/* fft/real_pass_n.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 void

FUNCTION(fft_real,pass_n) (const BASE in[],

                           const size_t istride,

                           BASE out[],

                           const size_t ostride,

                           const size_t factor,

                           const size_t product,

                           const size_t n,

                           const TYPE(gsl_complex) twiddle[])

{

  size_t k, k1;

  const size_t m = n / factor;

  const size_t q = n / product;

  const size_t product_1 = product / factor;

  size_t e1, e2;

  const double d_theta = 2.0 * M_PI / ((double) factor);

  const ATOMIC cos_d_theta = cos (d_theta);

  const ATOMIC sin_d_theta = sin (d_theta);

  for (k1 = 0; k1 < q; k1++)

    {

      /* compute x = W(factor) z, for z real */

      ATOMIC dw_real = 1.0, dw_imag = 0.0;

      for (e1 = 0; e1 <= factor - e1; e1++)

        {

          ATOMIC sum_real = 0.0;

          ATOMIC sum_imag = 0.0;

          ATOMIC w_real = 1.0, w_imag = 0.0;

          if (e1 > 0)

            {

              ATOMIC tmp_real = dw_real * cos_d_theta + dw_imag * sin_d_theta;

              ATOMIC tmp_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta;

              dw_real = tmp_real;

              dw_imag = tmp_imag;

            }

          for (e2 = 0; e2 < factor; e2++)

            {

              ATOMIC z_real = VECTOR(in,istride,k1 * product_1 + e2 * m);

              if (e2 > 0)

                {

                  ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;

                  ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;

                  w_real = tmp_real;

                  w_imag = tmp_imag;

                }

              sum_real += w_real * z_real;

              sum_imag += w_imag * z_real;

            }

          if (e1 == 0)

            {

              const size_t to0 = product * k1;

              VECTOR(out,ostride,to0) = sum_real;

            }

          else if (e1 < factor - e1)

            {

              const size_t to0 = k1 * product + 2 * e1 * product_1 - 1;

              VECTOR(out,ostride,to0) = sum_real;

              VECTOR(out,ostride,to0 + 1) = sum_imag;

            }

          else if (e1 == factor - e1)

            {

              const size_t to0 = k1 * product + 2 * e1 * product_1 - 1;

              VECTOR(out,ostride,to0) = sum_real;

            }

        }

    }

  if (product_1 == 1)

    return;

  for (k = 1; k < (product_1 + 1) / 2; k++)

    {

      for (k1 = 0; k1 < q; k1++)

        {

          ATOMIC dw_real = 1.0, dw_imag = 0.0;

          for (e1 = 0; e1 < factor; e1++)

            {

              ATOMIC sum_real = 0.0, sum_imag = 0.0;

              ATOMIC w_real = 1.0, w_imag = 0.0;

              if (e1 > 0)

                {

                  const ATOMIC tmp_real = dw_real * cos_d_theta + dw_imag * sin_d_theta;

                  const ATOMIC tmp_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta;

                  dw_real = tmp_real;

                  dw_imag = tmp_imag;

                }

              for (e2 = 0; e2 < factor; e2++)

                {

                  int tskip = (product_1 + 1) / 2 - 1;

                  const size_t from0 = k1 * product_1 + 2 * k + e2 * m - 1;

                  ATOMIC tw_real, tw_imag;

                  ATOMIC z_real, z_imag;

                  if (e2 == 0)

                    {

                      tw_real = 1.0;

                      tw_imag = 0.0;

                    }

                  else

                    {

                      const size_t t_index = (k - 1) + (e2 - 1) * tskip;

                      tw_real = GSL_REAL(twiddle[t_index]);

                      tw_imag = -GSL_IMAG(twiddle[t_index]);

                    }

                  {

                    const ATOMIC f0_real = VECTOR(in,istride,from0);

                    const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1);

                    z_real = tw_real * f0_real - tw_imag * f0_imag;

                    z_imag = tw_real * f0_imag + tw_imag * f0_real;

                  }

                  if (e2 > 0)

                    {

                      const ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;

                      const ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;

                      w_real = tmp_real;

                      w_imag = tmp_imag;

                    }

                  sum_real += w_real * z_real - w_imag * z_imag;

                  sum_imag += w_real * z_imag + w_imag * z_real;

                }

              if (e1 < factor - e1)

                {

                  const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k;

                  VECTOR(out,ostride,to0) = sum_real;

                  VECTOR(out,ostride,to0 + 1) = sum_imag;

                }

              else

                {

                  const size_t to0 = k1 * product - 1 + 2 * (factor - e1) * product_1 - 2 * k;

                  VECTOR(out,ostride,to0) = sum_real;

                  VECTOR(out,ostride,to0 + 1) = -sum_imag;

                }

            }

        }

    }

  if (product_1 % 2 == 1)

    return;

  {

    double tw_arg = M_PI / ((double) factor);

    ATOMIC cos_tw_arg = cos (tw_arg);

    ATOMIC sin_tw_arg = -sin (tw_arg);

    for (k1 = 0; k1 < q; k1++)

      {

        ATOMIC dw_real = 1.0, dw_imag = 0.0;

        for (e1 = 0; e1 < factor; e1++)

          {

            ATOMIC z_real, z_imag;

            ATOMIC sum_real = 0.0;

            ATOMIC sum_imag = 0.0;

            ATOMIC w_real = 1.0, w_imag = 0.0;

            ATOMIC tw_real = 1.0, tw_imag = 0.0;

            if (e1 > 0)

              {

                ATOMIC t_real = dw_real * cos_d_theta + dw_imag * sin_d_theta;

                ATOMIC t_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta;

                dw_real = t_real;

                dw_imag = t_imag;

              }

            for (e2 = 0; e2 < factor; e2++)

              {

                if (e2 > 0)

                  {

                    ATOMIC tmp_real = tw_real * cos_tw_arg - tw_imag * sin_tw_arg;

                    ATOMIC tmp_imag = tw_real * sin_tw_arg + tw_imag * cos_tw_arg;

                    tw_real = tmp_real;

                    tw_imag = tmp_imag;

                  }

                if (e2 > 0)

                  {

                    ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;

                    ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;

                    w_real = tmp_real;

                    w_imag = tmp_imag;

                  }

                {

                  const size_t from0 = k1 * product_1 + 2 * k + e2 * m - 1;

                  const ATOMIC f0_real = VECTOR(in,istride,from0);

                  z_real = tw_real * f0_real;

                  z_imag = tw_imag * f0_real;

                }

                sum_real += w_real * z_real - w_imag * z_imag;

                sum_imag += w_real * z_imag + w_imag * z_real;

              }

            if (e1 + 1 < factor - e1)

              {

                const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k;

                VECTOR(out,ostride,to0) = sum_real;

                VECTOR(out,ostride,to0 + 1) = sum_imag;

              }

            else if (e1 + 1 == factor - e1)

              {

                const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k;

                VECTOR(out,ostride,to0) = sum_real;

              }

            else

              {

                const size_t to0 = k1 * product - 1 + 2 * (factor - e1) * product_1 - 2 * k;

                VECTOR(out,ostride,to0) = sum_real;

                VECTOR(out,ostride,to0 + 1) = -sum_imag;

              }

          }

      }

  }

  return;

}