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dtoa.c
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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 
20 /* Please send bug reports to David M. Gay (dmg at acm dot org,
21  * with " at " changed at "@" and " dot " changed to "."). */
22 
23 /* On a machine with IEEE extended-precision registers, it is
24  * necessary to specify double-precision (53-bit) rounding precision
25  * before invoking strtod or dtoa. If the machine uses (the equivalent
26  * of) Intel 80x87 arithmetic, the call
27  * _control87(PC_53, MCW_PC);
28  * does this with many compilers. Whether this or another call is
29  * appropriate depends on the compiler; for this to work, it may be
30  * necessary to #include "float.h" or another system-dependent header
31  * file.
32  */
33 
34 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
35  *
36  * This strtod returns a nearest machine number to the input decimal
37  * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
38  * broken by the IEEE round-even rule. Otherwise ties are broken by
39  * biased rounding (add half and chop).
40  *
41  * Inspired loosely by William D. Clinger's paper "How to Read Floating
42  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
43  *
44  * Modifications:
45  *
46  * 1. We only require IEEE, IBM, or VAX double-precision
47  * arithmetic (not IEEE double-extended).
48  * 2. We get by with floating-point arithmetic in a case that
49  * Clinger missed -- when we're computing d * 10^n
50  * for a small integer d and the integer n is not too
51  * much larger than 22 (the maximum integer k for which
52  * we can represent 10^k exactly), we may be able to
53  * compute (d*10^k) * 10^(e-k) with just one roundoff.
54  * 3. Rather than a bit-at-a-time adjustment of the binary
55  * result in the hard case, we use floating-point
56  * arithmetic to determine the adjustment to within
57  * one bit; only in really hard cases do we need to
58  * compute a second residual.
59  * 4. Because of 3., we don't need a large table of powers of 10
60  * for ten-to-e (just some small tables, e.g. of 10^k
61  * for 0 <= k <= 22).
62  */
63 
64 /*
65  * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
66  * significant byte has the lowest address.
67  * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
68  * significant byte has the lowest address.
69  * #define Long int on machines with 32-bit ints and 64-bit longs.
70  * #define IBM for IBM mainframe-style floating-point arithmetic.
71  * #define VAX for VAX-style floating-point arithmetic (D_floating).
72  * #define No_leftright to omit left-right logic in fast floating-point
73  * computation of dtoa.
74  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
75  * and strtod and dtoa should round accordingly.
76  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
77  * and Honor_FLT_ROUNDS is not #defined.
78  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
79  * that use extended-precision instructions to compute rounded
80  * products and quotients) with IBM.
81  * #define ROUND_BIASED for IEEE-format with biased rounding.
82  * #define Inaccurate_Divide for IEEE-format with correctly rounded
83  * products but inaccurate quotients, e.g., for Intel i860.
84  * #define NO_LONG_LONG on machines that do not have a "long long"
85  * integer type (of >= 64 bits). On such machines, you can
86  * #define Just_16 to store 16 bits per 32-bit Long when doing
87  * high-precision integer arithmetic. Whether this speeds things
88  * up or slows things down depends on the machine and the number
89  * being converted. If long long is available and the name is
90  * something other than "long long", #define Llong to be the name,
91  * and if "unsigned Llong" does not work as an unsigned version of
92  * Llong, #define #ULLong to be the corresponding unsigned type.
93  * #define KR_headers for old-style C function headers.
94  * #define Bad_float_h if your system lacks a float.h or if it does not
95  * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
96  * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
97  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
98  * if memory is available and otherwise does something you deem
99  * appropriate. If MALLOC is undefined, malloc will be invoked
100  * directly -- and assumed always to succeed.
101  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
102  * memory allocations from a private pool of memory when possible.
103  * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
104  * unless #defined to be a different length. This default length
105  * suffices to get rid of MALLOC calls except for unusual cases,
106  * such as decimal-to-binary conversion of a very long string of
107  * digits. The longest string dtoa can return is about 751 bytes
108  * long. For conversions by strtod of strings of 800 digits and
109  * all dtoa conversions in single-threaded executions with 8-byte
110  * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
111  * pointers, PRIVATE_MEM >= 7112 appears adequate.
112  * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
113  * Infinity and NaN (case insensitively). On some systems (e.g.,
114  * some HP systems), it may be necessary to #define NAN_WORD0
115  * appropriately -- to the most significant word of a quiet NaN.
116  * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
117  * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
118  * strtod also accepts (case insensitively) strings of the form
119  * NaN(x), where x is a string of hexadecimal digits and spaces;
120  * if there is only one string of hexadecimal digits, it is taken
121  * for the 52 fraction bits of the resulting NaN; if there are two
122  * or more strings of hex digits, the first is for the high 20 bits,
123  * the second and subsequent for the low 32 bits, with intervening
124  * white space ignored; but if this results in none of the 52
125  * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
126  * and NAN_WORD1 are used instead.
127  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
128  * multiple threads. In this case, you must provide (or suitably
129  * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
130  * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
131  * in pow5mult, ensures lazy evaluation of only one copy of high
132  * powers of 5; omitting this lock would introduce a small
133  * probability of wasting memory, but would otherwise be harmless.)
134  * You must also invoke freedtoa(s) to free the value s returned by
135  * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
136  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
137  * avoids underflows on inputs whose result does not underflow.
138  * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
139  * floating-point numbers and flushes underflows to zero rather
140  * than implementing gradual underflow, then you must also #define
141  * Sudden_Underflow.
142  * #define YES_ALIAS to permit aliasing certain double values with
143  * arrays of ULongs. This leads to slightly better code with
144  * some compilers and was always used prior to 19990916, but it
145  * is not strictly legal and can cause trouble with aggressively
146  * optimizing compilers (e.g., gcc 2.95.1 under -O2).
147  * #define USE_LOCALE to use the current locale's decimal_point value.
148  * #define SET_INEXACT if IEEE arithmetic is being used and extra
149  * computation should be done to set the inexact flag when the
150  * result is inexact and avoid setting inexact when the result
151  * is exact. In this case, dtoa.c must be compiled in
152  * an environment, perhaps provided by #include "dtoa.c" in a
153  * suitable wrapper, that defines two functions,
154  * int get_inexact(void);
155  * void clear_inexact(void);
156  * such that get_inexact() returns a nonzero value if the
157  * inexact bit is already set, and clear_inexact() sets the
158  * inexact bit to 0. When SET_INEXACT is #defined, strtod
159  * also does extra computations to set the underflow and overflow
160  * flags when appropriate (i.e., when the result is tiny and
161  * inexact or when it is a numeric value rounded to +-infinity).
162  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
163  * the result overflows to +-Infinity or underflows to 0.
164  */
165 
166 #ifdef WORDS_BIGENDIAN
167 #define IEEE_BIG_ENDIAN
168 #else
169 #define IEEE_LITTLE_ENDIAN
170 #endif
171 
172 #ifdef __vax__
173 #define VAX
174 #undef IEEE_BIG_ENDIAN
175 #undef IEEE_LITTLE_ENDIAN
176 #endif
177 
178 #if defined(__arm__) && !defined(__VFP_FP__)
179 #define IEEE_BIG_ENDIAN
180 #undef IEEE_LITTLE_ENDIAN
181 #endif
182 
183 #undef Long
184 #undef ULong
185 
186 #if SIZEOF_INT == 4
187 #define Long int
188 #define ULong unsigned int
189 #elif SIZEOF_LONG == 4
190 #define Long long int
191 #define ULong unsigned long int
192 #endif
193 
194 #if HAVE_LONG_LONG
195 #define Llong LONG_LONG
196 #else
197 #define NO_LONG_LONG
198 #endif
199 
200 #ifdef DEBUG
201 #include <stdio.h>
202 #define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
203 #endif
204 
205 #include <stdlib.h>
206 #include <string.h>
207 
208 #ifdef USE_LOCALE
209 #include <locale.h>
210 #endif
211 
212 #ifdef MALLOC
213 extern void *MALLOC(size_t);
214 #else
215 #define MALLOC xmalloc
216 #endif
217 #ifdef FREE
218 extern void FREE(void*);
219 #else
220 #define FREE xfree
221 #endif
222 
223 #ifndef Omit_Private_Memory
224 #ifndef PRIVATE_MEM
225 #define PRIVATE_MEM 2304
226 #endif
227 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
228 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
229 #endif
230 
231 #undef IEEE_Arith
232 #undef Avoid_Underflow
233 #ifdef IEEE_BIG_ENDIAN
234 #define IEEE_Arith
235 #endif
236 #ifdef IEEE_LITTLE_ENDIAN
237 #define IEEE_Arith
238 #endif
239 
240 #ifdef Bad_float_h
241 
242 #ifdef IEEE_Arith
243 #define DBL_DIG 15
244 #define DBL_MAX_10_EXP 308
245 #define DBL_MAX_EXP 1024
246 #define FLT_RADIX 2
247 #endif /*IEEE_Arith*/
248 
249 #ifdef IBM
250 #define DBL_DIG 16
251 #define DBL_MAX_10_EXP 75
252 #define DBL_MAX_EXP 63
253 #define FLT_RADIX 16
254 #define DBL_MAX 7.2370055773322621e+75
255 #endif
256 
257 #ifdef VAX
258 #define DBL_DIG 16
259 #define DBL_MAX_10_EXP 38
260 #define DBL_MAX_EXP 127
261 #define FLT_RADIX 2
262 #define DBL_MAX 1.7014118346046923e+38
263 #endif
264 
265 #ifndef LONG_MAX
266 #define LONG_MAX 2147483647
267 #endif
268 
269 #else /* ifndef Bad_float_h */
270 #include <float.h>
271 #endif /* Bad_float_h */
272 
273 #include <math.h>
274 
275 #ifdef __cplusplus
276 extern "C" {
277 #if 0
278 } /* satisfy cc-mode */
279 #endif
280 #endif
281 
282 #ifndef hexdigit
283 static const char hexdigits[] = "0123456789abcdef0123456789ABCDEF";
284 #endif
285 
286 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
287 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
288 #endif
289 
290 typedef union { double d; ULong L[2]; } U;
291 
292 #ifdef YES_ALIAS
293 typedef double double_u;
294 # define dval(x) (x)
295 # ifdef IEEE_LITTLE_ENDIAN
296 # define word0(x) (((ULong *)&(x))[1])
297 # define word1(x) (((ULong *)&(x))[0])
298 # else
299 # define word0(x) (((ULong *)&(x))[0])
300 # define word1(x) (((ULong *)&(x))[1])
301 # endif
302 #else
303 typedef U double_u;
304 # ifdef IEEE_LITTLE_ENDIAN
305 # define word0(x) ((x).L[1])
306 # define word1(x) ((x).L[0])
307 # else
308 # define word0(x) ((x).L[0])
309 # define word1(x) ((x).L[1])
310 # endif
311 # define dval(x) ((x).d)
312 #endif
313 
314 /* The following definition of Storeinc is appropriate for MIPS processors.
315  * An alternative that might be better on some machines is
316  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
317  */
318 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
319 #define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
320 ((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
321 #else
322 #define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
323 ((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
324 #endif
325 
326 /* #define P DBL_MANT_DIG */
327 /* Ten_pmax = floor(P*log(2)/log(5)) */
328 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
329 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
330 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
331 
332 #ifdef IEEE_Arith
333 #define Exp_shift 20
334 #define Exp_shift1 20
335 #define Exp_msk1 0x100000
336 #define Exp_msk11 0x100000
337 #define Exp_mask 0x7ff00000
338 #define P 53
339 #define Bias 1023
340 #define Emin (-1022)
341 #define Exp_1 0x3ff00000
342 #define Exp_11 0x3ff00000
343 #define Ebits 11
344 #define Frac_mask 0xfffff
345 #define Frac_mask1 0xfffff
346 #define Ten_pmax 22
347 #define Bletch 0x10
348 #define Bndry_mask 0xfffff
349 #define Bndry_mask1 0xfffff
350 #define LSB 1
351 #define Sign_bit 0x80000000
352 #define Log2P 1
353 #define Tiny0 0
354 #define Tiny1 1
355 #define Quick_max 14
356 #define Int_max 14
357 #ifndef NO_IEEE_Scale
358 #define Avoid_Underflow
359 #ifdef Flush_Denorm /* debugging option */
360 #undef Sudden_Underflow
361 #endif
362 #endif
363 
364 #ifndef Flt_Rounds
365 #ifdef FLT_ROUNDS
366 #define Flt_Rounds FLT_ROUNDS
367 #else
368 #define Flt_Rounds 1
369 #endif
370 #endif /*Flt_Rounds*/
371 
372 #ifdef Honor_FLT_ROUNDS
373 #define Rounding rounding
374 #undef Check_FLT_ROUNDS
375 #define Check_FLT_ROUNDS
376 #else
377 #define Rounding Flt_Rounds
378 #endif
379 
380 #else /* ifndef IEEE_Arith */
381 #undef Check_FLT_ROUNDS
382 #undef Honor_FLT_ROUNDS
383 #undef SET_INEXACT
384 #undef Sudden_Underflow
385 #define Sudden_Underflow
386 #ifdef IBM
387 #undef Flt_Rounds
388 #define Flt_Rounds 0
389 #define Exp_shift 24
390 #define Exp_shift1 24
391 #define Exp_msk1 0x1000000
392 #define Exp_msk11 0x1000000
393 #define Exp_mask 0x7f000000
394 #define P 14
395 #define Bias 65
396 #define Exp_1 0x41000000
397 #define Exp_11 0x41000000
398 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
399 #define Frac_mask 0xffffff
400 #define Frac_mask1 0xffffff
401 #define Bletch 4
402 #define Ten_pmax 22
403 #define Bndry_mask 0xefffff
404 #define Bndry_mask1 0xffffff
405 #define LSB 1
406 #define Sign_bit 0x80000000
407 #define Log2P 4
408 #define Tiny0 0x100000
409 #define Tiny1 0
410 #define Quick_max 14
411 #define Int_max 15
412 #else /* VAX */
413 #undef Flt_Rounds
414 #define Flt_Rounds 1
415 #define Exp_shift 23
416 #define Exp_shift1 7
417 #define Exp_msk1 0x80
418 #define Exp_msk11 0x800000
419 #define Exp_mask 0x7f80
420 #define P 56
421 #define Bias 129
422 #define Exp_1 0x40800000
423 #define Exp_11 0x4080
424 #define Ebits 8
425 #define Frac_mask 0x7fffff
426 #define Frac_mask1 0xffff007f
427 #define Ten_pmax 24
428 #define Bletch 2
429 #define Bndry_mask 0xffff007f
430 #define Bndry_mask1 0xffff007f
431 #define LSB 0x10000
432 #define Sign_bit 0x8000
433 #define Log2P 1
434 #define Tiny0 0x80
435 #define Tiny1 0
436 #define Quick_max 15
437 #define Int_max 15
438 #endif /* IBM, VAX */
439 #endif /* IEEE_Arith */
440 
441 #ifndef IEEE_Arith
442 #define ROUND_BIASED
443 #endif
444 
445 #ifdef RND_PRODQUOT
446 #define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
447 #define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
448 extern double rnd_prod(double, double), rnd_quot(double, double);
449 #else
450 #define rounded_product(a,b) ((a) *= (b))
451 #define rounded_quotient(a,b) ((a) /= (b))
452 #endif
453 
454 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
455 #define Big1 0xffffffff
456 
457 #ifndef Pack_32
458 #define Pack_32
459 #endif
460 
461 #define FFFFFFFF 0xffffffffUL
462 
463 #ifdef NO_LONG_LONG
464 #undef ULLong
465 #ifdef Just_16
466 #undef Pack_32
467 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
468  * This makes some inner loops simpler and sometimes saves work
469  * during multiplications, but it often seems to make things slightly
470  * slower. Hence the default is now to store 32 bits per Long.
471  */
472 #endif
473 #else /* long long available */
474 #ifndef Llong
475 #define Llong long long
476 #endif
477 #ifndef ULLong
478 #define ULLong unsigned Llong
479 #endif
480 #endif /* NO_LONG_LONG */
481 
482 #define MULTIPLE_THREADS 1
483 
484 #ifndef MULTIPLE_THREADS
485 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
486 #define FREE_DTOA_LOCK(n) /*nothing*/
487 #else
488 #define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
489 #define FREE_DTOA_LOCK(n) /*unused right now*/
490 #endif
491 
492 #define Kmax 15
493 
494 struct Bigint {
495  struct Bigint *next;
496  int k, maxwds, sign, wds;
497  ULong x[1];
498 };
499 
500 typedef struct Bigint Bigint;
501 
502 static Bigint *freelist[Kmax+1];
503 
504 static Bigint *
505 Balloc(int k)
506 {
507  int x;
508  Bigint *rv;
509 #ifndef Omit_Private_Memory
510  size_t len;
511 #endif
512 
514  if (k <= Kmax && (rv = freelist[k]) != 0) {
515  freelist[k] = rv->next;
516  }
517  else {
518  x = 1 << k;
519 #ifdef Omit_Private_Memory
520  rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
521 #else
522  len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
523  /sizeof(double);
524  if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
525  rv = (Bigint*)pmem_next;
526  pmem_next += len;
527  }
528  else
529  rv = (Bigint*)MALLOC(len*sizeof(double));
530 #endif
531  rv->k = k;
532  rv->maxwds = x;
533  }
534  FREE_DTOA_LOCK(0);
535  rv->sign = rv->wds = 0;
536  return rv;
537 }
538 
539 static void
540 Bfree(Bigint *v)
541 {
542  if (v) {
543  if (v->k > Kmax) {
544  FREE(v);
545  return;
546  }
548  v->next = freelist[v->k];
549  freelist[v->k] = v;
550  FREE_DTOA_LOCK(0);
551  }
552 }
553 
554 #define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
555 (y)->wds*sizeof(Long) + 2*sizeof(int))
556 
557 static Bigint *
558 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
559 {
560  int i, wds;
561  ULong *x;
562 #ifdef ULLong
563  ULLong carry, y;
564 #else
565  ULong carry, y;
566 #ifdef Pack_32
567  ULong xi, z;
568 #endif
569 #endif
570  Bigint *b1;
571 
572  wds = b->wds;
573  x = b->x;
574  i = 0;
575  carry = a;
576  do {
577 #ifdef ULLong
578  y = *x * (ULLong)m + carry;
579  carry = y >> 32;
580  *x++ = (ULong)(y & FFFFFFFF);
581 #else
582 #ifdef Pack_32
583  xi = *x;
584  y = (xi & 0xffff) * m + carry;
585  z = (xi >> 16) * m + (y >> 16);
586  carry = z >> 16;
587  *x++ = (z << 16) + (y & 0xffff);
588 #else
589  y = *x * m + carry;
590  carry = y >> 16;
591  *x++ = y & 0xffff;
592 #endif
593 #endif
594  } while (++i < wds);
595  if (carry) {
596  if (wds >= b->maxwds) {
597  b1 = Balloc(b->k+1);
598  Bcopy(b1, b);
599  Bfree(b);
600  b = b1;
601  }
602  b->x[wds++] = (ULong)carry;
603  b->wds = wds;
604  }
605  return b;
606 }
607 
608 static Bigint *
609 s2b(const char *s, int nd0, int nd, ULong y9)
610 {
611  Bigint *b;
612  int i, k;
613  Long x, y;
614 
615  x = (nd + 8) / 9;
616  for (k = 0, y = 1; x > y; y <<= 1, k++) ;
617 #ifdef Pack_32
618  b = Balloc(k);
619  b->x[0] = y9;
620  b->wds = 1;
621 #else
622  b = Balloc(k+1);
623  b->x[0] = y9 & 0xffff;
624  b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
625 #endif
626 
627  i = 9;
628  if (9 < nd0) {
629  s += 9;
630  do {
631  b = multadd(b, 10, *s++ - '0');
632  } while (++i < nd0);
633  s++;
634  }
635  else
636  s += 10;
637  for (; i < nd; i++)
638  b = multadd(b, 10, *s++ - '0');
639  return b;
640 }
641 
642 static int
643 hi0bits(register ULong x)
644 {
645  register int k = 0;
646 
647  if (!(x & 0xffff0000)) {
648  k = 16;
649  x <<= 16;
650  }
651  if (!(x & 0xff000000)) {
652  k += 8;
653  x <<= 8;
654  }
655  if (!(x & 0xf0000000)) {
656  k += 4;
657  x <<= 4;
658  }
659  if (!(x & 0xc0000000)) {
660  k += 2;
661  x <<= 2;
662  }
663  if (!(x & 0x80000000)) {
664  k++;
665  if (!(x & 0x40000000))
666  return 32;
667  }
668  return k;
669 }
670 
671 static int
672 lo0bits(ULong *y)
673 {
674  register int k;
675  register ULong x = *y;
676 
677  if (x & 7) {
678  if (x & 1)
679  return 0;
680  if (x & 2) {
681  *y = x >> 1;
682  return 1;
683  }
684  *y = x >> 2;
685  return 2;
686  }
687  k = 0;
688  if (!(x & 0xffff)) {
689  k = 16;
690  x >>= 16;
691  }
692  if (!(x & 0xff)) {
693  k += 8;
694  x >>= 8;
695  }
696  if (!(x & 0xf)) {
697  k += 4;
698  x >>= 4;
699  }
700  if (!(x & 0x3)) {
701  k += 2;
702  x >>= 2;
703  }
704  if (!(x & 1)) {
705  k++;
706  x >>= 1;
707  if (!x)
708  return 32;
709  }
710  *y = x;
711  return k;
712 }
713 
714 static Bigint *
715 i2b(int i)
716 {
717  Bigint *b;
718 
719  b = Balloc(1);
720  b->x[0] = i;
721  b->wds = 1;
722  return b;
723 }
724 
725 static Bigint *
726 mult(Bigint *a, Bigint *b)
727 {
728  Bigint *c;
729  int k, wa, wb, wc;
730  ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
731  ULong y;
732 #ifdef ULLong
733  ULLong carry, z;
734 #else
735  ULong carry, z;
736 #ifdef Pack_32
737  ULong z2;
738 #endif
739 #endif
740 
741  if (a->wds < b->wds) {
742  c = a;
743  a = b;
744  b = c;
745  }
746  k = a->k;
747  wa = a->wds;
748  wb = b->wds;
749  wc = wa + wb;
750  if (wc > a->maxwds)
751  k++;
752  c = Balloc(k);
753  for (x = c->x, xa = x + wc; x < xa; x++)
754  *x = 0;
755  xa = a->x;
756  xae = xa + wa;
757  xb = b->x;
758  xbe = xb + wb;
759  xc0 = c->x;
760 #ifdef ULLong
761  for (; xb < xbe; xc0++) {
762  if ((y = *xb++) != 0) {
763  x = xa;
764  xc = xc0;
765  carry = 0;
766  do {
767  z = *x++ * (ULLong)y + *xc + carry;
768  carry = z >> 32;
769  *xc++ = (ULong)(z & FFFFFFFF);
770  } while (x < xae);
771  *xc = (ULong)carry;
772  }
773  }
774 #else
775 #ifdef Pack_32
776  for (; xb < xbe; xb++, xc0++) {
777  if ((y = *xb & 0xffff) != 0) {
778  x = xa;
779  xc = xc0;
780  carry = 0;
781  do {
782  z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
783  carry = z >> 16;
784  z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
785  carry = z2 >> 16;
786  Storeinc(xc, z2, z);
787  } while (x < xae);
788  *xc = (ULong)carry;
789  }
790  if ((y = *xb >> 16) != 0) {
791  x = xa;
792  xc = xc0;
793  carry = 0;
794  z2 = *xc;
795  do {
796  z = (*x & 0xffff) * y + (*xc >> 16) + carry;
797  carry = z >> 16;
798  Storeinc(xc, z, z2);
799  z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
800  carry = z2 >> 16;
801  } while (x < xae);
802  *xc = z2;
803  }
804  }
805 #else
806  for (; xb < xbe; xc0++) {
807  if (y = *xb++) {
808  x = xa;
809  xc = xc0;
810  carry = 0;
811  do {
812  z = *x++ * y + *xc + carry;
813  carry = z >> 16;
814  *xc++ = z & 0xffff;
815  } while (x < xae);
816  *xc = (ULong)carry;
817  }
818  }
819 #endif
820 #endif
821  for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
822  c->wds = wc;
823  return c;
824 }
825 
826 static Bigint *p5s;
827 
828 static Bigint *
829 pow5mult(Bigint *b, int k)
830 {
831  Bigint *b1, *p5, *p51;
832  int i;
833  static int p05[3] = { 5, 25, 125 };
834 
835  if ((i = k & 3) != 0)
836  b = multadd(b, p05[i-1], 0);
837 
838  if (!(k >>= 2))
839  return b;
840  if (!(p5 = p5s)) {
841  /* first time */
842 #ifdef MULTIPLE_THREADS
844  if (!(p5 = p5s)) {
845  p5 = p5s = i2b(625);
846  p5->next = 0;
847  }
848  FREE_DTOA_LOCK(1);
849 #else
850  p5 = p5s = i2b(625);
851  p5->next = 0;
852 #endif
853  }
854  for (;;) {
855  if (k & 1) {
856  b1 = mult(b, p5);
857  Bfree(b);
858  b = b1;
859  }
860  if (!(k >>= 1))
861  break;
862  if (!(p51 = p5->next)) {
863 #ifdef MULTIPLE_THREADS
865  if (!(p51 = p5->next)) {
866  p51 = p5->next = mult(p5,p5);
867  p51->next = 0;
868  }
869  FREE_DTOA_LOCK(1);
870 #else
871  p51 = p5->next = mult(p5,p5);
872  p51->next = 0;
873 #endif
874  }
875  p5 = p51;
876  }
877  return b;
878 }
879 
880 static Bigint *
881 lshift(Bigint *b, int k)
882 {
883  int i, k1, n, n1;
884  Bigint *b1;
885  ULong *x, *x1, *xe, z;
886 
887 #ifdef Pack_32
888  n = k >> 5;
889 #else
890  n = k >> 4;
891 #endif
892  k1 = b->k;
893  n1 = n + b->wds + 1;
894  for (i = b->maxwds; n1 > i; i <<= 1)
895  k1++;
896  b1 = Balloc(k1);
897  x1 = b1->x;
898  for (i = 0; i < n; i++)
899  *x1++ = 0;
900  x = b->x;
901  xe = x + b->wds;
902 #ifdef Pack_32
903  if (k &= 0x1f) {
904  k1 = 32 - k;
905  z = 0;
906  do {
907  *x1++ = *x << k | z;
908  z = *x++ >> k1;
909  } while (x < xe);
910  if ((*x1 = z) != 0)
911  ++n1;
912  }
913 #else
914  if (k &= 0xf) {
915  k1 = 16 - k;
916  z = 0;
917  do {
918  *x1++ = *x << k & 0xffff | z;
919  z = *x++ >> k1;
920  } while (x < xe);
921  if (*x1 = z)
922  ++n1;
923  }
924 #endif
925  else
926  do {
927  *x1++ = *x++;
928  } while (x < xe);
929  b1->wds = n1 - 1;
930  Bfree(b);
931  return b1;
932 }
933 
934 static int
935 cmp(Bigint *a, Bigint *b)
936 {
937  ULong *xa, *xa0, *xb, *xb0;
938  int i, j;
939 
940  i = a->wds;
941  j = b->wds;
942 #ifdef DEBUG
943  if (i > 1 && !a->x[i-1])
944  Bug("cmp called with a->x[a->wds-1] == 0");
945  if (j > 1 && !b->x[j-1])
946  Bug("cmp called with b->x[b->wds-1] == 0");
947 #endif
948  if (i -= j)
949  return i;
950  xa0 = a->x;
951  xa = xa0 + j;
952  xb0 = b->x;
953  xb = xb0 + j;
954  for (;;) {
955  if (*--xa != *--xb)
956  return *xa < *xb ? -1 : 1;
957  if (xa <= xa0)
958  break;
959  }
960  return 0;
961 }
962 
963 NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b));
964 static Bigint *
965 diff(Bigint *a, Bigint *b)
966 {
967  Bigint *c;
968  int i, wa, wb;
969  ULong *xa, *xae, *xb, *xbe, *xc;
970 #ifdef ULLong
971  ULLong borrow, y;
972 #else
973  ULong borrow, y;
974 #ifdef Pack_32
975  ULong z;
976 #endif
977 #endif
978 
979  i = cmp(a,b);
980  if (!i) {
981  c = Balloc(0);
982  c->wds = 1;
983  c->x[0] = 0;
984  return c;
985  }
986  if (i < 0) {
987  c = a;
988  a = b;
989  b = c;
990  i = 1;
991  }
992  else
993  i = 0;
994  c = Balloc(a->k);
995  c->sign = i;
996  wa = a->wds;
997  xa = a->x;
998  xae = xa + wa;
999  wb = b->wds;
1000  xb = b->x;
1001  xbe = xb + wb;
1002  xc = c->x;
1003  borrow = 0;
1004 #ifdef ULLong
1005  do {
1006  y = (ULLong)*xa++ - *xb++ - borrow;
1007  borrow = y >> 32 & (ULong)1;
1008  *xc++ = (ULong)(y & FFFFFFFF);
1009  } while (xb < xbe);
1010  while (xa < xae) {
1011  y = *xa++ - borrow;
1012  borrow = y >> 32 & (ULong)1;
1013  *xc++ = (ULong)(y & FFFFFFFF);
1014  }
1015 #else
1016 #ifdef Pack_32
1017  do {
1018  y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1019  borrow = (y & 0x10000) >> 16;
1020  z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1021  borrow = (z & 0x10000) >> 16;
1022  Storeinc(xc, z, y);
1023  } while (xb < xbe);
1024  while (xa < xae) {
1025  y = (*xa & 0xffff) - borrow;
1026  borrow = (y & 0x10000) >> 16;
1027  z = (*xa++ >> 16) - borrow;
1028  borrow = (z & 0x10000) >> 16;
1029  Storeinc(xc, z, y);
1030  }
1031 #else
1032  do {
1033  y = *xa++ - *xb++ - borrow;
1034  borrow = (y & 0x10000) >> 16;
1035  *xc++ = y & 0xffff;
1036  } while (xb < xbe);
1037  while (xa < xae) {
1038  y = *xa++ - borrow;
1039  borrow = (y & 0x10000) >> 16;
1040  *xc++ = y & 0xffff;
1041  }
1042 #endif
1043 #endif
1044  while (!*--xc)
1045  wa--;
1046  c->wds = wa;
1047  return c;
1048 }
1049 
1050 static double
1051 ulp(double x_)
1052 {
1053  register Long L;
1054  double_u x, a;
1055  dval(x) = x_;
1056 
1057  L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1058 #ifndef Avoid_Underflow
1059 #ifndef Sudden_Underflow
1060  if (L > 0) {
1061 #endif
1062 #endif
1063 #ifdef IBM
1064  L |= Exp_msk1 >> 4;
1065 #endif
1066  word0(a) = L;
1067  word1(a) = 0;
1068 #ifndef Avoid_Underflow
1069 #ifndef Sudden_Underflow
1070  }
1071  else {
1072  L = -L >> Exp_shift;
1073  if (L < Exp_shift) {
1074  word0(a) = 0x80000 >> L;
1075  word1(a) = 0;
1076  }
1077  else {
1078  word0(a) = 0;
1079  L -= Exp_shift;
1080  word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1081  }
1082  }
1083 #endif
1084 #endif
1085  return dval(a);
1086 }
1087 
1088 static double
1089 b2d(Bigint *a, int *e)
1090 {
1091  ULong *xa, *xa0, w, y, z;
1092  int k;
1093  double_u d;
1094 #ifdef VAX
1095  ULong d0, d1;
1096 #else
1097 #define d0 word0(d)
1098 #define d1 word1(d)
1099 #endif
1100 
1101  xa0 = a->x;
1102  xa = xa0 + a->wds;
1103  y = *--xa;
1104 #ifdef DEBUG
1105  if (!y) Bug("zero y in b2d");
1106 #endif
1107  k = hi0bits(y);
1108  *e = 32 - k;
1109 #ifdef Pack_32
1110  if (k < Ebits) {
1111  d0 = Exp_1 | y >> (Ebits - k);
1112  w = xa > xa0 ? *--xa : 0;
1113  d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1114  goto ret_d;
1115  }
1116  z = xa > xa0 ? *--xa : 0;
1117  if (k -= Ebits) {
1118  d0 = Exp_1 | y << k | z >> (32 - k);
1119  y = xa > xa0 ? *--xa : 0;
1120  d1 = z << k | y >> (32 - k);
1121  }
1122  else {
1123  d0 = Exp_1 | y;
1124  d1 = z;
1125  }
1126 #else
1127  if (k < Ebits + 16) {
1128  z = xa > xa0 ? *--xa : 0;
1129  d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1130  w = xa > xa0 ? *--xa : 0;
1131  y = xa > xa0 ? *--xa : 0;
1132  d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1133  goto ret_d;
1134  }
1135  z = xa > xa0 ? *--xa : 0;
1136  w = xa > xa0 ? *--xa : 0;
1137  k -= Ebits + 16;
1138  d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1139  y = xa > xa0 ? *--xa : 0;
1140  d1 = w << k + 16 | y << k;
1141 #endif
1142 ret_d:
1143 #ifdef VAX
1144  word0(d) = d0 >> 16 | d0 << 16;
1145  word1(d) = d1 >> 16 | d1 << 16;
1146 #else
1147 #undef d0
1148 #undef d1
1149 #endif
1150  return dval(d);
1151 }
1152 
1153 static Bigint *
1154 d2b(double d_, int *e, int *bits)
1155 {
1156  double_u d;
1157  Bigint *b;
1158  int de, k;
1159  ULong *x, y, z;
1160 #ifndef Sudden_Underflow
1161  int i;
1162 #endif
1163 #ifdef VAX
1164  ULong d0, d1;
1165 #endif
1166  dval(d) = d_;
1167 #ifdef VAX
1168  d0 = word0(d) >> 16 | word0(d) << 16;
1169  d1 = word1(d) >> 16 | word1(d) << 16;
1170 #else
1171 #define d0 word0(d)
1172 #define d1 word1(d)
1173 #endif
1174 
1175 #ifdef Pack_32
1176  b = Balloc(1);
1177 #else
1178  b = Balloc(2);
1179 #endif
1180  x = b->x;
1181 
1182  z = d0 & Frac_mask;
1183  d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1184 #ifdef Sudden_Underflow
1185  de = (int)(d0 >> Exp_shift);
1186 #ifndef IBM
1187  z |= Exp_msk11;
1188 #endif
1189 #else
1190  if ((de = (int)(d0 >> Exp_shift)) != 0)
1191  z |= Exp_msk1;
1192 #endif
1193 #ifdef Pack_32
1194  if ((y = d1) != 0) {
1195  if ((k = lo0bits(&y)) != 0) {
1196  x[0] = y | z << (32 - k);
1197  z >>= k;
1198  }
1199  else
1200  x[0] = y;
1201 #ifndef Sudden_Underflow
1202  i =
1203 #endif
1204  b->wds = (x[1] = z) ? 2 : 1;
1205  }
1206  else {
1207 #ifdef DEBUG
1208  if (!z)
1209  Bug("Zero passed to d2b");
1210 #endif
1211  k = lo0bits(&z);
1212  x[0] = z;
1213 #ifndef Sudden_Underflow
1214  i =
1215 #endif
1216  b->wds = 1;
1217  k += 32;
1218  }
1219 #else
1220  if (y = d1) {
1221  if (k = lo0bits(&y))
1222  if (k >= 16) {
1223  x[0] = y | z << 32 - k & 0xffff;
1224  x[1] = z >> k - 16 & 0xffff;
1225  x[2] = z >> k;
1226  i = 2;
1227  }
1228  else {
1229  x[0] = y & 0xffff;
1230  x[1] = y >> 16 | z << 16 - k & 0xffff;
1231  x[2] = z >> k & 0xffff;
1232  x[3] = z >> k+16;
1233  i = 3;
1234  }
1235  else {
1236  x[0] = y & 0xffff;
1237  x[1] = y >> 16;
1238  x[2] = z & 0xffff;
1239  x[3] = z >> 16;
1240  i = 3;
1241  }
1242  }
1243  else {
1244 #ifdef DEBUG
1245  if (!z)
1246  Bug("Zero passed to d2b");
1247 #endif
1248  k = lo0bits(&z);
1249  if (k >= 16) {
1250  x[0] = z;
1251  i = 0;
1252  }
1253  else {
1254  x[0] = z & 0xffff;
1255  x[1] = z >> 16;
1256  i = 1;
1257  }
1258  k += 32;
1259  }
1260  while (!x[i])
1261  --i;
1262  b->wds = i + 1;
1263 #endif
1264 #ifndef Sudden_Underflow
1265  if (de) {
1266 #endif
1267 #ifdef IBM
1268  *e = (de - Bias - (P-1) << 2) + k;
1269  *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1270 #else
1271  *e = de - Bias - (P-1) + k;
1272  *bits = P - k;
1273 #endif
1274 #ifndef Sudden_Underflow
1275  }
1276  else {
1277  *e = de - Bias - (P-1) + 1 + k;
1278 #ifdef Pack_32
1279  *bits = 32*i - hi0bits(x[i-1]);
1280 #else
1281  *bits = (i+2)*16 - hi0bits(x[i]);
1282 #endif
1283  }
1284 #endif
1285  return b;
1286 }
1287 #undef d0
1288 #undef d1
1289 
1290 static double
1291 ratio(Bigint *a, Bigint *b)
1292 {
1293  double_u da, db;
1294  int k, ka, kb;
1295 
1296  dval(da) = b2d(a, &ka);
1297  dval(db) = b2d(b, &kb);
1298 #ifdef Pack_32
1299  k = ka - kb + 32*(a->wds - b->wds);
1300 #else
1301  k = ka - kb + 16*(a->wds - b->wds);
1302 #endif
1303 #ifdef IBM
1304  if (k > 0) {
1305  word0(da) += (k >> 2)*Exp_msk1;
1306  if (k &= 3)
1307  dval(da) *= 1 << k;
1308  }
1309  else {
1310  k = -k;
1311  word0(db) += (k >> 2)*Exp_msk1;
1312  if (k &= 3)
1313  dval(db) *= 1 << k;
1314  }
1315 #else
1316  if (k > 0)
1317  word0(da) += k*Exp_msk1;
1318  else {
1319  k = -k;
1320  word0(db) += k*Exp_msk1;
1321  }
1322 #endif
1323  return dval(da) / dval(db);
1324 }
1325 
1326 static const double
1327 tens[] = {
1328  1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1329  1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1330  1e20, 1e21, 1e22
1331 #ifdef VAX
1332  , 1e23, 1e24
1333 #endif
1334 };
1335 
1336 static const double
1337 #ifdef IEEE_Arith
1338 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1339 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1340 #ifdef Avoid_Underflow
1341  9007199254740992.*9007199254740992.e-256
1342  /* = 2^106 * 1e-53 */
1343 #else
1344  1e-256
1345 #endif
1346 };
1347 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1348 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1349 #define Scale_Bit 0x10
1350 #define n_bigtens 5
1351 #else
1352 #ifdef IBM
1353 bigtens[] = { 1e16, 1e32, 1e64 };
1354 static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1355 #define n_bigtens 3
1356 #else
1357 bigtens[] = { 1e16, 1e32 };
1358 static const double tinytens[] = { 1e-16, 1e-32 };
1359 #define n_bigtens 2
1360 #endif
1361 #endif
1362 
1363 #ifndef IEEE_Arith
1364 #undef INFNAN_CHECK
1365 #endif
1366 
1367 #ifdef INFNAN_CHECK
1368 
1369 #ifndef NAN_WORD0
1370 #define NAN_WORD0 0x7ff80000
1371 #endif
1372 
1373 #ifndef NAN_WORD1
1374 #define NAN_WORD1 0
1375 #endif
1376 
1377 static int
1378 match(const char **sp, char *t)
1379 {
1380  int c, d;
1381  const char *s = *sp;
1382 
1383  while (d = *t++) {
1384  if ((c = *++s) >= 'A' && c <= 'Z')
1385  c += 'a' - 'A';
1386  if (c != d)
1387  return 0;
1388  }
1389  *sp = s + 1;
1390  return 1;
1391 }
1392 
1393 #ifndef No_Hex_NaN
1394 static void
1395 hexnan(double *rvp, const char **sp)
1396 {
1397  ULong c, x[2];
1398  const char *s;
1399  int havedig, udx0, xshift;
1400 
1401  x[0] = x[1] = 0;
1402  havedig = xshift = 0;
1403  udx0 = 1;
1404  s = *sp;
1405  while (c = *(const unsigned char*)++s) {
1406  if (c >= '0' && c <= '9')
1407  c -= '0';
1408  else if (c >= 'a' && c <= 'f')
1409  c += 10 - 'a';
1410  else if (c >= 'A' && c <= 'F')
1411  c += 10 - 'A';
1412  else if (c <= ' ') {
1413  if (udx0 && havedig) {
1414  udx0 = 0;
1415  xshift = 1;
1416  }
1417  continue;
1418  }
1419  else if (/*(*/ c == ')' && havedig) {
1420  *sp = s + 1;
1421  break;
1422  }
1423  else
1424  return; /* invalid form: don't change *sp */
1425  havedig = 1;
1426  if (xshift) {
1427  xshift = 0;
1428  x[0] = x[1];
1429  x[1] = 0;
1430  }
1431  if (udx0)
1432  x[0] = (x[0] << 4) | (x[1] >> 28);
1433  x[1] = (x[1] << 4) | c;
1434  }
1435  if ((x[0] &= 0xfffff) || x[1]) {
1436  word0(*rvp) = Exp_mask | x[0];
1437  word1(*rvp) = x[1];
1438  }
1439 }
1440 #endif /*No_Hex_NaN*/
1441 #endif /* INFNAN_CHECK */
1442 
1443 NO_SANITIZE("unsigned-integer-overflow", double strtod(const char *s00, char **se));
1444 double
1445 strtod(const char *s00, char **se)
1446 {
1447 #ifdef Avoid_Underflow
1448  int scale;
1449 #endif
1450  int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1451  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1452  const char *s, *s0, *s1;
1453  double aadj, adj;
1454  double_u aadj1, rv, rv0;
1455  Long L;
1456  ULong y, z;
1457  Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1458 #ifdef SET_INEXACT
1459  int inexact, oldinexact;
1460 #endif
1461 #ifdef Honor_FLT_ROUNDS
1462  int rounding;
1463 #endif
1464 #ifdef USE_LOCALE
1465  const char *s2;
1466 #endif
1467 
1468  errno = 0;
1469  sign = nz0 = nz = 0;
1470  dval(rv) = 0.;
1471  for (s = s00;;s++)
1472  switch (*s) {
1473  case '-':
1474  sign = 1;
1475  /* no break */
1476  case '+':
1477  if (*++s)
1478  goto break2;
1479  /* no break */
1480  case 0:
1481  goto ret0;
1482  case '\t':
1483  case '\n':
1484  case '\v':
1485  case '\f':
1486  case '\r':
1487  case ' ':
1488  continue;
1489  default:
1490  goto break2;
1491  }
1492 break2:
1493  if (*s == '0') {
1494  if (s[1] == 'x' || s[1] == 'X') {
1495  s0 = ++s;
1496  adj = 0;
1497  aadj = 1.0;
1498  nd0 = -4;
1499 
1500  if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
1501  if (*s == '0') {
1502  while (*++s == '0');
1503  s1 = strchr(hexdigit, *s);
1504  }
1505  if (s1 != NULL) {
1506  do {
1507  adj += aadj * ((s1 - hexdigit) & 15);
1508  nd0 += 4;
1509  aadj /= 16;
1510  } while (*++s && (s1 = strchr(hexdigit, *s)));
1511  }
1512 
1513  if (*s == '.') {
1514  dsign = 1;
1515  if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
1516  if (nd0 < 0) {
1517  while (*s == '0') {
1518  s++;
1519  nd0 -= 4;
1520  }
1521  }
1522  for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
1523  adj += aadj * ((s1 - hexdigit) & 15);
1524  if ((aadj /= 16) == 0.0) {
1525  while (strchr(hexdigit, *++s));
1526  break;
1527  }
1528  }
1529  }
1530  else {
1531  dsign = 0;
1532  }
1533 
1534  if (*s == 'P' || *s == 'p') {
1535  dsign = 0x2C - *++s; /* +: 2B, -: 2D */
1536  if (abs(dsign) == 1) s++;
1537  else dsign = 1;
1538 
1539  nd = 0;
1540  c = *s;
1541  if (c < '0' || '9' < c) goto ret0;
1542  do {
1543  nd *= 10;
1544  nd += c;
1545  nd -= '0';
1546  c = *++s;
1547  /* Float("0x0."+("0"*267)+"1fp2095") */
1548  if (nd + dsign * nd0 > 2095) {
1549  while ('0' <= c && c <= '9') c = *++s;
1550  break;
1551  }
1552  } while ('0' <= c && c <= '9');
1553  nd0 += nd * dsign;
1554  }
1555  else {
1556  if (dsign) goto ret0;
1557  }
1558  dval(rv) = ldexp(adj, nd0);
1559  goto ret;
1560  }
1561  nz0 = 1;
1562  while (*++s == '0') ;
1563  if (!*s)
1564  goto ret;
1565  }
1566  s0 = s;
1567  y = z = 0;
1568  for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1569  if (nd < 9)
1570  y = 10*y + c - '0';
1571  else if (nd < DBL_DIG + 2)
1572  z = 10*z + c - '0';
1573  nd0 = nd;
1574 #ifdef USE_LOCALE
1575  s1 = localeconv()->decimal_point;
1576  if (c == *s1) {
1577  c = '.';
1578  if (*++s1) {
1579  s2 = s;
1580  for (;;) {
1581  if (*++s2 != *s1) {
1582  c = 0;
1583  break;
1584  }
1585  if (!*++s1) {
1586  s = s2;
1587  break;
1588  }
1589  }
1590  }
1591  }
1592 #endif
1593  if (c == '.') {
1594  if (!ISDIGIT(s[1]))
1595  goto dig_done;
1596  c = *++s;
1597  if (!nd) {
1598  for (; c == '0'; c = *++s)
1599  nz++;
1600  if (c > '0' && c <= '9') {
1601  s0 = s;
1602  nf += nz;
1603  nz = 0;
1604  goto have_dig;
1605  }
1606  goto dig_done;
1607  }
1608  for (; c >= '0' && c <= '9'; c = *++s) {
1609 have_dig:
1610  nz++;
1611  if (nd > DBL_DIG * 4) {
1612  continue;
1613  }
1614  if (c -= '0') {
1615  nf += nz;
1616  for (i = 1; i < nz; i++)
1617  if (nd++ < 9)
1618  y *= 10;
1619  else if (nd <= DBL_DIG + 2)
1620  z *= 10;
1621  if (nd++ < 9)
1622  y = 10*y + c;
1623  else if (nd <= DBL_DIG + 2)
1624  z = 10*z + c;
1625  nz = 0;
1626  }
1627  }
1628  }
1629 dig_done:
1630  e = 0;
1631  if (c == 'e' || c == 'E') {
1632  if (!nd && !nz && !nz0) {
1633  goto ret0;
1634  }
1635  s00 = s;
1636  esign = 0;
1637  switch (c = *++s) {
1638  case '-':
1639  esign = 1;
1640  case '+':
1641  c = *++s;
1642  }
1643  if (c >= '0' && c <= '9') {
1644  while (c == '0')
1645  c = *++s;
1646  if (c > '0' && c <= '9') {
1647  L = c - '0';
1648  s1 = s;
1649  while ((c = *++s) >= '0' && c <= '9')
1650  L = 10*L + c - '0';
1651  if (s - s1 > 8 || L > 19999)
1652  /* Avoid confusion from exponents
1653  * so large that e might overflow.
1654  */
1655  e = 19999; /* safe for 16 bit ints */
1656  else
1657  e = (int)L;
1658  if (esign)
1659  e = -e;
1660  }
1661  else
1662  e = 0;
1663  }
1664  else
1665  s = s00;
1666  }
1667  if (!nd) {
1668  if (!nz && !nz0) {
1669 #ifdef INFNAN_CHECK
1670  /* Check for Nan and Infinity */
1671  switch (c) {
1672  case 'i':
1673  case 'I':
1674  if (match(&s,"nf")) {
1675  --s;
1676  if (!match(&s,"inity"))
1677  ++s;
1678  word0(rv) = 0x7ff00000;
1679  word1(rv) = 0;
1680  goto ret;
1681  }
1682  break;
1683  case 'n':
1684  case 'N':
1685  if (match(&s, "an")) {
1686  word0(rv) = NAN_WORD0;
1687  word1(rv) = NAN_WORD1;
1688 #ifndef No_Hex_NaN
1689  if (*s == '(') /*)*/
1690  hexnan(&rv, &s);
1691 #endif
1692  goto ret;
1693  }
1694  }
1695 #endif /* INFNAN_CHECK */
1696 ret0:
1697  s = s00;
1698  sign = 0;
1699  }
1700  goto ret;
1701  }
1702  e1 = e -= nf;
1703 
1704  /* Now we have nd0 digits, starting at s0, followed by a
1705  * decimal point, followed by nd-nd0 digits. The number we're
1706  * after is the integer represented by those digits times
1707  * 10**e */
1708 
1709  if (!nd0)
1710  nd0 = nd;
1711  k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
1712  dval(rv) = y;
1713  if (k > 9) {
1714 #ifdef SET_INEXACT
1715  if (k > DBL_DIG)
1716  oldinexact = get_inexact();
1717 #endif
1718  dval(rv) = tens[k - 9] * dval(rv) + z;
1719  }
1720  bd0 = bb = bd = bs = delta = 0;
1721  if (nd <= DBL_DIG
1722 #ifndef RND_PRODQUOT
1723 #ifndef Honor_FLT_ROUNDS
1724  && Flt_Rounds == 1
1725 #endif
1726 #endif
1727  ) {
1728  if (!e)
1729  goto ret;
1730  if (e > 0) {
1731  if (e <= Ten_pmax) {
1732 #ifdef VAX
1733  goto vax_ovfl_check;
1734 #else
1735 #ifdef Honor_FLT_ROUNDS
1736  /* round correctly FLT_ROUNDS = 2 or 3 */
1737  if (sign) {
1738  dval(rv) = -dval(rv);
1739  sign = 0;
1740  }
1741 #endif
1742  /* rv = */ rounded_product(dval(rv), tens[e]);
1743  goto ret;
1744 #endif
1745  }
1746  i = DBL_DIG - nd;
1747  if (e <= Ten_pmax + i) {
1748  /* A fancier test would sometimes let us do
1749  * this for larger i values.
1750  */
1751 #ifdef Honor_FLT_ROUNDS
1752  /* round correctly FLT_ROUNDS = 2 or 3 */
1753  if (sign) {
1754  dval(rv) = -dval(rv);
1755  sign = 0;
1756  }
1757 #endif
1758  e -= i;
1759  dval(rv) *= tens[i];
1760 #ifdef VAX
1761  /* VAX exponent range is so narrow we must
1762  * worry about overflow here...
1763  */
1764 vax_ovfl_check:
1765  word0(rv) -= P*Exp_msk1;
1766  /* rv = */ rounded_product(dval(rv), tens[e]);
1767  if ((word0(rv) & Exp_mask)
1768  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1769  goto ovfl;
1770  word0(rv) += P*Exp_msk1;
1771 #else
1772  /* rv = */ rounded_product(dval(rv), tens[e]);
1773 #endif
1774  goto ret;
1775  }
1776  }
1777 #ifndef Inaccurate_Divide
1778  else if (e >= -Ten_pmax) {
1779 #ifdef Honor_FLT_ROUNDS
1780  /* round correctly FLT_ROUNDS = 2 or 3 */
1781  if (sign) {
1782  dval(rv) = -dval(rv);
1783  sign = 0;
1784  }
1785 #endif
1786  /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1787  goto ret;
1788  }
1789 #endif
1790  }
1791  e1 += nd - k;
1792 
1793 #ifdef IEEE_Arith
1794 #ifdef SET_INEXACT
1795  inexact = 1;
1796  if (k <= DBL_DIG)
1797  oldinexact = get_inexact();
1798 #endif
1799 #ifdef Avoid_Underflow
1800  scale = 0;
1801 #endif
1802 #ifdef Honor_FLT_ROUNDS
1803  if ((rounding = Flt_Rounds) >= 2) {
1804  if (sign)
1805  rounding = rounding == 2 ? 0 : 2;
1806  else
1807  if (rounding != 2)
1808  rounding = 0;
1809  }
1810 #endif
1811 #endif /*IEEE_Arith*/
1812 
1813  /* Get starting approximation = rv * 10**e1 */
1814 
1815  if (e1 > 0) {
1816  if ((i = e1 & 15) != 0)
1817  dval(rv) *= tens[i];
1818  if (e1 &= ~15) {
1819  if (e1 > DBL_MAX_10_EXP) {
1820 ovfl:
1821 #ifndef NO_ERRNO
1822  errno = ERANGE;
1823 #endif
1824  /* Can't trust HUGE_VAL */
1825 #ifdef IEEE_Arith
1826 #ifdef Honor_FLT_ROUNDS
1827  switch (rounding) {
1828  case 0: /* toward 0 */
1829  case 3: /* toward -infinity */
1830  word0(rv) = Big0;
1831  word1(rv) = Big1;
1832  break;
1833  default:
1834  word0(rv) = Exp_mask;
1835  word1(rv) = 0;
1836  }
1837 #else /*Honor_FLT_ROUNDS*/
1838  word0(rv) = Exp_mask;
1839  word1(rv) = 0;
1840 #endif /*Honor_FLT_ROUNDS*/
1841 #ifdef SET_INEXACT
1842  /* set overflow bit */
1843  dval(rv0) = 1e300;
1844  dval(rv0) *= dval(rv0);
1845 #endif
1846 #else /*IEEE_Arith*/
1847  word0(rv) = Big0;
1848  word1(rv) = Big1;
1849 #endif /*IEEE_Arith*/
1850  if (bd0)
1851  goto retfree;
1852  goto ret;
1853  }
1854  e1 >>= 4;
1855  for (j = 0; e1 > 1; j++, e1 >>= 1)
1856  if (e1 & 1)
1857  dval(rv) *= bigtens[j];
1858  /* The last multiplication could overflow. */
1859  word0(rv) -= P*Exp_msk1;
1860  dval(rv) *= bigtens[j];
1861  if ((z = word0(rv) & Exp_mask)
1862  > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1863  goto ovfl;
1864  if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1865  /* set to largest number */
1866  /* (Can't trust DBL_MAX) */
1867  word0(rv) = Big0;
1868  word1(rv) = Big1;
1869  }
1870  else
1871  word0(rv) += P*Exp_msk1;
1872  }
1873  }
1874  else if (e1 < 0) {
1875  e1 = -e1;
1876  if ((i = e1 & 15) != 0)
1877  dval(rv) /= tens[i];
1878  if (e1 >>= 4) {
1879  if (e1 >= 1 << n_bigtens)
1880  goto undfl;
1881 #ifdef Avoid_Underflow
1882  if (e1 & Scale_Bit)
1883  scale = 2*P;
1884  for (j = 0; e1 > 0; j++, e1 >>= 1)
1885  if (e1 & 1)
1886  dval(rv) *= tinytens[j];
1887  if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1888  >> Exp_shift)) > 0) {
1889  /* scaled rv is denormal; zap j low bits */
1890  if (j >= 32) {
1891  word1(rv) = 0;
1892  if (j >= 53)
1893  word0(rv) = (P+2)*Exp_msk1;
1894  else
1895  word0(rv) &= 0xffffffff << (j-32);
1896  }
1897  else
1898  word1(rv) &= 0xffffffff << j;
1899  }
1900 #else
1901  for (j = 0; e1 > 1; j++, e1 >>= 1)
1902  if (e1 & 1)
1903  dval(rv) *= tinytens[j];
1904  /* The last multiplication could underflow. */
1905  dval(rv0) = dval(rv);
1906  dval(rv) *= tinytens[j];
1907  if (!dval(rv)) {
1908  dval(rv) = 2.*dval(rv0);
1909  dval(rv) *= tinytens[j];
1910 #endif
1911  if (!dval(rv)) {
1912 undfl:
1913  dval(rv) = 0.;
1914 #ifndef NO_ERRNO
1915  errno = ERANGE;
1916 #endif
1917  if (bd0)
1918  goto retfree;
1919  goto ret;
1920  }
1921 #ifndef Avoid_Underflow
1922  word0(rv) = Tiny0;
1923  word1(rv) = Tiny1;
1924  /* The refinement below will clean
1925  * this approximation up.
1926  */
1927  }
1928 #endif
1929  }
1930  }
1931 
1932  /* Now the hard part -- adjusting rv to the correct value.*/
1933 
1934  /* Put digits into bd: true value = bd * 10^e */
1935 
1936  bd0 = s2b(s0, nd0, nd, y);
1937 
1938  for (;;) {
1939  bd = Balloc(bd0->k);
1940  Bcopy(bd, bd0);
1941  bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1942  bs = i2b(1);
1943 
1944  if (e >= 0) {
1945  bb2 = bb5 = 0;
1946  bd2 = bd5 = e;
1947  }
1948  else {
1949  bb2 = bb5 = -e;
1950  bd2 = bd5 = 0;
1951  }
1952  if (bbe >= 0)
1953  bb2 += bbe;
1954  else
1955  bd2 -= bbe;
1956  bs2 = bb2;
1957 #ifdef Honor_FLT_ROUNDS
1958  if (rounding != 1)
1959  bs2++;
1960 #endif
1961 #ifdef Avoid_Underflow
1962  j = bbe - scale;
1963  i = j + bbbits - 1; /* logb(rv) */
1964  if (i < Emin) /* denormal */
1965  j += P - Emin;
1966  else
1967  j = P + 1 - bbbits;
1968 #else /*Avoid_Underflow*/
1969 #ifdef Sudden_Underflow
1970 #ifdef IBM
1971  j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1972 #else
1973  j = P + 1 - bbbits;
1974 #endif
1975 #else /*Sudden_Underflow*/
1976  j = bbe;
1977  i = j + bbbits - 1; /* logb(rv) */
1978  if (i < Emin) /* denormal */
1979  j += P - Emin;
1980  else
1981  j = P + 1 - bbbits;
1982 #endif /*Sudden_Underflow*/
1983 #endif /*Avoid_Underflow*/
1984  bb2 += j;
1985  bd2 += j;
1986 #ifdef Avoid_Underflow
1987  bd2 += scale;
1988 #endif
1989  i = bb2 < bd2 ? bb2 : bd2;
1990  if (i > bs2)
1991  i = bs2;
1992  if (i > 0) {
1993  bb2 -= i;
1994  bd2 -= i;
1995  bs2 -= i;
1996  }
1997  if (bb5 > 0) {
1998  bs = pow5mult(bs, bb5);
1999  bb1 = mult(bs, bb);
2000  Bfree(bb);
2001  bb = bb1;
2002  }
2003  if (bb2 > 0)
2004  bb = lshift(bb, bb2);
2005  if (bd5 > 0)
2006  bd = pow5mult(bd, bd5);
2007  if (bd2 > 0)
2008  bd = lshift(bd, bd2);
2009  if (bs2 > 0)
2010  bs = lshift(bs, bs2);
2011  delta = diff(bb, bd);
2012  dsign = delta->sign;
2013  delta->sign = 0;
2014  i = cmp(delta, bs);
2015 #ifdef Honor_FLT_ROUNDS
2016  if (rounding != 1) {
2017  if (i < 0) {
2018  /* Error is less than an ulp */
2019  if (!delta->x[0] && delta->wds <= 1) {
2020  /* exact */
2021 #ifdef SET_INEXACT
2022  inexact = 0;
2023 #endif
2024  break;
2025  }
2026  if (rounding) {
2027  if (dsign) {
2028  adj = 1.;
2029  goto apply_adj;
2030  }
2031  }
2032  else if (!dsign) {
2033  adj = -1.;
2034  if (!word1(rv)
2035  && !(word0(rv) & Frac_mask)) {
2036  y = word0(rv) & Exp_mask;
2037 #ifdef Avoid_Underflow
2038  if (!scale || y > 2*P*Exp_msk1)
2039 #else
2040  if (y)
2041 #endif
2042  {
2043  delta = lshift(delta,Log2P);
2044  if (cmp(delta, bs) <= 0)
2045  adj = -0.5;
2046  }
2047  }
2048 apply_adj:
2049 #ifdef Avoid_Underflow
2050  if (scale && (y = word0(rv) & Exp_mask)
2051  <= 2*P*Exp_msk1)
2052  word0(adj) += (2*P+1)*Exp_msk1 - y;
2053 #else
2054 #ifdef Sudden_Underflow
2055  if ((word0(rv) & Exp_mask) <=
2056  P*Exp_msk1) {
2057  word0(rv) += P*Exp_msk1;
2058  dval(rv) += adj*ulp(dval(rv));
2059  word0(rv) -= P*Exp_msk1;
2060  }
2061  else
2062 #endif /*Sudden_Underflow*/
2063 #endif /*Avoid_Underflow*/
2064  dval(rv) += adj*ulp(dval(rv));
2065  }
2066  break;
2067  }
2068  adj = ratio(delta, bs);
2069  if (adj < 1.)
2070  adj = 1.;
2071  if (adj <= 0x7ffffffe) {
2072  /* adj = rounding ? ceil(adj) : floor(adj); */
2073  y = adj;
2074  if (y != adj) {
2075  if (!((rounding>>1) ^ dsign))
2076  y++;
2077  adj = y;
2078  }
2079  }
2080 #ifdef Avoid_Underflow
2081  if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2082  word0(adj) += (2*P+1)*Exp_msk1 - y;
2083 #else
2084 #ifdef Sudden_Underflow
2085  if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2086  word0(rv) += P*Exp_msk1;
2087  adj *= ulp(dval(rv));
2088  if (dsign)
2089  dval(rv) += adj;
2090  else
2091  dval(rv) -= adj;
2092  word0(rv) -= P*Exp_msk1;
2093  goto cont;
2094  }
2095 #endif /*Sudden_Underflow*/
2096 #endif /*Avoid_Underflow*/
2097  adj *= ulp(dval(rv));
2098  if (dsign)
2099  dval(rv) += adj;
2100  else
2101  dval(rv) -= adj;
2102  goto cont;
2103  }
2104 #endif /*Honor_FLT_ROUNDS*/
2105 
2106  if (i < 0) {
2107  /* Error is less than half an ulp -- check for
2108  * special case of mantissa a power of two.
2109  */
2110  if (dsign || word1(rv) || word0(rv) & Bndry_mask
2111 #ifdef IEEE_Arith
2112 #ifdef Avoid_Underflow
2113  || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2114 #else
2115  || (word0(rv) & Exp_mask) <= Exp_msk1
2116 #endif
2117 #endif
2118  ) {
2119 #ifdef SET_INEXACT
2120  if (!delta->x[0] && delta->wds <= 1)
2121  inexact = 0;
2122 #endif
2123  break;
2124  }
2125  if (!delta->x[0] && delta->wds <= 1) {
2126  /* exact result */
2127 #ifdef SET_INEXACT
2128  inexact = 0;
2129 #endif
2130  break;
2131  }
2132  delta = lshift(delta,Log2P);
2133  if (cmp(delta, bs) > 0)
2134  goto drop_down;
2135  break;
2136  }
2137  if (i == 0) {
2138  /* exactly half-way between */
2139  if (dsign) {
2140  if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2141  && word1(rv) == (
2142 #ifdef Avoid_Underflow
2143  (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2144  ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2145 #endif
2146  0xffffffff)) {
2147  /*boundary case -- increment exponent*/
2148  word0(rv) = (word0(rv) & Exp_mask)
2149  + Exp_msk1
2150 #ifdef IBM
2151  | Exp_msk1 >> 4
2152 #endif
2153  ;
2154  word1(rv) = 0;
2155 #ifdef Avoid_Underflow
2156  dsign = 0;
2157 #endif
2158  break;
2159  }
2160  }
2161  else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2162 drop_down:
2163  /* boundary case -- decrement exponent */
2164 #ifdef Sudden_Underflow /*{{*/
2165  L = word0(rv) & Exp_mask;
2166 #ifdef IBM
2167  if (L < Exp_msk1)
2168 #else
2169 #ifdef Avoid_Underflow
2170  if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2171 #else
2172  if (L <= Exp_msk1)
2173 #endif /*Avoid_Underflow*/
2174 #endif /*IBM*/
2175  goto undfl;
2176  L -= Exp_msk1;
2177 #else /*Sudden_Underflow}{*/
2178 #ifdef Avoid_Underflow
2179  if (scale) {
2180  L = word0(rv) & Exp_mask;
2181  if (L <= (2*P+1)*Exp_msk1) {
2182  if (L > (P+2)*Exp_msk1)
2183  /* round even ==> */
2184  /* accept rv */
2185  break;
2186  /* rv = smallest denormal */
2187  goto undfl;
2188  }
2189  }
2190 #endif /*Avoid_Underflow*/
2191  L = (word0(rv) & Exp_mask) - Exp_msk1;
2192 #endif /*Sudden_Underflow}}*/
2193  word0(rv) = L | Bndry_mask1;
2194  word1(rv) = 0xffffffff;
2195 #ifdef IBM
2196  goto cont;
2197 #else
2198  break;
2199 #endif
2200  }
2201 #ifndef ROUND_BIASED
2202  if (!(word1(rv) & LSB))
2203  break;
2204 #endif
2205  if (dsign)
2206  dval(rv) += ulp(dval(rv));
2207 #ifndef ROUND_BIASED
2208  else {
2209  dval(rv) -= ulp(dval(rv));
2210 #ifndef Sudden_Underflow
2211  if (!dval(rv))
2212  goto undfl;
2213 #endif
2214  }
2215 #ifdef Avoid_Underflow
2216  dsign = 1 - dsign;
2217 #endif
2218 #endif
2219  break;
2220  }
2221  if ((aadj = ratio(delta, bs)) <= 2.) {
2222  if (dsign)
2223  aadj = dval(aadj1) = 1.;
2224  else if (word1(rv) || word0(rv) & Bndry_mask) {
2225 #ifndef Sudden_Underflow
2226  if (word1(rv) == Tiny1 && !word0(rv))
2227  goto undfl;
2228 #endif
2229  aadj = 1.;
2230  dval(aadj1) = -1.;
2231  }
2232  else {
2233  /* special case -- power of FLT_RADIX to be */
2234  /* rounded down... */
2235 
2236  if (aadj < 2./FLT_RADIX)
2237  aadj = 1./FLT_RADIX;
2238  else
2239  aadj *= 0.5;
2240  dval(aadj1) = -aadj;
2241  }
2242  }
2243  else {
2244  aadj *= 0.5;
2245  dval(aadj1) = dsign ? aadj : -aadj;
2246 #ifdef Check_FLT_ROUNDS
2247  switch (Rounding) {
2248  case 2: /* towards +infinity */
2249  dval(aadj1) -= 0.5;
2250  break;
2251  case 0: /* towards 0 */
2252  case 3: /* towards -infinity */
2253  dval(aadj1) += 0.5;
2254  }
2255 #else
2256  if (Flt_Rounds == 0)
2257  dval(aadj1) += 0.5;
2258 #endif /*Check_FLT_ROUNDS*/
2259  }
2260  y = word0(rv) & Exp_mask;
2261 
2262  /* Check for overflow */
2263 
2264  if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2265  dval(rv0) = dval(rv);
2266  word0(rv) -= P*Exp_msk1;
2267  adj = dval(aadj1) * ulp(dval(rv));
2268  dval(rv) += adj;
2269  if ((word0(rv) & Exp_mask) >=
2270  Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2271  if (word0(rv0) == Big0 && word1(rv0) == Big1)
2272  goto ovfl;
2273  word0(rv) = Big0;
2274  word1(rv) = Big1;
2275  goto cont;
2276  }
2277  else
2278  word0(rv) += P*Exp_msk1;
2279  }
2280  else {
2281 #ifdef Avoid_Underflow
2282  if (scale && y <= 2*P*Exp_msk1) {
2283  if (aadj <= 0x7fffffff) {
2284  if ((z = (int)aadj) <= 0)
2285  z = 1;
2286  aadj = z;
2287  dval(aadj1) = dsign ? aadj : -aadj;
2288  }
2289  word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2290  }
2291  adj = dval(aadj1) * ulp(dval(rv));
2292  dval(rv) += adj;
2293 #else
2294 #ifdef Sudden_Underflow
2295  if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2296  dval(rv0) = dval(rv);
2297  word0(rv) += P*Exp_msk1;
2298  adj = dval(aadj1) * ulp(dval(rv));
2299  dval(rv) += adj;
2300 #ifdef IBM
2301  if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2302 #else
2303  if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2304 #endif
2305  {
2306  if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2307  goto undfl;
2308  word0(rv) = Tiny0;
2309  word1(rv) = Tiny1;
2310  goto cont;
2311  }
2312  else
2313  word0(rv) -= P*Exp_msk1;
2314  }
2315  else {
2316  adj = dval(aadj1) * ulp(dval(rv));
2317  dval(rv) += adj;
2318  }
2319 #else /*Sudden_Underflow*/
2320  /* Compute adj so that the IEEE rounding rules will
2321  * correctly round rv + adj in some half-way cases.
2322  * If rv * ulp(rv) is denormalized (i.e.,
2323  * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2324  * trouble from bits lost to denormalization;
2325  * example: 1.2e-307 .
2326  */
2327  if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2328  dval(aadj1) = (double)(int)(aadj + 0.5);
2329  if (!dsign)
2330  dval(aadj1) = -dval(aadj1);
2331  }
2332  adj = dval(aadj1) * ulp(dval(rv));
2333  dval(rv) += adj;
2334 #endif /*Sudden_Underflow*/
2335 #endif /*Avoid_Underflow*/
2336  }
2337  z = word0(rv) & Exp_mask;
2338 #ifndef SET_INEXACT
2339 #ifdef Avoid_Underflow
2340  if (!scale)
2341 #endif
2342  if (y == z) {
2343  /* Can we stop now? */
2344  L = (Long)aadj;
2345  aadj -= L;
2346  /* The tolerances below are conservative. */
2347  if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2348  if (aadj < .4999999 || aadj > .5000001)
2349  break;
2350  }
2351  else if (aadj < .4999999/FLT_RADIX)
2352  break;
2353  }
2354 #endif
2355 cont:
2356  Bfree(bb);
2357  Bfree(bd);
2358  Bfree(bs);
2359  Bfree(delta);
2360  }
2361 #ifdef SET_INEXACT
2362  if (inexact) {
2363  if (!oldinexact) {
2364  word0(rv0) = Exp_1 + (70 << Exp_shift);
2365  word1(rv0) = 0;
2366  dval(rv0) += 1.;
2367  }
2368  }
2369  else if (!oldinexact)
2370  clear_inexact();
2371 #endif
2372 #ifdef Avoid_Underflow
2373  if (scale) {
2374  word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2375  word1(rv0) = 0;
2376  dval(rv) *= dval(rv0);
2377 #ifndef NO_ERRNO
2378  /* try to avoid the bug of testing an 8087 register value */
2379  if (word0(rv) == 0 && word1(rv) == 0)
2380  errno = ERANGE;
2381 #endif
2382  }
2383 #endif /* Avoid_Underflow */
2384 #ifdef SET_INEXACT
2385  if (inexact && !(word0(rv) & Exp_mask)) {
2386  /* set underflow bit */
2387  dval(rv0) = 1e-300;
2388  dval(rv0) *= dval(rv0);
2389  }
2390 #endif
2391 retfree:
2392  Bfree(bb);
2393  Bfree(bd);
2394  Bfree(bs);
2395  Bfree(bd0);
2396  Bfree(delta);
2397 ret:
2398  if (se)
2399  *se = (char *)s;
2400  return sign ? -dval(rv) : dval(rv);
2401 }
2402 
2403 NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S));
2404 static int
2405 quorem(Bigint *b, Bigint *S)
2406 {
2407  int n;
2408  ULong *bx, *bxe, q, *sx, *sxe;
2409 #ifdef ULLong
2410  ULLong borrow, carry, y, ys;
2411 #else
2412  ULong borrow, carry, y, ys;
2413 #ifdef Pack_32
2414  ULong si, z, zs;
2415 #endif
2416 #endif
2417 
2418  n = S->wds;
2419 #ifdef DEBUG
2420  /*debug*/ if (b->wds > n)
2421  /*debug*/ Bug("oversize b in quorem");
2422 #endif
2423  if (b->wds < n)
2424  return 0;
2425  sx = S->x;
2426  sxe = sx + --n;
2427  bx = b->x;
2428  bxe = bx + n;
2429  q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2430 #ifdef DEBUG
2431  /*debug*/ if (q > 9)
2432  /*debug*/ Bug("oversized quotient in quorem");
2433 #endif
2434  if (q) {
2435  borrow = 0;
2436  carry = 0;
2437  do {
2438 #ifdef ULLong
2439  ys = *sx++ * (ULLong)q + carry;
2440  carry = ys >> 32;
2441  y = *bx - (ys & FFFFFFFF) - borrow;
2442  borrow = y >> 32 & (ULong)1;
2443  *bx++ = (ULong)(y & FFFFFFFF);
2444 #else
2445 #ifdef Pack_32
2446  si = *sx++;
2447  ys = (si & 0xffff) * q + carry;
2448  zs = (si >> 16) * q + (ys >> 16);
2449  carry = zs >> 16;
2450  y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2451  borrow = (y & 0x10000) >> 16;
2452  z = (*bx >> 16) - (zs & 0xffff) - borrow;
2453  borrow = (z & 0x10000) >> 16;
2454  Storeinc(bx, z, y);
2455 #else
2456  ys = *sx++ * q + carry;
2457  carry = ys >> 16;
2458  y = *bx - (ys & 0xffff) - borrow;
2459  borrow = (y & 0x10000) >> 16;
2460  *bx++ = y & 0xffff;
2461 #endif
2462 #endif
2463  } while (sx <= sxe);
2464  if (!*bxe) {
2465  bx = b->x;
2466  while (--bxe > bx && !*bxe)
2467  --n;
2468  b->wds = n;
2469  }
2470  }
2471  if (cmp(b, S) >= 0) {
2472  q++;
2473  borrow = 0;
2474  carry = 0;
2475  bx = b->x;
2476  sx = S->x;
2477  do {
2478 #ifdef ULLong
2479  ys = *sx++ + carry;
2480  carry = ys >> 32;
2481  y = *bx - (ys & FFFFFFFF) - borrow;
2482  borrow = y >> 32 & (ULong)1;
2483  *bx++ = (ULong)(y & FFFFFFFF);
2484 #else
2485 #ifdef Pack_32
2486  si = *sx++;
2487  ys = (si & 0xffff) + carry;
2488  zs = (si >> 16) + (ys >> 16);
2489  carry = zs >> 16;
2490  y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2491  borrow = (y & 0x10000) >> 16;
2492  z = (*bx >> 16) - (zs & 0xffff) - borrow;
2493  borrow = (z & 0x10000) >> 16;
2494  Storeinc(bx, z, y);
2495 #else
2496  ys = *sx++ + carry;
2497  carry = ys >> 16;
2498  y = *bx - (ys & 0xffff) - borrow;
2499  borrow = (y & 0x10000) >> 16;
2500  *bx++ = y & 0xffff;
2501 #endif
2502 #endif
2503  } while (sx <= sxe);
2504  bx = b->x;
2505  bxe = bx + n;
2506  if (!*bxe) {
2507  while (--bxe > bx && !*bxe)
2508  --n;
2509  b->wds = n;
2510  }
2511  }
2512  return q;
2513 }
2514 
2515 #ifndef MULTIPLE_THREADS
2516 static char *dtoa_result;
2517 #endif
2518 
2519 #ifndef MULTIPLE_THREADS
2520 static char *
2521 rv_alloc(int i)
2522 {
2523  return dtoa_result = xmalloc(i);
2524 }
2525 #else
2526 #define rv_alloc(i) xmalloc(i)
2527 #endif
2528 
2529 static char *
2530 nrv_alloc(const char *s, char **rve, size_t n)
2531 {
2532  char *rv, *t;
2533 
2534  t = rv = rv_alloc(n);
2535  while ((*t = *s++) != 0) t++;
2536  if (rve)
2537  *rve = t;
2538  return rv;
2539 }
2540 
2541 #define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
2542 
2543 #ifndef MULTIPLE_THREADS
2544 /* freedtoa(s) must be used to free values s returned by dtoa
2545  * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2546  * but for consistency with earlier versions of dtoa, it is optional
2547  * when MULTIPLE_THREADS is not defined.
2548  */
2549 
2550 static void
2551 freedtoa(char *s)
2552 {
2553  xfree(s);
2554 }
2555 #endif
2556 
2557 static const char INFSTR[] = "Infinity";
2558 static const char NANSTR[] = "NaN";
2559 static const char ZEROSTR[] = "0";
2560 
2561 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2562  *
2563  * Inspired by "How to Print Floating-Point Numbers Accurately" by
2564  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2565  *
2566  * Modifications:
2567  * 1. Rather than iterating, we use a simple numeric overestimate
2568  * to determine k = floor(log10(d)). We scale relevant
2569  * quantities using O(log2(k)) rather than O(k) multiplications.
2570  * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2571  * try to generate digits strictly left to right. Instead, we
2572  * compute with fewer bits and propagate the carry if necessary
2573  * when rounding the final digit up. This is often faster.
2574  * 3. Under the assumption that input will be rounded nearest,
2575  * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2576  * That is, we allow equality in stopping tests when the
2577  * round-nearest rule will give the same floating-point value
2578  * as would satisfaction of the stopping test with strict
2579  * inequality.
2580  * 4. We remove common factors of powers of 2 from relevant
2581  * quantities.
2582  * 5. When converting floating-point integers less than 1e16,
2583  * we use floating-point arithmetic rather than resorting
2584  * to multiple-precision integers.
2585  * 6. When asked to produce fewer than 15 digits, we first try
2586  * to get by with floating-point arithmetic; we resort to
2587  * multiple-precision integer arithmetic only if we cannot
2588  * guarantee that the floating-point calculation has given
2589  * the correctly rounded result. For k requested digits and
2590  * "uniformly" distributed input, the probability is
2591  * something like 10^(k-15) that we must resort to the Long
2592  * calculation.
2593  */
2594 
2595 char *
2596 dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
2597 {
2598  /* Arguments ndigits, decpt, sign are similar to those
2599  of ecvt and fcvt; trailing zeros are suppressed from
2600  the returned string. If not null, *rve is set to point
2601  to the end of the return value. If d is +-Infinity or NaN,
2602  then *decpt is set to 9999.
2603 
2604  mode:
2605  0 ==> shortest string that yields d when read in
2606  and rounded to nearest.
2607  1 ==> like 0, but with Steele & White stopping rule;
2608  e.g. with IEEE P754 arithmetic , mode 0 gives
2609  1e23 whereas mode 1 gives 9.999999999999999e22.
2610  2 ==> max(1,ndigits) significant digits. This gives a
2611  return value similar to that of ecvt, except
2612  that trailing zeros are suppressed.
2613  3 ==> through ndigits past the decimal point. This
2614  gives a return value similar to that from fcvt,
2615  except that trailing zeros are suppressed, and
2616  ndigits can be negative.
2617  4,5 ==> similar to 2 and 3, respectively, but (in
2618  round-nearest mode) with the tests of mode 0 to
2619  possibly return a shorter string that rounds to d.
2620  With IEEE arithmetic and compilation with
2621  -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2622  as modes 2 and 3 when FLT_ROUNDS != 1.
2623  6-9 ==> Debugging modes similar to mode - 4: don't try
2624  fast floating-point estimate (if applicable).
2625 
2626  Values of mode other than 0-9 are treated as mode 0.
2627 
2628  Sufficient space is allocated to the return value
2629  to hold the suppressed trailing zeros.
2630  */
2631 
2632  int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2633  j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2634  spec_case, try_quick, half = 0;
2635  Long L;
2636 #ifndef Sudden_Underflow
2637  int denorm;
2638  ULong x;
2639 #endif
2640  Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
2641  double ds;
2642  double_u d, d2, eps;
2643  char *s, *s0;
2644 #ifdef Honor_FLT_ROUNDS
2645  int rounding;
2646 #endif
2647 #ifdef SET_INEXACT
2648  int inexact, oldinexact;
2649 #endif
2650 
2651  dval(d) = d_;
2652 
2653 #ifndef MULTIPLE_THREADS
2654  if (dtoa_result) {
2655  freedtoa(dtoa_result);
2656  dtoa_result = 0;
2657  }
2658 #endif
2659 
2660  if (word0(d) & Sign_bit) {
2661  /* set sign for everything, including 0's and NaNs */
2662  *sign = 1;
2663  word0(d) &= ~Sign_bit; /* clear sign bit */
2664  }
2665  else
2666  *sign = 0;
2667 
2668 #if defined(IEEE_Arith) + defined(VAX)
2669 #ifdef IEEE_Arith
2670  if ((word0(d) & Exp_mask) == Exp_mask)
2671 #else
2672  if (word0(d) == 0x8000)
2673 #endif
2674  {
2675  /* Infinity or NaN */
2676  *decpt = 9999;
2677 #ifdef IEEE_Arith
2678  if (!word1(d) && !(word0(d) & 0xfffff))
2679  return rv_strdup(INFSTR, rve);
2680 #endif
2681  return rv_strdup(NANSTR, rve);
2682  }
2683 #endif
2684 #ifdef IBM
2685  dval(d) += 0; /* normalize */
2686 #endif
2687  if (!dval(d)) {
2688  *decpt = 1;
2689  return rv_strdup(ZEROSTR, rve);
2690  }
2691 
2692 #ifdef SET_INEXACT
2693  try_quick = oldinexact = get_inexact();
2694  inexact = 1;
2695 #endif
2696 #ifdef Honor_FLT_ROUNDS
2697  if ((rounding = Flt_Rounds) >= 2) {
2698  if (*sign)
2699  rounding = rounding == 2 ? 0 : 2;
2700  else
2701  if (rounding != 2)
2702  rounding = 0;
2703  }
2704 #endif
2705 
2706  b = d2b(dval(d), &be, &bbits);
2707 #ifdef Sudden_Underflow
2708  i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2709 #else
2710  if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
2711 #endif
2712  dval(d2) = dval(d);
2713  word0(d2) &= Frac_mask1;
2714  word0(d2) |= Exp_11;
2715 #ifdef IBM
2716  if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2717  dval(d2) /= 1 << j;
2718 #endif
2719 
2720  /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2721  * log10(x) = log(x) / log(10)
2722  * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2723  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2724  *
2725  * This suggests computing an approximation k to log10(d) by
2726  *
2727  * k = (i - Bias)*0.301029995663981
2728  * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2729  *
2730  * We want k to be too large rather than too small.
2731  * The error in the first-order Taylor series approximation
2732  * is in our favor, so we just round up the constant enough
2733  * to compensate for any error in the multiplication of
2734  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2735  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2736  * adding 1e-13 to the constant term more than suffices.
2737  * Hence we adjust the constant term to 0.1760912590558.
2738  * (We could get a more accurate k by invoking log10,
2739  * but this is probably not worthwhile.)
2740  */
2741 
2742  i -= Bias;
2743 #ifdef IBM
2744  i <<= 2;
2745  i += j;
2746 #endif
2747 #ifndef Sudden_Underflow
2748  denorm = 0;
2749  }
2750  else {
2751  /* d is denormalized */
2752 
2753  i = bbits + be + (Bias + (P-1) - 1);
2754  x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2755  : word1(d) << (32 - i);
2756  dval(d2) = x;
2757  word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2758  i -= (Bias + (P-1) - 1) + 1;
2759  denorm = 1;
2760  }
2761 #endif
2762  ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2763  k = (int)ds;
2764  if (ds < 0. && ds != k)
2765  k--; /* want k = floor(ds) */
2766  k_check = 1;
2767  if (k >= 0 && k <= Ten_pmax) {
2768  if (dval(d) < tens[k])
2769  k--;
2770  k_check = 0;
2771  }
2772  j = bbits - i - 1;
2773  if (j >= 0) {
2774  b2 = 0;
2775  s2 = j;
2776  }
2777  else {
2778  b2 = -j;
2779  s2 = 0;
2780  }
2781  if (k >= 0) {
2782  b5 = 0;
2783  s5 = k;
2784  s2 += k;
2785  }
2786  else {
2787  b2 -= k;
2788  b5 = -k;
2789  s5 = 0;
2790  }
2791  if (mode < 0 || mode > 9)
2792  mode = 0;
2793 
2794 #ifndef SET_INEXACT
2795 #ifdef Check_FLT_ROUNDS
2796  try_quick = Rounding == 1;
2797 #else
2798  try_quick = 1;
2799 #endif
2800 #endif /*SET_INEXACT*/
2801 
2802  if (mode > 5) {
2803  mode -= 4;
2804  try_quick = 0;
2805  }
2806  leftright = 1;
2807  ilim = ilim1 = -1;
2808  switch (mode) {
2809  case 0:
2810  case 1:
2811  i = 18;
2812  ndigits = 0;
2813  break;
2814  case 2:
2815  leftright = 0;
2816  /* no break */
2817  case 4:
2818  if (ndigits <= 0)
2819  ndigits = 1;
2820  ilim = ilim1 = i = ndigits;
2821  break;
2822  case 3:
2823  leftright = 0;
2824  /* no break */
2825  case 5:
2826  i = ndigits + k + 1;
2827  ilim = i;
2828  ilim1 = i - 1;
2829  if (i <= 0)
2830  i = 1;
2831  }
2832  s = s0 = rv_alloc(i+1);
2833 
2834 #ifdef Honor_FLT_ROUNDS
2835  if (mode > 1 && rounding != 1)
2836  leftright = 0;
2837 #endif
2838 
2839  if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2840 
2841  /* Try to get by with floating-point arithmetic. */
2842 
2843  i = 0;
2844  dval(d2) = dval(d);
2845  k0 = k;
2846  ilim0 = ilim;
2847  ieps = 2; /* conservative */
2848  if (k > 0) {
2849  ds = tens[k&0xf];
2850  j = k >> 4;
2851  if (j & Bletch) {
2852  /* prevent overflows */
2853  j &= Bletch - 1;
2854  dval(d) /= bigtens[n_bigtens-1];
2855  ieps++;
2856  }
2857  for (; j; j >>= 1, i++)
2858  if (j & 1) {
2859  ieps++;
2860  ds *= bigtens[i];
2861  }
2862  dval(d) /= ds;
2863  }
2864  else if ((j1 = -k) != 0) {
2865  dval(d) *= tens[j1 & 0xf];
2866  for (j = j1 >> 4; j; j >>= 1, i++)
2867  if (j & 1) {
2868  ieps++;
2869  dval(d) *= bigtens[i];
2870  }
2871  }
2872  if (k_check && dval(d) < 1. && ilim > 0) {
2873  if (ilim1 <= 0)
2874  goto fast_failed;
2875  ilim = ilim1;
2876  k--;
2877  dval(d) *= 10.;
2878  ieps++;
2879  }
2880  dval(eps) = ieps*dval(d) + 7.;
2881  word0(eps) -= (P-1)*Exp_msk1;
2882  if (ilim == 0) {
2883  S = mhi = 0;
2884  dval(d) -= 5.;
2885  if (dval(d) > dval(eps))
2886  goto one_digit;
2887  if (dval(d) < -dval(eps))
2888  goto no_digits;
2889  goto fast_failed;
2890  }
2891 #ifndef No_leftright
2892  if (leftright) {
2893  /* Use Steele & White method of only
2894  * generating digits needed.
2895  */
2896  dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2897  for (i = 0;;) {
2898  L = (int)dval(d);
2899  dval(d) -= L;
2900  *s++ = '0' + (int)L;
2901  if (dval(d) < dval(eps))
2902  goto ret1;
2903  if (1. - dval(d) < dval(eps))
2904  goto bump_up;
2905  if (++i >= ilim)
2906  break;
2907  dval(eps) *= 10.;
2908  dval(d) *= 10.;
2909  }
2910  }
2911  else {
2912 #endif
2913  /* Generate ilim digits, then fix them up. */
2914  dval(eps) *= tens[ilim-1];
2915  for (i = 1;; i++, dval(d) *= 10.) {
2916  L = (Long)(dval(d));
2917  if (!(dval(d) -= L))
2918  ilim = i;
2919  *s++ = '0' + (int)L;
2920  if (i == ilim) {
2921  if (dval(d) > 0.5 + dval(eps))
2922  goto bump_up;
2923  else if (dval(d) < 0.5 - dval(eps)) {
2924  while (*--s == '0') ;
2925  s++;
2926  goto ret1;
2927  }
2928  half = 1;
2929  if ((*(s-1) - '0') & 1) {
2930  goto bump_up;
2931  }
2932  break;
2933  }
2934  }
2935 #ifndef No_leftright
2936  }
2937 #endif
2938 fast_failed:
2939  s = s0;
2940  dval(d) = dval(d2);
2941  k = k0;
2942  ilim = ilim0;
2943  }
2944 
2945  /* Do we have a "small" integer? */
2946 
2947  if (be >= 0 && k <= Int_max) {
2948  /* Yes. */
2949  ds = tens[k];
2950  if (ndigits < 0 && ilim <= 0) {
2951  S = mhi = 0;
2952  if (ilim < 0 || dval(d) <= 5*ds)
2953  goto no_digits;
2954  goto one_digit;
2955  }
2956  for (i = 1;; i++, dval(d) *= 10.) {
2957  L = (Long)(dval(d) / ds);
2958  dval(d) -= L*ds;
2959 #ifdef Check_FLT_ROUNDS
2960  /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2961  if (dval(d) < 0) {
2962  L--;
2963  dval(d) += ds;
2964  }
2965 #endif
2966  *s++ = '0' + (int)L;
2967  if (!dval(d)) {
2968 #ifdef SET_INEXACT
2969  inexact = 0;
2970 #endif
2971  break;
2972  }
2973  if (i == ilim) {
2974 #ifdef Honor_FLT_ROUNDS
2975  if (mode > 1)
2976  switch (rounding) {
2977  case 0: goto ret1;
2978  case 2: goto bump_up;
2979  }
2980 #endif
2981  dval(d) += dval(d);
2982  if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
2983 bump_up:
2984  while (*--s == '9')
2985  if (s == s0) {
2986  k++;
2987  *s = '0';
2988  break;
2989  }
2990  ++*s++;
2991  }
2992  break;
2993  }
2994  }
2995  goto ret1;
2996  }
2997 
2998  m2 = b2;
2999  m5 = b5;
3000  if (leftright) {
3001  i =
3002 #ifndef Sudden_Underflow
3003  denorm ? be + (Bias + (P-1) - 1 + 1) :
3004 #endif
3005 #ifdef IBM
3006  1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3007 #else
3008  1 + P - bbits;
3009 #endif
3010  b2 += i;
3011  s2 += i;
3012  mhi = i2b(1);
3013  }
3014  if (m2 > 0 && s2 > 0) {
3015  i = m2 < s2 ? m2 : s2;
3016  b2 -= i;
3017  m2 -= i;
3018  s2 -= i;
3019  }
3020  if (b5 > 0) {
3021  if (leftright) {
3022  if (m5 > 0) {
3023  mhi = pow5mult(mhi, m5);
3024  b1 = mult(mhi, b);
3025  Bfree(b);
3026  b = b1;
3027  }
3028  if ((j = b5 - m5) != 0)
3029  b = pow5mult(b, j);
3030  }
3031  else
3032  b = pow5mult(b, b5);
3033  }
3034  S = i2b(1);
3035  if (s5 > 0)
3036  S = pow5mult(S, s5);
3037 
3038  /* Check for special case that d is a normalized power of 2. */
3039 
3040  spec_case = 0;
3041  if ((mode < 2 || leftright)
3042 #ifdef Honor_FLT_ROUNDS
3043  && rounding == 1
3044 #endif
3045  ) {
3046  if (!word1(d) && !(word0(d) & Bndry_mask)
3047 #ifndef Sudden_Underflow
3048  && word0(d) & (Exp_mask & ~Exp_msk1)
3049 #endif
3050  ) {
3051  /* The special case */
3052  b2 += Log2P;
3053  s2 += Log2P;
3054  spec_case = 1;
3055  }
3056  }
3057 
3058  /* Arrange for convenient computation of quotients:
3059  * shift left if necessary so divisor has 4 leading 0 bits.
3060  *
3061  * Perhaps we should just compute leading 28 bits of S once
3062  * and for all and pass them and a shift to quorem, so it
3063  * can do shifts and ors to compute the numerator for q.
3064  */
3065 #ifdef Pack_32
3066  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3067  i = 32 - i;
3068 #else
3069  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3070  i = 16 - i;
3071 #endif
3072  if (i > 4) {
3073  i -= 4;
3074  b2 += i;
3075  m2 += i;
3076  s2 += i;
3077  }
3078  else if (i < 4) {
3079  i += 28;
3080  b2 += i;
3081  m2 += i;
3082  s2 += i;
3083  }
3084  if (b2 > 0)
3085  b = lshift(b, b2);
3086  if (s2 > 0)
3087  S = lshift(S, s2);
3088  if (k_check) {
3089  if (cmp(b,S) < 0) {
3090  k--;
3091  b = multadd(b, 10, 0); /* we botched the k estimate */
3092  if (leftright)
3093  mhi = multadd(mhi, 10, 0);
3094  ilim = ilim1;
3095  }
3096  }
3097  if (ilim <= 0 && (mode == 3 || mode == 5)) {
3098  if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3099  /* no digits, fcvt style */
3100 no_digits:
3101  k = -1 - ndigits;
3102  goto ret;
3103  }
3104 one_digit:
3105  *s++ = '1';
3106  k++;
3107  goto ret;
3108  }
3109  if (leftright) {
3110  if (m2 > 0)
3111  mhi = lshift(mhi, m2);
3112 
3113  /* Compute mlo -- check for special case
3114  * that d is a normalized power of 2.
3115  */
3116 
3117  mlo = mhi;
3118  if (spec_case) {
3119  mhi = Balloc(mhi->k);
3120  Bcopy(mhi, mlo);
3121  mhi = lshift(mhi, Log2P);
3122  }
3123 
3124  for (i = 1;;i++) {
3125  dig = quorem(b,S) + '0';
3126  /* Do we yet have the shortest decimal string
3127  * that will round to d?
3128  */
3129  j = cmp(b, mlo);
3130  delta = diff(S, mhi);
3131  j1 = delta->sign ? 1 : cmp(b, delta);
3132  Bfree(delta);
3133 #ifndef ROUND_BIASED
3134  if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3135 #ifdef Honor_FLT_ROUNDS
3136  && rounding >= 1
3137 #endif
3138  ) {
3139  if (dig == '9')
3140  goto round_9_up;
3141  if (j > 0)
3142  dig++;
3143 #ifdef SET_INEXACT
3144  else if (!b->x[0] && b->wds <= 1)
3145  inexact = 0;
3146 #endif
3147  *s++ = dig;
3148  goto ret;
3149  }
3150 #endif
3151  if (j < 0 || (j == 0 && mode != 1
3152 #ifndef ROUND_BIASED
3153  && !(word1(d) & 1)
3154 #endif
3155  )) {
3156  if (!b->x[0] && b->wds <= 1) {
3157 #ifdef SET_INEXACT
3158  inexact = 0;
3159 #endif
3160  goto accept_dig;
3161  }
3162 #ifdef Honor_FLT_ROUNDS
3163  if (mode > 1)
3164  switch (rounding) {
3165  case 0: goto accept_dig;
3166  case 2: goto keep_dig;
3167  }
3168 #endif /*Honor_FLT_ROUNDS*/
3169  if (j1 > 0) {
3170  b = lshift(b, 1);
3171  j1 = cmp(b, S);
3172  if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3173  goto round_9_up;
3174  }
3175 accept_dig:
3176  *s++ = dig;
3177  goto ret;
3178  }
3179  if (j1 > 0) {
3180 #ifdef Honor_FLT_ROUNDS
3181  if (!rounding)
3182  goto accept_dig;
3183 #endif
3184  if (dig == '9') { /* possible if i == 1 */
3185 round_9_up:
3186  *s++ = '9';
3187  goto roundoff;
3188  }
3189  *s++ = dig + 1;
3190  goto ret;
3191  }
3192 #ifdef Honor_FLT_ROUNDS
3193 keep_dig:
3194 #endif
3195  *s++ = dig;
3196  if (i == ilim)
3197  break;
3198  b = multadd(b, 10, 0);
3199  if (mlo == mhi)
3200  mlo = mhi = multadd(mhi, 10, 0);
3201  else {
3202  mlo = multadd(mlo, 10, 0);
3203  mhi = multadd(mhi, 10, 0);
3204  }
3205  }
3206  }
3207  else
3208  for (i = 1;; i++) {
3209  *s++ = dig = quorem(b,S) + '0';
3210  if (!b->x[0] && b->wds <= 1) {
3211 #ifdef SET_INEXACT
3212  inexact = 0;
3213 #endif
3214  goto ret;
3215  }
3216  if (i >= ilim)
3217  break;
3218  b = multadd(b, 10, 0);
3219  }
3220 
3221  /* Round off last digit */
3222 
3223 #ifdef Honor_FLT_ROUNDS
3224  switch (rounding) {
3225  case 0: goto trimzeros;
3226  case 2: goto roundoff;
3227  }
3228 #endif
3229  b = lshift(b, 1);
3230  j = cmp(b, S);
3231  if (j > 0 || (j == 0 && (dig & 1))) {
3232  roundoff:
3233  while (*--s == '9')
3234  if (s == s0) {
3235  k++;
3236  *s++ = '1';
3237  goto ret;
3238  }
3239  if (!half || (*s - '0') & 1)
3240  ++*s;
3241  }
3242  else {
3243  while (*--s == '0') ;
3244  }
3245  s++;
3246 ret:
3247  Bfree(S);
3248  if (mhi) {
3249  if (mlo && mlo != mhi)
3250  Bfree(mlo);
3251  Bfree(mhi);
3252  }
3253 ret1:
3254 #ifdef SET_INEXACT
3255  if (inexact) {
3256  if (!oldinexact) {
3257  word0(d) = Exp_1 + (70 << Exp_shift);
3258  word1(d) = 0;
3259  dval(d) += 1.;
3260  }
3261  }
3262  else if (!oldinexact)
3263  clear_inexact();
3264 #endif
3265  Bfree(b);
3266  *s = 0;
3267  *decpt = k + 1;
3268  if (rve)
3269  *rve = s;
3270  return s0;
3271 }
3272 
3273 /*-
3274  * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
3275  * All rights reserved.
3276  *
3277  * Redistribution and use in source and binary forms, with or without
3278  * modification, are permitted provided that the following conditions
3279  * are met:
3280  * 1. Redistributions of source code must retain the above copyright
3281  * notice, this list of conditions and the following disclaimer.
3282  * 2. Redistributions in binary form must reproduce the above copyright
3283  * notice, this list of conditions and the following disclaimer in the
3284  * documentation and/or other materials provided with the distribution.
3285  *
3286  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
3287  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
3288  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
3289  * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
3290  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
3291  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
3292  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
3293  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
3294  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
3295  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
3296  * SUCH DAMAGE.
3297  */
3298 
3299 #define DBL_MANH_SIZE 20
3300 #define DBL_MANL_SIZE 32
3301 #define DBL_ADJ (DBL_MAX_EXP - 2)
3302 #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3303 #define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3304 #define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3305 #define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3306 #define dmanl_get(u) ((uint32_t)word1(u))
3307 
3308 
3309 /*
3310  * This procedure converts a double-precision number in IEEE format
3311  * into a string of hexadecimal digits and an exponent of 2. Its
3312  * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
3313  * following exceptions:
3314  *
3315  * - An ndigits < 0 causes it to use as many digits as necessary to
3316  * represent the number exactly.
3317  * - The additional xdigs argument should point to either the string
3318  * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
3319  * which case is desired.
3320  * - This routine does not repeat dtoa's mistake of setting decpt
3321  * to 9999 in the case of an infinity or NaN. INT_MAX is used
3322  * for this purpose instead.
3323  *
3324  * Note that the C99 standard does not specify what the leading digit
3325  * should be for non-zero numbers. For instance, 0x1.3p3 is the same
3326  * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
3327  * the leading digit a 1. This ensures that the exponent printed is the
3328  * actual base-2 exponent, i.e., ilogb(d).
3329  *
3330  * Inputs: d, xdigs, ndigits
3331  * Outputs: decpt, sign, rve
3332  */
3333 char *
3334 hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve)
3335 {
3336  U u;
3337  char *s, *s0;
3338  int bufsize;
3339  uint32_t manh, manl;
3340 
3341  u.d = d;
3342  if (word0(u) & Sign_bit) {
3343  /* set sign for everything, including 0's and NaNs */
3344  *sign = 1;
3345  word0(u) &= ~Sign_bit; /* clear sign bit */
3346  }
3347  else
3348  *sign = 0;
3349 
3350  if (isinf(d)) { /* FP_INFINITE */
3351  *decpt = INT_MAX;
3352  return rv_strdup(INFSTR, rve);
3353  }
3354  else if (isnan(d)) { /* FP_NAN */
3355  *decpt = INT_MAX;
3356  return rv_strdup(NANSTR, rve);
3357  }
3358  else if (d == 0.0) { /* FP_ZERO */
3359  *decpt = 1;
3360  return rv_strdup(ZEROSTR, rve);
3361  }
3362  else if (dexp_get(u)) { /* FP_NORMAL */
3363  *decpt = dexp_get(u) - DBL_ADJ;
3364  }
3365  else { /* FP_SUBNORMAL */
3366  u.d *= 5.363123171977039e+154 /* 0x1p514 */;
3367  *decpt = dexp_get(u) - (514 + DBL_ADJ);
3368  }
3369 
3370  if (ndigits == 0) /* dtoa() compatibility */
3371  ndigits = 1;
3372 
3373  /*
3374  * If ndigits < 0, we are expected to auto-size, so we allocate
3375  * enough space for all the digits.
3376  */
3377  bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3378  s0 = rv_alloc(bufsize+1);
3379 
3380  /* Round to the desired number of digits. */
3381  if (SIGFIGS > ndigits && ndigits > 0) {
3382  float redux = 1.0f;
3383  int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3384  dexp_set(u, offset);
3385  u.d += redux;
3386  u.d -= redux;
3387  *decpt += dexp_get(u) - offset;
3388  }
3389 
3390  manh = dmanh_get(u);
3391  manl = dmanl_get(u);
3392  *s0 = '1';
3393  for (s = s0 + 1; s < s0 + bufsize; s++) {
3394  *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3395  manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3396  manl <<= 4;
3397  }
3398 
3399  /* If ndigits < 0, we are expected to auto-size the precision. */
3400  if (ndigits < 0) {
3401  for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
3402  ;
3403  }
3404 
3405  s = s0 + ndigits;
3406  *s = '\0';
3407  if (rve != NULL)
3408  *rve = s;
3409  return (s0);
3410 }
3411 
3412 #ifdef __cplusplus
3413 #if 0
3414 { /* satisfy cc-mode */
3415 #endif
3416 }
3417 #endif
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