Ruby: missing/dtoa.c Source File

Ruby 3.4.8p72 (2025-12-17 revision 995b59f66677d44767ce9faac6957e5543617ff9)

dtoa.c
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 David M. Gay (dmg at acm dot org,
21 * with " at " changed at "@" and " dot " changed to "."). */
22
23/* On a machine with IEEE extended-precision registers, it is
24 * necessary to specify double-precision (53-bit) rounding precision
25 * before invoking strtod or dtoa. If the machine uses (the equivalent
26 * of) Intel 80x87 arithmetic, the call
27 * _control87(PC_53, MCW_PC);
28 * does this with many compilers. Whether this or another call is
29 * appropriate depends on the compiler; for this to work, it may be
30 * necessary to #include "float.h" or another system-dependent header
31 * file.
32 */
33
34/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
35 *
36 * This strtod returns a nearest machine number to the input decimal
37 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
38 * broken by the IEEE round-even rule. Otherwise ties are broken by
39 * biased rounding (add half and chop).
40 *
41 * Inspired loosely by William D. Clinger's paper "How to Read Floating
42 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
43 *
44 * Modifications:
45 *
46 * 1. We only require IEEE, IBM, or VAX double-precision
47 * arithmetic (not IEEE double-extended).
48 * 2. We get by with floating-point arithmetic in a case that
49 * Clinger missed -- when we're computing d * 10^n
50 * for a small integer d and the integer n is not too
51 * much larger than 22 (the maximum integer k for which
52 * we can represent 10^k exactly), we may be able to
53 * compute (d*10^k) * 10^(e-k) with just one roundoff.
54 * 3. Rather than a bit-at-a-time adjustment of the binary
55 * result in the hard case, we use floating-point
56 * arithmetic to determine the adjustment to within
57 * one bit; only in really hard cases do we need to
58 * compute a second residual.
59 * 4. Because of 3., we don't need a large table of powers of 10
60 * for ten-to-e (just some small tables, e.g. of 10^k
61 * for 0 <= k <= 22).
62 */
63
64/*
65 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
66 * significant byte has the lowest address.
67 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
68 * significant byte has the lowest address.
69 * #define Long int on machines with 32-bit ints and 64-bit longs.
70 * #define IBM for IBM mainframe-style floating-point arithmetic.
71 * #define VAX for VAX-style floating-point arithmetic (D_floating).
72 * #define No_leftright to omit left-right logic in fast floating-point
73 * computation of dtoa.
74 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
75 * and strtod and dtoa should round accordingly.
76 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
77 * and Honor_FLT_ROUNDS is not #defined.
78 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
79 * that use extended-precision instructions to compute rounded
80 * products and quotients) with IBM.
81 * #define ROUND_BIASED for IEEE-format with biased rounding.
82 * #define Inaccurate_Divide for IEEE-format with correctly rounded
83 * products but inaccurate quotients, e.g., for Intel i860.
84 * #define NO_LONG_LONG on machines that do not have a "long long"
85 * integer type (of >= 64 bits). On such machines, you can
86 * #define Just_16 to store 16 bits per 32-bit Long when doing
87 * high-precision integer arithmetic. Whether this speeds things
88 * up or slows things down depends on the machine and the number
89 * being converted. If long long is available and the name is
90 * something other than "long long", #define Llong to be the name,
91 * and if "unsigned Llong" does not work as an unsigned version of
92 * Llong, #define #ULLong to be the corresponding unsigned type.
93 * #define KR_headers for old-style C function headers.
94 * #define Bad_float_h if your system lacks a float.h or if it does not
95 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
96 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
97 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
98 * if memory is available and otherwise does something you deem
99 * appropriate. If MALLOC is undefined, malloc will be invoked
100 * directly -- and assumed always to succeed.
101 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
102 * memory allocations from a private pool of memory when possible.
103 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
104 * unless #defined to be a different length. This default length
105 * suffices to get rid of MALLOC calls except for unusual cases,
106 * such as decimal-to-binary conversion of a very long string of
107 * digits. The longest string dtoa can return is about 751 bytes
108 * long. For conversions by strtod of strings of 800 digits and
109 * all dtoa conversions in single-threaded executions with 8-byte
110 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
111 * pointers, PRIVATE_MEM >= 7112 appears adequate.
112 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
113 * Infinity and NaN (case insensitively). On some systems (e.g.,
114 * some HP systems), it may be necessary to #define NAN_WORD0
115 * appropriately -- to the most significant word of a quiet NaN.
116 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
117 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
118 * strtod also accepts (case insensitively) strings of the form
119 * NaN(x), where x is a string of hexadecimal digits and spaces;
120 * if there is only one string of hexadecimal digits, it is taken
121 * for the 52 fraction bits of the resulting NaN; if there are two
122 * or more strings of hex digits, the first is for the high 20 bits,
123 * the second and subsequent for the low 32 bits, with intervening
124 * white space ignored; but if this results in none of the 52
125 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
126 * and NAN_WORD1 are used instead.
127 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
128 * multiple threads. In this case, you must provide (or suitably
129 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
130 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
131 * in pow5mult, ensures lazy evaluation of only one copy of high
132 * powers of 5; omitting this lock would introduce a small
133 * probability of wasting memory, but would otherwise be harmless.)
134 * You must also invoke freedtoa(s) to free the value s returned by
135 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
136 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
137 * avoids underflows on inputs whose result does not underflow.
138 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
139 * floating-point numbers and flushes underflows to zero rather
140 * than implementing gradual underflow, then you must also #define
141 * Sudden_Underflow.
142 * #define YES_ALIAS to permit aliasing certain double values with
143 * arrays of ULongs. This leads to slightly better code with
144 * some compilers and was always used prior to 19990916, but it
145 * is not strictly legal and can cause trouble with aggressively
146 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
147 * #define USE_LOCALE to use the current locale's decimal_point value.
148 * #define SET_INEXACT if IEEE arithmetic is being used and extra
149 * computation should be done to set the inexact flag when the
150 * result is inexact and avoid setting inexact when the result
151 * is exact. In this case, dtoa.c must be compiled in
152 * an environment, perhaps provided by #include "dtoa.c" in a
153 * suitable wrapper, that defines two functions,
154 * int get_inexact(void);
155 * void clear_inexact(void);
156 * such that get_inexact() returns a nonzero value if the
157 * inexact bit is already set, and clear_inexact() sets the
158 * inexact bit to 0. When SET_INEXACT is #defined, strtod
159 * also does extra computations to set the underflow and overflow
160 * flags when appropriate (i.e., when the result is tiny and
161 * inexact or when it is a numeric value rounded to +-infinity).
162 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
163 * the result overflows to +-Infinity or underflows to 0.
164 */
165
166#ifdef WORDS_BIGENDIAN
167#define IEEE_BIG_ENDIAN
168#else
169#define IEEE_LITTLE_ENDIAN
170#endif
171
172#ifdef __vax__
173#define VAX
174#undef IEEE_BIG_ENDIAN
175#undef IEEE_LITTLE_ENDIAN
176#endif
177
178#if defined(__arm__) && !defined(__VFP_FP__)
179#define IEEE_BIG_ENDIAN
180#undef IEEE_LITTLE_ENDIAN
181#endif
182
183#undef Long
184#undef ULong
185
186#include <assert.h>
187#include <limits.h>
188#include <stddef.h>
189#include <stdint.h>
190
191#if (INT_MAX >> 30) && !(INT_MAX >> 31)
192#define Long int
193#define ULong unsigned int
194#elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
195#define Long long int
196#define ULong unsigned long int
197#else
198#error No 32bit integer
199#endif
200
201#if defined(HAVE_LONG_LONG) && (HAVE_LONG_LONG)
202#define Llong LONG_LONG
203#else
204#define NO_LONG_LONG
205#endif
206
207#ifdef DEBUG
208#include <stdio.h>
209#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
210#endif
211
212#ifndef ISDIGIT
213#include <ctype.h>
214#define ISDIGIT(c) isdigit(c)
215#endif
216#include <errno.h>
217#include <stdlib.h>
218#include <string.h>
219
220#ifdef USE_LOCALE
221#include <locale.h>
222#endif
223
224#ifdef MALLOC
225extern void *MALLOC(size_t);
226#else
227#define MALLOC malloc
228#endif
229#ifdef FREE
230extern void FREE(void*);
231#else
232#define FREE free
233#endif
234#ifndef NO_SANITIZE
235#define NO_SANITIZE(x, y) y
236#endif
237
238#ifndef Omit_Private_Memory
239#ifndef PRIVATE_MEM
240#define PRIVATE_MEM 2304
241#endif
242#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
243static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
244#endif
245
246#undef IEEE_Arith
247#undef Avoid_Underflow
248#ifdef IEEE_BIG_ENDIAN
249#define IEEE_Arith
250#endif
251#ifdef IEEE_LITTLE_ENDIAN
252#define IEEE_Arith
253#endif
254
255#ifdef Bad_float_h
256
257#ifdef IEEE_Arith
258#define DBL_DIG 15
259#define DBL_MAX_10_EXP 308
260#define DBL_MAX_EXP 1024
261#define FLT_RADIX 2
262#endif /*IEEE_Arith*/
263
264#ifdef IBM
265#define DBL_DIG 16
266#define DBL_MAX_10_EXP 75
267#define DBL_MAX_EXP 63
268#define FLT_RADIX 16
269#define DBL_MAX 7.2370055773322621e+75
270#endif
271
272#ifdef VAX
273#define DBL_DIG 16
274#define DBL_MAX_10_EXP 38
275#define DBL_MAX_EXP 127
276#define FLT_RADIX 2
277#define DBL_MAX 1.7014118346046923e+38
278#endif
279
280#ifndef LONG_MAX
281#define LONG_MAX 2147483647
282#endif
283
284#else /* ifndef Bad_float_h */
285#include <float.h>
286#endif /* Bad_float_h */
287
288#include <math.h>
289
290#ifdef __cplusplus
291extern "C" {
292#if 0
293} /* satisfy cc-mode */
294#endif
295#endif
296
297#ifndef hexdigit
298static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
299#endif
300
301#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
302Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
303#endif
304
305 typedef union { double d; ULong L[2]; } U;
306
307#ifdef YES_ALIAS
308typedef double double_u;
309# define dval(x) (x)
310# ifdef IEEE_LITTLE_ENDIAN
311# define word0(x) (((ULong *)&(x))[1])
312# define word1(x) (((ULong *)&(x))[0])
313# else
314# define word0(x) (((ULong *)&(x))[0])
315# define word1(x) (((ULong *)&(x))[1])
316# endif
317#else
318typedef U double_u;
319# ifdef IEEE_LITTLE_ENDIAN
320# define word0(x) ((x).L[1])
321# define word1(x) ((x).L[0])
322# else
323# define word0(x) ((x).L[0])
324# define word1(x) ((x).L[1])
325# endif
326# define dval(x) ((x).d)
327#endif
328
329/* The following definition of Storeinc is appropriate for MIPS processors.
330 * An alternative that might be better on some machines is
331 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
332 */
333#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
334#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
335((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
336#else
337#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
338((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
339#endif
340
341/* #define P DBL_MANT_DIG */
342/* Ten_pmax = floor(P*log(2)/log(5)) */
343/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
344/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
345/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
346
347#ifdef IEEE_Arith
348#define Exp_shift 20
349#define Exp_shift1 20
350#define Exp_msk1 0x100000
351#define Exp_msk11 0x100000
352#define Exp_mask 0x7ff00000
353#define P 53
354#define Bias 1023
355#define Emin (-1022)
356#define Exp_1 0x3ff00000
357#define Exp_11 0x3ff00000
358#define Ebits 11
359#define Frac_mask 0xfffff
360#define Frac_mask1 0xfffff
361#define Ten_pmax 22
362#define Bletch 0x10
363#define Bndry_mask 0xfffff
364#define Bndry_mask1 0xfffff
365#define LSB 1
366#define Sign_bit 0x80000000
367#define Log2P 1
368#define Tiny0 0
369#define Tiny1 1
370#define Quick_max 14
371#define Int_max 14
372#ifndef NO_IEEE_Scale
373#define Avoid_Underflow
374#ifdef Flush_Denorm /* debugging option */
375#undef Sudden_Underflow
376#endif
377#endif
378
379#ifndef Flt_Rounds
380#ifdef FLT_ROUNDS
381#define Flt_Rounds FLT_ROUNDS
382#else
383#define Flt_Rounds 1
384#endif
385#endif /*Flt_Rounds*/
386
387#ifdef Honor_FLT_ROUNDS
388#define Rounding rounding
389#undef Check_FLT_ROUNDS
390#define Check_FLT_ROUNDS
391#else
392#define Rounding Flt_Rounds
393#endif
394
395#else /* ifndef IEEE_Arith */
396#undef Check_FLT_ROUNDS
397#undef Honor_FLT_ROUNDS
398#undef SET_INEXACT
399#undef Sudden_Underflow
400#define Sudden_Underflow
401#ifdef IBM
402#undef Flt_Rounds
403#define Flt_Rounds 0
404#define Exp_shift 24
405#define Exp_shift1 24
406#define Exp_msk1 0x1000000
407#define Exp_msk11 0x1000000
408#define Exp_mask 0x7f000000
409#define P 14
410#define Bias 65
411#define Exp_1 0x41000000
412#define Exp_11 0x41000000
413#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
414#define Frac_mask 0xffffff
415#define Frac_mask1 0xffffff
416#define Bletch 4
417#define Ten_pmax 22
418#define Bndry_mask 0xefffff
419#define Bndry_mask1 0xffffff
420#define LSB 1
421#define Sign_bit 0x80000000
422#define Log2P 4
423#define Tiny0 0x100000
424#define Tiny1 0
425#define Quick_max 14
426#define Int_max 15
427#else /* VAX */
428#undef Flt_Rounds
429#define Flt_Rounds 1
430#define Exp_shift 23
431#define Exp_shift1 7
432#define Exp_msk1 0x80
433#define Exp_msk11 0x800000
434#define Exp_mask 0x7f80
435#define P 56
436#define Bias 129
437#define Exp_1 0x40800000
438#define Exp_11 0x4080
439#define Ebits 8
440#define Frac_mask 0x7fffff
441#define Frac_mask1 0xffff007f
442#define Ten_pmax 24
443#define Bletch 2
444#define Bndry_mask 0xffff007f
445#define Bndry_mask1 0xffff007f
446#define LSB 0x10000
447#define Sign_bit 0x8000
448#define Log2P 1
449#define Tiny0 0x80
450#define Tiny1 0
451#define Quick_max 15
452#define Int_max 15
453#endif /* IBM, VAX */
454#endif /* IEEE_Arith */
455
456#ifndef IEEE_Arith
457#define ROUND_BIASED
458#endif
459
460#ifdef RND_PRODQUOT
461#define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
462#define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
463extern double rnd_prod(double, double), rnd_quot(double, double);
464#else
465#define rounded_product(a,b) ((a) *= (b))
466#define rounded_quotient(a,b) ((a) /= (b))
467#endif
468
469#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
470#define Big1 0xffffffff
471
472#ifndef Pack_32
473#define Pack_32
474#endif
475
476#define FFFFFFFF 0xffffffffUL
477
478#ifdef NO_LONG_LONG
479#undef ULLong
480#ifdef Just_16
481#undef Pack_32
482/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
483 * This makes some inner loops simpler and sometimes saves work
484 * during multiplications, but it often seems to make things slightly
485 * slower. Hence the default is now to store 32 bits per Long.
486 */
487#endif
488#else /* long long available */
489#ifndef Llong
490#define Llong long long
491#endif
492#ifndef ULLong
493#define ULLong unsigned Llong
494#endif
495#endif /* NO_LONG_LONG */
496
497#define MULTIPLE_THREADS 1
498
499#ifndef MULTIPLE_THREADS
500#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
501#define FREE_DTOA_LOCK(n) /*nothing*/
502#else
503#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
504#define FREE_DTOA_LOCK(n) /*unused right now*/
505#endif
506
507#ifndef ATOMIC_PTR_CAS
508#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (void *)(old))
509#endif
510#ifndef LIKELY
511#define LIKELY(x) (x)
512#endif
513#ifndef UNLIKELY
514#define UNLIKELY(x) (x)
515#endif
516#ifndef ASSUME
517#define ASSUME(x) (void)(x)
518#endif
519
520#define Kmax 15
521
522 struct Bigint {
523 struct Bigint *next;
524 int k, maxwds, sign, wds;
525 ULong x[1];
526};
527
528typedef struct Bigint Bigint;
529
530static Bigint *freelist[Kmax+1];
531
532#define BLOCKING_BIGINT ((Bigint *)(-1))
533
534static Bigint *
535Balloc(int k)
536{
537 int x;
538 Bigint *rv;
539#ifndef Omit_Private_Memory
540 size_t len;
541#endif
542
543 rv = 0;
544 ACQUIRE_DTOA_LOCK(0);
545 if (k <= Kmax) {
546 rv = freelist[k];
547 while (rv) {
548 Bigint *rvn = rv;
549 rv = ATOMIC_PTR_CAS(freelist[k], rv, BLOCKING_BIGINT);
550 if (LIKELY(rv != BLOCKING_BIGINT && rvn == rv)) {
551 rvn = ATOMIC_PTR_CAS(freelist[k], BLOCKING_BIGINT, rv->next);
552 assert(rvn == BLOCKING_BIGINT);
553 ASSUME(rv);
554 break;
555 }
556 }
557 }
558 if (!rv) {
559 x = 1 << k;
560#ifdef Omit_Private_Memory
561 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
562#else
563 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
564 /sizeof(double);
565 if (k <= Kmax) {
566 double *pnext = pmem_next;
567 while (pnext - private_mem + len <= PRIVATE_mem) {
568 double *p = pnext;
569 pnext = ATOMIC_PTR_CAS(pmem_next, pnext, pnext + len);
570 if (LIKELY(p == pnext)) {
571 rv = (Bigint*)pnext;
572 ASSUME(rv);
573 break;
574 }
575 }
576 }
577 if (!rv)
578 rv = (Bigint*)MALLOC(len*sizeof(double));
579#endif
580 rv->k = k;
581 rv->maxwds = x;
582 }
583 FREE_DTOA_LOCK(0);
584 rv->sign = rv->wds = 0;
585 return rv;
586}
587
588static void
589Bfree(Bigint *v)
590{
591 Bigint *vn;
592 if (v) {
593 if (v->k > Kmax) {
594 FREE(v);
595 return;
596 }
597 ACQUIRE_DTOA_LOCK(0);
598 do {
599 do {
600 vn = ATOMIC_PTR_CAS(freelist[v->k], 0, 0);
601 } while (UNLIKELY(vn == BLOCKING_BIGINT));
602 v->next = vn;
603 } while (UNLIKELY(ATOMIC_PTR_CAS(freelist[v->k], vn, v) != vn));
604 FREE_DTOA_LOCK(0);
605 }
606}
607
608#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
609(y)->wds*sizeof(Long) + 2*sizeof(int))
610
611static Bigint *
612multadd(Bigint *b, int m, int a) /* multiply by m and add a */
613{
614 int i, wds;
615 ULong *x;
616#ifdef ULLong
617 ULLong carry, y;
618#else
619 ULong carry, y;
620#ifdef Pack_32
621 ULong xi, z;
622#endif
623#endif
624 Bigint *b1;
625
626 wds = b->wds;
627 x = b->x;
628 i = 0;
629 carry = a;
630 do {
631#ifdef ULLong
632 y = *x * (ULLong)m + carry;
633 carry = y >> 32;
634 *x++ = (ULong)(y & FFFFFFFF);
635#else
636#ifdef Pack_32
637 xi = *x;
638 y = (xi & 0xffff) * m + carry;
639 z = (xi >> 16) * m + (y >> 16);
640 carry = z >> 16;
641 *x++ = (z << 16) + (y & 0xffff);
642#else
643 y = *x * m + carry;
644 carry = y >> 16;
645 *x++ = y & 0xffff;
646#endif
647#endif
648 } while (++i < wds);
649 if (carry) {
650 if (wds >= b->maxwds) {
651 b1 = Balloc(b->k+1);
652 Bcopy(b1, b);
653 Bfree(b);
654 b = b1;
655 }
656 b->x[wds++] = (ULong)carry;
657 b->wds = wds;
658 }
659 return b;
660}
661
662static Bigint *
663s2b(const char *s, int nd0, int nd, ULong y9)
664{
665 Bigint *b;
666 int i, k;
667 Long x, y;
668
669 x = (nd + 8) / 9;
670 for (k = 0, y = 1; x > y; y <<= 1, k++) ;
671#ifdef Pack_32
672 b = Balloc(k);
673 b->x[0] = y9;
674 b->wds = 1;
675#else
676 b = Balloc(k+1);
677 b->x[0] = y9 & 0xffff;
678 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
679#endif
680
681 i = 9;
682 if (9 < nd0) {
683 s += 9;
684 do {
685 b = multadd(b, 10, *s++ - '0');
686 } while (++i < nd0);
687 s++;
688 }
689 else
690 s += 10;
691 for (; i < nd; i++)
692 b = multadd(b, 10, *s++ - '0');
693 return b;
694}
695
696static int
697hi0bits(register ULong x)
698{
699 register int k = 0;
700
701 if (!(x & 0xffff0000)) {
702 k = 16;
703 x <<= 16;
704 }
705 if (!(x & 0xff000000)) {
706 k += 8;
707 x <<= 8;
708 }
709 if (!(x & 0xf0000000)) {
710 k += 4;
711 x <<= 4;
712 }
713 if (!(x & 0xc0000000)) {
714 k += 2;
715 x <<= 2;
716 }
717 if (!(x & 0x80000000)) {
718 k++;
719 if (!(x & 0x40000000))
720 return 32;
721 }
722 return k;
723}
724
725static int
726lo0bits(ULong *y)
727{
728 register int k;
729 register ULong x = *y;
730
731 if (x & 7) {
732 if (x & 1)
733 return 0;
734 if (x & 2) {
735 *y = x >> 1;
736 return 1;
737 }
738 *y = x >> 2;
739 return 2;
740 }
741 k = 0;
742 if (!(x & 0xffff)) {
743 k = 16;
744 x >>= 16;
745 }
746 if (!(x & 0xff)) {
747 k += 8;
748 x >>= 8;
749 }
750 if (!(x & 0xf)) {
751 k += 4;
752 x >>= 4;
753 }
754 if (!(x & 0x3)) {
755 k += 2;
756 x >>= 2;
757 }
758 if (!(x & 1)) {
759 k++;
760 x >>= 1;
761 if (!x)
762 return 32;
763 }
764 *y = x;
765 return k;
766}
767
768static Bigint *
769i2b(int i)
770{
771 Bigint *b;
772
773 b = Balloc(1);
774 b->x[0] = i;
775 b->wds = 1;
776 return b;
777}
778
779static Bigint *
780mult(Bigint *a, Bigint *b)
781{
782 Bigint *c;
783 int k, wa, wb, wc;
784 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
785 ULong y;
786#ifdef ULLong
787 ULLong carry, z;
788#else
789 ULong carry, z;
790#ifdef Pack_32
791 ULong z2;
792#endif
793#endif
794
795 if (a->wds < b->wds) {
796 c = a;
797 a = b;
798 b = c;
799 }
800 k = a->k;
801 wa = a->wds;
802 wb = b->wds;
803 wc = wa + wb;
804 if (wc > a->maxwds)
805 k++;
806 c = Balloc(k);
807 for (x = c->x, xa = x + wc; x < xa; x++)
808 *x = 0;
809 xa = a->x;
810 xae = xa + wa;
811 xb = b->x;
812 xbe = xb + wb;
813 xc0 = c->x;
814#ifdef ULLong
815 for (; xb < xbe; xc0++) {
816 if ((y = *xb++) != 0) {
817 x = xa;
818 xc = xc0;
819 carry = 0;
820 do {
821 z = *x++ * (ULLong)y + *xc + carry;
822 carry = z >> 32;
823 *xc++ = (ULong)(z & FFFFFFFF);
824 } while (x < xae);
825 *xc = (ULong)carry;
826 }
827 }
828#else
829#ifdef Pack_32
830 for (; xb < xbe; xb++, xc0++) {
831 if ((y = *xb & 0xffff) != 0) {
832 x = xa;
833 xc = xc0;
834 carry = 0;
835 do {
836 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
837 carry = z >> 16;
838 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
839 carry = z2 >> 16;
840 Storeinc(xc, z2, z);
841 } while (x < xae);
842 *xc = (ULong)carry;
843 }
844 if ((y = *xb >> 16) != 0) {
845 x = xa;
846 xc = xc0;
847 carry = 0;
848 z2 = *xc;
849 do {
850 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
851 carry = z >> 16;
852 Storeinc(xc, z, z2);
853 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
854 carry = z2 >> 16;
855 } while (x < xae);
856 *xc = z2;
857 }
858 }
859#else
860 for (; xb < xbe; xc0++) {
861 if (y = *xb++) {
862 x = xa;
863 xc = xc0;
864 carry = 0;
865 do {
866 z = *x++ * y + *xc + carry;
867 carry = z >> 16;
868 *xc++ = z & 0xffff;
869 } while (x < xae);
870 *xc = (ULong)carry;
871 }
872 }
873#endif
874#endif
875 for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
876 c->wds = wc;
877 return c;
878}
879
880static Bigint *p5s;
881
882static Bigint *
883pow5mult(Bigint *b, int k)
884{
885 Bigint *b1, *p5, *p51;
886 Bigint *p5tmp;
887 int i;
888 static const int p05[3] = { 5, 25, 125 };
889
890 if ((i = k & 3) != 0)
891 b = multadd(b, p05[i-1], 0);
892
893 if (!(k >>= 2))
894 return b;
895 if (!(p5 = p5s)) {
896 /* first time */
897 ACQUIRE_DTOA_LOCK(1);
898 if (!(p5 = p5s)) {
899 p5 = i2b(625);
900 p5->next = 0;
901 p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
902 if (UNLIKELY(p5tmp)) {
903 Bfree(p5);
904 p5 = p5tmp;
905 }
906 }
907 FREE_DTOA_LOCK(1);
908 }
909 for (;;) {
910 if (k & 1) {
911 b1 = mult(b, p5);
912 Bfree(b);
913 b = b1;
914 }
915 if (!(k >>= 1))
916 break;
917 if (!(p51 = p5->next)) {
918 ACQUIRE_DTOA_LOCK(1);
919 if (!(p51 = p5->next)) {
920 p51 = mult(p5,p5);
921 p51->next = 0;
922 p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
923 if (UNLIKELY(p5tmp)) {
924 Bfree(p51);
925 p51 = p5tmp;
926 }
927 }
928 FREE_DTOA_LOCK(1);
929 }
930 p5 = p51;
931 }
932 return b;
933}
934
935static Bigint *
936lshift(Bigint *b, int k)
937{
938 int i, k1, n, n1;
939 Bigint *b1;
940 ULong *x, *x1, *xe, z;
941
942#ifdef Pack_32
943 n = k >> 5;
944#else
945 n = k >> 4;
946#endif
947 k1 = b->k;
948 n1 = n + b->wds + 1;
949 for (i = b->maxwds; n1 > i; i <<= 1)
950 k1++;
951 b1 = Balloc(k1);
952 x1 = b1->x;
953 for (i = 0; i < n; i++)
954 *x1++ = 0;
955 x = b->x;
956 xe = x + b->wds;
957#ifdef Pack_32
958 if (k &= 0x1f) {
959 k1 = 32 - k;
960 z = 0;
961 do {
962 *x1++ = *x << k | z;
963 z = *x++ >> k1;
964 } while (x < xe);
965 if ((*x1 = z) != 0)
966 ++n1;
967 }
968#else
969 if (k &= 0xf) {
970 k1 = 16 - k;
971 z = 0;
972 do {
973 *x1++ = *x << k & 0xffff | z;
974 z = *x++ >> k1;
975 } while (x < xe);
976 if (*x1 = z)
977 ++n1;
978 }
979#endif
980 else
981 do {
982 *x1++ = *x++;
983 } while (x < xe);
984 b1->wds = n1 - 1;
985 Bfree(b);
986 return b1;
987}
988
989static int
990cmp(Bigint *a, Bigint *b)
991{
992 ULong *xa, *xa0, *xb, *xb0;
993 int i, j;
994
995 i = a->wds;
996 j = b->wds;
997#ifdef DEBUG
998 if (i > 1 && !a->x[i-1])
999 Bug("cmp called with a->x[a->wds-1] == 0");
1000 if (j > 1 && !b->x[j-1])
1001 Bug("cmp called with b->x[b->wds-1] == 0");
1002#endif
1003 if (i -= j)
1004 return i;
1005 xa0 = a->x;
1006 xa = xa0 + j;
1007 xb0 = b->x;
1008 xb = xb0 + j;
1009 for (;;) {
1010 if (*--xa != *--xb)
1011 return *xa < *xb ? -1 : 1;
1012 if (xa <= xa0)
1013 break;
1014 }
1015 return 0;
1016}
1017
1018NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b));
1019static Bigint *
1020diff(Bigint *a, Bigint *b)
1021{
1022 Bigint *c;
1023 int i, wa, wb;
1024 ULong *xa, *xae, *xb, *xbe, *xc;
1025#ifdef ULLong
1026 ULLong borrow, y;
1027#else
1028 ULong borrow, y;
1029#ifdef Pack_32
1030 ULong z;
1031#endif
1032#endif
1033
1034 i = cmp(a,b);
1035 if (!i) {
1036 c = Balloc(0);
1037 c->wds = 1;
1038 c->x[0] = 0;
1039 return c;
1040 }
1041 if (i < 0) {
1042 c = a;
1043 a = b;
1044 b = c;
1045 i = 1;
1046 }
1047 else
1048 i = 0;
1049 c = Balloc(a->k);
1050 c->sign = i;
1051 wa = a->wds;
1052 xa = a->x;
1053 xae = xa + wa;
1054 wb = b->wds;
1055 xb = b->x;
1056 xbe = xb + wb;
1057 xc = c->x;
1058 borrow = 0;
1059#ifdef ULLong
1060 do {
1061 y = (ULLong)*xa++ - *xb++ - borrow;
1062 borrow = y >> 32 & (ULong)1;
1063 *xc++ = (ULong)(y & FFFFFFFF);
1064 } while (xb < xbe);
1065 while (xa < xae) {
1066 y = *xa++ - borrow;
1067 borrow = y >> 32 & (ULong)1;
1068 *xc++ = (ULong)(y & FFFFFFFF);
1069 }
1070#else
1071#ifdef Pack_32
1072 do {
1073 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1074 borrow = (y & 0x10000) >> 16;
1075 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1076 borrow = (z & 0x10000) >> 16;
1077 Storeinc(xc, z, y);
1078 } while (xb < xbe);
1079 while (xa < xae) {
1080 y = (*xa & 0xffff) - borrow;
1081 borrow = (y & 0x10000) >> 16;
1082 z = (*xa++ >> 16) - borrow;
1083 borrow = (z & 0x10000) >> 16;
1084 Storeinc(xc, z, y);
1085 }
1086#else
1087 do {
1088 y = *xa++ - *xb++ - borrow;
1089 borrow = (y & 0x10000) >> 16;
1090 *xc++ = y & 0xffff;
1091 } while (xb < xbe);
1092 while (xa < xae) {
1093 y = *xa++ - borrow;
1094 borrow = (y & 0x10000) >> 16;
1095 *xc++ = y & 0xffff;
1096 }
1097#endif
1098#endif
1099 while (!*--xc)
1100 wa--;
1101 c->wds = wa;
1102 return c;
1103}
1104
1105static double
1106ulp(double x_)
1107{
1108 register Long L;
1109 double_u x, a;
1110 dval(x) = x_;
1111
1112 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1113#ifndef Avoid_Underflow
1114#ifndef Sudden_Underflow
1115 if (L > 0) {
1116#endif
1117#endif
1118#ifdef IBM
1119 L |= Exp_msk1 >> 4;
1120#endif
1121 word0(a) = L;
1122 word1(a) = 0;
1123#ifndef Avoid_Underflow
1124#ifndef Sudden_Underflow
1125 }
1126 else {
1127 L = -L >> Exp_shift;
1128 if (L < Exp_shift) {
1129 word0(a) = 0x80000 >> L;
1130 word1(a) = 0;
1131 }
1132 else {
1133 word0(a) = 0;
1134 L -= Exp_shift;
1135 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1136 }
1137 }
1138#endif
1139#endif
1140 return dval(a);
1141}
1142
1143static double
1144b2d(Bigint *a, int *e)
1145{
1146 ULong *xa, *xa0, w, y, z;
1147 int k;
1148 double_u d;
1149#ifdef VAX
1150 ULong d0, d1;
1151#else
1152#define d0 word0(d)
1153#define d1 word1(d)
1154#endif
1155
1156 xa0 = a->x;
1157 xa = xa0 + a->wds;
1158 y = *--xa;
1159#ifdef DEBUG
1160 if (!y) Bug("zero y in b2d");
1161#endif
1162 k = hi0bits(y);
1163 *e = 32 - k;
1164#ifdef Pack_32
1165 if (k < Ebits) {
1166 d0 = Exp_1 | y >> (Ebits - k);
1167 w = xa > xa0 ? *--xa : 0;
1168 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1169 goto ret_d;
1170 }
1171 z = xa > xa0 ? *--xa : 0;
1172 if (k -= Ebits) {
1173 d0 = Exp_1 | y << k | z >> (32 - k);
1174 y = xa > xa0 ? *--xa : 0;
1175 d1 = z << k | y >> (32 - k);
1176 }
1177 else {
1178 d0 = Exp_1 | y;
1179 d1 = z;
1180 }
1181#else
1182 if (k < Ebits + 16) {
1183 z = xa > xa0 ? *--xa : 0;
1184 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1185 w = xa > xa0 ? *--xa : 0;
1186 y = xa > xa0 ? *--xa : 0;
1187 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1188 goto ret_d;
1189 }
1190 z = xa > xa0 ? *--xa : 0;
1191 w = xa > xa0 ? *--xa : 0;
1192 k -= Ebits + 16;
1193 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1194 y = xa > xa0 ? *--xa : 0;
1195 d1 = w << k + 16 | y << k;
1196#endif
1197ret_d:
1198#ifdef VAX
1199 word0(d) = d0 >> 16 | d0 << 16;
1200 word1(d) = d1 >> 16 | d1 << 16;
1201#else
1202#undef d0
1203#undef d1
1204#endif
1205 return dval(d);
1206}
1207
1208static Bigint *
1209d2b(double d_, int *e, int *bits)
1210{
1211 double_u d;
1212 Bigint *b;
1213 int de, k;
1214 ULong *x, y, z;
1215#ifndef Sudden_Underflow
1216 int i;
1217#endif
1218#ifdef VAX
1219 ULong d0, d1;
1220#endif
1221 dval(d) = d_;
1222#ifdef VAX
1223 d0 = word0(d) >> 16 | word0(d) << 16;
1224 d1 = word1(d) >> 16 | word1(d) << 16;
1225#else
1226#define d0 word0(d)
1227#define d1 word1(d)
1228#endif
1229
1230#ifdef Pack_32
1231 b = Balloc(1);
1232#else
1233 b = Balloc(2);
1234#endif
1235 x = b->x;
1236
1237 z = d0 & Frac_mask;
1238 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1239#ifdef Sudden_Underflow
1240 de = (int)(d0 >> Exp_shift);
1241#ifndef IBM
1242 z |= Exp_msk11;
1243#endif
1244#else
1245 if ((de = (int)(d0 >> Exp_shift)) != 0)
1246 z |= Exp_msk1;
1247#endif
1248#ifdef Pack_32
1249 if ((y = d1) != 0) {
1250 if ((k = lo0bits(&y)) != 0) {
1251 x[0] = y | z << (32 - k);
1252 z >>= k;
1253 }
1254 else
1255 x[0] = y;
1256#ifndef Sudden_Underflow
1257 i =
1258#endif
1259 b->wds = (x[1] = z) ? 2 : 1;
1260 }
1261 else {
1262#ifdef DEBUG
1263 if (!z)
1264 Bug("Zero passed to d2b");
1265#endif
1266 k = lo0bits(&z);
1267 x[0] = z;
1268#ifndef Sudden_Underflow
1269 i =
1270#endif
1271 b->wds = 1;
1272 k += 32;
1273 }
1274#else
1275 if (y = d1) {
1276 if (k = lo0bits(&y))
1277 if (k >= 16) {
1278 x[0] = y | z << 32 - k & 0xffff;
1279 x[1] = z >> k - 16 & 0xffff;
1280 x[2] = z >> k;
1281 i = 2;
1282 }
1283 else {
1284 x[0] = y & 0xffff;
1285 x[1] = y >> 16 | z << 16 - k & 0xffff;
1286 x[2] = z >> k & 0xffff;
1287 x[3] = z >> k+16;
1288 i = 3;
1289 }
1290 else {
1291 x[0] = y & 0xffff;
1292 x[1] = y >> 16;
1293 x[2] = z & 0xffff;
1294 x[3] = z >> 16;
1295 i = 3;
1296 }
1297 }
1298 else {
1299#ifdef DEBUG
1300 if (!z)
1301 Bug("Zero passed to d2b");
1302#endif
1303 k = lo0bits(&z);
1304 if (k >= 16) {
1305 x[0] = z;
1306 i = 0;
1307 }
1308 else {
1309 x[0] = z & 0xffff;
1310 x[1] = z >> 16;
1311 i = 1;
1312 }
1313 k += 32;
1314 }
1315 while (!x[i])
1316 --i;
1317 b->wds = i + 1;
1318#endif
1319#ifndef Sudden_Underflow
1320 if (de) {
1321#endif
1322#ifdef IBM
1323 *e = (de - Bias - (P-1) << 2) + k;
1324 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1325#else
1326 *e = de - Bias - (P-1) + k;
1327 *bits = P - k;
1328#endif
1329#ifndef Sudden_Underflow
1330 }
1331 else {
1332 *e = de - Bias - (P-1) + 1 + k;
1333#ifdef Pack_32
1334 *bits = 32*i - hi0bits(x[i-1]);
1335#else
1336 *bits = (i+2)*16 - hi0bits(x[i]);
1337#endif
1338 }
1339#endif
1340 return b;
1341}
1342#undef d0
1343#undef d1
1344
1345static double
1346ratio(Bigint *a, Bigint *b)
1347{
1348 double_u da, db;
1349 int k, ka, kb;
1350
1351 dval(da) = b2d(a, &ka);
1352 dval(db) = b2d(b, &kb);
1353#ifdef Pack_32
1354 k = ka - kb + 32*(a->wds - b->wds);
1355#else
1356 k = ka - kb + 16*(a->wds - b->wds);
1357#endif
1358#ifdef IBM
1359 if (k > 0) {
1360 word0(da) += (k >> 2)*Exp_msk1;
1361 if (k &= 3)
1362 dval(da) *= 1 << k;
1363 }
1364 else {
1365 k = -k;
1366 word0(db) += (k >> 2)*Exp_msk1;
1367 if (k &= 3)
1368 dval(db) *= 1 << k;
1369 }
1370#else
1371 if (k > 0)
1372 word0(da) += k*Exp_msk1;
1373 else {
1374 k = -k;
1375 word0(db) += k*Exp_msk1;
1376 }
1377#endif
1378 return dval(da) / dval(db);
1379}
1380
1381static const double
1382tens[] = {
1383 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1384 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1385 1e20, 1e21, 1e22
1386#ifdef VAX
1387 , 1e23, 1e24
1388#endif
1389};
1390
1391static const double
1392#ifdef IEEE_Arith
1393bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1394static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1395#ifdef Avoid_Underflow
1396 9007199254740992.*9007199254740992.e-256
1397 /* = 2^106 * 1e-53 */
1398#else
1399 1e-256
1400#endif
1401};
1402/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1403/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1404#define Scale_Bit 0x10
1405#define n_bigtens 5
1406#else
1407#ifdef IBM
1408bigtens[] = { 1e16, 1e32, 1e64 };
1409static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1410#define n_bigtens 3
1411#else
1412bigtens[] = { 1e16, 1e32 };
1413static const double tinytens[] = { 1e-16, 1e-32 };
1414#define n_bigtens 2
1415#endif
1416#endif
1417
1418#ifndef IEEE_Arith
1419#undef INFNAN_CHECK
1420#endif
1421
1422#ifdef INFNAN_CHECK
1423
1424#ifndef NAN_WORD0
1425#define NAN_WORD0 0x7ff80000
1426#endif
1427
1428#ifndef NAN_WORD1
1429#define NAN_WORD1 0
1430#endif
1431
1432static int
1433match(const char **sp, char *t)
1434{
1435 int c, d;
1436 const char *s = *sp;
1437
1438 while (d = *t++) {
1439 if ((c = *++s) >= 'A' && c <= 'Z')
1440 c += 'a' - 'A';
1441 if (c != d)
1442 return 0;
1443 }
1444 *sp = s + 1;
1445 return 1;
1446}
1447
1448#ifndef No_Hex_NaN
1449static void
1450hexnan(double *rvp, const char **sp)
1451{
1452 ULong c, x[2];
1453 const char *s;
1454 int havedig, udx0, xshift;
1455
1456 x[0] = x[1] = 0;
1457 havedig = xshift = 0;
1458 udx0 = 1;
1459 s = *sp;
1460 while (c = *(const unsigned char*)++s) {
1461 if (c >= '0' && c <= '9')
1462 c -= '0';
1463 else if (c >= 'a' && c <= 'f')
1464 c += 10 - 'a';
1465 else if (c >= 'A' && c <= 'F')
1466 c += 10 - 'A';
1467 else if (c <= ' ') {
1468 if (udx0 && havedig) {
1469 udx0 = 0;
1470 xshift = 1;
1471 }
1472 continue;
1473 }
1474 else if (/*(*/ c == ')' && havedig) {
1475 *sp = s + 1;
1476 break;
1477 }
1478 else
1479 return; /* invalid form: don't change *sp */
1480 havedig = 1;
1481 if (xshift) {
1482 xshift = 0;
1483 x[0] = x[1];
1484 x[1] = 0;
1485 }
1486 if (udx0)
1487 x[0] = (x[0] << 4) | (x[1] >> 28);
1488 x[1] = (x[1] << 4) | c;
1489 }
1490 if ((x[0] &= 0xfffff) || x[1]) {
1491 word0(*rvp) = Exp_mask | x[0];
1492 word1(*rvp) = x[1];
1493 }
1494}
1495#endif /*No_Hex_NaN*/
1496#endif /* INFNAN_CHECK */
1497
1498NO_SANITIZE("unsigned-integer-overflow", double strtod(const char *s00, char **se));
1499double
1500 strtod(const char *s00, char **se)
1501{
1502#ifdef Avoid_Underflow
1503 int scale;
1504#endif
1505 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1506 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1507 const char *s, *s0, *s1;
1508 double aadj, adj;
1509 double_u aadj1, rv, rv0;
1510 Long L;
1511 ULong y, z;
1512 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1513#ifdef SET_INEXACT
1514 int inexact, oldinexact;
1515#endif
1516#ifdef Honor_FLT_ROUNDS
1517 int rounding;
1518#endif
1519#ifdef USE_LOCALE
1520 const char *s2;
1521#endif
1522
1523 errno = 0;
1524 sign = nz0 = nz = 0;
1525 dval(rv) = 0.;
1526 for (s = s00;;s++)
1527 switch (*s) {
1528 case '-':
1529 sign = 1;
1530 /* no break */
1531 case '+':
1532 if (*++s)
1533 goto break2;
1534 /* no break */
1535 case 0:
1536 goto ret0;
1537 case '\t':
1538 case '\n':
1539 case '\v':
1540 case '\f':
1541 case '\r':
1542 case ' ':
1543 continue;
1544 default:
1545 goto break2;
1546 }
1547break2:
1548 if (*s == '0') {
1549 if (s[1] == 'x' || s[1] == 'X') {
1550 s0 = ++s;
1551 adj = 0;
1552 aadj = 1.0;
1553 nd0 = -4;
1554
1555 if (!*++s || (!(s1 = strchr(hexdigit, *s)) && *s != '.')) goto ret0;
1556 if (*s == '0') {
1557 while (*++s == '0');
1558 if (!*s) goto ret;
1559 s1 = strchr(hexdigit, *s);
1560 }
1561 if (s1 != NULL) {
1562 do {
1563 adj += aadj * ((s1 - hexdigit) & 15);
1564 nd0 += 4;
1565 aadj /= 16;
1566 } while (*++s && (s1 = strchr(hexdigit, *s)));
1567 }
1568
1569 if ((*s == '.') && *++s && (s1 = strchr(hexdigit, *s))) {
1570 if (nd0 < 0) {
1571 while (*s == '0') {
1572 s++;
1573 nd0 -= 4;
1574 }
1575 }
1576 for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
1577 adj += aadj * ((s1 - hexdigit) & 15);
1578 if ((aadj /= 16) == 0.0) {
1579 while (*++s && strchr(hexdigit, *s));
1580 break;
1581 }
1582 }
1583 }
1584
1585 if (*s == 'P' || *s == 'p') {
1586 dsign = 0x2C - *++s; /* +: 2B, -: 2D */
1587 if (abs(dsign) == 1) s++;
1588 else dsign = 1;
1589
1590 nd = 0;
1591 c = *s;
1592 if (c < '0' || '9' < c) goto ret0;
1593 do {
1594 nd *= 10;
1595 nd += c;
1596 nd -= '0';
1597 c = *++s;
1598 /* Float("0x0."+("0"*267)+"1fp2095") */
1599 if (nd + dsign * nd0 > 2095) {
1600 while ('0' <= c && c <= '9') c = *++s;
1601 break;
1602 }
1603 } while ('0' <= c && c <= '9');
1604 nd0 += nd * dsign;
1605 }
1606 dval(rv) = ldexp(adj, nd0);
1607 goto ret;
1608 }
1609 nz0 = 1;
1610 while (*++s == '0') ;
1611 if (!*s)
1612 goto ret;
1613 }
1614 s0 = s;
1615 y = z = 0;
1616 for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1617 if (nd < 9)
1618 y = 10*y + c - '0';
1619 else if (nd < DBL_DIG + 2)
1620 z = 10*z + c - '0';
1621 nd0 = nd;
1622#ifdef USE_LOCALE
1623 s1 = localeconv()->decimal_point;
1624 if (c == *s1) {
1625 c = '.';
1626 if (*++s1) {
1627 s2 = s;
1628 for (;;) {
1629 if (*++s2 != *s1) {
1630 c = 0;
1631 break;
1632 }
1633 if (!*++s1) {
1634 s = s2;
1635 break;
1636 }
1637 }
1638 }
1639 }
1640#endif
1641 if (c == '.') {
1642 c = *++s;
1643 if (!ISDIGIT(c))
1644 goto dig_done;
1645 if (!nd) {
1646 for (; c == '0'; c = *++s)
1647 nz++;
1648 if (c > '0' && c <= '9') {
1649 s0 = s;
1650 nf += nz;
1651 nz = 0;
1652 goto have_dig;
1653 }
1654 goto dig_done;
1655 }
1656 for (; c >= '0' && c <= '9'; c = *++s) {
1657have_dig:
1658 nz++;
1659 if (nd > DBL_DIG * 4) {
1660 continue;
1661 }
1662 if (c -= '0') {
1663 nf += nz;
1664 for (i = 1; i < nz; i++)
1665 if (nd++ < 9)
1666 y *= 10;
1667 else if (nd <= DBL_DIG + 2)
1668 z *= 10;
1669 if (nd++ < 9)
1670 y = 10*y + c;
1671 else if (nd <= DBL_DIG + 2)
1672 z = 10*z + c;
1673 nz = 0;
1674 }
1675 }
1676 }
1677dig_done:
1678 e = 0;
1679 if (c == 'e' || c == 'E') {
1680 if (!nd && !nz && !nz0) {
1681 goto ret0;
1682 }
1683 s00 = s;
1684 esign = 0;
1685 switch (c = *++s) {
1686 case '-':
1687 esign = 1;
1688 case '+':
1689 c = *++s;
1690 }
1691 if (c >= '0' && c <= '9') {
1692 while (c == '0')
1693 c = *++s;
1694 if (c > '0' && c <= '9') {
1695 L = c - '0';
1696 s1 = s;
1697 while ((c = *++s) >= '0' && c <= '9')
1698 L = 10*L + c - '0';
1699 if (s - s1 > 8 || L > 19999)
1700 /* Avoid confusion from exponents
1701 * so large that e might overflow.
1702 */
1703 e = 19999; /* safe for 16 bit ints */
1704 else
1705 e = (int)L;
1706 if (esign)
1707 e = -e;
1708 }
1709 else
1710 e = 0;
1711 }
1712 else
1713 s = s00;
1714 }
1715 if (!nd) {
1716 if (!nz && !nz0) {
1717#ifdef INFNAN_CHECK
1718 /* Check for Nan and Infinity */
1719 switch (c) {
1720 case 'i':
1721 case 'I':
1722 if (match(&s,"nf")) {
1723 --s;
1724 if (!match(&s,"inity"))
1725 ++s;
1726 word0(rv) = 0x7ff00000;
1727 word1(rv) = 0;
1728 goto ret;
1729 }
1730 break;
1731 case 'n':
1732 case 'N':
1733 if (match(&s, "an")) {
1734 word0(rv) = NAN_WORD0;
1735 word1(rv) = NAN_WORD1;
1736#ifndef No_Hex_NaN
1737 if (*s == '(') /*)*/
1738 hexnan(&rv, &s);
1739#endif
1740 goto ret;
1741 }
1742 }
1743#endif /* INFNAN_CHECK */
1744ret0:
1745 s = s00;
1746 sign = 0;
1747 }
1748 goto ret;
1749 }
1750 e1 = e -= nf;
1751
1752 /* Now we have nd0 digits, starting at s0, followed by a
1753 * decimal point, followed by nd-nd0 digits. The number we're
1754 * after is the integer represented by those digits times
1755 * 10**e */
1756
1757 if (!nd0)
1758 nd0 = nd;
1759 k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
1760 dval(rv) = y;
1761 if (k > 9) {
1762#ifdef SET_INEXACT
1763 if (k > DBL_DIG)
1764 oldinexact = get_inexact();
1765#endif
1766 dval(rv) = tens[k - 9] * dval(rv) + z;
1767 }
1768 bd0 = bb = bd = bs = delta = 0;
1769 if (nd <= DBL_DIG
1770#ifndef RND_PRODQUOT
1771#ifndef Honor_FLT_ROUNDS
1772 && Flt_Rounds == 1
1773#endif
1774#endif
1775 ) {
1776 if (!e)
1777 goto ret;
1778 if (e > 0) {
1779 if (e <= Ten_pmax) {
1780#ifdef VAX
1781 goto vax_ovfl_check;
1782#else
1783#ifdef Honor_FLT_ROUNDS
1784 /* round correctly FLT_ROUNDS = 2 or 3 */
1785 if (sign) {
1786 dval(rv) = -dval(rv);
1787 sign = 0;
1788 }
1789#endif
1790 /* rv = */ rounded_product(dval(rv), tens[e]);
1791 goto ret;
1792#endif
1793 }
1794 i = DBL_DIG - nd;
1795 if (e <= Ten_pmax + i) {
1796 /* A fancier test would sometimes let us do
1797 * this for larger i values.
1798 */
1799#ifdef Honor_FLT_ROUNDS
1800 /* round correctly FLT_ROUNDS = 2 or 3 */
1801 if (sign) {
1802 dval(rv) = -dval(rv);
1803 sign = 0;
1804 }
1805#endif
1806 e -= i;
1807 dval(rv) *= tens[i];
1808#ifdef VAX
1809 /* VAX exponent range is so narrow we must
1810 * worry about overflow here...
1811 */
1812vax_ovfl_check:
1813 word0(rv) -= P*Exp_msk1;
1814 /* rv = */ rounded_product(dval(rv), tens[e]);
1815 if ((word0(rv) & Exp_mask)
1816 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1817 goto ovfl;
1818 word0(rv) += P*Exp_msk1;
1819#else
1820 /* rv = */ rounded_product(dval(rv), tens[e]);
1821#endif
1822 goto ret;
1823 }
1824 }
1825#ifndef Inaccurate_Divide
1826 else if (e >= -Ten_pmax) {
1827#ifdef Honor_FLT_ROUNDS
1828 /* round correctly FLT_ROUNDS = 2 or 3 */
1829 if (sign) {
1830 dval(rv) = -dval(rv);
1831 sign = 0;
1832 }
1833#endif
1834 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1835 goto ret;
1836 }
1837#endif
1838 }
1839 e1 += nd - k;
1840
1841#ifdef IEEE_Arith
1842#ifdef SET_INEXACT
1843 inexact = 1;
1844 if (k <= DBL_DIG)
1845 oldinexact = get_inexact();
1846#endif
1847#ifdef Avoid_Underflow
1848 scale = 0;
1849#endif
1850#ifdef Honor_FLT_ROUNDS
1851 if ((rounding = Flt_Rounds) >= 2) {
1852 if (sign)
1853 rounding = rounding == 2 ? 0 : 2;
1854 else
1855 if (rounding != 2)
1856 rounding = 0;
1857 }
1858#endif
1859#endif /*IEEE_Arith*/
1860
1861 /* Get starting approximation = rv * 10**e1 */
1862
1863 if (e1 > 0) {
1864 if ((i = e1 & 15) != 0)
1865 dval(rv) *= tens[i];
1866 if (e1 &= ~15) {
1867 if (e1 > DBL_MAX_10_EXP) {
1868ovfl:
1869#ifndef NO_ERRNO
1870 errno = ERANGE;
1871#endif
1872 /* Can't trust HUGE_VAL */
1873#ifdef IEEE_Arith
1874#ifdef Honor_FLT_ROUNDS
1875 switch (rounding) {
1876 case 0: /* toward 0 */
1877 case 3: /* toward -infinity */
1878 word0(rv) = Big0;
1879 word1(rv) = Big1;
1880 break;
1881 default:
1882 word0(rv) = Exp_mask;
1883 word1(rv) = 0;
1884 }
1885#else /*Honor_FLT_ROUNDS*/
1886 word0(rv) = Exp_mask;
1887 word1(rv) = 0;
1888#endif /*Honor_FLT_ROUNDS*/
1889#ifdef SET_INEXACT
1890 /* set overflow bit */
1891 dval(rv0) = 1e300;
1892 dval(rv0) *= dval(rv0);
1893#endif
1894#else /*IEEE_Arith*/
1895 word0(rv) = Big0;
1896 word1(rv) = Big1;
1897#endif /*IEEE_Arith*/
1898 if (bd0)
1899 goto retfree;
1900 goto ret;
1901 }
1902 e1 >>= 4;
1903 for (j = 0; e1 > 1; j++, e1 >>= 1)
1904 if (e1 & 1)
1905 dval(rv) *= bigtens[j];
1906 /* The last multiplication could overflow. */
1907 word0(rv) -= P*Exp_msk1;
1908 dval(rv) *= bigtens[j];
1909 if ((z = word0(rv) & Exp_mask)
1910 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1911 goto ovfl;
1912 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1913 /* set to largest number */
1914 /* (Can't trust DBL_MAX) */
1915 word0(rv) = Big0;
1916 word1(rv) = Big1;
1917 }
1918 else
1919 word0(rv) += P*Exp_msk1;
1920 }
1921 }
1922 else if (e1 < 0) {
1923 e1 = -e1;
1924 if ((i = e1 & 15) != 0)
1925 dval(rv) /= tens[i];
1926 if (e1 >>= 4) {
1927 if (e1 >= 1 << n_bigtens)
1928 goto undfl;
1929#ifdef Avoid_Underflow
1930 if (e1 & Scale_Bit)
1931 scale = 2*P;
1932 for (j = 0; e1 > 0; j++, e1 >>= 1)
1933 if (e1 & 1)
1934 dval(rv) *= tinytens[j];
1935 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1936 >> Exp_shift)) > 0) {
1937 /* scaled rv is denormal; zap j low bits */
1938 if (j >= 32) {
1939 word1(rv) = 0;
1940 if (j >= 53)
1941 word0(rv) = (P+2)*Exp_msk1;
1942 else
1943 word0(rv) &= 0xffffffff << (j-32);
1944 }
1945 else
1946 word1(rv) &= 0xffffffff << j;
1947 }
1948#else
1949 for (j = 0; e1 > 1; j++, e1 >>= 1)
1950 if (e1 & 1)
1951 dval(rv) *= tinytens[j];
1952 /* The last multiplication could underflow. */
1953 dval(rv0) = dval(rv);
1954 dval(rv) *= tinytens[j];
1955 if (!dval(rv)) {
1956 dval(rv) = 2.*dval(rv0);
1957 dval(rv) *= tinytens[j];
1958#endif
1959 if (!dval(rv)) {
1960undfl:
1961 dval(rv) = 0.;
1962#ifndef NO_ERRNO
1963 errno = ERANGE;
1964#endif
1965 if (bd0)
1966 goto retfree;
1967 goto ret;
1968 }
1969#ifndef Avoid_Underflow
1970 word0(rv) = Tiny0;
1971 word1(rv) = Tiny1;
1972 /* The refinement below will clean
1973 * this approximation up.
1974 */
1975 }
1976#endif
1977 }
1978 }
1979
1980 /* Now the hard part -- adjusting rv to the correct value.*/
1981
1982 /* Put digits into bd: true value = bd * 10^e */
1983
1984 bd0 = s2b(s0, nd0, nd, y);
1985
1986 for (;;) {
1987 bd = Balloc(bd0->k);
1988 Bcopy(bd, bd0);
1989 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1990 bs = i2b(1);
1991
1992 if (e >= 0) {
1993 bb2 = bb5 = 0;
1994 bd2 = bd5 = e;
1995 }
1996 else {
1997 bb2 = bb5 = -e;
1998 bd2 = bd5 = 0;
1999 }
2000 if (bbe >= 0)
2001 bb2 += bbe;
2002 else
2003 bd2 -= bbe;
2004 bs2 = bb2;
2005#ifdef Honor_FLT_ROUNDS
2006 if (rounding != 1)
2007 bs2++;
2008#endif
2009#ifdef Avoid_Underflow
2010 j = bbe - scale;
2011 i = j + bbbits - 1; /* logb(rv) */
2012 if (i < Emin) /* denormal */
2013 j += P - Emin;
2014 else
2015 j = P + 1 - bbbits;
2016#else /*Avoid_Underflow*/
2017#ifdef Sudden_Underflow
2018#ifdef IBM
2019 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2020#else
2021 j = P + 1 - bbbits;
2022#endif
2023#else /*Sudden_Underflow*/
2024 j = bbe;
2025 i = j + bbbits - 1; /* logb(rv) */
2026 if (i < Emin) /* denormal */
2027 j += P - Emin;
2028 else
2029 j = P + 1 - bbbits;
2030#endif /*Sudden_Underflow*/
2031#endif /*Avoid_Underflow*/
2032 bb2 += j;
2033 bd2 += j;
2034#ifdef Avoid_Underflow
2035 bd2 += scale;
2036#endif
2037 i = bb2 < bd2 ? bb2 : bd2;
2038 if (i > bs2)
2039 i = bs2;
2040 if (i > 0) {
2041 bb2 -= i;
2042 bd2 -= i;
2043 bs2 -= i;
2044 }
2045 if (bb5 > 0) {
2046 bs = pow5mult(bs, bb5);
2047 bb1 = mult(bs, bb);
2048 Bfree(bb);
2049 bb = bb1;
2050 }
2051 if (bb2 > 0)
2052 bb = lshift(bb, bb2);
2053 if (bd5 > 0)
2054 bd = pow5mult(bd, bd5);
2055 if (bd2 > 0)
2056 bd = lshift(bd, bd2);
2057 if (bs2 > 0)
2058 bs = lshift(bs, bs2);
2059 delta = diff(bb, bd);
2060 dsign = delta->sign;
2061 delta->sign = 0;
2062 i = cmp(delta, bs);
2063#ifdef Honor_FLT_ROUNDS
2064 if (rounding != 1) {
2065 if (i < 0) {
2066 /* Error is less than an ulp */
2067 if (!delta->x[0] && delta->wds <= 1) {
2068 /* exact */
2069#ifdef SET_INEXACT
2070 inexact = 0;
2071#endif
2072 break;
2073 }
2074 if (rounding) {
2075 if (dsign) {
2076 adj = 1.;
2077 goto apply_adj;
2078 }
2079 }
2080 else if (!dsign) {
2081 adj = -1.;
2082 if (!word1(rv)
2083 && !(word0(rv) & Frac_mask)) {
2084 y = word0(rv) & Exp_mask;
2085#ifdef Avoid_Underflow
2086 if (!scale || y > 2*P*Exp_msk1)
2087#else
2088 if (y)
2089#endif
2090 {
2091 delta = lshift(delta,Log2P);
2092 if (cmp(delta, bs) <= 0)
2093 adj = -0.5;
2094 }
2095 }
2096apply_adj:
2097#ifdef Avoid_Underflow
2098 if (scale && (y = word0(rv) & Exp_mask)
2099 <= 2*P*Exp_msk1)
2100 word0(adj) += (2*P+1)*Exp_msk1 - y;
2101#else
2102#ifdef Sudden_Underflow
2103 if ((word0(rv) & Exp_mask) <=
2104 P*Exp_msk1) {
2105 word0(rv) += P*Exp_msk1;
2106 dval(rv) += adj*ulp(dval(rv));
2107 word0(rv) -= P*Exp_msk1;
2108 }
2109 else
2110#endif /*Sudden_Underflow*/
2111#endif /*Avoid_Underflow*/
2112 dval(rv) += adj*ulp(dval(rv));
2113 }
2114 break;
2115 }
2116 adj = ratio(delta, bs);
2117 if (adj < 1.)
2118 adj = 1.;
2119 if (adj <= 0x7ffffffe) {
2120 /* adj = rounding ? ceil(adj) : floor(adj); */
2121 y = adj;
2122 if (y != adj) {
2123 if (!((rounding>>1) ^ dsign))
2124 y++;
2125 adj = y;
2126 }
2127 }
2128#ifdef Avoid_Underflow
2129 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2130 word0(adj) += (2*P+1)*Exp_msk1 - y;
2131#else
2132#ifdef Sudden_Underflow
2133 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2134 word0(rv) += P*Exp_msk1;
2135 adj *= ulp(dval(rv));
2136 if (dsign)
2137 dval(rv) += adj;
2138 else
2139 dval(rv) -= adj;
2140 word0(rv) -= P*Exp_msk1;
2141 goto cont;
2142 }
2143#endif /*Sudden_Underflow*/
2144#endif /*Avoid_Underflow*/
2145 adj *= ulp(dval(rv));
2146 if (dsign)
2147 dval(rv) += adj;
2148 else
2149 dval(rv) -= adj;
2150 goto cont;
2151 }
2152#endif /*Honor_FLT_ROUNDS*/
2153
2154 if (i < 0) {
2155 /* Error is less than half an ulp -- check for
2156 * special case of mantissa a power of two.
2157 */
2158 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2159#ifdef IEEE_Arith
2160#ifdef Avoid_Underflow
2161 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2162#else
2163 || (word0(rv) & Exp_mask) <= Exp_msk1
2164#endif
2165#endif
2166 ) {
2167#ifdef SET_INEXACT
2168 if (!delta->x[0] && delta->wds <= 1)
2169 inexact = 0;
2170#endif
2171 break;
2172 }
2173 if (!delta->x[0] && delta->wds <= 1) {
2174 /* exact result */
2175#ifdef SET_INEXACT
2176 inexact = 0;
2177#endif
2178 break;
2179 }
2180 delta = lshift(delta,Log2P);
2181 if (cmp(delta, bs) > 0)
2182 goto drop_down;
2183 break;
2184 }
2185 if (i == 0) {
2186 /* exactly half-way between */
2187 if (dsign) {
2188 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2189 && word1(rv) == (
2190#ifdef Avoid_Underflow
2191 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2192 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2193#endif
2194 0xffffffff)) {
2195 /*boundary case -- increment exponent*/
2196 word0(rv) = (word0(rv) & Exp_mask)
2197 + Exp_msk1
2198#ifdef IBM
2199 | Exp_msk1 >> 4
2200#endif
2201 ;
2202 word1(rv) = 0;
2203#ifdef Avoid_Underflow
2204 dsign = 0;
2205#endif
2206 break;
2207 }
2208 }
2209 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2210drop_down:
2211 /* boundary case -- decrement exponent */
2212#ifdef Sudden_Underflow /*{{*/
2213 L = word0(rv) & Exp_mask;
2214#ifdef IBM
2215 if (L < Exp_msk1)
2216#else
2217#ifdef Avoid_Underflow
2218 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2219#else
2220 if (L <= Exp_msk1)
2221#endif /*Avoid_Underflow*/
2222#endif /*IBM*/
2223 goto undfl;
2224 L -= Exp_msk1;
2225#else /*Sudden_Underflow}{*/
2226#ifdef Avoid_Underflow
2227 if (scale) {
2228 L = word0(rv) & Exp_mask;
2229 if (L <= (2*P+1)*Exp_msk1) {
2230 if (L > (P+2)*Exp_msk1)
2231 /* round even ==> */
2232 /* accept rv */
2233 break;
2234 /* rv = smallest denormal */
2235 goto undfl;
2236 }
2237 }
2238#endif /*Avoid_Underflow*/
2239 L = (word0(rv) & Exp_mask) - Exp_msk1;
2240#endif /*Sudden_Underflow}}*/
2241 word0(rv) = L | Bndry_mask1;
2242 word1(rv) = 0xffffffff;
2243#ifdef IBM
2244 goto cont;
2245#else
2246 break;
2247#endif
2248 }
2249#ifndef ROUND_BIASED
2250 if (!(word1(rv) & LSB))
2251 break;
2252#endif
2253 if (dsign)
2254 dval(rv) += ulp(dval(rv));
2255#ifndef ROUND_BIASED
2256 else {
2257 dval(rv) -= ulp(dval(rv));
2258#ifndef Sudden_Underflow
2259 if (!dval(rv))
2260 goto undfl;
2261#endif
2262 }
2263#ifdef Avoid_Underflow
2264 dsign = 1 - dsign;
2265#endif
2266#endif
2267 break;
2268 }
2269 if ((aadj = ratio(delta, bs)) <= 2.) {
2270 if (dsign)
2271 aadj = dval(aadj1) = 1.;
2272 else if (word1(rv) || word0(rv) & Bndry_mask) {
2273#ifndef Sudden_Underflow
2274 if (word1(rv) == Tiny1 && !word0(rv))
2275 goto undfl;
2276#endif
2277 aadj = 1.;
2278 dval(aadj1) = -1.;
2279 }
2280 else {
2281 /* special case -- power of FLT_RADIX to be */
2282 /* rounded down... */
2283
2284 if (aadj < 2./FLT_RADIX)
2285 aadj = 1./FLT_RADIX;
2286 else
2287 aadj *= 0.5;
2288 dval(aadj1) = -aadj;
2289 }
2290 }
2291 else {
2292 aadj *= 0.5;
2293 dval(aadj1) = dsign ? aadj : -aadj;
2294#ifdef Check_FLT_ROUNDS
2295 switch (Rounding) {
2296 case 2: /* towards +infinity */
2297 dval(aadj1) -= 0.5;
2298 break;
2299 case 0: /* towards 0 */
2300 case 3: /* towards -infinity */
2301 dval(aadj1) += 0.5;
2302 }
2303#else
2304 if (Flt_Rounds == 0)
2305 dval(aadj1) += 0.5;
2306#endif /*Check_FLT_ROUNDS*/
2307 }
2308 y = word0(rv) & Exp_mask;
2309
2310 /* Check for overflow */
2311
2312 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2313 dval(rv0) = dval(rv);
2314 word0(rv) -= P*Exp_msk1;
2315 adj = dval(aadj1) * ulp(dval(rv));
2316 dval(rv) += adj;
2317 if ((word0(rv) & Exp_mask) >=
2318 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2319 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2320 goto ovfl;
2321 word0(rv) = Big0;
2322 word1(rv) = Big1;
2323 goto cont;
2324 }
2325 else
2326 word0(rv) += P*Exp_msk1;
2327 }
2328 else {
2329#ifdef Avoid_Underflow
2330 if (scale && y <= 2*P*Exp_msk1) {
2331 if (aadj <= 0x7fffffff) {
2332 if ((z = (int)aadj) <= 0)
2333 z = 1;
2334 aadj = z;
2335 dval(aadj1) = dsign ? aadj : -aadj;
2336 }
2337 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2338 }
2339 adj = dval(aadj1) * ulp(dval(rv));
2340 dval(rv) += adj;
2341#else
2342#ifdef Sudden_Underflow
2343 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2344 dval(rv0) = dval(rv);
2345 word0(rv) += P*Exp_msk1;
2346 adj = dval(aadj1) * ulp(dval(rv));
2347 dval(rv) += adj;
2348#ifdef IBM
2349 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2350#else
2351 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2352#endif
2353 {
2354 if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2355 goto undfl;
2356 word0(rv) = Tiny0;
2357 word1(rv) = Tiny1;
2358 goto cont;
2359 }
2360 else
2361 word0(rv) -= P*Exp_msk1;
2362 }
2363 else {
2364 adj = dval(aadj1) * ulp(dval(rv));
2365 dval(rv) += adj;
2366 }
2367#else /*Sudden_Underflow*/
2368 /* Compute adj so that the IEEE rounding rules will
2369 * correctly round rv + adj in some half-way cases.
2370 * If rv * ulp(rv) is denormalized (i.e.,
2371 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2372 * trouble from bits lost to denormalization;
2373 * example: 1.2e-307 .
2374 */
2375 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2376 dval(aadj1) = (double)(int)(aadj + 0.5);
2377 if (!dsign)
2378 dval(aadj1) = -dval(aadj1);
2379 }
2380 adj = dval(aadj1) * ulp(dval(rv));
2381 dval(rv) += adj;
2382#endif /*Sudden_Underflow*/
2383#endif /*Avoid_Underflow*/
2384 }
2385 z = word0(rv) & Exp_mask;
2386#ifndef SET_INEXACT
2387#ifdef Avoid_Underflow
2388 if (!scale)
2389#endif
2390 if (y == z) {
2391 /* Can we stop now? */
2392 L = (Long)aadj;
2393 aadj -= L;
2394 /* The tolerances below are conservative. */
2395 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2396 if (aadj < .4999999 || aadj > .5000001)
2397 break;
2398 }
2399 else if (aadj < .4999999/FLT_RADIX)
2400 break;
2401 }
2402#endif
2403cont:
2404 Bfree(bb);
2405 Bfree(bd);
2406 Bfree(bs);
2407 Bfree(delta);
2408 }
2409#ifdef SET_INEXACT
2410 if (inexact) {
2411 if (!oldinexact) {
2412 word0(rv0) = Exp_1 + (70 << Exp_shift);
2413 word1(rv0) = 0;
2414 dval(rv0) += 1.;
2415 }
2416 }
2417 else if (!oldinexact)
2418 clear_inexact();
2419#endif
2420#ifdef Avoid_Underflow
2421 if (scale) {
2422 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2423 word1(rv0) = 0;
2424 dval(rv) *= dval(rv0);
2425#ifndef NO_ERRNO
2426 /* try to avoid the bug of testing an 8087 register value */
2427 if (word0(rv) == 0 && word1(rv) == 0)
2428 errno = ERANGE;
2429#endif
2430 }
2431#endif /* Avoid_Underflow */
2432#ifdef SET_INEXACT
2433 if (inexact && !(word0(rv) & Exp_mask)) {
2434 /* set underflow bit */
2435 dval(rv0) = 1e-300;
2436 dval(rv0) *= dval(rv0);
2437 }
2438#endif
2439retfree:
2440 Bfree(bb);
2441 Bfree(bd);
2442 Bfree(bs);
2443 Bfree(bd0);
2444 Bfree(delta);
2445ret:
2446 if (se)
2447 *se = (char *)s;
2448 return sign ? -dval(rv) : dval(rv);
2449}
2450
2451NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S));
2452static int
2453quorem(Bigint *b, Bigint *S)
2454{
2455 int n;
2456 ULong *bx, *bxe, q, *sx, *sxe;
2457#ifdef ULLong
2458 ULLong borrow, carry, y, ys;
2459#else
2460 ULong borrow, carry, y, ys;
2461#ifdef Pack_32
2462 ULong si, z, zs;
2463#endif
2464#endif
2465
2466 n = S->wds;
2467#ifdef DEBUG
2468 /*debug*/ if (b->wds > n)
2469 /*debug*/ Bug("oversize b in quorem");
2470#endif
2471 if (b->wds < n)
2472 return 0;
2473 sx = S->x;
2474 sxe = sx + --n;
2475 bx = b->x;
2476 bxe = bx + n;
2477 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2478#ifdef DEBUG
2479 /*debug*/ if (q > 9)
2480 /*debug*/ Bug("oversized quotient in quorem");
2481#endif
2482 if (q) {
2483 borrow = 0;
2484 carry = 0;
2485 do {
2486#ifdef ULLong
2487 ys = *sx++ * (ULLong)q + carry;
2488 carry = ys >> 32;
2489 y = *bx - (ys & FFFFFFFF) - borrow;
2490 borrow = y >> 32 & (ULong)1;
2491 *bx++ = (ULong)(y & FFFFFFFF);
2492#else
2493#ifdef Pack_32
2494 si = *sx++;
2495 ys = (si & 0xffff) * q + carry;
2496 zs = (si >> 16) * q + (ys >> 16);
2497 carry = zs >> 16;
2498 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2499 borrow = (y & 0x10000) >> 16;
2500 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2501 borrow = (z & 0x10000) >> 16;
2502 Storeinc(bx, z, y);
2503#else
2504 ys = *sx++ * q + carry;
2505 carry = ys >> 16;
2506 y = *bx - (ys & 0xffff) - borrow;
2507 borrow = (y & 0x10000) >> 16;
2508 *bx++ = y & 0xffff;
2509#endif
2510#endif
2511 } while (sx <= sxe);
2512 if (!*bxe) {
2513 bx = b->x;
2514 while (--bxe > bx && !*bxe)
2515 --n;
2516 b->wds = n;
2517 }
2518 }
2519 if (cmp(b, S) >= 0) {
2520 q++;
2521 borrow = 0;
2522 carry = 0;
2523 bx = b->x;
2524 sx = S->x;
2525 do {
2526#ifdef ULLong
2527 ys = *sx++ + carry;
2528 carry = ys >> 32;
2529 y = *bx - (ys & FFFFFFFF) - borrow;
2530 borrow = y >> 32 & (ULong)1;
2531 *bx++ = (ULong)(y & FFFFFFFF);
2532#else
2533#ifdef Pack_32
2534 si = *sx++;
2535 ys = (si & 0xffff) + carry;
2536 zs = (si >> 16) + (ys >> 16);
2537 carry = zs >> 16;
2538 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2539 borrow = (y & 0x10000) >> 16;
2540 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2541 borrow = (z & 0x10000) >> 16;
2542 Storeinc(bx, z, y);
2543#else
2544 ys = *sx++ + carry;
2545 carry = ys >> 16;
2546 y = *bx - (ys & 0xffff) - borrow;
2547 borrow = (y & 0x10000) >> 16;
2548 *bx++ = y & 0xffff;
2549#endif
2550#endif
2551 } while (sx <= sxe);
2552 bx = b->x;
2553 bxe = bx + n;
2554 if (!*bxe) {
2555 while (--bxe > bx && !*bxe)
2556 --n;
2557 b->wds = n;
2558 }
2559 }
2560 return q;
2561}
2562
2563#ifndef MULTIPLE_THREADS
2564static char *dtoa_result;
2565#endif
2566
2567#ifndef MULTIPLE_THREADS
2568static char *
2569rv_alloc(int i)
2570{
2571 return dtoa_result = MALLOC(i);
2572}
2573#else
2574#define rv_alloc(i) MALLOC(i)
2575#endif
2576
2577static char *
2578nrv_alloc(const char *s, char **rve, size_t n)
2579{
2580 char *rv, *t;
2581
2582 t = rv = rv_alloc(n);
2583 while ((*t = *s++) != 0) t++;
2584 if (rve)
2585 *rve = t;
2586 return rv;
2587}
2588
2589#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
2590
2591#ifndef MULTIPLE_THREADS
2592/* freedtoa(s) must be used to free values s returned by dtoa
2593 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2594 * but for consistency with earlier versions of dtoa, it is optional
2595 * when MULTIPLE_THREADS is not defined.
2596 */
2597
2598static void
2599freedtoa(char *s)
2600{
2601 FREE(s);
2602}
2603#endif
2604
2605static const char INFSTR[] = "Infinity";
2606static const char NANSTR[] = "NaN";
2607static const char ZEROSTR[] = "0";
2608
2609/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2610 *
2611 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2612 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2613 *
2614 * Modifications:
2615 * 1. Rather than iterating, we use a simple numeric overestimate
2616 * to determine k = floor(log10(d)). We scale relevant
2617 * quantities using O(log2(k)) rather than O(k) multiplications.
2618 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2619 * try to generate digits strictly left to right. Instead, we
2620 * compute with fewer bits and propagate the carry if necessary
2621 * when rounding the final digit up. This is often faster.
2622 * 3. Under the assumption that input will be rounded nearest,
2623 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2624 * That is, we allow equality in stopping tests when the
2625 * round-nearest rule will give the same floating-point value
2626 * as would satisfaction of the stopping test with strict
2627 * inequality.
2628 * 4. We remove common factors of powers of 2 from relevant
2629 * quantities.
2630 * 5. When converting floating-point integers less than 1e16,
2631 * we use floating-point arithmetic rather than resorting
2632 * to multiple-precision integers.
2633 * 6. When asked to produce fewer than 15 digits, we first try
2634 * to get by with floating-point arithmetic; we resort to
2635 * multiple-precision integer arithmetic only if we cannot
2636 * guarantee that the floating-point calculation has given
2637 * the correctly rounded result. For k requested digits and
2638 * "uniformly" distributed input, the probability is
2639 * something like 10^(k-15) that we must resort to the Long
2640 * calculation.
2641 */
2642
2643char *
2644dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
2645{
2646 /* Arguments ndigits, decpt, sign are similar to those
2647 of ecvt and fcvt; trailing zeros are suppressed from
2648 the returned string. If not null, *rve is set to point
2649 to the end of the return value. If d is +-Infinity or NaN,
2650 then *decpt is set to 9999.
2651
2652 mode:
2653 0 ==> shortest string that yields d when read in
2654 and rounded to nearest.
2655 1 ==> like 0, but with Steele & White stopping rule;
2656 e.g. with IEEE P754 arithmetic , mode 0 gives
2657 1e23 whereas mode 1 gives 9.999999999999999e22.
2658 2 ==> max(1,ndigits) significant digits. This gives a
2659 return value similar to that of ecvt, except
2660 that trailing zeros are suppressed.
2661 3 ==> through ndigits past the decimal point. This
2662 gives a return value similar to that from fcvt,
2663 except that trailing zeros are suppressed, and
2664 ndigits can be negative.
2665 4,5 ==> similar to 2 and 3, respectively, but (in
2666 round-nearest mode) with the tests of mode 0 to
2667 possibly return a shorter string that rounds to d.
2668 With IEEE arithmetic and compilation with
2669 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2670 as modes 2 and 3 when FLT_ROUNDS != 1.
2671 6-9 ==> Debugging modes similar to mode - 4: don't try
2672 fast floating-point estimate (if applicable).
2673
2674 Values of mode other than 0-9 are treated as mode 0.
2675
2676 Sufficient space is allocated to the return value
2677 to hold the suppressed trailing zeros.
2678 */
2679
2680 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2681 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2682 spec_case, try_quick, half = 0;
2683 Long L;
2684#ifndef Sudden_Underflow
2685 int denorm;
2686 ULong x;
2687#endif
2688 Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
2689 double ds;
2690 double_u d, d2, eps;
2691 char *s, *s0;
2692#ifdef Honor_FLT_ROUNDS
2693 int rounding;
2694#endif
2695#ifdef SET_INEXACT
2696 int inexact, oldinexact;
2697#endif
2698
2699 dval(d) = d_;
2700
2701#ifndef MULTIPLE_THREADS
2702 if (dtoa_result) {
2703 freedtoa(dtoa_result);
2704 dtoa_result = 0;
2705 }
2706#endif
2707
2708 if (word0(d) & Sign_bit) {
2709 /* set sign for everything, including 0's and NaNs */
2710 *sign = 1;
2711 word0(d) &= ~Sign_bit; /* clear sign bit */
2712 }
2713 else
2714 *sign = 0;
2715
2716#if defined(IEEE_Arith) + defined(VAX)
2717#ifdef IEEE_Arith
2718 if ((word0(d) & Exp_mask) == Exp_mask)
2719#else
2720 if (word0(d) == 0x8000)
2721#endif
2722 {
2723 /* Infinity or NaN */
2724 *decpt = 9999;
2725#ifdef IEEE_Arith
2726 if (!word1(d) && !(word0(d) & 0xfffff))
2727 return rv_strdup(INFSTR, rve);
2728#endif
2729 return rv_strdup(NANSTR, rve);
2730 }
2731#endif
2732#ifdef IBM
2733 dval(d) += 0; /* normalize */
2734#endif
2735 if (!dval(d)) {
2736 *decpt = 1;
2737 return rv_strdup(ZEROSTR, rve);
2738 }
2739
2740#ifdef SET_INEXACT
2741 try_quick = oldinexact = get_inexact();
2742 inexact = 1;
2743#endif
2744#ifdef Honor_FLT_ROUNDS
2745 if ((rounding = Flt_Rounds) >= 2) {
2746 if (*sign)
2747 rounding = rounding == 2 ? 0 : 2;
2748 else
2749 if (rounding != 2)
2750 rounding = 0;
2751 }
2752#endif
2753
2754 b = d2b(dval(d), &be, &bbits);
2755#ifdef Sudden_Underflow
2756 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2757#else
2758 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
2759#endif
2760 dval(d2) = dval(d);
2761 word0(d2) &= Frac_mask1;
2762 word0(d2) |= Exp_11;
2763#ifdef IBM
2764 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2765 dval(d2) /= 1 << j;
2766#endif
2767
2768 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2769 * log10(x) = log(x) / log(10)
2770 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2771 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2772 *
2773 * This suggests computing an approximation k to log10(d) by
2774 *
2775 * k = (i - Bias)*0.301029995663981
2776 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2777 *
2778 * We want k to be too large rather than too small.
2779 * The error in the first-order Taylor series approximation
2780 * is in our favor, so we just round up the constant enough
2781 * to compensate for any error in the multiplication of
2782 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2783 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2784 * adding 1e-13 to the constant term more than suffices.
2785 * Hence we adjust the constant term to 0.1760912590558.
2786 * (We could get a more accurate k by invoking log10,
2787 * but this is probably not worthwhile.)
2788 */
2789
2790 i -= Bias;
2791#ifdef IBM
2792 i <<= 2;
2793 i += j;
2794#endif
2795#ifndef Sudden_Underflow
2796 denorm = 0;
2797 }
2798 else {
2799 /* d is denormalized */
2800
2801 i = bbits + be + (Bias + (P-1) - 1);
2802 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2803 : word1(d) << (32 - i);
2804 dval(d2) = x;
2805 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2806 i -= (Bias + (P-1) - 1) + 1;
2807 denorm = 1;
2808 }
2809#endif
2810 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2811 k = (int)ds;
2812 if (ds < 0. && ds != k)
2813 k--; /* want k = floor(ds) */
2814 k_check = 1;
2815 if (k >= 0 && k <= Ten_pmax) {
2816 if (dval(d) < tens[k])
2817 k--;
2818 k_check = 0;
2819 }
2820 j = bbits - i - 1;
2821 if (j >= 0) {
2822 b2 = 0;
2823 s2 = j;
2824 }
2825 else {
2826 b2 = -j;
2827 s2 = 0;
2828 }
2829 if (k >= 0) {
2830 b5 = 0;
2831 s5 = k;
2832 s2 += k;
2833 }
2834 else {
2835 b2 -= k;
2836 b5 = -k;
2837 s5 = 0;
2838 }
2839 if (mode < 0 || mode > 9)
2840 mode = 0;
2841
2842#ifndef SET_INEXACT
2843#ifdef Check_FLT_ROUNDS
2844 try_quick = Rounding == 1;
2845#else
2846 try_quick = 1;
2847#endif
2848#endif /*SET_INEXACT*/
2849
2850 if (mode > 5) {
2851 mode -= 4;
2852 try_quick = 0;
2853 }
2854 leftright = 1;
2855 ilim = ilim1 = -1;
2856 switch (mode) {
2857 case 0:
2858 case 1:
2859 i = 18;
2860 ndigits = 0;
2861 break;
2862 case 2:
2863 leftright = 0;
2864 /* no break */
2865 case 4:
2866 if (ndigits <= 0)
2867 ndigits = 1;
2868 ilim = ilim1 = i = ndigits;
2869 break;
2870 case 3:
2871 leftright = 0;
2872 /* no break */
2873 case 5:
2874 i = ndigits + k + 1;
2875 ilim = i;
2876 ilim1 = i - 1;
2877 if (i <= 0)
2878 i = 1;
2879 }
2880 s = s0 = rv_alloc(i+1);
2881
2882#ifdef Honor_FLT_ROUNDS
2883 if (mode > 1 && rounding != 1)
2884 leftright = 0;
2885#endif
2886
2887 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2888
2889 /* Try to get by with floating-point arithmetic. */
2890
2891 i = 0;
2892 dval(d2) = dval(d);
2893 k0 = k;
2894 ilim0 = ilim;
2895 ieps = 2; /* conservative */
2896 if (k > 0) {
2897 ds = tens[k&0xf];
2898 j = k >> 4;
2899 if (j & Bletch) {
2900 /* prevent overflows */
2901 j &= Bletch - 1;
2902 dval(d) /= bigtens[n_bigtens-1];
2903 ieps++;
2904 }
2905 for (; j; j >>= 1, i++)
2906 if (j & 1) {
2907 ieps++;
2908 ds *= bigtens[i];
2909 }
2910 dval(d) /= ds;
2911 }
2912 else if ((j1 = -k) != 0) {
2913 dval(d) *= tens[j1 & 0xf];
2914 for (j = j1 >> 4; j; j >>= 1, i++)
2915 if (j & 1) {
2916 ieps++;
2917 dval(d) *= bigtens[i];
2918 }
2919 }
2920 if (k_check && dval(d) < 1. && ilim > 0) {
2921 if (ilim1 <= 0)
2922 goto fast_failed;
2923 ilim = ilim1;
2924 k--;
2925 dval(d) *= 10.;
2926 ieps++;
2927 }
2928 dval(eps) = ieps*dval(d) + 7.;
2929 word0(eps) -= (P-1)*Exp_msk1;
2930 if (ilim == 0) {
2931 S = mhi = 0;
2932 dval(d) -= 5.;
2933 if (dval(d) > dval(eps))
2934 goto one_digit;
2935 if (dval(d) < -dval(eps))
2936 goto no_digits;
2937 goto fast_failed;
2938 }
2939#ifndef No_leftright
2940 if (leftright) {
2941 /* Use Steele & White method of only
2942 * generating digits needed.
2943 */
2944 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2945 for (i = 0;;) {
2946 L = (int)dval(d);
2947 dval(d) -= L;
2948 *s++ = '0' + (int)L;
2949 if (dval(d) < dval(eps))
2950 goto ret1;
2951 if (1. - dval(d) < dval(eps))
2952 goto bump_up;
2953 if (++i >= ilim)
2954 break;
2955 dval(eps) *= 10.;
2956 dval(d) *= 10.;
2957 }
2958 }
2959 else {
2960#endif
2961 /* Generate ilim digits, then fix them up. */
2962 dval(eps) *= tens[ilim-1];
2963 for (i = 1;; i++, dval(d) *= 10.) {
2964 L = (Long)(dval(d));
2965 if (!(dval(d) -= L))
2966 ilim = i;
2967 *s++ = '0' + (int)L;
2968 if (i == ilim) {
2969 if (dval(d) > 0.5 + dval(eps))
2970 goto bump_up;
2971 else if (dval(d) < 0.5 - dval(eps)) {
2972 while (*--s == '0') ;
2973 s++;
2974 goto ret1;
2975 }
2976 half = 1;
2977 if ((*(s-1) - '0') & 1) {
2978 goto bump_up;
2979 }
2980 break;
2981 }
2982 }
2983#ifndef No_leftright
2984 }
2985#endif
2986fast_failed:
2987 s = s0;
2988 dval(d) = dval(d2);
2989 k = k0;
2990 ilim = ilim0;
2991 }
2992
2993 /* Do we have a "small" integer? */
2994
2995 if (be >= 0 && k <= Int_max) {
2996 /* Yes. */
2997 ds = tens[k];
2998 if (ndigits < 0 && ilim <= 0) {
2999 S = mhi = 0;
3000 if (ilim < 0 || dval(d) <= 5*ds)
3001 goto no_digits;
3002 goto one_digit;
3003 }
3004 for (i = 1;; i++, dval(d) *= 10.) {
3005 L = (Long)(dval(d) / ds);
3006 dval(d) -= L*ds;
3007#ifdef Check_FLT_ROUNDS
3008 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3009 if (dval(d) < 0) {
3010 L--;
3011 dval(d) += ds;
3012 }
3013#endif
3014 *s++ = '0' + (int)L;
3015 if (!dval(d)) {
3016#ifdef SET_INEXACT
3017 inexact = 0;
3018#endif
3019 break;
3020 }
3021 if (i == ilim) {
3022#ifdef Honor_FLT_ROUNDS
3023 if (mode > 1)
3024 switch (rounding) {
3025 case 0: goto ret1;
3026 case 2: goto bump_up;
3027 }
3028#endif
3029 dval(d) += dval(d);
3030 if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3031bump_up:
3032 while (*--s == '9')
3033 if (s == s0) {
3034 k++;
3035 *s = '0';
3036 break;
3037 }
3038 ++*s++;
3039 }
3040 break;
3041 }
3042 }
3043 goto ret1;
3044 }
3045
3046 m2 = b2;
3047 m5 = b5;
3048 if (leftright) {
3049 i =
3050#ifndef Sudden_Underflow
3051 denorm ? be + (Bias + (P-1) - 1 + 1) :
3052#endif
3053#ifdef IBM
3054 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3055#else
3056 1 + P - bbits;
3057#endif
3058 b2 += i;
3059 s2 += i;
3060 mhi = i2b(1);
3061 }
3062 if (m2 > 0 && s2 > 0) {
3063 i = m2 < s2 ? m2 : s2;
3064 b2 -= i;
3065 m2 -= i;
3066 s2 -= i;
3067 }
3068 if (b5 > 0) {
3069 if (leftright) {
3070 if (m5 > 0) {
3071 mhi = pow5mult(mhi, m5);
3072 b1 = mult(mhi, b);
3073 Bfree(b);
3074 b = b1;
3075 }
3076 if ((j = b5 - m5) != 0)
3077 b = pow5mult(b, j);
3078 }
3079 else
3080 b = pow5mult(b, b5);
3081 }
3082 S = i2b(1);
3083 if (s5 > 0)
3084 S = pow5mult(S, s5);
3085
3086 /* Check for special case that d is a normalized power of 2. */
3087
3088 spec_case = 0;
3089 if ((mode < 2 || leftright)
3090#ifdef Honor_FLT_ROUNDS
3091 && rounding == 1
3092#endif
3093 ) {
3094 if (!word1(d) && !(word0(d) & Bndry_mask)
3095#ifndef Sudden_Underflow
3096 && word0(d) & (Exp_mask & ~Exp_msk1)
3097#endif
3098 ) {
3099 /* The special case */
3100 b2 += Log2P;
3101 s2 += Log2P;
3102 spec_case = 1;
3103 }
3104 }
3105
3106 /* Arrange for convenient computation of quotients:
3107 * shift left if necessary so divisor has 4 leading 0 bits.
3108 *
3109 * Perhaps we should just compute leading 28 bits of S once
3110 * and for all and pass them and a shift to quorem, so it
3111 * can do shifts and ors to compute the numerator for q.
3112 */
3113#ifdef Pack_32
3114 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3115 i = 32 - i;
3116#else
3117 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3118 i = 16 - i;
3119#endif
3120 if (i > 4) {
3121 i -= 4;
3122 b2 += i;
3123 m2 += i;
3124 s2 += i;
3125 }
3126 else if (i < 4) {
3127 i += 28;
3128 b2 += i;
3129 m2 += i;
3130 s2 += i;
3131 }
3132 if (b2 > 0)
3133 b = lshift(b, b2);
3134 if (s2 > 0)
3135 S = lshift(S, s2);
3136 if (k_check) {
3137 if (cmp(b,S) < 0) {
3138 k--;
3139 b = multadd(b, 10, 0); /* we botched the k estimate */
3140 if (leftright)
3141 mhi = multadd(mhi, 10, 0);
3142 ilim = ilim1;
3143 }
3144 }
3145 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3146 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3147 /* no digits, fcvt style */
3148no_digits:
3149 k = -1 - ndigits;
3150 goto ret;
3151 }
3152one_digit:
3153 *s++ = '1';
3154 k++;
3155 goto ret;
3156 }
3157 if (leftright) {
3158 if (m2 > 0)
3159 mhi = lshift(mhi, m2);
3160
3161 /* Compute mlo -- check for special case
3162 * that d is a normalized power of 2.
3163 */
3164
3165 mlo = mhi;
3166 if (spec_case) {
3167 mhi = Balloc(mhi->k);
3168 Bcopy(mhi, mlo);
3169 mhi = lshift(mhi, Log2P);
3170 }
3171
3172 for (i = 1;;i++) {
3173 dig = quorem(b,S) + '0';
3174 /* Do we yet have the shortest decimal string
3175 * that will round to d?
3176 */
3177 j = cmp(b, mlo);
3178 delta = diff(S, mhi);
3179 j1 = delta->sign ? 1 : cmp(b, delta);
3180 Bfree(delta);
3181#ifndef ROUND_BIASED
3182 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3183#ifdef Honor_FLT_ROUNDS
3184 && rounding >= 1
3185#endif
3186 ) {
3187 if (dig == '9')
3188 goto round_9_up;
3189 if (j > 0)
3190 dig++;
3191#ifdef SET_INEXACT
3192 else if (!b->x[0] && b->wds <= 1)
3193 inexact = 0;
3194#endif
3195 *s++ = dig;
3196 goto ret;
3197 }
3198#endif
3199 if (j < 0 || (j == 0 && mode != 1
3200#ifndef ROUND_BIASED
3201 && !(word1(d) & 1)
3202#endif
3203 )) {
3204 if (!b->x[0] && b->wds <= 1) {
3205#ifdef SET_INEXACT
3206 inexact = 0;
3207#endif
3208 goto accept_dig;
3209 }
3210#ifdef Honor_FLT_ROUNDS
3211 if (mode > 1)
3212 switch (rounding) {
3213 case 0: goto accept_dig;
3214 case 2: goto keep_dig;
3215 }
3216#endif /*Honor_FLT_ROUNDS*/
3217 if (j1 > 0) {
3218 b = lshift(b, 1);
3219 j1 = cmp(b, S);
3220 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3221 goto round_9_up;
3222 }
3223accept_dig:
3224 *s++ = dig;
3225 goto ret;
3226 }
3227 if (j1 > 0) {
3228#ifdef Honor_FLT_ROUNDS
3229 if (!rounding)
3230 goto accept_dig;
3231#endif
3232 if (dig == '9') { /* possible if i == 1 */
3233round_9_up:
3234 *s++ = '9';
3235 goto roundoff;
3236 }
3237 *s++ = dig + 1;
3238 goto ret;
3239 }
3240#ifdef Honor_FLT_ROUNDS
3241keep_dig:
3242#endif
3243 *s++ = dig;
3244 if (i == ilim)
3245 break;
3246 b = multadd(b, 10, 0);
3247 if (mlo == mhi)
3248 mlo = mhi = multadd(mhi, 10, 0);
3249 else {
3250 mlo = multadd(mlo, 10, 0);
3251 mhi = multadd(mhi, 10, 0);
3252 }
3253 }
3254 }
3255 else
3256 for (i = 1;; i++) {
3257 *s++ = dig = quorem(b,S) + '0';
3258 if (!b->x[0] && b->wds <= 1) {
3259#ifdef SET_INEXACT
3260 inexact = 0;
3261#endif
3262 goto ret;
3263 }
3264 if (i >= ilim)
3265 break;
3266 b = multadd(b, 10, 0);
3267 }
3268
3269 /* Round off last digit */
3270
3271#ifdef Honor_FLT_ROUNDS
3272 switch (rounding) {
3273 case 0: goto trimzeros;
3274 case 2: goto roundoff;
3275 }
3276#endif
3277 b = lshift(b, 1);
3278 j = cmp(b, S);
3279 if (j > 0 || (j == 0 && (dig & 1))) {
3280 roundoff:
3281 while (*--s == '9')
3282 if (s == s0) {
3283 k++;
3284 *s++ = '1';
3285 goto ret;
3286 }
3287 if (!half || (*s - '0') & 1)
3288 ++*s;
3289 }
3290 else {
3291 while (*--s == '0') ;
3292 }
3293 s++;
3294ret:
3295 Bfree(S);
3296 if (mhi) {
3297 if (mlo && mlo != mhi)
3298 Bfree(mlo);
3299 Bfree(mhi);
3300 }
3301ret1:
3302#ifdef SET_INEXACT
3303 if (inexact) {
3304 if (!oldinexact) {
3305 word0(d) = Exp_1 + (70 << Exp_shift);
3306 word1(d) = 0;
3307 dval(d) += 1.;
3308 }
3309 }
3310 else if (!oldinexact)
3311 clear_inexact();
3312#endif
3313 Bfree(b);
3314 *s = 0;
3315 *decpt = k + 1;
3316 if (rve)
3317 *rve = s;
3318 return s0;
3319}
3320
3321/*-
3322 * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
3323 * All rights reserved.
3324 *
3325 * Redistribution and use in source and binary forms, with or without
3326 * modification, are permitted provided that the following conditions
3327 * are met:
3328 * 1. Redistributions of source code must retain the above copyright
3329 * notice, this list of conditions and the following disclaimer.
3330 * 2. Redistributions in binary form must reproduce the above copyright
3331 * notice, this list of conditions and the following disclaimer in the
3332 * documentation and/or other materials provided with the distribution.
3333 *
3334 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
3335 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
3336 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
3337 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
3338 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
3339 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
3340 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
3341 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
3342 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
3343 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
3344 * SUCH DAMAGE.
3345 */
3346
3347#define DBL_MANH_SIZE 20
3348#define DBL_MANL_SIZE 32
3349#define DBL_ADJ (DBL_MAX_EXP - 2)
3350#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3351#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3352#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3353#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3354#define dmanl_get(u) ((uint32_t)word1(u))
3355
3356
3357/*
3358 * This procedure converts a double-precision number in IEEE format
3359 * into a string of hexadecimal digits and an exponent of 2. Its
3360 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
3361 * following exceptions:
3362 *
3363 * - An ndigits < 0 causes it to use as many digits as necessary to
3364 * represent the number exactly.
3365 * - The additional xdigs argument should point to either the string
3366 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
3367 * which case is desired.
3368 * - This routine does not repeat dtoa's mistake of setting decpt
3369 * to 9999 in the case of an infinity or NaN. INT_MAX is used
3370 * for this purpose instead.
3371 *
3372 * Note that the C99 standard does not specify what the leading digit
3373 * should be for non-zero numbers. For instance, 0x1.3p3 is the same
3374 * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
3375 * the leading digit a 1. This ensures that the exponent printed is the
3376 * actual base-2 exponent, i.e., ilogb(d).
3377 *
3378 * Inputs: d, xdigs, ndigits
3379 * Outputs: decpt, sign, rve
3380 */
3381char *
3382hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve)
3383{
3384 U u;
3385 char *s, *s0;
3386 int bufsize;
3387 uint32_t manh, manl;
3388
3389 u.d = d;
3390 if (word0(u) & Sign_bit) {
3391 /* set sign for everything, including 0's and NaNs */
3392 *sign = 1;
3393 word0(u) &= ~Sign_bit; /* clear sign bit */
3394 }
3395 else
3396 *sign = 0;
3397
3398 if (isinf(d)) { /* FP_INFINITE */
3399 *decpt = INT_MAX;
3400 return rv_strdup(INFSTR, rve);
3401 }
3402 else if (isnan(d)) { /* FP_NAN */
3403 *decpt = INT_MAX;
3404 return rv_strdup(NANSTR, rve);
3405 }
3406 else if (d == 0.0) { /* FP_ZERO */
3407 *decpt = 1;
3408 return rv_strdup(ZEROSTR, rve);
3409 }
3410 else if (dexp_get(u)) { /* FP_NORMAL */
3411 *decpt = dexp_get(u) - DBL_ADJ;
3412 }
3413 else { /* FP_SUBNORMAL */
3414 u.d *= 5.363123171977039e+154 /* 0x1p514 */;
3415 *decpt = dexp_get(u) - (514 + DBL_ADJ);
3416 }
3417
3418 if (ndigits == 0) /* dtoa() compatibility */
3419 ndigits = 1;
3420
3421 /*
3422 * If ndigits < 0, we are expected to auto-size, so we allocate
3423 * enough space for all the digits.
3424 */
3425 bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3426 s0 = rv_alloc(bufsize+1);
3427
3428 /* Round to the desired number of digits. */
3429 if (SIGFIGS > ndigits && ndigits > 0) {
3430 float redux = 1.0f;
3431 int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3432 dexp_set(u, offset);
3433 u.d += redux;
3434 u.d -= redux;
3435 *decpt += dexp_get(u) - offset;
3436 }
3437
3438 manh = dmanh_get(u);
3439 manl = dmanl_get(u);
3440 *s0 = '1';
3441 for (s = s0 + 1; s < s0 + bufsize; s++) {
3442 *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3443 manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3444 manl <<= 4;
3445 }
3446
3447 /* If ndigits < 0, we are expected to auto-size the precision. */
3448 if (ndigits < 0) {
3449 for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
3450 ;
3451 }
3452
3453 s = s0 + ndigits;
3454 *s = '\0';
3455 if (rve != NULL)
3456 *rve = s;
3457 return (s0);
3458}
3459
3460#ifdef __cplusplus
3461#if 0
3462{ /* satisfy cc-mode */
3463#endif
3464}
3465#endif
assert.h
ISDIGIT
#define ISDIGIT
Old name of rb_isdigit.
Definition ctype.h:93
ASSUME
#define ASSUME
Old name of RBIMPL_ASSUME.
Definition assume.h:27
len
int len
Length of the buffer.
Definition io.h:8
strtod
#define strtod(s, e)
Just another name of ruby_strtod.
Definition util.h:223
errno
#define errno
Ractor-aware version of errno.
Definition ruby.h:388
Bigint
Definition dtoa.c:522
U
Definition dtoa.c:305