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2010-06-21 Rodrigo Kumpera <rkumpera@novell.com>
[mono.git] / mono / utils / strtod.c
blob71d1f08b9d1265c2bc71cce2d9807ed613cb083e
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 #define Omit_Private_Memory
25 #define MULTIPLE_THREADS 1
26 /* Lock 0 is not used because of USE_MALLOC, Lock 1 protects a lazy-initialized table */
27 #define ACQUIRE_DTOA_LOCK(n)
28 #define FREE_DTOA_LOCK(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 #ifdef Omit_Private_Memory
569 free (v);
570 #else
571 if (v) {
572 ACQUIRE_DTOA_LOCK(0);
573 v->next = freelist[v->k];
574 freelist[v->k] = v;
575 FREE_DTOA_LOCK(0);
576 }
577 #endif
578 }
579
580 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
581 y->wds*sizeof(Long) + 2*sizeof(int))
582
583 static Bigint *
584 multadd
585 #ifdef KR_headers
586 (b, m, a) Bigint *b; int m, a;
587 #else
588 (Bigint *b, int m, int a) /* multiply by m and add a */
589 #endif
590 {
591 int i, wds;
592 #ifdef ULLong
593 ULong *x;
594 ULLong carry, y;
595 #else
596 ULong carry, *x, y;
597 #ifdef Pack_32
598 ULong xi, z;
599 #endif
600 #endif
601 Bigint *b1;
602
603 wds = b->wds;
604 x = b->x;
605 i = 0;
606 carry = a;
607 do {
608 #ifdef ULLong
609 y = *x * (ULLong)m + carry;
610 carry = y >> 32;
611 *x++ = y & FFFFFFFF;
612 #else
613 #ifdef Pack_32
614 xi = *x;
615 y = (xi & 0xffff) * m + carry;
616 z = (xi >> 16) * m + (y >> 16);
617 carry = z >> 16;
618 *x++ = (z << 16) + (y & 0xffff);
619 #else
620 y = *x * m + carry;
621 carry = y >> 16;
622 *x++ = y & 0xffff;
623 #endif
624 #endif
625 }
626 while(++i < wds);
627 if (carry) {
628 if (wds >= b->maxwds) {
629 b1 = Balloc(b->k+1);
630 Bcopy(b1, b);
631 Bfree(b);
632 b = b1;
633 }
634 b->x[wds++] = carry;
635 b->wds = wds;
636 }
637 return b;
638 }
639
640 static Bigint *
641 s2b
642 #ifdef KR_headers
643 (s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
644 #else
645 (CONST char *s, int nd0, int nd, ULong y9)
646 #endif
647 {
648 Bigint *b;
649 int i, k;
650 Long x, y;
651
652 x = (nd + 8) / 9;
653 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
654 #ifdef Pack_32
655 b = Balloc(k);
656 b->x[0] = y9;
657 b->wds = 1;
658 #else
659 b = Balloc(k+1);
660 b->x[0] = y9 & 0xffff;
661 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
662 #endif
663
664 i = 9;
665 if (9 < nd0) {
666 s += 9;
667 do b = multadd(b, 10, *s++ - '0');
668 while(++i < nd0);
669 s++;
670 }
671 else
672 s += 10;
673 for(; i < nd; i++)
674 b = multadd(b, 10, *s++ - '0');
675 return b;
676 }
677
678 static int
679 hi0bits
680 #ifdef KR_headers
681 (x) register ULong x;
682 #else
683 (register ULong x)
684 #endif
685 {
686 register int k = 0;
687
688 if (!(x & 0xffff0000)) {
689 k = 16;
690 x <<= 16;
691 }
692 if (!(x & 0xff000000)) {
693 k += 8;
694 x <<= 8;
695 }
696 if (!(x & 0xf0000000)) {
697 k += 4;
698 x <<= 4;
699 }
700 if (!(x & 0xc0000000)) {
701 k += 2;
702 x <<= 2;
703 }
704 if (!(x & 0x80000000)) {
705 k++;
706 if (!(x & 0x40000000))
707 return 32;
708 }
709 return k;
710 }
711
712 static int
713 lo0bits
714 #ifdef KR_headers
715 (y) ULong *y;
716 #else
717 (ULong *y)
718 #endif
719 {
720 register int k;
721 register ULong x = *y;
722
723 if (x & 7) {
724 if (x & 1)
725 return 0;
726 if (x & 2) {
727 *y = x >> 1;
728 return 1;
729 }
730 *y = x >> 2;
731 return 2;
732 }
733 k = 0;
734 if (!(x & 0xffff)) {
735 k = 16;
736 x >>= 16;
737 }
738 if (!(x & 0xff)) {
739 k += 8;
740 x >>= 8;
741 }
742 if (!(x & 0xf)) {
743 k += 4;
744 x >>= 4;
745 }
746 if (!(x & 0x3)) {
747 k += 2;
748 x >>= 2;
749 }
750 if (!(x & 1)) {
751 k++;
752 x >>= 1;
753 if (!x)
754 return 32;
755 }
756 *y = x;
757 return k;
758 }
759
760 static Bigint *
761 i2b
762 #ifdef KR_headers
763 (i) int i;
764 #else
765 (int i)
766 #endif
767 {
768 Bigint *b;
769
770 b = Balloc(1);
771 b->x[0] = i;
772 b->wds = 1;
773 return b;
774 }
775
776 static Bigint *
777 mult
778 #ifdef KR_headers
779 (a, b) Bigint *a, *b;
780 #else
781 (Bigint *a, Bigint *b)
782 #endif
783 {
784 Bigint *c;
785 int k, wa, wb, wc;
786 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
787 ULong y;
788 #ifdef ULLong
789 ULLong carry, z;
790 #else
791 ULong carry, z;
792 #ifdef Pack_32
793 ULong z2;
794 #endif
795 #endif
796
797 if (a->wds < b->wds) {
798 c = a;
799 a = b;
800 b = c;
801 }
802 k = a->k;
803 wa = a->wds;
804 wb = b->wds;
805 wc = wa + wb;
806 if (wc > a->maxwds)
807 k++;
808 c = Balloc(k);
809 for(x = c->x, xa = x + wc; x < xa; x++)
810 *x = 0;
811 xa = a->x;
812 xae = xa + wa;
813 xb = b->x;
814 xbe = xb + wb;
815 xc0 = c->x;
816 #ifdef ULLong
817 for(; xb < xbe; xc0++) {
818 if ((y = *xb++)) {
819 x = xa;
820 xc = xc0;
821 carry = 0;
822 do {
823 z = *x++ * (ULLong)y + *xc + carry;
824 carry = z >> 32;
825 *xc++ = z & FFFFFFFF;
826 }
827 while(x < xae);
828 *xc = carry;
829 }
830 }
831 #else
832 #ifdef Pack_32
833 for(; xb < xbe; xb++, xc0++) {
834 if (y = *xb & 0xffff) {
835 x = xa;
836 xc = xc0;
837 carry = 0;
838 do {
839 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
840 carry = z >> 16;
841 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
842 carry = z2 >> 16;
843 Storeinc(xc, z2, z);
844 }
845 while(x < xae);
846 *xc = carry;
847 }
848 if (y = *xb >> 16) {
849 x = xa;
850 xc = xc0;
851 carry = 0;
852 z2 = *xc;
853 do {
854 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
855 carry = z >> 16;
856 Storeinc(xc, z, z2);
857 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
858 carry = z2 >> 16;
859 }
860 while(x < xae);
861 *xc = z2;
862 }
863 }
864 #else
865 for(; xb < xbe; xc0++) {
866 if (y = *xb++) {
867 x = xa;
868 xc = xc0;
869 carry = 0;
870 do {
871 z = *x++ * y + *xc + carry;
872 carry = z >> 16;
873 *xc++ = z & 0xffff;
874 }
875 while(x < xae);
876 *xc = carry;
877 }
878 }
879 #endif
880 #endif
881 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
882 c->wds = wc;
883 return c;
884 }
885
886 static Bigint *p5s;
887
888 static Bigint *
889 pow5mult
890 #ifdef KR_headers
891 (b, k) Bigint *b; int k;
892 #else
893 (Bigint *b, int k)
894 #endif
895 {
896 Bigint *b1, *p5, *p51;
897 int i;
898 static int p05[3] = { 5, 25, 125 };
899
900 if ((i = k & 3))
901 b = multadd(b, p05[i-1], 0);
902
903 if (!(k >>= 2))
904 return b;
905 if (!(p5 = p5s)) {
906 /* first time */
907 #ifdef MULTIPLE_THREADS
908 ACQUIRE_DTOA_LOCK(1);
909 if (!(p5 = p5s)) {
910 p5 = p5s = i2b(625);
911 p5->next = 0;
912 }
913 FREE_DTOA_LOCK(1);
914 #else
915 p5 = p5s = i2b(625);
916 p5->next = 0;
917 #endif
918 }
919 for(;;) {
920 if (k & 1) {
921 b1 = mult(b, p5);
922 Bfree(b);
923 b = b1;
924 }
925 if (!(k >>= 1))
926 break;
927 if (!(p51 = p5->next)) {
928 #ifdef MULTIPLE_THREADS
929 ACQUIRE_DTOA_LOCK(1);
930 if (!(p51 = p5->next)) {
931 p51 = p5->next = mult(p5,p5);
932 p51->next = 0;
933 }
934 FREE_DTOA_LOCK(1);
935 #else
936 p51 = p5->next = mult(p5,p5);
937 p51->next = 0;
938 #endif
939 }
940 p5 = p51;
941 }
942 return b;
943 }
944
945 static Bigint *
946 lshift
947 #ifdef KR_headers
948 (b, k) Bigint *b; int k;
949 #else
950 (Bigint *b, int k)
951 #endif
952 {
953 int i, k1, n, n1;
954 Bigint *b1;
955 ULong *x, *x1, *xe, z;
956
957 #ifdef Pack_32
958 n = k >> 5;
959 #else
960 n = k >> 4;
961 #endif
962 k1 = b->k;
963 n1 = n + b->wds + 1;
964 for(i = b->maxwds; n1 > i; i <<= 1)
965 k1++;
966 b1 = Balloc(k1);
967 x1 = b1->x;
968 for(i = 0; i < n; i++)
969 *x1++ = 0;
970 x = b->x;
971 xe = x + b->wds;
972 #ifdef Pack_32
973 if (k &= 0x1f) {
974 k1 = 32 - k;
975 z = 0;
976 do {
977 *x1++ = *x << k | z;
978 z = *x++ >> k1;
979 }
980 while(x < xe);
981 if ((*x1 = z))
982 ++n1;
983 }
984 #else
985 if (k &= 0xf) {
986 k1 = 16 - k;
987 z = 0;
988 do {
989 *x1++ = *x << k & 0xffff | z;
990 z = *x++ >> k1;
991 }
992 while(x < xe);
993 if (*x1 = z)
994 ++n1;
995 }
996 #endif
997 else do
998 *x1++ = *x++;
999 while(x < xe);
1000 b1->wds = n1 - 1;
1001 Bfree(b);
1002 return b1;
1003 }
1004
1005 static int
1006 cmp
1007 #ifdef KR_headers
1008 (a, b) Bigint *a, *b;
1009 #else
1010 (Bigint *a, Bigint *b)
1011 #endif
1012 {
1013 ULong *xa, *xa0, *xb, *xb0;
1014 int i, j;
1015
1016 i = a->wds;
1017 j = b->wds;
1018 #ifdef DEBUG
1019 if (i > 1 && !a->x[i-1])
1020 Bug("cmp called with a->x[a->wds-1] == 0");
1021 if (j > 1 && !b->x[j-1])
1022 Bug("cmp called with b->x[b->wds-1] == 0");
1023 #endif
1024 if (i -= j)
1025 return i;
1026 xa0 = a->x;
1027 xa = xa0 + j;
1028 xb0 = b->x;
1029 xb = xb0 + j;
1030 for(;;) {
1031 if (*--xa != *--xb)
1032 return *xa < *xb ? -1 : 1;
1033 if (xa <= xa0)
1034 break;
1035 }
1036 return 0;
1037 }
1038
1039 static Bigint *
1040 diff
1041 #ifdef KR_headers
1042 (a, b) Bigint *a, *b;
1043 #else
1044 (Bigint *a, Bigint *b)
1045 #endif
1046 {
1047 Bigint *c;
1048 int i, wa, wb;
1049 ULong *xa, *xae, *xb, *xbe, *xc;
1050 #ifdef ULLong
1051 ULLong borrow, y;
1052 #else
1053 ULong borrow, y;
1054 #ifdef Pack_32
1055 ULong z;
1056 #endif
1057 #endif
1058
1059 i = cmp(a,b);
1060 if (!i) {
1061 c = Balloc(0);
1062 c->wds = 1;
1063 c->x[0] = 0;
1064 return c;
1065 }
1066 if (i < 0) {
1067 c = a;
1068 a = b;
1069 b = c;
1070 i = 1;
1071 }
1072 else
1073 i = 0;
1074 c = Balloc(a->k);
1075 c->sign = i;
1076 wa = a->wds;
1077 xa = a->x;
1078 xae = xa + wa;
1079 wb = b->wds;
1080 xb = b->x;
1081 xbe = xb + wb;
1082 xc = c->x;
1083 borrow = 0;
1084 #ifdef ULLong
1085 do {
1086 y = (ULLong)*xa++ - *xb++ - borrow;
1087 borrow = y >> 32 & (ULong)1;
1088 *xc++ = y & FFFFFFFF;
1089 }
1090 while(xb < xbe);
1091 while(xa < xae) {
1092 y = *xa++ - borrow;
1093 borrow = y >> 32 & (ULong)1;
1094 *xc++ = y & FFFFFFFF;
1095 }
1096 #else
1097 #ifdef Pack_32
1098 do {
1099 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1100 borrow = (y & 0x10000) >> 16;
1101 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1102 borrow = (z & 0x10000) >> 16;
1103 Storeinc(xc, z, y);
1104 }
1105 while(xb < xbe);
1106 while(xa < xae) {
1107 y = (*xa & 0xffff) - borrow;
1108 borrow = (y & 0x10000) >> 16;
1109 z = (*xa++ >> 16) - borrow;
1110 borrow = (z & 0x10000) >> 16;
1111 Storeinc(xc, z, y);
1112 }
1113 #else
1114 do {
1115 y = *xa++ - *xb++ - borrow;
1116 borrow = (y & 0x10000) >> 16;
1117 *xc++ = y & 0xffff;
1118 }
1119 while(xb < xbe);
1120 while(xa < xae) {
1121 y = *xa++ - borrow;
1122 borrow = (y & 0x10000) >> 16;
1123 *xc++ = y & 0xffff;
1124 }
1125 #endif
1126 #endif
1127 while(!*--xc)
1128 wa--;
1129 c->wds = wa;
1130 return c;
1131 }
1132
1133 static double
1134 ulp
1135 #ifdef KR_headers
1136 (x) double x;
1137 #else
1138 (double x)
1139 #endif
1140 {
1141 register Long L;
1142 double a;
1143
1144 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1145 #ifndef Avoid_Underflow
1146 #ifndef Sudden_Underflow
1147 if (L > 0) {
1148 #endif
1149 #endif
1150 #ifdef IBM
1151 L |= Exp_msk1 >> 4;
1152 #endif
1153 word0(a) = L;
1154 word1(a) = 0;
1155 #ifndef Avoid_Underflow
1156 #ifndef Sudden_Underflow
1157 }
1158 else {
1159 L = -L >> Exp_shift;
1160 if (L < Exp_shift) {
1161 word0(a) = 0x80000 >> L;
1162 word1(a) = 0;
1163 }
1164 else {
1165 word0(a) = 0;
1166 L -= Exp_shift;
1167 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1168 }
1169 }
1170 #endif
1171 #endif
1172 return dval(a);
1173 }
1174
1175 static double
1176 b2d
1177 #ifdef KR_headers
1178 (a, e) Bigint *a; int *e;
1179 #else
1180 (Bigint *a, int *e)
1181 #endif
1182 {
1183 ULong *xa, *xa0, w, y, z;
1184 int k;
1185 double d;
1186 #ifdef VAX
1187 ULong d0, d1;
1188 #else
1189 #define d0 word0(d)
1190 #define d1 word1(d)
1191 #endif
1192
1193 xa0 = a->x;
1194 xa = xa0 + a->wds;
1195 y = *--xa;
1196 #ifdef DEBUG
1197 if (!y) Bug("zero y in b2d");
1198 #endif
1199 k = hi0bits(y);
1200 *e = 32 - k;
1201 #ifdef Pack_32
1202 if (k < Ebits) {
1203 d0 = Exp_1 | (y >> (Ebits - k));
1204 w = xa > xa0 ? *--xa : 0;
1205 d1 = y << ((32-Ebits) + k) | (w >> (Ebits - k));
1206 goto ret_d;
1207 }
1208 z = xa > xa0 ? *--xa : 0;
1209 if (k -= Ebits) {
1210 d0 = Exp_1 | y << k | (z >> (32 - k));
1211 y = xa > xa0 ? *--xa : 0;
1212 d1 = z << k | (y >> (32 - k));
1213 }
1214 else {
1215 d0 = Exp_1 | y;
1216 d1 = z;
1217 }
1218 #else
1219 if (k < Ebits + 16) {
1220 z = xa > xa0 ? *--xa : 0;
1221 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1222 w = xa > xa0 ? *--xa : 0;
1223 y = xa > xa0 ? *--xa : 0;
1224 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1225 goto ret_d;
1226 }
1227 z = xa > xa0 ? *--xa : 0;
1228 w = xa > xa0 ? *--xa : 0;
1229 k -= Ebits + 16;
1230 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1231 y = xa > xa0 ? *--xa : 0;
1232 d1 = w << k + 16 | y << k;
1233 #endif
1234 ret_d:
1235 #ifdef VAX
1236 word0(d) = d0 >> 16 | d0 << 16;
1237 word1(d) = d1 >> 16 | d1 << 16;
1238 #else
1239 #undef d0
1240 #undef d1
1241 #endif
1242 return dval(d);
1243 }
1244
1245 static Bigint *
1246 d2b
1247 #ifdef KR_headers
1248 (d, e, bits) double d; int *e, *bits;
1249 #else
1250 (double d, int *e, int *bits)
1251 #endif
1252 {
1253 Bigint *b;
1254 int de, k;
1255 ULong *x, y, z;
1256 #ifndef Sudden_Underflow
1257 int i;
1258 #endif
1259 #ifdef VAX
1260 ULong d0, d1;
1261 d0 = word0(d) >> 16 | word0(d) << 16;
1262 d1 = word1(d) >> 16 | word1(d) << 16;
1263 #else
1264 #define d0 word0(d)
1265 #define d1 word1(d)
1266 #endif
1267
1268 #ifdef Pack_32
1269 b = Balloc(1);
1270 #else
1271 b = Balloc(2);
1272 #endif
1273 x = b->x;
1274
1275 z = d0 & Frac_mask;
1276 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1277 #ifdef Sudden_Underflow
1278 de = (int)(d0 >> Exp_shift);
1279 #ifndef IBM
1280 z |= Exp_msk11;
1281 #endif
1282 #else
1283 if ((de = (int)(d0 >> Exp_shift)))
1284 z |= Exp_msk1;
1285 #endif
1286 #ifdef Pack_32
1287 if ((y = d1)) {
1288 if ((k = lo0bits(&y))) {
1289 x[0] = y | (z << (32 - k));
1290 z >>= k;
1291 }
1292 else
1293 x[0] = y;
1294 #ifndef Sudden_Underflow
1295 i =
1296 #endif
1297 b->wds = (x[1] = z) ? 2 : 1;
1298 }
1299 else {
1300 #ifdef DEBUG
1301 if (!z)
1302 Bug("Zero passed to d2b");
1303 #endif
1304 k = lo0bits(&z);
1305 x[0] = z;
1306 #ifndef Sudden_Underflow
1307 i =
1308 #endif
1309 b->wds = 1;
1310 k += 32;
1311 }
1312 #else
1313 if (y = d1) {
1314 if (k = lo0bits(&y))
1315 if (k >= 16) {
1316 x[0] = y | z << 32 - k & 0xffff;
1317 x[1] = z >> k - 16 & 0xffff;
1318 x[2] = z >> k;
1319 i = 2;
1320 }
1321 else {
1322 x[0] = y & 0xffff;
1323 x[1] = y >> 16 | z << 16 - k & 0xffff;
1324 x[2] = z >> k & 0xffff;
1325 x[3] = z >> k+16;
1326 i = 3;
1327 }
1328 else {
1329 x[0] = y & 0xffff;
1330 x[1] = y >> 16;
1331 x[2] = z & 0xffff;
1332 x[3] = z >> 16;
1333 i = 3;
1334 }
1335 }
1336 else {
1337 #ifdef DEBUG
1338 if (!z)
1339 Bug("Zero passed to d2b");
1340 #endif
1341 k = lo0bits(&z);
1342 if (k >= 16) {
1343 x[0] = z;
1344 i = 0;
1345 }
1346 else {
1347 x[0] = z & 0xffff;
1348 x[1] = z >> 16;
1349 i = 1;
1350 }
1351 k += 32;
1352 }
1353 while(!x[i])
1354 --i;
1355 b->wds = i + 1;
1356 #endif
1357 #ifndef Sudden_Underflow
1358 if (de) {
1359 #endif
1360 #ifdef IBM
1361 *e = (de - Bias - (P-1) << 2) + k;
1362 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1363 #else
1364 *e = de - Bias - (P-1) + k;
1365 *bits = P - k;
1366 #endif
1367 #ifndef Sudden_Underflow
1368 }
1369 else {
1370 *e = de - Bias - (P-1) + 1 + k;
1371 #ifdef Pack_32
1372 *bits = 32*i - hi0bits(x[i-1]);
1373 #else
1374 *bits = (i+2)*16 - hi0bits(x[i]);
1375 #endif
1376 }
1377 #endif
1378 return b;
1379 }
1380 #undef d0
1381 #undef d1
1382
1383 static double
1384 ratio
1385 #ifdef KR_headers
1386 (a, b) Bigint *a, *b;
1387 #else
1388 (Bigint *a, Bigint *b)
1389 #endif
1390 {
1391 double da, db;
1392 int k, ka, kb;
1393
1394 dval(da) = b2d(a, &ka);
1395 dval(db) = b2d(b, &kb);
1396 #ifdef Pack_32
1397 k = ka - kb + 32*(a->wds - b->wds);
1398 #else
1399 k = ka - kb + 16*(a->wds - b->wds);
1400 #endif
1401 #ifdef IBM
1402 if (k > 0) {
1403 word0(da) += (k >> 2)*Exp_msk1;
1404 if (k &= 3)
1405 dval(da) *= 1 << k;
1406 }
1407 else {
1408 k = -k;
1409 word0(db) += (k >> 2)*Exp_msk1;
1410 if (k &= 3)
1411 dval(db) *= 1 << k;
1412 }
1413 #else
1414 if (k > 0)
1415 word0(da) += k*Exp_msk1;
1416 else {
1417 k = -k;
1418 word0(db) += k*Exp_msk1;
1419 }
1420 #endif
1421 return dval(da) / dval(db);
1422 }
1423
1424 static CONST double
1425 tens[] = {
1426 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1427 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1428 1e20, 1e21, 1e22
1429 #ifdef VAX
1430 , 1e23, 1e24
1431 #endif
1432 };
1433
1434 static CONST double
1435 #ifdef IEEE_Arith
1436 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1437 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1438 #ifdef Avoid_Underflow
1439 9007199254740992.*9007199254740992.e-256
1440 /* = 2^106 * 1e-53 */
1441 #else
1442 1e-256
1443 #endif
1444 };
1445 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1446 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1447 #define Scale_Bit 0x10
1448 #define n_bigtens 5
1449 #else
1450 #ifdef IBM
1451 bigtens[] = { 1e16, 1e32, 1e64 };
1452 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1453 #define n_bigtens 3
1454 #else
1455 bigtens[] = { 1e16, 1e32 };
1456 static CONST double tinytens[] = { 1e-16, 1e-32 };
1457 #define n_bigtens 2
1458 #endif
1459 #endif
1460
1461 #ifndef IEEE_Arith
1462 #undef INFNAN_CHECK
1463 #endif
1464
1465 #ifdef INFNAN_CHECK
1466
1467 #ifndef NAN_WORD0
1468 #define NAN_WORD0 0x7ff80000
1469 #endif
1470
1471 #ifndef NAN_WORD1
1472 #define NAN_WORD1 0
1473 #endif
1474
1475 static int
1476 match
1477 #ifdef KR_headers
1478 (sp, t) char **sp, *t;
1479 #else
1480 (CONST char **sp, char *t)
1481 #endif
1482 {
1483 int c, d;
1484 CONST char *s = *sp;
1485
1486 while(d = *t++) {
1487 if ((c = *++s) >= 'A' && c <= 'Z')
1488 c += 'a' - 'A';
1489 if (c != d)
1490 return 0;
1491 }
1492 *sp = s + 1;
1493 return 1;
1494 }
1495
1496 #ifndef No_Hex_NaN
1497 static void
1498 hexnan
1499 #ifdef KR_headers
1500 (rvp, sp) double *rvp; CONST char **sp;
1501 #else
1502 (double *rvp, CONST char **sp)
1503 #endif
1504 {
1505 ULong c, x[2];
1506 CONST char *s;
1507 int havedig, udx0, xshift;
1508
1509 x[0] = x[1] = 0;
1510 havedig = xshift = 0;
1511 udx0 = 1;
1512 s = *sp;
1513 while(c = *(CONST unsigned char*)++s) {
1514 if (c >= '0' && c <= '9')
1515 c -= '0';
1516 else if (c >= 'a' && c <= 'f')
1517 c += 10 - 'a';
1518 else if (c >= 'A' && c <= 'F')
1519 c += 10 - 'A';
1520 else if (c <= ' ') {
1521 if (udx0 && havedig) {
1522 udx0 = 0;
1523 xshift = 1;
1524 }
1525 continue;
1526 }
1527 else if (/*(*/ c == ')' && havedig) {
1528 *sp = s + 1;
1529 break;
1530 }
1531 else
1532 return; /* invalid form: don't change *sp */
1533 havedig = 1;
1534 if (xshift) {
1535 xshift = 0;
1536 x[0] = x[1];
1537 x[1] = 0;
1538 }
1539 if (udx0)
1540 x[0] = (x[0] << 4) | (x[1] >> 28);
1541 x[1] = (x[1] << 4) | c;
1542 }
1543 if ((x[0] &= 0xfffff) || x[1]) {
1544 word0(*rvp) = Exp_mask | x[0];
1545 word1(*rvp) = x[1];
1546 }
1547 }
1548 #endif /*No_Hex_NaN*/
1549 #endif /* INFNAN_CHECK */
1550
1551 double
1552 mono_strtod
1553 #ifdef KR_headers
1554 (s00, se) CONST char *s00; char **se;
1555 #else
1556 (CONST char *s00, char **se)
1557 #endif
1558 {
1559 #ifdef Avoid_Underflow
1560 int scale;
1561 #endif
1562 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1563 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1564 CONST char *s, *s0, *s1;
1565 double aadj, aadj1, adj, rv, rv0;
1566 Long L;
1567 ULong y, z;
1568 Bigint *bb = NULL, *bb1, *bd = NULL, *bd0, *bs = NULL, *delta = NULL;
1569 #ifdef SET_INEXACT
1570 int inexact, oldinexact;
1571 #endif
1572 #ifdef Honor_FLT_ROUNDS
1573 int rounding;
1574 #endif
1575 #ifdef USE_LOCALE
1576 CONST char *s2;
1577 #endif
1578
1579 sign = nz0 = nz = 0;
1580 dval(rv) = 0.;
1581 for(s = s00;;s++) switch(*s) {
1582 case '-':
1583 sign = 1;
1584 /* no break */
1585 case '+':
1586 if (*++s)
1587 goto break2;
1588 /* no break */
1589 case 0:
1590 goto ret0;
1591 case '\t':
1592 case '\n':
1593 case '\v':
1594 case '\f':
1595 case '\r':
1596 case ' ':
1597 continue;
1598 default:
1599 goto break2;
1600 }
1601 break2:
1602 if (*s == '0') {
1603 nz0 = 1;
1604 while(*++s == '0') ;
1605 if (!*s)
1606 goto ret;
1607 }
1608 s0 = s;
1609 y = z = 0;
1610 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1611 if (nd < 9)
1612 y = 10*y + c - '0';
1613 else if (nd < 16)
1614 z = 10*z + c - '0';
1615 nd0 = nd;
1616 #ifdef USE_LOCALE
1617 s1 = localeconv()->decimal_point;
1618 if (c == *s1) {
1619 c = '.';
1620 if (*++s1) {
1621 s2 = s;
1622 for(;;) {
1623 if (*++s2 != *s1) {
1624 c = 0;
1625 break;
1626 }
1627 if (!*++s1) {
1628 s = s2;
1629 break;
1630 }
1631 }
1632 }
1633 }
1634 #endif
1635 if (c == '.') {
1636 c = *++s;
1637 if (!nd) {
1638 for(; c == '0'; c = *++s)
1639 nz++;
1640 if (c > '0' && c <= '9') {
1641 s0 = s;
1642 nf += nz;
1643 nz = 0;
1644 goto have_dig;
1645 }
1646 goto dig_done;
1647 }
1648 for(; c >= '0' && c <= '9'; c = *++s) {
1649 have_dig:
1650 nz++;
1651 if (c -= '0') {
1652 nf += nz;
1653 for(i = 1; i < nz; i++)
1654 if (nd++ < 9)
1655 y *= 10;
1656 else if (nd <= DBL_DIG + 1)
1657 z *= 10;
1658 if (nd++ < 9)
1659 y = 10*y + c;
1660 else if (nd <= DBL_DIG + 1)
1661 z = 10*z + c;
1662 nz = 0;
1663 }
1664 }
1665 }
1666 dig_done:
1667 e = 0;
1668 if (c == 'e' || c == 'E') {
1669 if (!nd && !nz && !nz0) {
1670 goto ret0;
1671 }
1672 s00 = s;
1673 esign = 0;
1674 switch(c = *++s) {
1675 case '-':
1676 esign = 1;
1677 case '+':
1678 c = *++s;
1679 }
1680 if (c >= '0' && c <= '9') {
1681 while(c == '0')
1682 c = *++s;
1683 if (c > '0' && c <= '9') {
1684 L = c - '0';
1685 s1 = s;
1686 while((c = *++s) >= '0' && c <= '9')
1687 L = 10*L + c - '0';
1688 if (s - s1 > 8 || L > 19999)
1689 /* Avoid confusion from exponents
1690 * so large that e might overflow.
1691 */
1692 e = 19999; /* safe for 16 bit ints */
1693 else
1694 e = (int)L;
1695 if (esign)
1696 e = -e;
1697 }
1698 else
1699 e = 0;
1700 }
1701 else
1702 s = s00;
1703 }
1704 if (!nd) {
1705 if (!nz && !nz0) {
1706 #ifdef INFNAN_CHECK
1707 /* Check for Nan and Infinity */
1708 switch(c) {
1709 case 'i':
1710 case 'I':
1711 if (match(&s,"nf")) {
1712 --s;
1713 if (!match(&s,"inity"))
1714 ++s;
1715 word0(rv) = 0x7ff00000;
1716 word1(rv) = 0;
1717 goto ret;
1718 }
1719 break;
1720 case 'n':
1721 case 'N':
1722 if (match(&s, "an")) {
1723 word0(rv) = NAN_WORD0;
1724 word1(rv) = NAN_WORD1;
1725 #ifndef No_Hex_NaN
1726 if (*s == '(') /*)*/
1727 hexnan(&rv, &s);
1728 #endif
1729 goto ret;
1730 }
1731 }
1732 #endif /* INFNAN_CHECK */
1733 ret0:
1734 s = s00;
1735 sign = 0;
1736 }
1737 goto ret;
1738 }
1739 e1 = e -= nf;
1740
1741 /* Now we have nd0 digits, starting at s0, followed by a
1742 * decimal point, followed by nd-nd0 digits. The number we're
1743 * after is the integer represented by those digits times
1744 * 10**e */
1745
1746 if (!nd0)
1747 nd0 = nd;
1748 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1749 dval(rv) = y;
1750 if (k > 9) {
1751 #ifdef SET_INEXACT
1752 if (k > DBL_DIG)
1753 oldinexact = get_inexact();
1754 #endif
1755 dval(rv) = tens[k - 9] * dval(rv) + z;
1756 }
1757 bd0 = 0;
1758 if (nd <= DBL_DIG
1759 #ifndef RND_PRODQUOT
1760 #ifndef Honor_FLT_ROUNDS
1761 && Flt_Rounds == 1
1762 #endif
1763 #endif
1764 ) {
1765 if (!e)
1766 goto ret;
1767 if (e > 0) {
1768 if (e <= Ten_pmax) {
1769 #ifdef VAX
1770 goto vax_ovfl_check;
1771 #else
1772 #ifdef Honor_FLT_ROUNDS
1773 /* round correctly FLT_ROUNDS = 2 or 3 */
1774 if (sign) {
1775 rv = -rv;
1776 sign = 0;
1777 }
1778 #endif
1779 /* rv = */ rounded_product(dval(rv), tens[e]);
1780 goto ret;
1781 #endif
1782 }
1783 i = DBL_DIG - nd;
1784 if (e <= Ten_pmax + i) {
1785 /* A fancier test would sometimes let us do
1786 * this for larger i values.
1787 */
1788 #ifdef Honor_FLT_ROUNDS
1789 /* round correctly FLT_ROUNDS = 2 or 3 */
1790 if (sign) {
1791 rv = -rv;
1792 sign = 0;
1793 }
1794 #endif
1795 e -= i;
1796 dval(rv) *= tens[i];
1797 #ifdef VAX
1798 /* VAX exponent range is so narrow we must
1799 * worry about overflow here...
1800 */
1801 vax_ovfl_check:
1802 word0(rv) -= P*Exp_msk1;
1803 /* rv = */ rounded_product(dval(rv), tens[e]);
1804 if ((word0(rv) & Exp_mask)
1805 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1806 goto ovfl;
1807 word0(rv) += P*Exp_msk1;
1808 #else
1809 /* rv = */ rounded_product(dval(rv), tens[e]);
1810 #endif
1811 goto ret;
1812 }
1813 }
1814 #ifndef Inaccurate_Divide
1815 else if (e >= -Ten_pmax) {
1816 #ifdef Honor_FLT_ROUNDS
1817 /* round correctly FLT_ROUNDS = 2 or 3 */
1818 if (sign) {
1819 rv = -rv;
1820 sign = 0;
1821 }
1822 #endif
1823 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1824 goto ret;
1825 }
1826 #endif
1827 }
1828 e1 += nd - k;
1829
1830 #ifdef IEEE_Arith
1831 #ifdef SET_INEXACT
1832 inexact = 1;
1833 if (k <= DBL_DIG)
1834 oldinexact = get_inexact();
1835 #endif
1836 #ifdef Avoid_Underflow
1837 scale = 0;
1838 #endif
1839 #ifdef Honor_FLT_ROUNDS
1840 if ((rounding = Flt_Rounds) >= 2) {
1841 if (sign)
1842 rounding = rounding == 2 ? 0 : 2;
1843 else
1844 if (rounding != 2)
1845 rounding = 0;
1846 }
1847 #endif
1848 #endif /*IEEE_Arith*/
1849
1850 /* Get starting approximation = rv * 10**e1 */
1851
1852 if (e1 > 0) {
1853 if ((i = e1 & 15))
1854 dval(rv) *= tens[i];
1855 if (e1 &= ~15) {
1856 if (e1 > DBL_MAX_10_EXP) {
1857 ovfl:
1858 #ifndef NO_ERRNO
1859 errno = ERANGE;
1860 #endif
1861 /* Can't trust HUGE_VAL */
1862 #ifdef IEEE_Arith
1863 #ifdef Honor_FLT_ROUNDS
1864 switch(rounding) {
1865 case 0: /* toward 0 */
1866 case 3: /* toward -infinity */
1867 word0(rv) = Big0;
1868 word1(rv) = Big1;
1869 break;
1870 default:
1871 word0(rv) = Exp_mask;
1872 word1(rv) = 0;
1873 }
1874 #else /*Honor_FLT_ROUNDS*/
1875 word0(rv) = Exp_mask;
1876 word1(rv) = 0;
1877 #endif /*Honor_FLT_ROUNDS*/
1878 #ifdef SET_INEXACT
1879 /* set overflow bit */
1880 dval(rv0) = 1e300;
1881 dval(rv0) *= dval(rv0);
1882 #endif
1883 #else /*IEEE_Arith*/
1884 word0(rv) = Big0;
1885 word1(rv) = Big1;
1886 #endif /*IEEE_Arith*/
1887 if (bd0)
1888 goto retfree;
1889 goto ret;
1890 }
1891 e1 >>= 4;
1892 for(j = 0; e1 > 1; j++, e1 >>= 1)
1893 if (e1 & 1)
1894 dval(rv) *= bigtens[j];
1895 /* The last multiplication could overflow. */
1896 word0(rv) -= P*Exp_msk1;
1897 dval(rv) *= bigtens[j];
1898 if ((z = word0(rv) & Exp_mask)
1899 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1900 goto ovfl;
1901 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1902 /* set to largest number */
1903 /* (Can't trust DBL_MAX) */
1904 word0(rv) = Big0;
1905 word1(rv) = Big1;
1906 }
1907 else
1908 word0(rv) += P*Exp_msk1;
1909 }
1910 }
1911 else if (e1 < 0) {
1912 e1 = -e1;
1913 if ((i = e1 & 15))
1914 dval(rv) /= tens[i];
1915 if (e1 >>= 4) {
1916 if (e1 >= 1 << n_bigtens)
1917 goto undfl;
1918 #ifdef Avoid_Underflow
1919 if (e1 & Scale_Bit)
1920 scale = 2*P;
1921 for(j = 0; e1 > 0; j++, e1 >>= 1)
1922 if (e1 & 1)
1923 dval(rv) *= tinytens[j];
1924 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1925 >> Exp_shift)) > 0) {
1926 /* scaled rv is denormal; zap j low bits */
1927 if (j >= 32) {
1928 word1(rv) = 0;
1929 if (j >= 53)
1930 word0(rv) = (P+2)*Exp_msk1;
1931 else
1932 word0(rv) &= 0xffffffff << (j-32);
1933 }
1934 else
1935 word1(rv) &= 0xffffffff << j;
1936 }
1937 #else
1938 for(j = 0; e1 > 1; j++, e1 >>= 1)
1939 if (e1 & 1)
1940 dval(rv) *= tinytens[j];
1941 /* The last multiplication could underflow. */
1942 dval(rv0) = dval(rv);
1943 dval(rv) *= tinytens[j];
1944 if (!dval(rv)) {
1945 dval(rv) = 2.*dval(rv0);
1946 dval(rv) *= tinytens[j];
1947 #endif
1948 if (!dval(rv)) {
1949 undfl:
1950 dval(rv) = 0.;
1951 #ifndef NO_ERRNO
1952 errno = ERANGE;
1953 #endif
1954 if (bd0)
1955 goto retfree;
1956 goto ret;
1957 }
1958 #ifndef Avoid_Underflow
1959 word0(rv) = Tiny0;
1960 word1(rv) = Tiny1;
1961 /* The refinement below will clean
1962 * this approximation up.
1963 */
1964 }
1965 #endif
1966 }
1967 }
1968
1969 /* Now the hard part -- adjusting rv to the correct value.*/
1970
1971 /* Put digits into bd: true value = bd * 10^e */
1972
1973 bd0 = s2b(s0, nd0, nd, y);
1974
1975 for(;;) {
1976 bd = Balloc(bd0->k);
1977 Bcopy(bd, bd0);
1978 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1979 bs = i2b(1);
1980
1981 if (e >= 0) {
1982 bb2 = bb5 = 0;
1983 bd2 = bd5 = e;
1984 }
1985 else {
1986 bb2 = bb5 = -e;
1987 bd2 = bd5 = 0;
1988 }
1989 if (bbe >= 0)
1990 bb2 += bbe;
1991 else
1992 bd2 -= bbe;
1993 bs2 = bb2;
1994 #ifdef Honor_FLT_ROUNDS
1995 if (rounding != 1)
1996 bs2++;
1997 #endif
1998 #ifdef Avoid_Underflow
1999 j = bbe - scale;
2000 i = j + bbbits - 1; /* logb(rv) */
2001 if (i < Emin) /* denormal */
2002 j += P - Emin;
2003 else
2004 j = P + 1 - bbbits;
2005 #else /*Avoid_Underflow*/
2006 #ifdef Sudden_Underflow
2007 #ifdef IBM
2008 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2009 #else
2010 j = P + 1 - bbbits;
2011 #endif
2012 #else /*Sudden_Underflow*/
2013 j = bbe;
2014 i = j + bbbits - 1; /* logb(rv) */
2015 if (i < Emin) /* denormal */
2016 j += P - Emin;
2017 else
2018 j = P + 1 - bbbits;
2019 #endif /*Sudden_Underflow*/
2020 #endif /*Avoid_Underflow*/
2021 bb2 += j;
2022 bd2 += j;
2023 #ifdef Avoid_Underflow
2024 bd2 += scale;
2025 #endif
2026 i = bb2 < bd2 ? bb2 : bd2;
2027 if (i > bs2)
2028 i = bs2;
2029 if (i > 0) {
2030 bb2 -= i;
2031 bd2 -= i;
2032 bs2 -= i;
2033 }
2034 if (bb5 > 0) {
2035 bs = pow5mult(bs, bb5);
2036 bb1 = mult(bs, bb);
2037 Bfree(bb);
2038 bb = bb1;
2039 }
2040 if (bb2 > 0)
2041 bb = lshift(bb, bb2);
2042 if (bd5 > 0)
2043 bd = pow5mult(bd, bd5);
2044 if (bd2 > 0)
2045 bd = lshift(bd, bd2);
2046 if (bs2 > 0)
2047 bs = lshift(bs, bs2);
2048 delta = diff(bb, bd);
2049 dsign = delta->sign;
2050 delta->sign = 0;
2051 i = cmp(delta, bs);
2052 #ifdef Honor_FLT_ROUNDS
2053 if (rounding != 1) {
2054 if (i < 0) {
2055 /* Error is less than an ulp */
2056 if (!delta->x[0] && delta->wds <= 1) {
2057 /* exact */
2058 #ifdef SET_INEXACT
2059 inexact = 0;
2060 #endif
2061 break;
2062 }
2063 if (rounding) {
2064 if (dsign) {
2065 adj = 1.;
2066 goto apply_adj;
2067 }
2068 }
2069 else if (!dsign) {
2070 adj = -1.;
2071 if (!word1(rv)
2072 && !(word0(rv) & Frac_mask)) {
2073 y = word0(rv) & Exp_mask;
2074 #ifdef Avoid_Underflow
2075 if (!scale || y > 2*P*Exp_msk1)
2076 #else
2077 if (y)
2078 #endif
2079 {
2080 delta = lshift(delta,Log2P);
2081 if (cmp(delta, bs) <= 0)
2082 adj = -0.5;
2083 }
2084 }
2085 apply_adj:
2086 #ifdef Avoid_Underflow
2087 if (scale && (y = word0(rv) & Exp_mask)
2088 <= 2*P*Exp_msk1)
2089 word0(adj) += (2*P+1)*Exp_msk1 - y;
2090 #else
2091 #ifdef Sudden_Underflow
2092 if ((word0(rv) & Exp_mask) <=
2093 P*Exp_msk1) {
2094 word0(rv) += P*Exp_msk1;
2095 dval(rv) += adj*ulp(dval(rv));
2096 word0(rv) -= P*Exp_msk1;
2097 }
2098 else
2099 #endif /*Sudden_Underflow*/
2100 #endif /*Avoid_Underflow*/
2101 dval(rv) += adj*ulp(dval(rv));
2102 }
2103 break;
2104 }
2105 adj = ratio(delta, bs);
2106 if (adj < 1.)
2107 adj = 1.;
2108 if (adj <= 0x7ffffffe) {
2109 /* adj = rounding ? ceil(adj) : floor(adj); */
2110 y = adj;
2111 if (y != adj) {
2112 if (!((rounding>>1) ^ dsign))
2113 y++;
2114 adj = y;
2115 }
2116 }
2117 #ifdef Avoid_Underflow
2118 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2119 word0(adj) += (2*P+1)*Exp_msk1 - y;
2120 #else
2121 #ifdef Sudden_Underflow
2122 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2123 word0(rv) += P*Exp_msk1;
2124 adj *= ulp(dval(rv));
2125 if (dsign)
2126 dval(rv) += adj;
2127 else
2128 dval(rv) -= adj;
2129 word0(rv) -= P*Exp_msk1;
2130 goto cont;
2131 }
2132 #endif /*Sudden_Underflow*/
2133 #endif /*Avoid_Underflow*/
2134 adj *= ulp(dval(rv));
2135 if (dsign)
2136 dval(rv) += adj;
2137 else
2138 dval(rv) -= adj;
2139 goto cont;
2140 }
2141 #endif /*Honor_FLT_ROUNDS*/
2142
2143 if (i < 0) {
2144 /* Error is less than half an ulp -- check for
2145 * special case of mantissa a power of two.
2146 */
2147 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2148 #ifdef IEEE_Arith
2149 #ifdef Avoid_Underflow
2150 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2151 #else
2152 || (word0(rv) & Exp_mask) <= Exp_msk1
2153 #endif
2154 #endif
2155 ) {
2156 #ifdef SET_INEXACT
2157 if (!delta->x[0] && delta->wds <= 1)
2158 inexact = 0;
2159 #endif
2160 break;
2161 }
2162 if (!delta->x[0] && delta->wds <= 1) {
2163 /* exact result */
2164 #ifdef SET_INEXACT
2165 inexact = 0;
2166 #endif
2167 break;
2168 }
2169 delta = lshift(delta,Log2P);
2170 if (cmp(delta, bs) > 0)
2171 goto drop_down;
2172 break;
2173 }
2174 if (i == 0) {
2175 /* exactly half-way between */
2176 if (dsign) {
2177 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2178 && word1(rv) == (
2179 #ifdef Avoid_Underflow
2180 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2181 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2182 #endif
2183 0xffffffff)) {
2184 /*boundary case -- increment exponent*/
2185 word0(rv) = (word0(rv) & Exp_mask)
2186 + Exp_msk1
2187 #ifdef IBM
2188 | Exp_msk1 >> 4
2189 #endif
2190 ;
2191 word1(rv) = 0;
2192 #ifdef Avoid_Underflow
2193 dsign = 0;
2194 #endif
2195 break;
2196 }
2197 }
2198 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2199 drop_down:
2200 /* boundary case -- decrement exponent */
2201 #ifdef Sudden_Underflow /*{{*/
2202 L = word0(rv) & Exp_mask;
2203 #ifdef IBM
2204 if (L < Exp_msk1)
2205 #else
2206 #ifdef Avoid_Underflow
2207 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2208 #else
2209 if (L <= Exp_msk1)
2210 #endif /*Avoid_Underflow*/
2211 #endif /*IBM*/
2212 goto undfl;
2213 L -= Exp_msk1;
2214 #else /*Sudden_Underflow}{*/
2215 #ifdef Avoid_Underflow
2216 if (scale) {
2217 L = word0(rv) & Exp_mask;
2218 if (L <= (2*P+1)*Exp_msk1) {
2219 if (L > (P+2)*Exp_msk1)
2220 /* round even ==> */
2221 /* accept rv */
2222 break;
2223 /* rv = smallest denormal */
2224 goto undfl;
2225 }
2226 }
2227 #endif /*Avoid_Underflow*/
2228 L = (word0(rv) & Exp_mask) - Exp_msk1;
2229 #endif /*Sudden_Underflow}}*/
2230 word0(rv) = L | Bndry_mask1;
2231 word1(rv) = 0xffffffff;
2232 #ifdef IBM
2233 goto cont;
2234 #else
2235 break;
2236 #endif
2237 }
2238 #ifndef ROUND_BIASED
2239 if (!(word1(rv) & LSB))
2240 break;
2241 #endif
2242 if (dsign)
2243 dval(rv) += ulp(dval(rv));
2244 #ifndef ROUND_BIASED
2245 else {
2246 dval(rv) -= ulp(dval(rv));
2247 #ifndef Sudden_Underflow
2248 if (!dval(rv))
2249 goto undfl;
2250 #endif
2251 }
2252 #ifdef Avoid_Underflow
2253 dsign = 1 - dsign;
2254 #endif
2255 #endif
2256 break;
2257 }
2258 if ((aadj = ratio(delta, bs)) <= 2.) {
2259 if (dsign)
2260 aadj = aadj1 = 1.;
2261 else if (word1(rv) || word0(rv) & Bndry_mask) {
2262 #ifndef Sudden_Underflow
2263 if (word1(rv) == Tiny1 && !word0(rv))
2264 goto undfl;
2265 #endif
2266 aadj = 1.;
2267 aadj1 = -1.;
2268 }
2269 else {
2270 /* special case -- power of FLT_RADIX to be */
2271 /* rounded down... */
2272
2273 if (aadj < 2./FLT_RADIX)
2274 aadj = 1./FLT_RADIX;
2275 else
2276 aadj *= 0.5;
2277 aadj1 = -aadj;
2278 }
2279 }
2280 else {
2281 aadj *= 0.5;
2282 aadj1 = dsign ? aadj : -aadj;
2283 #ifdef Check_FLT_ROUNDS
2284 switch(Rounding) {
2285 case 2: /* towards +infinity */
2286 aadj1 -= 0.5;
2287 break;
2288 case 0: /* towards 0 */
2289 case 3: /* towards -infinity */
2290 aadj1 += 0.5;
2291 }
2292 #else
2293 if (Flt_Rounds == 0)
2294 aadj1 += 0.5;
2295 #endif /*Check_FLT_ROUNDS*/
2296 }
2297 y = word0(rv) & Exp_mask;
2298
2299 /* Check for overflow */
2300
2301 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2302 dval(rv0) = dval(rv);
2303 word0(rv) -= P*Exp_msk1;
2304 adj = aadj1 * ulp(dval(rv));
2305 dval(rv) += adj;
2306 if ((word0(rv) & Exp_mask) >=
2307 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2308 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2309 goto ovfl;
2310 word0(rv) = Big0;
2311 word1(rv) = Big1;
2312 goto cont;
2313 }
2314 else
2315 word0(rv) += P*Exp_msk1;
2316 }
2317 else {
2318 #ifdef Avoid_Underflow
2319 if (scale && y <= 2*P*Exp_msk1) {
2320 if (aadj <= 0x7fffffff) {
2321 if ((z = aadj) <= 0)
2322 z = 1;
2323 aadj = z;
2324 aadj1 = dsign ? aadj : -aadj;
2325 }
2326 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2327 }
2328 adj = aadj1 * ulp(dval(rv));
2329 dval(rv) += adj;
2330 #else
2331 #ifdef Sudden_Underflow
2332 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2333 dval(rv0) = dval(rv);
2334 word0(rv) += P*Exp_msk1;
2335 adj = aadj1 * ulp(dval(rv));
2336 dval(rv) += adj;
2337 #ifdef IBM
2338 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2339 #else
2340 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2341 #endif
2342 {
2343 if (word0(rv0) == Tiny0
2344 && word1(rv0) == Tiny1)
2345 goto undfl;
2346 word0(rv) = Tiny0;
2347 word1(rv) = Tiny1;
2348 goto cont;
2349 }
2350 else
2351 word0(rv) -= P*Exp_msk1;
2352 }
2353 else {
2354 adj = aadj1 * ulp(dval(rv));
2355 dval(rv) += adj;
2356 }
2357 #else /*Sudden_Underflow*/
2358 /* Compute adj so that the IEEE rounding rules will
2359 * correctly round rv + adj in some half-way cases.
2360 * If rv * ulp(rv) is denormalized (i.e.,
2361 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2362 * trouble from bits lost to denormalization;
2363 * example: 1.2e-307 .
2364 */
2365 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2366 aadj1 = (double)(int)(aadj + 0.5);
2367 if (!dsign)
2368 aadj1 = -aadj1;
2369 }
2370 adj = aadj1 * ulp(dval(rv));
2371 dval(rv) += adj;
2372 #endif /*Sudden_Underflow*/
2373 #endif /*Avoid_Underflow*/
2374 }
2375 z = word0(rv) & Exp_mask;
2376 #ifndef SET_INEXACT
2377 #ifdef Avoid_Underflow
2378 if (!scale)
2379 #endif
2380 if (y == z) {
2381 /* Can we stop now? */
2382 L = (Long)aadj;
2383 aadj -= L;
2384 /* The tolerances below are conservative. */
2385 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2386 if (aadj < .4999999 || aadj > .5000001)
2387 break;
2388 }
2389 else if (aadj < .4999999/FLT_RADIX)
2390 break;
2391 }
2392 #endif
2393 cont:
2394 Bfree(bb);
2395 Bfree(bd);
2396 Bfree(bs);
2397 Bfree(delta);
2398 }
2399 #ifdef SET_INEXACT
2400 if (inexact) {
2401 if (!oldinexact) {
2402 word0(rv0) = Exp_1 + (70 << Exp_shift);
2403 word1(rv0) = 0;
2404 dval(rv0) += 1.;
2405 }
2406 }
2407 else if (!oldinexact)
2408 clear_inexact();
2409 #endif
2410 #ifdef Avoid_Underflow
2411 if (scale) {
2412 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2413 word1(rv0) = 0;
2414 dval(rv) *= dval(rv0);
2415 #ifndef NO_ERRNO
2416 /* try to avoid the bug of testing an 8087 register value */
2417 if (word0(rv) == 0 && word1(rv) == 0)
2418 errno = ERANGE;
2419 #endif
2420 }
2421 #endif /* Avoid_Underflow */
2422 #ifdef SET_INEXACT
2423 if (inexact && !(word0(rv) & Exp_mask)) {
2424 /* set underflow bit */
2425 dval(rv0) = 1e-300;
2426 dval(rv0) *= dval(rv0);
2427 }
2428 #endif
2429 retfree:
2430 Bfree(bb);
2431 Bfree(bd);
2432 Bfree(bs);
2433 Bfree(bd0);
2434 Bfree(delta);
2435 ret:
2436 if (se)
2437 *se = (char *)s;
2438 return sign ? -dval(rv) : dval(rv);
2439 }
2440
2441 static int
2442 quorem
2443 #ifdef KR_headers
2444 (b, S) Bigint *b, *S;
2445 #else
2446 (Bigint *b, Bigint *S)
2447 #endif
2448 {
2449 int n;
2450 ULong *bx, *bxe, q, *sx, *sxe;
2451 #ifdef ULLong
2452 ULLong borrow, carry, y, ys;
2453 #else
2454 ULong borrow, carry, y, ys;
2455 #ifdef Pack_32
2456 ULong si, z, zs;
2457 #endif
2458 #endif
2459
2460 n = S->wds;
2461 #ifdef DEBUG
2462 /*debug*/ if (b->wds > n)
2463 /*debug*/ Bug("oversize b in quorem");
2464 #endif
2465 if (b->wds < n)
2466 return 0;
2467 sx = S->x;
2468 sxe = sx + --n;
2469 bx = b->x;
2470 bxe = bx + n;
2471 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2472 #ifdef DEBUG
2473 /*debug*/ if (q > 9)
2474 /*debug*/ Bug("oversized quotient in quorem");
2475 #endif
2476 if (q) {
2477 borrow = 0;
2478 carry = 0;
2479 do {
2480 #ifdef ULLong
2481 ys = *sx++ * (ULLong)q + carry;
2482 carry = ys >> 32;
2483 y = *bx - (ys & FFFFFFFF) - borrow;
2484 borrow = y >> 32 & (ULong)1;
2485 *bx++ = y & FFFFFFFF;
2486 #else
2487 #ifdef Pack_32
2488 si = *sx++;
2489 ys = (si & 0xffff) * q + carry;
2490 zs = (si >> 16) * q + (ys >> 16);
2491 carry = zs >> 16;
2492 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2493 borrow = (y & 0x10000) >> 16;
2494 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2495 borrow = (z & 0x10000) >> 16;
2496 Storeinc(bx, z, y);
2497 #else
2498 ys = *sx++ * q + carry;
2499 carry = ys >> 16;
2500 y = *bx - (ys & 0xffff) - borrow;
2501 borrow = (y & 0x10000) >> 16;
2502 *bx++ = y & 0xffff;
2503 #endif
2504 #endif
2505 }
2506 while(sx <= sxe);
2507 if (!*bxe) {
2508 bx = b->x;
2509 while(--bxe > bx && !*bxe)
2510 --n;
2511 b->wds = n;
2512 }
2513 }
2514 if (cmp(b, S) >= 0) {
2515 q++;
2516 borrow = 0;
2517 carry = 0;
2518 bx = b->x;
2519 sx = S->x;
2520 do {
2521 #ifdef ULLong
2522 ys = *sx++ + carry;
2523 carry = ys >> 32;
2524 y = *bx - (ys & FFFFFFFF) - borrow;
2525 borrow = y >> 32 & (ULong)1;
2526 *bx++ = y & FFFFFFFF;
2527 #else
2528 #ifdef Pack_32
2529 si = *sx++;
2530 ys = (si & 0xffff) + carry;
2531 zs = (si >> 16) + (ys >> 16);
2532 carry = zs >> 16;
2533 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2534 borrow = (y & 0x10000) >> 16;
2535 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2536 borrow = (z & 0x10000) >> 16;
2537 Storeinc(bx, z, y);
2538 #else
2539 ys = *sx++ + carry;
2540 carry = ys >> 16;
2541 y = *bx - (ys & 0xffff) - borrow;
2542 borrow = (y & 0x10000) >> 16;
2543 *bx++ = y & 0xffff;
2544 #endif
2545 #endif
2546 }
2547 while(sx <= sxe);
2548 bx = b->x;
2549 bxe = bx + n;
2550 if (!*bxe) {
2551 while(--bxe > bx && !*bxe)
2552 --n;
2553 b->wds = n;
2554 }
2555 }
2556 return q;
2557 }
2558
2559 #ifndef MULTIPLE_THREADS
2560 static char *dtoa_result;
2561 #endif
2562
2563 static char *
2564 #ifdef KR_headers
2565 rv_alloc(i) int i;
2566 #else
2567 rv_alloc(int i)
2568 #endif
2569 {
2570 int j, k, *r;
2571
2572 j = sizeof(ULong);
2573 for(k = 0;
2574 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
2575 j <<= 1)
2576 k++;
2577 r = (int*)Balloc(k);
2578 *r = k;
2579 return
2580 #ifndef MULTIPLE_THREADS
2581 dtoa_result =
2582 #endif
2583 (char *)(r+1);
2584 }
2585
2586 static char *
2587 #ifdef KR_headers
2588 nrv_alloc(s, rve, n) char *s, **rve; int n;
2589 #else
2590 nrv_alloc(char *s, char **rve, int n)
2591 #endif
2592 {
2593 char *rv, *t;
2594
2595 t = rv = rv_alloc(n);
2596 while((*t = *s++)) t++;
2597 if (rve)
2598 *rve = t;
2599 return rv;
2600 }
2601
2602 /* freedtoa(s) must be used to free values s returned by dtoa
2603 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2604 * but for consistency with earlier versions of dtoa, it is optional
2605 * when MULTIPLE_THREADS is not defined.
2606 */
2607
2608 static void freedtoa (char *s);
2609
2610 static void
2611 #ifdef KR_headers
2612 freedtoa(s) char *s;
2613 #else
2614 freedtoa(char *s)
2615 #endif
2616 {
2617 Bigint *b = (Bigint *)((int *)s - 1);
2618 b->maxwds = 1 << (b->k = *(int*)b);
2619 Bfree(b);
2620 #ifndef MULTIPLE_THREADS
2621 if (s == dtoa_result)
2622 dtoa_result = 0;
2623 #endif
2624 }
2625
2626 #if 0
2627 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2628 *
2629 * Inspired by "How to Print Floating-Point Numbers Accurately" by
2630 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2631 *
2632 * Modifications:
2633 * 1. Rather than iterating, we use a simple numeric overestimate
2634 * to determine k = floor(log10(d)). We scale relevant
2635 * quantities using O(log2(k)) rather than O(k) multiplications.
2636 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2637 * try to generate digits strictly left to right. Instead, we
2638 * compute with fewer bits and propagate the carry if necessary
2639 * when rounding the final digit up. This is often faster.
2640 * 3. Under the assumption that input will be rounded nearest,
2641 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2642 * That is, we allow equality in stopping tests when the
2643 * round-nearest rule will give the same floating-point value
2644 * as would satisfaction of the stopping test with strict
2645 * inequality.
2646 * 4. We remove common factors of powers of 2 from relevant
2647 * quantities.
2648 * 5. When converting floating-point integers less than 1e16,
2649 * we use floating-point arithmetic rather than resorting
2650 * to multiple-precision integers.
2651 * 6. When asked to produce fewer than 15 digits, we first try
2652 * to get by with floating-point arithmetic; we resort to
2653 * multiple-precision integer arithmetic only if we cannot
2654 * guarantee that the floating-point calculation has given
2655 * the correctly rounded result. For k requested digits and
2656 * "uniformly" distributed input, the probability is
2657 * something like 10^(k-15) that we must resort to the Long
2658 * calculation.
2659 */
2660
2661 char *
2662 dtoa
2663 #ifdef KR_headers
2664 (d, mode, ndigits, decpt, sign, rve)
2665 double d; int mode, ndigits, *decpt, *sign; char **rve;
2666 #else
2667 (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
2668 #endif
2669 {
2670 /* Arguments ndigits, decpt, sign are similar to those
2671 of ecvt and fcvt; trailing zeros are suppressed from
2672 the returned string. If not null, *rve is set to point
2673 to the end of the return value. If d is +-Infinity or NaN,
2674 then *decpt is set to 9999.
2675
2676 mode:
2677 0 ==> shortest string that yields d when read in
2678 and rounded to nearest.
2679 1 ==> like 0, but with Steele & White stopping rule;
2680 e.g. with IEEE P754 arithmetic , mode 0 gives
2681 1e23 whereas mode 1 gives 9.999999999999999e22.
2682 2 ==> max(1,ndigits) significant digits. This gives a
2683 return value similar to that of ecvt, except
2684 that trailing zeros are suppressed.
2685 3 ==> through ndigits past the decimal point. This
2686 gives a return value similar to that from fcvt,
2687 except that trailing zeros are suppressed, and
2688 ndigits can be negative.
2689 4,5 ==> similar to 2 and 3, respectively, but (in
2690 round-nearest mode) with the tests of mode 0 to
2691 possibly return a shorter string that rounds to d.
2692 With IEEE arithmetic and compilation with
2693 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2694 as modes 2 and 3 when FLT_ROUNDS != 1.
2695 6-9 ==> Debugging modes similar to mode - 4: don't try
2696 fast floating-point estimate (if applicable).
2697
2698 Values of mode other than 0-9 are treated as mode 0.
2699
2700 Sufficient space is allocated to the return value
2701 to hold the suppressed trailing zeros.
2702 */
2703
2704 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2705 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2706 spec_case, try_quick;
2707 Long L;
2708 #ifndef Sudden_Underflow
2709 int denorm;
2710 ULong x;
2711 #endif
2712 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
2713 double d2, ds, eps;
2714 char *s, *s0;
2715 #ifdef Honor_FLT_ROUNDS
2716 int rounding;
2717 #endif
2718 #ifdef SET_INEXACT
2719 int inexact, oldinexact;
2720 #endif
2721
2722 #ifndef MULTIPLE_THREADS
2723 if (dtoa_result) {
2724 freedtoa(dtoa_result);
2725 dtoa_result = 0;
2726 }
2727 #endif
2728
2729 if (word0(d) & Sign_bit) {
2730 /* set sign for everything, including 0's and NaNs */
2731 *sign = 1;
2732 word0(d) &= ~Sign_bit; /* clear sign bit */
2733 }
2734 else
2735 *sign = 0;
2736
2737 #if defined(IEEE_Arith) + defined(VAX)
2738 #ifdef IEEE_Arith
2739 if ((word0(d) & Exp_mask) == Exp_mask)
2740 #else
2741 if (word0(d) == 0x8000)
2742 #endif
2743 {
2744 /* Infinity or NaN */
2745 *decpt = 9999;
2746 #ifdef IEEE_Arith
2747 if (!word1(d) && !(word0(d) & 0xfffff))
2748 return nrv_alloc("Infinity", rve, 8);
2749 #endif
2750 return nrv_alloc("NaN", rve, 3);
2751 }
2752 #endif
2753 #ifdef IBM
2754 dval(d) += 0; /* normalize */
2755 #endif
2756 if (!dval(d)) {
2757 *decpt = 1;
2758 return nrv_alloc("0", rve, 1);
2759 }
2760
2761 #ifdef SET_INEXACT
2762 try_quick = oldinexact = get_inexact();
2763 inexact = 1;
2764 #endif
2765 #ifdef Honor_FLT_ROUNDS
2766 if ((rounding = Flt_Rounds) >= 2) {
2767 if (*sign)
2768 rounding = rounding == 2 ? 0 : 2;
2769 else
2770 if (rounding != 2)
2771 rounding = 0;
2772 }
2773 #endif
2774
2775 b = d2b(dval(d), &be, &bbits);
2776 #ifdef Sudden_Underflow
2777 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2778 #else
2779 if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
2780 #endif
2781 dval(d2) = dval(d);
2782 word0(d2) &= Frac_mask1;
2783 word0(d2) |= Exp_11;
2784 #ifdef IBM
2785 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2786 dval(d2) /= 1 << j;
2787 #endif
2788
2789 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2790 * log10(x) = log(x) / log(10)
2791 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2792 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2793 *
2794 * This suggests computing an approximation k to log10(d) by
2795 *
2796 * k = (i - Bias)*0.301029995663981
2797 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2798 *
2799 * We want k to be too large rather than too small.
2800 * The error in the first-order Taylor series approximation
2801 * is in our favor, so we just round up the constant enough
2802 * to compensate for any error in the multiplication of
2803 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2804 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2805 * adding 1e-13 to the constant term more than suffices.
2806 * Hence we adjust the constant term to 0.1760912590558.
2807 * (We could get a more accurate k by invoking log10,
2808 * but this is probably not worthwhile.)
2809 */
2810
2811 i -= Bias;
2812 #ifdef IBM
2813 i <<= 2;
2814 i += j;
2815 #endif
2816 #ifndef Sudden_Underflow
2817 denorm = 0;
2818 }
2819 else {
2820 /* d is denormalized */
2821
2822 i = bbits + be + (Bias + (P-1) - 1);
2823 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
2824 : word1(d) << 32 - i;
2825 dval(d2) = x;
2826 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2827 i -= (Bias + (P-1) - 1) + 1;
2828 denorm = 1;
2829 }
2830 #endif
2831 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2832 k = (int)ds;
2833 if (ds < 0. && ds != k)
2834 k--; /* want k = floor(ds) */
2835 k_check = 1;
2836 if (k >= 0 && k <= Ten_pmax) {
2837 if (dval(d) < tens[k])
2838 k--;
2839 k_check = 0;
2840 }
2841 j = bbits - i - 1;
2842 if (j >= 0) {
2843 b2 = 0;
2844 s2 = j;
2845 }
2846 else {
2847 b2 = -j;
2848 s2 = 0;
2849 }
2850 if (k >= 0) {
2851 b5 = 0;
2852 s5 = k;
2853 s2 += k;
2854 }
2855 else {
2856 b2 -= k;
2857 b5 = -k;
2858 s5 = 0;
2859 }
2860 if (mode < 0 || mode > 9)
2861 mode = 0;
2862
2863 #ifndef SET_INEXACT
2864 #ifdef Check_FLT_ROUNDS
2865 try_quick = Rounding == 1;
2866 #else
2867 try_quick = 1;
2868 #endif
2869 #endif /*SET_INEXACT*/
2870
2871 if (mode > 5) {
2872 mode -= 4;
2873 try_quick = 0;
2874 }
2875 leftright = 1;
2876 switch(mode) {
2877 case 0:
2878 case 1:
2879 ilim = ilim1 = -1;
2880 i = 18;
2881 ndigits = 0;
2882 break;
2883 case 2:
2884 leftright = 0;
2885 /* no break */
2886 case 4:
2887 if (ndigits <= 0)
2888 ndigits = 1;
2889 ilim = ilim1 = i = ndigits;
2890 break;
2891 case 3:
2892 leftright = 0;
2893 /* no break */
2894 case 5:
2895 i = ndigits + k + 1;
2896 ilim = i;
2897 ilim1 = i - 1;
2898 if (i <= 0)
2899 i = 1;
2900 }
2901 s = s0 = rv_alloc(i);
2902
2903 #ifdef Honor_FLT_ROUNDS
2904 if (mode > 1 && rounding != 1)
2905 leftright = 0;
2906 #endif
2907
2908 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2909
2910 /* Try to get by with floating-point arithmetic. */
2911
2912 i = 0;
2913 dval(d2) = dval(d);
2914 k0 = k;
2915 ilim0 = ilim;
2916 ieps = 2; /* conservative */
2917 if (k > 0) {
2918 ds = tens[k&0xf];
2919 j = k >> 4;
2920 if (j & Bletch) {
2921 /* prevent overflows */
2922 j &= Bletch - 1;
2923 dval(d) /= bigtens[n_bigtens-1];
2924 ieps++;
2925 }
2926 for(; j; j >>= 1, i++)
2927 if (j & 1) {
2928 ieps++;
2929 ds *= bigtens[i];
2930 }
2931 dval(d) /= ds;
2932 }
2933 else if (j1 = -k) {
2934 dval(d) *= tens[j1 & 0xf];
2935 for(j = j1 >> 4; j; j >>= 1, i++)
2936 if (j & 1) {
2937 ieps++;
2938 dval(d) *= bigtens[i];
2939 }
2940 }
2941 if (k_check && dval(d) < 1. && ilim > 0) {
2942 if (ilim1 <= 0)
2943 goto fast_failed;
2944 ilim = ilim1;
2945 k--;
2946 dval(d) *= 10.;
2947 ieps++;
2948 }
2949 dval(eps) = ieps*dval(d) + 7.;
2950 word0(eps) -= (P-1)*Exp_msk1;
2951 if (ilim == 0) {
2952 S = mhi = 0;
2953 dval(d) -= 5.;
2954 if (dval(d) > dval(eps))
2955 goto one_digit;
2956 if (dval(d) < -dval(eps))
2957 goto no_digits;
2958 goto fast_failed;
2959 }
2960 #ifndef No_leftright
2961 if (leftright) {
2962 /* Use Steele & White method of only
2963 * generating digits needed.
2964 */
2965 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2966 for(i = 0;;) {
2967 L = dval(d);
2968 dval(d) -= L;
2969 *s++ = '0' + (int)L;
2970 if (dval(d) < dval(eps))
2971 goto ret1;
2972 if (1. - dval(d) < dval(eps))
2973 goto bump_up;
2974 if (++i >= ilim)
2975 break;
2976 dval(eps) *= 10.;
2977 dval(d) *= 10.;
2978 }
2979 }
2980 else {
2981 #endif
2982 /* Generate ilim digits, then fix them up. */
2983 dval(eps) *= tens[ilim-1];
2984 for(i = 1;; i++, dval(d) *= 10.) {
2985 L = (Long)(dval(d));
2986 if (!(dval(d) -= L))
2987 ilim = i;
2988 *s++ = '0' + (int)L;
2989 if (i == ilim) {
2990 if (dval(d) > 0.5 + dval(eps))
2991 goto bump_up;
2992 else if (dval(d) < 0.5 - dval(eps)) {
2993 while(*--s == '0');
2994 s++;
2995 goto ret1;
2996 }
2997 break;
2998 }
2999 }
3000 #ifndef No_leftright
3001 }
3002 #endif
3003 fast_failed:
3004 s = s0;
3005 dval(d) = dval(d2);
3006 k = k0;
3007 ilim = ilim0;
3008 }
3009
3010 /* Do we have a "small" integer? */
3011
3012 if (be >= 0 && k <= Int_max) {
3013 /* Yes. */
3014 ds = tens[k];
3015 if (ndigits < 0 && ilim <= 0) {
3016 S = mhi = 0;
3017 if (ilim < 0 || dval(d) <= 5*ds)
3018 goto no_digits;
3019 goto one_digit;
3020 }
3021 for(i = 1;; i++, dval(d) *= 10.) {
3022 L = (Long)(dval(d) / ds);
3023 dval(d) -= L*ds;
3024 #ifdef Check_FLT_ROUNDS
3025 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3026 if (dval(d) < 0) {
3027 L--;
3028 dval(d) += ds;
3029 }
3030 #endif
3031 *s++ = '0' + (int)L;
3032 if (!dval(d)) {
3033 #ifdef SET_INEXACT
3034 inexact = 0;
3035 #endif
3036 break;
3037 }
3038 if (i == ilim) {
3039 #ifdef Honor_FLT_ROUNDS
3040 if (mode > 1)
3041 switch(rounding) {
3042 case 0: goto ret1;
3043 case 2: goto bump_up;
3044 }
3045 #endif
3046 dval(d) += dval(d);
3047 if (dval(d) > ds || dval(d) == ds && L & 1) {
3048 bump_up:
3049 while(*--s == '9')
3050 if (s == s0) {
3051 k++;
3052 *s = '0';
3053 break;
3054 }
3055 ++*s++;
3056 }
3057 break;
3058 }
3059 }
3060 goto ret1;
3061 }
3062
3063 m2 = b2;
3064 m5 = b5;
3065 mhi = mlo = 0;
3066 if (leftright) {
3067 i =
3068 #ifndef Sudden_Underflow
3069 denorm ? be + (Bias + (P-1) - 1 + 1) :
3070 #endif
3071 #ifdef IBM
3072 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3073 #else
3074 1 + P - bbits;
3075 #endif
3076 b2 += i;
3077 s2 += i;
3078 mhi = i2b(1);
3079 }
3080 if (m2 > 0 && s2 > 0) {
3081 i = m2 < s2 ? m2 : s2;
3082 b2 -= i;
3083 m2 -= i;
3084 s2 -= i;
3085 }
3086 if (b5 > 0) {
3087 if (leftright) {
3088 if (m5 > 0) {
3089 mhi = pow5mult(mhi, m5);
3090 b1 = mult(mhi, b);
3091 Bfree(b);
3092 b = b1;
3093 }
3094 if (j = b5 - m5)
3095 b = pow5mult(b, j);
3096 }
3097 else
3098 b = pow5mult(b, b5);
3099 }
3100 S = i2b(1);
3101 if (s5 > 0)
3102 S = pow5mult(S, s5);
3103
3104 /* Check for special case that d is a normalized power of 2. */
3105
3106 spec_case = 0;
3107 if ((mode < 2 || leftright)
3108 #ifdef Honor_FLT_ROUNDS
3109 && rounding == 1
3110 #endif
3111 ) {
3112 if (!word1(d) && !(word0(d) & Bndry_mask)
3113 #ifndef Sudden_Underflow
3114 && word0(d) & (Exp_mask & ~Exp_msk1)
3115 #endif
3116 ) {
3117 /* The special case */
3118 b2 += Log2P;
3119 s2 += Log2P;
3120 spec_case = 1;
3121 }
3122 }
3123
3124 /* Arrange for convenient computation of quotients:
3125 * shift left if necessary so divisor has 4 leading 0 bits.
3126 *
3127 * Perhaps we should just compute leading 28 bits of S once
3128 * and for all and pass them and a shift to quorem, so it
3129 * can do shifts and ors to compute the numerator for q.
3130 */
3131 #ifdef Pack_32
3132 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
3133 i = 32 - i;
3134 #else
3135 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
3136 i = 16 - i;
3137 #endif
3138 if (i > 4) {
3139 i -= 4;
3140 b2 += i;
3141 m2 += i;
3142 s2 += i;
3143 }
3144 else if (i < 4) {
3145 i += 28;
3146 b2 += i;
3147 m2 += i;
3148 s2 += i;
3149 }
3150 if (b2 > 0)
3151 b = lshift(b, b2);
3152 if (s2 > 0)
3153 S = lshift(S, s2);
3154 if (k_check) {
3155 if (cmp(b,S) < 0) {
3156 k--;
3157 b = multadd(b, 10, 0); /* we botched the k estimate */
3158 if (leftright)
3159 mhi = multadd(mhi, 10, 0);
3160 ilim = ilim1;
3161 }
3162 }
3163 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3164 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3165 /* no digits, fcvt style */
3166 no_digits:
3167 k = -1 - ndigits;
3168 goto ret;
3169 }
3170 one_digit:
3171 *s++ = '1';
3172 k++;
3173 goto ret;
3174 }
3175 if (leftright) {
3176 if (m2 > 0)
3177 mhi = lshift(mhi, m2);
3178
3179 /* Compute mlo -- check for special case
3180 * that d is a normalized power of 2.
3181 */
3182
3183 mlo = mhi;
3184 if (spec_case) {
3185 mhi = Balloc(mhi->k);
3186 Bcopy(mhi, mlo);
3187 mhi = lshift(mhi, Log2P);
3188 }
3189
3190 for(i = 1;;i++) {
3191 dig = quorem(b,S) + '0';
3192 /* Do we yet have the shortest decimal string
3193 * that will round to d?
3194 */
3195 j = cmp(b, mlo);
3196 delta = diff(S, mhi);
3197 j1 = delta->sign ? 1 : cmp(b, delta);
3198 Bfree(delta);
3199 #ifndef ROUND_BIASED
3200 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3201 #ifdef Honor_FLT_ROUNDS
3202 && rounding >= 1
3203 #endif
3204 ) {
3205 if (dig == '9')
3206 goto round_9_up;
3207 if (j > 0)
3208 dig++;
3209 #ifdef SET_INEXACT
3210 else if (!b->x[0] && b->wds <= 1)
3211 inexact = 0;
3212 #endif
3213 *s++ = dig;
3214 goto ret;
3215 }
3216 #endif
3217 if (j < 0 || j == 0 && mode != 1
3218 #ifndef ROUND_BIASED
3219 && !(word1(d) & 1)
3220 #endif
3221 ) {
3222 if (!b->x[0] && b->wds <= 1) {
3223 #ifdef SET_INEXACT
3224 inexact = 0;
3225 #endif
3226 goto accept_dig;
3227 }
3228 #ifdef Honor_FLT_ROUNDS
3229 if (mode > 1)
3230 switch(rounding) {
3231 case 0: goto accept_dig;
3232 case 2: goto keep_dig;
3233 }
3234 #endif /*Honor_FLT_ROUNDS*/
3235 if (j1 > 0) {
3236 b = lshift(b, 1);
3237 j1 = cmp(b, S);
3238 if ((j1 > 0 || j1 == 0 && dig & 1)
3239 && dig++ == '9')
3240 goto round_9_up;
3241 }
3242 accept_dig:
3243 *s++ = dig;
3244 goto ret;
3245 }
3246 if (j1 > 0) {
3247 #ifdef Honor_FLT_ROUNDS
3248 if (!rounding)
3249 goto accept_dig;
3250 #endif
3251 if (dig == '9') { /* possible if i == 1 */
3252 round_9_up:
3253 *s++ = '9';
3254 goto roundoff;
3255 }
3256 *s++ = dig + 1;
3257 goto ret;
3258 }
3259 #ifdef Honor_FLT_ROUNDS
3260 keep_dig:
3261 #endif
3262 *s++ = dig;
3263 if (i == ilim)
3264 break;
3265 b = multadd(b, 10, 0);
3266 if (mlo == mhi)
3267 mlo = mhi = multadd(mhi, 10, 0);
3268 else {
3269 mlo = multadd(mlo, 10, 0);
3270 mhi = multadd(mhi, 10, 0);
3271 }
3272 }
3273 }
3274 else
3275 for(i = 1;; i++) {
3276 *s++ = dig = quorem(b,S) + '0';
3277 if (!b->x[0] && b->wds <= 1) {
3278 #ifdef SET_INEXACT
3279 inexact = 0;
3280 #endif
3281 goto ret;
3282 }
3283 if (i >= ilim)
3284 break;
3285 b = multadd(b, 10, 0);
3286 }
3287
3288 /* Round off last digit */
3289
3290 #ifdef Honor_FLT_ROUNDS
3291 switch(rounding) {
3292 case 0: goto trimzeros;
3293 case 2: goto roundoff;
3294 }
3295 #endif
3296 b = lshift(b, 1);
3297 j = cmp(b, S);
3298 if (j > 0 || j == 0 && dig & 1) {
3299 roundoff:
3300 while(*--s == '9')
3301 if (s == s0) {
3302 k++;
3303 *s++ = '1';
3304 goto ret;
3305 }
3306 ++*s++;
3307 }
3308 else {
3309 trimzeros:
3310 while(*--s == '0');
3311 s++;
3312 }
3313 ret:
3314 Bfree(S);
3315 if (mhi) {
3316 if (mlo && mlo != mhi)
3317 Bfree(mlo);
3318 Bfree(mhi);
3319 }
3320 ret1:
3321 #ifdef SET_INEXACT
3322 if (inexact) {
3323 if (!oldinexact) {
3324 word0(d) = Exp_1 + (70 << Exp_shift);
3325 word1(d) = 0;
3326 dval(d) += 1.;
3327 }
3328 }
3329 else if (!oldinexact)
3330 clear_inexact();
3331 #endif
3332 Bfree(b);
3333 *s = 0;
3334 *decpt = k + 1;
3335 if (rve)
3336 *rve = s;
3337 return s0;
3338 }
3339 #endif
3340
3341 #ifdef __cplusplus
3342 }
3343 #endif
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