text: /* fft/real_pass_2.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 void
  FUNCTION(fft_real,pass_2) (const BASE in[],
  			   const size_t istride,
  			   BASE out[],
  			   const size_t ostride,
  			   const size_t product,
  			   const size_t n,
  			   const TYPE(gsl_complex) twiddle[])
  {
    size_t k, k1;
  
    const size_t factor = 2;
    const size_t m = n / factor;
    const size_t q = n / product;
    const size_t product_1 = product / factor;
  
    for (k1 = 0; k1 < q; k1++)
      {
        const size_t from0 = k1 * product_1;
        const size_t from1 = from0 + m;
  
        const ATOMIC r0 = VECTOR(in,istride,from0);
        const ATOMIC r1 = VECTOR(in,istride,from1);
        
        const ATOMIC s0 = r0 + r1;
        const ATOMIC s1 = r0 - r1;
        
        const size_t to0 = product * k1;
        const size_t to1 = to0 + product - 1;
        
        VECTOR(out,ostride,to0) = s0;
        VECTOR(out,ostride,to1) = s1;
      }
  
    if (product_1 == 1)
      return;
  
    for (k = 1; k < (product_1 + 1) / 2; k++)
      {
  
        /* forward real transform: w -> conjugate(w) */
        const ATOMIC w_real = GSL_REAL(twiddle[k - 1]);
        const ATOMIC w_imag = -GSL_IMAG(twiddle[k - 1]);
  
        for (k1 = 0; k1 < q; k1++)
  	{
  	  const size_t from0 = k1 * product_1 + 2 * k - 1;
  	  const size_t from1 = from0 + m;
  
  	  const ATOMIC f0_real = VECTOR(in,istride,from0);
  	  const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1);
  
  	  const ATOMIC f1_real = VECTOR(in,istride,from1);
  	  const ATOMIC f1_imag = VECTOR(in,istride,from1 + 1);
  
  	  const ATOMIC z0_real = f0_real;
  	  const ATOMIC z0_imag = f0_imag;
  
  	  const ATOMIC z1_real = w_real * f1_real - w_imag * f1_imag;
  	  const ATOMIC z1_imag = w_real * f1_imag + w_imag * f1_real;
  
  	  /* compute x = W(2) z */
  
  	  /* x0 = z0 + z1 */
  	  const ATOMIC x0_real = z0_real + z1_real;
  	  const ATOMIC x0_imag = z0_imag + z1_imag;
  
  	  /* x1 = z0 - z1 */
  	  const ATOMIC x1_real = z0_real - z1_real;
  	  const ATOMIC x1_imag = z0_imag - z1_imag;
  
  	  const size_t to0 = k1 * product + 2 * k - 1;
  	  const size_t to1 = k1 * product + product - 2 * k - 1;
  	  
  	  VECTOR(out,ostride,to0) = x0_real;
  	  VECTOR(out,ostride,to0 + 1) = x0_imag;
  	  
  	  /* stored in conjugate location */
  	  VECTOR(out,ostride,to1) = x1_real;
  	  VECTOR(out,ostride,to1 + 1) = -x1_imag;
  	}
      }
    
    if (product_1 % 2 == 1)
      return;
  
    for (k1 = 0; k1 < q; k1++)
      {
        const size_t from0 = k1 * product_1 + product_1 - 1;
        const size_t from1 = from0 + m;
        const size_t to0 = k1 * product + product_1 - 1;
  
        VECTOR(out,ostride,to0) = VECTOR(in,istride,from0);
        VECTOR(out,ostride,to0 + 1) = -VECTOR(in,istride,from1);
      }
    return;
  }
  