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1/****************************************************************
2 *
3 * The author of this software is David M. Gay.
4 *
5 * Copyright (c) 1991 by AT&T.
6 *
7 * Permission to use, copy, modify, and distribute this software for any
8 * purpose without fee is hereby granted, provided that this entire notice
9 * is included in all copies of any software which is or includes a copy
10 * or modification of this software and in all copies of the supporting
11 * documentation for such software.
12 *
13 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
14 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
15 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
16 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
17 *
18 ***************************************************************/
19
20/* Please send bug reports to
21 David M. Gay
22 AT&T Bell Laboratories, Room 2C-463
23 600 Mountain Avenue
24 Murray Hill, NJ 07974-2070
25 U.S.A.
26 dmg@research.att.com or research!dmg
27 */
28
29/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
30 *
31 * This strtod returns a nearest machine number to the input decimal
32 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
33 * broken by the IEEE round-even rule. Otherwise ties are broken by
34 * biased rounding (add half and chop).
35 *
36 * Inspired loosely by William D. Clinger's paper "How to Read Floating
37 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
38 *
39 * Modifications:
40 *
41 * 1. We only require IEEE, IBM, or VAX double-precision
42 * arithmetic (not IEEE double-extended).
43 * 2. We get by with floating-point arithmetic in a case that
44 * Clinger missed -- when we're computing d * 10^n
45 * for a small integer d and the integer n is not too
46 * much larger than 22 (the maximum integer k for which
47 * we can represent 10^k exactly), we may be able to
48 * compute (d*10^k) * 10^(e-k) with just one roundoff.
49 * 3. Rather than a bit-at-a-time adjustment of the binary
50 * result in the hard case, we use floating-point
51 * arithmetic to determine the adjustment to within
52 * one bit; only in really hard cases do we need to
53 * compute a second residual.
54 * 4. Because of 3., we don't need a large table of powers of 10
55 * for ten-to-e (just some small tables, e.g. of 10^k
56 * for 0 <= k <= 22).
57 */
58
59/*
60 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
61 * significant byte has the lowest address.
62 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
63 * significant byte has the lowest address.
64 * #define Long int on machines with 32-bit ints and 64-bit longs.
65 * #define Sudden_Underflow for IEEE-format machines without gradual
66 * underflow (i.e., that flush to zero on underflow).
67 * #define IBM for IBM mainframe-style floating-point arithmetic.
68 * #define VAX for VAX-style floating-point arithmetic.
69 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
70 * #define No_leftright to omit left-right logic in fast floating-point
71 * computation of dtoa.
72 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
73 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
74 * that use extended-precision instructions to compute rounded
75 * products and quotients) with IBM.
76 * #define ROUND_BIASED for IEEE-format with biased rounding.
77 * #define Inaccurate_Divide for IEEE-format with correctly rounded
78 * products but inaccurate quotients, e.g., for Intel i860.
79 * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
80 * integer arithmetic. Whether this speeds things up or slows things
81 * down depends on the machine and the number being converted.
82 * #define KR_headers for old-style C function headers.
83 * #define Bad_float_h if your system lacks a float.h or if it does not
84 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
85 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
86 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
87 * if memory is available and otherwise does something you deem
88 * appropriate. If MALLOC is undefined, malloc will be invoked
89 * directly -- and assumed always to succeed.
90 */
91
92#if defined(LIBC_SCCS) && !defined(lint)
93static char *rcsid = "$OpenBSD: strtod.c,v 1.19 2004/02/03 16:52:11 drahn Exp $";
94#endif /* LIBC_SCCS and not lint */
95
96#if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \
97 defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \
98 defined(__powerpc__) || defined(__m88k__) || defined(__hppa__) || \
99 defined(__x86_64__) || (defined(__arm__) && defined(__VFP_FP__))
100#include <sys/types.h>
101#if BYTE_ORDER == BIG_ENDIAN
102#define IEEE_BIG_ENDIAN
103#else
104#define IEEE_LITTLE_ENDIAN
105#endif
106#endif
107
108#if defined(__arm__) && !defined(__VFP_FP__)
109/*
110 * Although the CPU is little endian the FP has different
111 * byte and word endianness. The byte order is still little endian
112 * but the word order is big endian.
113 */
114#define IEEE_BIG_ENDIAN
115#endif
116
117#ifdef __vax__
118#define VAX
119#endif
120
121#define Long int32_t
122#define ULong u_int32_t
123
124#ifdef DEBUG
125#include "stdio.h"
126#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
127#endif
128
129#ifdef __cplusplus
130#include "malloc.h"
131#include "memory.h"
132#else
133#ifndef KR_headers
134#include "stdlib.h"
135#include "string.h"
136#include "locale.h"
137#else
138#include "malloc.h"
139#include "memory.h"
140#endif
141#endif
142
143#ifdef MALLOC
144#ifdef KR_headers
145extern char *MALLOC();
146#else
147extern void *MALLOC(size_t);
148#endif
149#else
150#define MALLOC malloc
151#endif
152
153#include "ctype.h"
154#include "errno.h"
155
156#ifdef Bad_float_h
157#ifdef IEEE_BIG_ENDIAN
158#define IEEE_ARITHMETIC
159#endif
160#ifdef IEEE_LITTLE_ENDIAN
161#define IEEE_ARITHMETIC
162#endif
163
164#ifdef IEEE_ARITHMETIC
165#define DBL_DIG 15
166#define DBL_MAX_10_EXP 308
167#define DBL_MAX_EXP 1024
168#define FLT_RADIX 2
169#define FLT_ROUNDS 1
170#define DBL_MAX 1.7976931348623157e+308
171#endif
172
173#ifdef IBM
174#define DBL_DIG 16
175#define DBL_MAX_10_EXP 75
176#define DBL_MAX_EXP 63
177#define FLT_RADIX 16
178#define FLT_ROUNDS 0
179#define DBL_MAX 7.2370055773322621e+75
180#endif
181
182#ifdef VAX
183#define DBL_DIG 16
184#define DBL_MAX_10_EXP 38
185#define DBL_MAX_EXP 127
186#define FLT_RADIX 2
187#define FLT_ROUNDS 1
188#define DBL_MAX 1.7014118346046923e+38
189#endif
190
191#ifndef LONG_MAX
192#define LONG_MAX 2147483647
193#endif
194#else
195#include "float.h"
196#endif
197#ifndef __MATH_H__
198#include "math.h"
199#endif
200
201#ifdef __cplusplus
202extern "C" {
203#endif
204
205#ifndef CONST
206#ifdef KR_headers
207#define CONST /* blank */
208#else
209#define CONST const
210#endif
211#endif
212
213#ifdef Unsigned_Shifts
214#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
215#else
216#define Sign_Extend(a,b) /*no-op*/
217#endif
218
219#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
220 defined(IBM) != 1
221Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
222IBM should be defined.
223#endif
224
225typedef union {
226 double d;
227 ULong ul[2];
228} _double;
229#define value(x) ((x).d)
230#ifdef IEEE_LITTLE_ENDIAN
231#define word0(x) ((x).ul[1])
232#define word1(x) ((x).ul[0])
233#else
234#define word0(x) ((x).ul[0])
235#define word1(x) ((x).ul[1])
236#endif
237
238/* The following definition of Storeinc is appropriate for MIPS processors.
239 * An alternative that might be better on some machines is
240 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
241 */
242#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
243#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
244((unsigned short *)a)[0] = (unsigned short)c, a++)
245#else
246#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
247((unsigned short *)a)[1] = (unsigned short)c, a++)
248#endif
249
250/* #define P DBL_MANT_DIG */
251/* Ten_pmax = floor(P*log(2)/log(5)) */
252/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
253/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
254/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
255
256#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
257#define Exp_shift 20
258#define Exp_shift1 20
259#define Exp_msk1 0x100000
260#define Exp_msk11 0x100000
261#define Exp_mask 0x7ff00000
262#define P 53
263#define Bias 1023
264#define IEEE_Arith
265#define Emin (-1022)
266#define Exp_1 0x3ff00000
267#define Exp_11 0x3ff00000
268#define Ebits 11
269#define Frac_mask 0xfffff
270#define Frac_mask1 0xfffff
271#define Ten_pmax 22
272#define Bletch 0x10
273#define Bndry_mask 0xfffff
274#define Bndry_mask1 0xfffff
275#define LSB 1
276#define Sign_bit 0x80000000
277#define Log2P 1
278#define Tiny0 0
279#define Tiny1 1
280#define Quick_max 14
281#define Int_max 14
282#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
283#else
284#undef Sudden_Underflow
285#define Sudden_Underflow
286#ifdef IBM
287#define Exp_shift 24
288#define Exp_shift1 24
289#define Exp_msk1 0x1000000
290#define Exp_msk11 0x1000000
291#define Exp_mask 0x7f000000
292#define P 14
293#define Bias 65
294#define Exp_1 0x41000000
295#define Exp_11 0x41000000
296#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
297#define Frac_mask 0xffffff
298#define Frac_mask1 0xffffff
299#define Bletch 4
300#define Ten_pmax 22
301#define Bndry_mask 0xefffff
302#define Bndry_mask1 0xffffff
303#define LSB 1
304#define Sign_bit 0x80000000
305#define Log2P 4
306#define Tiny0 0x100000
307#define Tiny1 0
308#define Quick_max 14
309#define Int_max 15
310#else /* VAX */
311#define Exp_shift 23
312#define Exp_shift1 7
313#define Exp_msk1 0x80
314#define Exp_msk11 0x800000
315#define Exp_mask 0x7f80
316#define P 56
317#define Bias 129
318#define Exp_1 0x40800000
319#define Exp_11 0x4080
320#define Ebits 8
321#define Frac_mask 0x7fffff
322#define Frac_mask1 0xffff007f
323#define Ten_pmax 24
324#define Bletch 2
325#define Bndry_mask 0xffff007f
326#define Bndry_mask1 0xffff007f
327#define LSB 0x10000
328#define Sign_bit 0x8000
329#define Log2P 1
330#define Tiny0 0x80
331#define Tiny1 0
332#define Quick_max 15
333#define Int_max 15
334#endif
335#endif
336
337#ifndef IEEE_Arith
338#define ROUND_BIASED
339#endif
340
341#ifdef RND_PRODQUOT
342#define rounded_product(a,b) a = rnd_prod(a, b)
343#define rounded_quotient(a,b) a = rnd_quot(a, b)
344#ifdef KR_headers
345extern double rnd_prod(), rnd_quot();
346#else
347extern double rnd_prod(double, double), rnd_quot(double, double);
348#endif
349#else
350#define rounded_product(a,b) a *= b
351#define rounded_quotient(a,b) a /= b
352#endif
353
354#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
355#define Big1 0xffffffff
356
357#ifndef Just_16
358/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
359 * This makes some inner loops simpler and sometimes saves work
360 * during multiplications, but it often seems to make things slightly
361 * slower. Hence the default is now to store 32 bits per Long.
362 */
363#ifndef Pack_32
364#define Pack_32
365#endif
366#endif
367
368#define Kmax 15
369
370#ifdef __cplusplus
371extern "C" double strtod(const char *s00, char **se);
372extern "C" char *__dtoa(double d, int mode, int ndigits,
373 int *decpt, int *sign, char **rve);
374#endif
375
376 struct
377Bigint {
378 struct Bigint *next;
379 int k, maxwds, sign, wds;
380 ULong x[1];
381 };
382
383 typedef struct Bigint Bigint;
384
385 static Bigint *freelist[Kmax+1];
386
387 static Bigint *
388Balloc
389#ifdef KR_headers
390 (k) int k;
391#else
392 (int k)
393#endif
394{
395 int x;
396 Bigint *rv;
397
398 if ((rv = freelist[k])) {
399 freelist[k] = rv->next;
400 }
401 else {
402 x = 1 << k;
403 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
404 rv->k = k;
405 rv->maxwds = x;
406 }
407 rv->sign = rv->wds = 0;
408 return rv;
409 }
410
411 static void
412Bfree
413#ifdef KR_headers
414 (v) Bigint *v;
415#else
416 (Bigint *v)
417#endif
418{
419 if (v) {
420 v->next = freelist[v->k];
421 freelist[v->k] = v;
422 }
423 }
424
425#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
426y->wds*sizeof(Long) + 2*sizeof(int))
427
428 static Bigint *
429multadd
430#ifdef KR_headers
431 (b, m, a) Bigint *b; int m, a;
432#else
433 (Bigint *b, int m, int a) /* multiply by m and add a */
434#endif
435{
436 int i, wds;
437 ULong *x, y;
438#ifdef Pack_32
439 ULong xi, z;
440#endif
441 Bigint *b1;
442
443 wds = b->wds;
444 x = b->x;
445 i = 0;
446 do {
447#ifdef Pack_32
448 xi = *x;
449 y = (xi & 0xffff) * m + a;
450 z = (xi >> 16) * m + (y >> 16);
451 a = (int)(z >> 16);
452 *x++ = (z << 16) + (y & 0xffff);
453#else
454 y = *x * m + a;
455 a = (int)(y >> 16);
456 *x++ = y & 0xffff;
457#endif
458 }
459 while(++i < wds);
460 if (a) {
461 if (wds >= b->maxwds) {
462 b1 = Balloc(b->k+1);
463 Bcopy(b1, b);
464 Bfree(b);
465 b = b1;
466 }
467 b->x[wds++] = a;
468 b->wds = wds;
469 }
470 return b;
471 }
472
473 static Bigint *
474s2b
475#ifdef KR_headers
476 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
477#else
478 (CONST char *s, int nd0, int nd, ULong y9)
479#endif
480{
481 Bigint *b;
482 int i, k;
483 Long x, y;
484
485 x = (nd + 8) / 9;
486 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
487#ifdef Pack_32
488 b = Balloc(k);
489 b->x[0] = y9;
490 b->wds = 1;
491#else
492 b = Balloc(k+1);
493 b->x[0] = y9 & 0xffff;
494 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
495#endif
496
497 i = 9;
498 if (9 < nd0) {
499 s += 9;
500 do b = multadd(b, 10, *s++ - '0');
501 while(++i < nd0);
502 s++;
503 }
504 else
505 s += 10;
506 for(; i < nd; i++)
507 b = multadd(b, 10, *s++ - '0');
508 return b;
509 }
510
511 static int
512hi0bits
513#ifdef KR_headers
514 (x) register ULong x;
515#else
516 (register ULong x)
517#endif
518{
519 register int k = 0;
520
521 if (!(x & 0xffff0000)) {
522 k = 16;
523 x <<= 16;
524 }
525 if (!(x & 0xff000000)) {
526 k += 8;
527 x <<= 8;
528 }
529 if (!(x & 0xf0000000)) {
530 k += 4;
531 x <<= 4;
532 }
533 if (!(x & 0xc0000000)) {
534 k += 2;
535 x <<= 2;
536 }
537 if (!(x & 0x80000000)) {
538 k++;
539 if (!(x & 0x40000000))
540 return 32;
541 }
542 return k;
543 }
544
545 static int
546lo0bits
547#ifdef KR_headers
548 (y) ULong *y;
549#else
550 (ULong *y)
551#endif
552{
553 register int k;
554 register ULong x = *y;
555
556 if (x & 7) {
557 if (x & 1)
558 return 0;
559 if (x & 2) {
560 *y = x >> 1;
561 return 1;
562 }
563 *y = x >> 2;
564 return 2;
565 }
566 k = 0;
567 if (!(x & 0xffff)) {
568 k = 16;
569 x >>= 16;
570 }
571 if (!(x & 0xff)) {
572 k += 8;
573 x >>= 8;
574 }
575 if (!(x & 0xf)) {
576 k += 4;
577 x >>= 4;
578 }
579 if (!(x & 0x3)) {
580 k += 2;
581 x >>= 2;
582 }
583 if (!(x & 1)) {
584 k++;
585 x >>= 1;
586 if (!x & 1)
587 return 32;
588 }
589 *y = x;
590 return k;
591 }
592
593 static Bigint *
594i2b
595#ifdef KR_headers
596 (i) int i;
597#else
598 (int i)
599#endif
600{
601 Bigint *b;
602
603 b = Balloc(1);
604 b->x[0] = i;
605 b->wds = 1;
606 return b;
607 }
608
609 static Bigint *
610mult
611#ifdef KR_headers
612 (a, b) Bigint *a, *b;
613#else
614 (Bigint *a, Bigint *b)
615#endif
616{
617 Bigint *c;
618 int k, wa, wb, wc;
619 ULong carry, y, z;
620 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
621#ifdef Pack_32
622 ULong z2;
623#endif
624
625 if (a->wds < b->wds) {
626 c = a;
627 a = b;
628 b = c;
629 }
630 k = a->k;
631 wa = a->wds;
632 wb = b->wds;
633 wc = wa + wb;
634 if (wc > a->maxwds)
635 k++;
636 c = Balloc(k);
637 for(x = c->x, xa = x + wc; x < xa; x++)
638 *x = 0;
639 xa = a->x;
640 xae = xa + wa;
641 xb = b->x;
642 xbe = xb + wb;
643 xc0 = c->x;
644#ifdef Pack_32
645 for(; xb < xbe; xb++, xc0++) {
646 if ((y = *xb & 0xffff)) {
647 x = xa;
648 xc = xc0;
649 carry = 0;
650 do {
651 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
652 carry = z >> 16;
653 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
654 carry = z2 >> 16;
655 Storeinc(xc, z2, z);
656 }
657 while(x < xae);
658 *xc = carry;
659 }
660 if ((y = *xb >> 16)) {
661 x = xa;
662 xc = xc0;
663 carry = 0;
664 z2 = *xc;
665 do {
666 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
667 carry = z >> 16;
668 Storeinc(xc, z, z2);
669 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
670 carry = z2 >> 16;
671 }
672 while(x < xae);
673 *xc = z2;
674 }
675 }
676#else
677 for(; xb < xbe; xc0++) {
678 if (y = *xb++) {
679 x = xa;
680 xc = xc0;
681 carry = 0;
682 do {
683 z = *x++ * y + *xc + carry;
684 carry = z >> 16;
685 *xc++ = z & 0xffff;
686 }
687 while(x < xae);
688 *xc = carry;
689 }
690 }
691#endif
692 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
693 c->wds = wc;
694 return c;
695 }
696
697 static Bigint *p5s;
698
699 static Bigint *
700pow5mult
701#ifdef KR_headers
702 (b, k) Bigint *b; int k;
703#else
704 (Bigint *b, int k)
705#endif
706{
707 Bigint *b1, *p5, *p51;
708 int i;
709 static int p05[3] = { 5, 25, 125 };
710
711 if ((i = k & 3))
712 b = multadd(b, p05[i-1], 0);
713
714 if (!(k >>= 2))
715 return b;
716 if (!(p5 = p5s)) {
717 /* first time */
718 p5 = p5s = i2b(625);
719 p5->next = 0;
720 }
721 for(;;) {
722 if (k & 1) {
723 b1 = mult(b, p5);
724 Bfree(b);
725 b = b1;
726 }
727 if (!(k >>= 1))
728 break;
729 if (!(p51 = p5->next)) {
730 p51 = p5->next = mult(p5,p5);
731 p51->next = 0;
732 }
733 p5 = p51;
734 }
735 return b;
736 }
737
738 static Bigint *
739lshift
740#ifdef KR_headers
741 (b, k) Bigint *b; int k;
742#else
743 (Bigint *b, int k)
744#endif
745{
746 int i, k1, n, n1;
747 Bigint *b1;
748 ULong *x, *x1, *xe, z;
749
750#ifdef Pack_32
751 n = k >> 5;
752#else
753 n = k >> 4;
754#endif
755 k1 = b->k;
756 n1 = n + b->wds + 1;
757 for(i = b->maxwds; n1 > i; i <<= 1)
758 k1++;
759 b1 = Balloc(k1);
760 x1 = b1->x;
761 for(i = 0; i < n; i++)
762 *x1++ = 0;
763 x = b->x;
764 xe = x + b->wds;
765#ifdef Pack_32
766 if (k &= 0x1f) {
767 k1 = 32 - k;
768 z = 0;
769 do {
770 *x1++ = *x << k | z;
771 z = *x++ >> k1;
772 }
773 while(x < xe);
774 if ((*x1 = z))
775 ++n1;
776 }
777#else
778 if (k &= 0xf) {
779 k1 = 16 - k;
780 z = 0;
781 do {
782 *x1++ = *x << k & 0xffff | z;
783 z = *x++ >> k1;
784 }
785 while(x < xe);
786 if (*x1 = z)
787 ++n1;
788 }
789#endif
790 else do
791 *x1++ = *x++;
792 while(x < xe);
793 b1->wds = n1 - 1;
794 Bfree(b);
795 return b1;
796 }
797
798 static int
799cmp
800#ifdef KR_headers
801 (a, b) Bigint *a, *b;
802#else
803 (Bigint *a, Bigint *b)
804#endif
805{
806 ULong *xa, *xa0, *xb, *xb0;
807 int i, j;
808
809 i = a->wds;
810 j = b->wds;
811#ifdef DEBUG
812 if (i > 1 && !a->x[i-1])
813 Bug("cmp called with a->x[a->wds-1] == 0");
814 if (j > 1 && !b->x[j-1])
815 Bug("cmp called with b->x[b->wds-1] == 0");
816#endif
817 if (i -= j)
818 return i;
819 xa0 = a->x;
820 xa = xa0 + j;
821 xb0 = b->x;
822 xb = xb0 + j;
823 for(;;) {
824 if (*--xa != *--xb)
825 return *xa < *xb ? -1 : 1;
826 if (xa <= xa0)
827 break;
828 }
829 return 0;
830 }
831
832 static Bigint *
833diff
834#ifdef KR_headers
835 (a, b) Bigint *a, *b;
836#else
837 (Bigint *a, Bigint *b)
838#endif
839{
840 Bigint *c;
841 int i, wa, wb;
842 Long borrow, y; /* We need signed shifts here. */
843 ULong *xa, *xae, *xb, *xbe, *xc;
844#ifdef Pack_32
845 Long z;
846#endif
847
848 i = cmp(a,b);
849 if (!i) {
850 c = Balloc(0);
851 c->wds = 1;
852 c->x[0] = 0;
853 return c;
854 }
855 if (i < 0) {
856 c = a;
857 a = b;
858 b = c;
859 i = 1;
860 }
861 else
862 i = 0;
863 c = Balloc(a->k);
864 c->sign = i;
865 wa = a->wds;
866 xa = a->x;
867 xae = xa + wa;
868 wb = b->wds;
869 xb = b->x;
870 xbe = xb + wb;
871 xc = c->x;
872 borrow = 0;
873#ifdef Pack_32
874 do {
875 y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
876 borrow = y >> 16;
877 Sign_Extend(borrow, y);
878 z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
879 borrow = z >> 16;
880 Sign_Extend(borrow, z);
881 Storeinc(xc, z, y);
882 }
883 while(xb < xbe);
884 while(xa < xae) {
885 y = (*xa & 0xffff) + borrow;
886 borrow = y >> 16;
887 Sign_Extend(borrow, y);
888 z = (*xa++ >> 16) + borrow;
889 borrow = z >> 16;
890 Sign_Extend(borrow, z);
891 Storeinc(xc, z, y);
892 }
893#else
894 do {
895 y = *xa++ - *xb++ + borrow;
896 borrow = y >> 16;
897 Sign_Extend(borrow, y);
898 *xc++ = y & 0xffff;
899 }
900 while(xb < xbe);
901 while(xa < xae) {
902 y = *xa++ + borrow;
903 borrow = y >> 16;
904 Sign_Extend(borrow, y);
905 *xc++ = y & 0xffff;
906 }
907#endif
908 while(!*--xc)
909 wa--;
910 c->wds = wa;
911 return c;
912 }
913
914 static double
915ulp
916#ifdef KR_headers
917 (_x) double _x;
918#else
919 (double _x)
920#endif
921{
922 _double x;
923 register Long L;
924 _double a;
925
926 value(x) = _x;
927 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
928#ifndef Sudden_Underflow
929 if (L > 0) {
930#endif
931#ifdef IBM
932 L |= Exp_msk1 >> 4;
933#endif
934 word0(a) = L;
935 word1(a) = 0;
936#ifndef Sudden_Underflow
937 }
938 else {
939 L = -L >> Exp_shift;
940 if (L < Exp_shift) {
941 word0(a) = 0x80000 >> L;
942 word1(a) = 0;
943 }
944 else {
945 word0(a) = 0;
946 L -= Exp_shift;
947 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
948 }
949 }
950#endif
951 return value(a);
952 }
953
954 static double
955b2d
956#ifdef KR_headers
957 (a, e) Bigint *a; int *e;
958#else
959 (Bigint *a, int *e)
960#endif
961{
962 ULong *xa, *xa0, w, y, z;
963 int k;
964 _double d;
965#ifdef VAX
966 ULong d0, d1;
967#else
968#define d0 word0(d)
969#define d1 word1(d)
970#endif
971
972 xa0 = a->x;
973 xa = xa0 + a->wds;
974 y = *--xa;
975#ifdef DEBUG
976 if (!y) Bug("zero y in b2d");
977#endif
978 k = hi0bits(y);
979 *e = 32 - k;
980#ifdef Pack_32
981 if (k < Ebits) {
982 d0 = Exp_1 | y >> Ebits - k;
983 w = xa > xa0 ? *--xa : 0;
984 d1 = y << (32-Ebits) + k | w >> Ebits - k;
985 goto ret_d;
986 }
987 z = xa > xa0 ? *--xa : 0;
988 if (k -= Ebits) {
989 d0 = Exp_1 | y << k | z >> 32 - k;
990 y = xa > xa0 ? *--xa : 0;
991 d1 = z << k | y >> 32 - k;
992 }
993 else {
994 d0 = Exp_1 | y;
995 d1 = z;
996 }
997#else
998 if (k < Ebits + 16) {
999 z = xa > xa0 ? *--xa : 0;
1000 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1001 w = xa > xa0 ? *--xa : 0;
1002 y = xa > xa0 ? *--xa : 0;
1003 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1004 goto ret_d;
1005 }
1006 z = xa > xa0 ? *--xa : 0;
1007 w = xa > xa0 ? *--xa : 0;
1008 k -= Ebits + 16;
1009 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1010 y = xa > xa0 ? *--xa : 0;
1011 d1 = w << k + 16 | y << k;
1012#endif
1013 ret_d:
1014#ifdef VAX
1015 word0(d) = d0 >> 16 | d0 << 16;
1016 word1(d) = d1 >> 16 | d1 << 16;
1017#else
1018#undef d0
1019#undef d1
1020#endif
1021 return value(d);
1022 }
1023
1024 static Bigint *
1025d2b
1026#ifdef KR_headers
1027 (_d, e, bits) double d; int *e, *bits;
1028#else
1029 (double _d, int *e, int *bits)
1030#endif
1031{
1032 Bigint *b;
1033 int de, i, k;
1034 ULong *x, y, z;
1035 _double d;
1036#ifdef VAX
1037 ULong d0, d1;
1038#endif
1039
1040 value(d) = _d;
1041#ifdef VAX
1042 d0 = word0(d) >> 16 | word0(d) << 16;
1043 d1 = word1(d) >> 16 | word1(d) << 16;
1044#else
1045#define d0 word0(d)
1046#define d1 word1(d)
1047#endif
1048
1049#ifdef Pack_32
1050 b = Balloc(1);
1051#else
1052 b = Balloc(2);
1053#endif
1054 x = b->x;
1055
1056 z = d0 & Frac_mask;
1057 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1058#ifdef Sudden_Underflow
1059 de = (int)(d0 >> Exp_shift);
1060#ifndef IBM
1061 z |= Exp_msk11;
1062#endif
1063#else
1064 if (de = (int)(d0 >> Exp_shift))
1065 z |= Exp_msk1;
1066#endif
1067#ifdef Pack_32
1068 if (y = d1) {
1069 if (k = lo0bits(&y)) {
1070 x[0] = y | z << 32 - k;
1071 z >>= k;
1072 }
1073 else
1074 x[0] = y;
1075 i = b->wds = (x[1] = z) ? 2 : 1;
1076 }
1077 else {
1078#ifdef DEBUG
1079 if (!z)
1080 Bug("Zero passed to d2b");
1081#endif
1082 k = lo0bits(&z);
1083 x[0] = z;
1084 i = b->wds = 1;
1085 k += 32;
1086 }
1087#else
1088 if (y = d1) {
1089 if (k = lo0bits(&y))
1090 if (k >= 16) {
1091 x[0] = y | z << 32 - k & 0xffff;
1092 x[1] = z >> k - 16 & 0xffff;
1093 x[2] = z >> k;
1094 i = 2;
1095 }
1096 else {
1097 x[0] = y & 0xffff;
1098 x[1] = y >> 16 | z << 16 - k & 0xffff;
1099 x[2] = z >> k & 0xffff;
1100 x[3] = z >> k+16;
1101 i = 3;
1102 }
1103 else {
1104 x[0] = y & 0xffff;
1105 x[1] = y >> 16;
1106 x[2] = z & 0xffff;
1107 x[3] = z >> 16;
1108 i = 3;
1109 }
1110 }
1111 else {
1112#ifdef DEBUG
1113 if (!z)
1114 Bug("Zero passed to d2b");
1115#endif
1116 k = lo0bits(&z);
1117 if (k >= 16) {
1118 x[0] = z;
1119 i = 0;
1120 }
1121 else {
1122 x[0] = z & 0xffff;
1123 x[1] = z >> 16;
1124 i = 1;
1125 }
1126 k += 32;
1127 }
1128 while(!x[i])
1129 --i;
1130 b->wds = i + 1;
1131#endif
1132#ifndef Sudden_Underflow
1133 if (de) {
1134#endif
1135#ifdef IBM
1136 *e = (de - Bias - (P-1) << 2) + k;
1137 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1138#else
1139 *e = de - Bias - (P-1) + k;
1140 *bits = P - k;
1141#endif
1142#ifndef Sudden_Underflow
1143 }
1144 else {
1145 *e = de - Bias - (P-1) + 1 + k;
1146#ifdef Pack_32
1147 *bits = 32*i - hi0bits(x[i-1]);
1148#else
1149 *bits = (i+2)*16 - hi0bits(x[i]);
1150#endif
1151 }
1152#endif
1153 return b;
1154 }
1155#undef d0
1156#undef d1
1157
1158 static double
1159ratio
1160#ifdef KR_headers
1161 (a, b) Bigint *a, *b;
1162#else
1163 (Bigint *a, Bigint *b)
1164#endif
1165{
1166 _double da, db;
1167 int k, ka, kb;
1168
1169 value(da) = b2d(a, &ka);
1170 value(db) = b2d(b, &kb);
1171#ifdef Pack_32
1172 k = ka - kb + 32*(a->wds - b->wds);
1173#else
1174 k = ka - kb + 16*(a->wds - b->wds);
1175#endif
1176#ifdef IBM
1177 if (k > 0) {
1178 word0(da) += (k >> 2)*Exp_msk1;
1179 if (k &= 3)
1180 da *= 1 << k;
1181 }
1182 else {
1183 k = -k;
1184 word0(db) += (k >> 2)*Exp_msk1;
1185 if (k &= 3)
1186 db *= 1 << k;
1187 }
1188#else
1189 if (k > 0)
1190 word0(da) += k*Exp_msk1;
1191 else {
1192 k = -k;
1193 word0(db) += k*Exp_msk1;
1194 }
1195#endif
1196 return value(da) / value(db);
1197 }
1198
1199static CONST double
1200tens[] = {
1201 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1202 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1203 1e20, 1e21, 1e22
1204#ifdef VAX
1205 , 1e23, 1e24
1206#endif
1207 };
1208
1209#ifdef IEEE_Arith
1210static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1211static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1212#define n_bigtens 5
1213#else
1214#ifdef IBM
1215static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
1216static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1217#define n_bigtens 3
1218#else
1219static CONST double bigtens[] = { 1e16, 1e32 };
1220static CONST double tinytens[] = { 1e-16, 1e-32 };
1221#define n_bigtens 2
1222#endif
1223#endif
1224
1225 double
1226strtod
1227#ifdef KR_headers
1228 (s00, se) CONST char *s00; char **se;
1229#else
1230 (CONST char *s00, char **se)
1231#endif
1232{
1233 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1234 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1235 CONST char *s, *s0, *s1;
1236 double aadj, aadj1, adj;
1237 _double rv, rv0;
1238 Long L;
1239 ULong y, z;
1240 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1241
1242#ifndef KR_headers
1243 CONST char decimal_point = localeconv()->decimal_point[0];
1244#else
1245 CONST char decimal_point = '.';
1246#endif
1247
1248 sign = nz0 = nz = 0;
1249 value(rv) = 0.;
1250
1251
1252 for(s = s00; isspace((unsigned char) *s); s++)
1253 ;
1254
1255 if (*s == '-') {
1256 sign = 1;
1257 s++;
1258 } else if (*s == '+') {
1259 s++;
1260 }
1261
1262 if (*s == '\0') {
1263 s = s00;
1264 goto ret;
1265 }
1266
1267 if (*s == '0') {
1268 nz0 = 1;
1269 while(*++s == '0') ;
1270 if (!*s)
1271 goto ret;
1272 }
1273 s0 = s;
1274 y = z = 0;
1275 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1276 if (nd < 9)
1277 y = 10*y + c - '0';
1278 else if (nd < 16)
1279 z = 10*z + c - '0';
1280 nd0 = nd;
1281 if (c == decimal_point) {
1282 c = *++s;
1283 if (!nd) {
1284 for(; c == '0'; c = *++s)
1285 nz++;
1286 if (c > '0' && c <= '9') {
1287 s0 = s;
1288 nf += nz;
1289 nz = 0;
1290 goto have_dig;
1291 }
1292 goto dig_done;
1293 }
1294 for(; c >= '0' && c <= '9'; c = *++s) {
1295 have_dig:
1296 nz++;
1297 if (c -= '0') {
1298 nf += nz;
1299 for(i = 1; i < nz; i++)
1300 if (nd++ < 9)
1301 y *= 10;
1302 else if (nd <= DBL_DIG + 1)
1303 z *= 10;
1304 if (nd++ < 9)
1305 y = 10*y + c;
1306 else if (nd <= DBL_DIG + 1)
1307 z = 10*z + c;
1308 nz = 0;
1309 }
1310 }
1311 }
1312 dig_done:
1313 e = 0;
1314 if (c == 'e' || c == 'E') {
1315 if (!nd && !nz && !nz0) {
1316 s = s00;
1317 goto ret;
1318 }
1319 s00 = s;
1320 esign = 0;
1321 switch(c = *++s) {
1322 case '-':
1323 esign = 1;
1324 case '+':
1325 c = *++s;
1326 }
1327 if (c >= '0' && c <= '9') {
1328 while(c == '0')
1329 c = *++s;
1330 if (c > '0' && c <= '9') {
1331 L = c - '0';
1332 s1 = s;
1333 while((c = *++s) >= '0' && c <= '9')
1334 L = 10*L + c - '0';
1335 if (s - s1 > 8 || L > 19999)
1336 /* Avoid confusion from exponents
1337 * so large that e might overflow.
1338 */
1339 e = 19999; /* safe for 16 bit ints */
1340 else
1341 e = (int)L;
1342 if (esign)
1343 e = -e;
1344 }
1345 else
1346 e = 0;
1347 }
1348 else
1349 s = s00;
1350 }
1351 if (!nd) {
1352 if (!nz && !nz0)
1353 s = s00;
1354 goto ret;
1355 }
1356 e1 = e -= nf;
1357
1358 /* Now we have nd0 digits, starting at s0, followed by a
1359 * decimal point, followed by nd-nd0 digits. The number we're
1360 * after is the integer represented by those digits times
1361 * 10**e */
1362
1363 if (!nd0)
1364 nd0 = nd;
1365 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1366 value(rv) = y;
1367 if (k > 9)
1368 value(rv) = tens[k - 9] * value(rv) + z;
1369 bd0 = 0;
1370 if (nd <= DBL_DIG
1371#ifndef RND_PRODQUOT
1372 && FLT_ROUNDS == 1
1373#endif
1374 ) {
1375 if (!e)
1376 goto ret;
1377 if (e > 0) {
1378 if (e <= Ten_pmax) {
1379#ifdef VAX
1380 goto vax_ovfl_check;
1381#else
1382 /* value(rv) = */ rounded_product(value(rv),
1383 tens[e]);
1384 goto ret;
1385#endif
1386 }
1387 i = DBL_DIG - nd;
1388 if (e <= Ten_pmax + i) {
1389 /* A fancier test would sometimes let us do
1390 * this for larger i values.
1391 */
1392 e -= i;
1393 value(rv) *= tens[i];
1394#ifdef VAX
1395 /* VAX exponent range is so narrow we must
1396 * worry about overflow here...
1397 */
1398 vax_ovfl_check:
1399 word0(rv) -= P*Exp_msk1;
1400 /* value(rv) = */ rounded_product(value(rv),
1401 tens[e]);
1402 if ((word0(rv) & Exp_mask)
1403 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1404 goto ovfl;
1405 word0(rv) += P*Exp_msk1;
1406#else
1407 /* value(rv) = */ rounded_product(value(rv),
1408 tens[e]);
1409#endif
1410 goto ret;
1411 }
1412 }
1413#ifndef Inaccurate_Divide
1414 else if (e >= -Ten_pmax) {
1415 /* value(rv) = */ rounded_quotient(value(rv),
1416 tens[-e]);
1417 goto ret;
1418 }
1419#endif
1420 }
1421 e1 += nd - k;
1422
1423 /* Get starting approximation = rv * 10**e1 */
1424
1425 if (e1 > 0) {
1426 if (i = e1 & 15)
1427 value(rv) *= tens[i];
1428 if (e1 &= ~15) {
1429 if (e1 > DBL_MAX_10_EXP) {
1430 ovfl:
1431 errno = ERANGE;
1432#ifndef Bad_float_h
1433 value(rv) = HUGE_VAL;
1434#else
1435 /* Can't trust HUGE_VAL */
1436#ifdef IEEE_Arith
1437 word0(rv) = Exp_mask;
1438 word1(rv) = 0;
1439#else
1440 word0(rv) = Big0;
1441 word1(rv) = Big1;
1442#endif
1443#endif
1444 if (bd0)
1445 goto retfree;
1446 goto ret;
1447 }
1448 if (e1 >>= 4) {
1449 for(j = 0; e1 > 1; j++, e1 >>= 1)
1450 if (e1 & 1)
1451 value(rv) *= bigtens[j];
1452 /* The last multiplication could overflow. */
1453 word0(rv) -= P*Exp_msk1;
1454 value(rv) *= bigtens[j];
1455 if ((z = word0(rv) & Exp_mask)
1456 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1457 goto ovfl;
1458 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1459 /* set to largest number */
1460 /* (Can't trust DBL_MAX) */
1461 word0(rv) = Big0;
1462 word1(rv) = Big1;
1463 }
1464 else
1465 word0(rv) += P*Exp_msk1;
1466 }
1467
1468 }
1469 }
1470 else if (e1 < 0) {
1471 e1 = -e1;
1472 if (i = e1 & 15)
1473 value(rv) /= tens[i];
1474 if (e1 &= ~15) {
1475 e1 >>= 4;
1476 if (e1 >= 1 << n_bigtens)
1477 goto undfl;
1478 for(j = 0; e1 > 1; j++, e1 >>= 1)
1479 if (e1 & 1)
1480 value(rv) *= tinytens[j];
1481 /* The last multiplication could underflow. */
1482 value(rv0) = value(rv);
1483 value(rv) *= tinytens[j];
1484 if (!value(rv)) {
1485 value(rv) = 2.*value(rv0);
1486 value(rv) *= tinytens[j];
1487 if (!value(rv)) {
1488 undfl:
1489 value(rv) = 0.;
1490 errno = ERANGE;
1491 if (bd0)
1492 goto retfree;
1493 goto ret;
1494 }
1495 word0(rv) = Tiny0;
1496 word1(rv) = Tiny1;
1497 /* The refinement below will clean
1498 * this approximation up.
1499 */
1500 }
1501 }
1502 }
1503
1504 /* Now the hard part -- adjusting rv to the correct value.*/
1505
1506 /* Put digits into bd: true value = bd * 10^e */
1507
1508 bd0 = s2b(s0, nd0, nd, y);
1509
1510 for(;;) {
1511 bd = Balloc(bd0->k);
1512 Bcopy(bd, bd0);
1513 bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1514 bs = i2b(1);
1515
1516 if (e >= 0) {
1517 bb2 = bb5 = 0;
1518 bd2 = bd5 = e;
1519 }
1520 else {
1521 bb2 = bb5 = -e;
1522 bd2 = bd5 = 0;
1523 }
1524 if (bbe >= 0)
1525 bb2 += bbe;
1526 else
1527 bd2 -= bbe;
1528 bs2 = bb2;
1529#ifdef Sudden_Underflow
1530#ifdef IBM
1531 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1532#else
1533 j = P + 1 - bbbits;
1534#endif
1535#else
1536 i = bbe + bbbits - 1; /* logb(rv) */
1537 if (i < Emin) /* denormal */
1538 j = bbe + (P-Emin);
1539 else
1540 j = P + 1 - bbbits;
1541#endif
1542 bb2 += j;
1543 bd2 += j;
1544 i = bb2 < bd2 ? bb2 : bd2;
1545 if (i > bs2)
1546 i = bs2;
1547 if (i > 0) {
1548 bb2 -= i;
1549 bd2 -= i;
1550 bs2 -= i;
1551 }
1552 if (bb5 > 0) {
1553 bs = pow5mult(bs, bb5);
1554 bb1 = mult(bs, bb);
1555 Bfree(bb);
1556 bb = bb1;
1557 }
1558 if (bb2 > 0)
1559 bb = lshift(bb, bb2);
1560 if (bd5 > 0)
1561 bd = pow5mult(bd, bd5);
1562 if (bd2 > 0)
1563 bd = lshift(bd, bd2);
1564 if (bs2 > 0)
1565 bs = lshift(bs, bs2);
1566 delta = diff(bb, bd);
1567 dsign = delta->sign;
1568 delta->sign = 0;
1569 i = cmp(delta, bs);
1570 if (i < 0) {
1571 /* Error is less than half an ulp -- check for
1572 * special case of mantissa a power of two.
1573 */
1574 if (dsign || word1(rv) || word0(rv) & Bndry_mask)
1575 break;
1576 delta = lshift(delta,Log2P);
1577 if (cmp(delta, bs) > 0)
1578 goto drop_down;
1579 break;
1580 }
1581 if (i == 0) {
1582 /* exactly half-way between */
1583 if (dsign) {
1584 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
1585 && word1(rv) == 0xffffffff) {
1586 /*boundary case -- increment exponent*/
1587 word0(rv) = (word0(rv) & Exp_mask)
1588 + Exp_msk1
1589#ifdef IBM
1590 | Exp_msk1 >> 4
1591#endif
1592 ;
1593 word1(rv) = 0;
1594 break;
1595 }
1596 }
1597 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
1598 drop_down:
1599 /* boundary case -- decrement exponent */
1600#ifdef Sudden_Underflow
1601 L = word0(rv) & Exp_mask;
1602#ifdef IBM
1603 if (L < Exp_msk1)
1604#else
1605 if (L <= Exp_msk1)
1606#endif
1607 goto undfl;
1608 L -= Exp_msk1;
1609#else
1610 L = (word0(rv) & Exp_mask) - Exp_msk1;
1611#endif
1612 word0(rv) = L | Bndry_mask1;
1613 word1(rv) = 0xffffffff;
1614#ifdef IBM
1615 goto cont;
1616#else
1617 break;
1618#endif
1619 }
1620#ifndef ROUND_BIASED
1621 if (!(word1(rv) & LSB))
1622 break;
1623#endif
1624 if (dsign)
1625 value(rv) += ulp(value(rv));
1626#ifndef ROUND_BIASED
1627 else {
1628 value(rv) -= ulp(value(rv));
1629#ifndef Sudden_Underflow
1630 if (!value(rv))
1631 goto undfl;
1632#endif
1633 }
1634#endif
1635 break;
1636 }
1637 if ((aadj = ratio(delta, bs)) <= 2.) {
1638 if (dsign)
1639 aadj = aadj1 = 1.;
1640 else if (word1(rv) || word0(rv) & Bndry_mask) {
1641#ifndef Sudden_Underflow
1642 if (word1(rv) == Tiny1 && !word0(rv))
1643 goto undfl;
1644#endif
1645 aadj = 1.;
1646 aadj1 = -1.;
1647 }
1648 else {
1649 /* special case -- power of FLT_RADIX to be */
1650 /* rounded down... */
1651
1652 if (aadj < 2./FLT_RADIX)
1653 aadj = 1./FLT_RADIX;
1654 else
1655 aadj *= 0.5;
1656 aadj1 = -aadj;
1657 }
1658 }
1659 else {
1660 aadj *= 0.5;
1661 aadj1 = dsign ? aadj : -aadj;
1662#ifdef Check_FLT_ROUNDS
1663 switch(FLT_ROUNDS) {
1664 case 2: /* towards +infinity */
1665 aadj1 -= 0.5;
1666 break;
1667 case 0: /* towards 0 */
1668 case 3: /* towards -infinity */
1669 aadj1 += 0.5;
1670 }
1671#else
1672 if (FLT_ROUNDS == 0)
1673 aadj1 += 0.5;
1674#endif
1675 }
1676 y = word0(rv) & Exp_mask;
1677
1678 /* Check for overflow */
1679
1680 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
1681 value(rv0) = value(rv);
1682 word0(rv) -= P*Exp_msk1;
1683 adj = aadj1 * ulp(value(rv));
1684 value(rv) += adj;
1685 if ((word0(rv) & Exp_mask) >=
1686 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
1687 if (word0(rv0) == Big0 && word1(rv0) == Big1)
1688 goto ovfl;
1689 word0(rv) = Big0;
1690 word1(rv) = Big1;
1691 goto cont;
1692 }
1693 else
1694 word0(rv) += P*Exp_msk1;
1695 }
1696 else {
1697#ifdef Sudden_Underflow
1698 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
1699 value(rv0) = value(rv);
1700 word0(rv) += P*Exp_msk1;
1701 adj = aadj1 * ulp(value(rv));
1702 value(rv) += adj;
1703#ifdef IBM
1704 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
1705#else
1706 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
1707#endif
1708 {
1709 if (word0(rv0) == Tiny0
1710 && word1(rv0) == Tiny1)
1711 goto undfl;
1712 word0(rv) = Tiny0;
1713 word1(rv) = Tiny1;
1714 goto cont;
1715 }
1716 else
1717 word0(rv) -= P*Exp_msk1;
1718 }
1719 else {
1720 adj = aadj1 * ulp(value(rv));
1721 value(rv) += adj;
1722 }
1723#else
1724 /* Compute adj so that the IEEE rounding rules will
1725 * correctly round rv + adj in some half-way cases.
1726 * If rv * ulp(rv) is denormalized (i.e.,
1727 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
1728 * trouble from bits lost to denormalization;
1729 * example: 1.2e-307 .
1730 */
1731 if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
1732 aadj1 = (double)(int)(aadj + 0.5);
1733 if (!dsign)
1734 aadj1 = -aadj1;
1735 }
1736 adj = aadj1 * ulp(value(rv));
1737 value(rv) += adj;
1738#endif
1739 }
1740 z = word0(rv) & Exp_mask;
1741 if (y == z) {
1742 /* Can we stop now? */
1743 L = aadj;
1744 aadj -= L;
1745 /* The tolerances below are conservative. */
1746 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
1747 if (aadj < .4999999 || aadj > .5000001)
1748 break;
1749 }
1750 else if (aadj < .4999999/FLT_RADIX)
1751 break;
1752 }
1753 cont:
1754 Bfree(bb);
1755 Bfree(bd);
1756 Bfree(bs);
1757 Bfree(delta);
1758 }
1759 retfree:
1760 Bfree(bb);
1761 Bfree(bd);
1762 Bfree(bs);
1763 Bfree(bd0);
1764 Bfree(delta);
1765 ret:
1766 if (se)
1767 *se = (char *)s;
1768 return sign ? -value(rv) : value(rv);
1769 }
1770
1771 static int
1772quorem
1773#ifdef KR_headers
1774 (b, S) Bigint *b, *S;
1775#else
1776 (Bigint *b, Bigint *S)
1777#endif
1778{
1779 int n;
1780 Long borrow, y;
1781 ULong carry, q, ys;
1782 ULong *bx, *bxe, *sx, *sxe;
1783#ifdef Pack_32
1784 Long z;
1785 ULong si, zs;
1786#endif
1787
1788 n = S->wds;
1789#ifdef DEBUG
1790 /*debug*/ if (b->wds > n)
1791 /*debug*/ Bug("oversize b in quorem");
1792#endif
1793 if (b->wds < n)
1794 return 0;
1795 sx = S->x;
1796 sxe = sx + --n;
1797 bx = b->x;
1798 bxe = bx + n;
1799 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1800#ifdef DEBUG
1801 /*debug*/ if (q > 9)
1802 /*debug*/ Bug("oversized quotient in quorem");
1803#endif
1804 if (q) {
1805 borrow = 0;
1806 carry = 0;
1807 do {
1808#ifdef Pack_32
1809 si = *sx++;
1810 ys = (si & 0xffff) * q + carry;
1811 zs = (si >> 16) * q + (ys >> 16);
1812 carry = zs >> 16;
1813 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1814 borrow = y >> 16;
1815 Sign_Extend(borrow, y);
1816 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1817 borrow = z >> 16;
1818 Sign_Extend(borrow, z);
1819 Storeinc(bx, z, y);
1820#else
1821 ys = *sx++ * q + carry;
1822 carry = ys >> 16;
1823 y = *bx - (ys & 0xffff) + borrow;
1824 borrow = y >> 16;
1825 Sign_Extend(borrow, y);
1826 *bx++ = y & 0xffff;
1827#endif
1828 }
1829 while(sx <= sxe);
1830 if (!*bxe) {
1831 bx = b->x;
1832 while(--bxe > bx && !*bxe)
1833 --n;
1834 b->wds = n;
1835 }
1836 }
1837 if (cmp(b, S) >= 0) {
1838 q++;
1839 borrow = 0;
1840 carry = 0;
1841 bx = b->x;
1842 sx = S->x;
1843 do {
1844#ifdef Pack_32
1845 si = *sx++;
1846 ys = (si & 0xffff) + carry;
1847 zs = (si >> 16) + (ys >> 16);
1848 carry = zs >> 16;
1849 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1850 borrow = y >> 16;
1851 Sign_Extend(borrow, y);
1852 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1853 borrow = z >> 16;
1854 Sign_Extend(borrow, z);
1855 Storeinc(bx, z, y);
1856#else
1857 ys = *sx++ + carry;
1858 carry = ys >> 16;
1859 y = *bx - (ys & 0xffff) + borrow;
1860 borrow = y >> 16;
1861 Sign_Extend(borrow, y);
1862 *bx++ = y & 0xffff;
1863#endif
1864 }
1865 while(sx <= sxe);
1866 bx = b->x;
1867 bxe = bx + n;
1868 if (!*bxe) {
1869 while(--bxe > bx && !*bxe)
1870 --n;
1871 b->wds = n;
1872 }
1873 }
1874 return q;
1875 }
1876
1877/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1878 *
1879 * Inspired by "How to Print Floating-Point Numbers Accurately" by
1880 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1881 *
1882 * Modifications:
1883 * 1. Rather than iterating, we use a simple numeric overestimate
1884 * to determine k = floor(log10(d)). We scale relevant
1885 * quantities using O(log2(k)) rather than O(k) multiplications.
1886 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1887 * try to generate digits strictly left to right. Instead, we
1888 * compute with fewer bits and propagate the carry if necessary
1889 * when rounding the final digit up. This is often faster.
1890 * 3. Under the assumption that input will be rounded nearest,
1891 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1892 * That is, we allow equality in stopping tests when the
1893 * round-nearest rule will give the same floating-point value
1894 * as would satisfaction of the stopping test with strict
1895 * inequality.
1896 * 4. We remove common factors of powers of 2 from relevant
1897 * quantities.
1898 * 5. When converting floating-point integers less than 1e16,
1899 * we use floating-point arithmetic rather than resorting
1900 * to multiple-precision integers.
1901 * 6. When asked to produce fewer than 15 digits, we first try
1902 * to get by with floating-point arithmetic; we resort to
1903 * multiple-precision integer arithmetic only if we cannot
1904 * guarantee that the floating-point calculation has given
1905 * the correctly rounded result. For k requested digits and
1906 * "uniformly" distributed input, the probability is
1907 * something like 10^(k-15) that we must resort to the Long
1908 * calculation.
1909 */
1910
1911 char *
1912__dtoa
1913#ifdef KR_headers
1914 (_d, mode, ndigits, decpt, sign, rve)
1915 double _d; int mode, ndigits, *decpt, *sign; char **rve;
1916#else
1917 (double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
1918#endif
1919{
1920 /* Arguments ndigits, decpt, sign are similar to those
1921 of ecvt and fcvt; trailing zeros are suppressed from
1922 the returned string. If not null, *rve is set to point
1923 to the end of the return value. If d is +-Infinity or NaN,
1924 then *decpt is set to 9999.
1925
1926 mode:
1927 0 ==> shortest string that yields d when read in
1928 and rounded to nearest.
1929 1 ==> like 0, but with Steele & White stopping rule;
1930 e.g. with IEEE P754 arithmetic , mode 0 gives
1931 1e23 whereas mode 1 gives 9.999999999999999e22.
1932 2 ==> max(1,ndigits) significant digits. This gives a
1933 return value similar to that of ecvt, except
1934 that trailing zeros are suppressed.
1935 3 ==> through ndigits past the decimal point. This
1936 gives a return value similar to that from fcvt,
1937 except that trailing zeros are suppressed, and
1938 ndigits can be negative.
1939 4-9 should give the same return values as 2-3, i.e.,
1940 4 <= mode <= 9 ==> same return as mode
1941 2 + (mode & 1). These modes are mainly for
1942 debugging; often they run slower but sometimes
1943 faster than modes 2-3.
1944 4,5,8,9 ==> left-to-right digit generation.
1945 6-9 ==> don't try fast floating-point estimate
1946 (if applicable).
1947
1948 Values of mode other than 0-9 are treated as mode 0.
1949
1950 Sufficient space is allocated to the return value
1951 to hold the suppressed trailing zeros.
1952 */
1953
1954 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
1955 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1956 spec_case, try_quick;
1957 Long L;
1958#ifndef Sudden_Underflow
1959 int denorm;
1960 ULong x;
1961#endif
1962 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
1963 double ds;
1964 char *s, *s0;
1965 static Bigint *result;
1966 static int result_k;
1967 _double d, d2, eps;
1968
1969 value(d) = _d;
1970 if (result) {
1971 result->k = result_k;
1972 result->maxwds = 1 << result_k;
1973 Bfree(result);
1974 result = 0;
1975 }
1976
1977 if (word0(d) & Sign_bit) {
1978 /* set sign for everything, including 0's and NaNs */
1979 *sign = 1;
1980 word0(d) &= ~Sign_bit; /* clear sign bit */
1981 }
1982 else
1983 *sign = 0;
1984
1985#if defined(IEEE_Arith) + defined(VAX)
1986#ifdef IEEE_Arith
1987 if ((word0(d) & Exp_mask) == Exp_mask)
1988#else
1989 if (word0(d) == 0x8000)
1990#endif
1991 {
1992 /* Infinity or NaN */
1993 *decpt = 9999;
1994 s =
1995#ifdef IEEE_Arith
1996 !word1(d) && !(word0(d) & 0xfffff) ? ndigits < 8 ? "Inf" : "Infinity" :
1997#endif
1998 "NaN";
1999 if (rve)
2000 *rve =
2001#ifdef IEEE_Arith
2002 s[3] ? s + 8 :
2003#endif
2004 s + 3;
2005 return s;
2006 }
2007#endif
2008#ifdef IBM
2009 value(d) += 0; /* normalize */
2010#endif
2011 if (!value(d)) {
2012 *decpt = 1;
2013 s = "0";
2014 if (rve)
2015 *rve = s + 1;
2016 return s;
2017 }
2018
2019 b = d2b(value(d), &be, &bbits);
2020#ifdef Sudden_Underflow
2021 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2022#else
2023 if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
2024#endif
2025 value(d2) = value(d);
2026 word0(d2) &= Frac_mask1;
2027 word0(d2) |= Exp_11;
2028#ifdef IBM
2029 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2030 value(d2) /= 1 << j;
2031#endif
2032
2033 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2034 * log10(x) = log(x) / log(10)
2035 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2036 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2037 *
2038 * This suggests computing an approximation k to log10(d) by
2039 *
2040 * k = (i - Bias)*0.301029995663981
2041 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2042 *
2043 * We want k to be too large rather than too small.
2044 * The error in the first-order Taylor series approximation
2045 * is in our favor, so we just round up the constant enough
2046 * to compensate for any error in the multiplication of
2047 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2048 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2049 * adding 1e-13 to the constant term more than suffices.
2050 * Hence we adjust the constant term to 0.1760912590558.
2051 * (We could get a more accurate k by invoking log10,
2052 * but this is probably not worthwhile.)
2053 */
2054
2055 i -= Bias;
2056#ifdef IBM
2057 i <<= 2;
2058 i += j;
2059#endif
2060#ifndef Sudden_Underflow
2061 denorm = 0;
2062 }
2063 else {
2064 /* d is denormalized */
2065
2066 i = bbits + be + (Bias + (P-1) - 1);
2067 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2068 : word1(d) << 32 - i;
2069 value(d2) = x;
2070 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2071 i -= (Bias + (P-1) - 1) + 1;
2072 denorm = 1;
2073 }
2074#endif
2075 ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 +
2076 i*0.301029995663981;
2077 k = (int)ds;
2078 if (ds < 0. && ds != k)
2079 k--; /* want k = floor(ds) */
2080 k_check = 1;
2081 if (k >= 0 && k <= Ten_pmax) {
2082 if (value(d) < tens[k])
2083 k--;
2084 k_check = 0;
2085 }
2086 j = bbits - i - 1;
2087 if (j >= 0) {
2088 b2 = 0;
2089 s2 = j;
2090 }
2091 else {
2092 b2 = -j;
2093 s2 = 0;
2094 }
2095 if (k >= 0) {
2096 b5 = 0;
2097 s5 = k;
2098 s2 += k;
2099 }
2100 else {
2101 b2 -= k;
2102 b5 = -k;
2103 s5 = 0;
2104 }
2105 if (mode < 0 || mode > 9)
2106 mode = 0;
2107 try_quick = 1;
2108 if (mode > 5) {
2109 mode -= 4;
2110 try_quick = 0;
2111 }
2112 leftright = 1;
2113 switch(mode) {
2114 case 0:
2115 case 1:
2116 ilim = ilim1 = -1;
2117 i = 18;
2118 ndigits = 0;
2119 break;
2120 case 2:
2121 leftright = 0;
2122 /* no break */
2123 case 4:
2124 if (ndigits <= 0)
2125 ndigits = 1;
2126 ilim = ilim1 = i = ndigits;
2127 break;
2128 case 3:
2129 leftright = 0;
2130 /* no break */
2131 case 5:
2132 i = ndigits + k + 1;
2133 ilim = i;
2134 ilim1 = i - 1;
2135 if (i <= 0)
2136 i = 1;
2137 }
2138 j = sizeof(ULong);
2139 for(result_k = 0; sizeof(Bigint) - sizeof(ULong) + j <= i;
2140 j <<= 1) result_k++;
2141 result = Balloc(result_k);
2142 s = s0 = (char *)result;
2143
2144 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2145
2146 /* Try to get by with floating-point arithmetic. */
2147
2148 i = 0;
2149 value(d2) = value(d);
2150 k0 = k;
2151 ilim0 = ilim;
2152 ieps = 2; /* conservative */
2153 if (k > 0) {
2154 ds = tens[k&0xf];
2155 j = k >> 4;
2156 if (j & Bletch) {
2157 /* prevent overflows */
2158 j &= Bletch - 1;
2159 value(d) /= bigtens[n_bigtens-1];
2160 ieps++;
2161 }
2162 for(; j; j >>= 1, i++)
2163 if (j & 1) {
2164 ieps++;
2165 ds *= bigtens[i];
2166 }
2167 value(d) /= ds;
2168 }
2169 else if (j1 = -k) {
2170 value(d) *= tens[j1 & 0xf];
2171 for(j = j1 >> 4; j; j >>= 1, i++)
2172 if (j & 1) {
2173 ieps++;
2174 value(d) *= bigtens[i];
2175 }
2176 }
2177 if (k_check && value(d) < 1. && ilim > 0) {
2178 if (ilim1 <= 0)
2179 goto fast_failed;
2180 ilim = ilim1;
2181 k--;
2182 value(d) *= 10.;
2183 ieps++;
2184 }
2185 value(eps) = ieps*value(d) + 7.;
2186 word0(eps) -= (P-1)*Exp_msk1;
2187 if (ilim == 0) {
2188 S = mhi = 0;
2189 value(d) -= 5.;
2190 if (value(d) > value(eps))
2191 goto one_digit;
2192 if (value(d) < -value(eps))
2193 goto no_digits;
2194 goto fast_failed;
2195 }
2196#ifndef No_leftright
2197 if (leftright) {
2198 /* Use Steele & White method of only
2199 * generating digits needed.
2200 */
2201 value(eps) = 0.5/tens[ilim-1] - value(eps);
2202 for(i = 0;;) {
2203 L = value(d);
2204 value(d) -= L;
2205 *s++ = '0' + (int)L;
2206 if (value(d) < value(eps))
2207 goto ret1;
2208 if (1. - value(d) < value(eps))
2209 goto bump_up;
2210 if (++i >= ilim)
2211 break;
2212 value(eps) *= 10.;
2213 value(d) *= 10.;
2214 }
2215 }
2216 else {
2217#endif
2218 /* Generate ilim digits, then fix them up. */
2219 value(eps) *= tens[ilim-1];
2220 for(i = 1;; i++, value(d) *= 10.) {
2221 L = value(d);
2222 value(d) -= L;
2223 *s++ = '0' + (int)L;
2224 if (i == ilim) {
2225 if (value(d) > 0.5 + value(eps))
2226 goto bump_up;
2227 else if (value(d) < 0.5 - value(eps)) {
2228 while(*--s == '0');
2229 s++;
2230 goto ret1;
2231 }
2232 break;
2233 }
2234 }
2235#ifndef No_leftright
2236 }
2237#endif
2238 fast_failed:
2239 s = s0;
2240 value(d) = value(d2);
2241 k = k0;
2242 ilim = ilim0;
2243 }
2244
2245 /* Do we have a "small" integer? */
2246
2247 if (be >= 0 && k <= Int_max) {
2248 /* Yes. */
2249 ds = tens[k];
2250 if (ndigits < 0 && ilim <= 0) {
2251 S = mhi = 0;
2252 if (ilim < 0 || value(d) <= 5*ds)
2253 goto no_digits;
2254 goto one_digit;
2255 }
2256 for(i = 1;; i++) {
2257 L = value(d) / ds;
2258 value(d) -= L*ds;
2259#ifdef Check_FLT_ROUNDS
2260 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2261 if (value(d) < 0) {
2262 L--;
2263 value(d) += ds;
2264 }
2265#endif
2266 *s++ = '0' + (int)L;
2267 if (i == ilim) {
2268 value(d) += value(d);
2269 if (value(d) > ds || value(d) == ds && L & 1) {
2270 bump_up:
2271 while(*--s == '9')
2272 if (s == s0) {
2273 k++;
2274 *s = '0';
2275 break;
2276 }
2277 ++*s++;
2278 }
2279 break;
2280 }
2281 if (!(value(d) *= 10.))
2282 break;
2283 }
2284 goto ret1;
2285 }
2286
2287 m2 = b2;
2288 m5 = b5;
2289 mhi = mlo = 0;
2290 if (leftright) {
2291 if (mode < 2) {
2292 i =
2293#ifndef Sudden_Underflow
2294 denorm ? be + (Bias + (P-1) - 1 + 1) :
2295#endif
2296#ifdef IBM
2297 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2298#else
2299 1 + P - bbits;
2300#endif
2301 }
2302 else {
2303 j = ilim - 1;
2304 if (m5 >= j)
2305 m5 -= j;
2306 else {
2307 s5 += j -= m5;
2308 b5 += j;
2309 m5 = 0;
2310 }
2311 if ((i = ilim) < 0) {
2312 m2 -= i;
2313 i = 0;
2314 }
2315 }
2316 b2 += i;
2317 s2 += i;
2318 mhi = i2b(1);
2319 }
2320 if (m2 > 0 && s2 > 0) {
2321 i = m2 < s2 ? m2 : s2;
2322 b2 -= i;
2323 m2 -= i;
2324 s2 -= i;
2325 }
2326 if (b5 > 0) {
2327 if (leftright) {
2328 if (m5 > 0) {
2329 mhi = pow5mult(mhi, m5);
2330 b1 = mult(mhi, b);
2331 Bfree(b);
2332 b = b1;
2333 }
2334 if (j = b5 - m5)
2335 b = pow5mult(b, j);
2336 }
2337 else
2338 b = pow5mult(b, b5);
2339 }
2340 S = i2b(1);
2341 if (s5 > 0)
2342 S = pow5mult(S, s5);
2343
2344 /* Check for special case that d is a normalized power of 2. */
2345
2346 if (mode < 2) {
2347 if (!word1(d) && !(word0(d) & Bndry_mask)
2348#ifndef Sudden_Underflow
2349 && word0(d) & Exp_mask
2350#endif
2351 ) {
2352 /* The special case */
2353 b2 += Log2P;
2354 s2 += Log2P;
2355 spec_case = 1;
2356 }
2357 else
2358 spec_case = 0;
2359 }
2360
2361 /* Arrange for convenient computation of quotients:
2362 * shift left if necessary so divisor has 4 leading 0 bits.
2363 *
2364 * Perhaps we should just compute leading 28 bits of S once
2365 * and for all and pass them and a shift to quorem, so it
2366 * can do shifts and ors to compute the numerator for q.
2367 */
2368#ifdef Pack_32
2369 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
2370 i = 32 - i;
2371#else
2372 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
2373 i = 16 - i;
2374#endif
2375 if (i > 4) {
2376 i -= 4;
2377 b2 += i;
2378 m2 += i;
2379 s2 += i;
2380 }
2381 else if (i < 4) {
2382 i += 28;
2383 b2 += i;
2384 m2 += i;
2385 s2 += i;
2386 }
2387 if (b2 > 0)
2388 b = lshift(b, b2);
2389 if (s2 > 0)
2390 S = lshift(S, s2);
2391 if (k_check) {
2392 if (cmp(b,S) < 0) {
2393 k--;
2394 b = multadd(b, 10, 0); /* we botched the k estimate */
2395 if (leftright)
2396 mhi = multadd(mhi, 10, 0);
2397 ilim = ilim1;
2398 }
2399 }
2400 if (ilim <= 0 && mode > 2) {
2401 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
2402 /* no digits, fcvt style */
2403 no_digits:
2404 k = -1 - ndigits;
2405 goto ret;
2406 }
2407 one_digit:
2408 *s++ = '1';
2409 k++;
2410 goto ret;
2411 }
2412 if (leftright) {
2413 if (m2 > 0)
2414 mhi = lshift(mhi, m2);
2415
2416 /* Compute mlo -- check for special case
2417 * that d is a normalized power of 2.
2418 */
2419
2420 mlo = mhi;
2421 if (spec_case) {
2422 mhi = Balloc(mhi->k);
2423 Bcopy(mhi, mlo);
2424 mhi = lshift(mhi, Log2P);
2425 }
2426
2427 for(i = 1;;i++) {
2428 dig = quorem(b,S) + '0';
2429 /* Do we yet have the shortest decimal string
2430 * that will round to d?
2431 */
2432 j = cmp(b, mlo);
2433 delta = diff(S, mhi);
2434 j1 = delta->sign ? 1 : cmp(b, delta);
2435 Bfree(delta);
2436#ifndef ROUND_BIASED
2437 if (j1 == 0 && !mode && !(word1(d) & 1)) {
2438 if (dig == '9')
2439 goto round_9_up;
2440 if (j > 0)
2441 dig++;
2442 *s++ = dig;
2443 goto ret;
2444 }
2445#endif
2446 if (j < 0 || j == 0 && !mode
2447#ifndef ROUND_BIASED
2448 && !(word1(d) & 1)
2449#endif
2450 ) {
2451 if (j1 > 0) {
2452 b = lshift(b, 1);
2453 j1 = cmp(b, S);
2454 if ((j1 > 0 || j1 == 0 && dig & 1)
2455 && dig++ == '9')
2456 goto round_9_up;
2457 }
2458 *s++ = dig;
2459 goto ret;
2460 }
2461 if (j1 > 0) {
2462 if (dig == '9') { /* possible if i == 1 */
2463 round_9_up:
2464 *s++ = '9';
2465 goto roundoff;
2466 }
2467 *s++ = dig + 1;
2468 goto ret;
2469 }
2470 *s++ = dig;
2471 if (i == ilim)
2472 break;
2473 b = multadd(b, 10, 0);
2474 if (mlo == mhi)
2475 mlo = mhi = multadd(mhi, 10, 0);
2476 else {
2477 mlo = multadd(mlo, 10, 0);
2478 mhi = multadd(mhi, 10, 0);
2479 }
2480 }
2481 }
2482 else
2483 for(i = 1;; i++) {
2484 *s++ = dig = quorem(b,S) + '0';
2485 if (i >= ilim)
2486 break;
2487 b = multadd(b, 10, 0);
2488 }
2489
2490 /* Round off last digit */
2491
2492 b = lshift(b, 1);
2493 j = cmp(b, S);
2494 if (j > 0 || j == 0 && dig & 1) {
2495 roundoff:
2496 while(*--s == '9')
2497 if (s == s0) {
2498 k++;
2499 *s++ = '1';
2500 goto ret;
2501 }
2502 ++*s++;
2503 }
2504 else {
2505 while(*--s == '0');
2506 s++;
2507 }
2508 ret:
2509 Bfree(S);
2510 if (mhi) {
2511 if (mlo && mlo != mhi)
2512 Bfree(mlo);
2513 Bfree(mhi);
2514 }
2515 ret1:
2516 Bfree(b);
2517 if (s == s0) { /* don't return empty string */
2518 *s++ = '0';
2519 k = 0;
2520 }
2521 *s = 0;
2522 *decpt = k + 1;
2523 if (rve)
2524 *rve = s;
2525 return s0;
2526 }
2527#ifdef __cplusplus
2528}
2529#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-29 22:36:24 +0000