htswanalysis/MACS/lib/gsl/gsl-1.11/fft/c_pass_7.c

   1 /* fft/c_pass_7.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_7) (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                               const TYPE(gsl_complex) twiddle5[],
  33                               const TYPE(gsl_complex) twiddle6[])
  34 {
  35   size_t i = 0, j = 0;
  36   size_t k, k1;
  37
  38   const size_t factor = 7;
  39   const size_t m = n / factor;
  40   const size_t q = n / product;
  41   const size_t p_1 = product / factor;
  42   const size_t jump = (factor - 1) * p_1;
  43
  44   const ATOMIC c1 = cos(1.0 * 2.0 * M_PI / 7.0) ;
  45   const ATOMIC c2 = cos(2.0 * 2.0 * M_PI / 7.0) ;
  46   const ATOMIC c3 = cos(3.0 * 2.0 * M_PI / 7.0) ;
  47
  48   const ATOMIC s1 = sin(1.0 * 2.0 * M_PI / 7.0) ;
  49   const ATOMIC s2 = sin(2.0 * 2.0 * M_PI / 7.0) ;
  50   const ATOMIC s3 = sin(3.0 * 2.0 * M_PI / 7.0) ;
  51
  52   for (k = 0; k < q; k++)
  53     {
  54       ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real,
  55         w4_imag, w5_real, w5_imag, w6_real, w6_imag;
  56
  57       if (k == 0)
  58         {
  59           w1_real = 1.0;
  60           w1_imag = 0.0;
  61           w2_real = 1.0;
  62           w2_imag = 0.0;
  63           w3_real = 1.0;
  64           w3_imag = 0.0;
  65           w4_real = 1.0;
  66           w4_imag = 0.0;
  67           w5_real = 1.0;
  68           w5_imag = 0.0;
  69           w6_real = 1.0;
  70           w6_imag = 0.0;
  71         }
  72       else
  73         {
  74           if (sign == gsl_fft_forward)
  75             {
  76               /* forward tranform */
  77               w1_real = GSL_REAL(twiddle1[k - 1]);
  78               w1_imag = GSL_IMAG(twiddle1[k - 1]);
  79               w2_real = GSL_REAL(twiddle2[k - 1]);
  80               w2_imag = GSL_IMAG(twiddle2[k - 1]);
  81               w3_real = GSL_REAL(twiddle3[k - 1]);
  82               w3_imag = GSL_IMAG(twiddle3[k - 1]);
  83               w4_real = GSL_REAL(twiddle4[k - 1]);
  84               w4_imag = GSL_IMAG(twiddle4[k - 1]);
  85               w5_real = GSL_REAL(twiddle5[k - 1]);
  86               w5_imag = GSL_IMAG(twiddle5[k - 1]);
  87               w6_real = GSL_REAL(twiddle6[k - 1]);
  88               w6_imag = GSL_IMAG(twiddle6[k - 1]);
  89             }
  90           else
  91             {
  92               /* backward tranform: w -> conjugate(w) */
  93               w1_real = GSL_REAL(twiddle1[k - 1]);
  94               w1_imag = -GSL_IMAG(twiddle1[k - 1]);
  95               w2_real = GSL_REAL(twiddle2[k - 1]);
  96               w2_imag = -GSL_IMAG(twiddle2[k - 1]);
  97               w3_real = GSL_REAL(twiddle3[k - 1]);
  98               w3_imag = -GSL_IMAG(twiddle3[k - 1]);
  99               w4_real = GSL_REAL(twiddle4[k - 1]);
 100               w4_imag = -GSL_IMAG(twiddle4[k - 1]);
 101               w5_real = GSL_REAL(twiddle5[k - 1]);
 102               w5_imag = -GSL_IMAG(twiddle5[k - 1]);
 103               w6_real = GSL_REAL(twiddle6[k - 1]);
 104               w6_imag = -GSL_IMAG(twiddle6[k - 1]);
 105             }
 106         }
 107
 108       for (k1 = 0; k1 < p_1; k1++)
 109         {
 110           const ATOMIC z0_real = REAL(in,istride,i);
 111           const ATOMIC z0_imag = IMAG(in,istride,i);
 112           const ATOMIC z1_real = REAL(in,istride,i+m);
 113           const ATOMIC z1_imag = IMAG(in,istride,i+m);
 114           const ATOMIC z2_real = REAL(in,istride,i+2*m);
 115           const ATOMIC z2_imag = IMAG(in,istride,i+2*m);
 116           const ATOMIC z3_real = REAL(in,istride,i+3*m);
 117           const ATOMIC z3_imag = IMAG(in,istride,i+3*m);
 118           const ATOMIC z4_real = REAL(in,istride,i+4*m);
 119           const ATOMIC z4_imag = IMAG(in,istride,i+4*m);
 120           const ATOMIC z5_real = REAL(in,istride,i+5*m);
 121           const ATOMIC z5_imag = IMAG(in,istride,i+5*m);
 122           const ATOMIC z6_real = REAL(in,istride,i+6*m);
 123           const ATOMIC z6_imag = IMAG(in,istride,i+6*m);
 124
 125           /* compute x = W(7) z */
 126
 127           /* t0 = z1 + z6 */
 128           const ATOMIC t0_real = z1_real + z6_real ;
 129           const ATOMIC t0_imag = z1_imag + z6_imag ;
 130
 131           /* t1 = z1 - z6 */
 132           const ATOMIC t1_real = z1_real - z6_real ;
 133           const ATOMIC t1_imag = z1_imag - z6_imag ;
 134
 135           /* t2 = z2 + z5 */
 136           const ATOMIC t2_real = z2_real + z5_real ;
 137           const ATOMIC t2_imag = z2_imag + z5_imag ;
 138
 139           /* t3 = z2 - z5 */
 140           const ATOMIC t3_real = z2_real - z5_real ;
 141           const ATOMIC t3_imag = z2_imag - z5_imag ;
 142
 143           /* t4 = z4 + z3 */
 144           const ATOMIC t4_real = z4_real + z3_real ;
 145           const ATOMIC t4_imag = z4_imag + z3_imag ;
 146
 147           /* t5 = z4 - z3 */
 148           const ATOMIC t5_real = z4_real - z3_real ;
 149           const ATOMIC t5_imag = z4_imag - z3_imag ;
 150
 151           /* t6 = t2 + t0 */
 152           const ATOMIC t6_real = t2_real + t0_real ;
 153           const ATOMIC t6_imag = t2_imag + t0_imag ;
 154
 155           /* t7 = t5 + t3 */
 156           const ATOMIC t7_real = t5_real + t3_real ;
 157           const ATOMIC t7_imag = t5_imag + t3_imag ;
 158
 159           /* b0 = z0 + t6 + t4 */
 160           const ATOMIC b0_real = z0_real + t6_real + t4_real ;
 161           const ATOMIC b0_imag = z0_imag + t6_imag + t4_imag ;
 162
 163           /* b1 = ((cos(2pi/7) + cos(4pi/7) + cos(6pi/7))/3-1) (t6 + t4) */
 164           const ATOMIC b1_real = (((c1 + c2 + c3)/3.0 - 1.0) * (t6_real + t4_real));
 165           const ATOMIC b1_imag = (((c1 + c2 + c3)/3.0 - 1.0) * (t6_imag + t4_imag));
 166
 167           /* b2 = ((2*cos(2pi/7) - cos(4pi/7) - cos(6pi/7))/3) (t0 - t4) */
 168           const ATOMIC b2_real = (((2.0 * c1 - c2 - c3)/3.0) * (t0_real - t4_real));
 169           const ATOMIC b2_imag = (((2.0 * c1 - c2 - c3)/3.0) * (t0_imag - t4_imag));
 170
 171           /* b3 = ((cos(2pi/7) - 2*cos(4pi/7) + cos(6pi/7))/3) (t4 - t2) */
 172           const ATOMIC b3_real = (((c1 - 2.0*c2 + c3)/3.0) * (t4_real - t2_real));
 173           const ATOMIC b3_imag = (((c1 - 2.0*c2 + c3)/3.0) * (t4_imag - t2_imag));
 174
 175           /* b4 = ((cos(2pi/7) + cos(4pi/7) - 2*cos(6pi/7))/3) (t2 - t0) */
 176           const ATOMIC b4_real = (((c1 + c2 - 2.0 * c3)/3.0) * (t2_real - t0_real));
 177           const ATOMIC b4_imag = (((c1 + c2 - 2.0 * c3)/3.0) * (t2_imag - t0_imag));
 178
 179           /* b5 = sign * ((sin(2pi/7) + sin(4pi/7) - sin(6pi/7))/3) (t7 + t1) */
 180           const ATOMIC b5_real = (-(int)sign) * ((s1 + s2 - s3)/3.0) * (t7_real + t1_real) ;
 181           const ATOMIC b5_imag = (-(int)sign) * ((s1 + s2 - s3)/3.0) * (t7_imag + t1_imag) ;
 182
 183           /* b6 = sign * ((2sin(2pi/7) - sin(4pi/7) + sin(6pi/7))/3) (t1 - t5) */
 184           const ATOMIC b6_real = (-(int)sign) * ((2.0 * s1 - s2 + s3)/3.0) * (t1_real - t5_real) ;
 185           const ATOMIC b6_imag = (-(int)sign) * ((2.0 * s1 - s2 + s3)/3.0) * (t1_imag - t5_imag) ;
 186
 187           /* b7 = sign * ((sin(2pi/7) - 2sin(4pi/7) - sin(6pi/7))/3) (t5 - t3) */
 188           const ATOMIC b7_real = (-(int)sign) * ((s1 - 2.0 * s2 - s3)/3.0) * (t5_real - t3_real) ;
 189           const ATOMIC b7_imag = (-(int)sign) * ((s1 - 2.0 * s2 - s3)/3.0) * (t5_imag - t3_imag) ;
 190
 191           /* b8 = sign * ((sin(2pi/7) + sin(4pi/7) + 2sin(6pi/7))/3) (t3 - t1) */
 192           const ATOMIC b8_real = (-(int)sign) * ((s1 + s2 + 2.0 * s3)/3.0) * (t3_real - t1_real) ;
 193           const ATOMIC b8_imag = (-(int)sign) * ((s1 + s2 + 2.0 * s3)/3.0) * (t3_imag - t1_imag) ;
 194
 195
 196           /* T0 = b0 + b1 */
 197           const ATOMIC T0_real = b0_real + b1_real ;
 198           const ATOMIC T0_imag = b0_imag + b1_imag ;
 199
 200           /* T1 = b2 + b3 */
 201           const ATOMIC T1_real = b2_real + b3_real ;
 202           const ATOMIC T1_imag = b2_imag + b3_imag ;
 203
 204           /* T2 = b4 - b3 */
 205           const ATOMIC T2_real = b4_real - b3_real ;
 206           const ATOMIC T2_imag = b4_imag - b3_imag ;
 207
 208           /* T3 = -b2 - b4 */
 209           const ATOMIC T3_real = -b2_real - b4_real ;
 210           const ATOMIC T3_imag = -b2_imag - b4_imag ;
 211
 212           /* T4 = b6 + b7 */
 213           const ATOMIC T4_real = b6_real + b7_real ;
 214           const ATOMIC T4_imag = b6_imag + b7_imag ;
 215
 216           /* T5 = b8 - b7 */
 217           const ATOMIC T5_real = b8_real - b7_real ;
 218           const ATOMIC T5_imag = b8_imag - b7_imag ;
 219
 220           /* T6 = -b8 - b6 */
 221           const ATOMIC T6_real = -b8_real - b6_real ;
 222           const ATOMIC T6_imag = -b8_imag - b6_imag ;
 223
 224           /* T7 = T0 + T1 */
 225           const ATOMIC T7_real = T0_real + T1_real ;
 226           const ATOMIC T7_imag = T0_imag + T1_imag ;
 227
 228           /* T8 = T0 + T2 */
 229           const ATOMIC T8_real = T0_real + T2_real ;
 230           const ATOMIC T8_imag = T0_imag + T2_imag ;
 231
 232           /* T9 = T0 + T3 */
 233           const ATOMIC T9_real = T0_real + T3_real ;
 234           const ATOMIC T9_imag = T0_imag + T3_imag ;
 235
 236           /* T10 = T4 + b5 */
 237           const ATOMIC T10_real = T4_real + b5_real ;
 238           const ATOMIC T10_imag = T4_imag + b5_imag ;
 239
 240           /* T11 = T5 + b5 */
 241           const ATOMIC T11_real = T5_real + b5_real ;
 242           const ATOMIC T11_imag = T5_imag + b5_imag ;
 243
 244           /* T12 = T6 + b5 */
 245           const ATOMIC T12_real = T6_real + b5_real ;
 246           const ATOMIC T12_imag = T6_imag + b5_imag ;
 247
 248
 249           /* x0 = b0 */
 250           const ATOMIC x0_real = b0_real ;
 251           const ATOMIC x0_imag = b0_imag ;
 252
 253           /* x1 = T7 - i T10 */
 254           const ATOMIC x1_real = T7_real + T10_imag ;
 255           const ATOMIC x1_imag = T7_imag - T10_real ;
 256
 257           /* x2 = T9 - i T12 */
 258           const ATOMIC x2_real = T9_real + T12_imag ;
 259           const ATOMIC x2_imag = T9_imag - T12_real ;
 260
 261           /* x3 = T8 + i T11 */
 262           const ATOMIC x3_real = T8_real - T11_imag ;
 263           const ATOMIC x3_imag = T8_imag + T11_real ;
 264
 265           /* x4 = T8 - i T11 */
 266           const ATOMIC x4_real = T8_real + T11_imag ;
 267           const ATOMIC x4_imag = T8_imag - T11_real ;
 268
 269           /* x5 = T9 + i T12 */
 270           const ATOMIC x5_real = T9_real - T12_imag ;
 271           const ATOMIC x5_imag = T9_imag + T12_real ;
 272
 273           /* x6 = T7 + i T10 */
 274           const ATOMIC x6_real = T7_real - T10_imag ;
 275           const ATOMIC x6_imag = T7_imag + T10_real ;
 276
 277           /* apply twiddle factors */
 278
 279           /* to0 = 1 * x0 */
 280           REAL(out,ostride,j) = x0_real;
 281           IMAG(out,ostride,j) = x0_imag;
 282
 283           /* to1 = w1 * x1 */
 284           REAL(out,ostride,j+p_1) = w1_real * x1_real - w1_imag * x1_imag;
 285           IMAG(out,ostride,j+p_1) = w1_real * x1_imag + w1_imag * x1_real;
 286
 287           /* to2 = w2 * x2 */
 288           REAL(out,ostride,j+2*p_1) = w2_real * x2_real - w2_imag * x2_imag;
 289           IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real;
 290
 291           /* to3 = w3 * x3 */
 292           REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag;
 293           IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real;
 294
 295           /* to4 = w4 * x4 */
 296           REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag;
 297           IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real;
 298
 299           /* to5 = w5 * x5 */
 300           REAL(out,ostride,j+5*p_1) = w5_real * x5_real - w5_imag * x5_imag;
 301           IMAG(out,ostride,j+5*p_1) = w5_real * x5_imag + w5_imag * x5_real;
 302
 303           /* to6 = w6 * x6 */
 304           REAL(out,ostride,j+6*p_1) = w6_real * x6_real - w6_imag * x6_imag;
 305           IMAG(out,ostride,j+6*p_1) = w6_real * x6_imag + w6_imag * x6_real;
 306
 307           i++; j++;
 308         }
 309       j += jump;
 310     }
 311   return 0;
 312 }