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Bug 551763: Fix deletion of arguments ident. (r=Waldo)
[mozilla-central.git] / js / src / dtoa.c
blob76fc8cf08e626fe417aa227548149f16cd50ef31
1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
2 /****************************************************************
3 *
4 * The author of this software is David M. Gay.
5 *
6 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
7 *
8 * Permission to use, copy, modify, and distribute this software for any
9 * purpose without fee is hereby granted, provided that this entire notice
10 * is included in all copies of any software which is or includes a copy
11 * or modification of this software and in all copies of the supporting
12 * documentation for such software.
13 *
14 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
15 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
16 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
17 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
18 *
19 ***************************************************************/
20
21 /* Please send bug reports to David M. Gay (dmg at acm dot org,
22 * with " at " changed at "@" and " dot " changed to "."). */
23
24 /* On a machine with IEEE extended-precision registers, it is
25 * necessary to specify double-precision (53-bit) rounding precision
26 * before invoking strtod or dtoa. If the machine uses (the equivalent
27 * of) Intel 80x87 arithmetic, the call
28 * _control87(PC_53, MCW_PC);
29 * does this with many compilers. Whether this or another call is
30 * appropriate depends on the compiler; for this to work, it may be
31 * necessary to #include "float.h" or another system-dependent header
32 * file.
33 */
34
35 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
36 *
37 * This strtod returns a nearest machine number to the input decimal
38 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
39 * broken by the IEEE round-even rule. Otherwise ties are broken by
40 * biased rounding (add half and chop).
41 *
42 * Inspired loosely by William D. Clinger's paper "How to Read Floating
43 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
44 *
45 * Modifications:
46 *
47 * 1. We only require IEEE, IBM, or VAX double-precision
48 * arithmetic (not IEEE double-extended).
49 * 2. We get by with floating-point arithmetic in a case that
50 * Clinger missed -- when we're computing d * 10^n
51 * for a small integer d and the integer n is not too
52 * much larger than 22 (the maximum integer k for which
53 * we can represent 10^k exactly), we may be able to
54 * compute (d*10^k) * 10^(e-k) with just one roundoff.
55 * 3. Rather than a bit-at-a-time adjustment of the binary
56 * result in the hard case, we use floating-point
57 * arithmetic to determine the adjustment to within
58 * one bit; only in really hard cases do we need to
59 * compute a second residual.
60 * 4. Because of 3., we don't need a large table of powers of 10
61 * for ten-to-e (just some small tables, e.g. of 10^k
62 * for 0 <= k <= 22).
63 */
64
65 /*
66 * #define IEEE_8087 for IEEE-arithmetic machines where the least
67 * significant byte has the lowest address.
68 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
69 * significant byte has the lowest address.
70 * #define Long int on machines with 32-bit ints and 64-bit longs.
71 * #define IBM for IBM mainframe-style floating-point arithmetic.
72 * #define VAX for VAX-style floating-point arithmetic (D_floating).
73 * #define No_leftright to omit left-right logic in fast floating-point
74 * computation of dtoa.
75 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
76 * and strtod and dtoa should round accordingly.
77 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
78 * and Honor_FLT_ROUNDS is not #defined.
79 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
80 * that use extended-precision instructions to compute rounded
81 * products and quotients) with IBM.
82 * #define ROUND_BIASED for IEEE-format with biased rounding.
83 * #define Inaccurate_Divide for IEEE-format with correctly rounded
84 * products but inaccurate quotients, e.g., for Intel i860.
85 * #define NO_LONG_LONG on machines that do not have a "long long"
86 * integer type (of >= 64 bits). On such machines, you can
87 * #define Just_16 to store 16 bits per 32-bit Long when doing
88 * high-precision integer arithmetic. Whether this speeds things
89 * up or slows things down depends on the machine and the number
90 * being converted. If long long is available and the name is
91 * something other than "long long", #define Llong to be the name,
92 * and if "unsigned Llong" does not work as an unsigned version of
93 * Llong, #define #ULLong to be the corresponding unsigned type.
94 * #define KR_headers for old-style C function headers.
95 * #define Bad_float_h if your system lacks a float.h or if it does not
96 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
97 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
98 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
99 * if memory is available and otherwise does something you deem
100 * appropriate. If MALLOC is undefined, malloc will be invoked
101 * directly -- and assumed always to succeed. Similarly, if you
102 * want something other than the system's free() to be called to
103 * recycle memory acquired from MALLOC, #define FREE to be the
104 * name of the alternate routine. (Unless you #define
105 * NO_GLOBAL_STATE and call destroydtoa, FREE or free is only
106 * called in pathological cases, e.g., in a dtoa call after a dtoa
107 * return in mode 3 with thousands of digits requested.)
108 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
109 * memory allocations from a private pool of memory when possible.
110 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
111 * unless #defined to be a different length. This default length
112 * suffices to get rid of MALLOC calls except for unusual cases,
113 * such as decimal-to-binary conversion of a very long string of
114 * digits. The longest string dtoa can return is about 751 bytes
115 * long. For conversions by strtod of strings of 800 digits and
116 * all dtoa conversions in single-threaded executions with 8-byte
117 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
118 * pointers, PRIVATE_MEM >= 7112 appears adequate.
119 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
120 * #defined automatically on IEEE systems. On such systems,
121 * when INFNAN_CHECK is #defined, strtod checks
122 * for Infinity and NaN (case insensitively). On some systems
123 * (e.g., some HP systems), it may be necessary to #define NAN_WORD0
124 * appropriately -- to the most significant word of a quiet NaN.
125 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
126 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
127 * strtod also accepts (case insensitively) strings of the form
128 * NaN(x), where x is a string of hexadecimal digits and spaces;
129 * if there is only one string of hexadecimal digits, it is taken
130 * for the 52 fraction bits of the resulting NaN; if there are two
131 * or more strings of hex digits, the first is for the high 20 bits,
132 * the second and subsequent for the low 32 bits, with intervening
133 * white space ignored; but if this results in none of the 52
134 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
135 * and NAN_WORD1 are used instead.
136 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
137 * multiple threads. In this case, you must provide (or suitably
138 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
139 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
140 * in pow5mult, ensures lazy evaluation of only one copy of high
141 * powers of 5; omitting this lock would introduce a small
142 * probability of wasting memory, but would otherwise be harmless.)
143 * You must also invoke freedtoa(s) to free the value s returned by
144 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
145 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
146 * avoids underflows on inputs whose result does not underflow.
147 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
148 * floating-point numbers and flushes underflows to zero rather
149 * than implementing gradual underflow, then you must also #define
150 * Sudden_Underflow.
151 * #define USE_LOCALE to use the current locale's decimal_point value.
152 * #define SET_INEXACT if IEEE arithmetic is being used and extra
153 * computation should be done to set the inexact flag when the
154 * result is inexact and avoid setting inexact when the result
155 * is exact. In this case, dtoa.c must be compiled in
156 * an environment, perhaps provided by #include "dtoa.c" in a
157 * suitable wrapper, that defines two functions,
158 * int get_inexact(void);
159 * void clear_inexact(void);
160 * such that get_inexact() returns a nonzero value if the
161 * inexact bit is already set, and clear_inexact() sets the
162 * inexact bit to 0. When SET_INEXACT is #defined, strtod
163 * also does extra computations to set the underflow and overflow
164 * flags when appropriate (i.e., when the result is tiny and
165 * inexact or when it is a numeric value rounded to +-infinity).
166 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
167 * the result overflows to +-Infinity or underflows to 0.
168 * #define NO_GLOBAL_STATE to avoid defining any non-const global or
169 * static variables. Instead the necessary state is stored in an
170 * opaque struct, DtoaState, a pointer to which must be passed to
171 * every entry point. Two new functions are added to the API:
172 * DtoaState *newdtoa(void);
173 * void destroydtoa(DtoaState *);
174 */
175
176 #ifndef Long
177 #define Long long
178 #endif
179 #ifndef ULong
180 typedef unsigned Long ULong;
181 #endif
182
183 #ifdef DEBUG
184 #include "stdio.h"
185 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
186 #endif
187
188 #include "stdlib.h"
189 #include "string.h"
190
191 #ifdef USE_LOCALE
192 #include "locale.h"
193 #endif
194
195 #ifdef MALLOC
196 #ifdef KR_headers
197 extern char *MALLOC();
198 #else
199 extern void *MALLOC(size_t);
200 #endif
201 #else
202 #define MALLOC malloc
203 #endif
204
205 #ifndef FREE
206 #define FREE free
207 #endif
208
209 #ifndef Omit_Private_Memory
210 #ifndef PRIVATE_MEM
211 #define PRIVATE_MEM 2304
212 #endif
213 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
214 #endif
215
216 #undef IEEE_Arith
217 #undef Avoid_Underflow
218 #ifdef IEEE_MC68k
219 #define IEEE_Arith
220 #endif
221 #ifdef IEEE_8087
222 #define IEEE_Arith
223 #endif
224
225 #ifdef IEEE_Arith
226 #ifndef NO_INFNAN_CHECK
227 #undef INFNAN_CHECK
228 #define INFNAN_CHECK
229 #endif
230 #else
231 #undef INFNAN_CHECK
232 #endif
233
234 #include "errno.h"
235
236 #ifdef Bad_float_h
237
238 #ifdef IEEE_Arith
239 #define DBL_DIG 15
240 #define DBL_MAX_10_EXP 308
241 #define DBL_MAX_EXP 1024
242 #define FLT_RADIX 2
243 #endif /*IEEE_Arith*/
244
245 #ifdef IBM
246 #define DBL_DIG 16
247 #define DBL_MAX_10_EXP 75
248 #define DBL_MAX_EXP 63
249 #define FLT_RADIX 16
250 #define DBL_MAX 7.2370055773322621e+75
251 #endif
252
253 #ifdef VAX
254 #define DBL_DIG 16
255 #define DBL_MAX_10_EXP 38
256 #define DBL_MAX_EXP 127
257 #define FLT_RADIX 2
258 #define DBL_MAX 1.7014118346046923e+38
259 #endif
260
261 #ifndef LONG_MAX
262 #define LONG_MAX 2147483647
263 #endif
264
265 #else /* ifndef Bad_float_h */
266 #include "float.h"
267 #endif /* Bad_float_h */
268
269 #ifndef __MATH_H__
270 #include "math.h"
271 #endif
272
273 #ifdef __cplusplus
274 extern "C" {
275 #endif
276
277 #ifndef CONST
278 #ifdef KR_headers
279 #define CONST /* blank */
280 #else
281 #define CONST const
282 #endif
283 #endif
284
285 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
286 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
287 #endif
288
289 typedef union { double d; ULong L[2]; } U;
290
291 #define dval(x) ((x).d)
292 #ifdef IEEE_8087
293 #define word0(x) ((x).L[1])
294 #define word1(x) ((x).L[0])
295 #else
296 #define word0(x) ((x).L[0])
297 #define word1(x) ((x).L[1])
298 #endif
299
300 /* The following definition of Storeinc is appropriate for MIPS processors.
301 * An alternative that might be better on some machines is
302 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
303 */
304 #if defined(IEEE_8087) + defined(VAX)
305 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
306 ((unsigned short *)a)[0] = (unsigned short)c, a++)
307 #else
308 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
309 ((unsigned short *)a)[1] = (unsigned short)c, a++)
310 #endif
311
312 /* #define P DBL_MANT_DIG */
313 /* Ten_pmax = floor(P*log(2)/log(5)) */
314 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
315 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
316 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
317
318 #ifdef IEEE_Arith
319 #define Exp_shift 20
320 #define Exp_shift1 20
321 #define Exp_msk1 0x100000
322 #define Exp_msk11 0x100000
323 #define Exp_mask 0x7ff00000
324 #define P 53
325 #define Bias 1023
326 #define Emin (-1022)
327 #define Exp_1 0x3ff00000
328 #define Exp_11 0x3ff00000
329 #define Ebits 11
330 #define Frac_mask 0xfffff
331 #define Frac_mask1 0xfffff
332 #define Ten_pmax 22
333 #define Bletch 0x10
334 #define Bndry_mask 0xfffff
335 #define Bndry_mask1 0xfffff
336 #define LSB 1
337 #define Sign_bit 0x80000000
338 #define Log2P 1
339 #define Tiny0 0
340 #define Tiny1 1
341 #define Quick_max 14
342 #define Int_max 14
343 #ifndef NO_IEEE_Scale
344 #define Avoid_Underflow
345 #ifdef Flush_Denorm /* debugging option */
346 #undef Sudden_Underflow
347 #endif
348 #endif
349
350 #ifndef Flt_Rounds
351 #ifdef FLT_ROUNDS
352 #define Flt_Rounds FLT_ROUNDS
353 #else
354 #define Flt_Rounds 1
355 #endif
356 #endif /*Flt_Rounds*/
357
358 #ifdef Honor_FLT_ROUNDS
359 #define Rounding rounding
360 #undef Check_FLT_ROUNDS
361 #define Check_FLT_ROUNDS
362 #else
363 #define Rounding Flt_Rounds
364 #endif
365
366 #else /* ifndef IEEE_Arith */
367 #undef Check_FLT_ROUNDS
368 #undef Honor_FLT_ROUNDS
369 #undef SET_INEXACT
370 #undef Sudden_Underflow
371 #define Sudden_Underflow
372 #ifdef IBM
373 #undef Flt_Rounds
374 #define Flt_Rounds 0
375 #define Exp_shift 24
376 #define Exp_shift1 24
377 #define Exp_msk1 0x1000000
378 #define Exp_msk11 0x1000000
379 #define Exp_mask 0x7f000000
380 #define P 14
381 #define Bias 65
382 #define Exp_1 0x41000000
383 #define Exp_11 0x41000000
384 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
385 #define Frac_mask 0xffffff
386 #define Frac_mask1 0xffffff
387 #define Bletch 4
388 #define Ten_pmax 22
389 #define Bndry_mask 0xefffff
390 #define Bndry_mask1 0xffffff
391 #define LSB 1
392 #define Sign_bit 0x80000000
393 #define Log2P 4
394 #define Tiny0 0x100000
395 #define Tiny1 0
396 #define Quick_max 14
397 #define Int_max 15
398 #else /* VAX */
399 #undef Flt_Rounds
400 #define Flt_Rounds 1
401 #define Exp_shift 23
402 #define Exp_shift1 7
403 #define Exp_msk1 0x80
404 #define Exp_msk11 0x800000
405 #define Exp_mask 0x7f80
406 #define P 56
407 #define Bias 129
408 #define Exp_1 0x40800000
409 #define Exp_11 0x4080
410 #define Ebits 8
411 #define Frac_mask 0x7fffff
412 #define Frac_mask1 0xffff007f
413 #define Ten_pmax 24
414 #define Bletch 2
415 #define Bndry_mask 0xffff007f
416 #define Bndry_mask1 0xffff007f
417 #define LSB 0x10000
418 #define Sign_bit 0x8000
419 #define Log2P 1
420 #define Tiny0 0x80
421 #define Tiny1 0
422 #define Quick_max 15
423 #define Int_max 15
424 #endif /* IBM, VAX */
425 #endif /* IEEE_Arith */
426
427 #ifndef IEEE_Arith
428 #define ROUND_BIASED
429 #endif
430
431 #ifdef RND_PRODQUOT
432 #define rounded_product(a,b) a = rnd_prod(a, b)
433 #define rounded_quotient(a,b) a = rnd_quot(a, b)
434 #ifdef KR_headers
435 extern double rnd_prod(), rnd_quot();
436 #else
437 extern double rnd_prod(double, double), rnd_quot(double, double);
438 #endif
439 #else
440 #define rounded_product(a,b) a *= b
441 #define rounded_quotient(a,b) a /= b
442 #endif
443
444 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
445 #define Big1 0xffffffff
446
447 #ifndef Pack_32
448 #define Pack_32
449 #endif
450
451 #ifdef KR_headers
452 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
453 #else
454 #define FFFFFFFF 0xffffffffUL
455 #endif
456
457 #ifdef NO_LONG_LONG
458 #undef ULLong
459 #ifdef Just_16
460 #undef Pack_32
461 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
462 * This makes some inner loops simpler and sometimes saves work
463 * during multiplications, but it often seems to make things slightly
464 * slower. Hence the default is now to store 32 bits per Long.
465 */
466 #endif
467 #else /* long long available */
468 #ifndef Llong
469 #define Llong long long
470 #endif
471 #ifndef ULLong
472 #define ULLong unsigned Llong
473 #endif
474 #endif /* NO_LONG_LONG */
475
476 #ifndef MULTIPLE_THREADS
477 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
478 #define FREE_DTOA_LOCK(n) /*nothing*/
479 #endif
480
481 #define Kmax 7
482
483 struct
484 Bigint {
485 struct Bigint *next;
486 int k, maxwds, sign, wds;
487 ULong x[1];
488 };
489
490 typedef struct Bigint Bigint;
491
492 #ifdef NO_GLOBAL_STATE
493 #ifdef MULTIPLE_THREADS
494 #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"
495 #endif
496 struct
497 DtoaState {
498 #define DECLARE_GLOBAL_STATE /* nothing */
499 #else
500 #define DECLARE_GLOBAL_STATE static
501 #endif
502
503 DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];
504 DECLARE_GLOBAL_STATE Bigint *p5s;
505 #ifndef Omit_Private_Memory
506 DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];
507 DECLARE_GLOBAL_STATE double *pmem_next
508 #ifndef NO_GLOBAL_STATE
509 = private_mem
510 #endif
511 ;
512 #endif
513 #ifdef NO_GLOBAL_STATE
514 };
515 typedef struct DtoaState DtoaState;
516 #ifdef KR_headers
517 #define STATE_PARAM state,
518 #define STATE_PARAM_DECL DtoaState *state;
519 #else
520 #define STATE_PARAM DtoaState *state,
521 #endif
522 #define PASS_STATE state,
523 #define GET_STATE(field) (state->field)
524
525 static DtoaState *
526 newdtoa(void)
527 {
528 DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));
529 if (state) {
530 memset(state, 0, sizeof(DtoaState));
531 state->pmem_next = state->private_mem;
532 }
533 return state;
534 }
535
536 static void
537 destroydtoa
538 #ifdef KR_headers
539 (state) STATE_PARAM_DECL
540 #else
541 (DtoaState *state)
542 #endif
543 {
544 int i;
545 Bigint *v, *next;
546
547 for (i = 0; i <= Kmax; i++) {
548 for (v = GET_STATE(freelist)[i]; v; v = next) {
549 next = v->next;
550 #ifndef Omit_Private_Memory
551 if ((double*)v < GET_STATE(private_mem) ||
552 (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)
553 #endif
554 FREE((void*)v);
555 }
556 }
557 FREE((void *)state);
558 }
559
560 #else
561 #define STATE_PARAM /* nothing */
562 #define STATE_PARAM_DECL /* nothing */
563 #define PASS_STATE /* nothing */
564 #define GET_STATE(name) name
565 #endif
566
567 static Bigint *
568 Balloc
569 #ifdef KR_headers
570 (STATE_PARAM k) STATE_PARAM_DECL int k;
571 #else
572 (STATE_PARAM int k)
573 #endif
574 {
575 int x;
576 Bigint *rv;
577 #ifndef Omit_Private_Memory
578 size_t len;
579 #endif
580
581 ACQUIRE_DTOA_LOCK(0);
582 /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
583 /* but this case seems very unlikely. */
584 if (k <= Kmax && (rv = GET_STATE(freelist)[k]))
585 GET_STATE(freelist)[k] = rv->next;
586 else {
587 x = 1 << k;
588 #ifdef Omit_Private_Memory
589 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
590 #else
591 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
592 /sizeof(double);
593 if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
594 rv = (Bigint*)GET_STATE(pmem_next);
595 GET_STATE(pmem_next) += len;
596 }
597 else
598 rv = (Bigint*)MALLOC(len*sizeof(double));
599 #endif
600 rv->k = k;
601 rv->maxwds = x;
602 }
603 FREE_DTOA_LOCK(0);
604 rv->sign = rv->wds = 0;
605 return rv;
606 }
607
608 static void
609 Bfree
610 #ifdef KR_headers
611 (STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
612 #else
613 (STATE_PARAM Bigint *v)
614 #endif
615 {
616 if (v) {
617 if (v->k > Kmax)
618 FREE((void*)v);
619 else {
620 ACQUIRE_DTOA_LOCK(0);
621 v->next = GET_STATE(freelist)[v->k];
622 GET_STATE(freelist)[v->k] = v;
623 FREE_DTOA_LOCK(0);
624 }
625 }
626 }
627
628 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
629 y->wds*sizeof(Long) + 2*sizeof(int))
630
631 static Bigint *
632 multadd
633 #ifdef KR_headers
634 (STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
635 #else
636 (STATE_PARAM Bigint *b, int m, int a) /* multiply by m and add a */
637 #endif
638 {
639 int i, wds;
640 #ifdef ULLong
641 ULong *x;
642 ULLong carry, y;
643 #else
644 ULong carry, *x, y;
645 #ifdef Pack_32
646 ULong xi, z;
647 #endif
648 #endif
649 Bigint *b1;
650
651 wds = b->wds;
652 x = b->x;
653 i = 0;
654 carry = a;
655 do {
656 #ifdef ULLong
657 y = *x * (ULLong)m + carry;
658 carry = y >> 32;
659 *x++ = (ULong) y & FFFFFFFF;
660 #else
661 #ifdef Pack_32
662 xi = *x;
663 y = (xi & 0xffff) * m + carry;
664 z = (xi >> 16) * m + (y >> 16);
665 carry = z >> 16;
666 *x++ = (z << 16) + (y & 0xffff);
667 #else
668 y = *x * m + carry;
669 carry = y >> 16;
670 *x++ = y & 0xffff;
671 #endif
672 #endif
673 }
674 while(++i < wds);
675 if (carry) {
676 if (wds >= b->maxwds) {
677 b1 = Balloc(PASS_STATE b->k+1);
678 Bcopy(b1, b);
679 Bfree(PASS_STATE b);
680 b = b1;
681 }
682 b->x[wds++] = (ULong) carry;
683 b->wds = wds;
684 }
685 return b;
686 }
687
688 static Bigint *
689 s2b
690 #ifdef KR_headers
691 (STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9;
692 #else
693 (STATE_PARAM CONST char *s, int nd0, int nd, ULong y9)
694 #endif
695 {
696 Bigint *b;
697 int i, k;
698 Long x, y;
699
700 x = (nd + 8) / 9;
701 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
702 #ifdef Pack_32
703 b = Balloc(PASS_STATE k);
704 b->x[0] = y9;
705 b->wds = 1;
706 #else
707 b = Balloc(PASS_STATE k+1);
708 b->x[0] = y9 & 0xffff;
709 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
710 #endif
711
712 i = 9;
713 if (9 < nd0) {
714 s += 9;
715 do b = multadd(PASS_STATE b, 10, *s++ - '0');
716 while(++i < nd0);
717 s++;
718 }
719 else
720 s += 10;
721 for(; i < nd; i++)
722 b = multadd(PASS_STATE b, 10, *s++ - '0');
723 return b;
724 }
725
726 static int
727 hi0bits
728 #ifdef KR_headers
729 (x) register ULong x;
730 #else
731 (register ULong x)
732 #endif
733 {
734 register int k = 0;
735
736 if (!(x & 0xffff0000)) {
737 k = 16;
738 x <<= 16;
739 }
740 if (!(x & 0xff000000)) {
741 k += 8;
742 x <<= 8;
743 }
744 if (!(x & 0xf0000000)) {
745 k += 4;
746 x <<= 4;
747 }
748 if (!(x & 0xc0000000)) {
749 k += 2;
750 x <<= 2;
751 }
752 if (!(x & 0x80000000)) {
753 k++;
754 if (!(x & 0x40000000))
755 return 32;
756 }
757 return k;
758 }
759
760 static int
761 lo0bits
762 #ifdef KR_headers
763 (y) ULong *y;
764 #else
765 (ULong *y)
766 #endif
767 {
768 register int k;
769 register ULong x = *y;
770
771 if (x & 7) {
772 if (x & 1)
773 return 0;
774 if (x & 2) {
775 *y = x >> 1;
776 return 1;
777 }
778 *y = x >> 2;
779 return 2;
780 }
781 k = 0;
782 if (!(x & 0xffff)) {
783 k = 16;
784 x >>= 16;
785 }
786 if (!(x & 0xff)) {
787 k += 8;
788 x >>= 8;
789 }
790 if (!(x & 0xf)) {
791 k += 4;
792 x >>= 4;
793 }
794 if (!(x & 0x3)) {
795 k += 2;
796 x >>= 2;
797 }
798 if (!(x & 1)) {
799 k++;
800 x >>= 1;
801 if (!x)
802 return 32;
803 }
804 *y = x;
805 return k;
806 }
807
808 static Bigint *
809 i2b
810 #ifdef KR_headers
811 (STATE_PARAM i) STATE_PARAM_DECL int i;
812 #else
813 (STATE_PARAM int i)
814 #endif
815 {
816 Bigint *b;
817
818 b = Balloc(PASS_STATE 1);
819 b->x[0] = i;
820 b->wds = 1;
821 return b;
822 }
823
824 static Bigint *
825 mult
826 #ifdef KR_headers
827 (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
828 #else
829 (STATE_PARAM Bigint *a, Bigint *b)
830 #endif
831 {
832 Bigint *c;
833 int k, wa, wb, wc;
834 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
835 ULong y;
836 #ifdef ULLong
837 ULLong carry, z;
838 #else
839 ULong carry, z;
840 #ifdef Pack_32
841 ULong z2;
842 #endif
843 #endif
844
845 if (a->wds < b->wds) {
846 c = a;
847 a = b;
848 b = c;
849 }
850 k = a->k;
851 wa = a->wds;
852 wb = b->wds;
853 wc = wa + wb;
854 if (wc > a->maxwds)
855 k++;
856 c = Balloc(PASS_STATE k);
857 for(x = c->x, xa = x + wc; x < xa; x++)
858 *x = 0;
859 xa = a->x;
860 xae = xa + wa;
861 xb = b->x;
862 xbe = xb + wb;
863 xc0 = c->x;
864 #ifdef ULLong
865 for(; xb < xbe; xc0++) {
866 if ((y = *xb++)) {
867 x = xa;
868 xc = xc0;
869 carry = 0;
870 do {
871 z = *x++ * (ULLong)y + *xc + carry;
872 carry = z >> 32;
873 *xc++ = (ULong) z & FFFFFFFF;
874 }
875 while(x < xae);
876 *xc = (ULong) carry;
877 }
878 }
879 #else
880 #ifdef Pack_32
881 for(; xb < xbe; xb++, xc0++) {
882 if (y = *xb & 0xffff) {
883 x = xa;
884 xc = xc0;
885 carry = 0;
886 do {
887 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
888 carry = z >> 16;
889 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
890 carry = z2 >> 16;
891 Storeinc(xc, z2, z);
892 }
893 while(x < xae);
894 *xc = carry;
895 }
896 if (y = *xb >> 16) {
897 x = xa;
898 xc = xc0;
899 carry = 0;
900 z2 = *xc;
901 do {
902 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
903 carry = z >> 16;
904 Storeinc(xc, z, z2);
905 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
906 carry = z2 >> 16;
907 }
908 while(x < xae);
909 *xc = z2;
910 }
911 }
912 #else
913 for(; xb < xbe; xc0++) {
914 if (y = *xb++) {
915 x = xa;
916 xc = xc0;
917 carry = 0;
918 do {
919 z = *x++ * y + *xc + carry;
920 carry = z >> 16;
921 *xc++ = z & 0xffff;
922 }
923 while(x < xae);
924 *xc = carry;
925 }
926 }
927 #endif
928 #endif
929 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
930 c->wds = wc;
931 return c;
932 }
933
934 static Bigint *
935 pow5mult
936 #ifdef KR_headers
937 (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
938 #else
939 (STATE_PARAM Bigint *b, int k)
940 #endif
941 {
942 Bigint *b1, *p5, *p51;
943 int i;
944 static CONST int p05[3] = { 5, 25, 125 };
945
946 if ((i = k & 3))
947 b = multadd(PASS_STATE b, p05[i-1], 0);
948
949 if (!(k >>= 2))
950 return b;
951 if (!(p5 = GET_STATE(p5s))) {
952 /* first time */
953 #ifdef MULTIPLE_THREADS
954 ACQUIRE_DTOA_LOCK(1);
955 if (!(p5 = p5s)) {
956 p5 = p5s = i2b(625);
957 p5->next = 0;
958 }
959 FREE_DTOA_LOCK(1);
960 #else
961 p5 = GET_STATE(p5s) = i2b(PASS_STATE 625);
962 p5->next = 0;
963 #endif
964 }
965 for(;;) {
966 if (k & 1) {
967 b1 = mult(PASS_STATE b, p5);
968 Bfree(PASS_STATE b);
969 b = b1;
970 }
971 if (!(k >>= 1))
972 break;
973 if (!(p51 = p5->next)) {
974 #ifdef MULTIPLE_THREADS
975 ACQUIRE_DTOA_LOCK(1);
976 if (!(p51 = p5->next)) {
977 p51 = p5->next = mult(p5,p5);
978 p51->next = 0;
979 }
980 FREE_DTOA_LOCK(1);
981 #else
982 p51 = p5->next = mult(PASS_STATE p5,p5);
983 p51->next = 0;
984 #endif
985 }
986 p5 = p51;
987 }
988 return b;
989 }
990
991 static Bigint *
992 lshift
993 #ifdef KR_headers
994 (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
995 #else
996 (STATE_PARAM Bigint *b, int k)
997 #endif
998 {
999 int i, k1, n, n1;
1000 Bigint *b1;
1001 ULong *x, *x1, *xe, z;
1002
1003 #ifdef Pack_32
1004 n = k >> 5;
1005 #else
1006 n = k >> 4;
1007 #endif
1008 k1 = b->k;
1009 n1 = n + b->wds + 1;
1010 for(i = b->maxwds; n1 > i; i <<= 1)
1011 k1++;
1012 b1 = Balloc(PASS_STATE k1);
1013 x1 = b1->x;
1014 for(i = 0; i < n; i++)
1015 *x1++ = 0;
1016 x = b->x;
1017 xe = x + b->wds;
1018 #ifdef Pack_32
1019 if (k &= 0x1f) {
1020 k1 = 32 - k;
1021 z = 0;
1022 do {
1023 *x1++ = *x << k | z;
1024 z = *x++ >> k1;
1025 }
1026 while(x < xe);
1027 if ((*x1 = z))
1028 ++n1;
1029 }
1030 #else
1031 if (k &= 0xf) {
1032 k1 = 16 - k;
1033 z = 0;
1034 do {
1035 *x1++ = *x << k & 0xffff | z;
1036 z = *x++ >> k1;
1037 }
1038 while(x < xe);
1039 if (*x1 = z)
1040 ++n1;
1041 }
1042 #endif
1043 else do
1044 *x1++ = *x++;
1045 while(x < xe);
1046 b1->wds = n1 - 1;
1047 Bfree(PASS_STATE b);
1048 return b1;
1049 }
1050
1051 static int
1052 cmp
1053 #ifdef KR_headers
1054 (a, b) Bigint *a, *b;
1055 #else
1056 (Bigint *a, Bigint *b)
1057 #endif
1058 {
1059 ULong *xa, *xa0, *xb, *xb0;
1060 int i, j;
1061
1062 i = a->wds;
1063 j = b->wds;
1064 #ifdef DEBUG
1065 if (i > 1 && !a->x[i-1])
1066 Bug("cmp called with a->x[a->wds-1] == 0");
1067 if (j > 1 && !b->x[j-1])
1068 Bug("cmp called with b->x[b->wds-1] == 0");
1069 #endif
1070 if (i -= j)
1071 return i;
1072 xa0 = a->x;
1073 xa = xa0 + j;
1074 xb0 = b->x;
1075 xb = xb0 + j;
1076 for(;;) {
1077 if (*--xa != *--xb)
1078 return *xa < *xb ? -1 : 1;
1079 if (xa <= xa0)
1080 break;
1081 }
1082 return 0;
1083 }
1084
1085 static Bigint *
1086 diff
1087 #ifdef KR_headers
1088 (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
1089 #else
1090 (STATE_PARAM Bigint *a, Bigint *b)
1091 #endif
1092 {
1093 Bigint *c;
1094 int i, wa, wb;
1095 ULong *xa, *xae, *xb, *xbe, *xc;
1096 #ifdef ULLong
1097 ULLong borrow, y;
1098 #else
1099 ULong borrow, y;
1100 #ifdef Pack_32
1101 ULong z;
1102 #endif
1103 #endif
1104
1105 i = cmp(a,b);
1106 if (!i) {
1107 c = Balloc(PASS_STATE 0);
1108 c->wds = 1;
1109 c->x[0] = 0;
1110 return c;
1111 }
1112 if (i < 0) {
1113 c = a;
1114 a = b;
1115 b = c;
1116 i = 1;
1117 }
1118 else
1119 i = 0;
1120 c = Balloc(PASS_STATE a->k);
1121 c->sign = i;
1122 wa = a->wds;
1123 xa = a->x;
1124 xae = xa + wa;
1125 wb = b->wds;
1126 xb = b->x;
1127 xbe = xb + wb;
1128 xc = c->x;
1129 borrow = 0;
1130 #ifdef ULLong
1131 do {
1132 y = (ULLong)*xa++ - *xb++ - borrow;
1133 borrow = y >> 32 & (ULong)1;
1134 *xc++ = (ULong) y & FFFFFFFF;
1135 }
1136 while(xb < xbe);
1137 while(xa < xae) {
1138 y = *xa++ - borrow;
1139 borrow = y >> 32 & (ULong)1;
1140 *xc++ = (ULong) y & FFFFFFFF;
1141 }
1142 #else
1143 #ifdef Pack_32
1144 do {
1145 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1146 borrow = (y & 0x10000) >> 16;
1147 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1148 borrow = (z & 0x10000) >> 16;
1149 Storeinc(xc, z, y);
1150 }
1151 while(xb < xbe);
1152 while(xa < xae) {
1153 y = (*xa & 0xffff) - borrow;
1154 borrow = (y & 0x10000) >> 16;
1155 z = (*xa++ >> 16) - borrow;
1156 borrow = (z & 0x10000) >> 16;
1157 Storeinc(xc, z, y);
1158 }
1159 #else
1160 do {
1161 y = *xa++ - *xb++ - borrow;
1162 borrow = (y & 0x10000) >> 16;
1163 *xc++ = y & 0xffff;
1164 }
1165 while(xb < xbe);
1166 while(xa < xae) {
1167 y = *xa++ - borrow;
1168 borrow = (y & 0x10000) >> 16;
1169 *xc++ = y & 0xffff;
1170 }
1171 #endif
1172 #endif
1173 while(!*--xc)
1174 wa--;
1175 c->wds = wa;
1176 return c;
1177 }
1178
1179 static double
1180 ulp
1181 #ifdef KR_headers
1182 (x) U x;
1183 #else
1184 (U x)
1185 #endif
1186 {
1187 register Long L;
1188 U a;
1189
1190 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1191 #ifndef Avoid_Underflow
1192 #ifndef Sudden_Underflow
1193 if (L > 0) {
1194 #endif
1195 #endif
1196 #ifdef IBM
1197 L |= Exp_msk1 >> 4;
1198 #endif
1199 word0(a) = L;
1200 word1(a) = 0;
1201 #ifndef Avoid_Underflow
1202 #ifndef Sudden_Underflow
1203 }
1204 else {
1205 L = -L >> Exp_shift;
1206 if (L < Exp_shift) {
1207 word0(a) = 0x80000 >> L;
1208 word1(a) = 0;
1209 }
1210 else {
1211 word0(a) = 0;
1212 L -= Exp_shift;
1213 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1214 }
1215 }
1216 #endif
1217 #endif
1218 return dval(a);
1219 }
1220
1221 static double
1222 b2d
1223 #ifdef KR_headers
1224 (a, e) Bigint *a; int *e;
1225 #else
1226 (Bigint *a, int *e)
1227 #endif
1228 {
1229 ULong *xa, *xa0, w, y, z;
1230 int k;
1231 U d;
1232 #ifdef VAX
1233 ULong d0, d1;
1234 #else
1235 #define d0 word0(d)
1236 #define d1 word1(d)
1237 #endif
1238
1239 xa0 = a->x;
1240 xa = xa0 + a->wds;
1241 y = *--xa;
1242 #ifdef DEBUG
1243 if (!y) Bug("zero y in b2d");
1244 #endif
1245 k = hi0bits(y);
1246 *e = 32 - k;
1247 #ifdef Pack_32
1248 if (k < Ebits) {
1249 d0 = Exp_1 | y >> (Ebits - k);
1250 w = xa > xa0 ? *--xa : 0;
1251 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1252 goto ret_d;
1253 }
1254 z = xa > xa0 ? *--xa : 0;
1255 if (k -= Ebits) {
1256 d0 = Exp_1 | y << k | z >> (32 - k);
1257 y = xa > xa0 ? *--xa : 0;
1258 d1 = z << k | y >> (32 - k);
1259 }
1260 else {
1261 d0 = Exp_1 | y;
1262 d1 = z;
1263 }
1264 #else
1265 if (k < Ebits + 16) {
1266 z = xa > xa0 ? *--xa : 0;
1267 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1268 w = xa > xa0 ? *--xa : 0;
1269 y = xa > xa0 ? *--xa : 0;
1270 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1271 goto ret_d;
1272 }
1273 z = xa > xa0 ? *--xa : 0;
1274 w = xa > xa0 ? *--xa : 0;
1275 k -= Ebits + 16;
1276 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1277 y = xa > xa0 ? *--xa : 0;
1278 d1 = w << k + 16 | y << k;
1279 #endif
1280 ret_d:
1281 #ifdef VAX
1282 word0(d) = d0 >> 16 | d0 << 16;
1283 word1(d) = d1 >> 16 | d1 << 16;
1284 #else
1285 #undef d0
1286 #undef d1
1287 #endif
1288 return dval(d);
1289 }
1290
1291 static Bigint *
1292 d2b
1293 #ifdef KR_headers
1294 (STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
1295 #else
1296 (STATE_PARAM U d, int *e, int *bits)
1297 #endif
1298 {
1299 Bigint *b;
1300 int de, k;
1301 ULong *x, y, z;
1302 #ifndef Sudden_Underflow
1303 int i;
1304 #endif
1305 #ifdef VAX
1306 ULong d0, d1;
1307 d0 = word0(d) >> 16 | word0(d) << 16;
1308 d1 = word1(d) >> 16 | word1(d) << 16;
1309 #else
1310 #define d0 word0(d)
1311 #define d1 word1(d)
1312 #endif
1313
1314 #ifdef Pack_32
1315 b = Balloc(PASS_STATE 1);
1316 #else
1317 b = Balloc(PASS_STATE 2);
1318 #endif
1319 x = b->x;
1320
1321 z = d0 & Frac_mask;
1322 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1323 #ifdef Sudden_Underflow
1324 de = (int)(d0 >> Exp_shift);
1325 #ifndef IBM
1326 z |= Exp_msk11;
1327 #endif
1328 #else
1329 if ((de = (int)(d0 >> Exp_shift)))
1330 z |= Exp_msk1;
1331 #endif
1332 #ifdef Pack_32
1333 if ((y = d1)) {
1334 if ((k = lo0bits(&y))) {
1335 x[0] = y | z << (32 - k);
1336 z >>= k;
1337 }
1338 else
1339 x[0] = y;
1340 #ifndef Sudden_Underflow
1341 i =
1342 #endif
1343 b->wds = (x[1] = z) ? 2 : 1;
1344 }
1345 else {
1346 k = lo0bits(&z);
1347 x[0] = z;
1348 #ifndef Sudden_Underflow
1349 i =
1350 #endif
1351 b->wds = 1;
1352 k += 32;
1353 }
1354 #else
1355 if (y = d1) {
1356 if (k = lo0bits(&y))
1357 if (k >= 16) {
1358 x[0] = y | z << 32 - k & 0xffff;
1359 x[1] = z >> k - 16 & 0xffff;
1360 x[2] = z >> k;
1361 i = 2;
1362 }
1363 else {
1364 x[0] = y & 0xffff;
1365 x[1] = y >> 16 | z << 16 - k & 0xffff;
1366 x[2] = z >> k & 0xffff;
1367 x[3] = z >> k+16;
1368 i = 3;
1369 }
1370 else {
1371 x[0] = y & 0xffff;
1372 x[1] = y >> 16;
1373 x[2] = z & 0xffff;
1374 x[3] = z >> 16;
1375 i = 3;
1376 }
1377 }
1378 else {
1379 #ifdef DEBUG
1380 if (!z)
1381 Bug("Zero passed to d2b");
1382 #endif
1383 k = lo0bits(&z);
1384 if (k >= 16) {
1385 x[0] = z;
1386 i = 0;
1387 }
1388 else {
1389 x[0] = z & 0xffff;
1390 x[1] = z >> 16;
1391 i = 1;
1392 }
1393 k += 32;
1394 }
1395 while(!x[i])
1396 --i;
1397 b->wds = i + 1;
1398 #endif
1399 #ifndef Sudden_Underflow
1400 if (de) {
1401 #endif
1402 #ifdef IBM
1403 *e = (de - Bias - (P-1) << 2) + k;
1404 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1405 #else
1406 *e = de - Bias - (P-1) + k;
1407 *bits = P - k;
1408 #endif
1409 #ifndef Sudden_Underflow
1410 }
1411 else {
1412 *e = de - Bias - (P-1) + 1 + k;
1413 #ifdef Pack_32
1414 *bits = 32*i - hi0bits(x[i-1]);
1415 #else
1416 *bits = (i+2)*16 - hi0bits(x[i]);
1417 #endif
1418 }
1419 #endif
1420 return b;
1421 }
1422 #undef d0
1423 #undef d1
1424
1425 static double
1426 ratio
1427 #ifdef KR_headers
1428 (a, b) Bigint *a, *b;
1429 #else
1430 (Bigint *a, Bigint *b)
1431 #endif
1432 {
1433 U da, db;
1434 int k, ka, kb;
1435
1436 dval(da) = b2d(a, &ka);
1437 dval(db) = b2d(b, &kb);
1438 #ifdef Pack_32
1439 k = ka - kb + 32*(a->wds - b->wds);
1440 #else
1441 k = ka - kb + 16*(a->wds - b->wds);
1442 #endif
1443 #ifdef IBM
1444 if (k > 0) {
1445 word0(da) += (k >> 2)*Exp_msk1;
1446 if (k &= 3)
1447 dval(da) *= 1 << k;
1448 }
1449 else {
1450 k = -k;
1451 word0(db) += (k >> 2)*Exp_msk1;
1452 if (k &= 3)
1453 dval(db) *= 1 << k;
1454 }
1455 #else
1456 if (k > 0)
1457 word0(da) += k*Exp_msk1;
1458 else {
1459 k = -k;
1460 word0(db) += k*Exp_msk1;
1461 }
1462 #endif
1463 return dval(da) / dval(db);
1464 }
1465
1466 static CONST double
1467 tens[] = {
1468 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1469 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1470 1e20, 1e21, 1e22
1471 #ifdef VAX
1472 , 1e23, 1e24
1473 #endif
1474 };
1475
1476 static CONST double
1477 #ifdef IEEE_Arith
1478 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1479 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1480 #ifdef Avoid_Underflow
1481 9007199254740992.*9007199254740992.e-256
1482 /* = 2^106 * 1e-53 */
1483 #else
1484 1e-256
1485 #endif
1486 };
1487 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1488 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1489 #define Scale_Bit 0x10
1490 #define n_bigtens 5
1491 #else
1492 #ifdef IBM
1493 bigtens[] = { 1e16, 1e32, 1e64 };
1494 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1495 #define n_bigtens 3
1496 #else
1497 bigtens[] = { 1e16, 1e32 };
1498 static CONST double tinytens[] = { 1e-16, 1e-32 };
1499 #define n_bigtens 2
1500 #endif
1501 #endif
1502
1503 #ifdef INFNAN_CHECK
1504
1505 #ifndef NAN_WORD0
1506 #define NAN_WORD0 0x7ff80000
1507 #endif
1508
1509 #ifndef NAN_WORD1
1510 #define NAN_WORD1 0
1511 #endif
1512
1513 static int
1514 match
1515 #ifdef KR_headers
1516 (sp, t) char **sp, *t;
1517 #else
1518 (CONST char **sp, CONST char *t)
1519 #endif
1520 {
1521 int c, d;
1522 CONST char *s = *sp;
1523
1524 while((d = *t++)) {
1525 if ((c = *++s) >= 'A' && c <= 'Z')
1526 c += 'a' - 'A';
1527 if (c != d)
1528 return 0;
1529 }
1530 *sp = s + 1;
1531 return 1;
1532 }
1533
1534 #ifndef No_Hex_NaN
1535 static void
1536 hexnan
1537 #ifdef KR_headers
1538 (rvp, sp) U *rvp; CONST char **sp;
1539 #else
1540 (U *rvp, CONST char **sp)
1541 #endif
1542 {
1543 ULong c, x[2];
1544 CONST char *s;
1545 int havedig, udx0, xshift;
1546
1547 x[0] = x[1] = 0;
1548 havedig = xshift = 0;
1549 udx0 = 1;
1550 s = *sp;
1551 /* allow optional initial 0x or 0X */
1552 while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
1553 ++s;
1554 if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
1555 s += 2;
1556 while((c = *(CONST unsigned char*)++s)) {
1557 if (c >= '0' && c <= '9')
1558 c -= '0';
1559 else if (c >= 'a' && c <= 'f')
1560 c += 10 - 'a';
1561 else if (c >= 'A' && c <= 'F')
1562 c += 10 - 'A';
1563 else if (c <= ' ') {
1564 if (udx0 && havedig) {
1565 udx0 = 0;
1566 xshift = 1;
1567 }
1568 continue;
1569 }
1570 #ifdef GDTOA_NON_PEDANTIC_NANCHECK
1571 else if (/*(*/ c == ')' && havedig) {
1572 *sp = s + 1;
1573 break;
1574 }
1575 else
1576 return; /* invalid form: don't change *sp */
1577 #else
1578 else {
1579 do {
1580 if (/*(*/ c == ')') {
1581 *sp = s + 1;
1582 break;
1583 }
1584 } while((c = *++s));
1585 break;
1586 }
1587 #endif
1588 havedig = 1;
1589 if (xshift) {
1590 xshift = 0;
1591 x[0] = x[1];
1592 x[1] = 0;
1593 }
1594 if (udx0)
1595 x[0] = (x[0] << 4) | (x[1] >> 28);
1596 x[1] = (x[1] << 4) | c;
1597 }
1598 if ((x[0] &= 0xfffff) || x[1]) {
1599 word0(*rvp) = Exp_mask | x[0];
1600 word1(*rvp) = x[1];
1601 }
1602 }
1603 #endif /*No_Hex_NaN*/
1604 #endif /* INFNAN_CHECK */
1605
1606 static double
1607 _strtod
1608 #ifdef KR_headers
1609 (STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se;
1610 #else
1611 (STATE_PARAM CONST char *s00, char **se)
1612 #endif
1613 {
1614 #ifdef Avoid_Underflow
1615 int scale;
1616 #endif
1617 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1618 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1619 CONST char *s, *s0, *s1;
1620 double aadj, adj;
1621 U aadj1, rv, rv0;
1622 Long L;
1623 ULong y, z;
1624 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1625 #ifdef SET_INEXACT
1626 int inexact, oldinexact;
1627 #endif
1628 #ifdef Honor_FLT_ROUNDS
1629 int rounding;
1630 #endif
1631 #ifdef USE_LOCALE
1632 CONST char *s2;
1633 #endif
1634
1635 #ifdef __GNUC__
1636 delta = bb = bd = bs = 0;
1637 #endif
1638
1639 sign = nz0 = nz = 0;
1640 dval(rv) = 0.;
1641 for(s = s00;;s++) switch(*s) {
1642 case '-':
1643 sign = 1;
1644 /* no break */
1645 case '+':
1646 if (*++s)
1647 goto break2;
1648 /* no break */
1649 case 0:
1650 goto ret0;
1651 case '\t':
1652 case '\n':
1653 case '\v':
1654 case '\f':
1655 case '\r':
1656 case ' ':
1657 continue;
1658 default:
1659 goto break2;
1660 }
1661 break2:
1662 if (*s == '0') {
1663 nz0 = 1;
1664 while(*++s == '0') ;
1665 if (!*s)
1666 goto ret;
1667 }
1668 s0 = s;
1669 y = z = 0;
1670 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1671 if (nd < 9)
1672 y = 10*y + c - '0';
1673 else if (nd < 16)
1674 z = 10*z + c - '0';
1675 nd0 = nd;
1676 #ifdef USE_LOCALE
1677 s1 = localeconv()->decimal_point;
1678 if (c == *s1) {
1679 c = '.';
1680 if (*++s1) {
1681 s2 = s;
1682 for(;;) {
1683 if (*++s2 != *s1) {
1684 c = 0;
1685 break;
1686 }
1687 if (!*++s1) {
1688 s = s2;
1689 break;
1690 }
1691 }
1692 }
1693 }
1694 #endif
1695 if (c == '.') {
1696 c = *++s;
1697 if (!nd) {
1698 for(; c == '0'; c = *++s)
1699 nz++;
1700 if (c > '0' && c <= '9') {
1701 s0 = s;
1702 nf += nz;
1703 nz = 0;
1704 goto have_dig;
1705 }
1706 goto dig_done;
1707 }
1708 for(; c >= '0' && c <= '9'; c = *++s) {
1709 have_dig:
1710 nz++;
1711 if (c -= '0') {
1712 nf += nz;
1713 for(i = 1; i < nz; i++)
1714 if (nd++ < 9)
1715 y *= 10;
1716 else if (nd <= DBL_DIG + 1)
1717 z *= 10;
1718 if (nd++ < 9)
1719 y = 10*y + c;
1720 else if (nd <= DBL_DIG + 1)
1721 z = 10*z + c;
1722 nz = 0;
1723 }
1724 }
1725 }
1726 dig_done:
1727 e = 0;
1728 if (c == 'e' || c == 'E') {
1729 if (!nd && !nz && !nz0) {
1730 goto ret0;
1731 }
1732 s00 = s;
1733 esign = 0;
1734 switch(c = *++s) {
1735 case '-':
1736 esign = 1;
1737 case '+':
1738 c = *++s;
1739 }
1740 if (c >= '0' && c <= '9') {
1741 while(c == '0')
1742 c = *++s;
1743 if (c > '0' && c <= '9') {
1744 L = c - '0';
1745 s1 = s;
1746 while((c = *++s) >= '0' && c <= '9')
1747 L = 10*L + c - '0';
1748 if (s - s1 > 8 || L > 19999)
1749 /* Avoid confusion from exponents
1750 * so large that e might overflow.
1751 */
1752 e = 19999; /* safe for 16 bit ints */
1753 else
1754 e = (int)L;
1755 if (esign)
1756 e = -e;
1757 }
1758 else
1759 e = 0;
1760 }
1761 else
1762 s = s00;
1763 }
1764 if (!nd) {
1765 if (!nz && !nz0) {
1766 #ifdef INFNAN_CHECK
1767 /* Check for Nan and Infinity */
1768 switch(c) {
1769 case 'i':
1770 case 'I':
1771 if (match(&s,"nf")) {
1772 --s;
1773 if (!match(&s,"inity"))
1774 ++s;
1775 word0(rv) = 0x7ff00000;
1776 word1(rv) = 0;
1777 goto ret;
1778 }
1779 break;
1780 case 'n':
1781 case 'N':
1782 if (match(&s, "an")) {
1783 word0(rv) = NAN_WORD0;
1784 word1(rv) = NAN_WORD1;
1785 #ifndef No_Hex_NaN
1786 if (*s == '(') /*)*/
1787 hexnan(&rv, &s);
1788 #endif
1789 goto ret;
1790 }
1791 }
1792 #endif /* INFNAN_CHECK */
1793 ret0:
1794 s = s00;
1795 sign = 0;
1796 }
1797 goto ret;
1798 }
1799 e1 = e -= nf;
1800
1801 /* Now we have nd0 digits, starting at s0, followed by a
1802 * decimal point, followed by nd-nd0 digits. The number we're
1803 * after is the integer represented by those digits times
1804 * 10**e */
1805
1806 if (!nd0)
1807 nd0 = nd;
1808 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1809 dval(rv) = y;
1810 if (k > 9) {
1811 #ifdef SET_INEXACT
1812 if (k > DBL_DIG)
1813 oldinexact = get_inexact();
1814 #endif
1815 dval(rv) = tens[k - 9] * dval(rv) + z;
1816 }
1817 bd0 = 0;
1818 if (nd <= DBL_DIG
1819 #ifndef RND_PRODQUOT
1820 #ifndef Honor_FLT_ROUNDS
1821 && Flt_Rounds == 1
1822 #endif
1823 #endif
1824 ) {
1825 if (!e)
1826 goto ret;
1827 if (e > 0) {
1828 if (e <= Ten_pmax) {
1829 #ifdef VAX
1830 goto vax_ovfl_check;
1831 #else
1832 #ifdef Honor_FLT_ROUNDS
1833 /* round correctly FLT_ROUNDS = 2 or 3 */
1834 if (sign) {
1835 rv = -rv;
1836 sign = 0;
1837 }
1838 #endif
1839 /* rv = */ rounded_product(dval(rv), tens[e]);
1840 goto ret;
1841 #endif
1842 }
1843 i = DBL_DIG - nd;
1844 if (e <= Ten_pmax + i) {
1845 /* A fancier test would sometimes let us do
1846 * this for larger i values.
1847 */
1848 #ifdef Honor_FLT_ROUNDS
1849 /* round correctly FLT_ROUNDS = 2 or 3 */
1850 if (sign) {
1851 rv = -rv;
1852 sign = 0;
1853 }
1854 #endif
1855 e -= i;
1856 dval(rv) *= tens[i];
1857 #ifdef VAX
1858 /* VAX exponent range is so narrow we must
1859 * worry about overflow here...
1860 */
1861 vax_ovfl_check:
1862 word0(rv) -= P*Exp_msk1;
1863 /* rv = */ rounded_product(dval(rv), tens[e]);
1864 if ((word0(rv) & Exp_mask)
1865 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1866 goto ovfl;
1867 word0(rv) += P*Exp_msk1;
1868 #else
1869 /* rv = */ rounded_product(dval(rv), tens[e]);
1870 #endif
1871 goto ret;
1872 }
1873 }
1874 #ifndef Inaccurate_Divide
1875 else if (e >= -Ten_pmax) {
1876 #ifdef Honor_FLT_ROUNDS
1877 /* round correctly FLT_ROUNDS = 2 or 3 */
1878 if (sign) {
1879 rv = -rv;
1880 sign = 0;
1881 }
1882 #endif
1883 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1884 goto ret;
1885 }
1886 #endif
1887 }
1888 e1 += nd - k;
1889
1890 #ifdef IEEE_Arith
1891 #ifdef SET_INEXACT
1892 inexact = 1;
1893 if (k <= DBL_DIG)
1894 oldinexact = get_inexact();
1895 #endif
1896 #ifdef Avoid_Underflow
1897 scale = 0;
1898 #endif
1899 #ifdef Honor_FLT_ROUNDS
1900 if ((rounding = Flt_Rounds) >= 2) {
1901 if (sign)
1902 rounding = rounding == 2 ? 0 : 2;
1903 else
1904 if (rounding != 2)
1905 rounding = 0;
1906 }
1907 #endif
1908 #endif /*IEEE_Arith*/
1909
1910 /* Get starting approximation = rv * 10**e1 */
1911
1912 if (e1 > 0) {
1913 if ((i = e1 & 15))
1914 dval(rv) *= tens[i];
1915 if (e1 &= ~15) {
1916 if (e1 > DBL_MAX_10_EXP) {
1917 ovfl:
1918 #ifndef NO_ERRNO
1919 errno = ERANGE;
1920 #endif
1921 /* Can't trust HUGE_VAL */
1922 #ifdef IEEE_Arith
1923 #ifdef Honor_FLT_ROUNDS
1924 switch(rounding) {
1925 case 0: /* toward 0 */
1926 case 3: /* toward -infinity */
1927 word0(rv) = Big0;
1928 word1(rv) = Big1;
1929 break;
1930 default:
1931 word0(rv) = Exp_mask;
1932 word1(rv) = 0;
1933 }
1934 #else /*Honor_FLT_ROUNDS*/
1935 word0(rv) = Exp_mask;
1936 word1(rv) = 0;
1937 #endif /*Honor_FLT_ROUNDS*/
1938 #ifdef SET_INEXACT
1939 /* set overflow bit */
1940 dval(rv0) = 1e300;
1941 dval(rv0) *= dval(rv0);
1942 #endif
1943 #else /*IEEE_Arith*/
1944 word0(rv) = Big0;
1945 word1(rv) = Big1;
1946 #endif /*IEEE_Arith*/
1947 if (bd0)
1948 goto retfree;
1949 goto ret;
1950 }
1951 e1 >>= 4;
1952 for(j = 0; e1 > 1; j++, e1 >>= 1)
1953 if (e1 & 1)
1954 dval(rv) *= bigtens[j];
1955 /* The last multiplication could overflow. */
1956 word0(rv) -= P*Exp_msk1;
1957 dval(rv) *= bigtens[j];
1958 if ((z = word0(rv) & Exp_mask)
1959 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1960 goto ovfl;
1961 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1962 /* set to largest number */
1963 /* (Can't trust DBL_MAX) */
1964 word0(rv) = Big0;
1965 word1(rv) = Big1;
1966 }
1967 else
1968 word0(rv) += P*Exp_msk1;
1969 }
1970 }
1971 else if (e1 < 0) {
1972 e1 = -e1;
1973 if ((i = e1 & 15))
1974 dval(rv) /= tens[i];
1975 if (e1 >>= 4) {
1976 if (e1 >= 1 << n_bigtens)
1977 goto undfl;
1978 #ifdef Avoid_Underflow
1979 if (e1 & Scale_Bit)
1980 scale = 2*P;
1981 for(j = 0; e1 > 0; j++, e1 >>= 1)
1982 if (e1 & 1)
1983 dval(rv) *= tinytens[j];
1984 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1985 >> Exp_shift)) > 0) {
1986 /* scaled rv is denormal; zap j low bits */
1987 if (j >= 32) {
1988 word1(rv) = 0;
1989 if (j >= 53)
1990 word0(rv) = (P+2)*Exp_msk1;
1991 else
1992 word0(rv) &= 0xffffffff << (j-32);
1993 }
1994 else
1995 word1(rv) &= 0xffffffff << j;
1996 }
1997 #else
1998 for(j = 0; e1 > 1; j++, e1 >>= 1)
1999 if (e1 & 1)
2000 dval(rv) *= tinytens[j];
2001 /* The last multiplication could underflow. */
2002 dval(rv0) = dval(rv);
2003 dval(rv) *= tinytens[j];
2004 if (!dval(rv)) {
2005 dval(rv) = 2.*dval(rv0);
2006 dval(rv) *= tinytens[j];
2007 #endif
2008 if (!dval(rv)) {
2009 undfl:
2010 dval(rv) = 0.;
2011 #ifndef NO_ERRNO
2012 errno = ERANGE;
2013 #endif
2014 if (bd0)
2015 goto retfree;
2016 goto ret;
2017 }
2018 #ifndef Avoid_Underflow
2019 word0(rv) = Tiny0;
2020 word1(rv) = Tiny1;
2021 /* The refinement below will clean
2022 * this approximation up.
2023 */
2024 }
2025 #endif
2026 }
2027 }
2028
2029 /* Now the hard part -- adjusting rv to the correct value.*/
2030
2031 /* Put digits into bd: true value = bd * 10^e */
2032
2033 bd0 = s2b(PASS_STATE s0, nd0, nd, y);
2034
2035 for(;;) {
2036 bd = Balloc(PASS_STATE bd0->k);
2037 Bcopy(bd, bd0);
2038 bb = d2b(PASS_STATE rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
2039 bs = i2b(PASS_STATE 1);
2040
2041 if (e >= 0) {
2042 bb2 = bb5 = 0;
2043 bd2 = bd5 = e;
2044 }
2045 else {
2046 bb2 = bb5 = -e;
2047 bd2 = bd5 = 0;
2048 }
2049 if (bbe >= 0)
2050 bb2 += bbe;
2051 else
2052 bd2 -= bbe;
2053 bs2 = bb2;
2054 #ifdef Honor_FLT_ROUNDS
2055 if (rounding != 1)
2056 bs2++;
2057 #endif
2058 #ifdef Avoid_Underflow
2059 j = bbe - scale;
2060 i = j + bbbits - 1; /* logb(rv) */
2061 if (i < Emin) /* denormal */
2062 j += P - Emin;
2063 else
2064 j = P + 1 - bbbits;
2065 #else /*Avoid_Underflow*/
2066 #ifdef Sudden_Underflow
2067 #ifdef IBM
2068 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2069 #else
2070 j = P + 1 - bbbits;
2071 #endif
2072 #else /*Sudden_Underflow*/
2073 j = bbe;
2074 i = j + bbbits - 1; /* logb(rv) */
2075 if (i < Emin) /* denormal */
2076 j += P - Emin;
2077 else
2078 j = P + 1 - bbbits;
2079 #endif /*Sudden_Underflow*/
2080 #endif /*Avoid_Underflow*/
2081 bb2 += j;
2082 bd2 += j;
2083 #ifdef Avoid_Underflow
2084 bd2 += scale;
2085 #endif
2086 i = bb2 < bd2 ? bb2 : bd2;
2087 if (i > bs2)
2088 i = bs2;
2089 if (i > 0) {
2090 bb2 -= i;
2091 bd2 -= i;
2092 bs2 -= i;
2093 }
2094 if (bb5 > 0) {
2095 bs = pow5mult(PASS_STATE bs, bb5);
2096 bb1 = mult(PASS_STATE bs, bb);
2097 Bfree(PASS_STATE bb);
2098 bb = bb1;
2099 }
2100 if (bb2 > 0)
2101 bb = lshift(PASS_STATE bb, bb2);
2102 if (bd5 > 0)
2103 bd = pow5mult(PASS_STATE bd, bd5);
2104 if (bd2 > 0)
2105 bd = lshift(PASS_STATE bd, bd2);
2106 if (bs2 > 0)
2107 bs = lshift(PASS_STATE bs, bs2);
2108 delta = diff(PASS_STATE bb, bd);
2109 dsign = delta->sign;
2110 delta->sign = 0;
2111 i = cmp(delta, bs);
2112 #ifdef Honor_FLT_ROUNDS
2113 if (rounding != 1) {
2114 if (i < 0) {
2115 /* Error is less than an ulp */
2116 if (!delta->x[0] && delta->wds <= 1) {
2117 /* exact */
2118 #ifdef SET_INEXACT
2119 inexact = 0;
2120 #endif
2121 break;
2122 }
2123 if (rounding) {
2124 if (dsign) {
2125 adj = 1.;
2126 goto apply_adj;
2127 }
2128 }
2129 else if (!dsign) {
2130 adj = -1.;
2131 if (!word1(rv)
2132 && !(word0(rv) & Frac_mask)) {
2133 y = word0(rv) & Exp_mask;
2134 #ifdef Avoid_Underflow
2135 if (!scale || y > 2*P*Exp_msk1)
2136 #else
2137 if (y)
2138 #endif
2139 {
2140 delta = lshift(PASS_STATE delta,Log2P);
2141 if (cmp(delta, bs) <= 0)
2142 adj = -0.5;
2143 }
2144 }
2145 apply_adj:
2146 #ifdef Avoid_Underflow
2147 if (scale && (y = word0(rv) & Exp_mask)
2148 <= 2*P*Exp_msk1)
2149 word0(adj) += (2*P+1)*Exp_msk1 - y;
2150 #else
2151 #ifdef Sudden_Underflow
2152 if ((word0(rv) & Exp_mask) <=
2153 P*Exp_msk1) {
2154 word0(rv) += P*Exp_msk1;
2155 dval(rv) += adj*ulp(rv);
2156 word0(rv) -= P*Exp_msk1;
2157 }
2158 else
2159 #endif /*Sudden_Underflow*/
2160 #endif /*Avoid_Underflow*/
2161 dval(rv) += adj*ulp(rv);
2162 }
2163 break;
2164 }
2165 adj = ratio(delta, bs);
2166 if (adj < 1.)
2167 adj = 1.;
2168 if (adj <= 0x7ffffffe) {
2169 /* adj = rounding ? ceil(adj) : floor(adj); */
2170 y = adj;
2171 if (y != adj) {
2172 if (!((rounding>>1) ^ dsign))
2173 y++;
2174 adj = y;
2175 }
2176 }
2177 #ifdef Avoid_Underflow
2178 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2179 word0(adj) += (2*P+1)*Exp_msk1 - y;
2180 #else
2181 #ifdef Sudden_Underflow
2182 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2183 word0(rv) += P*Exp_msk1;
2184 adj *= ulp(rv);
2185 if (dsign)
2186 dval(rv) += adj;
2187 else
2188 dval(rv) -= adj;
2189 word0(rv) -= P*Exp_msk1;
2190 goto cont;
2191 }
2192 #endif /*Sudden_Underflow*/
2193 #endif /*Avoid_Underflow*/
2194 adj *= ulp(rv);
2195 if (dsign)
2196 dval(rv) += adj;
2197 else
2198 dval(rv) -= adj;
2199 goto cont;
2200 }
2201 #endif /*Honor_FLT_ROUNDS*/
2202
2203 if (i < 0) {
2204 /* Error is less than half an ulp -- check for
2205 * special case of mantissa a power of two.
2206 */
2207 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2208 #ifdef IEEE_Arith
2209 #ifdef Avoid_Underflow
2210 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2211 #else
2212 || (word0(rv) & Exp_mask) <= Exp_msk1
2213 #endif
2214 #endif
2215 ) {
2216 #ifdef SET_INEXACT
2217 if (!delta->x[0] && delta->wds <= 1)
2218 inexact = 0;
2219 #endif
2220 break;
2221 }
2222 if (!delta->x[0] && delta->wds <= 1) {
2223 /* exact result */
2224 #ifdef SET_INEXACT
2225 inexact = 0;
2226 #endif
2227 break;
2228 }
2229 delta = lshift(PASS_STATE delta,Log2P);
2230 if (cmp(delta, bs) > 0)
2231 goto drop_down;
2232 break;
2233 }
2234 if (i == 0) {
2235 /* exactly half-way between */
2236 if (dsign) {
2237 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2238 && word1(rv) == (
2239 #ifdef Avoid_Underflow
2240 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2241 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2242 #endif
2243 0xffffffff)) {
2244 /*boundary case -- increment exponent*/
2245 word0(rv) = (word0(rv) & Exp_mask)
2246 + Exp_msk1
2247 #ifdef IBM
2248 | Exp_msk1 >> 4
2249 #endif
2250 ;
2251 word1(rv) = 0;
2252 #ifdef Avoid_Underflow
2253 dsign = 0;
2254 #endif
2255 break;
2256 }
2257 }
2258 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2259 drop_down:
2260 /* boundary case -- decrement exponent */
2261 #ifdef Sudden_Underflow /*{{*/
2262 L = word0(rv) & Exp_mask;
2263 #ifdef IBM
2264 if (L < Exp_msk1)
2265 #else
2266 #ifdef Avoid_Underflow
2267 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2268 #else
2269 if (L <= Exp_msk1)
2270 #endif /*Avoid_Underflow*/
2271 #endif /*IBM*/
2272 goto undfl;
2273 L -= Exp_msk1;
2274 #else /*Sudden_Underflow}{*/
2275 #ifdef Avoid_Underflow
2276 if (scale) {
2277 L = word0(rv) & Exp_mask;
2278 if (L <= (2*P+1)*Exp_msk1) {
2279 if (L > (P+2)*Exp_msk1)
2280 /* round even ==> */
2281 /* accept rv */
2282 break;
2283 /* rv = smallest denormal */
2284 goto undfl;
2285 }
2286 }
2287 #endif /*Avoid_Underflow*/
2288 L = (word0(rv) & Exp_mask) - Exp_msk1;
2289 #endif /*Sudden_Underflow}}*/
2290 word0(rv) = L | Bndry_mask1;
2291 word1(rv) = 0xffffffff;
2292 #ifdef IBM
2293 goto cont;
2294 #else
2295 break;
2296 #endif
2297 }
2298 #ifndef ROUND_BIASED
2299 if (!(word1(rv) & LSB))
2300 break;
2301 #endif
2302 if (dsign)
2303 dval(rv) += ulp(rv);
2304 #ifndef ROUND_BIASED
2305 else {
2306 dval(rv) -= ulp(rv);
2307 #ifndef Sudden_Underflow
2308 if (!dval(rv))
2309 goto undfl;
2310 #endif
2311 }
2312 #ifdef Avoid_Underflow
2313 dsign = 1 - dsign;
2314 #endif
2315 #endif
2316 break;
2317 }
2318 if ((aadj = ratio(delta, bs)) <= 2.) {
2319 if (dsign)
2320 aadj = dval(aadj1) = 1.;
2321 else if (word1(rv) || word0(rv) & Bndry_mask) {
2322 #ifndef Sudden_Underflow
2323 if (word1(rv) == Tiny1 && !word0(rv))
2324 goto undfl;
2325 #endif
2326 aadj = 1.;
2327 dval(aadj1) = -1.;
2328 }
2329 else {
2330 /* special case -- power of FLT_RADIX to be */
2331 /* rounded down... */
2332
2333 if (aadj < 2./FLT_RADIX)
2334 aadj = 1./FLT_RADIX;
2335 else
2336 aadj *= 0.5;
2337 dval(aadj1) = -aadj;
2338 }
2339 }
2340 else {
2341 aadj *= 0.5;
2342 dval(aadj1) = dsign ? aadj : -aadj;
2343 #ifdef Check_FLT_ROUNDS
2344 switch(Rounding) {
2345 case 2: /* towards +infinity */
2346 dval(aadj1) -= 0.5;
2347 break;
2348 case 0: /* towards 0 */
2349 case 3: /* towards -infinity */
2350 dval(aadj1) += 0.5;
2351 }
2352 #else
2353 if (Flt_Rounds == 0)
2354 dval(aadj1) += 0.5;
2355 #endif /*Check_FLT_ROUNDS*/
2356 }
2357 y = word0(rv) & Exp_mask;
2358
2359 /* Check for overflow */
2360
2361 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2362 dval(rv0) = dval(rv);
2363 word0(rv) -= P*Exp_msk1;
2364 adj = dval(aadj1) * ulp(rv);
2365 dval(rv) += adj;
2366 if ((word0(rv) & Exp_mask) >=
2367 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2368 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2369 goto ovfl;
2370 word0(rv) = Big0;
2371 word1(rv) = Big1;
2372 goto cont;
2373 }
2374 else
2375 word0(rv) += P*Exp_msk1;
2376 }
2377 else {
2378 #ifdef Avoid_Underflow
2379 if (scale && y <= 2*P*Exp_msk1) {
2380 if (aadj <= 0x7fffffff) {
2381 if ((z = (ULong) aadj) <= 0)
2382 z = 1;
2383 aadj = z;
2384 dval(aadj1) = dsign ? aadj : -aadj;
2385 }
2386 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2387 }
2388 adj = dval(aadj1) * ulp(rv);
2389 dval(rv) += adj;
2390 #else
2391 #ifdef Sudden_Underflow
2392 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2393 dval(rv0) = dval(rv);
2394 word0(rv) += P*Exp_msk1;
2395 adj = dval(aadj1) * ulp(rv);
2396 dval(rv) += adj;
2397 #ifdef IBM
2398 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2399 #else
2400 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2401 #endif
2402 {
2403 if (word0(rv0) == Tiny0
2404 && word1(rv0) == Tiny1)
2405 goto undfl;
2406 word0(rv) = Tiny0;
2407 word1(rv) = Tiny1;
2408 goto cont;
2409 }
2410 else
2411 word0(rv) -= P*Exp_msk1;
2412 }
2413 else {
2414 adj = dval(aadj1) * ulp(rv);
2415 dval(rv) += adj;
2416 }
2417 #else /*Sudden_Underflow*/
2418 /* Compute adj so that the IEEE rounding rules will
2419 * correctly round rv + adj in some half-way cases.
2420 * If rv * ulp(rv) is denormalized (i.e.,
2421 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2422 * trouble from bits lost to denormalization;
2423 * example: 1.2e-307 .
2424 */
2425 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2426 dval(aadj1) = (double)(int)(aadj + 0.5);
2427 if (!dsign)
2428 dval(aadj1) = -dval(aadj1);
2429 }
2430 adj = dval(aadj1) * ulp(rv);
2431 dval(rv) += adj;
2432 #endif /*Sudden_Underflow*/
2433 #endif /*Avoid_Underflow*/
2434 }
2435 z = word0(rv) & Exp_mask;
2436 #ifndef SET_INEXACT
2437 #ifdef Avoid_Underflow
2438 if (!scale)
2439 #endif
2440 if (y == z) {
2441 /* Can we stop now? */
2442 L = (Long)aadj;
2443 aadj -= L;
2444 /* The tolerances below are conservative. */
2445 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2446 if (aadj < .4999999 || aadj > .5000001)
2447 break;
2448 }
2449 else if (aadj < .4999999/FLT_RADIX)
2450 break;
2451 }
2452 #endif
2453 cont:
2454 Bfree(PASS_STATE bb);
2455 Bfree(PASS_STATE bd);
2456 Bfree(PASS_STATE bs);
2457 Bfree(PASS_STATE delta);
2458 }
2459 #ifdef SET_INEXACT
2460 if (inexact) {
2461 if (!oldinexact) {
2462 word0(rv0) = Exp_1 + (70 << Exp_shift);
2463 word1(rv0) = 0;
2464 dval(rv0) += 1.;
2465 }
2466 }
2467 else if (!oldinexact)
2468 clear_inexact();
2469 #endif
2470 #ifdef Avoid_Underflow
2471 if (scale) {
2472 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2473 word1(rv0) = 0;
2474 dval(rv) *= dval(rv0);
2475 #ifndef NO_ERRNO
2476 /* try to avoid the bug of testing an 8087 register value */
2477 if (word0(rv) == 0 && word1(rv) == 0)
2478 errno = ERANGE;
2479 #endif
2480 }
2481 #endif /* Avoid_Underflow */
2482 #ifdef SET_INEXACT
2483 if (inexact && !(word0(rv) & Exp_mask)) {
2484 /* set underflow bit */
2485 dval(rv0) = 1e-300;
2486 dval(rv0) *= dval(rv0);
2487 }
2488 #endif
2489 retfree:
2490 Bfree(PASS_STATE bb);
2491 Bfree(PASS_STATE bd);
2492 Bfree(PASS_STATE bs);
2493 Bfree(PASS_STATE bd0);
2494 Bfree(PASS_STATE delta);
2495 ret:
2496 if (se)
2497 *se = (char *)s;
2498 return sign ? -dval(rv) : dval(rv);
2499 }
2500
2501 static int
2502 quorem
2503 #ifdef KR_headers
2504 (b, S) Bigint *b, *S;
2505 #else
2506 (Bigint *b, Bigint *S)
2507 #endif
2508 {
2509 int n;
2510 ULong *bx, *bxe, q, *sx, *sxe;
2511 #ifdef ULLong
2512 ULLong borrow, carry, y, ys;
2513 #else
2514 ULong borrow, carry, y, ys;
2515 #ifdef Pack_32
2516 ULong si, z, zs;
2517 #endif
2518 #endif
2519
2520 n = S->wds;
2521 #ifdef DEBUG
2522 /*debug*/ if (b->wds > n)
2523 /*debug*/ Bug("oversize b in quorem");
2524 #endif
2525 if (b->wds < n)
2526 return 0;
2527 sx = S->x;
2528 sxe = sx + --n;
2529 bx = b->x;
2530 bxe = bx + n;
2531 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2532 #ifdef DEBUG
2533 /*debug*/ if (q > 9)
2534 /*debug*/ Bug("oversized quotient in quorem");
2535 #endif
2536 if (q) {
2537 borrow = 0;
2538 carry = 0;
2539 do {
2540 #ifdef ULLong
2541 ys = *sx++ * (ULLong)q + carry;
2542 carry = ys >> 32;
2543 y = *bx - (ys & FFFFFFFF) - borrow;
2544 borrow = y >> 32 & (ULong)1;
2545 *bx++ = (ULong) y & FFFFFFFF;
2546 #else
2547 #ifdef Pack_32
2548 si = *sx++;
2549 ys = (si & 0xffff) * q + carry;
2550 zs = (si >> 16) * q + (ys >> 16);
2551 carry = zs >> 16;
2552 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2553 borrow = (y & 0x10000) >> 16;
2554 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2555 borrow = (z & 0x10000) >> 16;
2556 Storeinc(bx, z, y);
2557 #else
2558 ys = *sx++ * q + carry;
2559 carry = ys >> 16;
2560 y = *bx - (ys & 0xffff) - borrow;
2561 borrow = (y & 0x10000) >> 16;
2562 *bx++ = y & 0xffff;
2563 #endif
2564 #endif
2565 }
2566 while(sx <= sxe);
2567 if (!*bxe) {
2568 bx = b->x;
2569 while(--bxe > bx && !*bxe)
2570 --n;
2571 b->wds = n;
2572 }
2573 }
2574 if (cmp(b, S) >= 0) {
2575 q++;
2576 borrow = 0;
2577 carry = 0;
2578 bx = b->x;
2579 sx = S->x;
2580 do {
2581 #ifdef ULLong
2582 ys = *sx++ + carry;
2583 carry = ys >> 32;
2584 y = *bx - (ys & FFFFFFFF) - borrow;
2585 borrow = y >> 32 & (ULong)1;
2586 *bx++ = (ULong) y & FFFFFFFF;
2587 #else
2588 #ifdef Pack_32
2589 si = *sx++;
2590 ys = (si & 0xffff) + carry;
2591 zs = (si >> 16) + (ys >> 16);
2592 carry = zs >> 16;
2593 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2594 borrow = (y & 0x10000) >> 16;
2595 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2596 borrow = (z & 0x10000) >> 16;
2597 Storeinc(bx, z, y);
2598 #else
2599 ys = *sx++ + carry;
2600 carry = ys >> 16;
2601 y = *bx - (ys & 0xffff) - borrow;
2602 borrow = (y & 0x10000) >> 16;
2603 *bx++ = y & 0xffff;
2604 #endif
2605 #endif
2606 }
2607 while(sx <= sxe);
2608 bx = b->x;
2609 bxe = bx + n;
2610 if (!*bxe) {
2611 while(--bxe > bx && !*bxe)
2612 --n;
2613 b->wds = n;
2614 }
2615 }
2616 return q;
2617 }
2618
2619 #if !defined(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE)
2620 #define USE_DTOA_RESULT 1
2621 static char *dtoa_result;
2622 #endif
2623
2624 static char *
2625 #ifdef KR_headers
2626 rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i;
2627 #else
2628 rv_alloc(STATE_PARAM int i)
2629 #endif
2630 {
2631 int j, k, *r;
2632
2633 j = sizeof(ULong);
2634 for(k = 0;
2635 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i;
2636 j <<= 1)
2637 k++;
2638 r = (int*)Balloc(PASS_STATE k);
2639 *r = k;
2640 return
2641 #ifdef USE_DTOA_RESULT
2642 dtoa_result =
2643 #endif
2644 (char *)(r+1);
2645 }
2646
2647 static char *
2648 #ifdef KR_headers
2649 nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n;
2650 #else
2651 nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n)
2652 #endif
2653 {
2654 char *rv, *t;
2655
2656 t = rv = rv_alloc(PASS_STATE n);
2657 while((*t = *s++)) t++;
2658 if (rve)
2659 *rve = t;
2660 return rv;
2661 }
2662
2663 /* freedtoa(s) must be used to free values s returned by dtoa
2664 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2665 * but for consistency with earlier versions of dtoa, it is optional
2666 * when MULTIPLE_THREADS is not defined.
2667 */
2668
2669 static void
2670 #ifdef KR_headers
2671 freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s;
2672 #else
2673 freedtoa(STATE_PARAM char *s)
2674 #endif
2675 {
2676 Bigint *b = (Bigint *)((int *)s - 1);
2677 b->maxwds = 1 << (b->k = *(int*)b);
2678 Bfree(PASS_STATE b);
2679 #ifdef USE_DTOA_RESULT
2680 if (s == dtoa_result)
2681 dtoa_result = 0;
2682 #endif
2683 }
2684
2685 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2686 *
2687 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2688 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2689 *
2690 * Modifications:
2691 * 1. Rather than iterating, we use a simple numeric overestimate
2692 * to determine k = floor(log10(d)). We scale relevant
2693 * quantities using O(log2(k)) rather than O(k) multiplications.
2694 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2695 * try to generate digits strictly left to right. Instead, we
2696 * compute with fewer bits and propagate the carry if necessary
2697 * when rounding the final digit up. This is often faster.
2698 * 3. Under the assumption that input will be rounded nearest,
2699 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2700 * That is, we allow equality in stopping tests when the
2701 * round-nearest rule will give the same floating-point value
2702 * as would satisfaction of the stopping test with strict
2703 * inequality.
2704 * 4. We remove common factors of powers of 2 from relevant
2705 * quantities.
2706 * 5. When converting floating-point integers less than 1e16,
2707 * we use floating-point arithmetic rather than resorting
2708 * to multiple-precision integers.
2709 * 6. When asked to produce fewer than 15 digits, we first try
2710 * to get by with floating-point arithmetic; we resort to
2711 * multiple-precision integer arithmetic only if we cannot
2712 * guarantee that the floating-point calculation has given
2713 * the correctly rounded result. For k requested digits and
2714 * "uniformly" distributed input, the probability is
2715 * something like 10^(k-15) that we must resort to the Long
2716 * calculation.
2717 */
2718
2719 static char *
2720 dtoa
2721 #ifdef KR_headers
2722 (STATE_PARAM d, mode, ndigits, decpt, sign, rve)
2723 STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve;
2724 #else
2725 (STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2726 #endif
2727 {
2728 /* Arguments ndigits, decpt, sign are similar to those
2729 of ecvt and fcvt; trailing zeros are suppressed from
2730 the returned string. If not null, *rve is set to point
2731 to the end of the return value. If d is +-Infinity or NaN,
2732 then *decpt is set to 9999.
2733
2734 mode:
2735 0 ==> shortest string that yields d when read in
2736 and rounded to nearest.
2737 1 ==> like 0, but with Steele & White stopping rule;
2738 e.g. with IEEE P754 arithmetic , mode 0 gives
2739 1e23 whereas mode 1 gives 9.999999999999999e22.
2740 2 ==> max(1,ndigits) significant digits. This gives a
2741 return value similar to that of ecvt, except
2742 that trailing zeros are suppressed.
2743 3 ==> through ndigits past the decimal point. This
2744 gives a return value similar to that from fcvt,
2745 except that trailing zeros are suppressed, and
2746 ndigits can be negative.
2747 4,5 ==> similar to 2 and 3, respectively, but (in
2748 round-nearest mode) with the tests of mode 0 to
2749 possibly return a shorter string that rounds to d.
2750 With IEEE arithmetic and compilation with
2751 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2752 as modes 2 and 3 when FLT_ROUNDS != 1.
2753 6-9 ==> Debugging modes similar to mode - 4: don't try
2754 fast floating-point estimate (if applicable).
2755
2756 Values of mode other than 0-9 are treated as mode 0.
2757
2758 Sufficient space is allocated to the return value
2759 to hold the suppressed trailing zeros.
2760 */
2761
2762 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2763 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2764 spec_case, try_quick;
2765 Long L;
2766 #ifndef Sudden_Underflow
2767 int denorm;
2768 ULong x;
2769 #endif
2770 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2771 U d2, eps;
2772 double ds;
2773 char *s, *s0;
2774 #ifdef Honor_FLT_ROUNDS
2775 int rounding;
2776 #endif
2777 #ifdef SET_INEXACT
2778 int inexact, oldinexact;
2779 #endif
2780
2781 #ifdef __GNUC__
2782 ilim = ilim1 = 0;
2783 mlo = NULL;
2784 #endif
2785
2786 #ifdef USE_DTOA_RESULT
2787 if (dtoa_result) {
2788 freedtoa(PASS_STATE dtoa_result);
2789 dtoa_result = 0;
2790 }
2791 #endif
2792
2793 if (word0(d) & Sign_bit) {
2794 /* set sign for everything, including 0's and NaNs */
2795 *sign = 1;
2796 word0(d) &= ~Sign_bit; /* clear sign bit */
2797 }
2798 else
2799 *sign = 0;
2800
2801 #if defined(IEEE_Arith) + defined(VAX)
2802 #ifdef IEEE_Arith
2803 if ((word0(d) & Exp_mask) == Exp_mask)
2804 #else
2805 if (word0(d) == 0x8000)
2806 #endif
2807 {
2808 /* Infinity or NaN */
2809 *decpt = 9999;
2810 #ifdef IEEE_Arith
2811 if (!word1(d) && !(word0(d) & 0xfffff))
2812 return nrv_alloc(PASS_STATE "Infinity", rve, 8);
2813 #endif
2814 return nrv_alloc(PASS_STATE "NaN", rve, 3);
2815 }
2816 #endif
2817 #ifdef IBM
2818 dval(d) += 0; /* normalize */
2819 #endif
2820 if (!dval(d)) {
2821 *decpt = 1;
2822 return nrv_alloc(PASS_STATE "0", rve, 1);
2823 }
2824
2825 #ifdef SET_INEXACT
2826 try_quick = oldinexact = get_inexact();
2827 inexact = 1;
2828 #endif
2829 #ifdef Honor_FLT_ROUNDS
2830 if ((rounding = Flt_Rounds) >= 2) {
2831 if (*sign)
2832 rounding = rounding == 2 ? 0 : 2;
2833 else
2834 if (rounding != 2)
2835 rounding = 0;
2836 }
2837 #endif
2838
2839 b = d2b(PASS_STATE d, &be, &bbits);
2840 #ifdef Sudden_Underflow
2841 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2842 #else
2843 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2844 #endif
2845 dval(d2) = dval(d);
2846 word0(d2) &= Frac_mask1;
2847 word0(d2) |= Exp_11;
2848 #ifdef IBM
2849 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2850 dval(d2) /= 1 << j;
2851 #endif
2852
2853 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2854 * log10(x) = log(x) / log(10)
2855 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2856 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2857 *
2858 * This suggests computing an approximation k to log10(d) by
2859 *
2860 * k = (i - Bias)*0.301029995663981
2861 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2862 *
2863 * We want k to be too large rather than too small.
2864 * The error in the first-order Taylor series approximation
2865 * is in our favor, so we just round up the constant enough
2866 * to compensate for any error in the multiplication of
2867 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2868 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2869 * adding 1e-13 to the constant term more than suffices.
2870 * Hence we adjust the constant term to 0.1760912590558.
2871 * (We could get a more accurate k by invoking log10,
2872 * but this is probably not worthwhile.)
2873 */
2874
2875 i -= Bias;
2876 #ifdef IBM
2877 i <<= 2;
2878 i += j;
2879 #endif
2880 #ifndef Sudden_Underflow
2881 denorm = 0;
2882 }
2883 else {
2884 /* d is denormalized */
2885
2886 i = bbits + be + (Bias + (P-1) - 1);
2887 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2888 : word1(d) << (32 - i);
2889 dval(d2) = x;
2890 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2891 i -= (Bias + (P-1) - 1) + 1;
2892 denorm = 1;
2893 }
2894 #endif
2895 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2896 k = (int)ds;
2897 if (ds < 0. && ds != k)
2898 k--; /* want k = floor(ds) */
2899 k_check = 1;
2900 if (k >= 0 && k <= Ten_pmax) {
2901 if (dval(d) < tens[k])
2902 k--;
2903 k_check = 0;
2904 }
2905 j = bbits - i - 1;
2906 if (j >= 0) {
2907 b2 = 0;
2908 s2 = j;
2909 }
2910 else {
2911 b2 = -j;
2912 s2 = 0;
2913 }
2914 if (k >= 0) {
2915 b5 = 0;
2916 s5 = k;
2917 s2 += k;
2918 }
2919 else {
2920 b2 -= k;
2921 b5 = -k;
2922 s5 = 0;
2923 }
2924 if (mode < 0 || mode > 9)
2925 mode = 0;
2926
2927 #ifndef SET_INEXACT
2928 #ifdef Check_FLT_ROUNDS
2929 try_quick = Rounding == 1;
2930 #else
2931 try_quick = 1;
2932 #endif
2933 #endif /*SET_INEXACT*/
2934
2935 if (mode > 5) {
2936 mode -= 4;
2937 try_quick = 0;
2938 }
2939 leftright = 1;
2940 switch(mode) {
2941 case 0:
2942 case 1:
2943 ilim = ilim1 = -1;
2944 i = 18;
2945 ndigits = 0;
2946 break;
2947 case 2:
2948 leftright = 0;
2949 /* no break */
2950 case 4:
2951 if (ndigits <= 0)
2952 ndigits = 1;
2953 ilim = ilim1 = i = ndigits;
2954 break;
2955 case 3:
2956 leftright = 0;
2957 /* no break */
2958 case 5:
2959 i = ndigits + k + 1;
2960 ilim = i;
2961 ilim1 = i - 1;
2962 if (i <= 0)
2963 i = 1;
2964 }
2965 s = s0 = rv_alloc(PASS_STATE i);
2966
2967 #ifdef Honor_FLT_ROUNDS
2968 if (mode > 1 && rounding != 1)
2969 leftright = 0;
2970 #endif
2971
2972 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2973
2974 /* Try to get by with floating-point arithmetic. */
2975
2976 i = 0;
2977 dval(d2) = dval(d);
2978 k0 = k;
2979 ilim0 = ilim;
2980 ieps = 2; /* conservative */
2981 if (k > 0) {
2982 ds = tens[k&0xf];
2983 j = k >> 4;
2984 if (j & Bletch) {
2985 /* prevent overflows */
2986 j &= Bletch - 1;
2987 dval(d) /= bigtens[n_bigtens-1];
2988 ieps++;
2989 }
2990 for(; j; j >>= 1, i++)
2991 if (j & 1) {
2992 ieps++;
2993 ds *= bigtens[i];
2994 }
2995 dval(d) /= ds;
2996 }
2997 else if ((j1 = -k)) {
2998 dval(d) *= tens[j1 & 0xf];
2999 for(j = j1 >> 4; j; j >>= 1, i++)
3000 if (j & 1) {
3001 ieps++;
3002 dval(d) *= bigtens[i];
3003 }
3004 }
3005 if (k_check && dval(d) < 1. && ilim > 0) {
3006 if (ilim1 <= 0)
3007 goto fast_failed;
3008 ilim = ilim1;
3009 k--;
3010 dval(d) *= 10.;
3011 ieps++;
3012 }
3013 dval(eps) = ieps*dval(d) + 7.;
3014 word0(eps) -= (P-1)*Exp_msk1;
3015 if (ilim == 0) {
3016 S = mhi = 0;
3017 dval(d) -= 5.;
3018 if (dval(d) > dval(eps))
3019 goto one_digit;
3020 if (dval(d) < -dval(eps))
3021 goto no_digits;
3022 goto fast_failed;
3023 }
3024 #ifndef No_leftright
3025 if (leftright) {
3026 /* Use Steele & White method of only
3027 * generating digits needed.
3028 */
3029 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
3030 for(i = 0;;) {
3031 L = (ULong) dval(d);
3032 dval(d) -= L;
3033 *s++ = '0' + (int)L;
3034 if (dval(d) < dval(eps))
3035 goto ret1;
3036 if (1. - dval(d) < dval(eps))
3037 goto bump_up;
3038 if (++i >= ilim)
3039 break;
3040 dval(eps) *= 10.;
3041 dval(d) *= 10.;
3042 }
3043 }
3044 else {
3045 #endif
3046 /* Generate ilim digits, then fix them up. */
3047 dval(eps) *= tens[ilim-1];
3048 for(i = 1;; i++, dval(d) *= 10.) {
3049 L = (Long)(dval(d));
3050 if (!(dval(d) -= L))
3051 ilim = i;
3052 *s++ = '0' + (int)L;
3053 if (i == ilim) {
3054 if (dval(d) > 0.5 + dval(eps))
3055 goto bump_up;
3056 else if (dval(d) < 0.5 - dval(eps)) {
3057 while(*--s == '0');
3058 s++;
3059 goto ret1;
3060 }
3061 break;
3062 }
3063 }
3064 #ifndef No_leftright
3065 }
3066 #endif
3067 fast_failed:
3068 s = s0;
3069 dval(d) = dval(d2);
3070 k = k0;
3071 ilim = ilim0;
3072 }
3073
3074 /* Do we have a "small" integer? */
3075
3076 if (be >= 0 && k <= Int_max) {
3077 /* Yes. */
3078 ds = tens[k];
3079 if (ndigits < 0 && ilim <= 0) {
3080 S = mhi = 0;
3081 if (ilim < 0 || dval(d) < 5*ds)
3082 goto no_digits;
3083 goto one_digit;
3084 }
3085 for(i = 1;; i++, dval(d) *= 10.) {
3086 L = (Long)(dval(d) / ds);
3087 dval(d) -= L*ds;
3088 #ifdef Check_FLT_ROUNDS
3089 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3090 if (dval(d) < 0) {
3091 L--;
3092 dval(d) += ds;
3093 }
3094 #endif
3095 *s++ = '0' + (int)L;
3096 if (!dval(d)) {
3097 #ifdef SET_INEXACT
3098 inexact = 0;
3099 #endif
3100 break;
3101 }
3102 if (i == ilim) {
3103 #ifdef Honor_FLT_ROUNDS
3104 if (mode > 1)
3105 switch(rounding) {
3106 case 0: goto ret1;
3107 case 2: goto bump_up;
3108 }
3109 #endif
3110 dval(d) += dval(d);
3111 if (dval(d) > ds || (dval(d) == ds && L & 1)) {
3112 bump_up:
3113 while(*--s == '9')
3114 if (s == s0) {
3115 k++;
3116 *s = '0';
3117 break;
3118 }
3119 ++*s++;
3120 }
3121 break;
3122 }
3123 }
3124 goto ret1;
3125 }
3126
3127 m2 = b2;
3128 m5 = b5;
3129 mhi = mlo = 0;
3130 if (leftright) {
3131 i =
3132 #ifndef Sudden_Underflow
3133 denorm ? be + (Bias + (P-1) - 1 + 1) :
3134 #endif
3135 #ifdef IBM
3136 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3137 #else
3138 1 + P - bbits;
3139 #endif
3140 b2 += i;
3141 s2 += i;
3142 mhi = i2b(PASS_STATE 1);
3143 }
3144 if (m2 > 0 && s2 > 0) {
3145 i = m2 < s2 ? m2 : s2;
3146 b2 -= i;
3147 m2 -= i;
3148 s2 -= i;
3149 }
3150 if (b5 > 0) {
3151 if (leftright) {
3152 if (m5 > 0) {
3153 mhi = pow5mult(PASS_STATE mhi, m5);
3154 b1 = mult(PASS_STATE mhi, b);
3155 Bfree(PASS_STATE b);
3156 b = b1;
3157 }
3158 if ((j = b5 - m5))
3159 b = pow5mult(PASS_STATE b, j);
3160 }
3161 else
3162 b = pow5mult(PASS_STATE b, b5);
3163 }
3164 S = i2b(PASS_STATE 1);
3165 if (s5 > 0)
3166 S = pow5mult(PASS_STATE S, s5);
3167
3168 /* Check for special case that d is a normalized power of 2. */
3169
3170 spec_case = 0;
3171 if ((mode < 2 || leftright)
3172 #ifdef Honor_FLT_ROUNDS
3173 && rounding == 1
3174 #endif
3175 ) {
3176 if (!word1(d) && !(word0(d) & Bndry_mask)
3177 #ifndef Sudden_Underflow
3178 && word0(d) & (Exp_mask & ~Exp_msk1)
3179 #endif
3180 ) {
3181 /* The special case */
3182 b2 += Log2P;
3183 s2 += Log2P;
3184 spec_case = 1;
3185 }
3186 }
3187
3188 /* Arrange for convenient computation of quotients:
3189 * shift left if necessary so divisor has 4 leading 0 bits.
3190 *
3191 * Perhaps we should just compute leading 28 bits of S once
3192 * and for all and pass them and a shift to quorem, so it
3193 * can do shifts and ors to compute the numerator for q.
3194 */
3195 #ifdef Pack_32
3196 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3197 i = 32 - i;
3198 #else
3199 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3200 i = 16 - i;
3201 #endif
3202 if (i > 4) {
3203 i -= 4;
3204 b2 += i;
3205 m2 += i;
3206 s2 += i;
3207 }
3208 else if (i < 4) {
3209 i += 28;
3210 b2 += i;
3211 m2 += i;
3212 s2 += i;
3213 }
3214 if (b2 > 0)
3215 b = lshift(PASS_STATE b, b2);
3216 if (s2 > 0)
3217 S = lshift(PASS_STATE S, s2);
3218 if (k_check) {
3219 if (cmp(b,S) < 0) {
3220 k--;
3221 b = multadd(PASS_STATE b, 10, 0); /* we botched the k estimate */
3222 if (leftright)
3223 mhi = multadd(PASS_STATE mhi, 10, 0);
3224 ilim = ilim1;
3225 }
3226 }
3227 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3228 if (ilim < 0 || cmp(b,S = multadd(PASS_STATE S,5,0)) < 0) {
3229 /* no digits, fcvt style */
3230 no_digits:
3231 /* MOZILLA CHANGE: Always return a non-empty string. */
3232 *s++ = '0';
3233 k = 0;
3234 goto ret;
3235 }
3236 one_digit:
3237 *s++ = '1';
3238 k++;
3239 goto ret;
3240 }
3241 if (leftright) {
3242 if (m2 > 0)
3243 mhi = lshift(PASS_STATE mhi, m2);
3244
3245 /* Compute mlo -- check for special case
3246 * that d is a normalized power of 2.
3247 */
3248
3249 mlo = mhi;
3250 if (spec_case) {
3251 mhi = Balloc(PASS_STATE mhi->k);
3252 Bcopy(mhi, mlo);
3253 mhi = lshift(PASS_STATE mhi, Log2P);
3254 }
3255
3256 for(i = 1;;i++) {
3257 dig = quorem(b,S) + '0';
3258 /* Do we yet have the shortest decimal string
3259 * that will round to d?
3260 */
3261 j = cmp(b, mlo);
3262 delta = diff(PASS_STATE S, mhi);
3263 j1 = delta->sign ? 1 : cmp(b, delta);
3264 Bfree(PASS_STATE delta);
3265 #ifndef ROUND_BIASED
3266 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3267 #ifdef Honor_FLT_ROUNDS
3268 && rounding >= 1
3269 #endif
3270 ) {
3271 if (dig == '9')
3272 goto round_9_up;
3273 if (j > 0)
3274 dig++;
3275 #ifdef SET_INEXACT
3276 else if (!b->x[0] && b->wds <= 1)
3277 inexact = 0;
3278 #endif
3279 *s++ = dig;
3280 goto ret;
3281 }
3282 #endif
3283 if (j < 0 || (j == 0 && mode != 1
3284 #ifndef ROUND_BIASED
3285 && !(word1(d) & 1)
3286 #endif
3287 )) {
3288 if (!b->x[0] && b->wds <= 1) {
3289 #ifdef SET_INEXACT
3290 inexact = 0;
3291 #endif
3292 goto accept_dig;
3293 }
3294 #ifdef Honor_FLT_ROUNDS
3295 if (mode > 1)
3296 switch(rounding) {
3297 case 0: goto accept_dig;
3298 case 2: goto keep_dig;
3299 }
3300 #endif /*Honor_FLT_ROUNDS*/
3301 if (j1 > 0) {
3302 b = lshift(PASS_STATE b, 1);
3303 j1 = cmp(b, S);
3304 if ((j1 > 0 || (j1 == 0 && dig & 1))
3305 && dig++ == '9')
3306 goto round_9_up;
3307 }
3308 accept_dig:
3309 *s++ = dig;
3310 goto ret;
3311 }
3312 if (j1 > 0) {
3313 #ifdef Honor_FLT_ROUNDS
3314 if (!rounding)
3315 goto accept_dig;
3316 #endif
3317 if (dig == '9') { /* possible if i == 1 */
3318 round_9_up:
3319 *s++ = '9';
3320 goto roundoff;
3321 }
3322 *s++ = dig + 1;
3323 goto ret;
3324 }
3325 #ifdef Honor_FLT_ROUNDS
3326 keep_dig:
3327 #endif
3328 *s++ = dig;
3329 if (i == ilim)
3330 break;
3331 b = multadd(PASS_STATE b, 10, 0);
3332 if (mlo == mhi)
3333 mlo = mhi = multadd(PASS_STATE mhi, 10, 0);
3334 else {
3335 mlo = multadd(PASS_STATE mlo, 10, 0);
3336 mhi = multadd(PASS_STATE mhi, 10, 0);
3337 }
3338 }
3339 }
3340 else
3341 for(i = 1;; i++) {
3342 *s++ = dig = quorem(b,S) + '0';
3343 if (!b->x[0] && b->wds <= 1) {
3344 #ifdef SET_INEXACT
3345 inexact = 0;
3346 #endif
3347 goto ret;
3348 }
3349 if (i >= ilim)
3350 break;
3351 b = multadd(PASS_STATE b, 10, 0);
3352 }
3353
3354 /* Round off last digit */
3355
3356 #ifdef Honor_FLT_ROUNDS
3357 switch(rounding) {
3358 case 0: goto trimzeros;
3359 case 2: goto roundoff;
3360 }
3361 #endif
3362 b = lshift(PASS_STATE b, 1);
3363 j = cmp(b, S);
3364 if (j >= 0) { /* ECMA compatible rounding needed by Spidermonkey */
3365 roundoff:
3366 while(*--s == '9')
3367 if (s == s0) {
3368 k++;
3369 *s++ = '1';
3370 goto ret;
3371 }
3372 ++*s++;
3373 }
3374 else {
3375 #ifdef Honor_FLT_ROUNDS
3376 trimzeros:
3377 #endif
3378 while(*--s == '0');
3379 s++;
3380 }
3381 ret:
3382 Bfree(PASS_STATE S);
3383 if (mhi) {
3384 if (mlo && mlo != mhi)
3385 Bfree(PASS_STATE mlo);
3386 Bfree(PASS_STATE mhi);
3387 }
3388 ret1:
3389 #ifdef SET_INEXACT
3390 if (inexact) {
3391 if (!oldinexact) {
3392 word0(d) = Exp_1 + (70 << Exp_shift);
3393 word1(d) = 0;
3394 dval(d) += 1.;
3395 }
3396 }
3397 else if (!oldinexact)
3398 clear_inexact();
3399 #endif
3400 Bfree(PASS_STATE b);
3401 *s = 0;
3402 *decpt = k + 1;
3403 if (rve)
3404 *rve = s;
3405 return s0;
3406 }
3407 #ifdef __cplusplus
3408 }
3409 #endif
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