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