1 /* 2 * Copyright(c)1995,97 Mark Olesen <olesen (at) me.QueensU.CA> 3 * Queen's Univ at Kingston (Canada) 4 * 5 * Permission to use, copy, modify, and distribute this software for 6 * any purpose without fee is hereby granted, provided that this 7 * entire notice is included in all copies of any software which is 8 * or includes a copy or modification of this software and in all 9 * copies of the supporting documentation for such software. 10 * 11 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR 12 * IMPLIED WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR QUEEN'S 13 * UNIVERSITY AT KINGSTON MAKES ANY REPRESENTATION OR WARRANTY OF ANY 14 * KIND CONCERNING THE MERCHANTABILITY OF THIS SOFTWARE OR ITS 15 * FITNESS FOR ANY PARTICULAR PURPOSE. 16 * 17 * All of which is to say that you can do what you like with this 18 * source code provided you don't try to sell it as your own and you 19 * include an unaltered copy of this message (including the 20 * copyright). 21 * 22 * It is also implicitly understood that bug fixes and improvements 23 * should make their way back to the general Internet community so 24 * that everyone benefits. 25 * 26 * Changes: 27 * Trivial type modifications by the WebRTC authors. 28 */ 29 30 31 /* 32 * File: 33 * WebRtcIsac_Fftn.c 34 * 35 * Public: 36 * WebRtcIsac_Fftn / fftnf (); 37 * 38 * Private: 39 * WebRtcIsac_Fftradix / fftradixf (); 40 * 41 * Descript: 42 * multivariate complex Fourier transform, computed in place 43 * using mixed-radix Fast Fourier Transform algorithm. 44 * 45 * Fortran code by: 46 * RC Singleton, Stanford Research Institute, Sept. 1968 47 * 48 * translated by f2c (version 19950721). 49 * 50 * int WebRtcIsac_Fftn (int ndim, const int dims[], REAL Re[], REAL Im[], 51 * int iSign, double scaling); 52 * 53 * NDIM = the total number dimensions 54 * DIMS = a vector of array sizes 55 * if NDIM is zero then DIMS must be zero-terminated 56 * 57 * RE and IM hold the real and imaginary components of the data, and return 58 * the resulting real and imaginary Fourier coefficients. Multidimensional 59 * data *must* be allocated contiguously. There is no limit on the number 60 * of dimensions. 61 * 62 * ISIGN = the sign of the complex exponential (ie, forward or inverse FFT) 63 * the magnitude of ISIGN (normally 1) is used to determine the 64 * correct indexing increment (see below). 65 * 66 * SCALING = normalizing constant by which the final result is *divided* 67 * if SCALING == -1, normalize by total dimension of the transform 68 * if SCALING < -1, normalize by the square-root of the total dimension 69 * 70 * example: 71 * tri-variate transform with Re[n1][n2][n3], Im[n1][n2][n3] 72 * 73 * int dims[3] = {n1,n2,n3} 74 * WebRtcIsac_Fftn (3, dims, Re, Im, 1, scaling); 75 * 76 *-----------------------------------------------------------------------* 77 * int WebRtcIsac_Fftradix (REAL Re[], REAL Im[], size_t nTotal, size_t nPass, 78 * size_t nSpan, int iSign, size_t max_factors, 79 * size_t max_perm); 80 * 81 * RE, IM - see above documentation 82 * 83 * Although there is no limit on the number of dimensions, WebRtcIsac_Fftradix() must 84 * be called once for each dimension, but the calls may be in any order. 85 * 86 * NTOTAL = the total number of complex data values 87 * NPASS = the dimension of the current variable 88 * NSPAN/NPASS = the spacing of consecutive data values while indexing the 89 * current variable 90 * ISIGN - see above documentation 91 * 92 * example: 93 * tri-variate transform with Re[n1][n2][n3], Im[n1][n2][n3] 94 * 95 * WebRtcIsac_Fftradix (Re, Im, n1*n2*n3, n1, n1, 1, maxf, maxp); 96 * WebRtcIsac_Fftradix (Re, Im, n1*n2*n3, n2, n1*n2, 1, maxf, maxp); 97 * WebRtcIsac_Fftradix (Re, Im, n1*n2*n3, n3, n1*n2*n3, 1, maxf, maxp); 98 * 99 * single-variate transform, 100 * NTOTAL = N = NSPAN = (number of complex data values), 101 * 102 * WebRtcIsac_Fftradix (Re, Im, n, n, n, 1, maxf, maxp); 103 * 104 * The data can also be stored in a single array with alternating real and 105 * imaginary parts, the magnitude of ISIGN is changed to 2 to give correct 106 * indexing increment, and data [0] and data [1] used to pass the initial 107 * addresses for the sequences of real and imaginary values, 108 * 109 * example: 110 * REAL data [2*NTOTAL]; 111 * WebRtcIsac_Fftradix ( &data[0], &data[1], NTOTAL, nPass, nSpan, 2, maxf, maxp); 112 * 113 * for temporary allocation: 114 * 115 * MAX_FACTORS >= the maximum prime factor of NPASS 116 * MAX_PERM >= the number of prime factors of NPASS. In addition, 117 * if the square-free portion K of NPASS has two or more prime 118 * factors, then MAX_PERM >= (K-1) 119 * 120 * storage in FACTOR for a maximum of 15 prime factors of NPASS. if NPASS 121 * has more than one square-free factor, the product of the square-free 122 * factors must be <= 210 array storage for maximum prime factor of 23 the 123 * following two constants should agree with the array dimensions. 124 * 125 *----------------------------------------------------------------------*/ 126 #include "fft.h" 127 128 #include <stdlib.h> 129 #include <math.h> 130 131 132 133 /* double precision routine */ 134 static int 135 WebRtcIsac_Fftradix (double Re[], double Im[], 136 size_t nTotal, size_t nPass, size_t nSpan, int isign, 137 int max_factors, unsigned int max_perm, 138 FFTstr *fftstate); 139 140 141 142 #ifndef M_PI 143 # define M_PI 3.14159265358979323846264338327950288 144 #endif 145 146 #ifndef SIN60 147 # define SIN60 0.86602540378443865 /* sin(60 deg) */ 148 # define COS72 0.30901699437494742 /* cos(72 deg) */ 149 # define SIN72 0.95105651629515357 /* sin(72 deg) */ 150 #endif 151 152 # define REAL double 153 # define FFTN WebRtcIsac_Fftn 154 # define FFTNS "fftn" 155 # define FFTRADIX WebRtcIsac_Fftradix 156 # define FFTRADIXS "fftradix" 157 158 159 int WebRtcIsac_Fftns(unsigned int ndim, const int dims[], 160 double Re[], 161 double Im[], 162 int iSign, 163 double scaling, 164 FFTstr *fftstate) 165 { 166 167 size_t nSpan, nPass, nTotal; 168 unsigned int i; 169 int ret, max_factors, max_perm; 170 171 /* 172 * tally the number of elements in the data array 173 * and determine the number of dimensions 174 */ 175 nTotal = 1; 176 if (ndim && dims [0]) 177 { 178 for (i = 0; i < ndim; i++) 179 { 180 if (dims [i] <= 0) 181 { 182 return -1; 183 } 184 nTotal *= dims [i]; 185 } 186 } 187 else 188 { 189 ndim = 0; 190 for (i = 0; dims [i]; i++) 191 { 192 if (dims [i] <= 0) 193 { 194 return -1; 195 } 196 nTotal *= dims [i]; 197 ndim++; 198 } 199 } 200 201 /* determine maximum number of factors and permuations */ 202 #if 1 203 /* 204 * follow John Beale's example, just use the largest dimension and don't 205 * worry about excess allocation. May be someone else will do it? 206 */ 207 max_factors = max_perm = 1; 208 for (i = 0; i < ndim; i++) 209 { 210 nSpan = dims [i]; 211 if ((int)nSpan > max_factors) 212 { 213 max_factors = (int)nSpan; 214 } 215 if ((int)nSpan > max_perm) 216 { 217 max_perm = (int)nSpan; 218 } 219 } 220 #else 221 /* use the constants used in the original Fortran code */ 222 max_factors = 23; 223 max_perm = 209; 224 #endif 225 /* loop over the dimensions: */ 226 nPass = 1; 227 for (i = 0; i < ndim; i++) 228 { 229 nSpan = dims [i]; 230 nPass *= nSpan; 231 ret = FFTRADIX (Re, Im, nTotal, nSpan, nPass, iSign, 232 max_factors, max_perm, fftstate); 233 /* exit, clean-up already done */ 234 if (ret) 235 return ret; 236 } 237 238 /* Divide through by the normalizing constant: */ 239 if (scaling && scaling != 1.0) 240 { 241 if (iSign < 0) iSign = -iSign; 242 if (scaling < 0.0) 243 { 244 scaling = (double)nTotal; 245 if (scaling < -1.0) 246 scaling = sqrt (scaling); 247 } 248 scaling = 1.0 / scaling; /* multiply is often faster */ 249 for (i = 0; i < nTotal; i += iSign) 250 { 251 Re [i] *= scaling; 252 Im [i] *= scaling; 253 } 254 } 255 return 0; 256 } 257 258 /* 259 * singleton's mixed radix routine 260 * 261 * could move allocation out to WebRtcIsac_Fftn(), but leave it here so that it's 262 * possible to make this a standalone function 263 */ 264 265 static int FFTRADIX (REAL Re[], 266 REAL Im[], 267 size_t nTotal, 268 size_t nPass, 269 size_t nSpan, 270 int iSign, 271 int max_factors, 272 unsigned int max_perm, 273 FFTstr *fftstate) 274 { 275 int ii, mfactor, kspan, ispan, inc; 276 int j, jc, jf, jj, k, k1, k2, k3, k4, kk, kt, nn, ns, nt; 277 278 279 REAL radf; 280 REAL c1, c2, c3, cd, aa, aj, ak, ajm, ajp, akm, akp; 281 REAL s1, s2, s3, sd, bb, bj, bk, bjm, bjp, bkm, bkp; 282 283 REAL *Rtmp = NULL; /* temp space for real part*/ 284 REAL *Itmp = NULL; /* temp space for imaginary part */ 285 REAL *Cos = NULL; /* Cosine values */ 286 REAL *Sin = NULL; /* Sine values */ 287 288 REAL s60 = SIN60; /* sin(60 deg) */ 289 REAL c72 = COS72; /* cos(72 deg) */ 290 REAL s72 = SIN72; /* sin(72 deg) */ 291 REAL pi2 = M_PI; /* use PI first, 2 PI later */ 292 293 294 fftstate->SpaceAlloced = 0; 295 fftstate->MaxPermAlloced = 0; 296 297 298 // initialize to avoid warnings 299 k3 = c2 = c3 = s2 = s3 = 0.0; 300 301 if (nPass < 2) 302 return 0; 303 304 /* allocate storage */ 305 if (fftstate->SpaceAlloced < max_factors * sizeof (REAL)) 306 { 307 #ifdef SUN_BROKEN_REALLOC 308 if (!fftstate->SpaceAlloced) /* first time */ 309 { 310 fftstate->SpaceAlloced = max_factors * sizeof (REAL); 311 } 312 else 313 { 314 #endif 315 fftstate->SpaceAlloced = max_factors * sizeof (REAL); 316 #ifdef SUN_BROKEN_REALLOC 317 } 318 #endif 319 } 320 else 321 { 322 /* allow full use of alloc'd space */ 323 max_factors = fftstate->SpaceAlloced / sizeof (REAL); 324 } 325 if (fftstate->MaxPermAlloced < max_perm) 326 { 327 #ifdef SUN_BROKEN_REALLOC 328 if (!fftstate->MaxPermAlloced) /* first time */ 329 else 330 #endif 331 fftstate->MaxPermAlloced = max_perm; 332 } 333 else 334 { 335 /* allow full use of alloc'd space */ 336 max_perm = fftstate->MaxPermAlloced; 337 } 338 339 /* assign pointers */ 340 Rtmp = (REAL *) fftstate->Tmp0; 341 Itmp = (REAL *) fftstate->Tmp1; 342 Cos = (REAL *) fftstate->Tmp2; 343 Sin = (REAL *) fftstate->Tmp3; 344 345 /* 346 * Function Body 347 */ 348 inc = iSign; 349 if (iSign < 0) { 350 s72 = -s72; 351 s60 = -s60; 352 pi2 = -pi2; 353 inc = -inc; /* absolute value */ 354 } 355 356 /* adjust for strange increments */ 357 nt = inc * (int)nTotal; 358 ns = inc * (int)nSpan; 359 kspan = ns; 360 361 nn = nt - inc; 362 jc = ns / (int)nPass; 363 radf = pi2 * (double) jc; 364 pi2 *= 2.0; /* use 2 PI from here on */ 365 366 ii = 0; 367 jf = 0; 368 /* determine the factors of n */ 369 mfactor = 0; 370 k = (int)nPass; 371 while (k % 16 == 0) { 372 mfactor++; 373 fftstate->factor [mfactor - 1] = 4; 374 k /= 16; 375 } 376 j = 3; 377 jj = 9; 378 do { 379 while (k % jj == 0) { 380 mfactor++; 381 fftstate->factor [mfactor - 1] = j; 382 k /= jj; 383 } 384 j += 2; 385 jj = j * j; 386 } while (jj <= k); 387 if (k <= 4) { 388 kt = mfactor; 389 fftstate->factor [mfactor] = k; 390 if (k != 1) 391 mfactor++; 392 } else { 393 if (k - (k / 4 << 2) == 0) { 394 mfactor++; 395 fftstate->factor [mfactor - 1] = 2; 396 k /= 4; 397 } 398 kt = mfactor; 399 j = 2; 400 do { 401 if (k % j == 0) { 402 mfactor++; 403 fftstate->factor [mfactor - 1] = j; 404 k /= j; 405 } 406 j = ((j + 1) / 2 << 1) + 1; 407 } while (j <= k); 408 } 409 if (kt) { 410 j = kt; 411 do { 412 mfactor++; 413 fftstate->factor [mfactor - 1] = fftstate->factor [j - 1]; 414 j--; 415 } while (j); 416 } 417 418 /* test that mfactors is in range */ 419 if (mfactor > NFACTOR) 420 { 421 return -1; 422 } 423 424 /* compute fourier transform */ 425 for (;;) { 426 sd = radf / (double) kspan; 427 cd = sin(sd); 428 cd = 2.0 * cd * cd; 429 sd = sin(sd + sd); 430 kk = 0; 431 ii++; 432 433 switch (fftstate->factor [ii - 1]) { 434 case 2: 435 /* transform for factor of 2 (including rotation factor) */ 436 kspan /= 2; 437 k1 = kspan + 2; 438 do { 439 do { 440 k2 = kk + kspan; 441 ak = Re [k2]; 442 bk = Im [k2]; 443 Re [k2] = Re [kk] - ak; 444 Im [k2] = Im [kk] - bk; 445 Re [kk] += ak; 446 Im [kk] += bk; 447 kk = k2 + kspan; 448 } while (kk < nn); 449 kk -= nn; 450 } while (kk < jc); 451 if (kk >= kspan) 452 goto Permute_Results_Label; /* exit infinite loop */ 453 do { 454 c1 = 1.0 - cd; 455 s1 = sd; 456 do { 457 do { 458 do { 459 k2 = kk + kspan; 460 ak = Re [kk] - Re [k2]; 461 bk = Im [kk] - Im [k2]; 462 Re [kk] += Re [k2]; 463 Im [kk] += Im [k2]; 464 Re [k2] = c1 * ak - s1 * bk; 465 Im [k2] = s1 * ak + c1 * bk; 466 kk = k2 + kspan; 467 } while (kk < (nt-1)); 468 k2 = kk - nt; 469 c1 = -c1; 470 kk = k1 - k2; 471 } while (kk > k2); 472 ak = c1 - (cd * c1 + sd * s1); 473 s1 = sd * c1 - cd * s1 + s1; 474 c1 = 2.0 - (ak * ak + s1 * s1); 475 s1 *= c1; 476 c1 *= ak; 477 kk += jc; 478 } while (kk < k2); 479 k1 += inc + inc; 480 kk = (k1 - kspan + 1) / 2 + jc - 1; 481 } while (kk < (jc + jc)); 482 break; 483 484 case 4: /* transform for factor of 4 */ 485 ispan = kspan; 486 kspan /= 4; 487 488 do { 489 c1 = 1.0; 490 s1 = 0.0; 491 do { 492 do { 493 k1 = kk + kspan; 494 k2 = k1 + kspan; 495 k3 = k2 + kspan; 496 akp = Re [kk] + Re [k2]; 497 akm = Re [kk] - Re [k2]; 498 ajp = Re [k1] + Re [k3]; 499 ajm = Re [k1] - Re [k3]; 500 bkp = Im [kk] + Im [k2]; 501 bkm = Im [kk] - Im [k2]; 502 bjp = Im [k1] + Im [k3]; 503 bjm = Im [k1] - Im [k3]; 504 Re [kk] = akp + ajp; 505 Im [kk] = bkp + bjp; 506 ajp = akp - ajp; 507 bjp = bkp - bjp; 508 if (iSign < 0) { 509 akp = akm + bjm; 510 bkp = bkm - ajm; 511 akm -= bjm; 512 bkm += ajm; 513 } else { 514 akp = akm - bjm; 515 bkp = bkm + ajm; 516 akm += bjm; 517 bkm -= ajm; 518 } 519 /* avoid useless multiplies */ 520 if (s1 == 0.0) { 521 Re [k1] = akp; 522 Re [k2] = ajp; 523 Re [k3] = akm; 524 Im [k1] = bkp; 525 Im [k2] = bjp; 526 Im [k3] = bkm; 527 } else { 528 Re [k1] = akp * c1 - bkp * s1; 529 Re [k2] = ajp * c2 - bjp * s2; 530 Re [k3] = akm * c3 - bkm * s3; 531 Im [k1] = akp * s1 + bkp * c1; 532 Im [k2] = ajp * s2 + bjp * c2; 533 Im [k3] = akm * s3 + bkm * c3; 534 } 535 kk = k3 + kspan; 536 } while (kk < nt); 537 538 c2 = c1 - (cd * c1 + sd * s1); 539 s1 = sd * c1 - cd * s1 + s1; 540 c1 = 2.0 - (c2 * c2 + s1 * s1); 541 s1 *= c1; 542 c1 *= c2; 543 /* values of c2, c3, s2, s3 that will get used next time */ 544 c2 = c1 * c1 - s1 * s1; 545 s2 = 2.0 * c1 * s1; 546 c3 = c2 * c1 - s2 * s1; 547 s3 = c2 * s1 + s2 * c1; 548 kk = kk - nt + jc; 549 } while (kk < kspan); 550 kk = kk - kspan + inc; 551 } while (kk < jc); 552 if (kspan == jc) 553 goto Permute_Results_Label; /* exit infinite loop */ 554 break; 555 556 default: 557 /* transform for odd factors */ 558 #ifdef FFT_RADIX4 559 return -1; 560 break; 561 #else /* FFT_RADIX4 */ 562 k = fftstate->factor [ii - 1]; 563 ispan = kspan; 564 kspan /= k; 565 566 switch (k) { 567 case 3: /* transform for factor of 3 (optional code) */ 568 do { 569 do { 570 k1 = kk + kspan; 571 k2 = k1 + kspan; 572 ak = Re [kk]; 573 bk = Im [kk]; 574 aj = Re [k1] + Re [k2]; 575 bj = Im [k1] + Im [k2]; 576 Re [kk] = ak + aj; 577 Im [kk] = bk + bj; 578 ak -= 0.5 * aj; 579 bk -= 0.5 * bj; 580 aj = (Re [k1] - Re [k2]) * s60; 581 bj = (Im [k1] - Im [k2]) * s60; 582 Re [k1] = ak - bj; 583 Re [k2] = ak + bj; 584 Im [k1] = bk + aj; 585 Im [k2] = bk - aj; 586 kk = k2 + kspan; 587 } while (kk < (nn - 1)); 588 kk -= nn; 589 } while (kk < kspan); 590 break; 591 592 case 5: /* transform for factor of 5 (optional code) */ 593 c2 = c72 * c72 - s72 * s72; 594 s2 = 2.0 * c72 * s72; 595 do { 596 do { 597 k1 = kk + kspan; 598 k2 = k1 + kspan; 599 k3 = k2 + kspan; 600 k4 = k3 + kspan; 601 akp = Re [k1] + Re [k4]; 602 akm = Re [k1] - Re [k4]; 603 bkp = Im [k1] + Im [k4]; 604 bkm = Im [k1] - Im [k4]; 605 ajp = Re [k2] + Re [k3]; 606 ajm = Re [k2] - Re [k3]; 607 bjp = Im [k2] + Im [k3]; 608 bjm = Im [k2] - Im [k3]; 609 aa = Re [kk]; 610 bb = Im [kk]; 611 Re [kk] = aa + akp + ajp; 612 Im [kk] = bb + bkp + bjp; 613 ak = akp * c72 + ajp * c2 + aa; 614 bk = bkp * c72 + bjp * c2 + bb; 615 aj = akm * s72 + ajm * s2; 616 bj = bkm * s72 + bjm * s2; 617 Re [k1] = ak - bj; 618 Re [k4] = ak + bj; 619 Im [k1] = bk + aj; 620 Im [k4] = bk - aj; 621 ak = akp * c2 + ajp * c72 + aa; 622 bk = bkp * c2 + bjp * c72 + bb; 623 aj = akm * s2 - ajm * s72; 624 bj = bkm * s2 - bjm * s72; 625 Re [k2] = ak - bj; 626 Re [k3] = ak + bj; 627 Im [k2] = bk + aj; 628 Im [k3] = bk - aj; 629 kk = k4 + kspan; 630 } while (kk < (nn-1)); 631 kk -= nn; 632 } while (kk < kspan); 633 break; 634 635 default: 636 if (k != jf) { 637 jf = k; 638 s1 = pi2 / (double) k; 639 c1 = cos(s1); 640 s1 = sin(s1); 641 if (jf > max_factors){ 642 return -1; 643 } 644 Cos [jf - 1] = 1.0; 645 Sin [jf - 1] = 0.0; 646 j = 1; 647 do { 648 Cos [j - 1] = Cos [k - 1] * c1 + Sin [k - 1] * s1; 649 Sin [j - 1] = Cos [k - 1] * s1 - Sin [k - 1] * c1; 650 k--; 651 Cos [k - 1] = Cos [j - 1]; 652 Sin [k - 1] = -Sin [j - 1]; 653 j++; 654 } while (j < k); 655 } 656 do { 657 do { 658 k1 = kk; 659 k2 = kk + ispan; 660 ak = aa = Re [kk]; 661 bk = bb = Im [kk]; 662 j = 1; 663 k1 += kspan; 664 do { 665 k2 -= kspan; 666 j++; 667 Rtmp [j - 1] = Re [k1] + Re [k2]; 668 ak += Rtmp [j - 1]; 669 Itmp [j - 1] = Im [k1] + Im [k2]; 670 bk += Itmp [j - 1]; 671 j++; 672 Rtmp [j - 1] = Re [k1] - Re [k2]; 673 Itmp [j - 1] = Im [k1] - Im [k2]; 674 k1 += kspan; 675 } while (k1 < k2); 676 Re [kk] = ak; 677 Im [kk] = bk; 678 k1 = kk; 679 k2 = kk + ispan; 680 j = 1; 681 do { 682 k1 += kspan; 683 k2 -= kspan; 684 jj = j; 685 ak = aa; 686 bk = bb; 687 aj = 0.0; 688 bj = 0.0; 689 k = 1; 690 do { 691 k++; 692 ak += Rtmp [k - 1] * Cos [jj - 1]; 693 bk += Itmp [k - 1] * Cos [jj - 1]; 694 k++; 695 aj += Rtmp [k - 1] * Sin [jj - 1]; 696 bj += Itmp [k - 1] * Sin [jj - 1]; 697 jj += j; 698 if (jj > jf) { 699 jj -= jf; 700 } 701 } while (k < jf); 702 k = jf - j; 703 Re [k1] = ak - bj; 704 Im [k1] = bk + aj; 705 Re [k2] = ak + bj; 706 Im [k2] = bk - aj; 707 j++; 708 } while (j < k); 709 kk += ispan; 710 } while (kk < nn); 711 kk -= nn; 712 } while (kk < kspan); 713 break; 714 } 715 716 /* multiply by rotation factor (except for factors of 2 and 4) */ 717 if (ii == mfactor) 718 goto Permute_Results_Label; /* exit infinite loop */ 719 kk = jc; 720 do { 721 c2 = 1.0 - cd; 722 s1 = sd; 723 do { 724 c1 = c2; 725 s2 = s1; 726 kk += kspan; 727 do { 728 do { 729 ak = Re [kk]; 730 Re [kk] = c2 * ak - s2 * Im [kk]; 731 Im [kk] = s2 * ak + c2 * Im [kk]; 732 kk += ispan; 733 } while (kk < nt); 734 ak = s1 * s2; 735 s2 = s1 * c2 + c1 * s2; 736 c2 = c1 * c2 - ak; 737 kk = kk - nt + kspan; 738 } while (kk < ispan); 739 c2 = c1 - (cd * c1 + sd * s1); 740 s1 += sd * c1 - cd * s1; 741 c1 = 2.0 - (c2 * c2 + s1 * s1); 742 s1 *= c1; 743 c2 *= c1; 744 kk = kk - ispan + jc; 745 } while (kk < kspan); 746 kk = kk - kspan + jc + inc; 747 } while (kk < (jc + jc)); 748 break; 749 #endif /* FFT_RADIX4 */ 750 } 751 } 752 753 /* permute the results to normal order---done in two stages */ 754 /* permutation for square factors of n */ 755 Permute_Results_Label: 756 fftstate->Perm [0] = ns; 757 if (kt) { 758 k = kt + kt + 1; 759 if (mfactor < k) 760 k--; 761 j = 1; 762 fftstate->Perm [k] = jc; 763 do { 764 fftstate->Perm [j] = fftstate->Perm [j - 1] / fftstate->factor [j - 1]; 765 fftstate->Perm [k - 1] = fftstate->Perm [k] * fftstate->factor [j - 1]; 766 j++; 767 k--; 768 } while (j < k); 769 k3 = fftstate->Perm [k]; 770 kspan = fftstate->Perm [1]; 771 kk = jc; 772 k2 = kspan; 773 j = 1; 774 if (nPass != nTotal) { 775 /* permutation for multivariate transform */ 776 Permute_Multi_Label: 777 do { 778 do { 779 k = kk + jc; 780 do { 781 /* swap Re [kk] <> Re [k2], Im [kk] <> Im [k2] */ 782 ak = Re [kk]; Re [kk] = Re [k2]; Re [k2] = ak; 783 bk = Im [kk]; Im [kk] = Im [k2]; Im [k2] = bk; 784 kk += inc; 785 k2 += inc; 786 } while (kk < (k-1)); 787 kk += ns - jc; 788 k2 += ns - jc; 789 } while (kk < (nt-1)); 790 k2 = k2 - nt + kspan; 791 kk = kk - nt + jc; 792 } while (k2 < (ns-1)); 793 do { 794 do { 795 k2 -= fftstate->Perm [j - 1]; 796 j++; 797 k2 = fftstate->Perm [j] + k2; 798 } while (k2 > fftstate->Perm [j - 1]); 799 j = 1; 800 do { 801 if (kk < (k2-1)) 802 goto Permute_Multi_Label; 803 kk += jc; 804 k2 += kspan; 805 } while (k2 < (ns-1)); 806 } while (kk < (ns-1)); 807 } else { 808 /* permutation for single-variate transform (optional code) */ 809 Permute_Single_Label: 810 do { 811 /* swap Re [kk] <> Re [k2], Im [kk] <> Im [k2] */ 812 ak = Re [kk]; Re [kk] = Re [k2]; Re [k2] = ak; 813 bk = Im [kk]; Im [kk] = Im [k2]; Im [k2] = bk; 814 kk += inc; 815 k2 += kspan; 816 } while (k2 < (ns-1)); 817 do { 818 do { 819 k2 -= fftstate->Perm [j - 1]; 820 j++; 821 k2 = fftstate->Perm [j] + k2; 822 } while (k2 >= fftstate->Perm [j - 1]); 823 j = 1; 824 do { 825 if (kk < k2) 826 goto Permute_Single_Label; 827 kk += inc; 828 k2 += kspan; 829 } while (k2 < (ns-1)); 830 } while (kk < (ns-1)); 831 } 832 jc = k3; 833 } 834 835 if ((kt << 1) + 1 >= mfactor) 836 return 0; 837 ispan = fftstate->Perm [kt]; 838 /* permutation for square-free factors of n */ 839 j = mfactor - kt; 840 fftstate->factor [j] = 1; 841 do { 842 fftstate->factor [j - 1] *= fftstate->factor [j]; 843 j--; 844 } while (j != kt); 845 kt++; 846 nn = fftstate->factor [kt - 1] - 1; 847 if (nn > (int) max_perm) { 848 return -1; 849 } 850 j = jj = 0; 851 for (;;) { 852 k = kt + 1; 853 k2 = fftstate->factor [kt - 1]; 854 kk = fftstate->factor [k - 1]; 855 j++; 856 if (j > nn) 857 break; /* exit infinite loop */ 858 jj += kk; 859 while (jj >= k2) { 860 jj -= k2; 861 k2 = kk; 862 k++; 863 kk = fftstate->factor [k - 1]; 864 jj += kk; 865 } 866 fftstate->Perm [j - 1] = jj; 867 } 868 /* determine the permutation cycles of length greater than 1 */ 869 j = 0; 870 for (;;) { 871 do { 872 j++; 873 kk = fftstate->Perm [j - 1]; 874 } while (kk < 0); 875 if (kk != j) { 876 do { 877 k = kk; 878 kk = fftstate->Perm [k - 1]; 879 fftstate->Perm [k - 1] = -kk; 880 } while (kk != j); 881 k3 = kk; 882 } else { 883 fftstate->Perm [j - 1] = -j; 884 if (j == nn) 885 break; /* exit infinite loop */ 886 } 887 } 888 max_factors *= inc; 889 /* reorder a and b, following the permutation cycles */ 890 for (;;) { 891 j = k3 + 1; 892 nt -= ispan; 893 ii = nt - inc + 1; 894 if (nt < 0) 895 break; /* exit infinite loop */ 896 do { 897 do { 898 j--; 899 } while (fftstate->Perm [j - 1] < 0); 900 jj = jc; 901 do { 902 kspan = jj; 903 if (jj > max_factors) { 904 kspan = max_factors; 905 } 906 jj -= kspan; 907 k = fftstate->Perm [j - 1]; 908 kk = jc * k + ii + jj; 909 k1 = kk + kspan - 1; 910 k2 = 0; 911 do { 912 k2++; 913 Rtmp [k2 - 1] = Re [k1]; 914 Itmp [k2 - 1] = Im [k1]; 915 k1 -= inc; 916 } while (k1 != (kk-1)); 917 do { 918 k1 = kk + kspan - 1; 919 k2 = k1 - jc * (k + fftstate->Perm [k - 1]); 920 k = -fftstate->Perm [k - 1]; 921 do { 922 Re [k1] = Re [k2]; 923 Im [k1] = Im [k2]; 924 k1 -= inc; 925 k2 -= inc; 926 } while (k1 != (kk-1)); 927 kk = k2 + 1; 928 } while (k != j); 929 k1 = kk + kspan - 1; 930 k2 = 0; 931 do { 932 k2++; 933 Re [k1] = Rtmp [k2 - 1]; 934 Im [k1] = Itmp [k2 - 1]; 935 k1 -= inc; 936 } while (k1 != (kk-1)); 937 } while (jj); 938 } while (j != 1); 939 } 940 return 0; /* exit point here */ 941 } 942 /* ---------------------- end-of-file (c source) ---------------------- */ 943 944
