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Merge mozilla-central and tracemonkey. (a=blockers)
[mozilla-central.git] / js / src / dtoa.c
blob3940ccf184a703e9a0bdc9d0a6f185b8c853ee37
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 MULTIPLE_THREADS if the system offers preemptively scheduled
120 * multiple threads. In this case, you must provide (or suitably
121 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
122 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
123 * in pow5mult, ensures lazy evaluation of only one copy of high
124 * powers of 5; omitting this lock would introduce a small
125 * probability of wasting memory, but would otherwise be harmless.)
126 * You must also invoke freedtoa(s) to free the value s returned by
127 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
128 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
129 * avoids underflows on inputs whose result does not underflow.
130 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
131 * floating-point numbers and flushes underflows to zero rather
132 * than implementing gradual underflow, then you must also #define
133 * Sudden_Underflow.
134 * #define USE_LOCALE to use the current locale's decimal_point value.
135 * #define SET_INEXACT if IEEE arithmetic is being used and extra
136 * computation should be done to set the inexact flag when the
137 * result is inexact and avoid setting inexact when the result
138 * is exact. In this case, dtoa.c must be compiled in
139 * an environment, perhaps provided by #include "dtoa.c" in a
140 * suitable wrapper, that defines two functions,
141 * int get_inexact(void);
142 * void clear_inexact(void);
143 * such that get_inexact() returns a nonzero value if the
144 * inexact bit is already set, and clear_inexact() sets the
145 * inexact bit to 0. When SET_INEXACT is #defined, strtod
146 * also does extra computations to set the underflow and overflow
147 * flags when appropriate (i.e., when the result is tiny and
148 * inexact or when it is a numeric value rounded to +-infinity).
149 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
150 * the result overflows to +-Infinity or underflows to 0.
151 * #define NO_GLOBAL_STATE to avoid defining any non-const global or
152 * static variables. Instead the necessary state is stored in an
153 * opaque struct, DtoaState, a pointer to which must be passed to
154 * every entry point. Two new functions are added to the API:
155 * DtoaState *newdtoa(void);
156 * void destroydtoa(DtoaState *);
157 */
158
159 #ifndef Long
160 #define Long long
161 #endif
162 #ifndef ULong
163 typedef unsigned Long ULong;
164 #endif
165
166 #ifdef DEBUG
167 #include "stdio.h"
168 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
169 #endif
170
171 #include "stdlib.h"
172 #include "string.h"
173
174 #ifdef USE_LOCALE
175 #include "locale.h"
176 #endif
177
178 #ifdef MALLOC
179 #ifdef KR_headers
180 extern char *MALLOC();
181 #else
182 extern void *MALLOC(size_t);
183 #endif
184 #else
185 #define MALLOC malloc
186 #endif
187
188 #ifndef FREE
189 #define FREE free
190 #endif
191
192 #ifndef Omit_Private_Memory
193 #ifndef PRIVATE_MEM
194 #define PRIVATE_MEM 2304
195 #endif
196 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
197 #endif
198
199 #undef IEEE_Arith
200 #undef Avoid_Underflow
201 #ifdef IEEE_MC68k
202 #define IEEE_Arith
203 #endif
204 #ifdef IEEE_8087
205 #define IEEE_Arith
206 #endif
207
208 #include "errno.h"
209
210 #ifdef Bad_float_h
211
212 #ifdef IEEE_Arith
213 #define DBL_DIG 15
214 #define DBL_MAX_10_EXP 308
215 #define DBL_MAX_EXP 1024
216 #define FLT_RADIX 2
217 #endif /*IEEE_Arith*/
218
219 #ifdef IBM
220 #define DBL_DIG 16
221 #define DBL_MAX_10_EXP 75
222 #define DBL_MAX_EXP 63
223 #define FLT_RADIX 16
224 #define DBL_MAX 7.2370055773322621e+75
225 #endif
226
227 #ifdef VAX
228 #define DBL_DIG 16
229 #define DBL_MAX_10_EXP 38
230 #define DBL_MAX_EXP 127
231 #define FLT_RADIX 2
232 #define DBL_MAX 1.7014118346046923e+38
233 #endif
234
235 #ifndef LONG_MAX
236 #define LONG_MAX 2147483647
237 #endif
238
239 #else /* ifndef Bad_float_h */
240 #include "float.h"
241 #endif /* Bad_float_h */
242
243 #ifndef __MATH_H__
244 #include "math.h"
245 #endif
246
247 #ifdef __cplusplus
248 extern "C" {
249 #endif
250
251 #ifndef CONST
252 #ifdef KR_headers
253 #define CONST /* blank */
254 #else
255 #define CONST const
256 #endif
257 #endif
258
259 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
260 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
261 #endif
262
263 typedef union { double d; ULong L[2]; } U;
264
265 #define dval(x) ((x).d)
266 #ifdef IEEE_8087
267 #define word0(x) ((x).L[1])
268 #define word1(x) ((x).L[0])
269 #else
270 #define word0(x) ((x).L[0])
271 #define word1(x) ((x).L[1])
272 #endif
273
274 /* The following definition of Storeinc is appropriate for MIPS processors.
275 * An alternative that might be better on some machines is
276 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
277 */
278 #if defined(IEEE_8087) + defined(VAX)
279 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
280 ((unsigned short *)a)[0] = (unsigned short)c, a++)
281 #else
282 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
283 ((unsigned short *)a)[1] = (unsigned short)c, a++)
284 #endif
285
286 /* #define P DBL_MANT_DIG */
287 /* Ten_pmax = floor(P*log(2)/log(5)) */
288 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
289 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
290 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
291
292 #ifdef IEEE_Arith
293 #define Exp_shift 20
294 #define Exp_shift1 20
295 #define Exp_msk1 0x100000
296 #define Exp_msk11 0x100000
297 #define Exp_mask 0x7ff00000
298 #define P 53
299 #define Bias 1023
300 #define Emin (-1022)
301 #define Exp_1 0x3ff00000
302 #define Exp_11 0x3ff00000
303 #define Ebits 11
304 #define Frac_mask 0xfffff
305 #define Frac_mask1 0xfffff
306 #define Ten_pmax 22
307 #define Bletch 0x10
308 #define Bndry_mask 0xfffff
309 #define Bndry_mask1 0xfffff
310 #define LSB 1
311 #define Sign_bit 0x80000000
312 #define Log2P 1
313 #define Tiny0 0
314 #define Tiny1 1
315 #define Quick_max 14
316 #define Int_max 14
317 #ifndef NO_IEEE_Scale
318 #define Avoid_Underflow
319 #ifdef Flush_Denorm /* debugging option */
320 #undef Sudden_Underflow
321 #endif
322 #endif
323
324 #ifndef Flt_Rounds
325 #ifdef FLT_ROUNDS
326 #define Flt_Rounds FLT_ROUNDS
327 #else
328 #define Flt_Rounds 1
329 #endif
330 #endif /*Flt_Rounds*/
331
332 #ifdef Honor_FLT_ROUNDS
333 #define Rounding rounding
334 #undef Check_FLT_ROUNDS
335 #define Check_FLT_ROUNDS
336 #else
337 #define Rounding Flt_Rounds
338 #endif
339
340 #else /* ifndef IEEE_Arith */
341 #undef Check_FLT_ROUNDS
342 #undef Honor_FLT_ROUNDS
343 #undef SET_INEXACT
344 #undef Sudden_Underflow
345 #define Sudden_Underflow
346 #ifdef IBM
347 #undef Flt_Rounds
348 #define Flt_Rounds 0
349 #define Exp_shift 24
350 #define Exp_shift1 24
351 #define Exp_msk1 0x1000000
352 #define Exp_msk11 0x1000000
353 #define Exp_mask 0x7f000000
354 #define P 14
355 #define Bias 65
356 #define Exp_1 0x41000000
357 #define Exp_11 0x41000000
358 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
359 #define Frac_mask 0xffffff
360 #define Frac_mask1 0xffffff
361 #define Bletch 4
362 #define Ten_pmax 22
363 #define Bndry_mask 0xefffff
364 #define Bndry_mask1 0xffffff
365 #define LSB 1
366 #define Sign_bit 0x80000000
367 #define Log2P 4
368 #define Tiny0 0x100000
369 #define Tiny1 0
370 #define Quick_max 14
371 #define Int_max 15
372 #else /* VAX */
373 #undef Flt_Rounds
374 #define Flt_Rounds 1
375 #define Exp_shift 23
376 #define Exp_shift1 7
377 #define Exp_msk1 0x80
378 #define Exp_msk11 0x800000
379 #define Exp_mask 0x7f80
380 #define P 56
381 #define Bias 129
382 #define Exp_1 0x40800000
383 #define Exp_11 0x4080
384 #define Ebits 8
385 #define Frac_mask 0x7fffff
386 #define Frac_mask1 0xffff007f
387 #define Ten_pmax 24
388 #define Bletch 2
389 #define Bndry_mask 0xffff007f
390 #define Bndry_mask1 0xffff007f
391 #define LSB 0x10000
392 #define Sign_bit 0x8000
393 #define Log2P 1
394 #define Tiny0 0x80
395 #define Tiny1 0
396 #define Quick_max 15
397 #define Int_max 15
398 #endif /* IBM, VAX */
399 #endif /* IEEE_Arith */
400
401 #ifndef IEEE_Arith
402 #define ROUND_BIASED
403 #endif
404
405 #ifdef RND_PRODQUOT
406 #define rounded_product(a,b) a = rnd_prod(a, b)
407 #define rounded_quotient(a,b) a = rnd_quot(a, b)
408 #ifdef KR_headers
409 extern double rnd_prod(), rnd_quot();
410 #else
411 extern double rnd_prod(double, double), rnd_quot(double, double);
412 #endif
413 #else
414 #define rounded_product(a,b) a *= b
415 #define rounded_quotient(a,b) a /= b
416 #endif
417
418 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
419 #define Big1 0xffffffff
420
421 #ifndef Pack_32
422 #define Pack_32
423 #endif
424
425 #ifdef KR_headers
426 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
427 #else
428 #define FFFFFFFF 0xffffffffUL
429 #endif
430
431 #ifdef NO_LONG_LONG
432 #undef ULLong
433 #ifdef Just_16
434 #undef Pack_32
435 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
436 * This makes some inner loops simpler and sometimes saves work
437 * during multiplications, but it often seems to make things slightly
438 * slower. Hence the default is now to store 32 bits per Long.
439 */
440 #endif
441 #else /* long long available */
442 #ifndef Llong
443 #define Llong long long
444 #endif
445 #ifndef ULLong
446 #define ULLong unsigned Llong
447 #endif
448 #endif /* NO_LONG_LONG */
449
450 #ifndef MULTIPLE_THREADS
451 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
452 #define FREE_DTOA_LOCK(n) /*nothing*/
453 #endif
454
455 #define Kmax 7
456
457 struct
458 Bigint {
459 struct Bigint *next;
460 int k, maxwds, sign, wds;
461 ULong x[1];
462 };
463
464 typedef struct Bigint Bigint;
465
466 #ifdef NO_GLOBAL_STATE
467 #ifdef MULTIPLE_THREADS
468 #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"
469 #endif
470 struct
471 DtoaState {
472 #define DECLARE_GLOBAL_STATE /* nothing */
473 #else
474 #define DECLARE_GLOBAL_STATE static
475 #endif
476
477 DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];
478 DECLARE_GLOBAL_STATE Bigint *p5s;
479 #ifndef Omit_Private_Memory
480 DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];
481 DECLARE_GLOBAL_STATE double *pmem_next
482 #ifndef NO_GLOBAL_STATE
483 = private_mem
484 #endif
485 ;
486 #endif
487 #ifdef NO_GLOBAL_STATE
488 };
489 typedef struct DtoaState DtoaState;
490 #ifdef KR_headers
491 #define STATE_PARAM state,
492 #define STATE_PARAM_DECL DtoaState *state;
493 #else
494 #define STATE_PARAM DtoaState *state,
495 #endif
496 #define PASS_STATE state,
497 #define GET_STATE(field) (state->field)
498
499 static DtoaState *
500 newdtoa(void)
501 {
502 DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));
503 if (state) {
504 memset(state, 0, sizeof(DtoaState));
505 #ifndef Omit_Private_Memory
506 state->pmem_next = state->private_mem;
507 #endif
508 }
509 return state;
510 }
511
512 static void
513 destroydtoa
514 #ifdef KR_headers
515 (state) STATE_PARAM_DECL
516 #else
517 (DtoaState *state)
518 #endif
519 {
520 int i;
521 Bigint *v, *next;
522
523 for (i = 0; i <= Kmax; i++) {
524 for (v = GET_STATE(freelist)[i]; v; v = next) {
525 next = v->next;
526 #ifndef Omit_Private_Memory
527 if ((double*)v < GET_STATE(private_mem) ||
528 (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)
529 #endif
530 FREE((void*)v);
531 }
532 }
533 FREE((void *)state);
534 }
535
536 #else
537 #define STATE_PARAM /* nothing */
538 #define STATE_PARAM_DECL /* nothing */
539 #define PASS_STATE /* nothing */
540 #define GET_STATE(name) name
541 #endif
542
543 static Bigint *
544 Balloc
545 #ifdef KR_headers
546 (STATE_PARAM k) STATE_PARAM_DECL int k;
547 #else
548 (STATE_PARAM int k)
549 #endif
550 {
551 int x;
552 Bigint *rv;
553 #ifndef Omit_Private_Memory
554 size_t len;
555 #endif
556
557 ACQUIRE_DTOA_LOCK(0);
558 /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
559 /* but this case seems very unlikely. */
560 if (k <= Kmax && (rv = GET_STATE(freelist)[k]))
561 GET_STATE(freelist)[k] = rv->next;
562 else {
563 x = 1 << k;
564 #ifdef Omit_Private_Memory
565 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
566 #else
567 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
568 /sizeof(double);
569 if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
570 rv = (Bigint*)GET_STATE(pmem_next);
571 GET_STATE(pmem_next) += len;
572 }
573 else
574 rv = (Bigint*)MALLOC(len*sizeof(double));
575 #endif
576 rv->k = k;
577 rv->maxwds = x;
578 }
579 FREE_DTOA_LOCK(0);
580 rv->sign = rv->wds = 0;
581 return rv;
582 }
583
584 static void
585 Bfree
586 #ifdef KR_headers
587 (STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
588 #else
589 (STATE_PARAM Bigint *v)
590 #endif
591 {
592 if (v) {
593 if (v->k > Kmax)
594 FREE((void*)v);
595 else {
596 ACQUIRE_DTOA_LOCK(0);
597 v->next = GET_STATE(freelist)[v->k];
598 GET_STATE(freelist)[v->k] = v;
599 FREE_DTOA_LOCK(0);
600 }
601 }
602 }
603
604 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
605 y->wds*sizeof(Long) + 2*sizeof(int))
606
607 static Bigint *
608 multadd
609 #ifdef KR_headers
610 (STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
611 #else
612 (STATE_PARAM Bigint *b, int m, int a) /* multiply by m and add a */
613 #endif
614 {
615 int i, wds;
616 #ifdef ULLong
617 ULong *x;
618 ULLong carry, y;
619 #else
620 ULong carry, *x, y;
621 #ifdef Pack_32
622 ULong xi, z;
623 #endif
624 #endif
625 Bigint *b1;
626
627 wds = b->wds;
628 x = b->x;
629 i = 0;
630 carry = a;
631 do {
632 #ifdef ULLong
633 y = *x * (ULLong)m + carry;
634 carry = y >> 32;
635 *x++ = (ULong) y & FFFFFFFF;
636 #else
637 #ifdef Pack_32
638 xi = *x;
639 y = (xi & 0xffff) * m + carry;
640 z = (xi >> 16) * m + (y >> 16);
641 carry = z >> 16;
642 *x++ = (z << 16) + (y & 0xffff);
643 #else
644 y = *x * m + carry;
645 carry = y >> 16;
646 *x++ = y & 0xffff;
647 #endif
648 #endif
649 }
650 while(++i < wds);
651 if (carry) {
652 if (wds >= b->maxwds) {
653 b1 = Balloc(PASS_STATE b->k+1);
654 Bcopy(b1, b);
655 Bfree(PASS_STATE b);
656 b = b1;
657 }
658 b->x[wds++] = (ULong) carry;
659 b->wds = wds;
660 }
661 return b;
662 }
663
664 static Bigint *
665 s2b
666 #ifdef KR_headers
667 (STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9;
668 #else
669 (STATE_PARAM CONST char *s, int nd0, int nd, ULong y9)
670 #endif
671 {
672 Bigint *b;
673 int i, k;
674 Long x, y;
675
676 x = (nd + 8) / 9;
677 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
678 #ifdef Pack_32
679 b = Balloc(PASS_STATE k);
680 b->x[0] = y9;
681 b->wds = 1;
682 #else
683 b = Balloc(PASS_STATE k+1);
684 b->x[0] = y9 & 0xffff;
685 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
686 #endif
687
688 i = 9;
689 if (9 < nd0) {
690 s += 9;
691 do b = multadd(PASS_STATE b, 10, *s++ - '0');
692 while(++i < nd0);
693 s++;
694 }
695 else
696 s += 10;
697 for(; i < nd; i++)
698 b = multadd(PASS_STATE b, 10, *s++ - '0');
699 return b;
700 }
701
702 static int
703 hi0bits
704 #ifdef KR_headers
705 (x) register ULong x;
706 #else
707 (register ULong x)
708 #endif
709 {
710 register int k = 0;
711
712 if (!(x & 0xffff0000)) {
713 k = 16;
714 x <<= 16;
715 }
716 if (!(x & 0xff000000)) {
717 k += 8;
718 x <<= 8;
719 }
720 if (!(x & 0xf0000000)) {
721 k += 4;
722 x <<= 4;
723 }
724 if (!(x & 0xc0000000)) {
725 k += 2;
726 x <<= 2;
727 }
728 if (!(x & 0x80000000)) {
729 k++;
730 if (!(x & 0x40000000))
731 return 32;
732 }
733 return k;
734 }
735
736 static int
737 lo0bits
738 #ifdef KR_headers
739 (y) ULong *y;
740 #else
741 (ULong *y)
742 #endif
743 {
744 register int k;
745 register ULong x = *y;
746
747 if (x & 7) {
748 if (x & 1)
749 return 0;
750 if (x & 2) {
751 *y = x >> 1;
752 return 1;
753 }
754 *y = x >> 2;
755 return 2;
756 }
757 k = 0;
758 if (!(x & 0xffff)) {
759 k = 16;
760 x >>= 16;
761 }
762 if (!(x & 0xff)) {
763 k += 8;
764 x >>= 8;
765 }
766 if (!(x & 0xf)) {
767 k += 4;
768 x >>= 4;
769 }
770 if (!(x & 0x3)) {
771 k += 2;
772 x >>= 2;
773 }
774 if (!(x & 1)) {
775 k++;
776 x >>= 1;
777 if (!x)
778 return 32;
779 }
780 *y = x;
781 return k;
782 }
783
784 static Bigint *
785 i2b
786 #ifdef KR_headers
787 (STATE_PARAM i) STATE_PARAM_DECL int i;
788 #else
789 (STATE_PARAM int i)
790 #endif
791 {
792 Bigint *b;
793
794 b = Balloc(PASS_STATE 1);
795 b->x[0] = i;
796 b->wds = 1;
797 return b;
798 }
799
800 static Bigint *
801 mult
802 #ifdef KR_headers
803 (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
804 #else
805 (STATE_PARAM Bigint *a, Bigint *b)
806 #endif
807 {
808 Bigint *c;
809 int k, wa, wb, wc;
810 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
811 ULong y;
812 #ifdef ULLong
813 ULLong carry, z;
814 #else
815 ULong carry, z;
816 #ifdef Pack_32
817 ULong z2;
818 #endif
819 #endif
820
821 if (a->wds < b->wds) {
822 c = a;
823 a = b;
824 b = c;
825 }
826 k = a->k;
827 wa = a->wds;
828 wb = b->wds;
829 wc = wa + wb;
830 if (wc > a->maxwds)
831 k++;
832 c = Balloc(PASS_STATE k);
833 for(x = c->x, xa = x + wc; x < xa; x++)
834 *x = 0;
835 xa = a->x;
836 xae = xa + wa;
837 xb = b->x;
838 xbe = xb + wb;
839 xc0 = c->x;
840 #ifdef ULLong
841 for(; xb < xbe; xc0++) {
842 if ((y = *xb++)) {
843 x = xa;
844 xc = xc0;
845 carry = 0;
846 do {
847 z = *x++ * (ULLong)y + *xc + carry;
848 carry = z >> 32;
849 *xc++ = (ULong) z & FFFFFFFF;
850 }
851 while(x < xae);
852 *xc = (ULong) carry;
853 }
854 }
855 #else
856 #ifdef Pack_32
857 for(; xb < xbe; xb++, xc0++) {
858 if (y = *xb & 0xffff) {
859 x = xa;
860 xc = xc0;
861 carry = 0;
862 do {
863 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
864 carry = z >> 16;
865 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
866 carry = z2 >> 16;
867 Storeinc(xc, z2, z);
868 }
869 while(x < xae);
870 *xc = carry;
871 }
872 if (y = *xb >> 16) {
873 x = xa;
874 xc = xc0;
875 carry = 0;
876 z2 = *xc;
877 do {
878 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
879 carry = z >> 16;
880 Storeinc(xc, z, z2);
881 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
882 carry = z2 >> 16;
883 }
884 while(x < xae);
885 *xc = z2;
886 }
887 }
888 #else
889 for(; xb < xbe; xc0++) {
890 if (y = *xb++) {
891 x = xa;
892 xc = xc0;
893 carry = 0;
894 do {
895 z = *x++ * y + *xc + carry;
896 carry = z >> 16;
897 *xc++ = z & 0xffff;
898 }
899 while(x < xae);
900 *xc = carry;
901 }
902 }
903 #endif
904 #endif
905 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
906 c->wds = wc;
907 return c;
908 }
909
910 static Bigint *
911 pow5mult
912 #ifdef KR_headers
913 (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
914 #else
915 (STATE_PARAM Bigint *b, int k)
916 #endif
917 {
918 Bigint *b1, *p5, *p51;
919 int i;
920 static CONST int p05[3] = { 5, 25, 125 };
921
922 if ((i = k & 3))
923 b = multadd(PASS_STATE b, p05[i-1], 0);
924
925 if (!(k >>= 2))
926 return b;
927 if (!(p5 = GET_STATE(p5s))) {
928 /* first time */
929 #ifdef MULTIPLE_THREADS
930 ACQUIRE_DTOA_LOCK(1);
931 if (!(p5 = p5s)) {
932 p5 = p5s = i2b(625);
933 p5->next = 0;
934 }
935 FREE_DTOA_LOCK(1);
936 #else
937 p5 = GET_STATE(p5s) = i2b(PASS_STATE 625);
938 p5->next = 0;
939 #endif
940 }
941 for(;;) {
942 if (k & 1) {
943 b1 = mult(PASS_STATE b, p5);
944 Bfree(PASS_STATE b);
945 b = b1;
946 }
947 if (!(k >>= 1))
948 break;
949 if (!(p51 = p5->next)) {
950 #ifdef MULTIPLE_THREADS
951 ACQUIRE_DTOA_LOCK(1);
952 if (!(p51 = p5->next)) {
953 p51 = p5->next = mult(p5,p5);
954 p51->next = 0;
955 }
956 FREE_DTOA_LOCK(1);
957 #else
958 p51 = p5->next = mult(PASS_STATE p5,p5);
959 p51->next = 0;
960 #endif
961 }
962 p5 = p51;
963 }
964 return b;
965 }
966
967 static Bigint *
968 lshift
969 #ifdef KR_headers
970 (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
971 #else
972 (STATE_PARAM Bigint *b, int k)
973 #endif
974 {
975 int i, k1, n, n1;
976 Bigint *b1;
977 ULong *x, *x1, *xe, z;
978
979 #ifdef Pack_32
980 n = k >> 5;
981 #else
982 n = k >> 4;
983 #endif
984 k1 = b->k;
985 n1 = n + b->wds + 1;
986 for(i = b->maxwds; n1 > i; i <<= 1)
987 k1++;
988 b1 = Balloc(PASS_STATE k1);
989 x1 = b1->x;
990 for(i = 0; i < n; i++)
991 *x1++ = 0;
992 x = b->x;
993 xe = x + b->wds;
994 #ifdef Pack_32
995 if (k &= 0x1f) {
996 k1 = 32 - k;
997 z = 0;
998 do {
999 *x1++ = *x << k | z;
1000 z = *x++ >> k1;
1001 }
1002 while(x < xe);
1003 if ((*x1 = z))
1004 ++n1;
1005 }
1006 #else
1007 if (k &= 0xf) {
1008 k1 = 16 - k;
1009 z = 0;
1010 do {
1011 *x1++ = *x << k & 0xffff | z;
1012 z = *x++ >> k1;
1013 }
1014 while(x < xe);
1015 if (*x1 = z)
1016 ++n1;
1017 }
1018 #endif
1019 else do
1020 *x1++ = *x++;
1021 while(x < xe);
1022 b1->wds = n1 - 1;
1023 Bfree(PASS_STATE b);
1024 return b1;
1025 }
1026
1027 static int
1028 cmp
1029 #ifdef KR_headers
1030 (a, b) Bigint *a, *b;
1031 #else
1032 (Bigint *a, Bigint *b)
1033 #endif
1034 {
1035 ULong *xa, *xa0, *xb, *xb0;
1036 int i, j;
1037
1038 i = a->wds;
1039 j = b->wds;
1040 #ifdef DEBUG
1041 if (i > 1 && !a->x[i-1])
1042 Bug("cmp called with a->x[a->wds-1] == 0");
1043 if (j > 1 && !b->x[j-1])
1044 Bug("cmp called with b->x[b->wds-1] == 0");
1045 #endif
1046 if (i -= j)
1047 return i;
1048 xa0 = a->x;
1049 xa = xa0 + j;
1050 xb0 = b->x;
1051 xb = xb0 + j;
1052 for(;;) {
1053 if (*--xa != *--xb)
1054 return *xa < *xb ? -1 : 1;
1055 if (xa <= xa0)
1056 break;
1057 }
1058 return 0;
1059 }
1060
1061 static Bigint *
1062 diff
1063 #ifdef KR_headers
1064 (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
1065 #else
1066 (STATE_PARAM Bigint *a, Bigint *b)
1067 #endif
1068 {
1069 Bigint *c;
1070 int i, wa, wb;
1071 ULong *xa, *xae, *xb, *xbe, *xc;
1072 #ifdef ULLong
1073 ULLong borrow, y;
1074 #else
1075 ULong borrow, y;
1076 #ifdef Pack_32
1077 ULong z;
1078 #endif
1079 #endif
1080
1081 i = cmp(a,b);
1082 if (!i) {
1083 c = Balloc(PASS_STATE 0);
1084 c->wds = 1;
1085 c->x[0] = 0;
1086 return c;
1087 }
1088 if (i < 0) {
1089 c = a;
1090 a = b;
1091 b = c;
1092 i = 1;
1093 }
1094 else
1095 i = 0;
1096 c = Balloc(PASS_STATE a->k);
1097 c->sign = i;
1098 wa = a->wds;
1099 xa = a->x;
1100 xae = xa + wa;
1101 wb = b->wds;
1102 xb = b->x;
1103 xbe = xb + wb;
1104 xc = c->x;
1105 borrow = 0;
1106 #ifdef ULLong
1107 do {
1108 y = (ULLong)*xa++ - *xb++ - borrow;
1109 borrow = y >> 32 & (ULong)1;
1110 *xc++ = (ULong) y & FFFFFFFF;
1111 }
1112 while(xb < xbe);
1113 while(xa < xae) {
1114 y = *xa++ - borrow;
1115 borrow = y >> 32 & (ULong)1;
1116 *xc++ = (ULong) y & FFFFFFFF;
1117 }
1118 #else
1119 #ifdef Pack_32
1120 do {
1121 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1122 borrow = (y & 0x10000) >> 16;
1123 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1124 borrow = (z & 0x10000) >> 16;
1125 Storeinc(xc, z, y);
1126 }
1127 while(xb < xbe);
1128 while(xa < xae) {
1129 y = (*xa & 0xffff) - borrow;
1130 borrow = (y & 0x10000) >> 16;
1131 z = (*xa++ >> 16) - borrow;
1132 borrow = (z & 0x10000) >> 16;
1133 Storeinc(xc, z, y);
1134 }
1135 #else
1136 do {
1137 y = *xa++ - *xb++ - borrow;
1138 borrow = (y & 0x10000) >> 16;
1139 *xc++ = y & 0xffff;
1140 }
1141 while(xb < xbe);
1142 while(xa < xae) {
1143 y = *xa++ - borrow;
1144 borrow = (y & 0x10000) >> 16;
1145 *xc++ = y & 0xffff;
1146 }
1147 #endif
1148 #endif
1149 while(!*--xc)
1150 wa--;
1151 c->wds = wa;
1152 return c;
1153 }
1154
1155 static double
1156 ulp
1157 #ifdef KR_headers
1158 (x) U x;
1159 #else
1160 (U x)
1161 #endif
1162 {
1163 register Long L;
1164 U a;
1165
1166 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1167 #ifndef Avoid_Underflow
1168 #ifndef Sudden_Underflow
1169 if (L > 0) {
1170 #endif
1171 #endif
1172 #ifdef IBM
1173 L |= Exp_msk1 >> 4;
1174 #endif
1175 word0(a) = L;
1176 word1(a) = 0;
1177 #ifndef Avoid_Underflow
1178 #ifndef Sudden_Underflow
1179 }
1180 else {
1181 L = -L >> Exp_shift;
1182 if (L < Exp_shift) {
1183 word0(a) = 0x80000 >> L;
1184 word1(a) = 0;
1185 }
1186 else {
1187 word0(a) = 0;
1188 L -= Exp_shift;
1189 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1190 }
1191 }
1192 #endif
1193 #endif
1194 return dval(a);
1195 }
1196
1197 static double
1198 b2d
1199 #ifdef KR_headers
1200 (a, e) Bigint *a; int *e;
1201 #else
1202 (Bigint *a, int *e)
1203 #endif
1204 {
1205 ULong *xa, *xa0, w, y, z;
1206 int k;
1207 U d;
1208 #ifdef VAX
1209 ULong d0, d1;
1210 #else
1211 #define d0 word0(d)
1212 #define d1 word1(d)
1213 #endif
1214
1215 xa0 = a->x;
1216 xa = xa0 + a->wds;
1217 y = *--xa;
1218 #ifdef DEBUG
1219 if (!y) Bug("zero y in b2d");
1220 #endif
1221 k = hi0bits(y);
1222 *e = 32 - k;
1223 #ifdef Pack_32
1224 if (k < Ebits) {
1225 d0 = Exp_1 | y >> (Ebits - k);
1226 w = xa > xa0 ? *--xa : 0;
1227 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1228 goto ret_d;
1229 }
1230 z = xa > xa0 ? *--xa : 0;
1231 if (k -= Ebits) {
1232 d0 = Exp_1 | y << k | z >> (32 - k);
1233 y = xa > xa0 ? *--xa : 0;
1234 d1 = z << k | y >> (32 - k);
1235 }
1236 else {
1237 d0 = Exp_1 | y;
1238 d1 = z;
1239 }
1240 #else
1241 if (k < Ebits + 16) {
1242 z = xa > xa0 ? *--xa : 0;
1243 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1244 w = xa > xa0 ? *--xa : 0;
1245 y = xa > xa0 ? *--xa : 0;
1246 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1247 goto ret_d;
1248 }
1249 z = xa > xa0 ? *--xa : 0;
1250 w = xa > xa0 ? *--xa : 0;
1251 k -= Ebits + 16;
1252 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1253 y = xa > xa0 ? *--xa : 0;
1254 d1 = w << k + 16 | y << k;
1255 #endif
1256 ret_d:
1257 #ifdef VAX
1258 word0(d) = d0 >> 16 | d0 << 16;
1259 word1(d) = d1 >> 16 | d1 << 16;
1260 #else
1261 #undef d0
1262 #undef d1
1263 #endif
1264 return dval(d);
1265 }
1266
1267 static Bigint *
1268 d2b
1269 #ifdef KR_headers
1270 (STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
1271 #else
1272 (STATE_PARAM U d, int *e, int *bits)
1273 #endif
1274 {
1275 Bigint *b;
1276 int de, k;
1277 ULong *x, y, z;
1278 #ifndef Sudden_Underflow
1279 int i;
1280 #endif
1281 #ifdef VAX
1282 ULong d0, d1;
1283 d0 = word0(d) >> 16 | word0(d) << 16;
1284 d1 = word1(d) >> 16 | word1(d) << 16;
1285 #else
1286 #define d0 word0(d)
1287 #define d1 word1(d)
1288 #endif
1289
1290 #ifdef Pack_32
1291 b = Balloc(PASS_STATE 1);
1292 #else
1293 b = Balloc(PASS_STATE 2);
1294 #endif
1295 x = b->x;
1296
1297 z = d0 & Frac_mask;
1298 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1299 #ifdef Sudden_Underflow
1300 de = (int)(d0 >> Exp_shift);
1301 #ifndef IBM
1302 z |= Exp_msk11;
1303 #endif
1304 #else
1305 if ((de = (int)(d0 >> Exp_shift)))
1306 z |= Exp_msk1;
1307 #endif
1308 #ifdef Pack_32
1309 if ((y = d1)) {
1310 if ((k = lo0bits(&y))) {
1311 x[0] = y | z << (32 - k);
1312 z >>= k;
1313 }
1314 else
1315 x[0] = y;
1316 #ifndef Sudden_Underflow
1317 i =
1318 #endif
1319 b->wds = (x[1] = z) ? 2 : 1;
1320 }
1321 else {
1322 k = lo0bits(&z);
1323 x[0] = z;
1324 #ifndef Sudden_Underflow
1325 i =
1326 #endif
1327 b->wds = 1;
1328 k += 32;
1329 }
1330 #else
1331 if (y = d1) {
1332 if (k = lo0bits(&y))
1333 if (k >= 16) {
1334 x[0] = y | z << 32 - k & 0xffff;
1335 x[1] = z >> k - 16 & 0xffff;
1336 x[2] = z >> k;
1337 i = 2;
1338 }
1339 else {
1340 x[0] = y & 0xffff;
1341 x[1] = y >> 16 | z << 16 - k & 0xffff;
1342 x[2] = z >> k & 0xffff;
1343 x[3] = z >> k+16;
1344 i = 3;
1345 }
1346 else {
1347 x[0] = y & 0xffff;
1348 x[1] = y >> 16;
1349 x[2] = z & 0xffff;
1350 x[3] = z >> 16;
1351 i = 3;
1352 }
1353 }
1354 else {
1355 #ifdef DEBUG
1356 if (!z)
1357 Bug("Zero passed to d2b");
1358 #endif
1359 k = lo0bits(&z);
1360 if (k >= 16) {
1361 x[0] = z;
1362 i = 0;
1363 }
1364 else {
1365 x[0] = z & 0xffff;
1366 x[1] = z >> 16;
1367 i = 1;
1368 }
1369 k += 32;
1370 }
1371 while(!x[i])
1372 --i;
1373 b->wds = i + 1;
1374 #endif
1375 #ifndef Sudden_Underflow
1376 if (de) {
1377 #endif
1378 #ifdef IBM
1379 *e = (de - Bias - (P-1) << 2) + k;
1380 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1381 #else
1382 *e = de - Bias - (P-1) + k;
1383 *bits = P - k;
1384 #endif
1385 #ifndef Sudden_Underflow
1386 }
1387 else {
1388 *e = de - Bias - (P-1) + 1 + k;
1389 #ifdef Pack_32
1390 *bits = 32*i - hi0bits(x[i-1]);
1391 #else
1392 *bits = (i+2)*16 - hi0bits(x[i]);
1393 #endif
1394 }
1395 #endif
1396 return b;
1397 }
1398 #undef d0
1399 #undef d1
1400
1401 static double
1402 ratio
1403 #ifdef KR_headers
1404 (a, b) Bigint *a, *b;
1405 #else
1406 (Bigint *a, Bigint *b)
1407 #endif
1408 {
1409 U da, db;
1410 int k, ka, kb;
1411
1412 dval(da) = b2d(a, &ka);
1413 dval(db) = b2d(b, &kb);
1414 #ifdef Pack_32
1415 k = ka - kb + 32*(a->wds - b->wds);
1416 #else
1417 k = ka - kb + 16*(a->wds - b->wds);
1418 #endif
1419 #ifdef IBM
1420 if (k > 0) {
1421 word0(da) += (k >> 2)*Exp_msk1;
1422 if (k &= 3)
1423 dval(da) *= 1 << k;
1424 }
1425 else {
1426 k = -k;
1427 word0(db) += (k >> 2)*Exp_msk1;
1428 if (k &= 3)
1429 dval(db) *= 1 << k;
1430 }
1431 #else
1432 if (k > 0)
1433 word0(da) += k*Exp_msk1;
1434 else {
1435 k = -k;
1436 word0(db) += k*Exp_msk1;
1437 }
1438 #endif
1439 return dval(da) / dval(db);
1440 }
1441
1442 static CONST double
1443 tens[] = {
1444 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1445 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1446 1e20, 1e21, 1e22
1447 #ifdef VAX
1448 , 1e23, 1e24
1449 #endif
1450 };
1451
1452 static CONST double
1453 #ifdef IEEE_Arith
1454 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1455 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1456 #ifdef Avoid_Underflow
1457 9007199254740992.*9007199254740992.e-256
1458 /* = 2^106 * 1e-53 */
1459 #else
1460 1e-256
1461 #endif
1462 };
1463 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1464 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1465 #define Scale_Bit 0x10
1466 #define n_bigtens 5
1467 #else
1468 #ifdef IBM
1469 bigtens[] = { 1e16, 1e32, 1e64 };
1470 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1471 #define n_bigtens 3
1472 #else
1473 bigtens[] = { 1e16, 1e32 };
1474 static CONST double tinytens[] = { 1e-16, 1e-32 };
1475 #define n_bigtens 2
1476 #endif
1477 #endif
1478
1479 static double
1480 _strtod
1481 #ifdef KR_headers
1482 (STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se;
1483 #else
1484 (STATE_PARAM CONST char *s00, char **se)
1485 #endif
1486 {
1487 #ifdef Avoid_Underflow
1488 int scale;
1489 #endif
1490 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1491 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1492 CONST char *s, *s0, *s1;
1493 double aadj, adj;
1494 U aadj1, rv, rv0;
1495 Long L;
1496 ULong y, z;
1497 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1498 #ifdef SET_INEXACT
1499 int inexact, oldinexact;
1500 #endif
1501 #ifdef Honor_FLT_ROUNDS
1502 int rounding;
1503 #endif
1504 #ifdef USE_LOCALE
1505 CONST char *s2;
1506 #endif
1507
1508 #ifdef __GNUC__
1509 delta = bb = bd = bs = 0;
1510 #endif
1511
1512 sign = nz0 = nz = 0;
1513 dval(rv) = 0.;
1514 for(s = s00;;s++) switch(*s) {
1515 case '-':
1516 sign = 1;
1517 /* no break */
1518 case '+':
1519 if (*++s)
1520 goto break2;
1521 /* no break */
1522 case 0:
1523 goto ret0;
1524 case '\t':
1525 case '\n':
1526 case '\v':
1527 case '\f':
1528 case '\r':
1529 case ' ':
1530 continue;
1531 default:
1532 goto break2;
1533 }
1534 break2:
1535 if (*s == '0') {
1536 nz0 = 1;
1537 while(*++s == '0') ;
1538 if (!*s)
1539 goto ret;
1540 }
1541 s0 = s;
1542 y = z = 0;
1543 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1544 if (nd < 9)
1545 y = 10*y + c - '0';
1546 else if (nd < 16)
1547 z = 10*z + c - '0';
1548 nd0 = nd;
1549 #ifdef USE_LOCALE
1550 s1 = localeconv()->decimal_point;
1551 if (c == *s1) {
1552 c = '.';
1553 if (*++s1) {
1554 s2 = s;
1555 for(;;) {
1556 if (*++s2 != *s1) {
1557 c = 0;
1558 break;
1559 }
1560 if (!*++s1) {
1561 s = s2;
1562 break;
1563 }
1564 }
1565 }
1566 }
1567 #endif
1568 if (c == '.') {
1569 c = *++s;
1570 if (!nd) {
1571 for(; c == '0'; c = *++s)
1572 nz++;
1573 if (c > '0' && c <= '9') {
1574 s0 = s;
1575 nf += nz;
1576 nz = 0;
1577 goto have_dig;
1578 }
1579 goto dig_done;
1580 }
1581 for(; c >= '0' && c <= '9'; c = *++s) {
1582 have_dig:
1583 nz++;
1584 if (c -= '0') {
1585 nf += nz;
1586 for(i = 1; i < nz; i++)
1587 if (nd++ < 9)
1588 y *= 10;
1589 else if (nd <= DBL_DIG + 1)
1590 z *= 10;
1591 if (nd++ < 9)
1592 y = 10*y + c;
1593 else if (nd <= DBL_DIG + 1)
1594 z = 10*z + c;
1595 nz = 0;
1596 }
1597 }
1598 }
1599 dig_done:
1600 e = 0;
1601 if (c == 'e' || c == 'E') {
1602 if (!nd && !nz && !nz0) {
1603 goto ret0;
1604 }
1605 s00 = s;
1606 esign = 0;
1607 switch(c = *++s) {
1608 case '-':
1609 esign = 1;
1610 case '+':
1611 c = *++s;
1612 }
1613 if (c >= '0' && c <= '9') {
1614 while(c == '0')
1615 c = *++s;
1616 if (c > '0' && c <= '9') {
1617 L = c - '0';
1618 s1 = s;
1619 while((c = *++s) >= '0' && c <= '9')
1620 L = 10*L + c - '0';
1621 if (s - s1 > 8 || L > 19999)
1622 /* Avoid confusion from exponents
1623 * so large that e might overflow.
1624 */
1625 e = 19999; /* safe for 16 bit ints */
1626 else
1627 e = (int)L;
1628 if (esign)
1629 e = -e;
1630 }
1631 else
1632 e = 0;
1633 }
1634 else
1635 s = s00;
1636 }
1637 if (!nd) {
1638 if (!nz && !nz0) {
1639 ret0:
1640 s = s00;
1641 sign = 0;
1642 }
1643 goto ret;
1644 }
1645 e1 = e -= nf;
1646
1647 /* Now we have nd0 digits, starting at s0, followed by a
1648 * decimal point, followed by nd-nd0 digits. The number we're
1649 * after is the integer represented by those digits times
1650 * 10**e */
1651
1652 if (!nd0)
1653 nd0 = nd;
1654 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1655 dval(rv) = y;
1656 if (k > 9) {
1657 #ifdef SET_INEXACT
1658 if (k > DBL_DIG)
1659 oldinexact = get_inexact();
1660 #endif
1661 dval(rv) = tens[k - 9] * dval(rv) + z;
1662 }
1663 bd0 = 0;
1664 if (nd <= DBL_DIG
1665 #ifndef RND_PRODQUOT
1666 #ifndef Honor_FLT_ROUNDS
1667 && Flt_Rounds == 1
1668 #endif
1669 #endif
1670 ) {
1671 if (!e)
1672 goto ret;
1673 if (e > 0) {
1674 if (e <= Ten_pmax) {
1675 #ifdef VAX
1676 goto vax_ovfl_check;
1677 #else
1678 #ifdef Honor_FLT_ROUNDS
1679 /* round correctly FLT_ROUNDS = 2 or 3 */
1680 if (sign) {
1681 rv = -rv;
1682 sign = 0;
1683 }
1684 #endif
1685 /* rv = */ rounded_product(dval(rv), tens[e]);
1686 goto ret;
1687 #endif
1688 }
1689 i = DBL_DIG - nd;
1690 if (e <= Ten_pmax + i) {
1691 /* A fancier test would sometimes let us do
1692 * this for larger i values.
1693 */
1694 #ifdef Honor_FLT_ROUNDS
1695 /* round correctly FLT_ROUNDS = 2 or 3 */
1696 if (sign) {
1697 rv = -rv;
1698 sign = 0;
1699 }
1700 #endif
1701 e -= i;
1702 dval(rv) *= tens[i];
1703 #ifdef VAX
1704 /* VAX exponent range is so narrow we must
1705 * worry about overflow here...
1706 */
1707 vax_ovfl_check:
1708 word0(rv) -= P*Exp_msk1;
1709 /* rv = */ rounded_product(dval(rv), tens[e]);
1710 if ((word0(rv) & Exp_mask)
1711 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1712 goto ovfl;
1713 word0(rv) += P*Exp_msk1;
1714 #else
1715 /* rv = */ rounded_product(dval(rv), tens[e]);
1716 #endif
1717 goto ret;
1718 }
1719 }
1720 #ifndef Inaccurate_Divide
1721 else if (e >= -Ten_pmax) {
1722 #ifdef Honor_FLT_ROUNDS
1723 /* round correctly FLT_ROUNDS = 2 or 3 */
1724 if (sign) {
1725 rv = -rv;
1726 sign = 0;
1727 }
1728 #endif
1729 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1730 goto ret;
1731 }
1732 #endif
1733 }
1734 e1 += nd - k;
1735
1736 #ifdef IEEE_Arith
1737 #ifdef SET_INEXACT
1738 inexact = 1;
1739 if (k <= DBL_DIG)
1740 oldinexact = get_inexact();
1741 #endif
1742 #ifdef Avoid_Underflow
1743 scale = 0;
1744 #endif
1745 #ifdef Honor_FLT_ROUNDS
1746 if ((rounding = Flt_Rounds) >= 2) {
1747 if (sign)
1748 rounding = rounding == 2 ? 0 : 2;
1749 else
1750 if (rounding != 2)
1751 rounding = 0;
1752 }
1753 #endif
1754 #endif /*IEEE_Arith*/
1755
1756 /* Get starting approximation = rv * 10**e1 */
1757
1758 if (e1 > 0) {
1759 if ((i = e1 & 15))
1760 dval(rv) *= tens[i];
1761 if (e1 &= ~15) {
1762 if (e1 > DBL_MAX_10_EXP) {
1763 ovfl:
1764 #ifndef NO_ERRNO
1765 errno = ERANGE;
1766 #endif
1767 /* Can't trust HUGE_VAL */
1768 #ifdef IEEE_Arith
1769 #ifdef Honor_FLT_ROUNDS
1770 switch(rounding) {
1771 case 0: /* toward 0 */
1772 case 3: /* toward -infinity */
1773 word0(rv) = Big0;
1774 word1(rv) = Big1;
1775 break;
1776 default:
1777 word0(rv) = Exp_mask;
1778 word1(rv) = 0;
1779 }
1780 #else /*Honor_FLT_ROUNDS*/
1781 word0(rv) = Exp_mask;
1782 word1(rv) = 0;
1783 #endif /*Honor_FLT_ROUNDS*/
1784 #ifdef SET_INEXACT
1785 /* set overflow bit */
1786 dval(rv0) = 1e300;
1787 dval(rv0) *= dval(rv0);
1788 #endif
1789 #else /*IEEE_Arith*/
1790 word0(rv) = Big0;
1791 word1(rv) = Big1;
1792 #endif /*IEEE_Arith*/
1793 if (bd0)
1794 goto retfree;
1795 goto ret;
1796 }
1797 e1 >>= 4;
1798 for(j = 0; e1 > 1; j++, e1 >>= 1)
1799 if (e1 & 1)
1800 dval(rv) *= bigtens[j];
1801 /* The last multiplication could overflow. */
1802 word0(rv) -= P*Exp_msk1;
1803 dval(rv) *= bigtens[j];
1804 if ((z = word0(rv) & Exp_mask)
1805 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1806 goto ovfl;
1807 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1808 /* set to largest number */
1809 /* (Can't trust DBL_MAX) */
1810 word0(rv) = Big0;
1811 word1(rv) = Big1;
1812 }
1813 else
1814 word0(rv) += P*Exp_msk1;
1815 }
1816 }
1817 else if (e1 < 0) {
1818 e1 = -e1;
1819 if ((i = e1 & 15))
1820 dval(rv) /= tens[i];
1821 if (e1 >>= 4) {
1822 if (e1 >= 1 << n_bigtens)
1823 goto undfl;
1824 #ifdef Avoid_Underflow
1825 if (e1 & Scale_Bit)
1826 scale = 2*P;
1827 for(j = 0; e1 > 0; j++, e1 >>= 1)
1828 if (e1 & 1)
1829 dval(rv) *= tinytens[j];
1830 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1831 >> Exp_shift)) > 0) {
1832 /* scaled rv is denormal; zap j low bits */
1833 if (j >= 32) {
1834 word1(rv) = 0;
1835 if (j >= 53)
1836 word0(rv) = (P+2)*Exp_msk1;
1837 else
1838 word0(rv) &= 0xffffffff << (j-32);
1839 }
1840 else
1841 word1(rv) &= 0xffffffff << j;
1842 }
1843 #else
1844 for(j = 0; e1 > 1; j++, e1 >>= 1)
1845 if (e1 & 1)
1846 dval(rv) *= tinytens[j];
1847 /* The last multiplication could underflow. */
1848 dval(rv0) = dval(rv);
1849 dval(rv) *= tinytens[j];
1850 if (!dval(rv)) {
1851 dval(rv) = 2.*dval(rv0);
1852 dval(rv) *= tinytens[j];
1853 #endif
1854 if (!dval(rv)) {
1855 undfl:
1856 dval(rv) = 0.;
1857 #ifndef NO_ERRNO
1858 errno = ERANGE;
1859 #endif
1860 if (bd0)
1861 goto retfree;
1862 goto ret;
1863 }
1864 #ifndef Avoid_Underflow
1865 word0(rv) = Tiny0;
1866 word1(rv) = Tiny1;
1867 /* The refinement below will clean
1868 * this approximation up.
1869 */
1870 }
1871 #endif
1872 }
1873 }
1874
1875 /* Now the hard part -- adjusting rv to the correct value.*/
1876
1877 /* Put digits into bd: true value = bd * 10^e */
1878
1879 bd0 = s2b(PASS_STATE s0, nd0, nd, y);
1880
1881 for(;;) {
1882 bd = Balloc(PASS_STATE bd0->k);
1883 Bcopy(bd, bd0);
1884 bb = d2b(PASS_STATE rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
1885 bs = i2b(PASS_STATE 1);
1886
1887 if (e >= 0) {
1888 bb2 = bb5 = 0;
1889 bd2 = bd5 = e;
1890 }
1891 else {
1892 bb2 = bb5 = -e;
1893 bd2 = bd5 = 0;
1894 }
1895 if (bbe >= 0)
1896 bb2 += bbe;
1897 else
1898 bd2 -= bbe;
1899 bs2 = bb2;
1900 #ifdef Honor_FLT_ROUNDS
1901 if (rounding != 1)
1902 bs2++;
1903 #endif
1904 #ifdef Avoid_Underflow
1905 j = bbe - scale;
1906 i = j + bbbits - 1; /* logb(rv) */
1907 if (i < Emin) /* denormal */
1908 j += P - Emin;
1909 else
1910 j = P + 1 - bbbits;
1911 #else /*Avoid_Underflow*/
1912 #ifdef Sudden_Underflow
1913 #ifdef IBM
1914 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1915 #else
1916 j = P + 1 - bbbits;
1917 #endif
1918 #else /*Sudden_Underflow*/
1919 j = bbe;
1920 i = j + bbbits - 1; /* logb(rv) */
1921 if (i < Emin) /* denormal */
1922 j += P - Emin;
1923 else
1924 j = P + 1 - bbbits;
1925 #endif /*Sudden_Underflow*/
1926 #endif /*Avoid_Underflow*/
1927 bb2 += j;
1928 bd2 += j;
1929 #ifdef Avoid_Underflow
1930 bd2 += scale;
1931 #endif
1932 i = bb2 < bd2 ? bb2 : bd2;
1933 if (i > bs2)
1934 i = bs2;
1935 if (i > 0) {
1936 bb2 -= i;
1937 bd2 -= i;
1938 bs2 -= i;
1939 }
1940 if (bb5 > 0) {
1941 bs = pow5mult(PASS_STATE bs, bb5);
1942 bb1 = mult(PASS_STATE bs, bb);
1943 Bfree(PASS_STATE bb);
1944 bb = bb1;
1945 }
1946 if (bb2 > 0)
1947 bb = lshift(PASS_STATE bb, bb2);
1948 if (bd5 > 0)
1949 bd = pow5mult(PASS_STATE bd, bd5);
1950 if (bd2 > 0)
1951 bd = lshift(PASS_STATE bd, bd2);
1952 if (bs2 > 0)
1953 bs = lshift(PASS_STATE bs, bs2);
1954 delta = diff(PASS_STATE bb, bd);
1955 dsign = delta->sign;
1956 delta->sign = 0;
1957 i = cmp(delta, bs);
1958 #ifdef Honor_FLT_ROUNDS
1959 if (rounding != 1) {
1960 if (i < 0) {
1961 /* Error is less than an ulp */
1962 if (!delta->x[0] && delta->wds <= 1) {
1963 /* exact */
1964 #ifdef SET_INEXACT
1965 inexact = 0;
1966 #endif
1967 break;
1968 }
1969 if (rounding) {
1970 if (dsign) {
1971 adj = 1.;
1972 goto apply_adj;
1973 }
1974 }
1975 else if (!dsign) {
1976 adj = -1.;
1977 if (!word1(rv)
1978 && !(word0(rv) & Frac_mask)) {
1979 y = word0(rv) & Exp_mask;
1980 #ifdef Avoid_Underflow
1981 if (!scale || y > 2*P*Exp_msk1)
1982 #else
1983 if (y)
1984 #endif
1985 {
1986 delta = lshift(PASS_STATE delta,Log2P);
1987 if (cmp(delta, bs) <= 0)
1988 adj = -0.5;
1989 }
1990 }
1991 apply_adj:
1992 #ifdef Avoid_Underflow
1993 if (scale && (y = word0(rv) & Exp_mask)
1994 <= 2*P*Exp_msk1)
1995 word0(adj) += (2*P+1)*Exp_msk1 - y;
1996 #else
1997 #ifdef Sudden_Underflow
1998 if ((word0(rv) & Exp_mask) <=
1999 P*Exp_msk1) {
2000 word0(rv) += P*Exp_msk1;
2001 dval(rv) += adj*ulp(rv);
2002 word0(rv) -= P*Exp_msk1;
2003 }
2004 else
2005 #endif /*Sudden_Underflow*/
2006 #endif /*Avoid_Underflow*/
2007 dval(rv) += adj*ulp(rv);
2008 }
2009 break;
2010 }
2011 adj = ratio(delta, bs);
2012 if (adj < 1.)
2013 adj = 1.;
2014 if (adj <= 0x7ffffffe) {
2015 /* adj = rounding ? ceil(adj) : floor(adj); */
2016 y = adj;
2017 if (y != adj) {
2018 if (!((rounding>>1) ^ dsign))
2019 y++;
2020 adj = y;
2021 }
2022 }
2023 #ifdef Avoid_Underflow
2024 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2025 word0(adj) += (2*P+1)*Exp_msk1 - y;
2026 #else
2027 #ifdef Sudden_Underflow
2028 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2029 word0(rv) += P*Exp_msk1;
2030 adj *= ulp(rv);
2031 if (dsign)
2032 dval(rv) += adj;
2033 else
2034 dval(rv) -= adj;
2035 word0(rv) -= P*Exp_msk1;
2036 goto cont;
2037 }
2038 #endif /*Sudden_Underflow*/
2039 #endif /*Avoid_Underflow*/
2040 adj *= ulp(rv);
2041 if (dsign)
2042 dval(rv) += adj;
2043 else
2044 dval(rv) -= adj;
2045 goto cont;
2046 }
2047 #endif /*Honor_FLT_ROUNDS*/
2048
2049 if (i < 0) {
2050 /* Error is less than half an ulp -- check for
2051 * special case of mantissa a power of two.
2052 */
2053 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2054 #ifdef IEEE_Arith
2055 #ifdef Avoid_Underflow
2056 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2057 #else
2058 || (word0(rv) & Exp_mask) <= Exp_msk1
2059 #endif
2060 #endif
2061 ) {
2062 #ifdef SET_INEXACT
2063 if (!delta->x[0] && delta->wds <= 1)
2064 inexact = 0;
2065 #endif
2066 break;
2067 }
2068 if (!delta->x[0] && delta->wds <= 1) {
2069 /* exact result */
2070 #ifdef SET_INEXACT
2071 inexact = 0;
2072 #endif
2073 break;
2074 }
2075 delta = lshift(PASS_STATE delta,Log2P);
2076 if (cmp(delta, bs) > 0)
2077 goto drop_down;
2078 break;
2079 }
2080 if (i == 0) {
2081 /* exactly half-way between */
2082 if (dsign) {
2083 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2084 && word1(rv) == (
2085 #ifdef Avoid_Underflow
2086 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2087 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2088 #endif
2089 0xffffffff)) {
2090 /*boundary case -- increment exponent*/
2091 word0(rv) = (word0(rv) & Exp_mask)
2092 + Exp_msk1
2093 #ifdef IBM
2094 | Exp_msk1 >> 4
2095 #endif
2096 ;
2097 word1(rv) = 0;
2098 #ifdef Avoid_Underflow
2099 dsign = 0;
2100 #endif
2101 break;
2102 }
2103 }
2104 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2105 drop_down:
2106 /* boundary case -- decrement exponent */
2107 #ifdef Sudden_Underflow /*{{*/
2108 L = word0(rv) & Exp_mask;
2109 #ifdef IBM
2110 if (L < Exp_msk1)
2111 #else
2112 #ifdef Avoid_Underflow
2113 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2114 #else
2115 if (L <= Exp_msk1)
2116 #endif /*Avoid_Underflow*/
2117 #endif /*IBM*/
2118 goto undfl;
2119 L -= Exp_msk1;
2120 #else /*Sudden_Underflow}{*/
2121 #ifdef Avoid_Underflow
2122 if (scale) {
2123 L = word0(rv) & Exp_mask;
2124 if (L <= (2*P+1)*Exp_msk1) {
2125 if (L > (P+2)*Exp_msk1)
2126 /* round even ==> */
2127 /* accept rv */
2128 break;
2129 /* rv = smallest denormal */
2130 goto undfl;
2131 }
2132 }
2133 #endif /*Avoid_Underflow*/
2134 L = (word0(rv) & Exp_mask) - Exp_msk1;
2135 #endif /*Sudden_Underflow}}*/
2136 word0(rv) = L | Bndry_mask1;
2137 word1(rv) = 0xffffffff;
2138 #ifdef IBM
2139 goto cont;
2140 #else
2141 break;
2142 #endif
2143 }
2144 #ifndef ROUND_BIASED
2145 if (!(word1(rv) & LSB))
2146 break;
2147 #endif
2148 if (dsign)
2149 dval(rv) += ulp(rv);
2150 #ifndef ROUND_BIASED
2151 else {
2152 dval(rv) -= ulp(rv);
2153 #ifndef Sudden_Underflow
2154 if (!dval(rv))
2155 goto undfl;
2156 #endif
2157 }
2158 #ifdef Avoid_Underflow
2159 dsign = 1 - dsign;
2160 #endif
2161 #endif
2162 break;
2163 }
2164 if ((aadj = ratio(delta, bs)) <= 2.) {
2165 if (dsign)
2166 aadj = dval(aadj1) = 1.;
2167 else if (word1(rv) || word0(rv) & Bndry_mask) {
2168 #ifndef Sudden_Underflow
2169 if (word1(rv) == Tiny1 && !word0(rv))
2170 goto undfl;
2171 #endif
2172 aadj = 1.;
2173 dval(aadj1) = -1.;
2174 }
2175 else {
2176 /* special case -- power of FLT_RADIX to be */
2177 /* rounded down... */
2178
2179 if (aadj < 2./FLT_RADIX)
2180 aadj = 1./FLT_RADIX;
2181 else
2182 aadj *= 0.5;
2183 dval(aadj1) = -aadj;
2184 }
2185 }
2186 else {
2187 aadj *= 0.5;
2188 dval(aadj1) = dsign ? aadj : -aadj;
2189 #ifdef Check_FLT_ROUNDS
2190 switch(Rounding) {
2191 case 2: /* towards +infinity */
2192 dval(aadj1) -= 0.5;
2193 break;
2194 case 0: /* towards 0 */
2195 case 3: /* towards -infinity */
2196 dval(aadj1) += 0.5;
2197 }
2198 #else
2199 if (Flt_Rounds == 0)
2200 dval(aadj1) += 0.5;
2201 #endif /*Check_FLT_ROUNDS*/
2202 }
2203 y = word0(rv) & Exp_mask;
2204
2205 /* Check for overflow */
2206
2207 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2208 dval(rv0) = dval(rv);
2209 word0(rv) -= P*Exp_msk1;
2210 adj = dval(aadj1) * ulp(rv);
2211 dval(rv) += adj;
2212 if ((word0(rv) & Exp_mask) >=
2213 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2214 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2215 goto ovfl;
2216 word0(rv) = Big0;
2217 word1(rv) = Big1;
2218 goto cont;
2219 }
2220 else
2221 word0(rv) += P*Exp_msk1;
2222 }
2223 else {
2224 #ifdef Avoid_Underflow
2225 if (scale && y <= 2*P*Exp_msk1) {
2226 if (aadj <= 0x7fffffff) {
2227 if ((z = (ULong) aadj) <= 0)
2228 z = 1;
2229 aadj = z;
2230 dval(aadj1) = dsign ? aadj : -aadj;
2231 }
2232 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2233 }
2234 adj = dval(aadj1) * ulp(rv);
2235 dval(rv) += adj;
2236 #else
2237 #ifdef Sudden_Underflow
2238 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2239 dval(rv0) = dval(rv);
2240 word0(rv) += P*Exp_msk1;
2241 adj = dval(aadj1) * ulp(rv);
2242 dval(rv) += adj;
2243 #ifdef IBM
2244 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2245 #else
2246 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2247 #endif
2248 {
2249 if (word0(rv0) == Tiny0
2250 && word1(rv0) == Tiny1)
2251 goto undfl;
2252 word0(rv) = Tiny0;
2253 word1(rv) = Tiny1;
2254 goto cont;
2255 }
2256 else
2257 word0(rv) -= P*Exp_msk1;
2258 }
2259 else {
2260 adj = dval(aadj1) * ulp(rv);
2261 dval(rv) += adj;
2262 }
2263 #else /*Sudden_Underflow*/
2264 /* Compute adj so that the IEEE rounding rules will
2265 * correctly round rv + adj in some half-way cases.
2266 * If rv * ulp(rv) is denormalized (i.e.,
2267 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2268 * trouble from bits lost to denormalization;
2269 * example: 1.2e-307 .
2270 */
2271 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2272 dval(aadj1) = (double)(int)(aadj + 0.5);
2273 if (!dsign)
2274 dval(aadj1) = -dval(aadj1);
2275 }
2276 adj = dval(aadj1) * ulp(rv);
2277 dval(rv) += adj;
2278 #endif /*Sudden_Underflow*/
2279 #endif /*Avoid_Underflow*/
2280 }
2281 z = word0(rv) & Exp_mask;
2282 #ifndef SET_INEXACT
2283 #ifdef Avoid_Underflow
2284 if (!scale)
2285 #endif
2286 if (y == z) {
2287 /* Can we stop now? */
2288 L = (Long)aadj;
2289 aadj -= L;
2290 /* The tolerances below are conservative. */
2291 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2292 if (aadj < .4999999 || aadj > .5000001)
2293 break;
2294 }
2295 else if (aadj < .4999999/FLT_RADIX)
2296 break;
2297 }
2298 #endif
2299 cont:
2300 Bfree(PASS_STATE bb);
2301 Bfree(PASS_STATE bd);
2302 Bfree(PASS_STATE bs);
2303 Bfree(PASS_STATE delta);
2304 }
2305 #ifdef SET_INEXACT
2306 if (inexact) {
2307 if (!oldinexact) {
2308 word0(rv0) = Exp_1 + (70 << Exp_shift);
2309 word1(rv0) = 0;
2310 dval(rv0) += 1.;
2311 }
2312 }
2313 else if (!oldinexact)
2314 clear_inexact();
2315 #endif
2316 #ifdef Avoid_Underflow
2317 if (scale) {
2318 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2319 word1(rv0) = 0;
2320 dval(rv) *= dval(rv0);
2321 #ifndef NO_ERRNO
2322 /* try to avoid the bug of testing an 8087 register value */
2323 if (word0(rv) == 0 && word1(rv) == 0)
2324 errno = ERANGE;
2325 #endif
2326 }
2327 #endif /* Avoid_Underflow */
2328 #ifdef SET_INEXACT
2329 if (inexact && !(word0(rv) & Exp_mask)) {
2330 /* set underflow bit */
2331 dval(rv0) = 1e-300;
2332 dval(rv0) *= dval(rv0);
2333 }
2334 #endif
2335 retfree:
2336 Bfree(PASS_STATE bb);
2337 Bfree(PASS_STATE bd);
2338 Bfree(PASS_STATE bs);
2339 Bfree(PASS_STATE bd0);
2340 Bfree(PASS_STATE delta);
2341 ret:
2342 if (se)
2343 *se = (char *)s;
2344 return sign ? -dval(rv) : dval(rv);
2345 }
2346
2347 static int
2348 quorem
2349 #ifdef KR_headers
2350 (b, S) Bigint *b, *S;
2351 #else
2352 (Bigint *b, Bigint *S)
2353 #endif
2354 {
2355 int n;
2356 ULong *bx, *bxe, q, *sx, *sxe;
2357 #ifdef ULLong
2358 ULLong borrow, carry, y, ys;
2359 #else
2360 ULong borrow, carry, y, ys;
2361 #ifdef Pack_32
2362 ULong si, z, zs;
2363 #endif
2364 #endif
2365
2366 n = S->wds;
2367 #ifdef DEBUG
2368 /*debug*/ if (b->wds > n)
2369 /*debug*/ Bug("oversize b in quorem");
2370 #endif
2371 if (b->wds < n)
2372 return 0;
2373 sx = S->x;
2374 sxe = sx + --n;
2375 bx = b->x;
2376 bxe = bx + n;
2377 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2378 #ifdef DEBUG
2379 /*debug*/ if (q > 9)
2380 /*debug*/ Bug("oversized quotient in quorem");
2381 #endif
2382 if (q) {
2383 borrow = 0;
2384 carry = 0;
2385 do {
2386 #ifdef ULLong
2387 ys = *sx++ * (ULLong)q + carry;
2388 carry = ys >> 32;
2389 y = *bx - (ys & FFFFFFFF) - borrow;
2390 borrow = y >> 32 & (ULong)1;
2391 *bx++ = (ULong) y & FFFFFFFF;
2392 #else
2393 #ifdef Pack_32
2394 si = *sx++;
2395 ys = (si & 0xffff) * q + carry;
2396 zs = (si >> 16) * q + (ys >> 16);
2397 carry = zs >> 16;
2398 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2399 borrow = (y & 0x10000) >> 16;
2400 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2401 borrow = (z & 0x10000) >> 16;
2402 Storeinc(bx, z, y);
2403 #else
2404 ys = *sx++ * q + carry;
2405 carry = ys >> 16;
2406 y = *bx - (ys & 0xffff) - borrow;
2407 borrow = (y & 0x10000) >> 16;
2408 *bx++ = y & 0xffff;
2409 #endif
2410 #endif
2411 }
2412 while(sx <= sxe);
2413 if (!*bxe) {
2414 bx = b->x;
2415 while(--bxe > bx && !*bxe)
2416 --n;
2417 b->wds = n;
2418 }
2419 }
2420 if (cmp(b, S) >= 0) {
2421 q++;
2422 borrow = 0;
2423 carry = 0;
2424 bx = b->x;
2425 sx = S->x;
2426 do {
2427 #ifdef ULLong
2428 ys = *sx++ + carry;
2429 carry = ys >> 32;
2430 y = *bx - (ys & FFFFFFFF) - borrow;
2431 borrow = y >> 32 & (ULong)1;
2432 *bx++ = (ULong) y & FFFFFFFF;
2433 #else
2434 #ifdef Pack_32
2435 si = *sx++;
2436 ys = (si & 0xffff) + carry;
2437 zs = (si >> 16) + (ys >> 16);
2438 carry = zs >> 16;
2439 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2440 borrow = (y & 0x10000) >> 16;
2441 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2442 borrow = (z & 0x10000) >> 16;
2443 Storeinc(bx, z, y);
2444 #else
2445 ys = *sx++ + carry;
2446 carry = ys >> 16;
2447 y = *bx - (ys & 0xffff) - borrow;
2448 borrow = (y & 0x10000) >> 16;
2449 *bx++ = y & 0xffff;
2450 #endif
2451 #endif
2452 }
2453 while(sx <= sxe);
2454 bx = b->x;
2455 bxe = bx + n;
2456 if (!*bxe) {
2457 while(--bxe > bx && !*bxe)
2458 --n;
2459 b->wds = n;
2460 }
2461 }
2462 return q;
2463 }
2464
2465 #if !defined(MULTIPLE_THREADS) && !defined(NO_GLOBAL_STATE)
2466 #define USE_DTOA_RESULT 1
2467 static char *dtoa_result;
2468 #endif
2469
2470 static char *
2471 #ifdef KR_headers
2472 rv_alloc(STATE_PARAM i) STATE_PARAM_DECL int i;
2473 #else
2474 rv_alloc(STATE_PARAM int i)
2475 #endif
2476 {
2477 int j, k, *r;
2478
2479 j = sizeof(ULong);
2480 for(k = 0;
2481 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned) i;
2482 j <<= 1)
2483 k++;
2484 r = (int*)Balloc(PASS_STATE k);
2485 *r = k;
2486 return
2487 #ifdef USE_DTOA_RESULT
2488 dtoa_result =
2489 #endif
2490 (char *)(r+1);
2491 }
2492
2493 static char *
2494 #ifdef KR_headers
2495 nrv_alloc(STATE_PARAM s, rve, n) STATE_PARAM_DECL char *s, **rve; int n;
2496 #else
2497 nrv_alloc(STATE_PARAM CONST char *s, char **rve, int n)
2498 #endif
2499 {
2500 char *rv, *t;
2501
2502 t = rv = rv_alloc(PASS_STATE n);
2503 while((*t = *s++)) t++;
2504 if (rve)
2505 *rve = t;
2506 return rv;
2507 }
2508
2509 /* freedtoa(s) must be used to free values s returned by dtoa
2510 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2511 * but for consistency with earlier versions of dtoa, it is optional
2512 * when MULTIPLE_THREADS is not defined.
2513 */
2514
2515 static void
2516 #ifdef KR_headers
2517 freedtoa(STATE_PARAM s) STATE_PARAM_DECL char *s;
2518 #else
2519 freedtoa(STATE_PARAM char *s)
2520 #endif
2521 {
2522 Bigint *b = (Bigint *)((int *)s - 1);
2523 b->maxwds = 1 << (b->k = *(int*)b);
2524 Bfree(PASS_STATE b);
2525 #ifdef USE_DTOA_RESULT
2526 if (s == dtoa_result)
2527 dtoa_result = 0;
2528 #endif
2529 }
2530
2531 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2532 *
2533 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2534 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2535 *
2536 * Modifications:
2537 * 1. Rather than iterating, we use a simple numeric overestimate
2538 * to determine k = floor(log10(d)). We scale relevant
2539 * quantities using O(log2(k)) rather than O(k) multiplications.
2540 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2541 * try to generate digits strictly left to right. Instead, we
2542 * compute with fewer bits and propagate the carry if necessary
2543 * when rounding the final digit up. This is often faster.
2544 * 3. Under the assumption that input will be rounded nearest,
2545 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2546 * That is, we allow equality in stopping tests when the
2547 * round-nearest rule will give the same floating-point value
2548 * as would satisfaction of the stopping test with strict
2549 * inequality.
2550 * 4. We remove common factors of powers of 2 from relevant
2551 * quantities.
2552 * 5. When converting floating-point integers less than 1e16,
2553 * we use floating-point arithmetic rather than resorting
2554 * to multiple-precision integers.
2555 * 6. When asked to produce fewer than 15 digits, we first try
2556 * to get by with floating-point arithmetic; we resort to
2557 * multiple-precision integer arithmetic only if we cannot
2558 * guarantee that the floating-point calculation has given
2559 * the correctly rounded result. For k requested digits and
2560 * "uniformly" distributed input, the probability is
2561 * something like 10^(k-15) that we must resort to the Long
2562 * calculation.
2563 */
2564
2565 static char *
2566 dtoa
2567 #ifdef KR_headers
2568 (STATE_PARAM d, mode, ndigits, decpt, sign, rve)
2569 STATE_PARAM_DECL U d; int mode, ndigits, *decpt, *sign; char **rve;
2570 #else
2571 (STATE_PARAM U d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2572 #endif
2573 {
2574 /* Arguments ndigits, decpt, sign are similar to those
2575 of ecvt and fcvt; trailing zeros are suppressed from
2576 the returned string. If not null, *rve is set to point
2577 to the end of the return value. If d is +-Infinity or NaN,
2578 then *decpt is set to 9999.
2579
2580 mode:
2581 0 ==> shortest string that yields d when read in
2582 and rounded to nearest.
2583 1 ==> like 0, but with Steele & White stopping rule;
2584 e.g. with IEEE P754 arithmetic , mode 0 gives
2585 1e23 whereas mode 1 gives 9.999999999999999e22.
2586 2 ==> max(1,ndigits) significant digits. This gives a
2587 return value similar to that of ecvt, except
2588 that trailing zeros are suppressed.
2589 3 ==> through ndigits past the decimal point. This
2590 gives a return value similar to that from fcvt,
2591 except that trailing zeros are suppressed, and
2592 ndigits can be negative.
2593 4,5 ==> similar to 2 and 3, respectively, but (in
2594 round-nearest mode) with the tests of mode 0 to
2595 possibly return a shorter string that rounds to d.
2596 With IEEE arithmetic and compilation with
2597 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2598 as modes 2 and 3 when FLT_ROUNDS != 1.
2599 6-9 ==> Debugging modes similar to mode - 4: don't try
2600 fast floating-point estimate (if applicable).
2601
2602 Values of mode other than 0-9 are treated as mode 0.
2603
2604 Sufficient space is allocated to the return value
2605 to hold the suppressed trailing zeros.
2606 */
2607
2608 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2609 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2610 spec_case, try_quick;
2611 Long L;
2612 #ifndef Sudden_Underflow
2613 int denorm;
2614 ULong x;
2615 #endif
2616 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2617 U d2, eps;
2618 double ds;
2619 char *s, *s0;
2620 #ifdef Honor_FLT_ROUNDS
2621 int rounding;
2622 #endif
2623 #ifdef SET_INEXACT
2624 int inexact, oldinexact;
2625 #endif
2626
2627 #ifdef __GNUC__
2628 ilim = ilim1 = 0;
2629 mlo = NULL;
2630 #endif
2631
2632 #ifdef USE_DTOA_RESULT
2633 if (dtoa_result) {
2634 freedtoa(PASS_STATE dtoa_result);
2635 dtoa_result = 0;
2636 }
2637 #endif
2638
2639 if (word0(d) & Sign_bit) {
2640 /* set sign for everything, including 0's and NaNs */
2641 *sign = 1;
2642 word0(d) &= ~Sign_bit; /* clear sign bit */
2643 }
2644 else
2645 *sign = 0;
2646
2647 #if defined(IEEE_Arith) + defined(VAX)
2648 #ifdef IEEE_Arith
2649 if ((word0(d) & Exp_mask) == Exp_mask)
2650 #else
2651 if (word0(d) == 0x8000)
2652 #endif
2653 {
2654 /* Infinity or NaN */
2655 *decpt = 9999;
2656 #ifdef IEEE_Arith
2657 if (!word1(d) && !(word0(d) & 0xfffff))
2658 return nrv_alloc(PASS_STATE "Infinity", rve, 8);
2659 #endif
2660 return nrv_alloc(PASS_STATE "NaN", rve, 3);
2661 }
2662 #endif
2663 #ifdef IBM
2664 dval(d) += 0; /* normalize */
2665 #endif
2666 if (!dval(d)) {
2667 *decpt = 1;
2668 return nrv_alloc(PASS_STATE "0", rve, 1);
2669 }
2670
2671 #ifdef SET_INEXACT
2672 try_quick = oldinexact = get_inexact();
2673 inexact = 1;
2674 #endif
2675 #ifdef Honor_FLT_ROUNDS
2676 if ((rounding = Flt_Rounds) >= 2) {
2677 if (*sign)
2678 rounding = rounding == 2 ? 0 : 2;
2679 else
2680 if (rounding != 2)
2681 rounding = 0;
2682 }
2683 #endif
2684
2685 b = d2b(PASS_STATE d, &be, &bbits);
2686 #ifdef Sudden_Underflow
2687 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2688 #else
2689 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
2690 #endif
2691 dval(d2) = dval(d);
2692 word0(d2) &= Frac_mask1;
2693 word0(d2) |= Exp_11;
2694 #ifdef IBM
2695 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2696 dval(d2) /= 1 << j;
2697 #endif
2698
2699 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2700 * log10(x) = log(x) / log(10)
2701 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2702 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2703 *
2704 * This suggests computing an approximation k to log10(d) by
2705 *
2706 * k = (i - Bias)*0.301029995663981
2707 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2708 *
2709 * We want k to be too large rather than too small.
2710 * The error in the first-order Taylor series approximation
2711 * is in our favor, so we just round up the constant enough
2712 * to compensate for any error in the multiplication of
2713 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2714 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2715 * adding 1e-13 to the constant term more than suffices.
2716 * Hence we adjust the constant term to 0.1760912590558.
2717 * (We could get a more accurate k by invoking log10,
2718 * but this is probably not worthwhile.)
2719 */
2720
2721 i -= Bias;
2722 #ifdef IBM
2723 i <<= 2;
2724 i += j;
2725 #endif
2726 #ifndef Sudden_Underflow
2727 denorm = 0;
2728 }
2729 else {
2730 /* d is denormalized */
2731
2732 i = bbits + be + (Bias + (P-1) - 1);
2733 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2734 : word1(d) << (32 - i);
2735 dval(d2) = x;
2736 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2737 i -= (Bias + (P-1) - 1) + 1;
2738 denorm = 1;
2739 }
2740 #endif
2741 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2742 k = (int)ds;
2743 if (ds < 0. && ds != k)
2744 k--; /* want k = floor(ds) */
2745 k_check = 1;
2746 if (k >= 0 && k <= Ten_pmax) {
2747 if (dval(d) < tens[k])
2748 k--;
2749 k_check = 0;
2750 }
2751 j = bbits - i - 1;
2752 if (j >= 0) {
2753 b2 = 0;
2754 s2 = j;
2755 }
2756 else {
2757 b2 = -j;
2758 s2 = 0;
2759 }
2760 if (k >= 0) {
2761 b5 = 0;
2762 s5 = k;
2763 s2 += k;
2764 }
2765 else {
2766 b2 -= k;
2767 b5 = -k;
2768 s5 = 0;
2769 }
2770 if (mode < 0 || mode > 9)
2771 mode = 0;
2772
2773 #ifndef SET_INEXACT
2774 #ifdef Check_FLT_ROUNDS
2775 try_quick = Rounding == 1;
2776 #else
2777 try_quick = 1;
2778 #endif
2779 #endif /*SET_INEXACT*/
2780
2781 if (mode > 5) {
2782 mode -= 4;
2783 try_quick = 0;
2784 }
2785 leftright = 1;
2786 switch(mode) {
2787 case 0:
2788 case 1:
2789 ilim = ilim1 = -1;
2790 i = 18;
2791 ndigits = 0;
2792 break;
2793 case 2:
2794 leftright = 0;
2795 /* no break */
2796 case 4:
2797 if (ndigits <= 0)
2798 ndigits = 1;
2799 ilim = ilim1 = i = ndigits;
2800 break;
2801 case 3:
2802 leftright = 0;
2803 /* no break */
2804 case 5:
2805 i = ndigits + k + 1;
2806 ilim = i;
2807 ilim1 = i - 1;
2808 if (i <= 0)
2809 i = 1;
2810 }
2811 s = s0 = rv_alloc(PASS_STATE i);
2812
2813 #ifdef Honor_FLT_ROUNDS
2814 if (mode > 1 && rounding != 1)
2815 leftright = 0;
2816 #endif
2817
2818 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2819
2820 /* Try to get by with floating-point arithmetic. */
2821
2822 i = 0;
2823 dval(d2) = dval(d);
2824 k0 = k;
2825 ilim0 = ilim;
2826 ieps = 2; /* conservative */
2827 if (k > 0) {
2828 ds = tens[k&0xf];
2829 j = k >> 4;
2830 if (j & Bletch) {
2831 /* prevent overflows */
2832 j &= Bletch - 1;
2833 dval(d) /= bigtens[n_bigtens-1];
2834 ieps++;
2835 }
2836 for(; j; j >>= 1, i++)
2837 if (j & 1) {
2838 ieps++;
2839 ds *= bigtens[i];
2840 }
2841 dval(d) /= ds;
2842 }
2843 else if ((j1 = -k)) {
2844 dval(d) *= tens[j1 & 0xf];
2845 for(j = j1 >> 4; j; j >>= 1, i++)
2846 if (j & 1) {
2847 ieps++;
2848 dval(d) *= bigtens[i];
2849 }
2850 }
2851 if (k_check && dval(d) < 1. && ilim > 0) {
2852 if (ilim1 <= 0)
2853 goto fast_failed;
2854 ilim = ilim1;
2855 k--;
2856 dval(d) *= 10.;
2857 ieps++;
2858 }
2859 dval(eps) = ieps*dval(d) + 7.;
2860 word0(eps) -= (P-1)*Exp_msk1;
2861 if (ilim == 0) {
2862 S = mhi = 0;
2863 dval(d) -= 5.;
2864 if (dval(d) > dval(eps))
2865 goto one_digit;
2866 if (dval(d) < -dval(eps))
2867 goto no_digits;
2868 goto fast_failed;
2869 }
2870 #ifndef No_leftright
2871 if (leftright) {
2872 /* Use Steele & White method of only
2873 * generating digits needed.
2874 */
2875 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2876 for(i = 0;;) {
2877 L = (ULong) dval(d);
2878 dval(d) -= L;
2879 *s++ = '0' + (int)L;
2880 if (dval(d) < dval(eps))
2881 goto ret1;
2882 if (1. - dval(d) < dval(eps))
2883 goto bump_up;
2884 if (++i >= ilim)
2885 break;
2886 dval(eps) *= 10.;
2887 dval(d) *= 10.;
2888 }
2889 }
2890 else {
2891 #endif
2892 /* Generate ilim digits, then fix them up. */
2893 dval(eps) *= tens[ilim-1];
2894 for(i = 1;; i++, dval(d) *= 10.) {
2895 L = (Long)(dval(d));
2896 if (!(dval(d) -= L))
2897 ilim = i;
2898 *s++ = '0' + (int)L;
2899 if (i == ilim) {
2900 if (dval(d) > 0.5 + dval(eps))
2901 goto bump_up;
2902 else if (dval(d) < 0.5 - dval(eps)) {
2903 while(*--s == '0');
2904 s++;
2905 goto ret1;
2906 }
2907 break;
2908 }
2909 }
2910 #ifndef No_leftright
2911 }
2912 #endif
2913 fast_failed:
2914 s = s0;
2915 dval(d) = dval(d2);
2916 k = k0;
2917 ilim = ilim0;
2918 }
2919
2920 /* Do we have a "small" integer? */
2921
2922 if (be >= 0 && k <= Int_max) {
2923 /* Yes. */
2924 ds = tens[k];
2925 if (ndigits < 0 && ilim <= 0) {
2926 S = mhi = 0;
2927 if (ilim < 0 || dval(d) < 5*ds)
2928 goto no_digits;
2929 goto one_digit;
2930 }
2931 for(i = 1;; i++, dval(d) *= 10.) {
2932 L = (Long)(dval(d) / ds);
2933 dval(d) -= L*ds;
2934 #ifdef Check_FLT_ROUNDS
2935 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2936 if (dval(d) < 0) {
2937 L--;
2938 dval(d) += ds;
2939 }
2940 #endif
2941 *s++ = '0' + (int)L;
2942 if (!dval(d)) {
2943 #ifdef SET_INEXACT
2944 inexact = 0;
2945 #endif
2946 break;
2947 }
2948 if (i == ilim) {
2949 #ifdef Honor_FLT_ROUNDS
2950 if (mode > 1)
2951 switch(rounding) {
2952 case 0: goto ret1;
2953 case 2: goto bump_up;
2954 }
2955 #endif
2956 dval(d) += dval(d);
2957 if (dval(d) > ds || (dval(d) == ds && L & 1)) {
2958 bump_up:
2959 while(*--s == '9')
2960 if (s == s0) {
2961 k++;
2962 *s = '0';
2963 break;
2964 }
2965 ++*s++;
2966 }
2967 break;
2968 }
2969 }
2970 goto ret1;
2971 }
2972
2973 m2 = b2;
2974 m5 = b5;
2975 mhi = mlo = 0;
2976 if (leftright) {
2977 i =
2978 #ifndef Sudden_Underflow
2979 denorm ? be + (Bias + (P-1) - 1 + 1) :
2980 #endif
2981 #ifdef IBM
2982 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2983 #else
2984 1 + P - bbits;
2985 #endif
2986 b2 += i;
2987 s2 += i;
2988 mhi = i2b(PASS_STATE 1);
2989 }
2990 if (m2 > 0 && s2 > 0) {
2991 i = m2 < s2 ? m2 : s2;
2992 b2 -= i;
2993 m2 -= i;
2994 s2 -= i;
2995 }
2996 if (b5 > 0) {
2997 if (leftright) {
2998 if (m5 > 0) {
2999 mhi = pow5mult(PASS_STATE mhi, m5);
3000 b1 = mult(PASS_STATE mhi, b);
3001 Bfree(PASS_STATE b);
3002 b = b1;
3003 }
3004 if ((j = b5 - m5))
3005 b = pow5mult(PASS_STATE b, j);
3006 }
3007 else
3008 b = pow5mult(PASS_STATE b, b5);
3009 }
3010 S = i2b(PASS_STATE 1);
3011 if (s5 > 0)
3012 S = pow5mult(PASS_STATE S, s5);
3013
3014 /* Check for special case that d is a normalized power of 2. */
3015
3016 spec_case = 0;
3017 if ((mode < 2 || leftright)
3018 #ifdef Honor_FLT_ROUNDS
3019 && rounding == 1
3020 #endif
3021 ) {
3022 if (!word1(d) && !(word0(d) & Bndry_mask)
3023 #ifndef Sudden_Underflow
3024 && word0(d) & (Exp_mask & ~Exp_msk1)
3025 #endif
3026 ) {
3027 /* The special case */
3028 b2 += Log2P;
3029 s2 += Log2P;
3030 spec_case = 1;
3031 }
3032 }
3033
3034 /* Arrange for convenient computation of quotients:
3035 * shift left if necessary so divisor has 4 leading 0 bits.
3036 *
3037 * Perhaps we should just compute leading 28 bits of S once
3038 * and for all and pass them and a shift to quorem, so it
3039 * can do shifts and ors to compute the numerator for q.
3040 */
3041 #ifdef Pack_32
3042 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f))
3043 i = 32 - i;
3044 #else
3045 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3046 i = 16 - i;
3047 #endif
3048 if (i > 4) {
3049 i -= 4;
3050 b2 += i;
3051 m2 += i;
3052 s2 += i;
3053 }
3054 else if (i < 4) {
3055 i += 28;
3056 b2 += i;
3057 m2 += i;
3058 s2 += i;
3059 }
3060 if (b2 > 0)
3061 b = lshift(PASS_STATE b, b2);
3062 if (s2 > 0)
3063 S = lshift(PASS_STATE S, s2);
3064 if (k_check) {
3065 if (cmp(b,S) < 0) {
3066 k--;
3067 b = multadd(PASS_STATE b, 10, 0); /* we botched the k estimate */
3068 if (leftright)
3069 mhi = multadd(PASS_STATE mhi, 10, 0);
3070 ilim = ilim1;
3071 }
3072 }
3073 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3074 if (ilim < 0 || cmp(b,S = multadd(PASS_STATE S,5,0)) < 0) {
3075 /* no digits, fcvt style */
3076 no_digits:
3077 /* MOZILLA CHANGE: Always return a non-empty string. */
3078 *s++ = '0';
3079 k = 0;
3080 goto ret;
3081 }
3082 one_digit:
3083 *s++ = '1';
3084 k++;
3085 goto ret;
3086 }
3087 if (leftright) {
3088 if (m2 > 0)
3089 mhi = lshift(PASS_STATE mhi, m2);
3090
3091 /* Compute mlo -- check for special case
3092 * that d is a normalized power of 2.
3093 */
3094
3095 mlo = mhi;
3096 if (spec_case) {
3097 mhi = Balloc(PASS_STATE mhi->k);
3098 Bcopy(mhi, mlo);
3099 mhi = lshift(PASS_STATE mhi, Log2P);
3100 }
3101
3102 for(i = 1;;i++) {
3103 dig = quorem(b,S) + '0';
3104 /* Do we yet have the shortest decimal string
3105 * that will round to d?
3106 */
3107 j = cmp(b, mlo);
3108 delta = diff(PASS_STATE S, mhi);
3109 j1 = delta->sign ? 1 : cmp(b, delta);
3110 Bfree(PASS_STATE delta);
3111 #ifndef ROUND_BIASED
3112 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3113 #ifdef Honor_FLT_ROUNDS
3114 && rounding >= 1
3115 #endif
3116 ) {
3117 if (dig == '9')
3118 goto round_9_up;
3119 if (j > 0)
3120 dig++;
3121 #ifdef SET_INEXACT
3122 else if (!b->x[0] && b->wds <= 1)
3123 inexact = 0;
3124 #endif
3125 *s++ = dig;
3126 goto ret;
3127 }
3128 #endif
3129 if (j < 0 || (j == 0 && mode != 1
3130 #ifndef ROUND_BIASED
3131 && !(word1(d) & 1)
3132 #endif
3133 )) {
3134 if (!b->x[0] && b->wds <= 1) {
3135 #ifdef SET_INEXACT
3136 inexact = 0;
3137 #endif
3138 goto accept_dig;
3139 }
3140 #ifdef Honor_FLT_ROUNDS
3141 if (mode > 1)
3142 switch(rounding) {
3143 case 0: goto accept_dig;
3144 case 2: goto keep_dig;
3145 }
3146 #endif /*Honor_FLT_ROUNDS*/
3147 if (j1 > 0) {
3148 b = lshift(PASS_STATE b, 1);
3149 j1 = cmp(b, S);
3150 if ((j1 > 0 || (j1 == 0 && dig & 1))
3151 && dig++ == '9')
3152 goto round_9_up;
3153 }
3154 accept_dig:
3155 *s++ = dig;
3156 goto ret;
3157 }
3158 if (j1 > 0) {
3159 #ifdef Honor_FLT_ROUNDS
3160 if (!rounding)
3161 goto accept_dig;
3162 #endif
3163 if (dig == '9') { /* possible if i == 1 */
3164 round_9_up:
3165 *s++ = '9';
3166 goto roundoff;
3167 }
3168 *s++ = dig + 1;
3169 goto ret;
3170 }
3171 #ifdef Honor_FLT_ROUNDS
3172 keep_dig:
3173 #endif
3174 *s++ = dig;
3175 if (i == ilim)
3176 break;
3177 b = multadd(PASS_STATE b, 10, 0);
3178 if (mlo == mhi)
3179 mlo = mhi = multadd(PASS_STATE mhi, 10, 0);
3180 else {
3181 mlo = multadd(PASS_STATE mlo, 10, 0);
3182 mhi = multadd(PASS_STATE mhi, 10, 0);
3183 }
3184 }
3185 }
3186 else
3187 for(i = 1;; i++) {
3188 *s++ = dig = quorem(b,S) + '0';
3189 if (!b->x[0] && b->wds <= 1) {
3190 #ifdef SET_INEXACT
3191 inexact = 0;
3192 #endif
3193 goto ret;
3194 }
3195 if (i >= ilim)
3196 break;
3197 b = multadd(PASS_STATE b, 10, 0);
3198 }
3199
3200 /* Round off last digit */
3201
3202 #ifdef Honor_FLT_ROUNDS
3203 switch(rounding) {
3204 case 0: goto trimzeros;
3205 case 2: goto roundoff;
3206 }
3207 #endif
3208 b = lshift(PASS_STATE b, 1);
3209 j = cmp(b, S);
3210 if (j >= 0) { /* ECMA compatible rounding needed by Spidermonkey */
3211 roundoff:
3212 while(*--s == '9')
3213 if (s == s0) {
3214 k++;
3215 *s++ = '1';
3216 goto ret;
3217 }
3218 ++*s++;
3219 }
3220 else {
3221 #ifdef Honor_FLT_ROUNDS
3222 trimzeros:
3223 #endif
3224 while(*--s == '0');
3225 s++;
3226 }
3227 ret:
3228 Bfree(PASS_STATE S);
3229 if (mhi) {
3230 if (mlo && mlo != mhi)
3231 Bfree(PASS_STATE mlo);
3232 Bfree(PASS_STATE mhi);
3233 }
3234 ret1:
3235 #ifdef SET_INEXACT
3236 if (inexact) {
3237 if (!oldinexact) {
3238 word0(d) = Exp_1 + (70 << Exp_shift);
3239 word1(d) = 0;
3240 dval(d) += 1.;
3241 }
3242 }
3243 else if (!oldinexact)
3244 clear_inexact();
3245 #endif
3246 Bfree(PASS_STATE b);
3247 *s = 0;
3248 *decpt = k + 1;
3249 if (rve)
3250 *rve = s;
3251 return s0;
3252 }
3253 #ifdef __cplusplus
3254 }
3255 #endif
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