int
FUNCTION(fft_complex,pass_6) (const BASE in[],
			      const size_t istride,
			      BASE out[],
			      const size_t ostride,
			      const gsl_fft_direction sign,
			      const size_t product,
			      const size_t n,
			      const gsl_complex twiddle1[],
			      const gsl_complex twiddle2[],
			      const gsl_complex twiddle3[],
			      const gsl_complex twiddle4[],
			      const gsl_complex twiddle5[])
{

  size_t i = 0, j = 0;
  size_t k, k1;

  const size_t factor = 6;
  const size_t m = n / factor;
  const size_t q = n / product;
  const size_t p_1 = product / factor;
  const size_t jump = (factor - 1) * p_1;

  const double tau = sqrt (3.0) / 2.0;

  for (k = 0; k < q; k++)
    {
      double w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real,
        w4_imag, w5_real, w5_imag;

      if (k == 0)
	{
	  w1_real = 1.0;
	  w1_imag = 0.0;
	  w2_real = 1.0;
	  w2_imag = 0.0;
	  w3_real = 1.0;
	  w3_imag = 0.0;
	  w4_real = 1.0;
	  w4_imag = 0.0;
	  w5_real = 1.0;
	  w5_imag = 0.0;
	}
      else
	{
	  if (sign == forward)
	    {
	      /* forward tranform */
	      w1_real = GSL_REAL(twiddle1[k - 1]);
	      w1_imag = GSL_IMAG(twiddle1[k - 1]);
	      w2_real = GSL_REAL(twiddle2[k - 1]);
	      w2_imag = GSL_IMAG(twiddle2[k - 1]);
	      w3_real = GSL_REAL(twiddle3[k - 1]);
	      w3_imag = GSL_IMAG(twiddle3[k - 1]);
	      w4_real = GSL_REAL(twiddle4[k - 1]);
	      w4_imag = GSL_IMAG(twiddle4[k - 1]);
	      w5_real = GSL_REAL(twiddle5[k - 1]);
	      w5_imag = GSL_IMAG(twiddle5[k - 1]);
	    }
	  else
	    {
	      /* backward tranform: w -> conjugate(w) */
	      w1_real = GSL_REAL(twiddle1[k - 1]);
	      w1_imag = -GSL_IMAG(twiddle1[k - 1]);
	      w2_real = GSL_REAL(twiddle2[k - 1]);
	      w2_imag = -GSL_IMAG(twiddle2[k - 1]);
	      w3_real = GSL_REAL(twiddle3[k - 1]);
	      w3_imag = -GSL_IMAG(twiddle3[k - 1]);
	      w4_real = GSL_REAL(twiddle4[k - 1]);
	      w4_imag = -GSL_IMAG(twiddle4[k - 1]);
	      w5_real = GSL_REAL(twiddle5[k - 1]);
	      w5_imag = -GSL_IMAG(twiddle5[k - 1]);
	    }
	}

      for (k1 = 0; k1 < p_1; k1++)
	{
	  const double z0_real = REAL(in,istride,i);
	  const double z0_imag = IMAG(in,istride,i);
	  const double z1_real = REAL(in,istride,i+m);
	  const double z1_imag = IMAG(in,istride,i+m);
	  const double z2_real = REAL(in,istride,i+2*m);
	  const double z2_imag = IMAG(in,istride,i+2*m);
	  const double z3_real = REAL(in,istride,i+3*m);
	  const double z3_imag = IMAG(in,istride,i+3*m);
	  const double z4_real = REAL(in,istride,i+4*m);
	  const double z4_imag = IMAG(in,istride,i+4*m);
	  const double z5_real = REAL(in,istride,i+5*m);
	  const double z5_imag = IMAG(in,istride,i+5*m);

	  /* compute x = W(6) z */

	  /* W(6) is a combination of sums and differences of W(3) acting
	     on the even and odd elements of z */
	  
	  /* ta1 = z2 + z4 */
	  const double ta1_real = z2_real + z4_real;
	  const double ta1_imag = z2_imag + z4_imag;
	  
	  /* ta2 = z0 - ta1/2 */
	  const double ta2_real = z0_real - ta1_real / 2;
	  const double ta2_imag = z0_imag - ta1_imag / 2;
	  
	  /* ta3 = (+/-) sin(pi/3)*(z2 - z4) */
	  const double ta3_real = ((int) sign) * tau * (z2_real - z4_real);
	  const double ta3_imag = ((int) sign) * tau * (z2_imag - z4_imag);
	  
	  /* a0 = z0 + ta1 */
	  const double a0_real = z0_real + ta1_real;
	  const double a0_imag = z0_imag + ta1_imag;
	  
	  /* a1 = ta2 + i ta3 */
	  const double a1_real = ta2_real - ta3_imag;
	  const double a1_imag = ta2_imag + ta3_real;
	  
	  /* a2 = ta2 - i ta3 */
	  const double a2_real = ta2_real + ta3_imag;
	  const double a2_imag = ta2_imag - ta3_real;
	  
	  /* tb1 = z5 + z1 */
	  const double tb1_real = z5_real + z1_real;
	  const double tb1_imag = z5_imag + z1_imag;
	  
	  /* tb2 = z3 - tb1/2 */
	  const double tb2_real = z3_real - tb1_real / 2;
	  const double tb2_imag = z3_imag - tb1_imag / 2;
	  
	  /* tb3 = (+/-) sin(pi/3)*(z5 - z1) */
	  const double tb3_real = ((int) sign) * tau * (z5_real - z1_real);
	  const double tb3_imag = ((int) sign) * tau * (z5_imag - z1_imag);
	  
	  /* b0 = z3 + tb1 */
	  const double b0_real = z3_real + tb1_real;
	  const double b0_imag = z3_imag + tb1_imag;
	  
	  /* b1 = tb2 + i tb3 */
	  const double b1_real = tb2_real - tb3_imag;
	  const double b1_imag = tb2_imag + tb3_real;
	  
	  /* b2 = tb2 - i tb3 */
	  const double b2_real = tb2_real + tb3_imag;
	  const double b2_imag = tb2_imag - tb3_real;
	  
	  /* x0 = a0 + b0 */
	  const double x0_real = a0_real + b0_real;
	  const double x0_imag = a0_imag + b0_imag;
	  
	  /* x4 = a1 + b1 */
	  const double x4_real = a1_real + b1_real;
	  const double x4_imag = a1_imag + b1_imag;
	  
	  /* x2 = a2 + b2 */
	  const double x2_real = a2_real + b2_real;
	  const double x2_imag = a2_imag + b2_imag;
	  
	  /* x3 = a0 - b0 */
	  const double x3_real = a0_real - b0_real;
	  const double x3_imag = a0_imag - b0_imag;
	  
	  /* x1 = a1 - b1 */
	  const double x1_real = a1_real - b1_real;
	  const double x1_imag = a1_imag - b1_imag;
	  
	  /* x5 = a2 - b2 */
	  const double x5_real = a2_real - b2_real;
	  const double x5_imag = a2_imag - b2_imag;

	  /* apply twiddle factors */
	  
	  /* to0 = 1 * x0 */
	  REAL(out,ostride,j) = x0_real;
	  IMAG(out,ostride,j) = x0_imag;
	  
	  /* to1 = w1 * x1 */
	  REAL(out,ostride,j+p_1) = w1_real * x1_real - w1_imag * x1_imag;
	  IMAG(out,ostride,j+p_1) = w1_real * x1_imag + w1_imag * x1_real;
	  
	  /* to2 = w2 * x2 */
	  REAL(out,ostride,j+2*p_1) = w2_real * x2_real - w2_imag * x2_imag;
	  IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real;
	  
	  /* to3 = w3 * x3 */
	  REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag;
	  IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real;
	  
	  /* to4 = w4 * x4 */
	  REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag;
	  IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real;
	  
	  /* to5 = w5 * x5 */
	  REAL(out,ostride,j+5*p_1) = w5_real * x5_real - w5_imag * x5_imag;
	  IMAG(out,ostride,j+5*p_1) = w5_real * x5_imag + w5_imag * x5_real;

	  i++;
	  j++;
	}
      j += jump;
    }
  return 0;
}