msts/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_cfft_radix4_q31.c

/* ----------------------------------------------------------------------
 * 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  It has been superseded by \ref arm_cfft_q31 and will be removed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 */
}