Ruby  3.1.4p223 (2023-03-30 revision HEAD)
dtoa.c
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 #include <limits.h>
187 
188 #if (INT_MAX >> 30) && !(INT_MAX >> 31)
189 #define Long int
190 #define ULong unsigned int
191 #elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
192 #define Long long int
193 #define ULong unsigned long int
194 #else
195 #error No 32bit integer
196 #endif
197 
198 #if HAVE_LONG_LONG
199 #define Llong LONG_LONG
200 #else
201 #define NO_LONG_LONG
202 #endif
203 
204 #ifdef DEBUG
205 #include <stdio.h>
206 #define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
207 #endif
208 
209 #ifndef ISDIGIT
210 #include <ctype.h>
211 #define ISDIGIT(c) isdigit(c)
212 #endif
213 #include <errno.h>
214 #include <stdlib.h>
215 #include <string.h>
216 
217 #ifdef USE_LOCALE
218 #include <locale.h>
219 #endif
220 
221 #ifdef MALLOC
222 extern void *MALLOC(size_t);
223 #else
224 #define MALLOC xmalloc
225 #endif
226 #ifdef FREE
227 extern void FREE(void*);
228 #else
229 #define FREE xfree
230 #endif
231 #ifndef NO_SANITIZE
232 #define NO_SANITIZE(x, y) y
233 #endif
234 
235 #ifndef Omit_Private_Memory
236 #ifndef PRIVATE_MEM
237 #define PRIVATE_MEM 2304
238 #endif
239 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
240 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
241 #endif
242 
243 #undef IEEE_Arith
244 #undef Avoid_Underflow
245 #ifdef IEEE_BIG_ENDIAN
246 #define IEEE_Arith
247 #endif
248 #ifdef IEEE_LITTLE_ENDIAN
249 #define IEEE_Arith
250 #endif
251 
252 #ifdef Bad_float_h
253 
254 #ifdef IEEE_Arith
255 #define DBL_DIG 15
256 #define DBL_MAX_10_EXP 308
257 #define DBL_MAX_EXP 1024
258 #define FLT_RADIX 2
259 #endif /*IEEE_Arith*/
260 
261 #ifdef IBM
262 #define DBL_DIG 16
263 #define DBL_MAX_10_EXP 75
264 #define DBL_MAX_EXP 63
265 #define FLT_RADIX 16
266 #define DBL_MAX 7.2370055773322621e+75
267 #endif
268 
269 #ifdef VAX
270 #define DBL_DIG 16
271 #define DBL_MAX_10_EXP 38
272 #define DBL_MAX_EXP 127
273 #define FLT_RADIX 2
274 #define DBL_MAX 1.7014118346046923e+38
275 #endif
276 
277 #ifndef LONG_MAX
278 #define LONG_MAX 2147483647
279 #endif
280 
281 #else /* ifndef Bad_float_h */
282 #include <float.h>
283 #endif /* Bad_float_h */
284 
285 #include <math.h>
286 
287 #ifdef __cplusplus
288 extern "C" {
289 #if 0
290 } /* satisfy cc-mode */
291 #endif
292 #endif
293 
294 #ifndef hexdigit
295 static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
296 #endif
297 
298 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
299 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
300 #endif
301 
302 typedef union { double d; ULong L[2]; } U;
303 
304 #ifdef YES_ALIAS
305 typedef double double_u;
306 # define dval(x) (x)
307 # ifdef IEEE_LITTLE_ENDIAN
308 # define word0(x) (((ULong *)&(x))[1])
309 # define word1(x) (((ULong *)&(x))[0])
310 # else
311 # define word0(x) (((ULong *)&(x))[0])
312 # define word1(x) (((ULong *)&(x))[1])
313 # endif
314 #else
315 typedef U double_u;
316 # ifdef IEEE_LITTLE_ENDIAN
317 # define word0(x) ((x).L[1])
318 # define word1(x) ((x).L[0])
319 # else
320 # define word0(x) ((x).L[0])
321 # define word1(x) ((x).L[1])
322 # endif
323 # define dval(x) ((x).d)
324 #endif
325 
326 /* The following definition of Storeinc is appropriate for MIPS processors.
327  * An alternative that might be better on some machines is
328  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
329  */
330 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
331 #define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
332 ((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
333 #else
334 #define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
335 ((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
336 #endif
337 
338 /* #define P DBL_MANT_DIG */
339 /* Ten_pmax = floor(P*log(2)/log(5)) */
340 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
341 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
342 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
343 
344 #ifdef IEEE_Arith
345 #define Exp_shift 20
346 #define Exp_shift1 20
347 #define Exp_msk1 0x100000
348 #define Exp_msk11 0x100000
349 #define Exp_mask 0x7ff00000
350 #define P 53
351 #define Bias 1023
352 #define Emin (-1022)
353 #define Exp_1 0x3ff00000
354 #define Exp_11 0x3ff00000
355 #define Ebits 11
356 #define Frac_mask 0xfffff
357 #define Frac_mask1 0xfffff
358 #define Ten_pmax 22
359 #define Bletch 0x10
360 #define Bndry_mask 0xfffff
361 #define Bndry_mask1 0xfffff
362 #define LSB 1
363 #define Sign_bit 0x80000000
364 #define Log2P 1
365 #define Tiny0 0
366 #define Tiny1 1
367 #define Quick_max 14
368 #define Int_max 14
369 #ifndef NO_IEEE_Scale
370 #define Avoid_Underflow
371 #ifdef Flush_Denorm /* debugging option */
372 #undef Sudden_Underflow
373 #endif
374 #endif
375 
376 #ifndef Flt_Rounds
377 #ifdef FLT_ROUNDS
378 #define Flt_Rounds FLT_ROUNDS
379 #else
380 #define Flt_Rounds 1
381 #endif
382 #endif /*Flt_Rounds*/
383 
384 #ifdef Honor_FLT_ROUNDS
385 #define Rounding rounding
386 #undef Check_FLT_ROUNDS
387 #define Check_FLT_ROUNDS
388 #else
389 #define Rounding Flt_Rounds
390 #endif
391 
392 #else /* ifndef IEEE_Arith */
393 #undef Check_FLT_ROUNDS
394 #undef Honor_FLT_ROUNDS
395 #undef SET_INEXACT
396 #undef Sudden_Underflow
397 #define Sudden_Underflow
398 #ifdef IBM
399 #undef Flt_Rounds
400 #define Flt_Rounds 0
401 #define Exp_shift 24
402 #define Exp_shift1 24
403 #define Exp_msk1 0x1000000
404 #define Exp_msk11 0x1000000
405 #define Exp_mask 0x7f000000
406 #define P 14
407 #define Bias 65
408 #define Exp_1 0x41000000
409 #define Exp_11 0x41000000
410 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
411 #define Frac_mask 0xffffff
412 #define Frac_mask1 0xffffff
413 #define Bletch 4
414 #define Ten_pmax 22
415 #define Bndry_mask 0xefffff
416 #define Bndry_mask1 0xffffff
417 #define LSB 1
418 #define Sign_bit 0x80000000
419 #define Log2P 4
420 #define Tiny0 0x100000
421 #define Tiny1 0
422 #define Quick_max 14
423 #define Int_max 15
424 #else /* VAX */
425 #undef Flt_Rounds
426 #define Flt_Rounds 1
427 #define Exp_shift 23
428 #define Exp_shift1 7
429 #define Exp_msk1 0x80
430 #define Exp_msk11 0x800000
431 #define Exp_mask 0x7f80
432 #define P 56
433 #define Bias 129
434 #define Exp_1 0x40800000
435 #define Exp_11 0x4080
436 #define Ebits 8
437 #define Frac_mask 0x7fffff
438 #define Frac_mask1 0xffff007f
439 #define Ten_pmax 24
440 #define Bletch 2
441 #define Bndry_mask 0xffff007f
442 #define Bndry_mask1 0xffff007f
443 #define LSB 0x10000
444 #define Sign_bit 0x8000
445 #define Log2P 1
446 #define Tiny0 0x80
447 #define Tiny1 0
448 #define Quick_max 15
449 #define Int_max 15
450 #endif /* IBM, VAX */
451 #endif /* IEEE_Arith */
452 
453 #ifndef IEEE_Arith
454 #define ROUND_BIASED
455 #endif
456 
457 #ifdef RND_PRODQUOT
458 #define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
459 #define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
460 extern double rnd_prod(double, double), rnd_quot(double, double);
461 #else
462 #define rounded_product(a,b) ((a) *= (b))
463 #define rounded_quotient(a,b) ((a) /= (b))
464 #endif
465 
466 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
467 #define Big1 0xffffffff
468 
469 #ifndef Pack_32
470 #define Pack_32
471 #endif
472 
473 #define FFFFFFFF 0xffffffffUL
474 
475 #ifdef NO_LONG_LONG
476 #undef ULLong
477 #ifdef Just_16
478 #undef Pack_32
479 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
480  * This makes some inner loops simpler and sometimes saves work
481  * during multiplications, but it often seems to make things slightly
482  * slower. Hence the default is now to store 32 bits per Long.
483  */
484 #endif
485 #else /* long long available */
486 #ifndef Llong
487 #define Llong long long
488 #endif
489 #ifndef ULLong
490 #define ULLong unsigned Llong
491 #endif
492 #endif /* NO_LONG_LONG */
493 
494 #define MULTIPLE_THREADS 1
495 
496 #ifndef MULTIPLE_THREADS
497 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
498 #define FREE_DTOA_LOCK(n) /*nothing*/
499 #else
500 #define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
501 #define FREE_DTOA_LOCK(n) /*unused right now*/
502 #endif
503 
504 #ifndef ATOMIC_PTR_CAS
505 #define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (old))
506 #endif
507 #ifndef LIKELY
508 #define LIKELY(x) (x)
509 #endif
510 #ifndef UNLIKELY
511 #define UNLIKELY(x) (x)
512 #endif
513 #ifndef ASSUME
514 #define ASSUME(x) (void)(x)
515 #endif
516 
517 #define Kmax 15
518 
519 struct Bigint {
520  struct Bigint *next;
521  int k, maxwds, sign, wds;
522  ULong x[1];
523 };
524 
525 typedef struct Bigint Bigint;
526 
527 static Bigint *freelist[Kmax+1];
528 
529 #define BLOCKING_BIGINT ((Bigint *)(-1))
530 
531 static Bigint *
532 Balloc(int k)
533 {
534  int x;
535  Bigint *rv;
536 #ifndef Omit_Private_Memory
537  size_t len;
538 #endif
539 
540  rv = 0;
541  ACQUIRE_DTOA_LOCK(0);
542  if (k <= Kmax) {
543  rv = freelist[k];
544  while (rv) {
545  Bigint *rvn = rv;
546  rv = ATOMIC_PTR_CAS(freelist[k], rv, BLOCKING_BIGINT);
547  if (LIKELY(rv != BLOCKING_BIGINT && rvn == rv)) {
548  rvn = ATOMIC_PTR_CAS(freelist[k], BLOCKING_BIGINT, rv->next);
549  assert(rvn == BLOCKING_BIGINT);
550  ASSUME(rv);
551  break;
552  }
553  }
554  }
555  if (!rv) {
556  x = 1 << k;
557 #ifdef Omit_Private_Memory
558  rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
559 #else
560  len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
561  /sizeof(double);
562  if (k <= Kmax) {
563  double *pnext = pmem_next;
564  while (pnext - private_mem + len <= PRIVATE_mem) {
565  double *p = pnext;
566  pnext = ATOMIC_PTR_CAS(pmem_next, pnext, pnext + len);
567  if (LIKELY(p == pnext)) {
568  rv = (Bigint*)pnext;
569  ASSUME(rv);
570  break;
571  }
572  }
573  }
574  if (!rv)
575  rv = (Bigint*)MALLOC(len*sizeof(double));
576 #endif
577  rv->k = k;
578  rv->maxwds = x;
579  }
580  FREE_DTOA_LOCK(0);
581  rv->sign = rv->wds = 0;
582  return rv;
583 }
584 
585 static void
586 Bfree(Bigint *v)
587 {
588  Bigint *vn;
589  if (v) {
590  if (v->k > Kmax) {
591  FREE(v);
592  return;
593  }
594  ACQUIRE_DTOA_LOCK(0);
595  do {
596  do {
597  vn = ATOMIC_PTR_CAS(freelist[v->k], 0, 0);
598  } while (UNLIKELY(vn == BLOCKING_BIGINT));
599  v->next = vn;
600  } while (UNLIKELY(ATOMIC_PTR_CAS(freelist[v->k], vn, v) != vn));
601  FREE_DTOA_LOCK(0);
602  }
603 }
604 
605 #define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
606 (y)->wds*sizeof(Long) + 2*sizeof(int))
607 
608 static Bigint *
609 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
610 {
611  int i, wds;
612  ULong *x;
613 #ifdef ULLong
614  ULLong carry, y;
615 #else
616  ULong carry, y;
617 #ifdef Pack_32
618  ULong xi, z;
619 #endif
620 #endif
621  Bigint *b1;
622 
623  wds = b->wds;
624  x = b->x;
625  i = 0;
626  carry = a;
627  do {
628 #ifdef ULLong
629  y = *x * (ULLong)m + carry;
630  carry = y >> 32;
631  *x++ = (ULong)(y & FFFFFFFF);
632 #else
633 #ifdef Pack_32
634  xi = *x;
635  y = (xi & 0xffff) * m + carry;
636  z = (xi >> 16) * m + (y >> 16);
637  carry = z >> 16;
638  *x++ = (z << 16) + (y & 0xffff);
639 #else
640  y = *x * m + carry;
641  carry = y >> 16;
642  *x++ = y & 0xffff;
643 #endif
644 #endif
645  } while (++i < wds);
646  if (carry) {
647  if (wds >= b->maxwds) {
648  b1 = Balloc(b->k+1);
649  Bcopy(b1, b);
650  Bfree(b);
651  b = b1;
652  }
653  b->x[wds++] = (ULong)carry;
654  b->wds = wds;
655  }
656  return b;
657 }
658 
659 static Bigint *
660 s2b(const char *s, int nd0, int nd, ULong y9)
661 {
662  Bigint *b;
663  int i, k;
664  Long x, y;
665 
666  x = (nd + 8) / 9;
667  for (k = 0, y = 1; x > y; y <<= 1, k++) ;
668 #ifdef Pack_32
669  b = Balloc(k);
670  b->x[0] = y9;
671  b->wds = 1;
672 #else
673  b = Balloc(k+1);
674  b->x[0] = y9 & 0xffff;
675  b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
676 #endif
677 
678  i = 9;
679  if (9 < nd0) {
680  s += 9;
681  do {
682  b = multadd(b, 10, *s++ - '0');
683  } while (++i < nd0);
684  s++;
685  }
686  else
687  s += 10;
688  for (; i < nd; i++)
689  b = multadd(b, 10, *s++ - '0');
690  return b;
691 }
692 
693 static int
694 hi0bits(register ULong x)
695 {
696  register int k = 0;
697 
698  if (!(x & 0xffff0000)) {
699  k = 16;
700  x <<= 16;
701  }
702  if (!(x & 0xff000000)) {
703  k += 8;
704  x <<= 8;
705  }
706  if (!(x & 0xf0000000)) {
707  k += 4;
708  x <<= 4;
709  }
710  if (!(x & 0xc0000000)) {
711  k += 2;
712  x <<= 2;
713  }
714  if (!(x & 0x80000000)) {
715  k++;
716  if (!(x & 0x40000000))
717  return 32;
718  }
719  return k;
720 }
721 
722 static int
723 lo0bits(ULong *y)
724 {
725  register int k;
726  register ULong x = *y;
727 
728  if (x & 7) {
729  if (x & 1)
730  return 0;
731  if (x & 2) {
732  *y = x >> 1;
733  return 1;
734  }
735  *y = x >> 2;
736  return 2;
737  }
738  k = 0;
739  if (!(x & 0xffff)) {
740  k = 16;
741  x >>= 16;
742  }
743  if (!(x & 0xff)) {
744  k += 8;
745  x >>= 8;
746  }
747  if (!(x & 0xf)) {
748  k += 4;
749  x >>= 4;
750  }
751  if (!(x & 0x3)) {
752  k += 2;
753  x >>= 2;
754  }
755  if (!(x & 1)) {
756  k++;
757  x >>= 1;
758  if (!x)
759  return 32;
760  }
761  *y = x;
762  return k;
763 }
764 
765 static Bigint *
766 i2b(int i)
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(Bigint *a, Bigint *b)
778 {
779  Bigint *c;
780  int k, wa, wb, wc;
781  ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
782  ULong y;
783 #ifdef ULLong
784  ULLong carry, z;
785 #else
786  ULong carry, z;
787 #ifdef Pack_32
788  ULong z2;
789 #endif
790 #endif
791 
792  if (a->wds < b->wds) {
793  c = a;
794  a = b;
795  b = c;
796  }
797  k = a->k;
798  wa = a->wds;
799  wb = b->wds;
800  wc = wa + wb;
801  if (wc > a->maxwds)
802  k++;
803  c = Balloc(k);
804  for (x = c->x, xa = x + wc; x < xa; x++)
805  *x = 0;
806  xa = a->x;
807  xae = xa + wa;
808  xb = b->x;
809  xbe = xb + wb;
810  xc0 = c->x;
811 #ifdef ULLong
812  for (; xb < xbe; xc0++) {
813  if ((y = *xb++) != 0) {
814  x = xa;
815  xc = xc0;
816  carry = 0;
817  do {
818  z = *x++ * (ULLong)y + *xc + carry;
819  carry = z >> 32;
820  *xc++ = (ULong)(z & FFFFFFFF);
821  } while (x < xae);
822  *xc = (ULong)carry;
823  }
824  }
825 #else
826 #ifdef Pack_32
827  for (; xb < xbe; xb++, xc0++) {
828  if ((y = *xb & 0xffff) != 0) {
829  x = xa;
830  xc = xc0;
831  carry = 0;
832  do {
833  z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
834  carry = z >> 16;
835  z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
836  carry = z2 >> 16;
837  Storeinc(xc, z2, z);
838  } while (x < xae);
839  *xc = (ULong)carry;
840  }
841  if ((y = *xb >> 16) != 0) {
842  x = xa;
843  xc = xc0;
844  carry = 0;
845  z2 = *xc;
846  do {
847  z = (*x & 0xffff) * y + (*xc >> 16) + carry;
848  carry = z >> 16;
849  Storeinc(xc, z, z2);
850  z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
851  carry = z2 >> 16;
852  } while (x < xae);
853  *xc = z2;
854  }
855  }
856 #else
857  for (; xb < xbe; xc0++) {
858  if (y = *xb++) {
859  x = xa;
860  xc = xc0;
861  carry = 0;
862  do {
863  z = *x++ * y + *xc + carry;
864  carry = z >> 16;
865  *xc++ = z & 0xffff;
866  } while (x < xae);
867  *xc = (ULong)carry;
868  }
869  }
870 #endif
871 #endif
872  for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
873  c->wds = wc;
874  return c;
875 }
876 
877 static Bigint *p5s;
878 
879 static Bigint *
880 pow5mult(Bigint *b, int k)
881 {
882  Bigint *b1, *p5, *p51;
883  Bigint *p5tmp;
884  int i;
885  static const int p05[3] = { 5, 25, 125 };
886 
887  if ((i = k & 3) != 0)
888  b = multadd(b, p05[i-1], 0);
889 
890  if (!(k >>= 2))
891  return b;
892  if (!(p5 = p5s)) {
893  /* first time */
894  ACQUIRE_DTOA_LOCK(1);
895  if (!(p5 = p5s)) {
896  p5 = i2b(625);
897  p5->next = 0;
898  p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
899  if (UNLIKELY(p5tmp)) {
900  Bfree(p5);
901  p5 = p5tmp;
902  }
903  }
904  FREE_DTOA_LOCK(1);
905  }
906  for (;;) {
907  if (k & 1) {
908  b1 = mult(b, p5);
909  Bfree(b);
910  b = b1;
911  }
912  if (!(k >>= 1))
913  break;
914  if (!(p51 = p5->next)) {
915  ACQUIRE_DTOA_LOCK(1);
916  if (!(p51 = p5->next)) {
917  p51 = mult(p5,p5);
918  p51->next = 0;
919  p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
920  if (UNLIKELY(p5tmp)) {
921  Bfree(p51);
922  p51 = p5tmp;
923  }
924  }
925  FREE_DTOA_LOCK(1);
926  }
927  p5 = p51;
928  }
929  return b;
930 }
931 
932 static Bigint *
933 lshift(Bigint *b, int k)
934 {
935  int i, k1, n, n1;
936  Bigint *b1;
937  ULong *x, *x1, *xe, z;
938 
939 #ifdef Pack_32
940  n = k >> 5;
941 #else
942  n = k >> 4;
943 #endif
944  k1 = b->k;
945  n1 = n + b->wds + 1;
946  for (i = b->maxwds; n1 > i; i <<= 1)
947  k1++;
948  b1 = Balloc(k1);
949  x1 = b1->x;
950  for (i = 0; i < n; i++)
951  *x1++ = 0;
952  x = b->x;
953  xe = x + b->wds;
954 #ifdef Pack_32
955  if (k &= 0x1f) {
956  k1 = 32 - k;
957  z = 0;
958  do {
959  *x1++ = *x << k | z;
960  z = *x++ >> k1;
961  } while (x < xe);
962  if ((*x1 = z) != 0)
963  ++n1;
964  }
965 #else
966  if (k &= 0xf) {
967  k1 = 16 - k;
968  z = 0;
969  do {
970  *x1++ = *x << k & 0xffff | z;
971  z = *x++ >> k1;
972  } while (x < xe);
973  if (*x1 = z)
974  ++n1;
975  }
976 #endif
977  else
978  do {
979  *x1++ = *x++;
980  } while (x < xe);
981  b1->wds = n1 - 1;
982  Bfree(b);
983  return b1;
984 }
985 
986 static int
987 cmp(Bigint *a, Bigint *b)
988 {
989  ULong *xa, *xa0, *xb, *xb0;
990  int i, j;
991 
992  i = a->wds;
993  j = b->wds;
994 #ifdef DEBUG
995  if (i > 1 && !a->x[i-1])
996  Bug("cmp called with a->x[a->wds-1] == 0");
997  if (j > 1 && !b->x[j-1])
998  Bug("cmp called with b->x[b->wds-1] == 0");
999 #endif
1000  if (i -= j)
1001  return i;
1002  xa0 = a->x;
1003  xa = xa0 + j;
1004  xb0 = b->x;
1005  xb = xb0 + j;
1006  for (;;) {
1007  if (*--xa != *--xb)
1008  return *xa < *xb ? -1 : 1;
1009  if (xa <= xa0)
1010  break;
1011  }
1012  return 0;
1013 }
1014 
1015 NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b));
1016 static Bigint *
1017 diff(Bigint *a, Bigint *b)
1018 {
1019  Bigint *c;
1020  int i, wa, wb;
1021  ULong *xa, *xae, *xb, *xbe, *xc;
1022 #ifdef ULLong
1023  ULLong borrow, y;
1024 #else
1025  ULong borrow, y;
1026 #ifdef Pack_32
1027  ULong z;
1028 #endif
1029 #endif
1030 
1031  i = cmp(a,b);
1032  if (!i) {
1033  c = Balloc(0);
1034  c->wds = 1;
1035  c->x[0] = 0;
1036  return c;
1037  }
1038  if (i < 0) {
1039  c = a;
1040  a = b;
1041  b = c;
1042  i = 1;
1043  }
1044  else
1045  i = 0;
1046  c = Balloc(a->k);
1047  c->sign = i;
1048  wa = a->wds;
1049  xa = a->x;
1050  xae = xa + wa;
1051  wb = b->wds;
1052  xb = b->x;
1053  xbe = xb + wb;
1054  xc = c->x;
1055  borrow = 0;
1056 #ifdef ULLong
1057  do {
1058  y = (ULLong)*xa++ - *xb++ - borrow;
1059  borrow = y >> 32 & (ULong)1;
1060  *xc++ = (ULong)(y & FFFFFFFF);
1061  } while (xb < xbe);
1062  while (xa < xae) {
1063  y = *xa++ - borrow;
1064  borrow = y >> 32 & (ULong)1;
1065  *xc++ = (ULong)(y & FFFFFFFF);
1066  }
1067 #else
1068 #ifdef Pack_32
1069  do {
1070  y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1071  borrow = (y & 0x10000) >> 16;
1072  z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1073  borrow = (z & 0x10000) >> 16;
1074  Storeinc(xc, z, y);
1075  } while (xb < xbe);
1076  while (xa < xae) {
1077  y = (*xa & 0xffff) - borrow;
1078  borrow = (y & 0x10000) >> 16;
1079  z = (*xa++ >> 16) - borrow;
1080  borrow = (z & 0x10000) >> 16;
1081  Storeinc(xc, z, y);
1082  }
1083 #else
1084  do {
1085  y = *xa++ - *xb++ - borrow;
1086  borrow = (y & 0x10000) >> 16;
1087  *xc++ = y & 0xffff;
1088  } while (xb < xbe);
1089  while (xa < xae) {
1090  y = *xa++ - borrow;
1091  borrow = (y & 0x10000) >> 16;
1092  *xc++ = y & 0xffff;
1093  }
1094 #endif
1095 #endif
1096  while (!*--xc)
1097  wa--;
1098  c->wds = wa;
1099  return c;
1100 }
1101 
1102 static double
1103 ulp(double x_)
1104 {
1105  register Long L;
1106  double_u x, a;
1107  dval(x) = x_;
1108 
1109  L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1110 #ifndef Avoid_Underflow
1111 #ifndef Sudden_Underflow
1112  if (L > 0) {
1113 #endif
1114 #endif
1115 #ifdef IBM
1116  L |= Exp_msk1 >> 4;
1117 #endif
1118  word0(a) = L;
1119  word1(a) = 0;
1120 #ifndef Avoid_Underflow
1121 #ifndef Sudden_Underflow
1122  }
1123  else {
1124  L = -L >> Exp_shift;
1125  if (L < Exp_shift) {
1126  word0(a) = 0x80000 >> L;
1127  word1(a) = 0;
1128  }
1129  else {
1130  word0(a) = 0;
1131  L -= Exp_shift;
1132  word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1133  }
1134  }
1135 #endif
1136 #endif
1137  return dval(a);
1138 }
1139 
1140 static double
1141 b2d(Bigint *a, int *e)
1142 {
1143  ULong *xa, *xa0, w, y, z;
1144  int k;
1145  double_u d;
1146 #ifdef VAX
1147  ULong d0, d1;
1148 #else
1149 #define d0 word0(d)
1150 #define d1 word1(d)
1151 #endif
1152 
1153  xa0 = a->x;
1154  xa = xa0 + a->wds;
1155  y = *--xa;
1156 #ifdef DEBUG
1157  if (!y) Bug("zero y in b2d");
1158 #endif
1159  k = hi0bits(y);
1160  *e = 32 - k;
1161 #ifdef Pack_32
1162  if (k < Ebits) {
1163  d0 = Exp_1 | y >> (Ebits - k);
1164  w = xa > xa0 ? *--xa : 0;
1165  d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1166  goto ret_d;
1167  }
1168  z = xa > xa0 ? *--xa : 0;
1169  if (k -= Ebits) {
1170  d0 = Exp_1 | y << k | z >> (32 - k);
1171  y = xa > xa0 ? *--xa : 0;
1172  d1 = z << k | y >> (32 - k);
1173  }
1174  else {
1175  d0 = Exp_1 | y;
1176  d1 = z;
1177  }
1178 #else
1179  if (k < Ebits + 16) {
1180  z = xa > xa0 ? *--xa : 0;
1181  d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1182  w = xa > xa0 ? *--xa : 0;
1183  y = xa > xa0 ? *--xa : 0;
1184  d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1185  goto ret_d;
1186  }
1187  z = xa > xa0 ? *--xa : 0;
1188  w = xa > xa0 ? *--xa : 0;
1189  k -= Ebits + 16;
1190  d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1191  y = xa > xa0 ? *--xa : 0;
1192  d1 = w << k + 16 | y << k;
1193 #endif
1194 ret_d:
1195 #ifdef VAX
1196  word0(d) = d0 >> 16 | d0 << 16;
1197  word1(d) = d1 >> 16 | d1 << 16;
1198 #else
1199 #undef d0
1200 #undef d1
1201 #endif
1202  return dval(d);
1203 }
1204 
1205 static Bigint *
1206 d2b(double d_, int *e, int *bits)
1207 {
1208  double_u d;
1209  Bigint *b;
1210  int de, k;
1211  ULong *x, y, z;
1212 #ifndef Sudden_Underflow
1213  int i;
1214 #endif
1215 #ifdef VAX
1216  ULong d0, d1;
1217 #endif
1218  dval(d) = d_;
1219 #ifdef VAX
1220  d0 = word0(d) >> 16 | word0(d) << 16;
1221  d1 = word1(d) >> 16 | word1(d) << 16;
1222 #else
1223 #define d0 word0(d)
1224 #define d1 word1(d)
1225 #endif
1226 
1227 #ifdef Pack_32
1228  b = Balloc(1);
1229 #else
1230  b = Balloc(2);
1231 #endif
1232  x = b->x;
1233 
1234  z = d0 & Frac_mask;
1235  d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1236 #ifdef Sudden_Underflow
1237  de = (int)(d0 >> Exp_shift);
1238 #ifndef IBM
1239  z |= Exp_msk11;
1240 #endif
1241 #else
1242  if ((de = (int)(d0 >> Exp_shift)) != 0)
1243  z |= Exp_msk1;
1244 #endif
1245 #ifdef Pack_32
1246  if ((y = d1) != 0) {
1247  if ((k = lo0bits(&y)) != 0) {
1248  x[0] = y | z << (32 - k);
1249  z >>= k;
1250  }
1251  else
1252  x[0] = y;
1253 #ifndef Sudden_Underflow
1254  i =
1255 #endif
1256  b->wds = (x[1] = z) ? 2 : 1;
1257  }
1258  else {
1259 #ifdef DEBUG
1260  if (!z)
1261  Bug("Zero passed to d2b");
1262 #endif
1263  k = lo0bits(&z);
1264  x[0] = z;
1265 #ifndef Sudden_Underflow
1266  i =
1267 #endif
1268  b->wds = 1;
1269  k += 32;
1270  }
1271 #else
1272  if (y = d1) {
1273  if (k = lo0bits(&y))
1274  if (k >= 16) {
1275  x[0] = y | z << 32 - k & 0xffff;
1276  x[1] = z >> k - 16 & 0xffff;
1277  x[2] = z >> k;
1278  i = 2;
1279  }
1280  else {
1281  x[0] = y & 0xffff;
1282  x[1] = y >> 16 | z << 16 - k & 0xffff;
1283  x[2] = z >> k & 0xffff;
1284  x[3] = z >> k+16;
1285  i = 3;
1286  }
1287  else {
1288  x[0] = y & 0xffff;
1289  x[1] = y >> 16;
1290  x[2] = z & 0xffff;
1291  x[3] = z >> 16;
1292  i = 3;
1293  }
1294  }
1295  else {
1296 #ifdef DEBUG
1297  if (!z)
1298  Bug("Zero passed to d2b");
1299 #endif
1300  k = lo0bits(&z);
1301  if (k >= 16) {
1302  x[0] = z;
1303  i = 0;
1304  }
1305  else {
1306  x[0] = z & 0xffff;
1307  x[1] = z >> 16;
1308  i = 1;
1309  }
1310  k += 32;
1311  }
1312  while (!x[i])
1313  --i;
1314  b->wds = i + 1;
1315 #endif
1316 #ifndef Sudden_Underflow
1317  if (de) {
1318 #endif
1319 #ifdef IBM
1320  *e = (de - Bias - (P-1) << 2) + k;
1321  *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1322 #else
1323  *e = de - Bias - (P-1) + k;
1324  *bits = P - k;
1325 #endif
1326 #ifndef Sudden_Underflow
1327  }
1328  else {
1329  *e = de - Bias - (P-1) + 1 + k;
1330 #ifdef Pack_32
1331  *bits = 32*i - hi0bits(x[i-1]);
1332 #else
1333  *bits = (i+2)*16 - hi0bits(x[i]);
1334 #endif
1335  }
1336 #endif
1337  return b;
1338 }
1339 #undef d0
1340 #undef d1
1341 
1342 static double
1343 ratio(Bigint *a, Bigint *b)
1344 {
1345  double_u da, db;
1346  int k, ka, kb;
1347 
1348  dval(da) = b2d(a, &ka);
1349  dval(db) = b2d(b, &kb);
1350 #ifdef Pack_32
1351  k = ka - kb + 32*(a->wds - b->wds);
1352 #else
1353  k = ka - kb + 16*(a->wds - b->wds);
1354 #endif
1355 #ifdef IBM
1356  if (k > 0) {
1357  word0(da) += (k >> 2)*Exp_msk1;
1358  if (k &= 3)
1359  dval(da) *= 1 << k;
1360  }
1361  else {
1362  k = -k;
1363  word0(db) += (k >> 2)*Exp_msk1;
1364  if (k &= 3)
1365  dval(db) *= 1 << k;
1366  }
1367 #else
1368  if (k > 0)
1369  word0(da) += k*Exp_msk1;
1370  else {
1371  k = -k;
1372  word0(db) += k*Exp_msk1;
1373  }
1374 #endif
1375  return dval(da) / dval(db);
1376 }
1377 
1378 static const double
1379 tens[] = {
1380  1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1381  1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1382  1e20, 1e21, 1e22
1383 #ifdef VAX
1384  , 1e23, 1e24
1385 #endif
1386 };
1387 
1388 static const double
1389 #ifdef IEEE_Arith
1390 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1391 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1392 #ifdef Avoid_Underflow
1393  9007199254740992.*9007199254740992.e-256
1394  /* = 2^106 * 1e-53 */
1395 #else
1396  1e-256
1397 #endif
1398 };
1399 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1400 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1401 #define Scale_Bit 0x10
1402 #define n_bigtens 5
1403 #else
1404 #ifdef IBM
1405 bigtens[] = { 1e16, 1e32, 1e64 };
1406 static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1407 #define n_bigtens 3
1408 #else
1409 bigtens[] = { 1e16, 1e32 };
1410 static const double tinytens[] = { 1e-16, 1e-32 };
1411 #define n_bigtens 2
1412 #endif
1413 #endif
1414 
1415 #ifndef IEEE_Arith
1416 #undef INFNAN_CHECK
1417 #endif
1418 
1419 #ifdef INFNAN_CHECK
1420 
1421 #ifndef NAN_WORD0
1422 #define NAN_WORD0 0x7ff80000
1423 #endif
1424 
1425 #ifndef NAN_WORD1
1426 #define NAN_WORD1 0
1427 #endif
1428 
1429 static int
1430 match(const char **sp, char *t)
1431 {
1432  int c, d;
1433  const char *s = *sp;
1434 
1435  while (d = *t++) {
1436  if ((c = *++s) >= 'A' && c <= 'Z')
1437  c += 'a' - 'A';
1438  if (c != d)
1439  return 0;
1440  }
1441  *sp = s + 1;
1442  return 1;
1443 }
1444 
1445 #ifndef No_Hex_NaN
1446 static void
1447 hexnan(double *rvp, const char **sp)
1448 {
1449  ULong c, x[2];
1450  const char *s;
1451  int havedig, udx0, xshift;
1452 
1453  x[0] = x[1] = 0;
1454  havedig = xshift = 0;
1455  udx0 = 1;
1456  s = *sp;
1457  while (c = *(const unsigned char*)++s) {
1458  if (c >= '0' && c <= '9')
1459  c -= '0';
1460  else if (c >= 'a' && c <= 'f')
1461  c += 10 - 'a';
1462  else if (c >= 'A' && c <= 'F')
1463  c += 10 - 'A';
1464  else if (c <= ' ') {
1465  if (udx0 && havedig) {
1466  udx0 = 0;
1467  xshift = 1;
1468  }
1469  continue;
1470  }
1471  else if (/*(*/ c == ')' && havedig) {
1472  *sp = s + 1;
1473  break;
1474  }
1475  else
1476  return; /* invalid form: don't change *sp */
1477  havedig = 1;
1478  if (xshift) {
1479  xshift = 0;
1480  x[0] = x[1];
1481  x[1] = 0;
1482  }
1483  if (udx0)
1484  x[0] = (x[0] << 4) | (x[1] >> 28);
1485  x[1] = (x[1] << 4) | c;
1486  }
1487  if ((x[0] &= 0xfffff) || x[1]) {
1488  word0(*rvp) = Exp_mask | x[0];
1489  word1(*rvp) = x[1];
1490  }
1491 }
1492 #endif /*No_Hex_NaN*/
1493 #endif /* INFNAN_CHECK */
1494 
1495 NO_SANITIZE("unsigned-integer-overflow", double strtod(const char *s00, char **se));
1496 double
1497 strtod(const char *s00, char **se)
1498 {
1499 #ifdef Avoid_Underflow
1500  int scale;
1501 #endif
1502  int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1503  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1504  const char *s, *s0, *s1;
1505  double aadj, adj;
1506  double_u aadj1, rv, rv0;
1507  Long L;
1508  ULong y, z;
1509  Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1510 #ifdef SET_INEXACT
1511  int inexact, oldinexact;
1512 #endif
1513 #ifdef Honor_FLT_ROUNDS
1514  int rounding;
1515 #endif
1516 #ifdef USE_LOCALE
1517  const char *s2;
1518 #endif
1519 
1520  errno = 0;
1521  sign = nz0 = nz = 0;
1522  dval(rv) = 0.;
1523  for (s = s00;;s++)
1524  switch (*s) {
1525  case '-':
1526  sign = 1;
1527  /* no break */
1528  case '+':
1529  if (*++s)
1530  goto break2;
1531  /* no break */
1532  case 0:
1533  goto ret0;
1534  case '\t':
1535  case '\n':
1536  case '\v':
1537  case '\f':
1538  case '\r':
1539  case ' ':
1540  continue;
1541  default:
1542  goto break2;
1543  }
1544 break2:
1545  if (*s == '0') {
1546  if (s[1] == 'x' || s[1] == 'X') {
1547  s0 = ++s;
1548  adj = 0;
1549  aadj = 1.0;
1550  nd0 = -4;
1551 
1552  if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
1553  if (*s == '0') {
1554  while (*++s == '0');
1555  if (!*s) goto ret;
1556  s1 = strchr(hexdigit, *s);
1557  }
1558  if (s1 != NULL) {
1559  do {
1560  adj += aadj * ((s1 - hexdigit) & 15);
1561  nd0 += 4;
1562  aadj /= 16;
1563  } while (*++s && (s1 = strchr(hexdigit, *s)));
1564  }
1565 
1566  if (*s == '.') {
1567  dsign = 1;
1568  if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
1569  if (nd0 < 0) {
1570  while (*s == '0') {
1571  s++;
1572  nd0 -= 4;
1573  }
1574  }
1575  for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
1576  adj += aadj * ((s1 - hexdigit) & 15);
1577  if ((aadj /= 16) == 0.0) {
1578  while (*++s && strchr(hexdigit, *s));
1579  break;
1580  }
1581  }
1582  }
1583  else {
1584  dsign = 0;
1585  }
1586 
1587  if (*s == 'P' || *s == 'p') {
1588  dsign = 0x2C - *++s; /* +: 2B, -: 2D */
1589  if (abs(dsign) == 1) s++;
1590  else dsign = 1;
1591 
1592  nd = 0;
1593  c = *s;
1594  if (c < '0' || '9' < c) goto ret0;
1595  do {
1596  nd *= 10;
1597  nd += c;
1598  nd -= '0';
1599  c = *++s;
1600  /* Float("0x0."+("0"*267)+"1fp2095") */
1601  if (nd + dsign * nd0 > 2095) {
1602  while ('0' <= c && c <= '9') c = *++s;
1603  break;
1604  }
1605  } while ('0' <= c && c <= '9');
1606  nd0 += nd * dsign;
1607  }
1608  else {
1609  if (dsign) goto ret0;
1610  }
1611  dval(rv) = ldexp(adj, nd0);
1612  goto ret;
1613  }
1614  nz0 = 1;
1615  while (*++s == '0') ;
1616  if (!*s)
1617  goto ret;
1618  }
1619  s0 = s;
1620  y = z = 0;
1621  for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1622  if (nd < 9)
1623  y = 10*y + c - '0';
1624  else if (nd < DBL_DIG + 2)
1625  z = 10*z + c - '0';
1626  nd0 = nd;
1627 #ifdef USE_LOCALE
1628  s1 = localeconv()->decimal_point;
1629  if (c == *s1) {
1630  c = '.';
1631  if (*++s1) {
1632  s2 = s;
1633  for (;;) {
1634  if (*++s2 != *s1) {
1635  c = 0;
1636  break;
1637  }
1638  if (!*++s1) {
1639  s = s2;
1640  break;
1641  }
1642  }
1643  }
1644  }
1645 #endif
1646  if (c == '.') {
1647  if (!ISDIGIT(s[1]))
1648  goto dig_done;
1649  c = *++s;
1650  if (!nd) {
1651  for (; c == '0'; c = *++s)
1652  nz++;
1653  if (c > '0' && c <= '9') {
1654  s0 = s;
1655  nf += nz;
1656  nz = 0;
1657  goto have_dig;
1658  }
1659  goto dig_done;
1660  }
1661  for (; c >= '0' && c <= '9'; c = *++s) {
1662 have_dig:
1663  nz++;
1664  if (nd > DBL_DIG * 4) {
1665  continue;
1666  }
1667  if (c -= '0') {
1668  nf += nz;
1669  for (i = 1; i < nz; i++)
1670  if (nd++ < 9)
1671  y *= 10;
1672  else if (nd <= DBL_DIG + 2)
1673  z *= 10;
1674  if (nd++ < 9)
1675  y = 10*y + c;
1676  else if (nd <= DBL_DIG + 2)
1677  z = 10*z + c;
1678  nz = 0;
1679  }
1680  }
1681  }
1682 dig_done:
1683  e = 0;
1684  if (c == 'e' || c == 'E') {
1685  if (!nd && !nz && !nz0) {
1686  goto ret0;
1687  }
1688  s00 = s;
1689  esign = 0;
1690  switch (c = *++s) {
1691  case '-':
1692  esign = 1;
1693  case '+':
1694  c = *++s;
1695  }
1696  if (c >= '0' && c <= '9') {
1697  while (c == '0')
1698  c = *++s;
1699  if (c > '0' && c <= '9') {
1700  L = c - '0';
1701  s1 = s;
1702  while ((c = *++s) >= '0' && c <= '9')
1703  L = 10*L + c - '0';
1704  if (s - s1 > 8 || L > 19999)
1705  /* Avoid confusion from exponents
1706  * so large that e might overflow.
1707  */
1708  e = 19999; /* safe for 16 bit ints */
1709  else
1710  e = (int)L;
1711  if (esign)
1712  e = -e;
1713  }
1714  else
1715  e = 0;
1716  }
1717  else
1718  s = s00;
1719  }
1720  if (!nd) {
1721  if (!nz && !nz0) {
1722 #ifdef INFNAN_CHECK
1723  /* Check for Nan and Infinity */
1724  switch (c) {
1725  case 'i':
1726  case 'I':
1727  if (match(&s,"nf")) {
1728  --s;
1729  if (!match(&s,"inity"))
1730  ++s;
1731  word0(rv) = 0x7ff00000;
1732  word1(rv) = 0;
1733  goto ret;
1734  }
1735  break;
1736  case 'n':
1737  case 'N':
1738  if (match(&s, "an")) {
1739  word0(rv) = NAN_WORD0;
1740  word1(rv) = NAN_WORD1;
1741 #ifndef No_Hex_NaN
1742  if (*s == '(') /*)*/
1743  hexnan(&rv, &s);
1744 #endif
1745  goto ret;
1746  }
1747  }
1748 #endif /* INFNAN_CHECK */
1749 ret0:
1750  s = s00;
1751  sign = 0;
1752  }
1753  goto ret;
1754  }
1755  e1 = e -= nf;
1756 
1757  /* Now we have nd0 digits, starting at s0, followed by a
1758  * decimal point, followed by nd-nd0 digits. The number we're
1759  * after is the integer represented by those digits times
1760  * 10**e */
1761 
1762  if (!nd0)
1763  nd0 = nd;
1764  k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
1765  dval(rv) = y;
1766  if (k > 9) {
1767 #ifdef SET_INEXACT
1768  if (k > DBL_DIG)
1769  oldinexact = get_inexact();
1770 #endif
1771  dval(rv) = tens[k - 9] * dval(rv) + z;
1772  }
1773  bd0 = bb = bd = bs = delta = 0;
1774  if (nd <= DBL_DIG
1775 #ifndef RND_PRODQUOT
1776 #ifndef Honor_FLT_ROUNDS
1777  && Flt_Rounds == 1
1778 #endif
1779 #endif
1780  ) {
1781  if (!e)
1782  goto ret;
1783  if (e > 0) {
1784  if (e <= Ten_pmax) {
1785 #ifdef VAX
1786  goto vax_ovfl_check;
1787 #else
1788 #ifdef Honor_FLT_ROUNDS
1789  /* round correctly FLT_ROUNDS = 2 or 3 */
1790  if (sign) {
1791  dval(rv) = -dval(rv);
1792  sign = 0;
1793  }
1794 #endif
1795  /* rv = */ rounded_product(dval(rv), tens[e]);
1796  goto ret;
1797 #endif
1798  }
1799  i = DBL_DIG - nd;
1800  if (e <= Ten_pmax + i) {
1801  /* A fancier test would sometimes let us do
1802  * this for larger i values.
1803  */
1804 #ifdef Honor_FLT_ROUNDS
1805  /* round correctly FLT_ROUNDS = 2 or 3 */
1806  if (sign) {
1807  dval(rv) = -dval(rv);
1808  sign = 0;
1809  }
1810 #endif
1811  e -= i;
1812  dval(rv) *= tens[i];
1813 #ifdef VAX
1814  /* VAX exponent range is so narrow we must
1815  * worry about overflow here...
1816  */
1817 vax_ovfl_check:
1818  word0(rv) -= P*Exp_msk1;
1819  /* rv = */ rounded_product(dval(rv), tens[e]);
1820  if ((word0(rv) & Exp_mask)
1821  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1822  goto ovfl;
1823  word0(rv) += P*Exp_msk1;
1824 #else
1825  /* rv = */ rounded_product(dval(rv), tens[e]);
1826 #endif
1827  goto ret;
1828  }
1829  }
1830 #ifndef Inaccurate_Divide
1831  else if (e >= -Ten_pmax) {
1832 #ifdef Honor_FLT_ROUNDS
1833  /* round correctly FLT_ROUNDS = 2 or 3 */
1834  if (sign) {
1835  dval(rv) = -dval(rv);
1836  sign = 0;
1837  }
1838 #endif
1839  /* rv = */ rounded_quotient(dval(rv), tens[-e]);
1840  goto ret;
1841  }
1842 #endif
1843  }
1844  e1 += nd - k;
1845 
1846 #ifdef IEEE_Arith
1847 #ifdef SET_INEXACT
1848  inexact = 1;
1849  if (k <= DBL_DIG)
1850  oldinexact = get_inexact();
1851 #endif
1852 #ifdef Avoid_Underflow
1853  scale = 0;
1854 #endif
1855 #ifdef Honor_FLT_ROUNDS
1856  if ((rounding = Flt_Rounds) >= 2) {
1857  if (sign)
1858  rounding = rounding == 2 ? 0 : 2;
1859  else
1860  if (rounding != 2)
1861  rounding = 0;
1862  }
1863 #endif
1864 #endif /*IEEE_Arith*/
1865 
1866  /* Get starting approximation = rv * 10**e1 */
1867 
1868  if (e1 > 0) {
1869  if ((i = e1 & 15) != 0)
1870  dval(rv) *= tens[i];
1871  if (e1 &= ~15) {
1872  if (e1 > DBL_MAX_10_EXP) {
1873 ovfl:
1874 #ifndef NO_ERRNO
1875  errno = ERANGE;
1876 #endif
1877  /* Can't trust HUGE_VAL */
1878 #ifdef IEEE_Arith
1879 #ifdef Honor_FLT_ROUNDS
1880  switch (rounding) {
1881  case 0: /* toward 0 */
1882  case 3: /* toward -infinity */
1883  word0(rv) = Big0;
1884  word1(rv) = Big1;
1885  break;
1886  default:
1887  word0(rv) = Exp_mask;
1888  word1(rv) = 0;
1889  }
1890 #else /*Honor_FLT_ROUNDS*/
1891  word0(rv) = Exp_mask;
1892  word1(rv) = 0;
1893 #endif /*Honor_FLT_ROUNDS*/
1894 #ifdef SET_INEXACT
1895  /* set overflow bit */
1896  dval(rv0) = 1e300;
1897  dval(rv0) *= dval(rv0);
1898 #endif
1899 #else /*IEEE_Arith*/
1900  word0(rv) = Big0;
1901  word1(rv) = Big1;
1902 #endif /*IEEE_Arith*/
1903  if (bd0)
1904  goto retfree;
1905  goto ret;
1906  }
1907  e1 >>= 4;
1908  for (j = 0; e1 > 1; j++, e1 >>= 1)
1909  if (e1 & 1)
1910  dval(rv) *= bigtens[j];
1911  /* The last multiplication could overflow. */
1912  word0(rv) -= P*Exp_msk1;
1913  dval(rv) *= bigtens[j];
1914  if ((z = word0(rv) & Exp_mask)
1915  > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1916  goto ovfl;
1917  if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1918  /* set to largest number */
1919  /* (Can't trust DBL_MAX) */
1920  word0(rv) = Big0;
1921  word1(rv) = Big1;
1922  }
1923  else
1924  word0(rv) += P*Exp_msk1;
1925  }
1926  }
1927  else if (e1 < 0) {
1928  e1 = -e1;
1929  if ((i = e1 & 15) != 0)
1930  dval(rv) /= tens[i];
1931  if (e1 >>= 4) {
1932  if (e1 >= 1 << n_bigtens)
1933  goto undfl;
1934 #ifdef Avoid_Underflow
1935  if (e1 & Scale_Bit)
1936  scale = 2*P;
1937  for (j = 0; e1 > 0; j++, e1 >>= 1)
1938  if (e1 & 1)
1939  dval(rv) *= tinytens[j];
1940  if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
1941  >> Exp_shift)) > 0) {
1942  /* scaled rv is denormal; zap j low bits */
1943  if (j >= 32) {
1944  word1(rv) = 0;
1945  if (j >= 53)
1946  word0(rv) = (P+2)*Exp_msk1;
1947  else
1948  word0(rv) &= 0xffffffff << (j-32);
1949  }
1950  else
1951  word1(rv) &= 0xffffffff << j;
1952  }
1953 #else
1954  for (j = 0; e1 > 1; j++, e1 >>= 1)
1955  if (e1 & 1)
1956  dval(rv) *= tinytens[j];
1957  /* The last multiplication could underflow. */
1958  dval(rv0) = dval(rv);
1959  dval(rv) *= tinytens[j];
1960  if (!dval(rv)) {
1961  dval(rv) = 2.*dval(rv0);
1962  dval(rv) *= tinytens[j];
1963 #endif
1964  if (!dval(rv)) {
1965 undfl:
1966  dval(rv) = 0.;
1967 #ifndef NO_ERRNO
1968  errno = ERANGE;
1969 #endif
1970  if (bd0)
1971  goto retfree;
1972  goto ret;
1973  }
1974 #ifndef Avoid_Underflow
1975  word0(rv) = Tiny0;
1976  word1(rv) = Tiny1;
1977  /* The refinement below will clean
1978  * this approximation up.
1979  */
1980  }
1981 #endif
1982  }
1983  }
1984 
1985  /* Now the hard part -- adjusting rv to the correct value.*/
1986 
1987  /* Put digits into bd: true value = bd * 10^e */
1988 
1989  bd0 = s2b(s0, nd0, nd, y);
1990 
1991  for (;;) {
1992  bd = Balloc(bd0->k);
1993  Bcopy(bd, bd0);
1994  bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1995  bs = i2b(1);
1996 
1997  if (e >= 0) {
1998  bb2 = bb5 = 0;
1999  bd2 = bd5 = e;
2000  }
2001  else {
2002  bb2 = bb5 = -e;
2003  bd2 = bd5 = 0;
2004  }
2005  if (bbe >= 0)
2006  bb2 += bbe;
2007  else
2008  bd2 -= bbe;
2009  bs2 = bb2;
2010 #ifdef Honor_FLT_ROUNDS
2011  if (rounding != 1)
2012  bs2++;
2013 #endif
2014 #ifdef Avoid_Underflow
2015  j = bbe - scale;
2016  i = j + bbbits - 1; /* logb(rv) */
2017  if (i < Emin) /* denormal */
2018  j += P - Emin;
2019  else
2020  j = P + 1 - bbbits;
2021 #else /*Avoid_Underflow*/
2022 #ifdef Sudden_Underflow
2023 #ifdef IBM
2024  j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2025 #else
2026  j = P + 1 - bbbits;
2027 #endif
2028 #else /*Sudden_Underflow*/
2029  j = bbe;
2030  i = j + bbbits - 1; /* logb(rv) */
2031  if (i < Emin) /* denormal */
2032  j += P - Emin;
2033  else
2034  j = P + 1 - bbbits;
2035 #endif /*Sudden_Underflow*/
2036 #endif /*Avoid_Underflow*/
2037  bb2 += j;
2038  bd2 += j;
2039 #ifdef Avoid_Underflow
2040  bd2 += scale;
2041 #endif
2042  i = bb2 < bd2 ? bb2 : bd2;
2043  if (i > bs2)
2044  i = bs2;
2045  if (i > 0) {
2046  bb2 -= i;
2047  bd2 -= i;
2048  bs2 -= i;
2049  }
2050  if (bb5 > 0) {
2051  bs = pow5mult(bs, bb5);
2052  bb1 = mult(bs, bb);
2053  Bfree(bb);
2054  bb = bb1;
2055  }
2056  if (bb2 > 0)
2057  bb = lshift(bb, bb2);
2058  if (bd5 > 0)
2059  bd = pow5mult(bd, bd5);
2060  if (bd2 > 0)
2061  bd = lshift(bd, bd2);
2062  if (bs2 > 0)
2063  bs = lshift(bs, bs2);
2064  delta = diff(bb, bd);
2065  dsign = delta->sign;
2066  delta->sign = 0;
2067  i = cmp(delta, bs);
2068 #ifdef Honor_FLT_ROUNDS
2069  if (rounding != 1) {
2070  if (i < 0) {
2071  /* Error is less than an ulp */
2072  if (!delta->x[0] && delta->wds <= 1) {
2073  /* exact */
2074 #ifdef SET_INEXACT
2075  inexact = 0;
2076 #endif
2077  break;
2078  }
2079  if (rounding) {
2080  if (dsign) {
2081  adj = 1.;
2082  goto apply_adj;
2083  }
2084  }
2085  else if (!dsign) {
2086  adj = -1.;
2087  if (!word1(rv)
2088  && !(word0(rv) & Frac_mask)) {
2089  y = word0(rv) & Exp_mask;
2090 #ifdef Avoid_Underflow
2091  if (!scale || y > 2*P*Exp_msk1)
2092 #else
2093  if (y)
2094 #endif
2095  {
2096  delta = lshift(delta,Log2P);
2097  if (cmp(delta, bs) <= 0)
2098  adj = -0.5;
2099  }
2100  }
2101 apply_adj:
2102 #ifdef Avoid_Underflow
2103  if (scale && (y = word0(rv) & Exp_mask)
2104  <= 2*P*Exp_msk1)
2105  word0(adj) += (2*P+1)*Exp_msk1 - y;
2106 #else
2107 #ifdef Sudden_Underflow
2108  if ((word0(rv) & Exp_mask) <=
2109  P*Exp_msk1) {
2110  word0(rv) += P*Exp_msk1;
2111  dval(rv) += adj*ulp(dval(rv));
2112  word0(rv) -= P*Exp_msk1;
2113  }
2114  else
2115 #endif /*Sudden_Underflow*/
2116 #endif /*Avoid_Underflow*/
2117  dval(rv) += adj*ulp(dval(rv));
2118  }
2119  break;
2120  }
2121  adj = ratio(delta, bs);
2122  if (adj < 1.)
2123  adj = 1.;
2124  if (adj <= 0x7ffffffe) {
2125  /* adj = rounding ? ceil(adj) : floor(adj); */
2126  y = adj;
2127  if (y != adj) {
2128  if (!((rounding>>1) ^ dsign))
2129  y++;
2130  adj = y;
2131  }
2132  }
2133 #ifdef Avoid_Underflow
2134  if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2135  word0(adj) += (2*P+1)*Exp_msk1 - y;
2136 #else
2137 #ifdef Sudden_Underflow
2138  if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2139  word0(rv) += P*Exp_msk1;
2140  adj *= ulp(dval(rv));
2141  if (dsign)
2142  dval(rv) += adj;
2143  else
2144  dval(rv) -= adj;
2145  word0(rv) -= P*Exp_msk1;
2146  goto cont;
2147  }
2148 #endif /*Sudden_Underflow*/
2149 #endif /*Avoid_Underflow*/
2150  adj *= ulp(dval(rv));
2151  if (dsign)
2152  dval(rv) += adj;
2153  else
2154  dval(rv) -= adj;
2155  goto cont;
2156  }
2157 #endif /*Honor_FLT_ROUNDS*/
2158 
2159  if (i < 0) {
2160  /* Error is less than half an ulp -- check for
2161  * special case of mantissa a power of two.
2162  */
2163  if (dsign || word1(rv) || word0(rv) & Bndry_mask
2164 #ifdef IEEE_Arith
2165 #ifdef Avoid_Underflow
2166  || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2167 #else
2168  || (word0(rv) & Exp_mask) <= Exp_msk1
2169 #endif
2170 #endif
2171  ) {
2172 #ifdef SET_INEXACT
2173  if (!delta->x[0] && delta->wds <= 1)
2174  inexact = 0;
2175 #endif
2176  break;
2177  }
2178  if (!delta->x[0] && delta->wds <= 1) {
2179  /* exact result */
2180 #ifdef SET_INEXACT
2181  inexact = 0;
2182 #endif
2183  break;
2184  }
2185  delta = lshift(delta,Log2P);
2186  if (cmp(delta, bs) > 0)
2187  goto drop_down;
2188  break;
2189  }
2190  if (i == 0) {
2191  /* exactly half-way between */
2192  if (dsign) {
2193  if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2194  && word1(rv) == (
2195 #ifdef Avoid_Underflow
2196  (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2197  ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2198 #endif
2199  0xffffffff)) {
2200  /*boundary case -- increment exponent*/
2201  word0(rv) = (word0(rv) & Exp_mask)
2202  + Exp_msk1
2203 #ifdef IBM
2204  | Exp_msk1 >> 4
2205 #endif
2206  ;
2207  word1(rv) = 0;
2208 #ifdef Avoid_Underflow
2209  dsign = 0;
2210 #endif
2211  break;
2212  }
2213  }
2214  else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2215 drop_down:
2216  /* boundary case -- decrement exponent */
2217 #ifdef Sudden_Underflow /*{{*/
2218  L = word0(rv) & Exp_mask;
2219 #ifdef IBM
2220  if (L < Exp_msk1)
2221 #else
2222 #ifdef Avoid_Underflow
2223  if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2224 #else
2225  if (L <= Exp_msk1)
2226 #endif /*Avoid_Underflow*/
2227 #endif /*IBM*/
2228  goto undfl;
2229  L -= Exp_msk1;
2230 #else /*Sudden_Underflow}{*/
2231 #ifdef Avoid_Underflow
2232  if (scale) {
2233  L = word0(rv) & Exp_mask;
2234  if (L <= (2*P+1)*Exp_msk1) {
2235  if (L > (P+2)*Exp_msk1)
2236  /* round even ==> */
2237  /* accept rv */
2238  break;
2239  /* rv = smallest denormal */
2240  goto undfl;
2241  }
2242  }
2243 #endif /*Avoid_Underflow*/
2244  L = (word0(rv) & Exp_mask) - Exp_msk1;
2245 #endif /*Sudden_Underflow}}*/
2246  word0(rv) = L | Bndry_mask1;
2247  word1(rv) = 0xffffffff;
2248 #ifdef IBM
2249  goto cont;
2250 #else
2251  break;
2252 #endif
2253  }
2254 #ifndef ROUND_BIASED
2255  if (!(word1(rv) & LSB))
2256  break;
2257 #endif
2258  if (dsign)
2259  dval(rv) += ulp(dval(rv));
2260 #ifndef ROUND_BIASED
2261  else {
2262  dval(rv) -= ulp(dval(rv));
2263 #ifndef Sudden_Underflow
2264  if (!dval(rv))
2265  goto undfl;
2266 #endif
2267  }
2268 #ifdef Avoid_Underflow
2269  dsign = 1 - dsign;
2270 #endif
2271 #endif
2272  break;
2273  }
2274  if ((aadj = ratio(delta, bs)) <= 2.) {
2275  if (dsign)
2276  aadj = dval(aadj1) = 1.;
2277  else if (word1(rv) || word0(rv) & Bndry_mask) {
2278 #ifndef Sudden_Underflow
2279  if (word1(rv) == Tiny1 && !word0(rv))
2280  goto undfl;
2281 #endif
2282  aadj = 1.;
2283  dval(aadj1) = -1.;
2284  }
2285  else {
2286  /* special case -- power of FLT_RADIX to be */
2287  /* rounded down... */
2288 
2289  if (aadj < 2./FLT_RADIX)
2290  aadj = 1./FLT_RADIX;
2291  else
2292  aadj *= 0.5;
2293  dval(aadj1) = -aadj;
2294  }
2295  }
2296  else {
2297  aadj *= 0.5;
2298  dval(aadj1) = dsign ? aadj : -aadj;
2299 #ifdef Check_FLT_ROUNDS
2300  switch (Rounding) {
2301  case 2: /* towards +infinity */
2302  dval(aadj1) -= 0.5;
2303  break;
2304  case 0: /* towards 0 */
2305  case 3: /* towards -infinity */
2306  dval(aadj1) += 0.5;
2307  }
2308 #else
2309  if (Flt_Rounds == 0)
2310  dval(aadj1) += 0.5;
2311 #endif /*Check_FLT_ROUNDS*/
2312  }
2313  y = word0(rv) & Exp_mask;
2314 
2315  /* Check for overflow */
2316 
2317  if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2318  dval(rv0) = dval(rv);
2319  word0(rv) -= P*Exp_msk1;
2320  adj = dval(aadj1) * ulp(dval(rv));
2321  dval(rv) += adj;
2322  if ((word0(rv) & Exp_mask) >=
2323  Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2324  if (word0(rv0) == Big0 && word1(rv0) == Big1)
2325  goto ovfl;
2326  word0(rv) = Big0;
2327  word1(rv) = Big1;
2328  goto cont;
2329  }
2330  else
2331  word0(rv) += P*Exp_msk1;
2332  }
2333  else {
2334 #ifdef Avoid_Underflow
2335  if (scale && y <= 2*P*Exp_msk1) {
2336  if (aadj <= 0x7fffffff) {
2337  if ((z = (int)aadj) <= 0)
2338  z = 1;
2339  aadj = z;
2340  dval(aadj1) = dsign ? aadj : -aadj;
2341  }
2342  word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2343  }
2344  adj = dval(aadj1) * ulp(dval(rv));
2345  dval(rv) += adj;
2346 #else
2347 #ifdef Sudden_Underflow
2348  if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2349  dval(rv0) = dval(rv);
2350  word0(rv) += P*Exp_msk1;
2351  adj = dval(aadj1) * ulp(dval(rv));
2352  dval(rv) += adj;
2353 #ifdef IBM
2354  if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2355 #else
2356  if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2357 #endif
2358  {
2359  if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2360  goto undfl;
2361  word0(rv) = Tiny0;
2362  word1(rv) = Tiny1;
2363  goto cont;
2364  }
2365  else
2366  word0(rv) -= P*Exp_msk1;
2367  }
2368  else {
2369  adj = dval(aadj1) * ulp(dval(rv));
2370  dval(rv) += adj;
2371  }
2372 #else /*Sudden_Underflow*/
2373  /* Compute adj so that the IEEE rounding rules will
2374  * correctly round rv + adj in some half-way cases.
2375  * If rv * ulp(rv) is denormalized (i.e.,
2376  * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2377  * trouble from bits lost to denormalization;
2378  * example: 1.2e-307 .
2379  */
2380  if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2381  dval(aadj1) = (double)(int)(aadj + 0.5);
2382  if (!dsign)
2383  dval(aadj1) = -dval(aadj1);
2384  }
2385  adj = dval(aadj1) * ulp(dval(rv));
2386  dval(rv) += adj;
2387 #endif /*Sudden_Underflow*/
2388 #endif /*Avoid_Underflow*/
2389  }
2390  z = word0(rv) & Exp_mask;
2391 #ifndef SET_INEXACT
2392 #ifdef Avoid_Underflow
2393  if (!scale)
2394 #endif
2395  if (y == z) {
2396  /* Can we stop now? */
2397  L = (Long)aadj;
2398  aadj -= L;
2399  /* The tolerances below are conservative. */
2400  if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2401  if (aadj < .4999999 || aadj > .5000001)
2402  break;
2403  }
2404  else if (aadj < .4999999/FLT_RADIX)
2405  break;
2406  }
2407 #endif
2408 cont:
2409  Bfree(bb);
2410  Bfree(bd);
2411  Bfree(bs);
2412  Bfree(delta);
2413  }
2414 #ifdef SET_INEXACT
2415  if (inexact) {
2416  if (!oldinexact) {
2417  word0(rv0) = Exp_1 + (70 << Exp_shift);
2418  word1(rv0) = 0;
2419  dval(rv0) += 1.;
2420  }
2421  }
2422  else if (!oldinexact)
2423  clear_inexact();
2424 #endif
2425 #ifdef Avoid_Underflow
2426  if (scale) {
2427  word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2428  word1(rv0) = 0;
2429  dval(rv) *= dval(rv0);
2430 #ifndef NO_ERRNO
2431  /* try to avoid the bug of testing an 8087 register value */
2432  if (word0(rv) == 0 && word1(rv) == 0)
2433  errno = ERANGE;
2434 #endif
2435  }
2436 #endif /* Avoid_Underflow */
2437 #ifdef SET_INEXACT
2438  if (inexact && !(word0(rv) & Exp_mask)) {
2439  /* set underflow bit */
2440  dval(rv0) = 1e-300;
2441  dval(rv0) *= dval(rv0);
2442  }
2443 #endif
2444 retfree:
2445  Bfree(bb);
2446  Bfree(bd);
2447  Bfree(bs);
2448  Bfree(bd0);
2449  Bfree(delta);
2450 ret:
2451  if (se)
2452  *se = (char *)s;
2453  return sign ? -dval(rv) : dval(rv);
2454 }
2455 
2456 NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S));
2457 static int
2458 quorem(Bigint *b, Bigint *S)
2459 {
2460  int n;
2461  ULong *bx, *bxe, q, *sx, *sxe;
2462 #ifdef ULLong
2463  ULLong borrow, carry, y, ys;
2464 #else
2465  ULong borrow, carry, y, ys;
2466 #ifdef Pack_32
2467  ULong si, z, zs;
2468 #endif
2469 #endif
2470 
2471  n = S->wds;
2472 #ifdef DEBUG
2473  /*debug*/ if (b->wds > n)
2474  /*debug*/ Bug("oversize b in quorem");
2475 #endif
2476  if (b->wds < n)
2477  return 0;
2478  sx = S->x;
2479  sxe = sx + --n;
2480  bx = b->x;
2481  bxe = bx + n;
2482  q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2483 #ifdef DEBUG
2484  /*debug*/ if (q > 9)
2485  /*debug*/ Bug("oversized quotient in quorem");
2486 #endif
2487  if (q) {
2488  borrow = 0;
2489  carry = 0;
2490  do {
2491 #ifdef ULLong
2492  ys = *sx++ * (ULLong)q + carry;
2493  carry = ys >> 32;
2494  y = *bx - (ys & FFFFFFFF) - borrow;
2495  borrow = y >> 32 & (ULong)1;
2496  *bx++ = (ULong)(y & FFFFFFFF);
2497 #else
2498 #ifdef Pack_32
2499  si = *sx++;
2500  ys = (si & 0xffff) * q + carry;
2501  zs = (si >> 16) * q + (ys >> 16);
2502  carry = zs >> 16;
2503  y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2504  borrow = (y & 0x10000) >> 16;
2505  z = (*bx >> 16) - (zs & 0xffff) - borrow;
2506  borrow = (z & 0x10000) >> 16;
2507  Storeinc(bx, z, y);
2508 #else
2509  ys = *sx++ * q + carry;
2510  carry = ys >> 16;
2511  y = *bx - (ys & 0xffff) - borrow;
2512  borrow = (y & 0x10000) >> 16;
2513  *bx++ = y & 0xffff;
2514 #endif
2515 #endif
2516  } while (sx <= sxe);
2517  if (!*bxe) {
2518  bx = b->x;
2519  while (--bxe > bx && !*bxe)
2520  --n;
2521  b->wds = n;
2522  }
2523  }
2524  if (cmp(b, S) >= 0) {
2525  q++;
2526  borrow = 0;
2527  carry = 0;
2528  bx = b->x;
2529  sx = S->x;
2530  do {
2531 #ifdef ULLong
2532  ys = *sx++ + carry;
2533  carry = ys >> 32;
2534  y = *bx - (ys & FFFFFFFF) - borrow;
2535  borrow = y >> 32 & (ULong)1;
2536  *bx++ = (ULong)(y & FFFFFFFF);
2537 #else
2538 #ifdef Pack_32
2539  si = *sx++;
2540  ys = (si & 0xffff) + carry;
2541  zs = (si >> 16) + (ys >> 16);
2542  carry = zs >> 16;
2543  y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2544  borrow = (y & 0x10000) >> 16;
2545  z = (*bx >> 16) - (zs & 0xffff) - borrow;
2546  borrow = (z & 0x10000) >> 16;
2547  Storeinc(bx, z, y);
2548 #else
2549  ys = *sx++ + carry;
2550  carry = ys >> 16;
2551  y = *bx - (ys & 0xffff) - borrow;
2552  borrow = (y & 0x10000) >> 16;
2553  *bx++ = y & 0xffff;
2554 #endif
2555 #endif
2556  } while (sx <= sxe);
2557  bx = b->x;
2558  bxe = bx + n;
2559  if (!*bxe) {
2560  while (--bxe > bx && !*bxe)
2561  --n;
2562  b->wds = n;
2563  }
2564  }
2565  return q;
2566 }
2567 
2568 #ifndef MULTIPLE_THREADS
2569 static char *dtoa_result;
2570 #endif
2571 
2572 #ifndef MULTIPLE_THREADS
2573 static char *
2574 rv_alloc(int i)
2575 {
2576  return dtoa_result = MALLOC(i);
2577 }
2578 #else
2579 #define rv_alloc(i) MALLOC(i)
2580 #endif
2581 
2582 static char *
2583 nrv_alloc(const char *s, char **rve, size_t n)
2584 {
2585  char *rv, *t;
2586 
2587  t = rv = rv_alloc(n);
2588  while ((*t = *s++) != 0) t++;
2589  if (rve)
2590  *rve = t;
2591  return rv;
2592 }
2593 
2594 #define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
2595 
2596 #ifndef MULTIPLE_THREADS
2597 /* freedtoa(s) must be used to free values s returned by dtoa
2598  * when MULTIPLE_THREADS is #defined. It should be used in all cases,
2599  * but for consistency with earlier versions of dtoa, it is optional
2600  * when MULTIPLE_THREADS is not defined.
2601  */
2602 
2603 static void
2604 freedtoa(char *s)
2605 {
2606  FREE(s);
2607 }
2608 #endif
2609 
2610 static const char INFSTR[] = "Infinity";
2611 static const char NANSTR[] = "NaN";
2612 static const char ZEROSTR[] = "0";
2613 
2614 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
2615  *
2616  * Inspired by "How to Print Floating-Point Numbers Accurately" by
2617  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
2618  *
2619  * Modifications:
2620  * 1. Rather than iterating, we use a simple numeric overestimate
2621  * to determine k = floor(log10(d)). We scale relevant
2622  * quantities using O(log2(k)) rather than O(k) multiplications.
2623  * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
2624  * try to generate digits strictly left to right. Instead, we
2625  * compute with fewer bits and propagate the carry if necessary
2626  * when rounding the final digit up. This is often faster.
2627  * 3. Under the assumption that input will be rounded nearest,
2628  * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
2629  * That is, we allow equality in stopping tests when the
2630  * round-nearest rule will give the same floating-point value
2631  * as would satisfaction of the stopping test with strict
2632  * inequality.
2633  * 4. We remove common factors of powers of 2 from relevant
2634  * quantities.
2635  * 5. When converting floating-point integers less than 1e16,
2636  * we use floating-point arithmetic rather than resorting
2637  * to multiple-precision integers.
2638  * 6. When asked to produce fewer than 15 digits, we first try
2639  * to get by with floating-point arithmetic; we resort to
2640  * multiple-precision integer arithmetic only if we cannot
2641  * guarantee that the floating-point calculation has given
2642  * the correctly rounded result. For k requested digits and
2643  * "uniformly" distributed input, the probability is
2644  * something like 10^(k-15) that we must resort to the Long
2645  * calculation.
2646  */
2647 
2648 char *
2649 dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
2650 {
2651  /* Arguments ndigits, decpt, sign are similar to those
2652  of ecvt and fcvt; trailing zeros are suppressed from
2653  the returned string. If not null, *rve is set to point
2654  to the end of the return value. If d is +-Infinity or NaN,
2655  then *decpt is set to 9999.
2656 
2657  mode:
2658  0 ==> shortest string that yields d when read in
2659  and rounded to nearest.
2660  1 ==> like 0, but with Steele & White stopping rule;
2661  e.g. with IEEE P754 arithmetic , mode 0 gives
2662  1e23 whereas mode 1 gives 9.999999999999999e22.
2663  2 ==> max(1,ndigits) significant digits. This gives a
2664  return value similar to that of ecvt, except
2665  that trailing zeros are suppressed.
2666  3 ==> through ndigits past the decimal point. This
2667  gives a return value similar to that from fcvt,
2668  except that trailing zeros are suppressed, and
2669  ndigits can be negative.
2670  4,5 ==> similar to 2 and 3, respectively, but (in
2671  round-nearest mode) with the tests of mode 0 to
2672  possibly return a shorter string that rounds to d.
2673  With IEEE arithmetic and compilation with
2674  -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
2675  as modes 2 and 3 when FLT_ROUNDS != 1.
2676  6-9 ==> Debugging modes similar to mode - 4: don't try
2677  fast floating-point estimate (if applicable).
2678 
2679  Values of mode other than 0-9 are treated as mode 0.
2680 
2681  Sufficient space is allocated to the return value
2682  to hold the suppressed trailing zeros.
2683  */
2684 
2685  int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
2686  j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
2687  spec_case, try_quick, half = 0;
2688  Long L;
2689 #ifndef Sudden_Underflow
2690  int denorm;
2691  ULong x;
2692 #endif
2693  Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
2694  double ds;
2695  double_u d, d2, eps;
2696  char *s, *s0;
2697 #ifdef Honor_FLT_ROUNDS
2698  int rounding;
2699 #endif
2700 #ifdef SET_INEXACT
2701  int inexact, oldinexact;
2702 #endif
2703 
2704  dval(d) = d_;
2705 
2706 #ifndef MULTIPLE_THREADS
2707  if (dtoa_result) {
2708  freedtoa(dtoa_result);
2709  dtoa_result = 0;
2710  }
2711 #endif
2712 
2713  if (word0(d) & Sign_bit) {
2714  /* set sign for everything, including 0's and NaNs */
2715  *sign = 1;
2716  word0(d) &= ~Sign_bit; /* clear sign bit */
2717  }
2718  else
2719  *sign = 0;
2720 
2721 #if defined(IEEE_Arith) + defined(VAX)
2722 #ifdef IEEE_Arith
2723  if ((word0(d) & Exp_mask) == Exp_mask)
2724 #else
2725  if (word0(d) == 0x8000)
2726 #endif
2727  {
2728  /* Infinity or NaN */
2729  *decpt = 9999;
2730 #ifdef IEEE_Arith
2731  if (!word1(d) && !(word0(d) & 0xfffff))
2732  return rv_strdup(INFSTR, rve);
2733 #endif
2734  return rv_strdup(NANSTR, rve);
2735  }
2736 #endif
2737 #ifdef IBM
2738  dval(d) += 0; /* normalize */
2739 #endif
2740  if (!dval(d)) {
2741  *decpt = 1;
2742  return rv_strdup(ZEROSTR, rve);
2743  }
2744 
2745 #ifdef SET_INEXACT
2746  try_quick = oldinexact = get_inexact();
2747  inexact = 1;
2748 #endif
2749 #ifdef Honor_FLT_ROUNDS
2750  if ((rounding = Flt_Rounds) >= 2) {
2751  if (*sign)
2752  rounding = rounding == 2 ? 0 : 2;
2753  else
2754  if (rounding != 2)
2755  rounding = 0;
2756  }
2757 #endif
2758 
2759  b = d2b(dval(d), &be, &bbits);
2760 #ifdef Sudden_Underflow
2761  i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
2762 #else
2763  if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
2764 #endif
2765  dval(d2) = dval(d);
2766  word0(d2) &= Frac_mask1;
2767  word0(d2) |= Exp_11;
2768 #ifdef IBM
2769  if (j = 11 - hi0bits(word0(d2) & Frac_mask))
2770  dval(d2) /= 1 << j;
2771 #endif
2772 
2773  /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
2774  * log10(x) = log(x) / log(10)
2775  * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
2776  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
2777  *
2778  * This suggests computing an approximation k to log10(d) by
2779  *
2780  * k = (i - Bias)*0.301029995663981
2781  * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
2782  *
2783  * We want k to be too large rather than too small.
2784  * The error in the first-order Taylor series approximation
2785  * is in our favor, so we just round up the constant enough
2786  * to compensate for any error in the multiplication of
2787  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
2788  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
2789  * adding 1e-13 to the constant term more than suffices.
2790  * Hence we adjust the constant term to 0.1760912590558.
2791  * (We could get a more accurate k by invoking log10,
2792  * but this is probably not worthwhile.)
2793  */
2794 
2795  i -= Bias;
2796 #ifdef IBM
2797  i <<= 2;
2798  i += j;
2799 #endif
2800 #ifndef Sudden_Underflow
2801  denorm = 0;
2802  }
2803  else {
2804  /* d is denormalized */
2805 
2806  i = bbits + be + (Bias + (P-1) - 1);
2807  x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
2808  : word1(d) << (32 - i);
2809  dval(d2) = x;
2810  word0(d2) -= 31*Exp_msk1; /* adjust exponent */
2811  i -= (Bias + (P-1) - 1) + 1;
2812  denorm = 1;
2813  }
2814 #endif
2815  ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
2816  k = (int)ds;
2817  if (ds < 0. && ds != k)
2818  k--; /* want k = floor(ds) */
2819  k_check = 1;
2820  if (k >= 0 && k <= Ten_pmax) {
2821  if (dval(d) < tens[k])
2822  k--;
2823  k_check = 0;
2824  }
2825  j = bbits - i - 1;
2826  if (j >= 0) {
2827  b2 = 0;
2828  s2 = j;
2829  }
2830  else {
2831  b2 = -j;
2832  s2 = 0;
2833  }
2834  if (k >= 0) {
2835  b5 = 0;
2836  s5 = k;
2837  s2 += k;
2838  }
2839  else {
2840  b2 -= k;
2841  b5 = -k;
2842  s5 = 0;
2843  }
2844  if (mode < 0 || mode > 9)
2845  mode = 0;
2846 
2847 #ifndef SET_INEXACT
2848 #ifdef Check_FLT_ROUNDS
2849  try_quick = Rounding == 1;
2850 #else
2851  try_quick = 1;
2852 #endif
2853 #endif /*SET_INEXACT*/
2854 
2855  if (mode > 5) {
2856  mode -= 4;
2857  try_quick = 0;
2858  }
2859  leftright = 1;
2860  ilim = ilim1 = -1;
2861  switch (mode) {
2862  case 0:
2863  case 1:
2864  i = 18;
2865  ndigits = 0;
2866  break;
2867  case 2:
2868  leftright = 0;
2869  /* no break */
2870  case 4:
2871  if (ndigits <= 0)
2872  ndigits = 1;
2873  ilim = ilim1 = i = ndigits;
2874  break;
2875  case 3:
2876  leftright = 0;
2877  /* no break */
2878  case 5:
2879  i = ndigits + k + 1;
2880  ilim = i;
2881  ilim1 = i - 1;
2882  if (i <= 0)
2883  i = 1;
2884  }
2885  s = s0 = rv_alloc(i+1);
2886 
2887 #ifdef Honor_FLT_ROUNDS
2888  if (mode > 1 && rounding != 1)
2889  leftright = 0;
2890 #endif
2891 
2892  if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2893 
2894  /* Try to get by with floating-point arithmetic. */
2895 
2896  i = 0;
2897  dval(d2) = dval(d);
2898  k0 = k;
2899  ilim0 = ilim;
2900  ieps = 2; /* conservative */
2901  if (k > 0) {
2902  ds = tens[k&0xf];
2903  j = k >> 4;
2904  if (j & Bletch) {
2905  /* prevent overflows */
2906  j &= Bletch - 1;
2907  dval(d) /= bigtens[n_bigtens-1];
2908  ieps++;
2909  }
2910  for (; j; j >>= 1, i++)
2911  if (j & 1) {
2912  ieps++;
2913  ds *= bigtens[i];
2914  }
2915  dval(d) /= ds;
2916  }
2917  else if ((j1 = -k) != 0) {
2918  dval(d) *= tens[j1 & 0xf];
2919  for (j = j1 >> 4; j; j >>= 1, i++)
2920  if (j & 1) {
2921  ieps++;
2922  dval(d) *= bigtens[i];
2923  }
2924  }
2925  if (k_check && dval(d) < 1. && ilim > 0) {
2926  if (ilim1 <= 0)
2927  goto fast_failed;
2928  ilim = ilim1;
2929  k--;
2930  dval(d) *= 10.;
2931  ieps++;
2932  }
2933  dval(eps) = ieps*dval(d) + 7.;
2934  word0(eps) -= (P-1)*Exp_msk1;
2935  if (ilim == 0) {
2936  S = mhi = 0;
2937  dval(d) -= 5.;
2938  if (dval(d) > dval(eps))
2939  goto one_digit;
2940  if (dval(d) < -dval(eps))
2941  goto no_digits;
2942  goto fast_failed;
2943  }
2944 #ifndef No_leftright
2945  if (leftright) {
2946  /* Use Steele & White method of only
2947  * generating digits needed.
2948  */
2949  dval(eps) = 0.5/tens[ilim-1] - dval(eps);
2950  for (i = 0;;) {
2951  L = (int)dval(d);
2952  dval(d) -= L;
2953  *s++ = '0' + (int)L;
2954  if (dval(d) < dval(eps))
2955  goto ret1;
2956  if (1. - dval(d) < dval(eps))
2957  goto bump_up;
2958  if (++i >= ilim)
2959  break;
2960  dval(eps) *= 10.;
2961  dval(d) *= 10.;
2962  }
2963  }
2964  else {
2965 #endif
2966  /* Generate ilim digits, then fix them up. */
2967  dval(eps) *= tens[ilim-1];
2968  for (i = 1;; i++, dval(d) *= 10.) {
2969  L = (Long)(dval(d));
2970  if (!(dval(d) -= L))
2971  ilim = i;
2972  *s++ = '0' + (int)L;
2973  if (i == ilim) {
2974  if (dval(d) > 0.5 + dval(eps))
2975  goto bump_up;
2976  else if (dval(d) < 0.5 - dval(eps)) {
2977  while (*--s == '0') ;
2978  s++;
2979  goto ret1;
2980  }
2981  half = 1;
2982  if ((*(s-1) - '0') & 1) {
2983  goto bump_up;
2984  }
2985  break;
2986  }
2987  }
2988 #ifndef No_leftright
2989  }
2990 #endif
2991 fast_failed:
2992  s = s0;
2993  dval(d) = dval(d2);
2994  k = k0;
2995  ilim = ilim0;
2996  }
2997 
2998  /* Do we have a "small" integer? */
2999 
3000  if (be >= 0 && k <= Int_max) {
3001  /* Yes. */
3002  ds = tens[k];
3003  if (ndigits < 0 && ilim <= 0) {
3004  S = mhi = 0;
3005  if (ilim < 0 || dval(d) <= 5*ds)
3006  goto no_digits;
3007  goto one_digit;
3008  }
3009  for (i = 1;; i++, dval(d) *= 10.) {
3010  L = (Long)(dval(d) / ds);
3011  dval(d) -= L*ds;
3012 #ifdef Check_FLT_ROUNDS
3013  /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3014  if (dval(d) < 0) {
3015  L--;
3016  dval(d) += ds;
3017  }
3018 #endif
3019  *s++ = '0' + (int)L;
3020  if (!dval(d)) {
3021 #ifdef SET_INEXACT
3022  inexact = 0;
3023 #endif
3024  break;
3025  }
3026  if (i == ilim) {
3027 #ifdef Honor_FLT_ROUNDS
3028  if (mode > 1)
3029  switch (rounding) {
3030  case 0: goto ret1;
3031  case 2: goto bump_up;
3032  }
3033 #endif
3034  dval(d) += dval(d);
3035  if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3036 bump_up:
3037  while (*--s == '9')
3038  if (s == s0) {
3039  k++;
3040  *s = '0';
3041  break;
3042  }
3043  ++*s++;
3044  }
3045  break;
3046  }
3047  }
3048  goto ret1;
3049  }
3050 
3051  m2 = b2;
3052  m5 = b5;
3053  if (leftright) {
3054  i =
3055 #ifndef Sudden_Underflow
3056  denorm ? be + (Bias + (P-1) - 1 + 1) :
3057 #endif
3058 #ifdef IBM
3059  1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3060 #else
3061  1 + P - bbits;
3062 #endif
3063  b2 += i;
3064  s2 += i;
3065  mhi = i2b(1);
3066  }
3067  if (m2 > 0 && s2 > 0) {
3068  i = m2 < s2 ? m2 : s2;
3069  b2 -= i;
3070  m2 -= i;
3071  s2 -= i;
3072  }
3073  if (b5 > 0) {
3074  if (leftright) {
3075  if (m5 > 0) {
3076  mhi = pow5mult(mhi, m5);
3077  b1 = mult(mhi, b);
3078  Bfree(b);
3079  b = b1;
3080  }
3081  if ((j = b5 - m5) != 0)
3082  b = pow5mult(b, j);
3083  }
3084  else
3085  b = pow5mult(b, b5);
3086  }
3087  S = i2b(1);
3088  if (s5 > 0)
3089  S = pow5mult(S, s5);
3090 
3091  /* Check for special case that d is a normalized power of 2. */
3092 
3093  spec_case = 0;
3094  if ((mode < 2 || leftright)
3095 #ifdef Honor_FLT_ROUNDS
3096  && rounding == 1
3097 #endif
3098  ) {
3099  if (!word1(d) && !(word0(d) & Bndry_mask)
3100 #ifndef Sudden_Underflow
3101  && word0(d) & (Exp_mask & ~Exp_msk1)
3102 #endif
3103  ) {
3104  /* The special case */
3105  b2 += Log2P;
3106  s2 += Log2P;
3107  spec_case = 1;
3108  }
3109  }
3110 
3111  /* Arrange for convenient computation of quotients:
3112  * shift left if necessary so divisor has 4 leading 0 bits.
3113  *
3114  * Perhaps we should just compute leading 28 bits of S once
3115  * and for all and pass them and a shift to quorem, so it
3116  * can do shifts and ors to compute the numerator for q.
3117  */
3118 #ifdef Pack_32
3119  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3120  i = 32 - i;
3121 #else
3122  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3123  i = 16 - i;
3124 #endif
3125  if (i > 4) {
3126  i -= 4;
3127  b2 += i;
3128  m2 += i;
3129  s2 += i;
3130  }
3131  else if (i < 4) {
3132  i += 28;
3133  b2 += i;
3134  m2 += i;
3135  s2 += i;
3136  }
3137  if (b2 > 0)
3138  b = lshift(b, b2);
3139  if (s2 > 0)
3140  S = lshift(S, s2);
3141  if (k_check) {
3142  if (cmp(b,S) < 0) {
3143  k--;
3144  b = multadd(b, 10, 0); /* we botched the k estimate */
3145  if (leftright)
3146  mhi = multadd(mhi, 10, 0);
3147  ilim = ilim1;
3148  }
3149  }
3150  if (ilim <= 0 && (mode == 3 || mode == 5)) {
3151  if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3152  /* no digits, fcvt style */
3153 no_digits:
3154  k = -1 - ndigits;
3155  goto ret;
3156  }
3157 one_digit:
3158  *s++ = '1';
3159  k++;
3160  goto ret;
3161  }
3162  if (leftright) {
3163  if (m2 > 0)
3164  mhi = lshift(mhi, m2);
3165 
3166  /* Compute mlo -- check for special case
3167  * that d is a normalized power of 2.
3168  */
3169 
3170  mlo = mhi;
3171  if (spec_case) {
3172  mhi = Balloc(mhi->k);
3173  Bcopy(mhi, mlo);
3174  mhi = lshift(mhi, Log2P);
3175  }
3176 
3177  for (i = 1;;i++) {
3178  dig = quorem(b,S) + '0';
3179  /* Do we yet have the shortest decimal string
3180  * that will round to d?
3181  */
3182  j = cmp(b, mlo);
3183  delta = diff(S, mhi);
3184  j1 = delta->sign ? 1 : cmp(b, delta);
3185  Bfree(delta);
3186 #ifndef ROUND_BIASED
3187  if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3188 #ifdef Honor_FLT_ROUNDS
3189  && rounding >= 1
3190 #endif
3191  ) {
3192  if (dig == '9')
3193  goto round_9_up;
3194  if (j > 0)
3195  dig++;
3196 #ifdef SET_INEXACT
3197  else if (!b->x[0] && b->wds <= 1)
3198  inexact = 0;
3199 #endif
3200  *s++ = dig;
3201  goto ret;
3202  }
3203 #endif
3204  if (j < 0 || (j == 0 && mode != 1
3205 #ifndef ROUND_BIASED
3206  && !(word1(d) & 1)
3207 #endif
3208  )) {
3209  if (!b->x[0] && b->wds <= 1) {
3210 #ifdef SET_INEXACT
3211  inexact = 0;
3212 #endif
3213  goto accept_dig;
3214  }
3215 #ifdef Honor_FLT_ROUNDS
3216  if (mode > 1)
3217  switch (rounding) {
3218  case 0: goto accept_dig;
3219  case 2: goto keep_dig;
3220  }
3221 #endif /*Honor_FLT_ROUNDS*/
3222  if (j1 > 0) {
3223  b = lshift(b, 1);
3224  j1 = cmp(b, S);
3225  if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3226  goto round_9_up;
3227  }
3228 accept_dig:
3229  *s++ = dig;
3230  goto ret;
3231  }
3232  if (j1 > 0) {
3233 #ifdef Honor_FLT_ROUNDS
3234  if (!rounding)
3235  goto accept_dig;
3236 #endif
3237  if (dig == '9') { /* possible if i == 1 */
3238 round_9_up:
3239  *s++ = '9';
3240  goto roundoff;
3241  }
3242  *s++ = dig + 1;
3243  goto ret;
3244  }
3245 #ifdef Honor_FLT_ROUNDS
3246 keep_dig:
3247 #endif
3248  *s++ = dig;
3249  if (i == ilim)
3250  break;
3251  b = multadd(b, 10, 0);
3252  if (mlo == mhi)
3253  mlo = mhi = multadd(mhi, 10, 0);
3254  else {
3255  mlo = multadd(mlo, 10, 0);
3256  mhi = multadd(mhi, 10, 0);
3257  }
3258  }
3259  }
3260  else
3261  for (i = 1;; i++) {
3262  *s++ = dig = quorem(b,S) + '0';
3263  if (!b->x[0] && b->wds <= 1) {
3264 #ifdef SET_INEXACT
3265  inexact = 0;
3266 #endif
3267  goto ret;
3268  }
3269  if (i >= ilim)
3270  break;
3271  b = multadd(b, 10, 0);
3272  }
3273 
3274  /* Round off last digit */
3275 
3276 #ifdef Honor_FLT_ROUNDS
3277  switch (rounding) {
3278  case 0: goto trimzeros;
3279  case 2: goto roundoff;
3280  }
3281 #endif
3282  b = lshift(b, 1);
3283  j = cmp(b, S);
3284  if (j > 0 || (j == 0 && (dig & 1))) {
3285  roundoff:
3286  while (*--s == '9')
3287  if (s == s0) {
3288  k++;
3289  *s++ = '1';
3290  goto ret;
3291  }
3292  if (!half || (*s - '0') & 1)
3293  ++*s;
3294  }
3295  else {
3296  while (*--s == '0') ;
3297  }
3298  s++;
3299 ret:
3300  Bfree(S);
3301  if (mhi) {
3302  if (mlo && mlo != mhi)
3303  Bfree(mlo);
3304  Bfree(mhi);
3305  }
3306 ret1:
3307 #ifdef SET_INEXACT
3308  if (inexact) {
3309  if (!oldinexact) {
3310  word0(d) = Exp_1 + (70 << Exp_shift);
3311  word1(d) = 0;
3312  dval(d) += 1.;
3313  }
3314  }
3315  else if (!oldinexact)
3316  clear_inexact();
3317 #endif
3318  Bfree(b);
3319  *s = 0;
3320  *decpt = k + 1;
3321  if (rve)
3322  *rve = s;
3323  return s0;
3324 }
3325 
3326 /*-
3327  * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
3328  * All rights reserved.
3329  *
3330  * Redistribution and use in source and binary forms, with or without
3331  * modification, are permitted provided that the following conditions
3332  * are met:
3333  * 1. Redistributions of source code must retain the above copyright
3334  * notice, this list of conditions and the following disclaimer.
3335  * 2. Redistributions in binary form must reproduce the above copyright
3336  * notice, this list of conditions and the following disclaimer in the
3337  * documentation and/or other materials provided with the distribution.
3338  *
3339  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
3340  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
3341  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
3342  * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
3343  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
3344  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
3345  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
3346  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
3347  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
3348  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
3349  * SUCH DAMAGE.
3350  */
3351 
3352 #define DBL_MANH_SIZE 20
3353 #define DBL_MANL_SIZE 32
3354 #define DBL_ADJ (DBL_MAX_EXP - 2)
3355 #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3356 #define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3357 #define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3358 #define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3359 #define dmanl_get(u) ((uint32_t)word1(u))
3360 
3361 
3362 /*
3363  * This procedure converts a double-precision number in IEEE format
3364  * into a string of hexadecimal digits and an exponent of 2. Its
3365  * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
3366  * following exceptions:
3367  *
3368  * - An ndigits < 0 causes it to use as many digits as necessary to
3369  * represent the number exactly.
3370  * - The additional xdigs argument should point to either the string
3371  * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
3372  * which case is desired.
3373  * - This routine does not repeat dtoa's mistake of setting decpt
3374  * to 9999 in the case of an infinity or NaN. INT_MAX is used
3375  * for this purpose instead.
3376  *
3377  * Note that the C99 standard does not specify what the leading digit
3378  * should be for non-zero numbers. For instance, 0x1.3p3 is the same
3379  * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
3380  * the leading digit a 1. This ensures that the exponent printed is the
3381  * actual base-2 exponent, i.e., ilogb(d).
3382  *
3383  * Inputs: d, xdigs, ndigits
3384  * Outputs: decpt, sign, rve
3385  */
3386 char *
3387 hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve)
3388 {
3389  U u;
3390  char *s, *s0;
3391  int bufsize;
3392  uint32_t manh, manl;
3393 
3394  u.d = d;
3395  if (word0(u) & Sign_bit) {
3396  /* set sign for everything, including 0's and NaNs */
3397  *sign = 1;
3398  word0(u) &= ~Sign_bit; /* clear sign bit */
3399  }
3400  else
3401  *sign = 0;
3402 
3403  if (isinf(d)) { /* FP_INFINITE */
3404  *decpt = INT_MAX;
3405  return rv_strdup(INFSTR, rve);
3406  }
3407  else if (isnan(d)) { /* FP_NAN */
3408  *decpt = INT_MAX;
3409  return rv_strdup(NANSTR, rve);
3410  }
3411  else if (d == 0.0) { /* FP_ZERO */
3412  *decpt = 1;
3413  return rv_strdup(ZEROSTR, rve);
3414  }
3415  else if (dexp_get(u)) { /* FP_NORMAL */
3416  *decpt = dexp_get(u) - DBL_ADJ;
3417  }
3418  else { /* FP_SUBNORMAL */
3419  u.d *= 5.363123171977039e+154 /* 0x1p514 */;
3420  *decpt = dexp_get(u) - (514 + DBL_ADJ);
3421  }
3422 
3423  if (ndigits == 0) /* dtoa() compatibility */
3424  ndigits = 1;
3425 
3426  /*
3427  * If ndigits < 0, we are expected to auto-size, so we allocate
3428  * enough space for all the digits.
3429  */
3430  bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3431  s0 = rv_alloc(bufsize+1);
3432 
3433  /* Round to the desired number of digits. */
3434  if (SIGFIGS > ndigits && ndigits > 0) {
3435  float redux = 1.0f;
3436  int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3437  dexp_set(u, offset);
3438  u.d += redux;
3439  u.d -= redux;
3440  *decpt += dexp_get(u) - offset;
3441  }
3442 
3443  manh = dmanh_get(u);
3444  manl = dmanl_get(u);
3445  *s0 = '1';
3446  for (s = s0 + 1; s < s0 + bufsize; s++) {
3447  *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3448  manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3449  manl <<= 4;
3450  }
3451 
3452  /* If ndigits < 0, we are expected to auto-size the precision. */
3453  if (ndigits < 0) {
3454  for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
3455  ;
3456  }
3457 
3458  s = s0 + ndigits;
3459  *s = '\0';
3460  if (rve != NULL)
3461  *rve = s;
3462  return (s0);
3463 }
3464 
3465 #ifdef __cplusplus
3466 #if 0
3467 { /* satisfy cc-mode */
3468 #endif
3469 }
3470 #endif
#define ISDIGIT
Old name of rb_isdigit.
Definition: ctype.h:93
#define ASSUME
Old name of RBIMPL_ASSUME.
Definition: assume.h:29
#define strtod(s, e)
Just another name of ruby_strtod.
Definition: util.h:212
Definition: dtoa.c:519
Definition: dtoa.c:302