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

   1 /* fft/hc_pass_n.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 void
  21 FUNCTION(fft_halfcomplex,pass_n) (const BASE in[],
  22                                   const size_t istride,
  23                                   BASE out[],
  24                                   const size_t ostride,
  25                                   const size_t factor,
  26                                   const size_t product,
  27                                   const size_t n,
  28                                   const TYPE(gsl_complex) twiddle[])
  29 {
  30
  31   size_t k, k1;
  32
  33   const size_t m = n / factor;
  34   const size_t q = n / product;
  35   const size_t product_1 = product / factor;
  36
  37   size_t e1, e2;
  38
  39   const double d_theta = 2.0 * M_PI / ((double) factor);
  40   const ATOMIC cos_d_theta = cos (d_theta);
  41   const ATOMIC sin_d_theta = sin (d_theta);
  42
  43   for (k1 = 0; k1 < product_1; k1++)
  44     {
  45       /* compute z = W(factor) x, for x halfcomplex */
  46
  47       ATOMIC dw_real = 1.0, dw_imag = 0.0;
  48
  49       for (e1 = 0; e1 < factor; e1++)
  50         {
  51           ATOMIC sum_real = 0.0;
  52           ATOMIC w_real = 1.0, w_imag = 0.0;
  53
  54           if (e1 > 0)
  55             {
  56               ATOMIC tmp_real = dw_real * cos_d_theta - dw_imag * sin_d_theta;
  57               ATOMIC tmp_imag = dw_real * sin_d_theta + dw_imag * cos_d_theta;
  58               dw_real = tmp_real;
  59               dw_imag = tmp_imag;
  60             }
  61
  62           for (e2 = 0; e2 <= factor - e2; e2++)
  63             {
  64               ATOMIC z_real, z_imag;
  65
  66               if (e2 > 0)
  67                 {
  68                   ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;
  69                   ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;
  70                   w_real = tmp_real;
  71                   w_imag = tmp_imag;
  72                 }
  73
  74               if (e2 == 0)
  75                 {
  76                   size_t from_idx = factor * k1 * q;
  77                   z_real = VECTOR(in,istride,from_idx);
  78                   z_imag = 0.0;
  79                   sum_real += w_real * z_real - w_imag * z_imag;
  80                 }
  81               else if (e2 == factor - e2)
  82                 {
  83                   size_t from_idx = factor * q * k1 + 2 * e2 * q - 1;
  84                   z_real = VECTOR(in,istride,from_idx);
  85                   z_imag = 0.0;
  86                   sum_real += w_real * z_real;
  87                 }
  88               else
  89                 {
  90                   size_t from_idx = factor * q * k1 + 2 * e2 * q - 1;
  91                   z_real = VECTOR(in,istride,from_idx);
  92                   z_imag = VECTOR(in,istride,from_idx + 1);
  93                   sum_real += 2 * (w_real * z_real - w_imag * z_imag);
  94                 }
  95
  96             }
  97
  98           {
  99             const size_t to_idx = q * k1 + e1 * m;
 100             VECTOR(out,ostride,to_idx) = sum_real;
 101           }
 102         }
 103     }
 104
 105   if (q == 1)
 106     return;
 107
 108   for (k = 1; k < (q + 1) / 2; k++)
 109     {
 110       for (k1 = 0; k1 < product_1; k1++)
 111         {
 112
 113           ATOMIC dw_real = 1.0, dw_imag = 0.0;
 114
 115           for (e1 = 0; e1 < factor; e1++)
 116             {
 117               ATOMIC z_real, z_imag;
 118               ATOMIC sum_real = 0.0;
 119               ATOMIC sum_imag = 0.0;
 120               ATOMIC w_real = 1.0, w_imag = 0.0;
 121
 122               if (e1 > 0)
 123                 {
 124                   ATOMIC t_real = dw_real * cos_d_theta - dw_imag * sin_d_theta;
 125                   ATOMIC t_imag = dw_real * sin_d_theta + dw_imag * cos_d_theta;
 126                   dw_real = t_real;
 127                   dw_imag = t_imag;
 128                 }
 129
 130               for (e2 = 0; e2 < factor; e2++)
 131                 {
 132
 133                   if (e2 > 0)
 134                     {
 135                       ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;
 136                       ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;
 137                       w_real = tmp_real;
 138                       w_imag = tmp_imag;
 139                     }
 140
 141                   if (e2 < factor - e2)
 142                     {
 143                       const size_t from0 = factor * k1 * q + 2 * k + 2 * e2 * q - 1;
 144                       z_real = VECTOR(in,istride,from0);
 145                       z_imag = VECTOR(in,istride,from0 + 1);
 146                     }
 147                   else
 148                     {
 149                       const size_t from0 = factor * k1 * q - 2 * k + 2 * (factor - e2) * q - 1;
 150                       z_real = VECTOR(in,istride,from0);
 151                       z_imag = -VECTOR(in,istride,from0 + 1);
 152                     }
 153
 154                   sum_real += w_real * z_real - w_imag * z_imag;
 155                   sum_imag += w_real * z_imag + w_imag * z_real;
 156                 }
 157
 158               if (k == 0 || e1 == 0)
 159                 {
 160                   w_real = 1.0;
 161                   w_imag = 0.0;
 162                 }
 163               else
 164                 {
 165                   size_t tskip = (q + 1) / 2 - 1;
 166                   w_real = GSL_REAL(twiddle[k - 1 + tskip * (e1 - 1)]);
 167                   w_imag = GSL_IMAG(twiddle[k - 1 + tskip * (e1 - 1)]);
 168                 }
 169
 170               {
 171                 const size_t to0 = k1 * q + 2 * k + e1 * m - 1;
 172                 VECTOR(out,ostride,to0) = w_real * sum_real - w_imag * sum_imag;
 173                 VECTOR(out,ostride,to0 + 1) = w_real * sum_imag + w_imag * sum_real;
 174               }
 175
 176             }
 177         }
 178     }
 179
 180
 181   if (q % 2 == 1)
 182     return;
 183
 184   {
 185     double tw_arg = M_PI / ((double) factor);
 186     ATOMIC cos_tw_arg = cos (tw_arg);
 187     ATOMIC sin_tw_arg = sin (tw_arg);
 188
 189     for (k1 = 0; k1 < product_1; k1++)
 190       {
 191
 192         ATOMIC dw_real = 1.0, dw_imag = 0.0;
 193         ATOMIC tw_real = 1.0, tw_imag = 0.0;
 194
 195         for (e1 = 0; e1 < factor; e1++)
 196           {
 197             ATOMIC w_real, w_imag, z_real, z_imag;
 198
 199             ATOMIC sum_real = 0.0;
 200
 201             if (e1 > 0)
 202               {
 203                 ATOMIC tmp_real = tw_real * cos_tw_arg - tw_imag * sin_tw_arg;
 204                 ATOMIC tmp_imag = tw_real * sin_tw_arg + tw_imag * cos_tw_arg;
 205                 tw_real = tmp_real;
 206                 tw_imag = tmp_imag;
 207               }
 208
 209             w_real = tw_real;
 210             w_imag = tw_imag;
 211
 212             if (e1 > 0)
 213               {
 214                 ATOMIC t_real = dw_real * cos_d_theta - dw_imag * sin_d_theta;
 215                 ATOMIC t_imag = dw_real * sin_d_theta + dw_imag * cos_d_theta;
 216                 dw_real = t_real;
 217                 dw_imag = t_imag;
 218               }
 219
 220             for (e2 = 0; e2 <= factor - e2 - 1; e2++)
 221               {
 222
 223                 if (e2 > 0)
 224                   {
 225                     ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag;
 226                     ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real;
 227                     w_real = tmp_real;
 228                     w_imag = tmp_imag;
 229                   }
 230
 231
 232                 if (e2 == factor - e2 - 1)
 233                   {
 234                     const size_t from0 = factor * k1 * q + q + 2 * e2 * q - 1;
 235                     z_real = VECTOR(in,istride,from0);
 236                     z_imag = 0.0;
 237                     sum_real += w_real * z_real - w_imag * z_imag;
 238                   }
 239                 else
 240                   {
 241                     const size_t from0 = factor * k1 * q + q + 2 * e2 * q - 1;
 242                     z_real = VECTOR(in,istride,from0);
 243                     z_imag = VECTOR(in,istride,from0 + 1);
 244                     sum_real += 2 * (w_real * z_real - w_imag * z_imag);
 245                   }
 246
 247               }
 248
 249             {
 250               const size_t to0 = k1 * q + q + e1 * m - 1;
 251               VECTOR(out,ostride,to0) = sum_real;
 252             }
 253           }
 254       }
 255   }
 256   return;
 257 }