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| author | Ali Labbene <ali.labbene@st.com> | 2019-12-11 08:59:21 +0100 |
|---|---|---|
| committer | Ali Labbene <ali.labbene@st.com> | 2019-12-16 16:35:24 +0100 |
| commit | 9f95ff5b6ba01db09552b84a0ab79607060a2666 (patch) | |
| tree | 8a6e0dda832555c692307869aed49d07ee7facfe /DSP/Source/TransformFunctions | |
| parent | 76177aa280494bb36d7a0bcbda1078d4db717020 (diff) | |
| download | st-cmsis-core-lowfat-9f95ff5b6ba01db09552b84a0ab79607060a2666.tar.gz st-cmsis-core-lowfat-9f95ff5b6ba01db09552b84a0ab79607060a2666.tar.bz2 st-cmsis-core-lowfat-9f95ff5b6ba01db09552b84a0ab79607060a2666.zip | |
Official ARM version: v5.4.0
Add CMSIS V5.4.0, please refer to index.html available under \docs folder.
Note: content of \CMSIS\Core\Include has been copied under \Include to keep the same structure
used in existing projects, and thus avoid projects mass update
Note: the following components have been removed from ARM original delivery (as not used in ST packages)
- CMSIS_EW2018.pdf
- .gitattributes
- .gitignore
- \Device
- \CMSIS
- \CoreValidation
- \DAP
- \Documentation
- \DoxyGen
- \Driver
- \Pack
- \RTOS\CMSIS_RTOS_Tutorial.pdf
- \RTOS\RTX
- \RTOS\Template
- \RTOS2\RTX
- \Utilities
- All ARM/GCC projects files are deleted from \DSP, \RTOS and \RTOS2
Change-Id: Ia026c3f0f0d016627a4fb5a9032852c33d24b4d3
Diffstat (limited to 'DSP/Source/TransformFunctions')
32 files changed, 50916 insertions, 0 deletions
diff --git a/DSP/Source/TransformFunctions/arm_bitreversal.c b/DSP/Source/TransformFunctions/arm_bitreversal.c new file mode 100644 index 0000000..cea4821 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_bitreversal.c @@ -0,0 +1,230 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_bitreversal.c + * Description: Bitreversal functions + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.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. +* @return none. +*/ + +void arm_bitreversal_f32( +float32_t * pSrc, +uint16_t fftSize, +uint16_t bitRevFactor, +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; + } +} + + + +/* +* @brief In-place bit reversal function. +* @param[in, out] *pSrc points to the in-place buffer of Q31 data type. +* @param[in] fftLen 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 bit reversal table. +* @return none. +*/ + +void arm_bitreversal_q31( +q31_t * pSrc, +uint32_t fftLen, +uint16_t bitRevFactor, +uint16_t * pBitRevTable) +{ + 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 = *pBitRevTable; + + /* Updating the bit reversal index depending on the fft length */ + pBitRevTable += bitRevFactor; + } +} + + + +/* + * @brief In-place bit reversal function. + * @param[in, out] *pSrc points to the in-place buffer of Q15 data type. + * @param[in] fftLen 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 bit reversal table. + * @return none. +*/ + +void arm_bitreversal_q15( +q15_t * pSrc16, +uint32_t fftLen, +uint16_t bitRevFactor, +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/DSP/Source/TransformFunctions/arm_bitreversal2.S b/DSP/Source/TransformFunctions/arm_bitreversal2.S new file mode 100644 index 0000000..e0a82db --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_bitreversal2.S @@ -0,0 +1,216 @@ +;/* ---------------------------------------------------------------------- +; * Project: CMSIS DSP Library +; * Title: arm_bitreversal2.S +; * Description: arm_bitreversal_32 function done in assembly for maximum speed. +; * Called after doing an fft to reorder the output. +; * The function is loop unrolled by 2. arm_bitreversal_16 as well. +; * +; * $Date: 27. January 2017 +; * $Revision: V.1.5.1 +; * +; * Target Processor: Cortex-M cores +; * -------------------------------------------------------------------- */ +;/* +; * Copyright (C) 2010-2017 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. +; */ + +#if defined ( __CC_ARM ) /* Keil */ + #define CODESECT AREA ||.text||, CODE, READONLY, ALIGN=2 + #define LABEL +#elif defined ( __IASMARM__ ) /* IAR */ + #define CODESECT SECTION `.text`:CODE + #define PROC + #define LABEL + #define ENDP + #define EXPORT PUBLIC +#elif defined ( __CSMC__ ) /* Cosmic */ + #define CODESECT switch .text + #define THUMB + #define EXPORT xdef + #define PROC : + #define LABEL : + #define ENDP + #define arm_bitreversal_32 _arm_bitreversal_32 +#elif defined ( __TI_ARM__ ) /* TI ARM */ + #define THUMB .thumb + #define CODESECT .text + #define EXPORT .global + #define PROC : .asmfunc + #define LABEL : + #define ENDP .endasmfunc + #define END +#elif defined ( __GNUC__ ) /* GCC */ + #define THUMB .thumb + #define CODESECT .section .text + #define EXPORT .global + #define PROC : + #define LABEL : + #define ENDP + #define END + + .syntax unified +#endif + + CODESECT + THUMB + +;/* +;* @brief In-place bit reversal function. +;* @param[in, out] *pSrc points to the 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. +;*/ + EXPORT arm_bitreversal_32 + EXPORT arm_bitreversal_16 + +#if defined ( __CC_ARM ) /* Keil */ +#elif defined ( __IASMARM__ ) /* IAR */ +#elif defined ( __CSMC__ ) /* Cosmic */ +#elif defined ( __TI_ARM__ ) /* TI ARM */ +#elif defined ( __GNUC__ ) /* GCC */ + .type arm_bitreversal_16, %function + .type arm_bitreversal_32, %function +#endif + +#if defined(ARM_MATH_CM0) || defined(ARM_MATH_CM0PLUS) || defined(ARM_MATH_ARMV8MBL) + +arm_bitreversal_32 PROC + ADDS r3,r1,#1 + PUSH {r4-r6} + ADDS r1,r2,#0 + LSRS r3,r3,#1 +arm_bitreversal_32_0 LABEL + LDRH r2,[r1,#2] + LDRH r6,[r1,#0] + ADD r2,r0,r2 + ADD r6,r0,r6 + LDR r5,[r2,#0] + LDR r4,[r6,#0] + STR r5,[r6,#0] + STR r4,[r2,#0] + LDR r5,[r2,#4] + LDR r4,[r6,#4] + STR r5,[r6,#4] + STR r4,[r2,#4] + ADDS r1,r1,#4 + SUBS r3,r3,#1 + BNE arm_bitreversal_32_0 + POP {r4-r6} + BX lr + ENDP + +arm_bitreversal_16 PROC + ADDS r3,r1,#1 + PUSH {r4-r6} + ADDS r1,r2,#0 + LSRS r3,r3,#1 +arm_bitreversal_16_0 LABEL + LDRH r2,[r1,#2] + LDRH r6,[r1,#0] + LSRS r2,r2,#1 + LSRS r6,r6,#1 + ADD r2,r0,r2 + ADD r6,r0,r6 + LDR r5,[r2,#0] + LDR r4,[r6,#0] + STR r5,[r6,#0] + STR r4,[r2,#0] + ADDS r1,r1,#4 + SUBS r3,r3,#1 + BNE arm_bitreversal_16_0 + POP {r4-r6} + BX lr + ENDP + +#else + +arm_bitreversal_32 PROC + ADDS r3,r1,#1 + CMP r3,#1 + IT LS + BXLS lr + PUSH {r4-r9} + ADDS r1,r2,#2 + LSRS r3,r3,#2 +arm_bitreversal_32_0 LABEL ;/* loop unrolled by 2 */ + LDRH r8,[r1,#4] + LDRH r9,[r1,#2] + LDRH r2,[r1,#0] + LDRH r12,[r1,#-2] + ADD r8,r0,r8 + ADD r9,r0,r9 + ADD r2,r0,r2 + ADD r12,r0,r12 + LDR r7,[r9,#0] + LDR r6,[r8,#0] + LDR r5,[r2,#0] + LDR r4,[r12,#0] + STR r6,[r9,#0] + STR r7,[r8,#0] + STR r5,[r12,#0] + STR r4,[r2,#0] + LDR r7,[r9,#4] + LDR r6,[r8,#4] + LDR r5,[r2,#4] + LDR r4,[r12,#4] + STR r6,[r9,#4] + STR r7,[r8,#4] + STR r5,[r12,#4] + STR r4,[r2,#4] + ADDS r1,r1,#8 + SUBS r3,r3,#1 + BNE arm_bitreversal_32_0 + POP {r4-r9} + BX lr + ENDP + +arm_bitreversal_16 PROC + ADDS r3,r1,#1 + CMP r3,#1 + IT LS + BXLS lr + PUSH {r4-r9} + ADDS r1,r2,#2 + LSRS r3,r3,#2 +arm_bitreversal_16_0 LABEL ;/* loop unrolled by 2 */ + LDRH r8,[r1,#4] + LDRH r9,[r1,#2] + LDRH r2,[r1,#0] + LDRH r12,[r1,#-2] + ADD r8,r0,r8,LSR #1 + ADD r9,r0,r9,LSR #1 + ADD r2,r0,r2,LSR #1 + ADD r12,r0,r12,LSR #1 + LDR r7,[r9,#0] + LDR r6,[r8,#0] + LDR r5,[r2,#0] + LDR r4,[r12,#0] + STR r6,[r9,#0] + STR r7,[r8,#0] + STR r5,[r12,#0] + STR r4,[r2,#0] + ADDS r1,r1,#8 + SUBS r3,r3,#1 + BNE arm_bitreversal_16_0 + POP {r4-r9} + BX lr + ENDP + +#endif + + END diff --git a/DSP/Source/TransformFunctions/arm_cfft_f32.c b/DSP/Source/TransformFunctions/arm_cfft_f32.c new file mode 100644 index 0000000..4abb6f5 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_f32.c @@ -0,0 +1,620 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_f32.c + * Description: Combined Radix Decimation in Frequency CFFT Floating point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +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 <code>2*fftLen</code> interleaved values as shown below. +* <pre> {real[0], imag[0], real[1], imag[1],..} </pre> +* 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 <code>fftLen</code> when computing the forward transform. The +* inverse transform includes a scale of <code>1/fftLen</code> 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 <code>arm_const_structs.h</code>. Include +* this header in your function and then pass one of the constant structures as +* an argument to arm_cfft_f32. For example: +* \par +* <code>arm_cfft_f32(arm_cfft_sR_f32_len64, pSrc, 1, 1)</code> +* \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 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 <code>fftLen</code> when computing the forward transform. The +* inverse transform includes a scale of <code>1/fftLen</code> 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 <code>arm_const_structs.h</code>. Include +* this header in your function and then pass one of the constant structures as +* an argument to arm_cfft_q31. For example: +* \par +* <code>arm_cfft_q31(arm_cfft_sR_q31_len64, pSrc, 1, 1)</code> +* \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 +* +*/ + +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); +} + +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 ComplexFFT +* @{ +*/ + +/** +* @details +* @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 of size <code>2*fftLen</code>. Processing occurs in-place. +* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return none. +*/ + +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++; + } + } +} + +/** +* @} end of ComplexFFT group +*/ diff --git a/DSP/Source/TransformFunctions/arm_cfft_q15.c b/DSP/Source/TransformFunctions/arm_cfft_q15.c new file mode 100644 index 0000000..da76ddc --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_q15.c @@ -0,0 +1,345 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_q15.c + * Description: Combined Radix Decimation in Q15 Frequency CFFT processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +extern void arm_radix4_butterfly_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_radix4_butterfly_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_bitreversal_16( + uint16_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + +void arm_cfft_radix4by2_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef); + +void arm_cfft_radix4by2_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + const q15_t * pCoef); + +/** +* @ingroup groupTransforms +*/ + +/** +* @addtogroup ComplexFFT +* @{ +*/ + +/** +* @details +* @brief Processing function for the Q15 complex FFT. +* @param[in] *S points to an instance of the Q15 CFFT structure. +* @param[in, out] *p1 points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place. +* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return none. +*/ + +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); +} + +/** +* @} end of ComplexFFT group +*/ + +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 ia, l; + q15_t xt, yt, cosVal, sinVal; +#endif + + n2 = fftLen >> 1; + +#if defined (ARM_MATH_DSP) + + for (i = n2; i > 0; i--) + { + coeff = _SIMD32_OFFSET(pC); + pC += 2; + + T = _SIMD32_OFFSET(pSi); + T = __SHADD16(T, 0); // this is just a SIMD arithmetic shift right by 1 + + S = _SIMD32_OFFSET(pSl); + S = __SHADD16(S, 0); // this is just a SIMD arithmetic shift right by 1 + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(pSi) = __SHADD16(T, S); + pSi += 2; + + #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 + + _SIMD32_OFFSET(pSl) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSl += 2; + } + +#else // #if defined (ARM_MATH_DSP) + + ia = 0; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia++; + + 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[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) + + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1U] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) - + ((int16_t) (((q31_t) xt * sinVal) >> 16))); + } + +#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); + + for (i = 0; i < fftLen >> 1; i++) + { + p0 = pSrc[4*i+0]; + p1 = pSrc[4*i+1]; + p2 = pSrc[4*i+2]; + p3 = pSrc[4*i+3]; + + p0 <<= 1; + p1 <<= 1; + p2 <<= 1; + p3 <<= 1; + + pSrc[4*i+0] = p0; + pSrc[4*i+1] = p1; + pSrc[4*i+2] = p2; + pSrc[4*i+3] = p3; + } +} + +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 ia, l; + q15_t xt, yt, cosVal, sinVal; +#endif + + n2 = fftLen >> 1; + +#if defined (ARM_MATH_DSP) + + for (i = n2; i > 0; i--) + { + coeff = _SIMD32_OFFSET(pC); + pC += 2; + + T = _SIMD32_OFFSET(pSi); + T = __SHADD16(T, 0); // this is just a SIMD arithmetic shift right by 1 + + S = _SIMD32_OFFSET(pSl); + S = __SHADD16(S, 0); // this is just a SIMD arithmetic shift right by 1 + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(pSi) = __SHADD16(T, S); + pSi += 2; + + #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 + + _SIMD32_OFFSET(pSl) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSl += 2; + } + +#else // #if defined (ARM_MATH_DSP) + + ia = 0; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[ia * 2]; + sinVal = pCoef[(ia * 2) + 1]; + ia++; + + 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[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) - + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1U] = (((int16_t) (((q31_t) yt * cosVal) >> 16)) + + ((int16_t) (((q31_t) xt * sinVal) >> 16))); + } + +#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); + + for (i = 0; i < fftLen >> 1; i++) + { + p0 = pSrc[4*i+0]; + p1 = pSrc[4*i+1]; + p2 = pSrc[4*i+2]; + p3 = pSrc[4*i+3]; + + p0 <<= 1; + p1 <<= 1; + p2 <<= 1; + p3 <<= 1; + + pSrc[4*i+0] = p0; + pSrc[4*i+1] = p1; + pSrc[4*i+2] = p2; + pSrc[4*i+3] = p3; + } +} + diff --git a/DSP/Source/TransformFunctions/arm_cfft_q31.c b/DSP/Source/TransformFunctions/arm_cfft_q31.c new file mode 100644 index 0000000..ff4ff94 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_q31.c @@ -0,0 +1,252 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_q31.c + * Description: Combined Radix Decimation in Frequency CFFT fixed point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +extern void arm_radix4_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_radix4_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pCoef, + uint32_t twidCoefModifier); + +extern void arm_bitreversal_32( + uint32_t * pSrc, + const uint16_t bitRevLen, + const uint16_t * pBitRevTable); + +void arm_cfft_radix4by2_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef); + +void arm_cfft_radix4by2_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef); + +/** +* @ingroup groupTransforms +*/ + +/** +* @addtogroup ComplexFFT +* @{ +*/ + +/** +* @details +* @brief Processing function for the fixed-point complex FFT in Q31 format. +* @param[in] *S points to an instance of the fixed-point CFFT structure. +* @param[in, out] *p1 points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place. +* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return none. +*/ + +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); +} + +/** +* @} end of ComplexFFT group +*/ + +void arm_cfft_radix4by2_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef) +{ + uint32_t i, l; + uint32_t n2, ia; + q31_t xt, yt, cosVal, sinVal; + q31_t p0, p1; + + n2 = fftLen >> 1; + ia = 0; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2*ia]; + sinVal = pCoef[2*ia + 1]; + ia++; + + l = i + n2; + xt = (pSrc[2 * i] >> 2) - (pSrc[2 * l] >> 2); + pSrc[2 * i] = (pSrc[2 * i] >> 2) + (pSrc[2 * l] >> 2); + + yt = (pSrc[2 * i + 1] >> 2) - (pSrc[2 * l + 1] >> 2); + pSrc[2 * i + 1] = (pSrc[2 * l + 1] >> 2) + (pSrc[2 * i + 1] >> 2); + + 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 << 1; + pSrc[2U * l + 1U] = 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); + + for (i = 0; i < fftLen >> 1; i++) + { + p0 = pSrc[4*i+0]; + p1 = pSrc[4*i+1]; + xt = pSrc[4*i+2]; + yt = pSrc[4*i+3]; + + p0 <<= 1; + p1 <<= 1; + xt <<= 1; + yt <<= 1; + + pSrc[4*i+0] = p0; + pSrc[4*i+1] = p1; + pSrc[4*i+2] = xt; + pSrc[4*i+3] = yt; + } + +} + +void arm_cfft_radix4by2_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + const q31_t * pCoef) +{ + uint32_t i, l; + uint32_t n2, ia; + q31_t xt, yt, cosVal, sinVal; + q31_t p0, p1; + + n2 = fftLen >> 1; + ia = 0; + for (i = 0; i < n2; i++) + { + cosVal = pCoef[2*ia]; + sinVal = pCoef[2*ia + 1]; + ia++; + + l = i + n2; + xt = (pSrc[2 * i] >> 2) - (pSrc[2 * l] >> 2); + pSrc[2 * i] = (pSrc[2 * i] >> 2) + (pSrc[2 * l] >> 2); + + yt = (pSrc[2 * i + 1] >> 2) - (pSrc[2 * l + 1] >> 2); + pSrc[2 * i + 1] = (pSrc[2 * l + 1] >> 2) + (pSrc[2 * i + 1] >> 2); + + 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 << 1; + pSrc[2U * l + 1U] = p1 << 1; + + } + + // 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); + + for (i = 0; i < fftLen >> 1; i++) + { + p0 = pSrc[4*i+0]; + p1 = pSrc[4*i+1]; + xt = pSrc[4*i+2]; + yt = pSrc[4*i+3]; + + p0 <<= 1; + p1 <<= 1; + xt <<= 1; + yt <<= 1; + + pSrc[4*i+0] = p0; + pSrc[4*i+1] = p1; + pSrc[4*i+2] = xt; + pSrc[4*i+3] = yt; + } +} + diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix2_f32.c b/DSP/Source/TransformFunctions/arm_cfft_radix2_f32.c new file mode 100644 index 0000000..d35988d --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix2_f32.c @@ -0,0 +1,472 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_f32.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +void arm_radix2_butterfly_f32( + float32_t * pSrc, + uint32_t fftLen, + float32_t * pCoef, + uint16_t twidCoefModifier); + +void arm_radix2_butterfly_inverse_f32( + float32_t * pSrc, + uint32_t fftLen, + float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen); + +extern void arm_bitreversal_f32( + float32_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + uint16_t * pBitRevTab); + +/** +* @ingroup groupTransforms +*/ + +/** +* @addtogroup ComplexFFT +* @{ +*/ + +/** +* @details +* @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 <code>2*fftLen</code>. Processing occurs in-place. +* @return none. +*/ + +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 ComplexFFT 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. +*/ + +void arm_radix2_butterfly_f32( +float32_t * pSrc, +uint32_t fftLen, +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 + + 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) + +} + + +void arm_radix2_butterfly_inverse_f32( +float32_t * pSrc, +uint32_t fftLen, +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 + + 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[2U * l] = p2; + + pSrc[2 * i + 1] = p1; + pSrc[2U * l + 1U] = p3; + } // butterfly loop end + +#endif // #if defined (ARM_MATH_DSP) + +} diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix2_init_f32.c b/DSP/Source/TransformFunctions/arm_cfft_radix2_init_f32.c new file mode 100644 index 0000000..fdfa63e --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix2_init_f32.c @@ -0,0 +1,192 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_f32.c + * Description: Radix-2 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** +* @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 forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated +* \par +* The parameter <code>bitReverseFlag</code> 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 <code>fftLen</code> 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_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_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 ComplexFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix2_init_q15.c b/DSP/Source/TransformFunctions/arm_cfft_radix2_init_q15.c new file mode 100644 index 0000000..2646374 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix2_init_q15.c @@ -0,0 +1,177 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_q15.c + * Description: Radix-2 Decimation in Frequency Q15 FFT & IFFT initialization function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** +* @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 forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated +* \par +* The parameter <code>bitReverseFlag</code> 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 <code>fftLen</code> 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_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_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 ComplexFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix2_init_q31.c b/DSP/Source/TransformFunctions/arm_cfft_radix2_init_q31.c new file mode 100644 index 0000000..56fff4b --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix2_init_q31.c @@ -0,0 +1,174 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_init_q31.c + * Description: Radix-2 Decimation in Frequency Fixed-point CFFT & CIFFT Initialization function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + + +/** +* +* @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 +* @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 forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated +* \par +* The parameter <code>bitReverseFlag</code> 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 <code>fftLen</code> 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_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_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 ComplexFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix2_q15.c b/DSP/Source/TransformFunctions/arm_cfft_radix2_q15.c new file mode 100644 index 0000000..8880ab9 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix2_q15.c @@ -0,0 +1,729 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_q15.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +void arm_radix2_butterfly_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pCoef, + uint16_t twidCoefModifier); + +void arm_radix2_butterfly_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pCoef, + uint16_t twidCoefModifier); + +void arm_bitreversal_q15( + q15_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + uint16_t * pBitRevTab); + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** + * @details + * @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 + * @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 <code>2*fftLen</code>. Processing occurs in-place. + * @return none. + */ + +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 ComplexFFT group + */ + +void arm_radix2_butterfly_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pCoef, + uint16_t twidCoefModifier) +{ +#if defined (ARM_MATH_DSP) + + unsigned i, j, k, l; + unsigned 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 = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(pSrc + (2U * l)) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + + coeff = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + // loop for butterfly + i++; + l++; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(pSrc + (2U * l)) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + + i += n1; + + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = 0; i < fftLen; i += n1) + { + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S); + + _SIMD32_OFFSET(pSrc + (2U * l)) = R; + + i += n1; + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S); + + _SIMD32_OFFSET(pSrc + (2U * l)) = R; + + } // groups loop end + + +#else + + unsigned i, j, k, l; + unsigned 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[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) + + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1U] = (((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[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) + + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1U] = (((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[2U * l] = xt; + + pSrc[2U * l + 1U] = yt; + + } // butterfly loop end + + } // groups loop end + + twidCoefModifier = twidCoefModifier << 1U; + +#endif // #if defined (ARM_MATH_DSP) + +} + + +void arm_radix2_butterfly_inverse_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pCoef, + uint16_t twidCoefModifier) +{ +#if defined (ARM_MATH_DSP) + + unsigned i, j, k, l; + unsigned 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 = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(pSrc + (2U * l)) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + + coeff = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + // loop for butterfly + i++; + l++; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + in = ((int16_t) (T & 0xFFFF)) >> 1; + T = ((T >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + in = ((int16_t) (S & 0xFFFF)) >> 1; + S = ((S >> 1) & 0xFFFF0000) | (in & 0xFFFF); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(pSrc + (2U * l)) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + + i += n1; + + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(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 + + _SIMD32_OFFSET(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; + + // loop for groups + for (j = 0; j < n2; j++) + { + coeff = _SIMD32_OFFSET(pCoef + (ia * 2U)); + + ia = ia + twidCoefModifier; + + // loop for butterfly + for (i = j; i < fftLen; i += n1) + { + l = i + n2; + + T = _SIMD32_OFFSET(pSrc + (2 * i)); + + S = _SIMD32_OFFSET(pSrc + (2 * l)); + + R = __QSUB16(T, S); + + _SIMD32_OFFSET(pSrc + (2 * i)) = __QADD16(T, S); + + _SIMD32_OFFSET(pSrc + (2U * l)) = R; + + } // butterfly loop end + + } // groups loop end + + twidCoefModifier = twidCoefModifier << 1U; + +#else + + + unsigned i, j, k, l; + unsigned 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[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) - + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1U] = (((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[2U * l] = (((int16_t) (((q31_t) xt * cosVal) >> 16)) - + ((int16_t) (((q31_t) yt * sinVal) >> 16))); + + pSrc[2U * l + 1U] = (((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[2U * l] = xt; + + pSrc[2U * l + 1U] = yt; + + } // groups loop end + + +#endif // #if defined (ARM_MATH_DSP) + +} diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix2_q31.c b/DSP/Source/TransformFunctions/arm_cfft_radix2_q31.c new file mode 100644 index 0000000..c9b1537 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix2_q31.c @@ -0,0 +1,338 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix2_q31.c + * Description: Radix-2 Decimation in Frequency CFFT & CIFFT Fixed point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +void arm_radix2_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pCoef, + uint16_t twidCoefModifier); + +void arm_radix2_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pCoef, + uint16_t twidCoefModifier); + +void arm_bitreversal_q31( + q31_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + uint16_t * pBitRevTab); + +/** +* @ingroup groupTransforms +*/ + +/** +* @addtogroup ComplexFFT +* @{ +*/ + +/** +* @details +* @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 +* @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 <code>2*fftLen</code>. Processing occurs in-place. +* @return none. +*/ + +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 ComplexFFT group +*/ + +void arm_radix2_butterfly_q31( +q31_t * pSrc, +uint32_t fftLen, +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 + +} + + +void arm_radix2_butterfly_inverse_q31( +q31_t * pSrc, +uint32_t fftLen, +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/DSP/Source/TransformFunctions/arm_cfft_radix4_f32.c b/DSP/Source/TransformFunctions/arm_cfft_radix4_f32.c new file mode 100644 index 0000000..d6f66ae --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix4_f32.c @@ -0,0 +1,1209 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_f32.c + * Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +extern void arm_bitreversal_f32( +float32_t * pSrc, +uint16_t fftSize, +uint16_t bitRevFactor, +uint16_t * pBitRevTab); + +void arm_radix4_butterfly_f32( +float32_t * pSrc, +uint16_t fftLen, +float32_t * pCoef, +uint16_t twidCoefModifier); + +void arm_radix4_butterfly_inverse_f32( +float32_t * pSrc, +uint16_t fftLen, +float32_t * pCoef, +uint16_t twidCoefModifier, +float32_t onebyfftLen); + + +/** +* @ingroup groupTransforms +*/ + +/** +* @addtogroup ComplexFFT +* @{ +*/ + +/** +* @details +* @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 <code>2*fftLen</code>. Processing occurs in-place. +* @return none. +*/ + +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 ComplexFFT 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. +*/ + +void arm_radix4_butterfly_f32( +float32_t * pSrc, +uint16_t fftLen, +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_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + 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; + + /* 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 = 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_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. +* @return none. +*/ + +void arm_radix4_butterfly_inverse_f32( +float32_t * pSrc, +uint16_t fftLen, +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_DSP) + + 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; + + /* 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 = 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_DSP) */ +} + + diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix4_init_f32.c b/DSP/Source/TransformFunctions/arm_cfft_radix4_init_f32.c new file mode 100644 index 0000000..14ea487 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix4_init_f32.c @@ -0,0 +1,152 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_f32.c + * Description: Radix-4 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** +* @brief Initialization function for the floating-point CFFT/CIFFT. +* @deprecated Do not use this function. It has been superceded 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 forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated +* \par +* The parameter <code>bitReverseFlag</code> 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 <code>fftLen</code> 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_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_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 ComplexFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix4_init_q15.c b/DSP/Source/TransformFunctions/arm_cfft_radix4_init_q15.c new file mode 100644 index 0000000..ed78236 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix4_init_q15.c @@ -0,0 +1,140 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_q15.c + * Description: Radix-4 Decimation in Frequency Q15 FFT & IFFT initialization function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + + +/** + * @addtogroup ComplexFFT + * @{ + */ + + +/** +* @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 forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated +* \par +* The parameter <code>bitReverseFlag</code> 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 <code>fftLen</code> 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_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_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 ComplexFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix4_init_q31.c b/DSP/Source/TransformFunctions/arm_cfft_radix4_init_q31.c new file mode 100644 index 0000000..6f11763 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix4_init_q31.c @@ -0,0 +1,136 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix4_init_q31.c + * Description: Radix-4 Decimation in Frequency Q31 FFT & IFFT initialization function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** +* +* @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 +* @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 forward (ifftFlag=0) or inverse (ifftFlag=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated +* \par +* The parameter <code>bitReverseFlag</code> 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 <code>fftLen</code> 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_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_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 ComplexFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c b/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c new file mode 100644 index 0000000..f3451f7 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix4_q15.c @@ -0,0 +1,1910 @@ +/* ---------------------------------------------------------------------- + * 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: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + + +void arm_radix4_butterfly_q15( + q15_t * pSrc16, + uint32_t fftLen, + q15_t * pCoef16, + uint32_t twidCoefModifier); + +void arm_radix4_butterfly_inverse_q15( + q15_t * pSrc16, + uint32_t fftLen, + q15_t * pCoef16, + uint32_t twidCoefModifier); + +void arm_bitreversal_q15( + q15_t * pSrc, + uint32_t fftLen, + uint16_t bitRevFactor, + uint16_t * pBitRevTab); + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + + +/** + * @details + * @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 + * @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. + * @return none. + * + * \par Input and output formats: + * \par + * 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 + * \image html CFFTQ15.gif "Input and Output Formats for Q15 CFFT" + * \image html CIFFTQ15.gif "Input and Output Formats for Q15 CIFFT" + */ + +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 ComplexFFT 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. + * @return none. + */ + +void arm_radix4_butterfly_q15( + q15_t * pSrc16, + uint32_t fftLen, + q15_t * pCoef16, + uint32_t twidCoefModifier) +{ + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + 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 = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pSi1); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* Read yd (real), xd(imag) input */ + U = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi0) = __SHADD16(R, T); + pSi0 += 2; + + /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */ + R = __QSUB16(R, T); + + /* co2 & si2 are read from SIMD Coefficient pointer */ + C2 = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi1) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSi1 += 2; + + /* Butterfly calculations */ + /* U = packed(yd, xd) */ + U = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi2) = + ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF); + pSi2 += 2; + + + /* co3 & si3 are read from SIMD Coefficient pointer */ + C3 = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi3) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSi3 += 2; + + /* 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 = _SIMD32_OFFSET(pCoef16 + (2U * ic)); + C2 = _SIMD32_OFFSET(pCoef16 + (4U * ic)); + C3 = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pSi0); + + /* Read yc (real), xc(imag) input */ + S = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pSi1); + + /* Read yd (real), xd(imag) input */ + U = _SIMD32_OFFSET(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); + _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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) */ + _SIMD32_OFFSET(pSi1) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSi1 += 2 * n1; + + /* Butterfly calculations */ + + /* Read yd (real), xd(imag) input */ + U = _SIMD32_OFFSET(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) */ + _SIMD32_OFFSET(pSi2) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + 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) */ + _SIMD32_OFFSET(pSi3) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + 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 = *__SIMD32(ptr1)++; + + /* Read xb (real), yb(imag) input */ + xbyb = *__SIMD32(ptr1)++; + + /* Read xc (real), yc(imag) input */ + xcyc = *__SIMD32(ptr1)++; + + /* Read xd (real), yd(imag) input */ + xdyd = *__SIMD32(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 */ + *__SIMD32(ptr1)++ = __SHADD16(R, T); + + /* T = packed((yb + yd), (xb + xd)) */ + T = __QADD16(xbyb, xdyd); + + /* xc' = (xa-xb+xc-xd) */ + /* yc' = (ya-yb+yc-yd) */ + *__SIMD32(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) */ + *__SIMD32(ptr1)++ = __SHSAX(S, U); + + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + *__SIMD32(ptr1)++ = __SHASX(S, U); + +#else + + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + *__SIMD32(ptr1)++ = __SHASX(S, U); + + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + *__SIMD32(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 + + /* Run the below code for Cortex-M0 */ + + 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. + * @return none. + */ + +/* +* 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) +* +*/ + +void arm_radix4_butterfly_inverse_q15( + q15_t * pSrc16, + uint32_t fftLen, + q15_t * pCoef16, + uint32_t twidCoefModifier) +{ + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + 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 = _SIMD32_OFFSET(pSi0); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* Read yc (real), xc(imag) input */ + S = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pSi1); + T = __SHADD16(T, 0); + T = __SHADD16(T, 0); + + /* Read yd (real), xd(imag) input */ + U = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi0) = __SHADD16(R, T); + pSi0 += 2; + + /* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */ + R = __QSUB16(R, T); + + /* co2 & si2 are read from SIMD Coefficient pointer */ + C2 = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi1) = + (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSi1 += 2; + + /* Butterfly calculations */ + /* U = packed(yd, xd) */ + U = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi2) = + ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF); + pSi2 += 2; + + + /* co3 & si3 are read from SIMD Coefficient pointer */ + C3 = _SIMD32_OFFSET(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 */ + _SIMD32_OFFSET(pSi3) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSi3 += 2; + + /* 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 = _SIMD32_OFFSET(pCoef16 + (2U * ic)); + C2 = _SIMD32_OFFSET(pCoef16 + (4U * ic)); + C3 = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pSi0); + + /* Read yc (real), xc(imag) input */ + S = _SIMD32_OFFSET(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 = _SIMD32_OFFSET(pSi1); + + /* Read yd (real), xd(imag) input */ + U = _SIMD32_OFFSET(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); + _SIMD32_OFFSET(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 = _SIMD32_OFFSET(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) */ + _SIMD32_OFFSET(pSi1) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + pSi1 += 2 * n1; + + /* Butterfly calculations */ + + /* Read yd (real), xd(imag) input */ + U = _SIMD32_OFFSET(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) */ + _SIMD32_OFFSET(pSi2) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + 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) */ + _SIMD32_OFFSET(pSi3) = + ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF); + 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 = *__SIMD32(ptr1)++; + + /* Read xb (real), yb(imag) input */ + xbyb = *__SIMD32(ptr1)++; + + /* Read xc (real), yc(imag) input */ + xcyc = *__SIMD32(ptr1)++; + + /* Read xd (real), yd(imag) input */ + xdyd = *__SIMD32(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 */ + *__SIMD32(ptr1)++ = __SHADD16(R, T); + + /* T = packed((yb + yd), (xb + xd)) */ + T = __QADD16(xbyb, xdyd); + + /* xc' = (xa-xb+xc-xd) */ + /* yc' = (ya-yb+yc-yd) */ + *__SIMD32(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) */ + *__SIMD32(ptr1)++ = __SHASX(S, U); + + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + *__SIMD32(ptr1)++ = __SHSAX(S, U); + +#else + + /* xb' = (xa+yb-xc-yd) */ + /* yb' = (ya-xb-yc+xd) */ + *__SIMD32(ptr1)++ = __SHSAX(S, U); + + + /* xd' = (xa-yb-xc+yd) */ + /* yd' = (ya+xb-yc-xd) */ + *__SIMD32(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 + + /* Run the below code for Cortex-M0 */ + + 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/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c b/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c new file mode 100644 index 0000000..95292e4 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c @@ -0,0 +1,1389 @@ +/* ---------------------------------------------------------------------- + * 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: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +void arm_radix4_butterfly_inverse_q31( +q31_t * pSrc, +uint32_t fftLen, +q31_t * pCoef, +uint32_t twidCoefModifier); + +void arm_radix4_butterfly_q31( +q31_t * pSrc, +uint32_t fftLen, +q31_t * pCoef, +uint32_t twidCoefModifier); + +void arm_bitreversal_q31( +q31_t * pSrc, +uint32_t fftLen, +uint16_t bitRevFactor, +uint16_t * pBitRevTab); + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** + * @details + * @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 + * @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 <code>2*fftLen</code>. Processing occurs in-place. + * @return none. + * + * \par Input and output formats: + * \par + * 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 + * \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT" + * \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT" + * + */ + +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 ComplexFFT 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. + * @return none. + */ + +void arm_radix4_butterfly_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pCoef, + uint32_t twidCoefModifier) +{ +#if defined(ARM_MATH_CM7) + 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; + q63_t xaya, xbyb, xcyc, xdyd; + /* 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; + } +#else + uint32_t n1, n2, ia1, ia2, ia3, i0, 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; + q31_t *pSi0; + q31_t *pSi1; + q31_t *pSi2; + q31_t *pSi3; + q63_t xaya, xbyb, xcyc, xdyd; + /* 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; + + ia1 = 0U; + + j = n2; + + pSi0 = pSrc; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + /* Calculation of first stage */ + do + { + /* input is in 1.31(q31) format and provide 4 guard bits for the input */ + + /* Butterfly implementation */ + /* xa + xc */ + r1 = (pSi0[0] >> 4U) + (pSi2[0] >> 4U); + /* xa - xc */ + r2 = (pSi0[0] >> 4U) - (pSi2[0] >> 4U); + + /* xb + xd */ + t1 = (pSi1[0] >> 4U) + (pSi3[0] >> 4U); + + /* ya + yc */ + s1 = (pSi0[1] >> 4U) + (pSi2[1] >> 4U); + /* ya - yc */ + s2 = (pSi0[1] >> 4U) - (pSi2[1] >> 4U); + + /* xa' = xa + xb + xc + xd */ + *pSi0++ = (r1 + t1); + /* (xa + xc) - (xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = (pSi1[1] >> 4U) + (pSi3[1] >> 4U); + + /* ya' = ya + yb + yc + yd */ + *pSi0++ = (s1 + t2); + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* yb - yd */ + t1 = (pSi1[1] >> 4U) - (pSi3[1] >> 4U); + /* xb - xd */ + t2 = (pSi1[0] >> 4U) - (pSi3[0] >> 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) */ + *pSi1++ = (((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) */ + *pSi1++ = (((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) */ + *pSi2++ = (((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) */ + *pSi2++ = (((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) */ + *pSi3++ = (((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) */ + *pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) - + ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1U; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + } 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; + + pSi0 = pSrc + 2 * j; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSi0[0] + pSi2[0]; + + /* xa - xc */ + r2 = pSi0[0] - pSi2[0]; + + + /* ya + yc */ + s1 = pSi0[1] + pSi2[1]; + + /* ya - yc */ + s2 = pSi0[1] - pSi2[1]; + + + /* xb + xd */ + t1 = pSi1[0] + pSi3[0]; + + + /* xa' = xa + xb + xc + xd */ + pSi0[0] = (r1 + t1) >> 2U; + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSi1[1] + pSi3[1]; + + /* ya' = ya + yb + yc + yd */ + pSi0[1] = (s1 + t2) >> 2U; + pSi0 += 2 * n1; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSi1[1] - pSi3[1]; + + /* (xb - xd) */ + t2 = pSi1[0] - pSi3[0]; + + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSi1[0] = (((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) */ + pSi1[1] = (((int32_t) (((q63_t) s1 * co2) >> 32)) - + ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1U; + pSi1 += 2 * n1; + + /* (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) */ + pSi2[0] = (((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) */ + pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) - + ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1U; + pSi2 += 2 * n1; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSi3[0] = (((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) */ + pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) - + ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1U; + pSi3 += 2 * n1; + } + } + twidCoefModifier <<= 2U; + } +#endif + + /* 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 + { + +#ifndef ARM_MATH_BIG_ENDIAN + + /* Read xa (real), ya(imag) input */ + xaya = *__SIMD64(ptr1)++; + xa = (q31_t) xaya; + ya = (q31_t) (xaya >> 32); + + /* Read xb (real), yb(imag) input */ + xbyb = *__SIMD64(ptr1)++; + xb = (q31_t) xbyb; + yb = (q31_t) (xbyb >> 32); + + /* Read xc (real), yc(imag) input */ + xcyc = *__SIMD64(ptr1)++; + xc = (q31_t) xcyc; + yc = (q31_t) (xcyc >> 32); + + /* Read xc (real), yc(imag) input */ + xdyd = *__SIMD64(ptr1)++; + xd = (q31_t) xdyd; + yd = (q31_t) (xdyd >> 32); + +#else + + /* Read xa (real), ya(imag) input */ + xaya = *__SIMD64(ptr1)++; + ya = (q31_t) xaya; + xa = (q31_t) (xaya >> 32); + + /* Read xb (real), yb(imag) input */ + xbyb = *__SIMD64(ptr1)++; + yb = (q31_t) xbyb; + xb = (q31_t) (xbyb >> 32); + + /* Read xc (real), yc(imag) input */ + xcyc = *__SIMD64(ptr1)++; + yc = (q31_t) xcyc; + xc = (q31_t) (xcyc >> 32); + + /* Read xc (real), yc(imag) input */ + xdyd = *__SIMD64(ptr1)++; + yd = (q31_t) xdyd; + xd = (q31_t) (xdyd >> 32); + + +#endif + + /* 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. + * @return none. + */ + + +/* +* 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) +* +*/ + +void arm_radix4_butterfly_inverse_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pCoef, + uint32_t twidCoefModifier) +{ +#if defined(ARM_MATH_CM7) + 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; + q63_t xaya, xbyb, xcyc, xdyd; + + /* 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; + } +#else + uint32_t n1, n2, ia1, ia2, ia3, i0, 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; + q31_t *pSi0; + q31_t *pSi1; + q31_t *pSi2; + q31_t *pSi3; + q63_t xaya, xbyb, xcyc, xdyd; + + /* 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; + + ia1 = 0U; + + j = n2; + + pSi0 = pSrc; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + do + { + /* Butterfly implementation */ + /* xa + xc */ + r1 = (pSi0[0] >> 4U) + (pSi2[0] >> 4U); + /* xa - xc */ + r2 = (pSi0[0] >> 4U) - (pSi2[0] >> 4U); + + /* xb + xd */ + t1 = (pSi1[0] >> 4U) + (pSi3[0] >> 4U); + + /* ya + yc */ + s1 = (pSi0[1] >> 4U) + (pSi2[1] >> 4U); + /* ya - yc */ + s2 = (pSi0[1] >> 4U) - (pSi2[1] >> 4U); + + /* xa' = xa + xb + xc + xd */ + *pSi0++ = (r1 + t1); + /* (xa + xc) - (xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = (pSi1[1] >> 4U) + (pSi3[1] >> 4U); + /* ya' = ya + yb + yc + yd */ + *pSi0++ = (s1 + t2); + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* yb - yd */ + t1 = (pSi1[1] >> 4U) - (pSi3[1] >> 4U); + /* xb - xd */ + t2 = (pSi1[0] >> 4U) - (pSi3[0] >> 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) */ + *pSi1++ = (((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) */ + *pSi1++ = (((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) */ + *pSi2++ = (((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) */ + *pSi2++ = (((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) */ + *pSi3++ = (((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) */ + *pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) + + ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1U; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + } 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; + + pSi0 = pSrc + 2 * j; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSi0[0] + pSi2[0]; + + /* xa - xc */ + r2 = pSi0[0] - pSi2[0]; + + + /* ya + yc */ + s1 = pSi0[1] + pSi2[1]; + + /* ya - yc */ + s2 = pSi0[1] - pSi2[1]; + + + /* xb + xd */ + t1 = pSi1[0] + pSi3[0]; + + + /* xa' = xa + xb + xc + xd */ + pSi0[0] = (r1 + t1) >> 2U; + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = pSi1[1] + pSi3[1]; + + /* ya' = ya + yb + yc + yd */ + pSi0[1] = (s1 + t2) >> 2U; + pSi0 += 2 * n1; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSi1[1] - pSi3[1]; + + /* (xb - xd) */ + t2 = pSi1[0] - pSi3[0]; + + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSi1[0] = (((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) */ + pSi1[1] = + + (((int32_t) (((q63_t) s1 * co2) >> 32U)) + + ((int32_t) (((q63_t) r1 * si2) >> 32U))) >> 1U; + pSi1 += 2 * n1; + + /* (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) */ + pSi2[0] = (((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) */ + pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) + + ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1U; + pSi2 += 2 * n1; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSi3[0] = (((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) */ + pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) + + ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1U; + pSi3 += 2 * n1; + } + } + twidCoefModifier <<= 2U; + } +#endif + + /* 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 + { +#ifndef ARM_MATH_BIG_ENDIAN + /* Read xa (real), ya(imag) input */ + xaya = *__SIMD64(ptr1)++; + xa = (q31_t) xaya; + ya = (q31_t) (xaya >> 32); + + /* Read xb (real), yb(imag) input */ + xbyb = *__SIMD64(ptr1)++; + xb = (q31_t) xbyb; + yb = (q31_t) (xbyb >> 32); + + /* Read xc (real), yc(imag) input */ + xcyc = *__SIMD64(ptr1)++; + xc = (q31_t) xcyc; + yc = (q31_t) (xcyc >> 32); + + /* Read xc (real), yc(imag) input */ + xdyd = *__SIMD64(ptr1)++; + xd = (q31_t) xdyd; + yd = (q31_t) (xdyd >> 32); + +#else + + /* Read xa (real), ya(imag) input */ + xaya = *__SIMD64(ptr1)++; + ya = (q31_t) xaya; + xa = (q31_t) (xaya >> 32); + + /* Read xb (real), yb(imag) input */ + xbyb = *__SIMD64(ptr1)++; + yb = (q31_t) xbyb; + xb = (q31_t) (xbyb >> 32); + + /* Read xc (real), yc(imag) input */ + xcyc = *__SIMD64(ptr1)++; + yc = (q31_t) xcyc; + xc = (q31_t) (xcyc >> 32); + + /* Read xc (real), yc(imag) input */ + xdyd = *__SIMD64(ptr1)++; + yd = (q31_t) xdyd; + xd = (q31_t) (xdyd >> 32); + + +#endif + + /* 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/DSP/Source/TransformFunctions/arm_cfft_radix8_f32.c b/DSP/Source/TransformFunctions/arm_cfft_radix8_f32.c new file mode 100644 index 0000000..b70ab38 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_cfft_radix8_f32.c @@ -0,0 +1,285 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_radix8_f32.c + * Description: Radix-8 Decimation in Frequency CFFT & CIFFT Floating point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + + +/* ---------------------------------------------------------------------- + * 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. +*/ + +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/DSP/Source/TransformFunctions/arm_dct4_f32.c b/DSP/Source/TransformFunctions/arm_dct4_f32.c new file mode 100644 index 0000000..231c79a --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_dct4_f32.c @@ -0,0 +1,449 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_dct4_f32.c + * Description: Processing function of DCT4 & IDCT4 F32 + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @defgroup DCT4_IDCT4 DCT Type IV Functions + * Representation of signals by minimum number of values is important for storage and transmission. + * The possibility of large discontinuity between the beginning and end of a period of a signal + * in DFT can be avoided by extending the signal so that it is even-symmetric. + * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the + * spectrum and is very widely used in signal and image coding applications. + * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions. + * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular. + * + * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal. + * Reordering of the input data makes the computation of DCT just a problem of + * computing the DFT of a real signal with a few additional operations. + * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations. + * + * DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used. + * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing. + * DCT2 implementation can be described in the following steps: + * - Re-ordering input + * - Calculating Real FFT + * - Multiplication of weights and Real FFT output and getting real part from the product. + * + * This process is explained by the block diagram below: + * \image html DCT4.gif "Discrete Cosine Transform - type-IV" + * + * \par Algorithm: + * The N-point type-IV DCT is defined as a real, linear transformation by the formula: + * \image html DCT4Equation.gif + * where <code>k = 0,1,2,.....N-1</code> + *\par + * Its inverse is defined as follows: + * \image html IDCT4Equation.gif + * where <code>n = 0,1,2,.....N-1</code> + *\par + * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N). + * The symmetry of the transform matrix indicates that the fast algorithms for the forward + * and inverse transform computation are identical. + * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both. + * + * \par Lengths supported by the transform: + * As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192. + * The library provides separate functions for Q15, Q31, and floating-point data types. + * \par Instance Structure + * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure. + * A separate instance structure must be defined for each transform. + * There are separate instance structure declarations for each of the 3 supported data types. + * + * \par Initialization Functions + * 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 Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32(). + * \par + * Use of the initialization function is optional. + * However, if the initialization function is used, then the instance structure cannot be placed into a const data section. + * To place an instance structure into a const data section, the instance structure must be manually initialized. + * Manually initialize the instance structure as follows: + * <pre> + *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; + *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; + *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; + * </pre> + * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4; + * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>; + * \c pTwiddle points to the twiddle factor table; + * \c pCosFactor points to the cosFactor table; + * \c pRfft points to the real FFT instance; + * \c pCfft points to the complex FFT instance; + * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32() + * and arm_rfft_f32() respectively for details regarding static initialization. + * + * \par Fixed-Point Behavior + * Care must be taken when using the fixed-point versions of the DCT4 transform 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 DCT4_IDCT4 + * @{ + */ + +/** + * @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. + * @return none. + */ + +void arm_dct4_f32( + const arm_dct4_instance_f32 * S, + float32_t * pState, + float32_t * pInlineBuffer) +{ + uint32_t i; /* Loop counter */ + float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */ + float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ + float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ + float32_t in; /* Temporary variable */ + + + /* DCT4 computation involves DCT2 (which is calculated using RFFT) + * along with some pre-processing and post-processing. + * Computational procedure is explained as follows: + * (a) Pre-processing involves multiplying input with cos factor, + * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n)) + * where, + * r(n) -- output of preprocessing + * u(n) -- input to preprocessing(actual Source buffer) + * (b) Calculation of DCT2 using FFT is divided into three steps: + * Step1: Re-ordering of even and odd elements of input. + * Step2: Calculating FFT of the re-ordered input. + * Step3: Taking the real part of the product of FFT output and weights. + * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation: + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * where, + * Y4 -- DCT4 output, Y2 -- DCT2 output + * (d) Multiplying the output with the normalizing factor sqrt(2/N). + */ + + /*-------- Pre-processing ------------*/ + /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ + arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N); + arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N); + + /* ---------------------------------------------------------------- + * Step1: Re-ordering of even and odd elements as, + * pState[i] = pInlineBuffer[2*i] and + * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2 + ---------------------------------------------------------------------*/ + + /* pS1 initialized to pState */ + pS1 = pState; + + /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ + pS2 = pState + (S->N - 1U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ + i = (uint32_t) S->Nby2 >> 2U; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + do + { + /* Re-ordering of even and odd elements */ + /* pState[i] = pInlineBuffer[2*i] */ + *pS1++ = *pbuff++; + /* pState[N-i-1] = pInlineBuffer[2*i+1] */ + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Initializing the loop counter to N/4 instead of N for loop unrolling */ + i = (uint32_t) S->N >> 2U; + + /* Processing with loop unrolling 4 times as N is always multiple of 4. + * Compute 4 outputs at a time */ + do + { + /* Writing the re-ordered output back to inplace input buffer */ + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /* --------------------------------------------------------- + * Step2: Calculate RFFT for N-point input + * ---------------------------------------------------------- */ + /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ + arm_rfft_f32(S->pRfft, pInlineBuffer, pState); + + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); + + /* ----------- Post-processing ---------- */ + /* DCT-IV can be obtained from DCT-II by the equation, + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * Hence, Y4(0) = Y2(0)/2 */ + /* Getting only real part from the output and Converting to DCT-IV */ + + /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ + i = ((uint32_t) S->N - 1U) >> 2U; + + /* pbuff initialized to input buffer. */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ + in = *pS1++ * (float32_t) 0.5; + /* input buffer acts as inplace, so output values are stored in the input itself. */ + *pbuff++ = in; + + /* pState pointer is incremented twice as the real values are located alternatively in the array */ + pS1++; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + do + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + i = ((uint32_t) S->N - 1U) % 0x4U; + + while (i > 0U) + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + /* Decrement the loop counter */ + i--; + } + + + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + + /* Initializing the loop counter to N/4 instead of N for loop unrolling */ + i = (uint32_t) S->N >> 2U; + + /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + pbuff = pInlineBuffer; + + /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */ + do + { + /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ + in = *pbuff; + *pbuff++ = in * S->normalize; + + in = *pbuff; + *pbuff++ = in * S->normalize; + + in = *pbuff; + *pbuff++ = in * S->normalize; + + in = *pbuff; + *pbuff++ = in * S->normalize; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initializing the loop counter to N/2 */ + i = (uint32_t) S->Nby2; + + do + { + /* Re-ordering of even and odd elements */ + /* pState[i] = pInlineBuffer[2*i] */ + *pS1++ = *pbuff++; + /* pState[N-i-1] = pInlineBuffer[2*i+1] */ + *pS2-- = *pbuff++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Initializing the loop counter */ + i = (uint32_t) S->N; + + do + { + /* Writing the re-ordered output back to inplace input buffer */ + *pbuff++ = *pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /* --------------------------------------------------------- + * Step2: Calculate RFFT for N-point input + * ---------------------------------------------------------- */ + /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ + arm_rfft_f32(S->pRfft, pInlineBuffer, pState); + + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); + + /* ----------- Post-processing ---------- */ + /* DCT-IV can be obtained from DCT-II by the equation, + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * Hence, Y4(0) = Y2(0)/2 */ + /* Getting only real part from the output and Converting to DCT-IV */ + + /* pbuff initialized to input buffer. */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ + in = *pS1++ * (float32_t) 0.5; + /* input buffer acts as inplace, so output values are stored in the input itself. */ + *pbuff++ = in; + + /* pState pointer is incremented twice as the real values are located alternatively in the array */ + pS1++; + + /* Initializing the loop counter */ + i = ((uint32_t) S->N - 1U); + + do + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + + /* Initializing the loop counter */ + i = (uint32_t) S->N; + + /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + pbuff = pInlineBuffer; + + do + { + /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ + in = *pbuff; + *pbuff++ = in * S->normalize; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + +/** + * @} end of DCT4_IDCT4 group + */ diff --git a/DSP/Source/TransformFunctions/arm_dct4_init_f32.c b/DSP/Source/TransformFunctions/arm_dct4_init_f32.c new file mode 100644 index 0000000..9b39cd4 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_dct4_init_f32.c @@ -0,0 +1,16513 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_dct4_init_f32.c + * Description: Initialization function of DCT-4 & IDCT4 F32 + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @ingroup DCT4_IDCT4 + */ + +/** + * @addtogroup DCT4_IDCT4_Table DCT Type IV Tables + * @{ + */ + +/* +* @brief Weights Table +*/ + +/** + * \par + * Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre> + * \par + * C command to generate the table + * <pre> + * for(i = 0; i< N; i++) + * { + * weights[2*i]= cos(i*c); + * weights[(2*i)+1]= -sin(i * c); + * } </pre> + * \par + * Where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code> + * \par + * In the tables below the real and imaginary values are placed alternatively, hence the + * array length is <code>2*N</code>. + */ + +static const float32_t Weights_128[256] = { + 1.000000000000000000f, 0.000000000000000000f, 0.999924701839144500f, + -0.012271538285719925f, + 0.999698818696204250f, -0.024541228522912288f, 0.999322384588349540f, + -0.036807222941358832f, + 0.998795456205172410f, -0.049067674327418015f, 0.998118112900149180f, + -0.061320736302208578f, + 0.997290456678690210f, -0.073564563599667426f, 0.996312612182778000f, + -0.085797312344439894f, + 0.995184726672196930f, -0.098017140329560604f, 0.993906970002356060f, + -0.110222207293883060f, + 0.992479534598709970f, -0.122410675199216200f, 0.990902635427780010f, + -0.134580708507126170f, + 0.989176509964781010f, -0.146730474455361750f, 0.987301418157858430f, + -0.158858143333861450f, + 0.985277642388941220f, -0.170961888760301220f, 0.983105487431216290f, + -0.183039887955140950f, + 0.980785280403230430f, -0.195090322016128250f, 0.978317370719627650f, + -0.207111376192218560f, + 0.975702130038528570f, -0.219101240156869800f, 0.972939952205560180f, + -0.231058108280671110f, + 0.970031253194543970f, -0.242980179903263870f, 0.966976471044852070f, + -0.254865659604514570f, + 0.963776065795439840f, -0.266712757474898370f, 0.960430519415565790f, + -0.278519689385053060f, + 0.956940335732208820f, -0.290284677254462330f, 0.953306040354193860f, + -0.302005949319228080f, + 0.949528180593036670f, -0.313681740398891520f, 0.945607325380521280f, + -0.325310292162262930f, + 0.941544065183020810f, -0.336889853392220050f, 0.937339011912574960f, + -0.348418680249434560f, + 0.932992798834738960f, -0.359895036534988110f, 0.928506080473215590f, + -0.371317193951837540f, + 0.923879532511286740f, -0.382683432365089780f, 0.919113851690057770f, + -0.393992040061048100f, + 0.914209755703530690f, -0.405241314004989860f, 0.909167983090522380f, + -0.416429560097637150f, + 0.903989293123443340f, -0.427555093430282080f, 0.898674465693953820f, + -0.438616238538527660f, + 0.893224301195515320f, -0.449611329654606540f, 0.887639620402853930f, + -0.460538710958240010f, + 0.881921264348355050f, -0.471396736825997640f, 0.876070094195406600f, + -0.482183772079122720f, + 0.870086991108711460f, -0.492898192229784040f, 0.863972856121586810f, + -0.503538383725717580f, + 0.857728610000272120f, -0.514102744193221660f, 0.851355193105265200f, + -0.524589682678468950f, + 0.844853565249707120f, -0.534997619887097150f, 0.838224705554838080f, + -0.545324988422046460f, + 0.831469612302545240f, -0.555570233019602180f, 0.824589302785025290f, + -0.565731810783613120f, + 0.817584813151583710f, -0.575808191417845340f, 0.810457198252594770f, + -0.585797857456438860f, + 0.803207531480644940f, 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-0.999997775588762350f, + 0.001917474809855460f, -0.999998161643486980f, 0.001725727529795258f, + -0.999998510931137790f, + 0.001533980186284766f, -0.999998823451701880f, 0.001342232786374430f, + -0.999999099205167830f, + 0.001150485337113809f, -0.999999338191525530f, 0.000958737845553352f, + -0.999999540410766110f, + 0.000766990318742846f, -0.999999705862882230f, 0.000575242763732077f, + -0.999999834547867670f, + 0.000383495187571497f, -0.999999926465717890f, 0.000191747597310674f, + -0.999999981616429330f +}; + +/** +* \par +* cosFactor tables are generated using the formula : <pre>cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))</pre> +* \par +* C command to generate the table +* \par +* <pre> for(i = 0; i< N; i++) +* { +* cos_factors[i]= 2 * cos((2*i+1)*c/2); +* } </pre> +* \par +* where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code> +*/ +static const float32_t cos_factors_128[128] = { + 0.999981175282601110f, 0.999830581795823400f, 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0.030674803176636581f, 0.018406729905804820f, + 0.006135884649154515f +}; + +static const float32_t cos_factors_512[512] = { + 0.999998823451701880f, 0.999989411081928400f, 0.999970586430974140f, + 0.999942349676023910f, + 0.999904701082852900f, 0.999857641005823860f, 0.999801169887884260f, + 0.999735288260561680f, + 0.999659996743959220f, 0.999575296046749220f, 0.999481186966166950f, + 0.999377670388002850f, + 0.999264747286594420f, 0.999142418724816910f, 0.999010685854073380f, + 0.998869549914283560f, + 0.998719012233872940f, 0.998559074229759310f, 0.998389737407340160f, + 0.998211003360478190f, + 0.998022873771486240f, 0.997825350411111640f, 0.997618435138519550f, + 0.997402129901275300f, + 0.997176436735326190f, 0.996941357764982160f, 0.996696895202896060f, + 0.996443051350042630f, + 0.996179828595696980f, 0.995907229417411720f, 0.995625256380994310f, + 0.995333912140482280f, + 0.995033199438118630f, 0.994723121104325700f, 0.994403680057679100f, + 0.994074879304879370f, + 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0.075094300847921291f, + 0.072034653246889416f, 0.068974327628266732f, 0.065913352797003930f, + 0.062851757564161420f, + 0.059789570746640007f, 0.056726821166907783f, 0.053663537652730679f, + 0.050599749036899337f, + 0.047535484156959261f, 0.044470771854938744f, 0.041405640977076712f, + 0.038340120373552791f, + 0.035274238898213947f, 0.032208025408304704f, 0.029141508764193740f, + 0.026074717829104040f, + 0.023007681468839410f, 0.019940428551514598f, 0.016872987947281773f, + 0.013805388528060349f, + 0.010737659167264572f, 0.007669828739531077f, 0.004601926120448672f, + 0.001533980186284766f +}; + +static const float32_t cos_factors_2048[2048] = { + 0.999999926465717890f, 0.999999338191525530f, 0.999998161643486980f, + 0.999996396822294350f, + 0.999994043728985820f, 0.999991102364945590f, 0.999987572731904080f, + 0.999983454831937730f, + 0.999978748667468830f, 0.999973454241265940f, 0.999967571556443780f, + 0.999961100616462820f, + 0.999954041425129780f, 0.999946393986597460f, 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0.007094646264638386f, 0.006711153352455981f, + 0.006327660193523208f, + 0.005944166801940901f, 0.005560673191808128f, 0.005177179377225743f, + 0.004793685372293270f, + 0.004410191191110246f, 0.004026696847777542f, 0.003643202356394263f, + 0.003259707731061291f, + 0.002876212985878184f, 0.002492718134944503f, 0.002109223192361147f, + 0.001725728172227238f, + 0.001342233088643682f, 0.000958737955710053f, 0.000575242787525925f, + 0.000191747598192208f +}; + +/** + * @} end of DCT4_IDCT4_Table group + */ + +/** + * @addtogroup DCT4_IDCT4 + * @{ + */ + +/** + * @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 <code>fftLenReal</code> is not a supported transform length. + * \par Normalizing factor: + * The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>. + * Floating-point normalizing factors are mentioned in the table below for different DCT sizes: + * \image html dct4NormalizingF32Table.gif + */ + +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) +{ + /* Initialize the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializing the pointer array with the weight table base addresses of different lengths */ + float32_t *twiddlePtr[4] = + { (float32_t *) Weights_128, (float32_t *) Weights_512, + (float32_t *) Weights_2048, (float32_t *) Weights_8192 + }; + + /* Initializing the pointer array with the cos factor table base addresses of different lengths */ + float32_t *pCosFactor[4] = + { (float32_t *) cos_factors_128, (float32_t *) cos_factors_512, + (float32_t *) cos_factors_2048, (float32_t *) cos_factors_8192 + }; + + /* Initialize the DCT4 length */ + S->N = N; + + /* Initialize the half of DCT4 length */ + S->Nby2 = Nby2; + + /* Initialize the DCT4 Normalizing factor */ + S->normalize = normalize; + + /* Initialize Real FFT Instance */ + S->pRfft = S_RFFT; + + /* Initialize Complex FFT Instance */ + S->pCfft = S_CFFT; + + switch (N) + { + /* Initialize the table modifier values */ + case 8192U: + S->pTwiddle = twiddlePtr[3]; + S->pCosFactor = pCosFactor[3]; + break; + case 2048U: + S->pTwiddle = twiddlePtr[2]; + S->pCosFactor = pCosFactor[2]; + break; + case 512U: + S->pTwiddle = twiddlePtr[1]; + S->pCosFactor = pCosFactor[1]; + break; + case 128U: + S->pTwiddle = twiddlePtr[0]; + S->pCosFactor = pCosFactor[0]; + break; + default: + status = ARM_MATH_ARGUMENT_ERROR; + } + + /* Initialize the RFFT/RIFFT */ + arm_rfft_init_f32(S->pRfft, S->pCfft, S->N, 0U, 1U); + + /* return the status of DCT4 Init function */ + return (status); +} + +/** + * @} end of DCT4_IDCT4 group + */ diff --git a/DSP/Source/TransformFunctions/arm_dct4_init_q15.c b/DSP/Source/TransformFunctions/arm_dct4_init_q15.c new file mode 100644 index 0000000..e57541c --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_dct4_init_q15.c @@ -0,0 +1,4280 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_dct4_init_q15.c + * Description: Initialization function of DCT-4 & IDCT4 Q15 + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @ingroup DCT4_IDCT4 + */ + +/** + * @addtogroup DCT4_IDCT4_Table DCT Type IV Tables + * @{ + */ + +/* +* @brief Weights Table +*/ + +/** + * \par + * Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre> + * \par + * C command to generate the table + * <pre> + * for(i = 0; i< N; i++) + * { + * weights[2*i]= cos(i*c); + * weights[(2*i)+1]= -sin(i * c); + * } </pre> + * \par + * where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code> + * \par + * Converted the output to q15 format by multiplying with 2^31 and saturated if required. + * \par + * In the tables below the real and imaginary values are placed alternatively, hence the + * array length is <code>2*N</code>. + */ + +static const q15_t ALIGN4 WeightsQ15_128[256] = { + (q15_t)0x7fff, (q15_t)0x0, (q15_t)0x7ffd, (q15_t)0xfe6e, (q15_t)0x7ff6, (q15_t)0xfcdc, (q15_t)0x7fe9, (q15_t)0xfb4a, + (q15_t)0x7fd8, (q15_t)0xf9b9, (q15_t)0x7fc2, (q15_t)0xf827, (q15_t)0x7fa7, (q15_t)0xf696, (q15_t)0x7f87, (q15_t)0xf505, + (q15_t)0x7f62, (q15_t)0xf375, (q15_t)0x7f38, (q15_t)0xf1e5, (q15_t)0x7f09, (q15_t)0xf055, (q15_t)0x7ed5, (q15_t)0xeec7, + (q15_t)0x7e9d, (q15_t)0xed38, (q15_t)0x7e5f, (q15_t)0xebab, (q15_t)0x7e1d, (q15_t)0xea1e, (q15_t)0x7dd6, (q15_t)0xe893, + (q15_t)0x7d8a, (q15_t)0xe708, (q15_t)0x7d39, (q15_t)0xe57e, (q15_t)0x7ce3, (q15_t)0xe3f5, (q15_t)0x7c89, (q15_t)0xe26d, + (q15_t)0x7c29, (q15_t)0xe0e7, (q15_t)0x7bc5, (q15_t)0xdf61, (q15_t)0x7b5d, (q15_t)0xdddd, (q15_t)0x7aef, (q15_t)0xdc5a, + (q15_t)0x7a7d, (q15_t)0xdad8, (q15_t)0x7a05, (q15_t)0xd958, (q15_t)0x798a, (q15_t)0xd7da, (q15_t)0x7909, (q15_t)0xd65d, + (q15_t)0x7884, (q15_t)0xd4e1, (q15_t)0x77fa, (q15_t)0xd368, (q15_t)0x776c, (q15_t)0xd1ef, (q15_t)0x76d9, (q15_t)0xd079, + (q15_t)0x7641, (q15_t)0xcf05, (q15_t)0x75a5, (q15_t)0xcd92, (q15_t)0x7504, (q15_t)0xcc22, (q15_t)0x745f, (q15_t)0xcab3, + (q15_t)0x73b5, (q15_t)0xc946, (q15_t)0x7307, (q15_t)0xc7dc, (q15_t)0x7255, (q15_t)0xc674, (q15_t)0x719e, (q15_t)0xc50e, + (q15_t)0x70e2, (q15_t)0xc3aa, (q15_t)0x7023, (q15_t)0xc248, (q15_t)0x6f5f, (q15_t)0xc0e9, (q15_t)0x6e96, (q15_t)0xbf8d, + (q15_t)0x6dca, (q15_t)0xbe32, (q15_t)0x6cf9, (q15_t)0xbcdb, (q15_t)0x6c24, (q15_t)0xbb86, (q15_t)0x6b4a, (q15_t)0xba33, + (q15_t)0x6a6d, (q15_t)0xb8e4, (q15_t)0x698c, (q15_t)0xb797, (q15_t)0x68a6, (q15_t)0xb64c, (q15_t)0x67bd, (q15_t)0xb505, + (q15_t)0x66cf, (q15_t)0xb3c1, (q15_t)0x65dd, (q15_t)0xb27f, (q15_t)0x64e8, (q15_t)0xb141, (q15_t)0x63ef, (q15_t)0xb005, + (q15_t)0x62f2, (q15_t)0xaecd, (q15_t)0x61f1, (q15_t)0xad97, (q15_t)0x60ec, (q15_t)0xac65, (q15_t)0x5fe3, (q15_t)0xab36, + (q15_t)0x5ed7, (q15_t)0xaa0b, (q15_t)0x5dc7, (q15_t)0xa8e3, (q15_t)0x5cb4, (q15_t)0xa7be, (q15_t)0x5b9d, (q15_t)0xa69c, + (q15_t)0x5a82, (q15_t)0xa57e, (q15_t)0x5964, (q15_t)0xa463, (q15_t)0x5842, (q15_t)0xa34c, (q15_t)0x571d, (q15_t)0xa239, + (q15_t)0x55f5, (q15_t)0xa129, (q15_t)0x54ca, (q15_t)0xa01d, (q15_t)0x539b, (q15_t)0x9f14, (q15_t)0x5269, (q15_t)0x9e0f, + (q15_t)0x5133, (q15_t)0x9d0e, (q15_t)0x4ffb, (q15_t)0x9c11, (q15_t)0x4ebf, (q15_t)0x9b18, (q15_t)0x4d81, (q15_t)0x9a23, + (q15_t)0x4c3f, (q15_t)0x9931, (q15_t)0x4afb, (q15_t)0x9843, (q15_t)0x49b4, (q15_t)0x975a, (q15_t)0x4869, (q15_t)0x9674, + (q15_t)0x471c, (q15_t)0x9593, (q15_t)0x45cd, (q15_t)0x94b6, (q15_t)0x447a, (q15_t)0x93dc, (q15_t)0x4325, (q15_t)0x9307, + (q15_t)0x41ce, (q15_t)0x9236, (q15_t)0x4073, (q15_t)0x916a, (q15_t)0x3f17, (q15_t)0x90a1, (q15_t)0x3db8, (q15_t)0x8fdd, + (q15_t)0x3c56, (q15_t)0x8f1e, (q15_t)0x3af2, (q15_t)0x8e62, (q15_t)0x398c, (q15_t)0x8dab, (q15_t)0x3824, (q15_t)0x8cf9, + (q15_t)0x36ba, (q15_t)0x8c4b, (q15_t)0x354d, (q15_t)0x8ba1, (q15_t)0x33de, (q15_t)0x8afc, (q15_t)0x326e, (q15_t)0x8a5b, + (q15_t)0x30fb, (q15_t)0x89bf, (q15_t)0x2f87, (q15_t)0x8927, (q15_t)0x2e11, (q15_t)0x8894, (q15_t)0x2c98, (q15_t)0x8806, + (q15_t)0x2b1f, (q15_t)0x877c, (q15_t)0x29a3, (q15_t)0x86f7, (q15_t)0x2826, (q15_t)0x8676, (q15_t)0x26a8, (q15_t)0x85fb, + (q15_t)0x2528, (q15_t)0x8583, (q15_t)0x23a6, (q15_t)0x8511, (q15_t)0x2223, (q15_t)0x84a3, (q15_t)0x209f, (q15_t)0x843b, + (q15_t)0x1f19, (q15_t)0x83d7, (q15_t)0x1d93, (q15_t)0x8377, (q15_t)0x1c0b, (q15_t)0x831d, (q15_t)0x1a82, (q15_t)0x82c7, + (q15_t)0x18f8, (q15_t)0x8276, (q15_t)0x176d, (q15_t)0x822a, (q15_t)0x15e2, (q15_t)0x81e3, (q15_t)0x1455, (q15_t)0x81a1, + (q15_t)0x12c8, (q15_t)0x8163, (q15_t)0x1139, (q15_t)0x812b, (q15_t)0xfab, (q15_t)0x80f7, (q15_t)0xe1b, (q15_t)0x80c8, + (q15_t)0xc8b, (q15_t)0x809e, (q15_t)0xafb, (q15_t)0x8079, (q15_t)0x96a, (q15_t)0x8059, (q15_t)0x7d9, (q15_t)0x803e, + (q15_t)0x647, (q15_t)0x8028, (q15_t)0x4b6, (q15_t)0x8017, (q15_t)0x324, (q15_t)0x800a, (q15_t)0x192, (q15_t)0x8003 +}; + +static const q15_t ALIGN4 WeightsQ15_512[1024] = { + (q15_t)0x7fff, (q15_t)0x0, (q15_t)0x7fff, (q15_t)0xff9c, (q15_t)0x7fff, (q15_t)0xff37, (q15_t)0x7ffe, (q15_t)0xfed3, + (q15_t)0x7ffd, (q15_t)0xfe6e, (q15_t)0x7ffc, (q15_t)0xfe0a, (q15_t)0x7ffa, (q15_t)0xfda5, (q15_t)0x7ff8, (q15_t)0xfd41, + (q15_t)0x7ff6, (q15_t)0xfcdc, (q15_t)0x7ff3, (q15_t)0xfc78, (q15_t)0x7ff0, (q15_t)0xfc13, (q15_t)0x7fed, (q15_t)0xfbaf, + (q15_t)0x7fe9, (q15_t)0xfb4a, (q15_t)0x7fe5, (q15_t)0xfae6, (q15_t)0x7fe1, (q15_t)0xfa81, (q15_t)0x7fdd, (q15_t)0xfa1d, + (q15_t)0x7fd8, (q15_t)0xf9b9, (q15_t)0x7fd3, (q15_t)0xf954, (q15_t)0x7fce, (q15_t)0xf8f0, (q15_t)0x7fc8, (q15_t)0xf88b, + (q15_t)0x7fc2, (q15_t)0xf827, (q15_t)0x7fbc, (q15_t)0xf7c3, (q15_t)0x7fb5, (q15_t)0xf75e, (q15_t)0x7fae, (q15_t)0xf6fa, + (q15_t)0x7fa7, (q15_t)0xf696, (q15_t)0x7f9f, (q15_t)0xf632, (q15_t)0x7f97, (q15_t)0xf5cd, (q15_t)0x7f8f, (q15_t)0xf569, + (q15_t)0x7f87, (q15_t)0xf505, (q15_t)0x7f7e, (q15_t)0xf4a1, (q15_t)0x7f75, (q15_t)0xf43d, (q15_t)0x7f6b, (q15_t)0xf3d9, + (q15_t)0x7f62, (q15_t)0xf375, (q15_t)0x7f58, (q15_t)0xf311, (q15_t)0x7f4d, (q15_t)0xf2ad, (q15_t)0x7f43, (q15_t)0xf249, + (q15_t)0x7f38, (q15_t)0xf1e5, (q15_t)0x7f2d, (q15_t)0xf181, (q15_t)0x7f21, (q15_t)0xf11d, (q15_t)0x7f15, (q15_t)0xf0b9, + (q15_t)0x7f09, (q15_t)0xf055, (q15_t)0x7efd, (q15_t)0xeff2, (q15_t)0x7ef0, (q15_t)0xef8e, (q15_t)0x7ee3, (q15_t)0xef2a, + (q15_t)0x7ed5, (q15_t)0xeec7, (q15_t)0x7ec8, (q15_t)0xee63, (q15_t)0x7eba, (q15_t)0xedff, (q15_t)0x7eab, (q15_t)0xed9c, + (q15_t)0x7e9d, (q15_t)0xed38, (q15_t)0x7e8e, (q15_t)0xecd5, (q15_t)0x7e7f, (q15_t)0xec72, (q15_t)0x7e6f, (q15_t)0xec0e, + (q15_t)0x7e5f, (q15_t)0xebab, (q15_t)0x7e4f, (q15_t)0xeb48, (q15_t)0x7e3f, (q15_t)0xeae5, (q15_t)0x7e2e, (q15_t)0xea81, + (q15_t)0x7e1d, (q15_t)0xea1e, (q15_t)0x7e0c, (q15_t)0xe9bb, (q15_t)0x7dfa, (q15_t)0xe958, (q15_t)0x7de8, (q15_t)0xe8f6, + (q15_t)0x7dd6, (q15_t)0xe893, (q15_t)0x7dc3, (q15_t)0xe830, (q15_t)0x7db0, (q15_t)0xe7cd, (q15_t)0x7d9d, (q15_t)0xe76a, + (q15_t)0x7d8a, (q15_t)0xe708, (q15_t)0x7d76, (q15_t)0xe6a5, (q15_t)0x7d62, (q15_t)0xe643, (q15_t)0x7d4e, (q15_t)0xe5e0, + (q15_t)0x7d39, (q15_t)0xe57e, (q15_t)0x7d24, (q15_t)0xe51c, (q15_t)0x7d0f, (q15_t)0xe4b9, (q15_t)0x7cf9, (q15_t)0xe457, + (q15_t)0x7ce3, (q15_t)0xe3f5, (q15_t)0x7ccd, (q15_t)0xe393, (q15_t)0x7cb7, (q15_t)0xe331, (q15_t)0x7ca0, (q15_t)0xe2cf, + (q15_t)0x7c89, (q15_t)0xe26d, (q15_t)0x7c71, (q15_t)0xe20b, (q15_t)0x7c5a, (q15_t)0xe1aa, (q15_t)0x7c42, (q15_t)0xe148, + (q15_t)0x7c29, (q15_t)0xe0e7, (q15_t)0x7c11, (q15_t)0xe085, (q15_t)0x7bf8, (q15_t)0xe024, (q15_t)0x7bdf, (q15_t)0xdfc2, + (q15_t)0x7bc5, (q15_t)0xdf61, (q15_t)0x7bac, (q15_t)0xdf00, (q15_t)0x7b92, (q15_t)0xde9f, (q15_t)0x7b77, (q15_t)0xde3e, + (q15_t)0x7b5d, (q15_t)0xdddd, (q15_t)0x7b42, (q15_t)0xdd7c, (q15_t)0x7b26, (q15_t)0xdd1b, (q15_t)0x7b0b, (q15_t)0xdcbb, + (q15_t)0x7aef, (q15_t)0xdc5a, (q15_t)0x7ad3, (q15_t)0xdbf9, (q15_t)0x7ab6, (q15_t)0xdb99, (q15_t)0x7a9a, (q15_t)0xdb39, + (q15_t)0x7a7d, (q15_t)0xdad8, (q15_t)0x7a5f, (q15_t)0xda78, (q15_t)0x7a42, (q15_t)0xda18, (q15_t)0x7a24, (q15_t)0xd9b8, + (q15_t)0x7a05, (q15_t)0xd958, (q15_t)0x79e7, (q15_t)0xd8f9, (q15_t)0x79c8, (q15_t)0xd899, (q15_t)0x79a9, (q15_t)0xd839, + (q15_t)0x798a, (q15_t)0xd7da, (q15_t)0x796a, (q15_t)0xd77a, (q15_t)0x794a, (q15_t)0xd71b, (q15_t)0x792a, (q15_t)0xd6bc, + (q15_t)0x7909, (q15_t)0xd65d, (q15_t)0x78e8, (q15_t)0xd5fe, (q15_t)0x78c7, (q15_t)0xd59f, (q15_t)0x78a6, (q15_t)0xd540, + (q15_t)0x7884, (q15_t)0xd4e1, (q15_t)0x7862, (q15_t)0xd483, (q15_t)0x7840, (q15_t)0xd424, (q15_t)0x781d, (q15_t)0xd3c6, + (q15_t)0x77fa, (q15_t)0xd368, (q15_t)0x77d7, (q15_t)0xd309, (q15_t)0x77b4, (q15_t)0xd2ab, (q15_t)0x7790, (q15_t)0xd24d, + (q15_t)0x776c, (q15_t)0xd1ef, (q15_t)0x7747, (q15_t)0xd192, (q15_t)0x7723, (q15_t)0xd134, (q15_t)0x76fe, (q15_t)0xd0d7, + (q15_t)0x76d9, (q15_t)0xd079, (q15_t)0x76b3, (q15_t)0xd01c, (q15_t)0x768e, (q15_t)0xcfbf, (q15_t)0x7668, (q15_t)0xcf62, + (q15_t)0x7641, (q15_t)0xcf05, (q15_t)0x761b, (q15_t)0xcea8, (q15_t)0x75f4, (q15_t)0xce4b, (q15_t)0x75cc, (q15_t)0xcdef, + (q15_t)0x75a5, (q15_t)0xcd92, (q15_t)0x757d, (q15_t)0xcd36, (q15_t)0x7555, (q15_t)0xccda, (q15_t)0x752d, (q15_t)0xcc7e, + (q15_t)0x7504, (q15_t)0xcc22, (q15_t)0x74db, (q15_t)0xcbc6, (q15_t)0x74b2, (q15_t)0xcb6a, (q15_t)0x7489, (q15_t)0xcb0e, + (q15_t)0x745f, (q15_t)0xcab3, (q15_t)0x7435, (q15_t)0xca58, (q15_t)0x740b, (q15_t)0xc9fc, (q15_t)0x73e0, (q15_t)0xc9a1, + (q15_t)0x73b5, (q15_t)0xc946, (q15_t)0x738a, (q15_t)0xc8ec, (q15_t)0x735f, (q15_t)0xc891, (q15_t)0x7333, (q15_t)0xc836, + (q15_t)0x7307, (q15_t)0xc7dc, (q15_t)0x72db, (q15_t)0xc782, (q15_t)0x72af, (q15_t)0xc728, (q15_t)0x7282, (q15_t)0xc6ce, + (q15_t)0x7255, (q15_t)0xc674, (q15_t)0x7227, (q15_t)0xc61a, (q15_t)0x71fa, (q15_t)0xc5c0, (q15_t)0x71cc, (q15_t)0xc567, + (q15_t)0x719e, (q15_t)0xc50e, (q15_t)0x716f, (q15_t)0xc4b4, (q15_t)0x7141, (q15_t)0xc45b, (q15_t)0x7112, (q15_t)0xc403, + (q15_t)0x70e2, (q15_t)0xc3aa, (q15_t)0x70b3, (q15_t)0xc351, (q15_t)0x7083, (q15_t)0xc2f9, (q15_t)0x7053, (q15_t)0xc2a0, + (q15_t)0x7023, (q15_t)0xc248, (q15_t)0x6ff2, (q15_t)0xc1f0, (q15_t)0x6fc1, (q15_t)0xc198, (q15_t)0x6f90, (q15_t)0xc141, + (q15_t)0x6f5f, (q15_t)0xc0e9, (q15_t)0x6f2d, (q15_t)0xc092, (q15_t)0x6efb, (q15_t)0xc03b, (q15_t)0x6ec9, (q15_t)0xbfe3, + (q15_t)0x6e96, (q15_t)0xbf8d, (q15_t)0x6e63, (q15_t)0xbf36, (q15_t)0x6e30, (q15_t)0xbedf, (q15_t)0x6dfd, (q15_t)0xbe89, + (q15_t)0x6dca, (q15_t)0xbe32, (q15_t)0x6d96, (q15_t)0xbddc, (q15_t)0x6d62, (q15_t)0xbd86, (q15_t)0x6d2d, 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(q15_t)0x8b4e, (q15_t)0x343a, (q15_t)0x8b25, + (q15_t)0x33de, (q15_t)0x8afc, (q15_t)0x3382, (q15_t)0x8ad3, (q15_t)0x3326, (q15_t)0x8aab, (q15_t)0x32ca, (q15_t)0x8a83, + (q15_t)0x326e, (q15_t)0x8a5b, (q15_t)0x3211, (q15_t)0x8a34, (q15_t)0x31b5, (q15_t)0x8a0c, (q15_t)0x3158, (q15_t)0x89e5, + (q15_t)0x30fb, (q15_t)0x89bf, (q15_t)0x309e, (q15_t)0x8998, (q15_t)0x3041, (q15_t)0x8972, (q15_t)0x2fe4, (q15_t)0x894d, + (q15_t)0x2f87, (q15_t)0x8927, (q15_t)0x2f29, (q15_t)0x8902, (q15_t)0x2ecc, (q15_t)0x88dd, (q15_t)0x2e6e, (q15_t)0x88b9, + (q15_t)0x2e11, (q15_t)0x8894, (q15_t)0x2db3, (q15_t)0x8870, (q15_t)0x2d55, (q15_t)0x884c, (q15_t)0x2cf7, (q15_t)0x8829, + (q15_t)0x2c98, (q15_t)0x8806, (q15_t)0x2c3a, (q15_t)0x87e3, (q15_t)0x2bdc, (q15_t)0x87c0, (q15_t)0x2b7d, (q15_t)0x879e, + (q15_t)0x2b1f, (q15_t)0x877c, (q15_t)0x2ac0, (q15_t)0x875a, (q15_t)0x2a61, (q15_t)0x8739, (q15_t)0x2a02, (q15_t)0x8718, + (q15_t)0x29a3, (q15_t)0x86f7, (q15_t)0x2944, (q15_t)0x86d6, (q15_t)0x28e5, (q15_t)0x86b6, (q15_t)0x2886, (q15_t)0x8696, + (q15_t)0x2826, (q15_t)0x8676, (q15_t)0x27c7, (q15_t)0x8657, (q15_t)0x2767, (q15_t)0x8638, (q15_t)0x2707, (q15_t)0x8619, + (q15_t)0x26a8, (q15_t)0x85fb, (q15_t)0x2648, (q15_t)0x85dc, (q15_t)0x25e8, (q15_t)0x85be, (q15_t)0x2588, (q15_t)0x85a1, + (q15_t)0x2528, (q15_t)0x8583, (q15_t)0x24c7, (q15_t)0x8566, (q15_t)0x2467, (q15_t)0x854a, (q15_t)0x2407, (q15_t)0x852d, + (q15_t)0x23a6, (q15_t)0x8511, (q15_t)0x2345, (q15_t)0x84f5, (q15_t)0x22e5, (q15_t)0x84da, (q15_t)0x2284, (q15_t)0x84be, + (q15_t)0x2223, (q15_t)0x84a3, (q15_t)0x21c2, (q15_t)0x8489, (q15_t)0x2161, (q15_t)0x846e, (q15_t)0x2100, (q15_t)0x8454, + (q15_t)0x209f, (q15_t)0x843b, (q15_t)0x203e, (q15_t)0x8421, (q15_t)0x1fdc, (q15_t)0x8408, (q15_t)0x1f7b, (q15_t)0x83ef, + (q15_t)0x1f19, (q15_t)0x83d7, (q15_t)0x1eb8, (q15_t)0x83be, (q15_t)0x1e56, (q15_t)0x83a6, (q15_t)0x1df5, (q15_t)0x838f, + (q15_t)0x1d93, (q15_t)0x8377, (q15_t)0x1d31, (q15_t)0x8360, (q15_t)0x1ccf, (q15_t)0x8349, (q15_t)0x1c6d, (q15_t)0x8333, + (q15_t)0x1c0b, (q15_t)0x831d, (q15_t)0x1ba9, (q15_t)0x8307, (q15_t)0x1b47, (q15_t)0x82f1, (q15_t)0x1ae4, (q15_t)0x82dc, + (q15_t)0x1a82, (q15_t)0x82c7, (q15_t)0x1a20, (q15_t)0x82b2, (q15_t)0x19bd, (q15_t)0x829e, (q15_t)0x195b, (q15_t)0x828a, + (q15_t)0x18f8, (q15_t)0x8276, (q15_t)0x1896, (q15_t)0x8263, (q15_t)0x1833, (q15_t)0x8250, (q15_t)0x17d0, (q15_t)0x823d, + (q15_t)0x176d, (q15_t)0x822a, (q15_t)0x170a, (q15_t)0x8218, (q15_t)0x16a8, (q15_t)0x8206, (q15_t)0x1645, (q15_t)0x81f4, + (q15_t)0x15e2, (q15_t)0x81e3, (q15_t)0x157f, (q15_t)0x81d2, (q15_t)0x151b, (q15_t)0x81c1, (q15_t)0x14b8, (q15_t)0x81b1, + (q15_t)0x1455, (q15_t)0x81a1, (q15_t)0x13f2, (q15_t)0x8191, (q15_t)0x138e, (q15_t)0x8181, (q15_t)0x132b, (q15_t)0x8172, + (q15_t)0x12c8, (q15_t)0x8163, (q15_t)0x1264, (q15_t)0x8155, (q15_t)0x1201, (q15_t)0x8146, (q15_t)0x119d, (q15_t)0x8138, + (q15_t)0x1139, (q15_t)0x812b, (q15_t)0x10d6, (q15_t)0x811d, (q15_t)0x1072, (q15_t)0x8110, (q15_t)0x100e, (q15_t)0x8103, + (q15_t)0xfab, (q15_t)0x80f7, (q15_t)0xf47, (q15_t)0x80eb, (q15_t)0xee3, (q15_t)0x80df, (q15_t)0xe7f, (q15_t)0x80d3, + (q15_t)0xe1b, (q15_t)0x80c8, (q15_t)0xdb7, (q15_t)0x80bd, (q15_t)0xd53, (q15_t)0x80b3, (q15_t)0xcef, (q15_t)0x80a8, + (q15_t)0xc8b, (q15_t)0x809e, (q15_t)0xc27, (q15_t)0x8095, (q15_t)0xbc3, (q15_t)0x808b, (q15_t)0xb5f, (q15_t)0x8082, + (q15_t)0xafb, (q15_t)0x8079, (q15_t)0xa97, (q15_t)0x8071, (q15_t)0xa33, (q15_t)0x8069, (q15_t)0x9ce, (q15_t)0x8061, + (q15_t)0x96a, (q15_t)0x8059, (q15_t)0x906, (q15_t)0x8052, (q15_t)0x8a2, (q15_t)0x804b, (q15_t)0x83d, (q15_t)0x8044, + (q15_t)0x7d9, (q15_t)0x803e, (q15_t)0x775, (q15_t)0x8038, (q15_t)0x710, (q15_t)0x8032, (q15_t)0x6ac, (q15_t)0x802d, + (q15_t)0x647, (q15_t)0x8028, (q15_t)0x5e3, (q15_t)0x8023, (q15_t)0x57f, (q15_t)0x801f, (q15_t)0x51a, (q15_t)0x801b, + (q15_t)0x4b6, (q15_t)0x8017, (q15_t)0x451, (q15_t)0x8013, (q15_t)0x3ed, (q15_t)0x8010, (q15_t)0x388, (q15_t)0x800d, + (q15_t)0x324, (q15_t)0x800a, (q15_t)0x2bf, (q15_t)0x8008, (q15_t)0x25b, (q15_t)0x8006, (q15_t)0x1f6, (q15_t)0x8004, + (q15_t)0x192, (q15_t)0x8003, (q15_t)0x12d, (q15_t)0x8002, (q15_t)0xc9, (q15_t)0x8001, (q15_t)0x64, (q15_t)0x8001 +}; + +static const q15_t ALIGN4 WeightsQ15_2048[4096] = { + (q15_t)0x7fff, (q15_t)0x0, (q15_t)0x7fff, (q15_t)0xffe7, (q15_t)0x7fff, (q15_t)0xffce, (q15_t)0x7fff, (q15_t)0xffb5, + (q15_t)0x7fff, (q15_t)0xff9c, (q15_t)0x7fff, (q15_t)0xff83, (q15_t)0x7fff, (q15_t)0xff6a, (q15_t)0x7fff, (q15_t)0xff51, + (q15_t)0x7fff, (q15_t)0xff37, (q15_t)0x7fff, (q15_t)0xff1e, (q15_t)0x7fff, (q15_t)0xff05, (q15_t)0x7ffe, (q15_t)0xfeec, + (q15_t)0x7ffe, (q15_t)0xfed3, (q15_t)0x7ffe, (q15_t)0xfeba, (q15_t)0x7ffe, (q15_t)0xfea1, (q15_t)0x7ffd, (q15_t)0xfe88, + (q15_t)0x7ffd, (q15_t)0xfe6e, (q15_t)0x7ffd, (q15_t)0xfe55, (q15_t)0x7ffc, (q15_t)0xfe3c, (q15_t)0x7ffc, (q15_t)0xfe23, + (q15_t)0x7ffc, (q15_t)0xfe0a, (q15_t)0x7ffb, (q15_t)0xfdf1, (q15_t)0x7ffb, (q15_t)0xfdd8, (q15_t)0x7ffa, (q15_t)0xfdbe, + (q15_t)0x7ffa, (q15_t)0xfda5, (q15_t)0x7ff9, (q15_t)0xfd8c, (q15_t)0x7ff9, (q15_t)0xfd73, (q15_t)0x7ff8, (q15_t)0xfd5a, + (q15_t)0x7ff8, (q15_t)0xfd41, (q15_t)0x7ff7, (q15_t)0xfd28, (q15_t)0x7ff7, (q15_t)0xfd0f, (q15_t)0x7ff6, (q15_t)0xfcf5, + (q15_t)0x7ff6, (q15_t)0xfcdc, (q15_t)0x7ff5, (q15_t)0xfcc3, (q15_t)0x7ff4, (q15_t)0xfcaa, (q15_t)0x7ff4, (q15_t)0xfc91, + (q15_t)0x7ff3, (q15_t)0xfc78, (q15_t)0x7ff2, (q15_t)0xfc5f, (q15_t)0x7ff2, (q15_t)0xfc46, (q15_t)0x7ff1, (q15_t)0xfc2c, + (q15_t)0x7ff0, (q15_t)0xfc13, (q15_t)0x7fef, (q15_t)0xfbfa, (q15_t)0x7fee, (q15_t)0xfbe1, (q15_t)0x7fee, (q15_t)0xfbc8, + (q15_t)0x7fed, (q15_t)0xfbaf, (q15_t)0x7fec, (q15_t)0xfb96, (q15_t)0x7feb, (q15_t)0xfb7d, (q15_t)0x7fea, (q15_t)0xfb64, + (q15_t)0x7fe9, (q15_t)0xfb4a, (q15_t)0x7fe8, (q15_t)0xfb31, (q15_t)0x7fe7, (q15_t)0xfb18, (q15_t)0x7fe6, (q15_t)0xfaff, + (q15_t)0x7fe5, (q15_t)0xfae6, (q15_t)0x7fe4, (q15_t)0xfacd, (q15_t)0x7fe3, (q15_t)0xfab4, (q15_t)0x7fe2, (q15_t)0xfa9b, + (q15_t)0x7fe1, (q15_t)0xfa81, (q15_t)0x7fe0, (q15_t)0xfa68, (q15_t)0x7fdf, (q15_t)0xfa4f, (q15_t)0x7fde, (q15_t)0xfa36, + (q15_t)0x7fdd, (q15_t)0xfa1d, (q15_t)0x7fdc, (q15_t)0xfa04, (q15_t)0x7fda, (q15_t)0xf9eb, (q15_t)0x7fd9, (q15_t)0xf9d2, + (q15_t)0x7fd8, (q15_t)0xf9b9, (q15_t)0x7fd7, (q15_t)0xf9a0, (q15_t)0x7fd6, (q15_t)0xf986, (q15_t)0x7fd4, (q15_t)0xf96d, + (q15_t)0x7fd3, (q15_t)0xf954, (q15_t)0x7fd2, (q15_t)0xf93b, (q15_t)0x7fd0, (q15_t)0xf922, (q15_t)0x7fcf, (q15_t)0xf909, + (q15_t)0x7fce, (q15_t)0xf8f0, (q15_t)0x7fcc, (q15_t)0xf8d7, (q15_t)0x7fcb, (q15_t)0xf8be, (q15_t)0x7fc9, (q15_t)0xf8a5, + (q15_t)0x7fc8, (q15_t)0xf88b, (q15_t)0x7fc6, (q15_t)0xf872, (q15_t)0x7fc5, (q15_t)0xf859, (q15_t)0x7fc3, (q15_t)0xf840, + (q15_t)0x7fc2, (q15_t)0xf827, (q15_t)0x7fc0, (q15_t)0xf80e, (q15_t)0x7fbf, (q15_t)0xf7f5, (q15_t)0x7fbd, (q15_t)0xf7dc, + (q15_t)0x7fbc, (q15_t)0xf7c3, (q15_t)0x7fba, (q15_t)0xf7aa, (q15_t)0x7fb8, (q15_t)0xf791, (q15_t)0x7fb7, (q15_t)0xf778, + (q15_t)0x7fb5, (q15_t)0xf75e, (q15_t)0x7fb3, (q15_t)0xf745, (q15_t)0x7fb1, (q15_t)0xf72c, (q15_t)0x7fb0, (q15_t)0xf713, + (q15_t)0x7fae, (q15_t)0xf6fa, (q15_t)0x7fac, (q15_t)0xf6e1, (q15_t)0x7faa, (q15_t)0xf6c8, (q15_t)0x7fa9, (q15_t)0xf6af, + (q15_t)0x7fa7, (q15_t)0xf696, (q15_t)0x7fa5, (q15_t)0xf67d, (q15_t)0x7fa3, (q15_t)0xf664, (q15_t)0x7fa1, (q15_t)0xf64b, + (q15_t)0x7f9f, (q15_t)0xf632, (q15_t)0x7f9d, (q15_t)0xf619, (q15_t)0x7f9b, (q15_t)0xf600, (q15_t)0x7f99, (q15_t)0xf5e7, + (q15_t)0x7f97, (q15_t)0xf5cd, (q15_t)0x7f95, (q15_t)0xf5b4, (q15_t)0x7f93, (q15_t)0xf59b, (q15_t)0x7f91, (q15_t)0xf582, + (q15_t)0x7f8f, (q15_t)0xf569, (q15_t)0x7f8d, (q15_t)0xf550, (q15_t)0x7f8b, (q15_t)0xf537, (q15_t)0x7f89, (q15_t)0xf51e, + (q15_t)0x7f87, (q15_t)0xf505, (q15_t)0x7f85, (q15_t)0xf4ec, (q15_t)0x7f82, (q15_t)0xf4d3, (q15_t)0x7f80, (q15_t)0xf4ba, + (q15_t)0x7f7e, (q15_t)0xf4a1, (q15_t)0x7f7c, (q15_t)0xf488, (q15_t)0x7f79, (q15_t)0xf46f, (q15_t)0x7f77, (q15_t)0xf456, + (q15_t)0x7f75, (q15_t)0xf43d, (q15_t)0x7f72, (q15_t)0xf424, (q15_t)0x7f70, (q15_t)0xf40b, (q15_t)0x7f6e, (q15_t)0xf3f2, + (q15_t)0x7f6b, (q15_t)0xf3d9, (q15_t)0x7f69, (q15_t)0xf3c0, (q15_t)0x7f67, (q15_t)0xf3a7, (q15_t)0x7f64, (q15_t)0xf38e, + (q15_t)0x7f62, (q15_t)0xf375, (q15_t)0x7f5f, (q15_t)0xf35c, (q15_t)0x7f5d, (q15_t)0xf343, (q15_t)0x7f5a, (q15_t)0xf32a, + (q15_t)0x7f58, (q15_t)0xf311, (q15_t)0x7f55, (q15_t)0xf2f8, (q15_t)0x7f53, (q15_t)0xf2df, (q15_t)0x7f50, (q15_t)0xf2c6, + (q15_t)0x7f4d, (q15_t)0xf2ad, (q15_t)0x7f4b, (q15_t)0xf294, (q15_t)0x7f48, (q15_t)0xf27b, (q15_t)0x7f45, (q15_t)0xf262, + (q15_t)0x7f43, (q15_t)0xf249, (q15_t)0x7f40, (q15_t)0xf230, (q15_t)0x7f3d, (q15_t)0xf217, (q15_t)0x7f3b, (q15_t)0xf1fe, + (q15_t)0x7f38, (q15_t)0xf1e5, (q15_t)0x7f35, (q15_t)0xf1cc, (q15_t)0x7f32, (q15_t)0xf1b3, (q15_t)0x7f2f, (q15_t)0xf19a, + (q15_t)0x7f2d, (q15_t)0xf181, (q15_t)0x7f2a, (q15_t)0xf168, (q15_t)0x7f27, (q15_t)0xf14f, (q15_t)0x7f24, (q15_t)0xf136, + (q15_t)0x7f21, (q15_t)0xf11d, (q15_t)0x7f1e, (q15_t)0xf104, (q15_t)0x7f1b, (q15_t)0xf0eb, (q15_t)0x7f18, (q15_t)0xf0d2, + (q15_t)0x7f15, (q15_t)0xf0b9, (q15_t)0x7f12, (q15_t)0xf0a0, (q15_t)0x7f0f, (q15_t)0xf087, (q15_t)0x7f0c, (q15_t)0xf06e, + (q15_t)0x7f09, (q15_t)0xf055, (q15_t)0x7f06, (q15_t)0xf03c, (q15_t)0x7f03, (q15_t)0xf023, (q15_t)0x7f00, (q15_t)0xf00b, + (q15_t)0x7efd, (q15_t)0xeff2, (q15_t)0x7ef9, (q15_t)0xefd9, (q15_t)0x7ef6, (q15_t)0xefc0, (q15_t)0x7ef3, (q15_t)0xefa7, + (q15_t)0x7ef0, (q15_t)0xef8e, (q15_t)0x7eed, (q15_t)0xef75, (q15_t)0x7ee9, (q15_t)0xef5c, (q15_t)0x7ee6, (q15_t)0xef43, + (q15_t)0x7ee3, (q15_t)0xef2a, (q15_t)0x7edf, (q15_t)0xef11, (q15_t)0x7edc, (q15_t)0xeef8, (q15_t)0x7ed9, (q15_t)0xeedf, + (q15_t)0x7ed5, (q15_t)0xeec7, (q15_t)0x7ed2, (q15_t)0xeeae, (q15_t)0x7ecf, (q15_t)0xee95, (q15_t)0x7ecb, (q15_t)0xee7c, + (q15_t)0x7ec8, (q15_t)0xee63, (q15_t)0x7ec4, (q15_t)0xee4a, (q15_t)0x7ec1, (q15_t)0xee31, (q15_t)0x7ebd, (q15_t)0xee18, + (q15_t)0x7eba, (q15_t)0xedff, (q15_t)0x7eb6, (q15_t)0xede7, (q15_t)0x7eb3, (q15_t)0xedce, 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(q15_t)0x8031, (q15_t)0x6de, (q15_t)0x8030, (q15_t)0x6c5, (q15_t)0x802e, + (q15_t)0x6ac, (q15_t)0x802d, (q15_t)0x693, (q15_t)0x802c, (q15_t)0x67a, (q15_t)0x802a, (q15_t)0x660, (q15_t)0x8029, + (q15_t)0x647, (q15_t)0x8028, (q15_t)0x62e, (q15_t)0x8027, (q15_t)0x615, (q15_t)0x8026, (q15_t)0x5fc, (q15_t)0x8024, + (q15_t)0x5e3, (q15_t)0x8023, (q15_t)0x5ca, (q15_t)0x8022, (q15_t)0x5b1, (q15_t)0x8021, (q15_t)0x598, (q15_t)0x8020, + (q15_t)0x57f, (q15_t)0x801f, (q15_t)0x565, (q15_t)0x801e, (q15_t)0x54c, (q15_t)0x801d, (q15_t)0x533, (q15_t)0x801c, + (q15_t)0x51a, (q15_t)0x801b, (q15_t)0x501, (q15_t)0x801a, (q15_t)0x4e8, (q15_t)0x8019, (q15_t)0x4cf, (q15_t)0x8018, + (q15_t)0x4b6, (q15_t)0x8017, (q15_t)0x49c, (q15_t)0x8016, (q15_t)0x483, (q15_t)0x8015, (q15_t)0x46a, (q15_t)0x8014, + (q15_t)0x451, (q15_t)0x8013, (q15_t)0x438, (q15_t)0x8012, (q15_t)0x41f, (q15_t)0x8012, (q15_t)0x406, (q15_t)0x8011, + (q15_t)0x3ed, (q15_t)0x8010, (q15_t)0x3d4, (q15_t)0x800f, (q15_t)0x3ba, (q15_t)0x800e, (q15_t)0x3a1, (q15_t)0x800e, + (q15_t)0x388, (q15_t)0x800d, (q15_t)0x36f, (q15_t)0x800c, (q15_t)0x356, (q15_t)0x800c, (q15_t)0x33d, (q15_t)0x800b, + (q15_t)0x324, (q15_t)0x800a, (q15_t)0x30b, (q15_t)0x800a, (q15_t)0x2f1, (q15_t)0x8009, (q15_t)0x2d8, (q15_t)0x8009, + (q15_t)0x2bf, (q15_t)0x8008, (q15_t)0x2a6, (q15_t)0x8008, (q15_t)0x28d, (q15_t)0x8007, (q15_t)0x274, (q15_t)0x8007, + (q15_t)0x25b, (q15_t)0x8006, (q15_t)0x242, (q15_t)0x8006, (q15_t)0x228, (q15_t)0x8005, (q15_t)0x20f, (q15_t)0x8005, + (q15_t)0x1f6, (q15_t)0x8004, (q15_t)0x1dd, (q15_t)0x8004, (q15_t)0x1c4, (q15_t)0x8004, (q15_t)0x1ab, (q15_t)0x8003, + (q15_t)0x192, (q15_t)0x8003, (q15_t)0x178, (q15_t)0x8003, (q15_t)0x15f, (q15_t)0x8002, (q15_t)0x146, (q15_t)0x8002, + (q15_t)0x12d, (q15_t)0x8002, (q15_t)0x114, (q15_t)0x8002, (q15_t)0xfb, (q15_t)0x8001, (q15_t)0xe2, (q15_t)0x8001, + (q15_t)0xc9, (q15_t)0x8001, (q15_t)0xaf, (q15_t)0x8001, (q15_t)0x96, (q15_t)0x8001, (q15_t)0x7d, (q15_t)0x8001, + (q15_t)0x64, (q15_t)0x8001, (q15_t)0x4b, (q15_t)0x8001, (q15_t)0x32, (q15_t)0x8001, (q15_t)0x19, (q15_t)0x8001 +}; + +static const q15_t ALIGN4 WeightsQ15_8192[16384] = { + (q15_t)0x7fff, (q15_t)0x0, (q15_t)0x7fff, (q15_t)0xfffa, (q15_t)0x7fff, (q15_t)0xfff4, (q15_t)0x7fff, (q15_t)0xffee, + (q15_t)0x7fff, (q15_t)0xffe7, (q15_t)0x7fff, (q15_t)0xffe1, (q15_t)0x7fff, (q15_t)0xffdb, (q15_t)0x7fff, (q15_t)0xffd5, + (q15_t)0x7fff, (q15_t)0xffce, (q15_t)0x7fff, (q15_t)0xffc8, (q15_t)0x7fff, (q15_t)0xffc2, (q15_t)0x7fff, (q15_t)0xffbb, + (q15_t)0x7fff, (q15_t)0xffb5, (q15_t)0x7fff, (q15_t)0xffaf, (q15_t)0x7fff, (q15_t)0xffa9, (q15_t)0x7fff, (q15_t)0xffa2, + (q15_t)0x7fff, (q15_t)0xff9c, (q15_t)0x7fff, (q15_t)0xff96, (q15_t)0x7fff, (q15_t)0xff8f, (q15_t)0x7fff, (q15_t)0xff89, + (q15_t)0x7fff, (q15_t)0xff83, (q15_t)0x7fff, (q15_t)0xff7d, (q15_t)0x7fff, (q15_t)0xff76, (q15_t)0x7fff, (q15_t)0xff70, + (q15_t)0x7fff, (q15_t)0xff6a, (q15_t)0x7fff, (q15_t)0xff63, (q15_t)0x7fff, (q15_t)0xff5d, (q15_t)0x7fff, (q15_t)0xff57, + (q15_t)0x7fff, (q15_t)0xff51, (q15_t)0x7fff, (q15_t)0xff4a, (q15_t)0x7fff, (q15_t)0xff44, (q15_t)0x7fff, (q15_t)0xff3e, + (q15_t)0x7fff, (q15_t)0xff37, (q15_t)0x7fff, (q15_t)0xff31, (q15_t)0x7fff, (q15_t)0xff2b, (q15_t)0x7fff, (q15_t)0xff25, + (q15_t)0x7fff, (q15_t)0xff1e, (q15_t)0x7fff, (q15_t)0xff18, (q15_t)0x7fff, (q15_t)0xff12, (q15_t)0x7fff, (q15_t)0xff0b, + (q15_t)0x7fff, (q15_t)0xff05, (q15_t)0x7ffe, (q15_t)0xfeff, (q15_t)0x7ffe, (q15_t)0xfef9, (q15_t)0x7ffe, (q15_t)0xfef2, + (q15_t)0x7ffe, (q15_t)0xfeec, (q15_t)0x7ffe, (q15_t)0xfee6, (q15_t)0x7ffe, (q15_t)0xfedf, (q15_t)0x7ffe, (q15_t)0xfed9, + (q15_t)0x7ffe, (q15_t)0xfed3, (q15_t)0x7ffe, (q15_t)0xfecd, (q15_t)0x7ffe, (q15_t)0xfec6, (q15_t)0x7ffe, (q15_t)0xfec0, + (q15_t)0x7ffe, (q15_t)0xfeba, (q15_t)0x7ffe, (q15_t)0xfeb3, (q15_t)0x7ffe, (q15_t)0xfead, (q15_t)0x7ffe, (q15_t)0xfea7, + (q15_t)0x7ffe, (q15_t)0xfea1, (q15_t)0x7ffe, (q15_t)0xfe9a, (q15_t)0x7ffd, (q15_t)0xfe94, (q15_t)0x7ffd, (q15_t)0xfe8e, + (q15_t)0x7ffd, (q15_t)0xfe88, (q15_t)0x7ffd, (q15_t)0xfe81, (q15_t)0x7ffd, (q15_t)0xfe7b, (q15_t)0x7ffd, (q15_t)0xfe75, + (q15_t)0x7ffd, (q15_t)0xfe6e, (q15_t)0x7ffd, (q15_t)0xfe68, (q15_t)0x7ffd, (q15_t)0xfe62, (q15_t)0x7ffd, (q15_t)0xfe5c, + (q15_t)0x7ffd, (q15_t)0xfe55, (q15_t)0x7ffd, (q15_t)0xfe4f, (q15_t)0x7ffd, (q15_t)0xfe49, (q15_t)0x7ffc, (q15_t)0xfe42, + (q15_t)0x7ffc, (q15_t)0xfe3c, (q15_t)0x7ffc, (q15_t)0xfe36, (q15_t)0x7ffc, (q15_t)0xfe30, (q15_t)0x7ffc, (q15_t)0xfe29, + (q15_t)0x7ffc, (q15_t)0xfe23, (q15_t)0x7ffc, (q15_t)0xfe1d, (q15_t)0x7ffc, (q15_t)0xfe16, (q15_t)0x7ffc, (q15_t)0xfe10, + (q15_t)0x7ffc, (q15_t)0xfe0a, (q15_t)0x7ffc, (q15_t)0xfe04, (q15_t)0x7ffb, (q15_t)0xfdfd, (q15_t)0x7ffb, (q15_t)0xfdf7, + (q15_t)0x7ffb, (q15_t)0xfdf1, (q15_t)0x7ffb, (q15_t)0xfdea, (q15_t)0x7ffb, (q15_t)0xfde4, (q15_t)0x7ffb, (q15_t)0xfdde, + (q15_t)0x7ffb, (q15_t)0xfdd8, (q15_t)0x7ffb, (q15_t)0xfdd1, (q15_t)0x7ffb, (q15_t)0xfdcb, (q15_t)0x7ffb, (q15_t)0xfdc5, + (q15_t)0x7ffa, (q15_t)0xfdbe, (q15_t)0x7ffa, (q15_t)0xfdb8, (q15_t)0x7ffa, (q15_t)0xfdb2, (q15_t)0x7ffa, (q15_t)0xfdac, + (q15_t)0x7ffa, (q15_t)0xfda5, (q15_t)0x7ffa, (q15_t)0xfd9f, (q15_t)0x7ffa, (q15_t)0xfd99, (q15_t)0x7ffa, (q15_t)0xfd93, + (q15_t)0x7ff9, (q15_t)0xfd8c, (q15_t)0x7ff9, (q15_t)0xfd86, (q15_t)0x7ff9, (q15_t)0xfd80, (q15_t)0x7ff9, (q15_t)0xfd79, + (q15_t)0x7ff9, (q15_t)0xfd73, (q15_t)0x7ff9, (q15_t)0xfd6d, (q15_t)0x7ff9, (q15_t)0xfd67, (q15_t)0x7ff9, (q15_t)0xfd60, + (q15_t)0x7ff8, (q15_t)0xfd5a, (q15_t)0x7ff8, (q15_t)0xfd54, (q15_t)0x7ff8, (q15_t)0xfd4d, (q15_t)0x7ff8, (q15_t)0xfd47, + (q15_t)0x7ff8, (q15_t)0xfd41, (q15_t)0x7ff8, (q15_t)0xfd3b, (q15_t)0x7ff8, (q15_t)0xfd34, (q15_t)0x7ff8, (q15_t)0xfd2e, + (q15_t)0x7ff7, (q15_t)0xfd28, (q15_t)0x7ff7, (q15_t)0xfd21, (q15_t)0x7ff7, (q15_t)0xfd1b, (q15_t)0x7ff7, (q15_t)0xfd15, + (q15_t)0x7ff7, (q15_t)0xfd0f, (q15_t)0x7ff7, (q15_t)0xfd08, (q15_t)0x7ff7, (q15_t)0xfd02, (q15_t)0x7ff6, (q15_t)0xfcfc, + (q15_t)0x7ff6, (q15_t)0xfcf5, (q15_t)0x7ff6, (q15_t)0xfcef, (q15_t)0x7ff6, (q15_t)0xfce9, (q15_t)0x7ff6, (q15_t)0xfce3, + (q15_t)0x7ff6, (q15_t)0xfcdc, (q15_t)0x7ff5, (q15_t)0xfcd6, (q15_t)0x7ff5, (q15_t)0xfcd0, (q15_t)0x7ff5, (q15_t)0xfcc9, + (q15_t)0x7ff5, (q15_t)0xfcc3, (q15_t)0x7ff5, (q15_t)0xfcbd, (q15_t)0x7ff5, (q15_t)0xfcb7, (q15_t)0x7ff5, (q15_t)0xfcb0, + (q15_t)0x7ff4, (q15_t)0xfcaa, (q15_t)0x7ff4, (q15_t)0xfca4, (q15_t)0x7ff4, (q15_t)0xfc9e, (q15_t)0x7ff4, (q15_t)0xfc97, + (q15_t)0x7ff4, (q15_t)0xfc91, (q15_t)0x7ff4, (q15_t)0xfc8b, (q15_t)0x7ff3, (q15_t)0xfc84, (q15_t)0x7ff3, (q15_t)0xfc7e, + (q15_t)0x7ff3, (q15_t)0xfc78, (q15_t)0x7ff3, (q15_t)0xfc72, (q15_t)0x7ff3, (q15_t)0xfc6b, (q15_t)0x7ff2, (q15_t)0xfc65, + (q15_t)0x7ff2, (q15_t)0xfc5f, (q15_t)0x7ff2, (q15_t)0xfc58, (q15_t)0x7ff2, (q15_t)0xfc52, (q15_t)0x7ff2, (q15_t)0xfc4c, + (q15_t)0x7ff2, (q15_t)0xfc46, (q15_t)0x7ff1, (q15_t)0xfc3f, (q15_t)0x7ff1, (q15_t)0xfc39, (q15_t)0x7ff1, (q15_t)0xfc33, + (q15_t)0x7ff1, (q15_t)0xfc2c, (q15_t)0x7ff1, (q15_t)0xfc26, (q15_t)0x7ff0, (q15_t)0xfc20, (q15_t)0x7ff0, (q15_t)0xfc1a, + (q15_t)0x7ff0, (q15_t)0xfc13, (q15_t)0x7ff0, (q15_t)0xfc0d, (q15_t)0x7ff0, (q15_t)0xfc07, (q15_t)0x7fef, (q15_t)0xfc01, + (q15_t)0x7fef, (q15_t)0xfbfa, (q15_t)0x7fef, (q15_t)0xfbf4, (q15_t)0x7fef, (q15_t)0xfbee, (q15_t)0x7fef, (q15_t)0xfbe7, + (q15_t)0x7fee, (q15_t)0xfbe1, (q15_t)0x7fee, (q15_t)0xfbdb, (q15_t)0x7fee, (q15_t)0xfbd5, (q15_t)0x7fee, (q15_t)0xfbce, + (q15_t)0x7fee, (q15_t)0xfbc8, (q15_t)0x7fed, (q15_t)0xfbc2, (q15_t)0x7fed, (q15_t)0xfbbb, (q15_t)0x7fed, (q15_t)0xfbb5, + (q15_t)0x7fed, (q15_t)0xfbaf, (q15_t)0x7fed, (q15_t)0xfba9, (q15_t)0x7fec, (q15_t)0xfba2, (q15_t)0x7fec, (q15_t)0xfb9c, + (q15_t)0x7fec, (q15_t)0xfb96, (q15_t)0x7fec, (q15_t)0xfb8f, (q15_t)0x7fec, (q15_t)0xfb89, (q15_t)0x7feb, (q15_t)0xfb83, + (q15_t)0x7feb, (q15_t)0xfb7d, (q15_t)0x7feb, (q15_t)0xfb76, (q15_t)0x7feb, (q15_t)0xfb70, (q15_t)0x7fea, (q15_t)0xfb6a, + (q15_t)0x7fea, (q15_t)0xfb64, (q15_t)0x7fea, (q15_t)0xfb5d, (q15_t)0x7fea, (q15_t)0xfb57, (q15_t)0x7fea, (q15_t)0xfb51, + (q15_t)0x7fe9, (q15_t)0xfb4a, (q15_t)0x7fe9, (q15_t)0xfb44, (q15_t)0x7fe9, (q15_t)0xfb3e, (q15_t)0x7fe9, (q15_t)0xfb38, + (q15_t)0x7fe8, (q15_t)0xfb31, (q15_t)0x7fe8, (q15_t)0xfb2b, (q15_t)0x7fe8, (q15_t)0xfb25, (q15_t)0x7fe8, (q15_t)0xfb1e, + (q15_t)0x7fe7, (q15_t)0xfb18, (q15_t)0x7fe7, (q15_t)0xfb12, (q15_t)0x7fe7, (q15_t)0xfb0c, (q15_t)0x7fe7, (q15_t)0xfb05, + (q15_t)0x7fe6, (q15_t)0xfaff, (q15_t)0x7fe6, (q15_t)0xfaf9, (q15_t)0x7fe6, (q15_t)0xfaf3, (q15_t)0x7fe6, (q15_t)0xfaec, + (q15_t)0x7fe5, (q15_t)0xfae6, (q15_t)0x7fe5, (q15_t)0xfae0, (q15_t)0x7fe5, (q15_t)0xfad9, (q15_t)0x7fe5, (q15_t)0xfad3, + (q15_t)0x7fe4, (q15_t)0xfacd, (q15_t)0x7fe4, (q15_t)0xfac7, (q15_t)0x7fe4, (q15_t)0xfac0, (q15_t)0x7fe4, (q15_t)0xfaba, + (q15_t)0x7fe3, (q15_t)0xfab4, (q15_t)0x7fe3, (q15_t)0xfaad, (q15_t)0x7fe3, (q15_t)0xfaa7, (q15_t)0x7fe3, (q15_t)0xfaa1, + (q15_t)0x7fe2, (q15_t)0xfa9b, (q15_t)0x7fe2, (q15_t)0xfa94, (q15_t)0x7fe2, (q15_t)0xfa8e, (q15_t)0x7fe2, (q15_t)0xfa88, + (q15_t)0x7fe1, (q15_t)0xfa81, (q15_t)0x7fe1, (q15_t)0xfa7b, (q15_t)0x7fe1, (q15_t)0xfa75, (q15_t)0x7fe0, (q15_t)0xfa6f, + (q15_t)0x7fe0, (q15_t)0xfa68, (q15_t)0x7fe0, (q15_t)0xfa62, (q15_t)0x7fe0, (q15_t)0xfa5c, (q15_t)0x7fdf, (q15_t)0xfa56, + (q15_t)0x7fdf, (q15_t)0xfa4f, (q15_t)0x7fdf, (q15_t)0xfa49, (q15_t)0x7fdf, (q15_t)0xfa43, (q15_t)0x7fde, (q15_t)0xfa3c, + (q15_t)0x7fde, (q15_t)0xfa36, (q15_t)0x7fde, (q15_t)0xfa30, (q15_t)0x7fdd, (q15_t)0xfa2a, (q15_t)0x7fdd, (q15_t)0xfa23, + (q15_t)0x7fdd, (q15_t)0xfa1d, (q15_t)0x7fdd, (q15_t)0xfa17, (q15_t)0x7fdc, (q15_t)0xfa11, (q15_t)0x7fdc, (q15_t)0xfa0a, + (q15_t)0x7fdc, (q15_t)0xfa04, (q15_t)0x7fdb, (q15_t)0xf9fe, (q15_t)0x7fdb, (q15_t)0xf9f7, (q15_t)0x7fdb, (q15_t)0xf9f1, + (q15_t)0x7fda, (q15_t)0xf9eb, (q15_t)0x7fda, (q15_t)0xf9e5, (q15_t)0x7fda, (q15_t)0xf9de, (q15_t)0x7fda, (q15_t)0xf9d8, + (q15_t)0x7fd9, (q15_t)0xf9d2, (q15_t)0x7fd9, (q15_t)0xf9cb, (q15_t)0x7fd9, (q15_t)0xf9c5, (q15_t)0x7fd8, 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(q15_t)0x3c7, (q15_t)0x800f, (q15_t)0x3c1, (q15_t)0x800f, + (q15_t)0x3ba, (q15_t)0x800e, (q15_t)0x3b4, (q15_t)0x800e, (q15_t)0x3ae, (q15_t)0x800e, (q15_t)0x3a8, (q15_t)0x800e, + (q15_t)0x3a1, (q15_t)0x800e, (q15_t)0x39b, (q15_t)0x800e, (q15_t)0x395, (q15_t)0x800d, (q15_t)0x38e, (q15_t)0x800d, + (q15_t)0x388, (q15_t)0x800d, (q15_t)0x382, (q15_t)0x800d, (q15_t)0x37c, (q15_t)0x800d, (q15_t)0x375, (q15_t)0x800c, + (q15_t)0x36f, (q15_t)0x800c, (q15_t)0x369, (q15_t)0x800c, (q15_t)0x362, (q15_t)0x800c, (q15_t)0x35c, (q15_t)0x800c, + (q15_t)0x356, (q15_t)0x800c, (q15_t)0x350, (q15_t)0x800b, (q15_t)0x349, (q15_t)0x800b, (q15_t)0x343, (q15_t)0x800b, + (q15_t)0x33d, (q15_t)0x800b, (q15_t)0x337, (q15_t)0x800b, (q15_t)0x330, (q15_t)0x800b, (q15_t)0x32a, (q15_t)0x800b, + (q15_t)0x324, (q15_t)0x800a, (q15_t)0x31d, (q15_t)0x800a, (q15_t)0x317, (q15_t)0x800a, (q15_t)0x311, (q15_t)0x800a, + (q15_t)0x30b, (q15_t)0x800a, (q15_t)0x304, (q15_t)0x800a, (q15_t)0x2fe, (q15_t)0x8009, (q15_t)0x2f8, (q15_t)0x8009, + (q15_t)0x2f1, (q15_t)0x8009, (q15_t)0x2eb, (q15_t)0x8009, (q15_t)0x2e5, (q15_t)0x8009, (q15_t)0x2df, (q15_t)0x8009, + (q15_t)0x2d8, (q15_t)0x8009, (q15_t)0x2d2, (q15_t)0x8008, (q15_t)0x2cc, (q15_t)0x8008, (q15_t)0x2c5, (q15_t)0x8008, + (q15_t)0x2bf, (q15_t)0x8008, (q15_t)0x2b9, (q15_t)0x8008, (q15_t)0x2b3, (q15_t)0x8008, (q15_t)0x2ac, (q15_t)0x8008, + (q15_t)0x2a6, (q15_t)0x8008, (q15_t)0x2a0, (q15_t)0x8007, (q15_t)0x299, (q15_t)0x8007, (q15_t)0x293, (q15_t)0x8007, + (q15_t)0x28d, (q15_t)0x8007, (q15_t)0x287, (q15_t)0x8007, (q15_t)0x280, (q15_t)0x8007, (q15_t)0x27a, (q15_t)0x8007, + (q15_t)0x274, (q15_t)0x8007, (q15_t)0x26d, (q15_t)0x8006, (q15_t)0x267, (q15_t)0x8006, (q15_t)0x261, (q15_t)0x8006, + (q15_t)0x25b, (q15_t)0x8006, (q15_t)0x254, (q15_t)0x8006, (q15_t)0x24e, (q15_t)0x8006, (q15_t)0x248, (q15_t)0x8006, + (q15_t)0x242, (q15_t)0x8006, (q15_t)0x23b, (q15_t)0x8005, (q15_t)0x235, (q15_t)0x8005, (q15_t)0x22f, (q15_t)0x8005, + (q15_t)0x228, (q15_t)0x8005, (q15_t)0x222, (q15_t)0x8005, (q15_t)0x21c, (q15_t)0x8005, (q15_t)0x216, (q15_t)0x8005, + (q15_t)0x20f, (q15_t)0x8005, (q15_t)0x209, (q15_t)0x8005, (q15_t)0x203, (q15_t)0x8005, (q15_t)0x1fc, (q15_t)0x8004, + (q15_t)0x1f6, (q15_t)0x8004, (q15_t)0x1f0, (q15_t)0x8004, (q15_t)0x1ea, (q15_t)0x8004, (q15_t)0x1e3, (q15_t)0x8004, + (q15_t)0x1dd, (q15_t)0x8004, (q15_t)0x1d7, (q15_t)0x8004, (q15_t)0x1d0, (q15_t)0x8004, (q15_t)0x1ca, (q15_t)0x8004, + (q15_t)0x1c4, (q15_t)0x8004, (q15_t)0x1be, (q15_t)0x8004, (q15_t)0x1b7, (q15_t)0x8003, (q15_t)0x1b1, (q15_t)0x8003, + (q15_t)0x1ab, (q15_t)0x8003, (q15_t)0x1a4, (q15_t)0x8003, (q15_t)0x19e, (q15_t)0x8003, (q15_t)0x198, (q15_t)0x8003, + (q15_t)0x192, (q15_t)0x8003, (q15_t)0x18b, (q15_t)0x8003, (q15_t)0x185, (q15_t)0x8003, (q15_t)0x17f, (q15_t)0x8003, + (q15_t)0x178, (q15_t)0x8003, (q15_t)0x172, (q15_t)0x8003, (q15_t)0x16c, (q15_t)0x8003, (q15_t)0x166, (q15_t)0x8002, + (q15_t)0x15f, (q15_t)0x8002, (q15_t)0x159, (q15_t)0x8002, (q15_t)0x153, (q15_t)0x8002, (q15_t)0x14d, (q15_t)0x8002, + (q15_t)0x146, (q15_t)0x8002, (q15_t)0x140, (q15_t)0x8002, (q15_t)0x13a, (q15_t)0x8002, (q15_t)0x133, (q15_t)0x8002, + (q15_t)0x12d, (q15_t)0x8002, (q15_t)0x127, (q15_t)0x8002, (q15_t)0x121, (q15_t)0x8002, (q15_t)0x11a, (q15_t)0x8002, + (q15_t)0x114, (q15_t)0x8002, (q15_t)0x10e, (q15_t)0x8002, (q15_t)0x107, (q15_t)0x8002, (q15_t)0x101, (q15_t)0x8002, + (q15_t)0xfb, (q15_t)0x8001, (q15_t)0xf5, (q15_t)0x8001, (q15_t)0xee, (q15_t)0x8001, (q15_t)0xe8, (q15_t)0x8001, + (q15_t)0xe2, (q15_t)0x8001, (q15_t)0xdb, (q15_t)0x8001, (q15_t)0xd5, (q15_t)0x8001, (q15_t)0xcf, (q15_t)0x8001, + (q15_t)0xc9, (q15_t)0x8001, (q15_t)0xc2, (q15_t)0x8001, (q15_t)0xbc, (q15_t)0x8001, (q15_t)0xb6, (q15_t)0x8001, + (q15_t)0xaf, (q15_t)0x8001, (q15_t)0xa9, (q15_t)0x8001, (q15_t)0xa3, (q15_t)0x8001, (q15_t)0x9d, (q15_t)0x8001, + (q15_t)0x96, (q15_t)0x8001, (q15_t)0x90, (q15_t)0x8001, (q15_t)0x8a, (q15_t)0x8001, (q15_t)0x83, (q15_t)0x8001, + (q15_t)0x7d, (q15_t)0x8001, (q15_t)0x77, (q15_t)0x8001, (q15_t)0x71, (q15_t)0x8001, (q15_t)0x6a, (q15_t)0x8001, + (q15_t)0x64, (q15_t)0x8001, (q15_t)0x5e, (q15_t)0x8001, (q15_t)0x57, (q15_t)0x8001, (q15_t)0x51, (q15_t)0x8001, + (q15_t)0x4b, (q15_t)0x8001, (q15_t)0x45, (q15_t)0x8001, (q15_t)0x3e, (q15_t)0x8001, (q15_t)0x38, (q15_t)0x8001, + (q15_t)0x32, (q15_t)0x8001, (q15_t)0x2b, (q15_t)0x8001, (q15_t)0x25, (q15_t)0x8001, (q15_t)0x1f, (q15_t)0x8001, + (q15_t)0x19, (q15_t)0x8001, (q15_t)0x12, (q15_t)0x8001, (q15_t)0xc, (q15_t)0x8001, (q15_t)0x6, (q15_t)0x8001 +}; + + +/** +* \par +* cosFactor tables are generated using the formula : <pre> cos_factors[n] = 2 * cos((2n+1)*pi/(4*N)) </pre> +* \par +* C command to generate the table +* <pre> +* for(i = 0; i< N; i++) +* { +* cos_factors[i]= 2 * cos((2*i+1)*c/2); +* } </pre> +* \par +* where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code> +* \par +* Then converted to q15 format by multiplying with 2^31 and saturated if required. + +*/ + +static const q15_t ALIGN4 cos_factorsQ15_128[128] = { + (q15_t)0x7fff, (q15_t)0x7ffa, (q15_t)0x7ff0, (q15_t)0x7fe1, (q15_t)0x7fce, (q15_t)0x7fb5, (q15_t)0x7f97, (q15_t)0x7f75, + (q15_t)0x7f4d, (q15_t)0x7f21, (q15_t)0x7ef0, (q15_t)0x7eba, (q15_t)0x7e7f, (q15_t)0x7e3f, (q15_t)0x7dfa, (q15_t)0x7db0, + (q15_t)0x7d62, (q15_t)0x7d0f, (q15_t)0x7cb7, (q15_t)0x7c5a, (q15_t)0x7bf8, (q15_t)0x7b92, (q15_t)0x7b26, (q15_t)0x7ab6, + (q15_t)0x7a42, (q15_t)0x79c8, (q15_t)0x794a, (q15_t)0x78c7, (q15_t)0x7840, (q15_t)0x77b4, (q15_t)0x7723, (q15_t)0x768e, + (q15_t)0x75f4, (q15_t)0x7555, (q15_t)0x74b2, (q15_t)0x740b, (q15_t)0x735f, (q15_t)0x72af, (q15_t)0x71fa, (q15_t)0x7141, + (q15_t)0x7083, (q15_t)0x6fc1, (q15_t)0x6efb, (q15_t)0x6e30, (q15_t)0x6d62, (q15_t)0x6c8f, (q15_t)0x6bb8, (q15_t)0x6adc, + (q15_t)0x69fd, (q15_t)0x6919, (q15_t)0x6832, (q15_t)0x6746, (q15_t)0x6657, (q15_t)0x6563, (q15_t)0x646c, (q15_t)0x6371, + (q15_t)0x6271, (q15_t)0x616f, (q15_t)0x6068, (q15_t)0x5f5e, (q15_t)0x5e50, (q15_t)0x5d3e, (q15_t)0x5c29, (q15_t)0x5b10, + (q15_t)0x59f3, (q15_t)0x58d4, (q15_t)0x57b0, (q15_t)0x568a, (q15_t)0x5560, (q15_t)0x5433, (q15_t)0x5302, (q15_t)0x51ce, + (q15_t)0x5097, (q15_t)0x4f5e, (q15_t)0x4e21, (q15_t)0x4ce1, (q15_t)0x4b9e, (q15_t)0x4a58, (q15_t)0x490f, (q15_t)0x47c3, + (q15_t)0x4675, (q15_t)0x4524, (q15_t)0x43d0, (q15_t)0x427a, (q15_t)0x4121, (q15_t)0x3fc5, (q15_t)0x3e68, (q15_t)0x3d07, + (q15_t)0x3ba5, (q15_t)0x3a40, (q15_t)0x38d8, (q15_t)0x376f, (q15_t)0x3604, (q15_t)0x3496, (q15_t)0x3326, (q15_t)0x31b5, + (q15_t)0x3041, (q15_t)0x2ecc, (q15_t)0x2d55, (q15_t)0x2bdc, (q15_t)0x2a61, (q15_t)0x28e5, (q15_t)0x2767, (q15_t)0x25e8, + (q15_t)0x2467, (q15_t)0x22e5, (q15_t)0x2161, (q15_t)0x1fdc, (q15_t)0x1e56, (q15_t)0x1ccf, (q15_t)0x1b47, (q15_t)0x19bd, + (q15_t)0x1833, (q15_t)0x16a8, (q15_t)0x151b, (q15_t)0x138e, (q15_t)0x1201, (q15_t)0x1072, (q15_t)0xee3, (q15_t)0xd53, + (q15_t)0xbc3, (q15_t)0xa33, (q15_t)0x8a2, (q15_t)0x710, (q15_t)0x57f, (q15_t)0x3ed, (q15_t)0x25b, (q15_t)0xc9 +}; + +static const q15_t ALIGN4 cos_factorsQ15_512[512] = { + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7ffe, (q15_t)0x7ffc, (q15_t)0x7ffb, (q15_t)0x7ff9, (q15_t)0x7ff7, + (q15_t)0x7ff4, (q15_t)0x7ff2, (q15_t)0x7fee, (q15_t)0x7feb, (q15_t)0x7fe7, (q15_t)0x7fe3, (q15_t)0x7fdf, (q15_t)0x7fda, + (q15_t)0x7fd6, (q15_t)0x7fd0, (q15_t)0x7fcb, (q15_t)0x7fc5, (q15_t)0x7fbf, (q15_t)0x7fb8, (q15_t)0x7fb1, (q15_t)0x7faa, + (q15_t)0x7fa3, (q15_t)0x7f9b, (q15_t)0x7f93, (q15_t)0x7f8b, (q15_t)0x7f82, (q15_t)0x7f79, (q15_t)0x7f70, (q15_t)0x7f67, + (q15_t)0x7f5d, (q15_t)0x7f53, (q15_t)0x7f48, (q15_t)0x7f3d, (q15_t)0x7f32, (q15_t)0x7f27, (q15_t)0x7f1b, (q15_t)0x7f0f, + (q15_t)0x7f03, (q15_t)0x7ef6, (q15_t)0x7ee9, (q15_t)0x7edc, (q15_t)0x7ecf, (q15_t)0x7ec1, (q15_t)0x7eb3, (q15_t)0x7ea4, + (q15_t)0x7e95, (q15_t)0x7e86, (q15_t)0x7e77, (q15_t)0x7e67, (q15_t)0x7e57, (q15_t)0x7e47, (q15_t)0x7e37, (q15_t)0x7e26, + (q15_t)0x7e14, (q15_t)0x7e03, (q15_t)0x7df1, (q15_t)0x7ddf, (q15_t)0x7dcd, (q15_t)0x7dba, (q15_t)0x7da7, (q15_t)0x7d94, + (q15_t)0x7d80, (q15_t)0x7d6c, (q15_t)0x7d58, (q15_t)0x7d43, (q15_t)0x7d2f, (q15_t)0x7d19, (q15_t)0x7d04, (q15_t)0x7cee, + (q15_t)0x7cd8, (q15_t)0x7cc2, (q15_t)0x7cab, (q15_t)0x7c94, (q15_t)0x7c7d, (q15_t)0x7c66, (q15_t)0x7c4e, (q15_t)0x7c36, + (q15_t)0x7c1d, (q15_t)0x7c05, (q15_t)0x7beb, (q15_t)0x7bd2, (q15_t)0x7bb9, (q15_t)0x7b9f, (q15_t)0x7b84, (q15_t)0x7b6a, + (q15_t)0x7b4f, (q15_t)0x7b34, (q15_t)0x7b19, (q15_t)0x7afd, (q15_t)0x7ae1, (q15_t)0x7ac5, (q15_t)0x7aa8, (q15_t)0x7a8b, + (q15_t)0x7a6e, (q15_t)0x7a50, (q15_t)0x7a33, (q15_t)0x7a15, (q15_t)0x79f6, (q15_t)0x79d8, (q15_t)0x79b9, (q15_t)0x7999, + (q15_t)0x797a, (q15_t)0x795a, (q15_t)0x793a, (q15_t)0x7919, (q15_t)0x78f9, (q15_t)0x78d8, (q15_t)0x78b6, (q15_t)0x7895, + (q15_t)0x7873, (q15_t)0x7851, (q15_t)0x782e, (q15_t)0x780c, (q15_t)0x77e9, (q15_t)0x77c5, (q15_t)0x77a2, (q15_t)0x777e, + (q15_t)0x775a, (q15_t)0x7735, (q15_t)0x7710, (q15_t)0x76eb, (q15_t)0x76c6, (q15_t)0x76a0, (q15_t)0x767b, (q15_t)0x7654, + (q15_t)0x762e, (q15_t)0x7607, (q15_t)0x75e0, (q15_t)0x75b9, (q15_t)0x7591, (q15_t)0x7569, (q15_t)0x7541, (q15_t)0x7519, + (q15_t)0x74f0, (q15_t)0x74c7, (q15_t)0x749e, (q15_t)0x7474, (q15_t)0x744a, (q15_t)0x7420, (q15_t)0x73f6, (q15_t)0x73cb, + (q15_t)0x73a0, (q15_t)0x7375, (q15_t)0x7349, (q15_t)0x731d, (q15_t)0x72f1, (q15_t)0x72c5, (q15_t)0x7298, (q15_t)0x726b, + (q15_t)0x723e, (q15_t)0x7211, (q15_t)0x71e3, (q15_t)0x71b5, (q15_t)0x7186, (q15_t)0x7158, (q15_t)0x7129, (q15_t)0x70fa, + (q15_t)0x70cb, (q15_t)0x709b, (q15_t)0x706b, (q15_t)0x703b, (q15_t)0x700a, (q15_t)0x6fda, (q15_t)0x6fa9, (q15_t)0x6f77, + (q15_t)0x6f46, (q15_t)0x6f14, (q15_t)0x6ee2, (q15_t)0x6eaf, (q15_t)0x6e7d, (q15_t)0x6e4a, (q15_t)0x6e17, (q15_t)0x6de3, + (q15_t)0x6db0, (q15_t)0x6d7c, (q15_t)0x6d48, (q15_t)0x6d13, (q15_t)0x6cde, (q15_t)0x6ca9, (q15_t)0x6c74, (q15_t)0x6c3f, + (q15_t)0x6c09, (q15_t)0x6bd3, (q15_t)0x6b9c, (q15_t)0x6b66, (q15_t)0x6b2f, (q15_t)0x6af8, (q15_t)0x6ac1, (q15_t)0x6a89, + (q15_t)0x6a51, (q15_t)0x6a19, (q15_t)0x69e1, (q15_t)0x69a8, (q15_t)0x696f, (q15_t)0x6936, (q15_t)0x68fd, (q15_t)0x68c3, + (q15_t)0x6889, (q15_t)0x684f, (q15_t)0x6815, (q15_t)0x67da, (q15_t)0x679f, (q15_t)0x6764, (q15_t)0x6729, (q15_t)0x66ed, + (q15_t)0x66b1, (q15_t)0x6675, (q15_t)0x6639, (q15_t)0x65fc, (q15_t)0x65bf, (q15_t)0x6582, (q15_t)0x6545, (q15_t)0x6507, + (q15_t)0x64c9, (q15_t)0x648b, (q15_t)0x644d, (q15_t)0x640e, (q15_t)0x63cf, (q15_t)0x6390, (q15_t)0x6351, (q15_t)0x6311, + (q15_t)0x62d2, (q15_t)0x6292, (q15_t)0x6251, (q15_t)0x6211, (q15_t)0x61d0, (q15_t)0x618f, (q15_t)0x614e, (q15_t)0x610d, + (q15_t)0x60cb, (q15_t)0x6089, (q15_t)0x6047, (q15_t)0x6004, (q15_t)0x5fc2, (q15_t)0x5f7f, (q15_t)0x5f3c, (q15_t)0x5ef9, + (q15_t)0x5eb5, (q15_t)0x5e71, (q15_t)0x5e2d, (q15_t)0x5de9, (q15_t)0x5da5, (q15_t)0x5d60, (q15_t)0x5d1b, (q15_t)0x5cd6, + (q15_t)0x5c91, (q15_t)0x5c4b, (q15_t)0x5c06, (q15_t)0x5bc0, (q15_t)0x5b79, (q15_t)0x5b33, (q15_t)0x5aec, (q15_t)0x5aa5, + (q15_t)0x5a5e, (q15_t)0x5a17, (q15_t)0x59d0, (q15_t)0x5988, (q15_t)0x5940, (q15_t)0x58f8, (q15_t)0x58af, (q15_t)0x5867, + (q15_t)0x581e, (q15_t)0x57d5, (q15_t)0x578c, (q15_t)0x5742, (q15_t)0x56f9, (q15_t)0x56af, (q15_t)0x5665, (q15_t)0x561a, + (q15_t)0x55d0, (q15_t)0x5585, (q15_t)0x553a, (q15_t)0x54ef, (q15_t)0x54a4, (q15_t)0x5458, (q15_t)0x540d, (q15_t)0x53c1, + (q15_t)0x5375, (q15_t)0x5328, (q15_t)0x52dc, (q15_t)0x528f, (q15_t)0x5242, (q15_t)0x51f5, (q15_t)0x51a8, (q15_t)0x515a, + (q15_t)0x510c, (q15_t)0x50bf, (q15_t)0x5070, (q15_t)0x5022, (q15_t)0x4fd4, (q15_t)0x4f85, (q15_t)0x4f36, (q15_t)0x4ee7, + (q15_t)0x4e98, (q15_t)0x4e48, (q15_t)0x4df9, (q15_t)0x4da9, (q15_t)0x4d59, (q15_t)0x4d09, (q15_t)0x4cb8, (q15_t)0x4c68, + (q15_t)0x4c17, (q15_t)0x4bc6, (q15_t)0x4b75, (q15_t)0x4b24, (q15_t)0x4ad2, (q15_t)0x4a81, (q15_t)0x4a2f, (q15_t)0x49dd, + (q15_t)0x498a, (q15_t)0x4938, (q15_t)0x48e6, (q15_t)0x4893, (q15_t)0x4840, (q15_t)0x47ed, (q15_t)0x479a, (q15_t)0x4746, + (q15_t)0x46f3, (q15_t)0x469f, (q15_t)0x464b, (q15_t)0x45f7, (q15_t)0x45a3, (q15_t)0x454e, (q15_t)0x44fa, (q15_t)0x44a5, + (q15_t)0x4450, (q15_t)0x43fb, (q15_t)0x43a5, (q15_t)0x4350, (q15_t)0x42fa, (q15_t)0x42a5, (q15_t)0x424f, (q15_t)0x41f9, + (q15_t)0x41a2, (q15_t)0x414c, (q15_t)0x40f6, (q15_t)0x409f, (q15_t)0x4048, (q15_t)0x3ff1, (q15_t)0x3f9a, (q15_t)0x3f43, + (q15_t)0x3eeb, (q15_t)0x3e93, (q15_t)0x3e3c, (q15_t)0x3de4, (q15_t)0x3d8c, (q15_t)0x3d33, (q15_t)0x3cdb, (q15_t)0x3c83, + (q15_t)0x3c2a, (q15_t)0x3bd1, (q15_t)0x3b78, (q15_t)0x3b1f, (q15_t)0x3ac6, (q15_t)0x3a6c, (q15_t)0x3a13, (q15_t)0x39b9, + (q15_t)0x395f, (q15_t)0x3906, (q15_t)0x38ab, (q15_t)0x3851, (q15_t)0x37f7, (q15_t)0x379c, (q15_t)0x3742, (q15_t)0x36e7, + (q15_t)0x368c, (q15_t)0x3631, (q15_t)0x35d6, (q15_t)0x357b, (q15_t)0x351f, (q15_t)0x34c4, (q15_t)0x3468, (q15_t)0x340c, + (q15_t)0x33b0, (q15_t)0x3354, (q15_t)0x32f8, (q15_t)0x329c, (q15_t)0x3240, (q15_t)0x31e3, (q15_t)0x3186, (q15_t)0x312a, + (q15_t)0x30cd, (q15_t)0x3070, (q15_t)0x3013, (q15_t)0x2fb5, (q15_t)0x2f58, (q15_t)0x2efb, (q15_t)0x2e9d, (q15_t)0x2e3f, + (q15_t)0x2de2, (q15_t)0x2d84, (q15_t)0x2d26, (q15_t)0x2cc8, (q15_t)0x2c69, (q15_t)0x2c0b, (q15_t)0x2bad, (q15_t)0x2b4e, + (q15_t)0x2aef, (q15_t)0x2a91, (q15_t)0x2a32, (q15_t)0x29d3, (q15_t)0x2974, (q15_t)0x2915, (q15_t)0x28b5, (q15_t)0x2856, + (q15_t)0x27f6, (q15_t)0x2797, (q15_t)0x2737, (q15_t)0x26d8, (q15_t)0x2678, (q15_t)0x2618, (q15_t)0x25b8, (q15_t)0x2558, + (q15_t)0x24f7, (q15_t)0x2497, (q15_t)0x2437, (q15_t)0x23d6, (q15_t)0x2376, (q15_t)0x2315, (q15_t)0x22b4, (q15_t)0x2254, + (q15_t)0x21f3, (q15_t)0x2192, (q15_t)0x2131, (q15_t)0x20d0, (q15_t)0x206e, (q15_t)0x200d, (q15_t)0x1fac, (q15_t)0x1f4a, + (q15_t)0x1ee9, (q15_t)0x1e87, (q15_t)0x1e25, (q15_t)0x1dc4, (q15_t)0x1d62, (q15_t)0x1d00, (q15_t)0x1c9e, (q15_t)0x1c3c, + (q15_t)0x1bda, (q15_t)0x1b78, (q15_t)0x1b16, (q15_t)0x1ab3, (q15_t)0x1a51, (q15_t)0x19ef, (q15_t)0x198c, (q15_t)0x192a, + (q15_t)0x18c7, (q15_t)0x1864, (q15_t)0x1802, (q15_t)0x179f, (q15_t)0x173c, (q15_t)0x16d9, (q15_t)0x1676, (q15_t)0x1613, + (q15_t)0x15b0, (q15_t)0x154d, (q15_t)0x14ea, (q15_t)0x1487, (q15_t)0x1423, (q15_t)0x13c0, (q15_t)0x135d, (q15_t)0x12f9, + (q15_t)0x1296, (q15_t)0x1232, (q15_t)0x11cf, (q15_t)0x116b, (q15_t)0x1108, (q15_t)0x10a4, (q15_t)0x1040, (q15_t)0xfdd, + (q15_t)0xf79, (q15_t)0xf15, (q15_t)0xeb1, (q15_t)0xe4d, (q15_t)0xde9, (q15_t)0xd85, (q15_t)0xd21, (q15_t)0xcbd, + (q15_t)0xc59, (q15_t)0xbf5, (q15_t)0xb91, (q15_t)0xb2d, (q15_t)0xac9, (q15_t)0xa65, (q15_t)0xa00, (q15_t)0x99c, + (q15_t)0x938, (q15_t)0x8d4, (q15_t)0x86f, (q15_t)0x80b, (q15_t)0x7a7, (q15_t)0x742, (q15_t)0x6de, (q15_t)0x67a, + (q15_t)0x615, (q15_t)0x5b1, (q15_t)0x54c, (q15_t)0x4e8, (q15_t)0x483, (q15_t)0x41f, (q15_t)0x3ba, (q15_t)0x356, + (q15_t)0x2f1, (q15_t)0x28d, (q15_t)0x228, (q15_t)0x1c4, (q15_t)0x15f, (q15_t)0xfb, (q15_t)0x96, (q15_t)0x32 +}; + +static const q15_t ALIGN4 cos_factorsQ15_2048[2048] = { + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffd, (q15_t)0x7ffd, + (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffa, + (q15_t)0x7ffa, (q15_t)0x7ff9, (q15_t)0x7ff9, (q15_t)0x7ff8, (q15_t)0x7ff8, (q15_t)0x7ff7, (q15_t)0x7ff7, (q15_t)0x7ff6, + (q15_t)0x7ff5, (q15_t)0x7ff5, (q15_t)0x7ff4, (q15_t)0x7ff3, (q15_t)0x7ff3, (q15_t)0x7ff2, (q15_t)0x7ff1, (q15_t)0x7ff0, + (q15_t)0x7ff0, (q15_t)0x7fef, (q15_t)0x7fee, (q15_t)0x7fed, (q15_t)0x7fec, (q15_t)0x7fec, (q15_t)0x7feb, (q15_t)0x7fea, + (q15_t)0x7fe9, (q15_t)0x7fe8, (q15_t)0x7fe7, (q15_t)0x7fe6, (q15_t)0x7fe5, (q15_t)0x7fe4, (q15_t)0x7fe3, (q15_t)0x7fe2, + (q15_t)0x7fe1, (q15_t)0x7fe0, (q15_t)0x7fdf, (q15_t)0x7fdd, (q15_t)0x7fdc, (q15_t)0x7fdb, (q15_t)0x7fda, (q15_t)0x7fd9, + (q15_t)0x7fd7, (q15_t)0x7fd6, (q15_t)0x7fd5, (q15_t)0x7fd4, (q15_t)0x7fd2, (q15_t)0x7fd1, (q15_t)0x7fd0, (q15_t)0x7fce, + (q15_t)0x7fcd, (q15_t)0x7fcb, (q15_t)0x7fca, (q15_t)0x7fc9, (q15_t)0x7fc7, (q15_t)0x7fc6, (q15_t)0x7fc4, (q15_t)0x7fc3, + (q15_t)0x7fc1, (q15_t)0x7fc0, (q15_t)0x7fbe, (q15_t)0x7fbc, (q15_t)0x7fbb, (q15_t)0x7fb9, (q15_t)0x7fb7, (q15_t)0x7fb6, + (q15_t)0x7fb4, (q15_t)0x7fb2, (q15_t)0x7fb1, (q15_t)0x7faf, (q15_t)0x7fad, (q15_t)0x7fab, (q15_t)0x7fa9, (q15_t)0x7fa8, + (q15_t)0x7fa6, (q15_t)0x7fa4, (q15_t)0x7fa2, (q15_t)0x7fa0, (q15_t)0x7f9e, (q15_t)0x7f9c, (q15_t)0x7f9a, (q15_t)0x7f98, + (q15_t)0x7f96, (q15_t)0x7f94, (q15_t)0x7f92, (q15_t)0x7f90, (q15_t)0x7f8e, (q15_t)0x7f8c, (q15_t)0x7f8a, (q15_t)0x7f88, + (q15_t)0x7f86, (q15_t)0x7f83, (q15_t)0x7f81, (q15_t)0x7f7f, (q15_t)0x7f7d, (q15_t)0x7f7b, (q15_t)0x7f78, (q15_t)0x7f76, + (q15_t)0x7f74, (q15_t)0x7f71, (q15_t)0x7f6f, (q15_t)0x7f6d, (q15_t)0x7f6a, (q15_t)0x7f68, (q15_t)0x7f65, (q15_t)0x7f63, + (q15_t)0x7f60, (q15_t)0x7f5e, (q15_t)0x7f5b, (q15_t)0x7f59, (q15_t)0x7f56, (q15_t)0x7f54, (q15_t)0x7f51, (q15_t)0x7f4f, + (q15_t)0x7f4c, (q15_t)0x7f49, (q15_t)0x7f47, (q15_t)0x7f44, (q15_t)0x7f41, (q15_t)0x7f3f, (q15_t)0x7f3c, (q15_t)0x7f39, + (q15_t)0x7f36, (q15_t)0x7f34, (q15_t)0x7f31, (q15_t)0x7f2e, (q15_t)0x7f2b, (q15_t)0x7f28, (q15_t)0x7f25, (q15_t)0x7f23, + (q15_t)0x7f20, (q15_t)0x7f1d, (q15_t)0x7f1a, (q15_t)0x7f17, (q15_t)0x7f14, (q15_t)0x7f11, (q15_t)0x7f0e, (q15_t)0x7f0b, + (q15_t)0x7f08, (q15_t)0x7f04, (q15_t)0x7f01, (q15_t)0x7efe, (q15_t)0x7efb, (q15_t)0x7ef8, (q15_t)0x7ef5, (q15_t)0x7ef1, + (q15_t)0x7eee, (q15_t)0x7eeb, (q15_t)0x7ee8, (q15_t)0x7ee4, (q15_t)0x7ee1, (q15_t)0x7ede, (q15_t)0x7eda, (q15_t)0x7ed7, + (q15_t)0x7ed4, (q15_t)0x7ed0, (q15_t)0x7ecd, (q15_t)0x7ec9, (q15_t)0x7ec6, (q15_t)0x7ec3, (q15_t)0x7ebf, (q15_t)0x7ebb, + (q15_t)0x7eb8, (q15_t)0x7eb4, (q15_t)0x7eb1, (q15_t)0x7ead, (q15_t)0x7eaa, (q15_t)0x7ea6, (q15_t)0x7ea2, (q15_t)0x7e9f, + (q15_t)0x7e9b, (q15_t)0x7e97, (q15_t)0x7e94, (q15_t)0x7e90, (q15_t)0x7e8c, (q15_t)0x7e88, (q15_t)0x7e84, (q15_t)0x7e81, + (q15_t)0x7e7d, (q15_t)0x7e79, (q15_t)0x7e75, (q15_t)0x7e71, (q15_t)0x7e6d, (q15_t)0x7e69, (q15_t)0x7e65, (q15_t)0x7e61, + (q15_t)0x7e5d, (q15_t)0x7e59, (q15_t)0x7e55, (q15_t)0x7e51, (q15_t)0x7e4d, (q15_t)0x7e49, (q15_t)0x7e45, (q15_t)0x7e41, + (q15_t)0x7e3d, (q15_t)0x7e39, (q15_t)0x7e34, (q15_t)0x7e30, (q15_t)0x7e2c, (q15_t)0x7e28, (q15_t)0x7e24, (q15_t)0x7e1f, + (q15_t)0x7e1b, (q15_t)0x7e17, (q15_t)0x7e12, (q15_t)0x7e0e, (q15_t)0x7e0a, (q15_t)0x7e05, (q15_t)0x7e01, (q15_t)0x7dfc, + (q15_t)0x7df8, (q15_t)0x7df3, (q15_t)0x7def, (q15_t)0x7dea, (q15_t)0x7de6, (q15_t)0x7de1, (q15_t)0x7ddd, (q15_t)0x7dd8, + (q15_t)0x7dd4, (q15_t)0x7dcf, (q15_t)0x7dca, (q15_t)0x7dc6, (q15_t)0x7dc1, (q15_t)0x7dbc, (q15_t)0x7db8, (q15_t)0x7db3, + (q15_t)0x7dae, (q15_t)0x7da9, (q15_t)0x7da5, (q15_t)0x7da0, (q15_t)0x7d9b, (q15_t)0x7d96, (q15_t)0x7d91, (q15_t)0x7d8c, + (q15_t)0x7d87, (q15_t)0x7d82, (q15_t)0x7d7e, (q15_t)0x7d79, (q15_t)0x7d74, 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(q15_t)0x2290, (q15_t)0x2278, (q15_t)0x2260, (q15_t)0x2247, (q15_t)0x222f, + (q15_t)0x2217, (q15_t)0x21ff, (q15_t)0x21e7, (q15_t)0x21ce, (q15_t)0x21b6, (q15_t)0x219e, (q15_t)0x2186, (q15_t)0x216d, + (q15_t)0x2155, (q15_t)0x213d, (q15_t)0x2125, (q15_t)0x210c, (q15_t)0x20f4, (q15_t)0x20dc, (q15_t)0x20c3, (q15_t)0x20ab, + (q15_t)0x2093, (q15_t)0x207a, (q15_t)0x2062, (q15_t)0x204a, (q15_t)0x2032, (q15_t)0x2019, (q15_t)0x2001, (q15_t)0x1fe9, + (q15_t)0x1fd0, (q15_t)0x1fb8, (q15_t)0x1f9f, (q15_t)0x1f87, (q15_t)0x1f6f, (q15_t)0x1f56, (q15_t)0x1f3e, (q15_t)0x1f26, + (q15_t)0x1f0d, (q15_t)0x1ef5, (q15_t)0x1edd, (q15_t)0x1ec4, (q15_t)0x1eac, (q15_t)0x1e93, (q15_t)0x1e7b, (q15_t)0x1e62, + (q15_t)0x1e4a, (q15_t)0x1e32, (q15_t)0x1e19, (q15_t)0x1e01, (q15_t)0x1de8, (q15_t)0x1dd0, (q15_t)0x1db7, (q15_t)0x1d9f, + (q15_t)0x1d87, (q15_t)0x1d6e, (q15_t)0x1d56, (q15_t)0x1d3d, (q15_t)0x1d25, (q15_t)0x1d0c, (q15_t)0x1cf4, (q15_t)0x1cdb, + (q15_t)0x1cc3, (q15_t)0x1caa, (q15_t)0x1c92, (q15_t)0x1c79, (q15_t)0x1c61, (q15_t)0x1c48, (q15_t)0x1c30, (q15_t)0x1c17, + (q15_t)0x1bff, (q15_t)0x1be6, (q15_t)0x1bce, (q15_t)0x1bb5, (q15_t)0x1b9d, (q15_t)0x1b84, (q15_t)0x1b6c, (q15_t)0x1b53, + (q15_t)0x1b3a, (q15_t)0x1b22, (q15_t)0x1b09, (q15_t)0x1af1, (q15_t)0x1ad8, (q15_t)0x1ac0, (q15_t)0x1aa7, (q15_t)0x1a8e, + (q15_t)0x1a76, (q15_t)0x1a5d, (q15_t)0x1a45, (q15_t)0x1a2c, (q15_t)0x1a13, (q15_t)0x19fb, (q15_t)0x19e2, (q15_t)0x19ca, + (q15_t)0x19b1, (q15_t)0x1998, (q15_t)0x1980, (q15_t)0x1967, (q15_t)0x194e, (q15_t)0x1936, (q15_t)0x191d, (q15_t)0x1905, + (q15_t)0x18ec, (q15_t)0x18d3, (q15_t)0x18bb, (q15_t)0x18a2, (q15_t)0x1889, (q15_t)0x1871, (q15_t)0x1858, (q15_t)0x183f, + (q15_t)0x1827, (q15_t)0x180e, (q15_t)0x17f5, (q15_t)0x17dd, (q15_t)0x17c4, (q15_t)0x17ab, (q15_t)0x1792, (q15_t)0x177a, + (q15_t)0x1761, (q15_t)0x1748, (q15_t)0x1730, (q15_t)0x1717, (q15_t)0x16fe, (q15_t)0x16e5, (q15_t)0x16cd, (q15_t)0x16b4, + (q15_t)0x169b, (q15_t)0x1682, (q15_t)0x166a, (q15_t)0x1651, (q15_t)0x1638, (q15_t)0x161f, (q15_t)0x1607, (q15_t)0x15ee, + (q15_t)0x15d5, (q15_t)0x15bc, (q15_t)0x15a4, (q15_t)0x158b, (q15_t)0x1572, (q15_t)0x1559, (q15_t)0x1541, (q15_t)0x1528, + (q15_t)0x150f, (q15_t)0x14f6, (q15_t)0x14dd, (q15_t)0x14c5, (q15_t)0x14ac, (q15_t)0x1493, (q15_t)0x147a, (q15_t)0x1461, + (q15_t)0x1449, (q15_t)0x1430, (q15_t)0x1417, (q15_t)0x13fe, (q15_t)0x13e5, (q15_t)0x13cc, (q15_t)0x13b4, (q15_t)0x139b, + (q15_t)0x1382, (q15_t)0x1369, (q15_t)0x1350, (q15_t)0x1337, (q15_t)0x131f, (q15_t)0x1306, (q15_t)0x12ed, (q15_t)0x12d4, + (q15_t)0x12bb, (q15_t)0x12a2, (q15_t)0x1289, (q15_t)0x1271, (q15_t)0x1258, (q15_t)0x123f, (q15_t)0x1226, (q15_t)0x120d, + (q15_t)0x11f4, (q15_t)0x11db, (q15_t)0x11c2, (q15_t)0x11a9, (q15_t)0x1191, (q15_t)0x1178, (q15_t)0x115f, (q15_t)0x1146, + (q15_t)0x112d, (q15_t)0x1114, (q15_t)0x10fb, (q15_t)0x10e2, (q15_t)0x10c9, (q15_t)0x10b0, (q15_t)0x1098, (q15_t)0x107f, + (q15_t)0x1066, (q15_t)0x104d, (q15_t)0x1034, (q15_t)0x101b, (q15_t)0x1002, (q15_t)0xfe9, (q15_t)0xfd0, (q15_t)0xfb7, + (q15_t)0xf9e, (q15_t)0xf85, (q15_t)0xf6c, (q15_t)0xf53, (q15_t)0xf3a, (q15_t)0xf21, (q15_t)0xf08, (q15_t)0xef0, + (q15_t)0xed7, (q15_t)0xebe, (q15_t)0xea5, (q15_t)0xe8c, (q15_t)0xe73, (q15_t)0xe5a, (q15_t)0xe41, (q15_t)0xe28, + (q15_t)0xe0f, (q15_t)0xdf6, (q15_t)0xddd, (q15_t)0xdc4, (q15_t)0xdab, (q15_t)0xd92, (q15_t)0xd79, (q15_t)0xd60, + (q15_t)0xd47, (q15_t)0xd2e, (q15_t)0xd15, (q15_t)0xcfc, (q15_t)0xce3, (q15_t)0xcca, (q15_t)0xcb1, (q15_t)0xc98, + (q15_t)0xc7f, (q15_t)0xc66, (q15_t)0xc4d, (q15_t)0xc34, (q15_t)0xc1b, (q15_t)0xc02, (q15_t)0xbe9, (q15_t)0xbd0, + (q15_t)0xbb7, (q15_t)0xb9e, (q15_t)0xb85, (q15_t)0xb6c, (q15_t)0xb53, (q15_t)0xb3a, (q15_t)0xb20, (q15_t)0xb07, + (q15_t)0xaee, (q15_t)0xad5, (q15_t)0xabc, (q15_t)0xaa3, (q15_t)0xa8a, (q15_t)0xa71, (q15_t)0xa58, (q15_t)0xa3f, + (q15_t)0xa26, (q15_t)0xa0d, (q15_t)0x9f4, (q15_t)0x9db, (q15_t)0x9c2, (q15_t)0x9a9, (q15_t)0x990, (q15_t)0x977, + (q15_t)0x95e, (q15_t)0x944, (q15_t)0x92b, (q15_t)0x912, (q15_t)0x8f9, (q15_t)0x8e0, (q15_t)0x8c7, (q15_t)0x8ae, + (q15_t)0x895, (q15_t)0x87c, (q15_t)0x863, (q15_t)0x84a, (q15_t)0x831, (q15_t)0x818, (q15_t)0x7fe, (q15_t)0x7e5, + (q15_t)0x7cc, (q15_t)0x7b3, (q15_t)0x79a, (q15_t)0x781, (q15_t)0x768, (q15_t)0x74f, (q15_t)0x736, (q15_t)0x71d, + (q15_t)0x704, (q15_t)0x6ea, (q15_t)0x6d1, (q15_t)0x6b8, (q15_t)0x69f, (q15_t)0x686, (q15_t)0x66d, (q15_t)0x654, + (q15_t)0x63b, (q15_t)0x622, (q15_t)0x609, (q15_t)0x5ef, (q15_t)0x5d6, (q15_t)0x5bd, (q15_t)0x5a4, (q15_t)0x58b, + (q15_t)0x572, (q15_t)0x559, (q15_t)0x540, (q15_t)0x527, (q15_t)0x50d, (q15_t)0x4f4, (q15_t)0x4db, (q15_t)0x4c2, + (q15_t)0x4a9, (q15_t)0x490, (q15_t)0x477, (q15_t)0x45e, (q15_t)0x445, (q15_t)0x42b, (q15_t)0x412, (q15_t)0x3f9, + (q15_t)0x3e0, (q15_t)0x3c7, (q15_t)0x3ae, (q15_t)0x395, (q15_t)0x37c, (q15_t)0x362, (q15_t)0x349, (q15_t)0x330, + (q15_t)0x317, (q15_t)0x2fe, (q15_t)0x2e5, (q15_t)0x2cc, (q15_t)0x2b3, (q15_t)0x299, (q15_t)0x280, (q15_t)0x267, + (q15_t)0x24e, (q15_t)0x235, (q15_t)0x21c, (q15_t)0x203, (q15_t)0x1ea, (q15_t)0x1d0, (q15_t)0x1b7, (q15_t)0x19e, + (q15_t)0x185, (q15_t)0x16c, (q15_t)0x153, (q15_t)0x13a, (q15_t)0x121, (q15_t)0x107, (q15_t)0xee, (q15_t)0xd5, + (q15_t)0xbc, (q15_t)0xa3, (q15_t)0x8a, (q15_t)0x71, (q15_t)0x57, (q15_t)0x3e, (q15_t)0x25, (q15_t)0xc + +}; + +static const q15_t ALIGN4 cos_factorsQ15_8192[8192] = { + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, + (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, (q15_t)0x7fff, + (q15_t)0x7fff, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, + (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffe, + (q15_t)0x7ffe, (q15_t)0x7ffe, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, + (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffd, (q15_t)0x7ffc, + (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffc, (q15_t)0x7ffc, + (q15_t)0x7ffc, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, + (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffb, (q15_t)0x7ffa, (q15_t)0x7ffa, (q15_t)0x7ffa, (q15_t)0x7ffa, (q15_t)0x7ffa, + (q15_t)0x7ffa, (q15_t)0x7ffa, (q15_t)0x7ffa, (q15_t)0x7ffa, (q15_t)0x7ff9, (q15_t)0x7ff9, (q15_t)0x7ff9, (q15_t)0x7ff9, + (q15_t)0x7ff9, (q15_t)0x7ff9, (q15_t)0x7ff9, (q15_t)0x7ff9, (q15_t)0x7ff8, (q15_t)0x7ff8, (q15_t)0x7ff8, (q15_t)0x7ff8, + (q15_t)0x7ff8, (q15_t)0x7ff8, (q15_t)0x7ff8, (q15_t)0x7ff7, (q15_t)0x7ff7, (q15_t)0x7ff7, (q15_t)0x7ff7, (q15_t)0x7ff7, + (q15_t)0x7ff7, (q15_t)0x7ff7, (q15_t)0x7ff6, (q15_t)0x7ff6, (q15_t)0x7ff6, (q15_t)0x7ff6, (q15_t)0x7ff6, (q15_t)0x7ff6, + (q15_t)0x7ff6, (q15_t)0x7ff5, (q15_t)0x7ff5, (q15_t)0x7ff5, (q15_t)0x7ff5, (q15_t)0x7ff5, (q15_t)0x7ff5, (q15_t)0x7ff4, + (q15_t)0x7ff4, (q15_t)0x7ff4, (q15_t)0x7ff4, (q15_t)0x7ff4, (q15_t)0x7ff4, (q15_t)0x7ff3, (q15_t)0x7ff3, (q15_t)0x7ff3, + (q15_t)0x7ff3, (q15_t)0x7ff3, (q15_t)0x7ff3, (q15_t)0x7ff2, (q15_t)0x7ff2, (q15_t)0x7ff2, (q15_t)0x7ff2, (q15_t)0x7ff2, + (q15_t)0x7ff1, (q15_t)0x7ff1, (q15_t)0x7ff1, (q15_t)0x7ff1, (q15_t)0x7ff1, (q15_t)0x7ff1, (q15_t)0x7ff0, (q15_t)0x7ff0, + (q15_t)0x7ff0, (q15_t)0x7ff0, (q15_t)0x7ff0, (q15_t)0x7fef, (q15_t)0x7fef, (q15_t)0x7fef, (q15_t)0x7fef, (q15_t)0x7fef, + (q15_t)0x7fee, (q15_t)0x7fee, (q15_t)0x7fee, (q15_t)0x7fee, (q15_t)0x7fee, (q15_t)0x7fed, (q15_t)0x7fed, (q15_t)0x7fed, + (q15_t)0x7fed, (q15_t)0x7fed, (q15_t)0x7fec, (q15_t)0x7fec, (q15_t)0x7fec, (q15_t)0x7fec, (q15_t)0x7feb, (q15_t)0x7feb, + (q15_t)0x7feb, (q15_t)0x7feb, (q15_t)0x7feb, (q15_t)0x7fea, (q15_t)0x7fea, (q15_t)0x7fea, (q15_t)0x7fea, (q15_t)0x7fe9, + (q15_t)0x7fe9, (q15_t)0x7fe9, (q15_t)0x7fe9, (q15_t)0x7fe8, (q15_t)0x7fe8, (q15_t)0x7fe8, (q15_t)0x7fe8, (q15_t)0x7fe8, + (q15_t)0x7fe7, (q15_t)0x7fe7, (q15_t)0x7fe7, (q15_t)0x7fe7, (q15_t)0x7fe6, (q15_t)0x7fe6, (q15_t)0x7fe6, (q15_t)0x7fe6, + (q15_t)0x7fe5, (q15_t)0x7fe5, (q15_t)0x7fe5, (q15_t)0x7fe5, (q15_t)0x7fe4, (q15_t)0x7fe4, (q15_t)0x7fe4, (q15_t)0x7fe4, + (q15_t)0x7fe3, (q15_t)0x7fe3, (q15_t)0x7fe3, (q15_t)0x7fe2, (q15_t)0x7fe2, (q15_t)0x7fe2, (q15_t)0x7fe2, (q15_t)0x7fe1, + (q15_t)0x7fe1, (q15_t)0x7fe1, (q15_t)0x7fe1, (q15_t)0x7fe0, (q15_t)0x7fe0, (q15_t)0x7fe0, (q15_t)0x7fdf, (q15_t)0x7fdf, + (q15_t)0x7fdf, (q15_t)0x7fdf, (q15_t)0x7fde, (q15_t)0x7fde, (q15_t)0x7fde, (q15_t)0x7fde, (q15_t)0x7fdd, (q15_t)0x7fdd, + (q15_t)0x7fdd, (q15_t)0x7fdc, (q15_t)0x7fdc, (q15_t)0x7fdc, (q15_t)0x7fdb, (q15_t)0x7fdb, (q15_t)0x7fdb, (q15_t)0x7fdb, + (q15_t)0x7fda, (q15_t)0x7fda, (q15_t)0x7fda, (q15_t)0x7fd9, (q15_t)0x7fd9, (q15_t)0x7fd9, (q15_t)0x7fd8, (q15_t)0x7fd8, + (q15_t)0x7fd8, (q15_t)0x7fd8, (q15_t)0x7fd7, (q15_t)0x7fd7, (q15_t)0x7fd7, (q15_t)0x7fd6, (q15_t)0x7fd6, (q15_t)0x7fd6, + (q15_t)0x7fd5, (q15_t)0x7fd5, (q15_t)0x7fd5, (q15_t)0x7fd4, (q15_t)0x7fd4, (q15_t)0x7fd4, (q15_t)0x7fd3, (q15_t)0x7fd3, + (q15_t)0x7fd3, (q15_t)0x7fd2, (q15_t)0x7fd2, (q15_t)0x7fd2, (q15_t)0x7fd1, (q15_t)0x7fd1, (q15_t)0x7fd1, (q15_t)0x7fd0, + (q15_t)0x7fd0, (q15_t)0x7fd0, (q15_t)0x7fcf, (q15_t)0x7fcf, (q15_t)0x7fcf, (q15_t)0x7fce, (q15_t)0x7fce, (q15_t)0x7fce, + (q15_t)0x7fcd, (q15_t)0x7fcd, (q15_t)0x7fcd, (q15_t)0x7fcc, (q15_t)0x7fcc, (q15_t)0x7fcc, (q15_t)0x7fcb, (q15_t)0x7fcb, + (q15_t)0x7fcb, (q15_t)0x7fca, (q15_t)0x7fca, (q15_t)0x7fc9, (q15_t)0x7fc9, 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(q15_t)0x499, (q15_t)0x493, (q15_t)0x48d, (q15_t)0x487, + (q15_t)0x480, (q15_t)0x47a, (q15_t)0x474, (q15_t)0x46d, (q15_t)0x467, (q15_t)0x461, (q15_t)0x45b, (q15_t)0x454, + (q15_t)0x44e, (q15_t)0x448, (q15_t)0x441, (q15_t)0x43b, (q15_t)0x435, (q15_t)0x42f, (q15_t)0x428, (q15_t)0x422, + (q15_t)0x41c, (q15_t)0x415, (q15_t)0x40f, (q15_t)0x409, (q15_t)0x403, (q15_t)0x3fc, (q15_t)0x3f6, (q15_t)0x3f0, + (q15_t)0x3ea, (q15_t)0x3e3, (q15_t)0x3dd, (q15_t)0x3d7, (q15_t)0x3d0, (q15_t)0x3ca, (q15_t)0x3c4, (q15_t)0x3be, + (q15_t)0x3b7, (q15_t)0x3b1, (q15_t)0x3ab, (q15_t)0x3a4, (q15_t)0x39e, (q15_t)0x398, (q15_t)0x392, (q15_t)0x38b, + (q15_t)0x385, (q15_t)0x37f, (q15_t)0x378, (q15_t)0x372, (q15_t)0x36c, (q15_t)0x366, (q15_t)0x35f, (q15_t)0x359, + (q15_t)0x353, (q15_t)0x34c, (q15_t)0x346, (q15_t)0x340, (q15_t)0x33a, (q15_t)0x333, (q15_t)0x32d, (q15_t)0x327, + (q15_t)0x321, (q15_t)0x31a, (q15_t)0x314, (q15_t)0x30e, (q15_t)0x307, (q15_t)0x301, (q15_t)0x2fb, (q15_t)0x2f5, + (q15_t)0x2ee, (q15_t)0x2e8, (q15_t)0x2e2, (q15_t)0x2db, (q15_t)0x2d5, (q15_t)0x2cf, (q15_t)0x2c9, (q15_t)0x2c2, + (q15_t)0x2bc, (q15_t)0x2b6, (q15_t)0x2af, (q15_t)0x2a9, (q15_t)0x2a3, (q15_t)0x29d, (q15_t)0x296, (q15_t)0x290, + (q15_t)0x28a, (q15_t)0x283, (q15_t)0x27d, (q15_t)0x277, (q15_t)0x271, (q15_t)0x26a, (q15_t)0x264, (q15_t)0x25e, + (q15_t)0x258, (q15_t)0x251, (q15_t)0x24b, (q15_t)0x245, (q15_t)0x23e, (q15_t)0x238, (q15_t)0x232, (q15_t)0x22c, + (q15_t)0x225, (q15_t)0x21f, (q15_t)0x219, (q15_t)0x212, (q15_t)0x20c, (q15_t)0x206, (q15_t)0x200, (q15_t)0x1f9, + (q15_t)0x1f3, (q15_t)0x1ed, (q15_t)0x1e6, (q15_t)0x1e0, (q15_t)0x1da, (q15_t)0x1d4, (q15_t)0x1cd, (q15_t)0x1c7, + (q15_t)0x1c1, (q15_t)0x1ba, (q15_t)0x1b4, (q15_t)0x1ae, (q15_t)0x1a8, (q15_t)0x1a1, (q15_t)0x19b, (q15_t)0x195, + (q15_t)0x18e, (q15_t)0x188, (q15_t)0x182, (q15_t)0x17c, (q15_t)0x175, (q15_t)0x16f, (q15_t)0x169, (q15_t)0x162, + (q15_t)0x15c, (q15_t)0x156, (q15_t)0x150, (q15_t)0x149, (q15_t)0x143, (q15_t)0x13d, (q15_t)0x137, (q15_t)0x130, + (q15_t)0x12a, (q15_t)0x124, (q15_t)0x11d, (q15_t)0x117, (q15_t)0x111, (q15_t)0x10b, (q15_t)0x104, (q15_t)0xfe, + (q15_t)0xf8, (q15_t)0xf1, (q15_t)0xeb, (q15_t)0xe5, (q15_t)0xdf, (q15_t)0xd8, (q15_t)0xd2, (q15_t)0xcc, + (q15_t)0xc5, (q15_t)0xbf, (q15_t)0xb9, (q15_t)0xb3, (q15_t)0xac, (q15_t)0xa6, (q15_t)0xa0, (q15_t)0x99, + (q15_t)0x93, (q15_t)0x8d, (q15_t)0x87, (q15_t)0x80, (q15_t)0x7a, (q15_t)0x74, (q15_t)0x6d, (q15_t)0x67, + (q15_t)0x61, (q15_t)0x5b, (q15_t)0x54, (q15_t)0x4e, (q15_t)0x48, (q15_t)0x41, (q15_t)0x3b, (q15_t)0x35, + (q15_t)0x2f, (q15_t)0x28, (q15_t)0x22, (q15_t)0x1c, (q15_t)0x15, (q15_t)0xf, (q15_t)0x9, (q15_t)0x3 +}; + +/** + * @} end of DCT4_IDCT4_Table group + */ + +/** + * @addtogroup DCT4_IDCT4 + * @{ + */ + +/** + * @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 <code>N</code> is not a supported transform length. + * \par Normalizing factor: + * The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>. + * Normalizing factors in 1.15 format are mentioned in the table below for different DCT sizes: + * \image html dct4NormalizingQ15Table.gif + */ + +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) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializing the pointer array with the weight table base addresses of different lengths */ + q15_t *twiddlePtr[4] = { (q15_t *) WeightsQ15_128, (q15_t *) WeightsQ15_512, + (q15_t *) WeightsQ15_2048, (q15_t *) WeightsQ15_8192 + }; + + /* Initializing the pointer array with the cos factor table base addresses of different lengths */ + q15_t *pCosFactor[4] = + { (q15_t *) cos_factorsQ15_128, (q15_t *) cos_factorsQ15_512, + (q15_t *) cos_factorsQ15_2048, (q15_t *) cos_factorsQ15_8192 + }; + + /* Initialize the DCT4 length */ + S->N = N; + + /* Initialize the half of DCT4 length */ + S->Nby2 = Nby2; + + /* Initialize the DCT4 Normalizing factor */ + S->normalize = normalize; + + /* Initialize Real FFT Instance */ + S->pRfft = S_RFFT; + + /* Initialize Complex FFT Instance */ + S->pCfft = S_CFFT; + + switch (N) + { + /* Initialize the table modifier values */ + case 8192U: + S->pTwiddle = twiddlePtr[3]; + S->pCosFactor = pCosFactor[3]; + break; + case 2048U: + S->pTwiddle = twiddlePtr[2]; + S->pCosFactor = pCosFactor[2]; + break; + case 512U: + S->pTwiddle = twiddlePtr[1]; + S->pCosFactor = pCosFactor[1]; + break; + case 128U: + S->pTwiddle = twiddlePtr[0]; + S->pCosFactor = pCosFactor[0]; + break; + default: + status = ARM_MATH_ARGUMENT_ERROR; + } + + /* Initialize the RFFT/RIFFT */ + arm_rfft_init_q15(S->pRfft, S->N, 0U, 1U); + + /* return the status of DCT4 Init function */ + return (status); +} + +/** + * @} end of DCT4_IDCT4 group + */ diff --git a/DSP/Source/TransformFunctions/arm_dct4_init_q31.c b/DSP/Source/TransformFunctions/arm_dct4_init_q31.c new file mode 100644 index 0000000..8156844 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_dct4_init_q31.c @@ -0,0 +1,7686 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_dct4_init_q31.c + * Description: Initialization function of DCT-4 & IDCT4 Q31 + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @ingroup DCT4_IDCT4 + */ + +/** + * @addtogroup DCT4_IDCT4_Table DCT Type IV Tables + * @{ + */ + +/* +* @brief Weights Table +*/ + +/** + * \par + * Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre> + * \par + * C command to generate the table + * <pre> + * for(i = 0; i< N; i++) + * { + * weights[2*i]= cos(i*c); + * weights[(2*i)+1]= -sin(i * c); + * } </pre> + * \par + * where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code> + * \par + * Convert the output to q31 format by multiplying with 2^31 and saturated if required. + * \par + * In the tables below the real and imaginary values are placed alternatively, hence the + * array length is <code>2*N</code>. + */ + +static const q31_t WeightsQ31_128[256] = { + (q31_t)0x7fffffff, (q31_t)0x00000000, (q31_t)0x7ffd885a, (q31_t)0xfe6de2e0, (q31_t)0x7ff62182, (q31_t)0xfcdbd541, (q31_t)0x7fe9cbc0, (q31_t)0xfb49e6a3, + (q31_t)0x7fd8878e, (q31_t)0xf9b82684, (q31_t)0x7fc25596, (q31_t)0xf826a462, (q31_t)0x7fa736b4, (q31_t)0xf6956fb7, (q31_t)0x7f872bf3, (q31_t)0xf50497fb, + (q31_t)0x7f62368f, (q31_t)0xf3742ca2, (q31_t)0x7f3857f6, (q31_t)0xf1e43d1c, (q31_t)0x7f0991c4, (q31_t)0xf054d8d5, (q31_t)0x7ed5e5c6, (q31_t)0xeec60f31, + (q31_t)0x7e9d55fc, (q31_t)0xed37ef91, (q31_t)0x7e5fe493, (q31_t)0xebaa894f, (q31_t)0x7e1d93ea, (q31_t)0xea1debbb, (q31_t)0x7dd6668f, (q31_t)0xe8922622, + (q31_t)0x7d8a5f40, (q31_t)0xe70747c4, (q31_t)0x7d3980ec, (q31_t)0xe57d5fda, (q31_t)0x7ce3ceb2, (q31_t)0xe3f47d96, (q31_t)0x7c894bde, (q31_t)0xe26cb01b, + (q31_t)0x7c29fbee, (q31_t)0xe0e60685, (q31_t)0x7bc5e290, (q31_t)0xdf608fe4, (q31_t)0x7b5d039e, (q31_t)0xdddc5b3b, (q31_t)0x7aef6323, (q31_t)0xdc597781, + (q31_t)0x7a7d055b, (q31_t)0xdad7f3a2, (q31_t)0x7a05eead, (q31_t)0xd957de7a, (q31_t)0x798a23b1, (q31_t)0xd7d946d8, (q31_t)0x7909a92d, (q31_t)0xd65c3b7b, + (q31_t)0x78848414, (q31_t)0xd4e0cb15, (q31_t)0x77fab989, (q31_t)0xd3670446, (q31_t)0x776c4edb, (q31_t)0xd1eef59e, (q31_t)0x76d94989, (q31_t)0xd078ad9e, + (q31_t)0x7641af3d, (q31_t)0xcf043ab3, (q31_t)0x75a585cf, (q31_t)0xcd91ab39, (q31_t)0x7504d345, (q31_t)0xcc210d79, (q31_t)0x745f9dd1, (q31_t)0xcab26fa9, + (q31_t)0x73b5ebd1, (q31_t)0xc945dfec, (q31_t)0x7307c3d0, (q31_t)0xc7db6c50, (q31_t)0x72552c85, (q31_t)0xc67322ce, (q31_t)0x719e2cd2, (q31_t)0xc50d1149, + (q31_t)0x70e2cbc6, (q31_t)0xc3a94590, (q31_t)0x7023109a, (q31_t)0xc247cd5a, (q31_t)0x6f5f02b2, (q31_t)0xc0e8b648, (q31_t)0x6e96a99d, (q31_t)0xbf8c0de3, + (q31_t)0x6dca0d14, (q31_t)0xbe31e19b, (q31_t)0x6cf934fc, (q31_t)0xbcda3ecb, (q31_t)0x6c242960, (q31_t)0xbb8532b0, (q31_t)0x6b4af279, (q31_t)0xba32ca71, + (q31_t)0x6a6d98a4, (q31_t)0xb8e31319, (q31_t)0x698c246c, (q31_t)0xb796199b, (q31_t)0x68a69e81, (q31_t)0xb64beacd, (q31_t)0x67bd0fbd, (q31_t)0xb5049368, + (q31_t)0x66cf8120, (q31_t)0xb3c0200c, (q31_t)0x65ddfbd3, (q31_t)0xb27e9d3c, (q31_t)0x64e88926, (q31_t)0xb140175b, (q31_t)0x63ef3290, (q31_t)0xb0049ab3, + (q31_t)0x62f201ac, (q31_t)0xaecc336c, (q31_t)0x61f1003f, (q31_t)0xad96ed92, (q31_t)0x60ec3830, (q31_t)0xac64d510, (q31_t)0x5fe3b38d, (q31_t)0xab35f5b5, + (q31_t)0x5ed77c8a, (q31_t)0xaa0a5b2e, (q31_t)0x5dc79d7c, (q31_t)0xa8e21106, (q31_t)0x5cb420e0, (q31_t)0xa7bd22ac, (q31_t)0x5b9d1154, (q31_t)0xa69b9b68, + (q31_t)0x5a82799a, (q31_t)0xa57d8666, (q31_t)0x59646498, (q31_t)0xa462eeac, (q31_t)0x5842dd54, (q31_t)0xa34bdf20, (q31_t)0x571deefa, (q31_t)0xa2386284, + (q31_t)0x55f5a4d2, (q31_t)0xa1288376, (q31_t)0x54ca0a4b, (q31_t)0xa01c4c73, (q31_t)0x539b2af0, (q31_t)0x9f13c7d0, (q31_t)0x5269126e, (q31_t)0x9e0effc1, + (q31_t)0x5133cc94, (q31_t)0x9d0dfe54, (q31_t)0x4ffb654d, (q31_t)0x9c10cd70, (q31_t)0x4ebfe8a5, (q31_t)0x9b1776da, (q31_t)0x4d8162c4, (q31_t)0x9a22042d, + (q31_t)0x4c3fdff4, (q31_t)0x99307ee0, (q31_t)0x4afb6c98, (q31_t)0x9842f043, (q31_t)0x49b41533, (q31_t)0x9759617f, (q31_t)0x4869e665, (q31_t)0x9673db94, + (q31_t)0x471cece7, (q31_t)0x9592675c, (q31_t)0x45cd358f, (q31_t)0x94b50d87, (q31_t)0x447acd50, (q31_t)0x93dbd6a0, (q31_t)0x4325c135, (q31_t)0x9306cb04, + (q31_t)0x41ce1e65, (q31_t)0x9235f2ec, (q31_t)0x4073f21d, (q31_t)0x91695663, (q31_t)0x3f1749b8, (q31_t)0x90a0fd4e, (q31_t)0x3db832a6, (q31_t)0x8fdcef66, + (q31_t)0x3c56ba70, (q31_t)0x8f1d343a, (q31_t)0x3af2eeb7, (q31_t)0x8e61d32e, (q31_t)0x398cdd32, (q31_t)0x8daad37b, (q31_t)0x382493b0, (q31_t)0x8cf83c30, + (q31_t)0x36ba2014, (q31_t)0x8c4a142f, (q31_t)0x354d9057, (q31_t)0x8ba0622f, (q31_t)0x33def287, (q31_t)0x8afb2cbb, (q31_t)0x326e54c7, (q31_t)0x8a5a7a31, + (q31_t)0x30fbc54d, (q31_t)0x89be50c3, (q31_t)0x2f875262, (q31_t)0x8926b677, (q31_t)0x2e110a62, (q31_t)0x8893b125, (q31_t)0x2c98fbba, (q31_t)0x88054677, + (q31_t)0x2b1f34eb, (q31_t)0x877b7bec, (q31_t)0x29a3c485, (q31_t)0x86f656d3, (q31_t)0x2826b928, (q31_t)0x8675dc4f, (q31_t)0x26a82186, (q31_t)0x85fa1153, + (q31_t)0x25280c5e, (q31_t)0x8582faa5, (q31_t)0x23a6887f, (q31_t)0x85109cdd, (q31_t)0x2223a4c5, (q31_t)0x84a2fc62, (q31_t)0x209f701c, (q31_t)0x843a1d70, + (q31_t)0x1f19f97b, (q31_t)0x83d60412, (q31_t)0x1d934fe5, (q31_t)0x8376b422, (q31_t)0x1c0b826a, (q31_t)0x831c314e, (q31_t)0x1a82a026, (q31_t)0x82c67f14, + (q31_t)0x18f8b83c, (q31_t)0x8275a0c0, (q31_t)0x176dd9de, (q31_t)0x82299971, (q31_t)0x15e21445, (q31_t)0x81e26c16, (q31_t)0x145576b1, (q31_t)0x81a01b6d, + (q31_t)0x12c8106f, (q31_t)0x8162aa04, (q31_t)0x1139f0cf, (q31_t)0x812a1a3a, (q31_t)0xfab272b, (q31_t)0x80f66e3c, (q31_t)0xe1bc2e4, (q31_t)0x80c7a80a, + (q31_t)0xc8bd35e, (q31_t)0x809dc971, (q31_t)0xafb6805, (q31_t)0x8078d40d, (q31_t)0x96a9049, (q31_t)0x8058c94c, (q31_t)0x7d95b9e, (q31_t)0x803daa6a, + (q31_t)0x647d97c, (q31_t)0x80277872, (q31_t)0x4b6195d, (q31_t)0x80163440, (q31_t)0x3242abf, (q31_t)0x8009de7e, (q31_t)0x1921d20, (q31_t)0x800277a6 +}; + +static const q31_t WeightsQ31_512[1024] = { + (q31_t)0x7fffffff, (q31_t)0x00000000, (q31_t)0x7fffd886, (q31_t)0xff9b781d, (q31_t)0x7fff6216, (q31_t)0xff36f078, (q31_t)0x7ffe9cb2, (q31_t)0xfed2694f, + (q31_t)0x7ffd885a, (q31_t)0xfe6de2e0, (q31_t)0x7ffc250f, (q31_t)0xfe095d69, (q31_t)0x7ffa72d1, (q31_t)0xfda4d929, (q31_t)0x7ff871a2, (q31_t)0xfd40565c, + (q31_t)0x7ff62182, (q31_t)0xfcdbd541, (q31_t)0x7ff38274, (q31_t)0xfc775616, (q31_t)0x7ff09478, (q31_t)0xfc12d91a, (q31_t)0x7fed5791, (q31_t)0xfbae5e89, + (q31_t)0x7fe9cbc0, (q31_t)0xfb49e6a3, (q31_t)0x7fe5f108, (q31_t)0xfae571a4, (q31_t)0x7fe1c76b, (q31_t)0xfa80ffcb, (q31_t)0x7fdd4eec, (q31_t)0xfa1c9157, + (q31_t)0x7fd8878e, (q31_t)0xf9b82684, (q31_t)0x7fd37153, (q31_t)0xf953bf91, (q31_t)0x7fce0c3e, (q31_t)0xf8ef5cbb, (q31_t)0x7fc85854, (q31_t)0xf88afe42, + (q31_t)0x7fc25596, (q31_t)0xf826a462, (q31_t)0x7fbc040a, (q31_t)0xf7c24f59, (q31_t)0x7fb563b3, (q31_t)0xf75dff66, (q31_t)0x7fae7495, (q31_t)0xf6f9b4c6, + (q31_t)0x7fa736b4, (q31_t)0xf6956fb7, (q31_t)0x7f9faa15, (q31_t)0xf6313077, (q31_t)0x7f97cebd, (q31_t)0xf5ccf743, (q31_t)0x7f8fa4b0, (q31_t)0xf568c45b, + (q31_t)0x7f872bf3, (q31_t)0xf50497fb, (q31_t)0x7f7e648c, (q31_t)0xf4a07261, (q31_t)0x7f754e80, (q31_t)0xf43c53cb, (q31_t)0x7f6be9d4, (q31_t)0xf3d83c77, + (q31_t)0x7f62368f, (q31_t)0xf3742ca2, (q31_t)0x7f5834b7, (q31_t)0xf310248a, (q31_t)0x7f4de451, (q31_t)0xf2ac246e, (q31_t)0x7f434563, (q31_t)0xf2482c8a, + (q31_t)0x7f3857f6, (q31_t)0xf1e43d1c, (q31_t)0x7f2d1c0e, (q31_t)0xf1805662, (q31_t)0x7f2191b4, (q31_t)0xf11c789a, (q31_t)0x7f15b8ee, (q31_t)0xf0b8a401, + (q31_t)0x7f0991c4, (q31_t)0xf054d8d5, (q31_t)0x7efd1c3c, (q31_t)0xeff11753, (q31_t)0x7ef05860, (q31_t)0xef8d5fb8, (q31_t)0x7ee34636, (q31_t)0xef29b243, + (q31_t)0x7ed5e5c6, (q31_t)0xeec60f31, (q31_t)0x7ec8371a, (q31_t)0xee6276bf, (q31_t)0x7eba3a39, (q31_t)0xedfee92b, (q31_t)0x7eabef2c, (q31_t)0xed9b66b2, + (q31_t)0x7e9d55fc, (q31_t)0xed37ef91, (q31_t)0x7e8e6eb2, (q31_t)0xecd48407, (q31_t)0x7e7f3957, (q31_t)0xec71244f, (q31_t)0x7e6fb5f4, (q31_t)0xec0dd0a8, + (q31_t)0x7e5fe493, (q31_t)0xebaa894f, (q31_t)0x7e4fc53e, (q31_t)0xeb474e81, (q31_t)0x7e3f57ff, (q31_t)0xeae4207a, (q31_t)0x7e2e9cdf, (q31_t)0xea80ff7a, + (q31_t)0x7e1d93ea, (q31_t)0xea1debbb, (q31_t)0x7e0c3d29, (q31_t)0xe9bae57d, (q31_t)0x7dfa98a8, (q31_t)0xe957ecfb, (q31_t)0x7de8a670, (q31_t)0xe8f50273, + (q31_t)0x7dd6668f, (q31_t)0xe8922622, (q31_t)0x7dc3d90d, (q31_t)0xe82f5844, (q31_t)0x7db0fdf8, (q31_t)0xe7cc9917, (q31_t)0x7d9dd55a, (q31_t)0xe769e8d8, + (q31_t)0x7d8a5f40, (q31_t)0xe70747c4, (q31_t)0x7d769bb5, (q31_t)0xe6a4b616, (q31_t)0x7d628ac6, (q31_t)0xe642340d, (q31_t)0x7d4e2c7f, (q31_t)0xe5dfc1e5, + (q31_t)0x7d3980ec, (q31_t)0xe57d5fda, (q31_t)0x7d24881b, (q31_t)0xe51b0e2a, (q31_t)0x7d0f4218, (q31_t)0xe4b8cd11, (q31_t)0x7cf9aef0, (q31_t)0xe4569ccb, + (q31_t)0x7ce3ceb2, (q31_t)0xe3f47d96, (q31_t)0x7ccda169, (q31_t)0xe3926fad, (q31_t)0x7cb72724, (q31_t)0xe330734d, (q31_t)0x7ca05ff1, (q31_t)0xe2ce88b3, + (q31_t)0x7c894bde, (q31_t)0xe26cb01b, (q31_t)0x7c71eaf9, (q31_t)0xe20ae9c1, (q31_t)0x7c5a3d50, (q31_t)0xe1a935e2, (q31_t)0x7c4242f2, (q31_t)0xe14794ba, + (q31_t)0x7c29fbee, (q31_t)0xe0e60685, (q31_t)0x7c116853, (q31_t)0xe0848b7f, (q31_t)0x7bf88830, (q31_t)0xe02323e5, (q31_t)0x7bdf5b94, (q31_t)0xdfc1cff3, + (q31_t)0x7bc5e290, (q31_t)0xdf608fe4, (q31_t)0x7bac1d31, (q31_t)0xdeff63f4, (q31_t)0x7b920b89, (q31_t)0xde9e4c60, (q31_t)0x7b77ada8, (q31_t)0xde3d4964, + (q31_t)0x7b5d039e, (q31_t)0xdddc5b3b, (q31_t)0x7b420d7a, (q31_t)0xdd7b8220, (q31_t)0x7b26cb4f, (q31_t)0xdd1abe51, (q31_t)0x7b0b3d2c, (q31_t)0xdcba1008, + (q31_t)0x7aef6323, (q31_t)0xdc597781, (q31_t)0x7ad33d45, (q31_t)0xdbf8f4f8, (q31_t)0x7ab6cba4, (q31_t)0xdb9888a8, (q31_t)0x7a9a0e50, (q31_t)0xdb3832cd, + (q31_t)0x7a7d055b, (q31_t)0xdad7f3a2, (q31_t)0x7a5fb0d8, (q31_t)0xda77cb63, (q31_t)0x7a4210d8, (q31_t)0xda17ba4a, (q31_t)0x7a24256f, (q31_t)0xd9b7c094, + (q31_t)0x7a05eead, (q31_t)0xd957de7a, (q31_t)0x79e76ca7, (q31_t)0xd8f81439, (q31_t)0x79c89f6e, (q31_t)0xd898620c, (q31_t)0x79a98715, (q31_t)0xd838c82d, + (q31_t)0x798a23b1, (q31_t)0xd7d946d8, (q31_t)0x796a7554, (q31_t)0xd779de47, (q31_t)0x794a7c12, (q31_t)0xd71a8eb5, (q31_t)0x792a37fe, (q31_t)0xd6bb585e, + (q31_t)0x7909a92d, (q31_t)0xd65c3b7b, (q31_t)0x78e8cfb2, (q31_t)0xd5fd3848, (q31_t)0x78c7aba2, (q31_t)0xd59e4eff, (q31_t)0x78a63d11, (q31_t)0xd53f7fda, + (q31_t)0x78848414, (q31_t)0xd4e0cb15, (q31_t)0x786280bf, (q31_t)0xd48230e9, (q31_t)0x78403329, (q31_t)0xd423b191, (q31_t)0x781d9b65, (q31_t)0xd3c54d47, + (q31_t)0x77fab989, (q31_t)0xd3670446, (q31_t)0x77d78daa, (q31_t)0xd308d6c7, (q31_t)0x77b417df, (q31_t)0xd2aac504, (q31_t)0x7790583e, (q31_t)0xd24ccf39, + (q31_t)0x776c4edb, (q31_t)0xd1eef59e, (q31_t)0x7747fbce, (q31_t)0xd191386e, (q31_t)0x77235f2d, (q31_t)0xd13397e2, (q31_t)0x76fe790e, (q31_t)0xd0d61434, + (q31_t)0x76d94989, (q31_t)0xd078ad9e, (q31_t)0x76b3d0b4, (q31_t)0xd01b6459, (q31_t)0x768e0ea6, (q31_t)0xcfbe389f, (q31_t)0x76680376, (q31_t)0xcf612aaa, + (q31_t)0x7641af3d, (q31_t)0xcf043ab3, (q31_t)0x761b1211, (q31_t)0xcea768f2, (q31_t)0x75f42c0b, (q31_t)0xce4ab5a2, (q31_t)0x75ccfd42, (q31_t)0xcdee20fc, + (q31_t)0x75a585cf, (q31_t)0xcd91ab39, (q31_t)0x757dc5ca, (q31_t)0xcd355491, (q31_t)0x7555bd4c, (q31_t)0xccd91d3d, (q31_t)0x752d6c6c, (q31_t)0xcc7d0578, + (q31_t)0x7504d345, (q31_t)0xcc210d79, (q31_t)0x74dbf1ef, (q31_t)0xcbc53579, (q31_t)0x74b2c884, (q31_t)0xcb697db0, (q31_t)0x7489571c, (q31_t)0xcb0de658, + (q31_t)0x745f9dd1, (q31_t)0xcab26fa9, (q31_t)0x74359cbd, (q31_t)0xca5719db, (q31_t)0x740b53fb, (q31_t)0xc9fbe527, (q31_t)0x73e0c3a3, (q31_t)0xc9a0d1c5, + (q31_t)0x73b5ebd1, (q31_t)0xc945dfec, (q31_t)0x738acc9e, (q31_t)0xc8eb0fd6, (q31_t)0x735f6626, (q31_t)0xc89061ba, (q31_t)0x7333b883, (q31_t)0xc835d5d0, + (q31_t)0x7307c3d0, (q31_t)0xc7db6c50, (q31_t)0x72db8828, (q31_t)0xc7812572, (q31_t)0x72af05a7, (q31_t)0xc727016d, (q31_t)0x72823c67, (q31_t)0xc6cd0079, + (q31_t)0x72552c85, (q31_t)0xc67322ce, (q31_t)0x7227d61c, (q31_t)0xc61968a2, (q31_t)0x71fa3949, (q31_t)0xc5bfd22e, (q31_t)0x71cc5626, (q31_t)0xc5665fa9, + (q31_t)0x719e2cd2, (q31_t)0xc50d1149, (q31_t)0x716fbd68, (q31_t)0xc4b3e746, (q31_t)0x71410805, (q31_t)0xc45ae1d7, (q31_t)0x71120cc5, (q31_t)0xc4020133, + (q31_t)0x70e2cbc6, (q31_t)0xc3a94590, (q31_t)0x70b34525, (q31_t)0xc350af26, (q31_t)0x708378ff, (q31_t)0xc2f83e2a, (q31_t)0x70536771, (q31_t)0xc29ff2d4, + (q31_t)0x7023109a, (q31_t)0xc247cd5a, (q31_t)0x6ff27497, (q31_t)0xc1efcdf3, (q31_t)0x6fc19385, (q31_t)0xc197f4d4, (q31_t)0x6f906d84, (q31_t)0xc1404233, + (q31_t)0x6f5f02b2, (q31_t)0xc0e8b648, (q31_t)0x6f2d532c, (q31_t)0xc0915148, (q31_t)0x6efb5f12, (q31_t)0xc03a1368, (q31_t)0x6ec92683, (q31_t)0xbfe2fcdf, + (q31_t)0x6e96a99d, (q31_t)0xbf8c0de3, (q31_t)0x6e63e87f, (q31_t)0xbf3546a8, (q31_t)0x6e30e34a, (q31_t)0xbedea765, (q31_t)0x6dfd9a1c, (q31_t)0xbe88304f, + (q31_t)0x6dca0d14, (q31_t)0xbe31e19b, (q31_t)0x6d963c54, (q31_t)0xbddbbb7f, (q31_t)0x6d6227fa, (q31_t)0xbd85be30, (q31_t)0x6d2dd027, (q31_t)0xbd2fe9e2, + (q31_t)0x6cf934fc, (q31_t)0xbcda3ecb, (q31_t)0x6cc45698, (q31_t)0xbc84bd1f, (q31_t)0x6c8f351c, (q31_t)0xbc2f6513, (q31_t)0x6c59d0a9, (q31_t)0xbbda36dd, + (q31_t)0x6c242960, (q31_t)0xbb8532b0, (q31_t)0x6bee3f62, (q31_t)0xbb3058c0, (q31_t)0x6bb812d1, (q31_t)0xbadba943, (q31_t)0x6b81a3cd, (q31_t)0xba87246d, + (q31_t)0x6b4af279, (q31_t)0xba32ca71, (q31_t)0x6b13fef5, (q31_t)0xb9de9b83, (q31_t)0x6adcc964, (q31_t)0xb98a97d8, (q31_t)0x6aa551e9, (q31_t)0xb936bfa4, + (q31_t)0x6a6d98a4, (q31_t)0xb8e31319, (q31_t)0x6a359db9, (q31_t)0xb88f926d, (q31_t)0x69fd614a, (q31_t)0xb83c3dd1, (q31_t)0x69c4e37a, (q31_t)0xb7e9157a, + (q31_t)0x698c246c, (q31_t)0xb796199b, (q31_t)0x69532442, (q31_t)0xb7434a67, (q31_t)0x6919e320, (q31_t)0xb6f0a812, (q31_t)0x68e06129, (q31_t)0xb69e32cd, + (q31_t)0x68a69e81, (q31_t)0xb64beacd, (q31_t)0x686c9b4b, (q31_t)0xb5f9d043, (q31_t)0x683257ab, (q31_t)0xb5a7e362, (q31_t)0x67f7d3c5, (q31_t)0xb556245e, + (q31_t)0x67bd0fbd, (q31_t)0xb5049368, (q31_t)0x67820bb7, (q31_t)0xb4b330b3, (q31_t)0x6746c7d8, (q31_t)0xb461fc70, (q31_t)0x670b4444, (q31_t)0xb410f6d3, + (q31_t)0x66cf8120, (q31_t)0xb3c0200c, (q31_t)0x66937e91, (q31_t)0xb36f784f, (q31_t)0x66573cbb, (q31_t)0xb31effcc, (q31_t)0x661abbc5, (q31_t)0xb2ceb6b5, + (q31_t)0x65ddfbd3, (q31_t)0xb27e9d3c, (q31_t)0x65a0fd0b, (q31_t)0xb22eb392, (q31_t)0x6563bf92, (q31_t)0xb1def9e9, (q31_t)0x6526438f, (q31_t)0xb18f7071, + (q31_t)0x64e88926, (q31_t)0xb140175b, (q31_t)0x64aa907f, (q31_t)0xb0f0eeda, (q31_t)0x646c59bf, (q31_t)0xb0a1f71d, (q31_t)0x642de50d, (q31_t)0xb0533055, + (q31_t)0x63ef3290, (q31_t)0xb0049ab3, (q31_t)0x63b0426d, (q31_t)0xafb63667, (q31_t)0x637114cc, (q31_t)0xaf6803a2, (q31_t)0x6331a9d4, (q31_t)0xaf1a0293, + (q31_t)0x62f201ac, (q31_t)0xaecc336c, (q31_t)0x62b21c7b, (q31_t)0xae7e965b, (q31_t)0x6271fa69, (q31_t)0xae312b92, (q31_t)0x62319b9d, (q31_t)0xade3f33e, + (q31_t)0x61f1003f, (q31_t)0xad96ed92, (q31_t)0x61b02876, (q31_t)0xad4a1aba, (q31_t)0x616f146c, (q31_t)0xacfd7ae8, (q31_t)0x612dc447, (q31_t)0xacb10e4b, + (q31_t)0x60ec3830, (q31_t)0xac64d510, (q31_t)0x60aa7050, (q31_t)0xac18cf69, (q31_t)0x60686ccf, (q31_t)0xabccfd83, (q31_t)0x60262dd6, (q31_t)0xab815f8d, + (q31_t)0x5fe3b38d, (q31_t)0xab35f5b5, (q31_t)0x5fa0fe1f, (q31_t)0xaaeac02c, (q31_t)0x5f5e0db3, (q31_t)0xaa9fbf1e, (q31_t)0x5f1ae274, (q31_t)0xaa54f2ba, + (q31_t)0x5ed77c8a, (q31_t)0xaa0a5b2e, (q31_t)0x5e93dc1f, (q31_t)0xa9bff8a8, (q31_t)0x5e50015d, (q31_t)0xa975cb57, (q31_t)0x5e0bec6e, (q31_t)0xa92bd367, + (q31_t)0x5dc79d7c, (q31_t)0xa8e21106, 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(q31_t)0x84885258, (q31_t)0x2161b3a0, (q31_t)0x846df477, (q31_t)0x21009c0c, (q31_t)0x8453e2cf, + (q31_t)0x209f701c, (q31_t)0x843a1d70, (q31_t)0x203e300d, (q31_t)0x8420a46c, (q31_t)0x1fdcdc1b, (q31_t)0x840777d0, (q31_t)0x1f7b7481, (q31_t)0x83ee97ad, + (q31_t)0x1f19f97b, (q31_t)0x83d60412, (q31_t)0x1eb86b46, (q31_t)0x83bdbd0e, (q31_t)0x1e56ca1e, (q31_t)0x83a5c2b0, (q31_t)0x1df5163f, (q31_t)0x838e1507, + (q31_t)0x1d934fe5, (q31_t)0x8376b422, (q31_t)0x1d31774d, (q31_t)0x835fa00f, (q31_t)0x1ccf8cb3, (q31_t)0x8348d8dc, (q31_t)0x1c6d9053, (q31_t)0x83325e97, + (q31_t)0x1c0b826a, (q31_t)0x831c314e, (q31_t)0x1ba96335, (q31_t)0x83065110, (q31_t)0x1b4732ef, (q31_t)0x82f0bde8, (q31_t)0x1ae4f1d6, (q31_t)0x82db77e5, + (q31_t)0x1a82a026, (q31_t)0x82c67f14, (q31_t)0x1a203e1b, (q31_t)0x82b1d381, (q31_t)0x19bdcbf3, (q31_t)0x829d753a, (q31_t)0x195b49ea, (q31_t)0x8289644b, + (q31_t)0x18f8b83c, (q31_t)0x8275a0c0, (q31_t)0x18961728, (q31_t)0x82622aa6, (q31_t)0x183366e9, (q31_t)0x824f0208, (q31_t)0x17d0a7bc, (q31_t)0x823c26f3, + (q31_t)0x176dd9de, (q31_t)0x82299971, (q31_t)0x170afd8d, (q31_t)0x82175990, (q31_t)0x16a81305, (q31_t)0x82056758, (q31_t)0x16451a83, (q31_t)0x81f3c2d7, + (q31_t)0x15e21445, (q31_t)0x81e26c16, (q31_t)0x157f0086, (q31_t)0x81d16321, (q31_t)0x151bdf86, (q31_t)0x81c0a801, (q31_t)0x14b8b17f, (q31_t)0x81b03ac2, + (q31_t)0x145576b1, (q31_t)0x81a01b6d, (q31_t)0x13f22f58, (q31_t)0x81904a0c, (q31_t)0x138edbb1, (q31_t)0x8180c6a9, (q31_t)0x132b7bf9, (q31_t)0x8171914e, + (q31_t)0x12c8106f, (q31_t)0x8162aa04, (q31_t)0x1264994e, (q31_t)0x815410d4, (q31_t)0x120116d5, (q31_t)0x8145c5c7, (q31_t)0x119d8941, (q31_t)0x8137c8e6, + (q31_t)0x1139f0cf, (q31_t)0x812a1a3a, (q31_t)0x10d64dbd, (q31_t)0x811cb9ca, (q31_t)0x1072a048, (q31_t)0x810fa7a0, (q31_t)0x100ee8ad, (q31_t)0x8102e3c4, + (q31_t)0xfab272b, (q31_t)0x80f66e3c, (q31_t)0xf475bff, (q31_t)0x80ea4712, (q31_t)0xee38766, (q31_t)0x80de6e4c, (q31_t)0xe7fa99e, (q31_t)0x80d2e3f2, + (q31_t)0xe1bc2e4, (q31_t)0x80c7a80a, (q31_t)0xdb7d376, (q31_t)0x80bcba9d, (q31_t)0xd53db92, (q31_t)0x80b21baf, (q31_t)0xcefdb76, (q31_t)0x80a7cb49, + (q31_t)0xc8bd35e, (q31_t)0x809dc971, (q31_t)0xc27c389, (q31_t)0x8094162c, (q31_t)0xbc3ac35, (q31_t)0x808ab180, (q31_t)0xb5f8d9f, (q31_t)0x80819b74, + (q31_t)0xafb6805, (q31_t)0x8078d40d, (q31_t)0xa973ba5, (q31_t)0x80705b50, (q31_t)0xa3308bd, (q31_t)0x80683143, (q31_t)0x9cecf89, (q31_t)0x806055eb, + (q31_t)0x96a9049, (q31_t)0x8058c94c, (q31_t)0x9064b3a, (q31_t)0x80518b6b, (q31_t)0x8a2009a, (q31_t)0x804a9c4d, (q31_t)0x83db0a7, (q31_t)0x8043fbf6, + (q31_t)0x7d95b9e, (q31_t)0x803daa6a, (q31_t)0x77501be, (q31_t)0x8037a7ac, (q31_t)0x710a345, (q31_t)0x8031f3c2, (q31_t)0x6ac406f, (q31_t)0x802c8ead, + (q31_t)0x647d97c, (q31_t)0x80277872, (q31_t)0x5e36ea9, (q31_t)0x8022b114, (q31_t)0x57f0035, (q31_t)0x801e3895, (q31_t)0x51a8e5c, (q31_t)0x801a0ef8, + (q31_t)0x4b6195d, (q31_t)0x80163440, (q31_t)0x451a177, (q31_t)0x8012a86f, (q31_t)0x3ed26e6, (q31_t)0x800f6b88, (q31_t)0x388a9ea, (q31_t)0x800c7d8c, + (q31_t)0x3242abf, (q31_t)0x8009de7e, (q31_t)0x2bfa9a4, (q31_t)0x80078e5e, (q31_t)0x25b26d7, (q31_t)0x80058d2f, (q31_t)0x1f6a297, (q31_t)0x8003daf1, + (q31_t)0x1921d20, (q31_t)0x800277a6, (q31_t)0x12d96b1, (q31_t)0x8001634e, (q31_t)0xc90f88, (q31_t)0x80009dea, (q31_t)0x6487e3, (q31_t)0x8000277a +}; + +static const q31_t WeightsQ31_2048[4096] = { + (q31_t)0x7fffffff, (q31_t)0x00000000, (q31_t)0x7ffffd88, (q31_t)0xffe6de05, (q31_t)0x7ffff621, (q31_t)0xffcdbc0b, (q31_t)0x7fffe9cb, (q31_t)0xffb49a12, + (q31_t)0x7fffd886, (q31_t)0xff9b781d, (q31_t)0x7fffc251, (q31_t)0xff82562c, (q31_t)0x7fffa72c, (q31_t)0xff69343f, (q31_t)0x7fff8719, (q31_t)0xff501258, + (q31_t)0x7fff6216, (q31_t)0xff36f078, (q31_t)0x7fff3824, (q31_t)0xff1dcea0, (q31_t)0x7fff0943, (q31_t)0xff04acd0, (q31_t)0x7ffed572, (q31_t)0xfeeb8b0a, + (q31_t)0x7ffe9cb2, (q31_t)0xfed2694f, (q31_t)0x7ffe5f03, (q31_t)0xfeb947a0, (q31_t)0x7ffe1c65, (q31_t)0xfea025fd, (q31_t)0x7ffdd4d7, (q31_t)0xfe870467, + (q31_t)0x7ffd885a, (q31_t)0xfe6de2e0, (q31_t)0x7ffd36ee, (q31_t)0xfe54c169, (q31_t)0x7ffce093, (q31_t)0xfe3ba002, (q31_t)0x7ffc8549, (q31_t)0xfe227eac, + (q31_t)0x7ffc250f, (q31_t)0xfe095d69, (q31_t)0x7ffbbfe6, (q31_t)0xfdf03c3a, (q31_t)0x7ffb55ce, (q31_t)0xfdd71b1e, (q31_t)0x7ffae6c7, (q31_t)0xfdbdfa18, + (q31_t)0x7ffa72d1, (q31_t)0xfda4d929, (q31_t)0x7ff9f9ec, (q31_t)0xfd8bb850, (q31_t)0x7ff97c18, (q31_t)0xfd729790, (q31_t)0x7ff8f954, (q31_t)0xfd5976e9, + (q31_t)0x7ff871a2, (q31_t)0xfd40565c, (q31_t)0x7ff7e500, (q31_t)0xfd2735ea, (q31_t)0x7ff75370, (q31_t)0xfd0e1594, (q31_t)0x7ff6bcf0, (q31_t)0xfcf4f55c, + (q31_t)0x7ff62182, (q31_t)0xfcdbd541, (q31_t)0x7ff58125, (q31_t)0xfcc2b545, (q31_t)0x7ff4dbd9, (q31_t)0xfca9956a, (q31_t)0x7ff4319d, (q31_t)0xfc9075af, + (q31_t)0x7ff38274, (q31_t)0xfc775616, (q31_t)0x7ff2ce5b, (q31_t)0xfc5e36a0, (q31_t)0x7ff21553, (q31_t)0xfc45174e, (q31_t)0x7ff1575d, (q31_t)0xfc2bf821, + (q31_t)0x7ff09478, (q31_t)0xfc12d91a, (q31_t)0x7fefcca4, (q31_t)0xfbf9ba39, (q31_t)0x7feeffe1, (q31_t)0xfbe09b80, (q31_t)0x7fee2e30, (q31_t)0xfbc77cf0, + (q31_t)0x7fed5791, (q31_t)0xfbae5e89, (q31_t)0x7fec7c02, (q31_t)0xfb95404d, (q31_t)0x7feb9b85, (q31_t)0xfb7c223d, (q31_t)0x7feab61a, (q31_t)0xfb630459, + (q31_t)0x7fe9cbc0, (q31_t)0xfb49e6a3, (q31_t)0x7fe8dc78, (q31_t)0xfb30c91b, (q31_t)0x7fe7e841, (q31_t)0xfb17abc2, (q31_t)0x7fe6ef1c, (q31_t)0xfafe8e9b, + (q31_t)0x7fe5f108, (q31_t)0xfae571a4, (q31_t)0x7fe4ee06, (q31_t)0xfacc54e0, (q31_t)0x7fe3e616, (q31_t)0xfab3384f, (q31_t)0x7fe2d938, (q31_t)0xfa9a1bf3, + (q31_t)0x7fe1c76b, (q31_t)0xfa80ffcb, (q31_t)0x7fe0b0b1, (q31_t)0xfa67e3da, (q31_t)0x7fdf9508, (q31_t)0xfa4ec821, (q31_t)0x7fde7471, (q31_t)0xfa35ac9f, + (q31_t)0x7fdd4eec, (q31_t)0xfa1c9157, (q31_t)0x7fdc247a, (q31_t)0xfa037648, (q31_t)0x7fdaf519, (q31_t)0xf9ea5b75, (q31_t)0x7fd9c0ca, (q31_t)0xf9d140de, + (q31_t)0x7fd8878e, (q31_t)0xf9b82684, (q31_t)0x7fd74964, (q31_t)0xf99f0c68, (q31_t)0x7fd6064c, (q31_t)0xf985f28a, (q31_t)0x7fd4be46, (q31_t)0xf96cd8ed, + (q31_t)0x7fd37153, (q31_t)0xf953bf91, (q31_t)0x7fd21f72, (q31_t)0xf93aa676, (q31_t)0x7fd0c8a3, (q31_t)0xf9218d9e, (q31_t)0x7fcf6ce8, (q31_t)0xf908750a, + (q31_t)0x7fce0c3e, (q31_t)0xf8ef5cbb, (q31_t)0x7fcca6a7, (q31_t)0xf8d644b2, (q31_t)0x7fcb3c23, (q31_t)0xf8bd2cef, (q31_t)0x7fc9ccb2, (q31_t)0xf8a41574, + (q31_t)0x7fc85854, (q31_t)0xf88afe42, (q31_t)0x7fc6df08, (q31_t)0xf871e759, (q31_t)0x7fc560cf, (q31_t)0xf858d0bb, (q31_t)0x7fc3dda9, (q31_t)0xf83fba68, + (q31_t)0x7fc25596, (q31_t)0xf826a462, (q31_t)0x7fc0c896, (q31_t)0xf80d8ea9, (q31_t)0x7fbf36aa, (q31_t)0xf7f4793e, (q31_t)0x7fbd9fd0, (q31_t)0xf7db6423, + (q31_t)0x7fbc040a, (q31_t)0xf7c24f59, (q31_t)0x7fba6357, (q31_t)0xf7a93ae0, (q31_t)0x7fb8bdb8, (q31_t)0xf79026b9, (q31_t)0x7fb7132b, (q31_t)0xf77712e5, + (q31_t)0x7fb563b3, (q31_t)0xf75dff66, (q31_t)0x7fb3af4e, (q31_t)0xf744ec3b, (q31_t)0x7fb1f5fc, (q31_t)0xf72bd967, (q31_t)0x7fb037bf, (q31_t)0xf712c6ea, + (q31_t)0x7fae7495, (q31_t)0xf6f9b4c6, (q31_t)0x7facac7f, (q31_t)0xf6e0a2fa, (q31_t)0x7faadf7c, (q31_t)0xf6c79188, (q31_t)0x7fa90d8e, (q31_t)0xf6ae8071, + (q31_t)0x7fa736b4, (q31_t)0xf6956fb7, (q31_t)0x7fa55aee, (q31_t)0xf67c5f59, (q31_t)0x7fa37a3c, (q31_t)0xf6634f59, (q31_t)0x7fa1949e, (q31_t)0xf64a3fb8, + (q31_t)0x7f9faa15, (q31_t)0xf6313077, (q31_t)0x7f9dbaa0, (q31_t)0xf6182196, (q31_t)0x7f9bc640, (q31_t)0xf5ff1318, (q31_t)0x7f99ccf4, (q31_t)0xf5e604fc, + (q31_t)0x7f97cebd, (q31_t)0xf5ccf743, (q31_t)0x7f95cb9a, (q31_t)0xf5b3e9f0, (q31_t)0x7f93c38c, (q31_t)0xf59add02, (q31_t)0x7f91b694, (q31_t)0xf581d07b, + (q31_t)0x7f8fa4b0, (q31_t)0xf568c45b, (q31_t)0x7f8d8de1, (q31_t)0xf54fb8a4, (q31_t)0x7f8b7227, (q31_t)0xf536ad56, (q31_t)0x7f895182, (q31_t)0xf51da273, + (q31_t)0x7f872bf3, (q31_t)0xf50497fb, (q31_t)0x7f850179, (q31_t)0xf4eb8def, (q31_t)0x7f82d214, (q31_t)0xf4d28451, (q31_t)0x7f809dc5, (q31_t)0xf4b97b21, + (q31_t)0x7f7e648c, (q31_t)0xf4a07261, (q31_t)0x7f7c2668, (q31_t)0xf4876a10, (q31_t)0x7f79e35a, (q31_t)0xf46e6231, (q31_t)0x7f779b62, (q31_t)0xf4555ac5, + (q31_t)0x7f754e80, (q31_t)0xf43c53cb, (q31_t)0x7f72fcb4, (q31_t)0xf4234d45, (q31_t)0x7f70a5fe, (q31_t)0xf40a4735, (q31_t)0x7f6e4a5e, (q31_t)0xf3f1419a, + (q31_t)0x7f6be9d4, (q31_t)0xf3d83c77, (q31_t)0x7f698461, (q31_t)0xf3bf37cb, (q31_t)0x7f671a05, (q31_t)0xf3a63398, (q31_t)0x7f64aabf, (q31_t)0xf38d2fe0, + (q31_t)0x7f62368f, (q31_t)0xf3742ca2, (q31_t)0x7f5fbd77, (q31_t)0xf35b29e0, (q31_t)0x7f5d3f75, (q31_t)0xf342279b, (q31_t)0x7f5abc8a, (q31_t)0xf32925d3, + (q31_t)0x7f5834b7, (q31_t)0xf310248a, (q31_t)0x7f55a7fa, (q31_t)0xf2f723c1, (q31_t)0x7f531655, (q31_t)0xf2de2379, (q31_t)0x7f507fc7, (q31_t)0xf2c523b2, + (q31_t)0x7f4de451, (q31_t)0xf2ac246e, (q31_t)0x7f4b43f2, (q31_t)0xf29325ad, (q31_t)0x7f489eaa, (q31_t)0xf27a2771, (q31_t)0x7f45f47b, (q31_t)0xf26129ba, + (q31_t)0x7f434563, (q31_t)0xf2482c8a, (q31_t)0x7f409164, (q31_t)0xf22f2fe1, (q31_t)0x7f3dd87c, (q31_t)0xf21633c0, (q31_t)0x7f3b1aad, (q31_t)0xf1fd3829, + (q31_t)0x7f3857f6, (q31_t)0xf1e43d1c, (q31_t)0x7f359057, (q31_t)0xf1cb429a, (q31_t)0x7f32c3d1, (q31_t)0xf1b248a5, (q31_t)0x7f2ff263, (q31_t)0xf1994f3d, + (q31_t)0x7f2d1c0e, (q31_t)0xf1805662, (q31_t)0x7f2a40d2, (q31_t)0xf1675e17, (q31_t)0x7f2760af, (q31_t)0xf14e665c, (q31_t)0x7f247ba5, (q31_t)0xf1356f32, + (q31_t)0x7f2191b4, (q31_t)0xf11c789a, (q31_t)0x7f1ea2dc, (q31_t)0xf1038295, (q31_t)0x7f1baf1e, (q31_t)0xf0ea8d24, (q31_t)0x7f18b679, (q31_t)0xf0d19848, + (q31_t)0x7f15b8ee, (q31_t)0xf0b8a401, (q31_t)0x7f12b67c, (q31_t)0xf09fb051, (q31_t)0x7f0faf25, (q31_t)0xf086bd39, (q31_t)0x7f0ca2e7, (q31_t)0xf06dcaba, + (q31_t)0x7f0991c4, (q31_t)0xf054d8d5, (q31_t)0x7f067bba, (q31_t)0xf03be78a, (q31_t)0x7f0360cb, (q31_t)0xf022f6da, (q31_t)0x7f0040f6, (q31_t)0xf00a06c8, + (q31_t)0x7efd1c3c, (q31_t)0xeff11753, (q31_t)0x7ef9f29d, (q31_t)0xefd8287c, (q31_t)0x7ef6c418, (q31_t)0xefbf3a45, (q31_t)0x7ef390ae, (q31_t)0xefa64cae, + (q31_t)0x7ef05860, (q31_t)0xef8d5fb8, (q31_t)0x7eed1b2c, (q31_t)0xef747365, (q31_t)0x7ee9d914, (q31_t)0xef5b87b5, (q31_t)0x7ee69217, (q31_t)0xef429caa, + (q31_t)0x7ee34636, (q31_t)0xef29b243, (q31_t)0x7edff570, (q31_t)0xef10c883, (q31_t)0x7edc9fc6, (q31_t)0xeef7df6a, (q31_t)0x7ed94538, (q31_t)0xeedef6f9, + (q31_t)0x7ed5e5c6, (q31_t)0xeec60f31, (q31_t)0x7ed28171, (q31_t)0xeead2813, (q31_t)0x7ecf1837, (q31_t)0xee9441a0, (q31_t)0x7ecbaa1a, (q31_t)0xee7b5bd9, + (q31_t)0x7ec8371a, (q31_t)0xee6276bf, (q31_t)0x7ec4bf36, (q31_t)0xee499253, (q31_t)0x7ec14270, (q31_t)0xee30ae96, (q31_t)0x7ebdc0c6, (q31_t)0xee17cb88, + (q31_t)0x7eba3a39, (q31_t)0xedfee92b, (q31_t)0x7eb6aeca, (q31_t)0xede60780, (q31_t)0x7eb31e78, (q31_t)0xedcd2687, (q31_t)0x7eaf8943, (q31_t)0xedb44642, + (q31_t)0x7eabef2c, (q31_t)0xed9b66b2, (q31_t)0x7ea85033, (q31_t)0xed8287d7, (q31_t)0x7ea4ac58, (q31_t)0xed69a9b3, (q31_t)0x7ea1039b, (q31_t)0xed50cc46, + (q31_t)0x7e9d55fc, (q31_t)0xed37ef91, (q31_t)0x7e99a37c, (q31_t)0xed1f1396, (q31_t)0x7e95ec1a, (q31_t)0xed063856, (q31_t)0x7e922fd6, (q31_t)0xeced5dd0, + (q31_t)0x7e8e6eb2, (q31_t)0xecd48407, 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(q31_t)0x82eb652b, (q31_t)0x1b161479, (q31_t)0x82e61141, (q31_t)0x1afd83ad, (q31_t)0x82e0c22a, + (q31_t)0x1ae4f1d6, (q31_t)0x82db77e5, (q31_t)0x1acc5ef6, (q31_t)0x82d63274, (q31_t)0x1ab3cb0d, (q31_t)0x82d0f1d5, (q31_t)0x1a9b361d, (q31_t)0x82cbb60b, + (q31_t)0x1a82a026, (q31_t)0x82c67f14, (q31_t)0x1a6a0929, (q31_t)0x82c14cf1, (q31_t)0x1a517128, (q31_t)0x82bc1fa2, (q31_t)0x1a38d823, (q31_t)0x82b6f727, + (q31_t)0x1a203e1b, (q31_t)0x82b1d381, (q31_t)0x1a07a311, (q31_t)0x82acb4b0, (q31_t)0x19ef0707, (q31_t)0x82a79ab3, (q31_t)0x19d669fc, (q31_t)0x82a2858c, + (q31_t)0x19bdcbf3, (q31_t)0x829d753a, (q31_t)0x19a52ceb, (q31_t)0x829869be, (q31_t)0x198c8ce7, (q31_t)0x82936317, (q31_t)0x1973ebe6, (q31_t)0x828e6146, + (q31_t)0x195b49ea, (q31_t)0x8289644b, (q31_t)0x1942a6f3, (q31_t)0x82846c26, (q31_t)0x192a0304, (q31_t)0x827f78d8, (q31_t)0x19115e1c, (q31_t)0x827a8a61, + (q31_t)0x18f8b83c, (q31_t)0x8275a0c0, (q31_t)0x18e01167, (q31_t)0x8270bbf7, (q31_t)0x18c7699b, (q31_t)0x826bdc04, (q31_t)0x18aec0db, (q31_t)0x826700e9, + (q31_t)0x18961728, (q31_t)0x82622aa6, (q31_t)0x187d6c82, (q31_t)0x825d593a, (q31_t)0x1864c0ea, (q31_t)0x82588ca7, (q31_t)0x184c1461, (q31_t)0x8253c4eb, + (q31_t)0x183366e9, (q31_t)0x824f0208, (q31_t)0x181ab881, (q31_t)0x824a43fe, (q31_t)0x1802092c, (q31_t)0x82458acc, (q31_t)0x17e958ea, (q31_t)0x8240d673, + (q31_t)0x17d0a7bc, (q31_t)0x823c26f3, (q31_t)0x17b7f5a3, (q31_t)0x82377c4c, (q31_t)0x179f429f, (q31_t)0x8232d67f, (q31_t)0x17868eb3, (q31_t)0x822e358b, + (q31_t)0x176dd9de, (q31_t)0x82299971, (q31_t)0x17552422, (q31_t)0x82250232, (q31_t)0x173c6d80, (q31_t)0x82206fcc, (q31_t)0x1723b5f9, (q31_t)0x821be240, + (q31_t)0x170afd8d, (q31_t)0x82175990, (q31_t)0x16f2443e, (q31_t)0x8212d5b9, (q31_t)0x16d98a0c, (q31_t)0x820e56be, (q31_t)0x16c0cef9, (q31_t)0x8209dc9e, + (q31_t)0x16a81305, (q31_t)0x82056758, (q31_t)0x168f5632, (q31_t)0x8200f6ef, (q31_t)0x1676987f, (q31_t)0x81fc8b60, (q31_t)0x165dd9f0, (q31_t)0x81f824ae, + (q31_t)0x16451a83, (q31_t)0x81f3c2d7, (q31_t)0x162c5a3b, (q31_t)0x81ef65dc, (q31_t)0x16139918, (q31_t)0x81eb0dbe, (q31_t)0x15fad71b, (q31_t)0x81e6ba7c, + (q31_t)0x15e21445, (q31_t)0x81e26c16, (q31_t)0x15c95097, (q31_t)0x81de228d, (q31_t)0x15b08c12, (q31_t)0x81d9dde1, (q31_t)0x1597c6b7, (q31_t)0x81d59e13, + (q31_t)0x157f0086, (q31_t)0x81d16321, (q31_t)0x15663982, (q31_t)0x81cd2d0c, (q31_t)0x154d71aa, (q31_t)0x81c8fbd6, (q31_t)0x1534a901, (q31_t)0x81c4cf7d, + (q31_t)0x151bdf86, (q31_t)0x81c0a801, (q31_t)0x1503153a, (q31_t)0x81bc8564, (q31_t)0x14ea4a1f, (q31_t)0x81b867a5, (q31_t)0x14d17e36, (q31_t)0x81b44ec4, + (q31_t)0x14b8b17f, (q31_t)0x81b03ac2, (q31_t)0x149fe3fc, (q31_t)0x81ac2b9e, (q31_t)0x148715ae, (q31_t)0x81a82159, (q31_t)0x146e4694, (q31_t)0x81a41bf4, + (q31_t)0x145576b1, (q31_t)0x81a01b6d, (q31_t)0x143ca605, (q31_t)0x819c1fc5, (q31_t)0x1423d492, (q31_t)0x819828fd, (q31_t)0x140b0258, (q31_t)0x81943715, + (q31_t)0x13f22f58, (q31_t)0x81904a0c, (q31_t)0x13d95b93, (q31_t)0x818c61e3, (q31_t)0x13c0870a, (q31_t)0x81887e9a, (q31_t)0x13a7b1bf, (q31_t)0x8184a032, + (q31_t)0x138edbb1, (q31_t)0x8180c6a9, (q31_t)0x137604e2, (q31_t)0x817cf201, (q31_t)0x135d2d53, (q31_t)0x8179223a, (q31_t)0x13445505, (q31_t)0x81755754, + (q31_t)0x132b7bf9, (q31_t)0x8171914e, (q31_t)0x1312a230, (q31_t)0x816dd02a, (q31_t)0x12f9c7aa, (q31_t)0x816a13e6, (q31_t)0x12e0ec6a, (q31_t)0x81665c84, + (q31_t)0x12c8106f, (q31_t)0x8162aa04, (q31_t)0x12af33ba, (q31_t)0x815efc65, (q31_t)0x1296564d, (q31_t)0x815b53a8, (q31_t)0x127d7829, (q31_t)0x8157afcd, + (q31_t)0x1264994e, (q31_t)0x815410d4, (q31_t)0x124bb9be, (q31_t)0x815076bd, (q31_t)0x1232d979, (q31_t)0x814ce188, (q31_t)0x1219f880, (q31_t)0x81495136, + (q31_t)0x120116d5, (q31_t)0x8145c5c7, (q31_t)0x11e83478, (q31_t)0x81423f3a, (q31_t)0x11cf516a, (q31_t)0x813ebd90, (q31_t)0x11b66dad, (q31_t)0x813b40ca, + (q31_t)0x119d8941, (q31_t)0x8137c8e6, (q31_t)0x1184a427, (q31_t)0x813455e6, (q31_t)0x116bbe60, (q31_t)0x8130e7c9, (q31_t)0x1152d7ed, (q31_t)0x812d7e8f, + (q31_t)0x1139f0cf, (q31_t)0x812a1a3a, (q31_t)0x11210907, (q31_t)0x8126bac8, (q31_t)0x11082096, (q31_t)0x8123603a, (q31_t)0x10ef377d, (q31_t)0x81200a90, + (q31_t)0x10d64dbd, (q31_t)0x811cb9ca, (q31_t)0x10bd6356, (q31_t)0x81196de9, (q31_t)0x10a4784b, (q31_t)0x811626ec, (q31_t)0x108b8c9b, (q31_t)0x8112e4d4, + (q31_t)0x1072a048, (q31_t)0x810fa7a0, (q31_t)0x1059b352, (q31_t)0x810c6f52, (q31_t)0x1040c5bb, (q31_t)0x81093be8, (q31_t)0x1027d784, (q31_t)0x81060d63, + (q31_t)0x100ee8ad, (q31_t)0x8102e3c4, (q31_t)0xff5f938, (q31_t)0x80ffbf0a, (q31_t)0xfdd0926, (q31_t)0x80fc9f35, (q31_t)0xfc41876, (q31_t)0x80f98446, + (q31_t)0xfab272b, (q31_t)0x80f66e3c, (q31_t)0xf923546, (q31_t)0x80f35d19, (q31_t)0xf7942c7, (q31_t)0x80f050db, (q31_t)0xf604faf, (q31_t)0x80ed4984, + (q31_t)0xf475bff, (q31_t)0x80ea4712, (q31_t)0xf2e67b8, (q31_t)0x80e74987, (q31_t)0xf1572dc, (q31_t)0x80e450e2, (q31_t)0xefc7d6b, (q31_t)0x80e15d24, + (q31_t)0xee38766, (q31_t)0x80de6e4c, (q31_t)0xeca90ce, (q31_t)0x80db845b, (q31_t)0xeb199a4, (q31_t)0x80d89f51, (q31_t)0xe98a1e9, (q31_t)0x80d5bf2e, + (q31_t)0xe7fa99e, (q31_t)0x80d2e3f2, (q31_t)0xe66b0c3, (q31_t)0x80d00d9d, (q31_t)0xe4db75b, (q31_t)0x80cd3c2f, (q31_t)0xe34bd66, (q31_t)0x80ca6fa9, + (q31_t)0xe1bc2e4, (q31_t)0x80c7a80a, (q31_t)0xe02c7d7, (q31_t)0x80c4e553, (q31_t)0xde9cc40, (q31_t)0x80c22784, (q31_t)0xdd0d01f, (q31_t)0x80bf6e9c, + (q31_t)0xdb7d376, (q31_t)0x80bcba9d, (q31_t)0xd9ed646, (q31_t)0x80ba0b85, (q31_t)0xd85d88f, (q31_t)0x80b76156, (q31_t)0xd6cda53, (q31_t)0x80b4bc0e, + (q31_t)0xd53db92, (q31_t)0x80b21baf, (q31_t)0xd3adc4e, (q31_t)0x80af8039, (q31_t)0xd21dc87, (q31_t)0x80ace9ab, (q31_t)0xd08dc3f, (q31_t)0x80aa5806, + (q31_t)0xcefdb76, (q31_t)0x80a7cb49, (q31_t)0xcd6da2d, (q31_t)0x80a54376, (q31_t)0xcbdd865, (q31_t)0x80a2c08b, (q31_t)0xca4d620, (q31_t)0x80a04289, + (q31_t)0xc8bd35e, (q31_t)0x809dc971, (q31_t)0xc72d020, (q31_t)0x809b5541, (q31_t)0xc59cc68, (q31_t)0x8098e5fb, (q31_t)0xc40c835, (q31_t)0x80967b9f, + (q31_t)0xc27c389, (q31_t)0x8094162c, (q31_t)0xc0ebe66, (q31_t)0x8091b5a2, (q31_t)0xbf5b8cb, (q31_t)0x808f5a02, (q31_t)0xbdcb2bb, (q31_t)0x808d034c, + (q31_t)0xbc3ac35, (q31_t)0x808ab180, (q31_t)0xbaaa53b, (q31_t)0x8088649e, (q31_t)0xb919dcf, (q31_t)0x80861ca6, (q31_t)0xb7895f0, (q31_t)0x8083d998, + (q31_t)0xb5f8d9f, (q31_t)0x80819b74, (q31_t)0xb4684df, (q31_t)0x807f623b, (q31_t)0xb2d7baf, (q31_t)0x807d2dec, (q31_t)0xb147211, (q31_t)0x807afe87, + (q31_t)0xafb6805, (q31_t)0x8078d40d, (q31_t)0xae25d8d, (q31_t)0x8076ae7e, (q31_t)0xac952aa, (q31_t)0x80748dd9, (q31_t)0xab0475c, (q31_t)0x8072721f, + (q31_t)0xa973ba5, (q31_t)0x80705b50, (q31_t)0xa7e2f85, (q31_t)0x806e496c, (q31_t)0xa6522fe, (q31_t)0x806c3c74, (q31_t)0xa4c1610, (q31_t)0x806a3466, + (q31_t)0xa3308bd, (q31_t)0x80683143, (q31_t)0xa19fb04, (q31_t)0x8066330c, (q31_t)0xa00ece8, (q31_t)0x806439c0, (q31_t)0x9e7de6a, (q31_t)0x80624560, + (q31_t)0x9cecf89, (q31_t)0x806055eb, (q31_t)0x9b5c048, (q31_t)0x805e6b62, (q31_t)0x99cb0a7, (q31_t)0x805c85c4, (q31_t)0x983a0a7, (q31_t)0x805aa512, + (q31_t)0x96a9049, (q31_t)0x8058c94c, (q31_t)0x9517f8f, (q31_t)0x8056f272, (q31_t)0x9386e78, (q31_t)0x80552084, (q31_t)0x91f5d06, (q31_t)0x80535381, + (q31_t)0x9064b3a, (q31_t)0x80518b6b, (q31_t)0x8ed3916, (q31_t)0x804fc841, (q31_t)0x8d42699, (q31_t)0x804e0a04, (q31_t)0x8bb13c5, (q31_t)0x804c50b2, + (q31_t)0x8a2009a, (q31_t)0x804a9c4d, (q31_t)0x888ed1b, (q31_t)0x8048ecd5, (q31_t)0x86fd947, (q31_t)0x80474248, (q31_t)0x856c520, (q31_t)0x80459ca9, + (q31_t)0x83db0a7, (q31_t)0x8043fbf6, (q31_t)0x8249bdd, (q31_t)0x80426030, (q31_t)0x80b86c2, (q31_t)0x8040c956, (q31_t)0x7f27157, (q31_t)0x803f376a, + (q31_t)0x7d95b9e, (q31_t)0x803daa6a, (q31_t)0x7c04598, (q31_t)0x803c2257, (q31_t)0x7a72f45, (q31_t)0x803a9f31, (q31_t)0x78e18a7, (q31_t)0x803920f8, + (q31_t)0x77501be, (q31_t)0x8037a7ac, (q31_t)0x75bea8c, (q31_t)0x8036334e, (q31_t)0x742d311, (q31_t)0x8034c3dd, (q31_t)0x729bb4e, (q31_t)0x80335959, + (q31_t)0x710a345, (q31_t)0x8031f3c2, (q31_t)0x6f78af6, (q31_t)0x80309318, (q31_t)0x6de7262, (q31_t)0x802f375d, (q31_t)0x6c5598a, (q31_t)0x802de08e, + (q31_t)0x6ac406f, (q31_t)0x802c8ead, (q31_t)0x6932713, (q31_t)0x802b41ba, (q31_t)0x67a0d76, (q31_t)0x8029f9b4, (q31_t)0x660f398, (q31_t)0x8028b69c, + (q31_t)0x647d97c, (q31_t)0x80277872, (q31_t)0x62ebf22, (q31_t)0x80263f36, (q31_t)0x615a48b, (q31_t)0x80250ae7, (q31_t)0x5fc89b8, (q31_t)0x8023db86, + (q31_t)0x5e36ea9, (q31_t)0x8022b114, (q31_t)0x5ca5361, (q31_t)0x80218b8f, (q31_t)0x5b137df, (q31_t)0x80206af8, (q31_t)0x5981c26, (q31_t)0x801f4f4f, + (q31_t)0x57f0035, (q31_t)0x801e3895, (q31_t)0x565e40d, (q31_t)0x801d26c8, (q31_t)0x54cc7b1, (q31_t)0x801c19ea, (q31_t)0x533ab20, (q31_t)0x801b11fa, + (q31_t)0x51a8e5c, (q31_t)0x801a0ef8, (q31_t)0x5017165, (q31_t)0x801910e4, (q31_t)0x4e8543e, (q31_t)0x801817bf, (q31_t)0x4cf36e5, (q31_t)0x80172388, + (q31_t)0x4b6195d, (q31_t)0x80163440, (q31_t)0x49cfba7, (q31_t)0x801549e6, (q31_t)0x483ddc3, (q31_t)0x8014647b, (q31_t)0x46abfb3, (q31_t)0x801383fe, + (q31_t)0x451a177, (q31_t)0x8012a86f, (q31_t)0x4388310, (q31_t)0x8011d1d0, (q31_t)0x41f6480, (q31_t)0x8011001f, (q31_t)0x40645c7, (q31_t)0x8010335c, + (q31_t)0x3ed26e6, (q31_t)0x800f6b88, (q31_t)0x3d407df, (q31_t)0x800ea8a3, (q31_t)0x3bae8b2, (q31_t)0x800deaad, (q31_t)0x3a1c960, (q31_t)0x800d31a5, + (q31_t)0x388a9ea, (q31_t)0x800c7d8c, (q31_t)0x36f8a51, (q31_t)0x800bce63, (q31_t)0x3566a96, (q31_t)0x800b2427, (q31_t)0x33d4abb, (q31_t)0x800a7edb, + (q31_t)0x3242abf, (q31_t)0x8009de7e, (q31_t)0x30b0aa4, (q31_t)0x80094310, (q31_t)0x2f1ea6c, (q31_t)0x8008ac90, (q31_t)0x2d8ca16, (q31_t)0x80081b00, + (q31_t)0x2bfa9a4, (q31_t)0x80078e5e, (q31_t)0x2a68917, (q31_t)0x800706ac, (q31_t)0x28d6870, (q31_t)0x800683e8, (q31_t)0x27447b0, (q31_t)0x80060614, + (q31_t)0x25b26d7, (q31_t)0x80058d2f, (q31_t)0x24205e8, (q31_t)0x80051939, (q31_t)0x228e4e2, (q31_t)0x8004aa32, (q31_t)0x20fc3c6, (q31_t)0x8004401a, + (q31_t)0x1f6a297, (q31_t)0x8003daf1, (q31_t)0x1dd8154, (q31_t)0x80037ab7, (q31_t)0x1c45ffe, (q31_t)0x80031f6d, (q31_t)0x1ab3e97, (q31_t)0x8002c912, + (q31_t)0x1921d20, (q31_t)0x800277a6, (q31_t)0x178fb99, (q31_t)0x80022b29, (q31_t)0x15fda03, (q31_t)0x8001e39b, (q31_t)0x146b860, (q31_t)0x8001a0fd, + (q31_t)0x12d96b1, (q31_t)0x8001634e, (q31_t)0x11474f6, (q31_t)0x80012a8e, (q31_t)0xfb5330, (q31_t)0x8000f6bd, (q31_t)0xe23160, (q31_t)0x8000c7dc, + (q31_t)0xc90f88, (q31_t)0x80009dea, (q31_t)0xafeda8, (q31_t)0x800078e7, (q31_t)0x96cbc1, (q31_t)0x800058d4, (q31_t)0x7da9d4, (q31_t)0x80003daf, + (q31_t)0x6487e3, (q31_t)0x8000277a, (q31_t)0x4b65ee, (q31_t)0x80001635, (q31_t)0x3243f5, (q31_t)0x800009df, (q31_t)0x1921fb, (q31_t)0x80000278 +}; + +static const q31_t WeightsQ31_8192[16384] = { + (q31_t)0x7fffffff, (q31_t)0x0, (q31_t)0x7fffffd9, (q31_t)0xfff9b781, (q31_t)0x7fffff62, (q31_t)0xfff36f02, (q31_t)0x7ffffe9d, + (q31_t)0xffed2684, + (q31_t)0x7ffffd88, (q31_t)0xffe6de05, (q31_t)0x7ffffc25, (q31_t)0xffe09586, (q31_t)0x7ffffa73, (q31_t)0xffda4d08, + (q31_t)0x7ffff872, (q31_t)0xffd40489, + (q31_t)0x7ffff621, (q31_t)0xffcdbc0b, (q31_t)0x7ffff382, (q31_t)0xffc7738c, (q31_t)0x7ffff094, (q31_t)0xffc12b0e, + (q31_t)0x7fffed57, (q31_t)0xffbae290, + (q31_t)0x7fffe9cb, (q31_t)0xffb49a12, (q31_t)0x7fffe5f0, (q31_t)0xffae5195, (q31_t)0x7fffe1c6, (q31_t)0xffa80917, + (q31_t)0x7fffdd4d, (q31_t)0xffa1c09a, + (q31_t)0x7fffd886, (q31_t)0xff9b781d, (q31_t)0x7fffd36f, (q31_t)0xff952fa0, (q31_t)0x7fffce09, (q31_t)0xff8ee724, + (q31_t)0x7fffc854, (q31_t)0xff889ea7, + (q31_t)0x7fffc251, (q31_t)0xff82562c, (q31_t)0x7fffbbfe, (q31_t)0xff7c0db0, (q31_t)0x7fffb55c, (q31_t)0xff75c535, + (q31_t)0x7fffae6c, (q31_t)0xff6f7cba, + (q31_t)0x7fffa72c, (q31_t)0xff69343f, (q31_t)0x7fff9f9e, (q31_t)0xff62ebc5, (q31_t)0x7fff97c1, (q31_t)0xff5ca34b, + (q31_t)0x7fff8f94, (q31_t)0xff565ad1, + (q31_t)0x7fff8719, (q31_t)0xff501258, (q31_t)0x7fff7e4f, (q31_t)0xff49c9df, (q31_t)0x7fff7536, (q31_t)0xff438167, + (q31_t)0x7fff6bcd, (q31_t)0xff3d38ef, + (q31_t)0x7fff6216, (q31_t)0xff36f078, (q31_t)0x7fff5810, (q31_t)0xff30a801, (q31_t)0x7fff4dbb, (q31_t)0xff2a5f8b, + (q31_t)0x7fff4317, (q31_t)0xff241715, + (q31_t)0x7fff3824, (q31_t)0xff1dcea0, (q31_t)0x7fff2ce2, (q31_t)0xff17862b, (q31_t)0x7fff2151, (q31_t)0xff113db7, + (q31_t)0x7fff1572, (q31_t)0xff0af543, + (q31_t)0x7fff0943, (q31_t)0xff04acd0, (q31_t)0x7ffefcc5, (q31_t)0xfefe645e, (q31_t)0x7ffeeff8, (q31_t)0xfef81bec, + (q31_t)0x7ffee2dd, (q31_t)0xfef1d37b, + (q31_t)0x7ffed572, (q31_t)0xfeeb8b0a, (q31_t)0x7ffec7b9, (q31_t)0xfee5429a, (q31_t)0x7ffeb9b0, (q31_t)0xfedefa2b, + (q31_t)0x7ffeab59, (q31_t)0xfed8b1bd, + (q31_t)0x7ffe9cb2, (q31_t)0xfed2694f, (q31_t)0x7ffe8dbd, (q31_t)0xfecc20e2, (q31_t)0x7ffe7e79, (q31_t)0xfec5d876, + (q31_t)0x7ffe6ee5, (q31_t)0xfebf900a, + (q31_t)0x7ffe5f03, (q31_t)0xfeb947a0, (q31_t)0x7ffe4ed2, (q31_t)0xfeb2ff36, (q31_t)0x7ffe3e52, (q31_t)0xfeacb6cc, + (q31_t)0x7ffe2d83, (q31_t)0xfea66e64, + (q31_t)0x7ffe1c65, (q31_t)0xfea025fd, (q31_t)0x7ffe0af8, (q31_t)0xfe99dd96, (q31_t)0x7ffdf93c, (q31_t)0xfe939530, + (q31_t)0x7ffde731, (q31_t)0xfe8d4ccb, + (q31_t)0x7ffdd4d7, (q31_t)0xfe870467, (q31_t)0x7ffdc22e, (q31_t)0xfe80bc04, (q31_t)0x7ffdaf37, (q31_t)0xfe7a73a2, + (q31_t)0x7ffd9bf0, (q31_t)0xfe742b41, + (q31_t)0x7ffd885a, (q31_t)0xfe6de2e0, (q31_t)0x7ffd7476, (q31_t)0xfe679a81, (q31_t)0x7ffd6042, (q31_t)0xfe615223, + (q31_t)0x7ffd4bc0, (q31_t)0xfe5b09c5, + (q31_t)0x7ffd36ee, (q31_t)0xfe54c169, (q31_t)0x7ffd21ce, (q31_t)0xfe4e790d, (q31_t)0x7ffd0c5f, (q31_t)0xfe4830b3, + (q31_t)0x7ffcf6a0, (q31_t)0xfe41e85a, + (q31_t)0x7ffce093, (q31_t)0xfe3ba002, (q31_t)0x7ffcca37, (q31_t)0xfe3557ab, (q31_t)0x7ffcb38c, (q31_t)0xfe2f0f55, + (q31_t)0x7ffc9c92, (q31_t)0xfe28c700, + (q31_t)0x7ffc8549, (q31_t)0xfe227eac, (q31_t)0x7ffc6db1, (q31_t)0xfe1c365a, (q31_t)0x7ffc55ca, (q31_t)0xfe15ee09, + (q31_t)0x7ffc3d94, (q31_t)0xfe0fa5b8, + (q31_t)0x7ffc250f, (q31_t)0xfe095d69, (q31_t)0x7ffc0c3b, (q31_t)0xfe03151c, (q31_t)0x7ffbf319, (q31_t)0xfdfccccf, + (q31_t)0x7ffbd9a7, (q31_t)0xfdf68484, + (q31_t)0x7ffbbfe6, (q31_t)0xfdf03c3a, (q31_t)0x7ffba5d7, (q31_t)0xfde9f3f1, (q31_t)0x7ffb8b78, (q31_t)0xfde3aba9, + (q31_t)0x7ffb70cb, (q31_t)0xfddd6363, + (q31_t)0x7ffb55ce, (q31_t)0xfdd71b1e, (q31_t)0x7ffb3a83, (q31_t)0xfdd0d2db, (q31_t)0x7ffb1ee9, (q31_t)0xfdca8a99, + (q31_t)0x7ffb0300, (q31_t)0xfdc44258, + (q31_t)0x7ffae6c7, (q31_t)0xfdbdfa18, (q31_t)0x7ffaca40, (q31_t)0xfdb7b1da, (q31_t)0x7ffaad6a, (q31_t)0xfdb1699e, + (q31_t)0x7ffa9045, (q31_t)0xfdab2162, + (q31_t)0x7ffa72d1, (q31_t)0xfda4d929, (q31_t)0x7ffa550e, (q31_t)0xfd9e90f0, (q31_t)0x7ffa36fc, (q31_t)0xfd9848b9, + (q31_t)0x7ffa189c, (q31_t)0xfd920084, + (q31_t)0x7ff9f9ec, (q31_t)0xfd8bb850, (q31_t)0x7ff9daed, (q31_t)0xfd85701e, (q31_t)0x7ff9bba0, (q31_t)0xfd7f27ed, + (q31_t)0x7ff99c03, (q31_t)0xfd78dfbd, + (q31_t)0x7ff97c18, (q31_t)0xfd729790, (q31_t)0x7ff95bdd, (q31_t)0xfd6c4f64, (q31_t)0x7ff93b54, (q31_t)0xfd660739, + (q31_t)0x7ff91a7b, (q31_t)0xfd5fbf10, + (q31_t)0x7ff8f954, (q31_t)0xfd5976e9, (q31_t)0x7ff8d7de, (q31_t)0xfd532ec3, (q31_t)0x7ff8b619, (q31_t)0xfd4ce69f, + (q31_t)0x7ff89405, (q31_t)0xfd469e7c, + (q31_t)0x7ff871a2, (q31_t)0xfd40565c, (q31_t)0x7ff84ef0, (q31_t)0xfd3a0e3d, (q31_t)0x7ff82bef, (q31_t)0xfd33c61f, + (q31_t)0x7ff8089f, (q31_t)0xfd2d7e04, + (q31_t)0x7ff7e500, (q31_t)0xfd2735ea, (q31_t)0x7ff7c113, (q31_t)0xfd20edd2, (q31_t)0x7ff79cd6, (q31_t)0xfd1aa5bc, + (q31_t)0x7ff7784a, (q31_t)0xfd145da7, + (q31_t)0x7ff75370, (q31_t)0xfd0e1594, (q31_t)0x7ff72e46, (q31_t)0xfd07cd83, (q31_t)0x7ff708ce, (q31_t)0xfd018574, + (q31_t)0x7ff6e307, (q31_t)0xfcfb3d67, + (q31_t)0x7ff6bcf0, (q31_t)0xfcf4f55c, (q31_t)0x7ff6968b, (q31_t)0xfceead52, (q31_t)0x7ff66fd7, (q31_t)0xfce8654b, + (q31_t)0x7ff648d4, (q31_t)0xfce21d45, + (q31_t)0x7ff62182, (q31_t)0xfcdbd541, (q31_t)0x7ff5f9e1, (q31_t)0xfcd58d3f, (q31_t)0x7ff5d1f1, (q31_t)0xfccf453f, + (q31_t)0x7ff5a9b2, (q31_t)0xfcc8fd41, + (q31_t)0x7ff58125, (q31_t)0xfcc2b545, (q31_t)0x7ff55848, (q31_t)0xfcbc6d4c, (q31_t)0x7ff52f1d, (q31_t)0xfcb62554, + (q31_t)0x7ff505a2, (q31_t)0xfcafdd5e, + (q31_t)0x7ff4dbd9, (q31_t)0xfca9956a, (q31_t)0x7ff4b1c0, (q31_t)0xfca34d78, (q31_t)0x7ff48759, (q31_t)0xfc9d0588, + (q31_t)0x7ff45ca3, (q31_t)0xfc96bd9b, + (q31_t)0x7ff4319d, (q31_t)0xfc9075af, (q31_t)0x7ff40649, (q31_t)0xfc8a2dc6, (q31_t)0x7ff3daa6, (q31_t)0xfc83e5de, + (q31_t)0x7ff3aeb4, (q31_t)0xfc7d9df9, + (q31_t)0x7ff38274, (q31_t)0xfc775616, (q31_t)0x7ff355e4, (q31_t)0xfc710e36, (q31_t)0x7ff32905, (q31_t)0xfc6ac657, + (q31_t)0x7ff2fbd7, (q31_t)0xfc647e7b, + (q31_t)0x7ff2ce5b, (q31_t)0xfc5e36a0, (q31_t)0x7ff2a08f, (q31_t)0xfc57eec9, (q31_t)0x7ff27275, (q31_t)0xfc51a6f3, + (q31_t)0x7ff2440b, (q31_t)0xfc4b5f20, + (q31_t)0x7ff21553, (q31_t)0xfc45174e, (q31_t)0x7ff1e64c, (q31_t)0xfc3ecf80, (q31_t)0x7ff1b6f6, (q31_t)0xfc3887b3, + (q31_t)0x7ff18751, (q31_t)0xfc323fe9, + (q31_t)0x7ff1575d, (q31_t)0xfc2bf821, (q31_t)0x7ff1271a, (q31_t)0xfc25b05c, (q31_t)0x7ff0f688, (q31_t)0xfc1f6899, + (q31_t)0x7ff0c5a7, (q31_t)0xfc1920d8, + (q31_t)0x7ff09478, (q31_t)0xfc12d91a, (q31_t)0x7ff062f9, (q31_t)0xfc0c915e, (q31_t)0x7ff0312c, (q31_t)0xfc0649a5, + (q31_t)0x7fefff0f, (q31_t)0xfc0001ee, + (q31_t)0x7fefcca4, (q31_t)0xfbf9ba39, (q31_t)0x7fef99ea, (q31_t)0xfbf37287, (q31_t)0x7fef66e1, (q31_t)0xfbed2ad8, + (q31_t)0x7fef3388, (q31_t)0xfbe6e32b, + (q31_t)0x7feeffe1, (q31_t)0xfbe09b80, (q31_t)0x7feecbec, (q31_t)0xfbda53d8, (q31_t)0x7fee97a7, (q31_t)0xfbd40c33, + (q31_t)0x7fee6313, (q31_t)0xfbcdc490, + (q31_t)0x7fee2e30, (q31_t)0xfbc77cf0, (q31_t)0x7fedf8ff, (q31_t)0xfbc13552, (q31_t)0x7fedc37e, (q31_t)0xfbbaedb7, + (q31_t)0x7fed8daf, (q31_t)0xfbb4a61f, + (q31_t)0x7fed5791, (q31_t)0xfbae5e89, (q31_t)0x7fed2123, (q31_t)0xfba816f6, (q31_t)0x7fecea67, (q31_t)0xfba1cf66, + (q31_t)0x7fecb35c, (q31_t)0xfb9b87d8, + (q31_t)0x7fec7c02, (q31_t)0xfb95404d, (q31_t)0x7fec4459, (q31_t)0xfb8ef8c5, (q31_t)0x7fec0c62, (q31_t)0xfb88b13f, + (q31_t)0x7febd41b, (q31_t)0xfb8269bd, + (q31_t)0x7feb9b85, (q31_t)0xfb7c223d, (q31_t)0x7feb62a1, (q31_t)0xfb75dac0, (q31_t)0x7feb296d, 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(q31_t)0x8011001f, (q31_t)0x4191cd5, (q31_t)0x8010cc78, (q31_t)0x412d528, (q31_t)0x8010991f, + (q31_t)0x40c8d79, (q31_t)0x80106616, + (q31_t)0x40645c7, (q31_t)0x8010335c, (q31_t)0x3fffe12, (q31_t)0x801000f1, (q31_t)0x3f9b65b, (q31_t)0x800fced4, + (q31_t)0x3f36ea2, (q31_t)0x800f9d07, + (q31_t)0x3ed26e6, (q31_t)0x800f6b88, (q31_t)0x3e6df28, (q31_t)0x800f3a59, (q31_t)0x3e09767, (q31_t)0x800f0978, + (q31_t)0x3da4fa4, (q31_t)0x800ed8e6, + (q31_t)0x3d407df, (q31_t)0x800ea8a3, (q31_t)0x3cdc017, (q31_t)0x800e78af, (q31_t)0x3c7784d, (q31_t)0x800e490a, + (q31_t)0x3c13080, (q31_t)0x800e19b4, + (q31_t)0x3bae8b2, (q31_t)0x800deaad, (q31_t)0x3b4a0e0, (q31_t)0x800dbbf5, (q31_t)0x3ae590d, (q31_t)0x800d8d8b, + (q31_t)0x3a81137, (q31_t)0x800d5f71, + (q31_t)0x3a1c960, (q31_t)0x800d31a5, (q31_t)0x39b8185, (q31_t)0x800d0429, (q31_t)0x39539a9, (q31_t)0x800cd6fb, + (q31_t)0x38ef1ca, (q31_t)0x800caa1c, + (q31_t)0x388a9ea, (q31_t)0x800c7d8c, (q31_t)0x3826207, (q31_t)0x800c514c, (q31_t)0x37c1a22, (q31_t)0x800c255a, + (q31_t)0x375d23a, (q31_t)0x800bf9b7, + (q31_t)0x36f8a51, (q31_t)0x800bce63, (q31_t)0x3694265, (q31_t)0x800ba35d, (q31_t)0x362fa78, (q31_t)0x800b78a7, + (q31_t)0x35cb288, (q31_t)0x800b4e40, + (q31_t)0x3566a96, (q31_t)0x800b2427, (q31_t)0x35022a2, (q31_t)0x800afa5e, (q31_t)0x349daac, (q31_t)0x800ad0e3, + (q31_t)0x34392b4, (q31_t)0x800aa7b8, + (q31_t)0x33d4abb, (q31_t)0x800a7edb, (q31_t)0x33702bf, (q31_t)0x800a564e, (q31_t)0x330bac1, (q31_t)0x800a2e0f, + (q31_t)0x32a72c1, (q31_t)0x800a061f, + (q31_t)0x3242abf, (q31_t)0x8009de7e, (q31_t)0x31de2bb, (q31_t)0x8009b72c, (q31_t)0x3179ab5, (q31_t)0x80099029, + (q31_t)0x31152ae, (q31_t)0x80096975, + (q31_t)0x30b0aa4, (q31_t)0x80094310, (q31_t)0x304c299, (q31_t)0x80091cf9, (q31_t)0x2fe7a8c, (q31_t)0x8008f732, + (q31_t)0x2f8327d, (q31_t)0x8008d1ba, + (q31_t)0x2f1ea6c, (q31_t)0x8008ac90, (q31_t)0x2eba259, (q31_t)0x800887b6, (q31_t)0x2e55a44, (q31_t)0x8008632a, + (q31_t)0x2df122e, (q31_t)0x80083eed, + (q31_t)0x2d8ca16, (q31_t)0x80081b00, (q31_t)0x2d281fc, (q31_t)0x8007f761, (q31_t)0x2cc39e1, (q31_t)0x8007d411, + (q31_t)0x2c5f1c3, (q31_t)0x8007b110, + (q31_t)0x2bfa9a4, (q31_t)0x80078e5e, (q31_t)0x2b96184, (q31_t)0x80076bfb, (q31_t)0x2b31961, (q31_t)0x800749e7, + (q31_t)0x2acd13d, (q31_t)0x80072822, + (q31_t)0x2a68917, (q31_t)0x800706ac, (q31_t)0x2a040f0, (q31_t)0x8006e585, (q31_t)0x299f8c7, (q31_t)0x8006c4ac, + (q31_t)0x293b09c, (q31_t)0x8006a423, + (q31_t)0x28d6870, (q31_t)0x800683e8, (q31_t)0x2872043, (q31_t)0x800663fd, (q31_t)0x280d813, (q31_t)0x80064460, + (q31_t)0x27a8fe2, (q31_t)0x80062513, + (q31_t)0x27447b0, (q31_t)0x80060614, (q31_t)0x26dff7c, (q31_t)0x8005e764, (q31_t)0x267b747, (q31_t)0x8005c904, + (q31_t)0x2616f10, (q31_t)0x8005aaf2, + (q31_t)0x25b26d7, (q31_t)0x80058d2f, (q31_t)0x254de9e, (q31_t)0x80056fbb, (q31_t)0x24e9662, (q31_t)0x80055296, + (q31_t)0x2484e26, (q31_t)0x800535c0, + (q31_t)0x24205e8, (q31_t)0x80051939, (q31_t)0x23bbda8, (q31_t)0x8004fd00, (q31_t)0x2357567, (q31_t)0x8004e117, + (q31_t)0x22f2d25, (q31_t)0x8004c57d, + (q31_t)0x228e4e2, (q31_t)0x8004aa32, (q31_t)0x2229c9d, (q31_t)0x80048f35, (q31_t)0x21c5457, (q31_t)0x80047488, + (q31_t)0x2160c0f, (q31_t)0x80045a29, + (q31_t)0x20fc3c6, (q31_t)0x8004401a, (q31_t)0x2097b7c, (q31_t)0x80042659, (q31_t)0x2033331, (q31_t)0x80040ce7, + (q31_t)0x1fceae4, (q31_t)0x8003f3c5, + (q31_t)0x1f6a297, (q31_t)0x8003daf1, (q31_t)0x1f05a48, (q31_t)0x8003c26c, (q31_t)0x1ea11f7, (q31_t)0x8003aa36, + (q31_t)0x1e3c9a6, (q31_t)0x8003924f, + (q31_t)0x1dd8154, (q31_t)0x80037ab7, (q31_t)0x1d73900, (q31_t)0x8003636e, (q31_t)0x1d0f0ab, (q31_t)0x80034c74, + (q31_t)0x1caa855, (q31_t)0x800335c9, + (q31_t)0x1c45ffe, (q31_t)0x80031f6d, (q31_t)0x1be17a6, (q31_t)0x80030960, (q31_t)0x1b7cf4d, (q31_t)0x8002f3a1, + (q31_t)0x1b186f3, (q31_t)0x8002de32, + (q31_t)0x1ab3e97, (q31_t)0x8002c912, (q31_t)0x1a4f63b, (q31_t)0x8002b440, (q31_t)0x19eaddd, (q31_t)0x80029fbe, + (q31_t)0x198657f, (q31_t)0x80028b8a, + (q31_t)0x1921d20, (q31_t)0x800277a6, (q31_t)0x18bd4bf, (q31_t)0x80026410, (q31_t)0x1858c5e, (q31_t)0x800250c9, + (q31_t)0x17f43fc, (q31_t)0x80023dd2, + (q31_t)0x178fb99, (q31_t)0x80022b29, (q31_t)0x172b335, (q31_t)0x800218cf, (q31_t)0x16c6ad0, (q31_t)0x800206c4, + (q31_t)0x166226a, (q31_t)0x8001f508, + (q31_t)0x15fda03, (q31_t)0x8001e39b, (q31_t)0x159919c, (q31_t)0x8001d27d, (q31_t)0x1534934, (q31_t)0x8001c1ae, + (q31_t)0x14d00ca, (q31_t)0x8001b12e, + (q31_t)0x146b860, (q31_t)0x8001a0fd, (q31_t)0x1406ff6, (q31_t)0x8001911b, (q31_t)0x13a278a, (q31_t)0x80018187, + (q31_t)0x133df1e, (q31_t)0x80017243, + (q31_t)0x12d96b1, (q31_t)0x8001634e, (q31_t)0x1274e43, (q31_t)0x800154a7, (q31_t)0x12105d5, (q31_t)0x80014650, + (q31_t)0x11abd66, (q31_t)0x80013847, + (q31_t)0x11474f6, (q31_t)0x80012a8e, (q31_t)0x10e2c85, (q31_t)0x80011d23, (q31_t)0x107e414, (q31_t)0x80011008, + (q31_t)0x1019ba2, (q31_t)0x8001033b, + (q31_t)0xfb5330, (q31_t)0x8000f6bd, (q31_t)0xf50abd, (q31_t)0x8000ea8e, (q31_t)0xeec249, (q31_t)0x8000deaf, (q31_t)0xe879d5, + (q31_t)0x8000d31e, + (q31_t)0xe23160, (q31_t)0x8000c7dc, (q31_t)0xdbe8eb, (q31_t)0x8000bce9, (q31_t)0xd5a075, (q31_t)0x8000b245, (q31_t)0xcf57ff, + (q31_t)0x8000a7f0, + (q31_t)0xc90f88, (q31_t)0x80009dea, (q31_t)0xc2c711, (q31_t)0x80009433, (q31_t)0xbc7e99, (q31_t)0x80008aca, (q31_t)0xb63621, + (q31_t)0x800081b1, + (q31_t)0xafeda8, (q31_t)0x800078e7, (q31_t)0xa9a52f, (q31_t)0x8000706c, (q31_t)0xa35cb5, (q31_t)0x8000683f, (q31_t)0x9d143b, + (q31_t)0x80006062, + (q31_t)0x96cbc1, (q31_t)0x800058d4, (q31_t)0x908346, (q31_t)0x80005194, (q31_t)0x8a3acb, (q31_t)0x80004aa4, (q31_t)0x83f250, + (q31_t)0x80004402, + (q31_t)0x7da9d4, (q31_t)0x80003daf, (q31_t)0x776159, (q31_t)0x800037ac, (q31_t)0x7118dc, (q31_t)0x800031f7, (q31_t)0x6ad060, + (q31_t)0x80002c91, + (q31_t)0x6487e3, (q31_t)0x8000277a, (q31_t)0x5e3f66, (q31_t)0x800022b3, (q31_t)0x57f6e9, (q31_t)0x80001e3a, (q31_t)0x51ae6b, + (q31_t)0x80001a10, + (q31_t)0x4b65ee, (q31_t)0x80001635, (q31_t)0x451d70, (q31_t)0x800012a9, (q31_t)0x3ed4f2, (q31_t)0x80000f6c, (q31_t)0x388c74, + (q31_t)0x80000c7e, + (q31_t)0x3243f5, (q31_t)0x800009df, (q31_t)0x2bfb77, (q31_t)0x8000078e, (q31_t)0x25b2f8, (q31_t)0x8000058d, (q31_t)0x1f6a7a, + (q31_t)0x800003db, + (q31_t)0x1921fb, (q31_t)0x80000278, (q31_t)0x12d97c, (q31_t)0x80000163, (q31_t)0xc90fe, (q31_t)0x8000009e, (q31_t)0x6487f, + (q31_t)0x80000027 + +}; + +/** +* \par +* cosFactor tables are generated using the formula : <pre>cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))</pre> +* \par +* C command to generate the table +* <pre> +* for(i = 0; i< N; i++) +* { +* cos_factors[i]= 2 * cos((2*i+1)*c/2); +* } </pre> +* \par +* where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code> +* \par +* Then converted to q31 format by multiplying with 2^31 and saturated if required. +*/ + + +static const q31_t cos_factorsQ31_128[128] = { + (q31_t)0x7fff6216, (q31_t)0x7ffa72d1, (q31_t)0x7ff09478, (q31_t)0x7fe1c76b, (q31_t)0x7fce0c3e, (q31_t)0x7fb563b3, + (q31_t)0x7f97cebd, (q31_t)0x7f754e80, + (q31_t)0x7f4de451, (q31_t)0x7f2191b4, (q31_t)0x7ef05860, (q31_t)0x7eba3a39, (q31_t)0x7e7f3957, (q31_t)0x7e3f57ff, + (q31_t)0x7dfa98a8, (q31_t)0x7db0fdf8, + (q31_t)0x7d628ac6, (q31_t)0x7d0f4218, (q31_t)0x7cb72724, (q31_t)0x7c5a3d50, (q31_t)0x7bf88830, (q31_t)0x7b920b89, + (q31_t)0x7b26cb4f, (q31_t)0x7ab6cba4, + (q31_t)0x7a4210d8, (q31_t)0x79c89f6e, (q31_t)0x794a7c12, (q31_t)0x78c7aba2, (q31_t)0x78403329, (q31_t)0x77b417df, + (q31_t)0x77235f2d, (q31_t)0x768e0ea6, + (q31_t)0x75f42c0b, (q31_t)0x7555bd4c, (q31_t)0x74b2c884, (q31_t)0x740b53fb, (q31_t)0x735f6626, (q31_t)0x72af05a7, + (q31_t)0x71fa3949, (q31_t)0x71410805, + (q31_t)0x708378ff, (q31_t)0x6fc19385, (q31_t)0x6efb5f12, (q31_t)0x6e30e34a, (q31_t)0x6d6227fa, (q31_t)0x6c8f351c, + (q31_t)0x6bb812d1, (q31_t)0x6adcc964, + (q31_t)0x69fd614a, (q31_t)0x6919e320, (q31_t)0x683257ab, (q31_t)0x6746c7d8, (q31_t)0x66573cbb, (q31_t)0x6563bf92, + (q31_t)0x646c59bf, (q31_t)0x637114cc, + (q31_t)0x6271fa69, (q31_t)0x616f146c, (q31_t)0x60686ccf, (q31_t)0x5f5e0db3, (q31_t)0x5e50015d, (q31_t)0x5d3e5237, + (q31_t)0x5c290acc, (q31_t)0x5b1035cf, + (q31_t)0x59f3de12, (q31_t)0x58d40e8c, (q31_t)0x57b0d256, (q31_t)0x568a34a9, (q31_t)0x556040e2, (q31_t)0x5433027d, + (q31_t)0x53028518, (q31_t)0x51ced46e, + (q31_t)0x5097fc5e, (q31_t)0x4f5e08e3, (q31_t)0x4e210617, (q31_t)0x4ce10034, (q31_t)0x4b9e0390, (q31_t)0x4a581c9e, + (q31_t)0x490f57ee, (q31_t)0x47c3c22f, + (q31_t)0x46756828, (q31_t)0x452456bd, (q31_t)0x43d09aed, (q31_t)0x427a41d0, (q31_t)0x4121589b, (q31_t)0x3fc5ec98, + (q31_t)0x3e680b2c, (q31_t)0x3d07c1d6, + (q31_t)0x3ba51e29, (q31_t)0x3a402dd2, (q31_t)0x38d8fe93, (q31_t)0x376f9e46, (q31_t)0x36041ad9, (q31_t)0x34968250, + (q31_t)0x3326e2c3, (q31_t)0x31b54a5e, + (q31_t)0x3041c761, (q31_t)0x2ecc681e, (q31_t)0x2d553afc, (q31_t)0x2bdc4e6f, (q31_t)0x2a61b101, (q31_t)0x28e5714b, + (q31_t)0x27679df4, (q31_t)0x25e845b6, + (q31_t)0x24677758, (q31_t)0x22e541af, (q31_t)0x2161b3a0, (q31_t)0x1fdcdc1b, (q31_t)0x1e56ca1e, (q31_t)0x1ccf8cb3, + (q31_t)0x1b4732ef, (q31_t)0x19bdcbf3, + (q31_t)0x183366e9, (q31_t)0x16a81305, (q31_t)0x151bdf86, (q31_t)0x138edbb1, (q31_t)0x120116d5, (q31_t)0x1072a048, + (q31_t)0xee38766, (q31_t)0xd53db92, + (q31_t)0xbc3ac35, (q31_t)0xa3308bd, (q31_t)0x8a2009a, (q31_t)0x710a345, (q31_t)0x57f0035, (q31_t)0x3ed26e6, (q31_t)0x25b26d7, + (q31_t)0xc90f88 +}; + +static const q31_t cos_factorsQ31_512[512] = { + (q31_t)0x7ffff621, (q31_t)0x7fffa72c, (q31_t)0x7fff0943, (q31_t)0x7ffe1c65, (q31_t)0x7ffce093, (q31_t)0x7ffb55ce, + (q31_t)0x7ff97c18, (q31_t)0x7ff75370, + (q31_t)0x7ff4dbd9, (q31_t)0x7ff21553, (q31_t)0x7feeffe1, (q31_t)0x7feb9b85, (q31_t)0x7fe7e841, (q31_t)0x7fe3e616, + (q31_t)0x7fdf9508, (q31_t)0x7fdaf519, + (q31_t)0x7fd6064c, (q31_t)0x7fd0c8a3, (q31_t)0x7fcb3c23, (q31_t)0x7fc560cf, (q31_t)0x7fbf36aa, (q31_t)0x7fb8bdb8, + (q31_t)0x7fb1f5fc, (q31_t)0x7faadf7c, + (q31_t)0x7fa37a3c, (q31_t)0x7f9bc640, (q31_t)0x7f93c38c, (q31_t)0x7f8b7227, (q31_t)0x7f82d214, (q31_t)0x7f79e35a, + (q31_t)0x7f70a5fe, (q31_t)0x7f671a05, + (q31_t)0x7f5d3f75, (q31_t)0x7f531655, (q31_t)0x7f489eaa, (q31_t)0x7f3dd87c, (q31_t)0x7f32c3d1, (q31_t)0x7f2760af, + (q31_t)0x7f1baf1e, (q31_t)0x7f0faf25, + (q31_t)0x7f0360cb, (q31_t)0x7ef6c418, (q31_t)0x7ee9d914, (q31_t)0x7edc9fc6, (q31_t)0x7ecf1837, (q31_t)0x7ec14270, + (q31_t)0x7eb31e78, (q31_t)0x7ea4ac58, + (q31_t)0x7e95ec1a, (q31_t)0x7e86ddc6, (q31_t)0x7e778166, (q31_t)0x7e67d703, (q31_t)0x7e57dea7, (q31_t)0x7e47985b, + (q31_t)0x7e37042a, (q31_t)0x7e26221f, + (q31_t)0x7e14f242, (q31_t)0x7e0374a0, (q31_t)0x7df1a942, (q31_t)0x7ddf9034, (q31_t)0x7dcd2981, (q31_t)0x7dba7534, + (q31_t)0x7da77359, (q31_t)0x7d9423fc, + (q31_t)0x7d808728, (q31_t)0x7d6c9ce9, (q31_t)0x7d58654d, (q31_t)0x7d43e05e, (q31_t)0x7d2f0e2b, (q31_t)0x7d19eebf, + (q31_t)0x7d048228, (q31_t)0x7ceec873, + (q31_t)0x7cd8c1ae, (q31_t)0x7cc26de5, (q31_t)0x7cabcd28, (q31_t)0x7c94df83, (q31_t)0x7c7da505, (q31_t)0x7c661dbc, + (q31_t)0x7c4e49b7, (q31_t)0x7c362904, + (q31_t)0x7c1dbbb3, (q31_t)0x7c0501d2, (q31_t)0x7bebfb70, (q31_t)0x7bd2a89e, (q31_t)0x7bb9096b, (q31_t)0x7b9f1de6, + (q31_t)0x7b84e61f, (q31_t)0x7b6a6227, + (q31_t)0x7b4f920e, (q31_t)0x7b3475e5, (q31_t)0x7b190dbc, (q31_t)0x7afd59a4, (q31_t)0x7ae159ae, (q31_t)0x7ac50dec, + (q31_t)0x7aa8766f, (q31_t)0x7a8b9348, + (q31_t)0x7a6e648a, (q31_t)0x7a50ea47, (q31_t)0x7a332490, (q31_t)0x7a151378, (q31_t)0x79f6b711, (q31_t)0x79d80f6f, + (q31_t)0x79b91ca4, (q31_t)0x7999dec4, + (q31_t)0x797a55e0, (q31_t)0x795a820e, (q31_t)0x793a6361, (q31_t)0x7919f9ec, (q31_t)0x78f945c3, (q31_t)0x78d846fb, + (q31_t)0x78b6fda8, (q31_t)0x789569df, + (q31_t)0x78738bb3, (q31_t)0x7851633b, (q31_t)0x782ef08b, (q31_t)0x780c33b8, (q31_t)0x77e92cd9, (q31_t)0x77c5dc01, + (q31_t)0x77a24148, (q31_t)0x777e5cc3, + (q31_t)0x775a2e89, (q31_t)0x7735b6af, (q31_t)0x7710f54c, (q31_t)0x76ebea77, (q31_t)0x76c69647, (q31_t)0x76a0f8d2, + (q31_t)0x767b1231, (q31_t)0x7654e279, + (q31_t)0x762e69c4, (q31_t)0x7607a828, (q31_t)0x75e09dbd, (q31_t)0x75b94a9c, (q31_t)0x7591aedd, (q31_t)0x7569ca99, + (q31_t)0x75419de7, (q31_t)0x751928e0, + (q31_t)0x74f06b9e, (q31_t)0x74c7663a, (q31_t)0x749e18cd, (q31_t)0x74748371, (q31_t)0x744aa63f, (q31_t)0x74208150, + (q31_t)0x73f614c0, (q31_t)0x73cb60a8, + (q31_t)0x73a06522, (q31_t)0x73752249, (q31_t)0x73499838, (q31_t)0x731dc70a, (q31_t)0x72f1aed9, (q31_t)0x72c54fc1, + (q31_t)0x7298a9dd, (q31_t)0x726bbd48, + (q31_t)0x723e8a20, (q31_t)0x7211107e, (q31_t)0x71e35080, (q31_t)0x71b54a41, (q31_t)0x7186fdde, (q31_t)0x71586b74, + (q31_t)0x7129931f, (q31_t)0x70fa74fc, + (q31_t)0x70cb1128, (q31_t)0x709b67c0, (q31_t)0x706b78e3, (q31_t)0x703b44ad, (q31_t)0x700acb3c, (q31_t)0x6fda0cae, + (q31_t)0x6fa90921, (q31_t)0x6f77c0b3, + (q31_t)0x6f463383, (q31_t)0x6f1461b0, (q31_t)0x6ee24b57, (q31_t)0x6eaff099, (q31_t)0x6e7d5193, (q31_t)0x6e4a6e66, + (q31_t)0x6e174730, (q31_t)0x6de3dc11, + (q31_t)0x6db02d29, (q31_t)0x6d7c3a98, (q31_t)0x6d48047e, (q31_t)0x6d138afb, (q31_t)0x6cdece2f, (q31_t)0x6ca9ce3b, + (q31_t)0x6c748b3f, (q31_t)0x6c3f055d, + (q31_t)0x6c093cb6, (q31_t)0x6bd3316a, (q31_t)0x6b9ce39b, (q31_t)0x6b66536b, (q31_t)0x6b2f80fb, (q31_t)0x6af86c6c, + (q31_t)0x6ac115e2, (q31_t)0x6a897d7d, + (q31_t)0x6a51a361, (q31_t)0x6a1987b0, (q31_t)0x69e12a8c, (q31_t)0x69a88c19, (q31_t)0x696fac78, (q31_t)0x69368bce, + (q31_t)0x68fd2a3d, (q31_t)0x68c387e9, + (q31_t)0x6889a4f6, (q31_t)0x684f8186, (q31_t)0x68151dbe, (q31_t)0x67da79c3, (q31_t)0x679f95b7, (q31_t)0x676471c0, + (q31_t)0x67290e02, (q31_t)0x66ed6aa1, + (q31_t)0x66b187c3, (q31_t)0x6675658c, (q31_t)0x66390422, (q31_t)0x65fc63a9, (q31_t)0x65bf8447, (q31_t)0x65826622, + (q31_t)0x6545095f, (q31_t)0x65076e25, + (q31_t)0x64c99498, (q31_t)0x648b7ce0, (q31_t)0x644d2722, (q31_t)0x640e9386, (q31_t)0x63cfc231, (q31_t)0x6390b34a, + (q31_t)0x635166f9, (q31_t)0x6311dd64, + (q31_t)0x62d216b3, (q31_t)0x6292130c, (q31_t)0x6251d298, (q31_t)0x6211557e, (q31_t)0x61d09be5, (q31_t)0x618fa5f7, + (q31_t)0x614e73da, (q31_t)0x610d05b7, + (q31_t)0x60cb5bb7, (q31_t)0x60897601, (q31_t)0x604754bf, (q31_t)0x6004f819, (q31_t)0x5fc26038, (q31_t)0x5f7f8d46, + (q31_t)0x5f3c7f6b, (q31_t)0x5ef936d1, + (q31_t)0x5eb5b3a2, (q31_t)0x5e71f606, (q31_t)0x5e2dfe29, (q31_t)0x5de9cc33, (q31_t)0x5da5604f, (q31_t)0x5d60baa7, + (q31_t)0x5d1bdb65, (q31_t)0x5cd6c2b5, + (q31_t)0x5c9170bf, (q31_t)0x5c4be5b0, (q31_t)0x5c0621b2, (q31_t)0x5bc024f0, (q31_t)0x5b79ef96, (q31_t)0x5b3381ce, + (q31_t)0x5aecdbc5, (q31_t)0x5aa5fda5, + (q31_t)0x5a5ee79a, (q31_t)0x5a1799d1, (q31_t)0x59d01475, (q31_t)0x598857b2, (q31_t)0x594063b5, (q31_t)0x58f838a9, + (q31_t)0x58afd6bd, (q31_t)0x58673e1b, + (q31_t)0x581e6ef1, (q31_t)0x57d5696d, (q31_t)0x578c2dba, (q31_t)0x5742bc06, (q31_t)0x56f9147e, (q31_t)0x56af3750, + (q31_t)0x566524aa, (q31_t)0x561adcb9, + (q31_t)0x55d05faa, (q31_t)0x5585adad, (q31_t)0x553ac6ee, (q31_t)0x54efab9c, (q31_t)0x54a45be6, (q31_t)0x5458d7f9, + (q31_t)0x540d2005, (q31_t)0x53c13439, + (q31_t)0x537514c2, (q31_t)0x5328c1d0, (q31_t)0x52dc3b92, (q31_t)0x528f8238, (q31_t)0x524295f0, (q31_t)0x51f576ea, + (q31_t)0x51a82555, (q31_t)0x515aa162, + (q31_t)0x510ceb40, (q31_t)0x50bf031f, (q31_t)0x5070e92f, (q31_t)0x50229da1, (q31_t)0x4fd420a4, (q31_t)0x4f857269, + (q31_t)0x4f369320, (q31_t)0x4ee782fb, + (q31_t)0x4e984229, (q31_t)0x4e48d0dd, (q31_t)0x4df92f46, (q31_t)0x4da95d96, (q31_t)0x4d595bfe, (q31_t)0x4d092ab0, + (q31_t)0x4cb8c9dd, (q31_t)0x4c6839b7, + (q31_t)0x4c177a6e, (q31_t)0x4bc68c36, (q31_t)0x4b756f40, (q31_t)0x4b2423be, (q31_t)0x4ad2a9e2, (q31_t)0x4a8101de, + (q31_t)0x4a2f2be6, (q31_t)0x49dd282a, + (q31_t)0x498af6df, (q31_t)0x49389836, (q31_t)0x48e60c62, (q31_t)0x48935397, (q31_t)0x48406e08, (q31_t)0x47ed5be6, + (q31_t)0x479a1d67, (q31_t)0x4746b2bc, + (q31_t)0x46f31c1a, (q31_t)0x469f59b4, (q31_t)0x464b6bbe, (q31_t)0x45f7526b, (q31_t)0x45a30df0, (q31_t)0x454e9e80, + (q31_t)0x44fa0450, (q31_t)0x44a53f93, + (q31_t)0x4450507e, (q31_t)0x43fb3746, (q31_t)0x43a5f41e, (q31_t)0x4350873c, (q31_t)0x42faf0d4, (q31_t)0x42a5311b, + (q31_t)0x424f4845, (q31_t)0x41f93689, + (q31_t)0x41a2fc1a, (q31_t)0x414c992f, (q31_t)0x40f60dfb, (q31_t)0x409f5ab6, (q31_t)0x40487f94, (q31_t)0x3ff17cca, + (q31_t)0x3f9a5290, (q31_t)0x3f430119, + (q31_t)0x3eeb889c, (q31_t)0x3e93e950, (q31_t)0x3e3c2369, (q31_t)0x3de4371f, (q31_t)0x3d8c24a8, (q31_t)0x3d33ec39, + (q31_t)0x3cdb8e09, (q31_t)0x3c830a50, + (q31_t)0x3c2a6142, (q31_t)0x3bd19318, (q31_t)0x3b78a007, (q31_t)0x3b1f8848, (q31_t)0x3ac64c0f, (q31_t)0x3a6ceb96, + (q31_t)0x3a136712, (q31_t)0x39b9bebc, + (q31_t)0x395ff2c9, (q31_t)0x39060373, (q31_t)0x38abf0ef, (q31_t)0x3851bb77, (q31_t)0x37f76341, (q31_t)0x379ce885, + (q31_t)0x37424b7b, (q31_t)0x36e78c5b, + (q31_t)0x368cab5c, (q31_t)0x3631a8b8, (q31_t)0x35d684a6, (q31_t)0x357b3f5d, (q31_t)0x351fd918, (q31_t)0x34c4520d, + (q31_t)0x3468aa76, (q31_t)0x340ce28b, + (q31_t)0x33b0fa84, (q31_t)0x3354f29b, (q31_t)0x32f8cb07, (q31_t)0x329c8402, (q31_t)0x32401dc6, (q31_t)0x31e39889, + (q31_t)0x3186f487, (q31_t)0x312a31f8, + (q31_t)0x30cd5115, (q31_t)0x30705217, (q31_t)0x30133539, (q31_t)0x2fb5fab2, (q31_t)0x2f58a2be, (q31_t)0x2efb2d95, + (q31_t)0x2e9d9b70, (q31_t)0x2e3fec8b, + (q31_t)0x2de2211e, (q31_t)0x2d843964, (q31_t)0x2d263596, (q31_t)0x2cc815ee, (q31_t)0x2c69daa6, (q31_t)0x2c0b83fa, + (q31_t)0x2bad1221, (q31_t)0x2b4e8558, + (q31_t)0x2aefddd8, (q31_t)0x2a911bdc, (q31_t)0x2a323f9e, (q31_t)0x29d34958, (q31_t)0x29743946, (q31_t)0x29150fa1, + (q31_t)0x28b5cca5, (q31_t)0x2856708d, + (q31_t)0x27f6fb92, (q31_t)0x27976df1, (q31_t)0x2737c7e3, (q31_t)0x26d809a5, (q31_t)0x26783370, (q31_t)0x26184581, + (q31_t)0x25b84012, (q31_t)0x2558235f, + (q31_t)0x24f7efa2, (q31_t)0x2497a517, (q31_t)0x243743fa, (q31_t)0x23d6cc87, (q31_t)0x23763ef7, (q31_t)0x23159b88, + (q31_t)0x22b4e274, (q31_t)0x225413f8, + (q31_t)0x21f3304f, (q31_t)0x219237b5, (q31_t)0x21312a65, (q31_t)0x20d0089c, (q31_t)0x206ed295, (q31_t)0x200d888d, + (q31_t)0x1fac2abf, (q31_t)0x1f4ab968, + (q31_t)0x1ee934c3, (q31_t)0x1e879d0d, (q31_t)0x1e25f282, (q31_t)0x1dc4355e, (q31_t)0x1d6265dd, (q31_t)0x1d00843d, + (q31_t)0x1c9e90b8, (q31_t)0x1c3c8b8c, + (q31_t)0x1bda74f6, (q31_t)0x1b784d30, (q31_t)0x1b161479, (q31_t)0x1ab3cb0d, (q31_t)0x1a517128, (q31_t)0x19ef0707, + (q31_t)0x198c8ce7, (q31_t)0x192a0304, + (q31_t)0x18c7699b, (q31_t)0x1864c0ea, (q31_t)0x1802092c, (q31_t)0x179f429f, (q31_t)0x173c6d80, (q31_t)0x16d98a0c, + (q31_t)0x1676987f, (q31_t)0x16139918, + (q31_t)0x15b08c12, (q31_t)0x154d71aa, (q31_t)0x14ea4a1f, (q31_t)0x148715ae, (q31_t)0x1423d492, (q31_t)0x13c0870a, + (q31_t)0x135d2d53, (q31_t)0x12f9c7aa, + (q31_t)0x1296564d, (q31_t)0x1232d979, (q31_t)0x11cf516a, (q31_t)0x116bbe60, (q31_t)0x11082096, (q31_t)0x10a4784b, + (q31_t)0x1040c5bb, (q31_t)0xfdd0926, + (q31_t)0xf7942c7, (q31_t)0xf1572dc, (q31_t)0xeb199a4, (q31_t)0xe4db75b, (q31_t)0xde9cc40, (q31_t)0xd85d88f, (q31_t)0xd21dc87, + (q31_t)0xcbdd865, + (q31_t)0xc59cc68, (q31_t)0xbf5b8cb, (q31_t)0xb919dcf, (q31_t)0xb2d7baf, (q31_t)0xac952aa, (q31_t)0xa6522fe, (q31_t)0xa00ece8, + (q31_t)0x99cb0a7, + (q31_t)0x9386e78, (q31_t)0x8d42699, (q31_t)0x86fd947, (q31_t)0x80b86c2, (q31_t)0x7a72f45, (q31_t)0x742d311, (q31_t)0x6de7262, + (q31_t)0x67a0d76, + (q31_t)0x615a48b, (q31_t)0x5b137df, (q31_t)0x54cc7b1, (q31_t)0x4e8543e, (q31_t)0x483ddc3, (q31_t)0x41f6480, (q31_t)0x3bae8b2, + (q31_t)0x3566a96, + (q31_t)0x2f1ea6c, (q31_t)0x28d6870, (q31_t)0x228e4e2, (q31_t)0x1c45ffe, (q31_t)0x15fda03, (q31_t)0xfb5330, (q31_t)0x96cbc1, + (q31_t)0x3243f5 +}; + +static const q31_t cos_factorsQ31_2048[2048] = { + (q31_t)0x7fffff62, (q31_t)0x7ffffa73, (q31_t)0x7ffff094, (q31_t)0x7fffe1c6, (q31_t)0x7fffce09, (q31_t)0x7fffb55c, + (q31_t)0x7fff97c1, (q31_t)0x7fff7536, + (q31_t)0x7fff4dbb, (q31_t)0x7fff2151, (q31_t)0x7ffeeff8, (q31_t)0x7ffeb9b0, (q31_t)0x7ffe7e79, (q31_t)0x7ffe3e52, + (q31_t)0x7ffdf93c, (q31_t)0x7ffdaf37, + (q31_t)0x7ffd6042, (q31_t)0x7ffd0c5f, (q31_t)0x7ffcb38c, (q31_t)0x7ffc55ca, (q31_t)0x7ffbf319, (q31_t)0x7ffb8b78, + (q31_t)0x7ffb1ee9, (q31_t)0x7ffaad6a, + (q31_t)0x7ffa36fc, (q31_t)0x7ff9bba0, (q31_t)0x7ff93b54, (q31_t)0x7ff8b619, (q31_t)0x7ff82bef, (q31_t)0x7ff79cd6, + (q31_t)0x7ff708ce, (q31_t)0x7ff66fd7, + (q31_t)0x7ff5d1f1, (q31_t)0x7ff52f1d, (q31_t)0x7ff48759, (q31_t)0x7ff3daa6, (q31_t)0x7ff32905, (q31_t)0x7ff27275, + (q31_t)0x7ff1b6f6, (q31_t)0x7ff0f688, + (q31_t)0x7ff0312c, (q31_t)0x7fef66e1, (q31_t)0x7fee97a7, (q31_t)0x7fedc37e, (q31_t)0x7fecea67, (q31_t)0x7fec0c62, + (q31_t)0x7feb296d, (q31_t)0x7fea418b, + (q31_t)0x7fe954ba, (q31_t)0x7fe862fa, (q31_t)0x7fe76c4c, (q31_t)0x7fe670b0, (q31_t)0x7fe57025, (q31_t)0x7fe46aac, + (q31_t)0x7fe36045, (q31_t)0x7fe250ef, + (q31_t)0x7fe13cac, (q31_t)0x7fe0237a, (q31_t)0x7fdf055a, (q31_t)0x7fdde24d, (q31_t)0x7fdcba51, (q31_t)0x7fdb8d67, + (q31_t)0x7fda5b8f, (q31_t)0x7fd924ca, + (q31_t)0x7fd7e917, (q31_t)0x7fd6a875, (q31_t)0x7fd562e7, (q31_t)0x7fd4186a, (q31_t)0x7fd2c900, (q31_t)0x7fd174a8, + (q31_t)0x7fd01b63, (q31_t)0x7fcebd31, + (q31_t)0x7fcd5a11, (q31_t)0x7fcbf203, (q31_t)0x7fca8508, (q31_t)0x7fc91320, (q31_t)0x7fc79c4b, (q31_t)0x7fc62089, + (q31_t)0x7fc49fda, (q31_t)0x7fc31a3d, + (q31_t)0x7fc18fb4, (q31_t)0x7fc0003e, (q31_t)0x7fbe6bdb, (q31_t)0x7fbcd28b, (q31_t)0x7fbb344e, (q31_t)0x7fb99125, + (q31_t)0x7fb7e90f, (q31_t)0x7fb63c0d, + (q31_t)0x7fb48a1e, (q31_t)0x7fb2d343, (q31_t)0x7fb1177b, (q31_t)0x7faf56c7, (q31_t)0x7fad9127, (q31_t)0x7fabc69b, + (q31_t)0x7fa9f723, (q31_t)0x7fa822bf, + (q31_t)0x7fa6496e, (q31_t)0x7fa46b32, (q31_t)0x7fa2880b, (q31_t)0x7fa09ff7, (q31_t)0x7f9eb2f8, (q31_t)0x7f9cc10d, + (q31_t)0x7f9aca37, (q31_t)0x7f98ce76, + (q31_t)0x7f96cdc9, (q31_t)0x7f94c831, (q31_t)0x7f92bdad, (q31_t)0x7f90ae3f, (q31_t)0x7f8e99e6, (q31_t)0x7f8c80a1, + (q31_t)0x7f8a6272, (q31_t)0x7f883f58, + (q31_t)0x7f861753, (q31_t)0x7f83ea64, (q31_t)0x7f81b88a, (q31_t)0x7f7f81c6, (q31_t)0x7f7d4617, (q31_t)0x7f7b057e, + (q31_t)0x7f78bffb, (q31_t)0x7f76758e, + (q31_t)0x7f742637, (q31_t)0x7f71d1f6, (q31_t)0x7f6f78cb, (q31_t)0x7f6d1ab6, (q31_t)0x7f6ab7b8, (q31_t)0x7f684fd0, + (q31_t)0x7f65e2ff, (q31_t)0x7f637144, + (q31_t)0x7f60faa0, (q31_t)0x7f5e7f13, (q31_t)0x7f5bfe9d, (q31_t)0x7f59793e, (q31_t)0x7f56eef5, (q31_t)0x7f545fc5, + (q31_t)0x7f51cbab, (q31_t)0x7f4f32a9, + (q31_t)0x7f4c94be, (q31_t)0x7f49f1eb, (q31_t)0x7f474a30, (q31_t)0x7f449d8c, (q31_t)0x7f41ec01, (q31_t)0x7f3f358d, + (q31_t)0x7f3c7a31, (q31_t)0x7f39b9ee, + (q31_t)0x7f36f4c3, (q31_t)0x7f342ab1, (q31_t)0x7f315bb7, (q31_t)0x7f2e87d6, (q31_t)0x7f2baf0d, (q31_t)0x7f28d15d, + (q31_t)0x7f25eec7, (q31_t)0x7f230749, + (q31_t)0x7f201ae5, (q31_t)0x7f1d299a, (q31_t)0x7f1a3368, (q31_t)0x7f173850, (q31_t)0x7f143852, (q31_t)0x7f11336d, + (q31_t)0x7f0e29a3, (q31_t)0x7f0b1af2, + (q31_t)0x7f08075c, (q31_t)0x7f04eedf, (q31_t)0x7f01d17d, (q31_t)0x7efeaf36, (q31_t)0x7efb8809, (q31_t)0x7ef85bf7, + (q31_t)0x7ef52b00, (q31_t)0x7ef1f524, + (q31_t)0x7eeeba62, (q31_t)0x7eeb7abc, (q31_t)0x7ee83632, (q31_t)0x7ee4ecc3, (q31_t)0x7ee19e6f, (q31_t)0x7ede4b38, + (q31_t)0x7edaf31c, (q31_t)0x7ed7961c, + (q31_t)0x7ed43438, (q31_t)0x7ed0cd70, (q31_t)0x7ecd61c5, (q31_t)0x7ec9f137, (q31_t)0x7ec67bc5, (q31_t)0x7ec3016f, + (q31_t)0x7ebf8237, (q31_t)0x7ebbfe1c, + (q31_t)0x7eb8751e, (q31_t)0x7eb4e73d, (q31_t)0x7eb1547a, (q31_t)0x7eadbcd4, (q31_t)0x7eaa204c, (q31_t)0x7ea67ee2, + (q31_t)0x7ea2d896, (q31_t)0x7e9f2d68, + (q31_t)0x7e9b7d58, (q31_t)0x7e97c867, (q31_t)0x7e940e94, (q31_t)0x7e904fe0, (q31_t)0x7e8c8c4b, (q31_t)0x7e88c3d5, + (q31_t)0x7e84f67e, (q31_t)0x7e812447, + (q31_t)0x7e7d4d2f, (q31_t)0x7e797136, (q31_t)0x7e75905d, (q31_t)0x7e71aaa4, (q31_t)0x7e6dc00c, (q31_t)0x7e69d093, + (q31_t)0x7e65dc3b, (q31_t)0x7e61e303, + (q31_t)0x7e5de4ec, (q31_t)0x7e59e1f5, (q31_t)0x7e55da20, (q31_t)0x7e51cd6c, (q31_t)0x7e4dbbd9, (q31_t)0x7e49a567, + (q31_t)0x7e458a17, (q31_t)0x7e4169e9, + (q31_t)0x7e3d44dd, (q31_t)0x7e391af3, (q31_t)0x7e34ec2b, (q31_t)0x7e30b885, (q31_t)0x7e2c8002, (q31_t)0x7e2842a2, + (q31_t)0x7e240064, (q31_t)0x7e1fb94a, + (q31_t)0x7e1b6d53, (q31_t)0x7e171c7f, (q31_t)0x7e12c6ce, (q31_t)0x7e0e6c42, (q31_t)0x7e0a0cd9, (q31_t)0x7e05a894, + (q31_t)0x7e013f74, (q31_t)0x7dfcd178, + (q31_t)0x7df85ea0, (q31_t)0x7df3e6ee, (q31_t)0x7def6a60, (q31_t)0x7deae8f7, (q31_t)0x7de662b3, (q31_t)0x7de1d795, + (q31_t)0x7ddd479d, (q31_t)0x7dd8b2ca, + (q31_t)0x7dd4191d, (q31_t)0x7dcf7a96, (q31_t)0x7dcad736, (q31_t)0x7dc62efc, (q31_t)0x7dc181e8, (q31_t)0x7dbccffc, + (q31_t)0x7db81936, (q31_t)0x7db35d98, + (q31_t)0x7dae9d21, (q31_t)0x7da9d7d2, (q31_t)0x7da50dab, (q31_t)0x7da03eab, (q31_t)0x7d9b6ad3, (q31_t)0x7d969224, + (q31_t)0x7d91b49e, (q31_t)0x7d8cd240, + (q31_t)0x7d87eb0a, (q31_t)0x7d82fefe, (q31_t)0x7d7e0e1c, (q31_t)0x7d791862, (q31_t)0x7d741dd2, (q31_t)0x7d6f1e6c, + (q31_t)0x7d6a1a31, (q31_t)0x7d65111f, + (q31_t)0x7d600338, (q31_t)0x7d5af07b, (q31_t)0x7d55d8e9, (q31_t)0x7d50bc82, (q31_t)0x7d4b9b46, (q31_t)0x7d467536, + (q31_t)0x7d414a51, (q31_t)0x7d3c1a98, + (q31_t)0x7d36e60b, (q31_t)0x7d31acaa, (q31_t)0x7d2c6e76, (q31_t)0x7d272b6e, (q31_t)0x7d21e393, (q31_t)0x7d1c96e5, + (q31_t)0x7d174564, (q31_t)0x7d11ef11, + (q31_t)0x7d0c93eb, (q31_t)0x7d0733f3, (q31_t)0x7d01cf29, (q31_t)0x7cfc658d, (q31_t)0x7cf6f720, (q31_t)0x7cf183e1, + (q31_t)0x7cec0bd1, (q31_t)0x7ce68ef0, + (q31_t)0x7ce10d3f, (q31_t)0x7cdb86bd, (q31_t)0x7cd5fb6a, (q31_t)0x7cd06b48, (q31_t)0x7ccad656, (q31_t)0x7cc53c94, + (q31_t)0x7cbf9e03, (q31_t)0x7cb9faa2, + (q31_t)0x7cb45272, (q31_t)0x7caea574, (q31_t)0x7ca8f3a7, (q31_t)0x7ca33d0c, (q31_t)0x7c9d81a3, (q31_t)0x7c97c16b, + (q31_t)0x7c91fc66, (q31_t)0x7c8c3294, + (q31_t)0x7c8663f4, (q31_t)0x7c809088, (q31_t)0x7c7ab84e, (q31_t)0x7c74db48, (q31_t)0x7c6ef976, (q31_t)0x7c6912d7, + (q31_t)0x7c63276d, (q31_t)0x7c5d3737, + (q31_t)0x7c574236, (q31_t)0x7c514869, (q31_t)0x7c4b49d2, (q31_t)0x7c45466f, (q31_t)0x7c3f3e42, (q31_t)0x7c39314b, + (q31_t)0x7c331f8a, (q31_t)0x7c2d08ff, + (q31_t)0x7c26edab, (q31_t)0x7c20cd8d, (q31_t)0x7c1aa8a6, (q31_t)0x7c147ef6, (q31_t)0x7c0e507e, (q31_t)0x7c081d3d, + (q31_t)0x7c01e534, (q31_t)0x7bfba863, + (q31_t)0x7bf566cb, (q31_t)0x7bef206b, (q31_t)0x7be8d544, (q31_t)0x7be28556, (q31_t)0x7bdc30a1, (q31_t)0x7bd5d726, + (q31_t)0x7bcf78e5, (q31_t)0x7bc915dd, + (q31_t)0x7bc2ae10, (q31_t)0x7bbc417e, (q31_t)0x7bb5d026, (q31_t)0x7baf5a09, (q31_t)0x7ba8df28, (q31_t)0x7ba25f82, + (q31_t)0x7b9bdb18, (q31_t)0x7b9551ea, + (q31_t)0x7b8ec3f8, (q31_t)0x7b883143, (q31_t)0x7b8199ca, (q31_t)0x7b7afd8f, (q31_t)0x7b745c91, (q31_t)0x7b6db6d0, + (q31_t)0x7b670c4d, (q31_t)0x7b605d09, + (q31_t)0x7b59a902, (q31_t)0x7b52f03a, (q31_t)0x7b4c32b1, (q31_t)0x7b457068, (q31_t)0x7b3ea95d, (q31_t)0x7b37dd92, + (q31_t)0x7b310d07, (q31_t)0x7b2a37bc, + (q31_t)0x7b235db2, (q31_t)0x7b1c7ee8, (q31_t)0x7b159b5f, (q31_t)0x7b0eb318, (q31_t)0x7b07c612, (q31_t)0x7b00d44d, + (q31_t)0x7af9ddcb, (q31_t)0x7af2e28b, + (q31_t)0x7aebe28d, (q31_t)0x7ae4ddd2, (q31_t)0x7addd45b, (q31_t)0x7ad6c626, (q31_t)0x7acfb336, (q31_t)0x7ac89b89, + (q31_t)0x7ac17f20, (q31_t)0x7aba5dfc, + (q31_t)0x7ab3381d, (q31_t)0x7aac0d82, (q31_t)0x7aa4de2d, (q31_t)0x7a9daa1d, (q31_t)0x7a967153, 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(q31_t)0x25dc44d9, (q31_t)0x25c44207, (q31_t)0x25ac3dc0, (q31_t)0x25943806, (q31_t)0x257c30d8, (q31_t)0x25642839, + (q31_t)0x254c1e28, (q31_t)0x253412a8, + (q31_t)0x251c05b8, (q31_t)0x2503f75a, (q31_t)0x24ebe78f, (q31_t)0x24d3d657, (q31_t)0x24bbc3b4, (q31_t)0x24a3afa6, + (q31_t)0x248b9a2f, (q31_t)0x2473834f, + (q31_t)0x245b6b07, (q31_t)0x24435158, (q31_t)0x242b3644, (q31_t)0x241319ca, (q31_t)0x23fafbec, (q31_t)0x23e2dcac, + (q31_t)0x23cabc09, (q31_t)0x23b29a05, + (q31_t)0x239a76a0, (q31_t)0x238251dd, (q31_t)0x236a2bba, (q31_t)0x2352043b, (q31_t)0x2339db5e, (q31_t)0x2321b126, + (q31_t)0x23098593, (q31_t)0x22f158a7, + (q31_t)0x22d92a61, (q31_t)0x22c0fac4, (q31_t)0x22a8c9cf, (q31_t)0x22909785, (q31_t)0x227863e5, (q31_t)0x22602ef1, + (q31_t)0x2247f8aa, (q31_t)0x222fc111, + (q31_t)0x22178826, (q31_t)0x21ff4dea, (q31_t)0x21e71260, (q31_t)0x21ced586, (q31_t)0x21b6975f, (q31_t)0x219e57eb, + (q31_t)0x2186172b, (q31_t)0x216dd521, + (q31_t)0x215591cc, (q31_t)0x213d4d2f, (q31_t)0x21250749, (q31_t)0x210cc01d, (q31_t)0x20f477aa, (q31_t)0x20dc2df2, + (q31_t)0x20c3e2f5, (q31_t)0x20ab96b5, + (q31_t)0x20934933, (q31_t)0x207afa6f, (q31_t)0x2062aa6b, (q31_t)0x204a5927, (q31_t)0x203206a4, (q31_t)0x2019b2e4, + (q31_t)0x20015de7, (q31_t)0x1fe907ae, + (q31_t)0x1fd0b03a, (q31_t)0x1fb8578b, (q31_t)0x1f9ffda4, (q31_t)0x1f87a285, (q31_t)0x1f6f462f, (q31_t)0x1f56e8a2, + (q31_t)0x1f3e89e0, (q31_t)0x1f2629ea, + (q31_t)0x1f0dc8c0, (q31_t)0x1ef56664, (q31_t)0x1edd02d6, (q31_t)0x1ec49e17, (q31_t)0x1eac3829, (q31_t)0x1e93d10c, + (q31_t)0x1e7b68c2, (q31_t)0x1e62ff4a, + (q31_t)0x1e4a94a7, (q31_t)0x1e3228d9, (q31_t)0x1e19bbe0, (q31_t)0x1e014dbf, (q31_t)0x1de8de75, (q31_t)0x1dd06e04, + (q31_t)0x1db7fc6d, (q31_t)0x1d9f89b1, + (q31_t)0x1d8715d0, (q31_t)0x1d6ea0cc, (q31_t)0x1d562aa6, (q31_t)0x1d3db35e, (q31_t)0x1d253af5, (q31_t)0x1d0cc16c, + (q31_t)0x1cf446c5, (q31_t)0x1cdbcb00, + (q31_t)0x1cc34e1f, (q31_t)0x1caad021, (q31_t)0x1c925109, (q31_t)0x1c79d0d6, (q31_t)0x1c614f8b, (q31_t)0x1c48cd27, + (q31_t)0x1c3049ac, (q31_t)0x1c17c51b, + (q31_t)0x1bff3f75, (q31_t)0x1be6b8ba, (q31_t)0x1bce30ec, (q31_t)0x1bb5a80c, (q31_t)0x1b9d1e1a, (q31_t)0x1b849317, + (q31_t)0x1b6c0705, (q31_t)0x1b5379e5, + (q31_t)0x1b3aebb6, (q31_t)0x1b225c7b, (q31_t)0x1b09cc34, (q31_t)0x1af13ae3, (q31_t)0x1ad8a887, (q31_t)0x1ac01522, + (q31_t)0x1aa780b6, (q31_t)0x1a8eeb42, + (q31_t)0x1a7654c8, (q31_t)0x1a5dbd49, (q31_t)0x1a4524c6, (q31_t)0x1a2c8b3f, (q31_t)0x1a13f0b6, (q31_t)0x19fb552c, + (q31_t)0x19e2b8a2, (q31_t)0x19ca1b17, + (q31_t)0x19b17c8f, (q31_t)0x1998dd09, (q31_t)0x19803c86, (q31_t)0x19679b07, (q31_t)0x194ef88e, (q31_t)0x1936551b, + (q31_t)0x191db0af, (q31_t)0x19050b4b, + (q31_t)0x18ec64f0, (q31_t)0x18d3bda0, (q31_t)0x18bb155a, (q31_t)0x18a26c20, (q31_t)0x1889c1f3, (q31_t)0x187116d4, + (q31_t)0x18586ac3, (q31_t)0x183fbdc3, + (q31_t)0x18270fd3, (q31_t)0x180e60f4, (q31_t)0x17f5b129, (q31_t)0x17dd0070, (q31_t)0x17c44ecd, (q31_t)0x17ab9c3e, + (q31_t)0x1792e8c6, (q31_t)0x177a3466, + (q31_t)0x17617f1d, (q31_t)0x1748c8ee, (q31_t)0x173011d9, (q31_t)0x171759df, (q31_t)0x16fea102, (q31_t)0x16e5e741, + (q31_t)0x16cd2c9f, (q31_t)0x16b4711b, + (q31_t)0x169bb4b7, (q31_t)0x1682f774, (q31_t)0x166a3953, (q31_t)0x16517a55, (q31_t)0x1638ba7a, (q31_t)0x161ff9c4, + (q31_t)0x16073834, (q31_t)0x15ee75cb, + (q31_t)0x15d5b288, (q31_t)0x15bcee6f, (q31_t)0x15a4297f, (q31_t)0x158b63b9, (q31_t)0x15729d1f, (q31_t)0x1559d5b1, + (q31_t)0x15410d70, (q31_t)0x1528445d, + (q31_t)0x150f7a7a, (q31_t)0x14f6afc7, (q31_t)0x14dde445, (q31_t)0x14c517f4, (q31_t)0x14ac4ad7, (q31_t)0x14937cee, + (q31_t)0x147aae3a, (q31_t)0x1461debc, + (q31_t)0x14490e74, (q31_t)0x14303d65, (q31_t)0x14176b8e, (q31_t)0x13fe98f1, (q31_t)0x13e5c58e, (q31_t)0x13ccf167, + (q31_t)0x13b41c7d, (q31_t)0x139b46d0, + (q31_t)0x13827062, (q31_t)0x13699933, (q31_t)0x1350c144, (q31_t)0x1337e897, (q31_t)0x131f0f2c, (q31_t)0x13063505, + (q31_t)0x12ed5a21, (q31_t)0x12d47e83, + (q31_t)0x12bba22b, (q31_t)0x12a2c51b, (q31_t)0x1289e752, (q31_t)0x127108d2, (q31_t)0x1258299c, (q31_t)0x123f49b2, + (q31_t)0x12266913, (q31_t)0x120d87c1, + (q31_t)0x11f4a5bd, (q31_t)0x11dbc307, (q31_t)0x11c2dfa2, (q31_t)0x11a9fb8d, (q31_t)0x119116c9, (q31_t)0x11783159, + (q31_t)0x115f4b3c, (q31_t)0x11466473, + (q31_t)0x112d7d00, (q31_t)0x111494e4, (q31_t)0x10fbac1e, (q31_t)0x10e2c2b2, (q31_t)0x10c9d89e, (q31_t)0x10b0ede5, + (q31_t)0x10980287, (q31_t)0x107f1686, + (q31_t)0x106629e1, (q31_t)0x104d3c9b, (q31_t)0x10344eb4, (q31_t)0x101b602d, (q31_t)0x10027107, (q31_t)0xfe98143, + (q31_t)0xfd090e1, (q31_t)0xfb79fe4, + (q31_t)0xf9eae4c, (q31_t)0xf85bc19, (q31_t)0xf6cc94e, (q31_t)0xf53d5ea, (q31_t)0xf3ae1ee, (q31_t)0xf21ed5d, (q31_t)0xf08f836, + (q31_t)0xef0027b, + (q31_t)0xed70c2c, (q31_t)0xebe154b, (q31_t)0xea51dd8, (q31_t)0xe8c25d5, (q31_t)0xe732d42, (q31_t)0xe5a3421, (q31_t)0xe413a72, + (q31_t)0xe284036, + (q31_t)0xe0f456f, (q31_t)0xdf64a1c, (q31_t)0xddd4e40, (q31_t)0xdc451dc, (q31_t)0xdab54ef, (q31_t)0xd92577b, (q31_t)0xd795982, + (q31_t)0xd605b03, + (q31_t)0xd475c00, (q31_t)0xd2e5c7b, (q31_t)0xd155c73, (q31_t)0xcfc5bea, (q31_t)0xce35ae1, (q31_t)0xcca5959, (q31_t)0xcb15752, + (q31_t)0xc9854cf, + (q31_t)0xc7f51cf, (q31_t)0xc664e53, (q31_t)0xc4d4a5d, (q31_t)0xc3445ee, (q31_t)0xc1b4107, (q31_t)0xc023ba7, (q31_t)0xbe935d2, + (q31_t)0xbd02f87, + (q31_t)0xbb728c7, (q31_t)0xb9e2193, (q31_t)0xb8519ed, (q31_t)0xb6c11d5, (q31_t)0xb53094d, (q31_t)0xb3a0055, (q31_t)0xb20f6ee, + (q31_t)0xb07ed19, + (q31_t)0xaeee2d7, (q31_t)0xad5d829, (q31_t)0xabccd11, (q31_t)0xaa3c18e, (q31_t)0xa8ab5a2, (q31_t)0xa71a94f, (q31_t)0xa589c94, + (q31_t)0xa3f8f73, + (q31_t)0xa2681ed, (q31_t)0xa0d7403, (q31_t)0x9f465b5, (q31_t)0x9db5706, (q31_t)0x9c247f5, (q31_t)0x9a93884, (q31_t)0x99028b3, + (q31_t)0x9771884, + (q31_t)0x95e07f8, (q31_t)0x944f70f, (q31_t)0x92be5ca, (q31_t)0x912d42c, (q31_t)0x8f9c233, (q31_t)0x8e0afe2, (q31_t)0x8c79d3a, + (q31_t)0x8ae8a3a, + (q31_t)0x89576e5, (q31_t)0x87c633c, (q31_t)0x8634f3e, (q31_t)0x84a3aee, (q31_t)0x831264c, (q31_t)0x8181159, (q31_t)0x7fefc16, + (q31_t)0x7e5e685, + (q31_t)0x7ccd0a5, (q31_t)0x7b3ba78, (q31_t)0x79aa400, (q31_t)0x7818d3c, (q31_t)0x768762e, (q31_t)0x74f5ed7, (q31_t)0x7364738, + (q31_t)0x71d2f52, + (q31_t)0x7041726, (q31_t)0x6eafeb4, (q31_t)0x6d1e5fe, (q31_t)0x6b8cd05, (q31_t)0x69fb3c9, (q31_t)0x6869a4c, (q31_t)0x66d808f, + (q31_t)0x6546692, + (q31_t)0x63b4c57, (q31_t)0x62231de, (q31_t)0x6091729, (q31_t)0x5effc38, (q31_t)0x5d6e10c, (q31_t)0x5bdc5a7, (q31_t)0x5a4aa09, + (q31_t)0x58b8e34, + (q31_t)0x5727228, (q31_t)0x55955e6, (q31_t)0x540396f, (q31_t)0x5271cc4, (q31_t)0x50dffe7, (q31_t)0x4f4e2d8, (q31_t)0x4dbc597, + (q31_t)0x4c2a827, + (q31_t)0x4a98a88, (q31_t)0x4906cbb, (q31_t)0x4774ec1, (q31_t)0x45e309a, (q31_t)0x4451249, (q31_t)0x42bf3cd, (q31_t)0x412d528, + (q31_t)0x3f9b65b, + (q31_t)0x3e09767, (q31_t)0x3c7784d, (q31_t)0x3ae590d, (q31_t)0x39539a9, (q31_t)0x37c1a22, (q31_t)0x362fa78, (q31_t)0x349daac, + (q31_t)0x330bac1, + (q31_t)0x3179ab5, (q31_t)0x2fe7a8c, (q31_t)0x2e55a44, (q31_t)0x2cc39e1, (q31_t)0x2b31961, (q31_t)0x299f8c7, (q31_t)0x280d813, + (q31_t)0x267b747, + (q31_t)0x24e9662, (q31_t)0x2357567, (q31_t)0x21c5457, (q31_t)0x2033331, (q31_t)0x1ea11f7, (q31_t)0x1d0f0ab, (q31_t)0x1b7cf4d, + (q31_t)0x19eaddd, + (q31_t)0x1858c5e, (q31_t)0x16c6ad0, (q31_t)0x1534934, (q31_t)0x13a278a, (q31_t)0x12105d5, (q31_t)0x107e414, (q31_t)0xeec249, + (q31_t)0xd5a075, + (q31_t)0xbc7e99, (q31_t)0xa35cb5, (q31_t)0x8a3acb, (q31_t)0x7118dc, (q31_t)0x57f6e9, (q31_t)0x3ed4f2, (q31_t)0x25b2f8, + (q31_t)0xc90fe +}; + +static const q31_t cos_factorsQ31_8192[8192] = { + (q31_t)0x7ffffff6, (q31_t)0x7fffffa7, (q31_t)0x7fffff09, (q31_t)0x7ffffe1c, (q31_t)0x7ffffce1, (q31_t)0x7ffffb56, + (q31_t)0x7ffff97c, (q31_t)0x7ffff753, + (q31_t)0x7ffff4dc, (q31_t)0x7ffff215, (q31_t)0x7fffef00, (q31_t)0x7fffeb9b, (q31_t)0x7fffe7e8, (q31_t)0x7fffe3e5, + (q31_t)0x7fffdf94, (q31_t)0x7fffdaf3, + (q31_t)0x7fffd604, (q31_t)0x7fffd0c6, (q31_t)0x7fffcb39, (q31_t)0x7fffc55c, (q31_t)0x7fffbf31, (q31_t)0x7fffb8b7, + (q31_t)0x7fffb1ee, (q31_t)0x7fffaad6, + (q31_t)0x7fffa36f, (q31_t)0x7fff9bb9, (q31_t)0x7fff93b4, (q31_t)0x7fff8b61, (q31_t)0x7fff82be, (q31_t)0x7fff79cc, + (q31_t)0x7fff708b, (q31_t)0x7fff66fc, + (q31_t)0x7fff5d1d, (q31_t)0x7fff52ef, (q31_t)0x7fff4873, (q31_t)0x7fff3da8, (q31_t)0x7fff328d, (q31_t)0x7fff2724, + (q31_t)0x7fff1b6b, (q31_t)0x7fff0f64, + (q31_t)0x7fff030e, (q31_t)0x7ffef669, (q31_t)0x7ffee975, (q31_t)0x7ffedc31, (q31_t)0x7ffece9f, (q31_t)0x7ffec0be, + (q31_t)0x7ffeb28e, (q31_t)0x7ffea40f, + (q31_t)0x7ffe9542, (q31_t)0x7ffe8625, (q31_t)0x7ffe76b9, (q31_t)0x7ffe66fe, (q31_t)0x7ffe56f5, (q31_t)0x7ffe469c, + (q31_t)0x7ffe35f4, (q31_t)0x7ffe24fe, + (q31_t)0x7ffe13b8, (q31_t)0x7ffe0224, (q31_t)0x7ffdf040, (q31_t)0x7ffdde0e, (q31_t)0x7ffdcb8d, (q31_t)0x7ffdb8bc, + (q31_t)0x7ffda59d, (q31_t)0x7ffd922f, + (q31_t)0x7ffd7e72, (q31_t)0x7ffd6a66, (q31_t)0x7ffd560b, (q31_t)0x7ffd4161, (q31_t)0x7ffd2c68, (q31_t)0x7ffd1720, + (q31_t)0x7ffd0189, (q31_t)0x7ffceba4, + (q31_t)0x7ffcd56f, (q31_t)0x7ffcbeeb, (q31_t)0x7ffca819, (q31_t)0x7ffc90f7, (q31_t)0x7ffc7987, (q31_t)0x7ffc61c7, + (q31_t)0x7ffc49b9, (q31_t)0x7ffc315b, + (q31_t)0x7ffc18af, (q31_t)0x7ffbffb4, (q31_t)0x7ffbe66a, (q31_t)0x7ffbccd0, (q31_t)0x7ffbb2e8, (q31_t)0x7ffb98b1, + (q31_t)0x7ffb7e2b, (q31_t)0x7ffb6356, + (q31_t)0x7ffb4833, (q31_t)0x7ffb2cc0, (q31_t)0x7ffb10fe, (q31_t)0x7ffaf4ed, (q31_t)0x7ffad88e, (q31_t)0x7ffabbdf, + (q31_t)0x7ffa9ee2, (q31_t)0x7ffa8195, + (q31_t)0x7ffa63fa, (q31_t)0x7ffa460f, (q31_t)0x7ffa27d6, (q31_t)0x7ffa094e, (q31_t)0x7ff9ea76, (q31_t)0x7ff9cb50, + (q31_t)0x7ff9abdb, (q31_t)0x7ff98c17, + (q31_t)0x7ff96c04, (q31_t)0x7ff94ba2, (q31_t)0x7ff92af1, (q31_t)0x7ff909f2, (q31_t)0x7ff8e8a3, (q31_t)0x7ff8c705, + (q31_t)0x7ff8a519, (q31_t)0x7ff882dd, + (q31_t)0x7ff86053, (q31_t)0x7ff83d79, (q31_t)0x7ff81a51, (q31_t)0x7ff7f6da, (q31_t)0x7ff7d313, (q31_t)0x7ff7aefe, + (q31_t)0x7ff78a9a, (q31_t)0x7ff765e7, + (q31_t)0x7ff740e5, (q31_t)0x7ff71b94, (q31_t)0x7ff6f5f4, (q31_t)0x7ff6d005, (q31_t)0x7ff6a9c8, (q31_t)0x7ff6833b, + (q31_t)0x7ff65c5f, (q31_t)0x7ff63535, + (q31_t)0x7ff60dbb, (q31_t)0x7ff5e5f3, (q31_t)0x7ff5bddc, (q31_t)0x7ff59576, (q31_t)0x7ff56cc0, (q31_t)0x7ff543bc, + (q31_t)0x7ff51a69, (q31_t)0x7ff4f0c7, + (q31_t)0x7ff4c6d6, (q31_t)0x7ff49c96, (q31_t)0x7ff47208, (q31_t)0x7ff4472a, (q31_t)0x7ff41bfd, (q31_t)0x7ff3f082, + (q31_t)0x7ff3c4b7, (q31_t)0x7ff3989e, + (q31_t)0x7ff36c36, (q31_t)0x7ff33f7e, (q31_t)0x7ff31278, (q31_t)0x7ff2e523, (q31_t)0x7ff2b77f, (q31_t)0x7ff2898c, + (q31_t)0x7ff25b4a, (q31_t)0x7ff22cb9, + (q31_t)0x7ff1fdd9, (q31_t)0x7ff1ceab, (q31_t)0x7ff19f2d, (q31_t)0x7ff16f61, (q31_t)0x7ff13f45, (q31_t)0x7ff10edb, + (q31_t)0x7ff0de22, (q31_t)0x7ff0ad19, + (q31_t)0x7ff07bc2, (q31_t)0x7ff04a1c, (q31_t)0x7ff01827, (q31_t)0x7fefe5e4, (q31_t)0x7fefb351, (q31_t)0x7fef806f, + (q31_t)0x7fef4d3e, (q31_t)0x7fef19bf, + (q31_t)0x7feee5f0, (q31_t)0x7feeb1d3, (q31_t)0x7fee7d67, (q31_t)0x7fee48ac, (q31_t)0x7fee13a1, (q31_t)0x7fedde48, + (q31_t)0x7feda8a0, 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(q31_t)0x8925475, (q31_t)0x88c0f90, (q31_t)0x885caa5, (q31_t)0x87f85b5, (q31_t)0x87940c1, + (q31_t)0x872fbc6, + (q31_t)0x86cb6c7, (q31_t)0x86671c2, (q31_t)0x8602cb9, (q31_t)0x859e7aa, (q31_t)0x853a296, (q31_t)0x84d5d7d, (q31_t)0x847185e, + (q31_t)0x840d33b, + (q31_t)0x83a8e12, (q31_t)0x83448e5, (q31_t)0x82e03b2, (q31_t)0x827be7a, (q31_t)0x821793e, (q31_t)0x81b33fc, (q31_t)0x814eeb5, + (q31_t)0x80ea969, + (q31_t)0x8086419, (q31_t)0x8021ec3, (q31_t)0x7fbd968, (q31_t)0x7f59409, (q31_t)0x7ef4ea4, (q31_t)0x7e9093b, (q31_t)0x7e2c3cd, + (q31_t)0x7dc7e5a, + (q31_t)0x7d638e2, (q31_t)0x7cff365, (q31_t)0x7c9ade4, (q31_t)0x7c3685d, (q31_t)0x7bd22d2, (q31_t)0x7b6dd42, (q31_t)0x7b097ad, + (q31_t)0x7aa5214, + (q31_t)0x7a40c76, (q31_t)0x79dc6d3, (q31_t)0x797812b, (q31_t)0x7913b7f, (q31_t)0x78af5ce, (q31_t)0x784b019, (q31_t)0x77e6a5e, + (q31_t)0x77824a0, + (q31_t)0x771dedc, (q31_t)0x76b9914, (q31_t)0x7655347, (q31_t)0x75f0d76, (q31_t)0x758c7a1, (q31_t)0x75281c6, (q31_t)0x74c3be7, + (q31_t)0x745f604, + (q31_t)0x73fb01c, (q31_t)0x7396a30, (q31_t)0x733243f, (q31_t)0x72cde4a, (q31_t)0x7269851, (q31_t)0x7205253, (q31_t)0x71a0c50, + (q31_t)0x713c64a, + (q31_t)0x70d803f, (q31_t)0x7073a2f, (q31_t)0x700f41b, (q31_t)0x6faae03, (q31_t)0x6f467e7, (q31_t)0x6ee21c6, (q31_t)0x6e7dba1, + (q31_t)0x6e19578, + (q31_t)0x6db4f4a, (q31_t)0x6d50919, (q31_t)0x6cec2e3, (q31_t)0x6c87ca9, (q31_t)0x6c2366a, (q31_t)0x6bbf028, (q31_t)0x6b5a9e1, + (q31_t)0x6af6396, + (q31_t)0x6a91d47, (q31_t)0x6a2d6f4, (q31_t)0x69c909d, (q31_t)0x6964a42, (q31_t)0x69003e3, (q31_t)0x689bd80, (q31_t)0x6837718, + (q31_t)0x67d30ad, + (q31_t)0x676ea3d, (q31_t)0x670a3ca, (q31_t)0x66a5d53, (q31_t)0x66416d8, (q31_t)0x65dd058, (q31_t)0x65789d5, (q31_t)0x651434e, + (q31_t)0x64afcc3, + (q31_t)0x644b634, (q31_t)0x63e6fa2, (q31_t)0x638290b, (q31_t)0x631e271, (q31_t)0x62b9bd3, (q31_t)0x6255531, (q31_t)0x61f0e8b, + (q31_t)0x618c7e1, + (q31_t)0x6128134, (q31_t)0x60c3a83, (q31_t)0x605f3ce, (q31_t)0x5ffad15, (q31_t)0x5f96659, (q31_t)0x5f31f99, (q31_t)0x5ecd8d6, + (q31_t)0x5e6920e, + (q31_t)0x5e04b43, (q31_t)0x5da0475, (q31_t)0x5d3bda3, (q31_t)0x5cd76cd, (q31_t)0x5c72ff4, (q31_t)0x5c0e917, (q31_t)0x5baa237, + (q31_t)0x5b45b53, + (q31_t)0x5ae146b, (q31_t)0x5a7cd80, (q31_t)0x5a18692, (q31_t)0x59b3fa0, (q31_t)0x594f8aa, (q31_t)0x58eb1b2, (q31_t)0x5886ab5, + (q31_t)0x58223b6, + (q31_t)0x57bdcb3, (q31_t)0x57595ac, (q31_t)0x56f4ea2, (q31_t)0x5690795, (q31_t)0x562c085, (q31_t)0x55c7971, (q31_t)0x556325a, + (q31_t)0x54feb3f, + (q31_t)0x549a422, (q31_t)0x5435d01, (q31_t)0x53d15dd, (q31_t)0x536ceb5, (q31_t)0x530878a, (q31_t)0x52a405d, (q31_t)0x523f92c, + (q31_t)0x51db1f7, + (q31_t)0x5176ac0, (q31_t)0x5112385, (q31_t)0x50adc48, (q31_t)0x5049507, (q31_t)0x4fe4dc3, (q31_t)0x4f8067c, (q31_t)0x4f1bf32, + (q31_t)0x4eb77e5, + (q31_t)0x4e53095, (q31_t)0x4dee942, (q31_t)0x4d8a1ec, (q31_t)0x4d25a93, (q31_t)0x4cc1337, (q31_t)0x4c5cbd8, (q31_t)0x4bf8476, + (q31_t)0x4b93d11, + (q31_t)0x4b2f5a9, (q31_t)0x4acae3e, (q31_t)0x4a666d1, (q31_t)0x4a01f60, (q31_t)0x499d7ed, (q31_t)0x4939077, (q31_t)0x48d48fe, + (q31_t)0x4870182, + (q31_t)0x480ba04, (q31_t)0x47a7282, (q31_t)0x4742afe, (q31_t)0x46de377, (q31_t)0x4679bee, (q31_t)0x4615461, (q31_t)0x45b0cd2, + (q31_t)0x454c541, + (q31_t)0x44e7dac, (q31_t)0x4483615, (q31_t)0x441ee7c, (q31_t)0x43ba6df, (q31_t)0x4355f40, (q31_t)0x42f179f, (q31_t)0x428cffb, + (q31_t)0x4228854, + (q31_t)0x41c40ab, (q31_t)0x415f8ff, (q31_t)0x40fb151, (q31_t)0x40969a0, (q31_t)0x40321ed, (q31_t)0x3fcda37, (q31_t)0x3f6927f, + (q31_t)0x3f04ac4, + (q31_t)0x3ea0307, (q31_t)0x3e3bb48, (q31_t)0x3dd7386, (q31_t)0x3d72bc2, (q31_t)0x3d0e3fb, (q31_t)0x3ca9c32, (q31_t)0x3c45467, + (q31_t)0x3be0c99, + (q31_t)0x3b7c4c9, (q31_t)0x3b17cf7, (q31_t)0x3ab3523, (q31_t)0x3a4ed4c, (q31_t)0x39ea573, (q31_t)0x3985d97, (q31_t)0x39215ba, + (q31_t)0x38bcdda, + (q31_t)0x38585f8, (q31_t)0x37f3e14, (q31_t)0x378f62e, (q31_t)0x372ae46, (q31_t)0x36c665b, (q31_t)0x3661e6f, (q31_t)0x35fd680, + (q31_t)0x3598e8f, + (q31_t)0x353469c, (q31_t)0x34cfea8, (q31_t)0x346b6b1, (q31_t)0x3406eb8, (q31_t)0x33a26bd, (q31_t)0x333dec0, (q31_t)0x32d96c1, + (q31_t)0x3274ec0, + (q31_t)0x32106bd, (q31_t)0x31abeb9, (q31_t)0x31476b2, (q31_t)0x30e2ea9, (q31_t)0x307e69f, (q31_t)0x3019e93, (q31_t)0x2fb5684, + (q31_t)0x2f50e74, + (q31_t)0x2eec663, (q31_t)0x2e87e4f, (q31_t)0x2e2363a, (q31_t)0x2dbee22, (q31_t)0x2d5a609, (q31_t)0x2cf5def, (q31_t)0x2c915d2, + (q31_t)0x2c2cdb4, + (q31_t)0x2bc8594, (q31_t)0x2b63d73, (q31_t)0x2aff54f, (q31_t)0x2a9ad2a, (q31_t)0x2a36504, (q31_t)0x29d1cdc, (q31_t)0x296d4b2, + (q31_t)0x2908c87, + (q31_t)0x28a445a, (q31_t)0x283fc2b, (q31_t)0x27db3fb, (q31_t)0x2776bc9, (q31_t)0x2712396, (q31_t)0x26adb62, (q31_t)0x264932b, + (q31_t)0x25e4af4, + (q31_t)0x25802bb, (q31_t)0x251ba80, (q31_t)0x24b7244, (q31_t)0x2452a07, (q31_t)0x23ee1c8, (q31_t)0x2389988, (q31_t)0x2325147, + (q31_t)0x22c0904, + (q31_t)0x225c0bf, (q31_t)0x21f787a, (q31_t)0x2193033, (q31_t)0x212e7eb, (q31_t)0x20c9fa1, (q31_t)0x2065757, (q31_t)0x2000f0b, + (q31_t)0x1f9c6be, + (q31_t)0x1f37e6f, (q31_t)0x1ed3620, (q31_t)0x1e6edcf, (q31_t)0x1e0a57d, (q31_t)0x1da5d2a, (q31_t)0x1d414d6, (q31_t)0x1cdcc80, + (q31_t)0x1c7842a, + (q31_t)0x1c13bd2, (q31_t)0x1baf37a, (q31_t)0x1b4ab20, (q31_t)0x1ae62c5, (q31_t)0x1a81a69, (q31_t)0x1a1d20c, (q31_t)0x19b89ae, + (q31_t)0x1954150, + (q31_t)0x18ef8f0, (q31_t)0x188b08f, (q31_t)0x182682d, (q31_t)0x17c1fcb, (q31_t)0x175d767, (q31_t)0x16f8f03, (q31_t)0x169469d, + (q31_t)0x162fe37, + (q31_t)0x15cb5d0, (q31_t)0x1566d68, (q31_t)0x15024ff, (q31_t)0x149dc96, (q31_t)0x143942b, (q31_t)0x13d4bc0, (q31_t)0x1370354, + (q31_t)0x130bae7, + (q31_t)0x12a727a, (q31_t)0x1242a0c, (q31_t)0x11de19d, (q31_t)0x117992e, (q31_t)0x11150be, (q31_t)0x10b084d, (q31_t)0x104bfdb, + (q31_t)0xfe7769, + (q31_t)0xf82ef6, (q31_t)0xf1e683, (q31_t)0xeb9e0f, (q31_t)0xe5559b, (q31_t)0xdf0d26, (q31_t)0xd8c4b0, (q31_t)0xd27c3a, + (q31_t)0xcc33c3, + (q31_t)0xc5eb4c, (q31_t)0xbfa2d5, (q31_t)0xb95a5d, (q31_t)0xb311e4, (q31_t)0xacc96b, (q31_t)0xa680f2, (q31_t)0xa03878, + (q31_t)0x99effe, + (q31_t)0x93a784, (q31_t)0x8d5f09, (q31_t)0x87168e, (q31_t)0x80ce12, (q31_t)0x7a8597, (q31_t)0x743d1a, (q31_t)0x6df49e, + (q31_t)0x67ac21, + (q31_t)0x6163a5, (q31_t)0x5b1b27, (q31_t)0x54d2aa, (q31_t)0x4e8a2c, (q31_t)0x4841af, (q31_t)0x41f931, (q31_t)0x3bb0b3, + (q31_t)0x356835, + (q31_t)0x2f1fb6, (q31_t)0x28d738, (q31_t)0x228eb9, (q31_t)0x1c463b, (q31_t)0x15fdbc, (q31_t)0xfb53d, (q31_t)0x96cbe, (q31_t)0x3243f +}; + +/** + * @} end of DCT4_IDCT4_Table group + */ + +/** + * @addtogroup DCT4_IDCT4 + * @{ + */ + +/** + * @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 <code>N</code> is not a supported transform length. + * \par Normalizing factor: + * The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>. + * Normalizing factors in 1.31 format are mentioned in the table below for different DCT sizes: + * \image html dct4NormalizingQ31Table.gif + */ + +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) +{ + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initializing the pointer array with the weight table base addresses of different lengths */ + q31_t *twiddlePtr[4] = { (q31_t *) WeightsQ31_128, (q31_t *) WeightsQ31_512, + (q31_t *) WeightsQ31_2048, (q31_t *) WeightsQ31_8192 + }; + + /* Initializing the pointer array with the cos factor table base addresses of different lengths */ + q31_t *pCosFactor[4] = + { (q31_t *) cos_factorsQ31_128, (q31_t *) cos_factorsQ31_512, + (q31_t *) cos_factorsQ31_2048, (q31_t *) cos_factorsQ31_8192 + }; + + /* Initialize the DCT4 length */ + S->N = N; + + /* Initialize the half of DCT4 length */ + S->Nby2 = Nby2; + + /* Initialize the DCT4 Normalizing factor */ + S->normalize = normalize; + + /* Initialize Real FFT Instance */ + S->pRfft = S_RFFT; + + /* Initialize Complex FFT Instance */ + S->pCfft = S_CFFT; + + switch (N) + { + /* Initialize the table modifier values */ + case 8192U: + S->pTwiddle = twiddlePtr[3]; + S->pCosFactor = pCosFactor[3]; + break; + case 2048U: + S->pTwiddle = twiddlePtr[2]; + S->pCosFactor = pCosFactor[2]; + break; + case 512U: + S->pTwiddle = twiddlePtr[1]; + S->pCosFactor = pCosFactor[1]; + break; + case 128U: + S->pTwiddle = twiddlePtr[0]; + S->pCosFactor = pCosFactor[0]; + break; + default: + status = ARM_MATH_ARGUMENT_ERROR; + } + + /* Initialize the RFFT/RIFFT Function */ + arm_rfft_init_q31(S->pRfft, S->N, 0, 1); + + /* return the status of DCT4 Init function */ + return (status); +} + +/** + * @} end of DCT4_IDCT4 group + */ diff --git a/DSP/Source/TransformFunctions/arm_dct4_q15.c b/DSP/Source/TransformFunctions/arm_dct4_q15.c new file mode 100644 index 0000000..918f0bd --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_dct4_q15.c @@ -0,0 +1,382 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_dct4_q15.c + * Description: Processing function of DCT4 & IDCT4 Q15 + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @addtogroup DCT4_IDCT4 + * @{ + */ + +/** + * @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. + * @return none. + * + * \par Input an output formats: + * Internally inputs are downscaled in the RFFT process function to avoid overflows. + * Number of bits downscaled, depends on the size of the transform. + * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below: + * + * \image html dct4FormatsQ15Table.gif + */ + +void arm_dct4_q15( + const arm_dct4_instance_q15 * S, + q15_t * pState, + q15_t * pInlineBuffer) +{ + uint32_t i; /* Loop counter */ + q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */ + q15_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ + q15_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ + q15_t in; /* Temporary variable */ + + + /* DCT4 computation involves DCT2 (which is calculated using RFFT) + * along with some pre-processing and post-processing. + * Computational procedure is explained as follows: + * (a) Pre-processing involves multiplying input with cos factor, + * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n)) + * where, + * r(n) -- output of preprocessing + * u(n) -- input to preprocessing(actual Source buffer) + * (b) Calculation of DCT2 using FFT is divided into three steps: + * Step1: Re-ordering of even and odd elements of input. + * Step2: Calculating FFT of the re-ordered input. + * Step3: Taking the real part of the product of FFT output and weights. + * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation: + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * where, + * Y4 -- DCT4 output, Y2 -- DCT2 output + * (d) Multiplying the output with the normalizing factor sqrt(2/N). + */ + + /*-------- Pre-processing ------------*/ + /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ + arm_mult_q15(pInlineBuffer, cosFact, pInlineBuffer, S->N); + arm_shift_q15(pInlineBuffer, 1, pInlineBuffer, S->N); + + /* ---------------------------------------------------------------- + * Step1: Re-ordering of even and odd elements as + * pState[i] = pInlineBuffer[2*i] and + * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2 + ---------------------------------------------------------------------*/ + + /* pS1 initialized to pState */ + pS1 = pState; + + /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ + pS2 = pState + (S->N - 1U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ + i = (uint32_t) S->Nby2 >> 2U; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + do + { + /* Re-ordering of even and odd elements */ + /* pState[i] = pInlineBuffer[2*i] */ + *pS1++ = *pbuff++; + /* pState[N-i-1] = pInlineBuffer[2*i+1] */ + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Initializing the loop counter to N/4 instead of N for loop unrolling */ + i = (uint32_t) S->N >> 2U; + + /* Processing with loop unrolling 4 times as N is always multiple of 4. + * Compute 4 outputs at a time */ + do + { + /* Writing the re-ordered output back to inplace input buffer */ + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /* --------------------------------------------------------- + * Step2: Calculate RFFT for N-point input + * ---------------------------------------------------------- */ + /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ + arm_rfft_q15(S->pRfft, pInlineBuffer, pState); + + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N); + + /* The output of complex multiplication is in 3.13 format. + * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */ + arm_shift_q15(pState, 2, pState, S->N * 2); + + /* ----------- Post-processing ---------- */ + /* DCT-IV can be obtained from DCT-II by the equation, + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * Hence, Y4(0) = Y2(0)/2 */ + /* Getting only real part from the output and Converting to DCT-IV */ + + /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ + i = ((uint32_t) S->N - 1U) >> 2U; + + /* pbuff initialized to input buffer. */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ + in = *pS1++ >> 1U; + /* input buffer acts as inplace, so output values are stored in the input itself. */ + *pbuff++ = in; + + /* pState pointer is incremented twice as the real values are located alternatively in the array */ + pS1++; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + do + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + i = ((uint32_t) S->N - 1U) % 0x4U; + + while (i > 0U) + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + /* Decrement the loop counter */ + i--; + } + + + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + + /* Initializing the loop counter to N/4 instead of N for loop unrolling */ + i = (uint32_t) S->N >> 2U; + + /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + pbuff = pInlineBuffer; + + /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */ + do + { + /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ + in = *pbuff; + *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); + + in = *pbuff; + *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); + + in = *pbuff; + *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); + + in = *pbuff; + *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initializing the loop counter to N/2 */ + i = (uint32_t) S->Nby2; + + do + { + /* Re-ordering of even and odd elements */ + /* pState[i] = pInlineBuffer[2*i] */ + *pS1++ = *pbuff++; + /* pState[N-i-1] = pInlineBuffer[2*i+1] */ + *pS2-- = *pbuff++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Initializing the loop counter */ + i = (uint32_t) S->N; + + do + { + /* Writing the re-ordered output back to inplace input buffer */ + *pbuff++ = *pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /* --------------------------------------------------------- + * Step2: Calculate RFFT for N-point input + * ---------------------------------------------------------- */ + /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ + arm_rfft_q15(S->pRfft, pInlineBuffer, pState); + + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N); + + /* The output of complex multiplication is in 3.13 format. + * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */ + arm_shift_q15(pState, 2, pState, S->N * 2); + + /* ----------- Post-processing ---------- */ + /* DCT-IV can be obtained from DCT-II by the equation, + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * Hence, Y4(0) = Y2(0)/2 */ + /* Getting only real part from the output and Converting to DCT-IV */ + + /* Initializing the loop counter */ + i = ((uint32_t) S->N - 1U); + + /* pbuff initialized to input buffer. */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ + in = *pS1++ >> 1U; + /* input buffer acts as inplace, so output values are stored in the input itself. */ + *pbuff++ = in; + + /* pState pointer is incremented twice as the real values are located alternatively in the array */ + pS1++; + + do + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + + /* Initializing the loop counter */ + i = (uint32_t) S->N; + + /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + pbuff = pInlineBuffer; + + do + { + /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ + in = *pbuff; + *pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + +/** + * @} end of DCT4_IDCT4 group + */ diff --git a/DSP/Source/TransformFunctions/arm_dct4_q31.c b/DSP/Source/TransformFunctions/arm_dct4_q31.c new file mode 100644 index 0000000..0569778 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_dct4_q31.c @@ -0,0 +1,383 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_dct4_q31.c + * Description: Processing function of DCT4 & IDCT4 Q31 + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @addtogroup DCT4_IDCT4 + * @{ + */ + +/** + * @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. + * @return none. + * \par Input an output formats: + * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process, + * as the conversion from DCT2 to DCT4 involves one subtraction. + * Internally inputs are downscaled in the RFFT process function to avoid overflows. + * Number of bits downscaled, depends on the size of the transform. + * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below: + * + * \image html dct4FormatsQ31Table.gif + */ + +void arm_dct4_q31( + const arm_dct4_instance_q31 * S, + q31_t * pState, + q31_t * pInlineBuffer) +{ + uint16_t i; /* Loop counter */ + q31_t *weights = S->pTwiddle; /* Pointer to the Weights table */ + q31_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ + q31_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ + q31_t in; /* Temporary variable */ + + + /* DCT4 computation involves DCT2 (which is calculated using RFFT) + * along with some pre-processing and post-processing. + * Computational procedure is explained as follows: + * (a) Pre-processing involves multiplying input with cos factor, + * r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n)) + * where, + * r(n) -- output of preprocessing + * u(n) -- input to preprocessing(actual Source buffer) + * (b) Calculation of DCT2 using FFT is divided into three steps: + * Step1: Re-ordering of even and odd elements of input. + * Step2: Calculating FFT of the re-ordered input. + * Step3: Taking the real part of the product of FFT output and weights. + * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation: + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * where, + * Y4 -- DCT4 output, Y2 -- DCT2 output + * (d) Multiplying the output with the normalizing factor sqrt(2/N). + */ + + /*-------- Pre-processing ------------*/ + /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ + arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N); + arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N); + + /* ---------------------------------------------------------------- + * Step1: Re-ordering of even and odd elements as + * pState[i] = pInlineBuffer[2*i] and + * pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2 + ---------------------------------------------------------------------*/ + + /* pS1 initialized to pState */ + pS1 = pState; + + /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ + pS2 = pState + (S->N - 1U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ + i = S->Nby2 >> 2U; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + do + { + /* Re-ordering of even and odd elements */ + /* pState[i] = pInlineBuffer[2*i] */ + *pS1++ = *pbuff++; + /* pState[N-i-1] = pInlineBuffer[2*i+1] */ + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + *pS1++ = *pbuff++; + *pS2-- = *pbuff++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Initializing the loop counter to N/4 instead of N for loop unrolling */ + i = S->N >> 2U; + + /* Processing with loop unrolling 4 times as N is always multiple of 4. + * Compute 4 outputs at a time */ + do + { + /* Writing the re-ordered output back to inplace input buffer */ + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + *pbuff++ = *pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /* --------------------------------------------------------- + * Step2: Calculate RFFT for N-point input + * ---------------------------------------------------------- */ + /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ + arm_rfft_q31(S->pRfft, pInlineBuffer, pState); + + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); + + /* The output of complex multiplication is in 3.29 format. + * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ + arm_shift_q31(pState, 2, pState, S->N * 2); + + /* ----------- Post-processing ---------- */ + /* DCT-IV can be obtained from DCT-II by the equation, + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * Hence, Y4(0) = Y2(0)/2 */ + /* Getting only real part from the output and Converting to DCT-IV */ + + /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ + i = (S->N - 1U) >> 2U; + + /* pbuff initialized to input buffer. */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ + in = *pS1++ >> 1U; + /* input buffer acts as inplace, so output values are stored in the input itself. */ + *pbuff++ = in; + + /* pState pointer is incremented twice as the real values are located alternatively in the array */ + pS1++; + + /* First part of the processing with loop unrolling. Compute 4 outputs at a time. + ** a second loop below computes the remaining 1 to 3 samples. */ + do + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + in = *pS1++ - in; + *pbuff++ = in; + pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* If the blockSize is not a multiple of 4, compute any remaining output samples here. + ** No loop unrolling is used. */ + i = (S->N - 1U) % 0x4U; + + while (i > 0U) + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + /* Decrement the loop counter */ + i--; + } + + + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + + /* Initializing the loop counter to N/4 instead of N for loop unrolling */ + i = S->N >> 2U; + + /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + pbuff = pInlineBuffer; + + /* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */ + do + { + /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ + in = *pbuff; + *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); + + in = *pbuff; + *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); + + in = *pbuff; + *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); + + in = *pbuff; + *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + +#else + + /* Run the below code for Cortex-M0 */ + + /* Initializing the loop counter to N/2 */ + i = S->Nby2; + + do + { + /* Re-ordering of even and odd elements */ + /* pState[i] = pInlineBuffer[2*i] */ + *pS1++ = *pbuff++; + /* pState[N-i-1] = pInlineBuffer[2*i+1] */ + *pS2-- = *pbuff++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + /* pbuff initialized to input buffer */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Initializing the loop counter */ + i = S->N; + + do + { + /* Writing the re-ordered output back to inplace input buffer */ + *pbuff++ = *pS1++; + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + + + /* --------------------------------------------------------- + * Step2: Calculate RFFT for N-point input + * ---------------------------------------------------------- */ + /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ + arm_rfft_q31(S->pRfft, pInlineBuffer, pState); + + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); + + /* The output of complex multiplication is in 3.29 format. + * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ + arm_shift_q31(pState, 2, pState, S->N * 2); + + /* ----------- Post-processing ---------- */ + /* DCT-IV can be obtained from DCT-II by the equation, + * Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0) + * Hence, Y4(0) = Y2(0)/2 */ + /* Getting only real part from the output and Converting to DCT-IV */ + + /* pbuff initialized to input buffer. */ + pbuff = pInlineBuffer; + + /* pS1 initialized to pState */ + pS1 = pState; + + /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ + in = *pS1++ >> 1U; + /* input buffer acts as inplace, so output values are stored in the input itself. */ + *pbuff++ = in; + + /* pState pointer is incremented twice as the real values are located alternatively in the array */ + pS1++; + + /* Initializing the loop counter */ + i = (S->N - 1U); + + while (i > 0U) + { + /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ + /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ + in = *pS1++ - in; + *pbuff++ = in; + /* points to the next real value */ + pS1++; + + /* Decrement the loop counter */ + i--; + } + + + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + + /* Initializing the loop counter */ + i = S->N; + + /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + pbuff = pInlineBuffer; + + do + { + /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ + in = *pbuff; + *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); + + /* Decrement the loop counter */ + i--; + } while (i > 0U); + +#endif /* #if defined (ARM_MATH_DSP) */ + +} + +/** + * @} end of DCT4_IDCT4 group + */ diff --git a/DSP/Source/TransformFunctions/arm_rfft_f32.c b/DSP/Source/TransformFunctions/arm_rfft_f32.c new file mode 100644 index 0000000..a1bd81b --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_f32.c @@ -0,0 +1,318 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_f32.c + * Description: RFFT & RIFFT Floating point process function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/* ---------------------------------------------------------------------- + * Internal functions prototypes + * -------------------------------------------------------------------- */ + +extern void arm_radix4_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + float32_t * pCoef, + uint16_t twidCoefModifier); + +extern void arm_radix4_butterfly_inverse_f32( + float32_t * pSrc, + uint16_t fftLen, + float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen); + +extern void arm_bitreversal_f32( + float32_t * pSrc, + uint16_t fftSize, + uint16_t bitRevFactor, + uint16_t * pBitRevTab); + +void arm_split_rfft_f32( + float32_t * pSrc, + uint32_t fftLen, + float32_t * pATable, + float32_t * pBTable, + float32_t * pDst, + uint32_t modifier); + +void arm_split_rifft_f32( + float32_t * pSrc, + uint32_t fftLen, + float32_t * pATable, + float32_t * pBTable, + float32_t * pDst, + uint32_t modifier); + +/** +* @ingroup groupTransforms +*/ + +/** + * @addtogroup RealFFT + * @{ + */ + +/** + * @brief Processing function for the floating-point RFFT/RIFFT. + * @deprecated Do not use this function. It has been superceded by \ref arm_rfft_fast_f32 and will be removed + * in the future. + * @param[in] *S points to an instance of the floating-point RFFT/RIFFT structure. + * @param[in] *pSrc points to the input buffer. + * @param[out] *pDst points to the output buffer. + * @return none. + */ + +void arm_rfft_f32( + const arm_rfft_instance_f32 * S, + float32_t * pSrc, + float32_t * pDst) +{ + const arm_cfft_radix4_instance_f32 *S_CFFT = S->pCfft; + + + /* Calculation of Real IFFT of input */ + if (S->ifftFlagR == 1U) + { + /* Real IFFT core process */ + arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal, + S->pTwiddleBReal, pDst, S->twidCoefRModifier); + + + /* Complex radix-4 IFFT process */ + arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen, + S_CFFT->pTwiddle, + S_CFFT->twidCoefModifier, + S_CFFT->onebyfftLen); + + /* Bit reversal process */ + if (S->bitReverseFlagR == 1U) + { + arm_bitreversal_f32(pDst, S_CFFT->fftLen, + S_CFFT->bitRevFactor, S_CFFT->pBitRevTable); + } + } + else + { + + /* Calculation of RFFT of input */ + + /* Complex radix-4 FFT process */ + arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen, + S_CFFT->pTwiddle, S_CFFT->twidCoefModifier); + + /* Bit reversal process */ + if (S->bitReverseFlagR == 1U) + { + arm_bitreversal_f32(pSrc, S_CFFT->fftLen, + S_CFFT->bitRevFactor, S_CFFT->pBitRevTable); + } + + + /* Real FFT core process */ + arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal, + S->pTwiddleBReal, pDst, S->twidCoefRModifier); + } + +} + +/** + * @} end of RealFFT group + */ + +/** + * @brief Core Real FFT process + * @param[in] *pSrc points to the input buffer. + * @param[in] fftLen length of FFT. + * @param[in] *pATable points to the twiddle Coef A buffer. + * @param[in] *pBTable points to the twiddle Coef B buffer. + * @param[out] *pDst points to the output buffer. + * @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + * @return none. + */ + +void arm_split_rfft_f32( + float32_t * pSrc, + uint32_t fftLen, + float32_t * pATable, + float32_t * pBTable, + float32_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + float32_t outR, outI; /* Temporary variables for output */ + float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */ + float32_t *pDst1 = &pDst[2], *pDst2 = &pDst[(4U * fftLen) - 1U]; /* temp pointers for output buffer */ + float32_t *pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2U * fftLen) - 1U]; /* temp pointers for input buffer */ + + /* Init coefficient pointers */ + pCoefA = &pATable[modifier * 2U]; + pCoefB = &pBTable[modifier * 2U]; + + 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]); */ + + /* read pATable[2 * i] */ + CoefA1 = *pCoefA++; + /* pATable[2 * i + 1] */ + CoefA2 = *pCoefA; + + /* pSrc[2 * i] * pATable[2 * i] */ + outR = *pSrc1 * CoefA1; + /* pSrc[2 * i] * CoefA2 */ + outI = *pSrc1++ * CoefA2; + + /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */ + outR -= (*pSrc1 + *pSrc2) * CoefA2; + /* pSrc[2 * i + 1] * CoefA1 */ + outI += *pSrc1++ * CoefA1; + + CoefB1 = *pCoefB; + + /* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */ + outI -= *pSrc2-- * CoefB1; + /* pSrc[2 * fftLen - 2 * i] * CoefA2 */ + outI -= *pSrc2 * CoefA2; + + /* pSrc[2 * fftLen - 2 * i] * CoefB1 */ + outR += *pSrc2-- * CoefB1; + + /* write output */ + *pDst1++ = outR; + *pDst1++ = outI; + + /* write complex conjugate output */ + *pDst2-- = -outI; + *pDst2-- = outR; + + /* update coefficient pointer */ + pCoefB = pCoefB + (modifier * 2U); + pCoefA = pCoefA + ((modifier * 2U) - 1U); + + i--; + + } + + pDst[2U * fftLen] = pSrc[0] - pSrc[1]; + pDst[(2U * fftLen) + 1U] = 0.0f; + + pDst[0] = pSrc[0] + pSrc[1]; + pDst[1] = 0.0f; + +} + + +/** + * @brief Core Real IFFT process + * @param[in] *pSrc points to the input buffer. + * @param[in] fftLen length of FFT. + * @param[in] *pATable points to the twiddle Coef A buffer. + * @param[in] *pBTable points to the twiddle Coef B buffer. + * @param[out] *pDst points to the output buffer. + * @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + * @return none. + */ + +void arm_split_rifft_f32( + float32_t * pSrc, + uint32_t fftLen, + float32_t * pATable, + float32_t * pBTable, + float32_t * pDst, + uint32_t modifier) +{ + float32_t outR, outI; /* Temporary variables for output */ + float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */ + float32_t *pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2U * fftLen) + 1U]; + + 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 = (pSrc[2 * i] * CoefA1 */ + outR = *pSrc1 * CoefA1; + + /* - pSrc[2 * i] * CoefA2 */ + outI = -(*pSrc1++) * CoefA2; + + /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */ + outR += (*pSrc1 + *pSrc2) * CoefA2; + + /* pSrc[2 * i + 1] * CoefA1 */ + outI += (*pSrc1++) * CoefA1; + + CoefB1 = *pCoefB; + + /* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */ + outI -= *pSrc2-- * CoefB1; + + /* pSrc[2 * fftLen - 2 * i] * CoefB1 */ + outR += *pSrc2 * CoefB1; + + /* pSrc[2 * fftLen - 2 * i] * CoefA2 */ + outI += *pSrc2-- * CoefA2; + + /* write output */ + *pDst++ = outR; + *pDst++ = outI; + + /* update coefficient pointer */ + pCoefB = pCoefB + (modifier * 2U); + pCoefA = pCoefA + ((modifier * 2U) - 1U); + + /* Decrement loop count */ + fftLen--; + } + +} diff --git a/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c b/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c new file mode 100644 index 0000000..f7c52e9 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c @@ -0,0 +1,317 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_f32.c + * Description: RFFT & RIFFT Floating point process function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +void stage_rfft_f32( + arm_rfft_fast_instance_f32 * S, + float32_t * p, float32_t * pOut) +{ + uint32_t k; /* Loop Counter */ + float32_t twR, twI; /* RFFT Twiddle coefficients */ + float32_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + float32_t *pA = p; /* increasing pointer */ + 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 > 0U); +} + +/* Prepares data for inverse cfft */ +void merge_rfft_f32( +arm_rfft_fast_instance_f32 * S, +float32_t * p, float32_t * pOut) +{ + uint32_t k; /* Loop Counter */ + float32_t twR, twI; /* RFFT Twiddle coefficients */ + float32_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ + float32_t *pA = p; /* increasing pointer */ + 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 > 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++ = 0.5f * (xAR + xBR - r - s ); //xAR + *pOut++ = 0.5f * (xAI - xBI + t - u ); //xAI + + pA += 2; + pB -= 2; + k--; + } + +} + +/** +* @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 algorith 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. Except the first complex number that contains the two real numbers + * X[0] and X[N/2] all the data is complex. In other words, the first complex sample + * contains two real values packed. + * \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 arm_rfft_fast_f32() and arm_rfft_fast_init_f32(). + * The older functions arm_rfft_f32() and arm_rfft_init_f32() have been + * deprecated but are still documented. + * \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. Looking at the data, we see that we can + * uniquely represent the FFT using only N/2 complex numbers. These are + * packed into the output array in alternating real and imaginary + * components: + * \par + * X = { real[0], imag[0], real[1], imag[1], real[2], imag[2] ... + * real[(N/2)-1], imag[(N/2)-1 } + * \par + * It happens that the first complex number (real[0], imag[0]) is actually + * all real. real[0] represents the DC offset, and imag[0] should be 0. + * (real[1], imag[1]) is the fundamental frequency, (real[2], imag[2]) is + * the first harmonic and so on. + * \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 + * The complex transforms used internally include scaling to prevent fixed-point + * overflows. The overall scaling equals 1/(fftLen/2). + * \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. + * However, if the initialization function is used, then the instance structure + * cannot be placed into a const data section. To place an instance structure + * into a const data section, the instance structure should be manually + * initialized as follows: + * <pre> + *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}; + * </pre> + * where <code>fftLenReal</code> is the length of the real transform; + * <code>fftLenBy2</code> length of the internal complex transform. + * <code>ifftFlagR</code> Selects forward (=0) or inverse (=1) transform. + * <code>bitReverseFlagR</code> Selects bit reversed output (=0) or normal order + * output (=1). + * <code>twidCoefRModifier</code> stride modifier for the twiddle factor table. + * The value is based on the FFT length; + * <code>pTwiddleAReal</code>points to the A array of twiddle coefficients; + * <code>pTwiddleBReal</code>points to the B array of twiddle coefficients; + * <code>pCfft</code> points to the CFFT Instance structure. The CFFT structure + * must also be initialized. Refer to arm_cfft_radix4_f32() for details regarding + * static initialization of the complex FFT instance structure. + */ + +/** +* @addtogroup RealFFT +* @{ +*/ + +/** +* @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 the input buffer. +* @param[in] *pOut points to the output buffer. +* @param[in] ifftFlag RFFT if flag is 0, RIFFT if flag is 1 +* @return none. +*/ + +void arm_rfft_fast_f32( +arm_rfft_fast_instance_f32 * S, +float32_t * p, float32_t * pOut, +uint8_t ifftFlag) +{ + arm_cfft_instance_f32 * Sint = &(S->Sint); + Sint->fftLen = S->fftLenRFFT / 2; + + /* 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); + } +} + +/** +* @} end of RealFFT group +*/ diff --git a/DSP/Source/TransformFunctions/arm_rfft_fast_init_f32.c b/DSP/Source/TransformFunctions/arm_rfft_fast_init_f32.c new file mode 100644 index 0000000..2f8dfe6 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_fast_init_f32.c @@ -0,0 +1,131 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_cfft_init_f32.c + * Description: Split Radix Decimation in Frequency CFFT Floating point processing function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup RealFFT + * @{ + */ + +/** +* @brief 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 The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>fftLen</code> Specifies 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. +*/ +arm_status arm_rfft_fast_init_f32( + arm_rfft_fast_instance_f32 * S, + uint16_t fftLen) +{ + arm_cfft_instance_f32 * Sint; + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + /* Initialise the FFT length */ + Sint = &(S->Sint); + Sint->fftLen = fftLen/2; + S->fftLenRFFT = fftLen; + + /* Initializations of structure parameters depending on the FFT length */ + switch (Sint->fftLen) + { + case 2048U: + /* Initializations of structure parameters for 2048 point FFT */ + /* Initialise the bit reversal table length */ + Sint->bitRevLength = ARMBITREVINDEXTABLE_2048_TABLE_LENGTH; + /* Initialise the bit reversal table pointer */ + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable2048; + /* Initialise the Twiddle coefficient pointers */ + Sint->pTwiddle = (float32_t *) twiddleCoef_2048; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_4096; + break; + case 1024U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_1024_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable1024; + Sint->pTwiddle = (float32_t *) twiddleCoef_1024; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_2048; + break; + case 512U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_512_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable512; + Sint->pTwiddle = (float32_t *) twiddleCoef_512; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_1024; + break; + case 256U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_256_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable256; + Sint->pTwiddle = (float32_t *) twiddleCoef_256; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_512; + break; + case 128U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_128_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable128; + Sint->pTwiddle = (float32_t *) twiddleCoef_128; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_256; + break; + case 64U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_64_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable64; + Sint->pTwiddle = (float32_t *) twiddleCoef_64; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_128; + break; + case 32U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_32_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable32; + Sint->pTwiddle = (float32_t *) twiddleCoef_32; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_64; + break; + case 16U: + Sint->bitRevLength = ARMBITREVINDEXTABLE_16_TABLE_LENGTH; + Sint->pBitRevTable = (uint16_t *)armBitRevIndexTable16; + Sint->pTwiddle = (float32_t *) twiddleCoef_16; + S->pTwiddleRFFT = (float32_t *) twiddleCoef_rfft_32; + break; + default: + /* Reporting argument error if fftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + return (status); +} + +/** + * @} end of RealFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_rfft_init_f32.c b/DSP/Source/TransformFunctions/arm_rfft_init_f32.c new file mode 100644 index 0000000..bb3213a --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_init_f32.c @@ -0,0 +1,4273 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_init_f32.c + * Description: RFFT & RIFFT Floating point initialisation function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/** + * @ingroup RealFFT + */ + +/** + * @addtogroup RealFFT_Table Real FFT Tables + * @{ + */ + +/** +* \par +* Generation of realCoefA array: +* \par +* n = 4096 +* <pre>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)); +* } </pre> +*/ +static const float32_t realCoefA[8192] = { + 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, 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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 +* <pre>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)); +* } </pre> +* +*/ +static const float32_t realCoefB[8192] = { + 0.500000000000000f, 0.500000000000000f, 0.500383496284485f, 0.499999850988388f, + 0.500766992568970f, 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-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, +}; + + + +/** +* @brief Initialization function for the floating-point RFFT/RIFFT. +* @deprecated Do not use this function. It has been superceded by \ref arm_rfft_fast_init_f32 and will be removed +* in the future. +* @param[in,out] *S points to an instance of the floating-point RFFT/RIFFT structure. +* @param[in,out] *S_CFFT points to an instance of the floating-point CFFT/CIFFT structure. +* @param[in] fftLenReal length of the FFT. +* @param[in] ifftFlagR flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>fftLenReal</code> Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048. +* \par +* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. +* \par +* The parameter <code>bitReverseFlag</code> 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. +*/ + +/** +* @} end of RealFFT_Table group +*/ + +/** +* @addtogroup RealFFT +* @{ +*/ + +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) +{ + + /* Initialise the default arm status */ + arm_status status = ARM_MATH_SUCCESS; + + /* Initialize the Real FFT length */ + S->fftLenReal = (uint16_t) fftLenReal; + + /* Initialize the Complex FFT length */ + S->fftLenBy2 = (uint16_t) fftLenReal / 2U; + + /* Initialize the Twiddle coefficientA pointer */ + S->pTwiddleAReal = (float32_t *) realCoefA; + + /* Initialize the Twiddle coefficientB pointer */ + S->pTwiddleBReal = (float32_t *) realCoefB; + + /* 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; + + /* Initializations of structure parameters depending on the FFT length */ + switch (S->fftLenReal) + { + /* Init table modifier value */ + case 8192U: + S->twidCoefRModifier = 1U; + break; + case 2048U: + S->twidCoefRModifier = 4U; + break; + case 512U: + S->twidCoefRModifier = 16U; + break; + case 128U: + S->twidCoefRModifier = 64U; + break; + default: + /* Reporting argument error if rfftSize is not valid value */ + status = ARM_MATH_ARGUMENT_ERROR; + break; + } + + /* Init Complex FFT Instance */ + S->pCfft = S_CFFT; + + if (S->ifftFlagR) + { + /* Initializes the CIFFT Module for fftLenreal/2 length */ + arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 1U, 0U); + } + else + { + /* Initializes the CFFT Module for fftLenreal/2 length */ + arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 0U, 0U); + } + + /* return the status of RFFT Init function */ + return (status); + +} + + /** + * @} end of RealFFT group + */ diff --git a/DSP/Source/TransformFunctions/arm_rfft_init_q15.c b/DSP/Source/TransformFunctions/arm_rfft_init_q15.c new file mode 100644 index 0000000..0e09737 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_init_q15.c @@ -0,0 +1,2229 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_init_q15.c + * Description: RFFT & RIFFT Q15 initialisation function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + +/** +* @ingroup RealFFT +*/ + +/** + * @addtogroup RealFFT_Table Real FFT Tables +* @{ +*/ + +/** +* \par +* Generation fixed-point realCoefAQ15 array in Q15 format: +* \par +* n = 4096 +* <pre>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)); +* } </pre> +* \par +* Convert to fixed point Q15 format +* round(pATable[i] * pow(2, 15)) +*/ +const q15_t ALIGN4 realCoefAQ15[8192] = { + (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, 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(q15_t)0x3424, (q15_t)0x3ee4, (q15_t)0x3430, (q15_t)0x3ee7, (q15_t)0x343d, (q15_t)0x3ee9, + (q15_t)0x3449, (q15_t)0x3eeb, (q15_t)0x3455, (q15_t)0x3eed, (q15_t)0x3462, (q15_t)0x3ef0, (q15_t)0x346e, (q15_t)0x3ef2, + (q15_t)0x347b, (q15_t)0x3ef4, (q15_t)0x3487, (q15_t)0x3ef7, (q15_t)0x3493, (q15_t)0x3ef9, (q15_t)0x34a0, (q15_t)0x3efb, + (q15_t)0x34ac, (q15_t)0x3efd, (q15_t)0x34b8, (q15_t)0x3f00, (q15_t)0x34c5, (q15_t)0x3f02, (q15_t)0x34d1, (q15_t)0x3f04, + (q15_t)0x34dd, (q15_t)0x3f06, (q15_t)0x34ea, (q15_t)0x3f08, (q15_t)0x34f6, (q15_t)0x3f0a, (q15_t)0x3503, (q15_t)0x3f0d, + (q15_t)0x350f, (q15_t)0x3f0f, (q15_t)0x351b, (q15_t)0x3f11, (q15_t)0x3528, (q15_t)0x3f13, (q15_t)0x3534, (q15_t)0x3f15, + (q15_t)0x3540, (q15_t)0x3f17, (q15_t)0x354d, (q15_t)0x3f19, (q15_t)0x3559, (q15_t)0x3f1c, (q15_t)0x3566, (q15_t)0x3f1e, + (q15_t)0x3572, (q15_t)0x3f20, (q15_t)0x357e, (q15_t)0x3f22, (q15_t)0x358b, (q15_t)0x3f24, (q15_t)0x3597, (q15_t)0x3f26, + (q15_t)0x35a4, (q15_t)0x3f28, (q15_t)0x35b0, (q15_t)0x3f2a, (q15_t)0x35bc, (q15_t)0x3f2c, (q15_t)0x35c9, (q15_t)0x3f2e, + (q15_t)0x35d5, (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 +* <pre>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)); +* } </pre> +* \par +* Convert to fixed point Q15 format +* round(pBTable[i] * pow(2, 15)) +* +*/ +const q15_t ALIGN4 realCoefBQ15[8192] = { + (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, (q15_t)0x4620, (q15_t)0x3fb5, (q15_t)0x462d, (q15_t)0x3fb4, (q15_t)0x4639, (q15_t)0x3fb2, + (q15_t)0x4646, (q15_t)0x3fb1, (q15_t)0x4652, (q15_t)0x3fb0, (q15_t)0x465f, (q15_t)0x3faf, (q15_t)0x466b, (q15_t)0x3fad, + (q15_t)0x4678, (q15_t)0x3fac, (q15_t)0x4684, (q15_t)0x3fab, (q15_t)0x4691, (q15_t)0x3faa, (q15_t)0x469d, (q15_t)0x3fa8, + (q15_t)0x46aa, (q15_t)0x3fa7, (q15_t)0x46b6, (q15_t)0x3fa6, (q15_t)0x46c3, (q15_t)0x3fa4, (q15_t)0x46cf, (q15_t)0x3fa3, + (q15_t)0x46dc, (q15_t)0x3fa2, (q15_t)0x46e8, (q15_t)0x3fa0, (q15_t)0x46f5, (q15_t)0x3f9f, (q15_t)0x4701, (q15_t)0x3f9e, + (q15_t)0x470e, (q15_t)0x3f9c, (q15_t)0x471a, (q15_t)0x3f9b, (q15_t)0x4727, (q15_t)0x3f99, (q15_t)0x4733, (q15_t)0x3f98, + (q15_t)0x4740, (q15_t)0x3f97, (q15_t)0x474c, (q15_t)0x3f95, (q15_t)0x4759, (q15_t)0x3f94, (q15_t)0x4765, (q15_t)0x3f92, + (q15_t)0x4772, (q15_t)0x3f91, (q15_t)0x477e, (q15_t)0x3f8f, (q15_t)0x478b, (q15_t)0x3f8e, (q15_t)0x4797, (q15_t)0x3f8c, + (q15_t)0x47a4, (q15_t)0x3f8b, (q15_t)0x47b0, (q15_t)0x3f89, (q15_t)0x47bd, (q15_t)0x3f88, (q15_t)0x47c9, (q15_t)0x3f86, + (q15_t)0x47d6, (q15_t)0x3f85, (q15_t)0x47e2, (q15_t)0x3f83, (q15_t)0x47ef, (q15_t)0x3f82, (q15_t)0x47fb, (q15_t)0x3f80, + (q15_t)0x4807, (q15_t)0x3f7f, (q15_t)0x4814, (q15_t)0x3f7d, (q15_t)0x4820, (q15_t)0x3f7b, (q15_t)0x482d, (q15_t)0x3f7a, + (q15_t)0x4839, (q15_t)0x3f78, (q15_t)0x4846, (q15_t)0x3f77, (q15_t)0x4852, (q15_t)0x3f75, (q15_t)0x485f, (q15_t)0x3f73, + (q15_t)0x486b, (q15_t)0x3f72, (q15_t)0x4878, (q15_t)0x3f70, (q15_t)0x4884, (q15_t)0x3f6e, (q15_t)0x4891, (q15_t)0x3f6d, + (q15_t)0x489d, (q15_t)0x3f6b, (q15_t)0x48a9, (q15_t)0x3f69, (q15_t)0x48b6, (q15_t)0x3f68, (q15_t)0x48c2, (q15_t)0x3f66, + (q15_t)0x48cf, (q15_t)0x3f64, (q15_t)0x48db, (q15_t)0x3f62, (q15_t)0x48e8, (q15_t)0x3f61, (q15_t)0x48f4, (q15_t)0x3f5f, + (q15_t)0x4901, (q15_t)0x3f5d, (q15_t)0x490d, (q15_t)0x3f5b, (q15_t)0x4919, (q15_t)0x3f5a, (q15_t)0x4926, (q15_t)0x3f58, + (q15_t)0x4932, (q15_t)0x3f56, (q15_t)0x493f, (q15_t)0x3f54, (q15_t)0x494b, (q15_t)0x3f52, (q15_t)0x4958, (q15_t)0x3f51, + (q15_t)0x4964, (q15_t)0x3f4f, (q15_t)0x4970, (q15_t)0x3f4d, (q15_t)0x497d, (q15_t)0x3f4b, (q15_t)0x4989, (q15_t)0x3f49, + (q15_t)0x4996, (q15_t)0x3f47, (q15_t)0x49a2, (q15_t)0x3f45, (q15_t)0x49af, (q15_t)0x3f43, (q15_t)0x49bb, (q15_t)0x3f42, + (q15_t)0x49c7, (q15_t)0x3f40, (q15_t)0x49d4, (q15_t)0x3f3e, (q15_t)0x49e0, (q15_t)0x3f3c, (q15_t)0x49ed, (q15_t)0x3f3a, + (q15_t)0x49f9, (q15_t)0x3f38, (q15_t)0x4a06, (q15_t)0x3f36, (q15_t)0x4a12, (q15_t)0x3f34, (q15_t)0x4a1e, (q15_t)0x3f32, + (q15_t)0x4a2b, (q15_t)0x3f30, (q15_t)0x4a37, (q15_t)0x3f2e, (q15_t)0x4a44, (q15_t)0x3f2c, (q15_t)0x4a50, (q15_t)0x3f2a, + (q15_t)0x4a5c, (q15_t)0x3f28, (q15_t)0x4a69, (q15_t)0x3f26, (q15_t)0x4a75, (q15_t)0x3f24, (q15_t)0x4a82, (q15_t)0x3f22, + (q15_t)0x4a8e, (q15_t)0x3f20, (q15_t)0x4a9a, (q15_t)0x3f1e, (q15_t)0x4aa7, (q15_t)0x3f1c, (q15_t)0x4ab3, (q15_t)0x3f19, + (q15_t)0x4ac0, (q15_t)0x3f17, (q15_t)0x4acc, (q15_t)0x3f15, (q15_t)0x4ad8, (q15_t)0x3f13, (q15_t)0x4ae5, (q15_t)0x3f11, + (q15_t)0x4af1, (q15_t)0x3f0f, (q15_t)0x4afd, (q15_t)0x3f0d, (q15_t)0x4b0a, (q15_t)0x3f0a, (q15_t)0x4b16, (q15_t)0x3f08, + (q15_t)0x4b23, (q15_t)0x3f06, (q15_t)0x4b2f, (q15_t)0x3f04, (q15_t)0x4b3b, (q15_t)0x3f02, (q15_t)0x4b48, (q15_t)0x3f00, + (q15_t)0x4b54, (q15_t)0x3efd, (q15_t)0x4b60, (q15_t)0x3efb, (q15_t)0x4b6d, (q15_t)0x3ef9, (q15_t)0x4b79, (q15_t)0x3ef7, + (q15_t)0x4b85, (q15_t)0x3ef4, (q15_t)0x4b92, (q15_t)0x3ef2, (q15_t)0x4b9e, (q15_t)0x3ef0, (q15_t)0x4bab, (q15_t)0x3eed, + (q15_t)0x4bb7, (q15_t)0x3eeb, (q15_t)0x4bc3, (q15_t)0x3ee9, (q15_t)0x4bd0, (q15_t)0x3ee7, (q15_t)0x4bdc, (q15_t)0x3ee4, + (q15_t)0x4be8, (q15_t)0x3ee2, (q15_t)0x4bf5, (q15_t)0x3ee0, (q15_t)0x4c01, (q15_t)0x3edd, (q15_t)0x4c0d, (q15_t)0x3edb, + (q15_t)0x4c1a, (q15_t)0x3ed8, (q15_t)0x4c26, (q15_t)0x3ed6, (q15_t)0x4c32, (q15_t)0x3ed4, (q15_t)0x4c3f, (q15_t)0x3ed1, + (q15_t)0x4c4b, (q15_t)0x3ecf, (q15_t)0x4c57, (q15_t)0x3ecc, (q15_t)0x4c64, (q15_t)0x3eca, (q15_t)0x4c70, (q15_t)0x3ec8, + (q15_t)0x4c7c, (q15_t)0x3ec5, (q15_t)0x4c89, (q15_t)0x3ec3, (q15_t)0x4c95, (q15_t)0x3ec0, (q15_t)0x4ca1, (q15_t)0x3ebe, + (q15_t)0x4cae, (q15_t)0x3ebb, (q15_t)0x4cba, (q15_t)0x3eb9, (q15_t)0x4cc6, (q15_t)0x3eb6, (q15_t)0x4cd3, (q15_t)0x3eb4, + (q15_t)0x4cdf, (q15_t)0x3eb1, (q15_t)0x4ceb, (q15_t)0x3eaf, (q15_t)0x4cf8, (q15_t)0x3eac, (q15_t)0x4d04, (q15_t)0x3eaa, + (q15_t)0x4d10, (q15_t)0x3ea7, (q15_t)0x4d1c, (q15_t)0x3ea5, (q15_t)0x4d29, (q15_t)0x3ea2, (q15_t)0x4d35, (q15_t)0x3e9f, + (q15_t)0x4d41, (q15_t)0x3e9d, (q15_t)0x4d4e, (q15_t)0x3e9a, (q15_t)0x4d5a, (q15_t)0x3e98, (q15_t)0x4d66, (q15_t)0x3e95, + (q15_t)0x4d72, (q15_t)0x3e92, (q15_t)0x4d7f, (q15_t)0x3e90, (q15_t)0x4d8b, (q15_t)0x3e8d, (q15_t)0x4d97, (q15_t)0x3e8a, + (q15_t)0x4da4, (q15_t)0x3e88, (q15_t)0x4db0, (q15_t)0x3e85, (q15_t)0x4dbc, (q15_t)0x3e82, (q15_t)0x4dc8, (q15_t)0x3e80, + (q15_t)0x4dd5, (q15_t)0x3e7d, (q15_t)0x4de1, (q15_t)0x3e7a, (q15_t)0x4ded, (q15_t)0x3e77, (q15_t)0x4df9, (q15_t)0x3e75, + (q15_t)0x4e06, (q15_t)0x3e72, (q15_t)0x4e12, (q15_t)0x3e6f, (q15_t)0x4e1e, (q15_t)0x3e6c, (q15_t)0x4e2b, (q15_t)0x3e6a, + (q15_t)0x4e37, (q15_t)0x3e67, (q15_t)0x4e43, (q15_t)0x3e64, (q15_t)0x4e4f, (q15_t)0x3e61, (q15_t)0x4e5c, (q15_t)0x3e5e, + 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(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 +*/ + +/** +* @addtogroup RealFFT +* @{ +*/ + +/** +* @brief 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 forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>fftLenReal</code> Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192. +* \par +* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. +* \par +* The parameter <code>bitReverseFlag</code> 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. +*/ +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_SUCCESS; + + /* Initialize the Real FFT length */ + S->fftLenReal = (uint16_t) fftLenReal; + + /* 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; + + /* Initialization of coef modifier depending on the FFT length */ + switch (S->fftLenReal) + { + case 8192U: + S->twidCoefRModifier = 1U; + S->pCfft = &arm_cfft_sR_q15_len4096; + break; + case 4096U: + S->twidCoefRModifier = 2U; + S->pCfft = &arm_cfft_sR_q15_len2048; + break; + case 2048U: + S->twidCoefRModifier = 4U; + S->pCfft = &arm_cfft_sR_q15_len1024; + break; + case 1024U: + S->twidCoefRModifier = 8U; + S->pCfft = &arm_cfft_sR_q15_len512; + break; + case 512U: + S->twidCoefRModifier = 16U; + S->pCfft = &arm_cfft_sR_q15_len256; + break; + case 256U: + S->twidCoefRModifier = 32U; + S->pCfft = &arm_cfft_sR_q15_len128; + break; + case 128U: + S->twidCoefRModifier = 64U; + S->pCfft = &arm_cfft_sR_q15_len64; + break; + case 64U: + S->twidCoefRModifier = 128U; + S->pCfft = &arm_cfft_sR_q15_len32; + break; + case 32U: + S->twidCoefRModifier = 256U; + S->pCfft = &arm_cfft_sR_q15_len16; + 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); +} + +/** +* @} end of RealFFT group +*/ diff --git a/DSP/Source/TransformFunctions/arm_rfft_init_q31.c b/DSP/Source/TransformFunctions/arm_rfft_init_q31.c new file mode 100644 index 0000000..71ec4f5 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_init_q31.c @@ -0,0 +1,4280 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_init_q31.c + * Description: RFFT & RIFFT Q31 initialisation function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" +#include "arm_common_tables.h" +#include "arm_const_structs.h" + +/** +* @ingroup RealFFT +*/ + +/** + * @addtogroup RealFFT_Table Real FFT Tables +* @{ +*/ + +/** +* \par +* Generation fixed-point realCoefAQ31 array in Q31 format: +* \par +* n = 4096 +* <pre>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)); +* }</pre> +* \par +* Convert to fixed point Q31 format +* round(pATable[i] * pow(2, 31)) +*/ +const q31_t realCoefAQ31[8192] = { + (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, (q31_t)0x3c6b2259, (q31_t)0xc019acac, + (q31_t)0x3c5e9678, (q31_t)0xc01a61ee, (q31_t)0x3c520aba, (q31_t)0xc01b19a7, + (q31_t)0x3c457f21, (q31_t)0xc01bd3d6, (q31_t)0x3c38f3ac, (q31_t)0xc01c907c, + (q31_t)0x3c2c685d, (q31_t)0xc01d4f99, (q31_t)0x3c1fdd34, (q31_t)0xc01e112b, + (q31_t)0x3c135231, (q31_t)0xc01ed535, (q31_t)0x3c06c754, (q31_t)0xc01f9bb5, + (q31_t)0x3bfa3c9f, (q31_t)0xc02064ab, (q31_t)0x3bedb212, (q31_t)0xc0213018, + (q31_t)0x3be127ac, (q31_t)0xc021fdfb, (q31_t)0x3bd49d70, (q31_t)0xc022ce54, + (q31_t)0x3bc8135c, (q31_t)0xc023a124, (q31_t)0x3bbb8973, (q31_t)0xc024766a, + (q31_t)0x3baeffb3, (q31_t)0xc0254e27, (q31_t)0x3ba2761e, (q31_t)0xc0262859, + (q31_t)0x3b95ecb4, (q31_t)0xc0270502, (q31_t)0x3b896375, (q31_t)0xc027e421, + (q31_t)0x3b7cda63, (q31_t)0xc028c5b6, (q31_t)0x3b70517d, (q31_t)0xc029a9c1, + (q31_t)0x3b63c8c4, (q31_t)0xc02a9042, (q31_t)0x3b574039, (q31_t)0xc02b7939, + (q31_t)0x3b4ab7db, (q31_t)0xc02c64a6, (q31_t)0x3b3e2fac, (q31_t)0xc02d5289, + (q31_t)0x3b31a7ac, (q31_t)0xc02e42e2, (q31_t)0x3b251fdc, (q31_t)0xc02f35b1, + (q31_t)0x3b18983b, (q31_t)0xc0302af5, (q31_t)0x3b0c10cb, (q31_t)0xc03122b0, + (q31_t)0x3aff898c, (q31_t)0xc0321ce0, (q31_t)0x3af3027e, (q31_t)0xc0331986, + (q31_t)0x3ae67ba2, (q31_t)0xc03418a2, (q31_t)0x3ad9f4f8, (q31_t)0xc0351a33, + (q31_t)0x3acd6e81, (q31_t)0xc0361e3a, (q31_t)0x3ac0e83d, (q31_t)0xc03724b6, + (q31_t)0x3ab4622d, (q31_t)0xc0382da8, (q31_t)0x3aa7dc52, (q31_t)0xc0393910, + (q31_t)0x3a9b56ab, (q31_t)0xc03a46ed, (q31_t)0x3a8ed139, (q31_t)0xc03b573f, + (q31_t)0x3a824bfd, (q31_t)0xc03c6a07, (q31_t)0x3a75c6f8, (q31_t)0xc03d7f44, + (q31_t)0x3a694229, (q31_t)0xc03e96f6, (q31_t)0x3a5cbd91, (q31_t)0xc03fb11d, + (q31_t)0x3a503930, (q31_t)0xc040cdba, (q31_t)0x3a43b508, (q31_t)0xc041eccc, + (q31_t)0x3a373119, (q31_t)0xc0430e53, (q31_t)0x3a2aad62, (q31_t)0xc044324f, + (q31_t)0x3a1e29e5, (q31_t)0xc04558c0, (q31_t)0x3a11a6a3, 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(q31_t)0x3d1ad650, (q31_t)0x3fef3a39, + (q31_t)0x3d276410, (q31_t)0x3fefca84, (q31_t)0x3d33f1ed, (q31_t)0x3ff05858, + (q31_t)0x3d407fe6, (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 +* <pre>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)); +* } </pre> +* \par +* Convert to fixed point Q31 format +* round(pBTable[i] * pow(2, 31)) +* +*/ + +const q31_t realCoefBQ31[8192] = { + (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, (q31_t)0x3f3f9cab, (q31_t)0x49d3d8df, (q31_t)0x3f3dafe7, + (q31_t)0x49e04385, (q31_t)0x3f3bc0b3, (q31_t)0x49ecadc9, (q31_t)0x3f39cf0e, + (q31_t)0x49f917ac, (q31_t)0x3f37dafa, (q31_t)0x4a05812c, (q31_t)0x3f35e476, + (q31_t)0x4a11ea49, (q31_t)0x3f33eb81, (q31_t)0x4a1e5303, (q31_t)0x3f31f01d, + (q31_t)0x4a2abb59, (q31_t)0x3f2ff24a, (q31_t)0x4a37234a, (q31_t)0x3f2df206, + (q31_t)0x4a438ad7, (q31_t)0x3f2bef53, 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(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, +}; + +/** +* @} end of RealFFT_Table group +*/ + +/** +* @addtogroup RealFFT +* @{ +*/ + +/** +* @brief 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 forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. +* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. +* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value. +* +* \par Description: +* \par +* The parameter <code>fftLenReal</code> Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192. +* \par +* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed. +* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated. +* \par +* The parameter <code>bitReverseFlag</code> 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 7 +* This function also initializes Twiddle factor table. +*/ + +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_SUCCESS; + + /* Initialize the Real FFT length */ + S->fftLenReal = (uint16_t) fftLenReal; + + /* 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; + + /* Initialization of coef modifier depending on the FFT length */ + switch (S->fftLenReal) + { + case 8192U: + S->twidCoefRModifier = 1U; + S->pCfft = &arm_cfft_sR_q31_len4096; + break; + case 4096U: + S->twidCoefRModifier = 2U; + S->pCfft = &arm_cfft_sR_q31_len2048; + break; + case 2048U: + S->twidCoefRModifier = 4U; + S->pCfft = &arm_cfft_sR_q31_len1024; + break; + case 1024U: + S->twidCoefRModifier = 8U; + S->pCfft = &arm_cfft_sR_q31_len512; + break; + case 512U: + S->twidCoefRModifier = 16U; + S->pCfft = &arm_cfft_sR_q31_len256; + break; + case 256U: + S->twidCoefRModifier = 32U; + S->pCfft = &arm_cfft_sR_q31_len128; + break; + case 128U: + S->twidCoefRModifier = 64U; + S->pCfft = &arm_cfft_sR_q31_len64; + break; + case 64U: + S->twidCoefRModifier = 128U; + S->pCfft = &arm_cfft_sR_q31_len32; + break; + case 32U: + S->twidCoefRModifier = 256U; + S->pCfft = &arm_cfft_sR_q31_len16; + 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); +} + +/** +* @} end of RealFFT group +*/ diff --git a/DSP/Source/TransformFunctions/arm_rfft_q15.c b/DSP/Source/TransformFunctions/arm_rfft_q15.c new file mode 100644 index 0000000..f85cf30 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_q15.c @@ -0,0 +1,426 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_q15.c + * Description: RFFT & RIFFT Q15 process function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/* ---------------------------------------------------------------------- + * Internal functions prototypes + * -------------------------------------------------------------------- */ + +void arm_split_rfft_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pATable, + q15_t * pBTable, + q15_t * pDst, + uint32_t modifier); + +void arm_split_rifft_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pATable, + q15_t * pBTable, + q15_t * pDst, + uint32_t modifier); + +/** +* @addtogroup RealFFT +* @{ +*/ + +/** +* @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 the input buffer. +* @param[out] *pDst points to the output buffer. +* @return none. +* +* \par Input an output formats: +* \par +* 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 +* \image html RFFTQ15.gif "Input and Output Formats for Q15 RFFT" +* \par +* \image html RIFFTQ15.gif "Input and Output Formats for Q15 RIFFT" +*/ + +void arm_rfft_q15( + const arm_rfft_instance_q15 * S, + q15_t * pSrc, + q15_t * pDst) +{ + const arm_cfft_instance_q15 *S_CFFT = S->pCfft; + uint32_t i; + uint32_t L2 = S->fftLenReal >> 1; + + /* 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); + + for(i=0;i<S->fftLenReal;i++) + { + pDst[i] = pDst[i] << 1; + } + } + 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); + } +} + +/** +* @} end of RealFFT group +*/ + +/** +* @brief Core Real FFT process +* @param *pSrc points to the input buffer. +* @param fftLen length of FFT. +* @param *pATable points to the A twiddle Coef buffer. +* @param *pBTable points to the B twiddle Coef buffer. +* @param *pDst points to the output buffer. +* @param modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +* @return none. +* The function implements a Real FFT +*/ + +void arm_split_rfft_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pATable, + q15_t * pBTable, + q15_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + q31_t outR, outI; /* Temporary variables for output */ + q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */ + q15_t *pSrc1, *pSrc2; +#if defined (ARM_MATH_DSP) + q15_t *pD1, *pD2; +#endif + + // pSrc[2U * fftLen] = pSrc[0]; + // pSrc[(2U * fftLen) + 1U] = pSrc[1]; + + pCoefA = &pATable[modifier * 2U]; + pCoefB = &pBTable[modifier * 2U]; + + pSrc1 = &pSrc[2]; + pSrc2 = &pSrc[(2U * fftLen) - 2U]; + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + 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(*__SIMD32(pSrc1), *__SIMD32(pCoefA)); + +#else + + /* -(pSrc[2 * i + 1] * pATable[2 * i + 1] - pSrc[2 * i] * pATable[2 * i]) */ + outR = -(__SMUSD(*__SIMD32(pSrc1), *__SIMD32(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(*__SIMD32(pSrc2), *__SIMD32(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(*__SIMD32(pSrc2)--, *__SIMD32(pCoefB)); + +#else + + outI = __SMUSDX(*__SIMD32(pCoefB), *__SIMD32(pSrc2)--); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] */ + outI = __SMLADX(*__SIMD32(pSrc1)++, *__SIMD32(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]) >> 1; + pDst[(2U * fftLen) + 1U] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1; + pDst[1] = 0; + +#else + + /* Run the below code for Cortex-M0 */ + 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) */ +} + + +/** +* @brief Core Real IFFT process +* @param[in] *pSrc points to the input buffer. +* @param[in] fftLen length of FFT. +* @param[in] *pATable points to the twiddle Coef A buffer. +* @param[in] *pBTable points to the twiddle Coef B buffer. +* @param[out] *pDst points to the output buffer. +* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +* @return none. +* The function implements a Real IFFT +*/ +void arm_split_rifft_q15( + q15_t * pSrc, + uint32_t fftLen, + q15_t * pATable, + q15_t * pBTable, + q15_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + q31_t outR, outI; /* Temporary variables for output */ + 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[2U * fftLen]; + +#if defined (ARM_MATH_DSP) + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + 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]); + */ + + +#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(*__SIMD32(pSrc2), *__SIMD32(pCoefB)); + +#else + + /* -(-pIn[2 * n - 2 * i] * pBTable[2 * i] + + pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1])) */ + outR = -(__SMUSD(*__SIMD32(pSrc2), *__SIMD32(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(*__SIMD32(pSrc1), *__SIMD32(pCoefA), outR) >> 16U; + + /* + -pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + + pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */ + outI = __SMUADX(*__SIMD32(pSrc2)--, *__SIMD32(pCoefB)); + + /* pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] */ + +#ifndef ARM_MATH_BIG_ENDIAN + + outI = __SMLSDX(*__SIMD32(pCoefA), *__SIMD32(pSrc1)++, -outI); + +#else + + outI = __SMLSDX(*__SIMD32(pSrc1)++, *__SIMD32(pCoefA), -outI); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + /* write output */ + +#ifndef ARM_MATH_BIG_ENDIAN + + *__SIMD32(pDst1)++ = __PKHBT(outR, (outI >> 16U), 16); + +#else + + *__SIMD32(pDst1)++ = __PKHBT((outI >> 16U), outR, 16); + +#endif /* #ifndef ARM_MATH_BIG_ENDIAN */ + + /* update coefficient pointer */ + pCoefB = pCoefB + (2U * modifier); + pCoefA = pCoefA + (2U * modifier); + + i--; + } +#else + /* Run the below code for Cortex-M0 */ + 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]); + */ + + outR = *pSrc2 * *pCoefB; + outR = outR - (*(pSrc2 + 1) * *(pCoefB + 1)); + outR = outR + (*pSrc1 * *pCoefA); + outR = (outR + (*(pSrc1 + 1) * *(pCoefA + 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 = *(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); + + /* update coefficient pointer */ + pCoefB = pCoefB + (2U * modifier); + pCoefA = pCoefA + (2U * modifier); + + i--; + } +#endif /* #if defined (ARM_MATH_DSP) */ +} diff --git a/DSP/Source/TransformFunctions/arm_rfft_q31.c b/DSP/Source/TransformFunctions/arm_rfft_q31.c new file mode 100644 index 0000000..5386140 --- /dev/null +++ b/DSP/Source/TransformFunctions/arm_rfft_q31.c @@ -0,0 +1,283 @@ +/* ---------------------------------------------------------------------- + * Project: CMSIS DSP Library + * Title: arm_rfft_q31.c + * Description: FFT & RIFFT Q31 process function + * + * $Date: 27. January 2017 + * $Revision: V.1.5.1 + * + * Target Processor: Cortex-M cores + * -------------------------------------------------------------------- */ +/* + * Copyright (C) 2010-2017 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_math.h" + +/* ---------------------------------------------------------------------- + * Internal functions prototypes + * -------------------------------------------------------------------- */ + +void arm_split_rfft_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pATable, + q31_t * pBTable, + q31_t * pDst, + uint32_t modifier); + +void arm_split_rifft_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pATable, + q31_t * pBTable, + q31_t * pDst, + uint32_t modifier); + +/** +* @addtogroup RealFFT +* @{ +*/ + +/** +* @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 the input buffer. +* @param[out] *pDst points to the output buffer. +* @return none. +* +* \par Input an output formats: +* \par +* 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 +* \image html RFFTQ31.gif "Input and Output Formats for Q31 RFFT" +* +* \par +* \image html RIFFTQ31.gif "Input and Output Formats for Q31 RIFFT" +*/ +void arm_rfft_q31( + const arm_rfft_instance_q31 * S, + q31_t * pSrc, + q31_t * pDst) +{ + const arm_cfft_instance_q31 *S_CFFT = S->pCfft; + uint32_t i; + uint32_t L2 = S->fftLenReal >> 1; + + /* 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); + + for(i=0;i<S->fftLenReal;i++) + { + pDst[i] = pDst[i] << 1; + } + } + 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); + } +} + +/** +* @} end of RealFFT group +*/ + +/** +* @brief Core Real FFT process +* @param[in] *pSrc points to the input buffer. +* @param[in] fftLen length of FFT. +* @param[in] *pATable points to the twiddle Coef A buffer. +* @param[in] *pBTable points to the twiddle Coef B buffer. +* @param[out] *pDst points to the output buffer. +* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +* @return none. +*/ +void arm_split_rfft_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pATable, + q31_t * pBTable, + q31_t * pDst, + uint32_t modifier) +{ + uint32_t i; /* Loop Counter */ + q31_t outR, outI; /* Temporary variables for output */ + 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[(4U * fftLen) - 1U]; + q31_t *pIn1 = &pSrc[2], *pIn2 = &pSrc[(2U * fftLen) - 1U]; + + /* Init coefficient pointers */ + pCoefA = &pATable[modifier * 2U]; + pCoefB = &pBTable[modifier * 2U]; + + 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 + (modifier * 2U); + pCoefA = pCoefA + ((modifier * 2U) - 1U); + + i--; + } + pDst[2U * fftLen] = (pSrc[0] - pSrc[1]) >> 1; + pDst[(2U * fftLen) + 1U] = 0; + + pDst[0] = (pSrc[0] + pSrc[1]) >> 1; + pDst[1] = 0; +} + +/** +* @brief Core Real IFFT process +* @param[in] *pSrc points to the input buffer. +* @param[in] fftLen length of FFT. +* @param[in] *pATable points to the twiddle Coef A buffer. +* @param[in] *pBTable points to the twiddle Coef B buffer. +* @param[out] *pDst points to the output buffer. +* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. +* @return none. +*/ +void arm_split_rifft_q31( + q31_t * pSrc, + uint32_t fftLen, + q31_t * pATable, + q31_t * pBTable, + q31_t * pDst, + uint32_t modifier) +{ + q31_t outR, outI; /* Temporary variables for output */ + 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[(2U * fftLen) + 1U]; + + 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 * 2U); + pCoefA = pCoefA + ((modifier * 2U) - 1U); + + /* Decrement loop count */ + fftLen--; + } +} |