-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathModule_Random.F90
8718 lines (8715 loc) · 255 KB
/
Module_Random.F90
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
module Random
! ########################################################################
!
! Copyright 2020 IRD
!
! This file is part of statpack.
!
! statpack is free software: you can redistribute it and/or modify
! it under the terms of the GNU Lesser General Public License as
! published by the Free Software Foundation, either version 3 of
! the License, or (at your option) any later version.
!
! statpack is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU Lesser General Public License for more details.
!
! You can find a copy of the GNU Lesser General Public License
! in the statpack/doc directory.
!
! ########################################################################
! *
! ************************************************************************
! THIS MODULE REPLACES THE FORTRAN 90 INTRINSICS *
! random_number AND random_seed BY SEVERAL IMPLEMENTATIONS *
! OF THE KISS (Keep It Simple Stupid), L'Ecuyer's LFSR113, *
! MERSENNE TWISTER MT19937 AND MEMT19937-II RANDOM *
! NUMBER GENERATORS. *
! *
! IN ADDITION TO 10 DIFFERENT UNIFORM RANDOM GENERATORS, GAUSSIAN *
! RANDOM GENERATORS, SHUFFLING AND SAMPLING SUBROUTINES ARE ALSO *
! PROVIDED, AS WELL AS SUBROUTINES FOR GENERATING PSEUDO-RANDOM *
! ORTHOGONAL MATRICES FOLLOWING THE HAAR DISTRIBUTION OVER THE GROUP OF *
! ORTHOGONAL MATRICES, PSEUDO_RANDOM SYMMETRIC MATRICES WITH A *
! PRESCRIBED SPECTRUM OR PSEUDO_RANDOM MATRICES WITH A PRESCRIBED *
! SINGULAR VALUE DISTRIBUTION. *
! *
! MANY PARTS OF THIS MODULE ARE ADAPTED FROM : *
! *
! Hennecke, M., 1995: A Fortran90 interface to random *
! number generation. *
! Computer Physics Communications. *
! Volume 90, Number 1, 117-120 *
! *
! LATEST REVISION : 20/10/2020 *
! *
! ########################################################################
! *
! ************************************************************************
! *
! THE C PROCESSOR MACROS USED IN THIS MODULE ARE: *
! *
! _OPENMP FOR ACTIVATING OPENMP PARALLELIZATION *
! _ALLOC FOR ALLOCATING LOCAL VARIABLES INSTEAD OF PLACING *
! THEM ON THE STACK IN SOME SUBROUTINES AND FUNCTIONS *
! _BLAS FOR USING BLAS WHEN POSSIBLE *
! _MATMUL FOR REPLACING THE matmul INTRINSIC FUNCTION WITH *
! STATPACK matmul2 FUNCTION *
! _TRANSPOSE FOR REPLACING THE transpose INTRINSIC FUNCTION WITH *
! STATPACK transpose2 FUNCTION *
! _RANDOM_WITH0 FOR GENERATING REAL FLOATING POINT NUMBERS *
! IN THE [0,1[ INTERVAL INSTEAD OF ]0,1[ INTERVAL *
! _RANDOM_NOINT32 FOR SIGNALING THAT 32 BIT INTEGERS ARE NOT *
! AVAILABLE *
! _RANDOM_NOUNIX FOR SIGNALING THAT THE OPERATING SYSTEM IS NOT UNIX *
! _RANDOM_GFORTRAN FOR SIGNALING THAT THE INTEGER Unix FUNCTION getpid *
! IS CONSIDERED AS AN INTRINSIC RATHER AS AN EXTERNAL *
! PROCEDURE AS FOR THE gfortran COMPILER *
! _RANDOM_NAGWARE FOR SIGNALING THAT THE INTEGER Unix FUNCTION getpid *
! IS LOCATED IN THE f90_unix_env MODULE FOR THE NAG *
! FORTRAN COMPILER *
! _USE_GNU FOR SIGNALING THAT THE GNU GFORTRAN COMPILER IS *
! USED. HERE, THIS INCLUDES ONLY THE ACTIVATION OF *
! THE _RANDOM_GFORTRAN MACRO *
! _USE_NAGWARE FOR SIGNALING THAT THE NAG FORTRAN COMPILER IS *
! USED. HERE, THIS INCLUDES ONLY THE ACTIVATION OF *
! THE _RANDOM_NAGWARE MACRO *
! _USE_PGI FOR DESACTIVATING SOME OPENMP CONSTRUCTS FOR THE *
! PORTLAND PGFORTRAN COMPILER *
! *
! ************************************************************************
!
#ifdef _USE_GNU
#define _RANDOM_GFORTRAN
#endif
!
#ifdef _USE_NAGWARE
#define _RANDOM_NAGWARE
#endif
!
!
! USED MODULES
! ============
!
use Select_Parameters, only : lgl, stnd, extd, i4b, urandom_file
use Utilities, only : merror, arth
use Reals_Constants, only : zero, half, one, two, twopi
use Logical_Constants
#ifdef _MATMUL
use Utilities, only : matmul=>matmul2
#endif
#ifdef _TRANSPOSE
use Utilities, only : transpose=>transpose2
#endif
#ifdef _OPENMP
use Select_Parameters, only : omp_limit
use omp_lib, only : omp_get_max_threads, omp_in_parallel, omp_get_nested
#endif
#ifdef _RANDOM_NAGWARE
use f90_unix_env, only : getpid
#endif
#ifdef _BLAS
use BLAS_interfaces, only : gemm
#endif
!
! OTHER MODULES USED IN SPECIFIC SUBROUTINES
! ==========================================
!
! use Char_Constants
! use Prob_Procedures
! use Hous_Procedures
! use QR_Procedures
! use BLAS_interfaces
!
! STRONG TYPING IMPOSED
! =====================
!
implicit none
!
! PUBLIC ENTITIES
! ===============
!
! ALL SUBROUTINES, FUNCTIONS, VARIABLES AND PARAMETERS ARE PRIVATE BY DEFAULT.
!
private
public :: &
rand_number, rand_integer32, rand_integer31, &
random_number_, random_integer32_, random_integer31_, &
random_seed_, init_mt19937, init_memt19937, &
normal_rand_number, normal_random_number_, &
normal_rand_number2, normal_random_number2_, &
normal_rand_number3, normal_random_number3_, &
random_qr_cmp, ortho_gen_random_qr, &
gen_random_sym_mat, gen_random_mat, &
simple_shuffle, drawsample, drawbootsample
!
! GENERIC INTERFACES FOR ROUTINES WITH OVERLOADED VERSIONS
! ========================================================
!
interface random_number_
module procedure random_r0, &
random_r1, &
random_r2, &
random_r3, &
random_r4, &
random_r5, &
random_r6, &
random_r7
end interface
!
interface random_integer32_
module procedure random_i32_0, &
random_i32_1, &
random_i32_2, &
random_i32_3, &
random_i32_4, &
random_i32_5, &
random_i32_6, &
random_i32_7
end interface
!
interface random_integer31_
module procedure random_i31_0, &
random_i31_1, &
random_i31_2, &
random_i31_3, &
random_i31_4, &
random_i31_5, &
random_i31_6, &
random_i31_7
end interface
!
interface init_mt19937
module procedure init_mt19937_r0, &
init_mt19937_r1
end interface
!
interface init_memt19937
module procedure init_memt19937_r0, &
init_memt19937_r1
end interface
!
interface normal_random_number_
module procedure normal_random_r0, &
normal_random_r1, &
normal_random_r2
end interface
!
interface normal_random_number2_
module procedure normal_random2_r0, &
normal_random2_r1, &
normal_random2_r2
end interface
!
interface normal_random_number3_
module procedure normal_random3_r0, &
normal_random3_r1, &
normal_random3_r2
end interface
!
interface simple_shuffle
module procedure simple_shuffle_rv, simple_shuffle_cv, simple_shuffle_iv
end interface
!
!
! MODULE PARAMETERS
! =================
!
! ki_sel IS THE KIND PARAMETER FOR 32-BIT INTEGER.
!
integer, parameter :: ki0 = kind(0)
integer, parameter :: ki9 = selected_int_kind(9)
integer, parameter :: ki_sel = max(ki9,sign(ki0,-ki9))
!
integer, parameter :: ratio_i = (int(bit_size(0_ki_sel)) + bit_size(0) - 1)/bit_size(0)
!
! bit_size(0_ki_sel) MUST BE EQUAL TO fullbitsize IF 32_BIT INTEGERS ARE AVAILABLE.
!
integer(ki_sel), parameter :: fullbitsize = 32_ki_sel
!
! THE CONSTANTS fbs, hbs, qbs AND tbs ARE USED FOR EMULATING UNSIGNED 32-BIT INTEGER ARITHMETIC
! WITHOUT OVERFLOWS IN INTERNAL ROUTINES.
!
integer, parameter :: fbs = int(fullbitsize), hbs = fbs/2, qbs = hbs/2, tbs = 3*qbs, topbit = fbs - 1
!
! SPECIFY HERE THE LOCATION OF THE URANDOM DEVICE ON YOUR SYSTEM IF IT EXISTS.
! FOR UNIX SYSTEM, NORMALLY IT IS /dev/urandom .
!
! character(len=*), parameter :: urandom_file='/dev/urandom'
!
#ifdef _RANDOM_WITH0
! THE CONSTANT m_ran_32 IS 2^32.
! THE CONSTANT m_ran_invm32 IS THE RECIPROCAL OF 2^32.
!
real(stnd), parameter :: m_ran_32 = 4294967296.0_stnd, &
m_ran_invm32 = one/m_ran_32
#else
! THE CONSTANT m_ran_32 IS THE REAL NUMBER FOLLOWING 2^32.
! THE CONSTANT m_ran_invm32 IS THE RECIPROCAL OF THIS REAL NUMBER.
!
real(stnd), parameter :: m_ran_32 = 4294967296.0_stnd*(one + epsilon(half) ), &
m_ran_invm32 = one/m_ran_32
#endif
!
! num_bits_stnd IS THE NUMBER OF BITS IN THE MANTISSA OF REAL NUMBERS OF PRECISION stnd. WE
! ASSUME THAT THE MANTISSA IS NORMALIZED AS IN THE IEEE STANDARD.
!
integer, parameter :: num_bits_stnd = min(digits(half),64)-1, &
num_shift=max(min(num_bits_stnd-64,-1),-topbit)
!
! THE FOLLOWING INTEGER PARAMETERS ARE USED BY THE 32-BIT XORSHIFT RNG WHICH IS ONE OF THE
! COMPONENT RNGS IN THE KISS RANDOM NUMBER GENERATORS.
!
integer, parameter :: kiss_shift1 = 13, &
kiss_shift2 = -17, &
kiss_shift3 = 5
!
! THE FOLLOWING INTEGER PARAMETERS ARE USED BY THE MERSENNE TWISTER RANDOM NUMBER GENERATORS.
!
! PERIOD PARAMETERS FOR THE MERSENNE TWISTER MT19937 AND MEMT19937-II RNGS.
!
integer(ki_sel), parameter :: mt_n = 624_ki_sel, &
mt_m = 397_ki_sel
!
#ifdef _RANDOM_NOINT32
integer(ki_sel), parameter :: mt_upper_mask = ishft( 1_ki_sel, topbit), &
mt_lower_mask = ibits( not( mt_upper_mask ), 0, fbs ), &
mt_matrix_a = ior( 419999967_ki_sel, mt_upper_mask ), &
mt_mag01(0:1) = (/ 0_ki_sel, mt_matrix_a /)
#else
integer(ki_sel), parameter :: mt_upper_mask = ishft( 1_ki_sel, topbit), &
mt_lower_mask = not( mt_upper_mask ), &
mt_matrix_a = ior( 419999967_ki_sel, mt_upper_mask ), &
mt_mag01(0:1) = (/ 0_ki_sel, mt_matrix_a /)
#endif
!
! THESE PARAMETERS MAY BE ALSO SPECIFIED AS FOLLOW ASSUMING 32-BIT INTEGER AND INTEGER REPRESENTATION
! IS TWO'S COMPLEMENT. HOWEVER, THE INITIALIZATION OF mt_upper_mask TO THE NEGATIVE 32-BIT INTEGER
! OF THE LARGEST AMPLITUDE AT COMPILATION TIME MAY CAUSE PROBLEMS ON SOME SYSTEMS (E.G. SOME VERSIONS
! OF GFORTRAN FOR EXAMPLE). THIS IS DUE TO THE FACT THAT THE COMPILER WILL TRY TO FORM
! THE POSITIVE INTEGER 2147483648 (WHICH IS NOT REPRESENTABLE IF TWO'S COMPLEMENT NOTATION
! IS USED), BEFORE NEGATING IT. THIS WILL RESULT IN INTEGER OVERFLOW, WHICH IS USUALLY
! CHECKED AT COMPILATION TIME FOR CONSTANT PARAMETERS.
!
! integer(ki_sel), parameter :: mt_upper_mask = -2147483648_ki_sel, &
! mt_lower_mask = 2147483647_ki_sel, &
! mt_matrix_a = -1727483681_ki_sel, &
! mt_mag01(0:1) = (/ 0_ki_sel, mt_matrix_a /)
!
! THESE PARAMETERS MAY BE ALSO SPECIFIED AS FOLLOW, WITH HEXADECIMAL CONSTANTS. HOWEVER, THESE HEXADECIMAL
! CONSTANTS MAY CAUSE PROBLEMS ON SOME COMPILERS (E.G. GFORTRAN) BECAUSE THE "NEGATIVE" 32-BIT INTEGERS ARE
! CONSIDERED AS UNSIGNED 32-BIT INTEGERS INSTEAD OF SIGNED 32-BIT INTEGERS DURING COMPILATION. THIS WILL
! RESULT IN INTEGER OVERFLOW, WHICH IS USUALLY CHECKED AT COMPILATION TIME FOR CONSTANT PARAMETERS.
!
! integer(ki_sel), parameter :: mt_upper_mask = int( z'80000000', ki_sel), &
! mt_lower_mask = int( z'7fffffff', ki_sel), &
! mt_matrix_a = int( z'9908b0df', ki_sel), &
! mt_mag01(0:1) = (/ 0_ki_sel, mt_matrix_a /)
!
! DEFAULT SEEDS FOR THE MERSENNE TWISTER MT19937 AND MEMT19937-II RNGS.
!
integer(ki_sel), parameter :: mt_default_seed = 5489_ki_sel
! integer(ki_sel), parameter :: mt_default_seed = 21641_ki_sel
!
integer(ki_sel), dimension(4), parameter :: &
mt_default_seed_array = (/ 291_ki_sel, 564_ki_sel, 837_ki_sel, 1110_ki_sel /)
!
! TEMPERING PARAMETERS FOR THE MERSENNE TWISTER MT19937 RNG.
!
integer, parameter :: mt_t1_shift = 7, &
mt_t2_shift = 15, &
mt_shift0 = -11, &
mt_shift1 = -18
!
integer(ki_sel), parameter :: mt_t1_mask = ior( 489444992_ki_sel , mt_upper_mask), &
mt_t2_mask = ior( 1875247104_ki_sel, mt_upper_mask)
!
! THESE PARAMETERS MAY BE ALSO SPECIFIED AS FOLLOW ASSUMING 32-BIT INTEGER AND INTEGER REPRESENTATION
! IS TWO'S COMPLEMENT.
!
! integer(ki_sel), parameter :: mt_t1_mask = -1658038656_ki_sel, &
! mt_t2_mask = -272236544_ki_sel
!
! THESE PARAMETERS MAY BE ALSO SPECIFIED AS FOLLOW, WITH HEXADECIMAL CONSTANTS. HOWEVER, THESE HEXADECIMAL
! CONSTANTS MAY CAUSE PROBLEMS ON SOME COMPILERS (E.G. GFORTRAN) BECAUSE THE "NEGATIVE" 32-BIT INTEGERS ARE
! CONSIDERED AS UNSIGNED 32-BIT INTEGERS INSTEAD OF SIGNED 32-BIT INTEGERS DURING COMPILATION.
!
! integer(ki_sel), parameter :: mt_t1_mask = int( z'9d2c5680', ki_sel), &
! mt_t2_mask = int( z'efc60000', ki_sel)
!
! TEMPERING PARAMETERS FOR THE MERSENNE TWISTER MEMT19937-II RNG.
!
integer, parameter :: memt_lag1 = 151, &
memt_lag2 = 36, &
memt_lag1over = 473, &
memt_lag2over = 588, &
memt_shift1 = 8, &
memt_shift2 = 14
!
integer(ki_sel), parameter :: memt_mask1 = ior( 840548011_ki_sel, mt_upper_mask ), &
memt_mask2 = 1455285546_ki_sel
!
! THESE PARAMETERS MAY BE ALSO SPECIFIED AS FOLLOW ASSUMING 32-BIT INTEGER AND INTEGER REPRESENTATION
! IS TWO'S COMPLEMENT.
!
! integer(ki_sel), parameter :: memt_mask1 = -1306935637_ki_sel, &
! memt_mask2 = 1455285546_ki_sel
!
! THESE PARAMETERS MAY BE ALSO SPECIFIED AS FOLLOW, WITH HEXADECIMAL CONSTANTS. HOWEVER, THESE HEXADECIMAL
! CONSTANTS MAY CAUSE PROBLEMS ON SOME COMPILERS (E.G. GFORTRAN) BECAUSE THE "NEGATIVE" 32-BIT INTEGERS ARE
! CONSIDERED AS UNSIGNED 32-BIT INTEGERS INSTEAD OF SIGNED 32-BIT INTEGERS DURING COMPILATION.
!
! integer(ki_sel), parameter :: memt_mask1 = int( z'b219beab', ki_sel), &
! memt_mask2 = int( z'56bde52a', ki_sel)
!
#ifdef _RANDOM_NOINT32
! THE FOLLOWING PARAMETER IS USED TO SET THE LAST 32 BITS OF INTEGER OF KIND ki_sel TO 1,
! IF 32 BIT-INTEGERS ARE NOT AVAILABLE.
!
integer(ki_sel), parameter :: noint32_mask = not( ior( mt_lower_mask, mt_upper_mask ) )
!
#endif
!
!
! MODULE VARIABLES
! ================
!
! first = true MEANS THAT THE random_seed_ SUBROUTINE HAS NEVER BEEN CALLED BEFORE.
! test_kiss = true MEANS THAT THE KISS RNGS HAVE NOT BEEN YET TESTED FOR OVERFLOWS.
!
logical(lgl), save :: first = true, test_kiss = true
!
! THE PRIVATE INTEGER VARIABLE method SETS THE RANDOM NUMBER GENERATOR USED FOR SUBSEQUENT
! CALLS OF THE rand_number, rand_integer32, rand_integer31, random_number_, random_integer32_,
! random_integer31_ ROUTINES:
!
! method = 1 : THE Marsaglia's KISS RNG IS USED.
! method = 2 : THE FAST Marsaglia's KISS RNG, WHICH USES ONLY
! ADD, SHIFT, EXCLUSIVE-OR AND "AND" OPERATIONS,
! IS USED (SAME RESULTS AS THE C VERSION).
! method = 3 : THE L'Ecuyer's LFSR113 RNG IS USED.
! method = 4 : THE MERSENNE TWISTER MT19937 RNG IS USED.
! method = 5 : THE MERSENNE TWISTER MEMT19937-II RNG IS USED.
! method = 6 : THE EXTENDED VERSION OF THE Marsaglia's KISS RNG IS USED.
! method = 7 : THE EXTENDED VERSION OF THE FAST Marsaglia's KISS RNG IS USED.
! method = 8 : THE EXTENDED VERSION OF THE L'Ecuyer's LFSR113 RNG IS USED.
! method = 9 : THE EXTENDED VERSION OF THE MERSENNE TWISTER MT19937 RNG IS USED.
! method = 10 : THE EXTENDED VERSION OF THE MERSENNE TWISTER MEMT19937-II RNG IS USED.
!
! IN ORDER TO CHANGE THE RNG, YOU MUST USE A CALL TO THE random_seed_ SUBROUTINE WITH
! THE OPTIONAL alg ARGUMENT SET TO 1, 2, 3, 4, 5, 6, 7, 8, 9 OR 10. NOTE THAT FOR RANDOM INTEGER
! GENERATION, METHODS 6, 7, 8, 9 AND 10 ARE EXACTLY IDENTICAL TO METHODS 1, 2, 3, 4 AND 5,
! RESPECTIVELY. THEY DIFFER ONLY FOR RANDOM REAL GENERATION.
!
! THE PRIVATE INTEGER VARIABLE method STORED THE METHOD CURRENTLY IN USE, num_seeds
! STORED THE NUMBER OF SEEDS USED BY THIS METHOD AND seed_size IS THE CORRESPONDING SIZE
! OF THE SEED VECTOR AS RETURNED BY A CALL TO random_seed_ SUBROUTINE WITH ARGUMENT size.
!
! THE DEFAULT METHOD CAN BE SAFELY CHANGED HERE, BETWEEN 1, 2 AND 3.
! NOTE THAT THE OTHER METHODS CANNOT BE USED SAFELY AS THE DEFAULT METHOD.
! FURTHERMORE IF 32-BIT INTEGERS ARE NOT AVAILABLE THE DEFAULT METHOD MUST
! BE 3, BECAUSE THE KISS RNGS WORK PROPERLY ONLY WITH 32-BIT INTEGERS.
!
! integer, save :: method = 1
! integer, save :: method = 2
integer, save :: method = 3
!
! num_seeds IS THE SIZE OF THE STATE VECTOR OF THE CURRENT RNG.
! seed_size IS THE SIZE OF THE SEED ARRAY OF THE RANDOM GENERATOR AS
! RETURNED BY SUBROUTINE random_seed_. NOTE THAT THE seed_size IS NOT
! NECESSARILY EQUAL TO num_seeds DEPENDING ON THE RNG AND IF 32-BIT INTEGERS
! ARE OR NOT THE DEFAULT INTEGERS ON YOUR SYSTEM.
!
integer, save :: num_seeds, seed_size
!
! THE NEXT VARIABLES STORE THE STATE VARIABLES FOR EACH RANDOM NUMBER GENERATORS.
!
! PRIVATE INTEGER STATE VARIABLES USED BY THE Marsaglia's KISS RNG (method = 1 or 6).
!
integer(ki_sel), save :: x = 123456789_ki_sel, y = 362436069_ki_sel, &
z = 521288629_ki_sel, w = 916191069_ki_sel
!
! PRIVATE INTEGER STATE VARIABLES USED BY THE FAST Marsaglia's KISS RNG, WHICH USES ONLY
! ADD, SHIFT, EXCLUSIVE-OR AND "AND" OPERATIONS (method = 2 or 7).
!
integer(ki_sel), save :: x2 = 123456789_ki_sel, y2 = 362436069_ki_sel, &
z2 = 21288629_ki_sel, w2 = 14921776_ki_sel, c=0_ki_sel
!
! PRIVATE INTEGER STATE VARIABLES USED BY THE L'Ecuyer's LFSR113 RNG (method = 3 or 8).
!
integer(ki_sel), save :: s1 = 153587801_ki_sel, s2 = -759022222_ki_sel, &
s3 = 1288503317_ki_sel, s4 = -1718083407_ki_sel
!
! PRIVATE INTEGER STATE VARIABLES USED BY THE THE MERSENNE TWISTER MT19937 RNG (method = 4 or 9).
! mt_initialized = false MEANS THAT THE STATE OF MT19937 IS NOT INITIALIZED.
! mti = mt_n MEANS THAT THE ARRAY mt(:) IS NOT INITIALIZED.
! THE ARRAY mt(:) IS THE STATE VECTOR OF THE MERSENNE TWISTER MT19937 RNG.
!
logical(lgl), save :: mt_initialized = false
integer(ki_sel), save :: mti = mt_n, mt(0_ki_sel:mt_n-1_ki_sel) = 0_ki_sel
!
! PRIVATE INTEGER STATE VARIABLES USED BY THE THE MERSENNE TWISTER MEMT19937-II RNG (method = 5 or 10).
! memt_initialized = false MEANS THAT THE STATE OF MEMT19937-II IS NOT INITIALIZED.
! memti = -1_ki_sel MEANS THAT THE ARRAY memt(:) IS NOT INITIALIZED.
! THE ARRAY memt(:) IS THE STATE VECTOR OF THE MERSENNE TWISTER MEMT19937-II RNG.
!
logical(lgl), save :: memt_initialized = false
integer(ki_sel), save :: memti = -1_ki_sel, memt(0_ki_sel:mt_n-1_ki_sel) = 0_ki_sel
!
! THE FOLLOWING PRIVATE VARIABLE m_ran_invmbits IS USED TO TRANSFORM SIGNED 32-BIT INTEGERS
! INTO REAL FLOATING POINT NUMBERS FOR THE EXTENDED VERSIONS OF THE RNGS.
!
real(stnd), save :: m_ran_invmbits = -one
!
#ifndef _RANDOM_NOUNIX
!
! INTEGER Unix FUNCTION USED FOR INITIALIZING THE SEEDS OF THE RNGS ON UNIX SYSTEMS.
!
#ifdef _RANDOM_GFORTRAN
intrinsic getpid
#else
!
#ifndef _RANDOM_NAGWARE
!
integer :: getpid
!
external getpid
#endif
!
#endif
!
#endif
!
!
! =========================================================================================
!
contains
! ========
!
! =========================================================================================
! RANDOM FLOATING POINT NUMBER SUBROUTINES
! =========================================================================================
!
function rand_number() result( harvest )
!
! purpose
! _______
!
! This function returns a uniformly distributed random number between 0 and 1,
! exclusive of the two endpoints 0 and 1.
!
!
! Arguments
! _________
!
! None
!
!
! Further Details
! _______________
!
! If the CPP macro _RANDOM_WITH0 is used during compilation,
! this routine may return 0 value.
!
!
! __________________________________________________________________________________________
!
!
! USED MODULES
! ____________
!
#ifdef _RANDOM_NOINT32
use Char_Constants, only : random_error7, random_error9
#else
use Char_Constants, only : random_error1, random_error2, &
random_error7, random_error8
#endif
!
!
! SPECIFICATIONS FOR ARGUMENTS
! ____________________________
!
real(stnd) :: harvest
!
!
! SPECIFICATIONS FOR LOCAL VARIABLES
! __________________________________
!
integer(ki_sel) :: k, j, tmp
integer(ki_sel), dimension(2) :: tmpvec
!
!
! PARAMETERS
! __________
!
character(len=*), parameter :: name_proc='rand_number'
!
!
! EXECUTABLE STATEMENTS
! _____________________
!
if ( first ) then
#ifdef _RANDOM_NOINT32
!
! TEST IF THE DEFAULT RNG IS SET CORRECTLY.
!
if ( method/=3 ) then
call merror( name_proc//random_error9 )
endif
!
! TEST IF THE BASE OF THE INTEGER SYSTEM IS 2 AND
! IF INTEGER REPRESENTATION IS TWO'S COMPLEMENT NOTATION.
!
tmp = ibclr(-1_ki_sel, bit_size(tmp)-1_ki_sel)
!
if ( radix(tmp)/=2 .or. tmp/=huge(tmp) ) then
!
call merror( name_proc//random_error7 )
!
endif
!
#else
!
! TEST IF 32-BIT INTEGERS ARE AVAILABLE.
!
if ( bit_size( tmp )/=fullbitsize ) then
call merror( name_proc//random_error1 )
endif
!
! TEST IF THE DEFAULT RNG IS SET CORRECTLY.
!
if ( method<1 .or. method>3 ) then
call merror( name_proc//random_error2 )
endif
!
! TEST IF THE BASE OF THE INTEGER SYSTEM IS 2 AND
! IF INTEGER REPRESENTATION IS TWO'S COMPLEMENT NOTATION.
!
tmp = ishftc( -8_ki_sel, -3)
!
if ( radix(tmp)/=2 .or. tmp/=536870911_ki_sel ) then
!
call merror( name_proc//random_error7 )
!
endif
!
if ( method/=3 ) then
!
! TEST IF INTEGER OVERFLOWS ARE SAFE FOR THE MARSAGLIA'S KISS RNGS.
!
tmp = huge( tmp )
!
if ( integer_not_safe( tmp ) ) then
!
call merror( name_proc//random_error8 )
!
endif
!
endif
#endif
!
endif
!
!$OMP CRITICAL (ran_num_)
select case (method)
!
case (1)
!
! Marsaglia's KISS RNG.
!
x = 69069_ki_sel * x + 1327217885_ki_sel
y = ieor( y, ishft(y, kiss_shift1) )
y = ieor( y, ishft(y, kiss_shift2) )
y = ieor( y, ishft(y, kiss_shift3) )
! y = m( m( m( y, kiss_shift1), kiss_shift2), kiss_shift3)
z = 18000_ki_sel * iand( z, 65535_ki_sel) + ishft( z, -16)
w = 30903_ki_sel * iand( w, 65535_ki_sel) + ishft( w, -16)
!
tmp = x + y + ishft( z, 16) + w
!
case (2)
!
! FAST Marsaglia's KISS RNG WHICH USES ONLY ADD, SHIFT, EXCLUSIVE-OR AND "AND" OPERATIONS.
!
x2 = x2 + 545925293_ki_sel
! x2 = uiadd( x2, 545925293_ki_sel )
y2 = ieor( y2, ishft(y2, kiss_shift1) )
y2 = ieor( y2, ishft(y2, kiss_shift2) )
y2 = ieor( y2, ishft(y2, kiss_shift3) )
! y2 = m( m( m(y2, kiss_shift1), kiss_shift2), kiss_shift3)
tmp = z2 + w2 + c
z2 = w2
c = ishft( tmp, -topbit)
w2 = iand( tmp, 2147483647_ki_sel)
!
tmp = x2 + y2 + w2
!
case (3)
!
! L'Ecuyer's LFSR113 RNG.
!
#ifdef _RANDOM_NOINT32
tmp = ieor( ishft(s1,6), s1)
tmp = ishft( ibits( tmp, 0, fbs ), -13)
tmp = ieor( ishft( iand(s1,-2_ki_sel), 18), tmp)
s1 = ibits( tmp, 0, fbs )
!
tmp = ieor( ishft(s2,2), s2)
tmp = ishft( ibits( tmp, 0, fbs ), -27)
tmp = ieor( ishft( iand(s2,-8_ki_sel), 2), tmp)
s2 = ibits( tmp, 0, fbs )
!
tmp = ieor( ishft(s3,13), s3)
tmp = ishft( ibits( tmp, 0, fbs ), -21)
tmp = ieor( ishft( iand(s3,-16_ki_sel), 7), tmp)
s3 = ibits( tmp, 0, fbs )
!
tmp = ieor( ishft(s4,3), s4)
tmp = ishft( ibits( tmp, 0, fbs ), -12)
tmp = ieor( ishft( iand(s4,-128_ki_sel), 13), tmp)
s4 = ibits( tmp, 0, fbs )
#else
tmp = ishft( ieor( ishft(s1,6), s1), -13)
s1 = ieor( ishft( iand(s1,-2_ki_sel), 18), tmp)
!
tmp = ishft( ieor( ishft(s2,2), s2), -27)
s2 = ieor( ishft( iand(s2,-8_ki_sel), 2), tmp)
!
tmp = ishft( ieor( ishft(s3,13), s3), -21)
s3 = ieor( ishft( iand(s3,-16_ki_sel), 7), tmp)
!
tmp = ishft( ieor( ishft(s4,3), s4), -12)
s4 = ieor( ishft( iand(s4,-128_ki_sel), 13), tmp)
#endif
!
tmp = ieor( ieor( ieor(s1,s2), s3), s4)
!
case (4)
!
! MERSENNE TWISTER MT19937 RNG.
!
if ( mti>=mt_n ) then
!
! GENERATE mt_n WORDS AT ONE TIME.
!
do j = 0_ki_sel, mt_n - mt_m - 1_ki_sel
!
tmp = ior( iand(mt(j),mt_upper_mask), &
iand(mt(j+1_ki_sel),mt_lower_mask) )
!
mt(j) = ieor( ieor(mt(j+mt_m),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
end do
!
do j = mt_n - mt_m, mt_n - 2_ki_sel
!
tmp = ior( iand(mt(j),mt_upper_mask), &
iand(mt(j+1_ki_sel),mt_lower_mask) )
!
mt(j) = ieor( ieor(mt(j+(mt_m-mt_n)), ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
end do
!
tmp = ior( iand(mt(j),mt_upper_mask), &
iand(mt(0_ki_sel),mt_lower_mask) )
!
mt(j) = ieor( ieor(mt(mt_m-1_ki_sel),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
mti = 0_ki_sel
!
endif
!
tmp = mt(mti)
mti = mti + 1_ki_sel
!
! TEMPERING PHASE.
!
tmp = ieor( tmp, ishft(tmp,mt_shift0) )
tmp = ieor( tmp, iand(ishft(tmp,mt_t1_shift),mt_t1_mask) )
tmp = ieor( tmp, iand(ishft(tmp,mt_t2_shift),mt_t2_mask) )
tmp = ieor( tmp, ishft(tmp,mt_shift1) )
!
case (5)
!
! MERSENNE TWISTER MT19937-II RNG.
!
select case (memti)
!
case (0_ki_sel:mt_n-mt_m-1_ki_sel)
!
tmp = ior( iand(memt(memti),mt_upper_mask), &
iand(memt(memti+1_ki_sel),mt_lower_mask) )
!
memt(memti) = ieor( ieor(memt(memti+mt_m),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
! TEMPERING PHASE.
!
tmp = ieor( memt(memti), iand(memt(memti+memt_lag1),memt_mask1) )
tmp = ieor( tmp, ishft(tmp,memt_shift1) )
tmp = ieor( tmp, ishft(tmp,memt_shift2) )
tmp = ieor( tmp, iand(memt(memti+memt_lag2),memt_mask2) )
!
memti = memti + 1_ki_sel
!
case (mt_n-mt_m:memt_lag1over-1_ki_sel)
!
tmp = ior( iand(memt(memti),mt_upper_mask), &
iand(memt(memti+1_ki_sel),mt_lower_mask) )
!
memt(memti) = ieor( ieor(memt(memti+(mt_m-mt_n)),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
! TEMPERING PHASE.
!
tmp = ieor( memt(memti), iand(memt(memti+memt_lag1),memt_mask1) )
tmp = ieor( tmp, ishft(tmp,memt_shift1) )
tmp = ieor( tmp, ishft(tmp,memt_shift2) )
tmp = ieor( tmp, iand(memt(memti+memt_lag2),memt_mask2) )
!
memti = memti + 1_ki_sel
!
case (memt_lag1over:memt_lag2over-1_ki_sel)
!
tmp = ior( iand(memt(memti),mt_upper_mask), &
iand(memt(memti+1_ki_sel),mt_lower_mask) )
!
memt(memti) = ieor( ieor(memt(memti+(mt_m-mt_n)),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
! TEMPERING PHASE.
!
tmp = ieor( memt(memti), iand(memt(memti-memt_lag1over),memt_mask1) )
tmp = ieor( tmp, ishft(tmp,memt_shift1) )
tmp = ieor( tmp, ishft(tmp,memt_shift2) )
tmp = ieor( tmp, iand(memt(memti+memt_lag2),memt_mask2) )
!
memti = memti + 1_ki_sel
!
case (memt_lag2over:mt_n-2_ki_sel)
!
tmp = ior( iand(memt(memti),mt_upper_mask), &
iand(memt(memti+1_ki_sel),mt_lower_mask) )
!
memt(memti) = ieor( ieor(memt(memti+(mt_m-mt_n)),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
! TEMPERING PHASE.
!
tmp = ieor( memt(memti), iand(memt(memti-memt_lag1over),memt_mask1) )
tmp = ieor( tmp, ishft(tmp,memt_shift1) )
tmp = ieor( tmp, ishft(tmp,memt_shift2) )
tmp = ieor( tmp, iand(memt(memti-memt_lag2over),memt_mask2) )
!
memti = memti + 1_ki_sel
!
case (mt_n-1_ki_sel)
!
tmp = ior( iand(memt(mt_n-1_ki_sel),mt_upper_mask), &
iand(memt(0_ki_sel),mt_lower_mask) )
!
memt(mt_n-1_ki_sel) = ieor( ieor(memt(mt_m-1_ki_sel),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
! TEMPERING PHASE.
!
tmp = ieor( memt(memti), iand(memt(memti-memt_lag1over),memt_mask1) )
tmp = ieor( tmp, ishft(tmp,memt_shift1) )
tmp = ieor( tmp, ishft(tmp,memt_shift2) )
tmp = ieor( tmp, iand(memt(memti-memt_lag2over),memt_mask2) )
!
memti = 0_ki_sel
!
end select
!
#ifdef _RANDOM_NOINT32
tmp = ibits( tmp, 0, fbs )
#endif
!
case (6)
!
! EXTENDED PRECISION VERSION OF Marsaglia's KISS RNG.
!
do k = 1_ki_sel, 2_ki_sel
!
x = 69069_ki_sel * x + 1327217885_ki_sel
y = ieor( y, ishft(y, kiss_shift1) )
y = ieor( y, ishft(y, kiss_shift2) )
y = ieor( y, ishft(y, kiss_shift3) )
! y = m( m( m( y, kiss_shift1), kiss_shift2), kiss_shift3)
z = 18000_ki_sel * iand( z, 65535_ki_sel) + ishft( z, -16)
w = 30903_ki_sel * iand( w, 65535_ki_sel) + ishft( w, -16)
!
tmpvec(k) = x + y + ishft( z, 16) + w
!
end do
!
case (7)
!
! EXTENDED PRECISION VERSION OF THE FAST Marsaglia's KISS RNG,
! WHICH USES ONLY ADD, SHIFT, EXCLUSIVE-OR AND "AND" OPERATIONS.
!
do k = 1_ki_sel, 2_ki_sel
!
x2 = x2 + 545925293_ki_sel
! x2 = uiadd( x2, 545925293_ki_sel )
y2 = ieor( y2, ishft(y2, kiss_shift1) )
y2 = ieor( y2, ishft(y2, kiss_shift2) )
y2 = ieor( y2, ishft(y2, kiss_shift3) )
! y2 = m( m( m(y2, kiss_shift1), kiss_shift2), kiss_shift3)
tmp = z2 + w2 + c
z2 = w2
c = ishft( tmp, -topbit)
w2 = iand( tmp, 2147483647_ki_sel)
!
tmpvec(k) = x2 + y2 + w2
!
end do
!
case (8)
!
! EXTENDED PRECISION VERSION OF L'Ecuyer's LFSR113 RNG.
!
do k = 1_ki_sel, 2_ki_sel
!
#ifdef _RANDOM_NOINT32
tmp = ieor( ishft(s1,6), s1)
tmp = ishft( ibits( tmp, 0, fbs ), -13)
tmp = ieor( ishft( iand(s1,-2_ki_sel), 18), tmp)
s1 = ibits( tmp, 0, fbs )
!
tmp = ieor( ishft(s2,2), s2)
tmp = ishft( ibits( tmp, 0, fbs ), -27)
tmp = ieor( ishft( iand(s2,-8_ki_sel), 2), tmp)
s2 = ibits( tmp, 0, fbs )
!
tmp = ieor( ishft(s3,13), s3)
tmp = ishft( ibits( tmp, 0, fbs ), -21)
tmp = ieor( ishft( iand(s3,-16_ki_sel), 7), tmp)
s3 = ibits( tmp, 0, fbs )
!
tmp = ieor( ishft(s4,3), s4)
tmp = ishft( ibits( tmp, 0, fbs ), -12)
tmp = ieor( ishft( iand(s4,-128_ki_sel), 13), tmp)
s4 = ibits( tmp, 0, fbs )
#else
tmp = ishft( ieor( ishft(s1,6), s1), -13)
s1 = ieor( ishft( iand(s1,-2_ki_sel), 18), tmp)
!
tmp = ishft( ieor( ishft(s2,2), s2), -27)
s2 = ieor( ishft( iand(s2,-8_ki_sel), 2), tmp)
!
tmp = ishft( ieor( ishft(s3,13), s3), -21)
s3 = ieor( ishft( iand(s3,-16_ki_sel), 7), tmp)
!
tmp = ishft( ieor( ishft(s4,3), s4), -12)
s4 = ieor( ishft( iand(s4,-128_ki_sel), 13), tmp)
#endif
!
tmpvec(k) = ieor( ieor( ieor(s1,s2), s3), s4)
!
end do
!
case (9)
!
! EXTENDED PRECISION VERSION OF THE MERSENNE TWISTER MT19937 RNG.
!
do k = 1_ki_sel, 2_ki_sel
!
if ( mti>=mt_n ) then
!
! GENERATE mt_n WORDS AT ONE TIME.
!
do j = 0_ki_sel, mt_n - mt_m - 1_ki_sel
!
tmp = ior( iand(mt(j),mt_upper_mask), &
iand(mt(j+1_ki_sel),mt_lower_mask) )
!
mt(j) = ieor( ieor(mt(j+mt_m),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
end do
!
do j = mt_n - mt_m, mt_n - 2_ki_sel
!
tmp = ior( iand(mt(j),mt_upper_mask), &
iand(mt(j+1_ki_sel),mt_lower_mask) )
!
mt(j) = ieor( ieor(mt(j+(mt_m-mt_n)), ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
end do
!
tmp = ior( iand(mt(j),mt_upper_mask), &
iand(mt(0_ki_sel),mt_lower_mask) )
!
mt(j) = ieor( ieor(mt(mt_m-1_ki_sel),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
mti = 0_ki_sel
!
endif
!
tmp = mt(mti)
mti = mti + 1_ki_sel
!
! TEMPERING PHASE.
!
tmp = ieor( tmp, ishft(tmp,mt_shift0) )
tmp = ieor( tmp, iand(ishft(tmp,mt_t1_shift),mt_t1_mask) )
tmp = ieor( tmp, iand(ishft(tmp,mt_t2_shift),mt_t2_mask) )
!
tmpvec(k) = ieor( tmp, ishft(tmp,mt_shift1) )
!
end do
!
case (10)
!
! EXTENDED PRECISION VERSION OF THE MERSENNE TWISTER MEMT19937-II RNG.
!
do k = 1_ki_sel, 2_ki_sel
!
select case (memti)
!
case (0_ki_sel:mt_n-mt_m-1_ki_sel)
!
tmp = ior( iand(memt(memti),mt_upper_mask), &
iand(memt(memti+1_ki_sel),mt_lower_mask) )
!
memt(memti) = ieor( ieor(memt(memti+mt_m),ishft(tmp,-1)), &
mt_mag01(iand(tmp,1_ki_sel)) )
!
! TEMPERING PHASE.
!
tmp = ieor( memt(memti), iand(memt(memti+memt_lag1),memt_mask1) )
tmp = ieor( tmp, ishft(tmp,memt_shift1) )
tmp = ieor( tmp, ishft(tmp,memt_shift2) )
tmpvec(k) = ieor( tmp, iand(memt(memti+memt_lag2),memt_mask2) )
!
memti = memti + 1_ki_sel
!
case (mt_n-mt_m:memt_lag1over-1_ki_sel)
!
tmp = ior( iand(memt(memti),mt_upper_mask), &
iand(memt(memti+1_ki_sel),mt_lower_mask) )
!
memt(memti) = ieor( ieor(memt(memti+(mt_m-mt_n)),ishft(tmp,-1)), &