[ac5aaf]: fftn.c Maximize Restore History

Download this file

fftn.c    1199 lines (1125 with data), 29.8 kB

   1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
/*--------------------------------*-C-*---------------------------------*
* File:
* fftn.c
*
* multivariate complex Fourier transform, computed in place
* using mixed-radix Fast Fourier Transform algorithm.
*
* Fortran code by:
* RC Singleton, Stanford Research Institute, Sept. 1968
* NIST Guide to Available Math Software.
* Source for module FFT from package GO.
* Retrieved from NETLIB on Wed Jul 5 11:50:07 1995.
* translated by f2c (version 19950721) and with lots of cleanup
* to make it resemble C by:
* MJ Olesen, Queen's University at Kingston, 1995-97
*/
/*{{{ Copyright: */
/*
* Copyright(c)1995,97 Mark Olesen <olesen@me.QueensU.CA>
* Queen's Univ at Kingston (Canada)
*
* Permission to use, copy, modify, and distribute this software for
* any purpose without fee is hereby granted, provided that this
* entire notice is included in all copies of any software which is
* or includes a copy or modification of this software and in all
* copies of the supporting documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR QUEEN'S
* UNIVERSITY AT KINGSTON MAKES ANY REPRESENTATION OR WARRANTY OF ANY
* KIND CONCERNING THE MERCHANTABILITY OF THIS SOFTWARE OR ITS
* FITNESS FOR ANY PARTICULAR PURPOSE.
*
* All of which is to say that you can do what you like with this
* source code provided you don't try to sell it as your own and you
* include an unaltered copy of this message (including the
* copyright).
*
* It is also implicitly understood that bug fixes and improvements
* should make their way back to the general Internet community so
* that everyone benefits.
*----------------------------------------------------------------------*/
/*}}}*/
/*{{{ notes: */
/*
* Public:
* fft_free
* fftn / fftnf
* (these are documented in the header file)
*
* Private:
* fftradix / fftradixf
*
* ----------------------------------------------------------------------*
* int fftradix (REAL Re[], REAL Im[], unsigned int nTotal, unsigned int nPass,
* unsigned int nSpan, int iSign, unsigned int maxFactors,
* unsigned int maxPerm);
*
* RE and IM hold the real and imaginary components of the data, and
* return the resulting real and imaginary Fourier coefficients.
* Multidimensional data *must* be allocated contiguously. There is
* no limit on the number of dimensions.
*
*
* Although there is no limit on the number of dimensions, fftradix()
* must be called once for each dimension, but the calls may be in
* any order.
*
* NTOTAL = the total number of complex data values
* NPASS = the dimension of the current variable
* NSPAN/NPASS = the spacing of consecutive data values while indexing
* the current variable
* ISIGN - see above documentation
*
* example:
* tri-variate transform with Re[n1][n2][n3], Im[n1][n2][n3]
*
* fftradix (Re, Im, n1*n2*n3, n1, n1, 1, maxf, maxp);
* fftradix (Re, Im, n1*n2*n3, n2, n1*n2, 1, maxf, maxp);
* fftradix (Re, Im, n1*n2*n3, n3, n1*n2*n3, 1, maxf, maxp);
*
* single-variate transform,
* NTOTAL = N = NSPAN = (number of complex data values),
*
* fftradix (Re, Im, n, n, n, 1, maxf, maxp);
*
* The data can also be stored in a single array with alternating
* real and imaginary parts, the magnitude of ISIGN is changed to 2
* to give correct indexing increment, and data [0] and data [1] used
* to pass the initial addresses for the sequences of real and
* imaginary values,
*
* example:
* REAL data [2*NTOTAL];
* fftradix (&data[0], &data[1], NTOTAL, nPass, nSpan, 2, maxf, maxp);
*
* for temporary allocation:
*
* MAXFACTORS >= the maximum prime factor of NPASS
* MAXPERM >= the number of prime factors of NPASS. In addition,
* if the square-free portion K of NPASS has two or more prime
* factors, then MAXPERM >= (K-1)
*
* storage in FACTOR for a maximum of 15 prime factors of NPASS. if
* NPASS has more than one square-free factor, the product of the
* square-free factors must be <= 210 array storage for maximum prime
* factor of 23 the following two constants should agree with the
* array dimensions.
* ----------------------------------------------------------------------*/
/*}}}*/
/*{{{ Revisions: */
/*
* 26 July 95 John Beale
* - added maxf and maxp as parameters to fftradix()
*
* 28 July 95 Mark Olesen <olesen@me.QueensU.CA>
* - cleaned-up the Fortran 66 goto spaghetti, only 3 labels remain.
*
* - added fft_free() to provide some measure of control over
* allocation/deallocation.
*
* - added fftn() wrapper for multidimensional FFTs
*
* - use -DFFT_NOFLOAT or -DFFT_NODOUBLE to avoid compiling that
* precision. Note suffix `f' on the function names indicates
* float precision.
*
* - revised documentation
*
* 31 July 95 Mark Olesen <olesen@me.QueensU.CA>
* - added GNU Public License
* - more cleanup
* - define SUN_BROKEN_REALLOC to use malloc() instead of realloc()
* on the first pass through, apparently needed for old libc
* - removed #error directive in favour of some code that simply
* won't compile (generate an error that way)
*
* 1 Aug 95 Mark Olesen <olesen@me.QueensU.CA>
* - define FFT_RADIX4 to only have radix 2, radix 4 transforms
* - made fftradix /fftradixf () static scope, just use fftn()
* instead. If you have good ideas about fixing the factors
* in fftn() please do so.
*
* 8 Jan 95 mj olesen <olesen@me.QueensU.CA>
* - fixed typo's, including one that broke scaling for scaling by
* total number of matrix elements or the square root of same
* - removed unnecessary casts from allocations
*
* 10 Dec 96 mj olesen <olesen@me.QueensU.CA>
* - changes defines to compile *without* float support by default,
* use -DFFT_FLOAT to enable.
* - shifted some variables to local scope (better hints for optimizer)
* - added Michael Steffens <Michael.Steffens@mbox.muk.uni-hannover.de>
* Fortran 90 module
* - made it simpler to pass dimensions for 1D FFT.
*
* 23 Feb 97 Mark Olesen <olesen@me.QueensU.CA>
* - removed the GNU Public License (see 21 July 1995 entry),
* which should make it clear why I have the right to do so.
* - Added copyright notice and submitted to netlib
* - Moved documentation for the public functions to the header
* files where is will always be available.
* ----------------------------------------------------------------------*/
/*}}}*/
#ifndef _FFTN_C
#define _FFTN_C
/* we use CPP to re-include this same file for double/float cases */
//#if !defined (lint) && !defined (__FILE__)
//Error: your compiler is sick! define __FILE__ yourself (a string)
//eg, something like -D__FILE__=\"fftn.c\"
//#endif
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "fftn.h"
/*{{{ defines/constants */
#ifndef M_PI
# define M_PI 3.14159265358979323846264338327950288
#endif
#ifndef SIN60
# define SIN60 0.86602540378443865 /* sin(60 deg) */
# define COS72 0.30901699437494742 /* cos(72 deg) */
# define SIN72 0.95105651629515357 /* sin(72 deg) */
#endif
/*}}}*/
/*{{{ static parameters - for memory management */
static size_t SpaceAlloced = 0;
static size_t MaxPermAlloced = 0;
/* temp space, (void *) since both float and double routines use it */
static void * Tmp0 = NULL; /* temp space for real part */
static void * Tmp1 = NULL; /* temp space for imaginary part */
static void * Tmp2 = NULL; /* temp space for Cosine values */
static void * Tmp3 = NULL; /* temp space for Sine values */
static int * Perm = NULL; /* Permutation vector */
#define NFACTOR 11
static int factor [NFACTOR];
/*}}}*/
/*{{{ fft_free() */
void
fft_free (void)
{
SpaceAlloced = MaxPermAlloced = 0;
if (Tmp0) { free (Tmp0); Tmp0 = NULL; }
if (Tmp1) { free (Tmp1); Tmp1 = NULL; }
if (Tmp2) { free (Tmp2); Tmp2 = NULL; }
if (Tmp3) { free (Tmp3); Tmp3 = NULL; }
if (Perm) { free (Perm); Perm = NULL; }
}
/*}}}*/
/* return the number of factors */
static int
factorize (unsigned int nPass, int * kt)
{
int nFactor = 0;
int j;
unsigned int jj;
*kt = 0;
/* determine the factors of n */
while ((nPass % 16) == 0) /* factors of 4 */
{
factor [nFactor++] = 4;
nPass /= 16;
}
j = 3; jj = 9; /* factors of 3, 5, 7, ... */
do {
while ((nPass % jj) == 0)
{
factor [nFactor++] = j;
nPass /= jj;
}
j += 2;
jj = j * j;
} while (jj <= nPass);
if (nPass <= 4)
{
*kt = nFactor;
factor [nFactor] = nPass;
if (nPass != 1)
nFactor++;
}
else
{
if (nPass - (nPass / 4 << 2) == 0)
{
factor [nFactor++] = 2;
nPass /= 4;
}
*kt = nFactor;
j = 2;
do {
if ((nPass % j) == 0)
{
factor [nFactor++] = j;
nPass /= j;
}
j = ((j + 1) / 2 << 1) + 1;
} while (j <= nPass);
}
if (*kt)
{
j = *kt;
do
factor [nFactor++] = factor [--j];
while (j);
}
return nFactor;
}
/* re-include this source file on the second pass through */
/*{{{ defines for re-including double precision */
#ifdef FFT_NODOUBLE
# ifndef FFT_FLOAT
# define FFT_FLOAT
# endif
#else
# undef REAL
# undef FFTN
# undef FFTNS
# undef FFTRADIX
# undef FFTRADIXS
/* defines for double */
# define REAL double
# define FFTN fftn
# define FFTNS "fftn"
# define FFTRADIX fftradix
# define FFTRADIXS "fftradix"
/* double precision routine */
static int
fftradix (double Re[], double Im[],
unsigned int nTotal, unsigned int nPass, unsigned int nSpan, int isign,
unsigned int maxFactors, unsigned int maxPerm);
# include __FILE__ /* include this file again */
#endif
/*}}}*/
/*{{{ defines for re-including float precision */
#ifdef FFT_FLOAT
# undef REAL
# undef FFTN
# undef FFTNS
# undef FFTRADIX
# undef FFTRADIXS
/* defines for float */
# define REAL float
# define FFTN fftnf /* trailing 'f' for float */
# define FFTNS "fftnf" /* name for error message */
# define FFTRADIX fftradixf /* trailing 'f' for float */
# define FFTRADIXS "fftradixf" /* name for error message */
/* float precision routine */
static int
fftradixf (float Re[], float Im[],
unsigned int nTotal, unsigned int nPass, unsigned int nSpan, int isign,
unsigned int maxFactors, unsigned int maxPerm);
# include __FILE__ /* include this file again */
#endif
/*}}}*/
#else /* _FFTN_C */
/*
* use macros to access the Real/Imaginary parts so that it's possible
* to substitute different macros if a complex struct is used
*/
#ifndef Re_Data
# define Re_Data(i) Re[i]
# define Im_Data(i) Im[i]
#endif
/*
*
*/
int
FFTN (int ndim,
const unsigned int dims [],
REAL Re [],
REAL Im [],
int iSign,
double scaling)
{
unsigned int nTotal;
unsigned int maxFactors, maxPerm;
/*
* tally the number of elements in the data array
* and determine the number of dimensions
*/
nTotal = 1;
if (ndim)
{
if (dims != NULL)
{
int i;
/* number of dimensions was specified */
for (i = 0; i < ndim; i++)
{
if (dims [i] <= 0) goto Dimension_Error;
nTotal *= dims [i];
}
}
else
nTotal *= ndim;
}
else
{
int i;
/* determine # of dimensions from zero-terminated list */
if (dims == NULL) goto Dimension_Error;
for (ndim = i = 0; dims [i]; i++)
{
if (dims [i] <= 0)
goto Dimension_Error;
nTotal *= dims [i];
ndim++;
}
}
/* determine maximum number of factors and permuations */
#if 1
/*
* follow John Beale's example, just use the largest dimension and don't
* worry about excess allocation. May be someone else will do it?
*/
if (dims != NULL)
{
int i;
for (maxFactors = maxPerm = 1, i = 0; i < ndim; i++)
{
if (dims [i] > maxFactors) maxFactors = dims [i];
if (dims [i] > maxPerm) maxPerm = dims [i];
}
}
else
{
maxFactors = maxPerm = nTotal;
}
#else
/* use the constants used in the original Fortran code */
maxFactors = 23;
maxPerm = 209;
#endif
/* loop over the dimensions: */
if (dims != NULL)
{
unsigned int nSpan = 1;
int i;
for (i = 0; i < ndim; i++)
{
int ret;
nSpan *= dims [i];
ret = FFTRADIX (Re, Im, nTotal, dims [i], nSpan, iSign,
maxFactors, maxPerm);
/* exit, clean-up already done */
if (ret)
return ret;
}
}
else
{
int ret;
ret = FFTRADIX (Re, Im, nTotal, nTotal, nTotal, iSign,
maxFactors, maxPerm);
/* exit, clean-up already done */
if (ret)
return ret;
}
/* Divide through by the normalizing constant: */
if (scaling && scaling != 1.0)
{
size_t ist;
if (iSign < 0) iSign = -iSign;
if (scaling < 0.0)
scaling = (scaling < -1.0) ? sqrt (nTotal) : nTotal;
scaling = 1.0 / scaling; /* multiply is often faster */
for (ist = 0; ist < nTotal; ist += iSign)
{
Re_Data (ist) *= scaling;
Im_Data (ist) *= scaling;
}
}
return 0;
Dimension_Error:
fprintf (stderr, "Error: " FFTNS "() - dimension error\n");
fft_free (); /* free-up memory */
return -1;
}
/*----------------------------------------------------------------------*/
/*
* singleton's mixed radix routine
*
* could move allocation out to fftn(), but leave it here so that it's
* possible to make this a standalone function
*/
static int
FFTRADIX (REAL Re [],
REAL Im [],
unsigned int nTotal,
unsigned int nPass,
unsigned int nSpan,
int iSign,
unsigned int maxFactors,
unsigned int maxPerm)
{
int ii, nFactor, kspan, ispan, inc;
int j, jc, jf, jj, k, k1, k3, kk, kt, nn, ns, nt;
REAL radf;
REAL c1, c2, c3, cd;
REAL s1, s2, s3, sd;
REAL * Rtmp = NULL; /* temp space for real part*/
REAL * Itmp = NULL; /* temp space for imaginary part */
REAL * Cos = NULL; /* Cosine values */
REAL * Sin = NULL; /* Sine values */
#ifndef FFT_RADIX4
REAL s60 = SIN60; /* sin(60 deg) */
REAL s72 = SIN72; /* sin(72 deg) */
REAL c72 = COS72; /* cos(72 deg) */
#endif
REAL pi2 = M_PI; /* use PI first, 2 PI later */
/* gcc complains about k3 being uninitialized, but I can't find out where
* or why ... it looks okay to me.
*
* initialize to make gcc happy
*/
k3 = 0;
/* gcc complains about c2, c3, s2,s3 being uninitialized, but they're
* only used for the radix 4 case and only AFTER the (s1 == 0.0) pass
* through the loop at which point they will have been calculated.
*
* initialize to make gcc happy
*/
c2 = c3 = s2 = s3 = 0.0;
/* Parameter adjustments, was fortran so fix zero-offset */
Re--;
Im--;
if (nPass < 2)
return 0;
/* allocate storage */
if (SpaceAlloced < maxFactors * sizeof (REAL))
{
#ifdef SUN_BROKEN_REALLOC
if (!SpaceAlloced) /* first time */
{
SpaceAlloced = maxFactors * sizeof (REAL);
Tmp0 = malloc (SpaceAlloced);
Tmp1 = malloc (SpaceAlloced);
Tmp2 = malloc (SpaceAlloced);
Tmp3 = malloc (SpaceAlloced);
}
else
{
#endif
SpaceAlloced = maxFactors * sizeof (REAL);
Tmp0 = realloc (Tmp0, SpaceAlloced);
Tmp1 = realloc (Tmp1, SpaceAlloced);
Tmp2 = realloc (Tmp2, SpaceAlloced);
Tmp3 = realloc (Tmp3, SpaceAlloced);
#ifdef SUN_BROKEN_REALLOC
}
#endif
}
else
{
/* allow full use of alloc'd space */
maxFactors = SpaceAlloced / sizeof (REAL);
}
if (MaxPermAlloced < (size_t)maxPerm)
{
#ifdef SUN_BROKEN_REALLOC
if (!MaxPermAlloced) /* first time */
Perm = malloc (maxPerm * sizeof(int));
else
#endif
Perm = realloc (Perm, maxPerm * sizeof(int));
MaxPermAlloced = maxPerm;
}
else
{
/* allow full use of alloc'd space */
maxPerm = MaxPermAlloced;
}
if (!Tmp0 || !Tmp1 || !Tmp2 || !Tmp3 || !Perm) goto Memory_Error;
/* assign pointers */
Rtmp = (REAL *) Tmp0;
Itmp = (REAL *) Tmp1;
Cos = (REAL *) Tmp2;
Sin = (REAL *) Tmp3;
/*
* Function Body
*/
inc = iSign;
if (iSign < 0)
{
#ifndef FFT_RADIX4
s60 = -s60;
s72 = -s72;
#endif
pi2 = -pi2;
inc = -inc; /* absolute value */
}
/* adjust for strange increments */
nt = inc * nTotal;
ns = inc * nSpan;
kspan = ns;
nn = nt - inc;
jc = ns / nPass;
radf = pi2 * (double) jc;
pi2 *= 2.0; /* use 2 PI from here on */
ii = 0;
jf = 0;
/* determine the factors of n */
nFactor = factorize (nPass, &kt);
/* test that nFactors is in range */
if (nFactor > NFACTOR)
{
fprintf (stderr, "Error: " FFTRADIXS "() - exceeded number of factors\n");
goto Memory_Error;
}
/* compute fourier transform */
for (;;) {
sd = radf / (double) kspan;
cd = sin (sd);
cd = 2.0 * cd * cd;
sd = sin (sd + sd);
kk = 1;
ii++;
switch (factor [ii - 1]) {
case 2:
/* transform for factor of 2 (including rotation factor) */
kspan /= 2;
k1 = kspan + 2;
do {
do {
REAL tmpr;
REAL tmpi;
int k2;
k2 = kk + kspan;
tmpr = Re_Data (k2);
tmpi = Im_Data (k2);
Re_Data (k2) = Re_Data (kk) - tmpr;
Im_Data (k2) = Im_Data (kk) - tmpi;
Re_Data (kk) += tmpr;
Im_Data (kk) += tmpi;
kk = k2 + kspan;
} while (kk <= nn);
kk -= nn;
} while (kk <= jc);
if (kk > kspan)
goto Permute_Results; /* exit infinite loop */
do {
int k2;
c1 = 1.0 - cd;
s1 = sd;
do {
REAL tmp;
do {
do {
REAL tmpr;
REAL tmpi;
k2 = kk + kspan;
tmpr = Re_Data (kk) - Re_Data (k2);
tmpi = Im_Data (kk) - Im_Data (k2);
Re_Data (kk) += Re_Data (k2);
Im_Data (kk) += Im_Data (k2);
Re_Data (k2) = c1 * tmpr - s1 * tmpi;
Im_Data (k2) = s1 * tmpr + c1 * tmpi;
kk = k2 + kspan;
} while (kk < nt);
k2 = kk - nt;
c1 = -c1;
kk = k1 - k2;
} while (kk > k2);
tmp = c1 - (cd * c1 + sd * s1);
s1 = sd * c1 - cd * s1 + s1;
c1 = 2.0 - (tmp * tmp + s1 * s1);
s1 *= c1;
c1 *= tmp;
kk += jc;
} while (kk < k2);
k1 += (inc + inc);
kk = (k1 - kspan) / 2 + jc;
} while (kk <= jc + jc);
break;
case 4: /* transform for factor of 4 */
ispan = kspan;
kspan /= 4;
do {
c1 = 1.0;
s1 = 0.0;
do {
do {
REAL ajm, ajp, akm, akp;
REAL bjm, bjp, bkm, bkp;
int k2;
k1 = kk + kspan;
k2 = k1 + kspan;
k3 = k2 + kspan;
akp = Re_Data (kk) + Re_Data (k2);
akm = Re_Data (kk) - Re_Data (k2);
ajp = Re_Data (k1) + Re_Data (k3);
ajm = Re_Data (k1) - Re_Data (k3);
bkp = Im_Data (kk) + Im_Data (k2);
bkm = Im_Data (kk) - Im_Data (k2);
bjp = Im_Data (k1) + Im_Data (k3);
bjm = Im_Data (k1) - Im_Data (k3);
Re_Data (kk) = akp + ajp;
Im_Data (kk) = bkp + bjp;
ajp = akp - ajp;
bjp = bkp - bjp;
if (iSign < 0)
{
akp = akm + bjm;
bkp = bkm - ajm;
akm -= bjm;
bkm += ajm;
}
else
{
akp = akm - bjm;
bkp = bkm + ajm;
akm += bjm;
bkm -= ajm;
}
/* avoid useless multiplies */
if (s1 == 0.0)
{
Re_Data (k1) = akp;
Re_Data (k2) = ajp;
Re_Data (k3) = akm;
Im_Data (k1) = bkp;
Im_Data (k2) = bjp;
Im_Data (k3) = bkm;
}
else
{
Re_Data (k1) = akp * c1 - bkp * s1;
Re_Data (k2) = ajp * c2 - bjp * s2;
Re_Data (k3) = akm * c3 - bkm * s3;
Im_Data (k1) = akp * s1 + bkp * c1;
Im_Data (k2) = ajp * s2 + bjp * c2;
Im_Data (k3) = akm * s3 + bkm * c3;
}
kk = k3 + kspan;
} while (kk <= nt);
c2 = c1 - (cd * c1 + sd * s1);
s1 = sd * c1 - cd * s1 + s1;
c1 = 2.0 - (c2 * c2 + s1 * s1);
s1 *= c1;
c1 *= c2;
/* values of c2, c3, s2, s3 that will get used next time */
c2 = c1 * c1 - s1 * s1;
s2 = 2.0 * c1 * s1;
c3 = c2 * c1 - s2 * s1;
s3 = c2 * s1 + s2 * c1;
kk = kk - nt + jc;
} while (kk <= kspan);
kk = kk - kspan + inc;
} while (kk <= jc);
if (kspan == jc)
goto Permute_Results; /* exit infinite loop */
break;
default:
/* transform for odd factors */
#ifdef FFT_RADIX4
fprintf (stderr, "Error: " FFTRADIXS "(): compiled for radix 2/4 only\n");
fft_free (); /* free-up memory */
return -1;
break;
#else /* FFT_RADIX4 */
ispan = kspan;
k = factor [ii - 1];
kspan /= factor [ii - 1];
switch (factor [ii - 1]) {
case 3: /* transform for factor of 3 (optional code) */
do {
do {
REAL aj, tmpr;
REAL bj, tmpi;
int k2;
k1 = kk + kspan;
k2 = k1 + kspan;
tmpr = Re_Data (kk);
tmpi = Im_Data (kk);
aj = Re_Data (k1) + Re_Data (k2);
bj = Im_Data (k1) + Im_Data (k2);
Re_Data (kk) = tmpr + aj;
Im_Data (kk) = tmpi + bj;
tmpr -= 0.5 * aj;
tmpi -= 0.5 * bj;
aj = (Re_Data (k1) - Re_Data (k2)) * s60;
bj = (Im_Data (k1) - Im_Data (k2)) * s60;
Re_Data (k1) = tmpr - bj;
Re_Data (k2) = tmpr + bj;
Im_Data (k1) = tmpi + aj;
Im_Data (k2) = tmpi - aj;
kk = k2 + kspan;
} while (kk < nn);
kk -= nn;
} while (kk <= kspan);
break;
case 5: /* transform for factor of 5 (optional code) */
c2 = c72 * c72 - s72 * s72;
s2 = 2.0 * c72 * s72;
do {
do {
REAL aa, aj, ak, ajm, ajp, akm, akp;
REAL bb, bj, bk, bjm, bjp, bkm, bkp;
int k2, k4;
k1 = kk + kspan;
k2 = k1 + kspan;
k3 = k2 + kspan;
k4 = k3 + kspan;
akp = Re_Data (k1) + Re_Data (k4);
akm = Re_Data (k1) - Re_Data (k4);
bkp = Im_Data (k1) + Im_Data (k4);
bkm = Im_Data (k1) - Im_Data (k4);
ajp = Re_Data (k2) + Re_Data (k3);
ajm = Re_Data (k2) - Re_Data (k3);
bjp = Im_Data (k2) + Im_Data (k3);
bjm = Im_Data (k2) - Im_Data (k3);
aa = Re_Data (kk);
bb = Im_Data (kk);
Re_Data (kk) = aa + akp + ajp;
Im_Data (kk) = bb + bkp + bjp;
ak = akp * c72 + ajp * c2 + aa;
bk = bkp * c72 + bjp * c2 + bb;
aj = akm * s72 + ajm * s2;
bj = bkm * s72 + bjm * s2;
Re_Data (k1) = ak - bj;
Re_Data (k4) = ak + bj;
Im_Data (k1) = bk + aj;
Im_Data (k4) = bk - aj;
ak = akp * c2 + ajp * c72 + aa;
bk = bkp * c2 + bjp * c72 + bb;
aj = akm * s2 - ajm * s72;
bj = bkm * s2 - bjm * s72;
Re_Data (k2) = ak - bj;
Re_Data (k3) = ak + bj;
Im_Data (k2) = bk + aj;
Im_Data (k3) = bk - aj;
kk = k4 + kspan;
} while (kk < nn);
kk -= nn;
} while (kk <= kspan);
break;
default:
k = factor [ii - 1];
if (jf != k)
{
jf = k;
s1 = pi2 / (double) jf;
c1 = cos (s1);
s1 = sin (s1);
if (jf > maxFactors)
goto Memory_Error;
Cos [jf - 1] = 1.0;
Sin [jf - 1] = 0.0;
j = 1;
do {
Cos [j - 1] = Cos [k - 1] * c1 + Sin [k - 1] * s1;
Sin [j - 1] = Cos [k - 1] * s1 - Sin [k - 1] * c1;
k--;
Cos [k - 1] = Cos [j - 1];
Sin [k - 1] = -Sin [j - 1];
j++;
} while (j < k);
}
do {
do {
REAL aa, ak;
REAL bb, bk;
int k2;
aa = ak = Re_Data (kk);
bb = bk = Im_Data (kk);
k1 = kk;
k2 = kk + ispan;
j = 1;
k1 += kspan;
do {
k2 -= kspan;
Rtmp [j] = Re_Data (k1) + Re_Data (k2);
ak += Rtmp [j];
Itmp [j] = Im_Data (k1) + Im_Data (k2);
bk += Itmp [j];
j++;
Rtmp [j] = Re_Data (k1) - Re_Data (k2);
Itmp [j] = Im_Data (k1) - Im_Data (k2);
j++;
k1 += kspan;
} while (k1 < k2);
Re_Data (kk) = ak;
Im_Data (kk) = bk;
k1 = kk;
k2 = kk + ispan;
j = 1;
do {
REAL aj = 0.0;
REAL bj = 0.0;
k1 += kspan;
k2 -= kspan;
jj = j;
ak = aa;
bk = bb;
k = 1;
do {
ak += Rtmp [k] * Cos [jj - 1];
bk += Itmp [k] * Cos [jj - 1];
k++;
aj += Rtmp [k] * Sin [jj - 1];
bj += Itmp [k] * Sin [jj - 1];
k++;
jj += j;
if (jj > jf)
jj -= jf;
} while (k < jf);
k = jf - j;
Re_Data (k1) = ak - bj;
Im_Data (k1) = bk + aj;
Re_Data (k2) = ak + bj;
Im_Data (k2) = bk - aj;
j++;
} while (j < k);
kk += ispan;
} while (kk <= nn);
kk -= nn;
} while (kk <= kspan);
break;
}
/* multiply by rotation factor (except for factors of 2 and 4) */
if (ii == nFactor)
goto Permute_Results; /* exit infinite loop */
kk = jc + 1;
do {
c2 = 1.0 - cd;
s1 = sd;
do {
c1 = c2;
s2 = s1;
kk += kspan;
do {
REAL tmp;
do {
REAL ak;
ak = Re_Data (kk);
Re_Data (kk) = c2 * ak - s2 * Im_Data (kk);
Im_Data (kk) = s2 * ak + c2 * Im_Data (kk);
kk += ispan;
} while (kk <= nt);
tmp = s1 * s2;
s2 = s1 * c2 + c1 * s2;
c2 = c1 * c2 - tmp;
kk = kk - nt + kspan;
} while (kk <= ispan);
c2 = c1 - (cd * c1 + sd * s1);
s1 += sd * c1 - cd * s1;
c1 = 2.0 - (c2 * c2 + s1 * s1);
s1 *= c1;
c2 *= c1;
kk = kk - ispan + jc;
} while (kk <= kspan);
kk = kk - kspan + jc + inc;
} while (kk <= jc + jc);
break;
#endif /* FFT_RADIX4 */
}
}
/* permute the results to normal order -- done in two stages */
/* permutation for square factors of n */
Permute_Results:
Perm [0] = ns;
if (kt)
{
int k2;
k = kt + kt + 1;
if (k > nFactor)
k--;
Perm [k] = jc;
j = 1;
do {
Perm [j] = Perm [j - 1] / factor [j - 1];
Perm [k - 1] = Perm [k] * factor [j - 1];
j++;
k--;
} while (j < k);
k3 = Perm [k];
kspan = Perm [1];
kk = jc + 1;
k2 = kspan + 1;
j = 1;
if (nPass != nTotal)
{
/* permutation for multivariate transform */
Permute_Multi:
do {
do {
k = kk + jc;
do {
/* swap
* Re_Data (kk) <> Re_Data (k2)
* Im_Data (kk) <> Im_Data (k2)
*/
REAL tmp;
tmp = Re_Data (kk); Re_Data (kk) = Re_Data (k2); Re_Data (k2) = tmp;
tmp = Im_Data (kk); Im_Data (kk) = Im_Data (k2); Im_Data (k2) = tmp;
kk += inc;
k2 += inc;
} while (kk < k);
kk += (ns - jc);
k2 += (ns - jc);
} while (kk < nt);
k2 = k2 - nt + kspan;
kk = kk - nt + jc;
} while (k2 < ns);
do {
do {
k2 -= Perm [j - 1];
j++;
k2 = Perm [j] + k2;
} while (k2 > Perm [j - 1]);
j = 1;
do {
if (kk < k2)
goto Permute_Multi;
kk += jc;
k2 += kspan;
} while (k2 < ns);
} while (kk < ns);
}
else
{
/* permutation for single-variate transform (optional code) */
Permute_Single:
do {
/* swap
* Re_Data (kk) <> Re_Data (k2)
* Im_Data (kk) <> Im_Data (k2)
*/
REAL t;
t = Re_Data (kk); Re_Data (kk) = Re_Data (k2); Re_Data (k2) = t;
t = Im_Data (kk); Im_Data (kk) = Im_Data (k2); Im_Data (k2) = t;
kk += inc;
k2 += kspan;
} while (k2 < ns);
do {
do {
k2 -= Perm [j - 1];
j++;
k2 = Perm [j] + k2;
} while (k2 > Perm [j - 1]);
j = 1;
do {
if (kk < k2)
goto Permute_Single;
kk += inc;
k2 += kspan;
} while (k2 < ns);
} while (kk < ns);
}
jc = k3;
}
if ((kt << 1) + 1 >= nFactor)
return 0;
ispan = Perm [kt];
/* permutation for square-free factors of n */
j = nFactor - kt;
factor [j] = 1;
do {
factor [j - 1] *= factor [j];
j--;
} while (j != kt);
nn = factor [kt] - 1;
kt++;
if (nn > maxPerm)
goto Memory_Error;
j = jj = 0;
for (;;) {
int k2;
k = kt + 1;
k2 = factor [kt - 1];
kk = factor [k - 1];
j++;
if (j > nn)
break; /* exit infinite loop */
jj += kk;
while (jj >= k2)
{
jj -= k2;
k2 = kk;
kk = factor [k++];
jj += kk;
}
Perm [j - 1] = jj;
}
/* determine the permutation cycles of length greater than 1 */
j = 0;
for (;;) {
do {
kk = Perm [j++];
} while (kk < 0);
if (kk != j)
{
do {
k = kk;
kk = Perm [k - 1];
Perm [k - 1] = -kk;
} while (kk != j);
k3 = kk;
}
else
{
Perm [j - 1] = -j;
if (j == nn)
break; /* exit infinite loop */
}
}
maxFactors *= inc;
/* reorder a and b, following the permutation cycles */
for (;;) {
j = k3 + 1;
nt -= ispan;
ii = nt - inc + 1;
if (nt < 0)
break; /* exit infinite loop */
do {
do {
j--;
} while (Perm [j - 1] < 0);
jj = jc;
do {
int k2;
if (jj < maxFactors) kspan = jj; else kspan = maxFactors;
jj -= kspan;
k = Perm [j - 1];
kk = jc * k + ii + jj;
k1 = kk + kspan;
k2 = 0;
do {
Rtmp [k2] = Re_Data (k1);
Itmp [k2] = Im_Data (k1);
k2++;
k1 -= inc;
} while (k1 != kk);
do {
k1 = kk + kspan;
k2 = k1 - jc * (k + Perm [k - 1]);
k = -Perm [k - 1];
do {
Re_Data (k1) = Re_Data (k2);
Im_Data (k1) = Im_Data (k2);
k1 -= inc;
k2 -= inc;
} while (k1 != kk);
kk = k2;
} while (k != j);
k1 = kk + kspan;
k2 = 0;
do {
Re_Data (k1) = Rtmp [k2];
Im_Data (k1) = Itmp [k2];
k2++;
k1 -= inc;
} while (k1 != kk);
} while (jj);
} while (j != 1);
}
return 0; /* exit point here */
/* alloc or other problem, do some clean-up */
Memory_Error:
fprintf (stderr, "Error: " FFTRADIXS "() - insufficient memory.\n");
fft_free (); /* free-up memory */
return -1;
}
#endif /* _FFTN_C */
/*----------------------- end-of-file (C source) -----------------------*/