/* ----------------------------------------------------------------------   
* Copyright (C) 2010 ARM Limited. All rights reserved.   
*   
* $Date:        15. July 2011  
* $Revision: 	V1.0.10  
*   
* Project: 	    CMSIS DSP Library   
* Title:	    arm_cfft_radix4_f32.c   
*   
* Description:	Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function   
*   
*   
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* Version 1.0.10 2011/7/15 
*    Big Endian support added and Merged M0 and M3/M4 Source code.  
*   
* Version 1.0.3 2010/11/29  
*    Re-organized the CMSIS folders and updated documentation.   
*    
* Version 1.0.2 2010/11/11   
*    Documentation updated.    
*   
* Version 1.0.1 2010/10/05    
*    Production release and review comments incorporated.   
*   
* Version 1.0.0 2010/09/20    
*    Production release and review comments incorporated.   
*   
* Version 0.0.5  2010/04/26    
* 	 incorporated review comments and updated with latest CMSIS layer   
*   
* Version 0.0.3  2010/03/10    
*    Initial version   
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**   
 * @ingroup groupTransforms   
 */

/**   
 * @defgroup CFFT_CIFFT Complex FFT Functions   
 *   
 * \par   
 * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).   
 * Computational complexity of CFFT reduces drastically when compared to DFT.   
 * \par   
 * This set of functions implements CFFT/CIFFT   
 * for Q15, Q31, and floating-point data types.  The functions operates on in-place buffer which uses same buffer for input and output.   
 * Complex input is stored in input buffer in an interleaved fashion.   
 *   
 * \par   
 * The functions operate on blocks of input and output data and each call to the function processes   
 * <code>2*fftLen</code> samples through the transform.  <code>pSrc</code>  points to In-place arrays containing <code>2*fftLen</code> values.   
 * \par  
 * The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.   
 * <pre> {real[0], imag[0], real[1], imag[1],..} </pre>   
 *   
 * \par Lengths supported by the transform:  
 * \par   
 * Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm   
 * and the size of the FFT supported are of the lengths [16, 64, 256, 1024].  
 *    
 *   
 * \par Algorithm:   
 *   
 * <b>Complex Fast Fourier Transform:</b>   
 * \par    
 * Input real and imaginary data:   
 * <pre>   
 * 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   
 * </pre>   
 * where N is length of FFT   
 * \par   
 * Output real and imaginary data:   
 * <pre>   
 * X(4r) = xa'+ j * ya'   
 * X(4r+1) = xb'+ j * yb'   
 * X(4r+2) = xc'+ j * yc'   
 * X(4r+3) = xd'+ j * yd'   
 * </pre>   
 * \par   
 * Twiddle factors for radix-4 FFT:   
 * <pre>   
 * Wn = co1 + j * (- si1)   
 * W2n = co2 + j * (- si2)   
 * W3n = co3 + j * (- si3)   
 * </pre>   
 *   
 * \par   
 * \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform"   
 *   
 * \par   
 * Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.   
 * \par   
 * <b> Butterfly CFFT equations:</b>   
 * <pre>   
 * xa' = xa + xb + xc + xd   
 * ya' = ya + yb + yc + yd   
 * xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)   
 * yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)   
 * xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)   
 * yb' = (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)   
 * </pre>   
 *   
 *   
 * <b>Complex Inverse Fast Fourier Transform:</b>   
 * \par   
 * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.   
 *   
 * \par   
 * <b> Modified Butterfly CIFFT equations:</b>   
 * <pre>   
 * xa' = xa + xb + xc + xd   
 * ya' = ya + yb + yc + yd   
 * xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)   
 * yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)   
 * xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)   
 * yb' = (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)   
 * </pre>   
 *   
 * \par Instance Structure   
 * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.   
 * There are separate instance structure declarations for each of the 3 supported data types.   
 *   
 * \par Initialization Functions   
 * There is also an associated initialization function for each data type.   
 * The initialization function performs the following operations:   
 * - Sets the values of the internal structure fields.   
 * - Initializes twiddle factor table and bit reversal table pointers   
 * \par   
 * Use of the initialization function is optional.   
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.   
 * To place an instance structure into a const data section, the instance structure must be manually initialized.   
 * Manually initialize the instance structure as follows:   
 * <pre>   
 *arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};   
 *arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};   
 *arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};   
 * </pre>   
 * \par   
 * where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);   
 * <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);    
 * <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.   
 * <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;    
 * <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.   
 * <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;   
 *  
 * \par Fixed-Point Behavior   
 * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.   
 * Refer to the function specific documentation below for usage guidelines.   
 */


/**   
 * @addtogroup CFFT_CIFFT   
 * @{   
 */

/**   
 * @details   
 * @brief Processing function for the floating-point CFFT/CIFFT.  
 * @param[in]      *S    points to an instance of the floating-point CFFT/CIFFT structure.  
 * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.  
 * @return none.  
 */

void arm_cfft_radix4_f32(
  const arm_cfft_radix4_instance_f32 * S,
  float32_t * pSrc)
{

  if(S->ifftFlag == 1u)
  {
    /*  Complex IFFT radix-4  */
    arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
                                     S->twidCoefModifier, S->onebyfftLen);
  }
  else
  {
    /*  Complex FFT radix-4  */
    arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
                             S->twidCoefModifier);
  }

  if(S->bitReverseFlag == 1u)
  {
    /*  Bit Reversal */
    arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
  }

}


/**   
 * @} end of CFFT_CIFFT group   
 */



/* ----------------------------------------------------------------------   
** Internal helper function used by the FFTs   
** ------------------------------------------------------------------- */

/*   
 * @brief  Core function for the floating-point CFFT butterfly process.  
 * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.  
 * @param[in]      fftLen           length of the FFT.  
 * @param[in]      *pCoef           points to the twiddle coefficient buffer.  
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.  
 * @return none.  
 */

void arm_radix4_butterfly_f32(
  float32_t * pSrc,
  uint16_t fftLen,
  float32_t * pCoef,
  uint16_t twidCoefModifier)
{

  float32_t co1, co2, co3, si1, si2, si3;
  float32_t t1, t2, r1, r2, s1, s2;
  uint32_t ia1, ia2, ia3;
  uint32_t i0, i1, i2, i3;
  uint32_t n1, n2, j, k;

#ifndef ARM_MATH_CM0

  /* Run the below code for Cortex-M4 and Cortex-M3 */

  /*  Initializations for the first stage */
  n2 = fftLen;
  n1 = n2;

  /* n2 = fftLen/4 */
  n2 >>= 2u;
  i0 = 0u;
  ia1 = 0u;

  j = n2;

  /*  Calculation of first stage */
  do
  {
    /*  index calculation for the input as, */
    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
    i1 = i0 + n2;
    i2 = i1 + n2;
    i3 = i2 + n2;

    /*  Butterfly implementation */

    /* xa + xc */
    r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

    /* xa - xc */
    r2 = pSrc[2u * i0] - pSrc[2u * i2];

    /* ya + yc */
    s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

    /* ya - yc */
    s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

    /* xb + xd */
    t1 = pSrc[2u * i1] + pSrc[2u * i3];

    /* xa' = xa + xb + xc + xd */
    pSrc[2u * i0] = r1 + t1;

    /* (xa + xc) - (xb + xd) */
    r1 = r1 - t1;

    /* yb + yd */
    t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

    /* ya' = ya + yb + yc + yd */
    pSrc[(2u * i0) + 1u] = s1 + t2;

    /* (ya + yc) - (yb + yd) */
    s1 = s1 - t2;

    /* yb - yd */
    t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

    /* xb - xd */
    t2 = pSrc[2u * i1] - pSrc[2u * i3];

    /*  index calculation for the coefficients */
    ia2 = ia1 + ia1;
    co2 = pCoef[ia2 * 2u];
    si2 = pCoef[(ia2 * 2u) + 1u];

    /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
    pSrc[2u * i1] = (r1 * co2) + (s1 * si2);

    /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
    pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);

    /* (xa - xc) + (yb - yd) */
    r1 = r2 + t1;

    /* (xa - xc) - (yb - yd) */
    r2 = r2 - t1;

    /* (ya - yc) - (xb - xd) */
    s1 = s2 - t2;

    /* (ya - yc) + (xb - xd) */
    s2 = s2 + t2;

    co1 = pCoef[ia1 * 2u];
    si1 = pCoef[(ia1 * 2u) + 1u];

    /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
    pSrc[2u * i2] = (r1 * co1) + (s1 * si1);

    /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
    pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);

    /*  index calculation for the coefficients */
    ia3 = ia2 + ia1;
    co3 = pCoef[ia3 * 2u];
    si3 = pCoef[(ia3 * 2u) + 1u];


    /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
    pSrc[2u * i3] = (r2 * co3) + (s2 * si3);

    /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
    pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);

    /*  Twiddle coefficients index modifier */
    ia1 = ia1 + twidCoefModifier;

    /*  Updating input index */
    i0 = i0 + 1u;

  }
  while(--j);

  twidCoefModifier <<= 2u;

  /*  Calculation of second stage to excluding last stage */
  for (k = fftLen / 4; 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/2], pSrc[i0 + 3fftLen/4] */
        i1 = i0 + n2;
        i2 = i1 + n2;
        i3 = i2 + n2;

        /* xa + xc */
        r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

        /* xa - xc */
        r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];

        /* ya + yc */
        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

        /* ya - yc */
        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

        /* xb + xd */
        t1 = pSrc[2u * i1] + pSrc[2u * i3];

        /* xa' = xa + xb + xc + xd */
        pSrc[2u * i0] = r1 + t1;

        /* xa + xc -(xb + xd) */
        r1 = r1 - t1;

        /* yb + yd */
        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = s1 + t2;

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* (yb - yd) */
        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

        /* (xb - xd) */
        t2 = pSrc[2u * i1] - pSrc[2u * i3];

        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = (r1 * co2) + (s1 * si2);

        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);

        /* (xa - xc) + (yb - yd) */
        r1 = r2 + t1;

        /* (xa - xc) - (yb - yd) */
        r2 = r2 - t1;

        /* (ya - yc) -  (xb - xd) */
        s1 = s2 - t2;

        /* (ya - yc) +  (xb - xd) */
        s2 = s2 + t2;

        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = (r1 * co1) + (s1 * si1);

        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);

        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = (r2 * co3) + (s2 * si3);

        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
      }
    }
    twidCoefModifier <<= 2u;
  }

  /*  Initializations of last stage */
  n1 = n2;
  n2 >>= 2u;

  /*  Calculations of last stage */
  for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
  {
    /*  index calculation for the input as, */
    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
    i1 = i0 + n2;
    i2 = i1 + n2;
    i3 = i2 + n2;

    /*  Butterfly implementation */

    /* xa + xb */
    r1 = pSrc[2u * i0] + pSrc[2u * i2];

    /* xa - xb */
    r2 = pSrc[2u * i0] - pSrc[2u * i2];

    /* ya + yc */
    s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

    /* ya - yc */
    s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

    /* xc + xd */
    t1 = pSrc[2u * i1] + pSrc[2u * i3];

    /* xa' = xa + xb + xc + xd */
    pSrc[2u * i0] = r1 + t1;

    /* (xa + xb) - (xc + xd) */
    r1 = r1 - t1;

    /* yb + yd */
    t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

    /* ya' = ya + yb + yc + yd */
    pSrc[(2u * i0) + 1u] = s1 + t2;

    /* (ya + yc) - (yb + yd) */
    s1 = s1 - t2;

    /* (yb-yd) */
    t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

    /* (xb-xd) */
    t2 = pSrc[2u * i1] - pSrc[2u * i3];

    /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
    pSrc[2u * i1] = r1;

    /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
    pSrc[(2u * i1) + 1u] = s1;

    /* (xa+yb-xc-yd) */
    r1 = r2 + t1;

    /* (xa-yb-xc+yd) */
    r2 = r2 - t1;

    /* (ya-xb-yc+xd) */
    s1 = s2 - t2;

    /* (ya+xb-yc-xd) */
    s2 = s2 + t2;

    /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
    pSrc[2u * i2] = r1;

    /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
    pSrc[(2u * i2) + 1u] = s1;

    /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
    pSrc[2u * i3] = r2;

    /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
    pSrc[(2u * i3) + 1u] = s2;
  }


#else

  /* Run the below code for Cortex-M0 */

  /*  Initializations for the fft calculation */
  n2 = fftLen;
  n1 = n2;
  for (k = fftLen; k > 1u; k >>= 2u)
  {
    /*  Initializations for the fft calculation */
    n1 = n2;
    n2 >>= 2u;
    ia1 = 0u;

    /*  FFT Calculation */
    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/2], pSrc[i0 + 3fftLen/4] */
        i1 = i0 + n2;
        i2 = i1 + n2;
        i3 = i2 + n2;

        /* xa + xc */
        r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

        /* xa - xc */
        r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];

        /* ya + yc */
        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

        /* ya - yc */
        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

        /* xb + xd */
        t1 = pSrc[2u * i1] + pSrc[2u * i3];

        /* xa' = xa + xb + xc + xd */
        pSrc[2u * i0] = r1 + t1;

        /* xa + xc -(xb + xd) */
        r1 = r1 - t1;

        /* yb + yd */
        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = s1 + t2;

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* (yb - yd) */
        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

        /* (xb - xd) */
        t2 = pSrc[2u * i1] - pSrc[2u * i3];

        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = (r1 * co2) + (s1 * si2);

        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);

        /* (xa - xc) + (yb - yd) */
        r1 = r2 + t1;

        /* (xa - xc) - (yb - yd) */
        r2 = r2 - t1;

        /* (ya - yc) -  (xb - xd) */
        s1 = s2 - t2;

        /* (ya - yc) +  (xb - xd) */
        s2 = s2 + t2;

        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = (r1 * co1) + (s1 * si1);

        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);

        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = (r2 * co3) + (s2 * si3);

        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
      }
    }
    twidCoefModifier <<= 2u;
  }

#endif /* #ifndef ARM_MATH_CM0 */

}

/*   
 * @brief  Core function for the floating-point CIFFT butterfly process.  
 * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.  
 * @param[in]      fftLen           length of the FFT.  
 * @param[in]      *pCoef           points to twiddle coefficient buffer.  
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.  
 * @param[in]      onebyfftLen      value of 1/fftLen.  
 * @return none.  
 */

void arm_radix4_butterfly_inverse_f32(
  float32_t * pSrc,
  uint16_t fftLen,
  float32_t * pCoef,
  uint16_t twidCoefModifier,
  float32_t onebyfftLen)
{
  float32_t co1, co2, co3, si1, si2, si3;
  float32_t t1, t2, r1, r2, s1, s2;
  uint32_t ia1, ia2, ia3;
  uint32_t i0, i1, i2, i3;
  uint32_t n1, n2, j, k;

#ifndef ARM_MATH_CM0

  /* Run the below code for Cortex-M4 and Cortex-M3 */

  /*  Initializations for the first stage */
  n2 = fftLen;
  n1 = n2;

  /* n2 = fftLen/4 */
  n2 >>= 2u;
  i0 = 0u;
  ia1 = 0u;

  j = n2;

  /*  Calculation of first stage */
  do
  {
    /*  index calculation for the input as, */
    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
    i1 = i0 + n2;
    i2 = i1 + n2;
    i3 = i2 + n2;

    /*  Butterfly implementation */
    /* xa + xc */
    r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

    /* xa - xc */
    r2 = pSrc[2u * i0] - pSrc[2u * i2];

    /* ya + yc */
    s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

    /* ya - yc */
    s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

    /* xb + xd */
    t1 = pSrc[2u * i1] + pSrc[2u * i3];

    /* xa' = xa + xb + xc + xd */
    pSrc[2u * i0] = r1 + t1;

    /* (xa + xc) - (xb + xd) */
    r1 = r1 - t1;

    /* yb + yd */
    t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

    /* ya' = ya + yb + yc + yd */
    pSrc[(2u * i0) + 1u] = s1 + t2;

    /* (ya + yc) - (yb + yd) */
    s1 = s1 - t2;

    /* yb - yd */
    t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

    /* xb - xd */
    t2 = pSrc[2u * i1] - pSrc[2u * i3];

    /*  index calculation for the coefficients */
    ia2 = ia1 + ia1;
    co2 = pCoef[ia2 * 2u];
    si2 = pCoef[(ia2 * 2u) + 1u];

    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
    pSrc[2u * i1] = (r1 * co2) - (s1 * si2);

    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
    pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);

    /* (xa - xc) - (yb - yd) */
    r1 = r2 - t1;

    /* (xa - xc) + (yb - yd) */
    r2 = r2 + t1;

    /* (ya - yc) + (xb - xd) */
    s1 = s2 + t2;

    /* (ya - yc) - (xb - xd) */
    s2 = s2 - t2;

    co1 = pCoef[ia1 * 2u];
    si1 = pCoef[(ia1 * 2u) + 1u];

    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
    pSrc[2u * i2] = (r1 * co1) - (s1 * si1);

    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
    pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);

    /*  index calculation for the coefficients */
    ia3 = ia2 + ia1;
    co3 = pCoef[ia3 * 2u];
    si3 = pCoef[(ia3 * 2u) + 1u];

    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
    pSrc[2u * i3] = (r2 * co3) - (s2 * si3);

    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
    pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);

    /*  Twiddle coefficients index modifier */
    ia1 = ia1 + twidCoefModifier;

    /*  Updating input index */
    i0 = i0 + 1u;

  }
  while(--j);

  twidCoefModifier <<= 2u;

  /*  Calculation of second stage to excluding last stage */
  for (k = fftLen / 4; 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/2], pSrc[i0 + 3fftLen/4] */
        i1 = i0 + n2;
        i2 = i1 + n2;
        i3 = i2 + n2;

        /* xa + xc */
        r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

        /* xa - xc */
        r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];

        /* ya + yc */
        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

        /* ya - yc */
        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

        /* xb + xd */
        t1 = pSrc[2u * i1] + pSrc[2u * i3];

        /* xa' = xa + xb + xc + xd */
        pSrc[2u * i0] = r1 + t1;

        /* xa + xc -(xb + xd) */
        r1 = r1 - t1;

        /* yb + yd */
        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = s1 + t2;

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* (yb - yd) */
        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

        /* (xb - xd) */
        t2 = pSrc[2u * i1] - pSrc[2u * i3];

        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = (r1 * co2) - (s1 * si2);

        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);

        /* (xa - xc) - (yb - yd) */
        r1 = r2 - t1;

        /* (xa - xc) + (yb - yd) */
        r2 = r2 + t1;

        /* (ya - yc) +  (xb - xd) */
        s1 = s2 + t2;

        /* (ya - yc) -  (xb - xd) */
        s2 = s2 - t2;

        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = (r1 * co1) - (s1 * si1);

        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);

        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = (r2 * co3) - (s2 * si3);

        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
      }
    }
    twidCoefModifier <<= 2u;
  }

  /*  Initializations of last stage */
  n1 = n2;
  n2 >>= 2u;

  /*  Calculations of last stage */
  for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
  {
    /*  index calculation for the input as, */
    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
    i1 = i0 + n2;
    i2 = i1 + n2;
    i3 = i2 + n2;

    /*  Butterfly implementation */
    /* xa + xc */
    r1 = pSrc[2u * i0] + pSrc[2u * i2];

    /* xa - xc */
    r2 = pSrc[2u * i0] - pSrc[2u * i2];

    /* ya + yc */
    s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

    /* ya - yc */
    s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

    /* xc + xd */
    t1 = pSrc[2u * i1] + pSrc[2u * i3];

    /* xa' = xa + xb + xc + xd */
    pSrc[2u * i0] = (r1 + t1) * onebyfftLen;

    /* (xa + xb) - (xc + xd) */
    r1 = r1 - t1;

    /* yb + yd */
    t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

    /* ya' = ya + yb + yc + yd */
    pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;

    /* (ya + yc) - (yb + yd) */
    s1 = s1 - t2;

    /* (yb-yd) */
    t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

    /* (xb-xd) */
    t2 = pSrc[2u * i1] - pSrc[2u * i3];

    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
    pSrc[2u * i1] = r1 * onebyfftLen;

    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
    pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;


    /* (xa - xc) - (yb-yd) */
    r1 = r2 - t1;

    /* (xa - xc) + (yb-yd) */
    r2 = r2 + t1;

    /* (ya - yc) + (xb-xd) */
    s1 = s2 + t2;

    /* (ya - yc) - (xb-xd) */
    s2 = s2 - t2;

    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
    pSrc[2u * i2] = r1 * onebyfftLen;

    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
    pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;

    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
    pSrc[2u * i3] = r2 * onebyfftLen;

    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
    pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
  }


#else

  /* Run the below code for Cortex-M0 */

  /*  Initializations for the first stage */
  n2 = fftLen;
  n1 = n2;

  /*  Calculation of first stage */
  for (k = fftLen; k > 4u; k >>= 2u)
  {
    /*  Initializations for the first stage */
    n1 = n2;
    n2 >>= 2u;
    ia1 = 0u;

    /*  Calculation of first stage */
    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/2], pSrc[i0 + 3fftLen/4] */
        i1 = i0 + n2;
        i2 = i1 + n2;
        i3 = i2 + n2;

        /* xa + xc */
        r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

        /* xa - xc */
        r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];

        /* ya + yc */
        s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

        /* ya - yc */
        s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

        /* xb + xd */
        t1 = pSrc[2u * i1] + pSrc[2u * i3];

        /* xa' = xa + xb + xc + xd */
        pSrc[2u * i0] = r1 + t1;

        /* xa + xc -(xb + xd) */
        r1 = r1 - t1;

        /* yb + yd */
        t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = s1 + t2;

        /* (ya + yc) - (yb + yd) */
        s1 = s1 - t2;

        /* (yb - yd) */
        t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

        /* (xb - xd) */
        t2 = pSrc[2u * i1] - pSrc[2u * i3];

        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = (r1 * co2) - (s1 * si2);

        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);

        /* (xa - xc) - (yb - yd) */
        r1 = r2 - t1;

        /* (xa - xc) + (yb - yd) */
        r2 = r2 + t1;

        /* (ya - yc) +  (xb - xd) */
        s1 = s2 + t2;

        /* (ya - yc) -  (xb - xd) */
        s2 = s2 - t2;

        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = (r1 * co1) - (s1 * si1);

        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);

        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = (r2 * co3) - (s2 * si3);

        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
      }
    }
    twidCoefModifier <<= 2u;
  }
  /*  Initializations of last stage */
  n1 = n2;
  n2 >>= 2u;

  /*  Calculations of last stage */
  for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
  {
    /*  index calculation for the input as, */
    /*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
    i1 = i0 + n2;
    i2 = i1 + n2;
    i3 = i2 + n2;

    /*  Butterfly implementation */
    /* xa + xc */
    r1 = pSrc[2u * i0] + pSrc[2u * i2];

    /* xa - xc */
    r2 = pSrc[2u * i0] - pSrc[2u * i2];

    /* ya + yc */
    s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

    /* ya - yc */
    s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

    /* xc + xd */
    t1 = pSrc[2u * i1] + pSrc[2u * i3];

    /* xa' = xa + xb + xc + xd */
    pSrc[2u * i0] = (r1 + t1) * onebyfftLen;

    /* (xa + xb) - (xc + xd) */
    r1 = r1 - t1;

    /* yb + yd */
    t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

    /* ya' = ya + yb + yc + yd */
    pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;

    /* (ya + yc) - (yb + yd) */
    s1 = s1 - t2;

    /* (yb-yd) */
    t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

    /* (xb-xd) */
    t2 = pSrc[2u * i1] - pSrc[2u * i3];

    /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
    pSrc[2u * i1] = r1 * onebyfftLen;

    /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
    pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;


    /* (xa - xc) - (yb-yd) */
    r1 = r2 - t1;

    /* (xa - xc) + (yb-yd) */
    r2 = r2 + t1;

    /* (ya - yc) + (xb-xd) */
    s1 = s2 + t2;

    /* (ya - yc) - (xb-xd) */
    s2 = s2 - t2;

    /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
    pSrc[2u * i2] = r1 * onebyfftLen;

    /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
    pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;

    /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
    pSrc[2u * i3] = r2 * onebyfftLen;

    /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
    pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
  }

#endif /* #ifndef ARM_MATH_CM0 */

}

/*   
 * @brief  In-place bit reversal function.  
 * @param[in, out] *pSrc        points to the in-place buffer of floating-point data type.  
 * @param[in]      fftSize      length of the FFT.  
 * @param[in]      bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.  
 * @param[in]      *pBitRevTab  points to the bit reversal table.  
 * @return none.  
 */

void arm_bitreversal_f32(
  float32_t * pSrc,
  uint16_t fftSize,
  uint16_t bitRevFactor,
  uint16_t * pBitRevTab)
{
  uint16_t fftLenBy2, fftLenBy2p1;
  uint16_t i, j;
  float32_t in;

  /*  Initializations */
  j = 0u;
  fftLenBy2 = fftSize >> 1u;
  fftLenBy2p1 = (fftSize >> 1u) + 1u;

  /* Bit Reversal Implementation */
  for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
  {
    if(i < j)
    {
      /*  pSrc[i] <-> pSrc[j]; */
      in = pSrc[2u * i];
      pSrc[2u * i] = pSrc[2u * j];
      pSrc[2u * j] = in;

      /*  pSrc[i+1u] <-> pSrc[j+1u] */
      in = pSrc[(2u * i) + 1u];
      pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
      pSrc[(2u * j) + 1u] = in;

      /*  pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
      in = pSrc[2u * (i + fftLenBy2p1)];
      pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
      pSrc[2u * (j + fftLenBy2p1)] = in;

      /*  pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
      in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
      pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
        pSrc[(2u * (j + fftLenBy2p1)) + 1u];
      pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;

    }

    /*  pSrc[i+1u] <-> pSrc[j+1u] */
    in = pSrc[2u * (i + 1u)];
    pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
    pSrc[2u * (j + fftLenBy2)] = in;

    /*  pSrc[i+2u] <-> pSrc[j+2u] */
    in = pSrc[(2u * (i + 1u)) + 1u];
    pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
    pSrc[(2u * (j + fftLenBy2)) + 1u] = in;

    /*  Reading the index for the bit reversal */
    j = *pBitRevTab;

    /*  Updating the bit reversal index depending on the fft length  */
    pBitRevTab += bitRevFactor;
  }
}