.76021, -0.64968 + 0x3fe85bc51ae958cc, 0xbfe4c0a145ec0004, // 0.7612, -0.64851 + 0x3fe863e97db3d95a, 0xbfe4b70ee48fb869, // 0.7622, -0.64735 + 0x3fe86c0a1d9aa195, 0xbfe4ad79516722f0, // 0.76319, -0.64618 + 0x3fe87426f95cd5bd, 0xbfe4a3e08dec9ed6, // 0.76418, -0.645 + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383 + 0x3fe884555f72fa6b, 0xbfe490a57bedbcdf, // 0.76615, -0.64266 + 0x3fe88c66e7481ba1, 0xbfe48703306091fe, // 0.76714, -0.64148 + 0x3fe89474a5fb0a84, 0xbfe47d5dba6fde01, // 0.76812, -0.6403 + 0x3fe89c7e9a4dd4ab, 0xbfe473b51b987347, // 0.7691, -0.63912 + 0x3fe8a484c3031d50, 0xbfe46a095557a0f1, // 0.77008, -0.63794 + 0x3fe8ac871ede1d88, 0xbfe4605a692b32a2, // 0.77106, -0.63676 + 0x3fe8b485aca2a468, 0xbfe456a858917046, // 0.77204, -0.63558 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe8c47758fa71cb, 0xbfe4433ad0117b1d, // 0.77398, -0.63321 + 0x3fe8cc6a75184655, 0xbfe4397f5b2a4380, // 0.77495, -0.63202 + 0x3fe8d459be34bdfa, 0xbfe42fc0c7d3adbb, // 0.77592, -0.63083 + 0x3fe8dc45331698cc, 0xbfe425ff178e6bb1, // 0.77689, -0.62964 + 0x3fe8e42cd2852e0a, 0xbfe41c3a4bdbaa26, // 0.77785, -0.62845 + 0x3fe8ec109b486c49, 0xbfe41272663d108c, // 0.77882, -0.62725 + 0x3fe8f3f08c28d9ac, 0xbfe408a76834c0c0, // 0.77978, -0.62606 + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486 + 0x3fe903a4e1665133, 0xbfe3f50828f1e8d2, // 0.78169, -0.62366 + 0x3fe90b7943575efe, 0xbfe3eb33eabe0680, // 0.78265, -0.62246 + 0x3fe91349c88da398, 0xbfe3e15c9a2db922, // 0.7836, -0.62126 + 0x3fe91b166fd49da2, 0xbfe3d78238c58343, // 0.78456, -0.62006 + 0x3fe922df37f8646a, 0xbfe3cda4c80a6076, // 0.78551, -0.61885 + 0x3fe92aa41fc5a815, 0xbfe3c3c44981c517, // 0.78646, -0.61765 + 0x3fe932652609b1cf, 0xbfe3b9e0beb19e18, // 0.7874, -0.61644 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe941db892e3a65, 0xbfe3a6108a54ba58, // 0.78929, -0.61402 + 0x3fe94990e3ac4a6c, 0xbfe39c23e3d63029, // 0.79023, -0.61281 + 0x3fe9514257dc4335, 0xbfe39234372c7f04, // 0.79117, -0.6116 + 0x3fe958efe48e6dd7, 0xbfe3884185dfeb22, // 0.79211, -0.61038 + 0x3fe960998893ad8c, 0xbfe37e4bd1792fe2, // 0.79304, -0.60917 + 0x3fe9683f42bd7fe1, 0xbfe374531b817f8d, // 0.79398, -0.60795 + 0x3fe96fe111ddfce0, 0xbfe36a576582831b, // 0.79491, -0.60673 + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551 + 0x3fe97f18ea4e5c9e, 0xbfe35656ff9799ae, // 0.79676, -0.60429 + 0x3fe986aef1457594, 0xbfe34c5252c14de1, // 0.79769, -0.60307 + 0x3fe98e410881a600, 0xbfe3424aac0ef7d6, // 0.79861, -0.60184 + 0x3fe995cf2ed80d22, 0xbfe338400d0c8e57, // 0.79954, -0.60062 + 0x3fe99d59631e65d5, 0xbfe32e3277467d6b, // 0.80046, -0.59939 + 0x3fe9a4dfa42b06b2, 0xbfe32421ec49a620, // 0.80138, -0.59816 + 0x3fe9ac61f0d4e247, 0xbfe31a0e6da35e44, // 0.80229, -0.59693 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe9bb5aa85f2098, 0xbfe305de9b921a94, // 0.80412, -0.59447 + 0x3fe9c2d110f075c3, 0xbfe2fbc24b441015, // 0.80503, -0.59323 + 0x3fe9ca438080eadb, 0xbfe2f1a30d86773a, // 0.80594, -0.592 + 0x3fe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // 0.80685, -0.59076 + 0x3fe9d91c7007d5a6, 0xbfe2dd5bcffb7616, // 0.80775, -0.58952 + 0x3fe9e082edb42472, 0xbfe2d333d34e9bb7, // 0.80866, -0.58828 + 0x3fe9e7e56dcb45bd, 0xbfe2c908ef734e57, // 0.80956, -0.58704 + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858 + 0x3fe9f69e70ac75bc, 0xbfe2b4aa787764c4, // 0.81135, -0.58455 + 0x3fe9fdf4f13149de, 0xbfe2aa76e87aeb58, // 0.81225, -0.58331 + 0x3fea05476f967bb5, 0xbfe2a040779843fb, // 0.81314, -0.58206 + 0x3fea0c95eabaf937, 0xbfe2960727629ca8, // 0.81404, -0.58081 + 0x3fea13e0617e4ec7, 0xbfe28bcaf96d94ba, // 0.81493, -0.57956 + 0x3fea1b26d2c0a75e, 0xbfe2818bef4d3cba, // 0.81581, -0.57831 + 0x3fea22693d62ccb9, 0xbfe2774a0a961612, // 0.8167, -0.57706 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea30e1fa4cbf81, 0xbfe262bdb7b795a2, // 0.81847, -0.57455 + 0x3fea38184a593bc6, 0xbfe258734cbb7110, // 0.81935, -0.5733 + 0x3fea3f4a8f4ee2d2, 0xbfe24e260d7ee7c9, // 0.82023, -0.57204 + 0x3fea4678c8119ac8, 0xbfe243d5fb98ac1f, // 0.8211, -0.57078 + 0x3fea4da2f385e997, 0xbfe23983189fdfd5, // 0.82198, -0.56952 + 0x3fea54c91090f524, 0xbfe22f2d662c13e1, // 0.82285, -0.56826 + 0x3fea5beb1e188375, 0xbfe224d4e5d5482e, // 0.82372, -0.567 + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573 + 0x3fea6a230637623b, 0xbfe2101b81e0da78, // 0.82546, -0.56447 + 0x3fea7138de9d60f5, 0xbfe205baa17560d6, // 0.82632, -0.5632 + 0x3fea784aa31d3f55, 0xbfe1fb56f98b37b8, // 0.82718, -0.56193 + 0x3fea7f58529fe69d, 0xbfe1f0f08bbc861b, // 0.82805, -0.56066 + 0x3fea8661ec0ee133, 0xbfe1e68759a3e074, // 0.8289, -0.55939 + 0x3fea8d676e545ad2, 0xbfe1dc1b64dc4872, // 0.82976, -0.55812 + 0x3fea9468d85b20ae, 0xbfe1d1acaf012cc2, // 0.83062, -0.55685 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3feaa25f5f5aee60, 0xbfe1bcc706804467, // 0.83232, -0.55429 + 0x3feaa9547a2cb98e, 0xbfe1b250171373be, // 0.83317, -0.55302 + 0x3feab045787157ff, 0xbfe1a7d66d0516e6, // 0.83402, -0.55174 + 0x3feab7325916c0d4, 0xbfe19d5a09f2b9b8, // 0.83486, -0.55046 + 0x3feabe1b1b0b8dac, 0xbfe192daef7a5386, // 0.83571, -0.54918 + 0x3feac4ffbd3efac8, 0xbfe188591f3a46e5, // 0.83655, -0.54789 + 0x3feacbe03ea0e73b, 0xbfe17dd49ad16161, // 0.83739, -0.54661 + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532 + 0x3fead994dab2e979, 0xbfe168c37c025764, // 0.83906, -0.54404 + 0x3feae068f345ecef, 0xbfe15e36e4dbe2bc, // 0.83989, -0.54275 + 0x3feae738e6cd4b67, 0xbfe153a7a00bf453, // 0.84073, -0.54146 + 0x3feaee04b43c1474, 0xbfe14915af336ceb, // 0.84155, -0.54017 + 0x3feaf4cc5a85fb73, 0xbfe13e8113f396c1, // 0.84238, -0.53888 + 0x3feafb8fd89f57b6, 0xbfe133e9cfee254e, // 0.84321, -0.53759 + 0x3feb024f2d7d24a9, 0xbfe1294fe4c5350a, // 0.84403, -0.53629 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feb0fc1575d33db, 0xbfe114141f935545, // 0.84567, -0.5337 + 0x3feb16742a4ca2f5, 0xbfe1097248d0a956, // 0.84649, -0.5324 + 0x3feb1d22cfdadcc6, 0xbfe0fecdd1770537, // 0.84731, -0.5311 + 0x3feb23cd470013b4, 0xbfe0f426bb2a8e7d, // 0.84812, -0.5298 + 0x3feb2a738eb51f33, 0xbfe0e97d078fd23b, // 0.84893, -0.5285 + 0x3feb3115a5f37bf4, 0xbfe0ded0b84bc4b5, // 0.84974, -0.5272 + 0x3feb37b38bb54c09, 0xbfe0d421cf03c12b, // 0.85055, -0.5259 + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459 + 0x3feb44e2beaf0a61, 0xbfe0bebc34ff4646, // 0.85216, -0.52328 + 0x3feb4b7409de7925, 0xbfe0b405878f85ec, // 0.85296, -0.52198 + 0x3feb52011f805c92, 0xbfe0a94c46b53d0b, // 0.85376, -0.52067 + 0x3feb5889fe921405, 0xbfe09e907417c5e1, // 0.85456, -0.51936 + 0x3feb5f0ea611a532, 0xbfe093d2115ee018, // 0.85535, -0.51804 + 0x3feb658f14fdbc47, 0xbfe089112032b08c, // 0.85615, -0.51673 + 0x3feb6c0b4a55ac17, 0xbfe07e4da23bc102, // 0.85694, -0.51542 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feb78f70449a34b, 0xbfe068bf0691c028, // 0.85852, -0.51279 + 0x3feb7f6686e792ea, 0xbfe05df3ec31b8b6, // 0.8593, -0.51147 + 0x3feb85d1cbf52c02, 0xbfe053264bad0483, // 0.86009, -0.51015 + 0x3feb8c38d27504e9, 0xbfe0485626ae221a, // 0.86087, -0.50883 + 0x3feb929b996a5b7f, 0xbfe03d837edff370, // 0.86165, -0.50751 + 0x3feb98fa1fd9155e, 0xbfe032ae55edbd95, // 0.86242, -0.50619 + 0x3feb9f5464c5bffc, 0xbfe027d6ad83287e, // 0.8632, -0.50486 + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354 + 0x3febabfc262e6586, 0xbfe0121fe4f56d2c, // 0.86474, -0.50221 + 0x3febb249a0b6c40d, 0xbfe00740c82b82e0, // 0.86551, -0.50089 + 0x3febb892d5d5dad5, 0xbfdff8be6537615e, // 0.86628, -0.49956 + 0x3febbed7c49380ea, 0xbfdfe2f64be7120f, // 0.86705, -0.49823 + 0x3febc5186bf8361d, 0xbfdfcd2947c1ff57, // 0.86781, -0.4969 + 0x3febcb54cb0d2327, 0xbfdfb7575c24d2de, // 0.86857, -0.49557 + 0x3febd18ce0dc19d6, 0xbfdfa1808c6cf7e0, // 0.86933, -0.49423 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3febddf02cd2b983, 0xbfdf75c44e26a852, // 0.87084, -0.49156 + 0x3febe41b611154c1, 0xbfdf5fdee656cda3, // 0.8716, -0.49023 + 0x3febea424837de6d, 0xbfdf49f4a7e97729, // 0.87235, -0.48889 + 0x3febf064e15377dd, 0xbfdf3405963fd068, // 0.87309, -0.48755 + 0x3febf6832b71ec5b, 0xbfdf1e11b4bbc35c, // 0.87384, -0.48621 + 0x3febfc9d25a1b147, 0xbfdf081906bff7fd, // 0.87459, -0.48487 + 0x3fec02b2cef1e641, 0xbfdef21b8fafd3b5, // 0.87533, -0.48353 + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218 + 0x3fec0ed12b3372e9, 0xbfdec61253e3c61b, // 0.87681, -0.48084 + 0x3fec14d9dc465e58, 0xbfdeb00695f25620, // 0.87755, -0.47949 + 0x3fec1ade38bce19b, 0xbfde99f61c817eda, // 0.87828, -0.47815 + 0x3fec20de3fa971b0, 0xbfde83e0eaf85113, // 0.87901, -0.4768 + 0x3fec26d9f01f2eaf, 0xbfde6dc704be97e2, // 0.87974, -0.47545 + 0x3fec2cd14931e3f1, 0xbfde57a86d3cd824, // 0.88047, -0.4741 + 0x3fec32c449f60831, 0xbfde418527dc4ffa, // 0.8812, -0.47275 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec3e9d3ee7d262, 0xbfde1530a12779f4, // 0.88264, -0.47004 + 0x3fec44833141c004, 0xbfddfeff66a941de, // 0.88336, -0.46869 + 0x3fec4a64c7a5ac4c, 0xbfdde8c98bf86bd6, // 0.88408, -0.46733 + 0x3fec5042012b6907, 0xbfddd28f1481cc58, // 0.8848, -0.46598 + 0x3fec561adceb743e, 0xbfddbc5003b2edf8, // 0.88551, -0.46462 + 0x3fec5bef59fef85a, 0xbfdda60c5cfa10d8, // 0.88622, -0.46326 + 0x3fec61bf777fcc48, 0xbfdd8fc423c62a25, // 0.88693, -0.4619 + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054 + 0x3fec6d5290341eb2, 0xbfdd632607ac9aa9, // 0.88835, -0.45918 + 0x3fec7315899eaad7, 0xbfdd4cd02ba8609c, // 0.88905, -0.45781 + 0x3fec78d41fe4a267, 0xbfdd3675caebf962, // 0.88975, -0.45645 + 0x3fec7e8e52233cf3, 0xbfdd2016e8e9db5b, // 0.89045, -0.45508 + 0x3fec84441f785f61, 0xbfdd09b389152ec1, // 0.89115, -0.45372 + 0x3fec89f587029c13, 0xbfdcf34baee1cd21, // 0.89184, -0.45235 + 0x3fec8fa287e13305, 0xbfdcdcdf5dc440ce, // 0.89253, -0.45098 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3fec9aef521bd480, 0xbfdcaff964a0421d, // 0.89391, -0.44824 + 0x3feca08f19b9c449, 0xbfdc997fc3865388, // 0.8946, -0.44687 + 0x3feca62a772fd919, 0xbfdc8301b95b40c2, // 0.89528, -0.4455 + 0x3fecabc169a0b901, 0xbfdc6c7f4997000a, // 0.89597, -0.44412 + 0x3fecb153f02fb87d, 0xbfdc55f877b23537, // 0.89665, -0.44275 + 0x3fecb6e20a00da99, 0xbfdc3f6d47263129, // 0.89732, -0.44137 + 0x3fecbc6bb638d10b, 0xbfdc28ddbb6cf145, // 0.898, -0.43999 + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862 + 0x3fecc771c2736c09, 0xbfdbfbb1a05e0edc, // 0.89935, -0.43724 + 0x3fecccee20c2de9f, 0xbfdbe51517ffc0d9, // 0.90002, -0.43586 + 0x3fecd2660e12c1e6, 0xbfdbce744262deee, // 0.90068, -0.43448 + 0x3fecd7d9898b32f6, 0xbfdbb7cf2304bd01, // 0.90135, -0.43309 + 0x3fecdd489254fe65, 0xbfdba125bd63583e, // 0.90201, -0.43171 + 0x3fece2b32799a060, 0xbfdb8a7814fd5693, // 0.90267, -0.43033 + 0x3fece819488344ce, 0xbfdb73c62d520624, // 0.90333, -0.42894 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fecf2d829f1b40e, 0xbfdb4655ae2bf757, // 0.90464, -0.42617 + 0x3fecf830e8ce467b, 0xbfdb2f971db31972, // 0.9053, -0.42478 + 0x3fecfd852fff6ad4, 0xbfdb18d45bf8aca6, // 0.90595, -0.42339 + 0x3fed02d4feb2bd92, 0xbfdb020d6c7f4009, // 0.9066, -0.422 + 0x3fed082054168bac, 0xbfdaeb4252ca07ab, // 0.90724, -0.42061 + 0x3fed0d672f59d2b9, 0xbfdad473125cdc08, // 0.90789, -0.41922 + 0x3fed12a98fac410c, 0xbfdabd9faebc3980, // 0.90853, -0.41782 + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643 + 0x3fed1d20dc40c15c, 0xbfda8fec8bf5b166, // 0.90981, -0.41503 + 0x3fed2255c6e5a4e1, 0xbfda790cd3dbf31a, // 0.91044, -0.41364 + 0x3fed2786335f52fc, 0xbfda622906a70b63, // 0.91107, -0.41224 + 0x3fed2cb220e0ef9f, 0xbfda4b4127dea1e4, // 0.91171, -0.41084 + 0x3fed31d98e9e503a, 0xbfda34553b0afee5, // 0.91234, -0.40944 + 0x3fed36fc7bcbfbdc, 0xbfda1d6543b50ac0, // 0.91296, -0.40804 + 0x3fed3c1ae79f2b4e, 0xbfda067145664d57, // 0.91359, -0.40664 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed464a380e7242, 0xbfd9d87d4207b0ab, // 0.91483, -0.40384 + 0x3fed4b5b1b187524, 0xbfd9c17d440df9f2, // 0.91545, -0.40243 + 0x3fed506779a3d2d9, 0xbfd9aa794d47c9ee, // 0.91606, -0.40103 + 0x3fed556f52e93eb1, 0xbfd993716141bdfe, // 0.91668, -0.39962 + 0x3fed5a72a6221e73, 0xbfd97c6583890fc2, // 0.91729, -0.39822 + 0x3fed5f7172888a7f, 0xbfd96555b7ab948f, // 0.9179, -0.39681 + 0x3fed646bb7574de5, 0xbfd94e420137bce3, // 0.91851, -0.3954 + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399 + 0x3fed6e52a71c8547, 0xbfd9200ee2c9be97, // 0.91972, -0.39258 + 0x3fed733f508c0dff, 0xbfd908ef81ef7bd1, // 0.92032, -0.39117 + 0x3fed78276f5617c6, 0xbfd8f1cc44bea329, // 0.92092, -0.38976 + 0x3fed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // 0.92151, -0.38835 + 0x3fed81ea09f38b63, 0xbfd8c37a439f884f, // 0.92211, -0.38693 + 0x3fed86c48445a450, 0xbfd8ac4b86d5ed44, // 0.9227, -0.38552 + 0x3fed8b9a70ef9cb4, 0xbfd89518fbff098e, // 0.92329, -0.3841 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3fed95389e50429b, 0xbfd866a88a792ea0, // 0.92447, -0.38127 + 0x3fed9a00dd8b3d46, 0xbfd84f6aaaf3903f, // 0.92505, -0.37985 + 0x3fed9ec48c26b1f3, 0xbfd838290bb359c8, // 0.92563, -0.37843 + 0x3feda383a9668988, 0xbfd820e3b04eaac4, // 0.92621, -0.37701 + 0x3feda83e348f613b, 0xbfd8099a9c5c362d, // 0.92679, -0.37559 + 0x3fedacf42ce68ab9, 0xbfd7f24dd37341e3, // 0.92736, -0.37416 + 0x3fedb1a591b20c38, 0xbfd7dafd592ba621, // 0.92794, -0.37274 + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132 + 0x3fedbafa9dc1b78d, 0xbfd7ac515ee2b172, // 0.92907, -0.36989 + 0x3fedbf9e4395759a, 0xbfd794f5e613dfae, // 0.92964, -0.36847 + 0x3fedc43d52fcb453, 0xbfd77d96ca4b73a6, // 0.93021, -0.36704 + 0x3fedc8d7cb410260, 0xbfd766340f2418f6, // 0.93077, -0.36561 + 0x3fedcd6dabaca3a5, 0xbfd74ecdb8390a3e, // 0.93133, -0.36418 + 0x3fedd1fef38a915a, 0xbfd73763c9261092, // 0.93188, -0.36276 + 0x3fedd68ba2267a25, 0xbfd71ff6458782ec, // 0.93244, -0.36133 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3feddf9730ca837b, 0xbfd6f1108f1bc9c5, // 0.93354, -0.35846 + 0x3fede4160f6d8d81, 0xbfd6d998638a0cb5, // 0.93409, -0.35703 + 0x3fede890520465ce, 0xbfd6c21cb1e39771, // 0.93464, -0.3556 + 0x3feded05f7de47da, 0xbfd6aa9d7dc77e16, // 0.93518, -0.35416 + 0x3fedf177004b2534, 0xbfd6931acad55f51, // 0.93573, -0.35273 + 0x3fedf5e36a9ba59c, 0xbfd67b949cad63ca, // 0.93627, -0.35129 + 0x3fedfa4b3621271d, 0xbfd6640af6f03d9e, // 0.9368, -0.34986 + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842 + 0x3fee030cee1435b8, 0xbfd634ed533be58e, // 0.93787, -0.34698 + 0x3fee0766d9280f54, 0xbfd61d595c88c203, // 0.9384, -0.34554 + 0x3fee0bbc22bd8349, 0xbfd605c1fcc88f63, // 0.93893, -0.3441 + 0x3fee100cca2980ac, 0xbfd5ee27379ea693, // 0.93946, -0.34266 + 0x3fee1458cec1ad83, 0xbfd5d68910aee686, // 0.93998, -0.34122 + 0x3fee18a02fdc66d9, 0xbfd5bee78b9db3b6, // 0.94051, -0.33978 + 0x3fee1ce2ecd0c0d8, 0xbfd5a742ac0ff78d, // 0.94103, -0.33833 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee255a77a63bb8, 0xbfd577eeec151e47, // 0.94206, -0.33545 + 0x3fee298f4439197a, 0xbfd5604012f467b4, // 0.94257, -0.334 + 0x3fee2dbf6a0911d9, 0xbfd5488dedeff3be, // 0.94308, -0.33255 + 0x3fee31eae870ce25, 0xbfd530d880af3c24, // 0.94359, -0.33111 + 0x3fee3611becbaf69, 0xbfd5191fceda3c35, // 0.9441, -0.32966 + 0x3fee3a33ec75ce85, 0xbfd50163dc197047, // 0.9446, -0.32821 + 0x3fee3e5170cbfc46, 0xbfd4e9a4ac15d520, // 0.94511, -0.32676 + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531 + 0x3fee467e7af35f23, 0xbfd4ba1ca2eca31c, // 0.94611, -0.32386 + 0x3fee4a8dff81ce5e, 0xbfd4a253d11b82f3, // 0.9466, -0.32241 + 0x3fee4e98d836c0af, 0xbfd48a87d0b07fd7, // 0.94709, -0.32096 + 0x3fee529f04729ffc, 0xbfd472b8a5571054, // 0.94759, -0.3195 + 0x3fee56a083968eb1, 0xbfd45ae652bb2800, // 0.94807, -0.31805 + 0x3fee5a9d550467d3, 0xbfd44310dc8936f0, // 0.94856, -0.31659 + 0x3fee5e95781ebf1c, 0xbfd42b38466e2928, // 0.94905, -0.31514 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee6677b0e6d31e, 0xbfd3fb7dc932cfa4, // 0.95001, -0.31222 + 0x3fee6a61c55d53a7, 0xbfd3e39be96ec271, // 0.95049, -0.31077 + 0x3fee6e472911da27, 0xbfd3cbb6f87a146e, // 0.95096, -0.30931 + 0x3fee7227db6a9744, 0xbfd3b3cefa0414b7, // 0.95144, -0.30785 + 0x3fee7603dbce74e9, 0xbfd39be3f1bc8aef, // 0.95191, -0.30639 + 0x3fee79db29a5165a, 0xbfd383f5e353b6aa, // 0.95238, -0.30493 + 0x3fee7dadc456d850, 0xbfd36c04d27a4edf, // 0.95284, -0.30347 + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201 + 0x3fee8544ddf0d075, 0xbfd33c19b83af207, // 0.95377, -0.30054 + 0x3fee89095bad6025, 0xbfd3241fb638baaf, // 0.95423, -0.29908 + 0x3fee8cc923edc388, 0xbfd30c22c08d6a13, // 0.95469, -0.29762 + 0x3fee9084361df7f3, 0xbfd2f422daec0386, // 0.95514, -0.29615 + 0x3fee943a91aab4b4, 0xbfd2dc200907fe51, // 0.95559, -0.29469 + 0x3fee97ec36016b30, 0xbfd2c41a4e954520, // 0.95605, -0.29322 + 0x3fee9b99229046f8, 0xbfd2ac11af483572, // 0.95649, -0.29175 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3feea2e4d212c000, 0xbfd27bf7d0f2c346, // 0.95738, -0.28882 + 0x3feea68393e65800, 0xbfd263e6995554ba, // 0.95783, -0.28735 + 0x3feeaa1d9bb20af3, 0xbfd24bd28bb37672, // 0.95827, -0.28588 + 0x3feeadb2e8e7a88e, 0xbfd233bbabc3bb72, // 0.9587, -0.28441 + 0x3feeb1437af9bb34, 0xbfd21ba1fd3d2623, // 0.95914, -0.28294 + 0x3feeb4cf515b8811, 0xbfd2038583d727bd, // 0.95957, -0.28146 + 0x3feeb8566b810f2a, 0xbfd1eb6643499fbb, // 0.96, -0.27999 + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852 + 0x3feebf5668eaf2ef, 0xbfd1bb1f7b999480, // 0.96086, -0.27705 + 0x3feec2cf4b1af6b2, 0xbfd1a2f7fbe8f243, // 0.96128, -0.27557 + 0x3feec6436ee60309, 0xbfd18acdc3f4873a, // 0.9617, -0.2741 + 0x3feec9b2d3c3bf84, 0xbfd172a0d7765177, // 0.96212, -0.27262 + 0x3feecd1d792c8f10, 0xbfd15a713a28b9d9, // 0.96254, -0.27115 + 0x3feed0835e999009, 0xbfd1423eefc69378, // 0.96295, -0.26967 + 0x3feed3e483849c51, 0xbfd12a09fc0b1b12, // 0.96337, -0.26819 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3feeda9889bfe86a, 0xbfd0f998277733f7, // 0.96418, -0.26523 + 0x3feeddeb6a078651, 0xbfd0e15b4e1749cd, // 0.96459, -0.26375 + 0x3feee13987bbebdc, 0xbfd0c91bda4f158d, // 0.96499, -0.26227 + 0x3feee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // 0.96539, -0.26079 + 0x3feee7c77961dc9e, 0xbfd09895327b465e, // 0.96579, -0.25931 + 0x3feeeb074c50a544, 0xbfd0804e05eb661e, // 0.96619, -0.25783 + 0x3feeee425aa6b09a, 0xbfd068044deab002, // 0.96658, -0.25635 + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487 + 0x3feef4aa278b2032, 0xbfd037694a928cac, // 0.96737, -0.25338 + 0x3feef7d6e51ca3c0, 0xbfd01f1806b9fdd2, // 0.96775, -0.2519 + 0x3feefafedc1ba8b7, 0xbfd006c4466e54af, // 0.96814, -0.25041 + 0x3feefe220c0b95ec, 0xbfcfdcdc1adfedf8, // 0.96852, -0.24893 + 0x3fef014074708ed3, 0xbfcfac2abeff57ff, // 0.9689, -0.24744 + 0x3fef045a14cf738c, 0xbfcf7b7480bd3801, // 0.96928, -0.24596 + 0x3fef076eecade0fa, 0xbfcf4ab9679c9f5c, // 0.96966, -0.24447 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef0d8a410379c5, 0xbfcee934c2d006c7, // 0.9704, -0.24149 + 0x3fef1090bc898f5f, 0xbfceb86b462de348, // 0.97077, -0.24 + 0x3fef13926dad024e, 0xbfce879d0cc0fdaf, // 0.97114, -0.23851 + 0x3fef168f53f7205d, 0xbfce56ca1e101a1b, // 0.9715, -0.23702 + 0x3fef19876ef1f486, 0xbfce25f281a2b684, // 0.97187, -0.23553 + 0x3fef1c7abe284708, 0xbfcdf5163f01099a, // 0.97223, -0.23404 + 0x3fef1f6941259d7a, 0xbfcdc4355db40195, // 0.97258, -0.23255 + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106 + 0x3fef2537e0a71f9f, 0xbfcd6265dd3f27e3, // 0.97329, -0.22957 + 0x3fef2817fc4609ce, 0xbfcd31774d2cbdee, // 0.97364, -0.22807 + 0x3fef2af349e17507, 0xbfcd00843c99c5f9, // 0.97399, -0.22658 + 0x3fef2dc9c9089a9d, 0xbfcccf8cb312b286, // 0.97434, -0.22508 + 0x3fef309b794b719f, 0xbfcc9e90b824a6a9, // 0.97468, -0.22359 + 0x3fef33685a3aaef0, 0xbfcc6d90535d74dc, // 0.97503, -0.22209 + 0x3fef36306b67c556, 0xbfcc3c8b8c4b9dd7, // 0.97536, -0.2206 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef3bb21cc4fe47, 0xbfcbda74f5856330, // 0.97604, -0.2176 + 0x3fef3e6bbc1bbc65, 0xbfcba96334f15dad, // 0.97637, -0.21611 + 0x3fef412089fd8adc, 0xbfcb784d30536cda, // 0.9767, -0.21461 + 0x3fef43d085ff92dd, 0xbfcb4732ef3d6722, // 0.97703, -0.21311 + 0x3fef467bafb7bbe0, 0xbfcb16147941ca2a, // 0.97735, -0.21161 + 0x3fef492206bcabb4, 0xbfcae4f1d5f3b9ab, // 0.97768, -0.21011 + 0x3fef4bc38aa5c694, 0xbfcab3cb0ce6fe44, // 0.978, -0.20861 + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711 + 0x3fef50f81785c6b9, 0xbfca517127e3dabc, // 0.97863, -0.20561 + 0x3fef538b1faf2d07, 0xbfca203e1b1831da, // 0.97895, -0.20411 + 0x3fef56195321c090, 0xbfc9ef0706e35a35, // 0.97926, -0.20261 + 0x3fef58a2b1789e84, 0xbfc9bdcbf2dc4366, // 0.97957, -0.2011 + 0x3fef5b273a4fa2d9, 0xbfc98c8ce69a7aec, // 0.97988, -0.1996 + 0x3fef5da6ed43685d, 0xbfc95b49e9b62af9, // 0.98018, -0.1981 + 0x3fef6021c9f148c2, 0xbfc92a0303c8194f, // 0.98048, -0.19659 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef6508fef47bd5, 0xbfc8c7699b34ca7e, // 0.98108, -0.19359 + 0x3fef677556883cee, 0xbfc8961727c41804, // 0.98138, -0.19208 + 0x3fef69dcd652f5de, 0xbfc864c0e9b2b6cf, // 0.98167, -0.19057 + 0x3fef6c3f7df5bbb7, 0xbfc83366e89c64c5, // 0.98196, -0.18907 + 0x3fef6e9d4d1262ca, 0xbfc802092c1d744b, // 0.98225, -0.18756 + 0x3fef70f6434b7eb7, 0xbfc7d0a7bbd2cb1b, // 0.98254, -0.18606 + 0x3fef734a60446279, 0xbfc79f429f59e11d, // 0.98282, -0.18455 + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304 + 0x3fef77e40d068a90, 0xbfc73c6d8055fe0a, // 0.98339, -0.18153 + 0x3fef7a299c1a322a, 0xbfc70afd8d08c4ff, // 0.98366, -0.18002 + 0x3fef7c6a50826840, 0xbfc6d98a0c08c8da, // 0.98394, -0.17851 + 0x3fef7ea629e63d6e, 0xbfc6a81304f64ab2, // 0.98421, -0.177 + 0x3fef80dd27ed8204, 0xbfc676987f7216b8, // 0.98448, -0.17549 + 0x3fef830f4a40c60c, 0xbfc6451a831d830d, // 0.98475, -0.17398 + 0x3fef853c9089595e, 0xbfc61399179a6e94, // 0.98501, -0.17247 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef898887a36c84, 0xbfc5b08c1192e381, // 0.98554, -0.16945 + 0x3fef8ba737cb4b78, 0xbfc57f008654cbde, // 0.9858, -0.16794 + 0x3fef8dc10a95380d, 0xbfc54d71aa74ef02, // 0.98605, -0.16643 + 0x3fef8fd5ffae41db, 0xbfc51bdf8597c5f2, // 0.98631, -0.16491 + 0x3fef91e616c43891, 0xbfc4ea4a1f624b61, // 0.98656, -0.1634 + 0x3fef93f14f85ac08, 0xbfc4b8b17f79fa88, // 0.98681, -0.16189 + 0x3fef95f7a9a1ec47, 0xbfc48715ad84cdf5, // 0.98706, -0.16037 + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886 + 0x3fef99f5c0abd496, 0xbfc423d4920e4166, // 0.98754, -0.15734 + 0x3fef9bed7cfbde29, 0xbfc3f22f57db4893, // 0.98778, -0.15583 + 0x3fef9de0596b77a3, 0xbfc3c0870a383ff6, // 0.98802, -0.15431 + 0x3fef9fce55adb2c8, 0xbfc38edbb0cd8d14, // 0.98826, -0.1528 + 0x3fefa1b7717661d5, 0xbfc35d2d53440db2, // 0.98849, -0.15128 + 0x3fefa39bac7a1791, 0xbfc32b7bf94516a7, // 0.98872, -0.14976 + 0x3fefa57b066e2754, 0xbfc2f9c7aa7a72af, // 0.98895, -0.14825 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefa92b1600657c, 0xbfc296564d2b953e, // 0.9894, -0.14521 + 0x3fefaafbcb0cfddc, 0xbfc264994dfd340a, // 0.98962, -0.1437 + 0x3fefacc79de6c44f, 0xbfc232d978aed413, // 0.98984, -0.14218 + 0x3fefae8e8e46cfbb, 0xbfc20116d4ec7bce, // 0.99006, -0.14066 + 0x3fefb0509be6f7db, 0xbfc1cf516a62a077, // 0.99027, -0.13914 + 0x3fefb20dc681d54d, 0xbfc19d8940be24e7, // 0.99049, -0.13762 + 0x3fefb3c60dd2c199, 0xbfc16bbe5fac5865, // 0.9907, -0.1361 + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458 + 0x3fefb727f187f1c7, 0xbfc1082095f820b0, // 0.99111, -0.13306 + 0x3fefb8d18d66adb7, 0xbfc0d64dbcb26786, // 0.99131, -0.13154 + 0x3fefba7644f068b5, 0xbfc0a4784ab8bf1d, // 0.99151, -0.13002 + 0x3fefbc1617e44186, 0xbfc072a047ba831d, // 0.99171, -0.1285 + 0x3fefbdb106021816, 0xbfc040c5bb67747e, // 0.99191, -0.12698 + 0x3fefbf470f0a8d88, 0xbfc00ee8ad6fb85b, // 0.9921, -0.12545 + 0x3fefc0d832bf043a, 0xbfbfba124b07ad85, // 0.99229, -0.12393 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefc3ebc935454c, 0xbfbef2858d27561b, // 0.99267, -0.12089 + 0x3fefc56e3b7d9af6, 0xbfbe8eb7fde4aa3e, // 0.99285, -0.11937 + 0x3fefc6ebc77f0887, 0xbfbe2ae5b8457f77, // 0.99303, -0.11784 + 0x3fefc8646cfeb721, 0xbfbdc70ecbae9fc8, // 0.99321, -0.11632 + 0x3fefc9d82bc2915e, 0xbfbd633347858ce4, // 0.99339, -0.11479 + 0x3fefcb4703914354, 0xbfbcff533b307dc1, // 0.99356, -0.11327 + 0x3fefccb0f4323aa3, 0xbfbc9b6eb6165c42, // 0.99374, -0.11175 + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022 + 0x3fefcf761f0c77a3, 0xbfbbd3987f31fa0e, // 0.99407, -0.1087 + 0x3fefd0d158d86087, 0xbfbb6fa6ec38f64c, // 0.99424, -0.10717 + 0x3fefd227aa9bd53b, 0xbfbb0bb11e1d5559, // 0.9944, -0.10565 + 0x3fefd37914220b84, 0xbfbaa7b724495c04, // 0.99456, -0.10412 + 0x3fefd4c59536fae4, 0xbfba43b90e27f3c4, // 0.99472, -0.1026 + 0x3fefd60d2da75c9e, 0xbfb9dfb6eb24a85c, // 0.99488, -0.10107 + 0x3fefd74fdd40abbf, 0xbfb97bb0caaba56f, // 0.99503, -0.099544 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518, -0.098017 + 0x3fefd9c68127c78c, 0xbfb8b398cf0c38e0, // 0.99533, -0.09649 + 0x3fefdafa7514538c, 0xbfb84f8712c130a0, // 0.99548, -0.094963 + 0x3fefdc297f674ba9, 0xbfb7eb7196b72ee4, // 0.99563, -0.093436 + 0x3fefdd539ff1f456, 0xbfb787586a5d5b21, // 0.99577, -0.091909 + 0x3fefde78d68653fd, 0xbfb7233b9d236e71, // 0.99591, -0.090381 + 0x3fefdf9922f73307, 0xbfb6bf1b3e79b129, // 0.99604, -0.088854 + 0x3fefe0b485181be3, 0xbfb65af75dd0f87b, // 0.99618, -0.087326 + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631, -0.085797 + 0x3fefe2dc89bbff08, 0xbfb592a554489bc8, // 0.99644, -0.084269 + 0x3fefe3e92be9d886, 0xbfb52e774a4d4d0a, // 0.99657, -0.08274 + 0x3fefe4f0e31d7a4a, 0xbfb4ca45fc1ba8b6, // 0.9967, -0.081211 + 0x3fefe5f3af2e3940, 0xbfb4661179272096, // 0.99682, -0.079682 + 0x3fefe6f18ff42c84, 0xbfb401d9d0e3a507, // 0.99694, -0.078153 + 0x3fefe7ea85482d60, 0xbfb39d9f12c5a299, // 0.99706, -0.076624 + 0x3fefe8de8f03d75c, 0xbfb339614e41ffa5, // 0.99718, -0.075094 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729, -0.073565 + 0x3fefeab7df1c6005, 0xbfb270dcefdfc45b, // 0.9974, -0.072035 + 0x3fefeb9d2530410f, 0xbfb20c9674ed444c, // 0.99751, -0.070505 + 0x3fefec7d7f19cffc, 0xbfb1a84d316d4f8a, // 0.99762, -0.068974 + 0x3fefed58ecb673c4, 0xbfb1440134d709b2, // 0.99772, -0.067444 + 0x3fefee2f6de455ba, 0xbfb0dfb28ea201e6, // 0.99783, -0.065913 + 0x3fefef0102826191, 0xbfb07b614e463064, // 0.99793, -0.064383 + 0x3fefefcdaa704562, 0xbfb0170d833bf421, // 0.99802, -0.062852 + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812, -0.061321 + 0x3feff15833be1965, 0xbfae9cbd15ff5527, // 0.99821, -0.05979 + 0x3feff21614e131ed, 0xbfadd406f9808ec8, // 0.9983, -0.058258 + 0x3feff2cf08da7321, 0xbfad0b4c436f91d0, // 0.99839, -0.056727 + 0x3feff3830f8d575c, 0xbfac428d12c0d7e3, // 0.99848, -0.055195 + 0x3feff43228de1b77, 0xbfab79c986698b78, // 0.99856, -0.053664 + 0x3feff4dc54b1bed3, 0xbfaab101bd5f8317, // 0.99864, -0.052132 + 0x3feff58192ee0358, 0xbfa9e835d6993c87, // 0.99872, -0.0506 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988, -0.049068 + 0x3feff6bd463b444d, 0xbfa856922bb513c1, // 0.99887, -0.047535 + 0x3feff753bb1b9164, 0xbfa78dbaa5874685, // 0.99894, -0.046003 + 0x3feff7e5420320f9, 0xbfa6c4df7d7d5b84, // 0.99901, -0.044471 + 0x3feff871dadb81df, 0xbfa5fc00d290cd43, // 0.99908, -0.042938 + 0x3feff8f9858f058b, 0xbfa5331ec3bba0eb, // 0.99914, -0.041406 + 0x3feff97c4208c014, 0xbfa46a396ff86179, // 0.9992, -0.039873 + 0x3feff9fa10348837, 0xbfa3a150f6421afc, // 0.99926, -0.03834 + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932, -0.036807 + 0x3feffae6e1556998, 0xbfa20f770ceb11c6, // 0.99938, -0.035274 + 0x3feffb55e425fdae, 0xbfa14685db42c17e, // 0.99943, -0.033741 + 0x3feffbbff85f9515, 0xbfa07d91ff984580, // 0.99948, -0.032208 + 0x3feffc251df1d3f8, 0xbf9f693731d1cf01, // 0.99953, -0.030675 + 0x3feffc8554cd213a, 0xbf9dd7458c64ab39, // 0.99958, -0.029142 + 0x3feffce09ce2a679, 0xbf9c454f4ce53b1c, // 0.99962, -0.027608 + 0x3feffd36f624500c, 0xbf9ab354b1504fca, // 0.99966, -0.026075 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997, -0.024541 + 0x3feffdd4dbf78f52, 0xbf978f535ddc9f03, // 0.99974, -0.023008 + 0x3feffe1c6870cb77, 0xbf95fd4d21fab226, // 0.99977, -0.021474 + 0x3feffe5f05e578db, 0xbf946b4381fce81c, // 0.9998, -0.01994 + 0x3feffe9cb44b51a1, 0xbf92d936bbe30efd, // 0.99983, -0.018407 + 0x3feffed57398d2b7, 0xbf9147270dad7132, // 0.99986, -0.016873 + 0x3fefff0943c53bd1, 0xbf8f6a296ab997ca, // 0.99988, -0.015339 + 0x3fefff3824c88f6f, 0xbf8c45ffe1e48ad9, // 0.9999, -0.013805 + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992, -0.012272 + 0x3fefff871937ce2f, 0xbf85fda037ac05e0, // 0.99994, -0.010738 + 0x3fefffa72c978c4f, 0xbf82d96b0e509703, // 0.99996,-0.0092038 + 0x3fefffc250b5daef, 0xbf7f6a65f9a2a3c5, // 0.99997,-0.0076698 + 0x3fefffd8858e8a92, 0xbf7921f0fe670071, // 0.99998,-0.0061359 + 0x3fefffe9cb1e2e8d, 0xbf72d97822f996bc, // 0.99999,-0.0046019 + 0x3feffff621621d02, 0xbf6921f8becca4ba, // 1, -0.003068 + 0x3feffffd88586ee6, 0xbf5921faaee6472d, // 1, -0.001534 + + +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i < N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 16, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_16[32] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.923879533f, 0.382683432f, + 0.707106781f, 0.707106781f, + 0.382683432f, 0.923879533f, + 0.000000000f, 1.000000000f, + -0.382683432f, 0.923879533f, + -0.707106781f, 0.707106781f, + -0.923879533f, 0.382683432f, + -1.000000000f, 0.000000000f, + -0.923879533f, -0.382683432f, + -0.707106781f, -0.707106781f, + -0.382683432f, -0.923879533f, + -0.000000000f, -1.000000000f, + 0.382683432f, -0.923879533f, + 0.707106781f, -0.707106781f, + 0.923879533f, -0.382683432f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 32, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_32[64] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.980785280f, 0.195090322f, + 0.923879533f, 0.382683432f, + 0.831469612f, 0.555570233f, + 0.707106781f, 0.707106781f, + 0.555570233f, 0.831469612f, + 0.382683432f, 0.923879533f, + 0.195090322f, 0.980785280f, + 0.000000000f, 1.000000000f, + -0.195090322f, 0.980785280f, + -0.382683432f, 0.923879533f, + -0.555570233f, 0.831469612f, + -0.707106781f, 0.707106781f, + -0.831469612f, 0.555570233f, + -0.923879533f, 0.382683432f, + -0.980785280f, 0.195090322f, + -1.000000000f, 0.000000000f, + -0.980785280f, -0.195090322f, + -0.923879533f, -0.382683432f, + -0.831469612f, -0.555570233f, + -0.707106781f, -0.707106781f, + -0.555570233f, -0.831469612f, + -0.382683432f, -0.923879533f, + -0.195090322f, -0.980785280f, + -0.000000000f, -1.000000000f, + 0.195090322f, -0.980785280f, + 0.382683432f, -0.923879533f, + 0.555570233f, -0.831469612f, + 0.707106781f, -0.707106781f, + 0.831469612f, -0.555570233f, + 0.923879533f, -0.382683432f, + 0.980785280f, -0.195090322f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for(i = 0; i < N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 64, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_64[128] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.995184727f, 0.098017140f, + 0.980785280f, 0.195090322f, + 0.956940336f, 0.290284677f, + 0.923879533f, 0.382683432f, + 0.881921264f, 0.471396737f, + 0.831469612f, 0.555570233f, + 0.773010453f, 0.634393284f, + 0.707106781f, 0.707106781f, + 0.634393284f, 0.773010453f, + 0.555570233f, 0.831469612f, + 0.471396737f, 0.881921264f, + 0.382683432f, 0.923879533f, + 0.290284677f, 0.956940336f, + 0.195090322f, 0.980785280f, + 0.098017140f, 0.995184727f, + 0.000000000f, 1.000000000f, + -0.098017140f, 0.995184727f, + -0.195090322f, 0.980785280f, + -0.290284677f, 0.956940336f, + -0.382683432f, 0.923879533f, + -0.471396737f, 0.881921264f, + -0.555570233f, 0.831469612f, + -0.634393284f, 0.773010453f, + -0.707106781f, 0.707106781f, + -0.773010453f, 0.634393284f, + -0.831469612f, 0.555570233f, + -0.881921264f, 0.471396737f, + -0.923879533f, 0.382683432f, + -0.956940336f, 0.290284677f, + -0.980785280f, 0.195090322f, + -0.995184727f, 0.098017140f, + -1.000000000f, 0.000000000f, + -0.995184727f, -0.098017140f, + -0.980785280f, -0.195090322f, + -0.956940336f, -0.290284677f, + -0.923879533f, -0.382683432f, + -0.881921264f, -0.471396737f, + -0.831469612f, -0.555570233f, + -0.773010453f, -0.634393284f, + -0.707106781f, -0.707106781f, + -0.634393284f, -0.773010453f, + -0.555570233f, -0.831469612f, + -0.471396737f, -0.881921264f, + -0.382683432f, -0.923879533f, + -0.290284677f, -0.956940336f, + -0.195090322f, -0.980785280f, + -0.098017140f, -0.995184727f, + -0.000000000f, -1.000000000f, + 0.098017140f, -0.995184727f, + 0.195090322f, -0.980785280f, + 0.290284677f, -0.956940336f, + 0.382683432f, -0.923879533f, + 0.471396737f, -0.881921264f, + 0.555570233f, -0.831469612f, + 0.634393284f, -0.773010453f, + 0.707106781f, -0.707106781f, + 0.773010453f, -0.634393284f, + 0.831469612f, -0.555570233f, + 0.881921264f, -0.471396737f, + 0.923879533f, -0.382683432f, + 0.956940336f, -0.290284677f, + 0.980785280f, -0.195090322f, + 0.995184727f, -0.098017140f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 128, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_128[256] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.998795456f, 0.049067674f, + 0.995184727f, 0.098017140f, + 0.989176510f, 0.146730474f, + 0.980785280f, 0.195090322f, + 0.970031253f, 0.242980180f, + 0.956940336f, 0.290284677f, + 0.941544065f, 0.336889853f, + 0.923879533f, 0.382683432f, + 0.903989293f, 0.427555093f, + 0.881921264f, 0.471396737f, + 0.857728610f, 0.514102744f, + 0.831469612f, 0.555570233f, + 0.803207531f, 0.595699304f, + 0.773010453f, 0.634393284f, + 0.740951125f, 0.671558955f, + 0.707106781f, 0.707106781f, + 0.671558955f, 0.740951125f, + 0.634393284f, 0.773010453f, + 0.595699304f, 0.803207531f, + 0.555570233f, 0.831469612f, + 0.514102744f, 0.857728610f, + 0.471396737f, 0.881921264f, + 0.427555093f, 0.903989293f, + 0.382683432f, 0.923879533f, + 0.336889853f, 0.941544065f, + 0.290284677f, 0.956940336f, + 0.242980180f, 0.970031253f, + 0.195090322f, 0.980785280f, + 0.146730474f, 0.989176510f, + 0.098017140f, 0.995184727f, + 0.049067674f, 0.998795456f, + 0.000000000f, 1.000000000f, + -0.049067674f, 0.998795456f, + -0.098017140f, 0.995184727f, + -0.146730474f, 0.989176510f, + -0.195090322f, 0.980785280f, + -0.242980180f, 0.970031253f, + -0.290284677f, 0.956940336f, + -0.336889853f, 0.941544065f, + -0.382683432f, 0.923879533f, + -0.427555093f, 0.903989293f, + -0.471396737f, 0.881921264f, + -0.514102744f, 0.857728610f, + -0.555570233f, 0.831469612f, + -0.595699304f, 0.803207531f, + -0.634393284f, 0.773010453f, + -0.671558955f, 0.740951125f, + -0.707106781f, 0.707106781f, + -0.740951125f, 0.671558955f, + -0.773010453f, 0.634393284f, + -0.803207531f, 0.595699304f, + -0.831469612f, 0.555570233f, + -0.857728610f, 0.514102744f, + -0.881921264f, 0.471396737f, + -0.903989293f, 0.427555093f, + -0.923879533f, 0.382683432f, + -0.941544065f, 0.336889853f, + -0.956940336f, 0.290284677f, + -0.970031253f, 0.242980180f, + -0.980785280f, 0.195090322f, + -0.989176510f, 0.146730474f, + -0.995184727f, 0.098017140f, + -0.998795456f, 0.049067674f, + -1.000000000f, 0.000000000f, + -0.998795456f, -0.049067674f, + -0.995184727f, -0.098017140f, + -0.989176510f, -0.146730474f, + -0.980785280f, -0.195090322f, + -0.970031253f, -0.242980180f, + -0.956940336f, -0.290284677f, + -0.941544065f, -0.336889853f, + -0.923879533f, -0.382683432f, + -0.903989293f, -0.427555093f, + -0.881921264f, -0.471396737f, + -0.857728610f, -0.514102744f, + -0.831469612f, -0.555570233f, + -0.803207531f, -0.595699304f, + -0.773010453f, -0.634393284f, + -0.740951125f, -0.671558955f, + -0.707106781f, -0.707106781f, + -0.671558955f, -0.740951125f, + -0.634393284f, -0.773010453f, + -0.595699304f, -0.803207531f, + -0.555570233f, -0.831469612f, + -0.514102744f, -0.857728610f, + -0.471396737f, -0.881921264f, + -0.427555093f, -0.903989293f, + -0.382683432f, -0.923879533f, + -0.336889853f, -0.941544065f, + -0.290284677f, -0.956940336f, + -0.242980180f, -0.970031253f, + -0.195090322f, -0.980785280f, + -0.146730474f, -0.989176510f, + -0.098017140f, -0.995184727f, + -0.049067674f, -0.998795456f, + -0.000000000f, -1.000000000f, + 0.049067674f, -0.998795456f, + 0.098017140f, -0.995184727f, + 0.146730474f, -0.989176510f, + 0.195090322f, -0.980785280f, + 0.242980180f, -0.970031253f, + 0.290284677f, -0.956940336f, + 0.336889853f, -0.941544065f, + 0.382683432f, -0.923879533f, + 0.427555093f, -0.903989293f, + 0.471396737f, -0.881921264f, + 0.514102744f, -0.857728610f, + 0.555570233f, -0.831469612f, + 0.595699304f, -0.803207531f, + 0.634393284f, -0.773010453f, + 0.671558955f, -0.740951125f, + 0.707106781f, -0.707106781f, + 0.740951125f, -0.671558955f, + 0.773010453f, -0.634393284f, + 0.803207531f, -0.595699304f, + 0.831469612f, -0.555570233f, + 0.857728610f, -0.514102744f, + 0.881921264f, -0.471396737f, + 0.903989293f, -0.427555093f, + 0.923879533f, -0.382683432f, + 0.941544065f, -0.336889853f, + 0.956940336f, -0.290284677f, + 0.970031253f, -0.242980180f, + 0.980785280f, -0.195090322f, + 0.989176510f, -0.146730474f, + 0.995184727f, -0.098017140f, + 0.998795456f, -0.049067674f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for(i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 256, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_256[512] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.999698819f, 0.024541229f, + 0.998795456f, 0.049067674f, + 0.997290457f, 0.073564564f, + 0.995184727f, 0.098017140f, + 0.992479535f, 0.122410675f, + 0.989176510f, 0.146730474f, + 0.985277642f, 0.170961889f, + 0.980785280f, 0.195090322f, + 0.975702130f, 0.219101240f, + 0.970031253f, 0.242980180f, + 0.963776066f, 0.266712757f, + 0.956940336f, 0.290284677f, + 0.949528181f, 0.313681740f, + 0.941544065f, 0.336889853f, + 0.932992799f, 0.359895037f, + 0.923879533f, 0.382683432f, + 0.914209756f, 0.405241314f, + 0.903989293f, 0.427555093f, + 0.893224301f, 0.449611330f, + 0.881921264f, 0.471396737f, + 0.870086991f, 0.492898192f, + 0.857728610f, 0.514102744f, + 0.844853565f, 0.534997620f, + 0.831469612f, 0.555570233f, + 0.817584813f, 0.575808191f, + 0.803207531f, 0.595699304f, + 0.788346428f, 0.615231591f, + 0.773010453f, 0.634393284f, + 0.757208847f, 0.653172843f, + 0.740951125f, 0.671558955f, + 0.724247083f, 0.689540545f, + 0.707106781f, 0.707106781f, + 0.689540545f, 0.724247083f, + 0.671558955f, 0.740951125f, + 0.653172843f, 0.757208847f, + 0.634393284f, 0.773010453f, + 0.615231591f, 0.788346428f, + 0.595699304f, 0.803207531f, + 0.575808191f, 0.817584813f, + 0.555570233f, 0.831469612f, + 0.534997620f, 0.844853565f, + 0.514102744f, 0.857728610f, + 0.492898192f, 0.870086991f, + 0.471396737f, 0.881921264f, + 0.449611330f, 0.893224301f, + 0.427555093f, 0.903989293f, + 0.405241314f, 0.914209756f, + 0.382683432f, 0.923879533f, + 0.359895037f, 0.932992799f, + 0.336889853f, 0.941544065f, + 0.313681740f, 0.949528181f, + 0.290284677f, 0.956940336f, + 0.266712757f, 0.963776066f, + 0.242980180f, 0.970031253f, + 0.219101240f, 0.975702130f, + 0.195090322f, 0.980785280f, + 0.170961889f, 0.985277642f, + 0.146730474f, 0.989176510f, + 0.122410675f, 0.992479535f, + 0.098017140f, 0.995184727f, + 0.073564564f, 0.997290457f, + 0.049067674f, 0.998795456f, + 0.024541229f, 0.999698819f, + 0.000000000f, 1.000000000f, + -0.024541229f, 0.999698819f, + -0.049067674f, 0.998795456f, + -0.073564564f, 0.997290457f, + -0.098017140f, 0.995184727f, + -0.122410675f, 0.992479535f, + -0.146730474f, 0.989176510f, + -0.170961889f, 0.985277642f, + -0.195090322f, 0.980785280f, + -0.219101240f, 0.975702130f, + -0.242980180f, 0.970031253f, + -0.266712757f, 0.963776066f, + -0.290284677f, 0.956940336f, + -0.313681740f, 0.949528181f, + -0.336889853f, 0.941544065f, + -0.359895037f, 0.932992799f, + -0.382683432f, 0.923879533f, + -0.405241314f, 0.914209756f, + -0.427555093f, 0.903989293f, + -0.449611330f, 0.893224301f, + -0.471396737f, 0.881921264f, + -0.492898192f, 0.870086991f, + -0.514102744f, 0.857728610f, + -0.534997620f, 0.844853565f, + -0.555570233f, 0.831469612f, + -0.575808191f, 0.817584813f, + -0.595699304f, 0.803207531f, + -0.615231591f, 0.788346428f, + -0.634393284f, 0.773010453f, + -0.653172843f, 0.757208847f, + -0.671558955f, 0.740951125f, + -0.689540545f, 0.724247083f, + -0.707106781f, 0.707106781f, + -0.724247083f, 0.689540545f, + -0.740951125f, 0.671558955f, + -0.757208847f, 0.653172843f, + -0.773010453f, 0.634393284f, + -0.788346428f, 0.615231591f, + -0.803207531f, 0.595699304f, + -0.817584813f, 0.575808191f, + -0.831469612f, 0.555570233f, + -0.844853565f, 0.534997620f, + -0.857728610f, 0.514102744f, + -0.870086991f, 0.492898192f, + -0.881921264f, 0.471396737f, + -0.893224301f, 0.449611330f, + -0.903989293f, 0.427555093f, + -0.914209756f, 0.405241314f, + -0.923879533f, 0.382683432f, + -0.932992799f, 0.359895037f, + -0.941544065f, 0.336889853f, + -0.949528181f, 0.313681740f, + -0.956940336f, 0.290284677f, + -0.963776066f, 0.266712757f, + -0.970031253f, 0.242980180f, + -0.975702130f, 0.219101240f, + -0.980785280f, 0.195090322f, + -0.985277642f, 0.170961889f, + -0.989176510f, 0.146730474f, + -0.992479535f, 0.122410675f, + -0.995184727f, 0.098017140f, + -0.997290457f, 0.073564564f, + -0.998795456f, 0.049067674f, + -0.999698819f, 0.024541229f, + -1.000000000f, 0.000000000f, + -0.999698819f, -0.024541229f, + -0.998795456f, -0.049067674f, + -0.997290457f, -0.073564564f, + -0.995184727f, -0.098017140f, + -0.992479535f, -0.122410675f, + -0.989176510f, -0.146730474f, + -0.985277642f, -0.170961889f, + -0.980785280f, -0.195090322f, + -0.975702130f, -0.219101240f, + -0.970031253f, -0.242980180f, + -0.963776066f, -0.266712757f, + -0.956940336f, -0.290284677f, + -0.949528181f, -0.313681740f, + -0.941544065f, -0.336889853f, + -0.932992799f, -0.359895037f, + -0.923879533f, -0.382683432f, + -0.914209756f, -0.405241314f, + -0.903989293f, -0.427555093f, + -0.893224301f, -0.449611330f, + -0.881921264f, -0.471396737f, + -0.870086991f, -0.492898192f, + -0.857728610f, -0.514102744f, + -0.844853565f, -0.534997620f, + -0.831469612f, -0.555570233f, + -0.817584813f, -0.575808191f, + -0.803207531f, -0.595699304f, + -0.788346428f, -0.615231591f, + -0.773010453f, -0.634393284f, + -0.757208847f, -0.653172843f, + -0.740951125f, -0.671558955f, + -0.724247083f, -0.689540545f, + -0.707106781f, -0.707106781f, + -0.689540545f, -0.724247083f, + -0.671558955f, -0.740951125f, + -0.653172843f, -0.757208847f, + -0.634393284f, -0.773010453f, + -0.615231591f, -0.788346428f, + -0.595699304f, -0.803207531f, + -0.575808191f, -0.817584813f, + -0.555570233f, -0.831469612f, + -0.534997620f, -0.844853565f, + -0.514102744f, -0.857728610f, + -0.492898192f, -0.870086991f, + -0.471396737f, -0.881921264f, + -0.449611330f, -0.893224301f, + -0.427555093f, -0.903989293f, + -0.405241314f, -0.914209756f, + -0.382683432f, -0.923879533f, + -0.359895037f, -0.932992799f, + -0.336889853f, -0.941544065f, + -0.313681740f, -0.949528181f, + -0.290284677f, -0.956940336f, + -0.266712757f, -0.963776066f, + -0.242980180f, -0.970031253f, + -0.219101240f, -0.975702130f, + -0.195090322f, -0.980785280f, + -0.170961889f, -0.985277642f, + -0.146730474f, -0.989176510f, + -0.122410675f, -0.992479535f, + -0.098017140f, -0.995184727f, + -0.073564564f, -0.997290457f, + -0.049067674f, -0.998795456f, + -0.024541229f, -0.999698819f, + -0.000000000f, -1.000000000f, + 0.024541229f, -0.999698819f, + 0.049067674f, -0.998795456f, + 0.073564564f, -0.997290457f, + 0.098017140f, -0.995184727f, + 0.122410675f, -0.992479535f, + 0.146730474f, -0.989176510f, + 0.170961889f, -0.985277642f, + 0.195090322f, -0.980785280f, + 0.219101240f, -0.975702130f, + 0.242980180f, -0.970031253f, + 0.266712757f, -0.963776066f, + 0.290284677f, -0.956940336f, + 0.313681740f, -0.949528181f, + 0.336889853f, -0.941544065f, + 0.359895037f, -0.932992799f, + 0.382683432f, -0.923879533f, + 0.405241314f, -0.914209756f, + 0.427555093f, -0.903989293f, + 0.449611330f, -0.893224301f, + 0.471396737f, -0.881921264f, + 0.492898192f, -0.870086991f, + 0.514102744f, -0.857728610f, + 0.534997620f, -0.844853565f, + 0.555570233f, -0.831469612f, + 0.575808191f, -0.817584813f, + 0.595699304f, -0.803207531f, + 0.615231591f, -0.788346428f, + 0.634393284f, -0.773010453f, + 0.653172843f, -0.757208847f, + 0.671558955f, -0.740951125f, + 0.689540545f, -0.724247083f, + 0.707106781f, -0.707106781f, + 0.724247083f, -0.689540545f, + 0.740951125f, -0.671558955f, + 0.757208847f, -0.653172843f, + 0.773010453f, -0.634393284f, + 0.788346428f, -0.615231591f, + 0.803207531f, -0.595699304f, + 0.817584813f, -0.575808191f, + 0.831469612f, -0.555570233f, + 0.844853565f, -0.534997620f, + 0.857728610f, -0.514102744f, + 0.870086991f, -0.492898192f, + 0.881921264f, -0.471396737f, + 0.893224301f, -0.449611330f, + 0.903989293f, -0.427555093f, + 0.914209756f, -0.405241314f, + 0.923879533f, -0.382683432f, + 0.932992799f, -0.359895037f, + 0.941544065f, -0.336889853f, + 0.949528181f, -0.313681740f, + 0.956940336f, -0.290284677f, + 0.963776066f, -0.266712757f, + 0.970031253f, -0.242980180f, + 0.975702130f, -0.219101240f, + 0.980785280f, -0.195090322f, + 0.985277642f, -0.170961889f, + 0.989176510f, -0.146730474f, + 0.992479535f, -0.122410675f, + 0.995184727f, -0.098017140f, + 0.997290457f, -0.073564564f, + 0.998795456f, -0.049067674f, + 0.999698819f, -0.024541229f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 512, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_512[1024] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.999924702f, 0.012271538f, + 0.999698819f, 0.024541229f, + 0.999322385f, 0.036807223f, + 0.998795456f, 0.049067674f, + 0.998118113f, 0.061320736f, + 0.997290457f, 0.073564564f, + 0.996312612f, 0.085797312f, + 0.995184727f, 0.098017140f, + 0.993906970f, 0.110222207f, + 0.992479535f, 0.122410675f, + 0.990902635f, 0.134580709f, + 0.989176510f, 0.146730474f, + 0.987301418f, 0.158858143f, + 0.985277642f, 0.170961889f, + 0.983105487f, 0.183039888f, + 0.980785280f, 0.195090322f, + 0.978317371f, 0.207111376f, + 0.975702130f, 0.219101240f, + 0.972939952f, 0.231058108f, + 0.970031253f, 0.242980180f, + 0.966976471f, 0.254865660f, + 0.963776066f, 0.266712757f, + 0.960430519f, 0.278519689f, + 0.956940336f, 0.290284677f, + 0.953306040f, 0.302005949f, + 0.949528181f, 0.313681740f, + 0.945607325f, 0.325310292f, + 0.941544065f, 0.336889853f, + 0.937339012f, 0.348418680f, + 0.932992799f, 0.359895037f, + 0.928506080f, 0.371317194f, + 0.923879533f, 0.382683432f, + 0.919113852f, 0.393992040f, + 0.914209756f, 0.405241314f, + 0.909167983f, 0.416429560f, + 0.903989293f, 0.427555093f, + 0.898674466f, 0.438616239f, + 0.893224301f, 0.449611330f, + 0.887639620f, 0.460538711f, + 0.881921264f, 0.471396737f, + 0.876070094f, 0.482183772f, + 0.870086991f, 0.492898192f, + 0.863972856f, 0.503538384f, + 0.857728610f, 0.514102744f, + 0.851355193f, 0.524589683f, + 0.844853565f, 0.534997620f, + 0.838224706f, 0.545324988f, + 0.831469612f, 0.555570233f, + 0.824589303f, 0.565731811f, + 0.817584813f, 0.575808191f, + 0.810457198f, 0.585797857f, + 0.803207531f, 0.595699304f, + 0.795836905f, 0.605511041f, + 0.788346428f, 0.615231591f, + 0.780737229f, 0.624859488f, + 0.773010453f, 0.634393284f, + 0.765167266f, 0.643831543f, + 0.757208847f, 0.653172843f, + 0.749136395f, 0.662415778f, + 0.740951125f, 0.671558955f, + 0.732654272f, 0.680600998f, + 0.724247083f, 0.689540545f, + 0.715730825f, 0.698376249f, + 0.707106781f, 0.707106781f, + 0.698376249f, 0.715730825f, + 0.689540545f, 0.724247083f, + 0.680600998f, 0.732654272f, + 0.671558955f, 0.740951125f, + 0.662415778f, 0.749136395f, + 0.653172843f, 0.757208847f, + 0.643831543f, 0.765167266f, + 0.634393284f, 0.773010453f, + 0.624859488f, 0.780737229f, + 0.615231591f, 0.788346428f, + 0.605511041f, 0.795836905f, + 0.595699304f, 0.803207531f, + 0.585797857f, 0.810457198f, + 0.575808191f, 0.817584813f, + 0.565731811f, 0.824589303f, + 0.555570233f, 0.831469612f, + 0.545324988f, 0.838224706f, + 0.534997620f, 0.844853565f, + 0.524589683f, 0.851355193f, + 0.514102744f, 0.857728610f, + 0.503538384f, 0.863972856f, + 0.492898192f, 0.870086991f, + 0.482183772f, 0.876070094f, + 0.471396737f, 0.881921264f, + 0.460538711f, 0.887639620f, + 0.449611330f, 0.893224301f, + 0.438616239f, 0.898674466f, + 0.427555093f, 0.903989293f, + 0.416429560f, 0.909167983f, + 0.405241314f, 0.914209756f, + 0.393992040f, 0.919113852f, + 0.382683432f, 0.923879533f, + 0.371317194f, 0.928506080f, + 0.359895037f, 0.932992799f, + 0.348418680f, 0.937339012f, + 0.336889853f, 0.941544065f, + 0.325310292f, 0.945607325f, + 0.313681740f, 0.949528181f, + 0.302005949f, 0.953306040f, + 0.290284677f, 0.956940336f, + 0.278519689f, 0.960430519f, + 0.266712757f, 0.963776066f, + 0.254865660f, 0.966976471f, + 0.242980180f, 0.970031253f, + 0.231058108f, 0.972939952f, + 0.219101240f, 0.975702130f, + 0.207111376f, 0.978317371f, + 0.195090322f, 0.980785280f, + 0.183039888f, 0.983105487f, + 0.170961889f, 0.985277642f, + 0.158858143f, 0.987301418f, + 0.146730474f, 0.989176510f, + 0.134580709f, 0.990902635f, + 0.122410675f, 0.992479535f, + 0.110222207f, 0.993906970f, + 0.098017140f, 0.995184727f, + 0.085797312f, 0.996312612f, + 0.073564564f, 0.997290457f, + 0.061320736f, 0.998118113f, + 0.049067674f, 0.998795456f, + 0.036807223f, 0.999322385f, + 0.024541229f, 0.999698819f, + 0.012271538f, 0.999924702f, + 0.000000000f, 1.000000000f, + -0.012271538f, 0.999924702f, + -0.024541229f, 0.999698819f, + -0.036807223f, 0.999322385f, + -0.049067674f, 0.998795456f, + -0.061320736f, 0.998118113f, + -0.073564564f, 0.997290457f, + -0.085797312f, 0.996312612f, + -0.098017140f, 0.995184727f, + -0.110222207f, 0.993906970f, + -0.122410675f, 0.992479535f, + -0.134580709f, 0.990902635f, + -0.146730474f, 0.989176510f, + -0.158858143f, 0.987301418f, + -0.170961889f, 0.985277642f, + -0.183039888f, 0.983105487f, + -0.195090322f, 0.980785280f, + -0.207111376f, 0.978317371f, + -0.219101240f, 0.975702130f, + -0.231058108f, 0.972939952f, + -0.242980180f, 0.970031253f, + -0.254865660f, 0.966976471f, + -0.266712757f, 0.963776066f, + -0.278519689f, 0.960430519f, + -0.290284677f, 0.956940336f, + -0.302005949f, 0.953306040f, + -0.313681740f, 0.949528181f, + -0.325310292f, 0.945607325f, + -0.336889853f, 0.941544065f, + -0.348418680f, 0.937339012f, + -0.359895037f, 0.932992799f, + -0.371317194f, 0.928506080f, + -0.382683432f, 0.923879533f, + -0.393992040f, 0.919113852f, + -0.405241314f, 0.914209756f, + -0.416429560f, 0.909167983f, + -0.427555093f, 0.903989293f, + -0.438616239f, 0.898674466f, + -0.449611330f, 0.893224301f, + -0.460538711f, 0.887639620f, + -0.471396737f, 0.881921264f, + -0.482183772f, 0.876070094f, + -0.492898192f, 0.870086991f, + -0.503538384f, 0.863972856f, + -0.514102744f, 0.857728610f, + -0.524589683f, 0.851355193f, + -0.534997620f, 0.844853565f, + -0.545324988f, 0.838224706f, + -0.555570233f, 0.831469612f, + -0.565731811f, 0.824589303f, + -0.575808191f, 0.817584813f, + -0.585797857f, 0.810457198f, + -0.595699304f, 0.803207531f, + -0.605511041f, 0.795836905f, + -0.615231591f, 0.788346428f, + -0.624859488f, 0.780737229f, + -0.634393284f, 0.773010453f, + -0.643831543f, 0.765167266f, + -0.653172843f, 0.757208847f, + -0.662415778f, 0.749136395f, + -0.671558955f, 0.740951125f, + -0.680600998f, 0.732654272f, + -0.689540545f, 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-0.073564564f, + 0.998118113f, -0.061320736f, + 0.998795456f, -0.049067674f, + 0.999322385f, -0.036807223f, + 0.999698819f, -0.024541229f, + 0.999924702f, -0.012271538f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 1024, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_1024[2048] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.999981175f, 0.006135885f, + 0.999924702f, 0.012271538f, + 0.999830582f, 0.018406730f, + 0.999698819f, 0.024541229f, + 0.999529418f, 0.030674803f, + 0.999322385f, 0.036807223f, + 0.999077728f, 0.042938257f, + 0.998795456f, 0.049067674f, + 0.998475581f, 0.055195244f, + 0.998118113f, 0.061320736f, + 0.997723067f, 0.067443920f, + 0.997290457f, 0.073564564f, + 0.996820299f, 0.079682438f, + 0.996312612f, 0.085797312f, + 0.995767414f, 0.091908956f, + 0.995184727f, 0.098017140f, + 0.994564571f, 0.104121634f, + 0.993906970f, 0.110222207f, + 0.993211949f, 0.116318631f, + 0.992479535f, 0.122410675f, + 0.991709754f, 0.128498111f, + 0.990902635f, 0.134580709f, + 0.990058210f, 0.140658239f, + 0.989176510f, 0.146730474f, + 0.988257568f, 0.152797185f, + 0.987301418f, 0.158858143f, + 0.986308097f, 0.164913120f, + 0.985277642f, 0.170961889f, + 0.984210092f, 0.177004220f, + 0.983105487f, 0.183039888f, + 0.981963869f, 0.189068664f, + 0.980785280f, 0.195090322f, + 0.979569766f, 0.201104635f, + 0.978317371f, 0.207111376f, + 0.977028143f, 0.213110320f, + 0.975702130f, 0.219101240f, + 0.974339383f, 0.225083911f, + 0.972939952f, 0.231058108f, + 0.971503891f, 0.237023606f, + 0.970031253f, 0.242980180f, + 0.968522094f, 0.248927606f, + 0.966976471f, 0.254865660f, + 0.965394442f, 0.260794118f, + 0.963776066f, 0.266712757f, + 0.962121404f, 0.272621355f, + 0.960430519f, 0.278519689f, + 0.958703475f, 0.284407537f, + 0.956940336f, 0.290284677f, + 0.955141168f, 0.296150888f, + 0.953306040f, 0.302005949f, + 0.951435021f, 0.307849640f, + 0.949528181f, 0.313681740f, + 0.947585591f, 0.319502031f, + 0.945607325f, 0.325310292f, + 0.943593458f, 0.331106306f, + 0.941544065f, 0.336889853f, + 0.939459224f, 0.342660717f, + 0.937339012f, 0.348418680f, + 0.935183510f, 0.354163525f, + 0.932992799f, 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-0.036807223f, + 0.999529418f, -0.030674803f, + 0.999698819f, -0.024541229f, + 0.999830582f, -0.018406730f, + 0.999924702f, -0.012271538f, + 0.999981175f, -0.006135885f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 2048, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_2048[4096] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.999995294f, 0.003067957f, + 0.999981175f, 0.006135885f, + 0.999957645f, 0.009203755f, + 0.999924702f, 0.012271538f, + 0.999882347f, 0.015339206f, + 0.999830582f, 0.018406730f, + 0.999769405f, 0.021474080f, + 0.999698819f, 0.024541229f, + 0.999618822f, 0.027608146f, + 0.999529418f, 0.030674803f, + 0.999430605f, 0.033741172f, + 0.999322385f, 0.036807223f, + 0.999204759f, 0.039872928f, + 0.999077728f, 0.042938257f, + 0.998941293f, 0.046003182f, + 0.998795456f, 0.049067674f, + 0.998640218f, 0.052131705f, + 0.998475581f, 0.055195244f, + 0.998301545f, 0.058258265f, + 0.998118113f, 0.061320736f, + 0.997925286f, 0.064382631f, + 0.997723067f, 0.067443920f, + 0.997511456f, 0.070504573f, + 0.997290457f, 0.073564564f, + 0.997060070f, 0.076623861f, + 0.996820299f, 0.079682438f, + 0.996571146f, 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-0.018406730f, + 0.999882347f, -0.015339206f, + 0.999924702f, -0.012271538f, + 0.999957645f, -0.009203755f, + 0.999981175f, -0.006135885f, + 0.999995294f, -0.003067957f +}; + +/** + @par + Example code for Floating-point Twiddle factors Generation: + @par + 
for (i = 0; i< N/; i++)
+  {
+ 	twiddleCoef[2*i]   = cos(i * 2*PI/(float)N);
+ 	twiddleCoef[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 4096, PI = 3.14159265358979 + @par + Cos and Sin values are in interleaved fashion +*/ +const float32_t twiddleCoef_4096[8192] ARM_DSP_TABLE_ATTRIBUTE = { + 1.000000000f, 0.000000000f, + 0.999998823f, 0.001533980f, + 0.999995294f, 0.003067957f, + 0.999989411f, 0.004601926f, + 0.999981175f, 0.006135885f, + 0.999970586f, 0.007669829f, + 0.999957645f, 0.009203755f, + 0.999942350f, 0.010737659f, + 0.999924702f, 0.012271538f, + 0.999904701f, 0.013805389f, + 0.999882347f, 0.015339206f, + 0.999857641f, 0.016872988f, + 0.999830582f, 0.018406730f, + 0.999801170f, 0.019940429f, + 0.999769405f, 0.021474080f, + 0.999735288f, 0.023007681f, + 0.999698819f, 0.024541229f, + 0.999659997f, 0.026074718f, + 0.999618822f, 0.027608146f, + 0.999575296f, 0.029141509f, + 0.999529418f, 0.030674803f, + 0.999481187f, 0.032208025f, + 0.999430605f, 0.033741172f, + 0.999377670f, 0.035274239f, + 0.999322385f, 0.036807223f, + 0.999264747f, 0.038340120f, + 0.999204759f, 0.039872928f, + 0.999142419f, 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-0.059789571f, + 0.998301545f, -0.058258265f, + 0.998389737f, -0.056726821f, + 0.998475581f, -0.055195244f, + 0.998559074f, -0.053663538f, + 0.998640218f, -0.052131705f, + 0.998719012f, -0.050599749f, + 0.998795456f, -0.049067674f, + 0.998869550f, -0.047535484f, + 0.998941293f, -0.046003182f, + 0.999010686f, -0.044470772f, + 0.999077728f, -0.042938257f, + 0.999142419f, -0.041405641f, + 0.999204759f, -0.039872928f, + 0.999264747f, -0.038340120f, + 0.999322385f, -0.036807223f, + 0.999377670f, -0.035274239f, + 0.999430605f, -0.033741172f, + 0.999481187f, -0.032208025f, + 0.999529418f, -0.030674803f, + 0.999575296f, -0.029141509f, + 0.999618822f, -0.027608146f, + 0.999659997f, -0.026074718f, + 0.999698819f, -0.024541229f, + 0.999735288f, -0.023007681f, + 0.999769405f, -0.021474080f, + 0.999801170f, -0.019940429f, + 0.999830582f, -0.018406730f, + 0.999857641f, -0.016872988f, + 0.999882347f, -0.015339206f, + 0.999904701f, -0.013805389f, + 0.999924702f, -0.012271538f, + 0.999942350f, -0.010737659f, + 0.999957645f, -0.009203755f, + 0.999970586f, -0.007669829f, + 0.999981175f, -0.006135885f, + 0.999989411f, -0.004601926f, + 0.999995294f, -0.003067957f, + 0.999998823f, -0.001533980f +}; + + +/** + @brief Q31 Twiddle factors Table +*/ + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
 for(i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 16, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + */ +const q31_t twiddleCoef_16_q31[24] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, + (q31_t)0x7641AF3C, (q31_t)0x30FBC54D, + (q31_t)0x5A82799A, (q31_t)0x5A82799A, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, + (q31_t)0x00000000, (q31_t)0x7FFFFFFF, + (q31_t)0xCF043AB2, (q31_t)0x7641AF3C, + (q31_t)0xA57D8666, (q31_t)0x5A82799A, + (q31_t)0x89BE50C3, (q31_t)0x30FBC54D, + (q31_t)0x80000000, (q31_t)0x00000000, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, + (q31_t)0xA57D8666, (q31_t)0xA57D8666, + (q31_t)0xCF043AB2, (q31_t)0x89BE50C3 +}; + + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 32, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + */ +const q31_t twiddleCoef_32_q31[48] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, + (q31_t)0x7D8A5F3F, (q31_t)0x18F8B83C, + (q31_t)0x7641AF3C, (q31_t)0x30FBC54D, + (q31_t)0x6A6D98A4, (q31_t)0x471CECE6, + (q31_t)0x5A82799A, (q31_t)0x5A82799A, + (q31_t)0x471CECE6, (q31_t)0x6A6D98A4, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, + (q31_t)0x18F8B83C, (q31_t)0x7D8A5F3F, + (q31_t)0x00000000, (q31_t)0x7FFFFFFF, + (q31_t)0xE70747C3, (q31_t)0x7D8A5F3F, + (q31_t)0xCF043AB2, (q31_t)0x7641AF3C, + (q31_t)0xB8E31319, (q31_t)0x6A6D98A4, + (q31_t)0xA57D8666, (q31_t)0x5A82799A, + (q31_t)0x9592675B, (q31_t)0x471CECE6, + (q31_t)0x89BE50C3, (q31_t)0x30FBC54D, + (q31_t)0x8275A0C0, (q31_t)0x18F8B83C, + (q31_t)0x80000000, (q31_t)0x00000000, + (q31_t)0x8275A0C0, (q31_t)0xE70747C3, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, + (q31_t)0x9592675B, (q31_t)0xB8E31319, + (q31_t)0xA57D8666, (q31_t)0xA57D8666, + (q31_t)0xB8E31319, (q31_t)0x9592675B, + (q31_t)0xCF043AB2, (q31_t)0x89BE50C3, + (q31_t)0xE70747C3, (q31_t)0x8275A0C0 +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 64, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + */ +const q31_t twiddleCoef_64_q31[96] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7F62368F, + (q31_t)0x0C8BD35E, (q31_t)0x7D8A5F3F, (q31_t)0x18F8B83C, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x7641AF3C, + (q31_t)0x30FBC54D, (q31_t)0x70E2CBC6, (q31_t)0x3C56BA70, + (q31_t)0x6A6D98A4, (q31_t)0x471CECE6, (q31_t)0x62F201AC, + (q31_t)0x5133CC94, (q31_t)0x5A82799A, (q31_t)0x5A82799A, + (q31_t)0x5133CC94, (q31_t)0x62F201AC, (q31_t)0x471CECE6, + (q31_t)0x6A6D98A4, (q31_t)0x3C56BA70, (q31_t)0x70E2CBC6, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, (q31_t)0x25280C5D, + (q31_t)0x7A7D055B, (q31_t)0x18F8B83C, (q31_t)0x7D8A5F3F, + (q31_t)0x0C8BD35E, (q31_t)0x7F62368F, (q31_t)0x00000000, + (q31_t)0x7FFFFFFF, (q31_t)0xF3742CA1, (q31_t)0x7F62368F, + (q31_t)0xE70747C3, (q31_t)0x7D8A5F3F, (q31_t)0xDAD7F3A2, + (q31_t)0x7A7D055B, (q31_t)0xCF043AB2, (q31_t)0x7641AF3C, + (q31_t)0xC3A9458F, (q31_t)0x70E2CBC6, (q31_t)0xB8E31319, + (q31_t)0x6A6D98A4, (q31_t)0xAECC336B, (q31_t)0x62F201AC, + (q31_t)0xA57D8666, (q31_t)0x5A82799A, (q31_t)0x9D0DFE53, + (q31_t)0x5133CC94, (q31_t)0x9592675B, (q31_t)0x471CECE6, + (q31_t)0x8F1D343A, (q31_t)0x3C56BA70, (q31_t)0x89BE50C3, + (q31_t)0x30FBC54D, (q31_t)0x8582FAA4, (q31_t)0x25280C5D, + (q31_t)0x8275A0C0, (q31_t)0x18F8B83C, (q31_t)0x809DC970, + (q31_t)0x0C8BD35E, (q31_t)0x80000000, (q31_t)0x00000000, + (q31_t)0x809DC970, (q31_t)0xF3742CA1, (q31_t)0x8275A0C0, + (q31_t)0xE70747C3, (q31_t)0x8582FAA4, (q31_t)0xDAD7F3A2, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, (q31_t)0x8F1D343A, + (q31_t)0xC3A9458F, (q31_t)0x9592675B, (q31_t)0xB8E31319, + (q31_t)0x9D0DFE53, (q31_t)0xAECC336B, (q31_t)0xA57D8666, + (q31_t)0xA57D8666, (q31_t)0xAECC336B, (q31_t)0x9D0DFE53, + (q31_t)0xB8E31319, (q31_t)0x9592675B, (q31_t)0xC3A9458F, + (q31_t)0x8F1D343A, (q31_t)0xCF043AB2, (q31_t)0x89BE50C3, + (q31_t)0xDAD7F3A2, (q31_t)0x8582FAA4, (q31_t)0xE70747C3, + (q31_t)0x8275A0C0, (q31_t)0xF3742CA1, (q31_t)0x809DC970 +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i < 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 128, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + */ +const q31_t twiddleCoef_128_q31[192] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7FD8878D, + (q31_t)0x0647D97C, (q31_t)0x7F62368F, (q31_t)0x0C8BD35E, + (q31_t)0x7E9D55FC, (q31_t)0x12C8106E, (q31_t)0x7D8A5F3F, + (q31_t)0x18F8B83C, (q31_t)0x7C29FBEE, (q31_t)0x1F19F97B, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x78848413, + (q31_t)0x2B1F34EB, (q31_t)0x7641AF3C, (q31_t)0x30FBC54D, + (q31_t)0x73B5EBD0, (q31_t)0x36BA2013, (q31_t)0x70E2CBC6, + (q31_t)0x3C56BA70, (q31_t)0x6DCA0D14, (q31_t)0x41CE1E64, + (q31_t)0x6A6D98A4, (q31_t)0x471CECE6, (q31_t)0x66CF811F, + (q31_t)0x4C3FDFF3, (q31_t)0x62F201AC, (q31_t)0x5133CC94, + (q31_t)0x5ED77C89, (q31_t)0x55F5A4D2, (q31_t)0x5A82799A, + (q31_t)0x5A82799A, (q31_t)0x55F5A4D2, (q31_t)0x5ED77C89, + (q31_t)0x5133CC94, (q31_t)0x62F201AC, (q31_t)0x4C3FDFF3, + (q31_t)0x66CF811F, (q31_t)0x471CECE6, (q31_t)0x6A6D98A4, + (q31_t)0x41CE1E64, (q31_t)0x6DCA0D14, (q31_t)0x3C56BA70, + (q31_t)0x70E2CBC6, (q31_t)0x36BA2013, (q31_t)0x73B5EBD0, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, (q31_t)0x2B1F34EB, + (q31_t)0x78848413, (q31_t)0x25280C5D, (q31_t)0x7A7D055B, + (q31_t)0x1F19F97B, (q31_t)0x7C29FBEE, (q31_t)0x18F8B83C, + (q31_t)0x7D8A5F3F, (q31_t)0x12C8106E, (q31_t)0x7E9D55FC, + (q31_t)0x0C8BD35E, (q31_t)0x7F62368F, (q31_t)0x0647D97C, + (q31_t)0x7FD8878D, (q31_t)0x00000000, (q31_t)0x7FFFFFFF, + (q31_t)0xF9B82683, (q31_t)0x7FD8878D, (q31_t)0xF3742CA1, + (q31_t)0x7F62368F, (q31_t)0xED37EF91, (q31_t)0x7E9D55FC, + (q31_t)0xE70747C3, (q31_t)0x7D8A5F3F, (q31_t)0xE0E60684, + (q31_t)0x7C29FBEE, (q31_t)0xDAD7F3A2, (q31_t)0x7A7D055B, + (q31_t)0xD4E0CB14, (q31_t)0x78848413, (q31_t)0xCF043AB2, + (q31_t)0x7641AF3C, (q31_t)0xC945DFEC, (q31_t)0x73B5EBD0, + (q31_t)0xC3A9458F, (q31_t)0x70E2CBC6, (q31_t)0xBE31E19B, + (q31_t)0x6DCA0D14, (q31_t)0xB8E31319, (q31_t)0x6A6D98A4, + (q31_t)0xB3C0200C, (q31_t)0x66CF811F, (q31_t)0xAECC336B, + (q31_t)0x62F201AC, (q31_t)0xAA0A5B2D, (q31_t)0x5ED77C89, + (q31_t)0xA57D8666, (q31_t)0x5A82799A, (q31_t)0xA1288376, + (q31_t)0x55F5A4D2, (q31_t)0x9D0DFE53, (q31_t)0x5133CC94, + (q31_t)0x99307EE0, (q31_t)0x4C3FDFF3, (q31_t)0x9592675B, + (q31_t)0x471CECE6, (q31_t)0x9235F2EB, (q31_t)0x41CE1E64, + (q31_t)0x8F1D343A, (q31_t)0x3C56BA70, (q31_t)0x8C4A142F, + (q31_t)0x36BA2013, (q31_t)0x89BE50C3, (q31_t)0x30FBC54D, + (q31_t)0x877B7BEC, (q31_t)0x2B1F34EB, (q31_t)0x8582FAA4, + (q31_t)0x25280C5D, (q31_t)0x83D60411, (q31_t)0x1F19F97B, + (q31_t)0x8275A0C0, (q31_t)0x18F8B83C, (q31_t)0x8162AA03, + (q31_t)0x12C8106E, (q31_t)0x809DC970, (q31_t)0x0C8BD35E, + (q31_t)0x80277872, (q31_t)0x0647D97C, (q31_t)0x80000000, + (q31_t)0x00000000, (q31_t)0x80277872, (q31_t)0xF9B82683, + (q31_t)0x809DC970, (q31_t)0xF3742CA1, (q31_t)0x8162AA03, + (q31_t)0xED37EF91, (q31_t)0x8275A0C0, (q31_t)0xE70747C3, + (q31_t)0x83D60411, (q31_t)0xE0E60684, (q31_t)0x8582FAA4, + (q31_t)0xDAD7F3A2, (q31_t)0x877B7BEC, (q31_t)0xD4E0CB14, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, (q31_t)0x8C4A142F, + (q31_t)0xC945DFEC, (q31_t)0x8F1D343A, (q31_t)0xC3A9458F, + (q31_t)0x9235F2EB, (q31_t)0xBE31E19B, (q31_t)0x9592675B, + (q31_t)0xB8E31319, (q31_t)0x99307EE0, (q31_t)0xB3C0200C, + (q31_t)0x9D0DFE53, (q31_t)0xAECC336B, (q31_t)0xA1288376, + (q31_t)0xAA0A5B2D, (q31_t)0xA57D8666, (q31_t)0xA57D8666, + (q31_t)0xAA0A5B2D, (q31_t)0xA1288376, (q31_t)0xAECC336B, + (q31_t)0x9D0DFE53, (q31_t)0xB3C0200C, (q31_t)0x99307EE0, + (q31_t)0xB8E31319, (q31_t)0x9592675B, (q31_t)0xBE31E19B, + (q31_t)0x9235F2EB, (q31_t)0xC3A9458F, (q31_t)0x8F1D343A, + (q31_t)0xC945DFEC, (q31_t)0x8C4A142F, (q31_t)0xCF043AB2, + (q31_t)0x89BE50C3, (q31_t)0xD4E0CB14, (q31_t)0x877B7BEC, + (q31_t)0xDAD7F3A2, (q31_t)0x8582FAA4, (q31_t)0xE0E60684, + (q31_t)0x83D60411, (q31_t)0xE70747C3, (q31_t)0x8275A0C0, + (q31_t)0xED37EF91, (q31_t)0x8162AA03, (q31_t)0xF3742CA1, + (q31_t)0x809DC970, (q31_t)0xF9B82683, (q31_t)0x80277872 +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 256, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + + */ +const q31_t twiddleCoef_256_q31[384] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7FF62182, + (q31_t)0x03242ABF, (q31_t)0x7FD8878D, (q31_t)0x0647D97C, + (q31_t)0x7FA736B4, (q31_t)0x096A9049, (q31_t)0x7F62368F, + (q31_t)0x0C8BD35E, (q31_t)0x7F0991C3, (q31_t)0x0FAB272B, + (q31_t)0x7E9D55FC, (q31_t)0x12C8106E, (q31_t)0x7E1D93E9, + (q31_t)0x15E21444, (q31_t)0x7D8A5F3F, (q31_t)0x18F8B83C, + (q31_t)0x7CE3CEB1, (q31_t)0x1C0B826A, (q31_t)0x7C29FBEE, + (q31_t)0x1F19F97B, (q31_t)0x7B5D039D, (q31_t)0x2223A4C5, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x798A23B1, + (q31_t)0x2826B928, (q31_t)0x78848413, (q31_t)0x2B1F34EB, + (q31_t)0x776C4EDB, (q31_t)0x2E110A62, (q31_t)0x7641AF3C, + (q31_t)0x30FBC54D, (q31_t)0x7504D345, (q31_t)0x33DEF287, + (q31_t)0x73B5EBD0, (q31_t)0x36BA2013, (q31_t)0x72552C84, + (q31_t)0x398CDD32, (q31_t)0x70E2CBC6, (q31_t)0x3C56BA70, + (q31_t)0x6F5F02B1, (q31_t)0x3F1749B7, (q31_t)0x6DCA0D14, + (q31_t)0x41CE1E64, (q31_t)0x6C242960, (q31_t)0x447ACD50, + (q31_t)0x6A6D98A4, (q31_t)0x471CECE6, (q31_t)0x68A69E81, + (q31_t)0x49B41533, (q31_t)0x66CF811F, (q31_t)0x4C3FDFF3, + (q31_t)0x64E88926, (q31_t)0x4EBFE8A4, (q31_t)0x62F201AC, + (q31_t)0x5133CC94, (q31_t)0x60EC3830, (q31_t)0x539B2AEF, + (q31_t)0x5ED77C89, (q31_t)0x55F5A4D2, (q31_t)0x5CB420DF, + (q31_t)0x5842DD54, (q31_t)0x5A82799A, (q31_t)0x5A82799A, + (q31_t)0x5842DD54, (q31_t)0x5CB420DF, (q31_t)0x55F5A4D2, + (q31_t)0x5ED77C89, (q31_t)0x539B2AEF, (q31_t)0x60EC3830, + (q31_t)0x5133CC94, (q31_t)0x62F201AC, (q31_t)0x4EBFE8A4, + (q31_t)0x64E88926, (q31_t)0x4C3FDFF3, (q31_t)0x66CF811F, + (q31_t)0x49B41533, (q31_t)0x68A69E81, (q31_t)0x471CECE6, + (q31_t)0x6A6D98A4, (q31_t)0x447ACD50, (q31_t)0x6C242960, + (q31_t)0x41CE1E64, (q31_t)0x6DCA0D14, (q31_t)0x3F1749B7, + (q31_t)0x6F5F02B1, (q31_t)0x3C56BA70, (q31_t)0x70E2CBC6, + (q31_t)0x398CDD32, (q31_t)0x72552C84, (q31_t)0x36BA2013, + (q31_t)0x73B5EBD0, (q31_t)0x33DEF287, (q31_t)0x7504D345, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, (q31_t)0x2E110A62, + (q31_t)0x776C4EDB, (q31_t)0x2B1F34EB, (q31_t)0x78848413, + (q31_t)0x2826B928, (q31_t)0x798A23B1, (q31_t)0x25280C5D, + (q31_t)0x7A7D055B, (q31_t)0x2223A4C5, (q31_t)0x7B5D039D, + (q31_t)0x1F19F97B, (q31_t)0x7C29FBEE, (q31_t)0x1C0B826A, + (q31_t)0x7CE3CEB1, (q31_t)0x18F8B83C, (q31_t)0x7D8A5F3F, + (q31_t)0x15E21444, (q31_t)0x7E1D93E9, (q31_t)0x12C8106E, + (q31_t)0x7E9D55FC, (q31_t)0x0FAB272B, (q31_t)0x7F0991C3, + (q31_t)0x0C8BD35E, (q31_t)0x7F62368F, (q31_t)0x096A9049, + (q31_t)0x7FA736B4, (q31_t)0x0647D97C, (q31_t)0x7FD8878D, + (q31_t)0x03242ABF, (q31_t)0x7FF62182, (q31_t)0x00000000, + (q31_t)0x7FFFFFFF, (q31_t)0xFCDBD541, (q31_t)0x7FF62182, + (q31_t)0xF9B82683, (q31_t)0x7FD8878D, (q31_t)0xF6956FB6, + (q31_t)0x7FA736B4, (q31_t)0xF3742CA1, (q31_t)0x7F62368F, + (q31_t)0xF054D8D4, (q31_t)0x7F0991C3, (q31_t)0xED37EF91, + (q31_t)0x7E9D55FC, (q31_t)0xEA1DEBBB, (q31_t)0x7E1D93E9, + (q31_t)0xE70747C3, (q31_t)0x7D8A5F3F, (q31_t)0xE3F47D95, + (q31_t)0x7CE3CEB1, (q31_t)0xE0E60684, (q31_t)0x7C29FBEE, + (q31_t)0xDDDC5B3A, (q31_t)0x7B5D039D, (q31_t)0xDAD7F3A2, + (q31_t)0x7A7D055B, (q31_t)0xD7D946D7, (q31_t)0x798A23B1, + (q31_t)0xD4E0CB14, (q31_t)0x78848413, (q31_t)0xD1EEF59E, + (q31_t)0x776C4EDB, (q31_t)0xCF043AB2, (q31_t)0x7641AF3C, + (q31_t)0xCC210D78, (q31_t)0x7504D345, (q31_t)0xC945DFEC, + (q31_t)0x73B5EBD0, (q31_t)0xC67322CD, (q31_t)0x72552C84, + (q31_t)0xC3A9458F, (q31_t)0x70E2CBC6, (q31_t)0xC0E8B648, + (q31_t)0x6F5F02B1, (q31_t)0xBE31E19B, (q31_t)0x6DCA0D14, + (q31_t)0xBB8532AF, (q31_t)0x6C242960, (q31_t)0xB8E31319, + (q31_t)0x6A6D98A4, (q31_t)0xB64BEACC, (q31_t)0x68A69E81, + (q31_t)0xB3C0200C, (q31_t)0x66CF811F, (q31_t)0xB140175B, + (q31_t)0x64E88926, (q31_t)0xAECC336B, (q31_t)0x62F201AC, + (q31_t)0xAC64D510, (q31_t)0x60EC3830, (q31_t)0xAA0A5B2D, + (q31_t)0x5ED77C89, (q31_t)0xA7BD22AB, (q31_t)0x5CB420DF, + (q31_t)0xA57D8666, (q31_t)0x5A82799A, (q31_t)0xA34BDF20, + (q31_t)0x5842DD54, (q31_t)0xA1288376, (q31_t)0x55F5A4D2, + (q31_t)0x9F13C7D0, (q31_t)0x539B2AEF, (q31_t)0x9D0DFE53, + (q31_t)0x5133CC94, (q31_t)0x9B1776D9, (q31_t)0x4EBFE8A4, + (q31_t)0x99307EE0, (q31_t)0x4C3FDFF3, (q31_t)0x9759617E, + (q31_t)0x49B41533, (q31_t)0x9592675B, (q31_t)0x471CECE6, + (q31_t)0x93DBD69F, (q31_t)0x447ACD50, (q31_t)0x9235F2EB, + (q31_t)0x41CE1E64, (q31_t)0x90A0FD4E, (q31_t)0x3F1749B7, + (q31_t)0x8F1D343A, (q31_t)0x3C56BA70, (q31_t)0x8DAAD37B, + (q31_t)0x398CDD32, (q31_t)0x8C4A142F, (q31_t)0x36BA2013, + (q31_t)0x8AFB2CBA, (q31_t)0x33DEF287, (q31_t)0x89BE50C3, + (q31_t)0x30FBC54D, (q31_t)0x8893B124, (q31_t)0x2E110A62, + (q31_t)0x877B7BEC, (q31_t)0x2B1F34EB, (q31_t)0x8675DC4E, + (q31_t)0x2826B928, (q31_t)0x8582FAA4, (q31_t)0x25280C5D, + (q31_t)0x84A2FC62, (q31_t)0x2223A4C5, (q31_t)0x83D60411, + (q31_t)0x1F19F97B, (q31_t)0x831C314E, (q31_t)0x1C0B826A, + (q31_t)0x8275A0C0, (q31_t)0x18F8B83C, (q31_t)0x81E26C16, + (q31_t)0x15E21444, (q31_t)0x8162AA03, (q31_t)0x12C8106E, + (q31_t)0x80F66E3C, (q31_t)0x0FAB272B, (q31_t)0x809DC970, + (q31_t)0x0C8BD35E, (q31_t)0x8058C94C, (q31_t)0x096A9049, + (q31_t)0x80277872, (q31_t)0x0647D97C, (q31_t)0x8009DE7D, + (q31_t)0x03242ABF, (q31_t)0x80000000, (q31_t)0x00000000, + (q31_t)0x8009DE7D, (q31_t)0xFCDBD541, (q31_t)0x80277872, + (q31_t)0xF9B82683, (q31_t)0x8058C94C, (q31_t)0xF6956FB6, + (q31_t)0x809DC970, (q31_t)0xF3742CA1, (q31_t)0x80F66E3C, + (q31_t)0xF054D8D4, (q31_t)0x8162AA03, (q31_t)0xED37EF91, + (q31_t)0x81E26C16, (q31_t)0xEA1DEBBB, (q31_t)0x8275A0C0, + (q31_t)0xE70747C3, (q31_t)0x831C314E, (q31_t)0xE3F47D95, + (q31_t)0x83D60411, (q31_t)0xE0E60684, (q31_t)0x84A2FC62, + (q31_t)0xDDDC5B3A, (q31_t)0x8582FAA4, (q31_t)0xDAD7F3A2, + (q31_t)0x8675DC4E, (q31_t)0xD7D946D7, (q31_t)0x877B7BEC, + (q31_t)0xD4E0CB14, (q31_t)0x8893B124, (q31_t)0xD1EEF59E, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, (q31_t)0x8AFB2CBA, + (q31_t)0xCC210D78, (q31_t)0x8C4A142F, (q31_t)0xC945DFEC, + (q31_t)0x8DAAD37B, (q31_t)0xC67322CD, (q31_t)0x8F1D343A, + (q31_t)0xC3A9458F, (q31_t)0x90A0FD4E, (q31_t)0xC0E8B648, + (q31_t)0x9235F2EB, (q31_t)0xBE31E19B, (q31_t)0x93DBD69F, + (q31_t)0xBB8532AF, (q31_t)0x9592675B, (q31_t)0xB8E31319, + (q31_t)0x9759617E, (q31_t)0xB64BEACC, (q31_t)0x99307EE0, + (q31_t)0xB3C0200C, (q31_t)0x9B1776D9, (q31_t)0xB140175B, + (q31_t)0x9D0DFE53, (q31_t)0xAECC336B, (q31_t)0x9F13C7D0, + (q31_t)0xAC64D510, (q31_t)0xA1288376, (q31_t)0xAA0A5B2D, + (q31_t)0xA34BDF20, (q31_t)0xA7BD22AB, (q31_t)0xA57D8666, + (q31_t)0xA57D8666, (q31_t)0xA7BD22AB, (q31_t)0xA34BDF20, + (q31_t)0xAA0A5B2D, (q31_t)0xA1288376, (q31_t)0xAC64D510, + (q31_t)0x9F13C7D0, (q31_t)0xAECC336B, (q31_t)0x9D0DFE53, + (q31_t)0xB140175B, (q31_t)0x9B1776D9, (q31_t)0xB3C0200C, + (q31_t)0x99307EE0, (q31_t)0xB64BEACC, (q31_t)0x9759617E, + (q31_t)0xB8E31319, (q31_t)0x9592675B, (q31_t)0xBB8532AF, + (q31_t)0x93DBD69F, (q31_t)0xBE31E19B, (q31_t)0x9235F2EB, + (q31_t)0xC0E8B648, (q31_t)0x90A0FD4E, (q31_t)0xC3A9458F, + (q31_t)0x8F1D343A, (q31_t)0xC67322CD, (q31_t)0x8DAAD37B, + (q31_t)0xC945DFEC, (q31_t)0x8C4A142F, (q31_t)0xCC210D78, + (q31_t)0x8AFB2CBA, (q31_t)0xCF043AB2, (q31_t)0x89BE50C3, + (q31_t)0xD1EEF59E, (q31_t)0x8893B124, (q31_t)0xD4E0CB14, + (q31_t)0x877B7BEC, (q31_t)0xD7D946D7, (q31_t)0x8675DC4E, + (q31_t)0xDAD7F3A2, (q31_t)0x8582FAA4, (q31_t)0xDDDC5B3A, + (q31_t)0x84A2FC62, (q31_t)0xE0E60684, (q31_t)0x83D60411, + (q31_t)0xE3F47D95, (q31_t)0x831C314E, (q31_t)0xE70747C3, + (q31_t)0x8275A0C0, (q31_t)0xEA1DEBBB, (q31_t)0x81E26C16, + (q31_t)0xED37EF91, (q31_t)0x8162AA03, (q31_t)0xF054D8D4, + (q31_t)0x80F66E3C, (q31_t)0xF3742CA1, (q31_t)0x809DC970, + (q31_t)0xF6956FB6, (q31_t)0x8058C94C, (q31_t)0xF9B82683, + (q31_t)0x80277872, (q31_t)0xFCDBD541, (q31_t)0x8009DE7D +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 512, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + + */ +const q31_t twiddleCoef_512_q31[768] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7FFD885A, + (q31_t)0x01921D1F, (q31_t)0x7FF62182, (q31_t)0x03242ABF, + (q31_t)0x7FE9CBC0, (q31_t)0x04B6195D, (q31_t)0x7FD8878D, + (q31_t)0x0647D97C, (q31_t)0x7FC25596, (q31_t)0x07D95B9E, + (q31_t)0x7FA736B4, (q31_t)0x096A9049, (q31_t)0x7F872BF3, + (q31_t)0x0AFB6805, (q31_t)0x7F62368F, (q31_t)0x0C8BD35E, + (q31_t)0x7F3857F5, (q31_t)0x0E1BC2E3, (q31_t)0x7F0991C3, + (q31_t)0x0FAB272B, (q31_t)0x7ED5E5C6, (q31_t)0x1139F0CE, + (q31_t)0x7E9D55FC, (q31_t)0x12C8106E, (q31_t)0x7E5FE493, + (q31_t)0x145576B1, (q31_t)0x7E1D93E9, (q31_t)0x15E21444, + (q31_t)0x7DD6668E, (q31_t)0x176DD9DE, (q31_t)0x7D8A5F3F, + (q31_t)0x18F8B83C, (q31_t)0x7D3980EC, (q31_t)0x1A82A025, + (q31_t)0x7CE3CEB1, (q31_t)0x1C0B826A, (q31_t)0x7C894BDD, + (q31_t)0x1D934FE5, (q31_t)0x7C29FBEE, (q31_t)0x1F19F97B, + (q31_t)0x7BC5E28F, (q31_t)0x209F701C, (q31_t)0x7B5D039D, + (q31_t)0x2223A4C5, (q31_t)0x7AEF6323, (q31_t)0x23A6887E, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x7A05EEAD, + (q31_t)0x26A82185, (q31_t)0x798A23B1, (q31_t)0x2826B928, + (q31_t)0x7909A92C, (q31_t)0x29A3C484, (q31_t)0x78848413, + (q31_t)0x2B1F34EB, (q31_t)0x77FAB988, (q31_t)0x2C98FBBA, + (q31_t)0x776C4EDB, (q31_t)0x2E110A62, (q31_t)0x76D94988, + (q31_t)0x2F875262, (q31_t)0x7641AF3C, (q31_t)0x30FBC54D, + (q31_t)0x75A585CF, (q31_t)0x326E54C7, (q31_t)0x7504D345, + (q31_t)0x33DEF287, (q31_t)0x745F9DD1, (q31_t)0x354D9056, + (q31_t)0x73B5EBD0, (q31_t)0x36BA2013, (q31_t)0x7307C3D0, + (q31_t)0x382493B0, (q31_t)0x72552C84, (q31_t)0x398CDD32, + (q31_t)0x719E2CD2, (q31_t)0x3AF2EEB7, (q31_t)0x70E2CBC6, + (q31_t)0x3C56BA70, (q31_t)0x70231099, (q31_t)0x3DB832A5, + (q31_t)0x6F5F02B1, (q31_t)0x3F1749B7, (q31_t)0x6E96A99C, + (q31_t)0x4073F21D, (q31_t)0x6DCA0D14, (q31_t)0x41CE1E64, + (q31_t)0x6CF934FB, (q31_t)0x4325C135, (q31_t)0x6C242960, + (q31_t)0x447ACD50, (q31_t)0x6B4AF278, (q31_t)0x45CD358F, + (q31_t)0x6A6D98A4, (q31_t)0x471CECE6, (q31_t)0x698C246C, + (q31_t)0x4869E664, (q31_t)0x68A69E81, (q31_t)0x49B41533, + (q31_t)0x67BD0FBC, (q31_t)0x4AFB6C97, (q31_t)0x66CF811F, + (q31_t)0x4C3FDFF3, (q31_t)0x65DDFBD3, (q31_t)0x4D8162C4, + (q31_t)0x64E88926, (q31_t)0x4EBFE8A4, (q31_t)0x63EF328F, + (q31_t)0x4FFB654D, (q31_t)0x62F201AC, (q31_t)0x5133CC94, + (q31_t)0x61F1003E, (q31_t)0x5269126E, (q31_t)0x60EC3830, + (q31_t)0x539B2AEF, (q31_t)0x5FE3B38D, (q31_t)0x54CA0A4A, + (q31_t)0x5ED77C89, (q31_t)0x55F5A4D2, (q31_t)0x5DC79D7C, + (q31_t)0x571DEEF9, (q31_t)0x5CB420DF, (q31_t)0x5842DD54, + (q31_t)0x5B9D1153, (q31_t)0x59646497, (q31_t)0x5A82799A, + (q31_t)0x5A82799A, (q31_t)0x59646497, (q31_t)0x5B9D1153, + (q31_t)0x5842DD54, (q31_t)0x5CB420DF, (q31_t)0x571DEEF9, + (q31_t)0x5DC79D7C, (q31_t)0x55F5A4D2, (q31_t)0x5ED77C89, + (q31_t)0x54CA0A4A, (q31_t)0x5FE3B38D, (q31_t)0x539B2AEF, + (q31_t)0x60EC3830, (q31_t)0x5269126E, (q31_t)0x61F1003E, + (q31_t)0x5133CC94, (q31_t)0x62F201AC, (q31_t)0x4FFB654D, + (q31_t)0x63EF328F, (q31_t)0x4EBFE8A4, (q31_t)0x64E88926, + (q31_t)0x4D8162C4, (q31_t)0x65DDFBD3, (q31_t)0x4C3FDFF3, + (q31_t)0x66CF811F, (q31_t)0x4AFB6C97, (q31_t)0x67BD0FBC, + (q31_t)0x49B41533, (q31_t)0x68A69E81, (q31_t)0x4869E664, + (q31_t)0x698C246C, (q31_t)0x471CECE6, (q31_t)0x6A6D98A4, + (q31_t)0x45CD358F, (q31_t)0x6B4AF278, (q31_t)0x447ACD50, + (q31_t)0x6C242960, (q31_t)0x4325C135, (q31_t)0x6CF934FB, + (q31_t)0x41CE1E64, (q31_t)0x6DCA0D14, (q31_t)0x4073F21D, + (q31_t)0x6E96A99C, (q31_t)0x3F1749B7, (q31_t)0x6F5F02B1, + (q31_t)0x3DB832A5, (q31_t)0x70231099, (q31_t)0x3C56BA70, + (q31_t)0x70E2CBC6, (q31_t)0x3AF2EEB7, (q31_t)0x719E2CD2, + (q31_t)0x398CDD32, (q31_t)0x72552C84, (q31_t)0x382493B0, + (q31_t)0x7307C3D0, (q31_t)0x36BA2013, (q31_t)0x73B5EBD0, + (q31_t)0x354D9056, (q31_t)0x745F9DD1, (q31_t)0x33DEF287, + (q31_t)0x7504D345, (q31_t)0x326E54C7, (q31_t)0x75A585CF, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, (q31_t)0x2F875262, + (q31_t)0x76D94988, (q31_t)0x2E110A62, (q31_t)0x776C4EDB, + (q31_t)0x2C98FBBA, (q31_t)0x77FAB988, (q31_t)0x2B1F34EB, + (q31_t)0x78848413, (q31_t)0x29A3C484, (q31_t)0x7909A92C, + (q31_t)0x2826B928, (q31_t)0x798A23B1, (q31_t)0x26A82185, + (q31_t)0x7A05EEAD, (q31_t)0x25280C5D, (q31_t)0x7A7D055B, + (q31_t)0x23A6887E, (q31_t)0x7AEF6323, (q31_t)0x2223A4C5, + (q31_t)0x7B5D039D, (q31_t)0x209F701C, (q31_t)0x7BC5E28F, + (q31_t)0x1F19F97B, (q31_t)0x7C29FBEE, (q31_t)0x1D934FE5, + (q31_t)0x7C894BDD, (q31_t)0x1C0B826A, (q31_t)0x7CE3CEB1, + (q31_t)0x1A82A025, (q31_t)0x7D3980EC, (q31_t)0x18F8B83C, + (q31_t)0x7D8A5F3F, (q31_t)0x176DD9DE, (q31_t)0x7DD6668E, + (q31_t)0x15E21444, (q31_t)0x7E1D93E9, (q31_t)0x145576B1, + (q31_t)0x7E5FE493, (q31_t)0x12C8106E, (q31_t)0x7E9D55FC, + (q31_t)0x1139F0CE, (q31_t)0x7ED5E5C6, (q31_t)0x0FAB272B, + (q31_t)0x7F0991C3, (q31_t)0x0E1BC2E3, (q31_t)0x7F3857F5, + (q31_t)0x0C8BD35E, (q31_t)0x7F62368F, (q31_t)0x0AFB6805, + (q31_t)0x7F872BF3, (q31_t)0x096A9049, (q31_t)0x7FA736B4, + (q31_t)0x07D95B9E, (q31_t)0x7FC25596, (q31_t)0x0647D97C, + (q31_t)0x7FD8878D, (q31_t)0x04B6195D, (q31_t)0x7FE9CBC0, + (q31_t)0x03242ABF, (q31_t)0x7FF62182, (q31_t)0x01921D1F, + (q31_t)0x7FFD885A, (q31_t)0x00000000, (q31_t)0x7FFFFFFF, + (q31_t)0xFE6DE2E0, (q31_t)0x7FFD885A, (q31_t)0xFCDBD541, + (q31_t)0x7FF62182, (q31_t)0xFB49E6A2, (q31_t)0x7FE9CBC0, + (q31_t)0xF9B82683, (q31_t)0x7FD8878D, (q31_t)0xF826A461, + (q31_t)0x7FC25596, (q31_t)0xF6956FB6, (q31_t)0x7FA736B4, + (q31_t)0xF50497FA, (q31_t)0x7F872BF3, (q31_t)0xF3742CA1, + (q31_t)0x7F62368F, (q31_t)0xF1E43D1C, (q31_t)0x7F3857F5, + (q31_t)0xF054D8D4, (q31_t)0x7F0991C3, (q31_t)0xEEC60F31, + (q31_t)0x7ED5E5C6, (q31_t)0xED37EF91, (q31_t)0x7E9D55FC, + (q31_t)0xEBAA894E, (q31_t)0x7E5FE493, (q31_t)0xEA1DEBBB, + (q31_t)0x7E1D93E9, (q31_t)0xE8922621, (q31_t)0x7DD6668E, + (q31_t)0xE70747C3, (q31_t)0x7D8A5F3F, (q31_t)0xE57D5FDA, + (q31_t)0x7D3980EC, (q31_t)0xE3F47D95, (q31_t)0x7CE3CEB1, + (q31_t)0xE26CB01A, (q31_t)0x7C894BDD, (q31_t)0xE0E60684, + (q31_t)0x7C29FBEE, (q31_t)0xDF608FE3, (q31_t)0x7BC5E28F, + (q31_t)0xDDDC5B3A, (q31_t)0x7B5D039D, (q31_t)0xDC597781, + (q31_t)0x7AEF6323, (q31_t)0xDAD7F3A2, (q31_t)0x7A7D055B, + (q31_t)0xD957DE7A, (q31_t)0x7A05EEAD, (q31_t)0xD7D946D7, + (q31_t)0x798A23B1, (q31_t)0xD65C3B7B, (q31_t)0x7909A92C, + (q31_t)0xD4E0CB14, (q31_t)0x78848413, (q31_t)0xD3670445, + (q31_t)0x77FAB988, (q31_t)0xD1EEF59E, (q31_t)0x776C4EDB, + (q31_t)0xD078AD9D, (q31_t)0x76D94988, (q31_t)0xCF043AB2, + (q31_t)0x7641AF3C, (q31_t)0xCD91AB38, (q31_t)0x75A585CF, + (q31_t)0xCC210D78, (q31_t)0x7504D345, (q31_t)0xCAB26FA9, + (q31_t)0x745F9DD1, (q31_t)0xC945DFEC, (q31_t)0x73B5EBD0, + (q31_t)0xC7DB6C50, (q31_t)0x7307C3D0, (q31_t)0xC67322CD, + (q31_t)0x72552C84, (q31_t)0xC50D1148, (q31_t)0x719E2CD2, + (q31_t)0xC3A9458F, (q31_t)0x70E2CBC6, (q31_t)0xC247CD5A, + (q31_t)0x70231099, (q31_t)0xC0E8B648, (q31_t)0x6F5F02B1, + (q31_t)0xBF8C0DE2, (q31_t)0x6E96A99C, (q31_t)0xBE31E19B, + (q31_t)0x6DCA0D14, (q31_t)0xBCDA3ECA, (q31_t)0x6CF934FB, + (q31_t)0xBB8532AF, (q31_t)0x6C242960, (q31_t)0xBA32CA70, + (q31_t)0x6B4AF278, (q31_t)0xB8E31319, (q31_t)0x6A6D98A4, + (q31_t)0xB796199B, (q31_t)0x698C246C, (q31_t)0xB64BEACC, + (q31_t)0x68A69E81, (q31_t)0xB5049368, (q31_t)0x67BD0FBC, + (q31_t)0xB3C0200C, (q31_t)0x66CF811F, (q31_t)0xB27E9D3B, + (q31_t)0x65DDFBD3, (q31_t)0xB140175B, (q31_t)0x64E88926, + (q31_t)0xB0049AB2, (q31_t)0x63EF328F, (q31_t)0xAECC336B, + (q31_t)0x62F201AC, (q31_t)0xAD96ED91, (q31_t)0x61F1003E, + (q31_t)0xAC64D510, (q31_t)0x60EC3830, (q31_t)0xAB35F5B5, + (q31_t)0x5FE3B38D, (q31_t)0xAA0A5B2D, (q31_t)0x5ED77C89, + (q31_t)0xA8E21106, (q31_t)0x5DC79D7C, (q31_t)0xA7BD22AB, + (q31_t)0x5CB420DF, (q31_t)0xA69B9B68, (q31_t)0x5B9D1153, + (q31_t)0xA57D8666, (q31_t)0x5A82799A, (q31_t)0xA462EEAC, + (q31_t)0x59646497, (q31_t)0xA34BDF20, (q31_t)0x5842DD54, + (q31_t)0xA2386283, (q31_t)0x571DEEF9, (q31_t)0xA1288376, + (q31_t)0x55F5A4D2, (q31_t)0xA01C4C72, (q31_t)0x54CA0A4A, + (q31_t)0x9F13C7D0, (q31_t)0x539B2AEF, (q31_t)0x9E0EFFC1, + (q31_t)0x5269126E, (q31_t)0x9D0DFE53, (q31_t)0x5133CC94, + (q31_t)0x9C10CD70, (q31_t)0x4FFB654D, (q31_t)0x9B1776D9, + (q31_t)0x4EBFE8A4, (q31_t)0x9A22042C, (q31_t)0x4D8162C4, + (q31_t)0x99307EE0, (q31_t)0x4C3FDFF3, (q31_t)0x9842F043, + (q31_t)0x4AFB6C97, (q31_t)0x9759617E, (q31_t)0x49B41533, + (q31_t)0x9673DB94, (q31_t)0x4869E664, (q31_t)0x9592675B, + (q31_t)0x471CECE6, (q31_t)0x94B50D87, (q31_t)0x45CD358F, + (q31_t)0x93DBD69F, (q31_t)0x447ACD50, (q31_t)0x9306CB04, + (q31_t)0x4325C135, (q31_t)0x9235F2EB, (q31_t)0x41CE1E64, + (q31_t)0x91695663, (q31_t)0x4073F21D, (q31_t)0x90A0FD4E, + (q31_t)0x3F1749B7, (q31_t)0x8FDCEF66, (q31_t)0x3DB832A5, + (q31_t)0x8F1D343A, (q31_t)0x3C56BA70, (q31_t)0x8E61D32D, + (q31_t)0x3AF2EEB7, (q31_t)0x8DAAD37B, (q31_t)0x398CDD32, + (q31_t)0x8CF83C30, (q31_t)0x382493B0, (q31_t)0x8C4A142F, + (q31_t)0x36BA2013, (q31_t)0x8BA0622F, (q31_t)0x354D9056, + (q31_t)0x8AFB2CBA, (q31_t)0x33DEF287, (q31_t)0x8A5A7A30, + (q31_t)0x326E54C7, (q31_t)0x89BE50C3, (q31_t)0x30FBC54D, + (q31_t)0x8926B677, (q31_t)0x2F875262, (q31_t)0x8893B124, + (q31_t)0x2E110A62, (q31_t)0x88054677, (q31_t)0x2C98FBBA, + (q31_t)0x877B7BEC, (q31_t)0x2B1F34EB, (q31_t)0x86F656D3, + (q31_t)0x29A3C484, (q31_t)0x8675DC4E, (q31_t)0x2826B928, + (q31_t)0x85FA1152, (q31_t)0x26A82185, (q31_t)0x8582FAA4, + (q31_t)0x25280C5D, (q31_t)0x85109CDC, (q31_t)0x23A6887E, + (q31_t)0x84A2FC62, (q31_t)0x2223A4C5, (q31_t)0x843A1D70, + (q31_t)0x209F701C, (q31_t)0x83D60411, (q31_t)0x1F19F97B, + (q31_t)0x8376B422, (q31_t)0x1D934FE5, (q31_t)0x831C314E, + (q31_t)0x1C0B826A, (q31_t)0x82C67F13, (q31_t)0x1A82A025, + (q31_t)0x8275A0C0, (q31_t)0x18F8B83C, (q31_t)0x82299971, + (q31_t)0x176DD9DE, (q31_t)0x81E26C16, (q31_t)0x15E21444, + (q31_t)0x81A01B6C, (q31_t)0x145576B1, (q31_t)0x8162AA03, + (q31_t)0x12C8106E, (q31_t)0x812A1A39, (q31_t)0x1139F0CE, + (q31_t)0x80F66E3C, (q31_t)0x0FAB272B, (q31_t)0x80C7A80A, + (q31_t)0x0E1BC2E3, (q31_t)0x809DC970, (q31_t)0x0C8BD35E, + (q31_t)0x8078D40D, (q31_t)0x0AFB6805, (q31_t)0x8058C94C, + (q31_t)0x096A9049, (q31_t)0x803DAA69, (q31_t)0x07D95B9E, + (q31_t)0x80277872, (q31_t)0x0647D97C, (q31_t)0x80163440, + (q31_t)0x04B6195D, (q31_t)0x8009DE7D, (q31_t)0x03242ABF, + (q31_t)0x800277A5, (q31_t)0x01921D1F, (q31_t)0x80000000, + (q31_t)0x00000000, (q31_t)0x800277A5, (q31_t)0xFE6DE2E0, + (q31_t)0x8009DE7D, (q31_t)0xFCDBD541, (q31_t)0x80163440, + (q31_t)0xFB49E6A2, (q31_t)0x80277872, (q31_t)0xF9B82683, + (q31_t)0x803DAA69, (q31_t)0xF826A461, (q31_t)0x8058C94C, + (q31_t)0xF6956FB6, (q31_t)0x8078D40D, (q31_t)0xF50497FA, + (q31_t)0x809DC970, (q31_t)0xF3742CA1, (q31_t)0x80C7A80A, + (q31_t)0xF1E43D1C, (q31_t)0x80F66E3C, (q31_t)0xF054D8D4, + (q31_t)0x812A1A39, (q31_t)0xEEC60F31, (q31_t)0x8162AA03, + (q31_t)0xED37EF91, (q31_t)0x81A01B6C, (q31_t)0xEBAA894E, + (q31_t)0x81E26C16, (q31_t)0xEA1DEBBB, (q31_t)0x82299971, + (q31_t)0xE8922621, (q31_t)0x8275A0C0, (q31_t)0xE70747C3, + (q31_t)0x82C67F13, (q31_t)0xE57D5FDA, (q31_t)0x831C314E, + (q31_t)0xE3F47D95, (q31_t)0x8376B422, (q31_t)0xE26CB01A, + (q31_t)0x83D60411, (q31_t)0xE0E60684, (q31_t)0x843A1D70, + (q31_t)0xDF608FE3, (q31_t)0x84A2FC62, (q31_t)0xDDDC5B3A, + (q31_t)0x85109CDC, (q31_t)0xDC597781, (q31_t)0x8582FAA4, + (q31_t)0xDAD7F3A2, (q31_t)0x85FA1152, (q31_t)0xD957DE7A, + (q31_t)0x8675DC4E, (q31_t)0xD7D946D7, (q31_t)0x86F656D3, + (q31_t)0xD65C3B7B, (q31_t)0x877B7BEC, (q31_t)0xD4E0CB14, + (q31_t)0x88054677, (q31_t)0xD3670445, (q31_t)0x8893B124, + (q31_t)0xD1EEF59E, (q31_t)0x8926B677, (q31_t)0xD078AD9D, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, (q31_t)0x8A5A7A30, + (q31_t)0xCD91AB38, (q31_t)0x8AFB2CBA, (q31_t)0xCC210D78, + (q31_t)0x8BA0622F, (q31_t)0xCAB26FA9, (q31_t)0x8C4A142F, + (q31_t)0xC945DFEC, (q31_t)0x8CF83C30, (q31_t)0xC7DB6C50, + (q31_t)0x8DAAD37B, (q31_t)0xC67322CD, (q31_t)0x8E61D32D, + (q31_t)0xC50D1148, (q31_t)0x8F1D343A, (q31_t)0xC3A9458F, + (q31_t)0x8FDCEF66, (q31_t)0xC247CD5A, (q31_t)0x90A0FD4E, + (q31_t)0xC0E8B648, (q31_t)0x91695663, (q31_t)0xBF8C0DE2, + (q31_t)0x9235F2EB, (q31_t)0xBE31E19B, (q31_t)0x9306CB04, + (q31_t)0xBCDA3ECA, (q31_t)0x93DBD69F, (q31_t)0xBB8532AF, + (q31_t)0x94B50D87, (q31_t)0xBA32CA70, (q31_t)0x9592675B, + (q31_t)0xB8E31319, (q31_t)0x9673DB94, (q31_t)0xB796199B, + (q31_t)0x9759617E, (q31_t)0xB64BEACC, (q31_t)0x9842F043, + (q31_t)0xB5049368, (q31_t)0x99307EE0, (q31_t)0xB3C0200C, + (q31_t)0x9A22042C, (q31_t)0xB27E9D3B, (q31_t)0x9B1776D9, + (q31_t)0xB140175B, (q31_t)0x9C10CD70, (q31_t)0xB0049AB2, + (q31_t)0x9D0DFE53, (q31_t)0xAECC336B, (q31_t)0x9E0EFFC1, + (q31_t)0xAD96ED91, (q31_t)0x9F13C7D0, (q31_t)0xAC64D510, + (q31_t)0xA01C4C72, (q31_t)0xAB35F5B5, (q31_t)0xA1288376, + (q31_t)0xAA0A5B2D, (q31_t)0xA2386283, (q31_t)0xA8E21106, + (q31_t)0xA34BDF20, (q31_t)0xA7BD22AB, (q31_t)0xA462EEAC, + (q31_t)0xA69B9B68, (q31_t)0xA57D8666, (q31_t)0xA57D8666, + (q31_t)0xA69B9B68, (q31_t)0xA462EEAC, (q31_t)0xA7BD22AB, + (q31_t)0xA34BDF20, (q31_t)0xA8E21106, (q31_t)0xA2386283, + (q31_t)0xAA0A5B2D, (q31_t)0xA1288376, (q31_t)0xAB35F5B5, + (q31_t)0xA01C4C72, (q31_t)0xAC64D510, (q31_t)0x9F13C7D0, + (q31_t)0xAD96ED91, (q31_t)0x9E0EFFC1, (q31_t)0xAECC336B, + (q31_t)0x9D0DFE53, (q31_t)0xB0049AB2, (q31_t)0x9C10CD70, + (q31_t)0xB140175B, (q31_t)0x9B1776D9, (q31_t)0xB27E9D3B, + (q31_t)0x9A22042C, (q31_t)0xB3C0200C, (q31_t)0x99307EE0, + (q31_t)0xB5049368, (q31_t)0x9842F043, (q31_t)0xB64BEACC, + (q31_t)0x9759617E, (q31_t)0xB796199B, (q31_t)0x9673DB94, + (q31_t)0xB8E31319, (q31_t)0x9592675B, (q31_t)0xBA32CA70, + (q31_t)0x94B50D87, (q31_t)0xBB8532AF, (q31_t)0x93DBD69F, + (q31_t)0xBCDA3ECA, (q31_t)0x9306CB04, (q31_t)0xBE31E19B, + (q31_t)0x9235F2EB, (q31_t)0xBF8C0DE2, (q31_t)0x91695663, + (q31_t)0xC0E8B648, (q31_t)0x90A0FD4E, (q31_t)0xC247CD5A, + (q31_t)0x8FDCEF66, (q31_t)0xC3A9458F, (q31_t)0x8F1D343A, + (q31_t)0xC50D1148, (q31_t)0x8E61D32D, (q31_t)0xC67322CD, + (q31_t)0x8DAAD37B, (q31_t)0xC7DB6C50, (q31_t)0x8CF83C30, + (q31_t)0xC945DFEC, (q31_t)0x8C4A142F, (q31_t)0xCAB26FA9, + (q31_t)0x8BA0622F, (q31_t)0xCC210D78, (q31_t)0x8AFB2CBA, + (q31_t)0xCD91AB38, (q31_t)0x8A5A7A30, (q31_t)0xCF043AB2, + (q31_t)0x89BE50C3, (q31_t)0xD078AD9D, (q31_t)0x8926B677, + (q31_t)0xD1EEF59E, (q31_t)0x8893B124, (q31_t)0xD3670445, + (q31_t)0x88054677, (q31_t)0xD4E0CB14, (q31_t)0x877B7BEC, + (q31_t)0xD65C3B7B, (q31_t)0x86F656D3, (q31_t)0xD7D946D7, + (q31_t)0x8675DC4E, (q31_t)0xD957DE7A, (q31_t)0x85FA1152, + (q31_t)0xDAD7F3A2, (q31_t)0x8582FAA4, (q31_t)0xDC597781, + (q31_t)0x85109CDC, (q31_t)0xDDDC5B3A, (q31_t)0x84A2FC62, + (q31_t)0xDF608FE3, (q31_t)0x843A1D70, (q31_t)0xE0E60684, + (q31_t)0x83D60411, (q31_t)0xE26CB01A, (q31_t)0x8376B422, + (q31_t)0xE3F47D95, (q31_t)0x831C314E, (q31_t)0xE57D5FDA, + (q31_t)0x82C67F13, (q31_t)0xE70747C3, (q31_t)0x8275A0C0, + (q31_t)0xE8922621, (q31_t)0x82299971, (q31_t)0xEA1DEBBB, + (q31_t)0x81E26C16, (q31_t)0xEBAA894E, (q31_t)0x81A01B6C, + (q31_t)0xED37EF91, (q31_t)0x8162AA03, (q31_t)0xEEC60F31, + (q31_t)0x812A1A39, (q31_t)0xF054D8D4, (q31_t)0x80F66E3C, + (q31_t)0xF1E43D1C, (q31_t)0x80C7A80A, (q31_t)0xF3742CA1, + (q31_t)0x809DC970, (q31_t)0xF50497FA, (q31_t)0x8078D40D, + (q31_t)0xF6956FB6, (q31_t)0x8058C94C, (q31_t)0xF826A461, + (q31_t)0x803DAA69, (q31_t)0xF9B82683, (q31_t)0x80277872, + (q31_t)0xFB49E6A2, (q31_t)0x80163440, (q31_t)0xFCDBD541, + (q31_t)0x8009DE7D, (q31_t)0xFE6DE2E0, (q31_t)0x800277A5 +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 1024, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + + */ +const q31_t twiddleCoef_1024_q31[1536] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7FFF6216, + (q31_t)0x00C90F88, (q31_t)0x7FFD885A, (q31_t)0x01921D1F, + (q31_t)0x7FFA72D1, (q31_t)0x025B26D7, (q31_t)0x7FF62182, + (q31_t)0x03242ABF, (q31_t)0x7FF09477, (q31_t)0x03ED26E6, + (q31_t)0x7FE9CBC0, (q31_t)0x04B6195D, (q31_t)0x7FE1C76B, + (q31_t)0x057F0034, (q31_t)0x7FD8878D, (q31_t)0x0647D97C, + (q31_t)0x7FCE0C3E, (q31_t)0x0710A344, (q31_t)0x7FC25596, + (q31_t)0x07D95B9E, (q31_t)0x7FB563B2, (q31_t)0x08A2009A, + (q31_t)0x7FA736B4, (q31_t)0x096A9049, (q31_t)0x7F97CEBC, + (q31_t)0x0A3308BC, (q31_t)0x7F872BF3, (q31_t)0x0AFB6805, + (q31_t)0x7F754E7F, (q31_t)0x0BC3AC35, (q31_t)0x7F62368F, + (q31_t)0x0C8BD35E, (q31_t)0x7F4DE450, (q31_t)0x0D53DB92, + (q31_t)0x7F3857F5, (q31_t)0x0E1BC2E3, (q31_t)0x7F2191B4, + (q31_t)0x0EE38765, (q31_t)0x7F0991C3, (q31_t)0x0FAB272B, + (q31_t)0x7EF0585F, (q31_t)0x1072A047, (q31_t)0x7ED5E5C6, + (q31_t)0x1139F0CE, (q31_t)0x7EBA3A39, (q31_t)0x120116D4, + (q31_t)0x7E9D55FC, (q31_t)0x12C8106E, (q31_t)0x7E7F3956, + (q31_t)0x138EDBB0, (q31_t)0x7E5FE493, (q31_t)0x145576B1, + (q31_t)0x7E3F57FE, (q31_t)0x151BDF85, (q31_t)0x7E1D93E9, + (q31_t)0x15E21444, (q31_t)0x7DFA98A7, (q31_t)0x16A81305, + (q31_t)0x7DD6668E, (q31_t)0x176DD9DE, (q31_t)0x7DB0FDF7, + (q31_t)0x183366E8, (q31_t)0x7D8A5F3F, (q31_t)0x18F8B83C, + (q31_t)0x7D628AC5, (q31_t)0x19BDCBF2, (q31_t)0x7D3980EC, + (q31_t)0x1A82A025, (q31_t)0x7D0F4218, (q31_t)0x1B4732EF, + (q31_t)0x7CE3CEB1, (q31_t)0x1C0B826A, (q31_t)0x7CB72724, + (q31_t)0x1CCF8CB3, (q31_t)0x7C894BDD, (q31_t)0x1D934FE5, + (q31_t)0x7C5A3D4F, (q31_t)0x1E56CA1E, (q31_t)0x7C29FBEE, + (q31_t)0x1F19F97B, (q31_t)0x7BF88830, (q31_t)0x1FDCDC1A, + (q31_t)0x7BC5E28F, (q31_t)0x209F701C, (q31_t)0x7B920B89, + (q31_t)0x2161B39F, (q31_t)0x7B5D039D, (q31_t)0x2223A4C5, + (q31_t)0x7B26CB4F, (q31_t)0x22E541AE, (q31_t)0x7AEF6323, + (q31_t)0x23A6887E, (q31_t)0x7AB6CBA3, (q31_t)0x24677757, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x7A4210D8, + (q31_t)0x25E845B5, (q31_t)0x7A05EEAD, (q31_t)0x26A82185, + (q31_t)0x79C89F6D, (q31_t)0x27679DF4, (q31_t)0x798A23B1, + (q31_t)0x2826B928, (q31_t)0x794A7C11, (q31_t)0x28E5714A, + (q31_t)0x7909A92C, (q31_t)0x29A3C484, (q31_t)0x78C7ABA1, + (q31_t)0x2A61B101, (q31_t)0x78848413, (q31_t)0x2B1F34EB, + (q31_t)0x78403328, (q31_t)0x2BDC4E6F, (q31_t)0x77FAB988, + (q31_t)0x2C98FBBA, (q31_t)0x77B417DF, (q31_t)0x2D553AFB, + (q31_t)0x776C4EDB, (q31_t)0x2E110A62, (q31_t)0x77235F2D, + (q31_t)0x2ECC681E, (q31_t)0x76D94988, (q31_t)0x2F875262, + (q31_t)0x768E0EA5, (q31_t)0x3041C760, (q31_t)0x7641AF3C, + (q31_t)0x30FBC54D, (q31_t)0x75F42C0A, (q31_t)0x31B54A5D, + (q31_t)0x75A585CF, (q31_t)0x326E54C7, (q31_t)0x7555BD4B, + (q31_t)0x3326E2C2, (q31_t)0x7504D345, (q31_t)0x33DEF287, + (q31_t)0x74B2C883, (q31_t)0x3496824F, (q31_t)0x745F9DD1, + (q31_t)0x354D9056, (q31_t)0x740B53FA, (q31_t)0x36041AD9, + (q31_t)0x73B5EBD0, (q31_t)0x36BA2013, (q31_t)0x735F6626, + (q31_t)0x376F9E46, (q31_t)0x7307C3D0, (q31_t)0x382493B0, + (q31_t)0x72AF05A6, (q31_t)0x38D8FE93, (q31_t)0x72552C84, + (q31_t)0x398CDD32, (q31_t)0x71FA3948, (q31_t)0x3A402DD1, + (q31_t)0x719E2CD2, (q31_t)0x3AF2EEB7, (q31_t)0x71410804, + (q31_t)0x3BA51E29, (q31_t)0x70E2CBC6, (q31_t)0x3C56BA70, + (q31_t)0x708378FE, (q31_t)0x3D07C1D5, (q31_t)0x70231099, + (q31_t)0x3DB832A5, (q31_t)0x6FC19385, (q31_t)0x3E680B2C, + (q31_t)0x6F5F02B1, (q31_t)0x3F1749B7, (q31_t)0x6EFB5F12, + (q31_t)0x3FC5EC97, (q31_t)0x6E96A99C, (q31_t)0x4073F21D, + (q31_t)0x6E30E349, (q31_t)0x4121589A, (q31_t)0x6DCA0D14, + (q31_t)0x41CE1E64, (q31_t)0x6D6227FA, (q31_t)0x427A41D0, + (q31_t)0x6CF934FB, (q31_t)0x4325C135, (q31_t)0x6C8F351C, + (q31_t)0x43D09AEC, (q31_t)0x6C242960, (q31_t)0x447ACD50, + (q31_t)0x6BB812D0, (q31_t)0x452456BC, (q31_t)0x6B4AF278, + (q31_t)0x45CD358F, (q31_t)0x6ADCC964, (q31_t)0x46756827, + (q31_t)0x6A6D98A4, (q31_t)0x471CECE6, (q31_t)0x69FD614A, + (q31_t)0x47C3C22E, (q31_t)0x698C246C, (q31_t)0x4869E664, + (q31_t)0x6919E320, (q31_t)0x490F57EE, (q31_t)0x68A69E81, + (q31_t)0x49B41533, (q31_t)0x683257AA, (q31_t)0x4A581C9D, + (q31_t)0x67BD0FBC, (q31_t)0x4AFB6C97, (q31_t)0x6746C7D7, + (q31_t)0x4B9E038F, (q31_t)0x66CF811F, (q31_t)0x4C3FDFF3, + (q31_t)0x66573CBB, (q31_t)0x4CE10034, (q31_t)0x65DDFBD3, + (q31_t)0x4D8162C4, (q31_t)0x6563BF92, (q31_t)0x4E210617, + (q31_t)0x64E88926, (q31_t)0x4EBFE8A4, (q31_t)0x646C59BF, + (q31_t)0x4F5E08E3, (q31_t)0x63EF328F, (q31_t)0x4FFB654D, + (q31_t)0x637114CC, (q31_t)0x5097FC5E, (q31_t)0x62F201AC, + (q31_t)0x5133CC94, (q31_t)0x6271FA69, (q31_t)0x51CED46E, + (q31_t)0x61F1003E, (q31_t)0x5269126E, (q31_t)0x616F146B, + (q31_t)0x53028517, (q31_t)0x60EC3830, (q31_t)0x539B2AEF, + (q31_t)0x60686CCE, (q31_t)0x5433027D, (q31_t)0x5FE3B38D, + (q31_t)0x54CA0A4A, (q31_t)0x5F5E0DB3, (q31_t)0x556040E2, + (q31_t)0x5ED77C89, (q31_t)0x55F5A4D2, (q31_t)0x5E50015D, + (q31_t)0x568A34A9, (q31_t)0x5DC79D7C, (q31_t)0x571DEEF9, + (q31_t)0x5D3E5236, (q31_t)0x57B0D256, (q31_t)0x5CB420DF, + (q31_t)0x5842DD54, (q31_t)0x5C290ACC, (q31_t)0x58D40E8C, + (q31_t)0x5B9D1153, (q31_t)0x59646497, (q31_t)0x5B1035CF, + (q31_t)0x59F3DE12, (q31_t)0x5A82799A, (q31_t)0x5A82799A, + (q31_t)0x59F3DE12, (q31_t)0x5B1035CF, (q31_t)0x59646497, + (q31_t)0x5B9D1153, (q31_t)0x58D40E8C, (q31_t)0x5C290ACC, + (q31_t)0x5842DD54, (q31_t)0x5CB420DF, (q31_t)0x57B0D256, + (q31_t)0x5D3E5236, (q31_t)0x571DEEF9, (q31_t)0x5DC79D7C, + (q31_t)0x568A34A9, (q31_t)0x5E50015D, (q31_t)0x55F5A4D2, + (q31_t)0x5ED77C89, (q31_t)0x556040E2, (q31_t)0x5F5E0DB3, + (q31_t)0x54CA0A4A, (q31_t)0x5FE3B38D, (q31_t)0x5433027D, + (q31_t)0x60686CCE, (q31_t)0x539B2AEF, (q31_t)0x60EC3830, + (q31_t)0x53028517, (q31_t)0x616F146B, (q31_t)0x5269126E, + (q31_t)0x61F1003E, (q31_t)0x51CED46E, (q31_t)0x6271FA69, + (q31_t)0x5133CC94, (q31_t)0x62F201AC, (q31_t)0x5097FC5E, + (q31_t)0x637114CC, (q31_t)0x4FFB654D, (q31_t)0x63EF328F, + (q31_t)0x4F5E08E3, (q31_t)0x646C59BF, (q31_t)0x4EBFE8A4, + (q31_t)0x64E88926, (q31_t)0x4E210617, (q31_t)0x6563BF92, + (q31_t)0x4D8162C4, (q31_t)0x65DDFBD3, (q31_t)0x4CE10034, + (q31_t)0x66573CBB, (q31_t)0x4C3FDFF3, (q31_t)0x66CF811F, + (q31_t)0x4B9E038F, (q31_t)0x6746C7D7, (q31_t)0x4AFB6C97, + (q31_t)0x67BD0FBC, (q31_t)0x4A581C9D, (q31_t)0x683257AA, + (q31_t)0x49B41533, (q31_t)0x68A69E81, (q31_t)0x490F57EE, + (q31_t)0x6919E320, (q31_t)0x4869E664, (q31_t)0x698C246C, + (q31_t)0x47C3C22E, (q31_t)0x69FD614A, (q31_t)0x471CECE6, + (q31_t)0x6A6D98A4, (q31_t)0x46756827, (q31_t)0x6ADCC964, + (q31_t)0x45CD358F, (q31_t)0x6B4AF278, (q31_t)0x452456BC, + (q31_t)0x6BB812D0, (q31_t)0x447ACD50, (q31_t)0x6C242960, + (q31_t)0x43D09AEC, (q31_t)0x6C8F351C, (q31_t)0x4325C135, + (q31_t)0x6CF934FB, (q31_t)0x427A41D0, (q31_t)0x6D6227FA, + (q31_t)0x41CE1E64, (q31_t)0x6DCA0D14, (q31_t)0x4121589A, + (q31_t)0x6E30E349, (q31_t)0x4073F21D, (q31_t)0x6E96A99C, + (q31_t)0x3FC5EC97, (q31_t)0x6EFB5F12, (q31_t)0x3F1749B7, + (q31_t)0x6F5F02B1, (q31_t)0x3E680B2C, (q31_t)0x6FC19385, + (q31_t)0x3DB832A5, (q31_t)0x70231099, (q31_t)0x3D07C1D5, + (q31_t)0x708378FE, (q31_t)0x3C56BA70, (q31_t)0x70E2CBC6, + (q31_t)0x3BA51E29, (q31_t)0x71410804, (q31_t)0x3AF2EEB7, + (q31_t)0x719E2CD2, (q31_t)0x3A402DD1, (q31_t)0x71FA3948, + (q31_t)0x398CDD32, (q31_t)0x72552C84, (q31_t)0x38D8FE93, + (q31_t)0x72AF05A6, (q31_t)0x382493B0, (q31_t)0x7307C3D0, + (q31_t)0x376F9E46, (q31_t)0x735F6626, (q31_t)0x36BA2013, + (q31_t)0x73B5EBD0, (q31_t)0x36041AD9, (q31_t)0x740B53FA, + (q31_t)0x354D9056, (q31_t)0x745F9DD1, (q31_t)0x3496824F, + (q31_t)0x74B2C883, (q31_t)0x33DEF287, (q31_t)0x7504D345, + (q31_t)0x3326E2C2, (q31_t)0x7555BD4B, (q31_t)0x326E54C7, + (q31_t)0x75A585CF, (q31_t)0x31B54A5D, (q31_t)0x75F42C0A, + (q31_t)0x30FBC54D, (q31_t)0x7641AF3C, (q31_t)0x3041C760, + (q31_t)0x768E0EA5, (q31_t)0x2F875262, (q31_t)0x76D94988, + (q31_t)0x2ECC681E, (q31_t)0x77235F2D, (q31_t)0x2E110A62, + (q31_t)0x776C4EDB, (q31_t)0x2D553AFB, (q31_t)0x77B417DF, + (q31_t)0x2C98FBBA, (q31_t)0x77FAB988, (q31_t)0x2BDC4E6F, + (q31_t)0x78403328, (q31_t)0x2B1F34EB, (q31_t)0x78848413, + (q31_t)0x2A61B101, (q31_t)0x78C7ABA1, (q31_t)0x29A3C484, + (q31_t)0x7909A92C, (q31_t)0x28E5714A, (q31_t)0x794A7C11, + (q31_t)0x2826B928, (q31_t)0x798A23B1, (q31_t)0x27679DF4, + (q31_t)0x79C89F6D, (q31_t)0x26A82185, (q31_t)0x7A05EEAD, + (q31_t)0x25E845B5, (q31_t)0x7A4210D8, (q31_t)0x25280C5D, + (q31_t)0x7A7D055B, (q31_t)0x24677757, (q31_t)0x7AB6CBA3, + (q31_t)0x23A6887E, (q31_t)0x7AEF6323, (q31_t)0x22E541AE, + (q31_t)0x7B26CB4F, (q31_t)0x2223A4C5, (q31_t)0x7B5D039D, + (q31_t)0x2161B39F, (q31_t)0x7B920B89, (q31_t)0x209F701C, + (q31_t)0x7BC5E28F, (q31_t)0x1FDCDC1A, (q31_t)0x7BF88830, + (q31_t)0x1F19F97B, (q31_t)0x7C29FBEE, (q31_t)0x1E56CA1E, + (q31_t)0x7C5A3D4F, (q31_t)0x1D934FE5, (q31_t)0x7C894BDD, + (q31_t)0x1CCF8CB3, (q31_t)0x7CB72724, (q31_t)0x1C0B826A, + (q31_t)0x7CE3CEB1, (q31_t)0x1B4732EF, (q31_t)0x7D0F4218, + (q31_t)0x1A82A025, (q31_t)0x7D3980EC, (q31_t)0x19BDCBF2, + (q31_t)0x7D628AC5, (q31_t)0x18F8B83C, (q31_t)0x7D8A5F3F, + (q31_t)0x183366E8, (q31_t)0x7DB0FDF7, (q31_t)0x176DD9DE, + (q31_t)0x7DD6668E, (q31_t)0x16A81305, (q31_t)0x7DFA98A7, + (q31_t)0x15E21444, (q31_t)0x7E1D93E9, (q31_t)0x151BDF85, + (q31_t)0x7E3F57FE, (q31_t)0x145576B1, (q31_t)0x7E5FE493, + (q31_t)0x138EDBB0, (q31_t)0x7E7F3956, (q31_t)0x12C8106E, + (q31_t)0x7E9D55FC, (q31_t)0x120116D4, (q31_t)0x7EBA3A39, + (q31_t)0x1139F0CE, (q31_t)0x7ED5E5C6, (q31_t)0x1072A047, + (q31_t)0x7EF0585F, (q31_t)0x0FAB272B, (q31_t)0x7F0991C3, + (q31_t)0x0EE38765, (q31_t)0x7F2191B4, (q31_t)0x0E1BC2E3, + (q31_t)0x7F3857F5, (q31_t)0x0D53DB92, (q31_t)0x7F4DE450, + (q31_t)0x0C8BD35E, (q31_t)0x7F62368F, (q31_t)0x0BC3AC35, + (q31_t)0x7F754E7F, (q31_t)0x0AFB6805, (q31_t)0x7F872BF3, + (q31_t)0x0A3308BC, (q31_t)0x7F97CEBC, (q31_t)0x096A9049, + (q31_t)0x7FA736B4, (q31_t)0x08A2009A, (q31_t)0x7FB563B2, + (q31_t)0x07D95B9E, (q31_t)0x7FC25596, (q31_t)0x0710A344, + (q31_t)0x7FCE0C3E, (q31_t)0x0647D97C, (q31_t)0x7FD8878D, + (q31_t)0x057F0034, (q31_t)0x7FE1C76B, (q31_t)0x04B6195D, + (q31_t)0x7FE9CBC0, (q31_t)0x03ED26E6, (q31_t)0x7FF09477, + (q31_t)0x03242ABF, (q31_t)0x7FF62182, (q31_t)0x025B26D7, + (q31_t)0x7FFA72D1, (q31_t)0x01921D1F, (q31_t)0x7FFD885A, + (q31_t)0x00C90F88, (q31_t)0x7FFF6216, (q31_t)0x00000000, + (q31_t)0x7FFFFFFF, (q31_t)0xFF36F078, (q31_t)0x7FFF6216, + (q31_t)0xFE6DE2E0, (q31_t)0x7FFD885A, (q31_t)0xFDA4D928, + (q31_t)0x7FFA72D1, (q31_t)0xFCDBD541, (q31_t)0x7FF62182, + (q31_t)0xFC12D919, (q31_t)0x7FF09477, (q31_t)0xFB49E6A2, + (q31_t)0x7FE9CBC0, (q31_t)0xFA80FFCB, (q31_t)0x7FE1C76B, + (q31_t)0xF9B82683, (q31_t)0x7FD8878D, (q31_t)0xF8EF5CBB, + (q31_t)0x7FCE0C3E, (q31_t)0xF826A461, (q31_t)0x7FC25596, + (q31_t)0xF75DFF65, (q31_t)0x7FB563B2, (q31_t)0xF6956FB6, + (q31_t)0x7FA736B4, (q31_t)0xF5CCF743, (q31_t)0x7F97CEBC, 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+ (q31_t)0xB8E31319, (q31_t)0x9592675B, (q31_t)0xB98A97D8, + (q31_t)0x9523369B, (q31_t)0xBA32CA70, (q31_t)0x94B50D87, + (q31_t)0xBADBA943, (q31_t)0x9447ED2F, (q31_t)0xBB8532AF, + (q31_t)0x93DBD69F, (q31_t)0xBC2F6513, (q31_t)0x9370CAE4, + (q31_t)0xBCDA3ECA, (q31_t)0x9306CB04, (q31_t)0xBD85BE2F, + (q31_t)0x929DD805, (q31_t)0xBE31E19B, (q31_t)0x9235F2EB, + (q31_t)0xBEDEA765, (q31_t)0x91CF1CB6, (q31_t)0xBF8C0DE2, + (q31_t)0x91695663, (q31_t)0xC03A1368, (q31_t)0x9104A0ED, + (q31_t)0xC0E8B648, (q31_t)0x90A0FD4E, (q31_t)0xC197F4D3, + (q31_t)0x903E6C7A, (q31_t)0xC247CD5A, (q31_t)0x8FDCEF66, + (q31_t)0xC2F83E2A, (q31_t)0x8F7C8701, (q31_t)0xC3A9458F, + (q31_t)0x8F1D343A, (q31_t)0xC45AE1D7, (q31_t)0x8EBEF7FB, + (q31_t)0xC50D1148, (q31_t)0x8E61D32D, (q31_t)0xC5BFD22E, + (q31_t)0x8E05C6B7, (q31_t)0xC67322CD, (q31_t)0x8DAAD37B, + (q31_t)0xC727016C, (q31_t)0x8D50FA59, (q31_t)0xC7DB6C50, + (q31_t)0x8CF83C30, (q31_t)0xC89061BA, (q31_t)0x8CA099D9, + (q31_t)0xC945DFEC, (q31_t)0x8C4A142F, (q31_t)0xC9FBE527, + (q31_t)0x8BF4AC05, (q31_t)0xCAB26FA9, (q31_t)0x8BA0622F, + (q31_t)0xCB697DB0, (q31_t)0x8B4D377C, (q31_t)0xCC210D78, + (q31_t)0x8AFB2CBA, (q31_t)0xCCD91D3D, (q31_t)0x8AAA42B4, + (q31_t)0xCD91AB38, (q31_t)0x8A5A7A30, (q31_t)0xCE4AB5A2, + (q31_t)0x8A0BD3F5, (q31_t)0xCF043AB2, (q31_t)0x89BE50C3, + (q31_t)0xCFBE389F, (q31_t)0x8971F15A, (q31_t)0xD078AD9D, + (q31_t)0x8926B677, (q31_t)0xD13397E1, (q31_t)0x88DCA0D3, + (q31_t)0xD1EEF59E, (q31_t)0x8893B124, (q31_t)0xD2AAC504, + (q31_t)0x884BE820, (q31_t)0xD3670445, (q31_t)0x88054677, + (q31_t)0xD423B190, (q31_t)0x87BFCCD7, (q31_t)0xD4E0CB14, + (q31_t)0x877B7BEC, (q31_t)0xD59E4EFE, (q31_t)0x8738545E, + (q31_t)0xD65C3B7B, (q31_t)0x86F656D3, (q31_t)0xD71A8EB5, + (q31_t)0x86B583EE, (q31_t)0xD7D946D7, (q31_t)0x8675DC4E, + (q31_t)0xD898620C, (q31_t)0x86376092, (q31_t)0xD957DE7A, + (q31_t)0x85FA1152, (q31_t)0xDA17BA4A, (q31_t)0x85BDEF27, + (q31_t)0xDAD7F3A2, (q31_t)0x8582FAA4, (q31_t)0xDB9888A8, + (q31_t)0x8549345C, (q31_t)0xDC597781, (q31_t)0x85109CDC, + (q31_t)0xDD1ABE51, (q31_t)0x84D934B0, (q31_t)0xDDDC5B3A, + (q31_t)0x84A2FC62, (q31_t)0xDE9E4C60, (q31_t)0x846DF476, + (q31_t)0xDF608FE3, (q31_t)0x843A1D70, (q31_t)0xE02323E5, + (q31_t)0x840777CF, (q31_t)0xE0E60684, (q31_t)0x83D60411, + (q31_t)0xE1A935E1, (q31_t)0x83A5C2B0, (q31_t)0xE26CB01A, + (q31_t)0x8376B422, (q31_t)0xE330734C, (q31_t)0x8348D8DB, + (q31_t)0xE3F47D95, (q31_t)0x831C314E, (q31_t)0xE4B8CD10, + (q31_t)0x82F0BDE8, (q31_t)0xE57D5FDA, (q31_t)0x82C67F13, + (q31_t)0xE642340D, (q31_t)0x829D753A, (q31_t)0xE70747C3, + (q31_t)0x8275A0C0, (q31_t)0xE7CC9917, (q31_t)0x824F0208, + (q31_t)0xE8922621, (q31_t)0x82299971, (q31_t)0xE957ECFB, + (q31_t)0x82056758, (q31_t)0xEA1DEBBB, (q31_t)0x81E26C16, + (q31_t)0xEAE4207A, (q31_t)0x81C0A801, (q31_t)0xEBAA894E, + (q31_t)0x81A01B6C, (q31_t)0xEC71244F, (q31_t)0x8180C6A9, + (q31_t)0xED37EF91, (q31_t)0x8162AA03, (q31_t)0xEDFEE92B, + (q31_t)0x8145C5C6, (q31_t)0xEEC60F31, (q31_t)0x812A1A39, + (q31_t)0xEF8D5FB8, (q31_t)0x810FA7A0, (q31_t)0xF054D8D4, + (q31_t)0x80F66E3C, (q31_t)0xF11C789A, (q31_t)0x80DE6E4C, + (q31_t)0xF1E43D1C, (q31_t)0x80C7A80A, (q31_t)0xF2AC246D, + (q31_t)0x80B21BAF, (q31_t)0xF3742CA1, (q31_t)0x809DC970, + (q31_t)0xF43C53CA, (q31_t)0x808AB180, (q31_t)0xF50497FA, + (q31_t)0x8078D40D, (q31_t)0xF5CCF743, (q31_t)0x80683143, + (q31_t)0xF6956FB6, (q31_t)0x8058C94C, (q31_t)0xF75DFF65, + (q31_t)0x804A9C4D, (q31_t)0xF826A461, (q31_t)0x803DAA69, + (q31_t)0xF8EF5CBB, (q31_t)0x8031F3C1, (q31_t)0xF9B82683, + (q31_t)0x80277872, (q31_t)0xFA80FFCB, (q31_t)0x801E3894, + (q31_t)0xFB49E6A2, (q31_t)0x80163440, (q31_t)0xFC12D919, + (q31_t)0x800F6B88, (q31_t)0xFCDBD541, (q31_t)0x8009DE7D, + (q31_t)0xFDA4D928, (q31_t)0x80058D2E, (q31_t)0xFE6DE2E0, + (q31_t)0x800277A5, (q31_t)0xFF36F078, (q31_t)0x80009DE9 +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 2048, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + */ +const q31_t twiddleCoef_2048_q31[3072] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7FFFD885, + (q31_t)0x006487E3, (q31_t)0x7FFF6216, (q31_t)0x00C90F88, + (q31_t)0x7FFE9CB2, (q31_t)0x012D96B0, (q31_t)0x7FFD885A, + (q31_t)0x01921D1F, (q31_t)0x7FFC250F, (q31_t)0x01F6A296, + (q31_t)0x7FFA72D1, (q31_t)0x025B26D7, (q31_t)0x7FF871A1, + (q31_t)0x02BFA9A4, (q31_t)0x7FF62182, (q31_t)0x03242ABF, + (q31_t)0x7FF38273, (q31_t)0x0388A9E9, (q31_t)0x7FF09477, + (q31_t)0x03ED26E6, (q31_t)0x7FED5790, (q31_t)0x0451A176, + (q31_t)0x7FE9CBC0, (q31_t)0x04B6195D, (q31_t)0x7FE5F108, + (q31_t)0x051A8E5C, (q31_t)0x7FE1C76B, (q31_t)0x057F0034, + (q31_t)0x7FDD4EEC, (q31_t)0x05E36EA9, (q31_t)0x7FD8878D, + (q31_t)0x0647D97C, (q31_t)0x7FD37152, (q31_t)0x06AC406F, + (q31_t)0x7FCE0C3E, (q31_t)0x0710A344, (q31_t)0x7FC85853, + (q31_t)0x077501BE, (q31_t)0x7FC25596, (q31_t)0x07D95B9E, + (q31_t)0x7FBC040A, (q31_t)0x083DB0A7, (q31_t)0x7FB563B2, + (q31_t)0x08A2009A, (q31_t)0x7FAE7494, (q31_t)0x09064B3A, + (q31_t)0x7FA736B4, (q31_t)0x096A9049, (q31_t)0x7F9FAA15, + (q31_t)0x09CECF89, (q31_t)0x7F97CEBC, (q31_t)0x0A3308BC, + (q31_t)0x7F8FA4AF, (q31_t)0x0A973BA5, (q31_t)0x7F872BF3, + (q31_t)0x0AFB6805, (q31_t)0x7F7E648B, (q31_t)0x0B5F8D9F, + (q31_t)0x7F754E7F, (q31_t)0x0BC3AC35, (q31_t)0x7F6BE9D4, + (q31_t)0x0C27C389, (q31_t)0x7F62368F, (q31_t)0x0C8BD35E, + (q31_t)0x7F5834B6, (q31_t)0x0CEFDB75, (q31_t)0x7F4DE450, + (q31_t)0x0D53DB92, (q31_t)0x7F434563, (q31_t)0x0DB7D376, + (q31_t)0x7F3857F5, (q31_t)0x0E1BC2E3, (q31_t)0x7F2D1C0E, + (q31_t)0x0E7FA99D, (q31_t)0x7F2191B4, (q31_t)0x0EE38765, + (q31_t)0x7F15B8EE, (q31_t)0x0F475BFE, (q31_t)0x7F0991C3, + (q31_t)0x0FAB272B, (q31_t)0x7EFD1C3C, (q31_t)0x100EE8AD, + (q31_t)0x7EF0585F, (q31_t)0x1072A047, (q31_t)0x7EE34635, + (q31_t)0x10D64DBC, (q31_t)0x7ED5E5C6, (q31_t)0x1139F0CE, + (q31_t)0x7EC8371A, (q31_t)0x119D8940, (q31_t)0x7EBA3A39, + (q31_t)0x120116D4, (q31_t)0x7EABEF2C, (q31_t)0x1264994E, + (q31_t)0x7E9D55FC, (q31_t)0x12C8106E, (q31_t)0x7E8E6EB1, + (q31_t)0x132B7BF9, (q31_t)0x7E7F3956, (q31_t)0x138EDBB0, + (q31_t)0x7E6FB5F3, (q31_t)0x13F22F57, (q31_t)0x7E5FE493, + (q31_t)0x145576B1, (q31_t)0x7E4FC53E, (q31_t)0x14B8B17F, + (q31_t)0x7E3F57FE, (q31_t)0x151BDF85, (q31_t)0x7E2E9CDF, + (q31_t)0x157F0086, (q31_t)0x7E1D93E9, (q31_t)0x15E21444, + (q31_t)0x7E0C3D29, (q31_t)0x16451A83, (q31_t)0x7DFA98A7, + (q31_t)0x16A81305, (q31_t)0x7DE8A670, (q31_t)0x170AFD8D, + (q31_t)0x7DD6668E, (q31_t)0x176DD9DE, (q31_t)0x7DC3D90D, + (q31_t)0x17D0A7BB, (q31_t)0x7DB0FDF7, (q31_t)0x183366E8, + (q31_t)0x7D9DD55A, (q31_t)0x18961727, (q31_t)0x7D8A5F3F, + (q31_t)0x18F8B83C, (q31_t)0x7D769BB5, (q31_t)0x195B49E9, + (q31_t)0x7D628AC5, (q31_t)0x19BDCBF2, (q31_t)0x7D4E2C7E, + (q31_t)0x1A203E1B, (q31_t)0x7D3980EC, (q31_t)0x1A82A025, + (q31_t)0x7D24881A, (q31_t)0x1AE4F1D6, (q31_t)0x7D0F4218, + (q31_t)0x1B4732EF, (q31_t)0x7CF9AEF0, (q31_t)0x1BA96334, + (q31_t)0x7CE3CEB1, (q31_t)0x1C0B826A, (q31_t)0x7CCDA168, + (q31_t)0x1C6D9053, (q31_t)0x7CB72724, (q31_t)0x1CCF8CB3, + (q31_t)0x7CA05FF1, (q31_t)0x1D31774D, (q31_t)0x7C894BDD, + (q31_t)0x1D934FE5, (q31_t)0x7C71EAF8, (q31_t)0x1DF5163F, + (q31_t)0x7C5A3D4F, (q31_t)0x1E56CA1E, (q31_t)0x7C4242F2, + (q31_t)0x1EB86B46, (q31_t)0x7C29FBEE, (q31_t)0x1F19F97B, + (q31_t)0x7C116853, (q31_t)0x1F7B7480, (q31_t)0x7BF88830, + (q31_t)0x1FDCDC1A, (q31_t)0x7BDF5B94, (q31_t)0x203E300D, + (q31_t)0x7BC5E28F, (q31_t)0x209F701C, (q31_t)0x7BAC1D31, + (q31_t)0x21009C0B, (q31_t)0x7B920B89, (q31_t)0x2161B39F, + (q31_t)0x7B77ADA8, (q31_t)0x21C2B69C, (q31_t)0x7B5D039D, + (q31_t)0x2223A4C5, (q31_t)0x7B420D7A, (q31_t)0x22847DDF, + (q31_t)0x7B26CB4F, (q31_t)0x22E541AE, (q31_t)0x7B0B3D2C, + (q31_t)0x2345EFF7, (q31_t)0x7AEF6323, (q31_t)0x23A6887E, + (q31_t)0x7AD33D45, (q31_t)0x24070B07, (q31_t)0x7AB6CBA3, + (q31_t)0x24677757, (q31_t)0x7A9A0E4F, (q31_t)0x24C7CD32, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x7A5FB0D8, + (q31_t)0x2588349D, (q31_t)0x7A4210D8, (q31_t)0x25E845B5, + (q31_t)0x7A24256E, (q31_t)0x26483F6C, (q31_t)0x7A05EEAD, + (q31_t)0x26A82185, (q31_t)0x79E76CA6, (q31_t)0x2707EBC6, + (q31_t)0x79C89F6D, (q31_t)0x27679DF4, (q31_t)0x79A98715, + (q31_t)0x27C737D2, (q31_t)0x798A23B1, (q31_t)0x2826B928, + (q31_t)0x796A7554, (q31_t)0x288621B9, (q31_t)0x794A7C11, + (q31_t)0x28E5714A, (q31_t)0x792A37FE, (q31_t)0x2944A7A2, + (q31_t)0x7909A92C, (q31_t)0x29A3C484, (q31_t)0x78E8CFB1, + (q31_t)0x2A02C7B8, (q31_t)0x78C7ABA1, (q31_t)0x2A61B101, + (q31_t)0x78A63D10, (q31_t)0x2AC08025, (q31_t)0x78848413, + (q31_t)0x2B1F34EB, (q31_t)0x786280BF, (q31_t)0x2B7DCF17, + (q31_t)0x78403328, (q31_t)0x2BDC4E6F, (q31_t)0x781D9B64, + (q31_t)0x2C3AB2B9, (q31_t)0x77FAB988, (q31_t)0x2C98FBBA, + (q31_t)0x77D78DAA, (q31_t)0x2CF72939, (q31_t)0x77B417DF, + (q31_t)0x2D553AFB, (q31_t)0x7790583D, (q31_t)0x2DB330C7, + (q31_t)0x776C4EDB, (q31_t)0x2E110A62, (q31_t)0x7747FBCE, + (q31_t)0x2E6EC792, (q31_t)0x77235F2D, (q31_t)0x2ECC681E, + (q31_t)0x76FE790E, (q31_t)0x2F29EBCC, (q31_t)0x76D94988, + (q31_t)0x2F875262, (q31_t)0x76B3D0B3, (q31_t)0x2FE49BA6, + (q31_t)0x768E0EA5, (q31_t)0x3041C760, (q31_t)0x76680376, + (q31_t)0x309ED555, (q31_t)0x7641AF3C, (q31_t)0x30FBC54D, + (q31_t)0x761B1211, (q31_t)0x3158970D, (q31_t)0x75F42C0A, + (q31_t)0x31B54A5D, (q31_t)0x75CCFD42, (q31_t)0x3211DF03, + (q31_t)0x75A585CF, (q31_t)0x326E54C7, (q31_t)0x757DC5CA, + (q31_t)0x32CAAB6F, (q31_t)0x7555BD4B, (q31_t)0x3326E2C2, + (q31_t)0x752D6C6C, (q31_t)0x3382FA88, (q31_t)0x7504D345, + (q31_t)0x33DEF287, (q31_t)0x74DBF1EF, (q31_t)0x343ACA87, + (q31_t)0x74B2C883, (q31_t)0x3496824F, (q31_t)0x7489571B, + (q31_t)0x34F219A7, (q31_t)0x745F9DD1, (q31_t)0x354D9056, + (q31_t)0x74359CBD, (q31_t)0x35A8E624, (q31_t)0x740B53FA, + (q31_t)0x36041AD9, (q31_t)0x73E0C3A3, (q31_t)0x365F2E3B, + (q31_t)0x73B5EBD0, (q31_t)0x36BA2013, (q31_t)0x738ACC9E, + (q31_t)0x3714F02A, (q31_t)0x735F6626, (q31_t)0x376F9E46, + (q31_t)0x7333B883, (q31_t)0x37CA2A30, (q31_t)0x7307C3D0, + (q31_t)0x382493B0, (q31_t)0x72DB8828, (q31_t)0x387EDA8E, + (q31_t)0x72AF05A6, (q31_t)0x38D8FE93, (q31_t)0x72823C66, + (q31_t)0x3932FF87, (q31_t)0x72552C84, (q31_t)0x398CDD32, + (q31_t)0x7227D61C, (q31_t)0x39E6975D, (q31_t)0x71FA3948, + (q31_t)0x3A402DD1, (q31_t)0x71CC5626, (q31_t)0x3A99A057, + (q31_t)0x719E2CD2, (q31_t)0x3AF2EEB7, (q31_t)0x716FBD68, + (q31_t)0x3B4C18BA, (q31_t)0x71410804, (q31_t)0x3BA51E29, + (q31_t)0x71120CC5, (q31_t)0x3BFDFECD, (q31_t)0x70E2CBC6, + (q31_t)0x3C56BA70, (q31_t)0x70B34524, (q31_t)0x3CAF50DA, + (q31_t)0x708378FE, (q31_t)0x3D07C1D5, (q31_t)0x70536771, + (q31_t)0x3D600D2B, (q31_t)0x70231099, (q31_t)0x3DB832A5, + (q31_t)0x6FF27496, (q31_t)0x3E10320D, (q31_t)0x6FC19385, + (q31_t)0x3E680B2C, (q31_t)0x6F906D84, (q31_t)0x3EBFBDCC, + (q31_t)0x6F5F02B1, (q31_t)0x3F1749B7, (q31_t)0x6F2D532C, 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(q31_t)0x835FA00E, + (q31_t)0xE2CE88B2, (q31_t)0x8376B422, (q31_t)0xE26CB01A, + (q31_t)0x838E1507, (q31_t)0xE20AE9C1, (q31_t)0x83A5C2B0, + (q31_t)0xE1A935E1, (q31_t)0x83BDBD0D, (q31_t)0xE14794B9, + (q31_t)0x83D60411, (q31_t)0xE0E60684, (q31_t)0x83EE97AC, + (q31_t)0xE0848B7F, (q31_t)0x840777CF, (q31_t)0xE02323E5, + (q31_t)0x8420A46B, (q31_t)0xDFC1CFF2, (q31_t)0x843A1D70, + (q31_t)0xDF608FE3, (q31_t)0x8453E2CE, (q31_t)0xDEFF63F4, + (q31_t)0x846DF476, (q31_t)0xDE9E4C60, (q31_t)0x84885257, + (q31_t)0xDE3D4963, (q31_t)0x84A2FC62, (q31_t)0xDDDC5B3A, + (q31_t)0x84BDF285, (q31_t)0xDD7B8220, (q31_t)0x84D934B0, + (q31_t)0xDD1ABE51, (q31_t)0x84F4C2D3, (q31_t)0xDCBA1008, + (q31_t)0x85109CDC, (q31_t)0xDC597781, (q31_t)0x852CC2BA, + (q31_t)0xDBF8F4F8, (q31_t)0x8549345C, (q31_t)0xDB9888A8, + (q31_t)0x8565F1B0, (q31_t)0xDB3832CD, (q31_t)0x8582FAA4, + (q31_t)0xDAD7F3A2, (q31_t)0x85A04F28, (q31_t)0xDA77CB62, + (q31_t)0x85BDEF27, (q31_t)0xDA17BA4A, (q31_t)0x85DBDA91, + (q31_t)0xD9B7C093, (q31_t)0x85FA1152, (q31_t)0xD957DE7A, + (q31_t)0x86189359, (q31_t)0xD8F81439, (q31_t)0x86376092, + (q31_t)0xD898620C, (q31_t)0x865678EA, (q31_t)0xD838C82D, + (q31_t)0x8675DC4E, (q31_t)0xD7D946D7, (q31_t)0x86958AAB, + (q31_t)0xD779DE46, (q31_t)0x86B583EE, (q31_t)0xD71A8EB5, + (q31_t)0x86D5C802, (q31_t)0xD6BB585D, (q31_t)0x86F656D3, + (q31_t)0xD65C3B7B, (q31_t)0x8717304E, (q31_t)0xD5FD3847, + (q31_t)0x8738545E, (q31_t)0xD59E4EFE, (q31_t)0x8759C2EF, + (q31_t)0xD53F7FDA, (q31_t)0x877B7BEC, (q31_t)0xD4E0CB14, + (q31_t)0x879D7F40, (q31_t)0xD48230E8, (q31_t)0x87BFCCD7, + (q31_t)0xD423B190, (q31_t)0x87E2649B, (q31_t)0xD3C54D46, + (q31_t)0x88054677, (q31_t)0xD3670445, (q31_t)0x88287255, + (q31_t)0xD308D6C6, (q31_t)0x884BE820, (q31_t)0xD2AAC504, + (q31_t)0x886FA7C2, (q31_t)0xD24CCF38, (q31_t)0x8893B124, + (q31_t)0xD1EEF59E, (q31_t)0x88B80431, (q31_t)0xD191386D, + (q31_t)0x88DCA0D3, (q31_t)0xD13397E1, (q31_t)0x890186F1, + (q31_t)0xD0D61433, (q31_t)0x8926B677, (q31_t)0xD078AD9D, + (q31_t)0x894C2F4C, (q31_t)0xD01B6459, (q31_t)0x8971F15A, + (q31_t)0xCFBE389F, (q31_t)0x8997FC89, (q31_t)0xCF612AAA, + (q31_t)0x89BE50C3, (q31_t)0xCF043AB2, (q31_t)0x89E4EDEE, + (q31_t)0xCEA768F2, (q31_t)0x8A0BD3F5, (q31_t)0xCE4AB5A2, + (q31_t)0x8A3302BD, (q31_t)0xCDEE20FC, (q31_t)0x8A5A7A30, + (q31_t)0xCD91AB38, (q31_t)0x8A823A35, (q31_t)0xCD355490, + (q31_t)0x8AAA42B4, (q31_t)0xCCD91D3D, (q31_t)0x8AD29393, + (q31_t)0xCC7D0577, (q31_t)0x8AFB2CBA, (q31_t)0xCC210D78, + (q31_t)0x8B240E10, (q31_t)0xCBC53578, (q31_t)0x8B4D377C, + (q31_t)0xCB697DB0, (q31_t)0x8B76A8E4, (q31_t)0xCB0DE658, + (q31_t)0x8BA0622F, (q31_t)0xCAB26FA9, (q31_t)0x8BCA6342, + (q31_t)0xCA5719DB, (q31_t)0x8BF4AC05, (q31_t)0xC9FBE527, + (q31_t)0x8C1F3C5C, (q31_t)0xC9A0D1C4, (q31_t)0x8C4A142F, + (q31_t)0xC945DFEC, (q31_t)0x8C753361, (q31_t)0xC8EB0FD6, + (q31_t)0x8CA099D9, (q31_t)0xC89061BA, (q31_t)0x8CCC477D, + (q31_t)0xC835D5D0, (q31_t)0x8CF83C30, (q31_t)0xC7DB6C50, + (q31_t)0x8D2477D8, (q31_t)0xC7812571, (q31_t)0x8D50FA59, + (q31_t)0xC727016C, (q31_t)0x8D7DC399, (q31_t)0xC6CD0079, + (q31_t)0x8DAAD37B, (q31_t)0xC67322CD, (q31_t)0x8DD829E4, + (q31_t)0xC61968A2, (q31_t)0x8E05C6B7, (q31_t)0xC5BFD22E, + (q31_t)0x8E33A9D9, (q31_t)0xC5665FA8, (q31_t)0x8E61D32D, + (q31_t)0xC50D1148, (q31_t)0x8E904298, (q31_t)0xC4B3E746, + (q31_t)0x8EBEF7FB, (q31_t)0xC45AE1D7, (q31_t)0x8EEDF33B, + (q31_t)0xC4020132, (q31_t)0x8F1D343A, (q31_t)0xC3A9458F, + (q31_t)0x8F4CBADB, (q31_t)0xC350AF25, (q31_t)0x8F7C8701, + (q31_t)0xC2F83E2A, (q31_t)0x8FAC988E, (q31_t)0xC29FF2D4, + (q31_t)0x8FDCEF66, (q31_t)0xC247CD5A, (q31_t)0x900D8B69, + (q31_t)0xC1EFCDF2, (q31_t)0x903E6C7A, (q31_t)0xC197F4D3, + (q31_t)0x906F927B, (q31_t)0xC1404233, (q31_t)0x90A0FD4E, + (q31_t)0xC0E8B648, (q31_t)0x90D2ACD3, (q31_t)0xC0915147, + (q31_t)0x9104A0ED, (q31_t)0xC03A1368, (q31_t)0x9136D97D, + (q31_t)0xBFE2FCDF, (q31_t)0x91695663, (q31_t)0xBF8C0DE2, + (q31_t)0x919C1780, (q31_t)0xBF3546A8, (q31_t)0x91CF1CB6, + (q31_t)0xBEDEA765, (q31_t)0x920265E4, (q31_t)0xBE88304F, + (q31_t)0x9235F2EB, (q31_t)0xBE31E19B, (q31_t)0x9269C3AC, + (q31_t)0xBDDBBB7F, (q31_t)0x929DD805, (q31_t)0xBD85BE2F, + (q31_t)0x92D22FD8, (q31_t)0xBD2FE9E1, (q31_t)0x9306CB04, + (q31_t)0xBCDA3ECA, (q31_t)0x933BA968, (q31_t)0xBC84BD1E, + (q31_t)0x9370CAE4, (q31_t)0xBC2F6513, (q31_t)0x93A62F56, + (q31_t)0xBBDA36DC, (q31_t)0x93DBD69F, (q31_t)0xBB8532AF, + (q31_t)0x9411C09D, (q31_t)0xBB3058C0, (q31_t)0x9447ED2F, + (q31_t)0xBADBA943, (q31_t)0x947E5C32, (q31_t)0xBA87246C, + (q31_t)0x94B50D87, (q31_t)0xBA32CA70, (q31_t)0x94EC010B, + (q31_t)0xB9DE9B83, (q31_t)0x9523369B, (q31_t)0xB98A97D8, + (q31_t)0x955AAE17, (q31_t)0xB936BFA3, (q31_t)0x9592675B, + (q31_t)0xB8E31319, (q31_t)0x95CA6246, (q31_t)0xB88F926C, + (q31_t)0x96029EB5, (q31_t)0xB83C3DD1, (q31_t)0x963B1C85, + (q31_t)0xB7E9157A, (q31_t)0x9673DB94, (q31_t)0xB796199B, + (q31_t)0x96ACDBBD, (q31_t)0xB7434A67, (q31_t)0x96E61CDF, + (q31_t)0xB6F0A811, (q31_t)0x971F9ED6, (q31_t)0xB69E32CD, + (q31_t)0x9759617E, (q31_t)0xB64BEACC, (q31_t)0x979364B5, + (q31_t)0xB5F9D042, (q31_t)0x97CDA855, (q31_t)0xB5A7E362, + (q31_t)0x98082C3B, (q31_t)0xB556245E, (q31_t)0x9842F043, + (q31_t)0xB5049368, (q31_t)0x987DF449, (q31_t)0xB4B330B2, + (q31_t)0x98B93828, (q31_t)0xB461FC70, (q31_t)0x98F4BBBC, + (q31_t)0xB410F6D2, (q31_t)0x99307EE0, (q31_t)0xB3C0200C, + (q31_t)0x996C816F, (q31_t)0xB36F784E, (q31_t)0x99A8C344, + (q31_t)0xB31EFFCB, (q31_t)0x99E5443A, (q31_t)0xB2CEB6B5, + (q31_t)0x9A22042C, (q31_t)0xB27E9D3B, (q31_t)0x9A5F02F5, + (q31_t)0xB22EB392, (q31_t)0x9A9C406D, (q31_t)0xB1DEF9E8, + (q31_t)0x9AD9BC71, (q31_t)0xB18F7070, (q31_t)0x9B1776D9, + (q31_t)0xB140175B, (q31_t)0x9B556F80, (q31_t)0xB0F0EEDA, + (q31_t)0x9B93A640, (q31_t)0xB0A1F71C, (q31_t)0x9BD21AF2, + (q31_t)0xB0533055, (q31_t)0x9C10CD70, (q31_t)0xB0049AB2, + (q31_t)0x9C4FBD92, (q31_t)0xAFB63667, (q31_t)0x9C8EEB33, + (q31_t)0xAF6803A1, (q31_t)0x9CCE562B, (q31_t)0xAF1A0293, + (q31_t)0x9D0DFE53, (q31_t)0xAECC336B, (q31_t)0x9D4DE384, + (q31_t)0xAE7E965B, (q31_t)0x9D8E0596, (q31_t)0xAE312B91, + (q31_t)0x9DCE6462, (q31_t)0xADE3F33E, (q31_t)0x9E0EFFC1, + (q31_t)0xAD96ED91, (q31_t)0x9E4FD789, (q31_t)0xAD4A1ABA, + (q31_t)0x9E90EB94, (q31_t)0xACFD7AE8, (q31_t)0x9ED23BB9, + (q31_t)0xACB10E4A, (q31_t)0x9F13C7D0, (q31_t)0xAC64D510, + (q31_t)0x9F558FB0, (q31_t)0xAC18CF68, (q31_t)0x9F979331, + (q31_t)0xABCCFD82, (q31_t)0x9FD9D22A, (q31_t)0xAB815F8C, + (q31_t)0xA01C4C72, (q31_t)0xAB35F5B5, (q31_t)0xA05F01E1, + (q31_t)0xAAEAC02B, (q31_t)0xA0A1F24C, (q31_t)0xAA9FBF1D, + (q31_t)0xA0E51D8C, (q31_t)0xAA54F2B9, (q31_t)0xA1288376, + (q31_t)0xAA0A5B2D, (q31_t)0xA16C23E1, (q31_t)0xA9BFF8A8, + (q31_t)0xA1AFFEA2, (q31_t)0xA975CB56, (q31_t)0xA1F41391, + (q31_t)0xA92BD366, (q31_t)0xA2386283, (q31_t)0xA8E21106, + (q31_t)0xA27CEB4F, (q31_t)0xA8988463, (q31_t)0xA2C1ADC9, + (q31_t)0xA84F2DA9, (q31_t)0xA306A9C7, (q31_t)0xA8060D08, + (q31_t)0xA34BDF20, (q31_t)0xA7BD22AB, (q31_t)0xA3914DA7, + (q31_t)0xA7746EC0, (q31_t)0xA3D6F533, (q31_t)0xA72BF173, + (q31_t)0xA41CD598, (q31_t)0xA6E3AAF2, (q31_t)0xA462EEAC, + (q31_t)0xA69B9B68, (q31_t)0xA4A94042, (q31_t)0xA653C302, + (q31_t)0xA4EFCA31, (q31_t)0xA60C21ED, (q31_t)0xA5368C4B, + (q31_t)0xA5C4B855, (q31_t)0xA57D8666, (q31_t)0xA57D8666, + (q31_t)0xA5C4B855, (q31_t)0xA5368C4B, (q31_t)0xA60C21ED, + (q31_t)0xA4EFCA31, (q31_t)0xA653C302, (q31_t)0xA4A94042, + (q31_t)0xA69B9B68, (q31_t)0xA462EEAC, (q31_t)0xA6E3AAF2, + (q31_t)0xA41CD598, (q31_t)0xA72BF173, (q31_t)0xA3D6F533, + (q31_t)0xA7746EC0, (q31_t)0xA3914DA7, (q31_t)0xA7BD22AB, + (q31_t)0xA34BDF20, (q31_t)0xA8060D08, (q31_t)0xA306A9C7, + (q31_t)0xA84F2DA9, (q31_t)0xA2C1ADC9, (q31_t)0xA8988463, + (q31_t)0xA27CEB4F, (q31_t)0xA8E21106, (q31_t)0xA2386283, + (q31_t)0xA92BD366, (q31_t)0xA1F41391, (q31_t)0xA975CB56, + (q31_t)0xA1AFFEA2, (q31_t)0xA9BFF8A8, (q31_t)0xA16C23E1, + (q31_t)0xAA0A5B2D, (q31_t)0xA1288376, (q31_t)0xAA54F2B9, + (q31_t)0xA0E51D8C, (q31_t)0xAA9FBF1D, (q31_t)0xA0A1F24C, + (q31_t)0xAAEAC02B, (q31_t)0xA05F01E1, (q31_t)0xAB35F5B5, + (q31_t)0xA01C4C72, (q31_t)0xAB815F8C, (q31_t)0x9FD9D22A, + (q31_t)0xABCCFD82, (q31_t)0x9F979331, (q31_t)0xAC18CF68, + (q31_t)0x9F558FB0, (q31_t)0xAC64D510, (q31_t)0x9F13C7D0, + (q31_t)0xACB10E4A, (q31_t)0x9ED23BB9, (q31_t)0xACFD7AE8, + (q31_t)0x9E90EB94, (q31_t)0xAD4A1ABA, (q31_t)0x9E4FD789, + (q31_t)0xAD96ED91, (q31_t)0x9E0EFFC1, (q31_t)0xADE3F33E, + (q31_t)0x9DCE6462, (q31_t)0xAE312B91, (q31_t)0x9D8E0596, + (q31_t)0xAE7E965B, (q31_t)0x9D4DE384, (q31_t)0xAECC336B, + (q31_t)0x9D0DFE53, (q31_t)0xAF1A0293, (q31_t)0x9CCE562B, + (q31_t)0xAF6803A1, (q31_t)0x9C8EEB33, (q31_t)0xAFB63667, + (q31_t)0x9C4FBD92, (q31_t)0xB0049AB2, (q31_t)0x9C10CD70, + (q31_t)0xB0533055, (q31_t)0x9BD21AF2, (q31_t)0xB0A1F71C, + (q31_t)0x9B93A640, (q31_t)0xB0F0EEDA, (q31_t)0x9B556F80, + (q31_t)0xB140175B, (q31_t)0x9B1776D9, (q31_t)0xB18F7070, + (q31_t)0x9AD9BC71, (q31_t)0xB1DEF9E8, (q31_t)0x9A9C406D, + (q31_t)0xB22EB392, (q31_t)0x9A5F02F5, (q31_t)0xB27E9D3B, + (q31_t)0x9A22042C, (q31_t)0xB2CEB6B5, (q31_t)0x99E5443A, + (q31_t)0xB31EFFCB, (q31_t)0x99A8C344, (q31_t)0xB36F784E, + (q31_t)0x996C816F, (q31_t)0xB3C0200C, (q31_t)0x99307EE0, + (q31_t)0xB410F6D2, (q31_t)0x98F4BBBC, (q31_t)0xB461FC70, + (q31_t)0x98B93828, (q31_t)0xB4B330B2, (q31_t)0x987DF449, + (q31_t)0xB5049368, (q31_t)0x9842F043, (q31_t)0xB556245E, + (q31_t)0x98082C3B, (q31_t)0xB5A7E362, (q31_t)0x97CDA855, + (q31_t)0xB5F9D042, (q31_t)0x979364B5, (q31_t)0xB64BEACC, + (q31_t)0x9759617E, (q31_t)0xB69E32CD, (q31_t)0x971F9ED6, + (q31_t)0xB6F0A811, (q31_t)0x96E61CDF, (q31_t)0xB7434A67, + (q31_t)0x96ACDBBD, (q31_t)0xB796199B, (q31_t)0x9673DB94, + (q31_t)0xB7E9157A, (q31_t)0x963B1C85, (q31_t)0xB83C3DD1, + (q31_t)0x96029EB5, (q31_t)0xB88F926C, (q31_t)0x95CA6246, + (q31_t)0xB8E31319, (q31_t)0x9592675B, (q31_t)0xB936BFA3, + (q31_t)0x955AAE17, (q31_t)0xB98A97D8, (q31_t)0x9523369B, + (q31_t)0xB9DE9B83, (q31_t)0x94EC010B, (q31_t)0xBA32CA70, + (q31_t)0x94B50D87, (q31_t)0xBA87246C, (q31_t)0x947E5C32, + (q31_t)0xBADBA943, (q31_t)0x9447ED2F, (q31_t)0xBB3058C0, + (q31_t)0x9411C09D, (q31_t)0xBB8532AF, (q31_t)0x93DBD69F, + (q31_t)0xBBDA36DC, (q31_t)0x93A62F56, (q31_t)0xBC2F6513, + (q31_t)0x9370CAE4, (q31_t)0xBC84BD1E, (q31_t)0x933BA968, + (q31_t)0xBCDA3ECA, (q31_t)0x9306CB04, (q31_t)0xBD2FE9E1, + (q31_t)0x92D22FD8, (q31_t)0xBD85BE2F, (q31_t)0x929DD805, + (q31_t)0xBDDBBB7F, (q31_t)0x9269C3AC, (q31_t)0xBE31E19B, + (q31_t)0x9235F2EB, (q31_t)0xBE88304F, (q31_t)0x920265E4, + (q31_t)0xBEDEA765, (q31_t)0x91CF1CB6, (q31_t)0xBF3546A8, + (q31_t)0x919C1780, (q31_t)0xBF8C0DE2, (q31_t)0x91695663, + (q31_t)0xBFE2FCDF, (q31_t)0x9136D97D, (q31_t)0xC03A1368, + (q31_t)0x9104A0ED, (q31_t)0xC0915147, (q31_t)0x90D2ACD3, + (q31_t)0xC0E8B648, (q31_t)0x90A0FD4E, (q31_t)0xC1404233, + (q31_t)0x906F927B, (q31_t)0xC197F4D3, (q31_t)0x903E6C7A, + (q31_t)0xC1EFCDF2, (q31_t)0x900D8B69, (q31_t)0xC247CD5A, + (q31_t)0x8FDCEF66, (q31_t)0xC29FF2D4, (q31_t)0x8FAC988E, + (q31_t)0xC2F83E2A, (q31_t)0x8F7C8701, (q31_t)0xC350AF25, + (q31_t)0x8F4CBADB, (q31_t)0xC3A9458F, (q31_t)0x8F1D343A, + (q31_t)0xC4020132, (q31_t)0x8EEDF33B, (q31_t)0xC45AE1D7, + (q31_t)0x8EBEF7FB, (q31_t)0xC4B3E746, (q31_t)0x8E904298, + (q31_t)0xC50D1148, (q31_t)0x8E61D32D, (q31_t)0xC5665FA8, + (q31_t)0x8E33A9D9, (q31_t)0xC5BFD22E, (q31_t)0x8E05C6B7, + (q31_t)0xC61968A2, (q31_t)0x8DD829E4, (q31_t)0xC67322CD, + (q31_t)0x8DAAD37B, (q31_t)0xC6CD0079, (q31_t)0x8D7DC399, + (q31_t)0xC727016C, (q31_t)0x8D50FA59, (q31_t)0xC7812571, + (q31_t)0x8D2477D8, (q31_t)0xC7DB6C50, (q31_t)0x8CF83C30, + (q31_t)0xC835D5D0, (q31_t)0x8CCC477D, (q31_t)0xC89061BA, + (q31_t)0x8CA099D9, (q31_t)0xC8EB0FD6, (q31_t)0x8C753361, + (q31_t)0xC945DFEC, (q31_t)0x8C4A142F, (q31_t)0xC9A0D1C4, + (q31_t)0x8C1F3C5C, (q31_t)0xC9FBE527, (q31_t)0x8BF4AC05, + (q31_t)0xCA5719DB, (q31_t)0x8BCA6342, (q31_t)0xCAB26FA9, + (q31_t)0x8BA0622F, (q31_t)0xCB0DE658, (q31_t)0x8B76A8E4, + (q31_t)0xCB697DB0, (q31_t)0x8B4D377C, (q31_t)0xCBC53578, + (q31_t)0x8B240E10, (q31_t)0xCC210D78, (q31_t)0x8AFB2CBA, + (q31_t)0xCC7D0577, (q31_t)0x8AD29393, (q31_t)0xCCD91D3D, + (q31_t)0x8AAA42B4, (q31_t)0xCD355490, (q31_t)0x8A823A35, + (q31_t)0xCD91AB38, (q31_t)0x8A5A7A30, (q31_t)0xCDEE20FC, + (q31_t)0x8A3302BD, (q31_t)0xCE4AB5A2, (q31_t)0x8A0BD3F5, + (q31_t)0xCEA768F2, (q31_t)0x89E4EDEE, (q31_t)0xCF043AB2, + (q31_t)0x89BE50C3, (q31_t)0xCF612AAA, (q31_t)0x8997FC89, + (q31_t)0xCFBE389F, (q31_t)0x8971F15A, (q31_t)0xD01B6459, + (q31_t)0x894C2F4C, (q31_t)0xD078AD9D, (q31_t)0x8926B677, + (q31_t)0xD0D61433, (q31_t)0x890186F1, (q31_t)0xD13397E1, + (q31_t)0x88DCA0D3, (q31_t)0xD191386D, (q31_t)0x88B80431, + (q31_t)0xD1EEF59E, (q31_t)0x8893B124, (q31_t)0xD24CCF38, + (q31_t)0x886FA7C2, (q31_t)0xD2AAC504, (q31_t)0x884BE820, + (q31_t)0xD308D6C6, (q31_t)0x88287255, (q31_t)0xD3670445, + (q31_t)0x88054677, (q31_t)0xD3C54D46, (q31_t)0x87E2649B, + (q31_t)0xD423B190, (q31_t)0x87BFCCD7, (q31_t)0xD48230E8, + (q31_t)0x879D7F40, (q31_t)0xD4E0CB14, (q31_t)0x877B7BEC, + (q31_t)0xD53F7FDA, (q31_t)0x8759C2EF, (q31_t)0xD59E4EFE, + (q31_t)0x8738545E, (q31_t)0xD5FD3847, (q31_t)0x8717304E, + (q31_t)0xD65C3B7B, (q31_t)0x86F656D3, (q31_t)0xD6BB585D, + (q31_t)0x86D5C802, (q31_t)0xD71A8EB5, (q31_t)0x86B583EE, + (q31_t)0xD779DE46, (q31_t)0x86958AAB, (q31_t)0xD7D946D7, + (q31_t)0x8675DC4E, (q31_t)0xD838C82D, (q31_t)0x865678EA, + (q31_t)0xD898620C, (q31_t)0x86376092, (q31_t)0xD8F81439, + (q31_t)0x86189359, (q31_t)0xD957DE7A, (q31_t)0x85FA1152, + (q31_t)0xD9B7C093, (q31_t)0x85DBDA91, (q31_t)0xDA17BA4A, + (q31_t)0x85BDEF27, (q31_t)0xDA77CB62, (q31_t)0x85A04F28, + (q31_t)0xDAD7F3A2, (q31_t)0x8582FAA4, (q31_t)0xDB3832CD, + (q31_t)0x8565F1B0, (q31_t)0xDB9888A8, (q31_t)0x8549345C, + (q31_t)0xDBF8F4F8, (q31_t)0x852CC2BA, (q31_t)0xDC597781, + (q31_t)0x85109CDC, (q31_t)0xDCBA1008, (q31_t)0x84F4C2D3, + (q31_t)0xDD1ABE51, (q31_t)0x84D934B0, (q31_t)0xDD7B8220, + (q31_t)0x84BDF285, (q31_t)0xDDDC5B3A, (q31_t)0x84A2FC62, + (q31_t)0xDE3D4963, (q31_t)0x84885257, (q31_t)0xDE9E4C60, + (q31_t)0x846DF476, (q31_t)0xDEFF63F4, (q31_t)0x8453E2CE, + (q31_t)0xDF608FE3, (q31_t)0x843A1D70, (q31_t)0xDFC1CFF2, + (q31_t)0x8420A46B, (q31_t)0xE02323E5, (q31_t)0x840777CF, + (q31_t)0xE0848B7F, (q31_t)0x83EE97AC, (q31_t)0xE0E60684, + (q31_t)0x83D60411, (q31_t)0xE14794B9, (q31_t)0x83BDBD0D, + (q31_t)0xE1A935E1, (q31_t)0x83A5C2B0, (q31_t)0xE20AE9C1, + (q31_t)0x838E1507, (q31_t)0xE26CB01A, (q31_t)0x8376B422, + (q31_t)0xE2CE88B2, (q31_t)0x835FA00E, (q31_t)0xE330734C, + (q31_t)0x8348D8DB, (q31_t)0xE3926FAC, (q31_t)0x83325E97, + (q31_t)0xE3F47D95, (q31_t)0x831C314E, (q31_t)0xE4569CCB, + (q31_t)0x8306510F, (q31_t)0xE4B8CD10, (q31_t)0x82F0BDE8, + (q31_t)0xE51B0E2A, (q31_t)0x82DB77E5, (q31_t)0xE57D5FDA, + (q31_t)0x82C67F13, (q31_t)0xE5DFC1E4, (q31_t)0x82B1D381, + (q31_t)0xE642340D, (q31_t)0x829D753A, (q31_t)0xE6A4B616, + (q31_t)0x8289644A, (q31_t)0xE70747C3, (q31_t)0x8275A0C0, + (q31_t)0xE769E8D8, (q31_t)0x82622AA5, (q31_t)0xE7CC9917, + (q31_t)0x824F0208, (q31_t)0xE82F5844, (q31_t)0x823C26F2, + (q31_t)0xE8922621, (q31_t)0x82299971, (q31_t)0xE8F50273, + (q31_t)0x8217598F, (q31_t)0xE957ECFB, (q31_t)0x82056758, + (q31_t)0xE9BAE57C, (q31_t)0x81F3C2D7, (q31_t)0xEA1DEBBB, + (q31_t)0x81E26C16, (q31_t)0xEA80FF79, (q31_t)0x81D16320, + (q31_t)0xEAE4207A, (q31_t)0x81C0A801, (q31_t)0xEB474E80, + (q31_t)0x81B03AC1, (q31_t)0xEBAA894E, (q31_t)0x81A01B6C, + (q31_t)0xEC0DD0A8, (q31_t)0x81904A0C, (q31_t)0xEC71244F, + (q31_t)0x8180C6A9, (q31_t)0xECD48406, (q31_t)0x8171914E, + (q31_t)0xED37EF91, (q31_t)0x8162AA03, (q31_t)0xED9B66B2, + (q31_t)0x815410D3, (q31_t)0xEDFEE92B, (q31_t)0x8145C5C6, + (q31_t)0xEE6276BF, (q31_t)0x8137C8E6, (q31_t)0xEEC60F31, + (q31_t)0x812A1A39, (q31_t)0xEF29B243, (q31_t)0x811CB9CA, + (q31_t)0xEF8D5FB8, (q31_t)0x810FA7A0, (q31_t)0xEFF11752, + (q31_t)0x8102E3C3, (q31_t)0xF054D8D4, (q31_t)0x80F66E3C, + (q31_t)0xF0B8A401, (q31_t)0x80EA4712, (q31_t)0xF11C789A, + (q31_t)0x80DE6E4C, (q31_t)0xF1805662, (q31_t)0x80D2E3F1, + (q31_t)0xF1E43D1C, (q31_t)0x80C7A80A, (q31_t)0xF2482C89, + (q31_t)0x80BCBA9C, (q31_t)0xF2AC246D, (q31_t)0x80B21BAF, + (q31_t)0xF310248A, (q31_t)0x80A7CB49, (q31_t)0xF3742CA1, + (q31_t)0x809DC970, (q31_t)0xF3D83C76, (q31_t)0x8094162B, + (q31_t)0xF43C53CA, (q31_t)0x808AB180, (q31_t)0xF4A07260, + (q31_t)0x80819B74, (q31_t)0xF50497FA, (q31_t)0x8078D40D, + (q31_t)0xF568C45A, (q31_t)0x80705B50, (q31_t)0xF5CCF743, + (q31_t)0x80683143, (q31_t)0xF6313076, (q31_t)0x806055EA, + (q31_t)0xF6956FB6, (q31_t)0x8058C94C, (q31_t)0xF6F9B4C5, + (q31_t)0x80518B6B, (q31_t)0xF75DFF65, (q31_t)0x804A9C4D, + (q31_t)0xF7C24F58, (q31_t)0x8043FBF6, (q31_t)0xF826A461, + (q31_t)0x803DAA69, (q31_t)0xF88AFE41, (q31_t)0x8037A7AC, + (q31_t)0xF8EF5CBB, (q31_t)0x8031F3C1, (q31_t)0xF953BF90, + (q31_t)0x802C8EAD, (q31_t)0xF9B82683, (q31_t)0x80277872, + (q31_t)0xFA1C9156, (q31_t)0x8022B113, (q31_t)0xFA80FFCB, + (q31_t)0x801E3894, (q31_t)0xFAE571A4, (q31_t)0x801A0EF7, + (q31_t)0xFB49E6A2, (q31_t)0x80163440, (q31_t)0xFBAE5E89, + (q31_t)0x8012A86F, (q31_t)0xFC12D919, (q31_t)0x800F6B88, + (q31_t)0xFC775616, (q31_t)0x800C7D8C, (q31_t)0xFCDBD541, + (q31_t)0x8009DE7D, (q31_t)0xFD40565B, (q31_t)0x80078E5E, + (q31_t)0xFDA4D928, (q31_t)0x80058D2E, (q31_t)0xFE095D69, + (q31_t)0x8003DAF0, (q31_t)0xFE6DE2E0, (q31_t)0x800277A5, + (q31_t)0xFED2694F, (q31_t)0x8001634D, (q31_t)0xFF36F078, + (q31_t)0x80009DE9, (q31_t)0xFF9B781D, (q31_t)0x8000277A +}; + +/** + @par + Example code for Q31 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefQ31[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefQ31[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 4096, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to Q31(Fixed point 1.31): + round(twiddleCoefQ31(i) * pow(2, 31)) + */ +const q31_t twiddleCoef_4096_q31[6144] ARM_DSP_TABLE_ATTRIBUTE = +{ + (q31_t)0x7FFFFFFF, (q31_t)0x00000000, (q31_t)0x7FFFF621, + (q31_t)0x003243F5, (q31_t)0x7FFFD885, (q31_t)0x006487E3, + (q31_t)0x7FFFA72C, (q31_t)0x0096CBC1, (q31_t)0x7FFF6216, + (q31_t)0x00C90F88, (q31_t)0x7FFF0942, (q31_t)0x00FB532F, + (q31_t)0x7FFE9CB2, (q31_t)0x012D96B0, (q31_t)0x7FFE1C64, + (q31_t)0x015FDA03, (q31_t)0x7FFD885A, (q31_t)0x01921D1F, + (q31_t)0x7FFCE093, (q31_t)0x01C45FFE, (q31_t)0x7FFC250F, + (q31_t)0x01F6A296, (q31_t)0x7FFB55CE, (q31_t)0x0228E4E1, + (q31_t)0x7FFA72D1, (q31_t)0x025B26D7, (q31_t)0x7FF97C17, + (q31_t)0x028D6870, (q31_t)0x7FF871A1, (q31_t)0x02BFA9A4, + (q31_t)0x7FF7536F, (q31_t)0x02F1EA6B, (q31_t)0x7FF62182, + (q31_t)0x03242ABF, (q31_t)0x7FF4DBD8, (q31_t)0x03566A96, + (q31_t)0x7FF38273, (q31_t)0x0388A9E9, (q31_t)0x7FF21553, + (q31_t)0x03BAE8B1, (q31_t)0x7FF09477, (q31_t)0x03ED26E6, + (q31_t)0x7FEEFFE1, (q31_t)0x041F647F, (q31_t)0x7FED5790, + (q31_t)0x0451A176, (q31_t)0x7FEB9B85, (q31_t)0x0483DDC3, + (q31_t)0x7FE9CBC0, (q31_t)0x04B6195D, (q31_t)0x7FE7E840, + (q31_t)0x04E8543D, (q31_t)0x7FE5F108, (q31_t)0x051A8E5C, + (q31_t)0x7FE3E616, (q31_t)0x054CC7B0, (q31_t)0x7FE1C76B, + (q31_t)0x057F0034, (q31_t)0x7FDF9508, (q31_t)0x05B137DF, + (q31_t)0x7FDD4EEC, (q31_t)0x05E36EA9, (q31_t)0x7FDAF518, + (q31_t)0x0615A48A, (q31_t)0x7FD8878D, (q31_t)0x0647D97C, + (q31_t)0x7FD6064B, (q31_t)0x067A0D75, (q31_t)0x7FD37152, + (q31_t)0x06AC406F, (q31_t)0x7FD0C8A3, (q31_t)0x06DE7261, + (q31_t)0x7FCE0C3E, (q31_t)0x0710A344, (q31_t)0x7FCB3C23, + (q31_t)0x0742D310, (q31_t)0x7FC85853, (q31_t)0x077501BE, + (q31_t)0x7FC560CF, (q31_t)0x07A72F45, (q31_t)0x7FC25596, + (q31_t)0x07D95B9E, (q31_t)0x7FBF36A9, (q31_t)0x080B86C1, + (q31_t)0x7FBC040A, (q31_t)0x083DB0A7, (q31_t)0x7FB8BDB7, + (q31_t)0x086FD947, (q31_t)0x7FB563B2, (q31_t)0x08A2009A, + (q31_t)0x7FB1F5FC, (q31_t)0x08D42698, (q31_t)0x7FAE7494, + (q31_t)0x09064B3A, (q31_t)0x7FAADF7C, (q31_t)0x09386E77, + (q31_t)0x7FA736B4, (q31_t)0x096A9049, (q31_t)0x7FA37A3C, + (q31_t)0x099CB0A7, (q31_t)0x7F9FAA15, (q31_t)0x09CECF89, + (q31_t)0x7F9BC63F, (q31_t)0x0A00ECE8, (q31_t)0x7F97CEBC, + (q31_t)0x0A3308BC, (q31_t)0x7F93C38C, (q31_t)0x0A6522FE, + (q31_t)0x7F8FA4AF, (q31_t)0x0A973BA5, (q31_t)0x7F8B7226, + (q31_t)0x0AC952AA, (q31_t)0x7F872BF3, (q31_t)0x0AFB6805, + (q31_t)0x7F82D214, (q31_t)0x0B2D7BAE, (q31_t)0x7F7E648B, + (q31_t)0x0B5F8D9F, (q31_t)0x7F79E35A, (q31_t)0x0B919DCE, + (q31_t)0x7F754E7F, (q31_t)0x0BC3AC35, (q31_t)0x7F70A5FD, + (q31_t)0x0BF5B8CB, (q31_t)0x7F6BE9D4, (q31_t)0x0C27C389, + (q31_t)0x7F671A04, (q31_t)0x0C59CC67, (q31_t)0x7F62368F, + (q31_t)0x0C8BD35E, (q31_t)0x7F5D3F75, (q31_t)0x0CBDD865, + (q31_t)0x7F5834B6, (q31_t)0x0CEFDB75, (q31_t)0x7F531654, + (q31_t)0x0D21DC87, (q31_t)0x7F4DE450, (q31_t)0x0D53DB92, + (q31_t)0x7F489EAA, (q31_t)0x0D85D88F, (q31_t)0x7F434563, + (q31_t)0x0DB7D376, (q31_t)0x7F3DD87C, (q31_t)0x0DE9CC3F, + (q31_t)0x7F3857F5, (q31_t)0x0E1BC2E3, (q31_t)0x7F32C3D0, + (q31_t)0x0E4DB75B, (q31_t)0x7F2D1C0E, (q31_t)0x0E7FA99D, + (q31_t)0x7F2760AF, (q31_t)0x0EB199A3, (q31_t)0x7F2191B4, + (q31_t)0x0EE38765, (q31_t)0x7F1BAF1E, (q31_t)0x0F1572DC, + (q31_t)0x7F15B8EE, (q31_t)0x0F475BFE, (q31_t)0x7F0FAF24, + (q31_t)0x0F7942C6, (q31_t)0x7F0991C3, (q31_t)0x0FAB272B, + (q31_t)0x7F0360CB, (q31_t)0x0FDD0925, (q31_t)0x7EFD1C3C, + (q31_t)0x100EE8AD, (q31_t)0x7EF6C418, (q31_t)0x1040C5BB, + (q31_t)0x7EF0585F, (q31_t)0x1072A047, (q31_t)0x7EE9D913, + (q31_t)0x10A4784A, (q31_t)0x7EE34635, (q31_t)0x10D64DBC, + (q31_t)0x7EDC9FC6, (q31_t)0x11082096, (q31_t)0x7ED5E5C6, + (q31_t)0x1139F0CE, (q31_t)0x7ECF1837, (q31_t)0x116BBE5F, + (q31_t)0x7EC8371A, (q31_t)0x119D8940, (q31_t)0x7EC1426F, + (q31_t)0x11CF516A, (q31_t)0x7EBA3A39, (q31_t)0x120116D4, + (q31_t)0x7EB31E77, (q31_t)0x1232D978, (q31_t)0x7EABEF2C, + (q31_t)0x1264994E, (q31_t)0x7EA4AC58, (q31_t)0x1296564D, + (q31_t)0x7E9D55FC, (q31_t)0x12C8106E, (q31_t)0x7E95EC19, + (q31_t)0x12F9C7AA, (q31_t)0x7E8E6EB1, (q31_t)0x132B7BF9, + (q31_t)0x7E86DDC5, (q31_t)0x135D2D53, (q31_t)0x7E7F3956, + (q31_t)0x138EDBB0, (q31_t)0x7E778165, (q31_t)0x13C0870A, + (q31_t)0x7E6FB5F3, (q31_t)0x13F22F57, (q31_t)0x7E67D702, + (q31_t)0x1423D492, (q31_t)0x7E5FE493, (q31_t)0x145576B1, + (q31_t)0x7E57DEA6, (q31_t)0x148715AD, (q31_t)0x7E4FC53E, + (q31_t)0x14B8B17F, (q31_t)0x7E47985B, (q31_t)0x14EA4A1F, + (q31_t)0x7E3F57FE, (q31_t)0x151BDF85, (q31_t)0x7E37042A, + (q31_t)0x154D71AA, (q31_t)0x7E2E9CDF, (q31_t)0x157F0086, + (q31_t)0x7E26221E, (q31_t)0x15B08C11, (q31_t)0x7E1D93E9, + (q31_t)0x15E21444, (q31_t)0x7E14F242, (q31_t)0x16139917, + (q31_t)0x7E0C3D29, (q31_t)0x16451A83, (q31_t)0x7E03749F, + (q31_t)0x1676987F, (q31_t)0x7DFA98A7, (q31_t)0x16A81305, + (q31_t)0x7DF1A942, (q31_t)0x16D98A0C, (q31_t)0x7DE8A670, + (q31_t)0x170AFD8D, (q31_t)0x7DDF9034, (q31_t)0x173C6D80, + (q31_t)0x7DD6668E, (q31_t)0x176DD9DE, (q31_t)0x7DCD2981, + (q31_t)0x179F429F, (q31_t)0x7DC3D90D, (q31_t)0x17D0A7BB, + (q31_t)0x7DBA7534, (q31_t)0x1802092C, (q31_t)0x7DB0FDF7, + (q31_t)0x183366E8, (q31_t)0x7DA77359, (q31_t)0x1864C0E9, + (q31_t)0x7D9DD55A, (q31_t)0x18961727, (q31_t)0x7D9423FB, + (q31_t)0x18C7699B, (q31_t)0x7D8A5F3F, (q31_t)0x18F8B83C, + (q31_t)0x7D808727, (q31_t)0x192A0303, (q31_t)0x7D769BB5, + (q31_t)0x195B49E9, (q31_t)0x7D6C9CE9, (q31_t)0x198C8CE6, + (q31_t)0x7D628AC5, (q31_t)0x19BDCBF2, (q31_t)0x7D58654C, + (q31_t)0x19EF0706, (q31_t)0x7D4E2C7E, (q31_t)0x1A203E1B, + (q31_t)0x7D43E05E, (q31_t)0x1A517127, (q31_t)0x7D3980EC, + (q31_t)0x1A82A025, (q31_t)0x7D2F0E2A, (q31_t)0x1AB3CB0C, + (q31_t)0x7D24881A, (q31_t)0x1AE4F1D6, (q31_t)0x7D19EEBE, + (q31_t)0x1B161479, (q31_t)0x7D0F4218, (q31_t)0x1B4732EF, + (q31_t)0x7D048228, (q31_t)0x1B784D30, (q31_t)0x7CF9AEF0, + (q31_t)0x1BA96334, (q31_t)0x7CEEC873, (q31_t)0x1BDA74F5, + (q31_t)0x7CE3CEB1, (q31_t)0x1C0B826A, (q31_t)0x7CD8C1AD, + (q31_t)0x1C3C8B8C, (q31_t)0x7CCDA168, (q31_t)0x1C6D9053, + (q31_t)0x7CC26DE5, (q31_t)0x1C9E90B8, (q31_t)0x7CB72724, + (q31_t)0x1CCF8CB3, (q31_t)0x7CABCD27, (q31_t)0x1D00843C, + (q31_t)0x7CA05FF1, (q31_t)0x1D31774D, (q31_t)0x7C94DF82, + (q31_t)0x1D6265DD, (q31_t)0x7C894BDD, (q31_t)0x1D934FE5, + (q31_t)0x7C7DA504, (q31_t)0x1DC4355D, (q31_t)0x7C71EAF8, + (q31_t)0x1DF5163F, (q31_t)0x7C661DBB, (q31_t)0x1E25F281, + (q31_t)0x7C5A3D4F, (q31_t)0x1E56CA1E, (q31_t)0x7C4E49B6, + (q31_t)0x1E879D0C, (q31_t)0x7C4242F2, (q31_t)0x1EB86B46, + (q31_t)0x7C362904, (q31_t)0x1EE934C2, (q31_t)0x7C29FBEE, + (q31_t)0x1F19F97B, (q31_t)0x7C1DBBB2, (q31_t)0x1F4AB967, + (q31_t)0x7C116853, (q31_t)0x1F7B7480, (q31_t)0x7C0501D1, + (q31_t)0x1FAC2ABF, (q31_t)0x7BF88830, (q31_t)0x1FDCDC1A, + (q31_t)0x7BEBFB70, (q31_t)0x200D888C, (q31_t)0x7BDF5B94, + (q31_t)0x203E300D, (q31_t)0x7BD2A89E, (q31_t)0x206ED295, + (q31_t)0x7BC5E28F, (q31_t)0x209F701C, (q31_t)0x7BB9096A, + (q31_t)0x20D0089B, (q31_t)0x7BAC1D31, (q31_t)0x21009C0B, + (q31_t)0x7B9F1DE5, (q31_t)0x21312A65, (q31_t)0x7B920B89, + (q31_t)0x2161B39F, (q31_t)0x7B84E61E, (q31_t)0x219237B4, + (q31_t)0x7B77ADA8, (q31_t)0x21C2B69C, (q31_t)0x7B6A6227, + (q31_t)0x21F3304E, (q31_t)0x7B5D039D, (q31_t)0x2223A4C5, + (q31_t)0x7B4F920E, (q31_t)0x225413F8, (q31_t)0x7B420D7A, + (q31_t)0x22847DDF, (q31_t)0x7B3475E4, (q31_t)0x22B4E274, + (q31_t)0x7B26CB4F, (q31_t)0x22E541AE, (q31_t)0x7B190DBB, + (q31_t)0x23159B87, (q31_t)0x7B0B3D2C, (q31_t)0x2345EFF7, + (q31_t)0x7AFD59A3, (q31_t)0x23763EF7, (q31_t)0x7AEF6323, + (q31_t)0x23A6887E, (q31_t)0x7AE159AE, (q31_t)0x23D6CC86, + (q31_t)0x7AD33D45, (q31_t)0x24070B07, (q31_t)0x7AC50DEB, + (q31_t)0x243743FA, (q31_t)0x7AB6CBA3, (q31_t)0x24677757, + (q31_t)0x7AA8766E, (q31_t)0x2497A517, (q31_t)0x7A9A0E4F, + (q31_t)0x24C7CD32, (q31_t)0x7A8B9348, (q31_t)0x24F7EFA1, + (q31_t)0x7A7D055B, (q31_t)0x25280C5D, (q31_t)0x7A6E648A, + (q31_t)0x2558235E, (q31_t)0x7A5FB0D8, (q31_t)0x2588349D, + (q31_t)0x7A50EA46, (q31_t)0x25B84012, (q31_t)0x7A4210D8, + (q31_t)0x25E845B5, (q31_t)0x7A33248F, (q31_t)0x26184581, + (q31_t)0x7A24256E, (q31_t)0x26483F6C, (q31_t)0x7A151377, + (q31_t)0x26783370, (q31_t)0x7A05EEAD, (q31_t)0x26A82185, + (q31_t)0x79F6B711, (q31_t)0x26D809A5, (q31_t)0x79E76CA6, + (q31_t)0x2707EBC6, (q31_t)0x79D80F6F, (q31_t)0x2737C7E3, + (q31_t)0x79C89F6D, (q31_t)0x27679DF4, (q31_t)0x79B91CA4, + (q31_t)0x27976DF1, (q31_t)0x79A98715, (q31_t)0x27C737D2, + (q31_t)0x7999DEC3, (q31_t)0x27F6FB92, (q31_t)0x798A23B1, + (q31_t)0x2826B928, (q31_t)0x797A55E0, (q31_t)0x2856708C, + (q31_t)0x796A7554, (q31_t)0x288621B9, (q31_t)0x795A820E, + (q31_t)0x28B5CCA5, (q31_t)0x794A7C11, (q31_t)0x28E5714A, + (q31_t)0x793A6360, (q31_t)0x29150FA1, (q31_t)0x792A37FE, + (q31_t)0x2944A7A2, (q31_t)0x7919F9EB, (q31_t)0x29743945, + (q31_t)0x7909A92C, (q31_t)0x29A3C484, (q31_t)0x78F945C3, + (q31_t)0x29D34958, (q31_t)0x78E8CFB1, (q31_t)0x2A02C7B8, + (q31_t)0x78D846FB, (q31_t)0x2A323F9D, (q31_t)0x78C7ABA1, + (q31_t)0x2A61B101, (q31_t)0x78B6FDA8, (q31_t)0x2A911BDB, + (q31_t)0x78A63D10, (q31_t)0x2AC08025, (q31_t)0x789569DE, + (q31_t)0x2AEFDDD8, (q31_t)0x78848413, (q31_t)0x2B1F34EB, + (q31_t)0x78738BB3, (q31_t)0x2B4E8558, (q31_t)0x786280BF, + (q31_t)0x2B7DCF17, (q31_t)0x7851633B, (q31_t)0x2BAD1221, + (q31_t)0x78403328, (q31_t)0x2BDC4E6F, (q31_t)0x782EF08B, + (q31_t)0x2C0B83F9, (q31_t)0x781D9B64, (q31_t)0x2C3AB2B9, + (q31_t)0x780C33B8, (q31_t)0x2C69DAA6, (q31_t)0x77FAB988, + (q31_t)0x2C98FBBA, (q31_t)0x77E92CD8, (q31_t)0x2CC815ED, + (q31_t)0x77D78DAA, (q31_t)0x2CF72939, (q31_t)0x77C5DC01, + (q31_t)0x2D263595, (q31_t)0x77B417DF, (q31_t)0x2D553AFB, + (q31_t)0x77A24148, (q31_t)0x2D843963, (q31_t)0x7790583D, + (q31_t)0x2DB330C7, (q31_t)0x777E5CC3, (q31_t)0x2DE2211E, + (q31_t)0x776C4EDB, (q31_t)0x2E110A62, (q31_t)0x775A2E88, + (q31_t)0x2E3FEC8B, (q31_t)0x7747FBCE, (q31_t)0x2E6EC792, + (q31_t)0x7735B6AE, (q31_t)0x2E9D9B70, (q31_t)0x77235F2D, + (q31_t)0x2ECC681E, (q31_t)0x7710F54B, (q31_t)0x2EFB2D94, + (q31_t)0x76FE790E, (q31_t)0x2F29EBCC, (q31_t)0x76EBEA77, + (q31_t)0x2F58A2BD, (q31_t)0x76D94988, (q31_t)0x2F875262, + (q31_t)0x76C69646, (q31_t)0x2FB5FAB2, (q31_t)0x76B3D0B3, + (q31_t)0x2FE49BA6, (q31_t)0x76A0F8D2, (q31_t)0x30133538, + (q31_t)0x768E0EA5, (q31_t)0x3041C760, (q31_t)0x767B1230, + (q31_t)0x30705217, (q31_t)0x76680376, (q31_t)0x309ED555, + (q31_t)0x7654E279, (q31_t)0x30CD5114, (q31_t)0x7641AF3C, + (q31_t)0x30FBC54D, (q31_t)0x762E69C3, (q31_t)0x312A31F8, + (q31_t)0x761B1211, (q31_t)0x3158970D, (q31_t)0x7607A827, + (q31_t)0x3186F487, (q31_t)0x75F42C0A, (q31_t)0x31B54A5D, + (q31_t)0x75E09DBD, (q31_t)0x31E39889, (q31_t)0x75CCFD42, + (q31_t)0x3211DF03, (q31_t)0x75B94A9C, (q31_t)0x32401DC5, + (q31_t)0x75A585CF, (q31_t)0x326E54C7, (q31_t)0x7591AEDD, + (q31_t)0x329C8402, (q31_t)0x757DC5CA, (q31_t)0x32CAAB6F, + (q31_t)0x7569CA98, (q31_t)0x32F8CB07, (q31_t)0x7555BD4B, + (q31_t)0x3326E2C2, (q31_t)0x75419DE6, (q31_t)0x3354F29A, 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(q31_t)0x81B03AC1, (q31_t)0xEB474E80, (q31_t)0x81B867A4, + (q31_t)0xEB15B5E0, (q31_t)0x81C0A801, (q31_t)0xEAE4207A, + (q31_t)0x81C8FBD5, (q31_t)0xEAB28E55, (q31_t)0x81D16320, + (q31_t)0xEA80FF79, (q31_t)0x81D9DDE1, (q31_t)0xEA4F73EE, + (q31_t)0x81E26C16, (q31_t)0xEA1DEBBB, (q31_t)0x81EB0DBD, + (q31_t)0xE9EC66E8, (q31_t)0x81F3C2D7, (q31_t)0xE9BAE57C, + (q31_t)0x81FC8B60, (q31_t)0xE9896780, (q31_t)0x82056758, + (q31_t)0xE957ECFB, (q31_t)0x820E56BE, (q31_t)0xE92675F4, + (q31_t)0x8217598F, (q31_t)0xE8F50273, (q31_t)0x82206FCB, + (q31_t)0xE8C3927F, (q31_t)0x82299971, (q31_t)0xE8922621, + (q31_t)0x8232D67E, (q31_t)0xE860BD60, (q31_t)0x823C26F2, + (q31_t)0xE82F5844, (q31_t)0x82458ACB, (q31_t)0xE7FDF6D3, + (q31_t)0x824F0208, (q31_t)0xE7CC9917, (q31_t)0x82588CA6, + (q31_t)0xE79B3F16, (q31_t)0x82622AA5, (q31_t)0xE769E8D8, + (q31_t)0x826BDC04, (q31_t)0xE7389664, (q31_t)0x8275A0C0, + (q31_t)0xE70747C3, (q31_t)0x827F78D8, (q31_t)0xE6D5FCFC, + (q31_t)0x8289644A, (q31_t)0xE6A4B616, (q31_t)0x82936316, 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(q31_t)0xE1A935E1, + (q31_t)0x83B1B649, (q31_t)0xE17862F3, (q31_t)0x83BDBD0D, + (q31_t)0xE14794B9, (q31_t)0x83C9D6FB, (q31_t)0xE116CB3D, + (q31_t)0x83D60411, (q31_t)0xE0E60684, (q31_t)0x83E2444D, + (q31_t)0xE0B54698, (q31_t)0x83EE97AC, (q31_t)0xE0848B7F, + (q31_t)0x83FAFE2E, (q31_t)0xE053D541, (q31_t)0x840777CF, + (q31_t)0xE02323E5, (q31_t)0x8414048F, (q31_t)0xDFF27773, + (q31_t)0x8420A46B, (q31_t)0xDFC1CFF2, (q31_t)0x842D5761, + (q31_t)0xDF912D6A, (q31_t)0x843A1D70, (q31_t)0xDF608FE3, + (q31_t)0x8446F695, (q31_t)0xDF2FF764, (q31_t)0x8453E2CE, + (q31_t)0xDEFF63F4, (q31_t)0x8460E21A, (q31_t)0xDECED59B, + (q31_t)0x846DF476, (q31_t)0xDE9E4C60, (q31_t)0x847B19E1, + (q31_t)0xDE6DC84B, (q31_t)0x84885257, (q31_t)0xDE3D4963, + (q31_t)0x84959DD9, (q31_t)0xDE0CCFB1, (q31_t)0x84A2FC62, + (q31_t)0xDDDC5B3A, (q31_t)0x84B06DF1, (q31_t)0xDDABEC07, + (q31_t)0x84BDF285, (q31_t)0xDD7B8220, (q31_t)0x84CB8A1B, + (q31_t)0xDD4B1D8B, (q31_t)0x84D934B0, (q31_t)0xDD1ABE51, + (q31_t)0x84E6F244, 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(q31_t)0xE4E9EB86, (q31_t)0x82E61141, + (q31_t)0xE51B0E2A, (q31_t)0x82DB77E5, (q31_t)0xE54C34F3, + (q31_t)0x82D0F1D5, (q31_t)0xE57D5FDA, (q31_t)0x82C67F13, + (q31_t)0xE5AE8ED8, (q31_t)0x82BC1FA1, (q31_t)0xE5DFC1E4, + (q31_t)0x82B1D381, (q31_t)0xE610F8F9, (q31_t)0x82A79AB3, + (q31_t)0xE642340D, (q31_t)0x829D753A, (q31_t)0xE6737319, + (q31_t)0x82936316, (q31_t)0xE6A4B616, (q31_t)0x8289644A, + (q31_t)0xE6D5FCFC, (q31_t)0x827F78D8, (q31_t)0xE70747C3, + (q31_t)0x8275A0C0, (q31_t)0xE7389664, (q31_t)0x826BDC04, + (q31_t)0xE769E8D8, (q31_t)0x82622AA5, (q31_t)0xE79B3F16, + (q31_t)0x82588CA6, (q31_t)0xE7CC9917, (q31_t)0x824F0208, + (q31_t)0xE7FDF6D3, (q31_t)0x82458ACB, (q31_t)0xE82F5844, + (q31_t)0x823C26F2, (q31_t)0xE860BD60, (q31_t)0x8232D67E, + (q31_t)0xE8922621, (q31_t)0x82299971, (q31_t)0xE8C3927F, + (q31_t)0x82206FCB, (q31_t)0xE8F50273, (q31_t)0x8217598F, + (q31_t)0xE92675F4, (q31_t)0x820E56BE, (q31_t)0xE957ECFB, + (q31_t)0x82056758, (q31_t)0xE9896780, (q31_t)0x81FC8B60, + (q31_t)0xE9BAE57C, (q31_t)0x81F3C2D7, (q31_t)0xE9EC66E8, + (q31_t)0x81EB0DBD, (q31_t)0xEA1DEBBB, (q31_t)0x81E26C16, + (q31_t)0xEA4F73EE, (q31_t)0x81D9DDE1, (q31_t)0xEA80FF79, + (q31_t)0x81D16320, (q31_t)0xEAB28E55, (q31_t)0x81C8FBD5, + (q31_t)0xEAE4207A, (q31_t)0x81C0A801, (q31_t)0xEB15B5E0, + (q31_t)0x81B867A4, (q31_t)0xEB474E80, (q31_t)0x81B03AC1, + (q31_t)0xEB78EA52, (q31_t)0x81A82159, (q31_t)0xEBAA894E, + (q31_t)0x81A01B6C, (q31_t)0xEBDC2B6D, (q31_t)0x819828FD, + (q31_t)0xEC0DD0A8, (q31_t)0x81904A0C, (q31_t)0xEC3F78F5, + (q31_t)0x81887E9A, (q31_t)0xEC71244F, (q31_t)0x8180C6A9, + (q31_t)0xECA2D2AC, (q31_t)0x8179223A, (q31_t)0xECD48406, + (q31_t)0x8171914E, (q31_t)0xED063855, (q31_t)0x816A13E6, + (q31_t)0xED37EF91, (q31_t)0x8162AA03, (q31_t)0xED69A9B2, + (q31_t)0x815B53A8, (q31_t)0xED9B66B2, (q31_t)0x815410D3, + (q31_t)0xEDCD2687, (q31_t)0x814CE188, (q31_t)0xEDFEE92B, + (q31_t)0x8145C5C6, (q31_t)0xEE30AE95, (q31_t)0x813EBD90, + (q31_t)0xEE6276BF, (q31_t)0x8137C8E6, (q31_t)0xEE9441A0, + (q31_t)0x8130E7C8, (q31_t)0xEEC60F31, (q31_t)0x812A1A39, + (q31_t)0xEEF7DF6A, (q31_t)0x81236039, (q31_t)0xEF29B243, + (q31_t)0x811CB9CA, (q31_t)0xEF5B87B5, (q31_t)0x811626EC, + (q31_t)0xEF8D5FB8, (q31_t)0x810FA7A0, (q31_t)0xEFBF3A44, + (q31_t)0x81093BE8, (q31_t)0xEFF11752, (q31_t)0x8102E3C3, + (q31_t)0xF022F6DA, (q31_t)0x80FC9F35, (q31_t)0xF054D8D4, + (q31_t)0x80F66E3C, (q31_t)0xF086BD39, (q31_t)0x80F050DB, + (q31_t)0xF0B8A401, (q31_t)0x80EA4712, (q31_t)0xF0EA8D23, + (q31_t)0x80E450E2, (q31_t)0xF11C789A, (q31_t)0x80DE6E4C, + (q31_t)0xF14E665C, (q31_t)0x80D89F51, (q31_t)0xF1805662, + (q31_t)0x80D2E3F1, (q31_t)0xF1B248A5, (q31_t)0x80CD3C2F, + (q31_t)0xF1E43D1C, (q31_t)0x80C7A80A, (q31_t)0xF21633C0, + (q31_t)0x80C22783, (q31_t)0xF2482C89, (q31_t)0x80BCBA9C, + (q31_t)0xF27A2770, (q31_t)0x80B76155, (q31_t)0xF2AC246D, + (q31_t)0x80B21BAF, (q31_t)0xF2DE2378, (q31_t)0x80ACE9AB, + (q31_t)0xF310248A, (q31_t)0x80A7CB49, (q31_t)0xF342279A, + (q31_t)0x80A2C08B, (q31_t)0xF3742CA1, (q31_t)0x809DC970, + (q31_t)0xF3A63398, (q31_t)0x8098E5FB, (q31_t)0xF3D83C76, + (q31_t)0x8094162B, (q31_t)0xF40A4734, (q31_t)0x808F5A02, + (q31_t)0xF43C53CA, (q31_t)0x808AB180, (q31_t)0xF46E6231, + (q31_t)0x80861CA5, (q31_t)0xF4A07260, (q31_t)0x80819B74, + (q31_t)0xF4D28451, (q31_t)0x807D2DEB, (q31_t)0xF50497FA, + (q31_t)0x8078D40D, (q31_t)0xF536AD55, (q31_t)0x80748DD9, + (q31_t)0xF568C45A, (q31_t)0x80705B50, (q31_t)0xF59ADD01, + (q31_t)0x806C3C73, (q31_t)0xF5CCF743, (q31_t)0x80683143, + (q31_t)0xF5FF1317, (q31_t)0x806439C0, (q31_t)0xF6313076, + (q31_t)0x806055EA, (q31_t)0xF6634F58, (q31_t)0x805C85C3, + (q31_t)0xF6956FB6, (q31_t)0x8058C94C, (q31_t)0xF6C79188, + (q31_t)0x80552083, (q31_t)0xF6F9B4C5, (q31_t)0x80518B6B, + (q31_t)0xF72BD967, (q31_t)0x804E0A03, (q31_t)0xF75DFF65, + (q31_t)0x804A9C4D, (q31_t)0xF79026B8, (q31_t)0x80474248, + (q31_t)0xF7C24F58, (q31_t)0x8043FBF6, (q31_t)0xF7F4793E, + (q31_t)0x8040C956, (q31_t)0xF826A461, (q31_t)0x803DAA69, + (q31_t)0xF858D0BA, (q31_t)0x803A9F31, (q31_t)0xF88AFE41, + (q31_t)0x8037A7AC, (q31_t)0xF8BD2CEF, (q31_t)0x8034C3DC, + (q31_t)0xF8EF5CBB, (q31_t)0x8031F3C1, (q31_t)0xF9218D9E, + (q31_t)0x802F375C, (q31_t)0xF953BF90, (q31_t)0x802C8EAD, + (q31_t)0xF985F28A, (q31_t)0x8029F9B4, (q31_t)0xF9B82683, + (q31_t)0x80277872, (q31_t)0xF9EA5B75, (q31_t)0x80250AE7, + (q31_t)0xFA1C9156, (q31_t)0x8022B113, (q31_t)0xFA4EC820, + (q31_t)0x80206AF8, (q31_t)0xFA80FFCB, (q31_t)0x801E3894, + (q31_t)0xFAB3384F, (q31_t)0x801C19E9, (q31_t)0xFAE571A4, + (q31_t)0x801A0EF7, (q31_t)0xFB17ABC2, (q31_t)0x801817BF, + (q31_t)0xFB49E6A2, (q31_t)0x80163440, (q31_t)0xFB7C223C, + (q31_t)0x8014647A, (q31_t)0xFBAE5E89, (q31_t)0x8012A86F, + (q31_t)0xFBE09B80, (q31_t)0x8011001E, (q31_t)0xFC12D919, + (q31_t)0x800F6B88, (q31_t)0xFC45174E, (q31_t)0x800DEAAC, + (q31_t)0xFC775616, (q31_t)0x800C7D8C, (q31_t)0xFCA99569, + (q31_t)0x800B2427, (q31_t)0xFCDBD541, (q31_t)0x8009DE7D, + (q31_t)0xFD0E1594, (q31_t)0x8008AC90, (q31_t)0xFD40565B, + (q31_t)0x80078E5E, (q31_t)0xFD72978F, (q31_t)0x800683E8, + (q31_t)0xFDA4D928, (q31_t)0x80058D2E, (q31_t)0xFDD71B1E, + (q31_t)0x8004AA31, (q31_t)0xFE095D69, (q31_t)0x8003DAF0, + (q31_t)0xFE3BA001, (q31_t)0x80031F6C, (q31_t)0xFE6DE2E0, + (q31_t)0x800277A5, (q31_t)0xFEA025FC, (q31_t)0x8001E39B, + (q31_t)0xFED2694F, (q31_t)0x8001634D, (q31_t)0xFF04ACD0, + (q31_t)0x8000F6BD, (q31_t)0xFF36F078, (q31_t)0x80009DE9, + (q31_t)0xFF69343E, (q31_t)0x800058D3, (q31_t)0xFF9B781D, + (q31_t)0x8000277A, (q31_t)0xFFCDBC0A, (q31_t)0x800009DE +}; + +/** + @brief q15 Twiddle factors Table +*/ + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
fori = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 16, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_16_q15[24] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, + (q15_t)0x7641, (q15_t)0x30FB, + (q15_t)0x5A82, (q15_t)0x5A82, + (q15_t)0x30FB, (q15_t)0x7641, + (q15_t)0x0000, (q15_t)0x7FFF, + (q15_t)0xCF04, (q15_t)0x7641, + (q15_t)0xA57D, (q15_t)0x5A82, + (q15_t)0x89BE, (q15_t)0x30FB, + (q15_t)0x8000, (q15_t)0x0000, + (q15_t)0x89BE, (q15_t)0xCF04, + (q15_t)0xA57D, (q15_t)0xA57D, + (q15_t)0xCF04, (q15_t)0x89BE +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 32, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_32_q15[48] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, + (q15_t)0x7D8A, (q15_t)0x18F8, + (q15_t)0x7641, (q15_t)0x30FB, + (q15_t)0x6A6D, (q15_t)0x471C, + (q15_t)0x5A82, (q15_t)0x5A82, + (q15_t)0x471C, (q15_t)0x6A6D, + (q15_t)0x30FB, (q15_t)0x7641, + (q15_t)0x18F8, (q15_t)0x7D8A, + (q15_t)0x0000, (q15_t)0x7FFF, + (q15_t)0xE707, (q15_t)0x7D8A, + (q15_t)0xCF04, (q15_t)0x7641, + (q15_t)0xB8E3, (q15_t)0x6A6D, + (q15_t)0xA57D, (q15_t)0x5A82, + (q15_t)0x9592, (q15_t)0x471C, + (q15_t)0x89BE, (q15_t)0x30FB, + (q15_t)0x8275, (q15_t)0x18F8, + (q15_t)0x8000, (q15_t)0x0000, + (q15_t)0x8275, (q15_t)0xE707, + (q15_t)0x89BE, (q15_t)0xCF04, + (q15_t)0x9592, (q15_t)0xB8E3, + (q15_t)0xA57D, (q15_t)0xA57D, + (q15_t)0xB8E3, (q15_t)0x9592, + (q15_t)0xCF04, (q15_t)0x89BE, + (q15_t)0xE707, (q15_t)0x8275 +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 64, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_64_q15[96] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7F62, (q15_t)0x0C8B, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7A7D, (q15_t)0x2528, + (q15_t)0x7641, (q15_t)0x30FB, (q15_t)0x70E2, (q15_t)0x3C56, + (q15_t)0x6A6D, (q15_t)0x471C, (q15_t)0x62F2, (q15_t)0x5133, + (q15_t)0x5A82, (q15_t)0x5A82, (q15_t)0x5133, (q15_t)0x62F2, + (q15_t)0x471C, (q15_t)0x6A6D, (q15_t)0x3C56, (q15_t)0x70E2, + (q15_t)0x30FB, (q15_t)0x7641, (q15_t)0x2528, (q15_t)0x7A7D, + (q15_t)0x18F8, (q15_t)0x7D8A, (q15_t)0x0C8B, (q15_t)0x7F62, + (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0xF374, (q15_t)0x7F62, + (q15_t)0xE707, (q15_t)0x7D8A, (q15_t)0xDAD7, (q15_t)0x7A7D, + (q15_t)0xCF04, (q15_t)0x7641, (q15_t)0xC3A9, (q15_t)0x70E2, + (q15_t)0xB8E3, (q15_t)0x6A6D, (q15_t)0xAECC, (q15_t)0x62F2, + (q15_t)0xA57D, (q15_t)0x5A82, (q15_t)0x9D0D, (q15_t)0x5133, + (q15_t)0x9592, (q15_t)0x471C, (q15_t)0x8F1D, (q15_t)0x3C56, + (q15_t)0x89BE, (q15_t)0x30FB, (q15_t)0x8582, (q15_t)0x2528, + (q15_t)0x8275, (q15_t)0x18F8, (q15_t)0x809D, (q15_t)0x0C8B, + (q15_t)0x8000, (q15_t)0x0000, (q15_t)0x809D, (q15_t)0xF374, + (q15_t)0x8275, (q15_t)0xE707, (q15_t)0x8582, (q15_t)0xDAD7, + (q15_t)0x89BE, (q15_t)0xCF04, (q15_t)0x8F1D, (q15_t)0xC3A9, + (q15_t)0x9592, (q15_t)0xB8E3, (q15_t)0x9D0D, (q15_t)0xAECC, + (q15_t)0xA57D, (q15_t)0xA57D, (q15_t)0xAECC, (q15_t)0x9D0D, + (q15_t)0xB8E3, (q15_t)0x9592, (q15_t)0xC3A9, (q15_t)0x8F1D, + (q15_t)0xCF04, (q15_t)0x89BE, (q15_t)0xDAD7, (q15_t)0x8582, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xF374, (q15_t)0x809D +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 128, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_128_q15[192] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7FD8, (q15_t)0x0647, + (q15_t)0x7F62, (q15_t)0x0C8B, (q15_t)0x7E9D, (q15_t)0x12C8, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7C29, (q15_t)0x1F19, + (q15_t)0x7A7D, (q15_t)0x2528, (q15_t)0x7884, (q15_t)0x2B1F, + (q15_t)0x7641, (q15_t)0x30FB, (q15_t)0x73B5, (q15_t)0x36BA, + (q15_t)0x70E2, (q15_t)0x3C56, (q15_t)0x6DCA, (q15_t)0x41CE, + (q15_t)0x6A6D, (q15_t)0x471C, (q15_t)0x66CF, (q15_t)0x4C3F, + (q15_t)0x62F2, (q15_t)0x5133, (q15_t)0x5ED7, (q15_t)0x55F5, + (q15_t)0x5A82, (q15_t)0x5A82, (q15_t)0x55F5, (q15_t)0x5ED7, + (q15_t)0x5133, (q15_t)0x62F2, (q15_t)0x4C3F, (q15_t)0x66CF, + (q15_t)0x471C, (q15_t)0x6A6D, (q15_t)0x41CE, (q15_t)0x6DCA, + (q15_t)0x3C56, (q15_t)0x70E2, (q15_t)0x36BA, (q15_t)0x73B5, + (q15_t)0x30FB, (q15_t)0x7641, (q15_t)0x2B1F, (q15_t)0x7884, + (q15_t)0x2528, (q15_t)0x7A7D, (q15_t)0x1F19, (q15_t)0x7C29, + (q15_t)0x18F8, (q15_t)0x7D8A, (q15_t)0x12C8, (q15_t)0x7E9D, + (q15_t)0x0C8B, (q15_t)0x7F62, (q15_t)0x0647, (q15_t)0x7FD8, + (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0xF9B8, (q15_t)0x7FD8, + (q15_t)0xF374, (q15_t)0x7F62, (q15_t)0xED37, (q15_t)0x7E9D, + (q15_t)0xE707, (q15_t)0x7D8A, (q15_t)0xE0E6, (q15_t)0x7C29, + (q15_t)0xDAD7, (q15_t)0x7A7D, (q15_t)0xD4E0, (q15_t)0x7884, + (q15_t)0xCF04, (q15_t)0x7641, (q15_t)0xC945, (q15_t)0x73B5, + (q15_t)0xC3A9, (q15_t)0x70E2, (q15_t)0xBE31, (q15_t)0x6DCA, + (q15_t)0xB8E3, (q15_t)0x6A6D, (q15_t)0xB3C0, (q15_t)0x66CF, + (q15_t)0xAECC, (q15_t)0x62F2, (q15_t)0xAA0A, (q15_t)0x5ED7, + (q15_t)0xA57D, (q15_t)0x5A82, (q15_t)0xA128, (q15_t)0x55F5, + (q15_t)0x9D0D, (q15_t)0x5133, (q15_t)0x9930, (q15_t)0x4C3F, + (q15_t)0x9592, (q15_t)0x471C, (q15_t)0x9235, (q15_t)0x41CE, + (q15_t)0x8F1D, (q15_t)0x3C56, (q15_t)0x8C4A, (q15_t)0x36BA, + (q15_t)0x89BE, (q15_t)0x30FB, (q15_t)0x877B, (q15_t)0x2B1F, + (q15_t)0x8582, (q15_t)0x2528, (q15_t)0x83D6, (q15_t)0x1F19, + (q15_t)0x8275, (q15_t)0x18F8, (q15_t)0x8162, (q15_t)0x12C8, + (q15_t)0x809D, (q15_t)0x0C8B, (q15_t)0x8027, (q15_t)0x0647, + (q15_t)0x8000, (q15_t)0x0000, (q15_t)0x8027, (q15_t)0xF9B8, + (q15_t)0x809D, (q15_t)0xF374, (q15_t)0x8162, (q15_t)0xED37, + (q15_t)0x8275, (q15_t)0xE707, (q15_t)0x83D6, (q15_t)0xE0E6, + (q15_t)0x8582, (q15_t)0xDAD7, (q15_t)0x877B, (q15_t)0xD4E0, + (q15_t)0x89BE, (q15_t)0xCF04, (q15_t)0x8C4A, (q15_t)0xC945, + (q15_t)0x8F1D, (q15_t)0xC3A9, (q15_t)0x9235, (q15_t)0xBE31, + (q15_t)0x9592, (q15_t)0xB8E3, (q15_t)0x9930, (q15_t)0xB3C0, + (q15_t)0x9D0D, (q15_t)0xAECC, (q15_t)0xA128, (q15_t)0xAA0A, + (q15_t)0xA57D, (q15_t)0xA57D, (q15_t)0xAA0A, (q15_t)0xA128, + (q15_t)0xAECC, (q15_t)0x9D0D, (q15_t)0xB3C0, (q15_t)0x9930, + (q15_t)0xB8E3, (q15_t)0x9592, (q15_t)0xBE31, (q15_t)0x9235, + (q15_t)0xC3A9, (q15_t)0x8F1D, (q15_t)0xC945, (q15_t)0x8C4A, + (q15_t)0xCF04, (q15_t)0x89BE, (q15_t)0xD4E0, (q15_t)0x877B, + (q15_t)0xDAD7, (q15_t)0x8582, (q15_t)0xE0E6, (q15_t)0x83D6, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xED37, (q15_t)0x8162, + (q15_t)0xF374, (q15_t)0x809D, (q15_t)0xF9B8, (q15_t)0x8027 +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 256, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_256_q15[384] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7FF6, (q15_t)0x0324, + (q15_t)0x7FD8, (q15_t)0x0647, (q15_t)0x7FA7, (q15_t)0x096A, + (q15_t)0x7F62, (q15_t)0x0C8B, (q15_t)0x7F09, (q15_t)0x0FAB, + (q15_t)0x7E9D, (q15_t)0x12C8, (q15_t)0x7E1D, (q15_t)0x15E2, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7CE3, (q15_t)0x1C0B, + (q15_t)0x7C29, (q15_t)0x1F19, (q15_t)0x7B5D, (q15_t)0x2223, + (q15_t)0x7A7D, (q15_t)0x2528, (q15_t)0x798A, (q15_t)0x2826, + (q15_t)0x7884, (q15_t)0x2B1F, (q15_t)0x776C, (q15_t)0x2E11, + (q15_t)0x7641, (q15_t)0x30FB, (q15_t)0x7504, (q15_t)0x33DE, + (q15_t)0x73B5, (q15_t)0x36BA, (q15_t)0x7255, (q15_t)0x398C, + (q15_t)0x70E2, (q15_t)0x3C56, (q15_t)0x6F5F, (q15_t)0x3F17, + (q15_t)0x6DCA, (q15_t)0x41CE, (q15_t)0x6C24, (q15_t)0x447A, + (q15_t)0x6A6D, (q15_t)0x471C, (q15_t)0x68A6, (q15_t)0x49B4, + (q15_t)0x66CF, (q15_t)0x4C3F, (q15_t)0x64E8, (q15_t)0x4EBF, + (q15_t)0x62F2, (q15_t)0x5133, (q15_t)0x60EC, (q15_t)0x539B, + (q15_t)0x5ED7, (q15_t)0x55F5, (q15_t)0x5CB4, (q15_t)0x5842, + (q15_t)0x5A82, (q15_t)0x5A82, (q15_t)0x5842, (q15_t)0x5CB4, + (q15_t)0x55F5, (q15_t)0x5ED7, (q15_t)0x539B, (q15_t)0x60EC, + (q15_t)0x5133, (q15_t)0x62F2, (q15_t)0x4EBF, (q15_t)0x64E8, + (q15_t)0x4C3F, (q15_t)0x66CF, (q15_t)0x49B4, (q15_t)0x68A6, + (q15_t)0x471C, (q15_t)0x6A6D, (q15_t)0x447A, (q15_t)0x6C24, + (q15_t)0x41CE, (q15_t)0x6DCA, (q15_t)0x3F17, (q15_t)0x6F5F, + (q15_t)0x3C56, (q15_t)0x70E2, (q15_t)0x398C, (q15_t)0x7255, + (q15_t)0x36BA, (q15_t)0x73B5, (q15_t)0x33DE, (q15_t)0x7504, + (q15_t)0x30FB, (q15_t)0x7641, (q15_t)0x2E11, (q15_t)0x776C, + (q15_t)0x2B1F, (q15_t)0x7884, (q15_t)0x2826, (q15_t)0x798A, + (q15_t)0x2528, (q15_t)0x7A7D, (q15_t)0x2223, (q15_t)0x7B5D, + (q15_t)0x1F19, (q15_t)0x7C29, (q15_t)0x1C0B, (q15_t)0x7CE3, + (q15_t)0x18F8, (q15_t)0x7D8A, (q15_t)0x15E2, (q15_t)0x7E1D, + (q15_t)0x12C8, (q15_t)0x7E9D, (q15_t)0x0FAB, (q15_t)0x7F09, + (q15_t)0x0C8B, (q15_t)0x7F62, (q15_t)0x096A, (q15_t)0x7FA7, + (q15_t)0x0647, (q15_t)0x7FD8, (q15_t)0x0324, (q15_t)0x7FF6, + (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0xFCDB, (q15_t)0x7FF6, + (q15_t)0xF9B8, (q15_t)0x7FD8, (q15_t)0xF695, (q15_t)0x7FA7, + (q15_t)0xF374, (q15_t)0x7F62, (q15_t)0xF054, (q15_t)0x7F09, + (q15_t)0xED37, (q15_t)0x7E9D, (q15_t)0xEA1D, (q15_t)0x7E1D, + (q15_t)0xE707, (q15_t)0x7D8A, (q15_t)0xE3F4, (q15_t)0x7CE3, + (q15_t)0xE0E6, (q15_t)0x7C29, (q15_t)0xDDDC, (q15_t)0x7B5D, + (q15_t)0xDAD7, (q15_t)0x7A7D, (q15_t)0xD7D9, (q15_t)0x798A, + (q15_t)0xD4E0, (q15_t)0x7884, (q15_t)0xD1EE, (q15_t)0x776C, + (q15_t)0xCF04, (q15_t)0x7641, (q15_t)0xCC21, (q15_t)0x7504, + (q15_t)0xC945, (q15_t)0x73B5, (q15_t)0xC673, (q15_t)0x7255, + (q15_t)0xC3A9, (q15_t)0x70E2, (q15_t)0xC0E8, (q15_t)0x6F5F, + (q15_t)0xBE31, (q15_t)0x6DCA, (q15_t)0xBB85, (q15_t)0x6C24, + (q15_t)0xB8E3, (q15_t)0x6A6D, (q15_t)0xB64B, (q15_t)0x68A6, + (q15_t)0xB3C0, (q15_t)0x66CF, (q15_t)0xB140, (q15_t)0x64E8, + (q15_t)0xAECC, (q15_t)0x62F2, (q15_t)0xAC64, (q15_t)0x60EC, + (q15_t)0xAA0A, (q15_t)0x5ED7, (q15_t)0xA7BD, (q15_t)0x5CB4, + (q15_t)0xA57D, (q15_t)0x5A82, (q15_t)0xA34B, (q15_t)0x5842, + (q15_t)0xA128, (q15_t)0x55F5, (q15_t)0x9F13, (q15_t)0x539B, + (q15_t)0x9D0D, (q15_t)0x5133, (q15_t)0x9B17, (q15_t)0x4EBF, + (q15_t)0x9930, (q15_t)0x4C3F, (q15_t)0x9759, (q15_t)0x49B4, + (q15_t)0x9592, (q15_t)0x471C, (q15_t)0x93DB, (q15_t)0x447A, + (q15_t)0x9235, (q15_t)0x41CE, (q15_t)0x90A0, (q15_t)0x3F17, + (q15_t)0x8F1D, (q15_t)0x3C56, (q15_t)0x8DAA, (q15_t)0x398C, + (q15_t)0x8C4A, (q15_t)0x36BA, (q15_t)0x8AFB, (q15_t)0x33DE, + (q15_t)0x89BE, (q15_t)0x30FB, (q15_t)0x8893, (q15_t)0x2E11, + (q15_t)0x877B, (q15_t)0x2B1F, (q15_t)0x8675, (q15_t)0x2826, + (q15_t)0x8582, (q15_t)0x2528, (q15_t)0x84A2, (q15_t)0x2223, + (q15_t)0x83D6, (q15_t)0x1F19, (q15_t)0x831C, (q15_t)0x1C0B, + (q15_t)0x8275, (q15_t)0x18F8, (q15_t)0x81E2, (q15_t)0x15E2, + (q15_t)0x8162, (q15_t)0x12C8, (q15_t)0x80F6, (q15_t)0x0FAB, + (q15_t)0x809D, (q15_t)0x0C8B, (q15_t)0x8058, (q15_t)0x096A, + (q15_t)0x8027, (q15_t)0x0647, (q15_t)0x8009, (q15_t)0x0324, + (q15_t)0x8000, (q15_t)0x0000, (q15_t)0x8009, (q15_t)0xFCDB, + (q15_t)0x8027, (q15_t)0xF9B8, (q15_t)0x8058, (q15_t)0xF695, + (q15_t)0x809D, (q15_t)0xF374, (q15_t)0x80F6, (q15_t)0xF054, + (q15_t)0x8162, (q15_t)0xED37, (q15_t)0x81E2, (q15_t)0xEA1D, + (q15_t)0x8275, (q15_t)0xE707, (q15_t)0x831C, (q15_t)0xE3F4, + (q15_t)0x83D6, (q15_t)0xE0E6, (q15_t)0x84A2, (q15_t)0xDDDC, + (q15_t)0x8582, (q15_t)0xDAD7, (q15_t)0x8675, (q15_t)0xD7D9, + (q15_t)0x877B, (q15_t)0xD4E0, (q15_t)0x8893, (q15_t)0xD1EE, + (q15_t)0x89BE, (q15_t)0xCF04, (q15_t)0x8AFB, (q15_t)0xCC21, + (q15_t)0x8C4A, (q15_t)0xC945, (q15_t)0x8DAA, (q15_t)0xC673, + (q15_t)0x8F1D, (q15_t)0xC3A9, (q15_t)0x90A0, (q15_t)0xC0E8, + (q15_t)0x9235, (q15_t)0xBE31, (q15_t)0x93DB, (q15_t)0xBB85, + (q15_t)0x9592, (q15_t)0xB8E3, (q15_t)0x9759, (q15_t)0xB64B, + (q15_t)0x9930, (q15_t)0xB3C0, (q15_t)0x9B17, (q15_t)0xB140, + (q15_t)0x9D0D, (q15_t)0xAECC, (q15_t)0x9F13, (q15_t)0xAC64, + (q15_t)0xA128, (q15_t)0xAA0A, (q15_t)0xA34B, (q15_t)0xA7BD, + (q15_t)0xA57D, (q15_t)0xA57D, (q15_t)0xA7BD, (q15_t)0xA34B, + (q15_t)0xAA0A, (q15_t)0xA128, (q15_t)0xAC64, (q15_t)0x9F13, + (q15_t)0xAECC, (q15_t)0x9D0D, (q15_t)0xB140, (q15_t)0x9B17, + (q15_t)0xB3C0, (q15_t)0x9930, (q15_t)0xB64B, (q15_t)0x9759, + (q15_t)0xB8E3, (q15_t)0x9592, (q15_t)0xBB85, (q15_t)0x93DB, + (q15_t)0xBE31, (q15_t)0x9235, (q15_t)0xC0E8, (q15_t)0x90A0, + (q15_t)0xC3A9, (q15_t)0x8F1D, (q15_t)0xC673, (q15_t)0x8DAA, + (q15_t)0xC945, (q15_t)0x8C4A, (q15_t)0xCC21, (q15_t)0x8AFB, + (q15_t)0xCF04, (q15_t)0x89BE, (q15_t)0xD1EE, (q15_t)0x8893, + (q15_t)0xD4E0, (q15_t)0x877B, (q15_t)0xD7D9, (q15_t)0x8675, + (q15_t)0xDAD7, (q15_t)0x8582, (q15_t)0xDDDC, (q15_t)0x84A2, + (q15_t)0xE0E6, (q15_t)0x83D6, (q15_t)0xE3F4, (q15_t)0x831C, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xEA1D, (q15_t)0x81E2, + (q15_t)0xED37, (q15_t)0x8162, (q15_t)0xF054, (q15_t)0x80F6, + (q15_t)0xF374, (q15_t)0x809D, (q15_t)0xF695, (q15_t)0x8058, + (q15_t)0xF9B8, (q15_t)0x8027, (q15_t)0xFCDB, (q15_t)0x8009 +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 512, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_512_q15[768] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7FFD, (q15_t)0x0192, + (q15_t)0x7FF6, (q15_t)0x0324, (q15_t)0x7FE9, (q15_t)0x04B6, + (q15_t)0x7FD8, (q15_t)0x0647, (q15_t)0x7FC2, (q15_t)0x07D9, + (q15_t)0x7FA7, (q15_t)0x096A, (q15_t)0x7F87, (q15_t)0x0AFB, + (q15_t)0x7F62, (q15_t)0x0C8B, (q15_t)0x7F38, (q15_t)0x0E1B, + (q15_t)0x7F09, (q15_t)0x0FAB, (q15_t)0x7ED5, (q15_t)0x1139, + (q15_t)0x7E9D, (q15_t)0x12C8, (q15_t)0x7E5F, (q15_t)0x1455, + (q15_t)0x7E1D, (q15_t)0x15E2, (q15_t)0x7DD6, (q15_t)0x176D, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7D39, (q15_t)0x1A82, + (q15_t)0x7CE3, (q15_t)0x1C0B, (q15_t)0x7C89, (q15_t)0x1D93, + (q15_t)0x7C29, (q15_t)0x1F19, (q15_t)0x7BC5, (q15_t)0x209F, + (q15_t)0x7B5D, (q15_t)0x2223, (q15_t)0x7AEF, (q15_t)0x23A6, + (q15_t)0x7A7D, (q15_t)0x2528, (q15_t)0x7A05, (q15_t)0x26A8, + (q15_t)0x798A, (q15_t)0x2826, (q15_t)0x7909, (q15_t)0x29A3, + (q15_t)0x7884, (q15_t)0x2B1F, (q15_t)0x77FA, (q15_t)0x2C98, + (q15_t)0x776C, (q15_t)0x2E11, (q15_t)0x76D9, (q15_t)0x2F87, + (q15_t)0x7641, (q15_t)0x30FB, (q15_t)0x75A5, (q15_t)0x326E, + (q15_t)0x7504, (q15_t)0x33DE, (q15_t)0x745F, (q15_t)0x354D, + (q15_t)0x73B5, (q15_t)0x36BA, (q15_t)0x7307, (q15_t)0x3824, + (q15_t)0x7255, (q15_t)0x398C, (q15_t)0x719E, (q15_t)0x3AF2, + (q15_t)0x70E2, (q15_t)0x3C56, (q15_t)0x7023, (q15_t)0x3DB8, + (q15_t)0x6F5F, (q15_t)0x3F17, (q15_t)0x6E96, (q15_t)0x4073, + (q15_t)0x6DCA, (q15_t)0x41CE, (q15_t)0x6CF9, (q15_t)0x4325, + (q15_t)0x6C24, (q15_t)0x447A, (q15_t)0x6B4A, (q15_t)0x45CD, + (q15_t)0x6A6D, (q15_t)0x471C, (q15_t)0x698C, (q15_t)0x4869, + (q15_t)0x68A6, (q15_t)0x49B4, (q15_t)0x67BD, (q15_t)0x4AFB, + (q15_t)0x66CF, (q15_t)0x4C3F, (q15_t)0x65DD, (q15_t)0x4D81, + (q15_t)0x64E8, (q15_t)0x4EBF, (q15_t)0x63EF, (q15_t)0x4FFB, + (q15_t)0x62F2, (q15_t)0x5133, (q15_t)0x61F1, (q15_t)0x5269, + (q15_t)0x60EC, (q15_t)0x539B, (q15_t)0x5FE3, (q15_t)0x54CA, + (q15_t)0x5ED7, (q15_t)0x55F5, (q15_t)0x5DC7, (q15_t)0x571D, + (q15_t)0x5CB4, (q15_t)0x5842, (q15_t)0x5B9D, (q15_t)0x5964, + (q15_t)0x5A82, (q15_t)0x5A82, (q15_t)0x5964, (q15_t)0x5B9D, + (q15_t)0x5842, (q15_t)0x5CB4, (q15_t)0x571D, (q15_t)0x5DC7, + (q15_t)0x55F5, (q15_t)0x5ED7, (q15_t)0x54CA, (q15_t)0x5FE3, + (q15_t)0x539B, (q15_t)0x60EC, (q15_t)0x5269, (q15_t)0x61F1, + (q15_t)0x5133, (q15_t)0x62F2, (q15_t)0x4FFB, (q15_t)0x63EF, + (q15_t)0x4EBF, (q15_t)0x64E8, (q15_t)0x4D81, (q15_t)0x65DD, + (q15_t)0x4C3F, (q15_t)0x66CF, (q15_t)0x4AFB, (q15_t)0x67BD, + (q15_t)0x49B4, (q15_t)0x68A6, (q15_t)0x4869, (q15_t)0x698C, + (q15_t)0x471C, (q15_t)0x6A6D, (q15_t)0x45CD, (q15_t)0x6B4A, + (q15_t)0x447A, (q15_t)0x6C24, (q15_t)0x4325, (q15_t)0x6CF9, + (q15_t)0x41CE, (q15_t)0x6DCA, (q15_t)0x4073, (q15_t)0x6E96, + (q15_t)0x3F17, (q15_t)0x6F5F, (q15_t)0x3DB8, (q15_t)0x7023, + (q15_t)0x3C56, (q15_t)0x70E2, (q15_t)0x3AF2, (q15_t)0x719E, + (q15_t)0x398C, (q15_t)0x7255, (q15_t)0x3824, (q15_t)0x7307, + (q15_t)0x36BA, (q15_t)0x73B5, (q15_t)0x354D, (q15_t)0x745F, + (q15_t)0x33DE, (q15_t)0x7504, (q15_t)0x326E, (q15_t)0x75A5, + (q15_t)0x30FB, (q15_t)0x7641, (q15_t)0x2F87, (q15_t)0x76D9, + (q15_t)0x2E11, (q15_t)0x776C, (q15_t)0x2C98, (q15_t)0x77FA, + (q15_t)0x2B1F, (q15_t)0x7884, (q15_t)0x29A3, (q15_t)0x7909, + (q15_t)0x2826, (q15_t)0x798A, (q15_t)0x26A8, (q15_t)0x7A05, + (q15_t)0x2528, (q15_t)0x7A7D, (q15_t)0x23A6, (q15_t)0x7AEF, + (q15_t)0x2223, (q15_t)0x7B5D, (q15_t)0x209F, (q15_t)0x7BC5, + (q15_t)0x1F19, (q15_t)0x7C29, (q15_t)0x1D93, (q15_t)0x7C89, + (q15_t)0x1C0B, (q15_t)0x7CE3, (q15_t)0x1A82, (q15_t)0x7D39, + (q15_t)0x18F8, (q15_t)0x7D8A, (q15_t)0x176D, (q15_t)0x7DD6, + (q15_t)0x15E2, (q15_t)0x7E1D, (q15_t)0x1455, (q15_t)0x7E5F, + (q15_t)0x12C8, (q15_t)0x7E9D, (q15_t)0x1139, (q15_t)0x7ED5, + (q15_t)0x0FAB, (q15_t)0x7F09, (q15_t)0x0E1B, (q15_t)0x7F38, + (q15_t)0x0C8B, (q15_t)0x7F62, (q15_t)0x0AFB, (q15_t)0x7F87, + (q15_t)0x096A, (q15_t)0x7FA7, (q15_t)0x07D9, (q15_t)0x7FC2, + (q15_t)0x0647, (q15_t)0x7FD8, (q15_t)0x04B6, (q15_t)0x7FE9, + (q15_t)0x0324, (q15_t)0x7FF6, (q15_t)0x0192, (q15_t)0x7FFD, + (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0xFE6D, (q15_t)0x7FFD, + (q15_t)0xFCDB, (q15_t)0x7FF6, (q15_t)0xFB49, (q15_t)0x7FE9, + (q15_t)0xF9B8, (q15_t)0x7FD8, (q15_t)0xF826, (q15_t)0x7FC2, + (q15_t)0xF695, (q15_t)0x7FA7, (q15_t)0xF504, (q15_t)0x7F87, + (q15_t)0xF374, (q15_t)0x7F62, (q15_t)0xF1E4, (q15_t)0x7F38, + (q15_t)0xF054, (q15_t)0x7F09, (q15_t)0xEEC6, (q15_t)0x7ED5, + (q15_t)0xED37, (q15_t)0x7E9D, (q15_t)0xEBAA, (q15_t)0x7E5F, + (q15_t)0xEA1D, (q15_t)0x7E1D, (q15_t)0xE892, (q15_t)0x7DD6, + (q15_t)0xE707, (q15_t)0x7D8A, (q15_t)0xE57D, (q15_t)0x7D39, + (q15_t)0xE3F4, (q15_t)0x7CE3, (q15_t)0xE26C, (q15_t)0x7C89, + (q15_t)0xE0E6, (q15_t)0x7C29, (q15_t)0xDF60, (q15_t)0x7BC5, + (q15_t)0xDDDC, (q15_t)0x7B5D, (q15_t)0xDC59, (q15_t)0x7AEF, + (q15_t)0xDAD7, (q15_t)0x7A7D, (q15_t)0xD957, (q15_t)0x7A05, + (q15_t)0xD7D9, (q15_t)0x798A, (q15_t)0xD65C, (q15_t)0x7909, + (q15_t)0xD4E0, (q15_t)0x7884, (q15_t)0xD367, (q15_t)0x77FA, + (q15_t)0xD1EE, (q15_t)0x776C, (q15_t)0xD078, (q15_t)0x76D9, + (q15_t)0xCF04, (q15_t)0x7641, (q15_t)0xCD91, (q15_t)0x75A5, + (q15_t)0xCC21, (q15_t)0x7504, (q15_t)0xCAB2, (q15_t)0x745F, + (q15_t)0xC945, (q15_t)0x73B5, (q15_t)0xC7DB, (q15_t)0x7307, + (q15_t)0xC673, (q15_t)0x7255, (q15_t)0xC50D, (q15_t)0x719E, + (q15_t)0xC3A9, (q15_t)0x70E2, (q15_t)0xC247, (q15_t)0x7023, + (q15_t)0xC0E8, (q15_t)0x6F5F, (q15_t)0xBF8C, (q15_t)0x6E96, + (q15_t)0xBE31, (q15_t)0x6DCA, (q15_t)0xBCDA, (q15_t)0x6CF9, + (q15_t)0xBB85, (q15_t)0x6C24, (q15_t)0xBA32, (q15_t)0x6B4A, + (q15_t)0xB8E3, (q15_t)0x6A6D, (q15_t)0xB796, (q15_t)0x698C, + (q15_t)0xB64B, (q15_t)0x68A6, (q15_t)0xB504, (q15_t)0x67BD, + (q15_t)0xB3C0, (q15_t)0x66CF, (q15_t)0xB27E, (q15_t)0x65DD, + (q15_t)0xB140, (q15_t)0x64E8, (q15_t)0xB004, (q15_t)0x63EF, + (q15_t)0xAECC, (q15_t)0x62F2, (q15_t)0xAD96, (q15_t)0x61F1, + (q15_t)0xAC64, (q15_t)0x60EC, (q15_t)0xAB35, (q15_t)0x5FE3, + (q15_t)0xAA0A, (q15_t)0x5ED7, (q15_t)0xA8E2, (q15_t)0x5DC7, + (q15_t)0xA7BD, (q15_t)0x5CB4, (q15_t)0xA69B, (q15_t)0x5B9D, + (q15_t)0xA57D, (q15_t)0x5A82, (q15_t)0xA462, (q15_t)0x5964, + (q15_t)0xA34B, (q15_t)0x5842, (q15_t)0xA238, (q15_t)0x571D, + (q15_t)0xA128, (q15_t)0x55F5, (q15_t)0xA01C, (q15_t)0x54CA, + (q15_t)0x9F13, (q15_t)0x539B, (q15_t)0x9E0E, (q15_t)0x5269, + (q15_t)0x9D0D, (q15_t)0x5133, (q15_t)0x9C10, (q15_t)0x4FFB, + (q15_t)0x9B17, (q15_t)0x4EBF, (q15_t)0x9A22, (q15_t)0x4D81, + (q15_t)0x9930, (q15_t)0x4C3F, (q15_t)0x9842, (q15_t)0x4AFB, + (q15_t)0x9759, (q15_t)0x49B4, (q15_t)0x9673, (q15_t)0x4869, + (q15_t)0x9592, (q15_t)0x471C, (q15_t)0x94B5, (q15_t)0x45CD, + (q15_t)0x93DB, (q15_t)0x447A, (q15_t)0x9306, (q15_t)0x4325, + (q15_t)0x9235, (q15_t)0x41CE, (q15_t)0x9169, (q15_t)0x4073, + (q15_t)0x90A0, (q15_t)0x3F17, (q15_t)0x8FDC, (q15_t)0x3DB8, + (q15_t)0x8F1D, (q15_t)0x3C56, (q15_t)0x8E61, (q15_t)0x3AF2, + (q15_t)0x8DAA, (q15_t)0x398C, (q15_t)0x8CF8, (q15_t)0x3824, + (q15_t)0x8C4A, (q15_t)0x36BA, (q15_t)0x8BA0, (q15_t)0x354D, + (q15_t)0x8AFB, (q15_t)0x33DE, (q15_t)0x8A5A, (q15_t)0x326E, + (q15_t)0x89BE, (q15_t)0x30FB, (q15_t)0x8926, (q15_t)0x2F87, + (q15_t)0x8893, (q15_t)0x2E11, (q15_t)0x8805, (q15_t)0x2C98, + (q15_t)0x877B, (q15_t)0x2B1F, (q15_t)0x86F6, (q15_t)0x29A3, + (q15_t)0x8675, (q15_t)0x2826, (q15_t)0x85FA, (q15_t)0x26A8, + (q15_t)0x8582, (q15_t)0x2528, (q15_t)0x8510, (q15_t)0x23A6, + (q15_t)0x84A2, (q15_t)0x2223, (q15_t)0x843A, (q15_t)0x209F, + (q15_t)0x83D6, (q15_t)0x1F19, (q15_t)0x8376, (q15_t)0x1D93, + (q15_t)0x831C, (q15_t)0x1C0B, (q15_t)0x82C6, (q15_t)0x1A82, + (q15_t)0x8275, (q15_t)0x18F8, (q15_t)0x8229, (q15_t)0x176D, + (q15_t)0x81E2, (q15_t)0x15E2, (q15_t)0x81A0, (q15_t)0x1455, + (q15_t)0x8162, (q15_t)0x12C8, (q15_t)0x812A, (q15_t)0x1139, + (q15_t)0x80F6, (q15_t)0x0FAB, (q15_t)0x80C7, (q15_t)0x0E1B, + (q15_t)0x809D, (q15_t)0x0C8B, (q15_t)0x8078, (q15_t)0x0AFB, + (q15_t)0x8058, (q15_t)0x096A, (q15_t)0x803D, (q15_t)0x07D9, + (q15_t)0x8027, (q15_t)0x0647, (q15_t)0x8016, (q15_t)0x04B6, + (q15_t)0x8009, (q15_t)0x0324, (q15_t)0x8002, (q15_t)0x0192, + (q15_t)0x8000, (q15_t)0x0000, (q15_t)0x8002, (q15_t)0xFE6D, + (q15_t)0x8009, (q15_t)0xFCDB, (q15_t)0x8016, (q15_t)0xFB49, + (q15_t)0x8027, (q15_t)0xF9B8, (q15_t)0x803D, (q15_t)0xF826, + (q15_t)0x8058, (q15_t)0xF695, (q15_t)0x8078, (q15_t)0xF504, + (q15_t)0x809D, (q15_t)0xF374, (q15_t)0x80C7, (q15_t)0xF1E4, + (q15_t)0x80F6, (q15_t)0xF054, (q15_t)0x812A, (q15_t)0xEEC6, + (q15_t)0x8162, (q15_t)0xED37, (q15_t)0x81A0, (q15_t)0xEBAA, + (q15_t)0x81E2, (q15_t)0xEA1D, (q15_t)0x8229, (q15_t)0xE892, + (q15_t)0x8275, (q15_t)0xE707, (q15_t)0x82C6, (q15_t)0xE57D, + (q15_t)0x831C, (q15_t)0xE3F4, (q15_t)0x8376, (q15_t)0xE26C, + (q15_t)0x83D6, (q15_t)0xE0E6, (q15_t)0x843A, (q15_t)0xDF60, + (q15_t)0x84A2, (q15_t)0xDDDC, (q15_t)0x8510, (q15_t)0xDC59, + (q15_t)0x8582, (q15_t)0xDAD7, (q15_t)0x85FA, (q15_t)0xD957, + (q15_t)0x8675, (q15_t)0xD7D9, (q15_t)0x86F6, (q15_t)0xD65C, + (q15_t)0x877B, (q15_t)0xD4E0, (q15_t)0x8805, (q15_t)0xD367, + (q15_t)0x8893, (q15_t)0xD1EE, (q15_t)0x8926, (q15_t)0xD078, + (q15_t)0x89BE, (q15_t)0xCF04, (q15_t)0x8A5A, (q15_t)0xCD91, + (q15_t)0x8AFB, (q15_t)0xCC21, (q15_t)0x8BA0, (q15_t)0xCAB2, + (q15_t)0x8C4A, (q15_t)0xC945, (q15_t)0x8CF8, (q15_t)0xC7DB, + (q15_t)0x8DAA, (q15_t)0xC673, (q15_t)0x8E61, (q15_t)0xC50D, + (q15_t)0x8F1D, (q15_t)0xC3A9, (q15_t)0x8FDC, (q15_t)0xC247, + (q15_t)0x90A0, (q15_t)0xC0E8, (q15_t)0x9169, (q15_t)0xBF8C, + (q15_t)0x9235, (q15_t)0xBE31, (q15_t)0x9306, (q15_t)0xBCDA, + (q15_t)0x93DB, (q15_t)0xBB85, (q15_t)0x94B5, (q15_t)0xBA32, + (q15_t)0x9592, (q15_t)0xB8E3, (q15_t)0x9673, (q15_t)0xB796, + (q15_t)0x9759, (q15_t)0xB64B, (q15_t)0x9842, (q15_t)0xB504, + (q15_t)0x9930, (q15_t)0xB3C0, (q15_t)0x9A22, (q15_t)0xB27E, + (q15_t)0x9B17, (q15_t)0xB140, (q15_t)0x9C10, (q15_t)0xB004, + (q15_t)0x9D0D, (q15_t)0xAECC, (q15_t)0x9E0E, (q15_t)0xAD96, + (q15_t)0x9F13, (q15_t)0xAC64, (q15_t)0xA01C, (q15_t)0xAB35, + (q15_t)0xA128, (q15_t)0xAA0A, (q15_t)0xA238, (q15_t)0xA8E2, + (q15_t)0xA34B, (q15_t)0xA7BD, (q15_t)0xA462, (q15_t)0xA69B, + (q15_t)0xA57D, (q15_t)0xA57D, (q15_t)0xA69B, (q15_t)0xA462, + (q15_t)0xA7BD, (q15_t)0xA34B, (q15_t)0xA8E2, (q15_t)0xA238, + (q15_t)0xAA0A, (q15_t)0xA128, (q15_t)0xAB35, (q15_t)0xA01C, + (q15_t)0xAC64, (q15_t)0x9F13, (q15_t)0xAD96, (q15_t)0x9E0E, + (q15_t)0xAECC, (q15_t)0x9D0D, (q15_t)0xB004, (q15_t)0x9C10, + (q15_t)0xB140, (q15_t)0x9B17, (q15_t)0xB27E, (q15_t)0x9A22, + (q15_t)0xB3C0, (q15_t)0x9930, (q15_t)0xB504, (q15_t)0x9842, + (q15_t)0xB64B, (q15_t)0x9759, (q15_t)0xB796, (q15_t)0x9673, + (q15_t)0xB8E3, (q15_t)0x9592, (q15_t)0xBA32, (q15_t)0x94B5, + (q15_t)0xBB85, (q15_t)0x93DB, (q15_t)0xBCDA, (q15_t)0x9306, + (q15_t)0xBE31, (q15_t)0x9235, (q15_t)0xBF8C, (q15_t)0x9169, + (q15_t)0xC0E8, (q15_t)0x90A0, (q15_t)0xC247, (q15_t)0x8FDC, + (q15_t)0xC3A9, (q15_t)0x8F1D, (q15_t)0xC50D, (q15_t)0x8E61, + (q15_t)0xC673, (q15_t)0x8DAA, (q15_t)0xC7DB, (q15_t)0x8CF8, + (q15_t)0xC945, (q15_t)0x8C4A, (q15_t)0xCAB2, (q15_t)0x8BA0, + (q15_t)0xCC21, (q15_t)0x8AFB, (q15_t)0xCD91, (q15_t)0x8A5A, + (q15_t)0xCF04, (q15_t)0x89BE, (q15_t)0xD078, (q15_t)0x8926, + (q15_t)0xD1EE, (q15_t)0x8893, (q15_t)0xD367, (q15_t)0x8805, + (q15_t)0xD4E0, (q15_t)0x877B, (q15_t)0xD65C, (q15_t)0x86F6, + (q15_t)0xD7D9, (q15_t)0x8675, (q15_t)0xD957, (q15_t)0x85FA, + (q15_t)0xDAD7, (q15_t)0x8582, (q15_t)0xDC59, (q15_t)0x8510, + (q15_t)0xDDDC, (q15_t)0x84A2, (q15_t)0xDF60, (q15_t)0x843A, + (q15_t)0xE0E6, (q15_t)0x83D6, (q15_t)0xE26C, (q15_t)0x8376, + (q15_t)0xE3F4, (q15_t)0x831C, (q15_t)0xE57D, (q15_t)0x82C6, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xE892, (q15_t)0x8229, + (q15_t)0xEA1D, (q15_t)0x81E2, (q15_t)0xEBAA, (q15_t)0x81A0, + (q15_t)0xED37, (q15_t)0x8162, (q15_t)0xEEC6, (q15_t)0x812A, + (q15_t)0xF054, (q15_t)0x80F6, (q15_t)0xF1E4, (q15_t)0x80C7, + (q15_t)0xF374, (q15_t)0x809D, (q15_t)0xF504, (q15_t)0x8078, + (q15_t)0xF695, (q15_t)0x8058, (q15_t)0xF826, (q15_t)0x803D, + (q15_t)0xF9B8, (q15_t)0x8027, (q15_t)0xFB49, (q15_t)0x8016, + (q15_t)0xFCDB, (q15_t)0x8009, (q15_t)0xFE6D, (q15_t)0x8002 +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 1024, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + + */ +const q15_t twiddleCoef_1024_q15[1536] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0x00C9, + (q15_t)0x7FFD, (q15_t)0x0192, (q15_t)0x7FFA, (q15_t)0x025B, + (q15_t)0x7FF6, (q15_t)0x0324, (q15_t)0x7FF0, (q15_t)0x03ED, + (q15_t)0x7FE9, (q15_t)0x04B6, (q15_t)0x7FE1, (q15_t)0x057F, + (q15_t)0x7FD8, (q15_t)0x0647, (q15_t)0x7FCE, (q15_t)0x0710, + (q15_t)0x7FC2, (q15_t)0x07D9, (q15_t)0x7FB5, (q15_t)0x08A2, + (q15_t)0x7FA7, (q15_t)0x096A, (q15_t)0x7F97, (q15_t)0x0A33, + (q15_t)0x7F87, (q15_t)0x0AFB, (q15_t)0x7F75, (q15_t)0x0BC3, + (q15_t)0x7F62, (q15_t)0x0C8B, (q15_t)0x7F4D, (q15_t)0x0D53, + (q15_t)0x7F38, (q15_t)0x0E1B, (q15_t)0x7F21, (q15_t)0x0EE3, + (q15_t)0x7F09, (q15_t)0x0FAB, (q15_t)0x7EF0, (q15_t)0x1072, + (q15_t)0x7ED5, (q15_t)0x1139, (q15_t)0x7EBA, (q15_t)0x1201, + (q15_t)0x7E9D, (q15_t)0x12C8, (q15_t)0x7E7F, (q15_t)0x138E, + (q15_t)0x7E5F, (q15_t)0x1455, (q15_t)0x7E3F, (q15_t)0x151B, + (q15_t)0x7E1D, (q15_t)0x15E2, (q15_t)0x7DFA, (q15_t)0x16A8, + (q15_t)0x7DD6, (q15_t)0x176D, (q15_t)0x7DB0, (q15_t)0x1833, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7D62, (q15_t)0x19BD, + (q15_t)0x7D39, (q15_t)0x1A82, (q15_t)0x7D0F, (q15_t)0x1B47, + (q15_t)0x7CE3, (q15_t)0x1C0B, (q15_t)0x7CB7, (q15_t)0x1CCF, + (q15_t)0x7C89, (q15_t)0x1D93, (q15_t)0x7C5A, (q15_t)0x1E56, + (q15_t)0x7C29, (q15_t)0x1F19, (q15_t)0x7BF8, (q15_t)0x1FDC, + (q15_t)0x7BC5, (q15_t)0x209F, (q15_t)0x7B92, (q15_t)0x2161, + (q15_t)0x7B5D, (q15_t)0x2223, (q15_t)0x7B26, (q15_t)0x22E5, + (q15_t)0x7AEF, (q15_t)0x23A6, (q15_t)0x7AB6, (q15_t)0x2467, + (q15_t)0x7A7D, (q15_t)0x2528, (q15_t)0x7A42, (q15_t)0x25E8, + (q15_t)0x7A05, (q15_t)0x26A8, (q15_t)0x79C8, (q15_t)0x2767, + (q15_t)0x798A, (q15_t)0x2826, (q15_t)0x794A, (q15_t)0x28E5, + (q15_t)0x7909, (q15_t)0x29A3, (q15_t)0x78C7, (q15_t)0x2A61, + (q15_t)0x7884, (q15_t)0x2B1F, (q15_t)0x7840, (q15_t)0x2BDC, + (q15_t)0x77FA, (q15_t)0x2C98, (q15_t)0x77B4, (q15_t)0x2D55, + (q15_t)0x776C, (q15_t)0x2E11, (q15_t)0x7723, (q15_t)0x2ECC, + (q15_t)0x76D9, (q15_t)0x2F87, (q15_t)0x768E, (q15_t)0x3041, + (q15_t)0x7641, (q15_t)0x30FB, (q15_t)0x75F4, (q15_t)0x31B5, + (q15_t)0x75A5, (q15_t)0x326E, (q15_t)0x7555, (q15_t)0x3326, + (q15_t)0x7504, (q15_t)0x33DE, (q15_t)0x74B2, (q15_t)0x3496, + (q15_t)0x745F, (q15_t)0x354D, (q15_t)0x740B, (q15_t)0x3604, + (q15_t)0x73B5, (q15_t)0x36BA, (q15_t)0x735F, (q15_t)0x376F, + (q15_t)0x7307, (q15_t)0x3824, (q15_t)0x72AF, (q15_t)0x38D8, + (q15_t)0x7255, (q15_t)0x398C, (q15_t)0x71FA, (q15_t)0x3A40, + (q15_t)0x719E, (q15_t)0x3AF2, (q15_t)0x7141, (q15_t)0x3BA5, + (q15_t)0x70E2, (q15_t)0x3C56, (q15_t)0x7083, (q15_t)0x3D07, + (q15_t)0x7023, (q15_t)0x3DB8, (q15_t)0x6FC1, (q15_t)0x3E68, + (q15_t)0x6F5F, (q15_t)0x3F17, (q15_t)0x6EFB, (q15_t)0x3FC5, + (q15_t)0x6E96, (q15_t)0x4073, (q15_t)0x6E30, (q15_t)0x4121, + (q15_t)0x6DCA, (q15_t)0x41CE, (q15_t)0x6D62, (q15_t)0x427A, + (q15_t)0x6CF9, (q15_t)0x4325, (q15_t)0x6C8F, (q15_t)0x43D0, + (q15_t)0x6C24, (q15_t)0x447A, (q15_t)0x6BB8, (q15_t)0x4524, + (q15_t)0x6B4A, (q15_t)0x45CD, (q15_t)0x6ADC, (q15_t)0x4675, + (q15_t)0x6A6D, (q15_t)0x471C, (q15_t)0x69FD, (q15_t)0x47C3, + (q15_t)0x698C, (q15_t)0x4869, (q15_t)0x6919, (q15_t)0x490F, + (q15_t)0x68A6, (q15_t)0x49B4, (q15_t)0x6832, (q15_t)0x4A58, + (q15_t)0x67BD, (q15_t)0x4AFB, (q15_t)0x6746, (q15_t)0x4B9E, + (q15_t)0x66CF, (q15_t)0x4C3F, (q15_t)0x6657, (q15_t)0x4CE1, + (q15_t)0x65DD, (q15_t)0x4D81, (q15_t)0x6563, (q15_t)0x4E21, + (q15_t)0x64E8, (q15_t)0x4EBF, (q15_t)0x646C, (q15_t)0x4F5E, + (q15_t)0x63EF, (q15_t)0x4FFB, (q15_t)0x6371, (q15_t)0x5097, + (q15_t)0x62F2, (q15_t)0x5133, (q15_t)0x6271, (q15_t)0x51CE, + (q15_t)0x61F1, (q15_t)0x5269, (q15_t)0x616F, (q15_t)0x5302, + (q15_t)0x60EC, (q15_t)0x539B, (q15_t)0x6068, (q15_t)0x5433, + (q15_t)0x5FE3, (q15_t)0x54CA, (q15_t)0x5F5E, (q15_t)0x5560, + (q15_t)0x5ED7, (q15_t)0x55F5, (q15_t)0x5E50, (q15_t)0x568A, + (q15_t)0x5DC7, (q15_t)0x571D, (q15_t)0x5D3E, (q15_t)0x57B0, + (q15_t)0x5CB4, (q15_t)0x5842, (q15_t)0x5C29, (q15_t)0x58D4, + (q15_t)0x5B9D, (q15_t)0x5964, (q15_t)0x5B10, (q15_t)0x59F3, + (q15_t)0x5A82, (q15_t)0x5A82, (q15_t)0x59F3, (q15_t)0x5B10, + (q15_t)0x5964, (q15_t)0x5B9D, (q15_t)0x58D4, (q15_t)0x5C29, + (q15_t)0x5842, (q15_t)0x5CB4, (q15_t)0x57B0, (q15_t)0x5D3E, + (q15_t)0x571D, (q15_t)0x5DC7, (q15_t)0x568A, (q15_t)0x5E50, + (q15_t)0x55F5, (q15_t)0x5ED7, (q15_t)0x5560, (q15_t)0x5F5E, + (q15_t)0x54CA, (q15_t)0x5FE3, (q15_t)0x5433, (q15_t)0x6068, + (q15_t)0x539B, (q15_t)0x60EC, (q15_t)0x5302, (q15_t)0x616F, + (q15_t)0x5269, (q15_t)0x61F1, (q15_t)0x51CE, (q15_t)0x6271, + (q15_t)0x5133, (q15_t)0x62F2, (q15_t)0x5097, (q15_t)0x6371, + (q15_t)0x4FFB, (q15_t)0x63EF, (q15_t)0x4F5E, (q15_t)0x646C, + (q15_t)0x4EBF, (q15_t)0x64E8, (q15_t)0x4E21, (q15_t)0x6563, + (q15_t)0x4D81, (q15_t)0x65DD, (q15_t)0x4CE1, (q15_t)0x6657, + (q15_t)0x4C3F, (q15_t)0x66CF, (q15_t)0x4B9E, (q15_t)0x6746, + (q15_t)0x4AFB, (q15_t)0x67BD, (q15_t)0x4A58, (q15_t)0x6832, + (q15_t)0x49B4, (q15_t)0x68A6, (q15_t)0x490F, (q15_t)0x6919, + (q15_t)0x4869, (q15_t)0x698C, (q15_t)0x47C3, (q15_t)0x69FD, + (q15_t)0x471C, (q15_t)0x6A6D, (q15_t)0x4675, (q15_t)0x6ADC, + (q15_t)0x45CD, (q15_t)0x6B4A, (q15_t)0x4524, (q15_t)0x6BB8, + (q15_t)0x447A, (q15_t)0x6C24, (q15_t)0x43D0, (q15_t)0x6C8F, + (q15_t)0x4325, (q15_t)0x6CF9, (q15_t)0x427A, (q15_t)0x6D62, + (q15_t)0x41CE, (q15_t)0x6DCA, (q15_t)0x4121, (q15_t)0x6E30, + (q15_t)0x4073, (q15_t)0x6E96, (q15_t)0x3FC5, (q15_t)0x6EFB, + (q15_t)0x3F17, (q15_t)0x6F5F, (q15_t)0x3E68, (q15_t)0x6FC1, + (q15_t)0x3DB8, (q15_t)0x7023, (q15_t)0x3D07, (q15_t)0x7083, + (q15_t)0x3C56, (q15_t)0x70E2, (q15_t)0x3BA5, (q15_t)0x7141, + (q15_t)0x3AF2, (q15_t)0x719E, (q15_t)0x3A40, (q15_t)0x71FA, + (q15_t)0x398C, (q15_t)0x7255, (q15_t)0x38D8, (q15_t)0x72AF, + (q15_t)0x3824, (q15_t)0x7307, (q15_t)0x376F, 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(q15_t)0xAA9F, + (q15_t)0xA128, (q15_t)0xAA0A, (q15_t)0xA1AF, (q15_t)0xA975, + (q15_t)0xA238, (q15_t)0xA8E2, (q15_t)0xA2C1, (q15_t)0xA84F, + (q15_t)0xA34B, (q15_t)0xA7BD, (q15_t)0xA3D6, (q15_t)0xA72B, + (q15_t)0xA462, (q15_t)0xA69B, (q15_t)0xA4EF, (q15_t)0xA60C, + (q15_t)0xA57D, (q15_t)0xA57D, (q15_t)0xA60C, (q15_t)0xA4EF, + (q15_t)0xA69B, (q15_t)0xA462, (q15_t)0xA72B, (q15_t)0xA3D6, + (q15_t)0xA7BD, (q15_t)0xA34B, (q15_t)0xA84F, (q15_t)0xA2C1, + (q15_t)0xA8E2, (q15_t)0xA238, (q15_t)0xA975, (q15_t)0xA1AF, + (q15_t)0xAA0A, (q15_t)0xA128, (q15_t)0xAA9F, (q15_t)0xA0A1, + (q15_t)0xAB35, (q15_t)0xA01C, (q15_t)0xABCC, (q15_t)0x9F97, + (q15_t)0xAC64, (q15_t)0x9F13, (q15_t)0xACFD, (q15_t)0x9E90, + (q15_t)0xAD96, (q15_t)0x9E0E, (q15_t)0xAE31, (q15_t)0x9D8E, + (q15_t)0xAECC, (q15_t)0x9D0D, (q15_t)0xAF68, (q15_t)0x9C8E, + (q15_t)0xB004, (q15_t)0x9C10, (q15_t)0xB0A1, (q15_t)0x9B93, + (q15_t)0xB140, (q15_t)0x9B17, (q15_t)0xB1DE, (q15_t)0x9A9C, + (q15_t)0xB27E, (q15_t)0x9A22, (q15_t)0xB31E, (q15_t)0x99A8, + (q15_t)0xB3C0, (q15_t)0x9930, (q15_t)0xB461, (q15_t)0x98B9, + (q15_t)0xB504, (q15_t)0x9842, (q15_t)0xB5A7, (q15_t)0x97CD, + (q15_t)0xB64B, (q15_t)0x9759, (q15_t)0xB6F0, (q15_t)0x96E6, + (q15_t)0xB796, (q15_t)0x9673, (q15_t)0xB83C, (q15_t)0x9602, + (q15_t)0xB8E3, (q15_t)0x9592, (q15_t)0xB98A, (q15_t)0x9523, + (q15_t)0xBA32, (q15_t)0x94B5, (q15_t)0xBADB, (q15_t)0x9447, + (q15_t)0xBB85, (q15_t)0x93DB, (q15_t)0xBC2F, (q15_t)0x9370, + (q15_t)0xBCDA, (q15_t)0x9306, (q15_t)0xBD85, (q15_t)0x929D, + (q15_t)0xBE31, (q15_t)0x9235, (q15_t)0xBEDE, (q15_t)0x91CF, + (q15_t)0xBF8C, (q15_t)0x9169, (q15_t)0xC03A, (q15_t)0x9104, + (q15_t)0xC0E8, (q15_t)0x90A0, (q15_t)0xC197, (q15_t)0x903E, + (q15_t)0xC247, (q15_t)0x8FDC, (q15_t)0xC2F8, (q15_t)0x8F7C, + (q15_t)0xC3A9, (q15_t)0x8F1D, (q15_t)0xC45A, (q15_t)0x8EBE, + (q15_t)0xC50D, (q15_t)0x8E61, (q15_t)0xC5BF, (q15_t)0x8E05, + (q15_t)0xC673, (q15_t)0x8DAA, (q15_t)0xC727, (q15_t)0x8D50, + (q15_t)0xC7DB, (q15_t)0x8CF8, (q15_t)0xC890, (q15_t)0x8CA0, + (q15_t)0xC945, (q15_t)0x8C4A, (q15_t)0xC9FB, (q15_t)0x8BF4, + (q15_t)0xCAB2, (q15_t)0x8BA0, (q15_t)0xCB69, (q15_t)0x8B4D, + (q15_t)0xCC21, (q15_t)0x8AFB, (q15_t)0xCCD9, (q15_t)0x8AAA, + (q15_t)0xCD91, (q15_t)0x8A5A, (q15_t)0xCE4A, (q15_t)0x8A0B, + (q15_t)0xCF04, (q15_t)0x89BE, (q15_t)0xCFBE, (q15_t)0x8971, + (q15_t)0xD078, (q15_t)0x8926, (q15_t)0xD133, (q15_t)0x88DC, + (q15_t)0xD1EE, (q15_t)0x8893, (q15_t)0xD2AA, (q15_t)0x884B, + (q15_t)0xD367, (q15_t)0x8805, (q15_t)0xD423, (q15_t)0x87BF, + (q15_t)0xD4E0, (q15_t)0x877B, (q15_t)0xD59E, (q15_t)0x8738, + (q15_t)0xD65C, (q15_t)0x86F6, (q15_t)0xD71A, (q15_t)0x86B5, + (q15_t)0xD7D9, (q15_t)0x8675, (q15_t)0xD898, (q15_t)0x8637, + (q15_t)0xD957, (q15_t)0x85FA, (q15_t)0xDA17, (q15_t)0x85BD, + (q15_t)0xDAD7, (q15_t)0x8582, (q15_t)0xDB98, (q15_t)0x8549, + (q15_t)0xDC59, (q15_t)0x8510, (q15_t)0xDD1A, (q15_t)0x84D9, + (q15_t)0xDDDC, (q15_t)0x84A2, (q15_t)0xDE9E, (q15_t)0x846D, + (q15_t)0xDF60, (q15_t)0x843A, (q15_t)0xE023, (q15_t)0x8407, + (q15_t)0xE0E6, (q15_t)0x83D6, (q15_t)0xE1A9, (q15_t)0x83A5, + (q15_t)0xE26C, (q15_t)0x8376, (q15_t)0xE330, (q15_t)0x8348, + (q15_t)0xE3F4, (q15_t)0x831C, (q15_t)0xE4B8, (q15_t)0x82F0, + (q15_t)0xE57D, (q15_t)0x82C6, (q15_t)0xE642, (q15_t)0x829D, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xE7CC, (q15_t)0x824F, + (q15_t)0xE892, (q15_t)0x8229, (q15_t)0xE957, (q15_t)0x8205, + (q15_t)0xEA1D, (q15_t)0x81E2, (q15_t)0xEAE4, (q15_t)0x81C0, + (q15_t)0xEBAA, (q15_t)0x81A0, (q15_t)0xEC71, (q15_t)0x8180, + (q15_t)0xED37, (q15_t)0x8162, (q15_t)0xEDFE, (q15_t)0x8145, + (q15_t)0xEEC6, (q15_t)0x812A, (q15_t)0xEF8D, (q15_t)0x810F, + (q15_t)0xF054, (q15_t)0x80F6, (q15_t)0xF11C, (q15_t)0x80DE, + (q15_t)0xF1E4, (q15_t)0x80C7, (q15_t)0xF2AC, (q15_t)0x80B2, + (q15_t)0xF374, (q15_t)0x809D, (q15_t)0xF43C, (q15_t)0x808A, + (q15_t)0xF504, (q15_t)0x8078, (q15_t)0xF5CC, (q15_t)0x8068, + (q15_t)0xF695, (q15_t)0x8058, (q15_t)0xF75D, (q15_t)0x804A, + (q15_t)0xF826, (q15_t)0x803D, (q15_t)0xF8EF, (q15_t)0x8031, + (q15_t)0xF9B8, (q15_t)0x8027, (q15_t)0xFA80, (q15_t)0x801E, + (q15_t)0xFB49, (q15_t)0x8016, (q15_t)0xFC12, (q15_t)0x800F, + (q15_t)0xFCDB, (q15_t)0x8009, (q15_t)0xFDA4, (q15_t)0x8005, + (q15_t)0xFE6D, (q15_t)0x8002, (q15_t)0xFF36, (q15_t)0x8000 +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 2048, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_2048_q15[3072] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0x0064, + (q15_t)0x7FFF, (q15_t)0x00C9, (q15_t)0x7FFE, (q15_t)0x012D, + (q15_t)0x7FFD, (q15_t)0x0192, (q15_t)0x7FFC, (q15_t)0x01F6, + (q15_t)0x7FFA, (q15_t)0x025B, (q15_t)0x7FF8, (q15_t)0x02BF, + (q15_t)0x7FF6, (q15_t)0x0324, (q15_t)0x7FF3, (q15_t)0x0388, + (q15_t)0x7FF0, (q15_t)0x03ED, (q15_t)0x7FED, (q15_t)0x0451, + (q15_t)0x7FE9, (q15_t)0x04B6, (q15_t)0x7FE5, (q15_t)0x051A, + (q15_t)0x7FE1, (q15_t)0x057F, (q15_t)0x7FDD, (q15_t)0x05E3, + (q15_t)0x7FD8, (q15_t)0x0647, (q15_t)0x7FD3, (q15_t)0x06AC, + (q15_t)0x7FCE, (q15_t)0x0710, (q15_t)0x7FC8, (q15_t)0x0775, + (q15_t)0x7FC2, (q15_t)0x07D9, (q15_t)0x7FBC, (q15_t)0x083D, + (q15_t)0x7FB5, (q15_t)0x08A2, (q15_t)0x7FAE, (q15_t)0x0906, + (q15_t)0x7FA7, (q15_t)0x096A, (q15_t)0x7F9F, (q15_t)0x09CE, + (q15_t)0x7F97, (q15_t)0x0A33, (q15_t)0x7F8F, (q15_t)0x0A97, + (q15_t)0x7F87, (q15_t)0x0AFB, (q15_t)0x7F7E, (q15_t)0x0B5F, + (q15_t)0x7F75, (q15_t)0x0BC3, (q15_t)0x7F6B, (q15_t)0x0C27, + (q15_t)0x7F62, (q15_t)0x0C8B, (q15_t)0x7F58, (q15_t)0x0CEF, + (q15_t)0x7F4D, (q15_t)0x0D53, (q15_t)0x7F43, (q15_t)0x0DB7, + (q15_t)0x7F38, (q15_t)0x0E1B, (q15_t)0x7F2D, (q15_t)0x0E7F, + (q15_t)0x7F21, (q15_t)0x0EE3, (q15_t)0x7F15, (q15_t)0x0F47, + (q15_t)0x7F09, (q15_t)0x0FAB, (q15_t)0x7EFD, (q15_t)0x100E, + (q15_t)0x7EF0, (q15_t)0x1072, (q15_t)0x7EE3, (q15_t)0x10D6, + (q15_t)0x7ED5, (q15_t)0x1139, (q15_t)0x7EC8, (q15_t)0x119D, + (q15_t)0x7EBA, (q15_t)0x1201, (q15_t)0x7EAB, (q15_t)0x1264, + (q15_t)0x7E9D, (q15_t)0x12C8, (q15_t)0x7E8E, (q15_t)0x132B, + (q15_t)0x7E7F, (q15_t)0x138E, (q15_t)0x7E6F, (q15_t)0x13F2, + (q15_t)0x7E5F, (q15_t)0x1455, (q15_t)0x7E4F, (q15_t)0x14B8, + (q15_t)0x7E3F, (q15_t)0x151B, (q15_t)0x7E2E, (q15_t)0x157F, + (q15_t)0x7E1D, (q15_t)0x15E2, (q15_t)0x7E0C, (q15_t)0x1645, + (q15_t)0x7DFA, (q15_t)0x16A8, (q15_t)0x7DE8, (q15_t)0x170A, + (q15_t)0x7DD6, (q15_t)0x176D, (q15_t)0x7DC3, (q15_t)0x17D0, + (q15_t)0x7DB0, (q15_t)0x1833, (q15_t)0x7D9D, (q15_t)0x1896, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7D76, (q15_t)0x195B, + (q15_t)0x7D62, (q15_t)0x19BD, (q15_t)0x7D4E, (q15_t)0x1A20, + (q15_t)0x7D39, (q15_t)0x1A82, (q15_t)0x7D24, (q15_t)0x1AE4, + (q15_t)0x7D0F, (q15_t)0x1B47, (q15_t)0x7CF9, (q15_t)0x1BA9, + (q15_t)0x7CE3, (q15_t)0x1C0B, (q15_t)0x7CCD, (q15_t)0x1C6D, + (q15_t)0x7CB7, (q15_t)0x1CCF, (q15_t)0x7CA0, (q15_t)0x1D31, + (q15_t)0x7C89, (q15_t)0x1D93, (q15_t)0x7C71, (q15_t)0x1DF5, + (q15_t)0x7C5A, (q15_t)0x1E56, (q15_t)0x7C42, (q15_t)0x1EB8, + (q15_t)0x7C29, (q15_t)0x1F19, (q15_t)0x7C11, (q15_t)0x1F7B, + (q15_t)0x7BF8, (q15_t)0x1FDC, (q15_t)0x7BDF, (q15_t)0x203E, + (q15_t)0x7BC5, (q15_t)0x209F, (q15_t)0x7BAC, (q15_t)0x2100, + (q15_t)0x7B92, (q15_t)0x2161, (q15_t)0x7B77, (q15_t)0x21C2, + (q15_t)0x7B5D, (q15_t)0x2223, (q15_t)0x7B42, (q15_t)0x2284, + (q15_t)0x7B26, (q15_t)0x22E5, (q15_t)0x7B0B, (q15_t)0x2345, + (q15_t)0x7AEF, (q15_t)0x23A6, (q15_t)0x7AD3, (q15_t)0x2407, + (q15_t)0x7AB6, (q15_t)0x2467, (q15_t)0x7A9A, (q15_t)0x24C7, + (q15_t)0x7A7D, (q15_t)0x2528, (q15_t)0x7A5F, (q15_t)0x2588, + (q15_t)0x7A42, (q15_t)0x25E8, (q15_t)0x7A24, (q15_t)0x2648, + (q15_t)0x7A05, (q15_t)0x26A8, (q15_t)0x79E7, (q15_t)0x2707, + (q15_t)0x79C8, (q15_t)0x2767, (q15_t)0x79A9, (q15_t)0x27C7, + (q15_t)0x798A, (q15_t)0x2826, (q15_t)0x796A, (q15_t)0x2886, + (q15_t)0x794A, (q15_t)0x28E5, (q15_t)0x792A, (q15_t)0x2944, + (q15_t)0x7909, (q15_t)0x29A3, (q15_t)0x78E8, (q15_t)0x2A02, + (q15_t)0x78C7, (q15_t)0x2A61, (q15_t)0x78A6, (q15_t)0x2AC0, + (q15_t)0x7884, (q15_t)0x2B1F, (q15_t)0x7862, (q15_t)0x2B7D, + (q15_t)0x7840, (q15_t)0x2BDC, (q15_t)0x781D, (q15_t)0x2C3A, + (q15_t)0x77FA, (q15_t)0x2C98, (q15_t)0x77D7, (q15_t)0x2CF7, + (q15_t)0x77B4, (q15_t)0x2D55, (q15_t)0x7790, (q15_t)0x2DB3, + (q15_t)0x776C, (q15_t)0x2E11, (q15_t)0x7747, (q15_t)0x2E6E, + (q15_t)0x7723, (q15_t)0x2ECC, (q15_t)0x76FE, (q15_t)0x2F29, + (q15_t)0x76D9, (q15_t)0x2F87, (q15_t)0x76B3, (q15_t)0x2FE4, + (q15_t)0x768E, (q15_t)0x3041, (q15_t)0x7668, (q15_t)0x309E, + (q15_t)0x7641, (q15_t)0x30FB, (q15_t)0x761B, (q15_t)0x3158, + (q15_t)0x75F4, (q15_t)0x31B5, (q15_t)0x75CC, (q15_t)0x3211, + (q15_t)0x75A5, (q15_t)0x326E, (q15_t)0x757D, (q15_t)0x32CA, + (q15_t)0x7555, (q15_t)0x3326, (q15_t)0x752D, (q15_t)0x3382, + (q15_t)0x7504, (q15_t)0x33DE, (q15_t)0x74DB, (q15_t)0x343A, + (q15_t)0x74B2, (q15_t)0x3496, (q15_t)0x7489, (q15_t)0x34F2, + (q15_t)0x745F, (q15_t)0x354D, (q15_t)0x7435, (q15_t)0x35A8, + (q15_t)0x740B, (q15_t)0x3604, (q15_t)0x73E0, (q15_t)0x365F, + (q15_t)0x73B5, (q15_t)0x36BA, (q15_t)0x738A, (q15_t)0x3714, + (q15_t)0x735F, (q15_t)0x376F, (q15_t)0x7333, (q15_t)0x37CA, + (q15_t)0x7307, (q15_t)0x3824, (q15_t)0x72DB, (q15_t)0x387E, + (q15_t)0x72AF, (q15_t)0x38D8, (q15_t)0x7282, (q15_t)0x3932, + (q15_t)0x7255, (q15_t)0x398C, (q15_t)0x7227, (q15_t)0x39E6, + (q15_t)0x71FA, (q15_t)0x3A40, (q15_t)0x71CC, (q15_t)0x3A99, + (q15_t)0x719E, (q15_t)0x3AF2, (q15_t)0x716F, (q15_t)0x3B4C, + (q15_t)0x7141, (q15_t)0x3BA5, (q15_t)0x7112, (q15_t)0x3BFD, + (q15_t)0x70E2, (q15_t)0x3C56, (q15_t)0x70B3, (q15_t)0x3CAF, + (q15_t)0x7083, (q15_t)0x3D07, (q15_t)0x7053, (q15_t)0x3D60, + (q15_t)0x7023, (q15_t)0x3DB8, (q15_t)0x6FF2, (q15_t)0x3E10, + (q15_t)0x6FC1, (q15_t)0x3E68, (q15_t)0x6F90, (q15_t)0x3EBF, + (q15_t)0x6F5F, (q15_t)0x3F17, (q15_t)0x6F2D, (q15_t)0x3F6E, + (q15_t)0x6EFB, (q15_t)0x3FC5, (q15_t)0x6EC9, (q15_t)0x401D, + (q15_t)0x6E96, (q15_t)0x4073, (q15_t)0x6E63, (q15_t)0x40CA, + (q15_t)0x6E30, (q15_t)0x4121, (q15_t)0x6DFD, (q15_t)0x4177, + (q15_t)0x6DCA, (q15_t)0x41CE, (q15_t)0x6D96, (q15_t)0x4224, + (q15_t)0x6D62, (q15_t)0x427A, (q15_t)0x6D2D, (q15_t)0x42D0, + (q15_t)0x6CF9, (q15_t)0x4325, (q15_t)0x6CC4, (q15_t)0x437B, + (q15_t)0x6C8F, (q15_t)0x43D0, (q15_t)0x6C59, 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(q15_t)0x8332, + (q15_t)0xE3F4, (q15_t)0x831C, (q15_t)0xE456, (q15_t)0x8306, + (q15_t)0xE4B8, (q15_t)0x82F0, (q15_t)0xE51B, (q15_t)0x82DB, + (q15_t)0xE57D, (q15_t)0x82C6, (q15_t)0xE5DF, (q15_t)0x82B1, + (q15_t)0xE642, (q15_t)0x829D, (q15_t)0xE6A4, (q15_t)0x8289, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xE769, (q15_t)0x8262, + (q15_t)0xE7CC, (q15_t)0x824F, (q15_t)0xE82F, (q15_t)0x823C, + (q15_t)0xE892, (q15_t)0x8229, (q15_t)0xE8F5, (q15_t)0x8217, + (q15_t)0xE957, (q15_t)0x8205, (q15_t)0xE9BA, (q15_t)0x81F3, + (q15_t)0xEA1D, (q15_t)0x81E2, (q15_t)0xEA80, (q15_t)0x81D1, + (q15_t)0xEAE4, (q15_t)0x81C0, (q15_t)0xEB47, (q15_t)0x81B0, + (q15_t)0xEBAA, (q15_t)0x81A0, (q15_t)0xEC0D, (q15_t)0x8190, + (q15_t)0xEC71, (q15_t)0x8180, (q15_t)0xECD4, (q15_t)0x8171, + (q15_t)0xED37, (q15_t)0x8162, (q15_t)0xED9B, (q15_t)0x8154, + (q15_t)0xEDFE, (q15_t)0x8145, (q15_t)0xEE62, (q15_t)0x8137, + (q15_t)0xEEC6, (q15_t)0x812A, (q15_t)0xEF29, (q15_t)0x811C, + (q15_t)0xEF8D, (q15_t)0x810F, (q15_t)0xEFF1, (q15_t)0x8102, + (q15_t)0xF054, (q15_t)0x80F6, (q15_t)0xF0B8, (q15_t)0x80EA, + (q15_t)0xF11C, (q15_t)0x80DE, (q15_t)0xF180, (q15_t)0x80D2, + (q15_t)0xF1E4, (q15_t)0x80C7, (q15_t)0xF248, (q15_t)0x80BC, + (q15_t)0xF2AC, (q15_t)0x80B2, (q15_t)0xF310, (q15_t)0x80A7, + (q15_t)0xF374, (q15_t)0x809D, (q15_t)0xF3D8, (q15_t)0x8094, + (q15_t)0xF43C, (q15_t)0x808A, (q15_t)0xF4A0, (q15_t)0x8081, + (q15_t)0xF504, (q15_t)0x8078, (q15_t)0xF568, (q15_t)0x8070, + (q15_t)0xF5CC, (q15_t)0x8068, (q15_t)0xF631, (q15_t)0x8060, + (q15_t)0xF695, (q15_t)0x8058, (q15_t)0xF6F9, (q15_t)0x8051, + (q15_t)0xF75D, (q15_t)0x804A, (q15_t)0xF7C2, (q15_t)0x8043, + (q15_t)0xF826, (q15_t)0x803D, (q15_t)0xF88A, (q15_t)0x8037, + (q15_t)0xF8EF, (q15_t)0x8031, (q15_t)0xF953, (q15_t)0x802C, + (q15_t)0xF9B8, (q15_t)0x8027, (q15_t)0xFA1C, (q15_t)0x8022, + (q15_t)0xFA80, (q15_t)0x801E, (q15_t)0xFAE5, (q15_t)0x801A, + (q15_t)0xFB49, (q15_t)0x8016, (q15_t)0xFBAE, (q15_t)0x8012, + (q15_t)0xFC12, (q15_t)0x800F, (q15_t)0xFC77, (q15_t)0x800C, + (q15_t)0xFCDB, (q15_t)0x8009, (q15_t)0xFD40, (q15_t)0x8007, + (q15_t)0xFDA4, (q15_t)0x8005, (q15_t)0xFE09, (q15_t)0x8003, + (q15_t)0xFE6D, (q15_t)0x8002, (q15_t)0xFED2, (q15_t)0x8001, + (q15_t)0xFF36, (q15_t)0x8000, (q15_t)0xFF9B, (q15_t)0x8000 +}; + +/** + @par + Example code for q15 Twiddle factors Generation:: + @par + 
for (i = 0; i< 3N/4; i++)
+  {
+     twiddleCoefq15[2*i]   = cos(i * 2*PI/(float)N);
+     twiddleCoefq15[2*i+1] = sin(i * 2*PI/(float)N);
+  }
+ @par + where N = 4096, PI = 3.14159265358979 + @par + Cos and Sin values are interleaved fashion + @par + Convert Floating point to q15(Fixed point 1.15): + round(twiddleCoefq15(i) * pow(2, 15)) + */ +const q15_t twiddleCoef_4096_q15[6144] ARM_DSP_TABLE_ATTRIBUTE = +{ + (q15_t)0x7FFF, (q15_t)0x0000, (q15_t)0x7FFF, (q15_t)0x0032, + (q15_t)0x7FFF, (q15_t)0x0064, (q15_t)0x7FFF, (q15_t)0x0096, + (q15_t)0x7FFF, (q15_t)0x00C9, (q15_t)0x7FFF, (q15_t)0x00FB, + (q15_t)0x7FFE, (q15_t)0x012D, (q15_t)0x7FFE, (q15_t)0x015F, + (q15_t)0x7FFD, (q15_t)0x0192, (q15_t)0x7FFC, (q15_t)0x01C4, + (q15_t)0x7FFC, (q15_t)0x01F6, (q15_t)0x7FFB, (q15_t)0x0228, + (q15_t)0x7FFA, (q15_t)0x025B, (q15_t)0x7FF9, (q15_t)0x028D, + (q15_t)0x7FF8, (q15_t)0x02BF, (q15_t)0x7FF7, (q15_t)0x02F1, + (q15_t)0x7FF6, (q15_t)0x0324, (q15_t)0x7FF4, (q15_t)0x0356, + (q15_t)0x7FF3, (q15_t)0x0388, (q15_t)0x7FF2, (q15_t)0x03BA, + (q15_t)0x7FF0, (q15_t)0x03ED, (q15_t)0x7FEE, (q15_t)0x041F, + (q15_t)0x7FED, (q15_t)0x0451, (q15_t)0x7FEB, (q15_t)0x0483, + (q15_t)0x7FE9, (q15_t)0x04B6, (q15_t)0x7FE7, (q15_t)0x04E8, + (q15_t)0x7FE5, (q15_t)0x051A, (q15_t)0x7FE3, (q15_t)0x054C, + (q15_t)0x7FE1, (q15_t)0x057F, (q15_t)0x7FDF, (q15_t)0x05B1, + (q15_t)0x7FDD, (q15_t)0x05E3, (q15_t)0x7FDA, (q15_t)0x0615, + (q15_t)0x7FD8, (q15_t)0x0647, (q15_t)0x7FD6, (q15_t)0x067A, + (q15_t)0x7FD3, (q15_t)0x06AC, (q15_t)0x7FD0, (q15_t)0x06DE, + (q15_t)0x7FCE, (q15_t)0x0710, (q15_t)0x7FCB, (q15_t)0x0742, + (q15_t)0x7FC8, (q15_t)0x0775, (q15_t)0x7FC5, (q15_t)0x07A7, + (q15_t)0x7FC2, (q15_t)0x07D9, (q15_t)0x7FBF, (q15_t)0x080B, + (q15_t)0x7FBC, (q15_t)0x083D, (q15_t)0x7FB8, (q15_t)0x086F, + (q15_t)0x7FB5, (q15_t)0x08A2, (q15_t)0x7FB1, (q15_t)0x08D4, + (q15_t)0x7FAE, (q15_t)0x0906, (q15_t)0x7FAA, (q15_t)0x0938, + (q15_t)0x7FA7, (q15_t)0x096A, (q15_t)0x7FA3, (q15_t)0x099C, + (q15_t)0x7F9F, (q15_t)0x09CE, (q15_t)0x7F9B, (q15_t)0x0A00, + (q15_t)0x7F97, (q15_t)0x0A33, (q15_t)0x7F93, (q15_t)0x0A65, + (q15_t)0x7F8F, (q15_t)0x0A97, (q15_t)0x7F8B, (q15_t)0x0AC9, + (q15_t)0x7F87, (q15_t)0x0AFB, (q15_t)0x7F82, (q15_t)0x0B2D, + (q15_t)0x7F7E, (q15_t)0x0B5F, (q15_t)0x7F79, (q15_t)0x0B91, + (q15_t)0x7F75, (q15_t)0x0BC3, (q15_t)0x7F70, (q15_t)0x0BF5, + (q15_t)0x7F6B, (q15_t)0x0C27, (q15_t)0x7F67, (q15_t)0x0C59, + (q15_t)0x7F62, (q15_t)0x0C8B, (q15_t)0x7F5D, (q15_t)0x0CBD, + (q15_t)0x7F58, (q15_t)0x0CEF, (q15_t)0x7F53, (q15_t)0x0D21, + (q15_t)0x7F4D, (q15_t)0x0D53, (q15_t)0x7F48, (q15_t)0x0D85, + (q15_t)0x7F43, (q15_t)0x0DB7, (q15_t)0x7F3D, (q15_t)0x0DE9, + (q15_t)0x7F38, (q15_t)0x0E1B, (q15_t)0x7F32, (q15_t)0x0E4D, + (q15_t)0x7F2D, (q15_t)0x0E7F, (q15_t)0x7F27, (q15_t)0x0EB1, + (q15_t)0x7F21, (q15_t)0x0EE3, (q15_t)0x7F1B, (q15_t)0x0F15, + (q15_t)0x7F15, (q15_t)0x0F47, (q15_t)0x7F0F, (q15_t)0x0F79, + (q15_t)0x7F09, (q15_t)0x0FAB, (q15_t)0x7F03, (q15_t)0x0FDD, + (q15_t)0x7EFD, (q15_t)0x100E, (q15_t)0x7EF6, (q15_t)0x1040, + (q15_t)0x7EF0, (q15_t)0x1072, (q15_t)0x7EE9, (q15_t)0x10A4, + (q15_t)0x7EE3, (q15_t)0x10D6, (q15_t)0x7EDC, (q15_t)0x1108, + (q15_t)0x7ED5, (q15_t)0x1139, (q15_t)0x7ECF, (q15_t)0x116B, + (q15_t)0x7EC8, (q15_t)0x119D, (q15_t)0x7EC1, (q15_t)0x11CF, + (q15_t)0x7EBA, (q15_t)0x1201, (q15_t)0x7EB3, (q15_t)0x1232, + (q15_t)0x7EAB, (q15_t)0x1264, (q15_t)0x7EA4, (q15_t)0x1296, + (q15_t)0x7E9D, (q15_t)0x12C8, (q15_t)0x7E95, (q15_t)0x12F9, + (q15_t)0x7E8E, (q15_t)0x132B, (q15_t)0x7E86, (q15_t)0x135D, + (q15_t)0x7E7F, (q15_t)0x138E, (q15_t)0x7E77, (q15_t)0x13C0, + (q15_t)0x7E6F, (q15_t)0x13F2, (q15_t)0x7E67, (q15_t)0x1423, + (q15_t)0x7E5F, (q15_t)0x1455, (q15_t)0x7E57, (q15_t)0x1487, + (q15_t)0x7E4F, (q15_t)0x14B8, (q15_t)0x7E47, (q15_t)0x14EA, + (q15_t)0x7E3F, (q15_t)0x151B, (q15_t)0x7E37, (q15_t)0x154D, + (q15_t)0x7E2E, (q15_t)0x157F, (q15_t)0x7E26, (q15_t)0x15B0, + (q15_t)0x7E1D, (q15_t)0x15E2, (q15_t)0x7E14, (q15_t)0x1613, + (q15_t)0x7E0C, (q15_t)0x1645, (q15_t)0x7E03, (q15_t)0x1676, + (q15_t)0x7DFA, (q15_t)0x16A8, (q15_t)0x7DF1, (q15_t)0x16D9, + (q15_t)0x7DE8, (q15_t)0x170A, (q15_t)0x7DDF, (q15_t)0x173C, + (q15_t)0x7DD6, (q15_t)0x176D, (q15_t)0x7DCD, (q15_t)0x179F, + (q15_t)0x7DC3, (q15_t)0x17D0, (q15_t)0x7DBA, (q15_t)0x1802, + (q15_t)0x7DB0, (q15_t)0x1833, (q15_t)0x7DA7, (q15_t)0x1864, + (q15_t)0x7D9D, (q15_t)0x1896, (q15_t)0x7D94, (q15_t)0x18C7, + (q15_t)0x7D8A, (q15_t)0x18F8, (q15_t)0x7D80, (q15_t)0x192A, + (q15_t)0x7D76, (q15_t)0x195B, (q15_t)0x7D6C, (q15_t)0x198C, + (q15_t)0x7D62, (q15_t)0x19BD, (q15_t)0x7D58, (q15_t)0x19EF, + (q15_t)0x7D4E, (q15_t)0x1A20, (q15_t)0x7D43, (q15_t)0x1A51, + (q15_t)0x7D39, (q15_t)0x1A82, (q15_t)0x7D2F, (q15_t)0x1AB3, + (q15_t)0x7D24, (q15_t)0x1AE4, (q15_t)0x7D19, (q15_t)0x1B16, + (q15_t)0x7D0F, (q15_t)0x1B47, (q15_t)0x7D04, (q15_t)0x1B78, + (q15_t)0x7CF9, (q15_t)0x1BA9, (q15_t)0x7CEE, (q15_t)0x1BDA, + (q15_t)0x7CE3, (q15_t)0x1C0B, (q15_t)0x7CD8, (q15_t)0x1C3C, + (q15_t)0x7CCD, (q15_t)0x1C6D, (q15_t)0x7CC2, (q15_t)0x1C9E, + (q15_t)0x7CB7, (q15_t)0x1CCF, (q15_t)0x7CAB, (q15_t)0x1D00, + (q15_t)0x7CA0, (q15_t)0x1D31, (q15_t)0x7C94, (q15_t)0x1D62, + (q15_t)0x7C89, (q15_t)0x1D93, (q15_t)0x7C7D, (q15_t)0x1DC4, + (q15_t)0x7C71, (q15_t)0x1DF5, (q15_t)0x7C66, (q15_t)0x1E25, + (q15_t)0x7C5A, (q15_t)0x1E56, (q15_t)0x7C4E, (q15_t)0x1E87, + (q15_t)0x7C42, (q15_t)0x1EB8, (q15_t)0x7C36, (q15_t)0x1EE9, + (q15_t)0x7C29, (q15_t)0x1F19, (q15_t)0x7C1D, (q15_t)0x1F4A, + (q15_t)0x7C11, (q15_t)0x1F7B, (q15_t)0x7C05, (q15_t)0x1FAC, + (q15_t)0x7BF8, (q15_t)0x1FDC, (q15_t)0x7BEB, (q15_t)0x200D, + (q15_t)0x7BDF, (q15_t)0x203E, (q15_t)0x7BD2, (q15_t)0x206E, + (q15_t)0x7BC5, (q15_t)0x209F, (q15_t)0x7BB9, (q15_t)0x20D0, + (q15_t)0x7BAC, (q15_t)0x2100, (q15_t)0x7B9F, (q15_t)0x2131, + (q15_t)0x7B92, (q15_t)0x2161, (q15_t)0x7B84, (q15_t)0x2192, + (q15_t)0x7B77, (q15_t)0x21C2, (q15_t)0x7B6A, (q15_t)0x21F3, + (q15_t)0x7B5D, (q15_t)0x2223, (q15_t)0x7B4F, (q15_t)0x2254, + (q15_t)0x7B42, (q15_t)0x2284, (q15_t)0x7B34, (q15_t)0x22B4, + (q15_t)0x7B26, (q15_t)0x22E5, (q15_t)0x7B19, (q15_t)0x2315, + (q15_t)0x7B0B, (q15_t)0x2345, (q15_t)0x7AFD, (q15_t)0x2376, + (q15_t)0x7AEF, (q15_t)0x23A6, (q15_t)0x7AE1, (q15_t)0x23D6, + (q15_t)0x7AD3, (q15_t)0x2407, (q15_t)0x7AC5, (q15_t)0x2437, + (q15_t)0x7AB6, (q15_t)0x2467, (q15_t)0x7AA8, (q15_t)0x2497, + (q15_t)0x7A9A, (q15_t)0x24C7, (q15_t)0x7A8B, (q15_t)0x24F7, + (q15_t)0x7A7D, (q15_t)0x2528, (q15_t)0x7A6E, (q15_t)0x2558, + (q15_t)0x7A5F, (q15_t)0x2588, (q15_t)0x7A50, (q15_t)0x25B8, + (q15_t)0x7A42, (q15_t)0x25E8, (q15_t)0x7A33, (q15_t)0x2618, + (q15_t)0x7A24, (q15_t)0x2648, (q15_t)0x7A15, (q15_t)0x2678, + (q15_t)0x7A05, (q15_t)0x26A8, (q15_t)0x79F6, (q15_t)0x26D8, + (q15_t)0x79E7, (q15_t)0x2707, (q15_t)0x79D8, (q15_t)0x2737, + (q15_t)0x79C8, (q15_t)0x2767, (q15_t)0x79B9, (q15_t)0x2797, + (q15_t)0x79A9, (q15_t)0x27C7, (q15_t)0x7999, (q15_t)0x27F6, + (q15_t)0x798A, (q15_t)0x2826, (q15_t)0x797A, (q15_t)0x2856, + (q15_t)0x796A, (q15_t)0x2886, (q15_t)0x795A, (q15_t)0x28B5, + (q15_t)0x794A, (q15_t)0x28E5, (q15_t)0x793A, (q15_t)0x2915, + (q15_t)0x792A, (q15_t)0x2944, (q15_t)0x7919, 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(q15_t)0x8816, + (q15_t)0xD367, (q15_t)0x8805, (q15_t)0xD396, (q15_t)0x87F3, + (q15_t)0xD3C5, (q15_t)0x87E2, (q15_t)0xD3F4, (q15_t)0x87D1, + (q15_t)0xD423, (q15_t)0x87BF, (q15_t)0xD452, (q15_t)0x87AE, + (q15_t)0xD482, (q15_t)0x879D, (q15_t)0xD4B1, (q15_t)0x878C, + (q15_t)0xD4E0, (q15_t)0x877B, (q15_t)0xD510, (q15_t)0x876A, + (q15_t)0xD53F, (q15_t)0x8759, (q15_t)0xD56E, (q15_t)0x8749, + (q15_t)0xD59E, (q15_t)0x8738, (q15_t)0xD5CD, (q15_t)0x8727, + (q15_t)0xD5FD, (q15_t)0x8717, (q15_t)0xD62C, (q15_t)0x8706, + (q15_t)0xD65C, (q15_t)0x86F6, (q15_t)0xD68B, (q15_t)0x86E6, + (q15_t)0xD6BB, (q15_t)0x86D5, (q15_t)0xD6EA, (q15_t)0x86C5, + (q15_t)0xD71A, (q15_t)0x86B5, (q15_t)0xD74A, (q15_t)0x86A5, + (q15_t)0xD779, (q15_t)0x8695, (q15_t)0xD7A9, (q15_t)0x8685, + (q15_t)0xD7D9, (q15_t)0x8675, (q15_t)0xD809, (q15_t)0x8666, + (q15_t)0xD838, (q15_t)0x8656, (q15_t)0xD868, (q15_t)0x8646, + (q15_t)0xD898, (q15_t)0x8637, (q15_t)0xD8C8, (q15_t)0x8627, + (q15_t)0xD8F8, (q15_t)0x8618, (q15_t)0xD927, (q15_t)0x8609, + (q15_t)0xD957, (q15_t)0x85FA, (q15_t)0xD987, (q15_t)0x85EA, + (q15_t)0xD9B7, (q15_t)0x85DB, (q15_t)0xD9E7, (q15_t)0x85CC, + (q15_t)0xDA17, (q15_t)0x85BD, (q15_t)0xDA47, (q15_t)0x85AF, + (q15_t)0xDA77, (q15_t)0x85A0, (q15_t)0xDAA7, (q15_t)0x8591, + (q15_t)0xDAD7, (q15_t)0x8582, (q15_t)0xDB08, (q15_t)0x8574, + (q15_t)0xDB38, (q15_t)0x8565, (q15_t)0xDB68, (q15_t)0x8557, + (q15_t)0xDB98, (q15_t)0x8549, (q15_t)0xDBC8, (q15_t)0x853A, + (q15_t)0xDBF8, (q15_t)0x852C, (q15_t)0xDC29, (q15_t)0x851E, + (q15_t)0xDC59, (q15_t)0x8510, (q15_t)0xDC89, (q15_t)0x8502, + (q15_t)0xDCBA, (q15_t)0x84F4, (q15_t)0xDCEA, (q15_t)0x84E6, + (q15_t)0xDD1A, (q15_t)0x84D9, (q15_t)0xDD4B, (q15_t)0x84CB, + (q15_t)0xDD7B, (q15_t)0x84BD, (q15_t)0xDDAB, (q15_t)0x84B0, + (q15_t)0xDDDC, (q15_t)0x84A2, (q15_t)0xDE0C, (q15_t)0x8495, + (q15_t)0xDE3D, (q15_t)0x8488, (q15_t)0xDE6D, (q15_t)0x847B, + (q15_t)0xDE9E, (q15_t)0x846D, (q15_t)0xDECE, (q15_t)0x8460, + (q15_t)0xDEFF, (q15_t)0x8453, (q15_t)0xDF2F, (q15_t)0x8446, + (q15_t)0xDF60, (q15_t)0x843A, (q15_t)0xDF91, (q15_t)0x842D, + (q15_t)0xDFC1, (q15_t)0x8420, (q15_t)0xDFF2, (q15_t)0x8414, + (q15_t)0xE023, (q15_t)0x8407, (q15_t)0xE053, (q15_t)0x83FA, + (q15_t)0xE084, (q15_t)0x83EE, (q15_t)0xE0B5, (q15_t)0x83E2, + (q15_t)0xE0E6, (q15_t)0x83D6, (q15_t)0xE116, (q15_t)0x83C9, + (q15_t)0xE147, (q15_t)0x83BD, (q15_t)0xE178, (q15_t)0x83B1, + (q15_t)0xE1A9, (q15_t)0x83A5, (q15_t)0xE1DA, (q15_t)0x8399, + (q15_t)0xE20A, (q15_t)0x838E, (q15_t)0xE23B, (q15_t)0x8382, + (q15_t)0xE26C, (q15_t)0x8376, (q15_t)0xE29D, (q15_t)0x836B, + (q15_t)0xE2CE, (q15_t)0x835F, (q15_t)0xE2FF, (q15_t)0x8354, + (q15_t)0xE330, (q15_t)0x8348, (q15_t)0xE361, (q15_t)0x833D, + (q15_t)0xE392, (q15_t)0x8332, (q15_t)0xE3C3, (q15_t)0x8327, + (q15_t)0xE3F4, (q15_t)0x831C, (q15_t)0xE425, (q15_t)0x8311, + (q15_t)0xE456, (q15_t)0x8306, (q15_t)0xE487, (q15_t)0x82FB, + (q15_t)0xE4B8, (q15_t)0x82F0, (q15_t)0xE4E9, (q15_t)0x82E6, + (q15_t)0xE51B, (q15_t)0x82DB, (q15_t)0xE54C, (q15_t)0x82D0, + (q15_t)0xE57D, (q15_t)0x82C6, (q15_t)0xE5AE, (q15_t)0x82BC, + (q15_t)0xE5DF, (q15_t)0x82B1, (q15_t)0xE610, (q15_t)0x82A7, + (q15_t)0xE642, (q15_t)0x829D, (q15_t)0xE673, (q15_t)0x8293, + (q15_t)0xE6A4, (q15_t)0x8289, (q15_t)0xE6D5, (q15_t)0x827F, + (q15_t)0xE707, (q15_t)0x8275, (q15_t)0xE738, (q15_t)0x826B, + (q15_t)0xE769, (q15_t)0x8262, (q15_t)0xE79B, (q15_t)0x8258, + (q15_t)0xE7CC, (q15_t)0x824F, (q15_t)0xE7FD, (q15_t)0x8245, + (q15_t)0xE82F, (q15_t)0x823C, (q15_t)0xE860, (q15_t)0x8232, + (q15_t)0xE892, (q15_t)0x8229, (q15_t)0xE8C3, (q15_t)0x8220, + (q15_t)0xE8F5, (q15_t)0x8217, (q15_t)0xE926, (q15_t)0x820E, + (q15_t)0xE957, (q15_t)0x8205, (q15_t)0xE989, (q15_t)0x81FC, + (q15_t)0xE9BA, (q15_t)0x81F3, (q15_t)0xE9EC, (q15_t)0x81EB, + (q15_t)0xEA1D, (q15_t)0x81E2, (q15_t)0xEA4F, (q15_t)0x81D9, + (q15_t)0xEA80, (q15_t)0x81D1, (q15_t)0xEAB2, (q15_t)0x81C8, + (q15_t)0xEAE4, (q15_t)0x81C0, (q15_t)0xEB15, (q15_t)0x81B8, + (q15_t)0xEB47, (q15_t)0x81B0, (q15_t)0xEB78, (q15_t)0x81A8, + (q15_t)0xEBAA, (q15_t)0x81A0, (q15_t)0xEBDC, (q15_t)0x8198, + (q15_t)0xEC0D, (q15_t)0x8190, (q15_t)0xEC3F, (q15_t)0x8188, + (q15_t)0xEC71, (q15_t)0x8180, (q15_t)0xECA2, (q15_t)0x8179, + (q15_t)0xECD4, (q15_t)0x8171, (q15_t)0xED06, (q15_t)0x816A, + (q15_t)0xED37, (q15_t)0x8162, (q15_t)0xED69, (q15_t)0x815B, + (q15_t)0xED9B, (q15_t)0x8154, (q15_t)0xEDCD, (q15_t)0x814C, + (q15_t)0xEDFE, (q15_t)0x8145, (q15_t)0xEE30, (q15_t)0x813E, + (q15_t)0xEE62, (q15_t)0x8137, (q15_t)0xEE94, (q15_t)0x8130, + (q15_t)0xEEC6, (q15_t)0x812A, (q15_t)0xEEF7, (q15_t)0x8123, + (q15_t)0xEF29, (q15_t)0x811C, (q15_t)0xEF5B, (q15_t)0x8116, + (q15_t)0xEF8D, (q15_t)0x810F, (q15_t)0xEFBF, (q15_t)0x8109, + (q15_t)0xEFF1, (q15_t)0x8102, (q15_t)0xF022, (q15_t)0x80FC, + (q15_t)0xF054, (q15_t)0x80F6, (q15_t)0xF086, (q15_t)0x80F0, + (q15_t)0xF0B8, (q15_t)0x80EA, (q15_t)0xF0EA, (q15_t)0x80E4, + (q15_t)0xF11C, (q15_t)0x80DE, (q15_t)0xF14E, (q15_t)0x80D8, + (q15_t)0xF180, (q15_t)0x80D2, (q15_t)0xF1B2, (q15_t)0x80CD, + (q15_t)0xF1E4, (q15_t)0x80C7, (q15_t)0xF216, (q15_t)0x80C2, + (q15_t)0xF248, (q15_t)0x80BC, (q15_t)0xF27A, (q15_t)0x80B7, + (q15_t)0xF2AC, (q15_t)0x80B2, (q15_t)0xF2DE, (q15_t)0x80AC, + (q15_t)0xF310, (q15_t)0x80A7, (q15_t)0xF342, (q15_t)0x80A2, + (q15_t)0xF374, (q15_t)0x809D, (q15_t)0xF3A6, (q15_t)0x8098, + (q15_t)0xF3D8, (q15_t)0x8094, (q15_t)0xF40A, (q15_t)0x808F, + (q15_t)0xF43C, (q15_t)0x808A, (q15_t)0xF46E, (q15_t)0x8086, + (q15_t)0xF4A0, (q15_t)0x8081, (q15_t)0xF4D2, (q15_t)0x807D, + (q15_t)0xF504, (q15_t)0x8078, (q15_t)0xF536, (q15_t)0x8074, + (q15_t)0xF568, (q15_t)0x8070, (q15_t)0xF59A, (q15_t)0x806C, + (q15_t)0xF5CC, (q15_t)0x8068, (q15_t)0xF5FF, (q15_t)0x8064, + (q15_t)0xF631, (q15_t)0x8060, (q15_t)0xF663, (q15_t)0x805C, + (q15_t)0xF695, (q15_t)0x8058, (q15_t)0xF6C7, (q15_t)0x8055, + (q15_t)0xF6F9, (q15_t)0x8051, (q15_t)0xF72B, (q15_t)0x804E, + (q15_t)0xF75D, (q15_t)0x804A, (q15_t)0xF790, (q15_t)0x8047, + (q15_t)0xF7C2, (q15_t)0x8043, (q15_t)0xF7F4, (q15_t)0x8040, + (q15_t)0xF826, (q15_t)0x803D, (q15_t)0xF858, (q15_t)0x803A, + (q15_t)0xF88A, (q15_t)0x8037, (q15_t)0xF8BD, (q15_t)0x8034, + (q15_t)0xF8EF, (q15_t)0x8031, (q15_t)0xF921, (q15_t)0x802F, + (q15_t)0xF953, (q15_t)0x802C, (q15_t)0xF985, (q15_t)0x8029, + (q15_t)0xF9B8, (q15_t)0x8027, (q15_t)0xF9EA, (q15_t)0x8025, + (q15_t)0xFA1C, (q15_t)0x8022, (q15_t)0xFA4E, (q15_t)0x8020, + (q15_t)0xFA80, (q15_t)0x801E, (q15_t)0xFAB3, (q15_t)0x801C, + (q15_t)0xFAE5, (q15_t)0x801A, (q15_t)0xFB17, (q15_t)0x8018, + (q15_t)0xFB49, (q15_t)0x8016, (q15_t)0xFB7C, (q15_t)0x8014, + (q15_t)0xFBAE, (q15_t)0x8012, (q15_t)0xFBE0, (q15_t)0x8011, + (q15_t)0xFC12, (q15_t)0x800F, (q15_t)0xFC45, (q15_t)0x800D, + (q15_t)0xFC77, (q15_t)0x800C, (q15_t)0xFCA9, (q15_t)0x800B, + (q15_t)0xFCDB, (q15_t)0x8009, (q15_t)0xFD0E, (q15_t)0x8008, + (q15_t)0xFD40, (q15_t)0x8007, (q15_t)0xFD72, (q15_t)0x8006, + (q15_t)0xFDA4, (q15_t)0x8005, (q15_t)0xFDD7, (q15_t)0x8004, + (q15_t)0xFE09, (q15_t)0x8003, (q15_t)0xFE3B, (q15_t)0x8003, + (q15_t)0xFE6D, (q15_t)0x8002, (q15_t)0xFEA0, (q15_t)0x8001, + (q15_t)0xFED2, (q15_t)0x8001, (q15_t)0xFF04, (q15_t)0x8000, + (q15_t)0xFF36, (q15_t)0x8000, (q15_t)0xFF69, (q15_t)0x8000, + (q15_t)0xFF9B, (q15_t)0x8000, (q15_t)0xFFCD, (q15_t)0x8000 +}; + + +/** + @} end of CFFT_CIFFT group +*/ + + +const uint16_t armBitRevIndexTableF64_16[ARMBITREVINDEXTABLEF64_16_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 12 */ + 8,64, 16,32, 24,96, 40,80, 56,112, 88,104 +}; + +const uint16_t armBitRevIndexTableF64_32[ARMBITREVINDEXTABLEF64_32_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 24 */ + 8,128, 16,64, 24,192, 40,160, 48,96, 56,224, 72,144, + 88,208, 104,176, 120,240, 152,200, 184,232 +}; + +const uint16_t armBitRevIndexTableF64_64[ARMBITREVINDEXTABLEF64_64_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 56 */ + 8,256, 16,128, 24,384, 32,64, 40,320, 48,192, 56,448, 72,288, 80,160, 88,416, 104,352, + 112,224, 120,480, 136,272, 152,400, 168,336, 176,208, 184,464, 200,304, 216,432, + 232,368, 248,496, 280,392, 296,328, 312,456, 344,424, 376,488, 440,472 +}; + +const uint16_t armBitRevIndexTableF64_128[ARMBITREVINDEXTABLEF64_128_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 112 */ + 8,512, 16,256, 24,768, 32,128, 40,640, 48,384, 56,896, 72,576, 80,320, 88,832, 96,192, + 104,704, 112,448, 120,960, 136,544, 144,288, 152,800, 168,672, 176,416, 184,928, 200,608, + 208,352, 216,864, 232,736, 240,480, 248,992, 264,528, 280,784, 296,656, 304,400, 312,912, + 328,592, 344,848, 360,720, 368,464, 376,976, 392,560, 408,816, 424,688, 440,944, 456,624, + 472,880, 488,752, 504,1008, 536,776, 552,648, 568,904, 600,840, 616,712, 632,968, + 664,808, 696,936, 728,872, 760,1000, 824,920, 888,984 +}; + +const uint16_t armBitRevIndexTableF64_256[ARMBITREVINDEXTABLEF64_256_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 240 */ + 8,1024, 16,512, 24,1536, 32,256, 40,1280, 48,768, 56,1792, 64,128, 72,1152, 80,640, + 88,1664, 96,384, 104,1408, 112,896, 120,1920, 136,1088, 144,576, 152,1600, 160,320, + 168,1344, 176,832, 184,1856, 200,1216, 208,704, 216,1728, 224,448, 232,1472, 240,960, + 248,1984, 264,1056, 272,544, 280,1568, 296,1312, 304,800, 312,1824, 328,1184, 336,672, + 344,1696, 352,416, 360,1440, 368,928, 376,1952, 392,1120, 400,608, 408,1632, 424,1376, + 432,864, 440,1888, 456,1248, 464,736, 472,1760, 488,1504, 496,992, 504,2016, 520,1040, + 536,1552, 552,1296, 560,784, 568,1808, 584,1168, 592,656, 600,1680, 616,1424, 624,912, + 632,1936, 648,1104, 664,1616, 680,1360, 688,848, 696,1872, 712,1232, 728,1744, 744,1488, + 752,976, 760,2000, 776,1072, 792,1584, 808,1328, 824,1840, 840,1200, 856,1712, 872,1456, + 880,944, 888,1968, 904,1136, 920,1648, 936,1392, 952,1904, 968,1264, 984,1776, 1000,1520, + 1016,2032, 1048,1544, 1064,1288, 1080,1800, 1096,1160, 1112,1672, 1128,1416, 1144,1928, + 1176,1608, 1192,1352, 1208,1864, 1240,1736, 1256,1480, 1272,1992, 1304,1576, 1336,1832, + 1368,1704, 1384,1448, 1400,1960, 1432,1640, 1464,1896, 1496,1768, 1528,2024, 1592,1816, + 1624,1688, 1656,1944, 1720,1880, 1784,2008, 1912,1976 +}; + +const uint16_t armBitRevIndexTableF64_512[ARMBITREVINDEXTABLEF64_512_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 480 */ + 8,2048, 16,1024, 24,3072, 32,512, 40,2560, 48,1536, 56,3584, 64,256, 72,2304, 80,1280, + 88,3328, 96,768, 104,2816, 112,1792, 120,3840, 136,2176, 144,1152, 152,3200, 160,640, + 168,2688, 176,1664, 184,3712, 192,384, 200,2432, 208,1408, 216,3456, 224,896, 232,2944, + 240,1920, 248,3968, 264,2112, 272,1088, 280,3136, 288,576, 296,2624, 304,1600, 312,3648, + 328,2368, 336,1344, 344,3392, 352,832, 360,2880, 368,1856, 376,3904, 392,2240, 400,1216, + 408,3264, 416,704, 424,2752, 432,1728, 440,3776, 456,2496, 464,1472, 472,3520, 480,960, + 488,3008, 496,1984, 504,4032, 520,2080, 528,1056, 536,3104, 552,2592, 560,1568, 568,3616, + 584,2336, 592,1312, 600,3360, 608,800, 616,2848, 624,1824, 632,3872, 648,2208, 656,1184, + 664,3232, 680,2720, 688,1696, 696,3744, 712,2464, 720,1440, 728,3488, 736,928, 744,2976, + 752,1952, 760,4000, 776,2144, 784,1120, 792,3168, 808,2656, 816,1632, 824,3680, 840,2400, + 848,1376, 856,3424, 872,2912, 880,1888, 888,3936, 904,2272, 912,1248, 920,3296, 936,2784, + 944,1760, 952,3808, 968,2528, 976,1504, 984,3552, 1000,3040, 1008,2016, 1016,4064, + 1032,2064, 1048,3088, 1064,2576, 1072,1552, 1080,3600, 1096,2320, 1104,1296, 1112,3344, + 1128,2832, 1136,1808, 1144,3856, 1160,2192, 1176,3216, 1192,2704, 1200,1680, 1208,3728, + 1224,2448, 1232,1424, 1240,3472, 1256,2960, 1264,1936, 1272,3984, 1288,2128, 1304,3152, + 1320,2640, 1328,1616, 1336,3664, 1352,2384, 1368,3408, 1384,2896, 1392,1872, 1400,3920, + 1416,2256, 1432,3280, 1448,2768, 1456,1744, 1464,3792, 1480,2512, 1496,3536, 1512,3024, + 1520,2000, 1528,4048, 1544,2096, 1560,3120, 1576,2608, 1592,3632, 1608,2352, 1624,3376, + 1640,2864, 1648,1840, 1656,3888, 1672,2224, 1688,3248, 1704,2736, 1720,3760, 1736,2480, + 1752,3504, 1768,2992, 1776,1968, 1784,4016, 1800,2160, 1816,3184, 1832,2672, 1848,3696, + 1864,2416, 1880,3440, 1896,2928, 1912,3952, 1928,2288, 1944,3312, 1960,2800, 1976,3824, + 1992,2544, 2008,3568, 2024,3056, 2040,4080, 2072,3080, 2088,2568, 2104,3592, 2120,2312, + 2136,3336, 2152,2824, 2168,3848, 2200,3208, 2216,2696, 2232,3720, 2248,2440, 2264,3464, + 2280,2952, 2296,3976, 2328,3144, 2344,2632, 2360,3656, 2392,3400, 2408,2888, 2424,3912, + 2456,3272, 2472,2760, 2488,3784, 2520,3528, 2536,3016, 2552,4040, 2584,3112, 2616,3624, + 2648,3368, 2664,2856, 2680,3880, 2712,3240, 2744,3752, 2776,3496, 2792,2984, 2808,4008, + 2840,3176, 2872,3688, 2904,3432, 2936,3944, 2968,3304, 3000,3816, 3032,3560, 3064,4072, + 3128,3608, 3160,3352, 3192,3864, 3256,3736, 3288,3480, 3320,3992, 3384,3672, 3448,3928, + 3512,3800, 3576,4056, 3704,3896, 3832,4024 +}; + +const uint16_t armBitRevIndexTableF64_1024[ARMBITREVINDEXTABLEF64_1024_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 992 */ + 8,4096, 16,2048, 24,6144, 32,1024, 40,5120, 48,3072, 56,7168, 64,512, 72,4608, + 80,2560, 88,6656, 96,1536, 104,5632, 112,3584, 120,7680, 128,256, 136,4352, + 144,2304, 152,6400, 160,1280, 168,5376, 176,3328, 184,7424, 192,768, 200,4864, + 208,2816, 216,6912, 224,1792, 232,5888, 240,3840, 248,7936, 264,4224, 272,2176, + 280,6272, 288,1152, 296,5248, 304,3200, 312,7296, 320,640, 328,4736, 336,2688, + 344,6784, 352,1664, 360,5760, 368,3712, 376,7808, 392,4480, 400,2432, 408,6528, + 416,1408, 424,5504, 432,3456, 440,7552, 448,896, 456,4992, 464,2944, 472,7040, + 480,1920, 488,6016, 496,3968, 504,8064, 520,4160, 528,2112, 536,6208, 544,1088, + 552,5184, 560,3136, 568,7232, 584,4672, 592,2624, 600,6720, 608,1600, 616,5696, + 624,3648, 632,7744, 648,4416, 656,2368, 664,6464, 672,1344, 680,5440, 688,3392, + 696,7488, 704,832, 712,4928, 720,2880, 728,6976, 736,1856, 744,5952, 752,3904, + 760,8000, 776,4288, 784,2240, 792,6336, 800,1216, 808,5312, 816,3264, 824,7360, + 840,4800, 848,2752, 856,6848, 864,1728, 872,5824, 880,3776, 888,7872, 904,4544, + 912,2496, 920,6592, 928,1472, 936,5568, 944,3520, 952,7616, 968,5056, 976,3008, + 984,7104, 992,1984, 1000,6080, 1008,4032, 1016,8128, 1032,4128, 1040,2080, + 1048,6176, 1064,5152, 1072,3104, 1080,7200, 1096,4640, 1104,2592, 1112,6688, + 1120,1568, 1128,5664, 1136,3616, 1144,7712, 1160,4384, 1168,2336, 1176,6432, + 1184,1312, 1192,5408, 1200,3360, 1208,7456, 1224,4896, 1232,2848, 1240,6944, + 1248,1824, 1256,5920, 1264,3872, 1272,7968, 1288,4256, 1296,2208, 1304,6304, + 1320,5280, 1328,3232, 1336,7328, 1352,4768, 1360,2720, 1368,6816, 1376,1696, + 1384,5792, 1392,3744, 1400,7840, 1416,4512, 1424,2464, 1432,6560, 1448,5536, + 1456,3488, 1464,7584, 1480,5024, 1488,2976, 1496,7072, 1504,1952, 1512,6048, + 1520,4000, 1528,8096, 1544,4192, 1552,2144, 1560,6240, 1576,5216, 1584,3168, + 1592,7264, 1608,4704, 1616,2656, 1624,6752, 1640,5728, 1648,3680, 1656,7776, + 1672,4448, 1680,2400, 1688,6496, 1704,5472, 1712,3424, 1720,7520, 1736,4960, + 1744,2912, 1752,7008, 1760,1888, 1768,5984, 1776,3936, 1784,8032, 1800,4320, + 1808,2272, 1816,6368, 1832,5344, 1840,3296, 1848,7392, 1864,4832, 1872,2784, + 1880,6880, 1896,5856, 1904,3808, 1912,7904, 1928,4576, 1936,2528, 1944,6624, + 1960,5600, 1968,3552, 1976,7648, 1992,5088, 2000,3040, 2008,7136, 2024,6112, + 2032,4064, 2040,8160, 2056,4112, 2072,6160, 2088,5136, 2096,3088, 2104,7184, + 2120,4624, 2128,2576, 2136,6672, 2152,5648, 2160,3600, 2168,7696, 2184,4368, + 2192,2320, 2200,6416, 2216,5392, 2224,3344, 2232,7440, 2248,4880, 2256,2832, + 2264,6928, 2280,5904, 2288,3856, 2296,7952, 2312,4240, 2328,6288, 2344,5264, + 2352,3216, 2360,7312, 2376,4752, 2384,2704, 2392,6800, 2408,5776, 2416,3728, + 2424,7824, 2440,4496, 2456,6544, 2472,5520, 2480,3472, 2488,7568, 2504,5008, + 2512,2960, 2520,7056, 2536,6032, 2544,3984, 2552,8080, 2568,4176, 2584,6224, + 2600,5200, 2608,3152, 2616,7248, 2632,4688, 2648,6736, 2664,5712, 2672,3664, + 2680,7760, 2696,4432, 2712,6480, 2728,5456, 2736,3408, 2744,7504, 2760,4944, + 2768,2896, 2776,6992, 2792,5968, 2800,3920, 2808,8016, 2824,4304, 2840,6352, + 2856,5328, 2864,3280, 2872,7376, 2888,4816, 2904,6864, 2920,5840, 2928,3792, + 2936,7888, 2952,4560, 2968,6608, 2984,5584, 2992,3536, 3000,7632, 3016,5072, + 3032,7120, 3048,6096, 3056,4048, 3064,8144, 3080,4144, 3096,6192, 3112,5168, + 3128,7216, 3144,4656, 3160,6704, 3176,5680, 3184,3632, 3192,7728, 3208,4400, + 3224,6448, 3240,5424, 3248,3376, 3256,7472, 3272,4912, 3288,6960, 3304,5936, + 3312,3888, 3320,7984, 3336,4272, 3352,6320, 3368,5296, 3384,7344, 3400,4784, + 3416,6832, 3432,5808, 3440,3760, 3448,7856, 3464,4528, 3480,6576, 3496,5552, + 3512,7600, 3528,5040, 3544,7088, 3560,6064, 3568,4016, 3576,8112, 3592,4208, + 3608,6256, 3624,5232, 3640,7280, 3656,4720, 3672,6768, 3688,5744, 3704,7792, + 3720,4464, 3736,6512, 3752,5488, 3768,7536, 3784,4976, 3800,7024, 3816,6000, + 3824,3952, 3832,8048, 3848,4336, 3864,6384, 3880,5360, 3896,7408, 3912,4848, + 3928,6896, 3944,5872, 3960,7920, 3976,4592, 3992,6640, 4008,5616, 4024,7664, + 4040,5104, 4056,7152, 4072,6128, 4088,8176, 4120,6152, 4136,5128, 4152,7176, + 4168,4616, 4184,6664, 4200,5640, 4216,7688, 4232,4360, 4248,6408, 4264,5384, + 4280,7432, 4296,4872, 4312,6920, 4328,5896, 4344,7944, 4376,6280, 4392,5256, + 4408,7304, 4424,4744, 4440,6792, 4456,5768, 4472,7816, 4504,6536, 4520,5512, + 4536,7560, 4552,5000, 4568,7048, 4584,6024, 4600,8072, 4632,6216, 4648,5192, + 4664,7240, 4696,6728, 4712,5704, 4728,7752, 4760,6472, 4776,5448, 4792,7496, + 4808,4936, 4824,6984, 4840,5960, 4856,8008, 4888,6344, 4904,5320, 4920,7368, + 4952,6856, 4968,5832, 4984,7880, 5016,6600, 5032,5576, 5048,7624, 5080,7112, + 5096,6088, 5112,8136, 5144,6184, 5176,7208, 5208,6696, 5224,5672, 5240,7720, + 5272,6440, 5288,5416, 5304,7464, 5336,6952, 5352,5928, 5368,7976, 5400,6312, + 5432,7336, 5464,6824, 5480,5800, 5496,7848, 5528,6568, 5560,7592, 5592,7080, + 5608,6056, 5624,8104, 5656,6248, 5688,7272, 5720,6760, 5752,7784, 5784,6504, + 5816,7528, 5848,7016, 5864,5992, 5880,8040, 5912,6376, 5944,7400, 5976,6888, + 6008,7912, 6040,6632, 6072,7656, 6104,7144, 6136,8168, 6200,7192, 6232,6680, + 6264,7704, 6296,6424, 6328,7448, 6360,6936, 6392,7960, 6456,7320, 6488,6808, + 6520,7832, 6584,7576, 6616,7064, 6648,8088, 6712,7256, 6776,7768, 6840,7512, + 6872,7000, 6904,8024, 6968,7384, 7032,7896, 7096,7640, 7160,8152, 7288,7736, + 7352,7480, 7416,7992, 7544,7864, 7672,8120, 7928,8056 +}; + +const uint16_t armBitRevIndexTableF64_2048[ARMBITREVINDEXTABLEF64_2048_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 1984 */ + 8,8192, 16,4096, 24,12288, 32,2048, 40,10240, 48,6144, 56,14336, 64,1024, + 72,9216, 80,5120, 88,13312, 96,3072, 104,11264, 112,7168, 120,15360, 128,512, + 136,8704, 144,4608, 152,12800, 160,2560, 168,10752, 176,6656, 184,14848, + 192,1536, 200,9728, 208,5632, 216,13824, 224,3584, 232,11776, 240,7680, + 248,15872, 264,8448, 272,4352, 280,12544, 288,2304, 296,10496, 304,6400, + 312,14592, 320,1280, 328,9472, 336,5376, 344,13568, 352,3328, 360,11520, + 368,7424, 376,15616, 384,768, 392,8960, 400,4864, 408,13056, 416,2816, + 424,11008, 432,6912, 440,15104, 448,1792, 456,9984, 464,5888, 472,14080, + 480,3840, 488,12032, 496,7936, 504,16128, 520,8320, 528,4224, 536,12416, + 544,2176, 552,10368, 560,6272, 568,14464, 576,1152, 584,9344, 592,5248, + 600,13440, 608,3200, 616,11392, 624,7296, 632,15488, 648,8832, 656,4736, + 664,12928, 672,2688, 680,10880, 688,6784, 696,14976, 704,1664, 712,9856, + 720,5760, 728,13952, 736,3712, 744,11904, 752,7808, 760,16000, 776,8576, + 784,4480, 792,12672, 800,2432, 808,10624, 816,6528, 824,14720, 832,1408, + 840,9600, 848,5504, 856,13696, 864,3456, 872,11648, 880,7552, 888,15744, + 904,9088, 912,4992, 920,13184, 928,2944, 936,11136, 944,7040, 952,15232, + 960,1920, 968,10112, 976,6016, 984,14208, 992,3968, 1000,12160, 1008,8064, + 1016,16256, 1032,8256, 1040,4160, 1048,12352, 1056,2112, 1064,10304, 1072,6208, + 1080,14400, 1096,9280, 1104,5184, 1112,13376, 1120,3136, 1128,11328, 1136,7232, + 1144,15424, 1160,8768, 1168,4672, 1176,12864, 1184,2624, 1192,10816, 1200,6720, + 1208,14912, 1216,1600, 1224,9792, 1232,5696, 1240,13888, 1248,3648, 1256,11840, + 1264,7744, 1272,15936, 1288,8512, 1296,4416, 1304,12608, 1312,2368, 1320,10560, + 1328,6464, 1336,14656, 1352,9536, 1360,5440, 1368,13632, 1376,3392, 1384,11584, + 1392,7488, 1400,15680, 1416,9024, 1424,4928, 1432,13120, 1440,2880, 1448,11072, + 1456,6976, 1464,15168, 1472,1856, 1480,10048, 1488,5952, 1496,14144, 1504,3904, + 1512,12096, 1520,8000, 1528,16192, 1544,8384, 1552,4288, 1560,12480, 1568,2240, + 1576,10432, 1584,6336, 1592,14528, 1608,9408, 1616,5312, 1624,13504, 1632,3264, + 1640,11456, 1648,7360, 1656,15552, 1672,8896, 1680,4800, 1688,12992, 1696,2752, + 1704,10944, 1712,6848, 1720,15040, 1736,9920, 1744,5824, 1752,14016, 1760,3776, + 1768,11968, 1776,7872, 1784,16064, 1800,8640, 1808,4544, 1816,12736, 1824,2496, + 1832,10688, 1840,6592, 1848,14784, 1864,9664, 1872,5568, 1880,13760, 1888,3520, + 1896,11712, 1904,7616, 1912,15808, 1928,9152, 1936,5056, 1944,13248, 1952,3008, + 1960,11200, 1968,7104, 1976,15296, 1992,10176, 2000,6080, 2008,14272, 2016,4032, + 2024,12224, 2032,8128, 2040,16320, 2056,8224, 2064,4128, 2072,12320, 2088,10272, + 2096,6176, 2104,14368, 2120,9248, 2128,5152, 2136,13344, 2144,3104, 2152,11296, + 2160,7200, 2168,15392, 2184,8736, 2192,4640, 2200,12832, 2208,2592, 2216,10784, + 2224,6688, 2232,14880, 2248,9760, 2256,5664, 2264,13856, 2272,3616, 2280,11808, + 2288,7712, 2296,15904, 2312,8480, 2320,4384, 2328,12576, 2344,10528, 2352,6432, + 2360,14624, 2376,9504, 2384,5408, 2392,13600, 2400,3360, 2408,11552, 2416,7456, + 2424,15648, 2440,8992, 2448,4896, 2456,13088, 2464,2848, 2472,11040, 2480,6944, + 2488,15136, 2504,10016, 2512,5920, 2520,14112, 2528,3872, 2536,12064, 2544,7968, + 2552,16160, 2568,8352, 2576,4256, 2584,12448, 2600,10400, 2608,6304, 2616,14496, + 2632,9376, 2640,5280, 2648,13472, 2656,3232, 2664,11424, 2672,7328, 2680,15520, + 2696,8864, 2704,4768, 2712,12960, 2728,10912, 2736,6816, 2744,15008, 2760,9888, + 2768,5792, 2776,13984, 2784,3744, 2792,11936, 2800,7840, 2808,16032, 2824,8608, + 2832,4512, 2840,12704, 2856,10656, 2864,6560, 2872,14752, 2888,9632, 2896,5536, + 2904,13728, 2912,3488, 2920,11680, 2928,7584, 2936,15776, 2952,9120, 2960,5024, + 2968,13216, 2984,11168, 2992,7072, 3000,15264, 3016,10144, 3024,6048, + 3032,14240, 3040,4000, 3048,12192, 3056,8096, 3064,16288, 3080,8288, 3088,4192, + 3096,12384, 3112,10336, 3120,6240, 3128,14432, 3144,9312, 3152,5216, 3160,13408, + 3176,11360, 3184,7264, 3192,15456, 3208,8800, 3216,4704, 3224,12896, 3240,10848, + 3248,6752, 3256,14944, 3272,9824, 3280,5728, 3288,13920, 3296,3680, 3304,11872, + 3312,7776, 3320,15968, 3336,8544, 3344,4448, 3352,12640, 3368,10592, 3376,6496, + 3384,14688, 3400,9568, 3408,5472, 3416,13664, 3432,11616, 3440,7520, 3448,15712, + 3464,9056, 3472,4960, 3480,13152, 3496,11104, 3504,7008, 3512,15200, 3528,10080, + 3536,5984, 3544,14176, 3552,3936, 3560,12128, 3568,8032, 3576,16224, 3592,8416, + 3600,4320, 3608,12512, 3624,10464, 3632,6368, 3640,14560, 3656,9440, 3664,5344, + 3672,13536, 3688,11488, 3696,7392, 3704,15584, 3720,8928, 3728,4832, 3736,13024, + 3752,10976, 3760,6880, 3768,15072, 3784,9952, 3792,5856, 3800,14048, 3816,12000, + 3824,7904, 3832,16096, 3848,8672, 3856,4576, 3864,12768, 3880,10720, 3888,6624, + 3896,14816, 3912,9696, 3920,5600, 3928,13792, 3944,11744, 3952,7648, 3960,15840, + 3976,9184, 3984,5088, 3992,13280, 4008,11232, 4016,7136, 4024,15328, 4040,10208, + 4048,6112, 4056,14304, 4072,12256, 4080,8160, 4088,16352, 4104,8208, 4120,12304, + 4136,10256, 4144,6160, 4152,14352, 4168,9232, 4176,5136, 4184,13328, 4200,11280, + 4208,7184, 4216,15376, 4232,8720, 4240,4624, 4248,12816, 4264,10768, 4272,6672, + 4280,14864, 4296,9744, 4304,5648, 4312,13840, 4328,11792, 4336,7696, 4344,15888, + 4360,8464, 4376,12560, 4392,10512, 4400,6416, 4408,14608, 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13016,13976, 13048,16024, + 13112,14744, 13144,13720, 13176,15768, 13240,15256, 13272,14232, 13304,16280, + 13368,14424, 13432,15448, 13496,14936, 13528,13912, 13560,15960, 13624,14680, + 13688,15704, 13752,15192, 13784,14168, 13816,16216, 13880,14552, 13944,15576, + 14008,15064, 14072,16088, 14136,14808, 14200,15832, 14264,15320, 14328,16344, + 14456,15416, 14520,14904, 14584,15928, 14712,15672, 14776,15160, 14840,16184, + 14968,15544, 15096,16056, 15224,15800, 15352,16312, 15608,15992, 15864,16248 +}; + +const uint16_t armBitRevIndexTableF64_4096[ARMBITREVINDEXTABLEF64_4096_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 4032 */ + 8,16384, 16,8192, 24,24576, 32,4096, 40,20480, 48,12288, 56,28672, 64,2048, + 72,18432, 80,10240, 88,26624, 96,6144, 104,22528, 112,14336, 120,30720, + 128,1024, 136,17408, 144,9216, 152,25600, 160,5120, 168,21504, 176,13312, + 184,29696, 192,3072, 200,19456, 208,11264, 216,27648, 224,7168, 232,23552, + 240,15360, 248,31744, 256,512, 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25592,32536, 25656,28824, 25688,26776, 25720,30872, 25784,29848, + 25816,27800, 25848,31896, 25912,29336, 25944,27288, 25976,31384, 26008,26264, + 26040,30360, 26072,28312, 26104,32408, 26168,29080, 26200,27032, 26232,31128, + 26296,30104, 26328,28056, 26360,32152, 26424,29592, 26456,27544, 26488,31640, + 26552,30616, 26584,28568, 26616,32664, 26680,28760, 26744,30808, 26808,29784, + 26840,27736, 26872,31832, 26936,29272, 26968,27224, 27000,31320, 27064,30296, + 27096,28248, 27128,32344, 27192,29016, 27256,31064, 27320,30040, 27352,27992, + 27384,32088, 27448,29528, 27512,31576, 27576,30552, 27608,28504, 27640,32600, + 27704,28888, 27768,30936, 27832,29912, 27896,31960, 27960,29400, 28024,31448, + 28088,30424, 28120,28376, 28152,32472, 28216,29144, 28280,31192, 28344,30168, + 28408,32216, 28472,29656, 28536,31704, 28600,30680, 28664,32728, 28792,30776, + 28856,29752, 28920,31800, 28984,29240, 29048,31288, 29112,30264, 29176,32312, + 29304,31032, 29368,30008, 29432,32056, 29560,31544, 29624,30520, 29688,32568, + 29816,30904, 29944,31928, 30072,31416, 30136,30392, 30200,32440, 30328,31160, + 30456,32184, 30584,31672, 30712,32696, 30968,31864, 31096,31352, 31224,32376, + 31480,32120, 31736,32632, 32248,32504 +}; + +const uint16_t armBitRevIndexTable16[ARMBITREVINDEXTABLE_16_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 8x2, size 20 */ + 8,64, 24,72, 16,64, 40,80, 32,64, 56,88, 48,72, 88,104, 72,96, 104,112 +}; + +const uint16_t armBitRevIndexTable32[ARMBITREVINDEXTABLE_32_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 8x4, size 48 */ + 8,64, 16,128, 24,192, 32,64, 40,72, 48,136, 56,200, 64,128, 72,80, 88,208, + 80,144, 96,192, 104,208, 112,152, 120,216, 136,192, 144,160, 168,208, + 152,224, 176,208, 184,232, 216,240, 200,224, 232,240 +}; + +const uint16_t armBitRevIndexTable64[ARMBITREVINDEXTABLE_64_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 8, size 56 */ + 8,64, 16,128, 24,192, 32,256, 40,320, 48,384, 56,448, 80,136, 88,200, + 96,264, 104,328, 112,392, 120,456, 152,208, 160,272, 168,336, 176,400, + 184,464, 224,280, 232,344, 240,408, 248,472, 296,352, 304,416, 312,480, + 368,424, 376,488, 440,496 +}; + + +const uint16_t armBitRevIndexTable128[ARMBITREVINDEXTABLE_128_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 8x2, size 208 */ + 8,512, 16,64, 24,576, 32,128, 40,640, 48,192, 56,704, 64,256, 72,768, + 80,320, 88,832, 96,384, 104,896, 112,448, 120,960, 128,512, 136,520, + 144,768, 152,584, 160,520, 168,648, 176,200, 184,712, 192,264, 200,776, + 208,328, 216,840, 224,392, 232,904, 240,456, 248,968, 264,528, 272,320, + 280,592, 288,768, 296,656, 304,328, 312,720, 328,784, 344,848, 352,400, + 360,912, 368,464, 376,976, 384,576, 392,536, 400,832, 408,600, 416,584, + 424,664, 432,840, 440,728, 448,592, 456,792, 464,848, 472,856, 480,600, + 488,920, 496,856, 504,984, 520,544, 528,576, 536,608, 552,672, 560,608, + 568,736, 576,768, 584,800, 592,832, 600,864, 608,800, 616,928, 624,864, + 632,992, 648,672, 656,896, 664,928, 688,904, 696,744, 704,896, 712,808, + 720,912, 728,872, 736,928, 744,936, 752,920, 760,1000, 776,800, 784,832, + 792,864, 808,904, 816,864, 824,920, 840,864, 856,880, 872,944, 888,1008, + 904,928, 912,960, 920,992, 944,968, 952,1000, 968,992, 984,1008 +}; + +const uint16_t armBitRevIndexTable256[ARMBITREVINDEXTABLE_256_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 8x4, size 440 */ + 8,512, 16,1024, 24,1536, 32,64, 40,576, 48,1088, 56,1600, 64,128, 72,640, + 80,1152, 88,1664, 96,192, 104,704, 112,1216, 120,1728, 128,256, 136,768, + 144,1280, 152,1792, 160,320, 168,832, 176,1344, 184,1856, 192,384, + 200,896, 208,1408, 216,1920, 224,448, 232,960, 240,1472, 248,1984, + 256,512, 264,520, 272,1032, 280,1544, 288,640, 296,584, 304,1096, 312,1608, + 320,768, 328,648, 336,1160, 344,1672, 352,896, 360,712, 368,1224, 376,1736, + 384,520, 392,776, 400,1288, 408,1800, 416,648, 424,840, 432,1352, 440,1864, + 448,776, 456,904, 464,1416, 472,1928, 480,904, 488,968, 496,1480, 504,1992, + 520,528, 512,1024, 528,1040, 536,1552, 544,1152, 552,592, 560,1104, + 568,1616, 576,1280, 584,656, 592,1168, 600,1680, 608,1408, 616,720, + 624,1232, 632,1744, 640,1032, 648,784, 656,1296, 664,1808, 672,1160, + 680,848, 688,1360, 696,1872, 704,1288, 712,912, 720,1424, 728,1936, + 736,1416, 744,976, 752,1488, 760,2000, 768,1536, 776,1552, 784,1048, + 792,1560, 800,1664, 808,1680, 816,1112, 824,1624, 832,1792, 840,1808, + 848,1176, 856,1688, 864,1920, 872,1936, 880,1240, 888,1752, 896,1544, + 904,1560, 912,1304, 920,1816, 928,1672, 936,1688, 944,1368, 952,1880, + 960,1800, 968,1816, 976,1432, 984,1944, 992,1928, 1000,1944, 1008,1496, + 1016,2008, 1032,1152, 1040,1056, 1048,1568, 1064,1408, 1072,1120, + 1080,1632, 1088,1536, 1096,1160, 1104,1184, 1112,1696, 1120,1552, + 1128,1416, 1136,1248, 1144,1760, 1160,1664, 1168,1312, 1176,1824, + 1184,1544, 1192,1920, 1200,1376, 1208,1888, 1216,1568, 1224,1672, + 1232,1440, 1240,1952, 1248,1560, 1256,1928, 1264,1504, 1272,2016, + 1288,1312, 1296,1408, 1304,1576, 1320,1424, 1328,1416, 1336,1640, + 1344,1792, 1352,1824, 1360,1920, 1368,1704, 1376,1800, 1384,1432, + 1392,1928, 1400,1768, 1416,1680, 1432,1832, 1440,1576, 1448,1936, + 1456,1832, 1464,1896, 1472,1808, 1480,1688, 1488,1936, 1496,1960, + 1504,1816, 1512,1944, 1520,1944, 1528,2024, 1560,1584, 1592,1648, + 1600,1792, 1608,1920, 1616,1800, 1624,1712, 1632,1808, 1640,1936, + 1648,1816, 1656,1776, 1672,1696, 1688,1840, 1704,1952, 1712,1928, + 1720,1904, 1728,1824, 1736,1952, 1744,1832, 1752,1968, 1760,1840, + 1768,1960, 1776,1944, 1784,2032, 1864,1872, 1848,1944, 1872,1888, + 1880,1904, 1888,1984, 1896,2000, 1912,2032, 1904,2016, 1976,2032, + 1960,1968, 2008,2032, 1992,2016, 2024,2032 +}; + +const uint16_t armBitRevIndexTable512[ARMBITREVINDEXTABLE_512_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 8, size 448 */ + 8,512, 16,1024, 24,1536, 32,2048, 40,2560, 48,3072, 56,3584, 72,576, + 80,1088, 88,1600, 96,2112, 104,2624, 112,3136, 120,3648, 136,640, 144,1152, + 152,1664, 160,2176, 168,2688, 176,3200, 184,3712, 200,704, 208,1216, + 216,1728, 224,2240, 232,2752, 240,3264, 248,3776, 264,768, 272,1280, + 280,1792, 288,2304, 296,2816, 304,3328, 312,3840, 328,832, 336,1344, + 344,1856, 352,2368, 360,2880, 368,3392, 376,3904, 392,896, 400,1408, + 408,1920, 416,2432, 424,2944, 432,3456, 440,3968, 456,960, 464,1472, + 472,1984, 480,2496, 488,3008, 496,3520, 504,4032, 528,1032, 536,1544, + 544,2056, 552,2568, 560,3080, 568,3592, 592,1096, 600,1608, 608,2120, + 616,2632, 624,3144, 632,3656, 656,1160, 664,1672, 672,2184, 680,2696, + 688,3208, 696,3720, 720,1224, 728,1736, 736,2248, 744,2760, 752,3272, + 760,3784, 784,1288, 792,1800, 800,2312, 808,2824, 816,3336, 824,3848, + 848,1352, 856,1864, 864,2376, 872,2888, 880,3400, 888,3912, 912,1416, + 920,1928, 928,2440, 936,2952, 944,3464, 952,3976, 976,1480, 984,1992, + 992,2504, 1000,3016, 1008,3528, 1016,4040, 1048,1552, 1056,2064, 1064,2576, + 1072,3088, 1080,3600, 1112,1616, 1120,2128, 1128,2640, 1136,3152, + 1144,3664, 1176,1680, 1184,2192, 1192,2704, 1200,3216, 1208,3728, + 1240,1744, 1248,2256, 1256,2768, 1264,3280, 1272,3792, 1304,1808, + 1312,2320, 1320,2832, 1328,3344, 1336,3856, 1368,1872, 1376,2384, + 1384,2896, 1392,3408, 1400,3920, 1432,1936, 1440,2448, 1448,2960, + 1456,3472, 1464,3984, 1496,2000, 1504,2512, 1512,3024, 1520,3536, + 1528,4048, 1568,2072, 1576,2584, 1584,3096, 1592,3608, 1632,2136, + 1640,2648, 1648,3160, 1656,3672, 1696,2200, 1704,2712, 1712,3224, + 1720,3736, 1760,2264, 1768,2776, 1776,3288, 1784,3800, 1824,2328, + 1832,2840, 1840,3352, 1848,3864, 1888,2392, 1896,2904, 1904,3416, + 1912,3928, 1952,2456, 1960,2968, 1968,3480, 1976,3992, 2016,2520, + 2024,3032, 2032,3544, 2040,4056, 2088,2592, 2096,3104, 2104,3616, + 2152,2656, 2160,3168, 2168,3680, 2216,2720, 2224,3232, 2232,3744, + 2280,2784, 2288,3296, 2296,3808, 2344,2848, 2352,3360, 2360,3872, + 2408,2912, 2416,3424, 2424,3936, 2472,2976, 2480,3488, 2488,4000, + 2536,3040, 2544,3552, 2552,4064, 2608,3112, 2616,3624, 2672,3176, + 2680,3688, 2736,3240, 2744,3752, 2800,3304, 2808,3816, 2864,3368, + 2872,3880, 2928,3432, 2936,3944, 2992,3496, 3000,4008, 3056,3560, + 3064,4072, 3128,3632, 3192,3696, 3256,3760, 3320,3824, 3384,3888, + 3448,3952, 3512,4016, 3576,4080 +}; + +const uint16_t armBitRevIndexTable1024[ARMBITREVINDEXTABLE_1024_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 8x2, size 1800 */ + 8,4096, 16,512, 24,4608, 32,1024, 40,5120, 48,1536, 56,5632, 64,2048, + 72,6144, 80,2560, 88,6656, 96,3072, 104,7168, 112,3584, 120,7680, 128,2048, + 136,4160, 144,576, 152,4672, 160,1088, 168,5184, 176,1600, 184,5696, + 192,2112, 200,6208, 208,2624, 216,6720, 224,3136, 232,7232, 240,3648, + 248,7744, 256,2048, 264,4224, 272,640, 280,4736, 288,1152, 296,5248, + 304,1664, 312,5760, 320,2176, 328,6272, 336,2688, 344,6784, 352,3200, + 360,7296, 368,3712, 376,7808, 384,2112, 392,4288, 400,704, 408,4800, + 416,1216, 424,5312, 432,1728, 440,5824, 448,2240, 456,6336, 464,2752, + 472,6848, 480,3264, 488,7360, 496,3776, 504,7872, 512,2048, 520,4352, + 528,768, 536,4864, 544,1280, 552,5376, 560,1792, 568,5888, 576,2304, + 584,6400, 592,2816, 600,6912, 608,3328, 616,7424, 624,3840, 632,7936, + 640,2176, 648,4416, 656,832, 664,4928, 672,1344, 680,5440, 688,1856, + 696,5952, 704,2368, 712,6464, 720,2880, 728,6976, 736,3392, 744,7488, + 752,3904, 760,8000, 768,2112, 776,4480, 784,896, 792,4992, 800,1408, + 808,5504, 816,1920, 824,6016, 832,2432, 840,6528, 848,2944, 856,7040, + 864,3456, 872,7552, 880,3968, 888,8064, 896,2240, 904,4544, 912,960, + 920,5056, 928,1472, 936,5568, 944,1984, 952,6080, 960,2496, 968,6592, + 976,3008, 984,7104, 992,3520, 1000,7616, 1008,4032, 1016,8128, 1024,4096, + 1032,4104, 1040,4352, 1048,4616, 1056,4104, 1064,5128, 1072,1544, + 1080,5640, 1088,2056, 1096,6152, 1104,2568, 1112,6664, 1120,3080, + 1128,7176, 1136,3592, 1144,7688, 1152,6144, 1160,4168, 1168,6400, + 1176,4680, 1184,6152, 1192,5192, 1200,1608, 1208,5704, 1216,2120, + 1224,6216, 1232,2632, 1240,6728, 1248,3144, 1256,7240, 1264,3656, + 1272,7752, 1280,4160, 1288,4232, 1296,4416, 1304,4744, 1312,4168, + 1320,5256, 1328,1672, 1336,5768, 1344,2184, 1352,6280, 1360,2696, + 1368,6792, 1376,3208, 1384,7304, 1392,3720, 1400,7816, 1408,6208, + 1416,4296, 1424,6464, 1432,4808, 1440,6216, 1448,5320, 1456,1736, + 1464,5832, 1472,2248, 1480,6344, 1488,2760, 1496,6856, 1504,3272, + 1512,7368, 1520,3784, 1528,7880, 1536,4224, 1544,4360, 1552,4480, + 1560,4872, 1568,4232, 1576,5384, 1584,1800, 1592,5896, 1600,2312, + 1608,6408, 1616,2824, 1624,6920, 1632,3336, 1640,7432, 1648,3848, + 1656,7944, 1664,6272, 1672,4424, 1680,6528, 1688,4936, 1696,6280, + 1704,5448, 1712,1864, 1720,5960, 1728,2376, 1736,6472, 1744,2888, + 1752,6984, 1760,3400, 1768,7496, 1776,3912, 1784,8008, 1792,4288, + 1800,4488, 1808,4544, 1816,5000, 1824,4296, 1832,5512, 1840,1928, + 1848,6024, 1856,2440, 1864,6536, 1872,2952, 1880,7048, 1888,3464, + 1896,7560, 1904,3976, 1912,8072, 1920,6336, 1928,4552, 1936,6592, + 1944,5064, 1952,6344, 1960,5576, 1968,1992, 1976,6088, 1984,2504, + 1992,6600, 2000,3016, 2008,7112, 2016,3528, 2024,7624, 2032,4040, + 2040,8136, 2056,4112, 2064,2112, 2072,4624, 2080,4352, 2088,5136, + 2096,4480, 2104,5648, 2120,6160, 2128,2576, 2136,6672, 2144,3088, + 2152,7184, 2160,3600, 2168,7696, 2176,2560, 2184,4176, 2192,2816, + 2200,4688, 2208,2568, 2216,5200, 2224,2824, 2232,5712, 2240,2576, + 2248,6224, 2256,2640, 2264,6736, 2272,3152, 2280,7248, 2288,3664, + 2296,7760, 2312,4240, 2320,2432, 2328,4752, 2336,6400, 2344,5264, + 2352,6528, 2360,5776, 2368,2816, 2376,6288, 2384,2704, 2392,6800, + 2400,3216, 2408,7312, 2416,3728, 2424,7824, 2432,2624, 2440,4304, + 2448,2880, 2456,4816, 2464,2632, 2472,5328, 2480,2888, 2488,5840, + 2496,2640, 2504,6352, 2512,2768, 2520,6864, 2528,3280, 2536,7376, + 2544,3792, 2552,7888, 2568,4368, 2584,4880, 2592,4416, 2600,5392, + 2608,4544, 2616,5904, 2632,6416, 2640,2832, 2648,6928, 2656,3344, + 2664,7440, 2672,3856, 2680,7952, 2696,4432, 2704,2944, 2712,4944, + 2720,4432, 2728,5456, 2736,2952, 2744,5968, 2752,2944, 2760,6480, + 2768,2896, 2776,6992, 2784,3408, 2792,7504, 2800,3920, 2808,8016, + 2824,4496, 2840,5008, 2848,6464, 2856,5520, 2864,6592, 2872,6032, + 2888,6544, 2896,2960, 2904,7056, 2912,3472, 2920,7568, 2928,3984, + 2936,8080, 2952,4560, 2960,3008, 2968,5072, 2976,6480, 2984,5584, + 2992,3016, 3000,6096, 3016,6608, 3032,7120, 3040,3536, 3048,7632, + 3056,4048, 3064,8144, 3072,4608, 3080,4120, 3088,4864, 3096,4632, + 3104,4616, 3112,5144, 3120,4872, 3128,5656, 3136,4624, 3144,6168, + 3152,4880, 3160,6680, 3168,4632, 3176,7192, 3184,3608, 3192,7704, + 3200,6656, 3208,4184, 3216,6912, 3224,4696, 3232,6664, 3240,5208, + 3248,6920, 3256,5720, 3264,6672, 3272,6232, 3280,6928, 3288,6744, + 3296,6680, 3304,7256, 3312,3672, 3320,7768, 3328,4672, 3336,4248, + 3344,4928, 3352,4760, 3360,4680, 3368,5272, 3376,4936, 3384,5784, + 3392,4688, 3400,6296, 3408,4944, 3416,6808, 3424,4696, 3432,7320, + 3440,3736, 3448,7832, 3456,6720, 3464,4312, 3472,6976, 3480,4824, + 3488,6728, 3496,5336, 3504,6984, 3512,5848, 3520,6736, 3528,6360, + 3536,6992, 3544,6872, 3552,6744, 3560,7384, 3568,3800, 3576,7896, + 3584,4736, 3592,4376, 3600,4992, 3608,4888, 3616,4744, 3624,5400, + 3632,5000, 3640,5912, 3648,4752, 3656,6424, 3664,5008, 3672,6936, + 3680,4760, 3688,7448, 3696,3864, 3704,7960, 3712,6784, 3720,4440, + 3728,7040, 3736,4952, 3744,6792, 3752,5464, 3760,7048, 3768,5976, + 3776,6800, 3784,6488, 3792,7056, 3800,7000, 3808,6808, 3816,7512, + 3824,3928, 3832,8024, 3840,4800, 3848,4504, 3856,5056, 3864,5016, + 3872,4808, 3880,5528, 3888,5064, 3896,6040, 3904,4816, 3912,6552, + 3920,5072, 3928,7064, 3936,4824, 3944,7576, 3952,3992, 3960,8088, + 3968,6848, 3976,4568, 3984,7104, 3992,5080, 4000,6856, 4008,5592, + 4016,7112, 4024,6104, 4032,6864, 4040,6616, 4048,7120, 4056,7128, + 4064,6872, 4072,7640, 4080,7128, 4088,8152, 4104,4128, 4112,4160, + 4120,4640, 4136,5152, 4144,4232, 4152,5664, 4160,4352, 4168,6176, + 4176,4416, 4184,6688, 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7600,8008, 7608,8040, 7616,7760, 7624,7792, 7632,8016, 7640,8048, + 7648,7768, 7656,7800, 7664,8024, 7672,7928, 7688,7712, 7704,7728, + 7752,7776, 7768,7792, 7800,7992, 7816,7840, 7824,8064, 7832,8096, + 7856,8072, 7864,8104, 7872,8064, 7880,8072, 7888,8080, 7896,8112, + 7904,8096, 7912,8104, 7920,8088, 7928,8056, 7944,7968, 7960,7984, + 8008,8032, 8024,8048, 8056,8120, 8072,8096, 8080,8128, 8088,8160, + 8112,8136, 8120,8168, 8136,8160, 8152,8176 +}; + +const uint16_t armBitRevIndexTable2048[ARMBITREVINDEXTABLE_2048_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 8x2, size 3808 */ + 8,4096, 16,8192, 24,12288, 32,512, 40,4608, 48,8704, 56,12800, 64,1024, + 72,5120, 80,9216, 88,13312, 96,1536, 104,5632, 112,9728, 120,13824, + 128,2048, 136,6144, 144,10240, 152,14336, 160,2560, 168,6656, 176,10752, + 184,14848, 192,3072, 200,7168, 208,11264, 216,15360, 224,3584, 232,7680, + 240,11776, 248,15872, 256,1024, 264,4160, 272,8256, 280,12352, 288,576, + 296,4672, 304,8768, 312,12864, 320,1088, 328,5184, 336,9280, 344,13376, + 352,1600, 360,5696, 368,9792, 376,13888, 384,2112, 392,6208, 400,10304, + 408,14400, 416,2624, 424,6720, 432,10816, 440,14912, 448,3136, 456,7232, + 464,11328, 472,15424, 480,3648, 488,7744, 496,11840, 504,15936, 512,2048, + 520,4224, 528,8320, 536,12416, 544,640, 552,4736, 560,8832, 568,12928, + 576,1152, 584,5248, 592,9344, 600,13440, 608,1664, 616,5760, 624,9856, + 632,13952, 640,2176, 648,6272, 656,10368, 664,14464, 672,2688, 680,6784, + 688,10880, 696,14976, 704,3200, 712,7296, 720,11392, 728,15488, 736,3712, + 744,7808, 752,11904, 760,16000, 768,3072, 776,4288, 784,8384, 792,12480, + 800,3200, 808,4800, 816,8896, 824,12992, 832,1216, 840,5312, 848,9408, + 856,13504, 864,1728, 872,5824, 880,9920, 888,14016, 896,2240, 904,6336, + 912,10432, 920,14528, 928,2752, 936,6848, 944,10944, 952,15040, 960,3264, + 968,7360, 976,11456, 984,15552, 992,3776, 1000,7872, 1008,11968, 1016,16064, + 1032,4352, 1040,8448, 1048,12544, 1056,3072, 1064,4864, 1072,8960, + 1080,13056, 1088,1280, 1096,5376, 1104,9472, 1112,13568, 1120,1792, + 1128,5888, 1136,9984, 1144,14080, 1152,2304, 1160,6400, 1168,10496, + 1176,14592, 1184,2816, 1192,6912, 1200,11008, 1208,15104, 1216,3328, + 1224,7424, 1232,11520, 1240,15616, 1248,3840, 1256,7936, 1264,12032, + 1272,16128, 1288,4416, 1296,8512, 1304,12608, 1312,3328, 1320,4928, + 1328,9024, 1336,13120, 1352,5440, 1360,9536, 1368,13632, 1376,1856, + 1384,5952, 1392,10048, 1400,14144, 1408,2368, 1416,6464, 1424,10560, + 1432,14656, 1440,2880, 1448,6976, 1456,11072, 1464,15168, 1472,3392, + 1480,7488, 1488,11584, 1496,15680, 1504,3904, 1512,8000, 1520,12096, + 1528,16192, 1536,2112, 1544,4480, 1552,8576, 1560,12672, 1568,2240, + 1576,4992, 1584,9088, 1592,13184, 1600,2368, 1608,5504, 1616,9600, + 1624,13696, 1632,1920, 1640,6016, 1648,10112, 1656,14208, 1664,2432, + 1672,6528, 1680,10624, 1688,14720, 1696,2944, 1704,7040, 1712,11136, + 1720,15232, 1728,3456, 1736,7552, 1744,11648, 1752,15744, 1760,3968, + 1768,8064, 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25912,30896, 25968,27312, 25976,31408, 26032,27824, + 26040,31920, 26096,28336, 26104,32432, 26168,28912, 26232,29424, + 26296,29936, 26360,30448, 26416,26864, 26424,30960, 26480,27376, + 26488,31472, 26544,27888, 26552,31984, 26608,28400, 26616,32496, + 26680,28976, 26744,29488, 26808,30000, 26872,30512, 26936,31024, + 26992,27440, 27000,31536, 27056,27952, 27064,32048, 27120,28464, + 27128,32560, 27192,29040, 27256,29552, 27320,30064, 27384,30576, + 27448,31088, 27512,31600, 27568,28016, 27576,32112, 27632,28528, + 27640,32624, 27704,29104, 27768,29616, 27832,30128, 27896,30640, + 27960,31152, 28024,31664, 28088,32176, 28144,28592, 28152,32688, + 28216,29168, 28280,29680, 28344,30192, 28408,30704, 28472,31216, + 28536,31728, 28600,32240, 28664,32752, 28792,29240, 28856,29752, + 28920,30264, 28984,30776, 29048,31288, 29112,31800, 29176,32312, + 29368,29816, 29432,30328, 29496,30840, 29560,31352, 29624,31864, + 29688,32376, 29944,30392, 30008,30904, 30072,31416, 30136,31928, + 30200,32440, 30520,30968, 30584,31480, 30648,31992, 30712,32504, + 31096,31544, 31160,32056, 31224,32568, 31672,32120, 31736,32632, + 32248,32696 +}; + +const uint16_t armBitRevIndexTable_fixed_16[ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 12 */ + 8,64, 16,32, 24,96, 40,80, 56,112, 88,104 +}; + +const uint16_t armBitRevIndexTable_fixed_32[ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 24 */ + 8,128, 16,64, 24,192, 40,160, 48,96, 56,224, 72,144, + 88,208, 104,176, 120,240, 152,200, 184,232 +}; + +const uint16_t armBitRevIndexTable_fixed_64[ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 56 */ + 8,256, 16,128, 24,384, 32,64, 40,320, 48,192, 56,448, 72,288, 80,160, 88,416, 104,352, + 112,224, 120,480, 136,272, 152,400, 168,336, 176,208, 184,464, 200,304, 216,432, + 232,368, 248,496, 280,392, 296,328, 312,456, 344,424, 376,488, 440,472 +}; + +const uint16_t armBitRevIndexTable_fixed_128[ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 112 */ + 8,512, 16,256, 24,768, 32,128, 40,640, 48,384, 56,896, 72,576, 80,320, 88,832, 96,192, + 104,704, 112,448, 120,960, 136,544, 144,288, 152,800, 168,672, 176,416, 184,928, 200,608, + 208,352, 216,864, 232,736, 240,480, 248,992, 264,528, 280,784, 296,656, 304,400, 312,912, + 328,592, 344,848, 360,720, 368,464, 376,976, 392,560, 408,816, 424,688, 440,944, 456,624, + 472,880, 488,752, 504,1008, 536,776, 552,648, 568,904, 600,840, 616,712, 632,968, + 664,808, 696,936, 728,872, 760,1000, 824,920, 888,984 +}; + +const uint16_t armBitRevIndexTable_fixed_256[ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 240 */ + 8,1024, 16,512, 24,1536, 32,256, 40,1280, 48,768, 56,1792, 64,128, 72,1152, 80,640, + 88,1664, 96,384, 104,1408, 112,896, 120,1920, 136,1088, 144,576, 152,1600, 160,320, + 168,1344, 176,832, 184,1856, 200,1216, 208,704, 216,1728, 224,448, 232,1472, 240,960, + 248,1984, 264,1056, 272,544, 280,1568, 296,1312, 304,800, 312,1824, 328,1184, 336,672, + 344,1696, 352,416, 360,1440, 368,928, 376,1952, 392,1120, 400,608, 408,1632, 424,1376, + 432,864, 440,1888, 456,1248, 464,736, 472,1760, 488,1504, 496,992, 504,2016, 520,1040, + 536,1552, 552,1296, 560,784, 568,1808, 584,1168, 592,656, 600,1680, 616,1424, 624,912, + 632,1936, 648,1104, 664,1616, 680,1360, 688,848, 696,1872, 712,1232, 728,1744, 744,1488, + 752,976, 760,2000, 776,1072, 792,1584, 808,1328, 824,1840, 840,1200, 856,1712, 872,1456, + 880,944, 888,1968, 904,1136, 920,1648, 936,1392, 952,1904, 968,1264, 984,1776, 1000,1520, + 1016,2032, 1048,1544, 1064,1288, 1080,1800, 1096,1160, 1112,1672, 1128,1416, 1144,1928, + 1176,1608, 1192,1352, 1208,1864, 1240,1736, 1256,1480, 1272,1992, 1304,1576, 1336,1832, + 1368,1704, 1384,1448, 1400,1960, 1432,1640, 1464,1896, 1496,1768, 1528,2024, 1592,1816, + 1624,1688, 1656,1944, 1720,1880, 1784,2008, 1912,1976 +}; + +const uint16_t armBitRevIndexTable_fixed_512[ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 480 */ + 8,2048, 16,1024, 24,3072, 32,512, 40,2560, 48,1536, 56,3584, 64,256, 72,2304, 80,1280, + 88,3328, 96,768, 104,2816, 112,1792, 120,3840, 136,2176, 144,1152, 152,3200, 160,640, + 168,2688, 176,1664, 184,3712, 192,384, 200,2432, 208,1408, 216,3456, 224,896, 232,2944, + 240,1920, 248,3968, 264,2112, 272,1088, 280,3136, 288,576, 296,2624, 304,1600, 312,3648, + 328,2368, 336,1344, 344,3392, 352,832, 360,2880, 368,1856, 376,3904, 392,2240, 400,1216, + 408,3264, 416,704, 424,2752, 432,1728, 440,3776, 456,2496, 464,1472, 472,3520, 480,960, + 488,3008, 496,1984, 504,4032, 520,2080, 528,1056, 536,3104, 552,2592, 560,1568, 568,3616, + 584,2336, 592,1312, 600,3360, 608,800, 616,2848, 624,1824, 632,3872, 648,2208, 656,1184, + 664,3232, 680,2720, 688,1696, 696,3744, 712,2464, 720,1440, 728,3488, 736,928, 744,2976, + 752,1952, 760,4000, 776,2144, 784,1120, 792,3168, 808,2656, 816,1632, 824,3680, 840,2400, + 848,1376, 856,3424, 872,2912, 880,1888, 888,3936, 904,2272, 912,1248, 920,3296, 936,2784, + 944,1760, 952,3808, 968,2528, 976,1504, 984,3552, 1000,3040, 1008,2016, 1016,4064, + 1032,2064, 1048,3088, 1064,2576, 1072,1552, 1080,3600, 1096,2320, 1104,1296, 1112,3344, + 1128,2832, 1136,1808, 1144,3856, 1160,2192, 1176,3216, 1192,2704, 1200,1680, 1208,3728, + 1224,2448, 1232,1424, 1240,3472, 1256,2960, 1264,1936, 1272,3984, 1288,2128, 1304,3152, + 1320,2640, 1328,1616, 1336,3664, 1352,2384, 1368,3408, 1384,2896, 1392,1872, 1400,3920, + 1416,2256, 1432,3280, 1448,2768, 1456,1744, 1464,3792, 1480,2512, 1496,3536, 1512,3024, + 1520,2000, 1528,4048, 1544,2096, 1560,3120, 1576,2608, 1592,3632, 1608,2352, 1624,3376, + 1640,2864, 1648,1840, 1656,3888, 1672,2224, 1688,3248, 1704,2736, 1720,3760, 1736,2480, + 1752,3504, 1768,2992, 1776,1968, 1784,4016, 1800,2160, 1816,3184, 1832,2672, 1848,3696, + 1864,2416, 1880,3440, 1896,2928, 1912,3952, 1928,2288, 1944,3312, 1960,2800, 1976,3824, + 1992,2544, 2008,3568, 2024,3056, 2040,4080, 2072,3080, 2088,2568, 2104,3592, 2120,2312, + 2136,3336, 2152,2824, 2168,3848, 2200,3208, 2216,2696, 2232,3720, 2248,2440, 2264,3464, + 2280,2952, 2296,3976, 2328,3144, 2344,2632, 2360,3656, 2392,3400, 2408,2888, 2424,3912, + 2456,3272, 2472,2760, 2488,3784, 2520,3528, 2536,3016, 2552,4040, 2584,3112, 2616,3624, + 2648,3368, 2664,2856, 2680,3880, 2712,3240, 2744,3752, 2776,3496, 2792,2984, 2808,4008, + 2840,3176, 2872,3688, 2904,3432, 2936,3944, 2968,3304, 3000,3816, 3032,3560, 3064,4072, + 3128,3608, 3160,3352, 3192,3864, 3256,3736, 3288,3480, 3320,3992, 3384,3672, 3448,3928, + 3512,3800, 3576,4056, 3704,3896, 3832,4024 +}; + +const uint16_t armBitRevIndexTable_fixed_1024[ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 992 */ + 8,4096, 16,2048, 24,6144, 32,1024, 40,5120, 48,3072, 56,7168, 64,512, 72,4608, + 80,2560, 88,6656, 96,1536, 104,5632, 112,3584, 120,7680, 128,256, 136,4352, + 144,2304, 152,6400, 160,1280, 168,5376, 176,3328, 184,7424, 192,768, 200,4864, + 208,2816, 216,6912, 224,1792, 232,5888, 240,3840, 248,7936, 264,4224, 272,2176, + 280,6272, 288,1152, 296,5248, 304,3200, 312,7296, 320,640, 328,4736, 336,2688, + 344,6784, 352,1664, 360,5760, 368,3712, 376,7808, 392,4480, 400,2432, 408,6528, + 416,1408, 424,5504, 432,3456, 440,7552, 448,896, 456,4992, 464,2944, 472,7040, + 480,1920, 488,6016, 496,3968, 504,8064, 520,4160, 528,2112, 536,6208, 544,1088, + 552,5184, 560,3136, 568,7232, 584,4672, 592,2624, 600,6720, 608,1600, 616,5696, + 624,3648, 632,7744, 648,4416, 656,2368, 664,6464, 672,1344, 680,5440, 688,3392, + 696,7488, 704,832, 712,4928, 720,2880, 728,6976, 736,1856, 744,5952, 752,3904, + 760,8000, 776,4288, 784,2240, 792,6336, 800,1216, 808,5312, 816,3264, 824,7360, + 840,4800, 848,2752, 856,6848, 864,1728, 872,5824, 880,3776, 888,7872, 904,4544, + 912,2496, 920,6592, 928,1472, 936,5568, 944,3520, 952,7616, 968,5056, 976,3008, + 984,7104, 992,1984, 1000,6080, 1008,4032, 1016,8128, 1032,4128, 1040,2080, + 1048,6176, 1064,5152, 1072,3104, 1080,7200, 1096,4640, 1104,2592, 1112,6688, + 1120,1568, 1128,5664, 1136,3616, 1144,7712, 1160,4384, 1168,2336, 1176,6432, + 1184,1312, 1192,5408, 1200,3360, 1208,7456, 1224,4896, 1232,2848, 1240,6944, + 1248,1824, 1256,5920, 1264,3872, 1272,7968, 1288,4256, 1296,2208, 1304,6304, + 1320,5280, 1328,3232, 1336,7328, 1352,4768, 1360,2720, 1368,6816, 1376,1696, + 1384,5792, 1392,3744, 1400,7840, 1416,4512, 1424,2464, 1432,6560, 1448,5536, + 1456,3488, 1464,7584, 1480,5024, 1488,2976, 1496,7072, 1504,1952, 1512,6048, + 1520,4000, 1528,8096, 1544,4192, 1552,2144, 1560,6240, 1576,5216, 1584,3168, + 1592,7264, 1608,4704, 1616,2656, 1624,6752, 1640,5728, 1648,3680, 1656,7776, + 1672,4448, 1680,2400, 1688,6496, 1704,5472, 1712,3424, 1720,7520, 1736,4960, + 1744,2912, 1752,7008, 1760,1888, 1768,5984, 1776,3936, 1784,8032, 1800,4320, + 1808,2272, 1816,6368, 1832,5344, 1840,3296, 1848,7392, 1864,4832, 1872,2784, + 1880,6880, 1896,5856, 1904,3808, 1912,7904, 1928,4576, 1936,2528, 1944,6624, + 1960,5600, 1968,3552, 1976,7648, 1992,5088, 2000,3040, 2008,7136, 2024,6112, + 2032,4064, 2040,8160, 2056,4112, 2072,6160, 2088,5136, 2096,3088, 2104,7184, + 2120,4624, 2128,2576, 2136,6672, 2152,5648, 2160,3600, 2168,7696, 2184,4368, + 2192,2320, 2200,6416, 2216,5392, 2224,3344, 2232,7440, 2248,4880, 2256,2832, + 2264,6928, 2280,5904, 2288,3856, 2296,7952, 2312,4240, 2328,6288, 2344,5264, + 2352,3216, 2360,7312, 2376,4752, 2384,2704, 2392,6800, 2408,5776, 2416,3728, + 2424,7824, 2440,4496, 2456,6544, 2472,5520, 2480,3472, 2488,7568, 2504,5008, + 2512,2960, 2520,7056, 2536,6032, 2544,3984, 2552,8080, 2568,4176, 2584,6224, + 2600,5200, 2608,3152, 2616,7248, 2632,4688, 2648,6736, 2664,5712, 2672,3664, + 2680,7760, 2696,4432, 2712,6480, 2728,5456, 2736,3408, 2744,7504, 2760,4944, + 2768,2896, 2776,6992, 2792,5968, 2800,3920, 2808,8016, 2824,4304, 2840,6352, + 2856,5328, 2864,3280, 2872,7376, 2888,4816, 2904,6864, 2920,5840, 2928,3792, + 2936,7888, 2952,4560, 2968,6608, 2984,5584, 2992,3536, 3000,7632, 3016,5072, + 3032,7120, 3048,6096, 3056,4048, 3064,8144, 3080,4144, 3096,6192, 3112,5168, + 3128,7216, 3144,4656, 3160,6704, 3176,5680, 3184,3632, 3192,7728, 3208,4400, + 3224,6448, 3240,5424, 3248,3376, 3256,7472, 3272,4912, 3288,6960, 3304,5936, + 3312,3888, 3320,7984, 3336,4272, 3352,6320, 3368,5296, 3384,7344, 3400,4784, + 3416,6832, 3432,5808, 3440,3760, 3448,7856, 3464,4528, 3480,6576, 3496,5552, + 3512,7600, 3528,5040, 3544,7088, 3560,6064, 3568,4016, 3576,8112, 3592,4208, + 3608,6256, 3624,5232, 3640,7280, 3656,4720, 3672,6768, 3688,5744, 3704,7792, + 3720,4464, 3736,6512, 3752,5488, 3768,7536, 3784,4976, 3800,7024, 3816,6000, + 3824,3952, 3832,8048, 3848,4336, 3864,6384, 3880,5360, 3896,7408, 3912,4848, + 3928,6896, 3944,5872, 3960,7920, 3976,4592, 3992,6640, 4008,5616, 4024,7664, + 4040,5104, 4056,7152, 4072,6128, 4088,8176, 4120,6152, 4136,5128, 4152,7176, + 4168,4616, 4184,6664, 4200,5640, 4216,7688, 4232,4360, 4248,6408, 4264,5384, + 4280,7432, 4296,4872, 4312,6920, 4328,5896, 4344,7944, 4376,6280, 4392,5256, + 4408,7304, 4424,4744, 4440,6792, 4456,5768, 4472,7816, 4504,6536, 4520,5512, + 4536,7560, 4552,5000, 4568,7048, 4584,6024, 4600,8072, 4632,6216, 4648,5192, + 4664,7240, 4696,6728, 4712,5704, 4728,7752, 4760,6472, 4776,5448, 4792,7496, + 4808,4936, 4824,6984, 4840,5960, 4856,8008, 4888,6344, 4904,5320, 4920,7368, + 4952,6856, 4968,5832, 4984,7880, 5016,6600, 5032,5576, 5048,7624, 5080,7112, + 5096,6088, 5112,8136, 5144,6184, 5176,7208, 5208,6696, 5224,5672, 5240,7720, + 5272,6440, 5288,5416, 5304,7464, 5336,6952, 5352,5928, 5368,7976, 5400,6312, + 5432,7336, 5464,6824, 5480,5800, 5496,7848, 5528,6568, 5560,7592, 5592,7080, + 5608,6056, 5624,8104, 5656,6248, 5688,7272, 5720,6760, 5752,7784, 5784,6504, + 5816,7528, 5848,7016, 5864,5992, 5880,8040, 5912,6376, 5944,7400, 5976,6888, + 6008,7912, 6040,6632, 6072,7656, 6104,7144, 6136,8168, 6200,7192, 6232,6680, + 6264,7704, 6296,6424, 6328,7448, 6360,6936, 6392,7960, 6456,7320, 6488,6808, + 6520,7832, 6584,7576, 6616,7064, 6648,8088, 6712,7256, 6776,7768, 6840,7512, + 6872,7000, 6904,8024, 6968,7384, 7032,7896, 7096,7640, 7160,8152, 7288,7736, + 7352,7480, 7416,7992, 7544,7864, 7672,8120, 7928,8056 +}; + +const uint16_t armBitRevIndexTable_fixed_2048[ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* 4x2, size 1984 */ + 8,8192, 16,4096, 24,12288, 32,2048, 40,10240, 48,6144, 56,14336, 64,1024, + 72,9216, 80,5120, 88,13312, 96,3072, 104,11264, 112,7168, 120,15360, 128,512, + 136,8704, 144,4608, 152,12800, 160,2560, 168,10752, 176,6656, 184,14848, + 192,1536, 200,9728, 208,5632, 216,13824, 224,3584, 232,11776, 240,7680, + 248,15872, 264,8448, 272,4352, 280,12544, 288,2304, 296,10496, 304,6400, + 312,14592, 320,1280, 328,9472, 336,5376, 344,13568, 352,3328, 360,11520, + 368,7424, 376,15616, 384,768, 392,8960, 400,4864, 408,13056, 416,2816, + 424,11008, 432,6912, 440,15104, 448,1792, 456,9984, 464,5888, 472,14080, + 480,3840, 488,12032, 496,7936, 504,16128, 520,8320, 528,4224, 536,12416, + 544,2176, 552,10368, 560,6272, 568,14464, 576,1152, 584,9344, 592,5248, + 600,13440, 608,3200, 616,11392, 624,7296, 632,15488, 648,8832, 656,4736, + 664,12928, 672,2688, 680,10880, 688,6784, 696,14976, 704,1664, 712,9856, + 720,5760, 728,13952, 736,3712, 744,11904, 752,7808, 760,16000, 776,8576, + 784,4480, 792,12672, 800,2432, 808,10624, 816,6528, 824,14720, 832,1408, + 840,9600, 848,5504, 856,13696, 864,3456, 872,11648, 880,7552, 888,15744, + 904,9088, 912,4992, 920,13184, 928,2944, 936,11136, 944,7040, 952,15232, + 960,1920, 968,10112, 976,6016, 984,14208, 992,3968, 1000,12160, 1008,8064, + 1016,16256, 1032,8256, 1040,4160, 1048,12352, 1056,2112, 1064,10304, 1072,6208, + 1080,14400, 1096,9280, 1104,5184, 1112,13376, 1120,3136, 1128,11328, 1136,7232, + 1144,15424, 1160,8768, 1168,4672, 1176,12864, 1184,2624, 1192,10816, 1200,6720, + 1208,14912, 1216,1600, 1224,9792, 1232,5696, 1240,13888, 1248,3648, 1256,11840, + 1264,7744, 1272,15936, 1288,8512, 1296,4416, 1304,12608, 1312,2368, 1320,10560, + 1328,6464, 1336,14656, 1352,9536, 1360,5440, 1368,13632, 1376,3392, 1384,11584, + 1392,7488, 1400,15680, 1416,9024, 1424,4928, 1432,13120, 1440,2880, 1448,11072, + 1456,6976, 1464,15168, 1472,1856, 1480,10048, 1488,5952, 1496,14144, 1504,3904, + 1512,12096, 1520,8000, 1528,16192, 1544,8384, 1552,4288, 1560,12480, 1568,2240, + 1576,10432, 1584,6336, 1592,14528, 1608,9408, 1616,5312, 1624,13504, 1632,3264, + 1640,11456, 1648,7360, 1656,15552, 1672,8896, 1680,4800, 1688,12992, 1696,2752, + 1704,10944, 1712,6848, 1720,15040, 1736,9920, 1744,5824, 1752,14016, 1760,3776, + 1768,11968, 1776,7872, 1784,16064, 1800,8640, 1808,4544, 1816,12736, 1824,2496, + 1832,10688, 1840,6592, 1848,14784, 1864,9664, 1872,5568, 1880,13760, 1888,3520, + 1896,11712, 1904,7616, 1912,15808, 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13304,16280, + 13368,14424, 13432,15448, 13496,14936, 13528,13912, 13560,15960, 13624,14680, + 13688,15704, 13752,15192, 13784,14168, 13816,16216, 13880,14552, 13944,15576, + 14008,15064, 14072,16088, 14136,14808, 14200,15832, 14264,15320, 14328,16344, + 14456,15416, 14520,14904, 14584,15928, 14712,15672, 14776,15160, 14840,16184, + 14968,15544, 15096,16056, 15224,15800, 15352,16312, 15608,15992, 15864,16248 +}; + +const uint16_t armBitRevIndexTable_fixed_4096[ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH] ARM_DSP_TABLE_ATTRIBUTE = +{ + /* radix 4, size 4032 */ + 8,16384, 16,8192, 24,24576, 32,4096, 40,20480, 48,12288, 56,28672, 64,2048, + 72,18432, 80,10240, 88,26624, 96,6144, 104,22528, 112,14336, 120,30720, + 128,1024, 136,17408, 144,9216, 152,25600, 160,5120, 168,21504, 176,13312, + 184,29696, 192,3072, 200,19456, 208,11264, 216,27648, 224,7168, 232,23552, + 240,15360, 248,31744, 256,512, 264,16896, 272,8704, 280,25088, 288,4608, + 296,20992, 304,12800, 312,29184, 320,2560, 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17000,22792, + 17016,30984, 17032,17672, 17048,25864, 17064,21768, 17080,29960, 17096,19720, + 17112,27912, 17128,23816, 17144,32008, 17176,25352, 17192,21256, 17208,29448, + 17224,19208, 17240,27400, 17256,23304, 17272,31496, 17288,18184, 17304,26376, + 17320,22280, 17336,30472, 17352,20232, 17368,28424, 17384,24328, 17400,32520, + 17432,24712, 17448,20616, 17464,28808, 17480,18568, 17496,26760, 17512,22664, + 17528,30856, 17560,25736, 17576,21640, 17592,29832, 17608,19592, 17624,27784, + 17640,23688, 17656,31880, 17688,25224, 17704,21128, 17720,29320, 17736,19080, + 17752,27272, 17768,23176, 17784,31368, 17800,18056, 17816,26248, 17832,22152, + 17848,30344, 17864,20104, 17880,28296, 17896,24200, 17912,32392, 17944,24968, + 17960,20872, 17976,29064, 17992,18824, 18008,27016, 18024,22920, 18040,31112, + 18072,25992, 18088,21896, 18104,30088, 18120,19848, 18136,28040, 18152,23944, + 18168,32136, 18200,25480, 18216,21384, 18232,29576, 18248,19336, 18264,27528, + 18280,23432, 18296,31624, 18328,26504, 18344,22408, 18360,30600, 18376,20360, + 18392,28552, 18408,24456, 18424,32648, 18456,24648, 18472,20552, 18488,28744, + 18520,26696, 18536,22600, 18552,30792, 18584,25672, 18600,21576, 18616,29768, + 18632,19528, 18648,27720, 18664,23624, 18680,31816, 18712,25160, 18728,21064, + 18744,29256, 18760,19016, 18776,27208, 18792,23112, 18808,31304, 18840,26184, + 18856,22088, 18872,30280, 18888,20040, 18904,28232, 18920,24136, 18936,32328, + 18968,24904, 18984,20808, 19000,29000, 19032,26952, 19048,22856, 19064,31048, + 19096,25928, 19112,21832, 19128,30024, 19144,19784, 19160,27976, 19176,23880, + 19192,32072, 19224,25416, 19240,21320, 19256,29512, 19288,27464, 19304,23368, + 19320,31560, 19352,26440, 19368,22344, 19384,30536, 19400,20296, 19416,28488, + 19432,24392, 19448,32584, 19480,24776, 19496,20680, 19512,28872, 19544,26824, + 19560,22728, 19576,30920, 19608,25800, 19624,21704, 19640,29896, 19672,27848, + 19688,23752, 19704,31944, 19736,25288, 19752,21192, 19768,29384, 19800,27336, + 19816,23240, 19832,31432, 19864,26312, 19880,22216, 19896,30408, 19912,20168, + 19928,28360, 19944,24264, 19960,32456, 19992,25032, 20008,20936, 20024,29128, + 20056,27080, 20072,22984, 20088,31176, 20120,26056, 20136,21960, 20152,30152, + 20184,28104, 20200,24008, 20216,32200, 20248,25544, 20264,21448, 20280,29640, + 20312,27592, 20328,23496, 20344,31688, 20376,26568, 20392,22472, 20408,30664, + 20440,28616, 20456,24520, 20472,32712, 20504,24616, 20536,28712, 20568,26664, + 20584,22568, 20600,30760, 20632,25640, 20648,21544, 20664,29736, 20696,27688, + 20712,23592, 20728,31784, 20760,25128, 20776,21032, 20792,29224, 20824,27176, + 20840,23080, 20856,31272, 20888,26152, 20904,22056, 20920,30248, 20952,28200, + 20968,24104, 20984,32296, 21016,24872, 21048,28968, 21080,26920, 21096,22824, + 21112,31016, 21144,25896, 21160,21800, 21176,29992, 21208,27944, 21224,23848, + 21240,32040, 21272,25384, 21304,29480, 21336,27432, 21352,23336, 21368,31528, + 21400,26408, 21416,22312, 21432,30504, 21464,28456, 21480,24360, 21496,32552, + 21528,24744, 21560,28840, 21592,26792, 21608,22696, 21624,30888, 21656,25768, + 21688,29864, 21720,27816, 21736,23720, 21752,31912, 21784,25256, 21816,29352, + 21848,27304, 21864,23208, 21880,31400, 21912,26280, 21928,22184, 21944,30376, + 21976,28328, 21992,24232, 22008,32424, 22040,25000, 22072,29096, 22104,27048, + 22120,22952, 22136,31144, 22168,26024, 22200,30120, 22232,28072, 22248,23976, + 22264,32168, 22296,25512, 22328,29608, 22360,27560, 22376,23464, 22392,31656, + 22424,26536, 22456,30632, 22488,28584, 22504,24488, 22520,32680, 22552,24680, + 22584,28776, 22616,26728, 22648,30824, 22680,25704, 22712,29800, 22744,27752, + 22760,23656, 22776,31848, 22808,25192, 22840,29288, 22872,27240, 22888,23144, + 22904,31336, 22936,26216, 22968,30312, 23000,28264, 23016,24168, 23032,32360, + 23064,24936, 23096,29032, 23128,26984, 23160,31080, 23192,25960, 23224,30056, + 23256,28008, 23272,23912, 23288,32104, 23320,25448, 23352,29544, 23384,27496, + 23416,31592, 23448,26472, 23480,30568, 23512,28520, 23528,24424, 23544,32616, + 23576,24808, 23608,28904, 23640,26856, 23672,30952, 23704,25832, 23736,29928, + 23768,27880, 23800,31976, 23832,25320, 23864,29416, 23896,27368, 23928,31464, + 23960,26344, 23992,30440, 24024,28392, 24040,24296, 24056,32488, 24088,25064, + 24120,29160, 24152,27112, 24184,31208, 24216,26088, 24248,30184, 24280,28136, + 24312,32232, 24344,25576, 24376,29672, 24408,27624, 24440,31720, 24472,26600, + 24504,30696, 24536,28648, 24568,32744, 24632,28696, 24664,26648, 24696,30744, + 24728,25624, 24760,29720, 24792,27672, 24824,31768, 24856,25112, 24888,29208, + 24920,27160, 24952,31256, 24984,26136, 25016,30232, 25048,28184, 25080,32280, + 25144,28952, 25176,26904, 25208,31000, 25240,25880, 25272,29976, 25304,27928, + 25336,32024, 25400,29464, 25432,27416, 25464,31512, 25496,26392, 25528,30488, + 25560,28440, 25592,32536, 25656,28824, 25688,26776, 25720,30872, 25784,29848, + 25816,27800, 25848,31896, 25912,29336, 25944,27288, 25976,31384, 26008,26264, + 26040,30360, 26072,28312, 26104,32408, 26168,29080, 26200,27032, 26232,31128, + 26296,30104, 26328,28056, 26360,32152, 26424,29592, 26456,27544, 26488,31640, + 26552,30616, 26584,28568, 26616,32664, 26680,28760, 26744,30808, 26808,29784, + 26840,27736, 26872,31832, 26936,29272, 26968,27224, 27000,31320, 27064,30296, + 27096,28248, 27128,32344, 27192,29016, 27256,31064, 27320,30040, 27352,27992, + 27384,32088, 27448,29528, 27512,31576, 27576,30552, 27608,28504, 27640,32600, + 27704,28888, 27768,30936, 27832,29912, 27896,31960, 27960,29400, 28024,31448, + 28088,30424, 28120,28376, 28152,32472, 28216,29144, 28280,31192, 28344,30168, + 28408,32216, 28472,29656, 28536,31704, 28600,30680, 28664,32728, 28792,30776, + 28856,29752, 28920,31800, 28984,29240, 29048,31288, 29112,30264, 29176,32312, + 29304,31032, 29368,30008, 29432,32056, 29560,31544, 29624,30520, 29688,32568, + 29816,30904, 29944,31928, 30072,31416, 30136,30392, 30200,32440, 30328,31160, + 30456,32184, 30584,31672, 30712,32696, 30968,31864, 31096,31352, 31224,32376, + 31480,32120, 31736,32632, 32248,32504 +}; + +/** + @par + Example code for Double Precision Floating-point RFFT Twiddle factors Generation: + @par + 
TW = exp(pi/2*i-2*pi*i*[0:L/2-1]/L).'
+ @par + Real and Imag values are in interleaved fashion +*/ +const uint64_t twiddleCoefF64_rfft_32[32] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, //0.19509, 0.98079 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, //0.38268, 0.92388 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, //0.55557, 0.83147 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, //0.70711, 0.70711 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, //0.83147, 0.55557 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, //0.92388, 0.38268 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, //0.98079, 0.19509 + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, //0.98079,-0.19509 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, //0.92388,-0.38268 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, //0.83147,-0.55557 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, //0.70711,-0.70711 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, //0.55557,-0.83147 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, //0.38268,-0.92388 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, //0.19509,-0.98079 +}; + +const uint64_t twiddleCoefF64_rfft_64[64] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, //0.098017, 0.99518' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017' + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509' + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268' + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557' + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711' + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147' + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388' + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079' + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, //0.098017, -0.99518' +}; + +const uint64_t twiddleCoefF64_rfft_128[128] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, //0.049068, 0.9988' + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, //0.098017, 0.99518' + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003' + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694' + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399' + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192' + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321' + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301' + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156' + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439' + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141' + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714' + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689' + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028' + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673' + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017' + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068' + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988,-0.049068' + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017' + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509' + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298' + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028' + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268' + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756' + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714' + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557' + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957' + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439' + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711' + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095' + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301' + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147' + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773' + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192' + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388' + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154' + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694' + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079' + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918' + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, //0.098017, -0.99518' + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, //0.049068, -0.9988' +}; + +const uint64_t twiddleCoefF64_rfft_256[256] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, //0.024541, 0.9997 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, //0.049068, 0.9988 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, //0.073565, 0.99729 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, //0.098017, 0.99518 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997,-0.024541 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988,-0.049068 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729,-0.073565 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, //0.098017, -0.99518 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, //0.073565, -0.99729 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, //0.049068, -0.9988' + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, //0.024541, -0.9997 + + +}; + +const uint64_t twiddleCoefF64_rfft_512[512] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0x3f8921d1fcdec784, 0x3fefff62169b92db, //0.012272, 0.99992' + 0x3f992155f7a3667e, 0x3feffd886084cd0d, //0.024541, 0.9997' + 0x3fa2d865759455cd, 0x3feffa72effef75d, //0.036807, 0.99932' + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, //0.049068, 0.9988' + 0x3faf656e79f820e0, 0x3feff095658e71ad, //0.061321, 0.99812' + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, //0.073565, 0.99729' + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, //0.085797, 0.99631' + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, //0.098017, 0.99518' + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391' + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248' + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909' + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918' + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873' + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528' + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832' + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757' + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294' + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003' + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698' + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378' + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043' + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694' + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331' + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953' + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561' + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154' + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734' + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299' + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911' + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421' + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917' + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399' + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867' + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322' + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764' + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192' + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607' + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009' + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397' + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773' + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136' + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485' + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459' + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758' + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046' + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321' + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584' + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835' + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074' + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301' + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517' + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721' + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914' + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095' + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265' + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425' + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838' + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954' + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806' + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156' + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242' + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317' + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383' + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439' + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486' + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523' + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551' + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957' + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858' + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581' + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532' + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535' + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459' + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141' + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354' + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929' + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218' + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714' + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054' + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961' + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862' + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756' + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643' + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524' + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132' + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599' + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842' + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689' + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531' + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368' + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201' + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028' + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852' + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671' + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487' + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298' + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106' + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191' + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304' + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096' + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886' + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673' + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458' + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241' + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022' + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017' + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797' + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565' + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321' + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068' + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807' + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541' + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272' + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992,-0.012272' + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997,-0.024541' + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932,-0.036807' + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988,-0.049068' + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812,-0.061321' + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729,-0.073565' + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631,-0.085797' + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518,-0.098017' + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022' + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241' + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458' + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673' + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886' + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096' + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509' + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711' + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191' + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106' + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298' + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487' + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671' + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852' + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028' + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201' + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368' + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531' + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689' + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842' + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599' + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268' + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399' + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524' + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643' + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756' + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862' + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961' + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054' + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714' + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218' + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929' + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354' + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141' + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459' + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535' + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557' + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573' + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581' + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858' + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957' + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551' + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523' + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486' + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439' + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383' + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317' + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242' + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156' + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806' + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954' + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711' + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573' + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425' + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265' + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095' + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914' + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721' + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517' + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301' + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074' + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835' + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584' + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321' + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046' + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758' + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147' + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822' + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485' + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136' + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773' + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397' + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009' + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607' + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192' + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764' + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322' + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867' + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399' + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917' + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421' + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388' + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851' + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299' + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734' + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154' + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561' + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953' + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331' + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694' + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043' + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378' + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698' + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003' + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294' + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757' + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079' + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311' + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528' + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873' + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918' + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909' + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248' + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391' + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, //0.098017, -0.99518' + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, //0.085797, -0.99631' + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, //0.073565, -0.99729' + 0x3faf656e79f820e0, 0xbfeff095658e71ad, //0.061321, -0.99812' + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, //0.049068, -0.9988' + 0x3fa2d865759455cd, 0xbfeffa72effef75d, //0.036807, -0.99932' + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, //0.024541, -0.9997' + 0x3f8921d1fcdec784, 0xbfefff62169b92db, //0.012272, -0.99992' + + +}; + +const uint64_t twiddleCoefF64_rfft_1024[1024] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1' + 0x3f7921f0fe670071, 0x3fefffd8858e8a92, //0.0061359, 0.99998' + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992' + 0x3f92d936bbe30efd, 0x3feffe9cb44b51a1, // 0.018407, 0.99983' + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997' + 0x3f9f693731d1cf01, 0x3feffc251df1d3f8, // 0.030675, 0.99953' + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932' + 0x3fa5fc00d290cd43, 0x3feff871dadb81df, // 0.042938, 0.99908' + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988' + 0x3fac428d12c0d7e3, 0x3feff3830f8d575c, // 0.055195, 0.99848' + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812' + 0x3fb1440134d709b2, 0x3fefed58ecb673c4, // 0.067444, 0.99772' + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729' + 0x3fb4661179272096, 0x3fefe5f3af2e3940, // 0.079682, 0.99682' + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631' + 0x3fb787586a5d5b21, 0x3fefdd539ff1f456, // 0.091909, 0.99577' + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518' + 0x3fbaa7b724495c04, 0x3fefd37914220b84, // 0.10412, 0.99456' + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391' + 0x3fbdc70ecbae9fc8, 0x3fefc8646cfeb721, // 0.11632, 0.99321' + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248' + 0x3fc072a047ba831d, 0x3fefbc1617e44186, // 0.1285, 0.99171' + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909' + 0x3fc20116d4ec7bce, 0x3fefae8e8e46cfbb, // 0.14066, 0.99006' + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918' + 0x3fc38edbb0cd8d14, 0x3fef9fce55adb2c8, // 0.1528, 0.98826' + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873' + 0x3fc51bdf8597c5f2, 0x3fef8fd5ffae41db, // 0.16491, 0.98631' + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528' + 0x3fc6a81304f64ab2, 0x3fef7ea629e63d6e, // 0.177, 0.98421' + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311' + 0x3fc83366e89c64c5, 0x3fef6c3f7df5bbb7, // 0.18907, 0.98196' + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079' + 0x3fc9bdcbf2dc4366, 0x3fef58a2b1789e84, // 0.2011, 0.97957' + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832' + 0x3fcb4732ef3d6722, 0x3fef43d085ff92dd, // 0.21311, 0.97703' + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757' + 0x3fcccf8cb312b286, 0x3fef2dc9c9089a9d, // 0.22508, 0.97434' + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294' + 0x3fce56ca1e101a1b, 0x3fef168f53f7205d, // 0.23702, 0.9715' + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003' + 0x3fcfdcdc1adfedf8, 0x3feefe220c0b95ec, // 0.24893, 0.96852' + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698' + 0x3fd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // 0.26079, 0.96539' + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378' + 0x3fd172a0d7765177, 0x3feec9b2d3c3bf84, // 0.27262, 0.96212' + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043' + 0x3fd233bbabc3bb72, 0x3feeadb2e8e7a88e, // 0.28441, 0.9587' + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694' + 0x3fd2f422daec0386, 0x3fee9084361df7f3, // 0.29615, 0.95514' + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331' + 0x3fd3b3cefa0414b7, 0x3fee7227db6a9744, // 0.30785, 0.95144' + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953' + 0x3fd472b8a5571054, 0x3fee529f04729ffc, // 0.3195, 0.94759' + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561' + 0x3fd530d880af3c24, 0x3fee31eae870ce25, // 0.33111, 0.94359' + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154' + 0x3fd5ee27379ea693, 0x3fee100cca2980ac, // 0.34266, 0.93946' + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734' + 0x3fd6aa9d7dc77e16, 0x3feded05f7de47da, // 0.35416, 0.93518' + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299' + 0x3fd766340f2418f6, 0x3fedc8d7cb410260, // 0.36561, 0.93077' + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851' + 0x3fd820e3b04eaac4, 0x3feda383a9668988, // 0.37701, 0.92621' + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388' + 0x3fd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // 0.38835, 0.92151' + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911' + 0x3fd993716141bdfe, 0x3fed556f52e93eb1, // 0.39962, 0.91668' + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421' + 0x3fda4b4127dea1e4, 0x3fed2cb220e0ef9f, // 0.41084, 0.91171' + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917' + 0x3fdb020d6c7f4009, 0x3fed02d4feb2bd92, // 0.422, 0.9066' + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399' + 0x3fdbb7cf2304bd01, 0x3fecd7d9898b32f6, // 0.43309, 0.90135' + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867' + 0x3fdc6c7f4997000a, 0x3fecabc169a0b901, // 0.44412, 0.89597' + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322' + 0x3fdd2016e8e9db5b, 0x3fec7e8e52233cf3, // 0.45508, 0.89045' + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764' + 0x3fddd28f1481cc58, 0x3fec5042012b6907, // 0.46598, 0.8848' + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192' + 0x3fde83e0eaf85113, 0x3fec20de3fa971b0, // 0.4768, 0.87901' + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607' + 0x3fdf3405963fd068, 0x3febf064e15377dd, // 0.48755, 0.87309' + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009' + 0x3fdfe2f64be7120f, 0x3febbed7c49380ea, // 0.49823, 0.86705' + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397' + 0x3fe0485626ae221a, 0x3feb8c38d27504e9, // 0.50883, 0.86087' + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773' + 0x3fe09e907417c5e1, 0x3feb5889fe921405, // 0.51936, 0.85456' + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136' + 0x3fe0f426bb2a8e7d, 0x3feb23cd470013b4, // 0.5298, 0.84812' + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485' + 0x3fe14915af336ceb, 0x3feaee04b43c1474, // 0.54017, 0.84155' + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822' + 0x3fe19d5a09f2b9b8, 0x3feab7325916c0d4, // 0.55046, 0.83486' + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147' + 0x3fe1f0f08bbc861b, 0x3fea7f58529fe69d, // 0.56066, 0.82805' + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459' + 0x3fe243d5fb98ac1f, 0x3fea4678c8119ac8, // 0.57078, 0.8211' + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758' + 0x3fe2960727629ca8, 0x3fea0c95eabaf937, // 0.58081, 0.81404' + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046' + 0x3fe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // 0.59076, 0.80685' + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321' + 0x3fe338400d0c8e57, 0x3fe995cf2ed80d22, // 0.60062, 0.79954' + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584' + 0x3fe3884185dfeb22, 0x3fe958efe48e6dd7, // 0.61038, 0.79211' + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835' + 0x3fe3d78238c58343, 0x3fe91b166fd49da2, // 0.62006, 0.78456' + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074' + 0x3fe425ff178e6bb1, 0x3fe8dc45331698cc, // 0.62964, 0.77689' + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301' + 0x3fe473b51b987347, 0x3fe89c7e9a4dd4ab, // 0.63912, 0.7691' + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517' + 0x3fe4c0a145ec0004, 0x3fe85bc51ae958cc, // 0.64851, 0.7612' + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721' + 0x3fe50cc09f59a09b, 0x3fe81a1b33b57acc, // 0.65781, 0.75319' + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914' + 0x3fe5581038975137, 0x3fe7d7836cc33db2, // 0.667, 0.74506' + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095' + 0x3fe5a28d2a5d7250, 0x3fe79400574f55e4, // 0.67609, 0.73682' + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265' + 0x3fe5ec3495837074, 0x3fe74f948da8d28d, // 0.68508, 0.72846' + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425' + 0x3fe63503a31c1be8, 0x3fe70a42b3176d7a, // 0.69397, 0.72' + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573' + 0x3fe67cf78491af10, 0x3fe6c40d73c18275, // 0.70275, 0.71143' + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711' + 0x3fe6c40d73c18275, 0x3fe67cf78491af10, // 0.71143, 0.70275' + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838' + 0x3fe70a42b3176d7a, 0x3fe63503a31c1be8, // 0.72, 0.69397' + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954' + 0x3fe74f948da8d28d, 0x3fe5ec3495837074, // 0.72846, 0.68508' + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806' + 0x3fe79400574f55e4, 0x3fe5a28d2a5d7250, // 0.73682, 0.67609' + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156' + 0x3fe7d7836cc33db2, 0x3fe5581038975137, // 0.74506, 0.667' + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242' + 0x3fe81a1b33b57acc, 0x3fe50cc09f59a09b, // 0.75319, 0.65781' + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317' + 0x3fe85bc51ae958cc, 0x3fe4c0a145ec0004, // 0.7612, 0.64851' + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383' + 0x3fe89c7e9a4dd4ab, 0x3fe473b51b987347, // 0.7691, 0.63912' + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439' + 0x3fe8dc45331698cc, 0x3fe425ff178e6bb1, // 0.77689, 0.62964' + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486' + 0x3fe91b166fd49da2, 0x3fe3d78238c58343, // 0.78456, 0.62006' + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523' + 0x3fe958efe48e6dd7, 0x3fe3884185dfeb22, // 0.79211, 0.61038' + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551' + 0x3fe995cf2ed80d22, 0x3fe338400d0c8e57, // 0.79954, 0.60062' + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957' + 0x3fe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // 0.80685, 0.59076' + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858' + 0x3fea0c95eabaf937, 0x3fe2960727629ca8, // 0.81404, 0.58081' + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581' + 0x3fea4678c8119ac8, 0x3fe243d5fb98ac1f, // 0.8211, 0.57078' + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573' + 0x3fea7f58529fe69d, 0x3fe1f0f08bbc861b, // 0.82805, 0.56066' + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557' + 0x3feab7325916c0d4, 0x3fe19d5a09f2b9b8, // 0.83486, 0.55046' + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532' + 0x3feaee04b43c1474, 0x3fe14915af336ceb, // 0.84155, 0.54017' + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535' + 0x3feb23cd470013b4, 0x3fe0f426bb2a8e7d, // 0.84812, 0.5298' + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459' + 0x3feb5889fe921405, 0x3fe09e907417c5e1, // 0.85456, 0.51936' + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141' + 0x3feb8c38d27504e9, 0x3fe0485626ae221a, // 0.86087, 0.50883' + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354' + 0x3febbed7c49380ea, 0x3fdfe2f64be7120f, // 0.86705, 0.49823' + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929' + 0x3febf064e15377dd, 0x3fdf3405963fd068, // 0.87309, 0.48755' + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218' + 0x3fec20de3fa971b0, 0x3fde83e0eaf85113, // 0.87901, 0.4768' + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714' + 0x3fec5042012b6907, 0x3fddd28f1481cc58, // 0.8848, 0.46598' + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054' + 0x3fec7e8e52233cf3, 0x3fdd2016e8e9db5b, // 0.89045, 0.45508' + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961' + 0x3fecabc169a0b901, 0x3fdc6c7f4997000a, // 0.89597, 0.44412' + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862' + 0x3fecd7d9898b32f6, 0x3fdbb7cf2304bd01, // 0.90135, 0.43309' + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756' + 0x3fed02d4feb2bd92, 0x3fdb020d6c7f4009, // 0.9066, 0.422' + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643' + 0x3fed2cb220e0ef9f, 0x3fda4b4127dea1e4, // 0.91171, 0.41084' + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524' + 0x3fed556f52e93eb1, 0x3fd993716141bdfe, // 0.91668, 0.39962' + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399' + 0x3fed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // 0.92151, 0.38835' + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268' + 0x3feda383a9668988, 0x3fd820e3b04eaac4, // 0.92621, 0.37701' + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132' + 0x3fedc8d7cb410260, 0x3fd766340f2418f6, // 0.93077, 0.36561' + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599' + 0x3feded05f7de47da, 0x3fd6aa9d7dc77e16, // 0.93518, 0.35416' + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842' + 0x3fee100cca2980ac, 0x3fd5ee27379ea693, // 0.93946, 0.34266' + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689' + 0x3fee31eae870ce25, 0x3fd530d880af3c24, // 0.94359, 0.33111' + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531' + 0x3fee529f04729ffc, 0x3fd472b8a5571054, // 0.94759, 0.3195' + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368' + 0x3fee7227db6a9744, 0x3fd3b3cefa0414b7, // 0.95144, 0.30785' + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201' + 0x3fee9084361df7f3, 0x3fd2f422daec0386, // 0.95514, 0.29615' + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028' + 0x3feeadb2e8e7a88e, 0x3fd233bbabc3bb72, // 0.9587, 0.28441' + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852' + 0x3feec9b2d3c3bf84, 0x3fd172a0d7765177, // 0.96212, 0.27262' + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671' + 0x3feee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // 0.96539, 0.26079' + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487' + 0x3feefe220c0b95ec, 0x3fcfdcdc1adfedf8, // 0.96852, 0.24893' + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298' + 0x3fef168f53f7205d, 0x3fce56ca1e101a1b, // 0.9715, 0.23702' + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106' + 0x3fef2dc9c9089a9d, 0x3fcccf8cb312b286, // 0.97434, 0.22508' + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191' + 0x3fef43d085ff92dd, 0x3fcb4732ef3d6722, // 0.97703, 0.21311' + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711' + 0x3fef58a2b1789e84, 0x3fc9bdcbf2dc4366, // 0.97957, 0.2011' + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509' + 0x3fef6c3f7df5bbb7, 0x3fc83366e89c64c5, // 0.98196, 0.18907' + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304' + 0x3fef7ea629e63d6e, 0x3fc6a81304f64ab2, // 0.98421, 0.177' + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096' + 0x3fef8fd5ffae41db, 0x3fc51bdf8597c5f2, // 0.98631, 0.16491' + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886' + 0x3fef9fce55adb2c8, 0x3fc38edbb0cd8d14, // 0.98826, 0.1528' + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673' + 0x3fefae8e8e46cfbb, 0x3fc20116d4ec7bce, // 0.99006, 0.14066' + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458' + 0x3fefbc1617e44186, 0x3fc072a047ba831d, // 0.99171, 0.1285' + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241' + 0x3fefc8646cfeb721, 0x3fbdc70ecbae9fc8, // 0.99321, 0.11632' + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022' + 0x3fefd37914220b84, 0x3fbaa7b724495c04, // 0.99456, 0.10412' + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017' + 0x3fefdd539ff1f456, 0x3fb787586a5d5b21, // 0.99577, 0.091909' + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797' + 0x3fefe5f3af2e3940, 0x3fb4661179272096, // 0.99682, 0.079682' + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565' + 0x3fefed58ecb673c4, 0x3fb1440134d709b2, // 0.99772, 0.067444' + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321' + 0x3feff3830f8d575c, 0x3fac428d12c0d7e3, // 0.99848, 0.055195' + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068' + 0x3feff871dadb81df, 0x3fa5fc00d290cd43, // 0.99908, 0.042938' + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807' + 0x3feffc251df1d3f8, 0x3f9f693731d1cf01, // 0.99953, 0.030675' + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541' + 0x3feffe9cb44b51a1, 0x3f92d936bbe30efd, // 0.99983, 0.018407' + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272' + 0x3fefffd8858e8a92, 0x3f7921f0fe670071, // 0.99998, 0.0061359' + 0x3ff0000000000000, 0x0000000000000000, // 1, 0' + 0x3fefffd8858e8a92, 0xbf7921f0fe670071, // 0.99998,-0.0061359' + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992, -0.012272' + 0x3feffe9cb44b51a1, 0xbf92d936bbe30efd, // 0.99983, -0.018407' + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997, -0.024541' + 0x3feffc251df1d3f8, 0xbf9f693731d1cf01, // 0.99953, -0.030675' + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932, -0.036807' + 0x3feff871dadb81df, 0xbfa5fc00d290cd43, // 0.99908, -0.042938' + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988, -0.049068' + 0x3feff3830f8d575c, 0xbfac428d12c0d7e3, // 0.99848, -0.055195' + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812, -0.061321' + 0x3fefed58ecb673c4, 0xbfb1440134d709b2, // 0.99772, -0.067444' + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729, -0.073565' + 0x3fefe5f3af2e3940, 0xbfb4661179272096, // 0.99682, -0.079682' + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631, -0.085797' + 0x3fefdd539ff1f456, 0xbfb787586a5d5b21, // 0.99577, -0.091909' + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518, -0.098017' + 0x3fefd37914220b84, 0xbfbaa7b724495c04, // 0.99456, -0.10412' + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022' + 0x3fefc8646cfeb721, 0xbfbdc70ecbae9fc8, // 0.99321, -0.11632' + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241' + 0x3fefbc1617e44186, 0xbfc072a047ba831d, // 0.99171, -0.1285' + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458' + 0x3fefae8e8e46cfbb, 0xbfc20116d4ec7bce, // 0.99006, -0.14066' + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673' + 0x3fef9fce55adb2c8, 0xbfc38edbb0cd8d14, // 0.98826, -0.1528' + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886' + 0x3fef8fd5ffae41db, 0xbfc51bdf8597c5f2, // 0.98631, -0.16491' + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096' + 0x3fef7ea629e63d6e, 0xbfc6a81304f64ab2, // 0.98421, -0.177' + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304' + 0x3fef6c3f7df5bbb7, 0xbfc83366e89c64c5, // 0.98196, -0.18907' + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509' + 0x3fef58a2b1789e84, 0xbfc9bdcbf2dc4366, // 0.97957, -0.2011' + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711' + 0x3fef43d085ff92dd, 0xbfcb4732ef3d6722, // 0.97703, -0.21311' + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191' + 0x3fef2dc9c9089a9d, 0xbfcccf8cb312b286, // 0.97434, -0.22508' + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106' + 0x3fef168f53f7205d, 0xbfce56ca1e101a1b, // 0.9715, -0.23702' + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298' + 0x3feefe220c0b95ec, 0xbfcfdcdc1adfedf8, // 0.96852, -0.24893' + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487' + 0x3feee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // 0.96539, -0.26079' + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671' + 0x3feec9b2d3c3bf84, 0xbfd172a0d7765177, // 0.96212, -0.27262' + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852' + 0x3feeadb2e8e7a88e, 0xbfd233bbabc3bb72, // 0.9587, -0.28441' + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028' + 0x3fee9084361df7f3, 0xbfd2f422daec0386, // 0.95514, -0.29615' + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201' + 0x3fee7227db6a9744, 0xbfd3b3cefa0414b7, // 0.95144, -0.30785' + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368' + 0x3fee529f04729ffc, 0xbfd472b8a5571054, // 0.94759, -0.3195' + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531' + 0x3fee31eae870ce25, 0xbfd530d880af3c24, // 0.94359, -0.33111' + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689' + 0x3fee100cca2980ac, 0xbfd5ee27379ea693, // 0.93946, -0.34266' + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842' + 0x3feded05f7de47da, 0xbfd6aa9d7dc77e16, // 0.93518, -0.35416' + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599' + 0x3fedc8d7cb410260, 0xbfd766340f2418f6, // 0.93077, -0.36561' + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132' + 0x3feda383a9668988, 0xbfd820e3b04eaac4, // 0.92621, -0.37701' + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268' + 0x3fed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // 0.92151, -0.38835' + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399' + 0x3fed556f52e93eb1, 0xbfd993716141bdfe, // 0.91668, -0.39962' + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524' + 0x3fed2cb220e0ef9f, 0xbfda4b4127dea1e4, // 0.91171, -0.41084' + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643' + 0x3fed02d4feb2bd92, 0xbfdb020d6c7f4009, // 0.9066, -0.422' + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756' + 0x3fecd7d9898b32f6, 0xbfdbb7cf2304bd01, // 0.90135, -0.43309' + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862' + 0x3fecabc169a0b901, 0xbfdc6c7f4997000a, // 0.89597, -0.44412' + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961' + 0x3fec7e8e52233cf3, 0xbfdd2016e8e9db5b, // 0.89045, -0.45508' + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054' + 0x3fec5042012b6907, 0xbfddd28f1481cc58, // 0.8848, -0.46598' + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714' + 0x3fec20de3fa971b0, 0xbfde83e0eaf85113, // 0.87901, -0.4768' + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218' + 0x3febf064e15377dd, 0xbfdf3405963fd068, // 0.87309, -0.48755' + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929' + 0x3febbed7c49380ea, 0xbfdfe2f64be7120f, // 0.86705, -0.49823' + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354' + 0x3feb8c38d27504e9, 0xbfe0485626ae221a, // 0.86087, -0.50883' + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141' + 0x3feb5889fe921405, 0xbfe09e907417c5e1, // 0.85456, -0.51936' + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459' + 0x3feb23cd470013b4, 0xbfe0f426bb2a8e7d, // 0.84812, -0.5298' + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535' + 0x3feaee04b43c1474, 0xbfe14915af336ceb, // 0.84155, -0.54017' + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532' + 0x3feab7325916c0d4, 0xbfe19d5a09f2b9b8, // 0.83486, -0.55046' + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557' + 0x3fea7f58529fe69d, 0xbfe1f0f08bbc861b, // 0.82805, -0.56066' + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573' + 0x3fea4678c8119ac8, 0xbfe243d5fb98ac1f, // 0.8211, -0.57078' + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581' + 0x3fea0c95eabaf937, 0xbfe2960727629ca8, // 0.81404, -0.58081' + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858' + 0x3fe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // 0.80685, -0.59076' + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957' + 0x3fe995cf2ed80d22, 0xbfe338400d0c8e57, // 0.79954, -0.60062' + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551' + 0x3fe958efe48e6dd7, 0xbfe3884185dfeb22, // 0.79211, -0.61038' + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523' + 0x3fe91b166fd49da2, 0xbfe3d78238c58343, // 0.78456, -0.62006' + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486' + 0x3fe8dc45331698cc, 0xbfe425ff178e6bb1, // 0.77689, -0.62964' + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439' + 0x3fe89c7e9a4dd4ab, 0xbfe473b51b987347, // 0.7691, -0.63912' + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383' + 0x3fe85bc51ae958cc, 0xbfe4c0a145ec0004, // 0.7612, -0.64851' + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317' + 0x3fe81a1b33b57acc, 0xbfe50cc09f59a09b, // 0.75319, -0.65781' + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242' + 0x3fe7d7836cc33db2, 0xbfe5581038975137, // 0.74506, -0.667' + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156' + 0x3fe79400574f55e4, 0xbfe5a28d2a5d7250, // 0.73682, -0.67609' + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806' + 0x3fe74f948da8d28d, 0xbfe5ec3495837074, // 0.72846, -0.68508' + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954' + 0x3fe70a42b3176d7a, 0xbfe63503a31c1be8, // 0.72, -0.69397' + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838' + 0x3fe6c40d73c18275, 0xbfe67cf78491af10, // 0.71143, -0.70275' + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711' + 0x3fe67cf78491af10, 0xbfe6c40d73c18275, // 0.70275, -0.71143' + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573' + 0x3fe63503a31c1be8, 0xbfe70a42b3176d7a, // 0.69397, -0.72' + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425' + 0x3fe5ec3495837074, 0xbfe74f948da8d28d, // 0.68508, -0.72846' + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265' + 0x3fe5a28d2a5d7250, 0xbfe79400574f55e4, // 0.67609, -0.73682' + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095' + 0x3fe5581038975137, 0xbfe7d7836cc33db2, // 0.667, -0.74506' + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914' + 0x3fe50cc09f59a09b, 0xbfe81a1b33b57acc, // 0.65781, -0.75319' + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721' + 0x3fe4c0a145ec0004, 0xbfe85bc51ae958cc, // 0.64851, -0.7612' + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517' + 0x3fe473b51b987347, 0xbfe89c7e9a4dd4ab, // 0.63912, -0.7691' + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301' + 0x3fe425ff178e6bb1, 0xbfe8dc45331698cc, // 0.62964, -0.77689' + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074' + 0x3fe3d78238c58343, 0xbfe91b166fd49da2, // 0.62006, -0.78456' + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835' + 0x3fe3884185dfeb22, 0xbfe958efe48e6dd7, // 0.61038, -0.79211' + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584' + 0x3fe338400d0c8e57, 0xbfe995cf2ed80d22, // 0.60062, -0.79954' + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321' + 0x3fe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // 0.59076, -0.80685' + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046' + 0x3fe2960727629ca8, 0xbfea0c95eabaf937, // 0.58081, -0.81404' + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758' + 0x3fe243d5fb98ac1f, 0xbfea4678c8119ac8, // 0.57078, -0.8211' + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459' + 0x3fe1f0f08bbc861b, 0xbfea7f58529fe69d, // 0.56066, -0.82805' + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147' + 0x3fe19d5a09f2b9b8, 0xbfeab7325916c0d4, // 0.55046, -0.83486' + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822' + 0x3fe14915af336ceb, 0xbfeaee04b43c1474, // 0.54017, -0.84155' + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485' + 0x3fe0f426bb2a8e7d, 0xbfeb23cd470013b4, // 0.5298, -0.84812' + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136' + 0x3fe09e907417c5e1, 0xbfeb5889fe921405, // 0.51936, -0.85456' + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773' + 0x3fe0485626ae221a, 0xbfeb8c38d27504e9, // 0.50883, -0.86087' + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397' + 0x3fdfe2f64be7120f, 0xbfebbed7c49380ea, // 0.49823, -0.86705' + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009' + 0x3fdf3405963fd068, 0xbfebf064e15377dd, // 0.48755, -0.87309' + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607' + 0x3fde83e0eaf85113, 0xbfec20de3fa971b0, // 0.4768, -0.87901' + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192' + 0x3fddd28f1481cc58, 0xbfec5042012b6907, // 0.46598, -0.8848' + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764' + 0x3fdd2016e8e9db5b, 0xbfec7e8e52233cf3, // 0.45508, -0.89045' + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322' + 0x3fdc6c7f4997000a, 0xbfecabc169a0b901, // 0.44412, -0.89597' + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867' + 0x3fdbb7cf2304bd01, 0xbfecd7d9898b32f6, // 0.43309, -0.90135' + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399' + 0x3fdb020d6c7f4009, 0xbfed02d4feb2bd92, // 0.422, -0.9066' + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917' + 0x3fda4b4127dea1e4, 0xbfed2cb220e0ef9f, // 0.41084, -0.91171' + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421' + 0x3fd993716141bdfe, 0xbfed556f52e93eb1, // 0.39962, -0.91668' + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911' + 0x3fd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // 0.38835, -0.92151' + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388' + 0x3fd820e3b04eaac4, 0xbfeda383a9668988, // 0.37701, -0.92621' + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851' + 0x3fd766340f2418f6, 0xbfedc8d7cb410260, // 0.36561, -0.93077' + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299' + 0x3fd6aa9d7dc77e16, 0xbfeded05f7de47da, // 0.35416, -0.93518' + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734' + 0x3fd5ee27379ea693, 0xbfee100cca2980ac, // 0.34266, -0.93946' + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154' + 0x3fd530d880af3c24, 0xbfee31eae870ce25, // 0.33111, -0.94359' + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561' + 0x3fd472b8a5571054, 0xbfee529f04729ffc, // 0.3195, -0.94759' + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953' + 0x3fd3b3cefa0414b7, 0xbfee7227db6a9744, // 0.30785, -0.95144' + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331' + 0x3fd2f422daec0386, 0xbfee9084361df7f3, // 0.29615, -0.95514' + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694' + 0x3fd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // 0.28441, -0.9587' + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043' + 0x3fd172a0d7765177, 0xbfeec9b2d3c3bf84, // 0.27262, -0.96212' + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378' + 0x3fd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // 0.26079, -0.96539' + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698' + 0x3fcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // 0.24893, -0.96852' + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003' + 0x3fce56ca1e101a1b, 0xbfef168f53f7205d, // 0.23702, -0.9715' + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294' + 0x3fcccf8cb312b286, 0xbfef2dc9c9089a9d, // 0.22508, -0.97434' + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757' + 0x3fcb4732ef3d6722, 0xbfef43d085ff92dd, // 0.21311, -0.97703' + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832' + 0x3fc9bdcbf2dc4366, 0xbfef58a2b1789e84, // 0.2011, -0.97957' + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079' + 0x3fc83366e89c64c5, 0xbfef6c3f7df5bbb7, // 0.18907, -0.98196' + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311' + 0x3fc6a81304f64ab2, 0xbfef7ea629e63d6e, // 0.177, -0.98421' + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528' + 0x3fc51bdf8597c5f2, 0xbfef8fd5ffae41db, // 0.16491, -0.98631' + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873' + 0x3fc38edbb0cd8d14, 0xbfef9fce55adb2c8, // 0.1528, -0.98826' + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918' + 0x3fc20116d4ec7bce, 0xbfefae8e8e46cfbb, // 0.14066, -0.99006' + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909' + 0x3fc072a047ba831d, 0xbfefbc1617e44186, // 0.1285, -0.99171' + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248' + 0x3fbdc70ecbae9fc8, 0xbfefc8646cfeb721, // 0.11632, -0.99321' + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391' + 0x3fbaa7b724495c04, 0xbfefd37914220b84, // 0.10412, -0.99456' + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518' + 0x3fb787586a5d5b21, 0xbfefdd539ff1f456, // 0.091909, -0.99577' + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631' + 0x3fb4661179272096, 0xbfefe5f3af2e3940, // 0.079682, -0.99682' + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729' + 0x3fb1440134d709b2, 0xbfefed58ecb673c4, // 0.067444, -0.99772' + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812' + 0x3fac428d12c0d7e3, 0xbfeff3830f8d575c, // 0.055195, -0.99848' + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988' + 0x3fa5fc00d290cd43, 0xbfeff871dadb81df, // 0.042938, -0.99908' + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932' + 0x3f9f693731d1cf01, 0xbfeffc251df1d3f8, // 0.030675, -0.99953' + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997' + 0x3f92d936bbe30efd, 0xbfeffe9cb44b51a1, // 0.018407, -0.99983' + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992' + 0x3f7921f0fe670071, 0xbfefffd8858e8a92, //0.0061359, -0.99998' +}; + +const uint64_t twiddleCoefF64_rfft_2048[2048] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0x3f6921f8becca4ba, 0x3feffff621621d02, // 0.003068, 1 + 0x3f7921f0fe670071, 0x3fefffd8858e8a92, //0.0061359, 0.99998 + 0x3f82d96b0e509703, 0x3fefffa72c978c4f, //0.0092038, 0.99996 + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992 + 0x3f8f6a296ab997ca, 0x3fefff0943c53bd1, // 0.015339, 0.99988 + 0x3f92d936bbe30efd, 0x3feffe9cb44b51a1, // 0.018407, 0.99983 + 0x3f95fd4d21fab226, 0x3feffe1c6870cb77, // 0.021474, 0.99977 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x3f9c454f4ce53b1c, 0x3feffce09ce2a679, // 0.027608, 0.99962 + 0x3f9f693731d1cf01, 0x3feffc251df1d3f8, // 0.030675, 0.99953 + 0x3fa14685db42c17e, 0x3feffb55e425fdae, // 0.033741, 0.99943 + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932 + 0x3fa46a396ff86179, 0x3feff97c4208c014, // 0.039873, 0.9992 + 0x3fa5fc00d290cd43, 0x3feff871dadb81df, // 0.042938, 0.99908 + 0x3fa78dbaa5874685, 0x3feff753bb1b9164, // 0.046003, 0.99894 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3faab101bd5f8317, 0x3feff4dc54b1bed3, // 0.052132, 0.99864 + 0x3fac428d12c0d7e3, 0x3feff3830f8d575c, // 0.055195, 0.99848 + 0x3fadd406f9808ec8, 0x3feff21614e131ed, // 0.058258, 0.9983 + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812 + 0x3fb07b614e463064, 0x3fefef0102826191, // 0.064383, 0.99793 + 0x3fb1440134d709b2, 0x3fefed58ecb673c4, // 0.067444, 0.99772 + 0x3fb20c9674ed444c, 0x3fefeb9d2530410f, // 0.070505, 0.99751 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3fb39d9f12c5a299, 0x3fefe7ea85482d60, // 0.076624, 0.99706 + 0x3fb4661179272096, 0x3fefe5f3af2e3940, // 0.079682, 0.99682 + 0x3fb52e774a4d4d0a, 0x3fefe3e92be9d886, // 0.08274, 0.99657 + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631 + 0x3fb6bf1b3e79b129, 0x3fefdf9922f73307, // 0.088854, 0.99604 + 0x3fb787586a5d5b21, 0x3fefdd539ff1f456, // 0.091909, 0.99577 + 0x3fb84f8712c130a0, 0x3fefdafa7514538c, // 0.094963, 0.99548 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb9dfb6eb24a85c, 0x3fefd60d2da75c9e, // 0.10107, 0.99488 + 0x3fbaa7b724495c04, 0x3fefd37914220b84, // 0.10412, 0.99456 + 0x3fbb6fa6ec38f64c, 0x3fefd0d158d86087, // 0.10717, 0.99424 + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391 + 0x3fbcff533b307dc1, 0x3fefcb4703914354, // 0.11327, 0.99356 + 0x3fbdc70ecbae9fc8, 0x3fefc8646cfeb721, // 0.11632, 0.99321 + 0x3fbe8eb7fde4aa3e, 0x3fefc56e3b7d9af6, // 0.11937, 0.99285 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fc00ee8ad6fb85b, 0x3fefbf470f0a8d88, // 0.12545, 0.9921 + 0x3fc072a047ba831d, 0x3fefbc1617e44186, // 0.1285, 0.99171 + 0x3fc0d64dbcb26786, 0x3fefb8d18d66adb7, // 0.13154, 0.99131 + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909 + 0x3fc19d8940be24e7, 0x3fefb20dc681d54d, // 0.13762, 0.99049 + 0x3fc20116d4ec7bce, 0x3fefae8e8e46cfbb, // 0.14066, 0.99006 + 0x3fc264994dfd340a, 0x3fefaafbcb0cfddc, // 0.1437, 0.98962 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc32b7bf94516a7, 0x3fefa39bac7a1791, // 0.14976, 0.98872 + 0x3fc38edbb0cd8d14, 0x3fef9fce55adb2c8, // 0.1528, 0.98826 + 0x3fc3f22f57db4893, 0x3fef9bed7cfbde29, // 0.15583, 0.98778 + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873 + 0x3fc4b8b17f79fa88, 0x3fef93f14f85ac08, // 0.16189, 0.98681 + 0x3fc51bdf8597c5f2, 0x3fef8fd5ffae41db, // 0.16491, 0.98631 + 0x3fc57f008654cbde, 0x3fef8ba737cb4b78, // 0.16794, 0.9858 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc6451a831d830d, 0x3fef830f4a40c60c, // 0.17398, 0.98475 + 0x3fc6a81304f64ab2, 0x3fef7ea629e63d6e, // 0.177, 0.98421 + 0x3fc70afd8d08c4ff, 0x3fef7a299c1a322a, // 0.18002, 0.98366 + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311 + 0x3fc7d0a7bbd2cb1b, 0x3fef70f6434b7eb7, // 0.18606, 0.98254 + 0x3fc83366e89c64c5, 0x3fef6c3f7df5bbb7, // 0.18907, 0.98196 + 0x3fc8961727c41804, 0x3fef677556883cee, // 0.19208, 0.98138 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc95b49e9b62af9, 0x3fef5da6ed43685d, // 0.1981, 0.98018 + 0x3fc9bdcbf2dc4366, 0x3fef58a2b1789e84, // 0.2011, 0.97957 + 0x3fca203e1b1831da, 0x3fef538b1faf2d07, // 0.20411, 0.97895 + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832 + 0x3fcae4f1d5f3b9ab, 0x3fef492206bcabb4, // 0.21011, 0.97768 + 0x3fcb4732ef3d6722, 0x3fef43d085ff92dd, // 0.21311, 0.97703 + 0x3fcba96334f15dad, 0x3fef3e6bbc1bbc65, // 0.21611, 0.97637 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fcc6d90535d74dc, 0x3fef33685a3aaef0, // 0.22209, 0.97503 + 0x3fcccf8cb312b286, 0x3fef2dc9c9089a9d, // 0.22508, 0.97434 + 0x3fcd31774d2cbdee, 0x3fef2817fc4609ce, // 0.22807, 0.97364 + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294 + 0x3fcdf5163f01099a, 0x3fef1c7abe284708, // 0.23404, 0.97223 + 0x3fce56ca1e101a1b, 0x3fef168f53f7205d, // 0.23702, 0.9715 + 0x3fceb86b462de348, 0x3fef1090bc898f5f, // 0.24, 0.97077 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fcf7b7480bd3801, 0x3fef045a14cf738c, // 0.24596, 0.96928 + 0x3fcfdcdc1adfedf8, 0x3feefe220c0b95ec, // 0.24893, 0.96852 + 0x3fd01f1806b9fdd2, 0x3feef7d6e51ca3c0, // 0.2519, 0.96775 + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698 + 0x3fd0804e05eb661e, 0x3feeeb074c50a544, // 0.25783, 0.96619 + 0x3fd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // 0.26079, 0.96539 + 0x3fd0e15b4e1749cd, 0x3feeddeb6a078651, // 0.26375, 0.96459 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd1423eefc69378, 0x3feed0835e999009, // 0.26967, 0.96295 + 0x3fd172a0d7765177, 0x3feec9b2d3c3bf84, // 0.27262, 0.96212 + 0x3fd1a2f7fbe8f243, 0x3feec2cf4b1af6b2, // 0.27557, 0.96128 + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043 + 0x3fd2038583d727bd, 0x3feeb4cf515b8811, // 0.28146, 0.95957 + 0x3fd233bbabc3bb72, 0x3feeadb2e8e7a88e, // 0.28441, 0.9587 + 0x3fd263e6995554ba, 0x3feea68393e65800, // 0.28735, 0.95783 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd2c41a4e954520, 0x3fee97ec36016b30, // 0.29322, 0.95605 + 0x3fd2f422daec0386, 0x3fee9084361df7f3, // 0.29615, 0.95514 + 0x3fd3241fb638baaf, 0x3fee89095bad6025, // 0.29908, 0.95423 + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331 + 0x3fd383f5e353b6aa, 0x3fee79db29a5165a, // 0.30493, 0.95238 + 0x3fd3b3cefa0414b7, 0x3fee7227db6a9744, // 0.30785, 0.95144 + 0x3fd3e39be96ec271, 0x3fee6a61c55d53a7, // 0.31077, 0.95049 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd44310dc8936f0, 0x3fee5a9d550467d3, // 0.31659, 0.94856 + 0x3fd472b8a5571054, 0x3fee529f04729ffc, // 0.3195, 0.94759 + 0x3fd4a253d11b82f3, 0x3fee4a8dff81ce5e, // 0.32241, 0.9466 + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561 + 0x3fd50163dc197047, 0x3fee3a33ec75ce85, // 0.32821, 0.9446 + 0x3fd530d880af3c24, 0x3fee31eae870ce25, // 0.33111, 0.94359 + 0x3fd5604012f467b4, 0x3fee298f4439197a, // 0.334, 0.94257 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd5bee78b9db3b6, 0x3fee18a02fdc66d9, // 0.33978, 0.94051 + 0x3fd5ee27379ea693, 0x3fee100cca2980ac, // 0.34266, 0.93946 + 0x3fd61d595c88c203, 0x3fee0766d9280f54, // 0.34554, 0.9384 + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734 + 0x3fd67b949cad63ca, 0x3fedf5e36a9ba59c, // 0.35129, 0.93627 + 0x3fd6aa9d7dc77e16, 0x3feded05f7de47da, // 0.35416, 0.93518 + 0x3fd6d998638a0cb5, 0x3fede4160f6d8d81, // 0.35703, 0.93409 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd73763c9261092, 0x3fedd1fef38a915a, // 0.36276, 0.93188 + 0x3fd766340f2418f6, 0x3fedc8d7cb410260, // 0.36561, 0.93077 + 0x3fd794f5e613dfae, 0x3fedbf9e4395759a, // 0.36847, 0.92964 + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851 + 0x3fd7f24dd37341e3, 0x3fedacf42ce68ab9, // 0.37416, 0.92736 + 0x3fd820e3b04eaac4, 0x3feda383a9668988, // 0.37701, 0.92621 + 0x3fd84f6aaaf3903f, 0x3fed9a00dd8b3d46, // 0.37985, 0.92505 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd8ac4b86d5ed44, 0x3fed86c48445a450, // 0.38552, 0.9227 + 0x3fd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // 0.38835, 0.92151 + 0x3fd908ef81ef7bd1, 0x3fed733f508c0dff, // 0.39117, 0.92032 + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911 + 0x3fd96555b7ab948f, 0x3fed5f7172888a7f, // 0.39681, 0.9179 + 0x3fd993716141bdfe, 0x3fed556f52e93eb1, // 0.39962, 0.91668 + 0x3fd9c17d440df9f2, 0x3fed4b5b1b187524, // 0.40243, 0.91545 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fda1d6543b50ac0, 0x3fed36fc7bcbfbdc, // 0.40804, 0.91296 + 0x3fda4b4127dea1e4, 0x3fed2cb220e0ef9f, // 0.41084, 0.91171 + 0x3fda790cd3dbf31a, 0x3fed2255c6e5a4e1, // 0.41364, 0.91044 + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917 + 0x3fdad473125cdc08, 0x3fed0d672f59d2b9, // 0.41922, 0.90789 + 0x3fdb020d6c7f4009, 0x3fed02d4feb2bd92, // 0.422, 0.9066 + 0x3fdb2f971db31972, 0x3fecf830e8ce467b, // 0.42478, 0.9053 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdb8a7814fd5693, 0x3fece2b32799a060, // 0.43033, 0.90267 + 0x3fdbb7cf2304bd01, 0x3fecd7d9898b32f6, // 0.43309, 0.90135 + 0x3fdbe51517ffc0d9, 0x3fecccee20c2de9f, // 0.43586, 0.90002 + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867 + 0x3fdc3f6d47263129, 0x3fecb6e20a00da99, // 0.44137, 0.89732 + 0x3fdc6c7f4997000a, 0x3fecabc169a0b901, // 0.44412, 0.89597 + 0x3fdc997fc3865388, 0x3feca08f19b9c449, // 0.44687, 0.8946 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdcf34baee1cd21, 0x3fec89f587029c13, // 0.45235, 0.89184 + 0x3fdd2016e8e9db5b, 0x3fec7e8e52233cf3, // 0.45508, 0.89045 + 0x3fdd4cd02ba8609c, 0x3fec7315899eaad7, // 0.45781, 0.88905 + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764 + 0x3fdda60c5cfa10d8, 0x3fec5bef59fef85a, // 0.46326, 0.88622 + 0x3fddd28f1481cc58, 0x3fec5042012b6907, // 0.46598, 0.8848 + 0x3fddfeff66a941de, 0x3fec44833141c004, // 0.46869, 0.88336 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fde57a86d3cd824, 0x3fec2cd14931e3f1, // 0.4741, 0.88047 + 0x3fde83e0eaf85113, 0x3fec20de3fa971b0, // 0.4768, 0.87901 + 0x3fdeb00695f25620, 0x3fec14d9dc465e58, // 0.47949, 0.87755 + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607 + 0x3fdf081906bff7fd, 0x3febfc9d25a1b147, // 0.48487, 0.87459 + 0x3fdf3405963fd068, 0x3febf064e15377dd, // 0.48755, 0.87309 + 0x3fdf5fdee656cda3, 0x3febe41b611154c1, // 0.49023, 0.8716 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fdfb7575c24d2de, 0x3febcb54cb0d2327, // 0.49557, 0.86857 + 0x3fdfe2f64be7120f, 0x3febbed7c49380ea, // 0.49823, 0.86705 + 0x3fe00740c82b82e0, 0x3febb249a0b6c40d, // 0.50089, 0.86551 + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397 + 0x3fe032ae55edbd95, 0x3feb98fa1fd9155e, // 0.50619, 0.86242 + 0x3fe0485626ae221a, 0x3feb8c38d27504e9, // 0.50883, 0.86087 + 0x3fe05df3ec31b8b6, 0x3feb7f6686e792ea, // 0.51147, 0.8593 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe089112032b08c, 0x3feb658f14fdbc47, // 0.51673, 0.85615 + 0x3fe09e907417c5e1, 0x3feb5889fe921405, // 0.51936, 0.85456 + 0x3fe0b405878f85ec, 0x3feb4b7409de7925, // 0.52198, 0.85296 + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136 + 0x3fe0ded0b84bc4b5, 0x3feb3115a5f37bf4, // 0.5272, 0.84974 + 0x3fe0f426bb2a8e7d, 0x3feb23cd470013b4, // 0.5298, 0.84812 + 0x3fe1097248d0a956, 0x3feb16742a4ca2f5, // 0.5324, 0.84649 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe133e9cfee254e, 0x3feafb8fd89f57b6, // 0.53759, 0.84321 + 0x3fe14915af336ceb, 0x3feaee04b43c1474, // 0.54017, 0.84155 + 0x3fe15e36e4dbe2bc, 0x3feae068f345ecef, // 0.54275, 0.83989 + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822 + 0x3fe188591f3a46e5, 0x3feac4ffbd3efac8, // 0.54789, 0.83655 + 0x3fe19d5a09f2b9b8, 0x3feab7325916c0d4, // 0.55046, 0.83486 + 0x3fe1b250171373be, 0x3feaa9547a2cb98e, // 0.55302, 0.83317 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe1dc1b64dc4872, 0x3fea8d676e545ad2, // 0.55812, 0.82976 + 0x3fe1f0f08bbc861b, 0x3fea7f58529fe69d, // 0.56066, 0.82805 + 0x3fe205baa17560d6, 0x3fea7138de9d60f5, // 0.5632, 0.82632 + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459 + 0x3fe22f2d662c13e1, 0x3fea54c91090f524, // 0.56826, 0.82285 + 0x3fe243d5fb98ac1f, 0x3fea4678c8119ac8, // 0.57078, 0.8211 + 0x3fe258734cbb7110, 0x3fea38184a593bc6, // 0.5733, 0.81935 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe2818bef4d3cba, 0x3fea1b26d2c0a75e, // 0.57831, 0.81581 + 0x3fe2960727629ca8, 0x3fea0c95eabaf937, // 0.58081, 0.81404 + 0x3fe2aa76e87aeb58, 0x3fe9fdf4f13149de, // 0.58331, 0.81225 + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046 + 0x3fe2d333d34e9bb7, 0x3fe9e082edb42472, // 0.58828, 0.80866 + 0x3fe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // 0.59076, 0.80685 + 0x3fe2fbc24b441015, 0x3fe9c2d110f075c3, // 0.59323, 0.80503 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe32421ec49a620, 0x3fe9a4dfa42b06b2, // 0.59816, 0.80138 + 0x3fe338400d0c8e57, 0x3fe995cf2ed80d22, // 0.60062, 0.79954 + 0x3fe34c5252c14de1, 0x3fe986aef1457594, // 0.60307, 0.79769 + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584 + 0x3fe374531b817f8d, 0x3fe9683f42bd7fe1, // 0.60795, 0.79398 + 0x3fe3884185dfeb22, 0x3fe958efe48e6dd7, // 0.61038, 0.79211 + 0x3fe39c23e3d63029, 0x3fe94990e3ac4a6c, // 0.61281, 0.79023 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe3c3c44981c517, 0x3fe92aa41fc5a815, // 0.61765, 0.78646 + 0x3fe3d78238c58343, 0x3fe91b166fd49da2, // 0.62006, 0.78456 + 0x3fe3eb33eabe0680, 0x3fe90b7943575efe, // 0.62246, 0.78265 + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074 + 0x3fe41272663d108c, 0x3fe8ec109b486c49, // 0.62725, 0.77882 + 0x3fe425ff178e6bb1, 0x3fe8dc45331698cc, // 0.62964, 0.77689 + 0x3fe4397f5b2a4380, 0x3fe8cc6a75184655, // 0.63202, 0.77495 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe4605a692b32a2, 0x3fe8ac871ede1d88, // 0.63676, 0.77106 + 0x3fe473b51b987347, 0x3fe89c7e9a4dd4ab, // 0.63912, 0.7691 + 0x3fe48703306091fe, 0x3fe88c66e7481ba1, // 0.64148, 0.76714 + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517 + 0x3fe4ad79516722f0, 0x3fe86c0a1d9aa195, // 0.64618, 0.76319 + 0x3fe4c0a145ec0004, 0x3fe85bc51ae958cc, // 0.64851, 0.7612 + 0x3fe4d3bc6d589f80, 0x3fe84b7111af83f9, // 0.65085, 0.75921 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe4f9cc25cca486, 0x3fe82a9c13f545ff, // 0.65549, 0.7552 + 0x3fe50cc09f59a09b, 0x3fe81a1b33b57acc, // 0.65781, 0.75319 + 0x3fe51fa81cd99aa6, 0x3fe8098b756e52fa, // 0.66011, 0.75117 + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914 + 0x3fe5454ff5159dfb, 0x3fe7e83f87b03686, // 0.66471, 0.7471 + 0x3fe5581038975137, 0x3fe7d7836cc33db2, // 0.667, 0.74506 + 0x3fe56ac35197649e, 0x3fe7c6b89ce2d333, // 0.66928, 0.74301 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe59001d5f723df, 0x3fe7a4f707bf97d2, // 0.67383, 0.73889 + 0x3fe5a28d2a5d7250, 0x3fe79400574f55e4, // 0.67609, 0.73682 + 0x3fe5b50b264f7448, 0x3fe782fb1b90b35b, // 0.67835, 0.73474 + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265 + 0x3fe5d9dee73e345c, 0x3fe760c52c304764, // 0.68285, 0.73056 + 0x3fe5ec3495837074, 0x3fe74f948da8d28d, // 0.68508, 0.72846 + 0x3fe5fe7cbde56a0f, 0x3fe73e558e079942, // 0.68732, 0.72636 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe622e44fec22ff, 0x3fe71bac960e41bf, // 0.69176, 0.72213 + 0x3fe63503a31c1be8, 0x3fe70a42b3176d7a, // 0.69397, 0.72 + 0x3fe64715437f535b, 0x3fe6f8ca99c95b75, // 0.69618, 0.71787 + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573 + 0x3fe66b0f3f52b386, 0x3fe6d5afef4aafcc, // 0.70057, 0.71358 + 0x3fe67cf78491af10, 0x3fe6c40d73c18275, // 0.70275, 0.71143 + 0x3fe68ed1eaa19c71, 0x3fe6b25ced2fe29c, // 0.70493, 0.70927 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe6b25ced2fe29c, 0x3fe68ed1eaa19c71, // 0.70927, 0.70493 + 0x3fe6c40d73c18275, 0x3fe67cf78491af10, // 0.71143, 0.70275 + 0x3fe6d5afef4aafcc, 0x3fe66b0f3f52b386, // 0.71358, 0.70057 + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838 + 0x3fe6f8ca99c95b75, 0x3fe64715437f535b, // 0.71787, 0.69618 + 0x3fe70a42b3176d7a, 0x3fe63503a31c1be8, // 0.72, 0.69397 + 0x3fe71bac960e41bf, 0x3fe622e44fec22ff, // 0.72213, 0.69176 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe73e558e079942, 0x3fe5fe7cbde56a0f, // 0.72636, 0.68732 + 0x3fe74f948da8d28d, 0x3fe5ec3495837074, // 0.72846, 0.68508 + 0x3fe760c52c304764, 0x3fe5d9dee73e345c, // 0.73056, 0.68285 + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806 + 0x3fe782fb1b90b35b, 0x3fe5b50b264f7448, // 0.73474, 0.67835 + 0x3fe79400574f55e4, 0x3fe5a28d2a5d7250, // 0.73682, 0.67609 + 0x3fe7a4f707bf97d2, 0x3fe59001d5f723df, // 0.73889, 0.67383 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe7c6b89ce2d333, 0x3fe56ac35197649e, // 0.74301, 0.66928 + 0x3fe7d7836cc33db2, 0x3fe5581038975137, // 0.74506, 0.667 + 0x3fe7e83f87b03686, 0x3fe5454ff5159dfb, // 0.7471, 0.66471 + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242 + 0x3fe8098b756e52fa, 0x3fe51fa81cd99aa6, // 0.75117, 0.66011 + 0x3fe81a1b33b57acc, 0x3fe50cc09f59a09b, // 0.75319, 0.65781 + 0x3fe82a9c13f545ff, 0x3fe4f9cc25cca486, // 0.7552, 0.65549 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe84b7111af83f9, 0x3fe4d3bc6d589f80, // 0.75921, 0.65085 + 0x3fe85bc51ae958cc, 0x3fe4c0a145ec0004, // 0.7612, 0.64851 + 0x3fe86c0a1d9aa195, 0x3fe4ad79516722f0, // 0.76319, 0.64618 + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383 + 0x3fe88c66e7481ba1, 0x3fe48703306091fe, // 0.76714, 0.64148 + 0x3fe89c7e9a4dd4ab, 0x3fe473b51b987347, // 0.7691, 0.63912 + 0x3fe8ac871ede1d88, 0x3fe4605a692b32a2, // 0.77106, 0.63676 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe8cc6a75184655, 0x3fe4397f5b2a4380, // 0.77495, 0.63202 + 0x3fe8dc45331698cc, 0x3fe425ff178e6bb1, // 0.77689, 0.62964 + 0x3fe8ec109b486c49, 0x3fe41272663d108c, // 0.77882, 0.62725 + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486 + 0x3fe90b7943575efe, 0x3fe3eb33eabe0680, // 0.78265, 0.62246 + 0x3fe91b166fd49da2, 0x3fe3d78238c58343, // 0.78456, 0.62006 + 0x3fe92aa41fc5a815, 0x3fe3c3c44981c517, // 0.78646, 0.61765 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe94990e3ac4a6c, 0x3fe39c23e3d63029, // 0.79023, 0.61281 + 0x3fe958efe48e6dd7, 0x3fe3884185dfeb22, // 0.79211, 0.61038 + 0x3fe9683f42bd7fe1, 0x3fe374531b817f8d, // 0.79398, 0.60795 + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551 + 0x3fe986aef1457594, 0x3fe34c5252c14de1, // 0.79769, 0.60307 + 0x3fe995cf2ed80d22, 0x3fe338400d0c8e57, // 0.79954, 0.60062 + 0x3fe9a4dfa42b06b2, 0x3fe32421ec49a620, // 0.80138, 0.59816 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe9c2d110f075c3, 0x3fe2fbc24b441015, // 0.80503, 0.59323 + 0x3fe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // 0.80685, 0.59076 + 0x3fe9e082edb42472, 0x3fe2d333d34e9bb7, // 0.80866, 0.58828 + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858 + 0x3fe9fdf4f13149de, 0x3fe2aa76e87aeb58, // 0.81225, 0.58331 + 0x3fea0c95eabaf937, 0x3fe2960727629ca8, // 0.81404, 0.58081 + 0x3fea1b26d2c0a75e, 0x3fe2818bef4d3cba, // 0.81581, 0.57831 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fea38184a593bc6, 0x3fe258734cbb7110, // 0.81935, 0.5733 + 0x3fea4678c8119ac8, 0x3fe243d5fb98ac1f, // 0.8211, 0.57078 + 0x3fea54c91090f524, 0x3fe22f2d662c13e1, // 0.82285, 0.56826 + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573 + 0x3fea7138de9d60f5, 0x3fe205baa17560d6, // 0.82632, 0.5632 + 0x3fea7f58529fe69d, 0x3fe1f0f08bbc861b, // 0.82805, 0.56066 + 0x3fea8d676e545ad2, 0x3fe1dc1b64dc4872, // 0.82976, 0.55812 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3feaa9547a2cb98e, 0x3fe1b250171373be, // 0.83317, 0.55302 + 0x3feab7325916c0d4, 0x3fe19d5a09f2b9b8, // 0.83486, 0.55046 + 0x3feac4ffbd3efac8, 0x3fe188591f3a46e5, // 0.83655, 0.54789 + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532 + 0x3feae068f345ecef, 0x3fe15e36e4dbe2bc, // 0.83989, 0.54275 + 0x3feaee04b43c1474, 0x3fe14915af336ceb, // 0.84155, 0.54017 + 0x3feafb8fd89f57b6, 0x3fe133e9cfee254e, // 0.84321, 0.53759 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3feb16742a4ca2f5, 0x3fe1097248d0a956, // 0.84649, 0.5324 + 0x3feb23cd470013b4, 0x3fe0f426bb2a8e7d, // 0.84812, 0.5298 + 0x3feb3115a5f37bf4, 0x3fe0ded0b84bc4b5, // 0.84974, 0.5272 + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459 + 0x3feb4b7409de7925, 0x3fe0b405878f85ec, // 0.85296, 0.52198 + 0x3feb5889fe921405, 0x3fe09e907417c5e1, // 0.85456, 0.51936 + 0x3feb658f14fdbc47, 0x3fe089112032b08c, // 0.85615, 0.51673 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb7f6686e792ea, 0x3fe05df3ec31b8b6, // 0.8593, 0.51147 + 0x3feb8c38d27504e9, 0x3fe0485626ae221a, // 0.86087, 0.50883 + 0x3feb98fa1fd9155e, 0x3fe032ae55edbd95, // 0.86242, 0.50619 + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354 + 0x3febb249a0b6c40d, 0x3fe00740c82b82e0, // 0.86551, 0.50089 + 0x3febbed7c49380ea, 0x3fdfe2f64be7120f, // 0.86705, 0.49823 + 0x3febcb54cb0d2327, 0x3fdfb7575c24d2de, // 0.86857, 0.49557 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3febe41b611154c1, 0x3fdf5fdee656cda3, // 0.8716, 0.49023 + 0x3febf064e15377dd, 0x3fdf3405963fd068, // 0.87309, 0.48755 + 0x3febfc9d25a1b147, 0x3fdf081906bff7fd, // 0.87459, 0.48487 + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218 + 0x3fec14d9dc465e58, 0x3fdeb00695f25620, // 0.87755, 0.47949 + 0x3fec20de3fa971b0, 0x3fde83e0eaf85113, // 0.87901, 0.4768 + 0x3fec2cd14931e3f1, 0x3fde57a86d3cd824, // 0.88047, 0.4741 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec44833141c004, 0x3fddfeff66a941de, // 0.88336, 0.46869 + 0x3fec5042012b6907, 0x3fddd28f1481cc58, // 0.8848, 0.46598 + 0x3fec5bef59fef85a, 0x3fdda60c5cfa10d8, // 0.88622, 0.46326 + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054 + 0x3fec7315899eaad7, 0x3fdd4cd02ba8609c, // 0.88905, 0.45781 + 0x3fec7e8e52233cf3, 0x3fdd2016e8e9db5b, // 0.89045, 0.45508 + 0x3fec89f587029c13, 0x3fdcf34baee1cd21, // 0.89184, 0.45235 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3feca08f19b9c449, 0x3fdc997fc3865388, // 0.8946, 0.44687 + 0x3fecabc169a0b901, 0x3fdc6c7f4997000a, // 0.89597, 0.44412 + 0x3fecb6e20a00da99, 0x3fdc3f6d47263129, // 0.89732, 0.44137 + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862 + 0x3fecccee20c2de9f, 0x3fdbe51517ffc0d9, // 0.90002, 0.43586 + 0x3fecd7d9898b32f6, 0x3fdbb7cf2304bd01, // 0.90135, 0.43309 + 0x3fece2b32799a060, 0x3fdb8a7814fd5693, // 0.90267, 0.43033 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fecf830e8ce467b, 0x3fdb2f971db31972, // 0.9053, 0.42478 + 0x3fed02d4feb2bd92, 0x3fdb020d6c7f4009, // 0.9066, 0.422 + 0x3fed0d672f59d2b9, 0x3fdad473125cdc08, // 0.90789, 0.41922 + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643 + 0x3fed2255c6e5a4e1, 0x3fda790cd3dbf31a, // 0.91044, 0.41364 + 0x3fed2cb220e0ef9f, 0x3fda4b4127dea1e4, // 0.91171, 0.41084 + 0x3fed36fc7bcbfbdc, 0x3fda1d6543b50ac0, // 0.91296, 0.40804 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed4b5b1b187524, 0x3fd9c17d440df9f2, // 0.91545, 0.40243 + 0x3fed556f52e93eb1, 0x3fd993716141bdfe, // 0.91668, 0.39962 + 0x3fed5f7172888a7f, 0x3fd96555b7ab948f, // 0.9179, 0.39681 + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399 + 0x3fed733f508c0dff, 0x3fd908ef81ef7bd1, // 0.92032, 0.39117 + 0x3fed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // 0.92151, 0.38835 + 0x3fed86c48445a450, 0x3fd8ac4b86d5ed44, // 0.9227, 0.38552 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed9a00dd8b3d46, 0x3fd84f6aaaf3903f, // 0.92505, 0.37985 + 0x3feda383a9668988, 0x3fd820e3b04eaac4, // 0.92621, 0.37701 + 0x3fedacf42ce68ab9, 0x3fd7f24dd37341e3, // 0.92736, 0.37416 + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132 + 0x3fedbf9e4395759a, 0x3fd794f5e613dfae, // 0.92964, 0.36847 + 0x3fedc8d7cb410260, 0x3fd766340f2418f6, // 0.93077, 0.36561 + 0x3fedd1fef38a915a, 0x3fd73763c9261092, // 0.93188, 0.36276 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3fede4160f6d8d81, 0x3fd6d998638a0cb5, // 0.93409, 0.35703 + 0x3feded05f7de47da, 0x3fd6aa9d7dc77e16, // 0.93518, 0.35416 + 0x3fedf5e36a9ba59c, 0x3fd67b949cad63ca, // 0.93627, 0.35129 + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842 + 0x3fee0766d9280f54, 0x3fd61d595c88c203, // 0.9384, 0.34554 + 0x3fee100cca2980ac, 0x3fd5ee27379ea693, // 0.93946, 0.34266 + 0x3fee18a02fdc66d9, 0x3fd5bee78b9db3b6, // 0.94051, 0.33978 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fee298f4439197a, 0x3fd5604012f467b4, // 0.94257, 0.334 + 0x3fee31eae870ce25, 0x3fd530d880af3c24, // 0.94359, 0.33111 + 0x3fee3a33ec75ce85, 0x3fd50163dc197047, // 0.9446, 0.32821 + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531 + 0x3fee4a8dff81ce5e, 0x3fd4a253d11b82f3, // 0.9466, 0.32241 + 0x3fee529f04729ffc, 0x3fd472b8a5571054, // 0.94759, 0.3195 + 0x3fee5a9d550467d3, 0x3fd44310dc8936f0, // 0.94856, 0.31659 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee6a61c55d53a7, 0x3fd3e39be96ec271, // 0.95049, 0.31077 + 0x3fee7227db6a9744, 0x3fd3b3cefa0414b7, // 0.95144, 0.30785 + 0x3fee79db29a5165a, 0x3fd383f5e353b6aa, // 0.95238, 0.30493 + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201 + 0x3fee89095bad6025, 0x3fd3241fb638baaf, // 0.95423, 0.29908 + 0x3fee9084361df7f3, 0x3fd2f422daec0386, // 0.95514, 0.29615 + 0x3fee97ec36016b30, 0x3fd2c41a4e954520, // 0.95605, 0.29322 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3feea68393e65800, 0x3fd263e6995554ba, // 0.95783, 0.28735 + 0x3feeadb2e8e7a88e, 0x3fd233bbabc3bb72, // 0.9587, 0.28441 + 0x3feeb4cf515b8811, 0x3fd2038583d727bd, // 0.95957, 0.28146 + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852 + 0x3feec2cf4b1af6b2, 0x3fd1a2f7fbe8f243, // 0.96128, 0.27557 + 0x3feec9b2d3c3bf84, 0x3fd172a0d7765177, // 0.96212, 0.27262 + 0x3feed0835e999009, 0x3fd1423eefc69378, // 0.96295, 0.26967 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3feeddeb6a078651, 0x3fd0e15b4e1749cd, // 0.96459, 0.26375 + 0x3feee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // 0.96539, 0.26079 + 0x3feeeb074c50a544, 0x3fd0804e05eb661e, // 0.96619, 0.25783 + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487 + 0x3feef7d6e51ca3c0, 0x3fd01f1806b9fdd2, // 0.96775, 0.2519 + 0x3feefe220c0b95ec, 0x3fcfdcdc1adfedf8, // 0.96852, 0.24893 + 0x3fef045a14cf738c, 0x3fcf7b7480bd3801, // 0.96928, 0.24596 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3fef1090bc898f5f, 0x3fceb86b462de348, // 0.97077, 0.24 + 0x3fef168f53f7205d, 0x3fce56ca1e101a1b, // 0.9715, 0.23702 + 0x3fef1c7abe284708, 0x3fcdf5163f01099a, // 0.97223, 0.23404 + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106 + 0x3fef2817fc4609ce, 0x3fcd31774d2cbdee, // 0.97364, 0.22807 + 0x3fef2dc9c9089a9d, 0x3fcccf8cb312b286, // 0.97434, 0.22508 + 0x3fef33685a3aaef0, 0x3fcc6d90535d74dc, // 0.97503, 0.22209 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef3e6bbc1bbc65, 0x3fcba96334f15dad, // 0.97637, 0.21611 + 0x3fef43d085ff92dd, 0x3fcb4732ef3d6722, // 0.97703, 0.21311 + 0x3fef492206bcabb4, 0x3fcae4f1d5f3b9ab, // 0.97768, 0.21011 + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711 + 0x3fef538b1faf2d07, 0x3fca203e1b1831da, // 0.97895, 0.20411 + 0x3fef58a2b1789e84, 0x3fc9bdcbf2dc4366, // 0.97957, 0.2011 + 0x3fef5da6ed43685d, 0x3fc95b49e9b62af9, // 0.98018, 0.1981 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef677556883cee, 0x3fc8961727c41804, // 0.98138, 0.19208 + 0x3fef6c3f7df5bbb7, 0x3fc83366e89c64c5, // 0.98196, 0.18907 + 0x3fef70f6434b7eb7, 0x3fc7d0a7bbd2cb1b, // 0.98254, 0.18606 + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304 + 0x3fef7a299c1a322a, 0x3fc70afd8d08c4ff, // 0.98366, 0.18002 + 0x3fef7ea629e63d6e, 0x3fc6a81304f64ab2, // 0.98421, 0.177 + 0x3fef830f4a40c60c, 0x3fc6451a831d830d, // 0.98475, 0.17398 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef8ba737cb4b78, 0x3fc57f008654cbde, // 0.9858, 0.16794 + 0x3fef8fd5ffae41db, 0x3fc51bdf8597c5f2, // 0.98631, 0.16491 + 0x3fef93f14f85ac08, 0x3fc4b8b17f79fa88, // 0.98681, 0.16189 + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886 + 0x3fef9bed7cfbde29, 0x3fc3f22f57db4893, // 0.98778, 0.15583 + 0x3fef9fce55adb2c8, 0x3fc38edbb0cd8d14, // 0.98826, 0.1528 + 0x3fefa39bac7a1791, 0x3fc32b7bf94516a7, // 0.98872, 0.14976 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fefaafbcb0cfddc, 0x3fc264994dfd340a, // 0.98962, 0.1437 + 0x3fefae8e8e46cfbb, 0x3fc20116d4ec7bce, // 0.99006, 0.14066 + 0x3fefb20dc681d54d, 0x3fc19d8940be24e7, // 0.99049, 0.13762 + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458 + 0x3fefb8d18d66adb7, 0x3fc0d64dbcb26786, // 0.99131, 0.13154 + 0x3fefbc1617e44186, 0x3fc072a047ba831d, // 0.99171, 0.1285 + 0x3fefbf470f0a8d88, 0x3fc00ee8ad6fb85b, // 0.9921, 0.12545 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefc56e3b7d9af6, 0x3fbe8eb7fde4aa3e, // 0.99285, 0.11937 + 0x3fefc8646cfeb721, 0x3fbdc70ecbae9fc8, // 0.99321, 0.11632 + 0x3fefcb4703914354, 0x3fbcff533b307dc1, // 0.99356, 0.11327 + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022 + 0x3fefd0d158d86087, 0x3fbb6fa6ec38f64c, // 0.99424, 0.10717 + 0x3fefd37914220b84, 0x3fbaa7b724495c04, // 0.99456, 0.10412 + 0x3fefd60d2da75c9e, 0x3fb9dfb6eb24a85c, // 0.99488, 0.10107 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefdafa7514538c, 0x3fb84f8712c130a0, // 0.99548, 0.094963 + 0x3fefdd539ff1f456, 0x3fb787586a5d5b21, // 0.99577, 0.091909 + 0x3fefdf9922f73307, 0x3fb6bf1b3e79b129, // 0.99604, 0.088854 + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797 + 0x3fefe3e92be9d886, 0x3fb52e774a4d4d0a, // 0.99657, 0.08274 + 0x3fefe5f3af2e3940, 0x3fb4661179272096, // 0.99682, 0.079682 + 0x3fefe7ea85482d60, 0x3fb39d9f12c5a299, // 0.99706, 0.076624 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefeb9d2530410f, 0x3fb20c9674ed444c, // 0.99751, 0.070505 + 0x3fefed58ecb673c4, 0x3fb1440134d709b2, // 0.99772, 0.067444 + 0x3fefef0102826191, 0x3fb07b614e463064, // 0.99793, 0.064383 + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321 + 0x3feff21614e131ed, 0x3fadd406f9808ec8, // 0.9983, 0.058258 + 0x3feff3830f8d575c, 0x3fac428d12c0d7e3, // 0.99848, 0.055195 + 0x3feff4dc54b1bed3, 0x3faab101bd5f8317, // 0.99864, 0.052132 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feff753bb1b9164, 0x3fa78dbaa5874685, // 0.99894, 0.046003 + 0x3feff871dadb81df, 0x3fa5fc00d290cd43, // 0.99908, 0.042938 + 0x3feff97c4208c014, 0x3fa46a396ff86179, // 0.9992, 0.039873 + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807 + 0x3feffb55e425fdae, 0x3fa14685db42c17e, // 0.99943, 0.033741 + 0x3feffc251df1d3f8, 0x3f9f693731d1cf01, // 0.99953, 0.030675 + 0x3feffce09ce2a679, 0x3f9c454f4ce53b1c, // 0.99962, 0.027608 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feffe1c6870cb77, 0x3f95fd4d21fab226, // 0.99977, 0.021474 + 0x3feffe9cb44b51a1, 0x3f92d936bbe30efd, // 0.99983, 0.018407 + 0x3fefff0943c53bd1, 0x3f8f6a296ab997ca, // 0.99988, 0.015339 + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272 + 0x3fefffa72c978c4f, 0x3f82d96b0e509703, // 0.99996, 0.0092038 + 0x3fefffd8858e8a92, 0x3f7921f0fe670071, // 0.99998, 0.0061359 + 0x3feffff621621d02, 0x3f6921f8becca4ba, // 1, 0.003068 + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3feffff621621d02, 0xbf6921f8becca4ba, // 1, -0.003068 + 0x3fefffd8858e8a92, 0xbf7921f0fe670071, // 0.99998,-0.0061359 + 0x3fefffa72c978c4f, 0xbf82d96b0e509703, // 0.99996,-0.0092038 + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992, -0.012272 + 0x3fefff0943c53bd1, 0xbf8f6a296ab997ca, // 0.99988, -0.015339 + 0x3feffe9cb44b51a1, 0xbf92d936bbe30efd, // 0.99983, -0.018407 + 0x3feffe1c6870cb77, 0xbf95fd4d21fab226, // 0.99977, -0.021474 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997, -0.024541 + 0x3feffce09ce2a679, 0xbf9c454f4ce53b1c, // 0.99962, -0.027608 + 0x3feffc251df1d3f8, 0xbf9f693731d1cf01, // 0.99953, -0.030675 + 0x3feffb55e425fdae, 0xbfa14685db42c17e, // 0.99943, -0.033741 + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932, -0.036807 + 0x3feff97c4208c014, 0xbfa46a396ff86179, // 0.9992, -0.039873 + 0x3feff871dadb81df, 0xbfa5fc00d290cd43, // 0.99908, -0.042938 + 0x3feff753bb1b9164, 0xbfa78dbaa5874685, // 0.99894, -0.046003 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988, -0.049068 + 0x3feff4dc54b1bed3, 0xbfaab101bd5f8317, // 0.99864, -0.052132 + 0x3feff3830f8d575c, 0xbfac428d12c0d7e3, // 0.99848, -0.055195 + 0x3feff21614e131ed, 0xbfadd406f9808ec8, // 0.9983, -0.058258 + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812, -0.061321 + 0x3fefef0102826191, 0xbfb07b614e463064, // 0.99793, -0.064383 + 0x3fefed58ecb673c4, 0xbfb1440134d709b2, // 0.99772, -0.067444 + 0x3fefeb9d2530410f, 0xbfb20c9674ed444c, // 0.99751, -0.070505 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729, -0.073565 + 0x3fefe7ea85482d60, 0xbfb39d9f12c5a299, // 0.99706, -0.076624 + 0x3fefe5f3af2e3940, 0xbfb4661179272096, // 0.99682, -0.079682 + 0x3fefe3e92be9d886, 0xbfb52e774a4d4d0a, // 0.99657, -0.08274 + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631, -0.085797 + 0x3fefdf9922f73307, 0xbfb6bf1b3e79b129, // 0.99604, -0.088854 + 0x3fefdd539ff1f456, 0xbfb787586a5d5b21, // 0.99577, -0.091909 + 0x3fefdafa7514538c, 0xbfb84f8712c130a0, // 0.99548, -0.094963 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518, -0.098017 + 0x3fefd60d2da75c9e, 0xbfb9dfb6eb24a85c, // 0.99488, -0.10107 + 0x3fefd37914220b84, 0xbfbaa7b724495c04, // 0.99456, -0.10412 + 0x3fefd0d158d86087, 0xbfbb6fa6ec38f64c, // 0.99424, -0.10717 + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022 + 0x3fefcb4703914354, 0xbfbcff533b307dc1, // 0.99356, -0.11327 + 0x3fefc8646cfeb721, 0xbfbdc70ecbae9fc8, // 0.99321, -0.11632 + 0x3fefc56e3b7d9af6, 0xbfbe8eb7fde4aa3e, // 0.99285, -0.11937 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefbf470f0a8d88, 0xbfc00ee8ad6fb85b, // 0.9921, -0.12545 + 0x3fefbc1617e44186, 0xbfc072a047ba831d, // 0.99171, -0.1285 + 0x3fefb8d18d66adb7, 0xbfc0d64dbcb26786, // 0.99131, -0.13154 + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458 + 0x3fefb20dc681d54d, 0xbfc19d8940be24e7, // 0.99049, -0.13762 + 0x3fefae8e8e46cfbb, 0xbfc20116d4ec7bce, // 0.99006, -0.14066 + 0x3fefaafbcb0cfddc, 0xbfc264994dfd340a, // 0.98962, -0.1437 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefa39bac7a1791, 0xbfc32b7bf94516a7, // 0.98872, -0.14976 + 0x3fef9fce55adb2c8, 0xbfc38edbb0cd8d14, // 0.98826, -0.1528 + 0x3fef9bed7cfbde29, 0xbfc3f22f57db4893, // 0.98778, -0.15583 + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886 + 0x3fef93f14f85ac08, 0xbfc4b8b17f79fa88, // 0.98681, -0.16189 + 0x3fef8fd5ffae41db, 0xbfc51bdf8597c5f2, // 0.98631, -0.16491 + 0x3fef8ba737cb4b78, 0xbfc57f008654cbde, // 0.9858, -0.16794 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef830f4a40c60c, 0xbfc6451a831d830d, // 0.98475, -0.17398 + 0x3fef7ea629e63d6e, 0xbfc6a81304f64ab2, // 0.98421, -0.177 + 0x3fef7a299c1a322a, 0xbfc70afd8d08c4ff, // 0.98366, -0.18002 + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304 + 0x3fef70f6434b7eb7, 0xbfc7d0a7bbd2cb1b, // 0.98254, -0.18606 + 0x3fef6c3f7df5bbb7, 0xbfc83366e89c64c5, // 0.98196, -0.18907 + 0x3fef677556883cee, 0xbfc8961727c41804, // 0.98138, -0.19208 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef5da6ed43685d, 0xbfc95b49e9b62af9, // 0.98018, -0.1981 + 0x3fef58a2b1789e84, 0xbfc9bdcbf2dc4366, // 0.97957, -0.2011 + 0x3fef538b1faf2d07, 0xbfca203e1b1831da, // 0.97895, -0.20411 + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711 + 0x3fef492206bcabb4, 0xbfcae4f1d5f3b9ab, // 0.97768, -0.21011 + 0x3fef43d085ff92dd, 0xbfcb4732ef3d6722, // 0.97703, -0.21311 + 0x3fef3e6bbc1bbc65, 0xbfcba96334f15dad, // 0.97637, -0.21611 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef33685a3aaef0, 0xbfcc6d90535d74dc, // 0.97503, -0.22209 + 0x3fef2dc9c9089a9d, 0xbfcccf8cb312b286, // 0.97434, -0.22508 + 0x3fef2817fc4609ce, 0xbfcd31774d2cbdee, // 0.97364, -0.22807 + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106 + 0x3fef1c7abe284708, 0xbfcdf5163f01099a, // 0.97223, -0.23404 + 0x3fef168f53f7205d, 0xbfce56ca1e101a1b, // 0.9715, -0.23702 + 0x3fef1090bc898f5f, 0xbfceb86b462de348, // 0.97077, -0.24 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef045a14cf738c, 0xbfcf7b7480bd3801, // 0.96928, -0.24596 + 0x3feefe220c0b95ec, 0xbfcfdcdc1adfedf8, // 0.96852, -0.24893 + 0x3feef7d6e51ca3c0, 0xbfd01f1806b9fdd2, // 0.96775, -0.2519 + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487 + 0x3feeeb074c50a544, 0xbfd0804e05eb661e, // 0.96619, -0.25783 + 0x3feee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // 0.96539, -0.26079 + 0x3feeddeb6a078651, 0xbfd0e15b4e1749cd, // 0.96459, -0.26375 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3feed0835e999009, 0xbfd1423eefc69378, // 0.96295, -0.26967 + 0x3feec9b2d3c3bf84, 0xbfd172a0d7765177, // 0.96212, -0.27262 + 0x3feec2cf4b1af6b2, 0xbfd1a2f7fbe8f243, // 0.96128, -0.27557 + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852 + 0x3feeb4cf515b8811, 0xbfd2038583d727bd, // 0.95957, -0.28146 + 0x3feeadb2e8e7a88e, 0xbfd233bbabc3bb72, // 0.9587, -0.28441 + 0x3feea68393e65800, 0xbfd263e6995554ba, // 0.95783, -0.28735 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3fee97ec36016b30, 0xbfd2c41a4e954520, // 0.95605, -0.29322 + 0x3fee9084361df7f3, 0xbfd2f422daec0386, // 0.95514, -0.29615 + 0x3fee89095bad6025, 0xbfd3241fb638baaf, // 0.95423, -0.29908 + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201 + 0x3fee79db29a5165a, 0xbfd383f5e353b6aa, // 0.95238, -0.30493 + 0x3fee7227db6a9744, 0xbfd3b3cefa0414b7, // 0.95144, -0.30785 + 0x3fee6a61c55d53a7, 0xbfd3e39be96ec271, // 0.95049, -0.31077 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee5a9d550467d3, 0xbfd44310dc8936f0, // 0.94856, -0.31659 + 0x3fee529f04729ffc, 0xbfd472b8a5571054, // 0.94759, -0.3195 + 0x3fee4a8dff81ce5e, 0xbfd4a253d11b82f3, // 0.9466, -0.32241 + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531 + 0x3fee3a33ec75ce85, 0xbfd50163dc197047, // 0.9446, -0.32821 + 0x3fee31eae870ce25, 0xbfd530d880af3c24, // 0.94359, -0.33111 + 0x3fee298f4439197a, 0xbfd5604012f467b4, // 0.94257, -0.334 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee18a02fdc66d9, 0xbfd5bee78b9db3b6, // 0.94051, -0.33978 + 0x3fee100cca2980ac, 0xbfd5ee27379ea693, // 0.93946, -0.34266 + 0x3fee0766d9280f54, 0xbfd61d595c88c203, // 0.9384, -0.34554 + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842 + 0x3fedf5e36a9ba59c, 0xbfd67b949cad63ca, // 0.93627, -0.35129 + 0x3feded05f7de47da, 0xbfd6aa9d7dc77e16, // 0.93518, -0.35416 + 0x3fede4160f6d8d81, 0xbfd6d998638a0cb5, // 0.93409, -0.35703 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3fedd1fef38a915a, 0xbfd73763c9261092, // 0.93188, -0.36276 + 0x3fedc8d7cb410260, 0xbfd766340f2418f6, // 0.93077, -0.36561 + 0x3fedbf9e4395759a, 0xbfd794f5e613dfae, // 0.92964, -0.36847 + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132 + 0x3fedacf42ce68ab9, 0xbfd7f24dd37341e3, // 0.92736, -0.37416 + 0x3feda383a9668988, 0xbfd820e3b04eaac4, // 0.92621, -0.37701 + 0x3fed9a00dd8b3d46, 0xbfd84f6aaaf3903f, // 0.92505, -0.37985 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3fed86c48445a450, 0xbfd8ac4b86d5ed44, // 0.9227, -0.38552 + 0x3fed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // 0.92151, -0.38835 + 0x3fed733f508c0dff, 0xbfd908ef81ef7bd1, // 0.92032, -0.39117 + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399 + 0x3fed5f7172888a7f, 0xbfd96555b7ab948f, // 0.9179, -0.39681 + 0x3fed556f52e93eb1, 0xbfd993716141bdfe, // 0.91668, -0.39962 + 0x3fed4b5b1b187524, 0xbfd9c17d440df9f2, // 0.91545, -0.40243 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed36fc7bcbfbdc, 0xbfda1d6543b50ac0, // 0.91296, -0.40804 + 0x3fed2cb220e0ef9f, 0xbfda4b4127dea1e4, // 0.91171, -0.41084 + 0x3fed2255c6e5a4e1, 0xbfda790cd3dbf31a, // 0.91044, -0.41364 + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643 + 0x3fed0d672f59d2b9, 0xbfdad473125cdc08, // 0.90789, -0.41922 + 0x3fed02d4feb2bd92, 0xbfdb020d6c7f4009, // 0.9066, -0.422 + 0x3fecf830e8ce467b, 0xbfdb2f971db31972, // 0.9053, -0.42478 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fece2b32799a060, 0xbfdb8a7814fd5693, // 0.90267, -0.43033 + 0x3fecd7d9898b32f6, 0xbfdbb7cf2304bd01, // 0.90135, -0.43309 + 0x3fecccee20c2de9f, 0xbfdbe51517ffc0d9, // 0.90002, -0.43586 + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862 + 0x3fecb6e20a00da99, 0xbfdc3f6d47263129, // 0.89732, -0.44137 + 0x3fecabc169a0b901, 0xbfdc6c7f4997000a, // 0.89597, -0.44412 + 0x3feca08f19b9c449, 0xbfdc997fc3865388, // 0.8946, -0.44687 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3fec89f587029c13, 0xbfdcf34baee1cd21, // 0.89184, -0.45235 + 0x3fec7e8e52233cf3, 0xbfdd2016e8e9db5b, // 0.89045, -0.45508 + 0x3fec7315899eaad7, 0xbfdd4cd02ba8609c, // 0.88905, -0.45781 + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054 + 0x3fec5bef59fef85a, 0xbfdda60c5cfa10d8, // 0.88622, -0.46326 + 0x3fec5042012b6907, 0xbfddd28f1481cc58, // 0.8848, -0.46598 + 0x3fec44833141c004, 0xbfddfeff66a941de, // 0.88336, -0.46869 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec2cd14931e3f1, 0xbfde57a86d3cd824, // 0.88047, -0.4741 + 0x3fec20de3fa971b0, 0xbfde83e0eaf85113, // 0.87901, -0.4768 + 0x3fec14d9dc465e58, 0xbfdeb00695f25620, // 0.87755, -0.47949 + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218 + 0x3febfc9d25a1b147, 0xbfdf081906bff7fd, // 0.87459, -0.48487 + 0x3febf064e15377dd, 0xbfdf3405963fd068, // 0.87309, -0.48755 + 0x3febe41b611154c1, 0xbfdf5fdee656cda3, // 0.8716, -0.49023 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3febcb54cb0d2327, 0xbfdfb7575c24d2de, // 0.86857, -0.49557 + 0x3febbed7c49380ea, 0xbfdfe2f64be7120f, // 0.86705, -0.49823 + 0x3febb249a0b6c40d, 0xbfe00740c82b82e0, // 0.86551, -0.50089 + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354 + 0x3feb98fa1fd9155e, 0xbfe032ae55edbd95, // 0.86242, -0.50619 + 0x3feb8c38d27504e9, 0xbfe0485626ae221a, // 0.86087, -0.50883 + 0x3feb7f6686e792ea, 0xbfe05df3ec31b8b6, // 0.8593, -0.51147 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feb658f14fdbc47, 0xbfe089112032b08c, // 0.85615, -0.51673 + 0x3feb5889fe921405, 0xbfe09e907417c5e1, // 0.85456, -0.51936 + 0x3feb4b7409de7925, 0xbfe0b405878f85ec, // 0.85296, -0.52198 + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459 + 0x3feb3115a5f37bf4, 0xbfe0ded0b84bc4b5, // 0.84974, -0.5272 + 0x3feb23cd470013b4, 0xbfe0f426bb2a8e7d, // 0.84812, -0.5298 + 0x3feb16742a4ca2f5, 0xbfe1097248d0a956, // 0.84649, -0.5324 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feafb8fd89f57b6, 0xbfe133e9cfee254e, // 0.84321, -0.53759 + 0x3feaee04b43c1474, 0xbfe14915af336ceb, // 0.84155, -0.54017 + 0x3feae068f345ecef, 0xbfe15e36e4dbe2bc, // 0.83989, -0.54275 + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532 + 0x3feac4ffbd3efac8, 0xbfe188591f3a46e5, // 0.83655, -0.54789 + 0x3feab7325916c0d4, 0xbfe19d5a09f2b9b8, // 0.83486, -0.55046 + 0x3feaa9547a2cb98e, 0xbfe1b250171373be, // 0.83317, -0.55302 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3fea8d676e545ad2, 0xbfe1dc1b64dc4872, // 0.82976, -0.55812 + 0x3fea7f58529fe69d, 0xbfe1f0f08bbc861b, // 0.82805, -0.56066 + 0x3fea7138de9d60f5, 0xbfe205baa17560d6, // 0.82632, -0.5632 + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573 + 0x3fea54c91090f524, 0xbfe22f2d662c13e1, // 0.82285, -0.56826 + 0x3fea4678c8119ac8, 0xbfe243d5fb98ac1f, // 0.8211, -0.57078 + 0x3fea38184a593bc6, 0xbfe258734cbb7110, // 0.81935, -0.5733 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea1b26d2c0a75e, 0xbfe2818bef4d3cba, // 0.81581, -0.57831 + 0x3fea0c95eabaf937, 0xbfe2960727629ca8, // 0.81404, -0.58081 + 0x3fe9fdf4f13149de, 0xbfe2aa76e87aeb58, // 0.81225, -0.58331 + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858 + 0x3fe9e082edb42472, 0xbfe2d333d34e9bb7, // 0.80866, -0.58828 + 0x3fe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // 0.80685, -0.59076 + 0x3fe9c2d110f075c3, 0xbfe2fbc24b441015, // 0.80503, -0.59323 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe9a4dfa42b06b2, 0xbfe32421ec49a620, // 0.80138, -0.59816 + 0x3fe995cf2ed80d22, 0xbfe338400d0c8e57, // 0.79954, -0.60062 + 0x3fe986aef1457594, 0xbfe34c5252c14de1, // 0.79769, -0.60307 + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551 + 0x3fe9683f42bd7fe1, 0xbfe374531b817f8d, // 0.79398, -0.60795 + 0x3fe958efe48e6dd7, 0xbfe3884185dfeb22, // 0.79211, -0.61038 + 0x3fe94990e3ac4a6c, 0xbfe39c23e3d63029, // 0.79023, -0.61281 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe92aa41fc5a815, 0xbfe3c3c44981c517, // 0.78646, -0.61765 + 0x3fe91b166fd49da2, 0xbfe3d78238c58343, // 0.78456, -0.62006 + 0x3fe90b7943575efe, 0xbfe3eb33eabe0680, // 0.78265, -0.62246 + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486 + 0x3fe8ec109b486c49, 0xbfe41272663d108c, // 0.77882, -0.62725 + 0x3fe8dc45331698cc, 0xbfe425ff178e6bb1, // 0.77689, -0.62964 + 0x3fe8cc6a75184655, 0xbfe4397f5b2a4380, // 0.77495, -0.63202 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe8ac871ede1d88, 0xbfe4605a692b32a2, // 0.77106, -0.63676 + 0x3fe89c7e9a4dd4ab, 0xbfe473b51b987347, // 0.7691, -0.63912 + 0x3fe88c66e7481ba1, 0xbfe48703306091fe, // 0.76714, -0.64148 + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383 + 0x3fe86c0a1d9aa195, 0xbfe4ad79516722f0, // 0.76319, -0.64618 + 0x3fe85bc51ae958cc, 0xbfe4c0a145ec0004, // 0.7612, -0.64851 + 0x3fe84b7111af83f9, 0xbfe4d3bc6d589f80, // 0.75921, -0.65085 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe82a9c13f545ff, 0xbfe4f9cc25cca486, // 0.7552, -0.65549 + 0x3fe81a1b33b57acc, 0xbfe50cc09f59a09b, // 0.75319, -0.65781 + 0x3fe8098b756e52fa, 0xbfe51fa81cd99aa6, // 0.75117, -0.66011 + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242 + 0x3fe7e83f87b03686, 0xbfe5454ff5159dfb, // 0.7471, -0.66471 + 0x3fe7d7836cc33db2, 0xbfe5581038975137, // 0.74506, -0.667 + 0x3fe7c6b89ce2d333, 0xbfe56ac35197649e, // 0.74301, -0.66928 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe7a4f707bf97d2, 0xbfe59001d5f723df, // 0.73889, -0.67383 + 0x3fe79400574f55e4, 0xbfe5a28d2a5d7250, // 0.73682, -0.67609 + 0x3fe782fb1b90b35b, 0xbfe5b50b264f7448, // 0.73474, -0.67835 + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806 + 0x3fe760c52c304764, 0xbfe5d9dee73e345c, // 0.73056, -0.68285 + 0x3fe74f948da8d28d, 0xbfe5ec3495837074, // 0.72846, -0.68508 + 0x3fe73e558e079942, 0xbfe5fe7cbde56a0f, // 0.72636, -0.68732 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe71bac960e41bf, 0xbfe622e44fec22ff, // 0.72213, -0.69176 + 0x3fe70a42b3176d7a, 0xbfe63503a31c1be8, // 0.72, -0.69397 + 0x3fe6f8ca99c95b75, 0xbfe64715437f535b, // 0.71787, -0.69618 + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838 + 0x3fe6d5afef4aafcc, 0xbfe66b0f3f52b386, // 0.71358, -0.70057 + 0x3fe6c40d73c18275, 0xbfe67cf78491af10, // 0.71143, -0.70275 + 0x3fe6b25ced2fe29c, 0xbfe68ed1eaa19c71, // 0.70927, -0.70493 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe68ed1eaa19c71, 0xbfe6b25ced2fe29c, // 0.70493, -0.70927 + 0x3fe67cf78491af10, 0xbfe6c40d73c18275, // 0.70275, -0.71143 + 0x3fe66b0f3f52b386, 0xbfe6d5afef4aafcc, // 0.70057, -0.71358 + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573 + 0x3fe64715437f535b, 0xbfe6f8ca99c95b75, // 0.69618, -0.71787 + 0x3fe63503a31c1be8, 0xbfe70a42b3176d7a, // 0.69397, -0.72 + 0x3fe622e44fec22ff, 0xbfe71bac960e41bf, // 0.69176, -0.72213 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe5fe7cbde56a0f, 0xbfe73e558e079942, // 0.68732, -0.72636 + 0x3fe5ec3495837074, 0xbfe74f948da8d28d, // 0.68508, -0.72846 + 0x3fe5d9dee73e345c, 0xbfe760c52c304764, // 0.68285, -0.73056 + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265 + 0x3fe5b50b264f7448, 0xbfe782fb1b90b35b, // 0.67835, -0.73474 + 0x3fe5a28d2a5d7250, 0xbfe79400574f55e4, // 0.67609, -0.73682 + 0x3fe59001d5f723df, 0xbfe7a4f707bf97d2, // 0.67383, -0.73889 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe56ac35197649e, 0xbfe7c6b89ce2d333, // 0.66928, -0.74301 + 0x3fe5581038975137, 0xbfe7d7836cc33db2, // 0.667, -0.74506 + 0x3fe5454ff5159dfb, 0xbfe7e83f87b03686, // 0.66471, -0.7471 + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914 + 0x3fe51fa81cd99aa6, 0xbfe8098b756e52fa, // 0.66011, -0.75117 + 0x3fe50cc09f59a09b, 0xbfe81a1b33b57acc, // 0.65781, -0.75319 + 0x3fe4f9cc25cca486, 0xbfe82a9c13f545ff, // 0.65549, -0.7552 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe4d3bc6d589f80, 0xbfe84b7111af83f9, // 0.65085, -0.75921 + 0x3fe4c0a145ec0004, 0xbfe85bc51ae958cc, // 0.64851, -0.7612 + 0x3fe4ad79516722f0, 0xbfe86c0a1d9aa195, // 0.64618, -0.76319 + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517 + 0x3fe48703306091fe, 0xbfe88c66e7481ba1, // 0.64148, -0.76714 + 0x3fe473b51b987347, 0xbfe89c7e9a4dd4ab, // 0.63912, -0.7691 + 0x3fe4605a692b32a2, 0xbfe8ac871ede1d88, // 0.63676, -0.77106 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe4397f5b2a4380, 0xbfe8cc6a75184655, // 0.63202, -0.77495 + 0x3fe425ff178e6bb1, 0xbfe8dc45331698cc, // 0.62964, -0.77689 + 0x3fe41272663d108c, 0xbfe8ec109b486c49, // 0.62725, -0.77882 + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074 + 0x3fe3eb33eabe0680, 0xbfe90b7943575efe, // 0.62246, -0.78265 + 0x3fe3d78238c58343, 0xbfe91b166fd49da2, // 0.62006, -0.78456 + 0x3fe3c3c44981c517, 0xbfe92aa41fc5a815, // 0.61765, -0.78646 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe39c23e3d63029, 0xbfe94990e3ac4a6c, // 0.61281, -0.79023 + 0x3fe3884185dfeb22, 0xbfe958efe48e6dd7, // 0.61038, -0.79211 + 0x3fe374531b817f8d, 0xbfe9683f42bd7fe1, // 0.60795, -0.79398 + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584 + 0x3fe34c5252c14de1, 0xbfe986aef1457594, // 0.60307, -0.79769 + 0x3fe338400d0c8e57, 0xbfe995cf2ed80d22, // 0.60062, -0.79954 + 0x3fe32421ec49a620, 0xbfe9a4dfa42b06b2, // 0.59816, -0.80138 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe2fbc24b441015, 0xbfe9c2d110f075c3, // 0.59323, -0.80503 + 0x3fe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // 0.59076, -0.80685 + 0x3fe2d333d34e9bb7, 0xbfe9e082edb42472, // 0.58828, -0.80866 + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046 + 0x3fe2aa76e87aeb58, 0xbfe9fdf4f13149de, // 0.58331, -0.81225 + 0x3fe2960727629ca8, 0xbfea0c95eabaf937, // 0.58081, -0.81404 + 0x3fe2818bef4d3cba, 0xbfea1b26d2c0a75e, // 0.57831, -0.81581 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe258734cbb7110, 0xbfea38184a593bc6, // 0.5733, -0.81935 + 0x3fe243d5fb98ac1f, 0xbfea4678c8119ac8, // 0.57078, -0.8211 + 0x3fe22f2d662c13e1, 0xbfea54c91090f524, // 0.56826, -0.82285 + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459 + 0x3fe205baa17560d6, 0xbfea7138de9d60f5, // 0.5632, -0.82632 + 0x3fe1f0f08bbc861b, 0xbfea7f58529fe69d, // 0.56066, -0.82805 + 0x3fe1dc1b64dc4872, 0xbfea8d676e545ad2, // 0.55812, -0.82976 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe1b250171373be, 0xbfeaa9547a2cb98e, // 0.55302, -0.83317 + 0x3fe19d5a09f2b9b8, 0xbfeab7325916c0d4, // 0.55046, -0.83486 + 0x3fe188591f3a46e5, 0xbfeac4ffbd3efac8, // 0.54789, -0.83655 + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822 + 0x3fe15e36e4dbe2bc, 0xbfeae068f345ecef, // 0.54275, -0.83989 + 0x3fe14915af336ceb, 0xbfeaee04b43c1474, // 0.54017, -0.84155 + 0x3fe133e9cfee254e, 0xbfeafb8fd89f57b6, // 0.53759, -0.84321 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe1097248d0a956, 0xbfeb16742a4ca2f5, // 0.5324, -0.84649 + 0x3fe0f426bb2a8e7d, 0xbfeb23cd470013b4, // 0.5298, -0.84812 + 0x3fe0ded0b84bc4b5, 0xbfeb3115a5f37bf4, // 0.5272, -0.84974 + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136 + 0x3fe0b405878f85ec, 0xbfeb4b7409de7925, // 0.52198, -0.85296 + 0x3fe09e907417c5e1, 0xbfeb5889fe921405, // 0.51936, -0.85456 + 0x3fe089112032b08c, 0xbfeb658f14fdbc47, // 0.51673, -0.85615 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe05df3ec31b8b6, 0xbfeb7f6686e792ea, // 0.51147, -0.8593 + 0x3fe0485626ae221a, 0xbfeb8c38d27504e9, // 0.50883, -0.86087 + 0x3fe032ae55edbd95, 0xbfeb98fa1fd9155e, // 0.50619, -0.86242 + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397 + 0x3fe00740c82b82e0, 0xbfebb249a0b6c40d, // 0.50089, -0.86551 + 0x3fdfe2f64be7120f, 0xbfebbed7c49380ea, // 0.49823, -0.86705 + 0x3fdfb7575c24d2de, 0xbfebcb54cb0d2327, // 0.49557, -0.86857 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fdf5fdee656cda3, 0xbfebe41b611154c1, // 0.49023, -0.8716 + 0x3fdf3405963fd068, 0xbfebf064e15377dd, // 0.48755, -0.87309 + 0x3fdf081906bff7fd, 0xbfebfc9d25a1b147, // 0.48487, -0.87459 + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607 + 0x3fdeb00695f25620, 0xbfec14d9dc465e58, // 0.47949, -0.87755 + 0x3fde83e0eaf85113, 0xbfec20de3fa971b0, // 0.4768, -0.87901 + 0x3fde57a86d3cd824, 0xbfec2cd14931e3f1, // 0.4741, -0.88047 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fddfeff66a941de, 0xbfec44833141c004, // 0.46869, -0.88336 + 0x3fddd28f1481cc58, 0xbfec5042012b6907, // 0.46598, -0.8848 + 0x3fdda60c5cfa10d8, 0xbfec5bef59fef85a, // 0.46326, -0.88622 + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764 + 0x3fdd4cd02ba8609c, 0xbfec7315899eaad7, // 0.45781, -0.88905 + 0x3fdd2016e8e9db5b, 0xbfec7e8e52233cf3, // 0.45508, -0.89045 + 0x3fdcf34baee1cd21, 0xbfec89f587029c13, // 0.45235, -0.89184 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdc997fc3865388, 0xbfeca08f19b9c449, // 0.44687, -0.8946 + 0x3fdc6c7f4997000a, 0xbfecabc169a0b901, // 0.44412, -0.89597 + 0x3fdc3f6d47263129, 0xbfecb6e20a00da99, // 0.44137, -0.89732 + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867 + 0x3fdbe51517ffc0d9, 0xbfecccee20c2de9f, // 0.43586, -0.90002 + 0x3fdbb7cf2304bd01, 0xbfecd7d9898b32f6, // 0.43309, -0.90135 + 0x3fdb8a7814fd5693, 0xbfece2b32799a060, // 0.43033, -0.90267 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdb2f971db31972, 0xbfecf830e8ce467b, // 0.42478, -0.9053 + 0x3fdb020d6c7f4009, 0xbfed02d4feb2bd92, // 0.422, -0.9066 + 0x3fdad473125cdc08, 0xbfed0d672f59d2b9, // 0.41922, -0.90789 + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917 + 0x3fda790cd3dbf31a, 0xbfed2255c6e5a4e1, // 0.41364, -0.91044 + 0x3fda4b4127dea1e4, 0xbfed2cb220e0ef9f, // 0.41084, -0.91171 + 0x3fda1d6543b50ac0, 0xbfed36fc7bcbfbdc, // 0.40804, -0.91296 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fd9c17d440df9f2, 0xbfed4b5b1b187524, // 0.40243, -0.91545 + 0x3fd993716141bdfe, 0xbfed556f52e93eb1, // 0.39962, -0.91668 + 0x3fd96555b7ab948f, 0xbfed5f7172888a7f, // 0.39681, -0.9179 + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911 + 0x3fd908ef81ef7bd1, 0xbfed733f508c0dff, // 0.39117, -0.92032 + 0x3fd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // 0.38835, -0.92151 + 0x3fd8ac4b86d5ed44, 0xbfed86c48445a450, // 0.38552, -0.9227 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd84f6aaaf3903f, 0xbfed9a00dd8b3d46, // 0.37985, -0.92505 + 0x3fd820e3b04eaac4, 0xbfeda383a9668988, // 0.37701, -0.92621 + 0x3fd7f24dd37341e3, 0xbfedacf42ce68ab9, // 0.37416, -0.92736 + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851 + 0x3fd794f5e613dfae, 0xbfedbf9e4395759a, // 0.36847, -0.92964 + 0x3fd766340f2418f6, 0xbfedc8d7cb410260, // 0.36561, -0.93077 + 0x3fd73763c9261092, 0xbfedd1fef38a915a, // 0.36276, -0.93188 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd6d998638a0cb5, 0xbfede4160f6d8d81, // 0.35703, -0.93409 + 0x3fd6aa9d7dc77e16, 0xbfeded05f7de47da, // 0.35416, -0.93518 + 0x3fd67b949cad63ca, 0xbfedf5e36a9ba59c, // 0.35129, -0.93627 + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734 + 0x3fd61d595c88c203, 0xbfee0766d9280f54, // 0.34554, -0.9384 + 0x3fd5ee27379ea693, 0xbfee100cca2980ac, // 0.34266, -0.93946 + 0x3fd5bee78b9db3b6, 0xbfee18a02fdc66d9, // 0.33978, -0.94051 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd5604012f467b4, 0xbfee298f4439197a, // 0.334, -0.94257 + 0x3fd530d880af3c24, 0xbfee31eae870ce25, // 0.33111, -0.94359 + 0x3fd50163dc197047, 0xbfee3a33ec75ce85, // 0.32821, -0.9446 + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561 + 0x3fd4a253d11b82f3, 0xbfee4a8dff81ce5e, // 0.32241, -0.9466 + 0x3fd472b8a5571054, 0xbfee529f04729ffc, // 0.3195, -0.94759 + 0x3fd44310dc8936f0, 0xbfee5a9d550467d3, // 0.31659, -0.94856 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd3e39be96ec271, 0xbfee6a61c55d53a7, // 0.31077, -0.95049 + 0x3fd3b3cefa0414b7, 0xbfee7227db6a9744, // 0.30785, -0.95144 + 0x3fd383f5e353b6aa, 0xbfee79db29a5165a, // 0.30493, -0.95238 + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331 + 0x3fd3241fb638baaf, 0xbfee89095bad6025, // 0.29908, -0.95423 + 0x3fd2f422daec0386, 0xbfee9084361df7f3, // 0.29615, -0.95514 + 0x3fd2c41a4e954520, 0xbfee97ec36016b30, // 0.29322, -0.95605 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd263e6995554ba, 0xbfeea68393e65800, // 0.28735, -0.95783 + 0x3fd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // 0.28441, -0.9587 + 0x3fd2038583d727bd, 0xbfeeb4cf515b8811, // 0.28146, -0.95957 + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043 + 0x3fd1a2f7fbe8f243, 0xbfeec2cf4b1af6b2, // 0.27557, -0.96128 + 0x3fd172a0d7765177, 0xbfeec9b2d3c3bf84, // 0.27262, -0.96212 + 0x3fd1423eefc69378, 0xbfeed0835e999009, // 0.26967, -0.96295 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd0e15b4e1749cd, 0xbfeeddeb6a078651, // 0.26375, -0.96459 + 0x3fd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // 0.26079, -0.96539 + 0x3fd0804e05eb661e, 0xbfeeeb074c50a544, // 0.25783, -0.96619 + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698 + 0x3fd01f1806b9fdd2, 0xbfeef7d6e51ca3c0, // 0.2519, -0.96775 + 0x3fcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // 0.24893, -0.96852 + 0x3fcf7b7480bd3801, 0xbfef045a14cf738c, // 0.24596, -0.96928 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fceb86b462de348, 0xbfef1090bc898f5f, // 0.24, -0.97077 + 0x3fce56ca1e101a1b, 0xbfef168f53f7205d, // 0.23702, -0.9715 + 0x3fcdf5163f01099a, 0xbfef1c7abe284708, // 0.23404, -0.97223 + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294 + 0x3fcd31774d2cbdee, 0xbfef2817fc4609ce, // 0.22807, -0.97364 + 0x3fcccf8cb312b286, 0xbfef2dc9c9089a9d, // 0.22508, -0.97434 + 0x3fcc6d90535d74dc, 0xbfef33685a3aaef0, // 0.22209, -0.97503 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcba96334f15dad, 0xbfef3e6bbc1bbc65, // 0.21611, -0.97637 + 0x3fcb4732ef3d6722, 0xbfef43d085ff92dd, // 0.21311, -0.97703 + 0x3fcae4f1d5f3b9ab, 0xbfef492206bcabb4, // 0.21011, -0.97768 + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832 + 0x3fca203e1b1831da, 0xbfef538b1faf2d07, // 0.20411, -0.97895 + 0x3fc9bdcbf2dc4366, 0xbfef58a2b1789e84, // 0.2011, -0.97957 + 0x3fc95b49e9b62af9, 0xbfef5da6ed43685d, // 0.1981, -0.98018 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fc8961727c41804, 0xbfef677556883cee, // 0.19208, -0.98138 + 0x3fc83366e89c64c5, 0xbfef6c3f7df5bbb7, // 0.18907, -0.98196 + 0x3fc7d0a7bbd2cb1b, 0xbfef70f6434b7eb7, // 0.18606, -0.98254 + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311 + 0x3fc70afd8d08c4ff, 0xbfef7a299c1a322a, // 0.18002, -0.98366 + 0x3fc6a81304f64ab2, 0xbfef7ea629e63d6e, // 0.177, -0.98421 + 0x3fc6451a831d830d, 0xbfef830f4a40c60c, // 0.17398, -0.98475 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc57f008654cbde, 0xbfef8ba737cb4b78, // 0.16794, -0.9858 + 0x3fc51bdf8597c5f2, 0xbfef8fd5ffae41db, // 0.16491, -0.98631 + 0x3fc4b8b17f79fa88, 0xbfef93f14f85ac08, // 0.16189, -0.98681 + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873 + 0x3fc3f22f57db4893, 0xbfef9bed7cfbde29, // 0.15583, -0.98778 + 0x3fc38edbb0cd8d14, 0xbfef9fce55adb2c8, // 0.1528, -0.98826 + 0x3fc32b7bf94516a7, 0xbfefa39bac7a1791, // 0.14976, -0.98872 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc264994dfd340a, 0xbfefaafbcb0cfddc, // 0.1437, -0.98962 + 0x3fc20116d4ec7bce, 0xbfefae8e8e46cfbb, // 0.14066, -0.99006 + 0x3fc19d8940be24e7, 0xbfefb20dc681d54d, // 0.13762, -0.99049 + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909 + 0x3fc0d64dbcb26786, 0xbfefb8d18d66adb7, // 0.13154, -0.99131 + 0x3fc072a047ba831d, 0xbfefbc1617e44186, // 0.1285, -0.99171 + 0x3fc00ee8ad6fb85b, 0xbfefbf470f0a8d88, // 0.12545, -0.9921 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fbe8eb7fde4aa3e, 0xbfefc56e3b7d9af6, // 0.11937, -0.99285 + 0x3fbdc70ecbae9fc8, 0xbfefc8646cfeb721, // 0.11632, -0.99321 + 0x3fbcff533b307dc1, 0xbfefcb4703914354, // 0.11327, -0.99356 + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391 + 0x3fbb6fa6ec38f64c, 0xbfefd0d158d86087, // 0.10717, -0.99424 + 0x3fbaa7b724495c04, 0xbfefd37914220b84, // 0.10412, -0.99456 + 0x3fb9dfb6eb24a85c, 0xbfefd60d2da75c9e, // 0.10107, -0.99488 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fb84f8712c130a0, 0xbfefdafa7514538c, // 0.094963, -0.99548 + 0x3fb787586a5d5b21, 0xbfefdd539ff1f456, // 0.091909, -0.99577 + 0x3fb6bf1b3e79b129, 0xbfefdf9922f73307, // 0.088854, -0.99604 + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631 + 0x3fb52e774a4d4d0a, 0xbfefe3e92be9d886, // 0.08274, -0.99657 + 0x3fb4661179272096, 0xbfefe5f3af2e3940, // 0.079682, -0.99682 + 0x3fb39d9f12c5a299, 0xbfefe7ea85482d60, // 0.076624, -0.99706 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb20c9674ed444c, 0xbfefeb9d2530410f, // 0.070505, -0.99751 + 0x3fb1440134d709b2, 0xbfefed58ecb673c4, // 0.067444, -0.99772 + 0x3fb07b614e463064, 0xbfefef0102826191, // 0.064383, -0.99793 + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812 + 0x3fadd406f9808ec8, 0xbfeff21614e131ed, // 0.058258, -0.9983 + 0x3fac428d12c0d7e3, 0xbfeff3830f8d575c, // 0.055195, -0.99848 + 0x3faab101bd5f8317, 0xbfeff4dc54b1bed3, // 0.052132, -0.99864 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3fa78dbaa5874685, 0xbfeff753bb1b9164, // 0.046003, -0.99894 + 0x3fa5fc00d290cd43, 0xbfeff871dadb81df, // 0.042938, -0.99908 + 0x3fa46a396ff86179, 0xbfeff97c4208c014, // 0.039873, -0.9992 + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932 + 0x3fa14685db42c17e, 0xbfeffb55e425fdae, // 0.033741, -0.99943 + 0x3f9f693731d1cf01, 0xbfeffc251df1d3f8, // 0.030675, -0.99953 + 0x3f9c454f4ce53b1c, 0xbfeffce09ce2a679, // 0.027608, -0.99962 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3f95fd4d21fab226, 0xbfeffe1c6870cb77, // 0.021474, -0.99977 + 0x3f92d936bbe30efd, 0xbfeffe9cb44b51a1, // 0.018407, -0.99983 + 0x3f8f6a296ab997ca, 0xbfefff0943c53bd1, // 0.015339, -0.99988 + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992 + 0x3f82d96b0e509703, 0xbfefffa72c978c4f, //0.0092038, -0.99996 + 0x3f7921f0fe670071, 0xbfefffd8858e8a92, //0.0061359, -0.99998 + 0x3f6921f8becca4ba, 0xbfeffff621621d02, // 0.003068, -1 +}; + +const uint64_t twiddleCoefF64_rfft_4096[4096] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0000000000000000, 0x3ff0000000000000, // 0, 1 + 0x3f5921faaee6472d, 0x3feffffd88586ee6, // 0.001534, 1 + 0x3f6921f8becca4ba, 0x3feffff621621d02, // 0.003068, 1 + 0x3f72d97822f996bc, 0x3fefffe9cb1e2e8d, //0.0046019, 0.99999 + 0x3f7921f0fe670071, 0x3fefffd8858e8a92, //0.0061359, 0.99998 + 0x3f7f6a65f9a2a3c5, 0x3fefffc250b5daef, //0.0076698, 0.99997 + 0x3f82d96b0e509703, 0x3fefffa72c978c4f, //0.0092038, 0.99996 + 0x3f85fda037ac05e0, 0x3fefff871937ce2f, // 0.010738, 0.99994 + 0x3f8921d1fcdec784, 0x3fefff62169b92db, // 0.012272, 0.99992 + 0x3f8c45ffe1e48ad9, 0x3fefff3824c88f6f, // 0.013805, 0.9999 + 0x3f8f6a296ab997ca, 0x3fefff0943c53bd1, // 0.015339, 0.99988 + 0x3f9147270dad7132, 0x3feffed57398d2b7, // 0.016873, 0.99986 + 0x3f92d936bbe30efd, 0x3feffe9cb44b51a1, // 0.018407, 0.99983 + 0x3f946b4381fce81c, 0x3feffe5f05e578db, // 0.01994, 0.9998 + 0x3f95fd4d21fab226, 0x3feffe1c6870cb77, // 0.021474, 0.99977 + 0x3f978f535ddc9f03, 0x3feffdd4dbf78f52, // 0.023008, 0.99974 + 0x3f992155f7a3667e, 0x3feffd886084cd0d, // 0.024541, 0.9997 + 0x3f9ab354b1504fca, 0x3feffd36f624500c, // 0.026075, 0.99966 + 0x3f9c454f4ce53b1c, 0x3feffce09ce2a679, // 0.027608, 0.99962 + 0x3f9dd7458c64ab39, 0x3feffc8554cd213a, // 0.029142, 0.99958 + 0x3f9f693731d1cf01, 0x3feffc251df1d3f8, // 0.030675, 0.99953 + 0x3fa07d91ff984580, 0x3feffbbff85f9515, // 0.032208, 0.99948 + 0x3fa14685db42c17e, 0x3feffb55e425fdae, // 0.033741, 0.99943 + 0x3fa20f770ceb11c6, 0x3feffae6e1556998, // 0.035274, 0.99938 + 0x3fa2d865759455cd, 0x3feffa72effef75d, // 0.036807, 0.99932 + 0x3fa3a150f6421afc, 0x3feff9fa10348837, // 0.03834, 0.99926 + 0x3fa46a396ff86179, 0x3feff97c4208c014, // 0.039873, 0.9992 + 0x3fa5331ec3bba0eb, 0x3feff8f9858f058b, // 0.041406, 0.99914 + 0x3fa5fc00d290cd43, 0x3feff871dadb81df, // 0.042938, 0.99908 + 0x3fa6c4df7d7d5b84, 0x3feff7e5420320f9, // 0.044471, 0.99901 + 0x3fa78dbaa5874685, 0x3feff753bb1b9164, // 0.046003, 0.99894 + 0x3fa856922bb513c1, 0x3feff6bd463b444d, // 0.047535, 0.99887 + 0x3fa91f65f10dd814, 0x3feff621e3796d7e, // 0.049068, 0.9988 + 0x3fa9e835d6993c87, 0x3feff58192ee0358, // 0.0506, 0.99872 + 0x3faab101bd5f8317, 0x3feff4dc54b1bed3, // 0.052132, 0.99864 + 0x3fab79c986698b78, 0x3feff43228de1b77, // 0.053664, 0.99856 + 0x3fac428d12c0d7e3, 0x3feff3830f8d575c, // 0.055195, 0.99848 + 0x3fad0b4c436f91d0, 0x3feff2cf08da7321, // 0.056727, 0.99839 + 0x3fadd406f9808ec8, 0x3feff21614e131ed, // 0.058258, 0.9983 + 0x3fae9cbd15ff5527, 0x3feff15833be1965, // 0.05979, 0.99821 + 0x3faf656e79f820e0, 0x3feff095658e71ad, // 0.061321, 0.99812 + 0x3fb0170d833bf421, 0x3fefefcdaa704562, // 0.062852, 0.99802 + 0x3fb07b614e463064, 0x3fefef0102826191, // 0.064383, 0.99793 + 0x3fb0dfb28ea201e6, 0x3fefee2f6de455ba, // 0.065913, 0.99783 + 0x3fb1440134d709b2, 0x3fefed58ecb673c4, // 0.067444, 0.99772 + 0x3fb1a84d316d4f8a, 0x3fefec7d7f19cffc, // 0.068974, 0.99762 + 0x3fb20c9674ed444c, 0x3fefeb9d2530410f, // 0.070505, 0.99751 + 0x3fb270dcefdfc45b, 0x3fefeab7df1c6005, // 0.072035, 0.9974 + 0x3fb2d52092ce19f6, 0x3fefe9cdad01883a, // 0.073565, 0.99729 + 0x3fb339614e41ffa5, 0x3fefe8de8f03d75c, // 0.075094, 0.99718 + 0x3fb39d9f12c5a299, 0x3fefe7ea85482d60, // 0.076624, 0.99706 + 0x3fb401d9d0e3a507, 0x3fefe6f18ff42c84, // 0.078153, 0.99694 + 0x3fb4661179272096, 0x3fefe5f3af2e3940, // 0.079682, 0.99682 + 0x3fb4ca45fc1ba8b6, 0x3fefe4f0e31d7a4a, // 0.081211, 0.9967 + 0x3fb52e774a4d4d0a, 0x3fefe3e92be9d886, // 0.08274, 0.99657 + 0x3fb592a554489bc8, 0x3fefe2dc89bbff08, // 0.084269, 0.99644 + 0x3fb5f6d00a9aa419, 0x3fefe1cafcbd5b09, // 0.085797, 0.99631 + 0x3fb65af75dd0f87b, 0x3fefe0b485181be3, // 0.087326, 0.99618 + 0x3fb6bf1b3e79b129, 0x3fefdf9922f73307, // 0.088854, 0.99604 + 0x3fb7233b9d236e71, 0x3fefde78d68653fd, // 0.090381, 0.99591 + 0x3fb787586a5d5b21, 0x3fefdd539ff1f456, // 0.091909, 0.99577 + 0x3fb7eb7196b72ee4, 0x3fefdc297f674ba9, // 0.093436, 0.99563 + 0x3fb84f8712c130a0, 0x3fefdafa7514538c, // 0.094963, 0.99548 + 0x3fb8b398cf0c38e0, 0x3fefd9c68127c78c, // 0.09649, 0.99533 + 0x3fb917a6bc29b42c, 0x3fefd88da3d12526, // 0.098017, 0.99518 + 0x3fb97bb0caaba56f, 0x3fefd74fdd40abbf, // 0.099544, 0.99503 + 0x3fb9dfb6eb24a85c, 0x3fefd60d2da75c9e, // 0.10107, 0.99488 + 0x3fba43b90e27f3c4, 0x3fefd4c59536fae4, // 0.1026, 0.99472 + 0x3fbaa7b724495c04, 0x3fefd37914220b84, // 0.10412, 0.99456 + 0x3fbb0bb11e1d5559, 0x3fefd227aa9bd53b, // 0.10565, 0.9944 + 0x3fbb6fa6ec38f64c, 0x3fefd0d158d86087, // 0.10717, 0.99424 + 0x3fbbd3987f31fa0e, 0x3fefcf761f0c77a3, // 0.1087, 0.99407 + 0x3fbc3785c79ec2d5, 0x3fefce15fd6da67b, // 0.11022, 0.99391 + 0x3fbc9b6eb6165c42, 0x3fefccb0f4323aa3, // 0.11175, 0.99374 + 0x3fbcff533b307dc1, 0x3fefcb4703914354, // 0.11327, 0.99356 + 0x3fbd633347858ce4, 0x3fefc9d82bc2915e, // 0.11479, 0.99339 + 0x3fbdc70ecbae9fc8, 0x3fefc8646cfeb721, // 0.11632, 0.99321 + 0x3fbe2ae5b8457f77, 0x3fefc6ebc77f0887, // 0.11784, 0.99303 + 0x3fbe8eb7fde4aa3e, 0x3fefc56e3b7d9af6, // 0.11937, 0.99285 + 0x3fbef2858d27561b, 0x3fefc3ebc935454c, // 0.12089, 0.99267 + 0x3fbf564e56a9730e, 0x3fefc26470e19fd3, // 0.12241, 0.99248 + 0x3fbfba124b07ad85, 0x3fefc0d832bf043a, // 0.12393, 0.99229 + 0x3fc00ee8ad6fb85b, 0x3fefbf470f0a8d88, // 0.12545, 0.9921 + 0x3fc040c5bb67747e, 0x3fefbdb106021816, // 0.12698, 0.99191 + 0x3fc072a047ba831d, 0x3fefbc1617e44186, // 0.1285, 0.99171 + 0x3fc0a4784ab8bf1d, 0x3fefba7644f068b5, // 0.13002, 0.99151 + 0x3fc0d64dbcb26786, 0x3fefb8d18d66adb7, // 0.13154, 0.99131 + 0x3fc1082095f820b0, 0x3fefb727f187f1c7, // 0.13306, 0.99111 + 0x3fc139f0cedaf576, 0x3fefb5797195d741, // 0.13458, 0.9909 + 0x3fc16bbe5fac5865, 0x3fefb3c60dd2c199, // 0.1361, 0.9907 + 0x3fc19d8940be24e7, 0x3fefb20dc681d54d, // 0.13762, 0.99049 + 0x3fc1cf516a62a077, 0x3fefb0509be6f7db, // 0.13914, 0.99027 + 0x3fc20116d4ec7bce, 0x3fefae8e8e46cfbb, // 0.14066, 0.99006 + 0x3fc232d978aed413, 0x3fefacc79de6c44f, // 0.14218, 0.98984 + 0x3fc264994dfd340a, 0x3fefaafbcb0cfddc, // 0.1437, 0.98962 + 0x3fc296564d2b953e, 0x3fefa92b1600657c, // 0.14521, 0.9894 + 0x3fc2c8106e8e613a, 0x3fefa7557f08a517, // 0.14673, 0.98918 + 0x3fc2f9c7aa7a72af, 0x3fefa57b066e2754, // 0.14825, 0.98895 + 0x3fc32b7bf94516a7, 0x3fefa39bac7a1791, // 0.14976, 0.98872 + 0x3fc35d2d53440db2, 0x3fefa1b7717661d5, // 0.15128, 0.98849 + 0x3fc38edbb0cd8d14, 0x3fef9fce55adb2c8, // 0.1528, 0.98826 + 0x3fc3c0870a383ff6, 0x3fef9de0596b77a3, // 0.15431, 0.98802 + 0x3fc3f22f57db4893, 0x3fef9bed7cfbde29, // 0.15583, 0.98778 + 0x3fc423d4920e4166, 0x3fef99f5c0abd496, // 0.15734, 0.98754 + 0x3fc45576b1293e5a, 0x3fef97f924c9099b, // 0.15886, 0.9873 + 0x3fc48715ad84cdf5, 0x3fef95f7a9a1ec47, // 0.16037, 0.98706 + 0x3fc4b8b17f79fa88, 0x3fef93f14f85ac08, // 0.16189, 0.98681 + 0x3fc4ea4a1f624b61, 0x3fef91e616c43891, // 0.1634, 0.98656 + 0x3fc51bdf8597c5f2, 0x3fef8fd5ffae41db, // 0.16491, 0.98631 + 0x3fc54d71aa74ef02, 0x3fef8dc10a95380d, // 0.16643, 0.98605 + 0x3fc57f008654cbde, 0x3fef8ba737cb4b78, // 0.16794, 0.9858 + 0x3fc5b08c1192e381, 0x3fef898887a36c84, // 0.16945, 0.98554 + 0x3fc5e214448b3fc6, 0x3fef8764fa714ba9, // 0.17096, 0.98528 + 0x3fc61399179a6e94, 0x3fef853c9089595e, // 0.17247, 0.98501 + 0x3fc6451a831d830d, 0x3fef830f4a40c60c, // 0.17398, 0.98475 + 0x3fc676987f7216b8, 0x3fef80dd27ed8204, // 0.17549, 0.98448 + 0x3fc6a81304f64ab2, 0x3fef7ea629e63d6e, // 0.177, 0.98421 + 0x3fc6d98a0c08c8da, 0x3fef7c6a50826840, // 0.17851, 0.98394 + 0x3fc70afd8d08c4ff, 0x3fef7a299c1a322a, // 0.18002, 0.98366 + 0x3fc73c6d8055fe0a, 0x3fef77e40d068a90, // 0.18153, 0.98339 + 0x3fc76dd9de50bf31, 0x3fef7599a3a12077, // 0.18304, 0.98311 + 0x3fc79f429f59e11d, 0x3fef734a60446279, // 0.18455, 0.98282 + 0x3fc7d0a7bbd2cb1b, 0x3fef70f6434b7eb7, // 0.18606, 0.98254 + 0x3fc802092c1d744b, 0x3fef6e9d4d1262ca, // 0.18756, 0.98225 + 0x3fc83366e89c64c5, 0x3fef6c3f7df5bbb7, // 0.18907, 0.98196 + 0x3fc864c0e9b2b6cf, 0x3fef69dcd652f5de, // 0.19057, 0.98167 + 0x3fc8961727c41804, 0x3fef677556883cee, // 0.19208, 0.98138 + 0x3fc8c7699b34ca7e, 0x3fef6508fef47bd5, // 0.19359, 0.98108 + 0x3fc8f8b83c69a60a, 0x3fef6297cff75cb0, // 0.19509, 0.98079 + 0x3fc92a0303c8194f, 0x3fef6021c9f148c2, // 0.19659, 0.98048 + 0x3fc95b49e9b62af9, 0x3fef5da6ed43685d, // 0.1981, 0.98018 + 0x3fc98c8ce69a7aec, 0x3fef5b273a4fa2d9, // 0.1996, 0.97988 + 0x3fc9bdcbf2dc4366, 0x3fef58a2b1789e84, // 0.2011, 0.97957 + 0x3fc9ef0706e35a35, 0x3fef56195321c090, // 0.20261, 0.97926 + 0x3fca203e1b1831da, 0x3fef538b1faf2d07, // 0.20411, 0.97895 + 0x3fca517127e3dabc, 0x3fef50f81785c6b9, // 0.20561, 0.97863 + 0x3fca82a025b00451, 0x3fef4e603b0b2f2d, // 0.20711, 0.97832 + 0x3fcab3cb0ce6fe44, 0x3fef4bc38aa5c694, // 0.20861, 0.978 + 0x3fcae4f1d5f3b9ab, 0x3fef492206bcabb4, // 0.21011, 0.97768 + 0x3fcb16147941ca2a, 0x3fef467bafb7bbe0, // 0.21161, 0.97735 + 0x3fcb4732ef3d6722, 0x3fef43d085ff92dd, // 0.21311, 0.97703 + 0x3fcb784d30536cda, 0x3fef412089fd8adc, // 0.21461, 0.9767 + 0x3fcba96334f15dad, 0x3fef3e6bbc1bbc65, // 0.21611, 0.97637 + 0x3fcbda74f5856330, 0x3fef3bb21cc4fe47, // 0.2176, 0.97604 + 0x3fcc0b826a7e4f63, 0x3fef38f3ac64e589, // 0.2191, 0.9757 + 0x3fcc3c8b8c4b9dd7, 0x3fef36306b67c556, // 0.2206, 0.97536 + 0x3fcc6d90535d74dc, 0x3fef33685a3aaef0, // 0.22209, 0.97503 + 0x3fcc9e90b824a6a9, 0x3fef309b794b719f, // 0.22359, 0.97468 + 0x3fcccf8cb312b286, 0x3fef2dc9c9089a9d, // 0.22508, 0.97434 + 0x3fcd00843c99c5f9, 0x3fef2af349e17507, // 0.22658, 0.97399 + 0x3fcd31774d2cbdee, 0x3fef2817fc4609ce, // 0.22807, 0.97364 + 0x3fcd6265dd3f27e3, 0x3fef2537e0a71f9f, // 0.22957, 0.97329 + 0x3fcd934fe5454311, 0x3fef2252f7763ada, // 0.23106, 0.97294 + 0x3fcdc4355db40195, 0x3fef1f6941259d7a, // 0.23255, 0.97258 + 0x3fcdf5163f01099a, 0x3fef1c7abe284708, // 0.23404, 0.97223 + 0x3fce25f281a2b684, 0x3fef19876ef1f486, // 0.23553, 0.97187 + 0x3fce56ca1e101a1b, 0x3fef168f53f7205d, // 0.23702, 0.9715 + 0x3fce879d0cc0fdaf, 0x3fef13926dad024e, // 0.23851, 0.97114 + 0x3fceb86b462de348, 0x3fef1090bc898f5f, // 0.24, 0.97077 + 0x3fcee934c2d006c7, 0x3fef0d8a410379c5, // 0.24149, 0.9704 + 0x3fcf19f97b215f1a, 0x3fef0a7efb9230d7, // 0.24298, 0.97003 + 0x3fcf4ab9679c9f5c, 0x3fef076eecade0fa, // 0.24447, 0.96966 + 0x3fcf7b7480bd3801, 0x3fef045a14cf738c, // 0.24596, 0.96928 + 0x3fcfac2abeff57ff, 0x3fef014074708ed3, // 0.24744, 0.9689 + 0x3fcfdcdc1adfedf8, 0x3feefe220c0b95ec, // 0.24893, 0.96852 + 0x3fd006c4466e54af, 0x3feefafedc1ba8b7, // 0.25041, 0.96814 + 0x3fd01f1806b9fdd2, 0x3feef7d6e51ca3c0, // 0.2519, 0.96775 + 0x3fd037694a928cac, 0x3feef4aa278b2032, // 0.25338, 0.96737 + 0x3fd04fb80e37fdae, 0x3feef178a3e473c2, // 0.25487, 0.96698 + 0x3fd068044deab002, 0x3feeee425aa6b09a, // 0.25635, 0.96658 + 0x3fd0804e05eb661e, 0x3feeeb074c50a544, // 0.25783, 0.96619 + 0x3fd09895327b465e, 0x3feee7c77961dc9e, // 0.25931, 0.96579 + 0x3fd0b0d9cfdbdb90, 0x3feee482e25a9dbc, // 0.26079, 0.96539 + 0x3fd0c91bda4f158d, 0x3feee13987bbebdc, // 0.26227, 0.96499 + 0x3fd0e15b4e1749cd, 0x3feeddeb6a078651, // 0.26375, 0.96459 + 0x3fd0f998277733f7, 0x3feeda9889bfe86a, // 0.26523, 0.96418 + 0x3fd111d262b1f677, 0x3feed740e7684963, // 0.26671, 0.96378 + 0x3fd12a09fc0b1b12, 0x3feed3e483849c51, // 0.26819, 0.96337 + 0x3fd1423eefc69378, 0x3feed0835e999009, // 0.26967, 0.96295 + 0x3fd15a713a28b9d9, 0x3feecd1d792c8f10, // 0.27115, 0.96254 + 0x3fd172a0d7765177, 0x3feec9b2d3c3bf84, // 0.27262, 0.96212 + 0x3fd18acdc3f4873a, 0x3feec6436ee60309, // 0.2741, 0.9617 + 0x3fd1a2f7fbe8f243, 0x3feec2cf4b1af6b2, // 0.27557, 0.96128 + 0x3fd1bb1f7b999480, 0x3feebf5668eaf2ef, // 0.27705, 0.96086 + 0x3fd1d3443f4cdb3d, 0x3feebbd8c8df0b74, // 0.27852, 0.96043 + 0x3fd1eb6643499fbb, 0x3feeb8566b810f2a, // 0.27999, 0.96 + 0x3fd2038583d727bd, 0x3feeb4cf515b8811, // 0.28146, 0.95957 + 0x3fd21ba1fd3d2623, 0x3feeb1437af9bb34, // 0.28294, 0.95914 + 0x3fd233bbabc3bb72, 0x3feeadb2e8e7a88e, // 0.28441, 0.9587 + 0x3fd24bd28bb37672, 0x3feeaa1d9bb20af3, // 0.28588, 0.95827 + 0x3fd263e6995554ba, 0x3feea68393e65800, // 0.28735, 0.95783 + 0x3fd27bf7d0f2c346, 0x3feea2e4d212c000, // 0.28882, 0.95738 + 0x3fd294062ed59f05, 0x3fee9f4156c62dda, // 0.29028, 0.95694 + 0x3fd2ac11af483572, 0x3fee9b99229046f8, // 0.29175, 0.95649 + 0x3fd2c41a4e954520, 0x3fee97ec36016b30, // 0.29322, 0.95605 + 0x3fd2dc200907fe51, 0x3fee943a91aab4b4, // 0.29469, 0.95559 + 0x3fd2f422daec0386, 0x3fee9084361df7f3, // 0.29615, 0.95514 + 0x3fd30c22c08d6a13, 0x3fee8cc923edc388, // 0.29762, 0.95469 + 0x3fd3241fb638baaf, 0x3fee89095bad6025, // 0.29908, 0.95423 + 0x3fd33c19b83af207, 0x3fee8544ddf0d075, // 0.30054, 0.95377 + 0x3fd35410c2e18152, 0x3fee817bab4cd10d, // 0.30201, 0.95331 + 0x3fd36c04d27a4edf, 0x3fee7dadc456d850, // 0.30347, 0.95284 + 0x3fd383f5e353b6aa, 0x3fee79db29a5165a, // 0.30493, 0.95238 + 0x3fd39be3f1bc8aef, 0x3fee7603dbce74e9, // 0.30639, 0.95191 + 0x3fd3b3cefa0414b7, 0x3fee7227db6a9744, // 0.30785, 0.95144 + 0x3fd3cbb6f87a146e, 0x3fee6e472911da27, // 0.30931, 0.95096 + 0x3fd3e39be96ec271, 0x3fee6a61c55d53a7, // 0.31077, 0.95049 + 0x3fd3fb7dc932cfa4, 0x3fee6677b0e6d31e, // 0.31222, 0.95001 + 0x3fd4135c94176602, 0x3fee6288ec48e112, // 0.31368, 0.94953 + 0x3fd42b38466e2928, 0x3fee5e95781ebf1c, // 0.31514, 0.94905 + 0x3fd44310dc8936f0, 0x3fee5a9d550467d3, // 0.31659, 0.94856 + 0x3fd45ae652bb2800, 0x3fee56a083968eb1, // 0.31805, 0.94807 + 0x3fd472b8a5571054, 0x3fee529f04729ffc, // 0.3195, 0.94759 + 0x3fd48a87d0b07fd7, 0x3fee4e98d836c0af, // 0.32096, 0.94709 + 0x3fd4a253d11b82f3, 0x3fee4a8dff81ce5e, // 0.32241, 0.9466 + 0x3fd4ba1ca2eca31c, 0x3fee467e7af35f23, // 0.32386, 0.94611 + 0x3fd4d1e24278e76a, 0x3fee426a4b2bc17e, // 0.32531, 0.94561 + 0x3fd4e9a4ac15d520, 0x3fee3e5170cbfc46, // 0.32676, 0.94511 + 0x3fd50163dc197047, 0x3fee3a33ec75ce85, // 0.32821, 0.9446 + 0x3fd5191fceda3c35, 0x3fee3611becbaf69, // 0.32966, 0.9441 + 0x3fd530d880af3c24, 0x3fee31eae870ce25, // 0.33111, 0.94359 + 0x3fd5488dedeff3be, 0x3fee2dbf6a0911d9, // 0.33255, 0.94308 + 0x3fd5604012f467b4, 0x3fee298f4439197a, // 0.334, 0.94257 + 0x3fd577eeec151e47, 0x3fee255a77a63bb8, // 0.33545, 0.94206 + 0x3fd58f9a75ab1fdd, 0x3fee212104f686e5, // 0.33689, 0.94154 + 0x3fd5a742ac0ff78d, 0x3fee1ce2ecd0c0d8, // 0.33833, 0.94103 + 0x3fd5bee78b9db3b6, 0x3fee18a02fdc66d9, // 0.33978, 0.94051 + 0x3fd5d68910aee686, 0x3fee1458cec1ad83, // 0.34122, 0.93998 + 0x3fd5ee27379ea693, 0x3fee100cca2980ac, // 0.34266, 0.93946 + 0x3fd605c1fcc88f63, 0x3fee0bbc22bd8349, // 0.3441, 0.93893 + 0x3fd61d595c88c203, 0x3fee0766d9280f54, // 0.34554, 0.9384 + 0x3fd634ed533be58e, 0x3fee030cee1435b8, // 0.34698, 0.93787 + 0x3fd64c7ddd3f27c6, 0x3fedfeae622dbe2b, // 0.34842, 0.93734 + 0x3fd6640af6f03d9e, 0x3fedfa4b3621271d, // 0.34986, 0.9368 + 0x3fd67b949cad63ca, 0x3fedf5e36a9ba59c, // 0.35129, 0.93627 + 0x3fd6931acad55f51, 0x3fedf177004b2534, // 0.35273, 0.93573 + 0x3fd6aa9d7dc77e16, 0x3feded05f7de47da, // 0.35416, 0.93518 + 0x3fd6c21cb1e39771, 0x3fede890520465ce, // 0.3556, 0.93464 + 0x3fd6d998638a0cb5, 0x3fede4160f6d8d81, // 0.35703, 0.93409 + 0x3fd6f1108f1bc9c5, 0x3feddf9730ca837b, // 0.35846, 0.93354 + 0x3fd7088530fa459e, 0x3feddb13b6ccc23d, // 0.3599, 0.93299 + 0x3fd71ff6458782ec, 0x3fedd68ba2267a25, // 0.36133, 0.93244 + 0x3fd73763c9261092, 0x3fedd1fef38a915a, // 0.36276, 0.93188 + 0x3fd74ecdb8390a3e, 0x3fedcd6dabaca3a5, // 0.36418, 0.93133 + 0x3fd766340f2418f6, 0x3fedc8d7cb410260, // 0.36561, 0.93077 + 0x3fd77d96ca4b73a6, 0x3fedc43d52fcb453, // 0.36704, 0.93021 + 0x3fd794f5e613dfae, 0x3fedbf9e4395759a, // 0.36847, 0.92964 + 0x3fd7ac515ee2b172, 0x3fedbafa9dc1b78d, // 0.36989, 0.92907 + 0x3fd7c3a9311dcce7, 0x3fedb6526238a09b, // 0.37132, 0.92851 + 0x3fd7dafd592ba621, 0x3fedb1a591b20c38, // 0.37274, 0.92794 + 0x3fd7f24dd37341e3, 0x3fedacf42ce68ab9, // 0.37416, 0.92736 + 0x3fd8099a9c5c362d, 0x3feda83e348f613b, // 0.37559, 0.92679 + 0x3fd820e3b04eaac4, 0x3feda383a9668988, // 0.37701, 0.92621 + 0x3fd838290bb359c8, 0x3fed9ec48c26b1f3, // 0.37843, 0.92563 + 0x3fd84f6aaaf3903f, 0x3fed9a00dd8b3d46, // 0.37985, 0.92505 + 0x3fd866a88a792ea0, 0x3fed95389e50429b, // 0.38127, 0.92447 + 0x3fd87de2a6aea963, 0x3fed906bcf328d46, // 0.38268, 0.92388 + 0x3fd89518fbff098e, 0x3fed8b9a70ef9cb4, // 0.3841, 0.92329 + 0x3fd8ac4b86d5ed44, 0x3fed86c48445a450, // 0.38552, 0.9227 + 0x3fd8c37a439f884f, 0x3fed81ea09f38b63, // 0.38693, 0.92211 + 0x3fd8daa52ec8a4af, 0x3fed7d0b02b8ecf9, // 0.38835, 0.92151 + 0x3fd8f1cc44bea329, 0x3fed78276f5617c6, // 0.38976, 0.92092 + 0x3fd908ef81ef7bd1, 0x3fed733f508c0dff, // 0.39117, 0.92032 + 0x3fd9200ee2c9be97, 0x3fed6e52a71c8547, // 0.39258, 0.91972 + 0x3fd9372a63bc93d7, 0x3fed696173c9e68b, // 0.39399, 0.91911 + 0x3fd94e420137bce3, 0x3fed646bb7574de5, // 0.3954, 0.91851 + 0x3fd96555b7ab948f, 0x3fed5f7172888a7f, // 0.39681, 0.9179 + 0x3fd97c6583890fc2, 0x3fed5a72a6221e73, // 0.39822, 0.91729 + 0x3fd993716141bdfe, 0x3fed556f52e93eb1, // 0.39962, 0.91668 + 0x3fd9aa794d47c9ee, 0x3fed506779a3d2d9, // 0.40103, 0.91606 + 0x3fd9c17d440df9f2, 0x3fed4b5b1b187524, // 0.40243, 0.91545 + 0x3fd9d87d4207b0ab, 0x3fed464a380e7242, // 0.40384, 0.91483 + 0x3fd9ef7943a8ed8a, 0x3fed4134d14dc93a, // 0.40524, 0.91421 + 0x3fda067145664d57, 0x3fed3c1ae79f2b4e, // 0.40664, 0.91359 + 0x3fda1d6543b50ac0, 0x3fed36fc7bcbfbdc, // 0.40804, 0.91296 + 0x3fda34553b0afee5, 0x3fed31d98e9e503a, // 0.40944, 0.91234 + 0x3fda4b4127dea1e4, 0x3fed2cb220e0ef9f, // 0.41084, 0.91171 + 0x3fda622906a70b63, 0x3fed2786335f52fc, // 0.41224, 0.91107 + 0x3fda790cd3dbf31a, 0x3fed2255c6e5a4e1, // 0.41364, 0.91044 + 0x3fda8fec8bf5b166, 0x3fed1d20dc40c15c, // 0.41503, 0.90981 + 0x3fdaa6c82b6d3fc9, 0x3fed17e7743e35dc, // 0.41643, 0.90917 + 0x3fdabd9faebc3980, 0x3fed12a98fac410c, // 0.41782, 0.90853 + 0x3fdad473125cdc08, 0x3fed0d672f59d2b9, // 0.41922, 0.90789 + 0x3fdaeb4252ca07ab, 0x3fed082054168bac, // 0.42061, 0.90724 + 0x3fdb020d6c7f4009, 0x3fed02d4feb2bd92, // 0.422, 0.9066 + 0x3fdb18d45bf8aca6, 0x3fecfd852fff6ad4, // 0.42339, 0.90595 + 0x3fdb2f971db31972, 0x3fecf830e8ce467b, // 0.42478, 0.9053 + 0x3fdb4655ae2bf757, 0x3fecf2d829f1b40e, // 0.42617, 0.90464 + 0x3fdb5d1009e15cc0, 0x3feced7af43cc773, // 0.42756, 0.90399 + 0x3fdb73c62d520624, 0x3fece819488344ce, // 0.42894, 0.90333 + 0x3fdb8a7814fd5693, 0x3fece2b32799a060, // 0.43033, 0.90267 + 0x3fdba125bd63583e, 0x3fecdd489254fe65, // 0.43171, 0.90201 + 0x3fdbb7cf2304bd01, 0x3fecd7d9898b32f6, // 0.43309, 0.90135 + 0x3fdbce744262deee, 0x3fecd2660e12c1e6, // 0.43448, 0.90068 + 0x3fdbe51517ffc0d9, 0x3fecccee20c2de9f, // 0.43586, 0.90002 + 0x3fdbfbb1a05e0edc, 0x3fecc771c2736c09, // 0.43724, 0.89935 + 0x3fdc1249d8011ee7, 0x3fecc1f0f3fcfc5c, // 0.43862, 0.89867 + 0x3fdc28ddbb6cf145, 0x3fecbc6bb638d10b, // 0.43999, 0.898 + 0x3fdc3f6d47263129, 0x3fecb6e20a00da99, // 0.44137, 0.89732 + 0x3fdc55f877b23537, 0x3fecb153f02fb87d, // 0.44275, 0.89665 + 0x3fdc6c7f4997000a, 0x3fecabc169a0b901, // 0.44412, 0.89597 + 0x3fdc8301b95b40c2, 0x3feca62a772fd919, // 0.4455, 0.89528 + 0x3fdc997fc3865388, 0x3feca08f19b9c449, // 0.44687, 0.8946 + 0x3fdcaff964a0421d, 0x3fec9aef521bd480, // 0.44824, 0.89391 + 0x3fdcc66e9931c45d, 0x3fec954b213411f5, // 0.44961, 0.89322 + 0x3fdcdcdf5dc440ce, 0x3fec8fa287e13305, // 0.45098, 0.89253 + 0x3fdcf34baee1cd21, 0x3fec89f587029c13, // 0.45235, 0.89184 + 0x3fdd09b389152ec1, 0x3fec84441f785f61, // 0.45372, 0.89115 + 0x3fdd2016e8e9db5b, 0x3fec7e8e52233cf3, // 0.45508, 0.89045 + 0x3fdd3675caebf962, 0x3fec78d41fe4a267, // 0.45645, 0.88975 + 0x3fdd4cd02ba8609c, 0x3fec7315899eaad7, // 0.45781, 0.88905 + 0x3fdd632607ac9aa9, 0x3fec6d5290341eb2, // 0.45918, 0.88835 + 0x3fdd79775b86e389, 0x3fec678b3488739b, // 0.46054, 0.88764 + 0x3fdd8fc423c62a25, 0x3fec61bf777fcc48, // 0.4619, 0.88693 + 0x3fdda60c5cfa10d8, 0x3fec5bef59fef85a, // 0.46326, 0.88622 + 0x3fddbc5003b2edf8, 0x3fec561adceb743e, // 0.46462, 0.88551 + 0x3fddd28f1481cc58, 0x3fec5042012b6907, // 0.46598, 0.8848 + 0x3fdde8c98bf86bd6, 0x3fec4a64c7a5ac4c, // 0.46733, 0.88408 + 0x3fddfeff66a941de, 0x3fec44833141c004, // 0.46869, 0.88336 + 0x3fde1530a12779f4, 0x3fec3e9d3ee7d262, // 0.47004, 0.88264 + 0x3fde2b5d3806f63b, 0x3fec38b2f180bdb1, // 0.4714, 0.88192 + 0x3fde418527dc4ffa, 0x3fec32c449f60831, // 0.47275, 0.8812 + 0x3fde57a86d3cd824, 0x3fec2cd14931e3f1, // 0.4741, 0.88047 + 0x3fde6dc704be97e2, 0x3fec26d9f01f2eaf, // 0.47545, 0.87974 + 0x3fde83e0eaf85113, 0x3fec20de3fa971b0, // 0.4768, 0.87901 + 0x3fde99f61c817eda, 0x3fec1ade38bce19b, // 0.47815, 0.87828 + 0x3fdeb00695f25620, 0x3fec14d9dc465e58, // 0.47949, 0.87755 + 0x3fdec61253e3c61b, 0x3fec0ed12b3372e9, // 0.48084, 0.87681 + 0x3fdedc1952ef78d5, 0x3fec08c426725549, // 0.48218, 0.87607 + 0x3fdef21b8fafd3b5, 0x3fec02b2cef1e641, // 0.48353, 0.87533 + 0x3fdf081906bff7fd, 0x3febfc9d25a1b147, // 0.48487, 0.87459 + 0x3fdf1e11b4bbc35c, 0x3febf6832b71ec5b, // 0.48621, 0.87384 + 0x3fdf3405963fd068, 0x3febf064e15377dd, // 0.48755, 0.87309 + 0x3fdf49f4a7e97729, 0x3febea424837de6d, // 0.48889, 0.87235 + 0x3fdf5fdee656cda3, 0x3febe41b611154c1, // 0.49023, 0.8716 + 0x3fdf75c44e26a852, 0x3febddf02cd2b983, // 0.49156, 0.87084 + 0x3fdf8ba4dbf89aba, 0x3febd7c0ac6f952a, // 0.4929, 0.87009 + 0x3fdfa1808c6cf7e0, 0x3febd18ce0dc19d6, // 0.49423, 0.86933 + 0x3fdfb7575c24d2de, 0x3febcb54cb0d2327, // 0.49557, 0.86857 + 0x3fdfcd2947c1ff57, 0x3febc5186bf8361d, // 0.4969, 0.86781 + 0x3fdfe2f64be7120f, 0x3febbed7c49380ea, // 0.49823, 0.86705 + 0x3fdff8be6537615e, 0x3febb892d5d5dad5, // 0.49956, 0.86628 + 0x3fe00740c82b82e0, 0x3febb249a0b6c40d, // 0.50089, 0.86551 + 0x3fe0121fe4f56d2c, 0x3febabfc262e6586, // 0.50221, 0.86474 + 0x3fe01cfc874c3eb7, 0x3feba5aa673590d2, // 0.50354, 0.86397 + 0x3fe027d6ad83287e, 0x3feb9f5464c5bffc, // 0.50486, 0.8632 + 0x3fe032ae55edbd95, 0x3feb98fa1fd9155e, // 0.50619, 0.86242 + 0x3fe03d837edff370, 0x3feb929b996a5b7f, // 0.50751, 0.86165 + 0x3fe0485626ae221a, 0x3feb8c38d27504e9, // 0.50883, 0.86087 + 0x3fe053264bad0483, 0x3feb85d1cbf52c02, // 0.51015, 0.86009 + 0x3fe05df3ec31b8b6, 0x3feb7f6686e792ea, // 0.51147, 0.8593 + 0x3fe068bf0691c028, 0x3feb78f70449a34b, // 0.51279, 0.85852 + 0x3fe073879922ffed, 0x3feb728345196e3e, // 0.5141, 0.85773 + 0x3fe07e4da23bc102, 0x3feb6c0b4a55ac17, // 0.51542, 0.85694 + 0x3fe089112032b08c, 0x3feb658f14fdbc47, // 0.51673, 0.85615 + 0x3fe093d2115ee018, 0x3feb5f0ea611a532, // 0.51804, 0.85535 + 0x3fe09e907417c5e1, 0x3feb5889fe921405, // 0.51936, 0.85456 + 0x3fe0a94c46b53d0b, 0x3feb52011f805c92, // 0.52067, 0.85376 + 0x3fe0b405878f85ec, 0x3feb4b7409de7925, // 0.52198, 0.85296 + 0x3fe0bebc34ff4646, 0x3feb44e2beaf0a61, // 0.52328, 0.85216 + 0x3fe0c9704d5d898f, 0x3feb3e4d3ef55712, // 0.52459, 0.85136 + 0x3fe0d421cf03c12b, 0x3feb37b38bb54c09, // 0.5259, 0.85055 + 0x3fe0ded0b84bc4b5, 0x3feb3115a5f37bf4, // 0.5272, 0.84974 + 0x3fe0e97d078fd23b, 0x3feb2a738eb51f33, // 0.5285, 0.84893 + 0x3fe0f426bb2a8e7d, 0x3feb23cd470013b4, // 0.5298, 0.84812 + 0x3fe0fecdd1770537, 0x3feb1d22cfdadcc6, // 0.5311, 0.84731 + 0x3fe1097248d0a956, 0x3feb16742a4ca2f5, // 0.5324, 0.84649 + 0x3fe114141f935545, 0x3feb0fc1575d33db, // 0.5337, 0.84567 + 0x3fe11eb3541b4b22, 0x3feb090a58150200, // 0.535, 0.84485 + 0x3fe1294fe4c5350a, 0x3feb024f2d7d24a9, // 0.53629, 0.84403 + 0x3fe133e9cfee254e, 0x3feafb8fd89f57b6, // 0.53759, 0.84321 + 0x3fe13e8113f396c1, 0x3feaf4cc5a85fb73, // 0.53888, 0.84238 + 0x3fe14915af336ceb, 0x3feaee04b43c1474, // 0.54017, 0.84155 + 0x3fe153a7a00bf453, 0x3feae738e6cd4b67, // 0.54146, 0.84073 + 0x3fe15e36e4dbe2bc, 0x3feae068f345ecef, // 0.54275, 0.83989 + 0x3fe168c37c025764, 0x3fead994dab2e979, // 0.54404, 0.83906 + 0x3fe1734d63dedb49, 0x3fead2bc9e21d511, // 0.54532, 0.83822 + 0x3fe17dd49ad16161, 0x3feacbe03ea0e73b, // 0.54661, 0.83739 + 0x3fe188591f3a46e5, 0x3feac4ffbd3efac8, // 0.54789, 0.83655 + 0x3fe192daef7a5386, 0x3feabe1b1b0b8dac, // 0.54918, 0.83571 + 0x3fe19d5a09f2b9b8, 0x3feab7325916c0d4, // 0.55046, 0.83486 + 0x3fe1a7d66d0516e6, 0x3feab045787157ff, // 0.55174, 0.83402 + 0x3fe1b250171373be, 0x3feaa9547a2cb98e, // 0.55302, 0.83317 + 0x3fe1bcc706804467, 0x3feaa25f5f5aee60, // 0.55429, 0.83232 + 0x3fe1c73b39ae68c8, 0x3fea9b66290ea1a3, // 0.55557, 0.83147 + 0x3fe1d1acaf012cc2, 0x3fea9468d85b20ae, // 0.55685, 0.83062 + 0x3fe1dc1b64dc4872, 0x3fea8d676e545ad2, // 0.55812, 0.82976 + 0x3fe1e68759a3e074, 0x3fea8661ec0ee133, // 0.55939, 0.8289 + 0x3fe1f0f08bbc861b, 0x3fea7f58529fe69d, // 0.56066, 0.82805 + 0x3fe1fb56f98b37b8, 0x3fea784aa31d3f55, // 0.56193, 0.82718 + 0x3fe205baa17560d6, 0x3fea7138de9d60f5, // 0.5632, 0.82632 + 0x3fe2101b81e0da78, 0x3fea6a230637623b, // 0.56447, 0.82546 + 0x3fe21a799933eb58, 0x3fea63091b02fae2, // 0.56573, 0.82459 + 0x3fe224d4e5d5482e, 0x3fea5beb1e188375, // 0.567, 0.82372 + 0x3fe22f2d662c13e1, 0x3fea54c91090f524, // 0.56826, 0.82285 + 0x3fe23983189fdfd5, 0x3fea4da2f385e997, // 0.56952, 0.82198 + 0x3fe243d5fb98ac1f, 0x3fea4678c8119ac8, // 0.57078, 0.8211 + 0x3fe24e260d7ee7c9, 0x3fea3f4a8f4ee2d2, // 0.57204, 0.82023 + 0x3fe258734cbb7110, 0x3fea38184a593bc6, // 0.5733, 0.81935 + 0x3fe262bdb7b795a2, 0x3fea30e1fa4cbf81, // 0.57455, 0.81847 + 0x3fe26d054cdd12df, 0x3fea29a7a0462782, // 0.57581, 0.81758 + 0x3fe2774a0a961612, 0x3fea22693d62ccb9, // 0.57706, 0.8167 + 0x3fe2818bef4d3cba, 0x3fea1b26d2c0a75e, // 0.57831, 0.81581 + 0x3fe28bcaf96d94ba, 0x3fea13e0617e4ec7, // 0.57956, 0.81493 + 0x3fe2960727629ca8, 0x3fea0c95eabaf937, // 0.58081, 0.81404 + 0x3fe2a040779843fb, 0x3fea05476f967bb5, // 0.58206, 0.81314 + 0x3fe2aa76e87aeb58, 0x3fe9fdf4f13149de, // 0.58331, 0.81225 + 0x3fe2b4aa787764c4, 0x3fe9f69e70ac75bc, // 0.58455, 0.81135 + 0x3fe2bedb25faf3ea, 0x3fe9ef43ef29af94, // 0.5858, 0.81046 + 0x3fe2c908ef734e57, 0x3fe9e7e56dcb45bd, // 0.58704, 0.80956 + 0x3fe2d333d34e9bb7, 0x3fe9e082edb42472, // 0.58828, 0.80866 + 0x3fe2dd5bcffb7616, 0x3fe9d91c7007d5a6, // 0.58952, 0.80775 + 0x3fe2e780e3e8ea16, 0x3fe9d1b1f5ea80d6, // 0.59076, 0.80685 + 0x3fe2f1a30d86773a, 0x3fe9ca438080eadb, // 0.592, 0.80594 + 0x3fe2fbc24b441015, 0x3fe9c2d110f075c3, // 0.59323, 0.80503 + 0x3fe305de9b921a94, 0x3fe9bb5aa85f2098, // 0.59447, 0.80412 + 0x3fe30ff7fce17035, 0x3fe9b3e047f38741, // 0.5957, 0.80321 + 0x3fe31a0e6da35e44, 0x3fe9ac61f0d4e247, // 0.59693, 0.80229 + 0x3fe32421ec49a620, 0x3fe9a4dfa42b06b2, // 0.59816, 0.80138 + 0x3fe32e3277467d6b, 0x3fe99d59631e65d5, // 0.59939, 0.80046 + 0x3fe338400d0c8e57, 0x3fe995cf2ed80d22, // 0.60062, 0.79954 + 0x3fe3424aac0ef7d6, 0x3fe98e410881a600, // 0.60184, 0.79861 + 0x3fe34c5252c14de1, 0x3fe986aef1457594, // 0.60307, 0.79769 + 0x3fe35656ff9799ae, 0x3fe97f18ea4e5c9e, // 0.60429, 0.79676 + 0x3fe36058b10659f3, 0x3fe9777ef4c7d742, // 0.60551, 0.79584 + 0x3fe36a576582831b, 0x3fe96fe111ddfce0, // 0.60673, 0.79491 + 0x3fe374531b817f8d, 0x3fe9683f42bd7fe1, // 0.60795, 0.79398 + 0x3fe37e4bd1792fe2, 0x3fe960998893ad8c, // 0.60917, 0.79304 + 0x3fe3884185dfeb22, 0x3fe958efe48e6dd7, // 0.61038, 0.79211 + 0x3fe39234372c7f04, 0x3fe9514257dc4335, // 0.6116, 0.79117 + 0x3fe39c23e3d63029, 0x3fe94990e3ac4a6c, // 0.61281, 0.79023 + 0x3fe3a6108a54ba58, 0x3fe941db892e3a65, // 0.61402, 0.78929 + 0x3fe3affa292050b9, 0x3fe93a22499263fc, // 0.61523, 0.78835 + 0x3fe3b9e0beb19e18, 0x3fe932652609b1cf, // 0.61644, 0.7874 + 0x3fe3c3c44981c517, 0x3fe92aa41fc5a815, // 0.61765, 0.78646 + 0x3fe3cda4c80a6076, 0x3fe922df37f8646a, // 0.61885, 0.78551 + 0x3fe3d78238c58343, 0x3fe91b166fd49da2, // 0.62006, 0.78456 + 0x3fe3e15c9a2db922, 0x3fe91349c88da398, // 0.62126, 0.7836 + 0x3fe3eb33eabe0680, 0x3fe90b7943575efe, // 0.62246, 0.78265 + 0x3fe3f50828f1e8d2, 0x3fe903a4e1665133, // 0.62366, 0.78169 + 0x3fe3fed9534556d4, 0x3fe8fbcca3ef940d, // 0.62486, 0.78074 + 0x3fe408a76834c0c0, 0x3fe8f3f08c28d9ac, // 0.62606, 0.77978 + 0x3fe41272663d108c, 0x3fe8ec109b486c49, // 0.62725, 0.77882 + 0x3fe41c3a4bdbaa26, 0x3fe8e42cd2852e0a, // 0.62845, 0.77785 + 0x3fe425ff178e6bb1, 0x3fe8dc45331698cc, // 0.62964, 0.77689 + 0x3fe42fc0c7d3adbb, 0x3fe8d459be34bdfa, // 0.63083, 0.77592 + 0x3fe4397f5b2a4380, 0x3fe8cc6a75184655, // 0.63202, 0.77495 + 0x3fe4433ad0117b1d, 0x3fe8c47758fa71cb, // 0.63321, 0.77398 + 0x3fe44cf325091dd6, 0x3fe8bc806b151741, // 0.63439, 0.77301 + 0x3fe456a858917046, 0x3fe8b485aca2a468, // 0.63558, 0.77204 + 0x3fe4605a692b32a2, 0x3fe8ac871ede1d88, // 0.63676, 0.77106 + 0x3fe46a095557a0f1, 0x3fe8a484c3031d50, // 0.63794, 0.77008 + 0x3fe473b51b987347, 0x3fe89c7e9a4dd4ab, // 0.63912, 0.7691 + 0x3fe47d5dba6fde01, 0x3fe89474a5fb0a84, // 0.6403, 0.76812 + 0x3fe48703306091fe, 0x3fe88c66e7481ba1, // 0.64148, 0.76714 + 0x3fe490a57bedbcdf, 0x3fe884555f72fa6b, // 0.64266, 0.76615 + 0x3fe49a449b9b0938, 0x3fe87c400fba2ebf, // 0.64383, 0.76517 + 0x3fe4a3e08dec9ed6, 0x3fe87426f95cd5bd, // 0.645, 0.76418 + 0x3fe4ad79516722f0, 0x3fe86c0a1d9aa195, // 0.64618, 0.76319 + 0x3fe4b70ee48fb869, 0x3fe863e97db3d95a, // 0.64735, 0.7622 + 0x3fe4c0a145ec0004, 0x3fe85bc51ae958cc, // 0.64851, 0.7612 + 0x3fe4ca30740218a3, 0x3fe8539cf67c9029, // 0.64968, 0.76021 + 0x3fe4d3bc6d589f80, 0x3fe84b7111af83f9, // 0.65085, 0.75921 + 0x3fe4dd453076b064, 0x3fe843416dc4cce2, // 0.65201, 0.75821 + 0x3fe4e6cabbe3e5e9, 0x3fe83b0e0bff976e, // 0.65317, 0.75721 + 0x3fe4f04d0e2859aa, 0x3fe832d6eda3a3e0, // 0.65433, 0.75621 + 0x3fe4f9cc25cca486, 0x3fe82a9c13f545ff, // 0.65549, 0.7552 + 0x3fe503480159ded2, 0x3fe8225d803964e5, // 0.65665, 0.75419 + 0x3fe50cc09f59a09b, 0x3fe81a1b33b57acc, // 0.65781, 0.75319 + 0x3fe51635fe5601d7, 0x3fe811d52faf94dc, // 0.65896, 0.75218 + 0x3fe51fa81cd99aa6, 0x3fe8098b756e52fa, // 0.66011, 0.75117 + 0x3fe52916f96f8388, 0x3fe8013e0638e795, // 0.66127, 0.75015 + 0x3fe5328292a35596, 0x3fe7f8ece3571771, // 0.66242, 0.74914 + 0x3fe53beae7012abe, 0x3fe7f0980e113978, // 0.66356, 0.74812 + 0x3fe5454ff5159dfb, 0x3fe7e83f87b03686, // 0.66471, 0.7471 + 0x3fe54eb1bb6dcb8f, 0x3fe7dfe3517d8937, // 0.66586, 0.74608 + 0x3fe5581038975137, 0x3fe7d7836cc33db2, // 0.667, 0.74506 + 0x3fe5616b6b204e6e, 0x3fe7cf1fdacbf179, // 0.66814, 0.74403 + 0x3fe56ac35197649e, 0x3fe7c6b89ce2d333, // 0.66928, 0.74301 + 0x3fe57417ea8bb75c, 0x3fe7be4db453a27c, // 0.67042, 0.74198 + 0x3fe57d69348cec9f, 0x3fe7b5df226aafb0, // 0.67156, 0.74095 + 0x3fe586b72e2b2cfd, 0x3fe7ad6ce874dbb6, // 0.67269, 0.73992 + 0x3fe59001d5f723df, 0x3fe7a4f707bf97d2, // 0.67383, 0.73889 + 0x3fe599492a81ffbc, 0x3fe79c7d8198e56e, // 0.67496, 0.73785 + 0x3fe5a28d2a5d7250, 0x3fe79400574f55e4, // 0.67609, 0.73682 + 0x3fe5abcdd41bb0d8, 0x3fe78b7f8a320a52, // 0.67722, 0.73578 + 0x3fe5b50b264f7448, 0x3fe782fb1b90b35b, // 0.67835, 0.73474 + 0x3fe5be451f8bf980, 0x3fe77a730cbb9100, // 0.67948, 0.7337 + 0x3fe5c77bbe65018c, 0x3fe771e75f037261, // 0.6806, 0.73265 + 0x3fe5d0af016ed1d4, 0x3fe7695813b9b594, // 0.68172, 0.73161 + 0x3fe5d9dee73e345c, 0x3fe760c52c304764, // 0.68285, 0.73056 + 0x3fe5e30b6e6877f3, 0x3fe7582ea9b9a329, // 0.68397, 0.72951 + 0x3fe5ec3495837074, 0x3fe74f948da8d28d, // 0.68508, 0.72846 + 0x3fe5f55a5b2576f8, 0x3fe746f6d9516d59, // 0.6862, 0.72741 + 0x3fe5fe7cbde56a0f, 0x3fe73e558e079942, // 0.68732, 0.72636 + 0x3fe6079bbc5aadfa, 0x3fe735b0ad2009b2, // 0.68843, 0.7253 + 0x3fe610b7551d2cde, 0x3fe72d0837efff97, // 0.68954, 0.72425 + 0x3fe619cf86c55702, 0x3fe7245c2fcd492a, // 0.69065, 0.72319 + 0x3fe622e44fec22ff, 0x3fe71bac960e41bf, // 0.69176, 0.72213 + 0x3fe62bf5af2b0dfd, 0x3fe712f96c09d18d, // 0.69287, 0.72107 + 0x3fe63503a31c1be8, 0x3fe70a42b3176d7a, // 0.69397, 0.72 + 0x3fe63e0e2a59d7aa, 0x3fe701886c8f16e6, // 0.69508, 0.71894 + 0x3fe64715437f535b, 0x3fe6f8ca99c95b75, // 0.69618, 0.71787 + 0x3fe65018ed28287f, 0x3fe6f0093c1f54de, // 0.69728, 0.7168 + 0x3fe6591925f0783e, 0x3fe6e74454eaa8ae, // 0.69838, 0.71573 + 0x3fe66215ec74eb91, 0x3fe6de7be585881d, // 0.69947, 0.71466 + 0x3fe66b0f3f52b386, 0x3fe6d5afef4aafcc, // 0.70057, 0.71358 + 0x3fe674051d27896c, 0x3fe6cce07395679f, // 0.70166, 0.71251 + 0x3fe67cf78491af10, 0x3fe6c40d73c18275, // 0.70275, 0.71143 + 0x3fe685e6742feeef, 0x3fe6bb36f12b5e06, // 0.70385, 0.71035 + 0x3fe68ed1eaa19c71, 0x3fe6b25ced2fe29c, // 0.70493, 0.70927 + 0x3fe697b9e686941c, 0x3fe6a97f692c82ea, // 0.70602, 0.70819 + 0x3fe6a09e667f3bcc, 0x3fe6a09e667f3bcc, // 0.70711, 0.70711 + 0x3fe6a97f692c82ea, 0x3fe697b9e686941c, // 0.70819, 0.70602 + 0x3fe6b25ced2fe29c, 0x3fe68ed1eaa19c71, // 0.70927, 0.70493 + 0x3fe6bb36f12b5e06, 0x3fe685e6742feeef, // 0.71035, 0.70385 + 0x3fe6c40d73c18275, 0x3fe67cf78491af10, // 0.71143, 0.70275 + 0x3fe6cce07395679f, 0x3fe674051d27896c, // 0.71251, 0.70166 + 0x3fe6d5afef4aafcc, 0x3fe66b0f3f52b386, // 0.71358, 0.70057 + 0x3fe6de7be585881d, 0x3fe66215ec74eb91, // 0.71466, 0.69947 + 0x3fe6e74454eaa8ae, 0x3fe6591925f0783e, // 0.71573, 0.69838 + 0x3fe6f0093c1f54de, 0x3fe65018ed28287f, // 0.7168, 0.69728 + 0x3fe6f8ca99c95b75, 0x3fe64715437f535b, // 0.71787, 0.69618 + 0x3fe701886c8f16e6, 0x3fe63e0e2a59d7aa, // 0.71894, 0.69508 + 0x3fe70a42b3176d7a, 0x3fe63503a31c1be8, // 0.72, 0.69397 + 0x3fe712f96c09d18d, 0x3fe62bf5af2b0dfd, // 0.72107, 0.69287 + 0x3fe71bac960e41bf, 0x3fe622e44fec22ff, // 0.72213, 0.69176 + 0x3fe7245c2fcd492a, 0x3fe619cf86c55702, // 0.72319, 0.69065 + 0x3fe72d0837efff97, 0x3fe610b7551d2cde, // 0.72425, 0.68954 + 0x3fe735b0ad2009b2, 0x3fe6079bbc5aadfa, // 0.7253, 0.68843 + 0x3fe73e558e079942, 0x3fe5fe7cbde56a0f, // 0.72636, 0.68732 + 0x3fe746f6d9516d59, 0x3fe5f55a5b2576f8, // 0.72741, 0.6862 + 0x3fe74f948da8d28d, 0x3fe5ec3495837074, // 0.72846, 0.68508 + 0x3fe7582ea9b9a329, 0x3fe5e30b6e6877f3, // 0.72951, 0.68397 + 0x3fe760c52c304764, 0x3fe5d9dee73e345c, // 0.73056, 0.68285 + 0x3fe7695813b9b594, 0x3fe5d0af016ed1d4, // 0.73161, 0.68172 + 0x3fe771e75f037261, 0x3fe5c77bbe65018c, // 0.73265, 0.6806 + 0x3fe77a730cbb9100, 0x3fe5be451f8bf980, // 0.7337, 0.67948 + 0x3fe782fb1b90b35b, 0x3fe5b50b264f7448, // 0.73474, 0.67835 + 0x3fe78b7f8a320a52, 0x3fe5abcdd41bb0d8, // 0.73578, 0.67722 + 0x3fe79400574f55e4, 0x3fe5a28d2a5d7250, // 0.73682, 0.67609 + 0x3fe79c7d8198e56e, 0x3fe599492a81ffbc, // 0.73785, 0.67496 + 0x3fe7a4f707bf97d2, 0x3fe59001d5f723df, // 0.73889, 0.67383 + 0x3fe7ad6ce874dbb6, 0x3fe586b72e2b2cfd, // 0.73992, 0.67269 + 0x3fe7b5df226aafb0, 0x3fe57d69348cec9f, // 0.74095, 0.67156 + 0x3fe7be4db453a27c, 0x3fe57417ea8bb75c, // 0.74198, 0.67042 + 0x3fe7c6b89ce2d333, 0x3fe56ac35197649e, // 0.74301, 0.66928 + 0x3fe7cf1fdacbf179, 0x3fe5616b6b204e6e, // 0.74403, 0.66814 + 0x3fe7d7836cc33db2, 0x3fe5581038975137, // 0.74506, 0.667 + 0x3fe7dfe3517d8937, 0x3fe54eb1bb6dcb8f, // 0.74608, 0.66586 + 0x3fe7e83f87b03686, 0x3fe5454ff5159dfb, // 0.7471, 0.66471 + 0x3fe7f0980e113978, 0x3fe53beae7012abe, // 0.74812, 0.66356 + 0x3fe7f8ece3571771, 0x3fe5328292a35596, // 0.74914, 0.66242 + 0x3fe8013e0638e795, 0x3fe52916f96f8388, // 0.75015, 0.66127 + 0x3fe8098b756e52fa, 0x3fe51fa81cd99aa6, // 0.75117, 0.66011 + 0x3fe811d52faf94dc, 0x3fe51635fe5601d7, // 0.75218, 0.65896 + 0x3fe81a1b33b57acc, 0x3fe50cc09f59a09b, // 0.75319, 0.65781 + 0x3fe8225d803964e5, 0x3fe503480159ded2, // 0.75419, 0.65665 + 0x3fe82a9c13f545ff, 0x3fe4f9cc25cca486, // 0.7552, 0.65549 + 0x3fe832d6eda3a3e0, 0x3fe4f04d0e2859aa, // 0.75621, 0.65433 + 0x3fe83b0e0bff976e, 0x3fe4e6cabbe3e5e9, // 0.75721, 0.65317 + 0x3fe843416dc4cce2, 0x3fe4dd453076b064, // 0.75821, 0.65201 + 0x3fe84b7111af83f9, 0x3fe4d3bc6d589f80, // 0.75921, 0.65085 + 0x3fe8539cf67c9029, 0x3fe4ca30740218a3, // 0.76021, 0.64968 + 0x3fe85bc51ae958cc, 0x3fe4c0a145ec0004, // 0.7612, 0.64851 + 0x3fe863e97db3d95a, 0x3fe4b70ee48fb869, // 0.7622, 0.64735 + 0x3fe86c0a1d9aa195, 0x3fe4ad79516722f0, // 0.76319, 0.64618 + 0x3fe87426f95cd5bd, 0x3fe4a3e08dec9ed6, // 0.76418, 0.645 + 0x3fe87c400fba2ebf, 0x3fe49a449b9b0938, // 0.76517, 0.64383 + 0x3fe884555f72fa6b, 0x3fe490a57bedbcdf, // 0.76615, 0.64266 + 0x3fe88c66e7481ba1, 0x3fe48703306091fe, // 0.76714, 0.64148 + 0x3fe89474a5fb0a84, 0x3fe47d5dba6fde01, // 0.76812, 0.6403 + 0x3fe89c7e9a4dd4ab, 0x3fe473b51b987347, // 0.7691, 0.63912 + 0x3fe8a484c3031d50, 0x3fe46a095557a0f1, // 0.77008, 0.63794 + 0x3fe8ac871ede1d88, 0x3fe4605a692b32a2, // 0.77106, 0.63676 + 0x3fe8b485aca2a468, 0x3fe456a858917046, // 0.77204, 0.63558 + 0x3fe8bc806b151741, 0x3fe44cf325091dd6, // 0.77301, 0.63439 + 0x3fe8c47758fa71cb, 0x3fe4433ad0117b1d, // 0.77398, 0.63321 + 0x3fe8cc6a75184655, 0x3fe4397f5b2a4380, // 0.77495, 0.63202 + 0x3fe8d459be34bdfa, 0x3fe42fc0c7d3adbb, // 0.77592, 0.63083 + 0x3fe8dc45331698cc, 0x3fe425ff178e6bb1, // 0.77689, 0.62964 + 0x3fe8e42cd2852e0a, 0x3fe41c3a4bdbaa26, // 0.77785, 0.62845 + 0x3fe8ec109b486c49, 0x3fe41272663d108c, // 0.77882, 0.62725 + 0x3fe8f3f08c28d9ac, 0x3fe408a76834c0c0, // 0.77978, 0.62606 + 0x3fe8fbcca3ef940d, 0x3fe3fed9534556d4, // 0.78074, 0.62486 + 0x3fe903a4e1665133, 0x3fe3f50828f1e8d2, // 0.78169, 0.62366 + 0x3fe90b7943575efe, 0x3fe3eb33eabe0680, // 0.78265, 0.62246 + 0x3fe91349c88da398, 0x3fe3e15c9a2db922, // 0.7836, 0.62126 + 0x3fe91b166fd49da2, 0x3fe3d78238c58343, // 0.78456, 0.62006 + 0x3fe922df37f8646a, 0x3fe3cda4c80a6076, // 0.78551, 0.61885 + 0x3fe92aa41fc5a815, 0x3fe3c3c44981c517, // 0.78646, 0.61765 + 0x3fe932652609b1cf, 0x3fe3b9e0beb19e18, // 0.7874, 0.61644 + 0x3fe93a22499263fc, 0x3fe3affa292050b9, // 0.78835, 0.61523 + 0x3fe941db892e3a65, 0x3fe3a6108a54ba58, // 0.78929, 0.61402 + 0x3fe94990e3ac4a6c, 0x3fe39c23e3d63029, // 0.79023, 0.61281 + 0x3fe9514257dc4335, 0x3fe39234372c7f04, // 0.79117, 0.6116 + 0x3fe958efe48e6dd7, 0x3fe3884185dfeb22, // 0.79211, 0.61038 + 0x3fe960998893ad8c, 0x3fe37e4bd1792fe2, // 0.79304, 0.60917 + 0x3fe9683f42bd7fe1, 0x3fe374531b817f8d, // 0.79398, 0.60795 + 0x3fe96fe111ddfce0, 0x3fe36a576582831b, // 0.79491, 0.60673 + 0x3fe9777ef4c7d742, 0x3fe36058b10659f3, // 0.79584, 0.60551 + 0x3fe97f18ea4e5c9e, 0x3fe35656ff9799ae, // 0.79676, 0.60429 + 0x3fe986aef1457594, 0x3fe34c5252c14de1, // 0.79769, 0.60307 + 0x3fe98e410881a600, 0x3fe3424aac0ef7d6, // 0.79861, 0.60184 + 0x3fe995cf2ed80d22, 0x3fe338400d0c8e57, // 0.79954, 0.60062 + 0x3fe99d59631e65d5, 0x3fe32e3277467d6b, // 0.80046, 0.59939 + 0x3fe9a4dfa42b06b2, 0x3fe32421ec49a620, // 0.80138, 0.59816 + 0x3fe9ac61f0d4e247, 0x3fe31a0e6da35e44, // 0.80229, 0.59693 + 0x3fe9b3e047f38741, 0x3fe30ff7fce17035, // 0.80321, 0.5957 + 0x3fe9bb5aa85f2098, 0x3fe305de9b921a94, // 0.80412, 0.59447 + 0x3fe9c2d110f075c3, 0x3fe2fbc24b441015, // 0.80503, 0.59323 + 0x3fe9ca438080eadb, 0x3fe2f1a30d86773a, // 0.80594, 0.592 + 0x3fe9d1b1f5ea80d6, 0x3fe2e780e3e8ea16, // 0.80685, 0.59076 + 0x3fe9d91c7007d5a6, 0x3fe2dd5bcffb7616, // 0.80775, 0.58952 + 0x3fe9e082edb42472, 0x3fe2d333d34e9bb7, // 0.80866, 0.58828 + 0x3fe9e7e56dcb45bd, 0x3fe2c908ef734e57, // 0.80956, 0.58704 + 0x3fe9ef43ef29af94, 0x3fe2bedb25faf3ea, // 0.81046, 0.5858 + 0x3fe9f69e70ac75bc, 0x3fe2b4aa787764c4, // 0.81135, 0.58455 + 0x3fe9fdf4f13149de, 0x3fe2aa76e87aeb58, // 0.81225, 0.58331 + 0x3fea05476f967bb5, 0x3fe2a040779843fb, // 0.81314, 0.58206 + 0x3fea0c95eabaf937, 0x3fe2960727629ca8, // 0.81404, 0.58081 + 0x3fea13e0617e4ec7, 0x3fe28bcaf96d94ba, // 0.81493, 0.57956 + 0x3fea1b26d2c0a75e, 0x3fe2818bef4d3cba, // 0.81581, 0.57831 + 0x3fea22693d62ccb9, 0x3fe2774a0a961612, // 0.8167, 0.57706 + 0x3fea29a7a0462782, 0x3fe26d054cdd12df, // 0.81758, 0.57581 + 0x3fea30e1fa4cbf81, 0x3fe262bdb7b795a2, // 0.81847, 0.57455 + 0x3fea38184a593bc6, 0x3fe258734cbb7110, // 0.81935, 0.5733 + 0x3fea3f4a8f4ee2d2, 0x3fe24e260d7ee7c9, // 0.82023, 0.57204 + 0x3fea4678c8119ac8, 0x3fe243d5fb98ac1f, // 0.8211, 0.57078 + 0x3fea4da2f385e997, 0x3fe23983189fdfd5, // 0.82198, 0.56952 + 0x3fea54c91090f524, 0x3fe22f2d662c13e1, // 0.82285, 0.56826 + 0x3fea5beb1e188375, 0x3fe224d4e5d5482e, // 0.82372, 0.567 + 0x3fea63091b02fae2, 0x3fe21a799933eb58, // 0.82459, 0.56573 + 0x3fea6a230637623b, 0x3fe2101b81e0da78, // 0.82546, 0.56447 + 0x3fea7138de9d60f5, 0x3fe205baa17560d6, // 0.82632, 0.5632 + 0x3fea784aa31d3f55, 0x3fe1fb56f98b37b8, // 0.82718, 0.56193 + 0x3fea7f58529fe69d, 0x3fe1f0f08bbc861b, // 0.82805, 0.56066 + 0x3fea8661ec0ee133, 0x3fe1e68759a3e074, // 0.8289, 0.55939 + 0x3fea8d676e545ad2, 0x3fe1dc1b64dc4872, // 0.82976, 0.55812 + 0x3fea9468d85b20ae, 0x3fe1d1acaf012cc2, // 0.83062, 0.55685 + 0x3fea9b66290ea1a3, 0x3fe1c73b39ae68c8, // 0.83147, 0.55557 + 0x3feaa25f5f5aee60, 0x3fe1bcc706804467, // 0.83232, 0.55429 + 0x3feaa9547a2cb98e, 0x3fe1b250171373be, // 0.83317, 0.55302 + 0x3feab045787157ff, 0x3fe1a7d66d0516e6, // 0.83402, 0.55174 + 0x3feab7325916c0d4, 0x3fe19d5a09f2b9b8, // 0.83486, 0.55046 + 0x3feabe1b1b0b8dac, 0x3fe192daef7a5386, // 0.83571, 0.54918 + 0x3feac4ffbd3efac8, 0x3fe188591f3a46e5, // 0.83655, 0.54789 + 0x3feacbe03ea0e73b, 0x3fe17dd49ad16161, // 0.83739, 0.54661 + 0x3fead2bc9e21d511, 0x3fe1734d63dedb49, // 0.83822, 0.54532 + 0x3fead994dab2e979, 0x3fe168c37c025764, // 0.83906, 0.54404 + 0x3feae068f345ecef, 0x3fe15e36e4dbe2bc, // 0.83989, 0.54275 + 0x3feae738e6cd4b67, 0x3fe153a7a00bf453, // 0.84073, 0.54146 + 0x3feaee04b43c1474, 0x3fe14915af336ceb, // 0.84155, 0.54017 + 0x3feaf4cc5a85fb73, 0x3fe13e8113f396c1, // 0.84238, 0.53888 + 0x3feafb8fd89f57b6, 0x3fe133e9cfee254e, // 0.84321, 0.53759 + 0x3feb024f2d7d24a9, 0x3fe1294fe4c5350a, // 0.84403, 0.53629 + 0x3feb090a58150200, 0x3fe11eb3541b4b22, // 0.84485, 0.535 + 0x3feb0fc1575d33db, 0x3fe114141f935545, // 0.84567, 0.5337 + 0x3feb16742a4ca2f5, 0x3fe1097248d0a956, // 0.84649, 0.5324 + 0x3feb1d22cfdadcc6, 0x3fe0fecdd1770537, // 0.84731, 0.5311 + 0x3feb23cd470013b4, 0x3fe0f426bb2a8e7d, // 0.84812, 0.5298 + 0x3feb2a738eb51f33, 0x3fe0e97d078fd23b, // 0.84893, 0.5285 + 0x3feb3115a5f37bf4, 0x3fe0ded0b84bc4b5, // 0.84974, 0.5272 + 0x3feb37b38bb54c09, 0x3fe0d421cf03c12b, // 0.85055, 0.5259 + 0x3feb3e4d3ef55712, 0x3fe0c9704d5d898f, // 0.85136, 0.52459 + 0x3feb44e2beaf0a61, 0x3fe0bebc34ff4646, // 0.85216, 0.52328 + 0x3feb4b7409de7925, 0x3fe0b405878f85ec, // 0.85296, 0.52198 + 0x3feb52011f805c92, 0x3fe0a94c46b53d0b, // 0.85376, 0.52067 + 0x3feb5889fe921405, 0x3fe09e907417c5e1, // 0.85456, 0.51936 + 0x3feb5f0ea611a532, 0x3fe093d2115ee018, // 0.85535, 0.51804 + 0x3feb658f14fdbc47, 0x3fe089112032b08c, // 0.85615, 0.51673 + 0x3feb6c0b4a55ac17, 0x3fe07e4da23bc102, // 0.85694, 0.51542 + 0x3feb728345196e3e, 0x3fe073879922ffed, // 0.85773, 0.5141 + 0x3feb78f70449a34b, 0x3fe068bf0691c028, // 0.85852, 0.51279 + 0x3feb7f6686e792ea, 0x3fe05df3ec31b8b6, // 0.8593, 0.51147 + 0x3feb85d1cbf52c02, 0x3fe053264bad0483, // 0.86009, 0.51015 + 0x3feb8c38d27504e9, 0x3fe0485626ae221a, // 0.86087, 0.50883 + 0x3feb929b996a5b7f, 0x3fe03d837edff370, // 0.86165, 0.50751 + 0x3feb98fa1fd9155e, 0x3fe032ae55edbd95, // 0.86242, 0.50619 + 0x3feb9f5464c5bffc, 0x3fe027d6ad83287e, // 0.8632, 0.50486 + 0x3feba5aa673590d2, 0x3fe01cfc874c3eb7, // 0.86397, 0.50354 + 0x3febabfc262e6586, 0x3fe0121fe4f56d2c, // 0.86474, 0.50221 + 0x3febb249a0b6c40d, 0x3fe00740c82b82e0, // 0.86551, 0.50089 + 0x3febb892d5d5dad5, 0x3fdff8be6537615e, // 0.86628, 0.49956 + 0x3febbed7c49380ea, 0x3fdfe2f64be7120f, // 0.86705, 0.49823 + 0x3febc5186bf8361d, 0x3fdfcd2947c1ff57, // 0.86781, 0.4969 + 0x3febcb54cb0d2327, 0x3fdfb7575c24d2de, // 0.86857, 0.49557 + 0x3febd18ce0dc19d6, 0x3fdfa1808c6cf7e0, // 0.86933, 0.49423 + 0x3febd7c0ac6f952a, 0x3fdf8ba4dbf89aba, // 0.87009, 0.4929 + 0x3febddf02cd2b983, 0x3fdf75c44e26a852, // 0.87084, 0.49156 + 0x3febe41b611154c1, 0x3fdf5fdee656cda3, // 0.8716, 0.49023 + 0x3febea424837de6d, 0x3fdf49f4a7e97729, // 0.87235, 0.48889 + 0x3febf064e15377dd, 0x3fdf3405963fd068, // 0.87309, 0.48755 + 0x3febf6832b71ec5b, 0x3fdf1e11b4bbc35c, // 0.87384, 0.48621 + 0x3febfc9d25a1b147, 0x3fdf081906bff7fd, // 0.87459, 0.48487 + 0x3fec02b2cef1e641, 0x3fdef21b8fafd3b5, // 0.87533, 0.48353 + 0x3fec08c426725549, 0x3fdedc1952ef78d5, // 0.87607, 0.48218 + 0x3fec0ed12b3372e9, 0x3fdec61253e3c61b, // 0.87681, 0.48084 + 0x3fec14d9dc465e58, 0x3fdeb00695f25620, // 0.87755, 0.47949 + 0x3fec1ade38bce19b, 0x3fde99f61c817eda, // 0.87828, 0.47815 + 0x3fec20de3fa971b0, 0x3fde83e0eaf85113, // 0.87901, 0.4768 + 0x3fec26d9f01f2eaf, 0x3fde6dc704be97e2, // 0.87974, 0.47545 + 0x3fec2cd14931e3f1, 0x3fde57a86d3cd824, // 0.88047, 0.4741 + 0x3fec32c449f60831, 0x3fde418527dc4ffa, // 0.8812, 0.47275 + 0x3fec38b2f180bdb1, 0x3fde2b5d3806f63b, // 0.88192, 0.4714 + 0x3fec3e9d3ee7d262, 0x3fde1530a12779f4, // 0.88264, 0.47004 + 0x3fec44833141c004, 0x3fddfeff66a941de, // 0.88336, 0.46869 + 0x3fec4a64c7a5ac4c, 0x3fdde8c98bf86bd6, // 0.88408, 0.46733 + 0x3fec5042012b6907, 0x3fddd28f1481cc58, // 0.8848, 0.46598 + 0x3fec561adceb743e, 0x3fddbc5003b2edf8, // 0.88551, 0.46462 + 0x3fec5bef59fef85a, 0x3fdda60c5cfa10d8, // 0.88622, 0.46326 + 0x3fec61bf777fcc48, 0x3fdd8fc423c62a25, // 0.88693, 0.4619 + 0x3fec678b3488739b, 0x3fdd79775b86e389, // 0.88764, 0.46054 + 0x3fec6d5290341eb2, 0x3fdd632607ac9aa9, // 0.88835, 0.45918 + 0x3fec7315899eaad7, 0x3fdd4cd02ba8609c, // 0.88905, 0.45781 + 0x3fec78d41fe4a267, 0x3fdd3675caebf962, // 0.88975, 0.45645 + 0x3fec7e8e52233cf3, 0x3fdd2016e8e9db5b, // 0.89045, 0.45508 + 0x3fec84441f785f61, 0x3fdd09b389152ec1, // 0.89115, 0.45372 + 0x3fec89f587029c13, 0x3fdcf34baee1cd21, // 0.89184, 0.45235 + 0x3fec8fa287e13305, 0x3fdcdcdf5dc440ce, // 0.89253, 0.45098 + 0x3fec954b213411f5, 0x3fdcc66e9931c45d, // 0.89322, 0.44961 + 0x3fec9aef521bd480, 0x3fdcaff964a0421d, // 0.89391, 0.44824 + 0x3feca08f19b9c449, 0x3fdc997fc3865388, // 0.8946, 0.44687 + 0x3feca62a772fd919, 0x3fdc8301b95b40c2, // 0.89528, 0.4455 + 0x3fecabc169a0b901, 0x3fdc6c7f4997000a, // 0.89597, 0.44412 + 0x3fecb153f02fb87d, 0x3fdc55f877b23537, // 0.89665, 0.44275 + 0x3fecb6e20a00da99, 0x3fdc3f6d47263129, // 0.89732, 0.44137 + 0x3fecbc6bb638d10b, 0x3fdc28ddbb6cf145, // 0.898, 0.43999 + 0x3fecc1f0f3fcfc5c, 0x3fdc1249d8011ee7, // 0.89867, 0.43862 + 0x3fecc771c2736c09, 0x3fdbfbb1a05e0edc, // 0.89935, 0.43724 + 0x3fecccee20c2de9f, 0x3fdbe51517ffc0d9, // 0.90002, 0.43586 + 0x3fecd2660e12c1e6, 0x3fdbce744262deee, // 0.90068, 0.43448 + 0x3fecd7d9898b32f6, 0x3fdbb7cf2304bd01, // 0.90135, 0.43309 + 0x3fecdd489254fe65, 0x3fdba125bd63583e, // 0.90201, 0.43171 + 0x3fece2b32799a060, 0x3fdb8a7814fd5693, // 0.90267, 0.43033 + 0x3fece819488344ce, 0x3fdb73c62d520624, // 0.90333, 0.42894 + 0x3feced7af43cc773, 0x3fdb5d1009e15cc0, // 0.90399, 0.42756 + 0x3fecf2d829f1b40e, 0x3fdb4655ae2bf757, // 0.90464, 0.42617 + 0x3fecf830e8ce467b, 0x3fdb2f971db31972, // 0.9053, 0.42478 + 0x3fecfd852fff6ad4, 0x3fdb18d45bf8aca6, // 0.90595, 0.42339 + 0x3fed02d4feb2bd92, 0x3fdb020d6c7f4009, // 0.9066, 0.422 + 0x3fed082054168bac, 0x3fdaeb4252ca07ab, // 0.90724, 0.42061 + 0x3fed0d672f59d2b9, 0x3fdad473125cdc08, // 0.90789, 0.41922 + 0x3fed12a98fac410c, 0x3fdabd9faebc3980, // 0.90853, 0.41782 + 0x3fed17e7743e35dc, 0x3fdaa6c82b6d3fc9, // 0.90917, 0.41643 + 0x3fed1d20dc40c15c, 0x3fda8fec8bf5b166, // 0.90981, 0.41503 + 0x3fed2255c6e5a4e1, 0x3fda790cd3dbf31a, // 0.91044, 0.41364 + 0x3fed2786335f52fc, 0x3fda622906a70b63, // 0.91107, 0.41224 + 0x3fed2cb220e0ef9f, 0x3fda4b4127dea1e4, // 0.91171, 0.41084 + 0x3fed31d98e9e503a, 0x3fda34553b0afee5, // 0.91234, 0.40944 + 0x3fed36fc7bcbfbdc, 0x3fda1d6543b50ac0, // 0.91296, 0.40804 + 0x3fed3c1ae79f2b4e, 0x3fda067145664d57, // 0.91359, 0.40664 + 0x3fed4134d14dc93a, 0x3fd9ef7943a8ed8a, // 0.91421, 0.40524 + 0x3fed464a380e7242, 0x3fd9d87d4207b0ab, // 0.91483, 0.40384 + 0x3fed4b5b1b187524, 0x3fd9c17d440df9f2, // 0.91545, 0.40243 + 0x3fed506779a3d2d9, 0x3fd9aa794d47c9ee, // 0.91606, 0.40103 + 0x3fed556f52e93eb1, 0x3fd993716141bdfe, // 0.91668, 0.39962 + 0x3fed5a72a6221e73, 0x3fd97c6583890fc2, // 0.91729, 0.39822 + 0x3fed5f7172888a7f, 0x3fd96555b7ab948f, // 0.9179, 0.39681 + 0x3fed646bb7574de5, 0x3fd94e420137bce3, // 0.91851, 0.3954 + 0x3fed696173c9e68b, 0x3fd9372a63bc93d7, // 0.91911, 0.39399 + 0x3fed6e52a71c8547, 0x3fd9200ee2c9be97, // 0.91972, 0.39258 + 0x3fed733f508c0dff, 0x3fd908ef81ef7bd1, // 0.92032, 0.39117 + 0x3fed78276f5617c6, 0x3fd8f1cc44bea329, // 0.92092, 0.38976 + 0x3fed7d0b02b8ecf9, 0x3fd8daa52ec8a4af, // 0.92151, 0.38835 + 0x3fed81ea09f38b63, 0x3fd8c37a439f884f, // 0.92211, 0.38693 + 0x3fed86c48445a450, 0x3fd8ac4b86d5ed44, // 0.9227, 0.38552 + 0x3fed8b9a70ef9cb4, 0x3fd89518fbff098e, // 0.92329, 0.3841 + 0x3fed906bcf328d46, 0x3fd87de2a6aea963, // 0.92388, 0.38268 + 0x3fed95389e50429b, 0x3fd866a88a792ea0, // 0.92447, 0.38127 + 0x3fed9a00dd8b3d46, 0x3fd84f6aaaf3903f, // 0.92505, 0.37985 + 0x3fed9ec48c26b1f3, 0x3fd838290bb359c8, // 0.92563, 0.37843 + 0x3feda383a9668988, 0x3fd820e3b04eaac4, // 0.92621, 0.37701 + 0x3feda83e348f613b, 0x3fd8099a9c5c362d, // 0.92679, 0.37559 + 0x3fedacf42ce68ab9, 0x3fd7f24dd37341e3, // 0.92736, 0.37416 + 0x3fedb1a591b20c38, 0x3fd7dafd592ba621, // 0.92794, 0.37274 + 0x3fedb6526238a09b, 0x3fd7c3a9311dcce7, // 0.92851, 0.37132 + 0x3fedbafa9dc1b78d, 0x3fd7ac515ee2b172, // 0.92907, 0.36989 + 0x3fedbf9e4395759a, 0x3fd794f5e613dfae, // 0.92964, 0.36847 + 0x3fedc43d52fcb453, 0x3fd77d96ca4b73a6, // 0.93021, 0.36704 + 0x3fedc8d7cb410260, 0x3fd766340f2418f6, // 0.93077, 0.36561 + 0x3fedcd6dabaca3a5, 0x3fd74ecdb8390a3e, // 0.93133, 0.36418 + 0x3fedd1fef38a915a, 0x3fd73763c9261092, // 0.93188, 0.36276 + 0x3fedd68ba2267a25, 0x3fd71ff6458782ec, // 0.93244, 0.36133 + 0x3feddb13b6ccc23d, 0x3fd7088530fa459e, // 0.93299, 0.3599 + 0x3feddf9730ca837b, 0x3fd6f1108f1bc9c5, // 0.93354, 0.35846 + 0x3fede4160f6d8d81, 0x3fd6d998638a0cb5, // 0.93409, 0.35703 + 0x3fede890520465ce, 0x3fd6c21cb1e39771, // 0.93464, 0.3556 + 0x3feded05f7de47da, 0x3fd6aa9d7dc77e16, // 0.93518, 0.35416 + 0x3fedf177004b2534, 0x3fd6931acad55f51, // 0.93573, 0.35273 + 0x3fedf5e36a9ba59c, 0x3fd67b949cad63ca, // 0.93627, 0.35129 + 0x3fedfa4b3621271d, 0x3fd6640af6f03d9e, // 0.9368, 0.34986 + 0x3fedfeae622dbe2b, 0x3fd64c7ddd3f27c6, // 0.93734, 0.34842 + 0x3fee030cee1435b8, 0x3fd634ed533be58e, // 0.93787, 0.34698 + 0x3fee0766d9280f54, 0x3fd61d595c88c203, // 0.9384, 0.34554 + 0x3fee0bbc22bd8349, 0x3fd605c1fcc88f63, // 0.93893, 0.3441 + 0x3fee100cca2980ac, 0x3fd5ee27379ea693, // 0.93946, 0.34266 + 0x3fee1458cec1ad83, 0x3fd5d68910aee686, // 0.93998, 0.34122 + 0x3fee18a02fdc66d9, 0x3fd5bee78b9db3b6, // 0.94051, 0.33978 + 0x3fee1ce2ecd0c0d8, 0x3fd5a742ac0ff78d, // 0.94103, 0.33833 + 0x3fee212104f686e5, 0x3fd58f9a75ab1fdd, // 0.94154, 0.33689 + 0x3fee255a77a63bb8, 0x3fd577eeec151e47, // 0.94206, 0.33545 + 0x3fee298f4439197a, 0x3fd5604012f467b4, // 0.94257, 0.334 + 0x3fee2dbf6a0911d9, 0x3fd5488dedeff3be, // 0.94308, 0.33255 + 0x3fee31eae870ce25, 0x3fd530d880af3c24, // 0.94359, 0.33111 + 0x3fee3611becbaf69, 0x3fd5191fceda3c35, // 0.9441, 0.32966 + 0x3fee3a33ec75ce85, 0x3fd50163dc197047, // 0.9446, 0.32821 + 0x3fee3e5170cbfc46, 0x3fd4e9a4ac15d520, // 0.94511, 0.32676 + 0x3fee426a4b2bc17e, 0x3fd4d1e24278e76a, // 0.94561, 0.32531 + 0x3fee467e7af35f23, 0x3fd4ba1ca2eca31c, // 0.94611, 0.32386 + 0x3fee4a8dff81ce5e, 0x3fd4a253d11b82f3, // 0.9466, 0.32241 + 0x3fee4e98d836c0af, 0x3fd48a87d0b07fd7, // 0.94709, 0.32096 + 0x3fee529f04729ffc, 0x3fd472b8a5571054, // 0.94759, 0.3195 + 0x3fee56a083968eb1, 0x3fd45ae652bb2800, // 0.94807, 0.31805 + 0x3fee5a9d550467d3, 0x3fd44310dc8936f0, // 0.94856, 0.31659 + 0x3fee5e95781ebf1c, 0x3fd42b38466e2928, // 0.94905, 0.31514 + 0x3fee6288ec48e112, 0x3fd4135c94176602, // 0.94953, 0.31368 + 0x3fee6677b0e6d31e, 0x3fd3fb7dc932cfa4, // 0.95001, 0.31222 + 0x3fee6a61c55d53a7, 0x3fd3e39be96ec271, // 0.95049, 0.31077 + 0x3fee6e472911da27, 0x3fd3cbb6f87a146e, // 0.95096, 0.30931 + 0x3fee7227db6a9744, 0x3fd3b3cefa0414b7, // 0.95144, 0.30785 + 0x3fee7603dbce74e9, 0x3fd39be3f1bc8aef, // 0.95191, 0.30639 + 0x3fee79db29a5165a, 0x3fd383f5e353b6aa, // 0.95238, 0.30493 + 0x3fee7dadc456d850, 0x3fd36c04d27a4edf, // 0.95284, 0.30347 + 0x3fee817bab4cd10d, 0x3fd35410c2e18152, // 0.95331, 0.30201 + 0x3fee8544ddf0d075, 0x3fd33c19b83af207, // 0.95377, 0.30054 + 0x3fee89095bad6025, 0x3fd3241fb638baaf, // 0.95423, 0.29908 + 0x3fee8cc923edc388, 0x3fd30c22c08d6a13, // 0.95469, 0.29762 + 0x3fee9084361df7f3, 0x3fd2f422daec0386, // 0.95514, 0.29615 + 0x3fee943a91aab4b4, 0x3fd2dc200907fe51, // 0.95559, 0.29469 + 0x3fee97ec36016b30, 0x3fd2c41a4e954520, // 0.95605, 0.29322 + 0x3fee9b99229046f8, 0x3fd2ac11af483572, // 0.95649, 0.29175 + 0x3fee9f4156c62dda, 0x3fd294062ed59f05, // 0.95694, 0.29028 + 0x3feea2e4d212c000, 0x3fd27bf7d0f2c346, // 0.95738, 0.28882 + 0x3feea68393e65800, 0x3fd263e6995554ba, // 0.95783, 0.28735 + 0x3feeaa1d9bb20af3, 0x3fd24bd28bb37672, // 0.95827, 0.28588 + 0x3feeadb2e8e7a88e, 0x3fd233bbabc3bb72, // 0.9587, 0.28441 + 0x3feeb1437af9bb34, 0x3fd21ba1fd3d2623, // 0.95914, 0.28294 + 0x3feeb4cf515b8811, 0x3fd2038583d727bd, // 0.95957, 0.28146 + 0x3feeb8566b810f2a, 0x3fd1eb6643499fbb, // 0.96, 0.27999 + 0x3feebbd8c8df0b74, 0x3fd1d3443f4cdb3d, // 0.96043, 0.27852 + 0x3feebf5668eaf2ef, 0x3fd1bb1f7b999480, // 0.96086, 0.27705 + 0x3feec2cf4b1af6b2, 0x3fd1a2f7fbe8f243, // 0.96128, 0.27557 + 0x3feec6436ee60309, 0x3fd18acdc3f4873a, // 0.9617, 0.2741 + 0x3feec9b2d3c3bf84, 0x3fd172a0d7765177, // 0.96212, 0.27262 + 0x3feecd1d792c8f10, 0x3fd15a713a28b9d9, // 0.96254, 0.27115 + 0x3feed0835e999009, 0x3fd1423eefc69378, // 0.96295, 0.26967 + 0x3feed3e483849c51, 0x3fd12a09fc0b1b12, // 0.96337, 0.26819 + 0x3feed740e7684963, 0x3fd111d262b1f677, // 0.96378, 0.26671 + 0x3feeda9889bfe86a, 0x3fd0f998277733f7, // 0.96418, 0.26523 + 0x3feeddeb6a078651, 0x3fd0e15b4e1749cd, // 0.96459, 0.26375 + 0x3feee13987bbebdc, 0x3fd0c91bda4f158d, // 0.96499, 0.26227 + 0x3feee482e25a9dbc, 0x3fd0b0d9cfdbdb90, // 0.96539, 0.26079 + 0x3feee7c77961dc9e, 0x3fd09895327b465e, // 0.96579, 0.25931 + 0x3feeeb074c50a544, 0x3fd0804e05eb661e, // 0.96619, 0.25783 + 0x3feeee425aa6b09a, 0x3fd068044deab002, // 0.96658, 0.25635 + 0x3feef178a3e473c2, 0x3fd04fb80e37fdae, // 0.96698, 0.25487 + 0x3feef4aa278b2032, 0x3fd037694a928cac, // 0.96737, 0.25338 + 0x3feef7d6e51ca3c0, 0x3fd01f1806b9fdd2, // 0.96775, 0.2519 + 0x3feefafedc1ba8b7, 0x3fd006c4466e54af, // 0.96814, 0.25041 + 0x3feefe220c0b95ec, 0x3fcfdcdc1adfedf8, // 0.96852, 0.24893 + 0x3fef014074708ed3, 0x3fcfac2abeff57ff, // 0.9689, 0.24744 + 0x3fef045a14cf738c, 0x3fcf7b7480bd3801, // 0.96928, 0.24596 + 0x3fef076eecade0fa, 0x3fcf4ab9679c9f5c, // 0.96966, 0.24447 + 0x3fef0a7efb9230d7, 0x3fcf19f97b215f1a, // 0.97003, 0.24298 + 0x3fef0d8a410379c5, 0x3fcee934c2d006c7, // 0.9704, 0.24149 + 0x3fef1090bc898f5f, 0x3fceb86b462de348, // 0.97077, 0.24 + 0x3fef13926dad024e, 0x3fce879d0cc0fdaf, // 0.97114, 0.23851 + 0x3fef168f53f7205d, 0x3fce56ca1e101a1b, // 0.9715, 0.23702 + 0x3fef19876ef1f486, 0x3fce25f281a2b684, // 0.97187, 0.23553 + 0x3fef1c7abe284708, 0x3fcdf5163f01099a, // 0.97223, 0.23404 + 0x3fef1f6941259d7a, 0x3fcdc4355db40195, // 0.97258, 0.23255 + 0x3fef2252f7763ada, 0x3fcd934fe5454311, // 0.97294, 0.23106 + 0x3fef2537e0a71f9f, 0x3fcd6265dd3f27e3, // 0.97329, 0.22957 + 0x3fef2817fc4609ce, 0x3fcd31774d2cbdee, // 0.97364, 0.22807 + 0x3fef2af349e17507, 0x3fcd00843c99c5f9, // 0.97399, 0.22658 + 0x3fef2dc9c9089a9d, 0x3fcccf8cb312b286, // 0.97434, 0.22508 + 0x3fef309b794b719f, 0x3fcc9e90b824a6a9, // 0.97468, 0.22359 + 0x3fef33685a3aaef0, 0x3fcc6d90535d74dc, // 0.97503, 0.22209 + 0x3fef36306b67c556, 0x3fcc3c8b8c4b9dd7, // 0.97536, 0.2206 + 0x3fef38f3ac64e589, 0x3fcc0b826a7e4f63, // 0.9757, 0.2191 + 0x3fef3bb21cc4fe47, 0x3fcbda74f5856330, // 0.97604, 0.2176 + 0x3fef3e6bbc1bbc65, 0x3fcba96334f15dad, // 0.97637, 0.21611 + 0x3fef412089fd8adc, 0x3fcb784d30536cda, // 0.9767, 0.21461 + 0x3fef43d085ff92dd, 0x3fcb4732ef3d6722, // 0.97703, 0.21311 + 0x3fef467bafb7bbe0, 0x3fcb16147941ca2a, // 0.97735, 0.21161 + 0x3fef492206bcabb4, 0x3fcae4f1d5f3b9ab, // 0.97768, 0.21011 + 0x3fef4bc38aa5c694, 0x3fcab3cb0ce6fe44, // 0.978, 0.20861 + 0x3fef4e603b0b2f2d, 0x3fca82a025b00451, // 0.97832, 0.20711 + 0x3fef50f81785c6b9, 0x3fca517127e3dabc, // 0.97863, 0.20561 + 0x3fef538b1faf2d07, 0x3fca203e1b1831da, // 0.97895, 0.20411 + 0x3fef56195321c090, 0x3fc9ef0706e35a35, // 0.97926, 0.20261 + 0x3fef58a2b1789e84, 0x3fc9bdcbf2dc4366, // 0.97957, 0.2011 + 0x3fef5b273a4fa2d9, 0x3fc98c8ce69a7aec, // 0.97988, 0.1996 + 0x3fef5da6ed43685d, 0x3fc95b49e9b62af9, // 0.98018, 0.1981 + 0x3fef6021c9f148c2, 0x3fc92a0303c8194f, // 0.98048, 0.19659 + 0x3fef6297cff75cb0, 0x3fc8f8b83c69a60a, // 0.98079, 0.19509 + 0x3fef6508fef47bd5, 0x3fc8c7699b34ca7e, // 0.98108, 0.19359 + 0x3fef677556883cee, 0x3fc8961727c41804, // 0.98138, 0.19208 + 0x3fef69dcd652f5de, 0x3fc864c0e9b2b6cf, // 0.98167, 0.19057 + 0x3fef6c3f7df5bbb7, 0x3fc83366e89c64c5, // 0.98196, 0.18907 + 0x3fef6e9d4d1262ca, 0x3fc802092c1d744b, // 0.98225, 0.18756 + 0x3fef70f6434b7eb7, 0x3fc7d0a7bbd2cb1b, // 0.98254, 0.18606 + 0x3fef734a60446279, 0x3fc79f429f59e11d, // 0.98282, 0.18455 + 0x3fef7599a3a12077, 0x3fc76dd9de50bf31, // 0.98311, 0.18304 + 0x3fef77e40d068a90, 0x3fc73c6d8055fe0a, // 0.98339, 0.18153 + 0x3fef7a299c1a322a, 0x3fc70afd8d08c4ff, // 0.98366, 0.18002 + 0x3fef7c6a50826840, 0x3fc6d98a0c08c8da, // 0.98394, 0.17851 + 0x3fef7ea629e63d6e, 0x3fc6a81304f64ab2, // 0.98421, 0.177 + 0x3fef80dd27ed8204, 0x3fc676987f7216b8, // 0.98448, 0.17549 + 0x3fef830f4a40c60c, 0x3fc6451a831d830d, // 0.98475, 0.17398 + 0x3fef853c9089595e, 0x3fc61399179a6e94, // 0.98501, 0.17247 + 0x3fef8764fa714ba9, 0x3fc5e214448b3fc6, // 0.98528, 0.17096 + 0x3fef898887a36c84, 0x3fc5b08c1192e381, // 0.98554, 0.16945 + 0x3fef8ba737cb4b78, 0x3fc57f008654cbde, // 0.9858, 0.16794 + 0x3fef8dc10a95380d, 0x3fc54d71aa74ef02, // 0.98605, 0.16643 + 0x3fef8fd5ffae41db, 0x3fc51bdf8597c5f2, // 0.98631, 0.16491 + 0x3fef91e616c43891, 0x3fc4ea4a1f624b61, // 0.98656, 0.1634 + 0x3fef93f14f85ac08, 0x3fc4b8b17f79fa88, // 0.98681, 0.16189 + 0x3fef95f7a9a1ec47, 0x3fc48715ad84cdf5, // 0.98706, 0.16037 + 0x3fef97f924c9099b, 0x3fc45576b1293e5a, // 0.9873, 0.15886 + 0x3fef99f5c0abd496, 0x3fc423d4920e4166, // 0.98754, 0.15734 + 0x3fef9bed7cfbde29, 0x3fc3f22f57db4893, // 0.98778, 0.15583 + 0x3fef9de0596b77a3, 0x3fc3c0870a383ff6, // 0.98802, 0.15431 + 0x3fef9fce55adb2c8, 0x3fc38edbb0cd8d14, // 0.98826, 0.1528 + 0x3fefa1b7717661d5, 0x3fc35d2d53440db2, // 0.98849, 0.15128 + 0x3fefa39bac7a1791, 0x3fc32b7bf94516a7, // 0.98872, 0.14976 + 0x3fefa57b066e2754, 0x3fc2f9c7aa7a72af, // 0.98895, 0.14825 + 0x3fefa7557f08a517, 0x3fc2c8106e8e613a, // 0.98918, 0.14673 + 0x3fefa92b1600657c, 0x3fc296564d2b953e, // 0.9894, 0.14521 + 0x3fefaafbcb0cfddc, 0x3fc264994dfd340a, // 0.98962, 0.1437 + 0x3fefacc79de6c44f, 0x3fc232d978aed413, // 0.98984, 0.14218 + 0x3fefae8e8e46cfbb, 0x3fc20116d4ec7bce, // 0.99006, 0.14066 + 0x3fefb0509be6f7db, 0x3fc1cf516a62a077, // 0.99027, 0.13914 + 0x3fefb20dc681d54d, 0x3fc19d8940be24e7, // 0.99049, 0.13762 + 0x3fefb3c60dd2c199, 0x3fc16bbe5fac5865, // 0.9907, 0.1361 + 0x3fefb5797195d741, 0x3fc139f0cedaf576, // 0.9909, 0.13458 + 0x3fefb727f187f1c7, 0x3fc1082095f820b0, // 0.99111, 0.13306 + 0x3fefb8d18d66adb7, 0x3fc0d64dbcb26786, // 0.99131, 0.13154 + 0x3fefba7644f068b5, 0x3fc0a4784ab8bf1d, // 0.99151, 0.13002 + 0x3fefbc1617e44186, 0x3fc072a047ba831d, // 0.99171, 0.1285 + 0x3fefbdb106021816, 0x3fc040c5bb67747e, // 0.99191, 0.12698 + 0x3fefbf470f0a8d88, 0x3fc00ee8ad6fb85b, // 0.9921, 0.12545 + 0x3fefc0d832bf043a, 0x3fbfba124b07ad85, // 0.99229, 0.12393 + 0x3fefc26470e19fd3, 0x3fbf564e56a9730e, // 0.99248, 0.12241 + 0x3fefc3ebc935454c, 0x3fbef2858d27561b, // 0.99267, 0.12089 + 0x3fefc56e3b7d9af6, 0x3fbe8eb7fde4aa3e, // 0.99285, 0.11937 + 0x3fefc6ebc77f0887, 0x3fbe2ae5b8457f77, // 0.99303, 0.11784 + 0x3fefc8646cfeb721, 0x3fbdc70ecbae9fc8, // 0.99321, 0.11632 + 0x3fefc9d82bc2915e, 0x3fbd633347858ce4, // 0.99339, 0.11479 + 0x3fefcb4703914354, 0x3fbcff533b307dc1, // 0.99356, 0.11327 + 0x3fefccb0f4323aa3, 0x3fbc9b6eb6165c42, // 0.99374, 0.11175 + 0x3fefce15fd6da67b, 0x3fbc3785c79ec2d5, // 0.99391, 0.11022 + 0x3fefcf761f0c77a3, 0x3fbbd3987f31fa0e, // 0.99407, 0.1087 + 0x3fefd0d158d86087, 0x3fbb6fa6ec38f64c, // 0.99424, 0.10717 + 0x3fefd227aa9bd53b, 0x3fbb0bb11e1d5559, // 0.9944, 0.10565 + 0x3fefd37914220b84, 0x3fbaa7b724495c04, // 0.99456, 0.10412 + 0x3fefd4c59536fae4, 0x3fba43b90e27f3c4, // 0.99472, 0.1026 + 0x3fefd60d2da75c9e, 0x3fb9dfb6eb24a85c, // 0.99488, 0.10107 + 0x3fefd74fdd40abbf, 0x3fb97bb0caaba56f, // 0.99503, 0.099544 + 0x3fefd88da3d12526, 0x3fb917a6bc29b42c, // 0.99518, 0.098017 + 0x3fefd9c68127c78c, 0x3fb8b398cf0c38e0, // 0.99533, 0.09649 + 0x3fefdafa7514538c, 0x3fb84f8712c130a0, // 0.99548, 0.094963 + 0x3fefdc297f674ba9, 0x3fb7eb7196b72ee4, // 0.99563, 0.093436 + 0x3fefdd539ff1f456, 0x3fb787586a5d5b21, // 0.99577, 0.091909 + 0x3fefde78d68653fd, 0x3fb7233b9d236e71, // 0.99591, 0.090381 + 0x3fefdf9922f73307, 0x3fb6bf1b3e79b129, // 0.99604, 0.088854 + 0x3fefe0b485181be3, 0x3fb65af75dd0f87b, // 0.99618, 0.087326 + 0x3fefe1cafcbd5b09, 0x3fb5f6d00a9aa419, // 0.99631, 0.085797 + 0x3fefe2dc89bbff08, 0x3fb592a554489bc8, // 0.99644, 0.084269 + 0x3fefe3e92be9d886, 0x3fb52e774a4d4d0a, // 0.99657, 0.08274 + 0x3fefe4f0e31d7a4a, 0x3fb4ca45fc1ba8b6, // 0.9967, 0.081211 + 0x3fefe5f3af2e3940, 0x3fb4661179272096, // 0.99682, 0.079682 + 0x3fefe6f18ff42c84, 0x3fb401d9d0e3a507, // 0.99694, 0.078153 + 0x3fefe7ea85482d60, 0x3fb39d9f12c5a299, // 0.99706, 0.076624 + 0x3fefe8de8f03d75c, 0x3fb339614e41ffa5, // 0.99718, 0.075094 + 0x3fefe9cdad01883a, 0x3fb2d52092ce19f6, // 0.99729, 0.073565 + 0x3fefeab7df1c6005, 0x3fb270dcefdfc45b, // 0.9974, 0.072035 + 0x3fefeb9d2530410f, 0x3fb20c9674ed444c, // 0.99751, 0.070505 + 0x3fefec7d7f19cffc, 0x3fb1a84d316d4f8a, // 0.99762, 0.068974 + 0x3fefed58ecb673c4, 0x3fb1440134d709b2, // 0.99772, 0.067444 + 0x3fefee2f6de455ba, 0x3fb0dfb28ea201e6, // 0.99783, 0.065913 + 0x3fefef0102826191, 0x3fb07b614e463064, // 0.99793, 0.064383 + 0x3fefefcdaa704562, 0x3fb0170d833bf421, // 0.99802, 0.062852 + 0x3feff095658e71ad, 0x3faf656e79f820e0, // 0.99812, 0.061321 + 0x3feff15833be1965, 0x3fae9cbd15ff5527, // 0.99821, 0.05979 + 0x3feff21614e131ed, 0x3fadd406f9808ec8, // 0.9983, 0.058258 + 0x3feff2cf08da7321, 0x3fad0b4c436f91d0, // 0.99839, 0.056727 + 0x3feff3830f8d575c, 0x3fac428d12c0d7e3, // 0.99848, 0.055195 + 0x3feff43228de1b77, 0x3fab79c986698b78, // 0.99856, 0.053664 + 0x3feff4dc54b1bed3, 0x3faab101bd5f8317, // 0.99864, 0.052132 + 0x3feff58192ee0358, 0x3fa9e835d6993c87, // 0.99872, 0.0506 + 0x3feff621e3796d7e, 0x3fa91f65f10dd814, // 0.9988, 0.049068 + 0x3feff6bd463b444d, 0x3fa856922bb513c1, // 0.99887, 0.047535 + 0x3feff753bb1b9164, 0x3fa78dbaa5874685, // 0.99894, 0.046003 + 0x3feff7e5420320f9, 0x3fa6c4df7d7d5b84, // 0.99901, 0.044471 + 0x3feff871dadb81df, 0x3fa5fc00d290cd43, // 0.99908, 0.042938 + 0x3feff8f9858f058b, 0x3fa5331ec3bba0eb, // 0.99914, 0.041406 + 0x3feff97c4208c014, 0x3fa46a396ff86179, // 0.9992, 0.039873 + 0x3feff9fa10348837, 0x3fa3a150f6421afc, // 0.99926, 0.03834 + 0x3feffa72effef75d, 0x3fa2d865759455cd, // 0.99932, 0.036807 + 0x3feffae6e1556998, 0x3fa20f770ceb11c6, // 0.99938, 0.035274 + 0x3feffb55e425fdae, 0x3fa14685db42c17e, // 0.99943, 0.033741 + 0x3feffbbff85f9515, 0x3fa07d91ff984580, // 0.99948, 0.032208 + 0x3feffc251df1d3f8, 0x3f9f693731d1cf01, // 0.99953, 0.030675 + 0x3feffc8554cd213a, 0x3f9dd7458c64ab39, // 0.99958, 0.029142 + 0x3feffce09ce2a679, 0x3f9c454f4ce53b1c, // 0.99962, 0.027608 + 0x3feffd36f624500c, 0x3f9ab354b1504fca, // 0.99966, 0.026075 + 0x3feffd886084cd0d, 0x3f992155f7a3667e, // 0.9997, 0.024541 + 0x3feffdd4dbf78f52, 0x3f978f535ddc9f03, // 0.99974, 0.023008 + 0x3feffe1c6870cb77, 0x3f95fd4d21fab226, // 0.99977, 0.021474 + 0x3feffe5f05e578db, 0x3f946b4381fce81c, // 0.9998, 0.01994 + 0x3feffe9cb44b51a1, 0x3f92d936bbe30efd, // 0.99983, 0.018407 + 0x3feffed57398d2b7, 0x3f9147270dad7132, // 0.99986, 0.016873 + 0x3fefff0943c53bd1, 0x3f8f6a296ab997ca, // 0.99988, 0.015339 + 0x3fefff3824c88f6f, 0x3f8c45ffe1e48ad9, // 0.9999, 0.013805 + 0x3fefff62169b92db, 0x3f8921d1fcdec784, // 0.99992, 0.012272 + 0x3fefff871937ce2f, 0x3f85fda037ac05e0, // 0.99994, 0.010738 + 0x3fefffa72c978c4f, 0x3f82d96b0e509703, // 0.99996, 0.0092038 + 0x3fefffc250b5daef, 0x3f7f6a65f9a2a3c5, // 0.99997, 0.0076698 + 0x3fefffd8858e8a92, 0x3f7921f0fe670071, // 0.99998, 0.0061359 + 0x3fefffe9cb1e2e8d, 0x3f72d97822f996bc, // 0.99999, 0.0046019 + 0x3feffff621621d02, 0x3f6921f8becca4ba, // 1, 0.003068 + 0x3feffffd88586ee6, 0x3f5921faaee6472d, // 1, 0.001534 + 0x3ff0000000000000, 0x0000000000000000, // 1, 0 + 0x3feffffd88586ee6, 0xbf5921faaee6472d, // 1, -0.001534 + 0x3feffff621621d02, 0xbf6921f8becca4ba, // 1, -0.003068 + 0x3fefffe9cb1e2e8d, 0xbf72d97822f996bc, // 0.99999,-0.0046019 + 0x3fefffd8858e8a92, 0xbf7921f0fe670071, // 0.99998,-0.0061359 + 0x3fefffc250b5daef, 0xbf7f6a65f9a2a3c5, // 0.99997,-0.0076698 + 0x3fefffa72c978c4f, 0xbf82d96b0e509703, // 0.99996,-0.0092038 + 0x3fefff871937ce2f, 0xbf85fda037ac05e0, // 0.99994, -0.010738 + 0x3fefff62169b92db, 0xbf8921d1fcdec784, // 0.99992, -0.012272 + 0x3fefff3824c88f6f, 0xbf8c45ffe1e48ad9, // 0.9999, -0.013805 + 0x3fefff0943c53bd1, 0xbf8f6a296ab997ca, // 0.99988, -0.015339 + 0x3feffed57398d2b7, 0xbf9147270dad7132, // 0.99986, -0.016873 + 0x3feffe9cb44b51a1, 0xbf92d936bbe30efd, // 0.99983, -0.018407 + 0x3feffe5f05e578db, 0xbf946b4381fce81c, // 0.9998, -0.01994 + 0x3feffe1c6870cb77, 0xbf95fd4d21fab226, // 0.99977, -0.021474 + 0x3feffdd4dbf78f52, 0xbf978f535ddc9f03, // 0.99974, -0.023008 + 0x3feffd886084cd0d, 0xbf992155f7a3667e, // 0.9997, -0.024541 + 0x3feffd36f624500c, 0xbf9ab354b1504fca, // 0.99966, -0.026075 + 0x3feffce09ce2a679, 0xbf9c454f4ce53b1c, // 0.99962, -0.027608 + 0x3feffc8554cd213a, 0xbf9dd7458c64ab39, // 0.99958, -0.029142 + 0x3feffc251df1d3f8, 0xbf9f693731d1cf01, // 0.99953, -0.030675 + 0x3feffbbff85f9515, 0xbfa07d91ff984580, // 0.99948, -0.032208 + 0x3feffb55e425fdae, 0xbfa14685db42c17e, // 0.99943, -0.033741 + 0x3feffae6e1556998, 0xbfa20f770ceb11c6, // 0.99938, -0.035274 + 0x3feffa72effef75d, 0xbfa2d865759455cd, // 0.99932, -0.036807 + 0x3feff9fa10348837, 0xbfa3a150f6421afc, // 0.99926, -0.03834 + 0x3feff97c4208c014, 0xbfa46a396ff86179, // 0.9992, -0.039873 + 0x3feff8f9858f058b, 0xbfa5331ec3bba0eb, // 0.99914, -0.041406 + 0x3feff871dadb81df, 0xbfa5fc00d290cd43, // 0.99908, -0.042938 + 0x3feff7e5420320f9, 0xbfa6c4df7d7d5b84, // 0.99901, -0.044471 + 0x3feff753bb1b9164, 0xbfa78dbaa5874685, // 0.99894, -0.046003 + 0x3feff6bd463b444d, 0xbfa856922bb513c1, // 0.99887, -0.047535 + 0x3feff621e3796d7e, 0xbfa91f65f10dd814, // 0.9988, -0.049068 + 0x3feff58192ee0358, 0xbfa9e835d6993c87, // 0.99872, -0.0506 + 0x3feff4dc54b1bed3, 0xbfaab101bd5f8317, // 0.99864, -0.052132 + 0x3feff43228de1b77, 0xbfab79c986698b78, // 0.99856, -0.053664 + 0x3feff3830f8d575c, 0xbfac428d12c0d7e3, // 0.99848, -0.055195 + 0x3feff2cf08da7321, 0xbfad0b4c436f91d0, // 0.99839, -0.056727 + 0x3feff21614e131ed, 0xbfadd406f9808ec8, // 0.9983, -0.058258 + 0x3feff15833be1965, 0xbfae9cbd15ff5527, // 0.99821, -0.05979 + 0x3feff095658e71ad, 0xbfaf656e79f820e0, // 0.99812, -0.061321 + 0x3fefefcdaa704562, 0xbfb0170d833bf421, // 0.99802, -0.062852 + 0x3fefef0102826191, 0xbfb07b614e463064, // 0.99793, -0.064383 + 0x3fefee2f6de455ba, 0xbfb0dfb28ea201e6, // 0.99783, -0.065913 + 0x3fefed58ecb673c4, 0xbfb1440134d709b2, // 0.99772, -0.067444 + 0x3fefec7d7f19cffc, 0xbfb1a84d316d4f8a, // 0.99762, -0.068974 + 0x3fefeb9d2530410f, 0xbfb20c9674ed444c, // 0.99751, -0.070505 + 0x3fefeab7df1c6005, 0xbfb270dcefdfc45b, // 0.9974, -0.072035 + 0x3fefe9cdad01883a, 0xbfb2d52092ce19f6, // 0.99729, -0.073565 + 0x3fefe8de8f03d75c, 0xbfb339614e41ffa5, // 0.99718, -0.075094 + 0x3fefe7ea85482d60, 0xbfb39d9f12c5a299, // 0.99706, -0.076624 + 0x3fefe6f18ff42c84, 0xbfb401d9d0e3a507, // 0.99694, -0.078153 + 0x3fefe5f3af2e3940, 0xbfb4661179272096, // 0.99682, -0.079682 + 0x3fefe4f0e31d7a4a, 0xbfb4ca45fc1ba8b6, // 0.9967, -0.081211 + 0x3fefe3e92be9d886, 0xbfb52e774a4d4d0a, // 0.99657, -0.08274 + 0x3fefe2dc89bbff08, 0xbfb592a554489bc8, // 0.99644, -0.084269 + 0x3fefe1cafcbd5b09, 0xbfb5f6d00a9aa419, // 0.99631, -0.085797 + 0x3fefe0b485181be3, 0xbfb65af75dd0f87b, // 0.99618, -0.087326 + 0x3fefdf9922f73307, 0xbfb6bf1b3e79b129, // 0.99604, -0.088854 + 0x3fefde78d68653fd, 0xbfb7233b9d236e71, // 0.99591, -0.090381 + 0x3fefdd539ff1f456, 0xbfb787586a5d5b21, // 0.99577, -0.091909 + 0x3fefdc297f674ba9, 0xbfb7eb7196b72ee4, // 0.99563, -0.093436 + 0x3fefdafa7514538c, 0xbfb84f8712c130a0, // 0.99548, -0.094963 + 0x3fefd9c68127c78c, 0xbfb8b398cf0c38e0, // 0.99533, -0.09649 + 0x3fefd88da3d12526, 0xbfb917a6bc29b42c, // 0.99518, -0.098017 + 0x3fefd74fdd40abbf, 0xbfb97bb0caaba56f, // 0.99503, -0.099544 + 0x3fefd60d2da75c9e, 0xbfb9dfb6eb24a85c, // 0.99488, -0.10107 + 0x3fefd4c59536fae4, 0xbfba43b90e27f3c4, // 0.99472, -0.1026 + 0x3fefd37914220b84, 0xbfbaa7b724495c04, // 0.99456, -0.10412 + 0x3fefd227aa9bd53b, 0xbfbb0bb11e1d5559, // 0.9944, -0.10565 + 0x3fefd0d158d86087, 0xbfbb6fa6ec38f64c, // 0.99424, -0.10717 + 0x3fefcf761f0c77a3, 0xbfbbd3987f31fa0e, // 0.99407, -0.1087 + 0x3fefce15fd6da67b, 0xbfbc3785c79ec2d5, // 0.99391, -0.11022 + 0x3fefccb0f4323aa3, 0xbfbc9b6eb6165c42, // 0.99374, -0.11175 + 0x3fefcb4703914354, 0xbfbcff533b307dc1, // 0.99356, -0.11327 + 0x3fefc9d82bc2915e, 0xbfbd633347858ce4, // 0.99339, -0.11479 + 0x3fefc8646cfeb721, 0xbfbdc70ecbae9fc8, // 0.99321, -0.11632 + 0x3fefc6ebc77f0887, 0xbfbe2ae5b8457f77, // 0.99303, -0.11784 + 0x3fefc56e3b7d9af6, 0xbfbe8eb7fde4aa3e, // 0.99285, -0.11937 + 0x3fefc3ebc935454c, 0xbfbef2858d27561b, // 0.99267, -0.12089 + 0x3fefc26470e19fd3, 0xbfbf564e56a9730e, // 0.99248, -0.12241 + 0x3fefc0d832bf043a, 0xbfbfba124b07ad85, // 0.99229, -0.12393 + 0x3fefbf470f0a8d88, 0xbfc00ee8ad6fb85b, // 0.9921, -0.12545 + 0x3fefbdb106021816, 0xbfc040c5bb67747e, // 0.99191, -0.12698 + 0x3fefbc1617e44186, 0xbfc072a047ba831d, // 0.99171, -0.1285 + 0x3fefba7644f068b5, 0xbfc0a4784ab8bf1d, // 0.99151, -0.13002 + 0x3fefb8d18d66adb7, 0xbfc0d64dbcb26786, // 0.99131, -0.13154 + 0x3fefb727f187f1c7, 0xbfc1082095f820b0, // 0.99111, -0.13306 + 0x3fefb5797195d741, 0xbfc139f0cedaf576, // 0.9909, -0.13458 + 0x3fefb3c60dd2c199, 0xbfc16bbe5fac5865, // 0.9907, -0.1361 + 0x3fefb20dc681d54d, 0xbfc19d8940be24e7, // 0.99049, -0.13762 + 0x3fefb0509be6f7db, 0xbfc1cf516a62a077, // 0.99027, -0.13914 + 0x3fefae8e8e46cfbb, 0xbfc20116d4ec7bce, // 0.99006, -0.14066 + 0x3fefacc79de6c44f, 0xbfc232d978aed413, // 0.98984, -0.14218 + 0x3fefaafbcb0cfddc, 0xbfc264994dfd340a, // 0.98962, -0.1437 + 0x3fefa92b1600657c, 0xbfc296564d2b953e, // 0.9894, -0.14521 + 0x3fefa7557f08a517, 0xbfc2c8106e8e613a, // 0.98918, -0.14673 + 0x3fefa57b066e2754, 0xbfc2f9c7aa7a72af, // 0.98895, -0.14825 + 0x3fefa39bac7a1791, 0xbfc32b7bf94516a7, // 0.98872, -0.14976 + 0x3fefa1b7717661d5, 0xbfc35d2d53440db2, // 0.98849, -0.15128 + 0x3fef9fce55adb2c8, 0xbfc38edbb0cd8d14, // 0.98826, -0.1528 + 0x3fef9de0596b77a3, 0xbfc3c0870a383ff6, // 0.98802, -0.15431 + 0x3fef9bed7cfbde29, 0xbfc3f22f57db4893, // 0.98778, -0.15583 + 0x3fef99f5c0abd496, 0xbfc423d4920e4166, // 0.98754, -0.15734 + 0x3fef97f924c9099b, 0xbfc45576b1293e5a, // 0.9873, -0.15886 + 0x3fef95f7a9a1ec47, 0xbfc48715ad84cdf5, // 0.98706, -0.16037 + 0x3fef93f14f85ac08, 0xbfc4b8b17f79fa88, // 0.98681, -0.16189 + 0x3fef91e616c43891, 0xbfc4ea4a1f624b61, // 0.98656, -0.1634 + 0x3fef8fd5ffae41db, 0xbfc51bdf8597c5f2, // 0.98631, -0.16491 + 0x3fef8dc10a95380d, 0xbfc54d71aa74ef02, // 0.98605, -0.16643 + 0x3fef8ba737cb4b78, 0xbfc57f008654cbde, // 0.9858, -0.16794 + 0x3fef898887a36c84, 0xbfc5b08c1192e381, // 0.98554, -0.16945 + 0x3fef8764fa714ba9, 0xbfc5e214448b3fc6, // 0.98528, -0.17096 + 0x3fef853c9089595e, 0xbfc61399179a6e94, // 0.98501, -0.17247 + 0x3fef830f4a40c60c, 0xbfc6451a831d830d, // 0.98475, -0.17398 + 0x3fef80dd27ed8204, 0xbfc676987f7216b8, // 0.98448, -0.17549 + 0x3fef7ea629e63d6e, 0xbfc6a81304f64ab2, // 0.98421, -0.177 + 0x3fef7c6a50826840, 0xbfc6d98a0c08c8da, // 0.98394, -0.17851 + 0x3fef7a299c1a322a, 0xbfc70afd8d08c4ff, // 0.98366, -0.18002 + 0x3fef77e40d068a90, 0xbfc73c6d8055fe0a, // 0.98339, -0.18153 + 0x3fef7599a3a12077, 0xbfc76dd9de50bf31, // 0.98311, -0.18304 + 0x3fef734a60446279, 0xbfc79f429f59e11d, // 0.98282, -0.18455 + 0x3fef70f6434b7eb7, 0xbfc7d0a7bbd2cb1b, // 0.98254, -0.18606 + 0x3fef6e9d4d1262ca, 0xbfc802092c1d744b, // 0.98225, -0.18756 + 0x3fef6c3f7df5bbb7, 0xbfc83366e89c64c5, // 0.98196, -0.18907 + 0x3fef69dcd652f5de, 0xbfc864c0e9b2b6cf, // 0.98167, -0.19057 + 0x3fef677556883cee, 0xbfc8961727c41804, // 0.98138, -0.19208 + 0x3fef6508fef47bd5, 0xbfc8c7699b34ca7e, // 0.98108, -0.19359 + 0x3fef6297cff75cb0, 0xbfc8f8b83c69a60a, // 0.98079, -0.19509 + 0x3fef6021c9f148c2, 0xbfc92a0303c8194f, // 0.98048, -0.19659 + 0x3fef5da6ed43685d, 0xbfc95b49e9b62af9, // 0.98018, -0.1981 + 0x3fef5b273a4fa2d9, 0xbfc98c8ce69a7aec, // 0.97988, -0.1996 + 0x3fef58a2b1789e84, 0xbfc9bdcbf2dc4366, // 0.97957, -0.2011 + 0x3fef56195321c090, 0xbfc9ef0706e35a35, // 0.97926, -0.20261 + 0x3fef538b1faf2d07, 0xbfca203e1b1831da, // 0.97895, -0.20411 + 0x3fef50f81785c6b9, 0xbfca517127e3dabc, // 0.97863, -0.20561 + 0x3fef4e603b0b2f2d, 0xbfca82a025b00451, // 0.97832, -0.20711 + 0x3fef4bc38aa5c694, 0xbfcab3cb0ce6fe44, // 0.978, -0.20861 + 0x3fef492206bcabb4, 0xbfcae4f1d5f3b9ab, // 0.97768, -0.21011 + 0x3fef467bafb7bbe0, 0xbfcb16147941ca2a, // 0.97735, -0.21161 + 0x3fef43d085ff92dd, 0xbfcb4732ef3d6722, // 0.97703, -0.21311 + 0x3fef412089fd8adc, 0xbfcb784d30536cda, // 0.9767, -0.21461 + 0x3fef3e6bbc1bbc65, 0xbfcba96334f15dad, // 0.97637, -0.21611 + 0x3fef3bb21cc4fe47, 0xbfcbda74f5856330, // 0.97604, -0.2176 + 0x3fef38f3ac64e589, 0xbfcc0b826a7e4f63, // 0.9757, -0.2191 + 0x3fef36306b67c556, 0xbfcc3c8b8c4b9dd7, // 0.97536, -0.2206 + 0x3fef33685a3aaef0, 0xbfcc6d90535d74dc, // 0.97503, -0.22209 + 0x3fef309b794b719f, 0xbfcc9e90b824a6a9, // 0.97468, -0.22359 + 0x3fef2dc9c9089a9d, 0xbfcccf8cb312b286, // 0.97434, -0.22508 + 0x3fef2af349e17507, 0xbfcd00843c99c5f9, // 0.97399, -0.22658 + 0x3fef2817fc4609ce, 0xbfcd31774d2cbdee, // 0.97364, -0.22807 + 0x3fef2537e0a71f9f, 0xbfcd6265dd3f27e3, // 0.97329, -0.22957 + 0x3fef2252f7763ada, 0xbfcd934fe5454311, // 0.97294, -0.23106 + 0x3fef1f6941259d7a, 0xbfcdc4355db40195, // 0.97258, -0.23255 + 0x3fef1c7abe284708, 0xbfcdf5163f01099a, // 0.97223, -0.23404 + 0x3fef19876ef1f486, 0xbfce25f281a2b684, // 0.97187, -0.23553 + 0x3fef168f53f7205d, 0xbfce56ca1e101a1b, // 0.9715, -0.23702 + 0x3fef13926dad024e, 0xbfce879d0cc0fdaf, // 0.97114, -0.23851 + 0x3fef1090bc898f5f, 0xbfceb86b462de348, // 0.97077, -0.24 + 0x3fef0d8a410379c5, 0xbfcee934c2d006c7, // 0.9704, -0.24149 + 0x3fef0a7efb9230d7, 0xbfcf19f97b215f1a, // 0.97003, -0.24298 + 0x3fef076eecade0fa, 0xbfcf4ab9679c9f5c, // 0.96966, -0.24447 + 0x3fef045a14cf738c, 0xbfcf7b7480bd3801, // 0.96928, -0.24596 + 0x3fef014074708ed3, 0xbfcfac2abeff57ff, // 0.9689, -0.24744 + 0x3feefe220c0b95ec, 0xbfcfdcdc1adfedf8, // 0.96852, -0.24893 + 0x3feefafedc1ba8b7, 0xbfd006c4466e54af, // 0.96814, -0.25041 + 0x3feef7d6e51ca3c0, 0xbfd01f1806b9fdd2, // 0.96775, -0.2519 + 0x3feef4aa278b2032, 0xbfd037694a928cac, // 0.96737, -0.25338 + 0x3feef178a3e473c2, 0xbfd04fb80e37fdae, // 0.96698, -0.25487 + 0x3feeee425aa6b09a, 0xbfd068044deab002, // 0.96658, -0.25635 + 0x3feeeb074c50a544, 0xbfd0804e05eb661e, // 0.96619, -0.25783 + 0x3feee7c77961dc9e, 0xbfd09895327b465e, // 0.96579, -0.25931 + 0x3feee482e25a9dbc, 0xbfd0b0d9cfdbdb90, // 0.96539, -0.26079 + 0x3feee13987bbebdc, 0xbfd0c91bda4f158d, // 0.96499, -0.26227 + 0x3feeddeb6a078651, 0xbfd0e15b4e1749cd, // 0.96459, -0.26375 + 0x3feeda9889bfe86a, 0xbfd0f998277733f7, // 0.96418, -0.26523 + 0x3feed740e7684963, 0xbfd111d262b1f677, // 0.96378, -0.26671 + 0x3feed3e483849c51, 0xbfd12a09fc0b1b12, // 0.96337, -0.26819 + 0x3feed0835e999009, 0xbfd1423eefc69378, // 0.96295, -0.26967 + 0x3feecd1d792c8f10, 0xbfd15a713a28b9d9, // 0.96254, -0.27115 + 0x3feec9b2d3c3bf84, 0xbfd172a0d7765177, // 0.96212, -0.27262 + 0x3feec6436ee60309, 0xbfd18acdc3f4873a, // 0.9617, -0.2741 + 0x3feec2cf4b1af6b2, 0xbfd1a2f7fbe8f243, // 0.96128, -0.27557 + 0x3feebf5668eaf2ef, 0xbfd1bb1f7b999480, // 0.96086, -0.27705 + 0x3feebbd8c8df0b74, 0xbfd1d3443f4cdb3d, // 0.96043, -0.27852 + 0x3feeb8566b810f2a, 0xbfd1eb6643499fbb, // 0.96, -0.27999 + 0x3feeb4cf515b8811, 0xbfd2038583d727bd, // 0.95957, -0.28146 + 0x3feeb1437af9bb34, 0xbfd21ba1fd3d2623, // 0.95914, -0.28294 + 0x3feeadb2e8e7a88e, 0xbfd233bbabc3bb72, // 0.9587, -0.28441 + 0x3feeaa1d9bb20af3, 0xbfd24bd28bb37672, // 0.95827, -0.28588 + 0x3feea68393e65800, 0xbfd263e6995554ba, // 0.95783, -0.28735 + 0x3feea2e4d212c000, 0xbfd27bf7d0f2c346, // 0.95738, -0.28882 + 0x3fee9f4156c62dda, 0xbfd294062ed59f05, // 0.95694, -0.29028 + 0x3fee9b99229046f8, 0xbfd2ac11af483572, // 0.95649, -0.29175 + 0x3fee97ec36016b30, 0xbfd2c41a4e954520, // 0.95605, -0.29322 + 0x3fee943a91aab4b4, 0xbfd2dc200907fe51, // 0.95559, -0.29469 + 0x3fee9084361df7f3, 0xbfd2f422daec0386, // 0.95514, -0.29615 + 0x3fee8cc923edc388, 0xbfd30c22c08d6a13, // 0.95469, -0.29762 + 0x3fee89095bad6025, 0xbfd3241fb638baaf, // 0.95423, -0.29908 + 0x3fee8544ddf0d075, 0xbfd33c19b83af207, // 0.95377, -0.30054 + 0x3fee817bab4cd10d, 0xbfd35410c2e18152, // 0.95331, -0.30201 + 0x3fee7dadc456d850, 0xbfd36c04d27a4edf, // 0.95284, -0.30347 + 0x3fee79db29a5165a, 0xbfd383f5e353b6aa, // 0.95238, -0.30493 + 0x3fee7603dbce74e9, 0xbfd39be3f1bc8aef, // 0.95191, -0.30639 + 0x3fee7227db6a9744, 0xbfd3b3cefa0414b7, // 0.95144, -0.30785 + 0x3fee6e472911da27, 0xbfd3cbb6f87a146e, // 0.95096, -0.30931 + 0x3fee6a61c55d53a7, 0xbfd3e39be96ec271, // 0.95049, -0.31077 + 0x3fee6677b0e6d31e, 0xbfd3fb7dc932cfa4, // 0.95001, -0.31222 + 0x3fee6288ec48e112, 0xbfd4135c94176602, // 0.94953, -0.31368 + 0x3fee5e95781ebf1c, 0xbfd42b38466e2928, // 0.94905, -0.31514 + 0x3fee5a9d550467d3, 0xbfd44310dc8936f0, // 0.94856, -0.31659 + 0x3fee56a083968eb1, 0xbfd45ae652bb2800, // 0.94807, -0.31805 + 0x3fee529f04729ffc, 0xbfd472b8a5571054, // 0.94759, -0.3195 + 0x3fee4e98d836c0af, 0xbfd48a87d0b07fd7, // 0.94709, -0.32096 + 0x3fee4a8dff81ce5e, 0xbfd4a253d11b82f3, // 0.9466, -0.32241 + 0x3fee467e7af35f23, 0xbfd4ba1ca2eca31c, // 0.94611, -0.32386 + 0x3fee426a4b2bc17e, 0xbfd4d1e24278e76a, // 0.94561, -0.32531 + 0x3fee3e5170cbfc46, 0xbfd4e9a4ac15d520, // 0.94511, -0.32676 + 0x3fee3a33ec75ce85, 0xbfd50163dc197047, // 0.9446, -0.32821 + 0x3fee3611becbaf69, 0xbfd5191fceda3c35, // 0.9441, -0.32966 + 0x3fee31eae870ce25, 0xbfd530d880af3c24, // 0.94359, -0.33111 + 0x3fee2dbf6a0911d9, 0xbfd5488dedeff3be, // 0.94308, -0.33255 + 0x3fee298f4439197a, 0xbfd5604012f467b4, // 0.94257, -0.334 + 0x3fee255a77a63bb8, 0xbfd577eeec151e47, // 0.94206, -0.33545 + 0x3fee212104f686e5, 0xbfd58f9a75ab1fdd, // 0.94154, -0.33689 + 0x3fee1ce2ecd0c0d8, 0xbfd5a742ac0ff78d, // 0.94103, -0.33833 + 0x3fee18a02fdc66d9, 0xbfd5bee78b9db3b6, // 0.94051, -0.33978 + 0x3fee1458cec1ad83, 0xbfd5d68910aee686, // 0.93998, -0.34122 + 0x3fee100cca2980ac, 0xbfd5ee27379ea693, // 0.93946, -0.34266 + 0x3fee0bbc22bd8349, 0xbfd605c1fcc88f63, // 0.93893, -0.3441 + 0x3fee0766d9280f54, 0xbfd61d595c88c203, // 0.9384, -0.34554 + 0x3fee030cee1435b8, 0xbfd634ed533be58e, // 0.93787, -0.34698 + 0x3fedfeae622dbe2b, 0xbfd64c7ddd3f27c6, // 0.93734, -0.34842 + 0x3fedfa4b3621271d, 0xbfd6640af6f03d9e, // 0.9368, -0.34986 + 0x3fedf5e36a9ba59c, 0xbfd67b949cad63ca, // 0.93627, -0.35129 + 0x3fedf177004b2534, 0xbfd6931acad55f51, // 0.93573, -0.35273 + 0x3feded05f7de47da, 0xbfd6aa9d7dc77e16, // 0.93518, -0.35416 + 0x3fede890520465ce, 0xbfd6c21cb1e39771, // 0.93464, -0.3556 + 0x3fede4160f6d8d81, 0xbfd6d998638a0cb5, // 0.93409, -0.35703 + 0x3feddf9730ca837b, 0xbfd6f1108f1bc9c5, // 0.93354, -0.35846 + 0x3feddb13b6ccc23d, 0xbfd7088530fa459e, // 0.93299, -0.3599 + 0x3fedd68ba2267a25, 0xbfd71ff6458782ec, // 0.93244, -0.36133 + 0x3fedd1fef38a915a, 0xbfd73763c9261092, // 0.93188, -0.36276 + 0x3fedcd6dabaca3a5, 0xbfd74ecdb8390a3e, // 0.93133, -0.36418 + 0x3fedc8d7cb410260, 0xbfd766340f2418f6, // 0.93077, -0.36561 + 0x3fedc43d52fcb453, 0xbfd77d96ca4b73a6, // 0.93021, -0.36704 + 0x3fedbf9e4395759a, 0xbfd794f5e613dfae, // 0.92964, -0.36847 + 0x3fedbafa9dc1b78d, 0xbfd7ac515ee2b172, // 0.92907, -0.36989 + 0x3fedb6526238a09b, 0xbfd7c3a9311dcce7, // 0.92851, -0.37132 + 0x3fedb1a591b20c38, 0xbfd7dafd592ba621, // 0.92794, -0.37274 + 0x3fedacf42ce68ab9, 0xbfd7f24dd37341e3, // 0.92736, -0.37416 + 0x3feda83e348f613b, 0xbfd8099a9c5c362d, // 0.92679, -0.37559 + 0x3feda383a9668988, 0xbfd820e3b04eaac4, // 0.92621, -0.37701 + 0x3fed9ec48c26b1f3, 0xbfd838290bb359c8, // 0.92563, -0.37843 + 0x3fed9a00dd8b3d46, 0xbfd84f6aaaf3903f, // 0.92505, -0.37985 + 0x3fed95389e50429b, 0xbfd866a88a792ea0, // 0.92447, -0.38127 + 0x3fed906bcf328d46, 0xbfd87de2a6aea963, // 0.92388, -0.38268 + 0x3fed8b9a70ef9cb4, 0xbfd89518fbff098e, // 0.92329, -0.3841 + 0x3fed86c48445a450, 0xbfd8ac4b86d5ed44, // 0.9227, -0.38552 + 0x3fed81ea09f38b63, 0xbfd8c37a439f884f, // 0.92211, -0.38693 + 0x3fed7d0b02b8ecf9, 0xbfd8daa52ec8a4af, // 0.92151, -0.38835 + 0x3fed78276f5617c6, 0xbfd8f1cc44bea329, // 0.92092, -0.38976 + 0x3fed733f508c0dff, 0xbfd908ef81ef7bd1, // 0.92032, -0.39117 + 0x3fed6e52a71c8547, 0xbfd9200ee2c9be97, // 0.91972, -0.39258 + 0x3fed696173c9e68b, 0xbfd9372a63bc93d7, // 0.91911, -0.39399 + 0x3fed646bb7574de5, 0xbfd94e420137bce3, // 0.91851, -0.3954 + 0x3fed5f7172888a7f, 0xbfd96555b7ab948f, // 0.9179, -0.39681 + 0x3fed5a72a6221e73, 0xbfd97c6583890fc2, // 0.91729, -0.39822 + 0x3fed556f52e93eb1, 0xbfd993716141bdfe, // 0.91668, -0.39962 + 0x3fed506779a3d2d9, 0xbfd9aa794d47c9ee, // 0.91606, -0.40103 + 0x3fed4b5b1b187524, 0xbfd9c17d440df9f2, // 0.91545, -0.40243 + 0x3fed464a380e7242, 0xbfd9d87d4207b0ab, // 0.91483, -0.40384 + 0x3fed4134d14dc93a, 0xbfd9ef7943a8ed8a, // 0.91421, -0.40524 + 0x3fed3c1ae79f2b4e, 0xbfda067145664d57, // 0.91359, -0.40664 + 0x3fed36fc7bcbfbdc, 0xbfda1d6543b50ac0, // 0.91296, -0.40804 + 0x3fed31d98e9e503a, 0xbfda34553b0afee5, // 0.91234, -0.40944 + 0x3fed2cb220e0ef9f, 0xbfda4b4127dea1e4, // 0.91171, -0.41084 + 0x3fed2786335f52fc, 0xbfda622906a70b63, // 0.91107, -0.41224 + 0x3fed2255c6e5a4e1, 0xbfda790cd3dbf31a, // 0.91044, -0.41364 + 0x3fed1d20dc40c15c, 0xbfda8fec8bf5b166, // 0.90981, -0.41503 + 0x3fed17e7743e35dc, 0xbfdaa6c82b6d3fc9, // 0.90917, -0.41643 + 0x3fed12a98fac410c, 0xbfdabd9faebc3980, // 0.90853, -0.41782 + 0x3fed0d672f59d2b9, 0xbfdad473125cdc08, // 0.90789, -0.41922 + 0x3fed082054168bac, 0xbfdaeb4252ca07ab, // 0.90724, -0.42061 + 0x3fed02d4feb2bd92, 0xbfdb020d6c7f4009, // 0.9066, -0.422 + 0x3fecfd852fff6ad4, 0xbfdb18d45bf8aca6, // 0.90595, -0.42339 + 0x3fecf830e8ce467b, 0xbfdb2f971db31972, // 0.9053, -0.42478 + 0x3fecf2d829f1b40e, 0xbfdb4655ae2bf757, // 0.90464, -0.42617 + 0x3feced7af43cc773, 0xbfdb5d1009e15cc0, // 0.90399, -0.42756 + 0x3fece819488344ce, 0xbfdb73c62d520624, // 0.90333, -0.42894 + 0x3fece2b32799a060, 0xbfdb8a7814fd5693, // 0.90267, -0.43033 + 0x3fecdd489254fe65, 0xbfdba125bd63583e, // 0.90201, -0.43171 + 0x3fecd7d9898b32f6, 0xbfdbb7cf2304bd01, // 0.90135, -0.43309 + 0x3fecd2660e12c1e6, 0xbfdbce744262deee, // 0.90068, -0.43448 + 0x3fecccee20c2de9f, 0xbfdbe51517ffc0d9, // 0.90002, -0.43586 + 0x3fecc771c2736c09, 0xbfdbfbb1a05e0edc, // 0.89935, -0.43724 + 0x3fecc1f0f3fcfc5c, 0xbfdc1249d8011ee7, // 0.89867, -0.43862 + 0x3fecbc6bb638d10b, 0xbfdc28ddbb6cf145, // 0.898, -0.43999 + 0x3fecb6e20a00da99, 0xbfdc3f6d47263129, // 0.89732, -0.44137 + 0x3fecb153f02fb87d, 0xbfdc55f877b23537, // 0.89665, -0.44275 + 0x3fecabc169a0b901, 0xbfdc6c7f4997000a, // 0.89597, -0.44412 + 0x3feca62a772fd919, 0xbfdc8301b95b40c2, // 0.89528, -0.4455 + 0x3feca08f19b9c449, 0xbfdc997fc3865388, // 0.8946, -0.44687 + 0x3fec9aef521bd480, 0xbfdcaff964a0421d, // 0.89391, -0.44824 + 0x3fec954b213411f5, 0xbfdcc66e9931c45d, // 0.89322, -0.44961 + 0x3fec8fa287e13305, 0xbfdcdcdf5dc440ce, // 0.89253, -0.45098 + 0x3fec89f587029c13, 0xbfdcf34baee1cd21, // 0.89184, -0.45235 + 0x3fec84441f785f61, 0xbfdd09b389152ec1, // 0.89115, -0.45372 + 0x3fec7e8e52233cf3, 0xbfdd2016e8e9db5b, // 0.89045, -0.45508 + 0x3fec78d41fe4a267, 0xbfdd3675caebf962, // 0.88975, -0.45645 + 0x3fec7315899eaad7, 0xbfdd4cd02ba8609c, // 0.88905, -0.45781 + 0x3fec6d5290341eb2, 0xbfdd632607ac9aa9, // 0.88835, -0.45918 + 0x3fec678b3488739b, 0xbfdd79775b86e389, // 0.88764, -0.46054 + 0x3fec61bf777fcc48, 0xbfdd8fc423c62a25, // 0.88693, -0.4619 + 0x3fec5bef59fef85a, 0xbfdda60c5cfa10d8, // 0.88622, -0.46326 + 0x3fec561adceb743e, 0xbfddbc5003b2edf8, // 0.88551, -0.46462 + 0x3fec5042012b6907, 0xbfddd28f1481cc58, // 0.8848, -0.46598 + 0x3fec4a64c7a5ac4c, 0xbfdde8c98bf86bd6, // 0.88408, -0.46733 + 0x3fec44833141c004, 0xbfddfeff66a941de, // 0.88336, -0.46869 + 0x3fec3e9d3ee7d262, 0xbfde1530a12779f4, // 0.88264, -0.47004 + 0x3fec38b2f180bdb1, 0xbfde2b5d3806f63b, // 0.88192, -0.4714 + 0x3fec32c449f60831, 0xbfde418527dc4ffa, // 0.8812, -0.47275 + 0x3fec2cd14931e3f1, 0xbfde57a86d3cd824, // 0.88047, -0.4741 + 0x3fec26d9f01f2eaf, 0xbfde6dc704be97e2, // 0.87974, -0.47545 + 0x3fec20de3fa971b0, 0xbfde83e0eaf85113, // 0.87901, -0.4768 + 0x3fec1ade38bce19b, 0xbfde99f61c817eda, // 0.87828, -0.47815 + 0x3fec14d9dc465e58, 0xbfdeb00695f25620, // 0.87755, -0.47949 + 0x3fec0ed12b3372e9, 0xbfdec61253e3c61b, // 0.87681, -0.48084 + 0x3fec08c426725549, 0xbfdedc1952ef78d5, // 0.87607, -0.48218 + 0x3fec02b2cef1e641, 0xbfdef21b8fafd3b5, // 0.87533, -0.48353 + 0x3febfc9d25a1b147, 0xbfdf081906bff7fd, // 0.87459, -0.48487 + 0x3febf6832b71ec5b, 0xbfdf1e11b4bbc35c, // 0.87384, -0.48621 + 0x3febf064e15377dd, 0xbfdf3405963fd068, // 0.87309, -0.48755 + 0x3febea424837de6d, 0xbfdf49f4a7e97729, // 0.87235, -0.48889 + 0x3febe41b611154c1, 0xbfdf5fdee656cda3, // 0.8716, -0.49023 + 0x3febddf02cd2b983, 0xbfdf75c44e26a852, // 0.87084, -0.49156 + 0x3febd7c0ac6f952a, 0xbfdf8ba4dbf89aba, // 0.87009, -0.4929 + 0x3febd18ce0dc19d6, 0xbfdfa1808c6cf7e0, // 0.86933, -0.49423 + 0x3febcb54cb0d2327, 0xbfdfb7575c24d2de, // 0.86857, -0.49557 + 0x3febc5186bf8361d, 0xbfdfcd2947c1ff57, // 0.86781, -0.4969 + 0x3febbed7c49380ea, 0xbfdfe2f64be7120f, // 0.86705, -0.49823 + 0x3febb892d5d5dad5, 0xbfdff8be6537615e, // 0.86628, -0.49956 + 0x3febb249a0b6c40d, 0xbfe00740c82b82e0, // 0.86551, -0.50089 + 0x3febabfc262e6586, 0xbfe0121fe4f56d2c, // 0.86474, -0.50221 + 0x3feba5aa673590d2, 0xbfe01cfc874c3eb7, // 0.86397, -0.50354 + 0x3feb9f5464c5bffc, 0xbfe027d6ad83287e, // 0.8632, -0.50486 + 0x3feb98fa1fd9155e, 0xbfe032ae55edbd95, // 0.86242, -0.50619 + 0x3feb929b996a5b7f, 0xbfe03d837edff370, // 0.86165, -0.50751 + 0x3feb8c38d27504e9, 0xbfe0485626ae221a, // 0.86087, -0.50883 + 0x3feb85d1cbf52c02, 0xbfe053264bad0483, // 0.86009, -0.51015 + 0x3feb7f6686e792ea, 0xbfe05df3ec31b8b6, // 0.8593, -0.51147 + 0x3feb78f70449a34b, 0xbfe068bf0691c028, // 0.85852, -0.51279 + 0x3feb728345196e3e, 0xbfe073879922ffed, // 0.85773, -0.5141 + 0x3feb6c0b4a55ac17, 0xbfe07e4da23bc102, // 0.85694, -0.51542 + 0x3feb658f14fdbc47, 0xbfe089112032b08c, // 0.85615, -0.51673 + 0x3feb5f0ea611a532, 0xbfe093d2115ee018, // 0.85535, -0.51804 + 0x3feb5889fe921405, 0xbfe09e907417c5e1, // 0.85456, -0.51936 + 0x3feb52011f805c92, 0xbfe0a94c46b53d0b, // 0.85376, -0.52067 + 0x3feb4b7409de7925, 0xbfe0b405878f85ec, // 0.85296, -0.52198 + 0x3feb44e2beaf0a61, 0xbfe0bebc34ff4646, // 0.85216, -0.52328 + 0x3feb3e4d3ef55712, 0xbfe0c9704d5d898f, // 0.85136, -0.52459 + 0x3feb37b38bb54c09, 0xbfe0d421cf03c12b, // 0.85055, -0.5259 + 0x3feb3115a5f37bf4, 0xbfe0ded0b84bc4b5, // 0.84974, -0.5272 + 0x3feb2a738eb51f33, 0xbfe0e97d078fd23b, // 0.84893, -0.5285 + 0x3feb23cd470013b4, 0xbfe0f426bb2a8e7d, // 0.84812, -0.5298 + 0x3feb1d22cfdadcc6, 0xbfe0fecdd1770537, // 0.84731, -0.5311 + 0x3feb16742a4ca2f5, 0xbfe1097248d0a956, // 0.84649, -0.5324 + 0x3feb0fc1575d33db, 0xbfe114141f935545, // 0.84567, -0.5337 + 0x3feb090a58150200, 0xbfe11eb3541b4b22, // 0.84485, -0.535 + 0x3feb024f2d7d24a9, 0xbfe1294fe4c5350a, // 0.84403, -0.53629 + 0x3feafb8fd89f57b6, 0xbfe133e9cfee254e, // 0.84321, -0.53759 + 0x3feaf4cc5a85fb73, 0xbfe13e8113f396c1, // 0.84238, -0.53888 + 0x3feaee04b43c1474, 0xbfe14915af336ceb, // 0.84155, -0.54017 + 0x3feae738e6cd4b67, 0xbfe153a7a00bf453, // 0.84073, -0.54146 + 0x3feae068f345ecef, 0xbfe15e36e4dbe2bc, // 0.83989, -0.54275 + 0x3fead994dab2e979, 0xbfe168c37c025764, // 0.83906, -0.54404 + 0x3fead2bc9e21d511, 0xbfe1734d63dedb49, // 0.83822, -0.54532 + 0x3feacbe03ea0e73b, 0xbfe17dd49ad16161, // 0.83739, -0.54661 + 0x3feac4ffbd3efac8, 0xbfe188591f3a46e5, // 0.83655, -0.54789 + 0x3feabe1b1b0b8dac, 0xbfe192daef7a5386, // 0.83571, -0.54918 + 0x3feab7325916c0d4, 0xbfe19d5a09f2b9b8, // 0.83486, -0.55046 + 0x3feab045787157ff, 0xbfe1a7d66d0516e6, // 0.83402, -0.55174 + 0x3feaa9547a2cb98e, 0xbfe1b250171373be, // 0.83317, -0.55302 + 0x3feaa25f5f5aee60, 0xbfe1bcc706804467, // 0.83232, -0.55429 + 0x3fea9b66290ea1a3, 0xbfe1c73b39ae68c8, // 0.83147, -0.55557 + 0x3fea9468d85b20ae, 0xbfe1d1acaf012cc2, // 0.83062, -0.55685 + 0x3fea8d676e545ad2, 0xbfe1dc1b64dc4872, // 0.82976, -0.55812 + 0x3fea8661ec0ee133, 0xbfe1e68759a3e074, // 0.8289, -0.55939 + 0x3fea7f58529fe69d, 0xbfe1f0f08bbc861b, // 0.82805, -0.56066 + 0x3fea784aa31d3f55, 0xbfe1fb56f98b37b8, // 0.82718, -0.56193 + 0x3fea7138de9d60f5, 0xbfe205baa17560d6, // 0.82632, -0.5632 + 0x3fea6a230637623b, 0xbfe2101b81e0da78, // 0.82546, -0.56447 + 0x3fea63091b02fae2, 0xbfe21a799933eb58, // 0.82459, -0.56573 + 0x3fea5beb1e188375, 0xbfe224d4e5d5482e, // 0.82372, -0.567 + 0x3fea54c91090f524, 0xbfe22f2d662c13e1, // 0.82285, -0.56826 + 0x3fea4da2f385e997, 0xbfe23983189fdfd5, // 0.82198, -0.56952 + 0x3fea4678c8119ac8, 0xbfe243d5fb98ac1f, // 0.8211, -0.57078 + 0x3fea3f4a8f4ee2d2, 0xbfe24e260d7ee7c9, // 0.82023, -0.57204 + 0x3fea38184a593bc6, 0xbfe258734cbb7110, // 0.81935, -0.5733 + 0x3fea30e1fa4cbf81, 0xbfe262bdb7b795a2, // 0.81847, -0.57455 + 0x3fea29a7a0462782, 0xbfe26d054cdd12df, // 0.81758, -0.57581 + 0x3fea22693d62ccb9, 0xbfe2774a0a961612, // 0.8167, -0.57706 + 0x3fea1b26d2c0a75e, 0xbfe2818bef4d3cba, // 0.81581, -0.57831 + 0x3fea13e0617e4ec7, 0xbfe28bcaf96d94ba, // 0.81493, -0.57956 + 0x3fea0c95eabaf937, 0xbfe2960727629ca8, // 0.81404, -0.58081 + 0x3fea05476f967bb5, 0xbfe2a040779843fb, // 0.81314, -0.58206 + 0x3fe9fdf4f13149de, 0xbfe2aa76e87aeb58, // 0.81225, -0.58331 + 0x3fe9f69e70ac75bc, 0xbfe2b4aa787764c4, // 0.81135, -0.58455 + 0x3fe9ef43ef29af94, 0xbfe2bedb25faf3ea, // 0.81046, -0.5858 + 0x3fe9e7e56dcb45bd, 0xbfe2c908ef734e57, // 0.80956, -0.58704 + 0x3fe9e082edb42472, 0xbfe2d333d34e9bb7, // 0.80866, -0.58828 + 0x3fe9d91c7007d5a6, 0xbfe2dd5bcffb7616, // 0.80775, -0.58952 + 0x3fe9d1b1f5ea80d6, 0xbfe2e780e3e8ea16, // 0.80685, -0.59076 + 0x3fe9ca438080eadb, 0xbfe2f1a30d86773a, // 0.80594, -0.592 + 0x3fe9c2d110f075c3, 0xbfe2fbc24b441015, // 0.80503, -0.59323 + 0x3fe9bb5aa85f2098, 0xbfe305de9b921a94, // 0.80412, -0.59447 + 0x3fe9b3e047f38741, 0xbfe30ff7fce17035, // 0.80321, -0.5957 + 0x3fe9ac61f0d4e247, 0xbfe31a0e6da35e44, // 0.80229, -0.59693 + 0x3fe9a4dfa42b06b2, 0xbfe32421ec49a620, // 0.80138, -0.59816 + 0x3fe99d59631e65d5, 0xbfe32e3277467d6b, // 0.80046, -0.59939 + 0x3fe995cf2ed80d22, 0xbfe338400d0c8e57, // 0.79954, -0.60062 + 0x3fe98e410881a600, 0xbfe3424aac0ef7d6, // 0.79861, -0.60184 + 0x3fe986aef1457594, 0xbfe34c5252c14de1, // 0.79769, -0.60307 + 0x3fe97f18ea4e5c9e, 0xbfe35656ff9799ae, // 0.79676, -0.60429 + 0x3fe9777ef4c7d742, 0xbfe36058b10659f3, // 0.79584, -0.60551 + 0x3fe96fe111ddfce0, 0xbfe36a576582831b, // 0.79491, -0.60673 + 0x3fe9683f42bd7fe1, 0xbfe374531b817f8d, // 0.79398, -0.60795 + 0x3fe960998893ad8c, 0xbfe37e4bd1792fe2, // 0.79304, -0.60917 + 0x3fe958efe48e6dd7, 0xbfe3884185dfeb22, // 0.79211, -0.61038 + 0x3fe9514257dc4335, 0xbfe39234372c7f04, // 0.79117, -0.6116 + 0x3fe94990e3ac4a6c, 0xbfe39c23e3d63029, // 0.79023, -0.61281 + 0x3fe941db892e3a65, 0xbfe3a6108a54ba58, // 0.78929, -0.61402 + 0x3fe93a22499263fc, 0xbfe3affa292050b9, // 0.78835, -0.61523 + 0x3fe932652609b1cf, 0xbfe3b9e0beb19e18, // 0.7874, -0.61644 + 0x3fe92aa41fc5a815, 0xbfe3c3c44981c517, // 0.78646, -0.61765 + 0x3fe922df37f8646a, 0xbfe3cda4c80a6076, // 0.78551, -0.61885 + 0x3fe91b166fd49da2, 0xbfe3d78238c58343, // 0.78456, -0.62006 + 0x3fe91349c88da398, 0xbfe3e15c9a2db922, // 0.7836, -0.62126 + 0x3fe90b7943575efe, 0xbfe3eb33eabe0680, // 0.78265, -0.62246 + 0x3fe903a4e1665133, 0xbfe3f50828f1e8d2, // 0.78169, -0.62366 + 0x3fe8fbcca3ef940d, 0xbfe3fed9534556d4, // 0.78074, -0.62486 + 0x3fe8f3f08c28d9ac, 0xbfe408a76834c0c0, // 0.77978, -0.62606 + 0x3fe8ec109b486c49, 0xbfe41272663d108c, // 0.77882, -0.62725 + 0x3fe8e42cd2852e0a, 0xbfe41c3a4bdbaa26, // 0.77785, -0.62845 + 0x3fe8dc45331698cc, 0xbfe425ff178e6bb1, // 0.77689, -0.62964 + 0x3fe8d459be34bdfa, 0xbfe42fc0c7d3adbb, // 0.77592, -0.63083 + 0x3fe8cc6a75184655, 0xbfe4397f5b2a4380, // 0.77495, -0.63202 + 0x3fe8c47758fa71cb, 0xbfe4433ad0117b1d, // 0.77398, -0.63321 + 0x3fe8bc806b151741, 0xbfe44cf325091dd6, // 0.77301, -0.63439 + 0x3fe8b485aca2a468, 0xbfe456a858917046, // 0.77204, -0.63558 + 0x3fe8ac871ede1d88, 0xbfe4605a692b32a2, // 0.77106, -0.63676 + 0x3fe8a484c3031d50, 0xbfe46a095557a0f1, // 0.77008, -0.63794 + 0x3fe89c7e9a4dd4ab, 0xbfe473b51b987347, // 0.7691, -0.63912 + 0x3fe89474a5fb0a84, 0xbfe47d5dba6fde01, // 0.76812, -0.6403 + 0x3fe88c66e7481ba1, 0xbfe48703306091fe, // 0.76714, -0.64148 + 0x3fe884555f72fa6b, 0xbfe490a57bedbcdf, // 0.76615, -0.64266 + 0x3fe87c400fba2ebf, 0xbfe49a449b9b0938, // 0.76517, -0.64383 + 0x3fe87426f95cd5bd, 0xbfe4a3e08dec9ed6, // 0.76418, -0.645 + 0x3fe86c0a1d9aa195, 0xbfe4ad79516722f0, // 0.76319, -0.64618 + 0x3fe863e97db3d95a, 0xbfe4b70ee48fb869, // 0.7622, -0.64735 + 0x3fe85bc51ae958cc, 0xbfe4c0a145ec0004, // 0.7612, -0.64851 + 0x3fe8539cf67c9029, 0xbfe4ca30740218a3, // 0.76021, -0.64968 + 0x3fe84b7111af83f9, 0xbfe4d3bc6d589f80, // 0.75921, -0.65085 + 0x3fe843416dc4cce2, 0xbfe4dd453076b064, // 0.75821, -0.65201 + 0x3fe83b0e0bff976e, 0xbfe4e6cabbe3e5e9, // 0.75721, -0.65317 + 0x3fe832d6eda3a3e0, 0xbfe4f04d0e2859aa, // 0.75621, -0.65433 + 0x3fe82a9c13f545ff, 0xbfe4f9cc25cca486, // 0.7552, -0.65549 + 0x3fe8225d803964e5, 0xbfe503480159ded2, // 0.75419, -0.65665 + 0x3fe81a1b33b57acc, 0xbfe50cc09f59a09b, // 0.75319, -0.65781 + 0x3fe811d52faf94dc, 0xbfe51635fe5601d7, // 0.75218, -0.65896 + 0x3fe8098b756e52fa, 0xbfe51fa81cd99aa6, // 0.75117, -0.66011 + 0x3fe8013e0638e795, 0xbfe52916f96f8388, // 0.75015, -0.66127 + 0x3fe7f8ece3571771, 0xbfe5328292a35596, // 0.74914, -0.66242 + 0x3fe7f0980e113978, 0xbfe53beae7012abe, // 0.74812, -0.66356 + 0x3fe7e83f87b03686, 0xbfe5454ff5159dfb, // 0.7471, -0.66471 + 0x3fe7dfe3517d8937, 0xbfe54eb1bb6dcb8f, // 0.74608, -0.66586 + 0x3fe7d7836cc33db2, 0xbfe5581038975137, // 0.74506, -0.667 + 0x3fe7cf1fdacbf179, 0xbfe5616b6b204e6e, // 0.74403, -0.66814 + 0x3fe7c6b89ce2d333, 0xbfe56ac35197649e, // 0.74301, -0.66928 + 0x3fe7be4db453a27c, 0xbfe57417ea8bb75c, // 0.74198, -0.67042 + 0x3fe7b5df226aafb0, 0xbfe57d69348cec9f, // 0.74095, -0.67156 + 0x3fe7ad6ce874dbb6, 0xbfe586b72e2b2cfd, // 0.73992, -0.67269 + 0x3fe7a4f707bf97d2, 0xbfe59001d5f723df, // 0.73889, -0.67383 + 0x3fe79c7d8198e56e, 0xbfe599492a81ffbc, // 0.73785, -0.67496 + 0x3fe79400574f55e4, 0xbfe5a28d2a5d7250, // 0.73682, -0.67609 + 0x3fe78b7f8a320a52, 0xbfe5abcdd41bb0d8, // 0.73578, -0.67722 + 0x3fe782fb1b90b35b, 0xbfe5b50b264f7448, // 0.73474, -0.67835 + 0x3fe77a730cbb9100, 0xbfe5be451f8bf980, // 0.7337, -0.67948 + 0x3fe771e75f037261, 0xbfe5c77bbe65018c, // 0.73265, -0.6806 + 0x3fe7695813b9b594, 0xbfe5d0af016ed1d4, // 0.73161, -0.68172 + 0x3fe760c52c304764, 0xbfe5d9dee73e345c, // 0.73056, -0.68285 + 0x3fe7582ea9b9a329, 0xbfe5e30b6e6877f3, // 0.72951, -0.68397 + 0x3fe74f948da8d28d, 0xbfe5ec3495837074, // 0.72846, -0.68508 + 0x3fe746f6d9516d59, 0xbfe5f55a5b2576f8, // 0.72741, -0.6862 + 0x3fe73e558e079942, 0xbfe5fe7cbde56a0f, // 0.72636, -0.68732 + 0x3fe735b0ad2009b2, 0xbfe6079bbc5aadfa, // 0.7253, -0.68843 + 0x3fe72d0837efff97, 0xbfe610b7551d2cde, // 0.72425, -0.68954 + 0x3fe7245c2fcd492a, 0xbfe619cf86c55702, // 0.72319, -0.69065 + 0x3fe71bac960e41bf, 0xbfe622e44fec22ff, // 0.72213, -0.69176 + 0x3fe712f96c09d18d, 0xbfe62bf5af2b0dfd, // 0.72107, -0.69287 + 0x3fe70a42b3176d7a, 0xbfe63503a31c1be8, // 0.72, -0.69397 + 0x3fe701886c8f16e6, 0xbfe63e0e2a59d7aa, // 0.71894, -0.69508 + 0x3fe6f8ca99c95b75, 0xbfe64715437f535b, // 0.71787, -0.69618 + 0x3fe6f0093c1f54de, 0xbfe65018ed28287f, // 0.7168, -0.69728 + 0x3fe6e74454eaa8ae, 0xbfe6591925f0783e, // 0.71573, -0.69838 + 0x3fe6de7be585881d, 0xbfe66215ec74eb91, // 0.71466, -0.69947 + 0x3fe6d5afef4aafcc, 0xbfe66b0f3f52b386, // 0.71358, -0.70057 + 0x3fe6cce07395679f, 0xbfe674051d27896c, // 0.71251, -0.70166 + 0x3fe6c40d73c18275, 0xbfe67cf78491af10, // 0.71143, -0.70275 + 0x3fe6bb36f12b5e06, 0xbfe685e6742feeef, // 0.71035, -0.70385 + 0x3fe6b25ced2fe29c, 0xbfe68ed1eaa19c71, // 0.70927, -0.70493 + 0x3fe6a97f692c82ea, 0xbfe697b9e686941c, // 0.70819, -0.70602 + 0x3fe6a09e667f3bcc, 0xbfe6a09e667f3bcc, // 0.70711, -0.70711 + 0x3fe697b9e686941c, 0xbfe6a97f692c82ea, // 0.70602, -0.70819 + 0x3fe68ed1eaa19c71, 0xbfe6b25ced2fe29c, // 0.70493, -0.70927 + 0x3fe685e6742feeef, 0xbfe6bb36f12b5e06, // 0.70385, -0.71035 + 0x3fe67cf78491af10, 0xbfe6c40d73c18275, // 0.70275, -0.71143 + 0x3fe674051d27896c, 0xbfe6cce07395679f, // 0.70166, -0.71251 + 0x3fe66b0f3f52b386, 0xbfe6d5afef4aafcc, // 0.70057, -0.71358 + 0x3fe66215ec74eb91, 0xbfe6de7be585881d, // 0.69947, -0.71466 + 0x3fe6591925f0783e, 0xbfe6e74454eaa8ae, // 0.69838, -0.71573 + 0x3fe65018ed28287f, 0xbfe6f0093c1f54de, // 0.69728, -0.7168 + 0x3fe64715437f535b, 0xbfe6f8ca99c95b75, // 0.69618, -0.71787 + 0x3fe63e0e2a59d7aa, 0xbfe701886c8f16e6, // 0.69508, -0.71894 + 0x3fe63503a31c1be8, 0xbfe70a42b3176d7a, // 0.69397, -0.72 + 0x3fe62bf5af2b0dfd, 0xbfe712f96c09d18d, // 0.69287, -0.72107 + 0x3fe622e44fec22ff, 0xbfe71bac960e41bf, // 0.69176, -0.72213 + 0x3fe619cf86c55702, 0xbfe7245c2fcd492a, // 0.69065, -0.72319 + 0x3fe610b7551d2cde, 0xbfe72d0837efff97, // 0.68954, -0.72425 + 0x3fe6079bbc5aadfa, 0xbfe735b0ad2009b2, // 0.68843, -0.7253 + 0x3fe5fe7cbde56a0f, 0xbfe73e558e079942, // 0.68732, -0.72636 + 0x3fe5f55a5b2576f8, 0xbfe746f6d9516d59, // 0.6862, -0.72741 + 0x3fe5ec3495837074, 0xbfe74f948da8d28d, // 0.68508, -0.72846 + 0x3fe5e30b6e6877f3, 0xbfe7582ea9b9a329, // 0.68397, -0.72951 + 0x3fe5d9dee73e345c, 0xbfe760c52c304764, // 0.68285, -0.73056 + 0x3fe5d0af016ed1d4, 0xbfe7695813b9b594, // 0.68172, -0.73161 + 0x3fe5c77bbe65018c, 0xbfe771e75f037261, // 0.6806, -0.73265 + 0x3fe5be451f8bf980, 0xbfe77a730cbb9100, // 0.67948, -0.7337 + 0x3fe5b50b264f7448, 0xbfe782fb1b90b35b, // 0.67835, -0.73474 + 0x3fe5abcdd41bb0d8, 0xbfe78b7f8a320a52, // 0.67722, -0.73578 + 0x3fe5a28d2a5d7250, 0xbfe79400574f55e4, // 0.67609, -0.73682 + 0x3fe599492a81ffbc, 0xbfe79c7d8198e56e, // 0.67496, -0.73785 + 0x3fe59001d5f723df, 0xbfe7a4f707bf97d2, // 0.67383, -0.73889 + 0x3fe586b72e2b2cfd, 0xbfe7ad6ce874dbb6, // 0.67269, -0.73992 + 0x3fe57d69348cec9f, 0xbfe7b5df226aafb0, // 0.67156, -0.74095 + 0x3fe57417ea8bb75c, 0xbfe7be4db453a27c, // 0.67042, -0.74198 + 0x3fe56ac35197649e, 0xbfe7c6b89ce2d333, // 0.66928, -0.74301 + 0x3fe5616b6b204e6e, 0xbfe7cf1fdacbf179, // 0.66814, -0.74403 + 0x3fe5581038975137, 0xbfe7d7836cc33db2, // 0.667, -0.74506 + 0x3fe54eb1bb6dcb8f, 0xbfe7dfe3517d8937, // 0.66586, -0.74608 + 0x3fe5454ff5159dfb, 0xbfe7e83f87b03686, // 0.66471, -0.7471 + 0x3fe53beae7012abe, 0xbfe7f0980e113978, // 0.66356, -0.74812 + 0x3fe5328292a35596, 0xbfe7f8ece3571771, // 0.66242, -0.74914 + 0x3fe52916f96f8388, 0xbfe8013e0638e795, // 0.66127, -0.75015 + 0x3fe51fa81cd99aa6, 0xbfe8098b756e52fa, // 0.66011, -0.75117 + 0x3fe51635fe5601d7, 0xbfe811d52faf94dc, // 0.65896, -0.75218 + 0x3fe50cc09f59a09b, 0xbfe81a1b33b57acc, // 0.65781, -0.75319 + 0x3fe503480159ded2, 0xbfe8225d803964e5, // 0.65665, -0.75419 + 0x3fe4f9cc25cca486, 0xbfe82a9c13f545ff, // 0.65549, -0.7552 + 0x3fe4f04d0e2859aa, 0xbfe832d6eda3a3e0, // 0.65433, -0.75621 + 0x3fe4e6cabbe3e5e9, 0xbfe83b0e0bff976e, // 0.65317, -0.75721 + 0x3fe4dd453076b064, 0xbfe843416dc4cce2, // 0.65201, -0.75821 + 0x3fe4d3bc6d589f80, 0xbfe84b7111af83f9, // 0.65085, -0.75921 + 0x3fe4ca30740218a3, 0xbfe8539cf67c9029, // 0.64968, -0.76021 + 0x3fe4c0a145ec0004, 0xbfe85bc51ae958cc, // 0.64851, -0.7612 + 0x3fe4b70ee48fb869, 0xbfe863e97db3d95a, // 0.64735, -0.7622 + 0x3fe4ad79516722f0, 0xbfe86c0a1d9aa195, // 0.64618, -0.76319 + 0x3fe4a3e08dec9ed6, 0xbfe87426f95cd5bd, // 0.645, -0.76418 + 0x3fe49a449b9b0938, 0xbfe87c400fba2ebf, // 0.64383, -0.76517 + 0x3fe490a57bedbcdf, 0xbfe884555f72fa6b, // 0.64266, -0.76615 + 0x3fe48703306091fe, 0xbfe88c66e7481ba1, // 0.64148, -0.76714 + 0x3fe47d5dba6fde01, 0xbfe89474a5fb0a84, // 0.6403, -0.76812 + 0x3fe473b51b987347, 0xbfe89c7e9a4dd4ab, // 0.63912, -0.7691 + 0x3fe46a095557a0f1, 0xbfe8a484c3031d50, // 0.63794, -0.77008 + 0x3fe4605a692b32a2, 0xbfe8ac871ede1d88, // 0.63676, -0.77106 + 0x3fe456a858917046, 0xbfe8b485aca2a468, // 0.63558, -0.77204 + 0x3fe44cf325091dd6, 0xbfe8bc806b151741, // 0.63439, -0.77301 + 0x3fe4433ad0117b1d, 0xbfe8c47758fa71cb, // 0.63321, -0.77398 + 0x3fe4397f5b2a4380, 0xbfe8cc6a75184655, // 0.63202, -0.77495 + 0x3fe42fc0c7d3adbb, 0xbfe8d459be34bdfa, // 0.63083, -0.77592 + 0x3fe425ff178e6bb1, 0xbfe8dc45331698cc, // 0.62964, -0.77689 + 0x3fe41c3a4bdbaa26, 0xbfe8e42cd2852e0a, // 0.62845, -0.77785 + 0x3fe41272663d108c, 0xbfe8ec109b486c49, // 0.62725, -0.77882 + 0x3fe408a76834c0c0, 0xbfe8f3f08c28d9ac, // 0.62606, -0.77978 + 0x3fe3fed9534556d4, 0xbfe8fbcca3ef940d, // 0.62486, -0.78074 + 0x3fe3f50828f1e8d2, 0xbfe903a4e1665133, // 0.62366, -0.78169 + 0x3fe3eb33eabe0680, 0xbfe90b7943575efe, // 0.62246, -0.78265 + 0x3fe3e15c9a2db922, 0xbfe91349c88da398, // 0.62126, -0.7836 + 0x3fe3d78238c58343, 0xbfe91b166fd49da2, // 0.62006, -0.78456 + 0x3fe3cda4c80a6076, 0xbfe922df37f8646a, // 0.61885, -0.78551 + 0x3fe3c3c44981c517, 0xbfe92aa41fc5a815, // 0.61765, -0.78646 + 0x3fe3b9e0beb19e18, 0xbfe932652609b1cf, // 0.61644, -0.7874 + 0x3fe3affa292050b9, 0xbfe93a22499263fc, // 0.61523, -0.78835 + 0x3fe3a6108a54ba58, 0xbfe941db892e3a65, // 0.61402, -0.78929 + 0x3fe39c23e3d63029, 0xbfe94990e3ac4a6c, // 0.61281, -0.79023 + 0x3fe39234372c7f04, 0xbfe9514257dc4335, // 0.6116, -0.79117 + 0x3fe3884185dfeb22, 0xbfe958efe48e6dd7, // 0.61038, -0.79211 + 0x3fe37e4bd1792fe2, 0xbfe960998893ad8c, // 0.60917, -0.79304 + 0x3fe374531b817f8d, 0xbfe9683f42bd7fe1, // 0.60795, -0.79398 + 0x3fe36a576582831b, 0xbfe96fe111ddfce0, // 0.60673, -0.79491 + 0x3fe36058b10659f3, 0xbfe9777ef4c7d742, // 0.60551, -0.79584 + 0x3fe35656ff9799ae, 0xbfe97f18ea4e5c9e, // 0.60429, -0.79676 + 0x3fe34c5252c14de1, 0xbfe986aef1457594, // 0.60307, -0.79769 + 0x3fe3424aac0ef7d6, 0xbfe98e410881a600, // 0.60184, -0.79861 + 0x3fe338400d0c8e57, 0xbfe995cf2ed80d22, // 0.60062, -0.79954 + 0x3fe32e3277467d6b, 0xbfe99d59631e65d5, // 0.59939, -0.80046 + 0x3fe32421ec49a620, 0xbfe9a4dfa42b06b2, // 0.59816, -0.80138 + 0x3fe31a0e6da35e44, 0xbfe9ac61f0d4e247, // 0.59693, -0.80229 + 0x3fe30ff7fce17035, 0xbfe9b3e047f38741, // 0.5957, -0.80321 + 0x3fe305de9b921a94, 0xbfe9bb5aa85f2098, // 0.59447, -0.80412 + 0x3fe2fbc24b441015, 0xbfe9c2d110f075c3, // 0.59323, -0.80503 + 0x3fe2f1a30d86773a, 0xbfe9ca438080eadb, // 0.592, -0.80594 + 0x3fe2e780e3e8ea16, 0xbfe9d1b1f5ea80d6, // 0.59076, -0.80685 + 0x3fe2dd5bcffb7616, 0xbfe9d91c7007d5a6, // 0.58952, -0.80775 + 0x3fe2d333d34e9bb7, 0xbfe9e082edb42472, // 0.58828, -0.80866 + 0x3fe2c908ef734e57, 0xbfe9e7e56dcb45bd, // 0.58704, -0.80956 + 0x3fe2bedb25faf3ea, 0xbfe9ef43ef29af94, // 0.5858, -0.81046 + 0x3fe2b4aa787764c4, 0xbfe9f69e70ac75bc, // 0.58455, -0.81135 + 0x3fe2aa76e87aeb58, 0xbfe9fdf4f13149de, // 0.58331, -0.81225 + 0x3fe2a040779843fb, 0xbfea05476f967bb5, // 0.58206, -0.81314 + 0x3fe2960727629ca8, 0xbfea0c95eabaf937, // 0.58081, -0.81404 + 0x3fe28bcaf96d94ba, 0xbfea13e0617e4ec7, // 0.57956, -0.81493 + 0x3fe2818bef4d3cba, 0xbfea1b26d2c0a75e, // 0.57831, -0.81581 + 0x3fe2774a0a961612, 0xbfea22693d62ccb9, // 0.57706, -0.8167 + 0x3fe26d054cdd12df, 0xbfea29a7a0462782, // 0.57581, -0.81758 + 0x3fe262bdb7b795a2, 0xbfea30e1fa4cbf81, // 0.57455, -0.81847 + 0x3fe258734cbb7110, 0xbfea38184a593bc6, // 0.5733, -0.81935 + 0x3fe24e260d7ee7c9, 0xbfea3f4a8f4ee2d2, // 0.57204, -0.82023 + 0x3fe243d5fb98ac1f, 0xbfea4678c8119ac8, // 0.57078, -0.8211 + 0x3fe23983189fdfd5, 0xbfea4da2f385e997, // 0.56952, -0.82198 + 0x3fe22f2d662c13e1, 0xbfea54c91090f524, // 0.56826, -0.82285 + 0x3fe224d4e5d5482e, 0xbfea5beb1e188375, // 0.567, -0.82372 + 0x3fe21a799933eb58, 0xbfea63091b02fae2, // 0.56573, -0.82459 + 0x3fe2101b81e0da78, 0xbfea6a230637623b, // 0.56447, -0.82546 + 0x3fe205baa17560d6, 0xbfea7138de9d60f5, // 0.5632, -0.82632 + 0x3fe1fb56f98b37b8, 0xbfea784aa31d3f55, // 0.56193, -0.82718 + 0x3fe1f0f08bbc861b, 0xbfea7f58529fe69d, // 0.56066, -0.82805 + 0x3fe1e68759a3e074, 0xbfea8661ec0ee133, // 0.55939, -0.8289 + 0x3fe1dc1b64dc4872, 0xbfea8d676e545ad2, // 0.55812, -0.82976 + 0x3fe1d1acaf012cc2, 0xbfea9468d85b20ae, // 0.55685, -0.83062 + 0x3fe1c73b39ae68c8, 0xbfea9b66290ea1a3, // 0.55557, -0.83147 + 0x3fe1bcc706804467, 0xbfeaa25f5f5aee60, // 0.55429, -0.83232 + 0x3fe1b250171373be, 0xbfeaa9547a2cb98e, // 0.55302, -0.83317 + 0x3fe1a7d66d0516e6, 0xbfeab045787157ff, // 0.55174, -0.83402 + 0x3fe19d5a09f2b9b8, 0xbfeab7325916c0d4, // 0.55046, -0.83486 + 0x3fe192daef7a5386, 0xbfeabe1b1b0b8dac, // 0.54918, -0.83571 + 0x3fe188591f3a46e5, 0xbfeac4ffbd3efac8, // 0.54789, -0.83655 + 0x3fe17dd49ad16161, 0xbfeacbe03ea0e73b, // 0.54661, -0.83739 + 0x3fe1734d63dedb49, 0xbfead2bc9e21d511, // 0.54532, -0.83822 + 0x3fe168c37c025764, 0xbfead994dab2e979, // 0.54404, -0.83906 + 0x3fe15e36e4dbe2bc, 0xbfeae068f345ecef, // 0.54275, -0.83989 + 0x3fe153a7a00bf453, 0xbfeae738e6cd4b67, // 0.54146, -0.84073 + 0x3fe14915af336ceb, 0xbfeaee04b43c1474, // 0.54017, -0.84155 + 0x3fe13e8113f396c1, 0xbfeaf4cc5a85fb73, // 0.53888, -0.84238 + 0x3fe133e9cfee254e, 0xbfeafb8fd89f57b6, // 0.53759, -0.84321 + 0x3fe1294fe4c5350a, 0xbfeb024f2d7d24a9, // 0.53629, -0.84403 + 0x3fe11eb3541b4b22, 0xbfeb090a58150200, // 0.535, -0.84485 + 0x3fe114141f935545, 0xbfeb0fc1575d33db, // 0.5337, -0.84567 + 0x3fe1097248d0a956, 0xbfeb16742a4ca2f5, // 0.5324, -0.84649 + 0x3fe0fecdd1770537, 0xbfeb1d22cfdadcc6, // 0.5311, -0.84731 + 0x3fe0f426bb2a8e7d, 0xbfeb23cd470013b4, // 0.5298, -0.84812 + 0x3fe0e97d078fd23b, 0xbfeb2a738eb51f33, // 0.5285, -0.84893 + 0x3fe0ded0b84bc4b5, 0xbfeb3115a5f37bf4, // 0.5272, -0.84974 + 0x3fe0d421cf03c12b, 0xbfeb37b38bb54c09, // 0.5259, -0.85055 + 0x3fe0c9704d5d898f, 0xbfeb3e4d3ef55712, // 0.52459, -0.85136 + 0x3fe0bebc34ff4646, 0xbfeb44e2beaf0a61, // 0.52328, -0.85216 + 0x3fe0b405878f85ec, 0xbfeb4b7409de7925, // 0.52198, -0.85296 + 0x3fe0a94c46b53d0b, 0xbfeb52011f805c92, // 0.52067, -0.85376 + 0x3fe09e907417c5e1, 0xbfeb5889fe921405, // 0.51936, -0.85456 + 0x3fe093d2115ee018, 0xbfeb5f0ea611a532, // 0.51804, -0.85535 + 0x3fe089112032b08c, 0xbfeb658f14fdbc47, // 0.51673, -0.85615 + 0x3fe07e4da23bc102, 0xbfeb6c0b4a55ac17, // 0.51542, -0.85694 + 0x3fe073879922ffed, 0xbfeb728345196e3e, // 0.5141, -0.85773 + 0x3fe068bf0691c028, 0xbfeb78f70449a34b, // 0.51279, -0.85852 + 0x3fe05df3ec31b8b6, 0xbfeb7f6686e792ea, // 0.51147, -0.8593 + 0x3fe053264bad0483, 0xbfeb85d1cbf52c02, // 0.51015, -0.86009 + 0x3fe0485626ae221a, 0xbfeb8c38d27504e9, // 0.50883, -0.86087 + 0x3fe03d837edff370, 0xbfeb929b996a5b7f, // 0.50751, -0.86165 + 0x3fe032ae55edbd95, 0xbfeb98fa1fd9155e, // 0.50619, -0.86242 + 0x3fe027d6ad83287e, 0xbfeb9f5464c5bffc, // 0.50486, -0.8632 + 0x3fe01cfc874c3eb7, 0xbfeba5aa673590d2, // 0.50354, -0.86397 + 0x3fe0121fe4f56d2c, 0xbfebabfc262e6586, // 0.50221, -0.86474 + 0x3fe00740c82b82e0, 0xbfebb249a0b6c40d, // 0.50089, -0.86551 + 0x3fdff8be6537615e, 0xbfebb892d5d5dad5, // 0.49956, -0.86628 + 0x3fdfe2f64be7120f, 0xbfebbed7c49380ea, // 0.49823, -0.86705 + 0x3fdfcd2947c1ff57, 0xbfebc5186bf8361d, // 0.4969, -0.86781 + 0x3fdfb7575c24d2de, 0xbfebcb54cb0d2327, // 0.49557, -0.86857 + 0x3fdfa1808c6cf7e0, 0xbfebd18ce0dc19d6, // 0.49423, -0.86933 + 0x3fdf8ba4dbf89aba, 0xbfebd7c0ac6f952a, // 0.4929, -0.87009 + 0x3fdf75c44e26a852, 0xbfebddf02cd2b983, // 0.49156, -0.87084 + 0x3fdf5fdee656cda3, 0xbfebe41b611154c1, // 0.49023, -0.8716 + 0x3fdf49f4a7e97729, 0xbfebea424837de6d, // 0.48889, -0.87235 + 0x3fdf3405963fd068, 0xbfebf064e15377dd, // 0.48755, -0.87309 + 0x3fdf1e11b4bbc35c, 0xbfebf6832b71ec5b, // 0.48621, -0.87384 + 0x3fdf081906bff7fd, 0xbfebfc9d25a1b147, // 0.48487, -0.87459 + 0x3fdef21b8fafd3b5, 0xbfec02b2cef1e641, // 0.48353, -0.87533 + 0x3fdedc1952ef78d5, 0xbfec08c426725549, // 0.48218, -0.87607 + 0x3fdec61253e3c61b, 0xbfec0ed12b3372e9, // 0.48084, -0.87681 + 0x3fdeb00695f25620, 0xbfec14d9dc465e58, // 0.47949, -0.87755 + 0x3fde99f61c817eda, 0xbfec1ade38bce19b, // 0.47815, -0.87828 + 0x3fde83e0eaf85113, 0xbfec20de3fa971b0, // 0.4768, -0.87901 + 0x3fde6dc704be97e2, 0xbfec26d9f01f2eaf, // 0.47545, -0.87974 + 0x3fde57a86d3cd824, 0xbfec2cd14931e3f1, // 0.4741, -0.88047 + 0x3fde418527dc4ffa, 0xbfec32c449f60831, // 0.47275, -0.8812 + 0x3fde2b5d3806f63b, 0xbfec38b2f180bdb1, // 0.4714, -0.88192 + 0x3fde1530a12779f4, 0xbfec3e9d3ee7d262, // 0.47004, -0.88264 + 0x3fddfeff66a941de, 0xbfec44833141c004, // 0.46869, -0.88336 + 0x3fdde8c98bf86bd6, 0xbfec4a64c7a5ac4c, // 0.46733, -0.88408 + 0x3fddd28f1481cc58, 0xbfec5042012b6907, // 0.46598, -0.8848 + 0x3fddbc5003b2edf8, 0xbfec561adceb743e, // 0.46462, -0.88551 + 0x3fdda60c5cfa10d8, 0xbfec5bef59fef85a, // 0.46326, -0.88622 + 0x3fdd8fc423c62a25, 0xbfec61bf777fcc48, // 0.4619, -0.88693 + 0x3fdd79775b86e389, 0xbfec678b3488739b, // 0.46054, -0.88764 + 0x3fdd632607ac9aa9, 0xbfec6d5290341eb2, // 0.45918, -0.88835 + 0x3fdd4cd02ba8609c, 0xbfec7315899eaad7, // 0.45781, -0.88905 + 0x3fdd3675caebf962, 0xbfec78d41fe4a267, // 0.45645, -0.88975 + 0x3fdd2016e8e9db5b, 0xbfec7e8e52233cf3, // 0.45508, -0.89045 + 0x3fdd09b389152ec1, 0xbfec84441f785f61, // 0.45372, -0.89115 + 0x3fdcf34baee1cd21, 0xbfec89f587029c13, // 0.45235, -0.89184 + 0x3fdcdcdf5dc440ce, 0xbfec8fa287e13305, // 0.45098, -0.89253 + 0x3fdcc66e9931c45d, 0xbfec954b213411f5, // 0.44961, -0.89322 + 0x3fdcaff964a0421d, 0xbfec9aef521bd480, // 0.44824, -0.89391 + 0x3fdc997fc3865388, 0xbfeca08f19b9c449, // 0.44687, -0.8946 + 0x3fdc8301b95b40c2, 0xbfeca62a772fd919, // 0.4455, -0.89528 + 0x3fdc6c7f4997000a, 0xbfecabc169a0b901, // 0.44412, -0.89597 + 0x3fdc55f877b23537, 0xbfecb153f02fb87d, // 0.44275, -0.89665 + 0x3fdc3f6d47263129, 0xbfecb6e20a00da99, // 0.44137, -0.89732 + 0x3fdc28ddbb6cf145, 0xbfecbc6bb638d10b, // 0.43999, -0.898 + 0x3fdc1249d8011ee7, 0xbfecc1f0f3fcfc5c, // 0.43862, -0.89867 + 0x3fdbfbb1a05e0edc, 0xbfecc771c2736c09, // 0.43724, -0.89935 + 0x3fdbe51517ffc0d9, 0xbfecccee20c2de9f, // 0.43586, -0.90002 + 0x3fdbce744262deee, 0xbfecd2660e12c1e6, // 0.43448, -0.90068 + 0x3fdbb7cf2304bd01, 0xbfecd7d9898b32f6, // 0.43309, -0.90135 + 0x3fdba125bd63583e, 0xbfecdd489254fe65, // 0.43171, -0.90201 + 0x3fdb8a7814fd5693, 0xbfece2b32799a060, // 0.43033, -0.90267 + 0x3fdb73c62d520624, 0xbfece819488344ce, // 0.42894, -0.90333 + 0x3fdb5d1009e15cc0, 0xbfeced7af43cc773, // 0.42756, -0.90399 + 0x3fdb4655ae2bf757, 0xbfecf2d829f1b40e, // 0.42617, -0.90464 + 0x3fdb2f971db31972, 0xbfecf830e8ce467b, // 0.42478, -0.9053 + 0x3fdb18d45bf8aca6, 0xbfecfd852fff6ad4, // 0.42339, -0.90595 + 0x3fdb020d6c7f4009, 0xbfed02d4feb2bd92, // 0.422, -0.9066 + 0x3fdaeb4252ca07ab, 0xbfed082054168bac, // 0.42061, -0.90724 + 0x3fdad473125cdc08, 0xbfed0d672f59d2b9, // 0.41922, -0.90789 + 0x3fdabd9faebc3980, 0xbfed12a98fac410c, // 0.41782, -0.90853 + 0x3fdaa6c82b6d3fc9, 0xbfed17e7743e35dc, // 0.41643, -0.90917 + 0x3fda8fec8bf5b166, 0xbfed1d20dc40c15c, // 0.41503, -0.90981 + 0x3fda790cd3dbf31a, 0xbfed2255c6e5a4e1, // 0.41364, -0.91044 + 0x3fda622906a70b63, 0xbfed2786335f52fc, // 0.41224, -0.91107 + 0x3fda4b4127dea1e4, 0xbfed2cb220e0ef9f, // 0.41084, -0.91171 + 0x3fda34553b0afee5, 0xbfed31d98e9e503a, // 0.40944, -0.91234 + 0x3fda1d6543b50ac0, 0xbfed36fc7bcbfbdc, // 0.40804, -0.91296 + 0x3fda067145664d57, 0xbfed3c1ae79f2b4e, // 0.40664, -0.91359 + 0x3fd9ef7943a8ed8a, 0xbfed4134d14dc93a, // 0.40524, -0.91421 + 0x3fd9d87d4207b0ab, 0xbfed464a380e7242, // 0.40384, -0.91483 + 0x3fd9c17d440df9f2, 0xbfed4b5b1b187524, // 0.40243, -0.91545 + 0x3fd9aa794d47c9ee, 0xbfed506779a3d2d9, // 0.40103, -0.91606 + 0x3fd993716141bdfe, 0xbfed556f52e93eb1, // 0.39962, -0.91668 + 0x3fd97c6583890fc2, 0xbfed5a72a6221e73, // 0.39822, -0.91729 + 0x3fd96555b7ab948f, 0xbfed5f7172888a7f, // 0.39681, -0.9179 + 0x3fd94e420137bce3, 0xbfed646bb7574de5, // 0.3954, -0.91851 + 0x3fd9372a63bc93d7, 0xbfed696173c9e68b, // 0.39399, -0.91911 + 0x3fd9200ee2c9be97, 0xbfed6e52a71c8547, // 0.39258, -0.91972 + 0x3fd908ef81ef7bd1, 0xbfed733f508c0dff, // 0.39117, -0.92032 + 0x3fd8f1cc44bea329, 0xbfed78276f5617c6, // 0.38976, -0.92092 + 0x3fd8daa52ec8a4af, 0xbfed7d0b02b8ecf9, // 0.38835, -0.92151 + 0x3fd8c37a439f884f, 0xbfed81ea09f38b63, // 0.38693, -0.92211 + 0x3fd8ac4b86d5ed44, 0xbfed86c48445a450, // 0.38552, -0.9227 + 0x3fd89518fbff098e, 0xbfed8b9a70ef9cb4, // 0.3841, -0.92329 + 0x3fd87de2a6aea963, 0xbfed906bcf328d46, // 0.38268, -0.92388 + 0x3fd866a88a792ea0, 0xbfed95389e50429b, // 0.38127, -0.92447 + 0x3fd84f6aaaf3903f, 0xbfed9a00dd8b3d46, // 0.37985, -0.92505 + 0x3fd838290bb359c8, 0xbfed9ec48c26b1f3, // 0.37843, -0.92563 + 0x3fd820e3b04eaac4, 0xbfeda383a9668988, // 0.37701, -0.92621 + 0x3fd8099a9c5c362d, 0xbfeda83e348f613b, // 0.37559, -0.92679 + 0x3fd7f24dd37341e3, 0xbfedacf42ce68ab9, // 0.37416, -0.92736 + 0x3fd7dafd592ba621, 0xbfedb1a591b20c38, // 0.37274, -0.92794 + 0x3fd7c3a9311dcce7, 0xbfedb6526238a09b, // 0.37132, -0.92851 + 0x3fd7ac515ee2b172, 0xbfedbafa9dc1b78d, // 0.36989, -0.92907 + 0x3fd794f5e613dfae, 0xbfedbf9e4395759a, // 0.36847, -0.92964 + 0x3fd77d96ca4b73a6, 0xbfedc43d52fcb453, // 0.36704, -0.93021 + 0x3fd766340f2418f6, 0xbfedc8d7cb410260, // 0.36561, -0.93077 + 0x3fd74ecdb8390a3e, 0xbfedcd6dabaca3a5, // 0.36418, -0.93133 + 0x3fd73763c9261092, 0xbfedd1fef38a915a, // 0.36276, -0.93188 + 0x3fd71ff6458782ec, 0xbfedd68ba2267a25, // 0.36133, -0.93244 + 0x3fd7088530fa459e, 0xbfeddb13b6ccc23d, // 0.3599, -0.93299 + 0x3fd6f1108f1bc9c5, 0xbfeddf9730ca837b, // 0.35846, -0.93354 + 0x3fd6d998638a0cb5, 0xbfede4160f6d8d81, // 0.35703, -0.93409 + 0x3fd6c21cb1e39771, 0xbfede890520465ce, // 0.3556, -0.93464 + 0x3fd6aa9d7dc77e16, 0xbfeded05f7de47da, // 0.35416, -0.93518 + 0x3fd6931acad55f51, 0xbfedf177004b2534, // 0.35273, -0.93573 + 0x3fd67b949cad63ca, 0xbfedf5e36a9ba59c, // 0.35129, -0.93627 + 0x3fd6640af6f03d9e, 0xbfedfa4b3621271d, // 0.34986, -0.9368 + 0x3fd64c7ddd3f27c6, 0xbfedfeae622dbe2b, // 0.34842, -0.93734 + 0x3fd634ed533be58e, 0xbfee030cee1435b8, // 0.34698, -0.93787 + 0x3fd61d595c88c203, 0xbfee0766d9280f54, // 0.34554, -0.9384 + 0x3fd605c1fcc88f63, 0xbfee0bbc22bd8349, // 0.3441, -0.93893 + 0x3fd5ee27379ea693, 0xbfee100cca2980ac, // 0.34266, -0.93946 + 0x3fd5d68910aee686, 0xbfee1458cec1ad83, // 0.34122, -0.93998 + 0x3fd5bee78b9db3b6, 0xbfee18a02fdc66d9, // 0.33978, -0.94051 + 0x3fd5a742ac0ff78d, 0xbfee1ce2ecd0c0d8, // 0.33833, -0.94103 + 0x3fd58f9a75ab1fdd, 0xbfee212104f686e5, // 0.33689, -0.94154 + 0x3fd577eeec151e47, 0xbfee255a77a63bb8, // 0.33545, -0.94206 + 0x3fd5604012f467b4, 0xbfee298f4439197a, // 0.334, -0.94257 + 0x3fd5488dedeff3be, 0xbfee2dbf6a0911d9, // 0.33255, -0.94308 + 0x3fd530d880af3c24, 0xbfee31eae870ce25, // 0.33111, -0.94359 + 0x3fd5191fceda3c35, 0xbfee3611becbaf69, // 0.32966, -0.9441 + 0x3fd50163dc197047, 0xbfee3a33ec75ce85, // 0.32821, -0.9446 + 0x3fd4e9a4ac15d520, 0xbfee3e5170cbfc46, // 0.32676, -0.94511 + 0x3fd4d1e24278e76a, 0xbfee426a4b2bc17e, // 0.32531, -0.94561 + 0x3fd4ba1ca2eca31c, 0xbfee467e7af35f23, // 0.32386, -0.94611 + 0x3fd4a253d11b82f3, 0xbfee4a8dff81ce5e, // 0.32241, -0.9466 + 0x3fd48a87d0b07fd7, 0xbfee4e98d836c0af, // 0.32096, -0.94709 + 0x3fd472b8a5571054, 0xbfee529f04729ffc, // 0.3195, -0.94759 + 0x3fd45ae652bb2800, 0xbfee56a083968eb1, // 0.31805, -0.94807 + 0x3fd44310dc8936f0, 0xbfee5a9d550467d3, // 0.31659, -0.94856 + 0x3fd42b38466e2928, 0xbfee5e95781ebf1c, // 0.31514, -0.94905 + 0x3fd4135c94176602, 0xbfee6288ec48e112, // 0.31368, -0.94953 + 0x3fd3fb7dc932cfa4, 0xbfee6677b0e6d31e, // 0.31222, -0.95001 + 0x3fd3e39be96ec271, 0xbfee6a61c55d53a7, // 0.31077, -0.95049 + 0x3fd3cbb6f87a146e, 0xbfee6e472911da27, // 0.30931, -0.95096 + 0x3fd3b3cefa0414b7, 0xbfee7227db6a9744, // 0.30785, -0.95144 + 0x3fd39be3f1bc8aef, 0xbfee7603dbce74e9, // 0.30639, -0.95191 + 0x3fd383f5e353b6aa, 0xbfee79db29a5165a, // 0.30493, -0.95238 + 0x3fd36c04d27a4edf, 0xbfee7dadc456d850, // 0.30347, -0.95284 + 0x3fd35410c2e18152, 0xbfee817bab4cd10d, // 0.30201, -0.95331 + 0x3fd33c19b83af207, 0xbfee8544ddf0d075, // 0.30054, -0.95377 + 0x3fd3241fb638baaf, 0xbfee89095bad6025, // 0.29908, -0.95423 + 0x3fd30c22c08d6a13, 0xbfee8cc923edc388, // 0.29762, -0.95469 + 0x3fd2f422daec0386, 0xbfee9084361df7f3, // 0.29615, -0.95514 + 0x3fd2dc200907fe51, 0xbfee943a91aab4b4, // 0.29469, -0.95559 + 0x3fd2c41a4e954520, 0xbfee97ec36016b30, // 0.29322, -0.95605 + 0x3fd2ac11af483572, 0xbfee9b99229046f8, // 0.29175, -0.95649 + 0x3fd294062ed59f05, 0xbfee9f4156c62dda, // 0.29028, -0.95694 + 0x3fd27bf7d0f2c346, 0xbfeea2e4d212c000, // 0.28882, -0.95738 + 0x3fd263e6995554ba, 0xbfeea68393e65800, // 0.28735, -0.95783 + 0x3fd24bd28bb37672, 0xbfeeaa1d9bb20af3, // 0.28588, -0.95827 + 0x3fd233bbabc3bb72, 0xbfeeadb2e8e7a88e, // 0.28441, -0.9587 + 0x3fd21ba1fd3d2623, 0xbfeeb1437af9bb34, // 0.28294, -0.95914 + 0x3fd2038583d727bd, 0xbfeeb4cf515b8811, // 0.28146, -0.95957 + 0x3fd1eb6643499fbb, 0xbfeeb8566b810f2a, // 0.27999, -0.96 + 0x3fd1d3443f4cdb3d, 0xbfeebbd8c8df0b74, // 0.27852, -0.96043 + 0x3fd1bb1f7b999480, 0xbfeebf5668eaf2ef, // 0.27705, -0.96086 + 0x3fd1a2f7fbe8f243, 0xbfeec2cf4b1af6b2, // 0.27557, -0.96128 + 0x3fd18acdc3f4873a, 0xbfeec6436ee60309, // 0.2741, -0.9617 + 0x3fd172a0d7765177, 0xbfeec9b2d3c3bf84, // 0.27262, -0.96212 + 0x3fd15a713a28b9d9, 0xbfeecd1d792c8f10, // 0.27115, -0.96254 + 0x3fd1423eefc69378, 0xbfeed0835e999009, // 0.26967, -0.96295 + 0x3fd12a09fc0b1b12, 0xbfeed3e483849c51, // 0.26819, -0.96337 + 0x3fd111d262b1f677, 0xbfeed740e7684963, // 0.26671, -0.96378 + 0x3fd0f998277733f7, 0xbfeeda9889bfe86a, // 0.26523, -0.96418 + 0x3fd0e15b4e1749cd, 0xbfeeddeb6a078651, // 0.26375, -0.96459 + 0x3fd0c91bda4f158d, 0xbfeee13987bbebdc, // 0.26227, -0.96499 + 0x3fd0b0d9cfdbdb90, 0xbfeee482e25a9dbc, // 0.26079, -0.96539 + 0x3fd09895327b465e, 0xbfeee7c77961dc9e, // 0.25931, -0.96579 + 0x3fd0804e05eb661e, 0xbfeeeb074c50a544, // 0.25783, -0.96619 + 0x3fd068044deab002, 0xbfeeee425aa6b09a, // 0.25635, -0.96658 + 0x3fd04fb80e37fdae, 0xbfeef178a3e473c2, // 0.25487, -0.96698 + 0x3fd037694a928cac, 0xbfeef4aa278b2032, // 0.25338, -0.96737 + 0x3fd01f1806b9fdd2, 0xbfeef7d6e51ca3c0, // 0.2519, -0.96775 + 0x3fd006c4466e54af, 0xbfeefafedc1ba8b7, // 0.25041, -0.96814 + 0x3fcfdcdc1adfedf8, 0xbfeefe220c0b95ec, // 0.24893, -0.96852 + 0x3fcfac2abeff57ff, 0xbfef014074708ed3, // 0.24744, -0.9689 + 0x3fcf7b7480bd3801, 0xbfef045a14cf738c, // 0.24596, -0.96928 + 0x3fcf4ab9679c9f5c, 0xbfef076eecade0fa, // 0.24447, -0.96966 + 0x3fcf19f97b215f1a, 0xbfef0a7efb9230d7, // 0.24298, -0.97003 + 0x3fcee934c2d006c7, 0xbfef0d8a410379c5, // 0.24149, -0.9704 + 0x3fceb86b462de348, 0xbfef1090bc898f5f, // 0.24, -0.97077 + 0x3fce879d0cc0fdaf, 0xbfef13926dad024e, // 0.23851, -0.97114 + 0x3fce56ca1e101a1b, 0xbfef168f53f7205d, // 0.23702, -0.9715 + 0x3fce25f281a2b684, 0xbfef19876ef1f486, // 0.23553, -0.97187 + 0x3fcdf5163f01099a, 0xbfef1c7abe284708, // 0.23404, -0.97223 + 0x3fcdc4355db40195, 0xbfef1f6941259d7a, // 0.23255, -0.97258 + 0x3fcd934fe5454311, 0xbfef2252f7763ada, // 0.23106, -0.97294 + 0x3fcd6265dd3f27e3, 0xbfef2537e0a71f9f, // 0.22957, -0.97329 + 0x3fcd31774d2cbdee, 0xbfef2817fc4609ce, // 0.22807, -0.97364 + 0x3fcd00843c99c5f9, 0xbfef2af349e17507, // 0.22658, -0.97399 + 0x3fcccf8cb312b286, 0xbfef2dc9c9089a9d, // 0.22508, -0.97434 + 0x3fcc9e90b824a6a9, 0xbfef309b794b719f, // 0.22359, -0.97468 + 0x3fcc6d90535d74dc, 0xbfef33685a3aaef0, // 0.22209, -0.97503 + 0x3fcc3c8b8c4b9dd7, 0xbfef36306b67c556, // 0.2206, -0.97536 + 0x3fcc0b826a7e4f63, 0xbfef38f3ac64e589, // 0.2191, -0.9757 + 0x3fcbda74f5856330, 0xbfef3bb21cc4fe47, // 0.2176, -0.97604 + 0x3fcba96334f15dad, 0xbfef3e6bbc1bbc65, // 0.21611, -0.97637 + 0x3fcb784d30536cda, 0xbfef412089fd8adc, // 0.21461, -0.9767 + 0x3fcb4732ef3d6722, 0xbfef43d085ff92dd, // 0.21311, -0.97703 + 0x3fcb16147941ca2a, 0xbfef467bafb7bbe0, // 0.21161, -0.97735 + 0x3fcae4f1d5f3b9ab, 0xbfef492206bcabb4, // 0.21011, -0.97768 + 0x3fcab3cb0ce6fe44, 0xbfef4bc38aa5c694, // 0.20861, -0.978 + 0x3fca82a025b00451, 0xbfef4e603b0b2f2d, // 0.20711, -0.97832 + 0x3fca517127e3dabc, 0xbfef50f81785c6b9, // 0.20561, -0.97863 + 0x3fca203e1b1831da, 0xbfef538b1faf2d07, // 0.20411, -0.97895 + 0x3fc9ef0706e35a35, 0xbfef56195321c090, // 0.20261, -0.97926 + 0x3fc9bdcbf2dc4366, 0xbfef58a2b1789e84, // 0.2011, -0.97957 + 0x3fc98c8ce69a7aec, 0xbfef5b273a4fa2d9, // 0.1996, -0.97988 + 0x3fc95b49e9b62af9, 0xbfef5da6ed43685d, // 0.1981, -0.98018 + 0x3fc92a0303c8194f, 0xbfef6021c9f148c2, // 0.19659, -0.98048 + 0x3fc8f8b83c69a60a, 0xbfef6297cff75cb0, // 0.19509, -0.98079 + 0x3fc8c7699b34ca7e, 0xbfef6508fef47bd5, // 0.19359, -0.98108 + 0x3fc8961727c41804, 0xbfef677556883cee, // 0.19208, -0.98138 + 0x3fc864c0e9b2b6cf, 0xbfef69dcd652f5de, // 0.19057, -0.98167 + 0x3fc83366e89c64c5, 0xbfef6c3f7df5bbb7, // 0.18907, -0.98196 + 0x3fc802092c1d744b, 0xbfef6e9d4d1262ca, // 0.18756, -0.98225 + 0x3fc7d0a7bbd2cb1b, 0xbfef70f6434b7eb7, // 0.18606, -0.98254 + 0x3fc79f429f59e11d, 0xbfef734a60446279, // 0.18455, -0.98282 + 0x3fc76dd9de50bf31, 0xbfef7599a3a12077, // 0.18304, -0.98311 + 0x3fc73c6d8055fe0a, 0xbfef77e40d068a90, // 0.18153, -0.98339 + 0x3fc70afd8d08c4ff, 0xbfef7a299c1a322a, // 0.18002, -0.98366 + 0x3fc6d98a0c08c8da, 0xbfef7c6a50826840, // 0.17851, -0.98394 + 0x3fc6a81304f64ab2, 0xbfef7ea629e63d6e, // 0.177, -0.98421 + 0x3fc676987f7216b8, 0xbfef80dd27ed8204, // 0.17549, -0.98448 + 0x3fc6451a831d830d, 0xbfef830f4a40c60c, // 0.17398, -0.98475 + 0x3fc61399179a6e94, 0xbfef853c9089595e, // 0.17247, -0.98501 + 0x3fc5e214448b3fc6, 0xbfef8764fa714ba9, // 0.17096, -0.98528 + 0x3fc5b08c1192e381, 0xbfef898887a36c84, // 0.16945, -0.98554 + 0x3fc57f008654cbde, 0xbfef8ba737cb4b78, // 0.16794, -0.9858 + 0x3fc54d71aa74ef02, 0xbfef8dc10a95380d, // 0.16643, -0.98605 + 0x3fc51bdf8597c5f2, 0xbfef8fd5ffae41db, // 0.16491, -0.98631 + 0x3fc4ea4a1f624b61, 0xbfef91e616c43891, // 0.1634, -0.98656 + 0x3fc4b8b17f79fa88, 0xbfef93f14f85ac08, // 0.16189, -0.98681 + 0x3fc48715ad84cdf5, 0xbfef95f7a9a1ec47, // 0.16037, -0.98706 + 0x3fc45576b1293e5a, 0xbfef97f924c9099b, // 0.15886, -0.9873 + 0x3fc423d4920e4166, 0xbfef99f5c0abd496, // 0.15734, -0.98754 + 0x3fc3f22f57db4893, 0xbfef9bed7cfbde29, // 0.15583, -0.98778 + 0x3fc3c0870a383ff6, 0xbfef9de0596b77a3, // 0.15431, -0.98802 + 0x3fc38edbb0cd8d14, 0xbfef9fce55adb2c8, // 0.1528, -0.98826 + 0x3fc35d2d53440db2, 0xbfefa1b7717661d5, // 0.15128, -0.98849 + 0x3fc32b7bf94516a7, 0xbfefa39bac7a1791, // 0.14976, -0.98872 + 0x3fc2f9c7aa7a72af, 0xbfefa57b066e2754, // 0.14825, -0.98895 + 0x3fc2c8106e8e613a, 0xbfefa7557f08a517, // 0.14673, -0.98918 + 0x3fc296564d2b953e, 0xbfefa92b1600657c, // 0.14521, -0.9894 + 0x3fc264994dfd340a, 0xbfefaafbcb0cfddc, // 0.1437, -0.98962 + 0x3fc232d978aed413, 0xbfefacc79de6c44f, // 0.14218, -0.98984 + 0x3fc20116d4ec7bce, 0xbfefae8e8e46cfbb, // 0.14066, -0.99006 + 0x3fc1cf516a62a077, 0xbfefb0509be6f7db, // 0.13914, -0.99027 + 0x3fc19d8940be24e7, 0xbfefb20dc681d54d, // 0.13762, -0.99049 + 0x3fc16bbe5fac5865, 0xbfefb3c60dd2c199, // 0.1361, -0.9907 + 0x3fc139f0cedaf576, 0xbfefb5797195d741, // 0.13458, -0.9909 + 0x3fc1082095f820b0, 0xbfefb727f187f1c7, // 0.13306, -0.99111 + 0x3fc0d64dbcb26786, 0xbfefb8d18d66adb7, // 0.13154, -0.99131 + 0x3fc0a4784ab8bf1d, 0xbfefba7644f068b5, // 0.13002, -0.99151 + 0x3fc072a047ba831d, 0xbfefbc1617e44186, // 0.1285, -0.99171 + 0x3fc040c5bb67747e, 0xbfefbdb106021816, // 0.12698, -0.99191 + 0x3fc00ee8ad6fb85b, 0xbfefbf470f0a8d88, // 0.12545, -0.9921 + 0x3fbfba124b07ad85, 0xbfefc0d832bf043a, // 0.12393, -0.99229 + 0x3fbf564e56a9730e, 0xbfefc26470e19fd3, // 0.12241, -0.99248 + 0x3fbef2858d27561b, 0xbfefc3ebc935454c, // 0.12089, -0.99267 + 0x3fbe8eb7fde4aa3e, 0xbfefc56e3b7d9af6, // 0.11937, -0.99285 + 0x3fbe2ae5b8457f77, 0xbfefc6ebc77f0887, // 0.11784, -0.99303 + 0x3fbdc70ecbae9fc8, 0xbfefc8646cfeb721, // 0.11632, -0.99321 + 0x3fbd633347858ce4, 0xbfefc9d82bc2915e, // 0.11479, -0.99339 + 0x3fbcff533b307dc1, 0xbfefcb4703914354, // 0.11327, -0.99356 + 0x3fbc9b6eb6165c42, 0xbfefccb0f4323aa3, // 0.11175, -0.99374 + 0x3fbc3785c79ec2d5, 0xbfefce15fd6da67b, // 0.11022, -0.99391 + 0x3fbbd3987f31fa0e, 0xbfefcf761f0c77a3, // 0.1087, -0.99407 + 0x3fbb6fa6ec38f64c, 0xbfefd0d158d86087, // 0.10717, -0.99424 + 0x3fbb0bb11e1d5559, 0xbfefd227aa9bd53b, // 0.10565, -0.9944 + 0x3fbaa7b724495c04, 0xbfefd37914220b84, // 0.10412, -0.99456 + 0x3fba43b90e27f3c4, 0xbfefd4c59536fae4, // 0.1026, -0.99472 + 0x3fb9dfb6eb24a85c, 0xbfefd60d2da75c9e, // 0.10107, -0.99488 + 0x3fb97bb0caaba56f, 0xbfefd74fdd40abbf, // 0.099544, -0.99503 + 0x3fb917a6bc29b42c, 0xbfefd88da3d12526, // 0.098017, -0.99518 + 0x3fb8b398cf0c38e0, 0xbfefd9c68127c78c, // 0.09649, -0.99533 + 0x3fb84f8712c130a0, 0xbfefdafa7514538c, // 0.094963, -0.99548 + 0x3fb7eb7196b72ee4, 0xbfefdc297f674ba9, // 0.093436, -0.99563 + 0x3fb787586a5d5b21, 0xbfefdd539ff1f456, // 0.091909, -0.99577 + 0x3fb7233b9d236e71, 0xbfefde78d68653fd, // 0.090381, -0.99591 + 0x3fb6bf1b3e79b129, 0xbfefdf9922f73307, // 0.088854, -0.99604 + 0x3fb65af75dd0f87b, 0xbfefe0b485181be3, // 0.087326, -0.99618 + 0x3fb5f6d00a9aa419, 0xbfefe1cafcbd5b09, // 0.085797, -0.99631 + 0x3fb592a554489bc8, 0xbfefe2dc89bbff08, // 0.084269, -0.99644 + 0x3fb52e774a4d4d0a, 0xbfefe3e92be9d886, // 0.08274, -0.99657 + 0x3fb4ca45fc1ba8b6, 0xbfefe4f0e31d7a4a, // 0.081211, -0.9967 + 0x3fb4661179272096, 0xbfefe5f3af2e3940, // 0.079682, -0.99682 + 0x3fb401d9d0e3a507, 0xbfefe6f18ff42c84, // 0.078153, -0.99694 + 0x3fb39d9f12c5a299, 0xbfefe7ea85482d60, // 0.076624, -0.99706 + 0x3fb339614e41ffa5, 0xbfefe8de8f03d75c, // 0.075094, -0.99718 + 0x3fb2d52092ce19f6, 0xbfefe9cdad01883a, // 0.073565, -0.99729 + 0x3fb270dcefdfc45b, 0xbfefeab7df1c6005, // 0.072035, -0.9974 + 0x3fb20c9674ed444c, 0xbfefeb9d2530410f, // 0.070505, -0.99751 + 0x3fb1a84d316d4f8a, 0xbfefec7d7f19cffc, // 0.068974, -0.99762 + 0x3fb1440134d709b2, 0xbfefed58ecb673c4, // 0.067444, -0.99772 + 0x3fb0dfb28ea201e6, 0xbfefee2f6de455ba, // 0.065913, -0.99783 + 0x3fb07b614e463064, 0xbfefef0102826191, // 0.064383, -0.99793 + 0x3fb0170d833bf421, 0xbfefefcdaa704562, // 0.062852, -0.99802 + 0x3faf656e79f820e0, 0xbfeff095658e71ad, // 0.061321, -0.99812 + 0x3fae9cbd15ff5527, 0xbfeff15833be1965, // 0.05979, -0.99821 + 0x3fadd406f9808ec8, 0xbfeff21614e131ed, // 0.058258, -0.9983 + 0x3fad0b4c436f91d0, 0xbfeff2cf08da7321, // 0.056727, -0.99839 + 0x3fac428d12c0d7e3, 0xbfeff3830f8d575c, // 0.055195, -0.99848 + 0x3fab79c986698b78, 0xbfeff43228de1b77, // 0.053664, -0.99856 + 0x3faab101bd5f8317, 0xbfeff4dc54b1bed3, // 0.052132, -0.99864 + 0x3fa9e835d6993c87, 0xbfeff58192ee0358, // 0.0506, -0.99872 + 0x3fa91f65f10dd814, 0xbfeff621e3796d7e, // 0.049068, -0.9988 + 0x3fa856922bb513c1, 0xbfeff6bd463b444d, // 0.047535, -0.99887 + 0x3fa78dbaa5874685, 0xbfeff753bb1b9164, // 0.046003, -0.99894 + 0x3fa6c4df7d7d5b84, 0xbfeff7e5420320f9, // 0.044471, -0.99901 + 0x3fa5fc00d290cd43, 0xbfeff871dadb81df, // 0.042938, -0.99908 + 0x3fa5331ec3bba0eb, 0xbfeff8f9858f058b, // 0.041406, -0.99914 + 0x3fa46a396ff86179, 0xbfeff97c4208c014, // 0.039873, -0.9992 + 0x3fa3a150f6421afc, 0xbfeff9fa10348837, // 0.03834, -0.99926 + 0x3fa2d865759455cd, 0xbfeffa72effef75d, // 0.036807, -0.99932 + 0x3fa20f770ceb11c6, 0xbfeffae6e1556998, // 0.035274, -0.99938 + 0x3fa14685db42c17e, 0xbfeffb55e425fdae, // 0.033741, -0.99943 + 0x3fa07d91ff984580, 0xbfeffbbff85f9515, // 0.032208, -0.99948 + 0x3f9f693731d1cf01, 0xbfeffc251df1d3f8, // 0.030675, -0.99953 + 0x3f9dd7458c64ab39, 0xbfeffc8554cd213a, // 0.029142, -0.99958 + 0x3f9c454f4ce53b1c, 0xbfeffce09ce2a679, // 0.027608, -0.99962 + 0x3f9ab354b1504fca, 0xbfeffd36f624500c, // 0.026075, -0.99966 + 0x3f992155f7a3667e, 0xbfeffd886084cd0d, // 0.024541, -0.9997 + 0x3f978f535ddc9f03, 0xbfeffdd4dbf78f52, // 0.023008, -0.99974 + 0x3f95fd4d21fab226, 0xbfeffe1c6870cb77, // 0.021474, -0.99977 + 0x3f946b4381fce81c, 0xbfeffe5f05e578db, // 0.01994, -0.9998 + 0x3f92d936bbe30efd, 0xbfeffe9cb44b51a1, // 0.018407, -0.99983 + 0x3f9147270dad7132, 0xbfeffed57398d2b7, // 0.016873, -0.99986 + 0x3f8f6a296ab997ca, 0xbfefff0943c53bd1, // 0.015339, -0.99988 + 0x3f8c45ffe1e48ad9, 0xbfefff3824c88f6f, // 0.013805, -0.9999 + 0x3f8921d1fcdec784, 0xbfefff62169b92db, // 0.012272, -0.99992 + 0x3f85fda037ac05e0, 0xbfefff871937ce2f, // 0.010738, -0.99994 + 0x3f82d96b0e509703, 0xbfefffa72c978c4f, //0.0092038, -0.99996 + 0x3f7f6a65f9a2a3c5, 0xbfefffc250b5daef, //0.0076698, -0.99997 + 0x3f7921f0fe670071, 0xbfefffd8858e8a92, //0.0061359, -0.99998 + 0x3f72d97822f996bc, 0xbfefffe9cb1e2e8d, //0.0046019, -0.99999 + 0x3f6921f8becca4ba, 0xbfeffff621621d02, // 0.003068, -1 + 0x3f5921faaee6472d, 0xbfeffffd88586ee6, // 0.001534, -1 +}; + + +/** + @par + Example code for Floating-point RFFT Twiddle factors Generation: + @par + 
TW = exp(pi/2*i-2*pi*i*[0:L/2-1]/L).'
+ @par + Real and Imag values are in interleaved fashion +*/ +const float32_t twiddleCoef_rfft_32[32] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000f, 1.000000000f, + 0.195090322f, 0.980785280f, + 0.382683432f, 0.923879533f, + 0.555570233f, 0.831469612f, + 0.707106781f, 0.707106781f, + 0.831469612f, 0.555570233f, + 0.923879533f, 0.382683432f, + 0.980785280f, 0.195090322f, + 1.000000000f, 0.000000000f, + 0.980785280f, -0.195090322f, + 0.923879533f, -0.382683432f, + 0.831469612f, -0.555570233f, + 0.707106781f, -0.707106781f, + 0.555570233f, -0.831469612f, + 0.382683432f, -0.923879533f, + 0.195090322f, -0.980785280f +}; + +const float32_t twiddleCoef_rfft_64[64] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000000000f, 1.000000000000000f, + 0.098017140329561f, 0.995184726672197f, + 0.195090322016128f, 0.980785280403230f, + 0.290284677254462f, 0.956940335732209f, + 0.382683432365090f, 0.923879532511287f, + 0.471396736825998f, 0.881921264348355f, + 0.555570233019602f, 0.831469612302545f, + 0.634393284163645f, 0.773010453362737f, + 0.707106781186547f, 0.707106781186548f, + 0.773010453362737f, 0.634393284163645f, + 0.831469612302545f, 0.555570233019602f, + 0.881921264348355f, 0.471396736825998f, + 0.923879532511287f, 0.382683432365090f, + 0.956940335732209f, 0.290284677254462f, + 0.980785280403230f, 0.195090322016128f, + 0.995184726672197f, 0.098017140329561f, + 1.000000000000000f, 0.000000000000000f, + 0.995184726672197f, -0.098017140329561f, + 0.980785280403230f, -0.195090322016128f, + 0.956940335732209f, -0.290284677254462f, + 0.923879532511287f, -0.382683432365090f, + 0.881921264348355f, -0.471396736825998f, + 0.831469612302545f, -0.555570233019602f, + 0.773010453362737f, -0.634393284163645f, + 0.707106781186548f, -0.707106781186547f, + 0.634393284163645f, -0.773010453362737f, + 0.555570233019602f, -0.831469612302545f, + 0.471396736825998f, -0.881921264348355f, + 0.382683432365090f, -0.923879532511287f, + 0.290284677254462f, -0.956940335732209f, + 0.195090322016129f, -0.980785280403230f, + 0.098017140329561f, -0.995184726672197f +}; + +const float32_t twiddleCoef_rfft_128[128] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000f, 1.000000000f, + 0.049067674f, 0.998795456f, + 0.098017140f, 0.995184727f, + 0.146730474f, 0.989176510f, + 0.195090322f, 0.980785280f, + 0.242980180f, 0.970031253f, + 0.290284677f, 0.956940336f, + 0.336889853f, 0.941544065f, + 0.382683432f, 0.923879533f, + 0.427555093f, 0.903989293f, + 0.471396737f, 0.881921264f, + 0.514102744f, 0.857728610f, + 0.555570233f, 0.831469612f, + 0.595699304f, 0.803207531f, + 0.634393284f, 0.773010453f, + 0.671558955f, 0.740951125f, + 0.707106781f, 0.707106781f, + 0.740951125f, 0.671558955f, + 0.773010453f, 0.634393284f, + 0.803207531f, 0.595699304f, + 0.831469612f, 0.555570233f, + 0.857728610f, 0.514102744f, + 0.881921264f, 0.471396737f, + 0.903989293f, 0.427555093f, + 0.923879533f, 0.382683432f, + 0.941544065f, 0.336889853f, + 0.956940336f, 0.290284677f, + 0.970031253f, 0.242980180f, + 0.980785280f, 0.195090322f, + 0.989176510f, 0.146730474f, + 0.995184727f, 0.098017140f, + 0.998795456f, 0.049067674f, + 1.000000000f, 0.000000000f, + 0.998795456f, -0.049067674f, + 0.995184727f, -0.098017140f, + 0.989176510f, -0.146730474f, + 0.980785280f, -0.195090322f, + 0.970031253f, -0.242980180f, + 0.956940336f, -0.290284677f, + 0.941544065f, -0.336889853f, + 0.923879533f, -0.382683432f, + 0.903989293f, -0.427555093f, + 0.881921264f, -0.471396737f, + 0.857728610f, -0.514102744f, + 0.831469612f, -0.555570233f, + 0.803207531f, -0.595699304f, + 0.773010453f, -0.634393284f, + 0.740951125f, -0.671558955f, + 0.707106781f, -0.707106781f, + 0.671558955f, -0.740951125f, + 0.634393284f, -0.773010453f, + 0.595699304f, -0.803207531f, + 0.555570233f, -0.831469612f, + 0.514102744f, -0.857728610f, + 0.471396737f, -0.881921264f, + 0.427555093f, -0.903989293f, + 0.382683432f, -0.923879533f, + 0.336889853f, -0.941544065f, + 0.290284677f, -0.956940336f, + 0.242980180f, -0.970031253f, + 0.195090322f, -0.980785280f, + 0.146730474f, -0.989176510f, + 0.098017140f, -0.995184727f, + 0.049067674f, -0.998795456f +}; + +const float32_t twiddleCoef_rfft_256[256] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000f, 1.000000000f, + 0.024541229f, 0.999698819f, + 0.049067674f, 0.998795456f, + 0.073564564f, 0.997290457f, + 0.098017140f, 0.995184727f, + 0.122410675f, 0.992479535f, + 0.146730474f, 0.989176510f, + 0.170961889f, 0.985277642f, + 0.195090322f, 0.980785280f, + 0.219101240f, 0.975702130f, + 0.242980180f, 0.970031253f, + 0.266712757f, 0.963776066f, + 0.290284677f, 0.956940336f, + 0.313681740f, 0.949528181f, + 0.336889853f, 0.941544065f, + 0.359895037f, 0.932992799f, + 0.382683432f, 0.923879533f, + 0.405241314f, 0.914209756f, + 0.427555093f, 0.903989293f, + 0.449611330f, 0.893224301f, + 0.471396737f, 0.881921264f, + 0.492898192f, 0.870086991f, + 0.514102744f, 0.857728610f, + 0.534997620f, 0.844853565f, + 0.555570233f, 0.831469612f, + 0.575808191f, 0.817584813f, + 0.595699304f, 0.803207531f, + 0.615231591f, 0.788346428f, + 0.634393284f, 0.773010453f, + 0.653172843f, 0.757208847f, + 0.671558955f, 0.740951125f, + 0.689540545f, 0.724247083f, + 0.707106781f, 0.707106781f, + 0.724247083f, 0.689540545f, + 0.740951125f, 0.671558955f, + 0.757208847f, 0.653172843f, + 0.773010453f, 0.634393284f, + 0.788346428f, 0.615231591f, + 0.803207531f, 0.595699304f, + 0.817584813f, 0.575808191f, + 0.831469612f, 0.555570233f, + 0.844853565f, 0.534997620f, + 0.857728610f, 0.514102744f, + 0.870086991f, 0.492898192f, + 0.881921264f, 0.471396737f, + 0.893224301f, 0.449611330f, + 0.903989293f, 0.427555093f, + 0.914209756f, 0.405241314f, + 0.923879533f, 0.382683432f, + 0.932992799f, 0.359895037f, + 0.941544065f, 0.336889853f, + 0.949528181f, 0.313681740f, + 0.956940336f, 0.290284677f, + 0.963776066f, 0.266712757f, + 0.970031253f, 0.242980180f, + 0.975702130f, 0.219101240f, + 0.980785280f, 0.195090322f, + 0.985277642f, 0.170961889f, + 0.989176510f, 0.146730474f, + 0.992479535f, 0.122410675f, + 0.995184727f, 0.098017140f, + 0.997290457f, 0.073564564f, + 0.998795456f, 0.049067674f, + 0.999698819f, 0.024541229f, + 1.000000000f, 0.000000000f, + 0.999698819f, -0.024541229f, + 0.998795456f, -0.049067674f, + 0.997290457f, -0.073564564f, + 0.995184727f, -0.098017140f, + 0.992479535f, -0.122410675f, + 0.989176510f, -0.146730474f, + 0.985277642f, -0.170961889f, + 0.980785280f, -0.195090322f, + 0.975702130f, -0.219101240f, + 0.970031253f, -0.242980180f, + 0.963776066f, -0.266712757f, + 0.956940336f, -0.290284677f, + 0.949528181f, -0.313681740f, + 0.941544065f, -0.336889853f, + 0.932992799f, -0.359895037f, + 0.923879533f, -0.382683432f, + 0.914209756f, -0.405241314f, + 0.903989293f, -0.427555093f, + 0.893224301f, -0.449611330f, + 0.881921264f, -0.471396737f, + 0.870086991f, -0.492898192f, + 0.857728610f, -0.514102744f, + 0.844853565f, -0.534997620f, + 0.831469612f, -0.555570233f, + 0.817584813f, -0.575808191f, + 0.803207531f, -0.595699304f, + 0.788346428f, -0.615231591f, + 0.773010453f, -0.634393284f, + 0.757208847f, -0.653172843f, + 0.740951125f, -0.671558955f, + 0.724247083f, -0.689540545f, + 0.707106781f, -0.707106781f, + 0.689540545f, -0.724247083f, + 0.671558955f, -0.740951125f, + 0.653172843f, -0.757208847f, + 0.634393284f, -0.773010453f, + 0.615231591f, -0.788346428f, + 0.595699304f, -0.803207531f, + 0.575808191f, -0.817584813f, + 0.555570233f, -0.831469612f, + 0.534997620f, -0.844853565f, + 0.514102744f, -0.857728610f, + 0.492898192f, -0.870086991f, + 0.471396737f, -0.881921264f, + 0.449611330f, -0.893224301f, + 0.427555093f, -0.903989293f, + 0.405241314f, -0.914209756f, + 0.382683432f, -0.923879533f, + 0.359895037f, -0.932992799f, + 0.336889853f, -0.941544065f, + 0.313681740f, -0.949528181f, + 0.290284677f, -0.956940336f, + 0.266712757f, -0.963776066f, + 0.242980180f, -0.970031253f, + 0.219101240f, -0.975702130f, + 0.195090322f, -0.980785280f, + 0.170961889f, -0.985277642f, + 0.146730474f, -0.989176510f, + 0.122410675f, -0.992479535f, + 0.098017140f, -0.995184727f, + 0.073564564f, -0.997290457f, + 0.049067674f, -0.998795456f, + 0.024541229f, -0.999698819f +}; + +const float32_t twiddleCoef_rfft_512[512] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000f, 1.000000000f, + 0.012271538f, 0.999924702f, + 0.024541229f, 0.999698819f, + 0.036807223f, 0.999322385f, + 0.049067674f, 0.998795456f, + 0.061320736f, 0.998118113f, + 0.073564564f, 0.997290457f, + 0.085797312f, 0.996312612f, + 0.098017140f, 0.995184727f, + 0.110222207f, 0.993906970f, + 0.122410675f, 0.992479535f, + 0.134580709f, 0.990902635f, + 0.146730474f, 0.989176510f, + 0.158858143f, 0.987301418f, + 0.170961889f, 0.985277642f, + 0.183039888f, 0.983105487f, + 0.195090322f, 0.980785280f, + 0.207111376f, 0.978317371f, + 0.219101240f, 0.975702130f, + 0.231058108f, 0.972939952f, + 0.242980180f, 0.970031253f, + 0.254865660f, 0.966976471f, + 0.266712757f, 0.963776066f, + 0.278519689f, 0.960430519f, + 0.290284677f, 0.956940336f, + 0.302005949f, 0.953306040f, + 0.313681740f, 0.949528181f, + 0.325310292f, 0.945607325f, + 0.336889853f, 0.941544065f, + 0.348418680f, 0.937339012f, + 0.359895037f, 0.932992799f, + 0.371317194f, 0.928506080f, + 0.382683432f, 0.923879533f, + 0.393992040f, 0.919113852f, + 0.405241314f, 0.914209756f, + 0.416429560f, 0.909167983f, + 0.427555093f, 0.903989293f, + 0.438616239f, 0.898674466f, + 0.449611330f, 0.893224301f, + 0.460538711f, 0.887639620f, + 0.471396737f, 0.881921264f, + 0.482183772f, 0.876070094f, + 0.492898192f, 0.870086991f, + 0.503538384f, 0.863972856f, + 0.514102744f, 0.857728610f, + 0.524589683f, 0.851355193f, + 0.534997620f, 0.844853565f, + 0.545324988f, 0.838224706f, + 0.555570233f, 0.831469612f, + 0.565731811f, 0.824589303f, + 0.575808191f, 0.817584813f, + 0.585797857f, 0.810457198f, + 0.595699304f, 0.803207531f, + 0.605511041f, 0.795836905f, + 0.615231591f, 0.788346428f, + 0.624859488f, 0.780737229f, + 0.634393284f, 0.773010453f, + 0.643831543f, 0.765167266f, + 0.653172843f, 0.757208847f, + 0.662415778f, 0.749136395f, + 0.671558955f, 0.740951125f, + 0.680600998f, 0.732654272f, + 0.689540545f, 0.724247083f, + 0.698376249f, 0.715730825f, + 0.707106781f, 0.707106781f, + 0.715730825f, 0.698376249f, + 0.724247083f, 0.689540545f, + 0.732654272f, 0.680600998f, + 0.740951125f, 0.671558955f, + 0.749136395f, 0.662415778f, + 0.757208847f, 0.653172843f, + 0.765167266f, 0.643831543f, + 0.773010453f, 0.634393284f, + 0.780737229f, 0.624859488f, + 0.788346428f, 0.615231591f, + 0.795836905f, 0.605511041f, + 0.803207531f, 0.595699304f, + 0.810457198f, 0.585797857f, + 0.817584813f, 0.575808191f, + 0.824589303f, 0.565731811f, + 0.831469612f, 0.555570233f, + 0.838224706f, 0.545324988f, + 0.844853565f, 0.534997620f, + 0.851355193f, 0.524589683f, + 0.857728610f, 0.514102744f, + 0.863972856f, 0.503538384f, + 0.870086991f, 0.492898192f, + 0.876070094f, 0.482183772f, + 0.881921264f, 0.471396737f, + 0.887639620f, 0.460538711f, + 0.893224301f, 0.449611330f, + 0.898674466f, 0.438616239f, + 0.903989293f, 0.427555093f, + 0.909167983f, 0.416429560f, + 0.914209756f, 0.405241314f, + 0.919113852f, 0.393992040f, + 0.923879533f, 0.382683432f, + 0.928506080f, 0.371317194f, + 0.932992799f, 0.359895037f, + 0.937339012f, 0.348418680f, + 0.941544065f, 0.336889853f, + 0.945607325f, 0.325310292f, + 0.949528181f, 0.313681740f, + 0.953306040f, 0.302005949f, + 0.956940336f, 0.290284677f, + 0.960430519f, 0.278519689f, + 0.963776066f, 0.266712757f, + 0.966976471f, 0.254865660f, + 0.970031253f, 0.242980180f, + 0.972939952f, 0.231058108f, + 0.975702130f, 0.219101240f, + 0.978317371f, 0.207111376f, + 0.980785280f, 0.195090322f, + 0.983105487f, 0.183039888f, + 0.985277642f, 0.170961889f, + 0.987301418f, 0.158858143f, + 0.989176510f, 0.146730474f, + 0.990902635f, 0.134580709f, + 0.992479535f, 0.122410675f, + 0.993906970f, 0.110222207f, + 0.995184727f, 0.098017140f, + 0.996312612f, 0.085797312f, + 0.997290457f, 0.073564564f, + 0.998118113f, 0.061320736f, + 0.998795456f, 0.049067674f, + 0.999322385f, 0.036807223f, + 0.999698819f, 0.024541229f, + 0.999924702f, 0.012271538f, + 1.000000000f, 0.000000000f, + 0.999924702f, -0.012271538f, + 0.999698819f, -0.024541229f, + 0.999322385f, -0.036807223f, + 0.998795456f, -0.049067674f, + 0.998118113f, -0.061320736f, + 0.997290457f, -0.073564564f, + 0.996312612f, -0.085797312f, + 0.995184727f, -0.098017140f, + 0.993906970f, -0.110222207f, + 0.992479535f, -0.122410675f, + 0.990902635f, -0.134580709f, + 0.989176510f, -0.146730474f, + 0.987301418f, -0.158858143f, + 0.985277642f, -0.170961889f, + 0.983105487f, -0.183039888f, + 0.980785280f, -0.195090322f, + 0.978317371f, -0.207111376f, + 0.975702130f, -0.219101240f, + 0.972939952f, -0.231058108f, + 0.970031253f, -0.242980180f, + 0.966976471f, -0.254865660f, + 0.963776066f, -0.266712757f, + 0.960430519f, -0.278519689f, + 0.956940336f, -0.290284677f, + 0.953306040f, -0.302005949f, + 0.949528181f, -0.313681740f, + 0.945607325f, -0.325310292f, + 0.941544065f, -0.336889853f, + 0.937339012f, -0.348418680f, + 0.932992799f, -0.359895037f, + 0.928506080f, -0.371317194f, + 0.923879533f, -0.382683432f, + 0.919113852f, -0.393992040f, + 0.914209756f, -0.405241314f, + 0.909167983f, -0.416429560f, + 0.903989293f, -0.427555093f, + 0.898674466f, -0.438616239f, + 0.893224301f, -0.449611330f, + 0.887639620f, -0.460538711f, + 0.881921264f, -0.471396737f, + 0.876070094f, -0.482183772f, + 0.870086991f, -0.492898192f, + 0.863972856f, -0.503538384f, + 0.857728610f, -0.514102744f, + 0.851355193f, -0.524589683f, + 0.844853565f, -0.534997620f, + 0.838224706f, -0.545324988f, + 0.831469612f, -0.555570233f, + 0.824589303f, -0.565731811f, + 0.817584813f, -0.575808191f, + 0.810457198f, -0.585797857f, + 0.803207531f, -0.595699304f, + 0.795836905f, -0.605511041f, + 0.788346428f, -0.615231591f, + 0.780737229f, -0.624859488f, + 0.773010453f, -0.634393284f, + 0.765167266f, -0.643831543f, + 0.757208847f, -0.653172843f, + 0.749136395f, -0.662415778f, + 0.740951125f, -0.671558955f, + 0.732654272f, -0.680600998f, + 0.724247083f, -0.689540545f, + 0.715730825f, -0.698376249f, + 0.707106781f, -0.707106781f, + 0.698376249f, -0.715730825f, + 0.689540545f, -0.724247083f, + 0.680600998f, -0.732654272f, + 0.671558955f, -0.740951125f, + 0.662415778f, -0.749136395f, + 0.653172843f, -0.757208847f, + 0.643831543f, -0.765167266f, + 0.634393284f, -0.773010453f, + 0.624859488f, -0.780737229f, + 0.615231591f, -0.788346428f, + 0.605511041f, -0.795836905f, + 0.595699304f, -0.803207531f, + 0.585797857f, -0.810457198f, + 0.575808191f, -0.817584813f, + 0.565731811f, -0.824589303f, + 0.555570233f, -0.831469612f, + 0.545324988f, -0.838224706f, + 0.534997620f, -0.844853565f, + 0.524589683f, -0.851355193f, + 0.514102744f, -0.857728610f, + 0.503538384f, -0.863972856f, + 0.492898192f, -0.870086991f, + 0.482183772f, -0.876070094f, + 0.471396737f, -0.881921264f, + 0.460538711f, -0.887639620f, + 0.449611330f, -0.893224301f, + 0.438616239f, -0.898674466f, + 0.427555093f, -0.903989293f, + 0.416429560f, -0.909167983f, + 0.405241314f, -0.914209756f, + 0.393992040f, -0.919113852f, + 0.382683432f, -0.923879533f, + 0.371317194f, -0.928506080f, + 0.359895037f, -0.932992799f, + 0.348418680f, -0.937339012f, + 0.336889853f, -0.941544065f, + 0.325310292f, -0.945607325f, + 0.313681740f, -0.949528181f, + 0.302005949f, -0.953306040f, + 0.290284677f, -0.956940336f, + 0.278519689f, -0.960430519f, + 0.266712757f, -0.963776066f, + 0.254865660f, -0.966976471f, + 0.242980180f, -0.970031253f, + 0.231058108f, -0.972939952f, + 0.219101240f, -0.975702130f, + 0.207111376f, -0.978317371f, + 0.195090322f, -0.980785280f, + 0.183039888f, -0.983105487f, + 0.170961889f, -0.985277642f, + 0.158858143f, -0.987301418f, + 0.146730474f, -0.989176510f, + 0.134580709f, -0.990902635f, + 0.122410675f, -0.992479535f, + 0.110222207f, -0.993906970f, + 0.098017140f, -0.995184727f, + 0.085797312f, -0.996312612f, + 0.073564564f, -0.997290457f, + 0.061320736f, -0.998118113f, + 0.049067674f, -0.998795456f, + 0.036807223f, -0.999322385f, + 0.024541229f, -0.999698819f, + 0.012271538f, -0.999924702f +}; + +const float32_t twiddleCoef_rfft_1024[1024] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000f, 1.000000000f, + 0.006135885f, 0.999981175f, + 0.012271538f, 0.999924702f, + 0.018406730f, 0.999830582f, + 0.024541229f, 0.999698819f, + 0.030674803f, 0.999529418f, + 0.036807223f, 0.999322385f, + 0.042938257f, 0.999077728f, + 0.049067674f, 0.998795456f, + 0.055195244f, 0.998475581f, + 0.061320736f, 0.998118113f, + 0.067443920f, 0.997723067f, + 0.073564564f, 0.997290457f, + 0.079682438f, 0.996820299f, + 0.085797312f, 0.996312612f, + 0.091908956f, 0.995767414f, + 0.098017140f, 0.995184727f, + 0.104121634f, 0.994564571f, + 0.110222207f, 0.993906970f, + 0.116318631f, 0.993211949f, + 0.122410675f, 0.992479535f, + 0.128498111f, 0.991709754f, + 0.134580709f, 0.990902635f, + 0.140658239f, 0.990058210f, + 0.146730474f, 0.989176510f, + 0.152797185f, 0.988257568f, + 0.158858143f, 0.987301418f, + 0.164913120f, 0.986308097f, + 0.170961889f, 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0.078153242f, -0.996941358f, + 0.076623861f, -0.997060070f, + 0.075094301f, -0.997176437f, + 0.073564564f, -0.997290457f, + 0.072034653f, -0.997402130f, + 0.070504573f, -0.997511456f, + 0.068974328f, -0.997618435f, + 0.067443920f, -0.997723067f, + 0.065913353f, -0.997825350f, + 0.064382631f, -0.997925286f, + 0.062851758f, -0.998022874f, + 0.061320736f, -0.998118113f, + 0.059789571f, -0.998211003f, + 0.058258265f, -0.998301545f, + 0.056726821f, -0.998389737f, + 0.055195244f, -0.998475581f, + 0.053663538f, -0.998559074f, + 0.052131705f, -0.998640218f, + 0.050599749f, -0.998719012f, + 0.049067674f, -0.998795456f, + 0.047535484f, -0.998869550f, + 0.046003182f, -0.998941293f, + 0.044470772f, -0.999010686f, + 0.042938257f, -0.999077728f, + 0.041405641f, -0.999142419f, + 0.039872928f, -0.999204759f, + 0.038340120f, -0.999264747f, + 0.036807223f, -0.999322385f, + 0.035274239f, -0.999377670f, + 0.033741172f, -0.999430605f, + 0.032208025f, -0.999481187f, + 0.030674803f, -0.999529418f, + 0.029141509f, -0.999575296f, + 0.027608146f, -0.999618822f, + 0.026074718f, -0.999659997f, + 0.024541229f, -0.999698819f, + 0.023007681f, -0.999735288f, + 0.021474080f, -0.999769405f, + 0.019940429f, -0.999801170f, + 0.018406730f, -0.999830582f, + 0.016872988f, -0.999857641f, + 0.015339206f, -0.999882347f, + 0.013805389f, -0.999904701f, + 0.012271538f, -0.999924702f, + 0.010737659f, -0.999942350f, + 0.009203755f, -0.999957645f, + 0.007669829f, -0.999970586f, + 0.006135885f, -0.999981175f, + 0.004601926f, -0.999989411f, + 0.003067957f, -0.999995294f, + 0.001533980f, -0.999998823f +}; + + +/** + @ingroup RealFFT + */ + +/** + @addtogroup RealFFT_Table Real FFT Tables + @{ + */ + +/** + @par + Generation of realCoefA array: + @par + n = 4096 + 
for (i = 0; i < n; i++)
+  {
+     pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
+     pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }
+ */ + +const float32_t realCoefA[8192] ARM_DSP_TABLE_ATTRIBUTE = { + 0.500000000000000f, -0.500000000000000f, 0.499616503715515f, -0.499999850988388f, + 0.499233007431030f, -0.499999403953552f, 0.498849511146545f, -0.499998688697815f, + 0.498466014862061f, -0.499997645616531f, 0.498082518577576f, -0.499996334314346f, + 0.497699022293091f, -0.499994695186615f, 0.497315555810928f, -0.499992787837982f, + 0.496932059526443f, -0.499990582466125f, 0.496548563241959f, -0.499988079071045f, + 0.496165096759796f, -0.499985307455063f, 0.495781600475311f, -0.499982208013535f, + 0.495398133993149f, -0.499978810548782f, 0.495014637708664f, -0.499975144863129f, + 0.494631171226501f, -0.499971181154251f, 0.494247704744339f, -0.499966919422150f, + 0.493864238262177f, -0.499962359666824f, 0.493480771780014f, -0.499957501888275f, + 0.493097305297852f, -0.499952346086502f, 0.492713838815689f, -0.499946922063828f, + 0.492330402135849f, -0.499941170215607f, 0.491946935653687f, -0.499935150146484f, + 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0.476615339517593f, 0.499452859163284f, + 0.476998418569565f, 0.499470651149750f, 0.477381497621536f, 0.499488145112991f, + 0.477764606475830f, 0.499505341053009f, 0.478147745132446f, 0.499522238969803f, + 0.478530883789063f, 0.499538868665695f, 0.478914022445679f, 0.499555170536041f, + 0.479297190904617f, 0.499571204185486f, 0.479680359363556f, 0.499586939811707f, + 0.480063527822495f, 0.499602377414703f, 0.480446726083755f, 0.499617516994476f, + 0.480829954147339f, 0.499632388353348f, 0.481213152408600f, 0.499646931886673f, + 0.481596380472183f, 0.499661177396774f, 0.481979638338089f, 0.499675154685974f, + 0.482362866401672f, 0.499688833951950f, 0.482746154069901f, 0.499702215194702f, + 0.483129411935806f, 0.499715298414230f, 0.483512699604034f, 0.499728083610535f, + 0.483895987272263f, 0.499740600585938f, 0.484279274940491f, 0.499752789735794f, + 0.484662592411041f, 0.499764710664749f, 0.485045909881592f, 0.499776333570480f, + 0.485429257154465f, 0.499787658452988f, 0.485812574625015f, 0.499798685312271f, + 0.486195921897888f, 0.499809414148331f, 0.486579269170761f, 0.499819844961166f, + 0.486962646245956f, 0.499830007553101f, 0.487346023321152f, 0.499839842319489f, + 0.487729400396347f, 0.499849408864975f, 0.488112777471542f, 0.499858677387238f, + 0.488496154546738f, 0.499867647886276f, 0.488879561424255f, 0.499876320362091f, + 0.489262968301773f, 0.499884694814682f, 0.489646375179291f, 0.499892801046371f, + 0.490029782056808f, 0.499900579452515f, 0.490413218736649f, 0.499908089637756f, + 0.490796625614166f, 0.499915301799774f, 0.491180062294006f, 0.499922215938568f, + 0.491563498973846f, 0.499928832054138f, 0.491946935653687f, 0.499935150146484f, + 0.492330402135849f, 0.499941170215607f, 0.492713838815689f, 0.499946922063828f, + 0.493097305297852f, 0.499952346086502f, 0.493480771780014f, 0.499957501888275f, + 0.493864238262177f, 0.499962359666824f, 0.494247704744339f, 0.499966919422150f, + 0.494631171226501f, 0.499971181154251f, 0.495014637708664f, 0.499975144863129f, + 0.495398133993149f, 0.499978810548782f, 0.495781600475311f, 0.499982208013535f, + 0.496165096759796f, 0.499985307455063f, 0.496548563241959f, 0.499988079071045f, + 0.496932059526443f, 0.499990582466125f, 0.497315555810928f, 0.499992787837982f, + 0.497699022293091f, 0.499994695186615f, 0.498082518577576f, 0.499996334314346f, + 0.498466014862061f, 0.499997645616531f, 0.498849511146545f, 0.499998688697815f, + 0.499233007431030f, 0.499999403953552f, 0.499616503715515f, 0.499999850988388f, +}; + + +/** + @par + Generation of realCoefB array: + @par + n = 4096 + 
for (i = 0; i < n; i++)
+  {
+     pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
+     pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }
+ */ + +const float32_t realCoefB[8192] ARM_DSP_TABLE_ATTRIBUTE = { + 0.500000000000000f, 0.500000000000000f, 0.500383496284485f, 0.499999850988388f, + 0.500766992568970f, 0.499999403953552f, 0.501150488853455f, 0.499998688697815f, + 0.501533985137939f, 0.499997645616531f, 0.501917481422424f, 0.499996334314346f, + 0.502300977706909f, 0.499994695186615f, 0.502684473991394f, 0.499992787837982f, + 0.503067970275879f, 0.499990582466125f, 0.503451406955719f, 0.499988079071045f, + 0.503834903240204f, 0.499985307455063f, 0.504218399524689f, 0.499982208013535f, + 0.504601895809174f, 0.499978810548782f, 0.504985332489014f, 0.499975144863129f, + 0.505368828773499f, 0.499971181154251f, 0.505752325057983f, 0.499966919422150f, + 0.506135761737823f, 0.499962359666824f, 0.506519258022308f, 0.499957501888275f, + 0.506902694702148f, 0.499952346086502f, 0.507286131381989f, 0.499946922063828f, + 0.507669627666473f, 0.499941170215607f, 0.508053064346313f, 0.499935150146484f, + 0.508436501026154f, 0.499928832054138f, 0.508819937705994f, 0.499922215938568f, + 0.509203374385834f, 0.499915301799774f, 0.509586811065674f, 0.499908089637756f, + 0.509970188140869f, 0.499900579452515f, 0.510353624820709f, 0.499892801046371f, + 0.510737061500549f, 0.499884694814682f, 0.511120438575745f, 0.499876320362091f, + 0.511503815650940f, 0.499867647886276f, 0.511887252330780f, 0.499858677387238f, + 0.512270629405975f, 0.499849408864975f, 0.512654006481171f, 0.499839842319489f, + 0.513037383556366f, 0.499830007553101f, 0.513420701026917f, 0.499819844961166f, + 0.513804078102112f, 0.499809414148331f, 0.514187395572662f, 0.499798685312271f, + 0.514570772647858f, 0.499787658452988f, 0.514954090118408f, 0.499776333570480f, + 0.515337407588959f, 0.499764710664749f, 0.515720725059509f, 0.499752789735794f, + 0.516103982925415f, 0.499740600585938f, 0.516487300395966f, 0.499728083610535f, + 0.516870558261871f, 0.499715298414230f, 0.517253875732422f, 0.499702215194702f, + 0.517637133598328f, 0.499688833951950f, 0.518020391464233f, 0.499675154685974f, + 0.518403589725494f, 0.499661177396774f, 0.518786847591400f, 0.499646931886673f, + 0.519170045852661f, 0.499632388353348f, 0.519553244113922f, 0.499617516994476f, + 0.519936442375183f, 0.499602377414703f, 0.520319640636444f, 0.499586939811707f, + 0.520702838897705f, 0.499571204185486f, 0.521085977554321f, 0.499555170536041f, + 0.521469116210938f, 0.499538868665695f, 0.521852254867554f, 0.499522238969803f, + 0.522235393524170f, 0.499505341053009f, 0.522618472576141f, 0.499488145112991f, + 0.523001611232758f, 0.499470651149750f, 0.523384690284729f, 0.499452859163284f, + 0.523767769336700f, 0.499434769153595f, 0.524150788784027f, 0.499416410923004f, + 0.524533808231354f, 0.499397724866867f, 0.524916887283325f, 0.499378770589828f, + 0.525299847126007f, 0.499359518289566f, 0.525682866573334f, 0.499339967966080f, + 0.526065826416016f, 0.499320119619370f, 0.526448845863342f, 0.499299973249435f, + 0.526831746101379f, 0.499279528856277f, 0.527214705944061f, 0.499258816242218f, + 0.527597606182098f, 0.499237775802612f, 0.527980506420136f, 0.499216467142105f, + 0.528363406658173f, 0.499194860458374f, 0.528746306896210f, 0.499172955751419f, + 0.529129147529602f, 0.499150782823563f, 0.529511988162994f, 0.499128282070160f, + 0.529894769191742f, 0.499105513095856f, 0.530277609825134f, 0.499082416296005f, + 0.530660390853882f, 0.499059051275253f, 0.531043112277985f, 0.499035388231277f, + 0.531425893306732f, 0.499011427164078f, 0.531808614730835f, 0.498987197875977f, + 0.532191336154938f, 0.498962640762329f, 0.532573997974396f, 0.498937815427780f, + 0.532956659793854f, 0.498912662267685f, 0.533339321613312f, 0.498887240886688f, + 0.533721983432770f, 0.498861521482468f, 0.534104585647583f, 0.498835533857346f, + 0.534487187862396f, 0.498809218406677f, 0.534869730472565f, 0.498782604932785f, + 0.535252273082733f, 0.498755723237991f, 0.535634815692902f, 0.498728543519974f, + 0.536017298698425f, 0.498701065778732f, 0.536399841308594f, 0.498673290014267f, + 0.536782264709473f, 0.498645216226578f, 0.537164747714996f, 0.498616874217987f, + 0.537547171115875f, 0.498588204383850f, 0.537929534912109f, 0.498559266328812f, + 0.538311958312988f, 0.498530030250549f, 0.538694262504578f, 0.498500496149063f, + 0.539076626300812f, 0.498470664024353f, 0.539458930492401f, 0.498440563678741f, + 0.539841234683990f, 0.498410135507584f, 0.540223479270935f, 0.498379439115524f, + 0.540605723857880f, 0.498348444700241f, 0.540987968444824f, 0.498317152261734f, + 0.541370153427124f, 0.498285561800003f, 0.541752278804779f, 0.498253703117371f, + 0.542134463787079f, 0.498221516609192f, 0.542516589164734f, 0.498189061880112f, + 0.542898654937744f, 0.498156309127808f, 0.543280720710754f, 0.498123258352280f, + 0.543662786483765f, 0.498089909553528f, 0.544044792652130f, 0.498056292533875f, + 0.544426798820496f, 0.498022347688675f, 0.544808745384216f, 0.497988134622574f, + 0.545190691947937f, 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0.549771785736084f, -0.497516602277756f, 0.549390196800232f, -0.497554630041122f, + 0.549008548259735f, -0.497592359781265f, 0.548626899719238f, -0.497629791498184f, + 0.548245191574097f, -0.497666954994202f, 0.547863483428955f, -0.497703820466995f, + 0.547481775283813f, -0.497740387916565f, 0.547099947929382f, -0.497776657342911f, + 0.546718180179596f, -0.497812628746033f, 0.546336352825165f, -0.497848302125931f, + 0.545954465866089f, -0.497883707284927f, 0.545572578907013f, -0.497918814420700f, + 0.545190691947937f, -0.497953623533249f, 0.544808745384216f, -0.497988134622574f, + 0.544426798820496f, -0.498022347688675f, 0.544044792652130f, -0.498056292533875f, + 0.543662786483765f, -0.498089909553528f, 0.543280720710754f, -0.498123258352280f, + 0.542898654937744f, -0.498156309127808f, 0.542516589164734f, -0.498189061880112f, + 0.542134463787079f, -0.498221516609192f, 0.541752278804779f, -0.498253703117371f, + 0.541370153427124f, -0.498285561800003f, 0.540987968444824f, -0.498317152261734f, + 0.540605723857880f, -0.498348444700241f, 0.540223479270935f, -0.498379439115524f, + 0.539841234683990f, -0.498410135507584f, 0.539458930492401f, -0.498440563678741f, + 0.539076626300812f, -0.498470664024353f, 0.538694262504578f, -0.498500496149063f, + 0.538311958312988f, -0.498530030250549f, 0.537929534912109f, -0.498559266328812f, + 0.537547171115875f, -0.498588204383850f, 0.537164747714996f, -0.498616874217987f, + 0.536782264709473f, -0.498645216226578f, 0.536399841308594f, -0.498673290014267f, + 0.536017298698425f, -0.498701065778732f, 0.535634815692902f, -0.498728543519974f, + 0.535252273082733f, -0.498755723237991f, 0.534869730472565f, -0.498782604932785f, + 0.534487187862396f, -0.498809218406677f, 0.534104585647583f, -0.498835533857346f, + 0.533721983432770f, -0.498861521482468f, 0.533339321613312f, -0.498887240886688f, + 0.532956659793854f, -0.498912662267685f, 0.532573997974396f, -0.498937815427780f, + 0.532191336154938f, -0.498962640762329f, 0.531808614730835f, -0.498987197875977f, + 0.531425893306732f, -0.499011427164078f, 0.531043112277985f, -0.499035388231277f, + 0.530660390853882f, -0.499059051275253f, 0.530277609825134f, -0.499082416296005f, + 0.529894769191742f, -0.499105513095856f, 0.529511988162994f, -0.499128282070160f, + 0.529129147529602f, -0.499150782823563f, 0.528746306896210f, -0.499172955751419f, + 0.528363406658173f, -0.499194860458374f, 0.527980506420136f, -0.499216467142105f, + 0.527597606182098f, -0.499237775802612f, 0.527214705944061f, -0.499258816242218f, + 0.526831746101379f, -0.499279528856277f, 0.526448845863342f, -0.499299973249435f, + 0.526065826416016f, -0.499320119619370f, 0.525682866573334f, -0.499339967966080f, + 0.525299847126007f, -0.499359518289566f, 0.524916887283325f, -0.499378770589828f, + 0.524533808231354f, -0.499397724866867f, 0.524150788784027f, -0.499416410923004f, + 0.523767769336700f, -0.499434769153595f, 0.523384690284729f, -0.499452859163284f, + 0.523001611232758f, -0.499470651149750f, 0.522618472576141f, -0.499488145112991f, + 0.522235393524170f, -0.499505341053009f, 0.521852254867554f, -0.499522238969803f, + 0.521469116210938f, -0.499538868665695f, 0.521085977554321f, -0.499555170536041f, + 0.520702838897705f, -0.499571204185486f, 0.520319640636444f, -0.499586939811707f, + 0.519936442375183f, -0.499602377414703f, 0.519553244113922f, -0.499617516994476f, + 0.519170045852661f, -0.499632388353348f, 0.518786847591400f, -0.499646931886673f, + 0.518403589725494f, -0.499661177396774f, 0.518020391464233f, -0.499675154685974f, + 0.517637133598328f, -0.499688833951950f, 0.517253875732422f, -0.499702215194702f, + 0.516870558261871f, -0.499715298414230f, 0.516487300395966f, -0.499728083610535f, + 0.516103982925415f, -0.499740600585938f, 0.515720725059509f, -0.499752789735794f, + 0.515337407588959f, -0.499764710664749f, 0.514954090118408f, -0.499776333570480f, + 0.514570772647858f, -0.499787658452988f, 0.514187395572662f, -0.499798685312271f, + 0.513804078102112f, -0.499809414148331f, 0.513420701026917f, -0.499819844961166f, + 0.513037383556366f, -0.499830007553101f, 0.512654006481171f, -0.499839842319489f, + 0.512270629405975f, -0.499849408864975f, 0.511887252330780f, -0.499858677387238f, + 0.511503815650940f, -0.499867647886276f, 0.511120438575745f, -0.499876320362091f, + 0.510737061500549f, -0.499884694814682f, 0.510353624820709f, -0.499892801046371f, + 0.509970188140869f, -0.499900579452515f, 0.509586811065674f, -0.499908089637756f, + 0.509203374385834f, -0.499915301799774f, 0.508819937705994f, -0.499922215938568f, + 0.508436501026154f, -0.499928832054138f, 0.508053064346313f, -0.499935150146484f, + 0.507669627666473f, -0.499941170215607f, 0.507286131381989f, -0.499946922063828f, + 0.506902694702148f, -0.499952346086502f, 0.506519258022308f, -0.499957501888275f, + 0.506135761737823f, -0.499962359666824f, 0.505752325057983f, -0.499966919422150f, + 0.505368828773499f, -0.499971181154251f, 0.504985332489014f, -0.499975144863129f, + 0.504601895809174f, -0.499978810548782f, 0.504218399524689f, -0.499982208013535f, + 0.503834903240204f, -0.499985307455063f, 0.503451406955719f, -0.499988079071045f, + 0.503067970275879f, -0.499990582466125f, 0.502684473991394f, -0.499992787837982f, + 0.502300977706909f, -0.499994695186615f, 0.501917481422424f, -0.499996334314346f, + 0.501533985137939f, -0.499997645616531f, 0.501150488853455f, -0.499998688697815f, + 0.500766992568970f, -0.499999403953552f, 0.500383496284485f, -0.499999850988388f, +}; + +/** + @par + Generation fixed-point realCoefAQ31 array in Q31 format: + @par + n = 4096 + 
for (i = 0; i < n; i++)
+  {
+     pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
+     pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }
+ @par + Convert to fixed point Q31 format + round(pATable[i] * pow(2, 31)) +*/ +const q31_t realCoefAQ31[8192] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x40000000, (q31_t)0xc0000000, (q31_t)0x3ff36f02, (q31_t)0xc000013c, + (q31_t)0x3fe6de05, (q31_t)0xc00004ef, (q31_t)0x3fda4d09, (q31_t)0xc0000b1a, + (q31_t)0x3fcdbc0f, (q31_t)0xc00013bd, (q31_t)0x3fc12b16, (q31_t)0xc0001ed8, + (q31_t)0x3fb49a1f, (q31_t)0xc0002c6a, (q31_t)0x3fa8092c, (q31_t)0xc0003c74, + (q31_t)0x3f9b783c, (q31_t)0xc0004ef5, (q31_t)0x3f8ee750, (q31_t)0xc00063ee, + (q31_t)0x3f825668, (q31_t)0xc0007b5f, (q31_t)0x3f75c585, (q31_t)0xc0009547, + (q31_t)0x3f6934a8, (q31_t)0xc000b1a7, (q31_t)0x3f5ca3d0, (q31_t)0xc000d07e, + (q31_t)0x3f5012fe, (q31_t)0xc000f1ce, (q31_t)0x3f438234, (q31_t)0xc0011594, + (q31_t)0x3f36f170, (q31_t)0xc0013bd3, (q31_t)0x3f2a60b4, (q31_t)0xc0016489, + (q31_t)0x3f1dd001, (q31_t)0xc0018fb6, (q31_t)0x3f113f56, (q31_t)0xc001bd5c, + (q31_t)0x3f04aeb5, (q31_t)0xc001ed78, (q31_t)0x3ef81e1d, (q31_t)0xc002200d, + (q31_t)0x3eeb8d8f, (q31_t)0xc0025519, (q31_t)0x3edefd0c, (q31_t)0xc0028c9c, + (q31_t)0x3ed26c94, (q31_t)0xc002c697, (q31_t)0x3ec5dc28, (q31_t)0xc003030a, + (q31_t)0x3eb94bc8, (q31_t)0xc00341f4, (q31_t)0x3eacbb74, (q31_t)0xc0038356, + (q31_t)0x3ea02b2e, (q31_t)0xc003c72f, (q31_t)0x3e939af5, (q31_t)0xc0040d80, + (q31_t)0x3e870aca, (q31_t)0xc0045648, (q31_t)0x3e7a7aae, (q31_t)0xc004a188, + (q31_t)0x3e6deaa1, (q31_t)0xc004ef3f, (q31_t)0x3e615aa3, (q31_t)0xc0053f6e, + (q31_t)0x3e54cab5, (q31_t)0xc0059214, (q31_t)0x3e483ad8, (q31_t)0xc005e731, + (q31_t)0x3e3bab0b, (q31_t)0xc0063ec6, (q31_t)0x3e2f1b50, (q31_t)0xc00698d3, + (q31_t)0x3e228ba7, (q31_t)0xc006f556, (q31_t)0x3e15fc11, (q31_t)0xc0075452, + (q31_t)0x3e096c8d, (q31_t)0xc007b5c4, (q31_t)0x3dfcdd1d, (q31_t)0xc00819ae, + (q31_t)0x3df04dc0, (q31_t)0xc008800f, (q31_t)0x3de3be78, (q31_t)0xc008e8e8, + (q31_t)0x3dd72f45, (q31_t)0xc0095438, (q31_t)0x3dcaa027, (q31_t)0xc009c1ff, + (q31_t)0x3dbe111e, (q31_t)0xc00a323d, (q31_t)0x3db1822c, (q31_t)0xc00aa4f3, + (q31_t)0x3da4f351, (q31_t)0xc00b1a20, (q31_t)0x3d98648d, (q31_t)0xc00b91c4, + (q31_t)0x3d8bd5e1, (q31_t)0xc00c0be0, (q31_t)0x3d7f474d, (q31_t)0xc00c8872, + (q31_t)0x3d72b8d2, (q31_t)0xc00d077c, (q31_t)0x3d662a70, (q31_t)0xc00d88fd, + (q31_t)0x3d599c28, (q31_t)0xc00e0cf5, (q31_t)0x3d4d0df9, (q31_t)0xc00e9364, + (q31_t)0x3d407fe6, (q31_t)0xc00f1c4a, (q31_t)0x3d33f1ed, (q31_t)0xc00fa7a8, + (q31_t)0x3d276410, (q31_t)0xc010357c, (q31_t)0x3d1ad650, (q31_t)0xc010c5c7, + (q31_t)0x3d0e48ab, (q31_t)0xc011588a, (q31_t)0x3d01bb24, (q31_t)0xc011edc3, + (q31_t)0x3cf52dbb, (q31_t)0xc0128574, (q31_t)0x3ce8a06f, (q31_t)0xc0131f9b, + (q31_t)0x3cdc1342, (q31_t)0xc013bc39, (q31_t)0x3ccf8634, (q31_t)0xc0145b4e, + (q31_t)0x3cc2f945, (q31_t)0xc014fcda, (q31_t)0x3cb66c77, (q31_t)0xc015a0dd, + (q31_t)0x3ca9dfc8, (q31_t)0xc0164757, (q31_t)0x3c9d533b, (q31_t)0xc016f047, + (q31_t)0x3c90c6cf, (q31_t)0xc0179bae, (q31_t)0x3c843a85, (q31_t)0xc018498c, + (q31_t)0x3c77ae5e, (q31_t)0xc018f9e1, 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(q31_t)0x3ff0e3b6, (q31_t)0x3d4d0df9, (q31_t)0x3ff16c9c, + (q31_t)0x3d599c28, (q31_t)0x3ff1f30b, (q31_t)0x3d662a70, (q31_t)0x3ff27703, + (q31_t)0x3d72b8d2, (q31_t)0x3ff2f884, (q31_t)0x3d7f474d, (q31_t)0x3ff3778e, + (q31_t)0x3d8bd5e1, (q31_t)0x3ff3f420, (q31_t)0x3d98648d, (q31_t)0x3ff46e3c, + (q31_t)0x3da4f351, (q31_t)0x3ff4e5e0, (q31_t)0x3db1822c, (q31_t)0x3ff55b0d, + (q31_t)0x3dbe111e, (q31_t)0x3ff5cdc3, (q31_t)0x3dcaa027, (q31_t)0x3ff63e01, + (q31_t)0x3dd72f45, (q31_t)0x3ff6abc8, (q31_t)0x3de3be78, (q31_t)0x3ff71718, + (q31_t)0x3df04dc0, (q31_t)0x3ff77ff1, (q31_t)0x3dfcdd1d, (q31_t)0x3ff7e652, + (q31_t)0x3e096c8d, (q31_t)0x3ff84a3c, (q31_t)0x3e15fc11, (q31_t)0x3ff8abae, + (q31_t)0x3e228ba7, (q31_t)0x3ff90aaa, (q31_t)0x3e2f1b50, (q31_t)0x3ff9672d, + (q31_t)0x3e3bab0b, (q31_t)0x3ff9c13a, (q31_t)0x3e483ad8, (q31_t)0x3ffa18cf, + (q31_t)0x3e54cab5, (q31_t)0x3ffa6dec, (q31_t)0x3e615aa3, (q31_t)0x3ffac092, + (q31_t)0x3e6deaa1, (q31_t)0x3ffb10c1, (q31_t)0x3e7a7aae, (q31_t)0x3ffb5e78, + (q31_t)0x3e870aca, (q31_t)0x3ffba9b8, (q31_t)0x3e939af5, (q31_t)0x3ffbf280, + (q31_t)0x3ea02b2e, (q31_t)0x3ffc38d1, (q31_t)0x3eacbb74, (q31_t)0x3ffc7caa, + (q31_t)0x3eb94bc8, (q31_t)0x3ffcbe0c, (q31_t)0x3ec5dc28, (q31_t)0x3ffcfcf6, + (q31_t)0x3ed26c94, (q31_t)0x3ffd3969, (q31_t)0x3edefd0c, (q31_t)0x3ffd7364, + (q31_t)0x3eeb8d8f, (q31_t)0x3ffdaae7, (q31_t)0x3ef81e1d, (q31_t)0x3ffddff3, + (q31_t)0x3f04aeb5, (q31_t)0x3ffe1288, (q31_t)0x3f113f56, (q31_t)0x3ffe42a4, + (q31_t)0x3f1dd001, (q31_t)0x3ffe704a, (q31_t)0x3f2a60b4, (q31_t)0x3ffe9b77, + (q31_t)0x3f36f170, (q31_t)0x3ffec42d, (q31_t)0x3f438234, (q31_t)0x3ffeea6c, + (q31_t)0x3f5012fe, (q31_t)0x3fff0e32, (q31_t)0x3f5ca3d0, (q31_t)0x3fff2f82, + (q31_t)0x3f6934a8, (q31_t)0x3fff4e59, (q31_t)0x3f75c585, (q31_t)0x3fff6ab9, + (q31_t)0x3f825668, (q31_t)0x3fff84a1, (q31_t)0x3f8ee750, (q31_t)0x3fff9c12, + (q31_t)0x3f9b783c, (q31_t)0x3fffb10b, (q31_t)0x3fa8092c, (q31_t)0x3fffc38c, + (q31_t)0x3fb49a1f, (q31_t)0x3fffd396, (q31_t)0x3fc12b16, (q31_t)0x3fffe128, + (q31_t)0x3fcdbc0f, (q31_t)0x3fffec43, (q31_t)0x3fda4d09, (q31_t)0x3ffff4e6, + (q31_t)0x3fe6de05, (q31_t)0x3ffffb11, (q31_t)0x3ff36f02, (q31_t)0x3ffffec4, +}; + + +/** + @par + Generation of realCoefBQ31 array: + @par + n = 4096 + 
for (i = 0; i < n; i++)
+  {
+     pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
+     pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }
+ @par + Convert to fixed point Q31 format + round(pBTable[i] * pow(2, 31)) + */ + +const q31_t realCoefBQ31[8192] ARM_DSP_TABLE_ATTRIBUTE = { + (q31_t)0x40000000, (q31_t)0x40000000, (q31_t)0x400c90fe, (q31_t)0x3ffffec4, + (q31_t)0x401921fb, (q31_t)0x3ffffb11, (q31_t)0x4025b2f7, (q31_t)0x3ffff4e6, + (q31_t)0x403243f1, (q31_t)0x3fffec43, (q31_t)0x403ed4ea, (q31_t)0x3fffe128, + (q31_t)0x404b65e1, (q31_t)0x3fffd396, (q31_t)0x4057f6d4, (q31_t)0x3fffc38c, + (q31_t)0x406487c4, (q31_t)0x3fffb10b, (q31_t)0x407118b0, (q31_t)0x3fff9c12, + (q31_t)0x407da998, (q31_t)0x3fff84a1, (q31_t)0x408a3a7b, (q31_t)0x3fff6ab9, + (q31_t)0x4096cb58, (q31_t)0x3fff4e59, (q31_t)0x40a35c30, (q31_t)0x3fff2f82, + (q31_t)0x40afed02, (q31_t)0x3fff0e32, (q31_t)0x40bc7dcc, (q31_t)0x3ffeea6c, + (q31_t)0x40c90e90, (q31_t)0x3ffec42d, (q31_t)0x40d59f4c, (q31_t)0x3ffe9b77, + (q31_t)0x40e22fff, (q31_t)0x3ffe704a, (q31_t)0x40eec0aa, (q31_t)0x3ffe42a4, + (q31_t)0x40fb514b, (q31_t)0x3ffe1288, (q31_t)0x4107e1e3, (q31_t)0x3ffddff3, + (q31_t)0x41147271, (q31_t)0x3ffdaae7, (q31_t)0x412102f4, (q31_t)0x3ffd7364, + (q31_t)0x412d936c, (q31_t)0x3ffd3969, (q31_t)0x413a23d8, (q31_t)0x3ffcfcf6, + (q31_t)0x4146b438, (q31_t)0x3ffcbe0c, (q31_t)0x4153448c, (q31_t)0x3ffc7caa, + (q31_t)0x415fd4d2, (q31_t)0x3ffc38d1, (q31_t)0x416c650b, (q31_t)0x3ffbf280, + (q31_t)0x4178f536, (q31_t)0x3ffba9b8, (q31_t)0x41858552, (q31_t)0x3ffb5e78, + (q31_t)0x4192155f, (q31_t)0x3ffb10c1, (q31_t)0x419ea55d, (q31_t)0x3ffac092, + (q31_t)0x41ab354b, (q31_t)0x3ffa6dec, (q31_t)0x41b7c528, (q31_t)0x3ffa18cf, + (q31_t)0x41c454f5, (q31_t)0x3ff9c13a, (q31_t)0x41d0e4b0, (q31_t)0x3ff9672d, + (q31_t)0x41dd7459, (q31_t)0x3ff90aaa, (q31_t)0x41ea03ef, (q31_t)0x3ff8abae, + (q31_t)0x41f69373, (q31_t)0x3ff84a3c, (q31_t)0x420322e3, (q31_t)0x3ff7e652, + (q31_t)0x420fb240, (q31_t)0x3ff77ff1, (q31_t)0x421c4188, (q31_t)0x3ff71718, + (q31_t)0x4228d0bb, (q31_t)0x3ff6abc8, (q31_t)0x42355fd9, (q31_t)0x3ff63e01, + (q31_t)0x4241eee2, (q31_t)0x3ff5cdc3, (q31_t)0x424e7dd4, (q31_t)0x3ff55b0d, + (q31_t)0x425b0caf, (q31_t)0x3ff4e5e0, (q31_t)0x42679b73, (q31_t)0x3ff46e3c, + (q31_t)0x42742a1f, (q31_t)0x3ff3f420, (q31_t)0x4280b8b3, (q31_t)0x3ff3778e, + (q31_t)0x428d472e, (q31_t)0x3ff2f884, (q31_t)0x4299d590, (q31_t)0x3ff27703, + (q31_t)0x42a663d8, (q31_t)0x3ff1f30b, (q31_t)0x42b2f207, (q31_t)0x3ff16c9c, + (q31_t)0x42bf801a, (q31_t)0x3ff0e3b6, (q31_t)0x42cc0e13, (q31_t)0x3ff05858, + (q31_t)0x42d89bf0, (q31_t)0x3fefca84, (q31_t)0x42e529b0, (q31_t)0x3fef3a39, + (q31_t)0x42f1b755, (q31_t)0x3feea776, (q31_t)0x42fe44dc, (q31_t)0x3fee123d, + (q31_t)0x430ad245, (q31_t)0x3fed7a8c, (q31_t)0x43175f91, (q31_t)0x3fece065, + (q31_t)0x4323ecbe, (q31_t)0x3fec43c7, (q31_t)0x433079cc, (q31_t)0x3feba4b2, + (q31_t)0x433d06bb, (q31_t)0x3feb0326, (q31_t)0x43499389, (q31_t)0x3fea5f23, + (q31_t)0x43562038, (q31_t)0x3fe9b8a9, (q31_t)0x4362acc5, (q31_t)0x3fe90fb9, + (q31_t)0x436f3931, (q31_t)0x3fe86452, (q31_t)0x437bc57b, (q31_t)0x3fe7b674, + (q31_t)0x438851a2, (q31_t)0x3fe7061f, (q31_t)0x4394dda7, (q31_t)0x3fe65354, + (q31_t)0x43a16988, (q31_t)0x3fe59e12, (q31_t)0x43adf546, (q31_t)0x3fe4e659, + (q31_t)0x43ba80df, (q31_t)0x3fe42c2a, (q31_t)0x43c70c54, (q31_t)0x3fe36f84, + (q31_t)0x43d397a3, (q31_t)0x3fe2b067, (q31_t)0x43e022cc, (q31_t)0x3fe1eed5, + (q31_t)0x43ecadcf, (q31_t)0x3fe12acb, (q31_t)0x43f938ac, (q31_t)0x3fe0644b, + (q31_t)0x4405c361, (q31_t)0x3fdf9b55, (q31_t)0x44124dee, (q31_t)0x3fdecfe8, + (q31_t)0x441ed854, (q31_t)0x3fde0205, (q31_t)0x442b6290, (q31_t)0x3fdd31ac, + (q31_t)0x4437eca4, (q31_t)0x3fdc5edc, (q31_t)0x4444768d, (q31_t)0x3fdb8996, + (q31_t)0x4451004d, (q31_t)0x3fdab1d9, (q31_t)0x445d89e2, (q31_t)0x3fd9d7a7, + (q31_t)0x446a134c, (q31_t)0x3fd8fafe, (q31_t)0x44769c8b, (q31_t)0x3fd81bdf, + (q31_t)0x4483259d, (q31_t)0x3fd73a4a, (q31_t)0x448fae83, (q31_t)0x3fd6563f, + (q31_t)0x449c373c, (q31_t)0x3fd56fbe, (q31_t)0x44a8bfc7, (q31_t)0x3fd486c7, + (q31_t)0x44b54825, (q31_t)0x3fd39b5a, (q31_t)0x44c1d054, (q31_t)0x3fd2ad77, + (q31_t)0x44ce5854, (q31_t)0x3fd1bd1e, (q31_t)0x44dae024, (q31_t)0x3fd0ca4f, + (q31_t)0x44e767c5, (q31_t)0x3fcfd50b, (q31_t)0x44f3ef35, (q31_t)0x3fcedd50, + (q31_t)0x45007674, (q31_t)0x3fcde320, (q31_t)0x450cfd82, (q31_t)0x3fcce67a, + (q31_t)0x4519845e, (q31_t)0x3fcbe75e, (q31_t)0x45260b08, (q31_t)0x3fcae5cd, + (q31_t)0x4532917f, (q31_t)0x3fc9e1c6, (q31_t)0x453f17c3, (q31_t)0x3fc8db4a, + (q31_t)0x454b9dd3, (q31_t)0x3fc7d258, (q31_t)0x455823ae, (q31_t)0x3fc6c6f0, + (q31_t)0x4564a955, (q31_t)0x3fc5b913, (q31_t)0x45712ec7, (q31_t)0x3fc4a8c1, + (q31_t)0x457db403, (q31_t)0x3fc395f9, (q31_t)0x458a3908, (q31_t)0x3fc280bc, + (q31_t)0x4596bdd7, (q31_t)0x3fc1690a, (q31_t)0x45a3426f, (q31_t)0x3fc04ee3, + (q31_t)0x45afc6d0, (q31_t)0x3fbf3246, (q31_t)0x45bc4af8, (q31_t)0x3fbe1334, + (q31_t)0x45c8cee7, (q31_t)0x3fbcf1ad, (q31_t)0x45d5529e, (q31_t)0x3fbbcdb1, + (q31_t)0x45e1d61b, (q31_t)0x3fbaa740, (q31_t)0x45ee595d, (q31_t)0x3fb97e5a, + (q31_t)0x45fadc66, (q31_t)0x3fb852ff, (q31_t)0x46075f33, (q31_t)0x3fb7252f, + (q31_t)0x4613e1c5, (q31_t)0x3fb5f4ea, (q31_t)0x4620641a, (q31_t)0x3fb4c231, + (q31_t)0x462ce634, (q31_t)0x3fb38d02, (q31_t)0x46396810, (q31_t)0x3fb2555f, + (q31_t)0x4645e9af, (q31_t)0x3fb11b48, (q31_t)0x46526b10, (q31_t)0x3fafdebb, + (q31_t)0x465eec33, (q31_t)0x3fae9fbb, (q31_t)0x466b6d16, (q31_t)0x3fad5e45, + (q31_t)0x4677edbb, (q31_t)0x3fac1a5b, (q31_t)0x46846e1f, (q31_t)0x3faad3fd, + (q31_t)0x4690ee44, (q31_t)0x3fa98b2a, (q31_t)0x469d6e27, (q31_t)0x3fa83fe3, + (q31_t)0x46a9edc9, (q31_t)0x3fa6f228, (q31_t)0x46b66d29, (q31_t)0x3fa5a1f9, + (q31_t)0x46c2ec48, (q31_t)0x3fa44f55, (q31_t)0x46cf6b23, (q31_t)0x3fa2fa3d, + (q31_t)0x46dbe9bb, (q31_t)0x3fa1a2b2, (q31_t)0x46e86810, (q31_t)0x3fa048b2, + (q31_t)0x46f4e620, (q31_t)0x3f9eec3e, (q31_t)0x470163eb, (q31_t)0x3f9d8d56, + (q31_t)0x470de172, (q31_t)0x3f9c2bfb, (q31_t)0x471a5eb3, (q31_t)0x3f9ac82c, + (q31_t)0x4726dbae, (q31_t)0x3f9961e8, (q31_t)0x47335862, (q31_t)0x3f97f932, + (q31_t)0x473fd4cf, (q31_t)0x3f968e07, (q31_t)0x474c50f4, (q31_t)0x3f952069, + (q31_t)0x4758ccd2, (q31_t)0x3f93b058, (q31_t)0x47654867, (q31_t)0x3f923dd2, + (q31_t)0x4771c3b3, (q31_t)0x3f90c8da, (q31_t)0x477e3eb5, (q31_t)0x3f8f516e, + (q31_t)0x478ab96e, (q31_t)0x3f8dd78f, (q31_t)0x479733dc, (q31_t)0x3f8c5b3d, + (q31_t)0x47a3adff, (q31_t)0x3f8adc77, (q31_t)0x47b027d7, (q31_t)0x3f895b3e, + (q31_t)0x47bca163, (q31_t)0x3f87d792, (q31_t)0x47c91aa3, (q31_t)0x3f865174, + (q31_t)0x47d59396, (q31_t)0x3f84c8e2, (q31_t)0x47e20c3b, (q31_t)0x3f833ddd, + (q31_t)0x47ee8493, (q31_t)0x3f81b065, (q31_t)0x47fafc9c, (q31_t)0x3f80207b, + (q31_t)0x48077457, (q31_t)0x3f7e8e1e, (q31_t)0x4813ebc2, (q31_t)0x3f7cf94e, + (q31_t)0x482062de, (q31_t)0x3f7b620c, (q31_t)0x482cd9a9, (q31_t)0x3f79c857, + (q31_t)0x48395024, (q31_t)0x3f782c30, (q31_t)0x4845c64d, (q31_t)0x3f768d96, + (q31_t)0x48523c25, (q31_t)0x3f74ec8a, (q31_t)0x485eb1ab, (q31_t)0x3f73490b, + (q31_t)0x486b26de, (q31_t)0x3f71a31b, (q31_t)0x48779bbe, (q31_t)0x3f6ffab8, + (q31_t)0x4884104b, (q31_t)0x3f6e4fe3, (q31_t)0x48908483, (q31_t)0x3f6ca29c, + (q31_t)0x489cf867, (q31_t)0x3f6af2e3, (q31_t)0x48a96bf6, (q31_t)0x3f6940b8, + (q31_t)0x48b5df30, (q31_t)0x3f678c1c, (q31_t)0x48c25213, (q31_t)0x3f65d50d, + (q31_t)0x48cec4a0, (q31_t)0x3f641b8d, (q31_t)0x48db36d6, (q31_t)0x3f625f9b, + (q31_t)0x48e7a8b5, (q31_t)0x3f60a138, (q31_t)0x48f41a3c, (q31_t)0x3f5ee063, + (q31_t)0x49008b6a, (q31_t)0x3f5d1d1d, (q31_t)0x490cfc40, (q31_t)0x3f5b5765, + (q31_t)0x49196cbc, (q31_t)0x3f598f3c, (q31_t)0x4925dcdf, (q31_t)0x3f57c4a2, + (q31_t)0x49324ca7, (q31_t)0x3f55f796, (q31_t)0x493ebc14, (q31_t)0x3f54281a, + (q31_t)0x494b2b27, (q31_t)0x3f52562c, (q31_t)0x495799dd, (q31_t)0x3f5081cd, + (q31_t)0x49640837, (q31_t)0x3f4eaafe, (q31_t)0x49707635, (q31_t)0x3f4cd1be, + (q31_t)0x497ce3d5, (q31_t)0x3f4af60d, (q31_t)0x49895118, (q31_t)0x3f4917eb, + (q31_t)0x4995bdfd, (q31_t)0x3f473759, (q31_t)0x49a22a83, (q31_t)0x3f455456, + (q31_t)0x49ae96aa, (q31_t)0x3f436ee3, (q31_t)0x49bb0271, (q31_t)0x3f4186ff, + (q31_t)0x49c76dd8, 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(q31_t)0xc158e9c1, (q31_t)0x4d03d189, (q31_t)0xc1565a58, + (q31_t)0x4cf78383, (q31_t)0xc153cd5a, (q31_t)0x4ceb34fe, (q31_t)0xc15142c6, + (q31_t)0x4cdee5f9, (q31_t)0xc14eba9d, (q31_t)0x4cd29676, (q31_t)0xc14c34df, + (q31_t)0x4cc64673, (q31_t)0xc149b18b, (q31_t)0x4cb9f5f3, (q31_t)0xc14730a3, + (q31_t)0x4cada4f5, (q31_t)0xc144b225, (q31_t)0x4ca1537a, (q31_t)0xc1423613, + (q31_t)0x4c950182, (q31_t)0xc13fbc6c, (q31_t)0x4c88af0e, (q31_t)0xc13d4530, + (q31_t)0x4c7c5c1e, (q31_t)0xc13ad060, (q31_t)0x4c7008b3, (q31_t)0xc1385dfb, + (q31_t)0x4c63b4ce, (q31_t)0xc135ee02, (q31_t)0x4c57606e, (q31_t)0xc1338075, + (q31_t)0x4c4b0b94, (q31_t)0xc1311553, (q31_t)0x4c3eb641, (q31_t)0xc12eac9d, + (q31_t)0x4c326075, (q31_t)0xc12c4653, (q31_t)0x4c260a31, (q31_t)0xc129e276, + (q31_t)0x4c19b374, (q31_t)0xc1278104, (q31_t)0x4c0d5c41, (q31_t)0xc12521ff, + (q31_t)0x4c010496, (q31_t)0xc122c566, (q31_t)0x4bf4ac75, (q31_t)0xc1206b39, + (q31_t)0x4be853de, (q31_t)0xc11e1379, (q31_t)0x4bdbfad1, (q31_t)0xc11bbe26, + (q31_t)0x4bcfa150, (q31_t)0xc1196b3f, (q31_t)0x4bc34759, (q31_t)0xc1171ac6, + (q31_t)0x4bb6ecef, (q31_t)0xc114ccb9, (q31_t)0x4baa9211, (q31_t)0xc1128119, + (q31_t)0x4b9e36c0, (q31_t)0xc11037e6, (q31_t)0x4b91dafc, (q31_t)0xc10df120, + (q31_t)0x4b857ec7, (q31_t)0xc10bacc8, (q31_t)0x4b79221f, (q31_t)0xc1096add, + (q31_t)0x4b6cc506, (q31_t)0xc1072b5f, (q31_t)0x4b60677c, (q31_t)0xc104ee4f, + (q31_t)0x4b540982, (q31_t)0xc102b3ac, (q31_t)0x4b47ab19, (q31_t)0xc1007b77, + (q31_t)0x4b3b4c40, (q31_t)0xc0fe45b0, (q31_t)0x4b2eecf8, (q31_t)0xc0fc1257, + (q31_t)0x4b228d42, (q31_t)0xc0f9e16b, (q31_t)0x4b162d1d, (q31_t)0xc0f7b2ee, + (q31_t)0x4b09cc8c, (q31_t)0xc0f586df, (q31_t)0x4afd6b8d, (q31_t)0xc0f35d3e, + (q31_t)0x4af10a22, (q31_t)0xc0f1360b, (q31_t)0x4ae4a84b, (q31_t)0xc0ef1147, + (q31_t)0x4ad84609, (q31_t)0xc0eceef1, (q31_t)0x4acbe35b, (q31_t)0xc0eacf09, + (q31_t)0x4abf8043, (q31_t)0xc0e8b190, (q31_t)0x4ab31cc1, (q31_t)0xc0e69686, + (q31_t)0x4aa6b8d5, (q31_t)0xc0e47deb, (q31_t)0x4a9a5480, (q31_t)0xc0e267be, + (q31_t)0x4a8defc3, (q31_t)0xc0e05401, (q31_t)0x4a818a9d, (q31_t)0xc0de42b2, + (q31_t)0x4a752510, (q31_t)0xc0dc33d2, (q31_t)0x4a68bf1b, (q31_t)0xc0da2762, + (q31_t)0x4a5c58c0, (q31_t)0xc0d81d61, (q31_t)0x4a4ff1fe, (q31_t)0xc0d615cf, + (q31_t)0x4a438ad7, (q31_t)0xc0d410ad, (q31_t)0x4a37234a, (q31_t)0xc0d20dfa, + (q31_t)0x4a2abb59, (q31_t)0xc0d00db6, (q31_t)0x4a1e5303, (q31_t)0xc0ce0fe3, + (q31_t)0x4a11ea49, (q31_t)0xc0cc147f, (q31_t)0x4a05812c, (q31_t)0xc0ca1b8a, + (q31_t)0x49f917ac, (q31_t)0xc0c82506, (q31_t)0x49ecadc9, (q31_t)0xc0c630f2, + (q31_t)0x49e04385, (q31_t)0xc0c43f4d, (q31_t)0x49d3d8df, (q31_t)0xc0c25019, + (q31_t)0x49c76dd8, (q31_t)0xc0c06355, (q31_t)0x49bb0271, (q31_t)0xc0be7901, + (q31_t)0x49ae96aa, (q31_t)0xc0bc911d, (q31_t)0x49a22a83, (q31_t)0xc0baabaa, + (q31_t)0x4995bdfd, (q31_t)0xc0b8c8a7, (q31_t)0x49895118, (q31_t)0xc0b6e815, + (q31_t)0x497ce3d5, (q31_t)0xc0b509f3, (q31_t)0x49707635, (q31_t)0xc0b32e42, + (q31_t)0x49640837, (q31_t)0xc0b15502, (q31_t)0x495799dd, (q31_t)0xc0af7e33, + (q31_t)0x494b2b27, (q31_t)0xc0ada9d4, (q31_t)0x493ebc14, (q31_t)0xc0abd7e6, + (q31_t)0x49324ca7, (q31_t)0xc0aa086a, (q31_t)0x4925dcdf, (q31_t)0xc0a83b5e, + (q31_t)0x49196cbc, (q31_t)0xc0a670c4, (q31_t)0x490cfc40, (q31_t)0xc0a4a89b, + (q31_t)0x49008b6a, (q31_t)0xc0a2e2e3, (q31_t)0x48f41a3c, (q31_t)0xc0a11f9d, + (q31_t)0x48e7a8b5, (q31_t)0xc09f5ec8, (q31_t)0x48db36d6, (q31_t)0xc09da065, + (q31_t)0x48cec4a0, (q31_t)0xc09be473, (q31_t)0x48c25213, (q31_t)0xc09a2af3, + (q31_t)0x48b5df30, (q31_t)0xc09873e4, (q31_t)0x48a96bf6, (q31_t)0xc096bf48, + (q31_t)0x489cf867, (q31_t)0xc0950d1d, (q31_t)0x48908483, (q31_t)0xc0935d64, + (q31_t)0x4884104b, (q31_t)0xc091b01d, (q31_t)0x48779bbe, (q31_t)0xc0900548, + (q31_t)0x486b26de, (q31_t)0xc08e5ce5, (q31_t)0x485eb1ab, (q31_t)0xc08cb6f5, + (q31_t)0x48523c25, (q31_t)0xc08b1376, (q31_t)0x4845c64d, (q31_t)0xc089726a, + (q31_t)0x48395024, (q31_t)0xc087d3d0, (q31_t)0x482cd9a9, (q31_t)0xc08637a9, + (q31_t)0x482062de, (q31_t)0xc0849df4, (q31_t)0x4813ebc2, (q31_t)0xc08306b2, + (q31_t)0x48077457, (q31_t)0xc08171e2, (q31_t)0x47fafc9c, (q31_t)0xc07fdf85, + (q31_t)0x47ee8493, (q31_t)0xc07e4f9b, (q31_t)0x47e20c3b, (q31_t)0xc07cc223, + (q31_t)0x47d59396, (q31_t)0xc07b371e, (q31_t)0x47c91aa3, (q31_t)0xc079ae8c, + (q31_t)0x47bca163, (q31_t)0xc078286e, (q31_t)0x47b027d7, (q31_t)0xc076a4c2, + (q31_t)0x47a3adff, (q31_t)0xc0752389, (q31_t)0x479733dc, (q31_t)0xc073a4c3, + (q31_t)0x478ab96e, (q31_t)0xc0722871, (q31_t)0x477e3eb5, (q31_t)0xc070ae92, + (q31_t)0x4771c3b3, (q31_t)0xc06f3726, (q31_t)0x47654867, (q31_t)0xc06dc22e, + (q31_t)0x4758ccd2, (q31_t)0xc06c4fa8, (q31_t)0x474c50f4, (q31_t)0xc06adf97, + (q31_t)0x473fd4cf, (q31_t)0xc06971f9, (q31_t)0x47335862, (q31_t)0xc06806ce, + (q31_t)0x4726dbae, (q31_t)0xc0669e18, (q31_t)0x471a5eb3, (q31_t)0xc06537d4, + (q31_t)0x470de172, (q31_t)0xc063d405, (q31_t)0x470163eb, (q31_t)0xc06272aa, + (q31_t)0x46f4e620, (q31_t)0xc06113c2, (q31_t)0x46e86810, (q31_t)0xc05fb74e, + (q31_t)0x46dbe9bb, (q31_t)0xc05e5d4e, (q31_t)0x46cf6b23, (q31_t)0xc05d05c3, + (q31_t)0x46c2ec48, (q31_t)0xc05bb0ab, (q31_t)0x46b66d29, (q31_t)0xc05a5e07, + (q31_t)0x46a9edc9, (q31_t)0xc0590dd8, (q31_t)0x469d6e27, (q31_t)0xc057c01d, + (q31_t)0x4690ee44, (q31_t)0xc05674d6, (q31_t)0x46846e1f, (q31_t)0xc0552c03, + (q31_t)0x4677edbb, (q31_t)0xc053e5a5, (q31_t)0x466b6d16, (q31_t)0xc052a1bb, + (q31_t)0x465eec33, (q31_t)0xc0516045, (q31_t)0x46526b10, (q31_t)0xc0502145, + (q31_t)0x4645e9af, (q31_t)0xc04ee4b8, (q31_t)0x46396810, (q31_t)0xc04daaa1, + (q31_t)0x462ce634, (q31_t)0xc04c72fe, (q31_t)0x4620641a, (q31_t)0xc04b3dcf, + (q31_t)0x4613e1c5, (q31_t)0xc04a0b16, (q31_t)0x46075f33, (q31_t)0xc048dad1, + (q31_t)0x45fadc66, (q31_t)0xc047ad01, (q31_t)0x45ee595d, (q31_t)0xc04681a6, + (q31_t)0x45e1d61b, (q31_t)0xc04558c0, (q31_t)0x45d5529e, (q31_t)0xc044324f, + (q31_t)0x45c8cee7, (q31_t)0xc0430e53, (q31_t)0x45bc4af8, (q31_t)0xc041eccc, + (q31_t)0x45afc6d0, (q31_t)0xc040cdba, (q31_t)0x45a3426f, (q31_t)0xc03fb11d, + (q31_t)0x4596bdd7, (q31_t)0xc03e96f6, (q31_t)0x458a3908, (q31_t)0xc03d7f44, + (q31_t)0x457db403, (q31_t)0xc03c6a07, (q31_t)0x45712ec7, (q31_t)0xc03b573f, + (q31_t)0x4564a955, (q31_t)0xc03a46ed, (q31_t)0x455823ae, (q31_t)0xc0393910, + (q31_t)0x454b9dd3, (q31_t)0xc0382da8, (q31_t)0x453f17c3, (q31_t)0xc03724b6, + (q31_t)0x4532917f, (q31_t)0xc0361e3a, (q31_t)0x45260b08, (q31_t)0xc0351a33, + (q31_t)0x4519845e, (q31_t)0xc03418a2, (q31_t)0x450cfd82, (q31_t)0xc0331986, + (q31_t)0x45007674, (q31_t)0xc0321ce0, (q31_t)0x44f3ef35, (q31_t)0xc03122b0, + (q31_t)0x44e767c5, (q31_t)0xc0302af5, (q31_t)0x44dae024, (q31_t)0xc02f35b1, + (q31_t)0x44ce5854, (q31_t)0xc02e42e2, (q31_t)0x44c1d054, (q31_t)0xc02d5289, + (q31_t)0x44b54825, (q31_t)0xc02c64a6, (q31_t)0x44a8bfc7, (q31_t)0xc02b7939, + (q31_t)0x449c373c, (q31_t)0xc02a9042, (q31_t)0x448fae83, (q31_t)0xc029a9c1, + (q31_t)0x4483259d, (q31_t)0xc028c5b6, (q31_t)0x44769c8b, (q31_t)0xc027e421, + (q31_t)0x446a134c, (q31_t)0xc0270502, (q31_t)0x445d89e2, (q31_t)0xc0262859, + (q31_t)0x4451004d, (q31_t)0xc0254e27, (q31_t)0x4444768d, (q31_t)0xc024766a, + (q31_t)0x4437eca4, (q31_t)0xc023a124, (q31_t)0x442b6290, (q31_t)0xc022ce54, + (q31_t)0x441ed854, (q31_t)0xc021fdfb, (q31_t)0x44124dee, (q31_t)0xc0213018, + (q31_t)0x4405c361, (q31_t)0xc02064ab, (q31_t)0x43f938ac, (q31_t)0xc01f9bb5, + (q31_t)0x43ecadcf, (q31_t)0xc01ed535, (q31_t)0x43e022cc, (q31_t)0xc01e112b, + (q31_t)0x43d397a3, (q31_t)0xc01d4f99, (q31_t)0x43c70c54, (q31_t)0xc01c907c, + (q31_t)0x43ba80df, (q31_t)0xc01bd3d6, (q31_t)0x43adf546, (q31_t)0xc01b19a7, + (q31_t)0x43a16988, (q31_t)0xc01a61ee, (q31_t)0x4394dda7, (q31_t)0xc019acac, + (q31_t)0x438851a2, (q31_t)0xc018f9e1, (q31_t)0x437bc57b, (q31_t)0xc018498c, + (q31_t)0x436f3931, (q31_t)0xc0179bae, (q31_t)0x4362acc5, (q31_t)0xc016f047, + (q31_t)0x43562038, (q31_t)0xc0164757, (q31_t)0x43499389, (q31_t)0xc015a0dd, + (q31_t)0x433d06bb, (q31_t)0xc014fcda, (q31_t)0x433079cc, (q31_t)0xc0145b4e, + (q31_t)0x4323ecbe, (q31_t)0xc013bc39, (q31_t)0x43175f91, (q31_t)0xc0131f9b, + (q31_t)0x430ad245, (q31_t)0xc0128574, (q31_t)0x42fe44dc, (q31_t)0xc011edc3, + (q31_t)0x42f1b755, (q31_t)0xc011588a, (q31_t)0x42e529b0, (q31_t)0xc010c5c7, + (q31_t)0x42d89bf0, (q31_t)0xc010357c, (q31_t)0x42cc0e13, (q31_t)0xc00fa7a8, + (q31_t)0x42bf801a, (q31_t)0xc00f1c4a, (q31_t)0x42b2f207, (q31_t)0xc00e9364, + (q31_t)0x42a663d8, (q31_t)0xc00e0cf5, (q31_t)0x4299d590, (q31_t)0xc00d88fd, + (q31_t)0x428d472e, (q31_t)0xc00d077c, (q31_t)0x4280b8b3, (q31_t)0xc00c8872, + (q31_t)0x42742a1f, (q31_t)0xc00c0be0, (q31_t)0x42679b73, (q31_t)0xc00b91c4, + (q31_t)0x425b0caf, (q31_t)0xc00b1a20, (q31_t)0x424e7dd4, (q31_t)0xc00aa4f3, + (q31_t)0x4241eee2, (q31_t)0xc00a323d, (q31_t)0x42355fd9, (q31_t)0xc009c1ff, + (q31_t)0x4228d0bb, (q31_t)0xc0095438, (q31_t)0x421c4188, (q31_t)0xc008e8e8, + (q31_t)0x420fb240, (q31_t)0xc008800f, (q31_t)0x420322e3, (q31_t)0xc00819ae, + (q31_t)0x41f69373, (q31_t)0xc007b5c4, (q31_t)0x41ea03ef, (q31_t)0xc0075452, + (q31_t)0x41dd7459, (q31_t)0xc006f556, (q31_t)0x41d0e4b0, (q31_t)0xc00698d3, + (q31_t)0x41c454f5, (q31_t)0xc0063ec6, (q31_t)0x41b7c528, (q31_t)0xc005e731, + (q31_t)0x41ab354b, (q31_t)0xc0059214, (q31_t)0x419ea55d, (q31_t)0xc0053f6e, + (q31_t)0x4192155f, (q31_t)0xc004ef3f, (q31_t)0x41858552, (q31_t)0xc004a188, + (q31_t)0x4178f536, (q31_t)0xc0045648, (q31_t)0x416c650b, (q31_t)0xc0040d80, + (q31_t)0x415fd4d2, (q31_t)0xc003c72f, (q31_t)0x4153448c, (q31_t)0xc0038356, + (q31_t)0x4146b438, (q31_t)0xc00341f4, (q31_t)0x413a23d8, (q31_t)0xc003030a, + (q31_t)0x412d936c, (q31_t)0xc002c697, (q31_t)0x412102f4, (q31_t)0xc0028c9c, + (q31_t)0x41147271, (q31_t)0xc0025519, (q31_t)0x4107e1e3, (q31_t)0xc002200d, + (q31_t)0x40fb514b, (q31_t)0xc001ed78, (q31_t)0x40eec0aa, (q31_t)0xc001bd5c, + (q31_t)0x40e22fff, (q31_t)0xc0018fb6, (q31_t)0x40d59f4c, (q31_t)0xc0016489, + (q31_t)0x40c90e90, (q31_t)0xc0013bd3, (q31_t)0x40bc7dcc, (q31_t)0xc0011594, + (q31_t)0x40afed02, (q31_t)0xc000f1ce, (q31_t)0x40a35c30, (q31_t)0xc000d07e, + (q31_t)0x4096cb58, (q31_t)0xc000b1a7, (q31_t)0x408a3a7b, (q31_t)0xc0009547, + (q31_t)0x407da998, (q31_t)0xc0007b5f, (q31_t)0x407118b0, (q31_t)0xc00063ee, + (q31_t)0x406487c4, (q31_t)0xc0004ef5, (q31_t)0x4057f6d4, (q31_t)0xc0003c74, + (q31_t)0x404b65e1, (q31_t)0xc0002c6a, (q31_t)0x403ed4ea, (q31_t)0xc0001ed8, + (q31_t)0x403243f1, (q31_t)0xc00013bd, (q31_t)0x4025b2f7, (q31_t)0xc0000b1a, + (q31_t)0x401921fb, (q31_t)0xc00004ef, (q31_t)0x400c90fe, (q31_t)0xc000013c, +}; + +/** + @par + Generation fixed-point realCoefAQ15 array in Q15 format: + @par + n = 4096 + 
for (i = 0; i < n; i++)
+  {
+     pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
+     pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }
+ @par + Convert to fixed point Q15 format + round(pATable[i] * pow(2, 15)) + */ +const q15_t __ALIGNED(4) realCoefAQ15[8192] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x4000, (q15_t)0xc000, (q15_t)0x3ff3, (q15_t)0xc000, (q15_t)0x3fe7, (q15_t)0xc000, (q15_t)0x3fda, (q15_t)0xc000, + (q15_t)0x3fce, (q15_t)0xc000, (q15_t)0x3fc1, (q15_t)0xc000, (q15_t)0x3fb5, (q15_t)0xc000, (q15_t)0x3fa8, (q15_t)0xc000, + (q15_t)0x3f9b, (q15_t)0xc000, (q15_t)0x3f8f, (q15_t)0xc000, (q15_t)0x3f82, (q15_t)0xc000, (q15_t)0x3f76, (q15_t)0xc001, + (q15_t)0x3f69, (q15_t)0xc001, (q15_t)0x3f5d, (q15_t)0xc001, (q15_t)0x3f50, (q15_t)0xc001, (q15_t)0x3f44, (q15_t)0xc001, + (q15_t)0x3f37, (q15_t)0xc001, (q15_t)0x3f2a, (q15_t)0xc001, (q15_t)0x3f1e, (q15_t)0xc002, (q15_t)0x3f11, (q15_t)0xc002, + (q15_t)0x3f05, (q15_t)0xc002, (q15_t)0x3ef8, (q15_t)0xc002, (q15_t)0x3eec, (q15_t)0xc002, (q15_t)0x3edf, (q15_t)0xc003, + (q15_t)0x3ed2, (q15_t)0xc003, (q15_t)0x3ec6, (q15_t)0xc003, (q15_t)0x3eb9, (q15_t)0xc003, (q15_t)0x3ead, (q15_t)0xc004, + (q15_t)0x3ea0, (q15_t)0xc004, (q15_t)0x3e94, (q15_t)0xc004, (q15_t)0x3e87, (q15_t)0xc004, (q15_t)0x3e7a, (q15_t)0xc005, + (q15_t)0x3e6e, (q15_t)0xc005, (q15_t)0x3e61, (q15_t)0xc005, (q15_t)0x3e55, (q15_t)0xc006, (q15_t)0x3e48, (q15_t)0xc006, + (q15_t)0x3e3c, (q15_t)0xc006, (q15_t)0x3e2f, (q15_t)0xc007, (q15_t)0x3e23, (q15_t)0xc007, (q15_t)0x3e16, (q15_t)0xc007, + (q15_t)0x3e09, (q15_t)0xc008, (q15_t)0x3dfd, (q15_t)0xc008, (q15_t)0x3df0, (q15_t)0xc009, (q15_t)0x3de4, (q15_t)0xc009, + (q15_t)0x3dd7, (q15_t)0xc009, (q15_t)0x3dcb, (q15_t)0xc00a, (q15_t)0x3dbe, (q15_t)0xc00a, (q15_t)0x3db2, (q15_t)0xc00b, + (q15_t)0x3da5, (q15_t)0xc00b, (q15_t)0x3d98, (q15_t)0xc00c, (q15_t)0x3d8c, (q15_t)0xc00c, (q15_t)0x3d7f, (q15_t)0xc00d, + (q15_t)0x3d73, (q15_t)0xc00d, (q15_t)0x3d66, (q15_t)0xc00e, (q15_t)0x3d5a, (q15_t)0xc00e, (q15_t)0x3d4d, (q15_t)0xc00f, + (q15_t)0x3d40, (q15_t)0xc00f, (q15_t)0x3d34, (q15_t)0xc010, (q15_t)0x3d27, (q15_t)0xc010, (q15_t)0x3d1b, (q15_t)0xc011, + (q15_t)0x3d0e, (q15_t)0xc011, (q15_t)0x3d02, (q15_t)0xc012, (q15_t)0x3cf5, (q15_t)0xc013, (q15_t)0x3ce9, (q15_t)0xc013, + (q15_t)0x3cdc, (q15_t)0xc014, (q15_t)0x3cd0, (q15_t)0xc014, (q15_t)0x3cc3, (q15_t)0xc015, (q15_t)0x3cb6, (q15_t)0xc016, + (q15_t)0x3caa, (q15_t)0xc016, (q15_t)0x3c9d, (q15_t)0xc017, (q15_t)0x3c91, (q15_t)0xc018, (q15_t)0x3c84, (q15_t)0xc018, + (q15_t)0x3c78, (q15_t)0xc019, (q15_t)0x3c6b, (q15_t)0xc01a, (q15_t)0x3c5f, (q15_t)0xc01a, (q15_t)0x3c52, (q15_t)0xc01b, + (q15_t)0x3c45, (q15_t)0xc01c, (q15_t)0x3c39, (q15_t)0xc01d, (q15_t)0x3c2c, (q15_t)0xc01d, (q15_t)0x3c20, (q15_t)0xc01e, + (q15_t)0x3c13, (q15_t)0xc01f, (q15_t)0x3c07, (q15_t)0xc020, (q15_t)0x3bfa, (q15_t)0xc020, (q15_t)0x3bee, (q15_t)0xc021, + (q15_t)0x3be1, (q15_t)0xc022, (q15_t)0x3bd5, (q15_t)0xc023, (q15_t)0x3bc8, (q15_t)0xc024, (q15_t)0x3bbc, (q15_t)0xc024, + (q15_t)0x3baf, (q15_t)0xc025, (q15_t)0x3ba2, (q15_t)0xc026, (q15_t)0x3b96, (q15_t)0xc027, (q15_t)0x3b89, (q15_t)0xc028, + (q15_t)0x3b7d, (q15_t)0xc029, (q15_t)0x3b70, (q15_t)0xc02a, (q15_t)0x3b64, (q15_t)0xc02b, (q15_t)0x3b57, (q15_t)0xc02b, + (q15_t)0x3b4b, (q15_t)0xc02c, (q15_t)0x3b3e, (q15_t)0xc02d, (q15_t)0x3b32, (q15_t)0xc02e, (q15_t)0x3b25, (q15_t)0xc02f, + (q15_t)0x3b19, (q15_t)0xc030, (q15_t)0x3b0c, (q15_t)0xc031, (q15_t)0x3b00, (q15_t)0xc032, (q15_t)0x3af3, (q15_t)0xc033, + (q15_t)0x3ae6, (q15_t)0xc034, (q15_t)0x3ada, (q15_t)0xc035, (q15_t)0x3acd, (q15_t)0xc036, (q15_t)0x3ac1, (q15_t)0xc037, + (q15_t)0x3ab4, (q15_t)0xc038, (q15_t)0x3aa8, (q15_t)0xc039, (q15_t)0x3a9b, (q15_t)0xc03a, (q15_t)0x3a8f, (q15_t)0xc03b, + (q15_t)0x3a82, (q15_t)0xc03c, (q15_t)0x3a76, (q15_t)0xc03d, (q15_t)0x3a69, (q15_t)0xc03f, (q15_t)0x3a5d, (q15_t)0xc040, + (q15_t)0x3a50, (q15_t)0xc041, (q15_t)0x3a44, (q15_t)0xc042, (q15_t)0x3a37, (q15_t)0xc043, (q15_t)0x3a2b, (q15_t)0xc044, + (q15_t)0x3a1e, (q15_t)0xc045, (q15_t)0x3a12, (q15_t)0xc047, (q15_t)0x3a05, (q15_t)0xc048, (q15_t)0x39f9, (q15_t)0xc049, + (q15_t)0x39ec, (q15_t)0xc04a, (q15_t)0x39e0, (q15_t)0xc04b, (q15_t)0x39d3, (q15_t)0xc04c, (q15_t)0x39c7, (q15_t)0xc04e, + (q15_t)0x39ba, (q15_t)0xc04f, (q15_t)0x39ae, (q15_t)0xc050, (q15_t)0x39a1, (q15_t)0xc051, (q15_t)0x3995, (q15_t)0xc053, + (q15_t)0x3988, (q15_t)0xc054, (q15_t)0x397c, (q15_t)0xc055, (q15_t)0x396f, (q15_t)0xc056, (q15_t)0x3963, (q15_t)0xc058, + (q15_t)0x3956, (q15_t)0xc059, (q15_t)0x394a, (q15_t)0xc05a, (q15_t)0x393d, (q15_t)0xc05c, (q15_t)0x3931, (q15_t)0xc05d, + (q15_t)0x3924, (q15_t)0xc05e, (q15_t)0x3918, (q15_t)0xc060, (q15_t)0x390b, (q15_t)0xc061, (q15_t)0x38ff, (q15_t)0xc062, + (q15_t)0x38f2, (q15_t)0xc064, (q15_t)0x38e6, (q15_t)0xc065, (q15_t)0x38d9, (q15_t)0xc067, (q15_t)0x38cd, (q15_t)0xc068, + (q15_t)0x38c0, (q15_t)0xc069, (q15_t)0x38b4, (q15_t)0xc06b, (q15_t)0x38a7, (q15_t)0xc06c, (q15_t)0x389b, (q15_t)0xc06e, + (q15_t)0x388e, (q15_t)0xc06f, (q15_t)0x3882, (q15_t)0xc071, (q15_t)0x3875, (q15_t)0xc072, (q15_t)0x3869, (q15_t)0xc074, + (q15_t)0x385c, (q15_t)0xc075, (q15_t)0x3850, (q15_t)0xc077, (q15_t)0x3843, (q15_t)0xc078, (q15_t)0x3837, (q15_t)0xc07a, + (q15_t)0x382a, (q15_t)0xc07b, (q15_t)0x381e, (q15_t)0xc07d, (q15_t)0x3811, (q15_t)0xc07e, (q15_t)0x3805, (q15_t)0xc080, + (q15_t)0x37f9, (q15_t)0xc081, (q15_t)0x37ec, (q15_t)0xc083, (q15_t)0x37e0, (q15_t)0xc085, (q15_t)0x37d3, (q15_t)0xc086, + (q15_t)0x37c7, (q15_t)0xc088, (q15_t)0x37ba, (q15_t)0xc089, (q15_t)0x37ae, (q15_t)0xc08b, (q15_t)0x37a1, (q15_t)0xc08d, + (q15_t)0x3795, (q15_t)0xc08e, (q15_t)0x3788, (q15_t)0xc090, (q15_t)0x377c, (q15_t)0xc092, (q15_t)0x376f, (q15_t)0xc093, + (q15_t)0x3763, (q15_t)0xc095, (q15_t)0x3757, (q15_t)0xc097, (q15_t)0x374a, (q15_t)0xc098, (q15_t)0x373e, (q15_t)0xc09a, + (q15_t)0x3731, (q15_t)0xc09c, (q15_t)0x3725, (q15_t)0xc09e, (q15_t)0x3718, (q15_t)0xc09f, (q15_t)0x370c, (q15_t)0xc0a1, + (q15_t)0x36ff, (q15_t)0xc0a3, (q15_t)0x36f3, (q15_t)0xc0a5, (q15_t)0x36e7, (q15_t)0xc0a6, (q15_t)0x36da, (q15_t)0xc0a8, + (q15_t)0x36ce, (q15_t)0xc0aa, (q15_t)0x36c1, (q15_t)0xc0ac, (q15_t)0x36b5, (q15_t)0xc0ae, (q15_t)0x36a8, (q15_t)0xc0af, + (q15_t)0x369c, (q15_t)0xc0b1, (q15_t)0x3690, (q15_t)0xc0b3, (q15_t)0x3683, (q15_t)0xc0b5, (q15_t)0x3677, (q15_t)0xc0b7, + (q15_t)0x366a, (q15_t)0xc0b9, (q15_t)0x365e, (q15_t)0xc0bb, (q15_t)0x3651, (q15_t)0xc0bd, (q15_t)0x3645, (q15_t)0xc0be, + (q15_t)0x3639, (q15_t)0xc0c0, (q15_t)0x362c, (q15_t)0xc0c2, (q15_t)0x3620, (q15_t)0xc0c4, (q15_t)0x3613, (q15_t)0xc0c6, + (q15_t)0x3607, (q15_t)0xc0c8, (q15_t)0x35fa, (q15_t)0xc0ca, (q15_t)0x35ee, (q15_t)0xc0cc, (q15_t)0x35e2, (q15_t)0xc0ce, + (q15_t)0x35d5, (q15_t)0xc0d0, (q15_t)0x35c9, (q15_t)0xc0d2, (q15_t)0x35bc, (q15_t)0xc0d4, (q15_t)0x35b0, (q15_t)0xc0d6, + (q15_t)0x35a4, (q15_t)0xc0d8, (q15_t)0x3597, (q15_t)0xc0da, (q15_t)0x358b, (q15_t)0xc0dc, (q15_t)0x357e, (q15_t)0xc0de, + (q15_t)0x3572, (q15_t)0xc0e0, (q15_t)0x3566, (q15_t)0xc0e2, (q15_t)0x3559, (q15_t)0xc0e4, (q15_t)0x354d, (q15_t)0xc0e7, + (q15_t)0x3540, (q15_t)0xc0e9, (q15_t)0x3534, (q15_t)0xc0eb, (q15_t)0x3528, (q15_t)0xc0ed, (q15_t)0x351b, (q15_t)0xc0ef, + (q15_t)0x350f, (q15_t)0xc0f1, (q15_t)0x3503, (q15_t)0xc0f3, (q15_t)0x34f6, (q15_t)0xc0f6, (q15_t)0x34ea, (q15_t)0xc0f8, + (q15_t)0x34dd, (q15_t)0xc0fa, (q15_t)0x34d1, (q15_t)0xc0fc, (q15_t)0x34c5, (q15_t)0xc0fe, (q15_t)0x34b8, (q15_t)0xc100, + (q15_t)0x34ac, (q15_t)0xc103, (q15_t)0x34a0, (q15_t)0xc105, (q15_t)0x3493, (q15_t)0xc107, (q15_t)0x3487, (q15_t)0xc109, + (q15_t)0x347b, (q15_t)0xc10c, (q15_t)0x346e, (q15_t)0xc10e, (q15_t)0x3462, (q15_t)0xc110, (q15_t)0x3455, (q15_t)0xc113, + (q15_t)0x3449, (q15_t)0xc115, (q15_t)0x343d, (q15_t)0xc117, (q15_t)0x3430, (q15_t)0xc119, (q15_t)0x3424, (q15_t)0xc11c, + (q15_t)0x3418, (q15_t)0xc11e, (q15_t)0x340b, (q15_t)0xc120, (q15_t)0x33ff, (q15_t)0xc123, (q15_t)0x33f3, (q15_t)0xc125, + (q15_t)0x33e6, (q15_t)0xc128, (q15_t)0x33da, (q15_t)0xc12a, (q15_t)0x33ce, (q15_t)0xc12c, (q15_t)0x33c1, (q15_t)0xc12f, + (q15_t)0x33b5, (q15_t)0xc131, (q15_t)0x33a9, (q15_t)0xc134, (q15_t)0x339c, (q15_t)0xc136, (q15_t)0x3390, (q15_t)0xc138, + (q15_t)0x3384, (q15_t)0xc13b, (q15_t)0x3377, (q15_t)0xc13d, (q15_t)0x336b, (q15_t)0xc140, (q15_t)0x335f, (q15_t)0xc142, + (q15_t)0x3352, (q15_t)0xc145, (q15_t)0x3346, (q15_t)0xc147, (q15_t)0x333a, (q15_t)0xc14a, (q15_t)0x332d, (q15_t)0xc14c, + (q15_t)0x3321, (q15_t)0xc14f, (q15_t)0x3315, (q15_t)0xc151, (q15_t)0x3308, (q15_t)0xc154, (q15_t)0x32fc, (q15_t)0xc156, + (q15_t)0x32f0, (q15_t)0xc159, (q15_t)0x32e4, (q15_t)0xc15b, (q15_t)0x32d7, (q15_t)0xc15e, (q15_t)0x32cb, (q15_t)0xc161, + (q15_t)0x32bf, (q15_t)0xc163, (q15_t)0x32b2, (q15_t)0xc166, (q15_t)0x32a6, (q15_t)0xc168, (q15_t)0x329a, (q15_t)0xc16b, + (q15_t)0x328e, (q15_t)0xc16e, (q15_t)0x3281, (q15_t)0xc170, (q15_t)0x3275, (q15_t)0xc173, (q15_t)0x3269, (q15_t)0xc176, + (q15_t)0x325c, (q15_t)0xc178, (q15_t)0x3250, (q15_t)0xc17b, (q15_t)0x3244, (q15_t)0xc17e, (q15_t)0x3238, (q15_t)0xc180, + (q15_t)0x322b, (q15_t)0xc183, (q15_t)0x321f, (q15_t)0xc186, (q15_t)0x3213, (q15_t)0xc189, (q15_t)0x3207, (q15_t)0xc18b, + (q15_t)0x31fa, (q15_t)0xc18e, (q15_t)0x31ee, (q15_t)0xc191, (q15_t)0x31e2, (q15_t)0xc194, (q15_t)0x31d5, (q15_t)0xc196, + (q15_t)0x31c9, (q15_t)0xc199, (q15_t)0x31bd, (q15_t)0xc19c, (q15_t)0x31b1, (q15_t)0xc19f, (q15_t)0x31a4, (q15_t)0xc1a2, + (q15_t)0x3198, (q15_t)0xc1a4, (q15_t)0x318c, (q15_t)0xc1a7, (q15_t)0x3180, (q15_t)0xc1aa, (q15_t)0x3174, (q15_t)0xc1ad, + (q15_t)0x3167, (q15_t)0xc1b0, (q15_t)0x315b, (q15_t)0xc1b3, (q15_t)0x314f, (q15_t)0xc1b6, (q15_t)0x3143, (q15_t)0xc1b8, + (q15_t)0x3136, (q15_t)0xc1bb, (q15_t)0x312a, (q15_t)0xc1be, (q15_t)0x311e, (q15_t)0xc1c1, (q15_t)0x3112, (q15_t)0xc1c4, + (q15_t)0x3105, (q15_t)0xc1c7, (q15_t)0x30f9, (q15_t)0xc1ca, (q15_t)0x30ed, (q15_t)0xc1cd, (q15_t)0x30e1, (q15_t)0xc1d0, + (q15_t)0x30d5, (q15_t)0xc1d3, (q15_t)0x30c8, (q15_t)0xc1d6, (q15_t)0x30bc, (q15_t)0xc1d9, (q15_t)0x30b0, (q15_t)0xc1dc, + (q15_t)0x30a4, (q15_t)0xc1df, (q15_t)0x3098, (q15_t)0xc1e2, (q15_t)0x308b, (q15_t)0xc1e5, (q15_t)0x307f, (q15_t)0xc1e8, + (q15_t)0x3073, (q15_t)0xc1eb, (q15_t)0x3067, (q15_t)0xc1ee, (q15_t)0x305b, (q15_t)0xc1f1, (q15_t)0x304e, (q15_t)0xc1f4, + (q15_t)0x3042, (q15_t)0xc1f7, (q15_t)0x3036, (q15_t)0xc1fa, (q15_t)0x302a, (q15_t)0xc1fd, (q15_t)0x301e, (q15_t)0xc201, + (q15_t)0x3012, (q15_t)0xc204, (q15_t)0x3005, (q15_t)0xc207, (q15_t)0x2ff9, (q15_t)0xc20a, (q15_t)0x2fed, (q15_t)0xc20d, + (q15_t)0x2fe1, (q15_t)0xc210, (q15_t)0x2fd5, (q15_t)0xc213, (q15_t)0x2fc9, (q15_t)0xc217, (q15_t)0x2fbc, (q15_t)0xc21a, + (q15_t)0x2fb0, (q15_t)0xc21d, (q15_t)0x2fa4, (q15_t)0xc220, (q15_t)0x2f98, (q15_t)0xc223, (q15_t)0x2f8c, (q15_t)0xc227, + (q15_t)0x2f80, (q15_t)0xc22a, (q15_t)0x2f74, (q15_t)0xc22d, (q15_t)0x2f67, (q15_t)0xc230, (q15_t)0x2f5b, (q15_t)0xc234, + (q15_t)0x2f4f, (q15_t)0xc237, (q15_t)0x2f43, (q15_t)0xc23a, (q15_t)0x2f37, (q15_t)0xc23e, (q15_t)0x2f2b, (q15_t)0xc241, + (q15_t)0x2f1f, (q15_t)0xc244, (q15_t)0x2f13, (q15_t)0xc247, (q15_t)0x2f06, (q15_t)0xc24b, (q15_t)0x2efa, (q15_t)0xc24e, + (q15_t)0x2eee, 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(q15_t)0x3f30, (q15_t)0x35e2, (q15_t)0x3f32, (q15_t)0x35ee, (q15_t)0x3f34, (q15_t)0x35fa, (q15_t)0x3f36, + (q15_t)0x3607, (q15_t)0x3f38, (q15_t)0x3613, (q15_t)0x3f3a, (q15_t)0x3620, (q15_t)0x3f3c, (q15_t)0x362c, (q15_t)0x3f3e, + (q15_t)0x3639, (q15_t)0x3f40, (q15_t)0x3645, (q15_t)0x3f42, (q15_t)0x3651, (q15_t)0x3f43, (q15_t)0x365e, (q15_t)0x3f45, + (q15_t)0x366a, (q15_t)0x3f47, (q15_t)0x3677, (q15_t)0x3f49, (q15_t)0x3683, (q15_t)0x3f4b, (q15_t)0x3690, (q15_t)0x3f4d, + (q15_t)0x369c, (q15_t)0x3f4f, (q15_t)0x36a8, (q15_t)0x3f51, (q15_t)0x36b5, (q15_t)0x3f52, (q15_t)0x36c1, (q15_t)0x3f54, + (q15_t)0x36ce, (q15_t)0x3f56, (q15_t)0x36da, (q15_t)0x3f58, (q15_t)0x36e7, (q15_t)0x3f5a, (q15_t)0x36f3, (q15_t)0x3f5b, + (q15_t)0x36ff, (q15_t)0x3f5d, (q15_t)0x370c, (q15_t)0x3f5f, (q15_t)0x3718, (q15_t)0x3f61, (q15_t)0x3725, (q15_t)0x3f62, + (q15_t)0x3731, (q15_t)0x3f64, (q15_t)0x373e, (q15_t)0x3f66, (q15_t)0x374a, (q15_t)0x3f68, (q15_t)0x3757, (q15_t)0x3f69, + (q15_t)0x3763, (q15_t)0x3f6b, (q15_t)0x376f, (q15_t)0x3f6d, (q15_t)0x377c, (q15_t)0x3f6e, (q15_t)0x3788, (q15_t)0x3f70, + (q15_t)0x3795, (q15_t)0x3f72, (q15_t)0x37a1, (q15_t)0x3f73, (q15_t)0x37ae, (q15_t)0x3f75, (q15_t)0x37ba, (q15_t)0x3f77, + (q15_t)0x37c7, (q15_t)0x3f78, (q15_t)0x37d3, (q15_t)0x3f7a, (q15_t)0x37e0, (q15_t)0x3f7b, (q15_t)0x37ec, (q15_t)0x3f7d, + (q15_t)0x37f9, (q15_t)0x3f7f, (q15_t)0x3805, (q15_t)0x3f80, (q15_t)0x3811, (q15_t)0x3f82, (q15_t)0x381e, (q15_t)0x3f83, + (q15_t)0x382a, (q15_t)0x3f85, (q15_t)0x3837, (q15_t)0x3f86, (q15_t)0x3843, (q15_t)0x3f88, (q15_t)0x3850, (q15_t)0x3f89, + (q15_t)0x385c, (q15_t)0x3f8b, (q15_t)0x3869, (q15_t)0x3f8c, (q15_t)0x3875, (q15_t)0x3f8e, (q15_t)0x3882, (q15_t)0x3f8f, + (q15_t)0x388e, (q15_t)0x3f91, (q15_t)0x389b, (q15_t)0x3f92, (q15_t)0x38a7, (q15_t)0x3f94, (q15_t)0x38b4, (q15_t)0x3f95, + (q15_t)0x38c0, (q15_t)0x3f97, (q15_t)0x38cd, (q15_t)0x3f98, (q15_t)0x38d9, (q15_t)0x3f99, (q15_t)0x38e6, (q15_t)0x3f9b, + (q15_t)0x38f2, (q15_t)0x3f9c, (q15_t)0x38ff, (q15_t)0x3f9e, (q15_t)0x390b, (q15_t)0x3f9f, (q15_t)0x3918, (q15_t)0x3fa0, + (q15_t)0x3924, (q15_t)0x3fa2, (q15_t)0x3931, (q15_t)0x3fa3, (q15_t)0x393d, (q15_t)0x3fa4, (q15_t)0x394a, (q15_t)0x3fa6, + (q15_t)0x3956, (q15_t)0x3fa7, (q15_t)0x3963, (q15_t)0x3fa8, (q15_t)0x396f, (q15_t)0x3faa, (q15_t)0x397c, (q15_t)0x3fab, + (q15_t)0x3988, (q15_t)0x3fac, (q15_t)0x3995, (q15_t)0x3fad, (q15_t)0x39a1, (q15_t)0x3faf, (q15_t)0x39ae, (q15_t)0x3fb0, + (q15_t)0x39ba, (q15_t)0x3fb1, (q15_t)0x39c7, (q15_t)0x3fb2, (q15_t)0x39d3, (q15_t)0x3fb4, (q15_t)0x39e0, (q15_t)0x3fb5, + (q15_t)0x39ec, (q15_t)0x3fb6, (q15_t)0x39f9, (q15_t)0x3fb7, (q15_t)0x3a05, (q15_t)0x3fb8, (q15_t)0x3a12, (q15_t)0x3fb9, + (q15_t)0x3a1e, (q15_t)0x3fbb, (q15_t)0x3a2b, (q15_t)0x3fbc, (q15_t)0x3a37, (q15_t)0x3fbd, (q15_t)0x3a44, (q15_t)0x3fbe, + (q15_t)0x3a50, (q15_t)0x3fbf, (q15_t)0x3a5d, (q15_t)0x3fc0, (q15_t)0x3a69, (q15_t)0x3fc1, (q15_t)0x3a76, (q15_t)0x3fc3, + (q15_t)0x3a82, (q15_t)0x3fc4, (q15_t)0x3a8f, (q15_t)0x3fc5, (q15_t)0x3a9b, (q15_t)0x3fc6, (q15_t)0x3aa8, (q15_t)0x3fc7, + (q15_t)0x3ab4, (q15_t)0x3fc8, (q15_t)0x3ac1, (q15_t)0x3fc9, (q15_t)0x3acd, (q15_t)0x3fca, (q15_t)0x3ada, (q15_t)0x3fcb, + (q15_t)0x3ae6, (q15_t)0x3fcc, (q15_t)0x3af3, (q15_t)0x3fcd, (q15_t)0x3b00, (q15_t)0x3fce, (q15_t)0x3b0c, (q15_t)0x3fcf, + (q15_t)0x3b19, (q15_t)0x3fd0, (q15_t)0x3b25, (q15_t)0x3fd1, (q15_t)0x3b32, (q15_t)0x3fd2, (q15_t)0x3b3e, (q15_t)0x3fd3, + (q15_t)0x3b4b, (q15_t)0x3fd4, (q15_t)0x3b57, (q15_t)0x3fd5, (q15_t)0x3b64, (q15_t)0x3fd5, (q15_t)0x3b70, (q15_t)0x3fd6, + (q15_t)0x3b7d, (q15_t)0x3fd7, (q15_t)0x3b89, (q15_t)0x3fd8, (q15_t)0x3b96, (q15_t)0x3fd9, (q15_t)0x3ba2, (q15_t)0x3fda, + (q15_t)0x3baf, (q15_t)0x3fdb, (q15_t)0x3bbc, (q15_t)0x3fdc, (q15_t)0x3bc8, (q15_t)0x3fdc, (q15_t)0x3bd5, (q15_t)0x3fdd, + (q15_t)0x3be1, (q15_t)0x3fde, (q15_t)0x3bee, (q15_t)0x3fdf, (q15_t)0x3bfa, (q15_t)0x3fe0, (q15_t)0x3c07, (q15_t)0x3fe0, + (q15_t)0x3c13, (q15_t)0x3fe1, (q15_t)0x3c20, (q15_t)0x3fe2, (q15_t)0x3c2c, (q15_t)0x3fe3, (q15_t)0x3c39, (q15_t)0x3fe3, + (q15_t)0x3c45, (q15_t)0x3fe4, (q15_t)0x3c52, (q15_t)0x3fe5, (q15_t)0x3c5f, (q15_t)0x3fe6, (q15_t)0x3c6b, (q15_t)0x3fe6, + (q15_t)0x3c78, (q15_t)0x3fe7, (q15_t)0x3c84, (q15_t)0x3fe8, (q15_t)0x3c91, (q15_t)0x3fe8, (q15_t)0x3c9d, (q15_t)0x3fe9, + (q15_t)0x3caa, (q15_t)0x3fea, (q15_t)0x3cb6, (q15_t)0x3fea, (q15_t)0x3cc3, (q15_t)0x3feb, (q15_t)0x3cd0, (q15_t)0x3fec, + (q15_t)0x3cdc, (q15_t)0x3fec, (q15_t)0x3ce9, (q15_t)0x3fed, (q15_t)0x3cf5, (q15_t)0x3fed, (q15_t)0x3d02, (q15_t)0x3fee, + (q15_t)0x3d0e, (q15_t)0x3fef, (q15_t)0x3d1b, (q15_t)0x3fef, (q15_t)0x3d27, (q15_t)0x3ff0, (q15_t)0x3d34, (q15_t)0x3ff0, + (q15_t)0x3d40, (q15_t)0x3ff1, (q15_t)0x3d4d, (q15_t)0x3ff1, (q15_t)0x3d5a, (q15_t)0x3ff2, (q15_t)0x3d66, (q15_t)0x3ff2, + (q15_t)0x3d73, (q15_t)0x3ff3, (q15_t)0x3d7f, (q15_t)0x3ff3, (q15_t)0x3d8c, (q15_t)0x3ff4, (q15_t)0x3d98, (q15_t)0x3ff4, + (q15_t)0x3da5, (q15_t)0x3ff5, (q15_t)0x3db2, (q15_t)0x3ff5, (q15_t)0x3dbe, (q15_t)0x3ff6, (q15_t)0x3dcb, (q15_t)0x3ff6, + (q15_t)0x3dd7, (q15_t)0x3ff7, (q15_t)0x3de4, (q15_t)0x3ff7, (q15_t)0x3df0, (q15_t)0x3ff7, (q15_t)0x3dfd, (q15_t)0x3ff8, + (q15_t)0x3e09, (q15_t)0x3ff8, (q15_t)0x3e16, (q15_t)0x3ff9, (q15_t)0x3e23, (q15_t)0x3ff9, (q15_t)0x3e2f, (q15_t)0x3ff9, + (q15_t)0x3e3c, (q15_t)0x3ffa, (q15_t)0x3e48, (q15_t)0x3ffa, (q15_t)0x3e55, (q15_t)0x3ffa, (q15_t)0x3e61, (q15_t)0x3ffb, + (q15_t)0x3e6e, (q15_t)0x3ffb, (q15_t)0x3e7a, (q15_t)0x3ffb, (q15_t)0x3e87, (q15_t)0x3ffc, (q15_t)0x3e94, (q15_t)0x3ffc, + (q15_t)0x3ea0, (q15_t)0x3ffc, (q15_t)0x3ead, (q15_t)0x3ffc, (q15_t)0x3eb9, (q15_t)0x3ffd, (q15_t)0x3ec6, (q15_t)0x3ffd, + (q15_t)0x3ed2, (q15_t)0x3ffd, (q15_t)0x3edf, (q15_t)0x3ffd, (q15_t)0x3eec, (q15_t)0x3ffe, (q15_t)0x3ef8, (q15_t)0x3ffe, + (q15_t)0x3f05, (q15_t)0x3ffe, (q15_t)0x3f11, (q15_t)0x3ffe, (q15_t)0x3f1e, (q15_t)0x3ffe, (q15_t)0x3f2a, (q15_t)0x3fff, + (q15_t)0x3f37, (q15_t)0x3fff, (q15_t)0x3f44, (q15_t)0x3fff, (q15_t)0x3f50, (q15_t)0x3fff, (q15_t)0x3f5d, (q15_t)0x3fff, + (q15_t)0x3f69, (q15_t)0x3fff, (q15_t)0x3f76, (q15_t)0x3fff, (q15_t)0x3f82, (q15_t)0x4000, (q15_t)0x3f8f, (q15_t)0x4000, + (q15_t)0x3f9b, (q15_t)0x4000, (q15_t)0x3fa8, (q15_t)0x4000, (q15_t)0x3fb5, (q15_t)0x4000, (q15_t)0x3fc1, (q15_t)0x4000, + (q15_t)0x3fce, (q15_t)0x4000, (q15_t)0x3fda, (q15_t)0x4000, (q15_t)0x3fe7, (q15_t)0x4000, (q15_t)0x3ff3, (q15_t)0x4000, +}; + +/** + @par + Generation of real_CoefB array: + @par + n = 4096 + 
for (i = 0; i < n; i++)
+  {
+     pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
+     pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
+  }
+ @par + Convert to fixed point Q15 format + round(pBTable[i] * pow(2, 15)) +*/ +const q15_t __ALIGNED(4) realCoefBQ15[8192] ARM_DSP_TABLE_ATTRIBUTE = { + (q15_t)0x4000, (q15_t)0x4000, (q15_t)0x400d, (q15_t)0x4000, (q15_t)0x4019, (q15_t)0x4000, (q15_t)0x4026, (q15_t)0x4000, + (q15_t)0x4032, (q15_t)0x4000, (q15_t)0x403f, (q15_t)0x4000, (q15_t)0x404b, (q15_t)0x4000, (q15_t)0x4058, (q15_t)0x4000, + (q15_t)0x4065, (q15_t)0x4000, (q15_t)0x4071, (q15_t)0x4000, (q15_t)0x407e, (q15_t)0x4000, (q15_t)0x408a, (q15_t)0x3fff, + (q15_t)0x4097, (q15_t)0x3fff, (q15_t)0x40a3, (q15_t)0x3fff, (q15_t)0x40b0, (q15_t)0x3fff, (q15_t)0x40bc, (q15_t)0x3fff, + (q15_t)0x40c9, (q15_t)0x3fff, (q15_t)0x40d6, (q15_t)0x3fff, (q15_t)0x40e2, (q15_t)0x3ffe, (q15_t)0x40ef, (q15_t)0x3ffe, + (q15_t)0x40fb, (q15_t)0x3ffe, (q15_t)0x4108, (q15_t)0x3ffe, (q15_t)0x4114, (q15_t)0x3ffe, (q15_t)0x4121, (q15_t)0x3ffd, + (q15_t)0x412e, (q15_t)0x3ffd, (q15_t)0x413a, (q15_t)0x3ffd, (q15_t)0x4147, (q15_t)0x3ffd, (q15_t)0x4153, (q15_t)0x3ffc, + (q15_t)0x4160, (q15_t)0x3ffc, (q15_t)0x416c, (q15_t)0x3ffc, (q15_t)0x4179, (q15_t)0x3ffc, (q15_t)0x4186, (q15_t)0x3ffb, + (q15_t)0x4192, (q15_t)0x3ffb, (q15_t)0x419f, (q15_t)0x3ffb, (q15_t)0x41ab, (q15_t)0x3ffa, (q15_t)0x41b8, (q15_t)0x3ffa, + (q15_t)0x41c4, (q15_t)0x3ffa, (q15_t)0x41d1, (q15_t)0x3ff9, (q15_t)0x41dd, (q15_t)0x3ff9, (q15_t)0x41ea, (q15_t)0x3ff9, + (q15_t)0x41f7, (q15_t)0x3ff8, (q15_t)0x4203, (q15_t)0x3ff8, (q15_t)0x4210, (q15_t)0x3ff7, (q15_t)0x421c, (q15_t)0x3ff7, + (q15_t)0x4229, (q15_t)0x3ff7, (q15_t)0x4235, (q15_t)0x3ff6, (q15_t)0x4242, (q15_t)0x3ff6, (q15_t)0x424e, (q15_t)0x3ff5, + (q15_t)0x425b, (q15_t)0x3ff5, (q15_t)0x4268, (q15_t)0x3ff4, (q15_t)0x4274, (q15_t)0x3ff4, (q15_t)0x4281, (q15_t)0x3ff3, + (q15_t)0x428d, (q15_t)0x3ff3, (q15_t)0x429a, (q15_t)0x3ff2, (q15_t)0x42a6, (q15_t)0x3ff2, (q15_t)0x42b3, (q15_t)0x3ff1, + (q15_t)0x42c0, (q15_t)0x3ff1, (q15_t)0x42cc, (q15_t)0x3ff0, (q15_t)0x42d9, (q15_t)0x3ff0, (q15_t)0x42e5, (q15_t)0x3fef, + (q15_t)0x42f2, (q15_t)0x3fef, (q15_t)0x42fe, (q15_t)0x3fee, (q15_t)0x430b, (q15_t)0x3fed, (q15_t)0x4317, (q15_t)0x3fed, + (q15_t)0x4324, (q15_t)0x3fec, (q15_t)0x4330, (q15_t)0x3fec, (q15_t)0x433d, (q15_t)0x3feb, (q15_t)0x434a, (q15_t)0x3fea, + (q15_t)0x4356, (q15_t)0x3fea, (q15_t)0x4363, (q15_t)0x3fe9, (q15_t)0x436f, (q15_t)0x3fe8, (q15_t)0x437c, (q15_t)0x3fe8, + (q15_t)0x4388, (q15_t)0x3fe7, (q15_t)0x4395, (q15_t)0x3fe6, (q15_t)0x43a1, (q15_t)0x3fe6, (q15_t)0x43ae, (q15_t)0x3fe5, + (q15_t)0x43bb, (q15_t)0x3fe4, (q15_t)0x43c7, (q15_t)0x3fe3, (q15_t)0x43d4, (q15_t)0x3fe3, (q15_t)0x43e0, (q15_t)0x3fe2, + (q15_t)0x43ed, (q15_t)0x3fe1, (q15_t)0x43f9, (q15_t)0x3fe0, (q15_t)0x4406, (q15_t)0x3fe0, (q15_t)0x4412, (q15_t)0x3fdf, + (q15_t)0x441f, (q15_t)0x3fde, (q15_t)0x442b, (q15_t)0x3fdd, (q15_t)0x4438, (q15_t)0x3fdc, (q15_t)0x4444, (q15_t)0x3fdc, + (q15_t)0x4451, (q15_t)0x3fdb, (q15_t)0x445e, (q15_t)0x3fda, (q15_t)0x446a, (q15_t)0x3fd9, (q15_t)0x4477, (q15_t)0x3fd8, + (q15_t)0x4483, (q15_t)0x3fd7, (q15_t)0x4490, (q15_t)0x3fd6, (q15_t)0x449c, (q15_t)0x3fd5, (q15_t)0x44a9, (q15_t)0x3fd5, + (q15_t)0x44b5, (q15_t)0x3fd4, (q15_t)0x44c2, (q15_t)0x3fd3, (q15_t)0x44ce, (q15_t)0x3fd2, (q15_t)0x44db, (q15_t)0x3fd1, + (q15_t)0x44e7, (q15_t)0x3fd0, (q15_t)0x44f4, (q15_t)0x3fcf, (q15_t)0x4500, (q15_t)0x3fce, (q15_t)0x450d, (q15_t)0x3fcd, + (q15_t)0x451a, (q15_t)0x3fcc, (q15_t)0x4526, (q15_t)0x3fcb, (q15_t)0x4533, (q15_t)0x3fca, (q15_t)0x453f, (q15_t)0x3fc9, + (q15_t)0x454c, (q15_t)0x3fc8, (q15_t)0x4558, (q15_t)0x3fc7, (q15_t)0x4565, (q15_t)0x3fc6, (q15_t)0x4571, (q15_t)0x3fc5, + (q15_t)0x457e, (q15_t)0x3fc4, (q15_t)0x458a, (q15_t)0x3fc3, (q15_t)0x4597, (q15_t)0x3fc1, (q15_t)0x45a3, (q15_t)0x3fc0, + (q15_t)0x45b0, (q15_t)0x3fbf, (q15_t)0x45bc, (q15_t)0x3fbe, (q15_t)0x45c9, (q15_t)0x3fbd, (q15_t)0x45d5, (q15_t)0x3fbc, + (q15_t)0x45e2, (q15_t)0x3fbb, (q15_t)0x45ee, (q15_t)0x3fb9, (q15_t)0x45fb, (q15_t)0x3fb8, (q15_t)0x4607, (q15_t)0x3fb7, + (q15_t)0x4614, (q15_t)0x3fb6, 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(q15_t)0x4f8d, (q15_t)0xc1eb, (q15_t)0x4f81, (q15_t)0xc1e8, (q15_t)0x4f75, (q15_t)0xc1e5, (q15_t)0x4f68, (q15_t)0xc1e2, + (q15_t)0x4f5c, (q15_t)0xc1df, (q15_t)0x4f50, (q15_t)0xc1dc, (q15_t)0x4f44, (q15_t)0xc1d9, (q15_t)0x4f38, (q15_t)0xc1d6, + (q15_t)0x4f2b, (q15_t)0xc1d3, (q15_t)0x4f1f, (q15_t)0xc1d0, (q15_t)0x4f13, (q15_t)0xc1cd, (q15_t)0x4f07, (q15_t)0xc1ca, + (q15_t)0x4efb, (q15_t)0xc1c7, (q15_t)0x4eee, (q15_t)0xc1c4, (q15_t)0x4ee2, (q15_t)0xc1c1, (q15_t)0x4ed6, (q15_t)0xc1be, + (q15_t)0x4eca, (q15_t)0xc1bb, (q15_t)0x4ebd, (q15_t)0xc1b8, (q15_t)0x4eb1, (q15_t)0xc1b6, (q15_t)0x4ea5, (q15_t)0xc1b3, + (q15_t)0x4e99, (q15_t)0xc1b0, (q15_t)0x4e8c, (q15_t)0xc1ad, (q15_t)0x4e80, (q15_t)0xc1aa, (q15_t)0x4e74, (q15_t)0xc1a7, + (q15_t)0x4e68, (q15_t)0xc1a4, (q15_t)0x4e5c, (q15_t)0xc1a2, (q15_t)0x4e4f, (q15_t)0xc19f, (q15_t)0x4e43, (q15_t)0xc19c, + (q15_t)0x4e37, (q15_t)0xc199, (q15_t)0x4e2b, (q15_t)0xc196, (q15_t)0x4e1e, (q15_t)0xc194, (q15_t)0x4e12, (q15_t)0xc191, + (q15_t)0x4e06, (q15_t)0xc18e, (q15_t)0x4df9, (q15_t)0xc18b, (q15_t)0x4ded, (q15_t)0xc189, (q15_t)0x4de1, (q15_t)0xc186, + (q15_t)0x4dd5, (q15_t)0xc183, (q15_t)0x4dc8, (q15_t)0xc180, (q15_t)0x4dbc, (q15_t)0xc17e, (q15_t)0x4db0, (q15_t)0xc17b, + (q15_t)0x4da4, (q15_t)0xc178, (q15_t)0x4d97, (q15_t)0xc176, (q15_t)0x4d8b, (q15_t)0xc173, (q15_t)0x4d7f, (q15_t)0xc170, + (q15_t)0x4d72, (q15_t)0xc16e, (q15_t)0x4d66, (q15_t)0xc16b, (q15_t)0x4d5a, (q15_t)0xc168, (q15_t)0x4d4e, (q15_t)0xc166, + (q15_t)0x4d41, (q15_t)0xc163, (q15_t)0x4d35, (q15_t)0xc161, (q15_t)0x4d29, (q15_t)0xc15e, (q15_t)0x4d1c, (q15_t)0xc15b, + (q15_t)0x4d10, (q15_t)0xc159, (q15_t)0x4d04, (q15_t)0xc156, (q15_t)0x4cf8, (q15_t)0xc154, (q15_t)0x4ceb, (q15_t)0xc151, + (q15_t)0x4cdf, (q15_t)0xc14f, (q15_t)0x4cd3, (q15_t)0xc14c, (q15_t)0x4cc6, (q15_t)0xc14a, (q15_t)0x4cba, (q15_t)0xc147, + (q15_t)0x4cae, (q15_t)0xc145, (q15_t)0x4ca1, (q15_t)0xc142, (q15_t)0x4c95, (q15_t)0xc140, (q15_t)0x4c89, (q15_t)0xc13d, + (q15_t)0x4c7c, (q15_t)0xc13b, (q15_t)0x4c70, (q15_t)0xc138, (q15_t)0x4c64, (q15_t)0xc136, (q15_t)0x4c57, (q15_t)0xc134, + (q15_t)0x4c4b, (q15_t)0xc131, (q15_t)0x4c3f, (q15_t)0xc12f, (q15_t)0x4c32, (q15_t)0xc12c, (q15_t)0x4c26, (q15_t)0xc12a, + (q15_t)0x4c1a, (q15_t)0xc128, (q15_t)0x4c0d, (q15_t)0xc125, (q15_t)0x4c01, (q15_t)0xc123, (q15_t)0x4bf5, (q15_t)0xc120, + (q15_t)0x4be8, (q15_t)0xc11e, (q15_t)0x4bdc, (q15_t)0xc11c, (q15_t)0x4bd0, (q15_t)0xc119, (q15_t)0x4bc3, (q15_t)0xc117, + (q15_t)0x4bb7, (q15_t)0xc115, (q15_t)0x4bab, (q15_t)0xc113, (q15_t)0x4b9e, (q15_t)0xc110, (q15_t)0x4b92, (q15_t)0xc10e, + (q15_t)0x4b85, (q15_t)0xc10c, (q15_t)0x4b79, (q15_t)0xc109, (q15_t)0x4b6d, (q15_t)0xc107, (q15_t)0x4b60, (q15_t)0xc105, + (q15_t)0x4b54, (q15_t)0xc103, (q15_t)0x4b48, (q15_t)0xc100, (q15_t)0x4b3b, (q15_t)0xc0fe, (q15_t)0x4b2f, (q15_t)0xc0fc, + (q15_t)0x4b23, (q15_t)0xc0fa, (q15_t)0x4b16, (q15_t)0xc0f8, (q15_t)0x4b0a, (q15_t)0xc0f6, (q15_t)0x4afd, (q15_t)0xc0f3, + (q15_t)0x4af1, (q15_t)0xc0f1, (q15_t)0x4ae5, (q15_t)0xc0ef, (q15_t)0x4ad8, (q15_t)0xc0ed, (q15_t)0x4acc, (q15_t)0xc0eb, + (q15_t)0x4ac0, (q15_t)0xc0e9, (q15_t)0x4ab3, (q15_t)0xc0e7, (q15_t)0x4aa7, (q15_t)0xc0e4, (q15_t)0x4a9a, (q15_t)0xc0e2, + (q15_t)0x4a8e, (q15_t)0xc0e0, (q15_t)0x4a82, (q15_t)0xc0de, (q15_t)0x4a75, (q15_t)0xc0dc, (q15_t)0x4a69, (q15_t)0xc0da, + (q15_t)0x4a5c, (q15_t)0xc0d8, (q15_t)0x4a50, (q15_t)0xc0d6, (q15_t)0x4a44, (q15_t)0xc0d4, (q15_t)0x4a37, (q15_t)0xc0d2, + (q15_t)0x4a2b, (q15_t)0xc0d0, (q15_t)0x4a1e, (q15_t)0xc0ce, (q15_t)0x4a12, (q15_t)0xc0cc, (q15_t)0x4a06, (q15_t)0xc0ca, + (q15_t)0x49f9, (q15_t)0xc0c8, (q15_t)0x49ed, (q15_t)0xc0c6, (q15_t)0x49e0, (q15_t)0xc0c4, (q15_t)0x49d4, (q15_t)0xc0c2, + (q15_t)0x49c7, (q15_t)0xc0c0, (q15_t)0x49bb, (q15_t)0xc0be, (q15_t)0x49af, (q15_t)0xc0bd, (q15_t)0x49a2, (q15_t)0xc0bb, + (q15_t)0x4996, (q15_t)0xc0b9, (q15_t)0x4989, (q15_t)0xc0b7, (q15_t)0x497d, (q15_t)0xc0b5, (q15_t)0x4970, (q15_t)0xc0b3, + (q15_t)0x4964, (q15_t)0xc0b1, (q15_t)0x4958, (q15_t)0xc0af, (q15_t)0x494b, (q15_t)0xc0ae, (q15_t)0x493f, (q15_t)0xc0ac, + (q15_t)0x4932, (q15_t)0xc0aa, (q15_t)0x4926, (q15_t)0xc0a8, (q15_t)0x4919, (q15_t)0xc0a6, (q15_t)0x490d, (q15_t)0xc0a5, + (q15_t)0x4901, (q15_t)0xc0a3, (q15_t)0x48f4, (q15_t)0xc0a1, (q15_t)0x48e8, (q15_t)0xc09f, (q15_t)0x48db, (q15_t)0xc09e, + (q15_t)0x48cf, (q15_t)0xc09c, (q15_t)0x48c2, (q15_t)0xc09a, (q15_t)0x48b6, (q15_t)0xc098, (q15_t)0x48a9, (q15_t)0xc097, + (q15_t)0x489d, (q15_t)0xc095, (q15_t)0x4891, (q15_t)0xc093, (q15_t)0x4884, (q15_t)0xc092, (q15_t)0x4878, (q15_t)0xc090, + (q15_t)0x486b, (q15_t)0xc08e, (q15_t)0x485f, (q15_t)0xc08d, (q15_t)0x4852, (q15_t)0xc08b, (q15_t)0x4846, (q15_t)0xc089, + (q15_t)0x4839, (q15_t)0xc088, (q15_t)0x482d, (q15_t)0xc086, (q15_t)0x4820, (q15_t)0xc085, (q15_t)0x4814, (q15_t)0xc083, + (q15_t)0x4807, (q15_t)0xc081, (q15_t)0x47fb, (q15_t)0xc080, (q15_t)0x47ef, (q15_t)0xc07e, (q15_t)0x47e2, (q15_t)0xc07d, + (q15_t)0x47d6, (q15_t)0xc07b, (q15_t)0x47c9, (q15_t)0xc07a, (q15_t)0x47bd, (q15_t)0xc078, (q15_t)0x47b0, (q15_t)0xc077, + (q15_t)0x47a4, (q15_t)0xc075, (q15_t)0x4797, (q15_t)0xc074, (q15_t)0x478b, (q15_t)0xc072, (q15_t)0x477e, (q15_t)0xc071, + (q15_t)0x4772, (q15_t)0xc06f, (q15_t)0x4765, (q15_t)0xc06e, (q15_t)0x4759, (q15_t)0xc06c, (q15_t)0x474c, (q15_t)0xc06b, + (q15_t)0x4740, (q15_t)0xc069, (q15_t)0x4733, (q15_t)0xc068, (q15_t)0x4727, (q15_t)0xc067, (q15_t)0x471a, (q15_t)0xc065, + (q15_t)0x470e, (q15_t)0xc064, (q15_t)0x4701, (q15_t)0xc062, (q15_t)0x46f5, (q15_t)0xc061, (q15_t)0x46e8, (q15_t)0xc060, + (q15_t)0x46dc, (q15_t)0xc05e, (q15_t)0x46cf, (q15_t)0xc05d, (q15_t)0x46c3, (q15_t)0xc05c, (q15_t)0x46b6, (q15_t)0xc05a, + (q15_t)0x46aa, (q15_t)0xc059, (q15_t)0x469d, (q15_t)0xc058, (q15_t)0x4691, (q15_t)0xc056, (q15_t)0x4684, (q15_t)0xc055, + (q15_t)0x4678, (q15_t)0xc054, (q15_t)0x466b, (q15_t)0xc053, (q15_t)0x465f, (q15_t)0xc051, (q15_t)0x4652, (q15_t)0xc050, + (q15_t)0x4646, (q15_t)0xc04f, (q15_t)0x4639, (q15_t)0xc04e, (q15_t)0x462d, (q15_t)0xc04c, (q15_t)0x4620, (q15_t)0xc04b, + (q15_t)0x4614, (q15_t)0xc04a, (q15_t)0x4607, (q15_t)0xc049, (q15_t)0x45fb, (q15_t)0xc048, (q15_t)0x45ee, (q15_t)0xc047, + (q15_t)0x45e2, (q15_t)0xc045, (q15_t)0x45d5, (q15_t)0xc044, (q15_t)0x45c9, (q15_t)0xc043, (q15_t)0x45bc, (q15_t)0xc042, + (q15_t)0x45b0, (q15_t)0xc041, (q15_t)0x45a3, (q15_t)0xc040, (q15_t)0x4597, (q15_t)0xc03f, (q15_t)0x458a, (q15_t)0xc03d, + (q15_t)0x457e, (q15_t)0xc03c, (q15_t)0x4571, (q15_t)0xc03b, (q15_t)0x4565, (q15_t)0xc03a, (q15_t)0x4558, (q15_t)0xc039, + (q15_t)0x454c, (q15_t)0xc038, (q15_t)0x453f, (q15_t)0xc037, (q15_t)0x4533, (q15_t)0xc036, (q15_t)0x4526, (q15_t)0xc035, + (q15_t)0x451a, (q15_t)0xc034, (q15_t)0x450d, (q15_t)0xc033, (q15_t)0x4500, (q15_t)0xc032, (q15_t)0x44f4, (q15_t)0xc031, + (q15_t)0x44e7, (q15_t)0xc030, (q15_t)0x44db, (q15_t)0xc02f, (q15_t)0x44ce, (q15_t)0xc02e, (q15_t)0x44c2, (q15_t)0xc02d, + (q15_t)0x44b5, (q15_t)0xc02c, (q15_t)0x44a9, (q15_t)0xc02b, (q15_t)0x449c, (q15_t)0xc02b, (q15_t)0x4490, (q15_t)0xc02a, + (q15_t)0x4483, (q15_t)0xc029, (q15_t)0x4477, (q15_t)0xc028, (q15_t)0x446a, (q15_t)0xc027, (q15_t)0x445e, (q15_t)0xc026, + (q15_t)0x4451, (q15_t)0xc025, (q15_t)0x4444, (q15_t)0xc024, (q15_t)0x4438, (q15_t)0xc024, (q15_t)0x442b, (q15_t)0xc023, + (q15_t)0x441f, (q15_t)0xc022, (q15_t)0x4412, (q15_t)0xc021, (q15_t)0x4406, (q15_t)0xc020, (q15_t)0x43f9, (q15_t)0xc020, + (q15_t)0x43ed, (q15_t)0xc01f, (q15_t)0x43e0, (q15_t)0xc01e, (q15_t)0x43d4, (q15_t)0xc01d, (q15_t)0x43c7, (q15_t)0xc01d, + (q15_t)0x43bb, (q15_t)0xc01c, (q15_t)0x43ae, (q15_t)0xc01b, (q15_t)0x43a1, (q15_t)0xc01a, (q15_t)0x4395, (q15_t)0xc01a, + (q15_t)0x4388, (q15_t)0xc019, (q15_t)0x437c, (q15_t)0xc018, (q15_t)0x436f, (q15_t)0xc018, (q15_t)0x4363, (q15_t)0xc017, + (q15_t)0x4356, (q15_t)0xc016, (q15_t)0x434a, (q15_t)0xc016, (q15_t)0x433d, (q15_t)0xc015, (q15_t)0x4330, (q15_t)0xc014, + (q15_t)0x4324, (q15_t)0xc014, (q15_t)0x4317, (q15_t)0xc013, (q15_t)0x430b, (q15_t)0xc013, (q15_t)0x42fe, (q15_t)0xc012, + (q15_t)0x42f2, (q15_t)0xc011, (q15_t)0x42e5, (q15_t)0xc011, (q15_t)0x42d9, (q15_t)0xc010, (q15_t)0x42cc, (q15_t)0xc010, + (q15_t)0x42c0, (q15_t)0xc00f, (q15_t)0x42b3, (q15_t)0xc00f, (q15_t)0x42a6, (q15_t)0xc00e, (q15_t)0x429a, (q15_t)0xc00e, + (q15_t)0x428d, (q15_t)0xc00d, (q15_t)0x4281, (q15_t)0xc00d, (q15_t)0x4274, (q15_t)0xc00c, (q15_t)0x4268, (q15_t)0xc00c, + (q15_t)0x425b, (q15_t)0xc00b, (q15_t)0x424e, (q15_t)0xc00b, (q15_t)0x4242, (q15_t)0xc00a, (q15_t)0x4235, (q15_t)0xc00a, + (q15_t)0x4229, (q15_t)0xc009, (q15_t)0x421c, (q15_t)0xc009, (q15_t)0x4210, (q15_t)0xc009, (q15_t)0x4203, (q15_t)0xc008, + (q15_t)0x41f7, (q15_t)0xc008, (q15_t)0x41ea, (q15_t)0xc007, (q15_t)0x41dd, (q15_t)0xc007, (q15_t)0x41d1, (q15_t)0xc007, + (q15_t)0x41c4, (q15_t)0xc006, (q15_t)0x41b8, (q15_t)0xc006, (q15_t)0x41ab, (q15_t)0xc006, (q15_t)0x419f, (q15_t)0xc005, + (q15_t)0x4192, (q15_t)0xc005, (q15_t)0x4186, (q15_t)0xc005, (q15_t)0x4179, (q15_t)0xc004, (q15_t)0x416c, (q15_t)0xc004, + (q15_t)0x4160, (q15_t)0xc004, (q15_t)0x4153, (q15_t)0xc004, (q15_t)0x4147, (q15_t)0xc003, (q15_t)0x413a, (q15_t)0xc003, + (q15_t)0x412e, (q15_t)0xc003, (q15_t)0x4121, (q15_t)0xc003, (q15_t)0x4114, (q15_t)0xc002, (q15_t)0x4108, (q15_t)0xc002, + (q15_t)0x40fb, (q15_t)0xc002, (q15_t)0x40ef, (q15_t)0xc002, (q15_t)0x40e2, (q15_t)0xc002, (q15_t)0x40d6, (q15_t)0xc001, + (q15_t)0x40c9, (q15_t)0xc001, (q15_t)0x40bc, (q15_t)0xc001, (q15_t)0x40b0, (q15_t)0xc001, (q15_t)0x40a3, (q15_t)0xc001, + (q15_t)0x4097, (q15_t)0xc001, (q15_t)0x408a, (q15_t)0xc001, (q15_t)0x407e, (q15_t)0xc000, (q15_t)0x4071, (q15_t)0xc000, + (q15_t)0x4065, (q15_t)0xc000, (q15_t)0x4058, (q15_t)0xc000, (q15_t)0x404b, (q15_t)0xc000, (q15_t)0x403f, (q15_t)0xc000, + (q15_t)0x4032, (q15_t)0xc000, (q15_t)0x4026, (q15_t)0xc000, (q15_t)0x4019, (q15_t)0xc000, (q15_t)0x400d, (q15_t)0xc000, +}; + +/** + @} end of RealFFT_Table group + */ + + + +/** + @brief Q15 table for reciprocal +*/ +const q15_t __ALIGNED(4) armRecipTableQ15[64] ARM_DSP_TABLE_ATTRIBUTE = { + 0x7F03, 0x7D13, 0x7B31, 0x795E, 0x7798, 0x75E0, + 0x7434, 0x7294, 0x70FF, 0x6F76, 0x6DF6, 0x6C82, + 0x6B16, 0x69B5, 0x685C, 0x670C, 0x65C4, 0x6484, + 0x634C, 0x621C, 0x60F3, 0x5FD0, 0x5EB5, 0x5DA0, + 0x5C91, 0x5B88, 0x5A85, 0x5988, 0x5890, 0x579E, + 0x56B0, 0x55C8, 0x54E4, 0x5405, 0x532B, 0x5255, + 0x5183, 0x50B6, 0x4FEC, 0x4F26, 0x4E64, 0x4DA6, + 0x4CEC, 0x4C34, 0x4B81, 0x4AD0, 0x4A23, 0x4978, + 0x48D1, 0x482D, 0x478C, 0x46ED, 0x4651, 0x45B8, + 0x4521, 0x448D, 0x43FC, 0x436C, 0x42DF, 0x4255, + 0x41CC, 0x4146, 0x40C2, 0x4040 +}; + + + +/** + @brief Q31 table for reciprocal +*/ +const q31_t armRecipTableQ31[64] ARM_DSP_TABLE_ATTRIBUTE = { + 0x7F03F03F, 0x7D137420, 0x7B31E739, 0x795E9F94, 0x7798FD29, 0x75E06928, + 0x7434554D, 0x72943B4B, 0x70FF9C40, 0x6F760031, 0x6DF6F593, 0x6C8210E3, + 0x6B16EC3A, 0x69B526F6, 0x685C655F, 0x670C505D, 0x65C4952D, 0x6484E519, + 0x634CF53E, 0x621C7E4F, 0x60F33C61, 0x5FD0EEB3, 0x5EB55785, 0x5DA03BEB, + 0x5C9163A1, 0x5B8898E6, 0x5A85A85A, 0x598860DF, 0x58909373, 0x579E1318, + 0x56B0B4B8, 0x55C84F0B, 0x54E4BA80, 0x5405D124, 0x532B6E8F, 0x52556FD0, + 0x5183B35A, 0x50B618F3, 0x4FEC81A2, 0x4F26CFA2, 0x4E64E64E, 0x4DA6AA1D, + 0x4CEC008B, 0x4C34D010, 0x4B810016, 0x4AD078EF, 0x4A2323C4, 0x4978EA96, + 0x48D1B827, 0x482D77FE, 0x478C1657, 0x46ED801D, 0x4651A2E5, 0x45B86CE2, + 0x4521CCE1, 0x448DB244, 0x43FC0CFA, 0x436CCD78, 0x42DFE4B4, 0x42554426, + 0x41CCDDB6, 0x4146A3C6, 0x40C28923, 0x40408102 +}; + + +/** + @par + Example code for the generation of the floating-point sine table: + 
+  tableSize = 512;
+  for (n = 0; n < (tableSize + 1); n++)
+  {
+ 	sinTable[n] = sin(2*PI*n/tableSize);
+  }
+ @par + where PI value is 3.14159265358979 + */ +const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1] ARM_DSP_TABLE_ATTRIBUTE = { + 0.000000000f, 0.012271538f, 0.024541229f, 0.036807223f, 0.049067674f, 0.061320736f, + 0.073564564f, 0.085797312f, 0.098017140f, 0.110222207f, 0.122410675f, 0.134580709f, + 0.146730474f, 0.158858143f, 0.170961889f, 0.183039888f, 0.195090322f, 0.207111376f, + 0.219101240f, 0.231058108f, 0.242980180f, 0.254865660f, 0.266712757f, 0.278519689f, + 0.290284677f, 0.302005949f, 0.313681740f, 0.325310292f, 0.336889853f, 0.348418680f, + 0.359895037f, 0.371317194f, 0.382683432f, 0.393992040f, 0.405241314f, 0.416429560f, + 0.427555093f, 0.438616239f, 0.449611330f, 0.460538711f, 0.471396737f, 0.482183772f, + 0.492898192f, 0.503538384f, 0.514102744f, 0.524589683f, 0.534997620f, 0.545324988f, + 0.555570233f, 0.565731811f, 0.575808191f, 0.585797857f, 0.595699304f, 0.605511041f, + 0.615231591f, 0.624859488f, 0.634393284f, 0.643831543f, 0.653172843f, 0.662415778f, + 0.671558955f, 0.680600998f, 0.689540545f, 0.698376249f, 0.707106781f, 0.715730825f, + 0.724247083f, 0.732654272f, 0.740951125f, 0.749136395f, 0.757208847f, 0.765167266f, + 0.773010453f, 0.780737229f, 0.788346428f, 0.795836905f, 0.803207531f, 0.810457198f, + 0.817584813f, 0.824589303f, 0.831469612f, 0.838224706f, 0.844853565f, 0.851355193f, + 0.857728610f, 0.863972856f, 0.870086991f, 0.876070094f, 0.881921264f, 0.887639620f, + 0.893224301f, 0.898674466f, 0.903989293f, 0.909167983f, 0.914209756f, 0.919113852f, + 0.923879533f, 0.928506080f, 0.932992799f, 0.937339012f, 0.941544065f, 0.945607325f, + 0.949528181f, 0.953306040f, 0.956940336f, 0.960430519f, 0.963776066f, 0.966976471f, + 0.970031253f, 0.972939952f, 0.975702130f, 0.978317371f, 0.980785280f, 0.983105487f, + 0.985277642f, 0.987301418f, 0.989176510f, 0.990902635f, 0.992479535f, 0.993906970f, + 0.995184727f, 0.996312612f, 0.997290457f, 0.998118113f, 0.998795456f, 0.999322385f, + 0.999698819f, 0.999924702f, 1.000000000f, 0.999924702f, 0.999698819f, 0.999322385f, + 0.998795456f, 0.998118113f, 0.997290457f, 0.996312612f, 0.995184727f, 0.993906970f, + 0.992479535f, 0.990902635f, 0.989176510f, 0.987301418f, 0.985277642f, 0.983105487f, + 0.980785280f, 0.978317371f, 0.975702130f, 0.972939952f, 0.970031253f, 0.966976471f, + 0.963776066f, 0.960430519f, 0.956940336f, 0.953306040f, 0.949528181f, 0.945607325f, + 0.941544065f, 0.937339012f, 0.932992799f, 0.928506080f, 0.923879533f, 0.919113852f, + 0.914209756f, 0.909167983f, 0.903989293f, 0.898674466f, 0.893224301f, 0.887639620f, + 0.881921264f, 0.876070094f, 0.870086991f, 0.863972856f, 0.857728610f, 0.851355193f, + 0.844853565f, 0.838224706f, 0.831469612f, 0.824589303f, 0.817584813f, 0.810457198f, + 0.803207531f, 0.795836905f, 0.788346428f, 0.780737229f, 0.773010453f, 0.765167266f, + 0.757208847f, 0.749136395f, 0.740951125f, 0.732654272f, 0.724247083f, 0.715730825f, + 0.707106781f, 0.698376249f, 0.689540545f, 0.680600998f, 0.671558955f, 0.662415778f, + 0.653172843f, 0.643831543f, 0.634393284f, 0.624859488f, 0.615231591f, 0.605511041f, + 0.595699304f, 0.585797857f, 0.575808191f, 0.565731811f, 0.555570233f, 0.545324988f, + 0.534997620f, 0.524589683f, 0.514102744f, 0.503538384f, 0.492898192f, 0.482183772f, + 0.471396737f, 0.460538711f, 0.449611330f, 0.438616239f, 0.427555093f, 0.416429560f, + 0.405241314f, 0.393992040f, 0.382683432f, 0.371317194f, 0.359895037f, 0.348418680f, + 0.336889853f, 0.325310292f, 0.313681740f, 0.302005949f, 0.290284677f, 0.278519689f, + 0.266712757f, 0.254865660f, 0.242980180f, 0.231058108f, 0.219101240f, 0.207111376f, + 0.195090322f, 0.183039888f, 0.170961889f, 0.158858143f, 0.146730474f, 0.134580709f, + 0.122410675f, 0.110222207f, 0.098017140f, 0.085797312f, 0.073564564f, 0.061320736f, + 0.049067674f, 0.036807223f, 0.024541229f, 0.012271538f, 0.000000000f, -0.012271538f, + -0.024541229f, -0.036807223f, -0.049067674f, -0.061320736f, -0.073564564f, -0.085797312f, + -0.098017140f, -0.110222207f, -0.122410675f, -0.134580709f, -0.146730474f, -0.158858143f, + -0.170961889f, -0.183039888f, -0.195090322f, -0.207111376f, -0.219101240f, -0.231058108f, + -0.242980180f, -0.254865660f, -0.266712757f, -0.278519689f, -0.290284677f, -0.302005949f, + -0.313681740f, -0.325310292f, -0.336889853f, -0.348418680f, -0.359895037f, -0.371317194f, + -0.382683432f, -0.393992040f, -0.405241314f, -0.416429560f, -0.427555093f, -0.438616239f, + -0.449611330f, -0.460538711f, -0.471396737f, -0.482183772f, -0.492898192f, -0.503538384f, + -0.514102744f, -0.524589683f, -0.534997620f, -0.545324988f, -0.555570233f, -0.565731811f, + -0.575808191f, -0.585797857f, -0.595699304f, -0.605511041f, -0.615231591f, -0.624859488f, + -0.634393284f, -0.643831543f, -0.653172843f, -0.662415778f, -0.671558955f, -0.680600998f, + -0.689540545f, -0.698376249f, -0.707106781f, -0.715730825f, -0.724247083f, -0.732654272f, + -0.740951125f, -0.749136395f, -0.757208847f, -0.765167266f, -0.773010453f, -0.780737229f, + -0.788346428f, -0.795836905f, -0.803207531f, -0.810457198f, -0.817584813f, -0.824589303f, + -0.831469612f, -0.838224706f, -0.844853565f, -0.851355193f, -0.857728610f, -0.863972856f, + -0.870086991f, -0.876070094f, -0.881921264f, -0.887639620f, -0.893224301f, -0.898674466f, + -0.903989293f, -0.909167983f, -0.914209756f, -0.919113852f, -0.923879533f, -0.928506080f, + -0.932992799f, -0.937339012f, -0.941544065f, -0.945607325f, -0.949528181f, -0.953306040f, + -0.956940336f, -0.960430519f, -0.963776066f, -0.966976471f, -0.970031253f, -0.972939952f, + -0.975702130f, -0.978317371f, -0.980785280f, -0.983105487f, -0.985277642f, -0.987301418f, + -0.989176510f, -0.990902635f, -0.992479535f, -0.993906970f, -0.995184727f, -0.996312612f, + -0.997290457f, -0.998118113f, -0.998795456f, -0.999322385f, -0.999698819f, -0.999924702f, + -1.000000000f, -0.999924702f, -0.999698819f, -0.999322385f, -0.998795456f, -0.998118113f, + -0.997290457f, -0.996312612f, -0.995184727f, -0.993906970f, -0.992479535f, -0.990902635f, + -0.989176510f, -0.987301418f, -0.985277642f, -0.983105487f, -0.980785280f, -0.978317371f, + -0.975702130f, -0.972939952f, -0.970031253f, -0.966976471f, -0.963776066f, -0.960430519f, + -0.956940336f, -0.953306040f, -0.949528181f, -0.945607325f, -0.941544065f, -0.937339012f, + -0.932992799f, -0.928506080f, -0.923879533f, -0.919113852f, -0.914209756f, -0.909167983f, + -0.903989293f, -0.898674466f, -0.893224301f, -0.887639620f, -0.881921264f, -0.876070094f, + -0.870086991f, -0.863972856f, -0.857728610f, -0.851355193f, -0.844853565f, -0.838224706f, + -0.831469612f, -0.824589303f, -0.817584813f, -0.810457198f, -0.803207531f, -0.795836905f, + -0.788346428f, -0.780737229f, -0.773010453f, -0.765167266f, -0.757208847f, -0.749136395f, + -0.740951125f, -0.732654272f, -0.724247083f, -0.715730825f, -0.707106781f, -0.698376249f, + -0.689540545f, -0.680600998f, -0.671558955f, -0.662415778f, -0.653172843f, -0.643831543f, + -0.634393284f, -0.624859488f, -0.615231591f, -0.605511041f, -0.595699304f, -0.585797857f, + -0.575808191f, -0.565731811f, -0.555570233f, -0.545324988f, -0.534997620f, -0.524589683f, + -0.514102744f, -0.503538384f, -0.492898192f, -0.482183772f, -0.471396737f, -0.460538711f, + -0.449611330f, -0.438616239f, -0.427555093f, -0.416429560f, -0.405241314f, -0.393992040f, + -0.382683432f, -0.371317194f, -0.359895037f, -0.348418680f, -0.336889853f, -0.325310292f, + -0.313681740f, -0.302005949f, -0.290284677f, -0.278519689f, -0.266712757f, -0.254865660f, + -0.242980180f, -0.231058108f, -0.219101240f, -0.207111376f, -0.195090322f, -0.183039888f, + -0.170961889f, -0.158858143f, -0.146730474f, -0.134580709f, -0.122410675f, -0.110222207f, + -0.098017140f, -0.085797312f, -0.073564564f, -0.061320736f, -0.049067674f, -0.036807223f, + -0.024541229f, -0.012271538f, -0.000000000f +}; + +/** + @par + Table values are in Q31 (1.31 fixed-point format) and generation is done in + three steps. First, generate sin values in floating point: + 
+  tableSize = 512;
+  for (n = 0; n < (tableSize + 1); n++)
+  {
+ 	sinTable[n] = sin(2*PI*n/tableSize);
+  }
+ where PI value is 3.14159265358979 + @par + Second, convert floating-point to Q31 (Fixed point): + (sinTable[i] * pow(2, 31)) + @par + Finally, round to the nearest integer value: + sinTable[i] += (sinTable[i] > 0 ? 0.5 : -0.5); + */ +const q31_t sinTable_q31[FAST_MATH_TABLE_SIZE + 1] ARM_DSP_TABLE_ATTRIBUTE = { + 0L, 26352928L, 52701887L, 79042909L, 105372028L, 131685278L, 157978697L, + 184248325L, 210490206L, 236700388L, 262874923L, 289009871L, 315101295L, + 341145265L, 367137861L, 393075166L, 418953276L, 444768294L, 470516330L, + 496193509L, 521795963L, 547319836L, 572761285L, 598116479L, 623381598L, + 648552838L, 673626408L, 698598533L, 723465451L, 748223418L, 772868706L, + 797397602L, 821806413L, 846091463L, 870249095L, 894275671L, 918167572L, + 941921200L, 965532978L, 988999351L, 1012316784L, 1035481766L, 1058490808L, + 1081340445L, 1104027237L, 1126547765L, 1148898640L, 1171076495L, 1193077991L, + 1214899813L, 1236538675L, 1257991320L, 1279254516L, 1300325060L, 1321199781L, + 1341875533L, 1362349204L, 1382617710L, 1402678000L, 1422527051L, 1442161874L, + 1461579514L, 1480777044L, 1499751576L, 1518500250L, 1537020244L, 1555308768L, + 1573363068L, 1591180426L, 1608758157L, 1626093616L, 1643184191L, 1660027308L, + 1676620432L, 1692961062L, 1709046739L, 1724875040L, 1740443581L, 1755750017L, + 1770792044L, 1785567396L, 1800073849L, 1814309216L, 1828271356L, 1841958164L, + 1855367581L, 1868497586L, 1881346202L, 1893911494L, 1906191570L, 1918184581L, + 1929888720L, 1941302225L, 1952423377L, 1963250501L, 1973781967L, 1984016189L, + 1993951625L, 2003586779L, 2012920201L, 2021950484L, 2030676269L, 2039096241L, + 2047209133L, 2055013723L, 2062508835L, 2069693342L, 2076566160L, 2083126254L, + 2089372638L, 2095304370L, 2100920556L, 2106220352L, 2111202959L, 2115867626L, + 2120213651L, 2124240380L, 2127947206L, 2131333572L, 2134398966L, 2137142927L, + 2139565043L, 2141664948L, 2143442326L, 2144896910L, 2146028480L, 2146836866L, + 2147321946L, 2147483647L, 2147321946L, 2146836866L, 2146028480L, 2144896910L, + 2143442326L, 2141664948L, 2139565043L, 2137142927L, 2134398966L, 2131333572L, + 2127947206L, 2124240380L, 2120213651L, 2115867626L, 2111202959L, 2106220352L, + 2100920556L, 2095304370L, 2089372638L, 2083126254L, 2076566160L, 2069693342L, + 2062508835L, 2055013723L, 2047209133L, 2039096241L, 2030676269L, 2021950484L, + 2012920201L, 2003586779L, 1993951625L, 1984016189L, 1973781967L, 1963250501L, + 1952423377L, 1941302225L, 1929888720L, 1918184581L, 1906191570L, 1893911494L, + 1881346202L, 1868497586L, 1855367581L, 1841958164L, 1828271356L, 1814309216L, + 1800073849L, 1785567396L, 1770792044L, 1755750017L, 1740443581L, 1724875040L, + 1709046739L, 1692961062L, 1676620432L, 1660027308L, 1643184191L, 1626093616L, + 1608758157L, 1591180426L, 1573363068L, 1555308768L, 1537020244L, 1518500250L, + 1499751576L, 1480777044L, 1461579514L, 1442161874L, 1422527051L, 1402678000L, + 1382617710L, 1362349204L, 1341875533L, 1321199781L, 1300325060L, 1279254516L, + 1257991320L, 1236538675L, 1214899813L, 1193077991L, 1171076495L, 1148898640L, + 1126547765L, 1104027237L, 1081340445L, 1058490808L, 1035481766L, 1012316784L, + 988999351L, 965532978L, 941921200L, 918167572L, 894275671L, 870249095L, + 846091463L, 821806413L, 797397602L, 772868706L, 748223418L, 723465451L, + 698598533L, 673626408L, 648552838L, 623381598L, 598116479L, 572761285L, + 547319836L, 521795963L, 496193509L, 470516330L, 444768294L, 418953276L, + 393075166L, 367137861L, 341145265L, 315101295L, 289009871L, 262874923L, + 236700388L, 210490206L, 184248325L, 157978697L, 131685278L, 105372028L, + 79042909L, 52701887L, 26352928L, 0L, -26352928L, -52701887L, -79042909L, + -105372028L, -131685278L, -157978697L, -184248325L, -210490206L, -236700388L, + -262874923L, -289009871L, -315101295L, -341145265L, -367137861L, -393075166L, + -418953276L, -444768294L, -470516330L, -496193509L, -521795963L, -547319836L, + -572761285L, -598116479L, -623381598L, -648552838L, -673626408L, -698598533L, + -723465451L, -748223418L, -772868706L, -797397602L, -821806413L, -846091463L, + -870249095L, -894275671L, -918167572L, -941921200L, -965532978L, -988999351L, + -1012316784L, -1035481766L, -1058490808L, -1081340445L, -1104027237L, + -1126547765L, -1148898640L, -1171076495L, -1193077991L, -1214899813L, + -1236538675L, -1257991320L, -1279254516L, -1300325060L, -1321199781L, + -1341875533L, -1362349204L, -1382617710L, -1402678000L, -1422527051L, + -1442161874L, -1461579514L, -1480777044L, -1499751576L, -1518500250L, + -1537020244L, -1555308768L, -1573363068L, -1591180426L, -1608758157L, + -1626093616L, -1643184191L, -1660027308L, -1676620432L, -1692961062L, + -1709046739L, -1724875040L, -1740443581L, -1755750017L, -1770792044L, + -1785567396L, -1800073849L, -1814309216L, -1828271356L, -1841958164L, + -1855367581L, -1868497586L, -1881346202L, -1893911494L, -1906191570L, + -1918184581L, -1929888720L, -1941302225L, -1952423377L, -1963250501L, + -1973781967L, -1984016189L, -1993951625L, -2003586779L, -2012920201L, + -2021950484L, -2030676269L, -2039096241L, -2047209133L, -2055013723L, + -2062508835L, -2069693342L, -2076566160L, -2083126254L, -2089372638L, + -2095304370L, -2100920556L, -2106220352L, -2111202959L, -2115867626L, + -2120213651L, -2124240380L, -2127947206L, -2131333572L, -2134398966L, + -2137142927L, -2139565043L, -2141664948L, -2143442326L, -2144896910L, + -2146028480L, -2146836866L, -2147321946L, (q31_t)0x80000000, -2147321946L, + -2146836866L, -2146028480L, -2144896910L, -2143442326L, -2141664948L, + -2139565043L, -2137142927L, -2134398966L, -2131333572L, -2127947206L, + -2124240380L, -2120213651L, -2115867626L, -2111202959L, -2106220352L, + -2100920556L, -2095304370L, -2089372638L, -2083126254L, -2076566160L, + -2069693342L, -2062508835L, -2055013723L, -2047209133L, -2039096241L, + -2030676269L, -2021950484L, -2012920201L, -2003586779L, -1993951625L, + -1984016189L, -1973781967L, -1963250501L, -1952423377L, -1941302225L, + -1929888720L, -1918184581L, -1906191570L, -1893911494L, -1881346202L, + -1868497586L, -1855367581L, -1841958164L, -1828271356L, -1814309216L, + -1800073849L, -1785567396L, -1770792044L, -1755750017L, -1740443581L, + -1724875040L, -1709046739L, -1692961062L, -1676620432L, -1660027308L, + -1643184191L, -1626093616L, -1608758157L, -1591180426L, -1573363068L, + -1555308768L, -1537020244L, -1518500250L, -1499751576L, -1480777044L, + -1461579514L, -1442161874L, -1422527051L, -1402678000L, -1382617710L, + -1362349204L, -1341875533L, -1321199781L, -1300325060L, -1279254516L, + -1257991320L, -1236538675L, -1214899813L, -1193077991L, -1171076495L, + -1148898640L, -1126547765L, -1104027237L, -1081340445L, -1058490808L, + -1035481766L, -1012316784L, -988999351L, -965532978L, -941921200L, + -918167572L, -894275671L, -870249095L, -846091463L, -821806413L, -797397602L, + -772868706L, -748223418L, -723465451L, -698598533L, -673626408L, -648552838L, + -623381598L, -598116479L, -572761285L, -547319836L, -521795963L, -496193509L, + -470516330L, -444768294L, -418953276L, -393075166L, -367137861L, -341145265L, + -315101295L, -289009871L, -262874923L, -236700388L, -210490206L, -184248325L, + -157978697L, -131685278L, -105372028L, -79042909L, -52701887L, -26352928L, 0 +}; + + +/** + @par + Table values are in Q15 (1.15 fixed-point format) and generation is done in + three steps. First, generate sin values in floating point: + 
+  tableSize = 512;
+  for (n = 0; n < (tableSize + 1); n++)
+  {
+ 	sinTable[n] = sin(2*PI*n/tableSize);
+  }
+ where PI value is 3.14159265358979 + @par + Second, convert floating-point to Q15 (Fixed point): + (sinTable[i] * pow(2, 15)) + @par + Finally, round to the nearest integer value: + sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5); + */ +const q15_t sinTable_q15[FAST_MATH_TABLE_SIZE + 1] ARM_DSP_TABLE_ATTRIBUTE = { + 0, 402, 804, 1206, 1608, 2009, 2411, 2811, 3212, 3612, 4011, 4410, 4808, + 5205, 5602, 5998, 6393, 6787, 7180, 7571, 7962, 8351, 8740, 9127, 9512, + 9896, 10279, 10660, 11039, 11417, 11793, 12167, 12540, 12910, 13279, + 13646, 14010, 14373, 14733, 15091, 15447, 15800, 16151, 16500, 16846, + 17190, 17531, 17869, 18205, 18538, 18868, 19195, 19520, 19841, 20160, + 20475, 20788, 21097, 21403, 21706, 22006, 22302, 22595, 22884, 23170, + 23453, 23732, 24008, 24279, 24548, 24812, 25073, 25330, 25583, 25833, + 26078, 26320, 26557, 26791, 27020, 27246, 27467, 27684, 27897, 28106, + 28311, 28511, 28707, 28899, 29086, 29269, 29448, 29622, 29792, 29957, + 30118, 30274, 30425, 30572, 30715, 30853, 30986, 31114, 31238, 31357, + 31471, 31581, 31686, 31786, 31881, 31972, 32058, 32138, 32214, 32286, + 32352, 32413, 32470, 32522, 32568, 32610, 32647, 32679, 32706, 32729, + 32746, 32758, 32766, 32767, 32766, 32758, 32746, 32729, 32706, 32679, + 32647, 32610, 32568, 32522, 32470, 32413, 32352, 32286, 32214, 32138, + 32058, 31972, 31881, 31786, 31686, 31581, 31471, 31357, 31238, 31114, + 30986, 30853, 30715, 30572, 30425, 30274, 30118, 29957, 29792, 29622, + 29448, 29269, 29086, 28899, 28707, 28511, 28311, 28106, 27897, 27684, + 27467, 27246, 27020, 26791, 26557, 26320, 26078, 25833, 25583, 25330, + 25073, 24812, 24548, 24279, 24008, 23732, 23453, 23170, 22884, 22595, + 22302, 22006, 21706, 21403, 21097, 20788, 20475, 20160, 19841, 19520, + 19195, 18868, 18538, 18205, 17869, 17531, 17190, 16846, 16500, 16151, + 15800, 15447, 15091, 14733, 14373, 14010, 13646, 13279, 12910, 12540, + 12167, 11793, 11417, 11039, 10660, 10279, 9896, 9512, 9127, 8740, 8351, + 7962, 7571, 7180, 6787, 6393, 5998, 5602, 5205, 4808, 4410, 4011, 3612, + 3212, 2811, 2411, 2009, 1608, 1206, 804, 402, 0, -402, -804, -1206, + -1608, -2009, -2411, -2811, -3212, -3612, -4011, -4410, -4808, -5205, + -5602, -5998, -6393, -6787, -7180, -7571, -7962, -8351, -8740, -9127, + -9512, -9896, -10279, -10660, -11039, -11417, -11793, -12167, -12540, + -12910, -13279, -13646, -14010, -14373, -14733, -15091, -15447, -15800, + -16151, -16500, -16846, -17190, -17531, -17869, -18205, -18538, -18868, + -19195, -19520, -19841, -20160, -20475, -20788, -21097, -21403, -21706, + -22006, -22302, -22595, -22884, -23170, -23453, -23732, -24008, -24279, + -24548, -24812, -25073, -25330, -25583, -25833, -26078, -26320, -26557, + -26791, -27020, -27246, -27467, -27684, -27897, -28106, -28311, -28511, + -28707, -28899, -29086, -29269, -29448, -29622, -29792, -29957, -30118, + -30274, -30425, -30572, -30715, -30853, -30986, -31114, -31238, -31357, + -31471, -31581, -31686, -31786, -31881, -31972, -32058, -32138, -32214, + -32286, -32352, -32413, -32470, -32522, -32568, -32610, -32647, -32679, + -32706, -32729, -32746, -32758, -32766, -32768, -32766, -32758, -32746, + -32729, -32706, -32679, -32647, -32610, -32568, -32522, -32470, -32413, + -32352, -32286, -32214, -32138, -32058, -31972, -31881, -31786, -31686, + -31581, -31471, -31357, -31238, -31114, -30986, -30853, -30715, -30572, + -30425, -30274, -30118, -29957, -29792, -29622, -29448, -29269, -29086, + -28899, -28707, -28511, -28311, -28106, -27897, -27684, -27467, -27246, + -27020, -26791, -26557, -26320, -26078, -25833, -25583, -25330, -25073, + -24812, -24548, -24279, -24008, -23732, -23453, -23170, -22884, -22595, + -22302, -22006, -21706, -21403, -21097, -20788, -20475, -20160, -19841, + -19520, -19195, -18868, -18538, -18205, -17869, -17531, -17190, -16846, + -16500, -16151, -15800, -15447, -15091, -14733, -14373, -14010, -13646, + -13279, -12910, -12540, -12167, -11793, -11417, -11039, -10660, -10279, + -9896, -9512, -9127, -8740, -8351, -7962, -7571, -7180, -6787, -6393, + -5998, -5602, -5205, -4808, -4410, -4011, -3612, -3212, -2811, -2411, + -2009, -1608, -1206, -804, -402, 0 +}; + +#if (defined(ARM_MATH_MVEI) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + +const q31_t sqrtTable_Q31[256] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x5ffffffe, 0x7ffffffa, 0x5e88c596, 0x7a39e2ff, + 0x5d2238d8, 0x74dfa6b1, 0x5bcb268e, 0x6fe69562, + 0x5a827998, 0x6b454dba, 0x5947373a, 0x66f39063, + 0x58187bf8, 0x62ea1669, 0x56f578e6, 0x5f226e5f, + 0x55dd714e, 0x5b96df40, 0x54cfb8b0, 0x58424fca, + 0x53cbb102, 0x552031c7, 0x52d0c92c, 0x522c7048, + 0x51de7bb2, 0x4f6360a9, 0x50f44d86, 0x4cc1b594, + 0x5011cd0a, 0x4a4473f6, 0x4f36911a, 0x47e8e962, + 0x4e62384e, 0x45aca3d0, 0x4d946838, 0x438d6a6a, + 0x4cccccca, 0x41893746, 0x4c0b17c0, 0x3f9e31fa, + 0x4b4f0022, 0x3dcaaac3, 0x4a9841ce, 0x3c0d1660, + 0x49e69d14, 0x3a640a53, 0x4939d654, 0x38ce39a6, + 0x4891b5b2, 0x374a720b, 0x47ee06ba, 0x35d7993c, + 0x474e9830, 0x3474aacc, 0x46b33bc0, 0x3320b60c, + 0x461bc5d2, 0x31dadc4f, 0x45880d4c, 0x30a24f3c, + 0x44f7eb6a, 0x2f764f6a, 0x446b3b92, 0x2e562b0b, + 0x43e1db32, 0x2d413cc9, 0x435ba98a, 0x2c36eab0, + 0x42d887a4, 0x2b36a542, 0x42585824, 0x2a3fe69b, + 0x41daff34, 0x295231b0, 0x41606266, 0x286d118d, + 0x40e868a4, 0x279018c3, 0x4072fa10, 0x26bae0c8, + 0x3ffffffe, 0x25ed0979, 0x3f8f64d2, 0x25263894, + 0x3f2113f8, 0x24661958, 0x3eb4f9d8, 0x23ac5c10, + 0x3e4b03ba, 0x22f8b5bb, 0x3de31fc4, 0x224adfba, + 0x3d7d3cee, 0x21a2977a, 0x3d194ae8, 0x20ff9e30, + 0x3cb73a24, 0x2061b89a, 0x3c56fbba, 0x1fc8aebb, + 0x3bf88166, 0x1f344ba6, 0x3b9bbd80, 0x1ea45d4b, + 0x3b40a2f0, 0x1e18b448, 0x3ae7252e, 0x1d9123b9, + 0x3a8f382c, 0x1d0d8113, 0x3a38d062, 0x1c8da3fb, + 0x39e3e2b6, 0x1c116628, 0x39906482, 0x1b98a33c, + 0x393e4b8a, 0x1b2338aa, 0x38ed8df6, 0x1ab1059a, + 0x389e2250, 0x1a41eace, 0x384fff7a, 0x19d5ca89, + 0x38031cb2, 0x196c887b, 0x37b77184, 0x190609a9, + 0x376cf5ce, 0x18a2345b, 0x3723a1ba, 0x1840f00a, + 0x36db6db6, 0x17e22550, 0x36945276, 0x1785bdd2, + 0x364e48f4, 0x172ba43e, 0x36094a64, 0x16d3c42c, + 0x35c55036, 0x167e0a1f, 0x35825414, 0x162a6372, + 0x35404fde, 0x15d8be4d, 0x34ff3dac, 0x1589099d, + 0x34bf17c4, 0x153b3508, 0x347fd89e, 0x14ef30e4, + 0x34417ade, 0x14a4ee2a, 0x3403f956, 0x145c5e76, + 0x33c74f02, 0x141573fa, 0x338b7706, 0x13d02171, + 0x33506cae, 0x138c5a28, 0x33162b6a, 0x134a11e6, + 0x32dcaed0, 0x13093cee, 0x32a3f294, 0x12c9cffa, + 0x326bf292, 0x128bc034, 0x3234aac0, 0x124f0330, + 0x31fe1736, 0x12138ee5, 0x31c83428, 0x11d959b0, + 0x3192fde6, 0x11a05a45, 0x315e70de, 0x116887b5, + 0x312a8994, 0x1131d960, 0x30f744aa, 0x10fc46fd, + 0x30c49ed6, 0x10c7c88b, 0x309294ea, 0x10945653, + 0x306123cc, 0x1061e8e6, 0x30304878, 0x10307919 +}; + +const q15_t sqrtTable_Q15[256] ARM_DSP_TABLE_ATTRIBUTE = { + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x5fff, 0x7fff, 0x5e88, 0x7a39, + 0x5d22, 0x74df, 0x5bcb, 0x6fe6, + 0x5a82, 0x6b45, 0x5947, 0x66f3, + 0x5818, 0x62ea, 0x56f5, 0x5f22, + 0x55dd, 0x5b96, 0x54cf, 0x5842, + 0x53cb, 0x5520, 0x52d0, 0x522c, + 0x51de, 0x4f63, 0x50f4, 0x4cc1, + 0x5011, 0x4a44, 0x4f36, 0x47e8, + 0x4e62, 0x45ac, 0x4d94, 0x438d, + 0x4ccc, 0x4189, 0x4c0b, 0x3f9e, + 0x4b4f, 0x3dca, 0x4a98, 0x3c0d, + 0x49e6, 0x3a64, 0x4939, 0x38ce, + 0x4891, 0x374a, 0x47ee, 0x35d7, + 0x474e, 0x3474, 0x46b3, 0x3320, + 0x461b, 0x31da, 0x4588, 0x30a2, + 0x44f7, 0x2f76, 0x446b, 0x2e56, + 0x43e1, 0x2d41, 0x435b, 0x2c36, + 0x42d8, 0x2b36, 0x4258, 0x2a3f, + 0x41da, 0x2952, 0x4160, 0x286d, + 0x40e8, 0x2790, 0x4072, 0x26ba, + 0x3fff, 0x25ed, 0x3f8f, 0x2526, + 0x3f21, 0x2466, 0x3eb4, 0x23ac, + 0x3e4b, 0x22f8, 0x3de3, 0x224a, + 0x3d7d, 0x21a2, 0x3d19, 0x20ff, + 0x3cb7, 0x2061, 0x3c56, 0x1fc8, + 0x3bf8, 0x1f34, 0x3b9b, 0x1ea4, + 0x3b40, 0x1e18, 0x3ae7, 0x1d91, + 0x3a8f, 0x1d0d, 0x3a38, 0x1c8d, + 0x39e3, 0x1c11, 0x3990, 0x1b98, + 0x393e, 0x1b23, 0x38ed, 0x1ab1, + 0x389e, 0x1a41, 0x384f, 0x19d5, + 0x3803, 0x196c, 0x37b7, 0x1906, + 0x376c, 0x18a2, 0x3723, 0x1840, + 0x36db, 0x17e2, 0x3694, 0x1785, + 0x364e, 0x172b, 0x3609, 0x16d3, + 0x35c5, 0x167e, 0x3582, 0x162a, + 0x3540, 0x15d8, 0x34ff, 0x1589, + 0x34bf, 0x153b, 0x347f, 0x14ef, + 0x3441, 0x14a4, 0x3403, 0x145c, + 0x33c7, 0x1415, 0x338b, 0x13d0, + 0x3350, 0x138c, 0x3316, 0x134a, + 0x32dc, 0x1309, 0x32a3, 0x12c9, + 0x326b, 0x128b, 0x3234, 0x124f, + 0x31fe, 0x1213, 0x31c8, 0x11d9, + 0x3192, 0x11a0, 0x315e, 0x1168, + 0x312a, 0x1131, 0x30f7, 0x10fc, + 0x30c4, 0x10c7, 0x3092, 0x1094, + 0x3061, 0x1061, 0x3030, 0x1030 +}; + +/* haming weight LUT for bytes */ +#define B2(n) n, n + 1, n + 1, n + 2 +#define B4(n) B2(n) , B2(n + 1), B2(n + 1), B2(n + 2) +#define B6(n) B4(n) , B4(n + 1), B4(n + 1), B4(n + 2) + +// Lookup table that store the reverse of each table +const unsigned char hwLUT[256] ARM_DSP_TABLE_ATTRIBUTE = { B6(0), B6(1), B6(1), B6(2) }; + +#endif +/* +ClearAll[tofix]; +tofix[q_][a_] := With[{r = Round[a*2^q]}, + If[r > (2^q - 1), 2^q - 1, r] + ]; + +(* For q = format, 2^nb is length of the table *) +With[{q = 15, nb = 4, q12quarter = 16^^2000}, + With[{shift = Echo[q - nb]}, + Table[tofix[q][1.0/Sqrt[1.0*i/2^q]/8.0], {i, 2^(q - 2), + 2^q + q12quarter - 1, 2^shift}]] + ] // CopyToClipboard + +*/ +const q31_t sqrt_initial_lut_q31[32] ARM_DSP_TABLE_ATTRIBUTE = {536870912, 506166750, 480191942, 457845052, 438353264, 421156193, \ +405836263, 392075079, 379625062, 368290407, 357913941, 348367849, \ +339546978, 331363921, 323745341, 316629190, 309962566, 303700050, \ +297802400, 292235509, 286969573, 281978417, 277238947, 272730696, \ +268435456, 264336964, 260420644, 256673389, 253083375, 249639903, \ +246333269, 243154642}; + +const q15_t sqrt_initial_lut_q15[16] ARM_DSP_TABLE_ATTRIBUTE ={8192, 7327, 6689, 6193, 5793, 5461, 5181, 4940, 4730, 4544, 4379, \ +4230, 4096, 3974, 3862, 3759}; + + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + +const float32_t exp_tab[8] ARM_DSP_TABLE_ATTRIBUTE = { + (1.f), + (0.0416598916054f), + (0.500000596046f), + (0.0014122662833f), + (1.00000011921f), + (0.00833693705499f), + (0.166665703058f), + (0.000195780929062f), +}; + +const float32_t __logf_lut_f32[8] ARM_DSP_TABLE_ATTRIBUTE = { + -2.295614848256274f, /*p0*/ + -2.470711633419806f, /*p4*/ + -5.686926051100417f, /*p2*/ + -0.165253547131978f, /*p6*/ + +5.175912446351073f, /*p1*/ + +0.844006986174912f, /*p5*/ + +4.584458825456749f, /*p3*/ + +0.014127821926000f /*p7*/ +}; + + +#endif + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_common_tables_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_common_tables_f16.c new file mode 100755 index 0000000..7f75b0e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_common_tables_f16.c @@ -0,0 +1,12541 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_common_tables_f16.c + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "arm_math_types_f16.h" +/** + @ingroup ComplexFFT + */ + +/** + @addtogroup CFFT_CIFFT Complex FFT Tables + @{ + */ + + +/** + @brief Floating-point Twiddle factors Table Generation +*/ + +/* F16 */ +#if !defined(__CC_ARM) + +#if defined(ARM_FLOAT16_SUPPORTED) + +#include "arm_common_tables_f16.h" + + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 16 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_16[32] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)-0.382683432f, (float16_t)0.923879533f, + (float16_t)-0.707106781f, (float16_t)0.707106781f, + (float16_t)-0.923879533f, (float16_t)0.382683432f, + (float16_t)-1.000000000f, (float16_t)0.000000000f, + (float16_t)-0.923879533f, (float16_t)-0.382683432f, + (float16_t)-0.707106781f, (float16_t)-0.707106781f, + (float16_t)-0.382683432f, (float16_t)-0.923879533f, + (float16_t)-0.000000000f, (float16_t)-1.000000000f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.923879533f, (float16_t)-0.382683432f +}; + + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 32 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_32[64] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)-0.195090322f, (float16_t)0.980785280f, + (float16_t)-0.382683432f, (float16_t)0.923879533f, + (float16_t)-0.555570233f, (float16_t)0.831469612f, + (float16_t)-0.707106781f, (float16_t)0.707106781f, + (float16_t)-0.831469612f, (float16_t)0.555570233f, + (float16_t)-0.923879533f, (float16_t)0.382683432f, + (float16_t)-0.980785280f, (float16_t)0.195090322f, + (float16_t)-1.000000000f, (float16_t)0.000000000f, + (float16_t)-0.980785280f, (float16_t)-0.195090322f, + (float16_t)-0.923879533f, (float16_t)-0.382683432f, + (float16_t)-0.831469612f, (float16_t)-0.555570233f, + (float16_t)-0.707106781f, (float16_t)-0.707106781f, + (float16_t)-0.555570233f, (float16_t)-0.831469612f, + (float16_t)-0.382683432f, (float16_t)-0.923879533f, + (float16_t)-0.195090322f, (float16_t)-0.980785280f, + (float16_t)-0.000000000f, (float16_t)-1.000000000f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.980785280f, (float16_t)-0.195090322f +}; + + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 64 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_64[128] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)-0.098017140f, (float16_t)0.995184727f, + (float16_t)-0.195090322f, (float16_t)0.980785280f, + (float16_t)-0.290284677f, (float16_t)0.956940336f, + (float16_t)-0.382683432f, (float16_t)0.923879533f, + (float16_t)-0.471396737f, (float16_t)0.881921264f, + (float16_t)-0.555570233f, (float16_t)0.831469612f, + (float16_t)-0.634393284f, (float16_t)0.773010453f, + (float16_t)-0.707106781f, (float16_t)0.707106781f, + (float16_t)-0.773010453f, (float16_t)0.634393284f, + (float16_t)-0.831469612f, (float16_t)0.555570233f, + (float16_t)-0.881921264f, (float16_t)0.471396737f, + (float16_t)-0.923879533f, (float16_t)0.382683432f, + (float16_t)-0.956940336f, (float16_t)0.290284677f, + (float16_t)-0.980785280f, (float16_t)0.195090322f, + (float16_t)-0.995184727f, (float16_t)0.098017140f, + (float16_t)-1.000000000f, (float16_t)0.000000000f, + (float16_t)-0.995184727f, (float16_t)-0.098017140f, + (float16_t)-0.980785280f, (float16_t)-0.195090322f, + (float16_t)-0.956940336f, (float16_t)-0.290284677f, + (float16_t)-0.923879533f, (float16_t)-0.382683432f, + (float16_t)-0.881921264f, (float16_t)-0.471396737f, + (float16_t)-0.831469612f, (float16_t)-0.555570233f, + (float16_t)-0.773010453f, (float16_t)-0.634393284f, + (float16_t)-0.707106781f, (float16_t)-0.707106781f, + (float16_t)-0.634393284f, (float16_t)-0.773010453f, + (float16_t)-0.555570233f, (float16_t)-0.831469612f, + (float16_t)-0.471396737f, (float16_t)-0.881921264f, + (float16_t)-0.382683432f, (float16_t)-0.923879533f, + (float16_t)-0.290284677f, (float16_t)-0.956940336f, + (float16_t)-0.195090322f, (float16_t)-0.980785280f, + (float16_t)-0.098017140f, (float16_t)-0.995184727f, + (float16_t)-0.000000000f, (float16_t)-1.000000000f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.995184727f, (float16_t)-0.098017140f +}; + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 128 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ + +const float16_t twiddleCoefF16_128[256] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.857728610f, (float16_t)0.514102744f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)-0.049067674f, (float16_t)0.998795456f, + (float16_t)-0.098017140f, (float16_t)0.995184727f, + (float16_t)-0.146730474f, (float16_t)0.989176510f, + (float16_t)-0.195090322f, (float16_t)0.980785280f, + (float16_t)-0.242980180f, (float16_t)0.970031253f, + (float16_t)-0.290284677f, (float16_t)0.956940336f, + (float16_t)-0.336889853f, (float16_t)0.941544065f, + (float16_t)-0.382683432f, (float16_t)0.923879533f, + (float16_t)-0.427555093f, (float16_t)0.903989293f, + (float16_t)-0.471396737f, (float16_t)0.881921264f, + (float16_t)-0.514102744f, (float16_t)0.857728610f, + (float16_t)-0.555570233f, (float16_t)0.831469612f, + (float16_t)-0.595699304f, (float16_t)0.803207531f, + (float16_t)-0.634393284f, (float16_t)0.773010453f, + (float16_t)-0.671558955f, (float16_t)0.740951125f, + (float16_t)-0.707106781f, (float16_t)0.707106781f, + (float16_t)-0.740951125f, (float16_t)0.671558955f, + (float16_t)-0.773010453f, (float16_t)0.634393284f, + (float16_t)-0.803207531f, (float16_t)0.595699304f, + (float16_t)-0.831469612f, (float16_t)0.555570233f, + (float16_t)-0.857728610f, (float16_t)0.514102744f, + (float16_t)-0.881921264f, (float16_t)0.471396737f, + (float16_t)-0.903989293f, (float16_t)0.427555093f, + (float16_t)-0.923879533f, (float16_t)0.382683432f, + (float16_t)-0.941544065f, (float16_t)0.336889853f, + (float16_t)-0.956940336f, (float16_t)0.290284677f, + (float16_t)-0.970031253f, (float16_t)0.242980180f, + (float16_t)-0.980785280f, (float16_t)0.195090322f, + (float16_t)-0.989176510f, (float16_t)0.146730474f, + (float16_t)-0.995184727f, (float16_t)0.098017140f, + (float16_t)-0.998795456f, (float16_t)0.049067674f, + (float16_t)-1.000000000f, (float16_t)0.000000000f, + (float16_t)-0.998795456f, (float16_t)-0.049067674f, + (float16_t)-0.995184727f, (float16_t)-0.098017140f, + (float16_t)-0.989176510f, (float16_t)-0.146730474f, + (float16_t)-0.980785280f, (float16_t)-0.195090322f, + (float16_t)-0.970031253f, (float16_t)-0.242980180f, + (float16_t)-0.956940336f, (float16_t)-0.290284677f, + (float16_t)-0.941544065f, (float16_t)-0.336889853f, + (float16_t)-0.923879533f, (float16_t)-0.382683432f, + (float16_t)-0.903989293f, (float16_t)-0.427555093f, + (float16_t)-0.881921264f, (float16_t)-0.471396737f, + (float16_t)-0.857728610f, (float16_t)-0.514102744f, + (float16_t)-0.831469612f, (float16_t)-0.555570233f, + (float16_t)-0.803207531f, (float16_t)-0.595699304f, + (float16_t)-0.773010453f, (float16_t)-0.634393284f, + (float16_t)-0.740951125f, (float16_t)-0.671558955f, + (float16_t)-0.707106781f, (float16_t)-0.707106781f, + (float16_t)-0.671558955f, (float16_t)-0.740951125f, + (float16_t)-0.634393284f, (float16_t)-0.773010453f, + (float16_t)-0.595699304f, (float16_t)-0.803207531f, + (float16_t)-0.555570233f, (float16_t)-0.831469612f, + (float16_t)-0.514102744f, (float16_t)-0.857728610f, + (float16_t)-0.471396737f, (float16_t)-0.881921264f, + (float16_t)-0.427555093f, (float16_t)-0.903989293f, + (float16_t)-0.382683432f, (float16_t)-0.923879533f, + (float16_t)-0.336889853f, (float16_t)-0.941544065f, + (float16_t)-0.290284677f, (float16_t)-0.956940336f, + (float16_t)-0.242980180f, (float16_t)-0.970031253f, + (float16_t)-0.195090322f, (float16_t)-0.980785280f, + (float16_t)-0.146730474f, (float16_t)-0.989176510f, + (float16_t)-0.098017140f, (float16_t)-0.995184727f, + (float16_t)-0.049067674f, (float16_t)-0.998795456f, + (float16_t)-0.000000000f, (float16_t)-1.000000000f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.427555093f, (float16_t)-0.903989293f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.514102744f, (float16_t)-0.857728610f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.595699304f, (float16_t)-0.803207531f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.671558955f, (float16_t)-0.740951125f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.740951125f, (float16_t)-0.671558955f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.803207531f, (float16_t)-0.595699304f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.998795456f, (float16_t)-0.049067674f +}; + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 256 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_256[512] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.975702130f, (float16_t)0.219101240f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.963776066f, (float16_t)0.266712757f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.949528181f, (float16_t)0.313681740f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.932992799f, (float16_t)0.359895037f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.914209756f, (float16_t)0.405241314f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.893224301f, (float16_t)0.449611330f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.870086991f, (float16_t)0.492898192f, + (float16_t)0.857728610f, (float16_t)0.514102744f, + (float16_t)0.844853565f, (float16_t)0.534997620f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.817584813f, (float16_t)0.575808191f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.788346428f, (float16_t)0.615231591f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.757208847f, (float16_t)0.653172843f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.724247083f, (float16_t)0.689540545f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.689540545f, (float16_t)0.724247083f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.653172843f, (float16_t)0.757208847f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.615231591f, (float16_t)0.788346428f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.575808191f, (float16_t)0.817584813f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.534997620f, (float16_t)0.844853565f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.492898192f, (float16_t)0.870086991f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.449611330f, (float16_t)0.893224301f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.405241314f, (float16_t)0.914209756f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.359895037f, (float16_t)0.932992799f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.313681740f, (float16_t)0.949528181f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.266712757f, (float16_t)0.963776066f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.219101240f, (float16_t)0.975702130f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.170961889f, (float16_t)0.985277642f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.122410675f, (float16_t)0.992479535f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.073564564f, (float16_t)0.997290457f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.024541229f, (float16_t)0.999698819f, + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)-0.024541229f, (float16_t)0.999698819f, + (float16_t)-0.049067674f, (float16_t)0.998795456f, + (float16_t)-0.073564564f, (float16_t)0.997290457f, + (float16_t)-0.098017140f, (float16_t)0.995184727f, + (float16_t)-0.122410675f, (float16_t)0.992479535f, + (float16_t)-0.146730474f, (float16_t)0.989176510f, + (float16_t)-0.170961889f, (float16_t)0.985277642f, + (float16_t)-0.195090322f, 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(float16_t)-0.615231591f, (float16_t)0.788346428f, + (float16_t)-0.634393284f, (float16_t)0.773010453f, + (float16_t)-0.653172843f, (float16_t)0.757208847f, + (float16_t)-0.671558955f, (float16_t)0.740951125f, + (float16_t)-0.689540545f, (float16_t)0.724247083f, + (float16_t)-0.707106781f, (float16_t)0.707106781f, + (float16_t)-0.724247083f, (float16_t)0.689540545f, + (float16_t)-0.740951125f, (float16_t)0.671558955f, + (float16_t)-0.757208847f, (float16_t)0.653172843f, + (float16_t)-0.773010453f, (float16_t)0.634393284f, + (float16_t)-0.788346428f, (float16_t)0.615231591f, + (float16_t)-0.803207531f, (float16_t)0.595699304f, + (float16_t)-0.817584813f, (float16_t)0.575808191f, + (float16_t)-0.831469612f, (float16_t)0.555570233f, + (float16_t)-0.844853565f, (float16_t)0.534997620f, + (float16_t)-0.857728610f, (float16_t)0.514102744f, + (float16_t)-0.870086991f, (float16_t)0.492898192f, + (float16_t)-0.881921264f, (float16_t)0.471396737f, + (float16_t)-0.893224301f, (float16_t)0.449611330f, + (float16_t)-0.903989293f, (float16_t)0.427555093f, + (float16_t)-0.914209756f, (float16_t)0.405241314f, + (float16_t)-0.923879533f, (float16_t)0.382683432f, + (float16_t)-0.932992799f, (float16_t)0.359895037f, + (float16_t)-0.941544065f, (float16_t)0.336889853f, + (float16_t)-0.949528181f, (float16_t)0.313681740f, + (float16_t)-0.956940336f, (float16_t)0.290284677f, + (float16_t)-0.963776066f, (float16_t)0.266712757f, + (float16_t)-0.970031253f, (float16_t)0.242980180f, + (float16_t)-0.975702130f, (float16_t)0.219101240f, + (float16_t)-0.980785280f, (float16_t)0.195090322f, + (float16_t)-0.985277642f, (float16_t)0.170961889f, + (float16_t)-0.989176510f, (float16_t)0.146730474f, + (float16_t)-0.992479535f, (float16_t)0.122410675f, + (float16_t)-0.995184727f, (float16_t)0.098017140f, + (float16_t)-0.997290457f, (float16_t)0.073564564f, + (float16_t)-0.998795456f, (float16_t)0.049067674f, + (float16_t)-0.999698819f, (float16_t)0.024541229f, + (float16_t)-1.000000000f, (float16_t)0.000000000f, + (float16_t)-0.999698819f, (float16_t)-0.024541229f, + (float16_t)-0.998795456f, (float16_t)-0.049067674f, + (float16_t)-0.997290457f, (float16_t)-0.073564564f, + (float16_t)-0.995184727f, (float16_t)-0.098017140f, + (float16_t)-0.992479535f, (float16_t)-0.122410675f, + (float16_t)-0.989176510f, (float16_t)-0.146730474f, + (float16_t)-0.985277642f, (float16_t)-0.170961889f, + (float16_t)-0.980785280f, (float16_t)-0.195090322f, + (float16_t)-0.975702130f, (float16_t)-0.219101240f, + (float16_t)-0.970031253f, (float16_t)-0.242980180f, + (float16_t)-0.963776066f, (float16_t)-0.266712757f, + (float16_t)-0.956940336f, (float16_t)-0.290284677f, + (float16_t)-0.949528181f, (float16_t)-0.313681740f, + (float16_t)-0.941544065f, (float16_t)-0.336889853f, + (float16_t)-0.932992799f, (float16_t)-0.359895037f, + (float16_t)-0.923879533f, (float16_t)-0.382683432f, + (float16_t)-0.914209756f, (float16_t)-0.405241314f, + (float16_t)-0.903989293f, (float16_t)-0.427555093f, + (float16_t)-0.893224301f, (float16_t)-0.449611330f, + (float16_t)-0.881921264f, (float16_t)-0.471396737f, + (float16_t)-0.870086991f, (float16_t)-0.492898192f, + (float16_t)-0.857728610f, (float16_t)-0.514102744f, + (float16_t)-0.844853565f, (float16_t)-0.534997620f, + (float16_t)-0.831469612f, (float16_t)-0.555570233f, + (float16_t)-0.817584813f, (float16_t)-0.575808191f, + (float16_t)-0.803207531f, (float16_t)-0.595699304f, + (float16_t)-0.788346428f, (float16_t)-0.615231591f, + (float16_t)-0.773010453f, (float16_t)-0.634393284f, + (float16_t)-0.757208847f, (float16_t)-0.653172843f, + (float16_t)-0.740951125f, (float16_t)-0.671558955f, + (float16_t)-0.724247083f, (float16_t)-0.689540545f, + (float16_t)-0.707106781f, (float16_t)-0.707106781f, + (float16_t)-0.689540545f, (float16_t)-0.724247083f, + (float16_t)-0.671558955f, (float16_t)-0.740951125f, + (float16_t)-0.653172843f, (float16_t)-0.757208847f, + (float16_t)-0.634393284f, (float16_t)-0.773010453f, + (float16_t)-0.615231591f, (float16_t)-0.788346428f, + (float16_t)-0.595699304f, (float16_t)-0.803207531f, + (float16_t)-0.575808191f, (float16_t)-0.817584813f, + (float16_t)-0.555570233f, (float16_t)-0.831469612f, + (float16_t)-0.534997620f, (float16_t)-0.844853565f, + (float16_t)-0.514102744f, (float16_t)-0.857728610f, + (float16_t)-0.492898192f, (float16_t)-0.870086991f, + (float16_t)-0.471396737f, (float16_t)-0.881921264f, + (float16_t)-0.449611330f, (float16_t)-0.893224301f, + (float16_t)-0.427555093f, (float16_t)-0.903989293f, + (float16_t)-0.405241314f, (float16_t)-0.914209756f, + (float16_t)-0.382683432f, (float16_t)-0.923879533f, + (float16_t)-0.359895037f, (float16_t)-0.932992799f, + (float16_t)-0.336889853f, (float16_t)-0.941544065f, + (float16_t)-0.313681740f, (float16_t)-0.949528181f, + (float16_t)-0.290284677f, (float16_t)-0.956940336f, + (float16_t)-0.266712757f, (float16_t)-0.963776066f, + (float16_t)-0.242980180f, (float16_t)-0.970031253f, + (float16_t)-0.219101240f, (float16_t)-0.975702130f, + (float16_t)-0.195090322f, (float16_t)-0.980785280f, + (float16_t)-0.170961889f, (float16_t)-0.985277642f, + (float16_t)-0.146730474f, (float16_t)-0.989176510f, + (float16_t)-0.122410675f, (float16_t)-0.992479535f, + (float16_t)-0.098017140f, (float16_t)-0.995184727f, + (float16_t)-0.073564564f, (float16_t)-0.997290457f, + (float16_t)-0.049067674f, (float16_t)-0.998795456f, + (float16_t)-0.024541229f, (float16_t)-0.999698819f, + (float16_t)-0.000000000f, (float16_t)-1.000000000f, + (float16_t)0.024541229f, (float16_t)-0.999698819f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.122410675f, (float16_t)-0.992479535f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.170961889f, (float16_t)-0.985277642f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.219101240f, (float16_t)-0.975702130f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.266712757f, (float16_t)-0.963776066f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.313681740f, (float16_t)-0.949528181f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.359895037f, (float16_t)-0.932992799f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.405241314f, (float16_t)-0.914209756f, + (float16_t)0.427555093f, (float16_t)-0.903989293f, + (float16_t)0.449611330f, (float16_t)-0.893224301f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.492898192f, (float16_t)-0.870086991f, + (float16_t)0.514102744f, (float16_t)-0.857728610f, + (float16_t)0.534997620f, (float16_t)-0.844853565f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.575808191f, (float16_t)-0.817584813f, + (float16_t)0.595699304f, (float16_t)-0.803207531f, + (float16_t)0.615231591f, (float16_t)-0.788346428f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.653172843f, (float16_t)-0.757208847f, + (float16_t)0.671558955f, (float16_t)-0.740951125f, + (float16_t)0.689540545f, (float16_t)-0.724247083f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.724247083f, (float16_t)-0.689540545f, + (float16_t)0.740951125f, (float16_t)-0.671558955f, + (float16_t)0.757208847f, (float16_t)-0.653172843f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.788346428f, (float16_t)-0.615231591f, + (float16_t)0.803207531f, (float16_t)-0.595699304f, + (float16_t)0.817584813f, (float16_t)-0.575808191f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.844853565f, (float16_t)-0.534997620f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.870086991f, (float16_t)-0.492898192f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.893224301f, (float16_t)-0.449611330f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.914209756f, (float16_t)-0.405241314f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.932992799f, (float16_t)-0.359895037f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.949528181f, (float16_t)-0.313681740f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.963776066f, (float16_t)-0.266712757f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.975702130f, (float16_t)-0.219101240f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.985277642f, (float16_t)-0.170961889f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.992479535f, (float16_t)-0.122410675f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.997290457f, (float16_t)-0.073564564f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.999698819f, (float16_t)-0.024541229f +}; + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 512 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_512[1024] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999924702f, (float16_t)0.012271538f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)0.999322385f, (float16_t)0.036807223f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.998118113f, (float16_t)0.061320736f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.996312612f, (float16_t)0.085797312f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.993906970f, (float16_t)0.110222207f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.990902635f, (float16_t)0.134580709f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.987301418f, (float16_t)0.158858143f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.983105487f, 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(float16_t)-0.881921264f, (float16_t)-0.471396737f, + (float16_t)-0.876070094f, (float16_t)-0.482183772f, + (float16_t)-0.870086991f, (float16_t)-0.492898192f, + (float16_t)-0.863972856f, (float16_t)-0.503538384f, + (float16_t)-0.857728610f, (float16_t)-0.514102744f, + (float16_t)-0.851355193f, (float16_t)-0.524589683f, + (float16_t)-0.844853565f, (float16_t)-0.534997620f, + (float16_t)-0.838224706f, (float16_t)-0.545324988f, + (float16_t)-0.831469612f, (float16_t)-0.555570233f, + (float16_t)-0.824589303f, (float16_t)-0.565731811f, + (float16_t)-0.817584813f, (float16_t)-0.575808191f, + (float16_t)-0.810457198f, (float16_t)-0.585797857f, + (float16_t)-0.803207531f, (float16_t)-0.595699304f, + (float16_t)-0.795836905f, (float16_t)-0.605511041f, + (float16_t)-0.788346428f, (float16_t)-0.615231591f, + (float16_t)-0.780737229f, (float16_t)-0.624859488f, + (float16_t)-0.773010453f, (float16_t)-0.634393284f, + (float16_t)-0.765167266f, (float16_t)-0.643831543f, + (float16_t)-0.757208847f, (float16_t)-0.653172843f, + (float16_t)-0.749136395f, (float16_t)-0.662415778f, + (float16_t)-0.740951125f, (float16_t)-0.671558955f, + (float16_t)-0.732654272f, (float16_t)-0.680600998f, + (float16_t)-0.724247083f, (float16_t)-0.689540545f, + (float16_t)-0.715730825f, (float16_t)-0.698376249f, + (float16_t)-0.707106781f, (float16_t)-0.707106781f, + (float16_t)-0.698376249f, (float16_t)-0.715730825f, + (float16_t)-0.689540545f, (float16_t)-0.724247083f, + (float16_t)-0.680600998f, (float16_t)-0.732654272f, + (float16_t)-0.671558955f, (float16_t)-0.740951125f, + (float16_t)-0.662415778f, (float16_t)-0.749136395f, + (float16_t)-0.653172843f, (float16_t)-0.757208847f, + (float16_t)-0.643831543f, (float16_t)-0.765167266f, + (float16_t)-0.634393284f, (float16_t)-0.773010453f, + (float16_t)-0.624859488f, (float16_t)-0.780737229f, + (float16_t)-0.615231591f, (float16_t)-0.788346428f, + (float16_t)-0.605511041f, (float16_t)-0.795836905f, + (float16_t)-0.595699304f, (float16_t)-0.803207531f, + (float16_t)-0.585797857f, (float16_t)-0.810457198f, + (float16_t)-0.575808191f, (float16_t)-0.817584813f, + (float16_t)-0.565731811f, (float16_t)-0.824589303f, + (float16_t)-0.555570233f, (float16_t)-0.831469612f, + (float16_t)-0.545324988f, (float16_t)-0.838224706f, + (float16_t)-0.534997620f, (float16_t)-0.844853565f, + (float16_t)-0.524589683f, (float16_t)-0.851355193f, + (float16_t)-0.514102744f, (float16_t)-0.857728610f, + (float16_t)-0.503538384f, (float16_t)-0.863972856f, + (float16_t)-0.492898192f, (float16_t)-0.870086991f, + (float16_t)-0.482183772f, (float16_t)-0.876070094f, + (float16_t)-0.471396737f, (float16_t)-0.881921264f, + (float16_t)-0.460538711f, (float16_t)-0.887639620f, + (float16_t)-0.449611330f, (float16_t)-0.893224301f, + (float16_t)-0.438616239f, (float16_t)-0.898674466f, + (float16_t)-0.427555093f, (float16_t)-0.903989293f, + (float16_t)-0.416429560f, (float16_t)-0.909167983f, + (float16_t)-0.405241314f, (float16_t)-0.914209756f, + (float16_t)-0.393992040f, (float16_t)-0.919113852f, + (float16_t)-0.382683432f, (float16_t)-0.923879533f, + (float16_t)-0.371317194f, (float16_t)-0.928506080f, + (float16_t)-0.359895037f, (float16_t)-0.932992799f, + (float16_t)-0.348418680f, (float16_t)-0.937339012f, + (float16_t)-0.336889853f, (float16_t)-0.941544065f, + (float16_t)-0.325310292f, (float16_t)-0.945607325f, + (float16_t)-0.313681740f, (float16_t)-0.949528181f, + (float16_t)-0.302005949f, (float16_t)-0.953306040f, + (float16_t)-0.290284677f, (float16_t)-0.956940336f, + (float16_t)-0.278519689f, (float16_t)-0.960430519f, + (float16_t)-0.266712757f, (float16_t)-0.963776066f, + (float16_t)-0.254865660f, (float16_t)-0.966976471f, + (float16_t)-0.242980180f, (float16_t)-0.970031253f, + (float16_t)-0.231058108f, (float16_t)-0.972939952f, + (float16_t)-0.219101240f, (float16_t)-0.975702130f, + (float16_t)-0.207111376f, (float16_t)-0.978317371f, + (float16_t)-0.195090322f, (float16_t)-0.980785280f, + (float16_t)-0.183039888f, (float16_t)-0.983105487f, + (float16_t)-0.170961889f, (float16_t)-0.985277642f, + (float16_t)-0.158858143f, (float16_t)-0.987301418f, + (float16_t)-0.146730474f, (float16_t)-0.989176510f, + (float16_t)-0.134580709f, (float16_t)-0.990902635f, + (float16_t)-0.122410675f, (float16_t)-0.992479535f, + (float16_t)-0.110222207f, (float16_t)-0.993906970f, + (float16_t)-0.098017140f, (float16_t)-0.995184727f, + (float16_t)-0.085797312f, (float16_t)-0.996312612f, + (float16_t)-0.073564564f, (float16_t)-0.997290457f, + (float16_t)-0.061320736f, (float16_t)-0.998118113f, + (float16_t)-0.049067674f, (float16_t)-0.998795456f, + (float16_t)-0.036807223f, (float16_t)-0.999322385f, + (float16_t)-0.024541229f, (float16_t)-0.999698819f, + (float16_t)-0.012271538f, (float16_t)-0.999924702f, + (float16_t)-0.000000000f, (float16_t)-1.000000000f, + (float16_t)0.012271538f, (float16_t)-0.999924702f, + (float16_t)0.024541229f, (float16_t)-0.999698819f, + (float16_t)0.036807223f, (float16_t)-0.999322385f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.061320736f, (float16_t)-0.998118113f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.085797312f, (float16_t)-0.996312612f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.110222207f, (float16_t)-0.993906970f, + (float16_t)0.122410675f, (float16_t)-0.992479535f, + (float16_t)0.134580709f, (float16_t)-0.990902635f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.158858143f, (float16_t)-0.987301418f, + (float16_t)0.170961889f, (float16_t)-0.985277642f, + (float16_t)0.183039888f, (float16_t)-0.983105487f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.207111376f, (float16_t)-0.978317371f, + (float16_t)0.219101240f, (float16_t)-0.975702130f, + (float16_t)0.231058108f, (float16_t)-0.972939952f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.254865660f, (float16_t)-0.966976471f, + (float16_t)0.266712757f, (float16_t)-0.963776066f, + (float16_t)0.278519689f, (float16_t)-0.960430519f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.302005949f, (float16_t)-0.953306040f, + (float16_t)0.313681740f, (float16_t)-0.949528181f, + (float16_t)0.325310292f, (float16_t)-0.945607325f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.348418680f, (float16_t)-0.937339012f, + (float16_t)0.359895037f, (float16_t)-0.932992799f, + (float16_t)0.371317194f, (float16_t)-0.928506080f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.393992040f, (float16_t)-0.919113852f, + (float16_t)0.405241314f, (float16_t)-0.914209756f, + (float16_t)0.416429560f, (float16_t)-0.909167983f, + (float16_t)0.427555093f, (float16_t)-0.903989293f, + (float16_t)0.438616239f, (float16_t)-0.898674466f, + (float16_t)0.449611330f, (float16_t)-0.893224301f, + (float16_t)0.460538711f, (float16_t)-0.887639620f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.482183772f, (float16_t)-0.876070094f, + (float16_t)0.492898192f, (float16_t)-0.870086991f, + (float16_t)0.503538384f, (float16_t)-0.863972856f, + (float16_t)0.514102744f, (float16_t)-0.857728610f, + (float16_t)0.524589683f, (float16_t)-0.851355193f, + (float16_t)0.534997620f, (float16_t)-0.844853565f, + (float16_t)0.545324988f, (float16_t)-0.838224706f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.565731811f, (float16_t)-0.824589303f, + (float16_t)0.575808191f, (float16_t)-0.817584813f, + (float16_t)0.585797857f, (float16_t)-0.810457198f, + (float16_t)0.595699304f, (float16_t)-0.803207531f, + (float16_t)0.605511041f, (float16_t)-0.795836905f, + (float16_t)0.615231591f, (float16_t)-0.788346428f, + (float16_t)0.624859488f, (float16_t)-0.780737229f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.643831543f, (float16_t)-0.765167266f, + (float16_t)0.653172843f, (float16_t)-0.757208847f, + (float16_t)0.662415778f, (float16_t)-0.749136395f, + (float16_t)0.671558955f, (float16_t)-0.740951125f, + (float16_t)0.680600998f, (float16_t)-0.732654272f, + (float16_t)0.689540545f, (float16_t)-0.724247083f, + (float16_t)0.698376249f, (float16_t)-0.715730825f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.715730825f, (float16_t)-0.698376249f, + (float16_t)0.724247083f, (float16_t)-0.689540545f, + (float16_t)0.732654272f, (float16_t)-0.680600998f, + (float16_t)0.740951125f, (float16_t)-0.671558955f, + (float16_t)0.749136395f, (float16_t)-0.662415778f, + (float16_t)0.757208847f, (float16_t)-0.653172843f, + (float16_t)0.765167266f, (float16_t)-0.643831543f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.780737229f, (float16_t)-0.624859488f, + (float16_t)0.788346428f, (float16_t)-0.615231591f, + (float16_t)0.795836905f, (float16_t)-0.605511041f, + (float16_t)0.803207531f, (float16_t)-0.595699304f, + (float16_t)0.810457198f, (float16_t)-0.585797857f, + (float16_t)0.817584813f, (float16_t)-0.575808191f, + (float16_t)0.824589303f, (float16_t)-0.565731811f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.838224706f, (float16_t)-0.545324988f, + (float16_t)0.844853565f, (float16_t)-0.534997620f, + (float16_t)0.851355193f, (float16_t)-0.524589683f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.863972856f, (float16_t)-0.503538384f, + (float16_t)0.870086991f, (float16_t)-0.492898192f, + (float16_t)0.876070094f, (float16_t)-0.482183772f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.887639620f, (float16_t)-0.460538711f, + (float16_t)0.893224301f, (float16_t)-0.449611330f, + (float16_t)0.898674466f, (float16_t)-0.438616239f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.909167983f, (float16_t)-0.416429560f, + (float16_t)0.914209756f, (float16_t)-0.405241314f, + (float16_t)0.919113852f, (float16_t)-0.393992040f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.928506080f, (float16_t)-0.371317194f, + (float16_t)0.932992799f, (float16_t)-0.359895037f, + (float16_t)0.937339012f, (float16_t)-0.348418680f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.945607325f, (float16_t)-0.325310292f, + (float16_t)0.949528181f, (float16_t)-0.313681740f, + (float16_t)0.953306040f, (float16_t)-0.302005949f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.960430519f, (float16_t)-0.278519689f, + (float16_t)0.963776066f, (float16_t)-0.266712757f, + (float16_t)0.966976471f, (float16_t)-0.254865660f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.972939952f, (float16_t)-0.231058108f, + (float16_t)0.975702130f, (float16_t)-0.219101240f, + (float16_t)0.978317371f, (float16_t)-0.207111376f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.983105487f, (float16_t)-0.183039888f, + (float16_t)0.985277642f, (float16_t)-0.170961889f, + (float16_t)0.987301418f, (float16_t)-0.158858143f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.990902635f, (float16_t)-0.134580709f, + (float16_t)0.992479535f, (float16_t)-0.122410675f, + (float16_t)0.993906970f, (float16_t)-0.110222207f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.996312612f, (float16_t)-0.085797312f, + (float16_t)0.997290457f, (float16_t)-0.073564564f, + (float16_t)0.998118113f, (float16_t)-0.061320736f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.999322385f, (float16_t)-0.036807223f, + (float16_t)0.999698819f, (float16_t)-0.024541229f, + (float16_t)0.999924702f, (float16_t)-0.012271538f +}; + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 1024 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_1024[2048] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999981175f, (float16_t)0.006135885f, + (float16_t)0.999924702f, (float16_t)0.012271538f, + (float16_t)0.999830582f, (float16_t)0.018406730f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)0.999529418f, (float16_t)0.030674803f, + (float16_t)0.999322385f, (float16_t)0.036807223f, + (float16_t)0.999077728f, (float16_t)0.042938257f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.998475581f, (float16_t)0.055195244f, + (float16_t)0.998118113f, (float16_t)0.061320736f, + (float16_t)0.997723067f, (float16_t)0.067443920f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.996820299f, (float16_t)0.079682438f, + (float16_t)0.996312612f, (float16_t)0.085797312f, + (float16_t)0.995767414f, (float16_t)0.091908956f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.994564571f, (float16_t)0.104121634f, + (float16_t)0.993906970f, (float16_t)0.110222207f, + (float16_t)0.993211949f, (float16_t)0.116318631f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.991709754f, (float16_t)0.128498111f, + (float16_t)0.990902635f, (float16_t)0.134580709f, + (float16_t)0.990058210f, (float16_t)0.140658239f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.988257568f, (float16_t)0.152797185f, + (float16_t)0.987301418f, (float16_t)0.158858143f, + (float16_t)0.986308097f, (float16_t)0.164913120f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.984210092f, (float16_t)0.177004220f, + (float16_t)0.983105487f, (float16_t)0.183039888f, + (float16_t)0.981963869f, (float16_t)0.189068664f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.979569766f, (float16_t)0.201104635f, + (float16_t)0.978317371f, (float16_t)0.207111376f, + (float16_t)0.977028143f, (float16_t)0.213110320f, + (float16_t)0.975702130f, (float16_t)0.219101240f, + (float16_t)0.974339383f, (float16_t)0.225083911f, + (float16_t)0.972939952f, (float16_t)0.231058108f, + (float16_t)0.971503891f, (float16_t)0.237023606f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.968522094f, (float16_t)0.248927606f, + (float16_t)0.966976471f, (float16_t)0.254865660f, + (float16_t)0.965394442f, (float16_t)0.260794118f, + (float16_t)0.963776066f, (float16_t)0.266712757f, + (float16_t)0.962121404f, (float16_t)0.272621355f, + (float16_t)0.960430519f, (float16_t)0.278519689f, + (float16_t)0.958703475f, (float16_t)0.284407537f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.955141168f, (float16_t)0.296150888f, + (float16_t)0.953306040f, (float16_t)0.302005949f, + (float16_t)0.951435021f, (float16_t)0.307849640f, + (float16_t)0.949528181f, (float16_t)0.313681740f, + (float16_t)0.947585591f, (float16_t)0.319502031f, + (float16_t)0.945607325f, (float16_t)0.325310292f, + (float16_t)0.943593458f, (float16_t)0.331106306f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.939459224f, (float16_t)0.342660717f, + (float16_t)0.937339012f, (float16_t)0.348418680f, + (float16_t)0.935183510f, (float16_t)0.354163525f, + (float16_t)0.932992799f, (float16_t)0.359895037f, + (float16_t)0.930766961f, (float16_t)0.365612998f, + (float16_t)0.928506080f, (float16_t)0.371317194f, + (float16_t)0.926210242f, (float16_t)0.377007410f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.921514039f, (float16_t)0.388345047f, + (float16_t)0.919113852f, (float16_t)0.393992040f, + (float16_t)0.916679060f, (float16_t)0.399624200f, + (float16_t)0.914209756f, (float16_t)0.405241314f, + (float16_t)0.911706032f, (float16_t)0.410843171f, + (float16_t)0.909167983f, (float16_t)0.416429560f, + (float16_t)0.906595705f, (float16_t)0.422000271f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.901348847f, (float16_t)0.433093819f, + (float16_t)0.898674466f, (float16_t)0.438616239f, + (float16_t)0.895966250f, (float16_t)0.444122145f, + (float16_t)0.893224301f, (float16_t)0.449611330f, + (float16_t)0.890448723f, (float16_t)0.455083587f, + (float16_t)0.887639620f, (float16_t)0.460538711f, + (float16_t)0.884797098f, (float16_t)0.465976496f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.879012226f, (float16_t)0.476799230f, + (float16_t)0.876070094f, (float16_t)0.482183772f, + (float16_t)0.873094978f, (float16_t)0.487550160f, + (float16_t)0.870086991f, (float16_t)0.492898192f, + (float16_t)0.867046246f, (float16_t)0.498227667f, + (float16_t)0.863972856f, (float16_t)0.503538384f, + (float16_t)0.860866939f, (float16_t)0.508830143f, + (float16_t)0.857728610f, (float16_t)0.514102744f, + (float16_t)0.854557988f, (float16_t)0.519355990f, + (float16_t)0.851355193f, (float16_t)0.524589683f, + (float16_t)0.848120345f, (float16_t)0.529803625f, + (float16_t)0.844853565f, (float16_t)0.534997620f, + (float16_t)0.841554977f, (float16_t)0.540171473f, + (float16_t)0.838224706f, (float16_t)0.545324988f, + (float16_t)0.834862875f, (float16_t)0.550457973f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.828045045f, (float16_t)0.560661576f, + (float16_t)0.824589303f, (float16_t)0.565731811f, + (float16_t)0.821102515f, (float16_t)0.570780746f, + (float16_t)0.817584813f, (float16_t)0.575808191f, + (float16_t)0.814036330f, (float16_t)0.580813958f, + (float16_t)0.810457198f, (float16_t)0.585797857f, + (float16_t)0.806847554f, (float16_t)0.590759702f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.799537269f, (float16_t)0.600616479f, + (float16_t)0.795836905f, (float16_t)0.605511041f, + (float16_t)0.792106577f, (float16_t)0.610382806f, + (float16_t)0.788346428f, (float16_t)0.615231591f, + (float16_t)0.784556597f, (float16_t)0.620057212f, + (float16_t)0.780737229f, (float16_t)0.624859488f, + (float16_t)0.776888466f, (float16_t)0.629638239f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.769103338f, (float16_t)0.639124445f, + (float16_t)0.765167266f, (float16_t)0.643831543f, + (float16_t)0.761202385f, (float16_t)0.648514401f, + (float16_t)0.757208847f, (float16_t)0.653172843f, + (float16_t)0.753186799f, (float16_t)0.657806693f, + (float16_t)0.749136395f, (float16_t)0.662415778f, + (float16_t)0.745057785f, (float16_t)0.666999922f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.736816569f, (float16_t)0.676092704f, + (float16_t)0.732654272f, (float16_t)0.680600998f, + (float16_t)0.728464390f, (float16_t)0.685083668f, + (float16_t)0.724247083f, (float16_t)0.689540545f, + (float16_t)0.720002508f, (float16_t)0.693971461f, + (float16_t)0.715730825f, (float16_t)0.698376249f, + (float16_t)0.711432196f, (float16_t)0.702754744f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.702754744f, (float16_t)0.711432196f, + (float16_t)0.698376249f, (float16_t)0.715730825f, + (float16_t)0.693971461f, (float16_t)0.720002508f, + (float16_t)0.689540545f, (float16_t)0.724247083f, + (float16_t)0.685083668f, (float16_t)0.728464390f, + (float16_t)0.680600998f, (float16_t)0.732654272f, + (float16_t)0.676092704f, (float16_t)0.736816569f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.666999922f, (float16_t)0.745057785f, + (float16_t)0.662415778f, (float16_t)0.749136395f, + (float16_t)0.657806693f, (float16_t)0.753186799f, + (float16_t)0.653172843f, (float16_t)0.757208847f, + (float16_t)0.648514401f, (float16_t)0.761202385f, + (float16_t)0.643831543f, (float16_t)0.765167266f, + (float16_t)0.639124445f, (float16_t)0.769103338f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.629638239f, (float16_t)0.776888466f, + (float16_t)0.624859488f, (float16_t)0.780737229f, + (float16_t)0.620057212f, (float16_t)0.784556597f, + (float16_t)0.615231591f, (float16_t)0.788346428f, + (float16_t)0.610382806f, (float16_t)0.792106577f, + (float16_t)0.605511041f, (float16_t)0.795836905f, + (float16_t)0.600616479f, (float16_t)0.799537269f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.590759702f, (float16_t)0.806847554f, + (float16_t)0.585797857f, (float16_t)0.810457198f, + (float16_t)0.580813958f, (float16_t)0.814036330f, + (float16_t)0.575808191f, (float16_t)0.817584813f, + (float16_t)0.570780746f, (float16_t)0.821102515f, + (float16_t)0.565731811f, (float16_t)0.824589303f, + (float16_t)0.560661576f, (float16_t)0.828045045f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.550457973f, (float16_t)0.834862875f, + (float16_t)0.545324988f, (float16_t)0.838224706f, + (float16_t)0.540171473f, (float16_t)0.841554977f, + (float16_t)0.534997620f, (float16_t)0.844853565f, + (float16_t)0.529803625f, (float16_t)0.848120345f, + (float16_t)0.524589683f, (float16_t)0.851355193f, + (float16_t)0.519355990f, (float16_t)0.854557988f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.508830143f, (float16_t)0.860866939f, + (float16_t)0.503538384f, (float16_t)0.863972856f, + (float16_t)0.498227667f, (float16_t)0.867046246f, + (float16_t)0.492898192f, (float16_t)0.870086991f, + (float16_t)0.487550160f, (float16_t)0.873094978f, + (float16_t)0.482183772f, (float16_t)0.876070094f, + (float16_t)0.476799230f, (float16_t)0.879012226f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.465976496f, (float16_t)0.884797098f, + (float16_t)0.460538711f, (float16_t)0.887639620f, + (float16_t)0.455083587f, (float16_t)0.890448723f, + (float16_t)0.449611330f, (float16_t)0.893224301f, + (float16_t)0.444122145f, (float16_t)0.895966250f, + (float16_t)0.438616239f, (float16_t)0.898674466f, + (float16_t)0.433093819f, (float16_t)0.901348847f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.422000271f, (float16_t)0.906595705f, + (float16_t)0.416429560f, (float16_t)0.909167983f, + (float16_t)0.410843171f, (float16_t)0.911706032f, + (float16_t)0.405241314f, (float16_t)0.914209756f, + (float16_t)0.399624200f, (float16_t)0.916679060f, + (float16_t)0.393992040f, (float16_t)0.919113852f, + (float16_t)0.388345047f, (float16_t)0.921514039f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.377007410f, (float16_t)0.926210242f, + (float16_t)0.371317194f, (float16_t)0.928506080f, + (float16_t)0.365612998f, (float16_t)0.930766961f, + (float16_t)0.359895037f, (float16_t)0.932992799f, + (float16_t)0.354163525f, (float16_t)0.935183510f, + (float16_t)0.348418680f, (float16_t)0.937339012f, + (float16_t)0.342660717f, (float16_t)0.939459224f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.331106306f, (float16_t)0.943593458f, + (float16_t)0.325310292f, (float16_t)0.945607325f, + (float16_t)0.319502031f, (float16_t)0.947585591f, + (float16_t)0.313681740f, (float16_t)0.949528181f, + (float16_t)0.307849640f, (float16_t)0.951435021f, + (float16_t)0.302005949f, (float16_t)0.953306040f, + (float16_t)0.296150888f, (float16_t)0.955141168f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.284407537f, (float16_t)0.958703475f, + (float16_t)0.278519689f, (float16_t)0.960430519f, + (float16_t)0.272621355f, (float16_t)0.962121404f, + (float16_t)0.266712757f, (float16_t)0.963776066f, + (float16_t)0.260794118f, (float16_t)0.965394442f, + (float16_t)0.254865660f, (float16_t)0.966976471f, + (float16_t)0.248927606f, (float16_t)0.968522094f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.237023606f, (float16_t)0.971503891f, + (float16_t)0.231058108f, (float16_t)0.972939952f, + (float16_t)0.225083911f, (float16_t)0.974339383f, + (float16_t)0.219101240f, (float16_t)0.975702130f, + (float16_t)0.213110320f, (float16_t)0.977028143f, + (float16_t)0.207111376f, (float16_t)0.978317371f, + (float16_t)0.201104635f, (float16_t)0.979569766f, + (float16_t)0.195090322f, 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(float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.971503891f, (float16_t)-0.237023606f, + (float16_t)0.972939952f, (float16_t)-0.231058108f, + (float16_t)0.974339383f, (float16_t)-0.225083911f, + (float16_t)0.975702130f, (float16_t)-0.219101240f, + (float16_t)0.977028143f, (float16_t)-0.213110320f, + (float16_t)0.978317371f, (float16_t)-0.207111376f, + (float16_t)0.979569766f, (float16_t)-0.201104635f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.981963869f, (float16_t)-0.189068664f, + (float16_t)0.983105487f, (float16_t)-0.183039888f, + (float16_t)0.984210092f, (float16_t)-0.177004220f, + (float16_t)0.985277642f, (float16_t)-0.170961889f, + (float16_t)0.986308097f, (float16_t)-0.164913120f, + (float16_t)0.987301418f, (float16_t)-0.158858143f, + (float16_t)0.988257568f, (float16_t)-0.152797185f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.990058210f, (float16_t)-0.140658239f, + (float16_t)0.990902635f, (float16_t)-0.134580709f, + (float16_t)0.991709754f, (float16_t)-0.128498111f, + (float16_t)0.992479535f, (float16_t)-0.122410675f, + (float16_t)0.993211949f, (float16_t)-0.116318631f, + (float16_t)0.993906970f, (float16_t)-0.110222207f, + (float16_t)0.994564571f, (float16_t)-0.104121634f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.995767414f, (float16_t)-0.091908956f, + (float16_t)0.996312612f, (float16_t)-0.085797312f, + (float16_t)0.996820299f, (float16_t)-0.079682438f, + (float16_t)0.997290457f, (float16_t)-0.073564564f, + (float16_t)0.997723067f, (float16_t)-0.067443920f, + (float16_t)0.998118113f, (float16_t)-0.061320736f, + (float16_t)0.998475581f, (float16_t)-0.055195244f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.999077728f, (float16_t)-0.042938257f, + (float16_t)0.999322385f, (float16_t)-0.036807223f, + (float16_t)0.999529418f, (float16_t)-0.030674803f, + (float16_t)0.999698819f, (float16_t)-0.024541229f, + (float16_t)0.999830582f, (float16_t)-0.018406730f, + (float16_t)0.999924702f, (float16_t)-0.012271538f, + (float16_t)0.999981175f, (float16_t)-0.006135885f +}; + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 2048 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_2048[4096] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999995294f, (float16_t)0.003067957f, + (float16_t)0.999981175f, (float16_t)0.006135885f, + (float16_t)0.999957645f, (float16_t)0.009203755f, + (float16_t)0.999924702f, (float16_t)0.012271538f, + (float16_t)0.999882347f, (float16_t)0.015339206f, + (float16_t)0.999830582f, (float16_t)0.018406730f, + (float16_t)0.999769405f, (float16_t)0.021474080f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)0.999618822f, (float16_t)0.027608146f, + (float16_t)0.999529418f, (float16_t)0.030674803f, + (float16_t)0.999430605f, (float16_t)0.033741172f, + (float16_t)0.999322385f, (float16_t)0.036807223f, + (float16_t)0.999204759f, (float16_t)0.039872928f, + (float16_t)0.999077728f, (float16_t)0.042938257f, + (float16_t)0.998941293f, (float16_t)0.046003182f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.998640218f, (float16_t)0.052131705f, + (float16_t)0.998475581f, (float16_t)0.055195244f, + (float16_t)0.998301545f, (float16_t)0.058258265f, + (float16_t)0.998118113f, (float16_t)0.061320736f, + (float16_t)0.997925286f, (float16_t)0.064382631f, + (float16_t)0.997723067f, (float16_t)0.067443920f, + (float16_t)0.997511456f, (float16_t)0.070504573f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.997060070f, (float16_t)0.076623861f, + (float16_t)0.996820299f, (float16_t)0.079682438f, + (float16_t)0.996571146f, (float16_t)0.082740265f, + (float16_t)0.996312612f, (float16_t)0.085797312f, + (float16_t)0.996044701f, (float16_t)0.088853553f, + (float16_t)0.995767414f, (float16_t)0.091908956f, + (float16_t)0.995480755f, (float16_t)0.094963495f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.994879331f, (float16_t)0.101069863f, + (float16_t)0.994564571f, (float16_t)0.104121634f, + (float16_t)0.994240449f, (float16_t)0.107172425f, + (float16_t)0.993906970f, (float16_t)0.110222207f, + (float16_t)0.993564136f, (float16_t)0.113270952f, + (float16_t)0.993211949f, (float16_t)0.116318631f, + (float16_t)0.992850414f, (float16_t)0.119365215f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.992099313f, (float16_t)0.125454983f, + (float16_t)0.991709754f, (float16_t)0.128498111f, + (float16_t)0.991310860f, (float16_t)0.131540029f, + (float16_t)0.990902635f, (float16_t)0.134580709f, + (float16_t)0.990485084f, (float16_t)0.137620122f, + (float16_t)0.990058210f, (float16_t)0.140658239f, + (float16_t)0.989622017f, (float16_t)0.143695033f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.988721692f, (float16_t)0.149764535f, + (float16_t)0.988257568f, (float16_t)0.152797185f, + (float16_t)0.987784142f, (float16_t)0.155828398f, + (float16_t)0.987301418f, (float16_t)0.158858143f, + (float16_t)0.986809402f, (float16_t)0.161886394f, + (float16_t)0.986308097f, (float16_t)0.164913120f, + (float16_t)0.985797509f, (float16_t)0.167938295f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.984748502f, (float16_t)0.173983873f, + (float16_t)0.984210092f, (float16_t)0.177004220f, + (float16_t)0.983662419f, (float16_t)0.180022901f, + (float16_t)0.983105487f, (float16_t)0.183039888f, + (float16_t)0.982539302f, (float16_t)0.186055152f, + (float16_t)0.981963869f, (float16_t)0.189068664f, + (float16_t)0.981379193f, (float16_t)0.192080397f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.980182136f, (float16_t)0.198098411f, + (float16_t)0.979569766f, (float16_t)0.201104635f, + (float16_t)0.978948175f, (float16_t)0.204108966f, + (float16_t)0.978317371f, (float16_t)0.207111376f, + (float16_t)0.977677358f, (float16_t)0.210111837f, + (float16_t)0.977028143f, (float16_t)0.213110320f, + (float16_t)0.976369731f, (float16_t)0.216106797f, + (float16_t)0.975702130f, (float16_t)0.219101240f, + (float16_t)0.975025345f, (float16_t)0.222093621f, + (float16_t)0.974339383f, (float16_t)0.225083911f, + (float16_t)0.973644250f, (float16_t)0.228072083f, + (float16_t)0.972939952f, (float16_t)0.231058108f, + (float16_t)0.972226497f, (float16_t)0.234041959f, + (float16_t)0.971503891f, (float16_t)0.237023606f, + (float16_t)0.970772141f, (float16_t)0.240003022f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.969281235f, (float16_t)0.245955050f, + (float16_t)0.968522094f, (float16_t)0.248927606f, + (float16_t)0.967753837f, (float16_t)0.251897818f, + (float16_t)0.966976471f, (float16_t)0.254865660f, + (float16_t)0.966190003f, (float16_t)0.257831102f, + (float16_t)0.965394442f, (float16_t)0.260794118f, + (float16_t)0.964589793f, (float16_t)0.263754679f, + (float16_t)0.963776066f, (float16_t)0.266712757f, + (float16_t)0.962953267f, (float16_t)0.269668326f, + (float16_t)0.962121404f, (float16_t)0.272621355f, + (float16_t)0.961280486f, (float16_t)0.275571819f, + (float16_t)0.960430519f, (float16_t)0.278519689f, + (float16_t)0.959571513f, (float16_t)0.281464938f, + (float16_t)0.958703475f, (float16_t)0.284407537f, + (float16_t)0.957826413f, (float16_t)0.287347460f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.956045251f, (float16_t)0.293219163f, + (float16_t)0.955141168f, (float16_t)0.296150888f, + (float16_t)0.954228095f, (float16_t)0.299079826f, + (float16_t)0.953306040f, (float16_t)0.302005949f, + (float16_t)0.952375013f, (float16_t)0.304929230f, + (float16_t)0.951435021f, (float16_t)0.307849640f, + (float16_t)0.950486074f, (float16_t)0.310767153f, + (float16_t)0.949528181f, (float16_t)0.313681740f, + (float16_t)0.948561350f, (float16_t)0.316593376f, + (float16_t)0.947585591f, (float16_t)0.319502031f, + (float16_t)0.946600913f, (float16_t)0.322407679f, + (float16_t)0.945607325f, (float16_t)0.325310292f, + (float16_t)0.944604837f, (float16_t)0.328209844f, + (float16_t)0.943593458f, (float16_t)0.331106306f, + (float16_t)0.942573198f, (float16_t)0.333999651f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.940506071f, (float16_t)0.339776884f, + (float16_t)0.939459224f, (float16_t)0.342660717f, + (float16_t)0.938403534f, (float16_t)0.345541325f, + (float16_t)0.937339012f, (float16_t)0.348418680f, + (float16_t)0.936265667f, (float16_t)0.351292756f, + (float16_t)0.935183510f, (float16_t)0.354163525f, + (float16_t)0.934092550f, (float16_t)0.357030961f, + (float16_t)0.932992799f, (float16_t)0.359895037f, + (float16_t)0.931884266f, (float16_t)0.362755724f, + (float16_t)0.930766961f, (float16_t)0.365612998f, + (float16_t)0.929640896f, (float16_t)0.368466830f, + (float16_t)0.928506080f, (float16_t)0.371317194f, + (float16_t)0.927362526f, (float16_t)0.374164063f, + (float16_t)0.926210242f, (float16_t)0.377007410f, + (float16_t)0.925049241f, (float16_t)0.379847209f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.922701128f, (float16_t)0.385516054f, + (float16_t)0.921514039f, (float16_t)0.388345047f, + (float16_t)0.920318277f, (float16_t)0.391170384f, + (float16_t)0.919113852f, (float16_t)0.393992040f, + (float16_t)0.917900776f, (float16_t)0.396809987f, + (float16_t)0.916679060f, (float16_t)0.399624200f, + (float16_t)0.915448716f, (float16_t)0.402434651f, + (float16_t)0.914209756f, (float16_t)0.405241314f, + (float16_t)0.912962190f, (float16_t)0.408044163f, + (float16_t)0.911706032f, (float16_t)0.410843171f, + (float16_t)0.910441292f, (float16_t)0.413638312f, + (float16_t)0.909167983f, (float16_t)0.416429560f, + (float16_t)0.907886116f, (float16_t)0.419216888f, + (float16_t)0.906595705f, (float16_t)0.422000271f, + (float16_t)0.905296759f, (float16_t)0.424779681f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.902673318f, (float16_t)0.430326481f, + (float16_t)0.901348847f, (float16_t)0.433093819f, + (float16_t)0.900015892f, (float16_t)0.435857080f, + (float16_t)0.898674466f, 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(float16_t)0.838224706f, (float16_t)-0.545324988f, + (float16_t)0.839893794f, (float16_t)-0.542750785f, + (float16_t)0.841554977f, (float16_t)-0.540171473f, + (float16_t)0.843208240f, (float16_t)-0.537587076f, + (float16_t)0.844853565f, (float16_t)-0.534997620f, + (float16_t)0.846490939f, (float16_t)-0.532403128f, + (float16_t)0.848120345f, (float16_t)-0.529803625f, + (float16_t)0.849741768f, (float16_t)-0.527199135f, + (float16_t)0.851355193f, (float16_t)-0.524589683f, + (float16_t)0.852960605f, (float16_t)-0.521975293f, + (float16_t)0.854557988f, (float16_t)-0.519355990f, + (float16_t)0.856147328f, (float16_t)-0.516731799f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.859301818f, (float16_t)-0.511468850f, + (float16_t)0.860866939f, (float16_t)-0.508830143f, + (float16_t)0.862423956f, (float16_t)-0.506186645f, + (float16_t)0.863972856f, (float16_t)-0.503538384f, + (float16_t)0.865513624f, (float16_t)-0.500885383f, + (float16_t)0.867046246f, 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(float16_t)0.894599486f, (float16_t)-0.446868840f, + (float16_t)0.895966250f, (float16_t)-0.444122145f, + (float16_t)0.897324581f, (float16_t)-0.441371269f, + (float16_t)0.898674466f, (float16_t)-0.438616239f, + (float16_t)0.900015892f, (float16_t)-0.435857080f, + (float16_t)0.901348847f, (float16_t)-0.433093819f, + (float16_t)0.902673318f, (float16_t)-0.430326481f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.905296759f, (float16_t)-0.424779681f, + (float16_t)0.906595705f, (float16_t)-0.422000271f, + (float16_t)0.907886116f, (float16_t)-0.419216888f, + (float16_t)0.909167983f, (float16_t)-0.416429560f, + (float16_t)0.910441292f, (float16_t)-0.413638312f, + (float16_t)0.911706032f, (float16_t)-0.410843171f, + (float16_t)0.912962190f, (float16_t)-0.408044163f, + (float16_t)0.914209756f, (float16_t)-0.405241314f, + (float16_t)0.915448716f, (float16_t)-0.402434651f, + (float16_t)0.916679060f, (float16_t)-0.399624200f, + (float16_t)0.917900776f, (float16_t)-0.396809987f, + (float16_t)0.919113852f, (float16_t)-0.393992040f, + (float16_t)0.920318277f, (float16_t)-0.391170384f, + (float16_t)0.921514039f, (float16_t)-0.388345047f, + (float16_t)0.922701128f, (float16_t)-0.385516054f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.925049241f, (float16_t)-0.379847209f, + (float16_t)0.926210242f, (float16_t)-0.377007410f, + (float16_t)0.927362526f, (float16_t)-0.374164063f, + (float16_t)0.928506080f, (float16_t)-0.371317194f, + (float16_t)0.929640896f, (float16_t)-0.368466830f, + (float16_t)0.930766961f, (float16_t)-0.365612998f, + (float16_t)0.931884266f, (float16_t)-0.362755724f, + (float16_t)0.932992799f, (float16_t)-0.359895037f, + (float16_t)0.934092550f, (float16_t)-0.357030961f, + (float16_t)0.935183510f, (float16_t)-0.354163525f, + (float16_t)0.936265667f, (float16_t)-0.351292756f, + (float16_t)0.937339012f, (float16_t)-0.348418680f, + (float16_t)0.938403534f, (float16_t)-0.345541325f, + (float16_t)0.939459224f, (float16_t)-0.342660717f, + (float16_t)0.940506071f, (float16_t)-0.339776884f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.942573198f, (float16_t)-0.333999651f, + (float16_t)0.943593458f, (float16_t)-0.331106306f, + (float16_t)0.944604837f, (float16_t)-0.328209844f, + (float16_t)0.945607325f, (float16_t)-0.325310292f, + (float16_t)0.946600913f, (float16_t)-0.322407679f, + (float16_t)0.947585591f, (float16_t)-0.319502031f, + (float16_t)0.948561350f, (float16_t)-0.316593376f, + (float16_t)0.949528181f, (float16_t)-0.313681740f, + (float16_t)0.950486074f, (float16_t)-0.310767153f, + (float16_t)0.951435021f, (float16_t)-0.307849640f, + (float16_t)0.952375013f, (float16_t)-0.304929230f, + (float16_t)0.953306040f, (float16_t)-0.302005949f, + (float16_t)0.954228095f, (float16_t)-0.299079826f, + (float16_t)0.955141168f, (float16_t)-0.296150888f, + (float16_t)0.956045251f, (float16_t)-0.293219163f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.957826413f, (float16_t)-0.287347460f, + (float16_t)0.958703475f, (float16_t)-0.284407537f, + (float16_t)0.959571513f, (float16_t)-0.281464938f, + (float16_t)0.960430519f, (float16_t)-0.278519689f, + (float16_t)0.961280486f, (float16_t)-0.275571819f, + (float16_t)0.962121404f, (float16_t)-0.272621355f, + (float16_t)0.962953267f, (float16_t)-0.269668326f, + (float16_t)0.963776066f, (float16_t)-0.266712757f, + (float16_t)0.964589793f, (float16_t)-0.263754679f, + (float16_t)0.965394442f, (float16_t)-0.260794118f, + (float16_t)0.966190003f, (float16_t)-0.257831102f, + (float16_t)0.966976471f, (float16_t)-0.254865660f, + (float16_t)0.967753837f, (float16_t)-0.251897818f, + (float16_t)0.968522094f, (float16_t)-0.248927606f, + (float16_t)0.969281235f, (float16_t)-0.245955050f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.970772141f, (float16_t)-0.240003022f, + (float16_t)0.971503891f, (float16_t)-0.237023606f, + (float16_t)0.972226497f, (float16_t)-0.234041959f, + (float16_t)0.972939952f, (float16_t)-0.231058108f, + (float16_t)0.973644250f, (float16_t)-0.228072083f, + (float16_t)0.974339383f, (float16_t)-0.225083911f, + (float16_t)0.975025345f, (float16_t)-0.222093621f, + (float16_t)0.975702130f, (float16_t)-0.219101240f, + (float16_t)0.976369731f, (float16_t)-0.216106797f, + (float16_t)0.977028143f, (float16_t)-0.213110320f, + (float16_t)0.977677358f, (float16_t)-0.210111837f, + (float16_t)0.978317371f, (float16_t)-0.207111376f, + (float16_t)0.978948175f, (float16_t)-0.204108966f, + (float16_t)0.979569766f, (float16_t)-0.201104635f, + (float16_t)0.980182136f, (float16_t)-0.198098411f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.981379193f, (float16_t)-0.192080397f, + (float16_t)0.981963869f, (float16_t)-0.189068664f, + (float16_t)0.982539302f, (float16_t)-0.186055152f, + (float16_t)0.983105487f, (float16_t)-0.183039888f, + (float16_t)0.983662419f, (float16_t)-0.180022901f, + (float16_t)0.984210092f, (float16_t)-0.177004220f, + (float16_t)0.984748502f, (float16_t)-0.173983873f, + (float16_t)0.985277642f, (float16_t)-0.170961889f, + (float16_t)0.985797509f, (float16_t)-0.167938295f, + (float16_t)0.986308097f, (float16_t)-0.164913120f, + (float16_t)0.986809402f, (float16_t)-0.161886394f, + (float16_t)0.987301418f, (float16_t)-0.158858143f, + (float16_t)0.987784142f, (float16_t)-0.155828398f, + (float16_t)0.988257568f, (float16_t)-0.152797185f, + (float16_t)0.988721692f, (float16_t)-0.149764535f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.989622017f, (float16_t)-0.143695033f, + (float16_t)0.990058210f, (float16_t)-0.140658239f, + (float16_t)0.990485084f, (float16_t)-0.137620122f, + (float16_t)0.990902635f, (float16_t)-0.134580709f, + (float16_t)0.991310860f, (float16_t)-0.131540029f, + (float16_t)0.991709754f, (float16_t)-0.128498111f, + (float16_t)0.992099313f, (float16_t)-0.125454983f, + (float16_t)0.992479535f, (float16_t)-0.122410675f, + (float16_t)0.992850414f, (float16_t)-0.119365215f, + (float16_t)0.993211949f, (float16_t)-0.116318631f, + (float16_t)0.993564136f, (float16_t)-0.113270952f, + (float16_t)0.993906970f, (float16_t)-0.110222207f, + (float16_t)0.994240449f, (float16_t)-0.107172425f, + (float16_t)0.994564571f, (float16_t)-0.104121634f, + (float16_t)0.994879331f, (float16_t)-0.101069863f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.995480755f, (float16_t)-0.094963495f, + (float16_t)0.995767414f, (float16_t)-0.091908956f, + (float16_t)0.996044701f, (float16_t)-0.088853553f, + (float16_t)0.996312612f, (float16_t)-0.085797312f, + (float16_t)0.996571146f, (float16_t)-0.082740265f, + (float16_t)0.996820299f, (float16_t)-0.079682438f, + (float16_t)0.997060070f, (float16_t)-0.076623861f, + (float16_t)0.997290457f, (float16_t)-0.073564564f, + (float16_t)0.997511456f, (float16_t)-0.070504573f, + (float16_t)0.997723067f, (float16_t)-0.067443920f, + (float16_t)0.997925286f, (float16_t)-0.064382631f, + (float16_t)0.998118113f, (float16_t)-0.061320736f, + (float16_t)0.998301545f, (float16_t)-0.058258265f, + (float16_t)0.998475581f, (float16_t)-0.055195244f, + (float16_t)0.998640218f, (float16_t)-0.052131705f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.998941293f, (float16_t)-0.046003182f, + (float16_t)0.999077728f, (float16_t)-0.042938257f, + (float16_t)0.999204759f, (float16_t)-0.039872928f, + (float16_t)0.999322385f, (float16_t)-0.036807223f, + (float16_t)0.999430605f, (float16_t)-0.033741172f, + (float16_t)0.999529418f, (float16_t)-0.030674803f, + (float16_t)0.999618822f, (float16_t)-0.027608146f, + (float16_t)0.999698819f, (float16_t)-0.024541229f, + (float16_t)0.999769405f, (float16_t)-0.021474080f, + (float16_t)0.999830582f, (float16_t)-0.018406730f, + (float16_t)0.999882347f, (float16_t)-0.015339206f, + (float16_t)0.999924702f, (float16_t)-0.012271538f, + (float16_t)0.999957645f, (float16_t)-0.009203755f, + (float16_t)0.999981175f, (float16_t)-0.006135885f, + (float16_t)0.999995294f, (float16_t)-0.003067957f +}; + +/** +* \par +* Example code for Floating-point Twiddle factors Generation: +* \par +* 
for(i = 0; i< N/; i++)
+* {
+* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
+* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
+* }
+* \par +* where N = 4096 and PI = 3.14159265358979 +* \par +* Cos and Sin values are in interleaved fashion +* +*/ +const float16_t twiddleCoefF16_4096[8192] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999998823f, (float16_t)0.001533980f, + (float16_t)0.999995294f, (float16_t)0.003067957f, + (float16_t)0.999989411f, (float16_t)0.004601926f, + (float16_t)0.999981175f, (float16_t)0.006135885f, + (float16_t)0.999970586f, (float16_t)0.007669829f, + (float16_t)0.999957645f, (float16_t)0.009203755f, + (float16_t)0.999942350f, (float16_t)0.010737659f, + (float16_t)0.999924702f, (float16_t)0.012271538f, + (float16_t)0.999904701f, (float16_t)0.013805389f, + (float16_t)0.999882347f, (float16_t)0.015339206f, + (float16_t)0.999857641f, (float16_t)0.016872988f, + (float16_t)0.999830582f, (float16_t)0.018406730f, + (float16_t)0.999801170f, (float16_t)0.019940429f, + (float16_t)0.999769405f, (float16_t)0.021474080f, + (float16_t)0.999735288f, (float16_t)0.023007681f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)0.999659997f, (float16_t)0.026074718f, + (float16_t)0.999618822f, (float16_t)0.027608146f, + (float16_t)0.999575296f, (float16_t)0.029141509f, + (float16_t)0.999529418f, (float16_t)0.030674803f, + (float16_t)0.999481187f, (float16_t)0.032208025f, + (float16_t)0.999430605f, (float16_t)0.033741172f, + (float16_t)0.999377670f, (float16_t)0.035274239f, + (float16_t)0.999322385f, (float16_t)0.036807223f, + (float16_t)0.999264747f, (float16_t)0.038340120f, + (float16_t)0.999204759f, (float16_t)0.039872928f, + (float16_t)0.999142419f, (float16_t)0.041405641f, + (float16_t)0.999077728f, (float16_t)0.042938257f, + (float16_t)0.999010686f, (float16_t)0.044470772f, + (float16_t)0.998941293f, (float16_t)0.046003182f, + (float16_t)0.998869550f, (float16_t)0.047535484f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.998719012f, (float16_t)0.050599749f, + (float16_t)0.998640218f, (float16_t)0.052131705f, + (float16_t)0.998559074f, (float16_t)0.053663538f, + (float16_t)0.998475581f, (float16_t)0.055195244f, + (float16_t)0.998389737f, (float16_t)0.056726821f, + (float16_t)0.998301545f, (float16_t)0.058258265f, + (float16_t)0.998211003f, (float16_t)0.059789571f, + (float16_t)0.998118113f, (float16_t)0.061320736f, + (float16_t)0.998022874f, (float16_t)0.062851758f, + (float16_t)0.997925286f, (float16_t)0.064382631f, + (float16_t)0.997825350f, (float16_t)0.065913353f, + (float16_t)0.997723067f, (float16_t)0.067443920f, + (float16_t)0.997618435f, (float16_t)0.068974328f, + (float16_t)0.997511456f, (float16_t)0.070504573f, + (float16_t)0.997402130f, (float16_t)0.072034653f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.997176437f, (float16_t)0.075094301f, + (float16_t)0.997060070f, (float16_t)0.076623861f, + (float16_t)0.996941358f, (float16_t)0.078153242f, + (float16_t)0.996820299f, (float16_t)0.079682438f, + (float16_t)0.996696895f, (float16_t)0.081211447f, + (float16_t)0.996571146f, (float16_t)0.082740265f, + (float16_t)0.996443051f, (float16_t)0.084268888f, + (float16_t)0.996312612f, (float16_t)0.085797312f, + (float16_t)0.996179829f, (float16_t)0.087325535f, + (float16_t)0.996044701f, (float16_t)0.088853553f, + (float16_t)0.995907229f, (float16_t)0.090381361f, + (float16_t)0.995767414f, (float16_t)0.091908956f, + (float16_t)0.995625256f, (float16_t)0.093436336f, + (float16_t)0.995480755f, (float16_t)0.094963495f, + (float16_t)0.995333912f, (float16_t)0.096490431f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.995033199f, (float16_t)0.099543619f, + (float16_t)0.994879331f, (float16_t)0.101069863f, + (float16_t)0.994723121f, (float16_t)0.102595869f, + (float16_t)0.994564571f, (float16_t)0.104121634f, + (float16_t)0.994403680f, (float16_t)0.105647154f, + (float16_t)0.994240449f, (float16_t)0.107172425f, + (float16_t)0.994074879f, (float16_t)0.108697444f, + (float16_t)0.993906970f, (float16_t)0.110222207f, + (float16_t)0.993736722f, (float16_t)0.111746711f, + (float16_t)0.993564136f, (float16_t)0.113270952f, + (float16_t)0.993389211f, (float16_t)0.114794927f, + (float16_t)0.993211949f, (float16_t)0.116318631f, + (float16_t)0.993032350f, (float16_t)0.117842062f, + (float16_t)0.992850414f, (float16_t)0.119365215f, + (float16_t)0.992666142f, (float16_t)0.120888087f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.992290591f, (float16_t)0.123932975f, + (float16_t)0.992099313f, (float16_t)0.125454983f, + (float16_t)0.991905700f, (float16_t)0.126976696f, + (float16_t)0.991709754f, (float16_t)0.128498111f, + (float16_t)0.991511473f, (float16_t)0.130019223f, + (float16_t)0.991310860f, (float16_t)0.131540029f, + (float16_t)0.991107914f, (float16_t)0.133060525f, + (float16_t)0.990902635f, (float16_t)0.134580709f, + (float16_t)0.990695025f, (float16_t)0.136100575f, + (float16_t)0.990485084f, (float16_t)0.137620122f, + (float16_t)0.990272812f, (float16_t)0.139139344f, + (float16_t)0.990058210f, (float16_t)0.140658239f, + (float16_t)0.989841278f, (float16_t)0.142176804f, + (float16_t)0.989622017f, (float16_t)0.143695033f, + (float16_t)0.989400428f, (float16_t)0.145212925f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.988950265f, (float16_t)0.148247679f, + (float16_t)0.988721692f, (float16_t)0.149764535f, + (float16_t)0.988490793f, (float16_t)0.151281038f, + (float16_t)0.988257568f, (float16_t)0.152797185f, + (float16_t)0.988022017f, (float16_t)0.154312973f, + (float16_t)0.987784142f, (float16_t)0.155828398f, + (float16_t)0.987543942f, (float16_t)0.157343456f, + (float16_t)0.987301418f, (float16_t)0.158858143f, + (float16_t)0.987056571f, (float16_t)0.160372457f, + (float16_t)0.986809402f, (float16_t)0.161886394f, + (float16_t)0.986559910f, (float16_t)0.163399949f, + (float16_t)0.986308097f, (float16_t)0.164913120f, + (float16_t)0.986053963f, (float16_t)0.166425904f, + (float16_t)0.985797509f, (float16_t)0.167938295f, + (float16_t)0.985538735f, (float16_t)0.169450291f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.985014231f, (float16_t)0.172473084f, + (float16_t)0.984748502f, (float16_t)0.173983873f, + (float16_t)0.984480455f, (float16_t)0.175494253f, + (float16_t)0.984210092f, (float16_t)0.177004220f, + (float16_t)0.983937413f, (float16_t)0.178513771f, + (float16_t)0.983662419f, (float16_t)0.180022901f, + (float16_t)0.983385110f, (float16_t)0.181531608f, + (float16_t)0.983105487f, (float16_t)0.183039888f, + (float16_t)0.982823551f, (float16_t)0.184547737f, + (float16_t)0.982539302f, (float16_t)0.186055152f, + (float16_t)0.982252741f, (float16_t)0.187562129f, + (float16_t)0.981963869f, (float16_t)0.189068664f, + (float16_t)0.981672686f, (float16_t)0.190574755f, + (float16_t)0.981379193f, (float16_t)0.192080397f, + (float16_t)0.981083391f, (float16_t)0.193585587f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.980484862f, (float16_t)0.196594598f, + (float16_t)0.980182136f, (float16_t)0.198098411f, + (float16_t)0.979877104f, (float16_t)0.199601758f, + (float16_t)0.979569766f, (float16_t)0.201104635f, + (float16_t)0.979260123f, (float16_t)0.202607039f, + (float16_t)0.978948175f, (float16_t)0.204108966f, + (float16_t)0.978633924f, (float16_t)0.205610413f, + (float16_t)0.978317371f, (float16_t)0.207111376f, + (float16_t)0.977998515f, (float16_t)0.208611852f, + (float16_t)0.977677358f, (float16_t)0.210111837f, + (float16_t)0.977353900f, (float16_t)0.211611327f, + (float16_t)0.977028143f, (float16_t)0.213110320f, + (float16_t)0.976700086f, (float16_t)0.214608811f, + (float16_t)0.976369731f, (float16_t)0.216106797f, + (float16_t)0.976037079f, (float16_t)0.217604275f, + (float16_t)0.975702130f, (float16_t)0.219101240f, + (float16_t)0.975364885f, (float16_t)0.220597690f, + (float16_t)0.975025345f, (float16_t)0.222093621f, + (float16_t)0.974683511f, (float16_t)0.223589029f, + (float16_t)0.974339383f, (float16_t)0.225083911f, + (float16_t)0.973992962f, (float16_t)0.226578264f, + (float16_t)0.973644250f, (float16_t)0.228072083f, + (float16_t)0.973293246f, (float16_t)0.229565366f, + (float16_t)0.972939952f, (float16_t)0.231058108f, + (float16_t)0.972584369f, (float16_t)0.232550307f, + (float16_t)0.972226497f, (float16_t)0.234041959f, + (float16_t)0.971866337f, (float16_t)0.235533059f, + (float16_t)0.971503891f, (float16_t)0.237023606f, + (float16_t)0.971139158f, (float16_t)0.238513595f, + (float16_t)0.970772141f, (float16_t)0.240003022f, + (float16_t)0.970402839f, (float16_t)0.241491885f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.969657385f, (float16_t)0.244467903f, + (float16_t)0.969281235f, (float16_t)0.245955050f, + (float16_t)0.968902805f, (float16_t)0.247441619f, + (float16_t)0.968522094f, (float16_t)0.248927606f, + (float16_t)0.968139105f, (float16_t)0.250413007f, + (float16_t)0.967753837f, (float16_t)0.251897818f, + (float16_t)0.967366292f, (float16_t)0.253382037f, + (float16_t)0.966976471f, (float16_t)0.254865660f, + (float16_t)0.966584374f, (float16_t)0.256348682f, + (float16_t)0.966190003f, (float16_t)0.257831102f, + (float16_t)0.965793359f, (float16_t)0.259312915f, + (float16_t)0.965394442f, (float16_t)0.260794118f, + (float16_t)0.964993253f, (float16_t)0.262274707f, + (float16_t)0.964589793f, (float16_t)0.263754679f, + (float16_t)0.964184064f, (float16_t)0.265234030f, + (float16_t)0.963776066f, (float16_t)0.266712757f, + (float16_t)0.963365800f, (float16_t)0.268190857f, + (float16_t)0.962953267f, (float16_t)0.269668326f, + (float16_t)0.962538468f, (float16_t)0.271145160f, + (float16_t)0.962121404f, (float16_t)0.272621355f, + (float16_t)0.961702077f, (float16_t)0.274096910f, + (float16_t)0.961280486f, (float16_t)0.275571819f, + (float16_t)0.960856633f, (float16_t)0.277046080f, + (float16_t)0.960430519f, (float16_t)0.278519689f, + (float16_t)0.960002146f, (float16_t)0.279992643f, + (float16_t)0.959571513f, (float16_t)0.281464938f, + (float16_t)0.959138622f, (float16_t)0.282936570f, + (float16_t)0.958703475f, (float16_t)0.284407537f, + (float16_t)0.958266071f, (float16_t)0.285877835f, + (float16_t)0.957826413f, (float16_t)0.287347460f, + (float16_t)0.957384501f, (float16_t)0.288816408f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.956493919f, (float16_t)0.291752263f, + (float16_t)0.956045251f, (float16_t)0.293219163f, + (float16_t)0.955594334f, (float16_t)0.294685372f, + (float16_t)0.955141168f, (float16_t)0.296150888f, + (float16_t)0.954685755f, (float16_t)0.297615707f, + (float16_t)0.954228095f, (float16_t)0.299079826f, + (float16_t)0.953768190f, (float16_t)0.300543241f, + (float16_t)0.953306040f, (float16_t)0.302005949f, + (float16_t)0.952841648f, (float16_t)0.303467947f, + (float16_t)0.952375013f, (float16_t)0.304929230f, + (float16_t)0.951906137f, (float16_t)0.306389795f, + (float16_t)0.951435021f, (float16_t)0.307849640f, + (float16_t)0.950961666f, (float16_t)0.309308760f, + (float16_t)0.950486074f, (float16_t)0.310767153f, + (float16_t)0.950008245f, (float16_t)0.312224814f, + (float16_t)0.949528181f, (float16_t)0.313681740f, + (float16_t)0.949045882f, (float16_t)0.315137929f, + (float16_t)0.948561350f, (float16_t)0.316593376f, + (float16_t)0.948074586f, (float16_t)0.318048077f, + (float16_t)0.947585591f, (float16_t)0.319502031f, + (float16_t)0.947094366f, (float16_t)0.320955232f, + (float16_t)0.946600913f, (float16_t)0.322407679f, + (float16_t)0.946105232f, (float16_t)0.323859367f, + (float16_t)0.945607325f, (float16_t)0.325310292f, + (float16_t)0.945107193f, (float16_t)0.326760452f, + (float16_t)0.944604837f, (float16_t)0.328209844f, + (float16_t)0.944100258f, (float16_t)0.329658463f, + (float16_t)0.943593458f, (float16_t)0.331106306f, + (float16_t)0.943084437f, (float16_t)0.332553370f, + (float16_t)0.942573198f, (float16_t)0.333999651f, + (float16_t)0.942059740f, (float16_t)0.335445147f, + (float16_t)0.941544065f, 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(float16_t)0.999481187f, (float16_t)-0.032208025f, + (float16_t)0.999529418f, (float16_t)-0.030674803f, + (float16_t)0.999575296f, (float16_t)-0.029141509f, + (float16_t)0.999618822f, (float16_t)-0.027608146f, + (float16_t)0.999659997f, (float16_t)-0.026074718f, + (float16_t)0.999698819f, (float16_t)-0.024541229f, + (float16_t)0.999735288f, (float16_t)-0.023007681f, + (float16_t)0.999769405f, (float16_t)-0.021474080f, + (float16_t)0.999801170f, (float16_t)-0.019940429f, + (float16_t)0.999830582f, (float16_t)-0.018406730f, + (float16_t)0.999857641f, (float16_t)-0.016872988f, + (float16_t)0.999882347f, (float16_t)-0.015339206f, + (float16_t)0.999904701f, (float16_t)-0.013805389f, + (float16_t)0.999924702f, (float16_t)-0.012271538f, + (float16_t)0.999942350f, (float16_t)-0.010737659f, + (float16_t)0.999957645f, (float16_t)-0.009203755f, + (float16_t)0.999970586f, (float16_t)-0.007669829f, + (float16_t)0.999981175f, (float16_t)-0.006135885f, + (float16_t)0.999989411f, (float16_t)-0.004601926f, + (float16_t)0.999995294f, (float16_t)-0.003067957f, + (float16_t)0.999998823f, (float16_t)-0.001533980f +}; + +/** + @par + Example code for Floating-point RFFT Twiddle factors Generation: + @par + 
TW = exp(pi/2*i-2*pi*i*[0:L/2-1]/L).'
+ @par + Real and Imag values are in interleaved fashion +*/ +const float16_t twiddleCoefF16_rfft_32[32] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.195090322f, (float16_t)-0.980785280f +}; + +const float16_t twiddleCoefF16_rfft_64[64] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000000000f, (float16_t)1.000000000000000f, + (float16_t)0.098017140329561f, (float16_t)0.995184726672197f, + (float16_t)0.195090322016128f, (float16_t)0.980785280403230f, + (float16_t)0.290284677254462f, (float16_t)0.956940335732209f, + (float16_t)0.382683432365090f, (float16_t)0.923879532511287f, + (float16_t)0.471396736825998f, (float16_t)0.881921264348355f, + (float16_t)0.555570233019602f, (float16_t)0.831469612302545f, + (float16_t)0.634393284163645f, (float16_t)0.773010453362737f, + (float16_t)0.707106781186547f, (float16_t)0.707106781186548f, + (float16_t)0.773010453362737f, (float16_t)0.634393284163645f, + (float16_t)0.831469612302545f, (float16_t)0.555570233019602f, + (float16_t)0.881921264348355f, (float16_t)0.471396736825998f, + (float16_t)0.923879532511287f, (float16_t)0.382683432365090f, + (float16_t)0.956940335732209f, (float16_t)0.290284677254462f, + (float16_t)0.980785280403230f, (float16_t)0.195090322016128f, + (float16_t)0.995184726672197f, (float16_t)0.098017140329561f, + (float16_t)1.000000000000000f, (float16_t)0.000000000000000f, + (float16_t)0.995184726672197f, (float16_t)-0.098017140329561f, + (float16_t)0.980785280403230f, (float16_t)-0.195090322016128f, + (float16_t)0.956940335732209f, (float16_t)-0.290284677254462f, + (float16_t)0.923879532511287f, (float16_t)-0.382683432365090f, + (float16_t)0.881921264348355f, (float16_t)-0.471396736825998f, + (float16_t)0.831469612302545f, (float16_t)-0.555570233019602f, + (float16_t)0.773010453362737f, (float16_t)-0.634393284163645f, + (float16_t)0.707106781186548f, (float16_t)-0.707106781186547f, + (float16_t)0.634393284163645f, (float16_t)-0.773010453362737f, + (float16_t)0.555570233019602f, (float16_t)-0.831469612302545f, + (float16_t)0.471396736825998f, (float16_t)-0.881921264348355f, + (float16_t)0.382683432365090f, (float16_t)-0.923879532511287f, + (float16_t)0.290284677254462f, (float16_t)-0.956940335732209f, + (float16_t)0.195090322016129f, (float16_t)-0.980785280403230f, + (float16_t)0.098017140329561f, (float16_t)-0.995184726672197f +}; + +const float16_t twiddleCoefF16_rfft_128[128] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.857728610f, (float16_t)0.514102744f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.803207531f, (float16_t)-0.595699304f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.740951125f, (float16_t)-0.671558955f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.671558955f, (float16_t)-0.740951125f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.595699304f, (float16_t)-0.803207531f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.514102744f, (float16_t)-0.857728610f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.427555093f, (float16_t)-0.903989293f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.049067674f, (float16_t)-0.998795456f +}; + +const float16_t twiddleCoefF16_rfft_256[256] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.024541229f, (float16_t)0.999698819f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.073564564f, (float16_t)0.997290457f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.122410675f, (float16_t)0.992479535f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.170961889f, (float16_t)0.985277642f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.219101240f, (float16_t)0.975702130f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.266712757f, (float16_t)0.963776066f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.313681740f, (float16_t)0.949528181f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.359895037f, (float16_t)0.932992799f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.405241314f, (float16_t)0.914209756f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.449611330f, (float16_t)0.893224301f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.492898192f, (float16_t)0.870086991f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.534997620f, (float16_t)0.844853565f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.575808191f, (float16_t)0.817584813f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.615231591f, (float16_t)0.788346428f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.653172843f, (float16_t)0.757208847f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.689540545f, (float16_t)0.724247083f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.724247083f, (float16_t)0.689540545f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.757208847f, (float16_t)0.653172843f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.788346428f, (float16_t)0.615231591f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.817584813f, (float16_t)0.575808191f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.844853565f, (float16_t)0.534997620f, + (float16_t)0.857728610f, (float16_t)0.514102744f, + (float16_t)0.870086991f, (float16_t)0.492898192f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.893224301f, (float16_t)0.449611330f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.914209756f, (float16_t)0.405241314f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.932992799f, (float16_t)0.359895037f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.949528181f, (float16_t)0.313681740f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.963776066f, (float16_t)0.266712757f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.975702130f, (float16_t)0.219101240f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999698819f, (float16_t)-0.024541229f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.997290457f, (float16_t)-0.073564564f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.992479535f, (float16_t)-0.122410675f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.985277642f, (float16_t)-0.170961889f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.975702130f, (float16_t)-0.219101240f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.963776066f, (float16_t)-0.266712757f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.949528181f, (float16_t)-0.313681740f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.932992799f, (float16_t)-0.359895037f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.914209756f, (float16_t)-0.405241314f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.893224301f, (float16_t)-0.449611330f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.870086991f, (float16_t)-0.492898192f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.844853565f, (float16_t)-0.534997620f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.817584813f, (float16_t)-0.575808191f, + (float16_t)0.803207531f, (float16_t)-0.595699304f, + (float16_t)0.788346428f, (float16_t)-0.615231591f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.757208847f, (float16_t)-0.653172843f, + (float16_t)0.740951125f, (float16_t)-0.671558955f, + (float16_t)0.724247083f, (float16_t)-0.689540545f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.689540545f, (float16_t)-0.724247083f, + (float16_t)0.671558955f, (float16_t)-0.740951125f, + (float16_t)0.653172843f, (float16_t)-0.757208847f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.615231591f, (float16_t)-0.788346428f, + (float16_t)0.595699304f, (float16_t)-0.803207531f, + (float16_t)0.575808191f, (float16_t)-0.817584813f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.534997620f, (float16_t)-0.844853565f, + (float16_t)0.514102744f, (float16_t)-0.857728610f, + (float16_t)0.492898192f, (float16_t)-0.870086991f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.449611330f, (float16_t)-0.893224301f, + (float16_t)0.427555093f, (float16_t)-0.903989293f, + (float16_t)0.405241314f, (float16_t)-0.914209756f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.359895037f, (float16_t)-0.932992799f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.313681740f, (float16_t)-0.949528181f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.266712757f, (float16_t)-0.963776066f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.219101240f, (float16_t)-0.975702130f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.170961889f, (float16_t)-0.985277642f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.122410675f, (float16_t)-0.992479535f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.024541229f, (float16_t)-0.999698819f +}; + +const float16_t twiddleCoefF16_rfft_512[512] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.012271538f, (float16_t)0.999924702f, + (float16_t)0.024541229f, (float16_t)0.999698819f, + (float16_t)0.036807223f, (float16_t)0.999322385f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.061320736f, (float16_t)0.998118113f, + (float16_t)0.073564564f, (float16_t)0.997290457f, + (float16_t)0.085797312f, (float16_t)0.996312612f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.110222207f, (float16_t)0.993906970f, + (float16_t)0.122410675f, (float16_t)0.992479535f, + (float16_t)0.134580709f, (float16_t)0.990902635f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.158858143f, (float16_t)0.987301418f, + (float16_t)0.170961889f, (float16_t)0.985277642f, + (float16_t)0.183039888f, (float16_t)0.983105487f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.207111376f, (float16_t)0.978317371f, + (float16_t)0.219101240f, (float16_t)0.975702130f, + (float16_t)0.231058108f, (float16_t)0.972939952f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.254865660f, (float16_t)0.966976471f, + (float16_t)0.266712757f, (float16_t)0.963776066f, + (float16_t)0.278519689f, (float16_t)0.960430519f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.302005949f, (float16_t)0.953306040f, + (float16_t)0.313681740f, (float16_t)0.949528181f, + (float16_t)0.325310292f, (float16_t)0.945607325f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.348418680f, (float16_t)0.937339012f, + (float16_t)0.359895037f, (float16_t)0.932992799f, + (float16_t)0.371317194f, (float16_t)0.928506080f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.393992040f, (float16_t)0.919113852f, + (float16_t)0.405241314f, (float16_t)0.914209756f, + (float16_t)0.416429560f, (float16_t)0.909167983f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.438616239f, (float16_t)0.898674466f, + (float16_t)0.449611330f, (float16_t)0.893224301f, + (float16_t)0.460538711f, (float16_t)0.887639620f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.482183772f, (float16_t)0.876070094f, + (float16_t)0.492898192f, (float16_t)0.870086991f, + (float16_t)0.503538384f, (float16_t)0.863972856f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.524589683f, (float16_t)0.851355193f, + (float16_t)0.534997620f, (float16_t)0.844853565f, + (float16_t)0.545324988f, (float16_t)0.838224706f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.565731811f, (float16_t)0.824589303f, + (float16_t)0.575808191f, (float16_t)0.817584813f, + (float16_t)0.585797857f, (float16_t)0.810457198f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.605511041f, (float16_t)0.795836905f, + (float16_t)0.615231591f, (float16_t)0.788346428f, + (float16_t)0.624859488f, (float16_t)0.780737229f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.643831543f, (float16_t)0.765167266f, + (float16_t)0.653172843f, (float16_t)0.757208847f, + (float16_t)0.662415778f, (float16_t)0.749136395f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.680600998f, (float16_t)0.732654272f, + (float16_t)0.689540545f, (float16_t)0.724247083f, + (float16_t)0.698376249f, (float16_t)0.715730825f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.715730825f, (float16_t)0.698376249f, + (float16_t)0.724247083f, (float16_t)0.689540545f, + (float16_t)0.732654272f, (float16_t)0.680600998f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.749136395f, (float16_t)0.662415778f, + (float16_t)0.757208847f, (float16_t)0.653172843f, + (float16_t)0.765167266f, (float16_t)0.643831543f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.780737229f, (float16_t)0.624859488f, + (float16_t)0.788346428f, (float16_t)0.615231591f, + (float16_t)0.795836905f, (float16_t)0.605511041f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.810457198f, (float16_t)0.585797857f, + (float16_t)0.817584813f, (float16_t)0.575808191f, + (float16_t)0.824589303f, (float16_t)0.565731811f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.838224706f, (float16_t)0.545324988f, + (float16_t)0.844853565f, (float16_t)0.534997620f, + (float16_t)0.851355193f, (float16_t)0.524589683f, + (float16_t)0.857728610f, (float16_t)0.514102744f, + (float16_t)0.863972856f, (float16_t)0.503538384f, + (float16_t)0.870086991f, (float16_t)0.492898192f, + (float16_t)0.876070094f, (float16_t)0.482183772f, + (float16_t)0.881921264f, (float16_t)0.471396737f, + (float16_t)0.887639620f, (float16_t)0.460538711f, + (float16_t)0.893224301f, (float16_t)0.449611330f, + (float16_t)0.898674466f, (float16_t)0.438616239f, + (float16_t)0.903989293f, (float16_t)0.427555093f, + (float16_t)0.909167983f, (float16_t)0.416429560f, + (float16_t)0.914209756f, (float16_t)0.405241314f, + (float16_t)0.919113852f, (float16_t)0.393992040f, + (float16_t)0.923879533f, (float16_t)0.382683432f, + (float16_t)0.928506080f, (float16_t)0.371317194f, + (float16_t)0.932992799f, (float16_t)0.359895037f, + (float16_t)0.937339012f, (float16_t)0.348418680f, + (float16_t)0.941544065f, (float16_t)0.336889853f, + (float16_t)0.945607325f, (float16_t)0.325310292f, + (float16_t)0.949528181f, (float16_t)0.313681740f, + (float16_t)0.953306040f, (float16_t)0.302005949f, + (float16_t)0.956940336f, (float16_t)0.290284677f, + (float16_t)0.960430519f, (float16_t)0.278519689f, + (float16_t)0.963776066f, (float16_t)0.266712757f, + (float16_t)0.966976471f, (float16_t)0.254865660f, + (float16_t)0.970031253f, (float16_t)0.242980180f, + (float16_t)0.972939952f, (float16_t)0.231058108f, + (float16_t)0.975702130f, (float16_t)0.219101240f, + (float16_t)0.978317371f, (float16_t)0.207111376f, + (float16_t)0.980785280f, (float16_t)0.195090322f, + (float16_t)0.983105487f, (float16_t)0.183039888f, + (float16_t)0.985277642f, (float16_t)0.170961889f, + (float16_t)0.987301418f, (float16_t)0.158858143f, + (float16_t)0.989176510f, (float16_t)0.146730474f, + (float16_t)0.990902635f, (float16_t)0.134580709f, + (float16_t)0.992479535f, (float16_t)0.122410675f, + (float16_t)0.993906970f, (float16_t)0.110222207f, + (float16_t)0.995184727f, (float16_t)0.098017140f, + (float16_t)0.996312612f, (float16_t)0.085797312f, + (float16_t)0.997290457f, (float16_t)0.073564564f, + (float16_t)0.998118113f, (float16_t)0.061320736f, + (float16_t)0.998795456f, (float16_t)0.049067674f, + (float16_t)0.999322385f, (float16_t)0.036807223f, + (float16_t)0.999698819f, (float16_t)0.024541229f, + (float16_t)0.999924702f, (float16_t)0.012271538f, + (float16_t)1.000000000f, (float16_t)0.000000000f, + (float16_t)0.999924702f, (float16_t)-0.012271538f, + (float16_t)0.999698819f, (float16_t)-0.024541229f, + (float16_t)0.999322385f, (float16_t)-0.036807223f, + (float16_t)0.998795456f, (float16_t)-0.049067674f, + (float16_t)0.998118113f, (float16_t)-0.061320736f, + (float16_t)0.997290457f, (float16_t)-0.073564564f, + (float16_t)0.996312612f, (float16_t)-0.085797312f, + (float16_t)0.995184727f, (float16_t)-0.098017140f, + (float16_t)0.993906970f, (float16_t)-0.110222207f, + (float16_t)0.992479535f, (float16_t)-0.122410675f, + (float16_t)0.990902635f, (float16_t)-0.134580709f, + (float16_t)0.989176510f, (float16_t)-0.146730474f, + (float16_t)0.987301418f, (float16_t)-0.158858143f, + (float16_t)0.985277642f, (float16_t)-0.170961889f, + (float16_t)0.983105487f, (float16_t)-0.183039888f, + (float16_t)0.980785280f, (float16_t)-0.195090322f, + (float16_t)0.978317371f, (float16_t)-0.207111376f, + (float16_t)0.975702130f, (float16_t)-0.219101240f, + (float16_t)0.972939952f, (float16_t)-0.231058108f, + (float16_t)0.970031253f, (float16_t)-0.242980180f, + (float16_t)0.966976471f, (float16_t)-0.254865660f, + (float16_t)0.963776066f, (float16_t)-0.266712757f, + (float16_t)0.960430519f, (float16_t)-0.278519689f, + (float16_t)0.956940336f, (float16_t)-0.290284677f, + (float16_t)0.953306040f, (float16_t)-0.302005949f, + (float16_t)0.949528181f, (float16_t)-0.313681740f, + (float16_t)0.945607325f, (float16_t)-0.325310292f, + (float16_t)0.941544065f, (float16_t)-0.336889853f, + (float16_t)0.937339012f, (float16_t)-0.348418680f, + (float16_t)0.932992799f, (float16_t)-0.359895037f, + (float16_t)0.928506080f, (float16_t)-0.371317194f, + (float16_t)0.923879533f, (float16_t)-0.382683432f, + (float16_t)0.919113852f, (float16_t)-0.393992040f, + (float16_t)0.914209756f, (float16_t)-0.405241314f, + (float16_t)0.909167983f, (float16_t)-0.416429560f, + (float16_t)0.903989293f, (float16_t)-0.427555093f, + (float16_t)0.898674466f, (float16_t)-0.438616239f, + (float16_t)0.893224301f, (float16_t)-0.449611330f, + (float16_t)0.887639620f, (float16_t)-0.460538711f, + (float16_t)0.881921264f, (float16_t)-0.471396737f, + (float16_t)0.876070094f, (float16_t)-0.482183772f, + (float16_t)0.870086991f, (float16_t)-0.492898192f, + (float16_t)0.863972856f, (float16_t)-0.503538384f, + (float16_t)0.857728610f, (float16_t)-0.514102744f, + (float16_t)0.851355193f, (float16_t)-0.524589683f, + (float16_t)0.844853565f, (float16_t)-0.534997620f, + (float16_t)0.838224706f, (float16_t)-0.545324988f, + (float16_t)0.831469612f, (float16_t)-0.555570233f, + (float16_t)0.824589303f, (float16_t)-0.565731811f, + (float16_t)0.817584813f, (float16_t)-0.575808191f, + (float16_t)0.810457198f, (float16_t)-0.585797857f, + (float16_t)0.803207531f, (float16_t)-0.595699304f, + (float16_t)0.795836905f, (float16_t)-0.605511041f, + (float16_t)0.788346428f, (float16_t)-0.615231591f, + (float16_t)0.780737229f, (float16_t)-0.624859488f, + (float16_t)0.773010453f, (float16_t)-0.634393284f, + (float16_t)0.765167266f, (float16_t)-0.643831543f, + (float16_t)0.757208847f, (float16_t)-0.653172843f, + (float16_t)0.749136395f, (float16_t)-0.662415778f, + (float16_t)0.740951125f, (float16_t)-0.671558955f, + (float16_t)0.732654272f, (float16_t)-0.680600998f, + (float16_t)0.724247083f, (float16_t)-0.689540545f, + (float16_t)0.715730825f, (float16_t)-0.698376249f, + (float16_t)0.707106781f, (float16_t)-0.707106781f, + (float16_t)0.698376249f, (float16_t)-0.715730825f, + (float16_t)0.689540545f, (float16_t)-0.724247083f, + (float16_t)0.680600998f, (float16_t)-0.732654272f, + (float16_t)0.671558955f, (float16_t)-0.740951125f, + (float16_t)0.662415778f, (float16_t)-0.749136395f, + (float16_t)0.653172843f, (float16_t)-0.757208847f, + (float16_t)0.643831543f, (float16_t)-0.765167266f, + (float16_t)0.634393284f, (float16_t)-0.773010453f, + (float16_t)0.624859488f, (float16_t)-0.780737229f, + (float16_t)0.615231591f, (float16_t)-0.788346428f, + (float16_t)0.605511041f, (float16_t)-0.795836905f, + (float16_t)0.595699304f, (float16_t)-0.803207531f, + (float16_t)0.585797857f, (float16_t)-0.810457198f, + (float16_t)0.575808191f, (float16_t)-0.817584813f, + (float16_t)0.565731811f, (float16_t)-0.824589303f, + (float16_t)0.555570233f, (float16_t)-0.831469612f, + (float16_t)0.545324988f, (float16_t)-0.838224706f, + (float16_t)0.534997620f, (float16_t)-0.844853565f, + (float16_t)0.524589683f, (float16_t)-0.851355193f, + (float16_t)0.514102744f, (float16_t)-0.857728610f, + (float16_t)0.503538384f, (float16_t)-0.863972856f, + (float16_t)0.492898192f, (float16_t)-0.870086991f, + (float16_t)0.482183772f, (float16_t)-0.876070094f, + (float16_t)0.471396737f, (float16_t)-0.881921264f, + (float16_t)0.460538711f, (float16_t)-0.887639620f, + (float16_t)0.449611330f, (float16_t)-0.893224301f, + (float16_t)0.438616239f, (float16_t)-0.898674466f, + (float16_t)0.427555093f, (float16_t)-0.903989293f, + (float16_t)0.416429560f, (float16_t)-0.909167983f, + (float16_t)0.405241314f, (float16_t)-0.914209756f, + (float16_t)0.393992040f, (float16_t)-0.919113852f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.371317194f, (float16_t)-0.928506080f, + (float16_t)0.359895037f, (float16_t)-0.932992799f, + (float16_t)0.348418680f, (float16_t)-0.937339012f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.325310292f, (float16_t)-0.945607325f, + (float16_t)0.313681740f, (float16_t)-0.949528181f, + (float16_t)0.302005949f, (float16_t)-0.953306040f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.278519689f, (float16_t)-0.960430519f, + (float16_t)0.266712757f, (float16_t)-0.963776066f, + (float16_t)0.254865660f, (float16_t)-0.966976471f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.231058108f, (float16_t)-0.972939952f, + (float16_t)0.219101240f, (float16_t)-0.975702130f, + (float16_t)0.207111376f, (float16_t)-0.978317371f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.183039888f, (float16_t)-0.983105487f, + (float16_t)0.170961889f, (float16_t)-0.985277642f, + (float16_t)0.158858143f, (float16_t)-0.987301418f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.134580709f, (float16_t)-0.990902635f, + (float16_t)0.122410675f, (float16_t)-0.992479535f, + (float16_t)0.110222207f, (float16_t)-0.993906970f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.085797312f, (float16_t)-0.996312612f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.061320736f, (float16_t)-0.998118113f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.036807223f, (float16_t)-0.999322385f, + (float16_t)0.024541229f, (float16_t)-0.999698819f, + (float16_t)0.012271538f, (float16_t)-0.999924702f +}; + +const float16_t twiddleCoefF16_rfft_1024[1024] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.006135885f, (float16_t)0.999981175f, + (float16_t)0.012271538f, (float16_t)0.999924702f, + (float16_t)0.018406730f, (float16_t)0.999830582f, + (float16_t)0.024541229f, (float16_t)0.999698819f, + (float16_t)0.030674803f, (float16_t)0.999529418f, + (float16_t)0.036807223f, (float16_t)0.999322385f, + (float16_t)0.042938257f, (float16_t)0.999077728f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.055195244f, (float16_t)0.998475581f, + (float16_t)0.061320736f, (float16_t)0.998118113f, + (float16_t)0.067443920f, (float16_t)0.997723067f, + (float16_t)0.073564564f, (float16_t)0.997290457f, + (float16_t)0.079682438f, (float16_t)0.996820299f, + (float16_t)0.085797312f, (float16_t)0.996312612f, + (float16_t)0.091908956f, (float16_t)0.995767414f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.104121634f, (float16_t)0.994564571f, + (float16_t)0.110222207f, (float16_t)0.993906970f, + (float16_t)0.116318631f, (float16_t)0.993211949f, + (float16_t)0.122410675f, (float16_t)0.992479535f, + (float16_t)0.128498111f, (float16_t)0.991709754f, + (float16_t)0.134580709f, (float16_t)0.990902635f, + (float16_t)0.140658239f, (float16_t)0.990058210f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.152797185f, (float16_t)0.988257568f, + (float16_t)0.158858143f, (float16_t)0.987301418f, + (float16_t)0.164913120f, (float16_t)0.986308097f, + (float16_t)0.170961889f, (float16_t)0.985277642f, + (float16_t)0.177004220f, (float16_t)0.984210092f, + (float16_t)0.183039888f, (float16_t)0.983105487f, + (float16_t)0.189068664f, (float16_t)0.981963869f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.201104635f, (float16_t)0.979569766f, + (float16_t)0.207111376f, (float16_t)0.978317371f, + (float16_t)0.213110320f, (float16_t)0.977028143f, + (float16_t)0.219101240f, (float16_t)0.975702130f, + (float16_t)0.225083911f, (float16_t)0.974339383f, + (float16_t)0.231058108f, (float16_t)0.972939952f, + (float16_t)0.237023606f, (float16_t)0.971503891f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.248927606f, (float16_t)0.968522094f, + (float16_t)0.254865660f, (float16_t)0.966976471f, + (float16_t)0.260794118f, (float16_t)0.965394442f, + (float16_t)0.266712757f, (float16_t)0.963776066f, + (float16_t)0.272621355f, (float16_t)0.962121404f, + (float16_t)0.278519689f, (float16_t)0.960430519f, + (float16_t)0.284407537f, (float16_t)0.958703475f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.296150888f, (float16_t)0.955141168f, + (float16_t)0.302005949f, (float16_t)0.953306040f, + (float16_t)0.307849640f, (float16_t)0.951435021f, + (float16_t)0.313681740f, (float16_t)0.949528181f, + (float16_t)0.319502031f, (float16_t)0.947585591f, + (float16_t)0.325310292f, (float16_t)0.945607325f, + (float16_t)0.331106306f, (float16_t)0.943593458f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.342660717f, (float16_t)0.939459224f, + (float16_t)0.348418680f, (float16_t)0.937339012f, + (float16_t)0.354163525f, (float16_t)0.935183510f, + (float16_t)0.359895037f, (float16_t)0.932992799f, + (float16_t)0.365612998f, (float16_t)0.930766961f, + (float16_t)0.371317194f, (float16_t)0.928506080f, + (float16_t)0.377007410f, (float16_t)0.926210242f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.388345047f, (float16_t)0.921514039f, + (float16_t)0.393992040f, (float16_t)0.919113852f, + (float16_t)0.399624200f, (float16_t)0.916679060f, + (float16_t)0.405241314f, (float16_t)0.914209756f, + (float16_t)0.410843171f, (float16_t)0.911706032f, + (float16_t)0.416429560f, (float16_t)0.909167983f, + (float16_t)0.422000271f, (float16_t)0.906595705f, + (float16_t)0.427555093f, (float16_t)0.903989293f, + (float16_t)0.433093819f, (float16_t)0.901348847f, + (float16_t)0.438616239f, (float16_t)0.898674466f, + (float16_t)0.444122145f, (float16_t)0.895966250f, + (float16_t)0.449611330f, (float16_t)0.893224301f, + (float16_t)0.455083587f, (float16_t)0.890448723f, + (float16_t)0.460538711f, (float16_t)0.887639620f, + (float16_t)0.465976496f, (float16_t)0.884797098f, + (float16_t)0.471396737f, (float16_t)0.881921264f, + (float16_t)0.476799230f, (float16_t)0.879012226f, + (float16_t)0.482183772f, (float16_t)0.876070094f, + (float16_t)0.487550160f, (float16_t)0.873094978f, + (float16_t)0.492898192f, (float16_t)0.870086991f, + (float16_t)0.498227667f, (float16_t)0.867046246f, + (float16_t)0.503538384f, (float16_t)0.863972856f, + (float16_t)0.508830143f, (float16_t)0.860866939f, + (float16_t)0.514102744f, (float16_t)0.857728610f, + (float16_t)0.519355990f, (float16_t)0.854557988f, + (float16_t)0.524589683f, (float16_t)0.851355193f, + (float16_t)0.529803625f, (float16_t)0.848120345f, + (float16_t)0.534997620f, (float16_t)0.844853565f, + (float16_t)0.540171473f, (float16_t)0.841554977f, + (float16_t)0.545324988f, (float16_t)0.838224706f, + (float16_t)0.550457973f, (float16_t)0.834862875f, + (float16_t)0.555570233f, (float16_t)0.831469612f, + (float16_t)0.560661576f, (float16_t)0.828045045f, + (float16_t)0.565731811f, (float16_t)0.824589303f, + (float16_t)0.570780746f, (float16_t)0.821102515f, + (float16_t)0.575808191f, (float16_t)0.817584813f, + (float16_t)0.580813958f, (float16_t)0.814036330f, + (float16_t)0.585797857f, (float16_t)0.810457198f, + (float16_t)0.590759702f, (float16_t)0.806847554f, + (float16_t)0.595699304f, (float16_t)0.803207531f, + (float16_t)0.600616479f, (float16_t)0.799537269f, + (float16_t)0.605511041f, (float16_t)0.795836905f, + (float16_t)0.610382806f, (float16_t)0.792106577f, + (float16_t)0.615231591f, (float16_t)0.788346428f, + (float16_t)0.620057212f, (float16_t)0.784556597f, + (float16_t)0.624859488f, (float16_t)0.780737229f, + (float16_t)0.629638239f, (float16_t)0.776888466f, + (float16_t)0.634393284f, (float16_t)0.773010453f, + (float16_t)0.639124445f, (float16_t)0.769103338f, + (float16_t)0.643831543f, (float16_t)0.765167266f, + (float16_t)0.648514401f, (float16_t)0.761202385f, + (float16_t)0.653172843f, (float16_t)0.757208847f, + (float16_t)0.657806693f, (float16_t)0.753186799f, + (float16_t)0.662415778f, (float16_t)0.749136395f, + (float16_t)0.666999922f, (float16_t)0.745057785f, + (float16_t)0.671558955f, (float16_t)0.740951125f, + (float16_t)0.676092704f, (float16_t)0.736816569f, + (float16_t)0.680600998f, (float16_t)0.732654272f, + (float16_t)0.685083668f, (float16_t)0.728464390f, + (float16_t)0.689540545f, (float16_t)0.724247083f, + (float16_t)0.693971461f, (float16_t)0.720002508f, + (float16_t)0.698376249f, (float16_t)0.715730825f, + (float16_t)0.702754744f, (float16_t)0.711432196f, + (float16_t)0.707106781f, (float16_t)0.707106781f, + (float16_t)0.711432196f, (float16_t)0.702754744f, + (float16_t)0.715730825f, (float16_t)0.698376249f, + (float16_t)0.720002508f, (float16_t)0.693971461f, + (float16_t)0.724247083f, (float16_t)0.689540545f, + (float16_t)0.728464390f, (float16_t)0.685083668f, + (float16_t)0.732654272f, (float16_t)0.680600998f, + (float16_t)0.736816569f, (float16_t)0.676092704f, + (float16_t)0.740951125f, (float16_t)0.671558955f, + (float16_t)0.745057785f, (float16_t)0.666999922f, + (float16_t)0.749136395f, (float16_t)0.662415778f, + (float16_t)0.753186799f, (float16_t)0.657806693f, + (float16_t)0.757208847f, (float16_t)0.653172843f, + (float16_t)0.761202385f, (float16_t)0.648514401f, + (float16_t)0.765167266f, (float16_t)0.643831543f, + (float16_t)0.769103338f, (float16_t)0.639124445f, + (float16_t)0.773010453f, (float16_t)0.634393284f, + (float16_t)0.776888466f, (float16_t)0.629638239f, + (float16_t)0.780737229f, (float16_t)0.624859488f, + (float16_t)0.784556597f, (float16_t)0.620057212f, + (float16_t)0.788346428f, (float16_t)0.615231591f, + (float16_t)0.792106577f, (float16_t)0.610382806f, + (float16_t)0.795836905f, (float16_t)0.605511041f, + (float16_t)0.799537269f, (float16_t)0.600616479f, + (float16_t)0.803207531f, (float16_t)0.595699304f, + (float16_t)0.806847554f, (float16_t)0.590759702f, + (float16_t)0.810457198f, (float16_t)0.585797857f, + (float16_t)0.814036330f, (float16_t)0.580813958f, + (float16_t)0.817584813f, (float16_t)0.575808191f, + (float16_t)0.821102515f, (float16_t)0.570780746f, + (float16_t)0.824589303f, (float16_t)0.565731811f, + (float16_t)0.828045045f, (float16_t)0.560661576f, + (float16_t)0.831469612f, (float16_t)0.555570233f, + (float16_t)0.834862875f, (float16_t)0.550457973f, + (float16_t)0.838224706f, (float16_t)0.545324988f, + (float16_t)0.841554977f, (float16_t)0.540171473f, + (float16_t)0.844853565f, (float16_t)0.534997620f, + 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(float16_t)0.399624200f, (float16_t)-0.916679060f, + (float16_t)0.393992040f, (float16_t)-0.919113852f, + (float16_t)0.388345047f, (float16_t)-0.921514039f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.377007410f, (float16_t)-0.926210242f, + (float16_t)0.371317194f, (float16_t)-0.928506080f, + (float16_t)0.365612998f, (float16_t)-0.930766961f, + (float16_t)0.359895037f, (float16_t)-0.932992799f, + (float16_t)0.354163525f, (float16_t)-0.935183510f, + (float16_t)0.348418680f, (float16_t)-0.937339012f, + (float16_t)0.342660717f, (float16_t)-0.939459224f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.331106306f, (float16_t)-0.943593458f, + (float16_t)0.325310292f, (float16_t)-0.945607325f, + (float16_t)0.319502031f, (float16_t)-0.947585591f, + (float16_t)0.313681740f, (float16_t)-0.949528181f, + (float16_t)0.307849640f, (float16_t)-0.951435021f, + (float16_t)0.302005949f, (float16_t)-0.953306040f, + (float16_t)0.296150888f, (float16_t)-0.955141168f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.284407537f, (float16_t)-0.958703475f, + (float16_t)0.278519689f, (float16_t)-0.960430519f, + (float16_t)0.272621355f, (float16_t)-0.962121404f, + (float16_t)0.266712757f, (float16_t)-0.963776066f, + (float16_t)0.260794118f, (float16_t)-0.965394442f, + (float16_t)0.254865660f, (float16_t)-0.966976471f, + (float16_t)0.248927606f, (float16_t)-0.968522094f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.237023606f, (float16_t)-0.971503891f, + (float16_t)0.231058108f, (float16_t)-0.972939952f, + (float16_t)0.225083911f, (float16_t)-0.974339383f, + (float16_t)0.219101240f, (float16_t)-0.975702130f, + (float16_t)0.213110320f, (float16_t)-0.977028143f, + (float16_t)0.207111376f, (float16_t)-0.978317371f, + (float16_t)0.201104635f, (float16_t)-0.979569766f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.189068664f, (float16_t)-0.981963869f, + (float16_t)0.183039888f, (float16_t)-0.983105487f, + (float16_t)0.177004220f, (float16_t)-0.984210092f, + (float16_t)0.170961889f, (float16_t)-0.985277642f, + (float16_t)0.164913120f, (float16_t)-0.986308097f, + (float16_t)0.158858143f, (float16_t)-0.987301418f, + (float16_t)0.152797185f, (float16_t)-0.988257568f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.140658239f, (float16_t)-0.990058210f, + (float16_t)0.134580709f, (float16_t)-0.990902635f, + (float16_t)0.128498111f, (float16_t)-0.991709754f, + (float16_t)0.122410675f, (float16_t)-0.992479535f, + (float16_t)0.116318631f, (float16_t)-0.993211949f, + (float16_t)0.110222207f, (float16_t)-0.993906970f, + (float16_t)0.104121634f, (float16_t)-0.994564571f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.091908956f, (float16_t)-0.995767414f, + (float16_t)0.085797312f, (float16_t)-0.996312612f, + (float16_t)0.079682438f, (float16_t)-0.996820299f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.067443920f, (float16_t)-0.997723067f, + (float16_t)0.061320736f, (float16_t)-0.998118113f, + (float16_t)0.055195244f, (float16_t)-0.998475581f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.042938257f, (float16_t)-0.999077728f, + (float16_t)0.036807223f, (float16_t)-0.999322385f, + (float16_t)0.030674803f, (float16_t)-0.999529418f, + (float16_t)0.024541229f, (float16_t)-0.999698819f, + (float16_t)0.018406730f, (float16_t)-0.999830582f, + (float16_t)0.012271538f, (float16_t)-0.999924702f, + (float16_t)0.006135885f, (float16_t)-0.999981175f +}; + +const float16_t twiddleCoefF16_rfft_2048[2048] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.003067957f, (float16_t)0.999995294f, + (float16_t)0.006135885f, (float16_t)0.999981175f, + (float16_t)0.009203755f, (float16_t)0.999957645f, + (float16_t)0.012271538f, (float16_t)0.999924702f, + (float16_t)0.015339206f, (float16_t)0.999882347f, + (float16_t)0.018406730f, (float16_t)0.999830582f, + (float16_t)0.021474080f, (float16_t)0.999769405f, + (float16_t)0.024541229f, (float16_t)0.999698819f, + (float16_t)0.027608146f, (float16_t)0.999618822f, + (float16_t)0.030674803f, (float16_t)0.999529418f, + (float16_t)0.033741172f, (float16_t)0.999430605f, + (float16_t)0.036807223f, (float16_t)0.999322385f, + (float16_t)0.039872928f, (float16_t)0.999204759f, + (float16_t)0.042938257f, (float16_t)0.999077728f, + (float16_t)0.046003182f, (float16_t)0.998941293f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.052131705f, (float16_t)0.998640218f, + (float16_t)0.055195244f, (float16_t)0.998475581f, + (float16_t)0.058258265f, (float16_t)0.998301545f, + (float16_t)0.061320736f, (float16_t)0.998118113f, + (float16_t)0.064382631f, (float16_t)0.997925286f, + (float16_t)0.067443920f, (float16_t)0.997723067f, + (float16_t)0.070504573f, (float16_t)0.997511456f, + (float16_t)0.073564564f, (float16_t)0.997290457f, + (float16_t)0.076623861f, (float16_t)0.997060070f, + (float16_t)0.079682438f, (float16_t)0.996820299f, + (float16_t)0.082740265f, (float16_t)0.996571146f, + (float16_t)0.085797312f, (float16_t)0.996312612f, + (float16_t)0.088853553f, (float16_t)0.996044701f, + (float16_t)0.091908956f, (float16_t)0.995767414f, + (float16_t)0.094963495f, (float16_t)0.995480755f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.101069863f, (float16_t)0.994879331f, + (float16_t)0.104121634f, (float16_t)0.994564571f, + (float16_t)0.107172425f, (float16_t)0.994240449f, + (float16_t)0.110222207f, (float16_t)0.993906970f, + (float16_t)0.113270952f, (float16_t)0.993564136f, + (float16_t)0.116318631f, (float16_t)0.993211949f, + (float16_t)0.119365215f, (float16_t)0.992850414f, + (float16_t)0.122410675f, (float16_t)0.992479535f, + (float16_t)0.125454983f, (float16_t)0.992099313f, + (float16_t)0.128498111f, (float16_t)0.991709754f, + (float16_t)0.131540029f, (float16_t)0.991310860f, + (float16_t)0.134580709f, (float16_t)0.990902635f, + (float16_t)0.137620122f, (float16_t)0.990485084f, + (float16_t)0.140658239f, (float16_t)0.990058210f, + (float16_t)0.143695033f, (float16_t)0.989622017f, + (float16_t)0.146730474f, (float16_t)0.989176510f, + (float16_t)0.149764535f, (float16_t)0.988721692f, + (float16_t)0.152797185f, (float16_t)0.988257568f, + (float16_t)0.155828398f, (float16_t)0.987784142f, + (float16_t)0.158858143f, (float16_t)0.987301418f, + (float16_t)0.161886394f, (float16_t)0.986809402f, + (float16_t)0.164913120f, (float16_t)0.986308097f, + (float16_t)0.167938295f, (float16_t)0.985797509f, + (float16_t)0.170961889f, (float16_t)0.985277642f, + (float16_t)0.173983873f, (float16_t)0.984748502f, + (float16_t)0.177004220f, (float16_t)0.984210092f, + (float16_t)0.180022901f, (float16_t)0.983662419f, + (float16_t)0.183039888f, (float16_t)0.983105487f, + (float16_t)0.186055152f, (float16_t)0.982539302f, + (float16_t)0.189068664f, (float16_t)0.981963869f, + (float16_t)0.192080397f, (float16_t)0.981379193f, + (float16_t)0.195090322f, (float16_t)0.980785280f, + (float16_t)0.198098411f, (float16_t)0.980182136f, + (float16_t)0.201104635f, (float16_t)0.979569766f, + (float16_t)0.204108966f, (float16_t)0.978948175f, + (float16_t)0.207111376f, (float16_t)0.978317371f, + (float16_t)0.210111837f, (float16_t)0.977677358f, + (float16_t)0.213110320f, (float16_t)0.977028143f, + (float16_t)0.216106797f, (float16_t)0.976369731f, + (float16_t)0.219101240f, (float16_t)0.975702130f, + (float16_t)0.222093621f, (float16_t)0.975025345f, + (float16_t)0.225083911f, (float16_t)0.974339383f, + (float16_t)0.228072083f, (float16_t)0.973644250f, + (float16_t)0.231058108f, (float16_t)0.972939952f, + (float16_t)0.234041959f, (float16_t)0.972226497f, + (float16_t)0.237023606f, (float16_t)0.971503891f, + (float16_t)0.240003022f, (float16_t)0.970772141f, + (float16_t)0.242980180f, (float16_t)0.970031253f, + (float16_t)0.245955050f, (float16_t)0.969281235f, + (float16_t)0.248927606f, (float16_t)0.968522094f, + (float16_t)0.251897818f, (float16_t)0.967753837f, + (float16_t)0.254865660f, (float16_t)0.966976471f, + (float16_t)0.257831102f, (float16_t)0.966190003f, + (float16_t)0.260794118f, (float16_t)0.965394442f, + (float16_t)0.263754679f, (float16_t)0.964589793f, + (float16_t)0.266712757f, (float16_t)0.963776066f, + (float16_t)0.269668326f, (float16_t)0.962953267f, + (float16_t)0.272621355f, (float16_t)0.962121404f, + (float16_t)0.275571819f, (float16_t)0.961280486f, + (float16_t)0.278519689f, (float16_t)0.960430519f, + (float16_t)0.281464938f, (float16_t)0.959571513f, + (float16_t)0.284407537f, (float16_t)0.958703475f, + (float16_t)0.287347460f, (float16_t)0.957826413f, + (float16_t)0.290284677f, (float16_t)0.956940336f, + (float16_t)0.293219163f, (float16_t)0.956045251f, + (float16_t)0.296150888f, (float16_t)0.955141168f, + (float16_t)0.299079826f, (float16_t)0.954228095f, + (float16_t)0.302005949f, (float16_t)0.953306040f, + (float16_t)0.304929230f, (float16_t)0.952375013f, + (float16_t)0.307849640f, (float16_t)0.951435021f, + (float16_t)0.310767153f, (float16_t)0.950486074f, + (float16_t)0.313681740f, (float16_t)0.949528181f, + (float16_t)0.316593376f, (float16_t)0.948561350f, + (float16_t)0.319502031f, (float16_t)0.947585591f, + (float16_t)0.322407679f, (float16_t)0.946600913f, + (float16_t)0.325310292f, (float16_t)0.945607325f, + (float16_t)0.328209844f, (float16_t)0.944604837f, + (float16_t)0.331106306f, (float16_t)0.943593458f, + (float16_t)0.333999651f, (float16_t)0.942573198f, + (float16_t)0.336889853f, (float16_t)0.941544065f, + (float16_t)0.339776884f, (float16_t)0.940506071f, + (float16_t)0.342660717f, (float16_t)0.939459224f, + (float16_t)0.345541325f, (float16_t)0.938403534f, + (float16_t)0.348418680f, (float16_t)0.937339012f, + (float16_t)0.351292756f, (float16_t)0.936265667f, + (float16_t)0.354163525f, (float16_t)0.935183510f, + (float16_t)0.357030961f, (float16_t)0.934092550f, + (float16_t)0.359895037f, (float16_t)0.932992799f, + (float16_t)0.362755724f, (float16_t)0.931884266f, + (float16_t)0.365612998f, (float16_t)0.930766961f, + (float16_t)0.368466830f, (float16_t)0.929640896f, + (float16_t)0.371317194f, (float16_t)0.928506080f, + (float16_t)0.374164063f, (float16_t)0.927362526f, + (float16_t)0.377007410f, (float16_t)0.926210242f, + (float16_t)0.379847209f, (float16_t)0.925049241f, + (float16_t)0.382683432f, (float16_t)0.923879533f, + (float16_t)0.385516054f, (float16_t)0.922701128f, + (float16_t)0.388345047f, (float16_t)0.921514039f, + (float16_t)0.391170384f, (float16_t)0.920318277f, + (float16_t)0.393992040f, (float16_t)0.919113852f, + (float16_t)0.396809987f, (float16_t)0.917900776f, + (float16_t)0.399624200f, (float16_t)0.916679060f, + (float16_t)0.402434651f, (float16_t)0.915448716f, + (float16_t)0.405241314f, (float16_t)0.914209756f, + (float16_t)0.408044163f, (float16_t)0.912962190f, + (float16_t)0.410843171f, 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(float16_t)-0.914209756f, + (float16_t)0.402434651f, (float16_t)-0.915448716f, + (float16_t)0.399624200f, (float16_t)-0.916679060f, + (float16_t)0.396809987f, (float16_t)-0.917900776f, + (float16_t)0.393992040f, (float16_t)-0.919113852f, + (float16_t)0.391170384f, (float16_t)-0.920318277f, + (float16_t)0.388345047f, (float16_t)-0.921514039f, + (float16_t)0.385516054f, (float16_t)-0.922701128f, + (float16_t)0.382683432f, (float16_t)-0.923879533f, + (float16_t)0.379847209f, (float16_t)-0.925049241f, + (float16_t)0.377007410f, (float16_t)-0.926210242f, + (float16_t)0.374164063f, (float16_t)-0.927362526f, + (float16_t)0.371317194f, (float16_t)-0.928506080f, + (float16_t)0.368466830f, (float16_t)-0.929640896f, + (float16_t)0.365612998f, (float16_t)-0.930766961f, + (float16_t)0.362755724f, (float16_t)-0.931884266f, + (float16_t)0.359895037f, (float16_t)-0.932992799f, + (float16_t)0.357030961f, (float16_t)-0.934092550f, + (float16_t)0.354163525f, (float16_t)-0.935183510f, + (float16_t)0.351292756f, (float16_t)-0.936265667f, + (float16_t)0.348418680f, (float16_t)-0.937339012f, + (float16_t)0.345541325f, (float16_t)-0.938403534f, + (float16_t)0.342660717f, (float16_t)-0.939459224f, + (float16_t)0.339776884f, (float16_t)-0.940506071f, + (float16_t)0.336889853f, (float16_t)-0.941544065f, + (float16_t)0.333999651f, (float16_t)-0.942573198f, + (float16_t)0.331106306f, (float16_t)-0.943593458f, + (float16_t)0.328209844f, (float16_t)-0.944604837f, + (float16_t)0.325310292f, (float16_t)-0.945607325f, + (float16_t)0.322407679f, (float16_t)-0.946600913f, + (float16_t)0.319502031f, (float16_t)-0.947585591f, + (float16_t)0.316593376f, (float16_t)-0.948561350f, + (float16_t)0.313681740f, (float16_t)-0.949528181f, + (float16_t)0.310767153f, (float16_t)-0.950486074f, + (float16_t)0.307849640f, (float16_t)-0.951435021f, + (float16_t)0.304929230f, (float16_t)-0.952375013f, + (float16_t)0.302005949f, (float16_t)-0.953306040f, + (float16_t)0.299079826f, (float16_t)-0.954228095f, + (float16_t)0.296150888f, (float16_t)-0.955141168f, + (float16_t)0.293219163f, (float16_t)-0.956045251f, + (float16_t)0.290284677f, (float16_t)-0.956940336f, + (float16_t)0.287347460f, (float16_t)-0.957826413f, + (float16_t)0.284407537f, (float16_t)-0.958703475f, + (float16_t)0.281464938f, (float16_t)-0.959571513f, + (float16_t)0.278519689f, (float16_t)-0.960430519f, + (float16_t)0.275571819f, (float16_t)-0.961280486f, + (float16_t)0.272621355f, (float16_t)-0.962121404f, + (float16_t)0.269668326f, (float16_t)-0.962953267f, + (float16_t)0.266712757f, (float16_t)-0.963776066f, + (float16_t)0.263754679f, (float16_t)-0.964589793f, + (float16_t)0.260794118f, (float16_t)-0.965394442f, + (float16_t)0.257831102f, (float16_t)-0.966190003f, + (float16_t)0.254865660f, (float16_t)-0.966976471f, + (float16_t)0.251897818f, (float16_t)-0.967753837f, + (float16_t)0.248927606f, (float16_t)-0.968522094f, + (float16_t)0.245955050f, (float16_t)-0.969281235f, + (float16_t)0.242980180f, (float16_t)-0.970031253f, + (float16_t)0.240003022f, (float16_t)-0.970772141f, + (float16_t)0.237023606f, (float16_t)-0.971503891f, + (float16_t)0.234041959f, (float16_t)-0.972226497f, + (float16_t)0.231058108f, (float16_t)-0.972939952f, + (float16_t)0.228072083f, (float16_t)-0.973644250f, + (float16_t)0.225083911f, (float16_t)-0.974339383f, + (float16_t)0.222093621f, (float16_t)-0.975025345f, + (float16_t)0.219101240f, (float16_t)-0.975702130f, + (float16_t)0.216106797f, (float16_t)-0.976369731f, + (float16_t)0.213110320f, (float16_t)-0.977028143f, + (float16_t)0.210111837f, (float16_t)-0.977677358f, + (float16_t)0.207111376f, (float16_t)-0.978317371f, + (float16_t)0.204108966f, (float16_t)-0.978948175f, + (float16_t)0.201104635f, (float16_t)-0.979569766f, + (float16_t)0.198098411f, (float16_t)-0.980182136f, + (float16_t)0.195090322f, (float16_t)-0.980785280f, + (float16_t)0.192080397f, (float16_t)-0.981379193f, + (float16_t)0.189068664f, (float16_t)-0.981963869f, + (float16_t)0.186055152f, (float16_t)-0.982539302f, + (float16_t)0.183039888f, (float16_t)-0.983105487f, + (float16_t)0.180022901f, (float16_t)-0.983662419f, + (float16_t)0.177004220f, (float16_t)-0.984210092f, + (float16_t)0.173983873f, (float16_t)-0.984748502f, + (float16_t)0.170961889f, (float16_t)-0.985277642f, + (float16_t)0.167938295f, (float16_t)-0.985797509f, + (float16_t)0.164913120f, (float16_t)-0.986308097f, + (float16_t)0.161886394f, (float16_t)-0.986809402f, + (float16_t)0.158858143f, (float16_t)-0.987301418f, + (float16_t)0.155828398f, (float16_t)-0.987784142f, + (float16_t)0.152797185f, (float16_t)-0.988257568f, + (float16_t)0.149764535f, (float16_t)-0.988721692f, + (float16_t)0.146730474f, (float16_t)-0.989176510f, + (float16_t)0.143695033f, (float16_t)-0.989622017f, + (float16_t)0.140658239f, (float16_t)-0.990058210f, + (float16_t)0.137620122f, (float16_t)-0.990485084f, + (float16_t)0.134580709f, (float16_t)-0.990902635f, + (float16_t)0.131540029f, (float16_t)-0.991310860f, + (float16_t)0.128498111f, (float16_t)-0.991709754f, + (float16_t)0.125454983f, (float16_t)-0.992099313f, + (float16_t)0.122410675f, (float16_t)-0.992479535f, + (float16_t)0.119365215f, (float16_t)-0.992850414f, + (float16_t)0.116318631f, (float16_t)-0.993211949f, + (float16_t)0.113270952f, (float16_t)-0.993564136f, + (float16_t)0.110222207f, (float16_t)-0.993906970f, + (float16_t)0.107172425f, (float16_t)-0.994240449f, + (float16_t)0.104121634f, (float16_t)-0.994564571f, + (float16_t)0.101069863f, (float16_t)-0.994879331f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.094963495f, (float16_t)-0.995480755f, + (float16_t)0.091908956f, (float16_t)-0.995767414f, + (float16_t)0.088853553f, (float16_t)-0.996044701f, + (float16_t)0.085797312f, (float16_t)-0.996312612f, + (float16_t)0.082740265f, (float16_t)-0.996571146f, + (float16_t)0.079682438f, (float16_t)-0.996820299f, + (float16_t)0.076623861f, (float16_t)-0.997060070f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.070504573f, (float16_t)-0.997511456f, + (float16_t)0.067443920f, (float16_t)-0.997723067f, + (float16_t)0.064382631f, (float16_t)-0.997925286f, + (float16_t)0.061320736f, (float16_t)-0.998118113f, + (float16_t)0.058258265f, (float16_t)-0.998301545f, + (float16_t)0.055195244f, (float16_t)-0.998475581f, + (float16_t)0.052131705f, (float16_t)-0.998640218f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.046003182f, (float16_t)-0.998941293f, + (float16_t)0.042938257f, (float16_t)-0.999077728f, + (float16_t)0.039872928f, (float16_t)-0.999204759f, + (float16_t)0.036807223f, (float16_t)-0.999322385f, + (float16_t)0.033741172f, (float16_t)-0.999430605f, + (float16_t)0.030674803f, (float16_t)-0.999529418f, + (float16_t)0.027608146f, (float16_t)-0.999618822f, + (float16_t)0.024541229f, (float16_t)-0.999698819f, + (float16_t)0.021474080f, (float16_t)-0.999769405f, + (float16_t)0.018406730f, (float16_t)-0.999830582f, + (float16_t)0.015339206f, (float16_t)-0.999882347f, + (float16_t)0.012271538f, (float16_t)-0.999924702f, + (float16_t)0.009203755f, (float16_t)-0.999957645f, + (float16_t)0.006135885f, (float16_t)-0.999981175f, + (float16_t)0.003067957f, (float16_t)-0.999995294f +}; + +const float16_t twiddleCoefF16_rfft_4096[4096] ARM_DSP_TABLE_ATTRIBUTE = { + (float16_t)0.000000000f, (float16_t)1.000000000f, + (float16_t)0.001533980f, (float16_t)0.999998823f, + (float16_t)0.003067957f, (float16_t)0.999995294f, + (float16_t)0.004601926f, (float16_t)0.999989411f, + (float16_t)0.006135885f, (float16_t)0.999981175f, + (float16_t)0.007669829f, (float16_t)0.999970586f, + (float16_t)0.009203755f, (float16_t)0.999957645f, + (float16_t)0.010737659f, (float16_t)0.999942350f, + (float16_t)0.012271538f, (float16_t)0.999924702f, + (float16_t)0.013805389f, (float16_t)0.999904701f, + (float16_t)0.015339206f, (float16_t)0.999882347f, + (float16_t)0.016872988f, (float16_t)0.999857641f, + (float16_t)0.018406730f, (float16_t)0.999830582f, + (float16_t)0.019940429f, (float16_t)0.999801170f, + (float16_t)0.021474080f, (float16_t)0.999769405f, + (float16_t)0.023007681f, (float16_t)0.999735288f, + (float16_t)0.024541229f, (float16_t)0.999698819f, + (float16_t)0.026074718f, (float16_t)0.999659997f, + (float16_t)0.027608146f, (float16_t)0.999618822f, + (float16_t)0.029141509f, (float16_t)0.999575296f, + (float16_t)0.030674803f, (float16_t)0.999529418f, + (float16_t)0.032208025f, (float16_t)0.999481187f, + (float16_t)0.033741172f, (float16_t)0.999430605f, + (float16_t)0.035274239f, (float16_t)0.999377670f, + (float16_t)0.036807223f, (float16_t)0.999322385f, + (float16_t)0.038340120f, (float16_t)0.999264747f, + (float16_t)0.039872928f, (float16_t)0.999204759f, + (float16_t)0.041405641f, (float16_t)0.999142419f, + (float16_t)0.042938257f, (float16_t)0.999077728f, + (float16_t)0.044470772f, (float16_t)0.999010686f, + (float16_t)0.046003182f, (float16_t)0.998941293f, + (float16_t)0.047535484f, (float16_t)0.998869550f, + (float16_t)0.049067674f, (float16_t)0.998795456f, + (float16_t)0.050599749f, (float16_t)0.998719012f, + (float16_t)0.052131705f, (float16_t)0.998640218f, + (float16_t)0.053663538f, (float16_t)0.998559074f, + (float16_t)0.055195244f, (float16_t)0.998475581f, + (float16_t)0.056726821f, (float16_t)0.998389737f, + (float16_t)0.058258265f, (float16_t)0.998301545f, + (float16_t)0.059789571f, (float16_t)0.998211003f, + (float16_t)0.061320736f, (float16_t)0.998118113f, + (float16_t)0.062851758f, (float16_t)0.998022874f, + (float16_t)0.064382631f, (float16_t)0.997925286f, + (float16_t)0.065913353f, (float16_t)0.997825350f, + (float16_t)0.067443920f, (float16_t)0.997723067f, + (float16_t)0.068974328f, (float16_t)0.997618435f, + (float16_t)0.070504573f, (float16_t)0.997511456f, + (float16_t)0.072034653f, (float16_t)0.997402130f, + (float16_t)0.073564564f, (float16_t)0.997290457f, + (float16_t)0.075094301f, (float16_t)0.997176437f, + (float16_t)0.076623861f, (float16_t)0.997060070f, + (float16_t)0.078153242f, (float16_t)0.996941358f, + (float16_t)0.079682438f, (float16_t)0.996820299f, + (float16_t)0.081211447f, (float16_t)0.996696895f, + (float16_t)0.082740265f, (float16_t)0.996571146f, + (float16_t)0.084268888f, (float16_t)0.996443051f, + (float16_t)0.085797312f, (float16_t)0.996312612f, + (float16_t)0.087325535f, (float16_t)0.996179829f, + (float16_t)0.088853553f, (float16_t)0.996044701f, + (float16_t)0.090381361f, (float16_t)0.995907229f, + (float16_t)0.091908956f, (float16_t)0.995767414f, + (float16_t)0.093436336f, (float16_t)0.995625256f, + (float16_t)0.094963495f, (float16_t)0.995480755f, + (float16_t)0.096490431f, (float16_t)0.995333912f, + (float16_t)0.098017140f, (float16_t)0.995184727f, + (float16_t)0.099543619f, (float16_t)0.995033199f, + (float16_t)0.101069863f, (float16_t)0.994879331f, + (float16_t)0.102595869f, (float16_t)0.994723121f, + (float16_t)0.104121634f, 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(float16_t)0.102595869f, (float16_t)-0.994723121f, + (float16_t)0.101069863f, (float16_t)-0.994879331f, + (float16_t)0.099543619f, (float16_t)-0.995033199f, + (float16_t)0.098017140f, (float16_t)-0.995184727f, + (float16_t)0.096490431f, (float16_t)-0.995333912f, + (float16_t)0.094963495f, (float16_t)-0.995480755f, + (float16_t)0.093436336f, (float16_t)-0.995625256f, + (float16_t)0.091908956f, (float16_t)-0.995767414f, + (float16_t)0.090381361f, (float16_t)-0.995907229f, + (float16_t)0.088853553f, (float16_t)-0.996044701f, + (float16_t)0.087325535f, (float16_t)-0.996179829f, + (float16_t)0.085797312f, (float16_t)-0.996312612f, + (float16_t)0.084268888f, (float16_t)-0.996443051f, + (float16_t)0.082740265f, (float16_t)-0.996571146f, + (float16_t)0.081211447f, (float16_t)-0.996696895f, + (float16_t)0.079682438f, (float16_t)-0.996820299f, + (float16_t)0.078153242f, (float16_t)-0.996941358f, + (float16_t)0.076623861f, (float16_t)-0.997060070f, + (float16_t)0.075094301f, (float16_t)-0.997176437f, + (float16_t)0.073564564f, (float16_t)-0.997290457f, + (float16_t)0.072034653f, (float16_t)-0.997402130f, + (float16_t)0.070504573f, (float16_t)-0.997511456f, + (float16_t)0.068974328f, (float16_t)-0.997618435f, + (float16_t)0.067443920f, (float16_t)-0.997723067f, + (float16_t)0.065913353f, (float16_t)-0.997825350f, + (float16_t)0.064382631f, (float16_t)-0.997925286f, + (float16_t)0.062851758f, (float16_t)-0.998022874f, + (float16_t)0.061320736f, (float16_t)-0.998118113f, + (float16_t)0.059789571f, (float16_t)-0.998211003f, + (float16_t)0.058258265f, (float16_t)-0.998301545f, + (float16_t)0.056726821f, (float16_t)-0.998389737f, + (float16_t)0.055195244f, (float16_t)-0.998475581f, + (float16_t)0.053663538f, (float16_t)-0.998559074f, + (float16_t)0.052131705f, (float16_t)-0.998640218f, + (float16_t)0.050599749f, (float16_t)-0.998719012f, + (float16_t)0.049067674f, (float16_t)-0.998795456f, + (float16_t)0.047535484f, (float16_t)-0.998869550f, + (float16_t)0.046003182f, (float16_t)-0.998941293f, + (float16_t)0.044470772f, (float16_t)-0.999010686f, + (float16_t)0.042938257f, (float16_t)-0.999077728f, + (float16_t)0.041405641f, (float16_t)-0.999142419f, + (float16_t)0.039872928f, (float16_t)-0.999204759f, + (float16_t)0.038340120f, (float16_t)-0.999264747f, + (float16_t)0.036807223f, (float16_t)-0.999322385f, + (float16_t)0.035274239f, (float16_t)-0.999377670f, + (float16_t)0.033741172f, (float16_t)-0.999430605f, + (float16_t)0.032208025f, (float16_t)-0.999481187f, + (float16_t)0.030674803f, (float16_t)-0.999529418f, + (float16_t)0.029141509f, (float16_t)-0.999575296f, + (float16_t)0.027608146f, (float16_t)-0.999618822f, + (float16_t)0.026074718f, (float16_t)-0.999659997f, + (float16_t)0.024541229f, (float16_t)-0.999698819f, + (float16_t)0.023007681f, (float16_t)-0.999735288f, + (float16_t)0.021474080f, (float16_t)-0.999769405f, + (float16_t)0.019940429f, (float16_t)-0.999801170f, + (float16_t)0.018406730f, (float16_t)-0.999830582f, + (float16_t)0.016872988f, (float16_t)-0.999857641f, + (float16_t)0.015339206f, (float16_t)-0.999882347f, + (float16_t)0.013805389f, (float16_t)-0.999904701f, + (float16_t)0.012271538f, (float16_t)-0.999924702f, + (float16_t)0.010737659f, (float16_t)-0.999942350f, + (float16_t)0.009203755f, (float16_t)-0.999957645f, + (float16_t)0.007669829f, (float16_t)-0.999970586f, + (float16_t)0.006135885f, (float16_t)-0.999981175f, + (float16_t)0.004601926f, (float16_t)-0.999989411f, + (float16_t)0.003067957f, (float16_t)-0.999995294f, + (float16_t)0.001533980f, (float16_t)-0.999998823f +}; + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + +const float16_t exp_tab_f16[8] ARM_DSP_TABLE_ATTRIBUTE = { + (1.f16), + (0.0416598916054f16), + (0.500000596046f16), + (0.00138889f16), + (1.00000011921f16), + (0.00833693705499f16), + (0.166665703058f16), + (0.000195780929062f16), +}; + +const float16_t __logf_lut_f16[8] ARM_DSP_TABLE_ATTRIBUTE = { + -2.295614848256274f16, /*p0*/ + -2.470711633419806f16, /*p4*/ + -5.686926051100417f16, /*p2*/ + -0.165253547131978f16, /*p6*/ + +5.175912446351073f16, /*p1*/ + +0.844006986174912f16, /*p5*/ + +4.584458825456749f16, /*p3*/ + +0.014127821926000f16 /*p7*/ +}; + +#endif + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ + +#endif /* Not ARM AC5 */ + + +/** + @} end of CFFT_CIFFT group +*/ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_const_structs.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_const_structs.c new file mode 100755 index 0000000..b642a45 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_const_structs.c @@ -0,0 +1,519 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_const_structs.c + * Description: Constant structs that are initialized for user convenience. + * For example, some can be given as arguments to the arm_cfft_f32() or arm_rfft_f32() functions. + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include "arm_compiler_specific.h" +#include "arm_math_types.h" +#include "arm_const_structs.h" + +/* +ALLOW TABLE is true when config table is enabled and the Tramsform folder is included +for compilation. +*/ + +/* Floating-point structs */ +const arm_cfft_instance_f64 arm_cfft_sR_f64_len16 ARM_DSP_TABLE_ATTRIBUTE = { + 16, (const float64_t *)twiddleCoefF64_16, armBitRevIndexTableF64_16, ARMBITREVINDEXTABLEF64_16_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32, (const float64_t *)twiddleCoefF64_32, armBitRevIndexTableF64_32, ARMBITREVINDEXTABLEF64_32_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64, (const float64_t *)twiddleCoefF64_64, armBitRevIndexTableF64_64, ARMBITREVINDEXTABLEF64_64_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128, (const float64_t *)twiddleCoefF64_128, armBitRevIndexTableF64_128, ARMBITREVINDEXTABLEF64_128_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256, (const float64_t *)twiddleCoefF64_256, armBitRevIndexTableF64_256, ARMBITREVINDEXTABLEF64_256_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512, (const float64_t *)twiddleCoefF64_512, armBitRevIndexTableF64_512, ARMBITREVINDEXTABLEF64_512_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024, (const float64_t *)twiddleCoefF64_1024, armBitRevIndexTableF64_1024, ARMBITREVINDEXTABLEF64_1024_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048, (const float64_t *)twiddleCoefF64_2048, armBitRevIndexTableF64_2048, ARMBITREVINDEXTABLEF64_2048_TABLE_LENGTH +}; + +const arm_cfft_instance_f64 arm_cfft_sR_f64_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096, (const float64_t *)twiddleCoefF64_4096, armBitRevIndexTableF64_4096, ARMBITREVINDEXTABLEF64_4096_TABLE_LENGTH +}; + +/* Floating-point structs */ +#if (!defined(ARM_MATH_MVEF) || defined(ARM_MATH_AUTOVECTORIZE)) && !defined(ARM_MATH_NEON) + + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len16 ARM_DSP_TABLE_ATTRIBUTE = { + 16, twiddleCoef_16, armBitRevIndexTable16, ARMBITREVINDEXTABLE_16_TABLE_LENGTH +}; + + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32, twiddleCoef_32, armBitRevIndexTable32, ARMBITREVINDEXTABLE_32_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64, twiddleCoef_64, armBitRevIndexTable64, ARMBITREVINDEXTABLE_64_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128, twiddleCoef_128, armBitRevIndexTable128, ARMBITREVINDEXTABLE_128_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256, twiddleCoef_256, armBitRevIndexTable256, ARMBITREVINDEXTABLE_256_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512, twiddleCoef_512, armBitRevIndexTable512, ARMBITREVINDEXTABLE_512_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024, twiddleCoef_1024, armBitRevIndexTable1024, ARMBITREVINDEXTABLE_1024_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048, twiddleCoef_2048, armBitRevIndexTable2048, ARMBITREVINDEXTABLE_2048_TABLE_LENGTH +}; + +const arm_cfft_instance_f32 arm_cfft_sR_f32_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096, twiddleCoef_4096, armBitRevIndexTable4096, ARMBITREVINDEXTABLE_4096_TABLE_LENGTH +}; + +#endif /* !defined(ARM_MATH_MVEF) || defined(ARM_MATH_AUTOVECTORIZE) */ + +/* Fixed-point structs */ + +#if (!defined(ARM_MATH_MVEI) || defined(ARM_MATH_AUTOVECTORIZE)) && !defined(ARM_MATH_NEON) + +/* + +Those structures cannot be used to initialize the MVE version of the FFT Q31 instances. +So they are not compiled when MVE is defined. + +For the MVE version, the new arm_cfft_init_f32 must be used. + + +*/ + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len16 ARM_DSP_TABLE_ATTRIBUTE = { + 16, twiddleCoef_16_q31, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32, twiddleCoef_32_q31, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64, twiddleCoef_64_q31, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128, twiddleCoef_128_q31, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256, twiddleCoef_256_q31, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512, twiddleCoef_512_q31, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024, twiddleCoef_1024_q31, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048, twiddleCoef_2048_q31, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH +}; + +const arm_cfft_instance_q31 arm_cfft_sR_q31_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096, twiddleCoef_4096_q31, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH +}; +#endif + +#if (!defined(ARM_MATH_MVEI) || defined(ARM_MATH_AUTOVECTORIZE)) && !defined(ARM_MATH_NEON) + + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len16 ARM_DSP_TABLE_ATTRIBUTE = { + 16, twiddleCoef_16_q15, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32, twiddleCoef_32_q15, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64, twiddleCoef_64_q15, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128, twiddleCoef_128_q15, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256, twiddleCoef_256_q15, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512, twiddleCoef_512_q15, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024, twiddleCoef_1024_q15, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048, twiddleCoef_2048_q15, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH +}; + +const arm_cfft_instance_q15 arm_cfft_sR_q15_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096, twiddleCoef_4096_q15, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH +}; + +#endif /* !defined(ARM_MATH_MVEI) */ + +/* Structure for real-value inputs */ +/* Double precision strucs */ + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len32 ARM_DSP_TABLE_ATTRIBUTE = { + { 16, (const float64_t *)twiddleCoefF64_16, armBitRevIndexTableF64_16, ARMBITREVINDEXTABLEF64_16_TABLE_LENGTH }, + 32U, + (float64_t *)twiddleCoefF64_rfft_32 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len64 ARM_DSP_TABLE_ATTRIBUTE = { + { 32, (const float64_t *)twiddleCoefF64_32, armBitRevIndexTableF64_32, ARMBITREVINDEXTABLEF64_32_TABLE_LENGTH }, + 64U, + (float64_t *)twiddleCoefF64_rfft_64 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len128 ARM_DSP_TABLE_ATTRIBUTE = { + { 64, (const float64_t *)twiddleCoefF64_64, armBitRevIndexTableF64_64, ARMBITREVINDEXTABLEF64_64_TABLE_LENGTH }, + 128U, + (float64_t *)twiddleCoefF64_rfft_128 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len256 ARM_DSP_TABLE_ATTRIBUTE = { + { 128, (const float64_t *)twiddleCoefF64_128, armBitRevIndexTableF64_128, ARMBITREVINDEXTABLEF64_128_TABLE_LENGTH }, + 256U, + (float64_t *)twiddleCoefF64_rfft_256 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len512 ARM_DSP_TABLE_ATTRIBUTE = { + { 256, (const float64_t *)twiddleCoefF64_256, armBitRevIndexTableF64_256, ARMBITREVINDEXTABLEF64_256_TABLE_LENGTH }, + 512U, + (float64_t *)twiddleCoefF64_rfft_512 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + { 512, (const float64_t *)twiddleCoefF64_512, armBitRevIndexTableF64_512, ARMBITREVINDEXTABLEF64_512_TABLE_LENGTH }, + 1024U, + (float64_t *)twiddleCoefF64_rfft_1024 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + { 1024, (const float64_t *)twiddleCoefF64_1024, armBitRevIndexTableF64_1024, ARMBITREVINDEXTABLEF64_1024_TABLE_LENGTH }, + 2048U, + (float64_t *)twiddleCoefF64_rfft_2048 +}; + +const arm_rfft_fast_instance_f64 arm_rfft_fast_sR_f64_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + { 2048, (const float64_t *)twiddleCoefF64_2048, armBitRevIndexTableF64_2048, ARMBITREVINDEXTABLEF64_2048_TABLE_LENGTH }, + 4096U, + (float64_t *)twiddleCoefF64_rfft_4096 +}; + +/* Floating-point structs */ + +#if (!defined(ARM_MATH_MVEF) || defined(ARM_MATH_AUTOVECTORIZE)) && !defined(ARM_MATH_NEON) + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len32 ARM_DSP_TABLE_ATTRIBUTE = { + { 16, twiddleCoef_16, armBitRevIndexTable16, ARMBITREVINDEXTABLE_16_TABLE_LENGTH }, + 32U, + (float32_t *)twiddleCoef_rfft_32 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len64 ARM_DSP_TABLE_ATTRIBUTE = { + { 32, twiddleCoef_32, armBitRevIndexTable32, ARMBITREVINDEXTABLE_32_TABLE_LENGTH }, + 64U, + (float32_t *)twiddleCoef_rfft_64 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len128 ARM_DSP_TABLE_ATTRIBUTE = { + { 64, twiddleCoef_64, armBitRevIndexTable64, ARMBITREVINDEXTABLE_64_TABLE_LENGTH }, + 128U, + (float32_t *)twiddleCoef_rfft_128 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len256 ARM_DSP_TABLE_ATTRIBUTE = { + { 128, twiddleCoef_128, armBitRevIndexTable128, ARMBITREVINDEXTABLE_128_TABLE_LENGTH }, + 256U, + (float32_t *)twiddleCoef_rfft_256 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len512 ARM_DSP_TABLE_ATTRIBUTE = { + { 256, twiddleCoef_256, armBitRevIndexTable256, ARMBITREVINDEXTABLE_256_TABLE_LENGTH }, + 512U, + (float32_t *)twiddleCoef_rfft_512 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + { 512, twiddleCoef_512, armBitRevIndexTable512, ARMBITREVINDEXTABLE_512_TABLE_LENGTH }, + 1024U, + (float32_t *)twiddleCoef_rfft_1024 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + { 1024, twiddleCoef_1024, armBitRevIndexTable1024, ARMBITREVINDEXTABLE_1024_TABLE_LENGTH }, + 2048U, + (float32_t *)twiddleCoef_rfft_2048 +}; + +const arm_rfft_fast_instance_f32 arm_rfft_fast_sR_f32_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + { 2048, twiddleCoef_2048, armBitRevIndexTable2048, ARMBITREVINDEXTABLE_2048_TABLE_LENGTH }, + 4096U, + (float32_t *)twiddleCoef_rfft_4096 +}; + +#endif /* #if !defined(ARM_MATH_MVEF) || defined(ARM_MATH_AUTOVECTORIZE) */ + +/* Fixed-point structs */ +/* q31_t */ + +#if (!defined(ARM_MATH_MVEI) || defined(ARM_MATH_AUTOVECTORIZE)) && !defined(ARM_MATH_NEON) + +/* + +Those structures cannot be used to initialize the MVE version of the FFT Q31 instances. +So they are not compiled when MVE is defined. + +For the MVE version, the new arm_cfft_init_f32 must be used. + + +*/ + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32U, + 0, + 1, + 256U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len16 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64U, + 0, + 1, + 128U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len32 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128U, + 0, + 1, + 64U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len64 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256U, + 0, + 1, + 32U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len128 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512U, + 0, + 1, + 16U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len256 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024U, + 0, + 1, + 8U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len512 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048U, + 0, + 1, + 4U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len1024 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096U, + 0, + 1, + 2U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len2048 +}; + +const arm_rfft_instance_q31 arm_rfft_sR_q31_len8192 ARM_DSP_TABLE_ATTRIBUTE = { + 8192U, + 0, + 1, + 1U, + (q31_t*)realCoefAQ31, + (q31_t*)realCoefBQ31, + &arm_cfft_sR_q31_len4096 +}; + +#endif + +#if (!defined(ARM_MATH_MVEI) || defined(ARM_MATH_AUTOVECTORIZE)) && !defined(ARM_MATH_NEON) + + +/* q15_t */ +const arm_rfft_instance_q15 arm_rfft_sR_q15_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32U, + 0, + 1, + 256U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len16 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64U, + 0, + 1, + 128U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len32 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128U, + 0, + 1, + 64U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len64 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256U, + 0, + 1, + 32U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len128 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512U, + 0, + 1, + 16U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len256 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024U, + 0, + 1, + 8U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len512 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048U, + 0, + 1, + 4U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len1024 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096U, + 0, + 1, + 2U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len2048 +}; + +const arm_rfft_instance_q15 arm_rfft_sR_q15_len8192 ARM_DSP_TABLE_ATTRIBUTE = { + 8192U, + 0, + 1, + 1U, + (q15_t*)realCoefAQ15, + (q15_t*)realCoefBQ15, + &arm_cfft_sR_q15_len4096 +}; + +#endif /* !defined(ARM_MATH_MVEI) */ + + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_const_structs_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_const_structs_f16.c new file mode 100755 index 0000000..8749e7c --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_const_structs_f16.c @@ -0,0 +1,100 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_const_structs_f16.c + * Description: Constant structs that are initialized for user convenience. + * For example, some can be given as arguments to the arm_cfft_f32() or arm_rfft_f32() functions. + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "arm_math_types_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +#include "arm_const_structs_f16.h" + + + + +/* Floating-point structs */ +#if !defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_NEON_FLOAT16) + + +/* + +Those structures cannot be used to initialize the MVE version of the FFT F32 instances. +So they are not compiled when MVE is defined. + +For the MVE version, the new arm_cfft_init_f16 must be used. + + +*/ + +#if !defined(__CC_ARM) + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len16 ARM_DSP_TABLE_ATTRIBUTE = { + 16, twiddleCoefF16_16, armBitRevIndexTable_fixed_16, ARMBITREVINDEXTABLE_FIXED_16_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len32 ARM_DSP_TABLE_ATTRIBUTE = { + 32, twiddleCoefF16_32, armBitRevIndexTable_fixed_32, ARMBITREVINDEXTABLE_FIXED_32_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len64 ARM_DSP_TABLE_ATTRIBUTE = { + 64, twiddleCoefF16_64, armBitRevIndexTable_fixed_64, ARMBITREVINDEXTABLE_FIXED_64_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len128 ARM_DSP_TABLE_ATTRIBUTE = { + 128, twiddleCoefF16_128, armBitRevIndexTable_fixed_128, ARMBITREVINDEXTABLE_FIXED_128_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len256 ARM_DSP_TABLE_ATTRIBUTE = { + 256, twiddleCoefF16_256, armBitRevIndexTable_fixed_256, ARMBITREVINDEXTABLE_FIXED_256_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len512 ARM_DSP_TABLE_ATTRIBUTE = { + 512, twiddleCoefF16_512, armBitRevIndexTable_fixed_512, ARMBITREVINDEXTABLE_FIXED_512_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len1024 ARM_DSP_TABLE_ATTRIBUTE = { + 1024, twiddleCoefF16_1024, armBitRevIndexTable_fixed_1024, ARMBITREVINDEXTABLE_FIXED_1024_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len2048 ARM_DSP_TABLE_ATTRIBUTE = { + 2048, twiddleCoefF16_2048, armBitRevIndexTable_fixed_2048, ARMBITREVINDEXTABLE_FIXED_2048_TABLE_LENGTH +}; + +const arm_cfft_instance_f16 arm_cfft_sR_f16_len4096 ARM_DSP_TABLE_ATTRIBUTE = { + 4096, twiddleCoefF16_4096, armBitRevIndexTable_fixed_4096, ARMBITREVINDEXTABLE_FIXED_4096_TABLE_LENGTH +}; + + + +#endif + +#endif + +#endif diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_mve_tables.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_mve_tables.c new file mode 100755 index 0000000..c69f68e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_mve_tables.c @@ -0,0 +1,6484 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mve_tables.c + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for MVE implementation only + * + * @version V1.10.0 + * @date 04 October 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + #include "arm_compiler_specific.h" + + #include "arm_math_types.h" + + + + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + + + +const uint32_t rearranged_twiddle_tab_stride1_arr_16_f32[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_16_f32[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_16_f32[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const float32_t rearranged_twiddle_stride1_16_f32[8] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.92387950420379638672f, +0.38268342614173889160f,0.70710676908493041992f,0.70710676908493041992f, +0.38268342614173889160f,0.92387950420379638672f,}; + +const float32_t rearranged_twiddle_stride2_16_f32[8] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.70710676908493041992f, +0.70710676908493041992f,0.00000000000000006123f,1.00000000000000000000f, +-0.70710676908493041992f,0.70710676908493041992f,}; + +const float32_t rearranged_twiddle_stride3_16_f32[8] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.38268342614173889160f, +0.92387950420379638672f,-0.70710676908493041992f,0.70710676908493041992f, +-0.92387950420379638672f,-0.38268342614173889160f,}; + + + +const uint32_t rearranged_twiddle_tab_stride1_arr_64_f32[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_64_f32[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_64_f32[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const float32_t rearranged_twiddle_stride1_64_f32[40] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.99518471956253051758f, +0.09801714122295379639f,0.98078525066375732422f,0.19509032368659973145f, +0.95694035291671752930f,0.29028466343879699707f,0.92387950420379638672f, +0.38268342614173889160f,0.88192129135131835938f,0.47139674425125122070f, +0.83146959543228149414f,0.55557024478912353516f,0.77301043272018432617f, +0.63439327478408813477f,0.70710676908493041992f,0.70710676908493041992f, +0.63439327478408813477f,0.77301043272018432617f,0.55557024478912353516f, +0.83146959543228149414f,0.47139674425125122070f,0.88192129135131835938f, +0.38268342614173889160f,0.92387950420379638672f,0.29028466343879699707f, +0.95694035291671752930f,0.19509032368659973145f,0.98078525066375732422f, +0.09801714122295379639f,0.99518471956253051758f,1.00000000000000000000f, +0.00000000000000000000f,0.92387950420379638672f,0.38268342614173889160f, +0.70710676908493041992f,0.70710676908493041992f,0.38268342614173889160f, +0.92387950420379638672f,}; + +const float32_t rearranged_twiddle_stride2_64_f32[40] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.98078525066375732422f, +0.19509032368659973145f,0.92387950420379638672f,0.38268342614173889160f, +0.83146959543228149414f,0.55557024478912353516f,0.70710676908493041992f, +0.70710676908493041992f,0.55557024478912353516f,0.83146959543228149414f, +0.38268342614173889160f,0.92387950420379638672f,0.19509032368659973145f, +0.98078525066375732422f,0.00000000000000006123f,1.00000000000000000000f, +-0.19509032368659973145f,0.98078525066375732422f,-0.38268342614173889160f, +0.92387950420379638672f,-0.55557024478912353516f,0.83146959543228149414f, +-0.70710676908493041992f,0.70710676908493041992f,-0.83146959543228149414f, +0.55557024478912353516f,-0.92387950420379638672f,0.38268342614173889160f, +-0.98078525066375732422f,0.19509032368659973145f,1.00000000000000000000f, +0.00000000000000000000f,0.70710676908493041992f,0.70710676908493041992f, +0.00000000000000006123f,1.00000000000000000000f,-0.70710676908493041992f, +0.70710676908493041992f,}; + +const float32_t rearranged_twiddle_stride3_64_f32[40] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.95694035291671752930f, +0.29028466343879699707f,0.83146959543228149414f,0.55557024478912353516f, +0.63439327478408813477f,0.77301043272018432617f,0.38268342614173889160f, +0.92387950420379638672f,0.09801714122295379639f,0.99518471956253051758f, +-0.19509032368659973145f,0.98078525066375732422f,-0.47139674425125122070f, +0.88192129135131835938f,-0.70710676908493041992f,0.70710676908493041992f, +-0.88192129135131835938f,0.47139674425125122070f,-0.98078525066375732422f, +0.19509032368659973145f,-0.99518471956253051758f,-0.09801714122295379639f, +-0.92387950420379638672f,-0.38268342614173889160f,-0.77301043272018432617f, +-0.63439327478408813477f,-0.55557024478912353516f,-0.83146959543228149414f, +-0.29028466343879699707f,-0.95694035291671752930f,1.00000000000000000000f, +0.00000000000000000000f,0.38268342614173889160f,0.92387950420379638672f, +-0.70710676908493041992f,0.70710676908493041992f,-0.92387950420379638672f, +-0.38268342614173889160f,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_256_f32[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_256_f32[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_256_f32[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const float32_t rearranged_twiddle_stride1_256_f32[168] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.99969881772994995117f, +0.02454122900962829590f,0.99879544973373413086f,0.04906767606735229492f, +0.99729043245315551758f,0.07356456667184829712f,0.99518471956253051758f, +0.09801714122295379639f,0.99247956275939941406f,0.12241067737340927124f, +0.98917651176452636719f,0.14673046767711639404f,0.98527765274047851562f, +0.17096188664436340332f,0.98078525066375732422f,0.19509032368659973145f, +0.97570210695266723633f,0.21910123527050018311f,0.97003126144409179688f, +0.24298018217086791992f,0.96377605199813842773f,0.26671275496482849121f, +0.95694035291671752930f,0.29028466343879699707f,0.94952815771102905273f, +0.31368175148963928223f,0.94154405593872070312f,0.33688986301422119141f, +0.93299281597137451172f,0.35989505052566528320f,0.92387950420379638672f, +0.38268342614173889160f,0.91420978307723999023f,0.40524131059646606445f, +0.90398931503295898438f,0.42755508422851562500f,0.89322429895401000977f, +0.44961133599281311035f,0.88192129135131835938f,0.47139674425125122070f, +0.87008696794509887695f,0.49289819598197937012f,0.85772860050201416016f, +0.51410275697708129883f,0.84485357999801635742f,0.53499764204025268555f, +0.83146959543228149414f,0.55557024478912353516f,0.81758481264114379883f, +0.57580816745758056641f,0.80320751667022705078f,0.59569931030273437500f, +0.78834640979766845703f,0.61523157358169555664f,0.77301043272018432617f, +0.63439327478408813477f,0.75720882415771484375f,0.65317285060882568359f, +0.74095112085342407227f,0.67155897617340087891f,0.72424709796905517578f, +0.68954056501388549805f,0.70710676908493041992f,0.70710676908493041992f, +0.68954056501388549805f,0.72424709796905517578f,0.67155897617340087891f, +0.74095112085342407227f,0.65317285060882568359f,0.75720882415771484375f, +0.63439327478408813477f,0.77301043272018432617f,0.61523157358169555664f, +0.78834640979766845703f,0.59569931030273437500f,0.80320751667022705078f, +0.57580816745758056641f,0.81758481264114379883f,0.55557024478912353516f, +0.83146959543228149414f,0.53499764204025268555f,0.84485357999801635742f, +0.51410275697708129883f,0.85772860050201416016f,0.49289819598197937012f, +0.87008696794509887695f,0.47139674425125122070f,0.88192129135131835938f, +0.44961133599281311035f,0.89322429895401000977f,0.42755508422851562500f, +0.90398931503295898438f,0.40524131059646606445f,0.91420978307723999023f, +0.38268342614173889160f,0.92387950420379638672f,0.35989505052566528320f, +0.93299281597137451172f,0.33688986301422119141f,0.94154405593872070312f, +0.31368175148963928223f,0.94952815771102905273f,0.29028466343879699707f, +0.95694035291671752930f,0.26671275496482849121f,0.96377605199813842773f, +0.24298018217086791992f,0.97003126144409179688f,0.21910123527050018311f, +0.97570210695266723633f,0.19509032368659973145f,0.98078525066375732422f, +0.17096188664436340332f,0.98527765274047851562f,0.14673046767711639404f, +0.98917651176452636719f,0.12241067737340927124f,0.99247956275939941406f, +0.09801714122295379639f,0.99518471956253051758f,0.07356456667184829712f, +0.99729043245315551758f,0.04906767606735229492f,0.99879544973373413086f, +0.02454122900962829590f,0.99969881772994995117f,1.00000000000000000000f, +0.00000000000000000000f,0.99518471956253051758f,0.09801714122295379639f, +0.98078525066375732422f,0.19509032368659973145f,0.95694035291671752930f, +0.29028466343879699707f,0.92387950420379638672f,0.38268342614173889160f, +0.88192129135131835938f,0.47139674425125122070f,0.83146959543228149414f, +0.55557024478912353516f,0.77301043272018432617f,0.63439327478408813477f, +0.70710676908493041992f,0.70710676908493041992f,0.63439327478408813477f, +0.77301043272018432617f,0.55557024478912353516f,0.83146959543228149414f, +0.47139674425125122070f,0.88192129135131835938f,0.38268342614173889160f, +0.92387950420379638672f,0.29028466343879699707f,0.95694035291671752930f, +0.19509032368659973145f,0.98078525066375732422f,0.09801714122295379639f, +0.99518471956253051758f,1.00000000000000000000f,0.00000000000000000000f, +0.92387950420379638672f,0.38268342614173889160f,0.70710676908493041992f, +0.70710676908493041992f,0.38268342614173889160f,0.92387950420379638672f,}; + +const float32_t rearranged_twiddle_stride2_256_f32[168] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.99879544973373413086f, +0.04906767606735229492f,0.99518471956253051758f,0.09801714122295379639f, +0.98917651176452636719f,0.14673046767711639404f,0.98078525066375732422f, +0.19509032368659973145f,0.97003126144409179688f,0.24298018217086791992f, +0.95694035291671752930f,0.29028466343879699707f,0.94154405593872070312f, +0.33688986301422119141f,0.92387950420379638672f,0.38268342614173889160f, +0.90398931503295898438f,0.42755508422851562500f,0.88192129135131835938f, +0.47139674425125122070f,0.85772860050201416016f,0.51410275697708129883f, +0.83146959543228149414f,0.55557024478912353516f,0.80320751667022705078f, +0.59569931030273437500f,0.77301043272018432617f,0.63439327478408813477f, +0.74095112085342407227f,0.67155897617340087891f,0.70710676908493041992f, +0.70710676908493041992f,0.67155897617340087891f,0.74095112085342407227f, +0.63439327478408813477f,0.77301043272018432617f,0.59569931030273437500f, +0.80320751667022705078f,0.55557024478912353516f,0.83146959543228149414f, +0.51410275697708129883f,0.85772860050201416016f,0.47139674425125122070f, +0.88192129135131835938f,0.42755508422851562500f,0.90398931503295898438f, +0.38268342614173889160f,0.92387950420379638672f,0.33688986301422119141f, +0.94154405593872070312f,0.29028466343879699707f,0.95694035291671752930f, +0.24298018217086791992f,0.97003126144409179688f,0.19509032368659973145f, +0.98078525066375732422f,0.14673046767711639404f,0.98917651176452636719f, +0.09801714122295379639f,0.99518471956253051758f,0.04906767606735229492f, +0.99879544973373413086f,0.00000000000000006123f,1.00000000000000000000f, +-0.04906767606735229492f,0.99879544973373413086f,-0.09801714122295379639f, +0.99518471956253051758f,-0.14673046767711639404f,0.98917651176452636719f, +-0.19509032368659973145f,0.98078525066375732422f,-0.24298018217086791992f, +0.97003126144409179688f,-0.29028466343879699707f,0.95694035291671752930f, +-0.33688986301422119141f,0.94154405593872070312f,-0.38268342614173889160f, +0.92387950420379638672f,-0.42755508422851562500f,0.90398931503295898438f, +-0.47139674425125122070f,0.88192129135131835938f,-0.51410275697708129883f, +0.85772860050201416016f,-0.55557024478912353516f,0.83146959543228149414f, +-0.59569931030273437500f,0.80320751667022705078f,-0.63439327478408813477f, +0.77301043272018432617f,-0.67155897617340087891f,0.74095112085342407227f, +-0.70710676908493041992f,0.70710676908493041992f,-0.74095112085342407227f, +0.67155897617340087891f,-0.77301043272018432617f,0.63439327478408813477f, +-0.80320751667022705078f,0.59569931030273437500f,-0.83146959543228149414f, +0.55557024478912353516f,-0.85772860050201416016f,0.51410275697708129883f, +-0.88192129135131835938f,0.47139674425125122070f,-0.90398931503295898438f, +0.42755508422851562500f,-0.92387950420379638672f,0.38268342614173889160f, +-0.94154405593872070312f,0.33688986301422119141f,-0.95694035291671752930f, +0.29028466343879699707f,-0.97003126144409179688f,0.24298018217086791992f, +-0.98078525066375732422f,0.19509032368659973145f,-0.98917651176452636719f, +0.14673046767711639404f,-0.99518471956253051758f,0.09801714122295379639f, +-0.99879544973373413086f,0.04906767606735229492f,1.00000000000000000000f, +0.00000000000000000000f,0.98078525066375732422f,0.19509032368659973145f, +0.92387950420379638672f,0.38268342614173889160f,0.83146959543228149414f, +0.55557024478912353516f,0.70710676908493041992f,0.70710676908493041992f, +0.55557024478912353516f,0.83146959543228149414f,0.38268342614173889160f, +0.92387950420379638672f,0.19509032368659973145f,0.98078525066375732422f, +0.00000000000000006123f,1.00000000000000000000f,-0.19509032368659973145f, +0.98078525066375732422f,-0.38268342614173889160f,0.92387950420379638672f, +-0.55557024478912353516f,0.83146959543228149414f,-0.70710676908493041992f, +0.70710676908493041992f,-0.83146959543228149414f,0.55557024478912353516f, +-0.92387950420379638672f,0.38268342614173889160f,-0.98078525066375732422f, +0.19509032368659973145f,1.00000000000000000000f,0.00000000000000000000f, +0.70710676908493041992f,0.70710676908493041992f,0.00000000000000006123f, +1.00000000000000000000f,-0.70710676908493041992f,0.70710676908493041992f,}; + +const float32_t rearranged_twiddle_stride3_256_f32[168] ARM_DSP_TABLE_ATTRIBUTE ={ +1.00000000000000000000f,0.00000000000000000000f,0.99729043245315551758f, +0.07356456667184829712f,0.98917651176452636719f,0.14673046767711639404f, +0.97570210695266723633f,0.21910123527050018311f,0.95694035291671752930f, +0.29028466343879699707f,0.93299281597137451172f,0.35989505052566528320f, +0.90398931503295898438f,0.42755508422851562500f,0.87008696794509887695f, +0.49289819598197937012f,0.83146959543228149414f,0.55557024478912353516f, +0.78834640979766845703f,0.61523157358169555664f,0.74095112085342407227f, +0.67155897617340087891f,0.68954056501388549805f,0.72424709796905517578f, +0.63439327478408813477f,0.77301043272018432617f,0.57580816745758056641f, +0.81758481264114379883f,0.51410275697708129883f,0.85772860050201416016f, +0.44961133599281311035f,0.89322429895401000977f,0.38268342614173889160f, +0.92387950420379638672f,0.31368175148963928223f,0.94952815771102905273f, +0.24298018217086791992f,0.97003126144409179688f,0.17096188664436340332f, +0.98527765274047851562f,0.09801714122295379639f,0.99518471956253051758f, +0.02454122900962829590f,0.99969881772994995117f,-0.04906767606735229492f, +0.99879544973373413086f,-0.12241067737340927124f,0.99247956275939941406f, +-0.19509032368659973145f,0.98078525066375732422f,-0.26671275496482849121f, +0.96377605199813842773f,-0.33688986301422119141f,0.94154405593872070312f, +-0.40524131059646606445f,0.91420978307723999023f,-0.47139674425125122070f, +0.88192129135131835938f,-0.53499764204025268555f,0.84485357999801635742f, +-0.59569931030273437500f,0.80320751667022705078f,-0.65317285060882568359f, +0.75720882415771484375f,-0.70710676908493041992f,0.70710676908493041992f, +-0.75720882415771484375f,0.65317285060882568359f,-0.80320751667022705078f, +0.59569931030273437500f,-0.84485357999801635742f,0.53499764204025268555f, +-0.88192129135131835938f,0.47139674425125122070f,-0.91420978307723999023f, +0.40524131059646606445f,-0.94154405593872070312f,0.33688986301422119141f, +-0.96377605199813842773f,0.26671275496482849121f,-0.98078525066375732422f, +0.19509032368659973145f,-0.99247956275939941406f,0.12241067737340927124f, 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+-0.19509032368659973145f,0.98078525066375732422f,-0.47139674425125122070f, +0.88192129135131835938f,-0.70710676908493041992f,0.70710676908493041992f, +-0.88192129135131835938f,0.47139674425125122070f,-0.98078525066375732422f, +0.19509032368659973145f,-0.99518471956253051758f,-0.09801714122295379639f, +-0.92387950420379638672f,-0.38268342614173889160f,-0.77301043272018432617f, +-0.63439327478408813477f,-0.55557024478912353516f,-0.83146959543228149414f, +-0.29028466343879699707f,-0.95694035291671752930f,1.00000000000000000000f, +0.00000000000000000000f,0.38268342614173889160f,0.92387950420379638672f, +-0.70710676908493041992f,0.70710676908493041992f,-0.92387950420379638672f, +-0.38268342614173889160f,}; + + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + +const uint32_t rearranged_twiddle_tab_stride1_arr_16_q31[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_16_q31[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_16_q31[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const q31_t rearranged_twiddle_stride1_16_q31[8] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,}; + +const q31_t rearranged_twiddle_stride2_16_q31[8] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000,0xA57D8666, +0xA57D8666,}; + +const q31_t rearranged_twiddle_stride3_16_q31[8] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666,0xA57D8666,0x89BE50C3, +0x30FBC54D,}; + + + +const uint32_t rearranged_twiddle_tab_stride1_arr_64_q31[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_64_q31[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_64_q31[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const q31_t rearranged_twiddle_stride1_64_q31[40] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x7FFFFFFF,0x00000000,0x7641AF3D, +0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D,0x89BE50C3,}; + +const q31_t rearranged_twiddle_stride2_64_q31[40] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x5A82799A, +0xA57D8666,0x00000000,0x80000000,0xA57D8666,0xA57D8666,}; + +const q31_t rearranged_twiddle_stride3_64_q31[40] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7A7D055B,0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94, +0x9D0DFE54,0x30FBC54D,0x89BE50C3,0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0, +0xC3A94590,0x8F1D343A,0xA57D8666,0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0, +0xE70747C4,0x809DC971,0x0C8BD35E,0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94, +0xB8E31319,0x6A6D98A4,0xDAD7F3A2,0x7A7D055B,0x7FFFFFFF,0x00000000,0x30FBC54D, +0x89BE50C3,0xA57D8666,0xA57D8666,0x89BE50C3,0x30FBC54D,}; + + + +const uint32_t rearranged_twiddle_tab_stride1_arr_256_q31[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_256_q31[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_256_q31[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const q31_t rearranged_twiddle_stride1_256_q31[168] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684,0x7FA736B4, +0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC,0xED37EF91, +0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96,0x7C29FBEE, +0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1,0xD7D946D8, +0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3,0x7504D345, +0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6,0xC3A94590, +0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0,0x6A6D98A4, +0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926,0xB140175B, +0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E,0x5CB420E0, +0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2,0xA1288376, +0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA,0x4C3FDFF4, +0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50,0x93DBD6A0, +0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A,0x398CDD32, +0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D,0x89BE50C3, +0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F,0x25280C5E, +0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A,0x831C314E, +0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04,0x0FAB272B, +0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C,0x80277872, +0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40, +0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590, +0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94, +0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3, +0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x7FFFFFFF, +0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D,0x89BE50C3,}; + +const q31_t rearranged_twiddle_stride2_256_q31[168] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC, +0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2, +0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6, +0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C, +0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2, +0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C, +0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D, +0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412, +0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C, +0x80277872,0x00000000,0x80000000,0xF9B82684,0x80277872,0xF3742CA2,0x809DC971, +0xED37EF91,0x8162AA04,0xE70747C4,0x8275A0C0,0xE0E60685,0x83D60412,0xDAD7F3A2, +0x8582FAA5,0xD4E0CB15,0x877B7BEC,0xCF043AB3,0x89BE50C3,0xC945DFEC,0x8C4A142F, +0xC3A94590,0x8F1D343A,0xBE31E19B,0x9235F2EC,0xB8E31319,0x9592675C,0xB3C0200C, +0x99307EE0,0xAECC336C,0x9D0DFE54,0xAA0A5B2E,0xA1288376,0xA57D8666,0xA57D8666, +0xA1288376,0xAA0A5B2E,0x9D0DFE54,0xAECC336C,0x99307EE0,0xB3C0200C,0x9592675C, +0xB8E31319,0x9235F2EC,0xBE31E19B,0x8F1D343A,0xC3A94590,0x8C4A142F,0xC945DFEC, +0x89BE50C3,0xCF043AB3,0x877B7BEC,0xD4E0CB15,0x8582FAA5,0xDAD7F3A2,0x83D60412, +0xE0E60685,0x8275A0C0,0xE70747C4,0x8162AA04,0xED37EF91,0x809DC971,0xF3742CA2, +0x80277872,0xF9B82684,0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D, +0xCF043AB3,0x6A6D98A4,0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C, +0x30FBC54D,0x89BE50C3,0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4, +0x8275A0C0,0xCF043AB3,0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666, +0x9592675C,0xB8E31319,0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF, +0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000,0xA57D8666,0xA57D8666,}; + +const q31_t rearranged_twiddle_stride3_256_q31[168] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FA736B4,0xF6956FB7,0x7E9D55FC,0xED37EF91,0x7CE3CEB2, +0xE3F47D96,0x7A7D055B,0xDAD7F3A2,0x776C4EDB,0xD1EEF59E,0x73B5EBD1,0xC945DFEC, +0x6F5F02B2,0xC0E8B648,0x6A6D98A4,0xB8E31319,0x64E88926,0xB140175B,0x5ED77C8A, +0xAA0A5B2E,0x5842DD54,0xA34BDF20,0x5133CC94,0x9D0DFE54,0x49B41533,0x9759617F, +0x41CE1E65,0x9235F2EC,0x398CDD32,0x8DAAD37B,0x30FBC54D,0x89BE50C3,0x2826B928, +0x8675DC4F,0x1F19F97B,0x83D60412,0x15E21445,0x81E26C16,0x0C8BD35E,0x809DC971, +0x03242ABF,0x8009DE7E,0xF9B82684,0x80277872,0xF054D8D5,0x80F66E3C,0xE70747C4, +0x8275A0C0,0xDDDC5B3B,0x84A2FC62,0xD4E0CB15,0x877B7BEC,0xCC210D79,0x8AFB2CBB, +0xC3A94590,0x8F1D343A,0xBB8532B0,0x93DBD6A0,0xB3C0200C,0x99307EE0,0xAC64D510, +0x9F13C7D0,0xA57D8666,0xA57D8666,0x9F13C7D0,0xAC64D510,0x99307EE0,0xB3C0200C, +0x93DBD6A0,0xBB8532B0,0x8F1D343A,0xC3A94590,0x8AFB2CBB,0xCC210D79,0x877B7BEC, +0xD4E0CB15,0x84A2FC62,0xDDDC5B3B,0x8275A0C0,0xE70747C4,0x80F66E3C,0xF054D8D5, +0x80277872,0xF9B82684,0x8009DE7E,0x03242ABF,0x809DC971,0x0C8BD35E,0x81E26C16, +0x15E21445,0x83D60412,0x1F19F97B,0x8675DC4F,0x2826B928,0x89BE50C3,0x30FBC54D, +0x8DAAD37B,0x398CDD32,0x9235F2EC,0x41CE1E65,0x9759617F,0x49B41533,0x9D0DFE54, +0x5133CC94,0xA34BDF20,0x5842DD54,0xAA0A5B2E,0x5ED77C8A,0xB140175B,0x64E88926, +0xB8E31319,0x6A6D98A4,0xC0E8B648,0x6F5F02B2,0xC945DFEC,0x73B5EBD1,0xD1EEF59E, +0x776C4EDB,0xDAD7F3A2,0x7A7D055B,0xE3F47D96,0x7CE3CEB2,0xED37EF91,0x7E9D55FC, +0xF6956FB7,0x7FA736B4,0x7FFFFFFF,0x00000000,0x7A7D055B,0xDAD7F3A2,0x6A6D98A4, +0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3,0x0C8BD35E,0x809DC971, +0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666,0xA57D8666,0x8F1D343A, +0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E,0x89BE50C3,0x30FBC54D, +0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2,0x7A7D055B,0x7FFFFFFF, +0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666,0xA57D8666,0x89BE50C3,0x30FBC54D,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_1024_q31[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_1024_q31[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_1024_q31[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const q31_t rearranged_twiddle_stride1_1024_q31[680] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FFF6216,0xFF36F078,0x7FFD885A,0xFE6DE2E0,0x7FFA72D1, +0xFDA4D929,0x7FF62182,0xFCDBD541,0x7FF09478,0xFC12D91A,0x7FE9CBC0,0xFB49E6A3, +0x7FE1C76B,0xFA80FFCB,0x7FD8878E,0xF9B82684,0x7FCE0C3E,0xF8EF5CBB,0x7FC25596, +0xF826A462,0x7FB563B3,0xF75DFF66,0x7FA736B4,0xF6956FB7,0x7F97CEBD,0xF5CCF743, +0x7F872BF3,0xF50497FB,0x7F754E80,0xF43C53CB,0x7F62368F,0xF3742CA2,0x7F4DE451, +0xF2AC246E,0x7F3857F6,0xF1E43D1C,0x7F2191B4,0xF11C789A,0x7F0991C4,0xF054D8D5, +0x7EF05860,0xEF8D5FB8,0x7ED5E5C6,0xEEC60F31,0x7EBA3A39,0xEDFEE92B,0x7E9D55FC, +0xED37EF91,0x7E7F3957,0xEC71244F,0x7E5FE493,0xEBAA894F,0x7E3F57FF,0xEAE4207A, +0x7E1D93EA,0xEA1DEBBB,0x7DFA98A8,0xE957ECFB,0x7DD6668F,0xE8922622,0x7DB0FDF8, +0xE7CC9917,0x7D8A5F40,0xE70747C4,0x7D628AC6,0xE642340D,0x7D3980EC,0xE57D5FDA, +0x7D0F4218,0xE4B8CD11,0x7CE3CEB2,0xE3F47D96,0x7CB72724,0xE330734D,0x7C894BDE, +0xE26CB01B,0x7C5A3D50,0xE1A935E2,0x7C29FBEE,0xE0E60685,0x7BF88830,0xE02323E5, +0x7BC5E290,0xDF608FE4,0x7B920B89,0xDE9E4C60,0x7B5D039E,0xDDDC5B3B,0x7B26CB4F, +0xDD1ABE51,0x7AEF6323,0xDC597781,0x7AB6CBA4,0xDB9888A8,0x7A7D055B,0xDAD7F3A2, +0x7A4210D8,0xDA17BA4A,0x7A05EEAD,0xD957DE7A,0x79C89F6E,0xD898620C,0x798A23B1, +0xD7D946D8,0x794A7C12,0xD71A8EB5,0x7909A92D,0xD65C3B7B,0x78C7ABA2,0xD59E4EFF, +0x78848414,0xD4E0CB15,0x78403329,0xD423B191,0x77FAB989,0xD3670446,0x77B417DF, +0xD2AAC504,0x776C4EDB,0xD1EEF59E,0x77235F2D,0xD13397E2,0x76D94989,0xD078AD9E, +0x768E0EA6,0xCFBE389F,0x7641AF3D,0xCF043AB3,0x75F42C0B,0xCE4AB5A2,0x75A585CF, +0xCD91AB39,0x7555BD4C,0xCCD91D3D,0x7504D345,0xCC210D79,0x74B2C884,0xCB697DB0, +0x745F9DD1,0xCAB26FA9,0x740B53FB,0xC9FBE527,0x73B5EBD1,0xC945DFEC,0x735F6626, +0xC89061BA,0x7307C3D0,0xC7DB6C50,0x72AF05A7,0xC727016D,0x72552C85,0xC67322CE, +0x71FA3949,0xC5BFD22E,0x719E2CD2,0xC50D1149,0x71410805,0xC45AE1D7,0x70E2CBC6, +0xC3A94590,0x708378FF,0xC2F83E2A,0x7023109A,0xC247CD5A,0x6FC19385,0xC197F4D4, +0x6F5F02B2,0xC0E8B648,0x6EFB5F12,0xC03A1368,0x6E96A99D,0xBF8C0DE3,0x6E30E34A, +0xBEDEA765,0x6DCA0D14,0xBE31E19B,0x6D6227FA,0xBD85BE30,0x6CF934FC,0xBCDA3ECB, +0x6C8F351C,0xBC2F6513,0x6C242960,0xBB8532B0,0x6BB812D1,0xBADBA943,0x6B4AF279, +0xBA32CA71,0x6ADCC964,0xB98A97D8,0x6A6D98A4,0xB8E31319,0x69FD614A,0xB83C3DD1, +0x698C246C,0xB796199B,0x6919E320,0xB6F0A812,0x68A69E81,0xB64BEACD,0x683257AB, +0xB5A7E362,0x67BD0FBD,0xB5049368,0x6746C7D8,0xB461FC70,0x66CF8120,0xB3C0200C, +0x66573CBB,0xB31EFFCC,0x65DDFBD3,0xB27E9D3C,0x6563BF92,0xB1DEF9E9,0x64E88926, +0xB140175B,0x646C59BF,0xB0A1F71D,0x63EF3290,0xB0049AB3,0x637114CC,0xAF6803A2, +0x62F201AC,0xAECC336C,0x6271FA69,0xAE312B92,0x61F1003F,0xAD96ED92,0x616F146C, +0xACFD7AE8,0x60EC3830,0xAC64D510,0x60686CCF,0xABCCFD83,0x5FE3B38D,0xAB35F5B5, +0x5F5E0DB3,0xAA9FBF1E,0x5ED77C8A,0xAA0A5B2E,0x5E50015D,0xA975CB57,0x5DC79D7C, +0xA8E21106,0x5D3E5237,0xA84F2DAA,0x5CB420E0,0xA7BD22AC,0x5C290ACC,0xA72BF174, +0x5B9D1154,0xA69B9B68,0x5B1035CF,0xA60C21EE,0x5A82799A,0xA57D8666,0x59F3DE12, +0xA4EFCA31,0x59646498,0xA462EEAC,0x58D40E8C,0xA3D6F534,0x5842DD54,0xA34BDF20, +0x57B0D256,0xA2C1ADC9,0x571DEEFA,0xA2386284,0x568A34A9,0xA1AFFEA3,0x55F5A4D2, +0xA1288376,0x556040E2,0xA0A1F24D,0x54CA0A4B,0xA01C4C73,0x5433027D,0x9F979331, +0x539B2AF0,0x9F13C7D0,0x53028518,0x9E90EB94,0x5269126E,0x9E0EFFC1,0x51CED46E, +0x9D8E0597,0x5133CC94,0x9D0DFE54,0x5097FC5E,0x9C8EEB34,0x4FFB654D,0x9C10CD70, +0x4F5E08E3,0x9B93A641,0x4EBFE8A5,0x9B1776DA,0x4E210617,0x9A9C406E,0x4D8162C4, +0x9A22042D,0x4CE10034,0x99A8C345,0x4C3FDFF4,0x99307EE0,0x4B9E0390,0x98B93828, +0x4AFB6C98,0x9842F043,0x4A581C9E,0x97CDA855,0x49B41533,0x9759617F,0x490F57EE, +0x96E61CE0,0x4869E665,0x9673DB94,0x47C3C22F,0x96029EB6,0x471CECE7,0x9592675C, +0x46756828,0x9523369C,0x45CD358F,0x94B50D87,0x452456BD,0x9447ED2F,0x447ACD50, +0x93DBD6A0,0x43D09AED,0x9370CAE4,0x4325C135,0x9306CB04,0x427A41D0,0x929DD806, +0x41CE1E65,0x9235F2EC,0x4121589B,0x91CF1CB6,0x4073F21D,0x91695663,0x3FC5EC98, +0x9104A0EE,0x3F1749B8,0x90A0FD4E,0x3E680B2C,0x903E6C7B,0x3DB832A6,0x8FDCEF66, +0x3D07C1D6,0x8F7C8701,0x3C56BA70,0x8F1D343A,0x3BA51E29,0x8EBEF7FB,0x3AF2EEB7, +0x8E61D32E,0x3A402DD2,0x8E05C6B7,0x398CDD32,0x8DAAD37B,0x38D8FE93,0x8D50FA59, +0x382493B0,0x8CF83C30,0x376F9E46,0x8CA099DA,0x36BA2014,0x8C4A142F,0x36041AD9, +0x8BF4AC05,0x354D9057,0x8BA0622F,0x34968250,0x8B4D377C,0x33DEF287,0x8AFB2CBB, +0x3326E2C3,0x8AAA42B4,0x326E54C7,0x8A5A7A31,0x31B54A5E,0x8A0BD3F5,0x30FBC54D, +0x89BE50C3,0x3041C761,0x8971F15A,0x2F875262,0x8926B677,0x2ECC681E,0x88DCA0D3, +0x2E110A62,0x8893B125,0x2D553AFC,0x884BE821,0x2C98FBBA,0x88054677,0x2BDC4E6F, +0x87BFCCD7,0x2B1F34EB,0x877B7BEC,0x2A61B101,0x8738545E,0x29A3C485,0x86F656D3, +0x28E5714B,0x86B583EE,0x2826B928,0x8675DC4F,0x27679DF4,0x86376092,0x26A82186, +0x85FA1153,0x25E845B6,0x85BDEF28,0x25280C5E,0x8582FAA5,0x24677758,0x8549345C, +0x23A6887F,0x85109CDD,0x22E541AF,0x84D934B1,0x2223A4C5,0x84A2FC62,0x2161B3A0, +0x846DF477,0x209F701C,0x843A1D70,0x1FDCDC1B,0x840777D0,0x1F19F97B,0x83D60412, +0x1E56CA1E,0x83A5C2B0,0x1D934FE5,0x8376B422,0x1CCF8CB3,0x8348D8DC,0x1C0B826A, +0x831C314E,0x1B4732EF,0x82F0BDE8,0x1A82A026,0x82C67F14,0x19BDCBF3,0x829D753A, +0x18F8B83C,0x8275A0C0,0x183366E9,0x824F0208,0x176DD9DE,0x82299971,0x16A81305, +0x82056758,0x15E21445,0x81E26C16,0x151BDF86,0x81C0A801,0x145576B1,0x81A01B6D, +0x138EDBB1,0x8180C6A9,0x12C8106F,0x8162AA04,0x120116D5,0x8145C5C7,0x1139F0CF, +0x812A1A3A,0x1072A048,0x810FA7A0,0x0FAB272B,0x80F66E3C,0x0EE38766,0x80DE6E4C, +0x0E1BC2E4,0x80C7A80A,0x0D53DB92,0x80B21BAF,0x0C8BD35E,0x809DC971,0x0BC3AC35, +0x808AB180,0x0AFB6805,0x8078D40D,0x0A3308BD,0x80683143,0x096A9049,0x8058C94C, +0x08A2009A,0x804A9C4D,0x07D95B9E,0x803DAA6A,0x0710A345,0x8031F3C2,0x0647D97C, +0x80277872,0x057F0035,0x801E3895,0x04B6195D,0x80163440,0x03ED26E6,0x800F6B88, +0x03242ABF,0x8009DE7E,0x025B26D7,0x80058D2F,0x01921D20,0x800277A6,0x00C90F88, +0x80009DEA,0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684, +0x7FA736B4,0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC, +0xED37EF91,0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96, +0x7C29FBEE,0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1, +0xD7D946D8,0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3, +0x7504D345,0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6, +0xC3A94590,0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0, +0x6A6D98A4,0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926, +0xB140175B,0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E, +0x5CB420E0,0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2, +0xA1288376,0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA, +0x4C3FDFF4,0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50, +0x93DBD6A0,0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A, +0x398CDD32,0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D, +0x89BE50C3,0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F, +0x25280C5E,0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A, +0x831C314E,0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04, +0x0FAB272B,0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C, +0x80277872,0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,}; + +const q31_t rearranged_twiddle_stride2_1024_q31[680] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FFD885A,0xFE6DE2E0,0x7FF62182,0xFCDBD541,0x7FE9CBC0, +0xFB49E6A3,0x7FD8878E,0xF9B82684,0x7FC25596,0xF826A462,0x7FA736B4,0xF6956FB7, +0x7F872BF3,0xF50497FB,0x7F62368F,0xF3742CA2,0x7F3857F6,0xF1E43D1C,0x7F0991C4, +0xF054D8D5,0x7ED5E5C6,0xEEC60F31,0x7E9D55FC,0xED37EF91,0x7E5FE493,0xEBAA894F, +0x7E1D93EA,0xEA1DEBBB,0x7DD6668F,0xE8922622,0x7D8A5F40,0xE70747C4,0x7D3980EC, +0xE57D5FDA,0x7CE3CEB2,0xE3F47D96,0x7C894BDE,0xE26CB01B,0x7C29FBEE,0xE0E60685, +0x7BC5E290,0xDF608FE4,0x7B5D039E,0xDDDC5B3B,0x7AEF6323,0xDC597781,0x7A7D055B, +0xDAD7F3A2,0x7A05EEAD,0xD957DE7A,0x798A23B1,0xD7D946D8,0x7909A92D,0xD65C3B7B, +0x78848414,0xD4E0CB15,0x77FAB989,0xD3670446,0x776C4EDB,0xD1EEF59E,0x76D94989, +0xD078AD9E,0x7641AF3D,0xCF043AB3,0x75A585CF,0xCD91AB39,0x7504D345,0xCC210D79, +0x745F9DD1,0xCAB26FA9,0x73B5EBD1,0xC945DFEC,0x7307C3D0,0xC7DB6C50,0x72552C85, +0xC67322CE,0x719E2CD2,0xC50D1149,0x70E2CBC6,0xC3A94590,0x7023109A,0xC247CD5A, +0x6F5F02B2,0xC0E8B648,0x6E96A99D,0xBF8C0DE3,0x6DCA0D14,0xBE31E19B,0x6CF934FC, +0xBCDA3ECB,0x6C242960,0xBB8532B0,0x6B4AF279,0xBA32CA71,0x6A6D98A4,0xB8E31319, +0x698C246C,0xB796199B,0x68A69E81,0xB64BEACD,0x67BD0FBD,0xB5049368,0x66CF8120, +0xB3C0200C,0x65DDFBD3,0xB27E9D3C,0x64E88926,0xB140175B,0x63EF3290,0xB0049AB3, +0x62F201AC,0xAECC336C,0x61F1003F,0xAD96ED92,0x60EC3830,0xAC64D510,0x5FE3B38D, +0xAB35F5B5,0x5ED77C8A,0xAA0A5B2E,0x5DC79D7C,0xA8E21106,0x5CB420E0,0xA7BD22AC, +0x5B9D1154,0xA69B9B68,0x5A82799A,0xA57D8666,0x59646498,0xA462EEAC,0x5842DD54, +0xA34BDF20,0x571DEEFA,0xA2386284,0x55F5A4D2,0xA1288376,0x54CA0A4B,0xA01C4C73, +0x539B2AF0,0x9F13C7D0,0x5269126E,0x9E0EFFC1,0x5133CC94,0x9D0DFE54,0x4FFB654D, +0x9C10CD70,0x4EBFE8A5,0x9B1776DA,0x4D8162C4,0x9A22042D,0x4C3FDFF4,0x99307EE0, +0x4AFB6C98,0x9842F043,0x49B41533,0x9759617F,0x4869E665,0x9673DB94,0x471CECE7, +0x9592675C,0x45CD358F,0x94B50D87,0x447ACD50,0x93DBD6A0,0x4325C135,0x9306CB04, +0x41CE1E65,0x9235F2EC,0x4073F21D,0x91695663,0x3F1749B8,0x90A0FD4E,0x3DB832A6, +0x8FDCEF66,0x3C56BA70,0x8F1D343A,0x3AF2EEB7,0x8E61D32E,0x398CDD32,0x8DAAD37B, +0x382493B0,0x8CF83C30,0x36BA2014,0x8C4A142F,0x354D9057,0x8BA0622F,0x33DEF287, +0x8AFB2CBB,0x326E54C7,0x8A5A7A31,0x30FBC54D,0x89BE50C3,0x2F875262,0x8926B677, +0x2E110A62,0x8893B125,0x2C98FBBA,0x88054677,0x2B1F34EB,0x877B7BEC,0x29A3C485, +0x86F656D3,0x2826B928,0x8675DC4F,0x26A82186,0x85FA1153,0x25280C5E,0x8582FAA5, +0x23A6887F,0x85109CDD,0x2223A4C5,0x84A2FC62,0x209F701C,0x843A1D70,0x1F19F97B, +0x83D60412,0x1D934FE5,0x8376B422,0x1C0B826A,0x831C314E,0x1A82A026,0x82C67F14, +0x18F8B83C,0x8275A0C0,0x176DD9DE,0x82299971,0x15E21445,0x81E26C16,0x145576B1, +0x81A01B6D,0x12C8106F,0x8162AA04,0x1139F0CF,0x812A1A3A,0x0FAB272B,0x80F66E3C, +0x0E1BC2E4,0x80C7A80A,0x0C8BD35E,0x809DC971,0x0AFB6805,0x8078D40D,0x096A9049, +0x8058C94C,0x07D95B9E,0x803DAA6A,0x0647D97C,0x80277872,0x04B6195D,0x80163440, +0x03242ABF,0x8009DE7E,0x01921D20,0x800277A6,0x00000000,0x80000000,0xFE6DE2E0, +0x800277A6,0xFCDBD541,0x8009DE7E,0xFB49E6A3,0x80163440,0xF9B82684,0x80277872, +0xF826A462,0x803DAA6A,0xF6956FB7,0x8058C94C,0xF50497FB,0x8078D40D,0xF3742CA2, +0x809DC971,0xF1E43D1C,0x80C7A80A,0xF054D8D5,0x80F66E3C,0xEEC60F31,0x812A1A3A, +0xED37EF91,0x8162AA04,0xEBAA894F,0x81A01B6D,0xEA1DEBBB,0x81E26C16,0xE8922622, +0x82299971,0xE70747C4,0x8275A0C0,0xE57D5FDA,0x82C67F14,0xE3F47D96,0x831C314E, +0xE26CB01B,0x8376B422,0xE0E60685,0x83D60412,0xDF608FE4,0x843A1D70,0xDDDC5B3B, +0x84A2FC62,0xDC597781,0x85109CDD,0xDAD7F3A2,0x8582FAA5,0xD957DE7A,0x85FA1153, +0xD7D946D8,0x8675DC4F,0xD65C3B7B,0x86F656D3,0xD4E0CB15,0x877B7BEC,0xD3670446, +0x88054677,0xD1EEF59E,0x8893B125,0xD078AD9E,0x8926B677,0xCF043AB3,0x89BE50C3, +0xCD91AB39,0x8A5A7A31,0xCC210D79,0x8AFB2CBB,0xCAB26FA9,0x8BA0622F,0xC945DFEC, +0x8C4A142F,0xC7DB6C50,0x8CF83C30,0xC67322CE,0x8DAAD37B,0xC50D1149,0x8E61D32E, +0xC3A94590,0x8F1D343A,0xC247CD5A,0x8FDCEF66,0xC0E8B648,0x90A0FD4E,0xBF8C0DE3, +0x91695663,0xBE31E19B,0x9235F2EC,0xBCDA3ECB,0x9306CB04,0xBB8532B0,0x93DBD6A0, +0xBA32CA71,0x94B50D87,0xB8E31319,0x9592675C,0xB796199B,0x9673DB94,0xB64BEACD, +0x9759617F,0xB5049368,0x9842F043,0xB3C0200C,0x99307EE0,0xB27E9D3C,0x9A22042D, +0xB140175B,0x9B1776DA,0xB0049AB3,0x9C10CD70,0xAECC336C,0x9D0DFE54,0xAD96ED92, +0x9E0EFFC1,0xAC64D510,0x9F13C7D0,0xAB35F5B5,0xA01C4C73,0xAA0A5B2E,0xA1288376, +0xA8E21106,0xA2386284,0xA7BD22AC,0xA34BDF20,0xA69B9B68,0xA462EEAC,0xA57D8666, +0xA57D8666,0xA462EEAC,0xA69B9B68,0xA34BDF20,0xA7BD22AC,0xA2386284,0xA8E21106, +0xA1288376,0xAA0A5B2E,0xA01C4C73,0xAB35F5B5,0x9F13C7D0,0xAC64D510,0x9E0EFFC1, +0xAD96ED92,0x9D0DFE54,0xAECC336C,0x9C10CD70,0xB0049AB3,0x9B1776DA,0xB140175B, +0x9A22042D,0xB27E9D3C,0x99307EE0,0xB3C0200C,0x9842F043,0xB5049368,0x9759617F, +0xB64BEACD,0x9673DB94,0xB796199B,0x9592675C,0xB8E31319,0x94B50D87,0xBA32CA71, +0x93DBD6A0,0xBB8532B0,0x9306CB04,0xBCDA3ECB,0x9235F2EC,0xBE31E19B,0x91695663, +0xBF8C0DE3,0x90A0FD4E,0xC0E8B648,0x8FDCEF66,0xC247CD5A,0x8F1D343A,0xC3A94590, +0x8E61D32E,0xC50D1149,0x8DAAD37B,0xC67322CE,0x8CF83C30,0xC7DB6C50,0x8C4A142F, +0xC945DFEC,0x8BA0622F,0xCAB26FA9,0x8AFB2CBB,0xCC210D79,0x8A5A7A31,0xCD91AB39, +0x89BE50C3,0xCF043AB3,0x8926B677,0xD078AD9E,0x8893B125,0xD1EEF59E,0x88054677, +0xD3670446,0x877B7BEC,0xD4E0CB15,0x86F656D3,0xD65C3B7B,0x8675DC4F,0xD7D946D8, +0x85FA1153,0xD957DE7A,0x8582FAA5,0xDAD7F3A2,0x85109CDD,0xDC597781,0x84A2FC62, +0xDDDC5B3B,0x843A1D70,0xDF608FE4,0x83D60412,0xE0E60685,0x8376B422,0xE26CB01B, +0x831C314E,0xE3F47D96,0x82C67F14,0xE57D5FDA,0x8275A0C0,0xE70747C4,0x82299971, +0xE8922622,0x81E26C16,0xEA1DEBBB,0x81A01B6D,0xEBAA894F,0x8162AA04,0xED37EF91, +0x812A1A3A,0xEEC60F31,0x80F66E3C,0xF054D8D5,0x80C7A80A,0xF1E43D1C,0x809DC971, +0xF3742CA2,0x8078D40D,0xF50497FB,0x8058C94C,0xF6956FB7,0x803DAA6A,0xF826A462, +0x80277872,0xF9B82684,0x80163440,0xFB49E6A3,0x8009DE7E,0xFCDBD541,0x800277A6, +0xFE6DE2E0,0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2, +0x7E9D55FC,0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B, +0xDAD7F3A2,0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC, +0x70E2CBC6,0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120, +0xB3C0200C,0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666, +0x55F5A4D2,0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7, +0x9592675C,0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F, +0x30FBC54D,0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B, +0x83D60412,0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971, +0x0647D97C,0x80277872,0x00000000,0x80000000,0xF9B82684,0x80277872,0xF3742CA2, +0x809DC971,0xED37EF91,0x8162AA04,0xE70747C4,0x8275A0C0,0xE0E60685,0x83D60412, +0xDAD7F3A2,0x8582FAA5,0xD4E0CB15,0x877B7BEC,0xCF043AB3,0x89BE50C3,0xC945DFEC, +0x8C4A142F,0xC3A94590,0x8F1D343A,0xBE31E19B,0x9235F2EC,0xB8E31319,0x9592675C, +0xB3C0200C,0x99307EE0,0xAECC336C,0x9D0DFE54,0xAA0A5B2E,0xA1288376,0xA57D8666, +0xA57D8666,0xA1288376,0xAA0A5B2E,0x9D0DFE54,0xAECC336C,0x99307EE0,0xB3C0200C, +0x9592675C,0xB8E31319,0x9235F2EC,0xBE31E19B,0x8F1D343A,0xC3A94590,0x8C4A142F, +0xC945DFEC,0x89BE50C3,0xCF043AB3,0x877B7BEC,0xD4E0CB15,0x8582FAA5,0xDAD7F3A2, +0x83D60412,0xE0E60685,0x8275A0C0,0xE70747C4,0x8162AA04,0xED37EF91,0x809DC971, +0xF3742CA2,0x80277872,0xF9B82684,0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4, +0x7641AF3D,0xCF043AB3,0x6A6D98A4,0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7, +0x9592675C,0x30FBC54D,0x89BE50C3,0x18F8B83C,0x8275A0C0,0x00000000,0x80000000, +0xE70747C4,0x8275A0C0,0xCF043AB3,0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666, +0xA57D8666,0x9592675C,0xB8E31319,0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4, +0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000,0xA57D8666, +0xA57D8666,}; + +const q31_t rearranged_twiddle_stride3_1024_q31[680] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FFA72D1,0xFDA4D929,0x7FE9CBC0,0xFB49E6A3,0x7FCE0C3E, +0xF8EF5CBB,0x7FA736B4,0xF6956FB7,0x7F754E80,0xF43C53CB,0x7F3857F6,0xF1E43D1C, +0x7EF05860,0xEF8D5FB8,0x7E9D55FC,0xED37EF91,0x7E3F57FF,0xEAE4207A,0x7DD6668F, +0xE8922622,0x7D628AC6,0xE642340D,0x7CE3CEB2,0xE3F47D96,0x7C5A3D50,0xE1A935E2, +0x7BC5E290,0xDF608FE4,0x7B26CB4F,0xDD1ABE51,0x7A7D055B,0xDAD7F3A2,0x79C89F6E, +0xD898620C,0x7909A92D,0xD65C3B7B,0x78403329,0xD423B191,0x776C4EDB,0xD1EEF59E, +0x768E0EA6,0xCFBE389F,0x75A585CF,0xCD91AB39,0x74B2C884,0xCB697DB0,0x73B5EBD1, +0xC945DFEC,0x72AF05A7,0xC727016D,0x719E2CD2,0xC50D1149,0x708378FF,0xC2F83E2A, +0x6F5F02B2,0xC0E8B648,0x6E30E34A,0xBEDEA765,0x6CF934FC,0xBCDA3ECB,0x6BB812D1, +0xBADBA943,0x6A6D98A4,0xB8E31319,0x6919E320,0xB6F0A812,0x67BD0FBD,0xB5049368, +0x66573CBB,0xB31EFFCC,0x64E88926,0xB140175B,0x637114CC,0xAF6803A2,0x61F1003F, +0xAD96ED92,0x60686CCF,0xABCCFD83,0x5ED77C8A,0xAA0A5B2E,0x5D3E5237,0xA84F2DAA, +0x5B9D1154,0xA69B9B68,0x59F3DE12,0xA4EFCA31,0x5842DD54,0xA34BDF20,0x568A34A9, +0xA1AFFEA3,0x54CA0A4B,0xA01C4C73,0x53028518,0x9E90EB94,0x5133CC94,0x9D0DFE54, +0x4F5E08E3,0x9B93A641,0x4D8162C4,0x9A22042D,0x4B9E0390,0x98B93828,0x49B41533, +0x9759617F,0x47C3C22F,0x96029EB6,0x45CD358F,0x94B50D87,0x43D09AED,0x9370CAE4, +0x41CE1E65,0x9235F2EC,0x3FC5EC98,0x9104A0EE,0x3DB832A6,0x8FDCEF66,0x3BA51E29, +0x8EBEF7FB,0x398CDD32,0x8DAAD37B,0x376F9E46,0x8CA099DA,0x354D9057,0x8BA0622F, +0x3326E2C3,0x8AAA42B4,0x30FBC54D,0x89BE50C3,0x2ECC681E,0x88DCA0D3,0x2C98FBBA, +0x88054677,0x2A61B101,0x8738545E,0x2826B928,0x8675DC4F,0x25E845B6,0x85BDEF28, +0x23A6887F,0x85109CDD,0x2161B3A0,0x846DF477,0x1F19F97B,0x83D60412,0x1CCF8CB3, +0x8348D8DC,0x1A82A026,0x82C67F14,0x183366E9,0x824F0208,0x15E21445,0x81E26C16, +0x138EDBB1,0x8180C6A9,0x1139F0CF,0x812A1A3A,0x0EE38766,0x80DE6E4C,0x0C8BD35E, +0x809DC971,0x0A3308BD,0x80683143,0x07D95B9E,0x803DAA6A,0x057F0035,0x801E3895, +0x03242ABF,0x8009DE7E,0x00C90F88,0x80009DEA,0xFE6DE2E0,0x800277A6,0xFC12D91A, +0x800F6B88,0xF9B82684,0x80277872,0xF75DFF66,0x804A9C4D,0xF50497FB,0x8078D40D, +0xF2AC246E,0x80B21BAF,0xF054D8D5,0x80F66E3C,0xEDFEE92B,0x8145C5C7,0xEBAA894F, +0x81A01B6D,0xE957ECFB,0x82056758,0xE70747C4,0x8275A0C0,0xE4B8CD11,0x82F0BDE8, +0xE26CB01B,0x8376B422,0xE02323E5,0x840777D0,0xDDDC5B3B,0x84A2FC62,0xDB9888A8, +0x8549345C,0xD957DE7A,0x85FA1153,0xD71A8EB5,0x86B583EE,0xD4E0CB15,0x877B7BEC, +0xD2AAC504,0x884BE821,0xD078AD9E,0x8926B677,0xCE4AB5A2,0x8A0BD3F5,0xCC210D79, +0x8AFB2CBB,0xC9FBE527,0x8BF4AC05,0xC7DB6C50,0x8CF83C30,0xC5BFD22E,0x8E05C6B7, +0xC3A94590,0x8F1D343A,0xC197F4D4,0x903E6C7B,0xBF8C0DE3,0x91695663,0xBD85BE30, +0x929DD806,0xBB8532B0,0x93DBD6A0,0xB98A97D8,0x9523369C,0xB796199B,0x9673DB94, +0xB5A7E362,0x97CDA855,0xB3C0200C,0x99307EE0,0xB1DEF9E9,0x9A9C406E,0xB0049AB3, +0x9C10CD70,0xAE312B92,0x9D8E0597,0xAC64D510,0x9F13C7D0,0xAA9FBF1E,0xA0A1F24D, +0xA8E21106,0xA2386284,0xA72BF174,0xA3D6F534,0xA57D8666,0xA57D8666,0xA3D6F534, +0xA72BF174,0xA2386284,0xA8E21106,0xA0A1F24D,0xAA9FBF1E,0x9F13C7D0,0xAC64D510, +0x9D8E0597,0xAE312B92,0x9C10CD70,0xB0049AB3,0x9A9C406E,0xB1DEF9E9,0x99307EE0, +0xB3C0200C,0x97CDA855,0xB5A7E362,0x9673DB94,0xB796199B,0x9523369C,0xB98A97D8, +0x93DBD6A0,0xBB8532B0,0x929DD806,0xBD85BE30,0x91695663,0xBF8C0DE3,0x903E6C7B, +0xC197F4D4,0x8F1D343A,0xC3A94590,0x8E05C6B7,0xC5BFD22E,0x8CF83C30,0xC7DB6C50, +0x8BF4AC05,0xC9FBE527,0x8AFB2CBB,0xCC210D79,0x8A0BD3F5,0xCE4AB5A2,0x8926B677, +0xD078AD9E,0x884BE821,0xD2AAC504,0x877B7BEC,0xD4E0CB15,0x86B583EE,0xD71A8EB5, +0x85FA1153,0xD957DE7A,0x8549345C,0xDB9888A8,0x84A2FC62,0xDDDC5B3B,0x840777D0, +0xE02323E5,0x8376B422,0xE26CB01B,0x82F0BDE8,0xE4B8CD11,0x8275A0C0,0xE70747C4, +0x82056758,0xE957ECFB,0x81A01B6D,0xEBAA894F,0x8145C5C7,0xEDFEE92B,0x80F66E3C, +0xF054D8D5,0x80B21BAF,0xF2AC246E,0x8078D40D,0xF50497FB,0x804A9C4D,0xF75DFF66, +0x80277872,0xF9B82684,0x800F6B88,0xFC12D91A,0x800277A6,0xFE6DE2E0,0x80009DEA, +0x00C90F88,0x8009DE7E,0x03242ABF,0x801E3895,0x057F0035,0x803DAA6A,0x07D95B9E, +0x80683143,0x0A3308BD,0x809DC971,0x0C8BD35E,0x80DE6E4C,0x0EE38766,0x812A1A3A, +0x1139F0CF,0x8180C6A9,0x138EDBB1,0x81E26C16,0x15E21445,0x824F0208,0x183366E9, +0x82C67F14,0x1A82A026,0x8348D8DC,0x1CCF8CB3,0x83D60412,0x1F19F97B,0x846DF477, +0x2161B3A0,0x85109CDD,0x23A6887F,0x85BDEF28,0x25E845B6,0x8675DC4F,0x2826B928, +0x8738545E,0x2A61B101,0x88054677,0x2C98FBBA,0x88DCA0D3,0x2ECC681E,0x89BE50C3, +0x30FBC54D,0x8AAA42B4,0x3326E2C3,0x8BA0622F,0x354D9057,0x8CA099DA,0x376F9E46, +0x8DAAD37B,0x398CDD32,0x8EBEF7FB,0x3BA51E29,0x8FDCEF66,0x3DB832A6,0x9104A0EE, +0x3FC5EC98,0x9235F2EC,0x41CE1E65,0x9370CAE4,0x43D09AED,0x94B50D87,0x45CD358F, +0x96029EB6,0x47C3C22F,0x9759617F,0x49B41533,0x98B93828,0x4B9E0390,0x9A22042D, +0x4D8162C4,0x9B93A641,0x4F5E08E3,0x9D0DFE54,0x5133CC94,0x9E90EB94,0x53028518, +0xA01C4C73,0x54CA0A4B,0xA1AFFEA3,0x568A34A9,0xA34BDF20,0x5842DD54,0xA4EFCA31, +0x59F3DE12,0xA69B9B68,0x5B9D1154,0xA84F2DAA,0x5D3E5237,0xAA0A5B2E,0x5ED77C8A, +0xABCCFD83,0x60686CCF,0xAD96ED92,0x61F1003F,0xAF6803A2,0x637114CC,0xB140175B, +0x64E88926,0xB31EFFCC,0x66573CBB,0xB5049368,0x67BD0FBD,0xB6F0A812,0x6919E320, +0xB8E31319,0x6A6D98A4,0xBADBA943,0x6BB812D1,0xBCDA3ECB,0x6CF934FC,0xBEDEA765, +0x6E30E34A,0xC0E8B648,0x6F5F02B2,0xC2F83E2A,0x708378FF,0xC50D1149,0x719E2CD2, +0xC727016D,0x72AF05A7,0xC945DFEC,0x73B5EBD1,0xCB697DB0,0x74B2C884,0xCD91AB39, +0x75A585CF,0xCFBE389F,0x768E0EA6,0xD1EEF59E,0x776C4EDB,0xD423B191,0x78403329, +0xD65C3B7B,0x7909A92D,0xD898620C,0x79C89F6E,0xDAD7F3A2,0x7A7D055B,0xDD1ABE51, +0x7B26CB4F,0xDF608FE4,0x7BC5E290,0xE1A935E2,0x7C5A3D50,0xE3F47D96,0x7CE3CEB2, +0xE642340D,0x7D628AC6,0xE8922622,0x7DD6668F,0xEAE4207A,0x7E3F57FF,0xED37EF91, +0x7E9D55FC,0xEF8D5FB8,0x7EF05860,0xF1E43D1C,0x7F3857F6,0xF43C53CB,0x7F754E80, +0xF6956FB7,0x7FA736B4,0xF8EF5CBB,0x7FCE0C3E,0xFB49E6A3,0x7FE9CBC0,0xFDA4D929, +0x7FFA72D1,0x7FFFFFFF,0x00000000,0x7FA736B4,0xF6956FB7,0x7E9D55FC,0xED37EF91, +0x7CE3CEB2,0xE3F47D96,0x7A7D055B,0xDAD7F3A2,0x776C4EDB,0xD1EEF59E,0x73B5EBD1, +0xC945DFEC,0x6F5F02B2,0xC0E8B648,0x6A6D98A4,0xB8E31319,0x64E88926,0xB140175B, +0x5ED77C8A,0xAA0A5B2E,0x5842DD54,0xA34BDF20,0x5133CC94,0x9D0DFE54,0x49B41533, +0x9759617F,0x41CE1E65,0x9235F2EC,0x398CDD32,0x8DAAD37B,0x30FBC54D,0x89BE50C3, +0x2826B928,0x8675DC4F,0x1F19F97B,0x83D60412,0x15E21445,0x81E26C16,0x0C8BD35E, +0x809DC971,0x03242ABF,0x8009DE7E,0xF9B82684,0x80277872,0xF054D8D5,0x80F66E3C, +0xE70747C4,0x8275A0C0,0xDDDC5B3B,0x84A2FC62,0xD4E0CB15,0x877B7BEC,0xCC210D79, +0x8AFB2CBB,0xC3A94590,0x8F1D343A,0xBB8532B0,0x93DBD6A0,0xB3C0200C,0x99307EE0, +0xAC64D510,0x9F13C7D0,0xA57D8666,0xA57D8666,0x9F13C7D0,0xAC64D510,0x99307EE0, +0xB3C0200C,0x93DBD6A0,0xBB8532B0,0x8F1D343A,0xC3A94590,0x8AFB2CBB,0xCC210D79, +0x877B7BEC,0xD4E0CB15,0x84A2FC62,0xDDDC5B3B,0x8275A0C0,0xE70747C4,0x80F66E3C, +0xF054D8D5,0x80277872,0xF9B82684,0x8009DE7E,0x03242ABF,0x809DC971,0x0C8BD35E, +0x81E26C16,0x15E21445,0x83D60412,0x1F19F97B,0x8675DC4F,0x2826B928,0x89BE50C3, +0x30FBC54D,0x8DAAD37B,0x398CDD32,0x9235F2EC,0x41CE1E65,0x9759617F,0x49B41533, +0x9D0DFE54,0x5133CC94,0xA34BDF20,0x5842DD54,0xAA0A5B2E,0x5ED77C8A,0xB140175B, +0x64E88926,0xB8E31319,0x6A6D98A4,0xC0E8B648,0x6F5F02B2,0xC945DFEC,0x73B5EBD1, +0xD1EEF59E,0x776C4EDB,0xDAD7F3A2,0x7A7D055B,0xE3F47D96,0x7CE3CEB2,0xED37EF91, +0x7E9D55FC,0xF6956FB7,0x7FA736B4,0x7FFFFFFF,0x00000000,0x7A7D055B,0xDAD7F3A2, +0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3,0x0C8BD35E, +0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666,0xA57D8666, +0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E,0x89BE50C3, +0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2,0x7A7D055B, +0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666,0xA57D8666,0x89BE50C3, +0x30FBC54D,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_4096_q31[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_4096_q31[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_4096_q31[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const q31_t rearranged_twiddle_stride1_4096_q31[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FFFF621,0xFFCDBC0B,0x7FFFD886,0xFF9B781D,0x7FFFA72C, +0xFF69343F,0x7FFF6216,0xFF36F078,0x7FFF0943,0xFF04ACD0,0x7FFE9CB2,0xFED2694F, +0x7FFE1C65,0xFEA025FD,0x7FFD885A,0xFE6DE2E0,0x7FFCE093,0xFE3BA002,0x7FFC250F, +0xFE095D69,0x7FFB55CE,0xFDD71B1E,0x7FFA72D1,0xFDA4D929,0x7FF97C18,0xFD729790, +0x7FF871A2,0xFD40565C,0x7FF75370,0xFD0E1594,0x7FF62182,0xFCDBD541,0x7FF4DBD9, +0xFCA9956A,0x7FF38274,0xFC775616,0x7FF21553,0xFC45174E,0x7FF09478,0xFC12D91A, +0x7FEEFFE1,0xFBE09B80,0x7FED5791,0xFBAE5E89,0x7FEB9B85,0xFB7C223D,0x7FE9CBC0, +0xFB49E6A3,0x7FE7E841,0xFB17ABC2,0x7FE5F108,0xFAE571A4,0x7FE3E616,0xFAB3384F, +0x7FE1C76B,0xFA80FFCB,0x7FDF9508,0xFA4EC821,0x7FDD4EEC,0xFA1C9157,0x7FDAF519, +0xF9EA5B75,0x7FD8878E,0xF9B82684,0x7FD6064C,0xF985F28A,0x7FD37153,0xF953BF91, +0x7FD0C8A3,0xF9218D9E,0x7FCE0C3E,0xF8EF5CBB,0x7FCB3C23,0xF8BD2CEF,0x7FC85854, +0xF88AFE42,0x7FC560CF,0xF858D0BB,0x7FC25596,0xF826A462,0x7FBF36AA,0xF7F4793E, +0x7FBC040A,0xF7C24F59,0x7FB8BDB8,0xF79026B9,0x7FB563B3,0xF75DFF66,0x7FB1F5FC, +0xF72BD967,0x7FAE7495,0xF6F9B4C6,0x7FAADF7C,0xF6C79188,0x7FA736B4,0xF6956FB7, +0x7FA37A3C,0xF6634F59,0x7F9FAA15,0xF6313077,0x7F9BC640,0xF5FF1318,0x7F97CEBD, +0xF5CCF743,0x7F93C38C,0xF59ADD02,0x7F8FA4B0,0xF568C45B,0x7F8B7227,0xF536AD56, +0x7F872BF3,0xF50497FB,0x7F82D214,0xF4D28451,0x7F7E648C,0xF4A07261,0x7F79E35A, +0xF46E6231,0x7F754E80,0xF43C53CB,0x7F70A5FE,0xF40A4735,0x7F6BE9D4,0xF3D83C77, +0x7F671A05,0xF3A63398,0x7F62368F,0xF3742CA2,0x7F5D3F75,0xF342279B,0x7F5834B7, +0xF310248A,0x7F531655,0xF2DE2379,0x7F4DE451,0xF2AC246E,0x7F489EAA,0xF27A2771, +0x7F434563,0xF2482C8A,0x7F3DD87C,0xF21633C0,0x7F3857F6,0xF1E43D1C,0x7F32C3D1, +0xF1B248A5,0x7F2D1C0E,0xF1805662,0x7F2760AF,0xF14E665C,0x7F2191B4,0xF11C789A, +0x7F1BAF1E,0xF0EA8D24,0x7F15B8EE,0xF0B8A401,0x7F0FAF25,0xF086BD39,0x7F0991C4, +0xF054D8D5,0x7F0360CB,0xF022F6DA,0x7EFD1C3C,0xEFF11753,0x7EF6C418,0xEFBF3A45, +0x7EF05860,0xEF8D5FB8,0x7EE9D914,0xEF5B87B5,0x7EE34636,0xEF29B243,0x7EDC9FC6, +0xEEF7DF6A,0x7ED5E5C6,0xEEC60F31,0x7ECF1837,0xEE9441A0,0x7EC8371A,0xEE6276BF, +0x7EC14270,0xEE30AE96,0x7EBA3A39,0xEDFEE92B,0x7EB31E78,0xEDCD2687,0x7EABEF2C, +0xED9B66B2,0x7EA4AC58,0xED69A9B3,0x7E9D55FC,0xED37EF91,0x7E95EC1A,0xED063856, +0x7E8E6EB2,0xECD48407,0x7E86DDC6,0xECA2D2AD,0x7E7F3957,0xEC71244F,0x7E778166, +0xEC3F78F6,0x7E6FB5F4,0xEC0DD0A8,0x7E67D703,0xEBDC2B6E,0x7E5FE493,0xEBAA894F, +0x7E57DEA7,0xEB78EA52,0x7E4FC53E,0xEB474E81,0x7E47985B,0xEB15B5E1,0x7E3F57FF, +0xEAE4207A,0x7E37042A,0xEAB28E56,0x7E2E9CDF,0xEA80FF7A,0x7E26221F,0xEA4F73EE, +0x7E1D93EA,0xEA1DEBBB,0x7E14F242,0xE9EC66E8,0x7E0C3D29,0xE9BAE57D,0x7E0374A0, +0xE9896781,0x7DFA98A8,0xE957ECFB,0x7DF1A942,0xE92675F4,0x7DE8A670,0xE8F50273, +0x7DDF9034,0xE8C39280,0x7DD6668F,0xE8922622,0x7DCD2981,0xE860BD61,0x7DC3D90D, +0xE82F5844,0x7DBA7534,0xE7FDF6D4,0x7DB0FDF8,0xE7CC9917,0x7DA77359,0xE79B3F16, +0x7D9DD55A,0xE769E8D8,0x7D9423FC,0xE7389665,0x7D8A5F40,0xE70747C4,0x7D808728, +0xE6D5FCFC,0x7D769BB5,0xE6A4B616,0x7D6C9CE9,0xE6737319,0x7D628AC6,0xE642340D, +0x7D58654D,0xE610F8F9,0x7D4E2C7F,0xE5DFC1E5,0x7D43E05E,0xE5AE8ED8,0x7D3980EC, +0xE57D5FDA,0x7D2F0E2B,0xE54C34F3,0x7D24881B,0xE51B0E2A,0x7D19EEBF,0xE4E9EB87, +0x7D0F4218,0xE4B8CD11,0x7D048228,0xE487B2D0,0x7CF9AEF0,0xE4569CCB,0x7CEEC873, +0xE4258B0A,0x7CE3CEB2,0xE3F47D96,0x7CD8C1AE,0xE3C37474,0x7CCDA169,0xE3926FAD, +0x7CC26DE5,0xE3616F48,0x7CB72724,0xE330734D,0x7CABCD28,0xE2FF7BC3,0x7CA05FF1, +0xE2CE88B3,0x7C94DF83,0xE29D9A23,0x7C894BDE,0xE26CB01B,0x7C7DA505,0xE23BCAA2, +0x7C71EAF9,0xE20AE9C1,0x7C661DBC,0xE1DA0D7E,0x7C5A3D50,0xE1A935E2,0x7C4E49B7, +0xE17862F3,0x7C4242F2,0xE14794BA,0x7C362904,0xE116CB3D,0x7C29FBEE,0xE0E60685, +0x7C1DBBB3,0xE0B54698,0x7C116853,0xE0848B7F,0x7C0501D2,0xE053D541,0x7BF88830, +0xE02323E5,0x7BEBFB70,0xDFF27773,0x7BDF5B94,0xDFC1CFF3,0x7BD2A89E,0xDF912D6B, +0x7BC5E290,0xDF608FE4,0x7BB9096B,0xDF2FF764,0x7BAC1D31,0xDEFF63F4,0x7B9F1DE6, +0xDECED59B,0x7B920B89,0xDE9E4C60,0x7B84E61F,0xDE6DC84B,0x7B77ADA8,0xDE3D4964, +0x7B6A6227,0xDE0CCFB1,0x7B5D039E,0xDDDC5B3B,0x7B4F920E,0xDDABEC08,0x7B420D7A, +0xDD7B8220,0x7B3475E5,0xDD4B1D8C,0x7B26CB4F,0xDD1ABE51,0x7B190DBC,0xDCEA6478, +0x7B0B3D2C,0xDCBA1008,0x7AFD59A4,0xDC89C109,0x7AEF6323,0xDC597781,0x7AE159AE, +0xDC293379,0x7AD33D45,0xDBF8F4F8,0x7AC50DEC,0xDBC8BC06,0x7AB6CBA4,0xDB9888A8, +0x7AA8766F,0xDB685AE9,0x7A9A0E50,0xDB3832CD,0x7A8B9348,0xDB08105E,0x7A7D055B, +0xDAD7F3A2,0x7A6E648A,0xDAA7DCA1,0x7A5FB0D8,0xDA77CB63,0x7A50EA47,0xDA47BFEE, +0x7A4210D8,0xDA17BA4A,0x7A332490,0xD9E7BA7F,0x7A24256F,0xD9B7C094,0x7A151378, +0xD987CC90,0x7A05EEAD,0xD957DE7A,0x79F6B711,0xD927F65B,0x79E76CA7,0xD8F81439, +0x79D80F6F,0xD8C8381D,0x79C89F6E,0xD898620C,0x79B91CA4,0xD868920F,0x79A98715, +0xD838C82D,0x7999DEC4,0xD809046E,0x798A23B1,0xD7D946D8,0x797A55E0,0xD7A98F73, +0x796A7554,0xD779DE47,0x795A820E,0xD74A335B,0x794A7C12,0xD71A8EB5,0x793A6361, +0xD6EAF05F,0x792A37FE,0xD6BB585E,0x7919F9EC,0xD68BC6BA,0x7909A92D,0xD65C3B7B, +0x78F945C3,0xD62CB6A8,0x78E8CFB2,0xD5FD3848,0x78D846FB,0xD5CDC062,0x78C7ABA2, +0xD59E4EFF,0x78B6FDA8,0xD56EE424,0x78A63D11,0xD53F7FDA,0x789569DF,0xD5102228, +0x78848414,0xD4E0CB15,0x78738BB3,0xD4B17AA8,0x786280BF,0xD48230E9,0x7851633B, 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+0xA60C21EE,0x5A82799A,0xA57D8666,0x59F3DE12,0xA4EFCA31,0x59646498,0xA462EEAC, +0x58D40E8C,0xA3D6F534,0x5842DD54,0xA34BDF20,0x57B0D256,0xA2C1ADC9,0x571DEEFA, +0xA2386284,0x568A34A9,0xA1AFFEA3,0x55F5A4D2,0xA1288376,0x556040E2,0xA0A1F24D, +0x54CA0A4B,0xA01C4C73,0x5433027D,0x9F979331,0x539B2AF0,0x9F13C7D0,0x53028518, +0x9E90EB94,0x5269126E,0x9E0EFFC1,0x51CED46E,0x9D8E0597,0x5133CC94,0x9D0DFE54, +0x5097FC5E,0x9C8EEB34,0x4FFB654D,0x9C10CD70,0x4F5E08E3,0x9B93A641,0x4EBFE8A5, +0x9B1776DA,0x4E210617,0x9A9C406E,0x4D8162C4,0x9A22042D,0x4CE10034,0x99A8C345, +0x4C3FDFF4,0x99307EE0,0x4B9E0390,0x98B93828,0x4AFB6C98,0x9842F043,0x4A581C9E, +0x97CDA855,0x49B41533,0x9759617F,0x490F57EE,0x96E61CE0,0x4869E665,0x9673DB94, +0x47C3C22F,0x96029EB6,0x471CECE7,0x9592675C,0x46756828,0x9523369C,0x45CD358F, +0x94B50D87,0x452456BD,0x9447ED2F,0x447ACD50,0x93DBD6A0,0x43D09AED,0x9370CAE4, +0x4325C135,0x9306CB04,0x427A41D0,0x929DD806,0x41CE1E65,0x9235F2EC,0x4121589B, +0x91CF1CB6,0x4073F21D,0x91695663,0x3FC5EC98,0x9104A0EE,0x3F1749B8,0x90A0FD4E, +0x3E680B2C,0x903E6C7B,0x3DB832A6,0x8FDCEF66,0x3D07C1D6,0x8F7C8701,0x3C56BA70, +0x8F1D343A,0x3BA51E29,0x8EBEF7FB,0x3AF2EEB7,0x8E61D32E,0x3A402DD2,0x8E05C6B7, +0x398CDD32,0x8DAAD37B,0x38D8FE93,0x8D50FA59,0x382493B0,0x8CF83C30,0x376F9E46, +0x8CA099DA,0x36BA2014,0x8C4A142F,0x36041AD9,0x8BF4AC05,0x354D9057,0x8BA0622F, +0x34968250,0x8B4D377C,0x33DEF287,0x8AFB2CBB,0x3326E2C3,0x8AAA42B4,0x326E54C7, +0x8A5A7A31,0x31B54A5E,0x8A0BD3F5,0x30FBC54D,0x89BE50C3,0x3041C761,0x8971F15A, +0x2F875262,0x8926B677,0x2ECC681E,0x88DCA0D3,0x2E110A62,0x8893B125,0x2D553AFC, +0x884BE821,0x2C98FBBA,0x88054677,0x2BDC4E6F,0x87BFCCD7,0x2B1F34EB,0x877B7BEC, +0x2A61B101,0x8738545E,0x29A3C485,0x86F656D3,0x28E5714B,0x86B583EE,0x2826B928, +0x8675DC4F,0x27679DF4,0x86376092,0x26A82186,0x85FA1153,0x25E845B6,0x85BDEF28, +0x25280C5E,0x8582FAA5,0x24677758,0x8549345C,0x23A6887F,0x85109CDD,0x22E541AF, +0x84D934B1,0x2223A4C5,0x84A2FC62,0x2161B3A0,0x846DF477,0x209F701C,0x843A1D70, +0x1FDCDC1B,0x840777D0,0x1F19F97B,0x83D60412,0x1E56CA1E,0x83A5C2B0,0x1D934FE5, +0x8376B422,0x1CCF8CB3,0x8348D8DC,0x1C0B826A,0x831C314E,0x1B4732EF,0x82F0BDE8, +0x1A82A026,0x82C67F14,0x19BDCBF3,0x829D753A,0x18F8B83C,0x8275A0C0,0x183366E9, +0x824F0208,0x176DD9DE,0x82299971,0x16A81305,0x82056758,0x15E21445,0x81E26C16, +0x151BDF86,0x81C0A801,0x145576B1,0x81A01B6D,0x138EDBB1,0x8180C6A9,0x12C8106F, +0x8162AA04,0x120116D5,0x8145C5C7,0x1139F0CF,0x812A1A3A,0x1072A048,0x810FA7A0, +0x0FAB272B,0x80F66E3C,0x0EE38766,0x80DE6E4C,0x0E1BC2E4,0x80C7A80A,0x0D53DB92, +0x80B21BAF,0x0C8BD35E,0x809DC971,0x0BC3AC35,0x808AB180,0x0AFB6805,0x8078D40D, +0x0A3308BD,0x80683143,0x096A9049,0x8058C94C,0x08A2009A,0x804A9C4D,0x07D95B9E, +0x803DAA6A,0x0710A345,0x8031F3C2,0x0647D97C,0x80277872,0x057F0035,0x801E3895, +0x04B6195D,0x80163440,0x03ED26E6,0x800F6B88,0x03242ABF,0x8009DE7E,0x025B26D7, +0x80058D2F,0x01921D20,0x800277A6,0x00C90F88,0x80009DEA,0x7FFFFFFF,0x00000000, +0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684,0x7FA736B4,0xF6956FB7,0x7F62368F, +0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC,0xED37EF91,0x7E1D93EA,0xEA1DEBBB, +0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96,0x7C29FBEE,0xE0E60685,0x7B5D039E, +0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1,0xD7D946D8,0x78848414,0xD4E0CB15, +0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3,0x7504D345,0xCC210D79,0x73B5EBD1, +0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6,0xC3A94590,0x6F5F02B2,0xC0E8B648, +0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0,0x6A6D98A4,0xB8E31319,0x68A69E81, +0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926,0xB140175B,0x62F201AC,0xAECC336C, +0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E,0x5CB420E0,0xA7BD22AC,0x5A82799A, +0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2,0xA1288376,0x539B2AF0,0x9F13C7D0, +0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA,0x4C3FDFF4,0x99307EE0,0x49B41533, +0x9759617F,0x471CECE7,0x9592675C,0x447ACD50,0x93DBD6A0,0x41CE1E65,0x9235F2EC, +0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A,0x398CDD32,0x8DAAD37B,0x36BA2014, +0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D,0x89BE50C3,0x2E110A62,0x8893B125, +0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F,0x25280C5E,0x8582FAA5,0x2223A4C5, +0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A,0x831C314E,0x18F8B83C,0x8275A0C0, +0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04,0x0FAB272B,0x80F66E3C,0x0C8BD35E, +0x809DC971,0x096A9049,0x8058C94C,0x0647D97C,0x80277872,0x03242ABF,0x8009DE7E, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x7FFFFFFF,0x00000000,0x7641AF3D, +0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D,0x89BE50C3,}; + +const q31_t rearranged_twiddle_stride2_4096_q31[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FFFD886,0xFF9B781D,0x7FFF6216,0xFF36F078,0x7FFE9CB2, +0xFED2694F,0x7FFD885A,0xFE6DE2E0,0x7FFC250F,0xFE095D69,0x7FFA72D1,0xFDA4D929, +0x7FF871A2,0xFD40565C,0x7FF62182,0xFCDBD541,0x7FF38274,0xFC775616,0x7FF09478, +0xFC12D91A,0x7FED5791,0xFBAE5E89,0x7FE9CBC0,0xFB49E6A3,0x7FE5F108,0xFAE571A4, +0x7FE1C76B,0xFA80FFCB,0x7FDD4EEC,0xFA1C9157,0x7FD8878E,0xF9B82684,0x7FD37153, +0xF953BF91,0x7FCE0C3E,0xF8EF5CBB,0x7FC85854,0xF88AFE42,0x7FC25596,0xF826A462, +0x7FBC040A,0xF7C24F59,0x7FB563B3,0xF75DFF66,0x7FAE7495,0xF6F9B4C6,0x7FA736B4, +0xF6956FB7,0x7F9FAA15,0xF6313077,0x7F97CEBD,0xF5CCF743,0x7F8FA4B0,0xF568C45B, +0x7F872BF3,0xF50497FB,0x7F7E648C,0xF4A07261,0x7F754E80,0xF43C53CB,0x7F6BE9D4, +0xF3D83C77,0x7F62368F,0xF3742CA2,0x7F5834B7,0xF310248A,0x7F4DE451,0xF2AC246E, +0x7F434563,0xF2482C8A,0x7F3857F6,0xF1E43D1C,0x7F2D1C0E,0xF1805662,0x7F2191B4, +0xF11C789A,0x7F15B8EE,0xF0B8A401,0x7F0991C4,0xF054D8D5,0x7EFD1C3C,0xEFF11753, +0x7EF05860,0xEF8D5FB8,0x7EE34636,0xEF29B243,0x7ED5E5C6,0xEEC60F31,0x7EC8371A, +0xEE6276BF,0x7EBA3A39,0xEDFEE92B,0x7EABEF2C,0xED9B66B2,0x7E9D55FC,0xED37EF91, +0x7E8E6EB2,0xECD48407,0x7E7F3957,0xEC71244F,0x7E6FB5F4,0xEC0DD0A8,0x7E5FE493, +0xEBAA894F,0x7E4FC53E,0xEB474E81,0x7E3F57FF,0xEAE4207A,0x7E2E9CDF,0xEA80FF7A, +0x7E1D93EA,0xEA1DEBBB,0x7E0C3D29,0xE9BAE57D,0x7DFA98A8,0xE957ECFB,0x7DE8A670, +0xE8F50273,0x7DD6668F,0xE8922622,0x7DC3D90D,0xE82F5844,0x7DB0FDF8,0xE7CC9917, +0x7D9DD55A,0xE769E8D8,0x7D8A5F40,0xE70747C4,0x7D769BB5,0xE6A4B616,0x7D628AC6, +0xE642340D,0x7D4E2C7F,0xE5DFC1E5,0x7D3980EC,0xE57D5FDA,0x7D24881B,0xE51B0E2A, +0x7D0F4218,0xE4B8CD11,0x7CF9AEF0,0xE4569CCB,0x7CE3CEB2,0xE3F47D96,0x7CCDA169, +0xE3926FAD,0x7CB72724,0xE330734D,0x7CA05FF1,0xE2CE88B3,0x7C894BDE,0xE26CB01B, +0x7C71EAF9,0xE20AE9C1,0x7C5A3D50,0xE1A935E2,0x7C4242F2,0xE14794BA,0x7C29FBEE, +0xE0E60685,0x7C116853,0xE0848B7F,0x7BF88830,0xE02323E5,0x7BDF5B94,0xDFC1CFF3, +0x7BC5E290,0xDF608FE4,0x7BAC1D31,0xDEFF63F4,0x7B920B89,0xDE9E4C60,0x7B77ADA8, +0xDE3D4964,0x7B5D039E,0xDDDC5B3B,0x7B420D7A,0xDD7B8220,0x7B26CB4F,0xDD1ABE51, +0x7B0B3D2C,0xDCBA1008,0x7AEF6323,0xDC597781,0x7AD33D45,0xDBF8F4F8,0x7AB6CBA4, +0xDB9888A8,0x7A9A0E50,0xDB3832CD,0x7A7D055B,0xDAD7F3A2,0x7A5FB0D8,0xDA77CB63, +0x7A4210D8,0xDA17BA4A,0x7A24256F,0xD9B7C094,0x7A05EEAD,0xD957DE7A,0x79E76CA7, +0xD8F81439,0x79C89F6E,0xD898620C,0x79A98715,0xD838C82D,0x798A23B1,0xD7D946D8, +0x796A7554,0xD779DE47,0x794A7C12,0xD71A8EB5,0x792A37FE,0xD6BB585E,0x7909A92D, +0xD65C3B7B,0x78E8CFB2,0xD5FD3848,0x78C7ABA2,0xD59E4EFF,0x78A63D11,0xD53F7FDA, +0x78848414,0xD4E0CB15,0x786280BF,0xD48230E9,0x78403329,0xD423B191,0x781D9B65, +0xD3C54D47,0x77FAB989,0xD3670446,0x77D78DAA,0xD308D6C7,0x77B417DF,0xD2AAC504, 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+0x7C894BDE,0xE26CB01B,0x7C29FBEE,0xE0E60685,0x7BC5E290,0xDF608FE4,0x7B5D039E, +0xDDDC5B3B,0x7AEF6323,0xDC597781,0x7A7D055B,0xDAD7F3A2,0x7A05EEAD,0xD957DE7A, +0x798A23B1,0xD7D946D8,0x7909A92D,0xD65C3B7B,0x78848414,0xD4E0CB15,0x77FAB989, +0xD3670446,0x776C4EDB,0xD1EEF59E,0x76D94989,0xD078AD9E,0x7641AF3D,0xCF043AB3, +0x75A585CF,0xCD91AB39,0x7504D345,0xCC210D79,0x745F9DD1,0xCAB26FA9,0x73B5EBD1, +0xC945DFEC,0x7307C3D0,0xC7DB6C50,0x72552C85,0xC67322CE,0x719E2CD2,0xC50D1149, +0x70E2CBC6,0xC3A94590,0x7023109A,0xC247CD5A,0x6F5F02B2,0xC0E8B648,0x6E96A99D, +0xBF8C0DE3,0x6DCA0D14,0xBE31E19B,0x6CF934FC,0xBCDA3ECB,0x6C242960,0xBB8532B0, +0x6B4AF279,0xBA32CA71,0x6A6D98A4,0xB8E31319,0x698C246C,0xB796199B,0x68A69E81, +0xB64BEACD,0x67BD0FBD,0xB5049368,0x66CF8120,0xB3C0200C,0x65DDFBD3,0xB27E9D3C, +0x64E88926,0xB140175B,0x63EF3290,0xB0049AB3,0x62F201AC,0xAECC336C,0x61F1003F, +0xAD96ED92,0x60EC3830,0xAC64D510,0x5FE3B38D,0xAB35F5B5,0x5ED77C8A,0xAA0A5B2E, +0x5DC79D7C,0xA8E21106,0x5CB420E0,0xA7BD22AC,0x5B9D1154,0xA69B9B68,0x5A82799A, +0xA57D8666,0x59646498,0xA462EEAC,0x5842DD54,0xA34BDF20,0x571DEEFA,0xA2386284, +0x55F5A4D2,0xA1288376,0x54CA0A4B,0xA01C4C73,0x539B2AF0,0x9F13C7D0,0x5269126E, +0x9E0EFFC1,0x5133CC94,0x9D0DFE54,0x4FFB654D,0x9C10CD70,0x4EBFE8A5,0x9B1776DA, +0x4D8162C4,0x9A22042D,0x4C3FDFF4,0x99307EE0,0x4AFB6C98,0x9842F043,0x49B41533, +0x9759617F,0x4869E665,0x9673DB94,0x471CECE7,0x9592675C,0x45CD358F,0x94B50D87, +0x447ACD50,0x93DBD6A0,0x4325C135,0x9306CB04,0x41CE1E65,0x9235F2EC,0x4073F21D, +0x91695663,0x3F1749B8,0x90A0FD4E,0x3DB832A6,0x8FDCEF66,0x3C56BA70,0x8F1D343A, +0x3AF2EEB7,0x8E61D32E,0x398CDD32,0x8DAAD37B,0x382493B0,0x8CF83C30,0x36BA2014, +0x8C4A142F,0x354D9057,0x8BA0622F,0x33DEF287,0x8AFB2CBB,0x326E54C7,0x8A5A7A31, +0x30FBC54D,0x89BE50C3,0x2F875262,0x8926B677,0x2E110A62,0x8893B125,0x2C98FBBA, +0x88054677,0x2B1F34EB,0x877B7BEC,0x29A3C485,0x86F656D3,0x2826B928,0x8675DC4F, +0x26A82186,0x85FA1153,0x25280C5E,0x8582FAA5,0x23A6887F,0x85109CDD,0x2223A4C5, +0x84A2FC62,0x209F701C,0x843A1D70,0x1F19F97B,0x83D60412,0x1D934FE5,0x8376B422, +0x1C0B826A,0x831C314E,0x1A82A026,0x82C67F14,0x18F8B83C,0x8275A0C0,0x176DD9DE, +0x82299971,0x15E21445,0x81E26C16,0x145576B1,0x81A01B6D,0x12C8106F,0x8162AA04, +0x1139F0CF,0x812A1A3A,0x0FAB272B,0x80F66E3C,0x0E1BC2E4,0x80C7A80A,0x0C8BD35E, +0x809DC971,0x0AFB6805,0x8078D40D,0x096A9049,0x8058C94C,0x07D95B9E,0x803DAA6A, +0x0647D97C,0x80277872,0x04B6195D,0x80163440,0x03242ABF,0x8009DE7E,0x01921D20, +0x800277A6,0x00000000,0x80000000,0xFE6DE2E0,0x800277A6,0xFCDBD541,0x8009DE7E, +0xFB49E6A3,0x80163440,0xF9B82684,0x80277872,0xF826A462,0x803DAA6A,0xF6956FB7, +0x8058C94C,0xF50497FB,0x8078D40D,0xF3742CA2,0x809DC971,0xF1E43D1C,0x80C7A80A, +0xF054D8D5,0x80F66E3C,0xEEC60F31,0x812A1A3A,0xED37EF91,0x8162AA04,0xEBAA894F, +0x81A01B6D,0xEA1DEBBB,0x81E26C16,0xE8922622,0x82299971,0xE70747C4,0x8275A0C0, +0xE57D5FDA,0x82C67F14,0xE3F47D96,0x831C314E,0xE26CB01B,0x8376B422,0xE0E60685, +0x83D60412,0xDF608FE4,0x843A1D70,0xDDDC5B3B,0x84A2FC62,0xDC597781,0x85109CDD, +0xDAD7F3A2,0x8582FAA5,0xD957DE7A,0x85FA1153,0xD7D946D8,0x8675DC4F,0xD65C3B7B, +0x86F656D3,0xD4E0CB15,0x877B7BEC,0xD3670446,0x88054677,0xD1EEF59E,0x8893B125, +0xD078AD9E,0x8926B677,0xCF043AB3,0x89BE50C3,0xCD91AB39,0x8A5A7A31,0xCC210D79, +0x8AFB2CBB,0xCAB26FA9,0x8BA0622F,0xC945DFEC,0x8C4A142F,0xC7DB6C50,0x8CF83C30, +0xC67322CE,0x8DAAD37B,0xC50D1149,0x8E61D32E,0xC3A94590,0x8F1D343A,0xC247CD5A, +0x8FDCEF66,0xC0E8B648,0x90A0FD4E,0xBF8C0DE3,0x91695663,0xBE31E19B,0x9235F2EC, +0xBCDA3ECB,0x9306CB04,0xBB8532B0,0x93DBD6A0,0xBA32CA71,0x94B50D87,0xB8E31319, +0x9592675C,0xB796199B,0x9673DB94,0xB64BEACD,0x9759617F,0xB5049368,0x9842F043, +0xB3C0200C,0x99307EE0,0xB27E9D3C,0x9A22042D,0xB140175B,0x9B1776DA,0xB0049AB3, +0x9C10CD70,0xAECC336C,0x9D0DFE54,0xAD96ED92,0x9E0EFFC1,0xAC64D510,0x9F13C7D0, +0xAB35F5B5,0xA01C4C73,0xAA0A5B2E,0xA1288376,0xA8E21106,0xA2386284,0xA7BD22AC, +0xA34BDF20,0xA69B9B68,0xA462EEAC,0xA57D8666,0xA57D8666,0xA462EEAC,0xA69B9B68, +0xA34BDF20,0xA7BD22AC,0xA2386284,0xA8E21106,0xA1288376,0xAA0A5B2E,0xA01C4C73, +0xAB35F5B5,0x9F13C7D0,0xAC64D510,0x9E0EFFC1,0xAD96ED92,0x9D0DFE54,0xAECC336C, +0x9C10CD70,0xB0049AB3,0x9B1776DA,0xB140175B,0x9A22042D,0xB27E9D3C,0x99307EE0, +0xB3C0200C,0x9842F043,0xB5049368,0x9759617F,0xB64BEACD,0x9673DB94,0xB796199B, +0x9592675C,0xB8E31319,0x94B50D87,0xBA32CA71,0x93DBD6A0,0xBB8532B0,0x9306CB04, +0xBCDA3ECB,0x9235F2EC,0xBE31E19B,0x91695663,0xBF8C0DE3,0x90A0FD4E,0xC0E8B648, +0x8FDCEF66,0xC247CD5A,0x8F1D343A,0xC3A94590,0x8E61D32E,0xC50D1149,0x8DAAD37B, +0xC67322CE,0x8CF83C30,0xC7DB6C50,0x8C4A142F,0xC945DFEC,0x8BA0622F,0xCAB26FA9, +0x8AFB2CBB,0xCC210D79,0x8A5A7A31,0xCD91AB39,0x89BE50C3,0xCF043AB3,0x8926B677, +0xD078AD9E,0x8893B125,0xD1EEF59E,0x88054677,0xD3670446,0x877B7BEC,0xD4E0CB15, +0x86F656D3,0xD65C3B7B,0x8675DC4F,0xD7D946D8,0x85FA1153,0xD957DE7A,0x8582FAA5, +0xDAD7F3A2,0x85109CDD,0xDC597781,0x84A2FC62,0xDDDC5B3B,0x843A1D70,0xDF608FE4, +0x83D60412,0xE0E60685,0x8376B422,0xE26CB01B,0x831C314E,0xE3F47D96,0x82C67F14, +0xE57D5FDA,0x8275A0C0,0xE70747C4,0x82299971,0xE8922622,0x81E26C16,0xEA1DEBBB, +0x81A01B6D,0xEBAA894F,0x8162AA04,0xED37EF91,0x812A1A3A,0xEEC60F31,0x80F66E3C, +0xF054D8D5,0x80C7A80A,0xF1E43D1C,0x809DC971,0xF3742CA2,0x8078D40D,0xF50497FB, +0x8058C94C,0xF6956FB7,0x803DAA6A,0xF826A462,0x80277872,0xF9B82684,0x80163440, +0xFB49E6A3,0x8009DE7E,0xFCDBD541,0x800277A6,0xFE6DE2E0,0x7FFFFFFF,0x00000000, +0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91,0x7D8A5F40, +0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414,0xD4E0CB15, +0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590,0x6DCA0D14, +0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC,0xAECC336C, +0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376,0x5133CC94, +0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65,0x9235F2EC, +0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3,0x2B1F34EB, +0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C,0x8275A0C0, +0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872,0x00000000, +0x80000000,0xF9B82684,0x80277872,0xF3742CA2,0x809DC971,0xED37EF91,0x8162AA04, +0xE70747C4,0x8275A0C0,0xE0E60685,0x83D60412,0xDAD7F3A2,0x8582FAA5,0xD4E0CB15, +0x877B7BEC,0xCF043AB3,0x89BE50C3,0xC945DFEC,0x8C4A142F,0xC3A94590,0x8F1D343A, +0xBE31E19B,0x9235F2EC,0xB8E31319,0x9592675C,0xB3C0200C,0x99307EE0,0xAECC336C, +0x9D0DFE54,0xAA0A5B2E,0xA1288376,0xA57D8666,0xA57D8666,0xA1288376,0xAA0A5B2E, +0x9D0DFE54,0xAECC336C,0x99307EE0,0xB3C0200C,0x9592675C,0xB8E31319,0x9235F2EC, +0xBE31E19B,0x8F1D343A,0xC3A94590,0x8C4A142F,0xC945DFEC,0x89BE50C3,0xCF043AB3, +0x877B7BEC,0xD4E0CB15,0x8582FAA5,0xDAD7F3A2,0x83D60412,0xE0E60685,0x8275A0C0, +0xE70747C4,0x8162AA04,0xED37EF91,0x809DC971,0xF3742CA2,0x80277872,0xF9B82684, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x5A82799A, +0xA57D8666,0x00000000,0x80000000,0xA57D8666,0xA57D8666,}; + +const q31_t rearranged_twiddle_stride3_4096_q31[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFFFFFF,0x00000000,0x7FFFA72C,0xFF69343F,0x7FFE9CB2,0xFED2694F,0x7FFCE093, +0xFE3BA002,0x7FFA72D1,0xFDA4D929,0x7FF75370,0xFD0E1594,0x7FF38274,0xFC775616, +0x7FEEFFE1,0xFBE09B80,0x7FE9CBC0,0xFB49E6A3,0x7FE3E616,0xFAB3384F,0x7FDD4EEC, 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+0xE70747C4,0x809DC971,0x0C8BD35E,0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94, +0xB8E31319,0x6A6D98A4,0xDAD7F3A2,0x7A7D055B,0x7FFFFFFF,0x00000000,0x30FBC54D, +0x89BE50C3,0xA57D8666,0xA57D8666,0x89BE50C3,0x30FBC54D,}; + + +#endif /* defined(ARM_MATH_MVEI) */ + + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + +const uint32_t rearranged_twiddle_tab_stride1_arr_16_q15[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_16_q15[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_16_q15[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const q15_t rearranged_twiddle_stride1_16_q15[8] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,}; + +const q15_t rearranged_twiddle_stride2_16_q15[8] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x5A82,0xA57E,0x0000,0x8000,0xA57E,0xA57E,}; + +const q15_t rearranged_twiddle_stride3_16_q15[8] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E,0x89BE,0x30FC,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_64_q15[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_64_q15[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_64_q15[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const q15_t rearranged_twiddle_stride1_64_q15[40] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642,0xCF04,0x70E3, +0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E,0x471D,0x9592, +0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C,0x809E,0x7FFF, +0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,}; + +const q15_t rearranged_twiddle_stride2_64_q15[40] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04,0x89BE, +0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707,0x7FFF, +0x0000,0x5A82,0xA57E,0x0000,0x8000,0xA57E,0xA57E,}; + +const q15_t rearranged_twiddle_stride3_64_q15[40] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x30FC,0x89BE,0xA57E,0xA57E,0x89BE,0x30FC,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_256_q15[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_256_q15[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_256_q15[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const q15_t rearranged_twiddle_stride1_256_q15[168] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A, +0xF055,0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6, +0x7B5D,0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642, +0xCF04,0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9, +0x6DCA,0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9, +0xB140,0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E, +0x5843,0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40, +0x9930,0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1, +0x3C57,0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11, +0x8894,0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6, +0x1C0C,0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C, +0x809E,0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7F62,0xF374, +0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642,0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2, +0xAECC,0x5A82,0xA57E,0x5134,0x9D0E,0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE, +0x2528,0x8583,0x18F9,0x8276,0x0C8C,0x809E,0x7FFF,0x0000,0x7642,0xCF04,0x5A82, +0xA57E,0x30FC,0x89BE,}; + +const q15_t rearranged_twiddle_stride2_256_q15[168] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A, +0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9, +0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82, +0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236, +0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A, +0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000, +0xF9B8,0x8027,0xF374,0x809E,0xED38,0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8, +0x8583,0xD4E1,0x877B,0xCF04,0x89BE,0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236, +0xB8E3,0x9592,0xB3C0,0x9930,0xAECC,0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129, +0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0,0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9, +0x8C4A,0xC946,0x89BE,0xCF04,0x877B,0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276, +0xE707,0x8163,0xED38,0x809E,0xF374,0x8027,0xF9B8,0x7FFF,0x0000,0x7D8A,0xE707, +0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D,0x9592,0x30FC,0x89BE,0x18F9, +0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04,0x89BE,0xB8E3,0x9592,0xA57E,0xA57E, +0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707,0x7FFF,0x0000,0x5A82,0xA57E,0x0000, +0x8000,0xA57E,0xA57E,}; + +const q15_t rearranged_twiddle_stride3_256_q15[168] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D,0xDAD8,0x776C, +0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140,0x5ED7,0xAA0A, +0x5843,0xA34C,0x5134,0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D,0x8DAB,0x30FC, +0x89BE,0x2827,0x8676,0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E,0x0324,0x800A, +0xF9B8,0x8027,0xF055,0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1,0x877B,0xCC21, +0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14,0xA57E,0xA57E, +0x9F14,0xAC65,0x9930,0xB3C0,0x93DC,0xBB85,0x8F1D,0xC3A9,0x8AFB,0xCC21,0x877B, +0xD4E1,0x84A3,0xDDDC,0x8276,0xE707,0x80F6,0xF055,0x8027,0xF9B8,0x800A,0x0324, +0x809E,0x0C8C,0x81E2,0x15E2,0x83D6,0x1F1A,0x8676,0x2827,0x89BE,0x30FC,0x8DAB, +0x398D,0x9236,0x41CE,0x9759,0x49B4,0x9D0E,0x5134,0xA34C,0x5843,0xAA0A,0x5ED7, +0xB140,0x64E9,0xB8E3,0x6A6E,0xC0E9,0x6F5F,0xC946,0x73B6,0xD1EF,0x776C,0xDAD8, +0x7A7D,0xE3F4,0x7CE4,0xED38,0x7E9D,0xF695,0x7FA7,0x7FFF,0x0000,0x7A7D,0xDAD8, +0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C,0x809E,0xE707,0x8276,0xC3A9, +0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707,0x809E,0x0C8C,0x89BE,0x30FC, +0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E, +0xA57E,0x89BE,0x30FC,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_1024_q15[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_1024_q15[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_1024_q15[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const q15_t rearranged_twiddle_stride1_1024_q15[680] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FFF,0xFF37,0x7FFE,0xFE6E,0x7FFA,0xFDA5,0x7FF6,0xFCDC,0x7FF1, +0xFC13,0x7FEA,0xFB4A,0x7FE2,0xFA81,0x7FD9,0xF9B8,0x7FCE,0xF8EF,0x7FC2,0xF827, +0x7FB5,0xF75E,0x7FA7,0xF695,0x7F98,0xF5CD,0x7F87,0xF505,0x7F75,0xF43C,0x7F62, +0xF374,0x7F4E,0xF2AC,0x7F38,0xF1E4,0x7F22,0xF11C,0x7F0A,0xF055,0x7EF0,0xEF8D, +0x7ED6,0xEEC6,0x7EBA,0xEDFF,0x7E9D,0xED38,0x7E7F,0xEC71,0x7E60,0xEBAB,0x7E3F, +0xEAE4,0x7E1E,0xEA1E,0x7DFB,0xE958,0x7DD6,0xE892,0x7DB1,0xE7CD,0x7D8A,0xE707, +0x7D63,0xE642,0x7D3A,0xE57D,0x7D0F,0xE4B9,0x7CE4,0xE3F4,0x7CB7,0xE330,0x7C89, +0xE26D,0x7C5A,0xE1A9,0x7C2A,0xE0E6,0x7BF9,0xE023,0x7BC6,0xDF61,0x7B92,0xDE9E, +0x7B5D,0xDDDC,0x7B27,0xDD1B,0x7AEF,0xDC59,0x7AB7,0xDB99,0x7A7D,0xDAD8,0x7A42, +0xDA18,0x7A06,0xD958,0x79C9,0xD898,0x798A,0xD7D9,0x794A,0xD71B,0x790A,0xD65C, +0x78C8,0xD59E,0x7885,0xD4E1,0x7840,0xD424,0x77FB,0xD367,0x77B4,0xD2AB,0x776C, +0xD1EF,0x7723,0xD134,0x76D9,0xD079,0x768E,0xCFBE,0x7642,0xCF04,0x75F4,0xCE4B, +0x75A6,0xCD92,0x7556,0xCCD9,0x7505,0xCC21,0x74B3,0xCB69,0x7460,0xCAB2,0x740B, +0xC9FC,0x73B6,0xC946,0x735F,0xC890,0x7308,0xC7DB,0x72AF,0xC727,0x7255,0xC673, +0x71FA,0xC5C0,0x719E,0xC50D,0x7141,0xC45B,0x70E3,0xC3A9,0x7083,0xC2F8,0x7023, +0xC248,0x6FC2,0xC198,0x6F5F,0xC0E9,0x6EFB,0xC03A,0x6E97,0xBF8C,0x6E31,0xBEDF, +0x6DCA,0xBE32,0x6D62,0xBD86,0x6CF9,0xBCDA,0x6C8F,0xBC2F,0x6C24,0xBB85,0x6BB8, +0xBADC,0x6B4B,0xBA33,0x6ADD,0xB98B,0x6A6E,0xB8E3,0x69FD,0xB83C,0x698C,0xB796, +0x691A,0xB6F1,0x68A7,0xB64C,0x6832,0xB5A8,0x67BD,0xB505,0x6747,0xB462,0x66D0, +0xB3C0,0x6657,0xB31F,0x65DE,0xB27F,0x6564,0xB1DF,0x64E9,0xB140,0x646C,0xB0A2, +0x63EF,0xB005,0x6371,0xAF68,0x62F2,0xAECC,0x6272,0xAE31,0x61F1,0xAD97,0x616F, +0xACFD,0x60EC,0xAC65,0x6068,0xABCD,0x5FE4,0xAB36,0x5F5E,0xAAA0,0x5ED7,0xAA0A, +0x5E50,0xA976,0x5DC8,0xA8E2,0x5D3E,0xA84F,0x5CB4,0xA7BD,0x5C29,0xA72C,0x5B9D, +0xA69C,0x5B10,0xA60C,0x5A82,0xA57E,0x59F4,0xA4F0,0x5964,0xA463,0x58D4,0xA3D7, +0x5843,0xA34C,0x57B1,0xA2C2,0x571E,0xA238,0x568A,0xA1B0,0x55F6,0xA129,0x5560, +0xA0A2,0x54CA,0xA01C,0x5433,0x9F98,0x539B,0x9F14,0x5303,0x9E91,0x5269,0x9E0F, +0x51CF,0x9D8E,0x5134,0x9D0E,0x5098,0x9C8F,0x4FFB,0x9C11,0x4F5E,0x9B94,0x4EC0, +0x9B17,0x4E21,0x9A9C,0x4D81,0x9A22,0x4CE1,0x99A9,0x4C40,0x9930,0x4B9E,0x98B9, +0x4AFB,0x9843,0x4A58,0x97CE,0x49B4,0x9759,0x490F,0x96E6,0x486A,0x9674,0x47C4, +0x9603,0x471D,0x9592,0x4675,0x9523,0x45CD,0x94B5,0x4524,0x9448,0x447B,0x93DC, +0x43D1,0x9371,0x4326,0x9307,0x427A,0x929E,0x41CE,0x9236,0x4121,0x91CF,0x4074, +0x9169,0x3FC6,0x9105,0x3F17,0x90A1,0x3E68,0x903E,0x3DB8,0x8FDD,0x3D08,0x8F7D, +0x3C57,0x8F1D,0x3BA5,0x8EBF,0x3AF3,0x8E62,0x3A40,0x8E06,0x398D,0x8DAB,0x38D9, +0x8D51,0x3825,0x8CF8,0x3770,0x8CA1,0x36BA,0x8C4A,0x3604,0x8BF5,0x354E,0x8BA0, +0x3497,0x8B4D,0x33DF,0x8AFB,0x3327,0x8AAA,0x326E,0x8A5A,0x31B5,0x8A0C,0x30FC, +0x89BE,0x3042,0x8972,0x2F87,0x8927,0x2ECC,0x88DD,0x2E11,0x8894,0x2D55,0x884C, +0x2C99,0x8805,0x2BDC,0x87C0,0x2B1F,0x877B,0x2A62,0x8738,0x29A4,0x86F6,0x28E5, +0x86B6,0x2827,0x8676,0x2768,0x8637,0x26A8,0x85FA,0x25E8,0x85BE,0x2528,0x8583, +0x2467,0x8549,0x23A7,0x8511,0x22E5,0x84D9,0x2224,0x84A3,0x2162,0x846E,0x209F, +0x843A,0x1FDD,0x8407,0x1F1A,0x83D6,0x1E57,0x83A6,0x1D93,0x8377,0x1CD0,0x8349, +0x1C0C,0x831C,0x1B47,0x82F1,0x1A83,0x82C6,0x19BE,0x829D,0x18F9,0x8276,0x1833, +0x824F,0x176E,0x822A,0x16A8,0x8205,0x15E2,0x81E2,0x151C,0x81C1,0x1455,0x81A0, +0x138F,0x8181,0x12C8,0x8163,0x1201,0x8146,0x113A,0x812A,0x1073,0x8110,0x0FAB, +0x80F6,0x0EE4,0x80DE,0x0E1C,0x80C8,0x0D54,0x80B2,0x0C8C,0x809E,0x0BC4,0x808B, +0x0AFB,0x8079,0x0A33,0x8068,0x096B,0x8059,0x08A2,0x804B,0x07D9,0x803E,0x0711, +0x8032,0x0648,0x8027,0x057F,0x801E,0x04B6,0x8016,0x03ED,0x800F,0x0324,0x800A, +0x025B,0x8006,0x0192,0x8002,0x00C9,0x8001,0x7FFF,0x0000,0x7FF6,0xFCDC,0x7FD9, +0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055,0x7E9D,0xED38,0x7E1E,0xEA1E, +0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D,0xDDDC,0x7A7D,0xDAD8,0x798A, +0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04,0x7505,0xCC21,0x73B6,0xC946, +0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA,0xBE32,0x6C24,0xBB85,0x6A6E, +0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140,0x62F2,0xAECC,0x60EC,0xAC65, +0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843,0xA34C,0x55F6,0xA129,0x539B, +0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930,0x49B4,0x9759,0x471D,0x9592, +0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57,0x8F1D,0x398D,0x8DAB,0x36BA, +0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894,0x2B1F,0x877B,0x2827,0x8676, +0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C,0x831C,0x18F9,0x8276,0x15E2, +0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E,0x096B,0x8059,0x0648,0x8027, +0x0324,0x800A,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,}; + +const q15_t rearranged_twiddle_stride2_1024_q15[680] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FFE,0xFE6E,0x7FF6,0xFCDC,0x7FEA,0xFB4A,0x7FD9,0xF9B8,0x7FC2, +0xF827,0x7FA7,0xF695,0x7F87,0xF505,0x7F62,0xF374,0x7F38,0xF1E4,0x7F0A,0xF055, +0x7ED6,0xEEC6,0x7E9D,0xED38,0x7E60,0xEBAB,0x7E1E,0xEA1E,0x7DD6,0xE892,0x7D8A, +0xE707,0x7D3A,0xE57D,0x7CE4,0xE3F4,0x7C89,0xE26D,0x7C2A,0xE0E6,0x7BC6,0xDF61, +0x7B5D,0xDDDC,0x7AEF,0xDC59,0x7A7D,0xDAD8,0x7A06,0xD958,0x798A,0xD7D9,0x790A, +0xD65C,0x7885,0xD4E1,0x77FB,0xD367,0x776C,0xD1EF,0x76D9,0xD079,0x7642,0xCF04, +0x75A6,0xCD92,0x7505,0xCC21,0x7460,0xCAB2,0x73B6,0xC946,0x7308,0xC7DB,0x7255, +0xC673,0x719E,0xC50D,0x70E3,0xC3A9,0x7023,0xC248,0x6F5F,0xC0E9,0x6E97,0xBF8C, +0x6DCA,0xBE32,0x6CF9,0xBCDA,0x6C24,0xBB85,0x6B4B,0xBA33,0x6A6E,0xB8E3,0x698C, +0xB796,0x68A7,0xB64C,0x67BD,0xB505,0x66D0,0xB3C0,0x65DE,0xB27F,0x64E9,0xB140, +0x63EF,0xB005,0x62F2,0xAECC,0x61F1,0xAD97,0x60EC,0xAC65,0x5FE4,0xAB36,0x5ED7, +0xAA0A,0x5DC8,0xA8E2,0x5CB4,0xA7BD,0x5B9D,0xA69C,0x5A82,0xA57E,0x5964,0xA463, +0x5843,0xA34C,0x571E,0xA238,0x55F6,0xA129,0x54CA,0xA01C,0x539B,0x9F14,0x5269, +0x9E0F,0x5134,0x9D0E,0x4FFB,0x9C11,0x4EC0,0x9B17,0x4D81,0x9A22,0x4C40,0x9930, +0x4AFB,0x9843,0x49B4,0x9759,0x486A,0x9674,0x471D,0x9592,0x45CD,0x94B5,0x447B, +0x93DC,0x4326,0x9307,0x41CE,0x9236,0x4074,0x9169,0x3F17,0x90A1,0x3DB8,0x8FDD, +0x3C57,0x8F1D,0x3AF3,0x8E62,0x398D,0x8DAB,0x3825,0x8CF8,0x36BA,0x8C4A,0x354E, +0x8BA0,0x33DF,0x8AFB,0x326E,0x8A5A,0x30FC,0x89BE,0x2F87,0x8927,0x2E11,0x8894, +0x2C99,0x8805,0x2B1F,0x877B,0x29A4,0x86F6,0x2827,0x8676,0x26A8,0x85FA,0x2528, +0x8583,0x23A7,0x8511,0x2224,0x84A3,0x209F,0x843A,0x1F1A,0x83D6,0x1D93,0x8377, +0x1C0C,0x831C,0x1A83,0x82C6,0x18F9,0x8276,0x176E,0x822A,0x15E2,0x81E2,0x1455, +0x81A0,0x12C8,0x8163,0x113A,0x812A,0x0FAB,0x80F6,0x0E1C,0x80C8,0x0C8C,0x809E, +0x0AFB,0x8079,0x096B,0x8059,0x07D9,0x803E,0x0648,0x8027,0x04B6,0x8016,0x0324, +0x800A,0x0192,0x8002,0x0000,0x8000,0xFE6E,0x8002,0xFCDC,0x800A,0xFB4A,0x8016, +0xF9B8,0x8027,0xF827,0x803E,0xF695,0x8059,0xF505,0x8079,0xF374,0x809E,0xF1E4, +0x80C8,0xF055,0x80F6,0xEEC6,0x812A,0xED38,0x8163,0xEBAB,0x81A0,0xEA1E,0x81E2, +0xE892,0x822A,0xE707,0x8276,0xE57D,0x82C6,0xE3F4,0x831C,0xE26D,0x8377,0xE0E6, +0x83D6,0xDF61,0x843A,0xDDDC,0x84A3,0xDC59,0x8511,0xDAD8,0x8583,0xD958,0x85FA, +0xD7D9,0x8676,0xD65C,0x86F6,0xD4E1,0x877B,0xD367,0x8805,0xD1EF,0x8894,0xD079, +0x8927,0xCF04,0x89BE,0xCD92,0x8A5A,0xCC21,0x8AFB,0xCAB2,0x8BA0,0xC946,0x8C4A, +0xC7DB,0x8CF8,0xC673,0x8DAB,0xC50D,0x8E62,0xC3A9,0x8F1D,0xC248,0x8FDD,0xC0E9, +0x90A1,0xBF8C,0x9169,0xBE32,0x9236,0xBCDA,0x9307,0xBB85,0x93DC,0xBA33,0x94B5, +0xB8E3,0x9592,0xB796,0x9674,0xB64C,0x9759,0xB505,0x9843,0xB3C0,0x9930,0xB27F, +0x9A22,0xB140,0x9B17,0xB005,0x9C11,0xAECC,0x9D0E,0xAD97,0x9E0F,0xAC65,0x9F14, +0xAB36,0xA01C,0xAA0A,0xA129,0xA8E2,0xA238,0xA7BD,0xA34C,0xA69C,0xA463,0xA57E, +0xA57E,0xA463,0xA69C,0xA34C,0xA7BD,0xA238,0xA8E2,0xA129,0xAA0A,0xA01C,0xAB36, +0x9F14,0xAC65,0x9E0F,0xAD97,0x9D0E,0xAECC,0x9C11,0xB005,0x9B17,0xB140,0x9A22, +0xB27F,0x9930,0xB3C0,0x9843,0xB505,0x9759,0xB64C,0x9674,0xB796,0x9592,0xB8E3, +0x94B5,0xBA33,0x93DC,0xBB85,0x9307,0xBCDA,0x9236,0xBE32,0x9169,0xBF8C,0x90A1, +0xC0E9,0x8FDD,0xC248,0x8F1D,0xC3A9,0x8E62,0xC50D,0x8DAB,0xC673,0x8CF8,0xC7DB, +0x8C4A,0xC946,0x8BA0,0xCAB2,0x8AFB,0xCC21,0x8A5A,0xCD92,0x89BE,0xCF04,0x8927, +0xD079,0x8894,0xD1EF,0x8805,0xD367,0x877B,0xD4E1,0x86F6,0xD65C,0x8676,0xD7D9, +0x85FA,0xD958,0x8583,0xDAD8,0x8511,0xDC59,0x84A3,0xDDDC,0x843A,0xDF61,0x83D6, +0xE0E6,0x8377,0xE26D,0x831C,0xE3F4,0x82C6,0xE57D,0x8276,0xE707,0x822A,0xE892, +0x81E2,0xEA1E,0x81A0,0xEBAB,0x8163,0xED38,0x812A,0xEEC6,0x80F6,0xF055,0x80C8, +0xF1E4,0x809E,0xF374,0x8079,0xF505,0x8059,0xF695,0x803E,0xF827,0x8027,0xF9B8, +0x8016,0xFB4A,0x800A,0xFCDC,0x8002,0xFE6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82, +0xA57E,0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276, +0xCF04,0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276, +0xE707,0x7FFF,0x0000,0x5A82,0xA57E,0x0000,0x8000,0xA57E,0xA57E,}; + +const q15_t rearranged_twiddle_stride3_1024_q15[680] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FFA,0xFDA5,0x7FEA,0xFB4A,0x7FCE,0xF8EF,0x7FA7,0xF695,0x7F75, +0xF43C,0x7F38,0xF1E4,0x7EF0,0xEF8D,0x7E9D,0xED38,0x7E3F,0xEAE4,0x7DD6,0xE892, +0x7D63,0xE642,0x7CE4,0xE3F4,0x7C5A,0xE1A9,0x7BC6,0xDF61,0x7B27,0xDD1B,0x7A7D, +0xDAD8,0x79C9,0xD898,0x790A,0xD65C,0x7840,0xD424,0x776C,0xD1EF,0x768E,0xCFBE, +0x75A6,0xCD92,0x74B3,0xCB69,0x73B6,0xC946,0x72AF,0xC727,0x719E,0xC50D,0x7083, +0xC2F8,0x6F5F,0xC0E9,0x6E31,0xBEDF,0x6CF9,0xBCDA,0x6BB8,0xBADC,0x6A6E,0xB8E3, +0x691A,0xB6F1,0x67BD,0xB505,0x6657,0xB31F,0x64E9,0xB140,0x6371,0xAF68,0x61F1, +0xAD97,0x6068,0xABCD,0x5ED7,0xAA0A,0x5D3E,0xA84F,0x5B9D,0xA69C,0x59F4,0xA4F0, +0x5843,0xA34C,0x568A,0xA1B0,0x54CA,0xA01C,0x5303,0x9E91,0x5134,0x9D0E,0x4F5E, +0x9B94,0x4D81,0x9A22,0x4B9E,0x98B9,0x49B4,0x9759,0x47C4,0x9603,0x45CD,0x94B5, +0x43D1,0x9371,0x41CE,0x9236,0x3FC6,0x9105,0x3DB8,0x8FDD,0x3BA5,0x8EBF,0x398D, +0x8DAB,0x3770,0x8CA1,0x354E,0x8BA0,0x3327,0x8AAA,0x30FC,0x89BE,0x2ECC,0x88DD, +0x2C99,0x8805,0x2A62,0x8738,0x2827,0x8676,0x25E8,0x85BE,0x23A7,0x8511,0x2162, +0x846E,0x1F1A,0x83D6,0x1CD0,0x8349,0x1A83,0x82C6,0x1833,0x824F,0x15E2,0x81E2, +0x138F,0x8181,0x113A,0x812A,0x0EE4,0x80DE,0x0C8C,0x809E,0x0A33,0x8068,0x07D9, +0x803E,0x057F,0x801E,0x0324,0x800A,0x00C9,0x8001,0xFE6E,0x8002,0xFC13,0x800F, +0xF9B8,0x8027,0xF75E,0x804B,0xF505,0x8079,0xF2AC,0x80B2,0xF055,0x80F6,0xEDFF, +0x8146,0xEBAB,0x81A0,0xE958,0x8205,0xE707,0x8276,0xE4B9,0x82F1,0xE26D,0x8377, +0xE023,0x8407,0xDDDC,0x84A3,0xDB99,0x8549,0xD958,0x85FA,0xD71B,0x86B6,0xD4E1, +0x877B,0xD2AB,0x884C,0xD079,0x8927,0xCE4B,0x8A0C,0xCC21,0x8AFB,0xC9FC,0x8BF5, +0xC7DB,0x8CF8,0xC5C0,0x8E06,0xC3A9,0x8F1D,0xC198,0x903E,0xBF8C,0x9169,0xBD86, +0x929E,0xBB85,0x93DC,0xB98B,0x9523,0xB796,0x9674,0xB5A8,0x97CE,0xB3C0,0x9930, +0xB1DF,0x9A9C,0xB005,0x9C11,0xAE31,0x9D8E,0xAC65,0x9F14,0xAAA0,0xA0A2,0xA8E2, +0xA238,0xA72C,0xA3D7,0xA57E,0xA57E,0xA3D7,0xA72C,0xA238,0xA8E2,0xA0A2,0xAAA0, +0x9F14,0xAC65,0x9D8E,0xAE31,0x9C11,0xB005,0x9A9C,0xB1DF,0x9930,0xB3C0,0x97CE, +0xB5A8,0x9674,0xB796,0x9523,0xB98B,0x93DC,0xBB85,0x929E,0xBD86,0x9169,0xBF8C, +0x903E,0xC198,0x8F1D,0xC3A9,0x8E06,0xC5C0,0x8CF8,0xC7DB,0x8BF5,0xC9FC,0x8AFB, +0xCC21,0x8A0C,0xCE4B,0x8927,0xD079,0x884C,0xD2AB,0x877B,0xD4E1,0x86B6,0xD71B, +0x85FA,0xD958,0x8549,0xDB99,0x84A3,0xDDDC,0x8407,0xE023,0x8377,0xE26D,0x82F1, +0xE4B9,0x8276,0xE707,0x8205,0xE958,0x81A0,0xEBAB,0x8146,0xEDFF,0x80F6,0xF055, +0x80B2,0xF2AC,0x8079,0xF505,0x804B,0xF75E,0x8027,0xF9B8,0x800F,0xFC13,0x8002, +0xFE6E,0x8001,0x00C9,0x800A,0x0324,0x801E,0x057F,0x803E,0x07D9,0x8068,0x0A33, +0x809E,0x0C8C,0x80DE,0x0EE4,0x812A,0x113A,0x8181,0x138F,0x81E2,0x15E2,0x824F, +0x1833,0x82C6,0x1A83,0x8349,0x1CD0,0x83D6,0x1F1A,0x846E,0x2162,0x8511,0x23A7, +0x85BE,0x25E8,0x8676,0x2827,0x8738,0x2A62,0x8805,0x2C99,0x88DD,0x2ECC,0x89BE, +0x30FC,0x8AAA,0x3327,0x8BA0,0x354E,0x8CA1,0x3770,0x8DAB,0x398D,0x8EBF,0x3BA5, +0x8FDD,0x3DB8,0x9105,0x3FC6,0x9236,0x41CE,0x9371,0x43D1,0x94B5,0x45CD,0x9603, +0x47C4,0x9759,0x49B4,0x98B9,0x4B9E,0x9A22,0x4D81,0x9B94,0x4F5E,0x9D0E,0x5134, +0x9E91,0x5303,0xA01C,0x54CA,0xA1B0,0x568A,0xA34C,0x5843,0xA4F0,0x59F4,0xA69C, +0x5B9D,0xA84F,0x5D3E,0xAA0A,0x5ED7,0xABCD,0x6068,0xAD97,0x61F1,0xAF68,0x6371, +0xB140,0x64E9,0xB31F,0x6657,0xB505,0x67BD,0xB6F1,0x691A,0xB8E3,0x6A6E,0xBADC, +0x6BB8,0xBCDA,0x6CF9,0xBEDF,0x6E31,0xC0E9,0x6F5F,0xC2F8,0x7083,0xC50D,0x719E, +0xC727,0x72AF,0xC946,0x73B6,0xCB69,0x74B3,0xCD92,0x75A6,0xCFBE,0x768E,0xD1EF, +0x776C,0xD424,0x7840,0xD65C,0x790A,0xD898,0x79C9,0xDAD8,0x7A7D,0xDD1B,0x7B27, +0xDF61,0x7BC6,0xE1A9,0x7C5A,0xE3F4,0x7CE4,0xE642,0x7D63,0xE892,0x7DD6,0xEAE4, +0x7E3F,0xED38,0x7E9D,0xEF8D,0x7EF0,0xF1E4,0x7F38,0xF43C,0x7F75,0xF695,0x7FA7, +0xF8EF,0x7FCE,0xFB4A,0x7FEA,0xFDA5,0x7FFA,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D, +0xED38,0x7CE4,0xE3F4,0x7A7D,0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9, +0x6A6E,0xB8E3,0x64E9,0xB140,0x5ED7,0xAA0A,0x5843,0xA34C,0x5134,0x9D0E,0x49B4, +0x9759,0x41CE,0x9236,0x398D,0x8DAB,0x30FC,0x89BE,0x2827,0x8676,0x1F1A,0x83D6, +0x15E2,0x81E2,0x0C8C,0x809E,0x0324,0x800A,0xF9B8,0x8027,0xF055,0x80F6,0xE707, +0x8276,0xDDDC,0x84A3,0xD4E1,0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC, +0xB3C0,0x9930,0xAC65,0x9F14,0xA57E,0xA57E,0x9F14,0xAC65,0x9930,0xB3C0,0x93DC, +0xBB85,0x8F1D,0xC3A9,0x8AFB,0xCC21,0x877B,0xD4E1,0x84A3,0xDDDC,0x8276,0xE707, +0x80F6,0xF055,0x8027,0xF9B8,0x800A,0x0324,0x809E,0x0C8C,0x81E2,0x15E2,0x83D6, +0x1F1A,0x8676,0x2827,0x89BE,0x30FC,0x8DAB,0x398D,0x9236,0x41CE,0x9759,0x49B4, +0x9D0E,0x5134,0xA34C,0x5843,0xAA0A,0x5ED7,0xB140,0x64E9,0xB8E3,0x6A6E,0xC0E9, +0x6F5F,0xC946,0x73B6,0xD1EF,0x776C,0xDAD8,0x7A7D,0xE3F4,0x7CE4,0xED38,0x7E9D, +0xF695,0x7FA7,0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC, +0x89BE,0x0C8C,0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9, +0x8276,0xE707,0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8, +0x7A7D,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E,0x89BE,0x30FC,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_4096_q15[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_4096_q15[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_4096_q15[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const q15_t rearranged_twiddle_stride1_4096_q15[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FFF,0xFFCE,0x7FFF,0xFF9B,0x7FFF,0xFF69,0x7FFF,0xFF37,0x7FFF, +0xFF05,0x7FFF,0xFED2,0x7FFE,0xFEA0,0x7FFE,0xFE6E,0x7FFD,0xFE3C,0x7FFC,0xFE09, +0x7FFB,0xFDD7,0x7FFA,0xFDA5,0x7FF9,0xFD73,0x7FF8,0xFD40,0x7FF7,0xFD0E,0x7FF6, +0xFCDC,0x7FF5,0xFCAA,0x7FF4,0xFC77,0x7FF2,0xFC45,0x7FF1,0xFC13,0x7FEF,0xFBE1, +0x7FED,0xFBAE,0x7FEC,0xFB7C,0x7FEA,0xFB4A,0x7FE8,0xFB18,0x7FE6,0xFAE5,0x7FE4, +0xFAB3,0x7FE2,0xFA81,0x7FE0,0xFA4F,0x7FDD,0xFA1D,0x7FDB,0xF9EA,0x7FD9,0xF9B8, +0x7FD6,0xF986,0x7FD3,0xF954,0x7FD1,0xF922,0x7FCE,0xF8EF,0x7FCB,0xF8BD,0x7FC8, +0xF88B,0x7FC5,0xF859,0x7FC2,0xF827,0x7FBF,0xF7F4,0x7FBC,0xF7C2,0x7FB9,0xF790, +0x7FB5,0xF75E,0x7FB2,0xF72C,0x7FAE,0xF6FA,0x7FAB,0xF6C8,0x7FA7,0xF695,0x7FA3, +0xF663,0x7FA0,0xF631,0x7F9C,0xF5FF,0x7F98,0xF5CD,0x7F94,0xF59B,0x7F90,0xF569, +0x7F8B,0xF537,0x7F87,0xF505,0x7F83,0xF4D3,0x7F7E,0xF4A0,0x7F7A,0xF46E,0x7F75, +0xF43C,0x7F71,0xF40A,0x7F6C,0xF3D8,0x7F67,0xF3A6,0x7F62,0xF374,0x7F5D,0xF342, +0x7F58,0xF310,0x7F53,0xF2DE,0x7F4E,0xF2AC,0x7F49,0xF27A,0x7F43,0xF248,0x7F3E, +0xF216,0x7F38,0xF1E4,0x7F33,0xF1B2,0x7F2D,0xF180,0x7F27,0xF14E,0x7F22,0xF11C, +0x7F1C,0xF0EB,0x7F16,0xF0B9,0x7F10,0xF087,0x7F0A,0xF055,0x7F03,0xF023,0x7EFD, +0xEFF1,0x7EF7,0xEFBF,0x7EF0,0xEF8D,0x7EEA,0xEF5C,0x7EE3,0xEF2A,0x7EDD,0xEEF8, +0x7ED6,0xEEC6,0x7ECF,0xEE94,0x7EC8,0xEE62,0x7EC1,0xEE31,0x7EBA,0xEDFF,0x7EB3, +0xEDCD,0x7EAC,0xED9B,0x7EA5,0xED6A,0x7E9D,0xED38,0x7E96,0xED06,0x7E8E,0xECD5, +0x7E87,0xECA3,0x7E7F,0xEC71,0x7E78,0xEC3F,0x7E70,0xEC0E,0x7E68,0xEBDC,0x7E60, +0xEBAB,0x7E58,0xEB79,0x7E50,0xEB47,0x7E48,0xEB16,0x7E3F,0xEAE4,0x7E37,0xEAB3, +0x7E2F,0xEA81,0x7E26,0xEA4F,0x7E1E,0xEA1E,0x7E15,0xE9EC,0x7E0C,0xE9BB,0x7E03, +0xE989,0x7DFB,0xE958,0x7DF2,0xE926,0x7DE9,0xE8F5,0x7DE0,0xE8C4,0x7DD6,0xE892, +0x7DCD,0xE861,0x7DC4,0xE82F,0x7DBA,0xE7FE,0x7DB1,0xE7CD,0x7DA7,0xE79B,0x7D9E, +0xE76A,0x7D94,0xE739,0x7D8A,0xE707,0x7D81,0xE6D6,0x7D77,0xE6A5,0x7D6D,0xE673, +0x7D63,0xE642,0x7D58,0xE611,0x7D4E,0xE5E0,0x7D44,0xE5AF,0x7D3A,0xE57D,0x7D2F, +0xE54C,0x7D25,0xE51B,0x7D1A,0xE4EA,0x7D0F,0xE4B9,0x7D05,0xE488,0x7CFA,0xE457, +0x7CEF,0xE426,0x7CE4,0xE3F4,0x7CD9,0xE3C3,0x7CCE,0xE392,0x7CC2,0xE361,0x7CB7, +0xE330,0x7CAC,0xE2FF,0x7CA0,0xE2CF,0x7C95,0xE29E,0x7C89,0xE26D,0x7C7E,0xE23C, +0x7C72,0xE20B,0x7C66,0xE1DA,0x7C5A,0xE1A9,0x7C4E,0xE178,0x7C42,0xE148,0x7C36, +0xE117,0x7C2A,0xE0E6,0x7C1E,0xE0B5,0x7C11,0xE085,0x7C05,0xE054,0x7BF9,0xE023, +0x7BEC,0xDFF2,0x7BDF,0xDFC2,0x7BD3,0xDF91,0x7BC6,0xDF61,0x7BB9,0xDF30,0x7BAC, +0xDEFF,0x7B9F,0xDECF,0x7B92,0xDE9E,0x7B85,0xDE6E,0x7B78,0xDE3D,0x7B6A,0xDE0D, 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+0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA,0xBE32,0x6C24, +0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140,0x62F2,0xAECC, +0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843,0xA34C,0x55F6, +0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930,0x49B4,0x9759, +0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57,0x8F1D,0x398D, +0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894,0x2B1F,0x877B, +0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C,0x831C,0x18F9, +0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E,0x096B,0x8059, +0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D, +0xDAD8,0x7642,0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E, +0x5134,0x9D0E,0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9, +0x8276,0x0C8C,0x809E,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,}; + +const q15_t rearranged_twiddle_stride2_4096_q15[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FFF,0xFF9B,0x7FFF,0xFF37,0x7FFF,0xFED2,0x7FFE,0xFE6E,0x7FFC, +0xFE09,0x7FFA,0xFDA5,0x7FF8,0xFD40,0x7FF6,0xFCDC,0x7FF4,0xFC77,0x7FF1,0xFC13, +0x7FED,0xFBAE,0x7FEA,0xFB4A,0x7FE6,0xFAE5,0x7FE2,0xFA81,0x7FDD,0xFA1D,0x7FD9, +0xF9B8,0x7FD3,0xF954,0x7FCE,0xF8EF,0x7FC8,0xF88B,0x7FC2,0xF827,0x7FBC,0xF7C2, +0x7FB5,0xF75E,0x7FAE,0xF6FA,0x7FA7,0xF695,0x7FA0,0xF631,0x7F98,0xF5CD,0x7F90, +0xF569,0x7F87,0xF505,0x7F7E,0xF4A0,0x7F75,0xF43C,0x7F6C,0xF3D8,0x7F62,0xF374, +0x7F58,0xF310,0x7F4E,0xF2AC,0x7F43,0xF248,0x7F38,0xF1E4,0x7F2D,0xF180,0x7F22, +0xF11C,0x7F16,0xF0B9,0x7F0A,0xF055,0x7EFD,0xEFF1,0x7EF0,0xEF8D,0x7EE3,0xEF2A, +0x7ED6,0xEEC6,0x7EC8,0xEE62,0x7EBA,0xEDFF,0x7EAC,0xED9B,0x7E9D,0xED38,0x7E8E, +0xECD5,0x7E7F,0xEC71,0x7E70,0xEC0E,0x7E60,0xEBAB,0x7E50,0xEB47,0x7E3F,0xEAE4, +0x7E2F,0xEA81,0x7E1E,0xEA1E,0x7E0C,0xE9BB,0x7DFB,0xE958,0x7DE9,0xE8F5,0x7DD6, 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+0x809E,0xED38,0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B, +0xCF04,0x89BE,0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0, +0x9930,0xAECC,0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC, +0x9930,0xB3C0,0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE, +0xCF04,0x877B,0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38, +0x809E,0xF374,0x8027,0xF9B8,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E, +0xB8E3,0x5A82,0xA57E,0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000, +0xE707,0x8276,0xCF04,0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE, +0xCF04,0x8276,0xE707,0x7FFF,0x0000,0x5A82,0xA57E,0x0000,0x8000,0xA57E,0xA57E,}; + +const q15_t rearranged_twiddle_stride3_4096_q15[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +0x7FFF,0x0000,0x7FFF,0xFF69,0x7FFF,0xFED2,0x7FFD,0xFE3C,0x7FFA,0xFDA5,0x7FF7, +0xFD0E,0x7FF4,0xFC77,0x7FEF,0xFBE1,0x7FEA,0xFB4A,0x7FE4,0xFAB3,0x7FDD,0xFA1D, +0x7FD6,0xF986,0x7FCE,0xF8EF,0x7FC5,0xF859,0x7FBC,0xF7C2,0x7FB2,0xF72C,0x7FA7, +0xF695,0x7F9C,0xF5FF,0x7F90,0xF569,0x7F83,0xF4D3,0x7F75,0xF43C,0x7F67,0xF3A6, +0x7F58,0xF310,0x7F49,0xF27A,0x7F38,0xF1E4,0x7F27,0xF14E,0x7F16,0xF0B9,0x7F03, +0xF023,0x7EF0,0xEF8D,0x7EDD,0xEEF8,0x7EC8,0xEE62,0x7EB3,0xEDCD,0x7E9D,0xED38, +0x7E87,0xECA3,0x7E70,0xEC0E,0x7E58,0xEB79,0x7E3F,0xEAE4,0x7E26,0xEA4F,0x7E0C, +0xE9BB,0x7DF2,0xE926,0x7DD6,0xE892,0x7DBA,0xE7FE,0x7D9E,0xE76A,0x7D81,0xE6D6, +0x7D63,0xE642,0x7D44,0xE5AF,0x7D25,0xE51B,0x7D05,0xE488,0x7CE4,0xE3F4,0x7CC2, +0xE361,0x7CA0,0xE2CF,0x7C7E,0xE23C,0x7C5A,0xE1A9,0x7C36,0xE117,0x7C11,0xE085, +0x7BEC,0xDFF2,0x7BC6,0xDF61,0x7B9F,0xDECF,0x7B78,0xDE3D,0x7B50,0xDDAC,0x7B27, +0xDD1B,0x7AFD,0xDC8A,0x7AD3,0xDBF9,0x7AA8,0xDB68,0x7A7D,0xDAD8,0x7A51,0xDA48, +0x7A24,0xD9B8,0x79F7,0xD928,0x79C9,0xD898,0x799A,0xD809,0x796A,0xD77A,0x793A, +0xD6EB,0x790A,0xD65C,0x78D8,0xD5CE,0x78A6,0xD53F,0x7874,0xD4B1,0x7840,0xD424, +0x780C,0xD396,0x77D8,0xD309,0x77A2,0xD27C,0x776C,0xD1EF,0x7736,0xD162,0x76FE, +0xD0D6,0x76C7,0xD04A,0x768E,0xCFBE,0x7655,0xCF33,0x761B,0xCEA7,0x75E1,0xCE1C, +0x75A6,0xCD92,0x756A,0xCD07,0x752D,0xCC7D,0x74F0,0xCBF3,0x74B3,0xCB69,0x7475, +0xCAE0,0x7436,0xCA57,0x73F6,0xC9CE,0x73B6,0xC946,0x7375,0xC8BE,0x7334,0xC836, +0x72F2,0xC7AE,0x72AF,0xC727,0x726C,0xC6A0,0x7228,0xC619,0x71E3,0xC593,0x719E, +0xC50D,0x7158,0xC487,0x7112,0xC402,0x70CB,0xC37D,0x7083,0xC2F8,0x703B,0xC274, +0x6FF2,0xC1F0,0x6FA9,0xC16C,0x6F5F,0xC0E9,0x6F14,0xC066,0x6EC9,0xBFE3,0x6E7D, +0xBF61,0x6E31,0xBEDF,0x6DE4,0xBE5D,0x6D96,0xBDDC,0x6D48,0xBD5B,0x6CF9,0xBCDA, +0x6CAA,0xBC5A,0x6C5A,0xBBDA,0x6C09,0xBB5B,0x6BB8,0xBADC,0x6B66,0xBA5D,0x6B14, +0xB9DF,0x6AC1,0xB961,0x6A6E,0xB8E3,0x6A1A,0xB866,0x69C5,0xB7E9,0x6970,0xB76D, +0x691A,0xB6F1,0x68C4,0xB675,0x686D,0xB5FA,0x6815,0xB57F,0x67BD,0xB505,0x6764, +0xB48B,0x670B,0xB411,0x66B2,0xB398,0x6657,0xB31F,0x65FC,0xB2A7,0x65A1,0xB22F, +0x6545,0xB1B7,0x64E9,0xB140,0x648B,0xB0C9,0x642E,0xB053,0x63D0,0xAFDD,0x6371, +0xAF68,0x6312,0xAEF3,0x62B2,0xAE7F,0x6252,0xAE0B,0x61F1,0xAD97,0x6190,0xAD24, +0x612E,0xACB1,0x60CB,0xAC3F,0x6068,0xABCD,0x6005,0xAB5C,0x5FA1,0xAAEB,0x5F3C, +0xAA7A,0x5ED7,0xAA0A,0x5E72,0xA99B,0x5E0C,0xA92C,0x5DA5,0xA8BD,0x5D3E,0xA84F, +0x5CD7,0xA7E2,0x5C6F,0xA774,0x5C06,0xA708,0x5B9D,0xA69C,0x5B34,0xA630,0x5AC9, +0xA5C5,0x5A5F,0xA55A,0x59F4,0xA4F0,0x5988,0xA486,0x591C,0xA41D,0x58B0,0xA3B4, +0x5843,0xA34C,0x57D5,0xA2E4,0x5767,0xA27D,0x56F9,0xA216,0x568A,0xA1B0,0x561B, +0xA14A,0x55AB,0xA0E5,0x553B,0xA080,0x54CA,0xA01C,0x5459,0x9FB9,0x53E7,0x9F56, +0x5375,0x9EF3,0x5303,0x9E91,0x5290,0x9E2F,0x521C,0x9DCE,0x51A8,0x9D6E,0x5134, +0x9D0E,0x50BF,0x9CAF,0x504A,0x9C50,0x4FD4,0x9BF1,0x4F5E,0x9B94,0x4EE8,0x9B36, +0x4E71,0x9ADA,0x4DF9,0x9A7E,0x4D81,0x9A22,0x4D09,0x99C7,0x4C91,0x996D,0x4C17, +0x9913,0x4B9E,0x98B9,0x4B24,0x9860,0x4AAA,0x9808,0x4A2F,0x97B0,0x49B4,0x9759, +0x4939,0x9703,0x48BD,0x96AD,0x4840,0x9657,0x47C4,0x9603,0x4747,0x95AE,0x46C9, +0x955B,0x464B,0x9508,0x45CD,0x94B5,0x454F,0x9463,0x44D0,0x9412,0x4450,0x93C1, +0x43D1,0x9371,0x4351,0x9321,0x42D0,0x92D2,0x424F,0x9284,0x41CE,0x9236,0x414D, +0x91E9,0x40CB,0x919C,0x4048,0x9150,0x3FC6,0x9105,0x3F43,0x90BA,0x3EC0,0x9070, +0x3E3C,0x9026,0x3DB8,0x8FDD,0x3D34,0x8F95,0x3CAF,0x8F4D,0x3C2A,0x8F06,0x3BA5, +0x8EBF,0x3B20,0x8E79,0x3A9A,0x8E34,0x3A13,0x8DEF,0x398D,0x8DAB,0x3906,0x8D67, +0x387F,0x8D24,0x37F7,0x8CE2,0x3770,0x8CA1,0x36E8,0x8C60,0x365F,0x8C1F,0x35D7, +0x8BDF,0x354E,0x8BA0,0x34C4,0x8B62,0x343B,0x8B24,0x33B1,0x8AE7,0x3327,0x8AAA, +0x329D,0x8A6E,0x3212,0x8A33,0x3187,0x89F8,0x30FC,0x89BE,0x3070,0x8985,0x2FE5, +0x894C,0x2F59,0x8914,0x2ECC,0x88DD,0x2E40,0x88A6,0x2DB3,0x8870,0x2D26,0x883A, +0x2C99,0x8805,0x2C0C,0x87D1,0x2B7E,0x879D,0x2AF0,0x876B,0x2A62,0x8738,0x29D3, +0x8707,0x2945,0x86D6,0x28B6,0x86A5,0x2827,0x8676,0x2797,0x8647,0x2708,0x8619, +0x2678,0x85EB,0x25E8,0x85BE,0x2558,0x8592,0x24C8,0x8566,0x2437,0x853B,0x23A7, +0x8511,0x2316,0x84E7,0x2284,0x84BE,0x21F3,0x8496,0x2162,0x846E,0x20D0,0x8447, +0x203E,0x8421,0x1FAC,0x83FB,0x1F1A,0x83D6,0x1E88,0x83B2,0x1DF5,0x838E,0x1D62, +0x836B,0x1CD0,0x8349,0x1C3D,0x8327,0x1BA9,0x8306,0x1B16,0x82E6,0x1A83,0x82C6, +0x19EF,0x82A8,0x195B,0x8289,0x18C7,0x826C,0x1833,0x824F,0x179F,0x8233,0x170B, +0x8217,0x1677,0x81FD,0x15E2,0x81E2,0x154D,0x81C9,0x14B9,0x81B0,0x1424,0x8198, +0x138F,0x8181,0x12FA,0x816A,0x1265,0x8154,0x11CF,0x813F,0x113A,0x812A,0x10A4, +0x8116,0x100F,0x8103,0x0F79,0x80F0,0x0EE4,0x80DE,0x0E4E,0x80CD,0x0DB8,0x80BD, +0x0D22,0x80AD,0x0C8C,0x809E,0x0BF6,0x808F,0x0B60,0x8082,0x0AC9,0x8075,0x0A33, +0x8068,0x099D,0x805D,0x0906,0x8052,0x0870,0x8047,0x07D9,0x803E,0x0743,0x8035, +0x06AC,0x802D,0x0616,0x8025,0x057F,0x801E,0x04E8,0x8018,0x0452,0x8013,0x03BB, +0x800E,0x0324,0x800A,0x028D,0x8007,0x01F7,0x8004,0x0160,0x8002,0x00C9,0x8001, +0x0032,0x8000,0xFF9B,0x8000,0xFF05,0x8001,0xFE6E,0x8002,0xFDD7,0x8005,0xFD40, +0x8008,0xFCAA,0x800B,0xFC13,0x800F,0xFB7C,0x8014,0xFAE5,0x801A,0xFA4F,0x8020, +0xF9B8,0x8027,0xF922,0x802F,0xF88B,0x8038,0xF7F4,0x8041,0xF75E,0x804B,0xF6C8, +0x8055,0xF631,0x8060,0xF59B,0x806C,0xF505,0x8079,0xF46E,0x8086,0xF3D8,0x8094, +0xF342,0x80A3,0xF2AC,0x80B2,0xF216,0x80C2,0xF180,0x80D3,0xF0EB,0x80E4,0xF055, +0x80F6,0xEFBF,0x8109,0xEF2A,0x811D,0xEE94,0x8131,0xEDFF,0x8146,0xED6A,0x815B, +0xECD5,0x8172,0xEC3F,0x8188,0xEBAB,0x81A0,0xEB16,0x81B8,0xEA81,0x81D1,0xE9EC, +0x81EB,0xE958,0x8205,0xE8C4,0x8220,0xE82F,0x823C,0xE79B,0x8259,0xE707,0x8276, +0xE673,0x8293,0xE5E0,0x82B2,0xE54C,0x82D1,0xE4B9,0x82F1,0xE426,0x8311,0xE392, +0x8332,0xE2FF,0x8354,0xE26D,0x8377,0xE1DA,0x839A,0xE148,0x83BE,0xE0B5,0x83E2, +0xE023,0x8407,0xDF91,0x842D,0xDEFF,0x8454,0xDE6E,0x847B,0xDDDC,0x84A3,0xDD4B, +0x84CC,0xDCBA,0x84F5,0xDC29,0x851F,0xDB99,0x8549,0xDB08,0x8574,0xDA78,0x85A0, 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+0xC9FC,0x8BF5,0xC7DB,0x8CF8,0xC5C0,0x8E06,0xC3A9,0x8F1D,0xC198,0x903E,0xBF8C, +0x9169,0xBD86,0x929E,0xBB85,0x93DC,0xB98B,0x9523,0xB796,0x9674,0xB5A8,0x97CE, +0xB3C0,0x9930,0xB1DF,0x9A9C,0xB005,0x9C11,0xAE31,0x9D8E,0xAC65,0x9F14,0xAAA0, +0xA0A2,0xA8E2,0xA238,0xA72C,0xA3D7,0xA57E,0xA57E,0xA3D7,0xA72C,0xA238,0xA8E2, +0xA0A2,0xAAA0,0x9F14,0xAC65,0x9D8E,0xAE31,0x9C11,0xB005,0x9A9C,0xB1DF,0x9930, +0xB3C0,0x97CE,0xB5A8,0x9674,0xB796,0x9523,0xB98B,0x93DC,0xBB85,0x929E,0xBD86, +0x9169,0xBF8C,0x903E,0xC198,0x8F1D,0xC3A9,0x8E06,0xC5C0,0x8CF8,0xC7DB,0x8BF5, +0xC9FC,0x8AFB,0xCC21,0x8A0C,0xCE4B,0x8927,0xD079,0x884C,0xD2AB,0x877B,0xD4E1, +0x86B6,0xD71B,0x85FA,0xD958,0x8549,0xDB99,0x84A3,0xDDDC,0x8407,0xE023,0x8377, +0xE26D,0x82F1,0xE4B9,0x8276,0xE707,0x8205,0xE958,0x81A0,0xEBAB,0x8146,0xEDFF, +0x80F6,0xF055,0x80B2,0xF2AC,0x8079,0xF505,0x804B,0xF75E,0x8027,0xF9B8,0x800F, +0xFC13,0x8002,0xFE6E,0x8001,0x00C9,0x800A,0x0324,0x801E,0x057F,0x803E,0x07D9, +0x8068,0x0A33,0x809E,0x0C8C,0x80DE,0x0EE4,0x812A,0x113A,0x8181,0x138F,0x81E2, +0x15E2,0x824F,0x1833,0x82C6,0x1A83,0x8349,0x1CD0,0x83D6,0x1F1A,0x846E,0x2162, +0x8511,0x23A7,0x85BE,0x25E8,0x8676,0x2827,0x8738,0x2A62,0x8805,0x2C99,0x88DD, +0x2ECC,0x89BE,0x30FC,0x8AAA,0x3327,0x8BA0,0x354E,0x8CA1,0x3770,0x8DAB,0x398D, +0x8EBF,0x3BA5,0x8FDD,0x3DB8,0x9105,0x3FC6,0x9236,0x41CE,0x9371,0x43D1,0x94B5, +0x45CD,0x9603,0x47C4,0x9759,0x49B4,0x98B9,0x4B9E,0x9A22,0x4D81,0x9B94,0x4F5E, +0x9D0E,0x5134,0x9E91,0x5303,0xA01C,0x54CA,0xA1B0,0x568A,0xA34C,0x5843,0xA4F0, +0x59F4,0xA69C,0x5B9D,0xA84F,0x5D3E,0xAA0A,0x5ED7,0xABCD,0x6068,0xAD97,0x61F1, +0xAF68,0x6371,0xB140,0x64E9,0xB31F,0x6657,0xB505,0x67BD,0xB6F1,0x691A,0xB8E3, +0x6A6E,0xBADC,0x6BB8,0xBCDA,0x6CF9,0xBEDF,0x6E31,0xC0E9,0x6F5F,0xC2F8,0x7083, +0xC50D,0x719E,0xC727,0x72AF,0xC946,0x73B6,0xCB69,0x74B3,0xCD92,0x75A6,0xCFBE, +0x768E,0xD1EF,0x776C,0xD424,0x7840,0xD65C,0x790A,0xD898,0x79C9,0xDAD8,0x7A7D, +0xDD1B,0x7B27,0xDF61,0x7BC6,0xE1A9,0x7C5A,0xE3F4,0x7CE4,0xE642,0x7D63,0xE892, +0x7DD6,0xEAE4,0x7E3F,0xED38,0x7E9D,0xEF8D,0x7EF0,0xF1E4,0x7F38,0xF43C,0x7F75, +0xF695,0x7FA7,0xF8EF,0x7FCE,0xFB4A,0x7FEA,0xFDA5,0x7FFA,0x7FFF,0x0000,0x7FA7, +0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D,0xDAD8,0x776C,0xD1EF,0x73B6,0xC946, +0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140,0x5ED7,0xAA0A,0x5843,0xA34C,0x5134, +0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D,0x8DAB,0x30FC,0x89BE,0x2827,0x8676, +0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E,0x0324,0x800A,0xF9B8,0x8027,0xF055, +0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1,0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D, +0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14,0xA57E,0xA57E,0x9F14,0xAC65,0x9930, +0xB3C0,0x93DC,0xBB85,0x8F1D,0xC3A9,0x8AFB,0xCC21,0x877B,0xD4E1,0x84A3,0xDDDC, +0x8276,0xE707,0x80F6,0xF055,0x8027,0xF9B8,0x800A,0x0324,0x809E,0x0C8C,0x81E2, +0x15E2,0x83D6,0x1F1A,0x8676,0x2827,0x89BE,0x30FC,0x8DAB,0x398D,0x9236,0x41CE, +0x9759,0x49B4,0x9D0E,0x5134,0xA34C,0x5843,0xAA0A,0x5ED7,0xB140,0x64E9,0xB8E3, +0x6A6E,0xC0E9,0x6F5F,0xC946,0x73B6,0xD1EF,0x776C,0xDAD8,0x7A7D,0xE3F4,0x7CE4, +0xED38,0x7E9D,0xF695,0x7FA7,0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134, +0x9D0E,0x30FC,0x89BE,0x0C8C,0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E, +0x8F1D,0xC3A9,0x8276,0xE707,0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3, +0x6A6E,0xDAD8,0x7A7D,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E,0x89BE,0x30FC,}; + + +#endif /* defined(ARM_MATH_MVEI) */ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_mve_tables_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_mve_tables_f16.c new file mode 100755 index 0000000..e2ff0fd --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_mve_tables_f16.c @@ -0,0 +1,5558 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mve_tables_f16.c + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for MVE implementation only + * + * @version V1.10.0 + * @date 04 October 2021 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + #include "arm_math_types_f16.h" + + +#if defined(ARM_FLOAT16_SUPPORTED) + + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + + +const uint32_t rearranged_twiddle_tab_stride1_arr_16_f16[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_16_f16[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_16_f16[2] ARM_DSP_TABLE_ATTRIBUTE ={ +0,0,}; + +const float16_t rearranged_twiddle_stride1_16_f16[8] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f,}; + +const float16_t rearranged_twiddle_stride2_16_f16[8] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f,}; + +const float16_t rearranged_twiddle_stride3_16_f16[8] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_64_f16[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_64_f16[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_64_f16[3] ARM_DSP_TABLE_ATTRIBUTE ={ +0,32,0,}; + +const float16_t rearranged_twiddle_stride1_64_f16[40] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f,}; + +const float16_t rearranged_twiddle_stride2_64_f16[40] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f,}; + +const float16_t rearranged_twiddle_stride3_64_f16[40] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f,}; + +const uint32_t rearranged_twiddle_tab_stride1_arr_256_f16[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_256_f16[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_256_f16[4] ARM_DSP_TABLE_ATTRIBUTE ={ +0,128,160,0,}; + +const float16_t rearranged_twiddle_stride1_256_f16[168] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9995117187500f,(float16_t)0.0245361328125f, +(float16_t)0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)0.9970703125000f,(float16_t)0.0735473632812f, +(float16_t)0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.9926757812500f,(float16_t)0.1224365234375f, +(float16_t)0.9892578125000f,(float16_t)0.1467285156250f, +(float16_t)0.9853515625000f,(float16_t)0.1710205078125f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9755859375000f,(float16_t)0.2191162109375f, +(float16_t)0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)0.9638671875000f,(float16_t)0.2666015625000f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.9497070312500f,(float16_t)0.3137207031250f, +(float16_t)0.9414062500000f,(float16_t)0.3369140625000f, +(float16_t)0.9331054687500f,(float16_t)0.3598632812500f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.9140625000000f,(float16_t)0.4052734375000f, +(float16_t)0.9038085937500f,(float16_t)0.4274902343750f, +(float16_t)0.8930664062500f,(float16_t)0.4497070312500f, +(float16_t)0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)0.8701171875000f,(float16_t)0.4929199218750f, +(float16_t)0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)0.8447265625000f,(float16_t)0.5351562500000f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.8173828125000f,(float16_t)0.5756835937500f, +(float16_t)0.8032226562500f,(float16_t)0.5957031250000f, +(float16_t)0.7885742187500f,(float16_t)0.6152343750000f, +(float16_t)0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)0.7573242187500f,(float16_t)0.6533203125000f, +(float16_t)0.7407226562500f,(float16_t)0.6713867187500f, +(float16_t)0.7241210937500f,(float16_t)0.6894531250000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.6894531250000f,(float16_t)0.7241210937500f, +(float16_t)0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)0.6533203125000f,(float16_t)0.7573242187500f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.6152343750000f,(float16_t)0.7885742187500f, +(float16_t)0.5957031250000f,(float16_t)0.8032226562500f, +(float16_t)0.5756835937500f,(float16_t)0.8173828125000f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.5351562500000f,(float16_t)0.8447265625000f, +(float16_t)0.5141601562500f,(float16_t)0.8579101562500f, +(float16_t)0.4929199218750f,(float16_t)0.8701171875000f, +(float16_t)0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)0.4497070312500f,(float16_t)0.8930664062500f, +(float16_t)0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)0.4052734375000f,(float16_t)0.9140625000000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.3598632812500f,(float16_t)0.9331054687500f, +(float16_t)0.3369140625000f,(float16_t)0.9414062500000f, +(float16_t)0.3137207031250f,(float16_t)0.9497070312500f, +(float16_t)0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.2666015625000f,(float16_t)0.9638671875000f, +(float16_t)0.2429199218750f,(float16_t)0.9702148437500f, +(float16_t)0.2191162109375f,(float16_t)0.9755859375000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.1710205078125f,(float16_t)0.9853515625000f, +(float16_t)0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)0.1224365234375f,(float16_t)0.9926757812500f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)0.0735473632812f,(float16_t)0.9970703125000f, +(float16_t)0.0490722656250f,(float16_t)0.9990234375000f, +(float16_t)0.0245361328125f,(float16_t)0.9995117187500f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f,}; + +const float16_t rearranged_twiddle_stride2_256_f16[168] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)0.1467285156250f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)0.6713867187500f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)0.8032226562500f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)0.9702148437500f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)0.9990234375000f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.0490722656250f,(float16_t)0.9990234375000f, +(float16_t)-0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.2429199218750f,(float16_t)0.9702148437500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)-0.3369140625000f,(float16_t)0.9414062500000f, +(float16_t)-0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)-0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)-0.5141601562500f,(float16_t)0.8579101562500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.5957031250000f,(float16_t)0.8032226562500f, +(float16_t)-0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)-0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.7407226562500f,(float16_t)0.6713867187500f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.8032226562500f,(float16_t)0.5957031250000f, +(float16_t)-0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)-0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)-0.9038085937500f,(float16_t)0.4274902343750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.9414062500000f,(float16_t)0.3369140625000f, +(float16_t)-0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)-0.9892578125000f,(float16_t)0.1467285156250f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f,}; + +const float16_t rearranged_twiddle_stride3_256_f16[168] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9970703125000f,(float16_t)0.0735473632812f, +(float16_t)0.9892578125000f,(float16_t)0.1467285156250f, +(float16_t)0.9755859375000f,(float16_t)0.2191162109375f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.9331054687500f,(float16_t)0.3598632812500f, +(float16_t)0.9038085937500f,(float16_t)0.4274902343750f, +(float16_t)0.8701171875000f,(float16_t)0.4929199218750f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.7885742187500f,(float16_t)0.6152343750000f, +(float16_t)0.7407226562500f,(float16_t)0.6713867187500f, +(float16_t)0.6894531250000f,(float16_t)0.7241210937500f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.5756835937500f,(float16_t)0.8173828125000f, +(float16_t)0.5141601562500f,(float16_t)0.8579101562500f, +(float16_t)0.4497070312500f,(float16_t)0.8930664062500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.3137207031250f,(float16_t)0.9497070312500f, +(float16_t)0.2429199218750f,(float16_t)0.9702148437500f, +(float16_t)0.1710205078125f,(float16_t)0.9853515625000f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)0.0245361328125f,(float16_t)0.9995117187500f, +(float16_t)-0.0490722656250f,(float16_t)0.9990234375000f, +(float16_t)-0.1224365234375f,(float16_t)0.9926757812500f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.2666015625000f,(float16_t)0.9638671875000f, +(float16_t)-0.3369140625000f,(float16_t)0.9414062500000f, +(float16_t)-0.4052734375000f,(float16_t)0.9140625000000f, +(float16_t)-0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)-0.5351562500000f,(float16_t)0.8447265625000f, +(float16_t)-0.5957031250000f,(float16_t)0.8032226562500f, +(float16_t)-0.6533203125000f,(float16_t)0.7573242187500f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.7573242187500f,(float16_t)0.6533203125000f, +(float16_t)-0.8032226562500f,(float16_t)0.5957031250000f, +(float16_t)-0.8447265625000f,(float16_t)0.5351562500000f, +(float16_t)-0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)-0.9140625000000f,(float16_t)0.4052734375000f, +(float16_t)-0.9414062500000f,(float16_t)0.3369140625000f, +(float16_t)-0.9638671875000f,(float16_t)0.2666015625000f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)-0.9926757812500f,(float16_t)0.1224365234375f, +(float16_t)-0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)-0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.9853515625000f,(float16_t)-0.1710205078125f, +(float16_t)-0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)-0.9497070312500f,(float16_t)-0.3137207031250f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.8930664062500f,(float16_t)-0.4497070312500f, +(float16_t)-0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)-0.8173828125000f,(float16_t)-0.5756835937500f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)-0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)-0.6152343750000f,(float16_t)-0.7885742187500f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.4929199218750f,(float16_t)-0.8701171875000f, +(float16_t)-0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)-0.3598632812500f,(float16_t)-0.9331054687500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.2191162109375f,(float16_t)-0.9755859375000f, +(float16_t)-0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)-0.0735473632812f,(float16_t)-0.9970703125000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)0.7729492187500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f,}; + + +const uint32_t rearranged_twiddle_tab_stride1_arr_1024_f16[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_1024_f16[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_1024_f16[5] ARM_DSP_TABLE_ATTRIBUTE ={ +0,512,640,672,0,}; + +const float16_t rearranged_twiddle_stride1_1024_f16[680] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)0.0061340332031f, +(float16_t)1.0000000000000f,(float16_t)0.0122680664062f, +(float16_t)1.0000000000000f,(float16_t)0.0184020996094f, +(float16_t)0.9995117187500f,(float16_t)0.0245361328125f, +(float16_t)0.9995117187500f,(float16_t)0.0306701660156f, +(float16_t)0.9995117187500f,(float16_t)0.0368041992188f, +(float16_t)0.9990234375000f,(float16_t)0.0429382324219f, +(float16_t)0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)0.9985351562500f,(float16_t)0.0552062988281f, +(float16_t)0.9980468750000f,(float16_t)0.0613098144531f, +(float16_t)0.9975585937500f,(float16_t)0.0674438476562f, +(float16_t)0.9970703125000f,(float16_t)0.0735473632812f, +(float16_t)0.9965820312500f,(float16_t)0.0797119140625f, +(float16_t)0.9960937500000f,(float16_t)0.0858154296875f, +(float16_t)0.9956054687500f,(float16_t)0.0919189453125f, +(float16_t)0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.9946289062500f,(float16_t)0.1041259765625f, +(float16_t)0.9941406250000f,(float16_t)0.1102294921875f, +(float16_t)0.9931640625000f,(float16_t)0.1163330078125f, +(float16_t)0.9926757812500f,(float16_t)0.1224365234375f, +(float16_t)0.9916992187500f,(float16_t)0.1285400390625f, +(float16_t)0.9907226562500f,(float16_t)0.1345214843750f, +(float16_t)0.9902343750000f,(float16_t)0.1406250000000f, +(float16_t)0.9892578125000f,(float16_t)0.1467285156250f, +(float16_t)0.9882812500000f,(float16_t)0.1528320312500f, +(float16_t)0.9873046875000f,(float16_t)0.1588134765625f, +(float16_t)0.9863281250000f,(float16_t)0.1649169921875f, +(float16_t)0.9853515625000f,(float16_t)0.1710205078125f, +(float16_t)0.9843750000000f,(float16_t)0.1770019531250f, +(float16_t)0.9829101562500f,(float16_t)0.1829833984375f, +(float16_t)0.9819335937500f,(float16_t)0.1890869140625f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9794921875000f,(float16_t)0.2010498046875f, +(float16_t)0.9785156250000f,(float16_t)0.2071533203125f, +(float16_t)0.9770507812500f,(float16_t)0.2131347656250f, +(float16_t)0.9755859375000f,(float16_t)0.2191162109375f, +(float16_t)0.9741210937500f,(float16_t)0.2250976562500f, +(float16_t)0.9731445312500f,(float16_t)0.2310791015625f, +(float16_t)0.9716796875000f,(float16_t)0.2370605468750f, +(float16_t)0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)0.9687500000000f,(float16_t)0.2489013671875f, +(float16_t)0.9667968750000f,(float16_t)0.2548828125000f, +(float16_t)0.9653320312500f,(float16_t)0.2607421875000f, +(float16_t)0.9638671875000f,(float16_t)0.2666015625000f, +(float16_t)0.9619140625000f,(float16_t)0.2727050781250f, +(float16_t)0.9604492187500f,(float16_t)0.2785644531250f, +(float16_t)0.9584960937500f,(float16_t)0.2844238281250f, +(float16_t)0.9570312500000f,(float16_t)0.2902832031250f, +(float16_t)0.9550781250000f,(float16_t)0.2961425781250f, +(float16_t)0.9531250000000f,(float16_t)0.3020019531250f, +(float16_t)0.9516601562500f,(float16_t)0.3078613281250f, +(float16_t)0.9497070312500f,(float16_t)0.3137207031250f, +(float16_t)0.9477539062500f,(float16_t)0.3195800781250f, +(float16_t)0.9458007812500f,(float16_t)0.3251953125000f, +(float16_t)0.9433593750000f,(float16_t)0.3310546875000f, +(float16_t)0.9414062500000f,(float16_t)0.3369140625000f, +(float16_t)0.9394531250000f,(float16_t)0.3427734375000f, +(float16_t)0.9375000000000f,(float16_t)0.3483886718750f, +(float16_t)0.9350585937500f,(float16_t)0.3542480468750f, +(float16_t)0.9331054687500f,(float16_t)0.3598632812500f, +(float16_t)0.9306640625000f,(float16_t)0.3657226562500f, +(float16_t)0.9287109375000f,(float16_t)0.3713378906250f, +(float16_t)0.9262695312500f,(float16_t)0.3769531250000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.9213867187500f,(float16_t)0.3884277343750f, +(float16_t)0.9189453125000f,(float16_t)0.3940429687500f, +(float16_t)0.9165039062500f,(float16_t)0.3996582031250f, +(float16_t)0.9140625000000f,(float16_t)0.4052734375000f, +(float16_t)0.9116210937500f,(float16_t)0.4108886718750f, +(float16_t)0.9091796875000f,(float16_t)0.4165039062500f, +(float16_t)0.9067382812500f,(float16_t)0.4221191406250f, +(float16_t)0.9038085937500f,(float16_t)0.4274902343750f, +(float16_t)0.9013671875000f,(float16_t)0.4331054687500f, +(float16_t)0.8984375000000f,(float16_t)0.4387207031250f, +(float16_t)0.8959960937500f,(float16_t)0.4440917968750f, +(float16_t)0.8930664062500f,(float16_t)0.4497070312500f, +(float16_t)0.8906250000000f,(float16_t)0.4550781250000f, 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+(float16_t)0.6250000000000f,(float16_t)0.7807617187500f, +(float16_t)0.6201171875000f,(float16_t)0.7846679687500f, +(float16_t)0.6152343750000f,(float16_t)0.7885742187500f, +(float16_t)0.6103515625000f,(float16_t)0.7919921875000f, +(float16_t)0.6054687500000f,(float16_t)0.7958984375000f, +(float16_t)0.6005859375000f,(float16_t)0.7993164062500f, +(float16_t)0.5957031250000f,(float16_t)0.8032226562500f, +(float16_t)0.5908203125000f,(float16_t)0.8066406250000f, +(float16_t)0.5859375000000f,(float16_t)0.8105468750000f, +(float16_t)0.5810546875000f,(float16_t)0.8139648437500f, +(float16_t)0.5756835937500f,(float16_t)0.8173828125000f, +(float16_t)0.5708007812500f,(float16_t)0.8212890625000f, +(float16_t)0.5659179687500f,(float16_t)0.8247070312500f, +(float16_t)0.5605468750000f,(float16_t)0.8281250000000f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.5502929687500f,(float16_t)0.8349609375000f, +(float16_t)0.5454101562500f,(float16_t)0.8383789062500f, 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+(float16_t)0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f,}; + +const float16_t rearranged_twiddle_stride2_1024_f16[680] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)0.0122680664062f, +(float16_t)0.9995117187500f,(float16_t)0.0245361328125f, +(float16_t)0.9995117187500f,(float16_t)0.0368041992188f, +(float16_t)0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)0.9980468750000f,(float16_t)0.0613098144531f, +(float16_t)0.9970703125000f,(float16_t)0.0735473632812f, +(float16_t)0.9960937500000f,(float16_t)0.0858154296875f, 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+const float16_t rearranged_twiddle_stride3_1024_f16[680] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)0.0184020996094f, +(float16_t)0.9995117187500f,(float16_t)0.0368041992188f, +(float16_t)0.9985351562500f,(float16_t)0.0552062988281f, +(float16_t)0.9970703125000f,(float16_t)0.0735473632812f, +(float16_t)0.9956054687500f,(float16_t)0.0919189453125f, +(float16_t)0.9941406250000f,(float16_t)0.1102294921875f, +(float16_t)0.9916992187500f,(float16_t)0.1285400390625f, +(float16_t)0.9892578125000f,(float16_t)0.1467285156250f, +(float16_t)0.9863281250000f,(float16_t)0.1649169921875f, +(float16_t)0.9829101562500f,(float16_t)0.1829833984375f, +(float16_t)0.9794921875000f,(float16_t)0.2010498046875f, +(float16_t)0.9755859375000f,(float16_t)0.2191162109375f, +(float16_t)0.9716796875000f,(float16_t)0.2370605468750f, +(float16_t)0.9667968750000f,(float16_t)0.2548828125000f, 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+0,2048,2560,2688,2720,0,}; + +const uint32_t rearranged_twiddle_tab_stride2_arr_4096_f16[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const uint32_t rearranged_twiddle_tab_stride3_arr_4096_f16[6] ARM_DSP_TABLE_ATTRIBUTE ={ +0,2048,2560,2688,2720,0,}; + +const float16_t rearranged_twiddle_stride1_4096_f16[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)0.0015335083008f, +(float16_t)1.0000000000000f,(float16_t)0.0030670166016f, +(float16_t)1.0000000000000f,(float16_t)0.0046005249023f, +(float16_t)1.0000000000000f,(float16_t)0.0061340332031f, +(float16_t)1.0000000000000f,(float16_t)0.0076713562012f, +(float16_t)1.0000000000000f,(float16_t)0.0092010498047f, +(float16_t)1.0000000000000f,(float16_t)0.0107345581055f, +(float16_t)1.0000000000000f,(float16_t)0.0122680664062f, +(float16_t)1.0000000000000f,(float16_t)0.0138015747070f, +(float16_t)1.0000000000000f,(float16_t)0.0153427124023f, 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+(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f,}; + +const float16_t rearranged_twiddle_stride2_4096_f16[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)0.0030670166016f, +(float16_t)1.0000000000000f,(float16_t)0.0061340332031f, +(float16_t)1.0000000000000f,(float16_t)0.0092010498047f, +(float16_t)1.0000000000000f,(float16_t)0.0122680664062f, 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+(float16_t)-0.9990234375000f,(float16_t)0.0490722656250f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f,}; + +const float16_t rearranged_twiddle_stride3_4096_f16[2728] ARM_DSP_TABLE_ATTRIBUTE ={ +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)0.0046005249023f, +(float16_t)1.0000000000000f,(float16_t)0.0092010498047f, +(float16_t)1.0000000000000f,(float16_t)0.0138015747070f, +(float16_t)1.0000000000000f,(float16_t)0.0184020996094f, +(float16_t)0.9995117187500f,(float16_t)0.0230102539062f, +(float16_t)0.9995117187500f,(float16_t)0.0276031494141f, +(float16_t)0.9995117187500f,(float16_t)0.0321960449219f, +(float16_t)0.9995117187500f,(float16_t)0.0368041992188f, +(float16_t)0.9990234375000f,(float16_t)0.0414123535156f, +(float16_t)0.9990234375000f,(float16_t)0.0459899902344f, 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+(float16_t)-0.1950683593750f,(float16_t)0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)1.0000000000000f,(float16_t)0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f,}; + +#endif /* defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +#endif /* if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_neon_tables.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_neon_tables.c new file mode 100755 index 0000000..18e32b2 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_neon_tables.c @@ -0,0 +1,24169 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_neon_tables.c + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for NEON implementation only + * + * @date 02 October 2024 + * + * Target Processor: Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2024 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + + #include "arm_compiler_specific.h" + + #include "arm_math_types.h" + + + + +#if defined(ARM_MATH_NEON) + + +#include "arm_neon_tables.h" +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_16_f32[ARM_NEON_RFFT_TWIDDLES_16_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f,}; + +const uint32_t arm_neon_rfft_factors_16_f32[ARM_NEON_RFFT_FACTORS_16_F32_LEN]={ +2,4,4,4,}; + +const float32_t *arm_neon_rfft_twiddles_neon_16_f32=NULL; + +const uint32_t arm_neon_rfft_factors_neon_16_f32[ARM_NEON_RFFT_FACTORS_NEON_16_F32_LEN]={ +1,1,4,1,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_super_twiddles_neon_16_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_32_f32[ARM_NEON_RFFT_TWIDDLES_32_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.98078525066375732422f, +-0.19509032368659973145f,0.92387950420379638672f,-0.38268342614173889160f, +0.83146959543228149414f,-0.55557024478912353516f,0.70710676908493041992f, +-0.70710676908493041992f,0.55557024478912353516f,-0.83146959543228149414f, +0.38268342614173889160f,-0.92387950420379638672f,0.19509032368659973145f, +-0.98078525066375732422f,1.00000000000000000000f,-0.00000000000000000000f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.00000000000000006123f,-1.00000000000000000000f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.92387950420379638672f,-0.38268342614173889160f,1.00000000000000000000f, +-0.00000000000000000000f,0.83146959543228149414f,-0.55557024478912353516f, +0.38268342614173889160f,-0.92387950420379638672f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.98078525066375732422f,-0.19509032368659973145f,-0.92387950420379638672f, +0.38268342614173889160f,-0.55557024478912353516f,0.83146959543228149414f,}; + +const uint32_t arm_neon_rfft_factors_32_f32[ARM_NEON_RFFT_FACTORS_32_F32_LEN]={ +2,4,8,8,}; + +const float32_t *arm_neon_rfft_twiddles_neon_32_f32=NULL; + +const uint32_t arm_neon_rfft_factors_neon_32_f32[ARM_NEON_RFFT_FACTORS_NEON_32_F32_LEN]={ +1,1,8,1,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_super_twiddles_neon_32_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.98078525066375732422f, +-0.19509032368659973145f,0.92387950420379638672f,-0.38268342614173889160f, +0.83146959543228149414f,-0.55557024478912353516f,1.00000000000000000000f, +-0.00000000000000000000f,0.92387950420379638672f,-0.38268342614173889160f, +0.70710676908493041992f,-0.70710676908493041992f,0.38268342614173889160f, +-0.92387950420379638672f,1.00000000000000000000f,-0.00000000000000000000f, +0.83146959543228149414f,-0.55557024478912353516f,0.38268342614173889160f, +-0.92387950420379638672f,-0.19509032368659973145f,-0.98078525066375732422f,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_64_f32[ARM_NEON_RFFT_TWIDDLES_64_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f, +1.00000000000000000000f,-0.00000000000000000000f,0.99518471956253051758f, +-0.09801714122295379639f,0.98078525066375732422f,-0.19509032368659973145f, +0.95694035291671752930f,-0.29028466343879699707f,0.92387950420379638672f, +-0.38268342614173889160f,0.88192129135131835938f,-0.47139674425125122070f, +0.83146959543228149414f,-0.55557024478912353516f,0.77301043272018432617f, +-0.63439327478408813477f,0.70710676908493041992f,-0.70710676908493041992f, +0.63439327478408813477f,-0.77301043272018432617f,0.55557024478912353516f, +-0.83146959543228149414f,0.47139674425125122070f,-0.88192129135131835938f, +0.38268342614173889160f,-0.92387950420379638672f,0.29028466343879699707f, +-0.95694035291671752930f,0.19509032368659973145f,-0.98078525066375732422f, +0.09801714122295379639f,-0.99518471956253051758f,1.00000000000000000000f, +-0.00000000000000000000f,0.98078525066375732422f,-0.19509032368659973145f, +0.92387950420379638672f,-0.38268342614173889160f,0.83146959543228149414f, +-0.55557024478912353516f,0.70710676908493041992f,-0.70710676908493041992f, +0.55557024478912353516f,-0.83146959543228149414f,0.38268342614173889160f, +-0.92387950420379638672f,0.19509032368659973145f,-0.98078525066375732422f, +0.00000000000000006123f,-1.00000000000000000000f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.38268342614173889160f,-0.92387950420379638672f, +-0.55557024478912353516f,-0.83146959543228149414f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.83146959543228149414f,-0.55557024478912353516f, +-0.92387950420379638672f,-0.38268342614173889160f,-0.98078525066375732422f, +-0.19509032368659973145f,1.00000000000000000000f,-0.00000000000000000000f, +0.95694035291671752930f,-0.29028466343879699707f,0.83146959543228149414f, +-0.55557024478912353516f,0.63439327478408813477f,-0.77301043272018432617f, +0.38268342614173889160f,-0.92387950420379638672f,0.09801714122295379639f, +-0.99518471956253051758f,-0.19509032368659973145f,-0.98078525066375732422f, +-0.47139674425125122070f,-0.88192129135131835938f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.88192129135131835938f,-0.47139674425125122070f, +-0.98078525066375732422f,-0.19509032368659973145f,-0.99518471956253051758f, +0.09801714122295379639f,-0.92387950420379638672f,0.38268342614173889160f, +-0.77301043272018432617f,0.63439327478408813477f,-0.55557024478912353516f, +0.83146959543228149414f,-0.29028466343879699707f,0.95694035291671752930f,}; + +const uint32_t arm_neon_rfft_factors_64_f32[ARM_NEON_RFFT_FACTORS_64_F32_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_neon_64_f32[ARM_NEON_RFFT_TWIDDLES_NEON_64_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,1.00000000000000000000f, +-0.00000000000000000000f,1.00000000000000000000f,-0.00000000000000000000f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.70710676908493041992f,-0.70710676908493041992f,0.00000000000000006123f, +-1.00000000000000000000f,-0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f,}; + +const uint32_t arm_neon_rfft_factors_neon_64_f32[ARM_NEON_RFFT_FACTORS_NEON_64_F32_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_super_twiddles_neon_64_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.99518471956253051758f, +-0.09801714122295379639f,0.98078525066375732422f,-0.19509032368659973145f, +0.95694035291671752930f,-0.29028466343879699707f,1.00000000000000000000f, +-0.00000000000000000000f,0.98078525066375732422f,-0.19509032368659973145f, +0.92387950420379638672f,-0.38268342614173889160f,0.83146959543228149414f, +-0.55557024478912353516f,1.00000000000000000000f,-0.00000000000000000000f, +0.95694035291671752930f,-0.29028466343879699707f,0.83146959543228149414f, +-0.55557024478912353516f,0.63439327478408813477f,-0.77301043272018432617f, +0.92387950420379638672f,-0.38268345594406127930f,0.88192129135131835938f, +-0.47139671444892883301f,0.83146959543228149414f,-0.55557024478912353516f, +0.77301049232482910156f,-0.63439327478408813477f,0.70710676908493041992f, +-0.70710676908493041992f,0.55557024478912353516f,-0.83146959543228149414f, +0.38268342614173889160f,-0.92387950420379638672f,0.19509035348892211914f, +-0.98078525066375732422f,0.38268342614173889160f,-0.92387950420379638672f, +0.09801713377237319946f,-0.99518471956253051758f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.47139662504196166992f,-0.88192129135131835938f,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_128_f32[ARM_NEON_RFFT_TWIDDLES_128_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.98078525066375732422f, +-0.19509032368659973145f,0.92387950420379638672f,-0.38268342614173889160f, +0.83146959543228149414f,-0.55557024478912353516f,0.70710676908493041992f, +-0.70710676908493041992f,0.55557024478912353516f,-0.83146959543228149414f, +0.38268342614173889160f,-0.92387950420379638672f,0.19509032368659973145f, +-0.98078525066375732422f,1.00000000000000000000f,-0.00000000000000000000f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.00000000000000006123f,-1.00000000000000000000f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.92387950420379638672f,-0.38268342614173889160f,1.00000000000000000000f, +-0.00000000000000000000f,0.83146959543228149414f,-0.55557024478912353516f, +0.38268342614173889160f,-0.92387950420379638672f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.98078525066375732422f,-0.19509032368659973145f,-0.92387950420379638672f, +0.38268342614173889160f,-0.55557024478912353516f,0.83146959543228149414f, +1.00000000000000000000f,-0.00000000000000000000f,0.99879544973373413086f, +-0.04906767606735229492f,0.99518471956253051758f,-0.09801714122295379639f, +0.98917651176452636719f,-0.14673046767711639404f,0.98078525066375732422f, +-0.19509032368659973145f,0.97003126144409179688f,-0.24298018217086791992f, +0.95694035291671752930f,-0.29028466343879699707f,0.94154405593872070312f, +-0.33688986301422119141f,0.92387950420379638672f,-0.38268342614173889160f, +0.90398931503295898438f,-0.42755508422851562500f,0.88192129135131835938f, +-0.47139674425125122070f,0.85772860050201416016f,-0.51410275697708129883f, +0.83146959543228149414f,-0.55557024478912353516f,0.80320751667022705078f, +-0.59569931030273437500f,0.77301043272018432617f,-0.63439327478408813477f, +0.74095112085342407227f,-0.67155897617340087891f,0.70710676908493041992f, +-0.70710676908493041992f,0.67155897617340087891f,-0.74095112085342407227f, +0.63439327478408813477f,-0.77301043272018432617f,0.59569931030273437500f, +-0.80320751667022705078f,0.55557024478912353516f,-0.83146959543228149414f, +0.51410275697708129883f,-0.85772860050201416016f,0.47139674425125122070f, +-0.88192129135131835938f,0.42755508422851562500f,-0.90398931503295898438f, +0.38268342614173889160f,-0.92387950420379638672f,0.33688986301422119141f, +-0.94154405593872070312f,0.29028466343879699707f,-0.95694035291671752930f, +0.24298018217086791992f,-0.97003126144409179688f,0.19509032368659973145f, +-0.98078525066375732422f,0.14673046767711639404f,-0.98917651176452636719f, +0.09801714122295379639f,-0.99518471956253051758f,0.04906767606735229492f, +-0.99879544973373413086f,1.00000000000000000000f,-0.00000000000000000000f, +0.99518471956253051758f,-0.09801714122295379639f,0.98078525066375732422f, +-0.19509032368659973145f,0.95694035291671752930f,-0.29028466343879699707f, +0.92387950420379638672f,-0.38268342614173889160f,0.88192129135131835938f, +-0.47139674425125122070f,0.83146959543228149414f,-0.55557024478912353516f, +0.77301043272018432617f,-0.63439327478408813477f,0.70710676908493041992f, +-0.70710676908493041992f,0.63439327478408813477f,-0.77301043272018432617f, +0.55557024478912353516f,-0.83146959543228149414f,0.47139674425125122070f, +-0.88192129135131835938f,0.38268342614173889160f,-0.92387950420379638672f, +0.29028466343879699707f,-0.95694035291671752930f,0.19509032368659973145f, +-0.98078525066375732422f,0.09801714122295379639f,-0.99518471956253051758f, +0.00000000000000006123f,-1.00000000000000000000f,-0.09801714122295379639f, +-0.99518471956253051758f,-0.19509032368659973145f,-0.98078525066375732422f, +-0.29028466343879699707f,-0.95694035291671752930f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.47139674425125122070f,-0.88192129135131835938f, +-0.55557024478912353516f,-0.83146959543228149414f,-0.63439327478408813477f, +-0.77301043272018432617f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.77301043272018432617f,-0.63439327478408813477f,-0.83146959543228149414f, +-0.55557024478912353516f,-0.88192129135131835938f,-0.47139674425125122070f, +-0.92387950420379638672f,-0.38268342614173889160f,-0.95694035291671752930f, +-0.29028466343879699707f,-0.98078525066375732422f,-0.19509032368659973145f, +-0.99518471956253051758f,-0.09801714122295379639f,1.00000000000000000000f, +-0.00000000000000000000f,0.98917651176452636719f,-0.14673046767711639404f, +0.95694035291671752930f,-0.29028466343879699707f,0.90398931503295898438f, +-0.42755508422851562500f,0.83146959543228149414f,-0.55557024478912353516f, +0.74095112085342407227f,-0.67155897617340087891f,0.63439327478408813477f, +-0.77301043272018432617f,0.51410275697708129883f,-0.85772860050201416016f, +0.38268342614173889160f,-0.92387950420379638672f,0.24298018217086791992f, +-0.97003126144409179688f,0.09801714122295379639f,-0.99518471956253051758f, +-0.04906767606735229492f,-0.99879544973373413086f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.33688986301422119141f,-0.94154405593872070312f, +-0.47139674425125122070f,-0.88192129135131835938f,-0.59569931030273437500f, +-0.80320751667022705078f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.80320751667022705078f,-0.59569931030273437500f,-0.88192129135131835938f, +-0.47139674425125122070f,-0.94154405593872070312f,-0.33688986301422119141f, +-0.98078525066375732422f,-0.19509032368659973145f,-0.99879544973373413086f, +-0.04906767606735229492f,-0.99518471956253051758f,0.09801714122295379639f, +-0.97003126144409179688f,0.24298018217086791992f,-0.92387950420379638672f, +0.38268342614173889160f,-0.85772860050201416016f,0.51410275697708129883f, +-0.77301043272018432617f,0.63439327478408813477f,-0.67155897617340087891f, +0.74095112085342407227f,-0.55557024478912353516f,0.83146959543228149414f, +-0.42755508422851562500f,0.90398931503295898438f,-0.29028466343879699707f, +0.95694035291671752930f,-0.14673046767711639404f,0.98917651176452636719f,}; + +const uint32_t arm_neon_rfft_factors_128_f32[ARM_NEON_RFFT_FACTORS_128_F32_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_neon_128_f32[ARM_NEON_RFFT_TWIDDLES_NEON_128_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,1.00000000000000000000f, +-0.00000000000000000000f,1.00000000000000000000f,-0.00000000000000000000f, +0.98078525066375732422f,-0.19509032368659973145f,0.92387950420379638672f, +-0.38268342614173889160f,0.83146959543228149414f,-0.55557024478912353516f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.83146959543228149414f,-0.55557024478912353516f,0.38268342614173889160f, +-0.92387950420379638672f,-0.19509032368659973145f,-0.98078525066375732422f, +0.70710676908493041992f,-0.70710676908493041992f,0.00000000000000006123f, +-1.00000000000000000000f,-0.70710676908493041992f,-0.70710676908493041992f, +0.55557024478912353516f,-0.83146959543228149414f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.98078525066375732422f,-0.19509032368659973145f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, 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arm_neon_rfft_twiddles_256_f32[ARM_NEON_RFFT_TWIDDLES_256_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f, +1.00000000000000000000f,-0.00000000000000000000f,0.99518471956253051758f, +-0.09801714122295379639f,0.98078525066375732422f,-0.19509032368659973145f, +0.95694035291671752930f,-0.29028466343879699707f,0.92387950420379638672f, +-0.38268342614173889160f,0.88192129135131835938f,-0.47139674425125122070f, 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+0.09801714122295379639f,-0.98527765274047851562f,0.17096188664436340332f, +-0.97003126144409179688f,0.24298018217086791992f,-0.94952815771102905273f, +0.31368175148963928223f,-0.92387950420379638672f,0.38268342614173889160f, +-0.89322429895401000977f,0.44961133599281311035f,-0.85772860050201416016f, +0.51410275697708129883f,-0.81758481264114379883f,0.57580816745758056641f, +-0.77301043272018432617f,0.63439327478408813477f,-0.72424709796905517578f, +0.68954056501388549805f,-0.67155897617340087891f,0.74095112085342407227f, +-0.61523157358169555664f,0.78834640979766845703f,-0.55557024478912353516f, +0.83146959543228149414f,-0.49289819598197937012f,0.87008696794509887695f, +-0.42755508422851562500f,0.90398931503295898438f,-0.35989505052566528320f, +0.93299281597137451172f,-0.29028466343879699707f,0.95694035291671752930f, +-0.21910123527050018311f,0.97570210695266723633f,-0.14673046767711639404f, +0.98917651176452636719f,-0.07356456667184829712f,0.99729043245315551758f,}; + +const uint32_t arm_neon_rfft_factors_256_f32[ARM_NEON_RFFT_FACTORS_256_F32_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_neon_256_f32[ARM_NEON_RFFT_TWIDDLES_NEON_256_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,1.00000000000000000000f, +-0.00000000000000000000f,1.00000000000000000000f,-0.00000000000000000000f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.70710676908493041992f,-0.70710676908493041992f,0.00000000000000006123f, +-1.00000000000000000000f,-0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f, +1.00000000000000000000f,-0.00000000000000000000f,1.00000000000000000000f, +-0.00000000000000000000f,1.00000000000000000000f,-0.00000000000000000000f, +0.99518471956253051758f,-0.09801714122295379639f,0.98078525066375732422f, +-0.19509032368659973145f,0.95694035291671752930f,-0.29028466343879699707f, +0.98078525066375732422f,-0.19509032368659973145f,0.92387950420379638672f, +-0.38268342614173889160f,0.83146959543228149414f,-0.55557024478912353516f, +0.95694035291671752930f,-0.29028466343879699707f,0.83146959543228149414f, +-0.55557024478912353516f,0.63439327478408813477f,-0.77301043272018432617f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.88192129135131835938f,-0.47139674425125122070f,0.55557024478912353516f, +-0.83146959543228149414f,0.09801714122295379639f,-0.99518471956253051758f, +0.83146959543228149414f,-0.55557024478912353516f,0.38268342614173889160f, +-0.92387950420379638672f,-0.19509032368659973145f,-0.98078525066375732422f, +0.77301043272018432617f,-0.63439327478408813477f,0.19509032368659973145f, +-0.98078525066375732422f,-0.47139674425125122070f,-0.88192129135131835938f, +0.70710676908493041992f,-0.70710676908493041992f,0.00000000000000006123f, +-1.00000000000000000000f,-0.70710676908493041992f,-0.70710676908493041992f, +0.63439327478408813477f,-0.77301043272018432617f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.88192129135131835938f,-0.47139674425125122070f, +0.55557024478912353516f,-0.83146959543228149414f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.98078525066375732422f,-0.19509032368659973145f, +0.47139674425125122070f,-0.88192129135131835938f,-0.55557024478912353516f, +-0.83146959543228149414f,-0.99518471956253051758f,0.09801714122295379639f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f, +0.29028466343879699707f,-0.95694035291671752930f,-0.83146959543228149414f, +-0.55557024478912353516f,-0.77301043272018432617f,0.63439327478408813477f, +0.19509032368659973145f,-0.98078525066375732422f,-0.92387950420379638672f, +-0.38268342614173889160f,-0.55557024478912353516f,0.83146959543228149414f, +0.09801714122295379639f,-0.99518471956253051758f,-0.98078525066375732422f, +-0.19509032368659973145f,-0.29028466343879699707f,0.95694035291671752930f,}; + +const uint32_t arm_neon_rfft_factors_neon_256_f32[ARM_NEON_RFFT_FACTORS_NEON_256_F32_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_super_twiddles_neon_256_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.99969881772994995117f, +-0.02454122900962829590f,0.99879544973373413086f,-0.04906767606735229492f, +0.99729043245315551758f,-0.07356456667184829712f,1.00000000000000000000f, +-0.00000000000000000000f,0.99879544973373413086f,-0.04906767606735229492f, +0.99518471956253051758f,-0.09801714122295379639f,0.98917651176452636719f, +-0.14673046767711639404f,1.00000000000000000000f,-0.00000000000000000000f, 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+-0.38268345594406127930f,0.90398931503295898438f,-0.42755508422851562500f, +0.88192129135131835938f,-0.47139671444892883301f,0.85772860050201416016f, +-0.51410275697708129883f,0.83146959543228149414f,-0.55557024478912353516f, +0.78834646940231323242f,-0.61523157358169555664f,0.74095112085342407227f, +-0.67155897617340087891f,0.68954056501388549805f,-0.72424703836441040039f, +0.95694035291671752930f,-0.29028466343879699707f,0.94952815771102905273f, +-0.31368175148963928223f,0.94154405593872070312f,-0.33688983321189880371f, +0.93299281597137451172f,-0.35989505052566528320f,0.83146959543228149414f, +-0.55557024478912353516f,0.80320751667022705078f,-0.59569931030273437500f, +0.77301049232482910156f,-0.63439327478408813477f,0.74095112085342407227f, +-0.67155897617340087891f,0.63439327478408813477f,-0.77301043272018432617f, +0.57580822706222534180f,-0.81758481264114379883f,0.51410281658172607422f, +-0.85772860050201416016f,0.44961130619049072266f,-0.89322429895401000977f, 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+-0.90398931503295898438f,0.09801713377237319946f,-0.99518471956253051758f, +0.02454125508666038513f,-0.99969881772994995117f,-0.04906762018799781799f, +-0.99879544973373413086f,-0.12241070717573165894f,-0.99247950315475463867f, +0.83146959543228149414f,-0.55557024478912353516f,0.81758481264114379883f, +-0.57580822706222534180f,0.80320751667022705078f,-0.59569931030273437500f, +0.78834646940231323242f,-0.61523157358169555664f,0.38268342614173889160f, +-0.92387950420379638672f,0.33688983321189880371f,-0.94154405593872070312f, +0.29028463363647460938f,-0.95694035291671752930f,0.24298024177551269531f, +-0.97003126144409179688f,-0.19509032368659973145f,-0.98078525066375732422f, +-0.26671272516250610352f,-0.96377605199813842773f,-0.33688980340957641602f, +-0.94154405593872070312f,-0.40524134039878845215f,-0.91420972347259521484f, +0.77301049232482910156f,-0.63439327478408813477f,0.75720882415771484375f, +-0.65317285060882568359f,0.74095112085342407227f,-0.67155897617340087891f, +0.72424709796905517578f,-0.68954056501388549805f,0.19509035348892211914f, +-0.98078525066375732422f,0.14673049747943878174f,-0.98917651176452636719f, +0.09801713377237319946f,-0.99518471956253051758f,0.04906764999032020569f, +-0.99879544973373413086f,-0.47139662504196166992f,-0.88192129135131835938f, +-0.53499770164489746094f,-0.84485352039337158203f,-0.59569936990737915039f, +-0.80320751667022705078f,-0.65317285060882568359f,-0.75720882415771484375f,}; + +__ALIGNED(16) const float32_t arm_neon_rfft_twiddles_512_f32[ARM_NEON_RFFT_TWIDDLES_512_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.98078525066375732422f, +-0.19509032368659973145f,0.92387950420379638672f,-0.38268342614173889160f, +0.83146959543228149414f,-0.55557024478912353516f,0.70710676908493041992f, +-0.70710676908493041992f,0.55557024478912353516f,-0.83146959543228149414f, +0.38268342614173889160f,-0.92387950420379638672f,0.19509032368659973145f, 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arm_neon_rfft_super_twiddles_neon_512_f32[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.99992471933364868164f, +-0.01227153837680816650f,0.99969881772994995117f,-0.02454122900962829590f, +0.99932235479354858398f,-0.03680722415447235107f,1.00000000000000000000f, +-0.00000000000000000000f,0.99969881772994995117f,-0.02454122900962829590f, +0.99879544973373413086f,-0.04906767606735229492f,0.99729043245315551758f, +-0.07356456667184829712f,1.00000000000000000000f,-0.00000000000000000000f, +0.99932235479354858398f,-0.03680722415447235107f,0.99729043245315551758f, +-0.07356456667184829712f,0.99390697479248046875f,-0.11022220551967620850f, +0.99879544973373413086f,-0.04906767606735229492f,0.99811810255050659180f, +-0.06132073700428009033f,0.99729043245315551758f,-0.07356456667184829712f, +0.99631261825561523438f,-0.08579730987548828125f,0.99518471956253051758f, +-0.09801714122295379639f,0.99247956275939941406f,-0.12241066992282867432f, 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+-0.99961882829666137695f,-0.66699999570846557617f,-0.74505770206451416016f, +-0.67042165994644165039f,-0.74198037385940551758f,-0.67382907867431640625f, +-0.73888725042343139648f,-0.67722207307815551758f,-0.73577868938446044922f, +0.71573084592819213867f,-0.69837623834609985352f,0.71465867757797241211f, +-0.69947332143783569336f,0.71358489990234375000f,-0.70056879520416259766f, +0.71250939369201660156f,-0.70166260004043579102f,0.02454125508666038513f, +-0.99969881772994995117f,0.02147409692406654358f,-0.99976938962936401367f, +0.01840673759579658508f,-0.99983060359954833984f,0.01533920597285032272f, +-0.99988234043121337891f,-0.68060094118118286133f,-0.73265433311462402344f, +-0.68396532535552978516f,-0.72951447963714599609f,-0.68731528520584106445f, +-0.72635918855667114258f,-0.69065064191818237305f,-0.72318851947784423828f, +0.71143221855163574219f,-0.70275473594665527344f,0.71035331487655639648f, +-0.70384526252746582031f,0.70927280187606811523f,-0.70493406057357788086f, +0.70819061994552612305f,-0.70602124929428100586f,0.01227152906358242035f, +-0.99992471933364868164f,0.00920373760163784027f,-0.99995762109756469727f, +0.00613585812970995903f,-0.99998116493225097656f,0.00306792184710502625f, +-0.99999529123306274414f,-0.69397145509719848633f,-0.72000253200531005859f, +-0.69727748632431030273f,-0.71680128574371337891f,-0.70056879520416259766f, +-0.71358489990234375000f,-0.70384526252746582031f,-0.71035337448120117188f,}; + +const q31_t *arm_neon_rfft_twiddles_16_q31=NULL; + +const uint32_t arm_neon_rfft_factors_16_q31[ARM_NEON_RFFT_FACTORS_16_Q31_LEN]={ +1,1,8,1,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_16_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_Q31_LEN]={ +0xCF043AB3,0x89BE50C3,0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x80000000, +0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_32_q31[ARM_NEON_RFFT_TWIDDLES_32_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,}; + +const uint32_t arm_neon_rfft_factors_32_q31[ARM_NEON_RFFT_FACTORS_32_Q31_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_32_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_Q31_LEN]={ +0xE70747C4,0x8275A0C0,0xCF043AB3,0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666, +0xA57D8666,0x9592675C,0xB8E31319,0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4, +0x80000000,0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_64_q31[ARM_NEON_RFFT_TWIDDLES_64_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,}; + +const uint32_t arm_neon_rfft_factors_64_q31[ARM_NEON_RFFT_FACTORS_64_Q31_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_64_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_Q31_LEN]={ +0xF3742CA2,0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3, +0x89BE50C3,0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54, +0xA57D8666,0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A, +0xC3A94590,0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4, +0x809DC971,0xF3742CA2,0x80000000,0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_128_q31[ARM_NEON_RFFT_TWIDDLES_128_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,}; + +const uint32_t arm_neon_rfft_factors_128_q31[ARM_NEON_RFFT_FACTORS_128_Q31_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_128_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_Q31_LEN]={ +0xF9B82684,0x80277872,0xF3742CA2,0x809DC971,0xED37EF91,0x8162AA04,0xE70747C4, +0x8275A0C0,0xE0E60685,0x83D60412,0xDAD7F3A2,0x8582FAA5,0xD4E0CB15,0x877B7BEC, +0xCF043AB3,0x89BE50C3,0xC945DFEC,0x8C4A142F,0xC3A94590,0x8F1D343A,0xBE31E19B, +0x9235F2EC,0xB8E31319,0x9592675C,0xB3C0200C,0x99307EE0,0xAECC336C,0x9D0DFE54, +0xAA0A5B2E,0xA1288376,0xA57D8666,0xA57D8666,0xA1288376,0xAA0A5B2E,0x9D0DFE54, +0xAECC336C,0x99307EE0,0xB3C0200C,0x9592675C,0xB8E31319,0x9235F2EC,0xBE31E19B, +0x8F1D343A,0xC3A94590,0x8C4A142F,0xC945DFEC,0x89BE50C3,0xCF043AB3,0x877B7BEC, +0xD4E0CB15,0x8582FAA5,0xDAD7F3A2,0x83D60412,0xE0E60685,0x8275A0C0,0xE70747C4, +0x8162AA04,0xED37EF91,0x809DC971,0xF3742CA2,0x80277872,0xF9B82684,0x80000000, +0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_256_q31[ARM_NEON_RFFT_TWIDDLES_256_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,0x7FFFFFFF, +0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91, +0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414, +0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590, +0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC, +0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376, +0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65, +0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3, +0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C, +0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x00000000,0x80000000,0xF3742CA2, +0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3,0x89BE50C3, +0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54,0xA57D8666, +0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A,0xC3A94590, +0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4,0x809DC971, +0xF3742CA2,0x7FFFFFFF,0x00000000,0x7E9D55FC,0xED37EF91,0x7A7D055B,0xDAD7F3A2, +0x73B5EBD1,0xC945DFEC,0x6A6D98A4,0xB8E31319,0x5ED77C8A,0xAA0A5B2E,0x5133CC94, +0x9D0DFE54,0x41CE1E65,0x9235F2EC,0x30FBC54D,0x89BE50C3,0x1F19F97B,0x83D60412, +0x0C8BD35E,0x809DC971,0xF9B82684,0x80277872,0xE70747C4,0x8275A0C0,0xD4E0CB15, +0x877B7BEC,0xC3A94590,0x8F1D343A,0xB3C0200C,0x99307EE0,0xA57D8666,0xA57D8666, +0x99307EE0,0xB3C0200C,0x8F1D343A,0xC3A94590,0x877B7BEC,0xD4E0CB15,0x8275A0C0, +0xE70747C4,0x80277872,0xF9B82684,0x809DC971,0x0C8BD35E,0x83D60412,0x1F19F97B, +0x89BE50C3,0x30FBC54D,0x9235F2EC,0x41CE1E65,0x9D0DFE54,0x5133CC94,0xAA0A5B2E, +0x5ED77C8A,0xB8E31319,0x6A6D98A4,0xC945DFEC,0x73B5EBD1,0xDAD7F3A2,0x7A7D055B, +0xED37EF91,0x7E9D55FC,}; + +const uint32_t arm_neon_rfft_factors_256_q31[ARM_NEON_RFFT_FACTORS_256_Q31_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_256_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_Q31_LEN]={ +0xFCDBD541,0x8009DE7E,0xF9B82684,0x80277872,0xF6956FB7,0x8058C94C,0xF3742CA2, +0x809DC971,0xF054D8D5,0x80F66E3C,0xED37EF91,0x8162AA04,0xEA1DEBBB,0x81E26C16, +0xE70747C4,0x8275A0C0,0xE3F47D96,0x831C314E,0xE0E60685,0x83D60412,0xDDDC5B3B, +0x84A2FC62,0xDAD7F3A2,0x8582FAA5,0xD7D946D8,0x8675DC4F,0xD4E0CB15,0x877B7BEC, +0xD1EEF59E,0x8893B125,0xCF043AB3,0x89BE50C3,0xCC210D79,0x8AFB2CBB,0xC945DFEC, +0x8C4A142F,0xC67322CE,0x8DAAD37B,0xC3A94590,0x8F1D343A,0xC0E8B648,0x90A0FD4E, +0xBE31E19B,0x9235F2EC,0xBB8532B0,0x93DBD6A0,0xB8E31319,0x9592675C,0xB64BEACD, +0x9759617F,0xB3C0200C,0x99307EE0,0xB140175B,0x9B1776DA,0xAECC336C,0x9D0DFE54, +0xAC64D510,0x9F13C7D0,0xAA0A5B2E,0xA1288376,0xA7BD22AC,0xA34BDF20,0xA57D8666, +0xA57D8666,0xA34BDF20,0xA7BD22AC,0xA1288376,0xAA0A5B2E,0x9F13C7D0,0xAC64D510, +0x9D0DFE54,0xAECC336C,0x9B1776DA,0xB140175B,0x99307EE0,0xB3C0200C,0x9759617F, +0xB64BEACD,0x9592675C,0xB8E31319,0x93DBD6A0,0xBB8532B0,0x9235F2EC,0xBE31E19B, +0x90A0FD4E,0xC0E8B648,0x8F1D343A,0xC3A94590,0x8DAAD37B,0xC67322CE,0x8C4A142F, +0xC945DFEC,0x8AFB2CBB,0xCC210D79,0x89BE50C3,0xCF043AB3,0x8893B125,0xD1EEF59E, +0x877B7BEC,0xD4E0CB15,0x8675DC4F,0xD7D946D8,0x8582FAA5,0xDAD7F3A2,0x84A2FC62, +0xDDDC5B3B,0x83D60412,0xE0E60685,0x831C314E,0xE3F47D96,0x8275A0C0,0xE70747C4, +0x81E26C16,0xEA1DEBBB,0x8162AA04,0xED37EF91,0x80F66E3C,0xF054D8D5,0x809DC971, +0xF3742CA2,0x8058C94C,0xF6956FB7,0x80277872,0xF9B82684,0x8009DE7E,0xFCDBD541, +0x80000000,0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_512_q31[ARM_NEON_RFFT_TWIDDLES_512_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684, +0x7FA736B4,0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC, +0xED37EF91,0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96, +0x7C29FBEE,0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1, +0xD7D946D8,0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3, +0x7504D345,0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6, +0xC3A94590,0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0, +0x6A6D98A4,0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926, +0xB140175B,0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E, +0x5CB420E0,0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2, +0xA1288376,0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA, +0x4C3FDFF4,0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50, +0x93DBD6A0,0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A, +0x398CDD32,0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D, +0x89BE50C3,0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F, +0x25280C5E,0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A, +0x831C314E,0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04, +0x0FAB272B,0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C, +0x80277872,0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684, +0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE, +0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3, +0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4, +0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E, +0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4, +0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A, +0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E, +0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04, +0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872,0x00000000,0x80000000,0xF9B82684, +0x80277872,0xF3742CA2,0x809DC971,0xED37EF91,0x8162AA04,0xE70747C4,0x8275A0C0, +0xE0E60685,0x83D60412,0xDAD7F3A2,0x8582FAA5,0xD4E0CB15,0x877B7BEC,0xCF043AB3, +0x89BE50C3,0xC945DFEC,0x8C4A142F,0xC3A94590,0x8F1D343A,0xBE31E19B,0x9235F2EC, +0xB8E31319,0x9592675C,0xB3C0200C,0x99307EE0,0xAECC336C,0x9D0DFE54,0xAA0A5B2E, +0xA1288376,0xA57D8666,0xA57D8666,0xA1288376,0xAA0A5B2E,0x9D0DFE54,0xAECC336C, +0x99307EE0,0xB3C0200C,0x9592675C,0xB8E31319,0x9235F2EC,0xBE31E19B,0x8F1D343A, +0xC3A94590,0x8C4A142F,0xC945DFEC,0x89BE50C3,0xCF043AB3,0x877B7BEC,0xD4E0CB15, +0x8582FAA5,0xDAD7F3A2,0x83D60412,0xE0E60685,0x8275A0C0,0xE70747C4,0x8162AA04, +0xED37EF91,0x809DC971,0xF3742CA2,0x80277872,0xF9B82684,0x7FFFFFFF,0x00000000, +0x7FA736B4,0xF6956FB7,0x7E9D55FC,0xED37EF91,0x7CE3CEB2,0xE3F47D96,0x7A7D055B, +0xDAD7F3A2,0x776C4EDB,0xD1EEF59E,0x73B5EBD1,0xC945DFEC,0x6F5F02B2,0xC0E8B648, +0x6A6D98A4,0xB8E31319,0x64E88926,0xB140175B,0x5ED77C8A,0xAA0A5B2E,0x5842DD54, +0xA34BDF20,0x5133CC94,0x9D0DFE54,0x49B41533,0x9759617F,0x41CE1E65,0x9235F2EC, +0x398CDD32,0x8DAAD37B,0x30FBC54D,0x89BE50C3,0x2826B928,0x8675DC4F,0x1F19F97B, +0x83D60412,0x15E21445,0x81E26C16,0x0C8BD35E,0x809DC971,0x03242ABF,0x8009DE7E, +0xF9B82684,0x80277872,0xF054D8D5,0x80F66E3C,0xE70747C4,0x8275A0C0,0xDDDC5B3B, +0x84A2FC62,0xD4E0CB15,0x877B7BEC,0xCC210D79,0x8AFB2CBB,0xC3A94590,0x8F1D343A, +0xBB8532B0,0x93DBD6A0,0xB3C0200C,0x99307EE0,0xAC64D510,0x9F13C7D0,0xA57D8666, +0xA57D8666,0x9F13C7D0,0xAC64D510,0x99307EE0,0xB3C0200C,0x93DBD6A0,0xBB8532B0, +0x8F1D343A,0xC3A94590,0x8AFB2CBB,0xCC210D79,0x877B7BEC,0xD4E0CB15,0x84A2FC62, +0xDDDC5B3B,0x8275A0C0,0xE70747C4,0x80F66E3C,0xF054D8D5,0x80277872,0xF9B82684, +0x8009DE7E,0x03242ABF,0x809DC971,0x0C8BD35E,0x81E26C16,0x15E21445,0x83D60412, +0x1F19F97B,0x8675DC4F,0x2826B928,0x89BE50C3,0x30FBC54D,0x8DAAD37B,0x398CDD32, +0x9235F2EC,0x41CE1E65,0x9759617F,0x49B41533,0x9D0DFE54,0x5133CC94,0xA34BDF20, +0x5842DD54,0xAA0A5B2E,0x5ED77C8A,0xB140175B,0x64E88926,0xB8E31319,0x6A6D98A4, +0xC0E8B648,0x6F5F02B2,0xC945DFEC,0x73B5EBD1,0xD1EEF59E,0x776C4EDB,0xDAD7F3A2, +0x7A7D055B,0xE3F47D96,0x7CE3CEB2,0xED37EF91,0x7E9D55FC,0xF6956FB7,0x7FA736B4,}; + +const uint32_t arm_neon_rfft_factors_512_q31[ARM_NEON_RFFT_FACTORS_512_Q31_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_512_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_Q31_LEN]={ +0xFE6DE2E0,0x800277A6,0xFCDBD541,0x8009DE7E,0xFB49E6A3,0x80163440,0xF9B82684, +0x80277872,0xF826A462,0x803DAA6A,0xF6956FB7,0x8058C94C,0xF50497FB,0x8078D40D, +0xF3742CA2,0x809DC971,0xF1E43D1C,0x80C7A80A,0xF054D8D5,0x80F66E3C,0xEEC60F31, +0x812A1A3A,0xED37EF91,0x8162AA04,0xEBAA894F,0x81A01B6D,0xEA1DEBBB,0x81E26C16, +0xE8922622,0x82299971,0xE70747C4,0x8275A0C0,0xE57D5FDA,0x82C67F14,0xE3F47D96, +0x831C314E,0xE26CB01B,0x8376B422,0xE0E60685,0x83D60412,0xDF608FE4,0x843A1D70, +0xDDDC5B3B,0x84A2FC62,0xDC597781,0x85109CDD,0xDAD7F3A2,0x8582FAA5,0xD957DE7A, +0x85FA1153,0xD7D946D8,0x8675DC4F,0xD65C3B7B,0x86F656D3,0xD4E0CB15,0x877B7BEC, +0xD3670446,0x88054677,0xD1EEF59E,0x8893B125,0xD078AD9E,0x8926B677,0xCF043AB3, +0x89BE50C3,0xCD91AB39,0x8A5A7A31,0xCC210D79,0x8AFB2CBB,0xCAB26FA9,0x8BA0622F, +0xC945DFEC,0x8C4A142F,0xC7DB6C50,0x8CF83C30,0xC67322CE,0x8DAAD37B,0xC50D1149, +0x8E61D32E,0xC3A94590,0x8F1D343A,0xC247CD5A,0x8FDCEF66,0xC0E8B648,0x90A0FD4E, +0xBF8C0DE3,0x91695663,0xBE31E19B,0x9235F2EC,0xBCDA3ECB,0x9306CB04,0xBB8532B0, +0x93DBD6A0,0xBA32CA71,0x94B50D87,0xB8E31319,0x9592675C,0xB796199B,0x9673DB94, +0xB64BEACD,0x9759617F,0xB5049368,0x9842F043,0xB3C0200C,0x99307EE0,0xB27E9D3C, +0x9A22042D,0xB140175B,0x9B1776DA,0xB0049AB3,0x9C10CD70,0xAECC336C,0x9D0DFE54, +0xAD96ED92,0x9E0EFFC1,0xAC64D510,0x9F13C7D0,0xAB35F5B5,0xA01C4C73,0xAA0A5B2E, +0xA1288376,0xA8E21106,0xA2386284,0xA7BD22AC,0xA34BDF20,0xA69B9B68,0xA462EEAC, +0xA57D8666,0xA57D8666,0xA462EEAC,0xA69B9B68,0xA34BDF20,0xA7BD22AC,0xA2386284, +0xA8E21106,0xA1288376,0xAA0A5B2E,0xA01C4C73,0xAB35F5B5,0x9F13C7D0,0xAC64D510, +0x9E0EFFC1,0xAD96ED92,0x9D0DFE54,0xAECC336C,0x9C10CD70,0xB0049AB3,0x9B1776DA, +0xB140175B,0x9A22042D,0xB27E9D3C,0x99307EE0,0xB3C0200C,0x9842F043,0xB5049368, +0x9759617F,0xB64BEACD,0x9673DB94,0xB796199B,0x9592675C,0xB8E31319,0x94B50D87, +0xBA32CA71,0x93DBD6A0,0xBB8532B0,0x9306CB04,0xBCDA3ECB,0x9235F2EC,0xBE31E19B, +0x91695663,0xBF8C0DE3,0x90A0FD4E,0xC0E8B648,0x8FDCEF66,0xC247CD5A,0x8F1D343A, +0xC3A94590,0x8E61D32E,0xC50D1149,0x8DAAD37B,0xC67322CE,0x8CF83C30,0xC7DB6C50, +0x8C4A142F,0xC945DFEC,0x8BA0622F,0xCAB26FA9,0x8AFB2CBB,0xCC210D79,0x8A5A7A31, +0xCD91AB39,0x89BE50C3,0xCF043AB3,0x8926B677,0xD078AD9E,0x8893B125,0xD1EEF59E, +0x88054677,0xD3670446,0x877B7BEC,0xD4E0CB15,0x86F656D3,0xD65C3B7B,0x8675DC4F, +0xD7D946D8,0x85FA1153,0xD957DE7A,0x8582FAA5,0xDAD7F3A2,0x85109CDD,0xDC597781, +0x84A2FC62,0xDDDC5B3B,0x843A1D70,0xDF608FE4,0x83D60412,0xE0E60685,0x8376B422, +0xE26CB01B,0x831C314E,0xE3F47D96,0x82C67F14,0xE57D5FDA,0x8275A0C0,0xE70747C4, +0x82299971,0xE8922622,0x81E26C16,0xEA1DEBBB,0x81A01B6D,0xEBAA894F,0x8162AA04, +0xED37EF91,0x812A1A3A,0xEEC60F31,0x80F66E3C,0xF054D8D5,0x80C7A80A,0xF1E43D1C, +0x809DC971,0xF3742CA2,0x8078D40D,0xF50497FB,0x8058C94C,0xF6956FB7,0x803DAA6A, +0xF826A462,0x80277872,0xF9B82684,0x80163440,0xFB49E6A3,0x8009DE7E,0xFCDBD541, +0x800277A6,0xFE6DE2E0,0x80000000,0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_1024_q31[ARM_NEON_RFFT_TWIDDLES_1024_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,0x7FFFFFFF, +0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91, +0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414, +0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590, +0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC, +0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376, +0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65, +0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3, +0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C, +0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x00000000,0x80000000,0xF3742CA2, +0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3,0x89BE50C3, +0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54,0xA57D8666, +0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A,0xC3A94590, +0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4,0x809DC971, +0xF3742CA2,0x7FFFFFFF,0x00000000,0x7E9D55FC,0xED37EF91,0x7A7D055B,0xDAD7F3A2, +0x73B5EBD1,0xC945DFEC,0x6A6D98A4,0xB8E31319,0x5ED77C8A,0xAA0A5B2E,0x5133CC94, +0x9D0DFE54,0x41CE1E65,0x9235F2EC,0x30FBC54D,0x89BE50C3,0x1F19F97B,0x83D60412, +0x0C8BD35E,0x809DC971,0xF9B82684,0x80277872,0xE70747C4,0x8275A0C0,0xD4E0CB15, +0x877B7BEC,0xC3A94590,0x8F1D343A,0xB3C0200C,0x99307EE0,0xA57D8666,0xA57D8666, +0x99307EE0,0xB3C0200C,0x8F1D343A,0xC3A94590,0x877B7BEC,0xD4E0CB15,0x8275A0C0, +0xE70747C4,0x80277872,0xF9B82684,0x809DC971,0x0C8BD35E,0x83D60412,0x1F19F97B, +0x89BE50C3,0x30FBC54D,0x9235F2EC,0x41CE1E65,0x9D0DFE54,0x5133CC94,0xAA0A5B2E, +0x5ED77C8A,0xB8E31319,0x6A6D98A4,0xC945DFEC,0x73B5EBD1,0xDAD7F3A2,0x7A7D055B, +0xED37EF91,0x7E9D55FC,0x7FFFFFFF,0x00000000,0x7FFD885A,0xFE6DE2E0,0x7FF62182, +0xFCDBD541,0x7FE9CBC0,0xFB49E6A3,0x7FD8878E,0xF9B82684,0x7FC25596,0xF826A462, +0x7FA736B4,0xF6956FB7,0x7F872BF3,0xF50497FB,0x7F62368F,0xF3742CA2,0x7F3857F6, +0xF1E43D1C,0x7F0991C4,0xF054D8D5,0x7ED5E5C6,0xEEC60F31,0x7E9D55FC,0xED37EF91, +0x7E5FE493,0xEBAA894F,0x7E1D93EA,0xEA1DEBBB,0x7DD6668F,0xE8922622,0x7D8A5F40, +0xE70747C4,0x7D3980EC,0xE57D5FDA,0x7CE3CEB2,0xE3F47D96,0x7C894BDE,0xE26CB01B, +0x7C29FBEE,0xE0E60685,0x7BC5E290,0xDF608FE4,0x7B5D039E,0xDDDC5B3B,0x7AEF6323, +0xDC597781,0x7A7D055B,0xDAD7F3A2,0x7A05EEAD,0xD957DE7A,0x798A23B1,0xD7D946D8, +0x7909A92D,0xD65C3B7B,0x78848414,0xD4E0CB15,0x77FAB989,0xD3670446,0x776C4EDB, +0xD1EEF59E,0x76D94989,0xD078AD9E,0x7641AF3D,0xCF043AB3,0x75A585CF,0xCD91AB39, +0x7504D345,0xCC210D79,0x745F9DD1,0xCAB26FA9,0x73B5EBD1,0xC945DFEC,0x7307C3D0, +0xC7DB6C50,0x72552C85,0xC67322CE,0x719E2CD2,0xC50D1149,0x70E2CBC6,0xC3A94590, +0x7023109A,0xC247CD5A,0x6F5F02B2,0xC0E8B648,0x6E96A99D,0xBF8C0DE3,0x6DCA0D14, +0xBE31E19B,0x6CF934FC,0xBCDA3ECB,0x6C242960,0xBB8532B0,0x6B4AF279,0xBA32CA71, +0x6A6D98A4,0xB8E31319,0x698C246C,0xB796199B,0x68A69E81,0xB64BEACD,0x67BD0FBD, +0xB5049368,0x66CF8120,0xB3C0200C,0x65DDFBD3,0xB27E9D3C,0x64E88926,0xB140175B, +0x63EF3290,0xB0049AB3,0x62F201AC,0xAECC336C,0x61F1003F,0xAD96ED92,0x60EC3830, +0xAC64D510,0x5FE3B38D,0xAB35F5B5,0x5ED77C8A,0xAA0A5B2E,0x5DC79D7C,0xA8E21106, +0x5CB420E0,0xA7BD22AC,0x5B9D1154,0xA69B9B68,0x5A82799A,0xA57D8666,0x59646498, +0xA462EEAC,0x5842DD54,0xA34BDF20,0x571DEEFA,0xA2386284,0x55F5A4D2,0xA1288376, +0x54CA0A4B,0xA01C4C73,0x539B2AF0,0x9F13C7D0,0x5269126E,0x9E0EFFC1,0x5133CC94, +0x9D0DFE54,0x4FFB654D,0x9C10CD70,0x4EBFE8A5,0x9B1776DA,0x4D8162C4,0x9A22042D, +0x4C3FDFF4,0x99307EE0,0x4AFB6C98,0x9842F043,0x49B41533,0x9759617F,0x4869E665, +0x9673DB94,0x471CECE7,0x9592675C,0x45CD358F,0x94B50D87,0x447ACD50,0x93DBD6A0, +0x4325C135,0x9306CB04,0x41CE1E65,0x9235F2EC,0x4073F21D,0x91695663,0x3F1749B8, +0x90A0FD4E,0x3DB832A6,0x8FDCEF66,0x3C56BA70,0x8F1D343A,0x3AF2EEB7,0x8E61D32E, +0x398CDD32,0x8DAAD37B,0x382493B0,0x8CF83C30,0x36BA2014,0x8C4A142F,0x354D9057, +0x8BA0622F,0x33DEF287,0x8AFB2CBB,0x326E54C7,0x8A5A7A31,0x30FBC54D,0x89BE50C3, +0x2F875262,0x8926B677,0x2E110A62,0x8893B125,0x2C98FBBA,0x88054677,0x2B1F34EB, +0x877B7BEC,0x29A3C485,0x86F656D3,0x2826B928,0x8675DC4F,0x26A82186,0x85FA1153, +0x25280C5E,0x8582FAA5,0x23A6887F,0x85109CDD,0x2223A4C5,0x84A2FC62,0x209F701C, +0x843A1D70,0x1F19F97B,0x83D60412,0x1D934FE5,0x8376B422,0x1C0B826A,0x831C314E, +0x1A82A026,0x82C67F14,0x18F8B83C,0x8275A0C0,0x176DD9DE,0x82299971,0x15E21445, +0x81E26C16,0x145576B1,0x81A01B6D,0x12C8106F,0x8162AA04,0x1139F0CF,0x812A1A3A, +0x0FAB272B,0x80F66E3C,0x0E1BC2E4,0x80C7A80A,0x0C8BD35E,0x809DC971,0x0AFB6805, +0x8078D40D,0x096A9049,0x8058C94C,0x07D95B9E,0x803DAA6A,0x0647D97C,0x80277872, +0x04B6195D,0x80163440,0x03242ABF,0x8009DE7E,0x01921D20,0x800277A6,0x7FFFFFFF, +0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684,0x7FA736B4,0xF6956FB7, +0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC,0xED37EF91,0x7E1D93EA, +0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96,0x7C29FBEE,0xE0E60685, +0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1,0xD7D946D8,0x78848414, +0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3,0x7504D345,0xCC210D79, +0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6,0xC3A94590,0x6F5F02B2, +0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0,0x6A6D98A4,0xB8E31319, +0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926,0xB140175B,0x62F201AC, +0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E,0x5CB420E0,0xA7BD22AC, +0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2,0xA1288376,0x539B2AF0, +0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA,0x4C3FDFF4,0x99307EE0, +0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50,0x93DBD6A0,0x41CE1E65, +0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A,0x398CDD32,0x8DAAD37B, +0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D,0x89BE50C3,0x2E110A62, +0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F,0x25280C5E,0x8582FAA5, +0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A,0x831C314E,0x18F8B83C, +0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04,0x0FAB272B,0x80F66E3C, +0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C,0x80277872,0x03242ABF, +0x8009DE7E,0x00000000,0x80000000,0xFCDBD541,0x8009DE7E,0xF9B82684,0x80277872, +0xF6956FB7,0x8058C94C,0xF3742CA2,0x809DC971,0xF054D8D5,0x80F66E3C,0xED37EF91, +0x8162AA04,0xEA1DEBBB,0x81E26C16,0xE70747C4,0x8275A0C0,0xE3F47D96,0x831C314E, +0xE0E60685,0x83D60412,0xDDDC5B3B,0x84A2FC62,0xDAD7F3A2,0x8582FAA5,0xD7D946D8, +0x8675DC4F,0xD4E0CB15,0x877B7BEC,0xD1EEF59E,0x8893B125,0xCF043AB3,0x89BE50C3, +0xCC210D79,0x8AFB2CBB,0xC945DFEC,0x8C4A142F,0xC67322CE,0x8DAAD37B,0xC3A94590, +0x8F1D343A,0xC0E8B648,0x90A0FD4E,0xBE31E19B,0x9235F2EC,0xBB8532B0,0x93DBD6A0, +0xB8E31319,0x9592675C,0xB64BEACD,0x9759617F,0xB3C0200C,0x99307EE0,0xB140175B, +0x9B1776DA,0xAECC336C,0x9D0DFE54,0xAC64D510,0x9F13C7D0,0xAA0A5B2E,0xA1288376, +0xA7BD22AC,0xA34BDF20,0xA57D8666,0xA57D8666,0xA34BDF20,0xA7BD22AC,0xA1288376, +0xAA0A5B2E,0x9F13C7D0,0xAC64D510,0x9D0DFE54,0xAECC336C,0x9B1776DA,0xB140175B, +0x99307EE0,0xB3C0200C,0x9759617F,0xB64BEACD,0x9592675C,0xB8E31319,0x93DBD6A0, +0xBB8532B0,0x9235F2EC,0xBE31E19B,0x90A0FD4E,0xC0E8B648,0x8F1D343A,0xC3A94590, +0x8DAAD37B,0xC67322CE,0x8C4A142F,0xC945DFEC,0x8AFB2CBB,0xCC210D79,0x89BE50C3, +0xCF043AB3,0x8893B125,0xD1EEF59E,0x877B7BEC,0xD4E0CB15,0x8675DC4F,0xD7D946D8, +0x8582FAA5,0xDAD7F3A2,0x84A2FC62,0xDDDC5B3B,0x83D60412,0xE0E60685,0x831C314E, +0xE3F47D96,0x8275A0C0,0xE70747C4,0x81E26C16,0xEA1DEBBB,0x8162AA04,0xED37EF91, +0x80F66E3C,0xF054D8D5,0x809DC971,0xF3742CA2,0x8058C94C,0xF6956FB7,0x80277872, +0xF9B82684,0x8009DE7E,0xFCDBD541,0x7FFFFFFF,0x00000000,0x7FE9CBC0,0xFB49E6A3, +0x7FA736B4,0xF6956FB7,0x7F3857F6,0xF1E43D1C,0x7E9D55FC,0xED37EF91,0x7DD6668F, +0xE8922622,0x7CE3CEB2,0xE3F47D96,0x7BC5E290,0xDF608FE4,0x7A7D055B,0xDAD7F3A2, +0x7909A92D,0xD65C3B7B,0x776C4EDB,0xD1EEF59E,0x75A585CF,0xCD91AB39,0x73B5EBD1, +0xC945DFEC,0x719E2CD2,0xC50D1149,0x6F5F02B2,0xC0E8B648,0x6CF934FC,0xBCDA3ECB, +0x6A6D98A4,0xB8E31319,0x67BD0FBD,0xB5049368,0x64E88926,0xB140175B,0x61F1003F, +0xAD96ED92,0x5ED77C8A,0xAA0A5B2E,0x5B9D1154,0xA69B9B68,0x5842DD54,0xA34BDF20, +0x54CA0A4B,0xA01C4C73,0x5133CC94,0x9D0DFE54,0x4D8162C4,0x9A22042D,0x49B41533, +0x9759617F,0x45CD358F,0x94B50D87,0x41CE1E65,0x9235F2EC,0x3DB832A6,0x8FDCEF66, +0x398CDD32,0x8DAAD37B,0x354D9057,0x8BA0622F,0x30FBC54D,0x89BE50C3,0x2C98FBBA, +0x88054677,0x2826B928,0x8675DC4F,0x23A6887F,0x85109CDD,0x1F19F97B,0x83D60412, +0x1A82A026,0x82C67F14,0x15E21445,0x81E26C16,0x1139F0CF,0x812A1A3A,0x0C8BD35E, +0x809DC971,0x07D95B9E,0x803DAA6A,0x03242ABF,0x8009DE7E,0xFE6DE2E0,0x800277A6, +0xF9B82684,0x80277872,0xF50497FB,0x8078D40D,0xF054D8D5,0x80F66E3C,0xEBAA894F, +0x81A01B6D,0xE70747C4,0x8275A0C0,0xE26CB01B,0x8376B422,0xDDDC5B3B,0x84A2FC62, +0xD957DE7A,0x85FA1153,0xD4E0CB15,0x877B7BEC,0xD078AD9E,0x8926B677,0xCC210D79, +0x8AFB2CBB,0xC7DB6C50,0x8CF83C30,0xC3A94590,0x8F1D343A,0xBF8C0DE3,0x91695663, +0xBB8532B0,0x93DBD6A0,0xB796199B,0x9673DB94,0xB3C0200C,0x99307EE0,0xB0049AB3, +0x9C10CD70,0xAC64D510,0x9F13C7D0,0xA8E21106,0xA2386284,0xA57D8666,0xA57D8666, +0xA2386284,0xA8E21106,0x9F13C7D0,0xAC64D510,0x9C10CD70,0xB0049AB3,0x99307EE0, +0xB3C0200C,0x9673DB94,0xB796199B,0x93DBD6A0,0xBB8532B0,0x91695663,0xBF8C0DE3, +0x8F1D343A,0xC3A94590,0x8CF83C30,0xC7DB6C50,0x8AFB2CBB,0xCC210D79,0x8926B677, +0xD078AD9E,0x877B7BEC,0xD4E0CB15,0x85FA1153,0xD957DE7A,0x84A2FC62,0xDDDC5B3B, +0x8376B422,0xE26CB01B,0x8275A0C0,0xE70747C4,0x81A01B6D,0xEBAA894F,0x80F66E3C, +0xF054D8D5,0x8078D40D,0xF50497FB,0x80277872,0xF9B82684,0x800277A6,0xFE6DE2E0, +0x8009DE7E,0x03242ABF,0x803DAA6A,0x07D95B9E,0x809DC971,0x0C8BD35E,0x812A1A3A, +0x1139F0CF,0x81E26C16,0x15E21445,0x82C67F14,0x1A82A026,0x83D60412,0x1F19F97B, +0x85109CDD,0x23A6887F,0x8675DC4F,0x2826B928,0x88054677,0x2C98FBBA,0x89BE50C3, +0x30FBC54D,0x8BA0622F,0x354D9057,0x8DAAD37B,0x398CDD32,0x8FDCEF66,0x3DB832A6, +0x9235F2EC,0x41CE1E65,0x94B50D87,0x45CD358F,0x9759617F,0x49B41533,0x9A22042D, +0x4D8162C4,0x9D0DFE54,0x5133CC94,0xA01C4C73,0x54CA0A4B,0xA34BDF20,0x5842DD54, +0xA69B9B68,0x5B9D1154,0xAA0A5B2E,0x5ED77C8A,0xAD96ED92,0x61F1003F,0xB140175B, +0x64E88926,0xB5049368,0x67BD0FBD,0xB8E31319,0x6A6D98A4,0xBCDA3ECB,0x6CF934FC, +0xC0E8B648,0x6F5F02B2,0xC50D1149,0x719E2CD2,0xC945DFEC,0x73B5EBD1,0xCD91AB39, +0x75A585CF,0xD1EEF59E,0x776C4EDB,0xD65C3B7B,0x7909A92D,0xDAD7F3A2,0x7A7D055B, +0xDF608FE4,0x7BC5E290,0xE3F47D96,0x7CE3CEB2,0xE8922622,0x7DD6668F,0xED37EF91, +0x7E9D55FC,0xF1E43D1C,0x7F3857F6,0xF6956FB7,0x7FA736B4,0xFB49E6A3,0x7FE9CBC0,}; + +const uint32_t arm_neon_rfft_factors_1024_q31[ARM_NEON_RFFT_FACTORS_1024_Q31_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_1024_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_Q31_LEN]={ +0xFF36F078,0x80009DEA,0xFE6DE2E0,0x800277A6,0xFDA4D929,0x80058D2F,0xFCDBD541, +0x8009DE7E,0xFC12D91A,0x800F6B88,0xFB49E6A3,0x80163440,0xFA80FFCB,0x801E3895, +0xF9B82684,0x80277872,0xF8EF5CBB,0x8031F3C2,0xF826A462,0x803DAA6A,0xF75DFF66, +0x804A9C4D,0xF6956FB7,0x8058C94C,0xF5CCF743,0x80683143,0xF50497FB,0x8078D40D, +0xF43C53CB,0x808AB180,0xF3742CA2,0x809DC971,0xF2AC246E,0x80B21BAF,0xF1E43D1C, +0x80C7A80A,0xF11C789A,0x80DE6E4C,0xF054D8D5,0x80F66E3C,0xEF8D5FB8,0x810FA7A0, +0xEEC60F31,0x812A1A3A,0xEDFEE92B,0x8145C5C7,0xED37EF91,0x8162AA04,0xEC71244F, +0x8180C6A9,0xEBAA894F,0x81A01B6D,0xEAE4207A,0x81C0A801,0xEA1DEBBB,0x81E26C16, +0xE957ECFB,0x82056758,0xE8922622,0x82299971,0xE7CC9917,0x824F0208,0xE70747C4, +0x8275A0C0,0xE642340D,0x829D753A,0xE57D5FDA,0x82C67F14,0xE4B8CD11,0x82F0BDE8, +0xE3F47D96,0x831C314E,0xE330734D,0x8348D8DC,0xE26CB01B,0x8376B422,0xE1A935E2, +0x83A5C2B0,0xE0E60685,0x83D60412,0xE02323E5,0x840777D0,0xDF608FE4,0x843A1D70, +0xDE9E4C60,0x846DF477,0xDDDC5B3B,0x84A2FC62,0xDD1ABE51,0x84D934B1,0xDC597781, +0x85109CDD,0xDB9888A8,0x8549345C,0xDAD7F3A2,0x8582FAA5,0xDA17BA4A,0x85BDEF28, +0xD957DE7A,0x85FA1153,0xD898620C,0x86376092,0xD7D946D8,0x8675DC4F,0xD71A8EB5, +0x86B583EE,0xD65C3B7B,0x86F656D3,0xD59E4EFF,0x8738545E,0xD4E0CB15,0x877B7BEC, +0xD423B191,0x87BFCCD7,0xD3670446,0x88054677,0xD2AAC504,0x884BE821,0xD1EEF59E, +0x8893B125,0xD13397E2,0x88DCA0D3,0xD078AD9E,0x8926B677,0xCFBE389F,0x8971F15A, +0xCF043AB3,0x89BE50C3,0xCE4AB5A2,0x8A0BD3F5,0xCD91AB39,0x8A5A7A31,0xCCD91D3D, +0x8AAA42B4,0xCC210D79,0x8AFB2CBB,0xCB697DB0,0x8B4D377C,0xCAB26FA9,0x8BA0622F, +0xC9FBE527,0x8BF4AC05,0xC945DFEC,0x8C4A142F,0xC89061BA,0x8CA099DA,0xC7DB6C50, +0x8CF83C30,0xC727016D,0x8D50FA59,0xC67322CE,0x8DAAD37B,0xC5BFD22E,0x8E05C6B7, +0xC50D1149,0x8E61D32E,0xC45AE1D7,0x8EBEF7FB,0xC3A94590,0x8F1D343A,0xC2F83E2A, +0x8F7C8701,0xC247CD5A,0x8FDCEF66,0xC197F4D4,0x903E6C7B,0xC0E8B648,0x90A0FD4E, +0xC03A1368,0x9104A0EE,0xBF8C0DE3,0x91695663,0xBEDEA765,0x91CF1CB6,0xBE31E19B, +0x9235F2EC,0xBD85BE30,0x929DD806,0xBCDA3ECB,0x9306CB04,0xBC2F6513,0x9370CAE4, +0xBB8532B0,0x93DBD6A0,0xBADBA943,0x9447ED2F,0xBA32CA71,0x94B50D87,0xB98A97D8, +0x9523369C,0xB8E31319,0x9592675C,0xB83C3DD1,0x96029EB6,0xB796199B,0x9673DB94, +0xB6F0A812,0x96E61CE0,0xB64BEACD,0x9759617F,0xB5A7E362,0x97CDA855,0xB5049368, +0x9842F043,0xB461FC70,0x98B93828,0xB3C0200C,0x99307EE0,0xB31EFFCC,0x99A8C345, +0xB27E9D3C,0x9A22042D,0xB1DEF9E9,0x9A9C406E,0xB140175B,0x9B1776DA,0xB0A1F71D, +0x9B93A641,0xB0049AB3,0x9C10CD70,0xAF6803A2,0x9C8EEB34,0xAECC336C,0x9D0DFE54, +0xAE312B92,0x9D8E0597,0xAD96ED92,0x9E0EFFC1,0xACFD7AE8,0x9E90EB94,0xAC64D510, +0x9F13C7D0,0xABCCFD83,0x9F979331,0xAB35F5B5,0xA01C4C73,0xAA9FBF1E,0xA0A1F24D, +0xAA0A5B2E,0xA1288376,0xA975CB57,0xA1AFFEA3,0xA8E21106,0xA2386284,0xA84F2DAA, +0xA2C1ADC9,0xA7BD22AC,0xA34BDF20,0xA72BF174,0xA3D6F534,0xA69B9B68,0xA462EEAC, +0xA60C21EE,0xA4EFCA31,0xA57D8666,0xA57D8666,0xA4EFCA31,0xA60C21EE,0xA462EEAC, +0xA69B9B68,0xA3D6F534,0xA72BF174,0xA34BDF20,0xA7BD22AC,0xA2C1ADC9,0xA84F2DAA, +0xA2386284,0xA8E21106,0xA1AFFEA3,0xA975CB57,0xA1288376,0xAA0A5B2E,0xA0A1F24D, +0xAA9FBF1E,0xA01C4C73,0xAB35F5B5,0x9F979331,0xABCCFD83,0x9F13C7D0,0xAC64D510, +0x9E90EB94,0xACFD7AE8,0x9E0EFFC1,0xAD96ED92,0x9D8E0597,0xAE312B92,0x9D0DFE54, +0xAECC336C,0x9C8EEB34,0xAF6803A2,0x9C10CD70,0xB0049AB3,0x9B93A641,0xB0A1F71D, +0x9B1776DA,0xB140175B,0x9A9C406E,0xB1DEF9E9,0x9A22042D,0xB27E9D3C,0x99A8C345, +0xB31EFFCC,0x99307EE0,0xB3C0200C,0x98B93828,0xB461FC70,0x9842F043,0xB5049368, +0x97CDA855,0xB5A7E362,0x9759617F,0xB64BEACD,0x96E61CE0,0xB6F0A812,0x9673DB94, +0xB796199B,0x96029EB6,0xB83C3DD1,0x9592675C,0xB8E31319,0x9523369C,0xB98A97D8, +0x94B50D87,0xBA32CA71,0x9447ED2F,0xBADBA943,0x93DBD6A0,0xBB8532B0,0x9370CAE4, +0xBC2F6513,0x9306CB04,0xBCDA3ECB,0x929DD806,0xBD85BE30,0x9235F2EC,0xBE31E19B, +0x91CF1CB6,0xBEDEA765,0x91695663,0xBF8C0DE3,0x9104A0EE,0xC03A1368,0x90A0FD4E, +0xC0E8B648,0x903E6C7B,0xC197F4D4,0x8FDCEF66,0xC247CD5A,0x8F7C8701,0xC2F83E2A, +0x8F1D343A,0xC3A94590,0x8EBEF7FB,0xC45AE1D7,0x8E61D32E,0xC50D1149,0x8E05C6B7, +0xC5BFD22E,0x8DAAD37B,0xC67322CE,0x8D50FA59,0xC727016D,0x8CF83C30,0xC7DB6C50, +0x8CA099DA,0xC89061BA,0x8C4A142F,0xC945DFEC,0x8BF4AC05,0xC9FBE527,0x8BA0622F, +0xCAB26FA9,0x8B4D377C,0xCB697DB0,0x8AFB2CBB,0xCC210D79,0x8AAA42B4,0xCCD91D3D, +0x8A5A7A31,0xCD91AB39,0x8A0BD3F5,0xCE4AB5A2,0x89BE50C3,0xCF043AB3,0x8971F15A, +0xCFBE389F,0x8926B677,0xD078AD9E,0x88DCA0D3,0xD13397E2,0x8893B125,0xD1EEF59E, +0x884BE821,0xD2AAC504,0x88054677,0xD3670446,0x87BFCCD7,0xD423B191,0x877B7BEC, +0xD4E0CB15,0x8738545E,0xD59E4EFF,0x86F656D3,0xD65C3B7B,0x86B583EE,0xD71A8EB5, +0x8675DC4F,0xD7D946D8,0x86376092,0xD898620C,0x85FA1153,0xD957DE7A,0x85BDEF28, +0xDA17BA4A,0x8582FAA5,0xDAD7F3A2,0x8549345C,0xDB9888A8,0x85109CDD,0xDC597781, +0x84D934B1,0xDD1ABE51,0x84A2FC62,0xDDDC5B3B,0x846DF477,0xDE9E4C60,0x843A1D70, +0xDF608FE4,0x840777D0,0xE02323E5,0x83D60412,0xE0E60685,0x83A5C2B0,0xE1A935E2, +0x8376B422,0xE26CB01B,0x8348D8DC,0xE330734D,0x831C314E,0xE3F47D96,0x82F0BDE8, +0xE4B8CD11,0x82C67F14,0xE57D5FDA,0x829D753A,0xE642340D,0x8275A0C0,0xE70747C4, +0x824F0208,0xE7CC9917,0x82299971,0xE8922622,0x82056758,0xE957ECFB,0x81E26C16, +0xEA1DEBBB,0x81C0A801,0xEAE4207A,0x81A01B6D,0xEBAA894F,0x8180C6A9,0xEC71244F, +0x8162AA04,0xED37EF91,0x8145C5C7,0xEDFEE92B,0x812A1A3A,0xEEC60F31,0x810FA7A0, +0xEF8D5FB8,0x80F66E3C,0xF054D8D5,0x80DE6E4C,0xF11C789A,0x80C7A80A,0xF1E43D1C, +0x80B21BAF,0xF2AC246E,0x809DC971,0xF3742CA2,0x808AB180,0xF43C53CB,0x8078D40D, +0xF50497FB,0x80683143,0xF5CCF743,0x8058C94C,0xF6956FB7,0x804A9C4D,0xF75DFF66, +0x803DAA6A,0xF826A462,0x8031F3C2,0xF8EF5CBB,0x80277872,0xF9B82684,0x801E3895, +0xFA80FFCB,0x80163440,0xFB49E6A3,0x800F6B88,0xFC12D91A,0x8009DE7E,0xFCDBD541, +0x80058D2F,0xFDA4D929,0x800277A6,0xFE6DE2E0,0x80009DEA,0xFF36F078,0x80000000, +0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_2048_q31[ARM_NEON_RFFT_TWIDDLES_2048_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684, +0x7FA736B4,0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC, +0xED37EF91,0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96, +0x7C29FBEE,0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1, +0xD7D946D8,0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3, +0x7504D345,0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6, +0xC3A94590,0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0, +0x6A6D98A4,0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926, +0xB140175B,0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E, +0x5CB420E0,0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2, +0xA1288376,0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA, +0x4C3FDFF4,0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50, +0x93DBD6A0,0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A, +0x398CDD32,0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D, +0x89BE50C3,0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F, +0x25280C5E,0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A, +0x831C314E,0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04, +0x0FAB272B,0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C, +0x80277872,0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684, +0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE, +0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3, +0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4, +0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E, +0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4, +0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A, +0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E, +0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04, +0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872,0x00000000,0x80000000,0xF9B82684, +0x80277872,0xF3742CA2,0x809DC971,0xED37EF91,0x8162AA04,0xE70747C4,0x8275A0C0, +0xE0E60685,0x83D60412,0xDAD7F3A2,0x8582FAA5,0xD4E0CB15,0x877B7BEC,0xCF043AB3, +0x89BE50C3,0xC945DFEC,0x8C4A142F,0xC3A94590,0x8F1D343A,0xBE31E19B,0x9235F2EC, +0xB8E31319,0x9592675C,0xB3C0200C,0x99307EE0,0xAECC336C,0x9D0DFE54,0xAA0A5B2E, +0xA1288376,0xA57D8666,0xA57D8666,0xA1288376,0xAA0A5B2E,0x9D0DFE54,0xAECC336C, +0x99307EE0,0xB3C0200C,0x9592675C,0xB8E31319,0x9235F2EC,0xBE31E19B,0x8F1D343A, +0xC3A94590,0x8C4A142F,0xC945DFEC,0x89BE50C3,0xCF043AB3,0x877B7BEC,0xD4E0CB15, +0x8582FAA5,0xDAD7F3A2,0x83D60412,0xE0E60685,0x8275A0C0,0xE70747C4,0x8162AA04, +0xED37EF91,0x809DC971,0xF3742CA2,0x80277872,0xF9B82684,0x7FFFFFFF,0x00000000, +0x7FA736B4,0xF6956FB7,0x7E9D55FC,0xED37EF91,0x7CE3CEB2,0xE3F47D96,0x7A7D055B, +0xDAD7F3A2,0x776C4EDB,0xD1EEF59E,0x73B5EBD1,0xC945DFEC,0x6F5F02B2,0xC0E8B648, +0x6A6D98A4,0xB8E31319,0x64E88926,0xB140175B,0x5ED77C8A,0xAA0A5B2E,0x5842DD54, +0xA34BDF20,0x5133CC94,0x9D0DFE54,0x49B41533,0x9759617F,0x41CE1E65,0x9235F2EC, +0x398CDD32,0x8DAAD37B,0x30FBC54D,0x89BE50C3,0x2826B928,0x8675DC4F,0x1F19F97B, +0x83D60412,0x15E21445,0x81E26C16,0x0C8BD35E,0x809DC971,0x03242ABF,0x8009DE7E, +0xF9B82684,0x80277872,0xF054D8D5,0x80F66E3C,0xE70747C4,0x8275A0C0,0xDDDC5B3B, +0x84A2FC62,0xD4E0CB15,0x877B7BEC,0xCC210D79,0x8AFB2CBB,0xC3A94590,0x8F1D343A, +0xBB8532B0,0x93DBD6A0,0xB3C0200C,0x99307EE0,0xAC64D510,0x9F13C7D0,0xA57D8666, +0xA57D8666,0x9F13C7D0,0xAC64D510,0x99307EE0,0xB3C0200C,0x93DBD6A0,0xBB8532B0, +0x8F1D343A,0xC3A94590,0x8AFB2CBB,0xCC210D79,0x877B7BEC,0xD4E0CB15,0x84A2FC62, +0xDDDC5B3B,0x8275A0C0,0xE70747C4,0x80F66E3C,0xF054D8D5,0x80277872,0xF9B82684, +0x8009DE7E,0x03242ABF,0x809DC971,0x0C8BD35E,0x81E26C16,0x15E21445,0x83D60412, +0x1F19F97B,0x8675DC4F,0x2826B928,0x89BE50C3,0x30FBC54D,0x8DAAD37B,0x398CDD32, +0x9235F2EC,0x41CE1E65,0x9759617F,0x49B41533,0x9D0DFE54,0x5133CC94,0xA34BDF20, +0x5842DD54,0xAA0A5B2E,0x5ED77C8A,0xB140175B,0x64E88926,0xB8E31319,0x6A6D98A4, +0xC0E8B648,0x6F5F02B2,0xC945DFEC,0x73B5EBD1,0xD1EEF59E,0x776C4EDB,0xDAD7F3A2, +0x7A7D055B,0xE3F47D96,0x7CE3CEB2,0xED37EF91,0x7E9D55FC,0xF6956FB7,0x7FA736B4, +0x7FFFFFFF,0x00000000,0x7FFF6216,0xFF36F078,0x7FFD885A,0xFE6DE2E0,0x7FFA72D1, +0xFDA4D929,0x7FF62182,0xFCDBD541,0x7FF09478,0xFC12D91A,0x7FE9CBC0,0xFB49E6A3, +0x7FE1C76B,0xFA80FFCB,0x7FD8878E,0xF9B82684,0x7FCE0C3E,0xF8EF5CBB,0x7FC25596, +0xF826A462,0x7FB563B3,0xF75DFF66,0x7FA736B4,0xF6956FB7,0x7F97CEBD,0xF5CCF743, +0x7F872BF3,0xF50497FB,0x7F754E80,0xF43C53CB,0x7F62368F,0xF3742CA2,0x7F4DE451, +0xF2AC246E,0x7F3857F6,0xF1E43D1C,0x7F2191B4,0xF11C789A,0x7F0991C4,0xF054D8D5, +0x7EF05860,0xEF8D5FB8,0x7ED5E5C6,0xEEC60F31,0x7EBA3A39,0xEDFEE92B,0x7E9D55FC, +0xED37EF91,0x7E7F3957,0xEC71244F,0x7E5FE493,0xEBAA894F,0x7E3F57FF,0xEAE4207A, +0x7E1D93EA,0xEA1DEBBB,0x7DFA98A8,0xE957ECFB,0x7DD6668F,0xE8922622,0x7DB0FDF8, +0xE7CC9917,0x7D8A5F40,0xE70747C4,0x7D628AC6,0xE642340D,0x7D3980EC,0xE57D5FDA, +0x7D0F4218,0xE4B8CD11,0x7CE3CEB2,0xE3F47D96,0x7CB72724,0xE330734D,0x7C894BDE, +0xE26CB01B,0x7C5A3D50,0xE1A935E2,0x7C29FBEE,0xE0E60685,0x7BF88830,0xE02323E5, 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+0x67BD0FBD,0xB5049368,0x66573CBB,0xB31EFFCC,0x64E88926,0xB140175B,0x637114CC, +0xAF6803A2,0x61F1003F,0xAD96ED92,0x60686CCF,0xABCCFD83,0x5ED77C8A,0xAA0A5B2E, +0x5D3E5237,0xA84F2DAA,0x5B9D1154,0xA69B9B68,0x59F3DE12,0xA4EFCA31,0x5842DD54, +0xA34BDF20,0x568A34A9,0xA1AFFEA3,0x54CA0A4B,0xA01C4C73,0x53028518,0x9E90EB94, +0x5133CC94,0x9D0DFE54,0x4F5E08E3,0x9B93A641,0x4D8162C4,0x9A22042D,0x4B9E0390, +0x98B93828,0x49B41533,0x9759617F,0x47C3C22F,0x96029EB6,0x45CD358F,0x94B50D87, +0x43D09AED,0x9370CAE4,0x41CE1E65,0x9235F2EC,0x3FC5EC98,0x9104A0EE,0x3DB832A6, +0x8FDCEF66,0x3BA51E29,0x8EBEF7FB,0x398CDD32,0x8DAAD37B,0x376F9E46,0x8CA099DA, +0x354D9057,0x8BA0622F,0x3326E2C3,0x8AAA42B4,0x30FBC54D,0x89BE50C3,0x2ECC681E, +0x88DCA0D3,0x2C98FBBA,0x88054677,0x2A61B101,0x8738545E,0x2826B928,0x8675DC4F, +0x25E845B6,0x85BDEF28,0x23A6887F,0x85109CDD,0x2161B3A0,0x846DF477,0x1F19F97B, +0x83D60412,0x1CCF8CB3,0x8348D8DC,0x1A82A026,0x82C67F14,0x183366E9,0x824F0208, +0x15E21445,0x81E26C16,0x138EDBB1,0x8180C6A9,0x1139F0CF,0x812A1A3A,0x0EE38766, +0x80DE6E4C,0x0C8BD35E,0x809DC971,0x0A3308BD,0x80683143,0x07D95B9E,0x803DAA6A, +0x057F0035,0x801E3895,0x03242ABF,0x8009DE7E,0x00C90F88,0x80009DEA,0xFE6DE2E0, +0x800277A6,0xFC12D91A,0x800F6B88,0xF9B82684,0x80277872,0xF75DFF66,0x804A9C4D, +0xF50497FB,0x8078D40D,0xF2AC246E,0x80B21BAF,0xF054D8D5,0x80F66E3C,0xEDFEE92B, +0x8145C5C7,0xEBAA894F,0x81A01B6D,0xE957ECFB,0x82056758,0xE70747C4,0x8275A0C0, +0xE4B8CD11,0x82F0BDE8,0xE26CB01B,0x8376B422,0xE02323E5,0x840777D0,0xDDDC5B3B, +0x84A2FC62,0xDB9888A8,0x8549345C,0xD957DE7A,0x85FA1153,0xD71A8EB5,0x86B583EE, +0xD4E0CB15,0x877B7BEC,0xD2AAC504,0x884BE821,0xD078AD9E,0x8926B677,0xCE4AB5A2, +0x8A0BD3F5,0xCC210D79,0x8AFB2CBB,0xC9FBE527,0x8BF4AC05,0xC7DB6C50,0x8CF83C30, +0xC5BFD22E,0x8E05C6B7,0xC3A94590,0x8F1D343A,0xC197F4D4,0x903E6C7B,0xBF8C0DE3, +0x91695663,0xBD85BE30,0x929DD806,0xBB8532B0,0x93DBD6A0,0xB98A97D8,0x9523369C, +0xB796199B,0x9673DB94,0xB5A7E362,0x97CDA855,0xB3C0200C,0x99307EE0,0xB1DEF9E9, +0x9A9C406E,0xB0049AB3,0x9C10CD70,0xAE312B92,0x9D8E0597,0xAC64D510,0x9F13C7D0, +0xAA9FBF1E,0xA0A1F24D,0xA8E21106,0xA2386284,0xA72BF174,0xA3D6F534,0xA57D8666, +0xA57D8666,0xA3D6F534,0xA72BF174,0xA2386284,0xA8E21106,0xA0A1F24D,0xAA9FBF1E, +0x9F13C7D0,0xAC64D510,0x9D8E0597,0xAE312B92,0x9C10CD70,0xB0049AB3,0x9A9C406E, +0xB1DEF9E9,0x99307EE0,0xB3C0200C,0x97CDA855,0xB5A7E362,0x9673DB94,0xB796199B, +0x9523369C,0xB98A97D8,0x93DBD6A0,0xBB8532B0,0x929DD806,0xBD85BE30,0x91695663, +0xBF8C0DE3,0x903E6C7B,0xC197F4D4,0x8F1D343A,0xC3A94590,0x8E05C6B7,0xC5BFD22E, +0x8CF83C30,0xC7DB6C50,0x8BF4AC05,0xC9FBE527,0x8AFB2CBB,0xCC210D79,0x8A0BD3F5, +0xCE4AB5A2,0x8926B677,0xD078AD9E,0x884BE821,0xD2AAC504,0x877B7BEC,0xD4E0CB15, +0x86B583EE,0xD71A8EB5,0x85FA1153,0xD957DE7A,0x8549345C,0xDB9888A8,0x84A2FC62, +0xDDDC5B3B,0x840777D0,0xE02323E5,0x8376B422,0xE26CB01B,0x82F0BDE8,0xE4B8CD11, +0x8275A0C0,0xE70747C4,0x82056758,0xE957ECFB,0x81A01B6D,0xEBAA894F,0x8145C5C7, +0xEDFEE92B,0x80F66E3C,0xF054D8D5,0x80B21BAF,0xF2AC246E,0x8078D40D,0xF50497FB, +0x804A9C4D,0xF75DFF66,0x80277872,0xF9B82684,0x800F6B88,0xFC12D91A,0x800277A6, +0xFE6DE2E0,0x80009DEA,0x00C90F88,0x8009DE7E,0x03242ABF,0x801E3895,0x057F0035, +0x803DAA6A,0x07D95B9E,0x80683143,0x0A3308BD,0x809DC971,0x0C8BD35E,0x80DE6E4C, +0x0EE38766,0x812A1A3A,0x1139F0CF,0x8180C6A9,0x138EDBB1,0x81E26C16,0x15E21445, +0x824F0208,0x183366E9,0x82C67F14,0x1A82A026,0x8348D8DC,0x1CCF8CB3,0x83D60412, +0x1F19F97B,0x846DF477,0x2161B3A0,0x85109CDD,0x23A6887F,0x85BDEF28,0x25E845B6, +0x8675DC4F,0x2826B928,0x8738545E,0x2A61B101,0x88054677,0x2C98FBBA,0x88DCA0D3, +0x2ECC681E,0x89BE50C3,0x30FBC54D,0x8AAA42B4,0x3326E2C3,0x8BA0622F,0x354D9057, +0x8CA099DA,0x376F9E46,0x8DAAD37B,0x398CDD32,0x8EBEF7FB,0x3BA51E29,0x8FDCEF66, +0x3DB832A6,0x9104A0EE,0x3FC5EC98,0x9235F2EC,0x41CE1E65,0x9370CAE4,0x43D09AED, +0x94B50D87,0x45CD358F,0x96029EB6,0x47C3C22F,0x9759617F,0x49B41533,0x98B93828, +0x4B9E0390,0x9A22042D,0x4D8162C4,0x9B93A641,0x4F5E08E3,0x9D0DFE54,0x5133CC94, +0x9E90EB94,0x53028518,0xA01C4C73,0x54CA0A4B,0xA1AFFEA3,0x568A34A9,0xA34BDF20, +0x5842DD54,0xA4EFCA31,0x59F3DE12,0xA69B9B68,0x5B9D1154,0xA84F2DAA,0x5D3E5237, +0xAA0A5B2E,0x5ED77C8A,0xABCCFD83,0x60686CCF,0xAD96ED92,0x61F1003F,0xAF6803A2, +0x637114CC,0xB140175B,0x64E88926,0xB31EFFCC,0x66573CBB,0xB5049368,0x67BD0FBD, +0xB6F0A812,0x6919E320,0xB8E31319,0x6A6D98A4,0xBADBA943,0x6BB812D1,0xBCDA3ECB, +0x6CF934FC,0xBEDEA765,0x6E30E34A,0xC0E8B648,0x6F5F02B2,0xC2F83E2A,0x708378FF, +0xC50D1149,0x719E2CD2,0xC727016D,0x72AF05A7,0xC945DFEC,0x73B5EBD1,0xCB697DB0, +0x74B2C884,0xCD91AB39,0x75A585CF,0xCFBE389F,0x768E0EA6,0xD1EEF59E,0x776C4EDB, +0xD423B191,0x78403329,0xD65C3B7B,0x7909A92D,0xD898620C,0x79C89F6E,0xDAD7F3A2, +0x7A7D055B,0xDD1ABE51,0x7B26CB4F,0xDF608FE4,0x7BC5E290,0xE1A935E2,0x7C5A3D50, +0xE3F47D96,0x7CE3CEB2,0xE642340D,0x7D628AC6,0xE8922622,0x7DD6668F,0xEAE4207A, +0x7E3F57FF,0xED37EF91,0x7E9D55FC,0xEF8D5FB8,0x7EF05860,0xF1E43D1C,0x7F3857F6, +0xF43C53CB,0x7F754E80,0xF6956FB7,0x7FA736B4,0xF8EF5CBB,0x7FCE0C3E,0xFB49E6A3, +0x7FE9CBC0,0xFDA4D929,0x7FFA72D1,}; + +const uint32_t arm_neon_rfft_factors_2048_q31[ARM_NEON_RFFT_FACTORS_2048_Q31_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_2048_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_Q31_LEN]={ +0xFF9B781D,0x8000277A,0xFF36F078,0x80009DEA,0xFED2694F,0x8001634E,0xFE6DE2E0, +0x800277A6,0xFE095D69,0x8003DAF1,0xFDA4D929,0x80058D2F,0xFD40565C,0x80078E5E, +0xFCDBD541,0x8009DE7E,0xFC775616,0x800C7D8C,0xFC12D91A,0x800F6B88,0xFBAE5E89, +0x8012A86F,0xFB49E6A3,0x80163440,0xFAE571A4,0x801A0EF8,0xFA80FFCB,0x801E3895, +0xFA1C9157,0x8022B114,0xF9B82684,0x80277872,0xF953BF91,0x802C8EAD,0xF8EF5CBB, +0x8031F3C2,0xF88AFE42,0x8037A7AC,0xF826A462,0x803DAA6A,0xF7C24F59,0x8043FBF6, +0xF75DFF66,0x804A9C4D,0xF6F9B4C6,0x80518B6B,0xF6956FB7,0x8058C94C,0xF6313077, +0x806055EB,0xF5CCF743,0x80683143,0xF568C45B,0x80705B50,0xF50497FB,0x8078D40D, +0xF4A07261,0x80819B74,0xF43C53CB,0x808AB180,0xF3D83C77,0x8094162C,0xF3742CA2, +0x809DC971,0xF310248A,0x80A7CB49,0xF2AC246E,0x80B21BAF,0xF2482C8A,0x80BCBA9D, +0xF1E43D1C,0x80C7A80A,0xF1805662,0x80D2E3F2,0xF11C789A,0x80DE6E4C,0xF0B8A401, +0x80EA4712,0xF054D8D5,0x80F66E3C,0xEFF11753,0x8102E3C4,0xEF8D5FB8,0x810FA7A0, +0xEF29B243,0x811CB9CA,0xEEC60F31,0x812A1A3A,0xEE6276BF,0x8137C8E6,0xEDFEE92B, +0x8145C5C7,0xED9B66B2,0x815410D4,0xED37EF91,0x8162AA04,0xECD48407,0x8171914E, +0xEC71244F,0x8180C6A9,0xEC0DD0A8,0x81904A0C,0xEBAA894F,0x81A01B6D,0xEB474E81, +0x81B03AC2,0xEAE4207A,0x81C0A801,0xEA80FF7A,0x81D16321,0xEA1DEBBB,0x81E26C16, +0xE9BAE57D,0x81F3C2D7,0xE957ECFB,0x82056758,0xE8F50273,0x82175990,0xE8922622, +0x82299971,0xE82F5844,0x823C26F3,0xE7CC9917,0x824F0208,0xE769E8D8,0x82622AA6, +0xE70747C4,0x8275A0C0,0xE6A4B616,0x8289644B,0xE642340D,0x829D753A,0xE5DFC1E5, +0x82B1D381,0xE57D5FDA,0x82C67F14,0xE51B0E2A,0x82DB77E5,0xE4B8CD11,0x82F0BDE8, +0xE4569CCB,0x83065110,0xE3F47D96,0x831C314E,0xE3926FAD,0x83325E97,0xE330734D, +0x8348D8DC,0xE2CE88B3,0x835FA00F,0xE26CB01B,0x8376B422,0xE20AE9C1,0x838E1507, +0xE1A935E2,0x83A5C2B0,0xE14794BA,0x83BDBD0E,0xE0E60685,0x83D60412,0xE0848B7F, +0x83EE97AD,0xE02323E5,0x840777D0,0xDFC1CFF3,0x8420A46C,0xDF608FE4,0x843A1D70, +0xDEFF63F4,0x8453E2CF,0xDE9E4C60,0x846DF477,0xDE3D4964,0x84885258,0xDDDC5B3B, +0x84A2FC62,0xDD7B8220,0x84BDF286,0xDD1ABE51,0x84D934B1,0xDCBA1008,0x84F4C2D4, +0xDC597781,0x85109CDD,0xDBF8F4F8,0x852CC2BB,0xDB9888A8,0x8549345C,0xDB3832CD, +0x8565F1B0,0xDAD7F3A2,0x8582FAA5,0xDA77CB63,0x85A04F28,0xDA17BA4A,0x85BDEF28, +0xD9B7C094,0x85DBDA91,0xD957DE7A,0x85FA1153,0xD8F81439,0x86189359,0xD898620C, +0x86376092,0xD838C82D,0x865678EB,0xD7D946D8,0x8675DC4F,0xD779DE47,0x86958AAC, +0xD71A8EB5,0x86B583EE,0xD6BB585E,0x86D5C802,0xD65C3B7B,0x86F656D3,0xD5FD3848, +0x8717304E,0xD59E4EFF,0x8738545E,0xD53F7FDA,0x8759C2EF,0xD4E0CB15,0x877B7BEC, +0xD48230E9,0x879D7F41,0xD423B191,0x87BFCCD7,0xD3C54D47,0x87E2649B,0xD3670446, +0x88054677,0xD308D6C7,0x88287256,0xD2AAC504,0x884BE821,0xD24CCF39,0x886FA7C2, +0xD1EEF59E,0x8893B125,0xD191386E,0x88B80432,0xD13397E2,0x88DCA0D3,0xD0D61434, +0x890186F2,0xD078AD9E,0x8926B677,0xD01B6459,0x894C2F4C,0xCFBE389F,0x8971F15A, +0xCF612AAA,0x8997FC8A,0xCF043AB3,0x89BE50C3,0xCEA768F2,0x89E4EDEF,0xCE4AB5A2, +0x8A0BD3F5,0xCDEE20FC,0x8A3302BE,0xCD91AB39,0x8A5A7A31,0xCD355491,0x8A823A36, +0xCCD91D3D,0x8AAA42B4,0xCC7D0578,0x8AD29394,0xCC210D79,0x8AFB2CBB,0xCBC53579, +0x8B240E11,0xCB697DB0,0x8B4D377C,0xCB0DE658,0x8B76A8E4,0xCAB26FA9,0x8BA0622F, +0xCA5719DB,0x8BCA6343,0xC9FBE527,0x8BF4AC05,0xC9A0D1C5,0x8C1F3C5D,0xC945DFEC, +0x8C4A142F,0xC8EB0FD6,0x8C753362,0xC89061BA,0x8CA099DA,0xC835D5D0,0x8CCC477D, +0xC7DB6C50,0x8CF83C30,0xC7812572,0x8D2477D8,0xC727016D,0x8D50FA59,0xC6CD0079, +0x8D7DC399,0xC67322CE,0x8DAAD37B,0xC61968A2,0x8DD829E4,0xC5BFD22E,0x8E05C6B7, +0xC5665FA9,0x8E33A9DA,0xC50D1149,0x8E61D32E,0xC4B3E746,0x8E904298,0xC45AE1D7, +0x8EBEF7FB,0xC4020133,0x8EEDF33B,0xC3A94590,0x8F1D343A,0xC350AF26,0x8F4CBADB, +0xC2F83E2A,0x8F7C8701,0xC29FF2D4,0x8FAC988F,0xC247CD5A,0x8FDCEF66,0xC1EFCDF3, +0x900D8B69,0xC197F4D4,0x903E6C7B,0xC1404233,0x906F927C,0xC0E8B648,0x90A0FD4E, +0xC0915148,0x90D2ACD4,0xC03A1368,0x9104A0EE,0xBFE2FCDF,0x9136D97D,0xBF8C0DE3, +0x91695663,0xBF3546A8,0x919C1781,0xBEDEA765,0x91CF1CB6,0xBE88304F,0x920265E4, +0xBE31E19B,0x9235F2EC,0xBDDBBB7F,0x9269C3AC,0xBD85BE30,0x929DD806,0xBD2FE9E2, +0x92D22FD9,0xBCDA3ECB,0x9306CB04,0xBC84BD1F,0x933BA968,0xBC2F6513,0x9370CAE4, +0xBBDA36DD,0x93A62F57,0xBB8532B0,0x93DBD6A0,0xBB3058C0,0x9411C09E,0xBADBA943, +0x9447ED2F,0xBA87246D,0x947E5C33,0xBA32CA71,0x94B50D87,0xB9DE9B83,0x94EC010B, +0xB98A97D8,0x9523369C,0xB936BFA4,0x955AAE17,0xB8E31319,0x9592675C,0xB88F926D, +0x95CA6247,0xB83C3DD1,0x96029EB6,0xB7E9157A,0x963B1C86,0xB796199B,0x9673DB94, +0xB7434A67,0x96ACDBBE,0xB6F0A812,0x96E61CE0,0xB69E32CD,0x971F9ED7,0xB64BEACD, +0x9759617F,0xB5F9D043,0x979364B5,0xB5A7E362,0x97CDA855,0xB556245E,0x98082C3B, +0xB5049368,0x9842F043,0xB4B330B3,0x987DF449,0xB461FC70,0x98B93828,0xB410F6D3, +0x98F4BBBC,0xB3C0200C,0x99307EE0,0xB36F784F,0x996C816F,0xB31EFFCC,0x99A8C345, +0xB2CEB6B5,0x99E5443B,0xB27E9D3C,0x9A22042D,0xB22EB392,0x9A5F02F5,0xB1DEF9E9, +0x9A9C406E,0xB18F7071,0x9AD9BC71,0xB140175B,0x9B1776DA,0xB0F0EEDA,0x9B556F81, +0xB0A1F71D,0x9B93A641,0xB0533055,0x9BD21AF3,0xB0049AB3,0x9C10CD70,0xAFB63667, +0x9C4FBD93,0xAF6803A2,0x9C8EEB34,0xAF1A0293,0x9CCE562C,0xAECC336C,0x9D0DFE54, +0xAE7E965B,0x9D4DE385,0xAE312B92,0x9D8E0597,0xADE3F33E,0x9DCE6463,0xAD96ED92, +0x9E0EFFC1,0xAD4A1ABA,0x9E4FD78A,0xACFD7AE8,0x9E90EB94,0xACB10E4B,0x9ED23BB9, +0xAC64D510,0x9F13C7D0,0xAC18CF69,0x9F558FB0,0xABCCFD83,0x9F979331,0xAB815F8D, +0x9FD9D22A,0xAB35F5B5,0xA01C4C73,0xAAEAC02C,0xA05F01E1,0xAA9FBF1E,0xA0A1F24D, +0xAA54F2BA,0xA0E51D8C,0xAA0A5B2E,0xA1288376,0xA9BFF8A8,0xA16C23E1,0xA975CB57, +0xA1AFFEA3,0xA92BD367,0xA1F41392,0xA8E21106,0xA2386284,0xA8988463,0xA27CEB4F, +0xA84F2DAA,0xA2C1ADC9,0xA8060D08,0xA306A9C8,0xA7BD22AC,0xA34BDF20,0xA7746EC0, +0xA3914DA8,0xA72BF174,0xA3D6F534,0xA6E3AAF2,0xA41CD599,0xA69B9B68,0xA462EEAC, +0xA653C303,0xA4A94043,0xA60C21EE,0xA4EFCA31,0xA5C4B855,0xA5368C4B,0xA57D8666, +0xA57D8666,0xA5368C4B,0xA5C4B855,0xA4EFCA31,0xA60C21EE,0xA4A94043,0xA653C303, +0xA462EEAC,0xA69B9B68,0xA41CD599,0xA6E3AAF2,0xA3D6F534,0xA72BF174,0xA3914DA8, +0xA7746EC0,0xA34BDF20,0xA7BD22AC,0xA306A9C8,0xA8060D08,0xA2C1ADC9,0xA84F2DAA, +0xA27CEB4F,0xA8988463,0xA2386284,0xA8E21106,0xA1F41392,0xA92BD367,0xA1AFFEA3, +0xA975CB57,0xA16C23E1,0xA9BFF8A8,0xA1288376,0xAA0A5B2E,0xA0E51D8C,0xAA54F2BA, +0xA0A1F24D,0xAA9FBF1E,0xA05F01E1,0xAAEAC02C,0xA01C4C73,0xAB35F5B5,0x9FD9D22A, +0xAB815F8D,0x9F979331,0xABCCFD83,0x9F558FB0,0xAC18CF69,0x9F13C7D0,0xAC64D510, +0x9ED23BB9,0xACB10E4B,0x9E90EB94,0xACFD7AE8,0x9E4FD78A,0xAD4A1ABA,0x9E0EFFC1, +0xAD96ED92,0x9DCE6463,0xADE3F33E,0x9D8E0597,0xAE312B92,0x9D4DE385,0xAE7E965B, +0x9D0DFE54,0xAECC336C,0x9CCE562C,0xAF1A0293,0x9C8EEB34,0xAF6803A2,0x9C4FBD93, +0xAFB63667,0x9C10CD70,0xB0049AB3,0x9BD21AF3,0xB0533055,0x9B93A641,0xB0A1F71D, +0x9B556F81,0xB0F0EEDA,0x9B1776DA,0xB140175B,0x9AD9BC71,0xB18F7071,0x9A9C406E, +0xB1DEF9E9,0x9A5F02F5,0xB22EB392,0x9A22042D,0xB27E9D3C,0x99E5443B,0xB2CEB6B5, +0x99A8C345,0xB31EFFCC,0x996C816F,0xB36F784F,0x99307EE0,0xB3C0200C,0x98F4BBBC, +0xB410F6D3,0x98B93828,0xB461FC70,0x987DF449,0xB4B330B3,0x9842F043,0xB5049368, +0x98082C3B,0xB556245E,0x97CDA855,0xB5A7E362,0x979364B5,0xB5F9D043,0x9759617F, +0xB64BEACD,0x971F9ED7,0xB69E32CD,0x96E61CE0,0xB6F0A812,0x96ACDBBE,0xB7434A67, +0x9673DB94,0xB796199B,0x963B1C86,0xB7E9157A,0x96029EB6,0xB83C3DD1,0x95CA6247, +0xB88F926D,0x9592675C,0xB8E31319,0x955AAE17,0xB936BFA4,0x9523369C,0xB98A97D8, +0x94EC010B,0xB9DE9B83,0x94B50D87,0xBA32CA71,0x947E5C33,0xBA87246D,0x9447ED2F, +0xBADBA943,0x9411C09E,0xBB3058C0,0x93DBD6A0,0xBB8532B0,0x93A62F57,0xBBDA36DD, +0x9370CAE4,0xBC2F6513,0x933BA968,0xBC84BD1F,0x9306CB04,0xBCDA3ECB,0x92D22FD9, +0xBD2FE9E2,0x929DD806,0xBD85BE30,0x9269C3AC,0xBDDBBB7F,0x9235F2EC,0xBE31E19B, +0x920265E4,0xBE88304F,0x91CF1CB6,0xBEDEA765,0x919C1781,0xBF3546A8,0x91695663, +0xBF8C0DE3,0x9136D97D,0xBFE2FCDF,0x9104A0EE,0xC03A1368,0x90D2ACD4,0xC0915148, +0x90A0FD4E,0xC0E8B648,0x906F927C,0xC1404233,0x903E6C7B,0xC197F4D4,0x900D8B69, +0xC1EFCDF3,0x8FDCEF66,0xC247CD5A,0x8FAC988F,0xC29FF2D4,0x8F7C8701,0xC2F83E2A, +0x8F4CBADB,0xC350AF26,0x8F1D343A,0xC3A94590,0x8EEDF33B,0xC4020133,0x8EBEF7FB, +0xC45AE1D7,0x8E904298,0xC4B3E746,0x8E61D32E,0xC50D1149,0x8E33A9DA,0xC5665FA9, +0x8E05C6B7,0xC5BFD22E,0x8DD829E4,0xC61968A2,0x8DAAD37B,0xC67322CE,0x8D7DC399, +0xC6CD0079,0x8D50FA59,0xC727016D,0x8D2477D8,0xC7812572,0x8CF83C30,0xC7DB6C50, +0x8CCC477D,0xC835D5D0,0x8CA099DA,0xC89061BA,0x8C753362,0xC8EB0FD6,0x8C4A142F, +0xC945DFEC,0x8C1F3C5D,0xC9A0D1C5,0x8BF4AC05,0xC9FBE527,0x8BCA6343,0xCA5719DB, +0x8BA0622F,0xCAB26FA9,0x8B76A8E4,0xCB0DE658,0x8B4D377C,0xCB697DB0,0x8B240E11, +0xCBC53579,0x8AFB2CBB,0xCC210D79,0x8AD29394,0xCC7D0578,0x8AAA42B4,0xCCD91D3D, +0x8A823A36,0xCD355491,0x8A5A7A31,0xCD91AB39,0x8A3302BE,0xCDEE20FC,0x8A0BD3F5, +0xCE4AB5A2,0x89E4EDEF,0xCEA768F2,0x89BE50C3,0xCF043AB3,0x8997FC8A,0xCF612AAA, +0x8971F15A,0xCFBE389F,0x894C2F4C,0xD01B6459,0x8926B677,0xD078AD9E,0x890186F2, +0xD0D61434,0x88DCA0D3,0xD13397E2,0x88B80432,0xD191386E,0x8893B125,0xD1EEF59E, +0x886FA7C2,0xD24CCF39,0x884BE821,0xD2AAC504,0x88287256,0xD308D6C7,0x88054677, +0xD3670446,0x87E2649B,0xD3C54D47,0x87BFCCD7,0xD423B191,0x879D7F41,0xD48230E9, +0x877B7BEC,0xD4E0CB15,0x8759C2EF,0xD53F7FDA,0x8738545E,0xD59E4EFF,0x8717304E, +0xD5FD3848,0x86F656D3,0xD65C3B7B,0x86D5C802,0xD6BB585E,0x86B583EE,0xD71A8EB5, +0x86958AAC,0xD779DE47,0x8675DC4F,0xD7D946D8,0x865678EB,0xD838C82D,0x86376092, +0xD898620C,0x86189359,0xD8F81439,0x85FA1153,0xD957DE7A,0x85DBDA91,0xD9B7C094, +0x85BDEF28,0xDA17BA4A,0x85A04F28,0xDA77CB63,0x8582FAA5,0xDAD7F3A2,0x8565F1B0, +0xDB3832CD,0x8549345C,0xDB9888A8,0x852CC2BB,0xDBF8F4F8,0x85109CDD,0xDC597781, +0x84F4C2D4,0xDCBA1008,0x84D934B1,0xDD1ABE51,0x84BDF286,0xDD7B8220,0x84A2FC62, +0xDDDC5B3B,0x84885258,0xDE3D4964,0x846DF477,0xDE9E4C60,0x8453E2CF,0xDEFF63F4, +0x843A1D70,0xDF608FE4,0x8420A46C,0xDFC1CFF3,0x840777D0,0xE02323E5,0x83EE97AD, +0xE0848B7F,0x83D60412,0xE0E60685,0x83BDBD0E,0xE14794BA,0x83A5C2B0,0xE1A935E2, +0x838E1507,0xE20AE9C1,0x8376B422,0xE26CB01B,0x835FA00F,0xE2CE88B3,0x8348D8DC, +0xE330734D,0x83325E97,0xE3926FAD,0x831C314E,0xE3F47D96,0x83065110,0xE4569CCB, +0x82F0BDE8,0xE4B8CD11,0x82DB77E5,0xE51B0E2A,0x82C67F14,0xE57D5FDA,0x82B1D381, +0xE5DFC1E5,0x829D753A,0xE642340D,0x8289644B,0xE6A4B616,0x8275A0C0,0xE70747C4, +0x82622AA6,0xE769E8D8,0x824F0208,0xE7CC9917,0x823C26F3,0xE82F5844,0x82299971, +0xE8922622,0x82175990,0xE8F50273,0x82056758,0xE957ECFB,0x81F3C2D7,0xE9BAE57D, +0x81E26C16,0xEA1DEBBB,0x81D16321,0xEA80FF7A,0x81C0A801,0xEAE4207A,0x81B03AC2, +0xEB474E81,0x81A01B6D,0xEBAA894F,0x81904A0C,0xEC0DD0A8,0x8180C6A9,0xEC71244F, +0x8171914E,0xECD48407,0x8162AA04,0xED37EF91,0x815410D4,0xED9B66B2,0x8145C5C7, +0xEDFEE92B,0x8137C8E6,0xEE6276BF,0x812A1A3A,0xEEC60F31,0x811CB9CA,0xEF29B243, +0x810FA7A0,0xEF8D5FB8,0x8102E3C4,0xEFF11753,0x80F66E3C,0xF054D8D5,0x80EA4712, +0xF0B8A401,0x80DE6E4C,0xF11C789A,0x80D2E3F2,0xF1805662,0x80C7A80A,0xF1E43D1C, +0x80BCBA9D,0xF2482C8A,0x80B21BAF,0xF2AC246E,0x80A7CB49,0xF310248A,0x809DC971, +0xF3742CA2,0x8094162C,0xF3D83C77,0x808AB180,0xF43C53CB,0x80819B74,0xF4A07261, +0x8078D40D,0xF50497FB,0x80705B50,0xF568C45B,0x80683143,0xF5CCF743,0x806055EB, +0xF6313077,0x8058C94C,0xF6956FB7,0x80518B6B,0xF6F9B4C6,0x804A9C4D,0xF75DFF66, +0x8043FBF6,0xF7C24F59,0x803DAA6A,0xF826A462,0x8037A7AC,0xF88AFE42,0x8031F3C2, +0xF8EF5CBB,0x802C8EAD,0xF953BF91,0x80277872,0xF9B82684,0x8022B114,0xFA1C9157, +0x801E3895,0xFA80FFCB,0x801A0EF8,0xFAE571A4,0x80163440,0xFB49E6A3,0x8012A86F, +0xFBAE5E89,0x800F6B88,0xFC12D91A,0x800C7D8C,0xFC775616,0x8009DE7E,0xFCDBD541, +0x80078E5E,0xFD40565C,0x80058D2F,0xFDA4D929,0x8003DAF1,0xFE095D69,0x800277A6, +0xFE6DE2E0,0x8001634E,0xFED2694F,0x80009DEA,0xFF36F078,0x8000277A,0xFF9B781D, +0x80000000,0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_4096_q31[ARM_NEON_RFFT_TWIDDLES_4096_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,0x7FFFFFFF, +0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91, +0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414, +0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590, +0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC, +0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376, +0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65, +0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3, +0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C, +0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x00000000,0x80000000,0xF3742CA2, +0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3,0x89BE50C3, +0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54,0xA57D8666, +0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A,0xC3A94590, +0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4,0x809DC971, +0xF3742CA2,0x7FFFFFFF,0x00000000,0x7E9D55FC,0xED37EF91,0x7A7D055B,0xDAD7F3A2, +0x73B5EBD1,0xC945DFEC,0x6A6D98A4,0xB8E31319,0x5ED77C8A,0xAA0A5B2E,0x5133CC94, 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+0x9D8E0597,0xAD4A1ABA,0x9E4FD78A,0xAC64D510,0x9F13C7D0,0xAB815F8D,0x9FD9D22A, +0xAA9FBF1E,0xA0A1F24D,0xA9BFF8A8,0xA16C23E1,0xA8E21106,0xA2386284,0xA8060D08, +0xA306A9C8,0xA72BF174,0xA3D6F534,0xA653C303,0xA4A94043,0xA57D8666,0xA57D8666, +0xA4A94043,0xA653C303,0xA3D6F534,0xA72BF174,0xA306A9C8,0xA8060D08,0xA2386284, +0xA8E21106,0xA16C23E1,0xA9BFF8A8,0xA0A1F24D,0xAA9FBF1E,0x9FD9D22A,0xAB815F8D, +0x9F13C7D0,0xAC64D510,0x9E4FD78A,0xAD4A1ABA,0x9D8E0597,0xAE312B92,0x9CCE562C, +0xAF1A0293,0x9C10CD70,0xB0049AB3,0x9B556F81,0xB0F0EEDA,0x9A9C406E,0xB1DEF9E9, +0x99E5443B,0xB2CEB6B5,0x99307EE0,0xB3C0200C,0x987DF449,0xB4B330B3,0x97CDA855, +0xB5A7E362,0x971F9ED7,0xB69E32CD,0x9673DB94,0xB796199B,0x95CA6247,0xB88F926D, +0x9523369C,0xB98A97D8,0x947E5C33,0xBA87246D,0x93DBD6A0,0xBB8532B0,0x933BA968, +0xBC84BD1F,0x929DD806,0xBD85BE30,0x920265E4,0xBE88304F,0x91695663,0xBF8C0DE3, +0x90D2ACD4,0xC0915148,0x903E6C7B,0xC197F4D4,0x8FAC988F,0xC29FF2D4,0x8F1D343A, +0xC3A94590,0x8E904298,0xC4B3E746,0x8E05C6B7,0xC5BFD22E,0x8D7DC399,0xC6CD0079, +0x8CF83C30,0xC7DB6C50,0x8C753362,0xC8EB0FD6,0x8BF4AC05,0xC9FBE527,0x8B76A8E4, +0xCB0DE658,0x8AFB2CBB,0xCC210D79,0x8A823A36,0xCD355491,0x8A0BD3F5,0xCE4AB5A2, +0x8997FC8A,0xCF612AAA,0x8926B677,0xD078AD9E,0x88B80432,0xD191386E,0x884BE821, +0xD2AAC504,0x87E2649B,0xD3C54D47,0x877B7BEC,0xD4E0CB15,0x8717304E,0xD5FD3848, +0x86B583EE,0xD71A8EB5,0x865678EB,0xD838C82D,0x85FA1153,0xD957DE7A,0x85A04F28, +0xDA77CB63,0x8549345C,0xDB9888A8,0x84F4C2D4,0xDCBA1008,0x84A2FC62,0xDDDC5B3B, +0x8453E2CF,0xDEFF63F4,0x840777D0,0xE02323E5,0x83BDBD0E,0xE14794BA,0x8376B422, +0xE26CB01B,0x83325E97,0xE3926FAD,0x82F0BDE8,0xE4B8CD11,0x82B1D381,0xE5DFC1E5, +0x8275A0C0,0xE70747C4,0x823C26F3,0xE82F5844,0x82056758,0xE957ECFB,0x81D16321, +0xEA80FF7A,0x81A01B6D,0xEBAA894F,0x8171914E,0xECD48407,0x8145C5C7,0xEDFEE92B, +0x811CB9CA,0xEF29B243,0x80F66E3C,0xF054D8D5,0x80D2E3F2,0xF1805662,0x80B21BAF, +0xF2AC246E,0x8094162C,0xF3D83C77,0x8078D40D,0xF50497FB,0x806055EB,0xF6313077, +0x804A9C4D,0xF75DFF66,0x8037A7AC,0xF88AFE42,0x80277872,0xF9B82684,0x801A0EF8, +0xFAE571A4,0x800F6B88,0xFC12D91A,0x80078E5E,0xFD40565C,0x800277A6,0xFE6DE2E0, +0x8000277A,0xFF9B781D,0x80009DEA,0x00C90F88,0x8003DAF1,0x01F6A297,0x8009DE7E, +0x03242ABF,0x8012A86F,0x0451A177,0x801E3895,0x057F0035,0x802C8EAD,0x06AC406F, +0x803DAA6A,0x07D95B9E,0x80518B6B,0x09064B3A,0x80683143,0x0A3308BD,0x80819B74, +0x0B5F8D9F,0x809DC971,0x0C8BD35E,0x80BCBA9D,0x0DB7D376,0x80DE6E4C,0x0EE38766, +0x8102E3C4,0x100EE8AD,0x812A1A3A,0x1139F0CF,0x815410D4,0x1264994E,0x8180C6A9, +0x138EDBB1,0x81B03AC2,0x14B8B17F,0x81E26C16,0x15E21445,0x82175990,0x170AFD8D, +0x824F0208,0x183366E9,0x8289644B,0x195B49EA,0x82C67F14,0x1A82A026,0x83065110, +0x1BA96335,0x8348D8DC,0x1CCF8CB3,0x838E1507,0x1DF5163F,0x83D60412,0x1F19F97B, +0x8420A46C,0x203E300D,0x846DF477,0x2161B3A0,0x84BDF286,0x22847DE0,0x85109CDD, +0x23A6887F,0x8565F1B0,0x24C7CD33,0x85BDEF28,0x25E845B6,0x86189359,0x2707EBC7, +0x8675DC4F,0x2826B928,0x86D5C802,0x2944A7A2,0x8738545E,0x2A61B101,0x879D7F41, +0x2B7DCF17,0x88054677,0x2C98FBBA,0x886FA7C2,0x2DB330C7,0x88DCA0D3,0x2ECC681E, +0x894C2F4C,0x2FE49BA7,0x89BE50C3,0x30FBC54D,0x8A3302BE,0x3211DF04,0x8AAA42B4, +0x3326E2C3,0x8B240E11,0x343ACA87,0x8BA0622F,0x354D9057,0x8C1F3C5D,0x365F2E3B, +0x8CA099DA,0x376F9E46,0x8D2477D8,0x387EDA8E,0x8DAAD37B,0x398CDD32,0x8E33A9DA, +0x3A99A057,0x8EBEF7FB,0x3BA51E29,0x8F4CBADB,0x3CAF50DA,0x8FDCEF66,0x3DB832A6, +0x906F927C,0x3EBFBDCD,0x9104A0EE,0x3FC5EC98,0x919C1781,0x40CAB958,0x9235F2EC, +0x41CE1E65,0x92D22FD9,0x42D0161E,0x9370CAE4,0x43D09AED,0x9411C09E,0x44CFA740, +0x94B50D87,0x45CD358F,0x955AAE17,0x46C9405C,0x96029EB6,0x47C3C22F,0x96ACDBBE, +0x48BCB599,0x9759617F,0x49B41533,0x98082C3B,0x4AA9DBA2,0x98B93828,0x4B9E0390, +0x996C816F,0x4C9087B1,0x9A22042D,0x4D8162C4,0x9AD9BC71,0x4E708F8F,0x9B93A641, +0x4F5E08E3,0x9C4FBD93,0x5049C999,0x9D0DFE54,0x5133CC94,0x9DCE6463,0x521C0CC2, +0x9E90EB94,0x53028518,0x9F558FB0,0x53E73097,0xA01C4C73,0x54CA0A4B,0xA0E51D8C, +0x55AB0D46,0xA1AFFEA3,0x568A34A9,0xA27CEB4F,0x57677B9D,0xA34BDF20,0x5842DD54, +0xA41CD599,0x591C550E,0xA4EFCA31,0x59F3DE12,0xA5C4B855,0x5AC973B5,0xA69B9B68, +0x5B9D1154,0xA7746EC0,0x5C6EB258,0xA84F2DAA,0x5D3E5237,0xA92BD367,0x5E0BEC6E, +0xAA0A5B2E,0x5ED77C8A,0xAAEAC02C,0x5FA0FE1F,0xABCCFD83,0x60686CCF,0xACB10E4B, +0x612DC447,0xAD96ED92,0x61F1003F,0xAE7E965B,0x62B21C7B,0xAF6803A2,0x637114CC, +0xB0533055,0x642DE50D,0xB140175B,0x64E88926,0xB22EB392,0x65A0FD0B,0xB31EFFCC, +0x66573CBB,0xB410F6D3,0x670B4444,0xB5049368,0x67BD0FBD,0xB5F9D043,0x686C9B4B, +0xB6F0A812,0x6919E320,0xB7E9157A,0x69C4E37A,0xB8E31319,0x6A6D98A4,0xB9DE9B83, +0x6B13FEF5,0xBADBA943,0x6BB812D1,0xBBDA36DD,0x6C59D0A9,0xBCDA3ECB,0x6CF934FC, +0xBDDBBB7F,0x6D963C54,0xBEDEA765,0x6E30E34A,0xBFE2FCDF,0x6EC92683,0xC0E8B648, +0x6F5F02B2,0xC1EFCDF3,0x6FF27497,0xC2F83E2A,0x708378FF,0xC4020133,0x71120CC5, +0xC50D1149,0x719E2CD2,0xC61968A2,0x7227D61C,0xC727016D,0x72AF05A7,0xC835D5D0, +0x7333B883,0xC945DFEC,0x73B5EBD1,0xCA5719DB,0x74359CBD,0xCB697DB0,0x74B2C884, +0xCC7D0578,0x752D6C6C,0xCD91AB39,0x75A585CF,0xCEA768F2,0x761B1211,0xCFBE389F, +0x768E0EA6,0xD0D61434,0x76FE790E,0xD1EEF59E,0x776C4EDB,0xD308D6C7,0x77D78DAA, +0xD423B191,0x78403329,0xD53F7FDA,0x78A63D11,0xD65C3B7B,0x7909A92D,0xD779DE47, +0x796A7554,0xD898620C,0x79C89F6E,0xD9B7C094,0x7A24256F,0xDAD7F3A2,0x7A7D055B, +0xDBF8F4F8,0x7AD33D45,0xDD1ABE51,0x7B26CB4F,0xDE3D4964,0x7B77ADA8,0xDF608FE4, +0x7BC5E290,0xE0848B7F,0x7C116853,0xE1A935E2,0x7C5A3D50,0xE2CE88B3,0x7CA05FF1, +0xE3F47D96,0x7CE3CEB2,0xE51B0E2A,0x7D24881B,0xE642340D,0x7D628AC6,0xE769E8D8, +0x7D9DD55A,0xE8922622,0x7DD6668F,0xE9BAE57D,0x7E0C3D29,0xEAE4207A,0x7E3F57FF, +0xEC0DD0A8,0x7E6FB5F4,0xED37EF91,0x7E9D55FC,0xEE6276BF,0x7EC8371A,0xEF8D5FB8, +0x7EF05860,0xF0B8A401,0x7F15B8EE,0xF1E43D1C,0x7F3857F6,0xF310248A,0x7F5834B7, +0xF43C53CB,0x7F754E80,0xF568C45B,0x7F8FA4B0,0xF6956FB7,0x7FA736B4,0xF7C24F59, +0x7FBC040A,0xF8EF5CBB,0x7FCE0C3E,0xFA1C9157,0x7FDD4EEC,0xFB49E6A3,0x7FE9CBC0, +0xFC775616,0x7FF38274,0xFDA4D929,0x7FFA72D1,0xFED2694F,0x7FFE9CB2,}; + +const uint32_t arm_neon_rfft_factors_4096_q31[ARM_NEON_RFFT_FACTORS_4096_Q31_LEN]={ +5,256,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_4096_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_Q31_LEN]={ +0xFFCDBC0B,0x800009DF,0xFF9B781D,0x8000277A,0xFF69343F,0x800058D4,0xFF36F078, +0x80009DEA,0xFF04ACD0,0x8000F6BD,0xFED2694F,0x8001634E,0xFEA025FD,0x8001E39B, +0xFE6DE2E0,0x800277A6,0xFE3BA002,0x80031F6D,0xFE095D69,0x8003DAF1,0xFDD71B1E, +0x8004AA32,0xFDA4D929,0x80058D2F,0xFD729790,0x800683E8,0xFD40565C,0x80078E5E, +0xFD0E1594,0x8008AC90,0xFCDBD541,0x8009DE7E,0xFCA9956A,0x800B2427,0xFC775616, +0x800C7D8C,0xFC45174E,0x800DEAAD,0xFC12D91A,0x800F6B88,0xFBE09B80,0x8011001F, +0xFBAE5E89,0x8012A86F,0xFB7C223D,0x8014647B,0xFB49E6A3,0x80163440,0xFB17ABC2, +0x801817BF,0xFAE571A4,0x801A0EF8,0xFAB3384F,0x801C19EA,0xFA80FFCB,0x801E3895, +0xFA4EC821,0x80206AF8,0xFA1C9157,0x8022B114,0xF9EA5B75,0x80250AE7,0xF9B82684, +0x80277872,0xF985F28A,0x8029F9B4,0xF953BF91,0x802C8EAD,0xF9218D9E,0x802F375D, +0xF8EF5CBB,0x8031F3C2,0xF8BD2CEF,0x8034C3DD,0xF88AFE42,0x8037A7AC,0xF858D0BB, +0x803A9F31,0xF826A462,0x803DAA6A,0xF7F4793E,0x8040C956,0xF7C24F59,0x8043FBF6, +0xF79026B9,0x80474248,0xF75DFF66,0x804A9C4D,0xF72BD967,0x804E0A04,0xF6F9B4C6, +0x80518B6B,0xF6C79188,0x80552084,0xF6956FB7,0x8058C94C,0xF6634F59,0x805C85C4, +0xF6313077,0x806055EB,0xF5FF1318,0x806439C0,0xF5CCF743,0x80683143,0xF59ADD02, +0x806C3C74,0xF568C45B,0x80705B50,0xF536AD56,0x80748DD9,0xF50497FB,0x8078D40D, +0xF4D28451,0x807D2DEC,0xF4A07261,0x80819B74,0xF46E6231,0x80861CA6,0xF43C53CB, 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+0xF826A462,0x803A9F31,0xF858D0BB,0x8037A7AC,0xF88AFE42,0x8034C3DD,0xF8BD2CEF, +0x8031F3C2,0xF8EF5CBB,0x802F375D,0xF9218D9E,0x802C8EAD,0xF953BF91,0x8029F9B4, +0xF985F28A,0x80277872,0xF9B82684,0x80250AE7,0xF9EA5B75,0x8022B114,0xFA1C9157, +0x80206AF8,0xFA4EC821,0x801E3895,0xFA80FFCB,0x801C19EA,0xFAB3384F,0x801A0EF8, +0xFAE571A4,0x801817BF,0xFB17ABC2,0x80163440,0xFB49E6A3,0x8014647B,0xFB7C223D, +0x8012A86F,0xFBAE5E89,0x8011001F,0xFBE09B80,0x800F6B88,0xFC12D91A,0x800DEAAD, +0xFC45174E,0x800C7D8C,0xFC775616,0x800B2427,0xFCA9956A,0x8009DE7E,0xFCDBD541, +0x8008AC90,0xFD0E1594,0x80078E5E,0xFD40565C,0x800683E8,0xFD729790,0x80058D2F, +0xFDA4D929,0x8004AA32,0xFDD71B1E,0x8003DAF1,0xFE095D69,0x80031F6D,0xFE3BA002, +0x800277A6,0xFE6DE2E0,0x8001E39B,0xFEA025FD,0x8001634E,0xFED2694F,0x8000F6BD, +0xFF04ACD0,0x80009DEA,0xFF36F078,0x800058D4,0xFF69343F,0x8000277A,0xFF9B781D, +0x800009DF,0xFFCDBC0B,0x80000000,0x00000000,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_twiddles_8192_q31[ARM_NEON_RFFT_TWIDDLES_8192_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684, +0x7FA736B4,0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC, +0xED37EF91,0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96, +0x7C29FBEE,0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1, +0xD7D946D8,0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3, +0x7504D345,0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6, +0xC3A94590,0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0, +0x6A6D98A4,0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926, +0xB140175B,0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E, +0x5CB420E0,0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2, +0xA1288376,0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA, +0x4C3FDFF4,0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50, +0x93DBD6A0,0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A, +0x398CDD32,0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D, +0x89BE50C3,0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F, +0x25280C5E,0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A, +0x831C314E,0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04, +0x0FAB272B,0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C, +0x80277872,0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684, +0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE, +0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3, +0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4, +0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E, +0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4, +0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A, +0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E, +0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04, +0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872,0x00000000,0x80000000,0xF9B82684, +0x80277872,0xF3742CA2,0x809DC971,0xED37EF91,0x8162AA04,0xE70747C4,0x8275A0C0, +0xE0E60685,0x83D60412,0xDAD7F3A2,0x8582FAA5,0xD4E0CB15,0x877B7BEC,0xCF043AB3, +0x89BE50C3,0xC945DFEC,0x8C4A142F,0xC3A94590,0x8F1D343A,0xBE31E19B,0x9235F2EC, +0xB8E31319,0x9592675C,0xB3C0200C,0x99307EE0,0xAECC336C,0x9D0DFE54,0xAA0A5B2E, +0xA1288376,0xA57D8666,0xA57D8666,0xA1288376,0xAA0A5B2E,0x9D0DFE54,0xAECC336C, +0x99307EE0,0xB3C0200C,0x9592675C,0xB8E31319,0x9235F2EC,0xBE31E19B,0x8F1D343A, +0xC3A94590,0x8C4A142F,0xC945DFEC,0x89BE50C3,0xCF043AB3,0x877B7BEC,0xD4E0CB15, +0x8582FAA5,0xDAD7F3A2,0x83D60412,0xE0E60685,0x8275A0C0,0xE70747C4,0x8162AA04, +0xED37EF91,0x809DC971,0xF3742CA2,0x80277872,0xF9B82684,0x7FFFFFFF,0x00000000, +0x7FA736B4,0xF6956FB7,0x7E9D55FC,0xED37EF91,0x7CE3CEB2,0xE3F47D96,0x7A7D055B, +0xDAD7F3A2,0x776C4EDB,0xD1EEF59E,0x73B5EBD1,0xC945DFEC,0x6F5F02B2,0xC0E8B648, +0x6A6D98A4,0xB8E31319,0x64E88926,0xB140175B,0x5ED77C8A,0xAA0A5B2E,0x5842DD54, +0xA34BDF20,0x5133CC94,0x9D0DFE54,0x49B41533,0x9759617F,0x41CE1E65,0x9235F2EC, +0x398CDD32,0x8DAAD37B,0x30FBC54D,0x89BE50C3,0x2826B928,0x8675DC4F,0x1F19F97B, +0x83D60412,0x15E21445,0x81E26C16,0x0C8BD35E,0x809DC971,0x03242ABF,0x8009DE7E, +0xF9B82684,0x80277872,0xF054D8D5,0x80F66E3C,0xE70747C4,0x8275A0C0,0xDDDC5B3B, +0x84A2FC62,0xD4E0CB15,0x877B7BEC,0xCC210D79,0x8AFB2CBB,0xC3A94590,0x8F1D343A, +0xBB8532B0,0x93DBD6A0,0xB3C0200C,0x99307EE0,0xAC64D510,0x9F13C7D0,0xA57D8666, +0xA57D8666,0x9F13C7D0,0xAC64D510,0x99307EE0,0xB3C0200C,0x93DBD6A0,0xBB8532B0, +0x8F1D343A,0xC3A94590,0x8AFB2CBB,0xCC210D79,0x877B7BEC,0xD4E0CB15,0x84A2FC62, +0xDDDC5B3B,0x8275A0C0,0xE70747C4,0x80F66E3C,0xF054D8D5,0x80277872,0xF9B82684, +0x8009DE7E,0x03242ABF,0x809DC971,0x0C8BD35E,0x81E26C16,0x15E21445,0x83D60412, +0x1F19F97B,0x8675DC4F,0x2826B928,0x89BE50C3,0x30FBC54D,0x8DAAD37B,0x398CDD32, +0x9235F2EC,0x41CE1E65,0x9759617F,0x49B41533,0x9D0DFE54,0x5133CC94,0xA34BDF20, +0x5842DD54,0xAA0A5B2E,0x5ED77C8A,0xB140175B,0x64E88926,0xB8E31319,0x6A6D98A4, +0xC0E8B648,0x6F5F02B2,0xC945DFEC,0x73B5EBD1,0xD1EEF59E,0x776C4EDB,0xDAD7F3A2, +0x7A7D055B,0xE3F47D96,0x7CE3CEB2,0xED37EF91,0x7E9D55FC,0xF6956FB7,0x7FA736B4, +0x7FFFFFFF,0x00000000,0x7FFF6216,0xFF36F078,0x7FFD885A,0xFE6DE2E0,0x7FFA72D1, +0xFDA4D929,0x7FF62182,0xFCDBD541,0x7FF09478,0xFC12D91A,0x7FE9CBC0,0xFB49E6A3, +0x7FE1C76B,0xFA80FFCB,0x7FD8878E,0xF9B82684,0x7FCE0C3E,0xF8EF5CBB,0x7FC25596, +0xF826A462,0x7FB563B3,0xF75DFF66,0x7FA736B4,0xF6956FB7,0x7F97CEBD,0xF5CCF743, +0x7F872BF3,0xF50497FB,0x7F754E80,0xF43C53CB,0x7F62368F,0xF3742CA2,0x7F4DE451, +0xF2AC246E,0x7F3857F6,0xF1E43D1C,0x7F2191B4,0xF11C789A,0x7F0991C4,0xF054D8D5, +0x7EF05860,0xEF8D5FB8,0x7ED5E5C6,0xEEC60F31,0x7EBA3A39,0xEDFEE92B,0x7E9D55FC, +0xED37EF91,0x7E7F3957,0xEC71244F,0x7E5FE493,0xEBAA894F,0x7E3F57FF,0xEAE4207A, +0x7E1D93EA,0xEA1DEBBB,0x7DFA98A8,0xE957ECFB,0x7DD6668F,0xE8922622,0x7DB0FDF8, +0xE7CC9917,0x7D8A5F40,0xE70747C4,0x7D628AC6,0xE642340D,0x7D3980EC,0xE57D5FDA, +0x7D0F4218,0xE4B8CD11,0x7CE3CEB2,0xE3F47D96,0x7CB72724,0xE330734D,0x7C894BDE, 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+0xF6313077,0x80552084,0xF6C79188,0x804A9C4D,0xF75DFF66,0x8040C956,0xF7F4793E, +0x8037A7AC,0xF88AFE42,0x802F375D,0xF9218D9E,0x80277872,0xF9B82684,0x80206AF8, +0xFA4EC821,0x801A0EF8,0xFAE571A4,0x8014647B,0xFB7C223D,0x800F6B88,0xFC12D91A, +0x800B2427,0xFCA9956A,0x80078E5E,0xFD40565C,0x8004AA32,0xFDD71B1E,0x800277A6, +0xFE6DE2E0,0x8000F6BD,0xFF04ACD0,0x8000277A,0xFF9B781D,0x800009DF,0x003243F5, +0x80009DEA,0x00C90F88,0x8001E39B,0x015FDA03,0x8003DAF1,0x01F6A297,0x800683E8, +0x028D6870,0x8009DE7E,0x03242ABF,0x800DEAAD,0x03BAE8B2,0x8012A86F,0x0451A177, +0x801817BF,0x04E8543E,0x801E3895,0x057F0035,0x80250AE7,0x0615A48B,0x802C8EAD, +0x06AC406F,0x8034C3DD,0x0742D311,0x803DAA6A,0x07D95B9E,0x80474248,0x086FD947, +0x80518B6B,0x09064B3A,0x805C85C4,0x099CB0A7,0x80683143,0x0A3308BD,0x80748DD9, +0x0AC952AA,0x80819B74,0x0B5F8D9F,0x808F5A02,0x0BF5B8CB,0x809DC971,0x0C8BD35E, +0x80ACE9AB,0x0D21DC87,0x80BCBA9D,0x0DB7D376,0x80CD3C2F,0x0E4DB75B,0x80DE6E4C, +0x0EE38766,0x80F050DB,0x0F7942C7,0x8102E3C4,0x100EE8AD,0x811626EC,0x10A4784B, +0x812A1A3A,0x1139F0CF,0x813EBD90,0x11CF516A,0x815410D4,0x1264994E,0x816A13E6, +0x12F9C7AA,0x8180C6A9,0x138EDBB1,0x819828FD,0x1423D492,0x81B03AC2,0x14B8B17F, +0x81C8FBD6,0x154D71AA,0x81E26C16,0x15E21445,0x81FC8B60,0x1676987F,0x82175990, +0x170AFD8D,0x8232D67F,0x179F429F,0x824F0208,0x183366E9,0x826BDC04,0x18C7699B, +0x8289644B,0x195B49EA,0x82A79AB3,0x19EF0707,0x82C67F14,0x1A82A026,0x82E61141, +0x1B161479,0x83065110,0x1BA96335,0x83273E52,0x1C3C8B8C,0x8348D8DC,0x1CCF8CB3, +0x836B207D,0x1D6265DD,0x838E1507,0x1DF5163F,0x83B1B649,0x1E879D0D,0x83D60412, +0x1F19F97B,0x83FAFE2E,0x1FAC2ABF,0x8420A46C,0x203E300D,0x8446F695,0x20D0089C, +0x846DF477,0x2161B3A0,0x84959DD9,0x21F3304F,0x84BDF286,0x22847DE0,0x84E6F244, +0x23159B88,0x85109CDD,0x23A6887F,0x853AF214,0x243743FA,0x8565F1B0,0x24C7CD33, +0x85919B76,0x2558235F,0x85BDEF28,0x25E845B6,0x85EAEC88,0x26783370,0x86189359, +0x2707EBC7,0x8646E35C,0x27976DF1,0x8675DC4F,0x2826B928,0x86A57DF2,0x28B5CCA5, +0x86D5C802,0x2944A7A2,0x8706BA3D,0x29D34958,0x8738545E,0x2A61B101,0x876A9621, +0x2AEFDDD8,0x879D7F41,0x2B7DCF17,0x87D10F75,0x2C0B83FA,0x88054677,0x2C98FBBA, +0x883A23FF,0x2D263596,0x886FA7C2,0x2DB330C7,0x88A5D177,0x2E3FEC8B,0x88DCA0D3, +0x2ECC681E,0x89141589,0x2F58A2BE,0x894C2F4C,0x2FE49BA7,0x8984EDCF,0x30705217, +0x89BE50C3,0x30FBC54D,0x89F857D8,0x3186F487,0x8A3302BE,0x3211DF04,0x8A6E5123, +0x329C8402,0x8AAA42B4,0x3326E2C3,0x8AE6D720,0x33B0FA84,0x8B240E11,0x343ACA87, +0x8B61E733,0x34C4520D,0x8BA0622F,0x354D9057,0x8BDF7EB0,0x35D684A6,0x8C1F3C5D, +0x365F2E3B,0x8C5F9ADE,0x36E78C5B,0x8CA099DA,0x376F9E46,0x8CE238F6,0x37F76341, +0x8D2477D8,0x387EDA8E,0x8D675623,0x39060373,0x8DAAD37B,0x398CDD32,0x8DEEEF82, +0x3A136712,0x8E33A9DA,0x3A99A057,0x8E790222,0x3B1F8848,0x8EBEF7FB,0x3BA51E29, +0x8F058B04,0x3C2A6142,0x8F4CBADB,0x3CAF50DA,0x8F94871D,0x3D33EC39,0x8FDCEF66, +0x3DB832A6,0x9025F352,0x3E3C2369,0x906F927C,0x3EBFBDCD,0x90B9CC7D,0x3F430119, +0x9104A0EE,0x3FC5EC98,0x91500F67,0x40487F94,0x919C1781,0x40CAB958,0x91E8B8D0, +0x414C992F,0x9235F2EC,0x41CE1E65,0x9283C568,0x424F4845,0x92D22FD9,0x42D0161E, +0x932131D1,0x4350873C,0x9370CAE4,0x43D09AED,0x93C0FAA3,0x4450507E,0x9411C09E, +0x44CFA740,0x94631C65,0x454E9E80,0x94B50D87,0x45CD358F,0x95079394,0x464B6BBE, +0x955AAE17,0x46C9405C,0x95AE5C9F,0x4746B2BC,0x96029EB6,0x47C3C22F,0x965773E7, +0x48406E08,0x96ACDBBE,0x48BCB599,0x9702D5C3,0x49389836,0x9759617F,0x49B41533, +0x97B07E7A,0x4A2F2BE6,0x98082C3B,0x4AA9DBA2,0x98606A49,0x4B2423BE,0x98B93828, +0x4B9E0390,0x9912955F,0x4C177A6E,0x996C816F,0x4C9087B1,0x99C6FBDE,0x4D092AB0, +0x9A22042D,0x4D8162C4,0x9A7D99DE,0x4DF92F46,0x9AD9BC71,0x4E708F8F,0x9B366B68, +0x4EE782FB,0x9B93A641,0x4F5E08E3,0x9BF16C7A,0x4FD420A4,0x9C4FBD93,0x5049C999, +0x9CAE9907,0x50BF031F,0x9D0DFE54,0x5133CC94,0x9D6DECF4,0x51A82555,0x9DCE6463, +0x521C0CC2,0x9E2F641B,0x528F8238,0x9E90EB94,0x53028518,0x9EF2FA49,0x537514C2, +0x9F558FB0,0x53E73097,0x9FB8AB41,0x5458D7F9,0xA01C4C73,0x54CA0A4B,0xA08072BA, +0x553AC6EE,0xA0E51D8C,0x55AB0D46,0xA14A4C5E,0x561ADCB9,0xA1AFFEA3,0x568A34A9, +0xA21633CD,0x56F9147E,0xA27CEB4F,0x57677B9D,0xA2E4249B,0x57D5696D,0xA34BDF20, +0x5842DD54,0xA3B41A50,0x58AFD6BD,0xA41CD599,0x591C550E,0xA486106A,0x598857B2, +0xA4EFCA31,0x59F3DE12,0xA55A025B,0x5A5EE79A,0xA5C4B855,0x5AC973B5,0xA62FEB8B, +0x5B3381CE,0xA69B9B68,0x5B9D1154,0xA707C757,0x5C0621B2,0xA7746EC0,0x5C6EB258, +0xA7E1910F,0x5CD6C2B5,0xA84F2DAA,0x5D3E5237,0xA8BD43FA,0x5DA5604F,0xA92BD367, +0x5E0BEC6E,0xA99ADB56,0x5E71F606,0xAA0A5B2E,0x5ED77C8A,0xAA7A5253,0x5F3C7F6B, +0xAAEAC02C,0x5FA0FE1F,0xAB5BA41A,0x6004F819,0xABCCFD83,0x60686CCF,0xAC3ECBC7, +0x60CB5BB7,0xACB10E4B,0x612DC447,0xAD23C46E,0x618FA5F7,0xAD96ED92,0x61F1003F, +0xAE0A8916,0x6251D298,0xAE7E965B,0x62B21C7B,0xAEF314C0,0x6311DD64,0xAF6803A2, +0x637114CC,0xAFDD625F,0x63CFC231,0xB0533055,0x642DE50D,0xB0C96CE0,0x648B7CE0, +0xB140175B,0x64E88926,0xB1B72F23,0x6545095F,0xB22EB392,0x65A0FD0B,0xB2A6A402, +0x65FC63A9,0xB31EFFCC,0x66573CBB,0xB397C649,0x66B187C3,0xB410F6D3,0x670B4444, +0xB48A90C0,0x676471C0,0xB5049368,0x67BD0FBD,0xB57EFE22,0x68151DBE,0xB5F9D043, +0x686C9B4B,0xB6750921,0x68C387E9,0xB6F0A812,0x6919E320,0xB76CAC69,0x696FAC78, +0xB7E9157A,0x69C4E37A,0xB865E299,0x6A1987B0,0xB8E31319,0x6A6D98A4,0xB960A64C, +0x6AC115E2,0xB9DE9B83,0x6B13FEF5,0xBA5CF210,0x6B66536B,0xBADBA943,0x6BB812D1, +0xBB5AC06D,0x6C093CB6,0xBBDA36DD,0x6C59D0A9,0xBC5A0BE2,0x6CA9CE3B,0xBCDA3ECB, +0x6CF934FC,0xBD5ACEE5,0x6D48047E,0xBDDBBB7F,0x6D963C54,0xBE5D03E6,0x6DE3DC11, +0xBEDEA765,0x6E30E34A,0xBF60A54A,0x6E7D5193,0xBFE2FCDF,0x6EC92683,0xC065AD70, +0x6F1461B0,0xC0E8B648,0x6F5F02B2,0xC16C16B0,0x6FA90921,0xC1EFCDF3,0x6FF27497, +0xC273DB58,0x703B44AD,0xC2F83E2A,0x708378FF,0xC37CF5B0,0x70CB1128,0xC4020133, +0x71120CC5,0xC4875FF9,0x71586B74,0xC50D1149,0x719E2CD2,0xC593146A,0x71E35080, +0xC61968A2,0x7227D61C,0xC6A00D37,0x726BBD48,0xC727016D,0x72AF05A7,0xC7AE4489, +0x72F1AED9,0xC835D5D0,0x7333B883,0xC8BDB485,0x73752249,0xC945DFEC,0x73B5EBD1, +0xC9CE5748,0x73F614C0,0xCA5719DB,0x74359CBD,0xCAE026E8,0x74748371,0xCB697DB0, +0x74B2C884,0xCBF31D75,0x74F06B9E,0xCC7D0578,0x752D6C6C,0xCD0734F9,0x7569CA99, +0xCD91AB39,0x75A585CF,0xCE1C6777,0x75E09DBD,0xCEA768F2,0x761B1211,0xCF32AEEB, +0x7654E279,0xCFBE389F,0x768E0EA6,0xD04A054E,0x76C69647,0xD0D61434,0x76FE790E, +0xD1626490,0x7735B6AF,0xD1EEF59E,0x776C4EDB,0xD27BC69C,0x77A24148,0xD308D6C7, +0x77D78DAA,0xD396255A,0x780C33B8,0xD423B191,0x78403329,0xD4B17AA8,0x78738BB3, +0xD53F7FDA,0x78A63D11,0xD5CDC062,0x78D846FB,0xD65C3B7B,0x7909A92D,0xD6EAF05F, +0x793A6361,0xD779DE47,0x796A7554,0xD809046E,0x7999DEC4,0xD898620C,0x79C89F6E, +0xD927F65B,0x79F6B711,0xD9B7C094,0x7A24256F,0xDA47BFEE,0x7A50EA47,0xDAD7F3A2, +0x7A7D055B,0xDB685AE9,0x7AA8766F,0xDBF8F4F8,0x7AD33D45,0xDC89C109,0x7AFD59A4, +0xDD1ABE51,0x7B26CB4F,0xDDABEC08,0x7B4F920E,0xDE3D4964,0x7B77ADA8,0xDECED59B, +0x7B9F1DE6,0xDF608FE4,0x7BC5E290,0xDFF27773,0x7BEBFB70,0xE0848B7F,0x7C116853, +0xE116CB3D,0x7C362904,0xE1A935E2,0x7C5A3D50,0xE23BCAA2,0x7C7DA505,0xE2CE88B3, +0x7CA05FF1,0xE3616F48,0x7CC26DE5,0xE3F47D96,0x7CE3CEB2,0xE487B2D0,0x7D048228, +0xE51B0E2A,0x7D24881B,0xE5AE8ED8,0x7D43E05E,0xE642340D,0x7D628AC6,0xE6D5FCFC, +0x7D808728,0xE769E8D8,0x7D9DD55A,0xE7FDF6D4,0x7DBA7534,0xE8922622,0x7DD6668F, +0xE92675F4,0x7DF1A942,0xE9BAE57D,0x7E0C3D29,0xEA4F73EE,0x7E26221F,0xEAE4207A, +0x7E3F57FF,0xEB78EA52,0x7E57DEA7,0xEC0DD0A8,0x7E6FB5F4,0xECA2D2AD,0x7E86DDC6, +0xED37EF91,0x7E9D55FC,0xEDCD2687,0x7EB31E78,0xEE6276BF,0x7EC8371A,0xEEF7DF6A, +0x7EDC9FC6,0xEF8D5FB8,0x7EF05860,0xF022F6DA,0x7F0360CB,0xF0B8A401,0x7F15B8EE, +0xF14E665C,0x7F2760AF,0xF1E43D1C,0x7F3857F6,0xF27A2771,0x7F489EAA,0xF310248A, +0x7F5834B7,0xF3A63398,0x7F671A05,0xF43C53CB,0x7F754E80,0xF4D28451,0x7F82D214, +0xF568C45B,0x7F8FA4B0,0xF5FF1318,0x7F9BC640,0xF6956FB7,0x7FA736B4,0xF72BD967, +0x7FB1F5FC,0xF7C24F59,0x7FBC040A,0xF858D0BB,0x7FC560CF,0xF8EF5CBB,0x7FCE0C3E, +0xF985F28A,0x7FD6064C,0xFA1C9157,0x7FDD4EEC,0xFAB3384F,0x7FE3E616,0xFB49E6A3, +0x7FE9CBC0,0xFBE09B80,0x7FEEFFE1,0xFC775616,0x7FF38274,0xFD0E1594,0x7FF75370, +0xFDA4D929,0x7FFA72D1,0xFE3BA002,0x7FFCE093,0xFED2694F,0x7FFE9CB2,0xFF69343F, +0x7FFFA72C,}; + +const uint32_t arm_neon_rfft_factors_8192_q31[ARM_NEON_RFFT_FACTORS_8192_Q31_LEN]={ +6,1024,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_rfft_super_twiddles_neon_8192_q31[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_8192_Q31_LEN]={ +0xFFE6DE05,0x80000278,0xFFCDBC0B,0x800009DF,0xFFB49A12,0x80001635,0xFF9B781D, +0x8000277A,0xFF82562C,0x80003DAF,0xFF69343F,0x800058D4,0xFF501258,0x800078E7, +0xFF36F078,0x80009DEA,0xFF1DCEA0,0x8000C7DC,0xFF04ACD0,0x8000F6BD,0xFEEB8B0A, +0x80012A8E,0xFED2694F,0x8001634E,0xFEB947A0,0x8001A0FD,0xFEA025FD,0x8001E39B, +0xFE870467,0x80022B29,0xFE6DE2E0,0x800277A6,0xFE54C169,0x8002C912,0xFE3BA002, +0x80031F6D,0xFE227EAC,0x80037AB7,0xFE095D69,0x8003DAF1,0xFDF03C3A,0x8004401A, +0xFDD71B1E,0x8004AA32,0xFDBDFA18,0x80051939,0xFDA4D929,0x80058D2F,0xFD8BB850, +0x80060614,0xFD729790,0x800683E8,0xFD5976E9,0x800706AC,0xFD40565C,0x80078E5E, +0xFD2735EA,0x80081B00,0xFD0E1594,0x8008AC90,0xFCF4F55C,0x80094310,0xFCDBD541, +0x8009DE7E,0xFCC2B545,0x800A7EDB,0xFCA9956A,0x800B2427,0xFC9075AF,0x800BCE63, +0xFC775616,0x800C7D8C,0xFC5E36A0,0x800D31A5,0xFC45174E,0x800DEAAD,0xFC2BF821, +0x800EA8A3,0xFC12D91A,0x800F6B88,0xFBF9BA39,0x8010335C,0xFBE09B80,0x8011001F, +0xFBC77CF0,0x8011D1D0,0xFBAE5E89,0x8012A86F,0xFB95404D,0x801383FE,0xFB7C223D, +0x8014647B,0xFB630459,0x801549E6,0xFB49E6A3,0x80163440,0xFB30C91B,0x80172388, +0xFB17ABC2,0x801817BF,0xFAFE8E9B,0x801910E4,0xFAE571A4,0x801A0EF8,0xFACC54E0, +0x801B11FA,0xFAB3384F,0x801C19EA,0xFA9A1BF3,0x801D26C8,0xFA80FFCB,0x801E3895, +0xFA67E3DA,0x801F4F4F,0xFA4EC821,0x80206AF8,0xFA35AC9F,0x80218B8F,0xFA1C9157, +0x8022B114,0xFA037648,0x8023DB86,0xF9EA5B75,0x80250AE7,0xF9D140DE,0x80263F36, +0xF9B82684,0x80277872,0xF99F0C68,0x8028B69C,0xF985F28A,0x8029F9B4,0xF96CD8ED, +0x802B41BA,0xF953BF91,0x802C8EAD,0xF93AA676,0x802DE08E,0xF9218D9E,0x802F375D, +0xF908750A,0x80309318,0xF8EF5CBB,0x8031F3C2,0xF8D644B2,0x80335959,0xF8BD2CEF, +0x8034C3DD,0xF8A41574,0x8036334E,0xF88AFE42,0x8037A7AC,0xF871E759,0x803920F8, +0xF858D0BB,0x803A9F31,0xF83FBA68,0x803C2257,0xF826A462,0x803DAA6A,0xF80D8EA9, +0x803F376A,0xF7F4793E,0x8040C956,0xF7DB6423,0x80426030,0xF7C24F59,0x8043FBF6, +0xF7A93AE0,0x80459CA9,0xF79026B9,0x80474248,0xF77712E5,0x8048ECD5,0xF75DFF66, +0x804A9C4D,0xF744EC3B,0x804C50B2,0xF72BD967,0x804E0A04,0xF712C6EA,0x804FC841, +0xF6F9B4C6,0x80518B6B,0xF6E0A2FA,0x80535381,0xF6C79188,0x80552084,0xF6AE8071, +0x8056F272,0xF6956FB7,0x8058C94C,0xF67C5F59,0x805AA512,0xF6634F59,0x805C85C4, +0xF64A3FB8,0x805E6B62,0xF6313077,0x806055EB,0xF6182196,0x80624560,0xF5FF1318, +0x806439C0,0xF5E604FC,0x8066330C,0xF5CCF743,0x80683143,0xF5B3E9F0,0x806A3466, +0xF59ADD02,0x806C3C74,0xF581D07B,0x806E496C,0xF568C45B,0x80705B50,0xF54FB8A4, +0x8072721F,0xF536AD56,0x80748DD9,0xF51DA273,0x8076AE7E,0xF50497FB,0x8078D40D, +0xF4EB8DEF,0x807AFE87,0xF4D28451,0x807D2DEC,0xF4B97B21,0x807F623B,0xF4A07261, +0x80819B74,0xF4876A10,0x8083D998,0xF46E6231,0x80861CA6,0xF4555AC5,0x8088649E, +0xF43C53CB,0x808AB180,0xF4234D45,0x808D034C,0xF40A4735,0x808F5A02,0xF3F1419A, +0x8091B5A2,0xF3D83C77,0x8094162C,0xF3BF37CB,0x80967B9F,0xF3A63398,0x8098E5FB, +0xF38D2FE0,0x809B5541,0xF3742CA2,0x809DC971,0xF35B29E0,0x80A04289,0xF342279B, +0x80A2C08B,0xF32925D3,0x80A54376,0xF310248A,0x80A7CB49,0xF2F723C1,0x80AA5806, +0xF2DE2379,0x80ACE9AB,0xF2C523B2,0x80AF8039,0xF2AC246E,0x80B21BAF,0xF29325AD, +0x80B4BC0E,0xF27A2771,0x80B76156,0xF26129BA,0x80BA0B85,0xF2482C8A,0x80BCBA9D, +0xF22F2FE1,0x80BF6E9C,0xF21633C0,0x80C22784,0xF1FD3829,0x80C4E553,0xF1E43D1C, +0x80C7A80A,0xF1CB429A,0x80CA6FA9,0xF1B248A5,0x80CD3C2F,0xF1994F3D,0x80D00D9D, +0xF1805662,0x80D2E3F2,0xF1675E17,0x80D5BF2E,0xF14E665C,0x80D89F51,0xF1356F32, +0x80DB845B,0xF11C789A,0x80DE6E4C,0xF1038295,0x80E15D24,0xF0EA8D24,0x80E450E2, +0xF0D19848,0x80E74987,0xF0B8A401,0x80EA4712,0xF09FB051,0x80ED4984,0xF086BD39, +0x80F050DB,0xF06DCABA,0x80F35D19,0xF054D8D5,0x80F66E3C,0xF03BE78A,0x80F98446, +0xF022F6DA,0x80FC9F35,0xF00A06C8,0x80FFBF0A,0xEFF11753,0x8102E3C4,0xEFD8287C, +0x81060D63,0xEFBF3A45,0x81093BE8,0xEFA64CAE,0x810C6F52,0xEF8D5FB8,0x810FA7A0, +0xEF747365,0x8112E4D4,0xEF5B87B5,0x811626EC,0xEF429CAA,0x81196DE9,0xEF29B243, +0x811CB9CA,0xEF10C883,0x81200A90,0xEEF7DF6A,0x8123603A,0xEEDEF6F9,0x8126BAC8, +0xEEC60F31,0x812A1A3A,0xEEAD2813,0x812D7E8F,0xEE9441A0,0x8130E7C9,0xEE7B5BD9, +0x813455E6,0xEE6276BF,0x8137C8E6,0xEE499253,0x813B40CA,0xEE30AE96,0x813EBD90, +0xEE17CB88,0x81423F3A,0xEDFEE92B,0x8145C5C7,0xEDE60780,0x81495136,0xEDCD2687, +0x814CE188,0xEDB44642,0x815076BD,0xED9B66B2,0x815410D4,0xED8287D7,0x8157AFCD, +0xED69A9B3,0x815B53A8,0xED50CC46,0x815EFC65,0xED37EF91,0x8162AA04,0xED1F1396, +0x81665C84,0xED063856,0x816A13E6,0xECED5DD0,0x816DD02A,0xECD48407,0x8171914E, +0xECBBAAFB,0x81755754,0xECA2D2AD,0x8179223A,0xEC89FB1E,0x817CF201,0xEC71244F, +0x8180C6A9,0xEC584E41,0x8184A032,0xEC3F78F6,0x81887E9A,0xEC26A46D,0x818C61E3, +0xEC0DD0A8,0x81904A0C,0xEBF4FDA8,0x81943715,0xEBDC2B6E,0x819828FD,0xEBC359FB, +0x819C1FC5,0xEBAA894F,0x81A01B6D,0xEB91B96C,0x81A41BF4,0xEB78EA52,0x81A82159, +0xEB601C04,0x81AC2B9E,0xEB474E81,0x81B03AC2,0xEB2E81CA,0x81B44EC4,0xEB15B5E1, +0x81B867A5,0xEAFCEAC6,0x81BC8564,0xEAE4207A,0x81C0A801,0xEACB56FF,0x81C4CF7D, +0xEAB28E56,0x81C8FBD6,0xEA99C67E,0x81CD2D0C,0xEA80FF7A,0x81D16321,0xEA683949, +0x81D59E13,0xEA4F73EE,0x81D9DDE1,0xEA36AF69,0x81DE228D,0xEA1DEBBB,0x81E26C16, +0xEA0528E5,0x81E6BA7C,0xE9EC66E8,0x81EB0DBE,0xE9D3A5C5,0x81EF65DC,0xE9BAE57D, +0x81F3C2D7,0xE9A22610,0x81F824AE,0xE9896781,0x81FC8B60,0xE970A9CE,0x8200F6EF, +0xE957ECFB,0x82056758,0xE93F3107,0x8209DC9E,0xE92675F4,0x820E56BE,0xE90DBBC2, +0x8212D5B9,0xE8F50273,0x82175990,0xE8DC4A07,0x821BE240,0xE8C39280,0x82206FCC, +0xE8AADBDE,0x82250232,0xE8922622,0x82299971,0xE879714D,0x822E358B,0xE860BD61, +0x8232D67F,0xE8480A5D,0x82377C4C,0xE82F5844,0x823C26F3,0xE816A716,0x8240D673, +0xE7FDF6D4,0x82458ACC,0xE7E5477F,0x824A43FE,0xE7CC9917,0x824F0208,0xE7B3EB9F, +0x8253C4EB,0xE79B3F16,0x82588CA7,0xE782937E,0x825D593A,0xE769E8D8,0x82622AA6, +0xE7513F25,0x826700E9,0xE7389665,0x826BDC04,0xE71FEE99,0x8270BBF7,0xE70747C4, +0x8275A0C0,0xE6EEA1E4,0x827A8A61,0xE6D5FCFC,0x827F78D8,0xE6BD590D,0x82846C26, +0xE6A4B616,0x8289644B,0xE68C141A,0x828E6146,0xE6737319,0x82936317,0xE65AD315, +0x829869BE,0xE642340D,0x829D753A,0xE6299604,0x82A2858C,0xE610F8F9,0x82A79AB3, +0xE5F85CEF,0x82ACB4B0,0xE5DFC1E5,0x82B1D381,0xE5C727DD,0x82B6F727,0xE5AE8ED8, +0x82BC1FA2,0xE595F6D7,0x82C14CF1,0xE57D5FDA,0x82C67F14,0xE564C9E3,0x82CBB60B, +0xE54C34F3,0x82D0F1D5,0xE533A10A,0x82D63274,0xE51B0E2A,0x82DB77E5,0xE5027C53, +0x82E0C22A,0xE4E9EB87,0x82E61141,0xE4D15BC6,0x82EB652B,0xE4B8CD11,0x82F0BDE8, +0xE4A03F69,0x82F61B77,0xE487B2D0,0x82FB7DD8,0xE46F2745,0x8300E50B,0xE4569CCB, +0x83065110,0xE43E1362,0x830BC1E6,0xE4258B0A,0x8311378D,0xE40D03C6,0x8316B205, +0xE3F47D96,0x831C314E,0xE3DBF87A,0x8321B568,0xE3C37474,0x83273E52,0xE3AAF184, +0x832CCC0D,0xE3926FAD,0x83325E97,0xE379EEED,0x8337F5F1,0xE3616F48,0x833D921B, +0xE348F0BD,0x83433314,0xE330734D,0x8348D8DC,0xE317F6FA,0x834E8373,0xE2FF7BC3, +0x835432D8,0xE2E701AC,0x8359E70D,0xE2CE88B3,0x835FA00F,0xE2B610DA,0x83655DDF, +0xE29D9A23,0x836B207D,0xE285248D,0x8370E7E9,0xE26CB01B,0x8376B422,0xE2543CCC, +0x837C8528,0xE23BCAA2,0x83825AFB,0xE223599E,0x8388359B,0xE20AE9C1,0x838E1507, +0xE1F27B0B,0x8393F940,0xE1DA0D7E,0x8399E244,0xE1C1A11B,0x839FD014,0xE1A935E2, +0x83A5C2B0,0xE190CBD4,0x83ABBA17,0xE17862F3,0x83B1B649,0xE15FFB3F,0x83B7B746, +0xE14794BA,0x83BDBD0E,0xE12F2F63,0x83C3C7A0,0xE116CB3D,0x83C9D6FC,0xE0FE6848, +0x83CFEB22,0xE0E60685,0x83D60412,0xE0CDA5F5,0x83DC21CB,0xE0B54698,0x83E2444D, +0xE09CE871,0x83E86B99,0xE0848B7F,0x83EE97AD,0xE06C2FC4,0x83F4C889,0xE053D541, +0x83FAFE2E,0xE03B7BF6,0x8401389B,0xE02323E5,0x840777D0,0xE00ACD0E,0x840DBBCC, +0xDFF27773,0x84140490,0xDFDA2314,0x841A521A,0xDFC1CFF3,0x8420A46C,0xDFA97E0F, +0x8426FB84,0xDF912D6B,0x842D5762,0xDF78DE07,0x8433B806,0xDF608FE4,0x843A1D70, +0xDF484302,0x844087A0,0xDF2FF764,0x8446F695,0xDF17AD0A,0x844D6A50,0xDEFF63F4, +0x8453E2CF,0xDEE71C24,0x845A6012,0xDECED59B,0x8460E21A,0xDEB69059,0x846768E7, +0xDE9E4C60,0x846DF477,0xDE8609B1,0x847484CA,0xDE6DC84B,0x847B19E1,0xDE558831, +0x8481B3BB,0xDE3D4964,0x84885258,0xDE250BE3,0x848EF5B7,0xDE0CCFB1,0x84959DD9, +0xDDF494CE,0x849C4ABD,0xDDDC5B3B,0x84A2FC62,0xDDC422F8,0x84A9B2CA,0xDDABEC08, +0x84B06DF2,0xDD93B66A,0x84B72DDB,0xDD7B8220,0x84BDF286,0xDD634F2B,0x84C4BBF0, +0xDD4B1D8C,0x84CB8A1B,0xDD32ED43,0x84D25D06,0xDD1ABE51,0x84D934B1,0xDD0290B8, +0x84E0111B,0xDCEA6478,0x84E6F244,0xDCD23993,0x84EDD82D,0xDCBA1008,0x84F4C2D4, +0xDCA1E7DA,0x84FBB239,0xDC89C109,0x8502A65C,0xDC719B96,0x85099F3E,0xDC597781, +0x85109CDD,0xDC4154CD,0x85179F39,0xDC293379,0x851EA652,0xDC111388,0x8525B228, +0xDBF8F4F8,0x852CC2BB,0xDBE0D7CD,0x8533D809,0xDBC8BC06,0x853AF214,0xDBB0A1A4, +0x854210DB,0xDB9888A8,0x8549345C,0xDB807114,0x85505C99,0xDB685AE9,0x85578991, +0xDB504626,0x855EBB44,0xDB3832CD,0x8565F1B0,0xDB2020E0,0x856D2CD7,0xDB08105E, +0x85746CB8,0xDAF00149,0x857BB152,0xDAD7F3A2,0x8582FAA5,0xDABFE76A,0x858A48B1, +0xDAA7DCA1,0x85919B76,0xDA8FD349,0x8598F2F3,0xDA77CB63,0x85A04F28,0xDA5FC4EF, 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+0xE15FFB3F,0x83B1B649,0xE17862F3,0x83ABBA17,0xE190CBD4,0x83A5C2B0,0xE1A935E2, +0x839FD014,0xE1C1A11B,0x8399E244,0xE1DA0D7E,0x8393F940,0xE1F27B0B,0x838E1507, +0xE20AE9C1,0x8388359B,0xE223599E,0x83825AFB,0xE23BCAA2,0x837C8528,0xE2543CCC, +0x8376B422,0xE26CB01B,0x8370E7E9,0xE285248D,0x836B207D,0xE29D9A23,0x83655DDF, +0xE2B610DA,0x835FA00F,0xE2CE88B3,0x8359E70D,0xE2E701AC,0x835432D8,0xE2FF7BC3, +0x834E8373,0xE317F6FA,0x8348D8DC,0xE330734D,0x83433314,0xE348F0BD,0x833D921B, +0xE3616F48,0x8337F5F1,0xE379EEED,0x83325E97,0xE3926FAD,0x832CCC0D,0xE3AAF184, +0x83273E52,0xE3C37474,0x8321B568,0xE3DBF87A,0x831C314E,0xE3F47D96,0x8316B205, +0xE40D03C6,0x8311378D,0xE4258B0A,0x830BC1E6,0xE43E1362,0x83065110,0xE4569CCB, +0x8300E50B,0xE46F2745,0x82FB7DD8,0xE487B2D0,0x82F61B77,0xE4A03F69,0x82F0BDE8, +0xE4B8CD11,0x82EB652B,0xE4D15BC6,0x82E61141,0xE4E9EB87,0x82E0C22A,0xE5027C53, +0x82DB77E5,0xE51B0E2A,0x82D63274,0xE533A10A,0x82D0F1D5,0xE54C34F3,0x82CBB60B, +0xE564C9E3,0x82C67F14,0xE57D5FDA,0x82C14CF1,0xE595F6D7,0x82BC1FA2,0xE5AE8ED8, +0x82B6F727,0xE5C727DD,0x82B1D381,0xE5DFC1E5,0x82ACB4B0,0xE5F85CEF,0x82A79AB3, +0xE610F8F9,0x82A2858C,0xE6299604,0x829D753A,0xE642340D,0x829869BE,0xE65AD315, +0x82936317,0xE6737319,0x828E6146,0xE68C141A,0x8289644B,0xE6A4B616,0x82846C26, +0xE6BD590D,0x827F78D8,0xE6D5FCFC,0x827A8A61,0xE6EEA1E4,0x8275A0C0,0xE70747C4, +0x8270BBF7,0xE71FEE99,0x826BDC04,0xE7389665,0x826700E9,0xE7513F25,0x82622AA6, +0xE769E8D8,0x825D593A,0xE782937E,0x82588CA7,0xE79B3F16,0x8253C4EB,0xE7B3EB9F, +0x824F0208,0xE7CC9917,0x824A43FE,0xE7E5477F,0x82458ACC,0xE7FDF6D4,0x8240D673, +0xE816A716,0x823C26F3,0xE82F5844,0x82377C4C,0xE8480A5D,0x8232D67F,0xE860BD61, +0x822E358B,0xE879714D,0x82299971,0xE8922622,0x82250232,0xE8AADBDE,0x82206FCC, +0xE8C39280,0x821BE240,0xE8DC4A07,0x82175990,0xE8F50273,0x8212D5B9,0xE90DBBC2, +0x820E56BE,0xE92675F4,0x8209DC9E,0xE93F3107,0x82056758,0xE957ECFB,0x8200F6EF, +0xE970A9CE,0x81FC8B60,0xE9896781,0x81F824AE,0xE9A22610,0x81F3C2D7,0xE9BAE57D, +0x81EF65DC,0xE9D3A5C5,0x81EB0DBE,0xE9EC66E8,0x81E6BA7C,0xEA0528E5,0x81E26C16, +0xEA1DEBBB,0x81DE228D,0xEA36AF69,0x81D9DDE1,0xEA4F73EE,0x81D59E13,0xEA683949, +0x81D16321,0xEA80FF7A,0x81CD2D0C,0xEA99C67E,0x81C8FBD6,0xEAB28E56,0x81C4CF7D, +0xEACB56FF,0x81C0A801,0xEAE4207A,0x81BC8564,0xEAFCEAC6,0x81B867A5,0xEB15B5E1, +0x81B44EC4,0xEB2E81CA,0x81B03AC2,0xEB474E81,0x81AC2B9E,0xEB601C04,0x81A82159, +0xEB78EA52,0x81A41BF4,0xEB91B96C,0x81A01B6D,0xEBAA894F,0x819C1FC5,0xEBC359FB, +0x819828FD,0xEBDC2B6E,0x81943715,0xEBF4FDA8,0x81904A0C,0xEC0DD0A8,0x818C61E3, +0xEC26A46D,0x81887E9A,0xEC3F78F6,0x8184A032,0xEC584E41,0x8180C6A9,0xEC71244F, +0x817CF201,0xEC89FB1E,0x8179223A,0xECA2D2AD,0x81755754,0xECBBAAFB,0x8171914E, +0xECD48407,0x816DD02A,0xECED5DD0,0x816A13E6,0xED063856,0x81665C84,0xED1F1396, +0x8162AA04,0xED37EF91,0x815EFC65,0xED50CC46,0x815B53A8,0xED69A9B3,0x8157AFCD, +0xED8287D7,0x815410D4,0xED9B66B2,0x815076BD,0xEDB44642,0x814CE188,0xEDCD2687, +0x81495136,0xEDE60780,0x8145C5C7,0xEDFEE92B,0x81423F3A,0xEE17CB88,0x813EBD90, +0xEE30AE96,0x813B40CA,0xEE499253,0x8137C8E6,0xEE6276BF,0x813455E6,0xEE7B5BD9, +0x8130E7C9,0xEE9441A0,0x812D7E8F,0xEEAD2813,0x812A1A3A,0xEEC60F31,0x8126BAC8, +0xEEDEF6F9,0x8123603A,0xEEF7DF6A,0x81200A90,0xEF10C883,0x811CB9CA,0xEF29B243, +0x81196DE9,0xEF429CAA,0x811626EC,0xEF5B87B5,0x8112E4D4,0xEF747365,0x810FA7A0, +0xEF8D5FB8,0x810C6F52,0xEFA64CAE,0x81093BE8,0xEFBF3A45,0x81060D63,0xEFD8287C, +0x8102E3C4,0xEFF11753,0x80FFBF0A,0xF00A06C8,0x80FC9F35,0xF022F6DA,0x80F98446, +0xF03BE78A,0x80F66E3C,0xF054D8D5,0x80F35D19,0xF06DCABA,0x80F050DB,0xF086BD39, +0x80ED4984,0xF09FB051,0x80EA4712,0xF0B8A401,0x80E74987,0xF0D19848,0x80E450E2, +0xF0EA8D24,0x80E15D24,0xF1038295,0x80DE6E4C,0xF11C789A,0x80DB845B,0xF1356F32, +0x80D89F51,0xF14E665C,0x80D5BF2E,0xF1675E17,0x80D2E3F2,0xF1805662,0x80D00D9D, +0xF1994F3D,0x80CD3C2F,0xF1B248A5,0x80CA6FA9,0xF1CB429A,0x80C7A80A,0xF1E43D1C, +0x80C4E553,0xF1FD3829,0x80C22784,0xF21633C0,0x80BF6E9C,0xF22F2FE1,0x80BCBA9D, +0xF2482C8A,0x80BA0B85,0xF26129BA,0x80B76156,0xF27A2771,0x80B4BC0E,0xF29325AD, +0x80B21BAF,0xF2AC246E,0x80AF8039,0xF2C523B2,0x80ACE9AB,0xF2DE2379,0x80AA5806, +0xF2F723C1,0x80A7CB49,0xF310248A,0x80A54376,0xF32925D3,0x80A2C08B,0xF342279B, +0x80A04289,0xF35B29E0,0x809DC971,0xF3742CA2,0x809B5541,0xF38D2FE0,0x8098E5FB, +0xF3A63398,0x80967B9F,0xF3BF37CB,0x8094162C,0xF3D83C77,0x8091B5A2,0xF3F1419A, +0x808F5A02,0xF40A4735,0x808D034C,0xF4234D45,0x808AB180,0xF43C53CB,0x8088649E, +0xF4555AC5,0x80861CA6,0xF46E6231,0x8083D998,0xF4876A10,0x80819B74,0xF4A07261, +0x807F623B,0xF4B97B21,0x807D2DEC,0xF4D28451,0x807AFE87,0xF4EB8DEF,0x8078D40D, +0xF50497FB,0x8076AE7E,0xF51DA273,0x80748DD9,0xF536AD56,0x8072721F,0xF54FB8A4, +0x80705B50,0xF568C45B,0x806E496C,0xF581D07B,0x806C3C74,0xF59ADD02,0x806A3466, +0xF5B3E9F0,0x80683143,0xF5CCF743,0x8066330C,0xF5E604FC,0x806439C0,0xF5FF1318, +0x80624560,0xF6182196,0x806055EB,0xF6313077,0x805E6B62,0xF64A3FB8,0x805C85C4, +0xF6634F59,0x805AA512,0xF67C5F59,0x8058C94C,0xF6956FB7,0x8056F272,0xF6AE8071, +0x80552084,0xF6C79188,0x80535381,0xF6E0A2FA,0x80518B6B,0xF6F9B4C6,0x804FC841, +0xF712C6EA,0x804E0A04,0xF72BD967,0x804C50B2,0xF744EC3B,0x804A9C4D,0xF75DFF66, +0x8048ECD5,0xF77712E5,0x80474248,0xF79026B9,0x80459CA9,0xF7A93AE0,0x8043FBF6, +0xF7C24F59,0x80426030,0xF7DB6423,0x8040C956,0xF7F4793E,0x803F376A,0xF80D8EA9, +0x803DAA6A,0xF826A462,0x803C2257,0xF83FBA68,0x803A9F31,0xF858D0BB,0x803920F8, +0xF871E759,0x8037A7AC,0xF88AFE42,0x8036334E,0xF8A41574,0x8034C3DD,0xF8BD2CEF, +0x80335959,0xF8D644B2,0x8031F3C2,0xF8EF5CBB,0x80309318,0xF908750A,0x802F375D, +0xF9218D9E,0x802DE08E,0xF93AA676,0x802C8EAD,0xF953BF91,0x802B41BA,0xF96CD8ED, +0x8029F9B4,0xF985F28A,0x8028B69C,0xF99F0C68,0x80277872,0xF9B82684,0x80263F36, +0xF9D140DE,0x80250AE7,0xF9EA5B75,0x8023DB86,0xFA037648,0x8022B114,0xFA1C9157, +0x80218B8F,0xFA35AC9F,0x80206AF8,0xFA4EC821,0x801F4F4F,0xFA67E3DA,0x801E3895, +0xFA80FFCB,0x801D26C8,0xFA9A1BF3,0x801C19EA,0xFAB3384F,0x801B11FA,0xFACC54E0, +0x801A0EF8,0xFAE571A4,0x801910E4,0xFAFE8E9B,0x801817BF,0xFB17ABC2,0x80172388, +0xFB30C91B,0x80163440,0xFB49E6A3,0x801549E6,0xFB630459,0x8014647B,0xFB7C223D, +0x801383FE,0xFB95404D,0x8012A86F,0xFBAE5E89,0x8011D1D0,0xFBC77CF0,0x8011001F, +0xFBE09B80,0x8010335C,0xFBF9BA39,0x800F6B88,0xFC12D91A,0x800EA8A3,0xFC2BF821, +0x800DEAAD,0xFC45174E,0x800D31A5,0xFC5E36A0,0x800C7D8C,0xFC775616,0x800BCE63, +0xFC9075AF,0x800B2427,0xFCA9956A,0x800A7EDB,0xFCC2B545,0x8009DE7E,0xFCDBD541, +0x80094310,0xFCF4F55C,0x8008AC90,0xFD0E1594,0x80081B00,0xFD2735EA,0x80078E5E, +0xFD40565C,0x800706AC,0xFD5976E9,0x800683E8,0xFD729790,0x80060614,0xFD8BB850, +0x80058D2F,0xFDA4D929,0x80051939,0xFDBDFA18,0x8004AA32,0xFDD71B1E,0x8004401A, +0xFDF03C3A,0x8003DAF1,0xFE095D69,0x80037AB7,0xFE227EAC,0x80031F6D,0xFE3BA002, +0x8002C912,0xFE54C169,0x800277A6,0xFE6DE2E0,0x80022B29,0xFE870467,0x8001E39B, +0xFEA025FD,0x8001A0FD,0xFEB947A0,0x8001634E,0xFED2694F,0x80012A8E,0xFEEB8B0A, +0x8000F6BD,0xFF04ACD0,0x8000C7DC,0xFF1DCEA0,0x80009DEA,0xFF36F078,0x800078E7, +0xFF501258,0x800058D4,0xFF69343F,0x80003DAF,0xFF82562C,0x8000277A,0xFF9B781D, +0x80001635,0xFFB49A12,0x800009DF,0xFFCDBC0B,0x80000278,0xFFE6DE05,0x80000000, +0x00000000,}; + +const q15_t *arm_neon_rfft_twiddles_16_q15=NULL; + +const uint32_t arm_neon_rfft_factors_16_q15[ARM_NEON_RFFT_FACTORS_16_Q15_LEN]={ +1,1,8,1,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_16_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_Q15_LEN]={ +0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_32_q15[ARM_NEON_RFFT_TWIDDLES_32_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,}; + +const uint32_t arm_neon_rfft_factors_32_q15[ARM_NEON_RFFT_FACTORS_32_Q15_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_32_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_Q15_LEN]={ +0xE707,0x8276,0xCF04,0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE, +0xCF04,0x8276,0xE707,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_64_q15[ARM_NEON_RFFT_TWIDDLES_64_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,}; + +const uint32_t arm_neon_rfft_factors_64_q15[ARM_NEON_RFFT_FACTORS_64_Q15_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_64_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_Q15_LEN]={ +0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE,0xC3A9,0x8F1D,0xB8E3, +0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592,0xB8E3,0x8F1D,0xC3A9, +0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_128_q15[ARM_NEON_RFFT_TWIDDLES_128_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,}; + +const uint32_t arm_neon_rfft_factors_128_q15[ARM_NEON_RFFT_FACTORS_128_Q15_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_128_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_Q15_LEN]={ +0xF9B8,0x8027,0xF374,0x809E,0xED38,0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8, +0x8583,0xD4E1,0x877B,0xCF04,0x89BE,0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236, +0xB8E3,0x9592,0xB3C0,0x9930,0xAECC,0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129, +0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0,0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9, +0x8C4A,0xC946,0x89BE,0xCF04,0x877B,0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276, +0xE707,0x8163,0xED38,0x809E,0xF374,0x8027,0xF9B8,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_256_q15[ARM_NEON_RFFT_TWIDDLES_256_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D, +0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04, +0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2, +0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930, +0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F, +0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E, +0x0648,0x8027,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x0000,0x8000,0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE, +0xC3A9,0x8F1D,0xB8E3,0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592, +0xB8E3,0x8F1D,0xC3A9,0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374, +0x7FFF,0x0000,0x7E9D,0xED38,0x7A7D,0xDAD8,0x73B6,0xC946,0x6A6E,0xB8E3,0x5ED7, +0xAA0A,0x5134,0x9D0E,0x41CE,0x9236,0x30FC,0x89BE,0x1F1A,0x83D6,0x0C8C,0x809E, +0xF9B8,0x8027,0xE707,0x8276,0xD4E1,0x877B,0xC3A9,0x8F1D,0xB3C0,0x9930,0xA57E, +0xA57E,0x9930,0xB3C0,0x8F1D,0xC3A9,0x877B,0xD4E1,0x8276,0xE707,0x8027,0xF9B8, +0x809E,0x0C8C,0x83D6,0x1F1A,0x89BE,0x30FC,0x9236,0x41CE,0x9D0E,0x5134,0xAA0A, +0x5ED7,0xB8E3,0x6A6E,0xC946,0x73B6,0xDAD8,0x7A7D,0xED38,0x7E9D,}; + +const uint32_t arm_neon_rfft_factors_256_q15[ARM_NEON_RFFT_FACTORS_256_Q15_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_256_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_Q15_LEN]={ +0xFCDC,0x800A,0xF9B8,0x8027,0xF695,0x8059,0xF374,0x809E,0xF055,0x80F6,0xED38, +0x8163,0xEA1E,0x81E2,0xE707,0x8276,0xE3F4,0x831C,0xE0E6,0x83D6,0xDDDC,0x84A3, +0xDAD8,0x8583,0xD7D9,0x8676,0xD4E1,0x877B,0xD1EF,0x8894,0xCF04,0x89BE,0xCC21, +0x8AFB,0xC946,0x8C4A,0xC673,0x8DAB,0xC3A9,0x8F1D,0xC0E9,0x90A1,0xBE32,0x9236, +0xBB85,0x93DC,0xB8E3,0x9592,0xB64C,0x9759,0xB3C0,0x9930,0xB140,0x9B17,0xAECC, +0x9D0E,0xAC65,0x9F14,0xAA0A,0xA129,0xA7BD,0xA34C,0xA57E,0xA57E,0xA34C,0xA7BD, +0xA129,0xAA0A,0x9F14,0xAC65,0x9D0E,0xAECC,0x9B17,0xB140,0x9930,0xB3C0,0x9759, +0xB64C,0x9592,0xB8E3,0x93DC,0xBB85,0x9236,0xBE32,0x90A1,0xC0E9,0x8F1D,0xC3A9, +0x8DAB,0xC673,0x8C4A,0xC946,0x8AFB,0xCC21,0x89BE,0xCF04,0x8894,0xD1EF,0x877B, +0xD4E1,0x8676,0xD7D9,0x8583,0xDAD8,0x84A3,0xDDDC,0x83D6,0xE0E6,0x831C,0xE3F4, +0x8276,0xE707,0x81E2,0xEA1E,0x8163,0xED38,0x80F6,0xF055,0x809E,0xF374,0x8059, +0xF695,0x8027,0xF9B8,0x800A,0xFCDC,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_512_q15[ARM_NEON_RFFT_TWIDDLES_512_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055, +0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D, +0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04, +0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA, +0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140, +0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843, +0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930, +0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57, +0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894, +0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C, +0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E, +0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D, +0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140, +0x5ED7,0xAA0A,0x5843,0xA34C,0x5134,0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D, +0x8DAB,0x30FC,0x89BE,0x2827,0x8676,0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E, +0x0324,0x800A,0xF9B8,0x8027,0xF055,0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1, +0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14, +0xA57E,0xA57E,0x9F14,0xAC65,0x9930,0xB3C0,0x93DC,0xBB85,0x8F1D,0xC3A9,0x8AFB, +0xCC21,0x877B,0xD4E1,0x84A3,0xDDDC,0x8276,0xE707,0x80F6,0xF055,0x8027,0xF9B8, +0x800A,0x0324,0x809E,0x0C8C,0x81E2,0x15E2,0x83D6,0x1F1A,0x8676,0x2827,0x89BE, +0x30FC,0x8DAB,0x398D,0x9236,0x41CE,0x9759,0x49B4,0x9D0E,0x5134,0xA34C,0x5843, +0xAA0A,0x5ED7,0xB140,0x64E9,0xB8E3,0x6A6E,0xC0E9,0x6F5F,0xC946,0x73B6,0xD1EF, +0x776C,0xDAD8,0x7A7D,0xE3F4,0x7CE4,0xED38,0x7E9D,0xF695,0x7FA7,}; + +const uint32_t arm_neon_rfft_factors_512_q15[ARM_NEON_RFFT_FACTORS_512_Q15_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_512_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_Q15_LEN]={ +0xFE6E,0x8002,0xFCDC,0x800A,0xFB4A,0x8016,0xF9B8,0x8027,0xF827,0x803E,0xF695, +0x8059,0xF505,0x8079,0xF374,0x809E,0xF1E4,0x80C8,0xF055,0x80F6,0xEEC6,0x812A, +0xED38,0x8163,0xEBAB,0x81A0,0xEA1E,0x81E2,0xE892,0x822A,0xE707,0x8276,0xE57D, +0x82C6,0xE3F4,0x831C,0xE26D,0x8377,0xE0E6,0x83D6,0xDF61,0x843A,0xDDDC,0x84A3, +0xDC59,0x8511,0xDAD8,0x8583,0xD958,0x85FA,0xD7D9,0x8676,0xD65C,0x86F6,0xD4E1, +0x877B,0xD367,0x8805,0xD1EF,0x8894,0xD079,0x8927,0xCF04,0x89BE,0xCD92,0x8A5A, +0xCC21,0x8AFB,0xCAB2,0x8BA0,0xC946,0x8C4A,0xC7DB,0x8CF8,0xC673,0x8DAB,0xC50D, +0x8E62,0xC3A9,0x8F1D,0xC248,0x8FDD,0xC0E9,0x90A1,0xBF8C,0x9169,0xBE32,0x9236, +0xBCDA,0x9307,0xBB85,0x93DC,0xBA33,0x94B5,0xB8E3,0x9592,0xB796,0x9674,0xB64C, +0x9759,0xB505,0x9843,0xB3C0,0x9930,0xB27F,0x9A22,0xB140,0x9B17,0xB005,0x9C11, +0xAECC,0x9D0E,0xAD97,0x9E0F,0xAC65,0x9F14,0xAB36,0xA01C,0xAA0A,0xA129,0xA8E2, +0xA238,0xA7BD,0xA34C,0xA69C,0xA463,0xA57E,0xA57E,0xA463,0xA69C,0xA34C,0xA7BD, +0xA238,0xA8E2,0xA129,0xAA0A,0xA01C,0xAB36,0x9F14,0xAC65,0x9E0F,0xAD97,0x9D0E, +0xAECC,0x9C11,0xB005,0x9B17,0xB140,0x9A22,0xB27F,0x9930,0xB3C0,0x9843,0xB505, +0x9759,0xB64C,0x9674,0xB796,0x9592,0xB8E3,0x94B5,0xBA33,0x93DC,0xBB85,0x9307, +0xBCDA,0x9236,0xBE32,0x9169,0xBF8C,0x90A1,0xC0E9,0x8FDD,0xC248,0x8F1D,0xC3A9, +0x8E62,0xC50D,0x8DAB,0xC673,0x8CF8,0xC7DB,0x8C4A,0xC946,0x8BA0,0xCAB2,0x8AFB, +0xCC21,0x8A5A,0xCD92,0x89BE,0xCF04,0x8927,0xD079,0x8894,0xD1EF,0x8805,0xD367, +0x877B,0xD4E1,0x86F6,0xD65C,0x8676,0xD7D9,0x85FA,0xD958,0x8583,0xDAD8,0x8511, +0xDC59,0x84A3,0xDDDC,0x843A,0xDF61,0x83D6,0xE0E6,0x8377,0xE26D,0x831C,0xE3F4, +0x82C6,0xE57D,0x8276,0xE707,0x822A,0xE892,0x81E2,0xEA1E,0x81A0,0xEBAB,0x8163, +0xED38,0x812A,0xEEC6,0x80F6,0xF055,0x80C8,0xF1E4,0x809E,0xF374,0x8079,0xF505, +0x8059,0xF695,0x803E,0xF827,0x8027,0xF9B8,0x8016,0xFB4A,0x800A,0xFCDC,0x8002, +0xFE6E,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_1024_q15[ARM_NEON_RFFT_TWIDDLES_1024_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D, +0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04, +0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2, +0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930, +0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F, +0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E, +0x0648,0x8027,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x0000,0x8000,0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE, +0xC3A9,0x8F1D,0xB8E3,0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592, +0xB8E3,0x8F1D,0xC3A9,0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374, +0x7FFF,0x0000,0x7E9D,0xED38,0x7A7D,0xDAD8,0x73B6,0xC946,0x6A6E,0xB8E3,0x5ED7, +0xAA0A,0x5134,0x9D0E,0x41CE,0x9236,0x30FC,0x89BE,0x1F1A,0x83D6,0x0C8C,0x809E, +0xF9B8,0x8027,0xE707,0x8276,0xD4E1,0x877B,0xC3A9,0x8F1D,0xB3C0,0x9930,0xA57E, +0xA57E,0x9930,0xB3C0,0x8F1D,0xC3A9,0x877B,0xD4E1,0x8276,0xE707,0x8027,0xF9B8, +0x809E,0x0C8C,0x83D6,0x1F1A,0x89BE,0x30FC,0x9236,0x41CE,0x9D0E,0x5134,0xAA0A, +0x5ED7,0xB8E3,0x6A6E,0xC946,0x73B6,0xDAD8,0x7A7D,0xED38,0x7E9D,0x7FFF,0x0000, +0x7FFE,0xFE6E,0x7FF6,0xFCDC,0x7FEA,0xFB4A,0x7FD9,0xF9B8,0x7FC2,0xF827,0x7FA7, +0xF695,0x7F87,0xF505,0x7F62,0xF374,0x7F38,0xF1E4,0x7F0A,0xF055,0x7ED6,0xEEC6, +0x7E9D,0xED38,0x7E60,0xEBAB,0x7E1E,0xEA1E,0x7DD6,0xE892,0x7D8A,0xE707,0x7D3A, +0xE57D,0x7CE4,0xE3F4,0x7C89,0xE26D,0x7C2A,0xE0E6,0x7BC6,0xDF61,0x7B5D,0xDDDC, +0x7AEF,0xDC59,0x7A7D,0xDAD8,0x7A06,0xD958,0x798A,0xD7D9,0x790A,0xD65C,0x7885, +0xD4E1,0x77FB,0xD367,0x776C,0xD1EF,0x76D9,0xD079,0x7642,0xCF04,0x75A6,0xCD92, +0x7505,0xCC21,0x7460,0xCAB2,0x73B6,0xC946,0x7308,0xC7DB,0x7255,0xC673,0x719E, +0xC50D,0x70E3,0xC3A9,0x7023,0xC248,0x6F5F,0xC0E9,0x6E97,0xBF8C,0x6DCA,0xBE32, +0x6CF9,0xBCDA,0x6C24,0xBB85,0x6B4B,0xBA33,0x6A6E,0xB8E3,0x698C,0xB796,0x68A7, +0xB64C,0x67BD,0xB505,0x66D0,0xB3C0,0x65DE,0xB27F,0x64E9,0xB140,0x63EF,0xB005, +0x62F2,0xAECC,0x61F1,0xAD97,0x60EC,0xAC65,0x5FE4,0xAB36,0x5ED7,0xAA0A,0x5DC8, +0xA8E2,0x5CB4,0xA7BD,0x5B9D,0xA69C,0x5A82,0xA57E,0x5964,0xA463,0x5843,0xA34C, +0x571E,0xA238,0x55F6,0xA129,0x54CA,0xA01C,0x539B,0x9F14,0x5269,0x9E0F,0x5134, +0x9D0E,0x4FFB,0x9C11,0x4EC0,0x9B17,0x4D81,0x9A22,0x4C40,0x9930,0x4AFB,0x9843, +0x49B4,0x9759,0x486A,0x9674,0x471D,0x9592,0x45CD,0x94B5,0x447B,0x93DC,0x4326, +0x9307,0x41CE,0x9236,0x4074,0x9169,0x3F17,0x90A1,0x3DB8,0x8FDD,0x3C57,0x8F1D, +0x3AF3,0x8E62,0x398D,0x8DAB,0x3825,0x8CF8,0x36BA,0x8C4A,0x354E,0x8BA0,0x33DF, +0x8AFB,0x326E,0x8A5A,0x30FC,0x89BE,0x2F87,0x8927,0x2E11,0x8894,0x2C99,0x8805, +0x2B1F,0x877B,0x29A4,0x86F6,0x2827,0x8676,0x26A8,0x85FA,0x2528,0x8583,0x23A7, +0x8511,0x2224,0x84A3,0x209F,0x843A,0x1F1A,0x83D6,0x1D93,0x8377,0x1C0C,0x831C, +0x1A83,0x82C6,0x18F9,0x8276,0x176E,0x822A,0x15E2,0x81E2,0x1455,0x81A0,0x12C8, +0x8163,0x113A,0x812A,0x0FAB,0x80F6,0x0E1C,0x80C8,0x0C8C,0x809E,0x0AFB,0x8079, +0x096B,0x8059,0x07D9,0x803E,0x0648,0x8027,0x04B6,0x8016,0x0324,0x800A,0x0192, +0x8002,0x7FFF,0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374, +0x7F0A,0xF055,0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A, +0xE0E6,0x7B5D,0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF, +0x7642,0xCF04,0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F, +0xC0E9,0x6DCA,0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0, +0x64E9,0xB140,0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82, +0xA57E,0x5843,0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17, +0x4C40,0x9930,0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17, +0x90A1,0x3C57,0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE, +0x2E11,0x8894,0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A, +0x83D6,0x1C0C,0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6, +0x0C8C,0x809E,0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x0000,0x8000,0xFCDC, +0x800A,0xF9B8,0x8027,0xF695,0x8059,0xF374,0x809E,0xF055,0x80F6,0xED38,0x8163, +0xEA1E,0x81E2,0xE707,0x8276,0xE3F4,0x831C,0xE0E6,0x83D6,0xDDDC,0x84A3,0xDAD8, +0x8583,0xD7D9,0x8676,0xD4E1,0x877B,0xD1EF,0x8894,0xCF04,0x89BE,0xCC21,0x8AFB, +0xC946,0x8C4A,0xC673,0x8DAB,0xC3A9,0x8F1D,0xC0E9,0x90A1,0xBE32,0x9236,0xBB85, +0x93DC,0xB8E3,0x9592,0xB64C,0x9759,0xB3C0,0x9930,0xB140,0x9B17,0xAECC,0x9D0E, +0xAC65,0x9F14,0xAA0A,0xA129,0xA7BD,0xA34C,0xA57E,0xA57E,0xA34C,0xA7BD,0xA129, +0xAA0A,0x9F14,0xAC65,0x9D0E,0xAECC,0x9B17,0xB140,0x9930,0xB3C0,0x9759,0xB64C, +0x9592,0xB8E3,0x93DC,0xBB85,0x9236,0xBE32,0x90A1,0xC0E9,0x8F1D,0xC3A9,0x8DAB, +0xC673,0x8C4A,0xC946,0x8AFB,0xCC21,0x89BE,0xCF04,0x8894,0xD1EF,0x877B,0xD4E1, +0x8676,0xD7D9,0x8583,0xDAD8,0x84A3,0xDDDC,0x83D6,0xE0E6,0x831C,0xE3F4,0x8276, +0xE707,0x81E2,0xEA1E,0x8163,0xED38,0x80F6,0xF055,0x809E,0xF374,0x8059,0xF695, +0x8027,0xF9B8,0x800A,0xFCDC,0x7FFF,0x0000,0x7FEA,0xFB4A,0x7FA7,0xF695,0x7F38, +0xF1E4,0x7E9D,0xED38,0x7DD6,0xE892,0x7CE4,0xE3F4,0x7BC6,0xDF61,0x7A7D,0xDAD8, +0x790A,0xD65C,0x776C,0xD1EF,0x75A6,0xCD92,0x73B6,0xC946,0x719E,0xC50D,0x6F5F, +0xC0E9,0x6CF9,0xBCDA,0x6A6E,0xB8E3,0x67BD,0xB505,0x64E9,0xB140,0x61F1,0xAD97, +0x5ED7,0xAA0A,0x5B9D,0xA69C,0x5843,0xA34C,0x54CA,0xA01C,0x5134,0x9D0E,0x4D81, +0x9A22,0x49B4,0x9759,0x45CD,0x94B5,0x41CE,0x9236,0x3DB8,0x8FDD,0x398D,0x8DAB, +0x354E,0x8BA0,0x30FC,0x89BE,0x2C99,0x8805,0x2827,0x8676,0x23A7,0x8511,0x1F1A, +0x83D6,0x1A83,0x82C6,0x15E2,0x81E2,0x113A,0x812A,0x0C8C,0x809E,0x07D9,0x803E, +0x0324,0x800A,0xFE6E,0x8002,0xF9B8,0x8027,0xF505,0x8079,0xF055,0x80F6,0xEBAB, +0x81A0,0xE707,0x8276,0xE26D,0x8377,0xDDDC,0x84A3,0xD958,0x85FA,0xD4E1,0x877B, +0xD079,0x8927,0xCC21,0x8AFB,0xC7DB,0x8CF8,0xC3A9,0x8F1D,0xBF8C,0x9169,0xBB85, +0x93DC,0xB796,0x9674,0xB3C0,0x9930,0xB005,0x9C11,0xAC65,0x9F14,0xA8E2,0xA238, +0xA57E,0xA57E,0xA238,0xA8E2,0x9F14,0xAC65,0x9C11,0xB005,0x9930,0xB3C0,0x9674, +0xB796,0x93DC,0xBB85,0x9169,0xBF8C,0x8F1D,0xC3A9,0x8CF8,0xC7DB,0x8AFB,0xCC21, +0x8927,0xD079,0x877B,0xD4E1,0x85FA,0xD958,0x84A3,0xDDDC,0x8377,0xE26D,0x8276, +0xE707,0x81A0,0xEBAB,0x80F6,0xF055,0x8079,0xF505,0x8027,0xF9B8,0x8002,0xFE6E, +0x800A,0x0324,0x803E,0x07D9,0x809E,0x0C8C,0x812A,0x113A,0x81E2,0x15E2,0x82C6, +0x1A83,0x83D6,0x1F1A,0x8511,0x23A7,0x8676,0x2827,0x8805,0x2C99,0x89BE,0x30FC, +0x8BA0,0x354E,0x8DAB,0x398D,0x8FDD,0x3DB8,0x9236,0x41CE,0x94B5,0x45CD,0x9759, +0x49B4,0x9A22,0x4D81,0x9D0E,0x5134,0xA01C,0x54CA,0xA34C,0x5843,0xA69C,0x5B9D, +0xAA0A,0x5ED7,0xAD97,0x61F1,0xB140,0x64E9,0xB505,0x67BD,0xB8E3,0x6A6E,0xBCDA, +0x6CF9,0xC0E9,0x6F5F,0xC50D,0x719E,0xC946,0x73B6,0xCD92,0x75A6,0xD1EF,0x776C, +0xD65C,0x790A,0xDAD8,0x7A7D,0xDF61,0x7BC6,0xE3F4,0x7CE4,0xE892,0x7DD6,0xED38, +0x7E9D,0xF1E4,0x7F38,0xF695,0x7FA7,0xFB4A,0x7FEA,}; + +const uint32_t arm_neon_rfft_factors_1024_q15[ARM_NEON_RFFT_FACTORS_1024_Q15_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_1024_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_Q15_LEN]={ +0xFF37,0x8001,0xFE6E,0x8002,0xFDA5,0x8006,0xFCDC,0x800A,0xFC13,0x800F,0xFB4A, +0x8016,0xFA81,0x801E,0xF9B8,0x8027,0xF8EF,0x8032,0xF827,0x803E,0xF75E,0x804B, +0xF695,0x8059,0xF5CD,0x8068,0xF505,0x8079,0xF43C,0x808B,0xF374,0x809E,0xF2AC, +0x80B2,0xF1E4,0x80C8,0xF11C,0x80DE,0xF055,0x80F6,0xEF8D,0x8110,0xEEC6,0x812A, +0xEDFF,0x8146,0xED38,0x8163,0xEC71,0x8181,0xEBAB,0x81A0,0xEAE4,0x81C1,0xEA1E, +0x81E2,0xE958,0x8205,0xE892,0x822A,0xE7CD,0x824F,0xE707,0x8276,0xE642,0x829D, +0xE57D,0x82C6,0xE4B9,0x82F1,0xE3F4,0x831C,0xE330,0x8349,0xE26D,0x8377,0xE1A9, +0x83A6,0xE0E6,0x83D6,0xE023,0x8407,0xDF61,0x843A,0xDE9E,0x846E,0xDDDC,0x84A3, +0xDD1B,0x84D9,0xDC59,0x8511,0xDB99,0x8549,0xDAD8,0x8583,0xDA18,0x85BE,0xD958, +0x85FA,0xD898,0x8637,0xD7D9,0x8676,0xD71B,0x86B6,0xD65C,0x86F6,0xD59E,0x8738, +0xD4E1,0x877B,0xD424,0x87C0,0xD367,0x8805,0xD2AB,0x884C,0xD1EF,0x8894,0xD134, +0x88DD,0xD079,0x8927,0xCFBE,0x8972,0xCF04,0x89BE,0xCE4B,0x8A0C,0xCD92,0x8A5A, +0xCCD9,0x8AAA,0xCC21,0x8AFB,0xCB69,0x8B4D,0xCAB2,0x8BA0,0xC9FC,0x8BF5,0xC946, +0x8C4A,0xC890,0x8CA1,0xC7DB,0x8CF8,0xC727,0x8D51,0xC673,0x8DAB,0xC5C0,0x8E06, +0xC50D,0x8E62,0xC45B,0x8EBF,0xC3A9,0x8F1D,0xC2F8,0x8F7D,0xC248,0x8FDD,0xC198, +0x903E,0xC0E9,0x90A1,0xC03A,0x9105,0xBF8C,0x9169,0xBEDF,0x91CF,0xBE32,0x9236, +0xBD86,0x929E,0xBCDA,0x9307,0xBC2F,0x9371,0xBB85,0x93DC,0xBADC,0x9448,0xBA33, +0x94B5,0xB98B,0x9523,0xB8E3,0x9592,0xB83C,0x9603,0xB796,0x9674,0xB6F1,0x96E6, +0xB64C,0x9759,0xB5A8,0x97CE,0xB505,0x9843,0xB462,0x98B9,0xB3C0,0x9930,0xB31F, +0x99A9,0xB27F,0x9A22,0xB1DF,0x9A9C,0xB140,0x9B17,0xB0A2,0x9B94,0xB005,0x9C11, +0xAF68,0x9C8F,0xAECC,0x9D0E,0xAE31,0x9D8E,0xAD97,0x9E0F,0xACFD,0x9E91,0xAC65, +0x9F14,0xABCD,0x9F98,0xAB36,0xA01C,0xAAA0,0xA0A2,0xAA0A,0xA129,0xA976,0xA1B0, +0xA8E2,0xA238,0xA84F,0xA2C2,0xA7BD,0xA34C,0xA72C,0xA3D7,0xA69C,0xA463,0xA60C, +0xA4F0,0xA57E,0xA57E,0xA4F0,0xA60C,0xA463,0xA69C,0xA3D7,0xA72C,0xA34C,0xA7BD, +0xA2C2,0xA84F,0xA238,0xA8E2,0xA1B0,0xA976,0xA129,0xAA0A,0xA0A2,0xAAA0,0xA01C, +0xAB36,0x9F98,0xABCD,0x9F14,0xAC65,0x9E91,0xACFD,0x9E0F,0xAD97,0x9D8E,0xAE31, +0x9D0E,0xAECC,0x9C8F,0xAF68,0x9C11,0xB005,0x9B94,0xB0A2,0x9B17,0xB140,0x9A9C, +0xB1DF,0x9A22,0xB27F,0x99A9,0xB31F,0x9930,0xB3C0,0x98B9,0xB462,0x9843,0xB505, +0x97CE,0xB5A8,0x9759,0xB64C,0x96E6,0xB6F1,0x9674,0xB796,0x9603,0xB83C,0x9592, +0xB8E3,0x9523,0xB98B,0x94B5,0xBA33,0x9448,0xBADC,0x93DC,0xBB85,0x9371,0xBC2F, +0x9307,0xBCDA,0x929E,0xBD86,0x9236,0xBE32,0x91CF,0xBEDF,0x9169,0xBF8C,0x9105, +0xC03A,0x90A1,0xC0E9,0x903E,0xC198,0x8FDD,0xC248,0x8F7D,0xC2F8,0x8F1D,0xC3A9, +0x8EBF,0xC45B,0x8E62,0xC50D,0x8E06,0xC5C0,0x8DAB,0xC673,0x8D51,0xC727,0x8CF8, +0xC7DB,0x8CA1,0xC890,0x8C4A,0xC946,0x8BF5,0xC9FC,0x8BA0,0xCAB2,0x8B4D,0xCB69, +0x8AFB,0xCC21,0x8AAA,0xCCD9,0x8A5A,0xCD92,0x8A0C,0xCE4B,0x89BE,0xCF04,0x8972, +0xCFBE,0x8927,0xD079,0x88DD,0xD134,0x8894,0xD1EF,0x884C,0xD2AB,0x8805,0xD367, +0x87C0,0xD424,0x877B,0xD4E1,0x8738,0xD59E,0x86F6,0xD65C,0x86B6,0xD71B,0x8676, +0xD7D9,0x8637,0xD898,0x85FA,0xD958,0x85BE,0xDA18,0x8583,0xDAD8,0x8549,0xDB99, +0x8511,0xDC59,0x84D9,0xDD1B,0x84A3,0xDDDC,0x846E,0xDE9E,0x843A,0xDF61,0x8407, +0xE023,0x83D6,0xE0E6,0x83A6,0xE1A9,0x8377,0xE26D,0x8349,0xE330,0x831C,0xE3F4, +0x82F1,0xE4B9,0x82C6,0xE57D,0x829D,0xE642,0x8276,0xE707,0x824F,0xE7CD,0x822A, +0xE892,0x8205,0xE958,0x81E2,0xEA1E,0x81C1,0xEAE4,0x81A0,0xEBAB,0x8181,0xEC71, +0x8163,0xED38,0x8146,0xEDFF,0x812A,0xEEC6,0x8110,0xEF8D,0x80F6,0xF055,0x80DE, +0xF11C,0x80C8,0xF1E4,0x80B2,0xF2AC,0x809E,0xF374,0x808B,0xF43C,0x8079,0xF505, +0x8068,0xF5CD,0x8059,0xF695,0x804B,0xF75E,0x803E,0xF827,0x8032,0xF8EF,0x8027, +0xF9B8,0x801E,0xFA81,0x8016,0xFB4A,0x800F,0xFC13,0x800A,0xFCDC,0x8006,0xFDA5, +0x8002,0xFE6E,0x8001,0xFF37,0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_2048_q15[ARM_NEON_RFFT_TWIDDLES_2048_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055, +0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D, +0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04, +0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA, +0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140, +0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843, +0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930, +0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57, +0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894, +0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C, +0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E, +0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D, +0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140, 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+0x8276,0xE707,0x8205,0xE958,0x81A0,0xEBAB,0x8146,0xEDFF,0x80F6,0xF055,0x80B2, +0xF2AC,0x8079,0xF505,0x804B,0xF75E,0x8027,0xF9B8,0x800F,0xFC13,0x8002,0xFE6E, +0x8001,0x00C9,0x800A,0x0324,0x801E,0x057F,0x803E,0x07D9,0x8068,0x0A33,0x809E, +0x0C8C,0x80DE,0x0EE4,0x812A,0x113A,0x8181,0x138F,0x81E2,0x15E2,0x824F,0x1833, +0x82C6,0x1A83,0x8349,0x1CD0,0x83D6,0x1F1A,0x846E,0x2162,0x8511,0x23A7,0x85BE, +0x25E8,0x8676,0x2827,0x8738,0x2A62,0x8805,0x2C99,0x88DD,0x2ECC,0x89BE,0x30FC, +0x8AAA,0x3327,0x8BA0,0x354E,0x8CA1,0x3770,0x8DAB,0x398D,0x8EBF,0x3BA5,0x8FDD, +0x3DB8,0x9105,0x3FC6,0x9236,0x41CE,0x9371,0x43D1,0x94B5,0x45CD,0x9603,0x47C4, +0x9759,0x49B4,0x98B9,0x4B9E,0x9A22,0x4D81,0x9B94,0x4F5E,0x9D0E,0x5134,0x9E91, +0x5303,0xA01C,0x54CA,0xA1B0,0x568A,0xA34C,0x5843,0xA4F0,0x59F4,0xA69C,0x5B9D, +0xA84F,0x5D3E,0xAA0A,0x5ED7,0xABCD,0x6068,0xAD97,0x61F1,0xAF68,0x6371,0xB140, +0x64E9,0xB31F,0x6657,0xB505,0x67BD,0xB6F1,0x691A,0xB8E3,0x6A6E,0xBADC,0x6BB8, +0xBCDA,0x6CF9,0xBEDF,0x6E31,0xC0E9,0x6F5F,0xC2F8,0x7083,0xC50D,0x719E,0xC727, +0x72AF,0xC946,0x73B6,0xCB69,0x74B3,0xCD92,0x75A6,0xCFBE,0x768E,0xD1EF,0x776C, +0xD424,0x7840,0xD65C,0x790A,0xD898,0x79C9,0xDAD8,0x7A7D,0xDD1B,0x7B27,0xDF61, +0x7BC6,0xE1A9,0x7C5A,0xE3F4,0x7CE4,0xE642,0x7D63,0xE892,0x7DD6,0xEAE4,0x7E3F, +0xED38,0x7E9D,0xEF8D,0x7EF0,0xF1E4,0x7F38,0xF43C,0x7F75,0xF695,0x7FA7,0xF8EF, +0x7FCE,0xFB4A,0x7FEA,0xFDA5,0x7FFA,}; + +const uint32_t arm_neon_rfft_factors_2048_q15[ARM_NEON_RFFT_FACTORS_2048_Q15_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_2048_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_Q15_LEN]={ +0xFF9B,0x8000,0xFF37,0x8001,0xFED2,0x8001,0xFE6E,0x8002,0xFE09,0x8004,0xFDA5, +0x8006,0xFD40,0x8008,0xFCDC,0x800A,0xFC77,0x800C,0xFC13,0x800F,0xFBAE,0x8013, +0xFB4A,0x8016,0xFAE5,0x801A,0xFA81,0x801E,0xFA1D,0x8023,0xF9B8,0x8027,0xF954, +0x802D,0xF8EF,0x8032,0xF88B,0x8038,0xF827,0x803E,0xF7C2,0x8044,0xF75E,0x804B, +0xF6FA,0x8052,0xF695,0x8059,0xF631,0x8060,0xF5CD,0x8068,0xF569,0x8070,0xF505, +0x8079,0xF4A0,0x8082,0xF43C,0x808B,0xF3D8,0x8094,0xF374,0x809E,0xF310,0x80A8, +0xF2AC,0x80B2,0xF248,0x80BD,0xF1E4,0x80C8,0xF180,0x80D3,0xF11C,0x80DE,0xF0B9, +0x80EA,0xF055,0x80F6,0xEFF1,0x8103,0xEF8D,0x8110,0xEF2A,0x811D,0xEEC6,0x812A, +0xEE62,0x8138,0xEDFF,0x8146,0xED9B,0x8154,0xED38,0x8163,0xECD5,0x8172,0xEC71, +0x8181,0xEC0E,0x8190,0xEBAB,0x81A0,0xEB47,0x81B0,0xEAE4,0x81C1,0xEA81,0x81D1, +0xEA1E,0x81E2,0xE9BB,0x81F4,0xE958,0x8205,0xE8F5,0x8217,0xE892,0x822A,0xE82F, +0x823C,0xE7CD,0x824F,0xE76A,0x8262,0xE707,0x8276,0xE6A5,0x8289,0xE642,0x829D, +0xE5E0,0x82B2,0xE57D,0x82C6,0xE51B,0x82DB,0xE4B9,0x82F1,0xE457,0x8306,0xE3F4, +0x831C,0xE392,0x8332,0xE330,0x8349,0xE2CF,0x8360,0xE26D,0x8377,0xE20B,0x838E, +0xE1A9,0x83A6,0xE148,0x83BE,0xE0E6,0x83D6,0xE085,0x83EF,0xE023,0x8407,0xDFC2, +0x8421,0xDF61,0x843A,0xDEFF,0x8454,0xDE9E,0x846E,0xDE3D,0x8488,0xDDDC,0x84A3, +0xDD7C,0x84BE,0xDD1B,0x84D9,0xDCBA,0x84F5,0xDC59,0x8511,0xDBF9,0x852D,0xDB99, +0x8549,0xDB38,0x8566,0xDAD8,0x8583,0xDA78,0x85A0,0xDA18,0x85BE,0xD9B8,0x85DC, +0xD958,0x85FA,0xD8F8,0x8619,0xD898,0x8637,0xD839,0x8656,0xD7D9,0x8676,0xD77A, +0x8696,0xD71B,0x86B6,0xD6BB,0x86D6,0xD65C,0x86F6,0xD5FD,0x8717,0xD59E,0x8738, +0xD53F,0x875A,0xD4E1,0x877B,0xD482,0x879D,0xD424,0x87C0,0xD3C5,0x87E2,0xD367, +0x8805,0xD309,0x8828,0xD2AB,0x884C,0xD24D,0x8870,0xD1EF,0x8894,0xD191,0x88B8, +0xD134,0x88DD,0xD0D6,0x8902,0xD079,0x8927,0xD01B,0x894C,0xCFBE,0x8972,0xCF61, +0x8998,0xCF04,0x89BE,0xCEA7,0x89E5,0xCE4B,0x8A0C,0xCDEE,0x8A33,0xCD92,0x8A5A, +0xCD35,0x8A82,0xCCD9,0x8AAA,0xCC7D,0x8AD3,0xCC21,0x8AFB,0xCBC5,0x8B24,0xCB69, +0x8B4D,0xCB0E,0x8B77,0xCAB2,0x8BA0,0xCA57,0x8BCA,0xC9FC,0x8BF5,0xC9A1,0x8C1F, +0xC946,0x8C4A,0xC8EB,0x8C75,0xC890,0x8CA1,0xC836,0x8CCC,0xC7DB,0x8CF8,0xC781, +0x8D24,0xC727,0x8D51,0xC6CD,0x8D7E,0xC673,0x8DAB,0xC619,0x8DD8,0xC5C0,0x8E06, +0xC566,0x8E34,0xC50D,0x8E62,0xC4B4,0x8E90,0xC45B,0x8EBF,0xC402,0x8EEE,0xC3A9, +0x8F1D,0xC351,0x8F4D,0xC2F8,0x8F7D,0xC2A0,0x8FAD,0xC248,0x8FDD,0xC1F0,0x900E, +0xC198,0x903E,0xC140,0x9070,0xC0E9,0x90A1,0xC091,0x90D3,0xC03A,0x9105,0xBFE3, +0x9137,0xBF8C,0x9169,0xBF35,0x919C,0xBEDF,0x91CF,0xBE88,0x9202,0xBE32,0x9236, +0xBDDC,0x926A,0xBD86,0x929E,0xBD30,0x92D2,0xBCDA,0x9307,0xBC85,0x933C,0xBC2F, +0x9371,0xBBDA,0x93A6,0xBB85,0x93DC,0xBB30,0x9412,0xBADC,0x9448,0xBA87,0x947E, +0xBA33,0x94B5,0xB9DF,0x94EC,0xB98B,0x9523,0xB937,0x955B,0xB8E3,0x9592,0xB890, +0x95CA,0xB83C,0x9603,0xB7E9,0x963B,0xB796,0x9674,0xB743,0x96AD,0xB6F1,0x96E6, +0xB69E,0x9720,0xB64C,0x9759,0xB5FA,0x9793,0xB5A8,0x97CE,0xB556,0x9808,0xB505, +0x9843,0xB4B3,0x987E,0xB462,0x98B9,0xB411,0x98F5,0xB3C0,0x9930,0xB36F,0x996D, +0xB31F,0x99A9,0xB2CF,0x99E5,0xB27F,0x9A22,0xB22F,0x9A5F,0xB1DF,0x9A9C,0xB18F, +0x9ADA,0xB140,0x9B17,0xB0F1,0x9B55,0xB0A2,0x9B94,0xB053,0x9BD2,0xB005,0x9C11, +0xAFB6,0x9C50,0xAF68,0x9C8F,0xAF1A,0x9CCE,0xAECC,0x9D0E,0xAE7F,0x9D4E,0xAE31, +0x9D8E,0xADE4,0x9DCE,0xAD97,0x9E0F,0xAD4A,0x9E50,0xACFD,0x9E91,0xACB1,0x9ED2, +0xAC65,0x9F14,0xAC19,0x9F56,0xABCD,0x9F98,0xAB81,0x9FDA,0xAB36,0xA01C,0xAAEB, +0xA05F,0xAAA0,0xA0A2,0xAA55,0xA0E5,0xAA0A,0xA129,0xA9C0,0xA16C,0xA976,0xA1B0, +0xA92C,0xA1F4,0xA8E2,0xA238,0xA899,0xA27D,0xA84F,0xA2C2,0xA806,0xA307,0xA7BD, +0xA34C,0xA774,0xA391,0xA72C,0xA3D7,0xA6E4,0xA41D,0xA69C,0xA463,0xA654,0xA4A9, +0xA60C,0xA4F0,0xA5C5,0xA537,0xA57E,0xA57E,0xA537,0xA5C5,0xA4F0,0xA60C,0xA4A9, +0xA654,0xA463,0xA69C,0xA41D,0xA6E4,0xA3D7,0xA72C,0xA391,0xA774,0xA34C,0xA7BD, +0xA307,0xA806,0xA2C2,0xA84F,0xA27D,0xA899,0xA238,0xA8E2,0xA1F4,0xA92C,0xA1B0, +0xA976,0xA16C,0xA9C0,0xA129,0xAA0A,0xA0E5,0xAA55,0xA0A2,0xAAA0,0xA05F,0xAAEB, +0xA01C,0xAB36,0x9FDA,0xAB81,0x9F98,0xABCD,0x9F56,0xAC19,0x9F14,0xAC65,0x9ED2, +0xACB1,0x9E91,0xACFD,0x9E50,0xAD4A,0x9E0F,0xAD97,0x9DCE,0xADE4,0x9D8E,0xAE31, +0x9D4E,0xAE7F,0x9D0E,0xAECC,0x9CCE,0xAF1A,0x9C8F,0xAF68,0x9C50,0xAFB6,0x9C11, +0xB005,0x9BD2,0xB053,0x9B94,0xB0A2,0x9B55,0xB0F1,0x9B17,0xB140,0x9ADA,0xB18F, +0x9A9C,0xB1DF,0x9A5F,0xB22F,0x9A22,0xB27F,0x99E5,0xB2CF,0x99A9,0xB31F,0x996D, +0xB36F,0x9930,0xB3C0,0x98F5,0xB411,0x98B9,0xB462,0x987E,0xB4B3,0x9843,0xB505, +0x9808,0xB556,0x97CE,0xB5A8,0x9793,0xB5FA,0x9759,0xB64C,0x9720,0xB69E,0x96E6, +0xB6F1,0x96AD,0xB743,0x9674,0xB796,0x963B,0xB7E9,0x9603,0xB83C,0x95CA,0xB890, +0x9592,0xB8E3,0x955B,0xB937,0x9523,0xB98B,0x94EC,0xB9DF,0x94B5,0xBA33,0x947E, +0xBA87,0x9448,0xBADC,0x9412,0xBB30,0x93DC,0xBB85,0x93A6,0xBBDA,0x9371,0xBC2F, +0x933C,0xBC85,0x9307,0xBCDA,0x92D2,0xBD30,0x929E,0xBD86,0x926A,0xBDDC,0x9236, +0xBE32,0x9202,0xBE88,0x91CF,0xBEDF,0x919C,0xBF35,0x9169,0xBF8C,0x9137,0xBFE3, +0x9105,0xC03A,0x90D3,0xC091,0x90A1,0xC0E9,0x9070,0xC140,0x903E,0xC198,0x900E, +0xC1F0,0x8FDD,0xC248,0x8FAD,0xC2A0,0x8F7D,0xC2F8,0x8F4D,0xC351,0x8F1D,0xC3A9, +0x8EEE,0xC402,0x8EBF,0xC45B,0x8E90,0xC4B4,0x8E62,0xC50D,0x8E34,0xC566,0x8E06, +0xC5C0,0x8DD8,0xC619,0x8DAB,0xC673,0x8D7E,0xC6CD,0x8D51,0xC727,0x8D24,0xC781, +0x8CF8,0xC7DB,0x8CCC,0xC836,0x8CA1,0xC890,0x8C75,0xC8EB,0x8C4A,0xC946,0x8C1F, +0xC9A1,0x8BF5,0xC9FC,0x8BCA,0xCA57,0x8BA0,0xCAB2,0x8B77,0xCB0E,0x8B4D,0xCB69, +0x8B24,0xCBC5,0x8AFB,0xCC21,0x8AD3,0xCC7D,0x8AAA,0xCCD9,0x8A82,0xCD35,0x8A5A, +0xCD92,0x8A33,0xCDEE,0x8A0C,0xCE4B,0x89E5,0xCEA7,0x89BE,0xCF04,0x8998,0xCF61, +0x8972,0xCFBE,0x894C,0xD01B,0x8927,0xD079,0x8902,0xD0D6,0x88DD,0xD134,0x88B8, +0xD191,0x8894,0xD1EF,0x8870,0xD24D,0x884C,0xD2AB,0x8828,0xD309,0x8805,0xD367, +0x87E2,0xD3C5,0x87C0,0xD424,0x879D,0xD482,0x877B,0xD4E1,0x875A,0xD53F,0x8738, +0xD59E,0x8717,0xD5FD,0x86F6,0xD65C,0x86D6,0xD6BB,0x86B6,0xD71B,0x8696,0xD77A, +0x8676,0xD7D9,0x8656,0xD839,0x8637,0xD898,0x8619,0xD8F8,0x85FA,0xD958,0x85DC, +0xD9B8,0x85BE,0xDA18,0x85A0,0xDA78,0x8583,0xDAD8,0x8566,0xDB38,0x8549,0xDB99, +0x852D,0xDBF9,0x8511,0xDC59,0x84F5,0xDCBA,0x84D9,0xDD1B,0x84BE,0xDD7C,0x84A3, +0xDDDC,0x8488,0xDE3D,0x846E,0xDE9E,0x8454,0xDEFF,0x843A,0xDF61,0x8421,0xDFC2, +0x8407,0xE023,0x83EF,0xE085,0x83D6,0xE0E6,0x83BE,0xE148,0x83A6,0xE1A9,0x838E, +0xE20B,0x8377,0xE26D,0x8360,0xE2CF,0x8349,0xE330,0x8332,0xE392,0x831C,0xE3F4, +0x8306,0xE457,0x82F1,0xE4B9,0x82DB,0xE51B,0x82C6,0xE57D,0x82B2,0xE5E0,0x829D, +0xE642,0x8289,0xE6A5,0x8276,0xE707,0x8262,0xE76A,0x824F,0xE7CD,0x823C,0xE82F, +0x822A,0xE892,0x8217,0xE8F5,0x8205,0xE958,0x81F4,0xE9BB,0x81E2,0xEA1E,0x81D1, +0xEA81,0x81C1,0xEAE4,0x81B0,0xEB47,0x81A0,0xEBAB,0x8190,0xEC0E,0x8181,0xEC71, +0x8172,0xECD5,0x8163,0xED38,0x8154,0xED9B,0x8146,0xEDFF,0x8138,0xEE62,0x812A, +0xEEC6,0x811D,0xEF2A,0x8110,0xEF8D,0x8103,0xEFF1,0x80F6,0xF055,0x80EA,0xF0B9, +0x80DE,0xF11C,0x80D3,0xF180,0x80C8,0xF1E4,0x80BD,0xF248,0x80B2,0xF2AC,0x80A8, +0xF310,0x809E,0xF374,0x8094,0xF3D8,0x808B,0xF43C,0x8082,0xF4A0,0x8079,0xF505, +0x8070,0xF569,0x8068,0xF5CD,0x8060,0xF631,0x8059,0xF695,0x8052,0xF6FA,0x804B, +0xF75E,0x8044,0xF7C2,0x803E,0xF827,0x8038,0xF88B,0x8032,0xF8EF,0x802D,0xF954, +0x8027,0xF9B8,0x8023,0xFA1D,0x801E,0xFA81,0x801A,0xFAE5,0x8016,0xFB4A,0x8013, +0xFBAE,0x800F,0xFC13,0x800C,0xFC77,0x800A,0xFCDC,0x8008,0xFD40,0x8006,0xFDA5, +0x8004,0xFE09,0x8002,0xFE6E,0x8001,0xFED2,0x8001,0xFF37,0x8000,0xFF9B,0x8000, +0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_4096_q15[ARM_NEON_RFFT_TWIDDLES_4096_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D, +0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04, +0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2, +0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930, +0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F, +0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E, +0x0648,0x8027,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x0000,0x8000,0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE, +0xC3A9,0x8F1D,0xB8E3,0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592, +0xB8E3,0x8F1D,0xC3A9,0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374, +0x7FFF,0x0000,0x7E9D,0xED38,0x7A7D,0xDAD8,0x73B6,0xC946,0x6A6E,0xB8E3,0x5ED7, +0xAA0A,0x5134,0x9D0E,0x41CE,0x9236,0x30FC,0x89BE,0x1F1A,0x83D6,0x0C8C,0x809E, +0xF9B8,0x8027,0xE707,0x8276,0xD4E1,0x877B,0xC3A9,0x8F1D,0xB3C0,0x9930,0xA57E, +0xA57E,0x9930,0xB3C0,0x8F1D,0xC3A9,0x877B,0xD4E1,0x8276,0xE707,0x8027,0xF9B8, +0x809E,0x0C8C,0x83D6,0x1F1A,0x89BE,0x30FC,0x9236,0x41CE,0x9D0E,0x5134,0xAA0A, +0x5ED7,0xB8E3,0x6A6E,0xC946,0x73B6,0xDAD8,0x7A7D,0xED38,0x7E9D,0x7FFF,0x0000, +0x7FFE,0xFE6E,0x7FF6,0xFCDC,0x7FEA,0xFB4A,0x7FD9,0xF9B8,0x7FC2,0xF827,0x7FA7, +0xF695,0x7F87,0xF505,0x7F62,0xF374,0x7F38,0xF1E4,0x7F0A,0xF055,0x7ED6,0xEEC6, +0x7E9D,0xED38,0x7E60,0xEBAB,0x7E1E,0xEA1E,0x7DD6,0xE892,0x7D8A,0xE707,0x7D3A, +0xE57D,0x7CE4,0xE3F4,0x7C89,0xE26D,0x7C2A,0xE0E6,0x7BC6,0xDF61,0x7B5D,0xDDDC, +0x7AEF,0xDC59,0x7A7D,0xDAD8,0x7A06,0xD958,0x798A,0xD7D9,0x790A,0xD65C,0x7885, +0xD4E1,0x77FB,0xD367,0x776C,0xD1EF,0x76D9,0xD079,0x7642,0xCF04,0x75A6,0xCD92, +0x7505,0xCC21,0x7460,0xCAB2,0x73B6,0xC946,0x7308,0xC7DB,0x7255,0xC673,0x719E, +0xC50D,0x70E3,0xC3A9,0x7023,0xC248,0x6F5F,0xC0E9,0x6E97,0xBF8C,0x6DCA,0xBE32, +0x6CF9,0xBCDA,0x6C24,0xBB85,0x6B4B,0xBA33,0x6A6E,0xB8E3,0x698C,0xB796,0x68A7, +0xB64C,0x67BD,0xB505,0x66D0,0xB3C0,0x65DE,0xB27F,0x64E9,0xB140,0x63EF,0xB005, +0x62F2,0xAECC,0x61F1,0xAD97,0x60EC,0xAC65,0x5FE4,0xAB36,0x5ED7,0xAA0A,0x5DC8, +0xA8E2,0x5CB4,0xA7BD,0x5B9D,0xA69C,0x5A82,0xA57E,0x5964,0xA463,0x5843,0xA34C, +0x571E,0xA238,0x55F6,0xA129,0x54CA,0xA01C,0x539B,0x9F14,0x5269,0x9E0F,0x5134, +0x9D0E,0x4FFB,0x9C11,0x4EC0,0x9B17,0x4D81,0x9A22,0x4C40,0x9930,0x4AFB,0x9843, +0x49B4,0x9759,0x486A,0x9674,0x471D,0x9592,0x45CD,0x94B5,0x447B,0x93DC,0x4326, +0x9307,0x41CE,0x9236,0x4074,0x9169,0x3F17,0x90A1,0x3DB8,0x8FDD,0x3C57,0x8F1D, +0x3AF3,0x8E62,0x398D,0x8DAB,0x3825,0x8CF8,0x36BA,0x8C4A,0x354E,0x8BA0,0x33DF, +0x8AFB,0x326E,0x8A5A,0x30FC,0x89BE,0x2F87,0x8927,0x2E11,0x8894,0x2C99,0x8805, +0x2B1F,0x877B,0x29A4,0x86F6,0x2827,0x8676,0x26A8,0x85FA,0x2528,0x8583,0x23A7, +0x8511,0x2224,0x84A3,0x209F,0x843A,0x1F1A,0x83D6,0x1D93,0x8377,0x1C0C,0x831C, +0x1A83,0x82C6,0x18F9,0x8276,0x176E,0x822A,0x15E2,0x81E2,0x1455,0x81A0,0x12C8, +0x8163,0x113A,0x812A,0x0FAB,0x80F6,0x0E1C,0x80C8,0x0C8C,0x809E,0x0AFB,0x8079, +0x096B,0x8059,0x07D9,0x803E,0x0648,0x8027,0x04B6,0x8016,0x0324,0x800A,0x0192, +0x8002,0x7FFF,0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374, +0x7F0A,0xF055,0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A, +0xE0E6,0x7B5D,0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF, +0x7642,0xCF04,0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F, +0xC0E9,0x6DCA,0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0, +0x64E9,0xB140,0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82, +0xA57E,0x5843,0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17, +0x4C40,0x9930,0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17, +0x90A1,0x3C57,0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE, +0x2E11,0x8894,0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A, +0x83D6,0x1C0C,0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6, +0x0C8C,0x809E,0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x0000,0x8000,0xFCDC, +0x800A,0xF9B8,0x8027,0xF695,0x8059,0xF374,0x809E,0xF055,0x80F6,0xED38,0x8163, +0xEA1E,0x81E2,0xE707,0x8276,0xE3F4,0x831C,0xE0E6,0x83D6,0xDDDC,0x84A3,0xDAD8, +0x8583,0xD7D9,0x8676,0xD4E1,0x877B,0xD1EF,0x8894,0xCF04,0x89BE,0xCC21,0x8AFB, +0xC946,0x8C4A,0xC673,0x8DAB,0xC3A9,0x8F1D,0xC0E9,0x90A1,0xBE32,0x9236,0xBB85, +0x93DC,0xB8E3,0x9592,0xB64C,0x9759,0xB3C0,0x9930,0xB140,0x9B17,0xAECC,0x9D0E, +0xAC65,0x9F14,0xAA0A,0xA129,0xA7BD,0xA34C,0xA57E,0xA57E,0xA34C,0xA7BD,0xA129, +0xAA0A,0x9F14,0xAC65,0x9D0E,0xAECC,0x9B17,0xB140,0x9930,0xB3C0,0x9759,0xB64C, +0x9592,0xB8E3,0x93DC,0xBB85,0x9236,0xBE32,0x90A1,0xC0E9,0x8F1D,0xC3A9,0x8DAB, +0xC673,0x8C4A,0xC946,0x8AFB,0xCC21,0x89BE,0xCF04,0x8894,0xD1EF,0x877B,0xD4E1, +0x8676,0xD7D9,0x8583,0xDAD8,0x84A3,0xDDDC,0x83D6,0xE0E6,0x831C,0xE3F4,0x8276, +0xE707,0x81E2,0xEA1E,0x8163,0xED38,0x80F6,0xF055,0x809E,0xF374,0x8059,0xF695, +0x8027,0xF9B8,0x800A,0xFCDC,0x7FFF,0x0000,0x7FEA,0xFB4A,0x7FA7,0xF695,0x7F38, +0xF1E4,0x7E9D,0xED38,0x7DD6,0xE892,0x7CE4,0xE3F4,0x7BC6,0xDF61,0x7A7D,0xDAD8, +0x790A,0xD65C,0x776C,0xD1EF,0x75A6,0xCD92,0x73B6,0xC946,0x719E,0xC50D,0x6F5F, +0xC0E9,0x6CF9,0xBCDA,0x6A6E,0xB8E3,0x67BD,0xB505,0x64E9,0xB140,0x61F1,0xAD97, +0x5ED7,0xAA0A,0x5B9D,0xA69C,0x5843,0xA34C,0x54CA,0xA01C,0x5134,0x9D0E,0x4D81, +0x9A22,0x49B4,0x9759,0x45CD,0x94B5,0x41CE,0x9236,0x3DB8,0x8FDD,0x398D,0x8DAB, +0x354E,0x8BA0,0x30FC,0x89BE,0x2C99,0x8805,0x2827,0x8676,0x23A7,0x8511,0x1F1A, +0x83D6,0x1A83,0x82C6,0x15E2,0x81E2,0x113A,0x812A,0x0C8C,0x809E,0x07D9,0x803E, +0x0324,0x800A,0xFE6E,0x8002,0xF9B8,0x8027,0xF505,0x8079,0xF055,0x80F6,0xEBAB, +0x81A0,0xE707,0x8276,0xE26D,0x8377,0xDDDC,0x84A3,0xD958,0x85FA,0xD4E1,0x877B, 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+0xC6CD,0x8D7E,0xC5C0,0x8E06,0xC4B4,0x8E90,0xC3A9,0x8F1D,0xC2A0,0x8FAD,0xC198, +0x903E,0xC091,0x90D3,0xBF8C,0x9169,0xBE88,0x9202,0xBD86,0x929E,0xBC85,0x933C, +0xBB85,0x93DC,0xBA87,0x947E,0xB98B,0x9523,0xB890,0x95CA,0xB796,0x9674,0xB69E, +0x9720,0xB5A8,0x97CE,0xB4B3,0x987E,0xB3C0,0x9930,0xB2CF,0x99E5,0xB1DF,0x9A9C, +0xB0F1,0x9B55,0xB005,0x9C11,0xAF1A,0x9CCE,0xAE31,0x9D8E,0xAD4A,0x9E50,0xAC65, +0x9F14,0xAB81,0x9FDA,0xAAA0,0xA0A2,0xA9C0,0xA16C,0xA8E2,0xA238,0xA806,0xA307, +0xA72C,0xA3D7,0xA654,0xA4A9,0xA57E,0xA57E,0xA4A9,0xA654,0xA3D7,0xA72C,0xA307, +0xA806,0xA238,0xA8E2,0xA16C,0xA9C0,0xA0A2,0xAAA0,0x9FDA,0xAB81,0x9F14,0xAC65, +0x9E50,0xAD4A,0x9D8E,0xAE31,0x9CCE,0xAF1A,0x9C11,0xB005,0x9B55,0xB0F1,0x9A9C, +0xB1DF,0x99E5,0xB2CF,0x9930,0xB3C0,0x987E,0xB4B3,0x97CE,0xB5A8,0x9720,0xB69E, +0x9674,0xB796,0x95CA,0xB890,0x9523,0xB98B,0x947E,0xBA87,0x93DC,0xBB85,0x933C, +0xBC85,0x929E,0xBD86,0x9202,0xBE88,0x9169,0xBF8C,0x90D3,0xC091,0x903E,0xC198, +0x8FAD,0xC2A0,0x8F1D,0xC3A9,0x8E90,0xC4B4,0x8E06,0xC5C0,0x8D7E,0xC6CD,0x8CF8, +0xC7DB,0x8C75,0xC8EB,0x8BF5,0xC9FC,0x8B77,0xCB0E,0x8AFB,0xCC21,0x8A82,0xCD35, +0x8A0C,0xCE4B,0x8998,0xCF61,0x8927,0xD079,0x88B8,0xD191,0x884C,0xD2AB,0x87E2, +0xD3C5,0x877B,0xD4E1,0x8717,0xD5FD,0x86B6,0xD71B,0x8656,0xD839,0x85FA,0xD958, +0x85A0,0xDA78,0x8549,0xDB99,0x84F5,0xDCBA,0x84A3,0xDDDC,0x8454,0xDEFF,0x8407, +0xE023,0x83BE,0xE148,0x8377,0xE26D,0x8332,0xE392,0x82F1,0xE4B9,0x82B2,0xE5E0, +0x8276,0xE707,0x823C,0xE82F,0x8205,0xE958,0x81D1,0xEA81,0x81A0,0xEBAB,0x8172, +0xECD5,0x8146,0xEDFF,0x811D,0xEF2A,0x80F6,0xF055,0x80D3,0xF180,0x80B2,0xF2AC, +0x8094,0xF3D8,0x8079,0xF505,0x8060,0xF631,0x804B,0xF75E,0x8038,0xF88B,0x8027, +0xF9B8,0x801A,0xFAE5,0x800F,0xFC13,0x8008,0xFD40,0x8002,0xFE6E,0x8000,0xFF9B, +0x8001,0x00C9,0x8004,0x01F7,0x800A,0x0324,0x8013,0x0452,0x801E,0x057F,0x802D, +0x06AC,0x803E,0x07D9,0x8052,0x0906,0x8068,0x0A33,0x8082,0x0B60,0x809E,0x0C8C, +0x80BD,0x0DB8,0x80DE,0x0EE4,0x8103,0x100F,0x812A,0x113A,0x8154,0x1265,0x8181, +0x138F,0x81B0,0x14B9,0x81E2,0x15E2,0x8217,0x170B,0x824F,0x1833,0x8289,0x195B, +0x82C6,0x1A83,0x8306,0x1BA9,0x8349,0x1CD0,0x838E,0x1DF5,0x83D6,0x1F1A,0x8421, +0x203E,0x846E,0x2162,0x84BE,0x2284,0x8511,0x23A7,0x8566,0x24C8,0x85BE,0x25E8, +0x8619,0x2708,0x8676,0x2827,0x86D6,0x2945,0x8738,0x2A62,0x879D,0x2B7E,0x8805, +0x2C99,0x8870,0x2DB3,0x88DD,0x2ECC,0x894C,0x2FE5,0x89BE,0x30FC,0x8A33,0x3212, +0x8AAA,0x3327,0x8B24,0x343B,0x8BA0,0x354E,0x8C1F,0x365F,0x8CA1,0x3770,0x8D24, +0x387F,0x8DAB,0x398D,0x8E34,0x3A9A,0x8EBF,0x3BA5,0x8F4D,0x3CAF,0x8FDD,0x3DB8, +0x9070,0x3EC0,0x9105,0x3FC6,0x919C,0x40CB,0x9236,0x41CE,0x92D2,0x42D0,0x9371, +0x43D1,0x9412,0x44D0,0x94B5,0x45CD,0x955B,0x46C9,0x9603,0x47C4,0x96AD,0x48BD, +0x9759,0x49B4,0x9808,0x4AAA,0x98B9,0x4B9E,0x996D,0x4C91,0x9A22,0x4D81,0x9ADA, +0x4E71,0x9B94,0x4F5E,0x9C50,0x504A,0x9D0E,0x5134,0x9DCE,0x521C,0x9E91,0x5303, +0x9F56,0x53E7,0xA01C,0x54CA,0xA0E5,0x55AB,0xA1B0,0x568A,0xA27D,0x5767,0xA34C, +0x5843,0xA41D,0x591C,0xA4F0,0x59F4,0xA5C5,0x5AC9,0xA69C,0x5B9D,0xA774,0x5C6F, +0xA84F,0x5D3E,0xA92C,0x5E0C,0xAA0A,0x5ED7,0xAAEB,0x5FA1,0xABCD,0x6068,0xACB1, +0x612E,0xAD97,0x61F1,0xAE7F,0x62B2,0xAF68,0x6371,0xB053,0x642E,0xB140,0x64E9, +0xB22F,0x65A1,0xB31F,0x6657,0xB411,0x670B,0xB505,0x67BD,0xB5FA,0x686D,0xB6F1, +0x691A,0xB7E9,0x69C5,0xB8E3,0x6A6E,0xB9DF,0x6B14,0xBADC,0x6BB8,0xBBDA,0x6C5A, +0xBCDA,0x6CF9,0xBDDC,0x6D96,0xBEDF,0x6E31,0xBFE3,0x6EC9,0xC0E9,0x6F5F,0xC1F0, +0x6FF2,0xC2F8,0x7083,0xC402,0x7112,0xC50D,0x719E,0xC619,0x7228,0xC727,0x72AF, +0xC836,0x7334,0xC946,0x73B6,0xCA57,0x7436,0xCB69,0x74B3,0xCC7D,0x752D,0xCD92, +0x75A6,0xCEA7,0x761B,0xCFBE,0x768E,0xD0D6,0x76FE,0xD1EF,0x776C,0xD309,0x77D8, +0xD424,0x7840,0xD53F,0x78A6,0xD65C,0x790A,0xD77A,0x796A,0xD898,0x79C9,0xD9B8, +0x7A24,0xDAD8,0x7A7D,0xDBF9,0x7AD3,0xDD1B,0x7B27,0xDE3D,0x7B78,0xDF61,0x7BC6, +0xE085,0x7C11,0xE1A9,0x7C5A,0xE2CF,0x7CA0,0xE3F4,0x7CE4,0xE51B,0x7D25,0xE642, +0x7D63,0xE76A,0x7D9E,0xE892,0x7DD6,0xE9BB,0x7E0C,0xEAE4,0x7E3F,0xEC0E,0x7E70, +0xED38,0x7E9D,0xEE62,0x7EC8,0xEF8D,0x7EF0,0xF0B9,0x7F16,0xF1E4,0x7F38,0xF310, +0x7F58,0xF43C,0x7F75,0xF569,0x7F90,0xF695,0x7FA7,0xF7C2,0x7FBC,0xF8EF,0x7FCE, +0xFA1D,0x7FDD,0xFB4A,0x7FEA,0xFC77,0x7FF4,0xFDA5,0x7FFA,0xFED2,0x7FFF,}; + +const uint32_t arm_neon_rfft_factors_4096_q15[ARM_NEON_RFFT_FACTORS_4096_Q15_LEN]={ +5,256,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_4096_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_Q15_LEN]={ +0xFFCE,0x8000,0xFF9B,0x8000,0xFF69,0x8000,0xFF37,0x8001,0xFF05,0x8001,0xFED2, +0x8001,0xFEA0,0x8002,0xFE6E,0x8002,0xFE3C,0x8003,0xFE09,0x8004,0xFDD7,0x8005, +0xFDA5,0x8006,0xFD73,0x8007,0xFD40,0x8008,0xFD0E,0x8009,0xFCDC,0x800A,0xFCAA, +0x800B,0xFC77,0x800C,0xFC45,0x800E,0xFC13,0x800F,0xFBE1,0x8011,0xFBAE,0x8013, +0xFB7C,0x8014,0xFB4A,0x8016,0xFB18,0x8018,0xFAE5,0x801A,0xFAB3,0x801C,0xFA81, +0x801E,0xFA4F,0x8020,0xFA1D,0x8023,0xF9EA,0x8025,0xF9B8,0x8027,0xF986,0x802A, +0xF954,0x802D,0xF922,0x802F,0xF8EF,0x8032,0xF8BD,0x8035,0xF88B,0x8038,0xF859, +0x803B,0xF827,0x803E,0xF7F4,0x8041,0xF7C2,0x8044,0xF790,0x8047,0xF75E,0x804B, +0xF72C,0x804E,0xF6FA,0x8052,0xF6C8,0x8055,0xF695,0x8059,0xF663,0x805D,0xF631, +0x8060,0xF5FF,0x8064,0xF5CD,0x8068,0xF59B,0x806C,0xF569,0x8070,0xF537,0x8075, +0xF505,0x8079,0xF4D3,0x807D,0xF4A0,0x8082,0xF46E,0x8086,0xF43C,0x808B,0xF40A, +0x808F,0xF3D8,0x8094,0xF3A6,0x8099,0xF374,0x809E,0xF342,0x80A3,0xF310,0x80A8, +0xF2DE,0x80AD,0xF2AC,0x80B2,0xF27A,0x80B7,0xF248,0x80BD,0xF216,0x80C2,0xF1E4, +0x80C8,0xF1B2,0x80CD,0xF180,0x80D3,0xF14E,0x80D9,0xF11C,0x80DE,0xF0EB,0x80E4, +0xF0B9,0x80EA,0xF087,0x80F0,0xF055,0x80F6,0xF023,0x80FD,0xEFF1,0x8103,0xEFBF, +0x8109,0xEF8D,0x8110,0xEF5C,0x8116,0xEF2A,0x811D,0xEEF8,0x8123,0xEEC6,0x812A, +0xEE94,0x8131,0xEE62,0x8138,0xEE31,0x813F,0xEDFF,0x8146,0xEDCD,0x814D,0xED9B, +0x8154,0xED6A,0x815B,0xED38,0x8163,0xED06,0x816A,0xECD5,0x8172,0xECA3,0x8179, +0xEC71,0x8181,0xEC3F,0x8188,0xEC0E,0x8190,0xEBDC,0x8198,0xEBAB,0x81A0,0xEB79, +0x81A8,0xEB47,0x81B0,0xEB16,0x81B8,0xEAE4,0x81C1,0xEAB3,0x81C9,0xEA81,0x81D1, +0xEA4F,0x81DA,0xEA1E,0x81E2,0xE9EC,0x81EB,0xE9BB,0x81F4,0xE989,0x81FD,0xE958, +0x8205,0xE926,0x820E,0xE8F5,0x8217,0xE8C4,0x8220,0xE892,0x822A,0xE861,0x8233, +0xE82F,0x823C,0xE7FE,0x8246,0xE7CD,0x824F,0xE79B,0x8259,0xE76A,0x8262,0xE739, +0x826C,0xE707,0x8276,0xE6D6,0x827F,0xE6A5,0x8289,0xE673,0x8293,0xE642,0x829D, +0xE611,0x82A8,0xE5E0,0x82B2,0xE5AF,0x82BC,0xE57D,0x82C6,0xE54C,0x82D1,0xE51B, +0x82DB,0xE4EA,0x82E6,0xE4B9,0x82F1,0xE488,0x82FB,0xE457,0x8306,0xE426,0x8311, +0xE3F4,0x831C,0xE3C3,0x8327,0xE392,0x8332,0xE361,0x833E,0xE330,0x8349,0xE2FF, +0x8354,0xE2CF,0x8360,0xE29E,0x836B,0xE26D,0x8377,0xE23C,0x8382,0xE20B,0x838E, 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+0x8311,0xE426,0x8306,0xE457,0x82FB,0xE488,0x82F1,0xE4B9,0x82E6,0xE4EA,0x82DB, +0xE51B,0x82D1,0xE54C,0x82C6,0xE57D,0x82BC,0xE5AF,0x82B2,0xE5E0,0x82A8,0xE611, +0x829D,0xE642,0x8293,0xE673,0x8289,0xE6A5,0x827F,0xE6D6,0x8276,0xE707,0x826C, +0xE739,0x8262,0xE76A,0x8259,0xE79B,0x824F,0xE7CD,0x8246,0xE7FE,0x823C,0xE82F, +0x8233,0xE861,0x822A,0xE892,0x8220,0xE8C4,0x8217,0xE8F5,0x820E,0xE926,0x8205, +0xE958,0x81FD,0xE989,0x81F4,0xE9BB,0x81EB,0xE9EC,0x81E2,0xEA1E,0x81DA,0xEA4F, +0x81D1,0xEA81,0x81C9,0xEAB3,0x81C1,0xEAE4,0x81B8,0xEB16,0x81B0,0xEB47,0x81A8, +0xEB79,0x81A0,0xEBAB,0x8198,0xEBDC,0x8190,0xEC0E,0x8188,0xEC3F,0x8181,0xEC71, +0x8179,0xECA3,0x8172,0xECD5,0x816A,0xED06,0x8163,0xED38,0x815B,0xED6A,0x8154, +0xED9B,0x814D,0xEDCD,0x8146,0xEDFF,0x813F,0xEE31,0x8138,0xEE62,0x8131,0xEE94, +0x812A,0xEEC6,0x8123,0xEEF8,0x811D,0xEF2A,0x8116,0xEF5C,0x8110,0xEF8D,0x8109, +0xEFBF,0x8103,0xEFF1,0x80FD,0xF023,0x80F6,0xF055,0x80F0,0xF087,0x80EA,0xF0B9, +0x80E4,0xF0EB,0x80DE,0xF11C,0x80D9,0xF14E,0x80D3,0xF180,0x80CD,0xF1B2,0x80C8, +0xF1E4,0x80C2,0xF216,0x80BD,0xF248,0x80B7,0xF27A,0x80B2,0xF2AC,0x80AD,0xF2DE, +0x80A8,0xF310,0x80A3,0xF342,0x809E,0xF374,0x8099,0xF3A6,0x8094,0xF3D8,0x808F, +0xF40A,0x808B,0xF43C,0x8086,0xF46E,0x8082,0xF4A0,0x807D,0xF4D3,0x8079,0xF505, +0x8075,0xF537,0x8070,0xF569,0x806C,0xF59B,0x8068,0xF5CD,0x8064,0xF5FF,0x8060, +0xF631,0x805D,0xF663,0x8059,0xF695,0x8055,0xF6C8,0x8052,0xF6FA,0x804E,0xF72C, +0x804B,0xF75E,0x8047,0xF790,0x8044,0xF7C2,0x8041,0xF7F4,0x803E,0xF827,0x803B, +0xF859,0x8038,0xF88B,0x8035,0xF8BD,0x8032,0xF8EF,0x802F,0xF922,0x802D,0xF954, +0x802A,0xF986,0x8027,0xF9B8,0x8025,0xF9EA,0x8023,0xFA1D,0x8020,0xFA4F,0x801E, +0xFA81,0x801C,0xFAB3,0x801A,0xFAE5,0x8018,0xFB18,0x8016,0xFB4A,0x8014,0xFB7C, +0x8013,0xFBAE,0x8011,0xFBE1,0x800F,0xFC13,0x800E,0xFC45,0x800C,0xFC77,0x800B, +0xFCAA,0x800A,0xFCDC,0x8009,0xFD0E,0x8008,0xFD40,0x8007,0xFD73,0x8006,0xFDA5, +0x8005,0xFDD7,0x8004,0xFE09,0x8003,0xFE3C,0x8002,0xFE6E,0x8002,0xFEA0,0x8001, +0xFED2,0x8001,0xFF05,0x8001,0xFF37,0x8000,0xFF69,0x8000,0xFF9B,0x8000,0xFFCE, +0x8000,0x0000,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_twiddles_8192_q15[ARM_NEON_RFFT_TWIDDLES_8192_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055, +0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D, +0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04, +0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA, +0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140, +0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843, +0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930, +0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57, +0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894, +0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C, +0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E, +0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D, +0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140, +0x5ED7,0xAA0A,0x5843,0xA34C,0x5134,0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D, +0x8DAB,0x30FC,0x89BE,0x2827,0x8676,0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E, +0x0324,0x800A,0xF9B8,0x8027,0xF055,0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1, +0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14, +0xA57E,0xA57E,0x9F14,0xAC65,0x9930,0xB3C0,0x93DC,0xBB85,0x8F1D,0xC3A9,0x8AFB, +0xCC21,0x877B,0xD4E1,0x84A3,0xDDDC,0x8276,0xE707,0x80F6,0xF055,0x8027,0xF9B8, +0x800A,0x0324,0x809E,0x0C8C,0x81E2,0x15E2,0x83D6,0x1F1A,0x8676,0x2827,0x89BE, +0x30FC,0x8DAB,0x398D,0x9236,0x41CE,0x9759,0x49B4,0x9D0E,0x5134,0xA34C,0x5843, +0xAA0A,0x5ED7,0xB140,0x64E9,0xB8E3,0x6A6E,0xC0E9,0x6F5F,0xC946,0x73B6,0xD1EF, +0x776C,0xDAD8,0x7A7D,0xE3F4,0x7CE4,0xED38,0x7E9D,0xF695,0x7FA7,0x7FFF,0x0000, +0x7FFF,0xFF37,0x7FFE,0xFE6E,0x7FFA,0xFDA5,0x7FF6,0xFCDC,0x7FF1,0xFC13,0x7FEA, +0xFB4A,0x7FE2,0xFA81,0x7FD9,0xF9B8,0x7FCE,0xF8EF,0x7FC2,0xF827,0x7FB5,0xF75E, +0x7FA7,0xF695,0x7F98,0xF5CD,0x7F87,0xF505,0x7F75,0xF43C,0x7F62,0xF374,0x7F4E, +0xF2AC,0x7F38,0xF1E4,0x7F22,0xF11C,0x7F0A,0xF055,0x7EF0,0xEF8D,0x7ED6,0xEEC6, +0x7EBA,0xEDFF,0x7E9D,0xED38,0x7E7F,0xEC71,0x7E60,0xEBAB,0x7E3F,0xEAE4,0x7E1E, +0xEA1E,0x7DFB,0xE958,0x7DD6,0xE892,0x7DB1,0xE7CD,0x7D8A,0xE707,0x7D63,0xE642, +0x7D3A,0xE57D,0x7D0F,0xE4B9,0x7CE4,0xE3F4,0x7CB7,0xE330,0x7C89,0xE26D,0x7C5A, +0xE1A9,0x7C2A,0xE0E6,0x7BF9,0xE023,0x7BC6,0xDF61,0x7B92,0xDE9E,0x7B5D,0xDDDC, +0x7B27,0xDD1B,0x7AEF,0xDC59,0x7AB7,0xDB99,0x7A7D,0xDAD8,0x7A42,0xDA18,0x7A06, +0xD958,0x79C9,0xD898,0x798A,0xD7D9,0x794A,0xD71B,0x790A,0xD65C,0x78C8,0xD59E, +0x7885,0xD4E1,0x7840,0xD424,0x77FB,0xD367,0x77B4,0xD2AB,0x776C,0xD1EF,0x7723, 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+0x76C7,0xD0D6,0x76FE,0xD162,0x7736,0xD1EF,0x776C,0xD27C,0x77A2,0xD309,0x77D8, +0xD396,0x780C,0xD424,0x7840,0xD4B1,0x7874,0xD53F,0x78A6,0xD5CE,0x78D8,0xD65C, +0x790A,0xD6EB,0x793A,0xD77A,0x796A,0xD809,0x799A,0xD898,0x79C9,0xD928,0x79F7, +0xD9B8,0x7A24,0xDA48,0x7A51,0xDAD8,0x7A7D,0xDB68,0x7AA8,0xDBF9,0x7AD3,0xDC8A, +0x7AFD,0xDD1B,0x7B27,0xDDAC,0x7B50,0xDE3D,0x7B78,0xDECF,0x7B9F,0xDF61,0x7BC6, +0xDFF2,0x7BEC,0xE085,0x7C11,0xE117,0x7C36,0xE1A9,0x7C5A,0xE23C,0x7C7E,0xE2CF, +0x7CA0,0xE361,0x7CC2,0xE3F4,0x7CE4,0xE488,0x7D05,0xE51B,0x7D25,0xE5AF,0x7D44, +0xE642,0x7D63,0xE6D6,0x7D81,0xE76A,0x7D9E,0xE7FE,0x7DBA,0xE892,0x7DD6,0xE926, +0x7DF2,0xE9BB,0x7E0C,0xEA4F,0x7E26,0xEAE4,0x7E3F,0xEB79,0x7E58,0xEC0E,0x7E70, +0xECA3,0x7E87,0xED38,0x7E9D,0xEDCD,0x7EB3,0xEE62,0x7EC8,0xEEF8,0x7EDD,0xEF8D, +0x7EF0,0xF023,0x7F03,0xF0B9,0x7F16,0xF14E,0x7F27,0xF1E4,0x7F38,0xF27A,0x7F49, +0xF310,0x7F58,0xF3A6,0x7F67,0xF43C,0x7F75,0xF4D3,0x7F83,0xF569,0x7F90,0xF5FF, +0x7F9C,0xF695,0x7FA7,0xF72C,0x7FB2,0xF7C2,0x7FBC,0xF859,0x7FC5,0xF8EF,0x7FCE, +0xF986,0x7FD6,0xFA1D,0x7FDD,0xFAB3,0x7FE4,0xFB4A,0x7FEA,0xFBE1,0x7FEF,0xFC77, +0x7FF4,0xFD0E,0x7FF7,0xFDA5,0x7FFA,0xFE3C,0x7FFD,0xFED2,0x7FFF,0xFF69,0x7FFF,}; + +const uint32_t arm_neon_rfft_factors_8192_q15[ARM_NEON_RFFT_FACTORS_8192_Q15_LEN]={ +6,1024,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_rfft_super_twiddles_neon_8192_q15[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_8192_Q15_LEN]={ +0xFFE7,0x8000,0xFFCE,0x8000,0xFFB5,0x8000,0xFF9B,0x8000,0xFF82,0x8000,0xFF69, +0x8000,0xFF50,0x8000,0xFF37,0x8001,0xFF1E,0x8001,0xFF05,0x8001,0xFEEC,0x8001, +0xFED2,0x8001,0xFEB9,0x8002,0xFEA0,0x8002,0xFE87,0x8002,0xFE6E,0x8002,0xFE55, +0x8003,0xFE3C,0x8003,0xFE22,0x8003,0xFE09,0x8004,0xFDF0,0x8004,0xFDD7,0x8005, +0xFDBE,0x8005,0xFDA5,0x8006,0xFD8C,0x8006,0xFD73,0x8007,0xFD59,0x8007,0xFD40, +0x8008,0xFD27,0x8008,0xFD0E,0x8009,0xFCF5,0x8009,0xFCDC,0x800A,0xFCC3,0x800A, +0xFCAA,0x800B,0xFC90,0x800C,0xFC77,0x800C,0xFC5E,0x800D,0xFC45,0x800E,0xFC2C, +0x800F,0xFC13,0x800F,0xFBFA,0x8010,0xFBE1,0x8011,0xFBC7,0x8012,0xFBAE,0x8013, +0xFB95,0x8014,0xFB7C,0x8014,0xFB63,0x8015,0xFB4A,0x8016,0xFB31,0x8017,0xFB18, +0x8018,0xFAFF,0x8019,0xFAE5,0x801A,0xFACC,0x801B,0xFAB3,0x801C,0xFA9A,0x801D, +0xFA81,0x801E,0xFA68,0x801F,0xFA4F,0x8020,0xFA36,0x8022,0xFA1D,0x8023,0xFA03, +0x8024,0xF9EA,0x8025,0xF9D1,0x8026,0xF9B8,0x8027,0xF99F,0x8029,0xF986,0x802A, +0xF96D,0x802B,0xF954,0x802D,0xF93B,0x802E,0xF922,0x802F,0xF908,0x8031,0xF8EF, +0x8032,0xF8D6,0x8033,0xF8BD,0x8035,0xF8A4,0x8036,0xF88B,0x8038,0xF872,0x8039, +0xF859,0x803B,0xF840,0x803C,0xF827,0x803E,0xF80E,0x803F,0xF7F4,0x8041,0xF7DB, +0x8042,0xF7C2,0x8044,0xF7A9,0x8046,0xF790,0x8047,0xF777,0x8049,0xF75E,0x804B, +0xF745,0x804C,0xF72C,0x804E,0xF713,0x8050,0xF6FA,0x8052,0xF6E1,0x8053,0xF6C8, +0x8055,0xF6AF,0x8057,0xF695,0x8059,0xF67C,0x805B,0xF663,0x805D,0xF64A,0x805E, +0xF631,0x8060,0xF618,0x8062,0xF5FF,0x8064,0xF5E6,0x8066,0xF5CD,0x8068,0xF5B4, +0x806A,0xF59B,0x806C,0xF582,0x806E,0xF569,0x8070,0xF550,0x8072,0xF537,0x8075, +0xF51E,0x8077,0xF505,0x8079,0xF4EC,0x807B,0xF4D3,0x807D,0xF4B9,0x807F,0xF4A0, +0x8082,0xF487,0x8084,0xF46E,0x8086,0xF455,0x8088,0xF43C,0x808B,0xF423,0x808D, +0xF40A,0x808F,0xF3F1,0x8092,0xF3D8,0x8094,0xF3BF,0x8096,0xF3A6,0x8099,0xF38D, +0x809B,0xF374,0x809E,0xF35B,0x80A0,0xF342,0x80A3,0xF329,0x80A5,0xF310,0x80A8, +0xF2F7,0x80AA,0xF2DE,0x80AD,0xF2C5,0x80B0,0xF2AC,0x80B2,0xF293,0x80B5,0xF27A, +0x80B7,0xF261,0x80BA,0xF248,0x80BD,0xF22F,0x80BF,0xF216,0x80C2,0xF1FD,0x80C5, +0xF1E4,0x80C8,0xF1CB,0x80CA,0xF1B2,0x80CD,0xF199,0x80D0,0xF180,0x80D3,0xF167, +0x80D6,0xF14E,0x80D9,0xF135,0x80DC,0xF11C,0x80DE,0xF104,0x80E1,0xF0EB,0x80E4, +0xF0D2,0x80E7,0xF0B9,0x80EA,0xF0A0,0x80ED,0xF087,0x80F0,0xF06E,0x80F3,0xF055, +0x80F6,0xF03C,0x80FA,0xF023,0x80FD,0xF00A,0x8100,0xEFF1,0x8103,0xEFD8,0x8106, +0xEFBF,0x8109,0xEFA6,0x810C,0xEF8D,0x8110,0xEF74,0x8113,0xEF5C,0x8116,0xEF43, +0x8119,0xEF2A,0x811D,0xEF11,0x8120,0xEEF8,0x8123,0xEEDF,0x8127,0xEEC6,0x812A, +0xEEAD,0x812D,0xEE94,0x8131,0xEE7B,0x8134,0xEE62,0x8138,0xEE4A,0x813B,0xEE31, +0x813F,0xEE18,0x8142,0xEDFF,0x8146,0xEDE6,0x8149,0xEDCD,0x814D,0xEDB4,0x8150, +0xED9B,0x8154,0xED83,0x8158,0xED6A,0x815B,0xED51,0x815F,0xED38,0x8163,0xED1F, +0x8166,0xED06,0x816A,0xECED,0x816E,0xECD5,0x8172,0xECBC,0x8175,0xECA3,0x8179, +0xEC8A,0x817D,0xEC71,0x8181,0xEC58,0x8185,0xEC3F,0x8188,0xEC27,0x818C,0xEC0E, +0x8190,0xEBF5,0x8194,0xEBDC,0x8198,0xEBC3,0x819C,0xEBAB,0x81A0,0xEB92,0x81A4, +0xEB79,0x81A8,0xEB60,0x81AC,0xEB47,0x81B0,0xEB2F,0x81B4,0xEB16,0x81B8,0xEAFD, +0x81BD,0xEAE4,0x81C1,0xEACB,0x81C5,0xEAB3,0x81C9,0xEA9A,0x81CD,0xEA81,0x81D1, +0xEA68,0x81D6,0xEA4F,0x81DA,0xEA37,0x81DE,0xEA1E,0x81E2,0xEA05,0x81E7,0xE9EC, +0x81EB,0xE9D4,0x81EF,0xE9BB,0x81F4,0xE9A2,0x81F8,0xE989,0x81FD,0xE971,0x8201, +0xE958,0x8205,0xE93F,0x820A,0xE926,0x820E,0xE90E,0x8213,0xE8F5,0x8217,0xE8DC, +0x821C,0xE8C4,0x8220,0xE8AB,0x8225,0xE892,0x822A,0xE879,0x822E,0xE861,0x8233, +0xE848,0x8237,0xE82F,0x823C,0xE817,0x8241,0xE7FE,0x8246,0xE7E5,0x824A,0xE7CD, +0x824F,0xE7B4,0x8254,0xE79B,0x8259,0xE783,0x825D,0xE76A,0x8262,0xE751,0x8267, +0xE739,0x826C,0xE720,0x8271,0xE707,0x8276,0xE6EF,0x827B,0xE6D6,0x827F,0xE6BD, +0x8284,0xE6A5,0x8289,0xE68C,0x828E,0xE673,0x8293,0xE65B,0x8298,0xE642,0x829D, +0xE62A,0x82A3,0xE611,0x82A8,0xE5F8,0x82AD,0xE5E0,0x82B2,0xE5C7,0x82B7,0xE5AF, +0x82BC,0xE596,0x82C1,0xE57D,0x82C6,0xE565,0x82CC,0xE54C,0x82D1,0xE534,0x82D6, +0xE51B,0x82DB,0xE502,0x82E1,0xE4EA,0x82E6,0xE4D1,0x82EB,0xE4B9,0x82F1,0xE4A0, +0x82F6,0xE488,0x82FB,0xE46F,0x8301,0xE457,0x8306,0xE43E,0x830C,0xE426,0x8311, +0xE40D,0x8317,0xE3F4,0x831C,0xE3DC,0x8322,0xE3C3,0x8327,0xE3AB,0x832D,0xE392, +0x8332,0xE37A,0x8338,0xE361,0x833E,0xE349,0x8343,0xE330,0x8349,0xE318,0x834F, +0xE2FF,0x8354,0xE2E7,0x835A,0xE2CF,0x8360,0xE2B6,0x8365,0xE29E,0x836B,0xE285, +0x8371,0xE26D,0x8377,0xE254,0x837D,0xE23C,0x8382,0xE223,0x8388,0xE20B,0x838E, +0xE1F2,0x8394,0xE1DA,0x839A,0xE1C2,0x83A0,0xE1A9,0x83A6,0xE191,0x83AC,0xE178, +0x83B2,0xE160,0x83B8,0xE148,0x83BE,0xE12F,0x83C4,0xE117,0x83CA,0xE0FE,0x83D0, +0xE0E6,0x83D6,0xE0CE,0x83DC,0xE0B5,0x83E2,0xE09D,0x83E8,0xE085,0x83EF,0xE06C, +0x83F5,0xE054,0x83FB,0xE03B,0x8401,0xE023,0x8407,0xE00B,0x840E,0xDFF2,0x8414, +0xDFDA,0x841A,0xDFC2,0x8421,0xDFA9,0x8427,0xDF91,0x842D,0xDF79,0x8434,0xDF61, +0x843A,0xDF48,0x8441,0xDF30,0x8447,0xDF18,0x844D,0xDEFF,0x8454,0xDEE7,0x845A, +0xDECF,0x8461,0xDEB7,0x8467,0xDE9E,0x846E,0xDE86,0x8475,0xDE6E,0x847B,0xDE56, +0x8482,0xDE3D,0x8488,0xDE25,0x848F,0xDE0D,0x8496,0xDDF5,0x849C,0xDDDC,0x84A3, +0xDDC4,0x84AA,0xDDAC,0x84B0,0xDD94,0x84B7,0xDD7C,0x84BE,0xDD63,0x84C5,0xDD4B, +0x84CC,0xDD33,0x84D2,0xDD1B,0x84D9,0xDD03,0x84E0,0xDCEA,0x84E7,0xDCD2,0x84EE, 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+0x800B,0xFCAA,0x800A,0xFCC3,0x800A,0xFCDC,0x8009,0xFCF5,0x8009,0xFD0E,0x8008, +0xFD27,0x8008,0xFD40,0x8007,0xFD59,0x8007,0xFD73,0x8006,0xFD8C,0x8006,0xFDA5, +0x8005,0xFDBE,0x8005,0xFDD7,0x8004,0xFDF0,0x8004,0xFE09,0x8003,0xFE22,0x8003, +0xFE3C,0x8003,0xFE55,0x8002,0xFE6E,0x8002,0xFE87,0x8002,0xFEA0,0x8002,0xFEB9, +0x8001,0xFED2,0x8001,0xFEEC,0x8001,0xFF05,0x8001,0xFF1E,0x8001,0xFF37,0x8000, +0xFF50,0x8000,0xFF69,0x8000,0xFF82,0x8000,0xFF9B,0x8000,0xFFB5,0x8000,0xFFCE, +0x8000,0xFFE7,0x8000,0x0000,}; + +__ALIGNED(16) const float32_t arm_neon_twiddles_16_f32[ARM_NEON_TWIDDLES_16_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f,}; + +const uint32_t arm_neon_factors_16_f32[ARM_NEON_FACTORS_16_F32_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const float32_t arm_neon_twiddles_32_f32[ARM_NEON_TWIDDLES_32_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.98078525066375732422f, +-0.19509032368659973145f,0.92387950420379638672f,-0.38268342614173889160f, +0.83146959543228149414f,-0.55557024478912353516f,0.70710676908493041992f, +-0.70710676908493041992f,0.55557024478912353516f,-0.83146959543228149414f, +0.38268342614173889160f,-0.92387950420379638672f,0.19509032368659973145f, +-0.98078525066375732422f,1.00000000000000000000f,-0.00000000000000000000f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.00000000000000006123f,-1.00000000000000000000f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.92387950420379638672f,-0.38268342614173889160f,1.00000000000000000000f, +-0.00000000000000000000f,0.83146959543228149414f,-0.55557024478912353516f, +0.38268342614173889160f,-0.92387950420379638672f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.70710676908493041992f,-0.70710676908493041992f, +-0.98078525066375732422f,-0.19509032368659973145f,-0.92387950420379638672f, +0.38268342614173889160f,-0.55557024478912353516f,0.83146959543228149414f,}; + +const uint32_t arm_neon_factors_32_f32[ARM_NEON_FACTORS_32_F32_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const float32_t arm_neon_twiddles_64_f32[ARM_NEON_TWIDDLES_64_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f, +1.00000000000000000000f,-0.00000000000000000000f,0.99518471956253051758f, +-0.09801714122295379639f,0.98078525066375732422f,-0.19509032368659973145f, +0.95694035291671752930f,-0.29028466343879699707f,0.92387950420379638672f, +-0.38268342614173889160f,0.88192129135131835938f,-0.47139674425125122070f, +0.83146959543228149414f,-0.55557024478912353516f,0.77301043272018432617f, +-0.63439327478408813477f,0.70710676908493041992f,-0.70710676908493041992f, +0.63439327478408813477f,-0.77301043272018432617f,0.55557024478912353516f, +-0.83146959543228149414f,0.47139674425125122070f,-0.88192129135131835938f, +0.38268342614173889160f,-0.92387950420379638672f,0.29028466343879699707f, +-0.95694035291671752930f,0.19509032368659973145f,-0.98078525066375732422f, +0.09801714122295379639f,-0.99518471956253051758f,1.00000000000000000000f, +-0.00000000000000000000f,0.98078525066375732422f,-0.19509032368659973145f, +0.92387950420379638672f,-0.38268342614173889160f,0.83146959543228149414f, +-0.55557024478912353516f,0.70710676908493041992f,-0.70710676908493041992f, +0.55557024478912353516f,-0.83146959543228149414f,0.38268342614173889160f, +-0.92387950420379638672f,0.19509032368659973145f,-0.98078525066375732422f, +0.00000000000000006123f,-1.00000000000000000000f,-0.19509032368659973145f, +-0.98078525066375732422f,-0.38268342614173889160f,-0.92387950420379638672f, +-0.55557024478912353516f,-0.83146959543228149414f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.83146959543228149414f,-0.55557024478912353516f, +-0.92387950420379638672f,-0.38268342614173889160f,-0.98078525066375732422f, +-0.19509032368659973145f,1.00000000000000000000f,-0.00000000000000000000f, +0.95694035291671752930f,-0.29028466343879699707f,0.83146959543228149414f, +-0.55557024478912353516f,0.63439327478408813477f,-0.77301043272018432617f, +0.38268342614173889160f,-0.92387950420379638672f,0.09801714122295379639f, +-0.99518471956253051758f,-0.19509032368659973145f,-0.98078525066375732422f, +-0.47139674425125122070f,-0.88192129135131835938f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.88192129135131835938f,-0.47139674425125122070f, +-0.98078525066375732422f,-0.19509032368659973145f,-0.99518471956253051758f, +0.09801714122295379639f,-0.92387950420379638672f,0.38268342614173889160f, +-0.77301043272018432617f,0.63439327478408813477f,-0.55557024478912353516f, +0.83146959543228149414f,-0.29028466343879699707f,0.95694035291671752930f,}; + +const uint32_t arm_neon_factors_64_f32[ARM_NEON_FACTORS_64_F32_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const float32_t arm_neon_twiddles_128_f32[ARM_NEON_TWIDDLES_128_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.98078525066375732422f, +-0.19509032368659973145f,0.92387950420379638672f,-0.38268342614173889160f, +0.83146959543228149414f,-0.55557024478912353516f,0.70710676908493041992f, +-0.70710676908493041992f,0.55557024478912353516f,-0.83146959543228149414f, +0.38268342614173889160f,-0.92387950420379638672f,0.19509032368659973145f, +-0.98078525066375732422f,1.00000000000000000000f,-0.00000000000000000000f, +0.92387950420379638672f,-0.38268342614173889160f,0.70710676908493041992f, +-0.70710676908493041992f,0.38268342614173889160f,-0.92387950420379638672f, +0.00000000000000006123f,-1.00000000000000000000f,-0.38268342614173889160f, +-0.92387950420379638672f,-0.70710676908493041992f,-0.70710676908493041992f, 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arm_neon_factors_2048_f32[ARM_NEON_FACTORS_2048_F32_LEN]={ +5,256,8,8,}; + +__ALIGNED(16) const float32_t arm_neon_twiddles_4096_f32[ARM_NEON_TWIDDLES_4096_F32_LEN]={ +1.00000000000000000000f,-0.00000000000000000000f,0.92387950420379638672f, +-0.38268342614173889160f,0.70710676908493041992f,-0.70710676908493041992f, +0.38268342614173889160f,-0.92387950420379638672f,1.00000000000000000000f, +-0.00000000000000000000f,0.70710676908493041992f,-0.70710676908493041992f, +0.00000000000000006123f,-1.00000000000000000000f,-0.70710676908493041992f, +-0.70710676908493041992f,1.00000000000000000000f,-0.00000000000000000000f, +0.38268342614173889160f,-0.92387950420379638672f,-0.70710676908493041992f, +-0.70710676908493041992f,-0.92387950420379638672f,0.38268342614173889160f, +1.00000000000000000000f,-0.00000000000000000000f,0.99518471956253051758f, +-0.09801714122295379639f,0.98078525066375732422f,-0.19509032368659973145f, +0.95694035291671752930f,-0.29028466343879699707f,0.92387950420379638672f, 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+0.99576741456985473633f,-0.08732553571462631226f,0.99617981910705566406f, +-0.08274026215076446533f,0.99657112360000610352f,-0.07815324515104293823f, +0.99694132804870605469f,-0.07356456667184829712f,0.99729043245315551758f, +-0.06897433102130889893f,0.99761843681335449219f,-0.06438262760639190674f, +0.99792528152465820312f,-0.05978957191109657288f,0.99821102619171142578f, +-0.05519524589180946350f,0.99847555160522460938f,-0.05059975013136863708f, +0.99871903657913208008f,-0.04600318148732185364f,0.99894130229949951172f, +-0.04140564054250717163f,0.99914240837097167969f,-0.03680722415447235107f, +0.99932235479354858398f,-0.03220802545547485352f,0.99948120117187500000f, +-0.02760814502835273743f,0.99961882829666137695f,-0.02300768159329891205f, +0.99973529577255249023f,-0.01840673014521598816f,0.99983060359954833984f, +-0.01380538847297430038f,0.99990469217300415039f,-0.00920375436544418335f, +0.99995762109756469727f,-0.00460192607715725899f,0.99998939037322998047f,}; + +const uint32_t arm_neon_factors_4096_f32[ARM_NEON_FACTORS_4096_F32_LEN]={ +6,1024,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_16_q31[ARM_NEON_TWIDDLES_16_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,}; + +const uint32_t arm_neon_factors_16_q31[ARM_NEON_FACTORS_16_Q31_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_32_q31[ARM_NEON_TWIDDLES_32_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,}; + +const uint32_t arm_neon_factors_32_q31[ARM_NEON_FACTORS_32_Q31_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_64_q31[ARM_NEON_TWIDDLES_64_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,}; + +const uint32_t arm_neon_factors_64_q31[ARM_NEON_FACTORS_64_Q31_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_128_q31[ARM_NEON_TWIDDLES_128_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,0x7FFFFFFF, +0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91, +0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414, +0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590, +0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC, +0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376, +0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65, +0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3, +0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C, +0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x00000000,0x80000000,0xF3742CA2, +0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3,0x89BE50C3, +0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54,0xA57D8666, +0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A,0xC3A94590, +0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4,0x809DC971, +0xF3742CA2,0x7FFFFFFF,0x00000000,0x7E9D55FC,0xED37EF91,0x7A7D055B,0xDAD7F3A2, +0x73B5EBD1,0xC945DFEC,0x6A6D98A4,0xB8E31319,0x5ED77C8A,0xAA0A5B2E,0x5133CC94, +0x9D0DFE54,0x41CE1E65,0x9235F2EC,0x30FBC54D,0x89BE50C3,0x1F19F97B,0x83D60412, +0x0C8BD35E,0x809DC971,0xF9B82684,0x80277872,0xE70747C4,0x8275A0C0,0xD4E0CB15, +0x877B7BEC,0xC3A94590,0x8F1D343A,0xB3C0200C,0x99307EE0,0xA57D8666,0xA57D8666, +0x99307EE0,0xB3C0200C,0x8F1D343A,0xC3A94590,0x877B7BEC,0xD4E0CB15,0x8275A0C0, +0xE70747C4,0x80277872,0xF9B82684,0x809DC971,0x0C8BD35E,0x83D60412,0x1F19F97B, +0x89BE50C3,0x30FBC54D,0x9235F2EC,0x41CE1E65,0x9D0DFE54,0x5133CC94,0xAA0A5B2E, +0x5ED77C8A,0xB8E31319,0x6A6D98A4,0xC945DFEC,0x73B5EBD1,0xDAD7F3A2,0x7A7D055B, +0xED37EF91,0x7E9D55FC,}; + +const uint32_t arm_neon_factors_128_q31[ARM_NEON_FACTORS_128_Q31_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_256_q31[ARM_NEON_TWIDDLES_256_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684, +0x7FA736B4,0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC, +0xED37EF91,0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96, +0x7C29FBEE,0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1, +0xD7D946D8,0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3, +0x7504D345,0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6, +0xC3A94590,0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0, +0x6A6D98A4,0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926, +0xB140175B,0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E, +0x5CB420E0,0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2, +0xA1288376,0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA, +0x4C3FDFF4,0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50, +0x93DBD6A0,0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A, +0x398CDD32,0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D, +0x89BE50C3,0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F, +0x25280C5E,0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A, +0x831C314E,0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04, +0x0FAB272B,0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C, +0x80277872,0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684, +0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE, +0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3, +0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4, +0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E, +0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4, +0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A, +0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E, +0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04, +0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872,0x00000000,0x80000000,0xF9B82684, +0x80277872,0xF3742CA2,0x809DC971,0xED37EF91,0x8162AA04,0xE70747C4,0x8275A0C0, +0xE0E60685,0x83D60412,0xDAD7F3A2,0x8582FAA5,0xD4E0CB15,0x877B7BEC,0xCF043AB3, +0x89BE50C3,0xC945DFEC,0x8C4A142F,0xC3A94590,0x8F1D343A,0xBE31E19B,0x9235F2EC, +0xB8E31319,0x9592675C,0xB3C0200C,0x99307EE0,0xAECC336C,0x9D0DFE54,0xAA0A5B2E, +0xA1288376,0xA57D8666,0xA57D8666,0xA1288376,0xAA0A5B2E,0x9D0DFE54,0xAECC336C, +0x99307EE0,0xB3C0200C,0x9592675C,0xB8E31319,0x9235F2EC,0xBE31E19B,0x8F1D343A, +0xC3A94590,0x8C4A142F,0xC945DFEC,0x89BE50C3,0xCF043AB3,0x877B7BEC,0xD4E0CB15, +0x8582FAA5,0xDAD7F3A2,0x83D60412,0xE0E60685,0x8275A0C0,0xE70747C4,0x8162AA04, +0xED37EF91,0x809DC971,0xF3742CA2,0x80277872,0xF9B82684,0x7FFFFFFF,0x00000000, +0x7FA736B4,0xF6956FB7,0x7E9D55FC,0xED37EF91,0x7CE3CEB2,0xE3F47D96,0x7A7D055B, +0xDAD7F3A2,0x776C4EDB,0xD1EEF59E,0x73B5EBD1,0xC945DFEC,0x6F5F02B2,0xC0E8B648, +0x6A6D98A4,0xB8E31319,0x64E88926,0xB140175B,0x5ED77C8A,0xAA0A5B2E,0x5842DD54, +0xA34BDF20,0x5133CC94,0x9D0DFE54,0x49B41533,0x9759617F,0x41CE1E65,0x9235F2EC, +0x398CDD32,0x8DAAD37B,0x30FBC54D,0x89BE50C3,0x2826B928,0x8675DC4F,0x1F19F97B, +0x83D60412,0x15E21445,0x81E26C16,0x0C8BD35E,0x809DC971,0x03242ABF,0x8009DE7E, +0xF9B82684,0x80277872,0xF054D8D5,0x80F66E3C,0xE70747C4,0x8275A0C0,0xDDDC5B3B, +0x84A2FC62,0xD4E0CB15,0x877B7BEC,0xCC210D79,0x8AFB2CBB,0xC3A94590,0x8F1D343A, +0xBB8532B0,0x93DBD6A0,0xB3C0200C,0x99307EE0,0xAC64D510,0x9F13C7D0,0xA57D8666, +0xA57D8666,0x9F13C7D0,0xAC64D510,0x99307EE0,0xB3C0200C,0x93DBD6A0,0xBB8532B0, +0x8F1D343A,0xC3A94590,0x8AFB2CBB,0xCC210D79,0x877B7BEC,0xD4E0CB15,0x84A2FC62, +0xDDDC5B3B,0x8275A0C0,0xE70747C4,0x80F66E3C,0xF054D8D5,0x80277872,0xF9B82684, +0x8009DE7E,0x03242ABF,0x809DC971,0x0C8BD35E,0x81E26C16,0x15E21445,0x83D60412, +0x1F19F97B,0x8675DC4F,0x2826B928,0x89BE50C3,0x30FBC54D,0x8DAAD37B,0x398CDD32, +0x9235F2EC,0x41CE1E65,0x9759617F,0x49B41533,0x9D0DFE54,0x5133CC94,0xA34BDF20, +0x5842DD54,0xAA0A5B2E,0x5ED77C8A,0xB140175B,0x64E88926,0xB8E31319,0x6A6D98A4, +0xC0E8B648,0x6F5F02B2,0xC945DFEC,0x73B5EBD1,0xD1EEF59E,0x776C4EDB,0xDAD7F3A2, +0x7A7D055B,0xE3F47D96,0x7CE3CEB2,0xED37EF91,0x7E9D55FC,0xF6956FB7,0x7FA736B4,}; + +const uint32_t arm_neon_factors_256_q31[ARM_NEON_FACTORS_256_Q31_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_512_q31[ARM_NEON_TWIDDLES_512_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,0x7FFFFFFF, +0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91, +0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414, +0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590, +0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC, +0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376, +0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65, +0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3, +0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C, +0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x00000000,0x80000000,0xF3742CA2, +0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3,0x89BE50C3, +0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54,0xA57D8666, +0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A,0xC3A94590, +0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4,0x809DC971, +0xF3742CA2,0x7FFFFFFF,0x00000000,0x7E9D55FC,0xED37EF91,0x7A7D055B,0xDAD7F3A2, +0x73B5EBD1,0xC945DFEC,0x6A6D98A4,0xB8E31319,0x5ED77C8A,0xAA0A5B2E,0x5133CC94, +0x9D0DFE54,0x41CE1E65,0x9235F2EC,0x30FBC54D,0x89BE50C3,0x1F19F97B,0x83D60412, +0x0C8BD35E,0x809DC971,0xF9B82684,0x80277872,0xE70747C4,0x8275A0C0,0xD4E0CB15, +0x877B7BEC,0xC3A94590,0x8F1D343A,0xB3C0200C,0x99307EE0,0xA57D8666,0xA57D8666, +0x99307EE0,0xB3C0200C,0x8F1D343A,0xC3A94590,0x877B7BEC,0xD4E0CB15,0x8275A0C0, +0xE70747C4,0x80277872,0xF9B82684,0x809DC971,0x0C8BD35E,0x83D60412,0x1F19F97B, +0x89BE50C3,0x30FBC54D,0x9235F2EC,0x41CE1E65,0x9D0DFE54,0x5133CC94,0xAA0A5B2E, +0x5ED77C8A,0xB8E31319,0x6A6D98A4,0xC945DFEC,0x73B5EBD1,0xDAD7F3A2,0x7A7D055B, +0xED37EF91,0x7E9D55FC,0x7FFFFFFF,0x00000000,0x7FFD885A,0xFE6DE2E0,0x7FF62182, +0xFCDBD541,0x7FE9CBC0,0xFB49E6A3,0x7FD8878E,0xF9B82684,0x7FC25596,0xF826A462, +0x7FA736B4,0xF6956FB7,0x7F872BF3,0xF50497FB,0x7F62368F,0xF3742CA2,0x7F3857F6, +0xF1E43D1C,0x7F0991C4,0xF054D8D5,0x7ED5E5C6,0xEEC60F31,0x7E9D55FC,0xED37EF91, +0x7E5FE493,0xEBAA894F,0x7E1D93EA,0xEA1DEBBB,0x7DD6668F,0xE8922622,0x7D8A5F40, +0xE70747C4,0x7D3980EC,0xE57D5FDA,0x7CE3CEB2,0xE3F47D96,0x7C894BDE,0xE26CB01B, +0x7C29FBEE,0xE0E60685,0x7BC5E290,0xDF608FE4,0x7B5D039E,0xDDDC5B3B,0x7AEF6323, +0xDC597781,0x7A7D055B,0xDAD7F3A2,0x7A05EEAD,0xD957DE7A,0x798A23B1,0xD7D946D8, +0x7909A92D,0xD65C3B7B,0x78848414,0xD4E0CB15,0x77FAB989,0xD3670446,0x776C4EDB, +0xD1EEF59E,0x76D94989,0xD078AD9E,0x7641AF3D,0xCF043AB3,0x75A585CF,0xCD91AB39, +0x7504D345,0xCC210D79,0x745F9DD1,0xCAB26FA9,0x73B5EBD1,0xC945DFEC,0x7307C3D0, +0xC7DB6C50,0x72552C85,0xC67322CE,0x719E2CD2,0xC50D1149,0x70E2CBC6,0xC3A94590, +0x7023109A,0xC247CD5A,0x6F5F02B2,0xC0E8B648,0x6E96A99D,0xBF8C0DE3,0x6DCA0D14, +0xBE31E19B,0x6CF934FC,0xBCDA3ECB,0x6C242960,0xBB8532B0,0x6B4AF279,0xBA32CA71, +0x6A6D98A4,0xB8E31319,0x698C246C,0xB796199B,0x68A69E81,0xB64BEACD,0x67BD0FBD, +0xB5049368,0x66CF8120,0xB3C0200C,0x65DDFBD3,0xB27E9D3C,0x64E88926,0xB140175B, +0x63EF3290,0xB0049AB3,0x62F201AC,0xAECC336C,0x61F1003F,0xAD96ED92,0x60EC3830, +0xAC64D510,0x5FE3B38D,0xAB35F5B5,0x5ED77C8A,0xAA0A5B2E,0x5DC79D7C,0xA8E21106, +0x5CB420E0,0xA7BD22AC,0x5B9D1154,0xA69B9B68,0x5A82799A,0xA57D8666,0x59646498, +0xA462EEAC,0x5842DD54,0xA34BDF20,0x571DEEFA,0xA2386284,0x55F5A4D2,0xA1288376, +0x54CA0A4B,0xA01C4C73,0x539B2AF0,0x9F13C7D0,0x5269126E,0x9E0EFFC1,0x5133CC94, +0x9D0DFE54,0x4FFB654D,0x9C10CD70,0x4EBFE8A5,0x9B1776DA,0x4D8162C4,0x9A22042D, +0x4C3FDFF4,0x99307EE0,0x4AFB6C98,0x9842F043,0x49B41533,0x9759617F,0x4869E665, +0x9673DB94,0x471CECE7,0x9592675C,0x45CD358F,0x94B50D87,0x447ACD50,0x93DBD6A0, +0x4325C135,0x9306CB04,0x41CE1E65,0x9235F2EC,0x4073F21D,0x91695663,0x3F1749B8, +0x90A0FD4E,0x3DB832A6,0x8FDCEF66,0x3C56BA70,0x8F1D343A,0x3AF2EEB7,0x8E61D32E, +0x398CDD32,0x8DAAD37B,0x382493B0,0x8CF83C30,0x36BA2014,0x8C4A142F,0x354D9057, +0x8BA0622F,0x33DEF287,0x8AFB2CBB,0x326E54C7,0x8A5A7A31,0x30FBC54D,0x89BE50C3, +0x2F875262,0x8926B677,0x2E110A62,0x8893B125,0x2C98FBBA,0x88054677,0x2B1F34EB, +0x877B7BEC,0x29A3C485,0x86F656D3,0x2826B928,0x8675DC4F,0x26A82186,0x85FA1153, +0x25280C5E,0x8582FAA5,0x23A6887F,0x85109CDD,0x2223A4C5,0x84A2FC62,0x209F701C, +0x843A1D70,0x1F19F97B,0x83D60412,0x1D934FE5,0x8376B422,0x1C0B826A,0x831C314E, +0x1A82A026,0x82C67F14,0x18F8B83C,0x8275A0C0,0x176DD9DE,0x82299971,0x15E21445, +0x81E26C16,0x145576B1,0x81A01B6D,0x12C8106F,0x8162AA04,0x1139F0CF,0x812A1A3A, +0x0FAB272B,0x80F66E3C,0x0E1BC2E4,0x80C7A80A,0x0C8BD35E,0x809DC971,0x0AFB6805, +0x8078D40D,0x096A9049,0x8058C94C,0x07D95B9E,0x803DAA6A,0x0647D97C,0x80277872, +0x04B6195D,0x80163440,0x03242ABF,0x8009DE7E,0x01921D20,0x800277A6,0x7FFFFFFF, +0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684,0x7FA736B4,0xF6956FB7, +0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC,0xED37EF91,0x7E1D93EA, +0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96,0x7C29FBEE,0xE0E60685, +0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1,0xD7D946D8,0x78848414, +0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3,0x7504D345,0xCC210D79, +0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6,0xC3A94590,0x6F5F02B2, +0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0,0x6A6D98A4,0xB8E31319, +0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926,0xB140175B,0x62F201AC, +0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E,0x5CB420E0,0xA7BD22AC, +0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2,0xA1288376,0x539B2AF0, +0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA,0x4C3FDFF4,0x99307EE0, +0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50,0x93DBD6A0,0x41CE1E65, +0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A,0x398CDD32,0x8DAAD37B, +0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D,0x89BE50C3,0x2E110A62, +0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F,0x25280C5E,0x8582FAA5, +0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A,0x831C314E,0x18F8B83C, +0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04,0x0FAB272B,0x80F66E3C, +0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C,0x80277872,0x03242ABF, +0x8009DE7E,0x00000000,0x80000000,0xFCDBD541,0x8009DE7E,0xF9B82684,0x80277872, +0xF6956FB7,0x8058C94C,0xF3742CA2,0x809DC971,0xF054D8D5,0x80F66E3C,0xED37EF91, +0x8162AA04,0xEA1DEBBB,0x81E26C16,0xE70747C4,0x8275A0C0,0xE3F47D96,0x831C314E, +0xE0E60685,0x83D60412,0xDDDC5B3B,0x84A2FC62,0xDAD7F3A2,0x8582FAA5,0xD7D946D8, +0x8675DC4F,0xD4E0CB15,0x877B7BEC,0xD1EEF59E,0x8893B125,0xCF043AB3,0x89BE50C3, +0xCC210D79,0x8AFB2CBB,0xC945DFEC,0x8C4A142F,0xC67322CE,0x8DAAD37B,0xC3A94590, +0x8F1D343A,0xC0E8B648,0x90A0FD4E,0xBE31E19B,0x9235F2EC,0xBB8532B0,0x93DBD6A0, +0xB8E31319,0x9592675C,0xB64BEACD,0x9759617F,0xB3C0200C,0x99307EE0,0xB140175B, +0x9B1776DA,0xAECC336C,0x9D0DFE54,0xAC64D510,0x9F13C7D0,0xAA0A5B2E,0xA1288376, +0xA7BD22AC,0xA34BDF20,0xA57D8666,0xA57D8666,0xA34BDF20,0xA7BD22AC,0xA1288376, +0xAA0A5B2E,0x9F13C7D0,0xAC64D510,0x9D0DFE54,0xAECC336C,0x9B1776DA,0xB140175B, +0x99307EE0,0xB3C0200C,0x9759617F,0xB64BEACD,0x9592675C,0xB8E31319,0x93DBD6A0, +0xBB8532B0,0x9235F2EC,0xBE31E19B,0x90A0FD4E,0xC0E8B648,0x8F1D343A,0xC3A94590, +0x8DAAD37B,0xC67322CE,0x8C4A142F,0xC945DFEC,0x8AFB2CBB,0xCC210D79,0x89BE50C3, +0xCF043AB3,0x8893B125,0xD1EEF59E,0x877B7BEC,0xD4E0CB15,0x8675DC4F,0xD7D946D8, +0x8582FAA5,0xDAD7F3A2,0x84A2FC62,0xDDDC5B3B,0x83D60412,0xE0E60685,0x831C314E, +0xE3F47D96,0x8275A0C0,0xE70747C4,0x81E26C16,0xEA1DEBBB,0x8162AA04,0xED37EF91, +0x80F66E3C,0xF054D8D5,0x809DC971,0xF3742CA2,0x8058C94C,0xF6956FB7,0x80277872, +0xF9B82684,0x8009DE7E,0xFCDBD541,0x7FFFFFFF,0x00000000,0x7FE9CBC0,0xFB49E6A3, +0x7FA736B4,0xF6956FB7,0x7F3857F6,0xF1E43D1C,0x7E9D55FC,0xED37EF91,0x7DD6668F, +0xE8922622,0x7CE3CEB2,0xE3F47D96,0x7BC5E290,0xDF608FE4,0x7A7D055B,0xDAD7F3A2, +0x7909A92D,0xD65C3B7B,0x776C4EDB,0xD1EEF59E,0x75A585CF,0xCD91AB39,0x73B5EBD1, +0xC945DFEC,0x719E2CD2,0xC50D1149,0x6F5F02B2,0xC0E8B648,0x6CF934FC,0xBCDA3ECB, +0x6A6D98A4,0xB8E31319,0x67BD0FBD,0xB5049368,0x64E88926,0xB140175B,0x61F1003F, +0xAD96ED92,0x5ED77C8A,0xAA0A5B2E,0x5B9D1154,0xA69B9B68,0x5842DD54,0xA34BDF20, +0x54CA0A4B,0xA01C4C73,0x5133CC94,0x9D0DFE54,0x4D8162C4,0x9A22042D,0x49B41533, +0x9759617F,0x45CD358F,0x94B50D87,0x41CE1E65,0x9235F2EC,0x3DB832A6,0x8FDCEF66, +0x398CDD32,0x8DAAD37B,0x354D9057,0x8BA0622F,0x30FBC54D,0x89BE50C3,0x2C98FBBA, +0x88054677,0x2826B928,0x8675DC4F,0x23A6887F,0x85109CDD,0x1F19F97B,0x83D60412, +0x1A82A026,0x82C67F14,0x15E21445,0x81E26C16,0x1139F0CF,0x812A1A3A,0x0C8BD35E, +0x809DC971,0x07D95B9E,0x803DAA6A,0x03242ABF,0x8009DE7E,0xFE6DE2E0,0x800277A6, +0xF9B82684,0x80277872,0xF50497FB,0x8078D40D,0xF054D8D5,0x80F66E3C,0xEBAA894F, +0x81A01B6D,0xE70747C4,0x8275A0C0,0xE26CB01B,0x8376B422,0xDDDC5B3B,0x84A2FC62, +0xD957DE7A,0x85FA1153,0xD4E0CB15,0x877B7BEC,0xD078AD9E,0x8926B677,0xCC210D79, +0x8AFB2CBB,0xC7DB6C50,0x8CF83C30,0xC3A94590,0x8F1D343A,0xBF8C0DE3,0x91695663, +0xBB8532B0,0x93DBD6A0,0xB796199B,0x9673DB94,0xB3C0200C,0x99307EE0,0xB0049AB3, +0x9C10CD70,0xAC64D510,0x9F13C7D0,0xA8E21106,0xA2386284,0xA57D8666,0xA57D8666, +0xA2386284,0xA8E21106,0x9F13C7D0,0xAC64D510,0x9C10CD70,0xB0049AB3,0x99307EE0, +0xB3C0200C,0x9673DB94,0xB796199B,0x93DBD6A0,0xBB8532B0,0x91695663,0xBF8C0DE3, +0x8F1D343A,0xC3A94590,0x8CF83C30,0xC7DB6C50,0x8AFB2CBB,0xCC210D79,0x8926B677, +0xD078AD9E,0x877B7BEC,0xD4E0CB15,0x85FA1153,0xD957DE7A,0x84A2FC62,0xDDDC5B3B, +0x8376B422,0xE26CB01B,0x8275A0C0,0xE70747C4,0x81A01B6D,0xEBAA894F,0x80F66E3C, +0xF054D8D5,0x8078D40D,0xF50497FB,0x80277872,0xF9B82684,0x800277A6,0xFE6DE2E0, +0x8009DE7E,0x03242ABF,0x803DAA6A,0x07D95B9E,0x809DC971,0x0C8BD35E,0x812A1A3A, +0x1139F0CF,0x81E26C16,0x15E21445,0x82C67F14,0x1A82A026,0x83D60412,0x1F19F97B, +0x85109CDD,0x23A6887F,0x8675DC4F,0x2826B928,0x88054677,0x2C98FBBA,0x89BE50C3, +0x30FBC54D,0x8BA0622F,0x354D9057,0x8DAAD37B,0x398CDD32,0x8FDCEF66,0x3DB832A6, +0x9235F2EC,0x41CE1E65,0x94B50D87,0x45CD358F,0x9759617F,0x49B41533,0x9A22042D, +0x4D8162C4,0x9D0DFE54,0x5133CC94,0xA01C4C73,0x54CA0A4B,0xA34BDF20,0x5842DD54, +0xA69B9B68,0x5B9D1154,0xAA0A5B2E,0x5ED77C8A,0xAD96ED92,0x61F1003F,0xB140175B, +0x64E88926,0xB5049368,0x67BD0FBD,0xB8E31319,0x6A6D98A4,0xBCDA3ECB,0x6CF934FC, +0xC0E8B648,0x6F5F02B2,0xC50D1149,0x719E2CD2,0xC945DFEC,0x73B5EBD1,0xCD91AB39, +0x75A585CF,0xD1EEF59E,0x776C4EDB,0xD65C3B7B,0x7909A92D,0xDAD7F3A2,0x7A7D055B, +0xDF608FE4,0x7BC5E290,0xE3F47D96,0x7CE3CEB2,0xE8922622,0x7DD6668F,0xED37EF91, +0x7E9D55FC,0xF1E43D1C,0x7F3857F6,0xF6956FB7,0x7FA736B4,0xFB49E6A3,0x7FE9CBC0,}; + +const uint32_t arm_neon_factors_512_q31[ARM_NEON_FACTORS_512_Q31_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_1024_q31[ARM_NEON_TWIDDLES_1024_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, +0x5133CC94,0x9D0DFE54,0x471CECE7,0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D, +0x89BE50C3,0x25280C5E,0x8582FAA5,0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971, +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x00000000,0x80000000,0xE70747C4,0x8275A0C0,0xCF043AB3, +0x89BE50C3,0xB8E31319,0x9592675C,0xA57D8666,0xA57D8666,0x9592675C,0xB8E31319, +0x89BE50C3,0xCF043AB3,0x8275A0C0,0xE70747C4,0x7FFFFFFF,0x00000000,0x7A7D055B, +0xDAD7F3A2,0x6A6D98A4,0xB8E31319,0x5133CC94,0x9D0DFE54,0x30FBC54D,0x89BE50C3, +0x0C8BD35E,0x809DC971,0xE70747C4,0x8275A0C0,0xC3A94590,0x8F1D343A,0xA57D8666, +0xA57D8666,0x8F1D343A,0xC3A94590,0x8275A0C0,0xE70747C4,0x809DC971,0x0C8BD35E, +0x89BE50C3,0x30FBC54D,0x9D0DFE54,0x5133CC94,0xB8E31319,0x6A6D98A4,0xDAD7F3A2, +0x7A7D055B,0x7FFFFFFF,0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684, +0x7FA736B4,0xF6956FB7,0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC, +0xED37EF91,0x7E1D93EA,0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96, +0x7C29FBEE,0xE0E60685,0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1, +0xD7D946D8,0x78848414,0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3, +0x7504D345,0xCC210D79,0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6, +0xC3A94590,0x6F5F02B2,0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0, +0x6A6D98A4,0xB8E31319,0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926, +0xB140175B,0x62F201AC,0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E, +0x5CB420E0,0xA7BD22AC,0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2, +0xA1288376,0x539B2AF0,0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA, +0x4C3FDFF4,0x99307EE0,0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50, +0x93DBD6A0,0x41CE1E65,0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A, +0x398CDD32,0x8DAAD37B,0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D, +0x89BE50C3,0x2E110A62,0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F, +0x25280C5E,0x8582FAA5,0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A, +0x831C314E,0x18F8B83C,0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04, +0x0FAB272B,0x80F66E3C,0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C, +0x80277872,0x03242ABF,0x8009DE7E,0x7FFFFFFF,0x00000000,0x7FD8878E,0xF9B82684, +0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91,0x7D8A5F40,0xE70747C4,0x7C29FBEE, +0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414,0xD4E0CB15,0x7641AF3D,0xCF043AB3, +0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590,0x6DCA0D14,0xBE31E19B,0x6A6D98A4, +0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC,0xAECC336C,0x5ED77C8A,0xAA0A5B2E, +0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376,0x5133CC94,0x9D0DFE54,0x4C3FDFF4, +0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65,0x9235F2EC,0x3C56BA70,0x8F1D343A, +0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3,0x2B1F34EB,0x877B7BEC,0x25280C5E, +0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C,0x8275A0C0,0x12C8106F,0x8162AA04, +0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872,0x00000000,0x80000000,0xF9B82684, 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+0x85FA1153,0xD7D946D8,0x8675DC4F,0xD65C3B7B,0x86F656D3,0xD4E0CB15,0x877B7BEC, +0xD3670446,0x88054677,0xD1EEF59E,0x8893B125,0xD078AD9E,0x8926B677,0xCF043AB3, +0x89BE50C3,0xCD91AB39,0x8A5A7A31,0xCC210D79,0x8AFB2CBB,0xCAB26FA9,0x8BA0622F, +0xC945DFEC,0x8C4A142F,0xC7DB6C50,0x8CF83C30,0xC67322CE,0x8DAAD37B,0xC50D1149, +0x8E61D32E,0xC3A94590,0x8F1D343A,0xC247CD5A,0x8FDCEF66,0xC0E8B648,0x90A0FD4E, +0xBF8C0DE3,0x91695663,0xBE31E19B,0x9235F2EC,0xBCDA3ECB,0x9306CB04,0xBB8532B0, +0x93DBD6A0,0xBA32CA71,0x94B50D87,0xB8E31319,0x9592675C,0xB796199B,0x9673DB94, +0xB64BEACD,0x9759617F,0xB5049368,0x9842F043,0xB3C0200C,0x99307EE0,0xB27E9D3C, +0x9A22042D,0xB140175B,0x9B1776DA,0xB0049AB3,0x9C10CD70,0xAECC336C,0x9D0DFE54, +0xAD96ED92,0x9E0EFFC1,0xAC64D510,0x9F13C7D0,0xAB35F5B5,0xA01C4C73,0xAA0A5B2E, +0xA1288376,0xA8E21106,0xA2386284,0xA7BD22AC,0xA34BDF20,0xA69B9B68,0xA462EEAC, +0xA57D8666,0xA57D8666,0xA462EEAC,0xA69B9B68,0xA34BDF20,0xA7BD22AC,0xA2386284, +0xA8E21106,0xA1288376,0xAA0A5B2E,0xA01C4C73,0xAB35F5B5,0x9F13C7D0,0xAC64D510, +0x9E0EFFC1,0xAD96ED92,0x9D0DFE54,0xAECC336C,0x9C10CD70,0xB0049AB3,0x9B1776DA, +0xB140175B,0x9A22042D,0xB27E9D3C,0x99307EE0,0xB3C0200C,0x9842F043,0xB5049368, +0x9759617F,0xB64BEACD,0x9673DB94,0xB796199B,0x9592675C,0xB8E31319,0x94B50D87, +0xBA32CA71,0x93DBD6A0,0xBB8532B0,0x9306CB04,0xBCDA3ECB,0x9235F2EC,0xBE31E19B, +0x91695663,0xBF8C0DE3,0x90A0FD4E,0xC0E8B648,0x8FDCEF66,0xC247CD5A,0x8F1D343A, +0xC3A94590,0x8E61D32E,0xC50D1149,0x8DAAD37B,0xC67322CE,0x8CF83C30,0xC7DB6C50, +0x8C4A142F,0xC945DFEC,0x8BA0622F,0xCAB26FA9,0x8AFB2CBB,0xCC210D79,0x8A5A7A31, +0xCD91AB39,0x89BE50C3,0xCF043AB3,0x8926B677,0xD078AD9E,0x8893B125,0xD1EEF59E, +0x88054677,0xD3670446,0x877B7BEC,0xD4E0CB15,0x86F656D3,0xD65C3B7B,0x8675DC4F, +0xD7D946D8,0x85FA1153,0xD957DE7A,0x8582FAA5,0xDAD7F3A2,0x85109CDD,0xDC597781, +0x84A2FC62,0xDDDC5B3B,0x843A1D70,0xDF608FE4,0x83D60412,0xE0E60685,0x8376B422, +0xE26CB01B,0x831C314E,0xE3F47D96,0x82C67F14,0xE57D5FDA,0x8275A0C0,0xE70747C4, +0x82299971,0xE8922622,0x81E26C16,0xEA1DEBBB,0x81A01B6D,0xEBAA894F,0x8162AA04, +0xED37EF91,0x812A1A3A,0xEEC60F31,0x80F66E3C,0xF054D8D5,0x80C7A80A,0xF1E43D1C, +0x809DC971,0xF3742CA2,0x8078D40D,0xF50497FB,0x8058C94C,0xF6956FB7,0x803DAA6A, +0xF826A462,0x80277872,0xF9B82684,0x80163440,0xFB49E6A3,0x8009DE7E,0xFCDBD541, +0x800277A6,0xFE6DE2E0,0x7FFFFFFF,0x00000000,0x7FFA72D1,0xFDA4D929,0x7FE9CBC0, +0xFB49E6A3,0x7FCE0C3E,0xF8EF5CBB,0x7FA736B4,0xF6956FB7,0x7F754E80,0xF43C53CB, +0x7F3857F6,0xF1E43D1C,0x7EF05860,0xEF8D5FB8,0x7E9D55FC,0xED37EF91,0x7E3F57FF, +0xEAE4207A,0x7DD6668F,0xE8922622,0x7D628AC6,0xE642340D,0x7CE3CEB2,0xE3F47D96, +0x7C5A3D50,0xE1A935E2,0x7BC5E290,0xDF608FE4,0x7B26CB4F,0xDD1ABE51,0x7A7D055B, +0xDAD7F3A2,0x79C89F6E,0xD898620C,0x7909A92D,0xD65C3B7B,0x78403329,0xD423B191, +0x776C4EDB,0xD1EEF59E,0x768E0EA6,0xCFBE389F,0x75A585CF,0xCD91AB39,0x74B2C884, +0xCB697DB0,0x73B5EBD1,0xC945DFEC,0x72AF05A7,0xC727016D,0x719E2CD2,0xC50D1149, +0x708378FF,0xC2F83E2A,0x6F5F02B2,0xC0E8B648,0x6E30E34A,0xBEDEA765,0x6CF934FC, +0xBCDA3ECB,0x6BB812D1,0xBADBA943,0x6A6D98A4,0xB8E31319,0x6919E320,0xB6F0A812, +0x67BD0FBD,0xB5049368,0x66573CBB,0xB31EFFCC,0x64E88926,0xB140175B,0x637114CC, +0xAF6803A2,0x61F1003F,0xAD96ED92,0x60686CCF,0xABCCFD83,0x5ED77C8A,0xAA0A5B2E, +0x5D3E5237,0xA84F2DAA,0x5B9D1154,0xA69B9B68,0x59F3DE12,0xA4EFCA31,0x5842DD54, +0xA34BDF20,0x568A34A9,0xA1AFFEA3,0x54CA0A4B,0xA01C4C73,0x53028518,0x9E90EB94, +0x5133CC94,0x9D0DFE54,0x4F5E08E3,0x9B93A641,0x4D8162C4,0x9A22042D,0x4B9E0390, +0x98B93828,0x49B41533,0x9759617F,0x47C3C22F,0x96029EB6,0x45CD358F,0x94B50D87, +0x43D09AED,0x9370CAE4,0x41CE1E65,0x9235F2EC,0x3FC5EC98,0x9104A0EE,0x3DB832A6, +0x8FDCEF66,0x3BA51E29,0x8EBEF7FB,0x398CDD32,0x8DAAD37B,0x376F9E46,0x8CA099DA, +0x354D9057,0x8BA0622F,0x3326E2C3,0x8AAA42B4,0x30FBC54D,0x89BE50C3,0x2ECC681E, +0x88DCA0D3,0x2C98FBBA,0x88054677,0x2A61B101,0x8738545E,0x2826B928,0x8675DC4F, +0x25E845B6,0x85BDEF28,0x23A6887F,0x85109CDD,0x2161B3A0,0x846DF477,0x1F19F97B, +0x83D60412,0x1CCF8CB3,0x8348D8DC,0x1A82A026,0x82C67F14,0x183366E9,0x824F0208, +0x15E21445,0x81E26C16,0x138EDBB1,0x8180C6A9,0x1139F0CF,0x812A1A3A,0x0EE38766, +0x80DE6E4C,0x0C8BD35E,0x809DC971,0x0A3308BD,0x80683143,0x07D95B9E,0x803DAA6A, +0x057F0035,0x801E3895,0x03242ABF,0x8009DE7E,0x00C90F88,0x80009DEA,0xFE6DE2E0, +0x800277A6,0xFC12D91A,0x800F6B88,0xF9B82684,0x80277872,0xF75DFF66,0x804A9C4D, +0xF50497FB,0x8078D40D,0xF2AC246E,0x80B21BAF,0xF054D8D5,0x80F66E3C,0xEDFEE92B, +0x8145C5C7,0xEBAA894F,0x81A01B6D,0xE957ECFB,0x82056758,0xE70747C4,0x8275A0C0, +0xE4B8CD11,0x82F0BDE8,0xE26CB01B,0x8376B422,0xE02323E5,0x840777D0,0xDDDC5B3B, +0x84A2FC62,0xDB9888A8,0x8549345C,0xD957DE7A,0x85FA1153,0xD71A8EB5,0x86B583EE, +0xD4E0CB15,0x877B7BEC,0xD2AAC504,0x884BE821,0xD078AD9E,0x8926B677,0xCE4AB5A2, +0x8A0BD3F5,0xCC210D79,0x8AFB2CBB,0xC9FBE527,0x8BF4AC05,0xC7DB6C50,0x8CF83C30, +0xC5BFD22E,0x8E05C6B7,0xC3A94590,0x8F1D343A,0xC197F4D4,0x903E6C7B,0xBF8C0DE3, +0x91695663,0xBD85BE30,0x929DD806,0xBB8532B0,0x93DBD6A0,0xB98A97D8,0x9523369C, +0xB796199B,0x9673DB94,0xB5A7E362,0x97CDA855,0xB3C0200C,0x99307EE0,0xB1DEF9E9, +0x9A9C406E,0xB0049AB3,0x9C10CD70,0xAE312B92,0x9D8E0597,0xAC64D510,0x9F13C7D0, +0xAA9FBF1E,0xA0A1F24D,0xA8E21106,0xA2386284,0xA72BF174,0xA3D6F534,0xA57D8666, +0xA57D8666,0xA3D6F534,0xA72BF174,0xA2386284,0xA8E21106,0xA0A1F24D,0xAA9FBF1E, +0x9F13C7D0,0xAC64D510,0x9D8E0597,0xAE312B92,0x9C10CD70,0xB0049AB3,0x9A9C406E, +0xB1DEF9E9,0x99307EE0,0xB3C0200C,0x97CDA855,0xB5A7E362,0x9673DB94,0xB796199B, +0x9523369C,0xB98A97D8,0x93DBD6A0,0xBB8532B0,0x929DD806,0xBD85BE30,0x91695663, +0xBF8C0DE3,0x903E6C7B,0xC197F4D4,0x8F1D343A,0xC3A94590,0x8E05C6B7,0xC5BFD22E, +0x8CF83C30,0xC7DB6C50,0x8BF4AC05,0xC9FBE527,0x8AFB2CBB,0xCC210D79,0x8A0BD3F5, +0xCE4AB5A2,0x8926B677,0xD078AD9E,0x884BE821,0xD2AAC504,0x877B7BEC,0xD4E0CB15, +0x86B583EE,0xD71A8EB5,0x85FA1153,0xD957DE7A,0x8549345C,0xDB9888A8,0x84A2FC62, +0xDDDC5B3B,0x840777D0,0xE02323E5,0x8376B422,0xE26CB01B,0x82F0BDE8,0xE4B8CD11, +0x8275A0C0,0xE70747C4,0x82056758,0xE957ECFB,0x81A01B6D,0xEBAA894F,0x8145C5C7, +0xEDFEE92B,0x80F66E3C,0xF054D8D5,0x80B21BAF,0xF2AC246E,0x8078D40D,0xF50497FB, +0x804A9C4D,0xF75DFF66,0x80277872,0xF9B82684,0x800F6B88,0xFC12D91A,0x800277A6, +0xFE6DE2E0,0x80009DEA,0x00C90F88,0x8009DE7E,0x03242ABF,0x801E3895,0x057F0035, +0x803DAA6A,0x07D95B9E,0x80683143,0x0A3308BD,0x809DC971,0x0C8BD35E,0x80DE6E4C, +0x0EE38766,0x812A1A3A,0x1139F0CF,0x8180C6A9,0x138EDBB1,0x81E26C16,0x15E21445, +0x824F0208,0x183366E9,0x82C67F14,0x1A82A026,0x8348D8DC,0x1CCF8CB3,0x83D60412, +0x1F19F97B,0x846DF477,0x2161B3A0,0x85109CDD,0x23A6887F,0x85BDEF28,0x25E845B6, +0x8675DC4F,0x2826B928,0x8738545E,0x2A61B101,0x88054677,0x2C98FBBA,0x88DCA0D3, +0x2ECC681E,0x89BE50C3,0x30FBC54D,0x8AAA42B4,0x3326E2C3,0x8BA0622F,0x354D9057, +0x8CA099DA,0x376F9E46,0x8DAAD37B,0x398CDD32,0x8EBEF7FB,0x3BA51E29,0x8FDCEF66, +0x3DB832A6,0x9104A0EE,0x3FC5EC98,0x9235F2EC,0x41CE1E65,0x9370CAE4,0x43D09AED, +0x94B50D87,0x45CD358F,0x96029EB6,0x47C3C22F,0x9759617F,0x49B41533,0x98B93828, +0x4B9E0390,0x9A22042D,0x4D8162C4,0x9B93A641,0x4F5E08E3,0x9D0DFE54,0x5133CC94, +0x9E90EB94,0x53028518,0xA01C4C73,0x54CA0A4B,0xA1AFFEA3,0x568A34A9,0xA34BDF20, +0x5842DD54,0xA4EFCA31,0x59F3DE12,0xA69B9B68,0x5B9D1154,0xA84F2DAA,0x5D3E5237, +0xAA0A5B2E,0x5ED77C8A,0xABCCFD83,0x60686CCF,0xAD96ED92,0x61F1003F,0xAF6803A2, +0x637114CC,0xB140175B,0x64E88926,0xB31EFFCC,0x66573CBB,0xB5049368,0x67BD0FBD, +0xB6F0A812,0x6919E320,0xB8E31319,0x6A6D98A4,0xBADBA943,0x6BB812D1,0xBCDA3ECB, +0x6CF934FC,0xBEDEA765,0x6E30E34A,0xC0E8B648,0x6F5F02B2,0xC2F83E2A,0x708378FF, +0xC50D1149,0x719E2CD2,0xC727016D,0x72AF05A7,0xC945DFEC,0x73B5EBD1,0xCB697DB0, +0x74B2C884,0xCD91AB39,0x75A585CF,0xCFBE389F,0x768E0EA6,0xD1EEF59E,0x776C4EDB, +0xD423B191,0x78403329,0xD65C3B7B,0x7909A92D,0xD898620C,0x79C89F6E,0xDAD7F3A2, +0x7A7D055B,0xDD1ABE51,0x7B26CB4F,0xDF608FE4,0x7BC5E290,0xE1A935E2,0x7C5A3D50, +0xE3F47D96,0x7CE3CEB2,0xE642340D,0x7D628AC6,0xE8922622,0x7DD6668F,0xEAE4207A, +0x7E3F57FF,0xED37EF91,0x7E9D55FC,0xEF8D5FB8,0x7EF05860,0xF1E43D1C,0x7F3857F6, +0xF43C53CB,0x7F754E80,0xF6956FB7,0x7FA736B4,0xF8EF5CBB,0x7FCE0C3E,0xFB49E6A3, +0x7FE9CBC0,0xFDA4D929,0x7FFA72D1,}; + +const uint32_t arm_neon_factors_1024_q31[ARM_NEON_FACTORS_1024_Q31_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_2048_q31[ARM_NEON_TWIDDLES_2048_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7D8A5F40,0xE70747C4,0x7641AF3D,0xCF043AB3,0x6A6D98A4, +0xB8E31319,0x5A82799A,0xA57D8666,0x471CECE7,0x9592675C,0x30FBC54D,0x89BE50C3, +0x18F8B83C,0x8275A0C0,0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A, +0xA57D8666,0x30FBC54D,0x89BE50C3,0x00000000,0x80000000,0xCF043AB3,0x89BE50C3, +0xA57D8666,0xA57D8666,0x89BE50C3,0xCF043AB3,0x7FFFFFFF,0x00000000,0x6A6D98A4, +0xB8E31319,0x30FBC54D,0x89BE50C3,0xE70747C4,0x8275A0C0,0xA57D8666,0xA57D8666, +0x8275A0C0,0xE70747C4,0x89BE50C3,0x30FBC54D,0xB8E31319,0x6A6D98A4,0x7FFFFFFF, +0x00000000,0x7FD8878E,0xF9B82684,0x7F62368F,0xF3742CA2,0x7E9D55FC,0xED37EF91, +0x7D8A5F40,0xE70747C4,0x7C29FBEE,0xE0E60685,0x7A7D055B,0xDAD7F3A2,0x78848414, +0xD4E0CB15,0x7641AF3D,0xCF043AB3,0x73B5EBD1,0xC945DFEC,0x70E2CBC6,0xC3A94590, +0x6DCA0D14,0xBE31E19B,0x6A6D98A4,0xB8E31319,0x66CF8120,0xB3C0200C,0x62F201AC, +0xAECC336C,0x5ED77C8A,0xAA0A5B2E,0x5A82799A,0xA57D8666,0x55F5A4D2,0xA1288376, +0x5133CC94,0x9D0DFE54,0x4C3FDFF4,0x99307EE0,0x471CECE7,0x9592675C,0x41CE1E65, +0x9235F2EC,0x3C56BA70,0x8F1D343A,0x36BA2014,0x8C4A142F,0x30FBC54D,0x89BE50C3, +0x2B1F34EB,0x877B7BEC,0x25280C5E,0x8582FAA5,0x1F19F97B,0x83D60412,0x18F8B83C, +0x8275A0C0,0x12C8106F,0x8162AA04,0x0C8BD35E,0x809DC971,0x0647D97C,0x80277872, +0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2,0x7D8A5F40,0xE70747C4,0x7A7D055B, +0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6,0xC3A94590,0x6A6D98A4,0xB8E31319, +0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666,0x5133CC94,0x9D0DFE54,0x471CECE7, +0x9592675C,0x3C56BA70,0x8F1D343A,0x30FBC54D,0x89BE50C3,0x25280C5E,0x8582FAA5, +0x18F8B83C,0x8275A0C0,0x0C8BD35E,0x809DC971,0x00000000,0x80000000,0xF3742CA2, +0x809DC971,0xE70747C4,0x8275A0C0,0xDAD7F3A2,0x8582FAA5,0xCF043AB3,0x89BE50C3, +0xC3A94590,0x8F1D343A,0xB8E31319,0x9592675C,0xAECC336C,0x9D0DFE54,0xA57D8666, +0xA57D8666,0x9D0DFE54,0xAECC336C,0x9592675C,0xB8E31319,0x8F1D343A,0xC3A94590, +0x89BE50C3,0xCF043AB3,0x8582FAA5,0xDAD7F3A2,0x8275A0C0,0xE70747C4,0x809DC971, +0xF3742CA2,0x7FFFFFFF,0x00000000,0x7E9D55FC,0xED37EF91,0x7A7D055B,0xDAD7F3A2, +0x73B5EBD1,0xC945DFEC,0x6A6D98A4,0xB8E31319,0x5ED77C8A,0xAA0A5B2E,0x5133CC94, +0x9D0DFE54,0x41CE1E65,0x9235F2EC,0x30FBC54D,0x89BE50C3,0x1F19F97B,0x83D60412, +0x0C8BD35E,0x809DC971,0xF9B82684,0x80277872,0xE70747C4,0x8275A0C0,0xD4E0CB15, +0x877B7BEC,0xC3A94590,0x8F1D343A,0xB3C0200C,0x99307EE0,0xA57D8666,0xA57D8666, +0x99307EE0,0xB3C0200C,0x8F1D343A,0xC3A94590,0x877B7BEC,0xD4E0CB15,0x8275A0C0, +0xE70747C4,0x80277872,0xF9B82684,0x809DC971,0x0C8BD35E,0x83D60412,0x1F19F97B, +0x89BE50C3,0x30FBC54D,0x9235F2EC,0x41CE1E65,0x9D0DFE54,0x5133CC94,0xAA0A5B2E, +0x5ED77C8A,0xB8E31319,0x6A6D98A4,0xC945DFEC,0x73B5EBD1,0xDAD7F3A2,0x7A7D055B, +0xED37EF91,0x7E9D55FC,0x7FFFFFFF,0x00000000,0x7FFD885A,0xFE6DE2E0,0x7FF62182, +0xFCDBD541,0x7FE9CBC0,0xFB49E6A3,0x7FD8878E,0xF9B82684,0x7FC25596,0xF826A462, +0x7FA736B4,0xF6956FB7,0x7F872BF3,0xF50497FB,0x7F62368F,0xF3742CA2,0x7F3857F6, +0xF1E43D1C,0x7F0991C4,0xF054D8D5,0x7ED5E5C6,0xEEC60F31,0x7E9D55FC,0xED37EF91, +0x7E5FE493,0xEBAA894F,0x7E1D93EA,0xEA1DEBBB,0x7DD6668F,0xE8922622,0x7D8A5F40, +0xE70747C4,0x7D3980EC,0xE57D5FDA,0x7CE3CEB2,0xE3F47D96,0x7C894BDE,0xE26CB01B, +0x7C29FBEE,0xE0E60685,0x7BC5E290,0xDF608FE4,0x7B5D039E,0xDDDC5B3B,0x7AEF6323, +0xDC597781,0x7A7D055B,0xDAD7F3A2,0x7A05EEAD,0xD957DE7A,0x798A23B1,0xD7D946D8, +0x7909A92D,0xD65C3B7B,0x78848414,0xD4E0CB15,0x77FAB989,0xD3670446,0x776C4EDB, +0xD1EEF59E,0x76D94989,0xD078AD9E,0x7641AF3D,0xCF043AB3,0x75A585CF,0xCD91AB39, +0x7504D345,0xCC210D79,0x745F9DD1,0xCAB26FA9,0x73B5EBD1,0xC945DFEC,0x7307C3D0, +0xC7DB6C50,0x72552C85,0xC67322CE,0x719E2CD2,0xC50D1149,0x70E2CBC6,0xC3A94590, +0x7023109A,0xC247CD5A,0x6F5F02B2,0xC0E8B648,0x6E96A99D,0xBF8C0DE3,0x6DCA0D14, +0xBE31E19B,0x6CF934FC,0xBCDA3ECB,0x6C242960,0xBB8532B0,0x6B4AF279,0xBA32CA71, +0x6A6D98A4,0xB8E31319,0x698C246C,0xB796199B,0x68A69E81,0xB64BEACD,0x67BD0FBD, +0xB5049368,0x66CF8120,0xB3C0200C,0x65DDFBD3,0xB27E9D3C,0x64E88926,0xB140175B, +0x63EF3290,0xB0049AB3,0x62F201AC,0xAECC336C,0x61F1003F,0xAD96ED92,0x60EC3830, +0xAC64D510,0x5FE3B38D,0xAB35F5B5,0x5ED77C8A,0xAA0A5B2E,0x5DC79D7C,0xA8E21106, +0x5CB420E0,0xA7BD22AC,0x5B9D1154,0xA69B9B68,0x5A82799A,0xA57D8666,0x59646498, +0xA462EEAC,0x5842DD54,0xA34BDF20,0x571DEEFA,0xA2386284,0x55F5A4D2,0xA1288376, +0x54CA0A4B,0xA01C4C73,0x539B2AF0,0x9F13C7D0,0x5269126E,0x9E0EFFC1,0x5133CC94, +0x9D0DFE54,0x4FFB654D,0x9C10CD70,0x4EBFE8A5,0x9B1776DA,0x4D8162C4,0x9A22042D, +0x4C3FDFF4,0x99307EE0,0x4AFB6C98,0x9842F043,0x49B41533,0x9759617F,0x4869E665, +0x9673DB94,0x471CECE7,0x9592675C,0x45CD358F,0x94B50D87,0x447ACD50,0x93DBD6A0, +0x4325C135,0x9306CB04,0x41CE1E65,0x9235F2EC,0x4073F21D,0x91695663,0x3F1749B8, +0x90A0FD4E,0x3DB832A6,0x8FDCEF66,0x3C56BA70,0x8F1D343A,0x3AF2EEB7,0x8E61D32E, +0x398CDD32,0x8DAAD37B,0x382493B0,0x8CF83C30,0x36BA2014,0x8C4A142F,0x354D9057, +0x8BA0622F,0x33DEF287,0x8AFB2CBB,0x326E54C7,0x8A5A7A31,0x30FBC54D,0x89BE50C3, +0x2F875262,0x8926B677,0x2E110A62,0x8893B125,0x2C98FBBA,0x88054677,0x2B1F34EB, +0x877B7BEC,0x29A3C485,0x86F656D3,0x2826B928,0x8675DC4F,0x26A82186,0x85FA1153, +0x25280C5E,0x8582FAA5,0x23A6887F,0x85109CDD,0x2223A4C5,0x84A2FC62,0x209F701C, +0x843A1D70,0x1F19F97B,0x83D60412,0x1D934FE5,0x8376B422,0x1C0B826A,0x831C314E, +0x1A82A026,0x82C67F14,0x18F8B83C,0x8275A0C0,0x176DD9DE,0x82299971,0x15E21445, +0x81E26C16,0x145576B1,0x81A01B6D,0x12C8106F,0x8162AA04,0x1139F0CF,0x812A1A3A, +0x0FAB272B,0x80F66E3C,0x0E1BC2E4,0x80C7A80A,0x0C8BD35E,0x809DC971,0x0AFB6805, +0x8078D40D,0x096A9049,0x8058C94C,0x07D95B9E,0x803DAA6A,0x0647D97C,0x80277872, +0x04B6195D,0x80163440,0x03242ABF,0x8009DE7E,0x01921D20,0x800277A6,0x7FFFFFFF, +0x00000000,0x7FF62182,0xFCDBD541,0x7FD8878E,0xF9B82684,0x7FA736B4,0xF6956FB7, +0x7F62368F,0xF3742CA2,0x7F0991C4,0xF054D8D5,0x7E9D55FC,0xED37EF91,0x7E1D93EA, +0xEA1DEBBB,0x7D8A5F40,0xE70747C4,0x7CE3CEB2,0xE3F47D96,0x7C29FBEE,0xE0E60685, +0x7B5D039E,0xDDDC5B3B,0x7A7D055B,0xDAD7F3A2,0x798A23B1,0xD7D946D8,0x78848414, +0xD4E0CB15,0x776C4EDB,0xD1EEF59E,0x7641AF3D,0xCF043AB3,0x7504D345,0xCC210D79, +0x73B5EBD1,0xC945DFEC,0x72552C85,0xC67322CE,0x70E2CBC6,0xC3A94590,0x6F5F02B2, +0xC0E8B648,0x6DCA0D14,0xBE31E19B,0x6C242960,0xBB8532B0,0x6A6D98A4,0xB8E31319, +0x68A69E81,0xB64BEACD,0x66CF8120,0xB3C0200C,0x64E88926,0xB140175B,0x62F201AC, +0xAECC336C,0x60EC3830,0xAC64D510,0x5ED77C8A,0xAA0A5B2E,0x5CB420E0,0xA7BD22AC, +0x5A82799A,0xA57D8666,0x5842DD54,0xA34BDF20,0x55F5A4D2,0xA1288376,0x539B2AF0, +0x9F13C7D0,0x5133CC94,0x9D0DFE54,0x4EBFE8A5,0x9B1776DA,0x4C3FDFF4,0x99307EE0, +0x49B41533,0x9759617F,0x471CECE7,0x9592675C,0x447ACD50,0x93DBD6A0,0x41CE1E65, +0x9235F2EC,0x3F1749B8,0x90A0FD4E,0x3C56BA70,0x8F1D343A,0x398CDD32,0x8DAAD37B, +0x36BA2014,0x8C4A142F,0x33DEF287,0x8AFB2CBB,0x30FBC54D,0x89BE50C3,0x2E110A62, +0x8893B125,0x2B1F34EB,0x877B7BEC,0x2826B928,0x8675DC4F,0x25280C5E,0x8582FAA5, +0x2223A4C5,0x84A2FC62,0x1F19F97B,0x83D60412,0x1C0B826A,0x831C314E,0x18F8B83C, +0x8275A0C0,0x15E21445,0x81E26C16,0x12C8106F,0x8162AA04,0x0FAB272B,0x80F66E3C, +0x0C8BD35E,0x809DC971,0x096A9049,0x8058C94C,0x0647D97C,0x80277872,0x03242ABF, +0x8009DE7E,0x00000000,0x80000000,0xFCDBD541,0x8009DE7E,0xF9B82684,0x80277872, +0xF6956FB7,0x8058C94C,0xF3742CA2,0x809DC971,0xF054D8D5,0x80F66E3C,0xED37EF91, +0x8162AA04,0xEA1DEBBB,0x81E26C16,0xE70747C4,0x8275A0C0,0xE3F47D96,0x831C314E, +0xE0E60685,0x83D60412,0xDDDC5B3B,0x84A2FC62,0xDAD7F3A2,0x8582FAA5,0xD7D946D8, +0x8675DC4F,0xD4E0CB15,0x877B7BEC,0xD1EEF59E,0x8893B125,0xCF043AB3,0x89BE50C3, +0xCC210D79,0x8AFB2CBB,0xC945DFEC,0x8C4A142F,0xC67322CE,0x8DAAD37B,0xC3A94590, +0x8F1D343A,0xC0E8B648,0x90A0FD4E,0xBE31E19B,0x9235F2EC,0xBB8532B0,0x93DBD6A0, +0xB8E31319,0x9592675C,0xB64BEACD,0x9759617F,0xB3C0200C,0x99307EE0,0xB140175B, +0x9B1776DA,0xAECC336C,0x9D0DFE54,0xAC64D510,0x9F13C7D0,0xAA0A5B2E,0xA1288376, +0xA7BD22AC,0xA34BDF20,0xA57D8666,0xA57D8666,0xA34BDF20,0xA7BD22AC,0xA1288376, +0xAA0A5B2E,0x9F13C7D0,0xAC64D510,0x9D0DFE54,0xAECC336C,0x9B1776DA,0xB140175B, +0x99307EE0,0xB3C0200C,0x9759617F,0xB64BEACD,0x9592675C,0xB8E31319,0x93DBD6A0, +0xBB8532B0,0x9235F2EC,0xBE31E19B,0x90A0FD4E,0xC0E8B648,0x8F1D343A,0xC3A94590, +0x8DAAD37B,0xC67322CE,0x8C4A142F,0xC945DFEC,0x8AFB2CBB,0xCC210D79,0x89BE50C3, +0xCF043AB3,0x8893B125,0xD1EEF59E,0x877B7BEC,0xD4E0CB15,0x8675DC4F,0xD7D946D8, +0x8582FAA5,0xDAD7F3A2,0x84A2FC62,0xDDDC5B3B,0x83D60412,0xE0E60685,0x831C314E, +0xE3F47D96,0x8275A0C0,0xE70747C4,0x81E26C16,0xEA1DEBBB,0x8162AA04,0xED37EF91, +0x80F66E3C,0xF054D8D5,0x809DC971,0xF3742CA2,0x8058C94C,0xF6956FB7,0x80277872, +0xF9B82684,0x8009DE7E,0xFCDBD541,0x7FFFFFFF,0x00000000,0x7FE9CBC0,0xFB49E6A3, +0x7FA736B4,0xF6956FB7,0x7F3857F6,0xF1E43D1C,0x7E9D55FC,0xED37EF91,0x7DD6668F, +0xE8922622,0x7CE3CEB2,0xE3F47D96,0x7BC5E290,0xDF608FE4,0x7A7D055B,0xDAD7F3A2, +0x7909A92D,0xD65C3B7B,0x776C4EDB,0xD1EEF59E,0x75A585CF,0xCD91AB39,0x73B5EBD1, 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+0x85FA1153,0xD838C82D,0x865678EB,0xD71A8EB5,0x86B583EE,0xD5FD3848,0x8717304E, +0xD4E0CB15,0x877B7BEC,0xD3C54D47,0x87E2649B,0xD2AAC504,0x884BE821,0xD191386E, +0x88B80432,0xD078AD9E,0x8926B677,0xCF612AAA,0x8997FC8A,0xCE4AB5A2,0x8A0BD3F5, +0xCD355491,0x8A823A36,0xCC210D79,0x8AFB2CBB,0xCB0DE658,0x8B76A8E4,0xC9FBE527, +0x8BF4AC05,0xC8EB0FD6,0x8C753362,0xC7DB6C50,0x8CF83C30,0xC6CD0079,0x8D7DC399, +0xC5BFD22E,0x8E05C6B7,0xC4B3E746,0x8E904298,0xC3A94590,0x8F1D343A,0xC29FF2D4, +0x8FAC988F,0xC197F4D4,0x903E6C7B,0xC0915148,0x90D2ACD4,0xBF8C0DE3,0x91695663, +0xBE88304F,0x920265E4,0xBD85BE30,0x929DD806,0xBC84BD1F,0x933BA968,0xBB8532B0, +0x93DBD6A0,0xBA87246D,0x947E5C33,0xB98A97D8,0x9523369C,0xB88F926D,0x95CA6247, +0xB796199B,0x9673DB94,0xB69E32CD,0x971F9ED7,0xB5A7E362,0x97CDA855,0xB4B330B3, +0x987DF449,0xB3C0200C,0x99307EE0,0xB2CEB6B5,0x99E5443B,0xB1DEF9E9,0x9A9C406E, +0xB0F0EEDA,0x9B556F81,0xB0049AB3,0x9C10CD70,0xAF1A0293,0x9CCE562C,0xAE312B92, +0x9D8E0597,0xAD4A1ABA,0x9E4FD78A,0xAC64D510,0x9F13C7D0,0xAB815F8D,0x9FD9D22A, +0xAA9FBF1E,0xA0A1F24D,0xA9BFF8A8,0xA16C23E1,0xA8E21106,0xA2386284,0xA8060D08, +0xA306A9C8,0xA72BF174,0xA3D6F534,0xA653C303,0xA4A94043,0xA57D8666,0xA57D8666, +0xA4A94043,0xA653C303,0xA3D6F534,0xA72BF174,0xA306A9C8,0xA8060D08,0xA2386284, +0xA8E21106,0xA16C23E1,0xA9BFF8A8,0xA0A1F24D,0xAA9FBF1E,0x9FD9D22A,0xAB815F8D, +0x9F13C7D0,0xAC64D510,0x9E4FD78A,0xAD4A1ABA,0x9D8E0597,0xAE312B92,0x9CCE562C, +0xAF1A0293,0x9C10CD70,0xB0049AB3,0x9B556F81,0xB0F0EEDA,0x9A9C406E,0xB1DEF9E9, +0x99E5443B,0xB2CEB6B5,0x99307EE0,0xB3C0200C,0x987DF449,0xB4B330B3,0x97CDA855, +0xB5A7E362,0x971F9ED7,0xB69E32CD,0x9673DB94,0xB796199B,0x95CA6247,0xB88F926D, +0x9523369C,0xB98A97D8,0x947E5C33,0xBA87246D,0x93DBD6A0,0xBB8532B0,0x933BA968, +0xBC84BD1F,0x929DD806,0xBD85BE30,0x920265E4,0xBE88304F,0x91695663,0xBF8C0DE3, +0x90D2ACD4,0xC0915148,0x903E6C7B,0xC197F4D4,0x8FAC988F,0xC29FF2D4,0x8F1D343A, +0xC3A94590,0x8E904298,0xC4B3E746,0x8E05C6B7,0xC5BFD22E,0x8D7DC399,0xC6CD0079, +0x8CF83C30,0xC7DB6C50,0x8C753362,0xC8EB0FD6,0x8BF4AC05,0xC9FBE527,0x8B76A8E4, +0xCB0DE658,0x8AFB2CBB,0xCC210D79,0x8A823A36,0xCD355491,0x8A0BD3F5,0xCE4AB5A2, +0x8997FC8A,0xCF612AAA,0x8926B677,0xD078AD9E,0x88B80432,0xD191386E,0x884BE821, +0xD2AAC504,0x87E2649B,0xD3C54D47,0x877B7BEC,0xD4E0CB15,0x8717304E,0xD5FD3848, +0x86B583EE,0xD71A8EB5,0x865678EB,0xD838C82D,0x85FA1153,0xD957DE7A,0x85A04F28, +0xDA77CB63,0x8549345C,0xDB9888A8,0x84F4C2D4,0xDCBA1008,0x84A2FC62,0xDDDC5B3B, +0x8453E2CF,0xDEFF63F4,0x840777D0,0xE02323E5,0x83BDBD0E,0xE14794BA,0x8376B422, +0xE26CB01B,0x83325E97,0xE3926FAD,0x82F0BDE8,0xE4B8CD11,0x82B1D381,0xE5DFC1E5, +0x8275A0C0,0xE70747C4,0x823C26F3,0xE82F5844,0x82056758,0xE957ECFB,0x81D16321, +0xEA80FF7A,0x81A01B6D,0xEBAA894F,0x8171914E,0xECD48407,0x8145C5C7,0xEDFEE92B, +0x811CB9CA,0xEF29B243,0x80F66E3C,0xF054D8D5,0x80D2E3F2,0xF1805662,0x80B21BAF, +0xF2AC246E,0x8094162C,0xF3D83C77,0x8078D40D,0xF50497FB,0x806055EB,0xF6313077, +0x804A9C4D,0xF75DFF66,0x8037A7AC,0xF88AFE42,0x80277872,0xF9B82684,0x801A0EF8, +0xFAE571A4,0x800F6B88,0xFC12D91A,0x80078E5E,0xFD40565C,0x800277A6,0xFE6DE2E0, +0x8000277A,0xFF9B781D,0x80009DEA,0x00C90F88,0x8003DAF1,0x01F6A297,0x8009DE7E, +0x03242ABF,0x8012A86F,0x0451A177,0x801E3895,0x057F0035,0x802C8EAD,0x06AC406F, +0x803DAA6A,0x07D95B9E,0x80518B6B,0x09064B3A,0x80683143,0x0A3308BD,0x80819B74, +0x0B5F8D9F,0x809DC971,0x0C8BD35E,0x80BCBA9D,0x0DB7D376,0x80DE6E4C,0x0EE38766, +0x8102E3C4,0x100EE8AD,0x812A1A3A,0x1139F0CF,0x815410D4,0x1264994E,0x8180C6A9, +0x138EDBB1,0x81B03AC2,0x14B8B17F,0x81E26C16,0x15E21445,0x82175990,0x170AFD8D, +0x824F0208,0x183366E9,0x8289644B,0x195B49EA,0x82C67F14,0x1A82A026,0x83065110, +0x1BA96335,0x8348D8DC,0x1CCF8CB3,0x838E1507,0x1DF5163F,0x83D60412,0x1F19F97B, +0x8420A46C,0x203E300D,0x846DF477,0x2161B3A0,0x84BDF286,0x22847DE0,0x85109CDD, +0x23A6887F,0x8565F1B0,0x24C7CD33,0x85BDEF28,0x25E845B6,0x86189359,0x2707EBC7, +0x8675DC4F,0x2826B928,0x86D5C802,0x2944A7A2,0x8738545E,0x2A61B101,0x879D7F41, +0x2B7DCF17,0x88054677,0x2C98FBBA,0x886FA7C2,0x2DB330C7,0x88DCA0D3,0x2ECC681E, +0x894C2F4C,0x2FE49BA7,0x89BE50C3,0x30FBC54D,0x8A3302BE,0x3211DF04,0x8AAA42B4, +0x3326E2C3,0x8B240E11,0x343ACA87,0x8BA0622F,0x354D9057,0x8C1F3C5D,0x365F2E3B, +0x8CA099DA,0x376F9E46,0x8D2477D8,0x387EDA8E,0x8DAAD37B,0x398CDD32,0x8E33A9DA, +0x3A99A057,0x8EBEF7FB,0x3BA51E29,0x8F4CBADB,0x3CAF50DA,0x8FDCEF66,0x3DB832A6, +0x906F927C,0x3EBFBDCD,0x9104A0EE,0x3FC5EC98,0x919C1781,0x40CAB958,0x9235F2EC, +0x41CE1E65,0x92D22FD9,0x42D0161E,0x9370CAE4,0x43D09AED,0x9411C09E,0x44CFA740, +0x94B50D87,0x45CD358F,0x955AAE17,0x46C9405C,0x96029EB6,0x47C3C22F,0x96ACDBBE, +0x48BCB599,0x9759617F,0x49B41533,0x98082C3B,0x4AA9DBA2,0x98B93828,0x4B9E0390, +0x996C816F,0x4C9087B1,0x9A22042D,0x4D8162C4,0x9AD9BC71,0x4E708F8F,0x9B93A641, +0x4F5E08E3,0x9C4FBD93,0x5049C999,0x9D0DFE54,0x5133CC94,0x9DCE6463,0x521C0CC2, +0x9E90EB94,0x53028518,0x9F558FB0,0x53E73097,0xA01C4C73,0x54CA0A4B,0xA0E51D8C, +0x55AB0D46,0xA1AFFEA3,0x568A34A9,0xA27CEB4F,0x57677B9D,0xA34BDF20,0x5842DD54, +0xA41CD599,0x591C550E,0xA4EFCA31,0x59F3DE12,0xA5C4B855,0x5AC973B5,0xA69B9B68, +0x5B9D1154,0xA7746EC0,0x5C6EB258,0xA84F2DAA,0x5D3E5237,0xA92BD367,0x5E0BEC6E, +0xAA0A5B2E,0x5ED77C8A,0xAAEAC02C,0x5FA0FE1F,0xABCCFD83,0x60686CCF,0xACB10E4B, +0x612DC447,0xAD96ED92,0x61F1003F,0xAE7E965B,0x62B21C7B,0xAF6803A2,0x637114CC, +0xB0533055,0x642DE50D,0xB140175B,0x64E88926,0xB22EB392,0x65A0FD0B,0xB31EFFCC, +0x66573CBB,0xB410F6D3,0x670B4444,0xB5049368,0x67BD0FBD,0xB5F9D043,0x686C9B4B, +0xB6F0A812,0x6919E320,0xB7E9157A,0x69C4E37A,0xB8E31319,0x6A6D98A4,0xB9DE9B83, +0x6B13FEF5,0xBADBA943,0x6BB812D1,0xBBDA36DD,0x6C59D0A9,0xBCDA3ECB,0x6CF934FC, +0xBDDBBB7F,0x6D963C54,0xBEDEA765,0x6E30E34A,0xBFE2FCDF,0x6EC92683,0xC0E8B648, +0x6F5F02B2,0xC1EFCDF3,0x6FF27497,0xC2F83E2A,0x708378FF,0xC4020133,0x71120CC5, +0xC50D1149,0x719E2CD2,0xC61968A2,0x7227D61C,0xC727016D,0x72AF05A7,0xC835D5D0, +0x7333B883,0xC945DFEC,0x73B5EBD1,0xCA5719DB,0x74359CBD,0xCB697DB0,0x74B2C884, +0xCC7D0578,0x752D6C6C,0xCD91AB39,0x75A585CF,0xCEA768F2,0x761B1211,0xCFBE389F, +0x768E0EA6,0xD0D61434,0x76FE790E,0xD1EEF59E,0x776C4EDB,0xD308D6C7,0x77D78DAA, +0xD423B191,0x78403329,0xD53F7FDA,0x78A63D11,0xD65C3B7B,0x7909A92D,0xD779DE47, +0x796A7554,0xD898620C,0x79C89F6E,0xD9B7C094,0x7A24256F,0xDAD7F3A2,0x7A7D055B, +0xDBF8F4F8,0x7AD33D45,0xDD1ABE51,0x7B26CB4F,0xDE3D4964,0x7B77ADA8,0xDF608FE4, +0x7BC5E290,0xE0848B7F,0x7C116853,0xE1A935E2,0x7C5A3D50,0xE2CE88B3,0x7CA05FF1, +0xE3F47D96,0x7CE3CEB2,0xE51B0E2A,0x7D24881B,0xE642340D,0x7D628AC6,0xE769E8D8, +0x7D9DD55A,0xE8922622,0x7DD6668F,0xE9BAE57D,0x7E0C3D29,0xEAE4207A,0x7E3F57FF, +0xEC0DD0A8,0x7E6FB5F4,0xED37EF91,0x7E9D55FC,0xEE6276BF,0x7EC8371A,0xEF8D5FB8, +0x7EF05860,0xF0B8A401,0x7F15B8EE,0xF1E43D1C,0x7F3857F6,0xF310248A,0x7F5834B7, +0xF43C53CB,0x7F754E80,0xF568C45B,0x7F8FA4B0,0xF6956FB7,0x7FA736B4,0xF7C24F59, +0x7FBC040A,0xF8EF5CBB,0x7FCE0C3E,0xFA1C9157,0x7FDD4EEC,0xFB49E6A3,0x7FE9CBC0, +0xFC775616,0x7FF38274,0xFDA4D929,0x7FFA72D1,0xFED2694F,0x7FFE9CB2,}; + +const uint32_t arm_neon_factors_2048_q31[ARM_NEON_FACTORS_2048_Q31_LEN]={ +5,256,8,8,}; + +__ALIGNED(16) const q31_t arm_neon_twiddles_4096_q31[ARM_NEON_TWIDDLES_4096_Q31_LEN]={ +0x7FFFFFFF,0x00000000,0x7641AF3D,0xCF043AB3,0x5A82799A,0xA57D8666,0x30FBC54D, +0x89BE50C3,0x7FFFFFFF,0x00000000,0x5A82799A,0xA57D8666,0x00000000,0x80000000, +0xA57D8666,0xA57D8666,0x7FFFFFFF,0x00000000,0x30FBC54D,0x89BE50C3,0xA57D8666, +0xA57D8666,0x89BE50C3,0x30FBC54D,0x7FFFFFFF,0x00000000,0x7F62368F,0xF3742CA2, +0x7D8A5F40,0xE70747C4,0x7A7D055B,0xDAD7F3A2,0x7641AF3D,0xCF043AB3,0x70E2CBC6, +0xC3A94590,0x6A6D98A4,0xB8E31319,0x62F201AC,0xAECC336C,0x5A82799A,0xA57D8666, 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+0x97B07E7A,0x4A2F2BE6,0x98082C3B,0x4AA9DBA2,0x98606A49,0x4B2423BE,0x98B93828, +0x4B9E0390,0x9912955F,0x4C177A6E,0x996C816F,0x4C9087B1,0x99C6FBDE,0x4D092AB0, +0x9A22042D,0x4D8162C4,0x9A7D99DE,0x4DF92F46,0x9AD9BC71,0x4E708F8F,0x9B366B68, +0x4EE782FB,0x9B93A641,0x4F5E08E3,0x9BF16C7A,0x4FD420A4,0x9C4FBD93,0x5049C999, +0x9CAE9907,0x50BF031F,0x9D0DFE54,0x5133CC94,0x9D6DECF4,0x51A82555,0x9DCE6463, +0x521C0CC2,0x9E2F641B,0x528F8238,0x9E90EB94,0x53028518,0x9EF2FA49,0x537514C2, +0x9F558FB0,0x53E73097,0x9FB8AB41,0x5458D7F9,0xA01C4C73,0x54CA0A4B,0xA08072BA, +0x553AC6EE,0xA0E51D8C,0x55AB0D46,0xA14A4C5E,0x561ADCB9,0xA1AFFEA3,0x568A34A9, +0xA21633CD,0x56F9147E,0xA27CEB4F,0x57677B9D,0xA2E4249B,0x57D5696D,0xA34BDF20, +0x5842DD54,0xA3B41A50,0x58AFD6BD,0xA41CD599,0x591C550E,0xA486106A,0x598857B2, +0xA4EFCA31,0x59F3DE12,0xA55A025B,0x5A5EE79A,0xA5C4B855,0x5AC973B5,0xA62FEB8B, +0x5B3381CE,0xA69B9B68,0x5B9D1154,0xA707C757,0x5C0621B2,0xA7746EC0,0x5C6EB258, +0xA7E1910F,0x5CD6C2B5,0xA84F2DAA,0x5D3E5237,0xA8BD43FA,0x5DA5604F,0xA92BD367, +0x5E0BEC6E,0xA99ADB56,0x5E71F606,0xAA0A5B2E,0x5ED77C8A,0xAA7A5253,0x5F3C7F6B, +0xAAEAC02C,0x5FA0FE1F,0xAB5BA41A,0x6004F819,0xABCCFD83,0x60686CCF,0xAC3ECBC7, +0x60CB5BB7,0xACB10E4B,0x612DC447,0xAD23C46E,0x618FA5F7,0xAD96ED92,0x61F1003F, +0xAE0A8916,0x6251D298,0xAE7E965B,0x62B21C7B,0xAEF314C0,0x6311DD64,0xAF6803A2, +0x637114CC,0xAFDD625F,0x63CFC231,0xB0533055,0x642DE50D,0xB0C96CE0,0x648B7CE0, +0xB140175B,0x64E88926,0xB1B72F23,0x6545095F,0xB22EB392,0x65A0FD0B,0xB2A6A402, +0x65FC63A9,0xB31EFFCC,0x66573CBB,0xB397C649,0x66B187C3,0xB410F6D3,0x670B4444, +0xB48A90C0,0x676471C0,0xB5049368,0x67BD0FBD,0xB57EFE22,0x68151DBE,0xB5F9D043, +0x686C9B4B,0xB6750921,0x68C387E9,0xB6F0A812,0x6919E320,0xB76CAC69,0x696FAC78, +0xB7E9157A,0x69C4E37A,0xB865E299,0x6A1987B0,0xB8E31319,0x6A6D98A4,0xB960A64C, +0x6AC115E2,0xB9DE9B83,0x6B13FEF5,0xBA5CF210,0x6B66536B,0xBADBA943,0x6BB812D1, +0xBB5AC06D,0x6C093CB6,0xBBDA36DD,0x6C59D0A9,0xBC5A0BE2,0x6CA9CE3B,0xBCDA3ECB, +0x6CF934FC,0xBD5ACEE5,0x6D48047E,0xBDDBBB7F,0x6D963C54,0xBE5D03E6,0x6DE3DC11, +0xBEDEA765,0x6E30E34A,0xBF60A54A,0x6E7D5193,0xBFE2FCDF,0x6EC92683,0xC065AD70, +0x6F1461B0,0xC0E8B648,0x6F5F02B2,0xC16C16B0,0x6FA90921,0xC1EFCDF3,0x6FF27497, +0xC273DB58,0x703B44AD,0xC2F83E2A,0x708378FF,0xC37CF5B0,0x70CB1128,0xC4020133, +0x71120CC5,0xC4875FF9,0x71586B74,0xC50D1149,0x719E2CD2,0xC593146A,0x71E35080, +0xC61968A2,0x7227D61C,0xC6A00D37,0x726BBD48,0xC727016D,0x72AF05A7,0xC7AE4489, +0x72F1AED9,0xC835D5D0,0x7333B883,0xC8BDB485,0x73752249,0xC945DFEC,0x73B5EBD1, +0xC9CE5748,0x73F614C0,0xCA5719DB,0x74359CBD,0xCAE026E8,0x74748371,0xCB697DB0, +0x74B2C884,0xCBF31D75,0x74F06B9E,0xCC7D0578,0x752D6C6C,0xCD0734F9,0x7569CA99, +0xCD91AB39,0x75A585CF,0xCE1C6777,0x75E09DBD,0xCEA768F2,0x761B1211,0xCF32AEEB, +0x7654E279,0xCFBE389F,0x768E0EA6,0xD04A054E,0x76C69647,0xD0D61434,0x76FE790E, +0xD1626490,0x7735B6AF,0xD1EEF59E,0x776C4EDB,0xD27BC69C,0x77A24148,0xD308D6C7, +0x77D78DAA,0xD396255A,0x780C33B8,0xD423B191,0x78403329,0xD4B17AA8,0x78738BB3, +0xD53F7FDA,0x78A63D11,0xD5CDC062,0x78D846FB,0xD65C3B7B,0x7909A92D,0xD6EAF05F, +0x793A6361,0xD779DE47,0x796A7554,0xD809046E,0x7999DEC4,0xD898620C,0x79C89F6E, +0xD927F65B,0x79F6B711,0xD9B7C094,0x7A24256F,0xDA47BFEE,0x7A50EA47,0xDAD7F3A2, +0x7A7D055B,0xDB685AE9,0x7AA8766F,0xDBF8F4F8,0x7AD33D45,0xDC89C109,0x7AFD59A4, +0xDD1ABE51,0x7B26CB4F,0xDDABEC08,0x7B4F920E,0xDE3D4964,0x7B77ADA8,0xDECED59B, +0x7B9F1DE6,0xDF608FE4,0x7BC5E290,0xDFF27773,0x7BEBFB70,0xE0848B7F,0x7C116853, +0xE116CB3D,0x7C362904,0xE1A935E2,0x7C5A3D50,0xE23BCAA2,0x7C7DA505,0xE2CE88B3, +0x7CA05FF1,0xE3616F48,0x7CC26DE5,0xE3F47D96,0x7CE3CEB2,0xE487B2D0,0x7D048228, +0xE51B0E2A,0x7D24881B,0xE5AE8ED8,0x7D43E05E,0xE642340D,0x7D628AC6,0xE6D5FCFC, +0x7D808728,0xE769E8D8,0x7D9DD55A,0xE7FDF6D4,0x7DBA7534,0xE8922622,0x7DD6668F, +0xE92675F4,0x7DF1A942,0xE9BAE57D,0x7E0C3D29,0xEA4F73EE,0x7E26221F,0xEAE4207A, +0x7E3F57FF,0xEB78EA52,0x7E57DEA7,0xEC0DD0A8,0x7E6FB5F4,0xECA2D2AD,0x7E86DDC6, +0xED37EF91,0x7E9D55FC,0xEDCD2687,0x7EB31E78,0xEE6276BF,0x7EC8371A,0xEEF7DF6A, +0x7EDC9FC6,0xEF8D5FB8,0x7EF05860,0xF022F6DA,0x7F0360CB,0xF0B8A401,0x7F15B8EE, +0xF14E665C,0x7F2760AF,0xF1E43D1C,0x7F3857F6,0xF27A2771,0x7F489EAA,0xF310248A, +0x7F5834B7,0xF3A63398,0x7F671A05,0xF43C53CB,0x7F754E80,0xF4D28451,0x7F82D214, +0xF568C45B,0x7F8FA4B0,0xF5FF1318,0x7F9BC640,0xF6956FB7,0x7FA736B4,0xF72BD967, +0x7FB1F5FC,0xF7C24F59,0x7FBC040A,0xF858D0BB,0x7FC560CF,0xF8EF5CBB,0x7FCE0C3E, +0xF985F28A,0x7FD6064C,0xFA1C9157,0x7FDD4EEC,0xFAB3384F,0x7FE3E616,0xFB49E6A3, +0x7FE9CBC0,0xFBE09B80,0x7FEEFFE1,0xFC775616,0x7FF38274,0xFD0E1594,0x7FF75370, +0xFDA4D929,0x7FFA72D1,0xFE3BA002,0x7FFCE093,0xFED2694F,0x7FFE9CB2,0xFF69343F, +0x7FFFA72C,}; + +const uint32_t arm_neon_factors_4096_q31[ARM_NEON_FACTORS_4096_Q31_LEN]={ +6,1024,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_16_q15[ARM_NEON_TWIDDLES_16_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,}; + +const uint32_t arm_neon_factors_16_q15[ARM_NEON_FACTORS_16_Q15_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_32_q15[ARM_NEON_TWIDDLES_32_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,}; + +const uint32_t arm_neon_factors_32_q15[ARM_NEON_FACTORS_32_Q15_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_64_q15[ARM_NEON_TWIDDLES_64_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,}; + +const uint32_t arm_neon_factors_64_q15[ARM_NEON_FACTORS_64_Q15_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_128_q15[ARM_NEON_TWIDDLES_128_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D, +0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04, +0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2, +0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930, +0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F, +0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E, +0x0648,0x8027,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x0000,0x8000,0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE, +0xC3A9,0x8F1D,0xB8E3,0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592, +0xB8E3,0x8F1D,0xC3A9,0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374, +0x7FFF,0x0000,0x7E9D,0xED38,0x7A7D,0xDAD8,0x73B6,0xC946,0x6A6E,0xB8E3,0x5ED7, +0xAA0A,0x5134,0x9D0E,0x41CE,0x9236,0x30FC,0x89BE,0x1F1A,0x83D6,0x0C8C,0x809E, +0xF9B8,0x8027,0xE707,0x8276,0xD4E1,0x877B,0xC3A9,0x8F1D,0xB3C0,0x9930,0xA57E, +0xA57E,0x9930,0xB3C0,0x8F1D,0xC3A9,0x877B,0xD4E1,0x8276,0xE707,0x8027,0xF9B8, +0x809E,0x0C8C,0x83D6,0x1F1A,0x89BE,0x30FC,0x9236,0x41CE,0x9D0E,0x5134,0xAA0A, +0x5ED7,0xB8E3,0x6A6E,0xC946,0x73B6,0xDAD8,0x7A7D,0xED38,0x7E9D,}; + +const uint32_t arm_neon_factors_128_q15[ARM_NEON_FACTORS_128_Q15_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_256_q15[ARM_NEON_TWIDDLES_256_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055, +0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D, +0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04, +0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA, +0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140, +0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843, +0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930, +0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57, +0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894, +0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C, +0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E, +0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D, +0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140, +0x5ED7,0xAA0A,0x5843,0xA34C,0x5134,0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D, +0x8DAB,0x30FC,0x89BE,0x2827,0x8676,0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E, +0x0324,0x800A,0xF9B8,0x8027,0xF055,0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1, +0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14, +0xA57E,0xA57E,0x9F14,0xAC65,0x9930,0xB3C0,0x93DC,0xBB85,0x8F1D,0xC3A9,0x8AFB, +0xCC21,0x877B,0xD4E1,0x84A3,0xDDDC,0x8276,0xE707,0x80F6,0xF055,0x8027,0xF9B8, +0x800A,0x0324,0x809E,0x0C8C,0x81E2,0x15E2,0x83D6,0x1F1A,0x8676,0x2827,0x89BE, +0x30FC,0x8DAB,0x398D,0x9236,0x41CE,0x9759,0x49B4,0x9D0E,0x5134,0xA34C,0x5843, +0xAA0A,0x5ED7,0xB140,0x64E9,0xB8E3,0x6A6E,0xC0E9,0x6F5F,0xC946,0x73B6,0xD1EF, +0x776C,0xDAD8,0x7A7D,0xE3F4,0x7CE4,0xED38,0x7E9D,0xF695,0x7FA7,}; + +const uint32_t arm_neon_factors_256_q15[ARM_NEON_FACTORS_256_Q15_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_512_q15[ARM_NEON_TWIDDLES_512_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D, +0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04, +0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2, +0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930, +0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F, +0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E, +0x0648,0x8027,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x0000,0x8000,0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE, +0xC3A9,0x8F1D,0xB8E3,0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592, +0xB8E3,0x8F1D,0xC3A9,0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374, +0x7FFF,0x0000,0x7E9D,0xED38,0x7A7D,0xDAD8,0x73B6,0xC946,0x6A6E,0xB8E3,0x5ED7, +0xAA0A,0x5134,0x9D0E,0x41CE,0x9236,0x30FC,0x89BE,0x1F1A,0x83D6,0x0C8C,0x809E, +0xF9B8,0x8027,0xE707,0x8276,0xD4E1,0x877B,0xC3A9,0x8F1D,0xB3C0,0x9930,0xA57E, +0xA57E,0x9930,0xB3C0,0x8F1D,0xC3A9,0x877B,0xD4E1,0x8276,0xE707,0x8027,0xF9B8, +0x809E,0x0C8C,0x83D6,0x1F1A,0x89BE,0x30FC,0x9236,0x41CE,0x9D0E,0x5134,0xAA0A, +0x5ED7,0xB8E3,0x6A6E,0xC946,0x73B6,0xDAD8,0x7A7D,0xED38,0x7E9D,0x7FFF,0x0000, +0x7FFE,0xFE6E,0x7FF6,0xFCDC,0x7FEA,0xFB4A,0x7FD9,0xF9B8,0x7FC2,0xF827,0x7FA7, +0xF695,0x7F87,0xF505,0x7F62,0xF374,0x7F38,0xF1E4,0x7F0A,0xF055,0x7ED6,0xEEC6, +0x7E9D,0xED38,0x7E60,0xEBAB,0x7E1E,0xEA1E,0x7DD6,0xE892,0x7D8A,0xE707,0x7D3A, +0xE57D,0x7CE4,0xE3F4,0x7C89,0xE26D,0x7C2A,0xE0E6,0x7BC6,0xDF61,0x7B5D,0xDDDC, +0x7AEF,0xDC59,0x7A7D,0xDAD8,0x7A06,0xD958,0x798A,0xD7D9,0x790A,0xD65C,0x7885, +0xD4E1,0x77FB,0xD367,0x776C,0xD1EF,0x76D9,0xD079,0x7642,0xCF04,0x75A6,0xCD92, +0x7505,0xCC21,0x7460,0xCAB2,0x73B6,0xC946,0x7308,0xC7DB,0x7255,0xC673,0x719E, +0xC50D,0x70E3,0xC3A9,0x7023,0xC248,0x6F5F,0xC0E9,0x6E97,0xBF8C,0x6DCA,0xBE32, +0x6CF9,0xBCDA,0x6C24,0xBB85,0x6B4B,0xBA33,0x6A6E,0xB8E3,0x698C,0xB796,0x68A7, +0xB64C,0x67BD,0xB505,0x66D0,0xB3C0,0x65DE,0xB27F,0x64E9,0xB140,0x63EF,0xB005, +0x62F2,0xAECC,0x61F1,0xAD97,0x60EC,0xAC65,0x5FE4,0xAB36,0x5ED7,0xAA0A,0x5DC8, +0xA8E2,0x5CB4,0xA7BD,0x5B9D,0xA69C,0x5A82,0xA57E,0x5964,0xA463,0x5843,0xA34C, +0x571E,0xA238,0x55F6,0xA129,0x54CA,0xA01C,0x539B,0x9F14,0x5269,0x9E0F,0x5134, +0x9D0E,0x4FFB,0x9C11,0x4EC0,0x9B17,0x4D81,0x9A22,0x4C40,0x9930,0x4AFB,0x9843, +0x49B4,0x9759,0x486A,0x9674,0x471D,0x9592,0x45CD,0x94B5,0x447B,0x93DC,0x4326, +0x9307,0x41CE,0x9236,0x4074,0x9169,0x3F17,0x90A1,0x3DB8,0x8FDD,0x3C57,0x8F1D, +0x3AF3,0x8E62,0x398D,0x8DAB,0x3825,0x8CF8,0x36BA,0x8C4A,0x354E,0x8BA0,0x33DF, +0x8AFB,0x326E,0x8A5A,0x30FC,0x89BE,0x2F87,0x8927,0x2E11,0x8894,0x2C99,0x8805, +0x2B1F,0x877B,0x29A4,0x86F6,0x2827,0x8676,0x26A8,0x85FA,0x2528,0x8583,0x23A7, +0x8511,0x2224,0x84A3,0x209F,0x843A,0x1F1A,0x83D6,0x1D93,0x8377,0x1C0C,0x831C, +0x1A83,0x82C6,0x18F9,0x8276,0x176E,0x822A,0x15E2,0x81E2,0x1455,0x81A0,0x12C8, +0x8163,0x113A,0x812A,0x0FAB,0x80F6,0x0E1C,0x80C8,0x0C8C,0x809E,0x0AFB,0x8079, +0x096B,0x8059,0x07D9,0x803E,0x0648,0x8027,0x04B6,0x8016,0x0324,0x800A,0x0192, +0x8002,0x7FFF,0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374, +0x7F0A,0xF055,0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A, +0xE0E6,0x7B5D,0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF, +0x7642,0xCF04,0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F, +0xC0E9,0x6DCA,0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0, +0x64E9,0xB140,0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82, +0xA57E,0x5843,0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17, +0x4C40,0x9930,0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17, +0x90A1,0x3C57,0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE, +0x2E11,0x8894,0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A, +0x83D6,0x1C0C,0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6, +0x0C8C,0x809E,0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x0000,0x8000,0xFCDC, +0x800A,0xF9B8,0x8027,0xF695,0x8059,0xF374,0x809E,0xF055,0x80F6,0xED38,0x8163, +0xEA1E,0x81E2,0xE707,0x8276,0xE3F4,0x831C,0xE0E6,0x83D6,0xDDDC,0x84A3,0xDAD8, +0x8583,0xD7D9,0x8676,0xD4E1,0x877B,0xD1EF,0x8894,0xCF04,0x89BE,0xCC21,0x8AFB, +0xC946,0x8C4A,0xC673,0x8DAB,0xC3A9,0x8F1D,0xC0E9,0x90A1,0xBE32,0x9236,0xBB85, +0x93DC,0xB8E3,0x9592,0xB64C,0x9759,0xB3C0,0x9930,0xB140,0x9B17,0xAECC,0x9D0E, +0xAC65,0x9F14,0xAA0A,0xA129,0xA7BD,0xA34C,0xA57E,0xA57E,0xA34C,0xA7BD,0xA129, +0xAA0A,0x9F14,0xAC65,0x9D0E,0xAECC,0x9B17,0xB140,0x9930,0xB3C0,0x9759,0xB64C, +0x9592,0xB8E3,0x93DC,0xBB85,0x9236,0xBE32,0x90A1,0xC0E9,0x8F1D,0xC3A9,0x8DAB, +0xC673,0x8C4A,0xC946,0x8AFB,0xCC21,0x89BE,0xCF04,0x8894,0xD1EF,0x877B,0xD4E1, +0x8676,0xD7D9,0x8583,0xDAD8,0x84A3,0xDDDC,0x83D6,0xE0E6,0x831C,0xE3F4,0x8276, +0xE707,0x81E2,0xEA1E,0x8163,0xED38,0x80F6,0xF055,0x809E,0xF374,0x8059,0xF695, +0x8027,0xF9B8,0x800A,0xFCDC,0x7FFF,0x0000,0x7FEA,0xFB4A,0x7FA7,0xF695,0x7F38, +0xF1E4,0x7E9D,0xED38,0x7DD6,0xE892,0x7CE4,0xE3F4,0x7BC6,0xDF61,0x7A7D,0xDAD8, +0x790A,0xD65C,0x776C,0xD1EF,0x75A6,0xCD92,0x73B6,0xC946,0x719E,0xC50D,0x6F5F, +0xC0E9,0x6CF9,0xBCDA,0x6A6E,0xB8E3,0x67BD,0xB505,0x64E9,0xB140,0x61F1,0xAD97, +0x5ED7,0xAA0A,0x5B9D,0xA69C,0x5843,0xA34C,0x54CA,0xA01C,0x5134,0x9D0E,0x4D81, +0x9A22,0x49B4,0x9759,0x45CD,0x94B5,0x41CE,0x9236,0x3DB8,0x8FDD,0x398D,0x8DAB, +0x354E,0x8BA0,0x30FC,0x89BE,0x2C99,0x8805,0x2827,0x8676,0x23A7,0x8511,0x1F1A, +0x83D6,0x1A83,0x82C6,0x15E2,0x81E2,0x113A,0x812A,0x0C8C,0x809E,0x07D9,0x803E, +0x0324,0x800A,0xFE6E,0x8002,0xF9B8,0x8027,0xF505,0x8079,0xF055,0x80F6,0xEBAB, +0x81A0,0xE707,0x8276,0xE26D,0x8377,0xDDDC,0x84A3,0xD958,0x85FA,0xD4E1,0x877B, +0xD079,0x8927,0xCC21,0x8AFB,0xC7DB,0x8CF8,0xC3A9,0x8F1D,0xBF8C,0x9169,0xBB85, +0x93DC,0xB796,0x9674,0xB3C0,0x9930,0xB005,0x9C11,0xAC65,0x9F14,0xA8E2,0xA238, +0xA57E,0xA57E,0xA238,0xA8E2,0x9F14,0xAC65,0x9C11,0xB005,0x9930,0xB3C0,0x9674, +0xB796,0x93DC,0xBB85,0x9169,0xBF8C,0x8F1D,0xC3A9,0x8CF8,0xC7DB,0x8AFB,0xCC21, +0x8927,0xD079,0x877B,0xD4E1,0x85FA,0xD958,0x84A3,0xDDDC,0x8377,0xE26D,0x8276, +0xE707,0x81A0,0xEBAB,0x80F6,0xF055,0x8079,0xF505,0x8027,0xF9B8,0x8002,0xFE6E, +0x800A,0x0324,0x803E,0x07D9,0x809E,0x0C8C,0x812A,0x113A,0x81E2,0x15E2,0x82C6, +0x1A83,0x83D6,0x1F1A,0x8511,0x23A7,0x8676,0x2827,0x8805,0x2C99,0x89BE,0x30FC, +0x8BA0,0x354E,0x8DAB,0x398D,0x8FDD,0x3DB8,0x9236,0x41CE,0x94B5,0x45CD,0x9759, +0x49B4,0x9A22,0x4D81,0x9D0E,0x5134,0xA01C,0x54CA,0xA34C,0x5843,0xA69C,0x5B9D, +0xAA0A,0x5ED7,0xAD97,0x61F1,0xB140,0x64E9,0xB505,0x67BD,0xB8E3,0x6A6E,0xBCDA, +0x6CF9,0xC0E9,0x6F5F,0xC50D,0x719E,0xC946,0x73B6,0xCD92,0x75A6,0xD1EF,0x776C, +0xD65C,0x790A,0xDAD8,0x7A7D,0xDF61,0x7BC6,0xE3F4,0x7CE4,0xE892,0x7DD6,0xED38, +0x7E9D,0xF1E4,0x7F38,0xF695,0x7FA7,0xFB4A,0x7FEA,}; + +const uint32_t arm_neon_factors_512_q15[ARM_NEON_FACTORS_512_Q15_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_1024_q15[ARM_NEON_TWIDDLES_1024_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055, +0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D, +0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04, +0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA, +0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140, +0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843, +0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930, +0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57, +0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894, +0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C, +0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E, +0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D, +0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140, +0x5ED7,0xAA0A,0x5843,0xA34C,0x5134,0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D, +0x8DAB,0x30FC,0x89BE,0x2827,0x8676,0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E, +0x0324,0x800A,0xF9B8,0x8027,0xF055,0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1, +0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14, +0xA57E,0xA57E,0x9F14,0xAC65,0x9930,0xB3C0,0x93DC,0xBB85,0x8F1D,0xC3A9,0x8AFB, +0xCC21,0x877B,0xD4E1,0x84A3,0xDDDC,0x8276,0xE707,0x80F6,0xF055,0x8027,0xF9B8, +0x800A,0x0324,0x809E,0x0C8C,0x81E2,0x15E2,0x83D6,0x1F1A,0x8676,0x2827,0x89BE, +0x30FC,0x8DAB,0x398D,0x9236,0x41CE,0x9759,0x49B4,0x9D0E,0x5134,0xA34C,0x5843, +0xAA0A,0x5ED7,0xB140,0x64E9,0xB8E3,0x6A6E,0xC0E9,0x6F5F,0xC946,0x73B6,0xD1EF, +0x776C,0xDAD8,0x7A7D,0xE3F4,0x7CE4,0xED38,0x7E9D,0xF695,0x7FA7,0x7FFF,0x0000, +0x7FFF,0xFF37,0x7FFE,0xFE6E,0x7FFA,0xFDA5,0x7FF6,0xFCDC,0x7FF1,0xFC13,0x7FEA, +0xFB4A,0x7FE2,0xFA81,0x7FD9,0xF9B8,0x7FCE,0xF8EF,0x7FC2,0xF827,0x7FB5,0xF75E, +0x7FA7,0xF695,0x7F98,0xF5CD,0x7F87,0xF505,0x7F75,0xF43C,0x7F62,0xF374,0x7F4E, +0xF2AC,0x7F38,0xF1E4,0x7F22,0xF11C,0x7F0A,0xF055,0x7EF0,0xEF8D,0x7ED6,0xEEC6, +0x7EBA,0xEDFF,0x7E9D,0xED38,0x7E7F,0xEC71,0x7E60,0xEBAB,0x7E3F,0xEAE4,0x7E1E, +0xEA1E,0x7DFB,0xE958,0x7DD6,0xE892,0x7DB1,0xE7CD,0x7D8A,0xE707,0x7D63,0xE642, +0x7D3A,0xE57D,0x7D0F,0xE4B9,0x7CE4,0xE3F4,0x7CB7,0xE330,0x7C89,0xE26D,0x7C5A, +0xE1A9,0x7C2A,0xE0E6,0x7BF9,0xE023,0x7BC6,0xDF61,0x7B92,0xDE9E,0x7B5D,0xDDDC, +0x7B27,0xDD1B,0x7AEF,0xDC59,0x7AB7,0xDB99,0x7A7D,0xDAD8,0x7A42,0xDA18,0x7A06, +0xD958,0x79C9,0xD898,0x798A,0xD7D9,0x794A,0xD71B,0x790A,0xD65C,0x78C8,0xD59E, +0x7885,0xD4E1,0x7840,0xD424,0x77FB,0xD367,0x77B4,0xD2AB,0x776C,0xD1EF,0x7723, +0xD134,0x76D9,0xD079,0x768E,0xCFBE,0x7642,0xCF04,0x75F4,0xCE4B,0x75A6,0xCD92, +0x7556,0xCCD9,0x7505,0xCC21,0x74B3,0xCB69,0x7460,0xCAB2,0x740B,0xC9FC,0x73B6, +0xC946,0x735F,0xC890,0x7308,0xC7DB,0x72AF,0xC727,0x7255,0xC673,0x71FA,0xC5C0, +0x719E,0xC50D,0x7141,0xC45B,0x70E3,0xC3A9,0x7083,0xC2F8,0x7023,0xC248,0x6FC2, +0xC198,0x6F5F,0xC0E9,0x6EFB,0xC03A,0x6E97,0xBF8C,0x6E31,0xBEDF,0x6DCA,0xBE32, +0x6D62,0xBD86,0x6CF9,0xBCDA,0x6C8F,0xBC2F,0x6C24,0xBB85,0x6BB8,0xBADC,0x6B4B, +0xBA33,0x6ADD,0xB98B,0x6A6E,0xB8E3,0x69FD,0xB83C,0x698C,0xB796,0x691A,0xB6F1, +0x68A7,0xB64C,0x6832,0xB5A8,0x67BD,0xB505,0x6747,0xB462,0x66D0,0xB3C0,0x6657, +0xB31F,0x65DE,0xB27F,0x6564,0xB1DF,0x64E9,0xB140,0x646C,0xB0A2,0x63EF,0xB005, +0x6371,0xAF68,0x62F2,0xAECC,0x6272,0xAE31,0x61F1,0xAD97,0x616F,0xACFD,0x60EC, +0xAC65,0x6068,0xABCD,0x5FE4,0xAB36,0x5F5E,0xAAA0,0x5ED7,0xAA0A,0x5E50,0xA976, +0x5DC8,0xA8E2,0x5D3E,0xA84F,0x5CB4,0xA7BD,0x5C29,0xA72C,0x5B9D,0xA69C,0x5B10, +0xA60C,0x5A82,0xA57E,0x59F4,0xA4F0,0x5964,0xA463,0x58D4,0xA3D7,0x5843,0xA34C, +0x57B1,0xA2C2,0x571E,0xA238,0x568A,0xA1B0,0x55F6,0xA129,0x5560,0xA0A2,0x54CA, +0xA01C,0x5433,0x9F98,0x539B,0x9F14,0x5303,0x9E91,0x5269,0x9E0F,0x51CF,0x9D8E, +0x5134,0x9D0E,0x5098,0x9C8F,0x4FFB,0x9C11,0x4F5E,0x9B94,0x4EC0,0x9B17,0x4E21, +0x9A9C,0x4D81,0x9A22,0x4CE1,0x99A9,0x4C40,0x9930,0x4B9E,0x98B9,0x4AFB,0x9843, +0x4A58,0x97CE,0x49B4,0x9759,0x490F,0x96E6,0x486A,0x9674,0x47C4,0x9603,0x471D, +0x9592,0x4675,0x9523,0x45CD,0x94B5,0x4524,0x9448,0x447B,0x93DC,0x43D1,0x9371, +0x4326,0x9307,0x427A,0x929E,0x41CE,0x9236,0x4121,0x91CF,0x4074,0x9169,0x3FC6, +0x9105,0x3F17,0x90A1,0x3E68,0x903E,0x3DB8,0x8FDD,0x3D08,0x8F7D,0x3C57,0x8F1D, +0x3BA5,0x8EBF,0x3AF3,0x8E62,0x3A40,0x8E06,0x398D,0x8DAB,0x38D9,0x8D51,0x3825, +0x8CF8,0x3770,0x8CA1,0x36BA,0x8C4A,0x3604,0x8BF5,0x354E,0x8BA0,0x3497,0x8B4D, +0x33DF,0x8AFB,0x3327,0x8AAA,0x326E,0x8A5A,0x31B5,0x8A0C,0x30FC,0x89BE,0x3042, +0x8972,0x2F87,0x8927,0x2ECC,0x88DD,0x2E11,0x8894,0x2D55,0x884C,0x2C99,0x8805, +0x2BDC,0x87C0,0x2B1F,0x877B,0x2A62,0x8738,0x29A4,0x86F6,0x28E5,0x86B6,0x2827, +0x8676,0x2768,0x8637,0x26A8,0x85FA,0x25E8,0x85BE,0x2528,0x8583,0x2467,0x8549, +0x23A7,0x8511,0x22E5,0x84D9,0x2224,0x84A3,0x2162,0x846E,0x209F,0x843A,0x1FDD, 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+0xD958,0x798A,0xD7D9,0x790A,0xD65C,0x7885,0xD4E1,0x77FB,0xD367,0x776C,0xD1EF, +0x76D9,0xD079,0x7642,0xCF04,0x75A6,0xCD92,0x7505,0xCC21,0x7460,0xCAB2,0x73B6, +0xC946,0x7308,0xC7DB,0x7255,0xC673,0x719E,0xC50D,0x70E3,0xC3A9,0x7023,0xC248, +0x6F5F,0xC0E9,0x6E97,0xBF8C,0x6DCA,0xBE32,0x6CF9,0xBCDA,0x6C24,0xBB85,0x6B4B, +0xBA33,0x6A6E,0xB8E3,0x698C,0xB796,0x68A7,0xB64C,0x67BD,0xB505,0x66D0,0xB3C0, +0x65DE,0xB27F,0x64E9,0xB140,0x63EF,0xB005,0x62F2,0xAECC,0x61F1,0xAD97,0x60EC, +0xAC65,0x5FE4,0xAB36,0x5ED7,0xAA0A,0x5DC8,0xA8E2,0x5CB4,0xA7BD,0x5B9D,0xA69C, +0x5A82,0xA57E,0x5964,0xA463,0x5843,0xA34C,0x571E,0xA238,0x55F6,0xA129,0x54CA, +0xA01C,0x539B,0x9F14,0x5269,0x9E0F,0x5134,0x9D0E,0x4FFB,0x9C11,0x4EC0,0x9B17, +0x4D81,0x9A22,0x4C40,0x9930,0x4AFB,0x9843,0x49B4,0x9759,0x486A,0x9674,0x471D, +0x9592,0x45CD,0x94B5,0x447B,0x93DC,0x4326,0x9307,0x41CE,0x9236,0x4074,0x9169, +0x3F17,0x90A1,0x3DB8,0x8FDD,0x3C57,0x8F1D,0x3AF3,0x8E62,0x398D,0x8DAB,0x3825, 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+0x8805,0xD1EF,0x8894,0xD079,0x8927,0xCF04,0x89BE,0xCD92,0x8A5A,0xCC21,0x8AFB, +0xCAB2,0x8BA0,0xC946,0x8C4A,0xC7DB,0x8CF8,0xC673,0x8DAB,0xC50D,0x8E62,0xC3A9, +0x8F1D,0xC248,0x8FDD,0xC0E9,0x90A1,0xBF8C,0x9169,0xBE32,0x9236,0xBCDA,0x9307, +0xBB85,0x93DC,0xBA33,0x94B5,0xB8E3,0x9592,0xB796,0x9674,0xB64C,0x9759,0xB505, +0x9843,0xB3C0,0x9930,0xB27F,0x9A22,0xB140,0x9B17,0xB005,0x9C11,0xAECC,0x9D0E, +0xAD97,0x9E0F,0xAC65,0x9F14,0xAB36,0xA01C,0xAA0A,0xA129,0xA8E2,0xA238,0xA7BD, +0xA34C,0xA69C,0xA463,0xA57E,0xA57E,0xA463,0xA69C,0xA34C,0xA7BD,0xA238,0xA8E2, +0xA129,0xAA0A,0xA01C,0xAB36,0x9F14,0xAC65,0x9E0F,0xAD97,0x9D0E,0xAECC,0x9C11, +0xB005,0x9B17,0xB140,0x9A22,0xB27F,0x9930,0xB3C0,0x9843,0xB505,0x9759,0xB64C, +0x9674,0xB796,0x9592,0xB8E3,0x94B5,0xBA33,0x93DC,0xBB85,0x9307,0xBCDA,0x9236, +0xBE32,0x9169,0xBF8C,0x90A1,0xC0E9,0x8FDD,0xC248,0x8F1D,0xC3A9,0x8E62,0xC50D, +0x8DAB,0xC673,0x8CF8,0xC7DB,0x8C4A,0xC946,0x8BA0,0xCAB2,0x8AFB,0xCC21,0x8A5A, +0xCD92,0x89BE,0xCF04,0x8927,0xD079,0x8894,0xD1EF,0x8805,0xD367,0x877B,0xD4E1, +0x86F6,0xD65C,0x8676,0xD7D9,0x85FA,0xD958,0x8583,0xDAD8,0x8511,0xDC59,0x84A3, +0xDDDC,0x843A,0xDF61,0x83D6,0xE0E6,0x8377,0xE26D,0x831C,0xE3F4,0x82C6,0xE57D, +0x8276,0xE707,0x822A,0xE892,0x81E2,0xEA1E,0x81A0,0xEBAB,0x8163,0xED38,0x812A, +0xEEC6,0x80F6,0xF055,0x80C8,0xF1E4,0x809E,0xF374,0x8079,0xF505,0x8059,0xF695, +0x803E,0xF827,0x8027,0xF9B8,0x8016,0xFB4A,0x800A,0xFCDC,0x8002,0xFE6E,0x7FFF, +0x0000,0x7FFA,0xFDA5,0x7FEA,0xFB4A,0x7FCE,0xF8EF,0x7FA7,0xF695,0x7F75,0xF43C, +0x7F38,0xF1E4,0x7EF0,0xEF8D,0x7E9D,0xED38,0x7E3F,0xEAE4,0x7DD6,0xE892,0x7D63, +0xE642,0x7CE4,0xE3F4,0x7C5A,0xE1A9,0x7BC6,0xDF61,0x7B27,0xDD1B,0x7A7D,0xDAD8, +0x79C9,0xD898,0x790A,0xD65C,0x7840,0xD424,0x776C,0xD1EF,0x768E,0xCFBE,0x75A6, +0xCD92,0x74B3,0xCB69,0x73B6,0xC946,0x72AF,0xC727,0x719E,0xC50D,0x7083,0xC2F8, +0x6F5F,0xC0E9,0x6E31,0xBEDF,0x6CF9,0xBCDA,0x6BB8,0xBADC,0x6A6E,0xB8E3,0x691A, +0xB6F1,0x67BD,0xB505,0x6657,0xB31F,0x64E9,0xB140,0x6371,0xAF68,0x61F1,0xAD97, +0x6068,0xABCD,0x5ED7,0xAA0A,0x5D3E,0xA84F,0x5B9D,0xA69C,0x59F4,0xA4F0,0x5843, +0xA34C,0x568A,0xA1B0,0x54CA,0xA01C,0x5303,0x9E91,0x5134,0x9D0E,0x4F5E,0x9B94, +0x4D81,0x9A22,0x4B9E,0x98B9,0x49B4,0x9759,0x47C4,0x9603,0x45CD,0x94B5,0x43D1, +0x9371,0x41CE,0x9236,0x3FC6,0x9105,0x3DB8,0x8FDD,0x3BA5,0x8EBF,0x398D,0x8DAB, +0x3770,0x8CA1,0x354E,0x8BA0,0x3327,0x8AAA,0x30FC,0x89BE,0x2ECC,0x88DD,0x2C99, +0x8805,0x2A62,0x8738,0x2827,0x8676,0x25E8,0x85BE,0x23A7,0x8511,0x2162,0x846E, +0x1F1A,0x83D6,0x1CD0,0x8349,0x1A83,0x82C6,0x1833,0x824F,0x15E2,0x81E2,0x138F, +0x8181,0x113A,0x812A,0x0EE4,0x80DE,0x0C8C,0x809E,0x0A33,0x8068,0x07D9,0x803E, +0x057F,0x801E,0x0324,0x800A,0x00C9,0x8001,0xFE6E,0x8002,0xFC13,0x800F,0xF9B8, +0x8027,0xF75E,0x804B,0xF505,0x8079,0xF2AC,0x80B2,0xF055,0x80F6,0xEDFF,0x8146, +0xEBAB,0x81A0,0xE958,0x8205,0xE707,0x8276,0xE4B9,0x82F1,0xE26D,0x8377,0xE023, +0x8407,0xDDDC,0x84A3,0xDB99,0x8549,0xD958,0x85FA,0xD71B,0x86B6,0xD4E1,0x877B, +0xD2AB,0x884C,0xD079,0x8927,0xCE4B,0x8A0C,0xCC21,0x8AFB,0xC9FC,0x8BF5,0xC7DB, +0x8CF8,0xC5C0,0x8E06,0xC3A9,0x8F1D,0xC198,0x903E,0xBF8C,0x9169,0xBD86,0x929E, +0xBB85,0x93DC,0xB98B,0x9523,0xB796,0x9674,0xB5A8,0x97CE,0xB3C0,0x9930,0xB1DF, +0x9A9C,0xB005,0x9C11,0xAE31,0x9D8E,0xAC65,0x9F14,0xAAA0,0xA0A2,0xA8E2,0xA238, +0xA72C,0xA3D7,0xA57E,0xA57E,0xA3D7,0xA72C,0xA238,0xA8E2,0xA0A2,0xAAA0,0x9F14, +0xAC65,0x9D8E,0xAE31,0x9C11,0xB005,0x9A9C,0xB1DF,0x9930,0xB3C0,0x97CE,0xB5A8, +0x9674,0xB796,0x9523,0xB98B,0x93DC,0xBB85,0x929E,0xBD86,0x9169,0xBF8C,0x903E, +0xC198,0x8F1D,0xC3A9,0x8E06,0xC5C0,0x8CF8,0xC7DB,0x8BF5,0xC9FC,0x8AFB,0xCC21, +0x8A0C,0xCE4B,0x8927,0xD079,0x884C,0xD2AB,0x877B,0xD4E1,0x86B6,0xD71B,0x85FA, +0xD958,0x8549,0xDB99,0x84A3,0xDDDC,0x8407,0xE023,0x8377,0xE26D,0x82F1,0xE4B9, +0x8276,0xE707,0x8205,0xE958,0x81A0,0xEBAB,0x8146,0xEDFF,0x80F6,0xF055,0x80B2, +0xF2AC,0x8079,0xF505,0x804B,0xF75E,0x8027,0xF9B8,0x800F,0xFC13,0x8002,0xFE6E, +0x8001,0x00C9,0x800A,0x0324,0x801E,0x057F,0x803E,0x07D9,0x8068,0x0A33,0x809E, +0x0C8C,0x80DE,0x0EE4,0x812A,0x113A,0x8181,0x138F,0x81E2,0x15E2,0x824F,0x1833, +0x82C6,0x1A83,0x8349,0x1CD0,0x83D6,0x1F1A,0x846E,0x2162,0x8511,0x23A7,0x85BE, +0x25E8,0x8676,0x2827,0x8738,0x2A62,0x8805,0x2C99,0x88DD,0x2ECC,0x89BE,0x30FC, +0x8AAA,0x3327,0x8BA0,0x354E,0x8CA1,0x3770,0x8DAB,0x398D,0x8EBF,0x3BA5,0x8FDD, +0x3DB8,0x9105,0x3FC6,0x9236,0x41CE,0x9371,0x43D1,0x94B5,0x45CD,0x9603,0x47C4, +0x9759,0x49B4,0x98B9,0x4B9E,0x9A22,0x4D81,0x9B94,0x4F5E,0x9D0E,0x5134,0x9E91, +0x5303,0xA01C,0x54CA,0xA1B0,0x568A,0xA34C,0x5843,0xA4F0,0x59F4,0xA69C,0x5B9D, +0xA84F,0x5D3E,0xAA0A,0x5ED7,0xABCD,0x6068,0xAD97,0x61F1,0xAF68,0x6371,0xB140, +0x64E9,0xB31F,0x6657,0xB505,0x67BD,0xB6F1,0x691A,0xB8E3,0x6A6E,0xBADC,0x6BB8, +0xBCDA,0x6CF9,0xBEDF,0x6E31,0xC0E9,0x6F5F,0xC2F8,0x7083,0xC50D,0x719E,0xC727, +0x72AF,0xC946,0x73B6,0xCB69,0x74B3,0xCD92,0x75A6,0xCFBE,0x768E,0xD1EF,0x776C, +0xD424,0x7840,0xD65C,0x790A,0xD898,0x79C9,0xDAD8,0x7A7D,0xDD1B,0x7B27,0xDF61, +0x7BC6,0xE1A9,0x7C5A,0xE3F4,0x7CE4,0xE642,0x7D63,0xE892,0x7DD6,0xEAE4,0x7E3F, +0xED38,0x7E9D,0xEF8D,0x7EF0,0xF1E4,0x7F38,0xF43C,0x7F75,0xF695,0x7FA7,0xF8EF, +0x7FCE,0xFB4A,0x7FEA,0xFDA5,0x7FFA,}; + +const uint32_t arm_neon_factors_1024_q15[ARM_NEON_FACTORS_1024_Q15_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_2048_q15[ARM_NEON_TWIDDLES_2048_Q15_LEN]={ +0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E,0x471D, +0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E, +0x30FC,0x89BE,0x0000,0x8000,0xCF04,0x89BE,0xA57E,0xA57E,0x89BE,0xCF04,0x7FFF, +0x0000,0x6A6E,0xB8E3,0x30FC,0x89BE,0xE707,0x8276,0xA57E,0xA57E,0x8276,0xE707, +0x89BE,0x30FC,0xB8E3,0x6A6E,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62,0xF374,0x7E9D, +0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1,0x7642,0xCF04, +0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0,0xB3C0,0x62F2, +0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E,0x4C40,0x9930, +0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC,0x89BE,0x2B1F, +0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163,0x0C8C,0x809E, +0x0648,0x8027,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x0000,0x8000,0xF374,0x809E,0xE707,0x8276,0xDAD8,0x8583,0xCF04,0x89BE, +0xC3A9,0x8F1D,0xB8E3,0x9592,0xAECC,0x9D0E,0xA57E,0xA57E,0x9D0E,0xAECC,0x9592, +0xB8E3,0x8F1D,0xC3A9,0x89BE,0xCF04,0x8583,0xDAD8,0x8276,0xE707,0x809E,0xF374, +0x7FFF,0x0000,0x7E9D,0xED38,0x7A7D,0xDAD8,0x73B6,0xC946,0x6A6E,0xB8E3,0x5ED7, +0xAA0A,0x5134,0x9D0E,0x41CE,0x9236,0x30FC,0x89BE,0x1F1A,0x83D6,0x0C8C,0x809E, +0xF9B8,0x8027,0xE707,0x8276,0xD4E1,0x877B,0xC3A9,0x8F1D,0xB3C0,0x9930,0xA57E, +0xA57E,0x9930,0xB3C0,0x8F1D,0xC3A9,0x877B,0xD4E1,0x8276,0xE707,0x8027,0xF9B8, +0x809E,0x0C8C,0x83D6,0x1F1A,0x89BE,0x30FC,0x9236,0x41CE,0x9D0E,0x5134,0xAA0A, +0x5ED7,0xB8E3,0x6A6E,0xC946,0x73B6,0xDAD8,0x7A7D,0xED38,0x7E9D,0x7FFF,0x0000, +0x7FFE,0xFE6E,0x7FF6,0xFCDC,0x7FEA,0xFB4A,0x7FD9,0xF9B8,0x7FC2,0xF827,0x7FA7, +0xF695,0x7F87,0xF505,0x7F62,0xF374,0x7F38,0xF1E4,0x7F0A,0xF055,0x7ED6,0xEEC6, +0x7E9D,0xED38,0x7E60,0xEBAB,0x7E1E,0xEA1E,0x7DD6,0xE892,0x7D8A,0xE707,0x7D3A, +0xE57D,0x7CE4,0xE3F4,0x7C89,0xE26D,0x7C2A,0xE0E6,0x7BC6,0xDF61,0x7B5D,0xDDDC, +0x7AEF,0xDC59,0x7A7D,0xDAD8,0x7A06,0xD958,0x798A,0xD7D9,0x790A,0xD65C,0x7885, +0xD4E1,0x77FB,0xD367,0x776C,0xD1EF,0x76D9,0xD079,0x7642,0xCF04,0x75A6,0xCD92, +0x7505,0xCC21,0x7460,0xCAB2,0x73B6,0xC946,0x7308,0xC7DB,0x7255,0xC673,0x719E, +0xC50D,0x70E3,0xC3A9,0x7023,0xC248,0x6F5F,0xC0E9,0x6E97,0xBF8C,0x6DCA,0xBE32, +0x6CF9,0xBCDA,0x6C24,0xBB85,0x6B4B,0xBA33,0x6A6E,0xB8E3,0x698C,0xB796,0x68A7, +0xB64C,0x67BD,0xB505,0x66D0,0xB3C0,0x65DE,0xB27F,0x64E9,0xB140,0x63EF,0xB005, +0x62F2,0xAECC,0x61F1,0xAD97,0x60EC,0xAC65,0x5FE4,0xAB36,0x5ED7,0xAA0A,0x5DC8, +0xA8E2,0x5CB4,0xA7BD,0x5B9D,0xA69C,0x5A82,0xA57E,0x5964,0xA463,0x5843,0xA34C, +0x571E,0xA238,0x55F6,0xA129,0x54CA,0xA01C,0x539B,0x9F14,0x5269,0x9E0F,0x5134, +0x9D0E,0x4FFB,0x9C11,0x4EC0,0x9B17,0x4D81,0x9A22,0x4C40,0x9930,0x4AFB,0x9843, +0x49B4,0x9759,0x486A,0x9674,0x471D,0x9592,0x45CD,0x94B5,0x447B,0x93DC,0x4326, +0x9307,0x41CE,0x9236,0x4074,0x9169,0x3F17,0x90A1,0x3DB8,0x8FDD,0x3C57,0x8F1D, +0x3AF3,0x8E62,0x398D,0x8DAB,0x3825,0x8CF8,0x36BA,0x8C4A,0x354E,0x8BA0,0x33DF, +0x8AFB,0x326E,0x8A5A,0x30FC,0x89BE,0x2F87,0x8927,0x2E11,0x8894,0x2C99,0x8805, +0x2B1F,0x877B,0x29A4,0x86F6,0x2827,0x8676,0x26A8,0x85FA,0x2528,0x8583,0x23A7, +0x8511,0x2224,0x84A3,0x209F,0x843A,0x1F1A,0x83D6,0x1D93,0x8377,0x1C0C,0x831C, +0x1A83,0x82C6,0x18F9,0x8276,0x176E,0x822A,0x15E2,0x81E2,0x1455,0x81A0,0x12C8, +0x8163,0x113A,0x812A,0x0FAB,0x80F6,0x0E1C,0x80C8,0x0C8C,0x809E,0x0AFB,0x8079, +0x096B,0x8059,0x07D9,0x803E,0x0648,0x8027,0x04B6,0x8016,0x0324,0x800A,0x0192, +0x8002,0x7FFF,0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374, +0x7F0A,0xF055,0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A, +0xE0E6,0x7B5D,0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF, +0x7642,0xCF04,0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F, +0xC0E9,0x6DCA,0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0, +0x64E9,0xB140,0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82, +0xA57E,0x5843,0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17, +0x4C40,0x9930,0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17, +0x90A1,0x3C57,0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE, +0x2E11,0x8894,0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A, +0x83D6,0x1C0C,0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6, +0x0C8C,0x809E,0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x0000,0x8000,0xFCDC, +0x800A,0xF9B8,0x8027,0xF695,0x8059,0xF374,0x809E,0xF055,0x80F6,0xED38,0x8163, +0xEA1E,0x81E2,0xE707,0x8276,0xE3F4,0x831C,0xE0E6,0x83D6,0xDDDC,0x84A3,0xDAD8, +0x8583,0xD7D9,0x8676,0xD4E1,0x877B,0xD1EF,0x8894,0xCF04,0x89BE,0xCC21,0x8AFB, +0xC946,0x8C4A,0xC673,0x8DAB,0xC3A9,0x8F1D,0xC0E9,0x90A1,0xBE32,0x9236,0xBB85, +0x93DC,0xB8E3,0x9592,0xB64C,0x9759,0xB3C0,0x9930,0xB140,0x9B17,0xAECC,0x9D0E, +0xAC65,0x9F14,0xAA0A,0xA129,0xA7BD,0xA34C,0xA57E,0xA57E,0xA34C,0xA7BD,0xA129, +0xAA0A,0x9F14,0xAC65,0x9D0E,0xAECC,0x9B17,0xB140,0x9930,0xB3C0,0x9759,0xB64C, +0x9592,0xB8E3,0x93DC,0xBB85,0x9236,0xBE32,0x90A1,0xC0E9,0x8F1D,0xC3A9,0x8DAB, +0xC673,0x8C4A,0xC946,0x8AFB,0xCC21,0x89BE,0xCF04,0x8894,0xD1EF,0x877B,0xD4E1, +0x8676,0xD7D9,0x8583,0xDAD8,0x84A3,0xDDDC,0x83D6,0xE0E6,0x831C,0xE3F4,0x8276, +0xE707,0x81E2,0xEA1E,0x8163,0xED38,0x80F6,0xF055,0x809E,0xF374,0x8059,0xF695, +0x8027,0xF9B8,0x800A,0xFCDC,0x7FFF,0x0000,0x7FEA,0xFB4A,0x7FA7,0xF695,0x7F38, +0xF1E4,0x7E9D,0xED38,0x7DD6,0xE892,0x7CE4,0xE3F4,0x7BC6,0xDF61,0x7A7D,0xDAD8, +0x790A,0xD65C,0x776C,0xD1EF,0x75A6,0xCD92,0x73B6,0xC946,0x719E,0xC50D,0x6F5F, +0xC0E9,0x6CF9,0xBCDA,0x6A6E,0xB8E3,0x67BD,0xB505,0x64E9,0xB140,0x61F1,0xAD97, +0x5ED7,0xAA0A,0x5B9D,0xA69C,0x5843,0xA34C,0x54CA,0xA01C,0x5134,0x9D0E,0x4D81, +0x9A22,0x49B4,0x9759,0x45CD,0x94B5,0x41CE,0x9236,0x3DB8,0x8FDD,0x398D,0x8DAB, +0x354E,0x8BA0,0x30FC,0x89BE,0x2C99,0x8805,0x2827,0x8676,0x23A7,0x8511,0x1F1A, +0x83D6,0x1A83,0x82C6,0x15E2,0x81E2,0x113A,0x812A,0x0C8C,0x809E,0x07D9,0x803E, +0x0324,0x800A,0xFE6E,0x8002,0xF9B8,0x8027,0xF505,0x8079,0xF055,0x80F6,0xEBAB, +0x81A0,0xE707,0x8276,0xE26D,0x8377,0xDDDC,0x84A3,0xD958,0x85FA,0xD4E1,0x877B, +0xD079,0x8927,0xCC21,0x8AFB,0xC7DB,0x8CF8,0xC3A9,0x8F1D,0xBF8C,0x9169,0xBB85, +0x93DC,0xB796,0x9674,0xB3C0,0x9930,0xB005,0x9C11,0xAC65,0x9F14,0xA8E2,0xA238, +0xA57E,0xA57E,0xA238,0xA8E2,0x9F14,0xAC65,0x9C11,0xB005,0x9930,0xB3C0,0x9674, +0xB796,0x93DC,0xBB85,0x9169,0xBF8C,0x8F1D,0xC3A9,0x8CF8,0xC7DB,0x8AFB,0xCC21, +0x8927,0xD079,0x877B,0xD4E1,0x85FA,0xD958,0x84A3,0xDDDC,0x8377,0xE26D,0x8276, +0xE707,0x81A0,0xEBAB,0x80F6,0xF055,0x8079,0xF505,0x8027,0xF9B8,0x8002,0xFE6E, +0x800A,0x0324,0x803E,0x07D9,0x809E,0x0C8C,0x812A,0x113A,0x81E2,0x15E2,0x82C6, +0x1A83,0x83D6,0x1F1A,0x8511,0x23A7,0x8676,0x2827,0x8805,0x2C99,0x89BE,0x30FC, +0x8BA0,0x354E,0x8DAB,0x398D,0x8FDD,0x3DB8,0x9236,0x41CE,0x94B5,0x45CD,0x9759, +0x49B4,0x9A22,0x4D81,0x9D0E,0x5134,0xA01C,0x54CA,0xA34C,0x5843,0xA69C,0x5B9D, +0xAA0A,0x5ED7,0xAD97,0x61F1,0xB140,0x64E9,0xB505,0x67BD,0xB8E3,0x6A6E,0xBCDA, 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+0xBC85,0x929E,0xBD86,0x9202,0xBE88,0x9169,0xBF8C,0x90D3,0xC091,0x903E,0xC198, +0x8FAD,0xC2A0,0x8F1D,0xC3A9,0x8E90,0xC4B4,0x8E06,0xC5C0,0x8D7E,0xC6CD,0x8CF8, +0xC7DB,0x8C75,0xC8EB,0x8BF5,0xC9FC,0x8B77,0xCB0E,0x8AFB,0xCC21,0x8A82,0xCD35, +0x8A0C,0xCE4B,0x8998,0xCF61,0x8927,0xD079,0x88B8,0xD191,0x884C,0xD2AB,0x87E2, +0xD3C5,0x877B,0xD4E1,0x8717,0xD5FD,0x86B6,0xD71B,0x8656,0xD839,0x85FA,0xD958, +0x85A0,0xDA78,0x8549,0xDB99,0x84F5,0xDCBA,0x84A3,0xDDDC,0x8454,0xDEFF,0x8407, +0xE023,0x83BE,0xE148,0x8377,0xE26D,0x8332,0xE392,0x82F1,0xE4B9,0x82B2,0xE5E0, +0x8276,0xE707,0x823C,0xE82F,0x8205,0xE958,0x81D1,0xEA81,0x81A0,0xEBAB,0x8172, +0xECD5,0x8146,0xEDFF,0x811D,0xEF2A,0x80F6,0xF055,0x80D3,0xF180,0x80B2,0xF2AC, +0x8094,0xF3D8,0x8079,0xF505,0x8060,0xF631,0x804B,0xF75E,0x8038,0xF88B,0x8027, +0xF9B8,0x801A,0xFAE5,0x800F,0xFC13,0x8008,0xFD40,0x8002,0xFE6E,0x8000,0xFF9B, +0x8001,0x00C9,0x8004,0x01F7,0x800A,0x0324,0x8013,0x0452,0x801E,0x057F,0x802D, +0x06AC,0x803E,0x07D9,0x8052,0x0906,0x8068,0x0A33,0x8082,0x0B60,0x809E,0x0C8C, +0x80BD,0x0DB8,0x80DE,0x0EE4,0x8103,0x100F,0x812A,0x113A,0x8154,0x1265,0x8181, +0x138F,0x81B0,0x14B9,0x81E2,0x15E2,0x8217,0x170B,0x824F,0x1833,0x8289,0x195B, +0x82C6,0x1A83,0x8306,0x1BA9,0x8349,0x1CD0,0x838E,0x1DF5,0x83D6,0x1F1A,0x8421, +0x203E,0x846E,0x2162,0x84BE,0x2284,0x8511,0x23A7,0x8566,0x24C8,0x85BE,0x25E8, +0x8619,0x2708,0x8676,0x2827,0x86D6,0x2945,0x8738,0x2A62,0x879D,0x2B7E,0x8805, +0x2C99,0x8870,0x2DB3,0x88DD,0x2ECC,0x894C,0x2FE5,0x89BE,0x30FC,0x8A33,0x3212, +0x8AAA,0x3327,0x8B24,0x343B,0x8BA0,0x354E,0x8C1F,0x365F,0x8CA1,0x3770,0x8D24, +0x387F,0x8DAB,0x398D,0x8E34,0x3A9A,0x8EBF,0x3BA5,0x8F4D,0x3CAF,0x8FDD,0x3DB8, +0x9070,0x3EC0,0x9105,0x3FC6,0x919C,0x40CB,0x9236,0x41CE,0x92D2,0x42D0,0x9371, +0x43D1,0x9412,0x44D0,0x94B5,0x45CD,0x955B,0x46C9,0x9603,0x47C4,0x96AD,0x48BD, +0x9759,0x49B4,0x9808,0x4AAA,0x98B9,0x4B9E,0x996D,0x4C91,0x9A22,0x4D81,0x9ADA, +0x4E71,0x9B94,0x4F5E,0x9C50,0x504A,0x9D0E,0x5134,0x9DCE,0x521C,0x9E91,0x5303, +0x9F56,0x53E7,0xA01C,0x54CA,0xA0E5,0x55AB,0xA1B0,0x568A,0xA27D,0x5767,0xA34C, +0x5843,0xA41D,0x591C,0xA4F0,0x59F4,0xA5C5,0x5AC9,0xA69C,0x5B9D,0xA774,0x5C6F, +0xA84F,0x5D3E,0xA92C,0x5E0C,0xAA0A,0x5ED7,0xAAEB,0x5FA1,0xABCD,0x6068,0xACB1, +0x612E,0xAD97,0x61F1,0xAE7F,0x62B2,0xAF68,0x6371,0xB053,0x642E,0xB140,0x64E9, +0xB22F,0x65A1,0xB31F,0x6657,0xB411,0x670B,0xB505,0x67BD,0xB5FA,0x686D,0xB6F1, +0x691A,0xB7E9,0x69C5,0xB8E3,0x6A6E,0xB9DF,0x6B14,0xBADC,0x6BB8,0xBBDA,0x6C5A, +0xBCDA,0x6CF9,0xBDDC,0x6D96,0xBEDF,0x6E31,0xBFE3,0x6EC9,0xC0E9,0x6F5F,0xC1F0, +0x6FF2,0xC2F8,0x7083,0xC402,0x7112,0xC50D,0x719E,0xC619,0x7228,0xC727,0x72AF, +0xC836,0x7334,0xC946,0x73B6,0xCA57,0x7436,0xCB69,0x74B3,0xCC7D,0x752D,0xCD92, +0x75A6,0xCEA7,0x761B,0xCFBE,0x768E,0xD0D6,0x76FE,0xD1EF,0x776C,0xD309,0x77D8, +0xD424,0x7840,0xD53F,0x78A6,0xD65C,0x790A,0xD77A,0x796A,0xD898,0x79C9,0xD9B8, +0x7A24,0xDAD8,0x7A7D,0xDBF9,0x7AD3,0xDD1B,0x7B27,0xDE3D,0x7B78,0xDF61,0x7BC6, +0xE085,0x7C11,0xE1A9,0x7C5A,0xE2CF,0x7CA0,0xE3F4,0x7CE4,0xE51B,0x7D25,0xE642, +0x7D63,0xE76A,0x7D9E,0xE892,0x7DD6,0xE9BB,0x7E0C,0xEAE4,0x7E3F,0xEC0E,0x7E70, +0xED38,0x7E9D,0xEE62,0x7EC8,0xEF8D,0x7EF0,0xF0B9,0x7F16,0xF1E4,0x7F38,0xF310, +0x7F58,0xF43C,0x7F75,0xF569,0x7F90,0xF695,0x7FA7,0xF7C2,0x7FBC,0xF8EF,0x7FCE, +0xFA1D,0x7FDD,0xFB4A,0x7FEA,0xFC77,0x7FF4,0xFDA5,0x7FFA,0xFED2,0x7FFF,}; + +const uint32_t arm_neon_factors_2048_q15[ARM_NEON_FACTORS_2048_Q15_LEN]={ +5,256,8,8,}; + +__ALIGNED(16) const q15_t arm_neon_twiddles_4096_q15[ARM_NEON_TWIDDLES_4096_Q15_LEN]={ +0x7FFF,0x0000,0x7642,0xCF04,0x5A82,0xA57E,0x30FC,0x89BE,0x7FFF,0x0000,0x5A82, +0xA57E,0x0000,0x8000,0xA57E,0xA57E,0x7FFF,0x0000,0x30FC,0x89BE,0xA57E,0xA57E, +0x89BE,0x30FC,0x7FFF,0x0000,0x7F62,0xF374,0x7D8A,0xE707,0x7A7D,0xDAD8,0x7642, +0xCF04,0x70E3,0xC3A9,0x6A6E,0xB8E3,0x62F2,0xAECC,0x5A82,0xA57E,0x5134,0x9D0E, +0x471D,0x9592,0x3C57,0x8F1D,0x30FC,0x89BE,0x2528,0x8583,0x18F9,0x8276,0x0C8C, +0x809E,0x7FFF,0x0000,0x7D8A,0xE707,0x7642,0xCF04,0x6A6E,0xB8E3,0x5A82,0xA57E, +0x471D,0x9592,0x30FC,0x89BE,0x18F9,0x8276,0x0000,0x8000,0xE707,0x8276,0xCF04, +0x89BE,0xB8E3,0x9592,0xA57E,0xA57E,0x9592,0xB8E3,0x89BE,0xCF04,0x8276,0xE707, +0x7FFF,0x0000,0x7A7D,0xDAD8,0x6A6E,0xB8E3,0x5134,0x9D0E,0x30FC,0x89BE,0x0C8C, +0x809E,0xE707,0x8276,0xC3A9,0x8F1D,0xA57E,0xA57E,0x8F1D,0xC3A9,0x8276,0xE707, +0x809E,0x0C8C,0x89BE,0x30FC,0x9D0E,0x5134,0xB8E3,0x6A6E,0xDAD8,0x7A7D,0x7FFF, +0x0000,0x7FF6,0xFCDC,0x7FD9,0xF9B8,0x7FA7,0xF695,0x7F62,0xF374,0x7F0A,0xF055, +0x7E9D,0xED38,0x7E1E,0xEA1E,0x7D8A,0xE707,0x7CE4,0xE3F4,0x7C2A,0xE0E6,0x7B5D, +0xDDDC,0x7A7D,0xDAD8,0x798A,0xD7D9,0x7885,0xD4E1,0x776C,0xD1EF,0x7642,0xCF04, +0x7505,0xCC21,0x73B6,0xC946,0x7255,0xC673,0x70E3,0xC3A9,0x6F5F,0xC0E9,0x6DCA, +0xBE32,0x6C24,0xBB85,0x6A6E,0xB8E3,0x68A7,0xB64C,0x66D0,0xB3C0,0x64E9,0xB140, +0x62F2,0xAECC,0x60EC,0xAC65,0x5ED7,0xAA0A,0x5CB4,0xA7BD,0x5A82,0xA57E,0x5843, +0xA34C,0x55F6,0xA129,0x539B,0x9F14,0x5134,0x9D0E,0x4EC0,0x9B17,0x4C40,0x9930, +0x49B4,0x9759,0x471D,0x9592,0x447B,0x93DC,0x41CE,0x9236,0x3F17,0x90A1,0x3C57, +0x8F1D,0x398D,0x8DAB,0x36BA,0x8C4A,0x33DF,0x8AFB,0x30FC,0x89BE,0x2E11,0x8894, +0x2B1F,0x877B,0x2827,0x8676,0x2528,0x8583,0x2224,0x84A3,0x1F1A,0x83D6,0x1C0C, +0x831C,0x18F9,0x8276,0x15E2,0x81E2,0x12C8,0x8163,0x0FAB,0x80F6,0x0C8C,0x809E, +0x096B,0x8059,0x0648,0x8027,0x0324,0x800A,0x7FFF,0x0000,0x7FD9,0xF9B8,0x7F62, +0xF374,0x7E9D,0xED38,0x7D8A,0xE707,0x7C2A,0xE0E6,0x7A7D,0xDAD8,0x7885,0xD4E1, +0x7642,0xCF04,0x73B6,0xC946,0x70E3,0xC3A9,0x6DCA,0xBE32,0x6A6E,0xB8E3,0x66D0, +0xB3C0,0x62F2,0xAECC,0x5ED7,0xAA0A,0x5A82,0xA57E,0x55F6,0xA129,0x5134,0x9D0E, +0x4C40,0x9930,0x471D,0x9592,0x41CE,0x9236,0x3C57,0x8F1D,0x36BA,0x8C4A,0x30FC, +0x89BE,0x2B1F,0x877B,0x2528,0x8583,0x1F1A,0x83D6,0x18F9,0x8276,0x12C8,0x8163, +0x0C8C,0x809E,0x0648,0x8027,0x0000,0x8000,0xF9B8,0x8027,0xF374,0x809E,0xED38, +0x8163,0xE707,0x8276,0xE0E6,0x83D6,0xDAD8,0x8583,0xD4E1,0x877B,0xCF04,0x89BE, +0xC946,0x8C4A,0xC3A9,0x8F1D,0xBE32,0x9236,0xB8E3,0x9592,0xB3C0,0x9930,0xAECC, +0x9D0E,0xAA0A,0xA129,0xA57E,0xA57E,0xA129,0xAA0A,0x9D0E,0xAECC,0x9930,0xB3C0, +0x9592,0xB8E3,0x9236,0xBE32,0x8F1D,0xC3A9,0x8C4A,0xC946,0x89BE,0xCF04,0x877B, +0xD4E1,0x8583,0xDAD8,0x83D6,0xE0E6,0x8276,0xE707,0x8163,0xED38,0x809E,0xF374, +0x8027,0xF9B8,0x7FFF,0x0000,0x7FA7,0xF695,0x7E9D,0xED38,0x7CE4,0xE3F4,0x7A7D, +0xDAD8,0x776C,0xD1EF,0x73B6,0xC946,0x6F5F,0xC0E9,0x6A6E,0xB8E3,0x64E9,0xB140, +0x5ED7,0xAA0A,0x5843,0xA34C,0x5134,0x9D0E,0x49B4,0x9759,0x41CE,0x9236,0x398D, +0x8DAB,0x30FC,0x89BE,0x2827,0x8676,0x1F1A,0x83D6,0x15E2,0x81E2,0x0C8C,0x809E, +0x0324,0x800A,0xF9B8,0x8027,0xF055,0x80F6,0xE707,0x8276,0xDDDC,0x84A3,0xD4E1, +0x877B,0xCC21,0x8AFB,0xC3A9,0x8F1D,0xBB85,0x93DC,0xB3C0,0x9930,0xAC65,0x9F14, 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+0xE642,0x7D63,0xE6D6,0x7D81,0xE76A,0x7D9E,0xE7FE,0x7DBA,0xE892,0x7DD6,0xE926, +0x7DF2,0xE9BB,0x7E0C,0xEA4F,0x7E26,0xEAE4,0x7E3F,0xEB79,0x7E58,0xEC0E,0x7E70, +0xECA3,0x7E87,0xED38,0x7E9D,0xEDCD,0x7EB3,0xEE62,0x7EC8,0xEEF8,0x7EDD,0xEF8D, +0x7EF0,0xF023,0x7F03,0xF0B9,0x7F16,0xF14E,0x7F27,0xF1E4,0x7F38,0xF27A,0x7F49, +0xF310,0x7F58,0xF3A6,0x7F67,0xF43C,0x7F75,0xF4D3,0x7F83,0xF569,0x7F90,0xF5FF, +0x7F9C,0xF695,0x7FA7,0xF72C,0x7FB2,0xF7C2,0x7FBC,0xF859,0x7FC5,0xF8EF,0x7FCE, +0xF986,0x7FD6,0xFA1D,0x7FDD,0xFAB3,0x7FE4,0xFB4A,0x7FEA,0xFBE1,0x7FEF,0xFC77, +0x7FF4,0xFD0E,0x7FF7,0xFDA5,0x7FFA,0xFE3C,0x7FFD,0xFED2,0x7FFF,0xFF69,0x7FFF,}; + +const uint32_t arm_neon_factors_4096_q15[ARM_NEON_FACTORS_4096_Q15_LEN]={ +6,1024,4,4,}; + + + +#endif /* defined(ARM_MATH_NEON) */ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_neon_tables_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_neon_tables_f16.c new file mode 100755 index 0000000..a6ec6cd --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/CommonTables/arm_neon_tables_f16.c @@ -0,0 +1,21511 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_neon_tables_f16.c + * Description: common tables like fft twiddle factors, Bitreverse, reciprocal etc + * used for NEON implementation only + * + * @date 02 October 2024 + * + * Target Processor: Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2024 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + #include "arm_math_types_f16.h" + + +#if defined(ARM_FLOAT16_SUPPORTED) + + +#if defined(ARM_MATH_NEON_FLOAT16) + + +#include "arm_neon_tables_f16.h" +__ALIGNED(16) const float16_t arm_neon_twiddles_16_f16[ARM_NEON_TWIDDLES_16_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f,}; + +const uint32_t arm_neon_factors_16_f16[ARM_NEON_FACTORS_16_F16_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_32_f16[ARM_NEON_TWIDDLES_32_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f,}; + +const uint32_t arm_neon_factors_32_f16[ARM_NEON_FACTORS_32_F16_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_64_f16[ARM_NEON_TWIDDLES_64_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f,}; + +const uint32_t arm_neon_factors_64_f16[ARM_NEON_FACTORS_64_F16_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_128_f16[ARM_NEON_TWIDDLES_128_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f,}; + +const uint32_t arm_neon_factors_128_f16[ARM_NEON_FACTORS_128_F16_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_256_f16[ARM_NEON_TWIDDLES_256_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9853515625000f,(float16_t)-0.1710205078125f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9497070312500f,(float16_t)-0.3137207031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8930664062500f,(float16_t)-0.4497070312500f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8173828125000f,(float16_t)-0.5756835937500f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7573242187500f,(float16_t)-0.6533203125000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6894531250000f,(float16_t)-0.7241210937500f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6533203125000f,(float16_t)-0.7573242187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.6152343750000f,(float16_t)-0.7885742187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5756835937500f,(float16_t)-0.8173828125000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5351562500000f,(float16_t)-0.8447265625000f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4929199218750f,(float16_t)-0.8701171875000f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4497070312500f,(float16_t)-0.8930664062500f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.4052734375000f,(float16_t)-0.9140625000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3598632812500f,(float16_t)-0.9331054687500f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.3137207031250f,(float16_t)-0.9497070312500f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2666015625000f,(float16_t)-0.9638671875000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.2191162109375f,(float16_t)-0.9755859375000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1710205078125f,(float16_t)-0.9853515625000f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.1224365234375f,(float16_t)-0.9926757812500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0735473632812f,(float16_t)-0.9970703125000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, 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+(float16_t)-0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)-0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)-0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)-0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.9995117187500f,(float16_t)0.0245361328125f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9853515625000f,(float16_t)0.1710205078125f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)-0.9497070312500f,(float16_t)0.3137207031250f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.8930664062500f,(float16_t)0.4497070312500f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)-0.8173828125000f,(float16_t)0.5756835937500f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.7241210937500f,(float16_t)0.6894531250000f, +(float16_t)-0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)-0.6152343750000f,(float16_t)0.7885742187500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.4929199218750f,(float16_t)0.8701171875000f, +(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)-0.3598632812500f,(float16_t)0.9331054687500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)-0.2191162109375f,(float16_t)0.9755859375000f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f,}; + +const uint32_t arm_neon_factors_256_f16[ARM_NEON_FACTORS_256_F16_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_512_f16[ARM_NEON_TWIDDLES_512_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, 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+(float16_t)-0.3251953125000f,(float16_t)0.9458007812500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)-0.2548828125000f,(float16_t)0.9667968750000f, +(float16_t)-0.2191162109375f,(float16_t)0.9755859375000f, +(float16_t)-0.1829833984375f,(float16_t)0.9829101562500f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)-0.1102294921875f,(float16_t)0.9941406250000f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f, +(float16_t)-0.0368041992188f,(float16_t)0.9995117187500f,}; + +const uint32_t arm_neon_factors_512_f16[ARM_NEON_FACTORS_512_F16_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_1024_f16[ARM_NEON_TWIDDLES_1024_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, 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+(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)-0.1285400390625f,(float16_t)0.9916992187500f, +(float16_t)-0.1102294921875f,(float16_t)0.9941406250000f, +(float16_t)-0.0919189453125f,(float16_t)0.9956054687500f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f, +(float16_t)-0.0552062988281f,(float16_t)0.9985351562500f, +(float16_t)-0.0368041992188f,(float16_t)0.9995117187500f, +(float16_t)-0.0184020996094f,(float16_t)1.0000000000000f,}; + +const uint32_t arm_neon_factors_1024_f16[ARM_NEON_FACTORS_1024_F16_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_twiddles_2048_f16[ARM_NEON_TWIDDLES_2048_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, 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+(float16_t)-0.0827636718750f,(float16_t)0.9965820312500f, +(float16_t)-0.0781250000000f,(float16_t)0.9970703125000f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f, +(float16_t)-0.0689697265625f,(float16_t)0.9975585937500f, +(float16_t)-0.0643920898438f,(float16_t)0.9980468750000f, +(float16_t)-0.0597839355469f,(float16_t)0.9980468750000f, +(float16_t)-0.0552062988281f,(float16_t)0.9985351562500f, +(float16_t)-0.0505981445312f,(float16_t)0.9985351562500f, +(float16_t)-0.0459899902344f,(float16_t)0.9990234375000f, +(float16_t)-0.0414123535156f,(float16_t)0.9990234375000f, +(float16_t)-0.0368041992188f,(float16_t)0.9995117187500f, +(float16_t)-0.0321960449219f,(float16_t)0.9995117187500f, +(float16_t)-0.0276031494141f,(float16_t)0.9995117187500f, +(float16_t)-0.0230102539062f,(float16_t)0.9995117187500f, +(float16_t)-0.0184020996094f,(float16_t)1.0000000000000f, +(float16_t)-0.0138015747070f,(float16_t)1.0000000000000f, +(float16_t)-0.0092010498047f,(float16_t)1.0000000000000f, +(float16_t)-0.0046005249023f,(float16_t)1.0000000000000f,}; + +const uint32_t arm_neon_factors_4096_f16[ARM_NEON_FACTORS_4096_F16_LEN]={ +6,1024,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_16_f16[ARM_NEON_RFFT_TWIDDLES_16_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f,}; + +const uint32_t arm_neon_rfft_factors_16_f16[ARM_NEON_RFFT_FACTORS_16_F16_LEN]={ +2,4,4,4,}; + +const float16_t *arm_neon_rfft_twiddles_neon_16_f16=NULL; + +const uint32_t arm_neon_rfft_factors_neon_16_f16[ARM_NEON_RFFT_FACTORS_NEON_16_F16_LEN]={ +1,1,4,1,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_16_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_16_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_32_f16[ARM_NEON_RFFT_TWIDDLES_32_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f,}; + +const uint32_t arm_neon_rfft_factors_32_f16[ARM_NEON_RFFT_FACTORS_32_F16_LEN]={ +2,4,8,8,}; + +const float16_t *arm_neon_rfft_twiddles_neon_32_f16=NULL; + +const uint32_t arm_neon_rfft_factors_neon_32_f16[ARM_NEON_RFFT_FACTORS_NEON_32_F16_LEN]={ +1,1,8,1,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_32_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_32_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_64_f16[ARM_NEON_RFFT_TWIDDLES_64_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f,}; + +const uint32_t arm_neon_rfft_factors_64_f16[ARM_NEON_RFFT_FACTORS_64_F16_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_neon_64_f16[ARM_NEON_RFFT_TWIDDLES_NEON_64_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f,}; + +const uint32_t arm_neon_rfft_factors_neon_64_f16[ARM_NEON_RFFT_FACTORS_NEON_64_F16_LEN]={ +2,4,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_64_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_64_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_128_f16[ARM_NEON_RFFT_TWIDDLES_128_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f,}; + +const uint32_t arm_neon_rfft_factors_128_f16[ARM_NEON_RFFT_FACTORS_128_F16_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_neon_128_f16[ARM_NEON_RFFT_TWIDDLES_NEON_128_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f,}; + +const uint32_t arm_neon_rfft_factors_neon_128_f16[ARM_NEON_RFFT_FACTORS_NEON_128_F16_LEN]={ +2,4,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_128_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_128_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_256_f16[ARM_NEON_RFFT_TWIDDLES_256_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9853515625000f,(float16_t)-0.1710205078125f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9497070312500f,(float16_t)-0.3137207031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8930664062500f,(float16_t)-0.4497070312500f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8173828125000f,(float16_t)-0.5756835937500f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7573242187500f,(float16_t)-0.6533203125000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6894531250000f,(float16_t)-0.7241210937500f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6533203125000f,(float16_t)-0.7573242187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.6152343750000f,(float16_t)-0.7885742187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5756835937500f,(float16_t)-0.8173828125000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5351562500000f,(float16_t)-0.8447265625000f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4929199218750f,(float16_t)-0.8701171875000f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4497070312500f,(float16_t)-0.8930664062500f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.4052734375000f,(float16_t)-0.9140625000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3598632812500f,(float16_t)-0.9331054687500f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.3137207031250f,(float16_t)-0.9497070312500f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2666015625000f,(float16_t)-0.9638671875000f, 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+(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)-0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)-0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)-0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6894531250000f,(float16_t)-0.7241210937500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5756835937500f,(float16_t)-0.8173828125000f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4497070312500f,(float16_t)-0.8930664062500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3137207031250f,(float16_t)-0.9497070312500f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1710205078125f,(float16_t)-0.9853515625000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.1224365234375f,(float16_t)-0.9926757812500f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.2666015625000f,(float16_t)-0.9638671875000f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.4052734375000f,(float16_t)-0.9140625000000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5351562500000f,(float16_t)-0.8447265625000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.6533203125000f,(float16_t)-0.7573242187500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.7573242187500f,(float16_t)-0.6533203125000f, +(float16_t)-0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)-0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)-0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)-0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.9995117187500f,(float16_t)0.0245361328125f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9853515625000f,(float16_t)0.1710205078125f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)-0.9497070312500f,(float16_t)0.3137207031250f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.8930664062500f,(float16_t)0.4497070312500f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)-0.8173828125000f,(float16_t)0.5756835937500f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)-0.7241210937500f,(float16_t)0.6894531250000f, +(float16_t)-0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)-0.6152343750000f,(float16_t)0.7885742187500f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)-0.4929199218750f,(float16_t)0.8701171875000f, +(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)-0.3598632812500f,(float16_t)0.9331054687500f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)-0.2191162109375f,(float16_t)0.9755859375000f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f,}; + +const uint32_t arm_neon_rfft_factors_256_f16[ARM_NEON_RFFT_FACTORS_256_F16_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_neon_256_f16[ARM_NEON_RFFT_TWIDDLES_NEON_256_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f,}; + +const uint32_t arm_neon_rfft_factors_neon_256_f16[ARM_NEON_RFFT_FACTORS_NEON_256_F16_LEN]={ +3,16,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_256_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_256_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9853515625000f,(float16_t)-0.1710205078125f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6894531250000f,(float16_t)-0.7241210937500f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9497070312500f,(float16_t)-0.3137207031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5756835937500f,(float16_t)-0.8173828125000f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4497070312500f,(float16_t)-0.8930664062500f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8930664062500f,(float16_t)-0.4497070312500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3137207031250f,(float16_t)-0.9497070312500f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1710205078125f,(float16_t)-0.9853515625000f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.1224365234375f,(float16_t)-0.9926757812500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8173828125000f,(float16_t)-0.5756835937500f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.2666015625000f,(float16_t)-0.9638671875000f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.4052734375000f,(float16_t)-0.9140625000000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7573242187500f,(float16_t)-0.6533203125000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5351562500000f,(float16_t)-0.8447265625000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.6533203125000f,(float16_t)-0.7573242187500f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_512_f16[ARM_NEON_RFFT_TWIDDLES_512_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, 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+(float16_t)-0.2191162109375f,(float16_t)0.9755859375000f, +(float16_t)-0.1829833984375f,(float16_t)0.9829101562500f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)-0.1102294921875f,(float16_t)0.9941406250000f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f, +(float16_t)-0.0368041992188f,(float16_t)0.9995117187500f,}; + +const uint32_t arm_neon_rfft_factors_512_f16[ARM_NEON_RFFT_FACTORS_512_F16_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_neon_512_f16[ARM_NEON_RFFT_TWIDDLES_NEON_512_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, 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+(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)-0.9951171875000f,(float16_t)0.0980224609375f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)-0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)-0.9702148437500f,(float16_t)0.2429199218750f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, +(float16_t)0.3369140625000f,(float16_t)-0.9414062500000f, +(float16_t)-0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)-0.8579101562500f,(float16_t)0.5141601562500f, +(float16_t)0.2902832031250f,(float16_t)-0.9570312500000f, +(float16_t)-0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)-0.7729492187500f,(float16_t)0.6342773437500f, +(float16_t)0.2429199218750f,(float16_t)-0.9702148437500f, +(float16_t)-0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)-0.6713867187500f,(float16_t)0.7407226562500f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)-0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)-0.5556640625000f,(float16_t)0.8315429687500f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)-0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f,}; + +const uint32_t arm_neon_rfft_factors_neon_512_f16[ARM_NEON_RFFT_FACTORS_NEON_512_F16_LEN]={ +3,16,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_512_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_512_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0122680664062f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9995117187500f,(float16_t)-0.0368041992188f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9995117187500f,(float16_t)-0.0368041992188f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9941406250000f,(float16_t)-0.1102294921875f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9980468750000f,(float16_t)-0.0613098144531f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9960937500000f,(float16_t)-0.0858154296875f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9853515625000f,(float16_t)-0.1710205078125f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9829101562500f,(float16_t)-0.1829833984375f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9667968750000f,(float16_t)-0.2548828125000f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)0.9941406250000f,(float16_t)-0.1102294921875f, +(float16_t)0.9926757812500f,(float16_t)-0.1224365234375f, +(float16_t)0.9907226562500f,(float16_t)-0.1345214843750f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9458007812500f,(float16_t)-0.3251953125000f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9189453125000f,(float16_t)-0.3940429687500f, +(float16_t)0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)0.9873046875000f,(float16_t)-0.1588134765625f, +(float16_t)0.9853515625000f,(float16_t)-0.1710205078125f, +(float16_t)0.9829101562500f,(float16_t)-0.1829833984375f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9497070312500f,(float16_t)-0.3137207031250f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8876953125000f,(float16_t)-0.4604492187500f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.8515625000000f,(float16_t)-0.5244140625000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9785156250000f,(float16_t)-0.2071533203125f, +(float16_t)0.9755859375000f,(float16_t)-0.2191162109375f, +(float16_t)0.9731445312500f,(float16_t)-0.2310791015625f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)0.9038085937500f,(float16_t)-0.4274902343750f, +(float16_t)0.8930664062500f,(float16_t)-0.4497070312500f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8105468750000f,(float16_t)-0.5859375000000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.7651367187500f,(float16_t)-0.6440429687500f, +(float16_t)0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)0.9667968750000f,(float16_t)-0.2548828125000f, +(float16_t)0.9638671875000f,(float16_t)-0.2666015625000f, +(float16_t)0.9604492187500f,(float16_t)-0.2785644531250f, +(float16_t)0.8818359375000f,(float16_t)-0.4714355468750f, +(float16_t)0.8701171875000f,(float16_t)-0.4929199218750f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7158203125000f,(float16_t)-0.6982421875000f, +(float16_t)0.6894531250000f,(float16_t)-0.7241210937500f, +(float16_t)0.6625976562500f,(float16_t)-0.7490234375000f, +(float16_t)0.9570312500000f,(float16_t)-0.2902832031250f, +(float16_t)0.9531250000000f,(float16_t)-0.3020019531250f, +(float16_t)0.9497070312500f,(float16_t)-0.3137207031250f, +(float16_t)0.9458007812500f,(float16_t)-0.3251953125000f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.8173828125000f,(float16_t)-0.5756835937500f, +(float16_t)0.8032226562500f,(float16_t)-0.5957031250000f, +(float16_t)0.7885742187500f,(float16_t)-0.6152343750000f, +(float16_t)0.6342773437500f,(float16_t)-0.7729492187500f, +(float16_t)0.6054687500000f,(float16_t)-0.7958984375000f, +(float16_t)0.5756835937500f,(float16_t)-0.8173828125000f, +(float16_t)0.5454101562500f,(float16_t)-0.8383789062500f, +(float16_t)0.9414062500000f,(float16_t)-0.3369140625000f, +(float16_t)0.9375000000000f,(float16_t)-0.3483886718750f, +(float16_t)0.9331054687500f,(float16_t)-0.3598632812500f, +(float16_t)0.9287109375000f,(float16_t)-0.3713378906250f, +(float16_t)0.7729492187500f,(float16_t)-0.6342773437500f, +(float16_t)0.7573242187500f,(float16_t)-0.6533203125000f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4821777343750f,(float16_t)-0.8759765625000f, +(float16_t)0.4497070312500f,(float16_t)-0.8930664062500f, +(float16_t)0.4165039062500f,(float16_t)-0.9091796875000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.9189453125000f,(float16_t)-0.3940429687500f, +(float16_t)0.9140625000000f,(float16_t)-0.4052734375000f, +(float16_t)0.9091796875000f,(float16_t)-0.4165039062500f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.6894531250000f,(float16_t)-0.7241210937500f, +(float16_t)0.6713867187500f,(float16_t)-0.7407226562500f, +(float16_t)0.6533203125000f,(float16_t)-0.7573242187500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.3483886718750f,(float16_t)-0.9375000000000f, +(float16_t)0.3137207031250f,(float16_t)-0.9497070312500f, +(float16_t)0.2785644531250f,(float16_t)-0.9604492187500f, 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+(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.5351562500000f,(float16_t)-0.8447265625000f, +(float16_t)0.5141601562500f,(float16_t)-0.8579101562500f, +(float16_t)0.4929199218750f,(float16_t)-0.8701171875000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0613098144531f,(float16_t)-0.9980468750000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)-0.0122680664062f,(float16_t)-1.0000000000000f, +(float16_t)0.8579101562500f,(float16_t)-0.5141601562500f, +(float16_t)0.8515625000000f,(float16_t)-0.5244140625000f, +(float16_t)0.8447265625000f,(float16_t)-0.5351562500000f, +(float16_t)0.8383789062500f,(float16_t)-0.5454101562500f, +(float16_t)0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)0.4497070312500f,(float16_t)-0.8930664062500f, +(float16_t)0.4274902343750f,(float16_t)-0.9038085937500f, +(float16_t)0.4052734375000f,(float16_t)-0.9140625000000f, 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+(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)0.1710205078125f,(float16_t)-0.9853515625000f, +(float16_t)0.1467285156250f,(float16_t)-0.9892578125000f, +(float16_t)0.1224365234375f,(float16_t)-0.9926757812500f, +(float16_t)-0.4714355468750f,(float16_t)-0.8818359375000f, +(float16_t)-0.5034179687500f,(float16_t)-0.8637695312500f, +(float16_t)-0.5351562500000f,(float16_t)-0.8447265625000f, +(float16_t)-0.5659179687500f,(float16_t)-0.8247070312500f, +(float16_t)0.7407226562500f,(float16_t)-0.6713867187500f, +(float16_t)0.7324218750000f,(float16_t)-0.6806640625000f, +(float16_t)0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)0.7158203125000f,(float16_t)-0.6982421875000f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)0.0735473632812f,(float16_t)-0.9970703125000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.6250000000000f,(float16_t)-0.7807617187500f, +(float16_t)-0.6533203125000f,(float16_t)-0.7573242187500f, +(float16_t)-0.6806640625000f,(float16_t)-0.7324218750000f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_1024_f16[ARM_NEON_RFFT_TWIDDLES_1024_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, 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+(float16_t)-0.0184020996094f,(float16_t)1.0000000000000f,}; + +const uint32_t arm_neon_rfft_factors_1024_f16[ARM_NEON_RFFT_FACTORS_1024_F16_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_neon_1024_f16[ARM_NEON_RFFT_TWIDDLES_NEON_1024_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.0000000000000f,(float16_t)-1.0000000000000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)-0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)-0.9238281250000f,(float16_t)0.3825683593750f, 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+(float16_t)-0.4274902343750f,(float16_t)0.9038085937500f, +(float16_t)0.1224365234375f,(float16_t)-0.9926757812500f, +(float16_t)-0.9702148437500f,(float16_t)-0.2429199218750f, +(float16_t)-0.3598632812500f,(float16_t)0.9331054687500f, +(float16_t)0.0980224609375f,(float16_t)-0.9951171875000f, +(float16_t)-0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)-0.2902832031250f,(float16_t)0.9570312500000f, +(float16_t)0.0735473632812f,(float16_t)-0.9970703125000f, +(float16_t)-0.9892578125000f,(float16_t)-0.1467285156250f, +(float16_t)-0.2191162109375f,(float16_t)0.9755859375000f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)-0.9951171875000f,(float16_t)-0.0980224609375f, +(float16_t)-0.1467285156250f,(float16_t)0.9892578125000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f,}; + +const uint32_t arm_neon_rfft_factors_neon_1024_f16[ARM_NEON_RFFT_FACTORS_NEON_1024_F16_LEN]={ +4,64,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_1024_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_1024_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0061340332031f, +(float16_t)1.0000000000000f,(float16_t)-0.0122680664062f, +(float16_t)1.0000000000000f,(float16_t)-0.0184020996094f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0122680664062f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9995117187500f,(float16_t)-0.0368041992188f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0184020996094f, +(float16_t)0.9995117187500f,(float16_t)-0.0368041992188f, +(float16_t)0.9985351562500f,(float16_t)-0.0552062988281f, +(float16_t)0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)0.9995117187500f,(float16_t)-0.0306701660156f, +(float16_t)0.9995117187500f,(float16_t)-0.0368041992188f, +(float16_t)0.9990234375000f,(float16_t)-0.0429382324219f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9980468750000f,(float16_t)-0.0613098144531f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9960937500000f,(float16_t)-0.0858154296875f, +(float16_t)0.9970703125000f,(float16_t)-0.0735473632812f, +(float16_t)0.9956054687500f,(float16_t)-0.0919189453125f, +(float16_t)0.9941406250000f,(float16_t)-0.1102294921875f, +(float16_t)0.9916992187500f,(float16_t)-0.1285400390625f, +(float16_t)0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)0.9985351562500f,(float16_t)-0.0552062988281f, +(float16_t)0.9980468750000f,(float16_t)-0.0613098144531f, +(float16_t)0.9975585937500f,(float16_t)-0.0674438476562f, +(float16_t)0.9951171875000f,(float16_t)-0.0980224609375f, 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+(float16_t)0.0858154296875f,(float16_t)-0.9960937500000f, +(float16_t)0.0735473632812f,(float16_t)-0.9970703125000f, +(float16_t)0.0613098144531f,(float16_t)-0.9980468750000f, +(float16_t)-0.5957031250000f,(float16_t)-0.8032226562500f, +(float16_t)-0.6103515625000f,(float16_t)-0.7919921875000f, +(float16_t)-0.6250000000000f,(float16_t)-0.7807617187500f, +(float16_t)-0.6391601562500f,(float16_t)-0.7690429687500f, +(float16_t)0.7241210937500f,(float16_t)-0.6894531250000f, +(float16_t)0.7202148437500f,(float16_t)-0.6938476562500f, +(float16_t)0.7158203125000f,(float16_t)-0.6982421875000f, +(float16_t)0.7114257812500f,(float16_t)-0.7026367187500f, +(float16_t)0.0490722656250f,(float16_t)-0.9990234375000f, +(float16_t)0.0368041992188f,(float16_t)-0.9995117187500f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)0.0122680664062f,(float16_t)-1.0000000000000f, +(float16_t)-0.6533203125000f,(float16_t)-0.7573242187500f, +(float16_t)-0.6669921875000f,(float16_t)-0.7451171875000f, +(float16_t)-0.6806640625000f,(float16_t)-0.7324218750000f, +(float16_t)-0.6938476562500f,(float16_t)-0.7202148437500f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_2048_f16[ARM_NEON_RFFT_TWIDDLES_2048_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9809570312500f,(float16_t)-0.1950683593750f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.8315429687500f,(float16_t)-0.5556640625000f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.5556640625000f,(float16_t)-0.8315429687500f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, +(float16_t)0.1950683593750f,(float16_t)-0.9809570312500f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, 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+(float16_t)-0.1102294921875f,(float16_t)0.9941406250000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)-0.9990234375000f,(float16_t)-0.0490722656250f, +(float16_t)-0.0735473632812f,(float16_t)0.9970703125000f, +(float16_t)0.0122680664062f,(float16_t)-1.0000000000000f, +(float16_t)-0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)-0.0368041992188f,(float16_t)0.9995117187500f,}; + +const uint32_t arm_neon_rfft_factors_neon_2048_f16[ARM_NEON_RFFT_FACTORS_NEON_2048_F16_LEN]={ +4,64,8,8,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_2048_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_2048_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0030670166016f, +(float16_t)1.0000000000000f,(float16_t)-0.0061340332031f, +(float16_t)1.0000000000000f,(float16_t)-0.0092010498047f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, 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+(float16_t)0.7133789062500f,(float16_t)-0.7006835937500f, +(float16_t)0.7114257812500f,(float16_t)-0.7026367187500f, +(float16_t)0.7094726562500f,(float16_t)-0.7050781250000f, +(float16_t)0.0245361328125f,(float16_t)-0.9995117187500f, +(float16_t)0.0184020996094f,(float16_t)-1.0000000000000f, +(float16_t)0.0122680664062f,(float16_t)-1.0000000000000f, +(float16_t)0.0061340332031f,(float16_t)-1.0000000000000f, +(float16_t)-0.6806640625000f,(float16_t)-0.7324218750000f, +(float16_t)-0.6875000000000f,(float16_t)-0.7265625000000f, +(float16_t)-0.6938476562500f,(float16_t)-0.7202148437500f, +(float16_t)-0.7006835937500f,(float16_t)-0.7133789062500f,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_twiddles_4096_f16[ARM_NEON_RFFT_TWIDDLES_4096_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)0.9238281250000f,(float16_t)-0.3825683593750f, +(float16_t)0.7070312500000f,(float16_t)-0.7070312500000f, +(float16_t)0.3825683593750f,(float16_t)-0.9238281250000f, 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+(float16_t)-0.0552062988281f,(float16_t)0.9985351562500f, +(float16_t)0.0122680664062f,(float16_t)-1.0000000000000f, +(float16_t)-0.9995117187500f,(float16_t)-0.0245361328125f, +(float16_t)-0.0368041992188f,(float16_t)0.9995117187500f, +(float16_t)0.0061340332031f,(float16_t)-1.0000000000000f, +(float16_t)-1.0000000000000f,(float16_t)-0.0122680664062f, +(float16_t)-0.0184020996094f,(float16_t)1.0000000000000f,}; + +const uint32_t arm_neon_rfft_factors_neon_4096_f16[ARM_NEON_RFFT_FACTORS_NEON_4096_F16_LEN]={ +5,256,4,4,}; + +__ALIGNED(16) const float16_t arm_neon_rfft_super_twiddles_neon_4096_f16[ARM_NEON_RFFT_SUPER_TWIDDLES_NEON_4096_F16_LEN]={ +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, +(float16_t)1.0000000000000f,(float16_t)-0.0015335083008f, +(float16_t)1.0000000000000f,(float16_t)-0.0030670166016f, +(float16_t)1.0000000000000f,(float16_t)-0.0046005249023f, +(float16_t)1.0000000000000f,(float16_t)-0.0000000000000f, 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+(float16_t)0.7104492187500f,(float16_t)-0.7036132812500f, +(float16_t)0.7094726562500f,(float16_t)-0.7050781250000f, +(float16_t)0.7080078125000f,(float16_t)-0.7060546875000f, +(float16_t)0.0122680664062f,(float16_t)-1.0000000000000f, +(float16_t)0.0092010498047f,(float16_t)-1.0000000000000f, +(float16_t)0.0061340332031f,(float16_t)-1.0000000000000f, +(float16_t)0.0030670166016f,(float16_t)-1.0000000000000f, +(float16_t)-0.6938476562500f,(float16_t)-0.7202148437500f, +(float16_t)-0.6972656250000f,(float16_t)-0.7167968750000f, +(float16_t)-0.7006835937500f,(float16_t)-0.7133789062500f, +(float16_t)-0.7036132812500f,(float16_t)-0.7104492187500f,}; + + + +#endif /* defined(ARM_MATH_NEON_FLOAT16) && defined(ARM_FLOAT16_SUPPORTED) */ + +#endif /* if defined(ARM_MATH_NEON_FLOAT16) && defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_f16.c new file mode 100755 index 0000000..7522067 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_f16.c @@ -0,0 +1,165 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_conj_f16.c + * Description: Floating-point complex conjugate + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) +/** + @ingroup groupCmplxMath + */ + + +/** + @addtogroup cmplx_conj + @{ + */ + +/** + @brief Floating-point complex conjugate. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples) +{ + static const float16_t cmplx_conj_sign[8] = { 1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f }; + uint32_t blockSize = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + f16x8_t vecSrc; + f16x8_t vecSign; + + /* + * load sign vector + */ + vecSign = *(f16x8_t *) cmplx_conj_sign; + + /* Compute 4 real samples at a time */ + blkCnt = blockSize >> 3U; + + while (blkCnt > 0U) + { + vecSrc = vld1q(pSrc); + vst1q(pDst,vmulq(vecSrc, vecSign)); + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrc += 8; + pDst += 8; + blkCnt--; + } + + /* Tail */ + blkCnt = (blockSize & 0x7) >> 1; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + *pDst++ = -(_Float16)*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + *pDst++ = -(_Float16)*pSrc++; + + *pDst++ = *pSrc++; + *pDst++ = -(_Float16)*pSrc++; + + *pDst++ = *pSrc++; + *pDst++ = -(_Float16)*pSrc++; + + *pDst++ = *pSrc++; + *pDst++ = -(_Float16)*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + *pDst++ = -(_Float16)*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_conj group + */ +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c new file mode 100755 index 0000000..5c188a3 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c @@ -0,0 +1,215 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_conj_f32.c + * Description: Floating-point complex conjugate + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @defgroup cmplx_conj Complex Conjugate + + Conjugates the elements of a complex data vector. + + The pSrc points to the source data and + pDst points to the destination data where the result should be written. + numSamples specifies the number of complex samples + and the data in each array is stored in an interleaved fashion + (real, imag, real, imag, ...). + Each array has a total of 2*numSamples values. + + The underlying algorithm is used: + 
+  for (n = 0; n < numSamples; n++) {
+      pDst[(2*n)  ] =  pSrc[(2*n)  ];    // real part
+      pDst[(2*n)+1] = -pSrc[(2*n)+1];    // imag part
+  }
+
+ + There are separate functions for floating-point, Q15, and Q31 data types. + */ + +/** + @addtogroup cmplx_conj + @{ + */ + +/** + @brief Floating-point complex conjugate. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples) +{ + static const float32_t cmplx_conj_sign[4] = { 1.0f, -1.0f, 1.0f, -1.0f }; + uint32_t blockSize = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + f32x4_t vecSrc; + f32x4_t vecSign; + + /* + * load sign vector + */ + vecSign = *(f32x4_t *) cmplx_conj_sign; + + /* Compute 4 real samples at a time */ + blkCnt = blockSize >> 2U; + + while (blkCnt > 0U) + { + vecSrc = vld1q(pSrc); + vst1q(pDst,vmulq(vecSrc, vecSign)); + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrc += 4; + pDst += 4; + blkCnt--; + } + + /* Tail */ + blkCnt = (blockSize & 0x3) >> 1; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + *pDst++ = -*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + +#if defined(ARM_MATH_NEON) + float32x4_t zero; + float32x4x2_t vec; + + zero = vdupq_n_f32(0.0f); + + /* Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0]+jC[1] = A[0]+(-1)*jA[1] */ + /* Calculate Complex Conjugate and then store the results in the destination buffer. */ + vec = vld2q_f32(pSrc); + vec.val[1] = vsubq_f32(zero,vec.val[1]); + vst2q_f32(pDst,vec); + + /* Increment pointers */ + pSrc += 8; + pDst += 8; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* Tail */ + blkCnt = numSamples & 0x3; + +#else +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + *pDst++ = -*pSrc++; + + *pDst++ = *pSrc++; + *pDst++ = -*pSrc++; + + *pDst++ = *pSrc++; + *pDst++ = -*pSrc++; + + *pDst++ = *pSrc++; + *pDst++ = -*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +#endif /* #if defined (ARM_MATH_NEON) */ + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + *pDst++ = -*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_conj group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c new file mode 100755 index 0000000..cede0cf --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c @@ -0,0 +1,209 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_conj_q15.c + * Description: Q15 complex conjugate + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_conj + @{ + */ + +/** + @brief Q15 complex conjugate. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function uses saturating arithmetic. + The Q15 value -1 (0x8000) is saturated to the maximum allowable positive value 0x7FFF. + */ + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + uint32_t blockSize = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + q31_t in1; + + q15x8x2_t vecSrc; + q15x8_t zero; + + zero = vdupq_n_s16(0); + + /* Compute 8 real samples at a time */ + blkCnt = blockSize >> 4U; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + vecSrc.val[1] = vqsubq(zero, vecSrc.val[1]); + vst2q(pDst,vecSrc); + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrc += 16; + pDst += 16; + blkCnt --; + } + + /* Tail */ + blkCnt = (blockSize & 0xF) >> 1; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + in1 = *pSrc++; + *pDst++ = __SSAT(-in1, 16); + + /* Decrement loop counter */ + blkCnt--; + } +} +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q31_t in1; /* Temporary input variable */ + +#if defined (ARM_MATH_LOOPUNROLL) && defined (ARM_MATH_DSP) + q31_t in2, in3, in4; /* Temporary input variables */ +#endif + + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + +#if defined (ARM_MATH_DSP) + in1 = read_q15x2_ia (&pSrc); + in2 = read_q15x2_ia (&pSrc); + in3 = read_q15x2_ia (&pSrc); + in4 = read_q15x2_ia (&pSrc); + +#ifndef ARM_MATH_BIG_ENDIAN + in1 = __QASX(0, in1); + in2 = __QASX(0, in2); + in3 = __QASX(0, in3); + in4 = __QASX(0, in4); +#else + in1 = __QSAX(0, in1); + in2 = __QSAX(0, in2); + in3 = __QSAX(0, in3); + in4 = __QSAX(0, in4); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + in1 = ((uint32_t) in1 >> 16) | ((uint32_t) in1 << 16); + in2 = ((uint32_t) in2 >> 16) | ((uint32_t) in2 << 16); + in3 = ((uint32_t) in3 >> 16) | ((uint32_t) in3 << 16); + in4 = ((uint32_t) in4 >> 16) | ((uint32_t) in4 << 16); + + write_q15x2_ia (&pDst, in1); + write_q15x2_ia (&pDst, in2); + write_q15x2_ia (&pDst, in3); + write_q15x2_ia (&pDst, in4); +#else + *pDst++ = *pSrc++; + in1 = *pSrc++; + *pDst++ = (in1 == (q15_t) 0x8000) ? (q15_t) 0x7fff : -in1; + + *pDst++ = *pSrc++; + in1 = *pSrc++; + *pDst++ = (in1 == (q15_t) 0x8000) ? (q15_t) 0x7fff : -in1; + + *pDst++ = *pSrc++; + in1 = *pSrc++; + *pDst++ = (in1 == (q15_t) 0x8000) ? (q15_t) 0x7fff : -in1; + + *pDst++ = *pSrc++; + in1 = *pSrc++; + *pDst++ = (in1 == (q15_t) 0x8000) ? (q15_t) 0x7fff : -in1; + +#endif /* #if defined (ARM_MATH_DSP) */ + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + in1 = *pSrc++; +#if defined (ARM_MATH_DSP) + *pDst++ = __SSAT(-in1, 16); +#else + *pDst++ = (in1 == (q15_t) 0x8000) ? (q15_t) 0x7fff : -in1; +#endif + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_conj group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c new file mode 100755 index 0000000..02d19f4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c @@ -0,0 +1,195 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_conj_q31.c + * Description: Q31 complex conjugate + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_conj + @{ + */ + +/** + @brief Q31 complex conjugate. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function uses saturating arithmetic. + The Q31 value -1 (0x80000000) is saturated to the maximum allowable positive value 0x7FFFFFFF. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples) +{ + + uint32_t blockSize = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + q31x4x2_t vecSrc; + q31_t in; /* Temporary input variable */ + q31x4_t zero; + + zero = vdupq_n_s32(0); + + + /* Compute 4 real samples at a time */ + blkCnt = blockSize >> 3U; + + while (blkCnt > 0U) + { + + vecSrc = vld2q(pSrc); + vecSrc.val[1] = vqsubq(zero, vecSrc.val[1]); + vst2q(pDst,vecSrc); + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrc += 8; + pDst += 8; + blkCnt --; + } + + /* Tail */ + blkCnt = (blockSize & 0x7) >> 1; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + in = *pSrc++; + *pDst++ = __QSUB(0, in); + + /* Decrement loop counter */ + blkCnt--; + } + + +} +#else + +ARM_DSP_ATTRIBUTE void arm_cmplx_conj_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q31_t in; /* Temporary input variable */ + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + in = *pSrc++; +#if defined (ARM_MATH_DSP) + *pDst++ = __QSUB(0, in); +#else + *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in; +#endif + + *pDst++ = *pSrc++; + in = *pSrc++; +#if defined (ARM_MATH_DSP) + *pDst++ = __QSUB(0, in); +#else + *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in; +#endif + + *pDst++ = *pSrc++; + in = *pSrc++; +#if defined (ARM_MATH_DSP) + *pDst++ = __QSUB(0, in); +#else + *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in; +#endif + + *pDst++ = *pSrc++; + in = *pSrc++; +#if defined (ARM_MATH_DSP) + *pDst++ = __QSUB(0, in); +#else + *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in; +#endif + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] + jC[1] = A[0]+ j(-1)A[1] */ + + /* Calculate Complex Conjugate and store result in destination buffer. */ + *pDst++ = *pSrc++; + in = *pSrc++; +#if defined (ARM_MATH_DSP) + *pDst++ = __QSUB(0, in); +#else + *pDst++ = (in == INT32_MIN) ? INT32_MAX : -in; +#endif + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_conj group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f16.c new file mode 100755 index 0000000..07a057a --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f16.c @@ -0,0 +1,264 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_dot_prod_f16.c + * Description: Floating-point complex dot product + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + + +/** + @ingroup groupCmplxMath + */ + + +/** + @addtogroup cmplx_dot_prod + @{ + */ + +/** + @brief Floating-point complex dot product. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] numSamples number of samples in each vector + @param[out] realResult real part of the result returned here + @param[out] imagResult imaginary part of the result returned here + */ + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" + +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + uint32_t numSamples, + float16_t * realResult, + float16_t * imagResult) +{ + int32_t blkCnt; + float16_t real_sum, imag_sum; + f16x8_t vecSrcA, vecSrcB; + f16x8_t vec_acc = vdupq_n_f16(0.0f16); + f16x8_t vecSrcC, vecSrcD; + + blkCnt = (numSamples >> 3); + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q( pSrcA); + vecSrcB = vld1q( pSrcB); + pSrcA += 8; + pSrcB += 8; + + while (blkCnt > 0) { + vec_acc = vcmlaq(vec_acc, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 8; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 8; + + vec_acc = vcmlaq(vec_acc, vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 8; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + vec_acc = vcmlaq(vec_acc, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + + vec_acc = vcmlaq(vec_acc, vecSrcC, vecSrcD); + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 7); + while (blkCnt > 0) { + mve_pred16_t p = vctp16q(blkCnt); + pSrcA += 8; + pSrcB += 8; + + vecSrcA = vldrhq_z_f16(pSrcA, p); + vecSrcB = vldrhq_z_f16(pSrcB, p); + vec_acc = vcmlaq_m(vec_acc, vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + + blkCnt -= 8; + } + } else { + /* small vector */ + blkCnt = numSamples * CMPLX_DIM; + vec_acc = vdupq_n_f16(0.0f16); + + do { + mve_pred16_t p = vctp16q(blkCnt); + + vecSrcA = vldrhq_z_f16(pSrcA, p); + vecSrcB = vldrhq_z_f16(pSrcB, p); + + vec_acc = vcmlaq_m(vec_acc, vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrcA += 8; + pSrcB += 8; + blkCnt -= 8; + } + while (blkCnt > 0); + } + + /* Sum the partial parts */ + mve_cmplx_sum_intra_r_i_f16(vec_acc, real_sum, imag_sum); + + /* + * Store the real and imaginary results in the destination buffers + */ + *realResult = real_sum; + *imagResult = imag_sum; +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + uint32_t numSamples, + float16_t * realResult, + float16_t * imagResult) +{ + uint32_t blkCnt; /* Loop counter */ + _Float16 real_sum = 0.0f, imag_sum = 0.0f; /* Temporary result variables */ + _Float16 a0,b0,c0,d0; + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Store real and imaginary result in destination buffer. */ + *realResult = real_sum; + *imagResult = imag_sum; +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_dot_prod group + */ + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c new file mode 100755 index 0000000..18ee479 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c @@ -0,0 +1,342 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_dot_prod_f32.c + * Description: Floating-point complex dot product + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @defgroup cmplx_dot_prod Complex Dot Product + + Computes the dot product of two complex vectors. + The vectors are multiplied element-by-element and then summed. + + The pSrcA points to the first complex input vector and + pSrcB points to the second complex input vector. + numSamples specifies the number of complex samples + and the data in each array is stored in an interleaved fashion + (real, imag, real, imag, ...). + Each array has a total of 2*numSamples values. + + The underlying algorithm is used: + + 
+  realResult = 0;
+  imagResult = 0;
+  for (n = 0; n < numSamples; n++) {
+      realResult += pSrcA[(2*n)+0] * pSrcB[(2*n)+0] - pSrcA[(2*n)+1] * pSrcB[(2*n)+1];
+      imagResult += pSrcA[(2*n)+0] * pSrcB[(2*n)+1] + pSrcA[(2*n)+1] * pSrcB[(2*n)+0];
+  }
+
+ + There are separate functions for floating-point, Q15, and Q31 data types. + */ + +/** + @addtogroup cmplx_dot_prod + @{ + */ + +/** + @brief Floating-point complex dot product. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] numSamples number of samples in each vector + @param[out] realResult real part of the result returned here + @param[out] imagResult imaginary part of the result returned here + */ + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t numSamples, + float32_t * realResult, + float32_t * imagResult) +{ + int32_t blkCnt; + float32_t real_sum, imag_sum; + f32x4_t vecSrcA, vecSrcB; + f32x4_t vec_acc = vdupq_n_f32(0.0f); + f32x4_t vecSrcC, vecSrcD; + + blkCnt = numSamples >> 2; + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 4; + pSrcB += 4; + + while (blkCnt > 0) { + vec_acc = vcmlaq(vec_acc, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 4; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 4; + + vec_acc = vcmlaq(vec_acc, vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 4; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 4; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + vec_acc = vcmlaq(vec_acc, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + + vec_acc = vcmlaq(vec_acc, vecSrcC, vecSrcD); + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 3); + while (blkCnt > 0) { + mve_pred16_t p = vctp32q(blkCnt); + pSrcA += 4; + pSrcB += 4; + vecSrcA = vldrwq_z_f32(pSrcA, p); + vecSrcB = vldrwq_z_f32(pSrcB, p); + vec_acc = vcmlaq_m(vec_acc, vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + blkCnt -= 4; + } + } else { + /* small vector */ + blkCnt = numSamples * CMPLX_DIM; + vec_acc = vdupq_n_f32(0.0f); + + do { + mve_pred16_t p = vctp32q(blkCnt); + + vecSrcA = vldrwq_z_f32(pSrcA, p); + vecSrcB = vldrwq_z_f32(pSrcB, p); + + vec_acc = vcmlaq_m(vec_acc, vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrcA += 4; + pSrcB += 4; + blkCnt -= 4; + } + while (blkCnt > 0); + } + + real_sum = vgetq_lane(vec_acc, 0) + vgetq_lane(vec_acc, 2); + imag_sum = vgetq_lane(vec_acc, 1) + vgetq_lane(vec_acc, 3); + + /* + * Store the real and imaginary results in the destination buffers + */ + *realResult = real_sum; + *imagResult = imag_sum; +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + uint32_t numSamples, + float32_t * realResult, + float32_t * imagResult) +{ + uint32_t blkCnt; /* Loop counter */ + float32_t real_sum = 0.0f, imag_sum = 0.0f; /* Temporary result variables */ + float32_t a0,b0,c0,d0; + +#if defined(ARM_MATH_NEON) + float32x4x2_t vec1,vec2,vec3,vec4; + float32x4_t accR,accI; + float32x2_t accum = vdup_n_f32(0); + + accR = vdupq_n_f32(0.0f); + accI = vdupq_n_f32(0.0f); + + /* Loop unrolling: Compute 8 outputs at a time */ + blkCnt = numSamples >> 3U; + + while (blkCnt > 0U) + { + /* C = (A[0]+jA[1])*(B[0]+jB[1]) + ... */ + /* Calculate dot product and then store the result in a temporary buffer. */ + + vec1 = vld2q_f32(pSrcA); + vec2 = vld2q_f32(pSrcB); + + /* Increment pointers */ + pSrcA += 8; + pSrcB += 8; + + /* Re{C} = Re{A}*Re{B} - Im{A}*Im{B} */ + accR = vmlaq_f32(accR,vec1.val[0],vec2.val[0]); + accR = vmlsq_f32(accR,vec1.val[1],vec2.val[1]); + + /* Im{C} = Re{A}*Im{B} + Im{A}*Re{B} */ + accI = vmlaq_f32(accI,vec1.val[1],vec2.val[0]); + accI = vmlaq_f32(accI,vec1.val[0],vec2.val[1]); + + vec3 = vld2q_f32(pSrcA); + vec4 = vld2q_f32(pSrcB); + + /* Increment pointers */ + pSrcA += 8; + pSrcB += 8; + + /* Re{C} = Re{A}*Re{B} - Im{A}*Im{B} */ + accR = vmlaq_f32(accR,vec3.val[0],vec4.val[0]); + accR = vmlsq_f32(accR,vec3.val[1],vec4.val[1]); + + /* Im{C} = Re{A}*Im{B} + Im{A}*Re{B} */ + accI = vmlaq_f32(accI,vec3.val[1],vec4.val[0]); + accI = vmlaq_f32(accI,vec3.val[0],vec4.val[1]); + + /* Decrement the loop counter */ + blkCnt--; + } + + accum = vpadd_f32(vget_low_f32(accR), vget_high_f32(accR)); + real_sum += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1); + + accum = vpadd_f32(vget_low_f32(accI), vget_high_f32(accI)); + imag_sum += vget_lane_f32(accum, 0) + vget_lane_f32(accum, 1); + + /* Tail */ + blkCnt = numSamples & 0x7; + +#else +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +#endif /* #if defined(ARM_MATH_NEON) */ + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += a0 * c0; + imag_sum += a0 * d0; + real_sum -= b0 * d0; + imag_sum += b0 * c0; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Store real and imaginary result in destination buffer. */ + *realResult = real_sum; + *imagResult = imag_sum; +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_dot_prod group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c new file mode 100755 index 0000000..0d94ded --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c @@ -0,0 +1,258 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_dot_prod_q15.c + * Description: Processing function for the Q15 Complex Dot product + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_dot_prod + @{ + */ + +/** + @brief Q15 complex dot product. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] numSamples number of samples in each vector + @param[out] realResult real part of the result returned here + @param[out] imagResult imaginary part of the result returned her + + @par Scaling and Overflow Behavior + The function is implemented using an internal 64-bit accumulator. + The intermediate 1.15 by 1.15 multiplications are performed with full precision and yield a 2.30 result. + These are accumulated in a 64-bit accumulator with 34.30 precision. + As a final step, the accumulators are converted to 8.24 format. + The return results realResult and imagResult are in 8.24 format. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t numSamples, + q31_t * realResult, + q31_t * imagResult) +{ + int32_t blkCnt; + q63_t accReal = 0LL; + q63_t accImag = 0LL; + q15x8_t vecSrcA, vecSrcB; + q15x8_t vecSrcC, vecSrcD; + + blkCnt = (numSamples >> 3); + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 8; + pSrcB += 8; + + while (blkCnt > 0) { + + accReal = vmlsldavaq(accReal, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 8; + + accImag = vmlaldavaxq(accImag, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 8; + + accReal = vmlsldavaq(accReal, vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 8; + + accImag = vmlaldavaxq(accImag, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + accReal = vmlsldavaq(accReal, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + accImag = vmlaldavaxq(accImag, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + + accReal = vmlsldavaq(accReal, vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + + accImag = vmlaldavaxq(accImag, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 7); + do { + mve_pred16_t p = vctp16q(blkCnt); + + pSrcA += 8; + pSrcB += 8; + + vecSrcA = vldrhq_z_s16(pSrcA, p); + vecSrcB = vldrhq_z_s16(pSrcB, p); + + accReal = vmlsldavaq_p(accReal, vecSrcA, vecSrcB, p); + accImag = vmlaldavaxq_p(accImag, vecSrcA, vecSrcB, p); + + blkCnt -= 8; + } + while ((int32_t) blkCnt > 0); + } else { + blkCnt = numSamples * CMPLX_DIM; + while (blkCnt > 0) { + mve_pred16_t p = vctp16q(blkCnt); + + vecSrcA = vldrhq_z_s16(pSrcA, p); + vecSrcB = vldrhq_z_s16(pSrcB, p); + + accReal = vmlsldavaq_p(accReal, vecSrcA, vecSrcB, p); + accImag = vmlaldavaxq_p(accImag, vecSrcA, vecSrcB, p); + + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrcA += 8; + pSrcB += 8; + blkCnt -= 8; + } + } + *realResult = asrl(accReal, (14 - 8)); + *imagResult = asrl(accImag, (14 - 8)); +} +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + uint32_t numSamples, + q31_t * realResult, + q31_t * imagResult) +{ + uint32_t blkCnt; /* Loop counter */ + q63_t real_sum = 0, imag_sum = 0; /* Temporary result variables */ + q15_t a0,b0,c0,d0; + +#if defined (ARM_MATH_LOOPUNROLL) + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += (q31_t)a0 * c0; + imag_sum += (q31_t)a0 * d0; + real_sum -= (q31_t)b0 * d0; + imag_sum += (q31_t)b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += (q31_t)a0 * c0; + imag_sum += (q31_t)a0 * d0; + real_sum -= (q31_t)b0 * d0; + imag_sum += (q31_t)b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += (q31_t)a0 * c0; + imag_sum += (q31_t)a0 * d0; + real_sum -= (q31_t)b0 * d0; + imag_sum += (q31_t)b0 * c0; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += (q31_t)a0 * c0; + imag_sum += (q31_t)a0 * d0; + real_sum -= (q31_t)b0 * d0; + imag_sum += (q31_t)b0 * c0; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += (q31_t)a0 * c0; + imag_sum += (q31_t)a0 * d0; + real_sum -= (q31_t)b0 * d0; + imag_sum += (q31_t)b0 * c0; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Store real and imaginary result in 8.24 format */ + /* Convert real data in 34.30 to 8.24 by 6 right shifts */ + *realResult = (q31_t) (real_sum >> 6); + /* Convert imaginary data in 34.30 to 8.24 by 6 right shifts */ + *imagResult = (q31_t) (imag_sum >> 6); +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_dot_prod group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c new file mode 100755 index 0000000..752db99 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q31.c @@ -0,0 +1,261 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_dot_prod_q31.c + * Description: Q31 complex dot product + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_dot_prod + @{ + */ + +/** + @brief Q31 complex dot product. + @param[in] pSrcA points to the first input vector + @param[in] pSrcB points to the second input vector + @param[in] numSamples number of samples in each vector + @param[out] realResult real part of the result returned here + @param[out] imagResult imaginary part of the result returned here + + @par Scaling and Overflow Behavior + The function is implemented using an internal 64-bit accumulator. + The intermediate 1.31 by 1.31 multiplications are performed with 64-bit precision and then shifted to 16.48 format. + The internal real and imaginary accumulators are in 16.48 format and provide 15 guard bits. + Additions are nonsaturating and no overflow will occur as long as numSamples is less than 32768. + The return results realResult and imagResult are in 16.48 format. + Input down scaling is not required. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t numSamples, + q63_t * realResult, + q63_t * imagResult) +{ + int32_t blkCnt; + q63_t accReal = 0LL; + q63_t accImag = 0LL; + q31x4_t vecSrcA, vecSrcB; + q31x4_t vecSrcC, vecSrcD; + + blkCnt = numSamples >> 2; + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 4; + pSrcB += 4; + + while (blkCnt > 0) { + + accReal = vrmlsldavhaq(accReal, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 4; + + accImag = vrmlaldavhaxq(accImag, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 4; + + accReal = vrmlsldavhaq(accReal, vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 4; + + accImag = vrmlaldavhaxq(accImag, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 4; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + accReal = vrmlsldavhaq(accReal, vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + accImag = vrmlaldavhaxq(accImag, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + + accReal = vrmlsldavhaq(accReal, vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + + accImag = vrmlaldavhaxq(accImag, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 3); + do { + mve_pred16_t p = vctp32q(blkCnt); + + pSrcA += 4; + pSrcB += 4; + + vecSrcA = vldrwq_z_s32(pSrcA, p); + vecSrcB = vldrwq_z_s32(pSrcB, p); + + accReal = vrmlsldavhaq_p(accReal, vecSrcA, vecSrcB, p); + accImag = vrmlaldavhaxq_p(accImag, vecSrcA, vecSrcB, p); + + blkCnt -= 4; + } + while ((int32_t) blkCnt > 0); + } else { + blkCnt = numSamples * CMPLX_DIM; + while (blkCnt > 0) { + mve_pred16_t p = vctp32q(blkCnt); + + vecSrcA = vldrwq_z_s32(pSrcA, p); + vecSrcB = vldrwq_z_s32(pSrcB, p); + + accReal = vrmlsldavhaq_p(accReal, vecSrcA, vecSrcB, p); + accImag = vrmlaldavhaxq_p(accImag, vecSrcA, vecSrcB, p); + + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrcA += 4; + pSrcB += 4; + blkCnt -= 4; + } + } + *realResult = asrl(accReal, (14 - 8)); + *imagResult = asrl(accImag, (14 - 8)); + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_dot_prod_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + uint32_t numSamples, + q63_t * realResult, + q63_t * imagResult) +{ + uint32_t blkCnt; /* Loop counter */ + q63_t real_sum = 0, imag_sum = 0; /* Temporary result variables */ + q31_t a0,b0,c0,d0; + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += ((q63_t)a0 * c0) >> 14; + imag_sum += ((q63_t)a0 * d0) >> 14; + real_sum -= ((q63_t)b0 * d0) >> 14; + imag_sum += ((q63_t)b0 * c0) >> 14; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += ((q63_t)a0 * c0) >> 14; + imag_sum += ((q63_t)a0 * d0) >> 14; + real_sum -= ((q63_t)b0 * d0) >> 14; + imag_sum += ((q63_t)b0 * c0) >> 14; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += ((q63_t)a0 * c0) >> 14; + imag_sum += ((q63_t)a0 * d0) >> 14; + real_sum -= ((q63_t)b0 * d0) >> 14; + imag_sum += ((q63_t)b0 * c0) >> 14; + + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += ((q63_t)a0 * c0) >> 14; + imag_sum += ((q63_t)a0 * d0) >> 14; + real_sum -= ((q63_t)b0 * d0) >> 14; + imag_sum += ((q63_t)b0 * c0) >> 14; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + a0 = *pSrcA++; + b0 = *pSrcA++; + c0 = *pSrcB++; + d0 = *pSrcB++; + + real_sum += ((q63_t)a0 * c0) >> 14; + imag_sum += ((q63_t)a0 * d0) >> 14; + real_sum -= ((q63_t)b0 * d0) >> 14; + imag_sum += ((q63_t)b0 * c0) >> 14; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Store real and imaginary result in 16.48 format */ + *realResult = real_sum; + *imagResult = imag_sum; +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_dot_prod group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f16.c new file mode 100755 index 0000000..707bbc4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f16.c @@ -0,0 +1,221 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_f16.c + * Description: Floating-point complex magnitude + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) +/** + @ingroup groupCmplxMath + */ + + + +/** + @addtogroup cmplx_mag + @{ + */ + +/** + @brief Floating-point complex magnitude. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" + + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + f16x8x2_t vecSrc; + f16x8_t sum; + + /* Compute 4 complex samples at a time */ + blkCnt = blockSize >> 3; + while (blkCnt > 0U) + { + q15x8_t newtonStartVec; + f16x8_t sumHalf, invSqrt; + + vecSrc = vld2q(pSrc); + pSrc += 16; + sum = vmulq(vecSrc.val[0], vecSrc.val[0]); + sum = vfmaq(sum, vecSrc.val[1], vecSrc.val[1]); + + /* + * inlined Fast SQRT using inverse SQRT newton-raphson method + */ + + /* compute initial value */ + newtonStartVec = vdupq_n_s16(INVSQRT_MAGIC_F16) - vshrq((q15x8_t) sum, 1); + sumHalf = sum * 0.5f; + /* + * compute 3 x iterations + * + * The more iterations, the more accuracy. + * If you need to trade a bit of accuracy for more performance, + * you can comment out the 3rd use of the macro. + */ + INVSQRT_NEWTON_MVE_F16(invSqrt, sumHalf, (f16x8_t) newtonStartVec); + INVSQRT_NEWTON_MVE_F16(invSqrt, sumHalf, invSqrt); + INVSQRT_NEWTON_MVE_F16(invSqrt, sumHalf, invSqrt); + /* + * set negative values to 0 + */ + invSqrt = vdupq_m(invSqrt, (float16_t)0.0f, vcmpltq(invSqrt, (float16_t)0.0f)); + /* + * sqrt(x) = x * invSqrt(x) + */ + sum = vmulq(sum, invSqrt); + vstrhq_f16(pDst, sum); + pDst += 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + /* + * tail + */ + blkCnt = blockSize & 7; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp16q(blkCnt); + q15x8_t newtonStartVec; + f16x8_t sumHalf, invSqrt; + + vecSrc = vld2q((float16_t const *)pSrc); + sum = vmulq(vecSrc.val[0], vecSrc.val[0]); + sum = vfmaq(sum, vecSrc.val[1], vecSrc.val[1]); + + /* + * inlined Fast SQRT using inverse SQRT newton-raphson method + */ + + /* compute initial value */ + newtonStartVec = vdupq_n_s16(INVSQRT_MAGIC_F16) - vshrq((q15x8_t) sum, 1); + sumHalf = vmulq(sum, (float16_t)0.5); + /* + * compute 2 x iterations + */ + INVSQRT_NEWTON_MVE_F16(invSqrt, sumHalf, (f16x8_t) newtonStartVec); + INVSQRT_NEWTON_MVE_F16(invSqrt, sumHalf, invSqrt); + /* + * set negative values to 0 + */ + invSqrt = vdupq_m(invSqrt, (float16_t)0.0, vcmpltq(invSqrt, (float16_t)0.0)); + /* + * sqrt(x) = x * invSqrt(x) + */ + sum = vmulq(sum, invSqrt); + vstrhq_p_f16(pDst, sum, p0); + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* loop counter */ + _Float16 real, imag; /* Temporary variables to hold input values */ + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + arm_sqrt_f16((real * real) + (imag * imag), pDst++); + + real = *pSrc++; + imag = *pSrc++; + arm_sqrt_f16((real * real) + (imag * imag), pDst++); + + real = *pSrc++; + imag = *pSrc++; + arm_sqrt_f16((real * real) + (imag * imag), pDst++); + + real = *pSrc++; + imag = *pSrc++; + arm_sqrt_f16((real * real) + (imag * imag), pDst++); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + arm_sqrt_f16((real * real) + (imag * imag), pDst++); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_mag group + */ + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c new file mode 100755 index 0000000..9f06bb2 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c @@ -0,0 +1,275 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_f32.c + * Description: Floating-point complex magnitude + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @defgroup cmplx_mag Complex Magnitude + + Computes the magnitude of the elements of a complex data vector. + + The pSrc points to the source data and + pDst points to the where the result should be written. + numSamples specifies the number of complex samples + in the input array and the data is stored in an interleaved fashion + (real, imag, real, imag, ...). + The input array has a total of 2*numSamples values; + the output array has a total of numSamples values. + + The underlying algorithm is used: + + 
+  for (n = 0; n < numSamples; n++) {
+      pDst[n] = sqrt(pSrc[(2*n)+0]^2 + pSrc[(2*n)+1]^2);
+  }
+
+ + There are separate functions for floating-point, Q15, and Q31 data types. + */ + +/** + @addtogroup cmplx_mag + @{ + */ + +/** + @brief Floating-point complex magnitude. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_NEON) +#include "arm_vec_math.h" +#endif + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" + + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + f32x4x2_t vecSrc; + f32x4_t sum; + float32_t real, imag; /* Temporary variables to hold input values */ + + /* Compute 4 complex samples at a time */ + blkCnt = blockSize >> 2; + while (blkCnt > 0U) + { + q31x4_t newtonStartVec; + f32x4_t sumHalf, invSqrt; + + vecSrc = vld2q(pSrc); + pSrc += 8; + sum = vmulq(vecSrc.val[0], vecSrc.val[0]); + sum = vfmaq(sum, vecSrc.val[1], vecSrc.val[1]); + + /* + * inlined Fast SQRT using inverse SQRT newton-raphson method + */ + + /* compute initial value */ + newtonStartVec = vdupq_n_s32(INVSQRT_MAGIC_F32) - vshrq((q31x4_t) sum, 1); + sumHalf = sum * 0.5f; + /* + * compute 3 x iterations + * + * The more iterations, the more accuracy. + * If you need to trade a bit of accuracy for more performance, + * you can comment out the 3rd use of the macro. + */ + INVSQRT_NEWTON_MVE_F32(invSqrt, sumHalf, (f32x4_t) newtonStartVec); + INVSQRT_NEWTON_MVE_F32(invSqrt, sumHalf, invSqrt); + INVSQRT_NEWTON_MVE_F32(invSqrt, sumHalf, invSqrt); + /* + * set negative values to 0 + */ + invSqrt = vdupq_m(invSqrt, 0.0f, vcmpltq(invSqrt, 0.0f)); + /* + * sqrt(x) = x * invSqrt(x) + */ + sum = vmulq(sum, invSqrt); + vst1q(pDst, sum); + pDst += 4; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + /* + * tail + */ + blkCnt = blockSize & 3; + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + arm_sqrt_f32((real * real) + (imag * imag), pDst++); + + /* Decrement loop counter */ + blkCnt--; + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* loop counter */ + float32_t real, imag; /* Temporary variables to hold input values */ + +#if defined(ARM_MATH_NEON) + + float32x4x2_t vecA; + float32x4_t vRealA; + float32x4_t vImagA; + float32x4_t vMagSqA; + + float32x4x2_t vecB; + float32x4_t vRealB; + float32x4_t vImagB; + float32x4_t vMagSqB; + + /* Loop unrolling: Compute 8 outputs at a time */ + blkCnt = numSamples >> 3; + + while (blkCnt > 0U) + { + /* out = sqrt((real * real) + (imag * imag)) */ + + vecA = vld2q_f32(pSrc); + pSrc += 8; + + vecB = vld2q_f32(pSrc); + pSrc += 8; + + vRealA = vmulq_f32(vecA.val[0], vecA.val[0]); + vImagA = vmulq_f32(vecA.val[1], vecA.val[1]); + vMagSqA = vaddq_f32(vRealA, vImagA); + + vRealB = vmulq_f32(vecB.val[0], vecB.val[0]); + vImagB = vmulq_f32(vecB.val[1], vecB.val[1]); + vMagSqB = vaddq_f32(vRealB, vImagB); + + /* Store the result in the destination buffer. */ + vst1q_f32(pDst, __arm_vec_sqrt_f32_neon(vMagSqA)); + pDst += 4; + + vst1q_f32(pDst, __arm_vec_sqrt_f32_neon(vMagSqB)); + pDst += 4; + + /* Decrement the loop counter */ + blkCnt--; + } + + blkCnt = numSamples & 7; + +#else + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + arm_sqrt_f32((real * real) + (imag * imag), pDst++); + + real = *pSrc++; + imag = *pSrc++; + arm_sqrt_f32((real * real) + (imag * imag), pDst++); + + real = *pSrc++; + imag = *pSrc++; + arm_sqrt_f32((real * real) + (imag * imag), pDst++); + + real = *pSrc++; + imag = *pSrc++; + arm_sqrt_f32((real * real) + (imag * imag), pDst++); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +#endif /* #if defined(ARM_MATH_NEON) */ + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + arm_sqrt_f32((real * real) + (imag * imag), pDst++); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_mag group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f64.c new file mode 100755 index 0000000..7ab265e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_f64.c @@ -0,0 +1,80 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_f64.c + * Description: Floating-point complex magnitude + * + * $Date: 13 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + + + +/** + @addtogroup cmplx_mag + @{ + */ + +/** + @brief Floating-point complex magnitude. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* loop counter */ + float64_t real, imag; /* Temporary variables to hold input values */ + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + *pDst++ = sqrt((real * real) + (imag * imag)); + + /* Decrement loop counter */ + blkCnt--; + } + +} + +/** + @} end of cmplx_mag group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_fast_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_fast_q15.c new file mode 100755 index 0000000..326521e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_fast_q15.c @@ -0,0 +1,225 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_fast_q15.c + * Description: Q15 complex magnitude + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_mag + @{ + */ + +/** + @brief Q15 complex magnitude. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.15 by 1.15 multiplications and finally output is converted into 2.14 format. + Fast functions are less accurate. This function will tend to clamp to 0 + the too small values. So sqrt(x*x) = x will not always be true. + */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_fast_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + q15x8x2_t vecSrc; + q15x8_t sum; + q31_t in; + q31_t acc0; + + blkCnt = blockSize >> 3; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + pSrc += 16; + sum = vqaddq(vmulhq(vecSrc.val[0], vecSrc.val[0]), + vmulhq(vecSrc.val[1], vecSrc.val[1])); + + sum = vshrq(sum, 1); + + sum = FAST_VSQRT_Q15(sum); + + vst1q(pDst, sum); + pDst += 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* + * tail + */ + blkCnt = blockSize & 7; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + in = read_q15x2_ia ((q15_t **) &pSrc); + acc0 = __SMUAD(in, in); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++); + + + /* Decrement loop counter */ + blkCnt--; + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_fast_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + +#if defined (ARM_MATH_DSP) + q31_t in; + q31_t acc0; /* Accumulators */ +#else + q15_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ +#endif + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + +#if defined (ARM_MATH_DSP) + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++); + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++); + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++); + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++); +#else + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++); + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++); + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++); + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++); +#endif /* #if defined (ARM_MATH_DSP) */ + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + +#if defined (ARM_MATH_DSP) + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q15((q15_t) (acc0 >> 17), pDst++); +#else + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++); +#endif + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_mag group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c new file mode 100755 index 0000000..e130ecb --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c @@ -0,0 +1,269 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_q15.c + * Description: Q15 complex magnitude + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_mag + @{ + */ + +/** + @brief Q15 complex magnitude. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.15 by 1.15 multiplications and finally output is converted into 2.14 format. + */ + +/* Sqrt q31 is used otherwise accuracy is not good enough + for small values and for some applications it is + an issue. + */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + q15x8x2_t vecSrc; + q31x4_t prod0; + q31x4_t prod1; + + q31_t in; + q31_t acc0; + q31x4_t acc0V; + q31x4_t acc1V; + + q31_t res; + q15x8_t resV; + + blkCnt = blockSize >> 3; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + pSrc += 16; + + acc0V = vdupq_n_s32(0); + acc1V = vdupq_n_s32(0); + + prod0 = vmullbq_int_s16(vecSrc.val[0], vecSrc.val[0]); + acc0V = vqaddq_s32(acc0V,prod0); + + prod0 = vmullbq_int_s16(vecSrc.val[1], vecSrc.val[1]); + acc0V = vqaddq_s32(acc0V,prod0); + + + prod1 = vmulltq_int_s16(vecSrc.val[0], vecSrc.val[0]); + acc1V = vqaddq_s32(acc1V,prod1); + + prod1 = vmulltq_int_s16(vecSrc.val[1], vecSrc.val[1]); + acc1V = vqaddq_s32(acc1V,prod1); + + + + acc0V = vshrq(acc0V, 1); + acc1V = vshrq(acc1V, 1); + + acc0V = FAST_VSQRT_Q31(acc0V); + acc1V = FAST_VSQRT_Q31(acc1V); + + resV = vdupq_n_s16(0); + resV = vqshrnbq_n_s32(resV,acc0V,16); + resV = vqshrntq_n_s32(resV,acc1V,16); + + vst1q(pDst, resV); + pDst += 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* + * tail + */ + blkCnt = blockSize & 7; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + in = read_q15x2_ia ((q15_t **) &pSrc); + acc0 = __SMUAD(in, in); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q31((uint32_t)acc0 >> 1 , &res); + *pDst++ = res >> 16; + + + /* Decrement loop counter */ + blkCnt--; + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + q31_t res; /* temporary result */ + uint32_t blkCnt; /* Loop counter */ + +#if defined (ARM_MATH_DSP) + q31_t in; + q31_t acc0; /* Accumulators */ +#else + q15_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ +#endif + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + +#if defined (ARM_MATH_DSP) + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q31((uint32_t)acc0 >> 1 , &res); + *pDst++ = res >> 16; + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + arm_sqrt_q31((uint32_t)acc0 >> 1 , &res); + *pDst++ = res >> 16; + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + arm_sqrt_q31((uint32_t)acc0 >> 1 , &res); + *pDst++ = res >> 16; + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + arm_sqrt_q31((uint32_t)acc0 >> 1 , &res); + *pDst++ = res >> 16; +#else + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q31(((uint32_t)acc0 + (uint32_t)acc1) >> 1 , &res); + *pDst++ = res >> 16; + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + arm_sqrt_q31(((uint32_t)acc0 + (uint32_t)acc1) >> 1 , &res); + *pDst++ = res >> 16; + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + arm_sqrt_q31(((uint32_t)acc0 + (uint32_t)acc1) >> 1 , &res); + *pDst++ = res >> 16; + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + arm_sqrt_q31(((uint32_t)acc0 + (uint32_t)acc1) >> 1 , &res); + *pDst++ = res >> 16; +#endif /* #if defined (ARM_MATH_DSP) */ + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + +#if defined (ARM_MATH_DSP) + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q31((uint32_t)acc0 >> 1 , &res); + *pDst++ = res >> 16; +#else + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + + /* store result in 2.14 format in destination buffer. */ + arm_sqrt_q31(((uint32_t)acc0 + (uint32_t)acc1) >> 1 , &res); + *pDst++ = res >> 16; + +#endif + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_mag group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c new file mode 100755 index 0000000..db28961 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_q31.c @@ -0,0 +1,203 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_q31.c + * Description: Q31 complex magnitude + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_mag + @{ + */ + +/** + @brief Q31 complex magnitude. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.31 by 1.31 multiplications and finally output is converted into 2.30 format. + Input down scaling is not required. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + + q31x4x2_t vecSrc; + q31x4_t sum; + + q31_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ + + /* Compute 4 complex samples at a time */ + blkCnt = blockSize >> 2; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + + sum = vqaddq(vmulhq(vecSrc.val[0], vecSrc.val[0]), + vmulhq(vecSrc.val[1], vecSrc.val[1])); + + sum = vshrq(sum, 1); + + /* + + This function is using a table. There are compilations flags to avoid + including this table (and in this case, arm_cmplx_maq_q31 must not + be built and linked.) + + */ + sum = FAST_VSQRT_Q31(sum); + + vst1q(pDst, sum); + + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + pSrc += 8; + pDst += 4; + } + + /* + * tail + */ + blkCnt = blockSize & 3; + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + + /* store result in 2.30 format in destination buffer. */ + arm_sqrt_q31(acc0 + acc1, pDst++); + + /* Decrement loop counter */ + blkCnt--; + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q31_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + + /* store result in 2.30 format in destination buffer. */ + arm_sqrt_q31(acc0 + acc1, pDst++); + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + arm_sqrt_q31(acc0 + acc1, pDst++); + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + arm_sqrt_q31(acc0 + acc1, pDst++); + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + arm_sqrt_q31(acc0 + acc1, pDst++); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + + /* store result in 2.30 format in destination buffer. */ + arm_sqrt_q31(acc0 + acc1, pDst++); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_mag group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f16.c new file mode 100755 index 0000000..6e6848c --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f16.c @@ -0,0 +1,153 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_squared_f16.c + * Description: Floating-point complex magnitude squared + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + @ingroup groupCmplxMath + */ + + +/** + @addtogroup cmplx_mag_squared + @{ + */ + +/** + @brief Floating-point complex magnitude squared. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + f16x8x2_t vecSrc; + f16x8_t sum; + + /* Compute 4 complex samples at a time */ + while (blockSize > 0) + { + mve_pred16_t p = vctp16q(blockSize); + vecSrc = vld2q(pSrc); + sum = vmulq_m(vuninitializedq_f16(),vecSrc.val[0], vecSrc.val[0],p); + sum = vfmaq_m(sum, vecSrc.val[1], vecSrc.val[1],p); + vstrhq_p_f16(pDst, sum,p); + + pSrc += 16; + pDst += 8; + + /* + * Decrement the blockSize loop counter + */ + blockSize-= 8; + } + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + _Float16 real, imag; /* Temporary input variables */ + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + *pDst++ = (real * real) + (imag * imag); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_mag_squared group + */ + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c new file mode 100755 index 0000000..d87ed95 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c @@ -0,0 +1,237 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_squared_f32.c + * Description: Floating-point complex magnitude squared + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @defgroup cmplx_mag_squared Complex Magnitude Squared + + Computes the magnitude squared of the elements of a complex data vector. + + The pSrc points to the source data and + pDst points to the where the result should be written. + numSamples specifies the number of complex samples + in the input array and the data is stored in an interleaved fashion + (real, imag, real, imag, ...). + The input array has a total of 2*numSamples values; + the output array has a total of numSamples values. + + The underlying algorithm is used: + + 
+  for (n = 0; n < numSamples; n++) {
+      pDst[n] = pSrc[(2*n)+0]^2 + pSrc[(2*n)+1]^2;
+  }
+
+ + There are separate functions for floating-point, Q15, and Q31 data types. + */ + +/** + @addtogroup cmplx_mag_squared + @{ + */ + +/** + @brief Floating-point complex magnitude squared. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + f32x4x2_t vecSrc; + f32x4_t sum; + float32_t real, imag; /* Temporary input variables */ + + /* Compute 4 complex samples at a time */ + blkCnt = blockSize >> 2; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + sum = vmulq(vecSrc.val[0], vecSrc.val[0]); + sum = vfmaq(sum, vecSrc.val[1], vecSrc.val[1]); + vst1q(pDst, sum); + + pSrc += 8; + pDst += 4; + + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* Tail */ + blkCnt = blockSize & 3; + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + *pDst++ = (real * real) + (imag * imag); + + /* Decrement loop counter */ + blkCnt--; + } + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + float32_t real, imag; /* Temporary input variables */ + +#if defined(ARM_MATH_NEON) + float32x4x2_t vecA; + float32x4_t vRealA; + float32x4_t vImagA; + float32x4_t vMagSqA; + + float32x4x2_t vecB; + float32x4_t vRealB; + float32x4_t vImagB; + float32x4_t vMagSqB; + + /* Loop unrolling: Compute 8 outputs at a time */ + blkCnt = numSamples >> 3; + + while (blkCnt > 0U) + { + /* out = sqrt((real * real) + (imag * imag)) */ + + vecA = vld2q_f32(pSrc); + pSrc += 8; + + vRealA = vmulq_f32(vecA.val[0], vecA.val[0]); + vImagA = vmulq_f32(vecA.val[1], vecA.val[1]); + vMagSqA = vaddq_f32(vRealA, vImagA); + + vecB = vld2q_f32(pSrc); + pSrc += 8; + + vRealB = vmulq_f32(vecB.val[0], vecB.val[0]); + vImagB = vmulq_f32(vecB.val[1], vecB.val[1]); + vMagSqB = vaddq_f32(vRealB, vImagB); + + /* Store the result in the destination buffer. */ + vst1q_f32(pDst, vMagSqA); + pDst += 4; + + vst1q_f32(pDst, vMagSqB); + pDst += 4; + + /* Decrement the loop counter */ + blkCnt--; + } + + blkCnt = numSamples & 7; + +#else +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + real = *pSrc++; + imag = *pSrc++; + *pDst++ = (real * real) + (imag * imag); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +#endif /* #if defined(ARM_MATH_NEON) */ + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + *pDst++ = (real * real) + (imag * imag); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of cmplx_mag_squared group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f64.c new file mode 100755 index 0000000..314f855 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f64.c @@ -0,0 +1,78 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_squared_f64.c + * Description: Floating-point complex magnitude squared + * + * $Date: 13 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_mag_squared + @{ + */ + +/** + @brief Floating-point complex magnitude squared. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + float64_t real, imag; /* Temporary input variables */ + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + + /* store result in destination buffer. */ + *pDst++ = (real * real) + (imag * imag); + + /* Decrement loop counter */ + blkCnt--; + } + +} + +/** + @} end of cmplx_mag_squared group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c new file mode 100755 index 0000000..4c63f06 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c @@ -0,0 +1,223 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_squared_q15.c + * Description: Q15 complex magnitude squared + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_mag_squared + @{ + */ + +/** + @brief Q15 complex magnitude squared. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + q31_t in; + q31_t acc0; /* Accumulators */ + q15x8x2_t vecSrc; + q15x8_t vReal, vImag; + q15x8_t vMagSq; + + + blkCnt = blockSize >> 3; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + vReal = vmulhq(vecSrc.val[0], vecSrc.val[0]); + vImag = vmulhq(vecSrc.val[1], vecSrc.val[1]); + vMagSq = vqaddq(vReal, vImag); + vMagSq = vshrq(vMagSq, 1); + + vst1q(pDst, vMagSq); + + pSrc += 16; + pDst += 8; + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + blkCnt --; + } + + /* + * tail + */ + blkCnt = blockSize & 7; + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + in = read_q15x2_ia ((q15_t **) &pSrc); + acc0 = __SMUAD(in, in); + + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) (acc0 >> 17); + + + /* Decrement loop counter */ + blkCnt--; + } + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + +#if defined (ARM_MATH_DSP) + q31_t in; + q31_t acc0; /* Accumulators */ +#else + q15_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ +#endif + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + +#if defined (ARM_MATH_DSP) + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) (acc0 >> 17); + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + *pDst++ = (q15_t) (acc0 >> 17); + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + *pDst++ = (q15_t) (acc0 >> 17); + + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + *pDst++ = (q15_t) (acc0 >> 17); +#else + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17); + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17); + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17); + + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17); +#endif /* #if defined (ARM_MATH_DSP) */ + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + +#if defined (ARM_MATH_DSP) + in = read_q15x2_ia (&pSrc); + acc0 = __SMUAD(in, in); + + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) (acc0 >> 17); +#else + real = *pSrc++; + imag = *pSrc++; + acc0 = ((q31_t) real * real); + acc1 = ((q31_t) imag * imag); + + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17); +#endif + + /* Decrement loop counter */ + blkCnt--; + } + +} + +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_mag_squared group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c new file mode 100755 index 0000000..506efad --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c @@ -0,0 +1,189 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mag_squared_q31.c + * Description: Q31 complex magnitude squared + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup cmplx_mag_squared + @{ + */ + +/** + @brief Q31 complex magnitude squared. + @param[in] pSrc points to input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format. + Input down scaling is not required. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples) +{ + int32_t blockSize = numSamples; /* loop counters */ + uint32_t blkCnt; /* loop counters */ + q31x4x2_t vecSrc; + q31x4_t vReal, vImag; + q31x4_t vMagSq; + q31_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ + + /* Compute 4 complex samples at a time */ + blkCnt = blockSize >> 2; + while (blkCnt > 0U) + { + vecSrc = vld2q(pSrc); + vReal = vmulhq(vecSrc.val[0], vecSrc.val[0]); + vImag = vmulhq(vecSrc.val[1], vecSrc.val[1]); + vMagSq = vqaddq(vReal, vImag); + vMagSq = vshrq(vMagSq, 1); + + vst1q(pDst, vMagSq); + + pSrc += 8; + pDst += 4; + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + blkCnt --; + } + + /* Tail */ + blkCnt = blockSize & 3; + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + + /* store result in 3.29 format in destination buffer. */ + *pDst++ = acc0 + acc1; + + /* Decrement loop counter */ + blkCnt--; + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mag_squared_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q31_t real, imag; /* Temporary input variables */ + q31_t acc0, acc1; /* Accumulators */ + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + /* store the result in 3.29 format in the destination buffer. */ + *pDst++ = acc0 + acc1; + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + *pDst++ = acc0 + acc1; + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + *pDst++ = acc0 + acc1; + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + *pDst++ = acc0 + acc1; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[0] = (A[0] * A[0] + A[1] * A[1]) */ + + real = *pSrc++; + imag = *pSrc++; + acc0 = (q31_t) (((q63_t) real * real) >> 33); + acc1 = (q31_t) (((q63_t) imag * imag) >> 33); + + /* store result in 3.29 format in destination buffer. */ + *pDst++ = acc0 + acc1; + + /* Decrement loop counter */ + blkCnt--; + } + +} + +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of cmplx_mag_squared group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f16.c new file mode 100755 index 0000000..bcf7c38 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f16.c @@ -0,0 +1,253 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_cmplx_f16.c + * Description: Floating-point complex-by-complex multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + @ingroup groupCmplxMath + */ + + + +/** + @addtogroup CmplxByCmplxMult + @{ + */ + +/** + @brief Floating-point complex-by-complex multiplication. + @param[in] pSrcA points to first input vector + @param[in] pSrcB points to second input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + float16_t * pDst, + uint32_t numSamples) +{ + int32_t blkCnt; + f16x8_t vecSrcA, vecSrcB; + f16x8_t vecSrcC, vecSrcD; + f16x8_t vec_acc; + + blkCnt = (numSamples >> 3); + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 8; + pSrcB += 8; + + while (blkCnt > 0) { + vec_acc = vcmulq(vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 8; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 8; + vst1q(pDst, vec_acc); + pDst += 8; + + vec_acc = vcmulq(vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 8; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 8; + vst1q(pDst, vec_acc); + pDst += 8; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + vec_acc = vcmulq(vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + vst1q(pDst, vec_acc); + pDst += 8; + + vec_acc = vcmulq(vecSrcC, vecSrcD); + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + vst1q(pDst, vec_acc); + pDst += 8; + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 7); + while (blkCnt > 0) { + mve_pred16_t p = vctp16q(blkCnt); + pSrcA += 8; + pSrcB += 8; + + vecSrcA = vldrhq_z_f16(pSrcA, p); + vecSrcB = vldrhq_z_f16(pSrcB, p); + vec_acc = vcmulq_m(vuninitializedq_f16(),vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + + vstrhq_p_f16(pDst, vec_acc, p); + pDst += 8; + + blkCnt -= 8; + } + } else { + /* small vector */ + blkCnt = numSamples * CMPLX_DIM; + + do { + mve_pred16_t p = vctp16q(blkCnt); + + vecSrcA = vldrhq_z_f16(pSrcA, p); + vecSrcB = vldrhq_z_f16(pSrcB, p); + + vec_acc = vcmulq_m(vuninitializedq_f16(),vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + vstrhq_p_f16(pDst, vec_acc, p); + pDst += 8; + + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrcA += 8; + pSrcB += 8; + blkCnt -= 8; + } + while (blkCnt > 0); + } + +} + + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_f16( + const float16_t * pSrcA, + const float16_t * pSrcB, + float16_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + _Float16 a, b, c, d; /* Temporary variables to store real and imaginary values */ + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + /* store result in destination buffer. */ + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + + /* store result in destination buffer. */ + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of CmplxByCmplxMult group + */ + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c new file mode 100755 index 0000000..b9bb925 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c @@ -0,0 +1,307 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_cmplx_f32.c + * Description: Floating-point complex-by-complex multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @defgroup CmplxByCmplxMult Complex-by-Complex Multiplication + + Multiplies a complex vector by another complex vector and generates a complex result. + The data in the complex arrays is stored in an interleaved fashion + (real, imag, real, imag, ...). + The parameter numSamples represents the number of complex + samples processed. The complex arrays have a total of 2*numSamples + real values. + + The underlying algorithm is used: + + 
+  for (n = 0; n < numSamples; n++) {
+      pDst[(2*n)+0] = pSrcA[(2*n)+0] * pSrcB[(2*n)+0] - pSrcA[(2*n)+1] * pSrcB[(2*n)+1];
+      pDst[(2*n)+1] = pSrcA[(2*n)+0] * pSrcB[(2*n)+1] + pSrcA[(2*n)+1] * pSrcB[(2*n)+0];
+  }
+
+ + There are separate functions for floating-point, Q15, and Q31 data types. + */ + +/** + @addtogroup CmplxByCmplxMult + @{ + */ + +/** + @brief Floating-point complex-by-complex multiplication. + @param[in] pSrcA points to first input vector + @param[in] pSrcB points to second input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t numSamples) +{ + int32_t blkCnt; + f32x4_t vecSrcA, vecSrcB; + f32x4_t vecSrcC, vecSrcD; + f32x4_t vec_acc; + + blkCnt = numSamples >> 2; + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 4; + pSrcB += 4; + + while (blkCnt > 0) { + vec_acc = vcmulq(vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 4; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 4; + vst1q(pDst, vec_acc); + pDst += 4; + + vec_acc = vcmulq(vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 4; + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 4; + vst1q(pDst, vec_acc); + pDst += 4; + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + vec_acc = vcmulq(vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + vec_acc = vcmlaq_rot90(vec_acc, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + vst1q(pDst, vec_acc); + pDst += 4; + + vec_acc = vcmulq(vecSrcC, vecSrcD); + vec_acc = vcmlaq_rot90(vec_acc, vecSrcC, vecSrcD); + vst1q(pDst, vec_acc); + pDst += 4; + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 3); + while (blkCnt > 0) { + mve_pred16_t p = vctp32q(blkCnt); + pSrcA += 4; + pSrcB += 4; + + vecSrcA = vldrwq_z_f32(pSrcA, p); + vecSrcB = vldrwq_z_f32(pSrcB, p); + vec_acc = vcmulq_m(vuninitializedq_f32(),vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + + vstrwq_p_f32(pDst, vec_acc, p); + pDst += 4; + + blkCnt -= 4; + } + } else { + /* small vector */ + blkCnt = numSamples * CMPLX_DIM; + vec_acc = vdupq_n_f32(0.0f); + + do { + mve_pred16_t p = vctp32q(blkCnt); + + vecSrcA = vldrwq_z_f32(pSrcA, p); + vecSrcB = vldrwq_z_f32(pSrcB, p); + + vec_acc = vcmulq_m(vuninitializedq_f32(),vecSrcA, vecSrcB, p); + vec_acc = vcmlaq_rot90_m(vec_acc, vecSrcA, vecSrcB, p); + vstrwq_p_f32(pDst, vec_acc, p); + pDst += 4; + + /* + * Decrement the blkCnt loop counter + * Advance vector source and destination pointers + */ + pSrcA += 4; + pSrcB += 4; + blkCnt -= 4; + } + while (blkCnt > 0); + } + +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_f32( + const float32_t * pSrcA, + const float32_t * pSrcB, + float32_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + float32_t a, b, c, d; /* Temporary variables to store real and imaginary values */ + +#if defined(ARM_MATH_NEON) + float32x4x2_t va, vb; + float32x4x2_t outCplx; + + /* Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + va = vld2q_f32(pSrcA); // load & separate real/imag pSrcA (de-interleave 2) + vb = vld2q_f32(pSrcB); // load & separate real/imag pSrcB + + /* Increment pointers */ + pSrcA += 8; + pSrcB += 8; + + /* Re{C} = Re{A}*Re{B} - Im{A}*Im{B} */ + outCplx.val[0] = vmulq_f32(va.val[0], vb.val[0]); + outCplx.val[0] = vmlsq_f32(outCplx.val[0], va.val[1], vb.val[1]); + + /* Im{C} = Re{A}*Im{B} + Im{A}*Re{B} */ + outCplx.val[1] = vmulq_f32(va.val[0], vb.val[1]); + outCplx.val[1] = vmlaq_f32(outCplx.val[1], va.val[1], vb.val[0]); + + vst2q_f32(pDst, outCplx); + + /* Increment pointer */ + pDst += 8; + + /* Decrement the loop counter */ + blkCnt--; + } + + /* Tail */ + blkCnt = numSamples & 3; + +#else +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + /* store result in destination buffer. */ + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +#endif /* #if defined(ARM_MATH_NEON) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + + /* store result in destination buffer. */ + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of CmplxByCmplxMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f64.c new file mode 100755 index 0000000..493df89 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_f64.c @@ -0,0 +1,85 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_cmplx_f64.c + * Description: Floating-point complex-by-complex multiplication + * + * $Date: 13 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup CmplxByCmplxMult + @{ + */ + +/** + @brief Floating-point complex-by-complex multiplication. + @param[in] pSrcA points to first input vector + @param[in] pSrcB points to second input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + */ + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_f64( + const float64_t * pSrcA, + const float64_t * pSrcB, + float64_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + float64_t a, b, c, d; /* Temporary variables to store real and imaginary values */ + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + + /* store result in destination buffer. */ + *pDst++ = (a * c) - (b * d); + *pDst++ = (a * d) + (b * c); + + /* Decrement loop counter */ + blkCnt--; + } + +} + +/** + @} end of CmplxByCmplxMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c new file mode 100755 index 0000000..21ac664 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c @@ -0,0 +1,260 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_cmplx_q15.c + * Description: Q15 complex-by-complex multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup CmplxByCmplxMult + @{ + */ + +/** + @brief Q15 complex-by-complex multiplication. + @param[in] pSrcA points to first input vector + @param[in] pSrcB points to second input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t numSamples) +{ + int32_t blkCnt; + q15x8_t vecSrcA, vecSrcB; + q15x8_t vecSrcC, vecSrcD; + q15x8_t vecDst; + + blkCnt = (numSamples >> 3); + blkCnt -= 1; + if (blkCnt > 0) + { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 8; + pSrcB += 8; + + while (blkCnt > 0) + { + + /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1]. */ + vecDst = vqdmlsdhq(vuninitializedq_s16(), vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 8; + + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i]. */ + vecDst = vqdmladhxq(vecDst, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 8; + + vstrhq_s16(pDst, vshrq(vecDst, 2)); + pDst += 8; + + vecDst = vqdmlsdhq(vuninitializedq_s16(), vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 8; + + vecDst = vqdmladhxq(vecDst, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 8; + + vstrhq_s16(pDst, vshrq(vecDst, 2)); + pDst += 8; + + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + vecDst = vqdmlsdhq(vuninitializedq_s16(), vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + vecDst = vqdmladhxq(vecDst, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + + vstrhq_s16(pDst, vshrq(vecDst, 2)); + pDst += 8; + + vecDst = vqdmlsdhq(vuninitializedq_s16(), vecSrcC, vecSrcD); + vecDst = vqdmladhxq(vecDst, vecSrcC, vecSrcD); + + vstrhq_s16(pDst, vshrq(vecDst, 2)); + pDst += 8; + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 7); + do + { + mve_pred16_t p = vctp16q(blkCnt); + + pSrcA += 8; + pSrcB += 8; + + vecSrcA = vldrhq_z_s16(pSrcA, p); + vecSrcB = vldrhq_z_s16(pSrcB, p); + + vecDst = vqdmlsdhq_m(vuninitializedq_s16(), vecSrcA, vecSrcB, p); + vecDst = vqdmladhxq_m(vecDst, vecSrcA, vecSrcB, p); + + vecDst = vshrq_m(vuninitializedq_s16(), vecDst, 2, p); + vstrhq_p_s16(pDst, vecDst, p); + pDst += 8; + + blkCnt -= 8; + } + while ((int32_t) blkCnt > 0); + } + else + { + blkCnt = numSamples * CMPLX_DIM; + while (blkCnt > 0) { + mve_pred16_t p = vctp16q(blkCnt); + + vecSrcA = vldrhq_z_s16(pSrcA, p); + vecSrcB = vldrhq_z_s16(pSrcB, p); + + vecDst = vqdmlsdhq_m(vuninitializedq_s16(), vecSrcA, vecSrcB, p); + vecDst = vqdmladhxq_m(vecDst, vecSrcA, vecSrcB, p); + + vecDst = vshrq_m(vuninitializedq_s16(), vecDst, 2, p); + vstrhq_p_s16(pDst, vecDst, p); + + pDst += 8; + pSrcA += 8; + pSrcB += 8; + + blkCnt -= 8; + } + } +} +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_q15( + const q15_t * pSrcA, + const q15_t * pSrcB, + q15_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q15_t a, b, c, d; /* Temporary variables */ + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) ( (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17) ); + *pDst++ = (q15_t) ( (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17) ); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (q15_t) ( (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17) ); + *pDst++ = (q15_t) ( (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17) ); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (q15_t) ( (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17) ); + *pDst++ = (q15_t) ( (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17) ); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (q15_t) ( (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17) ); + *pDst++ = (q15_t) ( (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17) ); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + + /* store result in 3.13 format in destination buffer. */ + *pDst++ = (q15_t) ( (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17) ); + *pDst++ = (q15_t) ( (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17) ); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of CmplxByCmplxMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c new file mode 100755 index 0000000..6a5c5d2 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c @@ -0,0 +1,255 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_cmplx_q31.c + * Description: Q31 complex-by-complex multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup CmplxByCmplxMult + @{ + */ + +/** + @brief Q31 complex-by-complex multiplication. + @param[in] pSrcA points to first input vector + @param[in] pSrcB points to second input vector + @param[out] pDst points to output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format. + Input down scaling is not required. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t numSamples) +{ + int32_t blkCnt; + q31x4_t vecSrcA, vecSrcB; + q31x4_t vecSrcC, vecSrcD; + q31x4_t vecDst; + + blkCnt = numSamples >> 2; + blkCnt -= 1; + if (blkCnt > 0) { + /* should give more freedom to generate stall free code */ + vecSrcA = vld1q(pSrcA); + vecSrcB = vld1q(pSrcB); + pSrcA += 4; + pSrcB += 4; + + while (blkCnt > 0) { + + /* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1]. */ + vecDst = vqdmlsdhq(vuninitializedq_s32(), vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + pSrcA += 4; + + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i]. */ + vecDst = vqdmladhxq(vecDst, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + pSrcB += 4; + + vst1q(pDst, vshrq(vecDst, 2)); + pDst += 4; + + vecDst = vqdmlsdhq(vuninitializedq_s32(), vecSrcC, vecSrcD); + vecSrcA = vld1q(pSrcA); + pSrcA += 4; + + vecDst = vqdmladhxq(vecDst, vecSrcC, vecSrcD); + vecSrcB = vld1q(pSrcB); + pSrcB += 4; + + vst1q(pDst, vshrq(vecDst, 2)); + pDst += 4; + + /* + * Decrement the blockSize loop counter + */ + blkCnt--; + } + + /* process last elements out of the loop avoid the armclang breaking the SW pipeline */ + vecDst = vqdmlsdhq(vuninitializedq_s32(), vecSrcA, vecSrcB); + vecSrcC = vld1q(pSrcA); + + vecDst = vqdmladhxq(vecDst, vecSrcA, vecSrcB); + vecSrcD = vld1q(pSrcB); + + vst1q(pDst, vshrq(vecDst, 2)); + pDst += 4; + + vecDst = vqdmlsdhq(vuninitializedq_s32(), vecSrcC, vecSrcD); + vecDst = vqdmladhxq(vecDst, vecSrcC, vecSrcD); + + vst1q(pDst, vshrq(vecDst, 2)); + pDst += 4; + + /* + * tail + */ + blkCnt = CMPLX_DIM * (numSamples & 3); + do { + mve_pred16_t p = vctp32q(blkCnt); + + pSrcA += 4; + pSrcB += 4; + + vecSrcA = vldrwq_z_s32(pSrcA, p); + vecSrcB = vldrwq_z_s32(pSrcB, p); + + vecDst = vqdmlsdhq_m(vuninitializedq_s32(), vecSrcA, vecSrcB, p); + vecDst = vqdmladhxq_m(vecDst, vecSrcA, vecSrcB, p); + + vecDst = vshrq_m(vuninitializedq_s32(), vecDst, 2, p); + vstrwq_p_s32(pDst, vecDst, p); + pDst += 4; + + blkCnt -= 4; + } + while ((int32_t) blkCnt > 0); + } else { + blkCnt = numSamples * CMPLX_DIM; + while (blkCnt > 0) { + mve_pred16_t p = vctp32q(blkCnt); + + vecSrcA = vldrwq_z_s32(pSrcA, p); + vecSrcB = vldrwq_z_s32(pSrcB, p); + + vecDst = vqdmlsdhq_m(vuninitializedq_s32(), vecSrcA, vecSrcB, p); + vecDst = vqdmladhxq_m(vecDst, vecSrcA, vecSrcB, p); + + vecDst = vshrq_m(vuninitializedq_s32(), vecDst, 2, p); + vstrwq_p_s32(pDst, vecDst, p); + + pDst += 4; + pSrcA += 4; + pSrcB += 4; + + blkCnt -= 4; + } + } +} +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_cmplx_q31( + const q31_t * pSrcA, + const q31_t * pSrcB, + q31_t * pDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q31_t a, b, c, d; /* Temporary variables */ + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + /* store result in 3.29 format in destination buffer. */ + *pDst++ = (q31_t) ( (((q63_t) a * c) >> 33) - (((q63_t) b * d) >> 33) ); + *pDst++ = (q31_t) ( (((q63_t) a * d) >> 33) + (((q63_t) b * c) >> 33) ); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (q31_t) ( (((q63_t) a * c) >> 33) - (((q63_t) b * d) >> 33) ); + *pDst++ = (q31_t) ( (((q63_t) a * d) >> 33) + (((q63_t) b * c) >> 33) ); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (q31_t) ( (((q63_t) a * c) >> 33) - (((q63_t) b * d) >> 33) ); + *pDst++ = (q31_t) ( (((q63_t) a * d) >> 33) + (((q63_t) b * c) >> 33) ); + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + *pDst++ = (q31_t) ( (((q63_t) a * c) >> 33) - (((q63_t) b * d) >> 33) ); + *pDst++ = (q31_t) ( (((q63_t) a * d) >> 33) + (((q63_t) b * c) >> 33) ); + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i] * B[2 * i ] - A[2 * i + 1] * B[2 * i + 1]. */ + /* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i ]. */ + + a = *pSrcA++; + b = *pSrcA++; + c = *pSrcB++; + d = *pSrcB++; + + /* store result in 3.29 format in destination buffer. */ + *pDst++ = (q31_t) ( (((q63_t) a * c) >> 33) - (((q63_t) b * d) >> 33) ); + *pDst++ = (q31_t) ( (((q63_t) a * d) >> 33) + (((q63_t) b * c) >> 33) ); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of CmplxByCmplxMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_f16.c new file mode 100755 index 0000000..8b0a495 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_f16.c @@ -0,0 +1,174 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_real_f16.c + * Description: Floating-point complex by real multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + @ingroup groupCmplxMath + */ + + +/** + @addtogroup CmplxByRealMult + @{ + */ + +/** + @brief Floating-point complex-by-real multiplication. + @param[in] pSrcCmplx points to complex input vector + @param[in] pSrcReal points to real input vector + @param[out] pCmplxDst points to complex output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_f16( + const float16_t * pSrcCmplx, + const float16_t * pSrcReal, + float16_t * pCmplxDst, + uint32_t numSamples) +{ + static const uint16_t stride_cmplx_x_real_16[8] = { + 0, 0, 1, 1, 2, 2, 3, 3 + }; + uint32_t blockSizeC = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + f16x8_t rVec; + f16x8_t cmplxVec; + f16x8_t dstVec; + uint16x8_t strideVec; + + + /* stride vector for pairs of real generation */ + strideVec = vld1q(stride_cmplx_x_real_16); + + /* Compute 4 complex outputs at a time */ + blkCnt = blockSizeC >> 3; + while (blkCnt > 0U) + { + cmplxVec = vld1q(pSrcCmplx); + rVec = vldrhq_gather_shifted_offset_f16(pSrcReal, strideVec); + dstVec = vmulq(cmplxVec, rVec); + vst1q(pCmplxDst, dstVec); + + pSrcReal += 4; + pSrcCmplx += 8; + pCmplxDst += 8; + blkCnt--; + } + + blkCnt = blockSizeC & 7; + if (blkCnt > 0U) { + mve_pred16_t p0 = vctp16q(blkCnt); + + cmplxVec = vld1q(pSrcCmplx); + rVec = vldrhq_gather_shifted_offset_f16(pSrcReal, strideVec); + dstVec = vmulq(cmplxVec, rVec); + vstrhq_p_f16(pCmplxDst, dstVec, p0); + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_f16( + const float16_t * pSrcCmplx, + const float16_t * pSrcReal, + float16_t * pCmplxDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + float16_t in; /* Temporary variable */ + +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store result in destination buffer. */ + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + + in = *pSrcReal++; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + + in = *pSrcReal++; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + + in = *pSrcReal++; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store result in destination buffer. */ + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + *pCmplxDst++ = (_Float16)*pSrcCmplx++ * (_Float16)in; + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of CmplxByRealMult group + */ + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c new file mode 100755 index 0000000..68f18c6 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c @@ -0,0 +1,226 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_real_f32.c + * Description: Floating-point complex by real multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @defgroup CmplxByRealMult Complex-by-Real Multiplication + + Multiplies a complex vector by a real vector and generates a complex result. + The data in the complex arrays is stored in an interleaved fashion + (real, imag, real, imag, ...). + The parameter numSamples represents the number of complex + samples processed. The complex arrays have a total of 2*numSamples + real values while the real array has a total of numSamples + real values. + + The underlying algorithm is used: + + 
+  for (n = 0; n < numSamples; n++) {
+      pCmplxDst[(2*n)+0] = pSrcCmplx[(2*n)+0] * pSrcReal[n];
+      pCmplxDst[(2*n)+1] = pSrcCmplx[(2*n)+1] * pSrcReal[n];
+  }
+
+ + There are separate functions for floating-point, Q15, and Q31 data types. + */ + +/** + @addtogroup CmplxByRealMult + @{ + */ + +/** + @brief Floating-point complex-by-real multiplication. + @param[in] pSrcCmplx points to complex input vector + @param[in] pSrcReal points to real input vector + @param[out] pCmplxDst points to complex output vector + @param[in] numSamples number of samples in each vector + */ + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_f32( + const float32_t * pSrcCmplx, + const float32_t * pSrcReal, + float32_t * pCmplxDst, + uint32_t numSamples) +{ + static const uint32_t stride_cmplx_x_real_32[4] = { 0, 0, 1, 1 }; + + uint32_t blockSizeC = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + f32x4_t rVec; + f32x4_t cmplxVec; + f32x4_t dstVec; + uint32x4_t strideVec; + float32_t in; + + + /* stride vector for pairs of real generation */ + strideVec = vld1q(stride_cmplx_x_real_32); + + /* Compute 4 complex outputs at a time */ + blkCnt = blockSizeC >> 2; + while (blkCnt > 0U) + { + cmplxVec = vld1q(pSrcCmplx); + rVec = vldrwq_gather_shifted_offset_f32(pSrcReal, strideVec); + dstVec = vmulq(cmplxVec, rVec); + vst1q(pCmplxDst, dstVec); + + pSrcReal += 2; + pSrcCmplx += 4; + pCmplxDst += 4; + blkCnt--; + } + + blkCnt = (blockSizeC & 3) >> 1; + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store result in destination buffer. */ + *pCmplxDst++ = *pSrcCmplx++ * in; + *pCmplxDst++ = *pSrcCmplx++ * in; + + /* Decrement loop counter */ + blkCnt--; + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_f32( + const float32_t * pSrcCmplx, + const float32_t * pSrcReal, + float32_t * pCmplxDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + float32_t in; /* Temporary variable */ + +#if defined(ARM_MATH_NEON) + float32x4_t r; + float32x4x2_t ab,outCplx; + + /* Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + ab = vld2q_f32(pSrcCmplx); // load & separate real/imag pSrcA (de-interleave 2) + r = vld1q_f32(pSrcReal); // load & separate real/imag pSrcB + + /* Increment pointers */ + pSrcCmplx += 8; + pSrcReal += 4; + + outCplx.val[0] = vmulq_f32(ab.val[0], r); + outCplx.val[1] = vmulq_f32(ab.val[1], r); + + vst2q_f32(pCmplxDst, outCplx); + pCmplxDst += 8; + + blkCnt--; + } + + /* Tail */ + blkCnt = numSamples & 3; +#else +#if defined (ARM_MATH_LOOPUNROLL) && !defined(ARM_MATH_AUTOVECTORIZE) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store result in destination buffer. */ + *pCmplxDst++ = *pSrcCmplx++ * in; + *pCmplxDst++ = *pSrcCmplx++ * in; + + in = *pSrcReal++; + *pCmplxDst++ = *pSrcCmplx++ * in; + *pCmplxDst++ = *pSrcCmplx++ * in; + + in = *pSrcReal++; + *pCmplxDst++ = *pSrcCmplx++ * in; + *pCmplxDst++ = *pSrcCmplx++ * in; + + in = *pSrcReal++; + *pCmplxDst++ = *pSrcCmplx++* in; + *pCmplxDst++ = *pSrcCmplx++ * in; + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +#endif /* #if defined(ARM_MATH_NEON) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store result in destination buffer. */ + *pCmplxDst++ = *pSrcCmplx++ * in; + *pCmplxDst++ = *pSrcCmplx++ * in; + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of CmplxByRealMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c new file mode 100755 index 0000000..bf5074f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c @@ -0,0 +1,240 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_real_q15.c + * Description: Q15 complex by real multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup CmplxByRealMult + @{ + */ + +/** + @brief Q15 complex-by-real multiplication. + @param[in] pSrcCmplx points to complex input vector + @param[in] pSrcReal points to real input vector + @param[out] pCmplxDst points to complex output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function uses saturating arithmetic. + Results outside of the allowable Q15 range [0x8000 0x7FFF] are saturated. + */ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_q15( + const q15_t * pSrcCmplx, + const q15_t * pSrcReal, + q15_t * pCmplxDst, + uint32_t numSamples) +{ + static const uint16_t stride_cmplx_x_real_16[8] = { + 0, 0, 1, 1, 2, 2, 3, 3 + }; + q15x8_t rVec; + q15x8_t cmplxVec; + q15x8_t dstVec; + uint16x8_t strideVec; + uint32_t blockSizeC = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + q15_t in; + + /* + * stride vector for pairs of real generation + */ + strideVec = vld1q(stride_cmplx_x_real_16); + + blkCnt = blockSizeC >> 3; + + while (blkCnt > 0U) + { + cmplxVec = vld1q(pSrcCmplx); + rVec = vldrhq_gather_shifted_offset_s16(pSrcReal, strideVec); + dstVec = vqdmulhq(cmplxVec, rVec); + vst1q(pCmplxDst, dstVec); + + pSrcReal += 4; + pSrcCmplx += 8; + pCmplxDst += 8; + blkCnt --; + } + + /* Tail */ + blkCnt = (blockSizeC & 7) >> 1; + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store the result in the destination buffer. */ + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + + /* Decrement loop counter */ + blkCnt--; + } +} +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_q15( + const q15_t * pSrcCmplx, + const q15_t * pSrcReal, + q15_t * pCmplxDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q15_t in; /* Temporary variable */ + +#if defined (ARM_MATH_LOOPUNROLL) + +#if defined (ARM_MATH_DSP) + q31_t inA1, inA2; /* Temporary variables to hold input data */ + q31_t inB1; /* Temporary variables to hold input data */ + q15_t out1, out2, out3, out4; /* Temporary variables to hold output data */ + q31_t mul1, mul2, mul3, mul4; /* Temporary variables to hold intermediate data */ +#endif + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + +#if defined (ARM_MATH_DSP) + /* read 2 complex numbers both real and imaginary from complex input buffer */ + inA1 = read_q15x2_ia (&pSrcCmplx); + inA2 = read_q15x2_ia (&pSrcCmplx); + /* read 2 real values at a time from real input buffer */ + inB1 = read_q15x2_ia (&pSrcReal); + + /* multiply complex number with real numbers */ +#ifndef ARM_MATH_BIG_ENDIAN + mul1 = (q31_t) ((q15_t) (inA1) * (q15_t) (inB1)); + mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1)); + mul3 = (q31_t) ((q15_t) (inA2) * (q15_t) (inB1 >> 16)); + mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB1 >> 16)); +#else + mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16)); + mul1 = (q31_t) ((q15_t) inA1 * (q15_t) (inB1 >> 16)); + mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) inB1); + mul3 = (q31_t) ((q15_t) inA2 * (q15_t) inB1); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* saturate the result */ + out1 = (q15_t) __SSAT(mul1 >> 15U, 16); + out2 = (q15_t) __SSAT(mul2 >> 15U, 16); + out3 = (q15_t) __SSAT(mul3 >> 15U, 16); + out4 = (q15_t) __SSAT(mul4 >> 15U, 16); + + /* pack real and imaginary outputs and store them to destination */ + write_q15x2_ia (&pCmplxDst, __PKHBT(out1, out2, 16)); + write_q15x2_ia (&pCmplxDst, __PKHBT(out3, out4, 16)); + + inA1 = read_q15x2_ia (&pSrcCmplx); + inA2 = read_q15x2_ia (&pSrcCmplx); + inB1 = read_q15x2_ia (&pSrcReal); + +#ifndef ARM_MATH_BIG_ENDIAN + mul1 = (q31_t) ((q15_t) (inA1) * (q15_t) (inB1)); + mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1)); + mul3 = (q31_t) ((q15_t) (inA2) * (q15_t) (inB1 >> 16)); + mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) (inB1 >> 16)); +#else + mul2 = (q31_t) ((q15_t) (inA1 >> 16) * (q15_t) (inB1 >> 16)); + mul1 = (q31_t) ((q15_t) inA1 * (q15_t) (inB1 >> 16)); + mul4 = (q31_t) ((q15_t) (inA2 >> 16) * (q15_t) inB1); + mul3 = (q31_t) ((q15_t) inA2 * (q15_t) inB1); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + out1 = (q15_t) __SSAT(mul1 >> 15U, 16); + out2 = (q15_t) __SSAT(mul2 >> 15U, 16); + out3 = (q15_t) __SSAT(mul3 >> 15U, 16); + out4 = (q15_t) __SSAT(mul4 >> 15U, 16); + + write_q15x2_ia (&pCmplxDst, __PKHBT(out1, out2, 16)); + write_q15x2_ia (&pCmplxDst, __PKHBT(out3, out4, 16)); +#else + in = *pSrcReal++; + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + + in = *pSrcReal++; + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + + in = *pSrcReal++; + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + + in = *pSrcReal++; + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); +#endif + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store the result in the destination buffer. */ + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + *pCmplxDst++ = (q15_t) __SSAT((((q31_t) *pSrcCmplx++ * in) >> 15), 16); + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of CmplxByRealMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c new file mode 100755 index 0000000..8096ec6 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/ComplexMathFunctions/arm_cmplx_mult_real_q31.c @@ -0,0 +1,206 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cmplx_mult_real_q31.c + * Description: Q31 complex by real multiplication + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/complex_math_functions.h" + +/** + @ingroup groupCmplxMath + */ + +/** + @addtogroup CmplxByRealMult + @{ + */ + +/** + @brief Q31 complex-by-real multiplication. + @param[in] pSrcCmplx points to complex input vector + @param[in] pSrcReal points to real input vector + @param[out] pCmplxDst points to complex output vector + @param[in] numSamples number of samples in each vector + + @par Scaling and Overflow Behavior + The function uses saturating arithmetic. + Results outside of the allowable Q31 range[0x80000000 0x7FFFFFFF] are saturated. + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_q31( + const q31_t * pSrcCmplx, + const q31_t * pSrcReal, + q31_t * pCmplxDst, + uint32_t numSamples) +{ + + static const uint32_t stride_cmplx_x_real_32[4] = { + 0, 0, 1, 1 + }; + q31x4_t rVec; + q31x4_t cmplxVec; + q31x4_t dstVec; + uint32x4_t strideVec; + uint32_t blockSizeC = numSamples * CMPLX_DIM; /* loop counters */ + uint32_t blkCnt; + q31_t in; + + /* + * stride vector for pairs of real generation + */ + strideVec = vld1q(stride_cmplx_x_real_32); + + /* Compute 4 complex outputs at a time */ + blkCnt = blockSizeC >> 2; + while (blkCnt > 0U) + { + cmplxVec = vld1q(pSrcCmplx); + rVec = vldrwq_gather_shifted_offset_s32(pSrcReal, strideVec); + dstVec = vqdmulhq(cmplxVec, rVec); + vst1q(pCmplxDst, dstVec); + + pSrcReal += 2; + pSrcCmplx += 4; + pCmplxDst += 4; + blkCnt --; + } + + blkCnt = (blockSizeC & 3) >> 1; + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; + /* store saturated result in 1.31 format to destination buffer */ + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + + /* Decrement loop counter */ + blkCnt--; + } +} +#else +ARM_DSP_ATTRIBUTE void arm_cmplx_mult_real_q31( + const q31_t * pSrcCmplx, + const q31_t * pSrcReal, + q31_t * pCmplxDst, + uint32_t numSamples) +{ + uint32_t blkCnt; /* Loop counter */ + q31_t in; /* Temporary variable */ + +#if defined (ARM_MATH_LOOPUNROLL) + + /* Loop unrolling: Compute 4 outputs at a time */ + blkCnt = numSamples >> 2U; + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; +#if defined (ARM_MATH_DSP) + /* store saturated result in 1.31 format to destination buffer */ + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); +#else + /* store result in destination buffer. */ + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); +#endif + + in = *pSrcReal++; +#if defined (ARM_MATH_DSP) + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); +#else + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); +#endif + + in = *pSrcReal++; +#if defined (ARM_MATH_DSP) + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); +#else + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); +#endif + + in = *pSrcReal++; +#if defined (ARM_MATH_DSP) + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); +#else + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); +#endif + + /* Decrement loop counter */ + blkCnt--; + } + + /* Loop unrolling: Compute remaining outputs */ + blkCnt = numSamples % 0x4U; + +#else + + /* Initialize blkCnt with number of samples */ + blkCnt = numSamples; + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + + while (blkCnt > 0U) + { + /* C[2 * i ] = A[2 * i ] * B[i]. */ + /* C[2 * i + 1] = A[2 * i + 1] * B[i]. */ + + in = *pSrcReal++; +#if defined (ARM_MATH_DSP) + /* store saturated result in 1.31 format to destination buffer */ + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); + *pCmplxDst++ = (__SSAT((q31_t) (((q63_t) *pSrcCmplx++ * in) >> 32), 31) << 1); +#else + /* store result in destination buffer. */ + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); + *pCmplxDst++ = (q31_t) clip_q63_to_q31(((q63_t) *pSrcCmplx++ * in) >> 31); +#endif + + /* Decrement loop counter */ + blkCnt--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @} end of CmplxByRealMult group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_f16.c new file mode 100755 index 0000000..c4635f8 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_f16.c @@ -0,0 +1,174 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_atan2_f16.c + * Description: float16 Arc tangent of y/x + * + * $Date: 22 April 2022 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/* + +atan for argument between in [0, 1.0] + + +*/ + +#define PIF16 3.14f16 +#define PI16HALF 1.571f16 + +#define ATANHALFF16 0.463648f16 + +#define ATAN2_NB_COEFS_F16 5 + +static const float16_t atan2_coefs_f16[ATAN2_NB_COEFS_F16]={0.f16 +,1.f16 +,0.f16 +,-0.367f16 +,0.152f16 +}; + +__STATIC_FORCEINLINE float16_t arm_atan_limited_f16(float16_t x) +{ + float16_t res=atan2_coefs_f16[ATAN2_NB_COEFS_F16-1]; + int i=1; + for(i=1;i 1.0f16) + { + x = 1.0f16 / (_Float16)x; + res = (_Float16)PI16HALF - (_Float16)arm_atan_limited_f16(x); + } + else + { + res += (_Float16)arm_atan_limited_f16(x); + } + + + if (sign) + { + res = -(_Float16)res; + } + + return((float16_t)res); +} + +/** + @ingroup groupFastMath + */ + + +/** + @addtogroup atan2 + @{ + */ + +/** + @brief Arc Tangent of y/x using sign of y and x to get right quadrant + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result + @return error status. + + @par Compute the Arc tangent of y/x: + The sign of y and x are used to determine the right quadrant + and compute the right angle. Returned value is between -Pi and Pi. + +*/ +ARM_DSP_ATTRIBUTE arm_status arm_atan2_f16(float16_t y,float16_t x,float16_t *result) +{ + if ((_Float16)x > 0.0f16) + { + *result=arm_atan_f16((_Float16)y/(_Float16)x); + return(ARM_MATH_SUCCESS); + } + if ((_Float16)x < 0.0f16) + { + if ((_Float16)y > 0.0f16) + { + *result=(_Float16)arm_atan_f16((_Float16)y/(_Float16)x) + (_Float16)PIF16; + } + else if ((_Float16)y < 0.0f16) + { + *result=(_Float16)arm_atan_f16((_Float16)y/(_Float16)x) - (_Float16)PIF16; + } + else + { + if (signbit((float)y)) + { + *result= -(_Float16)PIF16; + } + else + { + *result= PIF16; + } + } + return(ARM_MATH_SUCCESS); + } + if ((_Float16)x == 0.0f16) + { + if ((_Float16)y > 0.0f16) + { + *result=PI16HALF; + return(ARM_MATH_SUCCESS); + } + if ((_Float16)y < 0.0f16) + { + *result=-(_Float16)PI16HALF; + return(ARM_MATH_SUCCESS); + } + } + + + return(ARM_MATH_NANINF); + +} + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ +/** + @} end of atan2 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_f32.c new file mode 100755 index 0000000..8927f4d --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_f32.c @@ -0,0 +1,186 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_atan2_f32.c + * Description: float32 Arc tangent of y/x + * + * $Date: 22 April 2022 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" + +/* + +atan for argument between in [0, 1.0] + + +*/ + +#define ATANHALFF32 0.463648f +#define PIHALFF32 1.5707963267948966192313f + +#define ATAN2_NB_COEFS_F32 10 + +static const float32_t atan2_coefs_f32[ATAN2_NB_COEFS_F32]={0.0f +,1.0000001638308195518f +,-0.0000228941363602264f +,-0.3328086544578890873f +,-0.004404814619311061f +,0.2162217461808173258f +,-0.0207504842057097504f +,-0.1745263362250363339f +,0.1340557235283553386f +,-0.0323664125927477625f +}; + +__STATIC_FORCEINLINE float32_t arm_atan_limited_f32(float32_t x) +{ + float32_t res=atan2_coefs_f32[ATAN2_NB_COEFS_F32-1]; + int i=1; + for(i=1;i 1.0f) + { + x = 1.0f / x; + res = PIHALFF32 - arm_atan_limited_f32(x); + } + else + { + res += arm_atan_limited_f32(x); + } + + + if (sign) + { + res = -res; + } + + return(res); +} + + +/** + @ingroup groupFastMath + */ + +/** + @defgroup atan2 ArcTan2 + + Computing Arc tangent only using the ratio y/x is not enough to determine the angle + since there is an indeterminacy. Opposite quadrants are giving the same ratio. + + ArcTan2 is not using y/x to compute the angle but y and x and use the sign of y and x + to determine the quadrant. + + */ + +/** + @addtogroup atan2 + @{ + */ + +/** + @brief Arc Tangent of y/x using sign of y and x to get right quadrant + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result + @return error status. + + @par Compute the Arc tangent of y/x: + The sign of y and x are used to determine the right quadrant + and compute the right angle. Returned value is between -Pi and Pi. +*/ + + +ARM_DSP_ATTRIBUTE arm_status arm_atan2_f32(float32_t y,float32_t x,float32_t *result) +{ + if (x > 0.0f) + { + *result=arm_atan_f32(y/x); + return(ARM_MATH_SUCCESS); + } + if (x < 0.0f) + { + if (y > 0.0f) + { + *result=arm_atan_f32(y/x) + PI; + } + else if (y < 0.0f) + { + *result=arm_atan_f32(y/x) - PI; + } + else + { + if (signbit(y)) + { + *result= -PI; + } + else + { + *result= PI; + } + } + return(ARM_MATH_SUCCESS); + } + if (x == 0.0f) + { + if (y > 0.0f) + { + *result=PIHALFF32; + return(ARM_MATH_SUCCESS); + } + if (y < 0.0f) + { + *result=-PIHALFF32; + return(ARM_MATH_SUCCESS); + } + } + + + return(ARM_MATH_NANINF); + +} + +/** + @} end of atan2 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_q15.c new file mode 100755 index 0000000..c507f3d --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_q15.c @@ -0,0 +1,232 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_atan2_q15.c + * Description: q15 Arc tangent of y/x + * + * $Date: 22 April 2022 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "dsp/utils.h" + +/* + +atan for argument between in [0, 1.0] + +*/ + + +/* Q2.13 */ +#define ATANHALFQ13 0xed6 +#define PIHALFQ13 0x3244 +#define PIQ13 0x6488 + +#define ATAN2_NB_COEFS_Q15 10 + +static const q15_t atan2_coefs_q15[ATAN2_NB_COEFS_Q15]={ + 0, // 0x0000 + 32767, // 0x7fff + -1, // 0xffff +-10905, // 0xd567 + -144, // 0xff70 + 7085, // 0x1bad + -680, // 0xfd58 + -5719, // 0xe9a9 + 4393, // 0x1129 + -1061 // 0xfbdb +}; + +__STATIC_FORCEINLINE q15_t arm_atan_limited_q15(q15_t x) +{ + q31_t res=(q31_t)atan2_coefs_q15[ATAN2_NB_COEFS_Q15-1]; + int i=1; + for(i=1;i> 15U; + res = res + ((q31_t) atan2_coefs_q15[ATAN2_NB_COEFS_Q15-1-i]) ; + } + + res = __SSAT(res>>2,16); + + + return(res); +} + + +__STATIC_FORCEINLINE q15_t arm_atan_q15(q15_t y,q15_t x) +{ + int sign=0; + q15_t res=0; + + if (y<0) + { + /* Negate y */ +#if defined (ARM_MATH_DSP) + y = __QSUB16(0, y); +#else + y = (y == (q15_t) 0x8000) ? (q15_t) 0x7fff : -y; +#endif + + sign=1-sign; + } + + if (x < 0) + { + sign=1 - sign; + + /* Negate x */ +#if defined (ARM_MATH_DSP) + x = __QSUB16(0, x); +#else + x = (x == (q15_t) 0x8000) ? (q15_t) 0x7fff : -x; +#endif + } + + if (y > x) + { + q15_t ratio; + int16_t shift; + + arm_divide_q15(x,y,&ratio,&shift); + + /* Shift ratio by shift */ + if (shift >=0) + { + ratio = __SSAT(((q31_t) ratio << shift), 16); + } + else + { + ratio = (ratio >> -shift); + } + + res = PIHALFQ13 - arm_atan_limited_q15(ratio); + + } + else + { + q15_t ratio; + int16_t shift; + + arm_divide_q15(y,x,&ratio,&shift); + + /* Shift ratio by shift */ + if (shift >=0) + { + ratio = __SSAT(((q31_t) ratio << shift), 16); + } + else + { + ratio = (ratio >> -shift); + } + + + res = arm_atan_limited_q15(ratio); + + } + + + if (sign) + { + /* Negate res */ +#if defined (ARM_MATH_DSP) + res = __QSUB16(0, res); +#else + res = (res == (q15_t) 0x8000) ? (q15_t) 0x7fff : -res; +#endif + } + + return(res); +} + + +/** + @ingroup groupFastMath + */ + + +/** + @addtogroup atan2 + @{ + */ + +/** + @brief Arc Tangent of y/x using sign of y and x to get right quadrant + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result in Q2.13 + @return error status. + + @par Compute the Arc tangent of y/x: + The sign of y and x are used to determine the right quadrant + and compute the right angle. Returned value is between -Pi and Pi. +*/ + + +ARM_DSP_ATTRIBUTE arm_status arm_atan2_q15(q15_t y,q15_t x,q15_t *result) +{ + if (x > 0) + { + *result=arm_atan_q15(y,x); + return(ARM_MATH_SUCCESS); + } + if (x < 0) + { + if (y > 0) + { + *result=arm_atan_q15(y,x) + PIQ13; + } + else if (y < 0) + { + *result=arm_atan_q15(y,x) - PIQ13; + } + else + { + *result= PIQ13; + } + return(ARM_MATH_SUCCESS); + } + if (x == 0) + { + if (y > 0) + { + *result=PIHALFQ13; + return(ARM_MATH_SUCCESS); + } + if (y < 0) + { + *result=-PIHALFQ13; + return(ARM_MATH_SUCCESS); + } + } + + + return(ARM_MATH_NANINF); + +} + +/** + @} end of atan2 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_q31.c new file mode 100755 index 0000000..848d1d3 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_atan2_q31.c @@ -0,0 +1,232 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_atan2_q31.c + * Description: q31 Arc tangent of y/x + * + * $Date: 22 April 2022 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "dsp/utils.h" + +/* + +atan for argument between in [0, 1.0] + +*/ + + +/* Q2.29 */ +#define ATANHALF_Q29 0xed63383 +#define PIHALF_Q29 0x3243f6a9 +#define PIQ29 0x6487ed51 + +#define ATAN2_NB_COEFS_Q31 13 + +static const q31_t atan2_coefs_q31[ATAN2_NB_COEFS_Q31]={0x00000000 +,0x7ffffffe +,0x000001b6 +,0xd555158e +,0x00036463 +,0x1985f617 +,0x001992ae +,0xeed53a7f +,0xf8f15245 +,0x2215a3a4 +,0xe0fab004 +,0x0cdd4825 +,0xfddbc054 +}; + + +__STATIC_FORCEINLINE q31_t arm_atan_limited_q31(q31_t x) +{ + q63_t res=(q63_t)atan2_coefs_q31[ATAN2_NB_COEFS_Q31-1]; + int i=1; + for(i=1;i> 31U; + res = res + ((q63_t) atan2_coefs_q31[ATAN2_NB_COEFS_Q31-1-i]) ; + } + + return(clip_q63_to_q31(res>>2)); +} + + +__STATIC_FORCEINLINE q31_t arm_atan_q31(q31_t y,q31_t x) +{ + int sign=0; + q31_t res=0; + + if (y<0) + { + /* Negate y */ +#if defined (ARM_MATH_DSP) + y = __QSUB(0, y); +#else + y = (y == INT32_MIN) ? INT32_MAX : -y; +#endif + + sign=1-sign; + } + + if (x < 0) + { + sign=1 - sign; + + /* Negate x */ +#if defined (ARM_MATH_DSP) + x = __QSUB(0, x); +#else + x = (x == INT32_MIN) ? INT32_MAX : -x; +#endif + } + + if (y > x) + { + q31_t ratio; + int16_t shift; + + arm_divide_q31(x,y,&ratio,&shift); + + /* Shift ratio by shift */ + if (shift >= 0) + { + ratio = clip_q63_to_q31((q63_t) ratio << shift); + } + else + { + ratio = (ratio >> -shift); + } + + res = PIHALF_Q29 - arm_atan_limited_q31(ratio); + + } + else + { + q31_t ratio; + int16_t shift; + + arm_divide_q31(y,x,&ratio,&shift); + + /* Shift ratio by shift */ + if (shift >= 0) + { + ratio = clip_q63_to_q31((q63_t) ratio << shift); + } + else + { + ratio = (ratio >> -shift); + } + + + res = arm_atan_limited_q31(ratio); + + } + + + if (sign) + { + /* Negate res */ +#if defined (ARM_MATH_DSP) + res = __QSUB(0, res); +#else + res = (res == INT32_MIN) ? INT32_MAX : -res; +#endif + } + + return(res); +} + + +/** + @ingroup groupFastMath + */ + + +/** + @addtogroup atan2 + @{ + */ + +/** + @brief Arc Tangent of y/x using sign of y and x to get right quadrant + @param[in] y y coordinate + @param[in] x x coordinate + @param[out] result Result in Q2.29 + @return error status. + + @par Compute the Arc tangent of y/x: + The sign of y and x are used to determine the right quadrant + and compute the right angle. Returned value is between -Pi and Pi. +*/ + + +ARM_DSP_ATTRIBUTE arm_status arm_atan2_q31(q31_t y,q31_t x,q31_t *result) +{ + if (x > 0) + { + *result=arm_atan_q31(y,x); + return(ARM_MATH_SUCCESS); + } + if (x < 0) + { + if (y > 0) + { + *result=arm_atan_q31(y,x) + PIQ29; + } + else if (y < 0) + { + *result=arm_atan_q31(y,x) - PIQ29; + } + else + { + *result= PIQ29; + } + return(ARM_MATH_SUCCESS); + } + if (x == 0) + { + if (y > 0) + { + *result=PIHALF_Q29; + return(ARM_MATH_SUCCESS); + } + if (y < 0) + { + *result=-PIHALF_Q29; + return(ARM_MATH_SUCCESS); + } + } + + + return(ARM_MATH_NANINF); + +} + +/** + @} end of atan2 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_f32.c new file mode 100755 index 0000000..d22cd84 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_f32.c @@ -0,0 +1,124 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cos_f32.c + * Description: Fast cosine calculation for floating-point values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup groupFastMath + */ + +/** + @defgroup cos Cosine + + Computes the trigonometric cosine function using a combination of table lookup + and linear interpolation. There are separate functions for + Q15, Q31, and floating-point data types. + The input to the floating-point version is in radians while the + fixed-point Q15 and Q31 have a scaled input with the range + [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a + value of 2*pi wraps around to 0. + + The implementation is based on table lookup using 512 values together with linear interpolation. + The steps used are: + -# Calculation of the nearest integer table index + -# Compute the fractional portion (fract) of the table index. + -# The final result equals (1.0f-fract)*a + fract*b; + + where + 
+     a = Table[index];
+     b = Table[index+1];
+
+ */ + +/** + @addtogroup cos + @{ + */ + +/** + @brief Fast approximation to the trigonometric cosine function for floating-point data. + @param[in] x input value in radians + @return cos(x) + */ +ARM_DSP_ATTRIBUTE float32_t arm_cos_f32( + float32_t x) +{ + float32_t cosVal, fract, in; /* Temporary input, output variables */ + uint16_t index; /* Index variable */ + float32_t a, b; /* Two nearest output values */ + int32_t n; + float32_t findex; + + /* input x is in radians */ + /* Scale input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */ + in = x * 0.159154943092f + 0.25f; + + /* Calculation of floor value of input */ + n = (int32_t) in; + + /* Make negative values towards -infinity */ + if (in < 0.0f) + { + n--; + } + + /* Map input value to [0 1] */ + in = in - (float32_t) n; + + /* Calculation of index of the table */ + findex = (float32_t)FAST_MATH_TABLE_SIZE * in; + index = (uint16_t)findex; + + /* when "in" is exactly 1, we need to rotate the index down to 0 */ + if (index >= FAST_MATH_TABLE_SIZE) { + index = 0; + findex -= (float32_t)FAST_MATH_TABLE_SIZE; + } + + /* fractional value calculation */ + fract = findex - (float32_t) index; + + /* Read two nearest values of input value from the cos table */ + a = sinTable_f32[index]; + b = sinTable_f32[index+1]; + + /* Linear interpolation process */ + cosVal = (1.0f - fract) * a + fract * b; + + /* Return output value */ + return (cosVal); +} + +/** + @} end of cos group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_q15.c new file mode 100755 index 0000000..db54632 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_q15.c @@ -0,0 +1,87 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cos_q15.c + * Description: Fast cosine calculation for Q15 values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup cos + @{ + */ + +/** + @brief Fast approximation to the trigonometric cosine function for Q15 data. + @param[in] x Scaled input value in radians + @return cos(x) + + The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*PI). + */ + +ARM_DSP_ATTRIBUTE q15_t arm_cos_q15( + q15_t x) +{ + q15_t cosVal; /* Temporary input, output variables */ + int32_t index; /* Index variable */ + q15_t a, b; /* Two nearest output values */ + q15_t fract; /* Temporary values for fractional values */ + + /* add 0.25 (pi/2) to read sine table */ + x = (uint16_t)x + 0x2000; + if (x < 0) + { /* convert negative numbers to corresponding positive ones */ + x = (uint16_t)x + 0x8000; + } + + /* Calculate the nearest index */ + index = (uint32_t)x >> FAST_MATH_Q15_SHIFT; + + /* Calculation of fractional value */ + fract = (x - (index << FAST_MATH_Q15_SHIFT)) << 9; + + /* Read two nearest values of input value from the sin table */ + a = sinTable_q15[index]; + b = sinTable_q15[index+1]; + + /* Linear interpolation process */ + cosVal = (q31_t) (0x8000 - fract) * a >> 16; + cosVal = (q15_t) ((((q31_t) cosVal << 16) + ((q31_t) fract * b)) >> 16); + + /* Return output value */ + return (cosVal << 1); +} + +/** + @} end of cos group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_q31.c new file mode 100755 index 0000000..7f47629 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_cos_q31.c @@ -0,0 +1,87 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cos_q31.c + * Description: Fast cosine calculation for Q31 values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup cos + @{ + */ + +/** + @brief Fast approximation to the trigonometric cosine function for Q31 data. + @param[in] x Scaled input value in radians + @return cos(x) + + The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*PI). + */ + +ARM_DSP_ATTRIBUTE q31_t arm_cos_q31( + q31_t x) +{ + q31_t cosVal; /* Temporary input, output variables */ + int32_t index; /* Index variable */ + q31_t a, b; /* Two nearest output values */ + q31_t fract; /* Temporary values for fractional values */ + + /* add 0.25 (pi/2) to read sine table */ + x = (uint32_t)x + 0x20000000; + if (x < 0) + { /* convert negative numbers to corresponding positive ones */ + x = (uint32_t)x + 0x80000000; + } + + /* Calculate the nearest index */ + index = (uint32_t)x >> FAST_MATH_Q31_SHIFT; + + /* Calculation of fractional value */ + fract = (x - (index << FAST_MATH_Q31_SHIFT)) << 9; + + /* Read two nearest values of input value from the sin table */ + a = sinTable_q31[index]; + b = sinTable_q31[index+1]; + + /* Linear interpolation process */ + cosVal = (q63_t) (0x80000000 - fract) * a >> 32; + cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) fract * b)) >> 32); + + /* Return output value */ + return (cosVal << 1); +} + +/** + @} end of cos group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_divide_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_divide_q15.c new file mode 100755 index 0000000..051d5a7 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_divide_q15.c @@ -0,0 +1,113 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cos_q15.c + * Description: Fast cosine calculation for Q15 values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +#include + +/** + @ingroup groupFastMath + */ + +/** + @defgroup divide Fixed point division + + */ + +/** + @addtogroup divide + @{ + */ + +/** + @brief Fixed point division + @param[in] numerator Numerator + @param[in] denominator Denominator + @param[out] quotient Quotient value normalized between -1.0 and 1.0 + @param[out] shift Shift left value to get the unnormalized quotient + @return error status + + When dividing by 0, an error ARM_MATH_NANINF is returned. And the quotient is forced + to the saturated negative or positive value. + */ + +ARM_DSP_ATTRIBUTE arm_status arm_divide_q15(q15_t numerator, + q15_t denominator, + q15_t *quotient, + int16_t *shift) +{ + int16_t sign=0; + q31_t temp; + int16_t shiftForNormalizing; + + *shift = 0; + + sign = (numerator<0) ^ (denominator<0); + + if (denominator == 0) + { + if (sign) + { + *quotient = -32768; + } + else + { + *quotient = 32767; + } + return(ARM_MATH_NANINF); + } + + arm_abs_q15(&numerator,&numerator,1); + arm_abs_q15(&denominator,&denominator,1); + + temp = ((q31_t)numerator << 15) / ((q31_t)denominator); + + shiftForNormalizing= 17 - __CLZ(temp); + if (shiftForNormalizing > 0) + { + *shift = shiftForNormalizing; + temp = temp >> shiftForNormalizing; + } + + if (sign) + { + temp = -temp; + } + + *quotient=temp; + + return(ARM_MATH_SUCCESS); +} + +/** + @} end of divide group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_divide_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_divide_q31.c new file mode 100755 index 0000000..4f7e1f4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_divide_q31.c @@ -0,0 +1,108 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cos_q31.c + * Description: Fast cosine calculation for Q31 values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +#include + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup divide + @{ + */ + +/** + @brief Fixed point division + @param[in] numerator Numerator + @param[in] denominator Denominator + @param[out] quotient Quotient value normalized between -1.0 and 1.0 + @param[out] shift Shift left value to get the unnormalized quotient + @return error status + + When dividing by 0, an error ARM_MATH_NANINF is returned. And the quotient is forced + to the saturated negative or positive value. + */ + +ARM_DSP_ATTRIBUTE arm_status arm_divide_q31(q31_t numerator, + q31_t denominator, + q31_t *quotient, + int16_t *shift) +{ + int16_t sign=0; + q63_t temp; + int16_t shiftForNormalizing; + + *shift = 0; + + sign = (numerator<0) ^ (denominator<0); + + if (denominator == 0) + { + if (sign) + { + *quotient = 0x80000000; + } + else + { + *quotient = 0x7FFFFFFF; + } + return(ARM_MATH_NANINF); + } + + arm_abs_q31(&numerator,&numerator,1); + arm_abs_q31(&denominator,&denominator,1); + + temp = ((q63_t)numerator << 31) / ((q63_t)denominator); + + shiftForNormalizing= 32 - __CLZ(temp >> 31); + if (shiftForNormalizing > 0) + { + *shift = shiftForNormalizing; + temp = temp >> shiftForNormalizing; + } + + if (sign) + { + temp = -temp; + } + + *quotient=(q31_t)temp; + + return(ARM_MATH_SUCCESS); +} + +/** + @} end of divide group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_f32.c new file mode 100755 index 0000000..15764b4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_f32.c @@ -0,0 +1,125 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_sin_f32.c + * Description: Fast sine calculation for floating-point values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup groupFastMath + */ + +/** + @defgroup sin Sine + + Computes the trigonometric sine function using a combination of table lookup + and linear interpolation. There are separate functions for + Q15, Q31, and floating-point data types. + The input to the floating-point version is in radians while the + fixed-point Q15 and Q31 have a scaled input with the range + [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a + value of 2*pi wraps around to 0. + + The implementation is based on table lookup using 512 values together with linear interpolation. + The steps used are: + -# Calculation of the nearest integer table index + -# Compute the fractional portion (fract) of the table index. + -# The final result equals (1.0f-fract)*a + fract*b; + + where + 
+     b = Table[index];
+     c = Table[index+1];
+
+ */ + +/** + @addtogroup sin + @{ + */ + +/** + @brief Fast approximation to the trigonometric sine function for floating-point data. + @param[in] x input value in radians. + @return sin(x) + */ + +ARM_DSP_ATTRIBUTE float32_t arm_sin_f32( + float32_t x) +{ + float32_t sinVal, fract, in; /* Temporary input, output variables */ + uint16_t index; /* Index variable */ + float32_t a, b; /* Two nearest output values */ + int32_t n; + float32_t findex; + + /* input x is in radians */ + /* Scale input to [0 1] range from [0 2*PI] , divide input by 2*pi */ + in = x * 0.159154943092f; + + /* Calculation of floor value of input */ + n = (int32_t) in; + + /* Make negative values towards -infinity */ + if (in < 0.0f) + { + n--; + } + + /* Map input value to [0 1] */ + in = in - (float32_t) n; + + /* Calculation of index of the table */ + findex = (float32_t)FAST_MATH_TABLE_SIZE * in; + index = (uint16_t)findex; + + /* when "in" is exactly 1, we need to rotate the index down to 0 */ + if (index >= FAST_MATH_TABLE_SIZE) { + index = 0; + findex -= (float32_t)FAST_MATH_TABLE_SIZE; + } + + /* fractional value calculation */ + fract = findex - (float32_t) index; + + /* Read two nearest values of input value from the sin table */ + a = sinTable_f32[index]; + b = sinTable_f32[index+1]; + + /* Linear interpolation process */ + sinVal = (1.0f - fract) * a + fract * b; + + /* Return output value */ + return (sinVal); +} + +/** + @} end of sin group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_q15.c new file mode 100755 index 0000000..9d7f105 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_q15.c @@ -0,0 +1,86 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_sin_q15.c + * Description: Fast sine calculation for Q15 values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup sin + @{ + */ + +/** + @brief Fast approximation to the trigonometric sine function for Q15 data. + @param[in] x Scaled input value in radians + @return sin(x) + + The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*PI). + */ + +ARM_DSP_ATTRIBUTE q15_t arm_sin_q15( + q15_t x) +{ + q15_t sinVal; /* Temporary input, output variables */ + int32_t index; /* Index variable */ + q15_t a, b; /* Two nearest output values */ + q15_t fract; /* Temporary values for fractional values */ + + + if (x < 0) + { /* convert negative numbers to corresponding positive ones */ + x = (uint16_t)x + 0x8000; + } + + /* Calculate the nearest index */ + index = (uint32_t)x >> FAST_MATH_Q15_SHIFT; + + /* Calculation of fractional value */ + fract = (x - (index << FAST_MATH_Q15_SHIFT)) << 9; + + /* Read two nearest values of input value from the sin table */ + a = sinTable_q15[index]; + b = sinTable_q15[index+1]; + + /* Linear interpolation process */ + sinVal = (q31_t) (0x8000 - fract) * a >> 16; + sinVal = (q15_t) ((((q31_t) sinVal << 16) + ((q31_t) fract * b)) >> 16); + + /* Return output value */ + return (sinVal << 1); +} + +/** + @} end of sin group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_q31.c new file mode 100755 index 0000000..a46ee67 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sin_q31.c @@ -0,0 +1,85 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_sin_q31.c + * Description: Fast sine calculation for Q31 values + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup sin + @{ + */ + +/** + @brief Fast approximation to the trigonometric sine function for Q31 data. + @param[in] x Scaled input value in radians + @return sin(x) + + The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*PI). + */ + +ARM_DSP_ATTRIBUTE q31_t arm_sin_q31( + q31_t x) +{ + q31_t sinVal; /* Temporary variables for input, output */ + int32_t index; /* Index variable */ + q31_t a, b; /* Two nearest output values */ + q31_t fract; /* Temporary values for fractional values */ + + if (x < 0) + { /* convert negative numbers to corresponding positive ones */ + x = (uint32_t)x + 0x80000000; + } + + /* Calculate the nearest index */ + index = (uint32_t)x >> FAST_MATH_Q31_SHIFT; + + /* Calculation of fractional value */ + fract = (x - (index << FAST_MATH_Q31_SHIFT)) << 9; + + /* Read two nearest values of input value from the sin table */ + a = sinTable_q31[index]; + b = sinTable_q31[index+1]; + + /* Linear interpolation process */ + sinVal = (q63_t) (0x80000000 - fract) * a >> 32; + sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) fract * b)) >> 32); + + /* Return output value */ + return (sinVal << 1); +} + +/** + @} end of sin group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sqrt_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sqrt_q15.c new file mode 100755 index 0000000..73eba0e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sqrt_q15.c @@ -0,0 +1,134 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_sqrt_q15.c + * Description: Q15 square root function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +#define Q12QUARTER 0x2000 + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup SQRT + @{ + */ + +/** + @brief Q15 square root function. + @param[in] in input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF + @param[out] pOut points to square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ + +ARM_DSP_ATTRIBUTE arm_status arm_sqrt_q15( + q15_t in, + q15_t * pOut) +{ + q15_t number, var1, signBits1,temp; + + number = in; + + /* If the input is a positive number then compute the signBits. */ + if (number > 0) + { + signBits1 = __CLZ(number) - 17; + + /* Shift by the number of signBits1 */ + if ((signBits1 % 2) == 0) + { + number = number << signBits1; + } + else + { + number = number << (signBits1 - 1); + } + /* Start value for 1/sqrt(x) for the Newton iteration */ + var1 = sqrt_initial_lut_q15[(number>> 11) - (Q12QUARTER >> 11)]; + + /* 0.5 var1 * (3 - number * var1 * var1) */ + /* 1st iteration */ + + temp = ((q31_t) var1 * var1) >> 12; + temp = ((q31_t) number * temp) >> 15; + temp = 0x3000 - temp; + var1 = ((q31_t) var1 * temp) >> 13; + + temp = ((q31_t) var1 * var1) >> 12; + temp = ((q31_t) number * temp) >> 15; + temp = 0x3000 - temp; + var1 = ((q31_t) var1 * temp) >> 13; + + temp = ((q31_t) var1 * var1) >> 12; + temp = ((q31_t) number * temp) >> 15; + temp = 0x3000 - temp; + var1 = ((q31_t) var1 * temp) >> 13; + + /* Multiply the inverse square root with the original value */ + + var1 = ((q15_t) (((q31_t) number * var1) >> 12)); + + /* Shift the output down accordingly */ + if ((signBits1 % 2) == 0) + { + var1 = var1 >> (signBits1 / 2); + } + else + { + var1 = var1 >> ((signBits1 - 1) / 2); + } + *pOut = var1; + + + return (ARM_MATH_SUCCESS); + } + /* If the number is a negative number then store zero as its square root value */ + else + { + *pOut = 0; + + if (number==0) + { + return (ARM_MATH_SUCCESS); + } + else + { + return (ARM_MATH_ARGUMENT_ERROR); + } + } +} + +/** + @} end of SQRT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sqrt_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sqrt_q31.c new file mode 100755 index 0000000..39c3af4 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_sqrt_q31.c @@ -0,0 +1,137 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_sqrt_q31.c + * Description: Q31 square root function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +#define Q28QUARTER 0x20000000 + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup SQRT + @{ + */ + +/** + @brief Q31 square root function. + @param[in] in input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF + @param[out] pOut points to square root of input value + @return execution status + - \ref ARM_MATH_SUCCESS : input value is positive + - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0 + */ + +ARM_DSP_ATTRIBUTE arm_status arm_sqrt_q31( + q31_t in, + q31_t * pOut) +{ + q31_t number, var1, signBits1 ,temp; + + number = in; + + /* If the input is a positive number then compute the signBits. */ + if (number > 0) + { + signBits1 = __CLZ(number) - 1; + + /* Shift by the number of signBits1 */ + if ((signBits1 % 2) == 0) + { + number = number << signBits1; + } + else + { + number = number << (signBits1 - 1); + } + + /* Start value for 1/sqrt(x) for the Newton iteration */ + var1 = sqrt_initial_lut_q31[(number>> 26) - (Q28QUARTER >> 26)]; + + /* 0.5 var1 * (3 - number * var1 * var1) */ + + /* 1st iteration */ + + temp = ((q63_t) var1 * var1) >> 28; + temp = ((q63_t) number * temp) >> 31; + temp = 0x30000000 - temp; + var1 = ((q63_t) var1 * temp) >> 29; + + + /* 2nd iteration */ + temp = ((q63_t) var1 * var1) >> 28; + temp = ((q63_t) number * temp) >> 31; + temp = 0x30000000 - temp; + var1 = ((q63_t) var1 * temp) >> 29; + + /* 3rd iteration */ + temp = ((q63_t) var1 * var1) >> 28; + temp = ((q63_t) number * temp) >> 31; + temp = 0x30000000 - temp; + var1 = ((q63_t) var1 * temp) >> 29; + + /* Multiply the inverse square root with the original value */ + var1 = ((q31_t) (((q63_t) number * var1) >> 28)); + + /* Shift the output down accordingly */ + if ((signBits1 % 2) == 0) + { + var1 = var1 >> (signBits1 / 2); + } + else + { + var1 = var1 >> ((signBits1 - 1) / 2); + } + *pOut = var1; + + return (ARM_MATH_SUCCESS); + } + /* If the number is a negative number then store zero as its square root value */ + else + { + *pOut = 0; + + if (number==0) + { + return (ARM_MATH_SUCCESS); + } + else + { + return (ARM_MATH_ARGUMENT_ERROR); + } + } +} + +/** + @} end of SQRT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f16.c new file mode 100755 index 0000000..410e922 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f16.c @@ -0,0 +1,98 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_f16.c + * Description: Fast vectorized log + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +#include "arm_common_tables.h" + +#include "arm_vec_math_f16.h" + +/** + @addtogroup vexp + @{ + */ + +/** + @brief Floating-point vector of exp values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ +ARM_DSP_ATTRIBUTE void arm_vexp_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + + f16x8_t src; + f16x8_t dst; + + blkCnt = blockSize >> 3; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vexpq_f16(src); + vst1q(pDst, dst); + + pSrc += 8; + pDst += 8; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 7; +#else + blkCnt = blockSize; +#endif + + while (blkCnt > 0U) + { + /* C = log(A) */ + + /* Calculate log and store result in destination buffer. */ + *pDst++ = (_Float16)expf((float32_t)*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ + +/** + @} end of vexp group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f32.c new file mode 100755 index 0000000..207b96e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f32.c @@ -0,0 +1,125 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_f32.c + * Description: Fast vectorized log + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +#if ((defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE)) || defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) +#include "arm_vec_math.h" +#endif + +/** + @ingroup groupFastMath + */ + +/** + @defgroup vexp Vector Exponential + + Compute the exp values of a vector of samples. +*/ + +/** + @addtogroup vexp + @{ + */ + +/** + @brief Floating-point vector of exp values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ +ARM_DSP_ATTRIBUTE void arm_vexp_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + f32x4_t src; + f32x4_t dst; + + blkCnt = blockSize >> 2; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vexpq_f32(src); + vst1q(pDst, dst); + + pSrc += 4; + pDst += 4; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 3; +#else +#if defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) + f32x4_t src; + f32x4_t dst; + + blkCnt = blockSize >> 2; + + while (blkCnt > 0U) + { + src = vld1q_f32(pSrc); + dst = vexpq_f32(src); + vst1q_f32(pDst, dst); + + pSrc += 4; + pDst += 4; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 3; +#else + blkCnt = blockSize; +#endif +#endif + + while (blkCnt > 0U) + { + /* C = log(A) */ + + /* Calculate log and store result in destination buffer. */ + *pDst++ = expf(*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} + +/** + @} end of vexp group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f64.c new file mode 100755 index 0000000..dea11fc --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vexp_f64.c @@ -0,0 +1,56 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_f64.c + * Description: Fast vectorized log + * + * $Date: 10 August 2022 + * $Revision: V1.10.1 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + + +ARM_DSP_ATTRIBUTE void arm_vexp_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + + blkCnt = blockSize; + + while (blkCnt > 0U) + { + /* C = log(A) */ + + + /* Calculate log and store result in destination buffer. */ + *pDst++ = exp(*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vinverse_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vinverse_f16.c new file mode 100755 index 0000000..6f29ced --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vinverse_f16.c @@ -0,0 +1,82 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vinverse_f16.c + * Description: Fast vectorized inverse + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +#include "arm_common_tables.h" + +#include "arm_vec_math_f16.h" + +ARM_DSP_ATTRIBUTE void arm_vinverse_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + + f16x8_t src; + f16x8_t dst; + + blkCnt = blockSize >> 3; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vrecip_hiprec_f16(src); + vst1q(pDst, dst); + + pSrc += 8; + pDst += 8; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 7; +#else + blkCnt = blockSize; +#endif + + while (blkCnt > 0U) + { + + *pDst++ = 1.0f16 / (_Float16)*pSrc++; + + /* Decrement loop counter */ + blkCnt--; + } +} + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f16.c new file mode 100755 index 0000000..01a1870 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f16.c @@ -0,0 +1,224 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_f16.c + * Description: Fast vectorized log + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions_f16.h" +#include "dsp/support_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/* Degree of the polynomial approximation */ +#define NB_DEG_LOGF16 3 + +/* +Related to the Log2 of the number of approximations. +For instance, with 3 there are 1 + 2^3 polynomials +*/ +#define NB_DIV_LOGF16 3 + +/* Length of the LUT table */ +#define NB_LUT_LOGF16 (NB_DEG_LOGF16+1)*(1 + (1< 1000][[2, 1]], {i, 1, 2, (1.0/2^nb)}]; +coefs = Chop@Flatten[CoefficientList[lut, x]]; + +*/ +static float16_t lut_logf16[NB_LUT_LOGF16]={ + 0,(float16_t)0.125,(float16_t)-0.00781197,(float16_t)0.00063974,(float16_t)0.117783,(float16_t) + 0.111111,(float16_t)-0.00617212,(float16_t)0.000447935,(float16_t)0.223144,(float16_t) + 0.1,(float16_t)-0.00499952,(float16_t)0.000327193,(float16_t)0.318454,(float16_t)0.0909091,(float16_t) + -0.00413191,(float16_t)0.000246234,(float16_t)0.405465,(float16_t)0.0833333,(float16_t) + -0.00347199,(float16_t)0.000189928,(float16_t)0.485508,(float16_t)0.0769231,(float16_t) + -0.00295841,(float16_t)0.00014956,(float16_t)0.559616,(float16_t)0.0714286,(float16_t) + -0.0025509,(float16_t)0.000119868,(float16_t)0.628609,(float16_t)0.0666667,(float16_t) + -0.00222213,(float16_t)0.0000975436,(float16_t)0.693147,(float16_t) + 0.0625,(float16_t)-0.00195305,(float16_t)0.0000804357}; + + +static float16_t logf16_scalar(float16_t x) +{ + int16_t i = arm_typecast_s16_f16(x); + + int32_t vecExpUnBiased = (i >> 10) - 15; + i = i - (vecExpUnBiased << 10); + float16_t vecTmpFlt1 = arm_typecast_f16_s16(i); + + float16_t *lut; + int n; + float16_t tmp,v; + + tmp = ((_Float16)vecTmpFlt1 - 1.0f16) * (1 << NB_DIV_LOGF16); + n = (int)floor((double)tmp); + v = (_Float16)tmp - (_Float16)n; + + lut = lut_logf16 + n * (1+NB_DEG_LOGF16); + + float16_t res = lut[NB_DEG_LOGF16-1]; + for(int j=NB_DEG_LOGF16-2; j >=0 ; j--) + { + res = (_Float16)lut[j] + (_Float16)v * (_Float16)res; + } + + res = (_Float16)res + 0.693147f16 * (_Float16)vecExpUnBiased; + + + return(res); +} + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_common_tables.h" +#include "arm_vec_math_f16.h" + + +static float16x8_t vlogq_lut_f16(float16x8_t vecIn) +{ + int16x8_t i = vreinterpretq_s16_f16(vecIn); + + int16x8_t vecExpUnBiased = vsubq_n_s16(vshrq_n_s16(i,10), 15); + i = vsubq_s16(i,vshlq_n_s16(vecExpUnBiased,10)); + float16x8_t vecTmpFlt1 = vreinterpretq_f16_s16(i); + + + float16x8_t lutV; + int16x8_t n; + int16x8_t offset; + + float16x8_t tmp,v,res; + + tmp = vmulq_n_f16(vsubq_n_f16(vecTmpFlt1,1.0f16),(_Float16)(1 << NB_DIV_LOGF16)); + + n = vcvtq_s16_f16(tmp); + v = vsubq_f16(tmp,vcvtq_f16_s16(n)); + + + offset = vmulq_n_s16(n,(1+NB_DEG_LOGF16)); + offset = vaddq_n_s16(offset,NB_DEG_LOGF16-1); + + res = vldrhq_gather_shifted_offset_f16(lut_logf16,(uint16x8_t)offset); + offset = vsubq_n_s16(offset,1); + + for(int j=NB_DEG_LOGF16-2; j >=0 ; j--) + { + lutV = vldrhq_gather_shifted_offset_f16(lut_logf16,(uint16x8_t)offset); + res = vfmaq_f16(lutV,v,res); + offset = vsubq_n_s16(offset,1); + + } + + res = vfmaq_n_f16(res,vcvtq_f16_s16(vecExpUnBiased),0.693147f16); + + + return(res); + +} + +#endif + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup vlog + @{ + */ + +/** + @brief Floating-point vector of log values. + @param[in] pSrc points to the input vector + @param[out] pDst points to the output vector + @param[in] blockSize number of samples in each vector + */ + + +ARM_DSP_ATTRIBUTE void arm_vlog_f16( + const float16_t * pSrc, + float16_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + f16x8_t src; + f16x8_t dst; + + blkCnt = blockSize >> 3; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vlogq_lut_f16(src); + vst1q(pDst, dst); + + pSrc += 8; + pDst += 8; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 7; +#else + blkCnt = blockSize; +#endif + + while (blkCnt > 0U) + { + /* C = log(A) */ + + /* Calculate log and store result in destination buffer. */ + *pDst++ = logf16_scalar(*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} + + + +/** + @} end of vlog group + */ + + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f32.c new file mode 100755 index 0000000..00622b9 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f32.c @@ -0,0 +1,122 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_f32.c + * Description: Fast vectorized log + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + + +/** + @ingroup groupFastMath + */ + + +/** + @defgroup vlog Vector Log + + Compute the log values of a vector of samples. + + */ + +/** + @addtogroup vlog + @{ + */ + +#if ((defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE)) || defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) +#include "arm_vec_math.h" +#endif + +ARM_DSP_ATTRIBUTE void arm_vlog_f32( + const float32_t * pSrc, + float32_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + +#if (defined(ARM_MATH_MVEF) || defined(ARM_MATH_HELIUM)) && !defined(ARM_MATH_AUTOVECTORIZE) + f32x4_t src; + f32x4_t dst; + + blkCnt = blockSize >> 2; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vlogq_f32(src); + vst1q(pDst, dst); + + pSrc += 4; + pDst += 4; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 3; +#else +#if defined(ARM_MATH_NEON) || defined(ARM_MATH_NEON_EXPERIMENTAL) + f32x4_t src; + f32x4_t dst; + + blkCnt = blockSize >> 2; + + while (blkCnt > 0U) + { + src = vld1q_f32(pSrc); + dst = vlogq_f32(src); + vst1q_f32(pDst, dst); + + pSrc += 4; + pDst += 4; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 3; +#else + blkCnt = blockSize; +#endif +#endif + + while (blkCnt > 0U) + { + /* C = log(A) */ + + /* Calculate log and store result in destination buffer. */ + *pDst++ = logf(*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} + +/** + @} end of vlog group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f64.c new file mode 100755 index 0000000..9f307a0 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_f64.c @@ -0,0 +1,55 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_f64.c + * Description: Fast vectorized log + * + * $Date: 10 August 2022 + * $Revision: V1.10.1 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" +#include "arm_common_tables.h" + +ARM_DSP_ATTRIBUTE void arm_vlog_f64( + const float64_t * pSrc, + float64_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; + + blkCnt = blockSize; + + + while (blkCnt > 0U) + { + /* C = log(A) */ + + /* Calculate log and store result in destination buffer. */ + *pDst++ = log(*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_q15.c new file mode 100755 index 0000000..6ead560 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_q15.c @@ -0,0 +1,265 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_q15 + * Description: Q15 vector log + * + * $Date: 19 July 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + +#include "dsp/fast_math_functions.h" + + +#define LOG_Q15_ACCURACY 15 + +/* Bit to represent the normalization factor + It is Ceiling[Log2[LOG_Q15_ACCURACY]] of the previous value. + The Log2 algorithm is assuming that the value x is + 1 <= x < 2. + + But input value could be as small a 2^-LOG_Q15_ACCURACY + which would give an integer part of -15. +*/ +#define LOG_Q15_INTEGER_PART 4 + +/* 2.0 in q14 */ +#define LOQ_Q15_THRESHOLD (1u << LOG_Q15_ACCURACY) + +/* HALF */ +#define LOQ_Q15_Q16_HALF LOQ_Q15_THRESHOLD +#define LOQ_Q15_Q14_HALF (LOQ_Q15_Q16_HALF >> 2) + + +/* 1.0 / Log2[Exp[1]] in q15 */ +#define LOG_Q15_INVLOG2EXP 0x58b9u + + +/* Clay Turner algorithm */ +static uint16_t arm_scalar_log_q15(uint16_t src) +{ + int i; + + int16_t c = __CLZ(src)-16; + int16_t normalization=0; + + /* 0.5 in q11 */ + uint16_t inc = LOQ_Q15_Q16_HALF >> (LOG_Q15_INTEGER_PART + 1); + + /* Will compute y = log2(x) for 1 <= x < 2.0 */ + uint16_t x; + + /* q11 */ + uint16_t y=0; + + /* q11 */ + int16_t tmp; + + + /* Normalize and convert to q14 format */ + x = src; + if ((c-1) < 0) + { + x = x >> (1-c); + } + else + { + x = x << (c-1); + } + normalization = c; + + + + /* Compute the Log2. Result is in q11 instead of q16 + because we know 0 <= y < 1.0 but + we want a result allowing to do a + product on int16 rather than having to go + through int32 + */ + for(i = 0; i < LOG_Q15_ACCURACY ; i++) + { + x = (((int32_t)x*x)) >> (LOG_Q15_ACCURACY - 1); + + if (x >= LOQ_Q15_THRESHOLD) + { + y += inc ; + x = x >> 1; + } + inc = inc >> 1; + } + + + /* + Convert the Log2 to Log and apply normalization. + We compute (y - normalisation) * (1 / Log2[e]). + + */ + + /* q11 */ + //tmp = y - ((int32_t)normalization << (LOG_Q15_ACCURACY + 1)); + tmp = (int16_t)y - (normalization << (LOG_Q15_ACCURACY - LOG_Q15_INTEGER_PART)); + + /* q4.11 */ + y = ((int32_t)tmp * LOG_Q15_INVLOG2EXP) >> 15; + + return(y); + +} + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + +static q15x8_t vlogq_q15(q15x8_t src) +{ + + int i; + + int16x8_t c = vclzq_s16(src); + int16x8_t normalization = c; + + + /* 0.5 in q11 */ + uint16_t inc = LOQ_Q15_Q16_HALF >> (LOG_Q15_INTEGER_PART + 1); + + /* Will compute y = log2(x) for 1 <= x < 2.0 */ + uint16x8_t x; + + + /* q11 */ + uint16x8_t y = vdupq_n_u16(0); + + + /* q11 */ + int16x8_t vtmp; + + + mve_pred16_t p; + + /* Normalize and convert to q14 format */ + + + vtmp = vsubq_n_s16(c,1); + x = vshlq_u16((uint16x8_t)src,vtmp); + + + /* Compute the Log2. Result is in q11 instead of q16 + because we know 0 <= y < 1.0 but + we want a result allowing to do a + product on int16 rather than having to go + through int32 + */ + for(i = 0; i < LOG_Q15_ACCURACY ; i++) + { + x = vmulhq_u16(x,x); + x = vshlq_n_u16(x,2); + + + p = vcmphiq_u16(x,vdupq_n_u16(LOQ_Q15_THRESHOLD)); + y = vaddq_m_n_u16(y, y,inc,p); + x = vshrq_m_n_u16(x,x,1,p); + + inc = inc >> 1; + } + + + /* + Convert the Log2 to Log and apply normalization. + We compute (y - normalisation) * (1 / Log2[e]). + + */ + + /* q11 */ + // tmp = (int16_t)y - (normalization << (LOG_Q15_ACCURACY - LOG_Q15_INTEGER_PART)); + vtmp = vshlq_n_s16(normalization,LOG_Q15_ACCURACY - LOG_Q15_INTEGER_PART); + vtmp = vsubq_s16((int16x8_t)y,vtmp); + + + + /* q4.11 */ + // y = ((int32_t)tmp * LOG_Q15_INVLOG2EXP) >> 15; + vtmp = vqdmulhq_n_s16(vtmp,LOG_Q15_INVLOG2EXP); + + return(vtmp); +} +#endif + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup vlog + @{ + */ + +/** + @brief q15 vector of log values. + @param[in] pSrc points to the input vector in q15 + @param[out] pDst points to the output vector in q4.11 + @param[in] blockSize number of samples in each vector + */ + +ARM_DSP_ATTRIBUTE void arm_vlog_q15( + const q15_t * pSrc, + q15_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counters */ + + #if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + q15x8_t src; + q15x8_t dst; + + blkCnt = blockSize >> 3; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vlogq_q15(src); + vst1q(pDst, dst); + + pSrc += 8; + pDst += 8; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 7; + #else + blkCnt = blockSize; + #endif + + while (blkCnt > 0U) + { + *pDst++ = arm_scalar_log_q15(*pSrc++); + + /* Decrement loop counter */ + blkCnt--; + } +} + +/** + @} end of vlog group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_q31.c new file mode 100755 index 0000000..9af99fc --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/FastMathFunctions/arm_vlog_q31.c @@ -0,0 +1,259 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_vlog_q31 + * Description: Q31 vector log + * + * $Date: 19 July 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/fast_math_functions.h" + +#define LOG_Q31_ACCURACY 31 + +/* Bit to represent the normalization factor + It is Ceiling[Log2[LOG_Q31_ACCURACY]] of the previous value. + The Log2 algorithm is assuming that the value x is + 1 <= x < 2. + + But input value could be as small a 2^-LOG_Q31_ACCURACY + which would give an integer part of -31. +*/ +#define LOG_Q31_INTEGER_PART 5 + +/* 2.0 in Q30 */ +#define LOQ_Q31_THRESHOLD (1u << LOG_Q31_ACCURACY) + +/* HALF */ +#define LOQ_Q31_Q32_HALF LOQ_Q31_THRESHOLD +#define LOQ_Q31_Q30_HALF (LOQ_Q31_Q32_HALF >> 2) + + +/* 1.0 / Log2[Exp[1]] in Q31 */ +#define LOG_Q31_INVLOG2EXP 0x58b90bfbuL + +/* Clay Turner algorithm */ +static uint32_t arm_scalar_log_q31(uint32_t src) +{ + int32_t i; + + int32_t c = __CLZ(src); + int32_t normalization=0; + + /* 0.5 in q26 */ + uint32_t inc = LOQ_Q31_Q32_HALF >> (LOG_Q31_INTEGER_PART + 1); + + /* Will compute y = log2(x) for 1 <= x < 2.0 */ + uint32_t x; + + /* q26 */ + uint32_t y=0; + + /* q26 */ + int32_t tmp; + + + /* Normalize and convert to q30 format */ + x = src; + if ((c-1) < 0) + { + x = x >> (1-c); + } + else + { + x = x << (c-1); + } + normalization = c; + + /* Compute the Log2. Result is in q26 + because we know 0 <= y < 1.0 but + do not want to use q32 to allow + following computation with less instructions. + */ + for(i = 0; i < LOG_Q31_ACCURACY ; i++) + { + x = ((int64_t)x*x) >> (LOG_Q31_ACCURACY - 1); + + if (x >= LOQ_Q31_THRESHOLD) + { + y += inc ; + x = x >> 1; + } + inc = inc >> 1; + } + + /* + Convert the Log2 to Log and apply normalization. + We compute (y - normalisation) * (1 / Log2[e]). + + */ + + /* q26 */ + tmp = (int32_t)y - (normalization << (LOG_Q31_ACCURACY - LOG_Q31_INTEGER_PART)); + + + /* q5.26 */ + y = ((int64_t)tmp * LOG_Q31_INVLOG2EXP) >> 31; + + + + return(y); + +} + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + +static q31x4_t vlogq_q31(q31x4_t src) +{ + + int32_t i; + + int32x4_t c = vclzq_s32(src); + int32x4_t normalization = c; + + + /* 0.5 in q11 */ + uint32_t inc = LOQ_Q31_Q32_HALF >> (LOG_Q31_INTEGER_PART + 1); + + /* Will compute y = log2(x) for 1 <= x < 2.0 */ + uint32x4_t x; + + + /* q11 */ + uint32x4_t y = vdupq_n_u32(0); + + + /* q11 */ + int32x4_t vtmp; + + + mve_pred16_t p; + + /* Normalize and convert to q14 format */ + + + vtmp = vsubq_n_s32(c,1); + x = vshlq_u32((uint32x4_t)src,vtmp); + + + /* Compute the Log2. Result is in Q26 + because we know 0 <= y < 1.0 but + do not want to use Q32 to allow + following computation with less instructions. + */ + for(i = 0; i < LOG_Q31_ACCURACY ; i++) + { + x = vmulhq_u32(x,x); + x = vshlq_n_u32(x,2); + + + p = vcmphiq_u32(x,vdupq_n_u32(LOQ_Q31_THRESHOLD)); + y = vaddq_m_n_u32(y, y,inc,p); + x = vshrq_m_n_u32(x,x,1,p); + + inc = inc >> 1; + } + + + /* + Convert the Log2 to Log and apply normalization. + We compute (y - normalisation) * (1 / Log2[e]). + + */ + + /* q11 */ + // tmp = (int16_t)y - (normalization << (LOG_Q15_ACCURACY - LOG_Q15_INTEGER_PART)); + vtmp = vshlq_n_s32(normalization,LOG_Q31_ACCURACY - LOG_Q31_INTEGER_PART); + vtmp = vsubq_s32((int32x4_t)y,vtmp); + + + + /* q4.11 */ + // y = ((int32_t)tmp * LOG_Q15_INVLOG2EXP) >> 15; + vtmp = vqdmulhq_n_s32(vtmp,LOG_Q31_INVLOG2EXP); + + return(vtmp); +} +#endif + +/** + @ingroup groupFastMath + */ + +/** + @addtogroup vlog + @{ + */ + +/** + @brief q31 vector of log values. + @param[in] pSrc points to the input vector in q31 + @param[out] pDst points to the output vector q5.26 + @param[in] blockSize number of samples in each vector + */ +ARM_DSP_ATTRIBUTE void arm_vlog_q31( + const q31_t * pSrc, + q31_t * pDst, + uint32_t blockSize) +{ + uint32_t blkCnt; /* loop counters */ + + #if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + + q31x4_t src; + q31x4_t dst; + + blkCnt = blockSize >> 2; + + while (blkCnt > 0U) + { + src = vld1q(pSrc); + dst = vlogq_q31(src); + vst1q(pDst, dst); + + pSrc += 4; + pDst += 4; + /* Decrement loop counter */ + blkCnt--; + } + + blkCnt = blockSize & 3; + #else + blkCnt = blockSize; + #endif + + while (blkCnt > 0U) + { + *pDst++=arm_scalar_log_q31(*pSrc++); + + blkCnt--; + } + +} + +/** + @} end of vlog group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal.c new file mode 100755 index 0000000..7ba683f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal.c @@ -0,0 +1,242 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_bitreversal.c + * Description: Bitreversal functions + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +void arm_bitreversal_f32( + float32_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + +/** + @brief In-place floating-point bit reversal function. + @param[in,out] pSrc points to in-place floating-point data buffer + @param[in] fftSize length of FFT + @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table + @param[in] pBitRevTab points to bit reversal table + */ + +ARM_DSP_ATTRIBUTE void arm_bitreversal_f32( + float32_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab) +{ + uint16_t fftLenBy2, fftLenBy2p1; + uint16_t i, j; + float32_t in; + + /* Initializations */ + j = 0U; + fftLenBy2 = fftSize >> 1U; + fftLenBy2p1 = (fftSize >> 1U) + 1U; + + /* Bit Reversal Implementation */ + for (i = 0U; i <= (fftLenBy2 - 2U); i += 2U) + { + if (i < j) + { + /* pSrc[i] <-> pSrc[j]; */ + in = pSrc[2U * i]; + pSrc[2U * i] = pSrc[2U * j]; + pSrc[2U * j] = in; + + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[(2U * i) + 1U]; + pSrc[(2U * i) + 1U] = pSrc[(2U * j) + 1U]; + pSrc[(2U * j) + 1U] = in; + + /* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */ + in = pSrc[2U * (i + fftLenBy2p1)]; + pSrc[2U * (i + fftLenBy2p1)] = pSrc[2U * (j + fftLenBy2p1)]; + pSrc[2U * (j + fftLenBy2p1)] = in; + + /* pSrc[i+fftLenBy2p1+1U] <-> pSrc[j+fftLenBy2p1+1U] */ + in = pSrc[(2U * (i + fftLenBy2p1)) + 1U]; + pSrc[(2U * (i + fftLenBy2p1)) + 1U] = + pSrc[(2U * (j + fftLenBy2p1)) + 1U]; + pSrc[(2U * (j + fftLenBy2p1)) + 1U] = in; + + } + + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[2U * (i + 1U)]; + pSrc[2U * (i + 1U)] = pSrc[2U * (j + fftLenBy2)]; + pSrc[2U * (j + fftLenBy2)] = in; + + /* pSrc[i+2U] <-> pSrc[j+2U] */ + in = pSrc[(2U * (i + 1U)) + 1U]; + pSrc[(2U * (i + 1U)) + 1U] = pSrc[(2U * (j + fftLenBy2)) + 1U]; + pSrc[(2U * (j + fftLenBy2)) + 1U] = in; + + /* Reading the index for the bit reversal */ + j = *pBitRevTab; + + /* Updating the bit reversal index depending on the fft length */ + pBitRevTab += bitRevFactor; + } +} + +void arm_bitreversal_q31( + q31_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + +/** + @brief In-place Q31 bit reversal function. + @param[in,out] pSrc points to in-place Q31 data buffer. + @param[in] fftLen length of FFT. + @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table + @param[in] pBitRevTab points to bit reversal table +*/ + +ARM_DSP_ATTRIBUTE void arm_bitreversal_q31( + q31_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab) +{ + uint32_t fftLenBy2, fftLenBy2p1, i, j; + q31_t in; + + /* Initializations */ + j = 0U; + fftLenBy2 = fftLen / 2U; + fftLenBy2p1 = (fftLen / 2U) + 1U; + + /* Bit Reversal Implementation */ + for (i = 0U; i <= (fftLenBy2 - 2U); i += 2U) + { + if (i < j) + { + /* pSrc[i] <-> pSrc[j]; */ + in = pSrc[2U * i]; + pSrc[2U * i] = pSrc[2U * j]; + pSrc[2U * j] = in; + + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[(2U * i) + 1U]; + pSrc[(2U * i) + 1U] = pSrc[(2U * j) + 1U]; + pSrc[(2U * j) + 1U] = in; + + /* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */ + in = pSrc[2U * (i + fftLenBy2p1)]; + pSrc[2U * (i + fftLenBy2p1)] = pSrc[2U * (j + fftLenBy2p1)]; + pSrc[2U * (j + fftLenBy2p1)] = in; + + /* pSrc[i+fftLenBy2p1+1U] <-> pSrc[j+fftLenBy2p1+1U] */ + in = pSrc[(2U * (i + fftLenBy2p1)) + 1U]; + pSrc[(2U * (i + fftLenBy2p1)) + 1U] = + pSrc[(2U * (j + fftLenBy2p1)) + 1U]; + pSrc[(2U * (j + fftLenBy2p1)) + 1U] = in; + + } + + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[2U * (i + 1U)]; + pSrc[2U * (i + 1U)] = pSrc[2U * (j + fftLenBy2)]; + pSrc[2U * (j + fftLenBy2)] = in; + + /* pSrc[i+2U] <-> pSrc[j+2U] */ + in = pSrc[(2U * (i + 1U)) + 1U]; + pSrc[(2U * (i + 1U)) + 1U] = pSrc[(2U * (j + fftLenBy2)) + 1U]; + pSrc[(2U * (j + fftLenBy2)) + 1U] = in; + + /* Reading the index for the bit reversal */ + j = *pBitRevTab; + + /* Updating the bit reversal index depending on the fft length */ + pBitRevTab += bitRevFactor; + } +} + +void arm_bitreversal_q15( + q15_t * pSrc16, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + + +/** + @brief In-place Q15 bit reversal function. + @param[in,out] pSrc16 points to in-place Q15 data buffer + @param[in] fftLen length of FFT + @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table + @param[in] pBitRevTab points to bit reversal table +*/ + +ARM_DSP_ATTRIBUTE void arm_bitreversal_q15( + q15_t * pSrc16, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab) +{ + q31_t *pSrc = (q31_t *) pSrc16; + q31_t in; + uint32_t fftLenBy2, fftLenBy2p1; + uint32_t i, j; + + /* Initializations */ + j = 0U; + fftLenBy2 = fftLen / 2U; + fftLenBy2p1 = (fftLen / 2U) + 1U; + + /* Bit Reversal Implementation */ + for (i = 0U; i <= (fftLenBy2 - 2U); i += 2U) + { + if (i < j) + { + /* pSrc[i] <-> pSrc[j]; */ + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[i]; + pSrc[i] = pSrc[j]; + pSrc[j] = in; + + /* pSrc[i + fftLenBy2p1] <-> pSrc[j + fftLenBy2p1]; */ + /* pSrc[i + fftLenBy2p1+1U] <-> pSrc[j + fftLenBy2p1+1U] */ + in = pSrc[i + fftLenBy2p1]; + pSrc[i + fftLenBy2p1] = pSrc[j + fftLenBy2p1]; + pSrc[j + fftLenBy2p1] = in; + } + + /* pSrc[i+1U] <-> pSrc[j+fftLenBy2]; */ + /* pSrc[i+2] <-> pSrc[j+fftLenBy2+1U] */ + in = pSrc[i + 1U]; + pSrc[i + 1U] = pSrc[j + fftLenBy2]; + pSrc[j + fftLenBy2] = in; + + /* Reading the index for the bit reversal */ + j = *pBitRevTab; + + /* Updating the bit reversal index depending on the fft length */ + pBitRevTab += bitRevFactor; + } +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal2.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal2.c new file mode 100755 index 0000000..fe63e97 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal2.c @@ -0,0 +1,148 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_bitreversal2.c + * Description: Bitreversal functions + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2019 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +void arm_bitreversal_64( + uint64_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab); + + +/** + @brief In-place 64 bit reversal function. + @param[in,out] pSrc points to in-place buffer of unknown 64-bit data type + @param[in] bitRevLen bit reversal table length + @param[in] pBitRevTab points to bit reversal table +*/ + +ARM_DSP_ATTRIBUTE void arm_bitreversal_64( + uint64_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab) +{ + uint64_t a, b, tmp; + uint32_t i; + + for (i = 0; i < bitRevLen; ) + { + a = pBitRevTab[i ] >> 2; + b = pBitRevTab[i + 1] >> 2; + + //real + tmp = pSrc[a]; + pSrc[a] = pSrc[b]; + pSrc[b] = tmp; + + //complex + tmp = pSrc[a+1]; + pSrc[a+1] = pSrc[b+1]; + pSrc[b+1] = tmp; + + i += 2; + } +} + +void arm_bitreversal_32( + uint32_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab); + +/** + @brief In-place 32 bit reversal function. + @param[in,out] pSrc points to in-place buffer of unknown 32-bit data type + @param[in] bitRevLen bit reversal table length + @param[in] pBitRevTab points to bit reversal table +*/ + +ARM_DSP_ATTRIBUTE void arm_bitreversal_32( + uint32_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab) +{ + uint32_t a, b, i, tmp; + + for (i = 0; i < bitRevLen; ) + { + a = pBitRevTab[i ] >> 2; + b = pBitRevTab[i + 1] >> 2; + + //real + tmp = pSrc[a]; + pSrc[a] = pSrc[b]; + pSrc[b] = tmp; + + //complex + tmp = pSrc[a+1]; + pSrc[a+1] = pSrc[b+1]; + pSrc[b+1] = tmp; + + i += 2; + } +} + +void arm_bitreversal_16( + uint16_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab); + + +/** + @brief In-place 16 bit reversal function. + @param[in,out] pSrc points to in-place buffer of unknown 16-bit data type + @param[in] bitRevLen bit reversal table length + @param[in] pBitRevTab points to bit reversal table +*/ + +ARM_DSP_ATTRIBUTE void arm_bitreversal_16( + uint16_t *pSrc, + const uint16_t bitRevLen, + const uint16_t *pBitRevTab) +{ + uint16_t a, b, tmp; + uint32_t i; + + for (i = 0; i < bitRevLen; ) + { + a = pBitRevTab[i ] >> 2; + b = pBitRevTab[i + 1] >> 2; + + //real + tmp = pSrc[a]; + pSrc[a] = pSrc[b]; + pSrc[b] = tmp; + + //complex + tmp = pSrc[a+1]; + pSrc[a+1] = pSrc[b+1]; + pSrc[b+1] = tmp; + + i += 2; + } +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal_f16.c new file mode 100755 index 0000000..80c5880 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_bitreversal_f16.c @@ -0,0 +1,112 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_bitreversal_f16.c + * Description: Bitreversal functions + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" + + + +/* +* @brief In-place bit reversal function. +* @param[in, out] *pSrc points to the in-place buffer of floating-point data type. +* @param[in] fftSize length of the FFT. +* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table. +* @param[in] *pBitRevTab points to the bit reversal table. +*/ + +#if defined(ARM_FLOAT16_SUPPORTED) + +void arm_bitreversal_f16( +float16_t * pSrc, +uint16_t fftSize, +uint16_t bitRevFactor, +const uint16_t * pBitRevTab); + +ARM_DSP_ATTRIBUTE void arm_bitreversal_f16( +float16_t * pSrc, +uint16_t fftSize, +uint16_t bitRevFactor, +const uint16_t * pBitRevTab) +{ + uint16_t fftLenBy2, fftLenBy2p1; + uint16_t i, j; + float16_t in; + + /* Initializations */ + j = 0U; + fftLenBy2 = fftSize >> 1U; + fftLenBy2p1 = (fftSize >> 1U) + 1U; + + /* Bit Reversal Implementation */ + for (i = 0U; i <= (fftLenBy2 - 2U); i += 2U) + { + if (i < j) + { + /* pSrc[i] <-> pSrc[j]; */ + in = pSrc[2U * i]; + pSrc[2U * i] = pSrc[2U * j]; + pSrc[2U * j] = in; + + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[(2U * i) + 1U]; + pSrc[(2U * i) + 1U] = pSrc[(2U * j) + 1U]; + pSrc[(2U * j) + 1U] = in; + + /* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */ + in = pSrc[2U * (i + fftLenBy2p1)]; + pSrc[2U * (i + fftLenBy2p1)] = pSrc[2U * (j + fftLenBy2p1)]; + pSrc[2U * (j + fftLenBy2p1)] = in; + + /* pSrc[i+fftLenBy2p1+1U] <-> pSrc[j+fftLenBy2p1+1U] */ + in = pSrc[(2U * (i + fftLenBy2p1)) + 1U]; + pSrc[(2U * (i + fftLenBy2p1)) + 1U] = + pSrc[(2U * (j + fftLenBy2p1)) + 1U]; + pSrc[(2U * (j + fftLenBy2p1)) + 1U] = in; + + } + + /* pSrc[i+1U] <-> pSrc[j+1U] */ + in = pSrc[2U * (i + 1U)]; + pSrc[2U * (i + 1U)] = pSrc[2U * (j + fftLenBy2)]; + pSrc[2U * (j + fftLenBy2)] = in; + + /* pSrc[i+2U] <-> pSrc[j+2U] */ + in = pSrc[(2U * (i + 1U)) + 1U]; + pSrc[(2U * (i + 1U)) + 1U] = pSrc[(2U * (j + fftLenBy2)) + 1U]; + pSrc[(2U * (j + fftLenBy2)) + 1U] = in; + + /* Reading the index for the bit reversal */ + j = *pBitRevTab; + + /* Updating the bit reversal index depending on the fft length */ + pBitRevTab += bitRevFactor; + } +} +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_f16.c new file mode 100755 index 0000000..2ddcff8 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_f16.c @@ -0,0 +1,753 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_f32.c + * Description: Combined Radix Decimation in Frequency CFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" +#include "arm_common_tables_f16.h" + + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" +#include "arm_vec_fft.h" +#include "arm_mve_tables_f16.h" + + +static float16_t arm_inverse_fft_length_f16(uint16_t fftLen) +{ + float16_t retValue=1.0; + + switch (fftLen) + { + + case 4096U: + retValue = (float16_t)0.000244140625f; + break; + + case 2048U: + retValue = (float16_t)0.00048828125f; + break; + + case 1024U: + retValue = (float16_t)0.0009765625f; + break; + + case 512U: + retValue = (float16_t)0.001953125f; + break; + + case 256U: + retValue = (float16_t)0.00390625f; + break; + + case 128U: + retValue = (float16_t)0.0078125f; + break; + + case 64U: + retValue = (float16_t)0.015625f; + break; + + case 32U: + retValue = (float16_t)0.03125f; + break; + + case 16U: + retValue = (float16_t)0.0625f; + break; + + + default: + break; + } + return(retValue); +} + + +static void _arm_radix4_butterfly_f16_mve(const arm_cfft_instance_f16 * S,float16_t * pSrc, uint32_t fftLen) +{ + f16x8_t vecTmp0, vecTmp1; + f16x8_t vecSum0, vecDiff0, vecSum1, vecDiff1; + f16x8_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = + { ( 0 - 16) * (int32_t)sizeof(float16_t *) + , ( 4 - 16) * (int32_t)sizeof(float16_t *) + , ( 8 - 16) * (int32_t)sizeof(float16_t *) + , (12 - 16) * (int32_t)sizeof(float16_t *)}; + + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + for (int k = fftLen / 4u; k > 1; k >>= 2) + { + float16_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + float16_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + float16_t const *p_rearranged_twiddle_tab_stride3 = + &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + float16_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + float16_t *inA = pBase; + float16_t *inB = inA + n2 * CMPLX_DIM; + float16_t *inC = inB + n2 * CMPLX_DIM; + float16_t *inD = inC + n2 * CMPLX_DIM; + float16_t const *pW1 = p_rearranged_twiddle_tab_stride1; + float16_t const *pW2 = p_rearranged_twiddle_tab_stride2; + float16_t const *pW3 = p_rearranged_twiddle_tab_stride3; + f16x8_t vecW; + + blkCnt = n2 / 4; + /* + * load 2 f16 complex pair + */ + vecA = vldrhq_f16(inA); + vecC = vldrhq_f16(inC); + while (blkCnt > 0U) + { + vecB = vldrhq_f16(inB); + vecD = vldrhq_f16(inD); + + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vecSum0 + vecSum1; + vst1q(inA, vecTmp0); + inA += 8; + + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vecSum0 - vecSum1; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW2); + pW2 += 8; + vecTmp1 = MVE_CMPLX_MULT_FLT_Conj_AxB(vecW, vecTmp0); + vst1q(inB, vecTmp1); + inB += 8; + + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW1); + pW1 +=8; + vecTmp1 = MVE_CMPLX_MULT_FLT_Conj_AxB(vecW, vecTmp0); + vst1q(inC, vecTmp1); + inC += 8; + + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 8; + vecTmp1 = MVE_CMPLX_MULT_FLT_Conj_AxB(vecW, vecTmp0); + vst1q(inD, vecTmp1); + inD += 8; + + vecA = vldrhq_f16(inA); + vecC = vldrhq_f16(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* load scheduling */ + vecA = (f16x8_t)vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 8); + + blkCnt = (fftLen >> 4); + while (blkCnt > 0U) + { + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecB = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 4); + vecD = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 12); + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + + /* pre-load for next iteration */ + vecA = (f16x8_t)vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 8); + + vecTmp0 = vecSum0 + vecSum1; + vstrwq_scatter_base_f32(vecScGathAddr, -64, (f32x4_t)vecTmp0); + + vecTmp0 = vecSum0 - vecSum1; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 4, (f32x4_t)vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 8, (f32x4_t)vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 12, (f32x4_t)vecTmp0); + + blkCnt--; + } + + /* + * End of last stage process + */ +} + +static void arm_cfft_radix4by2_f16_mve(const arm_cfft_instance_f16 * S, float16_t *pSrc, uint32_t fftLen) +{ + float16_t const *pCoefVec; + float16_t const *pCoef = S->pTwiddle; + float16_t *pIn0, *pIn1; + uint32_t n2; + uint32_t blkCnt; + f16x8_t vecIn0, vecIn1, vecSum, vecDiff; + f16x8_t vecCmplxTmp, vecTw; + + + n2 = fftLen >> 1; + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + pCoefVec = pCoef; + + blkCnt = n2 / 4; + while (blkCnt > 0U) + { + vecIn0 = *(f16x8_t *) pIn0; + vecIn1 = *(f16x8_t *) pIn1; + vecTw = vld1q(pCoefVec); + pCoefVec += 8; + + vecSum = vaddq(vecIn0, vecIn1); + vecDiff = vsubq(vecIn0, vecIn1); + + vecCmplxTmp = MVE_CMPLX_MULT_FLT_Conj_AxB(vecTw, vecDiff); + + vst1q(pIn0, vecSum); + pIn0 += 8; + vst1q(pIn1, vecCmplxTmp); + pIn1 += 8; + + blkCnt--; + } + + _arm_radix4_butterfly_f16_mve(S, pSrc, n2); + + _arm_radix4_butterfly_f16_mve(S, pSrc + fftLen, n2); + + pIn0 = pSrc; +} + +static void _arm_radix4_butterfly_inverse_f16_mve(const arm_cfft_instance_f16 * S,float16_t * pSrc, uint32_t fftLen, float16_t onebyfftLen) +{ + f16x8_t vecTmp0, vecTmp1; + f16x8_t vecSum0, vecDiff0, vecSum1, vecDiff1; + f16x8_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + ( 0 - 16) * (int32_t)sizeof(q31_t *), + ( 4 - 16) * (int32_t)sizeof(q31_t *), + ( 8 - 16) * (int32_t)sizeof(q31_t *), + (12 - 16) * (int32_t)sizeof(q31_t *) + }; + + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + for (int k = fftLen / 4; k > 1; k >>= 2) + { + float16_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + float16_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + float16_t const *p_rearranged_twiddle_tab_stride3 = + &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + + float16_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + float16_t *inA = pBase; + float16_t *inB = inA + n2 * CMPLX_DIM; + float16_t *inC = inB + n2 * CMPLX_DIM; + float16_t *inD = inC + n2 * CMPLX_DIM; + float16_t const *pW1 = p_rearranged_twiddle_tab_stride1; + float16_t const *pW2 = p_rearranged_twiddle_tab_stride2; + float16_t const *pW3 = p_rearranged_twiddle_tab_stride3; + f16x8_t vecW; + + blkCnt = n2 / 4; + /* + * load 2 f32 complex pair + */ + vecA = vldrhq_f16(inA); + vecC = vldrhq_f16(inC); + while (blkCnt > 0U) + { + vecB = vldrhq_f16(inB); + vecD = vldrhq_f16(inD); + + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vecSum0 + vecSum1; + vst1q(inA, vecTmp0); + inA += 8; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vecSum0 - vecSum1; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW2); + pW2 += 8; + vecTmp1 = MVE_CMPLX_MULT_FLT_AxB(vecW, vecTmp0); + vst1q(inB, vecTmp1); + inB += 8; + + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW1); + pW1 += 8; + vecTmp1 = MVE_CMPLX_MULT_FLT_AxB(vecW, vecTmp0); + vst1q(inC, vecTmp1); + inC += 8; + + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 8; + vecTmp1 = MVE_CMPLX_MULT_FLT_AxB(vecW, vecTmp0); + vst1q(inD, vecTmp1); + inD += 8; + + vecA = vldrhq_f16(inA); + vecC = vldrhq_f16(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* + * load scheduling + */ + vecA = (f16x8_t)vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 8); + + blkCnt = (fftLen >> 4); + while (blkCnt > 0U) + { + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecB = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 4); + vecD = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 12); + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + + vecA = (f16x8_t)vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = (f16x8_t)vldrwq_gather_base_f32(vecScGathAddr, 8); + + vecTmp0 = vecSum0 + vecSum1; + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64, (f32x4_t)vecTmp0); + + vecTmp0 = vecSum0 - vecSum1; + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 4, (f32x4_t)vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 8, (f32x4_t)vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 12, (f32x4_t)vecTmp0); + + blkCnt--; + } + + /* + * End of last stage process + */ +} + +static void arm_cfft_radix4by2_inverse_f16_mve(const arm_cfft_instance_f16 * S,float16_t *pSrc, uint32_t fftLen) +{ + float16_t const *pCoefVec; + float16_t const *pCoef = S->pTwiddle; + float16_t *pIn0, *pIn1; + uint32_t n2; + float16_t onebyfftLen = arm_inverse_fft_length_f16(fftLen); + uint32_t blkCnt; + f16x8_t vecIn0, vecIn1, vecSum, vecDiff; + f16x8_t vecCmplxTmp, vecTw; + + + n2 = fftLen >> 1; + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + pCoefVec = pCoef; + + blkCnt = n2 / 4; + while (blkCnt > 0U) + { + vecIn0 = *(f16x8_t *) pIn0; + vecIn1 = *(f16x8_t *) pIn1; + vecTw = vld1q(pCoefVec); + pCoefVec += 8; + + vecSum = vaddq(vecIn0, vecIn1); + vecDiff = vsubq(vecIn0, vecIn1); + + vecCmplxTmp = MVE_CMPLX_MULT_FLT_AxB(vecTw, vecDiff); + + vst1q(pIn0, vecSum); + pIn0 += 8; + vst1q(pIn1, vecCmplxTmp); + pIn1 += 8; + + blkCnt--; + } + + _arm_radix4_butterfly_inverse_f16_mve(S, pSrc, n2, onebyfftLen); + + _arm_radix4_butterfly_inverse_f16_mve(S, pSrc + fftLen, n2, onebyfftLen); +} + + +/** + @addtogroup ComplexFFTF16 + @{ + */ + +/** + @brief Processing function for the floating-point complex FFT. + @param[in] S points to an instance of the floating-point CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + +@par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is a temporary buffer. + The bit reverse flag is not more + available in Neon version. + + @code + void arm_cfft_f16( + const arm_cfft_instance_f16 * S, + const float16_t * pIn, + float16_t * pOut, + float16_t * pBuffer, + uint8_t ifftFlag); + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ + + +ARM_DSP_ATTRIBUTE void arm_cfft_f16( + const arm_cfft_instance_f16 * S, + float16_t * pSrc, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t fftLen = S->fftLen; + + if (ifftFlag == 1U) { + + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_inverse_f16_mve(S, pSrc, fftLen, arm_inverse_fft_length_f16(S->fftLen)); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_inverse_f16_mve(S, pSrc, fftLen); + break; + } + } else { + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_f16_mve(S, pSrc, fftLen); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_f16_mve(S, pSrc, fftLen); + break; + } + } + + + if (bitReverseFlag) + { + + arm_bitreversal_16_inpl_mve((uint16_t*)pSrc, S->bitRevLength, S->pBitRevTable); + + } +} +#elif defined(ARM_MATH_NEON_FLOAT16) && defined(ARM_FLOAT16_SUPPORTED) +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + + + +ARM_DSP_ATTRIBUTE void arm_cfft_f16( + const arm_cfft_instance_f16 * S, + const float16_t * pIn, + float16_t * pOut, + float16_t * pBuffer, /* When used, in is not modified */ + uint8_t ifftFlag) +{ + if (S->algorithm_flag == ARM_MIXED_RADIX_FFT) + { + if (ifftFlag) + { + arm_ne10_mixed_radix_generic_butterfly_inverse_float16_neon (S, + (ne10_fft_cpx_float16_t *)pIn, + (ne10_fft_cpx_float16_t *)pOut, + (ne10_fft_cpx_float16_t *)pBuffer); + } + else + { + arm_ne10_mixed_radix_generic_butterfly_float16_neon (S, + (ne10_fft_cpx_float16_t *)pIn, + (ne10_fft_cpx_float16_t *)pOut, + (ne10_fft_cpx_float16_t *)pBuffer); + } + } + else + { + if (ifftFlag == 0) + { + arm_ne10_mixed_radix_fft_forward_float16_neon (S, + (ne10_fft_cpx_float16_t *)pIn, + (ne10_fft_cpx_float16_t *)pOut, + (ne10_fft_cpx_float16_t *)pBuffer); + } + else + { + arm_ne10_mixed_radix_fft_backward_float16_neon (S, + (ne10_fft_cpx_float16_t *)pIn, + (ne10_fft_cpx_float16_t *)pOut, + (ne10_fft_cpx_float16_t *)pBuffer); + } + } +} +#else + +#if defined(ARM_FLOAT16_SUPPORTED) + +extern void arm_bitreversal_16( + uint16_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + + +extern void arm_cfft_radix4by2_f16( + float16_t * pSrc, + uint32_t fftLen, + const float16_t * pCoef); + +extern void arm_radix4_butterfly_f16( + float16_t * pSrc, + uint16_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier); + +/** + @addtogroup ComplexFFTF16 + @{ + */ + +/** + @brief Processing function for the floating-point complex FFT. + @param[in] S points to an instance of the floating-point CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_f16( + const arm_cfft_instance_f16 * S, + float16_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t L = S->fftLen, l; + float16_t invL, * pSrc; + + if (ifftFlag == 1U) + { + /* Conjugate input data */ + pSrc = p1 + 1; + for(l=0; lpTwiddle, 1U); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_f16 ( p1, L, (float16_t*)S->pTwiddle); + break; + + } + + if ( bitReverseFlag ) + arm_bitreversal_16((uint16_t*)p1, S->bitRevLength,(uint16_t*)S->pBitRevTable); + + if (ifftFlag == 1U) + { + invL = 1.0f16/(_Float16)L; + /* Conjugate and scale output data */ + pSrc = p1; + for(l=0; l + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" +#include "arm_vec_fft.h" +#include "arm_mve_tables.h" + + +static float32_t arm_inverse_fft_length_f32(uint16_t fftLen) +{ + float32_t retValue=1.0; + + switch (fftLen) + { + + case 4096U: + retValue = 0.000244140625; + break; + + case 2048U: + retValue = 0.00048828125; + break; + + case 1024U: + retValue = 0.0009765625f; + break; + + case 512U: + retValue = 0.001953125; + break; + + case 256U: + retValue = 0.00390625f; + break; + + case 128U: + retValue = 0.0078125; + break; + + case 64U: + retValue = 0.015625f; + break; + + case 32U: + retValue = 0.03125; + break; + + case 16U: + retValue = 0.0625f; + break; + + + default: + break; + } + return(retValue); +} + + + + +static void _arm_radix4_butterfly_f32_mve(const arm_cfft_instance_f32 * S,float32_t * pSrc, uint32_t fftLen) +{ + f32x4_t vecTmp0, vecTmp1; + f32x4_t vecSum0, vecDiff0, vecSum1, vecDiff1; + f32x4_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + (0 - 16) * (int32_t)sizeof(q31_t *), + (1 - 16) * (int32_t)sizeof(q31_t *), + (8 - 16) * (int32_t)sizeof(q31_t *), + (9 - 16) * (int32_t)sizeof(q31_t *) + }; + + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + for (int k = fftLen / 4u; k > 1; k >>= 2) + { + float32_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + float32_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + float32_t const *p_rearranged_twiddle_tab_stride3 = + &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + + float32_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + float32_t *inA = pBase; + float32_t *inB = inA + n2 * CMPLX_DIM; + float32_t *inC = inB + n2 * CMPLX_DIM; + float32_t *inD = inC + n2 * CMPLX_DIM; + float32_t const *pW1 = p_rearranged_twiddle_tab_stride1; + float32_t const *pW2 = p_rearranged_twiddle_tab_stride2; + float32_t const *pW3 = p_rearranged_twiddle_tab_stride3; + f32x4_t vecW; + + blkCnt = n2 / 2; + /* + * load 2 f32 complex pair + */ + vecA = vldrwq_f32(inA); + vecC = vldrwq_f32(inC); + while (blkCnt > 0U) + { + vecB = vldrwq_f32(inB); + vecD = vldrwq_f32(inD); + + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vecSum0 + vecSum1; + vst1q(inA, vecTmp0); + inA += 4; + + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vecSum0 - vecSum1; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW2); + pW2 += 4; + vecTmp1 = MVE_CMPLX_MULT_FLT_Conj_AxB(vecW, vecTmp0); + vst1q(inB, vecTmp1); + inB += 4; + + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW1); + pW1 +=4; + vecTmp1 = MVE_CMPLX_MULT_FLT_Conj_AxB(vecW, vecTmp0); + vst1q(inC, vecTmp1); + inC += 4; + + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 4; + vecTmp1 = MVE_CMPLX_MULT_FLT_Conj_AxB(vecW, vecTmp0); + vst1q(inD, vecTmp1); + inD += 4; + + vecA = vldrwq_f32(inA); + vecC = vldrwq_f32(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* load scheduling */ + vecA = vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_f32(vecScGathAddr, 16); + + blkCnt = (fftLen >> 3); + while (blkCnt > 0U) + { + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecB = vldrwq_gather_base_f32(vecScGathAddr, 8); + vecD = vldrwq_gather_base_f32(vecScGathAddr, 24); + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + + /* pre-load for next iteration */ + vecA = vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_f32(vecScGathAddr, 16); + + vecTmp0 = vecSum0 + vecSum1; + vstrwq_scatter_base_f32(vecScGathAddr, -64, vecTmp0); + + vecTmp0 = vecSum0 - vecSum1; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 8, vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 16, vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 24, vecTmp0); + + blkCnt--; + } + + /* + * End of last stage process + */ +} + +static void arm_cfft_radix4by2_f32_mve(const arm_cfft_instance_f32 * S, float32_t *pSrc, uint32_t fftLen) +{ + float32_t const *pCoefVec; + float32_t const *pCoef = S->pTwiddle; + float32_t *pIn0, *pIn1; + uint32_t n2; + uint32_t blkCnt; + f32x4_t vecIn0, vecIn1, vecSum, vecDiff; + f32x4_t vecCmplxTmp, vecTw; + + + n2 = fftLen >> 1; + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + pCoefVec = pCoef; + + blkCnt = n2 / 2; + while (blkCnt > 0U) + { + vecIn0 = *(f32x4_t *) pIn0; + vecIn1 = *(f32x4_t *) pIn1; + vecTw = vld1q(pCoefVec); + pCoefVec += 4; + + vecSum = vecIn0 + vecIn1; + vecDiff = vecIn0 - vecIn1; + + vecCmplxTmp = MVE_CMPLX_MULT_FLT_Conj_AxB(vecTw, vecDiff); + + vst1q(pIn0, vecSum); + pIn0 += 4; + vst1q(pIn1, vecCmplxTmp); + pIn1 += 4; + + blkCnt--; + } + + _arm_radix4_butterfly_f32_mve(S, pSrc, n2); + + _arm_radix4_butterfly_f32_mve(S, pSrc + fftLen, n2); + + pIn0 = pSrc; +} + +static void _arm_radix4_butterfly_inverse_f32_mve(const arm_cfft_instance_f32 * S,float32_t * pSrc, uint32_t fftLen, float32_t onebyfftLen) +{ + f32x4_t vecTmp0, vecTmp1; + f32x4_t vecSum0, vecDiff0, vecSum1, vecDiff1; + f32x4_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + (0 - 16) * (int32_t)sizeof(q31_t *), + (1 - 16) * (int32_t)sizeof(q31_t *), + (8 - 16) * (int32_t)sizeof(q31_t *), + (9 - 16) * (int32_t)sizeof(q31_t *) + }; + + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + for (int k = fftLen / 4; k > 1; k >>= 2) + { + float32_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + float32_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + float32_t const *p_rearranged_twiddle_tab_stride3 = + &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + + float32_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + float32_t *inA = pBase; + float32_t *inB = inA + n2 * CMPLX_DIM; + float32_t *inC = inB + n2 * CMPLX_DIM; + float32_t *inD = inC + n2 * CMPLX_DIM; + float32_t const *pW1 = p_rearranged_twiddle_tab_stride1; + float32_t const *pW2 = p_rearranged_twiddle_tab_stride2; + float32_t const *pW3 = p_rearranged_twiddle_tab_stride3; + f32x4_t vecW; + + blkCnt = n2 / 2; + /* + * load 2 f32 complex pair + */ + vecA = vldrwq_f32(inA); + vecC = vldrwq_f32(inC); + while (blkCnt > 0U) + { + vecB = vldrwq_f32(inB); + vecD = vldrwq_f32(inD); + + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vecSum0 + vecSum1; + vst1q(inA, vecTmp0); + inA += 4; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vecSum0 - vecSum1; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW2); + pW2 += 4; + vecTmp1 = MVE_CMPLX_MULT_FLT_AxB(vecW, vecTmp0); + vst1q(inB, vecTmp1); + inB += 4; + + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW1); + pW1 += 4; + vecTmp1 = MVE_CMPLX_MULT_FLT_AxB(vecW, vecTmp0); + vst1q(inC, vecTmp1); + inC += 4; + + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 4; + vecTmp1 = MVE_CMPLX_MULT_FLT_AxB(vecW, vecTmp0); + vst1q(inD, vecTmp1); + inD += 4; + + vecA = vldrwq_f32(inA); + vecC = vldrwq_f32(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32 ((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* + * load scheduling + */ + vecA = vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_f32(vecScGathAddr, 16); + + blkCnt = (fftLen >> 3); + while (blkCnt > 0U) + { + vecSum0 = vecA + vecC; /* vecSum0 = vaddq(vecA, vecC) */ + vecDiff0 = vecA - vecC; /* vecSum0 = vsubq(vecA, vecC) */ + + vecB = vldrwq_gather_base_f32(vecScGathAddr, 8); + vecD = vldrwq_gather_base_f32(vecScGathAddr, 24); + + vecSum1 = vecB + vecD; + vecDiff1 = vecB - vecD; + + vecA = vldrwq_gather_base_wb_f32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_f32(vecScGathAddr, 16); + + vecTmp0 = vecSum0 + vecSum1; + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64, vecTmp0); + + vecTmp0 = vecSum0 - vecSum1; + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 8, vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_A_ixB(vecDiff0, vecDiff1); + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 16, vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_A_ixB(vecDiff0, vecDiff1); + vecTmp0 = vecTmp0 * onebyfftLen; + vstrwq_scatter_base_f32(vecScGathAddr, -64 + 24, vecTmp0); + + blkCnt--; + } + + /* + * End of last stage process + */ +} + +static void arm_cfft_radix4by2_inverse_f32_mve(const arm_cfft_instance_f32 * S,float32_t *pSrc, uint32_t fftLen) +{ + float32_t const *pCoefVec; + float32_t const *pCoef = S->pTwiddle; + float32_t *pIn0, *pIn1; + uint32_t n2; + float32_t onebyfftLen = arm_inverse_fft_length_f32(fftLen); + uint32_t blkCnt; + f32x4_t vecIn0, vecIn1, vecSum, vecDiff; + f32x4_t vecCmplxTmp, vecTw; + + + n2 = fftLen >> 1; + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + pCoefVec = pCoef; + + blkCnt = n2 / 2; + while (blkCnt > 0U) + { + vecIn0 = *(f32x4_t *) pIn0; + vecIn1 = *(f32x4_t *) pIn1; + vecTw = vld1q(pCoefVec); + pCoefVec += 4; + + vecSum = vecIn0 + vecIn1; + vecDiff = vecIn0 - vecIn1; + + vecCmplxTmp = MVE_CMPLX_MULT_FLT_AxB(vecTw, vecDiff); + + vst1q(pIn0, vecSum); + pIn0 += 4; + vst1q(pIn1, vecCmplxTmp); + pIn1 += 4; + + blkCnt--; + } + + _arm_radix4_butterfly_inverse_f32_mve(S, pSrc, n2, onebyfftLen); + + _arm_radix4_butterfly_inverse_f32_mve(S, pSrc + fftLen, n2, onebyfftLen); +} + + +/** + @addtogroup ComplexFFTF32 + @{ + */ + +/** + @brief Processing function for the floating-point complex FFT. + @param[in] S points to an instance of the floating-point CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ + + +ARM_DSP_ATTRIBUTE void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + float32_t * pSrc, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t fftLen = S->fftLen; + + if (ifftFlag == 1U) { + + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_inverse_f32_mve(S, pSrc, fftLen, arm_inverse_fft_length_f32(S->fftLen)); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_inverse_f32_mve(S, pSrc, fftLen); + break; + } + } else { + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_f32_mve(S, pSrc, fftLen); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_f32_mve(S, pSrc, fftLen); + break; + } + } + + + if (bitReverseFlag) + { + + arm_bitreversal_32_inpl_mve((uint32_t*)pSrc, S->bitRevLength, S->pBitRevTable); + + } +} + + +#elif defined(ARM_MATH_NEON) +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + + + +ARM_DSP_ATTRIBUTE void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + const float32_t * pIn, + float32_t * pOut, + float32_t * pBuffer, /* When used, in is not modified */ + uint8_t ifftFlag) +{ + if (S->algorithm_flag == ARM_MIXED_RADIX_FFT) + { + if (ifftFlag) + { + arm_ne10_mixed_radix_generic_butterfly_inverse_float32_neon (S, + (ne10_fft_cpx_float32_t *)pIn, + (ne10_fft_cpx_float32_t *)pOut, + (ne10_fft_cpx_float32_t *)pBuffer); + } + else + { + arm_ne10_mixed_radix_generic_butterfly_float32_neon (S, + (ne10_fft_cpx_float32_t *)pIn, + (ne10_fft_cpx_float32_t *)pOut, + (ne10_fft_cpx_float32_t *)pBuffer); + } + } + else + { + if (ifftFlag == 0) + { + if (S->fftLen==16) + { + arm_ne10_fft16_forward_float32_neon (S, + (ne10_fft_cpx_float32_t *)pIn, + (ne10_fft_cpx_float32_t *)pOut + ); + } + else + { + arm_ne10_mixed_radix_fft_forward_float32_neon (S, + (ne10_fft_cpx_float32_t *)pIn, + (ne10_fft_cpx_float32_t *)pOut, + (ne10_fft_cpx_float32_t *)pBuffer); + } + } + else + { + if (S->fftLen==16) + { + arm_ne10_fft16_backward_float32_neon(S, + (ne10_fft_cpx_float32_t *)pIn, + (ne10_fft_cpx_float32_t *)pOut); + } + else + { + arm_ne10_mixed_radix_fft_backward_float32_neon (S, + (ne10_fft_cpx_float32_t *)pIn, + (ne10_fft_cpx_float32_t *)pOut, + (ne10_fft_cpx_float32_t *)pBuffer); + } + } + } +} +#else +extern void arm_radix8_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier); + +extern void arm_bitreversal_32( + uint32_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + +/** + @ingroup groupTransforms + */ + +/** + @defgroup ComplexFFT Complex FFT Functions + + @par + The Fast Fourier Transform (FFT) is an efficient algorithm for computing the + Discrete Fourier Transform (DFT). The FFT can be orders of magnitude faster + than the DFT, especially for long lengths. + The algorithms described in this section + operate on complex data. A separate set of functions is devoted to handling + of real sequences. + @par + There are separate algorithms for handling floating-point, Q15, and Q31 data + types. The algorithms available for each data type are described next. + @par + The FFT functions operate in-place. That is, the array holding the input data + will also be used to hold the corresponding result. The input data is complex + and contains 2*fftLen interleaved values as shown below. + 
{real[0], imag[0], real[1], imag[1], ...}
+ The FFT result will be contained in the same array and the frequency domain + values will have the same interleaving. + + @par Floating-point + The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-8 + stages are performed along with a single radix-2 or radix-4 stage, as needed. + The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses + a different twiddle factor table. + @par + The function uses the standard FFT definition and output values may grow by a + factor of fftLen when computing the forward transform. The + inverse transform includes a scale of 1/fftLen as part of the + calculation and this matches the textbook definition of the inverse FFT. + @par + For the MVE version, the new arm_cfft_init_f32 initialization function is + mandatory. Compilation flags are available to include only the required tables for the + needed FFTs. Other FFT versions can continue to be initialized as + explained below. + @par + For versions not targeting Helium or Neon, pre-initialized data structures containing twiddle factors + and bit reversal tables are provided and defined in arm_const_structs.h. Include + this header in your function and then pass one of the constant structures as + an argument to arm_cfft_f32. For example: + @par + arm_cfft_f32(arm_cfft_sR_f32_len64, pSrc, 1, 1) + @par + computes a 64-point inverse complex FFT including bit reversal. + The data structures are treated as constant data and not modified during the + calculation. The same data structure can be reused for multiple transforms + including mixing forward and inverse transforms. + @par + Earlier releases of the library provided separate radix-2 and radix-4 + algorithms that operated on floating-point data. These functions are still + provided but are deprecated. The older functions are slower and less general + than the new functions. + @par + An example of initialization of the constants for the arm_cfft_f32 function follows: + @code + const static arm_cfft_instance_f32 *S; + ... + switch (length) { + case 16: + S = &arm_cfft_sR_f32_len16; + break; + case 32: + S = &arm_cfft_sR_f32_len32; + break; + case 64: + S = &arm_cfft_sR_f32_len64; + break; + case 128: + S = &arm_cfft_sR_f32_len128; + break; + case 256: + S = &arm_cfft_sR_f32_len256; + break; + case 512: + S = &arm_cfft_sR_f32_len512; + break; + case 1024: + S = &arm_cfft_sR_f32_len1024; + break; + case 2048: + S = &arm_cfft_sR_f32_len2048; + break; + case 4096: + S = &arm_cfft_sR_f32_len4096; + break; + } + @endcode + + @par + The new arm_cfft_init_f32 can also be used. + @par Q15 and Q31 + The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-4 + stages are performed along with a single radix-2 stage, as needed. + The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses + a different twiddle factor table. + @par + The function uses the standard FFT definition and output values may grow by a + factor of fftLen when computing the forward transform. The + inverse transform includes a scale of 1/fftLen as part of the + calculation and this matches the textbook definition of the inverse FFT. + @par + Pre-initialized data structures containing twiddle factors and bit reversal + tables are provided and defined in arm_const_structs.h. Include + this header in your function and then pass one of the constant structures as + an argument to arm_cfft_q31 (except if you are targeting Helium or Neon). For example: + @par + arm_cfft_q31(arm_cfft_sR_q31_len64, pSrc, 1, 1) + @par + computes a 64-point inverse complex FFT including bit reversal. + The data structures are treated as constant data and not modified during the + calculation. The same data structure can be reused for multiple transforms + including mixing forward and inverse transforms. + @par + Earlier releases of the library provided separate radix-2 and radix-4 + algorithms that operated on floating-point data. These functions are still + provided but are deprecated. The older functions are slower and less general + than the new functions. + @par + An example of initialization of the constants for the arm_cfft_q31 function follows: + @code + const static arm_cfft_instance_q31 *S; + ... + switch (length) { + case 16: + S = &arm_cfft_sR_q31_len16; + break; + case 32: + S = &arm_cfft_sR_q31_len32; + break; + case 64: + S = &arm_cfft_sR_q31_len64; + break; + case 128: + S = &arm_cfft_sR_q31_len128; + break; + case 256: + S = &arm_cfft_sR_q31_len256; + break; + case 512: + S = &arm_cfft_sR_q31_len512; + break; + case 1024: + S = &arm_cfft_sR_q31_len1024; + break; + case 2048: + S = &arm_cfft_sR_q31_len2048; + break; + case 4096: + S = &arm_cfft_sR_q31_len4096; + break; + } + @endcode + + @par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is a temporary buffer. + The bit reverse flag is not more + available in Neon version. + + @code + void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + const float32_t * pIn, + float32_t * pOut, + float32_t * pBuffer, + uint8_t ifftFlag); + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ + +static void arm_cfft_radix8by2_f32 (arm_cfft_instance_f32 * S, float32_t * p1) +{ + uint32_t L = S->fftLen; + float32_t * pCol1, * pCol2, * pMid1, * pMid2; + float32_t * p2 = p1 + L; + const float32_t * tw = (float32_t *) S->pTwiddle; + float32_t t1[4], t2[4], t3[4], t4[4], twR, twI; + float32_t m0, m1, m2, m3; + uint32_t l; + + pCol1 = p1; + pCol2 = p2; + + /* Define new length */ + L >>= 1; + + /* Initialize mid pointers */ + pMid1 = p1 + L; + pMid2 = p2 + L; + + /* do two dot Fourier transform */ + for (l = L >> 2; l > 0; l-- ) + { + t1[0] = p1[0]; + t1[1] = p1[1]; + t1[2] = p1[2]; + t1[3] = p1[3]; + + t2[0] = p2[0]; + t2[1] = p2[1]; + t2[2] = p2[2]; + t2[3] = p2[3]; + + t3[0] = pMid1[0]; + t3[1] = pMid1[1]; + t3[2] = pMid1[2]; + t3[3] = pMid1[3]; + + t4[0] = pMid2[0]; + t4[1] = pMid2[1]; + t4[2] = pMid2[2]; + t4[3] = pMid2[3]; + + *p1++ = t1[0] + t2[0]; + *p1++ = t1[1] + t2[1]; + *p1++ = t1[2] + t2[2]; + *p1++ = t1[3] + t2[3]; /* col 1 */ + + t2[0] = t1[0] - t2[0]; + t2[1] = t1[1] - t2[1]; + t2[2] = t1[2] - t2[2]; + t2[3] = t1[3] - t2[3]; /* for col 2 */ + + *pMid1++ = t3[0] + t4[0]; + *pMid1++ = t3[1] + t4[1]; + *pMid1++ = t3[2] + t4[2]; + *pMid1++ = t3[3] + t4[3]; /* col 1 */ + + t4[0] = t4[0] - t3[0]; + t4[1] = t4[1] - t3[1]; + t4[2] = t4[2] - t3[2]; + t4[3] = t4[3] - t3[3]; /* for col 2 */ + + twR = *tw++; + twI = *tw++; + + /* multiply by twiddle factors */ + m0 = t2[0] * twR; + m1 = t2[1] * twI; + m2 = t2[1] * twR; + m3 = t2[0] * twI; + + /* R = R * Tr - I * Ti */ + *p2++ = m0 + m1; + /* I = I * Tr + R * Ti */ + *p2++ = m2 - m3; + + /* use vertical symmetry */ + /* 0.9988 - 0.0491i <==> -0.0491 - 0.9988i */ + m0 = t4[0] * twI; + m1 = t4[1] * twR; + m2 = t4[1] * twI; + m3 = t4[0] * twR; + + *pMid2++ = m0 - m1; + *pMid2++ = m2 + m3; + + twR = *tw++; + twI = *tw++; + + m0 = t2[2] * twR; + m1 = t2[3] * twI; + m2 = t2[3] * twR; + m3 = t2[2] * twI; + + *p2++ = m0 + m1; + *p2++ = m2 - m3; + + m0 = t4[2] * twI; + m1 = t4[3] * twR; + m2 = t4[3] * twI; + m3 = t4[2] * twR; + + *pMid2++ = m0 - m1; + *pMid2++ = m2 + m3; + } + + /* first col */ + arm_radix8_butterfly_f32 (pCol1, L, (float32_t *) S->pTwiddle, 2U); + + /* second col */ + arm_radix8_butterfly_f32 (pCol2, L, (float32_t *) S->pTwiddle, 2U); +} + +static void arm_cfft_radix8by4_f32 (arm_cfft_instance_f32 * S, float32_t * p1) +{ + uint32_t L = S->fftLen >> 1; + float32_t * pCol1, *pCol2, *pCol3, *pCol4, *pEnd1, *pEnd2, *pEnd3, *pEnd4; + const float32_t *tw2, *tw3, *tw4; + float32_t * p2 = p1 + L; + float32_t * p3 = p2 + L; + float32_t * p4 = p3 + L; + float32_t t2[4], t3[4], t4[4], twR, twI; + float32_t p1ap3_0, p1sp3_0, p1ap3_1, p1sp3_1; + float32_t m0, m1, m2, m3; + uint32_t l, twMod2, twMod3, twMod4; + + pCol1 = p1; /* points to real values by default */ + pCol2 = p2; + pCol3 = p3; + pCol4 = p4; + pEnd1 = p2 - 1; /* points to imaginary values by default */ + pEnd2 = p3 - 1; + pEnd3 = p4 - 1; + pEnd4 = pEnd3 + L; + + tw2 = tw3 = tw4 = (float32_t *) S->pTwiddle; + + L >>= 1; + + /* do four dot Fourier transform */ + + twMod2 = 2; + twMod3 = 4; + twMod4 = 6; + + /* TOP */ + p1ap3_0 = p1[0] + p3[0]; + p1sp3_0 = p1[0] - p3[0]; + p1ap3_1 = p1[1] + p3[1]; + p1sp3_1 = p1[1] - p3[1]; + + /* col 2 */ + t2[0] = p1sp3_0 + p2[1] - p4[1]; + t2[1] = p1sp3_1 - p2[0] + p4[0]; + /* col 3 */ + t3[0] = p1ap3_0 - p2[0] - p4[0]; + t3[1] = p1ap3_1 - p2[1] - p4[1]; + /* col 4 */ + t4[0] = p1sp3_0 - p2[1] + p4[1]; + t4[1] = p1sp3_1 + p2[0] - p4[0]; + /* col 1 */ + *p1++ = p1ap3_0 + p2[0] + p4[0]; + *p1++ = p1ap3_1 + p2[1] + p4[1]; + + /* Twiddle factors are ones */ + *p2++ = t2[0]; + *p2++ = t2[1]; + *p3++ = t3[0]; + *p3++ = t3[1]; + *p4++ = t4[0]; + *p4++ = t4[1]; + + tw2 += twMod2; + tw3 += twMod3; + tw4 += twMod4; + + for (l = (L - 2) >> 1; l > 0; l-- ) + { + /* TOP */ + p1ap3_0 = p1[0] + p3[0]; + p1sp3_0 = p1[0] - p3[0]; + p1ap3_1 = p1[1] + p3[1]; + p1sp3_1 = p1[1] - p3[1]; + /* col 2 */ + t2[0] = p1sp3_0 + p2[1] - p4[1]; + t2[1] = p1sp3_1 - p2[0] + p4[0]; + /* col 3 */ + t3[0] = p1ap3_0 - p2[0] - p4[0]; + t3[1] = p1ap3_1 - p2[1] - p4[1]; + /* col 4 */ + t4[0] = p1sp3_0 - p2[1] + p4[1]; + t4[1] = p1sp3_1 + p2[0] - p4[0]; + /* col 1 - top */ + *p1++ = p1ap3_0 + p2[0] + p4[0]; + *p1++ = p1ap3_1 + p2[1] + p4[1]; + + /* BOTTOM */ + p1ap3_1 = pEnd1[-1] + pEnd3[-1]; + p1sp3_1 = pEnd1[-1] - pEnd3[-1]; + p1ap3_0 = pEnd1[ 0] + pEnd3[0]; + p1sp3_0 = pEnd1[ 0] - pEnd3[0]; + /* col 2 */ + t2[2] = pEnd2[0] - pEnd4[0] + p1sp3_1; + t2[3] = pEnd1[0] - pEnd3[0] - pEnd2[-1] + pEnd4[-1]; + /* col 3 */ + t3[2] = p1ap3_1 - pEnd2[-1] - pEnd4[-1]; + t3[3] = p1ap3_0 - pEnd2[ 0] - pEnd4[ 0]; + /* col 4 */ + t4[2] = pEnd2[ 0] - pEnd4[ 0] - p1sp3_1; + t4[3] = pEnd4[-1] - pEnd2[-1] - p1sp3_0; + /* col 1 - Bottom */ + *pEnd1-- = p1ap3_0 + pEnd2[ 0] + pEnd4[ 0]; + *pEnd1-- = p1ap3_1 + pEnd2[-1] + pEnd4[-1]; + + /* COL 2 */ + /* read twiddle factors */ + twR = *tw2++; + twI = *tw2++; + /* multiply by twiddle factors */ + /* let Z1 = a + i(b), Z2 = c + i(d) */ + /* => Z1 * Z2 = (a*c - b*d) + i(b*c + a*d) */ + + /* Top */ + m0 = t2[0] * twR; + m1 = t2[1] * twI; + m2 = t2[1] * twR; + m3 = t2[0] * twI; + + *p2++ = m0 + m1; + *p2++ = m2 - m3; + /* use vertical symmetry col 2 */ + /* 0.9997 - 0.0245i <==> 0.0245 - 0.9997i */ + /* Bottom */ + m0 = t2[3] * twI; + m1 = t2[2] * twR; + m2 = t2[2] * twI; + m3 = t2[3] * twR; + + *pEnd2-- = m0 - m1; + *pEnd2-- = m2 + m3; + + /* COL 3 */ + twR = tw3[0]; + twI = tw3[1]; + tw3 += twMod3; + /* Top */ + m0 = t3[0] * twR; + m1 = t3[1] * twI; + m2 = t3[1] * twR; + m3 = t3[0] * twI; + + *p3++ = m0 + m1; + *p3++ = m2 - m3; + /* use vertical symmetry col 3 */ + /* 0.9988 - 0.0491i <==> -0.9988 - 0.0491i */ + /* Bottom */ + m0 = -t3[3] * twR; + m1 = t3[2] * twI; + m2 = t3[2] * twR; + m3 = t3[3] * twI; + + *pEnd3-- = m0 - m1; + *pEnd3-- = m3 - m2; + + /* COL 4 */ + twR = tw4[0]; + twI = tw4[1]; + tw4 += twMod4; + /* Top */ + m0 = t4[0] * twR; + m1 = t4[1] * twI; + m2 = t4[1] * twR; + m3 = t4[0] * twI; + + *p4++ = m0 + m1; + *p4++ = m2 - m3; + /* use vertical symmetry col 4 */ + /* 0.9973 - 0.0736i <==> -0.0736 + 0.9973i */ + /* Bottom */ + m0 = t4[3] * twI; + m1 = t4[2] * twR; + m2 = t4[2] * twI; + m3 = t4[3] * twR; + + *pEnd4-- = m0 - m1; + *pEnd4-- = m2 + m3; + } + + /* MIDDLE */ + /* Twiddle factors are */ + /* 1.0000 0.7071-0.7071i -1.0000i -0.7071-0.7071i */ + p1ap3_0 = p1[0] + p3[0]; + p1sp3_0 = p1[0] - p3[0]; + p1ap3_1 = p1[1] + p3[1]; + p1sp3_1 = p1[1] - p3[1]; + + /* col 2 */ + t2[0] = p1sp3_0 + p2[1] - p4[1]; + t2[1] = p1sp3_1 - p2[0] + p4[0]; + /* col 3 */ + t3[0] = p1ap3_0 - p2[0] - p4[0]; + t3[1] = p1ap3_1 - p2[1] - p4[1]; + /* col 4 */ + t4[0] = p1sp3_0 - p2[1] + p4[1]; + t4[1] = p1sp3_1 + p2[0] - p4[0]; + /* col 1 - Top */ + *p1++ = p1ap3_0 + p2[0] + p4[0]; + *p1++ = p1ap3_1 + p2[1] + p4[1]; + + /* COL 2 */ + twR = tw2[0]; + twI = tw2[1]; + + m0 = t2[0] * twR; + m1 = t2[1] * twI; + m2 = t2[1] * twR; + m3 = t2[0] * twI; + + *p2++ = m0 + m1; + *p2++ = m2 - m3; + /* COL 3 */ + twR = tw3[0]; + twI = tw3[1]; + + m0 = t3[0] * twR; + m1 = t3[1] * twI; + m2 = t3[1] * twR; + m3 = t3[0] * twI; + + *p3++ = m0 + m1; + *p3++ = m2 - m3; + /* COL 4 */ + twR = tw4[0]; + twI = tw4[1]; + + m0 = t4[0] * twR; + m1 = t4[1] * twI; + m2 = t4[1] * twR; + m3 = t4[0] * twI; + + *p4++ = m0 + m1; + *p4++ = m2 - m3; + + /* first col */ + arm_radix8_butterfly_f32 (pCol1, L, (float32_t *) S->pTwiddle, 4U); + + /* second col */ + arm_radix8_butterfly_f32 (pCol2, L, (float32_t *) S->pTwiddle, 4U); + + /* third col */ + arm_radix8_butterfly_f32 (pCol3, L, (float32_t *) S->pTwiddle, 4U); + + /* fourth col */ + arm_radix8_butterfly_f32 (pCol4, L, (float32_t *) S->pTwiddle, 4U); +} + +/** + @addtogroup ComplexFFTF32 + @{ + */ + +/** + @brief Processing function for the floating-point complex FFT. + @param[in] S points to an instance of the floating-point CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is an optional temporary buffer. + If the temporary buffer is not used, the + input buffer is modified. + The bit reverse flag is not more + available in Neon version. + + @par + @code + void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + float32_t * pIn, + float32_t * pOut, + float32_t * pBuffer, + uint8_t ifftFlag); + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_f32( + const arm_cfft_instance_f32 * S, + float32_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t L = S->fftLen, l; + float32_t invL, * pSrc; + + if (ifftFlag == 1U) + { + /* Conjugate input data */ + pSrc = p1 + 1; + for (l = 0; l < L; l++) + { + *pSrc = -*pSrc; + pSrc += 2; + } + } + + switch (L) + { + case 16: + case 128: + case 1024: + arm_cfft_radix8by2_f32 ( (arm_cfft_instance_f32 *) S, p1); + break; + case 32: + case 256: + case 2048: + arm_cfft_radix8by4_f32 ( (arm_cfft_instance_f32 *) S, p1); + break; + case 64: + case 512: + case 4096: + arm_radix8_butterfly_f32 ( p1, L, (float32_t *) S->pTwiddle, 1); + break; + } + + if ( bitReverseFlag ) + arm_bitreversal_32 ((uint32_t*) p1, S->bitRevLength, S->pBitRevTable); + + if (ifftFlag == 1U) + { + invL = 1.0f / (float32_t)L; + + /* Conjugate and scale output data */ + pSrc = p1; + for (l= 0; l < L; l++) + { + *pSrc++ *= invL ; + *pSrc = -(*pSrc) * invL; + pSrc++; + } + } +} +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @} end of ComplexFFTF32 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_f64.c new file mode 100755 index 0000000..4800165 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_f64.c @@ -0,0 +1,317 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_f64.c + * Description: Combined Radix Decimation in Frequency CFFT Double Precision Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + + +extern void arm_radix4_butterfly_f64( + float64_t * pSrc, + uint16_t fftLen, + const float64_t * pCoef, + uint16_t twidCoefModifier); + +extern void arm_bitreversal_64( + uint64_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + +/* ---------------------------------------------------------------------- + * Internal helper function used by the FFTs + * ---------------------------------------------------------------------- */ + +/* +* @brief Core function for the Double Precision floating-point CFFT butterfly process. +* @param[in, out] *pSrc points to the in-place buffer of F64 data type. +* @param[in] fftLen length of the FFT. +* @param[in] *pCoef points to the twiddle coefficient buffer. +* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +*/ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_f64( + float64_t * pSrc, + uint16_t fftLen, + const float64_t * pCoef, + uint16_t twidCoefModifier) +{ + + float64_t co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + + float64_t t1, t2, r1, r2, s1, s2; + + + /* Initializations for the fft calculation */ + n2 = fftLen; + n1 = n2; + for (k = fftLen; k > 1U; k >>= 2U) + { + /* Initializations for the fft calculation */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* FFT Calculation */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = pSrc[(2U * i0)] + pSrc[(2U * i2)]; + + /* xa - xc */ + r2 = pSrc[(2U * i0)] - pSrc[(2U * i2)]; + + /* ya + yc */ + s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = pSrc[2U * i1] + pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = r1 + t1; + + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = s1 + t2; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U]; + + /* (xb - xd) */ + t2 = pSrc[2U * i1] - pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (r1 * co2) + (s1 * si2); + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (s1 * co2) - (r1 * si2); + + /* (xa - xc) + (yb - yd) */ + r1 = r2 + t1; + + /* (xa - xc) - (yb - yd) */ + r2 = r2 - t1; + + /* (ya - yc) - (xb - xd) */ + s1 = s2 - t2; + + /* (ya - yc) + (xb - xd) */ + s2 = s2 + t2; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (r1 * co1) + (s1 * si1); + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (s1 * co1) - (r1 * si1); + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (r2 * co3) + (s2 * si3); + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (s2 * co3) - (r2 * si3); + + i0 += n1; + } while ( i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } +} + +/* +* @brief Core function for the Double Precision floating-point CFFT butterfly process. +* @param[in, out] *pSrc points to the in-place buffer of F64 data type. +* @param[in] fftLen length of the FFT. +* @param[in] *pCoef points to the twiddle coefficient buffer. +* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +*/ + +static void arm_cfft_radix4by2_f64( + float64_t * pSrc, + uint32_t fftLen, + const float64_t * pCoef) +{ + uint32_t i, l; + uint32_t n2, ia; + float64_t xt, yt, cosVal, sinVal; + float64_t p0, p1,p2,p3,a0,a1; + + n2 = fftLen >> 1; + ia = 0; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2*ia]; + sinVal = pCoef[2*ia + 1]; + ia++; + + l = i + n2; + + /* Butterfly implementation */ + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 + p1; + pSrc[2 * l + 1] = p2 - p3; + + } + + // first col + arm_radix4_butterfly_f64( pSrc, n2, (float64_t*)pCoef, 2U); + // second col + arm_radix4_butterfly_f64( pSrc + fftLen, n2, (float64_t*)pCoef, 2U); + +} + +/** + @addtogroup ComplexFFTF64 + @{ + */ + +/** + @brief Processing function for the Double Precision floating-point complex FFT. + @param[in] S points to an instance of the Double Precision floating-point CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_f64( + const arm_cfft_instance_f64 * S, + float64_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t L = S->fftLen, l; + float64_t invL, * pSrc; + + if (ifftFlag == 1U) + { + /* Conjugate input data */ + pSrc = p1 + 1; + for(l=0; lpTwiddle, 1U); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_f64 ( p1, L, (float64_t*)S->pTwiddle); + break; + + } + + if ( bitReverseFlag ) + arm_bitreversal_64((uint64_t*)p1, S->bitRevLength,S->pBitRevTable); + + if (ifftFlag == 1U) + { + invL = 1.0 / (float64_t)L; + /* Conjugate and scale output data */ + pSrc = p1; + for(l=0; lrearranged_twiddle_tab_stride1_arr = rearranged_twiddle_tab_stride1_arr_##LEN##_f16; \ + S->rearranged_twiddle_stride1 = rearranged_twiddle_stride1_##LEN##_f16; \ + \ + S->rearranged_twiddle_tab_stride2_arr = rearranged_twiddle_tab_stride2_arr_##LEN##_f16; \ + S->rearranged_twiddle_stride2 = rearranged_twiddle_stride2_##LEN##_f16; \ + \ + S->rearranged_twiddle_tab_stride3_arr = rearranged_twiddle_tab_stride3_arr_##LEN##_f16; \ + S->rearranged_twiddle_stride3 = rearranged_twiddle_stride3_##LEN##_f16; \ + return(ARM_MATH_SUCCESS); \ +} + +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F16(4096); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F16(1024); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F16(256); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F16(64); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F16(16); + + + +#define CFFTINIT_F16(LEN,LENTWIDDLE) \ +arm_status arm_cfft_init_##LEN##_f16( \ + arm_cfft_instance_f16 * S) \ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + /* Initialise the bit reversal table modifier */ \ + S->bitRevLength = ARMBITREVINDEXTABLE_FIXED_##LEN##_TABLE_LENGTH; \ + S->pBitRevTable = (uint16_t *)armBitRevIndexTable_fixed_##LEN; \ + S->pTwiddle = (float16_t *)twiddleCoefF16_##LEN; \ + status=arm_cfft_radix4by2_rearrange_twiddles_##LENTWIDDLE##_f16(S);\ + \ + return (status); \ +} + +#elif defined(ARM_MATH_NEON_FLOAT16) && defined(ARM_FLOAT16_SUPPORTED) +#include "arm_neon_tables_f16.h" + +#define CFFTINIT_F16(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_f16(arm_cfft_instance_f16 * S)\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + S->pTwiddle = arm_neon_twiddles_##LEN##_f16; \ + S->factors=arm_neon_factors_##LEN##_f16; \ + S->fftLen = LEN; \ + S->algorithm_flag = 0; \ + S->last_twiddles = NULL; \ + return status; \ +} +#else + +#if defined(ARM_FLOAT16_SUPPORTED) + +#define FFTINIT(EXT,SIZE) \ + S->bitRevLength = arm_cfft_sR_##EXT##_len##SIZE.bitRevLength; \ + S->pBitRevTable = arm_cfft_sR_##EXT##_len##SIZE.pBitRevTable; \ + S->pTwiddle = arm_cfft_sR_##EXT##_len##SIZE.pTwiddle; + +#define CFFTINIT_F16(LEN,LENTWIDDLE) \ +arm_status arm_cfft_init_##LEN##_f16(arm_cfft_instance_f16 * S) \ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + /* Initializations of Instance structure depending on the FFT length */\ + FFTINIT(f16,LEN); \ + \ + return (status); \ +} + + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +#if defined(ARM_MATH_MVE_FLOAT16) || defined(ARM_FLOAT16_SUPPORTED) +/** + @brief Initialization function for the cfft f16 function with 4096 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(4096,4096) + +/** + @brief Initialization function for the cfft f16 function with 2048 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(2048,1024) + + +/** + @brief Initialization function for the cfft f16 function with 1024 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(1024,1024) + + +/** + @brief Initialization function for the cfft f16 function with 512 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(512,256) + + +/** + @brief Initialization function for the cfft f16 function with 256 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(256,256) + + +/** + @brief Initialization function for the cfft f16 function with 128 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(128,64) + + +/** + @brief Initialization function for the cfft f16 function with 64 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(64,64) + + +/** + @brief Initialization function for the cfft f16 function with 32 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(32,16) + + +/** + @brief Initialization function for the cfft f16 function with 16 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F16(16,16) + + +/** + @brief Generic initialization function for the cfft f16 function + @param[in,out] S points to an instance of the floating-point CFFT structure + @param[in] fftLen fft length (number of complex samples) + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + + @par This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + */ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_f16( + arm_cfft_instance_f16 * S, + uint16_t fftLen) +{ + + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializations of Instance structure depending on the FFT length */ + switch (fftLen) { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_4096_f16(S); + break; + + /* Initializations of structure parameters for 2048 point FFT */ + case 2048U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_2048_f16(S); + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_1024_f16(S); + break; + + /* Initializations of structure parameters for 512 point FFT */ + case 512U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_512_f16(S); + break; + + case 256U: + status=arm_cfft_init_256_f16(S); + break; + + case 128U: + status=arm_cfft_init_128_f16(S); + break; + + case 64U: + status=arm_cfft_init_64_f16(S); + break; + + case 32U: + status=arm_cfft_init_32_f16(S); + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + status=arm_cfft_init_16_f16(S); + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} +#endif /* Float 16 used*/ + +/** + @} end of ComplexFFTF16 group + */ + +/** + @} end of ComplexFFT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_f32.c new file mode 100755 index 0000000..56e552e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_f32.c @@ -0,0 +1,365 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_init_f32.c + * Description: Initialization function for cfft f32 instance + * + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2024 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +/** + * @defgroup ComplexFFTF32 Complex FFT F32 + */ + +/** + @ingroup groupTransforms + */ + +/** + @addtogroup ComplexFFT + @{ + */ + +/** + @addtogroup ComplexFFTF32 + @{ + */ +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_vec_fft.h" +#include "arm_mve_tables.h" + + +#define CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F32(LEN) \ +static arm_status arm_cfft_radix4by2_rearrange_twiddles_##LEN##_f32(arm_cfft_instance_f32 *S)\ +{ \ + S->rearranged_twiddle_tab_stride1_arr = rearranged_twiddle_tab_stride1_arr_##LEN##_f32; \ + S->rearranged_twiddle_stride1 = rearranged_twiddle_stride1_##LEN##_f32; \ + \ + S->rearranged_twiddle_tab_stride2_arr = rearranged_twiddle_tab_stride2_arr_##LEN##_f32; \ + S->rearranged_twiddle_stride2 = rearranged_twiddle_stride2_##LEN##_f32; \ + \ + S->rearranged_twiddle_tab_stride3_arr = rearranged_twiddle_tab_stride3_arr_##LEN##_f32; \ + S->rearranged_twiddle_stride3 = rearranged_twiddle_stride3_##LEN##_f32; \ + return(ARM_MATH_SUCCESS); \ +} + +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F32(4096); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F32(1024); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F32(256); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F32(64); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_F32(16); + + +#define CFFTINIT_F32(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_f32( \ + arm_cfft_instance_f32 * S) \ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + /* Initialise the bit reversal table modifier */ \ + S->bitRevLength = ARMBITREVINDEXTABLE_FIXED_##LEN##_TABLE_LENGTH; \ + S->pBitRevTable = (uint16_t *)armBitRevIndexTable_fixed_##LEN; \ + S->pTwiddle = (float32_t *)twiddleCoef_##LEN; \ + status=arm_cfft_radix4by2_rearrange_twiddles_##LENTWIDDLE##_f32(S); \ + \ + return (status); \ +} + +#elif defined(ARM_MATH_NEON) + +#include "arm_neon_tables.h" + +#define CFFTINIT_F32(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_f32(arm_cfft_instance_f32 * S)\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + S->pTwiddle = arm_neon_twiddles_##LEN##_f32; \ + S->factors=arm_neon_factors_##LEN##_f32; \ + S->fftLen = LEN; \ + S->algorithm_flag = 0; \ + S->last_twiddles = NULL; \ + return status; \ +} +#else + +#define FFTINIT(EXT,SIZE) \ + S->bitRevLength = arm_cfft_sR_##EXT##_len##SIZE.bitRevLength; \ + S->pBitRevTable = arm_cfft_sR_##EXT##_len##SIZE.pBitRevTable; \ + S->pTwiddle = arm_cfft_sR_##EXT##_len##SIZE.pTwiddle; + +#define CFFTINIT_F32(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_f32(arm_cfft_instance_f32 * S)\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + FFTINIT(f32,LEN); \ + \ + return (status); \ +} + +#endif /* if not neon and not mve*/ + + +/** + @brief Initialization function for the cfft f32 function with 4096 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(4096,4096) + + +/** + @brief Initialization function for the cfft f32 function with 2048 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(2048,1024) + + +/** + @brief Initialization function for the cfft f32 function with 1024 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(1024,1024) + + +/** + @brief Initialization function for the cfft f32 function with 512 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(512,256) + + +/** + @brief Initialization function for the cfft f32 function with 256 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(256,256) + + +/** + @brief Initialization function for the cfft f32 function with 128 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(128,64) + + +/** + @brief Initialization function for the cfft f32 function with 64 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(64,64) + + +/** + @brief Initialization function for the cfft f32 function with 32 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(32,16) + + +/** + @brief Initialization function for the cfft f32 function with 16 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F32(16,16) + + +/** + @brief Generic initialization function for the cfft f32 function + @param[in,out] S points to an instance of the floating-point CFFT structure + @param[in] fftLen fft length (number of complex samples) + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par + Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + */ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_f32( + arm_cfft_instance_f32 * S, + uint16_t fftLen) +{ + + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializations of Instance structure depending on the FFT length */ + switch (fftLen) { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_4096_f32(S); + break; + + /* Initializations of structure parameters for 2048 point FFT */ + case 2048U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_2048_f32(S); + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_1024_f32(S); + break; + + /* Initializations of structure parameters for 512 point FFT */ + case 512U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_512_f32(S); + break; + + case 256U: + status=arm_cfft_init_256_f32(S); + break; + + case 128U: + status=arm_cfft_init_128_f32(S); + break; + + case 64U: + status=arm_cfft_init_64_f32(S); + break; + + case 32U: + status=arm_cfft_init_32_f32(S); + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + status=arm_cfft_init_16_f32(S); + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} + +/** + @} end of ComplexFFTF32 group + */ + +/** + @} end of ComplexFFT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_f64.c new file mode 100755 index 0000000..84a7b74 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_f64.c @@ -0,0 +1,289 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_init_f64.c + * Description: Initialization function for cfft f64 instance + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#define FFTINIT(EXT,SIZE) \ + S->bitRevLength = arm_cfft_sR_##EXT##_len##SIZE.bitRevLength; \ + S->pBitRevTable = arm_cfft_sR_##EXT##_len##SIZE.pBitRevTable; \ + S->pTwiddle = arm_cfft_sR_##EXT##_len##SIZE.pTwiddle; + +/** + * @defgroup ComplexFFTF64 Complex FFT F64 + */ + +/** + @ingroup groupTransforms + */ + +/** + @addtogroup ComplexFFT + @{ + */ + +/** + @addtogroup ComplexFFTF64 + @{ + */ + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + + +#define CFFTINIT_F64(LEN) \ +arm_status arm_cfft_init_##LEN##_f64(arm_cfft_instance_f64 * S)\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + FFTINIT(f64,LEN); \ + \ + return (status); \ +} + +/** + @brief Initialization function for the cfft f64 function with 4096 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(4096) + +/** + @brief Initialization function for the cfft f64 function with 2048 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(2048) + + +/** + @brief Initialization function for the cfft f64 function with 1024 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(1024) + +/** + @brief Initialization function for the cfft f64 function with 512 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(512) + +/** + @brief Initialization function for the cfft f64 function with 256 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(256) + +/** + @brief Initialization function for the cfft f64 function with 128 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(128) + +/** + @brief Initialization function for the cfft f64 function with 64 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(64) + +/** + @brief Initialization function for the cfft f64 function with 32 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(32) + +/** + @brief Initialization function for the cfft f64 function with 16 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_F64(16) + +/** + @brief Generic initialization function for the cfft f64 function + @param[in,out] S points to an instance of the floating-point CFFT structure + @param[in] fftLen fft length (number of complex samples) + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + + @par This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + + */ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_f64( + arm_cfft_instance_f64 * S, + uint16_t fftLen) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializations of Instance structure depending on the FFT length */ + switch (fftLen) { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the bit reversal table modifier */ + status = arm_cfft_init_4096_f64(S); + break; + + /* Initializations of structure parameters for 2048 point FFT */ + case 2048U: + /* Initialise the bit reversal table modifier */ + status = arm_cfft_init_2048_f64(S); + + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the bit reversal table modifier */ + status = arm_cfft_init_1024_f64(S); + + break; + + /* Initializations of structure parameters for 512 point FFT */ + case 512U: + /* Initialise the bit reversal table modifier */ + status = arm_cfft_init_512_f64(S); + break; + + case 256U: + status = arm_cfft_init_256_f64(S); + break; + + case 128U: + status = arm_cfft_init_128_f64(S); + break; + + case 64U: + status = arm_cfft_init_64_f64(S); + break; + + case 32U: + status = arm_cfft_init_32_f64(S); + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + status = arm_cfft_init_16_f64(S); + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} +/** + @} end of ComplexFFTF64 group + */ + +/** + @} end of ComplexFFT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_q15.c new file mode 100755 index 0000000..f1be0ae --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_q15.c @@ -0,0 +1,356 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_init_q15.c + * Description: Initialization function for cfft q15 instance + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + +/** + * @defgroup ComplexFFTQ15 Complex FFT Q15 + */ + +/** + @ingroup groupTransforms + */ + +/** + @addtogroup ComplexFFT + @{ + */ + +/** + @addtogroup ComplexFFTQ15 + @{ + */ +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_vec_fft.h" +#include "arm_mve_tables.h" + +#define CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q15(LEN) \ +static arm_status arm_cfft_radix4by2_rearrange_twiddles_##LEN##_q15(arm_cfft_instance_q15 *S)\ +{ \ + S->rearranged_twiddle_tab_stride1_arr = rearranged_twiddle_tab_stride1_arr_##LEN##_q15; \ + S->rearranged_twiddle_stride1 = rearranged_twiddle_stride1_##LEN##_q15; \ + \ + S->rearranged_twiddle_tab_stride2_arr = rearranged_twiddle_tab_stride2_arr_##LEN##_q15; \ + S->rearranged_twiddle_stride2 = rearranged_twiddle_stride2_##LEN##_q15; \ + \ + S->rearranged_twiddle_tab_stride3_arr = rearranged_twiddle_tab_stride3_arr_##LEN##_q15; \ + S->rearranged_twiddle_stride3 = rearranged_twiddle_stride3_##LEN##_q15; \ + return(ARM_MATH_SUCCESS); \ +} + +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q15(4096); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q15(1024); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q15(256); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q15(64); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q15(16); + + +#define CFFTINIT_Q15(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_q15( \ + arm_cfft_instance_q15 * S) \ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + /* Initialise the bit reversal table modifier */ \ + S->bitRevLength = ARMBITREVINDEXTABLE_FIXED_##LEN##_TABLE_LENGTH; \ + S->pBitRevTable = (uint16_t *)armBitRevIndexTable_fixed_##LEN; \ + S->pTwiddle = (q15_t *)twiddleCoef_##LEN##_q15; \ + status=arm_cfft_radix4by2_rearrange_twiddles_##LENTWIDDLE##_q15(S);\ + \ + return (status); \ +} + +#elif defined(ARM_MATH_NEON) + +#include "arm_neon_tables.h" + +#define CFFTINIT_Q15(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_q15(\ + arm_cfft_instance_q15 * S) \ +{ \ + arm_status status = ARM_MATH_SUCCESS; \ + S->pTwiddle = arm_neon_twiddles_##LEN##_q15; \ + S->factors=arm_neon_factors_##LEN##_q15; \ + S->fftLen = LEN; \ + S->algorithm_flag = 0; \ + S->last_twiddles = NULL; \ + return (status); \ +} +#else + +#define FFTINIT(EXT,SIZE) \ + S->bitRevLength = arm_cfft_sR_##EXT##_len##SIZE.bitRevLength;\ + S->pBitRevTable = arm_cfft_sR_##EXT##_len##SIZE.pBitRevTable;\ + S->pTwiddle = arm_cfft_sR_##EXT##_len##SIZE.pTwiddle; + +#define CFFTINIT_Q15(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_q15(arm_cfft_instance_q15 * S)\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + FFTINIT(q15,LEN); \ + \ + return (status); \ +} + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + + + +/** + @brief Initialization function for the cfft q15 function for 4096 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(4096,4096) + +/** + @brief Initialization function for the cfft q15 function for 2048 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(2048,1024) + +/** + @brief Initialization function for the cfft q15 function for 1024 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(1024,1024) + +/** + @brief Initialization function for the cfft q15 function for 512 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(512,256) + +/** + @brief Initialization function for the cfft q15 function for 256 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(256,256) + +/** + @brief Initialization function for the cfft q15 function for 128 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(128,64) + +/** + @brief Initialization function for the cfft q15 function for 64 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(64,64) + +/** + @brief Initialization function for the cfft q15 function for 32 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(32,16) + +/** + @brief Initialization function for the cfft q15 function for 16 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q15(16,16) + +/** + @brief Generic initialization function for the cfft q15 function + @param[in,out] S points to an instance of the floating-point CFFT structure + @param[in] fftLen fft length (number of complex samples) + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + */ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_q15( + arm_cfft_instance_q15 * S, + uint16_t fftLen) +{ + + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializations of Instance structure depending on the FFT length */ + switch (fftLen) { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_4096_q15(S); + break; + + /* Initializations of structure parameters for 2048 point FFT */ + case 2048U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_2048_q15(S); + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_1024_q15(S); + break; + + /* Initializations of structure parameters for 512 point FFT */ + case 512U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_512_q15(S); + break; + + case 256U: + status=arm_cfft_init_256_q15(S); + break; + + case 128U: + status=arm_cfft_init_128_q15(S); + break; + + case 64U: + status=arm_cfft_init_64_q15(S); + break; + + case 32U: + status=arm_cfft_init_32_q15(S); + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + status=arm_cfft_init_16_q15(S); + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} +/** + @} end of ComplexFFTQ15 group + */ + +/** + @} end of ComplexFFT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_q31.c new file mode 100755 index 0000000..d37876b --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_init_q31.c @@ -0,0 +1,359 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_init_q31.c + * Description: Initialization function for cfft q31 instance + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + +/** + * @defgroup ComplexFFTQ31 Complex FFT Q31 + */ + +/** + @ingroup groupTransforms + */ + +/** + @addtogroup ComplexFFT + @{ + */ + +/** + @addtogroup ComplexFFTQ31 + @{ + */ + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_vec_fft.h" +#include "arm_mve_tables.h" + +#define CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q31(LEN) \ +static arm_status arm_cfft_radix4by2_rearrange_twiddles_##LEN##_q31(arm_cfft_instance_q31 *S)\ +{ \ + S->rearranged_twiddle_tab_stride1_arr = rearranged_twiddle_tab_stride1_arr_##LEN##_q31; \ + S->rearranged_twiddle_stride1 = rearranged_twiddle_stride1_##LEN##_q31; \ + \ + S->rearranged_twiddle_tab_stride2_arr = rearranged_twiddle_tab_stride2_arr_##LEN##_q31; \ + S->rearranged_twiddle_stride2 = rearranged_twiddle_stride2_##LEN##_q31; \ + \ + S->rearranged_twiddle_tab_stride3_arr = rearranged_twiddle_tab_stride3_arr_##LEN##_q31; \ + S->rearranged_twiddle_stride3 = rearranged_twiddle_stride3_##LEN##_q31; \ + return(ARM_MATH_SUCCESS); \ +} + +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q31(4096); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q31(1024); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q31(256); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q31(64); +CFFT_RADIX4BY2_REARRANGE_TWIDDLES_Q31(16); + + +#define CFFTINIT_Q31(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_q31( \ + arm_cfft_instance_q31 * S) \ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + /* Initialise the bit reversal table modifier */ \ + S->bitRevLength = ARMBITREVINDEXTABLE_FIXED_##LEN##_TABLE_LENGTH; \ + S->pBitRevTable = (uint16_t *)armBitRevIndexTable_fixed_##LEN; \ + S->pTwiddle = (q31_t *)twiddleCoef_##LEN##_q31; \ + status=arm_cfft_radix4by2_rearrange_twiddles_##LENTWIDDLE##_q31(S);\ + \ + return (status); \ +} + +#elif defined(ARM_MATH_NEON) + +#include "arm_neon_tables.h" + +#define CFFTINIT_Q31(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_q31(\ + arm_cfft_instance_q31 * S) \ +{ \ + arm_status status = ARM_MATH_SUCCESS; \ + S->pTwiddle = arm_neon_twiddles_##LEN##_q31; \ + S->factors=arm_neon_factors_##LEN##_q31; \ + S->fftLen = LEN; \ + S->algorithm_flag = 0; \ + S->last_twiddles = NULL; \ + return (status); \ +} + +#else + +#define FFTINIT(EXT,SIZE) \ + S->bitRevLength = arm_cfft_sR_##EXT##_len##SIZE.bitRevLength; \ + S->pBitRevTable = arm_cfft_sR_##EXT##_len##SIZE.pBitRevTable; \ + S->pTwiddle = arm_cfft_sR_##EXT##_len##SIZE.pTwiddle; + +#define CFFTINIT_Q31(LEN,LENTWIDDLE) \ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_##LEN##_q31(arm_cfft_instance_q31 * S)\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialise the FFT length */ \ + S->fftLen = LEN; \ + \ + /* Initialise the Twiddle coefficient pointer */ \ + S->pTwiddle = NULL; \ + \ + FFTINIT(q31,LEN); \ + \ + return (status); \ +} + + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @brief Initialization function for the cfft q31 function for 4096 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(4096,4096) + +/** + @brief Initialization function for the cfft q31 function for 2048 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(2048,1024) + +/** + @brief Initialization function for the cfft q31 function for 1024 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(1024,1024) + +/** + @brief Initialization function for the cfft q31 function for 512 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(512,256) + +/** + @brief Initialization function for the cfft q31 function for 256 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(256,256) + +/** + @brief Initialization function for the cfft q31 function for 128 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(128,64) + +/** + @brief Initialization function for the cfft q31 function for 64 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(64,64) + +/** + @brief Initialization function for the cfft q31 function for 32 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(32,16) + +/** + @brief Initialization function for the cfft q31 function for 16 samples + @param[in,out] S points to an instance of the floating-point CFFT structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + */ +CFFTINIT_Q31(16,16) + +/** + @brief Generic initialization function for the cfft q31 function + @param[in,out] S points to an instance of the floating-point CFFT structure + @param[in] fftLen fft length (number of complex samples) + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + + @par Use of this function is mandatory only for the Helium and Neon versions of the FFT. + Other versions can still initialize directly the data structure using + variables declared in arm_const_structs.h + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + */ +ARM_DSP_ATTRIBUTE arm_status arm_cfft_init_q31( + arm_cfft_instance_q31 * S, + uint16_t fftLen) +{ + + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + + + /* Initializations of Instance structure depending on the FFT length */ + switch (fftLen) { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_4096_q31(S); + break; + + /* Initializations of structure parameters for 2048 point FFT */ + case 2048U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_2048_q31(S); + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_1024_q31(S); + break; + + /* Initializations of structure parameters for 512 point FFT */ + case 512U: + /* Initialise the bit reversal table modifier */ + status=arm_cfft_init_512_q31(S); + break; + + case 256U: + status=arm_cfft_init_256_q31(S); + break; + + case 128U: + status=arm_cfft_init_128_q31(S); + break; + + case 64U: + status=arm_cfft_init_64_q31(S); + break; + + case 32U: + status=arm_cfft_init_32_q31(S); + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + status=arm_cfft_init_16_q31(S); + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} +/** + @} end of ComplexFFTQ31 group + */ + +/** + @} end of ComplexFFT group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_q15.c new file mode 100755 index 0000000..5244a36 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_q15.c @@ -0,0 +1,932 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_q15.c + * Description: Combined Radix Decimation in Q15 Frequency CFFT processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_vec_fft.h" + + +static void _arm_radix4_butterfly_q15_mve( + const arm_cfft_instance_q15 * S, + q15_t *pSrc, + uint32_t fftLen) +{ + q15x8_t vecTmp0, vecTmp1; + q15x8_t vecSum0, vecDiff0, vecSum1, vecDiff1; + q15x8_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + (0 - 16) * (int32_t)sizeof(q15_t *), (4 - 16) * (int32_t)sizeof(q15_t *), + (8 - 16) * (int32_t)sizeof(q15_t *), (12 - 16) * (int32_t)sizeof(q15_t *) + }; + + /* + * Process first stages + * Each stage in middle stages provides two down scaling of the input + */ + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + + for (int k = fftLen / 4u; k > 1; k >>= 2u) + { + q15_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + q15_t const *p_rearranged_twiddle_tab_stride3 = &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + q15_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + + q15_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + q15_t *inA = pBase; + q15_t *inB = inA + n2 * CMPLX_DIM; + q15_t *inC = inB + n2 * CMPLX_DIM; + q15_t *inD = inC + n2 * CMPLX_DIM; + q15_t const *pW1 = p_rearranged_twiddle_tab_stride1; + q15_t const *pW2 = p_rearranged_twiddle_tab_stride2; + q15_t const *pW3 = p_rearranged_twiddle_tab_stride3; + q15x8_t vecW; + + blkCnt = n2 / 4; + /* + * load 4 x q15 complex pair + */ + vecA = vldrhq_s16(inA); + vecC = vldrhq_s16(inC); + while (blkCnt > 0U) + { + vecB = vldrhq_s16(inB); + vecD = vldrhq_s16(inD); + + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vhaddq(vecSum0, vecSum1); + vst1q(inA, vecTmp0); + inA += 8; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vhsubq(vecSum0, vecSum1); + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW2); + pW2 += 8; + vecTmp1 = MVE_CMPLX_MULT_FX_AxB(vecW, vecTmp0, q15x8_t); + + vst1q(inB, vecTmp1); + inB += 8; + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW1); + pW1 += 8; + vecTmp1 = MVE_CMPLX_MULT_FX_AxB(vecW, vecTmp0, q15x8_t); + vst1q(inC, vecTmp1); + inC += 8; + + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 8; + vecTmp1 = MVE_CMPLX_MULT_FX_AxB(vecW, vecTmp0, q15x8_t); + vst1q(inD, vecTmp1); + inD += 8; + + vecA = vldrhq_s16(inA); + vecC = vldrhq_s16(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32 ((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* + * load scheduling + */ + vecA = (q15x8_t) vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 8); + + blkCnt = (fftLen >> 4); + while (blkCnt > 0U) + { + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecB = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 4); + vecD = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 12); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * pre-load for next iteration + */ + vecA = (q15x8_t) vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 8); + + vecTmp0 = vhaddq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64, (int32x4_t) vecTmp0); + + vecTmp0 = vhsubq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 4, (int32x4_t) vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 8, (int32x4_t) vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 12, (int32x4_t) vecTmp0); + + blkCnt--; + } + +} + +static void arm_cfft_radix4by2_q15_mve(const arm_cfft_instance_q15 *S, q15_t *pSrc, uint32_t fftLen) +{ + uint32_t n2; + q15_t *pIn0; + q15_t *pIn1; + const q15_t *pCoef = S->pTwiddle; + uint32_t blkCnt; + q15x8_t vecIn0, vecIn1, vecSum, vecDiff; + q15x8_t vecCmplxTmp, vecTw; + q15_t const *pCoefVec; + + n2 = fftLen >> 1; + + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + pCoefVec = pCoef; + + blkCnt = n2 / 4; + + while (blkCnt > 0U) + { + vecIn0 = *(q15x8_t *) pIn0; + vecIn1 = *(q15x8_t *) pIn1; + + vecIn0 = vecIn0 >> 1; + vecIn1 = vecIn1 >> 1; + vecSum = vhaddq(vecIn0, vecIn1); + vst1q(pIn0, vecSum); + pIn0 += 8; + + vecTw = vld1q(pCoefVec); + pCoefVec += 8; + + vecDiff = vhsubq(vecIn0, vecIn1); + vecCmplxTmp = MVE_CMPLX_MULT_FX_AxConjB(vecDiff, vecTw, q15x8_t); + vst1q(pIn1, vecCmplxTmp); + pIn1 += 8; + + blkCnt--; + } + + _arm_radix4_butterfly_q15_mve(S, pSrc, n2); + + _arm_radix4_butterfly_q15_mve(S, pSrc + fftLen, n2); + + + pIn0 = pSrc; + blkCnt = (fftLen << 1) >> 3; + while (blkCnt > 0U) + { + vecIn0 = *(q15x8_t *) pIn0; + vecIn0 = vecIn0 << 1; + vst1q(pIn0, vecIn0); + pIn0 += 8; + blkCnt--; + } + /* + * tail + * (will be merged thru tail predication) + */ + blkCnt = (fftLen << 1) & 7; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp16q(blkCnt); + + vecIn0 = *(q15x8_t *) pIn0; + vecIn0 = vecIn0 << 1; + vstrhq_p(pIn0, vecIn0, p0); + } +} + +static void _arm_radix4_butterfly_inverse_q15_mve(const arm_cfft_instance_q15 *S,q15_t *pSrc, uint32_t fftLen) +{ + q15x8_t vecTmp0, vecTmp1; + q15x8_t vecSum0, vecDiff0, vecSum1, vecDiff1; + q15x8_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + (0 - 16) * (int32_t)sizeof(q15_t *), (4 - 16) * (int32_t)sizeof(q15_t *), + (8 - 16) * (int32_t)sizeof(q15_t *), (12 - 16) * (int32_t)sizeof(q15_t *) + }; + + + /* + * Process first stages + * Each stage in middle stages provides two down scaling of the input + */ + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + + for (int k = fftLen / 4u; k > 1; k >>= 2u) + { + q15_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + q15_t const *p_rearranged_twiddle_tab_stride3 = &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + q15_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + + q15_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + q15_t *inA = pBase; + q15_t *inB = inA + n2 * CMPLX_DIM; + q15_t *inC = inB + n2 * CMPLX_DIM; + q15_t *inD = inC + n2 * CMPLX_DIM; + q15_t const *pW1 = p_rearranged_twiddle_tab_stride1; + q15_t const *pW2 = p_rearranged_twiddle_tab_stride2; + q15_t const *pW3 = p_rearranged_twiddle_tab_stride3; + q15x8_t vecW; + + + blkCnt = n2 / 4; + /* + * load 4 x q15 complex pair + */ + vecA = vldrhq_s16(inA); + vecC = vldrhq_s16(inC); + while (blkCnt > 0U) + { + vecB = vldrhq_s16(inB); + vecD = vldrhq_s16(inD); + + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vhaddq(vecSum0, vecSum1); + vst1q(inA, vecTmp0); + inA += 8; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vhsubq(vecSum0, vecSum1); + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW2); + pW2 += 8; + vecTmp1 = MVE_CMPLX_MULT_FX_AxConjB(vecTmp0, vecW, q15x8_t); + + vst1q(inB, vecTmp1); + inB += 8; + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW1); + pW1 += 8; + vecTmp1 = MVE_CMPLX_MULT_FX_AxConjB(vecTmp0, vecW, q15x8_t); + vst1q(inC, vecTmp1); + inC += 8; + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 8; + vecTmp1 = MVE_CMPLX_MULT_FX_AxConjB(vecTmp0, vecW, q15x8_t); + vst1q(inD, vecTmp1); + inD += 8; + + vecA = vldrhq_s16(inA); + vecC = vldrhq_s16(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* + * load scheduling + */ + vecA = (q15x8_t) vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 8); + + blkCnt = (fftLen >> 4); + while (blkCnt > 0U) + { + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecB = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 4); + vecD = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 12); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * pre-load for next iteration + */ + vecA = (q15x8_t) vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = (q15x8_t) vldrwq_gather_base_s32(vecScGathAddr, 8); + + vecTmp0 = vhaddq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64, (int32x4_t) vecTmp0); + + vecTmp0 = vhsubq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 4, (int32x4_t) vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 8, (int32x4_t) vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 12, (int32x4_t) vecTmp0); + + blkCnt--; + } +} + +static void arm_cfft_radix4by2_inverse_q15_mve(const arm_cfft_instance_q15 *S, q15_t *pSrc, uint32_t fftLen) +{ + uint32_t n2; + q15_t *pIn0; + q15_t *pIn1; + const q15_t *pCoef = S->pTwiddle; + + uint32_t blkCnt; + q15x8_t vecIn0, vecIn1, vecSum, vecDiff; + q15x8_t vecCmplxTmp, vecTw; + q15_t const *pCoefVec; + + n2 = fftLen >> 1; + + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + pCoefVec = pCoef; + + blkCnt = n2 / 4; + + while (blkCnt > 0U) + { + vecIn0 = *(q15x8_t *) pIn0; + vecIn1 = *(q15x8_t *) pIn1; + + vecIn0 = vecIn0 >> 1; + vecIn1 = vecIn1 >> 1; + vecSum = vhaddq(vecIn0, vecIn1); + vst1q(pIn0, vecSum); + pIn0 += 8; + + vecTw = vld1q(pCoefVec); + pCoefVec += 8; + + vecDiff = vhsubq(vecIn0, vecIn1); + vecCmplxTmp = vqrdmlsdhq(vuninitializedq_s16() , vecDiff, vecTw); + vecCmplxTmp = vqrdmladhxq(vecCmplxTmp, vecDiff, vecTw); + vst1q(pIn1, vecCmplxTmp); + pIn1 += 8; + + blkCnt--; + } + + + _arm_radix4_butterfly_inverse_q15_mve(S, pSrc, n2); + + _arm_radix4_butterfly_inverse_q15_mve(S, pSrc + fftLen, n2); + + pIn0 = pSrc; + blkCnt = (fftLen << 1) >> 3; + while (blkCnt > 0U) + { + vecIn0 = *(q15x8_t *) pIn0; + vecIn0 = vecIn0 << 1; + vst1q(pIn0, vecIn0); + pIn0 += 8; + blkCnt--; + } + /* + * tail + * (will be merged thru tail predication) + */ + blkCnt = (fftLen << 1) & 7; + while (blkCnt > 0U) + { + mve_pred16_t p0 = vctp16q(blkCnt); + + vecIn0 = *(q15x8_t *) pIn0; + vecIn0 = vecIn0 << 1; + vstrhq_p(pIn0, vecIn0, p0); + } +} + +ARM_DSP_ATTRIBUTE void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + q15_t * pSrc, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t fftLen = S->fftLen; + + if (ifftFlag == 1U) { + + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_inverse_q15_mve(S, pSrc, fftLen); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_inverse_q15_mve(S, pSrc, fftLen); + break; + } + } else { + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_q15_mve(S, pSrc, fftLen); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_q15_mve(S, pSrc, fftLen); + break; + } + } + + + if (bitReverseFlag) + { + + arm_bitreversal_16_inpl_mve((uint16_t*)pSrc, S->bitRevLength, S->pBitRevTable); + + } +} + +#else + +#if !defined(ARM_MATH_NEON) + +extern void arm_radix4_butterfly_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_radix4_butterfly_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_bitreversal_16( + uint16_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef); + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef); + +#endif + +/** + @addtogroup ComplexFFTQ15 + @{ + */ + +/** + @brief Processing function for Q15 complex FFT. + @param[in] S points to an instance of Q15 CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + + @par Input and Output formats for CFFT Q15 + +| CFFT Size | Input Format | Output Format | Number of bits to upscale | +| ---------: | ------------: | -------------: | ------------------------: | +| 16 | 1.15 | 5.11 | 4 +| 64 | 1.15 | 7.9 | 6 +| 256 | 1.15 | 9.7 | 8 +| 1024 | 1.15 | 11.5 | 10 + + @par Input and Output formats for CIFFT Q15 + +| CIFFT Size | Input Format | Output Format | Number of bits to upscale | +| ----------: | ------------: | -------------: | ------------------------: | +| 16 | 1.15 | 5.11 | 0 +| 64 | 1.15 | 7.9 | 0 +| 256 | 1.15 | 9.7 | 0 +| 1024 | 1.15 | 11.5 | 0 + + @par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is a temporary buffer. + The bit reverse flag is not more + available in Neon version. + + @code + void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + const q15_t * src, + q15_t * dst, + q15_t *buffer, + uint8_t ifftFlag) + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ + +#if defined(ARM_MATH_NEON) +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + +ARM_DSP_ATTRIBUTE void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + const q15_t * src, + q15_t * dst, + q15_t *buffer, + uint8_t ifftFlag) +{ + arm_ne10_fft_c2c_1d_int16_neon (dst,src,S,ifftFlag,1,buffer); +} + +#else +ARM_DSP_ATTRIBUTE void arm_cfft_q15( + const arm_cfft_instance_q15 * S, + q15_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t L = S->fftLen; + + if (ifftFlag == 1U) + { + switch (L) + { + case 16: + case 64: + case 256: + case 1024: + case 4096: + arm_radix4_butterfly_inverse_q15 ( p1, L, (q15_t*)S->pTwiddle, 1 ); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_inverse_q15 ( p1, L, S->pTwiddle ); + break; + } + } + else + { + switch (L) + { + case 16: + case 64: + case 256: + case 1024: + case 4096: + arm_radix4_butterfly_q15 ( p1, L, (q15_t*)S->pTwiddle, 1 ); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_q15 ( p1, L, S->pTwiddle ); + break; + } + } + + if ( bitReverseFlag ) + arm_bitreversal_16 ((uint16_t*) p1, S->bitRevLength, S->pBitRevTable); +} + +#endif + +/** + @} end of ComplexFFTQ15 group + */ + +#if !defined(ARM_MATH_NEON) + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef) +{ + uint32_t i; + uint32_t n2; + q15_t p0, p1, p2, p3; +#if defined (ARM_MATH_DSP) + q31_t T, S, R; + q31_t coeff, out1, out2; + const q15_t *pC = pCoef; + q15_t *pSi = pSrc; + q15_t *pSl = pSrc + fftLen; +#else + uint32_t l; + q15_t xt, yt, cosVal, sinVal; +#endif + + n2 = fftLen >> 1U; + +#if defined (ARM_MATH_DSP) + + for (i = n2; i > 0; i--) + { + coeff = read_q15x2_ia (&pC); + + T = read_q15x2 (pSi); + T = __SHADD16(T, 0); /* this is just a SIMD arithmetic shift right by 1 */ + + S = read_q15x2 (pSl); + S = __SHADD16(S, 0); /* this is just a SIMD arithmetic shift right by 1 */ + + R = __QSUB16(T, S); + + write_q15x2_ia (&pSi, __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUAD(coeff, R) >> 16U; + out2 = __SMUSDX(coeff, R); +#else + out1 = __SMUSDX(R, coeff) >> 16U; + out2 = __SMUAD(coeff, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2_ia (&pSl, (q31_t)__PKHBT( out1, out2, 0 ) ); + } + +#else /* #if defined (ARM_MATH_DSP) */ + + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2 * i]; + sinVal = pCoef[2 * i + 1]; + + l = i + n2; + + xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U); + pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U; + + yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U); + pSrc[2 * i + 1] = ((pSrc[2 * l + 1] >> 1U) + (pSrc[2 * i + 1] >> 1U)) >> 1U; + + pSrc[2 * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16U)) + + ((int16_t) (((q31_t) yt * sinVal) >> 16U)) ); + + pSrc[2 * l + 1] = (((int16_t) (((q31_t) yt * cosVal) >> 16U)) - + ((int16_t) (((q31_t) xt * sinVal) >> 16U)) ); + } + +#endif /* #if defined (ARM_MATH_DSP) */ + + /* first col */ + arm_radix4_butterfly_q15( pSrc, n2, (q15_t*)pCoef, 2U); + + /* second col */ + arm_radix4_butterfly_q15( pSrc + fftLen, n2, (q15_t*)pCoef, 2U); + + n2 = fftLen >> 1U; + for (i = 0; i < n2; i++) + { + p0 = pSrc[4 * i + 0]; + p1 = pSrc[4 * i + 1]; + p2 = pSrc[4 * i + 2]; + p3 = pSrc[4 * i + 3]; + + p0 <<= 1U; + p1 <<= 1U; + p2 <<= 1U; + p3 <<= 1U; + + pSrc[4 * i + 0] = p0; + pSrc[4 * i + 1] = p1; + pSrc[4 * i + 2] = p2; + pSrc[4 * i + 3] = p3; + } + +} + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef) +{ + uint32_t i; + uint32_t n2; + q15_t p0, p1, p2, p3; +#if defined (ARM_MATH_DSP) + q31_t T, S, R; + q31_t coeff, out1, out2; + const q15_t *pC = pCoef; + q15_t *pSi = pSrc; + q15_t *pSl = pSrc + fftLen; +#else + uint32_t l; + q15_t xt, yt, cosVal, sinVal; +#endif + + n2 = fftLen >> 1U; + +#if defined (ARM_MATH_DSP) + + for (i = n2; i > 0; i--) + { + coeff = read_q15x2_ia (&pC); + + T = read_q15x2 (pSi); + T = __SHADD16(T, 0); /* this is just a SIMD arithmetic shift right by 1 */ + + S = read_q15x2 (pSl); + S = __SHADD16(S, 0); /* this is just a SIMD arithmetic shift right by 1 */ + + R = __QSUB16(T, S); + + write_q15x2_ia (&pSi, __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUSD(coeff, R) >> 16U; + out2 = __SMUADX(coeff, R); +#else + out1 = __SMUADX(R, coeff) >> 16U; + out2 = __SMUSD(__QSUB(0, coeff), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2_ia (&pSl, (q31_t)__PKHBT( out1, out2, 0 )); + } + +#else /* #if defined (ARM_MATH_DSP) */ + + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2 * i]; + sinVal = pCoef[2 * i + 1]; + + l = i + n2; + + xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U); + pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U; + + yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U); + pSrc[2 * i + 1] = ((pSrc[2 * l + 1] >> 1U) + (pSrc[2 * i + 1] >> 1U)) >> 1U; + + pSrc[2 * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16U)) - + ((int16_t) (((q31_t) yt * sinVal) >> 16U)) ); + + pSrc[2 * l + 1] = (((int16_t) (((q31_t) yt * cosVal) >> 16U)) + + ((int16_t) (((q31_t) xt * sinVal) >> 16U)) ); + } + +#endif /* #if defined (ARM_MATH_DSP) */ + + /* first col */ + arm_radix4_butterfly_inverse_q15( pSrc, n2, (q15_t*)pCoef, 2U); + + /* second col */ + arm_radix4_butterfly_inverse_q15( pSrc + fftLen, n2, (q15_t*)pCoef, 2U); + + n2 = fftLen >> 1U; + for (i = 0; i < n2; i++) + { + p0 = pSrc[4 * i + 0]; + p1 = pSrc[4 * i + 1]; + p2 = pSrc[4 * i + 2]; + p3 = pSrc[4 * i + 3]; + + p0 <<= 1U; + p1 <<= 1U; + p2 <<= 1U; + p3 <<= 1U; + + pSrc[4 * i + 0] = p0; + pSrc[4 * i + 1] = p1; + pSrc[4 * i + 2] = p2; + pSrc[4 * i + 3] = p3; + } +} +#endif /* defined NEON */ +#endif /* defined(ARM_MATH_MVEI) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_q31.c new file mode 100755 index 0000000..10bf8ef --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_q31.c @@ -0,0 +1,886 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_q31.c + * Description: Combined Radix Decimation in Frequency CFFT fixed point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_vec_fft.h" + + +static void _arm_radix4_butterfly_q31_mve( + const arm_cfft_instance_q31 * S, + q31_t *pSrc, + uint32_t fftLen) +{ + q31x4_t vecTmp0, vecTmp1; + q31x4_t vecSum0, vecDiff0, vecSum1, vecDiff1; + q31x4_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + (0 - 16) * (int32_t)sizeof(q31_t *), (1 - 16) * (int32_t)sizeof(q31_t *), + (8 - 16) * (int32_t)sizeof(q31_t *), (9 - 16) * (int32_t)sizeof(q31_t *) + }; + + + /* + * Process first stages + * Each stage in middle stages provides two down scaling of the input + */ + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + + for (int k = fftLen / 4u; k > 1; k >>= 2u) + { + q31_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + q31_t const *p_rearranged_twiddle_tab_stride3 = &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + q31_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + + q31_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + q31_t *inA = pBase; + q31_t *inB = inA + n2 * CMPLX_DIM; + q31_t *inC = inB + n2 * CMPLX_DIM; + q31_t *inD = inC + n2 * CMPLX_DIM; + q31_t const *pW1 = p_rearranged_twiddle_tab_stride1; + q31_t const *pW2 = p_rearranged_twiddle_tab_stride2; + q31_t const *pW3 = p_rearranged_twiddle_tab_stride3; + q31x4_t vecW; + + + blkCnt = n2 / 2; + /* + * load 2 x q31 complex pair + */ + vecA = vldrwq_s32(inA); + vecC = vldrwq_s32(inC); + while (blkCnt > 0U) + { + vecB = vldrwq_s32(inB); + vecD = vldrwq_s32(inD); + + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vhaddq(vecSum0, vecSum1); + vst1q(inA, vecTmp0); + inA += 4; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vhsubq(vecSum0, vecSum1); + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW2); + pW2 += 4; + vecTmp1 = MVE_CMPLX_MULT_FX_AxB(vecW, vecTmp0, q31x4_t); + + vst1q(inB, vecTmp1); + inB += 4; + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW1); + pW1 += 4; + vecTmp1 = MVE_CMPLX_MULT_FX_AxB(vecW, vecTmp0, q31x4_t); + vst1q(inC, vecTmp1); + inC += 4; + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 4; + vecTmp1 = MVE_CMPLX_MULT_FX_AxB(vecW, vecTmp0, q31x4_t); + vst1q(inD, vecTmp1); + inD += 4; + + vecA = vldrwq_s32(inA); + vecC = vldrwq_s32(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * End of 1st stages process + * data is in 11.21(q21) format for the 1024 point as there are 3 middle stages + * data is in 9.23(q23) format for the 256 point as there are 2 middle stages + * data is in 7.25(q25) format for the 64 point as there are 1 middle stage + * data is in 5.27(q27) format for the 16 point as there are no middle stages + */ + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* + * load scheduling + */ + vecA = vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_s32(vecScGathAddr, 16); + + blkCnt = (fftLen >> 3); + while (blkCnt > 0U) + { + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecB = vldrwq_gather_base_s32(vecScGathAddr, 8); + vecD = vldrwq_gather_base_s32(vecScGathAddr, 24); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * pre-load for next iteration + */ + vecA = vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_s32(vecScGathAddr, 16); + + vecTmp0 = vhaddq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64, vecTmp0); + + vecTmp0 = vhsubq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 8, vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 16, vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 24, vecTmp0); + + blkCnt--; + } + + /* + * output is in 11.21(q21) format for the 1024 point + * output is in 9.23(q23) format for the 256 point + * output is in 7.25(q25) format for the 64 point + * output is in 5.27(q27) format for the 16 point + */ +} + + +static void arm_cfft_radix4by2_q31_mve(const arm_cfft_instance_q31 *S, q31_t *pSrc, uint32_t fftLen) +{ + uint32_t n2; + q31_t *pIn0; + q31_t *pIn1; + const q31_t *pCoef = S->pTwiddle; + uint32_t blkCnt; + q31x4_t vecIn0, vecIn1, vecSum, vecDiff; + q31x4_t vecCmplxTmp, vecTw; + + n2 = fftLen >> 1; + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + + blkCnt = n2 / 2; + + while (blkCnt > 0U) + { + vecIn0 = vld1q_s32(pIn0); + vecIn1 = vld1q_s32(pIn1); + + vecIn0 = vecIn0 >> 1; + vecIn1 = vecIn1 >> 1; + vecSum = vhaddq(vecIn0, vecIn1); + vst1q(pIn0, vecSum); + pIn0 += 4; + + vecTw = vld1q_s32(pCoef); + pCoef += 4; + vecDiff = vhsubq(vecIn0, vecIn1); + + vecCmplxTmp = MVE_CMPLX_MULT_FX_AxConjB(vecDiff, vecTw, q31x4_t); + vst1q(pIn1, vecCmplxTmp); + pIn1 += 4; + + blkCnt--; + } + + _arm_radix4_butterfly_q31_mve(S, pSrc, n2); + + _arm_radix4_butterfly_q31_mve(S, pSrc + fftLen, n2); + + pIn0 = pSrc; + blkCnt = (fftLen << 1) >> 2; + while (blkCnt > 0U) + { + vecIn0 = vld1q_s32(pIn0); + vecIn0 = vecIn0 << 1; + vst1q(pIn0, vecIn0); + pIn0 += 4; + blkCnt--; + } + /* + * tail + * (will be merged thru tail predication) + */ + blkCnt = (fftLen << 1) & 3; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp32q(blkCnt); + + vecIn0 = vld1q_s32(pIn0); + vecIn0 = vecIn0 << 1; + vstrwq_p(pIn0, vecIn0, p0); + } + +} + +static void _arm_radix4_butterfly_inverse_q31_mve( + const arm_cfft_instance_q31 *S, + q31_t *pSrc, + uint32_t fftLen) +{ + q31x4_t vecTmp0, vecTmp1; + q31x4_t vecSum0, vecDiff0, vecSum1, vecDiff1; + q31x4_t vecA, vecB, vecC, vecD; + uint32_t blkCnt; + uint32_t n1, n2; + uint32_t stage = 0; + int32_t iter = 1; + static const int32_t strides[4] = { + (0 - 16) * (int32_t)sizeof(q31_t *), (1 - 16) * (int32_t)sizeof(q31_t *), + (8 - 16) * (int32_t)sizeof(q31_t *), (9 - 16) * (int32_t)sizeof(q31_t *) + }; + + /* + * Process first stages + * Each stage in middle stages provides two down scaling of the input + */ + n2 = fftLen; + n1 = n2; + n2 >>= 2u; + + for (int k = fftLen / 4u; k > 1; k >>= 2u) + { + q31_t const *p_rearranged_twiddle_tab_stride2 = + &S->rearranged_twiddle_stride2[ + S->rearranged_twiddle_tab_stride2_arr[stage]]; + q31_t const *p_rearranged_twiddle_tab_stride3 = &S->rearranged_twiddle_stride3[ + S->rearranged_twiddle_tab_stride3_arr[stage]]; + q31_t const *p_rearranged_twiddle_tab_stride1 = + &S->rearranged_twiddle_stride1[ + S->rearranged_twiddle_tab_stride1_arr[stage]]; + + q31_t * pBase = pSrc; + for (int i = 0; i < iter; i++) + { + q31_t *inA = pBase; + q31_t *inB = inA + n2 * CMPLX_DIM; + q31_t *inC = inB + n2 * CMPLX_DIM; + q31_t *inD = inC + n2 * CMPLX_DIM; + q31_t const *pW1 = p_rearranged_twiddle_tab_stride1; + q31_t const *pW2 = p_rearranged_twiddle_tab_stride2; + q31_t const *pW3 = p_rearranged_twiddle_tab_stride3; + q31x4_t vecW; + + blkCnt = n2 / 2; + /* + * load 2 x q31 complex pair + */ + vecA = vldrwq_s32(inA); + vecC = vldrwq_s32(inC); + while (blkCnt > 0U) + { + vecB = vldrwq_s32(inB); + vecD = vldrwq_s32(inD); + + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * [ 1 1 1 1 ] * [ A B C D ]' .* 1 + */ + vecTmp0 = vhaddq(vecSum0, vecSum1); + vst1q(inA, vecTmp0); + inA += 4; + /* + * [ 1 -1 1 -1 ] * [ A B C D ]' + */ + vecTmp0 = vhsubq(vecSum0, vecSum1); + /* + * [ 1 -1 1 -1 ] * [ A B C D ]'.* W2 + */ + vecW = vld1q(pW2); + pW2 += 4; + vecTmp1 = MVE_CMPLX_MULT_FX_AxConjB(vecTmp0, vecW, q31x4_t); + + vst1q(inB, vecTmp1); + inB += 4; + /* + * [ 1 -i -1 +i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 -i -1 +i ] * [ A B C D ]'.* W1 + */ + vecW = vld1q(pW1); + pW1 += 4; + vecTmp1 = MVE_CMPLX_MULT_FX_AxConjB(vecTmp0, vecW, q31x4_t); + vst1q(inC, vecTmp1); + inC += 4; + /* + * [ 1 +i -1 -i ] * [ A B C D ]' + */ + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + /* + * [ 1 +i -1 -i ] * [ A B C D ]'.* W3 + */ + vecW = vld1q(pW3); + pW3 += 4; + vecTmp1 = MVE_CMPLX_MULT_FX_AxConjB(vecTmp0, vecW, q31x4_t); + vst1q(inD, vecTmp1); + inD += 4; + + vecA = vldrwq_s32(inA); + vecC = vldrwq_s32(inC); + + blkCnt--; + } + pBase += CMPLX_DIM * n1; + } + n1 = n2; + n2 >>= 2u; + iter = iter << 2; + stage++; + } + + /* + * End of 1st stages process + * data is in 11.21(q21) format for the 1024 point as there are 3 middle stages + * data is in 9.23(q23) format for the 256 point as there are 2 middle stages + * data is in 7.25(q25) format for the 64 point as there are 1 middle stage + * data is in 5.27(q27) format for the 16 point as there are no middle stages + */ + + /* + * start of Last stage process + */ + uint32x4_t vecScGathAddr = vld1q_u32((uint32_t*)strides); + vecScGathAddr = vecScGathAddr + (uint32_t) pSrc; + + /* + * load scheduling + */ + vecA = vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_s32(vecScGathAddr, 16); + + blkCnt = (fftLen >> 3); + while (blkCnt > 0U) + { + vecSum0 = vhaddq(vecA, vecC); + vecDiff0 = vhsubq(vecA, vecC); + + vecB = vldrwq_gather_base_s32(vecScGathAddr, 8); + vecD = vldrwq_gather_base_s32(vecScGathAddr, 24); + + vecSum1 = vhaddq(vecB, vecD); + vecDiff1 = vhsubq(vecB, vecD); + /* + * pre-load for next iteration + */ + vecA = vldrwq_gather_base_wb_s32(&vecScGathAddr, 64); + vecC = vldrwq_gather_base_s32(vecScGathAddr, 16); + + vecTmp0 = vhaddq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64, vecTmp0); + + vecTmp0 = vhsubq(vecSum0, vecSum1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 8, vecTmp0); + + vecTmp0 = MVE_CMPLX_ADD_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 16, vecTmp0); + + vecTmp0 = MVE_CMPLX_SUB_FX_A_ixB(vecDiff0, vecDiff1); + vstrwq_scatter_base_s32(vecScGathAddr, -64 + 24, vecTmp0); + + blkCnt--; + } + /* + * output is in 11.21(q21) format for the 1024 point + * output is in 9.23(q23) format for the 256 point + * output is in 7.25(q25) format for the 64 point + * output is in 5.27(q27) format for the 16 point + */ +} + +static void arm_cfft_radix4by2_inverse_q31_mve(const arm_cfft_instance_q31 *S, q31_t *pSrc, uint32_t fftLen) +{ + uint32_t n2; + q31_t *pIn0; + q31_t *pIn1; + const q31_t *pCoef = S->pTwiddle; + + //uint16_t twidCoefModifier = arm_cfft_radix2_twiddle_factor(S->fftLen); + //q31_t twidIncr = (2 * twidCoefModifier * sizeof(q31_t)); + uint32_t blkCnt; + //uint64x2_t vecOffs; + q31x4_t vecIn0, vecIn1, vecSum, vecDiff; + q31x4_t vecCmplxTmp, vecTw; + + n2 = fftLen >> 1; + + pIn0 = pSrc; + pIn1 = pSrc + fftLen; + //vecOffs[0] = 0; + //vecOffs[1] = (uint64_t) twidIncr; + blkCnt = n2 / 2; + + while (blkCnt > 0U) + { + vecIn0 = vld1q_s32(pIn0); + vecIn1 = vld1q_s32(pIn1); + + vecIn0 = vecIn0 >> 1; + vecIn1 = vecIn1 >> 1; + vecSum = vhaddq(vecIn0, vecIn1); + vst1q(pIn0, vecSum); + pIn0 += 4; + + //vecTw = (q31x4_t) vldrdq_gather_offset_s64(pCoef, vecOffs); + vecTw = vld1q_s32(pCoef); + pCoef += 4; + vecDiff = vhsubq(vecIn0, vecIn1); + + vecCmplxTmp = MVE_CMPLX_MULT_FX_AxB(vecDiff, vecTw, q31x4_t); + vst1q(pIn1, vecCmplxTmp); + pIn1 += 4; + + //vecOffs = vaddq((q31x4_t) vecOffs, 2 * twidIncr); + blkCnt--; + } + + _arm_radix4_butterfly_inverse_q31_mve(S, pSrc, n2); + + _arm_radix4_butterfly_inverse_q31_mve(S, pSrc + fftLen, n2); + + pIn0 = pSrc; + blkCnt = (fftLen << 1) >> 2; + while (blkCnt > 0U) + { + vecIn0 = vld1q_s32(pIn0); + vecIn0 = vecIn0 << 1; + vst1q(pIn0, vecIn0); + pIn0 += 4; + blkCnt--; + } + /* + * tail + * (will be merged thru tail predication) + */ + blkCnt = (fftLen << 1) & 3; + if (blkCnt > 0U) + { + mve_pred16_t p0 = vctp32q(blkCnt); + + vecIn0 = vld1q_s32(pIn0); + vecIn0 = vecIn0 << 1; + vstrwq_p(pIn0, vecIn0, p0); + } + +} + + +ARM_DSP_ATTRIBUTE void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + q31_t * pSrc, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t fftLen = S->fftLen; + + if (ifftFlag == 1U) { + + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_inverse_q31_mve(S, pSrc, fftLen); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_inverse_q31_mve(S, pSrc, fftLen); + break; + } + } else { + switch (fftLen) { + case 16: + case 64: + case 256: + case 1024: + case 4096: + _arm_radix4_butterfly_q31_mve(S, pSrc, fftLen); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_q31_mve(S, pSrc, fftLen); + break; + } + } + + + if (bitReverseFlag) + { + + arm_bitreversal_32_inpl_mve((uint32_t*)pSrc, S->bitRevLength, S->pBitRevTable); + + } +} +#else + +#if !defined(ARM_MATH_NEON) +extern void arm_radix4_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_radix4_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_bitreversal_32( + uint32_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef); + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef); +#endif + +/** + @addtogroup ComplexFFTQ31 + @{ + */ + +/** + @brief Processing function for the Q31 complex FFT. + @param[in] S points to an instance of the fixed-point CFFT structure + @param[in,out] p1 points to the complex data buffer. Processing occurs in-place + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + +@par Input and Output formats for CFFT Q31 + +| CFFT Size | Input Format | Output Format | Number of bits to upscale | +| ---------: | ------------: | -------------: | ------------------------: | +| 16 | 1.31 | 5.27 | 4 +| 64 | 1.31 | 7.25 | 6 +| 256 | 1.31 | 9.23 | 8 +| 1024 | 1.31 | 11.21 | 10 + +@par Input and Output formats for CIFFT Q31 + +| CIFFT Size | Input Format | Output Format | Number of bits to upscale | +| ----------: | ------------: | -------------: | ------------------------: | +| 16 | 1.31 | 5.27 | 0 +| 64 | 1.31 | 7.25 | 0 +| 256 | 1.31 | 9.23 | 0 +| 1024 | 1.31 | 11.21 | 0 + + + @par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is a temporary buffer. + The bit reverse flag is not more + available in Neon version. + + @code + void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + const q31_t * src, + q31_t * dst, + q31_t *buffer, + uint8_t ifftFlag + ) + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ +#if defined(ARM_MATH_NEON) +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + +ARM_DSP_ATTRIBUTE void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + const q31_t * src, + q31_t * dst, + q31_t *buffer, + uint8_t ifftFlag + ) +{ + arm_ne10_fft_c2c_1d_int32_neon (dst,src,S,ifftFlag,1,buffer); +} + +#else +ARM_DSP_ATTRIBUTE void arm_cfft_q31( + const arm_cfft_instance_q31 * S, + q31_t * p1, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + uint32_t L = S->fftLen; + + if (ifftFlag == 1U) + { + switch (L) + { + case 16: + case 64: + case 256: + case 1024: + case 4096: + arm_radix4_butterfly_inverse_q31 ( p1, L, (q31_t*)S->pTwiddle, 1 ); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_inverse_q31 ( p1, L, S->pTwiddle ); + break; + } + } + else + { + switch (L) + { + case 16: + case 64: + case 256: + case 1024: + case 4096: + arm_radix4_butterfly_q31 ( p1, L, (q31_t*)S->pTwiddle, 1 ); + break; + + case 32: + case 128: + case 512: + case 2048: + arm_cfft_radix4by2_q31 ( p1, L, S->pTwiddle ); + break; + } + } + + if ( bitReverseFlag ) + arm_bitreversal_32 ((uint32_t*) p1, S->bitRevLength, S->pBitRevTable); +} +#endif + +/** + @} end of ComplexFFTQ31 group + */ + +#if !defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef) +{ + uint32_t i, l; + uint32_t n2; + q31_t xt, yt, cosVal, sinVal; + q31_t p0, p1; + + n2 = fftLen >> 1U; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2 * i]; + sinVal = pCoef[2 * i + 1]; + + l = i + n2; + + xt = (pSrc[2 * i] >> 2U) - (pSrc[2 * l] >> 2U); + pSrc[2 * i] = (pSrc[2 * i] >> 2U) + (pSrc[2 * l] >> 2U); + + yt = (pSrc[2 * i + 1] >> 2U) - (pSrc[2 * l + 1] >> 2U); + pSrc[2 * i + 1] = (pSrc[2 * l + 1] >> 2U) + (pSrc[2 * i + 1] >> 2U); + + mult_32x32_keep32_R(p0, xt, cosVal); + mult_32x32_keep32_R(p1, yt, cosVal); + multAcc_32x32_keep32_R(p0, yt, sinVal); + multSub_32x32_keep32_R(p1, xt, sinVal); + + pSrc[2 * l] = p0 << 1; + pSrc[2 * l + 1] = p1 << 1; + } + + + /* first col */ + arm_radix4_butterfly_q31 (pSrc, n2, (q31_t*)pCoef, 2U); + + /* second col */ + arm_radix4_butterfly_q31 (pSrc + fftLen, n2, (q31_t*)pCoef, 2U); + + n2 = fftLen >> 1U; + for (i = 0; i < n2; i++) + { + p0 = pSrc[4 * i + 0]; + p1 = pSrc[4 * i + 1]; + xt = pSrc[4 * i + 2]; + yt = pSrc[4 * i + 3]; + + p0 <<= 1U; + p1 <<= 1U; + xt <<= 1U; + yt <<= 1U; + + pSrc[4 * i + 0] = p0; + pSrc[4 * i + 1] = p1; + pSrc[4 * i + 2] = xt; + pSrc[4 * i + 3] = yt; + } + +} + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef) +{ + uint32_t i, l; + uint32_t n2; + q31_t xt, yt, cosVal, sinVal; + q31_t p0, p1; + + n2 = fftLen >> 1U; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2 * i]; + sinVal = pCoef[2 * i + 1]; + + l = i + n2; + + xt = (pSrc[2 * i] >> 2U) - (pSrc[2 * l] >> 2U); + pSrc[2 * i] = (pSrc[2 * i] >> 2U) + (pSrc[2 * l] >> 2U); + + yt = (pSrc[2 * i + 1] >> 2U) - (pSrc[2 * l + 1] >> 2U); + pSrc[2 * i + 1] = (pSrc[2 * l + 1] >> 2U) + (pSrc[2 * i + 1] >> 2U); + + mult_32x32_keep32_R(p0, xt, cosVal); + mult_32x32_keep32_R(p1, yt, cosVal); + multSub_32x32_keep32_R(p0, yt, sinVal); + multAcc_32x32_keep32_R(p1, xt, sinVal); + + pSrc[2 * l] = p0 << 1U; + pSrc[2 * l + 1] = p1 << 1U; + } + + /* first col */ + arm_radix4_butterfly_inverse_q31( pSrc, n2, (q31_t*)pCoef, 2U); + + /* second col */ + arm_radix4_butterfly_inverse_q31( pSrc + fftLen, n2, (q31_t*)pCoef, 2U); + + n2 = fftLen >> 1U; + for (i = 0; i < n2; i++) + { + p0 = pSrc[4 * i + 0]; + p1 = pSrc[4 * i + 1]; + xt = pSrc[4 * i + 2]; + yt = pSrc[4 * i + 3]; + + p0 <<= 1U; + p1 <<= 1U; + xt <<= 1U; + yt <<= 1U; + + pSrc[4 * i + 0] = p0; + pSrc[4 * i + 1] = p1; + pSrc[4 * i + 2] = xt; + pSrc[4 * i + 3] = yt; + } +} +#endif /* defined NEON */ +#endif /* defined(ARM_MATH_MVEI) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_f16.c new file mode 100755 index 0000000..23aa43c --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_f16.c @@ -0,0 +1,480 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_f16.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" + +/** + * @defgroup ComplexFFTDeprecated Deprecated Complex FFT functions + */ + +#if defined(ARM_FLOAT16_SUPPORTED) + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_f16( + float16_t * pSrc, + uint32_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_f16( + float16_t * pSrc, + uint32_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier, + float16_t onebyfftLen); + +extern void arm_bitreversal_f16( + float16_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + +/** + @ingroup ComplexFFT + */ + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Radix-2 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f16 and will be removed in the future + @param[in] S points to an instance of the floating-point Radix-2 CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix2_f16( +const arm_cfft_radix2_instance_f16 * S, + float16_t * pSrc) +{ + + if (S->ifftFlag == 1U) + { + /* Complex IFFT radix-2 */ + arm_radix2_butterfly_inverse_f16(pSrc, S->fftLen, S->pTwiddle, + S->twidCoefModifier, S->onebyfftLen); + } + else + { + /* Complex FFT radix-2 */ + arm_radix2_butterfly_f16(pSrc, S->fftLen, S->pTwiddle, + S->twidCoefModifier); + } + + if (S->bitReverseFlag == 1U) + { + /* Bit Reversal */ + arm_bitreversal_f16(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + + +/** + @} end of ComplexFFTDeprecated group + */ + + + +/* ---------------------------------------------------------------------- +** Internal helper function used by the FFTs +** ------------------------------------------------------------------- */ + +/* +* @brief Core function for the floating-point CFFT butterfly process. +* @param[in, out] *pSrc points to the in-place buffer of floating-point data type. +* @param[in] fftLen length of the FFT. +* @param[in] *pCoef points to the twiddle coefficient buffer. +* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +*/ + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_f16( +float16_t * pSrc, +uint32_t fftLen, +const float16_t * pCoef, +uint16_t twidCoefModifier) +{ + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + float16_t xt, yt, cosVal, sinVal; + float16_t p0, p1, p2, p3; + float16_t a0, a1; + +#if defined (ARM_MATH_DSP) + + /* Initializations for the first stage */ + n2 = fftLen >> 1; + ia = 0; + i = 0; + + // loop for groups + for (k = n2; k > 0; k--) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + + /* Twiddle coefficients index modifier */ + ia += twidCoefModifier; + + /* index calculation for the input as, */ + /* pSrc[i + 0], pSrc[i + fftLen/1] */ + l = i + n2; + + /* Butterfly implementation */ + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 + (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 - (_Float16)p3; + + i++; + } // groups loop end + + twidCoefModifier <<= 1U; + + // loop for stage + for (k = n2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 + (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 - (_Float16)p3; + + i += n1; + } while ( i < fftLen ); // butterfly loop end + j++; + } while ( j < n2); // groups loop end + twidCoefModifier <<= 1U; + } // stages loop end + + // loop for butterfly + for (i = 0; i < fftLen; i += 2) + { + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * i + 2]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * i + 2]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * i + 3]; + a1 = (_Float16)pSrc[2 * i + 3] + (_Float16)pSrc[2 * i + 1]; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + pSrc[2 * i + 2] = xt; + pSrc[2 * i + 3] = yt; + } // groups loop end + +#else + + n2 = fftLen; + + // loop for stage + for (k = fftLen; k > 1; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 + (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 - (_Float16)p3; + + i += n1; + } while (i < fftLen); + j++; + } while (j < n2); + twidCoefModifier <<= 1U; + } + +#endif // #if defined (ARM_MATH_DSP) + +} + + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_f16( +float16_t * pSrc, +uint32_t fftLen, +const float16_t * pCoef, +uint16_t twidCoefModifier, +float16_t onebyfftLen) +{ + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + float16_t xt, yt, cosVal, sinVal; + float16_t p0, p1, p2, p3; + float16_t a0, a1; + +#if defined (ARM_MATH_DSP) + + n2 = fftLen >> 1; + ia = 0; + + // loop for groups + for (i = 0; i < n2; i++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + l = i + n2; + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 - (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 + (_Float16)p3; + } // groups loop end + + twidCoefModifier <<= 1U; + + // loop for stage + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 - (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 + (_Float16)p3; + + i += n1; + } while ( i < fftLen ); // butterfly loop end + j++; + } while (j < n2); // groups loop end + + twidCoefModifier <<= 1U; + } // stages loop end + + // loop for butterfly + for (i = 0; i < fftLen; i += 2) + { + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * i + 2]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * i + 2]; + + a1 = (_Float16)pSrc[2 * i + 3] + (_Float16)pSrc[2 * i + 1]; + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * i + 3]; + + p0 = (_Float16)a0 * (_Float16)onebyfftLen; + p2 = (_Float16)xt * (_Float16)onebyfftLen; + p1 = (_Float16)a1 * (_Float16)onebyfftLen; + p3 = (_Float16)yt * (_Float16)onebyfftLen; + + pSrc[2 * i] = p0; + pSrc[2 * i + 1] = p1; + pSrc[2 * i + 2] = p2; + pSrc[2 * i + 3] = p3; + } // butterfly loop end + +#else + + n2 = fftLen; + + // loop for stage + for (k = fftLen; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 - (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 + (_Float16)p3; + + i += n1; + } while ( i < fftLen ); // butterfly loop end + j++; + } while ( j < n2 ); // groups loop end + + twidCoefModifier = twidCoefModifier << 1U; + } // stages loop end + + n1 = n2; + n2 = n2 >> 1; + + // loop for butterfly + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + + p0 = (_Float16)a0 * (_Float16)onebyfftLen; + p2 = (_Float16)xt * (_Float16)onebyfftLen; + p1 = (_Float16)a1 * (_Float16)onebyfftLen; + p3 = (_Float16)yt * (_Float16)onebyfftLen; + + pSrc[2 * i] = p0; + pSrc[2U * l] = p2; + + pSrc[2 * i + 1] = p1; + pSrc[2U * l + 1U] = p3; + } // butterfly loop end + +#endif // #if defined (ARM_MATH_DSP) + +} + + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_f32.c new file mode 100755 index 0000000..325d487 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_f32.c @@ -0,0 +1,470 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_f32.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_f32( + float32_t * pSrc, + uint32_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_f32( + float32_t * pSrc, + uint32_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen); + +extern void arm_bitreversal_f32( + float32_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Radix-2 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f32 and will be removed in the future + @param[in] S points to an instance of the floating-point Radix-2 CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix2_f32( +const arm_cfft_radix2_instance_f32 * S, + float32_t * pSrc) +{ + + if (S->ifftFlag == 1U) + { + /* Complex IFFT radix-2 */ + arm_radix2_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle, + S->twidCoefModifier, S->onebyfftLen); + } + else + { + /* Complex FFT radix-2 */ + arm_radix2_butterfly_f32(pSrc, S->fftLen, S->pTwiddle, + S->twidCoefModifier); + } + + if (S->bitReverseFlag == 1U) + { + /* Bit Reversal */ + arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + + +/** + @} end of ComplexFFTDeprecated group + */ + + + +/* ---------------------------------------------------------------------- + ** Internal helper function used by the FFTs + ** ------------------------------------------------------------------- */ + +/** + brief Core function for the floating-point CFFT butterfly process. + param[in,out] pSrc points to in-place buffer of floating-point data type + param[in] fftLen length of the FFT + param[in] pCoef points to twiddle coefficient buffer + param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + return none + */ + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_f32( + float32_t * pSrc, + uint32_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier) +{ + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + float32_t xt, yt, cosVal, sinVal; + float32_t p0, p1, p2, p3; + float32_t a0, a1; + +#if defined (ARM_MATH_DSP) + + /* Initializations for the first stage */ + n2 = fftLen >> 1; + ia = 0; + i = 0; + + // loop for groups + for (k = n2; k > 0; k--) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + + /* Twiddle coefficients index modifier */ + ia += twidCoefModifier; + + /* index calculation for the input as, */ + /* pSrc[i + 0], pSrc[i + fftLen/1] */ + l = i + n2; + + /* Butterfly implementation */ + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 + p1; + pSrc[2 * l + 1] = p2 - p3; + + i++; + } // groups loop end + + twidCoefModifier <<= 1U; + + // loop for stage + for (k = n2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 + p1; + pSrc[2 * l + 1] = p2 - p3; + + i += n1; + } while ( i < fftLen ); // butterfly loop end + j++; + } while ( j < n2); // groups loop end + twidCoefModifier <<= 1U; + } // stages loop end + + // loop for butterfly + for (i = 0; i < fftLen; i += 2) + { + a0 = pSrc[2 * i] + pSrc[2 * i + 2]; + xt = pSrc[2 * i] - pSrc[2 * i + 2]; + + yt = pSrc[2 * i + 1] - pSrc[2 * i + 3]; + a1 = pSrc[2 * i + 3] + pSrc[2 * i + 1]; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + pSrc[2 * i + 2] = xt; + pSrc[2 * i + 3] = yt; + } // groups loop end + +#else /* #if defined (ARM_MATH_DSP) */ + + n2 = fftLen; + + // loop for stage + for (k = fftLen; k > 1; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 + p1; + pSrc[2 * l + 1] = p2 - p3; + + i += n1; + } while (i < fftLen); + j++; + } while (j < n2); + twidCoefModifier <<= 1U; + } + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_f32( + float32_t * pSrc, + uint32_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen) +{ + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + float32_t xt, yt, cosVal, sinVal; + float32_t p0, p1, p2, p3; + float32_t a0, a1; + +#if defined (ARM_MATH_DSP) + + n2 = fftLen >> 1; + ia = 0; + + // loop for groups + for (i = 0; i < n2; i++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + l = i + n2; + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 - p1; + pSrc[2 * l + 1] = p2 + p3; + } // groups loop end + + twidCoefModifier <<= 1U; + + // loop for stage + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia += twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 - p1; + pSrc[2 * l + 1] = p2 + p3; + + i += n1; + } while ( i < fftLen ); // butterfly loop end + j++; + } while (j < n2); // groups loop end + + twidCoefModifier <<= 1U; + } // stages loop end + + // loop for butterfly + for (i = 0; i < fftLen; i += 2) + { + a0 = pSrc[2 * i] + pSrc[2 * i + 2]; + xt = pSrc[2 * i] - pSrc[2 * i + 2]; + + a1 = pSrc[2 * i + 3] + pSrc[2 * i + 1]; + yt = pSrc[2 * i + 1] - pSrc[2 * i + 3]; + + p0 = a0 * onebyfftLen; + p2 = xt * onebyfftLen; + p1 = a1 * onebyfftLen; + p3 = yt * onebyfftLen; + + pSrc[2 * i] = p0; + pSrc[2 * i + 1] = p1; + pSrc[2 * i + 2] = p2; + pSrc[2 * i + 3] = p3; + } // butterfly loop end + +#else /* #if defined (ARM_MATH_DSP) */ + + n2 = fftLen; + + // loop for stage + for (k = fftLen; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + j = 0; + do + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + // loop for butterfly + i = j; + do + { + l = i + n2; + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + + p0 = xt * cosVal; + p1 = yt * sinVal; + p2 = yt * cosVal; + p3 = xt * sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = p0 - p1; + pSrc[2 * l + 1] = p2 + p3; + + i += n1; + } while ( i < fftLen ); // butterfly loop end + j++; + } while ( j < n2 ); // groups loop end + + twidCoefModifier = twidCoefModifier << 1U; + } // stages loop end + + n1 = n2; + n2 = n2 >> 1; + + // loop for butterfly + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + + a0 = pSrc[2 * i] + pSrc[2 * l]; + xt = pSrc[2 * i] - pSrc[2 * l]; + + a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1]; + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + + p0 = a0 * onebyfftLen; + p2 = xt * onebyfftLen; + p1 = a1 * onebyfftLen; + p3 = yt * onebyfftLen; + + pSrc[2 * i] = p0; + pSrc[2 * l] = p2; + + pSrc[2 * i + 1] = p1; + pSrc[2 * l + 1] = p3; + } // butterfly loop end + +#endif /* #if defined (ARM_MATH_DSP) */ + +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_f16.c new file mode 100755 index 0000000..03b0e3f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_f16.c @@ -0,0 +1,207 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_f16.c + * Description: Radix-2 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" +#include "arm_common_tables.h" +#include "arm_common_tables_f16.h" + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Initialization function for the floating-point CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f16 and will be removed in the future. + @param[in,out] S points to an instance of the floating-point CFFT/CIFFT structure + @param[in] fftLen length of the FFT + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. +*/ + +#if defined(ARM_FLOAT16_SUPPORTED) + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix2_init_f16( + arm_cfft_radix2_instance_f16 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + + /* Initialise the FFT length */ + S->fftLen = fftLen; + + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (float16_t *) twiddleCoefF16_4096; + + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLen) + { + + case 4096U: + /* Initializations of structure parameters for 4096 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.000244140625; + break; + + case 2048U: + /* Initializations of structure parameters for 2048 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 2U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 2U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[1]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.00048828125; + break; + + case 1024U: + /* Initializations of structure parameters for 1024 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 4U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 4U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.0009765625f; + break; + + case 512U: + /* Initializations of structure parameters for 512 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 8U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 8U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[7]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.001953125; + break; + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + S->onebyfftLen = 0.00390625f; + break; + + case 128U: + /* Initializations of structure parameters for 128 point FFT */ + S->twidCoefModifier = 32U; + S->bitRevFactor = 32U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[31]; + S->onebyfftLen = 0.0078125; + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + S->onebyfftLen = 0.015625f; + break; + + case 32U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 128U; + S->bitRevFactor = 128U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[127]; + S->onebyfftLen = 0.03125; + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + S->onebyfftLen = 0.0625f; + break; + + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_f32.c new file mode 100755 index 0000000..409becb --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_f32.c @@ -0,0 +1,199 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_f32.c + * Description: Radix-2 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Initialization function for the floating-point CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f32 and will be removed in the future. + @param[in,out] S points to an instance of the floating-point CFFT/CIFFT structure + @param[in] fftLen length of the FFT + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. +*/ + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix2_init_f32( + arm_cfft_radix2_instance_f32 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + + /* Initialise the FFT length */ + S->fftLen = fftLen; + + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (float32_t *) twiddleCoef; + + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLen) + { + + case 4096U: + /* Initializations of structure parameters for 4096 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.000244140625; + break; + + case 2048U: + /* Initializations of structure parameters for 2048 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 2U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 2U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[1]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.00048828125; + break; + + case 1024U: + /* Initializations of structure parameters for 1024 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 4U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 4U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.0009765625f; + break; + + case 512U: + /* Initializations of structure parameters for 512 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 8U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 8U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[7]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.001953125; + break; + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + S->onebyfftLen = 0.00390625f; + break; + + case 128U: + /* Initializations of structure parameters for 128 point FFT */ + S->twidCoefModifier = 32U; + S->bitRevFactor = 32U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[31]; + S->onebyfftLen = 0.0078125; + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + S->onebyfftLen = 0.015625f; + break; + + case 32U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 128U; + S->bitRevFactor = 128U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[127]; + S->onebyfftLen = 0.03125; + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + S->onebyfftLen = 0.0625f; + break; + + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} + +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_q15.c new file mode 100755 index 0000000..3069239 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_q15.c @@ -0,0 +1,184 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_q15.c + * Description: Radix-2 Decimation in Frequency Q15 FFT & IFFT initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Initialization function for the Q15 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q15 and will be removed + @param[in,out] S points to an instance of the Q15 CFFT/CIFFT structure. + @param[in] fftLen length of the FFT. + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. +*/ + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix2_init_q15( + arm_cfft_radix2_instance_q15 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + + /* Initialise the FFT length */ + S->fftLen = fftLen; + + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (q15_t *) twiddleCoef_4096_q15; + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLen) + { + case 4096U: + /* Initializations of structure parameters for 4096 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + + break; + + case 2048U: + /* Initializations of structure parameters for 2048 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 2U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 2U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[1]; + + break; + + case 1024U: + /* Initializations of structure parameters for 1024 point FFT */ + S->twidCoefModifier = 4U; + S->bitRevFactor = 4U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + + break; + + case 512U: + /* Initializations of structure parameters for 512 point FFT */ + S->twidCoefModifier = 8U; + S->bitRevFactor = 8U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[7]; + + break; + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + + break; + + case 128U: + /* Initializations of structure parameters for 128 point FFT */ + S->twidCoefModifier = 32U; + S->bitRevFactor = 32U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[31]; + + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + + break; + + case 32U: + /* Initializations of structure parameters for 32 point FFT */ + S->twidCoefModifier = 128U; + S->bitRevFactor = 128U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[127]; + + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} + +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_q31.c new file mode 100755 index 0000000..b3b1aa1 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_init_q31.c @@ -0,0 +1,181 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_q31.c + * Description: Radix-2 Decimation in Frequency Fixed-point CFFT & CIFFT Initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Initialization function for the Q31 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q31 and will be removed in the future. + @param[in,out] S points to an instance of the Q31 CFFT/CIFFT structure + @param[in] fftLen length of the FFT + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. +*/ + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix2_init_q31( + arm_cfft_radix2_instance_q31 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + + /* Initialise the FFT length */ + S->fftLen = fftLen; + + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (q31_t *) twiddleCoef_4096_q31; + + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of Instance structure depending on the FFT length */ + switch (S->fftLen) + { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + break; + + /* Initializations of structure parameters for 2048 point FFT */ + case 2048U: + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 2U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 2U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[1]; + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 4U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 4U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + break; + + /* Initializations of structure parameters for 512 point FFT */ + case 512U: + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 8U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 8U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[7]; + break; + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + break; + + case 128U: + /* Initializations of structure parameters for 128 point FFT */ + S->twidCoefModifier = 32U; + S->bitRevFactor = 32U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[31]; + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + break; + + case 32U: + /* Initializations of structure parameters for 32 point FFT */ + S->twidCoefModifier = 128U; + S->bitRevFactor = 128U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[127]; + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + break; + + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} + +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_q15.c new file mode 100755 index 0000000..0b2dd2f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_q15.c @@ -0,0 +1,688 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_q15.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_bitreversal_q15( + q15_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Processing function for the fixed-point CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q15 and will be removed in the future. + @param[in] S points to an instance of the fixed-point CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix2_q15( + const arm_cfft_radix2_instance_q15 * S, + q15_t * pSrc) +{ + + if (S->ifftFlag == 1U) + { + arm_radix2_butterfly_inverse_q15 (pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + else + { + arm_radix2_butterfly_q15 (pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + + arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); +} + +/** + @} end of ComplexFFTDeprecated group + */ + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef, + uint16_t twidCoefModifier) +{ +#if defined (ARM_MATH_DSP) + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + q15_t in; + q31_t T, S, R; + q31_t coeff, out1, out2; + + //N = fftLen; + n2 = fftLen; + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + for (i = 0; i < n2; i++) + { + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = read_q15x2 (pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUAD(coeff, R) >> 16; + out2 = __SMUSDX(coeff, R); +#else + out1 = __SMUSDX(R, coeff) >> 16U; + out2 = __SMUAD(coeff, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2U * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + i++; + l++; + + T = read_q15x2 (pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = read_q15x2 (pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUAD(coeff, R) >> 16; + out2 = __SMUSDX(coeff, R); +#else + + out1 = __SMUSDX(R, coeff) >> 16U; + out2 = __SMUAD(coeff, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2U * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + + /* loop for stage */ + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUAD(coeff, R) >> 16; + out2 = __SMUSDX(coeff, R); +#else + out1 = __SMUSDX(R, coeff) >> 16U; + out2 = __SMUAD(coeff, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2U * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + i += n1; + + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUAD(coeff, R) >> 16; + out2 = __SMUSDX(coeff, R); +#else + out1 = __SMUSDX(R, coeff) >> 16U; + out2 = __SMUAD(coeff, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2U * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + } /* stages loop end */ + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __QADD16(T, S)); + + write_q15x2 (pSrc + (2 * l), R); + + i += n1; + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __QADD16(T, S)); + + write_q15x2 (pSrc + (2 * l), R); + + } /* groups loop end */ + + +#else /* #if defined (ARM_MATH_DSP) */ + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + q15_t xt, yt, cosVal, sinVal; + + + // N = fftLen; + n2 = fftLen; + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + cosVal = pCoef[(ia * 2)]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U); + pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U; + + yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U); + pSrc[2 * i + 1] = ((pSrc[2 * l + 1] >> 1U) + + (pSrc[2 * i + 1] >> 1U) ) >> 1U; + + pSrc[2 * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) + + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) - + ((int16_t) (((q31_t) xt * sinVal) >> 16))); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + + /* loop for stage */ + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1U; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1U; + + pSrc[2 * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) + + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) - + ((int16_t) (((q31_t) xt * sinVal) >> 16))); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + } /* stages loop end */ + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]); + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]); + + pSrc[2 * l] = xt; + + pSrc[2 * l + 1] = yt; + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef, + uint16_t twidCoefModifier) +{ +#if defined (ARM_MATH_DSP) + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + q15_t in; + q31_t T, S, R; + q31_t coeff, out1, out2; + + // N = fftLen; + n2 = fftLen; + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (i = 0; i < n2; i++) + { + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = read_q15x2 (pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUSD(coeff, R) >> 16; + out2 = __SMUADX(coeff, R); +#else + out1 = __SMUADX(R, coeff) >> 16U; + out2 = __SMUSD(__QSUB(0, coeff), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2 * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + i++; + l++; + + T = read_q15x2 (pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = read_q15x2 (pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUSD(coeff, R) >> 16; + out2 = __SMUADX(coeff, R); +#else + out1 = __SMUADX(R, coeff) >> 16U; + out2 = __SMUSD(__QSUB(0, coeff), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2 * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + + /* loop for stage */ + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUSD(coeff, R) >> 16; + out2 = __SMUADX(coeff, R); +#else + out1 = __SMUADX(R, coeff) >> 16U; + out2 = __SMUSD(__QSUB(0, coeff), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2 * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + i += n1; + + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __SHADD16(T, S)); + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUSD(coeff, R) >> 16; + out2 = __SMUADX(coeff, R); +#else + out1 = __SMUADX(R, coeff) >> 16U; + out2 = __SMUSD(__QSUB(0, coeff), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + write_q15x2 (pSrc + (2 * l), (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF)); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + } /* stages loop end */ + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + coeff = read_q15x2 ((q15_t *)pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + + T = read_q15x2 (pSrc + (2 * i)); + + S = read_q15x2 (pSrc + (2 * l)); + + R = __QSUB16(T, S); + + write_q15x2 (pSrc + (2 * i), __QADD16(T, S)); + + write_q15x2 (pSrc + (2 * l), R); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + +#else /* #if defined (ARM_MATH_DSP) */ + + uint32_t i, j, k, l; + uint32_t n1, n2, ia; + q15_t xt, yt, cosVal, sinVal; + + // N = fftLen; + n2 = fftLen; + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + cosVal = pCoef[(ia * 2)]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U); + pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U; + + yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U); + pSrc[2 * i + 1] = ((pSrc[2 * l + 1] >> 1U) + + (pSrc[2 * i + 1] >> 1U) ) >> 1U; + + pSrc[2 * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) - + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2 * l + 1] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) + + ((int16_t) (((q31_t) xt * sinVal) >> 16))); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + + /* loop for stage */ + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + /* loop for groups */ + for (j = 0; j < n2; j++) + { + cosVal = pCoef[(ia * 2)]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1U; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1U; + + pSrc[2 * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) - + ((int16_t) (((q31_t) yt * sinVal) >> 16)) ); + + pSrc[2 * l + 1] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) + + ((int16_t) (((q31_t) xt * sinVal) >> 16)) ); + + } /* butterfly loop end */ + + } /* groups loop end */ + + twidCoefModifier = twidCoefModifier << 1U; + } /* stages loop end */ + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + cosVal = pCoef[(ia * 2)]; + sinVal = pCoef[(ia * 2) + 1]; + + ia = ia + twidCoefModifier; + + /* loop for butterfly */ + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]); + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]); + + pSrc[2 * l] = xt; + + pSrc[2 * l + 1] = yt; + + } /* groups loop end */ + + +#endif /* #if defined (ARM_MATH_DSP) */ + +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_q31.c new file mode 100755 index 0000000..39eca83 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix2_q31.c @@ -0,0 +1,336 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_q31.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_bitreversal_q31( + q31_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Processing function for the fixed-point CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q31 and will be removed in the future. + @param[in] S points to an instance of the fixed-point CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix2_q31( + const arm_cfft_radix2_instance_q31 * S, + q31_t * pSrc) +{ + + if (S->ifftFlag == 1U) + { + arm_radix2_butterfly_inverse_q31(pSrc, S->fftLen, + S->pTwiddle, S->twidCoefModifier); + } + else + { + arm_radix2_butterfly_q31(pSrc, S->fftLen, + S->pTwiddle, S->twidCoefModifier); + } + + arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); +} + +/** + @} end of ComplexFFTDeprecated group + */ + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint16_t twidCoefModifier) +{ + + unsigned i, j, k, l, m; + unsigned n1, n2, ia; + q31_t xt, yt, cosVal, sinVal; + q31_t p0, p1; + + //N = fftLen; + n2 = fftLen; + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + for (i = 0; i < n2; i++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + l = i + n2; + xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U); + pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U; + + yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U); + pSrc[2 * i + 1] = + ((pSrc[2 * l + 1] >> 1U) + (pSrc[2 * i + 1] >> 1U)) >> 1U; + + mult_32x32_keep32_R(p0, xt, cosVal); + mult_32x32_keep32_R(p1, yt, cosVal); + multAcc_32x32_keep32_R(p0, yt, sinVal); + multSub_32x32_keep32_R(p1, xt, sinVal); + + pSrc[2U * l] = p0; + pSrc[2U * l + 1U] = p1; + + } // groups loop end + + twidCoefModifier <<= 1U; + + // loop for stage + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + for (j = 0; j < n2; j++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + // loop for butterfly + i = j; + m = fftLen / n1; + do + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1U; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1U; + + mult_32x32_keep32_R(p0, xt, cosVal); + mult_32x32_keep32_R(p1, yt, cosVal); + multAcc_32x32_keep32_R(p0, yt, sinVal); + multSub_32x32_keep32_R(p1, xt, sinVal); + + pSrc[2U * l] = p0; + pSrc[2U * l + 1U] = p1; + i += n1; + m--; + } while ( m > 0); // butterfly loop end + + } // groups loop end + + twidCoefModifier <<= 1U; + } // stages loop end + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]); + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]); + + pSrc[2U * l] = xt; + + pSrc[2U * l + 1U] = yt; + + i += n1; + l = i + n2; + + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]); + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]); + + pSrc[2U * l] = xt; + + pSrc[2U * l + 1U] = yt; + + } // butterfly loop end + +} + + +ARM_DSP_ATTRIBUTE void arm_radix2_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint16_t twidCoefModifier) +{ + + unsigned i, j, k, l; + unsigned n1, n2, ia; + q31_t xt, yt, cosVal, sinVal; + q31_t p0, p1; + + //N = fftLen; + n2 = fftLen; + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + for (i = 0; i < n2; i++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + l = i + n2; + xt = (pSrc[2 * i] >> 1U) - (pSrc[2 * l] >> 1U); + pSrc[2 * i] = ((pSrc[2 * i] >> 1U) + (pSrc[2 * l] >> 1U)) >> 1U; + + yt = (pSrc[2 * i + 1] >> 1U) - (pSrc[2 * l + 1] >> 1U); + pSrc[2 * i + 1] = + ((pSrc[2 * l + 1] >> 1U) + (pSrc[2 * i + 1] >> 1U)) >> 1U; + + mult_32x32_keep32_R(p0, xt, cosVal); + mult_32x32_keep32_R(p1, yt, cosVal); + multSub_32x32_keep32_R(p0, yt, sinVal); + multAcc_32x32_keep32_R(p1, xt, sinVal); + + pSrc[2U * l] = p0; + pSrc[2U * l + 1U] = p1; + } // groups loop end + + twidCoefModifier = twidCoefModifier << 1U; + + // loop for stage + for (k = fftLen / 2; k > 2; k = k >> 1) + { + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + // loop for groups + for (j = 0; j < n2; j++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]) >> 1U; + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]) >> 1U; + + mult_32x32_keep32_R(p0, xt, cosVal); + mult_32x32_keep32_R(p1, yt, cosVal); + multSub_32x32_keep32_R(p0, yt, sinVal); + multAcc_32x32_keep32_R(p1, xt, sinVal); + + pSrc[2U * l] = p0; + pSrc[2U * l + 1U] = p1; + } // butterfly loop end + + } // groups loop end + + twidCoefModifier = twidCoefModifier << 1U; + } // stages loop end + + n1 = n2; + n2 = n2 >> 1; + ia = 0; + + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]); + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]); + + pSrc[2U * l] = xt; + + pSrc[2U * l + 1U] = yt; + + i += n1; + l = i + n2; + + xt = pSrc[2 * i] - pSrc[2 * l]; + pSrc[2 * i] = (pSrc[2 * i] + pSrc[2 * l]); + + yt = pSrc[2 * i + 1] - pSrc[2 * l + 1]; + pSrc[2 * i + 1] = (pSrc[2 * l + 1] + pSrc[2 * i + 1]); + + pSrc[2U * l] = xt; + + pSrc[2U * l + 1U] = yt; + + } // butterfly loop end + +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_f16.c new file mode 100755 index 0000000..4096214 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_f16.c @@ -0,0 +1,1267 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_f16.c + * Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +extern void arm_bitreversal_f16( + float16_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_f16( + float16_t * pSrc, + uint16_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_f16( + float16_t * pSrc, + uint16_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier, + float16_t onebyfftLen); + + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_f16( + float16_t * pSrc, + uint32_t fftLen, + const float16_t * pCoef); + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/* +* @brief Core function for the floating-point CFFT butterfly process. +* @param[in, out] *pSrc points to the in-place buffer of floating-point data type. +* @param[in] fftLen length of the FFT. +* @param[in] *pCoef points to the twiddle coefficient buffer. +* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +*/ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4by2_f16( + float16_t * pSrc, + uint32_t fftLen, + const float16_t * pCoef) +{ + uint32_t i, l; + uint32_t n2, ia; + float16_t xt, yt, cosVal, sinVal; + float16_t p0, p1,p2,p3,a0,a1; + + n2 = fftLen >> 1; + ia = 0; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2*ia]; + sinVal = pCoef[2*ia + 1]; + ia++; + + l = i + n2; + + /* Butterfly implementation */ + a0 = (_Float16)pSrc[2 * i] + (_Float16)pSrc[2 * l]; + xt = (_Float16)pSrc[2 * i] - (_Float16)pSrc[2 * l]; + + yt = (_Float16)pSrc[2 * i + 1] - (_Float16)pSrc[2 * l + 1]; + a1 = (_Float16)pSrc[2 * l + 1] + (_Float16)pSrc[2 * i + 1]; + + p0 = (_Float16)xt * (_Float16)cosVal; + p1 = (_Float16)yt * (_Float16)sinVal; + p2 = (_Float16)yt * (_Float16)cosVal; + p3 = (_Float16)xt * (_Float16)sinVal; + + pSrc[2 * i] = a0; + pSrc[2 * i + 1] = a1; + + pSrc[2 * l] = (_Float16)p0 + (_Float16)p1; + pSrc[2 * l + 1] = (_Float16)p2 - (_Float16)p3; + + } + + // first col + arm_radix4_butterfly_f16( pSrc, n2, (float16_t*)pCoef, 2U); + // second col + arm_radix4_butterfly_f16( pSrc + fftLen, n2, (float16_t*)pCoef, 2U); + +} + + +/** + @brief Processing function for the floating-point Radix-4 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f16 and will be removed in the future. + @param[in] S points to an instance of the floating-point Radix-4 CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4_f16( + const arm_cfft_radix4_instance_f16 * S, + float16_t * pSrc) +{ + if (S->ifftFlag == 1U) + { + /* Complex IFFT radix-4 */ + arm_radix4_butterfly_inverse_f16(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier, S->onebyfftLen); + } + else + { + /* Complex FFT radix-4 */ + arm_radix4_butterfly_f16(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + + if (S->bitReverseFlag == 1U) + { + /* Bit Reversal */ + arm_bitreversal_f16(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + +/** + @} end of ComplexFFTDeprecated group + */ + +/* ---------------------------------------------------------------------- + * Internal helper function used by the FFTs + * ---------------------------------------------------------------------- */ + +/* +* @brief Core function for the floating-point CFFT butterfly process. +* @param[in, out] *pSrc points to the in-place buffer of floating-point data type. +* @param[in] fftLen length of the FFT. +* @param[in] *pCoef points to the twiddle coefficient buffer. +* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +*/ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_f16( +float16_t * pSrc, +uint16_t fftLen, +const float16_t * pCoef, +uint16_t twidCoefModifier) +{ + + _Float16 co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + _Float16 xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn; + _Float16 Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc, + Ybminusd; + _Float16 Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out; + _Float16 Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out; + float16_t *ptr1; + _Float16 p0,p1,p2,p3,p4,p5; + _Float16 a0,a1,a2,a3,a4,a5,a6,a7; + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + i0 = 0U; + ia1 = 0U; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa + xc */ + Xaplusc = (_Float16)xaIn + (_Float16)xcIn; + /* xb + xd */ + Xbplusd = (_Float16)xbIn + (_Float16)xdIn; + /* ya + yc */ + Yaplusc = (_Float16)yaIn + (_Float16)ycIn; + /* yb + yd */ + Ybplusd = (_Float16)ybIn + (_Float16)ydIn; + + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + + /* xa - xc */ + Xaminusc = (_Float16)xaIn - (_Float16)xcIn; + /* xb - xd */ + Xbminusd = (_Float16)xbIn - (_Float16)xdIn; + /* ya - yc */ + Yaminusc = (_Float16)yaIn - (_Float16)ycIn; + /* yb - yd */ + Ybminusd = (_Float16)ybIn - (_Float16)ydIn; + + /* xa' = xa + xb + xc + xd */ + pSrc[(2U * i0)] = (_Float16)Xaplusc + (_Float16)Xbplusd; + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (_Float16)Yaplusc + (_Float16)Ybplusd; + + /* (xa - xc) + (yb - yd) */ + Xb12C_out = ((_Float16)Xaminusc + (_Float16)Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = ((_Float16)Yaminusc - (_Float16)Xbminusd); + /* (xa + xc) - (xb + xd) */ + Xc12C_out = ((_Float16)Xaplusc - (_Float16)Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = ((_Float16)Yaplusc - (_Float16)Ybplusd); + /* (xa - xc) - (yb - yd) */ + Xd12C_out = ((_Float16)Xaminusc - (_Float16)Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yd12C_out = ((_Float16)Xbminusd + (_Float16)Yaminusc); + + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + + /* index calculation for the coefficients */ + ia3 = ia2 + ia1; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + Xb12_out = (_Float16)Xb12C_out * (_Float16)co1; + Yb12_out = (_Float16)Yb12C_out * (_Float16)co1; + Xc12_out = (_Float16)Xc12C_out * (_Float16)co2; + Yc12_out = (_Float16)Yc12C_out * (_Float16)co2; + Xd12_out = (_Float16)Xd12C_out * (_Float16)co3; + Yd12_out = (_Float16)Yd12C_out * (_Float16)co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = (_Float16)Yb12C_out * (_Float16)si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = (_Float16)Xb12C_out * (_Float16)si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = (_Float16)Yc12C_out * (_Float16)si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = (_Float16)Xc12C_out * (_Float16)si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = (_Float16)Yd12C_out * (_Float16)si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = (_Float16)Xd12C_out * (_Float16)si3; + + Xb12_out += (_Float16)p0; + Yb12_out -= (_Float16)p1; + Xc12_out += (_Float16)p2; + Yc12_out -= (_Float16)p3; + Xd12_out += (_Float16)p4; + Yd12_out -= (_Float16)p5; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + /* Twiddle coefficients index modifier */ + ia1 += twidCoefModifier; + + /* Updating input index */ + i0++; + + } + while (--j); + + twidCoefModifier <<= 2U; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen >> 2U; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 += twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa - xc */ + Xaminusc = (_Float16)xaIn - (_Float16)xcIn; + /* (xb - xd) */ + Xbminusd = (_Float16)xbIn - (_Float16)xdIn; + /* ya - yc */ + Yaminusc = (_Float16)yaIn - (_Float16)ycIn; + /* (yb - yd) */ + Ybminusd = (_Float16)ybIn - (_Float16)ydIn; + + /* xa + xc */ + Xaplusc = (_Float16)xaIn + (_Float16)xcIn; + /* xb + xd */ + Xbplusd = (_Float16)xbIn + (_Float16)xdIn; + /* ya + yc */ + Yaplusc = (_Float16)yaIn + (_Float16)ycIn; + /* yb + yd */ + Ybplusd = (_Float16)ybIn + (_Float16)ydIn; + + /* (xa - xc) + (yb - yd) */ + Xb12C_out = ((_Float16)Xaminusc + (_Float16)Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yb12C_out = ((_Float16)Yaminusc - (_Float16)Xbminusd); + /* xa + xc -(xb + xd) */ + Xc12C_out = ((_Float16)Xaplusc - (_Float16)Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = ((_Float16)Yaplusc - (_Float16)Ybplusd); + /* (xa - xc) - (yb - yd) */ + Xd12C_out = ((_Float16)Xaminusc - (_Float16)Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yd12C_out = ((_Float16)Xbminusd + (_Float16)Yaminusc); + + pSrc[(2U * i0)] = (_Float16)Xaplusc + (_Float16)Xbplusd; + pSrc[(2U * i0) + 1U] = (_Float16)Yaplusc + (_Float16)Ybplusd; + + Xb12_out = (_Float16)Xb12C_out * (_Float16)co1; + Yb12_out = (_Float16)Yb12C_out * (_Float16)co1; + Xc12_out = (_Float16)Xc12C_out * (_Float16)co2; + Yc12_out = (_Float16)Yc12C_out * (_Float16)co2; + Xd12_out = (_Float16)Xd12C_out * (_Float16)co3; + Yd12_out = (_Float16)Yd12C_out * (_Float16)co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = (_Float16)Yb12C_out * (_Float16)si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = (_Float16)Xb12C_out * (_Float16)si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = (_Float16)Yc12C_out * (_Float16)si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = (_Float16)Xc12C_out * (_Float16)si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = (_Float16)Yd12C_out * (_Float16)si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = (_Float16)Xd12C_out * (_Float16)si3; + + Xb12_out += (_Float16)p0; + Yb12_out -= (_Float16)p1; + Xc12_out += (_Float16)p2; + Yc12_out -= (_Float16)p3; + Xd12_out += (_Float16)p4; + Yd12_out -= (_Float16)p5; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + i0 += n1; + } while (i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + xaIn = ptr1[0]; + yaIn = ptr1[1]; + xbIn = ptr1[2]; + ybIn = ptr1[3]; + xcIn = ptr1[4]; + ycIn = ptr1[5]; + xdIn = ptr1[6]; + ydIn = ptr1[7]; + + /* xa + xc */ + Xaplusc = (_Float16)xaIn + (_Float16)xcIn; + + /* xa - xc */ + Xaminusc = (_Float16)xaIn - (_Float16)xcIn; + + /* ya + yc */ + Yaplusc = (_Float16)yaIn + (_Float16)ycIn; + + /* ya - yc */ + Yaminusc = (_Float16)yaIn - (_Float16)ycIn; + + /* xb + xd */ + Xbplusd = (_Float16)xbIn + (_Float16)xdIn; + + /* yb + yd */ + Ybplusd = (_Float16)ybIn + (_Float16)ydIn; + + /* (xb-xd) */ + Xbminusd = (_Float16)xbIn - (_Float16)xdIn; + + /* (yb-yd) */ + Ybminusd = (_Float16)ybIn - (_Float16)ydIn; + + /* xa' = xa + xb + xc + xd */ + a0 = ((_Float16)Xaplusc + (_Float16)Xbplusd); + /* ya' = ya + yb + yc + yd */ + a1 = ((_Float16)Yaplusc + (_Float16)Ybplusd); + /* xc' = (xa-xb+xc-xd) */ + a2 = ((_Float16)Xaplusc - (_Float16)Xbplusd); + /* yc' = (ya-yb+yc-yd) */ + a3 = ((_Float16)Yaplusc - (_Float16)Ybplusd); + /* xb' = (xa+yb-xc-yd) */ + a4 = ((_Float16)Xaminusc + (_Float16)Ybminusd); + /* yb' = (ya-xb-yc+xd) */ + a5 = ((_Float16)Yaminusc - (_Float16)Xbminusd); + /* xd' = (xa-yb-xc+yd)) */ + a6 = ((_Float16)Xaminusc - (_Float16)Ybminusd); + /* yd' = (ya+xb-yc-xd) */ + a7 = ((_Float16)Xbminusd + (_Float16)Yaminusc); + + ptr1[0] = a0; + ptr1[1] = a1; + ptr1[2] = a2; + ptr1[3] = a3; + ptr1[4] = a4; + ptr1[5] = a5; + ptr1[6] = a6; + ptr1[7] = a7; + + /* increment pointer by 8 */ + ptr1 += 8U; + } while (--j); + +#else + + _Float16 t1, t2, r1, r2, s1, s2; + + /* Run the below code for Cortex-M0 */ + + /* Initializations for the fft calculation */ + n2 = fftLen; + n1 = n2; + for (k = fftLen; k > 1U; k >>= 2U) + { + /* Initializations for the fft calculation */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* FFT Calculation */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = (_Float16)pSrc[(2U * i0)] + (_Float16)pSrc[(2U * i2)]; + + /* xa - xc */ + r2 = (_Float16)pSrc[(2U * i0)] - (_Float16)pSrc[(2U * i2)]; + + /* ya + yc */ + s1 = (_Float16)pSrc[(2U * i0) + 1U] + (_Float16)pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = (_Float16)pSrc[(2U * i0) + 1U] - (_Float16)pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = (_Float16)pSrc[2U * i1] + (_Float16)pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (_Float16)r1 + (_Float16)t1; + + /* xa + xc -(xb + xd) */ + r1 = (_Float16)r1 - (_Float16)t1; + + /* yb + yd */ + t2 = (_Float16)pSrc[(2U * i1) + 1U] + (_Float16)pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (_Float16)s1 + (_Float16)t2; + + /* (ya + yc) - (yb + yd) */ + s1 = (_Float16)s1 - (_Float16)t2; + + /* (yb - yd) */ + t1 = (_Float16)pSrc[(2U * i1) + 1U] - (_Float16)pSrc[(2U * i3) + 1U]; + + /* (xb - xd) */ + t2 = (_Float16)pSrc[2U * i1] - (_Float16)pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = ((_Float16)r1 * (_Float16)co2) + ((_Float16)s1 * (_Float16)si2); + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = ((_Float16)s1 * (_Float16)co2) - ((_Float16)r1 * (_Float16)si2); + + /* (xa - xc) + (yb - yd) */ + r1 = (_Float16)r2 + (_Float16)t1; + + /* (xa - xc) - (yb - yd) */ + r2 = (_Float16)r2 - (_Float16)t1; + + /* (ya - yc) - (xb - xd) */ + s1 = (_Float16)s2 - (_Float16)t2; + + /* (ya - yc) + (xb - xd) */ + s2 = (_Float16)s2 + (_Float16)t2; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = ((_Float16)r1 * (_Float16)co1) + ((_Float16)s1 * (_Float16)si1); + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = ((_Float16)s1 * (_Float16)co1) - ((_Float16)r1 * (_Float16)si1); + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = ((_Float16)r2 * (_Float16)co3) + ((_Float16)s2 * (_Float16)si3); + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = ((_Float16)s2 * (_Float16)co3) - ((_Float16)r2 * (_Float16)si3); + + i0 += n1; + } while ( i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + +/* +* @brief Core function for the floating-point CIFFT butterfly process. +* @param[in, out] *pSrc points to the in-place buffer of floating-point data type. +* @param[in] fftLen length of the FFT. +* @param[in] *pCoef points to twiddle coefficient buffer. +* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +* @param[in] onebyfftLen value of 1/fftLen. +*/ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_f16( +float16_t * pSrc, +uint16_t fftLen, +const float16_t * pCoef, +uint16_t twidCoefModifier, +float16_t onebyfftLen) +{ + _Float16 co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + +#if defined (ARM_MATH_DSP) + + _Float16 xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn; + _Float16 Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc, + Ybminusd; + _Float16 Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out; + _Float16 Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out; + float16_t *ptr1; + _Float16 p0,p1,p2,p3,p4,p5,p6,p7; + _Float16 a0,a1,a2,a3,a4,a5,a6,a7; + + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + i0 = 0U; + ia1 = 0U; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa + xc */ + Xaplusc = (_Float16)xaIn + (_Float16)xcIn; + /* xb + xd */ + Xbplusd = (_Float16)xbIn + (_Float16)xdIn; + /* ya + yc */ + Yaplusc = (_Float16)yaIn + (_Float16)ycIn; + /* yb + yd */ + Ybplusd = (_Float16)ybIn + (_Float16)ydIn; + + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + + /* xa - xc */ + Xaminusc = (_Float16)xaIn - (_Float16)xcIn; + /* xb - xd */ + Xbminusd = (_Float16)xbIn - (_Float16)xdIn; + /* ya - yc */ + Yaminusc = (_Float16)yaIn - (_Float16)ycIn; + /* yb - yd */ + Ybminusd = (_Float16)ybIn - (_Float16)ydIn; + + /* xa' = xa + xb + xc + xd */ + pSrc[(2U * i0)] = (_Float16)Xaplusc + (_Float16)Xbplusd; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (_Float16)Yaplusc + (_Float16)Ybplusd; + + /* (xa - xc) - (yb - yd) */ + Xb12C_out = ((_Float16)Xaminusc - (_Float16)Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = ((_Float16)Yaminusc + (_Float16)Xbminusd); + /* (xa + xc) - (xb + xd) */ + Xc12C_out = ((_Float16)Xaplusc - (_Float16)Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = ((_Float16)Yaplusc - (_Float16)Ybplusd); + /* (xa - xc) + (yb - yd) */ + Xd12C_out = ((_Float16)Xaminusc + (_Float16)Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yd12C_out = ((_Float16)Yaminusc - (_Float16)Xbminusd); + + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + + /* index calculation for the coefficients */ + ia3 = ia2 + ia1; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + Xb12_out = (_Float16)Xb12C_out * (_Float16)co1; + Yb12_out = (_Float16)Yb12C_out * (_Float16)co1; + Xc12_out = (_Float16)Xc12C_out * (_Float16)co2; + Yc12_out = (_Float16)Yc12C_out * (_Float16)co2; + Xd12_out = (_Float16)Xd12C_out * (_Float16)co3; + Yd12_out = (_Float16)Yd12C_out * (_Float16)co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = (_Float16)Yb12C_out * (_Float16)si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = (_Float16)Xb12C_out * (_Float16)si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = (_Float16)Yc12C_out * (_Float16)si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = (_Float16)Xc12C_out * (_Float16)si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = (_Float16)Yd12C_out * (_Float16)si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 =(_Float16) Xd12C_out * (_Float16)si3; + + Xb12_out -= (_Float16)p0; + Yb12_out += (_Float16)p1; + Xc12_out -= (_Float16)p2; + Yc12_out += (_Float16)p3; + Xd12_out -= (_Float16)p4; + Yd12_out += (_Float16)p5; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1U; + + } while (--j); + + twidCoefModifier <<= 2U; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen >> 2U; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa - xc */ + Xaminusc = (_Float16)xaIn - (_Float16)xcIn; + /* (xb - xd) */ + Xbminusd = (_Float16)xbIn - (_Float16)xdIn; + /* ya - yc */ + Yaminusc = (_Float16)yaIn - (_Float16)ycIn; + /* (yb - yd) */ + Ybminusd = (_Float16)ybIn - (_Float16)ydIn; + + /* xa + xc */ + Xaplusc = (_Float16)xaIn + (_Float16)xcIn; + /* xb + xd */ + Xbplusd = (_Float16)xbIn + (_Float16)xdIn; + /* ya + yc */ + Yaplusc = (_Float16)yaIn + (_Float16)ycIn; + /* yb + yd */ + Ybplusd = (_Float16)ybIn + (_Float16)ydIn; + + /* (xa - xc) - (yb - yd) */ + Xb12C_out = ((_Float16)Xaminusc - (_Float16)Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = ((_Float16)Yaminusc + (_Float16)Xbminusd); + /* xa + xc -(xb + xd) */ + Xc12C_out = ((_Float16)Xaplusc - (_Float16)Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = ((_Float16)Yaplusc - (_Float16)Ybplusd); + /* (xa - xc) + (yb - yd) */ + Xd12C_out = ((_Float16)Xaminusc + (_Float16)Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yd12C_out = ((_Float16)Yaminusc - (_Float16)Xbminusd); + + pSrc[(2U * i0)] = (_Float16)Xaplusc + (_Float16)Xbplusd; + pSrc[(2U * i0) + 1U] = (_Float16)Yaplusc + (_Float16)Ybplusd; + + Xb12_out = (_Float16)Xb12C_out * (_Float16)co1; + Yb12_out = (_Float16)Yb12C_out * (_Float16)co1; + Xc12_out = (_Float16)Xc12C_out * (_Float16)co2; + Yc12_out = (_Float16)Yc12C_out * (_Float16)co2; + Xd12_out = (_Float16)Xd12C_out * (_Float16)co3; + Yd12_out = (_Float16)Yd12C_out * (_Float16)co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = (_Float16)Yb12C_out * (_Float16)si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = (_Float16)Xb12C_out * (_Float16)si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = (_Float16)Yc12C_out * (_Float16)si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = (_Float16)Xc12C_out * (_Float16)si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = (_Float16)Yd12C_out * (_Float16)si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = (_Float16)Xd12C_out * (_Float16)si3; + + Xb12_out -= (_Float16)p0; + Yb12_out += (_Float16)p1; + Xc12_out -= (_Float16)p2; + Yc12_out += (_Float16)p3; + Xd12_out -= (_Float16)p4; + Yd12_out += (_Float16)p5; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + i0 += n1; + } while (i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + /* Initializations of last stage */ + + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + xaIn = ptr1[0]; + yaIn = ptr1[1]; + xbIn = ptr1[2]; + ybIn = ptr1[3]; + xcIn = ptr1[4]; + ycIn = ptr1[5]; + xdIn = ptr1[6]; + ydIn = ptr1[7]; + + /* Butterfly implementation */ + /* xa + xc */ + Xaplusc = (_Float16)xaIn + (_Float16)xcIn; + + /* xa - xc */ + Xaminusc = (_Float16)xaIn - (_Float16)xcIn; + + /* ya + yc */ + Yaplusc = (_Float16)yaIn + (_Float16)ycIn; + + /* ya - yc */ + Yaminusc = (_Float16)yaIn - (_Float16)ycIn; + + /* xb + xd */ + Xbplusd = (_Float16)xbIn + (_Float16)xdIn; + + /* yb + yd */ + Ybplusd = (_Float16)ybIn + (_Float16)ydIn; + + /* (xb-xd) */ + Xbminusd = (_Float16)xbIn - (_Float16)xdIn; + + /* (yb-yd) */ + Ybminusd = (_Float16)ybIn - (_Float16)ydIn; + + /* xa' = (xa+xb+xc+xd) * onebyfftLen */ + a0 = ((_Float16)Xaplusc + (_Float16)Xbplusd); + /* ya' = (ya+yb+yc+yd) * onebyfftLen */ + a1 = ((_Float16)Yaplusc + (_Float16)Ybplusd); + /* xc' = (xa-xb+xc-xd) * onebyfftLen */ + a2 = ((_Float16)Xaplusc - (_Float16)Xbplusd); + /* yc' = (ya-yb+yc-yd) * onebyfftLen */ + a3 = ((_Float16)Yaplusc - (_Float16)Ybplusd); + /* xb' = (xa-yb-xc+yd) * onebyfftLen */ + a4 = ((_Float16)Xaminusc - (_Float16)Ybminusd); + /* yb' = (ya+xb-yc-xd) * onebyfftLen */ + a5 = ((_Float16)Yaminusc + (_Float16)Xbminusd); + /* xd' = (xa-yb-xc+yd) * onebyfftLen */ + a6 = ((_Float16)Xaminusc + (_Float16)Ybminusd); + /* yd' = (ya-xb-yc+xd) * onebyfftLen */ + a7 = ((_Float16)Yaminusc - (_Float16)Xbminusd); + + p0 = (_Float16)a0 * (_Float16)onebyfftLen; + p1 = (_Float16)a1 * (_Float16)onebyfftLen; + p2 = (_Float16)a2 * (_Float16)onebyfftLen; + p3 = (_Float16)a3 * (_Float16)onebyfftLen; + p4 = (_Float16)a4 * (_Float16)onebyfftLen; + p5 = (_Float16)a5 * (_Float16)onebyfftLen; + p6 = (_Float16)a6 * (_Float16)onebyfftLen; + p7 = (_Float16)a7 * (_Float16)onebyfftLen; + + /* xa' = (xa+xb+xc+xd) * onebyfftLen */ + ptr1[0] = p0; + /* ya' = (ya+yb+yc+yd) * onebyfftLen */ + ptr1[1] = p1; + /* xc' = (xa-xb+xc-xd) * onebyfftLen */ + ptr1[2] = p2; + /* yc' = (ya-yb+yc-yd) * onebyfftLen */ + ptr1[3] = p3; + /* xb' = (xa-yb-xc+yd) * onebyfftLen */ + ptr1[4] = p4; + /* yb' = (ya+xb-yc-xd) * onebyfftLen */ + ptr1[5] = p5; + /* xd' = (xa-yb-xc+yd) * onebyfftLen */ + ptr1[6] = p6; + /* yd' = (ya-xb-yc+xd) * onebyfftLen */ + ptr1[7] = p7; + + /* increment source pointer by 8 for next calculations */ + ptr1 = ptr1 + 8U; + + } while (--j); + +#else + + float16_t t1, t2, r1, r2, s1, s2; + + /* Run the below code for Cortex-M0 */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* Calculation of first stage */ + for (k = fftLen; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = (_Float16)pSrc[(2U * i0)] + (_Float16)pSrc[(2U * i2)]; + + /* xa - xc */ + r2 = (_Float16)pSrc[(2U * i0)] - (_Float16)pSrc[(2U * i2)]; + + /* ya + yc */ + s1 = (_Float16)pSrc[(2U * i0) + 1U] + (_Float16)pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = (_Float16)pSrc[(2U * i0) + 1U] - (_Float16)pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = (_Float16)pSrc[2U * i1] + (_Float16)pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (_Float16)r1 + (_Float16)t1; + + /* xa + xc -(xb + xd) */ + r1 = (_Float16)r1 - (_Float16)t1; + + /* yb + yd */ + t2 = (_Float16)pSrc[(2U * i1) + 1U] + (_Float16)pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (_Float16)s1 + (_Float16)t2; + + /* (ya + yc) - (yb + yd) */ + s1 = (_Float16)s1 - (_Float16)t2; + + /* (yb - yd) */ + t1 = (_Float16)pSrc[(2U * i1) + 1U] - (_Float16)pSrc[(2U * i3) + 1U]; + + /* (xb - xd) */ + t2 = (_Float16)pSrc[2U * i1] - (_Float16)pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = ((_Float16)r1 * (_Float16)co2) - ((_Float16)s1 * (_Float16)si2); + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = ((_Float16)s1 * (_Float16)co2) + ((_Float16)r1 * (_Float16)si2); + + /* (xa - xc) - (yb - yd) */ + r1 = (_Float16)r2 - (_Float16)t1; + + /* (xa - xc) + (yb - yd) */ + r2 = (_Float16)r2 + (_Float16)t1; + + /* (ya - yc) + (xb - xd) */ + s1 = (_Float16)s2 + (_Float16)t2; + + /* (ya - yc) - (xb - xd) */ + s2 = (_Float16)s2 - (_Float16)t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = ((_Float16)r1 * (_Float16)co1) - ((_Float16)s1 * (_Float16)si1); + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = ((_Float16)s1 * (_Float16)co1) + ((_Float16)r1 * (_Float16)si1); + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = ((_Float16)r2 * (_Float16)co3) - ((_Float16)s2 * (_Float16)si3); + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = ((_Float16)s2 * (_Float16)co3) + ((_Float16)r2 * (_Float16)si3); + + i0 += n1; + } while ( i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + /* Initializations of last stage */ + n1 = n2; + n2 >>= 2U; + + /* Calculations of last stage */ + for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + /* xa + xc */ + r1 = (_Float16)pSrc[2U * i0] + (_Float16)pSrc[2U * i2]; + + /* xa - xc */ + r2 = (_Float16)pSrc[2U * i0] - (_Float16)pSrc[2U * i2]; + + /* ya + yc */ + s1 = (_Float16)pSrc[(2U * i0) + 1U] + (_Float16)pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = (_Float16)pSrc[(2U * i0) + 1U] - (_Float16)pSrc[(2U * i2) + 1U]; + + /* xc + xd */ + t1 = (_Float16)pSrc[2U * i1] + (_Float16)pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = ((_Float16)r1 + (_Float16)t1) * (_Float16)onebyfftLen; + + /* (xa + xb) - (xc + xd) */ + r1 = (_Float16)r1 - (_Float16)t1; + + /* yb + yd */ + t2 = (_Float16)pSrc[(2U * i1) + 1U] + (_Float16)pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = ((_Float16)s1 + (_Float16)t2) * (_Float16)onebyfftLen; + + /* (ya + yc) - (yb + yd) */ + s1 = (_Float16)s1 - (_Float16)t2; + + /* (yb-yd) */ + t1 = (_Float16)pSrc[(2U * i1) + 1U] - (_Float16)pSrc[(2U * i3) + 1U]; + + /* (xb-xd) */ + t2 = (_Float16)pSrc[2U * i1] - (_Float16)pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (_Float16)r1 * (_Float16)onebyfftLen; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (_Float16)s1 * (_Float16)onebyfftLen; + + /* (xa - xc) - (yb-yd) */ + r1 = (_Float16)r2 - (_Float16)t1; + + /* (xa - xc) + (yb-yd) */ + r2 = (_Float16)r2 + (_Float16)t1; + + /* (ya - yc) + (xb-xd) */ + s1 = (_Float16)s2 + (_Float16)t2; + + /* (ya - yc) - (xb-xd) */ + s2 = (_Float16)s2 - (_Float16)t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (_Float16)r1 * (_Float16)onebyfftLen; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (_Float16)s1 * (_Float16)onebyfftLen; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (_Float16)r2 * (_Float16)onebyfftLen; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (_Float16)s2 * (_Float16)onebyfftLen; + } + +#endif /* #if defined (ARM_MATH_DSP) */ +} + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_f32.c new file mode 100755 index 0000000..536ce0f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_f32.c @@ -0,0 +1,1201 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_f32.c + * Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +extern void arm_bitreversal_f32( + float32_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen); + + + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + + +/** + @brief Processing function for the floating-point Radix-4 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f32 and will be removed in the future. + @param[in] S points to an instance of the floating-point Radix-4 CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4_f32( + const arm_cfft_radix4_instance_f32 * S, + float32_t * pSrc) +{ + if (S->ifftFlag == 1U) + { + /* Complex IFFT radix-4 */ + arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier, S->onebyfftLen); + } + else + { + /* Complex FFT radix-4 */ + arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + + if (S->bitReverseFlag == 1U) + { + /* Bit Reversal */ + arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + +/** + @} end of ComplexFFTDeprecated group + */ + +/* ---------------------------------------------------------------------- + * Internal helper function used by the FFTs + * ---------------------------------------------------------------------- */ + +/** + brief Core function for the floating-point CFFT butterfly process. + param[in,out] pSrc points to the in-place buffer of floating-point data type + param[in] fftLen length of the FFT + param[in] pCoef points to the twiddle coefficient buffer + param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + return none + */ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier) +{ + float32_t co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + +#if defined (ARM_MATH_LOOPUNROLL) + + float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn; + float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc, + Ybminusd; + float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out; + float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out; + float32_t *ptr1; + float32_t p0,p1,p2,p3,p4,p5; + float32_t a0,a1,a2,a3,a4,a5,a6,a7; + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + i0 = 0U; + ia1 = 0U; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* xb - xd */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* yb - yd */ + Ybminusd = ybIn - ydIn; + + /* xa' = xa + xb + xc + xd */ + pSrc[(2U * i0)] = Xaplusc + Xbplusd; + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = Yaplusc + Ybplusd; + + /* (xa - xc) + (yb - yd) */ + Xb12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = (Yaminusc - Xbminusd); + /* (xa + xc) - (xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) - (yb - yd) */ + Xd12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yd12C_out = (Xbminusd + Yaminusc); + + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + + /* index calculation for the coefficients */ + ia3 = ia2 + ia1; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = Xd12C_out * si3; + + Xb12_out += p0; + Yb12_out -= p1; + Xc12_out += p2; + Yc12_out -= p3; + Xd12_out += p4; + Yd12_out -= p5; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + /* Twiddle coefficients index modifier */ + ia1 += twidCoefModifier; + + /* Updating input index */ + i0++; + + } + while (--j); + + twidCoefModifier <<= 2U; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen >> 2U; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[(ia1 * 2U)]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[(ia2 * 2U)]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[(ia3 * 2U)]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 += twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* (xb - xd) */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* (yb - yd) */ + Ybminusd = ybIn - ydIn; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* (xa - xc) + (yb - yd) */ + Xb12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yb12C_out = (Yaminusc - Xbminusd); + /* xa + xc -(xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) - (yb - yd) */ + Xd12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yd12C_out = (Xbminusd + Yaminusc); + + pSrc[(2U * i0)] = Xaplusc + Xbplusd; + pSrc[(2U * i0) + 1U] = Yaplusc + Ybplusd; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = Xd12C_out * si3; + + Xb12_out += p0; + Yb12_out -= p1; + Xc12_out += p2; + Yc12_out -= p3; + Xd12_out += p4; + Yd12_out -= p5; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + i0 += n1; + } while (i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + xaIn = ptr1[0]; + yaIn = ptr1[1]; + xbIn = ptr1[2]; + ybIn = ptr1[3]; + xcIn = ptr1[4]; + ycIn = ptr1[5]; + xdIn = ptr1[6]; + ydIn = ptr1[7]; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + + /* ya + yc */ + Yaplusc = yaIn + ycIn; + + /* ya - yc */ + Yaminusc = yaIn - ycIn; + + /* xb + xd */ + Xbplusd = xbIn + xdIn; + + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* (xb-xd) */ + Xbminusd = xbIn - xdIn; + + /* (yb-yd) */ + Ybminusd = ybIn - ydIn; + + /* xa' = xa + xb + xc + xd */ + a0 = (Xaplusc + Xbplusd); + /* ya' = ya + yb + yc + yd */ + a1 = (Yaplusc + Ybplusd); + /* xc' = (xa-xb+xc-xd) */ + a2 = (Xaplusc - Xbplusd); + /* yc' = (ya-yb+yc-yd) */ + a3 = (Yaplusc - Ybplusd); + /* xb' = (xa+yb-xc-yd) */ + a4 = (Xaminusc + Ybminusd); + /* yb' = (ya-xb-yc+xd) */ + a5 = (Yaminusc - Xbminusd); + /* xd' = (xa-yb-xc+yd)) */ + a6 = (Xaminusc - Ybminusd); + /* yd' = (ya+xb-yc-xd) */ + a7 = (Xbminusd + Yaminusc); + + ptr1[0] = a0; + ptr1[1] = a1; + ptr1[2] = a2; + ptr1[3] = a3; + ptr1[4] = a4; + ptr1[5] = a5; + ptr1[6] = a6; + ptr1[7] = a7; + + /* increment pointer by 8 */ + ptr1 += 8U; + } while (--j); + +#else + + float32_t t1, t2, r1, r2, s1, s2; + + /* Initializations for the fft calculation */ + n2 = fftLen; + n1 = n2; + for (k = fftLen; k > 1U; k >>= 2U) + { + /* Initializations for the fft calculation */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* FFT Calculation */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = pSrc[(2U * i0)] + pSrc[(2U * i2)]; + + /* xa - xc */ + r2 = pSrc[(2U * i0)] - pSrc[(2U * i2)]; + + /* ya + yc */ + s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = pSrc[2U * i1] + pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = r1 + t1; + + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = s1 + t2; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U]; + + /* (xb - xd) */ + t2 = pSrc[2U * i1] - pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (r1 * co2) + (s1 * si2); + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (s1 * co2) - (r1 * si2); + + /* (xa - xc) + (yb - yd) */ + r1 = r2 + t1; + + /* (xa - xc) - (yb - yd) */ + r2 = r2 - t1; + + /* (ya - yc) - (xb - xd) */ + s1 = s2 - t2; + + /* (ya - yc) + (xb - xd) */ + s2 = s2 + t2; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (r1 * co1) + (s1 * si1); + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (s1 * co1) - (r1 * si1); + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (r2 * co3) + (s2 * si3); + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (s2 * co3) - (r2 * si3); + + i0 += n1; + } while ( i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ + +} + +/** + brief Core function for the floating-point CIFFT butterfly process. + param[in,out] pSrc points to the in-place buffer of floating-point data type + param[in] fftLen length of the FFT + param[in] pCoef points to twiddle coefficient buffer + param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + param[in] onebyfftLen value of 1/fftLen + return none + */ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen) +{ + float32_t co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + +#if defined (ARM_MATH_LOOPUNROLL) + + float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn; + float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc, + Ybminusd; + float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out; + float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out; + float32_t *ptr1; + float32_t p0,p1,p2,p3,p4,p5,p6,p7; + float32_t a0,a1,a2,a3,a4,a5,a6,a7; + + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + i0 = 0U; + ia1 = 0U; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* xb - xd */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* yb - yd */ + Ybminusd = ybIn - ydIn; + + /* xa' = xa + xb + xc + xd */ + pSrc[(2U * i0)] = Xaplusc + Xbplusd; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = Yaplusc + Ybplusd; + + /* (xa - xc) - (yb - yd) */ + Xb12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = (Yaminusc + Xbminusd); + /* (xa + xc) - (xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) + (yb - yd) */ + Xd12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yd12C_out = (Yaminusc - Xbminusd); + + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + + /* index calculation for the coefficients */ + ia3 = ia2 + ia1; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = Xd12C_out * si3; + + Xb12_out -= p0; + Yb12_out += p1; + Xc12_out -= p2; + Yc12_out += p3; + Xd12_out -= p4; + Yd12_out += p5; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1U; + + } while (--j); + + twidCoefModifier <<= 2U; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen >> 2U; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2U * i0)]; + yaIn = pSrc[(2U * i0) + 1U]; + + xbIn = pSrc[(2U * i1)]; + ybIn = pSrc[(2U * i1) + 1U]; + + xcIn = pSrc[(2U * i2)]; + ycIn = pSrc[(2U * i2) + 1U]; + + xdIn = pSrc[(2U * i3)]; + ydIn = pSrc[(2U * i3) + 1U]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* (xb - xd) */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* (yb - yd) */ + Ybminusd = ybIn - ydIn; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* (xa - xc) - (yb - yd) */ + Xb12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = (Yaminusc + Xbminusd); + /* xa + xc -(xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) + (yb - yd) */ + Xd12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yd12C_out = (Yaminusc - Xbminusd); + + pSrc[(2U * i0)] = Xaplusc + Xbplusd; + pSrc[(2U * i0) + 1U] = Yaplusc + Ybplusd; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + //Xb12_out -= Yb12C_out * si1; + p0 = Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + //Yb12_out += Xb12C_out * si1; + p1 = Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + //Xc12_out -= Yc12C_out * si2; + p2 = Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + //Yc12_out += Xc12C_out * si2; + p3 = Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + //Xd12_out -= Yd12C_out * si3; + p4 = Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + //Yd12_out += Xd12C_out * si3; + p5 = Xd12C_out * si3; + + Xb12_out -= p0; + Yb12_out += p1; + Xc12_out -= p2; + Yc12_out += p3; + Xd12_out -= p4; + Yd12_out += p5; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = Yd12_out; + + i0 += n1; + } while (i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + /* Initializations of last stage */ + + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + xaIn = ptr1[0]; + yaIn = ptr1[1]; + xbIn = ptr1[2]; + ybIn = ptr1[3]; + xcIn = ptr1[4]; + ycIn = ptr1[5]; + xdIn = ptr1[6]; + ydIn = ptr1[7]; + + /* Butterfly implementation */ + /* xa + xc */ + Xaplusc = xaIn + xcIn; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + + /* ya + yc */ + Yaplusc = yaIn + ycIn; + + /* ya - yc */ + Yaminusc = yaIn - ycIn; + + /* xb + xd */ + Xbplusd = xbIn + xdIn; + + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* (xb-xd) */ + Xbminusd = xbIn - xdIn; + + /* (yb-yd) */ + Ybminusd = ybIn - ydIn; + + /* xa' = (xa+xb+xc+xd) * onebyfftLen */ + a0 = (Xaplusc + Xbplusd); + /* ya' = (ya+yb+yc+yd) * onebyfftLen */ + a1 = (Yaplusc + Ybplusd); + /* xc' = (xa-xb+xc-xd) * onebyfftLen */ + a2 = (Xaplusc - Xbplusd); + /* yc' = (ya-yb+yc-yd) * onebyfftLen */ + a3 = (Yaplusc - Ybplusd); + /* xb' = (xa-yb-xc+yd) * onebyfftLen */ + a4 = (Xaminusc - Ybminusd); + /* yb' = (ya+xb-yc-xd) * onebyfftLen */ + a5 = (Yaminusc + Xbminusd); + /* xd' = (xa-yb-xc+yd) * onebyfftLen */ + a6 = (Xaminusc + Ybminusd); + /* yd' = (ya-xb-yc+xd) * onebyfftLen */ + a7 = (Yaminusc - Xbminusd); + + p0 = a0 * onebyfftLen; + p1 = a1 * onebyfftLen; + p2 = a2 * onebyfftLen; + p3 = a3 * onebyfftLen; + p4 = a4 * onebyfftLen; + p5 = a5 * onebyfftLen; + p6 = a6 * onebyfftLen; + p7 = a7 * onebyfftLen; + + /* xa' = (xa+xb+xc+xd) * onebyfftLen */ + ptr1[0] = p0; + /* ya' = (ya+yb+yc+yd) * onebyfftLen */ + ptr1[1] = p1; + /* xc' = (xa-xb+xc-xd) * onebyfftLen */ + ptr1[2] = p2; + /* yc' = (ya-yb+yc-yd) * onebyfftLen */ + ptr1[3] = p3; + /* xb' = (xa-yb-xc+yd) * onebyfftLen */ + ptr1[4] = p4; + /* yb' = (ya+xb-yc-xd) * onebyfftLen */ + ptr1[5] = p5; + /* xd' = (xa-yb-xc+yd) * onebyfftLen */ + ptr1[6] = p6; + /* yd' = (ya-xb-yc+xd) * onebyfftLen */ + ptr1[7] = p7; + + /* increment source pointer by 8 for next calculations */ + ptr1 = ptr1 + 8U; + + } while (--j); + +#else + + float32_t t1, t2, r1, r2, s1, s2; + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* Calculation of first stage */ + for (k = fftLen; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + j = 0; + do + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + i0 = j; + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = pSrc[(2U * i0)] + pSrc[(2U * i2)]; + + /* xa - xc */ + r2 = pSrc[(2U * i0)] - pSrc[(2U * i2)]; + + /* ya + yc */ + s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = pSrc[2U * i1] + pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = r1 + t1; + + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = s1 + t2; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U]; + + /* (xb - xd) */ + t2 = pSrc[2U * i1] - pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (r1 * co2) - (s1 * si2); + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (s1 * co2) + (r1 * si2); + + /* (xa - xc) - (yb - yd) */ + r1 = r2 - t1; + + /* (xa - xc) + (yb - yd) */ + r2 = r2 + t1; + + /* (ya - yc) + (xb - xd) */ + s1 = s2 + t2; + + /* (ya - yc) - (xb - xd) */ + s2 = s2 - t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (r1 * co1) - (s1 * si1); + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (s1 * co1) + (r1 * si1); + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (r2 * co3) - (s2 * si3); + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (s2 * co3) + (r2 * si3); + + i0 += n1; + } while ( i0 < fftLen); + j++; + } while (j <= (n2 - 1U)); + twidCoefModifier <<= 2U; + } + /* Initializations of last stage */ + n1 = n2; + n2 >>= 2U; + + /* Calculations of last stage */ + for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSrc[2U * i0] + pSrc[2U * i2]; + + /* xa - xc */ + r2 = pSrc[2U * i0] - pSrc[2U * i2]; + + /* ya + yc */ + s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U]; + + /* ya - yc */ + s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U]; + + /* xc + xd */ + t1 = pSrc[2U * i1] + pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (r1 + t1) * onebyfftLen; + + /* (xa + xb) - (xc + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (s1 + t2) * onebyfftLen; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb-yd) */ + t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U]; + + /* (xb-xd) */ + t2 = pSrc[2U * i1] - pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = r1 * onebyfftLen; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = s1 * onebyfftLen; + + /* (xa - xc) - (yb-yd) */ + r1 = r2 - t1; + + /* (xa - xc) + (yb-yd) */ + r2 = r2 + t1; + + /* (ya - yc) + (xb-xd) */ + s1 = s2 + t2; + + /* (ya - yc) - (xb-xd) */ + s2 = s2 - t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = r1 * onebyfftLen; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = s1 * onebyfftLen; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = r2 * onebyfftLen; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = s2 * onebyfftLen; + } + +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ +} + + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_f16.c new file mode 100755 index 0000000..6c03dff --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_f16.c @@ -0,0 +1,162 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_f16.c + * Description: Radix-4 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" +#include "arm_common_tables.h" +#include "arm_common_tables_f16.h" + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Initialization function for the floating-point CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f16 and will be removed in the future. + @param[in,out] S points to an instance of the floating-point CFFT/CIFFT structure + @param[in] fftLen length of the FFT + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. + */ + +#if defined(ARM_FLOAT16_SUPPORTED) + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix4_init_f16( + arm_cfft_radix4_instance_f16 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + + /* Initialise the FFT length */ + S->fftLen = fftLen; + + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (float16_t *) twiddleCoefF16; + + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLen) + { + + case 4096U: + /* Initializations of structure parameters for 4096 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.000244140625; + break; + + case 1024U: + /* Initializations of structure parameters for 1024 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 4U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 4U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.0009765625f; + break; + + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + S->onebyfftLen = 0.00390625f; + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + S->onebyfftLen = 0.015625f; + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + S->onebyfftLen = 0.0625f; + break; + + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_f32.c new file mode 100755 index 0000000..2fdae65 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_f32.c @@ -0,0 +1,160 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_f32.c + * Description: Radix-4 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Initialization function for the floating-point CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_f32 and will be removed in the future. + @param[in,out] S points to an instance of the floating-point CFFT/CIFFT structure + @param[in] fftLen length of the FFT + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. + */ + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix4_init_f32( + arm_cfft_radix4_instance_f32 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + + /* Initialise the FFT length */ + S->fftLen = fftLen; + + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (float32_t *) twiddleCoef; + + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLen) + { + + case 4096U: + /* Initializations of structure parameters for 4096 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.000244140625; + break; + + case 1024U: + /* Initializations of structure parameters for 1024 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 4U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 4U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + /* Initialise the 1/fftLen Value */ + S->onebyfftLen = 0.0009765625f; + break; + + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + S->onebyfftLen = 0.00390625f; + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + S->onebyfftLen = 0.015625f; + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + S->onebyfftLen = 0.0625f; + break; + + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + + return (status); +} + +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_q15.c new file mode 100755 index 0000000..04de4ce --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_q15.c @@ -0,0 +1,147 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_q15.c + * Description: Radix-4 Decimation in Frequency Q15 FFT & IFFT initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + + +/** + @brief Initialization function for the Q15 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q15 and will be removed in the future. + @param[in,out] S points to an instance of the Q15 CFFT/CIFFT structure + @param[in] fftLen length of the FFT + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. + */ + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix4_init_q15( + arm_cfft_radix4_instance_q15 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + /* Initialise the FFT length */ + S->fftLen = fftLen; + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (q15_t *) twiddleCoef_4096_q15; + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLen) + { + case 4096U: + /* Initializations of structure parameters for 4096 point FFT */ + + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + + break; + + case 1024U: + /* Initializations of structure parameters for 1024 point FFT */ + S->twidCoefModifier = 4U; + S->bitRevFactor = 4U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + + break; + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} + +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_q31.c new file mode 100755 index 0000000..391931e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_init_q31.c @@ -0,0 +1,144 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_q31.c + * Description: Radix-4 Decimation in Frequency Q31 FFT & IFFT initialization function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + + @brief Initialization function for the Q31 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q31 and will be removed in the future. + @param[in,out] S points to an instance of the Q31 CFFT/CIFFT structure. + @param[in] fftLen length of the FFT. + @param[in] ifftFlag flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Details + The parameter ifftFlag controls whether a forward or inverse transform is computed. + Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024. + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. +*/ + +ARM_DSP_ATTRIBUTE arm_status arm_cfft_radix4_init_q31( + arm_cfft_radix4_instance_q31 * S, + uint16_t fftLen, + uint8_t ifftFlag, + uint8_t bitReverseFlag) +{ + + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialise the default arm status */ + status = ARM_MATH_SUCCESS; + /* Initialise the FFT length */ + S->fftLen = fftLen; + /* Initialise the Twiddle coefficient pointer */ + S->pTwiddle = (q31_t *) twiddleCoef_4096_q31; + /* Initialise the Flag for selection of CFFT or CIFFT */ + S->ifftFlag = ifftFlag; + /* Initialise the Flag for calculation Bit reversal or not */ + S->bitReverseFlag = bitReverseFlag; + + /* Initializations of Instance structure depending on the FFT length */ + switch (S->fftLen) + { + /* Initializations of structure parameters for 4096 point FFT */ + case 4096U: + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 1U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 1U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) armBitRevTable; + break; + + /* Initializations of structure parameters for 1024 point FFT */ + case 1024U: + /* Initialise the twiddle coef modifier value */ + S->twidCoefModifier = 4U; + /* Initialise the bit reversal table modifier */ + S->bitRevFactor = 4U; + /* Initialise the bit reversal table pointer */ + S->pBitRevTable = (uint16_t *) & armBitRevTable[3]; + break; + + case 256U: + /* Initializations of structure parameters for 256 point FFT */ + S->twidCoefModifier = 16U; + S->bitRevFactor = 16U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[15]; + break; + + case 64U: + /* Initializations of structure parameters for 64 point FFT */ + S->twidCoefModifier = 64U; + S->bitRevFactor = 64U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[63]; + break; + + case 16U: + /* Initializations of structure parameters for 16 point FFT */ + S->twidCoefModifier = 256U; + S->bitRevFactor = 256U; + S->pBitRevTable = (uint16_t *) & armBitRevTable[255]; + break; + + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} + +/** + @} end of ComplexFFTDeprecated group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_q15.c new file mode 100755 index 0000000..3567819 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_q15.c @@ -0,0 +1,1818 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_q15.c + * Description: This file has function definition of Radix-4 FFT & IFFT function and + * In-place bit reversal using bit reversal table + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_q15( + q15_t * pSrc16, + uint32_t fftLen, + const q15_t * pCoef16, + uint32_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_q15( + q15_t * pSrc16, + uint32_t fftLen, + const q15_t * pCoef16, + uint32_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_bitreversal_q15( + q15_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + + +/** + @brief Processing function for the Q15 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q15 and will be removed in the future. + @param[in] S points to an instance of the Q15 CFFT/CIFFT structure. + @param[in,out] pSrc points to the complex data buffer. Processing occurs in-place. + + @par Input and output formats: + Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. + Hence the output format is different for different FFT sizes. + The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT: + @par + +| CFFT Size | Input format | Output format | Number of bits to upscale | +| --------: | ------------: | ------------: | ------------------------: | +| 16 | 1.15 | 5.11 | 4 | +| 64 | 1.15 | 7.9 | 6 | +| 256 | 1.15 | 9.7 | 8 | +| 1024 | 1.15 | 11.5 | 10 | + +| CIFFT Size | Input format | Output format | Number of bits to upscale | +| ---------: | ------------: | ------------: | ------------------------: | +| 16 | 1.15 | 5.11 | 0 | +| 64 | 1.15 | 7.9 | 0 | +| 256 | 1.15 | 9.7 | 0 | +| 1024 | 1.15 | 11.5 | 0 | + + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4_q15( + const arm_cfft_radix4_instance_q15 * S, + q15_t * pSrc) +{ + if (S->ifftFlag == 1U) + { + /* Complex IFFT radix-4 */ + arm_radix4_butterfly_inverse_q15(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + else + { + /* Complex FFT radix-4 */ + arm_radix4_butterfly_q15(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + + if (S->bitReverseFlag == 1U) + { + /* Bit Reversal */ + arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + +/** + @} end of ComplexFFTDeprecated group + */ + +/* + * Radix-4 FFT algorithm used is : + * + * Input real and imaginary data: + * x(n) = xa + j * ya + * x(n+N/4 ) = xb + j * yb + * x(n+N/2 ) = xc + j * yc + * x(n+3N 4) = xd + j * yd + * + * + * Output real and imaginary data: + * x(4r) = xa'+ j * ya' + * x(4r+1) = xb'+ j * yb' + * x(4r+2) = xc'+ j * yc' + * x(4r+3) = xd'+ j * yd' + * + * + * Twiddle factors for radix-4 FFT: + * Wn = co1 + j * (- si1) + * W2n = co2 + j * (- si2) + * W3n = co3 + j * (- si3) + + * The real and imaginary output values for the radix-4 butterfly are + * xa' = xa + xb + xc + xd + * ya' = ya + yb + yc + yd + * xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) + * yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) + * xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) + * yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) + * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) + * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) + * + */ + +/** + @brief Core function for the Q15 CFFT butterfly process. + @param[in,out] pSrc16 points to the in-place buffer of Q15 data type + @param[in] fftLen length of the FFT + @param[in] pCoef16 points to twiddle coefficient buffer + @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + */ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_q15( + q15_t * pSrc16, + uint32_t fftLen, + const q15_t * pCoef16, + uint32_t twidCoefModifier) +{ + +#if defined (ARM_MATH_DSP) + + q31_t R, S, T, U; + q31_t C1, C2, C3, out1, out2; + uint32_t n1, n2, ic, i0, j, k; + + q15_t *ptr1; + q15_t *pSi0; + q15_t *pSi1; + q15_t *pSi2; + q15_t *pSi3; + + q31_t xaya, xbyb, xcyc, xdyd; + + /* Total process is divided into three stages */ + + /* process first stage, middle stages, & last stage */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + + /* Index for twiddle coefficient */ + ic = 0U; + + /* Index for input read and output write */ + j = n2; + + pSi0 = pSrc16; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + /* Input is in 1.15(q15) format */ + + /* start of first stage process */ + do + { + /* Butterfly implementation */ + + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T = read_q15x2 (pSi0); + T = __SHADD16(T, 0); /* this is just a SIMD arithmetic shift right by 1 */ + T = __SHADD16(T, 0); /* it turns out doing this twice is 2 cycles, the alternative takes 3 cycles */ +/* + in = ((int16_t) (T & 0xFFFF)) >> 2; // alternative code that takes 3 cycles + T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF); +*/ + + /* Read yc (real), xc(imag) input */ + S = read_q15x2 (pSi2); + S = __SHADD16(S, 0); + S = __SHADD16(S, 0); + + /* R = packed((ya + yc), (xa + xc) ) */ + R = __QADD16(T, S); + + /* S = packed((ya - yc), (xa - xc) ) */ + S = __QSUB16(T, S); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T = read_q15x2 (pSi1); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* Read yd (real), xd(imag) input */ + U = read_q15x2 (pSi3); + U = __SHADD16(U, 0); + U = __SHADD16(U, 0); + + /* T = packed((yb + yd), (xb + xd) ) */ + T = __QADD16(T, U); + + /* writing the butterfly processed i0 sample */ + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + write_q15x2_ia (&pSi0, __SHADD16(R, T)); + + /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */ + R = __QSUB16(R, T); + + /* co2 & si2 are read from SIMD Coefficient pointer */ + C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic)); + +#ifndef ARM_MATH_BIG_ENDIAN + /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + out1 = __SMUAD(C2, R) >> 16U; + /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out2 = __SMUSDX(C2, R); +#else + /* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out1 = __SMUSDX(R, C2) >> 16U; + /* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + out2 = __SMUAD(C2, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Reading i0+fftLen/4 */ + /* T = packed(yb, xb) */ + T = read_q15x2 (pSi1); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* writing output(xc', yc') in little endian format */ + write_q15x2_ia (&pSi1, (q31_t) __PKHBT( out1, out2, 0 )); + + /* Butterfly calculations */ + /* U = packed(yd, xd) */ + U = read_q15x2 (pSi3); + U = __SHADD16(U, 0); + U = __SHADD16(U, 0); + + /* T = packed(yb-yd, xb-xd) */ + T = __QSUB16(T, U); + +#ifndef ARM_MATH_BIG_ENDIAN + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __QASX(S, T); + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __QSAX(S, T); +#else + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __QSAX(S, T); + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __QASX(S, T); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* co1 & si1 are read from SIMD Coefficient pointer */ + C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic)); + /* Butterfly process for the i0+fftLen/2 sample */ + +#ifndef ARM_MATH_BIG_ENDIAN + /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + out1 = __SMUAD(C1, S) >> 16U; + /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + out2 = __SMUSDX(C1, S); +#else + /* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + out1 = __SMUSDX(S, C1) >> 16U; + /* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + out2 = __SMUAD(C1, S); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* writing output(xb', yb') in little endian format */ + write_q15x2_ia (&pSi2, __PKHBT( out1, out2, 0 )); + + /* co3 & si3 are read from SIMD Coefficient pointer */ + C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic)); + /* Butterfly process for the i0+3fftLen/4 sample */ + +#ifndef ARM_MATH_BIG_ENDIAN + /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */ + out1 = __SMUAD(C3, R) >> 16U; + /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */ + out2 = __SMUSDX(C3, R); +#else + /* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */ + out1 = __SMUSDX(R, C3) >> 16U; + /* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */ + out2 = __SMUAD(C3, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* writing output(xd', yd') in little endian format */ + write_q15x2_ia (&pSi3, __PKHBT( out1, out2, 0 )); + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + } while (--j); + /* data is in 4.11(q11) format */ + + /* end of first stage process */ + + + /* start of middle stage process */ + + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + + /* Calculation of Middle stage */ + for (k = fftLen / 4U; k > 4U; k >>= 2U) + { + /* Initializations for the middle stage */ + n1 = n2; + n2 >>= 2U; + ic = 0U; + + for (j = 0U; j <= (n2 - 1U); j++) + { + /* index calculation for the coefficients */ + C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic)); + C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic)); + C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic)); + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + pSi0 = pSrc16 + 2 * j; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + /* Butterfly implementation */ + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T = read_q15x2 (pSi0); + + /* Read yc (real), xc(imag) input */ + S = read_q15x2 (pSi2); + + /* R = packed( (ya + yc), (xa + xc)) */ + R = __QADD16(T, S); + + /* S = packed((ya - yc), (xa - xc)) */ + S = __QSUB16(T, S); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T = read_q15x2 (pSi1); + + /* Read yd (real), xd(imag) input */ + U = read_q15x2 (pSi3); + + /* T = packed( (yb + yd), (xb + xd)) */ + T = __QADD16(T, U); + + /* writing the butterfly processed i0 sample */ + + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + out1 = __SHADD16(R, T); + out1 = __SHADD16(out1, 0); + write_q15x2 (pSi0, out1); + pSi0 += 2 * n1; + + /* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */ + R = __SHSUB16(R, T); + +#ifndef ARM_MATH_BIG_ENDIAN + /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */ + out1 = __SMUAD(C2, R) >> 16U; + + /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out2 = __SMUSDX(C2, R); +#else + /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out1 = __SMUSDX(R, C2) >> 16U; + + /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */ + out2 = __SMUAD(C2, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Reading i0+3fftLen/4 */ + /* Read yb (real), xb(imag) input */ + T = read_q15x2 (pSi1); + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + write_q15x2 (pSi1, __PKHBT( out1, out2, 0 )); + pSi1 += 2 * n1; + + /* Butterfly calculations */ + + /* Read yd (real), xd(imag) input */ + U = read_q15x2 (pSi3); + + /* T = packed(yb-yd, xb-xd) */ + T = __QSUB16(T, U); + +#ifndef ARM_MATH_BIG_ENDIAN + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __SHASX(S, T); + + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __SHSAX(S, T); + + + /* Butterfly process for the i0+fftLen/2 sample */ + out1 = __SMUAD(C1, S) >> 16U; + out2 = __SMUSDX(C1, S); +#else + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __SHSAX(S, T); + + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __SHASX(S, T); + + + /* Butterfly process for the i0+fftLen/2 sample */ + out1 = __SMUSDX(S, C1) >> 16U; + out2 = __SMUAD(C1, S); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + write_q15x2 (pSi2, __PKHBT( out1, out2, 0 )); + pSi2 += 2 * n1; + + /* Butterfly process for the i0+3fftLen/4 sample */ + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUAD(C3, R) >> 16U; + out2 = __SMUSDX(C3, R); +#else + out1 = __SMUSDX(R, C3) >> 16U; + out2 = __SMUAD(C3, R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */ + /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */ + write_q15x2 (pSi3, __PKHBT( out1, out2, 0 )); + pSi3 += 2 * n1; + } + } + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + } + /* end of middle stage process */ + + + /* data is in 10.6(q6) format for the 1024 point */ + /* data is in 8.8(q8) format for the 256 point */ + /* data is in 6.10(q10) format for the 64 point */ + /* data is in 4.12(q12) format for the 16 point */ + + /* Initializations for the last stage */ + j = fftLen >> 2; + + ptr1 = &pSrc16[0]; + + /* start of last stage process */ + + /* Butterfly implementation */ + do + { + /* Read xa (real), ya(imag) input */ + xaya = read_q15x2_ia (&ptr1); + + /* Read xb (real), yb(imag) input */ + xbyb = read_q15x2_ia (&ptr1); + + /* Read xc (real), yc(imag) input */ + xcyc = read_q15x2_ia (&ptr1); + + /* Read xd (real), yd(imag) input */ + xdyd = read_q15x2_ia (&ptr1); + + /* R = packed((ya + yc), (xa + xc)) */ + R = __QADD16(xaya, xcyc); + + /* T = packed((yb + yd), (xb + xd)) */ + T = __QADD16(xbyb, xdyd); + + /* pointer updation for writing */ + ptr1 = ptr1 - 8U; + + + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + write_q15x2_ia (&ptr1, __SHADD16(R, T)); + + /* T = packed((yb + yd), (xb + xd)) */ + T = __QADD16(xbyb, xdyd); + + /* xc' = (xa-xb+xc-xd) */ + /* yc' = (ya-yb+yc-yd) */ + write_q15x2_ia (&ptr1, __SHSUB16(R, T)); + + /* S = packed((ya - yc), (xa - xc)) */ + S = __QSUB16(xaya, xcyc); + + /* Read yd (real), xd(imag) input */ + /* T = packed( (yb - yd), (xb - xd)) */ + U = __QSUB16(xbyb, xdyd); + +#ifndef ARM_MATH_BIG_ENDIAN + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + write_q15x2_ia (&ptr1, __SHSAX(S, U)); + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + write_q15x2_ia (&ptr1, __SHASX(S, U)); +#else + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + write_q15x2_ia (&ptr1, __SHASX(S, U)); + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + write_q15x2_ia (&ptr1, __SHSAX(S, U)); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + } while (--j); + + /* end of last stage process */ + + /* output is in 11.5(q5) format for the 1024 point */ + /* output is in 9.7(q7) format for the 256 point */ + /* output is in 7.9(q9) format for the 64 point */ + /* output is in 5.11(q11) format for the 16 point */ + + +#else /* #if defined (ARM_MATH_DSP) */ + + q15_t R0, R1, S0, S1, T0, T1, U0, U1; + q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2; + uint32_t n1, n2, ic, i0, i1, i2, i3, j, k; + + /* Total process is divided into three stages */ + + /* process first stage, middle stages, & last stage */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + + /* Index for twiddle coefficient */ + ic = 0U; + + /* Index for input read and output write */ + i0 = 0U; + j = n2; + + /* Input is in 1.15(q15) format */ + + /* start of first stage process */ + do + { + /* Butterfly implementation */ + + /* index calculation for the input as, */ + /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Reading i0, i0+fftLen/2 inputs */ + + /* input is down scale by 4 to avoid overflow */ + /* Read ya (real), xa(imag) input */ + T0 = pSrc16[i0 * 2U] >> 2U; + T1 = pSrc16[(i0 * 2U) + 1U] >> 2U; + + /* input is down scale by 4 to avoid overflow */ + /* Read yc (real), xc(imag) input */ + S0 = pSrc16[i2 * 2U] >> 2U; + S1 = pSrc16[(i2 * 2U) + 1U] >> 2U; + + /* R0 = (ya + yc) */ + R0 = __SSAT(T0 + S0, 16U); + /* R1 = (xa + xc) */ + R1 = __SSAT(T1 + S1, 16U); + + /* S0 = (ya - yc) */ + S0 = __SSAT(T0 - S0, 16); + /* S1 = (xa - xc) */ + S1 = __SSAT(T1 - S1, 16); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* input is down scale by 4 to avoid overflow */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U] >> 2U; + T1 = pSrc16[(i1 * 2U) + 1U] >> 2U; + + /* input is down scale by 4 to avoid overflow */ + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U] >> 2U; + U1 = pSrc16[(i3 * 2U) + 1] >> 2U; + + /* T0 = (yb + yd) */ + T0 = __SSAT(T0 + U0, 16U); + /* T1 = (xb + xd) */ + T1 = __SSAT(T1 + U1, 16U); + + /* writing the butterfly processed i0 sample */ + /* ya' = ya + yb + yc + yd */ + /* xa' = xa + xb + xc + xd */ + pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U); + pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U); + + /* R0 = (ya + yc) - (yb + yd) */ + /* R1 = (xa + xc) - (xb + xd) */ + R0 = __SSAT(R0 - T0, 16U); + R1 = __SSAT(R1 - T1, 16U); + + /* co2 & si2 are read from Coefficient pointer */ + Co2 = pCoef16[2U * ic * 2U]; + Si2 = pCoef16[(2U * ic * 2U) + 1]; + + /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + out1 = (q15_t) ((Co2 * R0 + Si2 * R1) >> 16U); + /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out2 = (q15_t) ((-Si2 * R0 + Co2 * R1) >> 16U); + + /* Reading i0+fftLen/4 */ + /* input is down scale by 4 to avoid overflow */ + /* T0 = yb, T1 = xb */ + T0 = pSrc16[i1 * 2U] >> 2; + T1 = pSrc16[(i1 * 2U) + 1] >> 2; + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* writing output(xc', yc') in little endian format */ + pSrc16[i1 * 2U] = out1; + pSrc16[(i1 * 2U) + 1] = out2; + + /* Butterfly calculations */ + /* input is down scale by 4 to avoid overflow */ + /* U0 = yd, U1 = xd */ + U0 = pSrc16[i3 * 2U] >> 2; + U1 = pSrc16[(i3 * 2U) + 1] >> 2; + /* T0 = yb-yd */ + T0 = __SSAT(T0 - U0, 16); + /* T1 = xb-xd */ + T1 = __SSAT(T1 - U1, 16); + + /* R1 = (ya-yc) + (xb- xd), R0 = (xa-xc) - (yb-yd)) */ + R0 = (q15_t) __SSAT((q31_t) (S0 - T1), 16); + R1 = (q15_t) __SSAT((q31_t) (S1 + T0), 16); + + /* S1 = (ya-yc) - (xb- xd), S0 = (xa-xc) + (yb-yd)) */ + S0 = (q15_t) __SSAT(((q31_t) S0 + T1), 16U); + S1 = (q15_t) __SSAT(((q31_t) S1 - T0), 16U); + + /* co1 & si1 are read from Coefficient pointer */ + Co1 = pCoef16[ic * 2U]; + Si1 = pCoef16[(ic * 2U) + 1]; + /* Butterfly process for the i0+fftLen/2 sample */ + /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + out1 = (q15_t) ((Si1 * S1 + Co1 * S0) >> 16); + /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + out2 = (q15_t) ((-Si1 * S0 + Co1 * S1) >> 16); + + /* writing output(xb', yb') in little endian format */ + pSrc16[i2 * 2U] = out1; + pSrc16[(i2 * 2U) + 1] = out2; + + /* Co3 & si3 are read from Coefficient pointer */ + Co3 = pCoef16[3U * (ic * 2U)]; + Si3 = pCoef16[(3U * (ic * 2U)) + 1]; + /* Butterfly process for the i0+3fftLen/4 sample */ + /* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */ + out1 = (q15_t) ((Si3 * R1 + Co3 * R0) >> 16U); + /* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */ + out2 = (q15_t) ((-Si3 * R0 + Co3 * R1) >> 16U); + /* writing output(xd', yd') in little endian format */ + pSrc16[i3 * 2U] = out1; + pSrc16[(i3 * 2U) + 1] = out2; + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1U; + + } while (--j); + /* data is in 4.11(q11) format */ + + /* end of first stage process */ + + + /* start of middle stage process */ + + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + + /* Calculation of Middle stage */ + for (k = fftLen / 4U; k > 4U; k >>= 2U) + { + /* Initializations for the middle stage */ + n1 = n2; + n2 >>= 2U; + ic = 0U; + + for (j = 0U; j <= (n2 - 1U); j++) + { + /* index calculation for the coefficients */ + Co1 = pCoef16[ic * 2U]; + Si1 = pCoef16[(ic * 2U) + 1U]; + Co2 = pCoef16[2U * (ic * 2U)]; + Si2 = pCoef16[(2U * (ic * 2U)) + 1U]; + Co3 = pCoef16[3U * (ic * 2U)]; + Si3 = pCoef16[(3U * (ic * 2U)) + 1U]; + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + /* Butterfly implementation */ + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T0 = pSrc16[i0 * 2U]; + T1 = pSrc16[(i0 * 2U) + 1U]; + + /* Read yc (real), xc(imag) input */ + S0 = pSrc16[i2 * 2U]; + S1 = pSrc16[(i2 * 2U) + 1U]; + + /* R0 = (ya + yc), R1 = (xa + xc) */ + R0 = __SSAT(T0 + S0, 16); + R1 = __SSAT(T1 + S1, 16); + + /* S0 = (ya - yc), S1 =(xa - xc) */ + S0 = __SSAT(T0 - S0, 16); + S1 = __SSAT(T1 - S1, 16); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + + + /* T0 = (yb + yd), T1 = (xb + xd) */ + T0 = __SSAT(T0 + U0, 16); + T1 = __SSAT(T1 + U1, 16); + + /* writing the butterfly processed i0 sample */ + + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + out1 = ((R0 >> 1U) + (T0 >> 1U)) >> 1U; + out2 = ((R1 >> 1U) + (T1 >> 1U)) >> 1U; + + pSrc16[i0 * 2U] = out1; + pSrc16[(2U * i0) + 1U] = out2; + + /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */ + R0 = (R0 >> 1U) - (T0 >> 1U); + R1 = (R1 >> 1U) - (T1 >> 1U); + + /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */ + out1 = (q15_t) ((Co2 * R0 + Si2 * R1) >> 16U); + + /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out2 = (q15_t) ((-Si2 * R0 + Co2 * R1) >> 16U); + + /* Reading i0+3fftLen/4 */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + pSrc16[i1 * 2U] = out1; + pSrc16[(i1 * 2U) + 1U] = out2; + + /* Butterfly calculations */ + + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + + /* T0 = yb-yd, T1 = xb-xd */ + T0 = __SSAT(T0 - U0, 16); + T1 = __SSAT(T1 - U1, 16); + + /* R0 = (ya-yc) + (xb- xd), R1 = (xa-xc) - (yb-yd)) */ + R0 = (S0 >> 1U) - (T1 >> 1U); + R1 = (S1 >> 1U) + (T0 >> 1U); + + /* S0 = (ya-yc) - (xb- xd), S1 = (xa-xc) + (yb-yd)) */ + S0 = (S0 >> 1U) + (T1 >> 1U); + S1 = (S1 >> 1U) - (T0 >> 1U); + + /* Butterfly process for the i0+fftLen/2 sample */ + out1 = (q15_t) ((Co1 * S0 + Si1 * S1) >> 16U); + + out2 = (q15_t) ((-Si1 * S0 + Co1 * S1) >> 16U); + + /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + pSrc16[i2 * 2U] = out1; + pSrc16[(i2 * 2U) + 1U] = out2; + + /* Butterfly process for the i0+3fftLen/4 sample */ + out1 = (q15_t) ((Si3 * R1 + Co3 * R0) >> 16U); + + out2 = (q15_t) ((-Si3 * R0 + Co3 * R1) >> 16U); + /* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */ + /* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */ + pSrc16[i3 * 2U] = out1; + pSrc16[(i3 * 2U) + 1U] = out2; + } + } + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + } + /* end of middle stage process */ + + + /* data is in 10.6(q6) format for the 1024 point */ + /* data is in 8.8(q8) format for the 256 point */ + /* data is in 6.10(q10) format for the 64 point */ + /* data is in 4.12(q12) format for the 16 point */ + + /* Initializations for the last stage */ + n1 = n2; + n2 >>= 2U; + + /* start of last stage process */ + + /* Butterfly implementation */ + for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T0 = pSrc16[i0 * 2U]; + T1 = pSrc16[(i0 * 2U) + 1U]; + + /* Read yc (real), xc(imag) input */ + S0 = pSrc16[i2 * 2U]; + S1 = pSrc16[(i2 * 2U) + 1U]; + + /* R0 = (ya + yc), R1 = (xa + xc) */ + R0 = __SSAT(T0 + S0, 16U); + R1 = __SSAT(T1 + S1, 16U); + + /* S0 = (ya - yc), S1 = (xa - xc) */ + S0 = __SSAT(T0 - S0, 16U); + S1 = __SSAT(T1 - S1, 16U); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + + /* T0 = (yb + yd), T1 = (xb + xd)) */ + T0 = __SSAT(T0 + U0, 16U); + T1 = __SSAT(T1 + U1, 16U); + + /* writing the butterfly processed i0 sample */ + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U); + pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U); + + /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */ + R0 = (R0 >> 1U) - (T0 >> 1U); + R1 = (R1 >> 1U) - (T1 >> 1U); + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* xc' = (xa-xb+xc-xd) */ + /* yc' = (ya-yb+yc-yd) */ + pSrc16[i1 * 2U] = R0; + pSrc16[(i1 * 2U) + 1U] = R1; + + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + /* T0 = (yb - yd), T1 = (xb - xd) */ + T0 = __SSAT(T0 - U0, 16U); + T1 = __SSAT(T1 - U1, 16U); + + /* writing the butterfly processed i0 + fftLen/2 sample */ + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + pSrc16[i2 * 2U] = (S0 >> 1U) + (T1 >> 1U); + pSrc16[(i2 * 2U) + 1U] = (S1 >> 1U) - (T0 >> 1U); + + /* writing the butterfly processed i0 + 3fftLen/4 sample */ + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + pSrc16[i3 * 2U] = (S0 >> 1U) - (T1 >> 1U); + pSrc16[(i3 * 2U) + 1U] = (S1 >> 1U) + (T0 >> 1U); + + } + + /* end of last stage process */ + + /* output is in 11.5(q5) format for the 1024 point */ + /* output is in 9.7(q7) format for the 256 point */ + /* output is in 7.9(q9) format for the 64 point */ + /* output is in 5.11(q11) format for the 16 point */ + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + + +/** + @brief Core function for the Q15 CIFFT butterfly process. + @param[in,out] pSrc16 points to the in-place buffer of Q15 data type + @param[in] fftLen length of the FFT + @param[in] pCoef16 points to twiddle coefficient buffer + @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + */ + +/* + * Radix-4 IFFT algorithm used is : + * + * CIFFT uses same twiddle coefficients as CFFT function + * x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4] + * + * + * IFFT is implemented with following changes in equations from FFT + * + * Input real and imaginary data: + * x(n) = xa + j * ya + * x(n+N/4 ) = xb + j * yb + * x(n+N/2 ) = xc + j * yc + * x(n+3N 4) = xd + j * yd + * + * + * Output real and imaginary data: + * x(4r) = xa'+ j * ya' + * x(4r+1) = xb'+ j * yb' + * x(4r+2) = xc'+ j * yc' + * x(4r+3) = xd'+ j * yd' + * + * + * Twiddle factors for radix-4 IFFT: + * Wn = co1 + j * (si1) + * W2n = co2 + j * (si2) + * W3n = co3 + j * (si3) + + * The real and imaginary output values for the radix-4 butterfly are + * xa' = xa + xb + xc + xd + * ya' = ya + yb + yc + yd + * xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) + * yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) + * xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) + * yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) + * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3) + * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3) + * + */ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_q15( + q15_t * pSrc16, + uint32_t fftLen, + const q15_t * pCoef16, + uint32_t twidCoefModifier) +{ + +#if defined (ARM_MATH_DSP) + + q31_t R, S, T, U; + q31_t C1, C2, C3, out1, out2; + uint32_t n1, n2, ic, i0, j, k; + + q15_t *ptr1; + q15_t *pSi0; + q15_t *pSi1; + q15_t *pSi2; + q15_t *pSi3; + + q31_t xaya, xbyb, xcyc, xdyd; + + /* Total process is divided into three stages */ + + /* process first stage, middle stages, & last stage */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + + /* Index for twiddle coefficient */ + ic = 0U; + + /* Index for input read and output write */ + j = n2; + + pSi0 = pSrc16; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + /* Input is in 1.15(q15) format */ + + /* start of first stage process */ + do + { + /* Butterfly implementation */ + + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T = read_q15x2 (pSi0); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* Read yc (real), xc(imag) input */ + S = read_q15x2 (pSi2); + S = __SHADD16(S, 0); + S = __SHADD16(S, 0); + + /* R = packed((ya + yc), (xa + xc) ) */ + R = __QADD16(T, S); + + /* S = packed((ya - yc), (xa - xc) ) */ + S = __QSUB16(T, S); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T = read_q15x2 (pSi1); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* Read yd (real), xd(imag) input */ + U = read_q15x2 (pSi3); + U = __SHADD16(U, 0); + U = __SHADD16(U, 0); + + /* T = packed((yb + yd), (xb + xd) ) */ + T = __QADD16(T, U); + + /* writing the butterfly processed i0 sample */ + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + write_q15x2_ia (&pSi0, __SHADD16(R, T)); + + /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */ + R = __QSUB16(R, T); + + /* co2 & si2 are read from SIMD Coefficient pointer */ + C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic)); + +#ifndef ARM_MATH_BIG_ENDIAN + /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + out1 = __SMUSD(C2, R) >> 16U; + /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out2 = __SMUADX(C2, R); +#else + /* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out1 = __SMUADX(C2, R) >> 16U; + /* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + out2 = __SMUSD(__QSUB16(0, C2), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Reading i0+fftLen/4 */ + /* T = packed(yb, xb) */ + T = read_q15x2 (pSi1); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* writing output(xc', yc') in little endian format */ + write_q15x2_ia (&pSi1, (q31_t) __PKHBT( out1, out2, 0 )); + + /* Butterfly calculations */ + /* U = packed(yd, xd) */ + U = read_q15x2 (pSi3); + U = __SHADD16(U, 0); + U = __SHADD16(U, 0); + + /* T = packed(yb-yd, xb-xd) */ + T = __QSUB16(T, U); + +#ifndef ARM_MATH_BIG_ENDIAN + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __QSAX(S, T); + /* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */ + S = __QASX(S, T); +#else + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __QASX(S, T); + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __QSAX(S, T); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* co1 & si1 are read from SIMD Coefficient pointer */ + C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic)); + /* Butterfly process for the i0+fftLen/2 sample */ + +#ifndef ARM_MATH_BIG_ENDIAN + /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + out1 = __SMUSD(C1, S) >> 16U; + /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + out2 = __SMUADX(C1, S); +#else + /* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + out1 = __SMUADX(C1, S) >> 16U; + /* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + out2 = __SMUSD(__QSUB16(0, C1), S); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* writing output(xb', yb') in little endian format */ + write_q15x2_ia (&pSi2, __PKHBT( out1, out2, 0 )); + + /* co3 & si3 are read from SIMD Coefficient pointer */ + C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic)); + /* Butterfly process for the i0+3fftLen/4 sample */ + +#ifndef ARM_MATH_BIG_ENDIAN + /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */ + out1 = __SMUSD(C3, R) >> 16U; + /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */ + out2 = __SMUADX(C3, R); +#else + /* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */ + out1 = __SMUADX(C3, R) >> 16U; + /* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */ + out2 = __SMUSD(__QSUB16(0, C3), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* writing output(xd', yd') in little endian format */ + write_q15x2_ia (&pSi3, __PKHBT( out1, out2, 0 )); + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + } while (--j); + /* data is in 4.11(q11) format */ + + /* end of first stage process */ + + + /* start of middle stage process */ + + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + + /* Calculation of Middle stage */ + for (k = fftLen / 4U; k > 4U; k >>= 2U) + { + /* Initializations for the middle stage */ + n1 = n2; + n2 >>= 2U; + ic = 0U; + + for (j = 0U; j <= (n2 - 1U); j++) + { + /* index calculation for the coefficients */ + C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic)); + C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic)); + C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic)); + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + pSi0 = pSrc16 + 2 * j; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + /* Butterfly implementation */ + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T = read_q15x2 (pSi0); + + /* Read yc (real), xc(imag) input */ + S = read_q15x2 (pSi2); + + /* R = packed( (ya + yc), (xa + xc)) */ + R = __QADD16(T, S); + + /* S = packed((ya - yc), (xa - xc)) */ + S = __QSUB16(T, S); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T = read_q15x2 (pSi1); + + /* Read yd (real), xd(imag) input */ + U = read_q15x2 (pSi3); + + /* T = packed( (yb + yd), (xb + xd)) */ + T = __QADD16(T, U); + + /* writing the butterfly processed i0 sample */ + + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + out1 = __SHADD16(R, T); + out1 = __SHADD16(out1, 0); + write_q15x2 (pSi0, out1); + pSi0 += 2 * n1; + + /* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */ + R = __SHSUB16(R, T); + +#ifndef ARM_MATH_BIG_ENDIAN + /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */ + out1 = __SMUSD(C2, R) >> 16U; + + /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out2 = __SMUADX(C2, R); +#else + /* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + out1 = __SMUADX(R, C2) >> 16U; + + /* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */ + out2 = __SMUSD(__QSUB16(0, C2), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* Reading i0+3fftLen/4 */ + /* Read yb (real), xb(imag) input */ + T = read_q15x2 (pSi1); + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */ + /* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */ + write_q15x2 (pSi1, __PKHBT( out1, out2, 0 )); + pSi1 += 2 * n1; + + /* Butterfly calculations */ + + /* Read yd (real), xd(imag) input */ + U = read_q15x2 (pSi3); + + /* T = packed(yb-yd, xb-xd) */ + T = __QSUB16(T, U); + +#ifndef ARM_MATH_BIG_ENDIAN + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __SHSAX(S, T); + + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __SHASX(S, T); + + /* Butterfly process for the i0+fftLen/2 sample */ + out1 = __SMUSD(C1, S) >> 16U; + out2 = __SMUADX(C1, S); +#else + /* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */ + R = __SHASX(S, T); + + /* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */ + S = __SHSAX(S, T); + + /* Butterfly process for the i0+fftLen/2 sample */ + out1 = __SMUADX(S, C1) >> 16U; + out2 = __SMUSD(__QSUB16(0, C1), S); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */ + /* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */ + write_q15x2 (pSi2, __PKHBT( out1, out2, 0 )); + pSi2 += 2 * n1; + + /* Butterfly process for the i0+3fftLen/4 sample */ + +#ifndef ARM_MATH_BIG_ENDIAN + out1 = __SMUSD(C3, R) >> 16U; + out2 = __SMUADX(C3, R); +#else + out1 = __SMUADX(C3, R) >> 16U; + out2 = __SMUSD(__QSUB16(0, C3), R); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */ + /* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */ + write_q15x2 (pSi3, __PKHBT( out1, out2, 0 )); + pSi3 += 2 * n1; + } + } + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + } + /* end of middle stage process */ + + /* data is in 10.6(q6) format for the 1024 point */ + /* data is in 8.8(q8) format for the 256 point */ + /* data is in 6.10(q10) format for the 64 point */ + /* data is in 4.12(q12) format for the 16 point */ + + /* Initializations for the last stage */ + j = fftLen >> 2; + + ptr1 = &pSrc16[0]; + + /* start of last stage process */ + + /* Butterfly implementation */ + do + { + /* Read xa (real), ya(imag) input */ + xaya = read_q15x2_ia (&ptr1); + + /* Read xb (real), yb(imag) input */ + xbyb = read_q15x2_ia (&ptr1); + + /* Read xc (real), yc(imag) input */ + xcyc = read_q15x2_ia (&ptr1); + + /* Read xd (real), yd(imag) input */ + xdyd = read_q15x2_ia (&ptr1); + + /* R = packed((ya + yc), (xa + xc)) */ + R = __QADD16(xaya, xcyc); + + /* T = packed((yb + yd), (xb + xd)) */ + T = __QADD16(xbyb, xdyd); + + /* pointer updation for writing */ + ptr1 = ptr1 - 8U; + + + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + write_q15x2_ia (&ptr1, __SHADD16(R, T)); + + /* T = packed((yb + yd), (xb + xd)) */ + T = __QADD16(xbyb, xdyd); + + /* xc' = (xa-xb+xc-xd) */ + /* yc' = (ya-yb+yc-yd) */ + write_q15x2_ia (&ptr1, __SHSUB16(R, T)); + + /* S = packed((ya - yc), (xa - xc)) */ + S = __QSUB16(xaya, xcyc); + + /* Read yd (real), xd(imag) input */ + /* T = packed( (yb - yd), (xb - xd)) */ + U = __QSUB16(xbyb, xdyd); + +#ifndef ARM_MATH_BIG_ENDIAN + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + write_q15x2_ia (&ptr1, __SHASX(S, U)); + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + write_q15x2_ia (&ptr1, __SHSAX(S, U)); +#else + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + write_q15x2_ia (&ptr1, __SHSAX(S, U)); + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + write_q15x2_ia (&ptr1, __SHASX(S, U)); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + } while (--j); + + /* end of last stage process */ + + /* output is in 11.5(q5) format for the 1024 point */ + /* output is in 9.7(q7) format for the 256 point */ + /* output is in 7.9(q9) format for the 64 point */ + /* output is in 5.11(q11) format for the 16 point */ + + +#else /* arm_radix4_butterfly_inverse_q15 */ + + q15_t R0, R1, S0, S1, T0, T1, U0, U1; + q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2; + uint32_t n1, n2, ic, i0, i1, i2, i3, j, k; + + /* Total process is divided into three stages */ + + /* process first stage, middle stages, & last stage */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2U; + + /* Index for twiddle coefficient */ + ic = 0U; + + /* Index for input read and output write */ + i0 = 0U; + + j = n2; + + /* Input is in 1.15(q15) format */ + + /* Start of first stage process */ + do + { + /* Butterfly implementation */ + + /* index calculation for the input as, */ + /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Reading i0, i0+fftLen/2 inputs */ + /* input is down scale by 4 to avoid overflow */ + /* Read ya (real), xa(imag) input */ + T0 = pSrc16[i0 * 2U] >> 2U; + T1 = pSrc16[(i0 * 2U) + 1U] >> 2U; + /* input is down scale by 4 to avoid overflow */ + /* Read yc (real), xc(imag) input */ + S0 = pSrc16[i2 * 2U] >> 2U; + S1 = pSrc16[(i2 * 2U) + 1U] >> 2U; + + /* R0 = (ya + yc), R1 = (xa + xc) */ + R0 = __SSAT(T0 + S0, 16U); + R1 = __SSAT(T1 + S1, 16U); + /* S0 = (ya - yc), S1 = (xa - xc) */ + S0 = __SSAT(T0 - S0, 16U); + S1 = __SSAT(T1 - S1, 16U); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* input is down scale by 4 to avoid overflow */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U] >> 2U; + T1 = pSrc16[(i1 * 2U) + 1U] >> 2U; + /* Read yd (real), xd(imag) input */ + /* input is down scale by 4 to avoid overflow */ + U0 = pSrc16[i3 * 2U] >> 2U; + U1 = pSrc16[(i3 * 2U) + 1U] >> 2U; + + /* T0 = (yb + yd), T1 = (xb + xd) */ + T0 = __SSAT(T0 + U0, 16U); + T1 = __SSAT(T1 + U1, 16U); + + /* writing the butterfly processed i0 sample */ + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U); + pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U); + + /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc)- (xb + xd) */ + R0 = __SSAT(R0 - T0, 16U); + R1 = __SSAT(R1 - T1, 16U); + /* co2 & si2 are read from Coefficient pointer */ + Co2 = pCoef16[2U * ic * 2U]; + Si2 = pCoef16[(2U * ic * 2U) + 1U]; + /* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */ + out1 = (q15_t) ((Co2 * R0 - Si2 * R1) >> 16U); + /* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */ + out2 = (q15_t) ((Si2 * R0 + Co2 * R1) >> 16U); + + /* Reading i0+fftLen/4 */ + /* input is down scale by 4 to avoid overflow */ + /* T0 = yb, T1 = xb */ + T0 = pSrc16[i1 * 2U] >> 2U; + T1 = pSrc16[(i1 * 2U) + 1U] >> 2U; + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* writing output(xc', yc') in little endian format */ + pSrc16[i1 * 2U] = out1; + pSrc16[(i1 * 2U) + 1U] = out2; + + /* Butterfly calculations */ + /* input is down scale by 4 to avoid overflow */ + /* U0 = yd, U1 = xd) */ + U0 = pSrc16[i3 * 2U] >> 2U; + U1 = pSrc16[(i3 * 2U) + 1U] >> 2U; + + /* T0 = yb-yd, T1 = xb-xd) */ + T0 = __SSAT(T0 - U0, 16U); + T1 = __SSAT(T1 - U1, 16U); + /* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */ + R0 = (q15_t) __SSAT((q31_t) (S0 + T1), 16); + R1 = (q15_t) __SSAT((q31_t) (S1 - T0), 16); + /* S = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */ + S0 = (q15_t) __SSAT((q31_t) (S0 - T1), 16); + S1 = (q15_t) __SSAT((q31_t) (S1 + T0), 16); + + /* co1 & si1 are read from Coefficient pointer */ + Co1 = pCoef16[ic * 2U]; + Si1 = pCoef16[(ic * 2U) + 1U]; + /* Butterfly process for the i0+fftLen/2 sample */ + /* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */ + out1 = (q15_t) ((Co1 * S0 - Si1 * S1) >> 16U); + /* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */ + out2 = (q15_t) ((Si1 * S0 + Co1 * S1) >> 16U); + /* writing output(xb', yb') in little endian format */ + pSrc16[i2 * 2U] = out1; + pSrc16[(i2 * 2U) + 1U] = out2; + + /* Co3 & si3 are read from Coefficient pointer */ + Co3 = pCoef16[3U * ic * 2U]; + Si3 = pCoef16[(3U * ic * 2U) + 1U]; + /* Butterfly process for the i0+3fftLen/4 sample */ + /* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */ + out1 = (q15_t) ((Co3 * R0 - Si3 * R1) >> 16U); + /* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */ + out2 = (q15_t) ((Si3 * R0 + Co3 * R1) >> 16U); + /* writing output(xd', yd') in little endian format */ + pSrc16[i3 * 2U] = out1; + pSrc16[(i3 * 2U) + 1U] = out2; + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1U; + + } while (--j); + + /* End of first stage process */ + + /* data is in 4.11(q11) format */ + + + /* Start of Middle stage process */ + + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + + /* Calculation of Middle stage */ + for (k = fftLen / 4U; k > 4U; k >>= 2U) + { + /* Initializations for the middle stage */ + n1 = n2; + n2 >>= 2U; + ic = 0U; + + for (j = 0U; j <= (n2 - 1U); j++) + { + /* index calculation for the coefficients */ + Co1 = pCoef16[ic * 2U]; + Si1 = pCoef16[(ic * 2U) + 1U]; + Co2 = pCoef16[2U * ic * 2U]; + Si2 = pCoef16[2U * ic * 2U + 1U]; + Co3 = pCoef16[3U * ic * 2U]; + Si3 = pCoef16[(3U * ic * 2U) + 1U]; + + /* Twiddle coefficients index modifier */ + ic = ic + twidCoefModifier; + + /* Butterfly implementation */ + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T0 = pSrc16[i0 * 2U]; + T1 = pSrc16[(i0 * 2U) + 1U]; + + /* Read yc (real), xc(imag) input */ + S0 = pSrc16[i2 * 2U]; + S1 = pSrc16[(i2 * 2U) + 1U]; + + + /* R0 = (ya + yc), R1 = (xa + xc) */ + R0 = __SSAT(T0 + S0, 16U); + R1 = __SSAT(T1 + S1, 16U); + /* S0 = (ya - yc), S1 = (xa - xc) */ + S0 = __SSAT(T0 - S0, 16U); + S1 = __SSAT(T1 - S1, 16U); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + + /* T0 = (yb + yd), T1 = (xb + xd) */ + T0 = __SSAT(T0 + U0, 16U); + T1 = __SSAT(T1 + U1, 16U); + + /* writing the butterfly processed i0 sample */ + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + pSrc16[i0 * 2U] = ((R0 >> 1U) + (T0 >> 1U)) >> 1U; + pSrc16[(i0 * 2U) + 1U] = ((R1 >> 1U) + (T1 >> 1U)) >> 1U; + + /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */ + R0 = (R0 >> 1U) - (T0 >> 1U); + R1 = (R1 >> 1U) - (T1 >> 1U); + + /* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */ + out1 = (q15_t) ((Co2 * R0 - Si2 * R1) >> 16); + /* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */ + out2 = (q15_t) ((Si2 * R0 + Co2 * R1) >> 16); + + /* Reading i0+3fftLen/4 */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */ + /* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */ + pSrc16[i1 * 2U] = out1; + pSrc16[(i1 * 2U) + 1U] = out2; + + /* Butterfly calculations */ + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + + /* T0 = yb-yd, T1 = xb-xd) */ + T0 = __SSAT(T0 - U0, 16U); + T1 = __SSAT(T1 - U1, 16U); + + /* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */ + R0 = (S0 >> 1U) + (T1 >> 1U); + R1 = (S1 >> 1U) - (T0 >> 1U); + + /* S1 = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */ + S0 = (S0 >> 1U) - (T1 >> 1U); + S1 = (S1 >> 1U) + (T0 >> 1U); + + /* Butterfly process for the i0+fftLen/2 sample */ + out1 = (q15_t) ((Co1 * S0 - Si1 * S1) >> 16U); + out2 = (q15_t) ((Si1 * S0 + Co1 * S1) >> 16U); + /* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */ + /* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */ + pSrc16[i2 * 2U] = out1; + pSrc16[(i2 * 2U) + 1U] = out2; + + /* Butterfly process for the i0+3fftLen/4 sample */ + out1 = (q15_t) ((Co3 * R0 - Si3 * R1) >> 16U); + + out2 = (q15_t) ((Si3 * R0 + Co3 * R1) >> 16U); + /* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */ + /* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */ + pSrc16[i3 * 2U] = out1; + pSrc16[(i3 * 2U) + 1U] = out2; + + + } + } + /* Twiddle coefficients index modifier */ + twidCoefModifier <<= 2U; + } + /* End of Middle stages process */ + + + /* data is in 10.6(q6) format for the 1024 point */ + /* data is in 8.8(q8) format for the 256 point */ + /* data is in 6.10(q10) format for the 64 point */ + /* data is in 4.12(q12) format for the 16 point */ + + /* start of last stage process */ + + + /* Initializations for the last stage */ + n1 = n2; + n2 >>= 2U; + + /* Butterfly implementation */ + for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Reading i0, i0+fftLen/2 inputs */ + /* Read ya (real), xa(imag) input */ + T0 = pSrc16[i0 * 2U]; + T1 = pSrc16[(i0 * 2U) + 1U]; + /* Read yc (real), xc(imag) input */ + S0 = pSrc16[i2 * 2U]; + S1 = pSrc16[(i2 * 2U) + 1U]; + + /* R0 = (ya + yc), R1 = (xa + xc) */ + R0 = __SSAT(T0 + S0, 16U); + R1 = __SSAT(T1 + S1, 16U); + /* S0 = (ya - yc), S1 = (xa - xc) */ + S0 = __SSAT(T0 - S0, 16U); + S1 = __SSAT(T1 - S1, 16U); + + /* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */ + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + + /* T0 = (yb + yd), T1 = (xb + xd) */ + T0 = __SSAT(T0 + U0, 16U); + T1 = __SSAT(T1 + U1, 16U); + + /* writing the butterfly processed i0 sample */ + /* xa' = xa + xb + xc + xd */ + /* ya' = ya + yb + yc + yd */ + pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U); + pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U); + + /* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */ + R0 = (R0 >> 1U) - (T0 >> 1U); + R1 = (R1 >> 1U) - (T1 >> 1U); + + /* Read yb (real), xb(imag) input */ + T0 = pSrc16[i1 * 2U]; + T1 = pSrc16[(i1 * 2U) + 1U]; + + /* writing the butterfly processed i0 + fftLen/4 sample */ + /* xc' = (xa-xb+xc-xd) */ + /* yc' = (ya-yb+yc-yd) */ + pSrc16[i1 * 2U] = R0; + pSrc16[(i1 * 2U) + 1U] = R1; + + /* Read yd (real), xd(imag) input */ + U0 = pSrc16[i3 * 2U]; + U1 = pSrc16[(i3 * 2U) + 1U]; + /* T0 = (yb - yd), T1 = (xb - xd) */ + T0 = __SSAT(T0 - U0, 16U); + T1 = __SSAT(T1 - U1, 16U); + + /* writing the butterfly processed i0 + fftLen/2 sample */ + /* xb' = (xa-yb-xc+yd) */ + /* yb' = (ya+xb-yc-xd) */ + pSrc16[i2 * 2U] = (S0 >> 1U) - (T1 >> 1U); + pSrc16[(i2 * 2U) + 1U] = (S1 >> 1U) + (T0 >> 1U); + + + /* writing the butterfly processed i0 + 3fftLen/4 sample */ + /* xd' = (xa+yb-xc-yd) */ + /* yd' = (ya-xb-yc+xd) */ + pSrc16[i3 * 2U] = (S0 >> 1U) + (T1 >> 1U); + pSrc16[(i3 * 2U) + 1U] = (S1 >> 1U) - (T0 >> 1U); + } + /* end of last stage process */ + + /* output is in 11.5(q5) format for the 1024 point */ + /* output is in 9.7(q7) format for the 256 point */ + /* output is in 7.9(q9) format for the 64 point */ + /* output is in 5.11(q11) format for the 16 point */ + +#endif /* #if defined (ARM_MATH_DSP) */ + +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_q31.c new file mode 100755 index 0000000..1cc502b --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix4_q31.c @@ -0,0 +1,837 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_q31.c + * Description: This file has function definition of Radix-4 FFT & IFFT function and + * In-place bit reversal using bit reversal table + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint32_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint32_t twidCoefModifier); + +ARM_DSP_ATTRIBUTE void arm_bitreversal_q31( + q31_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + const uint16_t * pBitRevTab); + + +/** + @addtogroup ComplexFFTDeprecated + @{ + */ + +/** + @brief Processing function for the Q31 CFFT/CIFFT. + @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q31 and will be removed in the future. + @param[in] S points to an instance of the Q31 CFFT/CIFFT structure + @param[in,out] pSrc points to the complex data buffer of size 2*fftLen. Processing occurs in-place + + @par Input and output formats: + Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. + Hence the output format is different for different FFT sizes. + The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT: + @par + +| CFFT Size | Input format | Output format | Number of bits to upscale | +| --------: | ------------: | ------------: | ------------------------: | +| 16 | 1.31 | 5.27 | 4 | +| 64 | 1.31 | 7.25 | 6 | +| 256 | 1.31 | 9.23 | 8 | +| 1024 | 1.31 | 11.21 | 10 | + +| CIFFT Size | Input format | Output format | Number of bits to upscale | +| ---------: | ------------: | ------------: | ------------------------: | +| 16 | 1.31 | 5.27 | 0 | +| 64 | 1.31 | 7.25 | 0 | +| 256 | 1.31 | 9.23 | 0 | +| 1024 | 1.31 | 11.21 | 0 | + + */ + +ARM_DSP_ATTRIBUTE void arm_cfft_radix4_q31( + const arm_cfft_radix4_instance_q31 * S, + q31_t * pSrc) +{ + if (S->ifftFlag == 1U) + { + /* Complex IFFT radix-4 */ + arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + else + { + /* Complex FFT radix-4 */ + arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier); + } + + if (S->bitReverseFlag == 1U) + { + /* Bit Reversal */ + arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + +/** + @} end of ComplexFFTDeprecated group + */ + +/* + * Radix-4 FFT algorithm used is : + * + * Input real and imaginary data: + * x(n) = xa + j * ya + * x(n+N/4 ) = xb + j * yb + * x(n+N/2 ) = xc + j * yc + * x(n+3N 4) = xd + j * yd + * + * + * Output real and imaginary data: + * x(4r) = xa'+ j * ya' + * x(4r+1) = xb'+ j * yb' + * x(4r+2) = xc'+ j * yc' + * x(4r+3) = xd'+ j * yd' + * + * + * Twiddle factors for radix-4 FFT: + * Wn = co1 + j * (- si1) + * W2n = co2 + j * (- si2) + * W3n = co3 + j * (- si3) + * + * Butterfly implementation: + * xa' = xa + xb + xc + xd + * ya' = ya + yb + yc + yd + * xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) + * yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) + * xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) + * yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) + * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) + * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) + * + */ + +/** + @brief Core function for the Q31 CFFT butterfly process. + @param[in,out] pSrc points to the in-place buffer of Q31 data type. + @param[in] fftLen length of the FFT. + @param[in] pCoef points to twiddle coefficient buffer. + @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + */ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint32_t twidCoefModifier) +{ + uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k; + q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3; + + q31_t xa, xb, xc, xd; + q31_t ya, yb, yc, yd; + q31_t xa_out, xb_out, xc_out, xd_out; + q31_t ya_out, yb_out, yc_out, yd_out; + + q31_t *ptr1; + + /* Total process is divided into three stages */ + + /* process first stage, middle stages, & last stage */ + + + /* start of first stage process */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + /* n2 = fftLen/4 */ + n2 >>= 2U; + i0 = 0U; + ia1 = 0U; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* input is in 1.31(q31) format and provide 4 guard bits for the input */ + + /* Butterfly implementation */ + /* xa + xc */ + r1 = (pSrc[(2U * i0)] >> 4U) + (pSrc[(2U * i2)] >> 4U); + /* xa - xc */ + r2 = (pSrc[(2U * i0)] >> 4U) - (pSrc[(2U * i2)] >> 4U); + + /* xb + xd */ + t1 = (pSrc[(2U * i1)] >> 4U) + (pSrc[(2U * i3)] >> 4U); + + /* ya + yc */ + s1 = (pSrc[(2U * i0) + 1U] >> 4U) + (pSrc[(2U * i2) + 1U] >> 4U); + /* ya - yc */ + s2 = (pSrc[(2U * i0) + 1U] >> 4U) - (pSrc[(2U * i2) + 1U] >> 4U); + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (r1 + t1); + /* (xa + xc) - (xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = (pSrc[(2U * i1) + 1U] >> 4U) + (pSrc[(2U * i3) + 1U] >> 4U); + + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (s1 + t2); + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* yb - yd */ + t1 = (pSrc[(2U * i1) + 1U] >> 4U) - (pSrc[(2U * i3) + 1U] >> 4U); + /* xb - xd */ + t2 = (pSrc[(2U * i1)] >> 4U) - (pSrc[(2U * i3)] >> 4U); + + /* index calculation for the coefficients */ + ia2 = 2U * ia1; + co2 = pCoef[(ia2 * 2U)]; + si2 = pCoef[(ia2 * 2U) + 1U]; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) + + ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1U; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32)) - + ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1U; + + /* (xa - xc) + (yb - yd) */ + r1 = r2 + t1; + /* (xa - xc) - (yb - yd) */ + r2 = r2 - t1; + + /* (ya - yc) - (xb - xd) */ + s1 = s2 - t2; + /* (ya - yc) + (xb - xd) */ + s2 = s2 + t2; + + co1 = pCoef[(ia1 * 2U)]; + si1 = pCoef[(ia1 * 2U) + 1U]; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) + + ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1U; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) - + ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1U; + + /* index calculation for the coefficients */ + ia3 = 3U * ia1; + co3 = pCoef[(ia3 * 2U)]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) + + ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1U; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) - + ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1U; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1U; + + } while (--j); + + /* end of first stage process */ + + /* data is in 5.27(q27) format */ + + + /* start of Middle stages process */ + + + /* each stage in middle stages provides two down scaling of the input */ + + twidCoefModifier <<= 2U; + + + for (k = fftLen / 4U; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + /* Calculation of first stage */ + for (j = 0U; j <= (n2 - 1U); j++) + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[(ia1 * 2U)]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[(ia2 * 2U)]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[(ia3 * 2U)]; + si3 = pCoef[(ia3 * 2U) + 1U]; + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSrc[2U * i0] + pSrc[2U * i2]; + /* xa - xc */ + r2 = pSrc[2U * i0] - pSrc[2U * i2]; + + /* ya + yc */ + s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U]; + /* ya - yc */ + s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = pSrc[2U * i1] + pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (r1 + t1) >> 2U; + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U]; + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (s1 + t2) >> 2U; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U]; + /* (xb - xd) */ + t2 = pSrc[2U * i1] - pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) + + ((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1U; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32)) - + ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1U; + + /* (xa - xc) + (yb - yd) */ + r1 = r2 + t1; + /* (xa - xc) - (yb - yd) */ + r2 = r2 - t1; + + /* (ya - yc) - (xb - xd) */ + s1 = s2 - t2; + /* (ya - yc) + (xb - xd) */ + s2 = s2 + t2; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) + + ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1U; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) - + ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1U; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) + + ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1U; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) - + ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1U; + } + } + twidCoefModifier <<= 2U; + } + + /* End of Middle stages process */ + + /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */ + /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */ + /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */ + /* data is in 5.27(q27) format for the 16 point as there are no middle stages */ + + + /* start of Last stage process */ + /* Initializations for the last stage */ + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + /* Read xa (real), ya(imag) input */ + xa = *ptr1++; + ya = *ptr1++; + + /* Read xb (real), yb(imag) input */ + xb = *ptr1++; + yb = *ptr1++; + + /* Read xc (real), yc(imag) input */ + xc = *ptr1++; + yc = *ptr1++; + + /* Read xc (real), yc(imag) input */ + xd = *ptr1++; + yd = *ptr1++; + + /* xa' = xa + xb + xc + xd */ + xa_out = xa + xb + xc + xd; + + /* ya' = ya + yb + yc + yd */ + ya_out = ya + yb + yc + yd; + + /* pointer updation for writing */ + ptr1 = ptr1 - 8U; + + /* writing xa' and ya' */ + *ptr1++ = xa_out; + *ptr1++ = ya_out; + + xc_out = (xa - xb + xc - xd); + yc_out = (ya - yb + yc - yd); + + /* writing xc' and yc' */ + *ptr1++ = xc_out; + *ptr1++ = yc_out; + + xb_out = (xa + yb - xc - yd); + yb_out = (ya - xb - yc + xd); + + /* writing xb' and yb' */ + *ptr1++ = xb_out; + *ptr1++ = yb_out; + + xd_out = (xa - yb - xc + yd); + yd_out = (ya + xb - yc - xd); + + /* writing xd' and yd' */ + *ptr1++ = xd_out; + *ptr1++ = yd_out; + + + } while (--j); + + /* output is in 11.21(q21) format for the 1024 point */ + /* output is in 9.23(q23) format for the 256 point */ + /* output is in 7.25(q25) format for the 64 point */ + /* output is in 5.27(q27) format for the 16 point */ + + /* End of last stage process */ + +} + + +/** + @brief Core function for the Q31 CIFFT butterfly process. + @param[in,out] pSrc points to the in-place buffer of Q31 data type. + @param[in] fftLen length of the FFT. + @param[in] pCoef points to twiddle coefficient buffer. + @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + */ + +/* + * Radix-4 IFFT algorithm used is : + * + * CIFFT uses same twiddle coefficients as CFFT Function + * x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4] + * + * + * IFFT is implemented with following changes in equations from FFT + * + * Input real and imaginary data: + * x(n) = xa + j * ya + * x(n+N/4 ) = xb + j * yb + * x(n+N/2 ) = xc + j * yc + * x(n+3N 4) = xd + j * yd + * + * + * Output real and imaginary data: + * x(4r) = xa'+ j * ya' + * x(4r+1) = xb'+ j * yb' + * x(4r+2) = xc'+ j * yc' + * x(4r+3) = xd'+ j * yd' + * + * + * Twiddle factors for radix-4 IFFT: + * Wn = co1 + j * (si1) + * W2n = co2 + j * (si2) + * W3n = co3 + j * (si3) + + * The real and imaginary output values for the radix-4 butterfly are + * xa' = xa + xb + xc + xd + * ya' = ya + yb + yc + yd + * xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) + * yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) + * xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) + * yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) + * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3) + * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3) + * + */ + +ARM_DSP_ATTRIBUTE void arm_radix4_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef, + uint32_t twidCoefModifier) +{ + uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k; + q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3; + q31_t xa, xb, xc, xd; + q31_t ya, yb, yc, yd; + q31_t xa_out, xb_out, xc_out, xd_out; + q31_t ya_out, yb_out, yc_out, yd_out; + + q31_t *ptr1; + + /* input is be 1.31(q31) format for all FFT sizes */ + /* Total process is divided into three stages */ + /* process first stage, middle stages, & last stage */ + + /* Start of first stage process */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + /* n2 = fftLen/4 */ + n2 >>= 2U; + i0 = 0U; + ia1 = 0U; + + j = n2; + + do + { + /* input is in 1.31(q31) format and provide 4 guard bits for the input */ + + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + /* xa + xc */ + r1 = (pSrc[2U * i0] >> 4U) + (pSrc[2U * i2] >> 4U); + /* xa - xc */ + r2 = (pSrc[2U * i0] >> 4U) - (pSrc[2U * i2] >> 4U); + + /* xb + xd */ + t1 = (pSrc[2U * i1] >> 4U) + (pSrc[2U * i3] >> 4U); + + /* ya + yc */ + s1 = (pSrc[(2U * i0) + 1U] >> 4U) + (pSrc[(2U * i2) + 1U] >> 4U); + /* ya - yc */ + s2 = (pSrc[(2U * i0) + 1U] >> 4U) - (pSrc[(2U * i2) + 1U] >> 4U); + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (r1 + t1); + /* (xa + xc) - (xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = (pSrc[(2U * i1) + 1U] >> 4U) + (pSrc[(2U * i3) + 1U] >> 4U); + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (s1 + t2); + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* yb - yd */ + t1 = (pSrc[(2U * i1) + 1U] >> 4U) - (pSrc[(2U * i3) + 1U] >> 4U); + /* xb - xd */ + t2 = (pSrc[2U * i1] >> 4U) - (pSrc[2U * i3] >> 4U); + + /* index calculation for the coefficients */ + ia2 = 2U * ia1; + co2 = pCoef[ia2 * 2U]; + si2 = pCoef[(ia2 * 2U) + 1U]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) - + ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1U; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[2U * i1 + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32)) + + ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1U; + + /* (xa - xc) - (yb - yd) */ + r1 = r2 - t1; + /* (xa - xc) + (yb - yd) */ + r2 = r2 + t1; + + /* (ya - yc) + (xb - xd) */ + s1 = s2 + t2; + /* (ya - yc) - (xb - xd) */ + s2 = s2 - t2; + + co1 = pCoef[ia1 * 2U]; + si1 = pCoef[(ia1 * 2U) + 1U]; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) - + ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1U; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) + + ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1U; + + /* index calculation for the coefficients */ + ia3 = 3U * ia1; + co3 = pCoef[ia3 * 2U]; + si3 = pCoef[(ia3 * 2U) + 1U]; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2U * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) - + ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1U; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) + + ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1U; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1U; + + } while (--j); + + /* data is in 5.27(q27) format */ + /* each stage provides two down scaling of the input */ + + + /* Start of Middle stages process */ + + twidCoefModifier <<= 2U; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen / 4U; k > 4U; k >>= 2U) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2U; + ia1 = 0U; + + for (j = 0; j <= (n2 - 1U); j++) + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[(ia1 * 2U)]; + si1 = pCoef[(ia1 * 2U) + 1U]; + co2 = pCoef[(ia2 * 2U)]; + si2 = pCoef[(ia2 * 2U) + 1U]; + co3 = pCoef[(ia3 * 2U)]; + si3 = pCoef[(ia3 * 2U) + 1U]; + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2U], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSrc[2U * i0] + pSrc[2U * i2]; + /* xa - xc */ + r2 = pSrc[2U * i0] - pSrc[2U * i2]; + + /* ya + yc */ + s1 = pSrc[(2U * i0) + 1U] + pSrc[(2U * i2) + 1U]; + /* ya - yc */ + s2 = pSrc[(2U * i0) + 1U] - pSrc[(2U * i2) + 1U]; + + /* xb + xd */ + t1 = pSrc[2U * i1] + pSrc[2U * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2U * i0] = (r1 + t1) >> 2U; + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = pSrc[(2U * i1) + 1U] + pSrc[(2U * i3) + 1U]; + /* ya' = ya + yb + yc + yd */ + pSrc[(2U * i0) + 1U] = (s1 + t2) >> 2U; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2U * i1) + 1U] - pSrc[(2U * i3) + 1U]; + /* (xb - xd) */ + t2 = pSrc[2U * i1] - pSrc[2U * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2U * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32U)) - + ((int32_t) (((q63_t) s1 * si2) >> 32U))) >> 1U; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2U * i1) + 1U] = (((int32_t) (((q63_t) s1 * co2) >> 32U)) + + ((int32_t) (((q63_t) r1 * si2) >> 32U))) >> 1U; + + /* (xa - xc) - (yb - yd) */ + r1 = r2 - t1; + /* (xa - xc) + (yb - yd) */ + r2 = r2 + t1; + + /* (ya - yc) + (xb - xd) */ + s1 = s2 + t2; + /* (ya - yc) - (xb - xd) */ + s2 = s2 - t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2U * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) - + ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1U; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2U * i2) + 1U] = (((int32_t) (((q63_t) s1 * co1) >> 32)) + + ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1U; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[(2U * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) - + ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1U; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2U * i3) + 1U] = (((int32_t) (((q63_t) s2 * co3) >> 32)) + + ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1U; + } + } + twidCoefModifier <<= 2U; + } + + /* End of Middle stages process */ + + /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */ + /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */ + /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */ + /* data is in 5.27(q27) format for the 16 point as there are no middle stages */ + + + /* Start of last stage process */ + + + /* Initializations for the last stage */ + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + /* Read xa (real), ya(imag) input */ + xa = *ptr1++; + ya = *ptr1++; + + /* Read xb (real), yb(imag) input */ + xb = *ptr1++; + yb = *ptr1++; + + /* Read xc (real), yc(imag) input */ + xc = *ptr1++; + yc = *ptr1++; + + /* Read xc (real), yc(imag) input */ + xd = *ptr1++; + yd = *ptr1++; + + /* xa' = xa + xb + xc + xd */ + xa_out = xa + xb + xc + xd; + + /* ya' = ya + yb + yc + yd */ + ya_out = ya + yb + yc + yd; + + /* pointer updation for writing */ + ptr1 = ptr1 - 8U; + + /* writing xa' and ya' */ + *ptr1++ = xa_out; + *ptr1++ = ya_out; + + xc_out = (xa - xb + xc - xd); + yc_out = (ya - yb + yc - yd); + + /* writing xc' and yc' */ + *ptr1++ = xc_out; + *ptr1++ = yc_out; + + xb_out = (xa - yb - xc + yd); + yb_out = (ya + xb - yc - xd); + + /* writing xb' and yb' */ + *ptr1++ = xb_out; + *ptr1++ = yb_out; + + xd_out = (xa + yb - xc - yd); + yd_out = (ya - xb - yc + xd); + + /* writing xd' and yd' */ + *ptr1++ = xd_out; + *ptr1++ = yd_out; + + } while (--j); + + /* output is in 11.21(q21) format for the 1024 point */ + /* output is in 9.23(q23) format for the 256 point */ + /* output is in 7.25(q25) format for the 64 point */ + /* output is in 5.27(q27) format for the 16 point */ + + /* End of last stage process */ +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix8_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix8_f16.c new file mode 100755 index 0000000..c700691 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix8_f16.c @@ -0,0 +1,297 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix8_f16.c + * Description: Radix-8 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +void arm_radix8_butterfly_f16( + float16_t * pSrc, + uint16_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier); + +/* ---------------------------------------------------------------------- + * Internal helper function used by the FFTs + * -------------------------------------------------------------------- */ + +/** + brief Core function for the floating-point CFFT butterfly process. + param[in,out] pSrc points to the in-place buffer of floating-point data type. + param[in] fftLen length of the FFT. + param[in] pCoef points to the twiddle coefficient buffer. + param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + return none +*/ + +ARM_DSP_ATTRIBUTE void arm_radix8_butterfly_f16( + float16_t * pSrc, + uint16_t fftLen, + const float16_t * pCoef, + uint16_t twidCoefModifier) +{ + uint32_t ia1, ia2, ia3, ia4, ia5, ia6, ia7; + uint32_t i1, i2, i3, i4, i5, i6, i7, i8; + uint32_t id; + uint32_t n1, n2, j; + + float16_t r1, r2, r3, r4, r5, r6, r7, r8; + float16_t t1, t2; + float16_t s1, s2, s3, s4, s5, s6, s7, s8; + float16_t p1, p2, p3, p4; + float16_t co2, co3, co4, co5, co6, co7, co8; + float16_t si2, si3, si4, si5, si6, si7, si8; + const float16_t C81 = 0.70710678118f16; + + n2 = fftLen; + + do + { + n1 = n2; + n2 = n2 >> 3; + i1 = 0; + + do + { + i2 = i1 + n2; + i3 = i2 + n2; + i4 = i3 + n2; + i5 = i4 + n2; + i6 = i5 + n2; + i7 = i6 + n2; + i8 = i7 + n2; + r1 = (_Float16)pSrc[2 * i1] + (_Float16)pSrc[2 * i5]; + r5 = (_Float16)pSrc[2 * i1] - (_Float16)pSrc[2 * i5]; + r2 = (_Float16)pSrc[2 * i2] + (_Float16)pSrc[2 * i6]; + r6 = (_Float16)pSrc[2 * i2] - (_Float16)pSrc[2 * i6]; + r3 = (_Float16)pSrc[2 * i3] + (_Float16)pSrc[2 * i7]; + r7 = (_Float16)pSrc[2 * i3] - (_Float16)pSrc[2 * i7]; + r4 = (_Float16)pSrc[2 * i4] + (_Float16)pSrc[2 * i8]; + r8 = (_Float16)pSrc[2 * i4] - (_Float16)pSrc[2 * i8]; + t1 = (_Float16)r1 - (_Float16)r3; + r1 = (_Float16)r1 + (_Float16)r3; + r3 = (_Float16)r2 - (_Float16)r4; + r2 = (_Float16)r2 + (_Float16)r4; + pSrc[2 * i1] = (_Float16)r1 + (_Float16)r2; + pSrc[2 * i5] = (_Float16)r1 - (_Float16)r2; + r1 = (_Float16)pSrc[2 * i1 + 1] + (_Float16)pSrc[2 * i5 + 1]; + s5 = (_Float16)pSrc[2 * i1 + 1] - (_Float16)pSrc[2 * i5 + 1]; + r2 = (_Float16)pSrc[2 * i2 + 1] + (_Float16)pSrc[2 * i6 + 1]; + s6 = (_Float16)pSrc[2 * i2 + 1] - (_Float16)pSrc[2 * i6 + 1]; + s3 = (_Float16)pSrc[2 * i3 + 1] + (_Float16)pSrc[2 * i7 + 1]; + s7 = (_Float16)pSrc[2 * i3 + 1] - (_Float16)pSrc[2 * i7 + 1]; + r4 = (_Float16)pSrc[2 * i4 + 1] + (_Float16)pSrc[2 * i8 + 1]; + s8 = (_Float16)pSrc[2 * i4 + 1] - (_Float16)pSrc[2 * i8 + 1]; + t2 = (_Float16)r1 - (_Float16)s3; + r1 = (_Float16)r1 + (_Float16)s3; + s3 = (_Float16)r2 - (_Float16)r4; + r2 = (_Float16)r2 + (_Float16)r4; + pSrc[2 * i1 + 1] = (_Float16)r1 + (_Float16)r2; + pSrc[2 * i5 + 1] = (_Float16)r1 - (_Float16)r2; + pSrc[2 * i3] = (_Float16)t1 + (_Float16)s3; + pSrc[2 * i7] = (_Float16)t1 - (_Float16)s3; + pSrc[2 * i3 + 1] = (_Float16)t2 - (_Float16)r3; + pSrc[2 * i7 + 1] = (_Float16)t2 + (_Float16)r3; + r1 = ((_Float16)r6 - (_Float16)r8) * (_Float16)C81; + r6 = ((_Float16)r6 + (_Float16)r8) * (_Float16)C81; + r2 = ((_Float16)s6 - (_Float16)s8) * (_Float16)C81; + s6 = ((_Float16)s6 + (_Float16)s8) * (_Float16)C81; + t1 = (_Float16)r5 - (_Float16)r1; + r5 = (_Float16)r5 + (_Float16)r1; + r8 = (_Float16)r7 - (_Float16)r6; + r7 = (_Float16)r7 + (_Float16)r6; + t2 = (_Float16)s5 - (_Float16)r2; + s5 = (_Float16)s5 + (_Float16)r2; + s8 = (_Float16)s7 - (_Float16)s6; + s7 = (_Float16)s7 + (_Float16)s6; + pSrc[2 * i2] = (_Float16)r5 + (_Float16)s7; + pSrc[2 * i8] = (_Float16)r5 - (_Float16)s7; + pSrc[2 * i6] = (_Float16)t1 + (_Float16)s8; + pSrc[2 * i4] = (_Float16)t1 - (_Float16)s8; + pSrc[2 * i2 + 1] = (_Float16)s5 - (_Float16)r7; + pSrc[2 * i8 + 1] = (_Float16)s5 + (_Float16)r7; + pSrc[2 * i6 + 1] = (_Float16)t2 - (_Float16)r8; + pSrc[2 * i4 + 1] = (_Float16)t2 + (_Float16)r8; + + i1 += n1; + } while (i1 < fftLen); + + if (n2 < 8) + break; + + ia1 = 0; + j = 1; + + do + { + /* index calculation for the coefficients */ + id = ia1 + twidCoefModifier; + ia1 = id; + ia2 = ia1 + id; + ia3 = ia2 + id; + ia4 = ia3 + id; + ia5 = ia4 + id; + ia6 = ia5 + id; + ia7 = ia6 + id; + + co2 = pCoef[2 * ia1]; + co3 = pCoef[2 * ia2]; + co4 = pCoef[2 * ia3]; + co5 = pCoef[2 * ia4]; + co6 = pCoef[2 * ia5]; + co7 = pCoef[2 * ia6]; + co8 = pCoef[2 * ia7]; + si2 = pCoef[2 * ia1 + 1]; + si3 = pCoef[2 * ia2 + 1]; + si4 = pCoef[2 * ia3 + 1]; + si5 = pCoef[2 * ia4 + 1]; + si6 = pCoef[2 * ia5 + 1]; + si7 = pCoef[2 * ia6 + 1]; + si8 = pCoef[2 * ia7 + 1]; + + i1 = j; + + do + { + /* index calculation for the input */ + i2 = i1 + n2; + i3 = i2 + n2; + i4 = i3 + n2; + i5 = i4 + n2; + i6 = i5 + n2; + i7 = i6 + n2; + i8 = i7 + n2; + r1 = (_Float16)pSrc[2 * i1] + (_Float16)pSrc[2 * i5]; + r5 = (_Float16)pSrc[2 * i1] - (_Float16)pSrc[2 * i5]; + r2 = (_Float16)pSrc[2 * i2] + (_Float16)pSrc[2 * i6]; + r6 = (_Float16)pSrc[2 * i2] - (_Float16)pSrc[2 * i6]; + r3 = (_Float16)pSrc[2 * i3] + (_Float16)pSrc[2 * i7]; + r7 = (_Float16)pSrc[2 * i3] - (_Float16)pSrc[2 * i7]; + r4 = (_Float16)pSrc[2 * i4] + (_Float16)pSrc[2 * i8]; + r8 = (_Float16)pSrc[2 * i4] - (_Float16)pSrc[2 * i8]; + t1 = (_Float16)r1 - (_Float16)r3; + r1 = (_Float16)r1 + (_Float16)r3; + r3 = (_Float16)r2 - (_Float16)r4; + r2 = (_Float16)r2 + (_Float16)r4; + pSrc[2 * i1] = (_Float16)r1 + (_Float16)r2; + r2 = (_Float16)r1 - (_Float16)r2; + s1 = (_Float16)pSrc[2 * i1 + 1] + (_Float16)pSrc[2 * i5 + 1]; + s5 = (_Float16)pSrc[2 * i1 + 1] - (_Float16)pSrc[2 * i5 + 1]; + s2 = (_Float16)pSrc[2 * i2 + 1] + (_Float16)pSrc[2 * i6 + 1]; + s6 = (_Float16)pSrc[2 * i2 + 1] - (_Float16)pSrc[2 * i6 + 1]; + s3 = (_Float16)pSrc[2 * i3 + 1] + (_Float16)pSrc[2 * i7 + 1]; + s7 = (_Float16)pSrc[2 * i3 + 1] - (_Float16)pSrc[2 * i7 + 1]; + s4 = (_Float16)pSrc[2 * i4 + 1] + (_Float16)pSrc[2 * i8 + 1]; + s8 = (_Float16)pSrc[2 * i4 + 1] - (_Float16)pSrc[2 * i8 + 1]; + t2 = (_Float16)s1 - (_Float16)s3; + s1 = (_Float16)s1 + (_Float16)s3; + s3 = (_Float16)s2 - (_Float16)s4; + s2 = (_Float16)s2 + (_Float16)s4; + r1 = (_Float16)t1 + (_Float16)s3; + t1 = (_Float16)t1 - (_Float16)s3; + pSrc[2 * i1 + 1] = (_Float16)s1 + (_Float16)s2; + s2 = (_Float16)s1 - (_Float16)s2; + s1 = (_Float16)t2 - (_Float16)r3; + t2 = (_Float16)t2 + (_Float16)r3; + p1 = (_Float16)co5 * (_Float16)r2; + p2 = (_Float16)si5 * (_Float16)s2; + p3 = (_Float16)co5 * (_Float16)s2; + p4 = (_Float16)si5 * (_Float16)r2; + pSrc[2 * i5] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i5 + 1] = (_Float16)p3 - (_Float16)p4; + p1 = (_Float16)co3 * (_Float16)r1; + p2 = (_Float16)si3 * (_Float16)s1; + p3 = (_Float16)co3 * (_Float16)s1; + p4 = (_Float16)si3 * (_Float16)r1; + pSrc[2 * i3] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i3 + 1] = (_Float16)p3 - (_Float16)p4; + p1 = (_Float16)co7 * (_Float16)t1; + p2 = (_Float16)si7 * (_Float16)t2; + p3 = (_Float16)co7 * (_Float16)t2; + p4 = (_Float16)si7 * (_Float16)t1; + pSrc[2 * i7] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i7 + 1] = (_Float16)p3 - (_Float16)p4; + r1 = ((_Float16)r6 - (_Float16)r8) * (_Float16)C81; + r6 = ((_Float16)r6 + (_Float16)r8) * (_Float16)C81; + s1 = ((_Float16)s6 - (_Float16)s8) * (_Float16)C81; + s6 = ((_Float16)s6 + (_Float16)s8) * (_Float16)C81; + t1 = (_Float16)r5 - (_Float16)r1; + r5 = (_Float16)r5 + (_Float16)r1; + r8 = (_Float16)r7 - (_Float16)r6; + r7 = (_Float16)r7 + (_Float16)r6; + t2 = (_Float16)s5 - (_Float16)s1; + s5 = (_Float16)s5 + (_Float16)s1; + s8 = (_Float16)s7 - (_Float16)s6; + s7 = (_Float16)s7 + (_Float16)s6; + r1 = (_Float16)r5 + (_Float16)s7; + r5 = (_Float16)r5 - (_Float16)s7; + r6 = (_Float16)t1 + (_Float16)s8; + t1 = (_Float16)t1 - (_Float16)s8; + s1 = (_Float16)s5 - (_Float16)r7; + s5 = (_Float16)s5 + (_Float16)r7; + s6 = (_Float16)t2 - (_Float16)r8; + t2 = (_Float16)t2 + (_Float16)r8; + p1 = (_Float16)co2 * (_Float16)r1; + p2 = (_Float16)si2 * (_Float16)s1; + p3 = (_Float16)co2 * (_Float16)s1; + p4 = (_Float16)si2 * (_Float16)r1; + pSrc[2 * i2] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i2 + 1] = (_Float16)p3 - (_Float16)p4; + p1 = (_Float16)co8 * (_Float16)r5; + p2 = (_Float16)si8 * (_Float16)s5; + p3 = (_Float16)co8 * (_Float16)s5; + p4 = (_Float16)si8 * (_Float16)r5; + pSrc[2 * i8] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i8 + 1] = (_Float16)p3 - (_Float16)p4; + p1 = (_Float16)co6 * (_Float16)r6; + p2 = (_Float16)si6 * (_Float16)s6; + p3 = (_Float16)co6 * (_Float16)s6; + p4 = (_Float16)si6 * (_Float16)r6; + pSrc[2 * i6] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i6 + 1] = (_Float16)p3 - (_Float16)p4; + p1 = (_Float16)co4 * (_Float16)t1; + p2 = (_Float16)si4 * (_Float16)t2; + p3 = (_Float16)co4 * (_Float16)t2; + p4 = (_Float16)si4 * (_Float16)t1; + pSrc[2 * i4] = (_Float16)p1 + (_Float16)p2; + pSrc[2 * i4 + 1] = (_Float16)p3 - (_Float16)p4; + + i1 += n1; + } while (i1 < fftLen); + + j++; + } while (j < n2); + + twidCoefModifier <<= 3; + } while (n2 > 7); +} + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix8_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix8_f32.c new file mode 100755 index 0000000..5920ccb --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_cfft_radix8_f32.c @@ -0,0 +1,294 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix8_f32.c + * Description: Radix-8 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + + +/* ---------------------------------------------------------------------- + * Internal helper function used by the FFTs + * -------------------------------------------------------------------- */ + +void arm_radix8_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier); + +/** + brief Core function for the floating-point CFFT butterfly process. + param[in,out] pSrc points to the in-place buffer of floating-point data type. + param[in] fftLen length of the FFT. + param[in] pCoef points to the twiddle coefficient buffer. + param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + return none +*/ + +ARM_DSP_ATTRIBUTE void arm_radix8_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + const float32_t * pCoef, + uint16_t twidCoefModifier) +{ + uint32_t ia1, ia2, ia3, ia4, ia5, ia6, ia7; + uint32_t i1, i2, i3, i4, i5, i6, i7, i8; + uint32_t id; + uint32_t n1, n2, j; + + float32_t r1, r2, r3, r4, r5, r6, r7, r8; + float32_t t1, t2; + float32_t s1, s2, s3, s4, s5, s6, s7, s8; + float32_t p1, p2, p3, p4; + float32_t co2, co3, co4, co5, co6, co7, co8; + float32_t si2, si3, si4, si5, si6, si7, si8; + const float32_t C81 = 0.70710678118f; + + n2 = fftLen; + + do + { + n1 = n2; + n2 = n2 >> 3; + i1 = 0; + + do + { + i2 = i1 + n2; + i3 = i2 + n2; + i4 = i3 + n2; + i5 = i4 + n2; + i6 = i5 + n2; + i7 = i6 + n2; + i8 = i7 + n2; + r1 = pSrc[2 * i1] + pSrc[2 * i5]; + r5 = pSrc[2 * i1] - pSrc[2 * i5]; + r2 = pSrc[2 * i2] + pSrc[2 * i6]; + r6 = pSrc[2 * i2] - pSrc[2 * i6]; + r3 = pSrc[2 * i3] + pSrc[2 * i7]; + r7 = pSrc[2 * i3] - pSrc[2 * i7]; + r4 = pSrc[2 * i4] + pSrc[2 * i8]; + r8 = pSrc[2 * i4] - pSrc[2 * i8]; + t1 = r1 - r3; + r1 = r1 + r3; + r3 = r2 - r4; + r2 = r2 + r4; + pSrc[2 * i1] = r1 + r2; + pSrc[2 * i5] = r1 - r2; + r1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1]; + s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1]; + r2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1]; + s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1]; + s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1]; + s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1]; + r4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1]; + s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1]; + t2 = r1 - s3; + r1 = r1 + s3; + s3 = r2 - r4; + r2 = r2 + r4; + pSrc[2 * i1 + 1] = r1 + r2; + pSrc[2 * i5 + 1] = r1 - r2; + pSrc[2 * i3] = t1 + s3; + pSrc[2 * i7] = t1 - s3; + pSrc[2 * i3 + 1] = t2 - r3; + pSrc[2 * i7 + 1] = t2 + r3; + r1 = (r6 - r8) * C81; + r6 = (r6 + r8) * C81; + r2 = (s6 - s8) * C81; + s6 = (s6 + s8) * C81; + t1 = r5 - r1; + r5 = r5 + r1; + r8 = r7 - r6; + r7 = r7 + r6; + t2 = s5 - r2; + s5 = s5 + r2; + s8 = s7 - s6; + s7 = s7 + s6; + pSrc[2 * i2] = r5 + s7; + pSrc[2 * i8] = r5 - s7; + pSrc[2 * i6] = t1 + s8; + pSrc[2 * i4] = t1 - s8; + pSrc[2 * i2 + 1] = s5 - r7; + pSrc[2 * i8 + 1] = s5 + r7; + pSrc[2 * i6 + 1] = t2 - r8; + pSrc[2 * i4 + 1] = t2 + r8; + + i1 += n1; + } while (i1 < fftLen); + + if (n2 < 8) + break; + + ia1 = 0; + j = 1; + + do + { + /* index calculation for the coefficients */ + id = ia1 + twidCoefModifier; + ia1 = id; + ia2 = ia1 + id; + ia3 = ia2 + id; + ia4 = ia3 + id; + ia5 = ia4 + id; + ia6 = ia5 + id; + ia7 = ia6 + id; + + co2 = pCoef[2 * ia1]; + co3 = pCoef[2 * ia2]; + co4 = pCoef[2 * ia3]; + co5 = pCoef[2 * ia4]; + co6 = pCoef[2 * ia5]; + co7 = pCoef[2 * ia6]; + co8 = pCoef[2 * ia7]; + si2 = pCoef[2 * ia1 + 1]; + si3 = pCoef[2 * ia2 + 1]; + si4 = pCoef[2 * ia3 + 1]; + si5 = pCoef[2 * ia4 + 1]; + si6 = pCoef[2 * ia5 + 1]; + si7 = pCoef[2 * ia6 + 1]; + si8 = pCoef[2 * ia7 + 1]; + + i1 = j; + + do + { + /* index calculation for the input */ + i2 = i1 + n2; + i3 = i2 + n2; + i4 = i3 + n2; + i5 = i4 + n2; + i6 = i5 + n2; + i7 = i6 + n2; + i8 = i7 + n2; + r1 = pSrc[2 * i1] + pSrc[2 * i5]; + r5 = pSrc[2 * i1] - pSrc[2 * i5]; + r2 = pSrc[2 * i2] + pSrc[2 * i6]; + r6 = pSrc[2 * i2] - pSrc[2 * i6]; + r3 = pSrc[2 * i3] + pSrc[2 * i7]; + r7 = pSrc[2 * i3] - pSrc[2 * i7]; + r4 = pSrc[2 * i4] + pSrc[2 * i8]; + r8 = pSrc[2 * i4] - pSrc[2 * i8]; + t1 = r1 - r3; + r1 = r1 + r3; + r3 = r2 - r4; + r2 = r2 + r4; + pSrc[2 * i1] = r1 + r2; + r2 = r1 - r2; + s1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1]; + s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1]; + s2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1]; + s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1]; + s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1]; + s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1]; + s4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1]; + s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1]; + t2 = s1 - s3; + s1 = s1 + s3; + s3 = s2 - s4; + s2 = s2 + s4; + r1 = t1 + s3; + t1 = t1 - s3; + pSrc[2 * i1 + 1] = s1 + s2; + s2 = s1 - s2; + s1 = t2 - r3; + t2 = t2 + r3; + p1 = co5 * r2; + p2 = si5 * s2; + p3 = co5 * s2; + p4 = si5 * r2; + pSrc[2 * i5] = p1 + p2; + pSrc[2 * i5 + 1] = p3 - p4; + p1 = co3 * r1; + p2 = si3 * s1; + p3 = co3 * s1; + p4 = si3 * r1; + pSrc[2 * i3] = p1 + p2; + pSrc[2 * i3 + 1] = p3 - p4; + p1 = co7 * t1; + p2 = si7 * t2; + p3 = co7 * t2; + p4 = si7 * t1; + pSrc[2 * i7] = p1 + p2; + pSrc[2 * i7 + 1] = p3 - p4; + r1 = (r6 - r8) * C81; + r6 = (r6 + r8) * C81; + s1 = (s6 - s8) * C81; + s6 = (s6 + s8) * C81; + t1 = r5 - r1; + r5 = r5 + r1; + r8 = r7 - r6; + r7 = r7 + r6; + t2 = s5 - s1; + s5 = s5 + s1; + s8 = s7 - s6; + s7 = s7 + s6; + r1 = r5 + s7; + r5 = r5 - s7; + r6 = t1 + s8; + t1 = t1 - s8; + s1 = s5 - r7; + s5 = s5 + r7; + s6 = t2 - r8; + t2 = t2 + r8; + p1 = co2 * r1; + p2 = si2 * s1; + p3 = co2 * s1; + p4 = si2 * r1; + pSrc[2 * i2] = p1 + p2; + pSrc[2 * i2 + 1] = p3 - p4; + p1 = co8 * r5; + p2 = si8 * s5; + p3 = co8 * s5; + p4 = si8 * r5; + pSrc[2 * i8] = p1 + p2; + pSrc[2 * i8 + 1] = p3 - p4; + p1 = co6 * r6; + p2 = si6 * s6; + p3 = co6 * s6; + p4 = si6 * r6; + pSrc[2 * i6] = p1 + p2; + pSrc[2 * i6 + 1] = p3 - p4; + p1 = co4 * t1; + p2 = si4 * t2; + p3 = co4 * t2; + p4 = si4 * t1; + pSrc[2 * i4] = p1 + p2; + pSrc[2 * i4 + 1] = p3 - p4; + + i1 += n1; + } while (i1 < fftLen); + + j++; + } while (j < n2); + + twidCoefModifier <<= 3; + } while (n2 > 7); +} diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_f16.c new file mode 100755 index 0000000..2fd668f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_f16.c @@ -0,0 +1,181 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_f16.c + * Description: MFCC function for the f16 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + +#include "dsp/transform_functions_f16.h" +#include "dsp/statistics_functions_f16.h" +#include "dsp/basic_math_functions_f16.h" +#include "dsp/complex_math_functions_f16.h" +#include "dsp/fast_math_functions_f16.h" +#include "dsp/matrix_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + @ingroup groupTransforms + */ + + +/** + @defgroup MFCC MFCC + + MFCC Transform + + There are separate functions for floating-point, Q15, and Q31 data types. + */ + + + +/** + @addtogroup MFCCF16 + @{ + */ + +/** + @brief MFCC F16 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples + @param[out] pDst points to the output MFCC values + @param[inout] pTmp points to a temporary buffer of complex + + @par Description + The number of input samples if the FFT length used + when initializing the instance data structure. + + The source buffer is modified by this function. + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ +#if defined(ARM_MATH_NEON_FLOAT16) +ARM_DSP_ATTRIBUTE void arm_mfcc_f16( + const arm_mfcc_instance_f16 * S, + float16_t *pSrc, + float16_t *pDst, + float16_t *pTmp, + float16_t *pTmp2 + ) +#else +ARM_DSP_ATTRIBUTE void arm_mfcc_f16( + const arm_mfcc_instance_f16 * S, + float16_t *pSrc, + float16_t *pDst, + float16_t *pTmp + ) +#endif +{ + float16_t maxValue; + uint32_t index; + uint32_t i; + float16_t result; + const float16_t *coefs=S->filterCoefs; + arm_matrix_instance_f16 pDctMat; + + /* Normalize */ + arm_absmax_f16(pSrc,S->fftLen,&maxValue,&index); + + if ((_Float16)maxValue != 0.0f16) + { + arm_scale_f16(pSrc,1.0f16/(_Float16)maxValue,pSrc,S->fftLen); + } + + /* Multiply by window */ + arm_mult_f16(pSrc,S->windowCoefs,pSrc,S->fftLen); + + /* Compute spectrum magnitude + */ +#if defined(ARM_MATH_NEON_FLOAT16) + arm_rfft_fast_f16(&(S->rfft),pSrc,pTmp,pTmp2,0); + pTmp[1]=0.0f16; +#else +#if defined(ARM_MFCC_USE_CFFT) + /* some HW accelerator for CMSIS-DSP used in some boards + are only providing acceleration for CFFT. + With ARM_MFCC_USE_CFFT enabled, CFFT is used and the MFCC + will be accelerated on those boards. + + The default is to use RFFT + */ + /* Convert from real to complex */ + for(i=0; i < S->fftLen ; i++) + { + pTmp[2*i] = pSrc[i]; + pTmp[2*i+1] = 0.0f16; + } + arm_cfft_f16(&(S->cfft),pTmp,0,1); +#else + /* Default RFFT based implementation */ + arm_rfft_fast_f16(&(S->rfft),pSrc,pTmp,0); + /* Unpack real values */ + pTmp[S->fftLen]=pTmp[1]; + pTmp[S->fftLen+1]=0.0f16; + pTmp[1]=0.0f; +#endif +#endif /* neon */ + arm_cmplx_mag_f16(pTmp,pSrc,S->fftLen); + if ((_Float16)maxValue != 0.0f16) + { + arm_scale_f16(pSrc,maxValue,pSrc,S->fftLen); + } + + /* Apply MEL filters */ + for(i=0; inbMelFilters; i++) + { + arm_dot_prod_f16(pSrc+S->filterPos[i], + coefs, + S->filterLengths[i], + &result); + + coefs += S->filterLengths[i]; + + pTmp[i] = result; + + } + + /* Compute the log */ + arm_offset_f16(pTmp,1.0e-4f16,pTmp,S->nbMelFilters); + arm_vlog_f16(pTmp,pTmp,S->nbMelFilters); + + /* Multiply with the DCT matrix */ + + pDctMat.numRows=S->nbDctOutputs; + pDctMat.numCols=S->nbMelFilters; + pDctMat.pData=(float16_t*)S->dctCoefs; + + arm_mat_vec_mult_f16(&pDctMat, pTmp, pDst); + + +} +#endif /* defined(ARM_FLOAT16_SUPPORTED) */ +/** + @} end of MFCC group +*/ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_f32.c new file mode 100755 index 0000000..6c121a7 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_f32.c @@ -0,0 +1,181 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_f32.c + * Description: MFCC function for the f32 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + + +#include "dsp/transform_functions.h" +#include "dsp/statistics_functions.h" +#include "dsp/basic_math_functions.h" +#include "dsp/complex_math_functions.h" +#include "dsp/fast_math_functions.h" +#include "dsp/matrix_functions.h" + +/** + @ingroup MFCC + */ + + + +/** + @addtogroup MFCCF32 + @{ + */ + +/** + @brief MFCC F32 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples + @param[out] pDst points to the output MFCC values + @param[inout] pTmp points to a temporary buffer of complex + + @par Description + The number of input samples if the FFT length used + when initializing the instance data structure. + + The source buffer is modified by this function. + + @par Neon implementation + The Neon implementation has a different API. + There is an additional temporary buffer pTmp2. + The source buffer is modified. + @code + void arm_mfcc_f32( + const arm_mfcc_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + float32_t *pTmp, + float32_t *pTmp2 + ); + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ +#if defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_mfcc_f32( + const arm_mfcc_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + float32_t *pTmp, + float32_t *pTmp2 + ) +#else +ARM_DSP_ATTRIBUTE void arm_mfcc_f32( + const arm_mfcc_instance_f32 * S, + float32_t *pSrc, + float32_t *pDst, + float32_t *pTmp + ) +#endif +{ + float32_t maxValue; + uint32_t index; + uint32_t i; + float32_t result; + const float32_t *coefs=S->filterCoefs; + arm_matrix_instance_f32 pDctMat; + + /* Normalize */ + arm_absmax_f32(pSrc,S->fftLen,&maxValue,&index); + + if (maxValue != 0.0f) + { + arm_scale_f32(pSrc,1.0f/maxValue,pSrc,S->fftLen); + } + + /* Multiply by window */ + arm_mult_f32(pSrc,S->windowCoefs,pSrc,S->fftLen); + + /* Compute spectrum magnitude + */ +#if defined(ARM_MATH_NEON) + arm_rfft_fast_f32(&(S->rfft),pSrc,pTmp,pTmp2,0); + pTmp[1]=0.0f; +#else +#if defined(ARM_MFCC_USE_CFFT) + /* some HW accelerator for CMSIS-DSP used in some boards + are only providing acceleration for CFFT. + With ARM_MFCC_USE_CFFT enabled, CFFT is used and the MFCC + will be accelerated on those boards. + + The default is to use RFFT + */ + /* Convert from real to complex */ + for(i=0; i < S->fftLen ; i++) + { + pTmp[2*i] = pSrc[i]; + pTmp[2*i+1] = 0.0f; + } + arm_cfft_f32(&(S->cfft),pTmp,0,1); +#else + /* Default RFFT based implementation */ + arm_rfft_fast_f32(&(S->rfft),pSrc,pTmp,0); + pTmp[1]=0.0f; +#endif /* ARM_MFCC_USE_CFFT */ +#endif /* ARM_MATH_NEON */ + arm_cmplx_mag_f32(pTmp,pSrc,S->fftLen); + if (maxValue != 0.0f) + { + arm_scale_f32(pSrc,maxValue,pSrc,S->fftLen); + } + + /* Apply MEL filters */ + for(i=0; inbMelFilters; i++) + { + arm_dot_prod_f32(pSrc+S->filterPos[i], + coefs, + S->filterLengths[i], + &result); + + coefs += S->filterLengths[i]; + + pTmp[i] = result; + + } + + /* Compute the log */ + arm_offset_f32(pTmp,1.0e-6f,pTmp,S->nbMelFilters); + arm_vlog_f32(pTmp,pTmp,S->nbMelFilters); + + /* Multiply with the DCT matrix */ + + pDctMat.numRows=S->nbDctOutputs; + pDctMat.numCols=S->nbMelFilters; + pDctMat.pData=(float32_t*)S->dctCoefs; + + arm_mat_vec_mult_f32(&pDctMat, pTmp, pDst); + + +} + +/** + @} end of MFCCF32 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_f16.c new file mode 100755 index 0000000..5f4b91c --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_f16.c @@ -0,0 +1,419 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_init_f16.c + * Description: MFCC initialization function for the f16 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + +/** + * @defgroup MFCCF16 MFCC F16 + */ + + +/** + @ingroup MFCC + */ + + +/** + @addtogroup MFCCF16 + @{ + */ + + +#include "dsp/transform_functions_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + @brief Generic initialization of the MFCC F16 instance structure + @param[out] S points to the mfcc instance structure + @param[in] fftLen fft length + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the MFCC sizes + that you need at build time, then it is better to use the initialization + functions defined for each MFCC size. + + */ + +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_f16( + arm_mfcc_instance_f16 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float16_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float16_t *filterCoefs, + const float16_t *windowCoefs + ) +{ + arm_status status; + + S->fftLen=fftLen; + S->nbMelFilters=nbMelFilters; + S->nbDctOutputs=nbDctOutputs; + S->dctCoefs=dctCoefs; + S->filterPos=filterPos; + S->filterLengths=filterLengths; + S->filterCoefs=filterCoefs; + S->windowCoefs=windowCoefs; + + #if defined(ARM_MFCC_USE_CFFT) + status=arm_cfft_init_f16(&(S->cfft),fftLen); + #else + status=arm_rfft_fast_init_f16(&(S->rfft),fftLen); + #endif + + return(status); +} + +#if defined(ARM_MFCC_USE_CFFT) +#define MFCC_INIT_F16(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_f16( \ + arm_mfcc_instance_f16 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const float16_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const float16_t *filterCoefs, \ + const float16_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + status=arm_cfft_init_##LEN##_f16(&(S->cfft));\ + \ + return(status); \ +} +#else +#define MFCC_INIT_F16(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_f16( \ + arm_mfcc_instance_f16 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const float16_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const float16_t *filterCoefs, \ + const float16_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + status=arm_rfft_fast_init_##LEN##_f16(&(S->rfft));\ + \ + return(status); \ +} +#endif + +/** + @brief Initialization of the MFCC F16 instance structure for 32 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(32) + +/** + @brief Initialization of the MFCC F16 instance structure for 64 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(64) + +/** + @brief Initialization of the MFCC F16 instance structure for 128 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(128) + +/** + @brief Initialization of the MFCC F16 instance structure for 256 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(256) + +/** + @brief Initialization of the MFCC F16 instance structure for 512 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(512) + +/** + @brief Initialization of the MFCC F16 instance structure for 1024 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(1024) + +/** + @brief Initialization of the MFCC F16 instance structure for 2048 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(2048) + +/** + @brief Initialization of the MFCC F16 instance structure for 4096 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script that can be used + to generate the filter, dct and window arrays. +*/ +MFCC_INIT_F16(4096) + +#endif /* defined(ARM_FLOAT16_SUPPORTED) */ +/** + @} end of MFCCF16 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_f32.c new file mode 100755 index 0000000..001e89f --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_f32.c @@ -0,0 +1,418 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_init_f32.c + * Description: MFCC initialization function for the f32 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + +/** + * @defgroup MFCCF32 MFCC F32 + */ + + +/** + @ingroup MFCC + */ + + +/** + @addtogroup MFCCF32 + @{ + */ + + +#include "dsp/transform_functions.h" + + + +/** + @brief Generic initialization of the MFCC F32 instance structure + @param[out] S points to the mfcc instance structure + @param[in] fftLen fft length + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the MFCC sizes + that you need at build time, then it is better to use the initialization + functions defined for each MFCC size. + + */ + +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_f32( + arm_mfcc_instance_f32 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const float32_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const float32_t *filterCoefs, + const float32_t *windowCoefs + ) +{ + arm_status status; + + S->fftLen=fftLen; + S->nbMelFilters=nbMelFilters; + S->nbDctOutputs=nbDctOutputs; + S->dctCoefs=dctCoefs; + S->filterPos=filterPos; + S->filterLengths=filterLengths; + S->filterCoefs=filterCoefs; + S->windowCoefs=windowCoefs; + + #if defined(ARM_MFCC_USE_CFFT) + status=arm_cfft_init_f32(&(S->cfft),fftLen); + #else + status=arm_rfft_fast_init_f32(&(S->rfft),fftLen); + #endif + + return(status); +} + +#if defined(ARM_MFCC_USE_CFFT) +#define MFCC_INIT_F32(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_f32( \ + arm_mfcc_instance_f32 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const float32_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const float32_t *filterCoefs, \ + const float32_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + status=arm_cfft_init_##LEN##_f32(&(S->cfft));\ + \ + return(status); \ +} +#else +#define MFCC_INIT_F32(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_f32( \ + arm_mfcc_instance_f32 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const float32_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const float32_t *filterCoefs, \ + const float32_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + status=arm_rfft_fast_init_##LEN##_f32(&(S->rfft));\ + \ + return(status); \ +} +#endif + +/** + @brief Initialization of the MFCC F32 instance structure for 32 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(32) + +/** + @brief Initialization of the MFCC F32 instance structure for 64 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(64) + +/** + @brief Initialization of the MFCC F32 instance structure for 128 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(128) + +/** + @brief Initialization of the MFCC F32 instance structure for 256 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(256) + +/** + @brief Initialization of the MFCC F32 instance structure for 512 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(512) + +/** + @brief Initialization of the MFCC F32 instance structure for 1024 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(1024) + +/** + @brief Initialization of the MFCC F32 instance structure for 2048 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(2048) + +/** + @brief Initialization of the MFCC F32 instance structure for 4096 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_F32(4096) + +/** + @} end of MFCCF32 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_q15.c new file mode 100755 index 0000000..e464b6e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_q15.c @@ -0,0 +1,432 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_init_q15.c + * Description: MFCC initialization function for the q15 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#if defined(ARM_MATH_NEON) +#define RFFT_INIT(L) \ + status=arm_rfft_init_q15(&(S->rfft),L); +#define RFFT_INIT_WITH_LEN(L) \ + status=arm_rfft_init_##L##_q15(&(S->rfft)); +#else +#define RFFT_INIT(L) \ + status=arm_rfft_init_q15(&(S->rfft),L,0,1); +#define RFFT_INIT_WITH_LEN(L) \ + status=arm_rfft_init_##L##_q15(&(S->rfft),0,1); +#endif + + + +/** + * @defgroup MFCCQ15 MFCC Q15 + */ + + +/** + @ingroup MFCC + */ + +/** + @addtogroup MFCCQ15 + @{ + */ + + +#include "dsp/transform_functions.h" + + + +/** + @brief Generic initialization of the MFCC Q15 instance structure + @param[out] S points to the mfcc instance structure + @param[in] fftLen fft length + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the MFCC sizes + that you need at build time, then it is better to use the initialization + functions defined for each MFCC size. + + + */ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_q15( + arm_mfcc_instance_q15 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q15_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q15_t *filterCoefs, + const q15_t *windowCoefs + ) +{ + arm_status status; + + S->fftLen=fftLen; + S->nbMelFilters=nbMelFilters; + S->nbDctOutputs=nbDctOutputs; + S->dctCoefs=dctCoefs; + S->filterPos=filterPos; + S->filterLengths=filterLengths; + S->filterCoefs=filterCoefs; + S->windowCoefs=windowCoefs; + + #if defined(ARM_MFCC_USE_CFFT) + status=arm_cfft_init_q15(&(S->cfft),fftLen); + #else + RFFT_INIT(fftLen); + #endif + + return(status); +} + +#if defined(ARM_MFCC_USE_CFFT) +#define MFCC_INIT_Q15(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_q15( \ + arm_mfcc_instance_q15 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const q15_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const q15_t *filterCoefs, \ + const q15_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + status=arm_cfft_init_##LEN##_q15(&(S->cfft));\ + \ + return(status); \ +} +#else +#define MFCC_INIT_Q15(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_q15( \ + arm_mfcc_instance_q15 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const q15_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const q15_t *filterCoefs, \ + const q15_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + RFFT_INIT_WITH_LEN(LEN); \ + \ + return(status); \ +} +#endif + +/** + @brief Initialization of the MFCC Q15 instance structure for 32 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(32) + +/** + @brief Initialization of the MFCC Q15 instance structure for 64 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(64) + +/** + @brief Initialization of the MFCC Q15 instance structure for 128 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(128) + +/** + @brief Initialization of the MFCC Q15 instance structure for 256 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(256) + +/** + @brief Initialization of the MFCC Q15 instance structure for 512 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(512) + +/** + @brief Initialization of the MFCC Q15 instance structure for 1024 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(1024) + +/** + @brief Initialization of the MFCC Q15 instance structure for 2048 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(2048) + +/** + @brief Initialization of the MFCC Q15 instance structure for 4096 samples MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q15(4096) + +#undef RFFT_INIT +#undef RFFT_INIT_WITH_LEN +/** + @} end of MFCCQ15 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_q31.c new file mode 100755 index 0000000..82d0156 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_init_q31.c @@ -0,0 +1,435 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_init_q31.c + * Description: MFCC initialization function for the q31 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#if defined(ARM_MATH_NEON) +#define RFFT_INIT(L) \ + status=arm_rfft_init_q31(&(S->rfft),L); +#define RFFT_INIT_WITH_LEN(L) \ + status=arm_rfft_init_##L##_q31(&(S->rfft)); +#else +#define RFFT_INIT(L) \ + status=arm_rfft_init_q31(&(S->rfft),L,0,1); +#define RFFT_INIT_WITH_LEN(L) \ + status=arm_rfft_init_##L##_q31(&(S->rfft),0,1); +#endif + + + + +/** + * @defgroup MFCCQ31 MFCC Q31 + */ + + +/** + @ingroup MFCC + */ + + +/** + @addtogroup MFCCQ31 + @{ + */ + + +#include "dsp/transform_functions.h" + + + +/** + @brief Generic initialization of the MFCC Q31 instance structure + @param[out] S points to the mfcc instance structure + @param[in] fftLen fft length + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the MFCC sizes + that you need at build time, then it is better to use the initialization + functions defined for each MFCC size. + + + */ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_q31( + arm_mfcc_instance_q31 * S, + uint32_t fftLen, + uint32_t nbMelFilters, + uint32_t nbDctOutputs, + const q31_t *dctCoefs, + const uint32_t *filterPos, + const uint32_t *filterLengths, + const q31_t *filterCoefs, + const q31_t *windowCoefs + ) +{ + arm_status status; + + S->fftLen=fftLen; + S->nbMelFilters=nbMelFilters; + S->nbDctOutputs=nbDctOutputs; + S->dctCoefs=dctCoefs; + S->filterPos=filterPos; + S->filterLengths=filterLengths; + S->filterCoefs=filterCoefs; + S->windowCoefs=windowCoefs; + + + #if defined(ARM_MFCC_USE_CFFT) + status=arm_cfft_init_q31(&(S->cfft),fftLen); + #else + RFFT_INIT(fftLen); + #endif + + return(status); +} + +#if defined(ARM_MFCC_USE_CFFT) +#define MFCC_INIT_Q31(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_q31( \ + arm_mfcc_instance_q31 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const q31_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const q31_t *filterCoefs, \ + const q31_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + status=arm_cfft_init_##LEN##_q31(&(S->cfft));\ + \ + return(status); \ +} +#else +#define MFCC_INIT_Q31(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_init_##LEN##_q31( \ + arm_mfcc_instance_q31 * S, \ + uint32_t nbMelFilters, \ + uint32_t nbDctOutputs, \ + const q31_t *dctCoefs, \ + const uint32_t *filterPos, \ + const uint32_t *filterLengths, \ + const q31_t *filterCoefs, \ + const q31_t *windowCoefs \ + ) \ +{ \ + arm_status status; \ + \ + S->fftLen=LEN; \ + S->nbMelFilters=nbMelFilters; \ + S->nbDctOutputs=nbDctOutputs; \ + S->dctCoefs=dctCoefs; \ + S->filterPos=filterPos; \ + S->filterLengths=filterLengths; \ + S->filterCoefs=filterCoefs; \ + S->windowCoefs=windowCoefs; \ + \ + RFFT_INIT_WITH_LEN(LEN); \ + \ + return(status); \ +} +#endif + +/** + @brief Initialization of the MFCC Q31 instance structure for 32 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(32) + +/** + @brief Initialization of the MFCC Q31 instance structure for 64 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(64) + +/** + @brief Initialization of the MFCC Q31 instance structure for 128 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(128) + +/** + @brief Initialization of the MFCC Q31 instance structure for 256 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(256) + +/** + @brief Initialization of the MFCC Q31 instance structure for 512 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(512) + +/** + @brief Initialization of the MFCC Q31 instance structure for 1024 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(1024) + +/** + @brief Initialization of the MFCC Q31 instance structure for 2048 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(2048) + +/** + @brief Initialization of the MFCC Q31 instance structure for 4096 sample MFCC + @param[out] S points to the mfcc instance structure + @param[in] nbMelFilters number of Mel filters + @param[in] nbDctOutputs number of Dct outputs + @param[in] dctCoefs points to an array of DCT coefficients + @param[in] filterPos points of the array of filter positions + @param[in] filterLengths points to the array of filter lengths + @param[in] filterCoefs points to the array of filter coefficients + @param[in] windowCoefs points to the array of window coefficients + + @return error status + + @par Description + The matrix of Mel filter coefficients is sparse. + Most of the coefficients are zero. + To avoid multiplying the spectrogram by those zeros, the + filter is applied only to a given position in the spectrogram + and on a given number of FFT bins (the filter length). + It is the reason for the arrays filterPos and filterLengths. + + window coefficients can describe (for instance) a Hamming window. + The array has the same size as the FFT length. + + The folder Scripts is containing a Python script which can be used + to generate the filter, dct and window arrays. + */ +MFCC_INIT_Q31(4096) + +#undef RFFT_INIT +#undef RFFT_INIT_WITH_LEN +/** + @} end of MFCCQ31 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_q15.c new file mode 100755 index 0000000..4037339 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_q15.c @@ -0,0 +1,234 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_q15.c + * Description: MFCC function for the q15 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + + +#include "dsp/transform_functions.h" +#include "dsp/statistics_functions.h" +#include "dsp/basic_math_functions.h" +#include "dsp/complex_math_functions.h" +#include "dsp/fast_math_functions.h" +#include "dsp/matrix_functions.h" + +/* Constants for Q15 implementation */ +#define LOG2TOLOG_Q15 0x02C5C860 +#define MICRO_Q15 0x00000219 +#define SHIFT_MELFILTER_SATURATION_Q15 10 +/** + @ingroup MFCC + */ + + + +/** + @addtogroup MFCCQ15 + @{ + */ + +/** + @brief MFCC Q15 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples in Q15 + @param[out] pDst points to the output MFCC values in q8.7 format + @param[inout] pTmp points to a temporary buffer of complex + @return error status + + @par Description + The number of input samples is the FFT length used + when initializing the instance data structure. + + The source buffer is modified by this function. + + The function may saturate. If the FFT length is too + big and the number of MEL filters too small then the fixed + point computations may saturate. + + @par Neon implementation + There is an additional temporary buffer used for the RFFT. + + + @code + arm_status arm_mfcc_q15( + const arm_mfcc_instance_q15 * S, + q15_t *pSrc, + q15_t *pDst, + q31_t *pTmp, + q15_t *pTmp_rfft + ) + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ +#if defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_q15( + const arm_mfcc_instance_q15 * S, + q15_t *pSrc, + q15_t *pDst, + q31_t *pTmp, + q15_t *pTmp_rfft + ) +#else +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_q15( + const arm_mfcc_instance_q15 * S, + q15_t *pSrc, + q15_t *pDst, + q31_t *pTmp + ) +#endif +{ + q15_t m; + uint32_t index; + uint32_t fftShift=0; + q31_t logExponent; + q63_t result; + arm_matrix_instance_q15 pDctMat; + uint32_t i; + uint32_t coefsPos; + uint32_t filterLimit; + q15_t *pTmp2=(q15_t*)pTmp; + + arm_status status = ARM_MATH_SUCCESS; + + // q15 + arm_absmax_q15(pSrc,S->fftLen,&m,&index); + + if ((m != 0) && (m != 0x7FFF)) + { + q15_t quotient; + int16_t shift; + + status = arm_divide_q15(0x7FFF,m,"ient,&shift); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + + arm_scale_q15(pSrc,quotient,shift,pSrc,S->fftLen); + } + + + // q15 + arm_mult_q15(pSrc,S->windowCoefs, pSrc, S->fftLen); + + + /* Compute spectrum magnitude + */ + fftShift = 31 - __CLZ(S->fftLen); +#if defined(ARM_MATH_NEON) + /* Default RFFT based implementation */ + arm_rfft_q15(&(S->rfft),pSrc,pTmp2,pTmp_rfft,0); +#else +#if defined(ARM_MFCC_USE_CFFT) + /* some HW accelerator for CMSIS-DSP used in some boards + are only providing acceleration for CFFT. + With ARM_MFCC_USE_CFFT enabled, CFFT is used and the MFCC + will be accelerated on those boards. + + The default is to use RFFT + */ + /* Convert from real to complex */ + for(i=0; i < S->fftLen ; i++) + { + pTmp2[2*i] = pSrc[i]; + pTmp2[2*i+1] = 0; + } + arm_cfft_q15(&(S->cfft),pTmp2,0,1); +#else + /* Default RFFT based implementation */ + arm_rfft_q15(&(S->rfft),pSrc,pTmp2); +#endif +#endif + filterLimit = 1 + (S->fftLen >> 1); + + + // q15 - fftShift + arm_cmplx_mag_q15(pTmp2,pSrc,filterLimit); + // q14 - fftShift + + /* Apply MEL filters */ + coefsPos = 0; + for(i=0; inbMelFilters; i++) + { + arm_dot_prod_q15(pSrc+S->filterPos[i], + &(S->filterCoefs[coefsPos]), + S->filterLengths[i], + &result); + + coefsPos += S->filterLengths[i]; + + // q34.29 - fftShift + result += MICRO_Q15; + result >>= SHIFT_MELFILTER_SATURATION_Q15; + // q34.29 - fftShift - satShift + pTmp[i] = __SSAT(result,31) ; + + } + + if ((m != 0) && (m != 0x7FFF)) + { + arm_scale_q31(pTmp,m<<16,0,pTmp,S->nbMelFilters); + } + + // q34.29 - fftShift - satShift + /* Compute the log */ + arm_vlog_q31(pTmp,pTmp,S->nbMelFilters); + + + // q5.26 + + logExponent = fftShift + 2 + SHIFT_MELFILTER_SATURATION_Q15; + logExponent = logExponent * LOG2TOLOG_Q15; + + + // q8.26 + arm_offset_q31(pTmp,logExponent,pTmp,S->nbMelFilters); + arm_shift_q31(pTmp,-19,pTmp,S->nbMelFilters); + for(i=0; inbMelFilters; i++) + { + pSrc[i] = __SSAT((q15_t)pTmp[i],16); + } + + // q8.7 + + pDctMat.numRows=S->nbDctOutputs; + pDctMat.numCols=S->nbMelFilters; + pDctMat.pData=(q15_t*)S->dctCoefs; + + arm_mat_vec_mult_q15(&pDctMat, pSrc, pDst); + + return(status); +} + +/** + @} end of MFCCQ15 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_q31.c new file mode 100755 index 0000000..043d408 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_mfcc_q31.c @@ -0,0 +1,233 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_mfcc_q31.c + * Description: MFCC function for the q31 version + * + * $Date: 07 September 2021 + * $Revision: V1.10.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + + + +#include "dsp/transform_functions.h" +#include "dsp/statistics_functions.h" +#include "dsp/basic_math_functions.h" +#include "dsp/complex_math_functions.h" +#include "dsp/fast_math_functions.h" +#include "dsp/matrix_functions.h" + +/* Constants for Q31 implementation */ +#define LOG2TOLOG_Q31 0x02C5C860 +#define MICRO_Q31 0x08637BD0 +#define SHIFT_MELFILTER_SATURATION_Q31 10 +/** + @ingroup MFCC + */ + + + +/** + @addtogroup MFCCQ31 + @{ + */ + +/** + @brief MFCC Q31 + @param[in] S points to the mfcc instance structure + @param[in] pSrc points to the input samples in Q31 + @param[out] pDst points to the output MFCC values in q8.23 format + @param[inout] pTmp points to a temporary buffer of complex + @return error status + + @par Description + The number of input samples is the FFT length used + when initializing the instance data structure. + + The source buffer is modified by this function. + + The function may saturate. If the FFT length is too + big and the number of MEL filters too small then the fixed + point computations may saturate. + + @par Neon implementation + There is an additional temporary buffer used for the RFFT. + + + @code + arm_status arm_mfcc_q31( + const arm_mfcc_instance_q31 * S, + q31_t *pSrc, + q31_t *pDst, + q31_t *pTmp, + q31_t *pTmp_rfft + ) + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ +#if defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_q31( + const arm_mfcc_instance_q31 * S, + q31_t *pSrc, + q31_t *pDst, + q31_t *pTmp, + q31_t *pTmp_rfft + ) +#else +ARM_DSP_ATTRIBUTE arm_status arm_mfcc_q31( + const arm_mfcc_instance_q31 * S, + q31_t *pSrc, + q31_t *pDst, + q31_t *pTmp + ) +#endif +{ + q31_t m; + uint32_t index; + uint32_t fftShift=0; + q31_t logExponent; + q63_t result; + arm_matrix_instance_q31 pDctMat; + uint32_t i; + uint32_t coefsPos; + uint32_t filterLimit; + q31_t *pTmp2=(q31_t*)pTmp; + + arm_status status = ARM_MATH_SUCCESS; + + // q31 + arm_absmax_q31(pSrc,S->fftLen,&m,&index); + + if ((m != 0) && (m != 0x7FFFFFFF)) + { + q31_t quotient; + int16_t shift; + + status = arm_divide_q31(0x7FFFFFFF,m,"ient,&shift); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + + arm_scale_q31(pSrc,quotient,shift,pSrc,S->fftLen); + } + + + // q31 + arm_mult_q31(pSrc,S->windowCoefs, pSrc, S->fftLen); + + + /* Compute spectrum magnitude + */ + fftShift = 31 - __CLZ(S->fftLen); +#if defined(ARM_MATH_NEON) + /* Default RFFT based implementation */ + arm_rfft_q31(&(S->rfft),pSrc,pTmp2,pTmp_rfft,0); +#else +#if defined(ARM_MFCC_USE_CFFT) + /* some HW accelerator for CMSIS-DSP used in some boards + are only providing acceleration for CFFT. + With ARM_MFCC_USE_CFFT enabled, CFFT is used and the MFCC + will be accelerated on those boards. + + The default is to use RFFT + */ + /* Convert from real to complex */ + for(i=0; i < S->fftLen ; i++) + { + pTmp2[2*i] = pSrc[i]; + pTmp2[2*i+1] = 0; + } + arm_cfft_q31(&(S->cfft),pTmp2,0,1); +#else + /* Default RFFT based implementation */ + arm_rfft_q31(&(S->rfft),pSrc,pTmp2); +#endif +#endif + filterLimit = 1 + (S->fftLen >> 1); + + + // q31 - fftShift + arm_cmplx_mag_q31(pTmp2,pSrc,filterLimit); + // q30 - fftShift + + + /* Apply MEL filters */ + coefsPos = 0; + for(i=0; inbMelFilters; i++) + { + arm_dot_prod_q31(pSrc+S->filterPos[i], + &(S->filterCoefs[coefsPos]), + S->filterLengths[i], + &result); + + + coefsPos += S->filterLengths[i]; + + // q16.48 - fftShift + result += MICRO_Q31; + result >>= (SHIFT_MELFILTER_SATURATION_Q31 + 18); + // q16.29 - fftShift - satShift + pTmp[i] = __SSAT(result,31) ; + + } + + if ((m != 0) && (m != 0x7FFFFFFF)) + { + arm_scale_q31(pTmp,m,0,pTmp,S->nbMelFilters); + } + + // q16.29 - fftShift - satShift + /* Compute the log */ + arm_vlog_q31(pTmp,pTmp,S->nbMelFilters); + + + // q5.26 + + logExponent = fftShift + 2 + SHIFT_MELFILTER_SATURATION_Q31; + logExponent = logExponent * LOG2TOLOG_Q31; + + + // q5.26 + arm_offset_q31(pTmp,logExponent,pTmp,S->nbMelFilters); + arm_shift_q31(pTmp,-3,pTmp,S->nbMelFilters); + + + // q8.23 + + pDctMat.numRows=S->nbDctOutputs; + pDctMat.numCols=S->nbMelFilters; + pDctMat.pData=(q31_t*)S->dctCoefs; + + arm_mat_vec_mult_q31(&pDctMat, pTmp, pDst); + + return(status); +} + +/** + @} end of MFCCQ31 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f16.c new file mode 100755 index 0000000..f39f844 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f16.c @@ -0,0 +1,556 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_fast_f16.c + * Description: RFFT & RIFFT Floating point process function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" +#include "arm_common_tables_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + + +#if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE) + +static void stage_rfft_f16( + const arm_rfft_fast_instance_f16 * S, + const float16_t * p, + float16_t * pOut) +{ + int32_t k; /* Loop Counter */ + float16_t twR, twI; /* RFFT Twiddle coefficients */ + const float16_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float16_t *pA = p; /* increasing pointer */ + const float16_t *pB = p; /* decreasing pointer */ + float16_t xAR, xAI, xBR, xBI; /* temporary variables */ + float16_t t1a, t1b; /* temporary variables */ + float16_t p0, p1, p2, p3; /* temporary variables */ + + float16x8x2_t tw,xA,xB; + float16x8x2_t tmp1, tmp2, res; + + uint16x8_t vecStridesBkwd; + + vecStridesBkwd = vddupq_u16((uint16_t)14, 2); + + + int blockCnt; + + + k = (S->Sint).fftLen - 1; + + /* Pack first and last sample of the frequency domain together */ + + xBR = pB[0]; + xBI = pB[1]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++ ; + twI = *pCoeff++ ; + + // U1 = XA(1) + XB(1); % It is real + t1a = (_Float16)xBR + (_Float16)xAR ; + + // U2 = XB(1) - XA(1); % It is imaginary + t1b = (_Float16)xBI + (_Float16)xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + *pOut++ = 0.5f16 * ( (_Float16)t1a + (_Float16)t1b ); + *pOut++ = 0.5f16 * ( (_Float16)t1a - (_Float16)t1b ); + + // XA(1) = 1/2*( U1 - imag(U2) + i*( U1 +imag(U2) )); + pB = p + 2*k - 14; + pA += 2; + + blockCnt = k >> 3; + while (blockCnt > 0) + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + + xA = vld2q_f16(pA); + pA += 16; + + xB = vld2q_f16(pB); + + xB.val[0] = vldrhq_gather_shifted_offset_f16(pB, vecStridesBkwd); + xB.val[1] = vldrhq_gather_shifted_offset_f16(&pB[1], vecStridesBkwd); + + xB.val[1] = vnegq_f16(xB.val[1]); + pB -= 16; + + + tw = vld2q_f16(pCoeff); + pCoeff += 16; + + + tmp1.val[0] = vaddq_f16(xA.val[0],xB.val[0]); + tmp1.val[1] = vaddq_f16(xA.val[1],xB.val[1]); + + tmp2.val[0] = vsubq_f16(xB.val[0],xA.val[0]); + tmp2.val[1] = vsubq_f16(xB.val[1],xA.val[1]); + + res.val[0] = vmulq(tw.val[0], tmp2.val[0]); + res.val[0] = vfmsq(res.val[0],tw.val[1], tmp2.val[1]); + + res.val[1] = vmulq(tw.val[0], tmp2.val[1]); + res.val[1] = vfmaq(res.val[1], tw.val[1], tmp2.val[0]); + + res.val[0] = vaddq_f16(res.val[0],tmp1.val[0] ); + res.val[1] = vaddq_f16(res.val[1],tmp1.val[1] ); + + res.val[0] = vmulq_n_f16(res.val[0], 0.5f); + res.val[1] = vmulq_n_f16(res.val[1], 0.5f); + + + vst2q_f16(pOut, res); + pOut += 16; + + + blockCnt--; + } + + pB += 14; + blockCnt = k & 7; + while (blockCnt > 0) + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + xBI = pB[1]; + xBR = pB[0]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = (_Float16)xBR - (_Float16)xAR ; + t1b = (_Float16)xBI + (_Float16)xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + p0 = (_Float16)twR * (_Float16)t1a; + p1 = (_Float16)twI * (_Float16)t1a; + p2 = (_Float16)twR * (_Float16)t1b; + p3 = (_Float16)twI * (_Float16)t1b; + + *pOut++ = 0.5f16 * ((_Float16)xAR + (_Float16)xBR + (_Float16)p0 + (_Float16)p3 ); //xAR + *pOut++ = 0.5f16 * ((_Float16)xAI - (_Float16)xBI + (_Float16)p1 - (_Float16)p2 ); //xAI + + pA += 2; + pB -= 2; + blockCnt--; + } +} + +/* Prepares data for inverse cfft */ +static void merge_rfft_f16( + const arm_rfft_fast_instance_f16 * S, + const float16_t * p, + float16_t * pOut) +{ + int32_t k; /* Loop Counter */ + float16_t twR, twI; /* RFFT Twiddle coefficients */ + const float16_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float16_t *pA = p; /* increasing pointer */ + const float16_t *pB = p; /* decreasing pointer */ + float16_t xAR, xAI, xBR, xBI; /* temporary variables */ + float16_t t1a, t1b, r, s, t, u; /* temporary variables */ + + float16x8x2_t tw,xA,xB; + float16x8x2_t tmp1, tmp2, res; + uint16x8_t vecStridesBkwd; + + vecStridesBkwd = vddupq_u16((uint16_t)14, 2); + + int blockCnt; + + + k = (S->Sint).fftLen - 1; + + xAR = pA[0]; + xAI = pA[1]; + + pCoeff += 2 ; + + *pOut++ = 0.5f16 * ( (_Float16)xAR + (_Float16)xAI ); + *pOut++ = 0.5f16 * ( (_Float16)xAR - (_Float16)xAI ); + + pB = p + 2*k - 14; + pA += 2 ; + + blockCnt = k >> 3; + while (blockCnt > 0) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xA = vld2q_f16(pA); + pA += 16; + + xB = vld2q_f16(pB); + + xB.val[0] = vldrhq_gather_shifted_offset_f16(pB, vecStridesBkwd); + xB.val[1] = vldrhq_gather_shifted_offset_f16(&pB[1], vecStridesBkwd); + + xB.val[1] = vnegq_f16(xB.val[1]); + pB -= 16; + + + tw = vld2q_f16(pCoeff); + tw.val[1] = vnegq_f16(tw.val[1]); + pCoeff += 16; + + + tmp1.val[0] = vaddq_f16(xA.val[0],xB.val[0]); + tmp1.val[1] = vaddq_f16(xA.val[1],xB.val[1]); + + tmp2.val[0] = vsubq_f16(xB.val[0],xA.val[0]); + tmp2.val[1] = vsubq_f16(xB.val[1],xA.val[1]); + + res.val[0] = vmulq(tw.val[0], tmp2.val[0]); + res.val[0] = vfmsq(res.val[0],tw.val[1], tmp2.val[1]); + + res.val[1] = vmulq(tw.val[0], tmp2.val[1]); + res.val[1] = vfmaq(res.val[1], tw.val[1], tmp2.val[0]); + + res.val[0] = vaddq_f16(res.val[0],tmp1.val[0] ); + res.val[1] = vaddq_f16(res.val[1],tmp1.val[1] ); + + res.val[0] = vmulq_n_f16(res.val[0], 0.5f); + res.val[1] = vmulq_n_f16(res.val[1], 0.5f); + + + vst2q_f16(pOut, res); + pOut += 16; + + + blockCnt--; + } + + pB += 14; + blockCnt = k & 7; + while (blockCnt > 0) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xBI = pB[1] ; + xBR = pB[0] ; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = (_Float16)xAR - (_Float16)xBR ; + t1b = (_Float16)xAI + (_Float16)xBI ; + + r = (_Float16)twR * (_Float16)t1a; + s = (_Float16)twI * (_Float16)t1b; + t = (_Float16)twI * (_Float16)t1a; + u = (_Float16)twR * (_Float16)t1b; + + // real(tw * (xA - xB)) = twR * (xAR - xBR) - twI * (xAI - xBI); + // imag(tw * (xA - xB)) = twI * (xAR - xBR) + twR * (xAI - xBI); + *pOut++ = 0.5f16 * ((_Float16)xAR + (_Float16)xBR - (_Float16)r - (_Float16)s ); //xAR + *pOut++ = 0.5f16 * ((_Float16)xAI - (_Float16)xBI + (_Float16)t - (_Float16)u ); //xAI + + pA += 2; + pB -= 2; + blockCnt--; + } + +} +#elif defined(ARM_MATH_NEON_FLOAT16) +/* + +No stage merge functions defined here for Neon. + +*/ +#else +static void stage_rfft_f16( + const arm_rfft_fast_instance_f16 * S, + const float16_t * p, + float16_t * pOut) +{ + int32_t k; /* Loop Counter */ + float16_t twR, twI; /* RFFT Twiddle coefficients */ + const float16_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float16_t *pA = p; /* increasing pointer */ + const float16_t *pB = p; /* decreasing pointer */ + float16_t xAR, xAI, xBR, xBI; /* temporary variables */ + float16_t t1a, t1b; /* temporary variables */ + float16_t p0, p1, p2, p3; /* temporary variables */ + + + k = (S->Sint).fftLen - 1; + + /* Pack first and last sample of the frequency domain together */ + + xBR = pB[0]; + xBI = pB[1]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++ ; + twI = *pCoeff++ ; + + + // U1 = XA(1) + XB(1); % It is real + t1a = (_Float16)xBR + (_Float16)xAR ; + + // U2 = XB(1) - XA(1); % It is imaginary + t1b = (_Float16)xBI + (_Float16)xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + *pOut++ = 0.5f16 * ( (_Float16)t1a + (_Float16)t1b ); + *pOut++ = 0.5f16 * ( (_Float16)t1a - (_Float16)t1b ); + + // XA(1) = 1/2*( U1 - imag(U2) + i*( U1 +imag(U2) )); + pB = p + 2*k; + pA += 2; + + do + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + xBI = pB[1]; + xBR = pB[0]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = (_Float16)xBR - (_Float16)xAR ; + t1b = (_Float16)xBI + (_Float16)xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + p0 = (_Float16)twR * (_Float16)t1a; + p1 = (_Float16)twI * (_Float16)t1a; + p2 = (_Float16)twR * (_Float16)t1b; + p3 = (_Float16)twI * (_Float16)t1b; + + *pOut++ = 0.5f16 * ((_Float16)xAR + (_Float16)xBR + (_Float16)p0 + (_Float16)p3 ); //xAR + *pOut++ = 0.5f16 * ((_Float16)xAI - (_Float16)xBI + (_Float16)p1 - (_Float16)p2 ); //xAI + + + pA += 2; + pB -= 2; + k--; + } while (k > 0); +} + +/* Prepares data for inverse cfft */ +static void merge_rfft_f16( + const arm_rfft_fast_instance_f16 * S, + const float16_t * p, + float16_t * pOut) +{ + int32_t k; /* Loop Counter */ + float16_t twR, twI; /* RFFT Twiddle coefficients */ + const float16_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float16_t *pA = p; /* increasing pointer */ + const float16_t *pB = p; /* decreasing pointer */ + float16_t xAR, xAI, xBR, xBI; /* temporary variables */ + float16_t t1a, t1b, r, s, t, u; /* temporary variables */ + + k = (S->Sint).fftLen - 1; + + xAR = pA[0]; + xAI = pA[1]; + + pCoeff += 2 ; + + *pOut++ = 0.5f16 * ( (_Float16)xAR + (_Float16)xAI ); + *pOut++ = 0.5f16 * ( (_Float16)xAR - (_Float16)xAI ); + + pB = p + 2*k ; + pA += 2 ; + + while (k > 0) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xBI = pB[1] ; + xBR = pB[0] ; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = (_Float16)xAR - (_Float16)xBR ; + t1b = (_Float16)xAI + (_Float16)xBI ; + + r = (_Float16)twR * (_Float16)t1a; + s = (_Float16)twI * (_Float16)t1b; + t = (_Float16)twI * (_Float16)t1a; + u = (_Float16)twR * (_Float16)t1b; + + // real(tw * (xA - xB)) = twR * (xAR - xBR) - twI * (xAI - xBI); + // imag(tw * (xA - xB)) = twI * (xAR - xBR) + twR * (xAI - xBI); + *pOut++ = 0.5f16 * ((_Float16)xAR + (_Float16)xBR - (_Float16)r - (_Float16)s ); //xAR + *pOut++ = 0.5f16 * ((_Float16)xAI - (_Float16)xBI + (_Float16)t - (_Float16)u ); //xAI + + pA += 2; + pB -= 2; + k--; + } + +} + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @ingroup RealFFT +*/ + +/** + @defgroup RealFFTF16 Real FFT F16 Functions +*/ + +/** + @addtogroup RealFFTF16 + @{ +*/ + +/** + @brief Processing function for the floating-point real FFT. + @param[in] S points to an arm_rfft_fast_instance_f16 structure + @param[in] p points to input buffer (Source buffer is modified by this function.) + @param[in] pOut points to output buffer + @param[in] ifftFlag + - value = 0: RFFT + - value = 1: RIFFT + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". +*/ +#if defined(ARM_MATH_NEON_FLOAT16) + +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + +ARM_DSP_ATTRIBUTE void arm_rfft_fast_f16( + const arm_rfft_fast_instance_f16 * S, + const float16_t * p, + float16_t * pOut, + float16_t *tmpbuf, + uint8_t ifftFlag) +{ +/* Calculation of Real FFT */ + if (!ifftFlag) + { + arm_ne10_fft_r2c_1d_float16_neon (S,p,pOut,tmpbuf); + } + else + { + arm_ne10_fft_c2r_1d_float16_neon (S,p,pOut,tmpbuf); + } +} + +#else +ARM_DSP_ATTRIBUTE void arm_rfft_fast_f16( + const arm_rfft_fast_instance_f16 * S, + float16_t * p, + float16_t * pOut, + uint8_t ifftFlag) +{ + const arm_cfft_instance_f16 * Sint = &(S->Sint); + + + /* Calculation of Real FFT */ + if (ifftFlag) + { + /* Real FFT compression */ + merge_rfft_f16(S, p, pOut); + /* Complex radix-4 IFFT process */ + arm_cfft_f16( Sint, pOut, ifftFlag, 1); + } + else + { + + /* Calculation of RFFT of input */ + arm_cfft_f16( Sint, p, ifftFlag, 1); + + /* Real FFT extraction */ + stage_rfft_f16(S, p, pOut); + } +} +#endif +/** +* @} end of RealFFTF16 group +*/ + +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f32.c new file mode 100755 index 0000000..7e6b029 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f32.c @@ -0,0 +1,706 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_fast_f32.c + * Description: RFFT & RIFFT Floating point process function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +#if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) +static void stage_rfft_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut) +{ + int32_t k; /* Loop Counter */ + float32_t twR, twI; /* RFFT Twiddle coefficients */ + const float32_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float32_t *pA = p; /* increasing pointer */ + const float32_t *pB = p; /* decreasing pointer */ + float32_t xAR, xAI, xBR, xBI; /* temporary variables */ + float32_t t1a, t1b; /* temporary variables */ + float32_t p0, p1, p2, p3; /* temporary variables */ + + float32x4x2_t tw,xA,xB; + float32x4x2_t tmp1, tmp2, res; + + uint32x4_t vecStridesFwd, vecStridesBkwd; + + vecStridesFwd = vidupq_u32((uint32_t)0, 2); + vecStridesBkwd = -vecStridesFwd; + + int blockCnt; + + + k = (S->Sint).fftLen - 1; + + /* Pack first and last sample of the frequency domain together */ + + xBR = pB[0]; + xBI = pB[1]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++ ; + twI = *pCoeff++ ; + + // U1 = XA(1) + XB(1); % It is real + t1a = xBR + xAR ; + + // U2 = XB(1) - XA(1); % It is imaginary + t1b = xBI + xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + *pOut++ = 0.5f * ( t1a + t1b ); + *pOut++ = 0.5f * ( t1a - t1b ); + + // XA(1) = 1/2*( U1 - imag(U2) + i*( U1 +imag(U2) )); + pB = p + 2*k; + pA += 2; + + blockCnt = k >> 2; + while (blockCnt > 0) + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + + xA = vld2q_f32(pA); + pA += 8; + + xB = vld2q_f32(pB); + + xB.val[0] = vldrwq_gather_shifted_offset_f32(pB, vecStridesBkwd); + xB.val[1] = vldrwq_gather_shifted_offset_f32(&pB[1], vecStridesBkwd); + + xB.val[1] = vnegq_f32(xB.val[1]); + pB -= 8; + + + tw = vld2q_f32(pCoeff); + pCoeff += 8; + + + tmp1.val[0] = vaddq_f32(xA.val[0],xB.val[0]); + tmp1.val[1] = vaddq_f32(xA.val[1],xB.val[1]); + + tmp2.val[0] = vsubq_f32(xB.val[0],xA.val[0]); + tmp2.val[1] = vsubq_f32(xB.val[1],xA.val[1]); + + res.val[0] = vmulq(tw.val[0], tmp2.val[0]); + res.val[0] = vfmsq(res.val[0],tw.val[1], tmp2.val[1]); + + res.val[1] = vmulq(tw.val[0], tmp2.val[1]); + res.val[1] = vfmaq(res.val[1], tw.val[1], tmp2.val[0]); + + res.val[0] = vaddq_f32(res.val[0],tmp1.val[0] ); + res.val[1] = vaddq_f32(res.val[1],tmp1.val[1] ); + + res.val[0] = vmulq_n_f32(res.val[0], 0.5f); + res.val[1] = vmulq_n_f32(res.val[1], 0.5f); + + + vst2q_f32(pOut, res); + pOut += 8; + + + blockCnt--; + } + + blockCnt = k & 3; + while (blockCnt > 0) + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + xBI = pB[1]; + xBR = pB[0]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = xBR - xAR ; + t1b = xBI + xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + p0 = twR * t1a; + p1 = twI * t1a; + p2 = twR * t1b; + p3 = twI * t1b; + + *pOut++ = 0.5f * (xAR + xBR + p0 + p3 ); //xAR + *pOut++ = 0.5f * (xAI - xBI + p1 - p2 ); //xAI + + pA += 2; + pB -= 2; + blockCnt--; + } +} + +/* Prepares data for inverse cfft */ +static void merge_rfft_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut) +{ + int32_t k; /* Loop Counter */ + float32_t twR, twI; /* RFFT Twiddle coefficients */ + const float32_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float32_t *pA = p; /* increasing pointer */ + const float32_t *pB = p; /* decreasing pointer */ + float32_t xAR, xAI, xBR, xBI; /* temporary variables */ + float32_t t1a, t1b, r, s, t, u; /* temporary variables */ + + float32x4x2_t tw,xA,xB; + float32x4x2_t tmp1, tmp2, res; + uint32x4_t vecStridesFwd, vecStridesBkwd; + + vecStridesFwd = vidupq_u32((uint32_t)0, 2); + vecStridesBkwd = -vecStridesFwd; + + int blockCnt; + + + k = (S->Sint).fftLen - 1; + + xAR = pA[0]; + xAI = pA[1]; + + pCoeff += 2 ; + + *pOut++ = 0.5f * ( xAR + xAI ); + *pOut++ = 0.5f * ( xAR - xAI ); + + pB = p + 2*k ; + pA += 2 ; + + blockCnt = k >> 2; + while (blockCnt > 0) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xA = vld2q_f32(pA); + pA += 8; + + xB = vld2q_f32(pB); + + xB.val[0] = vldrwq_gather_shifted_offset_f32(pB, vecStridesBkwd); + xB.val[1] = vldrwq_gather_shifted_offset_f32(&pB[1], vecStridesBkwd); + + xB.val[1] = vnegq_f32(xB.val[1]); + pB -= 8; + + + tw = vld2q_f32(pCoeff); + tw.val[1] = vnegq_f32(tw.val[1]); + pCoeff += 8; + + + tmp1.val[0] = vaddq_f32(xA.val[0],xB.val[0]); + tmp1.val[1] = vaddq_f32(xA.val[1],xB.val[1]); + + tmp2.val[0] = vsubq_f32(xB.val[0],xA.val[0]); + tmp2.val[1] = vsubq_f32(xB.val[1],xA.val[1]); + + res.val[0] = vmulq(tw.val[0], tmp2.val[0]); + res.val[0] = vfmsq(res.val[0],tw.val[1], tmp2.val[1]); + + res.val[1] = vmulq(tw.val[0], tmp2.val[1]); + res.val[1] = vfmaq(res.val[1], tw.val[1], tmp2.val[0]); + + res.val[0] = vaddq_f32(res.val[0],tmp1.val[0] ); + res.val[1] = vaddq_f32(res.val[1],tmp1.val[1] ); + + res.val[0] = vmulq_n_f32(res.val[0], 0.5f); + res.val[1] = vmulq_n_f32(res.val[1], 0.5f); + + + vst2q_f32(pOut, res); + pOut += 8; + + + blockCnt--; + } + + blockCnt = k & 3; + while (blockCnt > 0) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xBI = pB[1] ; + xBR = pB[0] ; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = xAR - xBR ; + t1b = xAI + xBI ; + + r = twR * t1a; + s = twI * t1b; + t = twI * t1a; + u = twR * t1b; + + // real(tw * (xA - xB)) = twR * (xAR - xBR) - twI * (xAI - xBI); + // imag(tw * (xA - xB)) = twI * (xAR - xBR) + twR * (xAI - xBI); + *pOut++ = 0.5f * (xAR + xBR - r - s ); //xAR + *pOut++ = 0.5f * (xAI - xBI + t - u ); //xAI + + pA += 2; + pB -= 2; + blockCnt--; + } + +} +#elif defined(ARM_MATH_NEON) +/* + +No stage merge functions defined here for Neon. + +*/ +#else +static void stage_rfft_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut) +{ + int32_t k; /* Loop Counter */ + float32_t twR, twI; /* RFFT Twiddle coefficients */ + const float32_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float32_t *pA = p; /* increasing pointer */ + const float32_t *pB = p; /* decreasing pointer */ + float32_t xAR, xAI, xBR, xBI; /* temporary variables */ + float32_t t1a, t1b; /* temporary variables */ + float32_t p0, p1, p2, p3; /* temporary variables */ + + + k = (S->Sint).fftLen - 1; + + /* Pack first and last sample of the frequency domain together */ + + xBR = pB[0]; + xBI = pB[1]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++ ; + twI = *pCoeff++ ; + + + // U1 = XA(1) + XB(1); % It is real + t1a = xBR + xAR ; + + // U2 = XB(1) - XA(1); % It is imaginary + t1b = xBI + xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + *pOut++ = 0.5f * ( t1a + t1b ); + *pOut++ = 0.5f * ( t1a - t1b ); + + // XA(1) = 1/2*( U1 - imag(U2) + i*( U1 +imag(U2) )); + pB = p + 2*k; + pA += 2; + + do + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + xBI = pB[1]; + xBR = pB[0]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = xBR - xAR ; + t1b = xBI + xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + p0 = twR * t1a; + p1 = twI * t1a; + p2 = twR * t1b; + p3 = twI * t1b; + + *pOut++ = 0.5f * (xAR + xBR + p0 + p3 ); //xAR + *pOut++ = 0.5f * (xAI - xBI + p1 - p2 ); //xAI + + + pA += 2; + pB -= 2; + k--; + } while (k > 0); +} + +/* Prepares data for inverse cfft */ +static void merge_rfft_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut) +{ + int32_t k; /* Loop Counter */ + float32_t twR, twI; /* RFFT Twiddle coefficients */ + const float32_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float32_t *pA = p; /* increasing pointer */ + const float32_t *pB = p; /* decreasing pointer */ + float32_t xAR, xAI, xBR, xBI; /* temporary variables */ + float32_t t1a, t1b, r, s, t, u; /* temporary variables */ + + k = (S->Sint).fftLen - 1; + + xAR = pA[0]; + xAI = pA[1]; + + pCoeff += 2 ; + + *pOut++ = 0.5f * ( xAR + xAI ); + *pOut++ = 0.5f * ( xAR - xAI ); + + pB = p + 2*k ; + pA += 2 ; + + while (k > 0) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xBI = pB[1] ; + xBR = pB[0] ; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = xAR - xBR ; + t1b = xAI + xBI ; + + r = twR * t1a; + s = twI * t1b; + t = twI * t1a; + u = twR * t1b; + + // real(tw * (xA - xB)) = twR * (xAR - xBR) - twI * (xAI - xBI); + // imag(tw * (xA - xB)) = twI * (xAR - xBR) + twR * (xAI - xBI); + *pOut++ = 0.5f * (xAR + xBR - r - s ); //xAR + *pOut++ = 0.5f * (xAI - xBI + t - u ); //xAI + + pA += 2; + pB -= 2; + k--; + } + +} + +#endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */ + +/** + @ingroup groupTransforms +*/ + +/** + @defgroup RealFFT Real FFT Functions + + @par + The CMSIS DSP library includes specialized algorithms for computing the + FFT of real data sequences. The FFT is defined over complex data but + in many applications the input is real. Real FFT algorithms take advantage + of the symmetry properties of the FFT and have a speed advantage over complex + algorithms of the same length. + @par + The Fast RFFT algorithm relays on the mixed radix CFFT that save processor usage. + @par + The real length N forward FFT of a sequence is computed using the steps shown below. + @par + \image html RFFT.gif "Real Fast Fourier Transform" + @par + The real sequence is initially treated as if it were complex to perform a CFFT. + Later, a processing stage reshapes the data to obtain half of the frequency spectrum + in complex format. + + @par + The input for the inverse RFFT should keep the same format as the output of the + forward RFFT. A first processing stage pre-process the data to later perform an + inverse CFFT. + @par + \image html RIFFT.gif "Real Inverse Fast Fourier Transform" + @par + The algorithms for floating-point, Q15, and Q31 data are slightly different + and we describe each algorithm in turn. + @par Floating-point + The main functions are \ref arm_rfft_fast_f32() and \ref arm_rfft_fast_init_f32(). + + For f16, the functions are \ref arm_rfft_fast_f16() and \ref arm_rfft_fast_init_f16(). + For f64, the functions are \ref arm_rfft_fast_f64() and \ref arm_rfft_fast_init_f64(). + @par + The FFT of a real N-point sequence has even symmetry in the frequency domain. + The second half of the data equals the conjugate of the first half flipped in frequency. + This conjugate part is not computed by the float RFFT. As consequence, the output of + a N point real FFT should be a N//2 + 1 complex numbers so N + 2 floats. + @par + It happens that the first complex of number of the RFFT output is actually + all real. Its real part represents the DC offset. + The value at Nyquist frequency is also real. + + @par + Those two complex numbers can be encoded with 2 floats rather than using two numbers + with an imaginary part set to zero. + @par + The implementation is using a trick so that the output buffer can be N float : + the last real is packaged in the imaginary part of the first complex (since + this imaginary part is not used and is zero). + + @par + The real FFT functions pack the frequency domain data in this fashion. + The forward transform outputs the data in this form and the inverse + transform expects input data in this form. The function always performs + the needed bitreversal so that the input and output data is always in + normal order. The functions support lengths of [32, 64, 128, ..., 4096] + samples. + @par Q15 and Q31 + The real algorithms are defined in a similar manner and utilize N/2 complex + transforms behind the scenes. + + @par + But warning, contrary to the float version, the fixed point implementation + RFFT is also computing the conjugate part (except for MVE version) so the + output buffer must be bigger. + Also the fixed point RFFTs are not using any trick to pack the DC and Nyquist + frequency in the same complex number. + The RIFFT is not using the conjugate part but it is still using the Nyquist + frequency value. The details are given in the documentation for the functions. + @par + The complex transforms used internally include scaling to prevent fixed-point + overflows. The overall scaling equals 1/(fftLen/2). + Due to the use of complex transform internally, the source buffer is + modified by the rfft. + @par + A separate instance structure must be defined for each transform used but + twiddle factor and bit reversal tables can be reused. + @par + There is also an associated initialization function for each data type. + The initialization function performs the following operations: + - Sets the values of the internal structure fields. + - Initializes twiddle factor table and bit reversal table pointers. + - Initializes the internal complex FFT data structure. + @par + Use of the initialization function is optional **except for MVE versions where it is mandatory**. + If you don't use the initialization functions, then the structures should be initialized with code + similar to the one below: + 
+      arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
+      arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
+
+ where fftLenReal is the length of the real transform; + fftLenBy2 length of the internal complex transform (fftLenReal/2). + ifftFlagR Selects forward (=0) or inverse (=1) transform. + bitReverseFlagR Selects bit reversed output (=0) or normal order + output (=1). + twidCoefRModifier stride modifier for the twiddle factor table. + The value is based on the FFT length; + pTwiddleARealpoints to the A array of twiddle coefficients; + pTwiddleBRealpoints to the B array of twiddle coefficients; + pCfft points to the CFFT Instance structure. The CFFT structure + must also be initialized. +@par + Note that with MVE versions you can't initialize instance structures directly and **must + use the initialization function**. + + @par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is a temporary buffer that is not optional. + + The bit reverse flag is not more + available in Neon version. + + + @code + void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + float32_t * p, + float32_t * pOut, + float32_t *tmpbuf, + uint8_t ifftFlag); + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + */ + +/** + @defgroup DeprecatedRealFFT Deprecated Real FFT Functions +*/ + +/** + @defgroup RealFFTF32 Real FFT F32 Functions +*/ +/** + @addtogroup RealFFTF32 + @{ +*/ + +/** + @brief Processing function for the floating-point real FFT. + @param[in] S points to an arm_rfft_fast_instance_f32 structure + @param[in] p points to input buffer (Source buffer is modified by this function.) + @param[in] pOut points to output buffer + @param[in] ifftFlag + - value = 0: RFFT + - value = 1: RIFFT + + @par Neon version + The neon version has a different API. + The input and output buffers must be + different. + There is a temporary buffer. + @par + The bit reverse flag is not more + available in Neon version. + + @par + @code + void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut, + float32_t *tmpbuf, + uint8_t ifftFlag); + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". +*/ + +#if defined(ARM_MATH_NEON) + +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + +/* + +p size : nfft reals +pOut size : nfft reals (nfft/2 complex) +tmpBuf size : 2*nfft reals (nfft complex) + +*/ +ARM_DSP_ATTRIBUTE void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + const float32_t * p, + float32_t * pOut, + float32_t *tmpbuf, + uint8_t ifftFlag) +{ +/* Calculation of Real FFT */ + if (!ifftFlag) + { + arm_ne10_fft_r2c_1d_float32_neon (S,p,pOut,tmpbuf); + } + else + { + arm_ne10_fft_c2r_1d_float32_neon (S,p,pOut,tmpbuf); + } +} +#else +ARM_DSP_ATTRIBUTE void arm_rfft_fast_f32( + const arm_rfft_fast_instance_f32 * S, + float32_t * p, + float32_t * pOut, + uint8_t ifftFlag) +{ + const arm_cfft_instance_f32 * Sint = &(S->Sint); + + /* Calculation of Real FFT */ + if (ifftFlag) + { + /* Real FFT compression */ + merge_rfft_f32(S, p, pOut); + /* Complex radix-4 IFFT process */ + arm_cfft_f32( Sint, pOut, ifftFlag, 1); + } + else + { + /* Calculation of RFFT of input */ + arm_cfft_f32( Sint, p, ifftFlag, 1); + + /* Real FFT extraction */ + stage_rfft_f32(S, p, pOut); + } +} +#endif +/** +* @} end of RealFFTF32 group +*/ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f64.c new file mode 100755 index 0000000..80fede3 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_f64.c @@ -0,0 +1,236 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_fast_f64.c + * Description: RFFT & RIFFT Double precision Floating point process function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +static void stage_rfft_f64( + const arm_rfft_fast_instance_f64 * S, + const float64_t * p, + float64_t * pOut) +{ + uint32_t k; /* Loop Counter */ + float64_t twR, twI; /* RFFT Twiddle coefficients */ + const float64_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float64_t *pA = p; /* increasing pointer */ + const float64_t *pB = p; /* decreasing pointer */ + float64_t xAR, xAI, xBR, xBI; /* temporary variables */ + float64_t t1a, t1b; /* temporary variables */ + float64_t p0, p1, p2, p3; /* temporary variables */ + + + k = (S->Sint).fftLen - 1; + + /* Pack first and last sample of the frequency domain together */ + + xBR = pB[0]; + xBI = pB[1]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++ ; + twI = *pCoeff++ ; + + // U1 = XA(1) + XB(1); % It is real + t1a = xBR + xAR ; + + // U2 = XB(1) - XA(1); % It is imaginary + t1b = xBI + xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + *pOut++ = 0.5 * ( t1a + t1b ); + *pOut++ = 0.5 * ( t1a - t1b ); + + // XA(1) = 1/2*( U1 - imag(U2) + i*( U1 +imag(U2) )); + pB = p + 2*k; + pA += 2; + + do + { + /* + function X = my_split_rfft(X, ifftFlag) + % X is a series of real numbers + L = length(X); + XC = X(1:2:end) +i*X(2:2:end); + XA = fft(XC); + XB = conj(XA([1 end:-1:2])); + TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; + for l = 2:L/2 + XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); + end + XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); + X = XA; + */ + + xBI = pB[1]; + xBR = pB[0]; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = xBR - xAR ; + t1b = xBI + xAI ; + + // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); + // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); + p0 = twR * t1a; + p1 = twI * t1a; + p2 = twR * t1b; + p3 = twI * t1b; + + *pOut++ = 0.5 * (xAR + xBR + p0 + p3 ); //xAR + *pOut++ = 0.5 * (xAI - xBI + p1 - p2 ); //xAI + + pA += 2; + pB -= 2; + k--; + } while (k > 0U); +} + +/* Prepares data for inverse cfft */ +static void merge_rfft_f64( + const arm_rfft_fast_instance_f64 * S, + const float64_t * p, + float64_t * pOut) +{ + uint32_t k; /* Loop Counter */ + float64_t twR, twI; /* RFFT Twiddle coefficients */ + const float64_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + const float64_t *pA = p; /* increasing pointer */ + const float64_t *pB = p; /* decreasing pointer */ + float64_t xAR, xAI, xBR, xBI; /* temporary variables */ + float64_t t1a, t1b, r, s, t, u; /* temporary variables */ + + k = (S->Sint).fftLen - 1; + + xAR = pA[0]; + xAI = pA[1]; + + pCoeff += 2 ; + + *pOut++ = 0.5 * ( xAR + xAI ); + *pOut++ = 0.5 * ( xAR - xAI ); + + pB = p + 2*k ; + pA += 2 ; + + while (k > 0U) + { + /* G is half of the frequency complex spectrum */ + //for k = 2:N + // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); + xBI = pB[1] ; + xBR = pB[0] ; + xAR = pA[0]; + xAI = pA[1]; + + twR = *pCoeff++; + twI = *pCoeff++; + + t1a = xAR - xBR ; + t1b = xAI + xBI ; + + r = twR * t1a; + s = twI * t1b; + t = twI * t1a; + u = twR * t1b; + + // real(tw * (xA - xB)) = twR * (xAR - xBR) - twI * (xAI - xBI); + // imag(tw * (xA - xB)) = twI * (xAR - xBR) + twR * (xAI - xBI); + *pOut++ = 0.5 * (xAR + xBR - r - s ); //xAR + *pOut++ = 0.5 * (xAI - xBI + t - u ); //xAI + + pA += 2; + pB -= 2; + k--; + } + +} + +/** + @ingroup RealFFT +*/ + +/** + @defgroup RealFFTF64 Real FFT F64 Functions +*/ + +/** + @addtogroup RealFFTF64 + @{ +*/ + +/** + @brief Processing function for the Double Precision floating-point real FFT. + @param[in] S points to an arm_rfft_fast_instance_f64 structure + @param[in] p points to input buffer (Source buffer is modified by this function.) + @param[in] pOut points to output buffer + @param[in] ifftFlag + - value = 0: RFFT + - value = 1: RIFFT + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". +*/ + +ARM_DSP_ATTRIBUTE void arm_rfft_fast_f64( + arm_rfft_fast_instance_f64 * S, + float64_t * p, + float64_t * pOut, + uint8_t ifftFlag) +{ + arm_cfft_instance_f64 * Sint = &(S->Sint); + Sint->fftLen = S->fftLenRFFT / 2; + + /* Calculation of Real FFT */ + if (ifftFlag) + { + /* Real FFT compression */ + merge_rfft_f64(S, p, pOut); + + /* Complex radix-4 IFFT process */ + arm_cfft_f64( Sint, pOut, ifftFlag, 1); + } + else + { + /* Calculation of RFFT of input */ + arm_cfft_f64( Sint, p, ifftFlag, 1); + + /* Real FFT extraction */ + stage_rfft_f64(S, p, pOut); + } +} + +/** +* @} end of RealFFTF64 group +*/ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f16.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f16.c new file mode 100755 index 0000000..14b855d --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f16.c @@ -0,0 +1,407 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_fast_init_f16.c + * Description: Split Radix Decimation in Frequency CFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2023 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions_f16.h" +#include "arm_common_tables_f16.h" +#include "arm_const_structs_f16.h" + +#if defined(ARM_FLOAT16_SUPPORTED) + +/** + @ingroup RealFFT + */ + +/** + @addtogroup RealFFTF16 + @{ + */ + + +/** + @brief Initialization function for the 32pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON_FLOAT16) +#include "arm_neon_tables_f16.h" +#define RFFT_INIT(LEN) \ + S->nfft = LEN; \ + S->r_twiddles = arm_neon_rfft_twiddles_##LEN##_f16; \ + S->r_factors = arm_neon_rfft_factors_##LEN##_f16; \ + \ + S->r_twiddles_neon = arm_neon_rfft_twiddles_neon_##LEN##_f16; \ + S->r_factors_neon = arm_neon_rfft_factors_neon_##LEN##_f16; \ + \ + S->r_twiddles_backward = S->r_twiddles + 2*ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_##LEN##_F16; \ + S->r_twiddles_neon_backward = S->r_twiddles_neon + 2*ARM_NE10_OFFSET_BACKWARD_TWID_NEON_##LEN##_F16;\ + \ + S->r_super_twiddles_neon = arm_neon_rfft_super_twiddles_neon_##LEN##_f16; + +#define FAST_INIT_FUNC(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_##LEN##_f16( arm_rfft_fast_instance_f16 * S )\ +{ \ + \ + if( !S ) return ARM_MATH_ARGUMENT_ERROR; \ + \ + RFFT_INIT(LEN); \ + \ + return ARM_MATH_SUCCESS; \ +} + +#endif + +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(32) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_32_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_16_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + + S->fftLenRFFT = 32U; + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_32; + + return ARM_MATH_SUCCESS; +} +#endif + +/** + @brief Initialization function for the 64pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(64) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_64_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_32_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 64U; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_64; + + return ARM_MATH_SUCCESS; +} +#endif + +/** + @brief Initialization function for the 128pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(128) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_128_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_64_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 128; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_128; + + return ARM_MATH_SUCCESS; +} +#endif + +/** + @brief Initialization function for the 256pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected +*/ +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(256) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_256_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_128_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 256U; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_256; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 512pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(512) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_512_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_256_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 512U; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_512; + + return ARM_MATH_SUCCESS; +} +#endif + +/** + @brief Initialization function for the 1024pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(1024) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_1024_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_512_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 1024U; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_1024; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 2048pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(2048) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_2048_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_1024_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 2048U; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_2048; + + return ARM_MATH_SUCCESS; +} +#endif +/** +* @brief Initialization function for the 4096pt floating-point real FFT. +* @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ +#if defined(ARM_MATH_NEON_FLOAT16) + +FAST_INIT_FUNC(4096) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_4096_f16( arm_rfft_fast_instance_f16 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_2048_f16(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 4096U; + + S->pTwiddleRFFT = (float16_t *) twiddleCoefF16_rfft_4096; + + return ARM_MATH_SUCCESS; +} +#endif + +/** + @brief Generic initialization function for the floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f16 structure + @param[in] fftLen length of the Real Sequence + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Description + The parameter fftLen specifies the length of RFFT/CIFFT process. + Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096. + + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_f16( + arm_rfft_fast_instance_f16 * S, + uint16_t fftLen) +{ + arm_status status; + + + switch (fftLen) + { + case 4096U: + status = arm_rfft_fast_init_4096_f16(S); + break; + case 2048U: + status = arm_rfft_fast_init_2048_f16(S); + break; + case 1024U: + status = arm_rfft_fast_init_1024_f16(S); + break; + case 512U: + status = arm_rfft_fast_init_512_f16(S); + break; + case 256U: + status = arm_rfft_fast_init_256_f16(S); + break; + case 128U: + status = arm_rfft_fast_init_128_f16(S); + break; + case 64U: + status = arm_rfft_fast_init_64_f16(S); + break; + case 32U: + status = arm_rfft_fast_init_32_f16(S); + break; + default: + return(ARM_MATH_ARGUMENT_ERROR); + break; + } + + return(status); + +} + +/** + @} end of RealFFTF16 group + */ + + #if defined(RFFT_INIT) + #undef RFFT_INIT + #endif + + #if defined(FAST_INIT_FUNC) + #undef FAST_INIT_FUNC + #endif +#endif /* #if defined(ARM_FLOAT16_SUPPORTED) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f32.c new file mode 100755 index 0000000..04052c5 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f32.c @@ -0,0 +1,386 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_fast_init_f32.c + * Description: Split Radix Decimation in Frequency CFFT Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup RealFFT + */ + +/** + @addtogroup RealFFTF32 + @{ + */ + + +/** + @brief Initialization function for the 32pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON) +#include "arm_neon_tables.h" +#define RFFT_INIT(LEN) \ + S->nfft = LEN; \ + S->r_twiddles = arm_neon_rfft_twiddles_##LEN##_f32; \ + S->r_factors = arm_neon_rfft_factors_##LEN##_f32; \ + \ + S->r_twiddles_neon = arm_neon_rfft_twiddles_neon_##LEN##_f32; \ + S->r_factors_neon = arm_neon_rfft_factors_neon_##LEN##_f32; \ + \ + S->r_twiddles_backward = S->r_twiddles + 2*ARM_NE10_OFFSET_BACKWARD_TWID_RFFT_##LEN##_F32; \ + S->r_twiddles_neon_backward = S->r_twiddles_neon + 2*ARM_NE10_OFFSET_BACKWARD_TWID_NEON_##LEN##_F32;\ + \ + S->r_super_twiddles_neon = arm_neon_rfft_super_twiddles_neon_##LEN##_f32; + +#define FAST_INIT_FUNC(LEN) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_##LEN##_f32( arm_rfft_fast_instance_f32 * S )\ +{ \ + \ + if( !S ) return ARM_MATH_ARGUMENT_ERROR; \ + \ + RFFT_INIT(LEN); \ + \ + return ARM_MATH_SUCCESS; \ +} + +#endif + +#if defined(ARM_MATH_NEON) + +FAST_INIT_FUNC(32) + +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_32_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_16_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + + S->fftLenRFFT = 32U; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_32; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 64pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(64) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_64_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_32_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 64U; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_64; + + return ARM_MATH_SUCCESS; +} +#endif + +/** + @brief Initialization function for the 128pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(128) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_128_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_64_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 128; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_128; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 256pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected +*/ + +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(256) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_256_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_128_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 256U; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_256; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 512pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(512) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_512_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_256_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 512U; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_512; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 1024pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(1024) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_1024_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_512_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 1024U; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_1024; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Initialization function for the 2048pt floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(2048) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_2048_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_1024_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 2048U; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_2048; + + return ARM_MATH_SUCCESS; +} +#endif +/** +* @brief Initialization function for the 4096pt floating-point real FFT. +* @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +#if defined(ARM_MATH_NEON) +FAST_INIT_FUNC(4096) +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_4096_f32( arm_rfft_fast_instance_f32 * S ) { + + arm_status status; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + status=arm_cfft_init_2048_f32(&(S->Sint)); + if (status != ARM_MATH_SUCCESS) + { + return(status); + } + S->fftLenRFFT = 4096U; + + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_4096; + + return ARM_MATH_SUCCESS; +} +#endif +/** + @brief Generic initialization function for the floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f32 structure + @param[in] fftLen length of the Real Sequence + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Description + The parameter fftLen specifies the length of RFFT/CIFFT process. + Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096. + + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_f32( + arm_rfft_fast_instance_f32 * S, + uint16_t fftLen) +{ + arm_status status; + + + switch (fftLen) + { + case 4096U: + status = arm_rfft_fast_init_4096_f32(S); + break; + case 2048U: + status = arm_rfft_fast_init_2048_f32(S); + break; + case 1024U: + status = arm_rfft_fast_init_1024_f32(S); + break; + case 512U: + status = arm_rfft_fast_init_512_f32(S); + break; + case 256U: + status = arm_rfft_fast_init_256_f32(S); + break; + case 128U: + status = arm_rfft_fast_init_128_f32(S); + break; + case 64U: + status = arm_rfft_fast_init_64_f32(S); + break; + case 32U: + status = arm_rfft_fast_init_32_f32(S); + break; + default: + return(ARM_MATH_ARGUMENT_ERROR); + break; + } + + return(status); + +} + +#if defined(RFFT_INIT) + #undef RFFT_INIT + #endif + + #if defined(FAST_INIT_FUNC) + #undef FAST_INIT_FUNC + #endif + +/** + @} end of RealFFTF32 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f64.c new file mode 100755 index 0000000..8f7c600 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_fast_init_f64.c @@ -0,0 +1,328 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_fast_init_f64.c + * Description: Split Radix Decimation in Frequency CFFT Double Precision Floating point processing function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" + +/** + @ingroup RealFFT + */ + +/** + @addtogroup RealFFTF64 + @{ + */ + + +/** + @brief Initialization function for the 32pt double precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_32_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 16U; + S->fftLenRFFT = 32U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_16_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_16; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_16; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_32; + + return ARM_MATH_SUCCESS; +} + + +/** + @brief Initialization function for the 64pt Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_64_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 32U; + S->fftLenRFFT = 64U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_32_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_32; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_32; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_64; + + return ARM_MATH_SUCCESS; +} + + +/** + @brief Initialization function for the 128pt Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_128_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 64U; + S->fftLenRFFT = 128U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_64_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_64; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_64; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_128; + + return ARM_MATH_SUCCESS; +} + + +/** + @brief Initialization function for the 256pt Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected +*/ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_256_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 128U; + S->fftLenRFFT = 256U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_128_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_128; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_128; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_256; + + return ARM_MATH_SUCCESS; +} + + +/** + @brief Initialization function for the 512pt Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_512_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 256U; + S->fftLenRFFT = 512U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_256_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_256; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_256; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_512; + + return ARM_MATH_SUCCESS; +} + +/** + @brief Initialization function for the 1024pt Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_1024_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 512U; + S->fftLenRFFT = 1024U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_512_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_512; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_512; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_1024; + + return ARM_MATH_SUCCESS; +} + +/** + @brief Initialization function for the 2048pt Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_2048_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 1024U; + S->fftLenRFFT = 2048U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_1024_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_1024; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_1024; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_2048; + + return ARM_MATH_SUCCESS; +} + +/** +* @brief Initialization function for the 4096pt Double Precision floating-point real FFT. +* @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : an error is detected + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_4096_f64( arm_rfft_fast_instance_f64 * S ) { + + arm_cfft_instance_f64 * Sint; + + if( !S ) return ARM_MATH_ARGUMENT_ERROR; + + Sint = &(S->Sint); + Sint->fftLen = 2048U; + S->fftLenRFFT = 4096U; + + Sint->bitRevLength = ARMBITREVINDEXTABLEF64_2048_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTableF64_2048; + Sint->pTwiddle = (float64_t *) twiddleCoefF64_2048; + S->pTwiddleRFFT = (float64_t *) twiddleCoefF64_rfft_4096; + + return ARM_MATH_SUCCESS; +} + +/** + @brief Generic initialization function for the Double Precision floating-point real FFT. + @param[in,out] S points to an arm_rfft_fast_instance_f64 structure + @param[in] fftLen length of the Real Sequence + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLen is not a supported length + + @par Description + The parameter fftLen specifies the length of RFFT/CIFFT process. + Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096. + + @par + This Function also initializes Twiddle factor table pointer and Bit reversal table pointer. + + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + + @par + If you use CMSIS-DSP as a library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + + */ + +ARM_DSP_ATTRIBUTE arm_status arm_rfft_fast_init_f64( + arm_rfft_fast_instance_f64 * S, + uint16_t fftLen) +{ + arm_status status; + + + switch (fftLen) + { + case 4096U: + status = arm_rfft_fast_init_4096_f64(S); + break; + case 2048U: + status = arm_rfft_fast_init_2048_f64(S); + break; + case 1024U: + status = arm_rfft_fast_init_1024_f64(S); + break; + case 512U: + status = arm_rfft_fast_init_512_f64(S); + break; + case 256U: + status = arm_rfft_fast_init_256_f64(S); + break; + case 128U: + status = arm_rfft_fast_init_128_f64(S); + break; + case 64U: + status = arm_rfft_fast_init_64_f64(S); + break; + case 32U: + status = arm_rfft_fast_init_32_f64(S); + break; + default: + return(ARM_MATH_ARGUMENT_ERROR); + break; + } + + return(status); + +} + +/** + @} end of RealFFTF64 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_init_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_init_q15.c new file mode 100755 index 0000000..4b0b783 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_init_q15.c @@ -0,0 +1,487 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_init_q15.c + * Description: RFFT & RIFFT Q15 initialisation function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2023 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + +/** + @ingroup RealFFT +*/ + +/** + @defgroup RealFFTQ15 Real FFT Q15 Functions +*/ + +/** + @addtogroup RealFFTQ15 + @{ + */ + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) +#define RFFTINIT_Q15(LEN,CFFTLEN,TWIDMOD) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_##LEN##_q15( arm_rfft_instance_q15 * S, \ + uint32_t ifftFlagR, \ + uint32_t bitReverseFlag ) \ +{ \ + \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + \ + /* Initialize the Real FFT length */ \ + S->fftLenReal = (uint16_t) LEN; \ + \ + /* Initialize the Twiddle coefficientA pointer */ \ + S->pTwiddleAReal = (q15_t *) realCoefAQ15; \ + \ + /* Initialize the Twiddle coefficientB pointer */ \ + S->pTwiddleBReal = (q15_t *) realCoefBQ15; \ + \ + /* Initialize the Flag for selection of RFFT or RIFFT */ \ + S->ifftFlagR = (uint8_t) ifftFlagR; \ + \ + /* Initialize the Flag for calculation Bit reversal or not */\ + S->bitReverseFlagR = (uint8_t) bitReverseFlag; \ + \ + S->twidCoefRModifier = TWIDMOD; \ + \ + status=arm_cfft_init_##CFFTLEN##_q15(&(S->cfftInst)); \ + \ + /* return the status of RFFT Init function */ \ + return (status); \ +} +#elif defined(ARM_MATH_NEON) +#define RFFTINIT_Q15(LEN,CFFTLEN,TWIDMOD) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_##LEN##_q15( arm_rfft_instance_q15 * S )\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + S->nfft = LEN; \ + S->ncfft = LEN >> 1; \ + \ + S->twiddles = arm_neon_rfft_twiddles_##LEN##_q15; \ + S->factors = arm_neon_rfft_factors_##LEN##_q15; \ + \ + S->super_twiddles = arm_neon_rfft_super_twiddles_neon_##LEN##_q15; \ + \ + /* return the status of RFFT Init function */ \ + return (status); \ +} +#include "arm_neon_tables.h" + + +#else +#define RFFTINIT_Q15(LEN,CFFTLEN,TWIDMOD) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_##LEN##_q15( arm_rfft_instance_q15 * S, \ + uint32_t ifftFlagR, \ + uint32_t bitReverseFlag ) \ +{ \ + /* Initialize the Real FFT length */ \ + S->fftLenReal = (uint16_t) LEN; \ + \ + /* Initialize the Twiddle coefficientA pointer */ \ + S->pTwiddleAReal = (q15_t *) realCoefAQ15; \ + \ + /* Initialize the Twiddle coefficientB pointer */ \ + S->pTwiddleBReal = (q15_t *) realCoefBQ15; \ + \ + /* Initialize the Flag for selection of RFFT or RIFFT */ \ + S->ifftFlagR = (uint8_t) ifftFlagR; \ + \ + /* Initialize the Flag for calculation Bit reversal or not */\ + S->bitReverseFlagR = (uint8_t) bitReverseFlag; \ + \ + S->twidCoefRModifier = TWIDMOD; \ + \ + S->pCfft = &arm_cfft_sR_q15_len##CFFTLEN; \ + \ + /* return the status of RFFT Init function */ \ + return (ARM_MATH_SUCCESS); \ +} +#endif + + +/** + @brief Initialization function for the 8192 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + + */ + +RFFTINIT_Q15(8192,4096,1) + +/** + @brief Initialization function for the 4096 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(4096,2048,2) + +/** + @brief Initialization function for the 2048 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(2048,1024,4) + +/** + @brief Initialization function for the 1024 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(1024,512,8) + +/** + @brief Initialization function for the 512 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(512,256,16) + +/** + @brief Initialization function for the 256 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(256,128,32) + +/** + @brief Initialization function for the 128 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(128,64,64) + +/** + @brief Initialization function for the 64 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(64,32,128) + +/** + @brief Initialization function for the 32 pt Q15 real FFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q15(32,16,256) + +/** + @brief Generic initialization function for the Q15 RFFT/RIFFT. + @param[in,out] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] fftLenReal length of the FFT + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par Details + The parameter fftLenReal specifies length of RFFT/RIFFT Process. + Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192. + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + + */ +#if defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_q15( + arm_rfft_instance_q15 * S, + uint32_t fftLenReal) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialization of coef modifier depending on the FFT length */ + switch (fftLenReal) + { + case 8192U: + status = arm_rfft_init_8192_q15( S ); + break; + case 4096U: + status = arm_rfft_init_4096_q15( S ); + break; + case 2048U: + status = arm_rfft_init_2048_q15( S ); + break; + case 1024U: + status = arm_rfft_init_1024_q15( S ); + break; + case 512U: + status = arm_rfft_init_512_q15( S ); + break; + case 256U: + status = arm_rfft_init_256_q15( S ); + break; + case 128U: + status = arm_rfft_init_128_q15( S ); + break; + case 64U: + status = arm_rfft_init_64_q15( S ); + break; + case 32U: + status = arm_rfft_init_32_q15( S ); + break; + default: + /* Reporting argument error if rfftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + /* return the status of RFFT Init function */ + return (status); +} +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_q15( + arm_rfft_instance_q15 * S, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + + /* Initialization of coef modifier depending on the FFT length */ + switch (fftLenReal) + { + case 8192U: + status = arm_rfft_init_8192_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 4096U: + status = arm_rfft_init_4096_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 2048U: + status = arm_rfft_init_2048_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 1024U: + status = arm_rfft_init_1024_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 512U: + status = arm_rfft_init_512_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 256U: + status = arm_rfft_init_256_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 128U: + status = arm_rfft_init_128_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 64U: + status = arm_rfft_init_64_q15( S,ifftFlagR,bitReverseFlag ); + break; + case 32U: + status = arm_rfft_init_32_q15( S,ifftFlagR,bitReverseFlag ); + break; + default: + /* Reporting argument error if rfftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + /* return the status of RFFT Init function */ + return (status); +} +#endif + +/** + @} end of RealFFTQ15 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_init_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_init_q31.c new file mode 100755 index 0000000..76fbcd1 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_init_q31.c @@ -0,0 +1,482 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_init_q31.c + * Description: RFFT & RIFFT Q31 initialisation function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + +/** + @ingroup RealFFT +*/ + +/** + @defgroup RealFFTQ31 Real FFT Q31 Functions +*/ + +/** + @addtogroup RealFFTQ31 + @{ + */ + + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) +#define RFFTINIT_Q31(LEN,CFFTLEN,TWIDMOD) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_##LEN##_q31( arm_rfft_instance_q31 * S, \ + uint32_t ifftFlagR, \ + uint32_t bitReverseFlag ) \ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_ARGUMENT_ERROR; \ + \ + /* Initialize the Real FFT length */ \ + S->fftLenReal = (uint16_t) LEN; \ + \ + /* Initialize the Twiddle coefficientA pointer */ \ + S->pTwiddleAReal = (q31_t *) realCoefAQ31; \ + \ + /* Initialize the Twiddle coefficientB pointer */ \ + S->pTwiddleBReal = (q31_t *) realCoefBQ31; \ + \ + /* Initialize the Flag for selection of RFFT or RIFFT */ \ + S->ifftFlagR = (uint8_t) ifftFlagR; \ + \ + /* Initialize the Flag for calculation Bit reversal or not */\ + S->bitReverseFlagR = (uint8_t) bitReverseFlag; \ + \ + S->twidCoefRModifier = TWIDMOD; \ + \ + status=arm_cfft_init_##CFFTLEN##_q31(&(S->cfftInst)); \ + \ + /* return the status of RFFT Init function */ \ + return (status); \ +} +#elif defined(ARM_MATH_NEON) +#define RFFTINIT_Q31(LEN,CFFTLEN,TWIDMOD) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_##LEN##_q31( arm_rfft_instance_q31 * S )\ +{ \ + /* Initialise the default arm status */ \ + arm_status status = ARM_MATH_SUCCESS; \ + S->nfft = LEN; \ + S->ncfft = LEN >> 1; \ + \ + S->twiddles = arm_neon_rfft_twiddles_##LEN##_q31; \ + S->factors = arm_neon_rfft_factors_##LEN##_q31; \ + \ + S->super_twiddles = arm_neon_rfft_super_twiddles_neon_##LEN##_q31; \ + \ + /* return the status of RFFT Init function */ \ + return (status); \ +} +#include "arm_neon_tables.h" + + +#else +#define RFFTINIT_Q31(LEN,CFFTLEN,TWIDMOD) \ +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_##LEN##_q31( arm_rfft_instance_q31 * S, \ + uint32_t ifftFlagR, \ + uint32_t bitReverseFlag ) \ +{ \ + /* Initialize the Real FFT length */ \ + S->fftLenReal = (uint16_t) LEN; \ + \ + /* Initialize the Twiddle coefficientA pointer */ \ + S->pTwiddleAReal = (q31_t *) realCoefAQ31; \ + \ + /* Initialize the Twiddle coefficientB pointer */ \ + S->pTwiddleBReal = (q31_t *) realCoefBQ31; \ + \ + /* Initialize the Flag for selection of RFFT or RIFFT */ \ + S->ifftFlagR = (uint8_t) ifftFlagR; \ + \ + /* Initialize the Flag for calculation Bit reversal or not */\ + S->bitReverseFlagR = (uint8_t) bitReverseFlag; \ + \ + S->twidCoefRModifier = TWIDMOD; \ + \ + S->pCfft = &arm_cfft_sR_q31_len##CFFTLEN; \ + \ + /* return the status of RFFT Init function */ \ + return (ARM_MATH_SUCCESS); \ +} +#endif + + +/** + @brief Initialization function for the 8192 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(8192,4096,1) + +/** + @brief Initialization function for the 4096 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(4096,2048,2) + +/** + @brief Initialization function for the 2048 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(2048,1024,4) + +/** + @brief Initialization function for the 1024 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(1024,512,8) + +/** + @brief Initialization function for the 512 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(512,256,16) + +/** + @brief Initialization function for the 256 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(256,128,32) + +/** + @brief Initialization function for the 128 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(128,64,64) + +/** + @brief Initialization function for the 64 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(64,32,128) + +/** + @brief Initialization function for the 32 pt Q31 real FFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + */ +RFFTINIT_Q31(32,16,256) + + +/** + @brief Generic initialization function for the Q31 RFFT/RIFFT. + @param[in,out] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] fftLenReal length of the FFT + @param[in] ifftFlagR flag that selects transform direction + - value = 0: forward transform + - value = 1: inverse transform + @param[in] bitReverseFlag flag that enables / disables bit reversal of output + - value = 0: disables bit reversal of output + - value = 1: enables bit reversal of output + @return execution status + - \ref ARM_MATH_SUCCESS : Operation successful + - \ref ARM_MATH_ARGUMENT_ERROR : fftLenReal is not a supported length + + @par Details + The parameter fftLenReal specifies length of RFFT/RIFFT Process. + Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192. + @par + The parameter ifftFlagR controls whether a forward or inverse transform is computed. + Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. + @par + The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. + Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order. + @par + This function also initializes Twiddle factor table. + @par + This function should be used only if you don't know the FFT sizes that + you'll need at build time. The use of this function will prevent the + linker from removing the FFT tables that are not needed and the library + code size will be bigger than needed. + @par + If you use CMSIS-DSP as a static library, and if you know the FFT sizes + that you need at build time, then it is better to use the initialization + functions defined for each FFT size. + +*/ +#if defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_q31( + arm_rfft_instance_q31 * S, + uint32_t fftLenReal) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + /* Initialization of coef modifier depending on the FFT length */ + switch (fftLenReal) + { + case 8192U: + status = arm_rfft_init_8192_q31( S ); + break; + case 4096U: + status = arm_rfft_init_4096_q31( S ); + break; + case 2048U: + status = arm_rfft_init_2048_q31( S ); + break; + case 1024U: + status = arm_rfft_init_1024_q31( S ); + break; + case 512U: + status = arm_rfft_init_512_q31( S ); + break; + case 256U: + status = arm_rfft_init_256_q31( S ); + break; + case 128U: + status = arm_rfft_init_128_q31( S ); + break; + case 64U: + status = arm_rfft_init_64_q31( S ); + break; + case 32U: + status = arm_rfft_init_32_q31( S ); + break; + default: + /* Reporting argument error if rfftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + /* return the status of RFFT Init function */ + return (status); +} +#else +ARM_DSP_ATTRIBUTE arm_status arm_rfft_init_q31( + arm_rfft_instance_q31 * S, + uint32_t fftLenReal, + uint32_t ifftFlagR, + uint32_t bitReverseFlag) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_ARGUMENT_ERROR; + /* Initialization of coef modifier depending on the FFT length */ + switch (fftLenReal) + { + case 8192U: + status = arm_rfft_init_8192_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 4096U: + status = arm_rfft_init_4096_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 2048U: + status = arm_rfft_init_2048_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 1024U: + status = arm_rfft_init_1024_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 512U: + status = arm_rfft_init_512_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 256U: + status = arm_rfft_init_256_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 128U: + status = arm_rfft_init_128_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 64U: + status = arm_rfft_init_64_q31( S,ifftFlagR,bitReverseFlag ); + break; + case 32U: + status = arm_rfft_init_32_q31( S,ifftFlagR,bitReverseFlag ); + break; + default: + /* Reporting argument error if rfftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + /* return the status of RFFT Init function */ + return (status); +} +#endif /* neon */ +/** + @} end of RealFFTQ31 group + */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_q15.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_q15.c new file mode 100755 index 0000000..cf52c5e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_q15.c @@ -0,0 +1,585 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_q15.c + * Description: RFFT & RIFFT Q15 process function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +/* ---------------------------------------------------------------------- + * Internal functions prototypes + * -------------------------------------------------------------------- */ + +#if !defined(ARM_MATH_NEON) + +ARM_DSP_ATTRIBUTE void arm_split_rfft_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pATable, + const q15_t * pBTable, + q15_t * pDst, + uint32_t modifier); + +ARM_DSP_ATTRIBUTE void arm_split_rifft_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pATable, + const q15_t * pBTable, + q15_t * pDst, + uint32_t modifier); +#endif + +/** + @addtogroup RealFFTQ15 + @{ + */ + +/** + @brief Processing function for the Q15 RFFT/RIFFT. + @param[in] S points to an instance of the Q15 RFFT/RIFFT structure + @param[in] pSrc points to input buffer (Source buffer is modified by this function.) + @param[out] pDst points to output buffer + + @par Input an output formats + Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. + Hence the output format is different for different RFFT sizes. + The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT: + @par Input and Output formats for RFFT Q15 + +| RFFT Size | Input Format | Output Format | Number of bits to upscale | +| ---------: | ------------: | -------------: | ------------------------: | +| 32 | 1.15 | 6.10 | 5 | +| 64 | 1.15 | 7.9 | 6 | +| 128 | 1.15 | 8.8 | 7 | +| 256 | 1.15 | 9.7 | 8 | +| 512 | 1.15 | 10.6 | 9 | +| 1024 | 1.15 | 11.5 | 10 | +| 2048 | 1.15 | 12.4 | 11 | +| 4096 | 1.15 | 13.3 | 12 | +| 8192 | 1.15 | 14.2 | 13 | + + @par Input and Output formats for RIFFT Q15 + +| RIFFT Size | Input Format | Output Format | Number of bits to upscale | +| ----------: | ------------: | -------------: | ------------------------: | +| 32 | 1.15 | 6.10 | 0 | +| 64 | 1.15 | 7.9 | 0 | +| 128 | 1.15 | 8.8 | 0 | +| 256 | 1.15 | 9.7 | 0 | +| 512 | 1.15 | 10.6 | 0 | +| 1024 | 1.15 | 11.5 | 0 | +| 2048 | 1.15 | 12.4 | 0 | +| 4096 | 1.15 | 13.3 | 0 | +| 8192 | 1.15 | 14.2 | 0 | + + + + @par Neon implementation + A temporary buffer is required + + @code + void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + q15_t *tmp, + uint8_t ifftFlag + ) + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ + +#if defined(ARM_MATH_NEON) +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + + +ARM_DSP_ATTRIBUTE void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + const q15_t * pSrc, + q15_t * pDst, + q15_t *tmp, + uint8_t ifftFlag + ) +{ + if (ifftFlag) + { + arm_ne10_fft_c2r_1d_int16_neon (pDst, + pSrc, + S, + 1, + tmp); + } + else + { + arm_ne10_fft_r2c_1d_int16_neon (pDst, + pSrc, + S, + 1, + tmp); + } +} +#else +ARM_DSP_ATTRIBUTE void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + q15_t * pSrc, + q15_t * pDst) +{ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + const arm_cfft_instance_q15 *S_CFFT = &(S->cfftInst); +#else + const arm_cfft_instance_q15 *S_CFFT = S->pCfft; +#endif + uint32_t L2 = S->fftLenReal >> 1U; + + /* Calculation of RIFFT of input */ + if (S->ifftFlagR == 1U) + { + /* Real IFFT core process */ + arm_split_rifft_q15 (pSrc, L2, S->pTwiddleAReal, S->pTwiddleBReal, pDst, S->twidCoefRModifier); + + /* Complex IFFT process */ + arm_cfft_q15 (S_CFFT, pDst, S->ifftFlagR, S->bitReverseFlagR); + + arm_shift_q15(pDst, 1, pDst, S->fftLenReal); + } + else + { + /* Calculation of RFFT of input */ + + /* Complex FFT process */ + arm_cfft_q15 (S_CFFT, pSrc, S->ifftFlagR, S->bitReverseFlagR); + + /* Real FFT core process */ + arm_split_rfft_q15 (pSrc, L2, S->pTwiddleAReal, S->pTwiddleBReal, pDst, S->twidCoefRModifier); + } + +} +#endif + +/** + @} end of RealFFTQ15 group + */ + +/** + @brief Core Real FFT process + @param[in] pSrc points to input buffer + @param[in] fftLen length of FFT + @param[in] pATable points to twiddle Coef A buffer + @param[in] pBTable points to twiddle Coef B buffer + @param[out] pDst points to output buffer + @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + + @par + The function implements a Real FFT + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" +#include "arm_vec_fft.h" + + +ARM_DSP_ATTRIBUTE void arm_split_rfft_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pATable, + const q15_t * pBTable, + q15_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q15_t *pOut1 = &pDst[2]; + q15_t *pIn1 = &pSrc[2]; + uint16x8_t offsetIn = { 6, 7, 4, 5, 2, 3, 0, 1 }; + uint16x8_t offsetCoef; + const uint16_t offsetCoefArr[16] = { + 0, 0, 2, 2, 4, 4, 6, 6, + 0, 1, 0, 1, 0, 1, 0, 1 + }; + + offsetCoef = vmulq_n_u16(vld1q_u16(offsetCoefArr), modifier) + vld1q_u16(offsetCoefArr + 8); + offsetIn = vaddq_n_u16(offsetIn, (2 * fftLen - 8)); + + /* Init coefficient pointers */ + pCoefA = &pATable[modifier * 2]; + pCoefB = &pBTable[modifier * 2]; + + const q15_t *pCoefAb, *pCoefBb; + pCoefAb = pCoefA; + pCoefBb = pCoefB; + + pIn1 = &pSrc[2]; + + i = fftLen - 1U; + i = i / 4 + 1; + while (i > 0U) { + q15x8_t in1 = vld1q_s16(pIn1); + q15x8_t in2 = vldrhq_gather_shifted_offset_s16(pSrc, offsetIn); + q15x8_t coefA = vldrhq_gather_shifted_offset_s16(pCoefAb, offsetCoef); + q15x8_t coefB = vldrhq_gather_shifted_offset_s16(pCoefBb, offsetCoef); + + + q15x8_t out = vhaddq_s16(MVE_CMPLX_MULT_FX_AxB(in1, coefA, q15x8_t), + MVE_CMPLX_MULT_FX_AxConjB(coefB, in2, q15x8_t)); + vst1q_s16(pOut1, out); + pOut1 += 8; + + offsetCoef = vaddq_n_u16(offsetCoef, modifier * 8); + offsetIn -= 8; + pIn1 += 8; + i -= 1; + } + + pDst[2 * fftLen] = (pSrc[0] - pSrc[1]) >> 1U; + pDst[2 * fftLen + 1] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1U; + pDst[1] = 0; +} +#elif !defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_split_rfft_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pATable, + const q15_t * pBTable, + q15_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + q31_t outR, outI; /* Temporary variables for output */ + const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q15_t *pSrc1, *pSrc2; +#if defined (ARM_MATH_DSP) + q15_t *pD1, *pD2; +#endif + + /* Init coefficient pointers */ + pCoefA = &pATable[modifier * 2]; + pCoefB = &pBTable[modifier * 2]; + + pSrc1 = &pSrc[2]; + pSrc2 = &pSrc[(2U * fftLen) - 2U]; + +#if defined (ARM_MATH_DSP) + + i = 1U; + pD1 = pDst + 2; + pD2 = pDst + (4U * fftLen) - 2; + + for (i = fftLen - 1; i > 0; i--) + { + /* + outR = ( pSrc[2 * i] * pATable[2 * i] + - pSrc[2 * i + 1] * pATable[2 * i + 1] + + pSrc[2 * n - 2 * i] * pBTable[2 * i] + + pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]); + + outI = ( pIn[2 * i + 1] * pATable[2 * i] + + pIn[2 * i] * pATable[2 * i + 1] + + pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i]) + */ + + +#ifndef ARM_MATH_BIG_ENDIAN + /* pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1] */ + outR = __SMUSD(read_q15x2 (pSrc1), read_q15x2((q15_t *) pCoefA)); +#else + /* -(pSrc[2 * i + 1] * pATable[2 * i + 1] - pSrc[2 * i] * pATable[2 * i]) */ + outR = -(__SMUSD(read_q15x2 (pSrc1), read_q15x2((q15_t *) pCoefA))); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* pSrc[2 * n - 2 * i] * pBTable[2 * i] + pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */ + outR = __SMLAD(read_q15x2 (pSrc2), read_q15x2((q15_t *) pCoefB), outR) >> 16U; + + /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] - pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */ +#ifndef ARM_MATH_BIG_ENDIAN + outI = __SMUSDX(read_q15x2_da (&pSrc2), read_q15x2((q15_t *) pCoefB)); +#else + outI = __SMUSDX(read_q15x2 ((q15_t *) pCoefB), read_q15x2_da (&pSrc2)); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] */ + outI = __SMLADX(read_q15x2_ia (&pSrc1), read_q15x2 ((q15_t *) pCoefA), outI); + + /* write output */ + *pD1++ = (q15_t) outR; + *pD1++ = outI >> 16U; + + /* write complex conjugate output */ + pD2[0] = (q15_t) outR; + pD2[1] = -(outI >> 16U); + pD2 -= 2; + + /* update coefficient pointer */ + pCoefB = pCoefB + (2U * modifier); + pCoefA = pCoefA + (2U * modifier); + } + + pDst[2U * fftLen] = (pSrc[0] - pSrc[1]) >> 1U; + pDst[2U * fftLen + 1U] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1U; + pDst[1] = 0; + +#else + + i = 1U; + + while (i < fftLen) + { + /* + outR = ( pSrc[2 * i] * pATable[2 * i] + - pSrc[2 * i + 1] * pATable[2 * i + 1] + + pSrc[2 * n - 2 * i] * pBTable[2 * i] + + pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]); + */ + + outR = *pSrc1 * *pCoefA; + outR = outR - (*(pSrc1 + 1) * *(pCoefA + 1)); + outR = outR + (*pSrc2 * *pCoefB); + outR = (outR + (*(pSrc2 + 1) * *(pCoefB + 1))) >> 16; + + /* + outI = ( pIn[2 * i + 1] * pATable[2 * i] + + pIn[2 * i] * pATable[2 * i + 1] + + pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); + */ + + outI = *pSrc2 * *(pCoefB + 1); + outI = outI - (*(pSrc2 + 1) * *pCoefB); + outI = outI + (*(pSrc1 + 1) * *pCoefA); + outI = outI + (*pSrc1 * *(pCoefA + 1)); + + /* update input pointers */ + pSrc1 += 2U; + pSrc2 -= 2U; + + /* write output */ + pDst[2U * i] = (q15_t) outR; + pDst[2U * i + 1U] = outI >> 16U; + + /* write complex conjugate output */ + pDst[(4U * fftLen) - (2U * i)] = (q15_t) outR; + pDst[((4U * fftLen) - (2U * i)) + 1U] = -(outI >> 16U); + + /* update coefficient pointer */ + pCoefB = pCoefB + (2U * modifier); + pCoefA = pCoefA + (2U * modifier); + + i++; + } + + pDst[2U * fftLen] = (pSrc[0] - pSrc[1]) >> 1; + pDst[2U * fftLen + 1U] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1; + pDst[1] = 0; + +#endif /* #if defined (ARM_MATH_DSP) */ +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @brief Core Real IFFT process + @param[in] pSrc points to input buffer + @param[in] fftLen length of FFT + @param[in] pATable points to twiddle Coef A buffer + @param[in] pBTable points to twiddle Coef B buffer + @param[out] pDst points to output buffer + @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + + @par + The function implements a Real IFFT + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" +#include "arm_vec_fft.h" + +ARM_DSP_ATTRIBUTE void arm_split_rifft_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pATable, + const q15_t * pBTable, + q15_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q15_t *pIn1; + uint16x8_t offset = { 6, 7, 4, 5, 2, 3, 0, 1 }; + uint16x8_t offsetCoef; + int16x8_t conj = { 1, -1, 1, -1, 1, -1, 1, -1 }; /* conjugate */ + const uint16_t offsetCoefArr[16] = { + 0, 0, 2, 2, 4, 4, 6, 6, + 0, 1, 0, 1, 0, 1, 0, 1 + }; + + offsetCoef = vmulq_n_u16(vld1q_u16(offsetCoefArr), modifier) + vld1q_u16(offsetCoefArr + 8); + + offset = vaddq_n_u16(offset, (2 * fftLen - 6)); + + /* Init coefficient pointers */ + pCoefA = &pATable[0]; + pCoefB = &pBTable[0]; + + const q15_t *pCoefAb, *pCoefBb; + pCoefAb = pCoefA; + pCoefBb = pCoefB; + + pIn1 = &pSrc[0]; + + i = fftLen; + i = i / 4; + + while (i > 0U) { + q15x8_t in1 = vld1q_s16(pIn1); + q15x8_t in2 = vldrhq_gather_shifted_offset_s16(pSrc, offset); + q15x8_t coefA = vldrhq_gather_shifted_offset_s16(pCoefAb, offsetCoef); + q15x8_t coefB = vldrhq_gather_shifted_offset_s16(pCoefBb, offsetCoef); + + /* can we avoid the conjugate here ? */ + q15x8_t out = vhaddq_s16(MVE_CMPLX_MULT_FX_AxConjB(in1, coefA, q15x8_t), + vmulq(conj, MVE_CMPLX_MULT_FX_AxB(in2, coefB, q15x8_t))); + + vst1q_s16(pDst, out); + pDst += 8; + + offsetCoef = vaddq_n_u16(offsetCoef, modifier * 8); + offset -= 8; + + pIn1 += 8; + i -= 1; + } +} +#elif !defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_split_rifft_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pATable, + const q15_t * pBTable, + q15_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + q31_t outR, outI; /* Temporary variables for output */ + const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q15_t *pSrc1, *pSrc2; + q15_t *pDst1 = &pDst[0]; + + pCoefA = &pATable[0]; + pCoefB = &pBTable[0]; + + pSrc1 = &pSrc[0]; + pSrc2 = &pSrc[2 * fftLen]; + + i = fftLen; + while (i > 0U) + { + /* + outR = ( pIn[2 * i] * pATable[2 * i] + + pIn[2 * i + 1] * pATable[2 * i + 1] + + pIn[2 * n - 2 * i] * pBTable[2 * i] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]); + + outI = ( pIn[2 * i + 1] * pATable[2 * i] + - pIn[2 * i] * pATable[2 * i + 1] + - pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); + */ + +#if defined (ARM_MATH_DSP) + +#ifndef ARM_MATH_BIG_ENDIAN + /* pIn[2 * n - 2 * i] * pBTable[2 * i] - pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */ + outR = __SMUSD(read_q15x2(pSrc2), read_q15x2((q15_t *) pCoefB)); +#else + /* -(-pIn[2 * n - 2 * i] * pBTable[2 * i] + pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1])) */ + outR = -(__SMUSD(read_q15x2(pSrc2), read_q15x2((q15_t *) pCoefB))); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] + pIn[2 * n - 2 * i] * pBTable[2 * i] */ + outR = __SMLAD(read_q15x2(pSrc1), read_q15x2 ((q15_t *) pCoefA), outR) >> 16U; + + /* -pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */ + outI = __SMUADX(read_q15x2_da (&pSrc2), read_q15x2((q15_t *) pCoefB)); + + /* pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] */ +#ifndef ARM_MATH_BIG_ENDIAN + outI = __SMLSDX(read_q15x2 ((q15_t *) pCoefA), read_q15x2_ia (&pSrc1), -outI); +#else + outI = __SMLSDX(read_q15x2_ia (&pSrc1), read_q15x2 ((q15_t *) pCoefA), -outI); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* write output */ +#ifndef ARM_MATH_BIG_ENDIAN + write_q15x2_ia (&pDst1, __PKHBT(outR, (outI >> 16U), 16)); +#else + write_q15x2_ia (&pDst1, __PKHBT((outI >> 16U), outR, 16)); +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + +#else /* #if defined (ARM_MATH_DSP) */ + + outR = *pSrc2 * *pCoefB; + outR = outR - (*(pSrc2 + 1) * *(pCoefB + 1)); + outR = outR + (*pSrc1 * *pCoefA); + outR = (outR + (*(pSrc1 + 1) * *(pCoefA + 1))) >> 16; + + outI = *(pSrc1 + 1) * *pCoefA; + outI = outI - (*pSrc1 * *(pCoefA + 1)); + outI = outI - (*pSrc2 * *(pCoefB + 1)); + outI = outI - (*(pSrc2 + 1) * *(pCoefB)); + + /* update input pointers */ + pSrc1 += 2U; + pSrc2 -= 2U; + + /* write output */ + *pDst1++ = (q15_t) outR; + *pDst1++ = (q15_t) (outI >> 16); + +#endif /* #if defined (ARM_MATH_DSP) */ + + /* update coefficient pointer */ + pCoefB = pCoefB + (2 * modifier); + pCoefA = pCoefA + (2 * modifier); + + i--; + } + +} +#endif /* defined(ARM_MATH_MVEI) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_q31.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_q31.c new file mode 100755 index 0000000..963f0a2 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_rfft_q31.c @@ -0,0 +1,481 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_q31.c + * Description: FFT & RIFFT Q31 process function + * + * $Date: 23 April 2021 + * $Revision: V1.9.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/transform_functions.h" + +/* ---------------------------------------------------------------------- + * Internal functions prototypes + * -------------------------------------------------------------------- */ + +#if !defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_split_rfft_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pATable, + const q31_t * pBTable, + q31_t * pDst, + uint32_t modifier); + +ARM_DSP_ATTRIBUTE void arm_split_rifft_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pATable, + const q31_t * pBTable, + q31_t * pDst, + uint32_t modifier); +#endif +/** + @addtogroup RealFFTQ31 + @{ + */ + +/** + @brief Processing function for the Q31 RFFT/RIFFT. + @param[in] S points to an instance of the Q31 RFFT/RIFFT structure + @param[in] pSrc points to input buffer (Source buffer is modified by this function) + @param[out] pDst points to output buffer + + @par Input an output formats + Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. + Hence the output format is different for different RFFT sizes. + The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT: + @par Input and Output formats for RFFT Q31 + +| RFFT Size | Input Format | Output Format | Number of bits to upscale | +| ---------: | ------------: | -------------: | ------------------------: | +| 32 | 1.31 | 6.26 | 5 | +| 64 | 1.31 | 7.25 | 6 | +| 128 | 1.31 | 8.24 | 7 | +| 256 | 1.31 | 9.23 | 8 | +| 512 | 1.31 | 10.22 | 9 | +| 1024 | 1.31 | 11.21 | 10 | +| 2048 | 1.31 | 12.20 | 11 | +| 4096 | 1.31 | 13.19 | 12 | +| 8192 | 1.31 | 14.18 | 13 | + + @par Input and Output formats for RIFFT Q31 + +| RIFFT Size | Input Format | Output Format | Number of bits to upscale | +| ----------: | ------------: | -------------: | ------------------------: | +| 32 | 1.31 | 6.26 | 0 | +| 64 | 1.31 | 7.25 | 0 | +| 128 | 1.31 | 8.24 | 0 | +| 256 | 1.31 | 9.23 | 0 | +| 512 | 1.31 | 10.22 | 0 | +| 1024 | 1.31 | 11.21 | 0 | +| 2048 | 1.31 | 12.20 | 0 | +| 4096 | 1.31 | 13.19 | 0 | +| 8192 | 1.31 | 14.18 | 0 | + + + @par Neon implementation + A temporary buffer is needed + + @code + void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + q31_t *tmp, + uint8_t ifftFlag + ) + @endcode + + @par Size of buffers according to the target architecture and datatype: + They are described on the page \ref transformbuffers "transform buffers". + + */ + +#if defined(ARM_MATH_NEON) +#include "CMSIS_NE10_types.h" +#include "CMSIS_NE10_fft.h" + + +ARM_DSP_ATTRIBUTE void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + const q31_t * pSrc, + q31_t * pDst, + q31_t *tmp, + uint8_t ifftFlag + ) +{ + if (ifftFlag) + { + arm_ne10_fft_c2r_1d_int32_neon (pDst, + pSrc, + S, + 1, + tmp); + } + else + { + arm_ne10_fft_r2c_1d_int32_neon (pDst, + pSrc, + S, + 1, + tmp); + } +} +#else +ARM_DSP_ATTRIBUTE void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + q31_t * pSrc, + q31_t * pDst) +{ +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + const arm_cfft_instance_q31 *S_CFFT = &(S->cfftInst); +#else + const arm_cfft_instance_q31 *S_CFFT = S->pCfft; +#endif + uint32_t L2 = S->fftLenReal >> 1U; + + /* Calculation of RIFFT of input */ + if (S->ifftFlagR == 1U) + { + /* Real IFFT core process */ + arm_split_rifft_q31 (pSrc, L2, S->pTwiddleAReal, S->pTwiddleBReal, pDst, S->twidCoefRModifier); + + /* Complex IFFT process */ + arm_cfft_q31 (S_CFFT, pDst, S->ifftFlagR, S->bitReverseFlagR); + + arm_shift_q31(pDst, 1, pDst, S->fftLenReal); + } + else + { + /* Calculation of RFFT of input */ + + /* Complex FFT process */ + arm_cfft_q31 (S_CFFT, pSrc, S->ifftFlagR, S->bitReverseFlagR); + + /* Real FFT core process */ + arm_split_rfft_q31 (pSrc, L2, S->pTwiddleAReal, S->pTwiddleBReal, pDst, S->twidCoefRModifier); + } + +} + +#endif +/** + @} end of RealFFTQ31 group + */ + +/** + @brief Core Real FFT process + @param[in] pSrc points to input buffer + @param[in] fftLen length of FFT + @param[in] pATable points to twiddle Coef A buffer + @param[in] pBTable points to twiddle Coef B buffer + @param[out] pDst points to output buffer + @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +#include "arm_helium_utils.h" +#include "arm_vec_fft.h" + + +ARM_DSP_ATTRIBUTE void arm_split_rfft_q31( + q31_t *pSrc, + uint32_t fftLen, + const q31_t *pATable, + const q31_t *pBTable, + q31_t *pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + const q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q31_t *pOut1 = &pDst[2]; + q31_t *pIn1 = &pSrc[2]; + uint32x4_t offset = { 2, 3, 0, 1 }; + uint32x4_t offsetCoef = { 0, 1, modifier * 2, modifier * 2 + 1 }; + + offset = offset + (2 * fftLen - 4); + + + /* Init coefficient pointers */ + pCoefA = &pATable[modifier * 2]; + pCoefB = &pBTable[modifier * 2]; + + const q31_t *pCoefAb, *pCoefBb; + pCoefAb = pCoefA; + pCoefBb = pCoefB; + + pIn1 = &pSrc[2]; + + i = fftLen - 1U; + i = i / 2 + 1; + while (i > 0U) { + q31x4_t in1 = vld1q_s32(pIn1); + q31x4_t in2 = vldrwq_gather_shifted_offset_s32(pSrc, offset); + q31x4_t coefA = vldrwq_gather_shifted_offset_s32(pCoefAb, offsetCoef); + q31x4_t coefB = vldrwq_gather_shifted_offset_s32(pCoefBb, offsetCoef); + + q31x4_t out = vhaddq_s32(MVE_CMPLX_MULT_FX_AxB(in1, coefA, q31x4_t), + MVE_CMPLX_MULT_FX_AxConjB(coefB, in2, q31x4_t)); + vst1q(pOut1, out); + pOut1 += 4; + + offsetCoef += modifier * 4; + offset -= 4; + + pIn1 += 4; + i -= 1; + } + + pDst[2 * fftLen] = (pSrc[0] - pSrc[1]) >> 1U; + pDst[2 * fftLen + 1] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1U; + pDst[1] = 0; +} +#elif !defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_split_rfft_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pATable, + const q31_t * pBTable, + q31_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + q31_t outR, outI; /* Temporary variables for output */ + const q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q31_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */ + q31_t *pOut1 = &pDst[2], *pOut2 = &pDst[4 * fftLen - 1]; + q31_t *pIn1 = &pSrc[2], *pIn2 = &pSrc[2 * fftLen - 1]; + + /* Init coefficient pointers */ + pCoefA = &pATable[modifier * 2]; + pCoefB = &pBTable[modifier * 2]; + + i = fftLen - 1U; + + while (i > 0U) + { + /* + outR = ( pSrc[2 * i] * pATable[2 * i] + - pSrc[2 * i + 1] * pATable[2 * i + 1] + + pSrc[2 * n - 2 * i] * pBTable[2 * i] + + pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]); + + outI = ( pIn[2 * i + 1] * pATable[2 * i] + + pIn[2 * i] * pATable[2 * i + 1] + + pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); + */ + + CoefA1 = *pCoefA++; + CoefA2 = *pCoefA; + + /* outR = (pSrc[2 * i] * pATable[2 * i] */ + mult_32x32_keep32_R (outR, *pIn1, CoefA1); + + /* outI = pIn[2 * i] * pATable[2 * i + 1] */ + mult_32x32_keep32_R (outI, *pIn1++, CoefA2); + + /* - pSrc[2 * i + 1] * pATable[2 * i + 1] */ + multSub_32x32_keep32_R (outR, *pIn1, CoefA2); + + /* (pIn[2 * i + 1] * pATable[2 * i] */ + multAcc_32x32_keep32_R (outI, *pIn1++, CoefA1); + + /* pSrc[2 * n - 2 * i] * pBTable[2 * i] */ + multSub_32x32_keep32_R (outR, *pIn2, CoefA2); + CoefB1 = *pCoefB; + + /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */ + multSub_32x32_keep32_R (outI, *pIn2--, CoefB1); + + /* pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */ + multAcc_32x32_keep32_R (outR, *pIn2, CoefB1); + + /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */ + multSub_32x32_keep32_R (outI, *pIn2--, CoefA2); + + /* write output */ + *pOut1++ = outR; + *pOut1++ = outI; + + /* write complex conjugate output */ + *pOut2-- = -outI; + *pOut2-- = outR; + + /* update coefficient pointer */ + pCoefB = pCoefB + (2 * modifier); + pCoefA = pCoefA + (2 * modifier - 1); + + /* Decrement loop count */ + i--; + } + + pDst[2 * fftLen] = (pSrc[0] - pSrc[1]) >> 1U; + pDst[2 * fftLen + 1] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1U; + pDst[1] = 0; +} +#endif /* defined(ARM_MATH_MVEI) */ + +/** + @brief Core Real IFFT process + @param[in] pSrc points to input buffer + @param[in] fftLen length of FFT + @param[in] pATable points to twiddle Coef A buffer + @param[in] pBTable points to twiddle Coef B buffer + @param[out] pDst points to output buffer + @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table + */ + +#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE) + +ARM_DSP_ATTRIBUTE void arm_split_rifft_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pATable, + const q31_t * pBTable, + q31_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + const q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q31_t *pIn1; + uint32x4_t offset = { 2, 3, 0, 1 }; + uint32x4_t offsetCoef = { 0, 1, modifier * 2, modifier * 2 + 1 }; + int32x4_t conj = { 1, -1, 1, -1 }; + + offset = offset + (2 * fftLen - 2); + + /* Init coefficient pointers */ + pCoefA = &pATable[0]; + pCoefB = &pBTable[0]; + + const q31_t *pCoefAb, *pCoefBb; + pCoefAb = pCoefA; + pCoefBb = pCoefB; + + pIn1 = &pSrc[0]; + + i = fftLen; + i = i >> 1; + while (i > 0U) { + q31x4_t in1 = vld1q_s32(pIn1); + q31x4_t in2 = vldrwq_gather_shifted_offset_s32(pSrc, offset); + q31x4_t coefA = vldrwq_gather_shifted_offset_s32(pCoefAb, offsetCoef); + q31x4_t coefB = vldrwq_gather_shifted_offset_s32(pCoefBb, offsetCoef); + + /* can we avoid the conjugate here ? */ + q31x4_t out = vhaddq_s32(MVE_CMPLX_MULT_FX_AxConjB(in1, coefA, q31x4_t), + vmulq_s32(conj, MVE_CMPLX_MULT_FX_AxB(in2, coefB, q31x4_t))); + + vst1q_s32(pDst, out); + pDst += 4; + + offsetCoef += modifier * 4; + offset -= 4; + + pIn1 += 4; + i -= 1; + } +} +#elif !defined(ARM_MATH_NEON) +ARM_DSP_ATTRIBUTE void arm_split_rifft_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pATable, + const q31_t * pBTable, + q31_t * pDst, + uint32_t modifier) +{ + q31_t outR, outI; /* Temporary variables for output */ + const q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q31_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */ + q31_t *pIn1 = &pSrc[0], *pIn2 = &pSrc[2 * fftLen + 1]; + + pCoefA = &pATable[0]; + pCoefB = &pBTable[0]; + + while (fftLen > 0U) + { + /* + outR = ( pIn[2 * i] * pATable[2 * i] + + pIn[2 * i + 1] * pATable[2 * i + 1] + + pIn[2 * n - 2 * i] * pBTable[2 * i] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]); + + outI = ( pIn[2 * i + 1] * pATable[2 * i] + - pIn[2 * i] * pATable[2 * i + 1] + - pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + - pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); + */ + + CoefA1 = *pCoefA++; + CoefA2 = *pCoefA; + + /* outR = (pIn[2 * i] * pATable[2 * i] */ + mult_32x32_keep32_R (outR, *pIn1, CoefA1); + + /* - pIn[2 * i] * pATable[2 * i + 1] */ + mult_32x32_keep32_R (outI, *pIn1++, -CoefA2); + + /* pIn[2 * i + 1] * pATable[2 * i + 1] */ + multAcc_32x32_keep32_R (outR, *pIn1, CoefA2); + + /* pIn[2 * i + 1] * pATable[2 * i] */ + multAcc_32x32_keep32_R (outI, *pIn1++, CoefA1); + + /* pIn[2 * n - 2 * i] * pBTable[2 * i] */ + multAcc_32x32_keep32_R (outR, *pIn2, CoefA2); + CoefB1 = *pCoefB; + + /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */ + multSub_32x32_keep32_R (outI, *pIn2--, CoefB1); + + /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */ + multAcc_32x32_keep32_R (outR, *pIn2, CoefB1); + + /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */ + multAcc_32x32_keep32_R (outI, *pIn2--, CoefA2); + + /* write output */ + *pDst++ = outR; + *pDst++ = outI; + + /* update coefficient pointer */ + pCoefB = pCoefB + (modifier * 2); + pCoefA = pCoefA + (modifier * 2 - 1); + + /* Decrement loop count */ + fftLen--; + } + +} + +#endif /* defined(ARM_MATH_MVEI) */ diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_transform_buffer_sizes.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_transform_buffer_sizes.c new file mode 100755 index 0000000..00c0805 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/TransformFunctions/arm_transform_buffer_sizes.c @@ -0,0 +1,346 @@ +#include "dsp/transform_functions.h" + +/** + @ingroup groupTransforms +*/ + +/** + @defgroup TransformBuffers Transform Buffer Sizes + @par + Functions to get the sizes of the buffers in the different transform functions + according to the datatype and target architecture. + + @par + The current architecture for the build is defined in `ARM_MATH_DEFAULT_TARGET_ARCH` + + @note All returned lengths are in real numbers and never in complex. So, for a complex buffer of S samples, the + returned length will be 2*S. + +*/ + +/** + @ingroup TransformBuffers +*/ + +/** + @defgroup CFFTBuffers Buffer Sizes for CFFT +*/ + + + +/** + @addtogroup CFFTBuffers + @{ +*/ + +/** + * @brief Calculate required length for the temporary buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples Number of samples + * @param[in] buf_id Identification for the temporary buffer + * @return Length in datatype elements (real numbers) for the temporary buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +int32_t arm_cfft_tmp_buffer_size(arm_math_target_arch arch,arm_math_datatype dt, + uint32_t nb_samples, + uint32_t buf_id) +{ + if (arch == ARM_MATH_NEON_ARCH) + { + if (buf_id != 1) + { + return 0; + } + switch(dt) + { + case ARM_MATH_F16: + /* Return values in float hence factor 2 */ + return(nb_samples * 2U); + case ARM_MATH_F32: + /* Return values in float hence factor 2 */ + return(nb_samples * 2U); + case ARM_MATH_Q31: + /* Return values in float hence factor 2 */ + return(nb_samples * 2U); + case ARM_MATH_Q15: + /* Return values in float hence factor 2 */ + return(nb_samples * 2U); + default: + return(0); + } + } + else + { + return(0); + } +} + +/** + * @brief Calculate required length for the output buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples Number of samples in the input data + * @return Length in datatype elements (real numbers) for the output buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +int32_t arm_cfft_output_buffer_size(arm_math_target_arch arch,arm_math_datatype dt, + uint32_t nb_samples) +{ + (void)arch; + switch(dt) + { + default: + return(nb_samples * 2U); + } +} + +/** + * @brief Calculate required length for the output buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples Number of samples in the input data + * @return Length in datatype elements (real numbers) for the output buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +int32_t arm_cifft_output_buffer_size(arm_math_target_arch arch,arm_math_datatype dt, + uint32_t nb_samples) +{ + (void)arch; + switch(dt) + { + default: + return(nb_samples * 2U); + } +} + +/** +* @} end of CFFTBuffers group +*/ + +/** + @ingroup TransformBuffers +*/ + +/** + @defgroup RFFTBuffers Buffer Sizes for RFFT +*/ + + +/** + @addtogroup RFFTBuffers + @{ +*/ + +/** + * @brief Calculate required length for the temporary buffer for both RFFT and RIFFT + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples Number of samples in the input data + * @param[in] buf_id Identification for the temporary buffer + * @return Length in datatype elements (real numbers) for the temporary buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +int32_t arm_rfft_tmp_buffer_size(arm_math_target_arch arch,arm_math_datatype dt, + uint32_t nb_samples, + uint32_t buf_id) +{ + switch(dt) + { + case ARM_MATH_F32: + case ARM_MATH_F16: + if (arch == ARM_MATH_NEON_ARCH) + { + if (buf_id != 1) + { + return 0; + } + return(nb_samples); + } + else + { + return 0; + } + break; + case ARM_MATH_Q31: + case ARM_MATH_Q15: + if (arch == ARM_MATH_NEON_ARCH) + { + if (buf_id != 1) + { + return 0; + } + return(2*nb_samples); + } + else + { + return 0; + } + break; + default: + return(0); + } +} + +/** + * @brief Calculate required length for the output buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples Number of samples in the input data + * @return Length in datatype elements (real numbers) for the output buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +int32_t arm_rfft_output_buffer_size(arm_math_target_arch arch,arm_math_datatype dt, + uint32_t nb_samples) +{ + switch(dt) + { + case ARM_MATH_F64: + case ARM_MATH_F32: + case ARM_MATH_F16: + return(nb_samples); + break; + case ARM_MATH_Q31: + case ARM_MATH_Q15: + if (arch == ARM_MATH_NEON_ARCH) + { + return(nb_samples+2); + } + else if (arch == ARM_MATH_HELIUM_ARCH) + { + return(nb_samples+2); + } + else + { + return(2*nb_samples); + } + + break; + default: + return 0; + } +} + +/** + * @brief Calculate required length for the input buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples RFFT length in samples + * @return Length in datatype elements (real numbers) for the input buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + */ +int32_t arm_rifft_input_buffer_size(arm_math_target_arch arch,arm_math_datatype dt, + uint32_t nb_samples) +{ + (void)arch; + switch(dt) + { + case ARM_MATH_F64: + case ARM_MATH_F32: + case ARM_MATH_F16: + return(nb_samples); + break; + case ARM_MATH_Q31: + case ARM_MATH_Q15: + return(nb_samples+2); + break; + default: + return 0; + } +} + +/** +* @} end of RFFTBuffers group +*/ + +/** + @ingroup TransformBuffers +*/ + +/** + @defgroup MFCCBuffers Buffer Sizes for MFCC +*/ + + +/** + @addtogroup MFCCBuffers + @{ +*/ + +/** + * @brief Calculate required length for the temporary buffer + * @param[in] arch Target architecture identification + * @param[in] dt Data type of the input data + * @param[in] nb_samples Number of samples in the input data + * @param[in] buf_id Identification for the temporary buffer + * @param[in] use_cfft 1 if implementastion uses CFFT, 0 if RFFT + * @return Length in datatype elements (real numbers) for the temporary buffer + * + * @note 0 means not applicable (temporary buffer not needed) + * @note -1 means error : configuration not supported + * @note The define `ARM_MFCC_USE_CFFT` can be checked to know the current MFCC mode (CFFT or RFFT) for the build + */ +int32_t arm_mfcc_tmp_buffer_size(arm_math_target_arch arch, + arm_math_datatype dt, + uint32_t nb_samples, + uint32_t buf_id, + uint32_t use_cfft) +{ + if (arch == ARM_MATH_NEON_ARCH) + { + if (use_cfft==1) + { + // Neon implementation is forcing the RFFT mode + // So an error is returned for this configuration + return(-1); + } + + if ((buf_id != 1) && (buf_id != 2)) + { + return 0; + } + } + else + { + if (buf_id != 1) + { + return 0; + } + } + + + switch(buf_id) + { + case 1: + if (use_cfft == 1) + { + return(arm_cfft_output_buffer_size(arch,dt, nb_samples)); + } + else + { + return(arm_rfft_output_buffer_size(arch,dt, nb_samples)); + } + case 2: + return(arm_rfft_tmp_buffer_size(arch,dt, nb_samples, 1)); + default: + return(0); + } + + +} + +/** +* @} end of MFCCBuffers group +*/ \ No newline at end of file diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_bartlett_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_bartlett_f32.c new file mode 100755 index 0000000..70a228e --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_bartlett_f32.c @@ -0,0 +1,95 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_bartlett_f32.c + * Description: Floating-point (f32) Bartlett window + * + * $Date: 14 December 2022 + * $Revision: v1.15.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/window_functions.h" + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowBARTLETT Bartlett window function (26.5 dB) + + */ + +/** + @ingroup WindowBARTLETT + */ + +/** + @brief Bartlett window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 26.5 dB | + | Normalized equivalent noise bandwidth | 1.3333 bins | + | 3 dB bandwidth | 1.2736 bins | + | Flatness | -1.8242 dB | + | Recommended overlap | 50.0 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_bartlett_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i 1.0f) + { + w = 2.0f - w; + } + pDst[i] = w; + } +} + +/** + @} end of WindowNormal group + */ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_bartlett_f64.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_bartlett_f64.c new file mode 100755 index 0000000..e409ac5 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_bartlett_f64.c @@ -0,0 +1,91 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_bartlett_f64.c + * Description: Floating-point (f64) Bartlett window + * + * $Date: 14 December 2022 + * $Revision: v1.15.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/window_functions.h" + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowBARTLETT + */ + +/** + @brief Bartlett window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 26.5 dB | + | Normalized equivalent noise bandwidth | 1.3333 bins | + | 3 dB bandwidth | 1.2736 bins | + | Flatness | -1.8242 dB | + | Recommended overlap | 50.0 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_bartlett_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i 1.0) + { + w = 2.0 - w; + } + pDst[i] = w; + } +} + +/** + @} end of WindowNormal group + */ + diff --git a/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_blackman_harris_92db_f32.c b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_blackman_harris_92db_f32.c new file mode 100755 index 0000000..e432a71 --- /dev/null +++ b/Middlewares/Third_Party/ARM/ARM.CMSIS-DSP.1.17.1/Source/WindowFunctions/arm_blackman_harris_92db_f32.c @@ -0,0 +1,95 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_blackman_harris_92db_f32.c + * Description: Floating-point (f32) 92 dB Blackman Harris window + * + * $Date: 14 December 2022 + * $Revision: v1.15.0 + * + * Target Processor: Cortex-M and Cortex-A cores + * -------------------------------------------------------------------- */ + +/* + * Copyright (C) 2010-2022 ARM Limited or its affiliates. All rights reserved. + * + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the License); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an AS IS BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +#include "arm_compiler_specific.h" + + +#include "dsp/window_functions.h" +#include "dsp/fast_math_functions.h" +#include +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowBLACKMAN_HARRIS_92DB Blackman Harris window function (92 dB) + + */ + +/** + @ingroup WindowBLACKMAN_HARRIS_92DB + */ + +/** + @brief 92 dB Blackman Harris window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 92.0 dB | + | Normalized equivalent noise bandwidth | 2.0044 bins | + | 3 dB bandwidth | 1.8962 bins | + | Flatness | -0.8256 dB | + | Recommended overlap | 66.1 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_blackman_harris_92db_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowBLACKMAN_HARRIS_92DB + */ + +/** + @brief 92 dB Blackman Harris window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 92.0 dB | + | Normalized equivalent noise bandwidth | 2.0044 bins | + | 3 dB bandwidth | 1.8962 bins | + | Flatness | -0.8256 dB | + | Recommended overlap | 66.1 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_blackman_harris_92db_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowHAMMING Hamming window function (42.7 dB) + + */ + +/** + @ingroup WindowHAMMING + */ + +/** + @brief Hamming window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 42.7 dB | + | Normalized equivalent noise bandwidth | 1.3628 bins | + | 3 dB bandwidth | 1.3008 bins | + | Flatness | -1.7514 dB | + | Recommended overlap | 50 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_hamming_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowHAMMING + */ + +/** + @brief Hamming window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 42.7 dB | + | Normalized equivalent noise bandwidth | 1.3628 bins | + | 3 dB bandwidth | 1.3008 bins | + | Flatness | -1.7514 dB | + | Recommended overlap | 50 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_hamming_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowHANNING Hanning window function (31.5 dB) + + */ + +/** + @ingroup WindowHANNING + */ + +/** + @brief Hanning window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 31.5 dB | + | Normalized equivalent noise bandwidth | 1.5 bins | + | 3 dB bandwidth | 1.4382 bins | + | Flatness | -1.4236 dB | + | Recommended overlap | 50 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_hanning_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowHANNING + */ + +/** + @brief Hanning window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 31.5 dB | + | Normalized equivalent noise bandwidth | 1.5 bins | + | 3 dB bandwidth | 1.4382 bins | + | Flatness | -1.4236 dB | + | Recommended overlap | 50 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_hanning_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT116D Hft116d window function (116.8 dB) + + */ + +/** + @ingroup WindowHFT116D + */ + +/** + @brief Hft116d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 116.8 dB | + | Normalized equivalent noise bandwidth | 4.2186 bins | + | 3 dB bandwidth | 4.1579 bins | + | Flatness | -0.0028 dB | + | Recommended overlap | 78.2 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft116d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT116D + */ + +/** + @brief Hft116d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 116.8 dB | + | Normalized equivalent noise bandwidth | 4.2186 bins | + | 3 dB bandwidth | 4.1579 bins | + | Flatness | -0.0028 dB | + | Recommended overlap | 78.2 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft116d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT144D Hft144d window function (144.1 dB) + + */ + +/** + @ingroup WindowHFT144D + */ + +/** + @brief Hft144d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 144.1 dB | + | Normalized equivalent noise bandwidth | 4.5386 bins | + | 3 dB bandwidth | 4.4697 bins | + | Flatness | 0.0021 dB | + | Recommended overlap | 79.9 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft144d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT144D + */ + +/** + @brief Hft144d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 144.1 dB | + | Normalized equivalent noise bandwidth | 4.5386 bins | + | 3 dB bandwidth | 4.4697 bins | + | Flatness | 0.0021 dB | + | Recommended overlap | 79.9 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft144d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT169D Hft169d window function (169.5 dB) + + */ + +/** + @ingroup WindowHFT169D + */ + +/** + @brief Hft169d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 169.5 dB | + | Normalized equivalent noise bandwidth | 4.8347 bins | + | 3 dB bandwidth | 4.7588 bins | + | Flatness | 0.0017 dB | + | Recommended overlap | 81.2 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft169d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT169D + */ + +/** + @brief Hft169d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 169.5 dB | + | Normalized equivalent noise bandwidth | 4.8347 bins | + | 3 dB bandwidth | 4.7588 bins | + | Flatness | 0.0017 dB | + | Recommended overlap | 81.2 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft169d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT196D Hft196d window function (196.2 dB) + + */ + +/** + @ingroup WindowHFT196D + */ + +/** + @brief Hft196d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 196.2 dB | + | Normalized equivalent noise bandwidth | 5.1134 bins | + | 3 dB bandwidth | 5.0308 bins | + | Flatness | 0.0013 dB | + | Recommended overlap | 82.3 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft196d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT196D + */ + +/** + @brief Hft196d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 196.2 dB | + | Normalized equivalent noise bandwidth | 5.1134 bins | + | 3 dB bandwidth | 5.0308 bins | + | Flatness | 0.0013 dB | + | Recommended overlap | 82.3 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft196d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT223D Hft223d window function (223.0 dB) + + */ + +/** + @ingroup WindowHFT223D + */ + +/** + @brief Hft223d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 223.0 dB | + | Normalized equivalent noise bandwidth | 5.3888 bins | + | 3 dB bandwidth | 5.3000 bins | + | Flatness | -0.0011 dB | + | Recommended overlap | 83.3 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft223d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT223D + */ + +/** + @brief Hft223d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 223.0 dB | + | Normalized equivalent noise bandwidth | 5.3888 bins | + | 3 dB bandwidth | 5.3000 bins | + | Flatness | 0.0011 dB | + | Recommended overlap | 83.3 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft223d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT248D Hft248d window function (248.4 dB) + + */ + +/** + @ingroup WindowHFT248D + */ + +/** + @brief Hft248d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 248.4 dB | + | Normalized equivalent noise bandwidth | 5.6512 bins | + | 3 dB bandwidth | 5.5567 bins | + | Flatness | 0.0009 dB | + | Recommended overlap | 84.1 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft248d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT248D + */ + +/** + @brief Hft248d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 248.4 dB | + | Normalized equivalent noise bandwidth | 5.6512 bins | + | 3 dB bandwidth | 5.5567 bins | + | Flatness | 0.0009 dB | + | Recommended overlap | 84.1 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft248d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT90D Hft90d window function (90.2 dB) + + */ + +/** + @ingroup WindowHFT90D + */ + +/** + @brief Hft90d window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 90.2 dB | + | Normalized equivalent noise bandwidth | 3.8832 bins | + | 3 dB bandwidth | 3.8320 bins | + | Flatness | -0.0039 dB | + | Recommended overlap | 76.0 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft90d_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + +/** + @defgroup WindowFlat Flat-top window functions + + Use those windows when you need to estimate the + amplitude of a tone. + + If just just need to detect a tone or estimate the + noise, you can use the regular windows. + + */ + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT90D + */ + +/** + @brief Hft90d window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 90.2 dB | + | Normalized equivalent noise bandwidth | 3.8832 bins | + | 3 dB bandwidth | 3.8320 bins | + | Flatness | -0.0039 dB | + | Recommended overlap | 76.0 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft90d_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + +/** + @defgroup WindowHFT95 Hft95 window function (95.0 dB) + + */ + +/** + @ingroup WindowHFT95 + */ + +/** + @brief Hft95 window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 95.0 dB | + | Normalized equivalent noise bandwidth | 3.8112 bins | + | 3 dB bandwidth | 3.7590 bins | + | Flatness | 0.0044 dB | + | Recommended overlap | 75.6 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft95_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowFlat + @{ + */ + + +/** + @ingroup WindowHFT95 + */ + +/** + @brief Hft95 window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 95.0 dB | + | Normalized equivalent noise bandwidth | 3.8112 bins | + | 3 dB bandwidth | 3.7590 bins | + | Flatness | 0.0044 dB | + | Recommended overlap | 75.6 % | + +Included in CMSIS-DSP with authorization from professor +Gerhard Heinzel. + +@par Original article: +Spectrum and spectral density estimation by the Discrete Fourier +transform (DFT), including a comprehensive list of window +functions and some new +flat-top windows. + +@par Authors: +G. Heinzel, A. Rudiger and R. Schilling, +Max-Planck-Institut fur Gravitationsphysik +(Albert-Einstein-Institut) +Teilinstitut Hannover + */ + + + +ARM_DSP_ATTRIBUTE void arm_hft95_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL3 Nuttall3 window function (46.7 dB) + + */ + +/** + @ingroup WindowNUTTALL3 + */ + +/** + @brief Nuttall3 window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 46.7 dB | + | Normalized equivalent noise bandwidth | 1.9444 bins | + | 3 dB bandwidth | 1.8496 bins | + | Flatness | -0.8630 dB | + | Recommended overlap | 64.7 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall3_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL3 + */ + +/** + @brief Nuttall3 window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 46.7 dB | + | Normalized equivalent noise bandwidth | 1.9444 bins | + | 3 dB bandwidth | 1.8496 bins | + | Flatness | -0.863 dB | + | Recommended overlap | 64.7 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall3_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL3A Nuttall3a window function (64.2 dB) + + */ + +/** + @ingroup WindowNUTTALL3A + */ + +/** + @brief Nuttall3a window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 64.2 dB | + | Normalized equivalent noise bandwidth | 1.7721 bins | + | 3 dB bandwidth | 1.6828 bins | + | Flatness | -1.0453 dB | + | Recommended overlap | 61.2 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall3a_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL3A + */ + +/** + @brief Nuttall3a window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 64.2 dB | + | Normalized equivalent noise bandwidth | 1.7721 bins | + | 3 dB bandwidth | 1.6828 bins | + | Flatness | -1.0453 dB | + | Recommended overlap | 61.2 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall3a_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL3B Nuttall3b window function (71.5 dB) + + */ + +/** + @ingroup WindowNUTTALL3B + */ + +/** + @brief Nuttall3b window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 71.5 dB | + | Normalized equivalent noise bandwidth | 1.7037 bins | + | 3 dB bandwidth | 1.6162 bins | + | Flatness | -1.1352 dB | + | Recommended overlap | 59.8 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall3b_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL3B + */ + +/** + @brief Nuttall3b window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 71.5 dB | + | Normalized equivalent noise bandwidth | 1.7037 bins | + | 3 dB bandwidth | 1.6162 bins | + | Flatness | -1.1352 dB | + | Recommended overlap | 59.8 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall3b_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL4 Nuttall4 window function (60.9 dB) + + */ + +/** + @ingroup WindowNUTTALL4 + */ + +/** + @brief Nuttall4 window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 60.9 dB | + | Normalized equivalent noise bandwidth | 2.31 bins | + | 3 dB bandwidth | 2.1884 bins | + | Flatness | -0.6184 dB | + | Recommended overlap | 70.5 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL4 + */ + +/** + @brief Nuttall4 window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 60.9 dB | + | Normalized equivalent noise bandwidth | 2.31 bins | + | 3 dB bandwidth | 2.1884 bins | + | Flatness | -0.6184 dB | + | Recommended overlap | 70.5 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL4A Nuttall4a window function (82.6 dB) + + */ + +/** + @ingroup WindowNUTTALL4A + */ + +/** + @brief Nuttall4a window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 82.6 dB | + | Normalized equivalent noise bandwidth | 2.1253 bins | + | 3 dB bandwidth | 2.0123 bins | + | Flatness | -0.7321 dB | + | Recommended overlap | 68.0 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4a_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL4A + */ + +/** + @brief Nuttall4a window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 82.6 dB | + | Normalized equivalent noise bandwidth | 2.1253 bins | + | 3 dB bandwidth | 2.0123 bins | + | Flatness | -0.7321 dB | + | Recommended overlap | 68.0 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4a_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL4B Nuttall4b window function (93.3 dB) + + */ + +/** + @ingroup WindowNUTTALL4B + */ + +/** + @brief Nuttall4b window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 93.3 dB | + | Normalized equivalent noise bandwidth | 2.0212 bins | + | 3 dB bandwidth | 1.9122 bins | + | Flatness | -0.8118 dB | + | Recommended overlap | 66.3 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4b_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i + +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL4B + */ + +/** + @brief Nuttall4b window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 93.3 dB | + | Normalized equivalent noise bandwidth | 2.0212 bins | + | 3 dB bandwidth | 1.9122 bins | + | Flatness | -0.8118 dB | + | Recommended overlap | 66.3 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4b_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2. / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + +/** + @defgroup WindowNUTTALL4C Nuttall4c window function (98.1 dB) + + */ + +/** + @ingroup WindowNUTTALL4C + */ + +/** + @brief Nuttall4c window generating function (f32). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 98.1 dB | + | Normalized equivalent noise bandwidth | 1.9761 bins | + | 3 dB bandwidth | 1.8687 bins | + | Flatness | -0.8506 dB | + | Recommended overlap | 65.6 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4c_f32( + float32_t * pDst, + uint32_t blockSize) +{ + float32_t k = 2.0f / ((float32_t) blockSize); + float32_t w; + + for(uint32_t i=0;i +/** + @ingroup groupWindow + */ + + + + +/** + @addtogroup WindowNormal + @{ + */ + + +/** + @ingroup WindowNUTTALL4C + */ + +/** + @brief Nuttall4c window generating function (f64). + @param[out] pDst points to the output generated window + @param[in] blockSize number of samples in the window + + @par Parameters of the window + + | Parameter | Value | + | ------------------------------------: | -----------------: | + | Peak sidelobe level | 98.1 dB | + | Normalized equivalent noise bandwidth | 1.9761 bins | + | 3 dB bandwidth | 1.8687 bins | + | Flatness | -0.8506 dB | + | Recommended overlap | 65.6 % | + + */ + + + +ARM_DSP_ATTRIBUTE void arm_nuttall4c_f64( + float64_t * pDst, + uint32_t blockSize) +{ + float64_t k = 2.0 / ((float64_t) blockSize); + float64_t w; + + for(uint32_t i=0;iSDRAM -} - + .RAM_D2 (NOLOAD) : + { + . = ALIGN(32); + _sram_d2 = .; + *(.RAM_D2) + *(.RAM_D2*) + . = ALIGN(32); + _eram_d2 = .; + } >RAM_D2 +} diff --git a/audio.ioc b/audio.ioc index d69b35c..4b525e7 100755 --- a/audio.ioc +++ b/audio.ioc @@ -1,7 +1,7 @@ #MicroXplorer Configuration settings - do not modify -CAD.formats= -CAD.pinconfig= -CAD.provider= +CAD.formats=[] +CAD.pinconfig=Dual +CAD.provider=Component Search Engine CORTEX_M7.AccessPermission_S-Cortex_Memory_Protection_Unit_Region1_Settings_S=MPU_REGION_FULL_ACCESS CORTEX_M7.AccessPermission_Spec=MPU_REGION_FULL_ACCESS CORTEX_M7.BaseAddress_S-Cortex_Memory_Protection_Unit_Region1_Settings_S=0x24000000 @@ -11,7 +11,8 @@ CORTEX_M7.CPU_ICache=Enabled CORTEX_M7.DisableExec_S-Cortex_Memory_Protection_Unit_Region1_Settings_S=MPU_INSTRUCTION_ACCESS_ENABLE CORTEX_M7.DisableExec_Spec=MPU_INSTRUCTION_ACCESS_ENABLE CORTEX_M7.Enable_S-Cortex_Memory_Protection_Unit_Region1_Settings_S=MPU_REGION_ENABLE -CORTEX_M7.IPParameters=default_mode_Activation,BaseAddress_Spec,Size_Spec,SubRegionDisable_Spec,AccessPermission_Spec,IsShareable_Spec,IsCacheable_Spec,IsBufferable_Spec,CPU_DCache,CPU_ICache,Enable_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,DisableExec_Spec,TypeExtField_Spec,BaseAddress_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,Size_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,TypeExtField_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,AccessPermission_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,DisableExec_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,IsShareable_S-Cortex_Memory_Protection_Unit_Region1_Settings_S +CORTEX_M7.Enable_S-Cortex_Memory_Protection_Unit_Region2_Settings_S=__NULL +CORTEX_M7.IPParameters=default_mode_Activation,BaseAddress_Spec,Size_Spec,SubRegionDisable_Spec,AccessPermission_Spec,IsShareable_Spec,IsCacheable_Spec,IsBufferable_Spec,CPU_DCache,CPU_ICache,Enable_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,DisableExec_Spec,TypeExtField_Spec,BaseAddress_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,Size_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,TypeExtField_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,AccessPermission_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,DisableExec_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,IsShareable_S-Cortex_Memory_Protection_Unit_Region1_Settings_S,Enable_S-Cortex_Memory_Protection_Unit_Region2_Settings_S CORTEX_M7.IsBufferable_Spec=MPU_ACCESS_BUFFERABLE CORTEX_M7.IsCacheable_Spec=MPU_ACCESS_CACHEABLE CORTEX_M7.IsShareable_S-Cortex_Memory_Protection_Unit_Region1_Settings_S=MPU_ACCESS_SHAREABLE @@ -86,7 +87,57 @@ I2C4.IPParameters=I2C_Speed_Mode,Speed,Timing I2C4.Speed=100 I2C4.Timing=0x307075B1 KeepUserPlacement=false -MMTAppRegionsCount=0 +MMTAppReg1.MEMORYMAP.AppRegionName=DTCMRAM +MMTAppReg1.MEMORYMAP.ContextName=Cortex-M7NS +MMTAppReg1.MEMORYMAP.CoreName=ARM Cortex-M7 +MMTAppReg1.MEMORYMAP.IPParameters=StartAddress,Size,CoreName,ContextName,Name +MMTAppReg1.MEMORYMAP.Name=DTCMRAM +MMTAppReg1.MEMORYMAP.Size=131072 +MMTAppReg1.MEMORYMAP.StartAddress=0x20000000 +MMTAppReg2.MEMORYMAP.AppRegionName=RAM +MMTAppReg2.MEMORYMAP.ContextName=Cortex-M7NS +MMTAppReg2.MEMORYMAP.CoreName=ARM Cortex-M7 +MMTAppReg2.MEMORYMAP.DefaultDataRegion=true +MMTAppReg2.MEMORYMAP.IPParameters=StartAddress,Size,CoreName,ContextName,Name,DefaultDataRegion +MMTAppReg2.MEMORYMAP.Name=RAM +MMTAppReg2.MEMORYMAP.Size=524288 +MMTAppReg2.MEMORYMAP.StartAddress=0x24000000 +MMTAppReg3.MEMORYMAP.AppRegionName=RAM_D2 +MMTAppReg3.MEMORYMAP.ContextName=Cortex-M7NS +MMTAppReg3.MEMORYMAP.CoreName=ARM Cortex-M7 +MMTAppReg3.MEMORYMAP.IPParameters=StartAddress,Size,CoreName,ContextName,Name +MMTAppReg3.MEMORYMAP.Name=RAM_D2 +MMTAppReg3.MEMORYMAP.Size=294912 +MMTAppReg3.MEMORYMAP.StartAddress=0x30000000 +MMTAppReg4.MEMORYMAP.AppRegionName=RAM_D3 +MMTAppReg4.MEMORYMAP.ContextName=Cortex-M7NS +MMTAppReg4.MEMORYMAP.CoreName=ARM Cortex-M7 +MMTAppReg4.MEMORYMAP.IPParameters=StartAddress,Size,CoreName,ContextName,Name +MMTAppReg4.MEMORYMAP.Name=RAM_D3 +MMTAppReg4.MEMORYMAP.Size=65536 +MMTAppReg4.MEMORYMAP.StartAddress=0x38000000 +MMTAppReg5.MEMORYMAP.AppRegionName=ITCMRAM +MMTAppReg5.MEMORYMAP.Cacheability=WTRA +MMTAppReg5.MEMORYMAP.ContextName=Cortex-M7NS +MMTAppReg5.MEMORYMAP.CoreName=ARM Cortex-M7 +MMTAppReg5.MEMORYMAP.IPParameters=StartAddress,Size,CoreName,ContextName,Name,Cacheability +MMTAppReg5.MEMORYMAP.Name=ITCMRAM +MMTAppReg5.MEMORYMAP.Size=65536 +MMTAppReg5.MEMORYMAP.StartAddress=0x00000000 +MMTAppReg6.MEMORYMAP.AP=RO_priv_only +MMTAppReg6.MEMORYMAP.AppRegionName=FLASH +MMTAppReg6.MEMORYMAP.Cacheability=WTRA +MMTAppReg6.MEMORYMAP.ContextName=Cortex-M7NS +MMTAppReg6.MEMORYMAP.CoreName=ARM Cortex-M7 +MMTAppReg6.MEMORYMAP.DefaultCodeRegion=true +MMTAppReg6.MEMORYMAP.IPParameters=StartAddress,Size,CoreName,MemType,ContextName,Name,AP,Cacheability,DefaultCodeRegion,ISRRegion,RootBootRegion +MMTAppReg6.MEMORYMAP.ISRRegion=true +MMTAppReg6.MEMORYMAP.MemType=ROM +MMTAppReg6.MEMORYMAP.Name=FLASH +MMTAppReg6.MEMORYMAP.RootBootRegion=true +MMTAppReg6.MEMORYMAP.Size=131072 +MMTAppReg6.MEMORYMAP.StartAddress=0x08000000 +MMTAppRegionsCount=6 MMTConfigApplied=false MMTSectionSuffix= Mcu.CPN=STM32H750ZBT6 @@ -159,46 +210,32 @@ Mcu.Pin52=PG2 Mcu.Pin53=PG4 Mcu.Pin54=PG5 Mcu.Pin55=PG6 -Mcu.Pin56=PG7 -Mcu.Pin57=PG8 -Mcu.Pin58=PC6 -Mcu.Pin59=PC7 +Mcu.Pin56=PG8 +Mcu.Pin57=PA13 (JTMS/SWDIO) +Mcu.Pin58=PA14 (JTCK/SWCLK) +Mcu.Pin59=PD0 Mcu.Pin6=PF1 -Mcu.Pin60=PC8 -Mcu.Pin61=PC9 -Mcu.Pin62=PA8 -Mcu.Pin63=PA9 -Mcu.Pin64=PA10 -Mcu.Pin65=PA11 -Mcu.Pin66=PA12 -Mcu.Pin67=PA13 (JTMS/SWDIO) -Mcu.Pin68=PA14 (JTCK/SWCLK) -Mcu.Pin69=PA15 (JTDI) +Mcu.Pin60=PD1 +Mcu.Pin61=PG15 +Mcu.Pin62=PB3 (JTDO/TRACESWO) +Mcu.Pin63=PB5 +Mcu.Pin64=PB7 +Mcu.Pin65=PB8 +Mcu.Pin66=PB9 +Mcu.Pin67=PE0 +Mcu.Pin68=PE1 +Mcu.Pin69=VP_SAI1_VP_$IpInstance_SAIA_SAI_BASIC Mcu.Pin7=PF2 -Mcu.Pin70=PC10 -Mcu.Pin71=PC11 -Mcu.Pin72=PC12 -Mcu.Pin73=PD0 -Mcu.Pin74=PD1 -Mcu.Pin75=PD3 -Mcu.Pin76=PD4 -Mcu.Pin77=PG15 -Mcu.Pin78=PB3 (JTDO/TRACESWO) -Mcu.Pin79=PB5 +Mcu.Pin70=VP_SAI1_VP_$IpInstance_SAIB_SAI_BASIC +Mcu.Pin71=VP_SYS_VS_Systick +Mcu.Pin72=VP_USB_DEVICE_VS_USB_DEVICE_MSC_HS +Mcu.Pin73=VP_MEMORYMAP_VS_MEMORYMAP +Mcu.Pin74=VP_STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.5.0_1.5.0 Mcu.Pin8=PF3 -Mcu.Pin80=PB7 -Mcu.Pin81=PB8 -Mcu.Pin82=PB9 -Mcu.Pin83=PE0 -Mcu.Pin84=PE1 -Mcu.Pin85=VP_SAI1_VP_$IpInstance_SAIA_SAI_BASIC -Mcu.Pin86=VP_SAI1_VP_$IpInstance_SAIB_SAI_BASIC -Mcu.Pin87=VP_SYS_VS_Systick -Mcu.Pin88=VP_USB_DEVICE_VS_USB_DEVICE_MSC_HS -Mcu.Pin89=VP_MEMORYMAP_VS_MEMORYMAP Mcu.Pin9=PF4 -Mcu.PinsNb=90 -Mcu.ThirdPartyNb=0 +Mcu.PinsNb=75 +Mcu.ThirdParty0=STMicroelectronics.X-CUBE-ALGOBUILD.1.5.0 +Mcu.ThirdPartyNb=1 Mcu.UserConstants= Mcu.UserName=STM32H750ZBTx MxCube.Version=6.17.0 @@ -219,39 +256,15 @@ NVIC.PriorityGroup=NVIC_PRIORITYGROUP_4 NVIC.SVCall_IRQn=true\:0\:0\:false\:false\:true\:false\:false\:false NVIC.SysTick_IRQn=true\:15\:0\:false\:false\:true\:false\:true\:false NVIC.UsageFault_IRQn=true\:0\:0\:false\:false\:true\:false\:false\:false -PA10.GPIOParameters=GPIO_Label -PA10.GPIO_Label=GPIO_IN4 -PA10.Locked=true -PA10.Signal=GPIO_Analog -PA11.GPIOParameters=GPIO_Label -PA11.GPIO_Label=GPIO_IN3 -PA11.Locked=true -PA11.Signal=GPIO_Analog -PA12.GPIOParameters=GPIO_Label -PA12.GPIO_Label=GPIO_IN2 -PA12.Locked=true -PA12.Signal=GPIO_Analog PA13\ (JTMS/SWDIO).Mode=Trace_Asynchronous_SW PA13\ (JTMS/SWDIO).Signal=DEBUG_JTMS-SWDIO PA14\ (JTCK/SWCLK).Mode=Trace_Asynchronous_SW PA14\ (JTCK/SWCLK).Signal=DEBUG_JTCK-SWCLK -PA15\ (JTDI).GPIOParameters=GPIO_Label -PA15\ (JTDI).GPIO_Label=GPIO_IN1 -PA15\ (JTDI).Locked=true -PA15\ (JTDI).Signal=GPIO_Analog PA3.Mode=Device_HS PA3.Signal=USB_OTG_HS_ULPI_D0 PA5.Mode=Device_HS PA5.Signal=USB_OTG_HS_ULPI_CK PA7.Signal=FMC_SDNWE -PA8.GPIOParameters=GPIO_Label -PA8.GPIO_Label=GPIO_IN6 -PA8.Locked=true -PA8.Signal=GPIO_Analog -PA9.GPIOParameters=GPIO_Label -PA9.GPIO_Label=GPIO_IN5 -PA9.Locked=true -PA9.Signal=GPIO_Analog PB0.Mode=Device_HS PB0.Signal=USB_OTG_HS_ULPI_D1 PB1.Mode=Device_HS @@ -280,18 +293,6 @@ PB9.Mode=I2C PB9.Signal=I2C4_SDA PC0.Mode=Device_HS PC0.Signal=USB_OTG_HS_ULPI_STP -PC10.GPIOParameters=GPIO_Label -PC10.GPIO_Label=GPIO_OUT3 -PC10.Locked=true -PC10.Signal=GPIO_Output -PC11.GPIOParameters=GPIO_Label -PC11.GPIO_Label=GPIO_OUT2 -PC11.Locked=true -PC11.Signal=GPIO_Output -PC12.GPIOParameters=GPIO_Label -PC12.GPIO_Label=GPIO_OUT1 -PC12.Locked=true -PC12.Signal=GPIO_Output PC2_C.Mode=Device_HS PC2_C.Signal=USB_OTG_HS_ULPI_DIR PC3_C.Mode=Device_HS @@ -300,35 +301,11 @@ PC4.Mode=SdramChipSelect1_1 PC4.Signal=FMC_SDNE0 PC5.Mode=SdramChipSelect1_1 PC5.Signal=FMC_SDCKE0 -PC6.GPIOParameters=GPIO_Label -PC6.GPIO_Label=GPIO_OUT7 -PC6.Locked=true -PC6.Signal=GPIO_Output -PC7.GPIOParameters=GPIO_Label -PC7.GPIO_Label=GPIO_OUT6 -PC7.Locked=true -PC7.Signal=GPIO_Output -PC8.GPIOParameters=GPIO_Label -PC8.GPIO_Label=GPIO_IN8 -PC8.Locked=true -PC8.Signal=GPIO_Analog -PC9.GPIOParameters=GPIO_Label -PC9.GPIO_Label=GPIO_IN7 -PC9.Locked=true -PC9.Signal=GPIO_Analog PD0.Signal=FMC_D2_DA2 PD1.Signal=FMC_D3_DA3 PD10.Signal=FMC_D15_DA15 PD14.Signal=FMC_D0_DA0 PD15.Signal=FMC_D1_DA1 -PD3.GPIOParameters=GPIO_Label -PD3.GPIO_Label=GPIO_OUT4 -PD3.Locked=true -PD3.Signal=GPIO_Output -PD4.GPIOParameters=GPIO_Label -PD4.GPIO_Label=GPIO_OUT5 -PD4.Locked=true -PD4.Signal=GPIO_Output PD8.Signal=FMC_D13_DA13 PD9.Signal=FMC_D14_DA14 PE0.Signal=FMC_NBL0 @@ -408,10 +385,6 @@ PG6.GPIOParameters=GPIO_Speed PG6.GPIO_Speed=GPIO_SPEED_FREQ_VERY_HIGH PG6.Mode=Single Bank 1 PG6.Signal=QUADSPI_BK1_NCS -PG7.GPIOParameters=GPIO_Label -PG7.GPIO_Label=GPIO_OUT8 -PG7.Locked=true -PG7.Signal=GPIO_Output PG8.Signal=FMC_SDCLK PH0-OSC_IN\ (PH0).Mode=HSE-External-Clock-Source PH0-OSC_IN\ (PH0).Signal=RCC_OSC_IN @@ -638,6 +611,10 @@ SH.FMC_SDNRAS.0=FMC_SDNRAS,13b-sda1 SH.FMC_SDNRAS.ConfNb=1 SH.FMC_SDNWE.0=FMC_SDNWE,13b-sda1 SH.FMC_SDNWE.ConfNb=1 +STMicroelectronics.X-CUBE-ALGOBUILD.1.5.0.DSPOoLibraryJjLibrary_Checked=true +STMicroelectronics.X-CUBE-ALGOBUILD.1.5.0.IPParameters=LibraryCcDSPOoLibraryJjDSPOoLibrary +STMicroelectronics.X-CUBE-ALGOBUILD.1.5.0.LibraryCcDSPOoLibraryJjDSPOoLibrary=true +STMicroelectronics.X-CUBE-ALGOBUILD.1.5.0_SwParameter=LibraryCcDSPOoLibraryJjDSPOoLibrary\:true; USB_DEVICE.CLASS_NAME_HS=MSC USB_DEVICE.IPParameters=VirtualModeHS,CLASS_NAME_HS,VirtualMode-MSC_HS USB_DEVICE.VirtualMode-MSC_HS=Msc @@ -651,6 +628,8 @@ VP_SAI1_VP_$IpInstance_SAIA_SAI_BASIC.Mode=SAI_A_BASIC VP_SAI1_VP_$IpInstance_SAIA_SAI_BASIC.Signal=SAI1_VP_$IpInstance_SAIA_SAI_BASIC VP_SAI1_VP_$IpInstance_SAIB_SAI_BASIC.Mode=SAI_B_BASIC VP_SAI1_VP_$IpInstance_SAIB_SAI_BASIC.Signal=SAI1_VP_$IpInstance_SAIB_SAI_BASIC +VP_STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.5.0_1.5.0.Mode=DSPOoLibraryJjLibrary +VP_STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.5.0_1.5.0.Signal=STMicroelectronics.X-CUBE-ALGOBUILD_VS_DSPOoLibraryJjLibrary_1.5.0_1.5.0 VP_SYS_VS_Systick.Mode=SysTick VP_SYS_VS_Systick.Signal=SYS_VS_Systick VP_USB_DEVICE_VS_USB_DEVICE_MSC_HS.Mode=MSC_HS -- cgit v1.2.3