text: /* ----------------------------------------------------------------------    
  * Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
  *    
  * $Date:        31. July 2014 
  * $Revision: 	V1.4.4  
  *    
  * 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
  *  
  * 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"
  
  extern void arm_bitreversal_f32(
  float32_t * pSrc,
  uint16_t fftSize,
  uint16_t bitRevFactor,
  uint16_t * pBitRevTab);
  
  /**    
  * @ingroup groupTransforms    
  */
  
  /* ----------------------------------------------------------------------    
  ** 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;
     uint32_t ia1, ia2, ia3;
     uint32_t i0, i1, i2, i3;
     uint32_t n1, n2, j, k;
  
  #ifndef ARM_MATH_CM0_FAMILY_FAMILY
  
     /* Run the below code for Cortex-M4 and Cortex-M3 */
  
     float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
     float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
     Ybminusd;
     float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
     float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
     float32_t *ptr1;
     float32_t p0,p1,p2,p3,p4,p5;
     float32_t a0,a1,a2,a3,a4,a5,a6,a7;
  
     /*  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;
  
        xaIn = pSrc[(2u * i0)];
        yaIn = pSrc[(2u * i0) + 1u];
  
        xbIn = pSrc[(2u * i1)];
        ybIn = pSrc[(2u * i1) + 1u];
  
        xcIn = pSrc[(2u * i2)];
        ycIn = pSrc[(2u * i2) + 1u];
  
        xdIn = pSrc[(2u * i3)];
        ydIn = pSrc[(2u * i3) + 1u];
  
        /* xa + xc */
        Xaplusc = xaIn + xcIn;
        /* xb + xd */
        Xbplusd = xbIn + xdIn;
        /* ya + yc */
        Yaplusc = yaIn + ycIn;
        /* yb + yd */
        Ybplusd = ybIn + ydIn;
  
        /*  index calculation for the coefficients */
        ia2 = ia1 + ia1;
        co2 = pCoef[ia2 * 2u];
        si2 = pCoef[(ia2 * 2u) + 1u];
  
        /* xa - xc */
        Xaminusc = xaIn - xcIn;
        /* xb - xd */
        Xbminusd = xbIn - xdIn;
        /* ya - yc */
        Yaminusc = yaIn - ycIn;
        /* yb - yd */
        Ybminusd = ybIn - ydIn;
  
        /* xa' = xa + xb + xc + xd */
        pSrc[(2u * i0)] = Xaplusc + Xbplusd;
        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
  
        /* (xa - xc) + (yb - yd) */
        Xb12C_out = (Xaminusc + Ybminusd);
        /* (ya - yc) + (xb - xd) */
        Yb12C_out = (Yaminusc - Xbminusd);
        /* (xa + xc) - (xb + xd) */
        Xc12C_out = (Xaplusc - Xbplusd);
        /* (ya + yc) - (yb + yd) */
        Yc12C_out = (Yaplusc - Ybplusd);
        /* (xa - xc) - (yb - yd) */
        Xd12C_out = (Xaminusc - Ybminusd);
        /* (ya - yc) + (xb - xd) */
        Yd12C_out = (Xbminusd + Yaminusc);
  
        co1 = pCoef[ia1 * 2u];
        si1 = pCoef[(ia1 * 2u) + 1u];
  
        /*  index calculation for the coefficients */
        ia3 = ia2 + ia1;
        co3 = pCoef[ia3 * 2u];
        si3 = pCoef[(ia3 * 2u) + 1u];
  
        Xb12_out = Xb12C_out * co1;
        Yb12_out = Yb12C_out * co1;
        Xc12_out = Xc12C_out * co2;
        Yc12_out = Yc12C_out * co2;
        Xd12_out = Xd12C_out * co3;
        Yd12_out = Yd12C_out * co3;
           
        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        //Xb12_out -= Yb12C_out * si1;
        p0 = Yb12C_out * si1;
        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        //Yb12_out += Xb12C_out * si1;
        p1 = Xb12C_out * si1;
        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        //Xc12_out -= Yc12C_out * si2;
        p2 = Yc12C_out * si2;
        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        //Yc12_out += Xc12C_out * si2;
        p3 = Xc12C_out * si2;
        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        //Xd12_out -= Yd12C_out * si3;
        p4 = Yd12C_out * si3;
        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        //Yd12_out += Xd12C_out * si3;
        p5 = Xd12C_out * si3;
        
        Xb12_out += p0;
        Yb12_out -= p1;
        Xc12_out += p2;
        Yc12_out -= p3;
        Xd12_out += p4;
        Yd12_out -= p5;
  
        /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = Xc12_out;
  
        /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = Yc12_out;
  
        /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = Xb12_out;
  
        /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = Yb12_out;
  
        /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = Xd12_out;
  
        /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = Yd12_out;
  
        /*  Twiddle coefficients index modifier */
        ia1 += twidCoefModifier;
  
        /*  Updating input index */
        i0++;
  
     }
     while(--j);
  
     twidCoefModifier <<= 2u;
  
     /*  Calculation of second stage to excluding last stage */
     for (k = fftLen >> 2u; k > 4u; k >>= 2u)
     {
        /*  Initializations for the first stage */
        n1 = n2;
        n2 >>= 2u;
        ia1 = 0u;
  
        /*  Calculation of first stage */
        j = 0;
        do
        {
           /*  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 += twidCoefModifier;
        
           i0 = j;
           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;
  
              xaIn = pSrc[(2u * i0)];
              yaIn = pSrc[(2u * i0) + 1u];
  
              xbIn = pSrc[(2u * i1)];
              ybIn = pSrc[(2u * i1) + 1u];
  
              xcIn = pSrc[(2u * i2)];
              ycIn = pSrc[(2u * i2) + 1u];
  
              xdIn = pSrc[(2u * i3)];
              ydIn = pSrc[(2u * i3) + 1u];
  
              /* xa - xc */
              Xaminusc = xaIn - xcIn;
              /* (xb - xd) */
              Xbminusd = xbIn - xdIn;
              /* ya - yc */
              Yaminusc = yaIn - ycIn;
              /* (yb - yd) */
              Ybminusd = ybIn - ydIn;
  
              /* xa + xc */
              Xaplusc = xaIn + xcIn;
              /* xb + xd */
              Xbplusd = xbIn + xdIn;
              /* ya + yc */
              Yaplusc = yaIn + ycIn;
              /* yb + yd */
              Ybplusd = ybIn + ydIn;
  
              /* (xa - xc) + (yb - yd) */
              Xb12C_out = (Xaminusc + Ybminusd);
              /* (ya - yc) -  (xb - xd) */
              Yb12C_out = (Yaminusc - Xbminusd);
              /* xa + xc -(xb + xd) */
              Xc12C_out = (Xaplusc - Xbplusd);
              /* (ya + yc) - (yb + yd) */
              Yc12C_out = (Yaplusc - Ybplusd);
              /* (xa - xc) - (yb - yd) */
              Xd12C_out = (Xaminusc - Ybminusd);
              /* (ya - yc) +  (xb - xd) */
              Yd12C_out = (Xbminusd + Yaminusc);
  
              pSrc[(2u * i0)] = Xaplusc + Xbplusd;
              pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
  
              Xb12_out = Xb12C_out * co1;
              Yb12_out = Yb12C_out * co1;
              Xc12_out = Xc12C_out * co2;
              Yc12_out = Yc12C_out * co2;
              Xd12_out = Xd12C_out * co3;
              Yd12_out = Yd12C_out * co3;
           
              /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
              //Xb12_out -= Yb12C_out * si1;
              p0 = Yb12C_out * si1;
              /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
              //Yb12_out += Xb12C_out * si1;
              p1 = Xb12C_out * si1;
              /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
              //Xc12_out -= Yc12C_out * si2;
              p2 = Yc12C_out * si2;
              /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
              //Yc12_out += Xc12C_out * si2;
              p3 = Xc12C_out * si2;
              /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
              //Xd12_out -= Yd12C_out * si3;
              p4 = Yd12C_out * si3;
              /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
              //Yd12_out += Xd12C_out * si3;
              p5 = Xd12C_out * si3;
              
              Xb12_out += p0;
              Yb12_out -= p1;
              Xc12_out += p2;
              Yc12_out -= p3;
              Xd12_out += p4;
              Yd12_out -= p5;
  
              /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
              pSrc[2u * i1] = Xc12_out;
  
              /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
              pSrc[(2u * i1) + 1u] = Yc12_out;
  
              /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
              pSrc[2u * i2] = Xb12_out;
  
              /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
              pSrc[(2u * i2) + 1u] = Yb12_out;
  
              /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
              pSrc[2u * i3] = Xd12_out;
  
              /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
              pSrc[(2u * i3) + 1u] = Yd12_out;
  
              i0 += n1;
           } while(i0 < fftLen);
           j++;
        } while(j <= (n2 - 1u));
        twidCoefModifier <<= 2u;
     }
  
     j = fftLen >> 2;
     ptr1 = &pSrc[0];
  
     /*  Calculations of last stage */
     do
     {
        xaIn = ptr1[0];
        yaIn = ptr1[1];
        xbIn = ptr1[2];
        ybIn = ptr1[3];
        xcIn = ptr1[4];
        ycIn = ptr1[5];
        xdIn = ptr1[6];
        ydIn = ptr1[7];
  
        /* xa + xc */
        Xaplusc = xaIn + xcIn;
  
        /* xa - xc */
        Xaminusc = xaIn - xcIn;
  
        /* ya + yc */
        Yaplusc = yaIn + ycIn;
  
        /* ya - yc */
        Yaminusc = yaIn - ycIn;
  
        /* xb + xd */
        Xbplusd = xbIn + xdIn;
  
        /* yb + yd */
        Ybplusd = ybIn + ydIn;
  
        /* (xb-xd) */
        Xbminusd = xbIn - xdIn;
  
        /* (yb-yd) */
        Ybminusd = ybIn - ydIn;
  
        /* xa' = xa + xb + xc + xd */
        a0 = (Xaplusc + Xbplusd);
        /* ya' = ya + yb + yc + yd */
        a1 = (Yaplusc + Ybplusd);
        /* xc' = (xa-xb+xc-xd) */
        a2 = (Xaplusc - Xbplusd);
        /* yc' = (ya-yb+yc-yd) */
        a3 = (Yaplusc - Ybplusd);
        /* xb' = (xa+yb-xc-yd) */
        a4 = (Xaminusc + Ybminusd);
        /* yb' = (ya-xb-yc+xd) */
        a5 = (Yaminusc - Xbminusd);
        /* xd' = (xa-yb-xc+yd)) */
        a6 = (Xaminusc - Ybminusd);
        /* yd' = (ya+xb-yc-xd) */
        a7 = (Xbminusd + Yaminusc);
     
        ptr1[0] = a0;
        ptr1[1] = a1;
        ptr1[2] = a2;
        ptr1[3] = a3;
        ptr1[4] = a4;
        ptr1[5] = a5;
        ptr1[6] = a6;
        ptr1[7] = a7;
  
        /* increment pointer by 8 */
        ptr1 += 8u;
     } while(--j);
  
  #else
  
     float32_t t1, t2, r1, r2, s1, s2;
  
     /* 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 */
        j = 0;
        do
        {
           /*  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;
  
           i0 = j;
           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;
  
              /* 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);
           
              i0 += n1;
           } while( i0 < fftLen);
           j++;
        } while(j <= (n2 - 1u));
        twidCoefModifier <<= 2u;
     }
  
  #endif /* #ifndef ARM_MATH_CM0_FAMILY_FAMILY */
  
  }
  
  /*    
  * @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;
     uint32_t ia1, ia2, ia3;
     uint32_t i0, i1, i2, i3;
     uint32_t n1, n2, j, k;
  
  #ifndef ARM_MATH_CM0_FAMILY_FAMILY
  
     float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
     float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
     Ybminusd;
     float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
     float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
     float32_t *ptr1;
     float32_t p0,p1,p2,p3,p4,p5,p6,p7;
     float32_t a0,a1,a2,a3,a4,a5,a6,a7;
  
  
     /*  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 */
        xaIn = pSrc[(2u * i0)];
        yaIn = pSrc[(2u * i0) + 1u];
  
        xcIn = pSrc[(2u * i2)];
        ycIn = pSrc[(2u * i2) + 1u];
  
        xbIn = pSrc[(2u * i1)];
        ybIn = pSrc[(2u * i1) + 1u];
  
        xdIn = pSrc[(2u * i3)];
        ydIn = pSrc[(2u * i3) + 1u];
  
        /* xa + xc */
        Xaplusc = xaIn + xcIn;
        /* xb + xd */
        Xbplusd = xbIn + xdIn;
        /* ya + yc */
        Yaplusc = yaIn + ycIn;
        /* yb + yd */
        Ybplusd = ybIn + ydIn;
  
        /*  index calculation for the coefficients */
        ia2 = ia1 + ia1;
        co2 = pCoef[ia2 * 2u];
        si2 = pCoef[(ia2 * 2u) + 1u];
  
        /* xa - xc */
        Xaminusc = xaIn - xcIn;
        /* xb - xd */
        Xbminusd = xbIn - xdIn;
        /* ya - yc */
        Yaminusc = yaIn - ycIn;
        /* yb - yd */
        Ybminusd = ybIn - ydIn;
  
        /* xa' = xa + xb + xc + xd */
        pSrc[(2u * i0)] = Xaplusc + Xbplusd;
  
        /* ya' = ya + yb + yc + yd */
        pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
  
        /* (xa - xc) - (yb - yd) */
        Xb12C_out = (Xaminusc - Ybminusd);
        /* (ya - yc) + (xb - xd) */
        Yb12C_out = (Yaminusc + Xbminusd);
        /* (xa + xc) - (xb + xd) */
        Xc12C_out = (Xaplusc - Xbplusd);
        /* (ya + yc) - (yb + yd) */
        Yc12C_out = (Yaplusc - Ybplusd);
        /* (xa - xc) + (yb - yd) */
        Xd12C_out = (Xaminusc + Ybminusd);
        /* (ya - yc) - (xb - xd) */
        Yd12C_out = (Yaminusc - Xbminusd);
  
        co1 = pCoef[ia1 * 2u];
        si1 = pCoef[(ia1 * 2u) + 1u];
  
        /*  index calculation for the coefficients */
        ia3 = ia2 + ia1;
        co3 = pCoef[ia3 * 2u];
        si3 = pCoef[(ia3 * 2u) + 1u];
  
        Xb12_out = Xb12C_out * co1;
        Yb12_out = Yb12C_out * co1;
        Xc12_out = Xc12C_out * co2;
        Yc12_out = Yc12C_out * co2;
        Xd12_out = Xd12C_out * co3;
        Yd12_out = Yd12C_out * co3;
     
        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        //Xb12_out -= Yb12C_out * si1;
        p0 = Yb12C_out * si1;
        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        //Yb12_out += Xb12C_out * si1;
        p1 = Xb12C_out * si1;
        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        //Xc12_out -= Yc12C_out * si2;
        p2 = Yc12C_out * si2;
        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        //Yc12_out += Xc12C_out * si2;
        p3 = Xc12C_out * si2;
        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        //Xd12_out -= Yd12C_out * si3;
        p4 = Yd12C_out * si3;
        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        //Yd12_out += Xd12C_out * si3;
        p5 = Xd12C_out * si3;
        
        Xb12_out -= p0;
        Yb12_out += p1;
        Xc12_out -= p2;
        Yc12_out += p3;
        Xd12_out -= p4;
        Yd12_out += p5;
  
        /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
        pSrc[2u * i1] = Xc12_out;
  
        /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
        pSrc[(2u * i1) + 1u] = Yc12_out;
  
        /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
        pSrc[2u * i2] = Xb12_out;
  
        /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
        pSrc[(2u * i2) + 1u] = Yb12_out;
  
        /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
        pSrc[2u * i3] = Xd12_out;
  
        /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
        pSrc[(2u * i3) + 1u] = Yd12_out;
  
        /*  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 >> 2u; k > 4u; k >>= 2u)
     {
        /*  Initializations for the first stage */
        n1 = n2;
        n2 >>= 2u;
        ia1 = 0u;
  
        /*  Calculation of first stage */
        j = 0;
        do
        {
           /*  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;
  
           i0 = j;
           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;
  
              xaIn = pSrc[(2u * i0)];
              yaIn = pSrc[(2u * i0) + 1u];
  
              xbIn = pSrc[(2u * i1)];
              ybIn = pSrc[(2u * i1) + 1u];
  
              xcIn = pSrc[(2u * i2)];
              ycIn = pSrc[(2u * i2) + 1u];
  
              xdIn = pSrc[(2u * i3)];
              ydIn = pSrc[(2u * i3) + 1u];
  
              /* xa - xc */
              Xaminusc = xaIn - xcIn;
              /* (xb - xd) */
              Xbminusd = xbIn - xdIn;
              /* ya - yc */
              Yaminusc = yaIn - ycIn;
              /* (yb - yd) */
              Ybminusd = ybIn - ydIn;
  
              /* xa + xc */
              Xaplusc = xaIn + xcIn;
              /* xb + xd */
              Xbplusd = xbIn + xdIn;
              /* ya + yc */
              Yaplusc = yaIn + ycIn;
              /* yb + yd */
              Ybplusd = ybIn + ydIn;
  
              /* (xa - xc) - (yb - yd) */
              Xb12C_out = (Xaminusc - Ybminusd);
              /* (ya - yc) +  (xb - xd) */
              Yb12C_out = (Yaminusc + Xbminusd);
              /* xa + xc -(xb + xd) */
              Xc12C_out = (Xaplusc - Xbplusd);
              /* (ya + yc) - (yb + yd) */
              Yc12C_out = (Yaplusc - Ybplusd);
              /* (xa - xc) + (yb - yd) */
              Xd12C_out = (Xaminusc + Ybminusd);
              /* (ya - yc) -  (xb - xd) */
              Yd12C_out = (Yaminusc - Xbminusd);
  
              pSrc[(2u * i0)] = Xaplusc + Xbplusd;
              pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
  
              Xb12_out = Xb12C_out * co1;
              Yb12_out = Yb12C_out * co1;
              Xc12_out = Xc12C_out * co2;
              Yc12_out = Yc12C_out * co2;
              Xd12_out = Xd12C_out * co3;
              Yd12_out = Yd12C_out * co3;
  
              /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
              //Xb12_out -= Yb12C_out * si1;
              p0 = Yb12C_out * si1;
              /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
              //Yb12_out += Xb12C_out * si1;
              p1 = Xb12C_out * si1;
              /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
              //Xc12_out -= Yc12C_out * si2;
              p2 = Yc12C_out * si2;
              /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
              //Yc12_out += Xc12C_out * si2;
              p3 = Xc12C_out * si2;
              /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
              //Xd12_out -= Yd12C_out * si3;
              p4 = Yd12C_out * si3;
              /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
              //Yd12_out += Xd12C_out * si3;
              p5 = Xd12C_out * si3;
              
              Xb12_out -= p0;
              Yb12_out += p1;
              Xc12_out -= p2;
              Yc12_out += p3;
              Xd12_out -= p4;
              Yd12_out += p5;
  
              /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
              pSrc[2u * i1] = Xc12_out;
  
              /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
              pSrc[(2u * i1) + 1u] = Yc12_out;
  
              /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
              pSrc[2u * i2] = Xb12_out;
  
              /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
              pSrc[(2u * i2) + 1u] = Yb12_out;
  
              /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
              pSrc[2u * i3] = Xd12_out;
  
              /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
              pSrc[(2u * i3) + 1u] = Yd12_out;
  
              i0 += n1;
           } while(i0 < fftLen);
           j++;
        } while(j <= (n2 - 1u));
        twidCoefModifier <<= 2u;
     }
     /*  Initializations of last stage */
  
     j = fftLen >> 2;
     ptr1 = &pSrc[0];
  
     /*  Calculations of last stage */
     do
     {
        xaIn = ptr1[0];
        yaIn = ptr1[1];
        xbIn = ptr1[2];
        ybIn = ptr1[3];
        xcIn = ptr1[4];
        ycIn = ptr1[5];
        xdIn = ptr1[6];
        ydIn = ptr1[7];
  
        /*  Butterfly implementation */
        /* xa + xc */
        Xaplusc = xaIn + xcIn;
  
        /* xa - xc */
        Xaminusc = xaIn - xcIn;
  
        /* ya + yc */
        Yaplusc = yaIn + ycIn;
  
        /* ya - yc */
        Yaminusc = yaIn - ycIn;
  
        /* xb + xd */
        Xbplusd = xbIn + xdIn;
  
        /* yb + yd */
        Ybplusd = ybIn + ydIn;
  
        /* (xb-xd) */
        Xbminusd = xbIn - xdIn;
  
        /* (yb-yd) */
        Ybminusd = ybIn - ydIn;
        
        /* xa' = (xa+xb+xc+xd) * onebyfftLen */
        a0 = (Xaplusc + Xbplusd);
        /* ya' = (ya+yb+yc+yd) * onebyfftLen */
        a1 = (Yaplusc + Ybplusd);
        /* xc' = (xa-xb+xc-xd) * onebyfftLen */
        a2 = (Xaplusc - Xbplusd);
        /* yc' = (ya-yb+yc-yd) * onebyfftLen  */
        a3 = (Yaplusc - Ybplusd);
        /* xb' = (xa-yb-xc+yd) * onebyfftLen */
        a4 = (Xaminusc - Ybminusd);
        /* yb' = (ya+xb-yc-xd) * onebyfftLen */
        a5 = (Yaminusc + Xbminusd);
        /* xd' = (xa-yb-xc+yd) * onebyfftLen */
        a6 = (Xaminusc + Ybminusd);
        /* yd' = (ya-xb-yc+xd) * onebyfftLen */
        a7 = (Yaminusc - Xbminusd);
     
        p0 = a0 * onebyfftLen;
        p1 = a1 * onebyfftLen;
        p2 = a2 * onebyfftLen;
        p3 = a3 * onebyfftLen;
        p4 = a4 * onebyfftLen;
        p5 = a5 * onebyfftLen;
        p6 = a6 * onebyfftLen;
        p7 = a7 * onebyfftLen;
     
        /* xa' = (xa+xb+xc+xd) * onebyfftLen */
        ptr1[0] = p0;
        /* ya' = (ya+yb+yc+yd) * onebyfftLen */
        ptr1[1] = p1;
        /* xc' = (xa-xb+xc-xd) * onebyfftLen */
        ptr1[2] = p2;
        /* yc' = (ya-yb+yc-yd) * onebyfftLen  */
        ptr1[3] = p3;
        /* xb' = (xa-yb-xc+yd) * onebyfftLen */
        ptr1[4] = p4;
        /* yb' = (ya+xb-yc-xd) * onebyfftLen */
        ptr1[5] = p5;
        /* xd' = (xa-yb-xc+yd) * onebyfftLen */
        ptr1[6] = p6;
        /* yd' = (ya-xb-yc+xd) * onebyfftLen */
        ptr1[7] = p7;
  
        /* increment source pointer by 8 for next calculations */
        ptr1 = ptr1 + 8u;
  
     } while(--j);
  
  #else
  
     float32_t t1, t2, r1, r2, s1, s2;
  
     /* 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 */
        j = 0;
        do
        {
           /*  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;
  
           i0 = j;
           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;
  
              /* 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);
           
              i0 += n1;
           } while( i0 < fftLen);
           j++;
        } while(j <= (n2 - 1u));
        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_FAMILY_FAMILY */
  }
  
  /**    
  * @addtogroup ComplexFFT    
  * @{    
  */
  
  /**    
  * @details    
  * @brief Processing function for the floating-point Radix-4 CFFT/CIFFT.   
  * @deprecated Do not use this function.  It has been superseded by \ref arm_cfft_f32 and will be removed
  * in the future.
  * @param[in]      *S    points to an instance of the floating-point Radix-4 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 ComplexFFT group    
  */
  
  