int
FUNCTION(fft_complex,pass_3) (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)
{
  size_t i = 0, j = 0;
  size_t k, k1;

  const size_t factor = 3;
  const size_t m = n / factor;
  const size_t q = n / product;
  const size_t product_1 = product / factor;
  const size_t jump = (factor - 1) * product_1;

  const double tau = sqrt (3.0) / 2.0;

  for (k = 0; k < q; k++)
    {
      double w1_real, w1_imag, w2_real, w2_imag;

      if (k == 0)
	{
	  w1_real = 1.0;
	  w1_imag = 0.0;
	  w2_real = 1.0;
	  w2_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]);
	    }
	  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]);
	    }
	}

      for (k1 = 0; k1 < product_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);

	  /* compute x = W(3) z */

	  /* t1 = z1 + z2 */
	  const double t1_real = z1_real + z2_real;
	  const double t1_imag = z1_imag + z2_imag;
	  
	  /* t2 = z0 - t1/2 */
	  const double t2_real = z0_real - t1_real / 2.0;
	  const double t2_imag = z0_imag - t1_imag / 2.0;
	  
	  /* t3 = (+/-) sin(pi/3)*(z1 - z2) */
	  const double t3_real = ((int) sign) * tau * (z1_real - z2_real);
	  const double t3_imag = ((int) sign) * tau * (z1_imag - z2_imag);
	  
	  /* x0 = z0 + t1 */
	  const double x0_real = z0_real + t1_real;
	  const double x0_imag = z0_imag + t1_imag;
	  
	  /* x1 = t2 + i t3 */
	  const double x1_real = t2_real - t3_imag;
	  const double x1_imag = t2_imag + t3_real;
	  
	  /* x2 = t2 - i t3 */
	  const double x2_real = t2_real + t3_imag;
	  const double x2_imag = t2_imag - t3_real;

	  /* 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+product_1) = w1_real * x1_real - w1_imag * x1_imag;
	  IMAG(out,ostride,j+product_1) = w1_real * x1_imag + w1_imag * x1_real;
	  
	  /* to2 = w2 * x2 */
	  REAL(out,ostride,j+2*product_1) = w2_real * x2_real - w2_imag * x2_imag;
	  IMAG(out,ostride,j+2*product_1) = w2_real * x2_imag + w2_imag * x2_real;

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