-
Notifications
You must be signed in to change notification settings - Fork 1
/
num.c
1665 lines (1537 loc) · 50.8 KB
/
num.c
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
/* This file is part of the MAYLIB libray.
Copyright 2007-2018 Patrick Pelissier
This Library 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.
This Library 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 should have received a copy of the GNU Lesser General Public License
along with th Library; see the file COPYING.LESSER.txt.
If not, write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include "may-impl.h"
/* All the functions accept unevaluated args.
Only simplify functions return evaluated args */
/* Support NON evaluated arg (May be called with MAY_DUMMY) */
MAY_REGPARM int
may_num_zero_p (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x))
{
case MAY_INT_T:
return mpz_sgn (MAY_INT (x)) == 0;
case MAY_RAT_T:
return mpq_sgn (MAY_RAT (x)) == 0;
case MAY_FLOAT_T:
return !mpfr_nan_p (MAY_FLOAT (x)) && mpfr_cmp_ui (MAY_FLOAT(x), 0) == 0;
default:
MAY_ASSERT (MAY_TYPE (x) == MAY_COMPLEX_T);
return may_num_zero_p (MAY_IM (x)) && may_num_zero_p (MAY_RE (x));
}
}
/* Support NON evaluated arg but must be NUMERICAL */
MAY_REGPARM int
may_num_pos_p (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x))
{
case MAY_INT_T:
return mpz_sgn (MAY_INT (x)) > 0;
case MAY_RAT_T:
return mpq_sgn (MAY_RAT (x)) > 0;
case MAY_FLOAT_T:
return !mpfr_nan_p (MAY_FLOAT (x)) && mpfr_sgn (MAY_FLOAT(x)) > 0;
default:
return 0;
}
}
/* Support NON evaluated arg but must be NUMERICAL */
MAY_REGPARM int
may_num_poszero_p (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x))
{
case MAY_INT_T:
return mpz_sgn (MAY_INT (x)) >= 0;
case MAY_RAT_T:
return mpq_sgn (MAY_RAT (x)) >= 0;
case MAY_FLOAT_T:
return !mpfr_nan_p (MAY_FLOAT (x)) && mpfr_sgn (MAY_FLOAT(x)) >= 0;
default:
return 0;
}
}
/* Support NON evaluated arg but must be NUMERICAL */
MAY_REGPARM int
may_num_neg_p (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x))
{
case MAY_INT_T:
return mpz_sgn (MAY_INT (x)) < 0;
case MAY_RAT_T:
return mpq_sgn (MAY_RAT (x)) < 0;
case MAY_FLOAT_T:
return !mpfr_nan_p (MAY_FLOAT (x)) && mpfr_sgn (MAY_FLOAT(x)) < 0;
default:
return 0;
}
}
/* Support NON evaluated arg but must be NUMERICAL */
MAY_REGPARM int
may_num_negzero_p (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x))
{
case MAY_INT_T:
return mpz_sgn (MAY_INT (x)) <= 0;
case MAY_RAT_T:
return mpq_sgn (MAY_RAT (x)) <= 0;
case MAY_FLOAT_T:
return !mpfr_nan_p (MAY_FLOAT (x)) && mpfr_sgn (MAY_FLOAT(x)) <= 0;
default:
return 0;
}
}
/* Support NON evaluated arg but must be NUMERICAL */
MAY_REGPARM int
may_num_one_p (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x))
{
case MAY_INT_T:
return mpz_cmp_ui (MAY_INT (x), 1) == 0;
case MAY_RAT_T:
return mpq_cmp_ui (MAY_RAT (x), 1, 1) == 0;
case MAY_FLOAT_T:
return !mpfr_nan_p (MAY_FLOAT (x)) && mpfr_cmp_ui (MAY_FLOAT(x), 1) == 0;
default:
MAY_ASSERT (MAY_TYPE (x) == MAY_COMPLEX_T);
return may_num_zero_p (MAY_IM (x)) && may_num_one_p (MAY_RE (x));
}
}
/* Compare two num args */
MAY_REGPARM int
may_num_cmp (may_t x, may_t y)
{
mpq_t q;
int i, sign;
/* FIXME: If y is float and is NAN, what to do? */
MAY_ASSERT (MAY_PURENUM_P (x));
MAY_ASSERT (MAY_PURENUM_P (y));
if (MAY_UNLIKELY (MAY_TYPE (x) > MAY_TYPE (y)))
swap (x, y), sign =-1;
else sign = 1;
/* Lexicographic order for complex */
if (MAY_UNLIKELY (MAY_TYPE (y) == MAY_COMPLEX_T)) {
i = may_num_cmp (x, MAY_RE (y));
if (i == 0)
i = may_num_cmp (MAY_ZERO, MAY_IM (y));
} else /* We compare real */
switch (MAY_TYPE (x)) {
case MAY_INT_T:
switch (MAY_TYPE (y)) {
case MAY_INT_T:
i = mpz_cmp (MAY_INT (x), MAY_INT (y));
break;
case MAY_RAT_T:
{
MAY_RECORD ();
mpq_init (q);
mpq_set_z (q, MAY_INT (x));
i = mpq_cmp (q, MAY_RAT (y));
MAY_CLEANUP ();
}
break;
default:
MAY_ASSERT (MAY_TYPE (y) == MAY_FLOAT_T);
i = -mpfr_cmp_z (MAY_FLOAT (y), MAY_INT (x));
break;
}
break;
case MAY_RAT_T:
switch (MAY_TYPE (y)) {
case MAY_RAT_T:
i = mpq_cmp (MAY_RAT (x), MAY_RAT (y));
break;
default:
MAY_ASSERT (MAY_TYPE (y) == MAY_FLOAT_T);
i = -mpfr_cmp_q (MAY_FLOAT (y), MAY_RAT (x));
break;
}
break;
default:
MAY_ASSERT (MAY_TYPE (x) == MAY_FLOAT_T);
MAY_ASSERT (MAY_TYPE (y) == MAY_FLOAT_T);
i = mpfr_cmp (MAY_FLOAT (x), MAY_FLOAT (y));
break;
}
return i*sign;
}
/* Simplify and return evaluated forms */
MAY_REGPARM may_t
may_mpz_simplify (may_t x)
{
MAY_ASSERT (MAY_TYPE (x) == MAY_INT_T);
#if defined(MAY_WANT_STAT_ON_INT)
static unsigned long count1[256];
static unsigned long count2[256];
static unsigned long count3[256];
static unsigned long count_bigger;
static unsigned long count_really_bigger;
long u;
if (mpz_fits_slong_p (MAY_INT (x))) {
u = mpz_get_si(MAY_INT(x));
if (u >= (1L<<24) || u <= -(1L<<24))
count_bigger++;
else {
/* abs doesn't work on LONG_MIN */
u = abs(u);
if (u >= (1L<<16))
count3 [ u >> 16 ] ++;
else if (u >= (1L<<8) )
count2 [ u >> 8 ] ++;
else
count1 [ u ] ++;
}
} else
count_really_bigger++;
auto void __attribute__((destructor)) __may_log_destruct (void);
auto void __attribute__((destructor)) __may_log_destruct (void) {
printf ("[MAYLIB]: Statistic usage of integers:\n");
for(int i = 0 ; i < 256; i++) {
if (count1[i] != 0)
printf (" %d is used %lu times.\n", i, count1[i]);
}
for(int i = 1 ; i < 256; i++) {
if (count2[i] != 0)
printf (" [%d-%d[ is used %lu times.\n", i<<8, (i+1)<<8, count2[i]);
}
for(int i = 1 ; i < 256; i++) {
if (count3[i] != 0)
printf (" [%d-%d[ is used %lu times.\n", i<<16, (i+1)<<16, count3[i]);
}
if (count_bigger != 0)
printf (" others (< long) are used %ld times.\n", count_bigger);
if (count_bigger != 0)
printf (" others (> long) are used %ld times.\n", count_really_bigger);
}
#endif
/* Arithemic in Z/nZ. Simplify number according to modulo */
if (MAY_UNLIKELY (may_g.frame.intmod != NULL)) {
mpz_t r;
mpz_init (r);
mpz_fdiv_r (r, MAY_INT (x), MAY_INT (may_g.frame.intmod));
x = MAY_MPZ_NOCOPY_C (r);
}
mp_limb_t t;
/* Simplify number: Don't use mpz_cmpabs_ui, but mpz_size and mpz_getlimbn which are inlined */
if (MAY_LIKELY (mpz_size (MAY_INT(x)) <= 1 && ( (t = mpz_getlimbn (MAY_INT (x), 0)) < MAY_MAX_MPZ_CONSTANT))) {
int sign = mpz_sgn (MAY_INT (x));
x = may_c.mpz_constant[t+MAY_MAX_MPZ_CONSTANT*(sign<0)];
}
else {
MAY_CLOSE_C (x, MAY_NUM_F|MAY_EVAL_F, may_mpz_hash (MAY_INT (x)));
MAY_SET_FLAG (x, MAY_EXPAND_F);
}
MAY_ASSERT (MAY_EVAL_P (x));
return x;
}
/* Simplify q and return evaluated form ('org' may be the 'may_t' container of 'q' if any,
or NULL if none ) */
MAY_REGPARM may_t
may_mpq_simplify (may_t org, mpq_t q)
{
MAY_ASSERT (org == NULL || MAY_TYPE (org) == MAY_RAT_T);
/* If modulo, converts n/d to an integer modulo */
if (MAY_UNLIKELY (may_g.frame.intmod != NULL))
return may_mpz_simplify (may_num_div (MAY_DUMMY,
MAY_MPZ_NOCOPY_C (mpq_numref (q)),
MAY_MPZ_NOCOPY_C (mpq_denref (q))));
if (MAY_UNLIKELY (mpz_sgn (mpq_denref (q)) == 0))
return (mpq_sgn (q) == 0 ? MAY_NAN
: mpq_sgn (q) > 0 ? MAY_P_INF : MAY_N_INF);
else if (MAY_UNLIKELY (mpz_cmp_ui (mpq_denref (q), 1) == 0))
return may_mpz_simplify (MAY_MPZ_NOCOPY_C (mpq_numref(q)));
else if (org == NULL)
org = MAY_MPQ_NOCOPY_C (q);
MAY_CLOSE_C (org, MAY_NUM_F|MAY_EVAL_F, may_mpq_hash (MAY_RAT (org)));
MAY_SET_FLAG (org, MAY_EXPAND_F);
MAY_ASSERT (MAY_EVAL_P (org));
return org;
}
/* Simplify and return evaluated form */
MAY_REGPARM may_t
may_mpfr_simplify (may_t x)
{
MAY_ASSERT (MAY_TYPE (x) == MAY_FLOAT_T);
MAY_CLOSE_C (x, MAY_NUM_F|MAY_EVAL_F, may_mpfr_hash (MAY_FLOAT (x)));
MAY_SET_FLAG (x, MAY_EXPAND_F);
MAY_ASSERT (MAY_EVAL_P (x));
return x;
}
/* Simplify and return evaluated form */
MAY_REGPARM may_t
may_cx_simplify (may_t x)
{
MAY_ASSERT (MAY_TYPE (x) == MAY_COMPLEX_T);
MAY_ASSERT (MAY_PURENUM_P (MAY_RE (x)));
MAY_ASSERT (MAY_PURENUM_P (MAY_IM (x)));
/* Simplify sub-args */
if (MAY_UNLIKELY (!MAY_EVAL_P (MAY_IM (x))))
MAY_SET_IM (x, may_num_simplify (MAY_IM (x)));
if (MAY_UNLIKELY (!MAY_EVAL_P (MAY_RE (x))))
MAY_SET_RE (x, may_num_simplify (MAY_RE (x)));
/* Check if Img = 0 */
if (MAY_UNLIKELY (may_num_zero_p (MAY_IM (x))))
return MAY_RE (x);
MAY_CLOSE_C (x, MAY_NUM_F|MAY_EVAL_F,
MAY_NEW_HASH2 (MAY_RE (x), MAY_IM (x)));
MAY_SET_FLAG (x, MAY_EXPAND_F);
MAY_ASSERT (MAY_EVAL_P (x));
return x;
}
MAY_REGPARM may_t
may_num_simplify (may_t x)
{
MAY_ASSERT (MAY_PURENUM_P (x));
switch (MAY_TYPE (x)) {
case MAY_INT_T:
return may_mpz_simplify (x);
case MAY_RAT_T:
return may_mpq_simplify (x, MAY_RAT(x));
case MAY_FLOAT_T:
return may_mpfr_simplify (x);
default:
MAY_ASSERT (MAY_TYPE (x) == MAY_COMPLEX_T);
return may_cx_simplify (x);
}
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_set (may_t dest, may_t op)
{
MAY_ASSERT (MAY_PURENUM_P (op));
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
switch (MAY_TYPE (op)) {
case MAY_INT_T:
if (MAY_LIKELY (MAY_TYPE (dest) != MAY_INT_T))
dest = MAY_INT_INIT_C ();
mpz_set (MAY_INT (dest), MAY_INT(op));
break;
case MAY_RAT_T:
if (MAY_LIKELY (MAY_TYPE (dest) != MAY_RAT_T))
dest = MAY_RAT_INIT_C ();
mpq_set (MAY_RAT(dest), MAY_RAT(op));
break;
case MAY_FLOAT_T:
if (MAY_LIKELY (MAY_TYPE (dest) != MAY_FLOAT_T))
dest = MAY_FLOAT_INIT_C ();
mpfr_set (MAY_FLOAT(dest), MAY_FLOAT(op), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op) == MAY_COMPLEX_T);
if (MAY_LIKELY (MAY_TYPE (dest) != MAY_COMPLEX_T))
dest = MAY_COMPLEX_INIT_C ();
may_t r = may_num_set (MAY_RE (dest), MAY_RE (op));
may_t i = may_num_set (MAY_IM (dest), MAY_IM (op));
MAY_SET_RE (dest, r);
MAY_SET_IM (dest, i);
break;
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
/* Warning: this function may return evaluated arg for complex number and
may return not a purenum for integer/rationnal complex number */
MAY_REGPARM may_t
may_num_abs (may_t dest, may_t x)
{
may_t r = may_num_set (dest, x);
MAY_ASSERT (MAY_PURENUM_P (r));
switch (MAY_TYPE(x))
{
case MAY_INT_T:
mpz_abs (MAY_INT (r), MAY_INT (r));
break;
case MAY_RAT_T:
mpq_abs (MAY_RAT (r), MAY_RAT (r));
break;
case MAY_FLOAT_T:
mpfr_abs (MAY_FLOAT (r), MAY_FLOAT (r), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (x) == MAY_COMPLEX_T);
/* abs(A+I*B) = sqrt(A^2+B^2) */
{
may_t AA = may_num_mul (MAY_DUMMY, MAY_RE (r), MAY_RE (r) );
may_t BB = may_num_mul (MAY_DUMMY, MAY_IM (r), MAY_IM (r) );
r = may_num_add (r, AA, BB);
/* It sucks: may_num_pow needs evaluated arg */
r = may_num_pow (may_num_simplify (r), MAY_HALF);
/* It may not be a pure num */
return r;
}
}
MAY_ASSERT (MAY_PURENUM_P (r));
return r;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_conj (may_t dest, may_t x)
{
may_t r = may_num_set (dest, x);
MAY_ASSERT (MAY_PURENUM_P (r));
if (MAY_TYPE (r) == MAY_COMPLEX_T) {
may_t i = may_num_neg (MAY_IM (r), MAY_IM (r));
UNUSED (i);
MAY_ASSERT (i == MAY_IM (r));
}
MAY_ASSERT (MAY_PURENUM_P (r));
return r;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_add (may_t dest, may_t op1, may_t op2)
{
MAY_ASSERT (MAY_PURENUM_P (op1));
MAY_ASSERT (MAY_PURENUM_P (op2));
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
/* Commun case where both types are equal */
if (MAY_LIKELY (MAY_TYPE (op1) == MAY_TYPE (op2))) {
switch (MAY_TYPE(op1)) {
case MAY_INT_T:
if (MAY_TYPE(dest) != MAY_INT_T)
dest = MAY_INT_INIT_C ();
mpz_add (MAY_INT (dest), MAY_INT (op1), MAY_INT (op2));
break;
case MAY_RAT_T:
if (MAY_TYPE(dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpq_add ( MAY_RAT(dest), MAY_RAT(op1), MAY_RAT(op2));
break;
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_add (MAY_FLOAT(dest), MAY_FLOAT(op1), MAY_FLOAT(op2), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
MAY_SET_RE (dest, may_num_add (MAY_RE(dest), MAY_RE(op1), MAY_RE(op2)));
MAY_SET_IM (dest, may_num_add (MAY_IM(dest), MAY_IM(op1), MAY_IM(op2)));
break;
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
if (MAY_UNLIKELY (MAY_TYPE(op1) > MAY_TYPE(op2)))
swap (op1, op2);
switch (MAY_TYPE(op1))
{
case MAY_INT_T:
switch (MAY_TYPE(op2))
{
case MAY_RAT_T:
if (MAY_TYPE(dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
{
mpz_t tmp;
mpz_init (tmp);
mpz_mul (tmp, mpq_denref(MAY_RAT(op2)), MAY_INT(op1));
mpz_add (mpq_numref(MAY_RAT(dest)), mpq_numref(MAY_RAT(op2)), tmp);
mpz_set (mpq_denref(MAY_RAT(dest)), mpq_denref(MAY_RAT(op2)));
mpq_canonicalize (MAY_RAT (dest));
mpz_clear (tmp);
}
break;
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_add_z (MAY_FLOAT(dest), MAY_FLOAT(op2), MAY_INT(op1), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE (dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
MAY_SET_RE (dest, may_num_add (MAY_RE (dest), op1, MAY_RE (op2)) );
MAY_SET_IM (dest, may_num_set (MAY_IM (dest), MAY_IM (op2)) );
break;
}
break;
case MAY_RAT_T:
switch (MAY_TYPE (op2))
{
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_add_q (MAY_FLOAT(dest), MAY_FLOAT(op2), MAY_RAT(op1), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
MAY_SET_RE (dest, may_num_add (MAY_RE(dest), op1, MAY_RE(op2)) );
MAY_SET_IM (dest, may_num_set (MAY_IM(dest), MAY_IM(op2)) );
break;
}
break;
default:
MAY_ASSERT (MAY_TYPE (op1) == MAY_FLOAT_T);
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C();
MAY_SET_RE (dest, may_num_add (MAY_RE(dest), op1, MAY_RE(op2)) );
MAY_SET_IM (dest, may_num_set (MAY_IM(dest), MAY_IM(op2)) );
break;
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_neg (may_t dest, may_t op)
{
MAY_ASSERT (MAY_TYPE(op) < MAY_NUM_LIMIT);
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
switch (MAY_TYPE(op))
{
case MAY_INT_T:
if (MAY_LIKELY (MAY_TYPE(dest) != MAY_INT_T))
dest = MAY_INT_INIT_C();
mpz_neg (MAY_INT(dest), MAY_INT(op));
break;
case MAY_RAT_T:
if (MAY_LIKELY (MAY_TYPE(dest) != MAY_RAT_T))
dest = MAY_RAT_INIT_C();
mpq_neg (MAY_RAT(dest), MAY_RAT(op));
break;
case MAY_FLOAT_T:
if (MAY_LIKELY (MAY_TYPE(dest) != MAY_FLOAT_T))
dest = MAY_FLOAT_INIT_C();
mpfr_neg (MAY_FLOAT(dest), MAY_FLOAT(op), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op) == MAY_COMPLEX_T);
if (MAY_LIKELY (MAY_TYPE(dest) != MAY_COMPLEX_T))
dest = MAY_COMPLEX_INIT_C ();
MAY_SET_RE (dest, may_num_neg (MAY_RE (dest), MAY_RE (op)) );
MAY_SET_IM (dest, may_num_neg (MAY_IM (dest), MAY_IM (op)) );
break;
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_sub (may_t dest, may_t op1, may_t op2)
{
MAY_ASSERT (MAY_PURENUM_P (op1));
MAY_ASSERT (MAY_PURENUM_P (op2));
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
/* Commun case where both types are equal */
if (MAY_LIKELY (MAY_TYPE (op1) == MAY_TYPE (op2))) {
switch (MAY_TYPE(op1)) {
case MAY_INT_T:
if (MAY_TYPE(dest) != MAY_INT_T)
dest = MAY_INT_INIT_C ();
mpz_sub (MAY_INT (dest), MAY_INT (op1), MAY_INT (op2));
break;
case MAY_RAT_T:
if (MAY_TYPE(dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpq_sub ( MAY_RAT(dest), MAY_RAT(op1), MAY_RAT(op2));
break;
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_sub (MAY_FLOAT(dest), MAY_FLOAT(op1), MAY_FLOAT(op2), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
MAY_SET_RE (dest, may_num_sub (MAY_RE(dest), MAY_RE(op1), MAY_RE(op2)));
MAY_SET_IM (dest, may_num_sub (MAY_IM(dest), MAY_IM(op1), MAY_IM(op2)));
break;
}
} else
/* Type are differents : fall back to generic way */
dest = may_num_add (dest, op1,
may_num_neg (dest != op1 ? dest : MAY_DUMMY, op2));
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_mul (may_t dest, may_t op1, may_t op2)
{
MAY_ASSERT (MAY_PURENUM_P (op1));
MAY_ASSERT (MAY_PURENUM_P (op2));
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
/* Commun case where both types are equals */
if (MAY_LIKELY (MAY_TYPE (op1) == MAY_TYPE (op2))) {
switch (MAY_TYPE (op1)) {
case MAY_INT_T:
if (MAY_TYPE (dest) != MAY_INT_T)
dest = MAY_INT_INIT_C ();
mpz_mul (MAY_INT (dest), MAY_INT (op1), MAY_INT (op2));
break;
case MAY_RAT_T:
if (MAY_TYPE (dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpq_mul (MAY_RAT (dest), MAY_RAT (op1), MAY_RAT (op2));
break;
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_mul (MAY_FLOAT(dest), MAY_FLOAT(op2), MAY_FLOAT(op1), MAY_RND);
break;
case MAY_COMPLEX_T:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C();
/* (A+B*I)*(C+I*D) = (A*C-B*D)+I*(B*C+A*D)
= (A*C-B*D)+I*((A+B)*(C+D)-(A*C+B*D))
No threeshold: Always Karatsuba ! */
{
may_t AxC = may_num_mul (MAY_DUMMY, MAY_RE(op1), MAY_RE(op2) );
may_t BxD = may_num_mul (MAY_DUMMY, MAY_IM(op1), MAY_IM(op2) );
may_t AB = may_num_add (MAY_DUMMY, MAY_RE(op1), MAY_IM(op1) );
may_t CD = may_num_add (MAY_DUMMY, MAY_RE(op2), MAY_IM(op2) );
AB = may_num_mul(AB, AB, CD);
CD = may_num_add(CD, AxC, BxD);
MAY_SET_RE (dest, may_num_sub (MAY_RE(dest), AxC, BxD) );
MAY_SET_IM (dest, may_num_sub (MAY_IM(dest), AB, CD ) );
}
break;
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Type are differents */
if (MAY_UNLIKELY (MAY_TYPE (op1) > MAY_TYPE (op2)))
swap (op1, op2);
switch (MAY_TYPE (op1))
{
case MAY_INT_T:
switch (MAY_TYPE (op2))
{
case MAY_RAT_T:
if (MAY_TYPE (dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpz_mul (mpq_numref (MAY_RAT(dest)),
MAY_INT (op1), mpq_numref (MAY_RAT (op2)));
mpz_set (mpq_denref (MAY_RAT (dest)), mpq_denref (MAY_RAT (op2)));
mpq_canonicalize (MAY_RAT (dest));
break;
case MAY_FLOAT_T:
if (MAY_TYPE (dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_mul_z (MAY_FLOAT(dest), MAY_FLOAT(op2), MAY_INT(op1), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE (dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
MAY_SET_IM (dest, may_num_mul (MAY_IM (dest), op1, MAY_IM (op2)) );
MAY_SET_RE (dest, may_num_mul (MAY_RE (dest), op1, MAY_RE (op2)) );
break;
}
break;
case MAY_RAT_T:
switch (MAY_TYPE (op2))
{
case MAY_FLOAT_T:
if (MAY_TYPE (dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_mul_q (MAY_FLOAT(dest), MAY_FLOAT(op2), MAY_RAT(op1), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE (dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
/* Before Im part since op1 may be dest[0]! */
MAY_SET_IM (dest, may_num_mul (MAY_IM(dest), op1, MAY_IM(op2)) );
MAY_SET_RE (dest, may_num_mul (MAY_RE(dest), op1, MAY_RE(op2)) );
break;
}
break;
default:
MAY_ASSERT (MAY_TYPE (op1) == MAY_FLOAT_T);
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
/* Before Im part since op1 may be dest[0]! */
MAY_SET_IM(dest, may_num_mul (MAY_IM(dest), op1, MAY_IM(op2)) );
MAY_SET_RE(dest, may_num_mul (MAY_RE(dest), op1, MAY_RE(op2)) );
break;
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_INLINE may_t
may_num_invmod (may_t dest, may_t op)
{
int i;
MAY_ASSERT (MAY_TYPE (op) == MAY_INT_T);
MAY_ASSERT (may_g.frame.intmod != NULL);
if (MAY_TYPE(dest) != MAY_INT_T)
dest = MAY_INT_INIT_C ();
i = mpz_invert (MAY_INT (dest), MAY_INT (op), MAY_INT (may_g.frame.intmod));
return i == 0 ? MAY_NAN : dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_inv (may_t dest, may_t op)
{
MAY_ASSERT(MAY_TYPE(op) < MAY_NUM_LIMIT);
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
switch (MAY_TYPE(op))
{
case MAY_INT_T:
if (MAY_UNLIKELY(mpz_sgn (MAY_INT (op)) == 0))
return may_num_set (dest, MAY_NAN);
if (MAY_UNLIKELY(mpz_cmp_ui (MAY_INT (op), 1) == 0))
return may_num_set (dest, MAY_ONE);
if (MAY_UNLIKELY (may_g.frame.intmod != NULL))
return may_num_invmod (dest, op);
if (MAY_UNLIKELY(mpz_cmp_si (MAY_INT (op), -1) == 0))
return may_num_set (dest, MAY_N_ONE);
if (MAY_TYPE(dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpz_set (mpq_numref (MAY_RAT (dest)), MAY_INT (MAY_ONE));
mpz_set (mpq_denref (MAY_RAT (dest)), MAY_INT (op));
mpq_canonicalize (MAY_RAT (dest));
break;
case MAY_RAT_T:
if (MAY_TYPE (dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpq_inv (MAY_RAT (dest), MAY_RAT (op));
break;
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_ui_div (MAY_FLOAT (dest), 1, MAY_FLOAT (op), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op) == MAY_COMPLEX_T);
/* 1/(C+I*D) = (C-I*D)/(C^2+D^2) */
{
if (MAY_TYPE(dest) != MAY_COMPLEX_T)
dest = MAY_COMPLEX_INIT_C ();
may_t n = may_num_add(MAY_DUMMY,
may_num_mul (MAY_DUMMY, MAY_RE(op), MAY_RE(op)),
may_num_mul (MAY_DUMMY, MAY_IM(op), MAY_IM(op)));
MAY_SET_RE (dest, may_num_div (MAY_RE (dest), MAY_RE (op), n));
MAY_SET_IM (dest, may_num_div (MAY_IM (dest), MAY_IM (op), n));
MAY_SET_IM (dest, may_num_neg (MAY_IM (dest), MAY_IM (dest)) );
break;
}
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Functions providing a wrapper to real functions.
dest may be MAY_DUMMY: it means create the destination
(It really allocates a new area of memory), otherwise
'dest' is a pool of memory the function tries to reuse */
MAY_REGPARM may_t
may_num_div (may_t dest, may_t op1, may_t op2)
{
MAY_ASSERT (MAY_PURENUM_P (op1));
MAY_ASSERT (MAY_PURENUM_P (op2));
MAY_ASSERT (dest == MAY_DUMMY
|| (!MAY_EVAL_P (dest) && MAY_PURENUM_P (dest)));
/* If the types are differents, it is quite uncommun, and quite
complicated to handle. Let's call only mul and inv */
if (MAY_TYPE(op1) != MAY_TYPE(op2)) {
div_by_mul_inverse:
dest = may_num_mul (dest, op1,
may_num_inv (dest != op1 ? dest : MAY_DUMMY, op2));
} else
switch (MAY_TYPE(op1))
{
case MAY_INT_T:
if (MAY_UNLIKELY(mpz_sgn (MAY_INT (op2)) == 0))
return may_num_set (dest, MAY_NAN);
if (MAY_UNLIKELY(mpz_cmp_ui (MAY_INT (op2), 1) == 0))
return may_num_set (dest, op1);
if (MAY_UNLIKELY (may_g.frame.intmod != NULL))
goto div_by_mul_inverse;
if (MAY_UNLIKELY(mpz_cmp_si (MAY_INT (op2), -1) == 0))
return may_num_neg (dest, op1);
if (MAY_TYPE (dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpz_set (mpq_numref (MAY_RAT (dest)), MAY_INT (op1));
mpz_set (mpq_denref (MAY_RAT (dest)), MAY_INT (op2));
mpq_canonicalize (MAY_RAT(dest));
break;
case MAY_RAT_T:
if (MAY_TYPE(dest) != MAY_RAT_T)
dest = MAY_RAT_INIT_C ();
mpq_div ( MAY_RAT (dest), MAY_RAT (op1), MAY_RAT (op2));
break;
case MAY_FLOAT_T:
if (MAY_TYPE(dest) != MAY_FLOAT_T)
dest = MAY_FLOAT_INIT_C ();
mpfr_div (MAY_FLOAT (dest), MAY_FLOAT (op1), MAY_FLOAT (op2), MAY_RND);
break;
default:
MAY_ASSERT (MAY_TYPE (op2) == MAY_COMPLEX_T);
dest = may_num_mul (dest, op1,
may_num_inv (dest != op1 ? dest : MAY_DUMMY, op2));
}
MAY_ASSERT (dest != MAY_DUMMY && !MAY_EVAL_P (dest) && MAY_PURENUM_P (dest));
return dest;
}
/* Eval a complex 'x' to an integer power 'n' using fast binary exponentiation */
static MAY_REGPARM may_t
complex_pow (may_t x, long n)
{
may_t r;
long i, m;
MAY_ASSERT (MAY_TYPE (x) == MAY_COMPLEX_T);
MAY_ASSERT (n != 0 && n != 1);
MAY_RECORD ();
if (n < 0) {
x = may_num_inv (MAY_DUMMY, x);
n = -n;
if (n == 1)
MAY_RET (may_cx_simplify (x));
}
for (i = 0, m = n; m != 0; i++)
m >>= 1;
r = may_num_set (MAY_DUMMY, x);
for (i -= 2; i >= 0; i--)
{
r = may_num_mul (r, r, r);
if (n & (1UL << i))
r = may_num_mul (r, r, x);
}
r = may_cx_simplify (r);
MAY_RET (r);
}
/* Try to eval INT^(1/N), in the INTEGER domain if INT > 0
if INT < 0 and N is even, it tries the INTEGER COMPLEX domain */
/* base = INT / expo = RAT = 1/N */
static MAY_REGPARM may_t
may_mpz_root (may_t base, may_t expo)
{
mpz_t z;
may_t y;
int i;
unsigned long n;
MAY_ASSERT (MAY_TYPE (base) == MAY_INT_T);
n = mpz_get_ui (mpq_denref (MAY_RAT (expo)));
if (MAY_UNLIKELY (n < 2))
return n == 0 ? MAY_NAN : base;
else if (MAY_UNLIKELY (base == MAY_N_ONE))
return NULL;
/* TODO: intmod. FIXME: what to do? */
MAY_RECORD ();
mpz_init (z);
mpz_abs (z, MAY_INT (base));
i = mpz_root (z, z, n);
if (i == 0)
y = NULL;
else {
y = may_num_pow (may_mpz_simplify (MAY_MPZ_NOCOPY_C (z)),
may_mpz_simplify (MAY_MPZ_NOCOPY_C (mpq_numref (MAY_RAT (expo)))));
/* If base < 0, returns (-1)^(1/N)*root */
if (mpz_sgn (MAY_INT (base)) < 0)
y = may_eval (may_mul_c (may_pow_c (MAY_N_ONE, expo), y));
}
MAY_RET (y);
}
/* This function tests if a^b fits as an integer.
It returns b as an unsigned long if successfull */
MAY_REGPARM unsigned long
may_test_overflow_pow_ui (mpz_srcptr a, mpz_srcptr b)
{
unsigned long c, sa;
/* If b doesn't fit in an unsigned long, fail */
if (!mpz_fits_ulong_p (b))
return 0;
c = mpz_get_ui (b);
/* If a == 0 or 1, it is ok . Or if c is 1 */
if (c <= 1 || mpz_cmpabs_ui (a, 1) <= 0)
return c;
/* Get log2(a) */
sa = mpz_sizeinbase (a, 2);
/* If a is a power of 2, we need to remove one bit.
In fact, the number of bits we want is for 'a-1', not 'a'.
This away avoids copying 'a' to remove 1 */
if (mpz_scan1 (a, 0) == (sa-1))
sa = sa -1;
sa = sa * c;
/* If there is an overflow in the product of sa is greater than intmaxsize */
if (sa < c || sa >= may_g.frame.intmaxsize) {
return 0;
} else
return c;
}
/* Return base^expo with base and expo evaluated pure numbers */
/* This function returns an evaluated form.
Expect evaluated form too. */
MAY_REGPARM may_t
may_num_pow (may_t base, may_t expo)
{
mpfr_t dest_fr;
mpq_t dest_q;
mpz_t dest_z;
may_t y;
unsigned long e;
MAY_ASSERT (MAY_PURENUM_P (base) && MAY_EVAL_P (base));
MAY_ASSERT (MAY_PURENUM_P (expo) && MAY_EVAL_P (expo));