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authorMark Pulford <mark@kyne.com.au>2011-12-29 08:10:57 +1030
committerMark Pulford <mark@kyne.com.au>2011-12-29 08:10:57 +1030
commit23d19ba2551e6f432ada6f7cd5ac3e874b4d35d1 (patch)
tree7fe925f57d9bc2bc91dcdb60f1d9df50360d22fa /dtoa.c
parenta336401403ed55ca1956c627a5413e456b1f87e8 (diff)
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Added Netlib dtoa.c/g_fmt.c routines (20110428)
See "www.netlib.org/fp/changes" for details.
Diffstat (limited to 'dtoa.c')
-rw-r--r--dtoa.c4356
1 files changed, 4356 insertions, 0 deletions
diff --git a/dtoa.c b/dtoa.c
new file mode 100644
index 0000000..4a458a4
--- /dev/null
+++ b/dtoa.c
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1/****************************************************************
2 *
3 * The author of this software is David M. Gay.
4 *
5 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
6 *
7 * Permission to use, copy, modify, and distribute this software for any
8 * purpose without fee is hereby granted, provided that this entire notice
9 * is included in all copies of any software which is or includes a copy
10 * or modification of this software and in all copies of the supporting
11 * documentation for such software.
12 *
13 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
14 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
15 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
16 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
17 *
18 ***************************************************************/
19
20/* Please send bug reports to David M. Gay (dmg at acm dot org,
21 * with " at " changed at "@" and " dot " changed to "."). */
22
23/* On a machine with IEEE extended-precision registers, it is
24 * necessary to specify double-precision (53-bit) rounding precision
25 * before invoking strtod or dtoa. If the machine uses (the equivalent
26 * of) Intel 80x87 arithmetic, the call
27 * _control87(PC_53, MCW_PC);
28 * does this with many compilers. Whether this or another call is
29 * appropriate depends on the compiler; for this to work, it may be
30 * necessary to #include "float.h" or another system-dependent header
31 * file.
32 */
33
34/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
35 *
36 * This strtod returns a nearest machine number to the input decimal
37 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
38 * broken by the IEEE round-even rule. Otherwise ties are broken by
39 * biased rounding (add half and chop).
40 *
41 * Inspired loosely by William D. Clinger's paper "How to Read Floating
42 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
43 *
44 * Modifications:
45 *
46 * 1. We only require IEEE, IBM, or VAX double-precision
47 * arithmetic (not IEEE double-extended).
48 * 2. We get by with floating-point arithmetic in a case that
49 * Clinger missed -- when we're computing d * 10^n
50 * for a small integer d and the integer n is not too
51 * much larger than 22 (the maximum integer k for which
52 * we can represent 10^k exactly), we may be able to
53 * compute (d*10^k) * 10^(e-k) with just one roundoff.
54 * 3. Rather than a bit-at-a-time adjustment of the binary
55 * result in the hard case, we use floating-point
56 * arithmetic to determine the adjustment to within
57 * one bit; only in really hard cases do we need to
58 * compute a second residual.
59 * 4. Because of 3., we don't need a large table of powers of 10
60 * for ten-to-e (just some small tables, e.g. of 10^k
61 * for 0 <= k <= 22).
62 */
63
64/*
65 * #define IEEE_8087 for IEEE-arithmetic machines where the least
66 * significant byte has the lowest address.
67 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
68 * significant byte has the lowest address.
69 * #define Long int on machines with 32-bit ints and 64-bit longs.
70 * #define IBM for IBM mainframe-style floating-point arithmetic.
71 * #define VAX for VAX-style floating-point arithmetic (D_floating).
72 * #define No_leftright to omit left-right logic in fast floating-point
73 * computation of dtoa. This will cause dtoa modes 4 and 5 to be
74 * treated the same as modes 2 and 3 for some inputs.
75 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
76 * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS
77 * is also #defined, fegetround() will be queried for the rounding mode.
78 * Note that both FLT_ROUNDS and fegetround() are specified by the C99
79 * standard (and are specified to be consistent, with fesetround()
80 * affecting the value of FLT_ROUNDS), but that some (Linux) systems
81 * do not work correctly in this regard, so using fegetround() is more
82 * portable than using FLT_ROUNDS directly.
83 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
84 * and Honor_FLT_ROUNDS is not #defined.
85 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
86 * that use extended-precision instructions to compute rounded
87 * products and quotients) with IBM.
88 * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic
89 * that rounds toward +Infinity.
90 * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased
91 * rounding when the underlying floating-point arithmetic uses
92 * unbiased rounding. This prevent using ordinary floating-point
93 * arithmetic when the result could be computed with one rounding error.
94 * #define Inaccurate_Divide for IEEE-format with correctly rounded
95 * products but inaccurate quotients, e.g., for Intel i860.
96 * #define NO_LONG_LONG on machines that do not have a "long long"
97 * integer type (of >= 64 bits). On such machines, you can
98 * #define Just_16 to store 16 bits per 32-bit Long when doing
99 * high-precision integer arithmetic. Whether this speeds things
100 * up or slows things down depends on the machine and the number
101 * being converted. If long long is available and the name is
102 * something other than "long long", #define Llong to be the name,
103 * and if "unsigned Llong" does not work as an unsigned version of
104 * Llong, #define #ULLong to be the corresponding unsigned type.
105 * #define KR_headers for old-style C function headers.
106 * #define Bad_float_h if your system lacks a float.h or if it does not
107 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
108 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
109 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
110 * if memory is available and otherwise does something you deem
111 * appropriate. If MALLOC is undefined, malloc will be invoked
112 * directly -- and assumed always to succeed. Similarly, if you
113 * want something other than the system's free() to be called to
114 * recycle memory acquired from MALLOC, #define FREE to be the
115 * name of the alternate routine. (FREE or free is only called in
116 * pathological cases, e.g., in a dtoa call after a dtoa return in
117 * mode 3 with thousands of digits requested.)
118 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
119 * memory allocations from a private pool of memory when possible.
120 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
121 * unless #defined to be a different length. This default length
122 * suffices to get rid of MALLOC calls except for unusual cases,
123 * such as decimal-to-binary conversion of a very long string of
124 * digits. The longest string dtoa can return is about 751 bytes
125 * long. For conversions by strtod of strings of 800 digits and
126 * all dtoa conversions in single-threaded executions with 8-byte
127 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
128 * pointers, PRIVATE_MEM >= 7112 appears adequate.
129 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
130 * #defined automatically on IEEE systems. On such systems,
131 * when INFNAN_CHECK is #defined, strtod checks
132 * for Infinity and NaN (case insensitively). On some systems
133 * (e.g., some HP systems), it may be necessary to #define NAN_WORD0
134 * appropriately -- to the most significant word of a quiet NaN.
135 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
136 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
137 * strtod also accepts (case insensitively) strings of the form
138 * NaN(x), where x is a string of hexadecimal digits and spaces;
139 * if there is only one string of hexadecimal digits, it is taken
140 * for the 52 fraction bits of the resulting NaN; if there are two
141 * or more strings of hex digits, the first is for the high 20 bits,
142 * the second and subsequent for the low 32 bits, with intervening
143 * white space ignored; but if this results in none of the 52
144 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
145 * and NAN_WORD1 are used instead.
146 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
147 * multiple threads. In this case, you must provide (or suitably
148 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
149 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
150 * in pow5mult, ensures lazy evaluation of only one copy of high
151 * powers of 5; omitting this lock would introduce a small
152 * probability of wasting memory, but would otherwise be harmless.)
153 * You must also invoke freedtoa(s) to free the value s returned by
154 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
155 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
156 * avoids underflows on inputs whose result does not underflow.
157 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
158 * floating-point numbers and flushes underflows to zero rather
159 * than implementing gradual underflow, then you must also #define
160 * Sudden_Underflow.
161 * #define USE_LOCALE to use the current locale's decimal_point value.
162 * #define SET_INEXACT if IEEE arithmetic is being used and extra
163 * computation should be done to set the inexact flag when the
164 * result is inexact and avoid setting inexact when the result
165 * is exact. In this case, dtoa.c must be compiled in
166 * an environment, perhaps provided by #include "dtoa.c" in a
167 * suitable wrapper, that defines two functions,
168 * int get_inexact(void);
169 * void clear_inexact(void);
170 * such that get_inexact() returns a nonzero value if the
171 * inexact bit is already set, and clear_inexact() sets the
172 * inexact bit to 0. When SET_INEXACT is #defined, strtod
173 * also does extra computations to set the underflow and overflow
174 * flags when appropriate (i.e., when the result is tiny and
175 * inexact or when it is a numeric value rounded to +-infinity).
176 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
177 * the result overflows to +-Infinity or underflows to 0.
178 * #define NO_HEX_FP to omit recognition of hexadecimal floating-point
179 * values by strtod.
180 * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
181 * to disable logic for "fast" testing of very long input strings
182 * to strtod. This testing proceeds by initially truncating the
183 * input string, then if necessary comparing the whole string with
184 * a decimal expansion to decide close cases. This logic is only
185 * used for input more than STRTOD_DIGLIM digits long (default 40).
186 */
187
188#ifndef Long
189#define Long long
190#endif
191#ifndef ULong
192typedef unsigned Long ULong;
193#endif
194
195#ifdef DEBUG
196#include "stdio.h"
197#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
198#endif
199
200#include "stdlib.h"
201#include "string.h"
202
203#ifdef USE_LOCALE
204#include "locale.h"
205#endif
206
207#ifdef Honor_FLT_ROUNDS
208#ifndef Trust_FLT_ROUNDS
209#include <fenv.h>
210#endif
211#endif
212
213#ifdef MALLOC
214#ifdef KR_headers
215extern char *MALLOC();
216#else
217extern void *MALLOC(size_t);
218#endif
219#else
220#define MALLOC malloc
221#endif
222
223#ifndef Omit_Private_Memory
224#ifndef PRIVATE_MEM
225#define PRIVATE_MEM 2304
226#endif
227#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
228static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
229#endif
230
231#undef IEEE_Arith
232#undef Avoid_Underflow
233#ifdef IEEE_MC68k
234#define IEEE_Arith
235#endif
236#ifdef IEEE_8087
237#define IEEE_Arith
238#endif
239
240#ifdef IEEE_Arith
241#ifndef NO_INFNAN_CHECK
242#undef INFNAN_CHECK
243#define INFNAN_CHECK
244#endif
245#else
246#undef INFNAN_CHECK
247#define NO_STRTOD_BIGCOMP
248#endif
249
250#include "errno.h"
251
252#ifdef Bad_float_h
253
254#ifdef IEEE_Arith
255#define DBL_DIG 15
256#define DBL_MAX_10_EXP 308
257#define DBL_MAX_EXP 1024
258#define FLT_RADIX 2
259#endif /*IEEE_Arith*/
260
261#ifdef IBM
262#define DBL_DIG 16
263#define DBL_MAX_10_EXP 75
264#define DBL_MAX_EXP 63
265#define FLT_RADIX 16
266#define DBL_MAX 7.2370055773322621e+75
267#endif
268
269#ifdef VAX
270#define DBL_DIG 16
271#define DBL_MAX_10_EXP 38
272#define DBL_MAX_EXP 127
273#define FLT_RADIX 2
274#define DBL_MAX 1.7014118346046923e+38
275#endif
276
277#ifndef LONG_MAX
278#define LONG_MAX 2147483647
279#endif
280
281#else /* ifndef Bad_float_h */
282#include "float.h"
283#endif /* Bad_float_h */
284
285#ifndef __MATH_H__
286#include "math.h"
287#endif
288
289#ifdef __cplusplus
290extern "C" {
291#endif
292
293#ifndef CONST
294#ifdef KR_headers
295#define CONST /* blank */
296#else
297#define CONST const
298#endif
299#endif
300
301#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
302Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
303#endif
304
305typedef union { double d; ULong L[2]; } U;
306
307#ifdef IEEE_8087
308#define word0(x) (x)->L[1]
309#define word1(x) (x)->L[0]
310#else
311#define word0(x) (x)->L[0]
312#define word1(x) (x)->L[1]
313#endif
314#define dval(x) (x)->d
315
316#ifndef STRTOD_DIGLIM
317#define STRTOD_DIGLIM 40
318#endif
319
320#ifdef DIGLIM_DEBUG
321extern int strtod_diglim;
322#else
323#define strtod_diglim STRTOD_DIGLIM
324#endif
325
326/* The following definition of Storeinc is appropriate for MIPS processors.
327 * An alternative that might be better on some machines is
328 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
329 */
330#if defined(IEEE_8087) + defined(VAX)
331#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
332((unsigned short *)a)[0] = (unsigned short)c, a++)
333#else
334#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
335((unsigned short *)a)[1] = (unsigned short)c, a++)
336#endif
337
338/* #define P DBL_MANT_DIG */
339/* Ten_pmax = floor(P*log(2)/log(5)) */
340/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
341/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
342/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
343
344#ifdef IEEE_Arith
345#define Exp_shift 20
346#define Exp_shift1 20
347#define Exp_msk1 0x100000
348#define Exp_msk11 0x100000
349#define Exp_mask 0x7ff00000
350#define P 53
351#define Nbits 53
352#define Bias 1023
353#define Emax 1023
354#define Emin (-1022)
355#define Exp_1 0x3ff00000
356#define Exp_11 0x3ff00000
357#define Ebits 11
358#define Frac_mask 0xfffff
359#define Frac_mask1 0xfffff
360#define Ten_pmax 22
361#define Bletch 0x10
362#define Bndry_mask 0xfffff
363#define Bndry_mask1 0xfffff
364#define LSB 1
365#define Sign_bit 0x80000000
366#define Log2P 1
367#define Tiny0 0
368#define Tiny1 1
369#define Quick_max 14
370#define Int_max 14
371#ifndef NO_IEEE_Scale
372#define Avoid_Underflow
373#ifdef Flush_Denorm /* debugging option */
374#undef Sudden_Underflow
375#endif
376#endif
377
378#ifndef Flt_Rounds
379#ifdef FLT_ROUNDS
380#define Flt_Rounds FLT_ROUNDS
381#else
382#define Flt_Rounds 1
383#endif
384#endif /*Flt_Rounds*/
385
386#ifdef Honor_FLT_ROUNDS
387#undef Check_FLT_ROUNDS
388#define Check_FLT_ROUNDS
389#else
390#define Rounding Flt_Rounds
391#endif
392
393#else /* ifndef IEEE_Arith */
394#undef Check_FLT_ROUNDS
395#undef Honor_FLT_ROUNDS
396#undef SET_INEXACT
397#undef Sudden_Underflow
398#define Sudden_Underflow
399#ifdef IBM
400#undef Flt_Rounds
401#define Flt_Rounds 0
402#define Exp_shift 24
403#define Exp_shift1 24
404#define Exp_msk1 0x1000000
405#define Exp_msk11 0x1000000
406#define Exp_mask 0x7f000000
407#define P 14
408#define Nbits 56
409#define Bias 65
410#define Emax 248
411#define Emin (-260)
412#define Exp_1 0x41000000
413#define Exp_11 0x41000000
414#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
415#define Frac_mask 0xffffff
416#define Frac_mask1 0xffffff
417#define Bletch 4
418#define Ten_pmax 22
419#define Bndry_mask 0xefffff
420#define Bndry_mask1 0xffffff
421#define LSB 1
422#define Sign_bit 0x80000000
423#define Log2P 4
424#define Tiny0 0x100000
425#define Tiny1 0
426#define Quick_max 14
427#define Int_max 15
428#else /* VAX */
429#undef Flt_Rounds
430#define Flt_Rounds 1
431#define Exp_shift 23
432#define Exp_shift1 7
433#define Exp_msk1 0x80
434#define Exp_msk11 0x800000
435#define Exp_mask 0x7f80
436#define P 56
437#define Nbits 56
438#define Bias 129
439#define Emax 126
440#define Emin (-129)
441#define Exp_1 0x40800000
442#define Exp_11 0x4080
443#define Ebits 8
444#define Frac_mask 0x7fffff
445#define Frac_mask1 0xffff007f
446#define Ten_pmax 24
447#define Bletch 2
448#define Bndry_mask 0xffff007f
449#define Bndry_mask1 0xffff007f
450#define LSB 0x10000
451#define Sign_bit 0x8000
452#define Log2P 1
453#define Tiny0 0x80
454#define Tiny1 0
455#define Quick_max 15
456#define Int_max 15
457#endif /* IBM, VAX */
458#endif /* IEEE_Arith */
459
460#ifndef IEEE_Arith
461#define ROUND_BIASED
462#else
463#ifdef ROUND_BIASED_without_Round_Up
464#undef ROUND_BIASED
465#define ROUND_BIASED
466#endif
467#endif
468
469#ifdef RND_PRODQUOT
470#define rounded_product(a,b) a = rnd_prod(a, b)
471#define rounded_quotient(a,b) a = rnd_quot(a, b)
472#ifdef KR_headers
473extern double rnd_prod(), rnd_quot();
474#else
475extern double rnd_prod(double, double), rnd_quot(double, double);
476#endif
477#else
478#define rounded_product(a,b) a *= b
479#define rounded_quotient(a,b) a /= b
480#endif
481
482#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
483#define Big1 0xffffffff
484
485#ifndef Pack_32
486#define Pack_32
487#endif
488
489typedef struct BCinfo BCinfo;
490 struct
491BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };
492
493#ifdef KR_headers
494#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
495#else
496#define FFFFFFFF 0xffffffffUL
497#endif
498
499#ifdef NO_LONG_LONG
500#undef ULLong
501#ifdef Just_16
502#undef Pack_32
503/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
504 * This makes some inner loops simpler and sometimes saves work
505 * during multiplications, but it often seems to make things slightly
506 * slower. Hence the default is now to store 32 bits per Long.
507 */
508#endif
509#else /* long long available */
510#ifndef Llong
511#define Llong long long
512#endif
513#ifndef ULLong
514#define ULLong unsigned Llong
515#endif
516#endif /* NO_LONG_LONG */
517
518#ifndef MULTIPLE_THREADS
519#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
520#define FREE_DTOA_LOCK(n) /*nothing*/
521#endif
522
523#define Kmax 7
524
525#ifdef __cplusplus
526extern "C" double strtod(const char *s00, char **se);
527extern "C" char *dtoa(double d, int mode, int ndigits,
528 int *decpt, int *sign, char **rve);
529#endif
530
531 struct
532Bigint {
533 struct Bigint *next;
534 int k, maxwds, sign, wds;
535 ULong x[1];
536 };
537
538 typedef struct Bigint Bigint;
539
540 static Bigint *freelist[Kmax+1];
541
542 static Bigint *
543Balloc
544#ifdef KR_headers
545 (k) int k;
546#else
547 (int k)
548#endif
549{
550 int x;
551 Bigint *rv;
552#ifndef Omit_Private_Memory
553 unsigned int len;
554#endif
555
556 ACQUIRE_DTOA_LOCK(0);
557 /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
558 /* but this case seems very unlikely. */
559 if (k <= Kmax && (rv = freelist[k]))
560 freelist[k] = rv->next;
561 else {
562 x = 1 << k;
563#ifdef Omit_Private_Memory
564 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
565#else
566 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
567 /sizeof(double);
568 if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
569 rv = (Bigint*)pmem_next;
570 pmem_next += len;
571 }
572 else
573 rv = (Bigint*)MALLOC(len*sizeof(double));
574#endif
575 rv->k = k;
576 rv->maxwds = x;
577 }
578 FREE_DTOA_LOCK(0);
579 rv->sign = rv->wds = 0;
580 return rv;
581 }
582
583 static void
584Bfree
585#ifdef KR_headers
586 (v) Bigint *v;
587#else
588 (Bigint *v)
589#endif
590{
591 if (v) {
592 if (v->k > Kmax)
593#ifdef FREE
594 FREE((void*)v);
595#else
596 free((void*)v);
597#endif
598 else {
599 ACQUIRE_DTOA_LOCK(0);
600 v->next = freelist[v->k];
601 freelist[v->k] = v;
602 FREE_DTOA_LOCK(0);
603 }
604 }
605 }
606
607#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
608y->wds*sizeof(Long) + 2*sizeof(int))
609
610 static Bigint *
611multadd
612#ifdef KR_headers
613 (b, m, a) Bigint *b; int m, a;
614#else
615 (Bigint *b, int m, int a) /* multiply by m and add a */
616#endif
617{
618 int i, wds;
619#ifdef ULLong
620 ULong *x;
621 ULLong carry, y;
622#else
623 ULong carry, *x, y;
624#ifdef Pack_32
625 ULong xi, z;
626#endif
627#endif
628 Bigint *b1;
629
630 wds = b->wds;
631 x = b->x;
632 i = 0;
633 carry = a;
634 do {
635#ifdef ULLong
636 y = *x * (ULLong)m + carry;
637 carry = y >> 32;
638 *x++ = y & FFFFFFFF;
639#else
640#ifdef Pack_32
641 xi = *x;
642 y = (xi & 0xffff) * m + carry;
643 z = (xi >> 16) * m + (y >> 16);
644 carry = z >> 16;
645 *x++ = (z << 16) + (y & 0xffff);
646#else
647 y = *x * m + carry;
648 carry = y >> 16;
649 *x++ = y & 0xffff;
650#endif
651#endif
652 }
653 while(++i < wds);
654 if (carry) {
655 if (wds >= b->maxwds) {
656 b1 = Balloc(b->k+1);
657 Bcopy(b1, b);
658 Bfree(b);
659 b = b1;
660 }
661 b->x[wds++] = carry;
662 b->wds = wds;
663 }
664 return b;
665 }
666
667 static Bigint *
668s2b
669#ifdef KR_headers
670 (s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9;
671#else
672 (const char *s, int nd0, int nd, ULong y9, int dplen)
673#endif
674{
675 Bigint *b;
676 int i, k;
677 Long x, y;
678
679 x = (nd + 8) / 9;
680 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
681#ifdef Pack_32
682 b = Balloc(k);
683 b->x[0] = y9;
684 b->wds = 1;
685#else
686 b = Balloc(k+1);
687 b->x[0] = y9 & 0xffff;
688 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
689#endif
690
691 i = 9;
692 if (9 < nd0) {
693 s += 9;
694 do b = multadd(b, 10, *s++ - '0');
695 while(++i < nd0);
696 s += dplen;
697 }
698 else
699 s += dplen + 9;
700 for(; i < nd; i++)
701 b = multadd(b, 10, *s++ - '0');
702 return b;
703 }
704
705 static int
706hi0bits
707#ifdef KR_headers
708 (x) ULong x;
709#else
710 (ULong x)
711#endif
712{
713 int k = 0;
714
715 if (!(x & 0xffff0000)) {
716 k = 16;
717 x <<= 16;
718 }
719 if (!(x & 0xff000000)) {
720 k += 8;
721 x <<= 8;
722 }
723 if (!(x & 0xf0000000)) {
724 k += 4;
725 x <<= 4;
726 }
727 if (!(x & 0xc0000000)) {
728 k += 2;
729 x <<= 2;
730 }
731 if (!(x & 0x80000000)) {
732 k++;
733 if (!(x & 0x40000000))
734 return 32;
735 }
736 return k;
737 }
738
739 static int
740lo0bits
741#ifdef KR_headers
742 (y) ULong *y;
743#else
744 (ULong *y)
745#endif
746{
747 int k;
748 ULong x = *y;
749
750 if (x & 7) {
751 if (x & 1)
752 return 0;
753 if (x & 2) {
754 *y = x >> 1;
755 return 1;
756 }
757 *y = x >> 2;
758 return 2;
759 }
760 k = 0;
761 if (!(x & 0xffff)) {
762 k = 16;
763 x >>= 16;
764 }
765 if (!(x & 0xff)) {
766 k += 8;
767 x >>= 8;
768 }
769 if (!(x & 0xf)) {
770 k += 4;
771 x >>= 4;
772 }
773 if (!(x & 0x3)) {
774 k += 2;
775 x >>= 2;
776 }
777 if (!(x & 1)) {
778 k++;
779 x >>= 1;
780 if (!x)
781 return 32;
782 }
783 *y = x;
784 return k;
785 }
786
787 static Bigint *
788i2b
789#ifdef KR_headers
790 (i) int i;
791#else
792 (int i)
793#endif
794{
795 Bigint *b;
796
797 b = Balloc(1);
798 b->x[0] = i;
799 b->wds = 1;
800 return b;
801 }
802
803 static Bigint *
804mult
805#ifdef KR_headers
806 (a, b) Bigint *a, *b;
807#else
808 (Bigint *a, Bigint *b)
809#endif
810{
811 Bigint *c;
812 int k, wa, wb, wc;
813 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
814 ULong y;
815#ifdef ULLong
816 ULLong carry, z;
817#else
818 ULong carry, z;
819#ifdef Pack_32
820 ULong z2;
821#endif
822#endif
823
824 if (a->wds < b->wds) {
825 c = a;
826 a = b;
827 b = c;
828 }
829 k = a->k;
830 wa = a->wds;
831 wb = b->wds;
832 wc = wa + wb;
833 if (wc > a->maxwds)
834 k++;
835 c = Balloc(k);
836 for(x = c->x, xa = x + wc; x < xa; x++)
837 *x = 0;
838 xa = a->x;
839 xae = xa + wa;
840 xb = b->x;
841 xbe = xb + wb;
842 xc0 = c->x;
843#ifdef ULLong
844 for(; xb < xbe; xc0++) {
845 if ((y = *xb++)) {
846 x = xa;
847 xc = xc0;
848 carry = 0;
849 do {
850 z = *x++ * (ULLong)y + *xc + carry;
851 carry = z >> 32;
852 *xc++ = z & FFFFFFFF;
853 }
854 while(x < xae);
855 *xc = carry;
856 }
857 }
858#else
859#ifdef Pack_32
860 for(; xb < xbe; xb++, xc0++) {
861 if (y = *xb & 0xffff) {
862 x = xa;
863 xc = xc0;
864 carry = 0;
865 do {
866 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
867 carry = z >> 16;
868 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
869 carry = z2 >> 16;
870 Storeinc(xc, z2, z);
871 }
872 while(x < xae);
873 *xc = carry;
874 }
875 if (y = *xb >> 16) {
876 x = xa;
877 xc = xc0;
878 carry = 0;
879 z2 = *xc;
880 do {
881 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
882 carry = z >> 16;
883 Storeinc(xc, z, z2);
884 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
885 carry = z2 >> 16;
886 }
887 while(x < xae);
888 *xc = z2;
889 }
890 }
891#else
892 for(; xb < xbe; xc0++) {
893 if (y = *xb++) {
894 x = xa;
895 xc = xc0;
896 carry = 0;
897 do {
898 z = *x++ * y + *xc + carry;
899 carry = z >> 16;
900 *xc++ = z & 0xffff;
901 }
902 while(x < xae);
903 *xc = carry;
904 }
905 }
906#endif
907#endif
908 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
909 c->wds = wc;
910 return c;
911 }
912
913 static Bigint *p5s;
914
915 static Bigint *
916pow5mult
917#ifdef KR_headers
918 (b, k) Bigint *b; int k;
919#else
920 (Bigint *b, int k)
921#endif
922{
923 Bigint *b1, *p5, *p51;
924 int i;
925 static int p05[3] = { 5, 25, 125 };
926
927 if ((i = k & 3))
928 b = multadd(b, p05[i-1], 0);
929
930 if (!(k >>= 2))
931 return b;
932 if (!(p5 = p5s)) {
933 /* first time */
934#ifdef MULTIPLE_THREADS
935 ACQUIRE_DTOA_LOCK(1);
936 if (!(p5 = p5s)) {
937 p5 = p5s = i2b(625);
938 p5->next = 0;
939 }
940 FREE_DTOA_LOCK(1);
941#else
942 p5 = p5s = i2b(625);
943 p5->next = 0;
944#endif
945 }
946 for(;;) {
947 if (k & 1) {
948 b1 = mult(b, p5);
949 Bfree(b);
950 b = b1;
951 }
952 if (!(k >>= 1))
953 break;
954 if (!(p51 = p5->next)) {
955#ifdef MULTIPLE_THREADS
956 ACQUIRE_DTOA_LOCK(1);
957 if (!(p51 = p5->next)) {
958 p51 = p5->next = mult(p5,p5);
959 p51->next = 0;
960 }
961 FREE_DTOA_LOCK(1);
962#else
963 p51 = p5->next = mult(p5,p5);
964 p51->next = 0;
965#endif
966 }
967 p5 = p51;
968 }
969 return b;
970 }
971
972 static Bigint *
973lshift
974#ifdef KR_headers
975 (b, k) Bigint *b; int k;
976#else
977 (Bigint *b, int k)
978#endif
979{
980 int i, k1, n, n1;
981 Bigint *b1;
982 ULong *x, *x1, *xe, z;
983
984#ifdef Pack_32
985 n = k >> 5;
986#else
987 n = k >> 4;
988#endif
989 k1 = b->k;
990 n1 = n + b->wds + 1;
991 for(i = b->maxwds; n1 > i; i <<= 1)
992 k1++;
993 b1 = Balloc(k1);
994 x1 = b1->x;
995 for(i = 0; i < n; i++)
996 *x1++ = 0;
997 x = b->x;
998 xe = x + b->wds;
999#ifdef Pack_32
1000 if (k &= 0x1f) {
1001 k1 = 32 - k;
1002 z = 0;
1003 do {
1004 *x1++ = *x << k | z;
1005 z = *x++ >> k1;
1006 }
1007 while(x < xe);
1008 if ((*x1 = z))
1009 ++n1;
1010 }
1011#else
1012 if (k &= 0xf) {
1013 k1 = 16 - k;
1014 z = 0;
1015 do {
1016 *x1++ = *x << k & 0xffff | z;
1017 z = *x++ >> k1;
1018 }
1019 while(x < xe);
1020 if (*x1 = z)
1021 ++n1;
1022 }
1023#endif
1024 else do
1025 *x1++ = *x++;
1026 while(x < xe);
1027 b1->wds = n1 - 1;
1028 Bfree(b);
1029 return b1;
1030 }
1031
1032 static int
1033cmp
1034#ifdef KR_headers
1035 (a, b) Bigint *a, *b;
1036#else
1037 (Bigint *a, Bigint *b)
1038#endif
1039{
1040 ULong *xa, *xa0, *xb, *xb0;
1041 int i, j;
1042
1043 i = a->wds;
1044 j = b->wds;
1045#ifdef DEBUG
1046 if (i > 1 && !a->x[i-1])
1047 Bug("cmp called with a->x[a->wds-1] == 0");
1048 if (j > 1 && !b->x[j-1])
1049 Bug("cmp called with b->x[b->wds-1] == 0");
1050#endif
1051 if (i -= j)
1052 return i;
1053 xa0 = a->x;
1054 xa = xa0 + j;
1055 xb0 = b->x;
1056 xb = xb0 + j;
1057 for(;;) {
1058 if (*--xa != *--xb)
1059 return *xa < *xb ? -1 : 1;
1060 if (xa <= xa0)
1061 break;
1062 }
1063 return 0;
1064 }
1065
1066 static Bigint *
1067diff
1068#ifdef KR_headers
1069 (a, b) Bigint *a, *b;
1070#else
1071 (Bigint *a, Bigint *b)
1072#endif
1073{
1074 Bigint *c;
1075 int i, wa, wb;
1076 ULong *xa, *xae, *xb, *xbe, *xc;
1077#ifdef ULLong
1078 ULLong borrow, y;
1079#else
1080 ULong borrow, y;
1081#ifdef Pack_32
1082 ULong z;
1083#endif
1084#endif
1085
1086 i = cmp(a,b);
1087 if (!i) {
1088 c = Balloc(0);
1089 c->wds = 1;
1090 c->x[0] = 0;
1091 return c;
1092 }
1093 if (i < 0) {
1094 c = a;
1095 a = b;
1096 b = c;
1097 i = 1;
1098 }
1099 else
1100 i = 0;
1101 c = Balloc(a->k);
1102 c->sign = i;
1103 wa = a->wds;
1104 xa = a->x;
1105 xae = xa + wa;
1106 wb = b->wds;
1107 xb = b->x;
1108 xbe = xb + wb;
1109 xc = c->x;
1110 borrow = 0;
1111#ifdef ULLong
1112 do {
1113 y = (ULLong)*xa++ - *xb++ - borrow;
1114 borrow = y >> 32 & (ULong)1;
1115 *xc++ = y & FFFFFFFF;
1116 }
1117 while(xb < xbe);
1118 while(xa < xae) {
1119 y = *xa++ - borrow;
1120 borrow = y >> 32 & (ULong)1;
1121 *xc++ = y & FFFFFFFF;
1122 }
1123#else
1124#ifdef Pack_32
1125 do {
1126 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1127 borrow = (y & 0x10000) >> 16;
1128 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1129 borrow = (z & 0x10000) >> 16;
1130 Storeinc(xc, z, y);
1131 }
1132 while(xb < xbe);
1133 while(xa < xae) {
1134 y = (*xa & 0xffff) - borrow;
1135 borrow = (y & 0x10000) >> 16;
1136 z = (*xa++ >> 16) - borrow;
1137 borrow = (z & 0x10000) >> 16;
1138 Storeinc(xc, z, y);
1139 }
1140#else
1141 do {
1142 y = *xa++ - *xb++ - borrow;
1143 borrow = (y & 0x10000) >> 16;
1144 *xc++ = y & 0xffff;
1145 }
1146 while(xb < xbe);
1147 while(xa < xae) {
1148 y = *xa++ - borrow;
1149 borrow = (y & 0x10000) >> 16;
1150 *xc++ = y & 0xffff;
1151 }
1152#endif
1153#endif
1154 while(!*--xc)
1155 wa--;
1156 c->wds = wa;
1157 return c;
1158 }
1159
1160 static double
1161ulp
1162#ifdef KR_headers
1163 (x) U *x;
1164#else
1165 (U *x)
1166#endif
1167{
1168 Long L;
1169 U u;
1170
1171 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1172#ifndef Avoid_Underflow
1173#ifndef Sudden_Underflow
1174 if (L > 0) {
1175#endif
1176#endif
1177#ifdef IBM
1178 L |= Exp_msk1 >> 4;
1179#endif
1180 word0(&u) = L;
1181 word1(&u) = 0;
1182#ifndef Avoid_Underflow
1183#ifndef Sudden_Underflow
1184 }
1185 else {
1186 L = -L >> Exp_shift;
1187 if (L < Exp_shift) {
1188 word0(&u) = 0x80000 >> L;
1189 word1(&u) = 0;
1190 }
1191 else {
1192 word0(&u) = 0;
1193 L -= Exp_shift;
1194 word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
1195 }
1196 }
1197#endif
1198#endif
1199 return dval(&u);
1200 }
1201
1202 static double
1203b2d
1204#ifdef KR_headers
1205 (a, e) Bigint *a; int *e;
1206#else
1207 (Bigint *a, int *e)
1208#endif
1209{
1210 ULong *xa, *xa0, w, y, z;
1211 int k;
1212 U d;
1213#ifdef VAX
1214 ULong d0, d1;
1215#else
1216#define d0 word0(&d)
1217#define d1 word1(&d)
1218#endif
1219
1220 xa0 = a->x;
1221 xa = xa0 + a->wds;
1222 y = *--xa;
1223#ifdef DEBUG
1224 if (!y) Bug("zero y in b2d");
1225#endif
1226 k = hi0bits(y);
1227 *e = 32 - k;
1228#ifdef Pack_32
1229 if (k < Ebits) {
1230 d0 = Exp_1 | y >> (Ebits - k);
1231 w = xa > xa0 ? *--xa : 0;
1232 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1233 goto ret_d;
1234 }
1235 z = xa > xa0 ? *--xa : 0;
1236 if (k -= Ebits) {
1237 d0 = Exp_1 | y << k | z >> (32 - k);
1238 y = xa > xa0 ? *--xa : 0;
1239 d1 = z << k | y >> (32 - k);
1240 }
1241 else {
1242 d0 = Exp_1 | y;
1243 d1 = z;
1244 }
1245#else
1246 if (k < Ebits + 16) {
1247 z = xa > xa0 ? *--xa : 0;
1248 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1249 w = xa > xa0 ? *--xa : 0;
1250 y = xa > xa0 ? *--xa : 0;
1251 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1252 goto ret_d;
1253 }
1254 z = xa > xa0 ? *--xa : 0;
1255 w = xa > xa0 ? *--xa : 0;
1256 k -= Ebits + 16;
1257 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1258 y = xa > xa0 ? *--xa : 0;
1259 d1 = w << k + 16 | y << k;
1260#endif
1261 ret_d:
1262#ifdef VAX
1263 word0(&d) = d0 >> 16 | d0 << 16;
1264 word1(&d) = d1 >> 16 | d1 << 16;
1265#else
1266#undef d0
1267#undef d1
1268#endif
1269 return dval(&d);
1270 }
1271
1272 static Bigint *
1273d2b
1274#ifdef KR_headers
1275 (d, e, bits) U *d; int *e, *bits;
1276#else
1277 (U *d, int *e, int *bits)
1278#endif
1279{
1280 Bigint *b;
1281 int de, k;
1282 ULong *x, y, z;
1283#ifndef Sudden_Underflow
1284 int i;
1285#endif
1286#ifdef VAX
1287 ULong d0, d1;
1288 d0 = word0(d) >> 16 | word0(d) << 16;
1289 d1 = word1(d) >> 16 | word1(d) << 16;
1290#else
1291#define d0 word0(d)
1292#define d1 word1(d)
1293#endif
1294
1295#ifdef Pack_32
1296 b = Balloc(1);
1297#else
1298 b = Balloc(2);
1299#endif
1300 x = b->x;
1301
1302 z = d0 & Frac_mask;
1303 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1304#ifdef Sudden_Underflow
1305 de = (int)(d0 >> Exp_shift);
1306#ifndef IBM
1307 z |= Exp_msk11;
1308#endif
1309#else
1310 if ((de = (int)(d0 >> Exp_shift)))
1311 z |= Exp_msk1;
1312#endif
1313#ifdef Pack_32
1314 if ((y = d1)) {
1315 if ((k = lo0bits(&y))) {
1316 x[0] = y | z << (32 - k);
1317 z >>= k;
1318 }
1319 else
1320 x[0] = y;
1321#ifndef Sudden_Underflow
1322 i =
1323#endif
1324 b->wds = (x[1] = z) ? 2 : 1;
1325 }
1326 else {
1327 k = lo0bits(&z);
1328 x[0] = z;
1329#ifndef Sudden_Underflow
1330 i =
1331#endif
1332 b->wds = 1;
1333 k += 32;
1334 }
1335#else
1336 if (y = d1) {
1337 if (k = lo0bits(&y))
1338 if (k >= 16) {
1339 x[0] = y | z << 32 - k & 0xffff;
1340 x[1] = z >> k - 16 & 0xffff;
1341 x[2] = z >> k;
1342 i = 2;
1343 }
1344 else {
1345 x[0] = y & 0xffff;
1346 x[1] = y >> 16 | z << 16 - k & 0xffff;
1347 x[2] = z >> k & 0xffff;
1348 x[3] = z >> k+16;
1349 i = 3;
1350 }
1351 else {
1352 x[0] = y & 0xffff;
1353 x[1] = y >> 16;
1354 x[2] = z & 0xffff;
1355 x[3] = z >> 16;
1356 i = 3;
1357 }
1358 }
1359 else {
1360#ifdef DEBUG
1361 if (!z)
1362 Bug("Zero passed to d2b");
1363#endif
1364 k = lo0bits(&z);
1365 if (k >= 16) {
1366 x[0] = z;
1367 i = 0;
1368 }
1369 else {
1370 x[0] = z & 0xffff;
1371 x[1] = z >> 16;
1372 i = 1;
1373 }
1374 k += 32;
1375 }
1376 while(!x[i])
1377 --i;
1378 b->wds = i + 1;
1379#endif
1380#ifndef Sudden_Underflow
1381 if (de) {
1382#endif
1383#ifdef IBM
1384 *e = (de - Bias - (P-1) << 2) + k;
1385 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1386#else
1387 *e = de - Bias - (P-1) + k;
1388 *bits = P - k;
1389#endif
1390#ifndef Sudden_Underflow
1391 }
1392 else {
1393 *e = de - Bias - (P-1) + 1 + k;
1394#ifdef Pack_32
1395 *bits = 32*i - hi0bits(x[i-1]);
1396#else
1397 *bits = (i+2)*16 - hi0bits(x[i]);
1398#endif
1399 }
1400#endif
1401 return b;
1402 }
1403#undef d0
1404#undef d1
1405
1406 static double
1407ratio
1408#ifdef KR_headers
1409 (a, b) Bigint *a, *b;
1410#else
1411 (Bigint *a, Bigint *b)
1412#endif
1413{
1414 U da, db;
1415 int k, ka, kb;
1416
1417 dval(&da) = b2d(a, &ka);
1418 dval(&db) = b2d(b, &kb);
1419#ifdef Pack_32
1420 k = ka - kb + 32*(a->wds - b->wds);
1421#else
1422 k = ka - kb + 16*(a->wds - b->wds);
1423#endif
1424#ifdef IBM
1425 if (k > 0) {
1426 word0(&da) += (k >> 2)*Exp_msk1;
1427 if (k &= 3)
1428 dval(&da) *= 1 << k;
1429 }
1430 else {
1431 k = -k;
1432 word0(&db) += (k >> 2)*Exp_msk1;
1433 if (k &= 3)
1434 dval(&db) *= 1 << k;
1435 }
1436#else
1437 if (k > 0)
1438 word0(&da) += k*Exp_msk1;
1439 else {
1440 k = -k;
1441 word0(&db) += k*Exp_msk1;
1442 }
1443#endif
1444 return dval(&da) / dval(&db);
1445 }
1446
1447 static CONST double
1448tens[] = {
1449 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1450 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1451 1e20, 1e21, 1e22
1452#ifdef VAX
1453 , 1e23, 1e24
1454#endif
1455 };
1456
1457 static CONST double
1458#ifdef IEEE_Arith
1459bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1460static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1461#ifdef Avoid_Underflow
1462 9007199254740992.*9007199254740992.e-256
1463 /* = 2^106 * 1e-256 */
1464#else
1465 1e-256
1466#endif
1467 };
1468/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1469/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1470#define Scale_Bit 0x10
1471#define n_bigtens 5
1472#else
1473#ifdef IBM
1474bigtens[] = { 1e16, 1e32, 1e64 };
1475static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1476#define n_bigtens 3
1477#else
1478bigtens[] = { 1e16, 1e32 };
1479static CONST double tinytens[] = { 1e-16, 1e-32 };
1480#define n_bigtens 2
1481#endif
1482#endif
1483
1484#undef Need_Hexdig
1485#ifdef INFNAN_CHECK
1486#ifndef No_Hex_NaN
1487#define Need_Hexdig
1488#endif
1489#endif
1490
1491#ifndef Need_Hexdig
1492#ifndef NO_HEX_FP
1493#define Need_Hexdig
1494#endif
1495#endif
1496
1497#ifdef Need_Hexdig /*{*/
1498static unsigned char hexdig[256];
1499
1500 static void
1501#ifdef KR_headers
1502htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;
1503#else
1504htinit(unsigned char *h, unsigned char *s, int inc)
1505#endif
1506{
1507 int i, j;
1508 for(i = 0; (j = s[i]) !=0; i++)
1509 h[j] = i + inc;
1510 }
1511
1512 static void
1513#ifdef KR_headers
1514hexdig_init()
1515#else
1516hexdig_init(void)
1517#endif
1518{
1519#define USC (unsigned char *)
1520 htinit(hexdig, USC "0123456789", 0x10);
1521 htinit(hexdig, USC "abcdef", 0x10 + 10);
1522 htinit(hexdig, USC "ABCDEF", 0x10 + 10);
1523 }
1524#endif /* } Need_Hexdig */
1525
1526#ifdef INFNAN_CHECK
1527
1528#ifndef NAN_WORD0
1529#define NAN_WORD0 0x7ff80000
1530#endif
1531
1532#ifndef NAN_WORD1
1533#define NAN_WORD1 0
1534#endif
1535
1536 static int
1537match
1538#ifdef KR_headers
1539 (sp, t) char **sp, *t;
1540#else
1541 (const char **sp, const char *t)
1542#endif
1543{
1544 int c, d;
1545 CONST char *s = *sp;
1546
1547 while((d = *t++)) {
1548 if ((c = *++s) >= 'A' && c <= 'Z')
1549 c += 'a' - 'A';
1550 if (c != d)
1551 return 0;
1552 }
1553 *sp = s + 1;
1554 return 1;
1555 }
1556
1557#ifndef No_Hex_NaN
1558 static void
1559hexnan
1560#ifdef KR_headers
1561 (rvp, sp) U *rvp; CONST char **sp;
1562#else
1563 (U *rvp, const char **sp)
1564#endif
1565{
1566 ULong c, x[2];
1567 CONST char *s;
1568 int c1, havedig, udx0, xshift;
1569
1570 if (!hexdig['0'])
1571 hexdig_init();
1572 x[0] = x[1] = 0;
1573 havedig = xshift = 0;
1574 udx0 = 1;
1575 s = *sp;
1576 /* allow optional initial 0x or 0X */
1577 while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
1578 ++s;
1579 if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
1580 s += 2;
1581 while((c = *(CONST unsigned char*)++s)) {
1582 if ((c1 = hexdig[c]))
1583 c = c1 & 0xf;
1584 else if (c <= ' ') {
1585 if (udx0 && havedig) {
1586 udx0 = 0;
1587 xshift = 1;
1588 }
1589 continue;
1590 }
1591#ifdef GDTOA_NON_PEDANTIC_NANCHECK
1592 else if (/*(*/ c == ')' && havedig) {
1593 *sp = s + 1;
1594 break;
1595 }
1596 else
1597 return; /* invalid form: don't change *sp */
1598#else
1599 else {
1600 do {
1601 if (/*(*/ c == ')') {
1602 *sp = s + 1;
1603 break;
1604 }
1605 } while((c = *++s));
1606 break;
1607 }
1608#endif
1609 havedig = 1;
1610 if (xshift) {
1611 xshift = 0;
1612 x[0] = x[1];
1613 x[1] = 0;
1614 }
1615 if (udx0)
1616 x[0] = (x[0] << 4) | (x[1] >> 28);
1617 x[1] = (x[1] << 4) | c;
1618 }
1619 if ((x[0] &= 0xfffff) || x[1]) {
1620 word0(rvp) = Exp_mask | x[0];
1621 word1(rvp) = x[1];
1622 }
1623 }
1624#endif /*No_Hex_NaN*/
1625#endif /* INFNAN_CHECK */
1626
1627#ifdef Pack_32
1628#define ULbits 32
1629#define kshift 5
1630#define kmask 31
1631#else
1632#define ULbits 16
1633#define kshift 4
1634#define kmask 15
1635#endif
1636
1637#if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/
1638 static Bigint *
1639#ifdef KR_headers
1640increment(b) Bigint *b;
1641#else
1642increment(Bigint *b)
1643#endif
1644{
1645 ULong *x, *xe;
1646 Bigint *b1;
1647
1648 x = b->x;
1649 xe = x + b->wds;
1650 do {
1651 if (*x < (ULong)0xffffffffL) {
1652 ++*x;
1653 return b;
1654 }
1655 *x++ = 0;
1656 } while(x < xe);
1657 {
1658 if (b->wds >= b->maxwds) {
1659 b1 = Balloc(b->k+1);
1660 Bcopy(b1,b);
1661 Bfree(b);
1662 b = b1;
1663 }
1664 b->x[b->wds++] = 1;
1665 }
1666 return b;
1667 }
1668
1669#endif /*}*/
1670
1671#ifndef NO_HEX_FP /*{*/
1672
1673 static void
1674#ifdef KR_headers
1675rshift(b, k) Bigint *b; int k;
1676#else
1677rshift(Bigint *b, int k)
1678#endif
1679{
1680 ULong *x, *x1, *xe, y;
1681 int n;
1682
1683 x = x1 = b->x;
1684 n = k >> kshift;
1685 if (n < b->wds) {
1686 xe = x + b->wds;
1687 x += n;
1688 if (k &= kmask) {
1689 n = 32 - k;
1690 y = *x++ >> k;
1691 while(x < xe) {
1692 *x1++ = (y | (*x << n)) & 0xffffffff;
1693 y = *x++ >> k;
1694 }
1695 if ((*x1 = y) !=0)
1696 x1++;
1697 }
1698 else
1699 while(x < xe)
1700 *x1++ = *x++;
1701 }
1702 if ((b->wds = x1 - b->x) == 0)
1703 b->x[0] = 0;
1704 }
1705
1706 static ULong
1707#ifdef KR_headers
1708any_on(b, k) Bigint *b; int k;
1709#else
1710any_on(Bigint *b, int k)
1711#endif
1712{
1713 int n, nwds;
1714 ULong *x, *x0, x1, x2;
1715
1716 x = b->x;
1717 nwds = b->wds;
1718 n = k >> kshift;
1719 if (n > nwds)
1720 n = nwds;
1721 else if (n < nwds && (k &= kmask)) {
1722 x1 = x2 = x[n];
1723 x1 >>= k;
1724 x1 <<= k;
1725 if (x1 != x2)
1726 return 1;
1727 }
1728 x0 = x;
1729 x += n;
1730 while(x > x0)
1731 if (*--x)
1732 return 1;
1733 return 0;
1734 }
1735
1736enum { /* rounding values: same as FLT_ROUNDS */
1737 Round_zero = 0,
1738 Round_near = 1,
1739 Round_up = 2,
1740 Round_down = 3
1741 };
1742
1743 void
1744#ifdef KR_headers
1745gethex(sp, rvp, rounding, sign)
1746 CONST char **sp; U *rvp; int rounding, sign;
1747#else
1748gethex( CONST char **sp, U *rvp, int rounding, int sign)
1749#endif
1750{
1751 Bigint *b;
1752 CONST unsigned char *decpt, *s0, *s, *s1;
1753 Long e, e1;
1754 ULong L, lostbits, *x;
1755 int big, denorm, esign, havedig, k, n, nbits, up, zret;
1756#ifdef IBM
1757 int j;
1758#endif
1759 enum {
1760#ifdef IEEE_Arith /*{{*/
1761 emax = 0x7fe - Bias - P + 1,
1762 emin = Emin - P + 1
1763#else /*}{*/
1764 emin = Emin - P,
1765#ifdef VAX
1766 emax = 0x7ff - Bias - P + 1
1767#endif
1768#ifdef IBM
1769 emax = 0x7f - Bias - P
1770#endif
1771#endif /*}}*/
1772 };
1773#ifdef USE_LOCALE
1774 int i;
1775#ifdef NO_LOCALE_CACHE
1776 const unsigned char *decimalpoint = (unsigned char*)
1777 localeconv()->decimal_point;
1778#else
1779 const unsigned char *decimalpoint;
1780 static unsigned char *decimalpoint_cache;
1781 if (!(s0 = decimalpoint_cache)) {
1782 s0 = (unsigned char*)localeconv()->decimal_point;
1783 if ((decimalpoint_cache = (unsigned char*)
1784 MALLOC(strlen((CONST char*)s0) + 1))) {
1785 strcpy((char*)decimalpoint_cache, (CONST char*)s0);
1786 s0 = decimalpoint_cache;
1787 }
1788 }
1789 decimalpoint = s0;
1790#endif
1791#endif
1792
1793 if (!hexdig['0'])
1794 hexdig_init();
1795 havedig = 0;
1796 s0 = *(CONST unsigned char **)sp + 2;
1797 while(s0[havedig] == '0')
1798 havedig++;
1799 s0 += havedig;
1800 s = s0;
1801 decpt = 0;
1802 zret = 0;
1803 e = 0;
1804 if (hexdig[*s])
1805 havedig++;
1806 else {
1807 zret = 1;
1808#ifdef USE_LOCALE
1809 for(i = 0; decimalpoint[i]; ++i) {
1810 if (s[i] != decimalpoint[i])
1811 goto pcheck;
1812 }
1813 decpt = s += i;
1814#else
1815 if (*s != '.')
1816 goto pcheck;
1817 decpt = ++s;
1818#endif
1819 if (!hexdig[*s])
1820 goto pcheck;
1821 while(*s == '0')
1822 s++;
1823 if (hexdig[*s])
1824 zret = 0;
1825 havedig = 1;
1826 s0 = s;
1827 }
1828 while(hexdig[*s])
1829 s++;
1830#ifdef USE_LOCALE
1831 if (*s == *decimalpoint && !decpt) {
1832 for(i = 1; decimalpoint[i]; ++i) {
1833 if (s[i] != decimalpoint[i])
1834 goto pcheck;
1835 }
1836 decpt = s += i;
1837#else
1838 if (*s == '.' && !decpt) {
1839 decpt = ++s;
1840#endif
1841 while(hexdig[*s])
1842 s++;
1843 }/*}*/
1844 if (decpt)
1845 e = -(((Long)(s-decpt)) << 2);
1846 pcheck:
1847 s1 = s;
1848 big = esign = 0;
1849 switch(*s) {
1850 case 'p':
1851 case 'P':
1852 switch(*++s) {
1853 case '-':
1854 esign = 1;
1855 /* no break */
1856 case '+':
1857 s++;
1858 }
1859 if ((n = hexdig[*s]) == 0 || n > 0x19) {
1860 s = s1;
1861 break;
1862 }
1863 e1 = n - 0x10;
1864 while((n = hexdig[*++s]) !=0 && n <= 0x19) {
1865 if (e1 & 0xf8000000)
1866 big = 1;
1867 e1 = 10*e1 + n - 0x10;
1868 }
1869 if (esign)
1870 e1 = -e1;
1871 e += e1;
1872 }
1873 *sp = (char*)s;
1874 if (!havedig)
1875 *sp = (char*)s0 - 1;
1876 if (zret)
1877 goto retz1;
1878 if (big) {
1879 if (esign) {
1880#ifdef IEEE_Arith
1881 switch(rounding) {
1882 case Round_up:
1883 if (sign)
1884 break;
1885 goto ret_tiny;
1886 case Round_down:
1887 if (!sign)
1888 break;
1889 goto ret_tiny;
1890 }
1891#endif
1892 goto retz;
1893#ifdef IEEE_Arith
1894 ret_tiny:
1895#ifndef NO_ERRNO
1896 errno = ERANGE;
1897#endif
1898 word0(rvp) = 0;
1899 word1(rvp) = 1;
1900 return;
1901#endif /* IEEE_Arith */
1902 }
1903 switch(rounding) {
1904 case Round_near:
1905 goto ovfl1;
1906 case Round_up:
1907 if (!sign)
1908 goto ovfl1;
1909 goto ret_big;
1910 case Round_down:
1911 if (sign)
1912 goto ovfl1;
1913 goto ret_big;
1914 }
1915 ret_big:
1916 word0(rvp) = Big0;
1917 word1(rvp) = Big1;
1918 return;
1919 }
1920 n = s1 - s0 - 1;
1921 for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
1922 k++;
1923 b = Balloc(k);
1924 x = b->x;
1925 n = 0;
1926 L = 0;
1927#ifdef USE_LOCALE
1928 for(i = 0; decimalpoint[i+1]; ++i);
1929#endif
1930 while(s1 > s0) {
1931#ifdef USE_LOCALE
1932 if (*--s1 == decimalpoint[i]) {
1933 s1 -= i;
1934 continue;
1935 }
1936#else
1937 if (*--s1 == '.')
1938 continue;
1939#endif
1940 if (n == ULbits) {
1941 *x++ = L;
1942 L = 0;
1943 n = 0;
1944 }
1945 L |= (hexdig[*s1] & 0x0f) << n;
1946 n += 4;
1947 }
1948 *x++ = L;
1949 b->wds = n = x - b->x;
1950 n = ULbits*n - hi0bits(L);
1951 nbits = Nbits;
1952 lostbits = 0;
1953 x = b->x;
1954 if (n > nbits) {
1955 n -= nbits;
1956 if (any_on(b,n)) {
1957 lostbits = 1;
1958 k = n - 1;
1959 if (x[k>>kshift] & 1 << (k & kmask)) {
1960 lostbits = 2;
1961 if (k > 0 && any_on(b,k))
1962 lostbits = 3;
1963 }
1964 }
1965 rshift(b, n);
1966 e += n;
1967 }
1968 else if (n < nbits) {
1969 n = nbits - n;
1970 b = lshift(b, n);
1971 e -= n;
1972 x = b->x;
1973 }
1974 if (e > Emax) {
1975 ovfl:
1976 Bfree(b);
1977 ovfl1:
1978#ifndef NO_ERRNO
1979 errno = ERANGE;
1980#endif
1981 word0(rvp) = Exp_mask;
1982 word1(rvp) = 0;
1983 return;
1984 }
1985 denorm = 0;
1986 if (e < emin) {
1987 denorm = 1;
1988 n = emin - e;
1989 if (n >= nbits) {
1990#ifdef IEEE_Arith /*{*/
1991 switch (rounding) {
1992 case Round_near:
1993 if (n == nbits && (n < 2 || any_on(b,n-1)))
1994 goto ret_tiny;
1995 break;
1996 case Round_up:
1997 if (!sign)
1998 goto ret_tiny;
1999 break;
2000 case Round_down:
2001 if (sign)
2002 goto ret_tiny;
2003 }
2004#endif /* } IEEE_Arith */
2005 Bfree(b);
2006 retz:
2007#ifndef NO_ERRNO
2008 errno = ERANGE;
2009#endif
2010 retz1:
2011 rvp->d = 0.;
2012 return;
2013 }
2014 k = n - 1;
2015 if (lostbits)
2016 lostbits = 1;
2017 else if (k > 0)
2018 lostbits = any_on(b,k);
2019 if (x[k>>kshift] & 1 << (k & kmask))
2020 lostbits |= 2;
2021 nbits -= n;
2022 rshift(b,n);
2023 e = emin;
2024 }
2025 if (lostbits) {
2026 up = 0;
2027 switch(rounding) {
2028 case Round_zero:
2029 break;
2030 case Round_near:
2031 if (lostbits & 2
2032 && (lostbits & 1) | (x[0] & 1))
2033 up = 1;
2034 break;
2035 case Round_up:
2036 up = 1 - sign;
2037 break;
2038 case Round_down:
2039 up = sign;
2040 }
2041 if (up) {
2042 k = b->wds;
2043 b = increment(b);
2044 x = b->x;
2045 if (denorm) {
2046#if 0
2047 if (nbits == Nbits - 1
2048 && x[nbits >> kshift] & 1 << (nbits & kmask))
2049 denorm = 0; /* not currently used */
2050#endif
2051 }
2052 else if (b->wds > k
2053 || ((n = nbits & kmask) !=0
2054 && hi0bits(x[k-1]) < 32-n)) {
2055 rshift(b,1);
2056 if (++e > Emax)
2057 goto ovfl;
2058 }
2059 }
2060 }
2061#ifdef IEEE_Arith
2062 if (denorm)
2063 word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
2064 else
2065 word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
2066 word1(rvp) = b->x[0];
2067#endif
2068#ifdef IBM
2069 if ((j = e & 3)) {
2070 k = b->x[0] & ((1 << j) - 1);
2071 rshift(b,j);
2072 if (k) {
2073 switch(rounding) {
2074 case Round_up:
2075 if (!sign)
2076 increment(b);
2077 break;
2078 case Round_down:
2079 if (sign)
2080 increment(b);
2081 break;
2082 case Round_near:
2083 j = 1 << (j-1);
2084 if (k & j && ((k & (j-1)) | lostbits))
2085 increment(b);
2086 }
2087 }
2088 }
2089 e >>= 2;
2090 word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
2091 word1(rvp) = b->x[0];
2092#endif
2093#ifdef VAX
2094 /* The next two lines ignore swap of low- and high-order 2 bytes. */
2095 /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
2096 /* word1(rvp) = b->x[0]; */
2097 word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
2098 word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
2099#endif
2100 Bfree(b);
2101 }
2102#endif /*!NO_HEX_FP}*/
2103
2104 static int
2105#ifdef KR_headers
2106dshift(b, p2) Bigint *b; int p2;
2107#else
2108dshift(Bigint *b, int p2)
2109#endif
2110{
2111 int rv = hi0bits(b->x[b->wds-1]) - 4;
2112 if (p2 > 0)
2113 rv -= p2;
2114 return rv & kmask;
2115 }
2116
2117 static int
2118quorem
2119#ifdef KR_headers
2120 (b, S) Bigint *b, *S;
2121#else
2122 (Bigint *b, Bigint *S)
2123#endif
2124{
2125 int n;
2126 ULong *bx, *bxe, q, *sx, *sxe;
2127#ifdef ULLong
2128 ULLong borrow, carry, y, ys;
2129#else
2130 ULong borrow, carry, y, ys;
2131#ifdef Pack_32
2132 ULong si, z, zs;
2133#endif
2134#endif
2135
2136 n = S->wds;
2137#ifdef DEBUG
2138 /*debug*/ if (b->wds > n)
2139 /*debug*/ Bug("oversize b in quorem");
2140#endif
2141 if (b->wds < n)
2142 return 0;
2143 sx = S->x;
2144 sxe = sx + --n;
2145 bx = b->x;
2146 bxe = bx + n;
2147 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2148#ifdef DEBUG
2149#ifdef NO_STRTOD_BIGCOMP
2150 /*debug*/ if (q > 9)
2151#else
2152 /* An oversized q is possible when quorem is called from bigcomp and */
2153 /* the input is near, e.g., twice the smallest denormalized number. */
2154 /*debug*/ if (q > 15)
2155#endif
2156 /*debug*/ Bug("oversized quotient in quorem");
2157#endif
2158 if (q) {
2159 borrow = 0;
2160 carry = 0;
2161 do {
2162#ifdef ULLong
2163 ys = *sx++ * (ULLong)q + carry;
2164 carry = ys >> 32;
2165 y = *bx - (ys & FFFFFFFF) - borrow;
2166 borrow = y >> 32 & (ULong)1;
2167 *bx++ = y & FFFFFFFF;
2168#else
2169#ifdef Pack_32
2170 si = *sx++;
2171 ys = (si & 0xffff) * q + carry;
2172 zs = (si >> 16) * q + (ys >> 16);
2173 carry = zs >> 16;
2174 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2175 borrow = (y & 0x10000) >> 16;
2176 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2177 borrow = (z & 0x10000) >> 16;
2178 Storeinc(bx, z, y);
2179#else
2180 ys = *sx++ * q + carry;
2181 carry = ys >> 16;
2182 y = *bx - (ys & 0xffff) - borrow;
2183 borrow = (y & 0x10000) >> 16;
2184 *bx++ = y & 0xffff;
2185#endif
2186#endif
2187 }
2188 while(sx <= sxe);
2189 if (!*bxe) {
2190 bx = b->x;
2191 while(--bxe > bx && !*bxe)
2192 --n;
2193 b->wds = n;
2194 }
2195 }
2196 if (cmp(b, S) >= 0) {
2197 q++;
2198 borrow = 0;
2199 carry = 0;
2200 bx = b->x;
2201 sx = S->x;
2202 do {
2203#ifdef ULLong
2204 ys = *sx++ + carry;
2205 carry = ys >> 32;
2206 y = *bx - (ys & FFFFFFFF) - borrow;
2207 borrow = y >> 32 & (ULong)1;
2208 *bx++ = y & FFFFFFFF;
2209#else
2210#ifdef Pack_32
2211 si = *sx++;
2212 ys = (si & 0xffff) + carry;
2213 zs = (si >> 16) + (ys >> 16);
2214 carry = zs >> 16;
2215 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2216 borrow = (y & 0x10000) >> 16;
2217 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2218 borrow = (z & 0x10000) >> 16;
2219 Storeinc(bx, z, y);
2220#else
2221 ys = *sx++ + carry;
2222 carry = ys >> 16;
2223 y = *bx - (ys & 0xffff) - borrow;
2224 borrow = (y & 0x10000) >> 16;
2225 *bx++ = y & 0xffff;
2226#endif
2227#endif
2228 }
2229 while(sx <= sxe);
2230 bx = b->x;
2231 bxe = bx + n;
2232 if (!*bxe) {
2233 while(--bxe > bx && !*bxe)
2234 --n;
2235 b->wds = n;
2236 }
2237 }
2238 return q;
2239 }
2240
2241#if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/
2242 static double
2243sulp
2244#ifdef KR_headers
2245 (x, bc) U *x; BCinfo *bc;
2246#else
2247 (U *x, BCinfo *bc)
2248#endif
2249{
2250 U u;
2251 double rv;
2252 int i;
2253
2254 rv = ulp(x);
2255 if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0)
2256 return rv; /* Is there an example where i <= 0 ? */
2257 word0(&u) = Exp_1 + (i << Exp_shift);
2258 word1(&u) = 0;
2259 return rv * u.d;
2260 }
2261#endif /*}*/
2262
2263#ifndef NO_STRTOD_BIGCOMP
2264 static void
2265bigcomp
2266#ifdef KR_headers
2267 (rv, s0, bc)
2268 U *rv; CONST char *s0; BCinfo *bc;
2269#else
2270 (U *rv, const char *s0, BCinfo *bc)
2271#endif
2272{
2273 Bigint *b, *d;
2274 int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
2275
2276 dsign = bc->dsign;
2277 nd = bc->nd;
2278 nd0 = bc->nd0;
2279 p5 = nd + bc->e0 - 1;
2280 speccase = 0;
2281#ifndef Sudden_Underflow
2282 if (rv->d == 0.) { /* special case: value near underflow-to-zero */
2283 /* threshold was rounded to zero */
2284 b = i2b(1);
2285 p2 = Emin - P + 1;
2286 bbits = 1;
2287#ifdef Avoid_Underflow
2288 word0(rv) = (P+2) << Exp_shift;
2289#else
2290 word1(rv) = 1;
2291#endif
2292 i = 0;
2293#ifdef Honor_FLT_ROUNDS
2294 if (bc->rounding == 1)
2295#endif
2296 {
2297 speccase = 1;
2298 --p2;
2299 dsign = 0;
2300 goto have_i;
2301 }
2302 }
2303 else
2304#endif
2305 b = d2b(rv, &p2, &bbits);
2306#ifdef Avoid_Underflow
2307 p2 -= bc->scale;
2308#endif
2309 /* floor(log2(rv)) == bbits - 1 + p2 */
2310 /* Check for denormal case. */
2311 i = P - bbits;
2312 if (i > (j = P - Emin - 1 + p2)) {
2313#ifdef Sudden_Underflow
2314 Bfree(b);
2315 b = i2b(1);
2316 p2 = Emin;
2317 i = P - 1;
2318#ifdef Avoid_Underflow
2319 word0(rv) = (1 + bc->scale) << Exp_shift;
2320#else
2321 word0(rv) = Exp_msk1;
2322#endif
2323 word1(rv) = 0;
2324#else
2325 i = j;
2326#endif
2327 }
2328#ifdef Honor_FLT_ROUNDS
2329 if (bc->rounding != 1) {
2330 if (i > 0)
2331 b = lshift(b, i);
2332 if (dsign)
2333 b = increment(b);
2334 }
2335 else
2336#endif
2337 {
2338 b = lshift(b, ++i);
2339 b->x[0] |= 1;
2340 }
2341#ifndef Sudden_Underflow
2342 have_i:
2343#endif
2344 p2 -= p5 + i;
2345 d = i2b(1);
2346 /* Arrange for convenient computation of quotients:
2347 * shift left if necessary so divisor has 4 leading 0 bits.
2348 */
2349 if (p5 > 0)
2350 d = pow5mult(d, p5);
2351 else if (p5 < 0)
2352 b = pow5mult(b, -p5);
2353 if (p2 > 0) {
2354 b2 = p2;
2355 d2 = 0;
2356 }
2357 else {
2358 b2 = 0;
2359 d2 = -p2;
2360 }
2361 i = dshift(d, d2);
2362 if ((b2 += i) > 0)
2363 b = lshift(b, b2);
2364 if ((d2 += i) > 0)
2365 d = lshift(d, d2);
2366
2367 /* Now b/d = exactly half-way between the two floating-point values */
2368 /* on either side of the input string. Compute first digit of b/d. */
2369
2370 if (!(dig = quorem(b,d))) {
2371 b = multadd(b, 10, 0); /* very unlikely */
2372 dig = quorem(b,d);
2373 }
2374
2375 /* Compare b/d with s0 */
2376
2377 for(i = 0; i < nd0; ) {
2378 if ((dd = s0[i++] - '0' - dig))
2379 goto ret;
2380 if (!b->x[0] && b->wds == 1) {
2381 if (i < nd)
2382 dd = 1;
2383 goto ret;
2384 }
2385 b = multadd(b, 10, 0);
2386 dig = quorem(b,d);
2387 }
2388 for(j = bc->dp1; i++ < nd;) {
2389 if ((dd = s0[j++] - '0' - dig))
2390 goto ret;
2391 if (!b->x[0] && b->wds == 1) {
2392 if (i < nd)
2393 dd = 1;
2394 goto ret;
2395 }
2396 b = multadd(b, 10, 0);
2397 dig = quorem(b,d);
2398 }
2399 if (b->x[0] || b->wds > 1)
2400 dd = -1;
2401 ret:
2402 Bfree(b);
2403 Bfree(d);
2404#ifdef Honor_FLT_ROUNDS
2405 if (bc->rounding != 1) {
2406 if (dd < 0) {
2407 if (bc->rounding == 0) {
2408 if (!dsign)
2409 goto retlow1;
2410 }
2411 else if (dsign)
2412 goto rethi1;
2413 }
2414 else if (dd > 0) {
2415 if (bc->rounding == 0) {
2416 if (dsign)
2417 goto rethi1;
2418 goto ret1;
2419 }
2420 if (!dsign)
2421 goto rethi1;
2422 dval(rv) += 2.*sulp(rv,bc);
2423 }
2424 else {
2425 bc->inexact = 0;
2426 if (dsign)
2427 goto rethi1;
2428 }
2429 }
2430 else
2431#endif
2432 if (speccase) {
2433 if (dd <= 0)
2434 rv->d = 0.;
2435 }
2436 else if (dd < 0) {
2437 if (!dsign) /* does not happen for round-near */
2438retlow1:
2439 dval(rv) -= sulp(rv,bc);
2440 }
2441 else if (dd > 0) {
2442 if (dsign) {
2443 rethi1:
2444 dval(rv) += sulp(rv,bc);
2445 }
2446 }
2447 else {
2448 /* Exact half-way case: apply round-even rule. */
2449 if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) {
2450 i = 1 - j;
2451 if (i <= 31) {
2452 if (word1(rv) & (0x1 << i))
2453 goto odd;
2454 }
2455 else if (word0(rv) & (0x1 << (i-32)))
2456 goto odd;
2457 }
2458 else if (word1(rv) & 1) {
2459 odd:
2460 if (dsign)
2461 goto rethi1;
2462 goto retlow1;
2463 }
2464 }
2465
2466#ifdef Honor_FLT_ROUNDS
2467 ret1:
2468#endif
2469 return;
2470 }
2471#endif /* NO_STRTOD_BIGCOMP */
2472
2473 double
2474strtod
2475#ifdef KR_headers
2476 (s00, se) CONST char *s00; char **se;
2477#else
2478 (const char *s00, char **se)
2479#endif
2480{
2481 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
2482 int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign;
2483 CONST char *s, *s0, *s1;
2484 double aadj, aadj1;
2485 Long L;
2486 U aadj2, adj, rv, rv0;
2487 ULong y, z;
2488 BCinfo bc;
2489 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
2490#ifdef Avoid_Underflow
2491 ULong Lsb, Lsb1;
2492#endif
2493#ifdef SET_INEXACT
2494 int oldinexact;
2495#endif
2496#ifndef NO_STRTOD_BIGCOMP
2497 int req_bigcomp = 0;
2498#endif
2499#ifdef Honor_FLT_ROUNDS /*{*/
2500#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
2501 bc.rounding = Flt_Rounds;
2502#else /*}{*/
2503 bc.rounding = 1;
2504 switch(fegetround()) {
2505 case FE_TOWARDZERO: bc.rounding = 0; break;
2506 case FE_UPWARD: bc.rounding = 2; break;
2507 case FE_DOWNWARD: bc.rounding = 3;
2508 }
2509#endif /*}}*/
2510#endif /*}*/
2511#ifdef USE_LOCALE
2512 CONST char *s2;
2513#endif
2514
2515 sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0;
2516 dval(&rv) = 0.;
2517 for(s = s00;;s++) switch(*s) {
2518 case '-':
2519 sign = 1;
2520 /* no break */
2521 case '+':
2522 if (*++s)
2523 goto break2;
2524 /* no break */
2525 case 0:
2526 goto ret0;
2527 case '\t':
2528 case '\n':
2529 case '\v':
2530 case '\f':
2531 case '\r':
2532 case ' ':
2533 continue;
2534 default:
2535 goto break2;
2536 }
2537 break2:
2538 if (*s == '0') {
2539#ifndef NO_HEX_FP /*{*/
2540 switch(s[1]) {
2541 case 'x':
2542 case 'X':
2543#ifdef Honor_FLT_ROUNDS
2544 gethex(&s, &rv, bc.rounding, sign);
2545#else
2546 gethex(&s, &rv, 1, sign);
2547#endif
2548 goto ret;
2549 }
2550#endif /*}*/
2551 nz0 = 1;
2552 while(*++s == '0') ;
2553 if (!*s)
2554 goto ret;
2555 }
2556 s0 = s;
2557 y = z = 0;
2558 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
2559 if (nd < 9)
2560 y = 10*y + c - '0';
2561 else if (nd < 16)
2562 z = 10*z + c - '0';
2563 nd0 = nd;
2564 bc.dp0 = bc.dp1 = s - s0;
2565 for(s1 = s; s1 > s0 && *--s1 == '0'; )
2566 ++nz1;
2567#ifdef USE_LOCALE
2568 s1 = localeconv()->decimal_point;
2569 if (c == *s1) {
2570 c = '.';
2571 if (*++s1) {
2572 s2 = s;
2573 for(;;) {
2574 if (*++s2 != *s1) {
2575 c = 0;
2576 break;
2577 }
2578 if (!*++s1) {
2579 s = s2;
2580 break;
2581 }
2582 }
2583 }
2584 }
2585#endif
2586 if (c == '.') {
2587 c = *++s;
2588 bc.dp1 = s - s0;
2589 bc.dplen = bc.dp1 - bc.dp0;
2590 if (!nd) {
2591 for(; c == '0'; c = *++s)
2592 nz++;
2593 if (c > '0' && c <= '9') {
2594 bc.dp0 = s0 - s;
2595 bc.dp1 = bc.dp0 + bc.dplen;
2596 s0 = s;
2597 nf += nz;
2598 nz = 0;
2599 goto have_dig;
2600 }
2601 goto dig_done;
2602 }
2603 for(; c >= '0' && c <= '9'; c = *++s) {
2604 have_dig:
2605 nz++;
2606 if (c -= '0') {
2607 nf += nz;
2608 for(i = 1; i < nz; i++)
2609 if (nd++ < 9)
2610 y *= 10;
2611 else if (nd <= DBL_DIG + 1)
2612 z *= 10;
2613 if (nd++ < 9)
2614 y = 10*y + c;
2615 else if (nd <= DBL_DIG + 1)
2616 z = 10*z + c;
2617 nz = nz1 = 0;
2618 }
2619 }
2620 }
2621 dig_done:
2622 e = 0;
2623 if (c == 'e' || c == 'E') {
2624 if (!nd && !nz && !nz0) {
2625 goto ret0;
2626 }
2627 s00 = s;
2628 esign = 0;
2629 switch(c = *++s) {
2630 case '-':
2631 esign = 1;
2632 case '+':
2633 c = *++s;
2634 }
2635 if (c >= '0' && c <= '9') {
2636 while(c == '0')
2637 c = *++s;
2638 if (c > '0' && c <= '9') {
2639 L = c - '0';
2640 s1 = s;
2641 while((c = *++s) >= '0' && c <= '9')
2642 L = 10*L + c - '0';
2643 if (s - s1 > 8 || L > 19999)
2644 /* Avoid confusion from exponents
2645 * so large that e might overflow.
2646 */
2647 e = 19999; /* safe for 16 bit ints */
2648 else
2649 e = (int)L;
2650 if (esign)
2651 e = -e;
2652 }
2653 else
2654 e = 0;
2655 }
2656 else
2657 s = s00;
2658 }
2659 if (!nd) {
2660 if (!nz && !nz0) {
2661#ifdef INFNAN_CHECK
2662 /* Check for Nan and Infinity */
2663 if (!bc.dplen)
2664 switch(c) {
2665 case 'i':
2666 case 'I':
2667 if (match(&s,"nf")) {
2668 --s;
2669 if (!match(&s,"inity"))
2670 ++s;
2671 word0(&rv) = 0x7ff00000;
2672 word1(&rv) = 0;
2673 goto ret;
2674 }
2675 break;
2676 case 'n':
2677 case 'N':
2678 if (match(&s, "an")) {
2679 word0(&rv) = NAN_WORD0;
2680 word1(&rv) = NAN_WORD1;
2681#ifndef No_Hex_NaN
2682 if (*s == '(') /*)*/
2683 hexnan(&rv, &s);
2684#endif
2685 goto ret;
2686 }
2687 }
2688#endif /* INFNAN_CHECK */
2689 ret0:
2690 s = s00;
2691 sign = 0;
2692 }
2693 goto ret;
2694 }
2695 bc.e0 = e1 = e -= nf;
2696
2697 /* Now we have nd0 digits, starting at s0, followed by a
2698 * decimal point, followed by nd-nd0 digits. The number we're
2699 * after is the integer represented by those digits times
2700 * 10**e */
2701
2702 if (!nd0)
2703 nd0 = nd;
2704 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2705 dval(&rv) = y;
2706 if (k > 9) {
2707#ifdef SET_INEXACT
2708 if (k > DBL_DIG)
2709 oldinexact = get_inexact();
2710#endif
2711 dval(&rv) = tens[k - 9] * dval(&rv) + z;
2712 }
2713 bd0 = 0;
2714 if (nd <= DBL_DIG
2715#ifndef RND_PRODQUOT
2716#ifndef Honor_FLT_ROUNDS
2717 && Flt_Rounds == 1
2718#endif
2719#endif
2720 ) {
2721 if (!e)
2722 goto ret;
2723#ifndef ROUND_BIASED_without_Round_Up
2724 if (e > 0) {
2725 if (e <= Ten_pmax) {
2726#ifdef VAX
2727 goto vax_ovfl_check;
2728#else
2729#ifdef Honor_FLT_ROUNDS
2730 /* round correctly FLT_ROUNDS = 2 or 3 */
2731 if (sign) {
2732 rv.d = -rv.d;
2733 sign = 0;
2734 }
2735#endif
2736 /* rv = */ rounded_product(dval(&rv), tens[e]);
2737 goto ret;
2738#endif
2739 }
2740 i = DBL_DIG - nd;
2741 if (e <= Ten_pmax + i) {
2742 /* A fancier test would sometimes let us do
2743 * this for larger i values.
2744 */
2745#ifdef Honor_FLT_ROUNDS
2746 /* round correctly FLT_ROUNDS = 2 or 3 */
2747 if (sign) {
2748 rv.d = -rv.d;
2749 sign = 0;
2750 }
2751#endif
2752 e -= i;
2753 dval(&rv) *= tens[i];
2754#ifdef VAX
2755 /* VAX exponent range is so narrow we must
2756 * worry about overflow here...
2757 */
2758 vax_ovfl_check:
2759 word0(&rv) -= P*Exp_msk1;
2760 /* rv = */ rounded_product(dval(&rv), tens[e]);
2761 if ((word0(&rv) & Exp_mask)
2762 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2763 goto ovfl;
2764 word0(&rv) += P*Exp_msk1;
2765#else
2766 /* rv = */ rounded_product(dval(&rv), tens[e]);
2767#endif
2768 goto ret;
2769 }
2770 }
2771#ifndef Inaccurate_Divide
2772 else if (e >= -Ten_pmax) {
2773#ifdef Honor_FLT_ROUNDS
2774 /* round correctly FLT_ROUNDS = 2 or 3 */
2775 if (sign) {
2776 rv.d = -rv.d;
2777 sign = 0;
2778 }
2779#endif
2780 /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
2781 goto ret;
2782 }
2783#endif
2784#endif /* ROUND_BIASED_without_Round_Up */
2785 }
2786 e1 += nd - k;
2787
2788#ifdef IEEE_Arith
2789#ifdef SET_INEXACT
2790 bc.inexact = 1;
2791 if (k <= DBL_DIG)
2792 oldinexact = get_inexact();
2793#endif
2794#ifdef Avoid_Underflow
2795 bc.scale = 0;
2796#endif
2797#ifdef Honor_FLT_ROUNDS
2798 if (bc.rounding >= 2) {
2799 if (sign)
2800 bc.rounding = bc.rounding == 2 ? 0 : 2;
2801 else
2802 if (bc.rounding != 2)
2803 bc.rounding = 0;
2804 }
2805#endif
2806#endif /*IEEE_Arith*/
2807
2808 /* Get starting approximation = rv * 10**e1 */
2809
2810 if (e1 > 0) {
2811 if ((i = e1 & 15))
2812 dval(&rv) *= tens[i];
2813 if (e1 &= ~15) {
2814 if (e1 > DBL_MAX_10_EXP) {
2815 ovfl:
2816 /* Can't trust HUGE_VAL */
2817#ifdef IEEE_Arith
2818#ifdef Honor_FLT_ROUNDS
2819 switch(bc.rounding) {
2820 case 0: /* toward 0 */
2821 case 3: /* toward -infinity */
2822 word0(&rv) = Big0;
2823 word1(&rv) = Big1;
2824 break;
2825 default:
2826 word0(&rv) = Exp_mask;
2827 word1(&rv) = 0;
2828 }
2829#else /*Honor_FLT_ROUNDS*/
2830 word0(&rv) = Exp_mask;
2831 word1(&rv) = 0;
2832#endif /*Honor_FLT_ROUNDS*/
2833#ifdef SET_INEXACT
2834 /* set overflow bit */
2835 dval(&rv0) = 1e300;
2836 dval(&rv0) *= dval(&rv0);
2837#endif
2838#else /*IEEE_Arith*/
2839 word0(&rv) = Big0;
2840 word1(&rv) = Big1;
2841#endif /*IEEE_Arith*/
2842 range_err:
2843 if (bd0) {
2844 Bfree(bb);
2845 Bfree(bd);
2846 Bfree(bs);
2847 Bfree(bd0);
2848 Bfree(delta);
2849 }
2850#ifndef NO_ERRNO
2851 errno = ERANGE;
2852#endif
2853 goto ret;
2854 }
2855 e1 >>= 4;
2856 for(j = 0; e1 > 1; j++, e1 >>= 1)
2857 if (e1 & 1)
2858 dval(&rv) *= bigtens[j];
2859 /* The last multiplication could overflow. */
2860 word0(&rv) -= P*Exp_msk1;
2861 dval(&rv) *= bigtens[j];
2862 if ((z = word0(&rv) & Exp_mask)
2863 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2864 goto ovfl;
2865 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2866 /* set to largest number */
2867 /* (Can't trust DBL_MAX) */
2868 word0(&rv) = Big0;
2869 word1(&rv) = Big1;
2870 }
2871 else
2872 word0(&rv) += P*Exp_msk1;
2873 }
2874 }
2875 else if (e1 < 0) {
2876 e1 = -e1;
2877 if ((i = e1 & 15))
2878 dval(&rv) /= tens[i];
2879 if (e1 >>= 4) {
2880 if (e1 >= 1 << n_bigtens)
2881 goto undfl;
2882#ifdef Avoid_Underflow
2883 if (e1 & Scale_Bit)
2884 bc.scale = 2*P;
2885 for(j = 0; e1 > 0; j++, e1 >>= 1)
2886 if (e1 & 1)
2887 dval(&rv) *= tinytens[j];
2888 if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
2889 >> Exp_shift)) > 0) {
2890 /* scaled rv is denormal; clear j low bits */
2891 if (j >= 32) {
2892 if (j > 54)
2893 goto undfl;
2894 word1(&rv) = 0;
2895 if (j >= 53)
2896 word0(&rv) = (P+2)*Exp_msk1;
2897 else
2898 word0(&rv) &= 0xffffffff << (j-32);
2899 }
2900 else
2901 word1(&rv) &= 0xffffffff << j;
2902 }
2903#else
2904 for(j = 0; e1 > 1; j++, e1 >>= 1)
2905 if (e1 & 1)
2906 dval(&rv) *= tinytens[j];
2907 /* The last multiplication could underflow. */
2908 dval(&rv0) = dval(&rv);
2909 dval(&rv) *= tinytens[j];
2910 if (!dval(&rv)) {
2911 dval(&rv) = 2.*dval(&rv0);
2912 dval(&rv) *= tinytens[j];
2913#endif
2914 if (!dval(&rv)) {
2915 undfl:
2916 dval(&rv) = 0.;
2917 goto range_err;
2918 }
2919#ifndef Avoid_Underflow
2920 word0(&rv) = Tiny0;
2921 word1(&rv) = Tiny1;
2922 /* The refinement below will clean
2923 * this approximation up.
2924 */
2925 }
2926#endif
2927 }
2928 }
2929
2930 /* Now the hard part -- adjusting rv to the correct value.*/
2931
2932 /* Put digits into bd: true value = bd * 10^e */
2933
2934 bc.nd = nd - nz1;
2935#ifndef NO_STRTOD_BIGCOMP
2936 bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */
2937 /* to silence an erroneous warning about bc.nd0 */
2938 /* possibly not being initialized. */
2939 if (nd > strtod_diglim) {
2940 /* ASSERT(strtod_diglim >= 18); 18 == one more than the */
2941 /* minimum number of decimal digits to distinguish double values */
2942 /* in IEEE arithmetic. */
2943 i = j = 18;
2944 if (i > nd0)
2945 j += bc.dplen;
2946 for(;;) {
2947 if (--j < bc.dp1 && j >= bc.dp0)
2948 j = bc.dp0 - 1;
2949 if (s0[j] != '0')
2950 break;
2951 --i;
2952 }
2953 e += nd - i;
2954 nd = i;
2955 if (nd0 > nd)
2956 nd0 = nd;
2957 if (nd < 9) { /* must recompute y */
2958 y = 0;
2959 for(i = 0; i < nd0; ++i)
2960 y = 10*y + s0[i] - '0';
2961 for(j = bc.dp1; i < nd; ++i)
2962 y = 10*y + s0[j++] - '0';
2963 }
2964 }
2965#endif
2966 bd0 = s2b(s0, nd0, nd, y, bc.dplen);
2967
2968 for(;;) {
2969 bd = Balloc(bd0->k);
2970 Bcopy(bd, bd0);
2971 bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
2972 bs = i2b(1);
2973
2974 if (e >= 0) {
2975 bb2 = bb5 = 0;
2976 bd2 = bd5 = e;
2977 }
2978 else {
2979 bb2 = bb5 = -e;
2980 bd2 = bd5 = 0;
2981 }
2982 if (bbe >= 0)
2983 bb2 += bbe;
2984 else
2985 bd2 -= bbe;
2986 bs2 = bb2;
2987#ifdef Honor_FLT_ROUNDS
2988 if (bc.rounding != 1)
2989 bs2++;
2990#endif
2991#ifdef Avoid_Underflow
2992 Lsb = LSB;
2993 Lsb1 = 0;
2994 j = bbe - bc.scale;
2995 i = j + bbbits - 1; /* logb(rv) */
2996 j = P + 1 - bbbits;
2997 if (i < Emin) { /* denormal */
2998 i = Emin - i;
2999 j -= i;
3000 if (i < 32)
3001 Lsb <<= i;
3002 else if (i < 52)
3003 Lsb1 = Lsb << (i-32);
3004 else
3005 Lsb1 = Exp_mask;
3006 }
3007#else /*Avoid_Underflow*/
3008#ifdef Sudden_Underflow
3009#ifdef IBM
3010 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
3011#else
3012 j = P + 1 - bbbits;
3013#endif
3014#else /*Sudden_Underflow*/
3015 j = bbe;
3016 i = j + bbbits - 1; /* logb(rv) */
3017 if (i < Emin) /* denormal */
3018 j += P - Emin;
3019 else
3020 j = P + 1 - bbbits;
3021#endif /*Sudden_Underflow*/
3022#endif /*Avoid_Underflow*/
3023 bb2 += j;
3024 bd2 += j;
3025#ifdef Avoid_Underflow
3026 bd2 += bc.scale;
3027#endif
3028 i = bb2 < bd2 ? bb2 : bd2;
3029 if (i > bs2)
3030 i = bs2;
3031 if (i > 0) {
3032 bb2 -= i;
3033 bd2 -= i;
3034 bs2 -= i;
3035 }
3036 if (bb5 > 0) {
3037 bs = pow5mult(bs, bb5);
3038 bb1 = mult(bs, bb);
3039 Bfree(bb);
3040 bb = bb1;
3041 }
3042 if (bb2 > 0)
3043 bb = lshift(bb, bb2);
3044 if (bd5 > 0)
3045 bd = pow5mult(bd, bd5);
3046 if (bd2 > 0)
3047 bd = lshift(bd, bd2);
3048 if (bs2 > 0)
3049 bs = lshift(bs, bs2);
3050 delta = diff(bb, bd);
3051 bc.dsign = delta->sign;
3052 delta->sign = 0;
3053 i = cmp(delta, bs);
3054#ifndef NO_STRTOD_BIGCOMP /*{*/
3055 if (bc.nd > nd && i <= 0) {
3056 if (bc.dsign) {
3057 /* Must use bigcomp(). */
3058 req_bigcomp = 1;
3059 break;
3060 }
3061#ifdef Honor_FLT_ROUNDS
3062 if (bc.rounding != 1) {
3063 if (i < 0) {
3064 req_bigcomp = 1;
3065 break;
3066 }
3067 }
3068 else
3069#endif
3070 i = -1; /* Discarded digits make delta smaller. */
3071 }
3072#endif /*}*/
3073#ifdef Honor_FLT_ROUNDS /*{*/
3074 if (bc.rounding != 1) {
3075 if (i < 0) {
3076 /* Error is less than an ulp */
3077 if (!delta->x[0] && delta->wds <= 1) {
3078 /* exact */
3079#ifdef SET_INEXACT
3080 bc.inexact = 0;
3081#endif
3082 break;
3083 }
3084 if (bc.rounding) {
3085 if (bc.dsign) {
3086 adj.d = 1.;
3087 goto apply_adj;
3088 }
3089 }
3090 else if (!bc.dsign) {
3091 adj.d = -1.;
3092 if (!word1(&rv)
3093 && !(word0(&rv) & Frac_mask)) {
3094 y = word0(&rv) & Exp_mask;
3095#ifdef Avoid_Underflow
3096 if (!bc.scale || y > 2*P*Exp_msk1)
3097#else
3098 if (y)
3099#endif
3100 {
3101 delta = lshift(delta,Log2P);
3102 if (cmp(delta, bs) <= 0)
3103 adj.d = -0.5;
3104 }
3105 }
3106 apply_adj:
3107#ifdef Avoid_Underflow /*{*/
3108 if (bc.scale && (y = word0(&rv) & Exp_mask)
3109 <= 2*P*Exp_msk1)
3110 word0(&adj) += (2*P+1)*Exp_msk1 - y;
3111#else
3112#ifdef Sudden_Underflow
3113 if ((word0(&rv) & Exp_mask) <=
3114 P*Exp_msk1) {
3115 word0(&rv) += P*Exp_msk1;
3116 dval(&rv) += adj.d*ulp(dval(&rv));
3117 word0(&rv) -= P*Exp_msk1;
3118 }
3119 else
3120#endif /*Sudden_Underflow*/
3121#endif /*Avoid_Underflow}*/
3122 dval(&rv) += adj.d*ulp(&rv);
3123 }
3124 break;
3125 }
3126 adj.d = ratio(delta, bs);
3127 if (adj.d < 1.)
3128 adj.d = 1.;
3129 if (adj.d <= 0x7ffffffe) {
3130 /* adj = rounding ? ceil(adj) : floor(adj); */
3131 y = adj.d;
3132 if (y != adj.d) {
3133 if (!((bc.rounding>>1) ^ bc.dsign))
3134 y++;
3135 adj.d = y;
3136 }
3137 }
3138#ifdef Avoid_Underflow /*{*/
3139 if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
3140 word0(&adj) += (2*P+1)*Exp_msk1 - y;
3141#else
3142#ifdef Sudden_Underflow
3143 if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
3144 word0(&rv) += P*Exp_msk1;
3145 adj.d *= ulp(dval(&rv));
3146 if (bc.dsign)
3147 dval(&rv) += adj.d;
3148 else
3149 dval(&rv) -= adj.d;
3150 word0(&rv) -= P*Exp_msk1;
3151 goto cont;
3152 }
3153#endif /*Sudden_Underflow*/
3154#endif /*Avoid_Underflow}*/
3155 adj.d *= ulp(&rv);
3156 if (bc.dsign) {
3157 if (word0(&rv) == Big0 && word1(&rv) == Big1)
3158 goto ovfl;
3159 dval(&rv) += adj.d;
3160 }
3161 else
3162 dval(&rv) -= adj.d;
3163 goto cont;
3164 }
3165#endif /*}Honor_FLT_ROUNDS*/
3166
3167 if (i < 0) {
3168 /* Error is less than half an ulp -- check for
3169 * special case of mantissa a power of two.
3170 */
3171 if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask
3172#ifdef IEEE_Arith /*{*/
3173#ifdef Avoid_Underflow
3174 || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
3175#else
3176 || (word0(&rv) & Exp_mask) <= Exp_msk1
3177#endif
3178#endif /*}*/
3179 ) {
3180#ifdef SET_INEXACT
3181 if (!delta->x[0] && delta->wds <= 1)
3182 bc.inexact = 0;
3183#endif
3184 break;
3185 }
3186 if (!delta->x[0] && delta->wds <= 1) {
3187 /* exact result */
3188#ifdef SET_INEXACT
3189 bc.inexact = 0;
3190#endif
3191 break;
3192 }
3193 delta = lshift(delta,Log2P);
3194 if (cmp(delta, bs) > 0)
3195 goto drop_down;
3196 break;
3197 }
3198 if (i == 0) {
3199 /* exactly half-way between */
3200 if (bc.dsign) {
3201 if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
3202 && word1(&rv) == (
3203#ifdef Avoid_Underflow
3204 (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
3205 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
3206#endif
3207 0xffffffff)) {
3208 /*boundary case -- increment exponent*/
3209 if (word0(&rv) == Big0 && word1(&rv) == Big1)
3210 goto ovfl;
3211 word0(&rv) = (word0(&rv) & Exp_mask)
3212 + Exp_msk1
3213#ifdef IBM
3214 | Exp_msk1 >> 4
3215#endif
3216 ;
3217 word1(&rv) = 0;
3218#ifdef Avoid_Underflow
3219 bc.dsign = 0;
3220#endif
3221 break;
3222 }
3223 }
3224 else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
3225 drop_down:
3226 /* boundary case -- decrement exponent */
3227#ifdef Sudden_Underflow /*{{*/
3228 L = word0(&rv) & Exp_mask;
3229#ifdef IBM
3230 if (L < Exp_msk1)
3231#else
3232#ifdef Avoid_Underflow
3233 if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
3234#else
3235 if (L <= Exp_msk1)
3236#endif /*Avoid_Underflow*/
3237#endif /*IBM*/
3238 {
3239 if (bc.nd >nd) {
3240 bc.uflchk = 1;
3241 break;
3242 }
3243 goto undfl;
3244 }
3245 L -= Exp_msk1;
3246#else /*Sudden_Underflow}{*/
3247#ifdef Avoid_Underflow
3248 if (bc.scale) {
3249 L = word0(&rv) & Exp_mask;
3250 if (L <= (2*P+1)*Exp_msk1) {
3251 if (L > (P+2)*Exp_msk1)
3252 /* round even ==> */
3253 /* accept rv */
3254 break;
3255 /* rv = smallest denormal */
3256 if (bc.nd >nd) {
3257 bc.uflchk = 1;
3258 break;
3259 }
3260 goto undfl;
3261 }
3262 }
3263#endif /*Avoid_Underflow*/
3264 L = (word0(&rv) & Exp_mask) - Exp_msk1;
3265#endif /*Sudden_Underflow}}*/
3266 word0(&rv) = L | Bndry_mask1;
3267 word1(&rv) = 0xffffffff;
3268#ifdef IBM
3269 goto cont;
3270#else
3271#ifndef NO_STRTOD_BIGCOMP
3272 if (bc.nd > nd)
3273 goto cont;
3274#endif
3275 break;
3276#endif
3277 }
3278#ifndef ROUND_BIASED
3279#ifdef Avoid_Underflow
3280 if (Lsb1) {
3281 if (!(word0(&rv) & Lsb1))
3282 break;
3283 }
3284 else if (!(word1(&rv) & Lsb))
3285 break;
3286#else
3287 if (!(word1(&rv) & LSB))
3288 break;
3289#endif
3290#endif
3291 if (bc.dsign)
3292#ifdef Avoid_Underflow
3293 dval(&rv) += sulp(&rv, &bc);
3294#else
3295 dval(&rv) += ulp(&rv);
3296#endif
3297#ifndef ROUND_BIASED
3298 else {
3299#ifdef Avoid_Underflow
3300 dval(&rv) -= sulp(&rv, &bc);
3301#else
3302 dval(&rv) -= ulp(&rv);
3303#endif
3304#ifndef Sudden_Underflow
3305 if (!dval(&rv)) {
3306 if (bc.nd >nd) {
3307 bc.uflchk = 1;
3308 break;
3309 }
3310 goto undfl;
3311 }
3312#endif
3313 }
3314#ifdef Avoid_Underflow
3315 bc.dsign = 1 - bc.dsign;
3316#endif
3317#endif
3318 break;
3319 }
3320 if ((aadj = ratio(delta, bs)) <= 2.) {
3321 if (bc.dsign)
3322 aadj = aadj1 = 1.;
3323 else if (word1(&rv) || word0(&rv) & Bndry_mask) {
3324#ifndef Sudden_Underflow
3325 if (word1(&rv) == Tiny1 && !word0(&rv)) {
3326 if (bc.nd >nd) {
3327 bc.uflchk = 1;
3328 break;
3329 }
3330 goto undfl;
3331 }
3332#endif
3333 aadj = 1.;
3334 aadj1 = -1.;
3335 }
3336 else {
3337 /* special case -- power of FLT_RADIX to be */
3338 /* rounded down... */
3339
3340 if (aadj < 2./FLT_RADIX)
3341 aadj = 1./FLT_RADIX;
3342 else
3343 aadj *= 0.5;
3344 aadj1 = -aadj;
3345 }
3346 }
3347 else {
3348 aadj *= 0.5;
3349 aadj1 = bc.dsign ? aadj : -aadj;
3350#ifdef Check_FLT_ROUNDS
3351 switch(bc.rounding) {
3352 case 2: /* towards +infinity */
3353 aadj1 -= 0.5;
3354 break;
3355 case 0: /* towards 0 */
3356 case 3: /* towards -infinity */
3357 aadj1 += 0.5;
3358 }
3359#else
3360 if (Flt_Rounds == 0)
3361 aadj1 += 0.5;
3362#endif /*Check_FLT_ROUNDS*/
3363 }
3364 y = word0(&rv) & Exp_mask;
3365
3366 /* Check for overflow */
3367
3368 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
3369 dval(&rv0) = dval(&rv);
3370 word0(&rv) -= P*Exp_msk1;
3371 adj.d = aadj1 * ulp(&rv);
3372 dval(&rv) += adj.d;
3373 if ((word0(&rv) & Exp_mask) >=
3374 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
3375 if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
3376 goto ovfl;
3377 word0(&rv) = Big0;
3378 word1(&rv) = Big1;
3379 goto cont;
3380 }
3381 else
3382 word0(&rv) += P*Exp_msk1;
3383 }
3384 else {
3385#ifdef Avoid_Underflow
3386 if (bc.scale && y <= 2*P*Exp_msk1) {
3387 if (aadj <= 0x7fffffff) {
3388 if ((z = aadj) <= 0)
3389 z = 1;
3390 aadj = z;
3391 aadj1 = bc.dsign ? aadj : -aadj;
3392 }
3393 dval(&aadj2) = aadj1;
3394 word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
3395 aadj1 = dval(&aadj2);
3396 adj.d = aadj1 * ulp(&rv);
3397 dval(&rv) += adj.d;
3398 if (rv.d == 0.)
3399#ifdef NO_STRTOD_BIGCOMP
3400 goto undfl;
3401#else
3402 {
3403 if (bc.nd > nd)
3404 bc.dsign = 1;
3405 break;
3406 }
3407#endif
3408 }
3409 else {
3410 adj.d = aadj1 * ulp(&rv);
3411 dval(&rv) += adj.d;
3412 }
3413#else
3414#ifdef Sudden_Underflow
3415 if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
3416 dval(&rv0) = dval(&rv);
3417 word0(&rv) += P*Exp_msk1;
3418 adj.d = aadj1 * ulp(&rv);
3419 dval(&rv) += adj.d;
3420#ifdef IBM
3421 if ((word0(&rv) & Exp_mask) < P*Exp_msk1)
3422#else
3423 if ((word0(&rv) & Exp_mask) <= P*Exp_msk1)
3424#endif
3425 {
3426 if (word0(&rv0) == Tiny0
3427 && word1(&rv0) == Tiny1) {
3428 if (bc.nd >nd) {
3429 bc.uflchk = 1;
3430 break;
3431 }
3432 goto undfl;
3433 }
3434 word0(&rv) = Tiny0;
3435 word1(&rv) = Tiny1;
3436 goto cont;
3437 }
3438 else
3439 word0(&rv) -= P*Exp_msk1;
3440 }
3441 else {
3442 adj.d = aadj1 * ulp(&rv);
3443 dval(&rv) += adj.d;
3444 }
3445#else /*Sudden_Underflow*/
3446 /* Compute adj so that the IEEE rounding rules will
3447 * correctly round rv + adj in some half-way cases.
3448 * If rv * ulp(rv) is denormalized (i.e.,
3449 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
3450 * trouble from bits lost to denormalization;
3451 * example: 1.2e-307 .
3452 */
3453 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
3454 aadj1 = (double)(int)(aadj + 0.5);
3455 if (!bc.dsign)
3456 aadj1 = -aadj1;
3457 }
3458 adj.d = aadj1 * ulp(&rv);
3459 dval(&rv) += adj.d;
3460#endif /*Sudden_Underflow*/
3461#endif /*Avoid_Underflow*/
3462 }
3463 z = word0(&rv) & Exp_mask;
3464#ifndef SET_INEXACT
3465 if (bc.nd == nd) {
3466#ifdef Avoid_Underflow
3467 if (!bc.scale)
3468#endif
3469 if (y == z) {
3470 /* Can we stop now? */
3471 L = (Long)aadj;
3472 aadj -= L;
3473 /* The tolerances below are conservative. */
3474 if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
3475 if (aadj < .4999999 || aadj > .5000001)
3476 break;
3477 }
3478 else if (aadj < .4999999/FLT_RADIX)
3479 break;
3480 }
3481 }
3482#endif
3483 cont:
3484 Bfree(bb);
3485 Bfree(bd);
3486 Bfree(bs);
3487 Bfree(delta);
3488 }
3489 Bfree(bb);
3490 Bfree(bd);
3491 Bfree(bs);
3492 Bfree(bd0);
3493 Bfree(delta);
3494#ifndef NO_STRTOD_BIGCOMP
3495 if (req_bigcomp) {
3496 bd0 = 0;
3497 bc.e0 += nz1;
3498 bigcomp(&rv, s0, &bc);
3499 y = word0(&rv) & Exp_mask;
3500 if (y == Exp_mask)
3501 goto ovfl;
3502 if (y == 0 && rv.d == 0.)
3503 goto undfl;
3504 }
3505#endif
3506#ifdef SET_INEXACT
3507 if (bc.inexact) {
3508 if (!oldinexact) {
3509 word0(&rv0) = Exp_1 + (70 << Exp_shift);
3510 word1(&rv0) = 0;
3511 dval(&rv0) += 1.;
3512 }
3513 }
3514 else if (!oldinexact)
3515 clear_inexact();
3516#endif
3517#ifdef Avoid_Underflow
3518 if (bc.scale) {
3519 word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
3520 word1(&rv0) = 0;
3521 dval(&rv) *= dval(&rv0);
3522#ifndef NO_ERRNO
3523 /* try to avoid the bug of testing an 8087 register value */
3524#ifdef IEEE_Arith
3525 if (!(word0(&rv) & Exp_mask))
3526#else
3527 if (word0(&rv) == 0 && word1(&rv) == 0)
3528#endif
3529 errno = ERANGE;
3530#endif
3531 }
3532#endif /* Avoid_Underflow */
3533#ifdef SET_INEXACT
3534 if (bc.inexact && !(word0(&rv) & Exp_mask)) {
3535 /* set underflow bit */
3536 dval(&rv0) = 1e-300;
3537 dval(&rv0) *= dval(&rv0);
3538 }
3539#endif
3540 ret:
3541 if (se)
3542 *se = (char *)s;
3543 return sign ? -dval(&rv) : dval(&rv);
3544 }
3545
3546#ifndef MULTIPLE_THREADS
3547 static char *dtoa_result;
3548#endif
3549
3550 static char *
3551#ifdef KR_headers
3552rv_alloc(i) int i;
3553#else
3554rv_alloc(int i)
3555#endif
3556{
3557 int j, k, *r;
3558
3559 j = sizeof(ULong);
3560 for(k = 0;
3561 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
3562 j <<= 1)
3563 k++;
3564 r = (int*)Balloc(k);
3565 *r = k;
3566 return
3567#ifndef MULTIPLE_THREADS
3568 dtoa_result =
3569#endif
3570 (char *)(r+1);
3571 }
3572
3573 static char *
3574#ifdef KR_headers
3575nrv_alloc(s, rve, n) char *s, **rve; int n;
3576#else
3577nrv_alloc(const char *s, char **rve, int n)
3578#endif
3579{
3580 char *rv, *t;
3581
3582 t = rv = rv_alloc(n);
3583 while((*t = *s++)) t++;
3584 if (rve)
3585 *rve = t;
3586 return rv;
3587 }
3588
3589/* freedtoa(s) must be used to free values s returned by dtoa
3590 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
3591 * but for consistency with earlier versions of dtoa, it is optional
3592 * when MULTIPLE_THREADS is not defined.
3593 */
3594
3595 void
3596#ifdef KR_headers
3597freedtoa(s) char *s;
3598#else
3599freedtoa(char *s)
3600#endif
3601{
3602 Bigint *b = (Bigint *)((int *)s - 1);
3603 b->maxwds = 1 << (b->k = *(int*)b);
3604 Bfree(b);
3605#ifndef MULTIPLE_THREADS
3606 if (s == dtoa_result)
3607 dtoa_result = 0;
3608#endif
3609 }
3610
3611/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
3612 *
3613 * Inspired by "How to Print Floating-Point Numbers Accurately" by
3614 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
3615 *
3616 * Modifications:
3617 * 1. Rather than iterating, we use a simple numeric overestimate
3618 * to determine k = floor(log10(d)). We scale relevant
3619 * quantities using O(log2(k)) rather than O(k) multiplications.
3620 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
3621 * try to generate digits strictly left to right. Instead, we
3622 * compute with fewer bits and propagate the carry if necessary
3623 * when rounding the final digit up. This is often faster.
3624 * 3. Under the assumption that input will be rounded nearest,
3625 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
3626 * That is, we allow equality in stopping tests when the
3627 * round-nearest rule will give the same floating-point value
3628 * as would satisfaction of the stopping test with strict
3629 * inequality.
3630 * 4. We remove common factors of powers of 2 from relevant
3631 * quantities.
3632 * 5. When converting floating-point integers less than 1e16,
3633 * we use floating-point arithmetic rather than resorting
3634 * to multiple-precision integers.
3635 * 6. When asked to produce fewer than 15 digits, we first try
3636 * to get by with floating-point arithmetic; we resort to
3637 * multiple-precision integer arithmetic only if we cannot
3638 * guarantee that the floating-point calculation has given
3639 * the correctly rounded result. For k requested digits and
3640 * "uniformly" distributed input, the probability is
3641 * something like 10^(k-15) that we must resort to the Long
3642 * calculation.
3643 */
3644
3645 char *
3646dtoa
3647#ifdef KR_headers
3648 (dd, mode, ndigits, decpt, sign, rve)
3649 double dd; int mode, ndigits, *decpt, *sign; char **rve;
3650#else
3651 (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
3652#endif
3653{
3654 /* Arguments ndigits, decpt, sign are similar to those
3655 of ecvt and fcvt; trailing zeros are suppressed from
3656 the returned string. If not null, *rve is set to point
3657 to the end of the return value. If d is +-Infinity or NaN,
3658 then *decpt is set to 9999.
3659
3660 mode:
3661 0 ==> shortest string that yields d when read in
3662 and rounded to nearest.
3663 1 ==> like 0, but with Steele & White stopping rule;
3664 e.g. with IEEE P754 arithmetic , mode 0 gives
3665 1e23 whereas mode 1 gives 9.999999999999999e22.
3666 2 ==> max(1,ndigits) significant digits. This gives a
3667 return value similar to that of ecvt, except
3668 that trailing zeros are suppressed.
3669 3 ==> through ndigits past the decimal point. This
3670 gives a return value similar to that from fcvt,
3671 except that trailing zeros are suppressed, and
3672 ndigits can be negative.
3673 4,5 ==> similar to 2 and 3, respectively, but (in
3674 round-nearest mode) with the tests of mode 0 to
3675 possibly return a shorter string that rounds to d.
3676 With IEEE arithmetic and compilation with
3677 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
3678 as modes 2 and 3 when FLT_ROUNDS != 1.
3679 6-9 ==> Debugging modes similar to mode - 4: don't try
3680 fast floating-point estimate (if applicable).
3681
3682 Values of mode other than 0-9 are treated as mode 0.
3683
3684 Sufficient space is allocated to the return value
3685 to hold the suppressed trailing zeros.
3686 */
3687
3688 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
3689 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
3690 spec_case, try_quick;
3691 Long L;
3692#ifndef Sudden_Underflow
3693 int denorm;
3694 ULong x;
3695#endif
3696 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
3697 U d2, eps, u;
3698 double ds;
3699 char *s, *s0;
3700#ifndef No_leftright
3701#ifdef IEEE_Arith
3702 U eps1;
3703#endif
3704#endif
3705#ifdef SET_INEXACT
3706 int inexact, oldinexact;
3707#endif
3708#ifdef Honor_FLT_ROUNDS /*{*/
3709 int Rounding;
3710#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
3711 Rounding = Flt_Rounds;
3712#else /*}{*/
3713 Rounding = 1;
3714 switch(fegetround()) {
3715 case FE_TOWARDZERO: Rounding = 0; break;
3716 case FE_UPWARD: Rounding = 2; break;
3717 case FE_DOWNWARD: Rounding = 3;
3718 }
3719#endif /*}}*/
3720#endif /*}*/
3721
3722#ifndef MULTIPLE_THREADS
3723 if (dtoa_result) {
3724 freedtoa(dtoa_result);
3725 dtoa_result = 0;
3726 }
3727#endif
3728
3729 u.d = dd;
3730 if (word0(&u) & Sign_bit) {
3731 /* set sign for everything, including 0's and NaNs */
3732 *sign = 1;
3733 word0(&u) &= ~Sign_bit; /* clear sign bit */
3734 }
3735 else
3736 *sign = 0;
3737
3738#if defined(IEEE_Arith) + defined(VAX)
3739#ifdef IEEE_Arith
3740 if ((word0(&u) & Exp_mask) == Exp_mask)
3741#else
3742 if (word0(&u) == 0x8000)
3743#endif
3744 {
3745 /* Infinity or NaN */
3746 *decpt = 9999;
3747#ifdef IEEE_Arith
3748 if (!word1(&u) && !(word0(&u) & 0xfffff))
3749 return nrv_alloc("Infinity", rve, 8);
3750#endif
3751 return nrv_alloc("NaN", rve, 3);
3752 }
3753#endif
3754#ifdef IBM
3755 dval(&u) += 0; /* normalize */
3756#endif
3757 if (!dval(&u)) {
3758 *decpt = 1;
3759 return nrv_alloc("0", rve, 1);
3760 }
3761
3762#ifdef SET_INEXACT
3763 try_quick = oldinexact = get_inexact();
3764 inexact = 1;
3765#endif
3766#ifdef Honor_FLT_ROUNDS
3767 if (Rounding >= 2) {
3768 if (*sign)
3769 Rounding = Rounding == 2 ? 0 : 2;
3770 else
3771 if (Rounding != 2)
3772 Rounding = 0;
3773 }
3774#endif
3775
3776 b = d2b(&u, &be, &bbits);
3777#ifdef Sudden_Underflow
3778 i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
3779#else
3780 if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
3781#endif
3782 dval(&d2) = dval(&u);
3783 word0(&d2) &= Frac_mask1;
3784 word0(&d2) |= Exp_11;
3785#ifdef IBM
3786 if (j = 11 - hi0bits(word0(&d2) & Frac_mask))
3787 dval(&d2) /= 1 << j;
3788#endif
3789
3790 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
3791 * log10(x) = log(x) / log(10)
3792 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
3793 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
3794 *
3795 * This suggests computing an approximation k to log10(d) by
3796 *
3797 * k = (i - Bias)*0.301029995663981
3798 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
3799 *
3800 * We want k to be too large rather than too small.
3801 * The error in the first-order Taylor series approximation
3802 * is in our favor, so we just round up the constant enough
3803 * to compensate for any error in the multiplication of
3804 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
3805 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
3806 * adding 1e-13 to the constant term more than suffices.
3807 * Hence we adjust the constant term to 0.1760912590558.
3808 * (We could get a more accurate k by invoking log10,
3809 * but this is probably not worthwhile.)
3810 */
3811
3812 i -= Bias;
3813#ifdef IBM
3814 i <<= 2;
3815 i += j;
3816#endif
3817#ifndef Sudden_Underflow
3818 denorm = 0;
3819 }
3820 else {
3821 /* d is denormalized */
3822
3823 i = bbits + be + (Bias + (P-1) - 1);
3824 x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
3825 : word1(&u) << (32 - i);
3826 dval(&d2) = x;
3827 word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
3828 i -= (Bias + (P-1) - 1) + 1;
3829 denorm = 1;
3830 }
3831#endif
3832 ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
3833 k = (int)ds;
3834 if (ds < 0. && ds != k)
3835 k--; /* want k = floor(ds) */
3836 k_check = 1;
3837 if (k >= 0 && k <= Ten_pmax) {
3838 if (dval(&u) < tens[k])
3839 k--;
3840 k_check = 0;
3841 }
3842 j = bbits - i - 1;
3843 if (j >= 0) {
3844 b2 = 0;
3845 s2 = j;
3846 }
3847 else {
3848 b2 = -j;
3849 s2 = 0;
3850 }
3851 if (k >= 0) {
3852 b5 = 0;
3853 s5 = k;
3854 s2 += k;
3855 }
3856 else {
3857 b2 -= k;
3858 b5 = -k;
3859 s5 = 0;
3860 }
3861 if (mode < 0 || mode > 9)
3862 mode = 0;
3863
3864#ifndef SET_INEXACT
3865#ifdef Check_FLT_ROUNDS
3866 try_quick = Rounding == 1;
3867#else
3868 try_quick = 1;
3869#endif
3870#endif /*SET_INEXACT*/
3871
3872 if (mode > 5) {
3873 mode -= 4;
3874 try_quick = 0;
3875 }
3876 leftright = 1;
3877 ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
3878 /* silence erroneous "gcc -Wall" warning. */
3879 switch(mode) {
3880 case 0:
3881 case 1:
3882 i = 18;
3883 ndigits = 0;
3884 break;
3885 case 2:
3886 leftright = 0;
3887 /* no break */
3888 case 4:
3889 if (ndigits <= 0)
3890 ndigits = 1;
3891 ilim = ilim1 = i = ndigits;
3892 break;
3893 case 3:
3894 leftright = 0;
3895 /* no break */
3896 case 5:
3897 i = ndigits + k + 1;
3898 ilim = i;
3899 ilim1 = i - 1;
3900 if (i <= 0)
3901 i = 1;
3902 }
3903 s = s0 = rv_alloc(i);
3904
3905#ifdef Honor_FLT_ROUNDS
3906 if (mode > 1 && Rounding != 1)
3907 leftright = 0;
3908#endif
3909
3910 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
3911
3912 /* Try to get by with floating-point arithmetic. */
3913
3914 i = 0;
3915 dval(&d2) = dval(&u);
3916 k0 = k;
3917 ilim0 = ilim;
3918 ieps = 2; /* conservative */
3919 if (k > 0) {
3920 ds = tens[k&0xf];
3921 j = k >> 4;
3922 if (j & Bletch) {
3923 /* prevent overflows */
3924 j &= Bletch - 1;
3925 dval(&u) /= bigtens[n_bigtens-1];
3926 ieps++;
3927 }
3928 for(; j; j >>= 1, i++)
3929 if (j & 1) {
3930 ieps++;
3931 ds *= bigtens[i];
3932 }
3933 dval(&u) /= ds;
3934 }
3935 else if ((j1 = -k)) {
3936 dval(&u) *= tens[j1 & 0xf];
3937 for(j = j1 >> 4; j; j >>= 1, i++)
3938 if (j & 1) {
3939 ieps++;
3940 dval(&u) *= bigtens[i];
3941 }
3942 }
3943 if (k_check && dval(&u) < 1. && ilim > 0) {
3944 if (ilim1 <= 0)
3945 goto fast_failed;
3946 ilim = ilim1;
3947 k--;
3948 dval(&u) *= 10.;
3949 ieps++;
3950 }
3951 dval(&eps) = ieps*dval(&u) + 7.;
3952 word0(&eps) -= (P-1)*Exp_msk1;
3953 if (ilim == 0) {
3954 S = mhi = 0;
3955 dval(&u) -= 5.;
3956 if (dval(&u) > dval(&eps))
3957 goto one_digit;
3958 if (dval(&u) < -dval(&eps))
3959 goto no_digits;
3960 goto fast_failed;
3961 }
3962#ifndef No_leftright
3963 if (leftright) {
3964 /* Use Steele & White method of only
3965 * generating digits needed.
3966 */
3967 dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
3968#ifdef IEEE_Arith
3969 if (k0 < 0 && j1 >= 307) {
3970 eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */
3971 word0(&eps1) -= Exp_msk1 * (Bias+P-1);
3972 dval(&eps1) *= tens[j1 & 0xf];
3973 for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++)
3974 if (j & 1)
3975 dval(&eps1) *= bigtens[i];
3976 if (eps.d < eps1.d)
3977 eps.d = eps1.d;
3978 }
3979#endif
3980 for(i = 0;;) {
3981 L = dval(&u);
3982 dval(&u) -= L;
3983 *s++ = '0' + (int)L;
3984 if (1. - dval(&u) < dval(&eps))
3985 goto bump_up;
3986 if (dval(&u) < dval(&eps))
3987 goto ret1;
3988 if (++i >= ilim)
3989 break;
3990 dval(&eps) *= 10.;
3991 dval(&u) *= 10.;
3992 }
3993 }
3994 else {
3995#endif
3996 /* Generate ilim digits, then fix them up. */
3997 dval(&eps) *= tens[ilim-1];
3998 for(i = 1;; i++, dval(&u) *= 10.) {
3999 L = (Long)(dval(&u));
4000 if (!(dval(&u) -= L))
4001 ilim = i;
4002 *s++ = '0' + (int)L;
4003 if (i == ilim) {
4004 if (dval(&u) > 0.5 + dval(&eps))
4005 goto bump_up;
4006 else if (dval(&u) < 0.5 - dval(&eps)) {
4007 while(*--s == '0');
4008 s++;
4009 goto ret1;
4010 }
4011 break;
4012 }
4013 }
4014#ifndef No_leftright
4015 }
4016#endif
4017 fast_failed:
4018 s = s0;
4019 dval(&u) = dval(&d2);
4020 k = k0;
4021 ilim = ilim0;
4022 }
4023
4024 /* Do we have a "small" integer? */
4025
4026 if (be >= 0 && k <= Int_max) {
4027 /* Yes. */
4028 ds = tens[k];
4029 if (ndigits < 0 && ilim <= 0) {
4030 S = mhi = 0;
4031 if (ilim < 0 || dval(&u) <= 5*ds)
4032 goto no_digits;
4033 goto one_digit;
4034 }
4035 for(i = 1;; i++, dval(&u) *= 10.) {
4036 L = (Long)(dval(&u) / ds);
4037 dval(&u) -= L*ds;
4038#ifdef Check_FLT_ROUNDS
4039 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
4040 if (dval(&u) < 0) {
4041 L--;
4042 dval(&u) += ds;
4043 }
4044#endif
4045 *s++ = '0' + (int)L;
4046 if (!dval(&u)) {
4047#ifdef SET_INEXACT
4048 inexact = 0;
4049#endif
4050 break;
4051 }
4052 if (i == ilim) {
4053#ifdef Honor_FLT_ROUNDS
4054 if (mode > 1)
4055 switch(Rounding) {
4056 case 0: goto ret1;
4057 case 2: goto bump_up;
4058 }
4059#endif
4060 dval(&u) += dval(&u);
4061#ifdef ROUND_BIASED
4062 if (dval(&u) >= ds)
4063#else
4064 if (dval(&u) > ds || (dval(&u) == ds && L & 1))
4065#endif
4066 {
4067 bump_up:
4068 while(*--s == '9')
4069 if (s == s0) {
4070 k++;
4071 *s = '0';
4072 break;
4073 }
4074 ++*s++;
4075 }
4076 break;
4077 }
4078 }
4079 goto ret1;
4080 }
4081
4082 m2 = b2;
4083 m5 = b5;
4084 mhi = mlo = 0;
4085 if (leftright) {
4086 i =
4087#ifndef Sudden_Underflow
4088 denorm ? be + (Bias + (P-1) - 1 + 1) :
4089#endif
4090#ifdef IBM
4091 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
4092#else
4093 1 + P - bbits;
4094#endif
4095 b2 += i;
4096 s2 += i;
4097 mhi = i2b(1);
4098 }
4099 if (m2 > 0 && s2 > 0) {
4100 i = m2 < s2 ? m2 : s2;
4101 b2 -= i;
4102 m2 -= i;
4103 s2 -= i;
4104 }
4105 if (b5 > 0) {
4106 if (leftright) {
4107 if (m5 > 0) {
4108 mhi = pow5mult(mhi, m5);
4109 b1 = mult(mhi, b);
4110 Bfree(b);
4111 b = b1;
4112 }
4113 if ((j = b5 - m5))
4114 b = pow5mult(b, j);
4115 }
4116 else
4117 b = pow5mult(b, b5);
4118 }
4119 S = i2b(1);
4120 if (s5 > 0)
4121 S = pow5mult(S, s5);
4122
4123 /* Check for special case that d is a normalized power of 2. */
4124
4125 spec_case = 0;
4126 if ((mode < 2 || leftright)
4127#ifdef Honor_FLT_ROUNDS
4128 && Rounding == 1
4129#endif
4130 ) {
4131 if (!word1(&u) && !(word0(&u) & Bndry_mask)
4132#ifndef Sudden_Underflow
4133 && word0(&u) & (Exp_mask & ~Exp_msk1)
4134#endif
4135 ) {
4136 /* The special case */
4137 b2 += Log2P;
4138 s2 += Log2P;
4139 spec_case = 1;
4140 }
4141 }
4142
4143 /* Arrange for convenient computation of quotients:
4144 * shift left if necessary so divisor has 4 leading 0 bits.
4145 *
4146 * Perhaps we should just compute leading 28 bits of S once
4147 * and for all and pass them and a shift to quorem, so it
4148 * can do shifts and ors to compute the numerator for q.
4149 */
4150 i = dshift(S, s2);
4151 b2 += i;
4152 m2 += i;
4153 s2 += i;
4154 if (b2 > 0)
4155 b = lshift(b, b2);
4156 if (s2 > 0)
4157 S = lshift(S, s2);
4158 if (k_check) {
4159 if (cmp(b,S) < 0) {
4160 k--;
4161 b = multadd(b, 10, 0); /* we botched the k estimate */
4162 if (leftright)
4163 mhi = multadd(mhi, 10, 0);
4164 ilim = ilim1;
4165 }
4166 }
4167 if (ilim <= 0 && (mode == 3 || mode == 5)) {
4168 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
4169 /* no digits, fcvt style */
4170 no_digits:
4171 k = -1 - ndigits;
4172 goto ret;
4173 }
4174 one_digit:
4175 *s++ = '1';
4176 k++;
4177 goto ret;
4178 }
4179 if (leftright) {
4180 if (m2 > 0)
4181 mhi = lshift(mhi, m2);
4182
4183 /* Compute mlo -- check for special case
4184 * that d is a normalized power of 2.
4185 */
4186
4187 mlo = mhi;
4188 if (spec_case) {
4189 mhi = Balloc(mhi->k);
4190 Bcopy(mhi, mlo);
4191 mhi = lshift(mhi, Log2P);
4192 }
4193
4194 for(i = 1;;i++) {
4195 dig = quorem(b,S) + '0';
4196 /* Do we yet have the shortest decimal string
4197 * that will round to d?
4198 */
4199 j = cmp(b, mlo);
4200 delta = diff(S, mhi);
4201 j1 = delta->sign ? 1 : cmp(b, delta);
4202 Bfree(delta);
4203#ifndef ROUND_BIASED
4204 if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
4205#ifdef Honor_FLT_ROUNDS
4206 && Rounding >= 1
4207#endif
4208 ) {
4209 if (dig == '9')
4210 goto round_9_up;
4211 if (j > 0)
4212 dig++;
4213#ifdef SET_INEXACT
4214 else if (!b->x[0] && b->wds <= 1)
4215 inexact = 0;
4216#endif
4217 *s++ = dig;
4218 goto ret;
4219 }
4220#endif
4221 if (j < 0 || (j == 0 && mode != 1
4222#ifndef ROUND_BIASED
4223 && !(word1(&u) & 1)
4224#endif
4225 )) {
4226 if (!b->x[0] && b->wds <= 1) {
4227#ifdef SET_INEXACT
4228 inexact = 0;
4229#endif
4230 goto accept_dig;
4231 }
4232#ifdef Honor_FLT_ROUNDS
4233 if (mode > 1)
4234 switch(Rounding) {
4235 case 0: goto accept_dig;
4236 case 2: goto keep_dig;
4237 }
4238#endif /*Honor_FLT_ROUNDS*/
4239 if (j1 > 0) {
4240 b = lshift(b, 1);
4241 j1 = cmp(b, S);
4242#ifdef ROUND_BIASED
4243 if (j1 >= 0 /*)*/
4244#else
4245 if ((j1 > 0 || (j1 == 0 && dig & 1))
4246#endif
4247 && dig++ == '9')
4248 goto round_9_up;
4249 }
4250 accept_dig:
4251 *s++ = dig;
4252 goto ret;
4253 }
4254 if (j1 > 0) {
4255#ifdef Honor_FLT_ROUNDS
4256 if (!Rounding)
4257 goto accept_dig;
4258#endif
4259 if (dig == '9') { /* possible if i == 1 */
4260 round_9_up:
4261 *s++ = '9';
4262 goto roundoff;
4263 }
4264 *s++ = dig + 1;
4265 goto ret;
4266 }
4267#ifdef Honor_FLT_ROUNDS
4268 keep_dig:
4269#endif
4270 *s++ = dig;
4271 if (i == ilim)
4272 break;
4273 b = multadd(b, 10, 0);
4274 if (mlo == mhi)
4275 mlo = mhi = multadd(mhi, 10, 0);
4276 else {
4277 mlo = multadd(mlo, 10, 0);
4278 mhi = multadd(mhi, 10, 0);
4279 }
4280 }
4281 }
4282 else
4283 for(i = 1;; i++) {
4284 *s++ = dig = quorem(b,S) + '0';
4285 if (!b->x[0] && b->wds <= 1) {
4286#ifdef SET_INEXACT
4287 inexact = 0;
4288#endif
4289 goto ret;
4290 }
4291 if (i >= ilim)
4292 break;
4293 b = multadd(b, 10, 0);
4294 }
4295
4296 /* Round off last digit */
4297
4298#ifdef Honor_FLT_ROUNDS
4299 switch(Rounding) {
4300 case 0: goto trimzeros;
4301 case 2: goto roundoff;
4302 }
4303#endif
4304 b = lshift(b, 1);
4305 j = cmp(b, S);
4306#ifdef ROUND_BIASED
4307 if (j >= 0)
4308#else
4309 if (j > 0 || (j == 0 && dig & 1))
4310#endif
4311 {
4312 roundoff:
4313 while(*--s == '9')
4314 if (s == s0) {
4315 k++;
4316 *s++ = '1';
4317 goto ret;
4318 }
4319 ++*s++;
4320 }
4321 else {
4322#ifdef Honor_FLT_ROUNDS
4323 trimzeros:
4324#endif
4325 while(*--s == '0');
4326 s++;
4327 }
4328 ret:
4329 Bfree(S);
4330 if (mhi) {
4331 if (mlo && mlo != mhi)
4332 Bfree(mlo);
4333 Bfree(mhi);
4334 }
4335 ret1:
4336#ifdef SET_INEXACT
4337 if (inexact) {
4338 if (!oldinexact) {
4339 word0(&u) = Exp_1 + (70 << Exp_shift);
4340 word1(&u) = 0;
4341 dval(&u) += 1.;
4342 }
4343 }
4344 else if (!oldinexact)
4345 clear_inexact();
4346#endif
4347 Bfree(b);
4348 *s = 0;
4349 *decpt = k + 1;
4350 if (rve)
4351 *rve = s;
4352 return s0;
4353 }
4354#ifdef __cplusplus
4355}
4356#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-03-15 21:24:18 +0000