1/****************************************************************
2 *
3 * The author of this software is David M. Gay.
4 *
5 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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 LUCENT 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 Bell Laboratories, Room 2C-463
23 600 Mountain Avenue
24 Murray Hill, NJ 07974-0636
25 U.S.A.
26 dmg@bell-labs.com
27 */
28
29/* On a machine with IEEE extended-precision registers, it is
30 * necessary to specify double-precision (53-bit) rounding precision
31 * before invoking strtod or dtoa. If the machine uses (the equivalent
32 * of) Intel 80x87 arithmetic, the call
33 * _control87(PC_53, MCW_PC);
34 * does this with many compilers. Whether this or another call is
35 * appropriate depends on the compiler; for this to work, it may be
36 * necessary to #include "float.h" or another system-dependent header
37 * file.
38 */
39
40/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
41 *
42 * This strtod returns a nearest machine number to the input decimal
43 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
44 * broken by the IEEE round-even rule. Otherwise ties are broken by
45 * biased rounding (add half and chop).
46 *
47 * Inspired loosely by William D. Clinger's paper "How to Read Floating
48 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
49 *
50 * Modifications:
51 *
52 * 1. We only require IEEE, IBM, or VAX double-precision
53 * arithmetic (not IEEE double-extended).
54 * 2. We get by with floating-point arithmetic in a case that
55 * Clinger missed -- when we're computing d * 10^n
56 * for a small integer d and the integer n is not too
57 * much larger than 22 (the maximum integer k for which
58 * we can represent 10^k exactly), we may be able to
59 * compute (d*10^k) * 10^(e-k) with just one roundoff.
60 * 3. Rather than a bit-at-a-time adjustment of the binary
61 * result in the hard case, we use floating-point
62 * arithmetic to determine the adjustment to within
63 * one bit; only in really hard cases do we need to
64 * compute a second residual.
65 * 4. Because of 3., we don't need a large table of powers of 10
66 * for ten-to-e (just some small tables, e.g. of 10^k
67 * for 0 <= k <= 22).
68 */
69
70/*
71 * #define IEEE_8087 for IEEE-arithmetic machines where the least
72 * significant byte has the lowest address.
73 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
74 * significant byte has the lowest address.
75 * #define Long int on machines with 32-bit ints and 64-bit longs.
76 * #define IBM for IBM mainframe-style floating-point arithmetic.
77 * #define VAX for VAX-style floating-point arithmetic (D_floating).
78 * #define No_leftright to omit left-right logic in fast floating-point
79 * computation of dtoa.
80 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
81 * and strtod and dtoa should round accordingly.
82 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
83 * and Honor_FLT_ROUNDS is not #defined.
84 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
85 * that use extended-precision instructions to compute rounded
86 * products and quotients) with IBM.
87 * #define ROUND_BIASED for IEEE-format with biased rounding.
88 * #define Inaccurate_Divide for IEEE-format with correctly rounded
89 * products but inaccurate quotients, e.g., for Intel i860.
90 * #define NO_LONG_LONG on machines that do not have a "long long"
91 * integer type (of >= 64 bits). On such machines, you can
92 * #define Just_16 to store 16 bits per 32-bit Long when doing
93 * high-precision integer arithmetic. Whether this speeds things
94 * up or slows things down depends on the machine and the number
95 * being converted. If long long is available and the name is
96 * something other than "long long", #define Llong to be the name,
97 * and if "unsigned Llong" does not work as an unsigned version of
98 * Llong, #define #ULLong to be the corresponding unsigned type.
99 * #define KR_headers for old-style C function headers.
100 * #define Bad_float_h if your system lacks a float.h or if it does not
101 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
102 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
103 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
104 * if memory is available and otherwise does something you deem
105 * appropriate. If MALLOC is undefined, malloc will be invoked
106 * directly -- and assumed always to succeed.
107 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
108 * memory allocations from a private pool of memory when possible.
109 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
110 * unless #defined to be a different length. This default length
111 * suffices to get rid of MALLOC calls except for unusual cases,
112 * such as decimal-to-binary conversion of a very long string of
113 * digits. The longest string dtoa can return is about 751 bytes
114 * long. For conversions by strtod of strings of 800 digits and
115 * all dtoa conversions in single-threaded executions with 8-byte
116 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
117 * pointers, PRIVATE_MEM >= 7112 appears adequate.
118 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
119 * Infinity and NaN (case insensitively). On some systems (e.g.,
120 * some HP systems), it may be necessary to #define NAN_WORD0
121 * appropriately -- to the most significant word of a quiet NaN.
122 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
123 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
124 * strtod also accepts (case insensitively) strings of the form
125 * NaN(x), where x is a string of hexadecimal digits and spaces;
126 * if there is only one string of hexadecimal digits, it is taken
127 * for the 52 fraction bits of the resulting NaN; if there are two
128 * or more strings of hex digits, the first is for the high 20 bits,
129 * the second and subsequent for the low 32 bits, with intervening
130 * white space ignored; but if this results in none of the 52
131 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
132 * and NAN_WORD1 are used instead.
133 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
134 * multiple threads. In this case, you must provide (or suitably
135 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
136 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
137 * in pow5mult, ensures lazy evaluation of only one copy of high
138 * powers of 5; omitting this lock would introduce a small
139 * probability of wasting memory, but would otherwise be harmless.)
140 * You must also invoke freedtoa(s) to free the value s returned by
141 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
142 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
143 * avoids underflows on inputs whose result does not underflow.
144 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
145 * floating-point numbers and flushes underflows to zero rather
146 * than implementing gradual underflow, then you must also #define
147 * Sudden_Underflow.
148 * #define YES_ALIAS to permit aliasing certain double values with
149 * arrays of ULongs. This leads to slightly better code with
150 * some compilers and was always used prior to 19990916, but it
151 * is not strictly legal and can cause trouble with aggressively
152 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
153 * #define USE_LOCALE to use the current locale's decimal_point value.
154 * #define SET_INEXACT if IEEE arithmetic is being used and extra
155 * computation should be done to set the inexact flag when the
156 * result is inexact and avoid setting inexact when the result
157 * is exact. In this case, dtoa.c must be compiled in
158 * an environment, perhaps provided by #include "dtoa.c" in a
159 * suitable wrapper, that defines two functions,
160 * int get_inexact(void);
161 * void clear_inexact(void);
162 * such that get_inexact() returns a nonzero value if the
163 * inexact bit is already set, and clear_inexact() sets the
164 * inexact bit to 0. When SET_INEXACT is #defined, strtod
165 * also does extra computations to set the underflow and overflow
166 * flags when appropriate (i.e., when the result is tiny and
167 * inexact or when it is a numeric value rounded to +-infinity).
168 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
169 * the result overflows to +-Infinity or underflows to 0.
170 */
171
172#include "dtoa.h"
173#include <config-kjs.h>
174
175#include "global.h"
176
177#if PLATFORM(BIG_ENDIAN)
178#define IEEE_MC68k
179#else
180#define IEEE_8087
181#endif
182#define INFNAN_CHECK
183
184
185
186#ifndef Long
187#define Long int
188#endif
189#ifndef ULong
190typedef unsigned Long ULong;
191#endif
192
193#ifdef DEBUG
194#include <stdio.h>
195#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
196#endif
197
198#include <stdlib.h>
199#include <string.h>
200
201#ifdef USE_LOCALE
202#include <locale.h>
203#endif
204
205#ifdef MALLOC
206extern void *MALLOC(size_t);
207#else
208#define MALLOC malloc
209#endif
210
211#ifndef Omit_Private_Memory
212#ifndef PRIVATE_MEM
213#define PRIVATE_MEM 2304
214#endif
215#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
216static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
217#endif
218
219#undef IEEE_Arith
220#undef Avoid_Underflow
221#ifdef IEEE_MC68k
222#define IEEE_Arith
223#endif
224#ifdef IEEE_8087
225#define IEEE_Arith
226#endif
227
228#include <errno.h>
229
230#ifdef Bad_float_h
231
232#ifdef IEEE_Arith
233#define DBL_DIG 15
234#define DBL_MAX_10_EXP 308
235#define DBL_MAX_EXP 1024
236#define FLT_RADIX 2
237#endif /*IEEE_Arith*/
238
239#ifdef IBM
240#define DBL_DIG 16
241#define DBL_MAX_10_EXP 75
242#define DBL_MAX_EXP 63
243#define FLT_RADIX 16
244#define DBL_MAX 7.2370055773322621e+75
245#endif
246
247#ifdef VAX
248#define DBL_DIG 16
249#define DBL_MAX_10_EXP 38
250#define DBL_MAX_EXP 127
251#define FLT_RADIX 2
252#define DBL_MAX 1.7014118346046923e+38
253#endif
254
255#ifndef LONG_MAX
256#define LONG_MAX 2147483647
257#endif
258
259#else /* ifndef Bad_float_h */
260#include <float.h>
261#endif /* Bad_float_h */
262
263#ifndef __MATH_H__
264#include <math.h>
265#endif
266
267#define strtod kjs_strtod
268#define dtoa kjs_dtoa
269#define freedtoa kjs_freedtoa
270
271#ifdef __cplusplus
272extern "C" {
273#endif
274
275#ifndef CONST
276#define CONST const
277#endif
278
279#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
280Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
281#endif
282
283typedef union { double d; ULong L[2]; } U;
284
285#define dval(x) (x).d
286#ifdef IEEE_8087
287#define word0(x) (x).L[1]
288#define word1(x) (x).L[0]
289#else
290#define word0(x) (x).L[0]
291#define word1(x) (x).L[1]
292#endif
293
294/* The following definition of Storeinc is appropriate for MIPS processors.
295 * An alternative that might be better on some machines is
296 */
297#define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
298
299/* #define P DBL_MANT_DIG */
300/* Ten_pmax = floor(P*log(2)/log(5)) */
301/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
302/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
303/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
304
305#ifdef IEEE_Arith
306#define Exp_shift 20
307#define Exp_shift1 20
308#define Exp_msk1 0x100000
309#define Exp_msk11 0x100000
310#define Exp_mask 0x7ff00000
311#define P 53
312#define Bias 1023
313#define Emin (-1022)
314#define Exp_1 0x3ff00000
315#define Exp_11 0x3ff00000
316#define Ebits 11
317#define Frac_mask 0xfffff
318#define Frac_mask1 0xfffff
319#define Ten_pmax 22
320#define Bletch 0x10
321#define Bndry_mask 0xfffff
322#define Bndry_mask1 0xfffff
323#define LSB 1
324#define Sign_bit 0x80000000
325#define Log2P 1
326#define Tiny0 0
327#define Tiny1 1
328#define Quick_max 14
329#define Int_max 14
330#ifndef NO_IEEE_Scale
331#define Avoid_Underflow
332#ifdef Flush_Denorm /* debugging option */
333#undef Sudden_Underflow
334#endif
335#endif
336
337#ifndef Flt_Rounds
338#ifdef FLT_ROUNDS
339#define Flt_Rounds FLT_ROUNDS
340#else
341#define Flt_Rounds 1
342#endif
343#endif /*Flt_Rounds*/
344
345#ifdef Honor_FLT_ROUNDS
346#define Rounding rounding
347#undef Check_FLT_ROUNDS
348#define Check_FLT_ROUNDS
349#else
350#define Rounding Flt_Rounds
351#endif
352
353#else /* ifndef IEEE_Arith */
354#undef Check_FLT_ROUNDS
355#undef Honor_FLT_ROUNDS
356#undef SET_INEXACT
357#undef Sudden_Underflow
358#define Sudden_Underflow
359#ifdef IBM
360#undef Flt_Rounds
361#define Flt_Rounds 0
362#define Exp_shift 24
363#define Exp_shift1 24
364#define Exp_msk1 0x1000000
365#define Exp_msk11 0x1000000
366#define Exp_mask 0x7f000000
367#define P 14
368#define Bias 65
369#define Exp_1 0x41000000
370#define Exp_11 0x41000000
371#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
372#define Frac_mask 0xffffff
373#define Frac_mask1 0xffffff
374#define Bletch 4
375#define Ten_pmax 22
376#define Bndry_mask 0xefffff
377#define Bndry_mask1 0xffffff
378#define LSB 1
379#define Sign_bit 0x80000000
380#define Log2P 4
381#define Tiny0 0x100000
382#define Tiny1 0
383#define Quick_max 14
384#define Int_max 15
385#else /* VAX */
386#undef Flt_Rounds
387#define Flt_Rounds 1
388#define Exp_shift 23
389#define Exp_shift1 7
390#define Exp_msk1 0x80
391#define Exp_msk11 0x800000
392#define Exp_mask 0x7f80
393#define P 56
394#define Bias 129
395#define Exp_1 0x40800000
396#define Exp_11 0x4080
397#define Ebits 8
398#define Frac_mask 0x7fffff
399#define Frac_mask1 0xffff007f
400#define Ten_pmax 24
401#define Bletch 2
402#define Bndry_mask 0xffff007f
403#define Bndry_mask1 0xffff007f
404#define LSB 0x10000
405#define Sign_bit 0x8000
406#define Log2P 1
407#define Tiny0 0x80
408#define Tiny1 0
409#define Quick_max 15
410#define Int_max 15
411#endif /* IBM, VAX */
412#endif /* IEEE_Arith */
413
414#ifndef IEEE_Arith
415#define ROUND_BIASED
416#endif
417
418#ifdef RND_PRODQUOT
419#define rounded_product(a,b) a = rnd_prod(a, b)
420#define rounded_quotient(a,b) a = rnd_quot(a, b)
421extern double rnd_prod(double, double), rnd_quot(double, double);
422#else
423#define rounded_product(a,b) a *= b
424#define rounded_quotient(a,b) a /= b
425#endif
426
427#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
428#define Big1 0xffffffff
429
430#ifndef Pack_32
431#define Pack_32
432#endif
433
434#define FFFFFFFF 0xffffffffUL
435
436#ifdef NO_LONG_LONG
437#undef ULLong
438#ifdef Just_16
439#undef Pack_32
440/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
441 * This makes some inner loops simpler and sometimes saves work
442 * during multiplications, but it often seems to make things slightly
443 * slower. Hence the default is now to store 32 bits per Long.
444 */
445#endif
446#else /* long long available */
447#ifndef Llong
448#define Llong long long
449#endif
450#ifndef ULLong
451#define ULLong unsigned Llong
452#endif
453#endif /* NO_LONG_LONG */
454
455#ifndef MULTIPLE_THREADS
456#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
457#define FREE_DTOA_LOCK(n) /*nothing*/
458#endif
459
460#define Kmax (sizeof(size_t) << 3)
461
462 struct
463Bigint {
464 struct Bigint *next;
465 int k, maxwds, sign, wds;
466 ULong x[1];
467 };
468
469 typedef struct Bigint Bigint;
470
471 static Bigint *freelist[Kmax+1];
472
473 static Bigint *
474Balloc
475 (int k)
476{
477 int x;
478 Bigint *rv;
479#ifndef Omit_Private_Memory
480 unsigned int len;
481#endif
482
483 ACQUIRE_DTOA_LOCK(0);
484 if ((rv = freelist[k])) {
485 freelist[k] = rv->next;
486 }
487 else {
488 x = 1 << k;
489#ifdef Omit_Private_Memory
490 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
491#else
492 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
493 /sizeof(double);
494 if (pmem_next - private_mem + len <= (unsigned)PRIVATE_mem) {
495 rv = (Bigint*)pmem_next;
496 pmem_next += len;
497 }
498 else
499 rv = (Bigint*)MALLOC(len*sizeof(double));
500#endif
501 rv->k = k;
502 rv->maxwds = x;
503 }
504 FREE_DTOA_LOCK(0);
505 rv->sign = rv->wds = 0;
506 return rv;
507 }
508
509 static void
510Bfree
511 (Bigint *v)
512{
513 if (v) {
514 ACQUIRE_DTOA_LOCK(0);
515 v->next = freelist[v->k];
516 freelist[v->k] = v;
517 FREE_DTOA_LOCK(0);
518 }
519 }
520
521#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
522y->wds*sizeof(Long) + 2*sizeof(int))
523
524 static Bigint *
525multadd
526 (Bigint *b, int m, int a) /* multiply by m and add a */
527{
528 int i, wds;
529#ifdef ULLong
530 ULong *x;
531 ULLong carry, y;
532#else
533 ULong carry, *x, y;
534#ifdef Pack_32
535 ULong xi, z;
536#endif
537#endif
538 Bigint *b1;
539
540 wds = b->wds;
541 x = b->x;
542 i = 0;
543 carry = a;
544 do {
545#ifdef ULLong
546 y = *x * (ULLong)m + carry;
547 carry = y >> 32;
548 *x++ = (ULong)y & FFFFFFFF;
549#else
550#ifdef Pack_32
551 xi = *x;
552 y = (xi & 0xffff) * m + carry;
553 z = (xi >> 16) * m + (y >> 16);
554 carry = z >> 16;
555 *x++ = (z << 16) + (y & 0xffff);
556#else
557 y = *x * m + carry;
558 carry = y >> 16;
559 *x++ = y & 0xffff;
560#endif
561#endif
562 }
563 while(++i < wds);
564 if (carry) {
565 if (wds >= b->maxwds) {
566 b1 = Balloc(b->k+1);
567 Bcopy(b1, b);
568 Bfree(b);
569 b = b1;
570 }
571 b->x[wds++] = (ULong)carry;
572 b->wds = wds;
573 }
574 return b;
575 }
576
577 static Bigint *
578s2b
579 (CONST char *s, int nd0, int nd, ULong y9)
580{
581 Bigint *b;
582 int i, k;
583 Long x, y;
584
585 x = (nd + 8) / 9;
586 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
587#ifdef Pack_32
588 b = Balloc(k);
589 b->x[0] = y9;
590 b->wds = 1;
591#else
592 b = Balloc(k+1);
593 b->x[0] = y9 & 0xffff;
594 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
595#endif
596
597 i = 9;
598 if (9 < nd0) {
599 s += 9;
600 do b = multadd(b, 10, *s++ - '0');
601 while(++i < nd0);
602 s++;
603 }
604 else
605 s += 10;
606 for(; i < nd; i++)
607 b = multadd(b, 10, *s++ - '0');
608 return b;
609 }
610
611 static int
612hi0bits
613 (register ULong x)
614{
615 register int k = 0;
616
617 if (!(x & 0xffff0000)) {
618 k = 16;
619 x <<= 16;
620 }
621 if (!(x & 0xff000000)) {
622 k += 8;
623 x <<= 8;
624 }
625 if (!(x & 0xf0000000)) {
626 k += 4;
627 x <<= 4;
628 }
629 if (!(x & 0xc0000000)) {
630 k += 2;
631 x <<= 2;
632 }
633 if (!(x & 0x80000000)) {
634 k++;
635 if (!(x & 0x40000000))
636 return 32;
637 }
638 return k;
639 }
640
641 static int
642lo0bits
643 (ULong *y)
644{
645 register int k;
646 register ULong x = *y;
647
648 if (x & 7) {
649 if (x & 1)
650 return 0;
651 if (x & 2) {
652 *y = x >> 1;
653 return 1;
654 }
655 *y = x >> 2;
656 return 2;
657 }
658 k = 0;
659 if (!(x & 0xffff)) {
660 k = 16;
661 x >>= 16;
662 }
663 if (!(x & 0xff)) {
664 k += 8;
665 x >>= 8;
666 }
667 if (!(x & 0xf)) {
668 k += 4;
669 x >>= 4;
670 }
671 if (!(x & 0x3)) {
672 k += 2;
673 x >>= 2;
674 }
675 if (!(x & 1)) {
676 k++;
677 x >>= 1;
678 if (!x & 1)
679 return 32;
680 }
681 *y = x;
682 return k;
683 }
684
685 static Bigint *
686i2b
687 (int i)
688{
689 Bigint *b;
690
691 b = Balloc(1);
692 b->x[0] = i;
693 b->wds = 1;
694 return b;
695 }
696
697 static Bigint *
698mult
699 (Bigint *a, Bigint *b)
700{
701 Bigint *c;
702 int k, wa, wb, wc;
703 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
704 ULong y;
705#ifdef ULLong
706 ULLong carry, z;
707#else
708 ULong carry, z;
709#ifdef Pack_32
710 ULong z2;
711#endif
712#endif
713
714 if (a->wds < b->wds) {
715 c = a;
716 a = b;
717 b = c;
718 }
719 k = a->k;
720 wa = a->wds;
721 wb = b->wds;
722 wc = wa + wb;
723 if (wc > a->maxwds)
724 k++;
725 c = Balloc(k);
726 for(x = c->x, xa = x + wc; x < xa; x++)
727 *x = 0;
728 xa = a->x;
729 xae = xa + wa;
730 xb = b->x;
731 xbe = xb + wb;
732 xc0 = c->x;
733#ifdef ULLong
734 for(; xb < xbe; xc0++) {
735 if ((y = *xb++)) {
736 x = xa;
737 xc = xc0;
738 carry = 0;
739 do {
740 z = *x++ * (ULLong)y + *xc + carry;
741 carry = z >> 32;
742 *xc++ = (ULong)z & FFFFFFFF;
743 }
744 while(x < xae);
745 *xc = (ULong)carry;
746 }
747 }
748#else
749#ifdef Pack_32
750 for(; xb < xbe; xb++, xc0++) {
751 if (y = *xb & 0xffff) {
752 x = xa;
753 xc = xc0;
754 carry = 0;
755 do {
756 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
757 carry = z >> 16;
758 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
759 carry = z2 >> 16;
760 Storeinc(xc, z2, z);
761 }
762 while(x < xae);
763 *xc = carry;
764 }
765 if (y = *xb >> 16) {
766 x = xa;
767 xc = xc0;
768 carry = 0;
769 z2 = *xc;
770 do {
771 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
772 carry = z >> 16;
773 Storeinc(xc, z, z2);
774 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
775 carry = z2 >> 16;
776 }
777 while(x < xae);
778 *xc = z2;
779 }
780 }
781#else
782 for(; xb < xbe; xc0++) {
783 if (y = *xb++) {
784 x = xa;
785 xc = xc0;
786 carry = 0;
787 do {
788 z = *x++ * y + *xc + carry;
789 carry = z >> 16;
790 *xc++ = z & 0xffff;
791 }
792 while(x < xae);
793 *xc = carry;
794 }
795 }
796#endif
797#endif
798 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
799 c->wds = wc;
800 return c;
801 }
802
803 static Bigint *p5s;
804
805 static Bigint *
806pow5mult
807 (Bigint *b, int k)
808{
809 Bigint *b1, *p5, *p51;
810 int i;
811 static int p05[3] = { 5, 25, 125 };
812
813 if ((i = k & 3))
814 b = multadd(b, p05[i-1], 0);
815
816 if (!(k >>= 2))
817 return b;
818 if (!(p5 = p5s)) {
819 /* first time */
820#ifdef MULTIPLE_THREADS
821 ACQUIRE_DTOA_LOCK(1);
822 if (!(p5 = p5s)) {
823 p5 = p5s = i2b(625);
824 p5->next = 0;
825 }
826 FREE_DTOA_LOCK(1);
827#else
828 p5 = p5s = i2b(625);
829 p5->next = 0;
830#endif
831 }
832 for(;;) {
833 if (k & 1) {
834 b1 = mult(b, p5);
835 Bfree(b);
836 b = b1;
837 }
838 if (!(k >>= 1))
839 break;
840 if (!(p51 = p5->next)) {
841#ifdef MULTIPLE_THREADS
842 ACQUIRE_DTOA_LOCK(1);
843 if (!(p51 = p5->next)) {
844 p51 = p5->next = mult(p5,p5);
845 p51->next = 0;
846 }
847 FREE_DTOA_LOCK(1);
848#else
849 p51 = p5->next = mult(p5,p5);
850 p51->next = 0;
851#endif
852 }
853 p5 = p51;
854 }
855 return b;
856 }
857
858 static Bigint *
859lshift
860 (Bigint *b, int k)
861{
862 int i, k1, n, n1;
863 Bigint *b1;
864 ULong *x, *x1, *xe, z;
865
866#ifdef Pack_32
867 n = k >> 5;
868#else
869 n = k >> 4;
870#endif
871 k1 = b->k;
872 n1 = n + b->wds + 1;
873 for(i = b->maxwds; n1 > i; i <<= 1)
874 k1++;
875 b1 = Balloc(k1);
876 x1 = b1->x;
877 for(i = 0; i < n; i++)
878 *x1++ = 0;
879 x = b->x;
880 xe = x + b->wds;
881#ifdef Pack_32
882 if (k &= 0x1f) {
883 k1 = 32 - k;
884 z = 0;
885 do {
886 *x1++ = *x << k | z;
887 z = *x++ >> k1;
888 }
889 while(x < xe);
890 if ((*x1 = z))
891 ++n1;
892 }
893#else
894 if (k &= 0xf) {
895 k1 = 16 - k;
896 z = 0;
897 do {
898 *x1++ = *x << k & 0xffff | z;
899 z = *x++ >> k1;
900 }
901 while(x < xe);
902 if (*x1 = z)
903 ++n1;
904 }
905#endif
906 else do
907 *x1++ = *x++;
908 while(x < xe);
909 b1->wds = n1 - 1;
910 Bfree(b);
911 return b1;
912 }
913
914 static int
915cmp
916 (Bigint *a, Bigint *b)
917{
918 ULong *xa, *xa0, *xb, *xb0;
919 int i, j;
920
921 i = a->wds;
922 j = b->wds;
923#ifdef DEBUG
924 if (i > 1 && !a->x[i-1])
925 Bug("cmp called with a->x[a->wds-1] == 0");
926 if (j > 1 && !b->x[j-1])
927 Bug("cmp called with b->x[b->wds-1] == 0");
928#endif
929 if (i -= j)
930 return i;
931 xa0 = a->x;
932 xa = xa0 + j;
933 xb0 = b->x;
934 xb = xb0 + j;
935 for(;;) {
936 if (*--xa != *--xb)
937 return *xa < *xb ? -1 : 1;
938 if (xa <= xa0)
939 break;
940 }
941 return 0;
942 }
943
944 static Bigint *
945diff
946 (Bigint *a, Bigint *b)
947{
948 Bigint *c;
949 int i, wa, wb;
950 ULong *xa, *xae, *xb, *xbe, *xc;
951#ifdef ULLong
952 ULLong borrow, y;
953#else
954 ULong borrow, y;
955#ifdef Pack_32
956 ULong z;
957#endif
958#endif
959
960 i = cmp(a,b);
961 if (!i) {
962 c = Balloc(0);
963 c->wds = 1;
964 c->x[0] = 0;
965 return c;
966 }
967 if (i < 0) {
968 c = a;
969 a = b;
970 b = c;
971 i = 1;
972 }
973 else
974 i = 0;
975 c = Balloc(a->k);
976 c->sign = i;
977 wa = a->wds;
978 xa = a->x;
979 xae = xa + wa;
980 wb = b->wds;
981 xb = b->x;
982 xbe = xb + wb;
983 xc = c->x;
984 borrow = 0;
985#ifdef ULLong
986 do {
987 y = (ULLong)*xa++ - *xb++ - borrow;
988 borrow = y >> 32 & (ULong)1;
989 *xc++ = (ULong)y & FFFFFFFF;
990 }
991 while(xb < xbe);
992 while(xa < xae) {
993 y = *xa++ - borrow;
994 borrow = y >> 32 & (ULong)1;
995 *xc++ = (ULong)y & FFFFFFFF;
996 }
997#else
998#ifdef Pack_32
999 do {
1000 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1001 borrow = (y & 0x10000) >> 16;
1002 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1003 borrow = (z & 0x10000) >> 16;
1004 Storeinc(xc, z, y);
1005 }
1006 while(xb < xbe);
1007 while(xa < xae) {
1008 y = (*xa & 0xffff) - borrow;
1009 borrow = (y & 0x10000) >> 16;
1010 z = (*xa++ >> 16) - borrow;
1011 borrow = (z & 0x10000) >> 16;
1012 Storeinc(xc, z, y);
1013 }
1014#else
1015 do {
1016 y = *xa++ - *xb++ - borrow;
1017 borrow = (y & 0x10000) >> 16;
1018 *xc++ = y & 0xffff;
1019 }
1020 while(xb < xbe);
1021 while(xa < xae) {
1022 y = *xa++ - borrow;
1023 borrow = (y & 0x10000) >> 16;
1024 *xc++ = y & 0xffff;
1025 }
1026#endif
1027#endif
1028 while(!*--xc)
1029 wa--;
1030 c->wds = wa;
1031 return c;
1032 }
1033
1034 static double
1035ulp
1036 (double dx)
1037{
1038 register Long L;
1039 U x, a;
1040
1041 dval(x) = dx;
1042 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1043#ifndef Avoid_Underflow
1044#ifndef Sudden_Underflow
1045 if (L > 0) {
1046#endif
1047#endif
1048#ifdef IBM
1049 L |= Exp_msk1 >> 4;
1050#endif
1051 word0(a) = L;
1052 word1(a) = 0;
1053#ifndef Avoid_Underflow
1054#ifndef Sudden_Underflow
1055 }
1056 else {
1057 L = -L >> Exp_shift;
1058 if (L < Exp_shift) {
1059 word0(a) = 0x80000 >> L;
1060 word1(a) = 0;
1061 }
1062 else {
1063 word0(a) = 0;
1064 L -= Exp_shift;
1065 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1066 }
1067 }
1068#endif
1069#endif
1070 return dval(a);
1071 }
1072
1073 static double
1074b2d
1075 (Bigint *a, int *e)
1076{
1077 ULong *xa, *xa0, w, y, z;
1078 int k;
1079 U d;
1080#ifdef VAX
1081 ULong d0, d1;
1082#else
1083#define d0 word0(d)
1084#define d1 word1(d)
1085#endif
1086
1087 xa0 = a->x;
1088 xa = xa0 + a->wds;
1089 y = *--xa;
1090#ifdef DEBUG
1091 if (!y) Bug("zero y in b2d");
1092#endif
1093 k = hi0bits(y);
1094 *e = 32 - k;
1095#ifdef Pack_32
1096 if (k < Ebits) {
1097 d0 = Exp_1 | y >> (Ebits - k);
1098 w = xa > xa0 ? *--xa : 0;
1099 d1 = y << (32-Ebits + k) | w >> (Ebits - k);
1100 goto ret_d;
1101 }
1102 z = xa > xa0 ? *--xa : 0;
1103 if (k -= Ebits) {
1104 d0 = Exp_1 | y << k | z >> (32 - k);
1105 y = xa > xa0 ? *--xa : 0;
1106 d1 = z << k | y >> (32 - k);
1107 }
1108 else {
1109 d0 = Exp_1 | y;
1110 d1 = z;
1111 }
1112#else
1113 if (k < Ebits + 16) {
1114 z = xa > xa0 ? *--xa : 0;
1115 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1116 w = xa > xa0 ? *--xa : 0;
1117 y = xa > xa0 ? *--xa : 0;
1118 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1119 goto ret_d;
1120 }
1121 z = xa > xa0 ? *--xa : 0;
1122 w = xa > xa0 ? *--xa : 0;
1123 k -= Ebits + 16;
1124 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1125 y = xa > xa0 ? *--xa : 0;
1126 d1 = w << k + 16 | y << k;
1127#endif
1128 ret_d:
1129#ifdef VAX
1130 word0(d) = d0 >> 16 | d0 << 16;
1131 word1(d) = d1 >> 16 | d1 << 16;
1132#else
1133#undef d0
1134#undef d1
1135#endif
1136 return dval(d);
1137 }
1138
1139 static Bigint *
1140d2b
1141 (double dd, int *e, int *bits)
1142{
1143 U d;
1144 Bigint *b;
1145 int de, k;
1146 ULong *x, y, z;
1147#ifndef Sudden_Underflow
1148 int i;
1149#endif
1150#ifdef VAX
1151 ULong d0, d1;
1152#endif
1153 dval(d) = dd;
1154#ifdef VAX
1155 d0 = word0(d) >> 16 | word0(d) << 16;
1156 d1 = word1(d) >> 16 | word1(d) << 16;
1157#else
1158#define d0 word0(d)
1159#define d1 word1(d)
1160#endif
1161
1162#ifdef Pack_32
1163 b = Balloc(1);
1164#else
1165 b = Balloc(2);
1166#endif
1167 x = b->x;
1168
1169 z = d0 & Frac_mask;
1170 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1171#ifdef Sudden_Underflow
1172 de = (int)(d0 >> Exp_shift);
1173#ifndef IBM
1174 z |= Exp_msk11;
1175#endif
1176#else
1177 if ((de = (int)(d0 >> Exp_shift)))
1178 z |= Exp_msk1;
1179#endif
1180#ifdef Pack_32
1181 if ((y = d1)) {
1182 if ((k = lo0bits(&y))) {
1183 x[0] = y | z << (32 - k);
1184 z >>= k;
1185 }
1186 else
1187 x[0] = y;
1188#ifndef Sudden_Underflow
1189 i =
1190#endif
1191 b->wds = (x[1] = z) ? 2 : 1;
1192 }
1193 else {
1194#ifdef DEBUG
1195 if (!z)
1196 Bug("Zero passed to d2b");
1197#endif
1198 k = lo0bits(&z);
1199 x[0] = z;
1200#ifndef Sudden_Underflow
1201 i =
1202#endif
1203 b->wds = 1;
1204 k += 32;
1205 }
1206#else
1207 if (y = d1) {
1208 if (k = lo0bits(&y))
1209 if (k >= 16) {
1210 x[0] = y | z << 32 - k & 0xffff;
1211 x[1] = z >> k - 16 & 0xffff;
1212 x[2] = z >> k;
1213 i = 2;
1214 }
1215 else {
1216 x[0] = y & 0xffff;
1217 x[1] = y >> 16 | z << 16 - k & 0xffff;
1218 x[2] = z >> k & 0xffff;
1219 x[3] = z >> k+16;
1220 i = 3;
1221 }
1222 else {
1223 x[0] = y & 0xffff;
1224 x[1] = y >> 16;
1225 x[2] = z & 0xffff;
1226 x[3] = z >> 16;
1227 i = 3;
1228 }
1229 }
1230 else {
1231#ifdef DEBUG
1232 if (!z)
1233 Bug("Zero passed to d2b");
1234#endif
1235 k = lo0bits(&z);
1236 if (k >= 16) {
1237 x[0] = z;
1238 i = 0;
1239 }
1240 else {
1241 x[0] = z & 0xffff;
1242 x[1] = z >> 16;
1243 i = 1;
1244 }
1245 k += 32;
1246 }
1247 while(!x[i])
1248 --i;
1249 b->wds = i + 1;
1250#endif
1251#ifndef Sudden_Underflow
1252 if (de) {
1253#endif
1254#ifdef IBM
1255 *e = (de - Bias - (P-1) << 2) + k;
1256 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1257#else
1258 *e = de - Bias - (P-1) + k;
1259 *bits = P - k;
1260#endif
1261#ifndef Sudden_Underflow
1262 }
1263 else {
1264 *e = de - Bias - (P-1) + 1 + k;
1265#ifdef Pack_32
1266 *bits = 32*i - hi0bits(x[i-1]);
1267#else
1268 *bits = (i+2)*16 - hi0bits(x[i]);
1269#endif
1270 }
1271#endif
1272 return b;
1273 }
1274#undef d0
1275#undef d1
1276
1277 static double
1278ratio
1279 (Bigint *a, Bigint *b)
1280{
1281 U da, db;
1282 int k, ka, kb;
1283
1284 dval(da) = b2d(a, &ka);
1285 dval(db) = b2d(b, &kb);
1286#ifdef Pack_32
1287 k = ka - kb + 32*(a->wds - b->wds);
1288#else
1289 k = ka - kb + 16*(a->wds - b->wds);
1290#endif
1291#ifdef IBM
1292 if (k > 0) {
1293 word0(da) += (k >> 2)*Exp_msk1;
1294 if (k &= 3)
1295 dval(da) *= 1 << k;
1296 }
1297 else {
1298 k = -k;
1299 word0(db) += (k >> 2)*Exp_msk1;
1300 if (k &= 3)
1301 dval(db) *= 1 << k;
1302 }
1303#else
1304 if (k > 0)
1305 word0(da) += k*Exp_msk1;
1306 else {
1307 k = -k;
1308 word0(db) += k*Exp_msk1;
1309 }
1310#endif
1311 return dval(da) / dval(db);
1312 }
1313
1314 static CONST double
1315tens[] = {
1316 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1317 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1318 1e20, 1e21, 1e22
1319#ifdef VAX
1320 , 1e23, 1e24
1321#endif
1322 };
1323
1324 static CONST double
1325#ifdef IEEE_Arith
1326bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1327static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1328#ifdef Avoid_Underflow
1329 9007199254740992.*9007199254740992.e-256
1330 /* = 2^106 * 1e-53 */
1331#else
1332 1e-256
1333#endif
1334 };
1335/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1336/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1337#define Scale_Bit 0x10
1338#define n_bigtens 5
1339#else
1340#ifdef IBM
1341bigtens[] = { 1e16, 1e32, 1e64 };
1342static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1343#define n_bigtens 3
1344#else
1345bigtens[] = { 1e16, 1e32 };
1346static CONST double tinytens[] = { 1e-16, 1e-32 };
1347#define n_bigtens 2
1348#endif
1349#endif
1350
1351#ifndef IEEE_Arith
1352#undef INFNAN_CHECK
1353#endif
1354
1355#ifdef INFNAN_CHECK
1356
1357#ifndef NAN_WORD0
1358#define NAN_WORD0 0x7ff80000
1359#endif
1360
1361#ifndef NAN_WORD1
1362#define NAN_WORD1 0
1363#endif
1364
1365 static int
1366match
1367 (CONST char **sp, CONST char *t)
1368{
1369 int c, d;
1370 CONST char *s = *sp;
1371
1372 while((d = *t++)) {
1373 if ((c = *++s) >= 'A' && c <= 'Z')
1374 c += 'a' - 'A';
1375 if (c != d)
1376 return 0;
1377 }
1378 *sp = s + 1;
1379 return 1;
1380 }
1381
1382#ifndef No_Hex_NaN
1383 static void
1384hexnan
1385 (U *rvp, CONST char **sp)
1386{
1387 ULong c, x[2];
1388 CONST char *s;
1389 int havedig, udx0, xshift;
1390
1391 x[0] = x[1] = 0;
1392 havedig = xshift = 0;
1393 udx0 = 1;
1394 s = *sp;
1395 while((c = *(CONST unsigned char*)++s)) {
1396 if (c >= '0' && c <= '9')
1397 c -= '0';
1398 else if (c >= 'a' && c <= 'f')
1399 c += 10 - 'a';
1400 else if (c >= 'A' && c <= 'F')
1401 c += 10 - 'A';
1402 else if (c <= ' ') {
1403 if (udx0 && havedig) {
1404 udx0 = 0;
1405 xshift = 1;
1406 }
1407 continue;
1408 }
1409 else if (/*(*/ c == ')' && havedig) {
1410 *sp = s + 1;
1411 break;
1412 }
1413 else
1414 return; /* invalid form: don't change *sp */
1415 havedig = 1;
1416 if (xshift) {
1417 xshift = 0;
1418 x[0] = x[1];
1419 x[1] = 0;
1420 }
1421 if (udx0)
1422 x[0] = (x[0] << 4) | (x[1] >> 28);
1423 x[1] = (x[1] << 4) | c;
1424 }
1425 if ((x[0] &= 0xfffff) || x[1]) {
1426 word0(*rvp) = Exp_mask | x[0];
1427 word1(*rvp) = x[1];
1428 }
1429 }
1430#endif /*No_Hex_NaN*/
1431#endif /* INFNAN_CHECK */
1432
1433 double
1434strtod
1435 (CONST char *s00, char **se)
1436{
1437#ifdef Avoid_Underflow
1438 int scale;
1439#endif
1440 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1441 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1442 CONST char *s, *s0, *s1;
1443 double aadj, aadj1, adj;
1444 U aadj2, rv, rv0;
1445 Long L;
1446 ULong y, z;
1447 Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
1448#ifdef SET_INEXACT
1449 int inexact, oldinexact;
1450#endif
1451#ifdef Honor_FLT_ROUNDS
1452 int rounding;
1453#endif
1454#ifdef USE_LOCALE
1455 CONST char *s2;
1456#endif
1457
1458 sign = nz0 = nz = 0;
1459 dval(rv) = 0.;
1460 for(s = s00;;s++) switch(*s) {
1461 case '-':
1462 sign = 1;
1463 /* no break */
1464 case '+':
1465 if (*++s)
1466 goto break2;
1467 /* no break */
1468 case 0:
1469 goto ret0;
1470 case '\t':
1471 case '\n':
1472 case '\v':
1473 case '\f':
1474 case '\r':
1475 case ' ':
1476 continue;
1477 default:
1478 goto break2;
1479 }
1480 break2:
1481 if (*s == '0') {
1482 nz0 = 1;
1483 while(*++s == '0') ;
1484 if (!*s)
1485 goto ret;
1486 }
1487 s0 = s;
1488 y = z = 0;
1489 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1490 if (nd < 9)
1491 y = 10*y + c - '0';
1492 else if (nd < 16)
1493 z = 10*z + c - '0';
1494 nd0 = nd;
1495#ifdef USE_LOCALE
1496 s1 = localeconv()->decimal_point;
1497 if (c == *s1) {
1498 c = '.';
1499 if (*++s1) {
1500 s2 = s;
1501 for(;;) {
1502 if (*++s2 != *s1) {
1503 c = 0;
1504 break;
1505 }
1506 if (!*++s1) {
1507 s = s2;
1508 break;
1509 }
1510 }
1511 }
1512 }
1513#endif
1514 if (c == '.') {
1515 c = *++s;
1516 if (!nd) {
1517 for(; c == '0'; c = *++s)
1518 nz++;
1519 if (c > '0' && c <= '9') {
1520 s0 = s;
1521 nf += nz;
1522 nz = 0;
1523 goto have_dig;
1524 }
1525 goto dig_done;
1526 }
1527 for(; c >= '0' && c <= '9'; c = *++s) {
1528 have_dig:
1529 nz++;
1530 if (c -= '0') {
1531 nf += nz;
1532 for(i = 1; i < nz; i++)
1533 if (nd++ < 9)
1534 y *= 10;
1535 else if (nd <= DBL_DIG + 1)
1536 z *= 10;
1537 if (nd++ < 9)
1538 y = 10*y + c;
1539 else if (nd <= DBL_DIG + 1)
1540 z = 10*z + c;
1541 nz = 0;
1542 }
1543 }
1544 }
1545 dig_done:
1546 e = 0;
1547 if (c == 'e' || c == 'E') {
1548 if (!nd && !nz && !nz0) {
1549 goto ret0;
1550 }
1551 s00 = s;
1552 esign = 0;
1553 switch(c = *++s) {
1554 case '-':
1555 esign = 1;
1556 case '+':
1557 c = *++s;
1558 }
1559 if (c >= '0' && c <= '9') {
1560 while(c == '0')
1561 c = *++s;
1562 if (c > '0' && c <= '9') {
1563 L = c - '0';
1564 s1 = s;
1565 while((c = *++s) >= '0' && c <= '9')
1566 L = 10*L + c - '0';
1567 if (s - s1 > 8 || L > 19999)
1568 /* Avoid confusion from exponents
1569 * so large that e might overflow.
1570 */
1571 e = 19999; /* safe for 16 bit ints */
1572 else
1573 e = (int)L;
1574 if (esign)
1575 e = -e;
1576 }
1577 else
1578 e = 0;
1579 }
1580 else
1581 s = s00;
1582 }
1583 if (!nd) {
1584 if (!nz && !nz0) {
1585#ifdef INFNAN_CHECK
1586 /* Check for Nan and Infinity */
1587 switch(c) {
1588 case 'i':
1589 case 'I':
1590 if (match(&s,"nf")) {
1591 --s;
1592 if (!match(&s,"inity"))
1593 ++s;
1594 word0(rv) = 0x7ff00000;
1595 word1(rv) = 0;
1596 goto ret;
1597 }
1598 break;
1599 case 'n':
1600 case 'N':
1601 if (match(&s, "an")) {
1602 word0(rv) = NAN_WORD0;
1603 word1(rv) = NAN_WORD1;
1604#ifndef No_Hex_NaN
1605 if (*s == '(') /*)*/
1606 hexnan(&rv, &s);
1607#endif
1608 goto ret;
1609 }
1610 }
1611#endif /* INFNAN_CHECK */
1612 ret0:
1613 s = s00;
1614 sign = 0;
1615 }
1616 goto ret;
1617 }
1618 e1 = e -= nf;
1619
1620 /* Now we have nd0 digits, starting at s0, followed by a
1621 * decimal point, followed by nd-nd0 digits. The number we're
1622 * after is the integer represented by those digits times
1623 * 10**e */
1624
1625 if (!nd0)
1626 nd0 = nd;
1627 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1628 dval(rv) = y;
1629 if (k > 9) {
1630#ifdef SET_INEXACT
1631 if (k > DBL_DIG)
1632 oldinexact = get_inexact();
1633#endif
1634 dval(rv) = tens[k - 9] * dval(rv) + z;
1635 }
1636 bd0 = 0;
1637 if (nd <= DBL_DIG
1638#ifndef RND_PRODQUOT
1639#ifndef Honor_FLT_ROUNDS
1640 && Flt_Rounds == 1
1641#endif
1642#endif
1643 ) {
1644 if (!e)
1645 goto ret;
1646 if (e > 0) {
1647 if (e <= Ten_pmax) {
1648#ifdef VAX
1649 goto vax_ovfl_check;
1650#else
1651#ifdef Honor_FLT_ROUNDS
1652 /* round correctly FLT_ROUNDS = 2 or 3 */
1653 if (sign) {
1654 rv = -rv;
1655 sign = 0;
1656 }
1657#endif
1658 /* rv = */ rounded_product(dval(rv), tens[e]);
1659 goto ret;
1660#endif
1661 }
1662 i = DBL_DIG - nd;
1663 if (e <= Ten_pmax + i) {
1664 /* A fancier test would sometimes let us do
1665 * this for larger i values.
1666 */
1667#ifdef Honor_FLT_ROUNDS
1668 /* round correctly FLT_ROUNDS = 2 or 3 */
1669 if (sign) {
1670 rv = -rv;
1671 sign = 0;
1672 }
1673#endif
1674 e -= i;
1675 dval(rv) *= tens[i];
1676#ifdef VAX
1677 /* VAX exponent range is so narrow we must
1678 * worry about overflow here...
1679 */
1680 vax_ovfl_check:
1681 word0(rv) -= P*Exp_msk1;
1682 /* rv = */ rounded_product(dval(rv), tens[e]);
1683 if ((word0(rv) & Exp_mask)
1684 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1685 goto ovfl;
1686 word0(rv) += P*Exp_msk1;
1687#else
1688 /* rv = */ rounded_product(dval(rv), tens[e]);
1689#endif
1690 goto ret;
1691 }
1692 }
1693#ifndef Inaccurate_Divide
1694 else if (e >= -Ten_pmax) {
1695#ifdef Honor_FLT_ROUNDS
1696 /* round correctly FLT_ROUNDS = 2 or 3 */
1697 if (sign) {
1698 rv = -rv;
1699 sign = 0;
1700 }
1701#endif
1702 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1703 goto ret;
1704 }
1705#endif
1706 }
1707 e1 += nd - k;
1708
1709#ifdef IEEE_Arith
1710#ifdef SET_INEXACT
1711 inexact = 1;
1712 if (k <= DBL_DIG)
1713 oldinexact = get_inexact();
1714#endif
1715#ifdef Avoid_Underflow
1716 scale = 0;
1717#endif
1718#ifdef Honor_FLT_ROUNDS
1719 if ((rounding = Flt_Rounds) >= 2) {
1720 if (sign)
1721 rounding = rounding == 2 ? 0 : 2;
1722 else
1723 if (rounding != 2)
1724 rounding = 0;
1725 }
1726#endif
1727#endif /*IEEE_Arith*/
1728
1729 /* Get starting approximation = rv * 10**e1 */
1730
1731 if (e1 > 0) {
1732 if ((i = e1 & 15))
1733 dval(rv) *= tens[i];
1734 if (e1 &= ~15) {
1735 if (e1 > DBL_MAX_10_EXP) {
1736 ovfl:
1737#ifndef NO_ERRNO
1738 errno = ERANGE;
1739#endif
1740 /* Can't trust HUGE_VAL */
1741#ifdef IEEE_Arith
1742#ifdef Honor_FLT_ROUNDS
1743 switch(rounding) {
1744 case 0: /* toward 0 */
1745 case 3: /* toward -infinity */
1746 word0(rv) = Big0;
1747 word1(rv) = Big1;
1748 break;
1749 default:
1750 word0(rv) = Exp_mask;
1751 word1(rv) = 0;
1752 }
1753#else /*Honor_FLT_ROUNDS*/
1754 word0(rv) = Exp_mask;
1755 word1(rv) = 0;
1756#endif /*Honor_FLT_ROUNDS*/
1757#ifdef SET_INEXACT
1758 /* set overflow bit */
1759 dval(rv0) = 1e300;
1760 dval(rv0) *= dval(rv0);
1761#endif
1762#else /*IEEE_Arith*/
1763 word0(rv) = Big0;
1764 word1(rv) = Big1;
1765#endif /*IEEE_Arith*/
1766 if (bd0)
1767 goto retfree;
1768 goto ret;
1769 }
1770 e1 >>= 4;
1771 for(j = 0; e1 > 1; j++, e1 >>= 1)
1772 if (e1 & 1)
1773 dval(rv) *= bigtens[j];
1774 /* The last multiplication could overflow. */
1775 word0(rv) -= P*Exp_msk1;
1776 dval(rv) *= bigtens[j];
1777 if ((z = word0(rv) & Exp_mask)
1778 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1779 goto ovfl;
1780 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1781 /* set to largest number */
1782 /* (Can't trust DBL_MAX) */
1783 word0(rv) = Big0;
1784 word1(rv) = Big1;
1785 }
1786 else
1787 word0(rv) += P*Exp_msk1;
1788 }
1789 }
1790 else if (e1 < 0) {
1791 e1 = -e1;
1792 if ((i = e1 & 15))
1793 dval(rv) /= tens[i];
1794 if (e1 >>= 4) {
1795 if (e1 >= 1 << n_bigtens)
1796 goto undfl;
1797#ifdef Avoid_Underflow
1798 if (e1 & Scale_Bit)
1799 scale = 2*P;
1800 for(j = 0; e1 > 0; j++, e1 >>= 1)
1801 if (e1 & 1)
1802 dval(rv) *= tinytens[j];
1803 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1804 >> Exp_shift)) > 0) {
1805 /* scaled rv is denormal; zap j low bits */
1806 if (j >= 32) {
1807 word1(rv) = 0;
1808 if (j >= 53)
1809 word0(rv) = (P+2)*Exp_msk1;
1810 else
1811 word0(rv) &= 0xffffffff << (j-32);
1812 }
1813 else
1814 word1(rv) &= 0xffffffff << j;
1815 }
1816#else
1817 for(j = 0; e1 > 1; j++, e1 >>= 1)
1818 if (e1 & 1)
1819 dval(rv) *= tinytens[j];
1820 /* The last multiplication could underflow. */
1821 dval(rv0) = dval(rv);
1822 dval(rv) *= tinytens[j];
1823 if (!dval(rv)) {
1824 dval(rv) = 2.*dval(rv0);
1825 dval(rv) *= tinytens[j];
1826#endif
1827 if (!dval(rv)) {
1828 undfl:
1829 dval(rv) = 0.;
1830#ifndef NO_ERRNO
1831 errno = ERANGE;
1832#endif
1833 if (bd0)
1834 goto retfree;
1835 goto ret;
1836 }
1837#ifndef Avoid_Underflow
1838 word0(rv) = Tiny0;
1839 word1(rv) = Tiny1;
1840 /* The refinement below will clean
1841 * this approximation up.
1842 */
1843 }
1844#endif
1845 }
1846 }
1847
1848 /* Now the hard part -- adjusting rv to the correct value.*/
1849
1850 /* Put digits into bd: true value = bd * 10^e */
1851
1852 bd0 = s2b(s0, nd0, nd, y);
1853
1854 for(;;) {
1855 bd = Balloc(bd0->k);
1856 Bcopy(bd, bd0);
1857 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1858 bs = i2b(1);
1859
1860 if (e >= 0) {
1861 bb2 = bb5 = 0;
1862 bd2 = bd5 = e;
1863 }
1864 else {
1865 bb2 = bb5 = -e;
1866 bd2 = bd5 = 0;
1867 }
1868 if (bbe >= 0)
1869 bb2 += bbe;
1870 else
1871 bd2 -= bbe;
1872 bs2 = bb2;
1873#ifdef Honor_FLT_ROUNDS
1874 if (rounding != 1)
1875 bs2++;
1876#endif
1877#ifdef Avoid_Underflow
1878 j = bbe - scale;
1879 i = j + bbbits - 1; /* logb(rv) */
1880 if (i < Emin) /* denormal */
1881 j += P - Emin;
1882 else
1883 j = P + 1 - bbbits;
1884#else /*Avoid_Underflow*/
1885#ifdef Sudden_Underflow
1886#ifdef IBM
1887 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1888#else
1889 j = P + 1 - bbbits;
1890#endif
1891#else /*Sudden_Underflow*/
1892 j = bbe;
1893 i = j + bbbits - 1; /* logb(rv) */
1894 if (i < Emin) /* denormal */
1895 j += P - Emin;
1896 else
1897 j = P + 1 - bbbits;
1898#endif /*Sudden_Underflow*/
1899#endif /*Avoid_Underflow*/
1900 bb2 += j;
1901 bd2 += j;
1902#ifdef Avoid_Underflow
1903 bd2 += scale;
1904#endif
1905 i = bb2 < bd2 ? bb2 : bd2;
1906 if (i > bs2)
1907 i = bs2;
1908 if (i > 0) {
1909 bb2 -= i;
1910 bd2 -= i;
1911 bs2 -= i;
1912 }
1913 if (bb5 > 0) {
1914 bs = pow5mult(bs, bb5);
1915 bb1 = mult(bs, bb);
1916 Bfree(bb);
1917 bb = bb1;
1918 }
1919 if (bb2 > 0)
1920 bb = lshift(bb, bb2);
1921 if (bd5 > 0)
1922 bd = pow5mult(bd, bd5);
1923 if (bd2 > 0)
1924 bd = lshift(bd, bd2);
1925 if (bs2 > 0)
1926 bs = lshift(bs, bs2);
1927 delta = diff(bb, bd);
1928 dsign = delta->sign;
1929 delta->sign = 0;
1930 i = cmp(delta, bs);
1931#ifdef Honor_FLT_ROUNDS
1932 if (rounding != 1) {
1933 if (i < 0) {
1934 /* Error is less than an ulp */
1935 if (!delta->x[0] && delta->wds <= 1) {
1936 /* exact */
1937#ifdef SET_INEXACT
1938 inexact = 0;
1939#endif
1940 break;
1941 }
1942 if (rounding) {
1943 if (dsign) {
1944 adj = 1.;
1945 goto apply_adj;
1946 }
1947 }
1948 else if (!dsign) {
1949 adj = -1.;
1950 if (!word1(rv)
1951 && !(word0(rv) & Frac_mask)) {
1952 y = word0(rv) & Exp_mask;
1953#ifdef Avoid_Underflow
1954 if (!scale || y > 2*P*Exp_msk1)
1955#else
1956 if (y)
1957#endif
1958 {
1959 delta = lshift(delta,Log2P);
1960 if (cmp(delta, bs) <= 0)
1961 adj = -0.5;
1962 }
1963 }
1964 apply_adj:
1965#ifdef Avoid_Underflow
1966 if (scale && (y = word0(rv) & Exp_mask)
1967 <= 2*P*Exp_msk1)
1968 word0(adj) += (2*P+1)*Exp_msk1 - y;
1969#else
1970#ifdef Sudden_Underflow
1971 if ((word0(rv) & Exp_mask) <=
1972 P*Exp_msk1) {
1973 word0(rv) += P*Exp_msk1;
1974 dval(rv) += adj*ulp(dval(rv));
1975 word0(rv) -= P*Exp_msk1;
1976 }
1977 else
1978#endif /*Sudden_Underflow*/
1979#endif /*Avoid_Underflow*/
1980 dval(rv) += adj*ulp(dval(rv));
1981 }
1982 break;
1983 }
1984 adj = ratio(delta, bs);
1985 if (adj < 1.)
1986 adj = 1.;
1987 if (adj <= 0x7ffffffe) {
1988 /* adj = rounding ? ceil(adj) : floor(adj); */
1989 y = adj;
1990 if (y != adj) {
1991 if (!((rounding>>1) ^ dsign))
1992 y++;
1993 adj = y;
1994 }
1995 }
1996#ifdef Avoid_Underflow
1997 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
1998 word0(adj) += (2*P+1)*Exp_msk1 - y;
1999#else
2000#ifdef Sudden_Underflow
2001 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2002 word0(rv) += P*Exp_msk1;
2003 adj *= ulp(dval(rv));
2004 if (dsign)
2005 dval(rv) += adj;
2006 else
2007 dval(rv) -= adj;
2008 word0(rv) -= P*Exp_msk1;
2009 goto cont;
2010 }
2011#endif /*Sudden_Underflow*/
2012#endif /*Avoid_Underflow*/
2013 adj *= ulp(dval(rv));
2014 if (dsign)
2015 dval(rv) += adj;
2016 else
2017 dval(rv) -= adj;
2018 goto cont;
2019 }
2020#endif /*Honor_FLT_ROUNDS*/
2021
2022 if (i < 0) {
2023 /* Error is less than half an ulp -- check for
2024 * special case of mantissa a power of two.
2025 */
2026 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2027#ifdef IEEE_Arith
2028#ifdef Avoid_Underflow
2029 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2030#else
2031 || (word0(rv) & Exp_mask) <= Exp_msk1
2032#endif
2033#endif
2034 ) {
2035#ifdef SET_INEXACT
2036 if (!delta->x[0] && delta->wds <= 1)
2037 inexact = 0;
2038#endif
2039 break;
2040 }
2041 if (!delta->x[0] && delta->wds <= 1) {
2042 /* exact result */
2043#ifdef SET_INEXACT
2044 inexact = 0;
2045#endif
2046 break;
2047 }
2048 delta = lshift(delta,Log2P);
2049 if (cmp(delta, bs) > 0)
2050 goto drop_down;
2051 break;
2052 }
2053 if (i == 0) {
2054 /* exactly half-way between */
2055 if (dsign) {
2056 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2057 && word1(rv) == (
2058#ifdef Avoid_Underflow
2059 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2060 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2061#endif
2062 0xffffffff)) {
2063 /*boundary case -- increment exponent*/
2064 word0(rv) = (word0(rv) & Exp_mask)
2065 + Exp_msk1
2066#ifdef IBM
2067 | Exp_msk1 >> 4
2068#endif
2069 ;
2070 word1(rv) = 0;
2071#ifdef Avoid_Underflow
2072 dsign = 0;
2073#endif
2074 break;
2075 }
2076 }
2077 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2078 drop_down:
2079 /* boundary case -- decrement exponent */
2080#ifdef Sudden_Underflow /*{{*/
2081 L = word0(rv) & Exp_mask;
2082#ifdef IBM
2083 if (L < Exp_msk1)
2084#else
2085#ifdef Avoid_Underflow
2086 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2087#else
2088 if (L <= Exp_msk1)
2089#endif /*Avoid_Underflow*/
2090#endif /*IBM*/
2091 goto undfl;
2092 L -= Exp_msk1;
2093#else /*Sudden_Underflow}{*/
2094#ifdef Avoid_Underflow
2095 if (scale) {
2096 L = word0(rv) & Exp_mask;
2097 if (L <= (2*P+1)*Exp_msk1) {
2098 if (L > (P+2)*Exp_msk1)
2099 /* round even ==> */
2100 /* accept rv */
2101 break;
2102 /* rv = smallest denormal */
2103 goto undfl;
2104 }
2105 }
2106#endif /*Avoid_Underflow*/
2107 L = (word0(rv) & Exp_mask) - Exp_msk1;
2108#endif /*Sudden_Underflow}}*/
2109 word0(rv) = L | Bndry_mask1;
2110 word1(rv) = 0xffffffff;
2111#ifdef IBM
2112 goto cont;
2113#else
2114 break;
2115#endif
2116 }
2117#ifndef ROUND_BIASED
2118 if (!(word1(rv) & LSB))
2119 break;
2120#endif
2121 if (dsign)
2122 dval(rv) += ulp(dval(rv));
2123#ifndef ROUND_BIASED
2124 else {
2125 dval(rv) -= ulp(dval(rv));
2126#ifndef Sudden_Underflow
2127 if (!dval(rv))
2128 goto undfl;
2129#endif
2130 }
2131#ifdef Avoid_Underflow
2132 dsign = 1 - dsign;
2133#endif
2134#endif
2135 break;
2136 }
2137 if ((aadj = ratio(delta, bs)) <= 2.) {
2138 if (dsign)
2139 aadj = aadj1 = 1.;
2140 else if (word1(rv) || word0(rv) & Bndry_mask) {
2141#ifndef Sudden_Underflow
2142 if (word1(rv) == Tiny1 && !word0(rv))
2143 goto undfl;
2144#endif
2145 aadj = 1.;
2146 aadj1 = -1.;
2147 }
2148 else {
2149 /* special case -- power of FLT_RADIX to be */
2150 /* rounded down... */
2151
2152 if (aadj < 2./FLT_RADIX)
2153 aadj = 1./FLT_RADIX;
2154 else
2155 aadj *= 0.5;
2156 aadj1 = -aadj;
2157 }
2158 }
2159 else {
2160 aadj *= 0.5;
2161 aadj1 = dsign ? aadj : -aadj;
2162#ifdef Check_FLT_ROUNDS
2163 switch(Rounding) {
2164 case 2: /* towards +infinity */
2165 aadj1 -= 0.5;
2166 break;
2167 case 0: /* towards 0 */
2168 case 3: /* towards -infinity */
2169 aadj1 += 0.5;
2170 }
2171#else
2172 if (Flt_Rounds == 0)
2173 aadj1 += 0.5;
2174#endif /*Check_FLT_ROUNDS*/
2175 }
2176 y = word0(rv) & Exp_mask;
2177
2178 /* Check for overflow */
2179
2180 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2181 dval(rv0) = dval(rv);
2182 word0(rv) -= P*Exp_msk1;
2183 adj = aadj1 * ulp(dval(rv));
2184 dval(rv) += adj;
2185 if ((word0(rv) & Exp_mask) >=
2186 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2187 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2188 goto ovfl;
2189 word0(rv) = Big0;
2190 word1(rv) = Big1;
2191 goto cont;
2192 }
2193 else
2194 word0(rv) += P*Exp_msk1;
2195 }
2196 else {
2197#ifdef Avoid_Underflow
2198 if (scale && y <= 2*P*Exp_msk1) {
2199 if (aadj <= 0x7fffffff) {
2200 if ((z = (ULong)aadj) <= 0)
2201 z = 1;
2202 aadj = z;
2203 aadj1 = dsign ? aadj : -aadj;
2204 }
2205 dval(aadj2) = aadj1;
2206 word0(aadj2) += (2*P+1)*Exp_msk1 - y;
2207 aadj1 = dval(aadj2);
2208 }
2209 adj = aadj1 * ulp(dval(rv));
2210 dval(rv) += adj;
2211#else
2212#ifdef Sudden_Underflow
2213 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2214 dval(rv0) = dval(rv);
2215 word0(rv) += P*Exp_msk1;
2216 adj = aadj1 * ulp(dval(rv));
2217 dval(rv) += adj;
2218#ifdef IBM
2219 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2220#else
2221 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2222#endif
2223 {
2224 if (word0(rv0) == Tiny0
2225 && word1(rv0) == Tiny1)
2226 goto undfl;
2227 word0(rv) = Tiny0;
2228 word1(rv) = Tiny1;
2229 goto cont;
2230 }
2231 else
2232 word0(rv) -= P*Exp_msk1;
2233 }
2234 else {
2235 adj = aadj1 * ulp(dval(rv));
2236 dval(rv) += adj;
2237 }
2238#else /*Sudden_Underflow*/
2239 /* Compute adj so that the IEEE rounding rules will
2240 * correctly round rv + adj in some half-way cases.
2241 * If rv * ulp(rv) is denormalized (i.e.,
2242 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2243 * trouble from bits lost to denormalization;
2244 * example: 1.2e-307 .
2245 */
2246 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2247 aadj1 = (double)(int)(aadj + 0.5);
2248 if (!dsign)
2249 aadj1 = -aadj1;
2250 }
2251 adj = aadj1 * ulp(dval(rv));
2252 dval(rv) += adj;
2253#endif /*Sudden_Underflow*/
2254#endif /*Avoid_Underflow*/
2255 }
2256 z = word0(rv) & Exp_mask;
2257#ifndef SET_INEXACT
2258#ifdef Avoid_Underflow
2259 if (!scale)
2260#endif
2261 if (y == z) {
2262 /* Can we stop now? */
2263 L = (Long)aadj;
2264 aadj -= L;
2265 /* The tolerances below are conservative. */
2266 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2267 if (aadj < .4999999 || aadj > .5000001)
2268 break;
2269 }
2270 else if (aadj < .4999999/FLT_RADIX)
2271 break;
2272 }
2273#endif
2274 cont:
2275 Bfree(bb);
2276 Bfree(bd);
2277 Bfree(bs);
2278 Bfree(delta);
2279 }
2280#ifdef SET_INEXACT
2281 if (inexact) {
2282 if (!oldinexact) {
2283 word0(rv0) = Exp_1 + (70 << Exp_shift);
2284 word1(rv0) = 0;
2285 dval(rv0) += 1.;
2286 }
2287 }
2288 else if (!oldinexact)
2289 clear_inexact();
2290#endif
2291#ifdef Avoid_Underflow
2292 if (scale) {
2293 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2294 word1(rv0) = 0;
2295 dval(rv) *= dval(rv0);
2296#ifndef NO_ERRNO
2297 /* try to avoid the bug of testing an 8087 register value */
2298 if (word0(rv) == 0 && word1(rv) == 0)
2299 errno = ERANGE;
2300#endif
2301 }
2302#endif /* Avoid_Underflow */
2303#ifdef SET_INEXACT
2304 if (inexact && !(word0(rv) & Exp_mask)) {
2305 /* set underflow bit */
2306 dval(rv0) = 1e-300;
2307 dval(rv0) *= dval(rv0);
2308 }
2309#endif
2310 retfree:
2311 Bfree(bb);
2312 Bfree(bd);
2313 Bfree(bs);
2314 Bfree(bd0);
2315 Bfree(delta);
2316 ret:
2317 if (se)
2318 *se = (char *)s;
2319 return sign ? -dval(rv) : dval(rv);
2320 }
2321
2322 static int
2323quorem
2324 (Bigint *b, Bigint *S)
2325{
2326 int n;
2327 ULong *bx, *bxe, q, *sx, *sxe;
2328#ifdef ULLong
2329 ULLong borrow, carry, y, ys;
2330#else
2331 ULong borrow, carry, y, ys;
2332#ifdef Pack_32
2333 ULong si, z, zs;
2334#endif
2335#endif
2336
2337 n = S->wds;
2338#ifdef DEBUG
2339 /*debug*/ if (b->wds > n)
2340 /*debug*/ Bug("oversize b in quorem");
2341#endif
2342 if (b->wds < n)
2343 return 0;
2344 sx = S->x;
2345 sxe = sx + --n;
2346 bx = b->x;
2347 bxe = bx + n;
2348 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2349#ifdef DEBUG
2350 /*debug*/ if (q > 9)
2351 /*debug*/ Bug("oversized quotient in quorem");
2352#endif
2353 if (q) {
2354 borrow = 0;
2355 carry = 0;
2356 do {
2357#ifdef ULLong
2358 ys = *sx++ * (ULLong)q + carry;
2359 carry = ys >> 32;
2360 y = *bx - (ys & FFFFFFFF) - borrow;
2361 borrow = y >> 32 & (ULong)1;
2362 *bx++ = (ULong)y & FFFFFFFF;
2363#else
2364#ifdef Pack_32
2365 si = *sx++;
2366 ys = (si & 0xffff) * q + carry;
2367 zs = (si >> 16) * q + (ys >> 16);
2368 carry = zs >> 16;
2369 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2370 borrow = (y & 0x10000) >> 16;
2371 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2372 borrow = (z & 0x10000) >> 16;
2373 Storeinc(bx, z, y);
2374#else
2375 ys = *sx++ * q + carry;
2376 carry = ys >> 16;
2377 y = *bx - (ys & 0xffff) - borrow;
2378 borrow = (y & 0x10000) >> 16;
2379 *bx++ = y & 0xffff;
2380#endif
2381#endif
2382 }
2383 while(sx <= sxe);
2384 if (!*bxe) {
2385 bx = b->x;
2386 while(--bxe > bx && !*bxe)
2387 --n;
2388 b->wds = n;
2389 }
2390 }
2391 if (cmp(b, S) >= 0) {
2392 q++;
2393 borrow = 0;
2394 carry = 0;
2395 bx = b->x;
2396 sx = S->x;
2397 do {
2398#ifdef ULLong
2399 ys = *sx++ + carry;
2400 carry = ys >> 32;
2401 y = *bx - (ys & FFFFFFFF) - borrow;
2402 borrow = y >> 32 & (ULong)1;
2403 *bx++ = (ULong)y & FFFFFFFF;
2404#else
2405#ifdef Pack_32
2406 si = *sx++;
2407 ys = (si & 0xffff) + carry;
2408 zs = (si >> 16) + (ys >> 16);
2409 carry = zs >> 16;
2410 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2411 borrow = (y & 0x10000) >> 16;
2412 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2413 borrow = (z & 0x10000) >> 16;
2414 Storeinc(bx, z, y);
2415#else
2416 ys = *sx++ + carry;
2417 carry = ys >> 16;
2418 y = *bx - (ys & 0xffff) - borrow;
2419 borrow = (y & 0x10000) >> 16;
2420 *bx++ = y & 0xffff;
2421#endif
2422#endif
2423 }
2424 while(sx <= sxe);
2425 bx = b->x;
2426 bxe = bx + n;
2427 if (!*bxe) {
2428 while(--bxe > bx && !*bxe)
2429 --n;
2430 b->wds = n;
2431 }
2432 }
2433 return q;
2434 }
2435
2436#ifndef MULTIPLE_THREADS
2437 static char *dtoa_result;
2438#endif
2439
2440 static char *
2441rv_alloc(int i)
2442{
2443 int j, k, *r;
2444
2445 j = sizeof(ULong);
2446 for(k = 0;
2447 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
2448 j <<= 1)
2449 k++;
2450 r = (int*)Balloc(k);
2451 *r = k;
2452 return
2453#ifndef MULTIPLE_THREADS
2454 dtoa_result =
2455#endif
2456 (char *)(r+1);
2457 }
2458
2459 static char *
2460nrv_alloc(CONST char *s, char **rve, int n)
2461{
2462 char *rv, *t;
2463
2464 t = rv = rv_alloc(n);
2465 while((*t = *s++)) t++;
2466 if (rve)
2467 *rve = t;
2468 return rv;
2469 }
2470
2471/* freedtoa(s) must be used to free values s returned by dtoa
2472 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2473 * but for consistency with earlier versions of dtoa, it is optional
2474 * when MULTIPLE_THREADS is not defined.
2475 */
2476
2477 void
2478freedtoa(char *s)
2479{
2480 Bigint *b = (Bigint *)((int *)s - 1);
2481 b->maxwds = 1 << (b->k = *(int*)b);
2482 Bfree(b);
2483#ifndef MULTIPLE_THREADS
2484 if (s == dtoa_result)
2485 dtoa_result = 0;
2486#endif
2487 }
2488
2489/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2490 *
2491 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2492 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
2493 *
2494 * Modifications:
2495 * 1. Rather than iterating, we use a simple numeric overestimate
2496 * to determine k = floor(log10(d)). We scale relevant
2497 * quantities using O(log2(k)) rather than O(k) multiplications.
2498 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2499 * try to generate digits strictly left to right. Instead, we
2500 * compute with fewer bits and propagate the carry if necessary
2501 * when rounding the final digit up. This is often faster.
2502 * 3. Under the assumption that input will be rounded nearest,
2503 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2504 * That is, we allow equality in stopping tests when the
2505 * round-nearest rule will give the same floating-point value
2506 * as would satisfaction of the stopping test with strict
2507 * inequality.
2508 * 4. We remove common factors of powers of 2 from relevant
2509 * quantities.
2510 * 5. When converting floating-point integers less than 1e16,
2511 * we use floating-point arithmetic rather than resorting
2512 * to multiple-precision integers.
2513 * 6. When asked to produce fewer than 15 digits, we first try
2514 * to get by with floating-point arithmetic; we resort to
2515 * multiple-precision integer arithmetic only if we cannot
2516 * guarantee that the floating-point calculation has given
2517 * the correctly rounded result. For k requested digits and
2518 * "uniformly" distributed input, the probability is
2519 * something like 10^(k-15) that we must resort to the Long
2520 * calculation.
2521 */
2522
2523 char *
2524dtoa
2525 (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
2526{
2527 /* Arguments ndigits, decpt, sign are similar to those
2528 of ecvt and fcvt; trailing zeros are suppressed from
2529 the returned string. If not null, *rve is set to point
2530 to the end of the return value. If d is +-Infinity or NaN,
2531 then *decpt is set to 9999.
2532
2533 mode:
2534 0 ==> shortest string that yields d when read in
2535 and rounded to nearest.
2536 1 ==> like 0, but with Steele & White stopping rule;
2537 e.g. with IEEE P754 arithmetic , mode 0 gives
2538 1e23 whereas mode 1 gives 9.999999999999999e22.
2539 2 ==> max(1,ndigits) significant digits. This gives a
2540 return value similar to that of ecvt, except
2541 that trailing zeros are suppressed.
2542 3 ==> through ndigits past the decimal point. This
2543 gives a return value similar to that from fcvt,
2544 except that trailing zeros are suppressed, and
2545 ndigits can be negative.
2546 4,5 ==> similar to 2 and 3, respectively, but (in
2547 round-nearest mode) with the tests of mode 0 to
2548 possibly return a shorter string that rounds to d.
2549 With IEEE arithmetic and compilation with
2550 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2551 as modes 2 and 3 when FLT_ROUNDS != 1.
2552 6-9 ==> Debugging modes similar to mode - 4: don't try
2553 fast floating-point estimate (if applicable).
2554
2555 Values of mode other than 0-9 are treated as mode 0.
2556
2557 Sufficient space is allocated to the return value
2558 to hold the suppressed trailing zeros.
2559 */
2560
2561 int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
2562 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2563 spec_case, try_quick;
2564 Long L;
2565#ifndef Sudden_Underflow
2566 int denorm;
2567 ULong x;
2568#endif
2569 Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
2570 U d, d2, eps;
2571 double ds;
2572 char *s, *s0;
2573#ifdef Honor_FLT_ROUNDS
2574 int rounding;
2575#endif
2576#ifdef SET_INEXACT
2577 int inexact, oldinexact;
2578#endif
2579
2580#ifndef MULTIPLE_THREADS
2581 if (dtoa_result) {
2582 freedtoa(dtoa_result);
2583 dtoa_result = 0;
2584 }
2585#endif
2586
2587 dval(d) = dd;
2588 if (word0(d) & Sign_bit) {
2589 /* set sign for everything, including 0's and NaNs */
2590 *sign = 1;
2591 word0(d) &= ~Sign_bit; /* clear sign bit */
2592 }
2593 else
2594 *sign = 0;
2595
2596#if defined(IEEE_Arith) + defined(VAX)
2597#ifdef IEEE_Arith
2598 if ((word0(d) & Exp_mask) == Exp_mask)
2599#else
2600 if (word0(d) == 0x8000)
2601#endif
2602 {
2603 /* Infinity or NaN */
2604 *decpt = 9999;
2605#ifdef IEEE_Arith
2606 if (!word1(d) && !(word0(d) & 0xfffff))
2607 return nrv_alloc("Infinity", rve, 8);
2608#endif
2609 return nrv_alloc("NaN", rve, 3);
2610 }
2611#endif
2612#ifdef IBM
2613 dval(d) += 0; /* normalize */
2614#endif
2615 if (!dval(d)) {
2616 *decpt = 1;
2617 return nrv_alloc("0", rve, 1);
2618 }
2619
2620#ifdef SET_INEXACT
2621 try_quick = oldinexact = get_inexact();
2622 inexact = 1;
2623#endif
2624#ifdef Honor_FLT_ROUNDS
2625 if ((rounding = Flt_Rounds) >= 2) {
2626 if (*sign)
2627 rounding = rounding == 2 ? 0 : 2;
2628 else
2629 if (rounding != 2)
2630 rounding = 0;
2631 }
2632#endif
2633
2634 b = d2b(dval(d), &be, &bbits);
2635#ifdef Sudden_Underflow
2636 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2637#else
2638 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2639#endif
2640 dval(d2) = dval(d);
2641 word0(d2) &= Frac_mask1;
2642 word0(d2) |= Exp_11;
2643#ifdef IBM
2644 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2645 dval(d2) /= 1 << j;
2646#endif
2647
2648 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2649 * log10(x) = log(x) / log(10)
2650 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2651 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2652 *
2653 * This suggests computing an approximation k to log10(d) by
2654 *
2655 * k = (i - Bias)*0.301029995663981
2656 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2657 *
2658 * We want k to be too large rather than too small.
2659 * The error in the first-order Taylor series approximation
2660 * is in our favor, so we just round up the constant enough
2661 * to compensate for any error in the multiplication of
2662 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2663 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2664 * adding 1e-13 to the constant term more than suffices.
2665 * Hence we adjust the constant term to 0.1760912590558.
2666 * (We could get a more accurate k by invoking log10,
2667 * but this is probably not worthwhile.)
2668 */
2669
2670 i -= Bias;
2671#ifdef IBM
2672 i <<= 2;
2673 i += j;
2674#endif
2675#ifndef Sudden_Underflow
2676 denorm = 0;
2677 }
2678 else {
2679 /* d is denormalized */
2680
2681 i = bbits + be + (Bias + (P-1) - 1);
2682 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2683 : word1(d) << (32 - i);
2684 dval(d2) = x;
2685 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2686 i -= (Bias + (P-1) - 1) + 1;
2687 denorm = 1;
2688 }
2689#endif
2690 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2691 k = (int)ds;
2692 if (ds < 0. && ds != k)
2693 k--; /* want k = floor(ds) */
2694 k_check = 1;
2695 if (k >= 0 && k <= Ten_pmax) {
2696 if (dval(d) < tens[k])
2697 k--;
2698 k_check = 0;
2699 }
2700 j = bbits - i - 1;
2701 if (j >= 0) {
2702 b2 = 0;
2703 s2 = j;
2704 }
2705 else {
2706 b2 = -j;
2707 s2 = 0;
2708 }
2709 if (k >= 0) {
2710 b5 = 0;
2711 s5 = k;
2712 s2 += k;
2713 }
2714 else {
2715 b2 -= k;
2716 b5 = -k;
2717 s5 = 0;
2718 }
2719 if (mode < 0 || mode > 9)
2720 mode = 0;
2721
2722#ifndef SET_INEXACT
2723#ifdef Check_FLT_ROUNDS
2724 try_quick = Rounding == 1;
2725#else
2726 try_quick = 1;
2727#endif
2728#endif /*SET_INEXACT*/
2729
2730 if (mode > 5) {
2731 mode -= 4;
2732 try_quick = 0;
2733 }
2734 leftright = 1;
2735 switch(mode) {
2736 case 0:
2737 case 1:
2738 ilim = ilim1 = -1;
2739 i = 18;
2740 ndigits = 0;
2741 break;
2742 case 2:
2743 leftright = 0;
2744 /* no break */
2745 case 4:
2746 if (ndigits <= 0)
2747 ndigits = 1;
2748 ilim = ilim1 = i = ndigits;
2749 break;
2750 case 3:
2751 leftright = 0;
2752 /* no break */
2753 case 5:
2754 i = ndigits + k + 1;
2755 ilim = i;
2756 ilim1 = i - 1;
2757 if (i <= 0)
2758 i = 1;
2759 }
2760 s = s0 = rv_alloc(i);
2761
2762#ifdef Honor_FLT_ROUNDS
2763 if (mode > 1 && rounding != 1)
2764 leftright = 0;
2765#endif
2766
2767 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2768
2769 /* Try to get by with floating-point arithmetic. */
2770
2771 i = 0;
2772 dval(d2) = dval(d);
2773 k0 = k;
2774 ilim0 = ilim;
2775 ieps = 2; /* conservative */
2776 if (k > 0) {
2777 ds = tens[k&0xf];
2778 j = k >> 4;
2779 if (j & Bletch) {
2780 /* prevent overflows */
2781 j &= Bletch - 1;
2782 dval(d) /= bigtens[n_bigtens-1];
2783 ieps++;
2784 }
2785 for(; j; j >>= 1, i++)
2786 if (j & 1) {
2787 ieps++;
2788 ds *= bigtens[i];
2789 }
2790 dval(d) /= ds;
2791 }
2792 else if ((j1 = -k)) {
2793 dval(d) *= tens[j1 & 0xf];
2794 for(j = j1 >> 4; j; j >>= 1, i++)
2795 if (j & 1) {
2796 ieps++;
2797 dval(d) *= bigtens[i];
2798 }
2799 }
2800 if (k_check && dval(d) < 1. && ilim > 0) {
2801 if (ilim1 <= 0)
2802 goto fast_failed;
2803 ilim = ilim1;
2804 k--;
2805 dval(d) *= 10.;
2806 ieps++;
2807 }
2808 dval(eps) = ieps*dval(d) + 7.;
2809 word0(eps) -= (P-1)*Exp_msk1;
2810 if (ilim == 0) {
2811 S = mhi = 0;
2812 dval(d) -= 5.;
2813 if (dval(d) > dval(eps))
2814 goto one_digit;
2815 if (dval(d) < -dval(eps))
2816 goto no_digits;
2817 goto fast_failed;
2818 }
2819#ifndef No_leftright
2820 if (leftright) {
2821 /* Use Steele & White method of only
2822 * generating digits needed.
2823 */
2824 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2825 for(i = 0;;) {
2826 L = (long int)dval(d);
2827 dval(d) -= L;
2828 *s++ = '0' + (int)L;
2829 if (dval(d) < dval(eps))
2830 goto ret1;
2831 if (1. - dval(d) < dval(eps))
2832 goto bump_up;
2833 if (++i >= ilim)
2834 break;
2835 dval(eps) *= 10.;
2836 dval(d) *= 10.;
2837 }
2838 }
2839 else {
2840#endif
2841 /* Generate ilim digits, then fix them up. */
2842 dval(eps) *= tens[ilim-1];
2843 for(i = 1;; i++, dval(d) *= 10.) {
2844 L = (Long)(dval(d));
2845 if (!(dval(d) -= L))
2846 ilim = i;
2847 *s++ = '0' + (int)L;
2848 if (i == ilim) {
2849 if (dval(d) > 0.5 + dval(eps))
2850 goto bump_up;
2851 else if (dval(d) < 0.5 - dval(eps)) {
2852 while(*--s == '0')
2853 ;
2854 s++;
2855 goto ret1;
2856 }
2857 break;
2858 }
2859 }
2860#ifndef No_leftright
2861 }
2862#endif
2863 fast_failed:
2864 s = s0;
2865 dval(d) = dval(d2);
2866 k = k0;
2867 ilim = ilim0;
2868 }
2869
2870 /* Do we have a "small" integer? */
2871
2872 if (be >= 0 && k <= Int_max) {
2873 /* Yes. */
2874 ds = tens[k];
2875 if (ndigits < 0 && ilim <= 0) {
2876 S = mhi = 0;
2877 if (ilim < 0 || dval(d) <= 5*ds)
2878 goto no_digits;
2879 goto one_digit;
2880 }
2881 for(i = 1;; i++, dval(d) *= 10.) {
2882 L = (Long)(dval(d) / ds);
2883 dval(d) -= L*ds;
2884#ifdef Check_FLT_ROUNDS
2885 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2886 if (dval(d) < 0) {
2887 L--;
2888 dval(d) += ds;
2889 }
2890#endif
2891 *s++ = '0' + (int)L;
2892 if (!dval(d)) {
2893#ifdef SET_INEXACT
2894 inexact = 0;
2895#endif
2896 break;
2897 }
2898 if (i == ilim) {
2899#ifdef Honor_FLT_ROUNDS
2900 if (mode > 1)
2901 switch(rounding) {
2902 case 0: goto ret1;
2903 case 2: goto bump_up;
2904 }
2905#endif
2906 dval(d) += dval(d);
2907 if (dval(d) > ds || (dval(d) == ds && L & 1)) {
2908 bump_up:
2909 while(*--s == '9')
2910 if (s == s0) {
2911 k++;
2912 *s = '0';
2913 break;
2914 }
2915 ++*s++;
2916 }
2917 break;
2918 }
2919 }
2920 goto ret1;
2921 }
2922
2923 m2 = b2;
2924 m5 = b5;
2925 mhi = mlo = 0;
2926 if (leftright) {
2927 i =
2928#ifndef Sudden_Underflow
2929 denorm ? be + (Bias + (P-1) - 1 + 1) :
2930#endif
2931#ifdef IBM
2932 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2933#else
2934 1 + P - bbits;
2935#endif
2936 b2 += i;
2937 s2 += i;
2938 mhi = i2b(1);
2939 }
2940 if (m2 > 0 && s2 > 0) {
2941 i = m2 < s2 ? m2 : s2;
2942 b2 -= i;
2943 m2 -= i;
2944 s2 -= i;
2945 }
2946 if (b5 > 0) {
2947 if (leftright) {
2948 if (m5 > 0) {
2949 mhi = pow5mult(mhi, m5);
2950 b1 = mult(mhi, b);
2951 Bfree(b);
2952 b = b1;
2953 }
2954 if ((j = b5 - m5))
2955 b = pow5mult(b, j);
2956 }
2957 else
2958 b = pow5mult(b, b5);
2959 }
2960 S = i2b(1);
2961 if (s5 > 0)
2962 S = pow5mult(S, s5);
2963
2964 /* Check for special case that d is a normalized power of 2. */
2965
2966 spec_case = 0;
2967 if ((mode < 2 || leftright)
2968#ifdef Honor_FLT_ROUNDS
2969 && rounding == 1
2970#endif
2971 ) {
2972 if (!word1(d) && !(word0(d) & Bndry_mask)
2973#ifndef Sudden_Underflow
2974 && word0(d) & (Exp_mask & ~Exp_msk1)
2975#endif
2976 ) {
2977 /* The special case */
2978 b2 += Log2P;
2979 s2 += Log2P;
2980 spec_case = 1;
2981 }
2982 }
2983
2984 /* Arrange for convenient computation of quotients:
2985 * shift left if necessary so divisor has 4 leading 0 bits.
2986 *
2987 * Perhaps we should just compute leading 28 bits of S once
2988 * and for all and pass them and a shift to quorem, so it
2989 * can do shifts and ors to compute the numerator for q.
2990 */
2991#ifdef Pack_32
2992 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
2993 i = 32 - i;
2994#else
2995 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
2996 i = 16 - i;
2997#endif
2998 if (i > 4) {
2999 i -= 4;
3000 b2 += i;
3001 m2 += i;
3002 s2 += i;
3003 }
3004 else if (i < 4) {
3005 i += 28;
3006 b2 += i;
3007 m2 += i;
3008 s2 += i;
3009 }
3010 if (b2 > 0)
3011 b = lshift(b, b2);
3012 if (s2 > 0)
3013 S = lshift(S, s2);
3014 if (k_check) {
3015 if (cmp(b,S) < 0) {
3016 k--;
3017 b = multadd(b, 10, 0); /* we botched the k estimate */
3018 if (leftright)
3019 mhi = multadd(mhi, 10, 0);
3020 ilim = ilim1;
3021 }
3022 }
3023 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3024 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3025 /* no digits, fcvt style */
3026 no_digits:
3027 k = -1 - ndigits;
3028 goto ret;
3029 }
3030 one_digit:
3031 *s++ = '1';
3032 k++;
3033 goto ret;
3034 }
3035 if (leftright) {
3036 if (m2 > 0)
3037 mhi = lshift(mhi, m2);
3038
3039 /* Compute mlo -- check for special case
3040 * that d is a normalized power of 2.
3041 */
3042
3043 mlo = mhi;
3044 if (spec_case) {
3045 mhi = Balloc(mhi->k);
3046 Bcopy(mhi, mlo);
3047 mhi = lshift(mhi, Log2P);
3048 }
3049
3050 for(i = 1;;i++) {
3051 dig = quorem(b,S) + '0';
3052 /* Do we yet have the shortest decimal string
3053 * that will round to d?
3054 */
3055 j = cmp(b, mlo);
3056 delta = diff(S, mhi);
3057 j1 = delta->sign ? 1 : cmp(b, delta);
3058 Bfree(delta);
3059#ifndef ROUND_BIASED
3060 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3061#ifdef Honor_FLT_ROUNDS
3062 && rounding >= 1
3063#endif
3064 ) {
3065 if (dig == '9')
3066 goto round_9_up;
3067 if (j > 0)
3068 dig++;
3069#ifdef SET_INEXACT
3070 else if (!b->x[0] && b->wds <= 1)
3071 inexact = 0;
3072#endif
3073 *s++ = dig;
3074 goto ret;
3075 }
3076#endif
3077 if (j < 0 || (j == 0 && mode != 1
3078#ifndef ROUND_BIASED
3079 && !(word1(d) & 1)
3080#endif
3081 )) {
3082 if (!b->x[0] && b->wds <= 1) {
3083#ifdef SET_INEXACT
3084 inexact = 0;
3085#endif
3086 goto accept_dig;
3087 }
3088#ifdef Honor_FLT_ROUNDS
3089 if (mode > 1)
3090 switch(rounding) {
3091 case 0: goto accept_dig;
3092 case 2: goto keep_dig;
3093 }
3094#endif /*Honor_FLT_ROUNDS*/
3095 if (j1 > 0) {
3096 b = lshift(b, 1);
3097 j1 = cmp(b, S);
3098 if ((j1 > 0 || (j1 == 0 && dig & 1))
3099 && dig++ == '9')
3100 goto round_9_up;
3101 }
3102 accept_dig:
3103 *s++ = dig;
3104 goto ret;
3105 }
3106 if (j1 > 0) {
3107#ifdef Honor_FLT_ROUNDS
3108 if (!rounding)
3109 goto accept_dig;
3110#endif
3111 if (dig == '9') { /* possible if i == 1 */
3112 round_9_up:
3113 *s++ = '9';
3114 goto roundoff;
3115 }
3116 *s++ = dig + 1;
3117 goto ret;
3118 }
3119#ifdef Honor_FLT_ROUNDS
3120 keep_dig:
3121#endif
3122 *s++ = dig;
3123 if (i == ilim)
3124 break;
3125 b = multadd(b, 10, 0);
3126 if (mlo == mhi)
3127 mlo = mhi = multadd(mhi, 10, 0);
3128 else {
3129 mlo = multadd(mlo, 10, 0);
3130 mhi = multadd(mhi, 10, 0);
3131 }
3132 }
3133 }
3134 else
3135 for(i = 1;; i++) {
3136 *s++ = dig = quorem(b,S) + '0';
3137 if (!b->x[0] && b->wds <= 1) {
3138#ifdef SET_INEXACT
3139 inexact = 0;
3140#endif
3141 goto ret;
3142 }
3143 if (i >= ilim)
3144 break;
3145 b = multadd(b, 10, 0);
3146 }
3147
3148 /* Round off last digit */
3149
3150#ifdef Honor_FLT_ROUNDS
3151 switch(rounding) {
3152 case 0: goto trimzeros;
3153 case 2: goto roundoff;
3154 }
3155#endif
3156 b = lshift(b, 1);
3157 j = cmp(b, S);
3158 if (j > 0 || (j == 0 && dig & 1)) {
3159 roundoff:
3160 while(*--s == '9')
3161 if (s == s0) {
3162 k++;
3163 *s++ = '1';
3164 goto ret;
3165 }
3166 ++*s++;
3167 }
3168 else {
3169#ifdef Honor_FLT_ROUNDS
3170trimzeros:
3171#endif
3172 while(*--s == '0')
3173 ;
3174 s++;
3175 }
3176 ret:
3177 Bfree(S);
3178 if (mhi) {
3179 if (mlo && mlo != mhi)
3180 Bfree(mlo);
3181 Bfree(mhi);
3182 }
3183 ret1:
3184#ifdef SET_INEXACT
3185 if (inexact) {
3186 if (!oldinexact) {
3187 word0(d) = Exp_1 + (70 << Exp_shift);
3188 word1(d) = 0;
3189 dval(d) += 1.;
3190 }
3191 }
3192 else if (!oldinexact)
3193 clear_inexact();
3194#endif
3195 Bfree(b);
3196 *s = 0;
3197 *decpt = k + 1;
3198 if (rve)
3199 *rve = s;
3200 return s0;
3201 }
3202#ifdef __cplusplus
3203}
3204#endif
3205