/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_rfft_q15.c
* Description: RFFT & RIFFT Q15 process function
*
* $Date: 23 April 2021
* $Revision: V1.9.0
*
* Target Processor: Cortex-M and Cortex-A cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "dsp/transform_functions.h"
/* ----------------------------------------------------------------------
* Internal functions prototypes
* -------------------------------------------------------------------- */
void arm_split_rfft_q15(
q15_t * pSrc,
uint32_t fftLen,
const q15_t * pATable,
const q15_t * pBTable,
q15_t * pDst,
uint32_t modifier);
void arm_split_rifft_q15(
q15_t * pSrc,
uint32_t fftLen,
const q15_t * pATable,
const q15_t * pBTable,
q15_t * pDst,
uint32_t modifier);
/**
@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 input buffer (Source buffer is modified by this function.)
@param[out] pDst points to output buffer
@return none
@par Input an output formats
Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
Hence the output format is different for different RFFT sizes.
The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT:
@par
\image html RFFTQ15.gif "Input and Output Formats for Q15 RFFT"
@par
\image html RIFFTQ15.gif "Input and Output Formats for Q15 RIFFT"
@par
If the input buffer is of length N, the output buffer must have length 2*N.
The input buffer is modified by this function.
@par
For the RIFFT, the source buffer must at least have length
fftLenReal + 2.
The last two elements must be equal to what would be generated
by the RFFT:
(pSrc[0] - pSrc[1]) >> 1 and 0
*/
void arm_rfft_q15(
const arm_rfft_instance_q15 * S,
q15_t * pSrc,
q15_t * pDst)
{
#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE)
const arm_cfft_instance_q15 *S_CFFT = &(S->cfftInst);
#else
const arm_cfft_instance_q15 *S_CFFT = S->pCfft;
#endif
uint32_t L2 = S->fftLenReal >> 1U;
/* Calculation of RIFFT of input */
if (S->ifftFlagR == 1U)
{
/* Real IFFT core process */
arm_split_rifft_q15 (pSrc, L2, S->pTwiddleAReal, S->pTwiddleBReal, pDst, S->twidCoefRModifier);
/* Complex IFFT process */
arm_cfft_q15 (S_CFFT, pDst, S->ifftFlagR, S->bitReverseFlagR);
arm_shift_q15(pDst, 1, pDst, S->fftLenReal);
}
else
{
/* Calculation of RFFT of input */
/* Complex FFT process */
arm_cfft_q15 (S_CFFT, pSrc, S->ifftFlagR, S->bitReverseFlagR);
/* Real FFT core process */
arm_split_rfft_q15 (pSrc, L2, S->pTwiddleAReal, S->pTwiddleBReal, pDst, S->twidCoefRModifier);
}
}
/**
@} end of RealFFT group
*/
/**
@brief Core Real FFT process
@param[in] pSrc points to input buffer
@param[in] fftLen length of FFT
@param[in] pATable points to twiddle Coef A buffer
@param[in] pBTable points to twiddle Coef B buffer
@param[out] pDst points to output buffer
@param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table
@return none
@par
The function implements a Real FFT
*/
#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE)
#include "arm_helium_utils.h"
#include "arm_vec_fft.h"
#if defined(__CMSIS_GCC_H)
#define MVE_CMPLX_MULT_FX_AxB_S16(A,B) vqdmladhxq_s16(vqdmlsdhq_s16((__typeof(A))vuninitializedq_s16(), A, B), A, B)
#define MVE_CMPLX_MULT_FX_AxConjB_S16(A,B) vqdmladhq_s16(vqdmlsdhxq_s16((__typeof(A))vuninitializedq_s16(), A, B), A, B)
#endif
void arm_split_rfft_q15(
q15_t * pSrc,
uint32_t fftLen,
const q15_t * pATable,
const q15_t * pBTable,
q15_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q15_t *pOut1 = &pDst[2];
q15_t *pIn1 = &pSrc[2];
uint16x8_t offsetIn = { 6, 7, 4, 5, 2, 3, 0, 1 };
uint16x8_t offsetCoef;
const uint16_t offsetCoefArr[16] = {
0, 0, 2, 2, 4, 4, 6, 6,
0, 1, 0, 1, 0, 1, 0, 1
};
offsetCoef = vmulq_n_u16(vld1q_u16(offsetCoefArr), modifier) + vld1q_u16(offsetCoefArr + 8);
offsetIn = vaddq_n_u16(offsetIn, (2 * fftLen - 8));
/* Init coefficient pointers */
pCoefA = &pATable[modifier * 2];
pCoefB = &pBTable[modifier * 2];
const q15_t *pCoefAb, *pCoefBb;
pCoefAb = pCoefA;
pCoefBb = pCoefB;
pIn1 = &pSrc[2];
i = fftLen - 1U;
i = i / 4 + 1;
while (i > 0U) {
q15x8_t in1 = vld1q_s16(pIn1);
q15x8_t in2 = vldrhq_gather_shifted_offset_s16(pSrc, offsetIn);
q15x8_t coefA = vldrhq_gather_shifted_offset_s16(pCoefAb, offsetCoef);
q15x8_t coefB = vldrhq_gather_shifted_offset_s16(pCoefBb, offsetCoef);
#if defined(__CMSIS_GCC_H)
q15x8_t out = vhaddq_s16(MVE_CMPLX_MULT_FX_AxB_S16(in1, coefA),
MVE_CMPLX_MULT_FX_AxConjB_S16(coefB, in2));
#else
q15x8_t out = vhaddq_s16(MVE_CMPLX_MULT_FX_AxB(in1, coefA, q15x8_t),
MVE_CMPLX_MULT_FX_AxConjB(coefB, in2, q15x8_t));
#endif
vst1q_s16(pOut1, out);
pOut1 += 8;
offsetCoef = vaddq_n_u16(offsetCoef, modifier * 8);
offsetIn -= 8;
pIn1 += 8;
i -= 1;
}
pDst[2 * fftLen] = (pSrc[0] - pSrc[1]) >> 1U;
pDst[2 * fftLen + 1] = 0;
pDst[0] = (pSrc[0] + pSrc[1]) >> 1U;
pDst[1] = 0;
}
#else
void arm_split_rfft_q15(
q15_t * pSrc,
uint32_t fftLen,
const q15_t * pATable,
const q15_t * pBTable,
q15_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
q31_t outR, outI; /* Temporary variables for output */
const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q15_t *pSrc1, *pSrc2;
#if defined (ARM_MATH_DSP)
q15_t *pD1, *pD2;
#endif
/* Init coefficient pointers */
pCoefA = &pATable[modifier * 2];
pCoefB = &pBTable[modifier * 2];
pSrc1 = &pSrc[2];
pSrc2 = &pSrc[(2U * fftLen) - 2U];
#if defined (ARM_MATH_DSP)
i = 1U;
pD1 = pDst + 2;
pD2 = pDst + (4U * fftLen) - 2;
for (i = fftLen - 1; i > 0; i--)
{
/*
outR = ( pSrc[2 * i] * pATable[2 * i]
- pSrc[2 * i + 1] * pATable[2 * i + 1]
+ pSrc[2 * n - 2 * i] * pBTable[2 * i]
+ pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
outI = ( pIn[2 * i + 1] * pATable[2 * i]
+ pIn[2 * i] * pATable[2 * i + 1]
+ pIn[2 * n - 2 * i] * pBTable[2 * i + 1]
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i])
*/
#ifndef ARM_MATH_BIG_ENDIAN
/* pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1] */
outR = __SMUSD(read_q15x2 (pSrc1), read_q15x2((q15_t *) pCoefA));
#else
/* -(pSrc[2 * i + 1] * pATable[2 * i + 1] - pSrc[2 * i] * pATable[2 * i]) */
outR = -(__SMUSD(read_q15x2 (pSrc1), read_q15x2((q15_t *) pCoefA)));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* pSrc[2 * n - 2 * i] * pBTable[2 * i] + pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */
outR = __SMLAD(read_q15x2 (pSrc2), read_q15x2((q15_t *) pCoefB), outR) >> 16U;
/* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] - pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
#ifndef ARM_MATH_BIG_ENDIAN
outI = __SMUSDX(read_q15x2_da (&pSrc2), read_q15x2((q15_t *) pCoefB));
#else
outI = __SMUSDX(read_q15x2 ((q15_t *) pCoefB), read_q15x2_da (&pSrc2));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] */
outI = __SMLADX(read_q15x2_ia (&pSrc1), read_q15x2 ((q15_t *) pCoefA), outI);
/* write output */
*pD1++ = (q15_t) outR;
*pD1++ = outI >> 16U;
/* write complex conjugate output */
pD2[0] = (q15_t) outR;
pD2[1] = -(outI >> 16U);
pD2 -= 2;
/* update coefficient pointer */
pCoefB = pCoefB + (2U * modifier);
pCoefA = pCoefA + (2U * modifier);
}
pDst[2U * fftLen] = (pSrc[0] - pSrc[1]) >> 1U;
pDst[2U * fftLen + 1U] = 0;
pDst[0] = (pSrc[0] + pSrc[1]) >> 1U;
pDst[1] = 0;
#else
i = 1U;
while (i < fftLen)
{
/*
outR = ( pSrc[2 * i] * pATable[2 * i]
- pSrc[2 * i + 1] * pATable[2 * i + 1]
+ pSrc[2 * n - 2 * i] * pBTable[2 * i]
+ pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
*/
outR = *pSrc1 * *pCoefA;
outR = outR - (*(pSrc1 + 1) * *(pCoefA + 1));
outR = outR + (*pSrc2 * *pCoefB);
outR = (outR + (*(pSrc2 + 1) * *(pCoefB + 1))) >> 16;
/*
outI = ( pIn[2 * i + 1] * pATable[2 * i]
+ pIn[2 * i] * pATable[2 * i + 1]
+ pIn[2 * n - 2 * i] * pBTable[2 * i + 1]
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
outI = *pSrc2 * *(pCoefB + 1);
outI = outI - (*(pSrc2 + 1) * *pCoefB);
outI = outI + (*(pSrc1 + 1) * *pCoefA);
outI = outI + (*pSrc1 * *(pCoefA + 1));
/* update input pointers */
pSrc1 += 2U;
pSrc2 -= 2U;
/* write output */
pDst[2U * i] = (q15_t) outR;
pDst[2U * i + 1U] = outI >> 16U;
/* write complex conjugate output */
pDst[(4U * fftLen) - (2U * i)] = (q15_t) outR;
pDst[((4U * fftLen) - (2U * i)) + 1U] = -(outI >> 16U);
/* update coefficient pointer */
pCoefB = pCoefB + (2U * modifier);
pCoefA = pCoefA + (2U * modifier);
i++;
}
pDst[2U * fftLen] = (pSrc[0] - pSrc[1]) >> 1;
pDst[2U * fftLen + 1U] = 0;
pDst[0] = (pSrc[0] + pSrc[1]) >> 1;
pDst[1] = 0;
#endif /* #if defined (ARM_MATH_DSP) */
}
#endif /* defined(ARM_MATH_MVEI) */
/**
@brief Core Real IFFT process
@param[in] pSrc points to input buffer
@param[in] fftLen length of FFT
@param[in] pATable points to twiddle Coef A buffer
@param[in] pBTable points to twiddle Coef B buffer
@param[out] pDst points to output buffer
@param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table
@return none
@par
The function implements a Real IFFT
*/
#if defined(ARM_MATH_MVEI) && !defined(ARM_MATH_AUTOVECTORIZE)
#include "arm_helium_utils.h"
#include "arm_vec_fft.h"
void arm_split_rifft_q15(
q15_t * pSrc,
uint32_t fftLen,
const q15_t * pATable,
const q15_t * pBTable,
q15_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q15_t *pIn1;
uint16x8_t offset = { 6, 7, 4, 5, 2, 3, 0, 1 };
uint16x8_t offsetCoef;
int16x8_t conj = { 1, -1, 1, -1, 1, -1, 1, -1 }; /* conjugate */
const uint16_t offsetCoefArr[16] = {
0, 0, 2, 2, 4, 4, 6, 6,
0, 1, 0, 1, 0, 1, 0, 1
};
offsetCoef = vmulq_n_u16(vld1q_u16(offsetCoefArr), modifier) + vld1q_u16(offsetCoefArr + 8);
offset = vaddq_n_u16(offset, (2 * fftLen - 6));
/* Init coefficient pointers */
pCoefA = &pATable[0];
pCoefB = &pBTable[0];
const q15_t *pCoefAb, *pCoefBb;
pCoefAb = pCoefA;
pCoefBb = pCoefB;
pIn1 = &pSrc[0];
i = fftLen;
i = i / 4;
while (i > 0U) {
q15x8_t in1 = vld1q_s16(pIn1);
q15x8_t in2 = vldrhq_gather_shifted_offset_s16(pSrc, offset);
q15x8_t coefA = vldrhq_gather_shifted_offset_s16(pCoefAb, offsetCoef);
q15x8_t coefB = vldrhq_gather_shifted_offset_s16(pCoefBb, offsetCoef);
/* can we avoid the conjugate here ? */
q15x8_t out = vhaddq_s16(MVE_CMPLX_MULT_FX_AxConjB(in1, coefA, q15x8_t),
vmulq(conj, MVE_CMPLX_MULT_FX_AxB(in2, coefB, q15x8_t)));
vst1q_s16(pDst, out);
pDst += 8;
offsetCoef = vaddq_n_u16(offsetCoef, modifier * 8);
offset -= 8;
pIn1 += 8;
i -= 1;
}
}
#else
void arm_split_rifft_q15(
q15_t * pSrc,
uint32_t fftLen,
const q15_t * pATable,
const q15_t * pBTable,
q15_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
q31_t outR, outI; /* Temporary variables for output */
const q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q15_t *pSrc1, *pSrc2;
q15_t *pDst1 = &pDst[0];
pCoefA = &pATable[0];
pCoefB = &pBTable[0];
pSrc1 = &pSrc[0];
pSrc2 = &pSrc[2 * fftLen];
i = fftLen;
while (i > 0U)
{
/*
outR = ( pIn[2 * i] * pATable[2 * i]
+ pIn[2 * i + 1] * pATable[2 * i + 1]
+ pIn[2 * n - 2 * i] * pBTable[2 * i]
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
outI = ( pIn[2 * i + 1] * pATable[2 * i]
- pIn[2 * i] * pATable[2 * i + 1]
- pIn[2 * n - 2 * i] * pBTable[2 * i + 1]
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
#if defined (ARM_MATH_DSP)
#ifndef ARM_MATH_BIG_ENDIAN
/* pIn[2 * n - 2 * i] * pBTable[2 * i] - pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */
outR = __SMUSD(read_q15x2(pSrc2), read_q15x2((q15_t *) pCoefB));
#else
/* -(-pIn[2 * n - 2 * i] * pBTable[2 * i] + pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1])) */
outR = -(__SMUSD(read_q15x2(pSrc2), read_q15x2((q15_t *) pCoefB)));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] + pIn[2 * n - 2 * i] * pBTable[2 * i] */
outR = __SMLAD(read_q15x2(pSrc1), read_q15x2 ((q15_t *) pCoefA), outR) >> 16U;
/* -pIn[2 * n - 2 * i] * pBTable[2 * i + 1] + pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
outI = __SMUADX(read_q15x2_da (&pSrc2), read_q15x2((q15_t *) pCoefB));
/* pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] */
#ifndef ARM_MATH_BIG_ENDIAN
outI = __SMLSDX(read_q15x2 ((q15_t *) pCoefA), read_q15x2_ia (&pSrc1), -outI);
#else
outI = __SMLSDX(read_q15x2_ia (&pSrc1), read_q15x2 ((q15_t *) pCoefA), -outI);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* write output */
#ifndef ARM_MATH_BIG_ENDIAN
write_q15x2_ia (&pDst1, __PKHBT(outR, (outI >> 16U), 16));
#else
write_q15x2_ia (&pDst1, __PKHBT((outI >> 16U), outR, 16));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
#else /* #if defined (ARM_MATH_DSP) */
outR = *pSrc2 * *pCoefB;
outR = outR - (*(pSrc2 + 1) * *(pCoefB + 1));
outR = outR + (*pSrc1 * *pCoefA);
outR = (outR + (*(pSrc1 + 1) * *(pCoefA + 1))) >> 16;
outI = *(pSrc1 + 1) * *pCoefA;
outI = outI - (*pSrc1 * *(pCoefA + 1));
outI = outI - (*pSrc2 * *(pCoefB + 1));
outI = outI - (*(pSrc2 + 1) * *(pCoefB));
/* update input pointers */
pSrc1 += 2U;
pSrc2 -= 2U;
/* write output */
*pDst1++ = (q15_t) outR;
*pDst1++ = (q15_t) (outI >> 16);
#endif /* #if defined (ARM_MATH_DSP) */
/* update coefficient pointer */
pCoefB = pCoefB + (2 * modifier);
pCoefA = pCoefA + (2 * modifier);
i--;
}
}
#endif /* defined(ARM_MATH_MVEI) */