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2009-03-04 Zoltan Varga <vargaz@gmail.com>
[mono-debugger.git] / mono / utils / strtod.c
blob76840194276682ceee8553fff3bd4860f3e9d548
1 /****************************************************************
2 *
3 * The author of this software is David M. Gay.
4 *
5 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
6 *
7 * Permission to use, copy, modify, and distribute this software for any
8 * purpose without fee is hereby granted, provided that this entire notice
9 * is included in all copies of any software which is or includes a copy
10 * or modification of this software and in all copies of the supporting
11 * documentation for such software.
12 *
13 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
14 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
15 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
16 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
17 *
18 ***************************************************************/
19 #include "strtod.h"
20 #include <glib.h>
21 #define freedtoa __freedtoa
22 #define dtoa __dtoa
23
24 G_LOCK_DEFINE_STATIC(str_mutex0);
25 G_LOCK_DEFINE_STATIC(str_mutex1);
26 #define MULTIPLE_THREADS 1
27 #define ACQUIRE_DTOA_LOCK(n) G_LOCK (str_mutex##n)
28 #define FREE_DTOA_LOCK(n) G_UNLOCK (str_mutex##n)
29
30 /* Please send bug reports to David M. Gay (dmg at acm dot org,
31 * with " at " changed at "@" and " dot " changed to "."). */
32
33 /* On a machine with IEEE extended-precision registers, it is
34 * necessary to specify double-precision (53-bit) rounding precision
35 * before invoking strtod or dtoa. If the machine uses (the equivalent
36 * of) Intel 80x87 arithmetic, the call
37 * _control87(PC_53, MCW_PC);
38 * does this with many compilers. Whether this or another call is
39 * appropriate depends on the compiler; for this to work, it may be
40 * necessary to #include "float.h" or another system-dependent header
41 * file.
42 */
43
44 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
45 *
46 * This strtod returns a nearest machine number to the input decimal
47 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
48 * broken by the IEEE round-even rule. Otherwise ties are broken by
49 * biased rounding (add half and chop).
50 *
51 * Inspired loosely by William D. Clinger's paper "How to Read Floating
52 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
53 *
54 * Modifications:
55 *
56 * 1. We only require IEEE, IBM, or VAX double-precision
57 * arithmetic (not IEEE double-extended).
58 * 2. We get by with floating-point arithmetic in a case that
59 * Clinger missed -- when we're computing d * 10^n
60 * for a small integer d and the integer n is not too
61 * much larger than 22 (the maximum integer k for which
62 * we can represent 10^k exactly), we may be able to
63 * compute (d*10^k) * 10^(e-k) with just one roundoff.
64 * 3. Rather than a bit-at-a-time adjustment of the binary
65 * result in the hard case, we use floating-point
66 * arithmetic to determine the adjustment to within
67 * one bit; only in really hard cases do we need to
68 * compute a second residual.
69 * 4. Because of 3., we don't need a large table of powers of 10
70 * for ten-to-e (just some small tables, e.g. of 10^k
71 * for 0 <= k <= 22).
72 */
73
74 /*
75 * #define IEEE_8087 for IEEE-arithmetic machines where the least
76 * significant byte has the lowest address.
77 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
78 * significant byte has the lowest address.
79 * #define Long int on machines with 32-bit ints and 64-bit longs.
80 * #define IBM for IBM mainframe-style floating-point arithmetic.
81 * #define VAX for VAX-style floating-point arithmetic (D_floating).
82 * #define No_leftright to omit left-right logic in fast floating-point
83 * computation of dtoa.
84 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
85 * and strtod and dtoa should round accordingly.
86 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
87 * and Honor_FLT_ROUNDS is not #defined.
88 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
89 * that use extended-precision instructions to compute rounded
90 * products and quotients) with IBM.
91 * #define ROUND_BIASED for IEEE-format with biased rounding.
92 * #define Inaccurate_Divide for IEEE-format with correctly rounded
93 * products but inaccurate quotients, e.g., for Intel i860.
94 * #define NO_LONG_LONG on machines that do not have a "long long"
95 * integer type (of >= 64 bits). On such machines, you can
96 * #define Just_16 to store 16 bits per 32-bit Long when doing
97 * high-precision integer arithmetic. Whether this speeds things
98 * up or slows things down depends on the machine and the number
99 * being converted. If long long is available and the name is
100 * something other than "long long", #define Llong to be the name,
101 * and if "unsigned Llong" does not work as an unsigned version of
102 * Llong, #define #ULLong to be the corresponding unsigned type.
103 * #define KR_headers for old-style C function headers.
104 * #define Bad_float_h if your system lacks a float.h or if it does not
105 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
106 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
107 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
108 * if memory is available and otherwise does something you deem
109 * appropriate. If MALLOC is undefined, malloc will be invoked
110 * directly -- and assumed always to succeed.
111 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
112 * memory allocations from a private pool of memory when possible.
113 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
114 * unless #defined to be a different length. This default length
115 * suffices to get rid of MALLOC calls except for unusual cases,
116 * such as decimal-to-binary conversion of a very long string of
117 * digits. The longest string dtoa can return is about 751 bytes
118 * long. For conversions by strtod of strings of 800 digits and
119 * all dtoa conversions in single-threaded executions with 8-byte
120 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
121 * pointers, PRIVATE_MEM >= 7112 appears adequate.
122 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
123 * Infinity and NaN (case insensitively). On some systems (e.g.,
124 * some HP systems), it may be necessary to #define NAN_WORD0
125 * appropriately -- to the most significant word of a quiet NaN.
126 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
127 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
128 * strtod also accepts (case insensitively) strings of the form
129 * NaN(x), where x is a string of hexadecimal digits and spaces;
130 * if there is only one string of hexadecimal digits, it is taken
131 * for the 52 fraction bits of the resulting NaN; if there are two
132 * or more strings of hex digits, the first is for the high 20 bits,
133 * the second and subsequent for the low 32 bits, with intervening
134 * white space ignored; but if this results in none of the 52
135 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
136 * and NAN_WORD1 are used instead.
137 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
138 * multiple threads. In this case, you must provide (or suitably
139 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
140 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
141 * in pow5mult, ensures lazy evaluation of only one copy of high
142 * powers of 5; omitting this lock would introduce a small
143 * probability of wasting memory, but would otherwise be harmless.)
144 * You must also invoke freedtoa(s) to free the value s returned by
145 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
146 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
147 * avoids underflows on inputs whose result does not underflow.
148 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
149 * floating-point numbers and flushes underflows to zero rather
150 * than implementing gradual underflow, then you must also #define
151 * Sudden_Underflow.
152 * #define YES_ALIAS to permit aliasing certain double values with
153 * arrays of ULongs. This leads to slightly better code with
154 * some compilers and was always used prior to 19990916, but it
155 * is not strictly legal and can cause trouble with aggressively
156 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
157 * #define USE_LOCALE to use the current locale's decimal_point value.
158 * #define SET_INEXACT if IEEE arithmetic is being used and extra
159 * computation should be done to set the inexact flag when the
160 * result is inexact and avoid setting inexact when the result
161 * is exact. In this case, dtoa.c must be compiled in
162 * an environment, perhaps provided by #include "dtoa.c" in a
163 * suitable wrapper, that defines two functions,
164 * int get_inexact(void);
165 * void clear_inexact(void);
166 * such that get_inexact() returns a nonzero value if the
167 * inexact bit is already set, and clear_inexact() sets the
168 * inexact bit to 0. When SET_INEXACT is #defined, strtod
169 * also does extra computations to set the underflow and overflow
170 * flags when appropriate (i.e., when the result is tiny and
171 * inexact or when it is a numeric value rounded to +-infinity).
172 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
173 * the result overflows to +-Infinity or underflows to 0.
174 */
175 #if defined(i386) || defined(mips) && defined(MIPSEL) || defined (__arm__)
176
177 # define IEEE_8087
178
179 #elif defined(__x86_64__) || defined(__alpha__)
180
181 # define IEEE_8087
182
183 #elif defined(__ia64)
184
185 # ifdef __hpux
186 # define IEEE_MC68k
187 # else
188 # define IEEE_8087
189 # endif
190
191 #elif defined(__hppa)
192
193 # define IEEE_MC68k
194
195 #else
196 #define IEEE_MC68k
197 #endif
198
199 #define Long gint32
200 #define ULong guint32
201
202 #ifdef DEBUG
203 #include "stdio.h"
204 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
205 #endif
206
207 #include "stdlib.h"
208 #include "string.h"
209
210 #undef USE_LOCALE
211 #ifdef USE_LOCALE
212 #include "locale.h"
213 #endif
214
215 #ifdef MALLOC
216 #ifdef KR_headers
217 extern char *MALLOC();
218 #else
219 extern void *MALLOC(size_t);
220 #endif
221 #else
222 #define MALLOC malloc
223 #endif
224
225 #define Omit_Private_Memory
226 #ifndef Omit_Private_Memory
227 #ifndef PRIVATE_MEM
228 #define PRIVATE_MEM 2304
229 #endif
230 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
231 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
232 #endif
233
234 #undef IEEE_Arith
235 #undef Avoid_Underflow
236 #ifdef IEEE_MC68k
237 #define IEEE_Arith
238 #endif
239 #ifdef IEEE_8087
240 #define IEEE_Arith
241 #endif
242
243 #include "errno.h"
244
245 #ifdef Bad_float_h
246
247 #ifdef IEEE_Arith
248 #define DBL_DIG 15
249 #define DBL_MAX_10_EXP 308
250 #define DBL_MAX_EXP 1024
251 #define FLT_RADIX 2
252 #endif /*IEEE_Arith*/
253
254 #ifdef IBM
255 #define DBL_DIG 16
256 #define DBL_MAX_10_EXP 75
257 #define DBL_MAX_EXP 63
258 #define FLT_RADIX 16
259 #define DBL_MAX 7.2370055773322621e+75
260 #endif
261
262 #ifdef VAX
263 #define DBL_DIG 16
264 #define DBL_MAX_10_EXP 38
265 #define DBL_MAX_EXP 127
266 #define FLT_RADIX 2
267 #define DBL_MAX 1.7014118346046923e+38
268 #endif
269
270 #ifndef LONG_MAX
271 #define LONG_MAX 2147483647
272 #endif
273
274 #else /* ifndef Bad_float_h */
275 #include "float.h"
276 #endif /* Bad_float_h */
277
278 #ifndef __MATH_H__
279 #include "math.h"
280 #endif
281
282 #ifdef __cplusplus
283 extern "C" {
284 #endif
285
286 #ifndef CONST
287 #ifdef KR_headers
288 #define CONST /* blank */
289 #else
290 #define CONST const
291 #endif
292 #endif
293
294 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
295 Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
296 #endif
297
298 typedef union { double d; ULong L[2]; } U;
299
300 #ifdef YES_ALIAS
301 #define dval(x) x
302 #ifdef IEEE_8087
303 #define word0(x) ((ULong *)&x)[1]
304 #define word1(x) ((ULong *)&x)[0]
305 #else
306 #define word0(x) ((ULong *)&x)[0]
307 #define word1(x) ((ULong *)&x)[1]
308 #endif
309 #else
310 #ifdef IEEE_8087
311 #define word0(x) ((U*)&x)->L[1]
312 #define word1(x) ((U*)&x)->L[0]
313 #else
314 #define word0(x) ((U*)&x)->L[0]
315 #define word1(x) ((U*)&x)->L[1]
316 #endif
317 #define dval(x) ((U*)&x)->d
318 #endif
319
320 /* The following definition of Storeinc is appropriate for MIPS processors.
321 * An alternative that might be better on some machines is
322 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
323 */
324 #if defined(IEEE_8087) + defined(VAX)
325 #define Storeinc(a,b,c) do { (((unsigned short *)a)[1] = (unsigned short)b, \
326 ((unsigned short *)a)[0] = (unsigned short)c, a++) } while (0)
327 #else
328 #define Storeinc(a,b,c) do { (((unsigned short *)a)[0] = (unsigned short)b, \
329 ((unsigned short *)a)[1] = (unsigned short)c, a++) } while (0)
330 #endif
331
332 /* #define P DBL_MANT_DIG */
333 /* Ten_pmax = floor(P*log(2)/log(5)) */
334 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
335 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
336 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
337
338 #ifdef IEEE_Arith
339 #define Exp_shift 20
340 #define Exp_shift1 20
341 #define Exp_msk1 0x100000
342 #define Exp_msk11 0x100000
343 #define Exp_mask 0x7ff00000
344 #define P 53
345 #define Bias 1023
346 #define Emin (-1022)
347 #define Exp_1 0x3ff00000
348 #define Exp_11 0x3ff00000
349 #define Ebits 11
350 #define Frac_mask 0xfffff
351 #define Frac_mask1 0xfffff
352 #define Ten_pmax 22
353 #define Bletch 0x10
354 #define Bndry_mask 0xfffff
355 #define Bndry_mask1 0xfffff
356 #define LSB 1
357 #define Sign_bit 0x80000000
358 #define Log2P 1
359 #define Tiny0 0
360 #define Tiny1 1
361 #define Quick_max 14
362 #define Int_max 14
363 #ifndef NO_IEEE_Scale
364 #define Avoid_Underflow
365 #ifdef Flush_Denorm /* debugging option */
366 #undef Sudden_Underflow
367 #endif
368 #endif
369
370 #ifndef Flt_Rounds
371 #ifdef FLT_ROUNDS
372 #define Flt_Rounds FLT_ROUNDS
373 #else
374 #define Flt_Rounds 1
375 #endif
376 #endif /*Flt_Rounds*/
377
378 #ifdef Honor_FLT_ROUNDS
379 #define Rounding rounding
380 #undef Check_FLT_ROUNDS
381 #define Check_FLT_ROUNDS
382 #else
383 #define Rounding Flt_Rounds
384 #endif
385
386 #else /* ifndef IEEE_Arith */
387 #undef Check_FLT_ROUNDS
388 #undef Honor_FLT_ROUNDS
389 #undef SET_INEXACT
390 #undef Sudden_Underflow
391 #define Sudden_Underflow
392 #ifdef IBM
393 #undef Flt_Rounds
394 #define Flt_Rounds 0
395 #define Exp_shift 24
396 #define Exp_shift1 24
397 #define Exp_msk1 0x1000000
398 #define Exp_msk11 0x1000000
399 #define Exp_mask 0x7f000000
400 #define P 14
401 #define Bias 65
402 #define Exp_1 0x41000000
403 #define Exp_11 0x41000000
404 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
405 #define Frac_mask 0xffffff
406 #define Frac_mask1 0xffffff
407 #define Bletch 4
408 #define Ten_pmax 22
409 #define Bndry_mask 0xefffff
410 #define Bndry_mask1 0xffffff
411 #define LSB 1
412 #define Sign_bit 0x80000000
413 #define Log2P 4
414 #define Tiny0 0x100000
415 #define Tiny1 0
416 #define Quick_max 14
417 #define Int_max 15
418 #else /* VAX */
419 #undef Flt_Rounds
420 #define Flt_Rounds 1
421 #define Exp_shift 23
422 #define Exp_shift1 7
423 #define Exp_msk1 0x80
424 #define Exp_msk11 0x800000
425 #define Exp_mask 0x7f80
426 #define P 56
427 #define Bias 129
428 #define Exp_1 0x40800000
429 #define Exp_11 0x4080
430 #define Ebits 8
431 #define Frac_mask 0x7fffff
432 #define Frac_mask1 0xffff007f
433 #define Ten_pmax 24
434 #define Bletch 2
435 #define Bndry_mask 0xffff007f
436 #define Bndry_mask1 0xffff007f
437 #define LSB 0x10000
438 #define Sign_bit 0x8000
439 #define Log2P 1
440 #define Tiny0 0x80
441 #define Tiny1 0
442 #define Quick_max 15
443 #define Int_max 15
444 #endif /* IBM, VAX */
445 #endif /* IEEE_Arith */
446
447 #ifndef IEEE_Arith
448 #define ROUND_BIASED
449 #endif
450
451 #ifdef RND_PRODQUOT
452 #define rounded_product(a,b) a = rnd_prod(a, b)
453 #define rounded_quotient(a,b) a = rnd_quot(a, b)
454 #ifdef KR_headers
455 extern double rnd_prod(), rnd_quot();
456 #else
457 extern double rnd_prod(double, double), rnd_quot(double, double);
458 #endif
459 #else
460 #define rounded_product(a,b) a *= b
461 #define rounded_quotient(a,b) a /= b
462 #endif
463
464 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
465 #define Big1 0xffffffff
466
467 #ifndef Pack_32
468 #define Pack_32
469 #endif
470
471 #ifdef KR_headers
472 #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
473 #else
474 #define FFFFFFFF 0xffffffffUL
475 #endif
476
477 #ifdef NO_LONG_LONG
478 #undef ULLong
479 #ifdef Just_16
480 #undef Pack_32
481 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
482 * This makes some inner loops simpler and sometimes saves work
483 * during multiplications, but it often seems to make things slightly
484 * slower. Hence the default is now to store 32 bits per Long.
485 */
486 #endif
487 #else /* long long available */
488 #ifndef Llong
489 #define Llong long long
490 #endif
491 #ifndef ULLong
492 #define ULLong unsigned Llong
493 #endif
494 #endif /* NO_LONG_LONG */
495
496 #ifndef MULTIPLE_THREADS
497 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
498 #define FREE_DTOA_LOCK(n) /*nothing*/
499 #endif
500
501 #define Kmax 15
502
503 #ifdef __cplusplus
504 extern "C" double strtod(const char *s00, char **se);
505 extern "C" char *dtoa(double d, int mode, int ndigits,
506 int *decpt, int *sign, char **rve);
507 #endif
508
509 struct
510 Bigint {
511 struct Bigint *next;
512 int k, maxwds, sign, wds;
513 ULong x[1];
514 };
515
516 typedef struct Bigint Bigint;
517
518 static Bigint *freelist[Kmax+1];
519
520 static Bigint *
521 Balloc
522 #ifdef KR_headers
523 (k) int k;
524 #else
525 (int k)
526 #endif
527 {
528 int x;
529 Bigint *rv;
530 #ifndef Omit_Private_Memory
531 unsigned int len;
532 #endif
533
534 ACQUIRE_DTOA_LOCK(0);
535 if ((rv = freelist[k])) {
536 freelist[k] = rv->next;
537 }
538 else {
539 x = 1 << k;
540 #ifdef Omit_Private_Memory
541 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
542 #else
543 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
544 /sizeof(double);
545 if (pmem_next - private_mem + len <= PRIVATE_mem) {
546 rv = (Bigint*)pmem_next;
547 pmem_next += len;
548 }
549 else
550 rv = (Bigint*)MALLOC(len*sizeof(double));
551 #endif
552 rv->k = k;
553 rv->maxwds = x;
554 }
555 FREE_DTOA_LOCK(0);
556 rv->sign = rv->wds = 0;
557 return rv;
558 }
559
560 static void
561 Bfree
562 #ifdef KR_headers
563 (v) Bigint *v;
564 #else
565 (Bigint *v)
566 #endif
567 {
568 if (v) {
569 ACQUIRE_DTOA_LOCK(0);
570 v->next = freelist[v->k];
571 freelist[v->k] = v;
572 FREE_DTOA_LOCK(0);
573 }
574 }
575
576 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
577 y->wds*sizeof(Long) + 2*sizeof(int))
578
579 static Bigint *
580 multadd
581 #ifdef KR_headers
582 (b, m, a) Bigint *b; int m, a;
583 #else
584 (Bigint *b, int m, int a) /* multiply by m and add a */
585 #endif
586 {
587 int i, wds;
588 #ifdef ULLong
589 ULong *x;
590 ULLong carry, y;
591 #else
592 ULong carry, *x, y;
593 #ifdef Pack_32
594 ULong xi, z;
595 #endif
596 #endif
597 Bigint *b1;
598
599 wds = b->wds;
600 x = b->x;
601 i = 0;
602 carry = a;
603 do {
604 #ifdef ULLong
605 y = *x * (ULLong)m + carry;
606 carry = y >> 32;
607 *x++ = y & FFFFFFFF;
608 #else
609 #ifdef Pack_32
610 xi = *x;
611 y = (xi & 0xffff) * m + carry;
612 z = (xi >> 16) * m + (y >> 16);
613 carry = z >> 16;
614 *x++ = (z << 16) + (y & 0xffff);
615 #else
616 y = *x * m + carry;
617 carry = y >> 16;
618 *x++ = y & 0xffff;
619 #endif
620 #endif
621 }
622 while(++i < wds);
623 if (carry) {
624 if (wds >= b->maxwds) {
625 b1 = Balloc(b->k+1);
626 Bcopy(b1, b);
627 Bfree(b);
628 b = b1;
629 }
630 b->x[wds++] = carry;
631 b->wds = wds;
632 }
633 return b;
634 }
635
636 static Bigint *
637 s2b
638 #ifdef KR_headers
639 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
640 #else
641 (CONST char *s, int nd0, int nd, ULong y9)
642 #endif
643 {
644 Bigint *b;
645 int i, k;
646 Long x, y;
647
648 x = (nd + 8) / 9;
649 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
650 #ifdef Pack_32
651 b = Balloc(k);
652 b->x[0] = y9;
653 b->wds = 1;
654 #else
655 b = Balloc(k+1);
656 b->x[0] = y9 & 0xffff;
657 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
658 #endif
659
660 i = 9;
661 if (9 < nd0) {
662 s += 9;
663 do b = multadd(b, 10, *s++ - '0');
664 while(++i < nd0);
665 s++;
666 }
667 else
668 s += 10;
669 for(; i < nd; i++)
670 b = multadd(b, 10, *s++ - '0');
671 return b;
672 }
673
674 static int
675 hi0bits
676 #ifdef KR_headers
677 (x) register ULong x;
678 #else
679 (register ULong x)
680 #endif
681 {
682 register int k = 0;
683
684 if (!(x & 0xffff0000)) {
685 k = 16;
686 x <<= 16;
687 }
688 if (!(x & 0xff000000)) {
689 k += 8;
690 x <<= 8;
691 }
692 if (!(x & 0xf0000000)) {
693 k += 4;
694 x <<= 4;
695 }
696 if (!(x & 0xc0000000)) {
697 k += 2;
698 x <<= 2;
699 }
700 if (!(x & 0x80000000)) {
701 k++;
702 if (!(x & 0x40000000))
703 return 32;
704 }
705 return k;
706 }
707
708 static int
709 lo0bits
710 #ifdef KR_headers
711 (y) ULong *y;
712 #else
713 (ULong *y)
714 #endif
715 {
716 register int k;
717 register ULong x = *y;
718
719 if (x & 7) {
720 if (x & 1)
721 return 0;
722 if (x & 2) {
723 *y = x >> 1;
724 return 1;
725 }
726 *y = x >> 2;
727 return 2;
728 }
729 k = 0;
730 if (!(x & 0xffff)) {
731 k = 16;
732 x >>= 16;
733 }
734 if (!(x & 0xff)) {
735 k += 8;
736 x >>= 8;
737 }
738 if (!(x & 0xf)) {
739 k += 4;
740 x >>= 4;
741 }
742 if (!(x & 0x3)) {
743 k += 2;
744 x >>= 2;
745 }
746 if (!(x & 1)) {
747 k++;
748 x >>= 1;
749 if (!x)
750 return 32;
751 }
752 *y = x;
753 return k;
754 }
755
756 static Bigint *
757 i2b
758 #ifdef KR_headers
759 (i) int i;
760 #else
761 (int i)
762 #endif
763 {
764 Bigint *b;
765
766 b = Balloc(1);
767 b->x[0] = i;
768 b->wds = 1;
769 return b;
770 }
771
772 static Bigint *
773 mult
774 #ifdef KR_headers
775 (a, b) Bigint *a, *b;
776 #else
777 (Bigint *a, Bigint *b)
778 #endif
779 {
780 Bigint *c;
781 int k, wa, wb, wc;
782 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
783 ULong y;
784 #ifdef ULLong
785 ULLong carry, z;
786 #else
787 ULong carry, z;
788 #ifdef Pack_32
789 ULong z2;
790 #endif
791 #endif
792
793 if (a->wds < b->wds) {
794 c = a;
795 a = b;
796 b = c;
797 }
798 k = a->k;
799 wa = a->wds;
800 wb = b->wds;
801 wc = wa + wb;
802 if (wc > a->maxwds)
803 k++;
804 c = Balloc(k);
805 for(x = c->x, xa = x + wc; x < xa; x++)
806 *x = 0;
807 xa = a->x;
808 xae = xa + wa;
809 xb = b->x;
810 xbe = xb + wb;
811 xc0 = c->x;
812 #ifdef ULLong
813 for(; xb < xbe; xc0++) {
814 if ((y = *xb++)) {
815 x = xa;
816 xc = xc0;
817 carry = 0;
818 do {
819 z = *x++ * (ULLong)y + *xc + carry;
820 carry = z >> 32;
821 *xc++ = z & FFFFFFFF;
822 }
823 while(x < xae);
824 *xc = carry;
825 }
826 }
827 #else
828 #ifdef Pack_32
829 for(; xb < xbe; xb++, xc0++) {
830 if (y = *xb & 0xffff) {
831 x = xa;
832 xc = xc0;
833 carry = 0;
834 do {
835 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
836 carry = z >> 16;
837 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
838 carry = z2 >> 16;
839 Storeinc(xc, z2, z);
840 }
841 while(x < xae);
842 *xc = carry;
843 }
844 if (y = *xb >> 16) {
845 x = xa;
846 xc = xc0;
847 carry = 0;
848 z2 = *xc;
849 do {
850 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
851 carry = z >> 16;
852 Storeinc(xc, z, z2);
853 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
854 carry = z2 >> 16;
855 }
856 while(x < xae);
857 *xc = z2;
858 }
859 }
860 #else
861 for(; xb < xbe; xc0++) {
862 if (y = *xb++) {
863 x = xa;
864 xc = xc0;
865 carry = 0;
866 do {
867 z = *x++ * y + *xc + carry;
868 carry = z >> 16;
869 *xc++ = z & 0xffff;
870 }
871 while(x < xae);
872 *xc = carry;
873 }
874 }
875 #endif
876 #endif
877 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
878 c->wds = wc;
879 return c;
880 }
881
882 static Bigint *p5s;
883
884 static Bigint *
885 pow5mult
886 #ifdef KR_headers
887 (b, k) Bigint *b; int k;
888 #else
889 (Bigint *b, int k)
890 #endif
891 {
892 Bigint *b1, *p5, *p51;
893 int i;
894 static int p05[3] = { 5, 25, 125 };
895
896 if ((i = k & 3))
897 b = multadd(b, p05[i-1], 0);
898
899 if (!(k >>= 2))
900 return b;
901 if (!(p5 = p5s)) {
902 /* first time */
903 #ifdef MULTIPLE_THREADS
904 ACQUIRE_DTOA_LOCK(1);
905 if (!(p5 = p5s)) {
906 p5 = p5s = i2b(625);
907 p5->next = 0;
908 }
909 FREE_DTOA_LOCK(1);
910 #else
911 p5 = p5s = i2b(625);
912 p5->next = 0;
913 #endif
914 }
915 for(;;) {
916 if (k & 1) {
917 b1 = mult(b, p5);
918 Bfree(b);
919 b = b1;
920 }
921 if (!(k >>= 1))
922 break;
923 if (!(p51 = p5->next)) {
924 #ifdef MULTIPLE_THREADS
925 ACQUIRE_DTOA_LOCK(1);
926 if (!(p51 = p5->next)) {
927 p51 = p5->next = mult(p5,p5);
928 p51->next = 0;
929 }
930 FREE_DTOA_LOCK(1);
931 #else
932 p51 = p5->next = mult(p5,p5);
933 p51->next = 0;
934 #endif
935 }
936 p5 = p51;
937 }
938 return b;
939 }
940
941 static Bigint *
942 lshift
943 #ifdef KR_headers
944 (b, k) Bigint *b; int k;
945 #else
946 (Bigint *b, int k)
947 #endif
948 {
949 int i, k1, n, n1;
950 Bigint *b1;
951 ULong *x, *x1, *xe, z;
952
953 #ifdef Pack_32
954 n = k >> 5;
955 #else
956 n = k >> 4;
957 #endif
958 k1 = b->k;
959 n1 = n + b->wds + 1;
960 for(i = b->maxwds; n1 > i; i <<= 1)
961 k1++;
962 b1 = Balloc(k1);
963 x1 = b1->x;
964 for(i = 0; i < n; i++)
965 *x1++ = 0;
966 x = b->x;
967 xe = x + b->wds;
968 #ifdef Pack_32
969 if (k &= 0x1f) {
970 k1 = 32 - k;
971 z = 0;
972 do {
973 *x1++ = *x << k | z;
974 z = *x++ >> k1;
975 }
976 while(x < xe);
977 if ((*x1 = z))
978 ++n1;
979 }
980 #else
981 if (k &= 0xf) {
982 k1 = 16 - k;
983 z = 0;
984 do {
985 *x1++ = *x << k & 0xffff | z;
986 z = *x++ >> k1;
987 }
988 while(x < xe);
989 if (*x1 = z)
990 ++n1;
991 }
992 #endif
993 else do
994 *x1++ = *x++;
995 while(x < xe);
996 b1->wds = n1 - 1;
997 Bfree(b);
998 return b1;
999 }
1000
1001 static int
1002 cmp
1003 #ifdef KR_headers
1004 (a, b) Bigint *a, *b;
1005 #else
1006 (Bigint *a, Bigint *b)
1007 #endif
1008 {
1009 ULong *xa, *xa0, *xb, *xb0;
1010 int i, j;
1011
1012 i = a->wds;
1013 j = b->wds;
1014 #ifdef DEBUG
1015 if (i > 1 && !a->x[i-1])
1016 Bug("cmp called with a->x[a->wds-1] == 0");
1017 if (j > 1 && !b->x[j-1])
1018 Bug("cmp called with b->x[b->wds-1] == 0");
1019 #endif
1020 if (i -= j)
1021 return i;
1022 xa0 = a->x;
1023 xa = xa0 + j;
1024 xb0 = b->x;
1025 xb = xb0 + j;
1026 for(;;) {
1027 if (*--xa != *--xb)
1028 return *xa < *xb ? -1 : 1;
1029 if (xa <= xa0)
1030 break;
1031 }
1032 return 0;
1033 }
1034
1035 static Bigint *
1036 diff
1037 #ifdef KR_headers
1038 (a, b) Bigint *a, *b;
1039 #else
1040 (Bigint *a, Bigint *b)
1041 #endif
1042 {
1043 Bigint *c;
1044 int i, wa, wb;
1045 ULong *xa, *xae, *xb, *xbe, *xc;
1046 #ifdef ULLong
1047 ULLong borrow, y;
1048 #else
1049 ULong borrow, y;
1050 #ifdef Pack_32
1051 ULong z;
1052 #endif
1053 #endif
1054
1055 i = cmp(a,b);
1056 if (!i) {
1057 c = Balloc(0);
1058 c->wds = 1;
1059 c->x[0] = 0;
1060 return c;
1061 }
1062 if (i < 0) {
1063 c = a;
1064 a = b;
1065 b = c;
1066 i = 1;
1067 }
1068 else
1069 i = 0;
1070 c = Balloc(a->k);
1071 c->sign = i;
1072 wa = a->wds;
1073 xa = a->x;
1074 xae = xa + wa;
1075 wb = b->wds;
1076 xb = b->x;
1077 xbe = xb + wb;
1078 xc = c->x;
1079 borrow = 0;
1080 #ifdef ULLong
1081 do {
1082 y = (ULLong)*xa++ - *xb++ - borrow;
1083 borrow = y >> 32 & (ULong)1;
1084 *xc++ = y & FFFFFFFF;
1085 }
1086 while(xb < xbe);
1087 while(xa < xae) {
1088 y = *xa++ - borrow;
1089 borrow = y >> 32 & (ULong)1;
1090 *xc++ = y & FFFFFFFF;
1091 }
1092 #else
1093 #ifdef Pack_32
1094 do {
1095 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1096 borrow = (y & 0x10000) >> 16;
1097 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1098 borrow = (z & 0x10000) >> 16;
1099 Storeinc(xc, z, y);
1100 }
1101 while(xb < xbe);
1102 while(xa < xae) {
1103 y = (*xa & 0xffff) - borrow;
1104 borrow = (y & 0x10000) >> 16;
1105 z = (*xa++ >> 16) - borrow;
1106 borrow = (z & 0x10000) >> 16;
1107 Storeinc(xc, z, y);
1108 }
1109 #else
1110 do {
1111 y = *xa++ - *xb++ - borrow;
1112 borrow = (y & 0x10000) >> 16;
1113 *xc++ = y & 0xffff;
1114 }
1115 while(xb < xbe);
1116 while(xa < xae) {
1117 y = *xa++ - borrow;
1118 borrow = (y & 0x10000) >> 16;
1119 *xc++ = y & 0xffff;
1120 }
1121 #endif
1122 #endif
1123 while(!*--xc)
1124 wa--;
1125 c->wds = wa;
1126 return c;
1127 }
1128
1129 static double
1130 ulp
1131 #ifdef KR_headers
1132 (x) double x;
1133 #else
1134 (double x)
1135 #endif
1136 {
1137 register Long L;
1138 double a;
1139
1140 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1141 #ifndef Avoid_Underflow
1142 #ifndef Sudden_Underflow
1143 if (L > 0) {
1144 #endif
1145 #endif
1146 #ifdef IBM
1147 L |= Exp_msk1 >> 4;
1148 #endif
1149 word0(a) = L;
1150 word1(a) = 0;
1151 #ifndef Avoid_Underflow
1152 #ifndef Sudden_Underflow
1153 }
1154 else {
1155 L = -L >> Exp_shift;
1156 if (L < Exp_shift) {
1157 word0(a) = 0x80000 >> L;
1158 word1(a) = 0;
1159 }
1160 else {
1161 word0(a) = 0;
1162 L -= Exp_shift;
1163 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1164 }
1165 }
1166 #endif
1167 #endif
1168 return dval(a);
1169 }
1170
1171 static double
1172 b2d
1173 #ifdef KR_headers
1174 (a, e) Bigint *a; int *e;
1175 #else
1176 (Bigint *a, int *e)
1177 #endif
1178 {
1179 ULong *xa, *xa0, w, y, z;
1180 int k;
1181 double d;
1182 #ifdef VAX
1183 ULong d0, d1;
1184 #else
1185 #define d0 word0(d)
1186 #define d1 word1(d)
1187 #endif
1188
1189 xa0 = a->x;
1190 xa = xa0 + a->wds;
1191 y = *--xa;
1192 #ifdef DEBUG
1193 if (!y) Bug("zero y in b2d");
1194 #endif
1195 k = hi0bits(y);
1196 *e = 32 - k;
1197 #ifdef Pack_32
1198 if (k < Ebits) {
1199 d0 = Exp_1 | (y >> (Ebits - k));
1200 w = xa > xa0 ? *--xa : 0;
1201 d1 = y << ((32-Ebits) + k) | (w >> (Ebits - k));
1202 goto ret_d;
1203 }
1204 z = xa > xa0 ? *--xa : 0;
1205 if (k -= Ebits) {
1206 d0 = Exp_1 | y << k | (z >> (32 - k));
1207 y = xa > xa0 ? *--xa : 0;
1208 d1 = z << k | (y >> (32 - k));
1209 }
1210 else {
1211 d0 = Exp_1 | y;
1212 d1 = z;
1213 }
1214 #else
1215 if (k < Ebits + 16) {
1216 z = xa > xa0 ? *--xa : 0;
1217 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1218 w = xa > xa0 ? *--xa : 0;
1219 y = xa > xa0 ? *--xa : 0;
1220 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1221 goto ret_d;
1222 }
1223 z = xa > xa0 ? *--xa : 0;
1224 w = xa > xa0 ? *--xa : 0;
1225 k -= Ebits + 16;
1226 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1227 y = xa > xa0 ? *--xa : 0;
1228 d1 = w << k + 16 | y << k;
1229 #endif
1230 ret_d:
1231 #ifdef VAX
1232 word0(d) = d0 >> 16 | d0 << 16;
1233 word1(d) = d1 >> 16 | d1 << 16;
1234 #else
1235 #undef d0
1236 #undef d1
1237 #endif
1238 return dval(d);
1239 }
1240
1241 static Bigint *
1242 d2b
1243 #ifdef KR_headers
1244 (d, e, bits) double d; int *e, *bits;
1245 #else
1246 (double d, int *e, int *bits)
1247 #endif
1248 {
1249 Bigint *b;
1250 int de, k;
1251 ULong *x, y, z;
1252 #ifndef Sudden_Underflow
1253 int i;
1254 #endif
1255 #ifdef VAX
1256 ULong d0, d1;
1257 d0 = word0(d) >> 16 | word0(d) << 16;
1258 d1 = word1(d) >> 16 | word1(d) << 16;
1259 #else
1260 #define d0 word0(d)
1261 #define d1 word1(d)
1262 #endif
1263
1264 #ifdef Pack_32
1265 b = Balloc(1);
1266 #else
1267 b = Balloc(2);
1268 #endif
1269 x = b->x;
1270
1271 z = d0 & Frac_mask;
1272 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1273 #ifdef Sudden_Underflow
1274 de = (int)(d0 >> Exp_shift);
1275 #ifndef IBM
1276 z |= Exp_msk11;
1277 #endif
1278 #else
1279 if ((de = (int)(d0 >> Exp_shift)))
1280 z |= Exp_msk1;
1281 #endif
1282 #ifdef Pack_32
1283 if ((y = d1)) {
1284 if ((k = lo0bits(&y))) {
1285 x[0] = y | (z << (32 - k));
1286 z >>= k;
1287 }
1288 else
1289 x[0] = y;
1290 #ifndef Sudden_Underflow
1291 i =
1292 #endif
1293 b->wds = (x[1] = z) ? 2 : 1;
1294 }
1295 else {
1296 #ifdef DEBUG
1297 if (!z)
1298 Bug("Zero passed to d2b");
1299 #endif
1300 k = lo0bits(&z);
1301 x[0] = z;
1302 #ifndef Sudden_Underflow
1303 i =
1304 #endif
1305 b->wds = 1;
1306 k += 32;
1307 }
1308 #else
1309 if (y = d1) {
1310 if (k = lo0bits(&y))
1311 if (k >= 16) {
1312 x[0] = y | z << 32 - k & 0xffff;
1313 x[1] = z >> k - 16 & 0xffff;
1314 x[2] = z >> k;
1315 i = 2;
1316 }
1317 else {
1318 x[0] = y & 0xffff;
1319 x[1] = y >> 16 | z << 16 - k & 0xffff;
1320 x[2] = z >> k & 0xffff;
1321 x[3] = z >> k+16;
1322 i = 3;
1323 }
1324 else {
1325 x[0] = y & 0xffff;
1326 x[1] = y >> 16;
1327 x[2] = z & 0xffff;
1328 x[3] = z >> 16;
1329 i = 3;
1330 }
1331 }
1332 else {
1333 #ifdef DEBUG
1334 if (!z)
1335 Bug("Zero passed to d2b");
1336 #endif
1337 k = lo0bits(&z);
1338 if (k >= 16) {
1339 x[0] = z;
1340 i = 0;
1341 }
1342 else {
1343 x[0] = z & 0xffff;
1344 x[1] = z >> 16;
1345 i = 1;
1346 }
1347 k += 32;
1348 }
1349 while(!x[i])
1350 --i;
1351 b->wds = i + 1;
1352 #endif
1353 #ifndef Sudden_Underflow
1354 if (de) {
1355 #endif
1356 #ifdef IBM
1357 *e = (de - Bias - (P-1) << 2) + k;
1358 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1359 #else
1360 *e = de - Bias - (P-1) + k;
1361 *bits = P - k;
1362 #endif
1363 #ifndef Sudden_Underflow
1364 }
1365 else {
1366 *e = de - Bias - (P-1) + 1 + k;
1367 #ifdef Pack_32
1368 *bits = 32*i - hi0bits(x[i-1]);
1369 #else
1370 *bits = (i+2)*16 - hi0bits(x[i]);
1371 #endif
1372 }
1373 #endif
1374 return b;
1375 }
1376 #undef d0
1377 #undef d1
1378
1379 static double
1380 ratio
1381 #ifdef KR_headers
1382 (a, b) Bigint *a, *b;
1383 #else
1384 (Bigint *a, Bigint *b)
1385 #endif
1386 {
1387 double da, db;
1388 int k, ka, kb;
1389
1390 dval(da) = b2d(a, &ka);
1391 dval(db) = b2d(b, &kb);
1392 #ifdef Pack_32
1393 k = ka - kb + 32*(a->wds - b->wds);
1394 #else
1395 k = ka - kb + 16*(a->wds - b->wds);
1396 #endif
1397 #ifdef IBM
1398 if (k > 0) {
1399 word0(da) += (k >> 2)*Exp_msk1;
1400 if (k &= 3)
1401 dval(da) *= 1 << k;
1402 }
1403 else {
1404 k = -k;
1405 word0(db) += (k >> 2)*Exp_msk1;
1406 if (k &= 3)
1407 dval(db) *= 1 << k;
1408 }
1409 #else
1410 if (k > 0)
1411 word0(da) += k*Exp_msk1;
1412 else {
1413 k = -k;
1414 word0(db) += k*Exp_msk1;
1415 }
1416 #endif
1417 return dval(da) / dval(db);
1418 }
1419
1420 static CONST double
1421 tens[] = {
1422 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1423 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1424 1e20, 1e21, 1e22
1425 #ifdef VAX
1426 , 1e23, 1e24
1427 #endif
1428 };
1429
1430 static CONST double
1431 #ifdef IEEE_Arith
1432 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1433 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1434 #ifdef Avoid_Underflow
1435 9007199254740992.*9007199254740992.e-256
1436 /* = 2^106 * 1e-53 */
1437 #else
1438 1e-256
1439 #endif
1440 };
1441 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1442 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1443 #define Scale_Bit 0x10
1444 #define n_bigtens 5
1445 #else
1446 #ifdef IBM
1447 bigtens[] = { 1e16, 1e32, 1e64 };
1448 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1449 #define n_bigtens 3
1450 #else
1451 bigtens[] = { 1e16, 1e32 };
1452 static CONST double tinytens[] = { 1e-16, 1e-32 };
1453 #define n_bigtens 2
1454 #endif
1455 #endif
1456
1457 #ifndef IEEE_Arith
1458 #undef INFNAN_CHECK
1459 #endif
1460
1461 #ifdef INFNAN_CHECK
1462
1463 #ifndef NAN_WORD0
1464 #define NAN_WORD0 0x7ff80000
1465 #endif
1466
1467 #ifndef NAN_WORD1
1468 #define NAN_WORD1 0
1469 #endif
1470
1471 static int
1472 match
1473 #ifdef KR_headers
1474 (sp, t) char **sp, *t;
1475 #else
1476 (CONST char **sp, char *t)
1477 #endif
1478 {
1479 int c, d;
1480 CONST char *s = *sp;
1481
1482 while(d = *t++) {
1483 if ((c = *++s) >= 'A' && c <= 'Z')
1484 c += 'a' - 'A';
1485 if (c != d)
1486 return 0;
1487 }
1488 *sp = s + 1;
1489 return 1;
1490 }
1491
1492 #ifndef No_Hex_NaN
1493 static void
1494 hexnan
1495 #ifdef KR_headers
1496 (rvp, sp) double *rvp; CONST char **sp;
1497 #else
1498 (double *rvp, CONST char **sp)
1499 #endif
1500 {
1501 ULong c, x[2];
1502 CONST char *s;
1503 int havedig, udx0, xshift;
1504
1505 x[0] = x[1] = 0;
1506 havedig = xshift = 0;
1507 udx0 = 1;
1508 s = *sp;
1509 while(c = *(CONST unsigned char*)++s) {
1510 if (c >= '0' && c <= '9')
1511 c -= '0';
1512 else if (c >= 'a' && c <= 'f')
1513 c += 10 - 'a';
1514 else if (c >= 'A' && c <= 'F')
1515 c += 10 - 'A';
1516 else if (c <= ' ') {
1517 if (udx0 && havedig) {
1518 udx0 = 0;
1519 xshift = 1;
1520 }
1521 continue;
1522 }
1523 else if (/*(*/ c == ')' && havedig) {
1524 *sp = s + 1;
1525 break;
1526 }
1527 else
1528 return; /* invalid form: don't change *sp */
1529 havedig = 1;
1530 if (xshift) {
1531 xshift = 0;
1532 x[0] = x[1];
1533 x[1] = 0;
1534 }
1535 if (udx0)
1536 x[0] = (x[0] << 4) | (x[1] >> 28);
1537 x[1] = (x[1] << 4) | c;
1538 }
1539 if ((x[0] &= 0xfffff) || x[1]) {
1540 word0(*rvp) = Exp_mask | x[0];
1541 word1(*rvp) = x[1];
1542 }
1543 }
1544 #endif /*No_Hex_NaN*/
1545 #endif /* INFNAN_CHECK */
1546
1547 double
1548 mono_strtod
1549 #ifdef KR_headers
1550 (s00, se) CONST char *s00; char **se;
1551 #else
1552 (CONST char *s00, char **se)
1553 #endif
1554 {
1555 #ifdef Avoid_Underflow
1556 int scale;
1557 #endif
1558 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1559 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1560 CONST char *s, *s0, *s1;
1561 double aadj, aadj1, adj, rv, rv0;
1562 Long L;
1563 ULong y, z;
1564 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1565 #ifdef SET_INEXACT
1566 int inexact, oldinexact;
1567 #endif
1568 #ifdef Honor_FLT_ROUNDS
1569 int rounding;
1570 #endif
1571 #ifdef USE_LOCALE
1572 CONST char *s2;
1573 #endif
1574
1575 sign = nz0 = nz = 0;
1576 dval(rv) = 0.;
1577 for(s = s00;;s++) switch(*s) {
1578 case '-':
1579 sign = 1;
1580 /* no break */
1581 case '+':
1582 if (*++s)
1583 goto break2;
1584 /* no break */
1585 case 0:
1586 goto ret0;
1587 case '\t':
1588 case '\n':
1589 case '\v':
1590 case '\f':
1591 case '\r':
1592 case ' ':
1593 continue;
1594 default:
1595 goto break2;
1596 }
1597 break2:
1598 if (*s == '0') {
1599 nz0 = 1;
1600 while(*++s == '0') ;
1601 if (!*s)
1602 goto ret;
1603 }
1604 s0 = s;
1605 y = z = 0;
1606 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1607 if (nd < 9)
1608 y = 10*y + c - '0';
1609 else if (nd < 16)
1610 z = 10*z + c - '0';
1611 nd0 = nd;
1612 #ifdef USE_LOCALE
1613 s1 = localeconv()->decimal_point;
1614 if (c == *s1) {
1615 c = '.';
1616 if (*++s1) {
1617 s2 = s;
1618 for(;;) {
1619 if (*++s2 != *s1) {
1620 c = 0;
1621 break;
1622 }
1623 if (!*++s1) {
1624 s = s2;
1625 break;
1626 }
1627 }
1628 }
1629 }
1630 #endif
1631 if (c == '.') {
1632 c = *++s;
1633 if (!nd) {
1634 for(; c == '0'; c = *++s)
1635 nz++;
1636 if (c > '0' && c <= '9') {
1637 s0 = s;
1638 nf += nz;
1639 nz = 0;
1640 goto have_dig;
1641 }
1642 goto dig_done;
1643 }
1644 for(; c >= '0' && c <= '9'; c = *++s) {
1645 have_dig:
1646 nz++;
1647 if (c -= '0') {
1648 nf += nz;
1649 for(i = 1; i < nz; i++)
1650 if (nd++ < 9)
1651 y *= 10;
1652 else if (nd <= DBL_DIG + 1)
1653 z *= 10;
1654 if (nd++ < 9)
1655 y = 10*y + c;
1656 else if (nd <= DBL_DIG + 1)
1657 z = 10*z + c;
1658 nz = 0;
1659 }
1660 }
1661 }
1662 dig_done:
1663 e = 0;
1664 if (c == 'e' || c == 'E') {
1665 if (!nd && !nz && !nz0) {
1666 goto ret0;
1667 }
1668 s00 = s;
1669 esign = 0;
1670 switch(c = *++s) {
1671 case '-':
1672 esign = 1;
1673 case '+':
1674 c = *++s;
1675 }
1676 if (c >= '0' && c <= '9') {
1677 while(c == '0')
1678 c = *++s;
1679 if (c > '0' && c <= '9') {
1680 L = c - '0';
1681 s1 = s;
1682 while((c = *++s) >= '0' && c <= '9')
1683 L = 10*L + c - '0';
1684 if (s - s1 > 8 || L > 19999)
1685 /* Avoid confusion from exponents
1686 * so large that e might overflow.
1687 */
1688 e = 19999; /* safe for 16 bit ints */
1689 else
1690 e = (int)L;
1691 if (esign)
1692 e = -e;
1693 }
1694 else
1695 e = 0;
1696 }
1697 else
1698 s = s00;
1699 }
1700 if (!nd) {
1701 if (!nz && !nz0) {
1702 #ifdef INFNAN_CHECK
1703 /* Check for Nan and Infinity */
1704 switch(c) {
1705 case 'i':
1706 case 'I':
1707 if (match(&s,"nf")) {
1708 --s;
1709 if (!match(&s,"inity"))
1710 ++s;
1711 word0(rv) = 0x7ff00000;
1712 word1(rv) = 0;
1713 goto ret;
1714 }
1715 break;
1716 case 'n':
1717 case 'N':
1718 if (match(&s, "an")) {
1719 word0(rv) = NAN_WORD0;
1720 word1(rv) = NAN_WORD1;
1721 #ifndef No_Hex_NaN
1722 if (*s == '(') /*)*/
1723 hexnan(&rv, &s);
1724 #endif
1725 goto ret;
1726 }
1727 }
1728 #endif /* INFNAN_CHECK */
1729 ret0:
1730 s = s00;
1731 sign = 0;
1732 }
1733 goto ret;
1734 }
1735 e1 = e -= nf;
1736
1737 /* Now we have nd0 digits, starting at s0, followed by a
1738 * decimal point, followed by nd-nd0 digits. The number we're
1739 * after is the integer represented by those digits times
1740 * 10**e */
1741
1742 if (!nd0)
1743 nd0 = nd;
1744 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1745 dval(rv) = y;
1746 if (k > 9) {
1747 #ifdef SET_INEXACT
1748 if (k > DBL_DIG)
1749 oldinexact = get_inexact();
1750 #endif
1751 dval(rv) = tens[k - 9] * dval(rv) + z;
1752 }
1753 bd0 = 0;
1754 if (nd <= DBL_DIG
1755 #ifndef RND_PRODQUOT
1756 #ifndef Honor_FLT_ROUNDS
1757 && Flt_Rounds == 1
1758 #endif
1759 #endif
1760 ) {
1761 if (!e)
1762 goto ret;
1763 if (e > 0) {
1764 if (e <= Ten_pmax) {
1765 #ifdef VAX
1766 goto vax_ovfl_check;
1767 #else
1768 #ifdef Honor_FLT_ROUNDS
1769 /* round correctly FLT_ROUNDS = 2 or 3 */
1770 if (sign) {
1771 rv = -rv;
1772 sign = 0;
1773 }
1774 #endif
1775 /* rv = */ rounded_product(dval(rv), tens[e]);
1776 goto ret;
1777 #endif
1778 }
1779 i = DBL_DIG - nd;
1780 if (e <= Ten_pmax + i) {
1781 /* A fancier test would sometimes let us do
1782 * this for larger i values.
1783 */
1784 #ifdef Honor_FLT_ROUNDS
1785 /* round correctly FLT_ROUNDS = 2 or 3 */
1786 if (sign) {
1787 rv = -rv;
1788 sign = 0;
1789 }
1790 #endif
1791 e -= i;
1792 dval(rv) *= tens[i];
1793 #ifdef VAX
1794 /* VAX exponent range is so narrow we must
1795 * worry about overflow here...
1796 */
1797 vax_ovfl_check:
1798 word0(rv) -= P*Exp_msk1;
1799 /* rv = */ rounded_product(dval(rv), tens[e]);
1800 if ((word0(rv) & Exp_mask)
1801 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1802 goto ovfl;
1803 word0(rv) += P*Exp_msk1;
1804 #else
1805 /* rv = */ rounded_product(dval(rv), tens[e]);
1806 #endif
1807 goto ret;
1808 }
1809 }
1810 #ifndef Inaccurate_Divide
1811 else if (e >= -Ten_pmax) {
1812 #ifdef Honor_FLT_ROUNDS
1813 /* round correctly FLT_ROUNDS = 2 or 3 */
1814 if (sign) {
1815 rv = -rv;
1816 sign = 0;
1817 }
1818 #endif
1819 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1820 goto ret;
1821 }
1822 #endif
1823 }
1824 e1 += nd - k;
1825
1826 #ifdef IEEE_Arith
1827 #ifdef SET_INEXACT
1828 inexact = 1;
1829 if (k <= DBL_DIG)
1830 oldinexact = get_inexact();
1831 #endif
1832 #ifdef Avoid_Underflow
1833 scale = 0;
1834 #endif
1835 #ifdef Honor_FLT_ROUNDS
1836 if ((rounding = Flt_Rounds) >= 2) {
1837 if (sign)
1838 rounding = rounding == 2 ? 0 : 2;
1839 else
1840 if (rounding != 2)
1841 rounding = 0;
1842 }
1843 #endif
1844 #endif /*IEEE_Arith*/
1845
1846 /* Get starting approximation = rv * 10**e1 */
1847
1848 if (e1 > 0) {
1849 if ((i = e1 & 15))
1850 dval(rv) *= tens[i];
1851 if (e1 &= ~15) {
1852 if (e1 > DBL_MAX_10_EXP) {
1853 ovfl:
1854 #ifndef NO_ERRNO
1855 errno = ERANGE;
1856 #endif
1857 /* Can't trust HUGE_VAL */
1858 #ifdef IEEE_Arith
1859 #ifdef Honor_FLT_ROUNDS
1860 switch(rounding) {
1861 case 0: /* toward 0 */
1862 case 3: /* toward -infinity */
1863 word0(rv) = Big0;
1864 word1(rv) = Big1;
1865 break;
1866 default:
1867 word0(rv) = Exp_mask;
1868 word1(rv) = 0;
1869 }
1870 #else /*Honor_FLT_ROUNDS*/
1871 word0(rv) = Exp_mask;
1872 word1(rv) = 0;
1873 #endif /*Honor_FLT_ROUNDS*/
1874 #ifdef SET_INEXACT
1875 /* set overflow bit */
1876 dval(rv0) = 1e300;
1877 dval(rv0) *= dval(rv0);
1878 #endif
1879 #else /*IEEE_Arith*/
1880 word0(rv) = Big0;
1881 word1(rv) = Big1;
1882 #endif /*IEEE_Arith*/
1883 if (bd0)
1884 goto retfree;
1885 goto ret;
1886 }
1887 e1 >>= 4;
1888 for(j = 0; e1 > 1; j++, e1 >>= 1)
1889 if (e1 & 1)
1890 dval(rv) *= bigtens[j];
1891 /* The last multiplication could overflow. */
1892 word0(rv) -= P*Exp_msk1;
1893 dval(rv) *= bigtens[j];
1894 if ((z = word0(rv) & Exp_mask)
1895 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1896 goto ovfl;
1897 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1898 /* set to largest number */
1899 /* (Can't trust DBL_MAX) */
1900 word0(rv) = Big0;
1901 word1(rv) = Big1;
1902 }
1903 else
1904 word0(rv) += P*Exp_msk1;
1905 }
1906 }
1907 else if (e1 < 0) {
1908 e1 = -e1;
1909 if ((i = e1 & 15))
1910 dval(rv) /= tens[i];
1911 if (e1 >>= 4) {
1912 if (e1 >= 1 << n_bigtens)
1913 goto undfl;
1914 #ifdef Avoid_Underflow
1915 if (e1 & Scale_Bit)
1916 scale = 2*P;
1917 for(j = 0; e1 > 0; j++, e1 >>= 1)
1918 if (e1 & 1)
1919 dval(rv) *= tinytens[j];
1920 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1921 >> Exp_shift)) > 0) {
1922 /* scaled rv is denormal; zap j low bits */
1923 if (j >= 32) {
1924 word1(rv) = 0;
1925 if (j >= 53)
1926 word0(rv) = (P+2)*Exp_msk1;
1927 else
1928 word0(rv) &= 0xffffffff << (j-32);
1929 }
1930 else
1931 word1(rv) &= 0xffffffff << j;
1932 }
1933 #else
1934 for(j = 0; e1 > 1; j++, e1 >>= 1)
1935 if (e1 & 1)
1936 dval(rv) *= tinytens[j];
1937 /* The last multiplication could underflow. */
1938 dval(rv0) = dval(rv);
1939 dval(rv) *= tinytens[j];
1940 if (!dval(rv)) {
1941 dval(rv) = 2.*dval(rv0);
1942 dval(rv) *= tinytens[j];
1943 #endif
1944 if (!dval(rv)) {
1945 undfl:
1946 dval(rv) = 0.;
1947 #ifndef NO_ERRNO
1948 errno = ERANGE;
1949 #endif
1950 if (bd0)
1951 goto retfree;
1952 goto ret;
1953 }
1954 #ifndef Avoid_Underflow
1955 word0(rv) = Tiny0;
1956 word1(rv) = Tiny1;
1957 /* The refinement below will clean
1958 * this approximation up.
1959 */
1960 }
1961 #endif
1962 }
1963 }
1964
1965 /* Now the hard part -- adjusting rv to the correct value.*/
1966
1967 /* Put digits into bd: true value = bd * 10^e */
1968
1969 bd0 = s2b(s0, nd0, nd, y);
1970
1971 for(;;) {
1972 bd = Balloc(bd0->k);
1973 Bcopy(bd, bd0);
1974 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1975 bs = i2b(1);
1976
1977 if (e >= 0) {
1978 bb2 = bb5 = 0;
1979 bd2 = bd5 = e;
1980 }
1981 else {
1982 bb2 = bb5 = -e;
1983 bd2 = bd5 = 0;
1984 }
1985 if (bbe >= 0)
1986 bb2 += bbe;
1987 else
1988 bd2 -= bbe;
1989 bs2 = bb2;
1990 #ifdef Honor_FLT_ROUNDS
1991 if (rounding != 1)
1992 bs2++;
1993 #endif
1994 #ifdef Avoid_Underflow
1995 j = bbe - scale;
1996 i = j + bbbits - 1; /* logb(rv) */
1997 if (i < Emin) /* denormal */
1998 j += P - Emin;
1999 else
2000 j = P + 1 - bbbits;
2001 #else /*Avoid_Underflow*/
2002 #ifdef Sudden_Underflow
2003 #ifdef IBM
2004 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2005 #else
2006 j = P + 1 - bbbits;
2007 #endif
2008 #else /*Sudden_Underflow*/
2009 j = bbe;
2010 i = j + bbbits - 1; /* logb(rv) */
2011 if (i < Emin) /* denormal */
2012 j += P - Emin;
2013 else
2014 j = P + 1 - bbbits;
2015 #endif /*Sudden_Underflow*/
2016 #endif /*Avoid_Underflow*/
2017 bb2 += j;
2018 bd2 += j;
2019 #ifdef Avoid_Underflow
2020 bd2 += scale;
2021 #endif
2022 i = bb2 < bd2 ? bb2 : bd2;
2023 if (i > bs2)
2024 i = bs2;
2025 if (i > 0) {
2026 bb2 -= i;
2027 bd2 -= i;
2028 bs2 -= i;
2029 }
2030 if (bb5 > 0) {
2031 bs = pow5mult(bs, bb5);
2032 bb1 = mult(bs, bb);
2033 Bfree(bb);
2034 bb = bb1;
2035 }
2036 if (bb2 > 0)
2037 bb = lshift(bb, bb2);
2038 if (bd5 > 0)
2039 bd = pow5mult(bd, bd5);
2040 if (bd2 > 0)
2041 bd = lshift(bd, bd2);
2042 if (bs2 > 0)
2043 bs = lshift(bs, bs2);
2044 delta = diff(bb, bd);
2045 dsign = delta->sign;
2046 delta->sign = 0;
2047 i = cmp(delta, bs);
2048 #ifdef Honor_FLT_ROUNDS
2049 if (rounding != 1) {
2050 if (i < 0) {
2051 /* Error is less than an ulp */
2052 if (!delta->x[0] && delta->wds <= 1) {
2053 /* exact */
2054 #ifdef SET_INEXACT
2055 inexact = 0;
2056 #endif
2057 break;
2058 }
2059 if (rounding) {
2060 if (dsign) {
2061 adj = 1.;
2062 goto apply_adj;
2063 }
2064 }
2065 else if (!dsign) {
2066 adj = -1.;
2067 if (!word1(rv)
2068 && !(word0(rv) & Frac_mask)) {
2069 y = word0(rv) & Exp_mask;
2070 #ifdef Avoid_Underflow
2071 if (!scale || y > 2*P*Exp_msk1)
2072 #else
2073 if (y)
2074 #endif
2075 {
2076 delta = lshift(delta,Log2P);
2077 if (cmp(delta, bs) <= 0)
2078 adj = -0.5;
2079 }
2080 }
2081 apply_adj:
2082 #ifdef Avoid_Underflow
2083 if (scale && (y = word0(rv) & Exp_mask)
2084 <= 2*P*Exp_msk1)
2085 word0(adj) += (2*P+1)*Exp_msk1 - y;
2086 #else
2087 #ifdef Sudden_Underflow
2088 if ((word0(rv) & Exp_mask) <=
2089 P*Exp_msk1) {
2090 word0(rv) += P*Exp_msk1;
2091 dval(rv) += adj*ulp(dval(rv));
2092 word0(rv) -= P*Exp_msk1;
2093 }
2094 else
2095 #endif /*Sudden_Underflow*/
2096 #endif /*Avoid_Underflow*/
2097 dval(rv) += adj*ulp(dval(rv));
2098 }
2099 break;
2100 }
2101 adj = ratio(delta, bs);
2102 if (adj < 1.)
2103 adj = 1.;
2104 if (adj <= 0x7ffffffe) {
2105 /* adj = rounding ? ceil(adj) : floor(adj); */
2106 y = adj;
2107 if (y != adj) {
2108 if (!((rounding>>1) ^ dsign))
2109 y++;
2110 adj = y;
2111 }
2112 }
2113 #ifdef Avoid_Underflow
2114 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2115 word0(adj) += (2*P+1)*Exp_msk1 - y;
2116 #else
2117 #ifdef Sudden_Underflow
2118 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2119 word0(rv) += P*Exp_msk1;
2120 adj *= ulp(dval(rv));
2121 if (dsign)
2122 dval(rv) += adj;
2123 else
2124 dval(rv) -= adj;
2125 word0(rv) -= P*Exp_msk1;
2126 goto cont;
2127 }
2128 #endif /*Sudden_Underflow*/
2129 #endif /*Avoid_Underflow*/
2130 adj *= ulp(dval(rv));
2131 if (dsign)
2132 dval(rv) += adj;
2133 else
2134 dval(rv) -= adj;
2135 goto cont;
2136 }
2137 #endif /*Honor_FLT_ROUNDS*/
2138
2139 if (i < 0) {
2140 /* Error is less than half an ulp -- check for
2141 * special case of mantissa a power of two.
2142 */
2143 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2144 #ifdef IEEE_Arith
2145 #ifdef Avoid_Underflow
2146 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2147 #else
2148 || (word0(rv) & Exp_mask) <= Exp_msk1
2149 #endif
2150 #endif
2151 ) {
2152 #ifdef SET_INEXACT
2153 if (!delta->x[0] && delta->wds <= 1)
2154 inexact = 0;
2155 #endif
2156 break;
2157 }
2158 if (!delta->x[0] && delta->wds <= 1) {
2159 /* exact result */
2160 #ifdef SET_INEXACT
2161 inexact = 0;
2162 #endif
2163 break;
2164 }
2165 delta = lshift(delta,Log2P);
2166 if (cmp(delta, bs) > 0)
2167 goto drop_down;
2168 break;
2169 }
2170 if (i == 0) {
2171 /* exactly half-way between */
2172 if (dsign) {
2173 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2174 && word1(rv) == (
2175 #ifdef Avoid_Underflow
2176 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2177 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2178 #endif
2179 0xffffffff)) {
2180 /*boundary case -- increment exponent*/
2181 word0(rv) = (word0(rv) & Exp_mask)
2182 + Exp_msk1
2183 #ifdef IBM
2184 | Exp_msk1 >> 4
2185 #endif
2186 ;
2187 word1(rv) = 0;
2188 #ifdef Avoid_Underflow
2189 dsign = 0;
2190 #endif
2191 break;
2192 }
2193 }
2194 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2195 drop_down:
2196 /* boundary case -- decrement exponent */
2197 #ifdef Sudden_Underflow /*{{*/
2198 L = word0(rv) & Exp_mask;
2199 #ifdef IBM
2200 if (L < Exp_msk1)
2201 #else
2202 #ifdef Avoid_Underflow
2203 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2204 #else
2205 if (L <= Exp_msk1)
2206 #endif /*Avoid_Underflow*/
2207 #endif /*IBM*/
2208 goto undfl;
2209 L -= Exp_msk1;
2210 #else /*Sudden_Underflow}{*/
2211 #ifdef Avoid_Underflow
2212 if (scale) {
2213 L = word0(rv) & Exp_mask;
2214 if (L <= (2*P+1)*Exp_msk1) {
2215 if (L > (P+2)*Exp_msk1)
2216 /* round even ==> */
2217 /* accept rv */
2218 break;
2219 /* rv = smallest denormal */
2220 goto undfl;
2221 }
2222 }
2223 #endif /*Avoid_Underflow*/
2224 L = (word0(rv) & Exp_mask) - Exp_msk1;
2225 #endif /*Sudden_Underflow}}*/
2226 word0(rv) = L | Bndry_mask1;
2227 word1(rv) = 0xffffffff;
2228 #ifdef IBM
2229 goto cont;
2230 #else
2231 break;
2232 #endif
2233 }
2234 #ifndef ROUND_BIASED
2235 if (!(word1(rv) & LSB))
2236 break;
2237 #endif
2238 if (dsign)
2239 dval(rv) += ulp(dval(rv));
2240 #ifndef ROUND_BIASED
2241 else {
2242 dval(rv) -= ulp(dval(rv));
2243 #ifndef Sudden_Underflow
2244 if (!dval(rv))
2245 goto undfl;
2246 #endif
2247 }
2248 #ifdef Avoid_Underflow
2249 dsign = 1 - dsign;
2250 #endif
2251 #endif
2252 break;
2253 }
2254 if ((aadj = ratio(delta, bs)) <= 2.) {
2255 if (dsign)
2256 aadj = aadj1 = 1.;
2257 else if (word1(rv) || word0(rv) & Bndry_mask) {
2258 #ifndef Sudden_Underflow
2259 if (word1(rv) == Tiny1 && !word0(rv))
2260 goto undfl;
2261 #endif
2262 aadj = 1.;
2263 aadj1 = -1.;
2264 }
2265 else {
2266 /* special case -- power of FLT_RADIX to be */
2267 /* rounded down... */
2268
2269 if (aadj < 2./FLT_RADIX)
2270 aadj = 1./FLT_RADIX;
2271 else
2272 aadj *= 0.5;
2273 aadj1 = -aadj;
2274 }
2275 }
2276 else {
2277 aadj *= 0.5;
2278 aadj1 = dsign ? aadj : -aadj;
2279 #ifdef Check_FLT_ROUNDS
2280 switch(Rounding) {
2281 case 2: /* towards +infinity */
2282 aadj1 -= 0.5;
2283 break;
2284 case 0: /* towards 0 */
2285 case 3: /* towards -infinity */
2286 aadj1 += 0.5;
2287 }
2288 #else
2289 if (Flt_Rounds == 0)
2290 aadj1 += 0.5;
2291 #endif /*Check_FLT_ROUNDS*/
2292 }
2293 y = word0(rv) & Exp_mask;
2294
2295 /* Check for overflow */
2296
2297 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2298 dval(rv0) = dval(rv);
2299 word0(rv) -= P*Exp_msk1;
2300 adj = aadj1 * ulp(dval(rv));
2301 dval(rv) += adj;
2302 if ((word0(rv) & Exp_mask) >=
2303 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2304 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2305 goto ovfl;
2306 word0(rv) = Big0;
2307 word1(rv) = Big1;
2308 goto cont;
2309 }
2310 else
2311 word0(rv) += P*Exp_msk1;
2312 }
2313 else {
2314 #ifdef Avoid_Underflow
2315 if (scale && y <= 2*P*Exp_msk1) {
2316 if (aadj <= 0x7fffffff) {
2317 if ((z = aadj) <= 0)
2318 z = 1;
2319 aadj = z;
2320 aadj1 = dsign ? aadj : -aadj;
2321 }
2322 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2323 }
2324 adj = aadj1 * ulp(dval(rv));
2325 dval(rv) += adj;
2326 #else
2327 #ifdef Sudden_Underflow
2328 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2329 dval(rv0) = dval(rv);
2330 word0(rv) += P*Exp_msk1;
2331 adj = aadj1 * ulp(dval(rv));
2332 dval(rv) += adj;
2333 #ifdef IBM
2334 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2335 #else
2336 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2337 #endif
2338 {
2339 if (word0(rv0) == Tiny0
2340 && word1(rv0) == Tiny1)
2341 goto undfl;
2342 word0(rv) = Tiny0;
2343 word1(rv) = Tiny1;
2344 goto cont;
2345 }
2346 else
2347 word0(rv) -= P*Exp_msk1;
2348 }
2349 else {
2350 adj = aadj1 * ulp(dval(rv));
2351 dval(rv) += adj;
2352 }
2353 #else /*Sudden_Underflow*/
2354 /* Compute adj so that the IEEE rounding rules will
2355 * correctly round rv + adj in some half-way cases.
2356 * If rv * ulp(rv) is denormalized (i.e.,
2357 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2358 * trouble from bits lost to denormalization;
2359 * example: 1.2e-307 .
2360 */
2361 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2362 aadj1 = (double)(int)(aadj + 0.5);
2363 if (!dsign)
2364 aadj1 = -aadj1;
2365 }
2366 adj = aadj1 * ulp(dval(rv));
2367 dval(rv) += adj;
2368 #endif /*Sudden_Underflow*/
2369 #endif /*Avoid_Underflow*/
2370 }
2371 z = word0(rv) & Exp_mask;
2372 #ifndef SET_INEXACT
2373 #ifdef Avoid_Underflow
2374 if (!scale)
2375 #endif
2376 if (y == z) {
2377 /* Can we stop now? */
2378 L = (Long)aadj;
2379 aadj -= L;
2380 /* The tolerances below are conservative. */
2381 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2382 if (aadj < .4999999 || aadj > .5000001)
2383 break;
2384 }
2385 else if (aadj < .4999999/FLT_RADIX)
2386 break;
2387 }
2388 #endif
2389 cont:
2390 Bfree(bb);
2391 Bfree(bd);
2392 Bfree(bs);
2393 Bfree(delta);
2394 }
2395 #ifdef SET_INEXACT
2396 if (inexact) {
2397 if (!oldinexact) {
2398 word0(rv0) = Exp_1 + (70 << Exp_shift);
2399 word1(rv0) = 0;
2400 dval(rv0) += 1.;
2401 }
2402 }
2403 else if (!oldinexact)
2404 clear_inexact();
2405 #endif
2406 #ifdef Avoid_Underflow
2407 if (scale) {
2408 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2409 word1(rv0) = 0;
2410 dval(rv) *= dval(rv0);
2411 #ifndef NO_ERRNO
2412 /* try to avoid the bug of testing an 8087 register value */
2413 if (word0(rv) == 0 && word1(rv) == 0)
2414 errno = ERANGE;
2415 #endif
2416 }
2417 #endif /* Avoid_Underflow */
2418 #ifdef SET_INEXACT
2419 if (inexact && !(word0(rv) & Exp_mask)) {
2420 /* set underflow bit */
2421 dval(rv0) = 1e-300;
2422 dval(rv0) *= dval(rv0);
2423 }
2424 #endif
2425 retfree:
2426 Bfree(bb);
2427 Bfree(bd);
2428 Bfree(bs);
2429 Bfree(bd0);
2430 Bfree(delta);
2431 ret:
2432 if (se)
2433 *se = (char *)s;
2434 return sign ? -dval(rv) : dval(rv);
2435 }
2436
2437 static int
2438 quorem
2439 #ifdef KR_headers
2440 (b, S) Bigint *b, *S;
2441 #else
2442 (Bigint *b, Bigint *S)
2443 #endif
2444 {
2445 int n;
2446 ULong *bx, *bxe, q, *sx, *sxe;
2447 #ifdef ULLong
2448 ULLong borrow, carry, y, ys;
2449 #else
2450 ULong borrow, carry, y, ys;
2451 #ifdef Pack_32
2452 ULong si, z, zs;
2453 #endif
2454 #endif
2455
2456 n = S->wds;
2457 #ifdef DEBUG
2458 /*debug*/ if (b->wds > n)
2459 /*debug*/ Bug("oversize b in quorem");
2460 #endif
2461 if (b->wds < n)
2462 return 0;
2463 sx = S->x;
2464 sxe = sx + --n;
2465 bx = b->x;
2466 bxe = bx + n;
2467 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2468 #ifdef DEBUG
2469 /*debug*/ if (q > 9)
2470 /*debug*/ Bug("oversized quotient in quorem");
2471 #endif
2472 if (q) {
2473 borrow = 0;
2474 carry = 0;
2475 do {
2476 #ifdef ULLong
2477 ys = *sx++ * (ULLong)q + carry;
2478 carry = ys >> 32;
2479 y = *bx - (ys & FFFFFFFF) - borrow;
2480 borrow = y >> 32 & (ULong)1;
2481 *bx++ = y & FFFFFFFF;
2482 #else
2483 #ifdef Pack_32
2484 si = *sx++;
2485 ys = (si & 0xffff) * q + carry;
2486 zs = (si >> 16) * q + (ys >> 16);
2487 carry = zs >> 16;
2488 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2489 borrow = (y & 0x10000) >> 16;
2490 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2491 borrow = (z & 0x10000) >> 16;
2492 Storeinc(bx, z, y);
2493 #else
2494 ys = *sx++ * q + carry;
2495 carry = ys >> 16;
2496 y = *bx - (ys & 0xffff) - borrow;
2497 borrow = (y & 0x10000) >> 16;
2498 *bx++ = y & 0xffff;
2499 #endif
2500 #endif
2501 }
2502 while(sx <= sxe);
2503 if (!*bxe) {
2504 bx = b->x;
2505 while(--bxe > bx && !*bxe)
2506 --n;
2507 b->wds = n;
2508 }
2509 }
2510 if (cmp(b, S) >= 0) {
2511 q++;
2512 borrow = 0;
2513 carry = 0;
2514 bx = b->x;
2515 sx = S->x;
2516 do {
2517 #ifdef ULLong
2518 ys = *sx++ + carry;
2519 carry = ys >> 32;
2520 y = *bx - (ys & FFFFFFFF) - borrow;
2521 borrow = y >> 32 & (ULong)1;
2522 *bx++ = y & FFFFFFFF;
2523 #else
2524 #ifdef Pack_32
2525 si = *sx++;
2526 ys = (si & 0xffff) + carry;
2527 zs = (si >> 16) + (ys >> 16);
2528 carry = zs >> 16;
2529 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2530 borrow = (y & 0x10000) >> 16;
2531 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2532 borrow = (z & 0x10000) >> 16;
2533 Storeinc(bx, z, y);
2534 #else
2535 ys = *sx++ + carry;
2536 carry = ys >> 16;
2537 y = *bx - (ys & 0xffff) - borrow;
2538 borrow = (y & 0x10000) >> 16;
2539 *bx++ = y & 0xffff;
2540 #endif
2541 #endif
2542 }
2543 while(sx <= sxe);
2544 bx = b->x;
2545 bxe = bx + n;
2546 if (!*bxe) {
2547 while(--bxe > bx && !*bxe)
2548 --n;
2549 b->wds = n;
2550 }
2551 }
2552 return q;
2553 }
2554
2555 #ifndef MULTIPLE_THREADS
2556 static char *dtoa_result;
2557 #endif
2558
2559 static char *
2560 #ifdef KR_headers
2561 rv_alloc(i) int i;
2562 #else
2563 rv_alloc(int i)
2564 #endif
2565 {
2566 int j, k, *r;
2567
2568 j = sizeof(ULong);
2569 for(k = 0;
2570 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
2571 j <<= 1)
2572 k++;
2573 r = (int*)Balloc(k);
2574 *r = k;
2575 return
2576 #ifndef MULTIPLE_THREADS
2577 dtoa_result =
2578 #endif
2579 (char *)(r+1);
2580 }
2581
2582 static char *
2583 #ifdef KR_headers
2584 nrv_alloc(s, rve, n) char *s, **rve; int n;
2585 #else
2586 nrv_alloc(char *s, char **rve, int n)
2587 #endif
2588 {
2589 char *rv, *t;
2590
2591 t = rv = rv_alloc(n);
2592 while((*t = *s++)) t++;
2593 if (rve)
2594 *rve = t;
2595 return rv;
2596 }
2597
2598 /* freedtoa(s) must be used to free values s returned by dtoa
2599 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2600 * but for consistency with earlier versions of dtoa, it is optional
2601 * when MULTIPLE_THREADS is not defined.
2602 */
2603
2604 static void freedtoa (char *s);
2605
2606 static void
2607 #ifdef KR_headers
2608 freedtoa(s) char *s;
2609 #else
2610 freedtoa(char *s)
2611 #endif
2612 {
2613 Bigint *b = (Bigint *)((int *)s - 1);
2614 b->maxwds = 1 << (b->k = *(int*)b);
2615 Bfree(b);
2616 #ifndef MULTIPLE_THREADS
2617 if (s == dtoa_result)
2618 dtoa_result = 0;
2619 #endif
2620 }
2621
2622 #if 0
2623 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2624 *
2625 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2626 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2627 *
2628 * Modifications:
2629 * 1. Rather than iterating, we use a simple numeric overestimate
2630 * to determine k = floor(log10(d)). We scale relevant
2631 * quantities using O(log2(k)) rather than O(k) multiplications.
2632 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2633 * try to generate digits strictly left to right. Instead, we
2634 * compute with fewer bits and propagate the carry if necessary
2635 * when rounding the final digit up. This is often faster.
2636 * 3. Under the assumption that input will be rounded nearest,
2637 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2638 * That is, we allow equality in stopping tests when the
2639 * round-nearest rule will give the same floating-point value
2640 * as would satisfaction of the stopping test with strict
2641 * inequality.
2642 * 4. We remove common factors of powers of 2 from relevant
2643 * quantities.
2644 * 5. When converting floating-point integers less than 1e16,
2645 * we use floating-point arithmetic rather than resorting
2646 * to multiple-precision integers.
2647 * 6. When asked to produce fewer than 15 digits, we first try
2648 * to get by with floating-point arithmetic; we resort to
2649 * multiple-precision integer arithmetic only if we cannot
2650 * guarantee that the floating-point calculation has given
2651 * the correctly rounded result. For k requested digits and
2652 * "uniformly" distributed input, the probability is
2653 * something like 10^(k-15) that we must resort to the Long
2654 * calculation.
2655 */
2656
2657 char *
2658 dtoa
2659 #ifdef KR_headers
2660 (d, mode, ndigits, decpt, sign, rve)
2661 double d; int mode, ndigits, *decpt, *sign; char **rve;
2662 #else
2663 (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2664 #endif
2665 {
2666 /* Arguments ndigits, decpt, sign are similar to those
2667 of ecvt and fcvt; trailing zeros are suppressed from
2668 the returned string. If not null, *rve is set to point
2669 to the end of the return value. If d is +-Infinity or NaN,
2670 then *decpt is set to 9999.
2671
2672 mode:
2673 0 ==> shortest string that yields d when read in
2674 and rounded to nearest.
2675 1 ==> like 0, but with Steele & White stopping rule;
2676 e.g. with IEEE P754 arithmetic , mode 0 gives
2677 1e23 whereas mode 1 gives 9.999999999999999e22.
2678 2 ==> max(1,ndigits) significant digits. This gives a
2679 return value similar to that of ecvt, except
2680 that trailing zeros are suppressed.
2681 3 ==> through ndigits past the decimal point. This
2682 gives a return value similar to that from fcvt,
2683 except that trailing zeros are suppressed, and
2684 ndigits can be negative.
2685 4,5 ==> similar to 2 and 3, respectively, but (in
2686 round-nearest mode) with the tests of mode 0 to
2687 possibly return a shorter string that rounds to d.
2688 With IEEE arithmetic and compilation with
2689 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2690 as modes 2 and 3 when FLT_ROUNDS != 1.
2691 6-9 ==> Debugging modes similar to mode - 4: don't try
2692 fast floating-point estimate (if applicable).
2693
2694 Values of mode other than 0-9 are treated as mode 0.
2695
2696 Sufficient space is allocated to the return value
2697 to hold the suppressed trailing zeros.
2698 */
2699
2700 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2701 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2702 spec_case, try_quick;
2703 Long L;
2704 #ifndef Sudden_Underflow
2705 int denorm;
2706 ULong x;
2707 #endif
2708 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2709 double d2, ds, eps;
2710 char *s, *s0;
2711 #ifdef Honor_FLT_ROUNDS
2712 int rounding;
2713 #endif
2714 #ifdef SET_INEXACT
2715 int inexact, oldinexact;
2716 #endif
2717
2718 #ifndef MULTIPLE_THREADS
2719 if (dtoa_result) {
2720 freedtoa(dtoa_result);
2721 dtoa_result = 0;
2722 }
2723 #endif
2724
2725 if (word0(d) & Sign_bit) {
2726 /* set sign for everything, including 0's and NaNs */
2727 *sign = 1;
2728 word0(d) &= ~Sign_bit; /* clear sign bit */
2729 }
2730 else
2731 *sign = 0;
2732
2733 #if defined(IEEE_Arith) + defined(VAX)
2734 #ifdef IEEE_Arith
2735 if ((word0(d) & Exp_mask) == Exp_mask)
2736 #else
2737 if (word0(d) == 0x8000)
2738 #endif
2739 {
2740 /* Infinity or NaN */
2741 *decpt = 9999;
2742 #ifdef IEEE_Arith
2743 if (!word1(d) && !(word0(d) & 0xfffff))
2744 return nrv_alloc("Infinity", rve, 8);
2745 #endif
2746 return nrv_alloc("NaN", rve, 3);
2747 }
2748 #endif
2749 #ifdef IBM
2750 dval(d) += 0; /* normalize */
2751 #endif
2752 if (!dval(d)) {
2753 *decpt = 1;
2754 return nrv_alloc("0", rve, 1);
2755 }
2756
2757 #ifdef SET_INEXACT
2758 try_quick = oldinexact = get_inexact();
2759 inexact = 1;
2760 #endif
2761 #ifdef Honor_FLT_ROUNDS
2762 if ((rounding = Flt_Rounds) >= 2) {
2763 if (*sign)
2764 rounding = rounding == 2 ? 0 : 2;
2765 else
2766 if (rounding != 2)
2767 rounding = 0;
2768 }
2769 #endif
2770
2771 b = d2b(dval(d), &be, &bbits);
2772 #ifdef Sudden_Underflow
2773 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2774 #else
2775 if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
2776 #endif
2777 dval(d2) = dval(d);
2778 word0(d2) &= Frac_mask1;
2779 word0(d2) |= Exp_11;
2780 #ifdef IBM
2781 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2782 dval(d2) /= 1 << j;
2783 #endif
2784
2785 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2786 * log10(x) = log(x) / log(10)
2787 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2788 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2789 *
2790 * This suggests computing an approximation k to log10(d) by
2791 *
2792 * k = (i - Bias)*0.301029995663981
2793 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2794 *
2795 * We want k to be too large rather than too small.
2796 * The error in the first-order Taylor series approximation
2797 * is in our favor, so we just round up the constant enough
2798 * to compensate for any error in the multiplication of
2799 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2800 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2801 * adding 1e-13 to the constant term more than suffices.
2802 * Hence we adjust the constant term to 0.1760912590558.
2803 * (We could get a more accurate k by invoking log10,
2804 * but this is probably not worthwhile.)
2805 */
2806
2807 i -= Bias;
2808 #ifdef IBM
2809 i <<= 2;
2810 i += j;
2811 #endif
2812 #ifndef Sudden_Underflow
2813 denorm = 0;
2814 }
2815 else {
2816 /* d is denormalized */
2817
2818 i = bbits + be + (Bias + (P-1) - 1);
2819 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2820 : word1(d) << 32 - i;
2821 dval(d2) = x;
2822 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2823 i -= (Bias + (P-1) - 1) + 1;
2824 denorm = 1;
2825 }
2826 #endif
2827 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2828 k = (int)ds;
2829 if (ds < 0. && ds != k)
2830 k--; /* want k = floor(ds) */
2831 k_check = 1;
2832 if (k >= 0 && k <= Ten_pmax) {
2833 if (dval(d) < tens[k])
2834 k--;
2835 k_check = 0;
2836 }
2837 j = bbits - i - 1;
2838 if (j >= 0) {
2839 b2 = 0;
2840 s2 = j;
2841 }
2842 else {
2843 b2 = -j;
2844 s2 = 0;
2845 }
2846 if (k >= 0) {
2847 b5 = 0;
2848 s5 = k;
2849 s2 += k;
2850 }
2851 else {
2852 b2 -= k;
2853 b5 = -k;
2854 s5 = 0;
2855 }
2856 if (mode < 0 || mode > 9)
2857 mode = 0;
2858
2859 #ifndef SET_INEXACT
2860 #ifdef Check_FLT_ROUNDS
2861 try_quick = Rounding == 1;
2862 #else
2863 try_quick = 1;
2864 #endif
2865 #endif /*SET_INEXACT*/
2866
2867 if (mode > 5) {
2868 mode -= 4;
2869 try_quick = 0;
2870 }
2871 leftright = 1;
2872 switch(mode) {
2873 case 0:
2874 case 1:
2875 ilim = ilim1 = -1;
2876 i = 18;
2877 ndigits = 0;
2878 break;
2879 case 2:
2880 leftright = 0;
2881 /* no break */
2882 case 4:
2883 if (ndigits <= 0)
2884 ndigits = 1;
2885 ilim = ilim1 = i = ndigits;
2886 break;
2887 case 3:
2888 leftright = 0;
2889 /* no break */
2890 case 5:
2891 i = ndigits + k + 1;
2892 ilim = i;
2893 ilim1 = i - 1;
2894 if (i <= 0)
2895 i = 1;
2896 }
2897 s = s0 = rv_alloc(i);
2898
2899 #ifdef Honor_FLT_ROUNDS
2900 if (mode > 1 && rounding != 1)
2901 leftright = 0;
2902 #endif
2903
2904 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2905
2906 /* Try to get by with floating-point arithmetic. */
2907
2908 i = 0;
2909 dval(d2) = dval(d);
2910 k0 = k;
2911 ilim0 = ilim;
2912 ieps = 2; /* conservative */
2913 if (k > 0) {
2914 ds = tens[k&0xf];
2915 j = k >> 4;
2916 if (j & Bletch) {
2917 /* prevent overflows */
2918 j &= Bletch - 1;
2919 dval(d) /= bigtens[n_bigtens-1];
2920 ieps++;
2921 }
2922 for(; j; j >>= 1, i++)
2923 if (j & 1) {
2924 ieps++;
2925 ds *= bigtens[i];
2926 }
2927 dval(d) /= ds;
2928 }
2929 else if (j1 = -k) {
2930 dval(d) *= tens[j1 & 0xf];
2931 for(j = j1 >> 4; j; j >>= 1, i++)
2932 if (j & 1) {
2933 ieps++;
2934 dval(d) *= bigtens[i];
2935 }
2936 }
2937 if (k_check && dval(d) < 1. && ilim > 0) {
2938 if (ilim1 <= 0)
2939 goto fast_failed;
2940 ilim = ilim1;
2941 k--;
2942 dval(d) *= 10.;
2943 ieps++;
2944 }
2945 dval(eps) = ieps*dval(d) + 7.;
2946 word0(eps) -= (P-1)*Exp_msk1;
2947 if (ilim == 0) {
2948 S = mhi = 0;
2949 dval(d) -= 5.;
2950 if (dval(d) > dval(eps))
2951 goto one_digit;
2952 if (dval(d) < -dval(eps))
2953 goto no_digits;
2954 goto fast_failed;
2955 }
2956 #ifndef No_leftright
2957 if (leftright) {
2958 /* Use Steele & White method of only
2959 * generating digits needed.
2960 */
2961 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2962 for(i = 0;;) {
2963 L = dval(d);
2964 dval(d) -= L;
2965 *s++ = '0' + (int)L;
2966 if (dval(d) < dval(eps))
2967 goto ret1;
2968 if (1. - dval(d) < dval(eps))
2969 goto bump_up;
2970 if (++i >= ilim)
2971 break;
2972 dval(eps) *= 10.;
2973 dval(d) *= 10.;
2974 }
2975 }
2976 else {
2977 #endif
2978 /* Generate ilim digits, then fix them up. */
2979 dval(eps) *= tens[ilim-1];
2980 for(i = 1;; i++, dval(d) *= 10.) {
2981 L = (Long)(dval(d));
2982 if (!(dval(d) -= L))
2983 ilim = i;
2984 *s++ = '0' + (int)L;
2985 if (i == ilim) {
2986 if (dval(d) > 0.5 + dval(eps))
2987 goto bump_up;
2988 else if (dval(d) < 0.5 - dval(eps)) {
2989 while(*--s == '0');
2990 s++;
2991 goto ret1;
2992 }
2993 break;
2994 }
2995 }
2996 #ifndef No_leftright
2997 }
2998 #endif
2999 fast_failed:
3000 s = s0;
3001 dval(d) = dval(d2);
3002 k = k0;
3003 ilim = ilim0;
3004 }
3005
3006 /* Do we have a "small" integer? */
3007
3008 if (be >= 0 && k <= Int_max) {
3009 /* Yes. */
3010 ds = tens[k];
3011 if (ndigits < 0 && ilim <= 0) {
3012 S = mhi = 0;
3013 if (ilim < 0 || dval(d) <= 5*ds)
3014 goto no_digits;
3015 goto one_digit;
3016 }
3017 for(i = 1;; i++, dval(d) *= 10.) {
3018 L = (Long)(dval(d) / ds);
3019 dval(d) -= L*ds;
3020 #ifdef Check_FLT_ROUNDS
3021 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3022 if (dval(d) < 0) {
3023 L--;
3024 dval(d) += ds;
3025 }
3026 #endif
3027 *s++ = '0' + (int)L;
3028 if (!dval(d)) {
3029 #ifdef SET_INEXACT
3030 inexact = 0;
3031 #endif
3032 break;
3033 }
3034 if (i == ilim) {
3035 #ifdef Honor_FLT_ROUNDS
3036 if (mode > 1)
3037 switch(rounding) {
3038 case 0: goto ret1;
3039 case 2: goto bump_up;
3040 }
3041 #endif
3042 dval(d) += dval(d);
3043 if (dval(d) > ds || dval(d) == ds && L & 1) {
3044 bump_up:
3045 while(*--s == '9')
3046 if (s == s0) {
3047 k++;
3048 *s = '0';
3049 break;
3050 }
3051 ++*s++;
3052 }
3053 break;
3054 }
3055 }
3056 goto ret1;
3057 }
3058
3059 m2 = b2;
3060 m5 = b5;
3061 mhi = mlo = 0;
3062 if (leftright) {
3063 i =
3064 #ifndef Sudden_Underflow
3065 denorm ? be + (Bias + (P-1) - 1 + 1) :
3066 #endif
3067 #ifdef IBM
3068 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3069 #else
3070 1 + P - bbits;
3071 #endif
3072 b2 += i;
3073 s2 += i;
3074 mhi = i2b(1);
3075 }
3076 if (m2 > 0 && s2 > 0) {
3077 i = m2 < s2 ? m2 : s2;
3078 b2 -= i;
3079 m2 -= i;
3080 s2 -= i;
3081 }
3082 if (b5 > 0) {
3083 if (leftright) {
3084 if (m5 > 0) {
3085 mhi = pow5mult(mhi, m5);
3086 b1 = mult(mhi, b);
3087 Bfree(b);
3088 b = b1;
3089 }
3090 if (j = b5 - m5)
3091 b = pow5mult(b, j);
3092 }
3093 else
3094 b = pow5mult(b, b5);
3095 }
3096 S = i2b(1);
3097 if (s5 > 0)
3098 S = pow5mult(S, s5);
3099
3100 /* Check for special case that d is a normalized power of 2. */
3101
3102 spec_case = 0;
3103 if ((mode < 2 || leftright)
3104 #ifdef Honor_FLT_ROUNDS
3105 && rounding == 1
3106 #endif
3107 ) {
3108 if (!word1(d) && !(word0(d) & Bndry_mask)
3109 #ifndef Sudden_Underflow
3110 && word0(d) & (Exp_mask & ~Exp_msk1)
3111 #endif
3112 ) {
3113 /* The special case */
3114 b2 += Log2P;
3115 s2 += Log2P;
3116 spec_case = 1;
3117 }
3118 }
3119
3120 /* Arrange for convenient computation of quotients:
3121 * shift left if necessary so divisor has 4 leading 0 bits.
3122 *
3123 * Perhaps we should just compute leading 28 bits of S once
3124 * and for all and pass them and a shift to quorem, so it
3125 * can do shifts and ors to compute the numerator for q.
3126 */
3127 #ifdef Pack_32
3128 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
3129 i = 32 - i;
3130 #else
3131 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3132 i = 16 - i;
3133 #endif
3134 if (i > 4) {
3135 i -= 4;
3136 b2 += i;
3137 m2 += i;
3138 s2 += i;
3139 }
3140 else if (i < 4) {
3141 i += 28;
3142 b2 += i;
3143 m2 += i;
3144 s2 += i;
3145 }
3146 if (b2 > 0)
3147 b = lshift(b, b2);
3148 if (s2 > 0)
3149 S = lshift(S, s2);
3150 if (k_check) {
3151 if (cmp(b,S) < 0) {
3152 k--;
3153 b = multadd(b, 10, 0); /* we botched the k estimate */
3154 if (leftright)
3155 mhi = multadd(mhi, 10, 0);
3156 ilim = ilim1;
3157 }
3158 }
3159 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3160 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3161 /* no digits, fcvt style */
3162 no_digits:
3163 k = -1 - ndigits;
3164 goto ret;
3165 }
3166 one_digit:
3167 *s++ = '1';
3168 k++;
3169 goto ret;
3170 }
3171 if (leftright) {
3172 if (m2 > 0)
3173 mhi = lshift(mhi, m2);
3174
3175 /* Compute mlo -- check for special case
3176 * that d is a normalized power of 2.
3177 */
3178
3179 mlo = mhi;
3180 if (spec_case) {
3181 mhi = Balloc(mhi->k);
3182 Bcopy(mhi, mlo);
3183 mhi = lshift(mhi, Log2P);
3184 }
3185
3186 for(i = 1;;i++) {
3187 dig = quorem(b,S) + '0';
3188 /* Do we yet have the shortest decimal string
3189 * that will round to d?
3190 */
3191 j = cmp(b, mlo);
3192 delta = diff(S, mhi);
3193 j1 = delta->sign ? 1 : cmp(b, delta);
3194 Bfree(delta);
3195 #ifndef ROUND_BIASED
3196 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3197 #ifdef Honor_FLT_ROUNDS
3198 && rounding >= 1
3199 #endif
3200 ) {
3201 if (dig == '9')
3202 goto round_9_up;
3203 if (j > 0)
3204 dig++;
3205 #ifdef SET_INEXACT
3206 else if (!b->x[0] && b->wds <= 1)
3207 inexact = 0;
3208 #endif
3209 *s++ = dig;
3210 goto ret;
3211 }
3212 #endif
3213 if (j < 0 || j == 0 && mode != 1
3214 #ifndef ROUND_BIASED
3215 && !(word1(d) & 1)
3216 #endif
3217 ) {
3218 if (!b->x[0] && b->wds <= 1) {
3219 #ifdef SET_INEXACT
3220 inexact = 0;
3221 #endif
3222 goto accept_dig;
3223 }
3224 #ifdef Honor_FLT_ROUNDS
3225 if (mode > 1)
3226 switch(rounding) {
3227 case 0: goto accept_dig;
3228 case 2: goto keep_dig;
3229 }
3230 #endif /*Honor_FLT_ROUNDS*/
3231 if (j1 > 0) {
3232 b = lshift(b, 1);
3233 j1 = cmp(b, S);
3234 if ((j1 > 0 || j1 == 0 && dig & 1)
3235 && dig++ == '9')
3236 goto round_9_up;
3237 }
3238 accept_dig:
3239 *s++ = dig;
3240 goto ret;
3241 }
3242 if (j1 > 0) {
3243 #ifdef Honor_FLT_ROUNDS
3244 if (!rounding)
3245 goto accept_dig;
3246 #endif
3247 if (dig == '9') { /* possible if i == 1 */
3248 round_9_up:
3249 *s++ = '9';
3250 goto roundoff;
3251 }
3252 *s++ = dig + 1;
3253 goto ret;
3254 }
3255 #ifdef Honor_FLT_ROUNDS
3256 keep_dig:
3257 #endif
3258 *s++ = dig;
3259 if (i == ilim)
3260 break;
3261 b = multadd(b, 10, 0);
3262 if (mlo == mhi)
3263 mlo = mhi = multadd(mhi, 10, 0);
3264 else {
3265 mlo = multadd(mlo, 10, 0);
3266 mhi = multadd(mhi, 10, 0);
3267 }
3268 }
3269 }
3270 else
3271 for(i = 1;; i++) {
3272 *s++ = dig = quorem(b,S) + '0';
3273 if (!b->x[0] && b->wds <= 1) {
3274 #ifdef SET_INEXACT
3275 inexact = 0;
3276 #endif
3277 goto ret;
3278 }
3279 if (i >= ilim)
3280 break;
3281 b = multadd(b, 10, 0);
3282 }
3283
3284 /* Round off last digit */
3285
3286 #ifdef Honor_FLT_ROUNDS
3287 switch(rounding) {
3288 case 0: goto trimzeros;
3289 case 2: goto roundoff;
3290 }
3291 #endif
3292 b = lshift(b, 1);
3293 j = cmp(b, S);
3294 if (j > 0 || j == 0 && dig & 1) {
3295 roundoff:
3296 while(*--s == '9')
3297 if (s == s0) {
3298 k++;
3299 *s++ = '1';
3300 goto ret;
3301 }
3302 ++*s++;
3303 }
3304 else {
3305 trimzeros:
3306 while(*--s == '0');
3307 s++;
3308 }
3309 ret:
3310 Bfree(S);
3311 if (mhi) {
3312 if (mlo && mlo != mhi)
3313 Bfree(mlo);
3314 Bfree(mhi);
3315 }
3316 ret1:
3317 #ifdef SET_INEXACT
3318 if (inexact) {
3319 if (!oldinexact) {
3320 word0(d) = Exp_1 + (70 << Exp_shift);
3321 word1(d) = 0;
3322 dval(d) += 1.;
3323 }
3324 }
3325 else if (!oldinexact)
3326 clear_inexact();
3327 #endif
3328 Bfree(b);
3329 *s = 0;
3330 *decpt = k + 1;
3331 if (rve)
3332 *rve = s;
3333 return s0;
3334 }
3335 #endif
3336
3337 #ifdef __cplusplus
3338 }
3339 #endif
Mono Debugger - Cloned from the original SVN repository at mono-cvs.ximian.com