#define __complex__ _Complex
#include <stdio.h>
#include <math.h>
#include "complex.h"
typedef _Complex float c;
void pc(c a){printf("%14.7e + %14.7ei\n", creal(a), cimag(a));}
c Sqrt(c x){
double A = crealf(x), B = cimag(x);
if(A < 0) return I* Sqrt(-x);
{double r = sqrt((A + sqrt(A*A + B*B))/2);
return r + I*(B/(2*r));}}

void fft(c a[], const int n){
  {int j=0, i; for(i=0; i<n-1; ++i) {
    if(i<j) {c t=a[j]; a[j]=a[i]; a[i]=t;}
    {int m=n/2; while(m<=j) {j -= m; m /= 2;} j += m;}}} 
  {int j=1, m; c b=-1; while(j<n) {c w = 1;
    for(m=0; m<j; ++m) {int i;
      for(i=m; i<n; i+=j+j)
        {c t = w*a[i+j]; a[i+j]=a[i]-t; a[i] += t;}
      w *= b;}
    j *= 2; b = Sqrt(b);}}}