#include <stdio.h>
#include <math.h>
#include <malloc.h>
#include <time.h>
#include <float.h>
#define N 1048576
#define N2 N/2
main()
{
/* 
   Generic version of cfft2 - no intrinsics
   from Section 3.5 in Petersen/Arbenz book,
   Oxford Uni. Press, 2004.

   W. Petersen, SAM. Math. ETHZ 1 June, 2002 
*/
   int first,i,icase,it,ln2,n;
/*
  repetition count:
                   16,    32,   64,  128,  256, 512, 1024, 2048,
                    |      |     |     |     |    |     |     | */
   int NX[17]={100000,100000,10000,10000,10000,1000, 1000, 1000,
           100,  100,  100,  100,   10,    10,     1,     1,      1};
/*           |     |     |     |     |      |      |      |       |
           4096,8192,16384,32768,65536,131072,262144,524288,1048576 */
   int nits;
   float error,fnm1,sign,z0,z1,ggl();
   float *x,*y,*z,*w;
   static float seed;
   double t1,mflops;
   void cffti(),cfft2();
/* allocate storage for x,y,z,w on 4-word bndr. */
   x = (float *) malloc(8*N);
   y = (float *) malloc(8*N);
   z = (float *) malloc(8*N);
   w = (float *) malloc(4*N);
   seed  = 331.0;
   n     = 16;
   for(ln2=4;ln2<21;ln2++){
      nits = NX[ln2-4];
      first = 1;
      for(icase=0;icase<2;icase++){
         if(first){
            for(i=0;i<2*n;i+=2){
               z0 = ggl(&seed);     /* real part of array */
               z1 = ggl(&seed);     /* imaginary part of array */
               x[i] = z0;
               z[i] = z0;           /* copy of initial real data */
               x[i+1] = z1;
               z[i+1] = z1;         /* copy of initial imag. data */
            }
         } else {
            for(i=0;i<2*n;i+=2){
               z0 = 0;              /* real part of array */
               z1 = 0;              /* imaginary part of array */
               x[i] = z0;
               z[i] = z0;           /* copy of initial real data */
               x[i+1] = z1;
               z[i+1] = z1;         /* copy of initial imag. data */
            }
         }
/* initialize sine/cosine tables */
         cffti(n,w);
/* transform forward, back */
         if(first){
            sign = 1.0;
            cfft2(n,x,y,w,sign);
            sign = -1.0;
            cfft2(n,y,x,w,sign);
/* results should be same as initial multiplied by n */
            fnm1 = 1.0/((float) n);
            error = 0.0;
            for(i=0;i<2*n;i+=2){
               error += (z[i] - fnm1*x[i])*(z[i] - fnm1*x[i]) +
                   (z[i+1] - fnm1*x[i+1])*(z[i+1] - fnm1*x[i+1]);
            }
            error = sqrt(fnm1*error);
            printf(" for n=%d, fwd/bck error=%e\n",n,error);
            first = 0;
         } else {
            t1   = ((double)clock())/((double) CLOCKS_PER_SEC);
            for(it=0;it<nits;it++){
               sign = +1.0;
               cfft2(n,x,y,w,sign);
               sign = -1.0;
               cfft2(n,y,x,w,sign);
            }
            t1   = ((double)clock())/((double) CLOCKS_PER_SEC) - t1;
            t1   = 0.5*t1/((double) nits);
            mflops = 5.0*((double) n)*((double) ln2)/((1.e+6)*t1);
            printf(" for n=%d, t1=%e, mflops=%e\n",n,t1,mflops);
         }
      }
      if((ln2%4)==0) nits /= 10;
      n *= 2;
   }
}
void cffti(int n, float w[][2])
{
   int i,n2;
   float aw,arg,pi;
   pi = 3.141592653589793;
   n2 = n/2;
   aw = 2.0*pi/((float)n);
   for(i=0;i<n2;i++){
      arg   = aw*((float)i);
      w[i][0] = cos(arg);
      w[i][1] = sin(arg);
   }
}
#include <math.h>
float ggl(float *ds)
{

/* generate u(0,1) distributed random numbers. 
   Seed ds must be saved between calls. ggl is 
   essentially the same as the IMSL routine RNUM. 

   W. Petersen and M. Troyer, 24 Oct. 2002, ETHZ: 
   a modification of a fortran version from 
   I. Vattulainen, Tampere Univ. of Technology, 
   Finland, 1992 */

   double t,d2=0.2147483647e10;
   t   = (float) *ds;
   t   = fmod(0.16807e5*t,d2);
   *ds = (float) t;
   return((float) ((t-1.0e0)/(d2-1.0e0)));
}
void cfft2(n,x,y,w,sign)
int n;
float x[][2],y[][2],w[][2],sign;
{
   int jb, m, j, mj, tgle;
   void ccopy(),step();
   m    = (int) (log((float) n)/log(1.99));
   mj   = 1;
   tgle = 1;  /* toggling switch for work array */
   step(n,mj,&x[0][0],&x[n/2][0],&y[0][0],&y[mj][0],w,sign);
   if(n==2)return;
   for(j=0;j<m-2;j++){
      mj *= 2;
      if(tgle){
         step(n,mj,&y[0][0],&y[n/2][0],&x[0][0],&x[mj][0],w,sign);
         tgle = 0;
      } else {
         step(n,mj,&x[0][0],&x[n/2][0],&y[0][0],&y[mj][0],w,sign);
         tgle = 1;
      }
   }
/* last pass thru data: move y to x if needed */
   if(tgle) {
      ccopy(n,y,x);
   }
   mj   = n/2;
   step(n,mj,&x[0][0],&x[n/2][0],&y[0][0],&y[mj][0],w,sign);
}
void ccopy(int n, float x[][2], float y[][2])
{
   int i;
   for(i=0;i<n;i++){
      y[i][0] = x[i][0];
      y[i][1] = x[i][1];
   }
}
void step(n,mj,a,b,c,d,w,sign)
int n,mj;
float a[][2],b[][2],c[][2],d[][2],w[][2];
float sign;
{
   float ambr, ambu, wjw[2];
   int j, k, ja, jb, jc, jd, jw, lj, mj2;
/* one step of workspace version of CFFT2 */
   mj2 = 2*mj; lj  = n/mj2;
   for(j=0;j<lj;j++){
      jw = j*mj; ja  = jw; jb  = ja; jc  = j*mj2; jd  = jc;
      wjw[0] = w[jw][0]; wjw[1] = w[jw][1];
      if(sign<0.) wjw[1]=-wjw[1];
      for(k=0; k<mj; k++){
         c[jc + k][0] = a[ja + k][0] + b[jb + k][0];
         c[jc + k][1] = a[ja + k][1] + b[jb + k][1];
         ambr = a[ja + k][0] - b[jb + k][0];
         ambu = a[ja + k][1] - b[jb + k][1];
         d[jd + k][0] = wjw[0]*ambr - wjw[1]*ambu;
         d[jd + k][1] = wjw[1]*ambr + wjw[0]*ambu;
      }
   }
}