/* fft16.c  complex data stored  re, im, re, im, re, ... im */

void fft16(float Z[32]) /* input data points and output  [0] to [31] */
{
  static float W[32];    /* scratch vector, used many times, */
  static float E[18] =   /* constants for FFT algorithm */
   { 1.0,       0.0,       0.92388,  0.382683,
     0.707107,  0.707107,  0.382683, 0.92388,
     0.0,       1.0,      -0.382683, 0.92388,
    -0.707107,  0.707107, -0.92388,  0.382683,
    -1.0,       0.0};
  float Tre, Tim;
  int i, j, k, l, m;

   m = 8;
   l = 1;
   while(1)
   { 
      k = 0;
      j = l;
      i = 0;
      while(1)
      { 
         while(1)
	 {
	   /* W[i+k] = Z[i] + Z[m+i]; complex */
           W[2*(i+k)]   = Z[2*i]   + Z[2*(m+i)];
           W[2*(i+k)+1] = Z[2*i+1] + Z[2*(m+i)+1];

           /* W[i+j] = E[k] * (Z[i] - Z[m+i]); complex */
           Tre = Z[2*i]   - Z[2*(m+i)];
           Tim = Z[2*i+1] - Z[2*(m+i)+1];
           W[2*(i+j)]   = E[2*k] * Tre - E[2*k+1] * Tim;
           W[2*(i+j)+1] = E[2*k] * Tim + E[2*k+1] * Tre; 
           i++;
           if(i >= j) break;
	 }
         k = j;
         j = k+l;
         if(j > m) break;
      }
      l = l+l;
                  /* work back other way without copying */
      k = 0;
      j = l;
      i = 0;
      while(1)
      {
        while(1)
	{
          /* Z[i+k] = W[i] + W[m+i]; complex */
          Z[2*(i+k)]   = W[2*i]   + W[2*(m+i)];
          Z[2*(i+k)+1] = W[2*i+1] + W[2*(m+i)+1];

          /* Z[i+j] = E[k] * (W[i] - W[m+i]); complex */
          Tre = W[2*i]   - W[2*(m+i)];
          Tim = W[2*i+1] - W[2*(m+i)+1];
          Z[2*(i+j)]   = E[2*k] * Tre - E[2*k+1] * Tim;
          Z[2*(i+j)+1] = E[2*k] * Tim + E[2*k+1] * Tre;
          i++;
          if(i >= j) break;
	}
        k = j;
        j = k+l;
        if(j > m) break;
      }
      l = l+l;
      if(l > m) break; // result is in Z
   }
} /* end fft16 */