// Copyright (c) 1996 Jens Jorgen Nielsen
// Written by Jens Jorgen Nielsen
// Optimizations by Janik Joire
//
// $History: $

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#ifndef PI
#define PI		3.14159265358979323846F
#endif

/************************************************************************
  fft(long n,float xRe[],float xIm[],float yRe[],float yIm[])
  ------------------------------------------------------------------------
  NOTE : This is copyrighted material, Not public domain. See below.
  ------------------------------------------------------------------------
  Input/output:
  long n        transformation length.
  float xRe[]   real part of input sequence.
  float xIm[]   imaginary part of input sequence.
  float yRe[]   real part of output sequence.
  float yIm[]   imaginary part of output sequence.
  ------------------------------------------------------------------------
  Function:
  The procedure performs a fast discrete Fourier transform (FFT) of
  a complex sequence, x, of an arbitrary length, n. The output, y,
  is also a complex sequence of length n.
  
  y[k] = sum(x[m]*exp(-i*2*pi*k*m/n), m=0..(n-1)), k=0,...,(n-1)
  
  The largest prime factor of n must be less than or equal to the
  constant maxPrimeFactor defined below.
  ------------------------------------------------------------------------
  Author:
  Jens Jorgen Nielsen             For non-commercial use only.
  Bakkehusene 54                  A $100 fee must be paid if used
  DK-2970 Horsholm                commercially. Please contact.
  DENMARK
  
  e-mail : jnielsen@internet.dk   All rights reserved. March 1996.
  ------------------------------------------------------------------------
  Implementation notes:
  The general idea is to factor the length of the DFT, n, into
  factors that are efficiently handled by the routines.
  
  A number of short DFT's are implemented with a minimum of
      arithmetical operations and using (almost) straight line code
      resulting in very fast execution when the factors of n belong
      to this set. Especially radix-10 is optimized.

      Prime factors, that are not in the set of short DFT's are handled
      with direct evaluation of the DFP expression.

      Please report any problems to the author. 
      Suggestions and improvements are welcomed.
 ------------------------------------------------------------------------
  Benchmarks:                   
      The Microsoft Visual C++ compiler was used with the following 
      compile options:
      /nologo /Gs /G2 /W4 /AH /Ox /D "NDEBUG" /D "_DOS" /FR
      and the FFTBENCH test executed on a 50MHz 486DX :
      
      Length  Time [s]  Accuracy [dB]

         128   0.0054     -314.8   
         256   0.0116     -309.8   
         512   0.0251     -290.8   
        1024   0.0567     -313.6   
        2048   0.1203     -306.4   
        4096   0.2600     -291.8   
        8192   0.5800     -305.1   
         100   0.0040     -278.5   
         200   0.0099     -280.3   
         500   0.0256     -278.5   
        1000   0.0540     -278.5   
        2000   0.1294     -280.6   
        5000   0.3300     -278.4   
       10000   0.7133     -278.5   
 ------------------------------------------------------------------------
  The following procedures are used :
      factorize       :  factor the transformation length.
      transTableSetup :  setup table with sofar-, actual-, and remainRadix.
      permute         :  permutation allows in-place calculations.
      twiddleTransf   :  twiddle multiplications and DFT's for one stage.
      initTrig        :  initialise sine/cosine table.
      fft_4           :  length 4 DFT, a la Nussbaumer.
      fft_5           :  length 5 DFT, a la Nussbaumer.
      fft_10          :  length 10 DFT using prime factor FFT.
      fft_odd         :  length n DFT, n odd.
*************************************************************************/

#define  maxPrimeFactor        37
#define  maxPrimeFactorDiv2    (maxPrimeFactor+1)/2
#define  maxFactorCount        20

static float  c3_1 = -1.5000000000000E+00F;  /*  c3_1 = cos(2*pi/3)-1;          */
static float  c3_2 =  8.6602540378444E-01F;  /*  c3_2 = sin(2*pi/3);            */
                                          
static float  u5   =  1.2566370614359E+00F;  /*  u5   = 2*pi/5;                 */
static float  c5_1 = -1.2500000000000E+00F;  /*  c5_1 = (cos(u5)+cos(2*u5))/2-1;*/
static float  c5_2 =  5.5901699437495E-01F;  /*  c5_2 = (cos(u5)-cos(2*u5))/2;  */
static float  c5_3 = -9.5105651629515E-01F;  /*  c5_3 = -sin(u5);               */
static float  c5_4 = -1.5388417685876E+00F;  /*  c5_4 = -(sin(u5)+sin(2*u5));   */
static float  c5_5 =  3.6327126400268E-01F;  /*  c5_5 = (sin(u5)-sin(2*u5));    */
static float  c8   =  7.0710678118655E-01F;  /*  c8 = 1/sqrt(2);    */

static float   pi;
static long      groupOffset,dataOffset,blockOffset,adr;
static long      groupNo,dataNo,blockNo,twNo;
static float   omega, tw_re,tw_im;
static float   twiddleRe[maxPrimeFactor], twiddleIm[maxPrimeFactor],
  trigRe[maxPrimeFactor], trigIm[maxPrimeFactor],
  zRe[maxPrimeFactor], zIm[maxPrimeFactor];
static float   vRe[maxPrimeFactorDiv2], vIm[maxPrimeFactorDiv2];
static float   wRe[maxPrimeFactorDiv2], wIm[maxPrimeFactorDiv2];

void factorize(long n, long *nFact, long fact[])
{
  long i,j,k;
  long nRadix;
  long radices[7];
  long factors[maxFactorCount];

  nRadix    =  6;  
  radices[1]=  2;
  radices[2]=  3;
  radices[3]=  4;
  radices[4]=  5;
  radices[5]=  8;
  radices[6]= 10;

  if (n==1)
    {
      j=1;
      factors[1]=1;
    }
  else j=0;
  i=nRadix;
  while ((n>1) && (i>0))
    {
      if ((n % radices[i]) == 0)
	{
	  n=n / radices[i];
	  j=j+1;
	  factors[j]=radices[i];
	}
      else  i=i-1;
    }
  if (factors[j] == 2)   /*substitute factors 2*8 with 4*4 */
    {   
      i = j-1;
      while ((i>0) && (factors[i] != 8)) i--;
      if (i>0)
	{
	  factors[j] = 4;
	  factors[i] = 4;
	}
    }
  if (n>1)
    {
      for (k=2; k<sqrt(n)+1; k++)
	while ((n % k) == 0)
	  {
	    n=n / k;
	    j=j+1;
	    factors[j]=k;
	  }
      if (n>1)
        {
	  j=j+1;
	  factors[j]=n;
        }
    }               
  for (i=1; i<=j; i++)         
    {
      fact[i] = factors[j-i+1];
    }
  *nFact=j;
}   /* factorize */

/****************************************************************************
  After N is factored the parameters that control the stages are generated.
  For each stage we have:
    sofar   : the product of the radices so far.
    actual  : the radix handled in this stage.
    remain  : the product of the remaining radices.
 ****************************************************************************/

void transTableSetup(long sofar[], long actual[], long remain[],
                     long *nFact,
                     long *nPoints)
{
  long i;

  factorize(*nPoints, nFact, actual);
  if (actual[*nFact] > maxPrimeFactor)
    {
      printf("\nPrime factor of FFT length too large : %6d",actual[*nFact]);
      exit(1);
    }
  remain[0]=*nPoints;
  sofar[1]=1;
  remain[1]=*nPoints / actual[1];
  for (i=2; i<=*nFact; i++)
    {
      sofar[i]=sofar[i-1]*actual[i-1];
      remain[i]=remain[i-1] / actual[i];
    }
}   /* transTableSetup */

/****************************************************************************
  The sequence y is the permuted input sequence x so that the following
  transformations can be performed in-place, and the final result is the
  normal order.
 ****************************************************************************/

void permute(long nPoint, long nFact,
             long fact[], long remain[],
             float xRe[], float xIm[],
             float yRe[], float yIm[])

{
  long i,j,k;
  long count[maxFactorCount]; 

  for (i=1; i<=nFact; i++) count[i]=0;
  k=0;
  for (i=0; i<=nPoint-2; i++)
    {
      yRe[i] = xRe[k];
      yIm[i] = xIm[k];
      j=1;
      k=k+remain[j];
      count[1] = count[1]+1;
      while (count[j] >= fact[j])
        {
	  count[j]=0;
	  k=k-remain[j-1]+remain[j+1];
	  j=j+1;
	  count[j]=count[j]+1;
        }
    }
  yRe[nPoint-1]=xRe[nPoint-1];
  yIm[nPoint-1]=xIm[nPoint-1];
}   /* permute */


/****************************************************************************
  Twiddle factor multiplications and transformations are performed on a
  group of data. The number of multiplications with 1 are reduced by skipping
  the twiddle multiplication of the first stage and of the first group of the
  following stages.
 ***************************************************************************/

void initTrig(long radix)
{
  long i;
  float w,xre,xim;

  w=2*pi/radix;
  trigRe[0]=1; trigIm[0]=0;
  xre=(float)cos(w); 
  xim=-(float)sin(w);
  trigRe[1]=xre; trigIm[1]=xim;
  for (i=2; i<radix; i++)
    {
      trigRe[i]=xre*trigRe[i-1] - xim*trigIm[i-1];
      trigIm[i]=xim*trigRe[i-1] + xre*trigIm[i-1];
    }
}   /* initTrig */

void fft_4(float aRe[], float aIm[])
{
  float  t1_re,t1_im, t2_re,t2_im;
  float  m2_re,m2_im, m3_re,m3_im;

  t1_re=aRe[0] + aRe[2]; t1_im=aIm[0] + aIm[2];
  t2_re=aRe[1] + aRe[3]; t2_im=aIm[1] + aIm[3];

  m2_re=aRe[0] - aRe[2]; m2_im=aIm[0] - aIm[2];
  m3_re=aIm[1] - aIm[3]; m3_im=aRe[3] - aRe[1];

  aRe[0]=t1_re + t2_re; aIm[0]=t1_im + t2_im;
  aRe[2]=t1_re - t2_re; aIm[2]=t1_im - t2_im;
  aRe[1]=m2_re + m3_re; aIm[1]=m2_im + m3_im;
  aRe[3]=m2_re - m3_re; aIm[3]=m2_im - m3_im;
}   /* fft_4 */


void fft_5(float aRe[], float aIm[])
{    
  float  t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
  float  t4_re,t4_im, t5_re,t5_im;
  float  m2_re,m2_im, m3_re,m3_im, m4_re,m4_im;
  float  m1_re,m1_im, m5_re,m5_im;
  float  s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
  float  s4_re,s4_im, s5_re,s5_im;

  t1_re=aRe[1] + aRe[4]; t1_im=aIm[1] + aIm[4];
  t2_re=aRe[2] + aRe[3]; t2_im=aIm[2] + aIm[3];
  t3_re=aRe[1] - aRe[4]; t3_im=aIm[1] - aIm[4];
  t4_re=aRe[3] - aRe[2]; t4_im=aIm[3] - aIm[2];
  t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
  aRe[0]=aRe[0] + t5_re; aIm[0]=aIm[0] + t5_im;
  m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
  m2_re=c5_2*(t1_re - t2_re); m2_im=c5_2*(t1_im - t2_im);

  m3_re=-c5_3*(t3_im + t4_im); m3_im=c5_3*(t3_re + t4_re);
  m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
  m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;

  s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
  s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
  s1_re=aRe[0] + m1_re; s1_im=aIm[0] + m1_im;
  s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
  s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;

  aRe[1]=s2_re + s3_re; aIm[1]=s2_im + s3_im;
  aRe[2]=s4_re + s5_re; aIm[2]=s4_im + s5_im;
  aRe[3]=s4_re - s5_re; aIm[3]=s4_im - s5_im;
  aRe[4]=s2_re - s3_re; aIm[4]=s2_im - s3_im;
}   /* fft_5 */

void fft_8()
{
  float  aRe[4], aIm[4], bRe[4], bIm[4], gem;

  aRe[0] = zRe[0];    bRe[0] = zRe[1];
  aRe[1] = zRe[2];    bRe[1] = zRe[3];
  aRe[2] = zRe[4];    bRe[2] = zRe[5];
  aRe[3] = zRe[6];    bRe[3] = zRe[7];

  aIm[0] = zIm[0];    bIm[0] = zIm[1];
  aIm[1] = zIm[2];    bIm[1] = zIm[3];
  aIm[2] = zIm[4];    bIm[2] = zIm[5];
  aIm[3] = zIm[6];    bIm[3] = zIm[7];

  fft_4(aRe, aIm); fft_4(bRe, bIm);

  gem    = c8*(bRe[1] + bIm[1]);
  bIm[1] = c8*(bIm[1] - bRe[1]);
  bRe[1] = gem;
  gem    = bIm[2];
  bIm[2] =-bRe[2];
  bRe[2] = gem;
  gem    = c8*(bIm[3] - bRe[3]);
  bIm[3] =-c8*(bRe[3] + bIm[3]);
  bRe[3] = gem;
    
  zRe[0] = aRe[0] + bRe[0]; zRe[4] = aRe[0] - bRe[0];
  zRe[1] = aRe[1] + bRe[1]; zRe[5] = aRe[1] - bRe[1];
  zRe[2] = aRe[2] + bRe[2]; zRe[6] = aRe[2] - bRe[2];
  zRe[3] = aRe[3] + bRe[3]; zRe[7] = aRe[3] - bRe[3];

  zIm[0] = aIm[0] + bIm[0]; zIm[4] = aIm[0] - bIm[0];
  zIm[1] = aIm[1] + bIm[1]; zIm[5] = aIm[1] - bIm[1];
  zIm[2] = aIm[2] + bIm[2]; zIm[6] = aIm[2] - bIm[2];
  zIm[3] = aIm[3] + bIm[3]; zIm[7] = aIm[3] - bIm[3];
}   /* fft_8 */

void fft_10()
{
  float  aRe[5], aIm[5], bRe[5], bIm[5];

  aRe[0] = zRe[0];    bRe[0] = zRe[5];
  aRe[1] = zRe[2];    bRe[1] = zRe[7];
  aRe[2] = zRe[4];    bRe[2] = zRe[9];
  aRe[3] = zRe[6];    bRe[3] = zRe[1];
  aRe[4] = zRe[8];    bRe[4] = zRe[3];

  aIm[0] = zIm[0];    bIm[0] = zIm[5];
  aIm[1] = zIm[2];    bIm[1] = zIm[7];
  aIm[2] = zIm[4];    bIm[2] = zIm[9];
  aIm[3] = zIm[6];    bIm[3] = zIm[1];
  aIm[4] = zIm[8];    bIm[4] = zIm[3];

  fft_5(aRe, aIm); fft_5(bRe, bIm);

  zRe[0] = aRe[0] + bRe[0]; zRe[5] = aRe[0] - bRe[0];
  zRe[6] = aRe[1] + bRe[1]; zRe[1] = aRe[1] - bRe[1];
  zRe[2] = aRe[2] + bRe[2]; zRe[7] = aRe[2] - bRe[2];
  zRe[8] = aRe[3] + bRe[3]; zRe[3] = aRe[3] - bRe[3];
  zRe[4] = aRe[4] + bRe[4]; zRe[9] = aRe[4] - bRe[4];

  zIm[0] = aIm[0] + bIm[0]; zIm[5] = aIm[0] - bIm[0];
  zIm[6] = aIm[1] + bIm[1]; zIm[1] = aIm[1] - bIm[1];
  zIm[2] = aIm[2] + bIm[2]; zIm[7] = aIm[2] - bIm[2];
  zIm[8] = aIm[3] + bIm[3]; zIm[3] = aIm[3] - bIm[3];
  zIm[4] = aIm[4] + bIm[4]; zIm[9] = aIm[4] - bIm[4];
}   /* fft_10 */

void fft_odd(long radix)
{
  float  rere, reim, imre, imim;
  long     i,j,k,n,max;

  n = radix;
  max = (n + 1)/2;
  for (j=1; j < max; j++)
    {
      vRe[j] = zRe[j] + zRe[n-j];
      vIm[j] = zIm[j] - zIm[n-j];
      wRe[j] = zRe[j] - zRe[n-j];
      wIm[j] = zIm[j] + zIm[n-j];
    }

  for (j=1; j < max; j++)
    {
      zRe[j]=zRe[0]; 
      zIm[j]=zIm[0];
      zRe[n-j]=zRe[0]; 
      zIm[n-j]=zIm[0];
      k=j;
      for (i=1; i < max; i++)
        {
	  rere = trigRe[k] * vRe[i];
	  imim = trigIm[k] * vIm[i];
	  reim = trigRe[k] * wIm[i];
	  imre = trigIm[k] * wRe[i];
            
	  zRe[n-j] += rere + imim;
	  zIm[n-j] += reim - imre;
	  zRe[j]   += rere - imim;
	  zIm[j]   += reim + imre;

	  k = k + j;
	  if (k >= n)  k = k - n;
        }
    }
  for (j=1; j < max; j++)
    {
      zRe[0]=zRe[0] + vRe[j]; 
      zIm[0]=zIm[0] + wIm[j];
    }
}   /* fft_odd */


void twiddleTransf(long sofarRadix, long radix, long remainRadix,
		   float yRe[], float yIm[])

{   /* twiddleTransf */ 
  float  cosw, sinw, gem;
  float  t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
  float  t4_re,t4_im, t5_re,t5_im;
  float  m2_re,m2_im, m3_re,m3_im, m4_re,m4_im;
  float  m1_re,m1_im, m5_re,m5_im;
  float  s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
  float  s4_re,s4_im, s5_re,s5_im;


  initTrig(radix);
  omega = 2*pi/(float)(sofarRadix*radix);
  cosw =  (float)cos(omega);
  sinw = -(float)sin(omega);
  tw_re = 1.0;
  tw_im = 0;
  dataOffset=0;
  groupOffset=dataOffset;
  adr=groupOffset;
  for (dataNo=0; dataNo<sofarRadix; dataNo++)
    {
      if (sofarRadix>1)
        {
	  twiddleRe[0] = 1.0; 
	  twiddleIm[0] = 0.0;
	  twiddleRe[1] = tw_re;
	  twiddleIm[1] = tw_im;
	  for (twNo=2; twNo<radix; twNo++)
            {
	      twiddleRe[twNo]=tw_re*twiddleRe[twNo-1]
		- tw_im*twiddleIm[twNo-1];
	      twiddleIm[twNo]=tw_im*twiddleRe[twNo-1]
		+ tw_re*twiddleIm[twNo-1];
            }
	  gem   = cosw*tw_re - sinw*tw_im;
	  tw_im = sinw*tw_re + cosw*tw_im;
	  tw_re = gem;                      
        }
      for (groupNo=0; groupNo<remainRadix; groupNo++)
        {
	  if ((sofarRadix>1) && (dataNo > 0))
            {
	      zRe[0]=yRe[adr];
	      zIm[0]=yIm[adr];
	      blockNo=1;
	      do {
		adr = adr + sofarRadix;
		zRe[blockNo]=  twiddleRe[blockNo] * yRe[adr]
		  - twiddleIm[blockNo] * yIm[adr];
		zIm[blockNo]=  twiddleRe[blockNo] * yIm[adr]
		  + twiddleIm[blockNo] * yRe[adr]; 
                    
		blockNo++;
	      } while (blockNo < radix);
            }
	  else
	    for (blockNo=0; blockNo<radix; blockNo++)
	      {
		zRe[blockNo]=yRe[adr];
		zIm[blockNo]=yIm[adr];
		adr=adr+sofarRadix;
	      }
	  switch(radix) {
	  case  2  : gem=zRe[0] + zRe[1];
	    zRe[1]=zRe[0] -  zRe[1]; zRe[0]=gem;
	    gem=zIm[0] + zIm[1];
	    zIm[1]=zIm[0] - zIm[1]; zIm[0]=gem;
	    break;
	  case  3  : t1_re=zRe[1] + zRe[2]; t1_im=zIm[1] + zIm[2];
	    zRe[0]=zRe[0] + t1_re; zIm[0]=zIm[0] + t1_im;
	    m1_re=c3_1*t1_re; m1_im=c3_1*t1_im;
	    m2_re=c3_2*(zIm[1] - zIm[2]); 
	    m2_im=c3_2*(zRe[2] -  zRe[1]);
	    s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
	    zRe[1]=s1_re + m2_re; zIm[1]=s1_im + m2_im;
	    zRe[2]=s1_re - m2_re; zIm[2]=s1_im - m2_im;
	    break;
	  case  4  : t1_re=zRe[0] + zRe[2]; t1_im=zIm[0] + zIm[2];
	    t2_re=zRe[1] + zRe[3]; t2_im=zIm[1] + zIm[3];

	    m2_re=zRe[0] - zRe[2]; m2_im=zIm[0] - zIm[2];
	    m3_re=zIm[1] - zIm[3]; m3_im=zRe[3] - zRe[1];

	    zRe[0]=t1_re + t2_re; zIm[0]=t1_im + t2_im;
	    zRe[2]=t1_re - t2_re; zIm[2]=t1_im - t2_im;
	    zRe[1]=m2_re + m3_re; zIm[1]=m2_im + m3_im;
	    zRe[3]=m2_re - m3_re; zIm[3]=m2_im - m3_im;
	    break;
	  case  5  : t1_re=zRe[1] + zRe[4]; t1_im=zIm[1] + zIm[4];
	    t2_re=zRe[2] + zRe[3]; t2_im=zIm[2] + zIm[3];
	    t3_re=zRe[1] - zRe[4]; t3_im=zIm[1] - zIm[4];
	    t4_re=zRe[3] - zRe[2]; t4_im=zIm[3] - zIm[2];
	    t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
	    zRe[0]=zRe[0] + t5_re; zIm[0]=zIm[0] + t5_im;
	    m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
	    m2_re=c5_2*(t1_re - t2_re); 
	    m2_im=c5_2*(t1_im - t2_im);

	    m3_re=-c5_3*(t3_im + t4_im); 
	    m3_im=c5_3*(t3_re + t4_re);
	    m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
	    m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;

	    s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
	    s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
	    s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
	    s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
	    s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;

	    zRe[1]=s2_re + s3_re; zIm[1]=s2_im + s3_im;
	    zRe[2]=s4_re + s5_re; zIm[2]=s4_im + s5_im;
	    zRe[3]=s4_re - s5_re; zIm[3]=s4_im - s5_im;
	    zRe[4]=s2_re - s3_re; zIm[4]=s2_im - s3_im;
	    break;
	  case  8  : fft_8(); break;
	  case 10  : fft_10(); break;
	  default  : fft_odd(radix); break;
	  }
	  adr=groupOffset;
	  for (blockNo=0; blockNo<radix; blockNo++)
            {
	      yRe[adr]=zRe[blockNo]; yIm[adr]=zIm[blockNo];
	      adr=adr+sofarRadix;
            }
	  groupOffset=groupOffset+sofarRadix*radix;
	  adr=groupOffset;
        }
      dataOffset=dataOffset+1;
      groupOffset=dataOffset;
      adr=groupOffset;
    }
}   /* twiddleTransf */

void fft(long n,float *xRe,float *xIm,float *yRe,float *yIm)
{
  long   sofarRadix[maxFactorCount], 
    actualRadix[maxFactorCount], 
    remainRadix[maxFactorCount];
  long   nFactor;
  long   count;

  pi = PI;    

  transTableSetup(sofarRadix, actualRadix, remainRadix, &nFactor, &n);
  permute(n, nFactor, actualRadix, remainRadix, xRe, xIm, yRe, yIm);

  for (count=1; count<=nFactor; count++)
    twiddleTransf(sofarRadix[count], actualRadix[count], remainRadix[count], 
		  yRe, yIm);
}   /* fft */

