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pigweed / third_party / github / STMicroelectronics / cmsis_core / aa27571dd348d8cfde415f2b83cda5e89527a72b / . / DSP / Source / TransformFunctions / arm_cfft_radix4_q31.c
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/* ----------------------------------------------------------------------
* 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 It has been superseded by \ref arm_cfft_q31 and will be removed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 */
}