| File: | root/firefox-clang/obj-x86_64-pc-linux-gnu/third_party/libwebrtc/modules/third_party/fft/fft_gn/./../../../../../../../third_party/libwebrtc/modules/third_party/fft/fft.c |
| Warning: | line 484, column 9 Value stored to 'ispan' is never read |
Press '?' to see keyboard shortcuts
Keyboard shortcuts:
| 1 | /* |
| 2 | * Copyright(c)1995,97 Mark Olesen <olesen@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 | |
| 127 | #include <stdlib.h> |
| 128 | #include <math.h> |
| 129 | |
| 130 | #include "modules/third_party/fft/fft.h" |
| 131 | |
| 132 | /* double precision routine */ |
| 133 | static int |
| 134 | WebRtcIsac_Fftradix (double Re[], double Im[], |
| 135 | size_t nTotal, size_t nPass, size_t nSpan, int isign, |
| 136 | int max_factors, unsigned int max_perm, |
| 137 | FFTstr *fftstate); |
| 138 | |
| 139 | |
| 140 | |
| 141 | #ifndef M_PI3.14159265358979323846 |
| 142 | # define M_PI3.14159265358979323846 3.14159265358979323846264338327950288 |
| 143 | #endif |
| 144 | |
| 145 | #ifndef SIN600.86602540378443865 |
| 146 | # define SIN600.86602540378443865 0.86602540378443865 /* sin(60 deg) */ |
| 147 | # define COS720.30901699437494742 0.30901699437494742 /* cos(72 deg) */ |
| 148 | # define SIN720.95105651629515357 0.95105651629515357 /* sin(72 deg) */ |
| 149 | #endif |
| 150 | |
| 151 | # define REALdouble double |
| 152 | # define FFTNWebRtcIsac_Fftn WebRtcIsac_Fftn |
| 153 | # define FFTNS"fftn" "fftn" |
| 154 | # define FFTRADIXWebRtcIsac_Fftradix WebRtcIsac_Fftradix |
| 155 | # define FFTRADIXS"fftradix" "fftradix" |
| 156 | |
| 157 | |
| 158 | int WebRtcIsac_Fftns(unsigned int ndim, const int dims[], |
| 159 | double Re[], |
| 160 | double Im[], |
| 161 | int iSign, |
| 162 | double scaling, |
| 163 | FFTstr *fftstate) |
| 164 | { |
| 165 | |
| 166 | size_t nSpan, nPass, nTotal; |
| 167 | unsigned int i; |
| 168 | int ret, max_factors, max_perm; |
| 169 | |
| 170 | /* |
| 171 | * tally the number of elements in the data array |
| 172 | * and determine the number of dimensions |
| 173 | */ |
| 174 | nTotal = 1; |
| 175 | if (ndim && dims [0]) |
| 176 | { |
| 177 | for (i = 0; i < ndim; i++) |
| 178 | { |
| 179 | if (dims [i] <= 0) |
| 180 | { |
| 181 | return -1; |
| 182 | } |
| 183 | nTotal *= dims [i]; |
| 184 | } |
| 185 | } |
| 186 | else |
| 187 | { |
| 188 | ndim = 0; |
| 189 | for (i = 0; dims [i]; i++) |
| 190 | { |
| 191 | if (dims [i] <= 0) |
| 192 | { |
| 193 | return -1; |
| 194 | } |
| 195 | nTotal *= dims [i]; |
| 196 | ndim++; |
| 197 | } |
| 198 | } |
| 199 | |
| 200 | /* determine maximum number of factors and permuations */ |
| 201 | #if 1 |
| 202 | /* |
| 203 | * follow John Beale's example, just use the largest dimension and don't |
| 204 | * worry about excess allocation. May be someone else will do it? |
| 205 | */ |
| 206 | max_factors = max_perm = 1; |
| 207 | for (i = 0; i < ndim; i++) |
| 208 | { |
| 209 | nSpan = dims [i]; |
| 210 | if ((int)nSpan > max_factors) |
| 211 | { |
| 212 | max_factors = (int)nSpan; |
| 213 | } |
| 214 | if ((int)nSpan > max_perm) |
| 215 | { |
| 216 | max_perm = (int)nSpan; |
| 217 | } |
| 218 | } |
| 219 | #else |
| 220 | /* use the constants used in the original Fortran code */ |
| 221 | max_factors = 23; |
| 222 | max_perm = 209; |
| 223 | #endif |
| 224 | /* loop over the dimensions: */ |
| 225 | nPass = 1; |
| 226 | for (i = 0; i < ndim; i++) |
| 227 | { |
| 228 | nSpan = dims [i]; |
| 229 | nPass *= nSpan; |
| 230 | ret = FFTRADIXWebRtcIsac_Fftradix (Re, Im, nTotal, nSpan, nPass, iSign, |
| 231 | max_factors, max_perm, fftstate); |
| 232 | /* exit, clean-up already done */ |
| 233 | if (ret) |
| 234 | return ret; |
| 235 | } |
| 236 | |
| 237 | /* Divide through by the normalizing constant: */ |
| 238 | if (scaling && scaling != 1.0) |
| 239 | { |
| 240 | if (iSign < 0) iSign = -iSign; |
| 241 | if (scaling < 0.0) |
| 242 | { |
| 243 | scaling = (double)nTotal; |
| 244 | if (scaling < -1.0) |
| 245 | scaling = sqrt (scaling); |
| 246 | } |
| 247 | scaling = 1.0 / scaling; /* multiply is often faster */ |
| 248 | for (i = 0; i < nTotal; i += iSign) |
| 249 | { |
| 250 | Re [i] *= scaling; |
| 251 | Im [i] *= scaling; |
| 252 | } |
| 253 | } |
| 254 | return 0; |
| 255 | } |
| 256 | |
| 257 | /* |
| 258 | * singleton's mixed radix routine |
| 259 | * |
| 260 | * could move allocation out to WebRtcIsac_Fftn(), but leave it here so that it's |
| 261 | * possible to make this a standalone function |
| 262 | */ |
| 263 | |
| 264 | static int FFTRADIXWebRtcIsac_Fftradix (REALdouble Re[], |
| 265 | REALdouble Im[], |
| 266 | size_t nTotal, |
| 267 | size_t nPass, |
| 268 | size_t nSpan, |
| 269 | int iSign, |
| 270 | int max_factors, |
| 271 | unsigned int max_perm, |
| 272 | FFTstr *fftstate) |
| 273 | { |
| 274 | int ii, mfactor, kspan, ispan, inc; |
| 275 | int j, jc, jf, jj, k, k1, k2, k3, k4, kk, kt, nn, ns, nt; |
| 276 | |
| 277 | |
| 278 | REALdouble radf; |
| 279 | REALdouble c1, c2, c3, cd, aa, aj, ak, ajm, ajp, akm, akp; |
| 280 | REALdouble s1, s2, s3, sd, bb, bj, bk, bjm, bjp, bkm, bkp; |
| 281 | |
| 282 | REALdouble *Rtmp = NULL((void*)0); /* temp space for real part*/ |
| 283 | REALdouble *Itmp = NULL((void*)0); /* temp space for imaginary part */ |
| 284 | REALdouble *Cos = NULL((void*)0); /* Cosine values */ |
| 285 | REALdouble *Sin = NULL((void*)0); /* Sine values */ |
| 286 | |
| 287 | REALdouble s60 = SIN600.86602540378443865; /* sin(60 deg) */ |
| 288 | REALdouble c72 = COS720.30901699437494742; /* cos(72 deg) */ |
| 289 | REALdouble s72 = SIN720.95105651629515357; /* sin(72 deg) */ |
| 290 | REALdouble pi2 = M_PI3.14159265358979323846; /* use PI first, 2 PI later */ |
| 291 | |
| 292 | |
| 293 | fftstate->SpaceAlloced = 0; |
| 294 | fftstate->MaxPermAlloced = 0; |
| 295 | |
| 296 | |
| 297 | // initialize to avoid warnings |
| 298 | k3 = c2 = c3 = s2 = s3 = 0.0; |
| 299 | |
| 300 | if (nPass < 2) |
| 301 | return 0; |
| 302 | |
| 303 | /* allocate storage */ |
| 304 | if (fftstate->SpaceAlloced < max_factors * sizeof (REALdouble)) |
| 305 | { |
| 306 | #ifdef SUN_BROKEN_REALLOC |
| 307 | if (!fftstate->SpaceAlloced) /* first time */ |
| 308 | { |
| 309 | fftstate->SpaceAlloced = max_factors * sizeof (REALdouble); |
| 310 | } |
| 311 | else |
| 312 | { |
| 313 | #endif |
| 314 | fftstate->SpaceAlloced = max_factors * sizeof (REALdouble); |
| 315 | #ifdef SUN_BROKEN_REALLOC |
| 316 | } |
| 317 | #endif |
| 318 | } |
| 319 | else |
| 320 | { |
| 321 | /* allow full use of alloc'd space */ |
| 322 | max_factors = fftstate->SpaceAlloced / sizeof (REALdouble); |
| 323 | } |
| 324 | if (fftstate->MaxPermAlloced < max_perm) |
| 325 | { |
| 326 | #ifdef SUN_BROKEN_REALLOC |
| 327 | if (!fftstate->MaxPermAlloced) /* first time */ |
| 328 | else |
| 329 | #endif |
| 330 | fftstate->MaxPermAlloced = max_perm; |
| 331 | } |
| 332 | else |
| 333 | { |
| 334 | /* allow full use of alloc'd space */ |
| 335 | max_perm = fftstate->MaxPermAlloced; |
| 336 | } |
| 337 | |
| 338 | /* assign pointers */ |
| 339 | Rtmp = (REALdouble *) fftstate->Tmp0; |
| 340 | Itmp = (REALdouble *) fftstate->Tmp1; |
| 341 | Cos = (REALdouble *) fftstate->Tmp2; |
| 342 | Sin = (REALdouble *) fftstate->Tmp3; |
| 343 | |
| 344 | /* |
| 345 | * Function Body |
| 346 | */ |
| 347 | inc = iSign; |
| 348 | if (iSign < 0) { |
| 349 | s72 = -s72; |
| 350 | s60 = -s60; |
| 351 | pi2 = -pi2; |
| 352 | inc = -inc; /* absolute value */ |
| 353 | } |
| 354 | |
| 355 | /* adjust for strange increments */ |
| 356 | nt = inc * (int)nTotal; |
| 357 | ns = inc * (int)nSpan; |
| 358 | kspan = ns; |
| 359 | |
| 360 | nn = nt - inc; |
| 361 | jc = ns / (int)nPass; |
| 362 | radf = pi2 * (double) jc; |
| 363 | pi2 *= 2.0; /* use 2 PI from here on */ |
| 364 | |
| 365 | ii = 0; |
| 366 | jf = 0; |
| 367 | /* determine the factors of n */ |
| 368 | mfactor = 0; |
| 369 | k = (int)nPass; |
| 370 | while (k % 16 == 0) { |
| 371 | mfactor++; |
| 372 | fftstate->factor [mfactor - 1] = 4; |
| 373 | k /= 16; |
| 374 | } |
| 375 | j = 3; |
| 376 | jj = 9; |
| 377 | do { |
| 378 | while (k % jj == 0) { |
| 379 | mfactor++; |
| 380 | fftstate->factor [mfactor - 1] = j; |
| 381 | k /= jj; |
| 382 | } |
| 383 | j += 2; |
| 384 | jj = j * j; |
| 385 | } while (jj <= k); |
| 386 | if (k <= 4) { |
| 387 | kt = mfactor; |
| 388 | fftstate->factor [mfactor] = k; |
| 389 | if (k != 1) |
| 390 | mfactor++; |
| 391 | } else { |
| 392 | if (k - (k / 4 << 2) == 0) { |
| 393 | mfactor++; |
| 394 | fftstate->factor [mfactor - 1] = 2; |
| 395 | k /= 4; |
| 396 | } |
| 397 | kt = mfactor; |
| 398 | j = 2; |
| 399 | do { |
| 400 | if (k % j == 0) { |
| 401 | mfactor++; |
| 402 | fftstate->factor [mfactor - 1] = j; |
| 403 | k /= j; |
| 404 | } |
| 405 | j = ((j + 1) / 2 << 1) + 1; |
| 406 | } while (j <= k); |
| 407 | } |
| 408 | if (kt) { |
| 409 | j = kt; |
| 410 | do { |
| 411 | mfactor++; |
| 412 | fftstate->factor [mfactor - 1] = fftstate->factor [j - 1]; |
| 413 | j--; |
| 414 | } while (j); |
| 415 | } |
| 416 | |
| 417 | /* test that mfactors is in range */ |
| 418 | if (mfactor > FFT_NFACTOR11) |
| 419 | { |
| 420 | return -1; |
| 421 | } |
| 422 | |
| 423 | /* compute fourier transform */ |
| 424 | for (;;) { |
| 425 | sd = radf / (double) kspan; |
| 426 | cd = sin(sd); |
| 427 | cd = 2.0 * cd * cd; |
| 428 | sd = sin(sd + sd); |
| 429 | kk = 0; |
| 430 | ii++; |
| 431 | |
| 432 | switch (fftstate->factor [ii - 1]) { |
| 433 | case 2: |
| 434 | /* transform for factor of 2 (including rotation factor) */ |
| 435 | kspan /= 2; |
| 436 | k1 = kspan + 2; |
| 437 | do { |
| 438 | do { |
| 439 | k2 = kk + kspan; |
| 440 | ak = Re [k2]; |
| 441 | bk = Im [k2]; |
| 442 | Re [k2] = Re [kk] - ak; |
| 443 | Im [k2] = Im [kk] - bk; |
| 444 | Re [kk] += ak; |
| 445 | Im [kk] += bk; |
| 446 | kk = k2 + kspan; |
| 447 | } while (kk < nn); |
| 448 | kk -= nn; |
| 449 | } while (kk < jc); |
| 450 | if (kk >= kspan) |
| 451 | goto Permute_Results_Label; /* exit infinite loop */ |
| 452 | do { |
| 453 | c1 = 1.0 - cd; |
| 454 | s1 = sd; |
| 455 | do { |
| 456 | do { |
| 457 | do { |
| 458 | k2 = kk + kspan; |
| 459 | ak = Re [kk] - Re [k2]; |
| 460 | bk = Im [kk] - Im [k2]; |
| 461 | Re [kk] += Re [k2]; |
| 462 | Im [kk] += Im [k2]; |
| 463 | Re [k2] = c1 * ak - s1 * bk; |
| 464 | Im [k2] = s1 * ak + c1 * bk; |
| 465 | kk = k2 + kspan; |
| 466 | } while (kk < (nt-1)); |
| 467 | k2 = kk - nt; |
| 468 | c1 = -c1; |
| 469 | kk = k1 - k2; |
| 470 | } while (kk > k2); |
| 471 | ak = c1 - (cd * c1 + sd * s1); |
| 472 | s1 = sd * c1 - cd * s1 + s1; |
| 473 | c1 = 2.0 - (ak * ak + s1 * s1); |
| 474 | s1 *= c1; |
| 475 | c1 *= ak; |
| 476 | kk += jc; |
| 477 | } while (kk < k2); |
| 478 | k1 += inc + inc; |
| 479 | kk = (k1 - kspan + 1) / 2 + jc - 1; |
| 480 | } while (kk < (jc + jc)); |
| 481 | break; |
| 482 | |
| 483 | case 4: /* transform for factor of 4 */ |
| 484 | ispan = kspan; |
Value stored to 'ispan' is never read | |
| 485 | kspan /= 4; |
| 486 | |
| 487 | do { |
| 488 | c1 = 1.0; |
| 489 | s1 = 0.0; |
| 490 | do { |
| 491 | do { |
| 492 | k1 = kk + kspan; |
| 493 | k2 = k1 + kspan; |
| 494 | k3 = k2 + kspan; |
| 495 | akp = Re [kk] + Re [k2]; |
| 496 | akm = Re [kk] - Re [k2]; |
| 497 | ajp = Re [k1] + Re [k3]; |
| 498 | ajm = Re [k1] - Re [k3]; |
| 499 | bkp = Im [kk] + Im [k2]; |
| 500 | bkm = Im [kk] - Im [k2]; |
| 501 | bjp = Im [k1] + Im [k3]; |
| 502 | bjm = Im [k1] - Im [k3]; |
| 503 | Re [kk] = akp + ajp; |
| 504 | Im [kk] = bkp + bjp; |
| 505 | ajp = akp - ajp; |
| 506 | bjp = bkp - bjp; |
| 507 | if (iSign < 0) { |
| 508 | akp = akm + bjm; |
| 509 | bkp = bkm - ajm; |
| 510 | akm -= bjm; |
| 511 | bkm += ajm; |
| 512 | } else { |
| 513 | akp = akm - bjm; |
| 514 | bkp = bkm + ajm; |
| 515 | akm += bjm; |
| 516 | bkm -= ajm; |
| 517 | } |
| 518 | /* avoid useless multiplies */ |
| 519 | if (s1 == 0.0) { |
| 520 | Re [k1] = akp; |
| 521 | Re [k2] = ajp; |
| 522 | Re [k3] = akm; |
| 523 | Im [k1] = bkp; |
| 524 | Im [k2] = bjp; |
| 525 | Im [k3] = bkm; |
| 526 | } else { |
| 527 | Re [k1] = akp * c1 - bkp * s1; |
| 528 | Re [k2] = ajp * c2 - bjp * s2; |
| 529 | Re [k3] = akm * c3 - bkm * s3; |
| 530 | Im [k1] = akp * s1 + bkp * c1; |
| 531 | Im [k2] = ajp * s2 + bjp * c2; |
| 532 | Im [k3] = akm * s3 + bkm * c3; |
| 533 | } |
| 534 | kk = k3 + kspan; |
| 535 | } while (kk < nt); |
| 536 | |
| 537 | c2 = c1 - (cd * c1 + sd * s1); |
| 538 | s1 = sd * c1 - cd * s1 + s1; |
| 539 | c1 = 2.0 - (c2 * c2 + s1 * s1); |
| 540 | s1 *= c1; |
| 541 | c1 *= c2; |
| 542 | /* values of c2, c3, s2, s3 that will get used next time */ |
| 543 | c2 = c1 * c1 - s1 * s1; |
| 544 | s2 = 2.0 * c1 * s1; |
| 545 | c3 = c2 * c1 - s2 * s1; |
| 546 | s3 = c2 * s1 + s2 * c1; |
| 547 | kk = kk - nt + jc; |
| 548 | } while (kk < kspan); |
| 549 | kk = kk - kspan + inc; |
| 550 | } while (kk < jc); |
| 551 | if (kspan == jc) |
| 552 | goto Permute_Results_Label; /* exit infinite loop */ |
| 553 | break; |
| 554 | |
| 555 | default: |
| 556 | /* transform for odd factors */ |
| 557 | #ifdef FFT_RADIX4 |
| 558 | return -1; |
| 559 | break; |
| 560 | #else /* FFT_RADIX4 */ |
| 561 | k = fftstate->factor [ii - 1]; |
| 562 | ispan = kspan; |
| 563 | kspan /= k; |
| 564 | |
| 565 | switch (k) { |
| 566 | case 3: /* transform for factor of 3 (optional code) */ |
| 567 | do { |
| 568 | do { |
| 569 | k1 = kk + kspan; |
| 570 | k2 = k1 + kspan; |
| 571 | ak = Re [kk]; |
| 572 | bk = Im [kk]; |
| 573 | aj = Re [k1] + Re [k2]; |
| 574 | bj = Im [k1] + Im [k2]; |
| 575 | Re [kk] = ak + aj; |
| 576 | Im [kk] = bk + bj; |
| 577 | ak -= 0.5 * aj; |
| 578 | bk -= 0.5 * bj; |
| 579 | aj = (Re [k1] - Re [k2]) * s60; |
| 580 | bj = (Im [k1] - Im [k2]) * s60; |
| 581 | Re [k1] = ak - bj; |
| 582 | Re [k2] = ak + bj; |
| 583 | Im [k1] = bk + aj; |
| 584 | Im [k2] = bk - aj; |
| 585 | kk = k2 + kspan; |
| 586 | } while (kk < (nn - 1)); |
| 587 | kk -= nn; |
| 588 | } while (kk < kspan); |
| 589 | break; |
| 590 | |
| 591 | case 5: /* transform for factor of 5 (optional code) */ |
| 592 | c2 = c72 * c72 - s72 * s72; |
| 593 | s2 = 2.0 * c72 * s72; |
| 594 | do { |
| 595 | do { |
| 596 | k1 = kk + kspan; |
| 597 | k2 = k1 + kspan; |
| 598 | k3 = k2 + kspan; |
| 599 | k4 = k3 + kspan; |
| 600 | akp = Re [k1] + Re [k4]; |
| 601 | akm = Re [k1] - Re [k4]; |
| 602 | bkp = Im [k1] + Im [k4]; |
| 603 | bkm = Im [k1] - Im [k4]; |
| 604 | ajp = Re [k2] + Re [k3]; |
| 605 | ajm = Re [k2] - Re [k3]; |
| 606 | bjp = Im [k2] + Im [k3]; |
| 607 | bjm = Im [k2] - Im [k3]; |
| 608 | aa = Re [kk]; |
| 609 | bb = Im [kk]; |
| 610 | Re [kk] = aa + akp + ajp; |
| 611 | Im [kk] = bb + bkp + bjp; |
| 612 | ak = akp * c72 + ajp * c2 + aa; |
| 613 | bk = bkp * c72 + bjp * c2 + bb; |
| 614 | aj = akm * s72 + ajm * s2; |
| 615 | bj = bkm * s72 + bjm * s2; |
| 616 | Re [k1] = ak - bj; |
| 617 | Re [k4] = ak + bj; |
| 618 | Im [k1] = bk + aj; |
| 619 | Im [k4] = bk - aj; |
| 620 | ak = akp * c2 + ajp * c72 + aa; |
| 621 | bk = bkp * c2 + bjp * c72 + bb; |
| 622 | aj = akm * s2 - ajm * s72; |
| 623 | bj = bkm * s2 - bjm * s72; |
| 624 | Re [k2] = ak - bj; |
| 625 | Re [k3] = ak + bj; |
| 626 | Im [k2] = bk + aj; |
| 627 | Im [k3] = bk - aj; |
| 628 | kk = k4 + kspan; |
| 629 | } while (kk < (nn-1)); |
| 630 | kk -= nn; |
| 631 | } while (kk < kspan); |
| 632 | break; |
| 633 | |
| 634 | default: |
| 635 | if (k != jf) { |
| 636 | jf = k; |
| 637 | s1 = pi2 / (double) k; |
| 638 | c1 = cos(s1); |
| 639 | s1 = sin(s1); |
| 640 | if (jf > max_factors){ |
| 641 | return -1; |
| 642 | } |
| 643 | Cos [jf - 1] = 1.0; |
| 644 | Sin [jf - 1] = 0.0; |
| 645 | j = 1; |
| 646 | do { |
| 647 | Cos [j - 1] = Cos [k - 1] * c1 + Sin [k - 1] * s1; |
| 648 | Sin [j - 1] = Cos [k - 1] * s1 - Sin [k - 1] * c1; |
| 649 | k--; |
| 650 | Cos [k - 1] = Cos [j - 1]; |
| 651 | Sin [k - 1] = -Sin [j - 1]; |
| 652 | j++; |
| 653 | } while (j < k); |
| 654 | } |
| 655 | do { |
| 656 | do { |
| 657 | k1 = kk; |
| 658 | k2 = kk + ispan; |
| 659 | ak = aa = Re [kk]; |
| 660 | bk = bb = Im [kk]; |
| 661 | j = 1; |
| 662 | k1 += kspan; |
| 663 | do { |
| 664 | k2 -= kspan; |
| 665 | j++; |
| 666 | Rtmp [j - 1] = Re [k1] + Re [k2]; |
| 667 | ak += Rtmp [j - 1]; |
| 668 | Itmp [j - 1] = Im [k1] + Im [k2]; |
| 669 | bk += Itmp [j - 1]; |
| 670 | j++; |
| 671 | Rtmp [j - 1] = Re [k1] - Re [k2]; |
| 672 | Itmp [j - 1] = Im [k1] - Im [k2]; |
| 673 | k1 += kspan; |
| 674 | } while (k1 < k2); |
| 675 | Re [kk] = ak; |
| 676 | Im [kk] = bk; |
| 677 | k1 = kk; |
| 678 | k2 = kk + ispan; |
| 679 | j = 1; |
| 680 | do { |
| 681 | k1 += kspan; |
| 682 | k2 -= kspan; |
| 683 | jj = j; |
| 684 | ak = aa; |
| 685 | bk = bb; |
| 686 | aj = 0.0; |
| 687 | bj = 0.0; |
| 688 | k = 1; |
| 689 | do { |
| 690 | k++; |
| 691 | ak += Rtmp [k - 1] * Cos [jj - 1]; |
| 692 | bk += Itmp [k - 1] * Cos [jj - 1]; |
| 693 | k++; |
| 694 | aj += Rtmp [k - 1] * Sin [jj - 1]; |
| 695 | bj += Itmp [k - 1] * Sin [jj - 1]; |
| 696 | jj += j; |
| 697 | if (jj > jf) { |
| 698 | jj -= jf; |
| 699 | } |
| 700 | } while (k < jf); |
| 701 | k = jf - j; |
| 702 | Re [k1] = ak - bj; |
| 703 | Im [k1] = bk + aj; |
| 704 | Re [k2] = ak + bj; |
| 705 | Im [k2] = bk - aj; |
| 706 | j++; |
| 707 | } while (j < k); |
| 708 | kk += ispan; |
| 709 | } while (kk < nn); |
| 710 | kk -= nn; |
| 711 | } while (kk < kspan); |
| 712 | break; |
| 713 | } |
| 714 | |
| 715 | /* multiply by rotation factor (except for factors of 2 and 4) */ |
| 716 | if (ii == mfactor) |
| 717 | goto Permute_Results_Label; /* exit infinite loop */ |
| 718 | kk = jc; |
| 719 | do { |
| 720 | c2 = 1.0 - cd; |
| 721 | s1 = sd; |
| 722 | do { |
| 723 | c1 = c2; |
| 724 | s2 = s1; |
| 725 | kk += kspan; |
| 726 | do { |
| 727 | do { |
| 728 | ak = Re [kk]; |
| 729 | Re [kk] = c2 * ak - s2 * Im [kk]; |
| 730 | Im [kk] = s2 * ak + c2 * Im [kk]; |
| 731 | kk += ispan; |
| 732 | } while (kk < nt); |
| 733 | ak = s1 * s2; |
| 734 | s2 = s1 * c2 + c1 * s2; |
| 735 | c2 = c1 * c2 - ak; |
| 736 | kk = kk - nt + kspan; |
| 737 | } while (kk < ispan); |
| 738 | c2 = c1 - (cd * c1 + sd * s1); |
| 739 | s1 += sd * c1 - cd * s1; |
| 740 | c1 = 2.0 - (c2 * c2 + s1 * s1); |
| 741 | s1 *= c1; |
| 742 | c2 *= c1; |
| 743 | kk = kk - ispan + jc; |
| 744 | } while (kk < kspan); |
| 745 | kk = kk - kspan + jc + inc; |
| 746 | } while (kk < (jc + jc)); |
| 747 | break; |
| 748 | #endif /* FFT_RADIX4 */ |
| 749 | } |
| 750 | } |
| 751 | |
| 752 | /* permute the results to normal order---done in two stages */ |
| 753 | /* permutation for square factors of n */ |
| 754 | Permute_Results_Label: |
| 755 | fftstate->Perm [0] = ns; |
| 756 | if (kt) { |
| 757 | k = kt + kt + 1; |
| 758 | if (mfactor < k) |
| 759 | k--; |
| 760 | j = 1; |
| 761 | fftstate->Perm [k] = jc; |
| 762 | do { |
| 763 | fftstate->Perm [j] = fftstate->Perm [j - 1] / fftstate->factor [j - 1]; |
| 764 | fftstate->Perm [k - 1] = fftstate->Perm [k] * fftstate->factor [j - 1]; |
| 765 | j++; |
| 766 | k--; |
| 767 | } while (j < k); |
| 768 | k3 = fftstate->Perm [k]; |
| 769 | kspan = fftstate->Perm [1]; |
| 770 | kk = jc; |
| 771 | k2 = kspan; |
| 772 | j = 1; |
| 773 | if (nPass != nTotal) { |
| 774 | /* permutation for multivariate transform */ |
| 775 | Permute_Multi_Label: |
| 776 | do { |
| 777 | do { |
| 778 | k = kk + jc; |
| 779 | do { |
| 780 | /* swap Re [kk] <> Re [k2], Im [kk] <> Im [k2] */ |
| 781 | ak = Re [kk]; Re [kk] = Re [k2]; Re [k2] = ak; |
| 782 | bk = Im [kk]; Im [kk] = Im [k2]; Im [k2] = bk; |
| 783 | kk += inc; |
| 784 | k2 += inc; |
| 785 | } while (kk < (k-1)); |
| 786 | kk += ns - jc; |
| 787 | k2 += ns - jc; |
| 788 | } while (kk < (nt-1)); |
| 789 | k2 = k2 - nt + kspan; |
| 790 | kk = kk - nt + jc; |
| 791 | } while (k2 < (ns-1)); |
| 792 | do { |
| 793 | do { |
| 794 | k2 -= fftstate->Perm [j - 1]; |
| 795 | j++; |
| 796 | k2 = fftstate->Perm [j] + k2; |
| 797 | } while (k2 > fftstate->Perm [j - 1]); |
| 798 | j = 1; |
| 799 | do { |
| 800 | if (kk < (k2-1)) |
| 801 | goto Permute_Multi_Label; |
| 802 | kk += jc; |
| 803 | k2 += kspan; |
| 804 | } while (k2 < (ns-1)); |
| 805 | } while (kk < (ns-1)); |
| 806 | } else { |
| 807 | /* permutation for single-variate transform (optional code) */ |
| 808 | Permute_Single_Label: |
| 809 | do { |
| 810 | /* swap Re [kk] <> Re [k2], Im [kk] <> Im [k2] */ |
| 811 | ak = Re [kk]; Re [kk] = Re [k2]; Re [k2] = ak; |
| 812 | bk = Im [kk]; Im [kk] = Im [k2]; Im [k2] = bk; |
| 813 | kk += inc; |
| 814 | k2 += kspan; |
| 815 | } while (k2 < (ns-1)); |
| 816 | do { |
| 817 | do { |
| 818 | k2 -= fftstate->Perm [j - 1]; |
| 819 | j++; |
| 820 | k2 = fftstate->Perm [j] + k2; |
| 821 | } while (k2 >= fftstate->Perm [j - 1]); |
| 822 | j = 1; |
| 823 | do { |
| 824 | if (kk < k2) |
| 825 | goto Permute_Single_Label; |
| 826 | kk += inc; |
| 827 | k2 += kspan; |
| 828 | } while (k2 < (ns-1)); |
| 829 | } while (kk < (ns-1)); |
| 830 | } |
| 831 | jc = k3; |
| 832 | } |
| 833 | |
| 834 | if ((kt << 1) + 1 >= mfactor) |
| 835 | return 0; |
| 836 | ispan = fftstate->Perm [kt]; |
| 837 | /* permutation for square-free factors of n */ |
| 838 | j = mfactor - kt; |
| 839 | fftstate->factor [j] = 1; |
| 840 | do { |
| 841 | fftstate->factor [j - 1] *= fftstate->factor [j]; |
| 842 | j--; |
| 843 | } while (j != kt); |
| 844 | kt++; |
| 845 | nn = fftstate->factor [kt - 1] - 1; |
| 846 | if (nn > (int) max_perm) { |
| 847 | return -1; |
| 848 | } |
| 849 | j = jj = 0; |
| 850 | for (;;) { |
| 851 | k = kt + 1; |
| 852 | k2 = fftstate->factor [kt - 1]; |
| 853 | kk = fftstate->factor [k - 1]; |
| 854 | j++; |
| 855 | if (j > nn) |
| 856 | break; /* exit infinite loop */ |
| 857 | jj += kk; |
| 858 | while (jj >= k2) { |
| 859 | jj -= k2; |
| 860 | k2 = kk; |
| 861 | k++; |
| 862 | kk = fftstate->factor [k - 1]; |
| 863 | jj += kk; |
| 864 | } |
| 865 | fftstate->Perm [j - 1] = jj; |
| 866 | } |
| 867 | /* determine the permutation cycles of length greater than 1 */ |
| 868 | j = 0; |
| 869 | for (;;) { |
| 870 | do { |
| 871 | j++; |
| 872 | kk = fftstate->Perm [j - 1]; |
| 873 | } while (kk < 0); |
| 874 | if (kk != j) { |
| 875 | do { |
| 876 | k = kk; |
| 877 | kk = fftstate->Perm [k - 1]; |
| 878 | fftstate->Perm [k - 1] = -kk; |
| 879 | } while (kk != j); |
| 880 | k3 = kk; |
| 881 | } else { |
| 882 | fftstate->Perm [j - 1] = -j; |
| 883 | if (j == nn) |
| 884 | break; /* exit infinite loop */ |
| 885 | } |
| 886 | } |
| 887 | max_factors *= inc; |
| 888 | /* reorder a and b, following the permutation cycles */ |
| 889 | for (;;) { |
| 890 | j = k3 + 1; |
| 891 | nt -= ispan; |
| 892 | ii = nt - inc + 1; |
| 893 | if (nt < 0) |
| 894 | break; /* exit infinite loop */ |
| 895 | do { |
| 896 | do { |
| 897 | j--; |
| 898 | } while (fftstate->Perm [j - 1] < 0); |
| 899 | jj = jc; |
| 900 | do { |
| 901 | kspan = jj; |
| 902 | if (jj > max_factors) { |
| 903 | kspan = max_factors; |
| 904 | } |
| 905 | jj -= kspan; |
| 906 | k = fftstate->Perm [j - 1]; |
| 907 | kk = jc * k + ii + jj; |
| 908 | k1 = kk + kspan - 1; |
| 909 | k2 = 0; |
| 910 | do { |
| 911 | k2++; |
| 912 | Rtmp [k2 - 1] = Re [k1]; |
| 913 | Itmp [k2 - 1] = Im [k1]; |
| 914 | k1 -= inc; |
| 915 | } while (k1 != (kk-1)); |
| 916 | do { |
| 917 | k1 = kk + kspan - 1; |
| 918 | k2 = k1 - jc * (k + fftstate->Perm [k - 1]); |
| 919 | k = -fftstate->Perm [k - 1]; |
| 920 | do { |
| 921 | Re [k1] = Re [k2]; |
| 922 | Im [k1] = Im [k2]; |
| 923 | k1 -= inc; |
| 924 | k2 -= inc; |
| 925 | } while (k1 != (kk-1)); |
| 926 | kk = k2 + 1; |
| 927 | } while (k != j); |
| 928 | k1 = kk + kspan - 1; |
| 929 | k2 = 0; |
| 930 | do { |
| 931 | k2++; |
| 932 | Re [k1] = Rtmp [k2 - 1]; |
| 933 | Im [k1] = Itmp [k2 - 1]; |
| 934 | k1 -= inc; |
| 935 | } while (k1 != (kk-1)); |
| 936 | } while (jj); |
| 937 | } while (j != 1); |
| 938 | } |
| 939 | return 0; /* exit point here */ |
| 940 | } |
| 941 | /* ---------------------- end-of-file (c source) ---------------------- */ |
| 942 |