c_pass_4.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* fft/c_pass_4.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

static int
FUNCTION(fft_complex,pass_4) (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[],
                              const TYPE(gsl_complex) twiddle3[])
{
  size_t i = 0, j = 0;
  size_t k, k1;

  const size_t factor = 4;
  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;

  for (k = 0; k < q; k++)
    {
      ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_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;
        }
      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]);
            }
          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]);
            }
        }

      for (k1 = 0; k1 < p_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);
          const ATOMIC z3_real = REAL(in,istride,i+3*m);
          const ATOMIC z3_imag = IMAG(in,istride,i+3*m);

          /* compute x = W(4) z */
          
          /* t1 = z0 + z2 */
          const ATOMIC t1_real = z0_real + z2_real;
          const ATOMIC t1_imag = z0_imag + z2_imag;
          
          /* t2 = z1 + z3 */
          const ATOMIC t2_real = z1_real + z3_real;
          const ATOMIC t2_imag = z1_imag + z3_imag;
          
          /* t3 = z0 - z2 */
          const ATOMIC t3_real = z0_real - z2_real;
          const ATOMIC t3_imag = z0_imag - z2_imag;
          
          /* t4 = (+/-) (z1 - z3) */
          const ATOMIC t4_real = ((int) sign) * (z1_real - z3_real);
          const ATOMIC t4_imag = ((int) sign) * (z1_imag - z3_imag);

            /* x0 = t1 + t2 */
          const ATOMIC x0_real = t1_real + t2_real;
          const ATOMIC x0_imag = t1_imag + t2_imag;

            /* x1 = t3 + i t4 */
          const ATOMIC x1_real = t3_real - t4_imag;
          const ATOMIC x1_imag = t3_imag + t4_real;

            /* x2 = t1 - t2 */
          const ATOMIC x2_real = t1_real - t2_real;
          const ATOMIC x2_imag = t1_imag - t2_imag;

            /* x3 = t3 - i t4 */
          const ATOMIC x3_real = t3_real + t4_imag;
          const ATOMIC x3_imag = t3_imag - t4_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 + 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;
          
          i++;
          j++;
        }
      j += jump;
    }
  return 0;
}