source: webkit/trunk/JavaScriptCore/kjs/dtoa.cpp@ 27031

Last change on this file since 27031 was 23955, checked in by weinig, 18 years ago

Reviewed by Brady Eidson.

Tenth round of fixes for implicit 64-32 bit conversion errors.
<rdar://problem/5292262>

  • Add explicit casts.
  • kjs/dtoa.cpp: (Bigint::):
  • Property allow-tabs set to x
  • Property svn:eol-style set to native
File size: 66.8 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#include "dtoa.h"
174
175#if COMPILER(MSVC)
176#pragma warning(disable: 4244)
177#pragma warning(disable: 4245)
178#pragma warning(disable: 4554)
179#endif
180
181#if PLATFORM(BIG_ENDIAN)
182#define IEEE_MC68k
183#else
184#define IEEE_8087
185#endif
186#define INFNAN_CHECK
187
188
189
190#ifndef Long
191#define Long int
192#endif
193#ifndef ULong
194typedef unsigned Long ULong;
195#endif
196
197#ifdef DEBUG
198#include <stdio.h>
199#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
200#endif
201
202#include <stdlib.h>
203#include <string.h>
204
205#ifdef USE_LOCALE
206#include <locale.h>
207#endif
208
209#ifdef MALLOC
210#ifdef KR_headers
211extern char *MALLOC();
212#else
213extern void *MALLOC(size_t);
214#endif
215#else
216#define MALLOC malloc
217#endif
218
219#ifndef Omit_Private_Memory
220#ifndef PRIVATE_MEM
221#define PRIVATE_MEM 2304
222#endif
223#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
224static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
225#endif
226
227#undef IEEE_Arith
228#undef Avoid_Underflow
229#ifdef IEEE_MC68k
230#define IEEE_Arith
231#endif
232#ifdef IEEE_8087
233#define IEEE_Arith
234#endif
235
236#include <errno.h>
237
238#ifdef Bad_float_h
239
240#ifdef IEEE_Arith
241#define DBL_DIG 15
242#define DBL_MAX_10_EXP 308
243#define DBL_MAX_EXP 1024
244#define FLT_RADIX 2
245#endif /*IEEE_Arith*/
246
247#ifdef IBM
248#define DBL_DIG 16
249#define DBL_MAX_10_EXP 75
250#define DBL_MAX_EXP 63
251#define FLT_RADIX 16
252#define DBL_MAX 7.2370055773322621e+75
253#endif
254
255#ifdef VAX
256#define DBL_DIG 16
257#define DBL_MAX_10_EXP 38
258#define DBL_MAX_EXP 127
259#define FLT_RADIX 2
260#define DBL_MAX 1.7014118346046923e+38
261#endif
262
263#ifndef LONG_MAX
264#define LONG_MAX 2147483647
265#endif
266
267#else /* ifndef Bad_float_h */
268#include <float.h>
269#endif /* Bad_float_h */
270
271#ifndef __MATH_H__
272#include <math.h>
273#endif
274
275#define strtod kjs_strtod
276#define dtoa kjs_dtoa
277#define freedtoa kjs_freedtoa
278
279#ifdef __cplusplus
280extern "C" {
281#endif
282
283#ifndef CONST_
284#ifdef KR_headers
285#define CONST_ /* blank */
286#else
287#define CONST_ const
288#endif
289#endif
290
291#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
292Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
293#endif
294
295typedef union { double d; ULong L[2]; } U;
296
297#ifdef YES_ALIAS
298#define dval(x) x
299#ifdef IEEE_8087
300#define word0(x) ((ULong *)&x)[1]
301#define word1(x) ((ULong *)&x)[0]
302#else
303#define word0(x) ((ULong *)&x)[0]
304#define word1(x) ((ULong *)&x)[1]
305#endif
306#else
307#ifdef IEEE_8087
308#define word0(x) ((U*)&x)->L[1]
309#define word1(x) ((U*)&x)->L[0]
310#else
311#define word0(x) ((U*)&x)->L[0]
312#define word1(x) ((U*)&x)->L[1]
313#endif
314#define dval(x) ((U*)&x)->d
315#endif
316
317/* The following definition of Storeinc is appropriate for MIPS processors.
318 * An alternative that might be better on some machines is
319 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
320 */
321#if defined(IEEE_8087) + defined(VAX)
322#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
323((unsigned short *)a)[0] = (unsigned short)c, a++)
324#else
325#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
326((unsigned short *)a)[1] = (unsigned short)c, a++)
327#endif
328
329/* #define P DBL_MANT_DIG */
330/* Ten_pmax = floor(P*log(2)/log(5)) */
331/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
332/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
333/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
334
335#ifdef IEEE_Arith
336#define Exp_shift 20
337#define Exp_shift1 20
338#define Exp_msk1 0x100000
339#define Exp_msk11 0x100000
340#define Exp_mask 0x7ff00000
341#define P 53
342#define Bias 1023
343#define Emin (-1022)
344#define Exp_1 0x3ff00000
345#define Exp_11 0x3ff00000
346#define Ebits 11
347#define Frac_mask 0xfffff
348#define Frac_mask1 0xfffff
349#define Ten_pmax 22
350#define Bletch 0x10
351#define Bndry_mask 0xfffff
352#define Bndry_mask1 0xfffff
353#define LSB 1
354#define Sign_bit 0x80000000
355#define Log2P 1
356#define Tiny0 0
357#define Tiny1 1
358#define Quick_max 14
359#define Int_max 14
360#ifndef NO_IEEE_Scale
361#define Avoid_Underflow
362#ifdef Flush_Denorm /* debugging option */
363#undef Sudden_Underflow
364#endif
365#endif
366
367#ifndef Flt_Rounds
368#ifdef FLT_ROUNDS
369#define Flt_Rounds FLT_ROUNDS
370#else
371#define Flt_Rounds 1
372#endif
373#endif /*Flt_Rounds*/
374
375#ifdef Honor_FLT_ROUNDS
376#define Rounding rounding
377#undef Check_FLT_ROUNDS
378#define Check_FLT_ROUNDS
379#else
380#define Rounding Flt_Rounds
381#endif
382
383#else /* ifndef IEEE_Arith */
384#undef Check_FLT_ROUNDS
385#undef Honor_FLT_ROUNDS
386#undef SET_INEXACT
387#undef Sudden_Underflow
388#define Sudden_Underflow
389#ifdef IBM
390#undef Flt_Rounds
391#define Flt_Rounds 0
392#define Exp_shift 24
393#define Exp_shift1 24
394#define Exp_msk1 0x1000000
395#define Exp_msk11 0x1000000
396#define Exp_mask 0x7f000000
397#define P 14
398#define Bias 65
399#define Exp_1 0x41000000
400#define Exp_11 0x41000000
401#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
402#define Frac_mask 0xffffff
403#define Frac_mask1 0xffffff
404#define Bletch 4
405#define Ten_pmax 22
406#define Bndry_mask 0xefffff
407#define Bndry_mask1 0xffffff
408#define LSB 1
409#define Sign_bit 0x80000000
410#define Log2P 4
411#define Tiny0 0x100000
412#define Tiny1 0
413#define Quick_max 14
414#define Int_max 15
415#else /* VAX */
416#undef Flt_Rounds
417#define Flt_Rounds 1
418#define Exp_shift 23
419#define Exp_shift1 7
420#define Exp_msk1 0x80
421#define Exp_msk11 0x800000
422#define Exp_mask 0x7f80
423#define P 56
424#define Bias 129
425#define Exp_1 0x40800000
426#define Exp_11 0x4080
427#define Ebits 8
428#define Frac_mask 0x7fffff
429#define Frac_mask1 0xffff007f
430#define Ten_pmax 24
431#define Bletch 2
432#define Bndry_mask 0xffff007f
433#define Bndry_mask1 0xffff007f
434#define LSB 0x10000
435#define Sign_bit 0x8000
436#define Log2P 1
437#define Tiny0 0x80
438#define Tiny1 0
439#define Quick_max 15
440#define Int_max 15
441#endif /* IBM, VAX */
442#endif /* IEEE_Arith */
443
444#ifndef IEEE_Arith
445#define ROUND_BIASED
446#endif
447
448#ifdef RND_PRODQUOT
449#define rounded_product(a,b) a = rnd_prod(a, b)
450#define rounded_quotient(a,b) a = rnd_quot(a, b)
451#ifdef KR_headers
452extern double rnd_prod(), rnd_quot();
453#else
454extern double rnd_prod(double, double), rnd_quot(double, double);
455#endif
456#else
457#define rounded_product(a,b) a *= b
458#define rounded_quotient(a,b) a /= b
459#endif
460
461#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
462#define Big1 0xffffffff
463
464#ifndef Pack_32
465#define Pack_32
466#endif
467
468#ifdef KR_headers
469#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
470#else
471#define FFFFFFFF 0xffffffffUL
472#endif
473
474#ifdef NO_LONG_LONG
475#undef ULLong
476#ifdef Just_16
477#undef Pack_32
478/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
479 * This makes some inner loops simpler and sometimes saves work
480 * during multiplications, but it often seems to make things slightly
481 * slower. Hence the default is now to store 32 bits per Long.
482 */
483#endif
484#else /* long long available */
485#ifndef Llong
486#define Llong long long
487#endif
488#ifndef ULLong
489#define ULLong unsigned Llong
490#endif
491#endif /* NO_LONG_LONG */
492
493#ifndef MULTIPLE_THREADS
494#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
495#define FREE_DTOA_LOCK(n) /*nothing*/
496#endif
497
498#define Kmax 15
499
500 struct
501Bigint {
502 struct Bigint *next;
503 int k, maxwds, sign, wds;
504 ULong x[1];
505 };
506
507 typedef struct Bigint Bigint;
508
509 static Bigint *freelist[Kmax+1];
510
511 static Bigint *
512Balloc
513#ifdef KR_headers
514 (k) int k;
515#else
516 (int k)
517#endif
518{
519 int x;
520 Bigint *rv;
521#ifndef Omit_Private_Memory
522 unsigned int len;
523#endif
524
525 ACQUIRE_DTOA_LOCK(0);
526 if ((rv = freelist[k])) {
527 freelist[k] = rv->next;
528 }
529 else {
530 x = 1 << k;
531#ifdef Omit_Private_Memory
532 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
533#else
534 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
535 /sizeof(double);
536 if (pmem_next - private_mem + len <= (unsigned)PRIVATE_mem) {
537 rv = (Bigint*)pmem_next;
538 pmem_next += len;
539 }
540 else
541 rv = (Bigint*)MALLOC(len*sizeof(double));
542#endif
543 rv->k = k;
544 rv->maxwds = x;
545 }
546 FREE_DTOA_LOCK(0);
547 rv->sign = rv->wds = 0;
548 return rv;
549 }
550
551 static void
552Bfree
553#ifdef KR_headers
554 (v) Bigint *v;
555#else
556 (Bigint *v)
557#endif
558{
559 if (v) {
560 ACQUIRE_DTOA_LOCK(0);
561 v->next = freelist[v->k];
562 freelist[v->k] = v;
563 FREE_DTOA_LOCK(0);
564 }
565 }
566
567#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
568y->wds*sizeof(Long) + 2*sizeof(int))
569
570 static Bigint *
571multadd
572#ifdef KR_headers
573 (b, m, a) Bigint *b; int m, a;
574#else
575 (Bigint *b, int m, int a) /* multiply by m and add a */
576#endif
577{
578 int i, wds;
579#ifdef ULLong
580 ULong *x;
581 ULLong carry, y;
582#else
583 ULong carry, *x, y;
584#ifdef Pack_32
585 ULong xi, z;
586#endif
587#endif
588 Bigint *b1;
589
590 wds = b->wds;
591 x = b->x;
592 i = 0;
593 carry = a;
594 do {
595#ifdef ULLong
596 y = *x * (ULLong)m + carry;
597 carry = y >> 32;
598 *x++ = (ULong)y & FFFFFFFF;
599#else
600#ifdef Pack_32
601 xi = *x;
602 y = (xi & 0xffff) * m + carry;
603 z = (xi >> 16) * m + (y >> 16);
604 carry = z >> 16;
605 *x++ = (z << 16) + (y & 0xffff);
606#else
607 y = *x * m + carry;
608 carry = y >> 16;
609 *x++ = y & 0xffff;
610#endif
611#endif
612 }
613 while(++i < wds);
614 if (carry) {
615 if (wds >= b->maxwds) {
616 b1 = Balloc(b->k+1);
617 Bcopy(b1, b);
618 Bfree(b);
619 b = b1;
620 }
621 b->x[wds++] = (ULong)carry;
622 b->wds = wds;
623 }
624 return b;
625 }
626
627 static Bigint *
628s2b
629#ifdef KR_headers
630 (s, nd0, nd, y9) CONST_ char *s; int nd0, nd; ULong y9;
631#else
632 (CONST_ char *s, int nd0, int nd, ULong y9)
633#endif
634{
635 Bigint *b;
636 int i, k;
637 Long x, y;
638
639 x = (nd + 8) / 9;
640 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
641#ifdef Pack_32
642 b = Balloc(k);
643 b->x[0] = y9;
644 b->wds = 1;
645#else
646 b = Balloc(k+1);
647 b->x[0] = y9 & 0xffff;
648 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
649#endif
650
651 i = 9;
652 if (9 < nd0) {
653 s += 9;
654 do b = multadd(b, 10, *s++ - '0');
655 while(++i < nd0);
656 s++;
657 }
658 else
659 s += 10;
660 for(; i < nd; i++)
661 b = multadd(b, 10, *s++ - '0');
662 return b;
663 }
664
665 static int
666hi0bits
667#ifdef KR_headers
668 (x) register ULong x;
669#else
670 (register ULong x)
671#endif
672{
673 register int k = 0;
674
675 if (!(x & 0xffff0000)) {
676 k = 16;
677 x <<= 16;
678 }
679 if (!(x & 0xff000000)) {
680 k += 8;
681 x <<= 8;
682 }
683 if (!(x & 0xf0000000)) {
684 k += 4;
685 x <<= 4;
686 }
687 if (!(x & 0xc0000000)) {
688 k += 2;
689 x <<= 2;
690 }
691 if (!(x & 0x80000000)) {
692 k++;
693 if (!(x & 0x40000000))
694 return 32;
695 }
696 return k;
697 }
698
699 static int
700lo0bits
701#ifdef KR_headers
702 (y) ULong *y;
703#else
704 (ULong *y)
705#endif
706{
707 register int k;
708 register ULong x = *y;
709
710 if (x & 7) {
711 if (x & 1)
712 return 0;
713 if (x & 2) {
714 *y = x >> 1;
715 return 1;
716 }
717 *y = x >> 2;
718 return 2;
719 }
720 k = 0;
721 if (!(x & 0xffff)) {
722 k = 16;
723 x >>= 16;
724 }
725 if (!(x & 0xff)) {
726 k += 8;
727 x >>= 8;
728 }
729 if (!(x & 0xf)) {
730 k += 4;
731 x >>= 4;
732 }
733 if (!(x & 0x3)) {
734 k += 2;
735 x >>= 2;
736 }
737 if (!(x & 1)) {
738 k++;
739 x >>= 1;
740 if (!x & 1)
741 return 32;
742 }
743 *y = x;
744 return k;
745 }
746
747 static Bigint *
748i2b
749#ifdef KR_headers
750 (i) int i;
751#else
752 (int i)
753#endif
754{
755 Bigint *b;
756
757 b = Balloc(1);
758 b->x[0] = i;
759 b->wds = 1;
760 return b;
761 }
762
763 static Bigint *
764mult
765#ifdef KR_headers
766 (a, b) Bigint *a, *b;
767#else
768 (Bigint *a, Bigint *b)
769#endif
770{
771 Bigint *c;
772 int k, wa, wb, wc;
773 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
774 ULong y;
775#ifdef ULLong
776 ULLong carry, z;
777#else
778 ULong carry, z;
779#ifdef Pack_32
780 ULong z2;
781#endif
782#endif
783
784 if (a->wds < b->wds) {
785 c = a;
786 a = b;
787 b = c;
788 }
789 k = a->k;
790 wa = a->wds;
791 wb = b->wds;
792 wc = wa + wb;
793 if (wc > a->maxwds)
794 k++;
795 c = Balloc(k);
796 for(x = c->x, xa = x + wc; x < xa; x++)
797 *x = 0;
798 xa = a->x;
799 xae = xa + wa;
800 xb = b->x;
801 xbe = xb + wb;
802 xc0 = c->x;
803#ifdef ULLong
804 for(; xb < xbe; xc0++) {
805 if ((y = *xb++)) {
806 x = xa;
807 xc = xc0;
808 carry = 0;
809 do {
810 z = *x++ * (ULLong)y + *xc + carry;
811 carry = z >> 32;
812 *xc++ = (ULong)z & FFFFFFFF;
813 }
814 while(x < xae);
815 *xc = (ULong)carry;
816 }
817 }
818#else
819#ifdef Pack_32
820 for(; xb < xbe; xb++, xc0++) {
821 if (y = *xb & 0xffff) {
822 x = xa;
823 xc = xc0;
824 carry = 0;
825 do {
826 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
827 carry = z >> 16;
828 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
829 carry = z2 >> 16;
830 Storeinc(xc, z2, z);
831 }
832 while(x < xae);
833 *xc = carry;
834 }
835 if (y = *xb >> 16) {
836 x = xa;
837 xc = xc0;
838 carry = 0;
839 z2 = *xc;
840 do {
841 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
842 carry = z >> 16;
843 Storeinc(xc, z, z2);
844 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
845 carry = z2 >> 16;
846 }
847 while(x < xae);
848 *xc = z2;
849 }
850 }
851#else
852 for(; xb < xbe; xc0++) {
853 if (y = *xb++) {
854 x = xa;
855 xc = xc0;
856 carry = 0;
857 do {
858 z = *x++ * y + *xc + carry;
859 carry = z >> 16;
860 *xc++ = z & 0xffff;
861 }
862 while(x < xae);
863 *xc = carry;
864 }
865 }
866#endif
867#endif
868 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
869 c->wds = wc;
870 return c;
871 }
872
873 static Bigint *p5s;
874
875 static Bigint *
876pow5mult
877#ifdef KR_headers
878 (b, k) Bigint *b; int k;
879#else
880 (Bigint *b, int k)
881#endif
882{
883 Bigint *b1, *p5, *p51;
884 int i;
885 static int p05[3] = { 5, 25, 125 };
886
887 if ((i = k & 3))
888 b = multadd(b, p05[i-1], 0);
889
890 if (!(k >>= 2))
891 return b;
892 if (!(p5 = p5s)) {
893 /* first time */
894#ifdef MULTIPLE_THREADS
895 ACQUIRE_DTOA_LOCK(1);
896 if (!(p5 = p5s)) {
897 p5 = p5s = i2b(625);
898 p5->next = 0;
899 }
900 FREE_DTOA_LOCK(1);
901#else
902 p5 = p5s = i2b(625);
903 p5->next = 0;
904#endif
905 }
906 for(;;) {
907 if (k & 1) {
908 b1 = mult(b, p5);
909 Bfree(b);
910 b = b1;
911 }
912 if (!(k >>= 1))
913 break;
914 if (!(p51 = p5->next)) {
915#ifdef MULTIPLE_THREADS
916 ACQUIRE_DTOA_LOCK(1);
917 if (!(p51 = p5->next)) {
918 p51 = p5->next = mult(p5,p5);
919 p51->next = 0;
920 }
921 FREE_DTOA_LOCK(1);
922#else
923 p51 = p5->next = mult(p5,p5);
924 p51->next = 0;
925#endif
926 }
927 p5 = p51;
928 }
929 return b;
930 }
931
932 static Bigint *
933lshift
934#ifdef KR_headers
935 (b, k) Bigint *b; int k;
936#else
937 (Bigint *b, int k)
938#endif
939{
940 int i, k1, n, n1;
941 Bigint *b1;
942 ULong *x, *x1, *xe, z;
943
944#ifdef Pack_32
945 n = k >> 5;
946#else
947 n = k >> 4;
948#endif
949 k1 = b->k;
950 n1 = n + b->wds + 1;
951 for(i = b->maxwds; n1 > i; i <<= 1)
952 k1++;
953 b1 = Balloc(k1);
954 x1 = b1->x;
955 for(i = 0; i < n; i++)
956 *x1++ = 0;
957 x = b->x;
958 xe = x + b->wds;
959#ifdef Pack_32
960 if (k &= 0x1f) {
961 k1 = 32 - k;
962 z = 0;
963 do {
964 *x1++ = *x << k | z;
965 z = *x++ >> k1;
966 }
967 while(x < xe);
968 if ((*x1 = z))
969 ++n1;
970 }
971#else
972 if (k &= 0xf) {
973 k1 = 16 - k;
974 z = 0;
975 do {
976 *x1++ = *x << k & 0xffff | z;
977 z = *x++ >> k1;
978 }
979 while(x < xe);
980 if (*x1 = z)
981 ++n1;
982 }
983#endif
984 else do
985 *x1++ = *x++;
986 while(x < xe);
987 b1->wds = n1 - 1;
988 Bfree(b);
989 return b1;
990 }
991
992 static int
993cmp
994#ifdef KR_headers
995 (a, b) Bigint *a, *b;
996#else
997 (Bigint *a, Bigint *b)
998#endif
999{
1000 ULong *xa, *xa0, *xb, *xb0;
1001 int i, j;
1002
1003 i = a->wds;
1004 j = b->wds;
1005#ifdef DEBUG
1006 if (i > 1 && !a->x[i-1])
1007 Bug("cmp called with a->x[a->wds-1] == 0");
1008 if (j > 1 && !b->x[j-1])
1009 Bug("cmp called with b->x[b->wds-1] == 0");
1010#endif
1011 if (i -= j)
1012 return i;
1013 xa0 = a->x;
1014 xa = xa0 + j;
1015 xb0 = b->x;
1016 xb = xb0 + j;
1017 for(;;) {
1018 if (*--xa != *--xb)
1019 return *xa < *xb ? -1 : 1;
1020 if (xa <= xa0)
1021 break;
1022 }
1023 return 0;
1024 }
1025
1026 static Bigint *
1027diff
1028#ifdef KR_headers
1029 (a, b) Bigint *a, *b;
1030#else
1031 (Bigint *a, Bigint *b)
1032#endif
1033{
1034 Bigint *c;
1035 int i, wa, wb;
1036 ULong *xa, *xae, *xb, *xbe, *xc;
1037#ifdef ULLong
1038 ULLong borrow, y;
1039#else
1040 ULong borrow, y;
1041#ifdef Pack_32
1042 ULong z;
1043#endif
1044#endif
1045
1046 i = cmp(a,b);
1047 if (!i) {
1048 c = Balloc(0);
1049 c->wds = 1;
1050 c->x[0] = 0;
1051 return c;
1052 }
1053 if (i < 0) {
1054 c = a;
1055 a = b;
1056 b = c;
1057 i = 1;
1058 }
1059 else
1060 i = 0;
1061 c = Balloc(a->k);
1062 c->sign = i;
1063 wa = a->wds;
1064 xa = a->x;
1065 xae = xa + wa;
1066 wb = b->wds;
1067 xb = b->x;
1068 xbe = xb + wb;
1069 xc = c->x;
1070 borrow = 0;
1071#ifdef ULLong
1072 do {
1073 y = (ULLong)*xa++ - *xb++ - borrow;
1074 borrow = y >> 32 & (ULong)1;
1075 *xc++ = (ULong)y & FFFFFFFF;
1076 }
1077 while(xb < xbe);
1078 while(xa < xae) {
1079 y = *xa++ - borrow;
1080 borrow = y >> 32 & (ULong)1;
1081 *xc++ = (ULong)y & FFFFFFFF;
1082 }
1083#else
1084#ifdef Pack_32
1085 do {
1086 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1087 borrow = (y & 0x10000) >> 16;
1088 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1089 borrow = (z & 0x10000) >> 16;
1090 Storeinc(xc, z, y);
1091 }
1092 while(xb < xbe);
1093 while(xa < xae) {
1094 y = (*xa & 0xffff) - borrow;
1095 borrow = (y & 0x10000) >> 16;
1096 z = (*xa++ >> 16) - borrow;
1097 borrow = (z & 0x10000) >> 16;
1098 Storeinc(xc, z, y);
1099 }
1100#else
1101 do {
1102 y = *xa++ - *xb++ - borrow;
1103 borrow = (y & 0x10000) >> 16;
1104 *xc++ = y & 0xffff;
1105 }
1106 while(xb < xbe);
1107 while(xa < xae) {
1108 y = *xa++ - borrow;
1109 borrow = (y & 0x10000) >> 16;
1110 *xc++ = y & 0xffff;
1111 }
1112#endif
1113#endif
1114 while(!*--xc)
1115 wa--;
1116 c->wds = wa;
1117 return c;
1118 }
1119
1120 static double
1121ulp
1122#ifdef KR_headers
1123 (x) double x;
1124#else
1125 (double x)
1126#endif
1127{
1128 register Long L;
1129 double a;
1130
1131 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1132#ifndef Avoid_Underflow
1133#ifndef Sudden_Underflow
1134 if (L > 0) {
1135#endif
1136#endif
1137#ifdef IBM
1138 L |= Exp_msk1 >> 4;
1139#endif
1140 word0(a) = L;
1141 word1(a) = 0;
1142#ifndef Avoid_Underflow
1143#ifndef Sudden_Underflow
1144 }
1145 else {
1146 L = -L >> Exp_shift;
1147 if (L < Exp_shift) {
1148 word0(a) = 0x80000 >> L;
1149 word1(a) = 0;
1150 }
1151 else {
1152 word0(a) = 0;
1153 L -= Exp_shift;
1154 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1155 }
1156 }
1157#endif
1158#endif
1159 return dval(a);
1160 }
1161
1162 static double
1163b2d
1164#ifdef KR_headers
1165 (a, e) Bigint *a; int *e;
1166#else
1167 (Bigint *a, int *e)
1168#endif
1169{
1170 ULong *xa, *xa0, w, y, z;
1171 int k;
1172 double d;
1173#ifdef VAX
1174 ULong d0, d1;
1175#else
1176#define d0 word0(d)
1177#define d1 word1(d)
1178#endif
1179
1180 xa0 = a->x;
1181 xa = xa0 + a->wds;
1182 y = *--xa;
1183#ifdef DEBUG
1184 if (!y) Bug("zero y in b2d");
1185#endif
1186 k = hi0bits(y);
1187 *e = 32 - k;
1188#ifdef Pack_32
1189 if (k < Ebits) {
1190 d0 = Exp_1 | y >> Ebits - k;
1191 w = xa > xa0 ? *--xa : 0;
1192 d1 = y << (32-Ebits) + k | w >> Ebits - k;
1193 goto ret_d;
1194 }
1195 z = xa > xa0 ? *--xa : 0;
1196 if (k -= Ebits) {
1197 d0 = Exp_1 | y << k | z >> 32 - k;
1198 y = xa > xa0 ? *--xa : 0;
1199 d1 = z << k | y >> 32 - k;
1200 }
1201 else {
1202 d0 = Exp_1 | y;
1203 d1 = z;
1204 }
1205#else
1206 if (k < Ebits + 16) {
1207 z = xa > xa0 ? *--xa : 0;
1208 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1209 w = xa > xa0 ? *--xa : 0;
1210 y = xa > xa0 ? *--xa : 0;
1211 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1212 goto ret_d;
1213 }
1214 z = xa > xa0 ? *--xa : 0;
1215 w = xa > xa0 ? *--xa : 0;
1216 k -= Ebits + 16;
1217 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1218 y = xa > xa0 ? *--xa : 0;
1219 d1 = w << k + 16 | y << k;
1220#endif
1221 ret_d:
1222#ifdef VAX
1223 word0(d) = d0 >> 16 | d0 << 16;
1224 word1(d) = d1 >> 16 | d1 << 16;
1225#else
1226#undef d0
1227#undef d1
1228#endif
1229 return dval(d);
1230 }
1231
1232 static Bigint *
1233d2b
1234#ifdef KR_headers
1235 (d, e, bits) double d; int *e, *bits;
1236#else
1237 (double d, int *e, int *bits)
1238#endif
1239{
1240 Bigint *b;
1241 int de, k;
1242 ULong *x, y, z;
1243#ifndef Sudden_Underflow
1244 int i;
1245#endif
1246#ifdef VAX
1247 ULong d0, d1;
1248 d0 = word0(d) >> 16 | word0(d) << 16;
1249 d1 = word1(d) >> 16 | word1(d) << 16;
1250#else
1251#define d0 word0(d)
1252#define d1 word1(d)
1253#endif
1254
1255#ifdef Pack_32
1256 b = Balloc(1);
1257#else
1258 b = Balloc(2);
1259#endif
1260 x = b->x;
1261
1262 z = d0 & Frac_mask;
1263 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1264#ifdef Sudden_Underflow
1265 de = (int)(d0 >> Exp_shift);
1266#ifndef IBM
1267 z |= Exp_msk11;
1268#endif
1269#else
1270 if ((de = (int)(d0 >> Exp_shift)))
1271 z |= Exp_msk1;
1272#endif
1273#ifdef Pack_32
1274 if ((y = d1)) {
1275 if ((k = lo0bits(&y))) {
1276 x[0] = y | z << 32 - k;
1277 z >>= k;
1278 }
1279 else
1280 x[0] = y;
1281#ifndef Sudden_Underflow
1282 i =
1283#endif
1284 b->wds = (x[1] = z) ? 2 : 1;
1285 }
1286 else {
1287#ifdef DEBUG
1288 if (!z)
1289 Bug("Zero passed to d2b");
1290#endif
1291 k = lo0bits(&z);
1292 x[0] = z;
1293#ifndef Sudden_Underflow
1294 i =
1295#endif
1296 b->wds = 1;
1297 k += 32;
1298 }
1299#else
1300 if (y = d1) {
1301 if (k = lo0bits(&y))
1302 if (k >= 16) {
1303 x[0] = y | z << 32 - k & 0xffff;
1304 x[1] = z >> k - 16 & 0xffff;
1305 x[2] = z >> k;
1306 i = 2;
1307 }
1308 else {
1309 x[0] = y & 0xffff;
1310 x[1] = y >> 16 | z << 16 - k & 0xffff;
1311 x[2] = z >> k & 0xffff;
1312 x[3] = z >> k+16;
1313 i = 3;
1314 }
1315 else {
1316 x[0] = y & 0xffff;
1317 x[1] = y >> 16;
1318 x[2] = z & 0xffff;
1319 x[3] = z >> 16;
1320 i = 3;
1321 }
1322 }
1323 else {
1324#ifdef DEBUG
1325 if (!z)
1326 Bug("Zero passed to d2b");
1327#endif
1328 k = lo0bits(&z);
1329 if (k >= 16) {
1330 x[0] = z;
1331 i = 0;
1332 }
1333 else {
1334 x[0] = z & 0xffff;
1335 x[1] = z >> 16;
1336 i = 1;
1337 }
1338 k += 32;
1339 }
1340 while(!x[i])
1341 --i;
1342 b->wds = i + 1;
1343#endif
1344#ifndef Sudden_Underflow
1345 if (de) {
1346#endif
1347#ifdef IBM
1348 *e = (de - Bias - (P-1) << 2) + k;
1349 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1350#else
1351 *e = de - Bias - (P-1) + k;
1352 *bits = P - k;
1353#endif
1354#ifndef Sudden_Underflow
1355 }
1356 else {
1357 *e = de - Bias - (P-1) + 1 + k;
1358#ifdef Pack_32
1359 *bits = 32*i - hi0bits(x[i-1]);
1360#else
1361 *bits = (i+2)*16 - hi0bits(x[i]);
1362#endif
1363 }
1364#endif
1365 return b;
1366 }
1367#undef d0
1368#undef d1
1369
1370 static double
1371ratio
1372#ifdef KR_headers
1373 (a, b) Bigint *a, *b;
1374#else
1375 (Bigint *a, Bigint *b)
1376#endif
1377{
1378 double da, db;
1379 int k, ka, kb;
1380
1381 dval(da) = b2d(a, &ka);
1382 dval(db) = b2d(b, &kb);
1383#ifdef Pack_32
1384 k = ka - kb + 32*(a->wds - b->wds);
1385#else
1386 k = ka - kb + 16*(a->wds - b->wds);
1387#endif
1388#ifdef IBM
1389 if (k > 0) {
1390 word0(da) += (k >> 2)*Exp_msk1;
1391 if (k &= 3)
1392 dval(da) *= 1 << k;
1393 }
1394 else {
1395 k = -k;
1396 word0(db) += (k >> 2)*Exp_msk1;
1397 if (k &= 3)
1398 dval(db) *= 1 << k;
1399 }
1400#else
1401 if (k > 0)
1402 word0(da) += k*Exp_msk1;
1403 else {
1404 k = -k;
1405 word0(db) += k*Exp_msk1;
1406 }
1407#endif
1408 return dval(da) / dval(db);
1409 }
1410
1411 static CONST_ double
1412tens[] = {
1413 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1414 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1415 1e20, 1e21, 1e22
1416#ifdef VAX
1417 , 1e23, 1e24
1418#endif
1419 };
1420
1421 static CONST_ double
1422#ifdef IEEE_Arith
1423bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1424static CONST_ double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1425#ifdef Avoid_Underflow
1426 9007199254740992.*9007199254740992.e-256
1427 /* = 2^106 * 1e-53 */
1428#else
1429 1e-256
1430#endif
1431 };
1432/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1433/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1434#define Scale_Bit 0x10
1435#define n_bigtens 5
1436#else
1437#ifdef IBM
1438bigtens[] = { 1e16, 1e32, 1e64 };
1439static CONST_ double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1440#define n_bigtens 3
1441#else
1442bigtens[] = { 1e16, 1e32 };
1443static CONST_ double tinytens[] = { 1e-16, 1e-32 };
1444#define n_bigtens 2
1445#endif
1446#endif
1447
1448#ifndef IEEE_Arith
1449#undef INFNAN_CHECK
1450#endif
1451
1452#ifdef INFNAN_CHECK
1453
1454#ifndef NAN_WORD0
1455#define NAN_WORD0 0x7ff80000
1456#endif
1457
1458#ifndef NAN_WORD1
1459#define NAN_WORD1 0
1460#endif
1461
1462 static int
1463match
1464#ifdef KR_headers
1465 (sp, t) char **sp, *t;
1466#else
1467 (CONST_ char **sp, CONST_ char *t)
1468#endif
1469{
1470 int c, d;
1471 CONST_ char *s = *sp;
1472
1473 while((d = *t++)) {
1474 if ((c = *++s) >= 'A' && c <= 'Z')
1475 c += 'a' - 'A';
1476 if (c != d)
1477 return 0;
1478 }
1479 *sp = s + 1;
1480 return 1;
1481 }
1482
1483#ifndef No_Hex_NaN
1484 static void
1485hexnan
1486#ifdef KR_headers
1487 (rvp, sp) double *rvp; CONST_ char **sp;
1488#else
1489 (double *rvp, CONST_ char **sp)
1490#endif
1491{
1492 ULong c, x[2];
1493 CONST_ char *s;
1494 int havedig, udx0, xshift;
1495
1496 x[0] = x[1] = 0;
1497 havedig = xshift = 0;
1498 udx0 = 1;
1499 s = *sp;
1500 while((c = *(CONST_ unsigned char*)++s)) {
1501 if (c >= '0' && c <= '9')
1502 c -= '0';
1503 else if (c >= 'a' && c <= 'f')
1504 c += 10 - 'a';
1505 else if (c >= 'A' && c <= 'F')
1506 c += 10 - 'A';
1507 else if (c <= ' ') {
1508 if (udx0 && havedig) {
1509 udx0 = 0;
1510 xshift = 1;
1511 }
1512 continue;
1513 }
1514 else if (/*(*/ c == ')' && havedig) {
1515 *sp = s + 1;
1516 break;
1517 }
1518 else
1519 return; /* invalid form: don't change *sp */
1520 havedig = 1;
1521 if (xshift) {
1522 xshift = 0;
1523 x[0] = x[1];
1524 x[1] = 0;
1525 }
1526 if (udx0)
1527 x[0] = (x[0] << 4) | (x[1] >> 28);
1528 x[1] = (x[1] << 4) | c;
1529 }
1530 if ((x[0] &= 0xfffff) || x[1]) {
1531 word0(*rvp) = Exp_mask | x[0];
1532 word1(*rvp) = x[1];
1533 }
1534 }
1535#endif /*No_Hex_NaN*/
1536#endif /* INFNAN_CHECK */
1537
1538 double
1539strtod
1540#ifdef KR_headers
1541 (s00, se) CONST_ char *s00; char **se;
1542#else
1543 (CONST_ char *s00, char **se)
1544#endif
1545{
1546#ifdef Avoid_Underflow
1547 int scale;
1548#endif
1549 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1550 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1551 CONST_ char *s, *s0, *s1;
1552 double aadj, aadj1, adj, rv, rv0;
1553 Long L;
1554 ULong y, z;
1555 Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
1556#ifdef SET_INEXACT
1557 int inexact, oldinexact;
1558#endif
1559#ifdef Honor_FLT_ROUNDS
1560 int rounding;
1561#endif
1562#ifdef USE_LOCALE
1563 CONST_ char *s2;
1564#endif
1565
1566 sign = nz0 = nz = 0;
1567 dval(rv) = 0.;
1568 for(s = s00;;s++) switch(*s) {
1569 case '-':
1570 sign = 1;
1571 /* no break */
1572 case '+':
1573 if (*++s)
1574 goto break2;
1575 /* no break */
1576 case 0:
1577 goto ret0;
1578 case '\t':
1579 case '\n':
1580 case '\v':
1581 case '\f':
1582 case '\r':
1583 case ' ':
1584 continue;
1585 default:
1586 goto break2;
1587 }
1588 break2:
1589 if (*s == '0') {
1590 nz0 = 1;
1591 while(*++s == '0') ;
1592 if (!*s)
1593 goto ret;
1594 }
1595 s0 = s;
1596 y = z = 0;
1597 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1598 if (nd < 9)
1599 y = 10*y + c - '0';
1600 else if (nd < 16)
1601 z = 10*z + c - '0';
1602 nd0 = nd;
1603#ifdef USE_LOCALE
1604 s1 = localeconv()->decimal_point;
1605 if (c == *s1) {
1606 c = '.';
1607 if (*++s1) {
1608 s2 = s;
1609 for(;;) {
1610 if (*++s2 != *s1) {
1611 c = 0;
1612 break;
1613 }
1614 if (!*++s1) {
1615 s = s2;
1616 break;
1617 }
1618 }
1619 }
1620 }
1621#endif
1622 if (c == '.') {
1623 c = *++s;
1624 if (!nd) {
1625 for(; c == '0'; c = *++s)
1626 nz++;
1627 if (c > '0' && c <= '9') {
1628 s0 = s;
1629 nf += nz;
1630 nz = 0;
1631 goto have_dig;
1632 }
1633 goto dig_done;
1634 }
1635 for(; c >= '0' && c <= '9'; c = *++s) {
1636 have_dig:
1637 nz++;
1638 if (c -= '0') {
1639 nf += nz;
1640 for(i = 1; i < nz; i++)
1641 if (nd++ < 9)
1642 y *= 10;
1643 else if (nd <= DBL_DIG + 1)
1644 z *= 10;
1645 if (nd++ < 9)
1646 y = 10*y + c;
1647 else if (nd <= DBL_DIG + 1)
1648 z = 10*z + c;
1649 nz = 0;
1650 }
1651 }
1652 }
1653 dig_done:
1654 e = 0;
1655 if (c == 'e' || c == 'E') {
1656 if (!nd && !nz && !nz0) {
1657 goto ret0;
1658 }
1659 s00 = s;
1660 esign = 0;
1661 switch(c = *++s) {
1662 case '-':
1663 esign = 1;
1664 case '+':
1665 c = *++s;
1666 }
1667 if (c >= '0' && c <= '9') {
1668 while(c == '0')
1669 c = *++s;
1670 if (c > '0' && c <= '9') {
1671 L = c - '0';
1672 s1 = s;
1673 while((c = *++s) >= '0' && c <= '9')
1674 L = 10*L + c - '0';
1675 if (s - s1 > 8 || L > 19999)
1676 /* Avoid confusion from exponents
1677 * so large that e might overflow.
1678 */
1679 e = 19999; /* safe for 16 bit ints */
1680 else
1681 e = (int)L;
1682 if (esign)
1683 e = -e;
1684 }
1685 else
1686 e = 0;
1687 }
1688 else
1689 s = s00;
1690 }
1691 if (!nd) {
1692 if (!nz && !nz0) {
1693#ifdef INFNAN_CHECK
1694 /* Check for Nan and Infinity */
1695 switch(c) {
1696 case 'i':
1697 case 'I':
1698 if (match(&s,"nf")) {
1699 --s;
1700 if (!match(&s,"inity"))
1701 ++s;
1702 word0(rv) = 0x7ff00000;
1703 word1(rv) = 0;
1704 goto ret;
1705 }
1706 break;
1707 case 'n':
1708 case 'N':
1709 if (match(&s, "an")) {
1710 word0(rv) = NAN_WORD0;
1711 word1(rv) = NAN_WORD1;
1712#ifndef No_Hex_NaN
1713 if (*s == '(') /*)*/
1714 hexnan(&rv, &s);
1715#endif
1716 goto ret;
1717 }
1718 }
1719#endif /* INFNAN_CHECK */
1720 ret0:
1721 s = s00;
1722 sign = 0;
1723 }
1724 goto ret;
1725 }
1726 e1 = e -= nf;
1727
1728 /* Now we have nd0 digits, starting at s0, followed by a
1729 * decimal point, followed by nd-nd0 digits. The number we're
1730 * after is the integer represented by those digits times
1731 * 10**e */
1732
1733 if (!nd0)
1734 nd0 = nd;
1735 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1736 dval(rv) = y;
1737 if (k > 9) {
1738#ifdef SET_INEXACT
1739 if (k > DBL_DIG)
1740 oldinexact = get_inexact();
1741#endif
1742 dval(rv) = tens[k - 9] * dval(rv) + z;
1743 }
1744 bd0 = 0;
1745 if (nd <= DBL_DIG
1746#ifndef RND_PRODQUOT
1747#ifndef Honor_FLT_ROUNDS
1748 && Flt_Rounds == 1
1749#endif
1750#endif
1751 ) {
1752 if (!e)
1753 goto ret;
1754 if (e > 0) {
1755 if (e <= Ten_pmax) {
1756#ifdef VAX
1757 goto vax_ovfl_check;
1758#else
1759#ifdef Honor_FLT_ROUNDS
1760 /* round correctly FLT_ROUNDS = 2 or 3 */
1761 if (sign) {
1762 rv = -rv;
1763 sign = 0;
1764 }
1765#endif
1766 /* rv = */ rounded_product(dval(rv), tens[e]);
1767 goto ret;
1768#endif
1769 }
1770 i = DBL_DIG - nd;
1771 if (e <= Ten_pmax + i) {
1772 /* A fancier test would sometimes let us do
1773 * this for larger i values.
1774 */
1775#ifdef Honor_FLT_ROUNDS
1776 /* round correctly FLT_ROUNDS = 2 or 3 */
1777 if (sign) {
1778 rv = -rv;
1779 sign = 0;
1780 }
1781#endif
1782 e -= i;
1783 dval(rv) *= tens[i];
1784#ifdef VAX
1785 /* VAX exponent range is so narrow we must
1786 * worry about overflow here...
1787 */
1788 vax_ovfl_check:
1789 word0(rv) -= P*Exp_msk1;
1790 /* rv = */ rounded_product(dval(rv), tens[e]);
1791 if ((word0(rv) & Exp_mask)
1792 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1793 goto ovfl;
1794 word0(rv) += P*Exp_msk1;
1795#else
1796 /* rv = */ rounded_product(dval(rv), tens[e]);
1797#endif
1798 goto ret;
1799 }
1800 }
1801#ifndef Inaccurate_Divide
1802 else if (e >= -Ten_pmax) {
1803#ifdef Honor_FLT_ROUNDS
1804 /* round correctly FLT_ROUNDS = 2 or 3 */
1805 if (sign) {
1806 rv = -rv;
1807 sign = 0;
1808 }
1809#endif
1810 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1811 goto ret;
1812 }
1813#endif
1814 }
1815 e1 += nd - k;
1816
1817#ifdef IEEE_Arith
1818#ifdef SET_INEXACT
1819 inexact = 1;
1820 if (k <= DBL_DIG)
1821 oldinexact = get_inexact();
1822#endif
1823#ifdef Avoid_Underflow
1824 scale = 0;
1825#endif
1826#ifdef Honor_FLT_ROUNDS
1827 if ((rounding = Flt_Rounds) >= 2) {
1828 if (sign)
1829 rounding = rounding == 2 ? 0 : 2;
1830 else
1831 if (rounding != 2)
1832 rounding = 0;
1833 }
1834#endif
1835#endif /*IEEE_Arith*/
1836
1837 /* Get starting approximation = rv * 10**e1 */
1838
1839 if (e1 > 0) {
1840 if ((i = e1 & 15))
1841 dval(rv) *= tens[i];
1842 if (e1 &= ~15) {
1843 if (e1 > DBL_MAX_10_EXP) {
1844 ovfl:
1845#ifndef NO_ERRNO
1846 errno = ERANGE;
1847#endif
1848 /* Can't trust HUGE_VAL */
1849#ifdef IEEE_Arith
1850#ifdef Honor_FLT_ROUNDS
1851 switch(rounding) {
1852 case 0: /* toward 0 */
1853 case 3: /* toward -infinity */
1854 word0(rv) = Big0;
1855 word1(rv) = Big1;
1856 break;
1857 default:
1858 word0(rv) = Exp_mask;
1859 word1(rv) = 0;
1860 }
1861#else /*Honor_FLT_ROUNDS*/
1862 word0(rv) = Exp_mask;
1863 word1(rv) = 0;
1864#endif /*Honor_FLT_ROUNDS*/
1865#ifdef SET_INEXACT
1866 /* set overflow bit */
1867 dval(rv0) = 1e300;
1868 dval(rv0) *= dval(rv0);
1869#endif
1870#else /*IEEE_Arith*/
1871 word0(rv) = Big0;
1872 word1(rv) = Big1;
1873#endif /*IEEE_Arith*/
1874 if (bd0)
1875 goto retfree;
1876 goto ret;
1877 }
1878 e1 >>= 4;
1879 for(j = 0; e1 > 1; j++, e1 >>= 1)
1880 if (e1 & 1)
1881 dval(rv) *= bigtens[j];
1882 /* The last multiplication could overflow. */
1883 word0(rv) -= P*Exp_msk1;
1884 dval(rv) *= bigtens[j];
1885 if ((z = word0(rv) & Exp_mask)
1886 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1887 goto ovfl;
1888 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1889 /* set to largest number */
1890 /* (Can't trust DBL_MAX) */
1891 word0(rv) = Big0;
1892 word1(rv) = Big1;
1893 }
1894 else
1895 word0(rv) += P*Exp_msk1;
1896 }
1897 }
1898 else if (e1 < 0) {
1899 e1 = -e1;
1900 if ((i = e1 & 15))
1901 dval(rv) /= tens[i];
1902 if (e1 >>= 4) {
1903 if (e1 >= 1 << n_bigtens)
1904 goto undfl;
1905#ifdef Avoid_Underflow
1906 if (e1 & Scale_Bit)
1907 scale = 2*P;
1908 for(j = 0; e1 > 0; j++, e1 >>= 1)
1909 if (e1 & 1)
1910 dval(rv) *= tinytens[j];
1911 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1912 >> Exp_shift)) > 0) {
1913 /* scaled rv is denormal; zap j low bits */
1914 if (j >= 32) {
1915 word1(rv) = 0;
1916 if (j >= 53)
1917 word0(rv) = (P+2)*Exp_msk1;
1918 else
1919 word0(rv) &= 0xffffffff << j-32;
1920 }
1921 else
1922 word1(rv) &= 0xffffffff << j;
1923 }
1924#else
1925 for(j = 0; e1 > 1; j++, e1 >>= 1)
1926 if (e1 & 1)
1927 dval(rv) *= tinytens[j];
1928 /* The last multiplication could underflow. */
1929 dval(rv0) = dval(rv);
1930 dval(rv) *= tinytens[j];
1931 if (!dval(rv)) {
1932 dval(rv) = 2.*dval(rv0);
1933 dval(rv) *= tinytens[j];
1934#endif
1935 if (!dval(rv)) {
1936 undfl:
1937 dval(rv) = 0.;
1938#ifndef NO_ERRNO
1939 errno = ERANGE;
1940#endif
1941 if (bd0)
1942 goto retfree;
1943 goto ret;
1944 }
1945#ifndef Avoid_Underflow
1946 word0(rv) = Tiny0;
1947 word1(rv) = Tiny1;
1948 /* The refinement below will clean
1949 * this approximation up.
1950 */
1951 }
1952#endif
1953 }
1954 }
1955
1956 /* Now the hard part -- adjusting rv to the correct value.*/
1957
1958 /* Put digits into bd: true value = bd * 10^e */
1959
1960 bd0 = s2b(s0, nd0, nd, y);
1961
1962 for(;;) {
1963 bd = Balloc(bd0->k);
1964 Bcopy(bd, bd0);
1965 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1966 bs = i2b(1);
1967
1968 if (e >= 0) {
1969 bb2 = bb5 = 0;
1970 bd2 = bd5 = e;
1971 }
1972 else {
1973 bb2 = bb5 = -e;
1974 bd2 = bd5 = 0;
1975 }
1976 if (bbe >= 0)
1977 bb2 += bbe;
1978 else
1979 bd2 -= bbe;
1980 bs2 = bb2;
1981#ifdef Honor_FLT_ROUNDS
1982 if (rounding != 1)
1983 bs2++;
1984#endif
1985#ifdef Avoid_Underflow
1986 j = bbe - scale;
1987 i = j + bbbits - 1; /* logb(rv) */
1988 if (i < Emin) /* denormal */
1989 j += P - Emin;
1990 else
1991 j = P + 1 - bbbits;
1992#else /*Avoid_Underflow*/
1993#ifdef Sudden_Underflow
1994#ifdef IBM
1995 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1996#else
1997 j = P + 1 - bbbits;
1998#endif
1999#else /*Sudden_Underflow*/
2000 j = bbe;
2001 i = j + bbbits - 1; /* logb(rv) */
2002 if (i < Emin) /* denormal */
2003 j += P - Emin;
2004 else
2005 j = P + 1 - bbbits;
2006#endif /*Sudden_Underflow*/
2007#endif /*Avoid_Underflow*/
2008 bb2 += j;
2009 bd2 += j;
2010#ifdef Avoid_Underflow
2011 bd2 += scale;
2012#endif
2013 i = bb2 < bd2 ? bb2 : bd2;
2014 if (i > bs2)
2015 i = bs2;
2016 if (i > 0) {
2017 bb2 -= i;
2018 bd2 -= i;
2019 bs2 -= i;
2020 }
2021 if (bb5 > 0) {
2022 bs = pow5mult(bs, bb5);
2023 bb1 = mult(bs, bb);
2024 Bfree(bb);
2025 bb = bb1;
2026 }
2027 if (bb2 > 0)
2028 bb = lshift(bb, bb2);
2029 if (bd5 > 0)
2030 bd = pow5mult(bd, bd5);
2031 if (bd2 > 0)
2032 bd = lshift(bd, bd2);
2033 if (bs2 > 0)
2034 bs = lshift(bs, bs2);
2035 delta = diff(bb, bd);
2036 dsign = delta->sign;
2037 delta->sign = 0;
2038 i = cmp(delta, bs);
2039#ifdef Honor_FLT_ROUNDS
2040 if (rounding != 1) {
2041 if (i < 0) {
2042 /* Error is less than an ulp */
2043 if (!delta->x[0] && delta->wds <= 1) {
2044 /* exact */
2045#ifdef SET_INEXACT
2046 inexact = 0;
2047#endif
2048 break;
2049 }
2050 if (rounding) {
2051 if (dsign) {
2052 adj = 1.;
2053 goto apply_adj;
2054 }
2055 }
2056 else if (!dsign) {
2057 adj = -1.;
2058 if (!word1(rv)
2059 && !(word0(rv) & Frac_mask)) {
2060 y = word0(rv) & Exp_mask;
2061#ifdef Avoid_Underflow
2062 if (!scale || y > 2*P*Exp_msk1)
2063#else
2064 if (y)
2065#endif
2066 {
2067 delta = lshift(delta,Log2P);
2068 if (cmp(delta, bs) <= 0)
2069 adj = -0.5;
2070 }
2071 }
2072 apply_adj:
2073#ifdef Avoid_Underflow
2074 if (scale && (y = word0(rv) & Exp_mask)
2075 <= 2*P*Exp_msk1)
2076 word0(adj) += (2*P+1)*Exp_msk1 - y;
2077#else
2078#ifdef Sudden_Underflow
2079 if ((word0(rv) & Exp_mask) <=
2080 P*Exp_msk1) {
2081 word0(rv) += P*Exp_msk1;
2082 dval(rv) += adj*ulp(dval(rv));
2083 word0(rv) -= P*Exp_msk1;
2084 }
2085 else
2086#endif /*Sudden_Underflow*/
2087#endif /*Avoid_Underflow*/
2088 dval(rv) += adj*ulp(dval(rv));
2089 }
2090 break;
2091 }
2092 adj = ratio(delta, bs);
2093 if (adj < 1.)
2094 adj = 1.;
2095 if (adj <= 0x7ffffffe) {
2096 /* adj = rounding ? ceil(adj) : floor(adj); */
2097 y = adj;
2098 if (y != adj) {
2099 if (!((rounding>>1) ^ dsign))
2100 y++;
2101 adj = y;
2102 }
2103 }
2104#ifdef Avoid_Underflow
2105 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2106 word0(adj) += (2*P+1)*Exp_msk1 - y;
2107#else
2108#ifdef Sudden_Underflow
2109 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2110 word0(rv) += P*Exp_msk1;
2111 adj *= ulp(dval(rv));
2112 if (dsign)
2113 dval(rv) += adj;
2114 else
2115 dval(rv) -= adj;
2116 word0(rv) -= P*Exp_msk1;
2117 goto cont;
2118 }
2119#endif /*Sudden_Underflow*/
2120#endif /*Avoid_Underflow*/
2121 adj *= ulp(dval(rv));
2122 if (dsign)
2123 dval(rv) += adj;
2124 else
2125 dval(rv) -= adj;
2126 goto cont;
2127 }
2128#endif /*Honor_FLT_ROUNDS*/
2129
2130 if (i < 0) {
2131 /* Error is less than half an ulp -- check for
2132 * special case of mantissa a power of two.
2133 */
2134 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2135#ifdef IEEE_Arith
2136#ifdef Avoid_Underflow
2137 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2138#else
2139 || (word0(rv) & Exp_mask) <= Exp_msk1
2140#endif
2141#endif
2142 ) {
2143#ifdef SET_INEXACT
2144 if (!delta->x[0] && delta->wds <= 1)
2145 inexact = 0;
2146#endif
2147 break;
2148 }
2149 if (!delta->x[0] && delta->wds <= 1) {
2150 /* exact result */
2151#ifdef SET_INEXACT
2152 inexact = 0;
2153#endif
2154 break;
2155 }
2156 delta = lshift(delta,Log2P);
2157 if (cmp(delta, bs) > 0)
2158 goto drop_down;
2159 break;
2160 }
2161 if (i == 0) {
2162 /* exactly half-way between */
2163 if (dsign) {
2164 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2165 && word1(rv) == (
2166#ifdef Avoid_Underflow
2167 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2168 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2169#endif
2170 0xffffffff)) {
2171 /*boundary case -- increment exponent*/
2172 word0(rv) = (word0(rv) & Exp_mask)
2173 + Exp_msk1
2174#ifdef IBM
2175 | Exp_msk1 >> 4
2176#endif
2177 ;
2178 word1(rv) = 0;
2179#ifdef Avoid_Underflow
2180 dsign = 0;
2181#endif
2182 break;
2183 }
2184 }
2185 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2186 drop_down:
2187 /* boundary case -- decrement exponent */
2188#ifdef Sudden_Underflow /*{{*/
2189 L = word0(rv) & Exp_mask;
2190#ifdef IBM
2191 if (L < Exp_msk1)
2192#else
2193#ifdef Avoid_Underflow
2194 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2195#else
2196 if (L <= Exp_msk1)
2197#endif /*Avoid_Underflow*/
2198#endif /*IBM*/
2199 goto undfl;
2200 L -= Exp_msk1;
2201#else /*Sudden_Underflow}{*/
2202#ifdef Avoid_Underflow
2203 if (scale) {
2204 L = word0(rv) & Exp_mask;
2205 if (L <= (2*P+1)*Exp_msk1) {
2206 if (L > (P+2)*Exp_msk1)
2207 /* round even ==> */
2208 /* accept rv */
2209 break;
2210 /* rv = smallest denormal */
2211 goto undfl;
2212 }
2213 }
2214#endif /*Avoid_Underflow*/
2215 L = (word0(rv) & Exp_mask) - Exp_msk1;
2216#endif /*Sudden_Underflow}}*/
2217 word0(rv) = L | Bndry_mask1;
2218 word1(rv) = 0xffffffff;
2219#ifdef IBM
2220 goto cont;
2221#else
2222 break;
2223#endif
2224 }
2225#ifndef ROUND_BIASED
2226 if (!(word1(rv) & LSB))
2227 break;
2228#endif
2229 if (dsign)
2230 dval(rv) += ulp(dval(rv));
2231#ifndef ROUND_BIASED
2232 else {
2233 dval(rv) -= ulp(dval(rv));
2234#ifndef Sudden_Underflow
2235 if (!dval(rv))
2236 goto undfl;
2237#endif
2238 }
2239#ifdef Avoid_Underflow
2240 dsign = 1 - dsign;
2241#endif
2242#endif
2243 break;
2244 }
2245 if ((aadj = ratio(delta, bs)) <= 2.) {
2246 if (dsign)
2247 aadj = aadj1 = 1.;
2248 else if (word1(rv) || word0(rv) & Bndry_mask) {
2249#ifndef Sudden_Underflow
2250 if (word1(rv) == Tiny1 && !word0(rv))
2251 goto undfl;
2252#endif
2253 aadj = 1.;
2254 aadj1 = -1.;
2255 }
2256 else {
2257 /* special case -- power of FLT_RADIX to be */
2258 /* rounded down... */
2259
2260 if (aadj < 2./FLT_RADIX)
2261 aadj = 1./FLT_RADIX;
2262 else
2263 aadj *= 0.5;
2264 aadj1 = -aadj;
2265 }
2266 }
2267 else {
2268 aadj *= 0.5;
2269 aadj1 = dsign ? aadj : -aadj;
2270#ifdef Check_FLT_ROUNDS
2271 switch(Rounding) {
2272 case 2: /* towards +infinity */
2273 aadj1 -= 0.5;
2274 break;
2275 case 0: /* towards 0 */
2276 case 3: /* towards -infinity */
2277 aadj1 += 0.5;
2278 }
2279#else
2280 if (Flt_Rounds == 0)
2281 aadj1 += 0.5;
2282#endif /*Check_FLT_ROUNDS*/
2283 }
2284 y = word0(rv) & Exp_mask;
2285
2286 /* Check for overflow */
2287
2288 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2289 dval(rv0) = dval(rv);
2290 word0(rv) -= P*Exp_msk1;
2291 adj = aadj1 * ulp(dval(rv));
2292 dval(rv) += adj;
2293 if ((word0(rv) & Exp_mask) >=
2294 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2295 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2296 goto ovfl;
2297 word0(rv) = Big0;
2298 word1(rv) = Big1;
2299 goto cont;
2300 }
2301 else
2302 word0(rv) += P*Exp_msk1;
2303 }
2304 else {
2305#ifdef Avoid_Underflow
2306 if (scale && y <= 2*P*Exp_msk1) {
2307 if (aadj <= 0x7fffffff) {
2308 if ((z = (ULong)aadj) <= 0)
2309 z = 1;
2310 aadj = z;
2311 aadj1 = dsign ? aadj : -aadj;
2312 }
2313 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2314 }
2315 adj = aadj1 * ulp(dval(rv));
2316 dval(rv) += adj;
2317#else
2318#ifdef Sudden_Underflow
2319 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2320 dval(rv0) = dval(rv);
2321 word0(rv) += P*Exp_msk1;
2322 adj = aadj1 * ulp(dval(rv));
2323 dval(rv) += adj;
2324#ifdef IBM
2325 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2326#else
2327 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2328#endif
2329 {
2330 if (word0(rv0) == Tiny0
2331 && word1(rv0) == Tiny1)
2332 goto undfl;
2333 word0(rv) = Tiny0;
2334 word1(rv) = Tiny1;
2335 goto cont;
2336 }
2337 else
2338 word0(rv) -= P*Exp_msk1;
2339 }
2340 else {
2341 adj = aadj1 * ulp(dval(rv));
2342 dval(rv) += adj;
2343 }
2344#else /*Sudden_Underflow*/
2345 /* Compute adj so that the IEEE rounding rules will
2346 * correctly round rv + adj in some half-way cases.
2347 * If rv * ulp(rv) is denormalized (i.e.,
2348 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2349 * trouble from bits lost to denormalization;
2350 * example: 1.2e-307 .
2351 */
2352 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2353 aadj1 = (double)(int)(aadj + 0.5);
2354 if (!dsign)
2355 aadj1 = -aadj1;
2356 }
2357 adj = aadj1 * ulp(dval(rv));
2358 dval(rv) += adj;
2359#endif /*Sudden_Underflow*/
2360#endif /*Avoid_Underflow*/
2361 }
2362 z = word0(rv) & Exp_mask;
2363#ifndef SET_INEXACT
2364#ifdef Avoid_Underflow
2365 if (!scale)
2366#endif
2367 if (y == z) {
2368 /* Can we stop now? */
2369 L = (Long)aadj;
2370 aadj -= L;
2371 /* The tolerances below are conservative. */
2372 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2373 if (aadj < .4999999 || aadj > .5000001)
2374 break;
2375 }
2376 else if (aadj < .4999999/FLT_RADIX)
2377 break;
2378 }
2379#endif
2380 cont:
2381 Bfree(bb);
2382 Bfree(bd);
2383 Bfree(bs);
2384 Bfree(delta);
2385 }
2386#ifdef SET_INEXACT
2387 if (inexact) {
2388 if (!oldinexact) {
2389 word0(rv0) = Exp_1 + (70 << Exp_shift);
2390 word1(rv0) = 0;
2391 dval(rv0) += 1.;
2392 }
2393 }
2394 else if (!oldinexact)
2395 clear_inexact();
2396#endif
2397#ifdef Avoid_Underflow
2398 if (scale) {
2399 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2400 word1(rv0) = 0;
2401 dval(rv) *= dval(rv0);
2402#ifndef NO_ERRNO
2403 /* try to avoid the bug of testing an 8087 register value */
2404 if (word0(rv) == 0 && word1(rv) == 0)
2405 errno = ERANGE;
2406#endif
2407 }
2408#endif /* Avoid_Underflow */
2409#ifdef SET_INEXACT
2410 if (inexact && !(word0(rv) & Exp_mask)) {
2411 /* set underflow bit */
2412 dval(rv0) = 1e-300;
2413 dval(rv0) *= dval(rv0);
2414 }
2415#endif
2416 retfree:
2417 Bfree(bb);
2418 Bfree(bd);
2419 Bfree(bs);
2420 Bfree(bd0);
2421 Bfree(delta);
2422 ret:
2423 if (se)
2424 *se = (char *)s;
2425 return sign ? -dval(rv) : dval(rv);
2426 }
2427
2428 static int
2429quorem
2430#ifdef KR_headers
2431 (b, S) Bigint *b, *S;
2432#else
2433 (Bigint *b, Bigint *S)
2434#endif
2435{
2436 int n;
2437 ULong *bx, *bxe, q, *sx, *sxe;
2438#ifdef ULLong
2439 ULLong borrow, carry, y, ys;
2440#else
2441 ULong borrow, carry, y, ys;
2442#ifdef Pack_32
2443 ULong si, z, zs;
2444#endif
2445#endif
2446
2447 n = S->wds;
2448#ifdef DEBUG
2449 /*debug*/ if (b->wds > n)
2450 /*debug*/ Bug("oversize b in quorem");
2451#endif
2452 if (b->wds < n)
2453 return 0;
2454 sx = S->x;
2455 sxe = sx + --n;
2456 bx = b->x;
2457 bxe = bx + n;
2458 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2459#ifdef DEBUG
2460 /*debug*/ if (q > 9)
2461 /*debug*/ Bug("oversized quotient in quorem");
2462#endif
2463 if (q) {
2464 borrow = 0;
2465 carry = 0;
2466 do {
2467#ifdef ULLong
2468 ys = *sx++ * (ULLong)q + carry;
2469 carry = ys >> 32;
2470 y = *bx - (ys & FFFFFFFF) - borrow;
2471 borrow = y >> 32 & (ULong)1;
2472 *bx++ = (ULong)y & FFFFFFFF;
2473#else
2474#ifdef Pack_32
2475 si = *sx++;
2476 ys = (si & 0xffff) * q + carry;
2477 zs = (si >> 16) * q + (ys >> 16);
2478 carry = zs >> 16;
2479 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2480 borrow = (y & 0x10000) >> 16;
2481 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2482 borrow = (z & 0x10000) >> 16;
2483 Storeinc(bx, z, y);
2484#else
2485 ys = *sx++ * q + carry;
2486 carry = ys >> 16;
2487 y = *bx - (ys & 0xffff) - borrow;
2488 borrow = (y & 0x10000) >> 16;
2489 *bx++ = y & 0xffff;
2490#endif
2491#endif
2492 }
2493 while(sx <= sxe);
2494 if (!*bxe) {
2495 bx = b->x;
2496 while(--bxe > bx && !*bxe)
2497 --n;
2498 b->wds = n;
2499 }
2500 }
2501 if (cmp(b, S) >= 0) {
2502 q++;
2503 borrow = 0;
2504 carry = 0;
2505 bx = b->x;
2506 sx = S->x;
2507 do {
2508#ifdef ULLong
2509 ys = *sx++ + carry;
2510 carry = ys >> 32;
2511 y = *bx - (ys & FFFFFFFF) - borrow;
2512 borrow = y >> 32 & (ULong)1;
2513 *bx++ = (ULong)y & FFFFFFFF;
2514#else
2515#ifdef Pack_32
2516 si = *sx++;
2517 ys = (si & 0xffff) + carry;
2518 zs = (si >> 16) + (ys >> 16);
2519 carry = zs >> 16;
2520 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2521 borrow = (y & 0x10000) >> 16;
2522 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2523 borrow = (z & 0x10000) >> 16;
2524 Storeinc(bx, z, y);
2525#else
2526 ys = *sx++ + carry;
2527 carry = ys >> 16;
2528 y = *bx - (ys & 0xffff) - borrow;
2529 borrow = (y & 0x10000) >> 16;
2530 *bx++ = y & 0xffff;
2531#endif
2532#endif
2533 }
2534 while(sx <= sxe);
2535 bx = b->x;
2536 bxe = bx + n;
2537 if (!*bxe) {
2538 while(--bxe > bx && !*bxe)
2539 --n;
2540 b->wds = n;
2541 }
2542 }
2543 return q;
2544 }
2545
2546#ifndef MULTIPLE_THREADS
2547 static char *dtoa_result;
2548#endif
2549
2550 static char *
2551#ifdef KR_headers
2552rv_alloc(i) int i;
2553#else
2554rv_alloc(int i)
2555#endif
2556{
2557 int j, k, *r;
2558
2559 j = sizeof(ULong);
2560 for(k = 0;
2561 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i;
2562 j <<= 1)
2563 k++;
2564 r = (int*)Balloc(k);
2565 *r = k;
2566 return
2567#ifndef MULTIPLE_THREADS
2568 dtoa_result =
2569#endif
2570 (char *)(r+1);
2571 }
2572
2573 static char *
2574#ifdef KR_headers
2575nrv_alloc(s, rve, n) char *s, **rve; int n;
2576#else
2577nrv_alloc(CONST_ char *s, char **rve, int n)
2578#endif
2579{
2580 char *rv, *t;
2581
2582 t = rv = rv_alloc(n);
2583 while((*t = *s++)) t++;
2584 if (rve)
2585 *rve = t;
2586 return rv;
2587 }
2588
2589/* freedtoa(s) must be used to free values s returned by dtoa
2590 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2591 * but for consistency with earlier versions of dtoa, it is optional
2592 * when MULTIPLE_THREADS is not defined.
2593 */
2594
2595 void
2596#ifdef KR_headers
2597freedtoa(s) char *s;
2598#else
2599freedtoa(char *s)
2600#endif
2601{
2602 Bigint *b = (Bigint *)((int *)s - 1);
2603 b->maxwds = 1 << (b->k = *(int*)b);
2604 Bfree(b);
2605#ifndef MULTIPLE_THREADS
2606 if (s == dtoa_result)
2607 dtoa_result = 0;
2608#endif
2609 }
2610
2611/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2612 *
2613 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2614 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
2615 *
2616 * Modifications:
2617 * 1. Rather than iterating, we use a simple numeric overestimate
2618 * to determine k = floor(log10(d)). We scale relevant
2619 * quantities using O(log2(k)) rather than O(k) multiplications.
2620 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2621 * try to generate digits strictly left to right. Instead, we
2622 * compute with fewer bits and propagate the carry if necessary
2623 * when rounding the final digit up. This is often faster.
2624 * 3. Under the assumption that input will be rounded nearest,
2625 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2626 * That is, we allow equality in stopping tests when the
2627 * round-nearest rule will give the same floating-point value
2628 * as would satisfaction of the stopping test with strict
2629 * inequality.
2630 * 4. We remove common factors of powers of 2 from relevant
2631 * quantities.
2632 * 5. When converting floating-point integers less than 1e16,
2633 * we use floating-point arithmetic rather than resorting
2634 * to multiple-precision integers.
2635 * 6. When asked to produce fewer than 15 digits, we first try
2636 * to get by with floating-point arithmetic; we resort to
2637 * multiple-precision integer arithmetic only if we cannot
2638 * guarantee that the floating-point calculation has given
2639 * the correctly rounded result. For k requested digits and
2640 * "uniformly" distributed input, the probability is
2641 * something like 10^(k-15) that we must resort to the Long
2642 * calculation.
2643 */
2644
2645 char *
2646dtoa
2647#ifdef KR_headers
2648 (d, mode, ndigits, decpt, sign, rve)
2649 double d; int mode, ndigits, *decpt, *sign; char **rve;
2650#else
2651 (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2652#endif
2653{
2654 /* Arguments ndigits, decpt, sign are similar to those
2655 of ecvt and fcvt; trailing zeros are suppressed from
2656 the returned string. If not null, *rve is set to point
2657 to the end of the return value. If d is +-Infinity or NaN,
2658 then *decpt is set to 9999.
2659
2660 mode:
2661 0 ==> shortest string that yields d when read in
2662 and rounded to nearest.
2663 1 ==> like 0, but with Steele & White stopping rule;
2664 e.g. with IEEE P754 arithmetic , mode 0 gives
2665 1e23 whereas mode 1 gives 9.999999999999999e22.
2666 2 ==> max(1,ndigits) significant digits. This gives a
2667 return value similar to that of ecvt, except
2668 that trailing zeros are suppressed.
2669 3 ==> through ndigits past the decimal point. This
2670 gives a return value similar to that from fcvt,
2671 except that trailing zeros are suppressed, and
2672 ndigits can be negative.
2673 4,5 ==> similar to 2 and 3, respectively, but (in
2674 round-nearest mode) with the tests of mode 0 to
2675 possibly return a shorter string that rounds to d.
2676 With IEEE arithmetic and compilation with
2677 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2678 as modes 2 and 3 when FLT_ROUNDS != 1.
2679 6-9 ==> Debugging modes similar to mode - 4: don't try
2680 fast floating-point estimate (if applicable).
2681
2682 Values of mode other than 0-9 are treated as mode 0.
2683
2684 Sufficient space is allocated to the return value
2685 to hold the suppressed trailing zeros.
2686 */
2687
2688 int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
2689 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2690 spec_case, try_quick;
2691 Long L;
2692#ifndef Sudden_Underflow
2693 int denorm;
2694 ULong x;
2695#endif
2696 Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
2697 double d2, ds, eps;
2698 char *s, *s0;
2699#ifdef Honor_FLT_ROUNDS
2700 int rounding;
2701#endif
2702#ifdef SET_INEXACT
2703 int inexact, oldinexact;
2704#endif
2705
2706#ifndef MULTIPLE_THREADS
2707 if (dtoa_result) {
2708 freedtoa(dtoa_result);
2709 dtoa_result = 0;
2710 }
2711#endif
2712
2713 if (word0(d) & Sign_bit) {
2714 /* set sign for everything, including 0's and NaNs */
2715 *sign = 1;
2716 word0(d) &= ~Sign_bit; /* clear sign bit */
2717 }
2718 else
2719 *sign = 0;
2720
2721#if defined(IEEE_Arith) + defined(VAX)
2722#ifdef IEEE_Arith
2723 if ((word0(d) & Exp_mask) == Exp_mask)
2724#else
2725 if (word0(d) == 0x8000)
2726#endif
2727 {
2728 /* Infinity or NaN */
2729 *decpt = 9999;
2730#ifdef IEEE_Arith
2731 if (!word1(d) && !(word0(d) & 0xfffff))
2732 return nrv_alloc("Infinity", rve, 8);
2733#endif
2734 return nrv_alloc("NaN", rve, 3);
2735 }
2736#endif
2737#ifdef IBM
2738 dval(d) += 0; /* normalize */
2739#endif
2740 if (!dval(d)) {
2741 *decpt = 1;
2742 return nrv_alloc("0", rve, 1);
2743 }
2744
2745#ifdef SET_INEXACT
2746 try_quick = oldinexact = get_inexact();
2747 inexact = 1;
2748#endif
2749#ifdef Honor_FLT_ROUNDS
2750 if ((rounding = Flt_Rounds) >= 2) {
2751 if (*sign)
2752 rounding = rounding == 2 ? 0 : 2;
2753 else
2754 if (rounding != 2)
2755 rounding = 0;
2756 }
2757#endif
2758
2759 b = d2b(dval(d), &be, &bbits);
2760#ifdef Sudden_Underflow
2761 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2762#else
2763 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2764#endif
2765 dval(d2) = dval(d);
2766 word0(d2) &= Frac_mask1;
2767 word0(d2) |= Exp_11;
2768#ifdef IBM
2769 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2770 dval(d2) /= 1 << j;
2771#endif
2772
2773 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2774 * log10(x) = log(x) / log(10)
2775 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2776 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2777 *
2778 * This suggests computing an approximation k to log10(d) by
2779 *
2780 * k = (i - Bias)*0.301029995663981
2781 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2782 *
2783 * We want k to be too large rather than too small.
2784 * The error in the first-order Taylor series approximation
2785 * is in our favor, so we just round up the constant enough
2786 * to compensate for any error in the multiplication of
2787 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2788 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2789 * adding 1e-13 to the constant term more than suffices.
2790 * Hence we adjust the constant term to 0.1760912590558.
2791 * (We could get a more accurate k by invoking log10,
2792 * but this is probably not worthwhile.)
2793 */
2794
2795 i -= Bias;
2796#ifdef IBM
2797 i <<= 2;
2798 i += j;
2799#endif
2800#ifndef Sudden_Underflow
2801 denorm = 0;
2802 }
2803 else {
2804 /* d is denormalized */
2805
2806 i = bbits + be + (Bias + (P-1) - 1);
2807 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2808 : word1(d) << 32 - i;
2809 dval(d2) = x;
2810 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2811 i -= (Bias + (P-1) - 1) + 1;
2812 denorm = 1;
2813 }
2814#endif
2815 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2816 k = (int)ds;
2817 if (ds < 0. && ds != k)
2818 k--; /* want k = floor(ds) */
2819 k_check = 1;
2820 if (k >= 0 && k <= Ten_pmax) {
2821 if (dval(d) < tens[k])
2822 k--;
2823 k_check = 0;
2824 }
2825 j = bbits - i - 1;
2826 if (j >= 0) {
2827 b2 = 0;
2828 s2 = j;
2829 }
2830 else {
2831 b2 = -j;
2832 s2 = 0;
2833 }
2834 if (k >= 0) {
2835 b5 = 0;
2836 s5 = k;
2837 s2 += k;
2838 }
2839 else {
2840 b2 -= k;
2841 b5 = -k;
2842 s5 = 0;
2843 }
2844 if (mode < 0 || mode > 9)
2845 mode = 0;
2846
2847#ifndef SET_INEXACT
2848#ifdef Check_FLT_ROUNDS
2849 try_quick = Rounding == 1;
2850#else
2851 try_quick = 1;
2852#endif
2853#endif /*SET_INEXACT*/
2854
2855 if (mode > 5) {
2856 mode -= 4;
2857 try_quick = 0;
2858 }
2859 leftright = 1;
2860 switch(mode) {
2861 case 0:
2862 case 1:
2863 ilim = ilim1 = -1;
2864 i = 18;
2865 ndigits = 0;
2866 break;
2867 case 2:
2868 leftright = 0;
2869 /* no break */
2870 case 4:
2871 if (ndigits <= 0)
2872 ndigits = 1;
2873 ilim = ilim1 = i = ndigits;
2874 break;
2875 case 3:
2876 leftright = 0;
2877 /* no break */
2878 case 5:
2879 i = ndigits + k + 1;
2880 ilim = i;
2881 ilim1 = i - 1;
2882 if (i <= 0)
2883 i = 1;
2884 }
2885 s = s0 = rv_alloc(i);
2886
2887#ifdef Honor_FLT_ROUNDS
2888 if (mode > 1 && rounding != 1)
2889 leftright = 0;
2890#endif
2891
2892 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2893
2894 /* Try to get by with floating-point arithmetic. */
2895
2896 i = 0;
2897 dval(d2) = dval(d);
2898 k0 = k;
2899 ilim0 = ilim;
2900 ieps = 2; /* conservative */
2901 if (k > 0) {
2902 ds = tens[k&0xf];
2903 j = k >> 4;
2904 if (j & Bletch) {
2905 /* prevent overflows */
2906 j &= Bletch - 1;
2907 dval(d) /= bigtens[n_bigtens-1];
2908 ieps++;
2909 }
2910 for(; j; j >>= 1, i++)
2911 if (j & 1) {
2912 ieps++;
2913 ds *= bigtens[i];
2914 }
2915 dval(d) /= ds;
2916 }
2917 else if ((j1 = -k)) {
2918 dval(d) *= tens[j1 & 0xf];
2919 for(j = j1 >> 4; j; j >>= 1, i++)
2920 if (j & 1) {
2921 ieps++;
2922 dval(d) *= bigtens[i];
2923 }
2924 }
2925 if (k_check && dval(d) < 1. && ilim > 0) {
2926 if (ilim1 <= 0)
2927 goto fast_failed;
2928 ilim = ilim1;
2929 k--;
2930 dval(d) *= 10.;
2931 ieps++;
2932 }
2933 dval(eps) = ieps*dval(d) + 7.;
2934 word0(eps) -= (P-1)*Exp_msk1;
2935 if (ilim == 0) {
2936 S = mhi = 0;
2937 dval(d) -= 5.;
2938 if (dval(d) > dval(eps))
2939 goto one_digit;
2940 if (dval(d) < -dval(eps))
2941 goto no_digits;
2942 goto fast_failed;
2943 }
2944#ifndef No_leftright
2945 if (leftright) {
2946 /* Use Steele & White method of only
2947 * generating digits needed.
2948 */
2949 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2950 for(i = 0;;) {
2951 L = (long int)dval(d);
2952 dval(d) -= L;
2953 *s++ = '0' + (int)L;
2954 if (dval(d) < dval(eps))
2955 goto ret1;
2956 if (1. - dval(d) < dval(eps))
2957 goto bump_up;
2958 if (++i >= ilim)
2959 break;
2960 dval(eps) *= 10.;
2961 dval(d) *= 10.;
2962 }
2963 }
2964 else {
2965#endif
2966 /* Generate ilim digits, then fix them up. */
2967 dval(eps) *= tens[ilim-1];
2968 for(i = 1;; i++, dval(d) *= 10.) {
2969 L = (Long)(dval(d));
2970 if (!(dval(d) -= L))
2971 ilim = i;
2972 *s++ = '0' + (int)L;
2973 if (i == ilim) {
2974 if (dval(d) > 0.5 + dval(eps))
2975 goto bump_up;
2976 else if (dval(d) < 0.5 - dval(eps)) {
2977 while(*--s == '0');
2978 s++;
2979 goto ret1;
2980 }
2981 break;
2982 }
2983 }
2984#ifndef No_leftright
2985 }
2986#endif
2987 fast_failed:
2988 s = s0;
2989 dval(d) = dval(d2);
2990 k = k0;
2991 ilim = ilim0;
2992 }
2993
2994 /* Do we have a "small" integer? */
2995
2996 if (be >= 0 && k <= Int_max) {
2997 /* Yes. */
2998 ds = tens[k];
2999 if (ndigits < 0 && ilim <= 0) {
3000 S = mhi = 0;
3001 if (ilim < 0 || dval(d) <= 5*ds)
3002 goto no_digits;
3003 goto one_digit;
3004 }
3005 for(i = 1;; i++, dval(d) *= 10.) {
3006 L = (Long)(dval(d) / ds);
3007 dval(d) -= L*ds;
3008#ifdef Check_FLT_ROUNDS
3009 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3010 if (dval(d) < 0) {
3011 L--;
3012 dval(d) += ds;
3013 }
3014#endif
3015 *s++ = '0' + (int)L;
3016 if (!dval(d)) {
3017#ifdef SET_INEXACT
3018 inexact = 0;
3019#endif
3020 break;
3021 }
3022 if (i == ilim) {
3023#ifdef Honor_FLT_ROUNDS
3024 if (mode > 1)
3025 switch(rounding) {
3026 case 0: goto ret1;
3027 case 2: goto bump_up;
3028 }
3029#endif
3030 dval(d) += dval(d);
3031 if (dval(d) > ds || dval(d) == ds && L & 1) {
3032 bump_up:
3033 while(*--s == '9')
3034 if (s == s0) {
3035 k++;
3036 *s = '0';
3037 break;
3038 }
3039 ++*s++;
3040 }
3041 break;
3042 }
3043 }
3044 goto ret1;
3045 }
3046
3047 m2 = b2;
3048 m5 = b5;
3049 mhi = mlo = 0;
3050 if (leftright) {
3051 i =
3052#ifndef Sudden_Underflow
3053 denorm ? be + (Bias + (P-1) - 1 + 1) :
3054#endif
3055#ifdef IBM
3056 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3057#else
3058 1 + P - bbits;
3059#endif
3060 b2 += i;
3061 s2 += i;
3062 mhi = i2b(1);
3063 }
3064 if (m2 > 0 && s2 > 0) {
3065 i = m2 < s2 ? m2 : s2;
3066 b2 -= i;
3067 m2 -= i;
3068 s2 -= i;
3069 }
3070 if (b5 > 0) {
3071 if (leftright) {
3072 if (m5 > 0) {
3073 mhi = pow5mult(mhi, m5);
3074 b1 = mult(mhi, b);
3075 Bfree(b);
3076 b = b1;
3077 }
3078 if ((j = b5 - m5))
3079 b = pow5mult(b, j);
3080 }
3081 else
3082 b = pow5mult(b, b5);
3083 }
3084 S = i2b(1);
3085 if (s5 > 0)
3086 S = pow5mult(S, s5);
3087
3088 /* Check for special case that d is a normalized power of 2. */
3089
3090 spec_case = 0;
3091 if ((mode < 2 || leftright)
3092#ifdef Honor_FLT_ROUNDS
3093 && rounding == 1
3094#endif
3095 ) {
3096 if (!word1(d) && !(word0(d) & Bndry_mask)
3097#ifndef Sudden_Underflow
3098 && word0(d) & (Exp_mask & ~Exp_msk1)
3099#endif
3100 ) {
3101 /* The special case */
3102 b2 += Log2P;
3103 s2 += Log2P;
3104 spec_case = 1;
3105 }
3106 }
3107
3108 /* Arrange for convenient computation of quotients:
3109 * shift left if necessary so divisor has 4 leading 0 bits.
3110 *
3111 * Perhaps we should just compute leading 28 bits of S once
3112 * and for all and pass them and a shift to quorem, so it
3113 * can do shifts and ors to compute the numerator for q.
3114 */
3115#ifdef Pack_32
3116 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3117 i = 32 - i;
3118#else
3119 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3120 i = 16 - i;
3121#endif
3122 if (i > 4) {
3123 i -= 4;
3124 b2 += i;
3125 m2 += i;
3126 s2 += i;
3127 }
3128 else if (i < 4) {
3129 i += 28;
3130 b2 += i;
3131 m2 += i;
3132 s2 += i;
3133 }
3134 if (b2 > 0)
3135 b = lshift(b, b2);
3136 if (s2 > 0)
3137 S = lshift(S, s2);
3138 if (k_check) {
3139 if (cmp(b,S) < 0) {
3140 k--;
3141 b = multadd(b, 10, 0); /* we botched the k estimate */
3142 if (leftright)
3143 mhi = multadd(mhi, 10, 0);
3144 ilim = ilim1;
3145 }
3146 }
3147 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3148 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3149 /* no digits, fcvt style */
3150 no_digits:
3151 k = -1 - ndigits;
3152 goto ret;
3153 }
3154 one_digit:
3155 *s++ = '1';
3156 k++;
3157 goto ret;
3158 }
3159 if (leftright) {
3160 if (m2 > 0)
3161 mhi = lshift(mhi, m2);
3162
3163 /* Compute mlo -- check for special case
3164 * that d is a normalized power of 2.
3165 */
3166
3167 mlo = mhi;
3168 if (spec_case) {
3169 mhi = Balloc(mhi->k);
3170 Bcopy(mhi, mlo);
3171 mhi = lshift(mhi, Log2P);
3172 }
3173
3174 for(i = 1;;i++) {
3175 dig = quorem(b,S) + '0';
3176 /* Do we yet have the shortest decimal string
3177 * that will round to d?
3178 */
3179 j = cmp(b, mlo);
3180 delta = diff(S, mhi);
3181 j1 = delta->sign ? 1 : cmp(b, delta);
3182 Bfree(delta);
3183#ifndef ROUND_BIASED
3184 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3185#ifdef Honor_FLT_ROUNDS
3186 && rounding >= 1
3187#endif
3188 ) {
3189 if (dig == '9')
3190 goto round_9_up;
3191 if (j > 0)
3192 dig++;
3193#ifdef SET_INEXACT
3194 else if (!b->x[0] && b->wds <= 1)
3195 inexact = 0;
3196#endif
3197 *s++ = dig;
3198 goto ret;
3199 }
3200#endif
3201 if (j < 0 || j == 0 && mode != 1
3202#ifndef ROUND_BIASED
3203 && !(word1(d) & 1)
3204#endif
3205 ) {
3206 if (!b->x[0] && b->wds <= 1) {
3207#ifdef SET_INEXACT
3208 inexact = 0;
3209#endif
3210 goto accept_dig;
3211 }
3212#ifdef Honor_FLT_ROUNDS
3213 if (mode > 1)
3214 switch(rounding) {
3215 case 0: goto accept_dig;
3216 case 2: goto keep_dig;
3217 }
3218#endif /*Honor_FLT_ROUNDS*/
3219 if (j1 > 0) {
3220 b = lshift(b, 1);
3221 j1 = cmp(b, S);
3222 if ((j1 > 0 || j1 == 0 && dig & 1)
3223 && dig++ == '9')
3224 goto round_9_up;
3225 }
3226 accept_dig:
3227 *s++ = dig;
3228 goto ret;
3229 }
3230 if (j1 > 0) {
3231#ifdef Honor_FLT_ROUNDS
3232 if (!rounding)
3233 goto accept_dig;
3234#endif
3235 if (dig == '9') { /* possible if i == 1 */
3236 round_9_up:
3237 *s++ = '9';
3238 goto roundoff;
3239 }
3240 *s++ = dig + 1;
3241 goto ret;
3242 }
3243#ifdef Honor_FLT_ROUNDS
3244 keep_dig:
3245#endif
3246 *s++ = dig;
3247 if (i == ilim)
3248 break;
3249 b = multadd(b, 10, 0);
3250 if (mlo == mhi)
3251 mlo = mhi = multadd(mhi, 10, 0);
3252 else {
3253 mlo = multadd(mlo, 10, 0);
3254 mhi = multadd(mhi, 10, 0);
3255 }
3256 }
3257 }
3258 else
3259 for(i = 1;; i++) {
3260 *s++ = dig = quorem(b,S) + '0';
3261 if (!b->x[0] && b->wds <= 1) {
3262#ifdef SET_INEXACT
3263 inexact = 0;
3264#endif
3265 goto ret;
3266 }
3267 if (i >= ilim)
3268 break;
3269 b = multadd(b, 10, 0);
3270 }
3271
3272 /* Round off last digit */
3273
3274#ifdef Honor_FLT_ROUNDS
3275 switch(rounding) {
3276 case 0: goto trimzeros;
3277 case 2: goto roundoff;
3278 }
3279#endif
3280 b = lshift(b, 1);
3281 j = cmp(b, S);
3282 if (j > 0 || j == 0 && dig & 1) {
3283 roundoff:
3284 while(*--s == '9')
3285 if (s == s0) {
3286 k++;
3287 *s++ = '1';
3288 goto ret;
3289 }
3290 ++*s++;
3291 }
3292 else {
3293#ifdef Honor_FLT_ROUNDS
3294trimzeros:
3295#endif
3296 while(*--s == '0');
3297 s++;
3298 }
3299 ret:
3300 Bfree(S);
3301 if (mhi) {
3302 if (mlo && mlo != mhi)
3303 Bfree(mlo);
3304 Bfree(mhi);
3305 }
3306 ret1:
3307#ifdef SET_INEXACT
3308 if (inexact) {
3309 if (!oldinexact) {
3310 word0(d) = Exp_1 + (70 << Exp_shift);
3311 word1(d) = 0;
3312 dval(d) += 1.;
3313 }
3314 }
3315 else if (!oldinexact)
3316 clear_inexact();
3317#endif
3318 Bfree(b);
3319 *s = 0;
3320 *decpt = k + 1;
3321 if (rve)
3322 *rve = s;
3323 return s0;
3324 }
3325#ifdef __cplusplus
3326}
3327#endif
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