forked from php/php-src
-
Notifications
You must be signed in to change notification settings - Fork 0
/
zend_strtod.c
2708 lines (2526 loc) · 53 KB
/
zend_strtod.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
/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991 by AT&T.
*
* 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 AT&T MAKES ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
***************************************************************/
/* Please send bug reports to
David M. Gay
AT&T Bell Laboratories, Room 2C-463
600 Mountain Avenue
Murray Hill, NJ 07974-2070
U.S.A.
dmg@research.att.com or research!dmg
*/
/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
*
* This strtod returns a nearest machine number to the input decimal
* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
* broken by the IEEE round-even rule. Otherwise ties are broken by
* biased rounding (add half and chop).
*
* Inspired loosely by William D. Clinger's paper "How to Read Floating
* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
*
* Modifications:
*
* 1. We only require IEEE, IBM, or VAX double-precision
* arithmetic (not IEEE double-extended).
* 2. We get by with floating-point arithmetic in a case that
* Clinger missed -- when we're computing d * 10^n
* for a small integer d and the integer n is not too
* much larger than 22 (the maximum integer k for which
* we can represent 10^k exactly), we may be able to
* compute (d*10^k) * 10^(e-k) with just one roundoff.
* 3. Rather than a bit-at-a-time adjustment of the binary
* result in the hard case, we use floating-point
* arithmetic to determine the adjustment to within
* one bit; only in really hard cases do we need to
* compute a second residual.
* 4. Because of 3., we don't need a large table of powers of 10
* for ten-to-e (just some small tables, e.g. of 10^k
* for 0 <= k <= 22).
*/
/*
* #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
* significant byte has the lowest address.
* #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
* significant byte has the lowest address.
* #define Long int on machines with 32-bit ints and 64-bit longs.
* #define Sudden_Underflow for IEEE-format machines without gradual
* underflow (i.e., that flush to zero on underflow).
* #define IBM for IBM mainframe-style floating-point arithmetic.
* #define VAX for VAX-style floating-point arithmetic.
* #define Unsigned_Shifts if >> does treats its left operand as unsigned.
* #define No_leftright to omit left-right logic in fast floating-point
* computation of dtoa.
* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
* that use extended-precision instructions to compute rounded
* products and quotients) with IBM.
* #define ROUND_BIASED for IEEE-format with biased rounding.
* #define Inaccurate_Divide for IEEE-format with correctly rounded
* products but inaccurate quotients, e.g., for Intel i860.
* #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
* integer arithmetic. Whether this speeds things up or slows things
* down depends on the machine and the number being converted.
* #define KR_headers for old-style C function headers.
* #define Bad_float_h if your system lacks a float.h or if it does not
* define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
* FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
* #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
* if memory is available and otherwise does something you deem
* appropriate. If MALLOC is undefined, malloc will be invoked
* directly -- and assumed always to succeed.
*/
/* $Id$ */
#include <zend_operators.h>
#include <zend_strtod.h>
#ifdef ZTS
#include <TSRM.h>
#endif
#include <stddef.h>
#include <stdio.h>
#include <ctype.h>
#include <stdarg.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#ifdef HAVE_LOCALE_H
#include <locale.h>
#endif
#ifdef HAVE_SYS_TYPES_H
#include <sys/types.h>
#endif
#if defined(HAVE_INTTYPES_H)
#include <inttypes.h>
#elif defined(HAVE_STDINT_H)
#include <stdint.h>
#endif
#ifndef HAVE_INT32_T
# if SIZEOF_INT == 4
typedef int int32_t;
# elif SIZEOF_LONG == 4
typedef long int int32_t;
# endif
#endif
#ifndef HAVE_UINT32_T
# if SIZEOF_INT == 4
typedef unsigned int uint32_t;
# elif SIZEOF_LONG == 4
typedef unsigned long int uint32_t;
# endif
#endif
#if (defined(__APPLE__) || defined(__APPLE_CC__)) && (defined(__BIG_ENDIAN__) || defined(__LITTLE_ENDIAN__))
# if defined(__LITTLE_ENDIAN__)
# undef WORDS_BIGENDIAN
# else
# if defined(__BIG_ENDIAN__)
# define WORDS_BIGENDIAN
# endif
# endif
#endif
#ifdef WORDS_BIGENDIAN
#define IEEE_BIG_ENDIAN
#else
#define IEEE_LITTLE_ENDIAN
#endif
#if defined(__arm__) && !defined(__VFP_FP__)
/*
* * Although the CPU is little endian the FP has different
* * byte and word endianness. The byte order is still little endian
* * but the word order is big endian.
* */
#define IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#ifdef __vax__
#define VAX
#undef IEEE_LITTLE_ENDIAN
#endif
#if defined(_MSC_VER)
#define int32_t __int32
#define uint32_t unsigned __int32
#define IEEE_LITTLE_ENDIAN
#endif
#define Long int32_t
#define ULong uint32_t
#ifdef __cplusplus
#include "malloc.h"
#include "memory.h"
#else
#ifndef KR_headers
#include "stdlib.h"
#include "string.h"
#include "locale.h"
#else
#include "malloc.h"
#include "memory.h"
#endif
#endif
#ifdef MALLOC
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#else
#define MALLOC malloc
#endif
#include "ctype.h"
#include "errno.h"
#ifdef Bad_float_h
#ifdef IEEE_BIG_ENDIAN
#define IEEE_ARITHMETIC
#endif
#ifdef IEEE_LITTLE_ENDIAN
#define IEEE_ARITHMETIC
#endif
#ifdef IEEE_ARITHMETIC
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#define FLT_ROUNDS 1
#define DBL_MAX 1.7976931348623157e+308
#endif
#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define FLT_ROUNDS 0
#define DBL_MAX 7.2370055773322621e+75
#endif
#ifdef VAX
#define DBL_DIG 16
#define DBL_MAX_10_EXP 38
#define DBL_MAX_EXP 127
#define FLT_RADIX 2
#define FLT_ROUNDS 1
#define DBL_MAX 1.7014118346046923e+38
#endif
#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else
#include "float.h"
#endif
#ifndef __MATH_H__
#include "math.h"
#endif
BEGIN_EXTERN_C()
#ifndef CONST
#ifdef KR_headers
#define CONST /* blank */
#else
#define CONST const
#endif
#endif
#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#endif
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
defined(IBM) != 1
Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
IBM should be defined.
#endif
typedef union {
double d;
ULong ul[2];
} _double;
#define value(x) ((x).d)
#ifdef IEEE_LITTLE_ENDIAN
#define word0(x) ((x).ul[1])
#define word1(x) ((x).ul[0])
#else
#define word0(x) ((x).ul[0])
#define word1(x) ((x).ul[1])
#endif
/* The following definition of Storeinc is appropriate for MIPS processors.
* An alternative that might be better on some machines is
* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
*/
#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#else
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#endif
/* #define P DBL_MANT_DIG */
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
#define Exp_shift 20
#define Exp_shift1 20
#define Exp_msk1 0x100000
#define Exp_msk11 0x100000
#define Exp_mask 0x7ff00000
#define P 53
#define Bias 1023
#define IEEE_Arith
#define Emin (-1022)
#define Exp_1 0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask 0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask 0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
#else
#undef Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#define Exp_shift 24
#define Exp_shift1 24
#define Exp_msk1 0x1000000
#define Exp_msk11 0x1000000
#define Exp_mask 0x7f000000
#define P 14
#define Bias 65
#define Exp_1 0x41000000
#define Exp_11 0x41000000
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
#define Frac_mask 0xffffff
#define Frac_mask1 0xffffff
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask 0xefffff
#define Bndry_mask1 0xffffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 4
#define Tiny0 0x100000
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else /* VAX */
#define Exp_shift 23
#define Exp_shift1 7
#define Exp_msk1 0x80
#define Exp_msk11 0x800000
#define Exp_mask 0x7f80
#define P 56
#define Bias 129
#define Exp_1 0x40800000
#define Exp_11 0x4080
#define Ebits 8
#define Frac_mask 0x7fffff
#define Frac_mask1 0xffff007f
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask 0xffff007f
#define Bndry_mask1 0xffff007f
#define LSB 0x10000
#define Sign_bit 0x8000
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif
#endif
#ifndef IEEE_Arith
#define ROUND_BIASED
#endif
#ifdef RND_PRODQUOT
#define rounded_product(a,b) a = rnd_prod(a, b)
#define rounded_quotient(a,b) a = rnd_quot(a, b)
#ifdef KR_headers
extern double rnd_prod(), rnd_quot();
#else
extern double rnd_prod(double, double), rnd_quot(double, double);
#endif
#else
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#endif
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff
#ifndef Just_16
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
* * This makes some inner loops simpler and sometimes saves work
* * during multiplications, but it often seems to make things slightly
* * slower. Hence the default is now to store 32 bits per Long.
* */
#ifndef Pack_32
#define Pack_32
#endif
#endif
#define Kmax 15
struct Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
/* static variables, multithreading fun! */
static Bigint *freelist[Kmax+1];
static Bigint *p5s;
static void destroy_freelist(void);
#ifdef ZTS
static MUTEX_T dtoa_mutex;
static MUTEX_T pow5mult_mutex;
#define _THREAD_PRIVATE_MUTEX_LOCK(x) tsrm_mutex_lock(x);
#define _THREAD_PRIVATE_MUTEX_UNLOCK(x) tsrm_mutex_unlock(x);
#else
#define _THREAD_PRIVATE_MUTEX_LOCK(x)
#define _THREAD_PRIVATE_MUTEX_UNLOCK(x)
#endif /* ZTS */
#ifdef DEBUG
static void Bug(const char *message) {
fprintf(stderr, "%s\n", message);
}
#endif
ZEND_API int zend_startup_strtod(void) /* {{{ */
{
#ifdef ZTS
dtoa_mutex = tsrm_mutex_alloc();
pow5mult_mutex = tsrm_mutex_alloc();
#endif
return 1;
}
/* }}} */
ZEND_API int zend_shutdown_strtod(void) /* {{{ */
{
destroy_freelist();
#ifdef ZTS
tsrm_mutex_free(dtoa_mutex);
dtoa_mutex = NULL;
tsrm_mutex_free(pow5mult_mutex);
pow5mult_mutex = NULL;
#endif
return 1;
}
/* }}} */
static Bigint * Balloc(int k)
{
int x;
Bigint *rv;
if (k > Kmax) {
zend_error(E_ERROR, "Balloc() allocation exceeds list boundary");
}
_THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex);
if ((rv = freelist[k])) {
freelist[k] = rv->next;
} else {
x = 1 << k;
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
if (!rv) {
_THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
zend_error(E_ERROR, "Balloc() failed to allocate memory");
}
rv->k = k;
rv->maxwds = x;
}
_THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
rv->sign = rv->wds = 0;
return rv;
}
static void Bfree(Bigint *v)
{
if (v) {
_THREAD_PRIVATE_MUTEX_LOCK(dtoa_mutex);
v->next = freelist[v->k];
freelist[v->k] = v;
_THREAD_PRIVATE_MUTEX_UNLOCK(dtoa_mutex);
}
}
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(Long) + 2*sizeof(int))
/* return value is only used as a simple string, so mis-aligned parts
* inside the Bigint are not at risk on strict align architectures
*/
static char * rv_alloc(int i) {
int j, k, *r;
j = sizeof(ULong);
for(k = 0;
sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
j <<= 1) {
k++;
}
r = (int*)Balloc(k);
*r = k;
return (char *)(r+1);
}
static char * nrv_alloc(char *s, char **rve, int n)
{
char *rv, *t;
t = rv = rv_alloc(n);
while((*t = *s++) !=0) {
t++;
}
if (rve) {
*rve = t;
}
return rv;
}
static Bigint * multadd(Bigint *b, int m, int a) /* multiply by m and add a */
{
int i, wds;
ULong *x, y;
#ifdef Pack_32
ULong xi, z;
#endif
Bigint *b1;
wds = b->wds;
x = b->x;
i = 0;
do {
#ifdef Pack_32
xi = *x;
y = (xi & 0xffff) * m + a;
z = (xi >> 16) * m + (y >> 16);
a = (int)(z >> 16);
*x++ = (z << 16) + (y & 0xffff);
#else
y = *x * m + a;
a = (int)(y >> 16);
*x++ = y & 0xffff;
#endif
}
while(++i < wds);
if (a) {
if (wds >= b->maxwds) {
b1 = Balloc(b->k+1);
Bcopy(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = a;
b->wds = wds;
}
return b;
}
static int hi0bits(ULong x)
{
int k = 0;
if (!(x & 0xffff0000)) {
k = 16;
x <<= 16;
}
if (!(x & 0xff000000)) {
k += 8;
x <<= 8;
}
if (!(x & 0xf0000000)) {
k += 4;
x <<= 4;
}
if (!(x & 0xc0000000)) {
k += 2;
x <<= 2;
}
if (!(x & 0x80000000)) {
k++;
if (!(x & 0x40000000)) {
return 32;
}
}
return k;
}
static int lo0bits(ULong *y)
{
int k;
ULong x = *y;
if (x & 7) {
if (x & 1) {
return 0;
}
if (x & 2) {
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if (!(x & 0xffff)) {
k = 16;
x >>= 16;
}
if (!(x & 0xff)) {
k += 8;
x >>= 8;
}
if (!(x & 0xf)) {
k += 4;
x >>= 4;
}
if (!(x & 0x3)) {
k += 2;
x >>= 2;
}
if (!(x & 1)) {
k++;
x >>= 1;
if (!(x & 1)) {
return 32;
}
}
*y = x;
return k;
}
static Bigint * i2b(int i)
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static Bigint * mult(Bigint *a, Bigint *b)
{
Bigint *c;
int k, wa, wb, wc;
ULong carry, y, z;
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
ULong z2;
#endif
if (a->wds < b->wds) {
c = a;
a = b;
b = c;
}
k = a->k;
wa = a->wds;
wb = b->wds;
wc = wa + wb;
if (wc > a->maxwds) {
k++;
}
c = Balloc(k);
for(x = c->x, xa = x + wc; x < xa; x++) {
*x = 0;
}
xa = a->x;
xae = xa + wa;
xb = b->x;
xbe = xb + wb;
xc0 = c->x;
#ifdef Pack_32
for(; xb < xbe; xb++, xc0++) {
if ((y = *xb & 0xffff)) {
x = xa;
xc = xc0;
carry = 0;
do {
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc(xc, z2, z);
}
while(x < xae);
*xc = carry;
}
if ((y = *xb >> 16)) {
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do {
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
Storeinc(xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
}
while(x < xae);
*xc = z2;
}
}
#else
for(; xb < xbe; xc0++) {
if (y = *xb++) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
}
while(x < xae);
*xc = carry;
}
}
#endif
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
static Bigint * s2b (CONST char *s, int nd0, int nd, ULong y9)
{
Bigint *b;
int i, k;
Long x, y;
x = (nd + 8) / 9;
for(k = 0, y = 1; x > y; y <<= 1, k++) ;
#ifdef Pack_32
b = Balloc(k);
b->x[0] = y9;
b->wds = 1;
#else
b = Balloc(k+1);
b->x[0] = y9 & 0xffff;
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
#endif
i = 9;
if (9 < nd0) {
s += 9;
do b = multadd(b, 10, *s++ - '0');
while(++i < nd0);
s++;
} else {
s += 10;
}
for(; i < nd; i++) {
b = multadd(b, 10, *s++ - '0');
}
return b;
}
static Bigint * pow5mult(Bigint *b, int k)
{
Bigint *b1, *p5, *p51;
int i;
static int p05[3] = { 5, 25, 125 };
_THREAD_PRIVATE_MUTEX_LOCK(pow5mult_mutex);
if ((i = k & 3)) {
b = multadd(b, p05[i-1], 0);
}
if (!(k >>= 2)) {
_THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex);
return b;
}
if (!(p5 = p5s)) {
/* first time */
p5 = p5s = i2b(625);
p5->next = 0;
}
for(;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1)) {
break;
}
if (!(p51 = p5->next)) {
if (!(p51 = p5->next)) {
p51 = p5->next = mult(p5,p5);
p51->next = 0;
}
}
p5 = p51;
}
_THREAD_PRIVATE_MUTEX_UNLOCK(pow5mult_mutex);
return b;
}
static Bigint *lshift(Bigint *b, int k)
{
int i, k1, n, n1;
Bigint *b1;
ULong *x, *x1, *xe, z;
#ifdef Pack_32
n = k >> 5;
#else
n = k >> 4;
#endif
k1 = b->k;
n1 = n + b->wds + 1;
for(i = b->maxwds; n1 > i; i <<= 1) {
k1++;
}
b1 = Balloc(k1);
x1 = b1->x;
for(i = 0; i < n; i++) {
*x1++ = 0;
}
x = b->x;
xe = x + b->wds;
#ifdef Pack_32
if (k &= 0x1f) {
k1 = 32 - k;
z = 0;
do {
*x1++ = *x << k | z;
z = *x++ >> k1;
}
while(x < xe);
if ((*x1 = z)) {
++n1;
}
}
#else
if (k &= 0xf) {
k1 = 16 - k;
z = 0;
do {
*x1++ = *x << k & 0xffff | z;
z = *x++ >> k1;
}
while(x < xe);
if (*x1 = z) {
++n1;
}
}
#endif
else do
*x1++ = *x++;
while(x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
static int cmp(Bigint *a, Bigint *b)
{
ULong *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef DEBUG
if (i > 1 && !a->x[i-1])
Bug("cmp called with a->x[a->wds-1] == 0");
if (j > 1 && !b->x[j-1])
Bug("cmp called with b->x[b->wds-1] == 0");
#endif
if (i -= j)
return i;
xa0 = a->x;
xa = xa0 + j;
xb0 = b->x;
xb = xb0 + j;
for(;;) {
if (*--xa != *--xb)
return *xa < *xb ? -1 : 1;
if (xa <= xa0)
break;
}
return 0;
}
static Bigint * diff(Bigint *a, Bigint *b)
{
Bigint *c;
int i, wa, wb;
Long borrow, y; /* We need signed shifts here. */
ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
Long z;
#endif
i = cmp(a,b);
if (!i) {
c = Balloc(0);
c->wds = 1;
c->x[0] = 0;
return c;
}
if (i < 0) {
c = a;
a = b;
b = c;
i = 1;
} else {
i = 0;
}
c = Balloc(a->k);
c->sign = i;
wa = a->wds;
xa = a->x;
xae = xa + wa;
wb = b->wds;
xb = b->x;
xbe = xb + wb;
xc = c->x;
borrow = 0;
#ifdef Pack_32
do {
y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
borrow = z >> 16;
Sign_Extend(borrow, z);
Storeinc(xc, z, y);
} while(xb < xbe);
while(xa < xae) {
y = (*xa & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
z = (*xa++ >> 16) + borrow;
borrow = z >> 16;
Sign_Extend(borrow, z);
Storeinc(xc, z, y);
}
#else
do {
y = *xa++ - *xb++ + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
*xc++ = y & 0xffff;
} while(xb < xbe);
while(xa < xae) {
y = *xa++ + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
*xc++ = y & 0xffff;
}
#endif
while(!*--xc) {
wa--;
}
c->wds = wa;
return c;
}
static double ulp (double _x)
{
volatile _double x;
register Long L;
volatile _double a;
value(x) = _x;
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Sudden_Underflow