source: webkit/trunk/JavaScriptCore/kjs/dtoa.cpp@ 12908

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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 [email protected]
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 "config.h"
173#include "dtoa.h"
174
175#ifdef WORDS_BIGENDIAN
176#define IEEE_MC68k
177#else
178#define IEEE_8087
179#endif
180#define INFNAN_CHECK
181
182
183
184#ifndef Long
185#define Long long
186#endif
187#ifndef ULong
188typedef unsigned Long ULong;
189#endif
190
191#ifdef DEBUG
192#include <stdio.h>
193#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
194#endif
195
196#include <stdlib.h>
197#include <string.h>
198
199#ifdef USE_LOCALE
200#include <locale.h>
201#endif
202
203#ifdef MALLOC
204#ifdef KR_headers
205extern char *MALLOC();
206#else
207extern void *MALLOC(size_t);
208#endif
209#else
210#define MALLOC malloc
211#endif
212
213#ifndef Omit_Private_Memory
214#ifndef PRIVATE_MEM
215#define PRIVATE_MEM 2304
216#endif
217#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
218static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
219#endif
220
221#undef IEEE_Arith
222#undef Avoid_Underflow
223#ifdef IEEE_MC68k
224#define IEEE_Arith
225#endif
226#ifdef IEEE_8087
227#define IEEE_Arith
228#endif
229
230#include <errno.h>
231
232#ifdef Bad_float_h
233
234#ifdef IEEE_Arith
235#define DBL_DIG 15
236#define DBL_MAX_10_EXP 308
237#define DBL_MAX_EXP 1024
238#define FLT_RADIX 2
239#endif /*IEEE_Arith*/
240
241#ifdef IBM
242#define DBL_DIG 16
243#define DBL_MAX_10_EXP 75
244#define DBL_MAX_EXP 63
245#define FLT_RADIX 16
246#define DBL_MAX 7.2370055773322621e+75
247#endif
248
249#ifdef VAX
250#define DBL_DIG 16
251#define DBL_MAX_10_EXP 38
252#define DBL_MAX_EXP 127
253#define FLT_RADIX 2
254#define DBL_MAX 1.7014118346046923e+38
255#endif
256
257#ifndef LONG_MAX
258#define LONG_MAX 2147483647
259#endif
260
261#else /* ifndef Bad_float_h */
262#include <float.h>
263#endif /* Bad_float_h */
264
265#ifndef __MATH_H__
266#include <math.h>
267#endif
268
269#define strtod kjs_strtod
270#define dtoa kjs_dtoa
271#define freedtoa kjs_freedtoa
272
273#ifdef __cplusplus
274extern "C" {
275#endif
276
277#ifndef CONST
278#ifdef KR_headers
279#define CONST /* blank */
280#else
281#define CONST const
282#endif
283#endif
284
285#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
286Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
287#endif
288
289typedef union { double d; ULong L[2]; } U;
290
291#ifdef YES_ALIAS
292#define dval(x) x
293#ifdef IEEE_8087
294#define word0(x) ((ULong *)&x)[1]
295#define word1(x) ((ULong *)&x)[0]
296#else
297#define word0(x) ((ULong *)&x)[0]
298#define word1(x) ((ULong *)&x)[1]
299#endif
300#else
301#ifdef IEEE_8087
302#define word0(x) ((U*)&x)->L[1]
303#define word1(x) ((U*)&x)->L[0]
304#else
305#define word0(x) ((U*)&x)->L[0]
306#define word1(x) ((U*)&x)->L[1]
307#endif
308#define dval(x) ((U*)&x)->d
309#endif
310
311/* The following definition of Storeinc is appropriate for MIPS processors.
312 * An alternative that might be better on some machines is
313 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
314 */
315#if defined(IEEE_8087) + defined(VAX)
316#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
317((unsigned short *)a)[0] = (unsigned short)c, a++)
318#else
319#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
320((unsigned short *)a)[1] = (unsigned short)c, a++)
321#endif
322
323/* #define P DBL_MANT_DIG */
324/* Ten_pmax = floor(P*log(2)/log(5)) */
325/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
326/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
327/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
328
329#ifdef IEEE_Arith
330#define Exp_shift 20
331#define Exp_shift1 20
332#define Exp_msk1 0x100000
333#define Exp_msk11 0x100000
334#define Exp_mask 0x7ff00000
335#define P 53
336#define Bias 1023
337#define Emin (-1022)
338#define Exp_1 0x3ff00000
339#define Exp_11 0x3ff00000
340#define Ebits 11
341#define Frac_mask 0xfffff
342#define Frac_mask1 0xfffff
343#define Ten_pmax 22
344#define Bletch 0x10
345#define Bndry_mask 0xfffff
346#define Bndry_mask1 0xfffff
347#define LSB 1
348#define Sign_bit 0x80000000
349#define Log2P 1
350#define Tiny0 0
351#define Tiny1 1
352#define Quick_max 14
353#define Int_max 14
354#ifndef NO_IEEE_Scale
355#define Avoid_Underflow
356#ifdef Flush_Denorm /* debugging option */
357#undef Sudden_Underflow
358#endif
359#endif
360
361#ifndef Flt_Rounds
362#ifdef FLT_ROUNDS
363#define Flt_Rounds FLT_ROUNDS
364#else
365#define Flt_Rounds 1
366#endif
367#endif /*Flt_Rounds*/
368
369#ifdef Honor_FLT_ROUNDS
370#define Rounding rounding
371#undef Check_FLT_ROUNDS
372#define Check_FLT_ROUNDS
373#else
374#define Rounding Flt_Rounds
375#endif
376
377#else /* ifndef IEEE_Arith */
378#undef Check_FLT_ROUNDS
379#undef Honor_FLT_ROUNDS
380#undef SET_INEXACT
381#undef Sudden_Underflow
382#define Sudden_Underflow
383#ifdef IBM
384#undef Flt_Rounds
385#define Flt_Rounds 0
386#define Exp_shift 24
387#define Exp_shift1 24
388#define Exp_msk1 0x1000000
389#define Exp_msk11 0x1000000
390#define Exp_mask 0x7f000000
391#define P 14
392#define Bias 65
393#define Exp_1 0x41000000
394#define Exp_11 0x41000000
395#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
396#define Frac_mask 0xffffff
397#define Frac_mask1 0xffffff
398#define Bletch 4
399#define Ten_pmax 22
400#define Bndry_mask 0xefffff
401#define Bndry_mask1 0xffffff
402#define LSB 1
403#define Sign_bit 0x80000000
404#define Log2P 4
405#define Tiny0 0x100000
406#define Tiny1 0
407#define Quick_max 14
408#define Int_max 15
409#else /* VAX */
410#undef Flt_Rounds
411#define Flt_Rounds 1
412#define Exp_shift 23
413#define Exp_shift1 7
414#define Exp_msk1 0x80
415#define Exp_msk11 0x800000
416#define Exp_mask 0x7f80
417#define P 56
418#define Bias 129
419#define Exp_1 0x40800000
420#define Exp_11 0x4080
421#define Ebits 8
422#define Frac_mask 0x7fffff
423#define Frac_mask1 0xffff007f
424#define Ten_pmax 24
425#define Bletch 2
426#define Bndry_mask 0xffff007f
427#define Bndry_mask1 0xffff007f
428#define LSB 0x10000
429#define Sign_bit 0x8000
430#define Log2P 1
431#define Tiny0 0x80
432#define Tiny1 0
433#define Quick_max 15
434#define Int_max 15
435#endif /* IBM, VAX */
436#endif /* IEEE_Arith */
437
438#ifndef IEEE_Arith
439#define ROUND_BIASED
440#endif
441
442#ifdef RND_PRODQUOT
443#define rounded_product(a,b) a = rnd_prod(a, b)
444#define rounded_quotient(a,b) a = rnd_quot(a, b)
445#ifdef KR_headers
446extern double rnd_prod(), rnd_quot();
447#else
448extern double rnd_prod(double, double), rnd_quot(double, double);
449#endif
450#else
451#define rounded_product(a,b) a *= b
452#define rounded_quotient(a,b) a /= b
453#endif
454
455#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
456#define Big1 0xffffffff
457
458#ifndef Pack_32
459#define Pack_32
460#endif
461
462#ifdef KR_headers
463#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
464#else
465#define FFFFFFFF 0xffffffffUL
466#endif
467
468#ifdef NO_LONG_LONG
469#undef ULLong
470#ifdef Just_16
471#undef Pack_32
472/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
473 * This makes some inner loops simpler and sometimes saves work
474 * during multiplications, but it often seems to make things slightly
475 * slower. Hence the default is now to store 32 bits per Long.
476 */
477#endif
478#else /* long long available */
479#ifndef Llong
480#define Llong long long
481#endif
482#ifndef ULLong
483#define ULLong unsigned Llong
484#endif
485#endif /* NO_LONG_LONG */
486
487#ifndef MULTIPLE_THREADS
488#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
489#define FREE_DTOA_LOCK(n) /*nothing*/
490#endif
491
492#define Kmax 15
493
494 struct
495Bigint {
496 struct Bigint *next;
497 int k, maxwds, sign, wds;
498 ULong x[1];
499 };
500
501 typedef struct Bigint Bigint;
502
503 static Bigint *freelist[Kmax+1];
504
505 static Bigint *
506Balloc
507#ifdef KR_headers
508 (k) int k;
509#else
510 (int k)
511#endif
512{
513 int x;
514 Bigint *rv;
515#ifndef Omit_Private_Memory
516 unsigned int len;
517#endif
518
519 ACQUIRE_DTOA_LOCK(0);
520 if ((rv = freelist[k])) {
521 freelist[k] = rv->next;
522 }
523 else {
524 x = 1 << k;
525#ifdef Omit_Private_Memory
526 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
527#else
528 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
529 /sizeof(double);
530 if (pmem_next - private_mem + len <= PRIVATE_mem) {
531 rv = (Bigint*)pmem_next;
532 pmem_next += len;
533 }
534 else
535 rv = (Bigint*)MALLOC(len*sizeof(double));
536#endif
537 rv->k = k;
538 rv->maxwds = x;
539 }
540 FREE_DTOA_LOCK(0);
541 rv->sign = rv->wds = 0;
542 return rv;
543 }
544
545 static void
546Bfree
547#ifdef KR_headers
548 (v) Bigint *v;
549#else
550 (Bigint *v)
551#endif
552{
553 if (v) {
554 ACQUIRE_DTOA_LOCK(0);
555 v->next = freelist[v->k];
556 freelist[v->k] = v;
557 FREE_DTOA_LOCK(0);
558 }
559 }
560
561#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
562y->wds*sizeof(Long) + 2*sizeof(int))
563
564 static Bigint *
565multadd
566#ifdef KR_headers
567 (b, m, a) Bigint *b; int m, a;
568#else
569 (Bigint *b, int m, int a) /* multiply by m and add a */
570#endif
571{
572 int i, wds;
573#ifdef ULLong
574 ULong *x;
575 ULLong carry, y;
576#else
577 ULong carry, *x, y;
578#ifdef Pack_32
579 ULong xi, z;
580#endif
581#endif
582 Bigint *b1;
583
584 wds = b->wds;
585 x = b->x;
586 i = 0;
587 carry = a;
588 do {
589#ifdef ULLong
590 y = *x * (ULLong)m + carry;
591 carry = y >> 32;
592 *x++ = y & FFFFFFFF;
593#else
594#ifdef Pack_32
595 xi = *x;
596 y = (xi & 0xffff) * m + carry;
597 z = (xi >> 16) * m + (y >> 16);
598 carry = z >> 16;
599 *x++ = (z << 16) + (y & 0xffff);
600#else
601 y = *x * m + carry;
602 carry = y >> 16;
603 *x++ = y & 0xffff;
604#endif
605#endif
606 }
607 while(++i < wds);
608 if (carry) {
609 if (wds >= b->maxwds) {
610 b1 = Balloc(b->k+1);
611 Bcopy(b1, b);
612 Bfree(b);
613 b = b1;
614 }
615 b->x[wds++] = carry;
616 b->wds = wds;
617 }
618 return b;
619 }
620
621 static Bigint *
622s2b
623#ifdef KR_headers
624 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
625#else
626 (CONST char *s, int nd0, int nd, ULong y9)
627#endif
628{
629 Bigint *b;
630 int i, k;
631 Long x, y;
632
633 x = (nd + 8) / 9;
634 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
635#ifdef Pack_32
636 b = Balloc(k);
637 b->x[0] = y9;
638 b->wds = 1;
639#else
640 b = Balloc(k+1);
641 b->x[0] = y9 & 0xffff;
642 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
643#endif
644
645 i = 9;
646 if (9 < nd0) {
647 s += 9;
648 do b = multadd(b, 10, *s++ - '0');
649 while(++i < nd0);
650 s++;
651 }
652 else
653 s += 10;
654 for(; i < nd; i++)
655 b = multadd(b, 10, *s++ - '0');
656 return b;
657 }
658
659 static int
660hi0bits
661#ifdef KR_headers
662 (x) register ULong x;
663#else
664 (register ULong x)
665#endif
666{
667 register int k = 0;
668
669 if (!(x & 0xffff0000)) {
670 k = 16;
671 x <<= 16;
672 }
673 if (!(x & 0xff000000)) {
674 k += 8;
675 x <<= 8;
676 }
677 if (!(x & 0xf0000000)) {
678 k += 4;
679 x <<= 4;
680 }
681 if (!(x & 0xc0000000)) {
682 k += 2;
683 x <<= 2;
684 }
685 if (!(x & 0x80000000)) {
686 k++;
687 if (!(x & 0x40000000))
688 return 32;
689 }
690 return k;
691 }
692
693 static int
694lo0bits
695#ifdef KR_headers
696 (y) ULong *y;
697#else
698 (ULong *y)
699#endif
700{
701 register int k;
702 register ULong x = *y;
703
704 if (x & 7) {
705 if (x & 1)
706 return 0;
707 if (x & 2) {
708 *y = x >> 1;
709 return 1;
710 }
711 *y = x >> 2;
712 return 2;
713 }
714 k = 0;
715 if (!(x & 0xffff)) {
716 k = 16;
717 x >>= 16;
718 }
719 if (!(x & 0xff)) {
720 k += 8;
721 x >>= 8;
722 }
723 if (!(x & 0xf)) {
724 k += 4;
725 x >>= 4;
726 }
727 if (!(x & 0x3)) {
728 k += 2;
729 x >>= 2;
730 }
731 if (!(x & 1)) {
732 k++;
733 x >>= 1;
734 if (!x & 1)
735 return 32;
736 }
737 *y = x;
738 return k;
739 }
740
741 static Bigint *
742i2b
743#ifdef KR_headers
744 (i) int i;
745#else
746 (int i)
747#endif
748{
749 Bigint *b;
750
751 b = Balloc(1);
752 b->x[0] = i;
753 b->wds = 1;
754 return b;
755 }
756
757 static Bigint *
758mult
759#ifdef KR_headers
760 (a, b) Bigint *a, *b;
761#else
762 (Bigint *a, Bigint *b)
763#endif
764{
765 Bigint *c;
766 int k, wa, wb, wc;
767 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
768 ULong y;
769#ifdef ULLong
770 ULLong carry, z;
771#else
772 ULong carry, z;
773#ifdef Pack_32
774 ULong z2;
775#endif
776#endif
777
778 if (a->wds < b->wds) {
779 c = a;
780 a = b;
781 b = c;
782 }
783 k = a->k;
784 wa = a->wds;
785 wb = b->wds;
786 wc = wa + wb;
787 if (wc > a->maxwds)
788 k++;
789 c = Balloc(k);
790 for(x = c->x, xa = x + wc; x < xa; x++)
791 *x = 0;
792 xa = a->x;
793 xae = xa + wa;
794 xb = b->x;
795 xbe = xb + wb;
796 xc0 = c->x;
797#ifdef ULLong
798 for(; xb < xbe; xc0++) {
799 if ((y = *xb++)) {
800 x = xa;
801 xc = xc0;
802 carry = 0;
803 do {
804 z = *x++ * (ULLong)y + *xc + carry;
805 carry = z >> 32;
806 *xc++ = z & FFFFFFFF;
807 }
808 while(x < xae);
809 *xc = carry;
810 }
811 }
812#else
813#ifdef Pack_32
814 for(; xb < xbe; xb++, xc0++) {
815 if (y = *xb & 0xffff) {
816 x = xa;
817 xc = xc0;
818 carry = 0;
819 do {
820 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
821 carry = z >> 16;
822 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
823 carry = z2 >> 16;
824 Storeinc(xc, z2, z);
825 }
826 while(x < xae);
827 *xc = carry;
828 }
829 if (y = *xb >> 16) {
830 x = xa;
831 xc = xc0;
832 carry = 0;
833 z2 = *xc;
834 do {
835 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
836 carry = z >> 16;
837 Storeinc(xc, z, z2);
838 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
839 carry = z2 >> 16;
840 }
841 while(x < xae);
842 *xc = z2;
843 }
844 }
845#else
846 for(; xb < xbe; xc0++) {
847 if (y = *xb++) {
848 x = xa;
849 xc = xc0;
850 carry = 0;
851 do {
852 z = *x++ * y + *xc + carry;
853 carry = z >> 16;
854 *xc++ = z & 0xffff;
855 }
856 while(x < xae);
857 *xc = carry;
858 }
859 }
860#endif
861#endif
862 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
863 c->wds = wc;
864 return c;
865 }
866
867 static Bigint *p5s;
868
869 static Bigint *
870pow5mult
871#ifdef KR_headers
872 (b, k) Bigint *b; int k;
873#else
874 (Bigint *b, int k)
875#endif
876{
877 Bigint *b1, *p5, *p51;
878 int i;
879 static int p05[3] = { 5, 25, 125 };
880
881 if ((i = k & 3))
882 b = multadd(b, p05[i-1], 0);
883
884 if (!(k >>= 2))
885 return b;
886 if (!(p5 = p5s)) {
887 /* first time */
888#ifdef MULTIPLE_THREADS
889 ACQUIRE_DTOA_LOCK(1);
890 if (!(p5 = p5s)) {
891 p5 = p5s = i2b(625);
892 p5->next = 0;
893 }
894 FREE_DTOA_LOCK(1);
895#else
896 p5 = p5s = i2b(625);
897 p5->next = 0;
898#endif
899 }
900 for(;;) {
901 if (k & 1) {
902 b1 = mult(b, p5);
903 Bfree(b);
904 b = b1;
905 }
906 if (!(k >>= 1))
907 break;
908 if (!(p51 = p5->next)) {
909#ifdef MULTIPLE_THREADS
910 ACQUIRE_DTOA_LOCK(1);
911 if (!(p51 = p5->next)) {
912 p51 = p5->next = mult(p5,p5);
913 p51->next = 0;
914 }
915 FREE_DTOA_LOCK(1);
916#else
917 p51 = p5->next = mult(p5,p5);
918 p51->next = 0;
919#endif
920 }
921 p5 = p51;
922 }
923 return b;
924 }
925
926 static Bigint *
927lshift
928#ifdef KR_headers
929 (b, k) Bigint *b; int k;
930#else
931 (Bigint *b, int k)
932#endif
933{
934 int i, k1, n, n1;
935 Bigint *b1;
936 ULong *x, *x1, *xe, z;
937
938#ifdef Pack_32
939 n = k >> 5;
940#else
941 n = k >> 4;
942#endif
943 k1 = b->k;
944 n1 = n + b->wds + 1;
945 for(i = b->maxwds; n1 > i; i <<= 1)
946 k1++;
947 b1 = Balloc(k1);
948 x1 = b1->x;
949 for(i = 0; i < n; i++)
950 *x1++ = 0;
951 x = b->x;
952 xe = x + b->wds;
953#ifdef Pack_32
954 if (k &= 0x1f) {
955 k1 = 32 - k;
956 z = 0;
957 do {
958 *x1++ = *x << k | z;
959 z = *x++ >> k1;
960 }
961 while(x < xe);
962 if ((*x1 = z))
963 ++n1;
964 }
965#else
966 if (k &= 0xf) {
967 k1 = 16 - k;
968 z = 0;
969 do {
970 *x1++ = *x << k & 0xffff | z;
971 z = *x++ >> k1;
972 }
973 while(x < xe);
974 if (*x1 = z)
975 ++n1;
976 }
977#endif
978 else do
979 *x1++ = *x++;
980 while(x < xe);
981 b1->wds = n1 - 1;
982 Bfree(b);
983 return b1;
984 }
985
986 static int
987cmp
988#ifdef KR_headers
989 (a, b) Bigint *a, *b;
990#else
991 (Bigint *a, Bigint *b)
992#endif
993{
994 ULong *xa, *xa0, *xb, *xb0;
995 int i, j;
996
997 i = a->wds;
998 j = b->wds;
999#ifdef DEBUG
1000 if (i > 1 && !a->x[i-1])
1001 Bug("cmp called with a->x[a->wds-1] == 0");
1002 if (j > 1 && !b->x[j-1])
1003 Bug("cmp called with b->x[b->wds-1] == 0");
1004#endif
1005 if (i -= j)
1006 return i;
1007 xa0 = a->x;
1008 xa = xa0 + j;
1009 xb0 = b->x;
1010 xb = xb0 + j;
1011 for(;;) {
1012 if (*--xa != *--xb)
1013 return *xa < *xb ? -1 : 1;
1014 if (xa <= xa0)
1015 break;
1016 }
1017 return 0;
1018 }
1019
1020 static Bigint *
1021diff
1022#ifdef KR_headers
1023 (a, b) Bigint *a, *b;
1024#else
1025 (Bigint *a, Bigint *b)
1026#endif
1027{
1028 Bigint *c;
1029 int i, wa, wb;
1030 ULong *xa, *xae, *xb, *xbe, *xc;
1031#ifdef ULLong
1032 ULLong borrow, y;
1033#else
1034 ULong borrow, y;
1035#ifdef Pack_32
1036 ULong z;
1037#endif
1038#endif
1039
1040 i = cmp(a,b);
1041 if (!i) {
1042 c = Balloc(0);
1043 c->wds = 1;
1044 c->x[0] = 0;
1045 return c;
1046 }
1047 if (i < 0) {
1048 c = a;
1049 a = b;
1050 b = c;
1051 i = 1;
1052 }
1053 else
1054 i = 0;
1055 c = Balloc(a->k);
1056 c->sign = i;
1057 wa = a->wds;
1058 xa = a->x;
1059 xae = xa + wa;
1060 wb = b->wds;
1061 xb = b->x;
1062 xbe = xb + wb;
1063 xc = c->x;
1064 borrow = 0;
1065#ifdef ULLong
1066 do {
1067 y = (ULLong)*xa++ - *xb++ - borrow;
1068 borrow = y >> 32 & (ULong)1;
1069 *xc++ = y & FFFFFFFF;
1070 }
1071 while(xb < xbe);
1072 while(xa < xae) {
1073 y = *xa++ - borrow;
1074 borrow = y >> 32 & (ULong)1;
1075 *xc++ = y & FFFFFFFF;
1076 }
1077#else
1078#ifdef Pack_32
1079 do {
1080 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1081 borrow = (y & 0x10000) >> 16;
1082 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1083 borrow = (z & 0x10000) >> 16;
1084 Storeinc(xc, z, y);
1085 }
1086 while(xb < xbe);
1087 while(xa < xae) {
1088 y = (*xa & 0xffff) - borrow;
1089 borrow = (y & 0x10000) >> 16;
1090 z = (*xa++ >> 16) - borrow;
1091 borrow = (z & 0x10000) >> 16;
1092 Storeinc(xc, z, y);
1093 }
1094#else
1095 do {
1096 y = *xa++ - *xb++ - borrow;
1097 borrow = (y & 0x10000) >> 16;
1098 *xc++ = y & 0xffff;
1099 }
1100 while(xb < xbe);
1101 while(xa < xae) {
1102 y = *xa++ - borrow;
1103 borrow = (y & 0x10000) >> 16;
1104 *xc++ = y & 0xffff;
1105 }
1106#endif
1107#endif
1108 while(!*--xc)
1109 wa--;
1110 c->wds = wa;
1111 return c;
1112 }
1113
1114 static double
1115ulp
1116#ifdef KR_headers
1117 (x) double x;
1118#else
1119 (double x)
1120#endif
1121{
1122 register Long L;
1123 double a;
1124
1125 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1126#ifndef Avoid_Underflow
1127#ifndef Sudden_Underflow
1128 if (L > 0) {
1129#endif
1130#endif
1131#ifdef IBM
1132 L |= Exp_msk1 >> 4;
1133#endif
1134 word0(a) = L;
1135 word1(a) = 0;
1136#ifndef Avoid_Underflow
1137#ifndef Sudden_Underflow
1138 }
1139 else {
1140 L = -L >> Exp_shift;
1141 if (L < Exp_shift) {
1142 word0(a) = 0x80000 >> L;
1143 word1(a) = 0;
1144 }
1145 else {
1146 word0(a) = 0;
1147 L -= Exp_shift;
1148 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1149 }
1150 }
1151#endif
1152#endif
1153 return dval(a);
1154 }
1155
1156 static double
1157b2d
1158#ifdef KR_headers
1159 (a, e) Bigint *a; int *e;
1160#else
1161 (Bigint *a, int *e)
1162#endif
1163{
1164 ULong *xa, *xa0, w, y, z;
1165 int k;
1166 double d;
1167#ifdef VAX
1168 ULong d0, d1;
1169#else
1170#define d0 word0(d)
1171#define d1 word1(d)
1172#endif
1173
1174 xa0 = a->x;
1175 xa = xa0 + a->wds;
1176 y = *--xa;
1177#ifdef DEBUG
1178 if (!y) Bug("zero y in b2d");
1179#endif
1180 k = hi0bits(y);
1181 *e = 32 - k;
1182#ifdef Pack_32
1183 if (k < Ebits) {
1184 d0 = Exp_1 | y >> Ebits - k;
1185 w = xa > xa0 ? *--xa : 0;
1186 d1 = y << (32-Ebits) + k | w >> Ebits - k;
1187 goto ret_d;
1188 }
1189 z = xa > xa0 ? *--xa : 0;
1190 if (k -= Ebits) {
1191 d0 = Exp_1 | y << k | z >> 32 - k;
1192 y = xa > xa0 ? *--xa : 0;
1193 d1 = z << k | y >> 32 - k;
1194 }
1195 else {
1196 d0 = Exp_1 | y;
1197 d1 = z;
1198 }
1199#else
1200 if (k < Ebits + 16) {
1201 z = xa > xa0 ? *--xa : 0;
1202 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1203 w = xa > xa0 ? *--xa : 0;
1204 y = xa > xa0 ? *--xa : 0;
1205 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1206 goto ret_d;
1207 }
1208 z = xa > xa0 ? *--xa : 0;
1209 w = xa > xa0 ? *--xa : 0;
1210 k -= Ebits + 16;
1211 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1212 y = xa > xa0 ? *--xa : 0;
1213 d1 = w << k + 16 | y << k;
1214#endif
1215 ret_d:
1216#ifdef VAX
1217 word0(d) = d0 >> 16 | d0 << 16;
1218 word1(d) = d1 >> 16 | d1 << 16;
1219#else
1220#undef d0
1221#undef d1
1222#endif
1223 return dval(d);
1224 }
1225
1226 static Bigint *
1227d2b
1228#ifdef KR_headers
1229 (d, e, bits) double d; int *e, *bits;
1230#else
1231 (double d, int *e, int *bits)
1232#endif
1233{
1234 Bigint *b;
1235 int de, k;
1236 ULong *x, y, z;
1237#ifndef Sudden_Underflow
1238 int i;
1239#endif
1240#ifdef VAX
1241 ULong d0, d1;
1242 d0 = word0(d) >> 16 | word0(d) << 16;
1243 d1 = word1(d) >> 16 | word1(d) << 16;
1244#else
1245#define d0 word0(d)
1246#define d1 word1(d)
1247#endif
1248
1249#ifdef Pack_32
1250 b = Balloc(1);
1251#else
1252 b = Balloc(2);
1253#endif
1254 x = b->x;
1255
1256 z = d0 & Frac_mask;
1257 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1258#ifdef Sudden_Underflow
1259 de = (int)(d0 >> Exp_shift);
1260#ifndef IBM
1261 z |= Exp_msk11;
1262#endif
1263#else
1264 if ((de = (int)(d0 >> Exp_shift)))
1265 z |= Exp_msk1;
1266#endif
1267#ifdef Pack_32
1268 if ((y = d1)) {
1269 if ((k = lo0bits(&y))) {
1270 x[0] = y | z << 32 - k;
1271 z >>= k;
1272 }
1273 else
1274 x[0] = y;
1275#ifndef Sudden_Underflow
1276 i =
1277#endif
1278 b->wds = (x[1] = z) ? 2 : 1;
1279 }
1280 else {
1281#ifdef DEBUG
1282 if (!z)
1283 Bug("Zero passed to d2b");
1284#endif
1285 k = lo0bits(&z);
1286 x[0] = z;
1287#ifndef Sudden_Underflow
1288 i =
1289#endif
1290 b->wds = 1;
1291 k += 32;
1292 }
1293#else
1294 if (y = d1) {
1295 if (k = lo0bits(&y))
1296 if (k >= 16) {
1297 x[0] = y | z << 32 - k & 0xffff;
1298 x[1] = z >> k - 16 & 0xffff;
1299 x[2] = z >> k;
1300 i = 2;
1301 }
1302 else {
1303 x[0] = y & 0xffff;
1304 x[1] = y >> 16 | z << 16 - k & 0xffff;
1305 x[2] = z >> k & 0xffff;
1306 x[3] = z >> k+16;
1307 i = 3;
1308 }
1309 else {
1310 x[0] = y & 0xffff;
1311 x[1] = y >> 16;
1312 x[2] = z & 0xffff;
1313 x[3] = z >> 16;
1314 i = 3;
1315 }
1316 }
1317 else {
1318#ifdef DEBUG
1319 if (!z)
1320 Bug("Zero passed to d2b");
1321#endif
1322 k = lo0bits(&z);
1323 if (k >= 16) {
1324 x[0] = z;
1325 i = 0;
1326 }
1327 else {
1328 x[0] = z & 0xffff;
1329 x[1] = z >> 16;
1330 i = 1;
1331 }
1332 k += 32;
1333 }
1334 while(!x[i])
1335 --i;
1336 b->wds = i + 1;
1337#endif
1338#ifndef Sudden_Underflow
1339 if (de) {
1340#endif
1341#ifdef IBM
1342 *e = (de - Bias - (P-1) << 2) + k;
1343 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1344#else
1345 *e = de - Bias - (P-1) + k;
1346 *bits = P - k;
1347#endif
1348#ifndef Sudden_Underflow
1349 }
1350 else {
1351 *e = de - Bias - (P-1) + 1 + k;
1352#ifdef Pack_32
1353 *bits = 32*i - hi0bits(x[i-1]);
1354#else
1355 *bits = (i+2)*16 - hi0bits(x[i]);
1356#endif
1357 }
1358#endif
1359 return b;
1360 }
1361#undef d0
1362#undef d1
1363
1364 static double
1365ratio
1366#ifdef KR_headers
1367 (a, b) Bigint *a, *b;
1368#else
1369 (Bigint *a, Bigint *b)
1370#endif
1371{
1372 double da, db;
1373 int k, ka, kb;
1374
1375 dval(da) = b2d(a, &ka);
1376 dval(db) = b2d(b, &kb);
1377#ifdef Pack_32
1378 k = ka - kb + 32*(a->wds - b->wds);
1379#else
1380 k = ka - kb + 16*(a->wds - b->wds);
1381#endif
1382#ifdef IBM
1383 if (k > 0) {
1384 word0(da) += (k >> 2)*Exp_msk1;
1385 if (k &= 3)
1386 dval(da) *= 1 << k;
1387 }
1388 else {
1389 k = -k;
1390 word0(db) += (k >> 2)*Exp_msk1;
1391 if (k &= 3)
1392 dval(db) *= 1 << k;
1393 }
1394#else
1395 if (k > 0)
1396 word0(da) += k*Exp_msk1;
1397 else {
1398 k = -k;
1399 word0(db) += k*Exp_msk1;
1400 }
1401#endif
1402 return dval(da) / dval(db);
1403 }
1404
1405 static CONST double
1406tens[] = {
1407 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1408 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1409 1e20, 1e21, 1e22
1410#ifdef VAX
1411 , 1e23, 1e24
1412#endif
1413 };
1414
1415 static CONST double
1416#ifdef IEEE_Arith
1417bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1418static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1419#ifdef Avoid_Underflow
1420 9007199254740992.*9007199254740992.e-256
1421 /* = 2^106 * 1e-53 */
1422#else
1423 1e-256
1424#endif
1425 };
1426/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1427/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1428#define Scale_Bit 0x10
1429#define n_bigtens 5
1430#else
1431#ifdef IBM
1432bigtens[] = { 1e16, 1e32, 1e64 };
1433static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1434#define n_bigtens 3
1435#else
1436bigtens[] = { 1e16, 1e32 };
1437static CONST double tinytens[] = { 1e-16, 1e-32 };
1438#define n_bigtens 2
1439#endif
1440#endif
1441
1442#ifndef IEEE_Arith
1443#undef INFNAN_CHECK
1444#endif
1445
1446#ifdef INFNAN_CHECK
1447
1448#ifndef NAN_WORD0
1449#define NAN_WORD0 0x7ff80000
1450#endif
1451
1452#ifndef NAN_WORD1
1453#define NAN_WORD1 0
1454#endif
1455
1456 static int
1457match
1458#ifdef KR_headers
1459 (sp, t) char **sp, *t;
1460#else
1461 (CONST char **sp, CONST char *t)
1462#endif
1463{
1464 int c, d;
1465 CONST char *s = *sp;
1466
1467 while((d = *t++)) {
1468 if ((c = *++s) >= 'A' && c <= 'Z')
1469 c += 'a' - 'A';
1470 if (c != d)
1471 return 0;
1472 }
1473 *sp = s + 1;
1474 return 1;
1475 }
1476
1477#ifndef No_Hex_NaN
1478 static void
1479hexnan
1480#ifdef KR_headers
1481 (rvp, sp) double *rvp; CONST char **sp;
1482#else
1483 (double *rvp, CONST char **sp)
1484#endif
1485{
1486 ULong c, x[2];
1487 CONST char *s;
1488 int havedig, udx0, xshift;
1489
1490 x[0] = x[1] = 0;
1491 havedig = xshift = 0;
1492 udx0 = 1;
1493 s = *sp;
1494 while((c = *(CONST unsigned char*)++s)) {
1495 if (c >= '0' && c <= '9')
1496 c -= '0';
1497 else if (c >= 'a' && c <= 'f')
1498 c += 10 - 'a';
1499 else if (c >= 'A' && c <= 'F')
1500 c += 10 - 'A';
1501 else if (c <= ' ') {
1502 if (udx0 && havedig) {
1503 udx0 = 0;
1504 xshift = 1;
1505 }
1506 continue;
1507 }
1508 else if (/*(*/ c == ')' && havedig) {
1509 *sp = s + 1;
1510 break;
1511 }
1512 else
1513 return; /* invalid form: don't change *sp */
1514 havedig = 1;
1515 if (xshift) {
1516 xshift = 0;
1517 x[0] = x[1];
1518 x[1] = 0;
1519 }
1520 if (udx0)
1521 x[0] = (x[0] << 4) | (x[1] >> 28);
1522 x[1] = (x[1] << 4) | c;
1523 }
1524 if ((x[0] &= 0xfffff) || x[1]) {
1525 word0(*rvp) = Exp_mask | x[0];
1526 word1(*rvp) = x[1];
1527 }
1528 }
1529#endif /*No_Hex_NaN*/
1530#endif /* INFNAN_CHECK */
1531
1532 double
1533strtod
1534#ifdef KR_headers
1535 (s00, se) CONST char *s00; char **se;
1536#else
1537 (CONST char *s00, char **se)
1538#endif
1539{
1540#ifdef Avoid_Underflow
1541 int scale;
1542#endif
1543 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1544 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1545 CONST char *s, *s0, *s1;
1546 double aadj, aadj1, adj, rv, rv0;
1547 Long L;
1548 ULong y, z;
1549 Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
1550#ifdef SET_INEXACT
1551 int inexact, oldinexact;
1552#endif
1553#ifdef Honor_FLT_ROUNDS
1554 int rounding;
1555#endif
1556#ifdef USE_LOCALE
1557 CONST char *s2;
1558#endif
1559
1560 sign = nz0 = nz = 0;
1561 dval(rv) = 0.;
1562 for(s = s00;;s++) switch(*s) {
1563 case '-':
1564 sign = 1;
1565 /* no break */
1566 case '+':
1567 if (*++s)
1568 goto break2;
1569 /* no break */
1570 case 0:
1571 goto ret0;
1572 case '\t':
1573 case '\n':
1574 case '\v':
1575 case '\f':
1576 case '\r':
1577 case ' ':
1578 continue;
1579 default:
1580 goto break2;
1581 }
1582 break2:
1583 if (*s == '0') {
1584 nz0 = 1;
1585 while(*++s == '0') ;
1586 if (!*s)
1587 goto ret;
1588 }
1589 s0 = s;
1590 y = z = 0;
1591 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1592 if (nd < 9)
1593 y = 10*y + c - '0';
1594 else if (nd < 16)
1595 z = 10*z + c - '0';
1596 nd0 = nd;
1597#ifdef USE_LOCALE
1598 s1 = localeconv()->decimal_point;
1599 if (c == *s1) {
1600 c = '.';
1601 if (*++s1) {
1602 s2 = s;
1603 for(;;) {
1604 if (*++s2 != *s1) {
1605 c = 0;
1606 break;
1607 }
1608 if (!*++s1) {
1609 s = s2;
1610 break;
1611 }
1612 }
1613 }
1614 }
1615#endif
1616 if (c == '.') {
1617 c = *++s;
1618 if (!nd) {
1619 for(; c == '0'; c = *++s)
1620 nz++;
1621 if (c > '0' && c <= '9') {
1622 s0 = s;
1623 nf += nz;
1624 nz = 0;
1625 goto have_dig;
1626 }
1627 goto dig_done;
1628 }
1629 for(; c >= '0' && c <= '9'; c = *++s) {
1630 have_dig:
1631 nz++;
1632 if (c -= '0') {
1633 nf += nz;
1634 for(i = 1; i < nz; i++)
1635 if (nd++ < 9)
1636 y *= 10;
1637 else if (nd <= DBL_DIG + 1)
1638 z *= 10;
1639 if (nd++ < 9)
1640 y = 10*y + c;
1641 else if (nd <= DBL_DIG + 1)
1642 z = 10*z + c;
1643 nz = 0;
1644 }
1645 }
1646 }
1647 dig_done:
1648 e = 0;
1649 if (c == 'e' || c == 'E') {
1650 if (!nd && !nz && !nz0) {
1651 goto ret0;
1652 }
1653 s00 = s;
1654 esign = 0;
1655 switch(c = *++s) {
1656 case '-':
1657 esign = 1;
1658 case '+':
1659 c = *++s;
1660 }
1661 if (c >= '0' && c <= '9') {
1662 while(c == '0')
1663 c = *++s;
1664 if (c > '0' && c <= '9') {
1665 L = c - '0';
1666 s1 = s;
1667 while((c = *++s) >= '0' && c <= '9')
1668 L = 10*L + c - '0';
1669 if (s - s1 > 8 || L > 19999)
1670 /* Avoid confusion from exponents
1671 * so large that e might overflow.
1672 */
1673 e = 19999; /* safe for 16 bit ints */
1674 else
1675 e = (int)L;
1676 if (esign)
1677 e = -e;
1678 }
1679 else
1680 e = 0;
1681 }
1682 else
1683 s = s00;
1684 }
1685 if (!nd) {
1686 if (!nz && !nz0) {
1687#ifdef INFNAN_CHECK
1688 /* Check for Nan and Infinity */
1689 switch(c) {
1690 case 'i':
1691 case 'I':
1692 if (match(&s,"nf")) {
1693 --s;
1694 if (!match(&s,"inity"))
1695 ++s;
1696 word0(rv) = 0x7ff00000;
1697 word1(rv) = 0;
1698 goto ret;
1699 }
1700 break;
1701 case 'n':
1702 case 'N':
1703 if (match(&s, "an")) {
1704 word0(rv) = NAN_WORD0;
1705 word1(rv) = NAN_WORD1;
1706#ifndef No_Hex_NaN
1707 if (*s == '(') /*)*/
1708 hexnan(&rv, &s);
1709#endif
1710 goto ret;
1711 }
1712 }
1713#endif /* INFNAN_CHECK */
1714 ret0:
1715 s = s00;
1716 sign = 0;
1717 }
1718 goto ret;
1719 }
1720 e1 = e -= nf;
1721
1722 /* Now we have nd0 digits, starting at s0, followed by a
1723 * decimal point, followed by nd-nd0 digits. The number we're
1724 * after is the integer represented by those digits times
1725 * 10**e */
1726
1727 if (!nd0)
1728 nd0 = nd;
1729 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1730 dval(rv) = y;
1731 if (k > 9) {
1732#ifdef SET_INEXACT
1733 if (k > DBL_DIG)
1734 oldinexact = get_inexact();
1735#endif
1736 dval(rv) = tens[k - 9] * dval(rv) + z;
1737 }
1738 bd0 = 0;
1739 if (nd <= DBL_DIG
1740#ifndef RND_PRODQUOT
1741#ifndef Honor_FLT_ROUNDS
1742 && Flt_Rounds == 1
1743#endif
1744#endif
1745 ) {
1746 if (!e)
1747 goto ret;
1748 if (e > 0) {
1749 if (e <= Ten_pmax) {
1750#ifdef VAX
1751 goto vax_ovfl_check;
1752#else
1753#ifdef Honor_FLT_ROUNDS
1754 /* round correctly FLT_ROUNDS = 2 or 3 */
1755 if (sign) {
1756 rv = -rv;
1757 sign = 0;
1758 }
1759#endif
1760 /* rv = */ rounded_product(dval(rv), tens[e]);
1761 goto ret;
1762#endif
1763 }
1764 i = DBL_DIG - nd;
1765 if (e <= Ten_pmax + i) {
1766 /* A fancier test would sometimes let us do
1767 * this for larger i values.
1768 */
1769#ifdef Honor_FLT_ROUNDS
1770 /* round correctly FLT_ROUNDS = 2 or 3 */
1771 if (sign) {
1772 rv = -rv;
1773 sign = 0;
1774 }
1775#endif
1776 e -= i;
1777 dval(rv) *= tens[i];
1778#ifdef VAX
1779 /* VAX exponent range is so narrow we must
1780 * worry about overflow here...
1781 */
1782 vax_ovfl_check:
1783 word0(rv) -= P*Exp_msk1;
1784 /* rv = */ rounded_product(dval(rv), tens[e]);
1785 if ((word0(rv) & Exp_mask)
1786 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1787 goto ovfl;
1788 word0(rv) += P*Exp_msk1;
1789#else
1790 /* rv = */ rounded_product(dval(rv), tens[e]);
1791#endif
1792 goto ret;
1793 }
1794 }
1795#ifndef Inaccurate_Divide
1796 else if (e >= -Ten_pmax) {
1797#ifdef Honor_FLT_ROUNDS
1798 /* round correctly FLT_ROUNDS = 2 or 3 */
1799 if (sign) {
1800 rv = -rv;
1801 sign = 0;
1802 }
1803#endif
1804 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1805 goto ret;
1806 }
1807#endif
1808 }
1809 e1 += nd - k;
1810
1811#ifdef IEEE_Arith
1812#ifdef SET_INEXACT
1813 inexact = 1;
1814 if (k <= DBL_DIG)
1815 oldinexact = get_inexact();
1816#endif
1817#ifdef Avoid_Underflow
1818 scale = 0;
1819#endif
1820#ifdef Honor_FLT_ROUNDS
1821 if ((rounding = Flt_Rounds) >= 2) {
1822 if (sign)
1823 rounding = rounding == 2 ? 0 : 2;
1824 else
1825 if (rounding != 2)
1826 rounding = 0;
1827 }
1828#endif
1829#endif /*IEEE_Arith*/
1830
1831 /* Get starting approximation = rv * 10**e1 */
1832
1833 if (e1 > 0) {
1834 if ((i = e1 & 15))
1835 dval(rv) *= tens[i];
1836 if (e1 &= ~15) {
1837 if (e1 > DBL_MAX_10_EXP) {
1838 ovfl:
1839#ifndef NO_ERRNO
1840 errno = ERANGE;
1841#endif
1842 /* Can't trust HUGE_VAL */
1843#ifdef IEEE_Arith
1844#ifdef Honor_FLT_ROUNDS
1845 switch(rounding) {
1846 case 0: /* toward 0 */
1847 case 3: /* toward -infinity */
1848 word0(rv) = Big0;
1849 word1(rv) = Big1;
1850 break;
1851 default:
1852 word0(rv) = Exp_mask;
1853 word1(rv) = 0;
1854 }
1855#else /*Honor_FLT_ROUNDS*/
1856 word0(rv) = Exp_mask;
1857 word1(rv) = 0;
1858#endif /*Honor_FLT_ROUNDS*/
1859#ifdef SET_INEXACT
1860 /* set overflow bit */
1861 dval(rv0) = 1e300;
1862 dval(rv0) *= dval(rv0);
1863#endif
1864#else /*IEEE_Arith*/
1865 word0(rv) = Big0;
1866 word1(rv) = Big1;
1867#endif /*IEEE_Arith*/
1868 if (bd0)
1869 goto retfree;
1870 goto ret;
1871 }
1872 e1 >>= 4;
1873 for(j = 0; e1 > 1; j++, e1 >>= 1)
1874 if (e1 & 1)
1875 dval(rv) *= bigtens[j];
1876 /* The last multiplication could overflow. */
1877 word0(rv) -= P*Exp_msk1;
1878 dval(rv) *= bigtens[j];
1879 if ((z = word0(rv) & Exp_mask)
1880 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1881 goto ovfl;
1882 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1883 /* set to largest number */
1884 /* (Can't trust DBL_MAX) */
1885 word0(rv) = Big0;
1886 word1(rv) = Big1;
1887 }
1888 else
1889 word0(rv) += P*Exp_msk1;
1890 }
1891 }
1892 else if (e1 < 0) {
1893 e1 = -e1;
1894 if ((i = e1 & 15))
1895 dval(rv) /= tens[i];
1896 if (e1 >>= 4) {
1897 if (e1 >= 1 << n_bigtens)
1898 goto undfl;
1899#ifdef Avoid_Underflow
1900 if (e1 & Scale_Bit)
1901 scale = 2*P;
1902 for(j = 0; e1 > 0; j++, e1 >>= 1)
1903 if (e1 & 1)
1904 dval(rv) *= tinytens[j];
1905 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1906 >> Exp_shift)) > 0) {
1907 /* scaled rv is denormal; zap j low bits */
1908 if (j >= 32) {
1909 word1(rv) = 0;
1910 if (j >= 53)
1911 word0(rv) = (P+2)*Exp_msk1;
1912 else
1913 word0(rv) &= 0xffffffff << j-32;
1914 }
1915 else
1916 word1(rv) &= 0xffffffff << j;
1917 }
1918#else
1919 for(j = 0; e1 > 1; j++, e1 >>= 1)
1920 if (e1 & 1)
1921 dval(rv) *= tinytens[j];
1922 /* The last multiplication could underflow. */
1923 dval(rv0) = dval(rv);
1924 dval(rv) *= tinytens[j];
1925 if (!dval(rv)) {
1926 dval(rv) = 2.*dval(rv0);
1927 dval(rv) *= tinytens[j];
1928#endif
1929 if (!dval(rv)) {
1930 undfl:
1931 dval(rv) = 0.;
1932#ifndef NO_ERRNO
1933 errno = ERANGE;
1934#endif
1935 if (bd0)
1936 goto retfree;
1937 goto ret;
1938 }
1939#ifndef Avoid_Underflow
1940 word0(rv) = Tiny0;
1941 word1(rv) = Tiny1;
1942 /* The refinement below will clean
1943 * this approximation up.
1944 */
1945 }
1946#endif
1947 }
1948 }
1949
1950 /* Now the hard part -- adjusting rv to the correct value.*/
1951
1952 /* Put digits into bd: true value = bd * 10^e */
1953
1954 bd0 = s2b(s0, nd0, nd, y);
1955
1956 for(;;) {
1957 bd = Balloc(bd0->k);
1958 Bcopy(bd, bd0);
1959 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1960 bs = i2b(1);
1961
1962 if (e >= 0) {
1963 bb2 = bb5 = 0;
1964 bd2 = bd5 = e;
1965 }
1966 else {
1967 bb2 = bb5 = -e;
1968 bd2 = bd5 = 0;
1969 }
1970 if (bbe >= 0)
1971 bb2 += bbe;
1972 else
1973 bd2 -= bbe;
1974 bs2 = bb2;
1975#ifdef Honor_FLT_ROUNDS
1976 if (rounding != 1)
1977 bs2++;
1978#endif
1979#ifdef Avoid_Underflow
1980 j = bbe - scale;
1981 i = j + bbbits - 1; /* logb(rv) */
1982 if (i < Emin) /* denormal */
1983 j += P - Emin;
1984 else
1985 j = P + 1 - bbbits;
1986#else /*Avoid_Underflow*/
1987#ifdef Sudden_Underflow
1988#ifdef IBM
1989 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1990#else
1991 j = P + 1 - bbbits;
1992#endif
1993#else /*Sudden_Underflow*/
1994 j = bbe;
1995 i = j + bbbits - 1; /* logb(rv) */
1996 if (i < Emin) /* denormal */
1997 j += P - Emin;
1998 else
1999 j = P + 1 - bbbits;
2000#endif /*Sudden_Underflow*/
2001#endif /*Avoid_Underflow*/
2002 bb2 += j;
2003 bd2 += j;
2004#ifdef Avoid_Underflow
2005 bd2 += scale;
2006#endif
2007 i = bb2 < bd2 ? bb2 : bd2;
2008 if (i > bs2)
2009 i = bs2;
2010 if (i > 0) {
2011 bb2 -= i;
2012 bd2 -= i;
2013 bs2 -= i;
2014 }
2015 if (bb5 > 0) {
2016 bs = pow5mult(bs, bb5);
2017 bb1 = mult(bs, bb);
2018 Bfree(bb);
2019 bb = bb1;
2020 }
2021 if (bb2 > 0)
2022 bb = lshift(bb, bb2);
2023 if (bd5 > 0)
2024 bd = pow5mult(bd, bd5);
2025 if (bd2 > 0)
2026 bd = lshift(bd, bd2);
2027 if (bs2 > 0)
2028 bs = lshift(bs, bs2);
2029 delta = diff(bb, bd);
2030 dsign = delta->sign;
2031 delta->sign = 0;
2032 i = cmp(delta, bs);
2033#ifdef Honor_FLT_ROUNDS
2034 if (rounding != 1) {
2035 if (i < 0) {
2036 /* Error is less than an ulp */
2037 if (!delta->x[0] && delta->wds <= 1) {
2038 /* exact */
2039#ifdef SET_INEXACT
2040 inexact = 0;
2041#endif
2042 break;
2043 }
2044 if (rounding) {
2045 if (dsign) {
2046 adj = 1.;
2047 goto apply_adj;
2048 }
2049 }
2050 else if (!dsign) {
2051 adj = -1.;
2052 if (!word1(rv)
2053 && !(word0(rv) & Frac_mask)) {
2054 y = word0(rv) & Exp_mask;
2055#ifdef Avoid_Underflow
2056 if (!scale || y > 2*P*Exp_msk1)
2057#else
2058 if (y)
2059#endif
2060 {
2061 delta = lshift(delta,Log2P);
2062 if (cmp(delta, bs) <= 0)
2063 adj = -0.5;
2064 }
2065 }
2066 apply_adj:
2067#ifdef Avoid_Underflow
2068 if (scale && (y = word0(rv) & Exp_mask)
2069 <= 2*P*Exp_msk1)
2070 word0(adj) += (2*P+1)*Exp_msk1 - y;
2071#else
2072#ifdef Sudden_Underflow
2073 if ((word0(rv) & Exp_mask) <=
2074 P*Exp_msk1) {
2075 word0(rv) += P*Exp_msk1;
2076 dval(rv) += adj*ulp(dval(rv));
2077 word0(rv) -= P*Exp_msk1;
2078 }
2079 else
2080#endif /*Sudden_Underflow*/
2081#endif /*Avoid_Underflow*/
2082 dval(rv) += adj*ulp(dval(rv));
2083 }
2084 break;
2085 }
2086 adj = ratio(delta, bs);
2087 if (adj < 1.)
2088 adj = 1.;
2089 if (adj <= 0x7ffffffe) {
2090 /* adj = rounding ? ceil(adj) : floor(adj); */
2091 y = adj;
2092 if (y != adj) {
2093 if (!((rounding>>1) ^ dsign))
2094 y++;
2095 adj = y;
2096 }
2097 }
2098#ifdef Avoid_Underflow
2099 if (scale && (y = word0(rv) & Exp_mask) <= 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) <= P*Exp_msk1) {
2104 word0(rv) += P*Exp_msk1;
2105 adj *= ulp(dval(rv));
2106 if (dsign)
2107 dval(rv) += adj;
2108 else
2109 dval(rv) -= adj;
2110 word0(rv) -= P*Exp_msk1;
2111 goto cont;
2112 }
2113#endif /*Sudden_Underflow*/
2114#endif /*Avoid_Underflow*/
2115 adj *= ulp(dval(rv));
2116 if (dsign)
2117 dval(rv) += adj;
2118 else
2119 dval(rv) -= adj;
2120 goto cont;
2121 }
2122#endif /*Honor_FLT_ROUNDS*/
2123
2124 if (i < 0) {
2125 /* Error is less than half an ulp -- check for
2126 * special case of mantissa a power of two.
2127 */
2128 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2129#ifdef IEEE_Arith
2130#ifdef Avoid_Underflow
2131 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2132#else
2133 || (word0(rv) & Exp_mask) <= Exp_msk1
2134#endif
2135#endif
2136 ) {
2137#ifdef SET_INEXACT
2138 if (!delta->x[0] && delta->wds <= 1)
2139 inexact = 0;
2140#endif
2141 break;
2142 }
2143 if (!delta->x[0] && delta->wds <= 1) {
2144 /* exact result */
2145#ifdef SET_INEXACT
2146 inexact = 0;
2147#endif
2148 break;
2149 }
2150 delta = lshift(delta,Log2P);
2151 if (cmp(delta, bs) > 0)
2152 goto drop_down;
2153 break;
2154 }
2155 if (i == 0) {
2156 /* exactly half-way between */
2157 if (dsign) {
2158 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2159 && word1(rv) == (
2160#ifdef Avoid_Underflow
2161 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2162 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2163#endif
2164 0xffffffff)) {
2165 /*boundary case -- increment exponent*/
2166 word0(rv) = (word0(rv) & Exp_mask)
2167 + Exp_msk1
2168#ifdef IBM
2169 | Exp_msk1 >> 4
2170#endif
2171 ;
2172 word1(rv) = 0;
2173#ifdef Avoid_Underflow
2174 dsign = 0;
2175#endif
2176 break;
2177 }
2178 }
2179 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2180 drop_down:
2181 /* boundary case -- decrement exponent */
2182#ifdef Sudden_Underflow /*{{*/
2183 L = word0(rv) & Exp_mask;
2184#ifdef IBM
2185 if (L < Exp_msk1)
2186#else
2187#ifdef Avoid_Underflow
2188 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2189#else
2190 if (L <= Exp_msk1)
2191#endif /*Avoid_Underflow*/
2192#endif /*IBM*/
2193 goto undfl;
2194 L -= Exp_msk1;
2195#else /*Sudden_Underflow}{*/
2196#ifdef Avoid_Underflow
2197 if (scale) {
2198 L = word0(rv) & Exp_mask;
2199 if (L <= (2*P+1)*Exp_msk1) {
2200 if (L > (P+2)*Exp_msk1)
2201 /* round even ==> */
2202 /* accept rv */
2203 break;
2204 /* rv = smallest denormal */
2205 goto undfl;
2206 }
2207 }
2208#endif /*Avoid_Underflow*/
2209 L = (word0(rv) & Exp_mask) - Exp_msk1;
2210#endif /*Sudden_Underflow}}*/
2211 word0(rv) = L | Bndry_mask1;
2212 word1(rv) = 0xffffffff;
2213#ifdef IBM
2214 goto cont;
2215#else
2216 break;
2217#endif
2218 }
2219#ifndef ROUND_BIASED
2220 if (!(word1(rv) & LSB))
2221 break;
2222#endif
2223 if (dsign)
2224 dval(rv) += ulp(dval(rv));
2225#ifndef ROUND_BIASED
2226 else {
2227 dval(rv) -= ulp(dval(rv));
2228#ifndef Sudden_Underflow
2229 if (!dval(rv))
2230 goto undfl;
2231#endif
2232 }
2233#ifdef Avoid_Underflow
2234 dsign = 1 - dsign;
2235#endif
2236#endif
2237 break;
2238 }
2239 if ((aadj = ratio(delta, bs)) <= 2.) {
2240 if (dsign)
2241 aadj = aadj1 = 1.;
2242 else if (word1(rv) || word0(rv) & Bndry_mask) {
2243#ifndef Sudden_Underflow
2244 if (word1(rv) == Tiny1 && !word0(rv))
2245 goto undfl;
2246#endif
2247 aadj = 1.;
2248 aadj1 = -1.;
2249 }
2250 else {
2251 /* special case -- power of FLT_RADIX to be */
2252 /* rounded down... */
2253
2254 if (aadj < 2./FLT_RADIX)
2255 aadj = 1./FLT_RADIX;
2256 else
2257 aadj *= 0.5;
2258 aadj1 = -aadj;
2259 }
2260 }
2261 else {
2262 aadj *= 0.5;
2263 aadj1 = dsign ? aadj : -aadj;
2264#ifdef Check_FLT_ROUNDS
2265 switch(Rounding) {
2266 case 2: /* towards +infinity */
2267 aadj1 -= 0.5;
2268 break;
2269 case 0: /* towards 0 */
2270 case 3: /* towards -infinity */
2271 aadj1 += 0.5;
2272 }
2273#else
2274 if (Flt_Rounds == 0)
2275 aadj1 += 0.5;
2276#endif /*Check_FLT_ROUNDS*/
2277 }
2278 y = word0(rv) & Exp_mask;
2279
2280 /* Check for overflow */
2281
2282 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2283 dval(rv0) = dval(rv);
2284 word0(rv) -= P*Exp_msk1;
2285 adj = aadj1 * ulp(dval(rv));
2286 dval(rv) += adj;
2287 if ((word0(rv) & Exp_mask) >=
2288 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2289 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2290 goto ovfl;
2291 word0(rv) = Big0;
2292 word1(rv) = Big1;
2293 goto cont;
2294 }
2295 else
2296 word0(rv) += P*Exp_msk1;
2297 }
2298 else {
2299#ifdef Avoid_Underflow
2300 if (scale && y <= 2*P*Exp_msk1) {
2301 if (aadj <= 0x7fffffff) {
2302 if ((z = (ULong)aadj) <= 0)
2303 z = 1;
2304 aadj = z;
2305 aadj1 = dsign ? aadj : -aadj;
2306 }
2307 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2308 }
2309 adj = aadj1 * ulp(dval(rv));
2310 dval(rv) += adj;
2311#else
2312#ifdef Sudden_Underflow
2313 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2314 dval(rv0) = dval(rv);
2315 word0(rv) += P*Exp_msk1;
2316 adj = aadj1 * ulp(dval(rv));
2317 dval(rv) += adj;
2318#ifdef IBM
2319 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2320#else
2321 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2322#endif
2323 {
2324 if (word0(rv0) == Tiny0
2325 && word1(rv0) == Tiny1)
2326 goto undfl;
2327 word0(rv) = Tiny0;
2328 word1(rv) = Tiny1;
2329 goto cont;
2330 }
2331 else
2332 word0(rv) -= P*Exp_msk1;
2333 }
2334 else {
2335 adj = aadj1 * ulp(dval(rv));
2336 dval(rv) += adj;
2337 }
2338#else /*Sudden_Underflow*/
2339 /* Compute adj so that the IEEE rounding rules will
2340 * correctly round rv + adj in some half-way cases.
2341 * If rv * ulp(rv) is denormalized (i.e.,
2342 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2343 * trouble from bits lost to denormalization;
2344 * example: 1.2e-307 .
2345 */
2346 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2347 aadj1 = (double)(int)(aadj + 0.5);
2348 if (!dsign)
2349 aadj1 = -aadj1;
2350 }
2351 adj = aadj1 * ulp(dval(rv));
2352 dval(rv) += adj;
2353#endif /*Sudden_Underflow*/
2354#endif /*Avoid_Underflow*/
2355 }
2356 z = word0(rv) & Exp_mask;
2357#ifndef SET_INEXACT
2358#ifdef Avoid_Underflow
2359 if (!scale)
2360#endif
2361 if (y == z) {
2362 /* Can we stop now? */
2363 L = (Long)aadj;
2364 aadj -= L;
2365 /* The tolerances below are conservative. */
2366 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2367 if (aadj < .4999999 || aadj > .5000001)
2368 break;
2369 }
2370 else if (aadj < .4999999/FLT_RADIX)
2371 break;
2372 }
2373#endif
2374 cont:
2375 Bfree(bb);
2376 Bfree(bd);
2377 Bfree(bs);
2378 Bfree(delta);
2379 }
2380#ifdef SET_INEXACT
2381 if (inexact) {
2382 if (!oldinexact) {
2383 word0(rv0) = Exp_1 + (70 << Exp_shift);
2384 word1(rv0) = 0;
2385 dval(rv0) += 1.;
2386 }
2387 }
2388 else if (!oldinexact)
2389 clear_inexact();
2390#endif
2391#ifdef Avoid_Underflow
2392 if (scale) {
2393 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2394 word1(rv0) = 0;
2395 dval(rv) *= dval(rv0);
2396#ifndef NO_ERRNO
2397 /* try to avoid the bug of testing an 8087 register value */
2398 if (word0(rv) == 0 && word1(rv) == 0)
2399 errno = ERANGE;
2400#endif
2401 }
2402#endif /* Avoid_Underflow */
2403#ifdef SET_INEXACT
2404 if (inexact && !(word0(rv) & Exp_mask)) {
2405 /* set underflow bit */
2406 dval(rv0) = 1e-300;
2407 dval(rv0) *= dval(rv0);
2408 }
2409#endif
2410 retfree:
2411 Bfree(bb);
2412 Bfree(bd);
2413 Bfree(bs);
2414 Bfree(bd0);
2415 Bfree(delta);
2416 ret:
2417 if (se)
2418 *se = (char *)s;
2419 return sign ? -dval(rv) : dval(rv);
2420 }
2421
2422 static int
2423quorem
2424#ifdef KR_headers
2425 (b, S) Bigint *b, *S;
2426#else
2427 (Bigint *b, Bigint *S)
2428#endif
2429{
2430 int n;
2431 ULong *bx, *bxe, q, *sx, *sxe;
2432#ifdef ULLong
2433 ULLong borrow, carry, y, ys;
2434#else
2435 ULong borrow, carry, y, ys;
2436#ifdef Pack_32
2437 ULong si, z, zs;
2438#endif
2439#endif
2440
2441 n = S->wds;
2442#ifdef DEBUG
2443 /*debug*/ if (b->wds > n)
2444 /*debug*/ Bug("oversize b in quorem");
2445#endif
2446 if (b->wds < n)
2447 return 0;
2448 sx = S->x;
2449 sxe = sx + --n;
2450 bx = b->x;
2451 bxe = bx + n;
2452 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2453#ifdef DEBUG
2454 /*debug*/ if (q > 9)
2455 /*debug*/ Bug("oversized quotient in quorem");
2456#endif
2457 if (q) {
2458 borrow = 0;
2459 carry = 0;
2460 do {
2461#ifdef ULLong
2462 ys = *sx++ * (ULLong)q + carry;
2463 carry = ys >> 32;
2464 y = *bx - (ys & FFFFFFFF) - borrow;
2465 borrow = y >> 32 & (ULong)1;
2466 *bx++ = y & FFFFFFFF;
2467#else
2468#ifdef Pack_32
2469 si = *sx++;
2470 ys = (si & 0xffff) * q + carry;
2471 zs = (si >> 16) * q + (ys >> 16);
2472 carry = zs >> 16;
2473 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2474 borrow = (y & 0x10000) >> 16;
2475 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2476 borrow = (z & 0x10000) >> 16;
2477 Storeinc(bx, z, y);
2478#else
2479 ys = *sx++ * q + carry;
2480 carry = ys >> 16;
2481 y = *bx - (ys & 0xffff) - borrow;
2482 borrow = (y & 0x10000) >> 16;
2483 *bx++ = y & 0xffff;
2484#endif
2485#endif
2486 }
2487 while(sx <= sxe);
2488 if (!*bxe) {
2489 bx = b->x;
2490 while(--bxe > bx && !*bxe)
2491 --n;
2492 b->wds = n;
2493 }
2494 }
2495 if (cmp(b, S) >= 0) {
2496 q++;
2497 borrow = 0;
2498 carry = 0;
2499 bx = b->x;
2500 sx = S->x;
2501 do {
2502#ifdef ULLong
2503 ys = *sx++ + carry;
2504 carry = ys >> 32;
2505 y = *bx - (ys & FFFFFFFF) - borrow;
2506 borrow = y >> 32 & (ULong)1;
2507 *bx++ = y & FFFFFFFF;
2508#else
2509#ifdef Pack_32
2510 si = *sx++;
2511 ys = (si & 0xffff) + carry;
2512 zs = (si >> 16) + (ys >> 16);
2513 carry = zs >> 16;
2514 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2515 borrow = (y & 0x10000) >> 16;
2516 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2517 borrow = (z & 0x10000) >> 16;
2518 Storeinc(bx, z, y);
2519#else
2520 ys = *sx++ + carry;
2521 carry = ys >> 16;
2522 y = *bx - (ys & 0xffff) - borrow;
2523 borrow = (y & 0x10000) >> 16;
2524 *bx++ = y & 0xffff;
2525#endif
2526#endif
2527 }
2528 while(sx <= sxe);
2529 bx = b->x;
2530 bxe = bx + n;
2531 if (!*bxe) {
2532 while(--bxe > bx && !*bxe)
2533 --n;
2534 b->wds = n;
2535 }
2536 }
2537 return q;
2538 }
2539
2540#ifndef MULTIPLE_THREADS
2541 static char *dtoa_result;
2542#endif
2543
2544 static char *
2545#ifdef KR_headers
2546rv_alloc(i) int i;
2547#else
2548rv_alloc(int i)
2549#endif
2550{
2551 int j, k, *r;
2552
2553 j = sizeof(ULong);
2554 for(k = 0;
2555 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
2556 j <<= 1)
2557 k++;
2558 r = (int*)Balloc(k);
2559 *r = k;
2560 return
2561#ifndef MULTIPLE_THREADS
2562 dtoa_result =
2563#endif
2564 (char *)(r+1);
2565 }
2566
2567 static char *
2568#ifdef KR_headers
2569nrv_alloc(s, rve, n) char *s, **rve; int n;
2570#else
2571nrv_alloc(CONST char *s, char **rve, int n)
2572#endif
2573{
2574 char *rv, *t;
2575
2576 t = rv = rv_alloc(n);
2577 while((*t = *s++)) t++;
2578 if (rve)
2579 *rve = t;
2580 return rv;
2581 }
2582
2583/* freedtoa(s) must be used to free values s returned by dtoa
2584 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2585 * but for consistency with earlier versions of dtoa, it is optional
2586 * when MULTIPLE_THREADS is not defined.
2587 */
2588
2589 void
2590#ifdef KR_headers
2591freedtoa(s) char *s;
2592#else
2593freedtoa(char *s)
2594#endif
2595{
2596 Bigint *b = (Bigint *)((int *)s - 1);
2597 b->maxwds = 1 << (b->k = *(int*)b);
2598 Bfree(b);
2599#ifndef MULTIPLE_THREADS
2600 if (s == dtoa_result)
2601 dtoa_result = 0;
2602#endif
2603 }
2604
2605/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2606 *
2607 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2608 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
2609 *
2610 * Modifications:
2611 * 1. Rather than iterating, we use a simple numeric overestimate
2612 * to determine k = floor(log10(d)). We scale relevant
2613 * quantities using O(log2(k)) rather than O(k) multiplications.
2614 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2615 * try to generate digits strictly left to right. Instead, we
2616 * compute with fewer bits and propagate the carry if necessary
2617 * when rounding the final digit up. This is often faster.
2618 * 3. Under the assumption that input will be rounded nearest,
2619 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2620 * That is, we allow equality in stopping tests when the
2621 * round-nearest rule will give the same floating-point value
2622 * as would satisfaction of the stopping test with strict
2623 * inequality.
2624 * 4. We remove common factors of powers of 2 from relevant
2625 * quantities.
2626 * 5. When converting floating-point integers less than 1e16,
2627 * we use floating-point arithmetic rather than resorting
2628 * to multiple-precision integers.
2629 * 6. When asked to produce fewer than 15 digits, we first try
2630 * to get by with floating-point arithmetic; we resort to
2631 * multiple-precision integer arithmetic only if we cannot
2632 * guarantee that the floating-point calculation has given
2633 * the correctly rounded result. For k requested digits and
2634 * "uniformly" distributed input, the probability is
2635 * something like 10^(k-15) that we must resort to the Long
2636 * calculation.
2637 */
2638
2639 char *
2640dtoa
2641#ifdef KR_headers
2642 (d, mode, ndigits, decpt, sign, rve)
2643 double d; int mode, ndigits, *decpt, *sign; char **rve;
2644#else
2645 (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2646#endif
2647{
2648 /* Arguments ndigits, decpt, sign are similar to those
2649 of ecvt and fcvt; trailing zeros are suppressed from
2650 the returned string. If not null, *rve is set to point
2651 to the end of the return value. If d is +-Infinity or NaN,
2652 then *decpt is set to 9999.
2653
2654 mode:
2655 0 ==> shortest string that yields d when read in
2656 and rounded to nearest.
2657 1 ==> like 0, but with Steele & White stopping rule;
2658 e.g. with IEEE P754 arithmetic , mode 0 gives
2659 1e23 whereas mode 1 gives 9.999999999999999e22.
2660 2 ==> max(1,ndigits) significant digits. This gives a
2661 return value similar to that of ecvt, except
2662 that trailing zeros are suppressed.
2663 3 ==> through ndigits past the decimal point. This
2664 gives a return value similar to that from fcvt,
2665 except that trailing zeros are suppressed, and
2666 ndigits can be negative.
2667 4,5 ==> similar to 2 and 3, respectively, but (in
2668 round-nearest mode) with the tests of mode 0 to
2669 possibly return a shorter string that rounds to d.
2670 With IEEE arithmetic and compilation with
2671 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2672 as modes 2 and 3 when FLT_ROUNDS != 1.
2673 6-9 ==> Debugging modes similar to mode - 4: don't try
2674 fast floating-point estimate (if applicable).
2675
2676 Values of mode other than 0-9 are treated as mode 0.
2677
2678 Sufficient space is allocated to the return value
2679 to hold the suppressed trailing zeros.
2680 */
2681
2682 int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
2683 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2684 spec_case, try_quick;
2685 Long L;
2686#ifndef Sudden_Underflow
2687 int denorm;
2688 ULong x;
2689#endif
2690 Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
2691 double d2, ds, eps;
2692 char *s, *s0;
2693#ifdef Honor_FLT_ROUNDS
2694 int rounding;
2695#endif
2696#ifdef SET_INEXACT
2697 int inexact, oldinexact;
2698#endif
2699
2700#ifndef MULTIPLE_THREADS
2701 if (dtoa_result) {
2702 freedtoa(dtoa_result);
2703 dtoa_result = 0;
2704 }
2705#endif
2706
2707 if (word0(d) & Sign_bit) {
2708 /* set sign for everything, including 0's and NaNs */
2709 *sign = 1;
2710 word0(d) &= ~Sign_bit; /* clear sign bit */
2711 }
2712 else
2713 *sign = 0;
2714
2715#if defined(IEEE_Arith) + defined(VAX)
2716#ifdef IEEE_Arith
2717 if ((word0(d) & Exp_mask) == Exp_mask)
2718#else
2719 if (word0(d) == 0x8000)
2720#endif
2721 {
2722 /* Infinity or NaN */
2723 *decpt = 9999;
2724#ifdef IEEE_Arith
2725 if (!word1(d) && !(word0(d) & 0xfffff))
2726 return nrv_alloc("Infinity", rve, 8);
2727#endif
2728 return nrv_alloc("NaN", rve, 3);
2729 }
2730#endif
2731#ifdef IBM
2732 dval(d) += 0; /* normalize */
2733#endif
2734 if (!dval(d)) {
2735 *decpt = 1;
2736 return nrv_alloc("0", rve, 1);
2737 }
2738
2739#ifdef SET_INEXACT
2740 try_quick = oldinexact = get_inexact();
2741 inexact = 1;
2742#endif
2743#ifdef Honor_FLT_ROUNDS
2744 if ((rounding = Flt_Rounds) >= 2) {
2745 if (*sign)
2746 rounding = rounding == 2 ? 0 : 2;
2747 else
2748 if (rounding != 2)
2749 rounding = 0;
2750 }
2751#endif
2752
2753 b = d2b(dval(d), &be, &bbits);
2754#ifdef Sudden_Underflow
2755 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2756#else
2757 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2758#endif
2759 dval(d2) = dval(d);
2760 word0(d2) &= Frac_mask1;
2761 word0(d2) |= Exp_11;
2762#ifdef IBM
2763 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2764 dval(d2) /= 1 << j;
2765#endif
2766
2767 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2768 * log10(x) = log(x) / log(10)
2769 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2770 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2771 *
2772 * This suggests computing an approximation k to log10(d) by
2773 *
2774 * k = (i - Bias)*0.301029995663981
2775 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2776 *
2777 * We want k to be too large rather than too small.
2778 * The error in the first-order Taylor series approximation
2779 * is in our favor, so we just round up the constant enough
2780 * to compensate for any error in the multiplication of
2781 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2782 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2783 * adding 1e-13 to the constant term more than suffices.
2784 * Hence we adjust the constant term to 0.1760912590558.
2785 * (We could get a more accurate k by invoking log10,
2786 * but this is probably not worthwhile.)
2787 */
2788
2789 i -= Bias;
2790#ifdef IBM
2791 i <<= 2;
2792 i += j;
2793#endif
2794#ifndef Sudden_Underflow
2795 denorm = 0;
2796 }
2797 else {
2798 /* d is denormalized */
2799
2800 i = bbits + be + (Bias + (P-1) - 1);
2801 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2802 : word1(d) << 32 - i;
2803 dval(d2) = x;
2804 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2805 i -= (Bias + (P-1) - 1) + 1;
2806 denorm = 1;
2807 }
2808#endif
2809 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2810 k = (int)ds;
2811 if (ds < 0. && ds != k)
2812 k--; /* want k = floor(ds) */
2813 k_check = 1;
2814 if (k >= 0 && k <= Ten_pmax) {
2815 if (dval(d) < tens[k])
2816 k--;
2817 k_check = 0;
2818 }
2819 j = bbits - i - 1;
2820 if (j >= 0) {
2821 b2 = 0;
2822 s2 = j;
2823 }
2824 else {
2825 b2 = -j;
2826 s2 = 0;
2827 }
2828 if (k >= 0) {
2829 b5 = 0;
2830 s5 = k;
2831 s2 += k;
2832 }
2833 else {
2834 b2 -= k;
2835 b5 = -k;
2836 s5 = 0;
2837 }
2838 if (mode < 0 || mode > 9)
2839 mode = 0;
2840
2841#ifndef SET_INEXACT
2842#ifdef Check_FLT_ROUNDS
2843 try_quick = Rounding == 1;
2844#else
2845 try_quick = 1;
2846#endif
2847#endif /*SET_INEXACT*/
2848
2849 if (mode > 5) {
2850 mode -= 4;
2851 try_quick = 0;
2852 }
2853 leftright = 1;
2854 switch(mode) {
2855 case 0:
2856 case 1:
2857 ilim = ilim1 = -1;
2858 i = 18;
2859 ndigits = 0;
2860 break;
2861 case 2:
2862 leftright = 0;
2863 /* no break */
2864 case 4:
2865 if (ndigits <= 0)
2866 ndigits = 1;
2867 ilim = ilim1 = i = ndigits;
2868 break;
2869 case 3:
2870 leftright = 0;
2871 /* no break */
2872 case 5:
2873 i = ndigits + k + 1;
2874 ilim = i;
2875 ilim1 = i - 1;
2876 if (i <= 0)
2877 i = 1;
2878 }
2879 s = s0 = rv_alloc(i);
2880
2881#ifdef Honor_FLT_ROUNDS
2882 if (mode > 1 && rounding != 1)
2883 leftright = 0;
2884#endif
2885
2886 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2887
2888 /* Try to get by with floating-point arithmetic. */
2889
2890 i = 0;
2891 dval(d2) = dval(d);
2892 k0 = k;
2893 ilim0 = ilim;
2894 ieps = 2; /* conservative */
2895 if (k > 0) {
2896 ds = tens[k&0xf];
2897 j = k >> 4;
2898 if (j & Bletch) {
2899 /* prevent overflows */
2900 j &= Bletch - 1;
2901 dval(d) /= bigtens[n_bigtens-1];
2902 ieps++;
2903 }
2904 for(; j; j >>= 1, i++)
2905 if (j & 1) {
2906 ieps++;
2907 ds *= bigtens[i];
2908 }
2909 dval(d) /= ds;
2910 }
2911 else if ((j1 = -k)) {
2912 dval(d) *= tens[j1 & 0xf];
2913 for(j = j1 >> 4; j; j >>= 1, i++)
2914 if (j & 1) {
2915 ieps++;
2916 dval(d) *= bigtens[i];
2917 }
2918 }
2919 if (k_check && dval(d) < 1. && ilim > 0) {
2920 if (ilim1 <= 0)
2921 goto fast_failed;
2922 ilim = ilim1;
2923 k--;
2924 dval(d) *= 10.;
2925 ieps++;
2926 }
2927 dval(eps) = ieps*dval(d) + 7.;
2928 word0(eps) -= (P-1)*Exp_msk1;
2929 if (ilim == 0) {
2930 S = mhi = 0;
2931 dval(d) -= 5.;
2932 if (dval(d) > dval(eps))
2933 goto one_digit;
2934 if (dval(d) < -dval(eps))
2935 goto no_digits;
2936 goto fast_failed;
2937 }
2938#ifndef No_leftright
2939 if (leftright) {
2940 /* Use Steele & White method of only
2941 * generating digits needed.
2942 */
2943 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2944 for(i = 0;;) {
2945 L = (long int)dval(d);
2946 dval(d) -= L;
2947 *s++ = '0' + (int)L;
2948 if (dval(d) < dval(eps))
2949 goto ret1;
2950 if (1. - dval(d) < dval(eps))
2951 goto bump_up;
2952 if (++i >= ilim)
2953 break;
2954 dval(eps) *= 10.;
2955 dval(d) *= 10.;
2956 }
2957 }
2958 else {
2959#endif
2960 /* Generate ilim digits, then fix them up. */
2961 dval(eps) *= tens[ilim-1];
2962 for(i = 1;; i++, dval(d) *= 10.) {
2963 L = (Long)(dval(d));
2964 if (!(dval(d) -= L))
2965 ilim = i;
2966 *s++ = '0' + (int)L;
2967 if (i == ilim) {
2968 if (dval(d) > 0.5 + dval(eps))
2969 goto bump_up;
2970 else if (dval(d) < 0.5 - dval(eps)) {
2971 while(*--s == '0');
2972 s++;
2973 goto ret1;
2974 }
2975 break;
2976 }
2977 }
2978#ifndef No_leftright
2979 }
2980#endif
2981 fast_failed:
2982 s = s0;
2983 dval(d) = dval(d2);
2984 k = k0;
2985 ilim = ilim0;
2986 }
2987
2988 /* Do we have a "small" integer? */
2989
2990 if (be >= 0 && k <= Int_max) {
2991 /* Yes. */
2992 ds = tens[k];
2993 if (ndigits < 0 && ilim <= 0) {
2994 S = mhi = 0;
2995 if (ilim < 0 || dval(d) <= 5*ds)
2996 goto no_digits;
2997 goto one_digit;
2998 }
2999 for(i = 1;; i++, dval(d) *= 10.) {
3000 L = (Long)(dval(d) / ds);
3001 dval(d) -= L*ds;
3002#ifdef Check_FLT_ROUNDS
3003 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3004 if (dval(d) < 0) {
3005 L--;
3006 dval(d) += ds;
3007 }
3008#endif
3009 *s++ = '0' + (int)L;
3010 if (!dval(d)) {
3011#ifdef SET_INEXACT
3012 inexact = 0;
3013#endif
3014 break;
3015 }
3016 if (i == ilim) {
3017#ifdef Honor_FLT_ROUNDS
3018 if (mode > 1)
3019 switch(rounding) {
3020 case 0: goto ret1;
3021 case 2: goto bump_up;
3022 }
3023#endif
3024 dval(d) += dval(d);
3025 if (dval(d) > ds || dval(d) == ds && L & 1) {
3026 bump_up:
3027 while(*--s == '9')
3028 if (s == s0) {
3029 k++;
3030 *s = '0';
3031 break;
3032 }
3033 ++*s++;
3034 }
3035 break;
3036 }
3037 }
3038 goto ret1;
3039 }
3040
3041 m2 = b2;
3042 m5 = b5;
3043 mhi = mlo = 0;
3044 if (leftright) {
3045 i =
3046#ifndef Sudden_Underflow
3047 denorm ? be + (Bias + (P-1) - 1 + 1) :
3048#endif
3049#ifdef IBM
3050 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3051#else
3052 1 + P - bbits;
3053#endif
3054 b2 += i;
3055 s2 += i;
3056 mhi = i2b(1);
3057 }
3058 if (m2 > 0 && s2 > 0) {
3059 i = m2 < s2 ? m2 : s2;
3060 b2 -= i;
3061 m2 -= i;
3062 s2 -= i;
3063 }
3064 if (b5 > 0) {
3065 if (leftright) {
3066 if (m5 > 0) {
3067 mhi = pow5mult(mhi, m5);
3068 b1 = mult(mhi, b);
3069 Bfree(b);
3070 b = b1;
3071 }
3072 if ((j = b5 - m5))
3073 b = pow5mult(b, j);
3074 }
3075 else
3076 b = pow5mult(b, b5);
3077 }
3078 S = i2b(1);
3079 if (s5 > 0)
3080 S = pow5mult(S, s5);
3081
3082 /* Check for special case that d is a normalized power of 2. */
3083
3084 spec_case = 0;
3085 if ((mode < 2 || leftright)
3086#ifdef Honor_FLT_ROUNDS
3087 && rounding == 1
3088#endif
3089 ) {
3090 if (!word1(d) && !(word0(d) & Bndry_mask)
3091#ifndef Sudden_Underflow
3092 && word0(d) & (Exp_mask & ~Exp_msk1)
3093#endif
3094 ) {
3095 /* The special case */
3096 b2 += Log2P;
3097 s2 += Log2P;
3098 spec_case = 1;
3099 }
3100 }
3101
3102 /* Arrange for convenient computation of quotients:
3103 * shift left if necessary so divisor has 4 leading 0 bits.
3104 *
3105 * Perhaps we should just compute leading 28 bits of S once
3106 * and for all and pass them and a shift to quorem, so it
3107 * can do shifts and ors to compute the numerator for q.
3108 */
3109#ifdef Pack_32
3110 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3111 i = 32 - i;
3112#else
3113 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3114 i = 16 - i;
3115#endif
3116 if (i > 4) {
3117 i -= 4;
3118 b2 += i;
3119 m2 += i;
3120 s2 += i;
3121 }
3122 else if (i < 4) {
3123 i += 28;
3124 b2 += i;
3125 m2 += i;
3126 s2 += i;
3127 }
3128 if (b2 > 0)
3129 b = lshift(b, b2);
3130 if (s2 > 0)
3131 S = lshift(S, s2);
3132 if (k_check) {
3133 if (cmp(b,S) < 0) {
3134 k--;
3135 b = multadd(b, 10, 0); /* we botched the k estimate */
3136 if (leftright)
3137 mhi = multadd(mhi, 10, 0);
3138 ilim = ilim1;
3139 }
3140 }
3141 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3142 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3143 /* no digits, fcvt style */
3144 no_digits:
3145 k = -1 - ndigits;
3146 goto ret;
3147 }
3148 one_digit:
3149 *s++ = '1';
3150 k++;
3151 goto ret;
3152 }
3153 if (leftright) {
3154 if (m2 > 0)
3155 mhi = lshift(mhi, m2);
3156
3157 /* Compute mlo -- check for special case
3158 * that d is a normalized power of 2.
3159 */
3160
3161 mlo = mhi;
3162 if (spec_case) {
3163 mhi = Balloc(mhi->k);
3164 Bcopy(mhi, mlo);
3165 mhi = lshift(mhi, Log2P);
3166 }
3167
3168 for(i = 1;;i++) {
3169 dig = quorem(b,S) + '0';
3170 /* Do we yet have the shortest decimal string
3171 * that will round to d?
3172 */
3173 j = cmp(b, mlo);
3174 delta = diff(S, mhi);
3175 j1 = delta->sign ? 1 : cmp(b, delta);
3176 Bfree(delta);
3177#ifndef ROUND_BIASED
3178 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3179#ifdef Honor_FLT_ROUNDS
3180 && rounding >= 1
3181#endif
3182 ) {
3183 if (dig == '9')
3184 goto round_9_up;
3185 if (j > 0)
3186 dig++;
3187#ifdef SET_INEXACT
3188 else if (!b->x[0] && b->wds <= 1)
3189 inexact = 0;
3190#endif
3191 *s++ = dig;
3192 goto ret;
3193 }
3194#endif
3195 if (j < 0 || j == 0 && mode != 1
3196#ifndef ROUND_BIASED
3197 && !(word1(d) & 1)
3198#endif
3199 ) {
3200 if (!b->x[0] && b->wds <= 1) {
3201#ifdef SET_INEXACT
3202 inexact = 0;
3203#endif
3204 goto accept_dig;
3205 }
3206#ifdef Honor_FLT_ROUNDS
3207 if (mode > 1)
3208 switch(rounding) {
3209 case 0: goto accept_dig;
3210 case 2: goto keep_dig;
3211 }
3212#endif /*Honor_FLT_ROUNDS*/
3213 if (j1 > 0) {
3214 b = lshift(b, 1);
3215 j1 = cmp(b, S);
3216 if ((j1 > 0 || j1 == 0 && dig & 1)
3217 && dig++ == '9')
3218 goto round_9_up;
3219 }
3220 accept_dig:
3221 *s++ = dig;
3222 goto ret;
3223 }
3224 if (j1 > 0) {
3225#ifdef Honor_FLT_ROUNDS
3226 if (!rounding)
3227 goto accept_dig;
3228#endif
3229 if (dig == '9') { /* possible if i == 1 */
3230 round_9_up:
3231 *s++ = '9';
3232 goto roundoff;
3233 }
3234 *s++ = dig + 1;
3235 goto ret;
3236 }
3237#ifdef Honor_FLT_ROUNDS
3238 keep_dig:
3239#endif
3240 *s++ = dig;
3241 if (i == ilim)
3242 break;
3243 b = multadd(b, 10, 0);
3244 if (mlo == mhi)
3245 mlo = mhi = multadd(mhi, 10, 0);
3246 else {
3247 mlo = multadd(mlo, 10, 0);
3248 mhi = multadd(mhi, 10, 0);
3249 }
3250 }
3251 }
3252 else
3253 for(i = 1;; i++) {
3254 *s++ = dig = quorem(b,S) + '0';
3255 if (!b->x[0] && b->wds <= 1) {
3256#ifdef SET_INEXACT
3257 inexact = 0;
3258#endif
3259 goto ret;
3260 }
3261 if (i >= ilim)
3262 break;
3263 b = multadd(b, 10, 0);
3264 }
3265
3266 /* Round off last digit */
3267
3268#ifdef Honor_FLT_ROUNDS
3269 switch(rounding) {
3270 case 0: goto trimzeros;
3271 case 2: goto roundoff;
3272 }
3273#endif
3274 b = lshift(b, 1);
3275 j = cmp(b, S);
3276 if (j > 0 || j == 0 && dig & 1) {
3277 roundoff:
3278 while(*--s == '9')
3279 if (s == s0) {
3280 k++;
3281 *s++ = '1';
3282 goto ret;
3283 }
3284 ++*s++;
3285 }
3286 else {
3287#ifdef Honor_FLT_ROUNDS
3288trimzeros:
3289#endif
3290 while(*--s == '0');
3291 s++;
3292 }
3293 ret:
3294 Bfree(S);
3295 if (mhi) {
3296 if (mlo && mlo != mhi)
3297 Bfree(mlo);
3298 Bfree(mhi);
3299 }
3300 ret1:
3301#ifdef SET_INEXACT
3302 if (inexact) {
3303 if (!oldinexact) {
3304 word0(d) = Exp_1 + (70 << Exp_shift);
3305 word1(d) = 0;
3306 dval(d) += 1.;
3307 }
3308 }
3309 else if (!oldinexact)
3310 clear_inexact();
3311#endif
3312 Bfree(b);
3313 *s = 0;
3314 *decpt = k + 1;
3315 if (rve)
3316 *rve = s;
3317 return s0;
3318 }
3319#ifdef __cplusplus
3320}
3321#endif
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