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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 1.15 2002/02/19 19:39:37 millert 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#include <sys/types.h>
100#if BYTE_ORDER == BIG_ENDIAN
101#define IEEE_BIG_ENDIAN
102#else
103#define IEEE_LITTLE_ENDIAN
104#endif
105#endif
106
107#ifdef __arm32__
108/*
109 * Although the CPU is little endian the FP has different
110 * byte and word endianness. The byte order is still little endian
111 * but the word order is big endian.
112 */
113#define IEEE_BIG_ENDIAN
114#endif
115
116#ifdef __vax__
117#define VAX
118#endif
119
120#define Long int32_t
121#define ULong u_int32_t
122
123#ifdef DEBUG
124#include "stdio.h"
125#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
126#endif
127
128#ifdef __cplusplus
129#include "malloc.h"
130#include "memory.h"
131#else
132#ifndef KR_headers
133#include "stdlib.h"
134#include "string.h"
135#include "locale.h"
136#else
137#include "malloc.h"
138#include "memory.h"
139#endif
140#endif
141
142#ifdef MALLOC
143#ifdef KR_headers
144extern char *MALLOC();
145#else
146extern void *MALLOC(size_t);
147#endif
148#else
149#define MALLOC malloc
150#endif
151
152#include "ctype.h"
153#include "errno.h"
154
155#ifdef Bad_float_h
156#ifdef IEEE_BIG_ENDIAN
157#define IEEE_ARITHMETIC
158#endif
159#ifdef IEEE_LITTLE_ENDIAN
160#define IEEE_ARITHMETIC
161#endif
162
163#ifdef IEEE_ARITHMETIC
164#define DBL_DIG 15
165#define DBL_MAX_10_EXP 308
166#define DBL_MAX_EXP 1024
167#define FLT_RADIX 2
168#define FLT_ROUNDS 1
169#define DBL_MAX 1.7976931348623157e+308
170#endif
171
172#ifdef IBM
173#define DBL_DIG 16
174#define DBL_MAX_10_EXP 75
175#define DBL_MAX_EXP 63
176#define FLT_RADIX 16
177#define FLT_ROUNDS 0
178#define DBL_MAX 7.2370055773322621e+75
179#endif
180
181#ifdef VAX
182#define DBL_DIG 16
183#define DBL_MAX_10_EXP 38
184#define DBL_MAX_EXP 127
185#define FLT_RADIX 2
186#define FLT_ROUNDS 1
187#define DBL_MAX 1.7014118346046923e+38
188#endif
189
190#ifndef LONG_MAX
191#define LONG_MAX 2147483647
192#endif
193#else
194#include "float.h"
195#endif
196#ifndef __MATH_H__
197#include "math.h"
198#endif
199
200#ifdef __cplusplus
201extern "C" {
202#endif
203
204#ifndef CONST
205#ifdef KR_headers
206#define CONST /* blank */
207#else
208#define CONST const
209#endif
210#endif
211
212#ifdef Unsigned_Shifts
213#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
214#else
215#define Sign_Extend(a,b) /*no-op*/
216#endif
217
218#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
219 defined(IBM) != 1
220Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
221IBM should be defined.
222#endif
223
224typedef union {
225 double d;
226 ULong ul[2];
227} _double;
228#define value(x) ((x).d)
229#ifdef IEEE_LITTLE_ENDIAN
230#define word0(x) ((x).ul[1])
231#define word1(x) ((x).ul[0])
232#else
233#define word0(x) ((x).ul[0])
234#define word1(x) ((x).ul[1])
235#endif
236
237/* The following definition of Storeinc is appropriate for MIPS processors.
238 * An alternative that might be better on some machines is
239 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
240 */
241#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm32__)
242#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
243((unsigned short *)a)[0] = (unsigned short)c, a++)
244#else
245#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
246((unsigned short *)a)[1] = (unsigned short)c, a++)
247#endif
248
249/* #define P DBL_MANT_DIG */
250/* Ten_pmax = floor(P*log(2)/log(5)) */
251/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
252/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
253/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
254
255#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
256#define Exp_shift 20
257#define Exp_shift1 20
258#define Exp_msk1 0x100000
259#define Exp_msk11 0x100000
260#define Exp_mask 0x7ff00000
261#define P 53
262#define Bias 1023
263#define IEEE_Arith
264#define Emin (-1022)
265#define Exp_1 0x3ff00000
266#define Exp_11 0x3ff00000
267#define Ebits 11
268#define Frac_mask 0xfffff
269#define Frac_mask1 0xfffff
270#define Ten_pmax 22
271#define Bletch 0x10
272#define Bndry_mask 0xfffff
273#define Bndry_mask1 0xfffff
274#define LSB 1
275#define Sign_bit 0x80000000
276#define Log2P 1
277#define Tiny0 0
278#define Tiny1 1
279#define Quick_max 14
280#define Int_max 14
281#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
282#else
283#undef Sudden_Underflow
284#define Sudden_Underflow
285#ifdef IBM
286#define Exp_shift 24
287#define Exp_shift1 24
288#define Exp_msk1 0x1000000
289#define Exp_msk11 0x1000000
290#define Exp_mask 0x7f000000
291#define P 14
292#define Bias 65
293#define Exp_1 0x41000000
294#define Exp_11 0x41000000
295#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
296#define Frac_mask 0xffffff
297#define Frac_mask1 0xffffff
298#define Bletch 4
299#define Ten_pmax 22
300#define Bndry_mask 0xefffff
301#define Bndry_mask1 0xffffff
302#define LSB 1
303#define Sign_bit 0x80000000
304#define Log2P 4
305#define Tiny0 0x100000
306#define Tiny1 0
307#define Quick_max 14
308#define Int_max 15
309#else /* VAX */
310#define Exp_shift 23
311#define Exp_shift1 7
312#define Exp_msk1 0x80
313#define Exp_msk11 0x800000
314#define Exp_mask 0x7f80
315#define P 56
316#define Bias 129
317#define Exp_1 0x40800000
318#define Exp_11 0x4080
319#define Ebits 8
320#define Frac_mask 0x7fffff
321#define Frac_mask1 0xffff007f
322#define Ten_pmax 24
323#define Bletch 2
324#define Bndry_mask 0xffff007f
325#define Bndry_mask1 0xffff007f
326#define LSB 0x10000
327#define Sign_bit 0x8000
328#define Log2P 1
329#define Tiny0 0x80
330#define Tiny1 0
331#define Quick_max 15
332#define Int_max 15
333#endif
334#endif
335
336#ifndef IEEE_Arith
337#define ROUND_BIASED
338#endif
339
340#ifdef RND_PRODQUOT
341#define rounded_product(a,b) a = rnd_prod(a, b)
342#define rounded_quotient(a,b) a = rnd_quot(a, b)
343#ifdef KR_headers
344extern double rnd_prod(), rnd_quot();
345#else
346extern double rnd_prod(double, double), rnd_quot(double, double);
347#endif
348#else
349#define rounded_product(a,b) a *= b
350#define rounded_quotient(a,b) a /= b
351#endif
352
353#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
354#define Big1 0xffffffff
355
356#ifndef Just_16
357/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
358 * This makes some inner loops simpler and sometimes saves work
359 * during multiplications, but it often seems to make things slightly
360 * slower. Hence the default is now to store 32 bits per Long.
361 */
362#ifndef Pack_32
363#define Pack_32
364#endif
365#endif
366
367#define Kmax 15
368
369#ifdef __cplusplus
370extern "C" double strtod(const char *s00, char **se);
371extern "C" char *__dtoa(double d, int mode, int ndigits,
372 int *decpt, int *sign, char **rve);
373#endif
374
375 struct
376Bigint {
377 struct Bigint *next;
378 int k, maxwds, sign, wds;
379 ULong x[1];
380 };
381
382 typedef struct Bigint Bigint;
383
384 static Bigint *freelist[Kmax+1];
385
386 static Bigint *
387Balloc
388#ifdef KR_headers
389 (k) int k;
390#else
391 (int k)
392#endif
393{
394 int x;
395 Bigint *rv;
396
397 if ((rv = freelist[k])) {
398 freelist[k] = rv->next;
399 }
400 else {
401 x = 1 << k;
402 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
403 rv->k = k;
404 rv->maxwds = x;
405 }
406 rv->sign = rv->wds = 0;
407 return rv;
408 }
409
410 static void
411Bfree
412#ifdef KR_headers
413 (v) Bigint *v;
414#else
415 (Bigint *v)
416#endif
417{
418 if (v) {
419 v->next = freelist[v->k];
420 freelist[v->k] = v;
421 }
422 }
423
424#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
425y->wds*sizeof(Long) + 2*sizeof(int))
426
427 static Bigint *
428multadd
429#ifdef KR_headers
430 (b, m, a) Bigint *b; int m, a;
431#else
432 (Bigint *b, int m, int a) /* multiply by m and add a */
433#endif
434{
435 int i, wds;
436 ULong *x, y;
437#ifdef Pack_32
438 ULong xi, z;
439#endif
440 Bigint *b1;
441
442 wds = b->wds;
443 x = b->x;
444 i = 0;
445 do {
446#ifdef Pack_32
447 xi = *x;
448 y = (xi & 0xffff) * m + a;
449 z = (xi >> 16) * m + (y >> 16);
450 a = (int)(z >> 16);
451 *x++ = (z << 16) + (y & 0xffff);
452#else
453 y = *x * m + a;
454 a = (int)(y >> 16);
455 *x++ = y & 0xffff;
456#endif
457 }
458 while(++i < wds);
459 if (a) {
460 if (wds >= b->maxwds) {
461 b1 = Balloc(b->k+1);
462 Bcopy(b1, b);
463 Bfree(b);
464 b = b1;
465 }
466 b->x[wds++] = a;
467 b->wds = wds;
468 }
469 return b;
470 }
471
472 static Bigint *
473s2b
474#ifdef KR_headers
475 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
476#else
477 (CONST char *s, int nd0, int nd, ULong y9)
478#endif
479{
480 Bigint *b;
481 int i, k;
482 Long x, y;
483
484 x = (nd + 8) / 9;
485 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
486#ifdef Pack_32
487 b = Balloc(k);
488 b->x[0] = y9;
489 b->wds = 1;
490#else
491 b = Balloc(k+1);
492 b->x[0] = y9 & 0xffff;
493 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
494#endif
495
496 i = 9;
497 if (9 < nd0) {
498 s += 9;
499 do b = multadd(b, 10, *s++ - '0');
500 while(++i < nd0);
501 s++;
502 }
503 else
504 s += 10;
505 for(; i < nd; i++)
506 b = multadd(b, 10, *s++ - '0');
507 return b;
508 }
509
510 static int
511hi0bits
512#ifdef KR_headers
513 (x) register ULong x;
514#else
515 (register ULong x)
516#endif
517{
518 register int k = 0;
519
520 if (!(x & 0xffff0000)) {
521 k = 16;
522 x <<= 16;
523 }
524 if (!(x & 0xff000000)) {
525 k += 8;
526 x <<= 8;
527 }
528 if (!(x & 0xf0000000)) {
529 k += 4;
530 x <<= 4;
531 }
532 if (!(x & 0xc0000000)) {
533 k += 2;
534 x <<= 2;
535 }
536 if (!(x & 0x80000000)) {
537 k++;
538 if (!(x & 0x40000000))
539 return 32;
540 }
541 return k;
542 }
543
544 static int
545lo0bits
546#ifdef KR_headers
547 (y) ULong *y;
548#else
549 (ULong *y)
550#endif
551{
552 register int k;
553 register ULong x = *y;
554
555 if (x & 7) {
556 if (x & 1)
557 return 0;
558 if (x & 2) {
559 *y = x >> 1;
560 return 1;
561 }
562 *y = x >> 2;
563 return 2;
564 }
565 k = 0;
566 if (!(x & 0xffff)) {
567 k = 16;
568 x >>= 16;
569 }
570 if (!(x & 0xff)) {
571 k += 8;
572 x >>= 8;
573 }
574 if (!(x & 0xf)) {
575 k += 4;
576 x >>= 4;
577 }
578 if (!(x & 0x3)) {
579 k += 2;
580 x >>= 2;
581 }
582 if (!(x & 1)) {
583 k++;
584 x >>= 1;
585 if (!x & 1)
586 return 32;
587 }
588 *y = x;
589 return k;
590 }
591
592 static Bigint *
593i2b
594#ifdef KR_headers
595 (i) int i;
596#else
597 (int i)
598#endif
599{
600 Bigint *b;
601
602 b = Balloc(1);
603 b->x[0] = i;
604 b->wds = 1;
605 return b;
606 }
607
608 static Bigint *
609mult
610#ifdef KR_headers
611 (a, b) Bigint *a, *b;
612#else
613 (Bigint *a, Bigint *b)
614#endif
615{
616 Bigint *c;
617 int k, wa, wb, wc;
618 ULong carry, y, z;
619 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
620#ifdef Pack_32
621 ULong z2;
622#endif
623
624 if (a->wds < b->wds) {
625 c = a;
626 a = b;
627 b = c;
628 }
629 k = a->k;
630 wa = a->wds;
631 wb = b->wds;
632 wc = wa + wb;
633 if (wc > a->maxwds)
634 k++;
635 c = Balloc(k);
636 for(x = c->x, xa = x + wc; x < xa; x++)
637 *x = 0;
638 xa = a->x;
639 xae = xa + wa;
640 xb = b->x;
641 xbe = xb + wb;
642 xc0 = c->x;
643#ifdef Pack_32
644 for(; xb < xbe; xb++, xc0++) {
645 if ((y = *xb & 0xffff)) {
646 x = xa;
647 xc = xc0;
648 carry = 0;
649 do {
650 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
651 carry = z >> 16;
652 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
653 carry = z2 >> 16;
654 Storeinc(xc, z2, z);
655 }
656 while(x < xae);
657 *xc = carry;
658 }
659 if ((y = *xb >> 16)) {
660 x = xa;
661 xc = xc0;
662 carry = 0;
663 z2 = *xc;
664 do {
665 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
666 carry = z >> 16;
667 Storeinc(xc, z, z2);
668 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
669 carry = z2 >> 16;
670 }
671 while(x < xae);
672 *xc = z2;
673 }
674 }
675#else
676 for(; xb < xbe; xc0++) {
677 if (y = *xb++) {
678 x = xa;
679 xc = xc0;
680 carry = 0;
681 do {
682 z = *x++ * y + *xc + carry;
683 carry = z >> 16;
684 *xc++ = z & 0xffff;
685 }
686 while(x < xae);
687 *xc = carry;
688 }
689 }
690#endif
691 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
692 c->wds = wc;
693 return c;
694 }
695
696 static Bigint *p5s;
697
698 static Bigint *
699pow5mult
700#ifdef KR_headers
701 (b, k) Bigint *b; int k;
702#else
703 (Bigint *b, int k)
704#endif
705{
706 Bigint *b1, *p5, *p51;
707 int i;
708 static int p05[3] = { 5, 25, 125 };
709
710 if ((i = k & 3))
711 b = multadd(b, p05[i-1], 0);
712
713 if (!(k >>= 2))
714 return b;
715 if (!(p5 = p5s)) {
716 /* first time */
717 p5 = p5s = i2b(625);
718 p5->next = 0;
719 }
720 for(;;) {
721 if (k & 1) {
722 b1 = mult(b, p5);
723 Bfree(b);
724 b = b1;
725 }
726 if (!(k >>= 1))
727 break;
728 if (!(p51 = p5->next)) {
729 p51 = p5->next = mult(p5,p5);
730 p51->next = 0;
731 }
732 p5 = p51;
733 }
734 return b;
735 }
736
737 static Bigint *
738lshift
739#ifdef KR_headers
740 (b, k) Bigint *b; int k;
741#else
742 (Bigint *b, int k)
743#endif
744{
745 int i, k1, n, n1;
746 Bigint *b1;
747 ULong *x, *x1, *xe, z;
748
749#ifdef Pack_32
750 n = k >> 5;
751#else
752 n = k >> 4;
753#endif
754 k1 = b->k;
755 n1 = n + b->wds + 1;
756 for(i = b->maxwds; n1 > i; i <<= 1)
757 k1++;
758 b1 = Balloc(k1);
759 x1 = b1->x;
760 for(i = 0; i < n; i++)
761 *x1++ = 0;
762 x = b->x;
763 xe = x + b->wds;
764#ifdef Pack_32
765 if (k &= 0x1f) {
766 k1 = 32 - k;
767 z = 0;
768 do {
769 *x1++ = *x << k | z;
770 z = *x++ >> k1;
771 }
772 while(x < xe);
773 if ((*x1 = z))
774 ++n1;
775 }
776#else
777 if (k &= 0xf) {
778 k1 = 16 - k;
779 z = 0;
780 do {
781 *x1++ = *x << k & 0xffff | z;
782 z = *x++ >> k1;
783 }
784 while(x < xe);
785 if (*x1 = z)
786 ++n1;
787 }
788#endif
789 else do
790 *x1++ = *x++;
791 while(x < xe);
792 b1->wds = n1 - 1;
793 Bfree(b);
794 return b1;
795 }
796
797 static int
798cmp
799#ifdef KR_headers
800 (a, b) Bigint *a, *b;
801#else
802 (Bigint *a, Bigint *b)
803#endif
804{
805 ULong *xa, *xa0, *xb, *xb0;
806 int i, j;
807
808 i = a->wds;
809 j = b->wds;
810#ifdef DEBUG
811 if (i > 1 && !a->x[i-1])
812 Bug("cmp called with a->x[a->wds-1] == 0");
813 if (j > 1 && !b->x[j-1])
814 Bug("cmp called with b->x[b->wds-1] == 0");
815#endif
816 if (i -= j)
817 return i;
818 xa0 = a->x;
819 xa = xa0 + j;
820 xb0 = b->x;
821 xb = xb0 + j;
822 for(;;) {
823 if (*--xa != *--xb)
824 return *xa < *xb ? -1 : 1;
825 if (xa <= xa0)
826 break;
827 }
828 return 0;
829 }
830
831 static Bigint *
832diff
833#ifdef KR_headers
834 (a, b) Bigint *a, *b;
835#else
836 (Bigint *a, Bigint *b)
837#endif
838{
839 Bigint *c;
840 int i, wa, wb;
841 Long borrow, y; /* We need signed shifts here. */
842 ULong *xa, *xae, *xb, *xbe, *xc;
843#ifdef Pack_32
844 Long z;
845#endif
846
847 i = cmp(a,b);
848 if (!i) {
849 c = Balloc(0);
850 c->wds = 1;
851 c->x[0] = 0;
852 return c;
853 }
854 if (i < 0) {
855 c = a;
856 a = b;
857 b = c;
858 i = 1;
859 }
860 else
861 i = 0;
862 c = Balloc(a->k);
863 c->sign = i;
864 wa = a->wds;
865 xa = a->x;
866 xae = xa + wa;
867 wb = b->wds;
868 xb = b->x;
869 xbe = xb + wb;
870 xc = c->x;
871 borrow = 0;
872#ifdef Pack_32
873 do {
874 y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
875 borrow = y >> 16;
876 Sign_Extend(borrow, y);
877 z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
878 borrow = z >> 16;
879 Sign_Extend(borrow, z);
880 Storeinc(xc, z, y);
881 }
882 while(xb < xbe);
883 while(xa < xae) {
884 y = (*xa & 0xffff) + borrow;
885 borrow = y >> 16;
886 Sign_Extend(borrow, y);
887 z = (*xa++ >> 16) + borrow;
888 borrow = z >> 16;
889 Sign_Extend(borrow, z);
890 Storeinc(xc, z, y);
891 }
892#else
893 do {
894 y = *xa++ - *xb++ + borrow;
895 borrow = y >> 16;
896 Sign_Extend(borrow, y);
897 *xc++ = y & 0xffff;
898 }
899 while(xb < xbe);
900 while(xa < xae) {
901 y = *xa++ + borrow;
902 borrow = y >> 16;
903 Sign_Extend(borrow, y);
904 *xc++ = y & 0xffff;
905 }
906#endif
907 while(!*--xc)
908 wa--;
909 c->wds = wa;
910 return c;
911 }
912
913 static double
914ulp
915#ifdef KR_headers
916 (_x) double _x;
917#else
918 (double _x)
919#endif
920{
921 _double x;
922 register Long L;
923 _double a;
924
925 value(x) = _x;
926 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
927#ifndef Sudden_Underflow
928 if (L > 0) {
929#endif
930#ifdef IBM
931 L |= Exp_msk1 >> 4;
932#endif
933 word0(a) = L;
934 word1(a) = 0;
935#ifndef Sudden_Underflow
936 }
937 else {
938 L = -L >> Exp_shift;
939 if (L < Exp_shift) {
940 word0(a) = 0x80000 >> L;
941 word1(a) = 0;
942 }
943 else {
944 word0(a) = 0;
945 L -= Exp_shift;
946 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
947 }
948 }
949#endif
950 return value(a);
951 }
952
953 static double
954b2d
955#ifdef KR_headers
956 (a, e) Bigint *a; int *e;
957#else
958 (Bigint *a, int *e)
959#endif
960{
961 ULong *xa, *xa0, w, y, z;
962 int k;
963 _double d;
964#ifdef VAX
965 ULong d0, d1;
966#else
967#define d0 word0(d)
968#define d1 word1(d)
969#endif
970
971 xa0 = a->x;
972 xa = xa0 + a->wds;
973 y = *--xa;
974#ifdef DEBUG
975 if (!y) Bug("zero y in b2d");
976#endif
977 k = hi0bits(y);
978 *e = 32 - k;
979#ifdef Pack_32
980 if (k < Ebits) {
981 d0 = Exp_1 | y >> Ebits - k;
982 w = xa > xa0 ? *--xa : 0;
983 d1 = y << (32-Ebits) + k | w >> Ebits - k;
984 goto ret_d;
985 }
986 z = xa > xa0 ? *--xa : 0;
987 if (k -= Ebits) {
988 d0 = Exp_1 | y << k | z >> 32 - k;
989 y = xa > xa0 ? *--xa : 0;
990 d1 = z << k | y >> 32 - k;
991 }
992 else {
993 d0 = Exp_1 | y;
994 d1 = z;
995 }
996#else
997 if (k < Ebits + 16) {
998 z = xa > xa0 ? *--xa : 0;
999 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1000 w = xa > xa0 ? *--xa : 0;
1001 y = xa > xa0 ? *--xa : 0;
1002 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1003 goto ret_d;
1004 }
1005 z = xa > xa0 ? *--xa : 0;
1006 w = xa > xa0 ? *--xa : 0;
1007 k -= Ebits + 16;
1008 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1009 y = xa > xa0 ? *--xa : 0;
1010 d1 = w << k + 16 | y << k;
1011#endif
1012 ret_d:
1013#ifdef VAX
1014 word0(d) = d0 >> 16 | d0 << 16;
1015 word1(d) = d1 >> 16 | d1 << 16;
1016#else
1017#undef d0
1018#undef d1
1019#endif
1020 return value(d);
1021 }
1022
1023 static Bigint *
1024d2b
1025#ifdef KR_headers
1026 (_d, e, bits) double d; int *e, *bits;
1027#else
1028 (double _d, int *e, int *bits)
1029#endif
1030{
1031 Bigint *b;
1032 int de, i, k;
1033 ULong *x, y, z;
1034 _double d;
1035#ifdef VAX
1036 ULong d0, d1;
1037#endif
1038
1039 value(d) = _d;
1040#ifdef VAX
1041 d0 = word0(d) >> 16 | word0(d) << 16;
1042 d1 = word1(d) >> 16 | word1(d) << 16;
1043#else
1044#define d0 word0(d)
1045#define d1 word1(d)
1046#endif
1047
1048#ifdef Pack_32
1049 b = Balloc(1);
1050#else
1051 b = Balloc(2);
1052#endif
1053 x = b->x;
1054
1055 z = d0 & Frac_mask;
1056 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1057#ifdef Sudden_Underflow
1058 de = (int)(d0 >> Exp_shift);
1059#ifndef IBM
1060 z |= Exp_msk11;
1061#endif
1062#else
1063 if (de = (int)(d0 >> Exp_shift))
1064 z |= Exp_msk1;
1065#endif
1066#ifdef Pack_32
1067 if (y = d1) {
1068 if (k = lo0bits(&y)) {
1069 x[0] = y | z << 32 - k;
1070 z >>= k;
1071 }
1072 else
1073 x[0] = y;
1074 i = b->wds = (x[1] = z) ? 2 : 1;
1075 }
1076 else {
1077#ifdef DEBUG
1078 if (!z)
1079 Bug("Zero passed to d2b");
1080#endif
1081 k = lo0bits(&z);
1082 x[0] = z;
1083 i = b->wds = 1;
1084 k += 32;
1085 }
1086#else
1087 if (y = d1) {
1088 if (k = lo0bits(&y))
1089 if (k >= 16) {
1090 x[0] = y | z << 32 - k & 0xffff;
1091 x[1] = z >> k - 16 & 0xffff;
1092 x[2] = z >> k;
1093 i = 2;
1094 }
1095 else {
1096 x[0] = y & 0xffff;
1097 x[1] = y >> 16 | z << 16 - k & 0xffff;
1098 x[2] = z >> k & 0xffff;
1099 x[3] = z >> k+16;
1100 i = 3;
1101 }
1102 else {
1103 x[0] = y & 0xffff;
1104 x[1] = y >> 16;
1105 x[2] = z & 0xffff;
1106 x[3] = z >> 16;
1107 i = 3;
1108 }
1109 }
1110 else {
1111#ifdef DEBUG
1112 if (!z)
1113 Bug("Zero passed to d2b");
1114#endif
1115 k = lo0bits(&z);
1116 if (k >= 16) {
1117 x[0] = z;
1118 i = 0;
1119 }
1120 else {
1121 x[0] = z & 0xffff;
1122 x[1] = z >> 16;
1123 i = 1;
1124 }
1125 k += 32;
1126 }
1127 while(!x[i])
1128 --i;
1129 b->wds = i + 1;
1130#endif
1131#ifndef Sudden_Underflow
1132 if (de) {
1133#endif
1134#ifdef IBM
1135 *e = (de - Bias - (P-1) << 2) + k;
1136 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1137#else
1138 *e = de - Bias - (P-1) + k;
1139 *bits = P - k;
1140#endif
1141#ifndef Sudden_Underflow
1142 }
1143 else {
1144 *e = de - Bias - (P-1) + 1 + k;
1145#ifdef Pack_32
1146 *bits = 32*i - hi0bits(x[i-1]);
1147#else
1148 *bits = (i+2)*16 - hi0bits(x[i]);
1149#endif
1150 }
1151#endif
1152 return b;
1153 }
1154#undef d0
1155#undef d1
1156
1157 static double
1158ratio
1159#ifdef KR_headers
1160 (a, b) Bigint *a, *b;
1161#else
1162 (Bigint *a, Bigint *b)
1163#endif
1164{
1165 _double da, db;
1166 int k, ka, kb;
1167
1168 value(da) = b2d(a, &ka);
1169 value(db) = b2d(b, &kb);
1170#ifdef Pack_32
1171 k = ka - kb + 32*(a->wds - b->wds);
1172#else
1173 k = ka - kb + 16*(a->wds - b->wds);
1174#endif
1175#ifdef IBM
1176 if (k > 0) {
1177 word0(da) += (k >> 2)*Exp_msk1;
1178 if (k &= 3)
1179 da *= 1 << k;
1180 }
1181 else {
1182 k = -k;
1183 word0(db) += (k >> 2)*Exp_msk1;
1184 if (k &= 3)
1185 db *= 1 << k;
1186 }
1187#else
1188 if (k > 0)
1189 word0(da) += k*Exp_msk1;
1190 else {
1191 k = -k;
1192 word0(db) += k*Exp_msk1;
1193 }
1194#endif
1195 return value(da) / value(db);
1196 }
1197
1198static CONST double
1199tens[] = {
1200 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1201 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1202 1e20, 1e21, 1e22
1203#ifdef VAX
1204 , 1e23, 1e24
1205#endif
1206 };
1207
1208#ifdef IEEE_Arith
1209static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1210static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1211#define n_bigtens 5
1212#else
1213#ifdef IBM
1214static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
1215static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1216#define n_bigtens 3
1217#else
1218static CONST double bigtens[] = { 1e16, 1e32 };
1219static CONST double tinytens[] = { 1e-16, 1e-32 };
1220#define n_bigtens 2
1221#endif
1222#endif
1223
1224 double
1225strtod
1226#ifdef KR_headers
1227 (s00, se) CONST char *s00; char **se;
1228#else
1229 (CONST char *s00, char **se)
1230#endif
1231{
1232 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1233 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1234 CONST char *s, *s0, *s1;
1235 double aadj, aadj1, adj;
1236 _double rv, rv0;
1237 Long L;
1238 ULong y, z;
1239 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1240
1241#ifndef KR_headers
1242 CONST char decimal_point = localeconv()->decimal_point[0];
1243#else
1244 CONST char decimal_point = '.';
1245#endif
1246
1247 sign = nz0 = nz = 0;
1248 value(rv) = 0.;
1249
1250
1251 for(s = s00; isspace((unsigned char) *s); s++)
1252 ;
1253
1254 if (*s == '-') {
1255 sign = 1;
1256 s++;
1257 } else if (*s == '+') {
1258 s++;
1259 }
1260
1261 if (*s == '\0') {
1262 s = s00;
1263 goto ret;
1264 }
1265
1266 if (*s == '0') {
1267 nz0 = 1;
1268 while(*++s == '0') ;
1269 if (!*s)
1270 goto ret;
1271 }
1272 s0 = s;
1273 y = z = 0;
1274 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1275 if (nd < 9)
1276 y = 10*y + c - '0';
1277 else if (nd < 16)
1278 z = 10*z + c - '0';
1279 nd0 = nd;
1280 if (c == decimal_point) {
1281 c = *++s;
1282 if (!nd) {
1283 for(; c == '0'; c = *++s)
1284 nz++;
1285 if (c > '0' && c <= '9') {
1286 s0 = s;
1287 nf += nz;
1288 nz = 0;
1289 goto have_dig;
1290 }
1291 goto dig_done;
1292 }
1293 for(; c >= '0' && c <= '9'; c = *++s) {
1294 have_dig:
1295 nz++;
1296 if (c -= '0') {
1297 nf += nz;
1298 for(i = 1; i < nz; i++)
1299 if (nd++ < 9)
1300 y *= 10;
1301 else if (nd <= DBL_DIG + 1)
1302 z *= 10;
1303 if (nd++ < 9)
1304 y = 10*y + c;
1305 else if (nd <= DBL_DIG + 1)
1306 z = 10*z + c;
1307 nz = 0;
1308 }
1309 }
1310 }
1311 dig_done:
1312 e = 0;
1313 if (c == 'e' || c == 'E') {
1314 if (!nd && !nz && !nz0) {
1315 s = s00;
1316 goto ret;
1317 }
1318 s00 = s;
1319 esign = 0;
1320 switch(c = *++s) {
1321 case '-':
1322 esign = 1;
1323 case '+':
1324 c = *++s;
1325 }
1326 if (c >= '0' && c <= '9') {
1327 while(c == '0')
1328 c = *++s;
1329 if (c > '0' && c <= '9') {
1330 L = c - '0';
1331 s1 = s;
1332 while((c = *++s) >= '0' && c <= '9')
1333 L = 10*L + c - '0';
1334 if (s - s1 > 8 || L > 19999)
1335 /* Avoid confusion from exponents
1336 * so large that e might overflow.
1337 */
1338 e = 19999; /* safe for 16 bit ints */
1339 else
1340 e = (int)L;
1341 if (esign)
1342 e = -e;
1343 }
1344 else
1345 e = 0;
1346 }
1347 else
1348 s = s00;
1349 }
1350 if (!nd) {
1351 if (!nz && !nz0)
1352 s = s00;
1353 goto ret;
1354 }
1355 e1 = e -= nf;
1356
1357 /* Now we have nd0 digits, starting at s0, followed by a
1358 * decimal point, followed by nd-nd0 digits. The number we're
1359 * after is the integer represented by those digits times
1360 * 10**e */
1361
1362 if (!nd0)
1363 nd0 = nd;
1364 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1365 value(rv) = y;
1366 if (k > 9)
1367 value(rv) = tens[k - 9] * value(rv) + z;
1368 bd0 = 0;
1369 if (nd <= DBL_DIG
1370#ifndef RND_PRODQUOT
1371 && FLT_ROUNDS == 1
1372#endif
1373 ) {
1374 if (!e)
1375 goto ret;
1376 if (e > 0) {
1377 if (e <= Ten_pmax) {
1378#ifdef VAX
1379 goto vax_ovfl_check;
1380#else
1381 /* value(rv) = */ rounded_product(value(rv),
1382 tens[e]);
1383 goto ret;
1384#endif
1385 }
1386 i = DBL_DIG - nd;
1387 if (e <= Ten_pmax + i) {
1388 /* A fancier test would sometimes let us do
1389 * this for larger i values.
1390 */
1391 e -= i;
1392 value(rv) *= tens[i];
1393#ifdef VAX
1394 /* VAX exponent range is so narrow we must
1395 * worry about overflow here...
1396 */
1397 vax_ovfl_check:
1398 word0(rv) -= P*Exp_msk1;
1399 /* value(rv) = */ rounded_product(value(rv),
1400 tens[e]);
1401 if ((word0(rv) & Exp_mask)
1402 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1403 goto ovfl;
1404 word0(rv) += P*Exp_msk1;
1405#else
1406 /* value(rv) = */ rounded_product(value(rv),
1407 tens[e]);
1408#endif
1409 goto ret;
1410 }
1411 }
1412#ifndef Inaccurate_Divide
1413 else if (e >= -Ten_pmax) {
1414 /* value(rv) = */ rounded_quotient(value(rv),
1415 tens[-e]);
1416 goto ret;
1417 }
1418#endif
1419 }
1420 e1 += nd - k;
1421
1422 /* Get starting approximation = rv * 10**e1 */
1423
1424 if (e1 > 0) {
1425 if (i = e1 & 15)
1426 value(rv) *= tens[i];
1427 if (e1 &= ~15) {
1428 if (e1 > DBL_MAX_10_EXP) {
1429 ovfl:
1430 errno = ERANGE;
1431#ifndef Bad_float_h
1432 value(rv) = HUGE_VAL;
1433#else
1434 /* Can't trust HUGE_VAL */
1435#ifdef IEEE_Arith
1436 word0(rv) = Exp_mask;
1437 word1(rv) = 0;
1438#else
1439 word0(rv) = Big0;
1440 word1(rv) = Big1;
1441#endif
1442#endif
1443 if (bd0)
1444 goto retfree;
1445 goto ret;
1446 }
1447 if (e1 >>= 4) {
1448 for(j = 0; e1 > 1; j++, e1 >>= 1)
1449 if (e1 & 1)
1450 value(rv) *= bigtens[j];
1451 /* The last multiplication could overflow. */
1452 word0(rv) -= P*Exp_msk1;
1453 value(rv) *= bigtens[j];
1454 if ((z = word0(rv) & Exp_mask)
1455 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1456 goto ovfl;
1457 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1458 /* set to largest number */
1459 /* (Can't trust DBL_MAX) */
1460 word0(rv) = Big0;
1461 word1(rv) = Big1;
1462 }
1463 else
1464 word0(rv) += P*Exp_msk1;
1465 }
1466
1467 }
1468 }
1469 else if (e1 < 0) {
1470 e1 = -e1;
1471 if (i = e1 & 15)
1472 value(rv) /= tens[i];
1473 if (e1 &= ~15) {
1474 e1 >>= 4;
1475 if (e1 >= 1 << n_bigtens)
1476 goto undfl;
1477 for(j = 0; e1 > 1; j++, e1 >>= 1)
1478 if (e1 & 1)
1479 value(rv) *= tinytens[j];
1480 /* The last multiplication could underflow. */
1481 value(rv0) = value(rv);
1482 value(rv) *= tinytens[j];
1483 if (!value(rv)) {
1484 value(rv) = 2.*value(rv0);
1485 value(rv) *= tinytens[j];
1486 if (!value(rv)) {
1487 undfl:
1488 value(rv) = 0.;
1489 errno = ERANGE;
1490 if (bd0)
1491 goto retfree;
1492 goto ret;
1493 }
1494 word0(rv) = Tiny0;
1495 word1(rv) = Tiny1;
1496 /* The refinement below will clean
1497 * this approximation up.
1498 */
1499 }
1500 }
1501 }
1502
1503 /* Now the hard part -- adjusting rv to the correct value.*/
1504
1505 /* Put digits into bd: true value = bd * 10^e */
1506
1507 bd0 = s2b(s0, nd0, nd, y);
1508
1509 for(;;) {
1510 bd = Balloc(bd0->k);
1511 Bcopy(bd, bd0);
1512 bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1513 bs = i2b(1);
1514
1515 if (e >= 0) {
1516 bb2 = bb5 = 0;
1517 bd2 = bd5 = e;
1518 }
1519 else {
1520 bb2 = bb5 = -e;
1521 bd2 = bd5 = 0;
1522 }
1523 if (bbe >= 0)
1524 bb2 += bbe;
1525 else
1526 bd2 -= bbe;
1527 bs2 = bb2;
1528#ifdef Sudden_Underflow
1529#ifdef IBM
1530 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1531#else
1532 j = P + 1 - bbbits;
1533#endif
1534#else
1535 i = bbe + bbbits - 1; /* logb(rv) */
1536 if (i < Emin) /* denormal */
1537 j = bbe + (P-Emin);
1538 else
1539 j = P + 1 - bbbits;
1540#endif
1541 bb2 += j;
1542 bd2 += j;
1543 i = bb2 < bd2 ? bb2 : bd2;
1544 if (i > bs2)
1545 i = bs2;
1546 if (i > 0) {
1547 bb2 -= i;
1548 bd2 -= i;
1549 bs2 -= i;
1550 }
1551 if (bb5 > 0) {
1552 bs = pow5mult(bs, bb5);
1553 bb1 = mult(bs, bb);
1554 Bfree(bb);
1555 bb = bb1;
1556 }
1557 if (bb2 > 0)
1558 bb = lshift(bb, bb2);
1559 if (bd5 > 0)
1560 bd = pow5mult(bd, bd5);
1561 if (bd2 > 0)
1562 bd = lshift(bd, bd2);
1563 if (bs2 > 0)
1564 bs = lshift(bs, bs2);
1565 delta = diff(bb, bd);
1566 dsign = delta->sign;
1567 delta->sign = 0;
1568 i = cmp(delta, bs);
1569 if (i < 0) {
1570 /* Error is less than half an ulp -- check for
1571 * special case of mantissa a power of two.
1572 */
1573 if (dsign || word1(rv) || word0(rv) & Bndry_mask)
1574 break;
1575 delta = lshift(delta,Log2P);
1576 if (cmp(delta, bs) > 0)
1577 goto drop_down;
1578 break;
1579 }
1580 if (i == 0) {
1581 /* exactly half-way between */
1582 if (dsign) {
1583 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
1584 && word1(rv) == 0xffffffff) {
1585 /*boundary case -- increment exponent*/
1586 word0(rv) = (word0(rv) & Exp_mask)
1587 + Exp_msk1
1588#ifdef IBM
1589 | Exp_msk1 >> 4
1590#endif
1591 ;
1592 word1(rv) = 0;
1593 break;
1594 }
1595 }
1596 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
1597 drop_down:
1598 /* boundary case -- decrement exponent */
1599#ifdef Sudden_Underflow
1600 L = word0(rv) & Exp_mask;
1601#ifdef IBM
1602 if (L < Exp_msk1)
1603#else
1604 if (L <= Exp_msk1)
1605#endif
1606 goto undfl;
1607 L -= Exp_msk1;
1608#else
1609 L = (word0(rv) & Exp_mask) - Exp_msk1;
1610#endif
1611 word0(rv) = L | Bndry_mask1;
1612 word1(rv) = 0xffffffff;
1613#ifdef IBM
1614 goto cont;
1615#else
1616 break;
1617#endif
1618 }
1619#ifndef ROUND_BIASED
1620 if (!(word1(rv) & LSB))
1621 break;
1622#endif
1623 if (dsign)
1624 value(rv) += ulp(value(rv));
1625#ifndef ROUND_BIASED
1626 else {
1627 value(rv) -= ulp(value(rv));
1628#ifndef Sudden_Underflow
1629 if (!value(rv))
1630 goto undfl;
1631#endif
1632 }
1633#endif
1634 break;
1635 }
1636 if ((aadj = ratio(delta, bs)) <= 2.) {
1637 if (dsign)
1638 aadj = aadj1 = 1.;
1639 else if (word1(rv) || word0(rv) & Bndry_mask) {
1640#ifndef Sudden_Underflow
1641 if (word1(rv) == Tiny1 && !word0(rv))
1642 goto undfl;
1643#endif
1644 aadj = 1.;
1645 aadj1 = -1.;
1646 }
1647 else {
1648 /* special case -- power of FLT_RADIX to be */
1649 /* rounded down... */
1650
1651 if (aadj < 2./FLT_RADIX)
1652 aadj = 1./FLT_RADIX;
1653 else
1654 aadj *= 0.5;
1655 aadj1 = -aadj;
1656 }
1657 }
1658 else {
1659 aadj *= 0.5;
1660 aadj1 = dsign ? aadj : -aadj;
1661#ifdef Check_FLT_ROUNDS
1662 switch(FLT_ROUNDS) {
1663 case 2: /* towards +infinity */
1664 aadj1 -= 0.5;
1665 break;
1666 case 0: /* towards 0 */
1667 case 3: /* towards -infinity */
1668 aadj1 += 0.5;
1669 }
1670#else
1671 if (FLT_ROUNDS == 0)
1672 aadj1 += 0.5;
1673#endif
1674 }
1675 y = word0(rv) & Exp_mask;
1676
1677 /* Check for overflow */
1678
1679 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
1680 value(rv0) = value(rv);
1681 word0(rv) -= P*Exp_msk1;
1682 adj = aadj1 * ulp(value(rv));
1683 value(rv) += adj;
1684 if ((word0(rv) & Exp_mask) >=
1685 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
1686 if (word0(rv0) == Big0 && word1(rv0) == Big1)
1687 goto ovfl;
1688 word0(rv) = Big0;
1689 word1(rv) = Big1;
1690 goto cont;
1691 }
1692 else
1693 word0(rv) += P*Exp_msk1;
1694 }
1695 else {
1696#ifdef Sudden_Underflow
1697 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
1698 value(rv0) = value(rv);
1699 word0(rv) += P*Exp_msk1;
1700 adj = aadj1 * ulp(value(rv));
1701 value(rv) += adj;
1702#ifdef IBM
1703 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
1704#else
1705 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
1706#endif
1707 {
1708 if (word0(rv0) == Tiny0
1709 && word1(rv0) == Tiny1)
1710 goto undfl;
1711 word0(rv) = Tiny0;
1712 word1(rv) = Tiny1;
1713 goto cont;
1714 }
1715 else
1716 word0(rv) -= P*Exp_msk1;
1717 }
1718 else {
1719 adj = aadj1 * ulp(value(rv));
1720 value(rv) += adj;
1721 }
1722#else
1723 /* Compute adj so that the IEEE rounding rules will
1724 * correctly round rv + adj in some half-way cases.
1725 * If rv * ulp(rv) is denormalized (i.e.,
1726 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
1727 * trouble from bits lost to denormalization;
1728 * example: 1.2e-307 .
1729 */
1730 if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
1731 aadj1 = (double)(int)(aadj + 0.5);
1732 if (!dsign)
1733 aadj1 = -aadj1;
1734 }
1735 adj = aadj1 * ulp(value(rv));
1736 value(rv) += adj;
1737#endif
1738 }
1739 z = word0(rv) & Exp_mask;
1740 if (y == z) {
1741 /* Can we stop now? */
1742 L = aadj;
1743 aadj -= L;
1744 /* The tolerances below are conservative. */
1745 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
1746 if (aadj < .4999999 || aadj > .5000001)
1747 break;
1748 }
1749 else if (aadj < .4999999/FLT_RADIX)
1750 break;
1751 }
1752 cont:
1753 Bfree(bb);
1754 Bfree(bd);
1755 Bfree(bs);
1756 Bfree(delta);
1757 }
1758 retfree:
1759 Bfree(bb);
1760 Bfree(bd);
1761 Bfree(bs);
1762 Bfree(bd0);
1763 Bfree(delta);
1764 ret:
1765 if (se)
1766 *se = (char *)s;
1767 return sign ? -value(rv) : value(rv);
1768 }
1769
1770 static int
1771quorem
1772#ifdef KR_headers
1773 (b, S) Bigint *b, *S;
1774#else
1775 (Bigint *b, Bigint *S)
1776#endif
1777{
1778 int n;
1779 Long borrow, y;
1780 ULong carry, q, ys;
1781 ULong *bx, *bxe, *sx, *sxe;
1782#ifdef Pack_32
1783 Long z;
1784 ULong si, zs;
1785#endif
1786
1787 n = S->wds;
1788#ifdef DEBUG
1789 /*debug*/ if (b->wds > n)
1790 /*debug*/ Bug("oversize b in quorem");
1791#endif
1792 if (b->wds < n)
1793 return 0;
1794 sx = S->x;
1795 sxe = sx + --n;
1796 bx = b->x;
1797 bxe = bx + n;
1798 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1799#ifdef DEBUG
1800 /*debug*/ if (q > 9)
1801 /*debug*/ Bug("oversized quotient in quorem");
1802#endif
1803 if (q) {
1804 borrow = 0;
1805 carry = 0;
1806 do {
1807#ifdef Pack_32
1808 si = *sx++;
1809 ys = (si & 0xffff) * q + carry;
1810 zs = (si >> 16) * q + (ys >> 16);
1811 carry = zs >> 16;
1812 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1813 borrow = y >> 16;
1814 Sign_Extend(borrow, y);
1815 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1816 borrow = z >> 16;
1817 Sign_Extend(borrow, z);
1818 Storeinc(bx, z, y);
1819#else
1820 ys = *sx++ * q + carry;
1821 carry = ys >> 16;
1822 y = *bx - (ys & 0xffff) + borrow;
1823 borrow = y >> 16;
1824 Sign_Extend(borrow, y);
1825 *bx++ = y & 0xffff;
1826#endif
1827 }
1828 while(sx <= sxe);
1829 if (!*bxe) {
1830 bx = b->x;
1831 while(--bxe > bx && !*bxe)
1832 --n;
1833 b->wds = n;
1834 }
1835 }
1836 if (cmp(b, S) >= 0) {
1837 q++;
1838 borrow = 0;
1839 carry = 0;
1840 bx = b->x;
1841 sx = S->x;
1842 do {
1843#ifdef Pack_32
1844 si = *sx++;
1845 ys = (si & 0xffff) + carry;
1846 zs = (si >> 16) + (ys >> 16);
1847 carry = zs >> 16;
1848 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1849 borrow = y >> 16;
1850 Sign_Extend(borrow, y);
1851 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1852 borrow = z >> 16;
1853 Sign_Extend(borrow, z);
1854 Storeinc(bx, z, y);
1855#else
1856 ys = *sx++ + carry;
1857 carry = ys >> 16;
1858 y = *bx - (ys & 0xffff) + borrow;
1859 borrow = y >> 16;
1860 Sign_Extend(borrow, y);
1861 *bx++ = y & 0xffff;
1862#endif
1863 }
1864 while(sx <= sxe);
1865 bx = b->x;
1866 bxe = bx + n;
1867 if (!*bxe) {
1868 while(--bxe > bx && !*bxe)
1869 --n;
1870 b->wds = n;
1871 }
1872 }
1873 return q;
1874 }
1875
1876/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1877 *
1878 * Inspired by "How to Print Floating-Point Numbers Accurately" by
1879 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1880 *
1881 * Modifications:
1882 * 1. Rather than iterating, we use a simple numeric overestimate
1883 * to determine k = floor(log10(d)). We scale relevant
1884 * quantities using O(log2(k)) rather than O(k) multiplications.
1885 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1886 * try to generate digits strictly left to right. Instead, we
1887 * compute with fewer bits and propagate the carry if necessary
1888 * when rounding the final digit up. This is often faster.
1889 * 3. Under the assumption that input will be rounded nearest,
1890 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1891 * That is, we allow equality in stopping tests when the
1892 * round-nearest rule will give the same floating-point value
1893 * as would satisfaction of the stopping test with strict
1894 * inequality.
1895 * 4. We remove common factors of powers of 2 from relevant
1896 * quantities.
1897 * 5. When converting floating-point integers less than 1e16,
1898 * we use floating-point arithmetic rather than resorting
1899 * to multiple-precision integers.
1900 * 6. When asked to produce fewer than 15 digits, we first try
1901 * to get by with floating-point arithmetic; we resort to
1902 * multiple-precision integer arithmetic only if we cannot
1903 * guarantee that the floating-point calculation has given
1904 * the correctly rounded result. For k requested digits and
1905 * "uniformly" distributed input, the probability is
1906 * something like 10^(k-15) that we must resort to the Long
1907 * calculation.
1908 */
1909
1910 char *
1911__dtoa
1912#ifdef KR_headers
1913 (_d, mode, ndigits, decpt, sign, rve)
1914 double _d; int mode, ndigits, *decpt, *sign; char **rve;
1915#else
1916 (double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
1917#endif
1918{
1919 /* Arguments ndigits, decpt, sign are similar to those
1920 of ecvt and fcvt; trailing zeros are suppressed from
1921 the returned string. If not null, *rve is set to point
1922 to the end of the return value. If d is +-Infinity or NaN,
1923 then *decpt is set to 9999.
1924
1925 mode:
1926 0 ==> shortest string that yields d when read in
1927 and rounded to nearest.
1928 1 ==> like 0, but with Steele & White stopping rule;
1929 e.g. with IEEE P754 arithmetic , mode 0 gives
1930 1e23 whereas mode 1 gives 9.999999999999999e22.
1931 2 ==> max(1,ndigits) significant digits. This gives a
1932 return value similar to that of ecvt, except
1933 that trailing zeros are suppressed.
1934 3 ==> through ndigits past the decimal point. This
1935 gives a return value similar to that from fcvt,
1936 except that trailing zeros are suppressed, and
1937 ndigits can be negative.
1938 4-9 should give the same return values as 2-3, i.e.,
1939 4 <= mode <= 9 ==> same return as mode
1940 2 + (mode & 1). These modes are mainly for
1941 debugging; often they run slower but sometimes
1942 faster than modes 2-3.
1943 4,5,8,9 ==> left-to-right digit generation.
1944 6-9 ==> don't try fast floating-point estimate
1945 (if applicable).
1946
1947 Values of mode other than 0-9 are treated as mode 0.
1948
1949 Sufficient space is allocated to the return value
1950 to hold the suppressed trailing zeros.
1951 */
1952
1953 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
1954 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1955 spec_case, try_quick;
1956 Long L;
1957#ifndef Sudden_Underflow
1958 int denorm;
1959 ULong x;
1960#endif
1961 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
1962 double ds;
1963 char *s, *s0;
1964 static Bigint *result;
1965 static int result_k;
1966 _double d, d2, eps;
1967
1968 value(d) = _d;
1969 if (result) {
1970 result->k = result_k;
1971 result->maxwds = 1 << result_k;
1972 Bfree(result);
1973 result = 0;
1974 }
1975
1976 if (word0(d) & Sign_bit) {
1977 /* set sign for everything, including 0's and NaNs */
1978 *sign = 1;
1979 word0(d) &= ~Sign_bit; /* clear sign bit */
1980 }
1981 else
1982 *sign = 0;
1983
1984#if defined(IEEE_Arith) + defined(VAX)
1985#ifdef IEEE_Arith
1986 if ((word0(d) & Exp_mask) == Exp_mask)
1987#else
1988 if (word0(d) == 0x8000)
1989#endif
1990 {
1991 /* Infinity or NaN */
1992 *decpt = 9999;
1993 s =
1994#ifdef IEEE_Arith
1995 !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
1996#endif
1997 "NaN";
1998 if (rve)
1999 *rve =
2000#ifdef IEEE_Arith
2001 s[3] ? s + 8 :
2002#endif
2003 s + 3;
2004 return s;
2005 }
2006#endif
2007#ifdef IBM
2008 value(d) += 0; /* normalize */
2009#endif
2010 if (!value(d)) {
2011 *decpt = 1;
2012 s = "0";
2013 if (rve)
2014 *rve = s + 1;
2015 return s;
2016 }
2017
2018 b = d2b(value(d), &be, &bbits);
2019#ifdef Sudden_Underflow
2020 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2021#else
2022 if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
2023#endif
2024 value(d2) = value(d);
2025 word0(d2) &= Frac_mask1;
2026 word0(d2) |= Exp_11;
2027#ifdef IBM
2028 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2029 value(d2) /= 1 << j;
2030#endif
2031
2032 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2033 * log10(x) = log(x) / log(10)
2034 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2035 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2036 *
2037 * This suggests computing an approximation k to log10(d) by
2038 *
2039 * k = (i - Bias)*0.301029995663981
2040 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2041 *
2042 * We want k to be too large rather than too small.
2043 * The error in the first-order Taylor series approximation
2044 * is in our favor, so we just round up the constant enough
2045 * to compensate for any error in the multiplication of
2046 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2047 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2048 * adding 1e-13 to the constant term more than suffices.
2049 * Hence we adjust the constant term to 0.1760912590558.
2050 * (We could get a more accurate k by invoking log10,
2051 * but this is probably not worthwhile.)
2052 */
2053
2054 i -= Bias;
2055#ifdef IBM
2056 i <<= 2;
2057 i += j;
2058#endif
2059#ifndef Sudden_Underflow
2060 denorm = 0;
2061 }
2062 else {
2063 /* d is denormalized */
2064
2065 i = bbits + be + (Bias + (P-1) - 1);
2066 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2067 : word1(d) << 32 - i;
2068 value(d2) = x;
2069 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2070 i -= (Bias + (P-1) - 1) + 1;
2071 denorm = 1;
2072 }
2073#endif
2074 ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 +
2075 i*0.301029995663981;
2076 k = (int)ds;
2077 if (ds < 0. && ds != k)
2078 k--; /* want k = floor(ds) */
2079 k_check = 1;
2080 if (k >= 0 && k <= Ten_pmax) {
2081 if (value(d) < tens[k])
2082 k--;
2083 k_check = 0;
2084 }
2085 j = bbits - i - 1;
2086 if (j >= 0) {
2087 b2 = 0;
2088 s2 = j;
2089 }
2090 else {
2091 b2 = -j;
2092 s2 = 0;
2093 }
2094 if (k >= 0) {
2095 b5 = 0;
2096 s5 = k;
2097 s2 += k;
2098 }
2099 else {
2100 b2 -= k;
2101 b5 = -k;
2102 s5 = 0;
2103 }
2104 if (mode < 0 || mode > 9)
2105 mode = 0;
2106 try_quick = 1;
2107 if (mode > 5) {
2108 mode -= 4;
2109 try_quick = 0;
2110 }
2111 leftright = 1;
2112 switch(mode) {
2113 case 0:
2114 case 1:
2115 ilim = ilim1 = -1;
2116 i = 18;
2117 ndigits = 0;
2118 break;
2119 case 2:
2120 leftright = 0;
2121 /* no break */
2122 case 4:
2123 if (ndigits <= 0)
2124 ndigits = 1;
2125 ilim = ilim1 = i = ndigits;
2126 break;
2127 case 3:
2128 leftright = 0;
2129 /* no break */
2130 case 5:
2131 i = ndigits + k + 1;
2132 ilim = i;
2133 ilim1 = i - 1;
2134 if (i <= 0)
2135 i = 1;
2136 }
2137 j = sizeof(ULong);
2138 for(result_k = 0; sizeof(Bigint) - sizeof(ULong) + j <= i;
2139 j <<= 1) result_k++;
2140 result = Balloc(result_k);
2141 s = s0 = (char *)result;
2142
2143 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2144
2145 /* Try to get by with floating-point arithmetic. */
2146
2147 i = 0;
2148 value(d2) = value(d);
2149 k0 = k;
2150 ilim0 = ilim;
2151 ieps = 2; /* conservative */
2152 if (k > 0) {
2153 ds = tens[k&0xf];
2154 j = k >> 4;
2155 if (j & Bletch) {
2156 /* prevent overflows */
2157 j &= Bletch - 1;
2158 value(d) /= bigtens[n_bigtens-1];
2159 ieps++;
2160 }
2161 for(; j; j >>= 1, i++)
2162 if (j & 1) {
2163 ieps++;
2164 ds *= bigtens[i];
2165 }
2166 value(d) /= ds;
2167 }
2168 else if (j1 = -k) {
2169 value(d) *= tens[j1 & 0xf];
2170 for(j = j1 >> 4; j; j >>= 1, i++)
2171 if (j & 1) {
2172 ieps++;
2173 value(d) *= bigtens[i];
2174 }
2175 }
2176 if (k_check && value(d) < 1. && ilim > 0) {
2177 if (ilim1 <= 0)
2178 goto fast_failed;
2179 ilim = ilim1;
2180 k--;
2181 value(d) *= 10.;
2182 ieps++;
2183 }
2184 value(eps) = ieps*value(d) + 7.;
2185 word0(eps) -= (P-1)*Exp_msk1;
2186 if (ilim == 0) {
2187 S = mhi = 0;
2188 value(d) -= 5.;
2189 if (value(d) > value(eps))
2190 goto one_digit;
2191 if (value(d) < -value(eps))
2192 goto no_digits;
2193 goto fast_failed;
2194 }
2195#ifndef No_leftright
2196 if (leftright) {
2197 /* Use Steele & White method of only
2198 * generating digits needed.
2199 */
2200 value(eps) = 0.5/tens[ilim-1] - value(eps);
2201 for(i = 0;;) {
2202 L = value(d);
2203 value(d) -= L;
2204 *s++ = '0' + (int)L;
2205 if (value(d) < value(eps))
2206 goto ret1;
2207 if (1. - value(d) < value(eps))
2208 goto bump_up;
2209 if (++i >= ilim)
2210 break;
2211 value(eps) *= 10.;
2212 value(d) *= 10.;
2213 }
2214 }
2215 else {
2216#endif
2217 /* Generate ilim digits, then fix them up. */
2218 value(eps) *= tens[ilim-1];
2219 for(i = 1;; i++, value(d) *= 10.) {
2220 L = value(d);
2221 value(d) -= L;
2222 *s++ = '0' + (int)L;
2223 if (i == ilim) {
2224 if (value(d) > 0.5 + value(eps))
2225 goto bump_up;
2226 else if (value(d) < 0.5 - value(eps)) {
2227 while(*--s == '0');
2228 s++;
2229 goto ret1;
2230 }
2231 break;
2232 }
2233 }
2234#ifndef No_leftright
2235 }
2236#endif
2237 fast_failed:
2238 s = s0;
2239 value(d) = value(d2);
2240 k = k0;
2241 ilim = ilim0;
2242 }
2243
2244 /* Do we have a "small" integer? */
2245
2246 if (be >= 0 && k <= Int_max) {
2247 /* Yes. */
2248 ds = tens[k];
2249 if (ndigits < 0 && ilim <= 0) {
2250 S = mhi = 0;
2251 if (ilim < 0 || value(d) <= 5*ds)
2252 goto no_digits;
2253 goto one_digit;
2254 }
2255 for(i = 1;; i++) {
2256 L = value(d) / ds;
2257 value(d) -= L*ds;
2258#ifdef Check_FLT_ROUNDS
2259 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2260 if (value(d) < 0) {
2261 L--;
2262 value(d) += ds;
2263 }
2264#endif
2265 *s++ = '0' + (int)L;
2266 if (i == ilim) {
2267 value(d) += value(d);
2268 if (value(d) > ds || value(d) == ds && L & 1) {
2269 bump_up:
2270 while(*--s == '9')
2271 if (s == s0) {
2272 k++;
2273 *s = '0';
2274 break;
2275 }
2276 ++*s++;
2277 }
2278 break;
2279 }
2280 if (!(value(d) *= 10.))
2281 break;
2282 }
2283 goto ret1;
2284 }
2285
2286 m2 = b2;
2287 m5 = b5;
2288 mhi = mlo = 0;
2289 if (leftright) {
2290 if (mode < 2) {
2291 i =
2292#ifndef Sudden_Underflow
2293 denorm ? be + (Bias + (P-1) - 1 + 1) :
2294#endif
2295#ifdef IBM
2296 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2297#else
2298 1 + P - bbits;
2299#endif
2300 }
2301 else {
2302 j = ilim - 1;
2303 if (m5 >= j)
2304 m5 -= j;
2305 else {
2306 s5 += j -= m5;
2307 b5 += j;
2308 m5 = 0;
2309 }
2310 if ((i = ilim) < 0) {
2311 m2 -= i;
2312 i = 0;
2313 }
2314 }
2315 b2 += i;
2316 s2 += i;
2317 mhi = i2b(1);
2318 }
2319 if (m2 > 0 && s2 > 0) {
2320 i = m2 < s2 ? m2 : s2;
2321 b2 -= i;
2322 m2 -= i;
2323 s2 -= i;
2324 }
2325 if (b5 > 0) {
2326 if (leftright) {
2327 if (m5 > 0) {
2328 mhi = pow5mult(mhi, m5);
2329 b1 = mult(mhi, b);
2330 Bfree(b);
2331 b = b1;
2332 }
2333 if (j = b5 - m5)
2334 b = pow5mult(b, j);
2335 }
2336 else
2337 b = pow5mult(b, b5);
2338 }
2339 S = i2b(1);
2340 if (s5 > 0)
2341 S = pow5mult(S, s5);
2342
2343 /* Check for special case that d is a normalized power of 2. */
2344
2345 if (mode < 2) {
2346 if (!word1(d) && !(word0(d) & Bndry_mask)
2347#ifndef Sudden_Underflow
2348 && word0(d) & Exp_mask
2349#endif
2350 ) {
2351 /* The special case */
2352 b2 += Log2P;
2353 s2 += Log2P;
2354 spec_case = 1;
2355 }
2356 else
2357 spec_case = 0;
2358 }
2359
2360 /* Arrange for convenient computation of quotients:
2361 * shift left if necessary so divisor has 4 leading 0 bits.
2362 *
2363 * Perhaps we should just compute leading 28 bits of S once
2364 * and for all and pass them and a shift to quorem, so it
2365 * can do shifts and ors to compute the numerator for q.
2366 */
2367#ifdef Pack_32
2368 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
2369 i = 32 - i;
2370#else
2371 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
2372 i = 16 - i;
2373#endif
2374 if (i > 4) {
2375 i -= 4;
2376 b2 += i;
2377 m2 += i;
2378 s2 += i;
2379 }
2380 else if (i < 4) {
2381 i += 28;
2382 b2 += i;
2383 m2 += i;
2384 s2 += i;
2385 }
2386 if (b2 > 0)
2387 b = lshift(b, b2);
2388 if (s2 > 0)
2389 S = lshift(S, s2);
2390 if (k_check) {
2391 if (cmp(b,S) < 0) {
2392 k--;
2393 b = multadd(b, 10, 0); /* we botched the k estimate */
2394 if (leftright)
2395 mhi = multadd(mhi, 10, 0);
2396 ilim = ilim1;
2397 }
2398 }
2399 if (ilim <= 0 && mode > 2) {
2400 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
2401 /* no digits, fcvt style */
2402 no_digits:
2403 k = -1 - ndigits;
2404 goto ret;
2405 }
2406 one_digit:
2407 *s++ = '1';
2408 k++;
2409 goto ret;
2410 }
2411 if (leftright) {
2412 if (m2 > 0)
2413 mhi = lshift(mhi, m2);
2414
2415 /* Compute mlo -- check for special case
2416 * that d is a normalized power of 2.
2417 */
2418
2419 mlo = mhi;
2420 if (spec_case) {
2421 mhi = Balloc(mhi->k);
2422 Bcopy(mhi, mlo);
2423 mhi = lshift(mhi, Log2P);
2424 }
2425
2426 for(i = 1;;i++) {
2427 dig = quorem(b,S) + '0';
2428 /* Do we yet have the shortest decimal string
2429 * that will round to d?
2430 */
2431 j = cmp(b, mlo);
2432 delta = diff(S, mhi);
2433 j1 = delta->sign ? 1 : cmp(b, delta);
2434 Bfree(delta);
2435#ifndef ROUND_BIASED
2436 if (j1 == 0 && !mode && !(word1(d) & 1)) {
2437 if (dig == '9')
2438 goto round_9_up;
2439 if (j > 0)
2440 dig++;
2441 *s++ = dig;
2442 goto ret;
2443 }
2444#endif
2445 if (j < 0 || j == 0 && !mode
2446#ifndef ROUND_BIASED
2447 && !(word1(d) & 1)
2448#endif
2449 ) {
2450 if (j1 > 0) {
2451 b = lshift(b, 1);
2452 j1 = cmp(b, S);
2453 if ((j1 > 0 || j1 == 0 && dig & 1)
2454 && dig++ == '9')
2455 goto round_9_up;
2456 }
2457 *s++ = dig;
2458 goto ret;
2459 }
2460 if (j1 > 0) {
2461 if (dig == '9') { /* possible if i == 1 */
2462 round_9_up:
2463 *s++ = '9';
2464 goto roundoff;
2465 }
2466 *s++ = dig + 1;
2467 goto ret;
2468 }
2469 *s++ = dig;
2470 if (i == ilim)
2471 break;
2472 b = multadd(b, 10, 0);
2473 if (mlo == mhi)
2474 mlo = mhi = multadd(mhi, 10, 0);
2475 else {
2476 mlo = multadd(mlo, 10, 0);
2477 mhi = multadd(mhi, 10, 0);
2478 }
2479 }
2480 }
2481 else
2482 for(i = 1;; i++) {
2483 *s++ = dig = quorem(b,S) + '0';
2484 if (i >= ilim)
2485 break;
2486 b = multadd(b, 10, 0);
2487 }
2488
2489 /* Round off last digit */
2490
2491 b = lshift(b, 1);
2492 j = cmp(b, S);
2493 if (j > 0 || j == 0 && dig & 1) {
2494 roundoff:
2495 while(*--s == '9')
2496 if (s == s0) {
2497 k++;
2498 *s++ = '1';
2499 goto ret;
2500 }
2501 ++*s++;
2502 }
2503 else {
2504 while(*--s == '0');
2505 s++;
2506 }
2507 ret:
2508 Bfree(S);
2509 if (mhi) {
2510 if (mlo && mlo != mhi)
2511 Bfree(mlo);
2512 Bfree(mhi);
2513 }
2514 ret1:
2515 Bfree(b);
2516 if (s == s0) { /* don't return empty string */
2517 *s++ = '0';
2518 k = 0;
2519 }
2520 *s = 0;
2521 *decpt = k + 1;
2522 if (rve)
2523 *rve = s;
2524 return s0;
2525 }
2526#ifdef __cplusplus
2527}
2528#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-27 08:12:13 +0000