htswanalysis/MACS/lib/gsl/gsl-1.11/fft/c_pass_5.c

   1 /* fft/c_pass_5.c
   2  *
   3  * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
   4  *
   5  * This program is free software; you can redistribute it and/or modify
   6  * it under the terms of the GNU General Public License as published by
   7  * the Free Software Foundation; either version 3 of the License, or (at
   8  * your option) any later version.
   9  *
  10  * This program is distributed in the hope that it will be useful, but
  11  * WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13  * General Public License for more details.
  14  *
  15  * You should have received a copy of the GNU General Public License
  16  * along with this program; if not, write to the Free Software
  17  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
  18  */
  19
  20 static int
  21 FUNCTION(fft_complex,pass_5) (const BASE in[],
  22                               const size_t istride,
  23                               BASE out[],
  24                               const size_t ostride,
  25                               const gsl_fft_direction sign,
  26                               const size_t product,
  27                               const size_t n,
  28                               const TYPE(gsl_complex) twiddle1[],
  29                               const TYPE(gsl_complex) twiddle2[],
  30                               const TYPE(gsl_complex) twiddle3[],
  31                               const TYPE(gsl_complex) twiddle4[])
  32 {
  33   size_t i = 0, j = 0;
  34   size_t k, k1;
  35
  36   const size_t factor = 5;
  37   const size_t m = n / factor;
  38   const size_t q = n / product;
  39   const size_t p_1 = product / factor;
  40   const size_t jump = (factor - 1) * p_1;
  41
  42   const ATOMIC sin_2pi_by_5 = sin (2.0 * M_PI / 5.0);
  43   const ATOMIC sin_2pi_by_10 = sin (2.0 * M_PI / 10.0);
  44
  45   for (k = 0; k < q; k++)
  46     {
  47
  48       ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real,
  49         w4_imag;
  50
  51       if (k == 0)
  52         {
  53           w1_real = 1.0;
  54           w1_imag = 0.0;
  55           w2_real = 1.0;
  56           w2_imag = 0.0;
  57           w3_real = 1.0;
  58           w3_imag = 0.0;
  59           w4_real = 1.0;
  60           w4_imag = 0.0;
  61         }
  62       else
  63         {
  64           if (sign == gsl_fft_forward)
  65             {
  66               /* forward tranform */
  67               w1_real = GSL_REAL(twiddle1[k - 1]);
  68               w1_imag = GSL_IMAG(twiddle1[k - 1]);
  69               w2_real = GSL_REAL(twiddle2[k - 1]);
  70               w2_imag = GSL_IMAG(twiddle2[k - 1]);
  71               w3_real = GSL_REAL(twiddle3[k - 1]);
  72               w3_imag = GSL_IMAG(twiddle3[k - 1]);
  73               w4_real = GSL_REAL(twiddle4[k - 1]);
  74               w4_imag = GSL_IMAG(twiddle4[k - 1]);
  75             }
  76           else
  77             {
  78               /* backward tranform: w -> conjugate(w) */
  79               w1_real = GSL_REAL(twiddle1[k - 1]);
  80               w1_imag = -GSL_IMAG(twiddle1[k - 1]);
  81               w2_real = GSL_REAL(twiddle2[k - 1]);
  82               w2_imag = -GSL_IMAG(twiddle2[k - 1]);
  83               w3_real = GSL_REAL(twiddle3[k - 1]);
  84               w3_imag = -GSL_IMAG(twiddle3[k - 1]);
  85               w4_real = GSL_REAL(twiddle4[k - 1]);
  86               w4_imag = -GSL_IMAG(twiddle4[k - 1]);
  87             }
  88         }
  89
  90       for (k1 = 0; k1 < p_1; k1++)
  91         {
  92
  93           ATOMIC x0_real, x0_imag, x1_real, x1_imag, x2_real, x2_imag,
  94             x3_real, x3_imag, x4_real, x4_imag;
  95
  96           const ATOMIC z0_real = REAL(in,istride,i);
  97           const ATOMIC z0_imag = IMAG(in,istride,i);
  98           const ATOMIC z1_real = REAL(in,istride,i + m);
  99           const ATOMIC z1_imag = IMAG(in,istride,i + m);
 100           const ATOMIC z2_real = REAL(in,istride,i + 2*m);
 101           const ATOMIC z2_imag = IMAG(in,istride,i + 2*m);
 102           const ATOMIC z3_real = REAL(in,istride,i + 3*m);
 103           const ATOMIC z3_imag = IMAG(in,istride,i + 3*m);
 104           const ATOMIC z4_real = REAL(in,istride,i + 4*m);
 105           const ATOMIC z4_imag = IMAG(in,istride,i + 4*m);
 106
 107           /* compute x = W(5) z */
 108
 109           /* t1 = z1 + z4 */
 110           const ATOMIC t1_real = z1_real + z4_real;
 111           const ATOMIC t1_imag = z1_imag + z4_imag;
 112
 113           /* t2 = z2 + z3 */
 114           const ATOMIC t2_real = z2_real + z3_real;
 115           const ATOMIC t2_imag = z2_imag + z3_imag;
 116
 117           /* t3 = z1 - z4 */
 118           const ATOMIC t3_real = z1_real - z4_real;
 119           const ATOMIC t3_imag = z1_imag - z4_imag;
 120
 121           /* t4 = z2 - z3 */
 122           const ATOMIC t4_real = z2_real - z3_real;
 123           const ATOMIC t4_imag = z2_imag - z3_imag;
 124
 125           /* t5 = t1 + t2 */
 126           const ATOMIC t5_real = t1_real + t2_real;
 127           const ATOMIC t5_imag = t1_imag + t2_imag;
 128
 129           /* t6 = (sqrt(5)/4)(t1 - t2) */
 130           const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real);
 131           const ATOMIC t6_imag = (sqrt (5.0) / 4.0) * (t1_imag - t2_imag);
 132
 133           /* t7 = z0 - ((t5)/4) */
 134           const ATOMIC t7_real = z0_real - t5_real / 4.0;
 135           const ATOMIC t7_imag = z0_imag - t5_imag / 4.0;
 136
 137           /* t8 = t7 + t6 */
 138           const ATOMIC t8_real = t7_real + t6_real;
 139           const ATOMIC t8_imag = t7_imag + t6_imag;
 140
 141           /* t9 = t7 - t6 */
 142           const ATOMIC t9_real = t7_real - t6_real;
 143           const ATOMIC t9_imag = t7_imag - t6_imag;
 144
 145           /* t10 = sin(2 pi/5) t3 + sin(2 pi/10) t4 */
 146           const ATOMIC t10_real = ((int) sign) * (sin_2pi_by_5 * t3_real +
 147                                                   sin_2pi_by_10 * t4_real);
 148           const ATOMIC t10_imag = ((int) sign) * (sin_2pi_by_5 * t3_imag +
 149                                                   sin_2pi_by_10 * t4_imag);
 150
 151           /* t11 = sin(2 pi/10) t3 - sin(2 pi/5) t4 */
 152           const ATOMIC t11_real = ((int) sign) * (sin_2pi_by_10 * t3_real -
 153                                                   sin_2pi_by_5 * t4_real);
 154           const ATOMIC t11_imag = ((int) sign) * (sin_2pi_by_10 * t3_imag -
 155                                                   sin_2pi_by_5 * t4_imag);
 156
 157           /* x0 = z0 + t5 */
 158           x0_real = z0_real + t5_real;
 159           x0_imag = z0_imag + t5_imag;
 160
 161           /* x1 = t8 + i t10 */
 162           x1_real = t8_real - t10_imag;
 163           x1_imag = t8_imag + t10_real;
 164
 165           /* x2 = t9 + i t11 */
 166           x2_real = t9_real - t11_imag;
 167           x2_imag = t9_imag + t11_real;
 168
 169           /* x3 = t9 - i t11 */
 170           x3_real = t9_real + t11_imag;
 171           x3_imag = t9_imag - t11_real;
 172
 173           /* x4 = t8 - i t10 */
 174           x4_real = t8_real + t10_imag;
 175           x4_imag = t8_imag - t10_real;
 176
 177           /* apply twiddle factors */
 178
 179           /* to0 = 1 * x0 */
 180           REAL(out,ostride,j) = x0_real;
 181           IMAG(out,ostride,j) = x0_imag;
 182
 183           /* to1 = w1 * x1 */
 184           REAL(out,ostride,j + p_1) = w1_real * x1_real - w1_imag * x1_imag;
 185           IMAG(out,ostride,j + p_1) = w1_real * x1_imag + w1_imag * x1_real;
 186
 187           /* to2 = w2 * x2 */
 188           REAL(out,ostride,j + 2*p_1) = w2_real * x2_real - w2_imag * x2_imag;
 189           IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real;
 190
 191           /* to3 = w3 * x3 */
 192           REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag;
 193           IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real;
 194
 195           /* to4 = w4 * x4 */
 196           REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag;
 197           IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real;
 198
 199           i++;
 200           j++;
 201         }
 202       j += jump;
 203     }
 204   return 0;
 205 }