1 /* $NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $ */
2
3 /****************************************************************
4 *
5 * The author of this software is David M. Gay.
6 *
7 * Copyright (c) 1991 by AT&T.
8 *
9 * Permission to use, copy, modify, and distribute this software for any
10 * purpose without fee is hereby granted, provided that this entire notice
11 * is included in all copies of any software which is or includes a copy
12 * or modification of this software and in all copies of the supporting
13 * documentation for such software.
14 *
15 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
16 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
17 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
18 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
19 *
20 ***************************************************************/
21
22 /* Please send bug reports to
23 David M. Gay
24 AT&T Bell Laboratories, Room 2C-463
25 600 Mountain Avenue
26 Murray Hill, NJ 07974-2070
27 U.S.A.
28 dmg@research.att.com or research!dmg
29 */
30
31 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
32 *
33 * This strtod returns a nearest machine number to the input decimal
34 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
35 * broken by the IEEE round-even rule. Otherwise ties are broken by
36 * biased rounding (add half and chop).
37 *
38 * Inspired loosely by William D. Clinger's paper "How to Read Floating
39 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
40 *
41 * Modifications:
42 *
43 * 1. We only require IEEE, IBM, or VAX double-precision
44 * arithmetic (not IEEE double-extended).
45 * 2. We get by with floating-point arithmetic in a case that
46 * Clinger missed -- when we're computing d * 10^n
47 * for a small integer d and the integer n is not too
48 * much larger than 22 (the maximum integer k for which
49 * we can represent 10^k exactly), we may be able to
50 * compute (d*10^k) * 10^(e-k) with just one roundoff.
51 * 3. Rather than a bit-at-a-time adjustment of the binary
52 * result in the hard case, we use floating-point
53 * arithmetic to determine the adjustment to within
54 * one bit; only in really hard cases do we need to
55 * compute a second residual.
56 * 4. Because of 3., we don't need a large table of powers of 10
57 * for ten-to-e (just some small tables, e.g. of 10^k
58 * for 0 <= k <= 22).
59 */
60
61 /*
62 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
63 * significant byte has the lowest address.
64 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
65 * significant byte has the lowest address.
66 * #define Long int on machines with 32-bit ints and 64-bit longs.
67 * #define Sudden_Underflow for IEEE-format machines without gradual
68 * underflow (i.e., that flush to zero on underflow).
69 * #define IBM for IBM mainframe-style floating-point arithmetic.
70 * #define VAX for VAX-style floating-point arithmetic.
71 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
72 * #define No_leftright to omit left-right logic in fast floating-point
73 * computation of dtoa.
74 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
75 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
76 * that use extended-precision instructions to compute rounded
77 * products and quotients) with IBM.
78 * #define ROUND_BIASED for IEEE-format with biased rounding.
79 * #define Inaccurate_Divide for IEEE-format with correctly rounded
80 * products but inaccurate quotients, e.g., for Intel i860.
81 * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
82 * integer arithmetic. Whether this speeds things up or slows things
83 * down depends on the machine and the number being converted.
84 * #define KR_headers for old-style C function headers.
85 * #define Bad_float_h if your system lacks a float.h or if it does not
86 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
87 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
88 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
89 * if memory is available and otherwise does something you deem
90 * appropriate. If MALLOC is undefined, malloc will be invoked
91 * directly -- and assumed always to succeed.
92 */
93
94 #ifdef ANDROID_CHANGES
95 #include <pthread.h>
96 #define mutex_lock(x) pthread_mutex_lock(x)
97 #define mutex_unlock(x) pthread_mutex_unlock(x)
98 #endif
99
100 #include <sys/cdefs.h>
101 #if defined(LIBC_SCCS) && !defined(lint)
102 __RCSID("$NetBSD: strtod.c,v 1.45.2.1 2005/04/19 13:35:54 tron Exp $");
103 #endif /* LIBC_SCCS and not lint */
104
105 #define Unsigned_Shifts
106 #if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \
107 defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \
108 defined(__powerpc__) || defined(__sh__) || defined(__x86_64__) || \
109 defined(__hppa__) || \
110 (defined(__arm__) && defined(__VFP_FP__))
111 #include <endian.h>
112 #if BYTE_ORDER == BIG_ENDIAN
113 #define IEEE_BIG_ENDIAN
114 #else
115 #define IEEE_LITTLE_ENDIAN
116 #endif
117 #endif
118
119 #if defined(__arm__) && !defined(__VFP_FP__)
120 /*
121 * Although the CPU is little endian the FP has different
122 * byte and word endianness. The byte order is still little endian
123 * but the word order is big endian.
124 */
125 #define IEEE_BIG_ENDIAN
126 #endif
127
128 #ifdef __vax__
129 #define VAX
130 #endif
131
132 #if defined(__hppa__) || defined(__mips__) || defined(__sh__)
133 #define NAN_WORD0 0x7ff40000
134 #else
135 #define NAN_WORD0 0x7ff80000
136 #endif
137 #define NAN_WORD1 0
138
139 #define Long int32_t
140 #define ULong u_int32_t
141
142 #ifdef DEBUG
143 #include "stdio.h"
144 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
145 #endif
146
147 #ifdef __cplusplus
148 #include "malloc.h"
149 #include "memory.h"
150 #else
151 #ifndef KR_headers
152 #include "stdlib.h"
153 #include "string.h"
154 #ifndef ANDROID_CHANGES
155 #include "locale.h"
156 #endif /* ANDROID_CHANGES */
157 #else
158 #include "malloc.h"
159 #include "memory.h"
160 #endif
161 #endif
162 #ifndef ANDROID_CHANGES
163 #include "extern.h"
164 #include "reentrant.h"
165 #endif /* ANDROID_CHANGES */
166
167 #ifdef MALLOC
168 #ifdef KR_headers
169 extern char *MALLOC();
170 #else
171 extern void *MALLOC(size_t);
172 #endif
173 #else
174 #define MALLOC malloc
175 #endif
176
177 #include "ctype.h"
178 #include "errno.h"
179 #include "float.h"
180
181 #ifndef __MATH_H__
182 #include "math.h"
183 #endif
184
185 #ifdef __cplusplus
186 extern "C" {
187 #endif
188
189 #ifndef CONST
190 #ifdef KR_headers
191 #define CONST /* blank */
192 #else
193 #define CONST const
194 #endif
195 #endif
196
197 #ifdef Unsigned_Shifts
198 #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
199 #else
200 #define Sign_Extend(a,b) /*no-op*/
201 #endif
202
203 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
204 defined(IBM) != 1
205 Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
206 IBM should be defined.
207 #endif
208
209 typedef union {
210 double d;
211 ULong ul[2];
212 } _double;
213 #define value(x) ((x).d)
214 #ifdef IEEE_LITTLE_ENDIAN
215 #define word0(x) ((x).ul[1])
216 #define word1(x) ((x).ul[0])
217 #else
218 #define word0(x) ((x).ul[0])
219 #define word1(x) ((x).ul[1])
220 #endif
221
222 /* The following definition of Storeinc is appropriate for MIPS processors.
223 * An alternative that might be better on some machines is
224 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
225 */
226 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
227 #define Storeinc(a,b,c) \
228 (((u_short *)(void *)a)[1] = \
229 (u_short)b, ((u_short *)(void *)a)[0] = (u_short)c, a++)
230 #else
231 #define Storeinc(a,b,c) \
232 (((u_short *)(void *)a)[0] = \
233 (u_short)b, ((u_short *)(void *)a)[1] = (u_short)c, a++)
234 #endif
235
236 /* #define P DBL_MANT_DIG */
237 /* Ten_pmax = floor(P*log(2)/log(5)) */
238 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
239 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
240 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
241
242 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
243 #define Exp_shift 20
244 #define Exp_shift1 20
245 #define Exp_msk1 0x100000
246 #define Exp_msk11 0x100000
247 #define Exp_mask 0x7ff00000
248 #define P 53
249 #define Bias 1023
250 #define IEEE_Arith
251 #define Emin (-1022)
252 #define Exp_1 0x3ff00000
253 #define Exp_11 0x3ff00000
254 #define Ebits 11
255 #define Frac_mask 0xfffff
256 #define Frac_mask1 0xfffff
257 #define Ten_pmax 22
258 #define Bletch 0x10
259 #define Bndry_mask 0xfffff
260 #define Bndry_mask1 0xfffff
261 #define LSB 1
262 #define Sign_bit 0x80000000
263 #define Log2P 1
264 #define Tiny0 0
265 #define Tiny1 1
266 #define Quick_max 14
267 #define Int_max 14
268 #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
269 #else
270 #undef Sudden_Underflow
271 #define Sudden_Underflow
272 #ifdef IBM
273 #define Exp_shift 24
274 #define Exp_shift1 24
275 #define Exp_msk1 0x1000000
276 #define Exp_msk11 0x1000000
277 #define Exp_mask 0x7f000000
278 #define P 14
279 #define Bias 65
280 #define Exp_1 0x41000000
281 #define Exp_11 0x41000000
282 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
283 #define Frac_mask 0xffffff
284 #define Frac_mask1 0xffffff
285 #define Bletch 4
286 #define Ten_pmax 22
287 #define Bndry_mask 0xefffff
288 #define Bndry_mask1 0xffffff
289 #define LSB 1
290 #define Sign_bit 0x80000000
291 #define Log2P 4
292 #define Tiny0 0x100000
293 #define Tiny1 0
294 #define Quick_max 14
295 #define Int_max 15
296 #else /* VAX */
297 #define Exp_shift 23
298 #define Exp_shift1 7
299 #define Exp_msk1 0x80
300 #define Exp_msk11 0x800000
301 #define Exp_mask 0x7f80
302 #define P 56
303 #define Bias 129
304 #define Exp_1 0x40800000
305 #define Exp_11 0x4080
306 #define Ebits 8
307 #define Frac_mask 0x7fffff
308 #define Frac_mask1 0xffff007f
309 #define Ten_pmax 24
310 #define Bletch 2
311 #define Bndry_mask 0xffff007f
312 #define Bndry_mask1 0xffff007f
313 #define LSB 0x10000
314 #define Sign_bit 0x8000
315 #define Log2P 1
316 #define Tiny0 0x80
317 #define Tiny1 0
318 #define Quick_max 15
319 #define Int_max 15
320 #endif
321 #endif
322
323 #ifndef IEEE_Arith
324 #define ROUND_BIASED
325 #endif
326
327 #ifdef RND_PRODQUOT
328 #define rounded_product(a,b) a = rnd_prod(a, b)
329 #define rounded_quotient(a,b) a = rnd_quot(a, b)
330 #ifdef KR_headers
331 extern double rnd_prod(), rnd_quot();
332 #else
333 extern double rnd_prod(double, double), rnd_quot(double, double);
334 #endif
335 #else
336 #define rounded_product(a,b) a *= b
337 #define rounded_quotient(a,b) a /= b
338 #endif
339
340 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
341 #define Big1 0xffffffff
342
343 #ifndef Just_16
344 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
345 * This makes some inner loops simpler and sometimes saves work
346 * during multiplications, but it often seems to make things slightly
347 * slower. Hence the default is now to store 32 bits per Long.
348 */
349 #ifndef Pack_32
350 #define Pack_32
351 #endif
352 #endif
353
354 #define Kmax 15
355
356 #ifdef __cplusplus
357 extern "C" double strtod(const char *s00, char **se);
358 extern "C" char *__dtoa(double d, int mode, int ndigits,
359 int *decpt, int *sign, char **rve);
360 #endif
361
362 struct
363 Bigint {
364 struct Bigint *next;
365 int k, maxwds, sign, wds;
366 ULong x[1];
367 };
368
369 typedef struct Bigint Bigint;
370
371 static Bigint *freelist[Kmax+1];
372
373 #ifdef ANDROID_CHANGES
374 static pthread_mutex_t freelist_mutex = PTHREAD_MUTEX_INITIALIZER;
375 #else
376 #ifdef _REENTRANT
377 static mutex_t freelist_mutex = MUTEX_INITIALIZER;
378 #endif
379 #endif
380
381 /* Special value used to indicate an invalid Bigint value,
382 * e.g. when a memory allocation fails. The idea is that we
383 * want to avoid introducing NULL checks everytime a bigint
384 * computation is performed. Also the NULL value can also be
385 * already used to indicate "value not initialized yet" and
386 * returning NULL might alter the execution code path in
387 * case of OOM.
388 */
389 #define BIGINT_INVALID ((Bigint *)&bigint_invalid_value)
390
391 static const Bigint bigint_invalid_value;
392
393
394 /* Return BIGINT_INVALID on allocation failure.
395 *
396 * Most of the code here depends on the fact that this function
397 * never returns NULL.
398 */
399 static Bigint *
Balloc(k)400 Balloc
401 #ifdef KR_headers
402 (k) int k;
403 #else
404 (int k)
405 #endif
406 {
407 int x;
408 Bigint *rv;
409
410 mutex_lock(&freelist_mutex);
411
412 if ((rv = freelist[k]) != NULL) {
413 freelist[k] = rv->next;
414 }
415 else {
416 x = 1 << k;
417 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
418 if (rv == NULL) {
419 rv = BIGINT_INVALID;
420 goto EXIT;
421 }
422 rv->k = k;
423 rv->maxwds = x;
424 }
425 rv->sign = rv->wds = 0;
426 EXIT:
427 mutex_unlock(&freelist_mutex);
428
429 return rv;
430 }
431
432 static void
Bfree(v)433 Bfree
434 #ifdef KR_headers
435 (v) Bigint *v;
436 #else
437 (Bigint *v)
438 #endif
439 {
440 if (v && v != BIGINT_INVALID) {
441 mutex_lock(&freelist_mutex);
442
443 v->next = freelist[v->k];
444 freelist[v->k] = v;
445
446 mutex_unlock(&freelist_mutex);
447 }
448 }
449
450 #define Bcopy_valid(x,y) memcpy(&(x)->sign, &(y)->sign, \
451 (y)->wds*sizeof(Long) + 2*sizeof(int))
452
453 #define Bcopy(x,y) Bcopy_ptr(&(x),(y))
454
455 static void
Bcopy_ptr(Bigint ** px,Bigint * y)456 Bcopy_ptr(Bigint **px, Bigint *y)
457 {
458 if (*px == BIGINT_INVALID)
459 return; /* no space to store copy */
460 if (y == BIGINT_INVALID) {
461 Bfree(*px); /* invalid input */
462 *px = BIGINT_INVALID;
463 } else {
464 Bcopy_valid(*px,y);
465 }
466 }
467
468 static Bigint *
multadd(b,m,a)469 multadd
470 #ifdef KR_headers
471 (b, m, a) Bigint *b; int m, a;
472 #else
473 (Bigint *b, int m, int a) /* multiply by m and add a */
474 #endif
475 {
476 int i, wds;
477 ULong *x, y;
478 #ifdef Pack_32
479 ULong xi, z;
480 #endif
481 Bigint *b1;
482
483 if (b == BIGINT_INVALID)
484 return b;
485
486 wds = b->wds;
487 x = b->x;
488 i = 0;
489 do {
490 #ifdef Pack_32
491 xi = *x;
492 y = (xi & 0xffff) * m + a;
493 z = (xi >> 16) * m + (y >> 16);
494 a = (int)(z >> 16);
495 *x++ = (z << 16) + (y & 0xffff);
496 #else
497 y = *x * m + a;
498 a = (int)(y >> 16);
499 *x++ = y & 0xffff;
500 #endif
501 }
502 while(++i < wds);
503 if (a) {
504 if (wds >= b->maxwds) {
505 b1 = Balloc(b->k+1);
506 if (b1 == BIGINT_INVALID) {
507 Bfree(b);
508 return b1;
509 }
510 Bcopy_valid(b1, b);
511 Bfree(b);
512 b = b1;
513 }
514 b->x[wds++] = a;
515 b->wds = wds;
516 }
517 return b;
518 }
519
520 static Bigint *
s2b(s,nd0,nd,y9)521 s2b
522 #ifdef KR_headers
523 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
524 #else
525 (CONST char *s, int nd0, int nd, ULong y9)
526 #endif
527 {
528 Bigint *b;
529 int i, k;
530 Long x, y;
531
532 x = (nd + 8) / 9;
533 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
534 #ifdef Pack_32
535 b = Balloc(k);
536 if (b == BIGINT_INVALID)
537 return b;
538 b->x[0] = y9;
539 b->wds = 1;
540 #else
541 b = Balloc(k+1);
542 if (b == BIGINT_INVALID)
543 return b;
544
545 b->x[0] = y9 & 0xffff;
546 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
547 #endif
548
549 i = 9;
550 if (9 < nd0) {
551 s += 9;
552 do b = multadd(b, 10, *s++ - '0');
553 while(++i < nd0);
554 s++;
555 }
556 else
557 s += 10;
558 for(; i < nd; i++)
559 b = multadd(b, 10, *s++ - '0');
560 return b;
561 }
562
563 static int
hi0bits(x)564 hi0bits
565 #ifdef KR_headers
566 (x) ULong x;
567 #else
568 (ULong x)
569 #endif
570 {
571 int k = 0;
572
573 if (!(x & 0xffff0000)) {
574 k = 16;
575 x <<= 16;
576 }
577 if (!(x & 0xff000000)) {
578 k += 8;
579 x <<= 8;
580 }
581 if (!(x & 0xf0000000)) {
582 k += 4;
583 x <<= 4;
584 }
585 if (!(x & 0xc0000000)) {
586 k += 2;
587 x <<= 2;
588 }
589 if (!(x & 0x80000000)) {
590 k++;
591 if (!(x & 0x40000000))
592 return 32;
593 }
594 return k;
595 }
596
597 static int
lo0bits(y)598 lo0bits
599 #ifdef KR_headers
600 (y) ULong *y;
601 #else
602 (ULong *y)
603 #endif
604 {
605 int k;
606 ULong x = *y;
607
608 if (x & 7) {
609 if (x & 1)
610 return 0;
611 if (x & 2) {
612 *y = x >> 1;
613 return 1;
614 }
615 *y = x >> 2;
616 return 2;
617 }
618 k = 0;
619 if (!(x & 0xffff)) {
620 k = 16;
621 x >>= 16;
622 }
623 if (!(x & 0xff)) {
624 k += 8;
625 x >>= 8;
626 }
627 if (!(x & 0xf)) {
628 k += 4;
629 x >>= 4;
630 }
631 if (!(x & 0x3)) {
632 k += 2;
633 x >>= 2;
634 }
635 if (!(x & 1)) {
636 k++;
637 x >>= 1;
638 if (!x & 1)
639 return 32;
640 }
641 *y = x;
642 return k;
643 }
644
645 static Bigint *
i2b(i)646 i2b
647 #ifdef KR_headers
648 (i) int i;
649 #else
650 (int i)
651 #endif
652 {
653 Bigint *b;
654
655 b = Balloc(1);
656 if (b != BIGINT_INVALID) {
657 b->x[0] = i;
658 b->wds = 1;
659 }
660 return b;
661 }
662
663 static Bigint *
mult(a,b)664 mult
665 #ifdef KR_headers
666 (a, b) Bigint *a, *b;
667 #else
668 (Bigint *a, Bigint *b)
669 #endif
670 {
671 Bigint *c;
672 int k, wa, wb, wc;
673 ULong carry, y, z;
674 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
675 #ifdef Pack_32
676 ULong z2;
677 #endif
678
679 if (a == BIGINT_INVALID || b == BIGINT_INVALID)
680 return BIGINT_INVALID;
681
682 if (a->wds < b->wds) {
683 c = a;
684 a = b;
685 b = c;
686 }
687 k = a->k;
688 wa = a->wds;
689 wb = b->wds;
690 wc = wa + wb;
691 if (wc > a->maxwds)
692 k++;
693 c = Balloc(k);
694 if (c == BIGINT_INVALID)
695 return c;
696 for(x = c->x, xa = x + wc; x < xa; x++)
697 *x = 0;
698 xa = a->x;
699 xae = xa + wa;
700 xb = b->x;
701 xbe = xb + wb;
702 xc0 = c->x;
703 #ifdef Pack_32
704 for(; xb < xbe; xb++, xc0++) {
705 if ((y = *xb & 0xffff) != 0) {
706 x = xa;
707 xc = xc0;
708 carry = 0;
709 do {
710 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
711 carry = z >> 16;
712 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
713 carry = z2 >> 16;
714 Storeinc(xc, z2, z);
715 }
716 while(x < xae);
717 *xc = carry;
718 }
719 if ((y = *xb >> 16) != 0) {
720 x = xa;
721 xc = xc0;
722 carry = 0;
723 z2 = *xc;
724 do {
725 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
726 carry = z >> 16;
727 Storeinc(xc, z, z2);
728 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
729 carry = z2 >> 16;
730 }
731 while(x < xae);
732 *xc = z2;
733 }
734 }
735 #else
736 for(; xb < xbe; xc0++) {
737 if (y = *xb++) {
738 x = xa;
739 xc = xc0;
740 carry = 0;
741 do {
742 z = *x++ * y + *xc + carry;
743 carry = z >> 16;
744 *xc++ = z & 0xffff;
745 }
746 while(x < xae);
747 *xc = carry;
748 }
749 }
750 #endif
751 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
752 c->wds = wc;
753 return c;
754 }
755
756 static Bigint *p5s;
757
758 static Bigint *
pow5mult(b,k)759 pow5mult
760 #ifdef KR_headers
761 (b, k) Bigint *b; int k;
762 #else
763 (Bigint *b, int k)
764 #endif
765 {
766 Bigint *b1, *p5, *p51;
767 int i;
768 static const int p05[3] = { 5, 25, 125 };
769
770 if (b == BIGINT_INVALID)
771 return b;
772
773 if ((i = k & 3) != 0)
774 b = multadd(b, p05[i-1], 0);
775
776 if (!(k = (unsigned int) k >> 2))
777 return b;
778 if (!(p5 = p5s)) {
779 /* first time */
780 p5 = i2b(625);
781 if (p5 == BIGINT_INVALID) {
782 Bfree(b);
783 return p5;
784 }
785 p5s = p5;
786 p5->next = 0;
787 }
788 for(;;) {
789 if (k & 1) {
790 b1 = mult(b, p5);
791 Bfree(b);
792 b = b1;
793 }
794 if (!(k = (unsigned int) k >> 1))
795 break;
796 if (!(p51 = p5->next)) {
797 p51 = mult(p5,p5);
798 if (p51 == BIGINT_INVALID) {
799 Bfree(b);
800 return p51;
801 }
802 p5->next = p51;
803 p51->next = 0;
804 }
805 p5 = p51;
806 }
807 return b;
808 }
809
810 static Bigint *
lshift(b,k)811 lshift
812 #ifdef KR_headers
813 (b, k) Bigint *b; int k;
814 #else
815 (Bigint *b, int k)
816 #endif
817 {
818 int i, k1, n, n1;
819 Bigint *b1;
820 ULong *x, *x1, *xe, z;
821
822 if (b == BIGINT_INVALID)
823 return b;
824
825 #ifdef Pack_32
826 n = (unsigned int)k >> 5;
827 #else
828 n = (unsigned int)k >> 4;
829 #endif
830 k1 = b->k;
831 n1 = n + b->wds + 1;
832 for(i = b->maxwds; n1 > i; i <<= 1)
833 k1++;
834 b1 = Balloc(k1);
835 if (b1 == BIGINT_INVALID) {
836 Bfree(b);
837 return b1;
838 }
839 x1 = b1->x;
840 for(i = 0; i < n; i++)
841 *x1++ = 0;
842 x = b->x;
843 xe = x + b->wds;
844 #ifdef Pack_32
845 if (k &= 0x1f) {
846 k1 = 32 - k;
847 z = 0;
848 do {
849 *x1++ = *x << k | z;
850 z = *x++ >> k1;
851 }
852 while(x < xe);
853 if ((*x1 = z) != 0)
854 ++n1;
855 }
856 #else
857 if (k &= 0xf) {
858 k1 = 16 - k;
859 z = 0;
860 do {
861 *x1++ = *x << k & 0xffff | z;
862 z = *x++ >> k1;
863 }
864 while(x < xe);
865 if (*x1 = z)
866 ++n1;
867 }
868 #endif
869 else do
870 *x1++ = *x++;
871 while(x < xe);
872 b1->wds = n1 - 1;
873 Bfree(b);
874 return b1;
875 }
876
877 static int
cmp(a,b)878 cmp
879 #ifdef KR_headers
880 (a, b) Bigint *a, *b;
881 #else
882 (Bigint *a, Bigint *b)
883 #endif
884 {
885 ULong *xa, *xa0, *xb, *xb0;
886 int i, j;
887
888 if (a == BIGINT_INVALID || b == BIGINT_INVALID)
889 #ifdef DEBUG
890 Bug("cmp called with a or b invalid");
891 #else
892 return 0; /* equal - the best we can do right now */
893 #endif
894
895 i = a->wds;
896 j = b->wds;
897 #ifdef DEBUG
898 if (i > 1 && !a->x[i-1])
899 Bug("cmp called with a->x[a->wds-1] == 0");
900 if (j > 1 && !b->x[j-1])
901 Bug("cmp called with b->x[b->wds-1] == 0");
902 #endif
903 if (i -= j)
904 return i;
905 xa0 = a->x;
906 xa = xa0 + j;
907 xb0 = b->x;
908 xb = xb0 + j;
909 for(;;) {
910 if (*--xa != *--xb)
911 return *xa < *xb ? -1 : 1;
912 if (xa <= xa0)
913 break;
914 }
915 return 0;
916 }
917
918 static Bigint *
diff(a,b)919 diff
920 #ifdef KR_headers
921 (a, b) Bigint *a, *b;
922 #else
923 (Bigint *a, Bigint *b)
924 #endif
925 {
926 Bigint *c;
927 int i, wa, wb;
928 Long borrow, y; /* We need signed shifts here. */
929 ULong *xa, *xae, *xb, *xbe, *xc;
930 #ifdef Pack_32
931 Long z;
932 #endif
933
934 if (a == BIGINT_INVALID || b == BIGINT_INVALID)
935 return BIGINT_INVALID;
936
937 i = cmp(a,b);
938 if (!i) {
939 c = Balloc(0);
940 if (c != BIGINT_INVALID) {
941 c->wds = 1;
942 c->x[0] = 0;
943 }
944 return c;
945 }
946 if (i < 0) {
947 c = a;
948 a = b;
949 b = c;
950 i = 1;
951 }
952 else
953 i = 0;
954 c = Balloc(a->k);
955 if (c == BIGINT_INVALID)
956 return c;
957 c->sign = i;
958 wa = a->wds;
959 xa = a->x;
960 xae = xa + wa;
961 wb = b->wds;
962 xb = b->x;
963 xbe = xb + wb;
964 xc = c->x;
965 borrow = 0;
966 #ifdef Pack_32
967 do {
968 y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
969 borrow = (ULong)y >> 16;
970 Sign_Extend(borrow, y);
971 z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
972 borrow = (ULong)z >> 16;
973 Sign_Extend(borrow, z);
974 Storeinc(xc, z, y);
975 }
976 while(xb < xbe);
977 while(xa < xae) {
978 y = (*xa & 0xffff) + borrow;
979 borrow = (ULong)y >> 16;
980 Sign_Extend(borrow, y);
981 z = (*xa++ >> 16) + borrow;
982 borrow = (ULong)z >> 16;
983 Sign_Extend(borrow, z);
984 Storeinc(xc, z, y);
985 }
986 #else
987 do {
988 y = *xa++ - *xb++ + borrow;
989 borrow = y >> 16;
990 Sign_Extend(borrow, y);
991 *xc++ = y & 0xffff;
992 }
993 while(xb < xbe);
994 while(xa < xae) {
995 y = *xa++ + borrow;
996 borrow = y >> 16;
997 Sign_Extend(borrow, y);
998 *xc++ = y & 0xffff;
999 }
1000 #endif
1001 while(!*--xc)
1002 wa--;
1003 c->wds = wa;
1004 return c;
1005 }
1006
1007 static double
ulp(_x)1008 ulp
1009 #ifdef KR_headers
1010 (_x) double _x;
1011 #else
1012 (double _x)
1013 #endif
1014 {
1015 _double x;
1016 Long L;
1017 _double a;
1018
1019 value(x) = _x;
1020 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1021 #ifndef Sudden_Underflow
1022 if (L > 0) {
1023 #endif
1024 #ifdef IBM
1025 L |= Exp_msk1 >> 4;
1026 #endif
1027 word0(a) = L;
1028 word1(a) = 0;
1029 #ifndef Sudden_Underflow
1030 }
1031 else {
1032 L = (ULong)-L >> Exp_shift;
1033 if (L < Exp_shift) {
1034 word0(a) = 0x80000 >> L;
1035 word1(a) = 0;
1036 }
1037 else {
1038 word0(a) = 0;
1039 L -= Exp_shift;
1040 word1(a) = L >= 31 ? 1 : 1 << (31 - L);
1041 }
1042 }
1043 #endif
1044 return value(a);
1045 }
1046
1047 static double
b2d(a,e)1048 b2d
1049 #ifdef KR_headers
1050 (a, e) Bigint *a; int *e;
1051 #else
1052 (Bigint *a, int *e)
1053 #endif
1054 {
1055 ULong *xa, *xa0, w, y, z;
1056 int k;
1057 _double d;
1058 #ifdef VAX
1059 ULong d0, d1;
1060 #else
1061 #define d0 word0(d)
1062 #define d1 word1(d)
1063 #endif
1064
1065 if (a == BIGINT_INVALID)
1066 return NAN;
1067
1068 xa0 = a->x;
1069 xa = xa0 + a->wds;
1070 y = *--xa;
1071 #ifdef DEBUG
1072 if (!y) Bug("zero y in b2d");
1073 #endif
1074 k = hi0bits(y);
1075 *e = 32 - k;
1076 #ifdef Pack_32
1077 if (k < Ebits) {
1078 d0 = Exp_1 | y >> (Ebits - k);
1079 w = xa > xa0 ? *--xa : 0;
1080 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1081 goto ret_d;
1082 }
1083 z = xa > xa0 ? *--xa : 0;
1084 if (k -= Ebits) {
1085 d0 = Exp_1 | y << k | z >> (32 - k);
1086 y = xa > xa0 ? *--xa : 0;
1087 d1 = z << k | y >> (32 - k);
1088 }
1089 else {
1090 d0 = Exp_1 | y;
1091 d1 = z;
1092 }
1093 #else
1094 if (k < Ebits + 16) {
1095 z = xa > xa0 ? *--xa : 0;
1096 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1097 w = xa > xa0 ? *--xa : 0;
1098 y = xa > xa0 ? *--xa : 0;
1099 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1100 goto ret_d;
1101 }
1102 z = xa > xa0 ? *--xa : 0;
1103 w = xa > xa0 ? *--xa : 0;
1104 k -= Ebits + 16;
1105 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1106 y = xa > xa0 ? *--xa : 0;
1107 d1 = w << k + 16 | y << k;
1108 #endif
1109 ret_d:
1110 #ifdef VAX
1111 word0(d) = d0 >> 16 | d0 << 16;
1112 word1(d) = d1 >> 16 | d1 << 16;
1113 #else
1114 #undef d0
1115 #undef d1
1116 #endif
1117 return value(d);
1118 }
1119
1120 static Bigint *
d2b(_d,e,bits)1121 d2b
1122 #ifdef KR_headers
1123 (_d, e, bits) double d; int *e, *bits;
1124 #else
1125 (double _d, int *e, int *bits)
1126 #endif
1127 {
1128 Bigint *b;
1129 int de, i, k;
1130 ULong *x, y, z;
1131 _double d;
1132 #ifdef VAX
1133 ULong d0, d1;
1134 #endif
1135
1136 value(d) = _d;
1137 #ifdef VAX
1138 d0 = word0(d) >> 16 | word0(d) << 16;
1139 d1 = word1(d) >> 16 | word1(d) << 16;
1140 #else
1141 #define d0 word0(d)
1142 #define d1 word1(d)
1143 #endif
1144
1145 #ifdef Pack_32
1146 b = Balloc(1);
1147 #else
1148 b = Balloc(2);
1149 #endif
1150 if (b == BIGINT_INVALID)
1151 return b;
1152 x = b->x;
1153
1154 z = d0 & Frac_mask;
1155 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1156 #ifdef Sudden_Underflow
1157 de = (int)(d0 >> Exp_shift);
1158 #ifndef IBM
1159 z |= Exp_msk11;
1160 #endif
1161 #else
1162 if ((de = (int)(d0 >> Exp_shift)) != 0)
1163 z |= Exp_msk1;
1164 #endif
1165 #ifdef Pack_32
1166 if ((y = d1) != 0) {
1167 if ((k = lo0bits(&y)) != 0) {
1168 x[0] = y | z << (32 - k);
1169 z >>= k;
1170 }
1171 else
1172 x[0] = y;
1173 i = b->wds = (x[1] = z) ? 2 : 1;
1174 }
1175 else {
1176 #ifdef DEBUG
1177 if (!z)
1178 Bug("Zero passed to d2b");
1179 #endif
1180 k = lo0bits(&z);
1181 x[0] = z;
1182 i = b->wds = 1;
1183 k += 32;
1184 }
1185 #else
1186 if (y = d1) {
1187 if (k = lo0bits(&y))
1188 if (k >= 16) {
1189 x[0] = y | z << 32 - k & 0xffff;
1190 x[1] = z >> k - 16 & 0xffff;
1191 x[2] = z >> k;
1192 i = 2;
1193 }
1194 else {
1195 x[0] = y & 0xffff;
1196 x[1] = y >> 16 | z << 16 - k & 0xffff;
1197 x[2] = z >> k & 0xffff;
1198 x[3] = z >> k+16;
1199 i = 3;
1200 }
1201 else {
1202 x[0] = y & 0xffff;
1203 x[1] = y >> 16;
1204 x[2] = z & 0xffff;
1205 x[3] = z >> 16;
1206 i = 3;
1207 }
1208 }
1209 else {
1210 #ifdef DEBUG
1211 if (!z)
1212 Bug("Zero passed to d2b");
1213 #endif
1214 k = lo0bits(&z);
1215 if (k >= 16) {
1216 x[0] = z;
1217 i = 0;
1218 }
1219 else {
1220 x[0] = z & 0xffff;
1221 x[1] = z >> 16;
1222 i = 1;
1223 }
1224 k += 32;
1225 }
1226 while(!x[i])
1227 --i;
1228 b->wds = i + 1;
1229 #endif
1230 #ifndef Sudden_Underflow
1231 if (de) {
1232 #endif
1233 #ifdef IBM
1234 *e = (de - Bias - (P-1) << 2) + k;
1235 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1236 #else
1237 *e = de - Bias - (P-1) + k;
1238 *bits = P - k;
1239 #endif
1240 #ifndef Sudden_Underflow
1241 }
1242 else {
1243 *e = de - Bias - (P-1) + 1 + k;
1244 #ifdef Pack_32
1245 *bits = 32*i - hi0bits(x[i-1]);
1246 #else
1247 *bits = (i+2)*16 - hi0bits(x[i]);
1248 #endif
1249 }
1250 #endif
1251 return b;
1252 }
1253 #undef d0
1254 #undef d1
1255
1256 static double
ratio(a,b)1257 ratio
1258 #ifdef KR_headers
1259 (a, b) Bigint *a, *b;
1260 #else
1261 (Bigint *a, Bigint *b)
1262 #endif
1263 {
1264 _double da, db;
1265 int k, ka, kb;
1266
1267 if (a == BIGINT_INVALID || b == BIGINT_INVALID)
1268 return NAN; /* for lack of better value ? */
1269
1270 value(da) = b2d(a, &ka);
1271 value(db) = b2d(b, &kb);
1272 #ifdef Pack_32
1273 k = ka - kb + 32*(a->wds - b->wds);
1274 #else
1275 k = ka - kb + 16*(a->wds - b->wds);
1276 #endif
1277 #ifdef IBM
1278 if (k > 0) {
1279 word0(da) += (k >> 2)*Exp_msk1;
1280 if (k &= 3)
1281 da *= 1 << k;
1282 }
1283 else {
1284 k = -k;
1285 word0(db) += (k >> 2)*Exp_msk1;
1286 if (k &= 3)
1287 db *= 1 << k;
1288 }
1289 #else
1290 if (k > 0)
1291 word0(da) += k*Exp_msk1;
1292 else {
1293 k = -k;
1294 word0(db) += k*Exp_msk1;
1295 }
1296 #endif
1297 return value(da) / value(db);
1298 }
1299
1300 static CONST double
1301 tens[] = {
1302 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1303 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1304 1e20, 1e21, 1e22
1305 #ifdef VAX
1306 , 1e23, 1e24
1307 #endif
1308 };
1309
1310 #ifdef IEEE_Arith
1311 static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1312 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1313 #define n_bigtens 5
1314 #else
1315 #ifdef IBM
1316 static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
1317 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1318 #define n_bigtens 3
1319 #else
1320 static CONST double bigtens[] = { 1e16, 1e32 };
1321 static CONST double tinytens[] = { 1e-16, 1e-32 };
1322 #define n_bigtens 2
1323 #endif
1324 #endif
1325
1326 double
strtod(s00,se)1327 strtod
1328 #ifdef KR_headers
1329 (s00, se) CONST char *s00; char **se;
1330 #else
1331 (CONST char *s00, char **se)
1332 #endif
1333 {
1334 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1335 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1336 CONST char *s, *s0, *s1;
1337 double aadj, aadj1, adj;
1338 _double rv, rv0;
1339 Long L;
1340 ULong y, z;
1341 Bigint *bb1, *bd0;
1342 Bigint *bb = NULL, *bd = NULL, *bs = NULL, *delta = NULL;/* pacify gcc */
1343
1344 #ifdef ANDROID_CHANGES
1345 CONST char decimal_point = '.';
1346 #else /* ANDROID_CHANGES */
1347 #ifndef KR_headers
1348 CONST char decimal_point = localeconv()->decimal_point[0];
1349 #else
1350 CONST char decimal_point = '.';
1351 #endif
1352
1353 #endif /* ANDROID_CHANGES */
1354
1355 sign = nz0 = nz = 0;
1356 value(rv) = 0.;
1357
1358
1359 for(s = s00; isspace((unsigned char) *s); s++)
1360 ;
1361
1362 if (*s == '-') {
1363 sign = 1;
1364 s++;
1365 } else if (*s == '+') {
1366 s++;
1367 }
1368
1369 if (*s == '\0') {
1370 s = s00;
1371 goto ret;
1372 }
1373
1374 /* "INF" or "INFINITY" */
1375 if (tolower((unsigned char)*s) == 'i' && strncasecmp(s, "inf", 3) == 0) {
1376 if (strncasecmp(s + 3, "inity", 5) == 0)
1377 s += 8;
1378 else
1379 s += 3;
1380
1381 value(rv) = HUGE_VAL;
1382 goto ret;
1383 }
1384
1385 #ifdef IEEE_Arith
1386 /* "NAN" or "NAN(n-char-sequence-opt)" */
1387 if (tolower((unsigned char)*s) == 'n' && strncasecmp(s, "nan", 3) == 0) {
1388 /* Build a quiet NaN. */
1389 word0(rv) = NAN_WORD0;
1390 word1(rv) = NAN_WORD1;
1391 s+= 3;
1392
1393 /* Don't interpret (n-char-sequence-opt), for now. */
1394 if (*s == '(') {
1395 s0 = s;
1396 for (s++; *s != ')' && *s != '\0'; s++)
1397 ;
1398 if (*s == ')')
1399 s++; /* Skip over closing paren ... */
1400 else
1401 s = s0; /* ... otherwise go back. */
1402 }
1403
1404 goto ret;
1405 }
1406 #endif
1407
1408 if (*s == '0') {
1409 nz0 = 1;
1410 while(*++s == '0') ;
1411 if (!*s)
1412 goto ret;
1413 }
1414 s0 = s;
1415 y = z = 0;
1416 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1417 if (nd < 9)
1418 y = 10*y + c - '0';
1419 else if (nd < 16)
1420 z = 10*z + c - '0';
1421 nd0 = nd;
1422 if (c == decimal_point) {
1423 c = *++s;
1424 if (!nd) {
1425 for(; c == '0'; c = *++s)
1426 nz++;
1427 if (c > '0' && c <= '9') {
1428 s0 = s;
1429 nf += nz;
1430 nz = 0;
1431 goto have_dig;
1432 }
1433 goto dig_done;
1434 }
1435 for(; c >= '0' && c <= '9'; c = *++s) {
1436 have_dig:
1437 nz++;
1438 if (c -= '0') {
1439 nf += nz;
1440 for(i = 1; i < nz; i++)
1441 if (nd++ < 9)
1442 y *= 10;
1443 else if (nd <= DBL_DIG + 1)
1444 z *= 10;
1445 if (nd++ < 9)
1446 y = 10*y + c;
1447 else if (nd <= DBL_DIG + 1)
1448 z = 10*z + c;
1449 nz = 0;
1450 }
1451 }
1452 }
1453 dig_done:
1454 e = 0;
1455 if (c == 'e' || c == 'E') {
1456 if (!nd && !nz && !nz0) {
1457 s = s00;
1458 goto ret;
1459 }
1460 s00 = s;
1461 esign = 0;
1462 switch(c = *++s) {
1463 case '-':
1464 esign = 1;
1465 /* FALLTHROUGH */
1466 case '+':
1467 c = *++s;
1468 }
1469 if (c >= '0' && c <= '9') {
1470 while(c == '0')
1471 c = *++s;
1472 if (c > '0' && c <= '9') {
1473 L = c - '0';
1474 s1 = s;
1475 while((c = *++s) >= '0' && c <= '9')
1476 L = 10*L + c - '0';
1477 if (s - s1 > 8 || L > 19999)
1478 /* Avoid confusion from exponents
1479 * so large that e might overflow.
1480 */
1481 e = 19999; /* safe for 16 bit ints */
1482 else
1483 e = (int)L;
1484 if (esign)
1485 e = -e;
1486 }
1487 else
1488 e = 0;
1489 }
1490 else
1491 s = s00;
1492 }
1493 if (!nd) {
1494 if (!nz && !nz0)
1495 s = s00;
1496 goto ret;
1497 }
1498 e1 = e -= nf;
1499
1500 /* Now we have nd0 digits, starting at s0, followed by a
1501 * decimal point, followed by nd-nd0 digits. The number we're
1502 * after is the integer represented by those digits times
1503 * 10**e */
1504
1505 if (!nd0)
1506 nd0 = nd;
1507 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1508 value(rv) = y;
1509 if (k > 9)
1510 value(rv) = tens[k - 9] * value(rv) + z;
1511 bd0 = 0;
1512 if (nd <= DBL_DIG
1513 #ifndef RND_PRODQUOT
1514 && FLT_ROUNDS == 1
1515 #endif
1516 ) {
1517 if (!e)
1518 goto ret;
1519 if (e > 0) {
1520 if (e <= Ten_pmax) {
1521 #ifdef VAX
1522 goto vax_ovfl_check;
1523 #else
1524 /* value(rv) = */ rounded_product(value(rv),
1525 tens[e]);
1526 goto ret;
1527 #endif
1528 }
1529 i = DBL_DIG - nd;
1530 if (e <= Ten_pmax + i) {
1531 /* A fancier test would sometimes let us do
1532 * this for larger i values.
1533 */
1534 e -= i;
1535 value(rv) *= tens[i];
1536 #ifdef VAX
1537 /* VAX exponent range is so narrow we must
1538 * worry about overflow here...
1539 */
1540 vax_ovfl_check:
1541 word0(rv) -= P*Exp_msk1;
1542 /* value(rv) = */ rounded_product(value(rv),
1543 tens[e]);
1544 if ((word0(rv) & Exp_mask)
1545 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1546 goto ovfl;
1547 word0(rv) += P*Exp_msk1;
1548 #else
1549 /* value(rv) = */ rounded_product(value(rv),
1550 tens[e]);
1551 #endif
1552 goto ret;
1553 }
1554 }
1555 #ifndef Inaccurate_Divide
1556 else if (e >= -Ten_pmax) {
1557 /* value(rv) = */ rounded_quotient(value(rv),
1558 tens[-e]);
1559 goto ret;
1560 }
1561 #endif
1562 }
1563 e1 += nd - k;
1564
1565 /* Get starting approximation = rv * 10**e1 */
1566
1567 if (e1 > 0) {
1568 if ((i = e1 & 15) != 0)
1569 value(rv) *= tens[i];
1570 if (e1 &= ~15) {
1571 if (e1 > DBL_MAX_10_EXP) {
1572 ovfl:
1573 errno = ERANGE;
1574 value(rv) = HUGE_VAL;
1575 if (bd0)
1576 goto retfree;
1577 goto ret;
1578 }
1579 if ((e1 = (unsigned int)e1 >> 4) != 0) {
1580 for(j = 0; e1 > 1; j++,
1581 e1 = (unsigned int)e1 >> 1)
1582 if (e1 & 1)
1583 value(rv) *= bigtens[j];
1584 /* The last multiplication could overflow. */
1585 word0(rv) -= P*Exp_msk1;
1586 value(rv) *= bigtens[j];
1587 if ((z = word0(rv) & Exp_mask)
1588 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1589 goto ovfl;
1590 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1591 /* set to largest number */
1592 /* (Can't trust DBL_MAX) */
1593 word0(rv) = Big0;
1594 word1(rv) = Big1;
1595 }
1596 else
1597 word0(rv) += P*Exp_msk1;
1598 }
1599 }
1600 }
1601 else if (e1 < 0) {
1602 e1 = -e1;
1603 if ((i = e1 & 15) != 0)
1604 value(rv) /= tens[i];
1605 if (e1 &= ~15) {
1606 e1 = (unsigned int)e1 >> 4;
1607 if (e1 >= 1 << n_bigtens)
1608 goto undfl;
1609 for(j = 0; e1 > 1; j++,
1610 e1 = (unsigned int)e1 >> 1)
1611 if (e1 & 1)
1612 value(rv) *= tinytens[j];
1613 /* The last multiplication could underflow. */
1614 value(rv0) = value(rv);
1615 value(rv) *= tinytens[j];
1616 if (!value(rv)) {
1617 value(rv) = 2.*value(rv0);
1618 value(rv) *= tinytens[j];
1619 if (!value(rv)) {
1620 undfl:
1621 value(rv) = 0.;
1622 errno = ERANGE;
1623 if (bd0)
1624 goto retfree;
1625 goto ret;
1626 }
1627 word0(rv) = Tiny0;
1628 word1(rv) = Tiny1;
1629 /* The refinement below will clean
1630 * this approximation up.
1631 */
1632 }
1633 }
1634 }
1635
1636 /* Now the hard part -- adjusting rv to the correct value.*/
1637
1638 /* Put digits into bd: true value = bd * 10^e */
1639
1640 bd0 = s2b(s0, nd0, nd, y);
1641
1642 for(;;) {
1643 bd = Balloc(bd0->k);
1644 Bcopy(bd, bd0);
1645 bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1646 bs = i2b(1);
1647
1648 if (e >= 0) {
1649 bb2 = bb5 = 0;
1650 bd2 = bd5 = e;
1651 }
1652 else {
1653 bb2 = bb5 = -e;
1654 bd2 = bd5 = 0;
1655 }
1656 if (bbe >= 0)
1657 bb2 += bbe;
1658 else
1659 bd2 -= bbe;
1660 bs2 = bb2;
1661 #ifdef Sudden_Underflow
1662 #ifdef IBM
1663 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1664 #else
1665 j = P + 1 - bbbits;
1666 #endif
1667 #else
1668 i = bbe + bbbits - 1; /* logb(rv) */
1669 if (i < Emin) /* denormal */
1670 j = bbe + (P-Emin);
1671 else
1672 j = P + 1 - bbbits;
1673 #endif
1674 bb2 += j;
1675 bd2 += j;
1676 i = bb2 < bd2 ? bb2 : bd2;
1677 if (i > bs2)
1678 i = bs2;
1679 if (i > 0) {
1680 bb2 -= i;
1681 bd2 -= i;
1682 bs2 -= i;
1683 }
1684 if (bb5 > 0) {
1685 bs = pow5mult(bs, bb5);
1686 bb1 = mult(bs, bb);
1687 Bfree(bb);
1688 bb = bb1;
1689 }
1690 if (bb2 > 0)
1691 bb = lshift(bb, bb2);
1692 if (bd5 > 0)
1693 bd = pow5mult(bd, bd5);
1694 if (bd2 > 0)
1695 bd = lshift(bd, bd2);
1696 if (bs2 > 0)
1697 bs = lshift(bs, bs2);
1698 delta = diff(bb, bd);
1699 dsign = delta->sign;
1700 delta->sign = 0;
1701 i = cmp(delta, bs);
1702 if (i < 0) {
1703 /* Error is less than half an ulp -- check for
1704 * special case of mantissa a power of two.
1705 */
1706 if (dsign || word1(rv) || word0(rv) & Bndry_mask)
1707 break;
1708 delta = lshift(delta,Log2P);
1709 if (cmp(delta, bs) > 0)
1710 goto drop_down;
1711 break;
1712 }
1713 if (i == 0) {
1714 /* exactly half-way between */
1715 if (dsign) {
1716 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
1717 && word1(rv) == 0xffffffff) {
1718 /*boundary case -- increment exponent*/
1719 word0(rv) = (word0(rv) & Exp_mask)
1720 + Exp_msk1
1721 #ifdef IBM
1722 | Exp_msk1 >> 4
1723 #endif
1724 ;
1725 word1(rv) = 0;
1726 break;
1727 }
1728 }
1729 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
1730 drop_down:
1731 /* boundary case -- decrement exponent */
1732 #ifdef Sudden_Underflow
1733 L = word0(rv) & Exp_mask;
1734 #ifdef IBM
1735 if (L < Exp_msk1)
1736 #else
1737 if (L <= Exp_msk1)
1738 #endif
1739 goto undfl;
1740 L -= Exp_msk1;
1741 #else
1742 L = (word0(rv) & Exp_mask) - Exp_msk1;
1743 #endif
1744 word0(rv) = L | Bndry_mask1;
1745 word1(rv) = 0xffffffff;
1746 #ifdef IBM
1747 goto cont;
1748 #else
1749 break;
1750 #endif
1751 }
1752 #ifndef ROUND_BIASED
1753 if (!(word1(rv) & LSB))
1754 break;
1755 #endif
1756 if (dsign)
1757 value(rv) += ulp(value(rv));
1758 #ifndef ROUND_BIASED
1759 else {
1760 value(rv) -= ulp(value(rv));
1761 #ifndef Sudden_Underflow
1762 if (!value(rv))
1763 goto undfl;
1764 #endif
1765 }
1766 #endif
1767 break;
1768 }
1769 if ((aadj = ratio(delta, bs)) <= 2.) {
1770 if (dsign)
1771 aadj = aadj1 = 1.;
1772 else if (word1(rv) || word0(rv) & Bndry_mask) {
1773 #ifndef Sudden_Underflow
1774 if (word1(rv) == Tiny1 && !word0(rv))
1775 goto undfl;
1776 #endif
1777 aadj = 1.;
1778 aadj1 = -1.;
1779 }
1780 else {
1781 /* special case -- power of FLT_RADIX to be */
1782 /* rounded down... */
1783
1784 if (aadj < 2./FLT_RADIX)
1785 aadj = 1./FLT_RADIX;
1786 else
1787 aadj *= 0.5;
1788 aadj1 = -aadj;
1789 }
1790 }
1791 else {
1792 aadj *= 0.5;
1793 aadj1 = dsign ? aadj : -aadj;
1794 #ifdef Check_FLT_ROUNDS
1795 switch(FLT_ROUNDS) {
1796 case 2: /* towards +infinity */
1797 aadj1 -= 0.5;
1798 break;
1799 case 0: /* towards 0 */
1800 case 3: /* towards -infinity */
1801 aadj1 += 0.5;
1802 }
1803 #else
1804 if (FLT_ROUNDS == 0)
1805 aadj1 += 0.5;
1806 #endif
1807 }
1808 y = word0(rv) & Exp_mask;
1809
1810 /* Check for overflow */
1811
1812 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
1813 value(rv0) = value(rv);
1814 word0(rv) -= P*Exp_msk1;
1815 adj = aadj1 * ulp(value(rv));
1816 value(rv) += adj;
1817 if ((word0(rv) & Exp_mask) >=
1818 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
1819 if (word0(rv0) == Big0 && word1(rv0) == Big1)
1820 goto ovfl;
1821 word0(rv) = Big0;
1822 word1(rv) = Big1;
1823 goto cont;
1824 }
1825 else
1826 word0(rv) += P*Exp_msk1;
1827 }
1828 else {
1829 #ifdef Sudden_Underflow
1830 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
1831 value(rv0) = value(rv);
1832 word0(rv) += P*Exp_msk1;
1833 adj = aadj1 * ulp(value(rv));
1834 value(rv) += adj;
1835 #ifdef IBM
1836 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
1837 #else
1838 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
1839 #endif
1840 {
1841 if (word0(rv0) == Tiny0
1842 && word1(rv0) == Tiny1)
1843 goto undfl;
1844 word0(rv) = Tiny0;
1845 word1(rv) = Tiny1;
1846 goto cont;
1847 }
1848 else
1849 word0(rv) -= P*Exp_msk1;
1850 }
1851 else {
1852 adj = aadj1 * ulp(value(rv));
1853 value(rv) += adj;
1854 }
1855 #else
1856 /* Compute adj so that the IEEE rounding rules will
1857 * correctly round rv + adj in some half-way cases.
1858 * If rv * ulp(rv) is denormalized (i.e.,
1859 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
1860 * trouble from bits lost to denormalization;
1861 * example: 1.2e-307 .
1862 */
1863 if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
1864 aadj1 = (double)(int)(aadj + 0.5);
1865 if (!dsign)
1866 aadj1 = -aadj1;
1867 }
1868 adj = aadj1 * ulp(value(rv));
1869 value(rv) += adj;
1870 #endif
1871 }
1872 z = word0(rv) & Exp_mask;
1873 if (y == z) {
1874 /* Can we stop now? */
1875 L = aadj;
1876 aadj -= L;
1877 /* The tolerances below are conservative. */
1878 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
1879 if (aadj < .4999999 || aadj > .5000001)
1880 break;
1881 }
1882 else if (aadj < .4999999/FLT_RADIX)
1883 break;
1884 }
1885 cont:
1886 Bfree(bb);
1887 Bfree(bd);
1888 Bfree(bs);
1889 Bfree(delta);
1890 }
1891 retfree:
1892 Bfree(bb);
1893 Bfree(bd);
1894 Bfree(bs);
1895 Bfree(bd0);
1896 Bfree(delta);
1897 ret:
1898 if (se)
1899 /* LINTED interface specification */
1900 *se = (char *)s;
1901 return sign ? -value(rv) : value(rv);
1902 }
1903
1904 static int
quorem(b,S)1905 quorem
1906 #ifdef KR_headers
1907 (b, S) Bigint *b, *S;
1908 #else
1909 (Bigint *b, Bigint *S)
1910 #endif
1911 {
1912 int n;
1913 Long borrow, y;
1914 ULong carry, q, ys;
1915 ULong *bx, *bxe, *sx, *sxe;
1916 #ifdef Pack_32
1917 Long z;
1918 ULong si, zs;
1919 #endif
1920
1921 if (b == BIGINT_INVALID || S == BIGINT_INVALID)
1922 return 0;
1923
1924 n = S->wds;
1925 #ifdef DEBUG
1926 /*debug*/ if (b->wds > n)
1927 /*debug*/ Bug("oversize b in quorem");
1928 #endif
1929 if (b->wds < n)
1930 return 0;
1931 sx = S->x;
1932 sxe = sx + --n;
1933 bx = b->x;
1934 bxe = bx + n;
1935 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1936 #ifdef DEBUG
1937 /*debug*/ if (q > 9)
1938 /*debug*/ Bug("oversized quotient in quorem");
1939 #endif
1940 if (q) {
1941 borrow = 0;
1942 carry = 0;
1943 do {
1944 #ifdef Pack_32
1945 si = *sx++;
1946 ys = (si & 0xffff) * q + carry;
1947 zs = (si >> 16) * q + (ys >> 16);
1948 carry = zs >> 16;
1949 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1950 borrow = (ULong)y >> 16;
1951 Sign_Extend(borrow, y);
1952 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1953 borrow = (ULong)z >> 16;
1954 Sign_Extend(borrow, z);
1955 Storeinc(bx, z, y);
1956 #else
1957 ys = *sx++ * q + carry;
1958 carry = ys >> 16;
1959 y = *bx - (ys & 0xffff) + borrow;
1960 borrow = y >> 16;
1961 Sign_Extend(borrow, y);
1962 *bx++ = y & 0xffff;
1963 #endif
1964 }
1965 while(sx <= sxe);
1966 if (!*bxe) {
1967 bx = b->x;
1968 while(--bxe > bx && !*bxe)
1969 --n;
1970 b->wds = n;
1971 }
1972 }
1973 if (cmp(b, S) >= 0) {
1974 q++;
1975 borrow = 0;
1976 carry = 0;
1977 bx = b->x;
1978 sx = S->x;
1979 do {
1980 #ifdef Pack_32
1981 si = *sx++;
1982 ys = (si & 0xffff) + carry;
1983 zs = (si >> 16) + (ys >> 16);
1984 carry = zs >> 16;
1985 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1986 borrow = (ULong)y >> 16;
1987 Sign_Extend(borrow, y);
1988 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1989 borrow = (ULong)z >> 16;
1990 Sign_Extend(borrow, z);
1991 Storeinc(bx, z, y);
1992 #else
1993 ys = *sx++ + carry;
1994 carry = ys >> 16;
1995 y = *bx - (ys & 0xffff) + borrow;
1996 borrow = y >> 16;
1997 Sign_Extend(borrow, y);
1998 *bx++ = y & 0xffff;
1999 #endif
2000 }
2001 while(sx <= sxe);
2002 bx = b->x;
2003 bxe = bx + n;
2004 if (!*bxe) {
2005 while(--bxe > bx && !*bxe)
2006 --n;
2007 b->wds = n;
2008 }
2009 }
2010 return q;
2011 }
2012
2013 /* freedtoa(s) must be used to free values s returned by dtoa
2014 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2015 * but for consistency with earlier versions of dtoa, it is optional
2016 * when MULTIPLE_THREADS is not defined.
2017 */
2018
2019 void
2020 #ifdef KR_headers
freedtoa(s)2021 freedtoa(s) char *s;
2022 #else
2023 freedtoa(char *s)
2024 #endif
2025 {
2026 free(s);
2027 }
2028
2029
2030
2031 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2032 *
2033 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2034 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
2035 *
2036 * Modifications:
2037 * 1. Rather than iterating, we use a simple numeric overestimate
2038 * to determine k = floor(log10(d)). We scale relevant
2039 * quantities using O(log2(k)) rather than O(k) multiplications.
2040 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2041 * try to generate digits strictly left to right. Instead, we
2042 * compute with fewer bits and propagate the carry if necessary
2043 * when rounding the final digit up. This is often faster.
2044 * 3. Under the assumption that input will be rounded nearest,
2045 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2046 * That is, we allow equality in stopping tests when the
2047 * round-nearest rule will give the same floating-point value
2048 * as would satisfaction of the stopping test with strict
2049 * inequality.
2050 * 4. We remove common factors of powers of 2 from relevant
2051 * quantities.
2052 * 5. When converting floating-point integers less than 1e16,
2053 * we use floating-point arithmetic rather than resorting
2054 * to multiple-precision integers.
2055 * 6. When asked to produce fewer than 15 digits, we first try
2056 * to get by with floating-point arithmetic; we resort to
2057 * multiple-precision integer arithmetic only if we cannot
2058 * guarantee that the floating-point calculation has given
2059 * the correctly rounded result. For k requested digits and
2060 * "uniformly" distributed input, the probability is
2061 * something like 10^(k-15) that we must resort to the Long
2062 * calculation.
2063 */
2064
2065 char *
__dtoa(_d,mode,ndigits,decpt,sign,rve)2066 __dtoa
2067 #ifdef KR_headers
2068 (_d, mode, ndigits, decpt, sign, rve)
2069 double _d; int mode, ndigits, *decpt, *sign; char **rve;
2070 #else
2071 (double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2072 #endif
2073 {
2074 /* Arguments ndigits, decpt, sign are similar to those
2075 of ecvt and fcvt; trailing zeros are suppressed from
2076 the returned string. If not null, *rve is set to point
2077 to the end of the return value. If d is +-Infinity or NaN,
2078 then *decpt is set to 9999.
2079
2080 mode:
2081 0 ==> shortest string that yields d when read in
2082 and rounded to nearest.
2083 1 ==> like 0, but with Steele & White stopping rule;
2084 e.g. with IEEE P754 arithmetic , mode 0 gives
2085 1e23 whereas mode 1 gives 9.999999999999999e22.
2086 2 ==> max(1,ndigits) significant digits. This gives a
2087 return value similar to that of ecvt, except
2088 that trailing zeros are suppressed.
2089 3 ==> through ndigits past the decimal point. This
2090 gives a return value similar to that from fcvt,
2091 except that trailing zeros are suppressed, and
2092 ndigits can be negative.
2093 4-9 should give the same return values as 2-3, i.e.,
2094 4 <= mode <= 9 ==> same return as mode
2095 2 + (mode & 1). These modes are mainly for
2096 debugging; often they run slower but sometimes
2097 faster than modes 2-3.
2098 4,5,8,9 ==> left-to-right digit generation.
2099 6-9 ==> don't try fast floating-point estimate
2100 (if applicable).
2101
2102 Values of mode other than 0-9 are treated as mode 0.
2103
2104 Sufficient space is allocated to the return value
2105 to hold the suppressed trailing zeros.
2106 */
2107
2108 int bbits, b2, b5, be, dig, i, ieps, ilim0,
2109 j, jj1, k, k0, k_check, leftright, m2, m5, s2, s5,
2110 try_quick;
2111 int ilim = 0, ilim1 = 0, spec_case = 0; /* pacify gcc */
2112 Long L;
2113 #ifndef Sudden_Underflow
2114 int denorm;
2115 ULong x;
2116 #endif
2117 Bigint *b, *b1, *delta, *mhi, *S;
2118 Bigint *mlo = NULL; /* pacify gcc */
2119 double ds;
2120 char *s, *s0;
2121 Bigint *result = NULL;
2122 int result_k = 0;
2123 _double d, d2, eps;
2124
2125 value(d) = _d;
2126
2127 if (word0(d) & Sign_bit) {
2128 /* set sign for everything, including 0's and NaNs */
2129 *sign = 1;
2130 word0(d) &= ~Sign_bit; /* clear sign bit */
2131 }
2132 else
2133 *sign = 0;
2134
2135 #if defined(IEEE_Arith) + defined(VAX)
2136 #ifdef IEEE_Arith
2137 if ((word0(d) & Exp_mask) == Exp_mask)
2138 #else
2139 if (word0(d) == 0x8000)
2140 #endif
2141 {
2142 /* Infinity or NaN */
2143 *decpt = 9999;
2144 s =
2145 #ifdef IEEE_Arith
2146 !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
2147 #endif
2148 "NaN";
2149 result = Balloc(strlen(s)+1);
2150 if (result == BIGINT_INVALID)
2151 return NULL;
2152 s0 = (char *)(void *)result;
2153 strcpy(s0, s);
2154 if (rve)
2155 *rve =
2156 #ifdef IEEE_Arith
2157 s0[3] ? s0 + 8 :
2158 #endif
2159 s0 + 3;
2160 return s0;
2161 }
2162 #endif
2163 #ifdef IBM
2164 value(d) += 0; /* normalize */
2165 #endif
2166 if (!value(d)) {
2167 *decpt = 1;
2168 result = Balloc(2);
2169 if (result == BIGINT_INVALID)
2170 return NULL;
2171 s0 = (char *)(void *)result;
2172 strcpy(s0, "0");
2173 if (rve)
2174 *rve = s0 + 1;
2175 return s0;
2176 }
2177
2178 b = d2b(value(d), &be, &bbits);
2179 #ifdef Sudden_Underflow
2180 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2181 #else
2182 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
2183 #endif
2184 value(d2) = value(d);
2185 word0(d2) &= Frac_mask1;
2186 word0(d2) |= Exp_11;
2187 #ifdef IBM
2188 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2189 value(d2) /= 1 << j;
2190 #endif
2191
2192 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2193 * log10(x) = log(x) / log(10)
2194 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2195 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2196 *
2197 * This suggests computing an approximation k to log10(d) by
2198 *
2199 * k = (i - Bias)*0.301029995663981
2200 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2201 *
2202 * We want k to be too large rather than too small.
2203 * The error in the first-order Taylor series approximation
2204 * is in our favor, so we just round up the constant enough
2205 * to compensate for any error in the multiplication of
2206 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2207 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2208 * adding 1e-13 to the constant term more than suffices.
2209 * Hence we adjust the constant term to 0.1760912590558.
2210 * (We could get a more accurate k by invoking log10,
2211 * but this is probably not worthwhile.)
2212 */
2213
2214 i -= Bias;
2215 #ifdef IBM
2216 i <<= 2;
2217 i += j;
2218 #endif
2219 #ifndef Sudden_Underflow
2220 denorm = 0;
2221 }
2222 else {
2223 /* d is denormalized */
2224
2225 i = bbits + be + (Bias + (P-1) - 1);
2226 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2227 : word1(d) << (32 - i);
2228 value(d2) = x;
2229 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2230 i -= (Bias + (P-1) - 1) + 1;
2231 denorm = 1;
2232 }
2233 #endif
2234 ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 +
2235 i*0.301029995663981;
2236 k = (int)ds;
2237 if (ds < 0. && ds != k)
2238 k--; /* want k = floor(ds) */
2239 k_check = 1;
2240 if (k >= 0 && k <= Ten_pmax) {
2241 if (value(d) < tens[k])
2242 k--;
2243 k_check = 0;
2244 }
2245 j = bbits - i - 1;
2246 if (j >= 0) {
2247 b2 = 0;
2248 s2 = j;
2249 }
2250 else {
2251 b2 = -j;
2252 s2 = 0;
2253 }
2254 if (k >= 0) {
2255 b5 = 0;
2256 s5 = k;
2257 s2 += k;
2258 }
2259 else {
2260 b2 -= k;
2261 b5 = -k;
2262 s5 = 0;
2263 }
2264 if (mode < 0 || mode > 9)
2265 mode = 0;
2266 try_quick = 1;
2267 if (mode > 5) {
2268 mode -= 4;
2269 try_quick = 0;
2270 }
2271 leftright = 1;
2272 switch(mode) {
2273 case 0:
2274 case 1:
2275 ilim = ilim1 = -1;
2276 i = 18;
2277 ndigits = 0;
2278 break;
2279 case 2:
2280 leftright = 0;
2281 /* FALLTHROUGH */
2282 case 4:
2283 if (ndigits <= 0)
2284 ndigits = 1;
2285 ilim = ilim1 = i = ndigits;
2286 break;
2287 case 3:
2288 leftright = 0;
2289 /* FALLTHROUGH */
2290 case 5:
2291 i = ndigits + k + 1;
2292 ilim = i;
2293 ilim1 = i - 1;
2294 if (i <= 0)
2295 i = 1;
2296 }
2297 j = sizeof(ULong);
2298 for(result_k = 0; (int)(sizeof(Bigint) - sizeof(ULong)) + j <= i;
2299 j <<= 1) result_k++;
2300 // this is really a ugly hack, the code uses Balloc
2301 // instead of malloc, but casts the result into a char*
2302 // it seems the only reason to do that is due to the
2303 // complicated way the block size need to be computed
2304 // buuurk....
2305 result = Balloc(result_k);
2306 if (result == BIGINT_INVALID) {
2307 Bfree(b);
2308 return NULL;
2309 }
2310 s = s0 = (char *)(void *)result;
2311
2312 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2313
2314 /* Try to get by with floating-point arithmetic. */
2315
2316 i = 0;
2317 value(d2) = value(d);
2318 k0 = k;
2319 ilim0 = ilim;
2320 ieps = 2; /* conservative */
2321 if (k > 0) {
2322 ds = tens[k&0xf];
2323 j = (unsigned int)k >> 4;
2324 if (j & Bletch) {
2325 /* prevent overflows */
2326 j &= Bletch - 1;
2327 value(d) /= bigtens[n_bigtens-1];
2328 ieps++;
2329 }
2330 for(; j; j = (unsigned int)j >> 1, i++)
2331 if (j & 1) {
2332 ieps++;
2333 ds *= bigtens[i];
2334 }
2335 value(d) /= ds;
2336 }
2337 else if ((jj1 = -k) != 0) {
2338 value(d) *= tens[jj1 & 0xf];
2339 for(j = (unsigned int)jj1 >> 4; j;
2340 j = (unsigned int)j >> 1, i++)
2341 if (j & 1) {
2342 ieps++;
2343 value(d) *= bigtens[i];
2344 }
2345 }
2346 if (k_check && value(d) < 1. && ilim > 0) {
2347 if (ilim1 <= 0)
2348 goto fast_failed;
2349 ilim = ilim1;
2350 k--;
2351 value(d) *= 10.;
2352 ieps++;
2353 }
2354 value(eps) = ieps*value(d) + 7.;
2355 word0(eps) -= (P-1)*Exp_msk1;
2356 if (ilim == 0) {
2357 S = mhi = 0;
2358 value(d) -= 5.;
2359 if (value(d) > value(eps))
2360 goto one_digit;
2361 if (value(d) < -value(eps))
2362 goto no_digits;
2363 goto fast_failed;
2364 }
2365 #ifndef No_leftright
2366 if (leftright) {
2367 /* Use Steele & White method of only
2368 * generating digits needed.
2369 */
2370 value(eps) = 0.5/tens[ilim-1] - value(eps);
2371 for(i = 0;;) {
2372 L = value(d);
2373 value(d) -= L;
2374 *s++ = '0' + (int)L;
2375 if (value(d) < value(eps))
2376 goto ret1;
2377 if (1. - value(d) < value(eps))
2378 goto bump_up;
2379 if (++i >= ilim)
2380 break;
2381 value(eps) *= 10.;
2382 value(d) *= 10.;
2383 }
2384 }
2385 else {
2386 #endif
2387 /* Generate ilim digits, then fix them up. */
2388 value(eps) *= tens[ilim-1];
2389 for(i = 1;; i++, value(d) *= 10.) {
2390 L = value(d);
2391 value(d) -= L;
2392 *s++ = '0' + (int)L;
2393 if (i == ilim) {
2394 if (value(d) > 0.5 + value(eps))
2395 goto bump_up;
2396 else if (value(d) < 0.5 - value(eps)) {
2397 while(*--s == '0');
2398 s++;
2399 goto ret1;
2400 }
2401 break;
2402 }
2403 }
2404 #ifndef No_leftright
2405 }
2406 #endif
2407 fast_failed:
2408 s = s0;
2409 value(d) = value(d2);
2410 k = k0;
2411 ilim = ilim0;
2412 }
2413
2414 /* Do we have a "small" integer? */
2415
2416 if (be >= 0 && k <= Int_max) {
2417 /* Yes. */
2418 ds = tens[k];
2419 if (ndigits < 0 && ilim <= 0) {
2420 S = mhi = 0;
2421 if (ilim < 0 || value(d) <= 5*ds)
2422 goto no_digits;
2423 goto one_digit;
2424 }
2425 for(i = 1;; i++) {
2426 L = value(d) / ds;
2427 value(d) -= L*ds;
2428 #ifdef Check_FLT_ROUNDS
2429 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2430 if (value(d) < 0) {
2431 L--;
2432 value(d) += ds;
2433 }
2434 #endif
2435 *s++ = '0' + (int)L;
2436 if (i == ilim) {
2437 value(d) += value(d);
2438 if (value(d) > ds || (value(d) == ds && L & 1)) {
2439 bump_up:
2440 while(*--s == '9')
2441 if (s == s0) {
2442 k++;
2443 *s = '0';
2444 break;
2445 }
2446 ++*s++;
2447 }
2448 break;
2449 }
2450 if (!(value(d) *= 10.))
2451 break;
2452 }
2453 goto ret1;
2454 }
2455
2456 m2 = b2;
2457 m5 = b5;
2458 mhi = mlo = 0;
2459 if (leftright) {
2460 if (mode < 2) {
2461 i =
2462 #ifndef Sudden_Underflow
2463 denorm ? be + (Bias + (P-1) - 1 + 1) :
2464 #endif
2465 #ifdef IBM
2466 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2467 #else
2468 1 + P - bbits;
2469 #endif
2470 }
2471 else {
2472 j = ilim - 1;
2473 if (m5 >= j)
2474 m5 -= j;
2475 else {
2476 s5 += j -= m5;
2477 b5 += j;
2478 m5 = 0;
2479 }
2480 if ((i = ilim) < 0) {
2481 m2 -= i;
2482 i = 0;
2483 }
2484 }
2485 b2 += i;
2486 s2 += i;
2487 mhi = i2b(1);
2488 }
2489 if (m2 > 0 && s2 > 0) {
2490 i = m2 < s2 ? m2 : s2;
2491 b2 -= i;
2492 m2 -= i;
2493 s2 -= i;
2494 }
2495 if (b5 > 0) {
2496 if (leftright) {
2497 if (m5 > 0) {
2498 mhi = pow5mult(mhi, m5);
2499 b1 = mult(mhi, b);
2500 Bfree(b);
2501 b = b1;
2502 }
2503 if ((j = b5 - m5) != 0)
2504 b = pow5mult(b, j);
2505 }
2506 else
2507 b = pow5mult(b, b5);
2508 }
2509 S = i2b(1);
2510 if (s5 > 0)
2511 S = pow5mult(S, s5);
2512
2513 /* Check for special case that d is a normalized power of 2. */
2514
2515 if (mode < 2) {
2516 if (!word1(d) && !(word0(d) & Bndry_mask)
2517 #ifndef Sudden_Underflow
2518 && word0(d) & Exp_mask
2519 #endif
2520 ) {
2521 /* The special case */
2522 b2 += Log2P;
2523 s2 += Log2P;
2524 spec_case = 1;
2525 }
2526 else
2527 spec_case = 0;
2528 }
2529
2530 /* Arrange for convenient computation of quotients:
2531 * shift left if necessary so divisor has 4 leading 0 bits.
2532 *
2533 * Perhaps we should just compute leading 28 bits of S once
2534 * and for all and pass them and a shift to quorem, so it
2535 * can do shifts and ors to compute the numerator for q.
2536 */
2537 if (S == BIGINT_INVALID) {
2538 i = 0;
2539 } else {
2540 #ifdef Pack_32
2541 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
2542 i = 32 - i;
2543 #else
2544 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
2545 i = 16 - i;
2546 #endif
2547 }
2548
2549 if (i > 4) {
2550 i -= 4;
2551 b2 += i;
2552 m2 += i;
2553 s2 += i;
2554 }
2555 else if (i < 4) {
2556 i += 28;
2557 b2 += i;
2558 m2 += i;
2559 s2 += i;
2560 }
2561 if (b2 > 0)
2562 b = lshift(b, b2);
2563 if (s2 > 0)
2564 S = lshift(S, s2);
2565 if (k_check) {
2566 if (cmp(b,S) < 0) {
2567 k--;
2568 b = multadd(b, 10, 0); /* we botched the k estimate */
2569 if (leftright)
2570 mhi = multadd(mhi, 10, 0);
2571 ilim = ilim1;
2572 }
2573 }
2574 if (ilim <= 0 && mode > 2) {
2575 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
2576 /* no digits, fcvt style */
2577 no_digits:
2578 k = -1 - ndigits;
2579 goto ret;
2580 }
2581 one_digit:
2582 *s++ = '1';
2583 k++;
2584 goto ret;
2585 }
2586 if (leftright) {
2587 if (m2 > 0)
2588 mhi = lshift(mhi, m2);
2589
2590 /* Compute mlo -- check for special case
2591 * that d is a normalized power of 2.
2592 */
2593
2594 mlo = mhi;
2595 if (spec_case) {
2596 mhi = Balloc(mhi->k);
2597 Bcopy(mhi, mlo);
2598 mhi = lshift(mhi, Log2P);
2599 }
2600
2601 for(i = 1;;i++) {
2602 dig = quorem(b,S) + '0';
2603 /* Do we yet have the shortest decimal string
2604 * that will round to d?
2605 */
2606 j = cmp(b, mlo);
2607 delta = diff(S, mhi);
2608 jj1 = delta->sign ? 1 : cmp(b, delta);
2609 Bfree(delta);
2610 #ifndef ROUND_BIASED
2611 if (jj1 == 0 && !mode && !(word1(d) & 1)) {
2612 if (dig == '9')
2613 goto round_9_up;
2614 if (j > 0)
2615 dig++;
2616 *s++ = dig;
2617 goto ret;
2618 }
2619 #endif
2620 if (j < 0 || (j == 0 && !mode
2621 #ifndef ROUND_BIASED
2622 && !(word1(d) & 1)
2623 #endif
2624 )) {
2625 if (jj1 > 0) {
2626 b = lshift(b, 1);
2627 jj1 = cmp(b, S);
2628 if ((jj1 > 0 || (jj1 == 0 && dig & 1))
2629 && dig++ == '9')
2630 goto round_9_up;
2631 }
2632 *s++ = dig;
2633 goto ret;
2634 }
2635 if (jj1 > 0) {
2636 if (dig == '9') { /* possible if i == 1 */
2637 round_9_up:
2638 *s++ = '9';
2639 goto roundoff;
2640 }
2641 *s++ = dig + 1;
2642 goto ret;
2643 }
2644 *s++ = dig;
2645 if (i == ilim)
2646 break;
2647 b = multadd(b, 10, 0);
2648 if (mlo == mhi)
2649 mlo = mhi = multadd(mhi, 10, 0);
2650 else {
2651 mlo = multadd(mlo, 10, 0);
2652 mhi = multadd(mhi, 10, 0);
2653 }
2654 }
2655 }
2656 else
2657 for(i = 1;; i++) {
2658 *s++ = dig = quorem(b,S) + '0';
2659 if (i >= ilim)
2660 break;
2661 b = multadd(b, 10, 0);
2662 }
2663
2664 /* Round off last digit */
2665
2666 b = lshift(b, 1);
2667 j = cmp(b, S);
2668 if (j > 0 || (j == 0 && dig & 1)) {
2669 roundoff:
2670 while(*--s == '9')
2671 if (s == s0) {
2672 k++;
2673 *s++ = '1';
2674 goto ret;
2675 }
2676 ++*s++;
2677 }
2678 else {
2679 while(*--s == '0');
2680 s++;
2681 }
2682 ret:
2683 Bfree(S);
2684 if (mhi) {
2685 if (mlo && mlo != mhi)
2686 Bfree(mlo);
2687 Bfree(mhi);
2688 }
2689 ret1:
2690 Bfree(b);
2691 if (s == s0) { /* don't return empty string */
2692 *s++ = '0';
2693 k = 0;
2694 }
2695 *s = 0;
2696 *decpt = k + 1;
2697 if (rve)
2698 *rve = s;
2699 return s0;
2700 }
2701 #ifdef __cplusplus
2702 }
2703 #endif
2704