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/* ----------------------------------------------------------------------    

* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    

*    

* $Date:        19. March 2015

* $Revision:    V.1.4.5  

*    

* 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    

*    

* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0

*  

* Redistribution and use in source and binary forms, with or without

* modification, are permitted provided that the following conditions

* are met:

*   - Redistributions of source code must retain the above copyright

*     notice, this list of conditions and the following disclaimer.

*   - Redistributions in binary form must reproduce the above copyright

*     notice, this list of conditions and the following disclaimer in

*     the documentation and/or other materials provided with the

*     distribution.

*   - Neither the name of ARM LIMITED nor the names of its contributors

*     may be used to endorse or promote products derived from this

*     software without specific prior written permission.

*

* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT

* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS

* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE

* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,

* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,

* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;

* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER

* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN

* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE

* POSSIBILITY OF SUCH DAMAGE.    

* -------------------------------------------------------------------- */

#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);