/* fft/c_pass_3.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program is distributed in the hope that it will be useful, but

 * WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

static 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 TYPE(gsl_complex) * twiddle1,

                              const TYPE(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 ATOMIC tau = sqrt (3.0) / 2.0;

  for (k = 0; k < q; k++)

    {

      ATOMIC 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 == gsl_fft_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 ATOMIC z0_real = REAL(in,istride,i);

          const ATOMIC z0_imag = IMAG(in,istride,i);

          const ATOMIC z1_real = REAL(in,istride,i+m);

          const ATOMIC z1_imag = IMAG(in,istride,i+m);

          const ATOMIC z2_real = REAL(in,istride,i+2*m);

          const ATOMIC z2_imag = IMAG(in,istride,i+2*m);

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

          /* t1 = z1 + z2 */

          const ATOMIC t1_real = z1_real + z2_real;

          const ATOMIC t1_imag = z1_imag + z2_imag;

          /* t2 = z0 - t1/2 */

          const ATOMIC t2_real = z0_real - t1_real / 2.0;

          const ATOMIC t2_imag = z0_imag - t1_imag / 2.0;

          /* t3 = (+/-) sin(pi/3)*(z1 - z2) */

          const ATOMIC t3_real = ((int) sign) * tau * (z1_real - z2_real);

          const ATOMIC t3_imag = ((int) sign) * tau * (z1_imag - z2_imag);

          /* x0 = z0 + t1 */

          const ATOMIC x0_real = z0_real + t1_real;

          const ATOMIC x0_imag = z0_imag + t1_imag;

          /* x1 = t2 + i t3 */

          const ATOMIC x1_real = t2_real - t3_imag;

          const ATOMIC x1_imag = t2_imag + t3_real;

          /* x2 = t2 - i t3 */

          const ATOMIC x2_real = t2_real + t3_imag;

          const ATOMIC 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;

}