source: webkit/trunk/JavaScriptCore/kjs/dtoa.cpp@ 7245

Last change on this file since 7245 was 2913, checked in by mjs, 22 years ago

Reviewed by: Darin Adler

  • fixed Deployment build.
  • kjs/dtoa.cpp: Work around warnings.
  • Property svn:eol-style set to native
  • Property svn:keywords set to Author Date Id Revision
File size: 66.6 KB
Line 
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#ifdef WORDS_BIGENDIAN
174#define IEEE_MC68k
175#else
176#define IEEE_8087
177#endif
178#define INFNAN_CHECK
179#include "dtoa.h"
180#define strtod kjs_strtod
181#define dtoa kjs_dtoa
182#define freedtoa kjs_freedtoa
183
184
185
186#ifndef Long
187#define Long long
188#endif
189#ifndef ULong
190typedef unsigned Long ULong;
191#endif
192
193#ifdef DEBUG
194#include "stdio.h"
195#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
196#endif
197
198#include "stdlib.h"
199#include "string.h"
200
201#ifdef USE_LOCALE
202#include "locale.h"
203#endif
204
205#ifdef MALLOC
206#ifdef KR_headers
207extern char *MALLOC();
208#else
209extern void *MALLOC(size_t);
210#endif
211#else
212#define MALLOC malloc
213#endif
214
215#ifndef Omit_Private_Memory
216#ifndef PRIVATE_MEM
217#define PRIVATE_MEM 2304
218#endif
219#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
220static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
221#endif
222
223#undef IEEE_Arith
224#undef Avoid_Underflow
225#ifdef IEEE_MC68k
226#define IEEE_Arith
227#endif
228#ifdef IEEE_8087
229#define IEEE_Arith
230#endif
231
232#include "errno.h"
233
234#ifdef Bad_float_h
235
236#ifdef IEEE_Arith
237#define DBL_DIG 15
238#define DBL_MAX_10_EXP 308
239#define DBL_MAX_EXP 1024
240#define FLT_RADIX 2
241#endif /*IEEE_Arith*/
242
243#ifdef IBM
244#define DBL_DIG 16
245#define DBL_MAX_10_EXP 75
246#define DBL_MAX_EXP 63
247#define FLT_RADIX 16
248#define DBL_MAX 7.2370055773322621e+75
249#endif
250
251#ifdef VAX
252#define DBL_DIG 16
253#define DBL_MAX_10_EXP 38
254#define DBL_MAX_EXP 127
255#define FLT_RADIX 2
256#define DBL_MAX 1.7014118346046923e+38
257#endif
258
259#ifndef LONG_MAX
260#define LONG_MAX 2147483647
261#endif
262
263#else /* ifndef Bad_float_h */
264#include "float.h"
265#endif /* Bad_float_h */
266
267#ifndef __MATH_H__
268#include "math.h"
269#endif
270
271#ifdef __cplusplus
272extern "C" {
273#endif
274
275#ifndef CONST
276#ifdef KR_headers
277#define CONST /* blank */
278#else
279#define CONST const
280#endif
281#endif
282
283#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
284Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
285#endif
286
287typedef union { double d; ULong L[2]; } U;
288
289#ifdef YES_ALIAS
290#define dval(x) x
291#ifdef IEEE_8087
292#define word0(x) ((ULong *)&x)[1]
293#define word1(x) ((ULong *)&x)[0]
294#else
295#define word0(x) ((ULong *)&x)[0]
296#define word1(x) ((ULong *)&x)[1]
297#endif
298#else
299#ifdef IEEE_8087
300#define word0(x) ((U*)&x)->L[1]
301#define word1(x) ((U*)&x)->L[0]
302#else
303#define word0(x) ((U*)&x)->L[0]
304#define word1(x) ((U*)&x)->L[1]
305#endif
306#define dval(x) ((U*)&x)->d
307#endif
308
309/* The following definition of Storeinc is appropriate for MIPS processors.
310 * An alternative that might be better on some machines is
311 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
312 */
313#if defined(IEEE_8087) + defined(VAX)
314#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
315((unsigned short *)a)[0] = (unsigned short)c, a++)
316#else
317#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
318((unsigned short *)a)[1] = (unsigned short)c, a++)
319#endif
320
321/* #define P DBL_MANT_DIG */
322/* Ten_pmax = floor(P*log(2)/log(5)) */
323/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
324/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
325/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
326
327#ifdef IEEE_Arith
328#define Exp_shift 20
329#define Exp_shift1 20
330#define Exp_msk1 0x100000
331#define Exp_msk11 0x100000
332#define Exp_mask 0x7ff00000
333#define P 53
334#define Bias 1023
335#define Emin (-1022)
336#define Exp_1 0x3ff00000
337#define Exp_11 0x3ff00000
338#define Ebits 11
339#define Frac_mask 0xfffff
340#define Frac_mask1 0xfffff
341#define Ten_pmax 22
342#define Bletch 0x10
343#define Bndry_mask 0xfffff
344#define Bndry_mask1 0xfffff
345#define LSB 1
346#define Sign_bit 0x80000000
347#define Log2P 1
348#define Tiny0 0
349#define Tiny1 1
350#define Quick_max 14
351#define Int_max 14
352#ifndef NO_IEEE_Scale
353#define Avoid_Underflow
354#ifdef Flush_Denorm /* debugging option */
355#undef Sudden_Underflow
356#endif
357#endif
358
359#ifndef Flt_Rounds
360#ifdef FLT_ROUNDS
361#define Flt_Rounds FLT_ROUNDS
362#else
363#define Flt_Rounds 1
364#endif
365#endif /*Flt_Rounds*/
366
367#ifdef Honor_FLT_ROUNDS
368#define Rounding rounding
369#undef Check_FLT_ROUNDS
370#define Check_FLT_ROUNDS
371#else
372#define Rounding Flt_Rounds
373#endif
374
375#else /* ifndef IEEE_Arith */
376#undef Check_FLT_ROUNDS
377#undef Honor_FLT_ROUNDS
378#undef SET_INEXACT
379#undef Sudden_Underflow
380#define Sudden_Underflow
381#ifdef IBM
382#undef Flt_Rounds
383#define Flt_Rounds 0
384#define Exp_shift 24
385#define Exp_shift1 24
386#define Exp_msk1 0x1000000
387#define Exp_msk11 0x1000000
388#define Exp_mask 0x7f000000
389#define P 14
390#define Bias 65
391#define Exp_1 0x41000000
392#define Exp_11 0x41000000
393#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
394#define Frac_mask 0xffffff
395#define Frac_mask1 0xffffff
396#define Bletch 4
397#define Ten_pmax 22
398#define Bndry_mask 0xefffff
399#define Bndry_mask1 0xffffff
400#define LSB 1
401#define Sign_bit 0x80000000
402#define Log2P 4
403#define Tiny0 0x100000
404#define Tiny1 0
405#define Quick_max 14
406#define Int_max 15
407#else /* VAX */
408#undef Flt_Rounds
409#define Flt_Rounds 1
410#define Exp_shift 23
411#define Exp_shift1 7
412#define Exp_msk1 0x80
413#define Exp_msk11 0x800000
414#define Exp_mask 0x7f80
415#define P 56
416#define Bias 129
417#define Exp_1 0x40800000
418#define Exp_11 0x4080
419#define Ebits 8
420#define Frac_mask 0x7fffff
421#define Frac_mask1 0xffff007f
422#define Ten_pmax 24
423#define Bletch 2
424#define Bndry_mask 0xffff007f
425#define Bndry_mask1 0xffff007f
426#define LSB 0x10000
427#define Sign_bit 0x8000
428#define Log2P 1
429#define Tiny0 0x80
430#define Tiny1 0
431#define Quick_max 15
432#define Int_max 15
433#endif /* IBM, VAX */
434#endif /* IEEE_Arith */
435
436#ifndef IEEE_Arith
437#define ROUND_BIASED
438#endif
439
440#ifdef RND_PRODQUOT
441#define rounded_product(a,b) a = rnd_prod(a, b)
442#define rounded_quotient(a,b) a = rnd_quot(a, b)
443#ifdef KR_headers
444extern double rnd_prod(), rnd_quot();
445#else
446extern double rnd_prod(double, double), rnd_quot(double, double);
447#endif
448#else
449#define rounded_product(a,b) a *= b
450#define rounded_quotient(a,b) a /= b
451#endif
452
453#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
454#define Big1 0xffffffff
455
456#ifndef Pack_32
457#define Pack_32
458#endif
459
460#ifdef KR_headers
461#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
462#else
463#define FFFFFFFF 0xffffffffUL
464#endif
465
466#ifdef NO_LONG_LONG
467#undef ULLong
468#ifdef Just_16
469#undef Pack_32
470/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
471 * This makes some inner loops simpler and sometimes saves work
472 * during multiplications, but it often seems to make things slightly
473 * slower. Hence the default is now to store 32 bits per Long.
474 */
475#endif
476#else /* long long available */
477#ifndef Llong
478#define Llong long long
479#endif
480#ifndef ULLong
481#define ULLong unsigned Llong
482#endif
483#endif /* NO_LONG_LONG */
484
485#ifndef MULTIPLE_THREADS
486#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
487#define FREE_DTOA_LOCK(n) /*nothing*/
488#endif
489
490#define Kmax 15
491
492 struct
493Bigint {
494 struct Bigint *next;
495 int k, maxwds, sign, wds;
496 ULong x[1];
497 };
498
499 typedef struct Bigint Bigint;
500
501 static Bigint *freelist[Kmax+1];
502
503 static Bigint *
504Balloc
505#ifdef KR_headers
506 (k) int k;
507#else
508 (int k)
509#endif
510{
511 int x;
512 Bigint *rv;
513#ifndef Omit_Private_Memory
514 unsigned int len;
515#endif
516
517 ACQUIRE_DTOA_LOCK(0);
518 if ((rv = freelist[k])) {
519 freelist[k] = rv->next;
520 }
521 else {
522 x = 1 << k;
523#ifdef Omit_Private_Memory
524 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
525#else
526 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
527 /sizeof(double);
528 if (pmem_next - private_mem + len <= PRIVATE_mem) {
529 rv = (Bigint*)pmem_next;
530 pmem_next += len;
531 }
532 else
533 rv = (Bigint*)MALLOC(len*sizeof(double));
534#endif
535 rv->k = k;
536 rv->maxwds = x;
537 }
538 FREE_DTOA_LOCK(0);
539 rv->sign = rv->wds = 0;
540 return rv;
541 }
542
543 static void
544Bfree
545#ifdef KR_headers
546 (v) Bigint *v;
547#else
548 (Bigint *v)
549#endif
550{
551 if (v) {
552 ACQUIRE_DTOA_LOCK(0);
553 v->next = freelist[v->k];
554 freelist[v->k] = v;
555 FREE_DTOA_LOCK(0);
556 }
557 }
558
559#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
560y->wds*sizeof(Long) + 2*sizeof(int))
561
562 static Bigint *
563multadd
564#ifdef KR_headers
565 (b, m, a) Bigint *b; int m, a;
566#else
567 (Bigint *b, int m, int a) /* multiply by m and add a */
568#endif
569{
570 int i, wds;
571#ifdef ULLong
572 ULong *x;
573 ULLong carry, y;
574#else
575 ULong carry, *x, y;
576#ifdef Pack_32
577 ULong xi, z;
578#endif
579#endif
580 Bigint *b1;
581
582 wds = b->wds;
583 x = b->x;
584 i = 0;
585 carry = a;
586 do {
587#ifdef ULLong
588 y = *x * (ULLong)m + carry;
589 carry = y >> 32;
590 *x++ = y & FFFFFFFF;
591#else
592#ifdef Pack_32
593 xi = *x;
594 y = (xi & 0xffff) * m + carry;
595 z = (xi >> 16) * m + (y >> 16);
596 carry = z >> 16;
597 *x++ = (z << 16) + (y & 0xffff);
598#else
599 y = *x * m + carry;
600 carry = y >> 16;
601 *x++ = y & 0xffff;
602#endif
603#endif
604 }
605 while(++i < wds);
606 if (carry) {
607 if (wds >= b->maxwds) {
608 b1 = Balloc(b->k+1);
609 Bcopy(b1, b);
610 Bfree(b);
611 b = b1;
612 }
613 b->x[wds++] = carry;
614 b->wds = wds;
615 }
616 return b;
617 }
618
619 static Bigint *
620s2b
621#ifdef KR_headers
622 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
623#else
624 (CONST char *s, int nd0, int nd, ULong y9)
625#endif
626{
627 Bigint *b;
628 int i, k;
629 Long x, y;
630
631 x = (nd + 8) / 9;
632 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
633#ifdef Pack_32
634 b = Balloc(k);
635 b->x[0] = y9;
636 b->wds = 1;
637#else
638 b = Balloc(k+1);
639 b->x[0] = y9 & 0xffff;
640 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
641#endif
642
643 i = 9;
644 if (9 < nd0) {
645 s += 9;
646 do b = multadd(b, 10, *s++ - '0');
647 while(++i < nd0);
648 s++;
649 }
650 else
651 s += 10;
652 for(; i < nd; i++)
653 b = multadd(b, 10, *s++ - '0');
654 return b;
655 }
656
657 static int
658hi0bits
659#ifdef KR_headers
660 (x) register ULong x;
661#else
662 (register ULong x)
663#endif
664{
665 register int k = 0;
666
667 if (!(x & 0xffff0000)) {
668 k = 16;
669 x <<= 16;
670 }
671 if (!(x & 0xff000000)) {
672 k += 8;
673 x <<= 8;
674 }
675 if (!(x & 0xf0000000)) {
676 k += 4;
677 x <<= 4;
678 }
679 if (!(x & 0xc0000000)) {
680 k += 2;
681 x <<= 2;
682 }
683 if (!(x & 0x80000000)) {
684 k++;
685 if (!(x & 0x40000000))
686 return 32;
687 }
688 return k;
689 }
690
691 static int
692lo0bits
693#ifdef KR_headers
694 (y) ULong *y;
695#else
696 (ULong *y)
697#endif
698{
699 register int k;
700 register ULong x = *y;
701
702 if (x & 7) {
703 if (x & 1)
704 return 0;
705 if (x & 2) {
706 *y = x >> 1;
707 return 1;
708 }
709 *y = x >> 2;
710 return 2;
711 }
712 k = 0;
713 if (!(x & 0xffff)) {
714 k = 16;
715 x >>= 16;
716 }
717 if (!(x & 0xff)) {
718 k += 8;
719 x >>= 8;
720 }
721 if (!(x & 0xf)) {
722 k += 4;
723 x >>= 4;
724 }
725 if (!(x & 0x3)) {
726 k += 2;
727 x >>= 2;
728 }
729 if (!(x & 1)) {
730 k++;
731 x >>= 1;
732 if (!x & 1)
733 return 32;
734 }
735 *y = x;
736 return k;
737 }
738
739 static Bigint *
740i2b
741#ifdef KR_headers
742 (i) int i;
743#else
744 (int i)
745#endif
746{
747 Bigint *b;
748
749 b = Balloc(1);
750 b->x[0] = i;
751 b->wds = 1;
752 return b;
753 }
754
755 static Bigint *
756mult
757#ifdef KR_headers
758 (a, b) Bigint *a, *b;
759#else
760 (Bigint *a, Bigint *b)
761#endif
762{
763 Bigint *c;
764 int k, wa, wb, wc;
765 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
766 ULong y;
767#ifdef ULLong
768 ULLong carry, z;
769#else
770 ULong carry, z;
771#ifdef Pack_32
772 ULong z2;
773#endif
774#endif
775
776 if (a->wds < b->wds) {
777 c = a;
778 a = b;
779 b = c;
780 }
781 k = a->k;
782 wa = a->wds;
783 wb = b->wds;
784 wc = wa + wb;
785 if (wc > a->maxwds)
786 k++;
787 c = Balloc(k);
788 for(x = c->x, xa = x + wc; x < xa; x++)
789 *x = 0;
790 xa = a->x;
791 xae = xa + wa;
792 xb = b->x;
793 xbe = xb + wb;
794 xc0 = c->x;
795#ifdef ULLong
796 for(; xb < xbe; xc0++) {
797 if ((y = *xb++)) {
798 x = xa;
799 xc = xc0;
800 carry = 0;
801 do {
802 z = *x++ * (ULLong)y + *xc + carry;
803 carry = z >> 32;
804 *xc++ = z & FFFFFFFF;
805 }
806 while(x < xae);
807 *xc = carry;
808 }
809 }
810#else
811#ifdef Pack_32
812 for(; xb < xbe; xb++, xc0++) {
813 if (y = *xb & 0xffff) {
814 x = xa;
815 xc = xc0;
816 carry = 0;
817 do {
818 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
819 carry = z >> 16;
820 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
821 carry = z2 >> 16;
822 Storeinc(xc, z2, z);
823 }
824 while(x < xae);
825 *xc = carry;
826 }
827 if (y = *xb >> 16) {
828 x = xa;
829 xc = xc0;
830 carry = 0;
831 z2 = *xc;
832 do {
833 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
834 carry = z >> 16;
835 Storeinc(xc, z, z2);
836 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
837 carry = z2 >> 16;
838 }
839 while(x < xae);
840 *xc = z2;
841 }
842 }
843#else
844 for(; xb < xbe; xc0++) {
845 if (y = *xb++) {
846 x = xa;
847 xc = xc0;
848 carry = 0;
849 do {
850 z = *x++ * y + *xc + carry;
851 carry = z >> 16;
852 *xc++ = z & 0xffff;
853 }
854 while(x < xae);
855 *xc = carry;
856 }
857 }
858#endif
859#endif
860 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
861 c->wds = wc;
862 return c;
863 }
864
865 static Bigint *p5s;
866
867 static Bigint *
868pow5mult
869#ifdef KR_headers
870 (b, k) Bigint *b; int k;
871#else
872 (Bigint *b, int k)
873#endif
874{
875 Bigint *b1, *p5, *p51;
876 int i;
877 static int p05[3] = { 5, 25, 125 };
878
879 if ((i = k & 3))
880 b = multadd(b, p05[i-1], 0);
881
882 if (!(k >>= 2))
883 return b;
884 if (!(p5 = p5s)) {
885 /* first time */
886#ifdef MULTIPLE_THREADS
887 ACQUIRE_DTOA_LOCK(1);
888 if (!(p5 = p5s)) {
889 p5 = p5s = i2b(625);
890 p5->next = 0;
891 }
892 FREE_DTOA_LOCK(1);
893#else
894 p5 = p5s = i2b(625);
895 p5->next = 0;
896#endif
897 }
898 for(;;) {
899 if (k & 1) {
900 b1 = mult(b, p5);
901 Bfree(b);
902 b = b1;
903 }
904 if (!(k >>= 1))
905 break;
906 if (!(p51 = p5->next)) {
907#ifdef MULTIPLE_THREADS
908 ACQUIRE_DTOA_LOCK(1);
909 if (!(p51 = p5->next)) {
910 p51 = p5->next = mult(p5,p5);
911 p51->next = 0;
912 }
913 FREE_DTOA_LOCK(1);
914#else
915 p51 = p5->next = mult(p5,p5);
916 p51->next = 0;
917#endif
918 }
919 p5 = p51;
920 }
921 return b;
922 }
923
924 static Bigint *
925lshift
926#ifdef KR_headers
927 (b, k) Bigint *b; int k;
928#else
929 (Bigint *b, int k)
930#endif
931{
932 int i, k1, n, n1;
933 Bigint *b1;
934 ULong *x, *x1, *xe, z;
935
936#ifdef Pack_32
937 n = k >> 5;
938#else
939 n = k >> 4;
940#endif
941 k1 = b->k;
942 n1 = n + b->wds + 1;
943 for(i = b->maxwds; n1 > i; i <<= 1)
944 k1++;
945 b1 = Balloc(k1);
946 x1 = b1->x;
947 for(i = 0; i < n; i++)
948 *x1++ = 0;
949 x = b->x;
950 xe = x + b->wds;
951#ifdef Pack_32
952 if (k &= 0x1f) {
953 k1 = 32 - k;
954 z = 0;
955 do {
956 *x1++ = *x << k | z;
957 z = *x++ >> k1;
958 }
959 while(x < xe);
960 if ((*x1 = z))
961 ++n1;
962 }
963#else
964 if (k &= 0xf) {
965 k1 = 16 - k;
966 z = 0;
967 do {
968 *x1++ = *x << k & 0xffff | z;
969 z = *x++ >> k1;
970 }
971 while(x < xe);
972 if (*x1 = z)
973 ++n1;
974 }
975#endif
976 else do
977 *x1++ = *x++;
978 while(x < xe);
979 b1->wds = n1 - 1;
980 Bfree(b);
981 return b1;
982 }
983
984 static int
985cmp
986#ifdef KR_headers
987 (a, b) Bigint *a, *b;
988#else
989 (Bigint *a, Bigint *b)
990#endif
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
1018 static Bigint *
1019diff
1020#ifdef KR_headers
1021 (a, b) Bigint *a, *b;
1022#else
1023 (Bigint *a, Bigint *b)
1024#endif
1025{
1026 Bigint *c;
1027 int i, wa, wb;
1028 ULong *xa, *xae, *xb, *xbe, *xc;
1029#ifdef ULLong
1030 ULLong borrow, y;
1031#else
1032 ULong borrow, y;
1033#ifdef Pack_32
1034 ULong z;
1035#endif
1036#endif
1037
1038 i = cmp(a,b);
1039 if (!i) {
1040 c = Balloc(0);
1041 c->wds = 1;
1042 c->x[0] = 0;
1043 return c;
1044 }
1045 if (i < 0) {
1046 c = a;
1047 a = b;
1048 b = c;
1049 i = 1;
1050 }
1051 else
1052 i = 0;
1053 c = Balloc(a->k);
1054 c->sign = i;
1055 wa = a->wds;
1056 xa = a->x;
1057 xae = xa + wa;
1058 wb = b->wds;
1059 xb = b->x;
1060 xbe = xb + wb;
1061 xc = c->x;
1062 borrow = 0;
1063#ifdef ULLong
1064 do {
1065 y = (ULLong)*xa++ - *xb++ - borrow;
1066 borrow = y >> 32 & (ULong)1;
1067 *xc++ = y & FFFFFFFF;
1068 }
1069 while(xb < xbe);
1070 while(xa < xae) {
1071 y = *xa++ - borrow;
1072 borrow = y >> 32 & (ULong)1;
1073 *xc++ = y & FFFFFFFF;
1074 }
1075#else
1076#ifdef Pack_32
1077 do {
1078 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1079 borrow = (y & 0x10000) >> 16;
1080 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1081 borrow = (z & 0x10000) >> 16;
1082 Storeinc(xc, z, y);
1083 }
1084 while(xb < xbe);
1085 while(xa < xae) {
1086 y = (*xa & 0xffff) - borrow;
1087 borrow = (y & 0x10000) >> 16;
1088 z = (*xa++ >> 16) - borrow;
1089 borrow = (z & 0x10000) >> 16;
1090 Storeinc(xc, z, y);
1091 }
1092#else
1093 do {
1094 y = *xa++ - *xb++ - borrow;
1095 borrow = (y & 0x10000) >> 16;
1096 *xc++ = y & 0xffff;
1097 }
1098 while(xb < xbe);
1099 while(xa < xae) {
1100 y = *xa++ - borrow;
1101 borrow = (y & 0x10000) >> 16;
1102 *xc++ = y & 0xffff;
1103 }
1104#endif
1105#endif
1106 while(!*--xc)
1107 wa--;
1108 c->wds = wa;
1109 return c;
1110 }
1111
1112 static double
1113ulp
1114#ifdef KR_headers
1115 (x) double x;
1116#else
1117 (double x)
1118#endif
1119{
1120 register Long L;
1121 double a;
1122
1123 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1124#ifndef Avoid_Underflow
1125#ifndef Sudden_Underflow
1126 if (L > 0) {
1127#endif
1128#endif
1129#ifdef IBM
1130 L |= Exp_msk1 >> 4;
1131#endif
1132 word0(a) = L;
1133 word1(a) = 0;
1134#ifndef Avoid_Underflow
1135#ifndef Sudden_Underflow
1136 }
1137 else {
1138 L = -L >> Exp_shift;
1139 if (L < Exp_shift) {
1140 word0(a) = 0x80000 >> L;
1141 word1(a) = 0;
1142 }
1143 else {
1144 word0(a) = 0;
1145 L -= Exp_shift;
1146 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1147 }
1148 }
1149#endif
1150#endif
1151 return dval(a);
1152 }
1153
1154 static double
1155b2d
1156#ifdef KR_headers
1157 (a, e) Bigint *a; int *e;
1158#else
1159 (Bigint *a, int *e)
1160#endif
1161{
1162 ULong *xa, *xa0, w, y, z;
1163 int k;
1164 double d;
1165#ifdef VAX
1166 ULong d0, d1;
1167#else
1168#define d0 word0(d)
1169#define d1 word1(d)
1170#endif
1171
1172 xa0 = a->x;
1173 xa = xa0 + a->wds;
1174 y = *--xa;
1175#ifdef DEBUG
1176 if (!y) Bug("zero y in b2d");
1177#endif
1178 k = hi0bits(y);
1179 *e = 32 - k;
1180#ifdef Pack_32
1181 if (k < Ebits) {
1182 d0 = Exp_1 | y >> Ebits - k;
1183 w = xa > xa0 ? *--xa : 0;
1184 d1 = y << (32-Ebits) + k | w >> Ebits - k;
1185 goto ret_d;
1186 }
1187 z = xa > xa0 ? *--xa : 0;
1188 if (k -= Ebits) {
1189 d0 = Exp_1 | y << k | z >> 32 - k;
1190 y = xa > xa0 ? *--xa : 0;
1191 d1 = z << k | y >> 32 - k;
1192 }
1193 else {
1194 d0 = Exp_1 | y;
1195 d1 = z;
1196 }
1197#else
1198 if (k < Ebits + 16) {
1199 z = xa > xa0 ? *--xa : 0;
1200 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1201 w = xa > xa0 ? *--xa : 0;
1202 y = xa > xa0 ? *--xa : 0;
1203 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1204 goto ret_d;
1205 }
1206 z = xa > xa0 ? *--xa : 0;
1207 w = xa > xa0 ? *--xa : 0;
1208 k -= Ebits + 16;
1209 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1210 y = xa > xa0 ? *--xa : 0;
1211 d1 = w << k + 16 | y << k;
1212#endif
1213 ret_d:
1214#ifdef VAX
1215 word0(d) = d0 >> 16 | d0 << 16;
1216 word1(d) = d1 >> 16 | d1 << 16;
1217#else
1218#undef d0
1219#undef d1
1220#endif
1221 return dval(d);
1222 }
1223
1224 static Bigint *
1225d2b
1226#ifdef KR_headers
1227 (d, e, bits) double d; int *e, *bits;
1228#else
1229 (double d, int *e, int *bits)
1230#endif
1231{
1232 Bigint *b;
1233 int de, k;
1234 ULong *x, y, z;
1235#ifndef Sudden_Underflow
1236 int i;
1237#endif
1238#ifdef VAX
1239 ULong d0, d1;
1240 d0 = word0(d) >> 16 | word0(d) << 16;
1241 d1 = word1(d) >> 16 | word1(d) << 16;
1242#else
1243#define d0 word0(d)
1244#define d1 word1(d)
1245#endif
1246
1247#ifdef Pack_32
1248 b = Balloc(1);
1249#else
1250 b = Balloc(2);
1251#endif
1252 x = b->x;
1253
1254 z = d0 & Frac_mask;
1255 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1256#ifdef Sudden_Underflow
1257 de = (int)(d0 >> Exp_shift);
1258#ifndef IBM
1259 z |= Exp_msk11;
1260#endif
1261#else
1262 if ((de = (int)(d0 >> Exp_shift)))
1263 z |= Exp_msk1;
1264#endif
1265#ifdef Pack_32
1266 if ((y = d1)) {
1267 if ((k = lo0bits(&y))) {
1268 x[0] = y | z << 32 - k;
1269 z >>= k;
1270 }
1271 else
1272 x[0] = y;
1273#ifndef Sudden_Underflow
1274 i =
1275#endif
1276 b->wds = (x[1] = z) ? 2 : 1;
1277 }
1278 else {
1279#ifdef DEBUG
1280 if (!z)
1281 Bug("Zero passed to d2b");
1282#endif
1283 k = lo0bits(&z);
1284 x[0] = z;
1285#ifndef Sudden_Underflow
1286 i =
1287#endif
1288 b->wds = 1;
1289 k += 32;
1290 }
1291#else
1292 if (y = d1) {
1293 if (k = lo0bits(&y))
1294 if (k >= 16) {
1295 x[0] = y | z << 32 - k & 0xffff;
1296 x[1] = z >> k - 16 & 0xffff;
1297 x[2] = z >> k;
1298 i = 2;
1299 }
1300 else {
1301 x[0] = y & 0xffff;
1302 x[1] = y >> 16 | z << 16 - k & 0xffff;
1303 x[2] = z >> k & 0xffff;
1304 x[3] = z >> k+16;
1305 i = 3;
1306 }
1307 else {
1308 x[0] = y & 0xffff;
1309 x[1] = y >> 16;
1310 x[2] = z & 0xffff;
1311 x[3] = z >> 16;
1312 i = 3;
1313 }
1314 }
1315 else {
1316#ifdef DEBUG
1317 if (!z)
1318 Bug("Zero passed to d2b");
1319#endif
1320 k = lo0bits(&z);
1321 if (k >= 16) {
1322 x[0] = z;
1323 i = 0;
1324 }
1325 else {
1326 x[0] = z & 0xffff;
1327 x[1] = z >> 16;
1328 i = 1;
1329 }
1330 k += 32;
1331 }
1332 while(!x[i])
1333 --i;
1334 b->wds = i + 1;
1335#endif
1336#ifndef Sudden_Underflow
1337 if (de) {
1338#endif
1339#ifdef IBM
1340 *e = (de - Bias - (P-1) << 2) + k;
1341 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1342#else
1343 *e = de - Bias - (P-1) + k;
1344 *bits = P - k;
1345#endif
1346#ifndef Sudden_Underflow
1347 }
1348 else {
1349 *e = de - Bias - (P-1) + 1 + k;
1350#ifdef Pack_32
1351 *bits = 32*i - hi0bits(x[i-1]);
1352#else
1353 *bits = (i+2)*16 - hi0bits(x[i]);
1354#endif
1355 }
1356#endif
1357 return b;
1358 }
1359#undef d0
1360#undef d1
1361
1362 static double
1363ratio
1364#ifdef KR_headers
1365 (a, b) Bigint *a, *b;
1366#else
1367 (Bigint *a, Bigint *b)
1368#endif
1369{
1370 double da, db;
1371 int k, ka, kb;
1372
1373 dval(da) = b2d(a, &ka);
1374 dval(db) = b2d(b, &kb);
1375#ifdef Pack_32
1376 k = ka - kb + 32*(a->wds - b->wds);
1377#else
1378 k = ka - kb + 16*(a->wds - b->wds);
1379#endif
1380#ifdef IBM
1381 if (k > 0) {
1382 word0(da) += (k >> 2)*Exp_msk1;
1383 if (k &= 3)
1384 dval(da) *= 1 << k;
1385 }
1386 else {
1387 k = -k;
1388 word0(db) += (k >> 2)*Exp_msk1;
1389 if (k &= 3)
1390 dval(db) *= 1 << k;
1391 }
1392#else
1393 if (k > 0)
1394 word0(da) += k*Exp_msk1;
1395 else {
1396 k = -k;
1397 word0(db) += k*Exp_msk1;
1398 }
1399#endif
1400 return dval(da) / dval(db);
1401 }
1402
1403 static CONST double
1404tens[] = {
1405 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1406 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1407 1e20, 1e21, 1e22
1408#ifdef VAX
1409 , 1e23, 1e24
1410#endif
1411 };
1412
1413 static CONST double
1414#ifdef IEEE_Arith
1415bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1416static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1417#ifdef Avoid_Underflow
1418 9007199254740992.*9007199254740992.e-256
1419 /* = 2^106 * 1e-53 */
1420#else
1421 1e-256
1422#endif
1423 };
1424/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1425/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1426#define Scale_Bit 0x10
1427#define n_bigtens 5
1428#else
1429#ifdef IBM
1430bigtens[] = { 1e16, 1e32, 1e64 };
1431static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1432#define n_bigtens 3
1433#else
1434bigtens[] = { 1e16, 1e32 };
1435static CONST double tinytens[] = { 1e-16, 1e-32 };
1436#define n_bigtens 2
1437#endif
1438#endif
1439
1440#ifndef IEEE_Arith
1441#undef INFNAN_CHECK
1442#endif
1443
1444#ifdef INFNAN_CHECK
1445
1446#ifndef NAN_WORD0
1447#define NAN_WORD0 0x7ff80000
1448#endif
1449
1450#ifndef NAN_WORD1
1451#define NAN_WORD1 0
1452#endif
1453
1454 static int
1455match
1456#ifdef KR_headers
1457 (sp, t) char **sp, *t;
1458#else
1459 (CONST char **sp, CONST char *t)
1460#endif
1461{
1462 int c, d;
1463 CONST char *s = *sp;
1464
1465 while((d = *t++)) {
1466 if ((c = *++s) >= 'A' && c <= 'Z')
1467 c += 'a' - 'A';
1468 if (c != d)
1469 return 0;
1470 }
1471 *sp = s + 1;
1472 return 1;
1473 }
1474
1475#ifndef No_Hex_NaN
1476 static void
1477hexnan
1478#ifdef KR_headers
1479 (rvp, sp) double *rvp; CONST char **sp;
1480#else
1481 (double *rvp, CONST char **sp)
1482#endif
1483{
1484 ULong c, x[2];
1485 CONST char *s;
1486 int havedig, udx0, xshift;
1487
1488 x[0] = x[1] = 0;
1489 havedig = xshift = 0;
1490 udx0 = 1;
1491 s = *sp;
1492 while((c = *(CONST unsigned char*)++s)) {
1493 if (c >= '0' && c <= '9')
1494 c -= '0';
1495 else if (c >= 'a' && c <= 'f')
1496 c += 10 - 'a';
1497 else if (c >= 'A' && c <= 'F')
1498 c += 10 - 'A';
1499 else if (c <= ' ') {
1500 if (udx0 && havedig) {
1501 udx0 = 0;
1502 xshift = 1;
1503 }
1504 continue;
1505 }
1506 else if (/*(*/ c == ')' && havedig) {
1507 *sp = s + 1;
1508 break;
1509 }
1510 else
1511 return; /* invalid form: don't change *sp */
1512 havedig = 1;
1513 if (xshift) {
1514 xshift = 0;
1515 x[0] = x[1];
1516 x[1] = 0;
1517 }
1518 if (udx0)
1519 x[0] = (x[0] << 4) | (x[1] >> 28);
1520 x[1] = (x[1] << 4) | c;
1521 }
1522 if ((x[0] &= 0xfffff) || x[1]) {
1523 word0(*rvp) = Exp_mask | x[0];
1524 word1(*rvp) = x[1];
1525 }
1526 }
1527#endif /*No_Hex_NaN*/
1528#endif /* INFNAN_CHECK */
1529
1530 double
1531strtod
1532#ifdef KR_headers
1533 (s00, se) CONST char *s00; char **se;
1534#else
1535 (CONST char *s00, char **se)
1536#endif
1537{
1538#ifdef Avoid_Underflow
1539 int scale;
1540#endif
1541 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1542 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1543 CONST char *s, *s0, *s1;
1544 double aadj, aadj1, adj, rv, rv0;
1545 Long L;
1546 ULong y, z;
1547 Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
1548#ifdef SET_INEXACT
1549 int inexact, oldinexact;
1550#endif
1551#ifdef Honor_FLT_ROUNDS
1552 int rounding;
1553#endif
1554#ifdef USE_LOCALE
1555 CONST char *s2;
1556#endif
1557
1558 sign = nz0 = nz = 0;
1559 dval(rv) = 0.;
1560 for(s = s00;;s++) switch(*s) {
1561 case '-':
1562 sign = 1;
1563 /* no break */
1564 case '+':
1565 if (*++s)
1566 goto break2;
1567 /* no break */
1568 case 0:
1569 goto ret0;
1570 case '\t':
1571 case '\n':
1572 case '\v':
1573 case '\f':
1574 case '\r':
1575 case ' ':
1576 continue;
1577 default:
1578 goto break2;
1579 }
1580 break2:
1581 if (*s == '0') {
1582 nz0 = 1;
1583 while(*++s == '0') ;
1584 if (!*s)
1585 goto ret;
1586 }
1587 s0 = s;
1588 y = z = 0;
1589 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1590 if (nd < 9)
1591 y = 10*y + c - '0';
1592 else if (nd < 16)
1593 z = 10*z + c - '0';
1594 nd0 = nd;
1595#ifdef USE_LOCALE
1596 s1 = localeconv()->decimal_point;
1597 if (c == *s1) {
1598 c = '.';
1599 if (*++s1) {
1600 s2 = s;
1601 for(;;) {
1602 if (*++s2 != *s1) {
1603 c = 0;
1604 break;
1605 }
1606 if (!*++s1) {
1607 s = s2;
1608 break;
1609 }
1610 }
1611 }
1612 }
1613#endif
1614 if (c == '.') {
1615 c = *++s;
1616 if (!nd) {
1617 for(; c == '0'; c = *++s)
1618 nz++;
1619 if (c > '0' && c <= '9') {
1620 s0 = s;
1621 nf += nz;
1622 nz = 0;
1623 goto have_dig;
1624 }
1625 goto dig_done;
1626 }
1627 for(; c >= '0' && c <= '9'; c = *++s) {
1628 have_dig:
1629 nz++;
1630 if (c -= '0') {
1631 nf += nz;
1632 for(i = 1; i < nz; i++)
1633 if (nd++ < 9)
1634 y *= 10;
1635 else if (nd <= DBL_DIG + 1)
1636 z *= 10;
1637 if (nd++ < 9)
1638 y = 10*y + c;
1639 else if (nd <= DBL_DIG + 1)
1640 z = 10*z + c;
1641 nz = 0;
1642 }
1643 }
1644 }
1645 dig_done:
1646 e = 0;
1647 if (c == 'e' || c == 'E') {
1648 if (!nd && !nz && !nz0) {
1649 goto ret0;
1650 }
1651 s00 = s;
1652 esign = 0;
1653 switch(c = *++s) {
1654 case '-':
1655 esign = 1;
1656 case '+':
1657 c = *++s;
1658 }
1659 if (c >= '0' && c <= '9') {
1660 while(c == '0')
1661 c = *++s;
1662 if (c > '0' && c <= '9') {
1663 L = c - '0';
1664 s1 = s;
1665 while((c = *++s) >= '0' && c <= '9')
1666 L = 10*L + c - '0';
1667 if (s - s1 > 8 || L > 19999)
1668 /* Avoid confusion from exponents
1669 * so large that e might overflow.
1670 */
1671 e = 19999; /* safe for 16 bit ints */
1672 else
1673 e = (int)L;
1674 if (esign)
1675 e = -e;
1676 }
1677 else
1678 e = 0;
1679 }
1680 else
1681 s = s00;
1682 }
1683 if (!nd) {
1684 if (!nz && !nz0) {
1685#ifdef INFNAN_CHECK
1686 /* Check for Nan and Infinity */
1687 switch(c) {
1688 case 'i':
1689 case 'I':
1690 if (match(&s,"nf")) {
1691 --s;
1692 if (!match(&s,"inity"))
1693 ++s;
1694 word0(rv) = 0x7ff00000;
1695 word1(rv) = 0;
1696 goto ret;
1697 }
1698 break;
1699 case 'n':
1700 case 'N':
1701 if (match(&s, "an")) {
1702 word0(rv) = NAN_WORD0;
1703 word1(rv) = NAN_WORD1;
1704#ifndef No_Hex_NaN
1705 if (*s == '(') /*)*/
1706 hexnan(&rv, &s);
1707#endif
1708 goto ret;
1709 }
1710 }
1711#endif /* INFNAN_CHECK */
1712 ret0:
1713 s = s00;
1714 sign = 0;
1715 }
1716 goto ret;
1717 }
1718 e1 = e -= nf;
1719
1720 /* Now we have nd0 digits, starting at s0, followed by a
1721 * decimal point, followed by nd-nd0 digits. The number we're
1722 * after is the integer represented by those digits times
1723 * 10**e */
1724
1725 if (!nd0)
1726 nd0 = nd;
1727 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1728 dval(rv) = y;
1729 if (k > 9) {
1730#ifdef SET_INEXACT
1731 if (k > DBL_DIG)
1732 oldinexact = get_inexact();
1733#endif
1734 dval(rv) = tens[k - 9] * dval(rv) + z;
1735 }
1736 bd0 = 0;
1737 if (nd <= DBL_DIG
1738#ifndef RND_PRODQUOT
1739#ifndef Honor_FLT_ROUNDS
1740 && Flt_Rounds == 1
1741#endif
1742#endif
1743 ) {
1744 if (!e)
1745 goto ret;
1746 if (e > 0) {
1747 if (e <= Ten_pmax) {
1748#ifdef VAX
1749 goto vax_ovfl_check;
1750#else
1751#ifdef Honor_FLT_ROUNDS
1752 /* round correctly FLT_ROUNDS = 2 or 3 */
1753 if (sign) {
1754 rv = -rv;
1755 sign = 0;
1756 }
1757#endif
1758 /* rv = */ rounded_product(dval(rv), tens[e]);
1759 goto ret;
1760#endif
1761 }
1762 i = DBL_DIG - nd;
1763 if (e <= Ten_pmax + i) {
1764 /* A fancier test would sometimes let us do
1765 * this for larger i values.
1766 */
1767#ifdef Honor_FLT_ROUNDS
1768 /* round correctly FLT_ROUNDS = 2 or 3 */
1769 if (sign) {
1770 rv = -rv;
1771 sign = 0;
1772 }
1773#endif
1774 e -= i;
1775 dval(rv) *= tens[i];
1776#ifdef VAX
1777 /* VAX exponent range is so narrow we must
1778 * worry about overflow here...
1779 */
1780 vax_ovfl_check:
1781 word0(rv) -= P*Exp_msk1;
1782 /* rv = */ rounded_product(dval(rv), tens[e]);
1783 if ((word0(rv) & Exp_mask)
1784 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1785 goto ovfl;
1786 word0(rv) += P*Exp_msk1;
1787#else
1788 /* rv = */ rounded_product(dval(rv), tens[e]);
1789#endif
1790 goto ret;
1791 }
1792 }
1793#ifndef Inaccurate_Divide
1794 else if (e >= -Ten_pmax) {
1795#ifdef Honor_FLT_ROUNDS
1796 /* round correctly FLT_ROUNDS = 2 or 3 */
1797 if (sign) {
1798 rv = -rv;
1799 sign = 0;
1800 }
1801#endif
1802 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1803 goto ret;
1804 }
1805#endif
1806 }
1807 e1 += nd - k;
1808
1809#ifdef IEEE_Arith
1810#ifdef SET_INEXACT
1811 inexact = 1;
1812 if (k <= DBL_DIG)
1813 oldinexact = get_inexact();
1814#endif
1815#ifdef Avoid_Underflow
1816 scale = 0;
1817#endif
1818#ifdef Honor_FLT_ROUNDS
1819 if ((rounding = Flt_Rounds) >= 2) {
1820 if (sign)
1821 rounding = rounding == 2 ? 0 : 2;
1822 else
1823 if (rounding != 2)
1824 rounding = 0;
1825 }
1826#endif
1827#endif /*IEEE_Arith*/
1828
1829 /* Get starting approximation = rv * 10**e1 */
1830
1831 if (e1 > 0) {
1832 if ((i = e1 & 15))
1833 dval(rv) *= tens[i];
1834 if (e1 &= ~15) {
1835 if (e1 > DBL_MAX_10_EXP) {
1836 ovfl:
1837#ifndef NO_ERRNO
1838 errno = ERANGE;
1839#endif
1840 /* Can't trust HUGE_VAL */
1841#ifdef IEEE_Arith
1842#ifdef Honor_FLT_ROUNDS
1843 switch(rounding) {
1844 case 0: /* toward 0 */
1845 case 3: /* toward -infinity */
1846 word0(rv) = Big0;
1847 word1(rv) = Big1;
1848 break;
1849 default:
1850 word0(rv) = Exp_mask;
1851 word1(rv) = 0;
1852 }
1853#else /*Honor_FLT_ROUNDS*/
1854 word0(rv) = Exp_mask;
1855 word1(rv) = 0;
1856#endif /*Honor_FLT_ROUNDS*/
1857#ifdef SET_INEXACT
1858 /* set overflow bit */
1859 dval(rv0) = 1e300;
1860 dval(rv0) *= dval(rv0);
1861#endif
1862#else /*IEEE_Arith*/
1863 word0(rv) = Big0;
1864 word1(rv) = Big1;
1865#endif /*IEEE_Arith*/
1866 if (bd0)
1867 goto retfree;
1868 goto ret;
1869 }
1870 e1 >>= 4;
1871 for(j = 0; e1 > 1; j++, e1 >>= 1)
1872 if (e1 & 1)
1873 dval(rv) *= bigtens[j];
1874 /* The last multiplication could overflow. */
1875 word0(rv) -= P*Exp_msk1;
1876 dval(rv) *= bigtens[j];
1877 if ((z = word0(rv) & Exp_mask)
1878 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1879 goto ovfl;
1880 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1881 /* set to largest number */
1882 /* (Can't trust DBL_MAX) */
1883 word0(rv) = Big0;
1884 word1(rv) = Big1;
1885 }
1886 else
1887 word0(rv) += P*Exp_msk1;
1888 }
1889 }
1890 else if (e1 < 0) {
1891 e1 = -e1;
1892 if ((i = e1 & 15))
1893 dval(rv) /= tens[i];
1894 if (e1 >>= 4) {
1895 if (e1 >= 1 << n_bigtens)
1896 goto undfl;
1897#ifdef Avoid_Underflow
1898 if (e1 & Scale_Bit)
1899 scale = 2*P;
1900 for(j = 0; e1 > 0; j++, e1 >>= 1)
1901 if (e1 & 1)
1902 dval(rv) *= tinytens[j];
1903 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1904 >> Exp_shift)) > 0) {
1905 /* scaled rv is denormal; zap j low bits */
1906 if (j >= 32) {
1907 word1(rv) = 0;
1908 if (j >= 53)
1909 word0(rv) = (P+2)*Exp_msk1;
1910 else
1911 word0(rv) &= 0xffffffff << j-32;
1912 }
1913 else
1914 word1(rv) &= 0xffffffff << j;
1915 }
1916#else
1917 for(j = 0; e1 > 1; j++, e1 >>= 1)
1918 if (e1 & 1)
1919 dval(rv) *= tinytens[j];
1920 /* The last multiplication could underflow. */
1921 dval(rv0) = dval(rv);
1922 dval(rv) *= tinytens[j];
1923 if (!dval(rv)) {
1924 dval(rv) = 2.*dval(rv0);
1925 dval(rv) *= tinytens[j];
1926#endif
1927 if (!dval(rv)) {
1928 undfl:
1929 dval(rv) = 0.;
1930#ifndef NO_ERRNO
1931 errno = ERANGE;
1932#endif
1933 if (bd0)
1934 goto retfree;
1935 goto ret;
1936 }
1937#ifndef Avoid_Underflow
1938 word0(rv) = Tiny0;
1939 word1(rv) = Tiny1;
1940 /* The refinement below will clean
1941 * this approximation up.
1942 */
1943 }
1944#endif
1945 }
1946 }
1947
1948 /* Now the hard part -- adjusting rv to the correct value.*/
1949
1950 /* Put digits into bd: true value = bd * 10^e */
1951
1952 bd0 = s2b(s0, nd0, nd, y);
1953
1954 for(;;) {
1955 bd = Balloc(bd0->k);
1956 Bcopy(bd, bd0);
1957 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1958 bs = i2b(1);
1959
1960 if (e >= 0) {
1961 bb2 = bb5 = 0;
1962 bd2 = bd5 = e;
1963 }
1964 else {
1965 bb2 = bb5 = -e;
1966 bd2 = bd5 = 0;
1967 }
1968 if (bbe >= 0)
1969 bb2 += bbe;
1970 else
1971 bd2 -= bbe;
1972 bs2 = bb2;
1973#ifdef Honor_FLT_ROUNDS
1974 if (rounding != 1)
1975 bs2++;
1976#endif
1977#ifdef Avoid_Underflow
1978 j = bbe - scale;
1979 i = j + bbbits - 1; /* logb(rv) */
1980 if (i < Emin) /* denormal */
1981 j += P - Emin;
1982 else
1983 j = P + 1 - bbbits;
1984#else /*Avoid_Underflow*/
1985#ifdef Sudden_Underflow
1986#ifdef IBM
1987 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1988#else
1989 j = P + 1 - bbbits;
1990#endif
1991#else /*Sudden_Underflow*/
1992 j = bbe;
1993 i = j + bbbits - 1; /* logb(rv) */
1994 if (i < Emin) /* denormal */
1995 j += P - Emin;
1996 else
1997 j = P + 1 - bbbits;
1998#endif /*Sudden_Underflow*/
1999#endif /*Avoid_Underflow*/
2000 bb2 += j;
2001 bd2 += j;
2002#ifdef Avoid_Underflow
2003 bd2 += scale;
2004#endif
2005 i = bb2 < bd2 ? bb2 : bd2;
2006 if (i > bs2)
2007 i = bs2;
2008 if (i > 0) {
2009 bb2 -= i;
2010 bd2 -= i;
2011 bs2 -= i;
2012 }
2013 if (bb5 > 0) {
2014 bs = pow5mult(bs, bb5);
2015 bb1 = mult(bs, bb);
2016 Bfree(bb);
2017 bb = bb1;
2018 }
2019 if (bb2 > 0)
2020 bb = lshift(bb, bb2);
2021 if (bd5 > 0)
2022 bd = pow5mult(bd, bd5);
2023 if (bd2 > 0)
2024 bd = lshift(bd, bd2);
2025 if (bs2 > 0)
2026 bs = lshift(bs, bs2);
2027 delta = diff(bb, bd);
2028 dsign = delta->sign;
2029 delta->sign = 0;
2030 i = cmp(delta, bs);
2031#ifdef Honor_FLT_ROUNDS
2032 if (rounding != 1) {
2033 if (i < 0) {
2034 /* Error is less than an ulp */
2035 if (!delta->x[0] && delta->wds <= 1) {
2036 /* exact */
2037#ifdef SET_INEXACT
2038 inexact = 0;
2039#endif
2040 break;
2041 }
2042 if (rounding) {
2043 if (dsign) {
2044 adj = 1.;
2045 goto apply_adj;
2046 }
2047 }
2048 else if (!dsign) {
2049 adj = -1.;
2050 if (!word1(rv)
2051 && !(word0(rv) & Frac_mask)) {
2052 y = word0(rv) & Exp_mask;
2053#ifdef Avoid_Underflow
2054 if (!scale || y > 2*P*Exp_msk1)
2055#else
2056 if (y)
2057#endif
2058 {
2059 delta = lshift(delta,Log2P);
2060 if (cmp(delta, bs) <= 0)
2061 adj = -0.5;
2062 }
2063 }
2064 apply_adj:
2065#ifdef Avoid_Underflow
2066 if (scale && (y = word0(rv) & Exp_mask)
2067 <= 2*P*Exp_msk1)
2068 word0(adj) += (2*P+1)*Exp_msk1 - y;
2069#else
2070#ifdef Sudden_Underflow
2071 if ((word0(rv) & Exp_mask) <=
2072 P*Exp_msk1) {
2073 word0(rv) += P*Exp_msk1;
2074 dval(rv) += adj*ulp(dval(rv));
2075 word0(rv) -= P*Exp_msk1;
2076 }
2077 else
2078#endif /*Sudden_Underflow*/
2079#endif /*Avoid_Underflow*/
2080 dval(rv) += adj*ulp(dval(rv));
2081 }
2082 break;
2083 }
2084 adj = ratio(delta, bs);
2085 if (adj < 1.)
2086 adj = 1.;
2087 if (adj <= 0x7ffffffe) {
2088 /* adj = rounding ? ceil(adj) : floor(adj); */
2089 y = adj;
2090 if (y != adj) {
2091 if (!((rounding>>1) ^ dsign))
2092 y++;
2093 adj = y;
2094 }
2095 }
2096#ifdef Avoid_Underflow
2097 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2098 word0(adj) += (2*P+1)*Exp_msk1 - y;
2099#else
2100#ifdef Sudden_Underflow
2101 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2102 word0(rv) += P*Exp_msk1;
2103 adj *= ulp(dval(rv));
2104 if (dsign)
2105 dval(rv) += adj;
2106 else
2107 dval(rv) -= adj;
2108 word0(rv) -= P*Exp_msk1;
2109 goto cont;
2110 }
2111#endif /*Sudden_Underflow*/
2112#endif /*Avoid_Underflow*/
2113 adj *= ulp(dval(rv));
2114 if (dsign)
2115 dval(rv) += adj;
2116 else
2117 dval(rv) -= adj;
2118 goto cont;
2119 }
2120#endif /*Honor_FLT_ROUNDS*/
2121
2122 if (i < 0) {
2123 /* Error is less than half an ulp -- check for
2124 * special case of mantissa a power of two.
2125 */
2126 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2127#ifdef IEEE_Arith
2128#ifdef Avoid_Underflow
2129 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2130#else
2131 || (word0(rv) & Exp_mask) <= Exp_msk1
2132#endif
2133#endif
2134 ) {
2135#ifdef SET_INEXACT
2136 if (!delta->x[0] && delta->wds <= 1)
2137 inexact = 0;
2138#endif
2139 break;
2140 }
2141 if (!delta->x[0] && delta->wds <= 1) {
2142 /* exact result */
2143#ifdef SET_INEXACT
2144 inexact = 0;
2145#endif
2146 break;
2147 }
2148 delta = lshift(delta,Log2P);
2149 if (cmp(delta, bs) > 0)
2150 goto drop_down;
2151 break;
2152 }
2153 if (i == 0) {
2154 /* exactly half-way between */
2155 if (dsign) {
2156 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2157 && word1(rv) == (
2158#ifdef Avoid_Underflow
2159 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2160 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2161#endif
2162 0xffffffff)) {
2163 /*boundary case -- increment exponent*/
2164 word0(rv) = (word0(rv) & Exp_mask)
2165 + Exp_msk1
2166#ifdef IBM
2167 | Exp_msk1 >> 4
2168#endif
2169 ;
2170 word1(rv) = 0;
2171#ifdef Avoid_Underflow
2172 dsign = 0;
2173#endif
2174 break;
2175 }
2176 }
2177 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2178 drop_down:
2179 /* boundary case -- decrement exponent */
2180#ifdef Sudden_Underflow /*{{*/
2181 L = word0(rv) & Exp_mask;
2182#ifdef IBM
2183 if (L < Exp_msk1)
2184#else
2185#ifdef Avoid_Underflow
2186 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2187#else
2188 if (L <= Exp_msk1)
2189#endif /*Avoid_Underflow*/
2190#endif /*IBM*/
2191 goto undfl;
2192 L -= Exp_msk1;
2193#else /*Sudden_Underflow}{*/
2194#ifdef Avoid_Underflow
2195 if (scale) {
2196 L = word0(rv) & Exp_mask;
2197 if (L <= (2*P+1)*Exp_msk1) {
2198 if (L > (P+2)*Exp_msk1)
2199 /* round even ==> */
2200 /* accept rv */
2201 break;
2202 /* rv = smallest denormal */
2203 goto undfl;
2204 }
2205 }
2206#endif /*Avoid_Underflow*/
2207 L = (word0(rv) & Exp_mask) - Exp_msk1;
2208#endif /*Sudden_Underflow}}*/
2209 word0(rv) = L | Bndry_mask1;
2210 word1(rv) = 0xffffffff;
2211#ifdef IBM
2212 goto cont;
2213#else
2214 break;
2215#endif
2216 }
2217#ifndef ROUND_BIASED
2218 if (!(word1(rv) & LSB))
2219 break;
2220#endif
2221 if (dsign)
2222 dval(rv) += ulp(dval(rv));
2223#ifndef ROUND_BIASED
2224 else {
2225 dval(rv) -= ulp(dval(rv));
2226#ifndef Sudden_Underflow
2227 if (!dval(rv))
2228 goto undfl;
2229#endif
2230 }
2231#ifdef Avoid_Underflow
2232 dsign = 1 - dsign;
2233#endif
2234#endif
2235 break;
2236 }
2237 if ((aadj = ratio(delta, bs)) <= 2.) {
2238 if (dsign)
2239 aadj = aadj1 = 1.;
2240 else if (word1(rv) || word0(rv) & Bndry_mask) {
2241#ifndef Sudden_Underflow
2242 if (word1(rv) == Tiny1 && !word0(rv))
2243 goto undfl;
2244#endif
2245 aadj = 1.;
2246 aadj1 = -1.;
2247 }
2248 else {
2249 /* special case -- power of FLT_RADIX to be */
2250 /* rounded down... */
2251
2252 if (aadj < 2./FLT_RADIX)
2253 aadj = 1./FLT_RADIX;
2254 else
2255 aadj *= 0.5;
2256 aadj1 = -aadj;
2257 }
2258 }
2259 else {
2260 aadj *= 0.5;
2261 aadj1 = dsign ? aadj : -aadj;
2262#ifdef Check_FLT_ROUNDS
2263 switch(Rounding) {
2264 case 2: /* towards +infinity */
2265 aadj1 -= 0.5;
2266 break;
2267 case 0: /* towards 0 */
2268 case 3: /* towards -infinity */
2269 aadj1 += 0.5;
2270 }
2271#else
2272 if (Flt_Rounds == 0)
2273 aadj1 += 0.5;
2274#endif /*Check_FLT_ROUNDS*/
2275 }
2276 y = word0(rv) & Exp_mask;
2277
2278 /* Check for overflow */
2279
2280 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2281 dval(rv0) = dval(rv);
2282 word0(rv) -= P*Exp_msk1;
2283 adj = aadj1 * ulp(dval(rv));
2284 dval(rv) += adj;
2285 if ((word0(rv) & Exp_mask) >=
2286 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2287 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2288 goto ovfl;
2289 word0(rv) = Big0;
2290 word1(rv) = Big1;
2291 goto cont;
2292 }
2293 else
2294 word0(rv) += P*Exp_msk1;
2295 }
2296 else {
2297#ifdef Avoid_Underflow
2298 if (scale && y <= 2*P*Exp_msk1) {
2299 if (aadj <= 0x7fffffff) {
2300 if ((z = (ULong)aadj) <= 0)
2301 z = 1;
2302 aadj = z;
2303 aadj1 = dsign ? aadj : -aadj;
2304 }
2305 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2306 }
2307 adj = aadj1 * ulp(dval(rv));
2308 dval(rv) += adj;
2309#else
2310#ifdef Sudden_Underflow
2311 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2312 dval(rv0) = dval(rv);
2313 word0(rv) += P*Exp_msk1;
2314 adj = aadj1 * ulp(dval(rv));
2315 dval(rv) += adj;
2316#ifdef IBM
2317 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2318#else
2319 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2320#endif
2321 {
2322 if (word0(rv0) == Tiny0
2323 && word1(rv0) == Tiny1)
2324 goto undfl;
2325 word0(rv) = Tiny0;
2326 word1(rv) = Tiny1;
2327 goto cont;
2328 }
2329 else
2330 word0(rv) -= P*Exp_msk1;
2331 }
2332 else {
2333 adj = aadj1 * ulp(dval(rv));
2334 dval(rv) += adj;
2335 }
2336#else /*Sudden_Underflow*/
2337 /* Compute adj so that the IEEE rounding rules will
2338 * correctly round rv + adj in some half-way cases.
2339 * If rv * ulp(rv) is denormalized (i.e.,
2340 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2341 * trouble from bits lost to denormalization;
2342 * example: 1.2e-307 .
2343 */
2344 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2345 aadj1 = (double)(int)(aadj + 0.5);
2346 if (!dsign)
2347 aadj1 = -aadj1;
2348 }
2349 adj = aadj1 * ulp(dval(rv));
2350 dval(rv) += adj;
2351#endif /*Sudden_Underflow*/
2352#endif /*Avoid_Underflow*/
2353 }
2354 z = word0(rv) & Exp_mask;
2355#ifndef SET_INEXACT
2356#ifdef Avoid_Underflow
2357 if (!scale)
2358#endif
2359 if (y == z) {
2360 /* Can we stop now? */
2361 L = (Long)aadj;
2362 aadj -= L;
2363 /* The tolerances below are conservative. */
2364 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2365 if (aadj < .4999999 || aadj > .5000001)
2366 break;
2367 }
2368 else if (aadj < .4999999/FLT_RADIX)
2369 break;
2370 }
2371#endif
2372 cont:
2373 Bfree(bb);
2374 Bfree(bd);
2375 Bfree(bs);
2376 Bfree(delta);
2377 }
2378#ifdef SET_INEXACT
2379 if (inexact) {
2380 if (!oldinexact) {
2381 word0(rv0) = Exp_1 + (70 << Exp_shift);
2382 word1(rv0) = 0;
2383 dval(rv0) += 1.;
2384 }
2385 }
2386 else if (!oldinexact)
2387 clear_inexact();
2388#endif
2389#ifdef Avoid_Underflow
2390 if (scale) {
2391 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2392 word1(rv0) = 0;
2393 dval(rv) *= dval(rv0);
2394#ifndef NO_ERRNO
2395 /* try to avoid the bug of testing an 8087 register value */
2396 if (word0(rv) == 0 && word1(rv) == 0)
2397 errno = ERANGE;
2398#endif
2399 }
2400#endif /* Avoid_Underflow */
2401#ifdef SET_INEXACT
2402 if (inexact && !(word0(rv) & Exp_mask)) {
2403 /* set underflow bit */
2404 dval(rv0) = 1e-300;
2405 dval(rv0) *= dval(rv0);
2406 }
2407#endif
2408 retfree:
2409 Bfree(bb);
2410 Bfree(bd);
2411 Bfree(bs);
2412 Bfree(bd0);
2413 Bfree(delta);
2414 ret:
2415 if (se)
2416 *se = (char *)s;
2417 return sign ? -dval(rv) : dval(rv);
2418 }
2419
2420 static int
2421quorem
2422#ifdef KR_headers
2423 (b, S) Bigint *b, *S;
2424#else
2425 (Bigint *b, Bigint *S)
2426#endif
2427{
2428 int n;
2429 ULong *bx, *bxe, q, *sx, *sxe;
2430#ifdef ULLong
2431 ULLong borrow, carry, y, ys;
2432#else
2433 ULong borrow, carry, y, ys;
2434#ifdef Pack_32
2435 ULong si, z, zs;
2436#endif
2437#endif
2438
2439 n = S->wds;
2440#ifdef DEBUG
2441 /*debug*/ if (b->wds > n)
2442 /*debug*/ Bug("oversize b in quorem");
2443#endif
2444 if (b->wds < n)
2445 return 0;
2446 sx = S->x;
2447 sxe = sx + --n;
2448 bx = b->x;
2449 bxe = bx + n;
2450 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2451#ifdef DEBUG
2452 /*debug*/ if (q > 9)
2453 /*debug*/ Bug("oversized quotient in quorem");
2454#endif
2455 if (q) {
2456 borrow = 0;
2457 carry = 0;
2458 do {
2459#ifdef ULLong
2460 ys = *sx++ * (ULLong)q + carry;
2461 carry = ys >> 32;
2462 y = *bx - (ys & FFFFFFFF) - borrow;
2463 borrow = y >> 32 & (ULong)1;
2464 *bx++ = y & FFFFFFFF;
2465#else
2466#ifdef Pack_32
2467 si = *sx++;
2468 ys = (si & 0xffff) * q + carry;
2469 zs = (si >> 16) * q + (ys >> 16);
2470 carry = zs >> 16;
2471 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2472 borrow = (y & 0x10000) >> 16;
2473 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2474 borrow = (z & 0x10000) >> 16;
2475 Storeinc(bx, z, y);
2476#else
2477 ys = *sx++ * q + carry;
2478 carry = ys >> 16;
2479 y = *bx - (ys & 0xffff) - borrow;
2480 borrow = (y & 0x10000) >> 16;
2481 *bx++ = y & 0xffff;
2482#endif
2483#endif
2484 }
2485 while(sx <= sxe);
2486 if (!*bxe) {
2487 bx = b->x;
2488 while(--bxe > bx && !*bxe)
2489 --n;
2490 b->wds = n;
2491 }
2492 }
2493 if (cmp(b, S) >= 0) {
2494 q++;
2495 borrow = 0;
2496 carry = 0;
2497 bx = b->x;
2498 sx = S->x;
2499 do {
2500#ifdef ULLong
2501 ys = *sx++ + carry;
2502 carry = ys >> 32;
2503 y = *bx - (ys & FFFFFFFF) - borrow;
2504 borrow = y >> 32 & (ULong)1;
2505 *bx++ = y & FFFFFFFF;
2506#else
2507#ifdef Pack_32
2508 si = *sx++;
2509 ys = (si & 0xffff) + carry;
2510 zs = (si >> 16) + (ys >> 16);
2511 carry = zs >> 16;
2512 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2513 borrow = (y & 0x10000) >> 16;
2514 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2515 borrow = (z & 0x10000) >> 16;
2516 Storeinc(bx, z, y);
2517#else
2518 ys = *sx++ + carry;
2519 carry = ys >> 16;
2520 y = *bx - (ys & 0xffff) - borrow;
2521 borrow = (y & 0x10000) >> 16;
2522 *bx++ = y & 0xffff;
2523#endif
2524#endif
2525 }
2526 while(sx <= sxe);
2527 bx = b->x;
2528 bxe = bx + n;
2529 if (!*bxe) {
2530 while(--bxe > bx && !*bxe)
2531 --n;
2532 b->wds = n;
2533 }
2534 }
2535 return q;
2536 }
2537
2538#ifndef MULTIPLE_THREADS
2539 static char *dtoa_result;
2540#endif
2541
2542 static char *
2543#ifdef KR_headers
2544rv_alloc(i) int i;
2545#else
2546rv_alloc(int i)
2547#endif
2548{
2549 int j, k, *r;
2550
2551 j = sizeof(ULong);
2552 for(k = 0;
2553 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
2554 j <<= 1)
2555 k++;
2556 r = (int*)Balloc(k);
2557 *r = k;
2558 return
2559#ifndef MULTIPLE_THREADS
2560 dtoa_result =
2561#endif
2562 (char *)(r+1);
2563 }
2564
2565 static char *
2566#ifdef KR_headers
2567nrv_alloc(s, rve, n) char *s, **rve; int n;
2568#else
2569nrv_alloc(CONST char *s, char **rve, int n)
2570#endif
2571{
2572 char *rv, *t;
2573
2574 t = rv = rv_alloc(n);
2575 while((*t = *s++)) t++;
2576 if (rve)
2577 *rve = t;
2578 return rv;
2579 }
2580
2581/* freedtoa(s) must be used to free values s returned by dtoa
2582 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2583 * but for consistency with earlier versions of dtoa, it is optional
2584 * when MULTIPLE_THREADS is not defined.
2585 */
2586
2587 void
2588#ifdef KR_headers
2589freedtoa(s) char *s;
2590#else
2591freedtoa(char *s)
2592#endif
2593{
2594 Bigint *b = (Bigint *)((int *)s - 1);
2595 b->maxwds = 1 << (b->k = *(int*)b);
2596 Bfree(b);
2597#ifndef MULTIPLE_THREADS
2598 if (s == dtoa_result)
2599 dtoa_result = 0;
2600#endif
2601 }
2602
2603/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2604 *
2605 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2606 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
2607 *
2608 * Modifications:
2609 * 1. Rather than iterating, we use a simple numeric overestimate
2610 * to determine k = floor(log10(d)). We scale relevant
2611 * quantities using O(log2(k)) rather than O(k) multiplications.
2612 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2613 * try to generate digits strictly left to right. Instead, we
2614 * compute with fewer bits and propagate the carry if necessary
2615 * when rounding the final digit up. This is often faster.
2616 * 3. Under the assumption that input will be rounded nearest,
2617 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2618 * That is, we allow equality in stopping tests when the
2619 * round-nearest rule will give the same floating-point value
2620 * as would satisfaction of the stopping test with strict
2621 * inequality.
2622 * 4. We remove common factors of powers of 2 from relevant
2623 * quantities.
2624 * 5. When converting floating-point integers less than 1e16,
2625 * we use floating-point arithmetic rather than resorting
2626 * to multiple-precision integers.
2627 * 6. When asked to produce fewer than 15 digits, we first try
2628 * to get by with floating-point arithmetic; we resort to
2629 * multiple-precision integer arithmetic only if we cannot
2630 * guarantee that the floating-point calculation has given
2631 * the correctly rounded result. For k requested digits and
2632 * "uniformly" distributed input, the probability is
2633 * something like 10^(k-15) that we must resort to the Long
2634 * calculation.
2635 */
2636
2637 char *
2638dtoa
2639#ifdef KR_headers
2640 (d, mode, ndigits, decpt, sign, rve)
2641 double d; int mode, ndigits, *decpt, *sign; char **rve;
2642#else
2643 (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2644#endif
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 = 0, ilim0, ilim1 = 0,
2681 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2682 spec_case, try_quick;
2683 Long L;
2684#ifndef Sudden_Underflow
2685 int denorm;
2686 ULong x;
2687#endif
2688 Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
2689 double d2, ds, eps;
2690 char *s, *s0;
2691#ifdef Honor_FLT_ROUNDS
2692 int rounding;
2693#endif
2694#ifdef SET_INEXACT
2695 int inexact, oldinexact;
2696#endif
2697
2698#ifndef MULTIPLE_THREADS
2699 if (dtoa_result) {
2700 freedtoa(dtoa_result);
2701 dtoa_result = 0;
2702 }
2703#endif
2704
2705 if (word0(d) & Sign_bit) {
2706 /* set sign for everything, including 0's and NaNs */
2707 *sign = 1;
2708 word0(d) &= ~Sign_bit; /* clear sign bit */
2709 }
2710 else
2711 *sign = 0;
2712
2713#if defined(IEEE_Arith) + defined(VAX)
2714#ifdef IEEE_Arith
2715 if ((word0(d) & Exp_mask) == Exp_mask)
2716#else
2717 if (word0(d) == 0x8000)
2718#endif
2719 {
2720 /* Infinity or NaN */
2721 *decpt = 9999;
2722#ifdef IEEE_Arith
2723 if (!word1(d) && !(word0(d) & 0xfffff))
2724 return nrv_alloc("Infinity", rve, 8);
2725#endif
2726 return nrv_alloc("NaN", rve, 3);
2727 }
2728#endif
2729#ifdef IBM
2730 dval(d) += 0; /* normalize */
2731#endif
2732 if (!dval(d)) {
2733 *decpt = 1;
2734 return nrv_alloc("0", rve, 1);
2735 }
2736
2737#ifdef SET_INEXACT
2738 try_quick = oldinexact = get_inexact();
2739 inexact = 1;
2740#endif
2741#ifdef Honor_FLT_ROUNDS
2742 if ((rounding = Flt_Rounds) >= 2) {
2743 if (*sign)
2744 rounding = rounding == 2 ? 0 : 2;
2745 else
2746 if (rounding != 2)
2747 rounding = 0;
2748 }
2749#endif
2750
2751 b = d2b(dval(d), &be, &bbits);
2752#ifdef Sudden_Underflow
2753 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2754#else
2755 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2756#endif
2757 dval(d2) = dval(d);
2758 word0(d2) &= Frac_mask1;
2759 word0(d2) |= Exp_11;
2760#ifdef IBM
2761 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2762 dval(d2) /= 1 << j;
2763#endif
2764
2765 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2766 * log10(x) = log(x) / log(10)
2767 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2768 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2769 *
2770 * This suggests computing an approximation k to log10(d) by
2771 *
2772 * k = (i - Bias)*0.301029995663981
2773 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2774 *
2775 * We want k to be too large rather than too small.
2776 * The error in the first-order Taylor series approximation
2777 * is in our favor, so we just round up the constant enough
2778 * to compensate for any error in the multiplication of
2779 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2780 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2781 * adding 1e-13 to the constant term more than suffices.
2782 * Hence we adjust the constant term to 0.1760912590558.
2783 * (We could get a more accurate k by invoking log10,
2784 * but this is probably not worthwhile.)
2785 */
2786
2787 i -= Bias;
2788#ifdef IBM
2789 i <<= 2;
2790 i += j;
2791#endif
2792#ifndef Sudden_Underflow
2793 denorm = 0;
2794 }
2795 else {
2796 /* d is denormalized */
2797
2798 i = bbits + be + (Bias + (P-1) - 1);
2799 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2800 : word1(d) << 32 - i;
2801 dval(d2) = x;
2802 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2803 i -= (Bias + (P-1) - 1) + 1;
2804 denorm = 1;
2805 }
2806#endif
2807 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2808 k = (int)ds;
2809 if (ds < 0. && ds != k)
2810 k--; /* want k = floor(ds) */
2811 k_check = 1;
2812 if (k >= 0 && k <= Ten_pmax) {
2813 if (dval(d) < tens[k])
2814 k--;
2815 k_check = 0;
2816 }
2817 j = bbits - i - 1;
2818 if (j >= 0) {
2819 b2 = 0;
2820 s2 = j;
2821 }
2822 else {
2823 b2 = -j;
2824 s2 = 0;
2825 }
2826 if (k >= 0) {
2827 b5 = 0;
2828 s5 = k;
2829 s2 += k;
2830 }
2831 else {
2832 b2 -= k;
2833 b5 = -k;
2834 s5 = 0;
2835 }
2836 if (mode < 0 || mode > 9)
2837 mode = 0;
2838
2839#ifndef SET_INEXACT
2840#ifdef Check_FLT_ROUNDS
2841 try_quick = Rounding == 1;
2842#else
2843 try_quick = 1;
2844#endif
2845#endif /*SET_INEXACT*/
2846
2847 if (mode > 5) {
2848 mode -= 4;
2849 try_quick = 0;
2850 }
2851 leftright = 1;
2852 switch(mode) {
2853 case 0:
2854 case 1:
2855 ilim = ilim1 = -1;
2856 i = 18;
2857 ndigits = 0;
2858 break;
2859 case 2:
2860 leftright = 0;
2861 /* no break */
2862 case 4:
2863 if (ndigits <= 0)
2864 ndigits = 1;
2865 ilim = ilim1 = i = ndigits;
2866 break;
2867 case 3:
2868 leftright = 0;
2869 /* no break */
2870 case 5:
2871 i = ndigits + k + 1;
2872 ilim = i;
2873 ilim1 = i - 1;
2874 if (i <= 0)
2875 i = 1;
2876 }
2877 s = s0 = rv_alloc(i);
2878
2879#ifdef Honor_FLT_ROUNDS
2880 if (mode > 1 && rounding != 1)
2881 leftright = 0;
2882#endif
2883
2884 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2885
2886 /* Try to get by with floating-point arithmetic. */
2887
2888 i = 0;
2889 dval(d2) = dval(d);
2890 k0 = k;
2891 ilim0 = ilim;
2892 ieps = 2; /* conservative */
2893 if (k > 0) {
2894 ds = tens[k&0xf];
2895 j = k >> 4;
2896 if (j & Bletch) {
2897 /* prevent overflows */
2898 j &= Bletch - 1;
2899 dval(d) /= bigtens[n_bigtens-1];
2900 ieps++;
2901 }
2902 for(; j; j >>= 1, i++)
2903 if (j & 1) {
2904 ieps++;
2905 ds *= bigtens[i];
2906 }
2907 dval(d) /= ds;
2908 }
2909 else if ((j1 = -k)) {
2910 dval(d) *= tens[j1 & 0xf];
2911 for(j = j1 >> 4; j; j >>= 1, i++)
2912 if (j & 1) {
2913 ieps++;
2914 dval(d) *= bigtens[i];
2915 }
2916 }
2917 if (k_check && dval(d) < 1. && ilim > 0) {
2918 if (ilim1 <= 0)
2919 goto fast_failed;
2920 ilim = ilim1;
2921 k--;
2922 dval(d) *= 10.;
2923 ieps++;
2924 }
2925 dval(eps) = ieps*dval(d) + 7.;
2926 word0(eps) -= (P-1)*Exp_msk1;
2927 if (ilim == 0) {
2928 S = mhi = 0;
2929 dval(d) -= 5.;
2930 if (dval(d) > dval(eps))
2931 goto one_digit;
2932 if (dval(d) < -dval(eps))
2933 goto no_digits;
2934 goto fast_failed;
2935 }
2936#ifndef No_leftright
2937 if (leftright) {
2938 /* Use Steele & White method of only
2939 * generating digits needed.
2940 */
2941 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2942 for(i = 0;;) {
2943 L = (long int)dval(d);
2944 dval(d) -= L;
2945 *s++ = '0' + (int)L;
2946 if (dval(d) < dval(eps))
2947 goto ret1;
2948 if (1. - dval(d) < dval(eps))
2949 goto bump_up;
2950 if (++i >= ilim)
2951 break;
2952 dval(eps) *= 10.;
2953 dval(d) *= 10.;
2954 }
2955 }
2956 else {
2957#endif
2958 /* Generate ilim digits, then fix them up. */
2959 dval(eps) *= tens[ilim-1];
2960 for(i = 1;; i++, dval(d) *= 10.) {
2961 L = (Long)(dval(d));
2962 if (!(dval(d) -= L))
2963 ilim = i;
2964 *s++ = '0' + (int)L;
2965 if (i == ilim) {
2966 if (dval(d) > 0.5 + dval(eps))
2967 goto bump_up;
2968 else if (dval(d) < 0.5 - dval(eps)) {
2969 while(*--s == '0');
2970 s++;
2971 goto ret1;
2972 }
2973 break;
2974 }
2975 }
2976#ifndef No_leftright
2977 }
2978#endif
2979 fast_failed:
2980 s = s0;
2981 dval(d) = dval(d2);
2982 k = k0;
2983 ilim = ilim0;
2984 }
2985
2986 /* Do we have a "small" integer? */
2987
2988 if (be >= 0 && k <= Int_max) {
2989 /* Yes. */
2990 ds = tens[k];
2991 if (ndigits < 0 && ilim <= 0) {
2992 S = mhi = 0;
2993 if (ilim < 0 || dval(d) <= 5*ds)
2994 goto no_digits;
2995 goto one_digit;
2996 }
2997 for(i = 1;; i++, dval(d) *= 10.) {
2998 L = (Long)(dval(d) / ds);
2999 dval(d) -= L*ds;
3000#ifdef Check_FLT_ROUNDS
3001 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3002 if (dval(d) < 0) {
3003 L--;
3004 dval(d) += ds;
3005 }
3006#endif
3007 *s++ = '0' + (int)L;
3008 if (!dval(d)) {
3009#ifdef SET_INEXACT
3010 inexact = 0;
3011#endif
3012 break;
3013 }
3014 if (i == ilim) {
3015#ifdef Honor_FLT_ROUNDS
3016 if (mode > 1)
3017 switch(rounding) {
3018 case 0: goto ret1;
3019 case 2: goto bump_up;
3020 }
3021#endif
3022 dval(d) += dval(d);
3023 if (dval(d) > ds || dval(d) == ds && L & 1) {
3024 bump_up:
3025 while(*--s == '9')
3026 if (s == s0) {
3027 k++;
3028 *s = '0';
3029 break;
3030 }
3031 ++*s++;
3032 }
3033 break;
3034 }
3035 }
3036 goto ret1;
3037 }
3038
3039 m2 = b2;
3040 m5 = b5;
3041 mhi = mlo = 0;
3042 if (leftright) {
3043 i =
3044#ifndef Sudden_Underflow
3045 denorm ? be + (Bias + (P-1) - 1 + 1) :
3046#endif
3047#ifdef IBM
3048 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3049#else
3050 1 + P - bbits;
3051#endif
3052 b2 += i;
3053 s2 += i;
3054 mhi = i2b(1);
3055 }
3056 if (m2 > 0 && s2 > 0) {
3057 i = m2 < s2 ? m2 : s2;
3058 b2 -= i;
3059 m2 -= i;
3060 s2 -= i;
3061 }
3062 if (b5 > 0) {
3063 if (leftright) {
3064 if (m5 > 0) {
3065 mhi = pow5mult(mhi, m5);
3066 b1 = mult(mhi, b);
3067 Bfree(b);
3068 b = b1;
3069 }
3070 if ((j = b5 - m5))
3071 b = pow5mult(b, j);
3072 }
3073 else
3074 b = pow5mult(b, b5);
3075 }
3076 S = i2b(1);
3077 if (s5 > 0)
3078 S = pow5mult(S, s5);
3079
3080 /* Check for special case that d is a normalized power of 2. */
3081
3082 spec_case = 0;
3083 if ((mode < 2 || leftright)
3084#ifdef Honor_FLT_ROUNDS
3085 && rounding == 1
3086#endif
3087 ) {
3088 if (!word1(d) && !(word0(d) & Bndry_mask)
3089#ifndef Sudden_Underflow
3090 && word0(d) & (Exp_mask & ~Exp_msk1)
3091#endif
3092 ) {
3093 /* The special case */
3094 b2 += Log2P;
3095 s2 += Log2P;
3096 spec_case = 1;
3097 }
3098 }
3099
3100 /* Arrange for convenient computation of quotients:
3101 * shift left if necessary so divisor has 4 leading 0 bits.
3102 *
3103 * Perhaps we should just compute leading 28 bits of S once
3104 * and for all and pass them and a shift to quorem, so it
3105 * can do shifts and ors to compute the numerator for q.
3106 */
3107#ifdef Pack_32
3108 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3109 i = 32 - i;
3110#else
3111 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3112 i = 16 - i;
3113#endif
3114 if (i > 4) {
3115 i -= 4;
3116 b2 += i;
3117 m2 += i;
3118 s2 += i;
3119 }
3120 else if (i < 4) {
3121 i += 28;
3122 b2 += i;
3123 m2 += i;
3124 s2 += i;
3125 }
3126 if (b2 > 0)
3127 b = lshift(b, b2);
3128 if (s2 > 0)
3129 S = lshift(S, s2);
3130 if (k_check) {
3131 if (cmp(b,S) < 0) {
3132 k--;
3133 b = multadd(b, 10, 0); /* we botched the k estimate */
3134 if (leftright)
3135 mhi = multadd(mhi, 10, 0);
3136 ilim = ilim1;
3137 }
3138 }
3139 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3140 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3141 /* no digits, fcvt style */
3142 no_digits:
3143 k = -1 - ndigits;
3144 goto ret;
3145 }
3146 one_digit:
3147 *s++ = '1';
3148 k++;
3149 goto ret;
3150 }
3151 if (leftright) {
3152 if (m2 > 0)
3153 mhi = lshift(mhi, m2);
3154
3155 /* Compute mlo -- check for special case
3156 * that d is a normalized power of 2.
3157 */
3158
3159 mlo = mhi;
3160 if (spec_case) {
3161 mhi = Balloc(mhi->k);
3162 Bcopy(mhi, mlo);
3163 mhi = lshift(mhi, Log2P);
3164 }
3165
3166 for(i = 1;;i++) {
3167 dig = quorem(b,S) + '0';
3168 /* Do we yet have the shortest decimal string
3169 * that will round to d?
3170 */
3171 j = cmp(b, mlo);
3172 delta = diff(S, mhi);
3173 j1 = delta->sign ? 1 : cmp(b, delta);
3174 Bfree(delta);
3175#ifndef ROUND_BIASED
3176 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3177#ifdef Honor_FLT_ROUNDS
3178 && rounding >= 1
3179#endif
3180 ) {
3181 if (dig == '9')
3182 goto round_9_up;
3183 if (j > 0)
3184 dig++;
3185#ifdef SET_INEXACT
3186 else if (!b->x[0] && b->wds <= 1)
3187 inexact = 0;
3188#endif
3189 *s++ = dig;
3190 goto ret;
3191 }
3192#endif
3193 if (j < 0 || j == 0 && mode != 1
3194#ifndef ROUND_BIASED
3195 && !(word1(d) & 1)
3196#endif
3197 ) {
3198 if (!b->x[0] && b->wds <= 1) {
3199#ifdef SET_INEXACT
3200 inexact = 0;
3201#endif
3202 goto accept_dig;
3203 }
3204#ifdef Honor_FLT_ROUNDS
3205 if (mode > 1)
3206 switch(rounding) {
3207 case 0: goto accept_dig;
3208 case 2: goto keep_dig;
3209 }
3210#endif /*Honor_FLT_ROUNDS*/
3211 if (j1 > 0) {
3212 b = lshift(b, 1);
3213 j1 = cmp(b, S);
3214 if ((j1 > 0 || j1 == 0 && dig & 1)
3215 && dig++ == '9')
3216 goto round_9_up;
3217 }
3218 accept_dig:
3219 *s++ = dig;
3220 goto ret;
3221 }
3222 if (j1 > 0) {
3223#ifdef Honor_FLT_ROUNDS
3224 if (!rounding)
3225 goto accept_dig;
3226#endif
3227 if (dig == '9') { /* possible if i == 1 */
3228 round_9_up:
3229 *s++ = '9';
3230 goto roundoff;
3231 }
3232 *s++ = dig + 1;
3233 goto ret;
3234 }
3235#ifdef Honor_FLT_ROUNDS
3236 keep_dig:
3237#endif
3238 *s++ = dig;
3239 if (i == ilim)
3240 break;
3241 b = multadd(b, 10, 0);
3242 if (mlo == mhi)
3243 mlo = mhi = multadd(mhi, 10, 0);
3244 else {
3245 mlo = multadd(mlo, 10, 0);
3246 mhi = multadd(mhi, 10, 0);
3247 }
3248 }
3249 }
3250 else
3251 for(i = 1;; i++) {
3252 *s++ = dig = quorem(b,S) + '0';
3253 if (!b->x[0] && b->wds <= 1) {
3254#ifdef SET_INEXACT
3255 inexact = 0;
3256#endif
3257 goto ret;
3258 }
3259 if (i >= ilim)
3260 break;
3261 b = multadd(b, 10, 0);
3262 }
3263
3264 /* Round off last digit */
3265
3266#ifdef Honor_FLT_ROUNDS
3267 switch(rounding) {
3268 case 0: goto trimzeros;
3269 case 2: goto roundoff;
3270 }
3271#endif
3272 b = lshift(b, 1);
3273 j = cmp(b, S);
3274 if (j > 0 || j == 0 && dig & 1) {
3275 roundoff:
3276 while(*--s == '9')
3277 if (s == s0) {
3278 k++;
3279 *s++ = '1';
3280 goto ret;
3281 }
3282 ++*s++;
3283 }
3284 else {
3285#ifdef Honor_FLT_ROUNDS
3286trimzeros:
3287#endif
3288 while(*--s == '0');
3289 s++;
3290 }
3291 ret:
3292 Bfree(S);
3293 if (mhi) {
3294 if (mlo && mlo != mhi)
3295 Bfree(mlo);
3296 Bfree(mhi);
3297 }
3298 ret1:
3299#ifdef SET_INEXACT
3300 if (inexact) {
3301 if (!oldinexact) {
3302 word0(d) = Exp_1 + (70 << Exp_shift);
3303 word1(d) = 0;
3304 dval(d) += 1.;
3305 }
3306 }
3307 else if (!oldinexact)
3308 clear_inexact();
3309#endif
3310 Bfree(b);
3311 *s = 0;
3312 *decpt = k + 1;
3313 if (rve)
3314 *rve = s;
3315 return s0;
3316 }
3317#ifdef __cplusplus
3318}
3319#endif
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