Ruby  2.0.0p594(2014-10-27revision48167)
util.c
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1 /**********************************************************************
2 
3  util.c -
4 
5  $Author: nagachika $
6  created at: Fri Mar 10 17:22:34 JST 1995
7 
8  Copyright (C) 1993-2008 Yukihiro Matsumoto
9 
10 **********************************************************************/
11 
12 #include "ruby/ruby.h"
13 #include "internal.h"
14 
15 #include <ctype.h>
16 #include <stdio.h>
17 #include <errno.h>
18 #include <math.h>
19 #include <float.h>
20 
21 #ifdef _WIN32
22 #include "missing/file.h"
23 #endif
24 
25 #include "ruby/util.h"
26 
27 unsigned long
28 ruby_scan_oct(const char *start, size_t len, size_t *retlen)
29 {
30  register const char *s = start;
31  register unsigned long retval = 0;
32 
33  while (len-- && *s >= '0' && *s <= '7') {
34  retval <<= 3;
35  retval |= *s++ - '0';
36  }
37  *retlen = (int)(s - start); /* less than len */
38  return retval;
39 }
40 
41 unsigned long
42 ruby_scan_hex(const char *start, size_t len, size_t *retlen)
43 {
44  static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
45  register const char *s = start;
46  register unsigned long retval = 0;
47  const char *tmp;
48 
49  while (len-- && *s && (tmp = strchr(hexdigit, *s))) {
50  retval <<= 4;
51  retval |= (tmp - hexdigit) & 15;
52  s++;
53  }
54  *retlen = (int)(s - start); /* less than len */
55  return retval;
56 }
57 
58 static unsigned long
59 scan_digits(const char *str, int base, size_t *retlen, int *overflow)
60 {
61  static signed char table[] = {
62  /* 0 1 2 3 4 5 6 7 8 9 a b c d e f */
63  /*0*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
64  /*1*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
65  /*2*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
66  /*3*/ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,-1,-1,-1,-1,-1,-1,
67  /*4*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
68  /*5*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
69  /*6*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
70  /*7*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
71  /*8*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
72  /*9*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
73  /*a*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
74  /*b*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
75  /*c*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
76  /*d*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
77  /*e*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
78  /*f*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
79  };
80 
81  const char *start = str;
82  unsigned long ret = 0, x;
83  unsigned long mul_overflow = (~(unsigned long)0) / base;
84  int c;
85  *overflow = 0;
86 
87  while ((c = (unsigned char)*str++) != '\0') {
88  int d = table[c];
89  if (d == -1 || base <= d) {
90  *retlen = (str-1) - start;
91  return ret;
92  }
93  if (mul_overflow < ret)
94  *overflow = 1;
95  ret *= base;
96  x = ret;
97  ret += d;
98  if (ret < x)
99  *overflow = 1;
100  }
101  *retlen = (str-1) - start;
102  return ret;
103 }
104 
105 unsigned long
106 ruby_strtoul(const char *str, char **endptr, int base)
107 {
108  int c, b, overflow;
109  int sign = 0;
110  size_t len;
111  unsigned long ret;
112  const char *subject_found = str;
113 
114  if (base == 1 || 36 < base) {
115  errno = EINVAL;
116  return 0;
117  }
118 
119  while ((c = *str) && ISSPACE(c))
120  str++;
121 
122  if (c == '+') {
123  sign = 1;
124  str++;
125  }
126  else if (c == '-') {
127  sign = -1;
128  str++;
129  }
130 
131  if (str[0] == '0') {
132  subject_found = str+1;
133  if (base == 0 || base == 16) {
134  if (str[1] == 'x' || str[1] == 'X') {
135  b = 16;
136  str += 2;
137  }
138  else {
139  b = base == 0 ? 8 : 16;
140  str++;
141  }
142  }
143  else {
144  b = base;
145  str++;
146  }
147  }
148  else {
149  b = base == 0 ? 10 : base;
150  }
151 
152  ret = scan_digits(str, b, &len, &overflow);
153 
154  if (0 < len)
155  subject_found = str+len;
156 
157  if (endptr)
158  *endptr = (char*)subject_found;
159 
160  if (overflow) {
161  errno = ERANGE;
162  return ULONG_MAX;
163  }
164 
165  if (sign < 0) {
166  ret = (unsigned long)(-(long)ret);
167  return ret;
168  }
169  else {
170  return ret;
171  }
172 }
173 
174 #include <sys/types.h>
175 #include <sys/stat.h>
176 #ifdef HAVE_UNISTD_H
177 #include <unistd.h>
178 #endif
179 #if defined(HAVE_FCNTL_H)
180 #include <fcntl.h>
181 #endif
182 
183 #ifndef S_ISDIR
184 # define S_ISDIR(m) (((m) & S_IFMT) == S_IFDIR)
185 #endif
186 
187 
188 /* mm.c */
189 
190 #define mmtype long
191 #define mmcount (16 / SIZEOF_LONG)
192 #define A ((mmtype*)a)
193 #define B ((mmtype*)b)
194 #define C ((mmtype*)c)
195 #define D ((mmtype*)d)
196 
197 #define mmstep (sizeof(mmtype) * mmcount)
198 #define mmprepare(base, size) do {\
199  if (((VALUE)(base) % sizeof(mmtype)) == 0 && ((size) % sizeof(mmtype)) == 0) \
200  if ((size) >= mmstep) mmkind = 1;\
201  else mmkind = 0;\
202  else mmkind = -1;\
203  high = ((size) / mmstep) * mmstep;\
204  low = ((size) % mmstep);\
205 } while (0)\
206 
207 #define mmarg mmkind, size, high, low
208 #define mmargdecl int mmkind, size_t size, size_t high, size_t low
209 
210 static void mmswap_(register char *a, register char *b, mmargdecl)
211 {
212  if (a == b) return;
213  if (mmkind >= 0) {
214  register mmtype s;
215 #if mmcount > 1
216  if (mmkind > 0) {
217  register char *t = a + high;
218  do {
219  s = A[0]; A[0] = B[0]; B[0] = s;
220  s = A[1]; A[1] = B[1]; B[1] = s;
221 #if mmcount > 2
222  s = A[2]; A[2] = B[2]; B[2] = s;
223 #if mmcount > 3
224  s = A[3]; A[3] = B[3]; B[3] = s;
225 #endif
226 #endif
227  a += mmstep; b += mmstep;
228  } while (a < t);
229  }
230 #endif
231  if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = s;
232 #if mmcount > 2
233  if (low >= 2 * sizeof(mmtype)) { s = A[1]; A[1] = B[1]; B[1] = s;
234 #if mmcount > 3
235  if (low >= 3 * sizeof(mmtype)) {s = A[2]; A[2] = B[2]; B[2] = s;}
236 #endif
237  }
238 #endif
239  }
240  }
241  else {
242  register char *t = a + size, s;
243  do {s = *a; *a++ = *b; *b++ = s;} while (a < t);
244  }
245 }
246 #define mmswap(a,b) mmswap_((a),(b),mmarg)
247 
248 /* a, b, c = b, c, a */
249 static void mmrot3_(register char *a, register char *b, register char *c, mmargdecl)
250 {
251  if (mmkind >= 0) {
252  register mmtype s;
253 #if mmcount > 1
254  if (mmkind > 0) {
255  register char *t = a + high;
256  do {
257  s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
258  s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
259 #if mmcount > 2
260  s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;
261 #if mmcount > 3
262  s = A[3]; A[3] = B[3]; B[3] = C[3]; C[3] = s;
263 #endif
264 #endif
265  a += mmstep; b += mmstep; c += mmstep;
266  } while (a < t);
267  }
268 #endif
269  if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
270 #if mmcount > 2
271  if (low >= 2 * sizeof(mmtype)) { s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
272 #if mmcount > 3
273  if (low == 3 * sizeof(mmtype)) {s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;}
274 #endif
275  }
276 #endif
277  }
278  }
279  else {
280  register char *t = a + size, s;
281  do {s = *a; *a++ = *b; *b++ = *c; *c++ = s;} while (a < t);
282  }
283 }
284 #define mmrot3(a,b,c) mmrot3_((a),(b),(c),mmarg)
285 
286 /* qs6.c */
287 /*****************************************************/
288 /* */
289 /* qs6 (Quick sort function) */
290 /* */
291 /* by Tomoyuki Kawamura 1995.4.21 */
292 /* kawamura@tokuyama.ac.jp */
293 /*****************************************************/
294 
295 typedef struct { char *LL, *RR; } stack_node; /* Stack structure for L,l,R,r */
296 #define PUSH(ll,rr) do { top->LL = (ll); top->RR = (rr); ++top; } while (0) /* Push L,l,R,r */
297 #define POP(ll,rr) do { --top; (ll) = top->LL; (rr) = top->RR; } while (0) /* Pop L,l,R,r */
298 
299 #define med3(a,b,c) ((*cmp)((a),(b),d)<0 ? \
300  ((*cmp)((b),(c),d)<0 ? (b) : ((*cmp)((a),(c),d)<0 ? (c) : (a))) : \
301  ((*cmp)((b),(c),d)>0 ? (b) : ((*cmp)((a),(c),d)<0 ? (a) : (c))))
302 
303 typedef int (cmpfunc_t)(const void*, const void*, void*);
304 void
305 ruby_qsort(void* base, const size_t nel, const size_t size, cmpfunc_t *cmp, void *d)
306 {
307  register char *l, *r, *m; /* l,r:left,right group m:median point */
308  register int t, eq_l, eq_r; /* eq_l: all items in left group are equal to S */
309  char *L = base; /* left end of current region */
310  char *R = (char*)base + size*(nel-1); /* right end of current region */
311  size_t chklim = 63; /* threshold of ordering element check */
312  enum {size_bits = sizeof(size) * CHAR_BIT};
313  stack_node stack[size_bits]; /* enough for size_t size */
314  stack_node *top = stack;
315  int mmkind;
316  size_t high, low, n;
317 
318  if (nel <= 1) return; /* need not to sort */
319  mmprepare(base, size);
320  goto start;
321 
322  nxt:
323  if (stack == top) return; /* return if stack is empty */
324  POP(L,R);
325 
326  for (;;) {
327  start:
328  if (L + size == R) { /* 2 elements */
329  if ((*cmp)(L,R,d) > 0) mmswap(L,R); goto nxt;
330  }
331 
332  l = L; r = R;
333  n = (r - l + size) / size; /* number of elements */
334  m = l + size * (n >> 1); /* calculate median value */
335 
336  if (n >= 60) {
337  register char *m1;
338  register char *m3;
339  if (n >= 200) {
340  n = size*(n>>3); /* number of bytes in splitting 8 */
341  {
342  register char *p1 = l + n;
343  register char *p2 = p1 + n;
344  register char *p3 = p2 + n;
345  m1 = med3(p1, p2, p3);
346  p1 = m + n;
347  p2 = p1 + n;
348  p3 = p2 + n;
349  m3 = med3(p1, p2, p3);
350  }
351  }
352  else {
353  n = size*(n>>2); /* number of bytes in splitting 4 */
354  m1 = l + n;
355  m3 = m + n;
356  }
357  m = med3(m1, m, m3);
358  }
359 
360  if ((t = (*cmp)(l,m,d)) < 0) { /*3-5-?*/
361  if ((t = (*cmp)(m,r,d)) < 0) { /*3-5-7*/
362  if (chklim && nel >= chklim) { /* check if already ascending order */
363  char *p;
364  chklim = 0;
365  for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) > 0) goto fail;
366  goto nxt;
367  }
368  fail: goto loopA; /*3-5-7*/
369  }
370  if (t > 0) {
371  if ((*cmp)(l,r,d) <= 0) {mmswap(m,r); goto loopA;} /*3-5-4*/
372  mmrot3(r,m,l); goto loopA; /*3-5-2*/
373  }
374  goto loopB; /*3-5-5*/
375  }
376 
377  if (t > 0) { /*7-5-?*/
378  if ((t = (*cmp)(m,r,d)) > 0) { /*7-5-3*/
379  if (chklim && nel >= chklim) { /* check if already ascending order */
380  char *p;
381  chklim = 0;
382  for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) < 0) goto fail2;
383  while (l<r) {mmswap(l,r); l+=size; r-=size;} /* reverse region */
384  goto nxt;
385  }
386  fail2: mmswap(l,r); goto loopA; /*7-5-3*/
387  }
388  if (t < 0) {
389  if ((*cmp)(l,r,d) <= 0) {mmswap(l,m); goto loopB;} /*7-5-8*/
390  mmrot3(l,m,r); goto loopA; /*7-5-6*/
391  }
392  mmswap(l,r); goto loopA; /*7-5-5*/
393  }
394 
395  if ((t = (*cmp)(m,r,d)) < 0) {goto loopA;} /*5-5-7*/
396  if (t > 0) {mmswap(l,r); goto loopB;} /*5-5-3*/
397 
398  /* determining splitting type in case 5-5-5 */ /*5-5-5*/
399  for (;;) {
400  if ((l += size) == r) goto nxt; /*5-5-5*/
401  if (l == m) continue;
402  if ((t = (*cmp)(l,m,d)) > 0) {mmswap(l,r); l = L; goto loopA;}/*575-5*/
403  if (t < 0) {mmswap(L,l); l = L; goto loopB;} /*535-5*/
404  }
405 
406  loopA: eq_l = 1; eq_r = 1; /* splitting type A */ /* left <= median < right */
407  for (;;) {
408  for (;;) {
409  if ((l += size) == r)
410  {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
411  if (l == m) continue;
412  if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
413  if (t < 0) eq_l = 0;
414  }
415  for (;;) {
416  if (l == (r -= size))
417  {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
418  if (r == m) {m = l; break;}
419  if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
420  if (t == 0) break;
421  }
422  mmswap(l,r); /* swap left and right */
423  }
424 
425  loopB: eq_l = 1; eq_r = 1; /* splitting type B */ /* left < median <= right */
426  for (;;) {
427  for (;;) {
428  if (l == (r -= size))
429  {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
430  if (r == m) continue;
431  if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
432  if (t > 0) eq_r = 0;
433  }
434  for (;;) {
435  if ((l += size) == r)
436  {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
437  if (l == m) {m = r; break;}
438  if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
439  if (t == 0) break;
440  }
441  mmswap(l,r); /* swap left and right */
442  }
443 
444  fin:
445  if (eq_l == 0) /* need to sort left side */
446  if (eq_r == 0) /* need to sort right side */
447  if (l-L < R-r) {PUSH(r,R); R = l;} /* sort left side first */
448  else {PUSH(L,l); L = r;} /* sort right side first */
449  else R = l; /* need to sort left side only */
450  else if (eq_r == 0) L = r; /* need to sort right side only */
451  else goto nxt; /* need not to sort both sides */
452  }
453 }
454 
455 char *
456 ruby_strdup(const char *str)
457 {
458  char *tmp;
459  size_t len = strlen(str) + 1;
460 
461  tmp = xmalloc(len);
462  memcpy(tmp, str, len);
463 
464  return tmp;
465 }
466 
467 #ifdef __native_client__
468 char *
469 ruby_getcwd(void)
470 {
471  char *buf = xmalloc(2);
472  strcpy(buf, ".");
473  return buf;
474 }
475 #else
476 char *
478 {
479 #ifdef HAVE_GETCWD
480  int size = 200;
481  char *buf = xmalloc(size);
482 
483  while (!getcwd(buf, size)) {
484  if (errno != ERANGE) {
485  xfree(buf);
486  rb_sys_fail("getcwd");
487  }
488  size *= 2;
489  buf = xrealloc(buf, size);
490  }
491 #else
492 # ifndef PATH_MAX
493 # define PATH_MAX 8192
494 # endif
495  char *buf = xmalloc(PATH_MAX+1);
496 
497  if (!getwd(buf)) {
498  xfree(buf);
499  rb_sys_fail("getwd");
500  }
501 #endif
502  return buf;
503 }
504 #endif
505 
506 /****************************************************************
507  *
508  * The author of this software is David M. Gay.
509  *
510  * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
511  *
512  * Permission to use, copy, modify, and distribute this software for any
513  * purpose without fee is hereby granted, provided that this entire notice
514  * is included in all copies of any software which is or includes a copy
515  * or modification of this software and in all copies of the supporting
516  * documentation for such software.
517  *
518  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
519  * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
520  * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
521  * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
522  *
523  ***************************************************************/
524 
525 /* Please send bug reports to David M. Gay (dmg at acm dot org,
526  * with " at " changed at "@" and " dot " changed to "."). */
527 
528 /* On a machine with IEEE extended-precision registers, it is
529  * necessary to specify double-precision (53-bit) rounding precision
530  * before invoking strtod or dtoa. If the machine uses (the equivalent
531  * of) Intel 80x87 arithmetic, the call
532  * _control87(PC_53, MCW_PC);
533  * does this with many compilers. Whether this or another call is
534  * appropriate depends on the compiler; for this to work, it may be
535  * necessary to #include "float.h" or another system-dependent header
536  * file.
537  */
538 
539 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
540  *
541  * This strtod returns a nearest machine number to the input decimal
542  * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
543  * broken by the IEEE round-even rule. Otherwise ties are broken by
544  * biased rounding (add half and chop).
545  *
546  * Inspired loosely by William D. Clinger's paper "How to Read Floating
547  * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
548  *
549  * Modifications:
550  *
551  * 1. We only require IEEE, IBM, or VAX double-precision
552  * arithmetic (not IEEE double-extended).
553  * 2. We get by with floating-point arithmetic in a case that
554  * Clinger missed -- when we're computing d * 10^n
555  * for a small integer d and the integer n is not too
556  * much larger than 22 (the maximum integer k for which
557  * we can represent 10^k exactly), we may be able to
558  * compute (d*10^k) * 10^(e-k) with just one roundoff.
559  * 3. Rather than a bit-at-a-time adjustment of the binary
560  * result in the hard case, we use floating-point
561  * arithmetic to determine the adjustment to within
562  * one bit; only in really hard cases do we need to
563  * compute a second residual.
564  * 4. Because of 3., we don't need a large table of powers of 10
565  * for ten-to-e (just some small tables, e.g. of 10^k
566  * for 0 <= k <= 22).
567  */
568 
569 /*
570  * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
571  * significant byte has the lowest address.
572  * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
573  * significant byte has the lowest address.
574  * #define Long int on machines with 32-bit ints and 64-bit longs.
575  * #define IBM for IBM mainframe-style floating-point arithmetic.
576  * #define VAX for VAX-style floating-point arithmetic (D_floating).
577  * #define No_leftright to omit left-right logic in fast floating-point
578  * computation of dtoa.
579  * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
580  * and strtod and dtoa should round accordingly.
581  * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
582  * and Honor_FLT_ROUNDS is not #defined.
583  * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
584  * that use extended-precision instructions to compute rounded
585  * products and quotients) with IBM.
586  * #define ROUND_BIASED for IEEE-format with biased rounding.
587  * #define Inaccurate_Divide for IEEE-format with correctly rounded
588  * products but inaccurate quotients, e.g., for Intel i860.
589  * #define NO_LONG_LONG on machines that do not have a "long long"
590  * integer type (of >= 64 bits). On such machines, you can
591  * #define Just_16 to store 16 bits per 32-bit Long when doing
592  * high-precision integer arithmetic. Whether this speeds things
593  * up or slows things down depends on the machine and the number
594  * being converted. If long long is available and the name is
595  * something other than "long long", #define Llong to be the name,
596  * and if "unsigned Llong" does not work as an unsigned version of
597  * Llong, #define #ULLong to be the corresponding unsigned type.
598  * #define KR_headers for old-style C function headers.
599  * #define Bad_float_h if your system lacks a float.h or if it does not
600  * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
601  * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
602  * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
603  * if memory is available and otherwise does something you deem
604  * appropriate. If MALLOC is undefined, malloc will be invoked
605  * directly -- and assumed always to succeed.
606  * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
607  * memory allocations from a private pool of memory when possible.
608  * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
609  * unless #defined to be a different length. This default length
610  * suffices to get rid of MALLOC calls except for unusual cases,
611  * such as decimal-to-binary conversion of a very long string of
612  * digits. The longest string dtoa can return is about 751 bytes
613  * long. For conversions by strtod of strings of 800 digits and
614  * all dtoa conversions in single-threaded executions with 8-byte
615  * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
616  * pointers, PRIVATE_MEM >= 7112 appears adequate.
617  * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
618  * Infinity and NaN (case insensitively). On some systems (e.g.,
619  * some HP systems), it may be necessary to #define NAN_WORD0
620  * appropriately -- to the most significant word of a quiet NaN.
621  * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
622  * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
623  * strtod also accepts (case insensitively) strings of the form
624  * NaN(x), where x is a string of hexadecimal digits and spaces;
625  * if there is only one string of hexadecimal digits, it is taken
626  * for the 52 fraction bits of the resulting NaN; if there are two
627  * or more strings of hex digits, the first is for the high 20 bits,
628  * the second and subsequent for the low 32 bits, with intervening
629  * white space ignored; but if this results in none of the 52
630  * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
631  * and NAN_WORD1 are used instead.
632  * #define MULTIPLE_THREADS if the system offers preemptively scheduled
633  * multiple threads. In this case, you must provide (or suitably
634  * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
635  * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
636  * in pow5mult, ensures lazy evaluation of only one copy of high
637  * powers of 5; omitting this lock would introduce a small
638  * probability of wasting memory, but would otherwise be harmless.)
639  * You must also invoke freedtoa(s) to free the value s returned by
640  * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
641  * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
642  * avoids underflows on inputs whose result does not underflow.
643  * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
644  * floating-point numbers and flushes underflows to zero rather
645  * than implementing gradual underflow, then you must also #define
646  * Sudden_Underflow.
647  * #define YES_ALIAS to permit aliasing certain double values with
648  * arrays of ULongs. This leads to slightly better code with
649  * some compilers and was always used prior to 19990916, but it
650  * is not strictly legal and can cause trouble with aggressively
651  * optimizing compilers (e.g., gcc 2.95.1 under -O2).
652  * #define USE_LOCALE to use the current locale's decimal_point value.
653  * #define SET_INEXACT if IEEE arithmetic is being used and extra
654  * computation should be done to set the inexact flag when the
655  * result is inexact and avoid setting inexact when the result
656  * is exact. In this case, dtoa.c must be compiled in
657  * an environment, perhaps provided by #include "dtoa.c" in a
658  * suitable wrapper, that defines two functions,
659  * int get_inexact(void);
660  * void clear_inexact(void);
661  * such that get_inexact() returns a nonzero value if the
662  * inexact bit is already set, and clear_inexact() sets the
663  * inexact bit to 0. When SET_INEXACT is #defined, strtod
664  * also does extra computations to set the underflow and overflow
665  * flags when appropriate (i.e., when the result is tiny and
666  * inexact or when it is a numeric value rounded to +-infinity).
667  * #define NO_ERRNO if strtod should not assign errno = ERANGE when
668  * the result overflows to +-Infinity or underflows to 0.
669  */
670 
671 #ifdef WORDS_BIGENDIAN
672 #define IEEE_BIG_ENDIAN
673 #else
674 #define IEEE_LITTLE_ENDIAN
675 #endif
676 
677 #ifdef __vax__
678 #define VAX
679 #undef IEEE_BIG_ENDIAN
680 #undef IEEE_LITTLE_ENDIAN
681 #endif
682 
683 #if defined(__arm__) && !defined(__VFP_FP__)
684 #define IEEE_BIG_ENDIAN
685 #undef IEEE_LITTLE_ENDIAN
686 #endif
687 
688 #undef Long
689 #undef ULong
690 
691 #if SIZEOF_INT == 4
692 #define Long int
693 #define ULong unsigned int
694 #elif SIZEOF_LONG == 4
695 #define Long long int
696 #define ULong unsigned long int
697 #endif
698 
699 #if HAVE_LONG_LONG
700 #define Llong LONG_LONG
701 #endif
702 
703 #ifdef DEBUG
704 #include "stdio.h"
705 #define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
706 #endif
707 
708 #include "stdlib.h"
709 #include "string.h"
710 
711 #ifdef USE_LOCALE
712 #include "locale.h"
713 #endif
714 
715 #ifdef MALLOC
716 extern void *MALLOC(size_t);
717 #else
718 #define MALLOC malloc
719 #endif
720 #ifdef FREE
721 extern void FREE(void*);
722 #else
723 #define FREE free
724 #endif
725 
726 #ifndef Omit_Private_Memory
727 #ifndef PRIVATE_MEM
728 #define PRIVATE_MEM 2304
729 #endif
730 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
732 #endif
733 
734 #undef IEEE_Arith
735 #undef Avoid_Underflow
736 #ifdef IEEE_BIG_ENDIAN
737 #define IEEE_Arith
738 #endif
739 #ifdef IEEE_LITTLE_ENDIAN
740 #define IEEE_Arith
741 #endif
742 
743 #ifdef Bad_float_h
744 
745 #ifdef IEEE_Arith
746 #define DBL_DIG 15
747 #define DBL_MAX_10_EXP 308
748 #define DBL_MAX_EXP 1024
749 #define FLT_RADIX 2
750 #endif /*IEEE_Arith*/
751 
752 #ifdef IBM
753 #define DBL_DIG 16
754 #define DBL_MAX_10_EXP 75
755 #define DBL_MAX_EXP 63
756 #define FLT_RADIX 16
757 #define DBL_MAX 7.2370055773322621e+75
758 #endif
759 
760 #ifdef VAX
761 #define DBL_DIG 16
762 #define DBL_MAX_10_EXP 38
763 #define DBL_MAX_EXP 127
764 #define FLT_RADIX 2
765 #define DBL_MAX 1.7014118346046923e+38
766 #endif
767 
768 #ifndef LONG_MAX
769 #define LONG_MAX 2147483647
770 #endif
771 
772 #else /* ifndef Bad_float_h */
773 #include "float.h"
774 #endif /* Bad_float_h */
775 
776 #ifndef __MATH_H__
777 #include "math.h"
778 #endif
779 
780 #ifdef __cplusplus
781 extern "C" {
782 #if 0
783 } /* satisfy cc-mode */
784 #endif
785 #endif
786 
787 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
788 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
789 #endif
790 
791 typedef union { double d; ULong L[2]; } U;
792 
793 #ifdef YES_ALIAS
794 typedef double double_u;
795 # define dval(x) (x)
796 # ifdef IEEE_LITTLE_ENDIAN
797 # define word0(x) (((ULong *)&(x))[1])
798 # define word1(x) (((ULong *)&(x))[0])
799 # else
800 # define word0(x) (((ULong *)&(x))[0])
801 # define word1(x) (((ULong *)&(x))[1])
802 # endif
803 #else
804 typedef U double_u;
805 # ifdef IEEE_LITTLE_ENDIAN
806 # define word0(x) ((x).L[1])
807 # define word1(x) ((x).L[0])
808 # else
809 # define word0(x) ((x).L[0])
810 # define word1(x) ((x).L[1])
811 # endif
812 # define dval(x) ((x).d)
813 #endif
814 
815 /* The following definition of Storeinc is appropriate for MIPS processors.
816  * An alternative that might be better on some machines is
817  * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
818  */
819 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
820 #define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
821 ((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
822 #else
823 #define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
824 ((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
825 #endif
826 
827 /* #define P DBL_MANT_DIG */
828 /* Ten_pmax = floor(P*log(2)/log(5)) */
829 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
830 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
831 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
832 
833 #ifdef IEEE_Arith
834 #define Exp_shift 20
835 #define Exp_shift1 20
836 #define Exp_msk1 0x100000
837 #define Exp_msk11 0x100000
838 #define Exp_mask 0x7ff00000
839 #define P 53
840 #define Bias 1023
841 #define Emin (-1022)
842 #define Exp_1 0x3ff00000
843 #define Exp_11 0x3ff00000
844 #define Ebits 11
845 #define Frac_mask 0xfffff
846 #define Frac_mask1 0xfffff
847 #define Ten_pmax 22
848 #define Bletch 0x10
849 #define Bndry_mask 0xfffff
850 #define Bndry_mask1 0xfffff
851 #define LSB 1
852 #define Sign_bit 0x80000000
853 #define Log2P 1
854 #define Tiny0 0
855 #define Tiny1 1
856 #define Quick_max 14
857 #define Int_max 14
858 #ifndef NO_IEEE_Scale
859 #define Avoid_Underflow
860 #ifdef Flush_Denorm /* debugging option */
861 #undef Sudden_Underflow
862 #endif
863 #endif
864 
865 #ifndef Flt_Rounds
866 #ifdef FLT_ROUNDS
867 #define Flt_Rounds FLT_ROUNDS
868 #else
869 #define Flt_Rounds 1
870 #endif
871 #endif /*Flt_Rounds*/
872 
873 #ifdef Honor_FLT_ROUNDS
874 #define Rounding rounding
875 #undef Check_FLT_ROUNDS
876 #define Check_FLT_ROUNDS
877 #else
878 #define Rounding Flt_Rounds
879 #endif
880 
881 #else /* ifndef IEEE_Arith */
882 #undef Check_FLT_ROUNDS
883 #undef Honor_FLT_ROUNDS
884 #undef SET_INEXACT
885 #undef Sudden_Underflow
886 #define Sudden_Underflow
887 #ifdef IBM
888 #undef Flt_Rounds
889 #define Flt_Rounds 0
890 #define Exp_shift 24
891 #define Exp_shift1 24
892 #define Exp_msk1 0x1000000
893 #define Exp_msk11 0x1000000
894 #define Exp_mask 0x7f000000
895 #define P 14
896 #define Bias 65
897 #define Exp_1 0x41000000
898 #define Exp_11 0x41000000
899 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
900 #define Frac_mask 0xffffff
901 #define Frac_mask1 0xffffff
902 #define Bletch 4
903 #define Ten_pmax 22
904 #define Bndry_mask 0xefffff
905 #define Bndry_mask1 0xffffff
906 #define LSB 1
907 #define Sign_bit 0x80000000
908 #define Log2P 4
909 #define Tiny0 0x100000
910 #define Tiny1 0
911 #define Quick_max 14
912 #define Int_max 15
913 #else /* VAX */
914 #undef Flt_Rounds
915 #define Flt_Rounds 1
916 #define Exp_shift 23
917 #define Exp_shift1 7
918 #define Exp_msk1 0x80
919 #define Exp_msk11 0x800000
920 #define Exp_mask 0x7f80
921 #define P 56
922 #define Bias 129
923 #define Exp_1 0x40800000
924 #define Exp_11 0x4080
925 #define Ebits 8
926 #define Frac_mask 0x7fffff
927 #define Frac_mask1 0xffff007f
928 #define Ten_pmax 24
929 #define Bletch 2
930 #define Bndry_mask 0xffff007f
931 #define Bndry_mask1 0xffff007f
932 #define LSB 0x10000
933 #define Sign_bit 0x8000
934 #define Log2P 1
935 #define Tiny0 0x80
936 #define Tiny1 0
937 #define Quick_max 15
938 #define Int_max 15
939 #endif /* IBM, VAX */
940 #endif /* IEEE_Arith */
941 
942 #ifndef IEEE_Arith
943 #define ROUND_BIASED
944 #endif
945 
946 #ifdef RND_PRODQUOT
947 #define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
948 #define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
949 extern double rnd_prod(double, double), rnd_quot(double, double);
950 #else
951 #define rounded_product(a,b) ((a) *= (b))
952 #define rounded_quotient(a,b) ((a) /= (b))
953 #endif
954 
955 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
956 #define Big1 0xffffffff
957 
958 #ifndef Pack_32
959 #define Pack_32
960 #endif
961 
962 #define FFFFFFFF 0xffffffffUL
963 
964 #ifdef NO_LONG_LONG
965 #undef ULLong
966 #ifdef Just_16
967 #undef Pack_32
968 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
969  * This makes some inner loops simpler and sometimes saves work
970  * during multiplications, but it often seems to make things slightly
971  * slower. Hence the default is now to store 32 bits per Long.
972  */
973 #endif
974 #else /* long long available */
975 #ifndef Llong
976 #define Llong long long
977 #endif
978 #ifndef ULLong
979 #define ULLong unsigned Llong
980 #endif
981 #endif /* NO_LONG_LONG */
982 
983 #define MULTIPLE_THREADS 1
984 
985 #ifndef MULTIPLE_THREADS
986 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
987 #define FREE_DTOA_LOCK(n) /*nothing*/
988 #else
989 #define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
990 #define FREE_DTOA_LOCK(n) /*unused right now*/
991 #endif
992 
993 #define Kmax 15
994 
995 struct Bigint {
996  struct Bigint *next;
997  int k, maxwds, sign, wds;
998  ULong x[1];
999 };
1000 
1001 typedef struct Bigint Bigint;
1002 
1003 static Bigint *freelist[Kmax+1];
1004 
1005 static Bigint *
1006 Balloc(int k)
1007 {
1008  int x;
1009  Bigint *rv;
1010 #ifndef Omit_Private_Memory
1011  size_t len;
1012 #endif
1013 
1014  ACQUIRE_DTOA_LOCK(0);
1015  if (k <= Kmax && (rv = freelist[k]) != 0) {
1016  freelist[k] = rv->next;
1017  }
1018  else {
1019  x = 1 << k;
1020 #ifdef Omit_Private_Memory
1021  rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
1022 #else
1023  len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
1024  /sizeof(double);
1025  if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
1026  rv = (Bigint*)pmem_next;
1027  pmem_next += len;
1028  }
1029  else
1030  rv = (Bigint*)MALLOC(len*sizeof(double));
1031 #endif
1032  rv->k = k;
1033  rv->maxwds = x;
1034  }
1035  FREE_DTOA_LOCK(0);
1036  rv->sign = rv->wds = 0;
1037  return rv;
1038 }
1039 
1040 static void
1042 {
1043  if (v) {
1044  if (v->k > Kmax) {
1045  FREE(v);
1046  return;
1047  }
1048  ACQUIRE_DTOA_LOCK(0);
1049  v->next = freelist[v->k];
1050  freelist[v->k] = v;
1051  FREE_DTOA_LOCK(0);
1052  }
1053 }
1054 
1055 #define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
1056 (y)->wds*sizeof(Long) + 2*sizeof(int))
1057 
1058 static Bigint *
1059 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
1060 {
1061  int i, wds;
1062  ULong *x;
1063 #ifdef ULLong
1064  ULLong carry, y;
1065 #else
1066  ULong carry, y;
1067 #ifdef Pack_32
1068  ULong xi, z;
1069 #endif
1070 #endif
1071  Bigint *b1;
1072 
1073  wds = b->wds;
1074  x = b->x;
1075  i = 0;
1076  carry = a;
1077  do {
1078 #ifdef ULLong
1079  y = *x * (ULLong)m + carry;
1080  carry = y >> 32;
1081  *x++ = (ULong)(y & FFFFFFFF);
1082 #else
1083 #ifdef Pack_32
1084  xi = *x;
1085  y = (xi & 0xffff) * m + carry;
1086  z = (xi >> 16) * m + (y >> 16);
1087  carry = z >> 16;
1088  *x++ = (z << 16) + (y & 0xffff);
1089 #else
1090  y = *x * m + carry;
1091  carry = y >> 16;
1092  *x++ = y & 0xffff;
1093 #endif
1094 #endif
1095  } while (++i < wds);
1096  if (carry) {
1097  if (wds >= b->maxwds) {
1098  b1 = Balloc(b->k+1);
1099  Bcopy(b1, b);
1100  Bfree(b);
1101  b = b1;
1102  }
1103  b->x[wds++] = (ULong)carry;
1104  b->wds = wds;
1105  }
1106  return b;
1107 }
1108 
1109 static Bigint *
1110 s2b(const char *s, int nd0, int nd, ULong y9)
1111 {
1112  Bigint *b;
1113  int i, k;
1114  Long x, y;
1115 
1116  x = (nd + 8) / 9;
1117  for (k = 0, y = 1; x > y; y <<= 1, k++) ;
1118 #ifdef Pack_32
1119  b = Balloc(k);
1120  b->x[0] = y9;
1121  b->wds = 1;
1122 #else
1123  b = Balloc(k+1);
1124  b->x[0] = y9 & 0xffff;
1125  b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
1126 #endif
1127 
1128  i = 9;
1129  if (9 < nd0) {
1130  s += 9;
1131  do {
1132  b = multadd(b, 10, *s++ - '0');
1133  } while (++i < nd0);
1134  s++;
1135  }
1136  else
1137  s += 10;
1138  for (; i < nd; i++)
1139  b = multadd(b, 10, *s++ - '0');
1140  return b;
1141 }
1142 
1143 static int
1144 hi0bits(register ULong x)
1145 {
1146  register int k = 0;
1147 
1148  if (!(x & 0xffff0000)) {
1149  k = 16;
1150  x <<= 16;
1151  }
1152  if (!(x & 0xff000000)) {
1153  k += 8;
1154  x <<= 8;
1155  }
1156  if (!(x & 0xf0000000)) {
1157  k += 4;
1158  x <<= 4;
1159  }
1160  if (!(x & 0xc0000000)) {
1161  k += 2;
1162  x <<= 2;
1163  }
1164  if (!(x & 0x80000000)) {
1165  k++;
1166  if (!(x & 0x40000000))
1167  return 32;
1168  }
1169  return k;
1170 }
1171 
1172 static int
1173 lo0bits(ULong *y)
1174 {
1175  register int k;
1176  register ULong x = *y;
1177 
1178  if (x & 7) {
1179  if (x & 1)
1180  return 0;
1181  if (x & 2) {
1182  *y = x >> 1;
1183  return 1;
1184  }
1185  *y = x >> 2;
1186  return 2;
1187  }
1188  k = 0;
1189  if (!(x & 0xffff)) {
1190  k = 16;
1191  x >>= 16;
1192  }
1193  if (!(x & 0xff)) {
1194  k += 8;
1195  x >>= 8;
1196  }
1197  if (!(x & 0xf)) {
1198  k += 4;
1199  x >>= 4;
1200  }
1201  if (!(x & 0x3)) {
1202  k += 2;
1203  x >>= 2;
1204  }
1205  if (!(x & 1)) {
1206  k++;
1207  x >>= 1;
1208  if (!x)
1209  return 32;
1210  }
1211  *y = x;
1212  return k;
1213 }
1214 
1215 static Bigint *
1216 i2b(int i)
1217 {
1218  Bigint *b;
1219 
1220  b = Balloc(1);
1221  b->x[0] = i;
1222  b->wds = 1;
1223  return b;
1224 }
1225 
1226 static Bigint *
1228 {
1229  Bigint *c;
1230  int k, wa, wb, wc;
1231  ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
1232  ULong y;
1233 #ifdef ULLong
1234  ULLong carry, z;
1235 #else
1236  ULong carry, z;
1237 #ifdef Pack_32
1238  ULong z2;
1239 #endif
1240 #endif
1241 
1242  if (a->wds < b->wds) {
1243  c = a;
1244  a = b;
1245  b = c;
1246  }
1247  k = a->k;
1248  wa = a->wds;
1249  wb = b->wds;
1250  wc = wa + wb;
1251  if (wc > a->maxwds)
1252  k++;
1253  c = Balloc(k);
1254  for (x = c->x, xa = x + wc; x < xa; x++)
1255  *x = 0;
1256  xa = a->x;
1257  xae = xa + wa;
1258  xb = b->x;
1259  xbe = xb + wb;
1260  xc0 = c->x;
1261 #ifdef ULLong
1262  for (; xb < xbe; xc0++) {
1263  if ((y = *xb++) != 0) {
1264  x = xa;
1265  xc = xc0;
1266  carry = 0;
1267  do {
1268  z = *x++ * (ULLong)y + *xc + carry;
1269  carry = z >> 32;
1270  *xc++ = (ULong)(z & FFFFFFFF);
1271  } while (x < xae);
1272  *xc = (ULong)carry;
1273  }
1274  }
1275 #else
1276 #ifdef Pack_32
1277  for (; xb < xbe; xb++, xc0++) {
1278  if (y = *xb & 0xffff) {
1279  x = xa;
1280  xc = xc0;
1281  carry = 0;
1282  do {
1283  z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
1284  carry = z >> 16;
1285  z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
1286  carry = z2 >> 16;
1287  Storeinc(xc, z2, z);
1288  } while (x < xae);
1289  *xc = (ULong)carry;
1290  }
1291  if (y = *xb >> 16) {
1292  x = xa;
1293  xc = xc0;
1294  carry = 0;
1295  z2 = *xc;
1296  do {
1297  z = (*x & 0xffff) * y + (*xc >> 16) + carry;
1298  carry = z >> 16;
1299  Storeinc(xc, z, z2);
1300  z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
1301  carry = z2 >> 16;
1302  } while (x < xae);
1303  *xc = z2;
1304  }
1305  }
1306 #else
1307  for (; xb < xbe; xc0++) {
1308  if (y = *xb++) {
1309  x = xa;
1310  xc = xc0;
1311  carry = 0;
1312  do {
1313  z = *x++ * y + *xc + carry;
1314  carry = z >> 16;
1315  *xc++ = z & 0xffff;
1316  } while (x < xae);
1317  *xc = (ULong)carry;
1318  }
1319  }
1320 #endif
1321 #endif
1322  for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
1323  c->wds = wc;
1324  return c;
1325 }
1326 
1327 static Bigint *p5s;
1328 
1329 static Bigint *
1331 {
1332  Bigint *b1, *p5, *p51;
1333  int i;
1334  static int p05[3] = { 5, 25, 125 };
1335 
1336  if ((i = k & 3) != 0)
1337  b = multadd(b, p05[i-1], 0);
1338 
1339  if (!(k >>= 2))
1340  return b;
1341  if (!(p5 = p5s)) {
1342  /* first time */
1343 #ifdef MULTIPLE_THREADS
1344  ACQUIRE_DTOA_LOCK(1);
1345  if (!(p5 = p5s)) {
1346  p5 = p5s = i2b(625);
1347  p5->next = 0;
1348  }
1349  FREE_DTOA_LOCK(1);
1350 #else
1351  p5 = p5s = i2b(625);
1352  p5->next = 0;
1353 #endif
1354  }
1355  for (;;) {
1356  if (k & 1) {
1357  b1 = mult(b, p5);
1358  Bfree(b);
1359  b = b1;
1360  }
1361  if (!(k >>= 1))
1362  break;
1363  if (!(p51 = p5->next)) {
1364 #ifdef MULTIPLE_THREADS
1365  ACQUIRE_DTOA_LOCK(1);
1366  if (!(p51 = p5->next)) {
1367  p51 = p5->next = mult(p5,p5);
1368  p51->next = 0;
1369  }
1370  FREE_DTOA_LOCK(1);
1371 #else
1372  p51 = p5->next = mult(p5,p5);
1373  p51->next = 0;
1374 #endif
1375  }
1376  p5 = p51;
1377  }
1378  return b;
1379 }
1380 
1381 static Bigint *
1383 {
1384  int i, k1, n, n1;
1385  Bigint *b1;
1386  ULong *x, *x1, *xe, z;
1387 
1388 #ifdef Pack_32
1389  n = k >> 5;
1390 #else
1391  n = k >> 4;
1392 #endif
1393  k1 = b->k;
1394  n1 = n + b->wds + 1;
1395  for (i = b->maxwds; n1 > i; i <<= 1)
1396  k1++;
1397  b1 = Balloc(k1);
1398  x1 = b1->x;
1399  for (i = 0; i < n; i++)
1400  *x1++ = 0;
1401  x = b->x;
1402  xe = x + b->wds;
1403 #ifdef Pack_32
1404  if (k &= 0x1f) {
1405  k1 = 32 - k;
1406  z = 0;
1407  do {
1408  *x1++ = *x << k | z;
1409  z = *x++ >> k1;
1410  } while (x < xe);
1411  if ((*x1 = z) != 0)
1412  ++n1;
1413  }
1414 #else
1415  if (k &= 0xf) {
1416  k1 = 16 - k;
1417  z = 0;
1418  do {
1419  *x1++ = *x << k & 0xffff | z;
1420  z = *x++ >> k1;
1421  } while (x < xe);
1422  if (*x1 = z)
1423  ++n1;
1424  }
1425 #endif
1426  else
1427  do {
1428  *x1++ = *x++;
1429  } while (x < xe);
1430  b1->wds = n1 - 1;
1431  Bfree(b);
1432  return b1;
1433 }
1434 
1435 static int
1437 {
1438  ULong *xa, *xa0, *xb, *xb0;
1439  int i, j;
1440 
1441  i = a->wds;
1442  j = b->wds;
1443 #ifdef DEBUG
1444  if (i > 1 && !a->x[i-1])
1445  Bug("cmp called with a->x[a->wds-1] == 0");
1446  if (j > 1 && !b->x[j-1])
1447  Bug("cmp called with b->x[b->wds-1] == 0");
1448 #endif
1449  if (i -= j)
1450  return i;
1451  xa0 = a->x;
1452  xa = xa0 + j;
1453  xb0 = b->x;
1454  xb = xb0 + j;
1455  for (;;) {
1456  if (*--xa != *--xb)
1457  return *xa < *xb ? -1 : 1;
1458  if (xa <= xa0)
1459  break;
1460  }
1461  return 0;
1462 }
1463 
1464 static Bigint *
1466 {
1467  Bigint *c;
1468  int i, wa, wb;
1469  ULong *xa, *xae, *xb, *xbe, *xc;
1470 #ifdef ULLong
1471  ULLong borrow, y;
1472 #else
1473  ULong borrow, y;
1474 #ifdef Pack_32
1475  ULong z;
1476 #endif
1477 #endif
1478 
1479  i = cmp(a,b);
1480  if (!i) {
1481  c = Balloc(0);
1482  c->wds = 1;
1483  c->x[0] = 0;
1484  return c;
1485  }
1486  if (i < 0) {
1487  c = a;
1488  a = b;
1489  b = c;
1490  i = 1;
1491  }
1492  else
1493  i = 0;
1494  c = Balloc(a->k);
1495  c->sign = i;
1496  wa = a->wds;
1497  xa = a->x;
1498  xae = xa + wa;
1499  wb = b->wds;
1500  xb = b->x;
1501  xbe = xb + wb;
1502  xc = c->x;
1503  borrow = 0;
1504 #ifdef ULLong
1505  do {
1506  y = (ULLong)*xa++ - *xb++ - borrow;
1507  borrow = y >> 32 & (ULong)1;
1508  *xc++ = (ULong)(y & FFFFFFFF);
1509  } while (xb < xbe);
1510  while (xa < xae) {
1511  y = *xa++ - borrow;
1512  borrow = y >> 32 & (ULong)1;
1513  *xc++ = (ULong)(y & FFFFFFFF);
1514  }
1515 #else
1516 #ifdef Pack_32
1517  do {
1518  y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1519  borrow = (y & 0x10000) >> 16;
1520  z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1521  borrow = (z & 0x10000) >> 16;
1522  Storeinc(xc, z, y);
1523  } while (xb < xbe);
1524  while (xa < xae) {
1525  y = (*xa & 0xffff) - borrow;
1526  borrow = (y & 0x10000) >> 16;
1527  z = (*xa++ >> 16) - borrow;
1528  borrow = (z & 0x10000) >> 16;
1529  Storeinc(xc, z, y);
1530  }
1531 #else
1532  do {
1533  y = *xa++ - *xb++ - borrow;
1534  borrow = (y & 0x10000) >> 16;
1535  *xc++ = y & 0xffff;
1536  } while (xb < xbe);
1537  while (xa < xae) {
1538  y = *xa++ - borrow;
1539  borrow = (y & 0x10000) >> 16;
1540  *xc++ = y & 0xffff;
1541  }
1542 #endif
1543 #endif
1544  while (!*--xc)
1545  wa--;
1546  c->wds = wa;
1547  return c;
1548 }
1549 
1550 static double
1551 ulp(double x_)
1552 {
1553  register Long L;
1554  double_u x, a;
1555  dval(x) = x_;
1556 
1557  L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1558 #ifndef Avoid_Underflow
1559 #ifndef Sudden_Underflow
1560  if (L > 0) {
1561 #endif
1562 #endif
1563 #ifdef IBM
1564  L |= Exp_msk1 >> 4;
1565 #endif
1566  word0(a) = L;
1567  word1(a) = 0;
1568 #ifndef Avoid_Underflow
1569 #ifndef Sudden_Underflow
1570  }
1571  else {
1572  L = -L >> Exp_shift;
1573  if (L < Exp_shift) {
1574  word0(a) = 0x80000 >> L;
1575  word1(a) = 0;
1576  }
1577  else {
1578  word0(a) = 0;
1579  L -= Exp_shift;
1580  word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1581  }
1582  }
1583 #endif
1584 #endif
1585  return dval(a);
1586 }
1587 
1588 static double
1589 b2d(Bigint *a, int *e)
1590 {
1591  ULong *xa, *xa0, w, y, z;
1592  int k;
1593  double_u d;
1594 #ifdef VAX
1595  ULong d0, d1;
1596 #else
1597 #define d0 word0(d)
1598 #define d1 word1(d)
1599 #endif
1600 
1601  xa0 = a->x;
1602  xa = xa0 + a->wds;
1603  y = *--xa;
1604 #ifdef DEBUG
1605  if (!y) Bug("zero y in b2d");
1606 #endif
1607  k = hi0bits(y);
1608  *e = 32 - k;
1609 #ifdef Pack_32
1610  if (k < Ebits) {
1611  d0 = Exp_1 | y >> (Ebits - k);
1612  w = xa > xa0 ? *--xa : 0;
1613  d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1614  goto ret_d;
1615  }
1616  z = xa > xa0 ? *--xa : 0;
1617  if (k -= Ebits) {
1618  d0 = Exp_1 | y << k | z >> (32 - k);
1619  y = xa > xa0 ? *--xa : 0;
1620  d1 = z << k | y >> (32 - k);
1621  }
1622  else {
1623  d0 = Exp_1 | y;
1624  d1 = z;
1625  }
1626 #else
1627  if (k < Ebits + 16) {
1628  z = xa > xa0 ? *--xa : 0;
1629  d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1630  w = xa > xa0 ? *--xa : 0;
1631  y = xa > xa0 ? *--xa : 0;
1632  d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1633  goto ret_d;
1634  }
1635  z = xa > xa0 ? *--xa : 0;
1636  w = xa > xa0 ? *--xa : 0;
1637  k -= Ebits + 16;
1638  d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1639  y = xa > xa0 ? *--xa : 0;
1640  d1 = w << k + 16 | y << k;
1641 #endif
1642 ret_d:
1643 #ifdef VAX
1644  word0(d) = d0 >> 16 | d0 << 16;
1645  word1(d) = d1 >> 16 | d1 << 16;
1646 #else
1647 #undef d0
1648 #undef d1
1649 #endif
1650  return dval(d);
1651 }
1652 
1653 static Bigint *
1654 d2b(double d_, int *e, int *bits)
1655 {
1656  double_u d;
1657  Bigint *b;
1658  int de, k;
1659  ULong *x, y, z;
1660 #ifndef Sudden_Underflow
1661  int i;
1662 #endif
1663 #ifdef VAX
1664  ULong d0, d1;
1665 #endif
1666  dval(d) = d_;
1667 #ifdef VAX
1668  d0 = word0(d) >> 16 | word0(d) << 16;
1669  d1 = word1(d) >> 16 | word1(d) << 16;
1670 #else
1671 #define d0 word0(d)
1672 #define d1 word1(d)
1673 #endif
1674 
1675 #ifdef Pack_32
1676  b = Balloc(1);
1677 #else
1678  b = Balloc(2);
1679 #endif
1680  x = b->x;
1681 
1682  z = d0 & Frac_mask;
1683  d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1684 #ifdef Sudden_Underflow
1685  de = (int)(d0 >> Exp_shift);
1686 #ifndef IBM
1687  z |= Exp_msk11;
1688 #endif
1689 #else
1690  if ((de = (int)(d0 >> Exp_shift)) != 0)
1691  z |= Exp_msk1;
1692 #endif
1693 #ifdef Pack_32
1694  if ((y = d1) != 0) {
1695  if ((k = lo0bits(&y)) != 0) {
1696  x[0] = y | z << (32 - k);
1697  z >>= k;
1698  }
1699  else
1700  x[0] = y;
1701 #ifndef Sudden_Underflow
1702  i =
1703 #endif
1704  b->wds = (x[1] = z) ? 2 : 1;
1705  }
1706  else {
1707 #ifdef DEBUG
1708  if (!z)
1709  Bug("Zero passed to d2b");
1710 #endif
1711  k = lo0bits(&z);
1712  x[0] = z;
1713 #ifndef Sudden_Underflow
1714  i =
1715 #endif
1716  b->wds = 1;
1717  k += 32;
1718  }
1719 #else
1720  if (y = d1) {
1721  if (k = lo0bits(&y))
1722  if (k >= 16) {
1723  x[0] = y | z << 32 - k & 0xffff;
1724  x[1] = z >> k - 16 & 0xffff;
1725  x[2] = z >> k;
1726  i = 2;
1727  }
1728  else {
1729  x[0] = y & 0xffff;
1730  x[1] = y >> 16 | z << 16 - k & 0xffff;
1731  x[2] = z >> k & 0xffff;
1732  x[3] = z >> k+16;
1733  i = 3;
1734  }
1735  else {
1736  x[0] = y & 0xffff;
1737  x[1] = y >> 16;
1738  x[2] = z & 0xffff;
1739  x[3] = z >> 16;
1740  i = 3;
1741  }
1742  }
1743  else {
1744 #ifdef DEBUG
1745  if (!z)
1746  Bug("Zero passed to d2b");
1747 #endif
1748  k = lo0bits(&z);
1749  if (k >= 16) {
1750  x[0] = z;
1751  i = 0;
1752  }
1753  else {
1754  x[0] = z & 0xffff;
1755  x[1] = z >> 16;
1756  i = 1;
1757  }
1758  k += 32;
1759  }
1760  while (!x[i])
1761  --i;
1762  b->wds = i + 1;
1763 #endif
1764 #ifndef Sudden_Underflow
1765  if (de) {
1766 #endif
1767 #ifdef IBM
1768  *e = (de - Bias - (P-1) << 2) + k;
1769  *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1770 #else
1771  *e = de - Bias - (P-1) + k;
1772  *bits = P - k;
1773 #endif
1774 #ifndef Sudden_Underflow
1775  }
1776  else {
1777  *e = de - Bias - (P-1) + 1 + k;
1778 #ifdef Pack_32
1779  *bits = 32*i - hi0bits(x[i-1]);
1780 #else
1781  *bits = (i+2)*16 - hi0bits(x[i]);
1782 #endif
1783  }
1784 #endif
1785  return b;
1786 }
1787 #undef d0
1788 #undef d1
1789 
1790 static double
1792 {
1793  double_u da, db;
1794  int k, ka, kb;
1795 
1796  dval(da) = b2d(a, &ka);
1797  dval(db) = b2d(b, &kb);
1798 #ifdef Pack_32
1799  k = ka - kb + 32*(a->wds - b->wds);
1800 #else
1801  k = ka - kb + 16*(a->wds - b->wds);
1802 #endif
1803 #ifdef IBM
1804  if (k > 0) {
1805  word0(da) += (k >> 2)*Exp_msk1;
1806  if (k &= 3)
1807  dval(da) *= 1 << k;
1808  }
1809  else {
1810  k = -k;
1811  word0(db) += (k >> 2)*Exp_msk1;
1812  if (k &= 3)
1813  dval(db) *= 1 << k;
1814  }
1815 #else
1816  if (k > 0)
1817  word0(da) += k*Exp_msk1;
1818  else {
1819  k = -k;
1820  word0(db) += k*Exp_msk1;
1821  }
1822 #endif
1823  return dval(da) / dval(db);
1824 }
1825 
1826 static const double
1827 tens[] = {
1828  1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1829  1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1830  1e20, 1e21, 1e22
1831 #ifdef VAX
1832  , 1e23, 1e24
1833 #endif
1834 };
1835 
1836 static const double
1837 #ifdef IEEE_Arith
1838 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1839 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1840 #ifdef Avoid_Underflow
1841  9007199254740992.*9007199254740992.e-256
1842  /* = 2^106 * 1e-53 */
1843 #else
1844  1e-256
1845 #endif
1846 };
1847 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1848 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1849 #define Scale_Bit 0x10
1850 #define n_bigtens 5
1851 #else
1852 #ifdef IBM
1853 bigtens[] = { 1e16, 1e32, 1e64 };
1854 static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1855 #define n_bigtens 3
1856 #else
1857 bigtens[] = { 1e16, 1e32 };
1858 static const double tinytens[] = { 1e-16, 1e-32 };
1859 #define n_bigtens 2
1860 #endif
1861 #endif
1862 
1863 #ifndef IEEE_Arith
1864 #undef INFNAN_CHECK
1865 #endif
1866 
1867 #ifdef INFNAN_CHECK
1868 
1869 #ifndef NAN_WORD0
1870 #define NAN_WORD0 0x7ff80000
1871 #endif
1872 
1873 #ifndef NAN_WORD1
1874 #define NAN_WORD1 0
1875 #endif
1876 
1877 static int
1878 match(const char **sp, char *t)
1879 {
1880  int c, d;
1881  const char *s = *sp;
1882 
1883  while (d = *t++) {
1884  if ((c = *++s) >= 'A' && c <= 'Z')
1885  c += 'a' - 'A';
1886  if (c != d)
1887  return 0;
1888  }
1889  *sp = s + 1;
1890  return 1;
1891 }
1892 
1893 #ifndef No_Hex_NaN
1894 static void
1895 hexnan(double *rvp, const char **sp)
1896 {
1897  ULong c, x[2];
1898  const char *s;
1899  int havedig, udx0, xshift;
1900 
1901  x[0] = x[1] = 0;
1902  havedig = xshift = 0;
1903  udx0 = 1;
1904  s = *sp;
1905  while (c = *(const unsigned char*)++s) {
1906  if (c >= '0' && c <= '9')
1907  c -= '0';
1908  else if (c >= 'a' && c <= 'f')
1909  c += 10 - 'a';
1910  else if (c >= 'A' && c <= 'F')
1911  c += 10 - 'A';
1912  else if (c <= ' ') {
1913  if (udx0 && havedig) {
1914  udx0 = 0;
1915  xshift = 1;
1916  }
1917  continue;
1918  }
1919  else if (/*(*/ c == ')' && havedig) {
1920  *sp = s + 1;
1921  break;
1922  }
1923  else
1924  return; /* invalid form: don't change *sp */
1925  havedig = 1;
1926  if (xshift) {
1927  xshift = 0;
1928  x[0] = x[1];
1929  x[1] = 0;
1930  }
1931  if (udx0)
1932  x[0] = (x[0] << 4) | (x[1] >> 28);
1933  x[1] = (x[1] << 4) | c;
1934  }
1935  if ((x[0] &= 0xfffff) || x[1]) {
1936  word0(*rvp) = Exp_mask | x[0];
1937  word1(*rvp) = x[1];
1938  }
1939 }
1940 #endif /*No_Hex_NaN*/
1941 #endif /* INFNAN_CHECK */
1942 
1943 double
1944 ruby_strtod(const char *s00, char **se)
1945 {
1946 #ifdef Avoid_Underflow
1947  int scale;
1948 #endif
1949  int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1950  e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1951  const char *s, *s0, *s1;
1952  double aadj, adj;
1953  double_u aadj1, rv, rv0;
1954  Long L;
1955  ULong y, z;
1956  Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1957 #ifdef SET_INEXACT
1958  int inexact, oldinexact;
1959 #endif
1960 #ifdef Honor_FLT_ROUNDS
1961  int rounding;
1962 #endif
1963 #ifdef USE_LOCALE
1964  const char *s2;
1965 #endif
1966 
1967  errno = 0;
1968  sign = nz0 = nz = 0;
1969  dval(rv) = 0.;
1970  for (s = s00;;s++)
1971  switch (*s) {
1972  case '-':
1973  sign = 1;
1974  /* no break */
1975  case '+':
1976  if (*++s)
1977  goto break2;
1978  /* no break */
1979  case 0:
1980  goto ret0;
1981  case '\t':
1982  case '\n':
1983  case '\v':
1984  case '\f':
1985  case '\r':
1986  case ' ':
1987  continue;
1988  default:
1989  goto break2;
1990  }
1991 break2:
1992  if (*s == '0') {
1993  if (s[1] == 'x' || s[1] == 'X') {
1994  static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
1995  s0 = ++s;
1996  adj = 0;
1997  aadj = 1.0;
1998  nd0 = -4;
1999 
2000  if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
2001  if (*s == '0') {
2002  while (*++s == '0');
2003  s1 = strchr(hexdigit, *s);
2004  }
2005  if (s1 != NULL) {
2006  do {
2007  adj += aadj * ((s1 - hexdigit) & 15);
2008  nd0 += 4;
2009  aadj /= 16;
2010  } while (*++s && (s1 = strchr(hexdigit, *s)));
2011  }
2012 
2013  if (*s == '.') {
2014  dsign = 1;
2015  if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
2016  if (nd0 < 0) {
2017  while (*s == '0') {
2018  s++;
2019  nd0 -= 4;
2020  }
2021  }
2022  for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
2023  adj += aadj * ((s1 - hexdigit) & 15);
2024  if ((aadj /= 16) == 0.0) {
2025  while (strchr(hexdigit, *++s));
2026  break;
2027  }
2028  }
2029  }
2030  else {
2031  dsign = 0;
2032  }
2033 
2034  if (*s == 'P' || *s == 'p') {
2035  dsign = 0x2C - *++s; /* +: 2B, -: 2D */
2036  if (abs(dsign) == 1) s++;
2037  else dsign = 1;
2038 
2039  nd = 0;
2040  c = *s;
2041  if (c < '0' || '9' < c) goto ret0;
2042  do {
2043  nd *= 10;
2044  nd += c;
2045  nd -= '0';
2046  c = *++s;
2047  /* Float("0x0."+("0"*267)+"1fp2095") */
2048  if (nd + dsign * nd0 > 2095) {
2049  while ('0' <= c && c <= '9') c = *++s;
2050  break;
2051  }
2052  } while ('0' <= c && c <= '9');
2053  nd0 += nd * dsign;
2054  }
2055  else {
2056  if (dsign) goto ret0;
2057  }
2058  dval(rv) = ldexp(adj, nd0);
2059  goto ret;
2060  }
2061  nz0 = 1;
2062  while (*++s == '0') ;
2063  if (!*s)
2064  goto ret;
2065  }
2066  s0 = s;
2067  y = z = 0;
2068  for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
2069  if (nd < 9)
2070  y = 10*y + c - '0';
2071  else if (nd < 16)
2072  z = 10*z + c - '0';
2073  nd0 = nd;
2074 #ifdef USE_LOCALE
2075  s1 = localeconv()->decimal_point;
2076  if (c == *s1) {
2077  c = '.';
2078  if (*++s1) {
2079  s2 = s;
2080  for (;;) {
2081  if (*++s2 != *s1) {
2082  c = 0;
2083  break;
2084  }
2085  if (!*++s1) {
2086  s = s2;
2087  break;
2088  }
2089  }
2090  }
2091  }
2092 #endif
2093  if (c == '.') {
2094  if (!ISDIGIT(s[1]))
2095  goto dig_done;
2096  c = *++s;
2097  if (!nd) {
2098  for (; c == '0'; c = *++s)
2099  nz++;
2100  if (c > '0' && c <= '9') {
2101  s0 = s;
2102  nf += nz;
2103  nz = 0;
2104  goto have_dig;
2105  }
2106  goto dig_done;
2107  }
2108  for (; c >= '0' && c <= '9'; c = *++s) {
2109 have_dig:
2110  nz++;
2111  if (nf > DBL_DIG * 4) continue;
2112  if (c -= '0') {
2113  nf += nz;
2114  for (i = 1; i < nz; i++)
2115  if (nd++ < 9)
2116  y *= 10;
2117  else if (nd <= DBL_DIG + 1)
2118  z *= 10;
2119  if (nd++ < 9)
2120  y = 10*y + c;
2121  else if (nd <= DBL_DIG + 1)
2122  z = 10*z + c;
2123  nz = 0;
2124  }
2125  }
2126  }
2127 dig_done:
2128  e = 0;
2129  if (c == 'e' || c == 'E') {
2130  if (!nd && !nz && !nz0) {
2131  goto ret0;
2132  }
2133  s00 = s;
2134  esign = 0;
2135  switch (c = *++s) {
2136  case '-':
2137  esign = 1;
2138  case '+':
2139  c = *++s;
2140  }
2141  if (c >= '0' && c <= '9') {
2142  while (c == '0')
2143  c = *++s;
2144  if (c > '0' && c <= '9') {
2145  L = c - '0';
2146  s1 = s;
2147  while ((c = *++s) >= '0' && c <= '9')
2148  L = 10*L + c - '0';
2149  if (s - s1 > 8 || L > 19999)
2150  /* Avoid confusion from exponents
2151  * so large that e might overflow.
2152  */
2153  e = 19999; /* safe for 16 bit ints */
2154  else
2155  e = (int)L;
2156  if (esign)
2157  e = -e;
2158  }
2159  else
2160  e = 0;
2161  }
2162  else
2163  s = s00;
2164  }
2165  if (!nd) {
2166  if (!nz && !nz0) {
2167 #ifdef INFNAN_CHECK
2168  /* Check for Nan and Infinity */
2169  switch (c) {
2170  case 'i':
2171  case 'I':
2172  if (match(&s,"nf")) {
2173  --s;
2174  if (!match(&s,"inity"))
2175  ++s;
2176  word0(rv) = 0x7ff00000;
2177  word1(rv) = 0;
2178  goto ret;
2179  }
2180  break;
2181  case 'n':
2182  case 'N':
2183  if (match(&s, "an")) {
2184  word0(rv) = NAN_WORD0;
2185  word1(rv) = NAN_WORD1;
2186 #ifndef No_Hex_NaN
2187  if (*s == '(') /*)*/
2188  hexnan(&rv, &s);
2189 #endif
2190  goto ret;
2191  }
2192  }
2193 #endif /* INFNAN_CHECK */
2194 ret0:
2195  s = s00;
2196  sign = 0;
2197  }
2198  goto ret;
2199  }
2200  e1 = e -= nf;
2201 
2202  /* Now we have nd0 digits, starting at s0, followed by a
2203  * decimal point, followed by nd-nd0 digits. The number we're
2204  * after is the integer represented by those digits times
2205  * 10**e */
2206 
2207  if (!nd0)
2208  nd0 = nd;
2209  k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2210  dval(rv) = y;
2211  if (k > 9) {
2212 #ifdef SET_INEXACT
2213  if (k > DBL_DIG)
2214  oldinexact = get_inexact();
2215 #endif
2216  dval(rv) = tens[k - 9] * dval(rv) + z;
2217  }
2218  bd0 = bb = bd = bs = delta = 0;
2219  if (nd <= DBL_DIG
2220 #ifndef RND_PRODQUOT
2221 #ifndef Honor_FLT_ROUNDS
2222  && Flt_Rounds == 1
2223 #endif
2224 #endif
2225  ) {
2226  if (!e)
2227  goto ret;
2228  if (e > 0) {
2229  if (e <= Ten_pmax) {
2230 #ifdef VAX
2231  goto vax_ovfl_check;
2232 #else
2233 #ifdef Honor_FLT_ROUNDS
2234  /* round correctly FLT_ROUNDS = 2 or 3 */
2235  if (sign) {
2236  dval(rv) = -dval(rv);
2237  sign = 0;
2238  }
2239 #endif
2240  /* rv = */ rounded_product(dval(rv), tens[e]);
2241  goto ret;
2242 #endif
2243  }
2244  i = DBL_DIG - nd;
2245  if (e <= Ten_pmax + i) {
2246  /* A fancier test would sometimes let us do
2247  * this for larger i values.
2248  */
2249 #ifdef Honor_FLT_ROUNDS
2250  /* round correctly FLT_ROUNDS = 2 or 3 */
2251  if (sign) {
2252  dval(rv) = -dval(rv);
2253  sign = 0;
2254  }
2255 #endif
2256  e -= i;
2257  dval(rv) *= tens[i];
2258 #ifdef VAX
2259  /* VAX exponent range is so narrow we must
2260  * worry about overflow here...
2261  */
2262 vax_ovfl_check:
2263  word0(rv) -= P*Exp_msk1;
2264  /* rv = */ rounded_product(dval(rv), tens[e]);
2265  if ((word0(rv) & Exp_mask)
2266  > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2267  goto ovfl;
2268  word0(rv) += P*Exp_msk1;
2269 #else
2270  /* rv = */ rounded_product(dval(rv), tens[e]);
2271 #endif
2272  goto ret;
2273  }
2274  }
2275 #ifndef Inaccurate_Divide
2276  else if (e >= -Ten_pmax) {
2277 #ifdef Honor_FLT_ROUNDS
2278  /* round correctly FLT_ROUNDS = 2 or 3 */
2279  if (sign) {
2280  dval(rv) = -dval(rv);
2281  sign = 0;
2282  }
2283 #endif
2284  /* rv = */ rounded_quotient(dval(rv), tens[-e]);
2285  goto ret;
2286  }
2287 #endif
2288  }
2289  e1 += nd - k;
2290 
2291 #ifdef IEEE_Arith
2292 #ifdef SET_INEXACT
2293  inexact = 1;
2294  if (k <= DBL_DIG)
2295  oldinexact = get_inexact();
2296 #endif
2297 #ifdef Avoid_Underflow
2298  scale = 0;
2299 #endif
2300 #ifdef Honor_FLT_ROUNDS
2301  if ((rounding = Flt_Rounds) >= 2) {
2302  if (sign)
2303  rounding = rounding == 2 ? 0 : 2;
2304  else
2305  if (rounding != 2)
2306  rounding = 0;
2307  }
2308 #endif
2309 #endif /*IEEE_Arith*/
2310 
2311  /* Get starting approximation = rv * 10**e1 */
2312 
2313  if (e1 > 0) {
2314  if ((i = e1 & 15) != 0)
2315  dval(rv) *= tens[i];
2316  if (e1 &= ~15) {
2317  if (e1 > DBL_MAX_10_EXP) {
2318 ovfl:
2319 #ifndef NO_ERRNO
2320  errno = ERANGE;
2321 #endif
2322  /* Can't trust HUGE_VAL */
2323 #ifdef IEEE_Arith
2324 #ifdef Honor_FLT_ROUNDS
2325  switch (rounding) {
2326  case 0: /* toward 0 */
2327  case 3: /* toward -infinity */
2328  word0(rv) = Big0;
2329  word1(rv) = Big1;
2330  break;
2331  default:
2332  word0(rv) = Exp_mask;
2333  word1(rv) = 0;
2334  }
2335 #else /*Honor_FLT_ROUNDS*/
2336  word0(rv) = Exp_mask;
2337  word1(rv) = 0;
2338 #endif /*Honor_FLT_ROUNDS*/
2339 #ifdef SET_INEXACT
2340  /* set overflow bit */
2341  dval(rv0) = 1e300;
2342  dval(rv0) *= dval(rv0);
2343 #endif
2344 #else /*IEEE_Arith*/
2345  word0(rv) = Big0;
2346  word1(rv) = Big1;
2347 #endif /*IEEE_Arith*/
2348  if (bd0)
2349  goto retfree;
2350  goto ret;
2351  }
2352  e1 >>= 4;
2353  for (j = 0; e1 > 1; j++, e1 >>= 1)
2354  if (e1 & 1)
2355  dval(rv) *= bigtens[j];
2356  /* The last multiplication could overflow. */
2357  word0(rv) -= P*Exp_msk1;
2358  dval(rv) *= bigtens[j];
2359  if ((z = word0(rv) & Exp_mask)
2360  > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2361  goto ovfl;
2362  if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2363  /* set to largest number */
2364  /* (Can't trust DBL_MAX) */
2365  word0(rv) = Big0;
2366  word1(rv) = Big1;
2367  }
2368  else
2369  word0(rv) += P*Exp_msk1;
2370  }
2371  }
2372  else if (e1 < 0) {
2373  e1 = -e1;
2374  if ((i = e1 & 15) != 0)
2375  dval(rv) /= tens[i];
2376  if (e1 >>= 4) {
2377  if (e1 >= 1 << n_bigtens)
2378  goto undfl;
2379 #ifdef Avoid_Underflow
2380  if (e1 & Scale_Bit)
2381  scale = 2*P;
2382  for (j = 0; e1 > 0; j++, e1 >>= 1)
2383  if (e1 & 1)
2384  dval(rv) *= tinytens[j];
2385  if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
2386  >> Exp_shift)) > 0) {
2387  /* scaled rv is denormal; zap j low bits */
2388  if (j >= 32) {
2389  word1(rv) = 0;
2390  if (j >= 53)
2391  word0(rv) = (P+2)*Exp_msk1;
2392  else
2393  word0(rv) &= 0xffffffff << (j-32);
2394  }
2395  else
2396  word1(rv) &= 0xffffffff << j;
2397  }
2398 #else
2399  for (j = 0; e1 > 1; j++, e1 >>= 1)
2400  if (e1 & 1)
2401  dval(rv) *= tinytens[j];
2402  /* The last multiplication could underflow. */
2403  dval(rv0) = dval(rv);
2404  dval(rv) *= tinytens[j];
2405  if (!dval(rv)) {
2406  dval(rv) = 2.*dval(rv0);
2407  dval(rv) *= tinytens[j];
2408 #endif
2409  if (!dval(rv)) {
2410 undfl:
2411  dval(rv) = 0.;
2412 #ifndef NO_ERRNO
2413  errno = ERANGE;
2414 #endif
2415  if (bd0)
2416  goto retfree;
2417  goto ret;
2418  }
2419 #ifndef Avoid_Underflow
2420  word0(rv) = Tiny0;
2421  word1(rv) = Tiny1;
2422  /* The refinement below will clean
2423  * this approximation up.
2424  */
2425  }
2426 #endif
2427  }
2428  }
2429 
2430  /* Now the hard part -- adjusting rv to the correct value.*/
2431 
2432  /* Put digits into bd: true value = bd * 10^e */
2433 
2434  bd0 = s2b(s0, nd0, nd, y);
2435 
2436  for (;;) {
2437  bd = Balloc(bd0->k);
2438  Bcopy(bd, bd0);
2439  bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
2440  bs = i2b(1);
2441 
2442  if (e >= 0) {
2443  bb2 = bb5 = 0;
2444  bd2 = bd5 = e;
2445  }
2446  else {
2447  bb2 = bb5 = -e;
2448  bd2 = bd5 = 0;
2449  }
2450  if (bbe >= 0)
2451  bb2 += bbe;
2452  else
2453  bd2 -= bbe;
2454  bs2 = bb2;
2455 #ifdef Honor_FLT_ROUNDS
2456  if (rounding != 1)
2457  bs2++;
2458 #endif
2459 #ifdef Avoid_Underflow
2460  j = bbe - scale;
2461  i = j + bbbits - 1; /* logb(rv) */
2462  if (i < Emin) /* denormal */
2463  j += P - Emin;
2464  else
2465  j = P + 1 - bbbits;
2466 #else /*Avoid_Underflow*/
2467 #ifdef Sudden_Underflow
2468 #ifdef IBM
2469  j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2470 #else
2471  j = P + 1 - bbbits;
2472 #endif
2473 #else /*Sudden_Underflow*/
2474  j = bbe;
2475  i = j + bbbits - 1; /* logb(rv) */
2476  if (i < Emin) /* denormal */
2477  j += P - Emin;
2478  else
2479  j = P + 1 - bbbits;
2480 #endif /*Sudden_Underflow*/
2481 #endif /*Avoid_Underflow*/
2482  bb2 += j;
2483  bd2 += j;
2484 #ifdef Avoid_Underflow
2485  bd2 += scale;
2486 #endif
2487  i = bb2 < bd2 ? bb2 : bd2;
2488  if (i > bs2)
2489  i = bs2;
2490  if (i > 0) {
2491  bb2 -= i;
2492  bd2 -= i;
2493  bs2 -= i;
2494  }
2495  if (bb5 > 0) {
2496  bs = pow5mult(bs, bb5);
2497  bb1 = mult(bs, bb);
2498  Bfree(bb);
2499  bb = bb1;
2500  }
2501  if (bb2 > 0)
2502  bb = lshift(bb, bb2);
2503  if (bd5 > 0)
2504  bd = pow5mult(bd, bd5);
2505  if (bd2 > 0)
2506  bd = lshift(bd, bd2);
2507  if (bs2 > 0)
2508  bs = lshift(bs, bs2);
2509  delta = diff(bb, bd);
2510  dsign = delta->sign;
2511  delta->sign = 0;
2512  i = cmp(delta, bs);
2513 #ifdef Honor_FLT_ROUNDS
2514  if (rounding != 1) {
2515  if (i < 0) {
2516  /* Error is less than an ulp */
2517  if (!delta->x[0] && delta->wds <= 1) {
2518  /* exact */
2519 #ifdef SET_INEXACT
2520  inexact = 0;
2521 #endif
2522  break;
2523  }
2524  if (rounding) {
2525  if (dsign) {
2526  adj = 1.;
2527  goto apply_adj;
2528  }
2529  }
2530  else if (!dsign) {
2531  adj = -1.;
2532  if (!word1(rv)
2533  && !(word0(rv) & Frac_mask)) {
2534  y = word0(rv) & Exp_mask;
2535 #ifdef Avoid_Underflow
2536  if (!scale || y > 2*P*Exp_msk1)
2537 #else
2538  if (y)
2539 #endif
2540  {
2541  delta = lshift(delta,Log2P);
2542  if (cmp(delta, bs) <= 0)
2543  adj = -0.5;
2544  }
2545  }
2546 apply_adj:
2547 #ifdef Avoid_Underflow
2548  if (scale && (y = word0(rv) & Exp_mask)
2549  <= 2*P*Exp_msk1)
2550  word0(adj) += (2*P+1)*Exp_msk1 - y;
2551 #else
2552 #ifdef Sudden_Underflow
2553  if ((word0(rv) & Exp_mask) <=
2554  P*Exp_msk1) {
2555  word0(rv) += P*Exp_msk1;
2556  dval(rv) += adj*ulp(dval(rv));
2557  word0(rv) -= P*Exp_msk1;
2558  }
2559  else
2560 #endif /*Sudden_Underflow*/
2561 #endif /*Avoid_Underflow*/
2562  dval(rv) += adj*ulp(dval(rv));
2563  }
2564  break;
2565  }
2566  adj = ratio(delta, bs);
2567  if (adj < 1.)
2568  adj = 1.;
2569  if (adj <= 0x7ffffffe) {
2570  /* adj = rounding ? ceil(adj) : floor(adj); */
2571  y = adj;
2572  if (y != adj) {
2573  if (!((rounding>>1) ^ dsign))
2574  y++;
2575  adj = y;
2576  }
2577  }
2578 #ifdef Avoid_Underflow
2579  if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2580  word0(adj) += (2*P+1)*Exp_msk1 - y;
2581 #else
2582 #ifdef Sudden_Underflow
2583  if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2584  word0(rv) += P*Exp_msk1;
2585  adj *= ulp(dval(rv));
2586  if (dsign)
2587  dval(rv) += adj;
2588  else
2589  dval(rv) -= adj;
2590  word0(rv) -= P*Exp_msk1;
2591  goto cont;
2592  }
2593 #endif /*Sudden_Underflow*/
2594 #endif /*Avoid_Underflow*/
2595  adj *= ulp(dval(rv));
2596  if (dsign)
2597  dval(rv) += adj;
2598  else
2599  dval(rv) -= adj;
2600  goto cont;
2601  }
2602 #endif /*Honor_FLT_ROUNDS*/
2603 
2604  if (i < 0) {
2605  /* Error is less than half an ulp -- check for
2606  * special case of mantissa a power of two.
2607  */
2608  if (dsign || word1(rv) || word0(rv) & Bndry_mask
2609 #ifdef IEEE_Arith
2610 #ifdef Avoid_Underflow
2611  || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2612 #else
2613  || (word0(rv) & Exp_mask) <= Exp_msk1
2614 #endif
2615 #endif
2616  ) {
2617 #ifdef SET_INEXACT
2618  if (!delta->x[0] && delta->wds <= 1)
2619  inexact = 0;
2620 #endif
2621  break;
2622  }
2623  if (!delta->x[0] && delta->wds <= 1) {
2624  /* exact result */
2625 #ifdef SET_INEXACT
2626  inexact = 0;
2627 #endif
2628  break;
2629  }
2630  delta = lshift(delta,Log2P);
2631  if (cmp(delta, bs) > 0)
2632  goto drop_down;
2633  break;
2634  }
2635  if (i == 0) {
2636  /* exactly half-way between */
2637  if (dsign) {
2638  if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2639  && word1(rv) == (
2640 #ifdef Avoid_Underflow
2641  (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2642  ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2643 #endif
2644  0xffffffff)) {
2645  /*boundary case -- increment exponent*/
2646  word0(rv) = (word0(rv) & Exp_mask)
2647  + Exp_msk1
2648 #ifdef IBM
2649  | Exp_msk1 >> 4
2650 #endif
2651  ;
2652  word1(rv) = 0;
2653 #ifdef Avoid_Underflow
2654  dsign = 0;
2655 #endif
2656  break;
2657  }
2658  }
2659  else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2660 drop_down:
2661  /* boundary case -- decrement exponent */
2662 #ifdef Sudden_Underflow /*{{*/
2663  L = word0(rv) & Exp_mask;
2664 #ifdef IBM
2665  if (L < Exp_msk1)
2666 #else
2667 #ifdef Avoid_Underflow
2668  if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2669 #else
2670  if (L <= Exp_msk1)
2671 #endif /*Avoid_Underflow*/
2672 #endif /*IBM*/
2673  goto undfl;
2674  L -= Exp_msk1;
2675 #else /*Sudden_Underflow}{*/
2676 #ifdef Avoid_Underflow
2677  if (scale) {
2678  L = word0(rv) & Exp_mask;
2679  if (L <= (2*P+1)*Exp_msk1) {
2680  if (L > (P+2)*Exp_msk1)
2681  /* round even ==> */
2682  /* accept rv */
2683  break;
2684  /* rv = smallest denormal */
2685  goto undfl;
2686  }
2687  }
2688 #endif /*Avoid_Underflow*/
2689  L = (word0(rv) & Exp_mask) - Exp_msk1;
2690 #endif /*Sudden_Underflow}}*/
2691  word0(rv) = L | Bndry_mask1;
2692  word1(rv) = 0xffffffff;
2693 #ifdef IBM
2694  goto cont;
2695 #else
2696  break;
2697 #endif
2698  }
2699 #ifndef ROUND_BIASED
2700  if (!(word1(rv) & LSB))
2701  break;
2702 #endif
2703  if (dsign)
2704  dval(rv) += ulp(dval(rv));
2705 #ifndef ROUND_BIASED
2706  else {
2707  dval(rv) -= ulp(dval(rv));
2708 #ifndef Sudden_Underflow
2709  if (!dval(rv))
2710  goto undfl;
2711 #endif
2712  }
2713 #ifdef Avoid_Underflow
2714  dsign = 1 - dsign;
2715 #endif
2716 #endif
2717  break;
2718  }
2719  if ((aadj = ratio(delta, bs)) <= 2.) {
2720  if (dsign)
2721  aadj = dval(aadj1) = 1.;
2722  else if (word1(rv) || word0(rv) & Bndry_mask) {
2723 #ifndef Sudden_Underflow
2724  if (word1(rv) == Tiny1 && !word0(rv))
2725  goto undfl;
2726 #endif
2727  aadj = 1.;
2728  dval(aadj1) = -1.;
2729  }
2730  else {
2731  /* special case -- power of FLT_RADIX to be */
2732  /* rounded down... */
2733 
2734  if (aadj < 2./FLT_RADIX)
2735  aadj = 1./FLT_RADIX;
2736  else
2737  aadj *= 0.5;
2738  dval(aadj1) = -aadj;
2739  }
2740  }
2741  else {
2742  aadj *= 0.5;
2743  dval(aadj1) = dsign ? aadj : -aadj;
2744 #ifdef Check_FLT_ROUNDS
2745  switch (Rounding) {
2746  case 2: /* towards +infinity */
2747  dval(aadj1) -= 0.5;
2748  break;
2749  case 0: /* towards 0 */
2750  case 3: /* towards -infinity */
2751  dval(aadj1) += 0.5;
2752  }
2753 #else
2754  if (Flt_Rounds == 0)
2755  dval(aadj1) += 0.5;
2756 #endif /*Check_FLT_ROUNDS*/
2757  }
2758  y = word0(rv) & Exp_mask;
2759 
2760  /* Check for overflow */
2761 
2762  if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2763  dval(rv0) = dval(rv);
2764  word0(rv) -= P*Exp_msk1;
2765  adj = dval(aadj1) * ulp(dval(rv));
2766  dval(rv) += adj;
2767  if ((word0(rv) & Exp_mask) >=
2768  Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2769  if (word0(rv0) == Big0 && word1(rv0) == Big1)
2770  goto ovfl;
2771  word0(rv) = Big0;
2772  word1(rv) = Big1;
2773  goto cont;
2774  }
2775  else
2776  word0(rv) += P*Exp_msk1;
2777  }
2778  else {
2779 #ifdef Avoid_Underflow
2780  if (scale && y <= 2*P*Exp_msk1) {
2781  if (aadj <= 0x7fffffff) {
2782  if ((z = (int)aadj) <= 0)
2783  z = 1;
2784  aadj = z;
2785  dval(aadj1) = dsign ? aadj : -aadj;
2786  }
2787  word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2788  }
2789  adj = dval(aadj1) * ulp(dval(rv));
2790  dval(rv) += adj;
2791 #else
2792 #ifdef Sudden_Underflow
2793  if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2794  dval(rv0) = dval(rv);
2795  word0(rv) += P*Exp_msk1;
2796  adj = dval(aadj1) * ulp(dval(rv));
2797  dval(rv) += adj;
2798 #ifdef IBM
2799  if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2800 #else
2801  if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2802 #endif
2803  {
2804  if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2805  goto undfl;
2806  word0(rv) = Tiny0;
2807  word1(rv) = Tiny1;
2808  goto cont;
2809  }
2810  else
2811  word0(rv) -= P*Exp_msk1;
2812  }
2813  else {
2814  adj = dval(aadj1) * ulp(dval(rv));
2815  dval(rv) += adj;
2816  }
2817 #else /*Sudden_Underflow*/
2818  /* Compute adj so that the IEEE rounding rules will
2819  * correctly round rv + adj in some half-way cases.
2820  * If rv * ulp(rv) is denormalized (i.e.,
2821  * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2822  * trouble from bits lost to denormalization;
2823  * example: 1.2e-307 .
2824  */
2825  if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2826  dval(aadj1) = (double)(int)(aadj + 0.5);
2827  if (!dsign)
2828  dval(aadj1) = -dval(aadj1);
2829  }
2830  adj = dval(aadj1) * ulp(dval(rv));
2831  dval(rv) += adj;
2832 #endif /*Sudden_Underflow*/
2833 #endif /*Avoid_Underflow*/
2834  }
2835  z = word0(rv) & Exp_mask;
2836 #ifndef SET_INEXACT
2837 #ifdef Avoid_Underflow
2838  if (!scale)
2839 #endif
2840  if (y == z) {
2841  /* Can we stop now? */
2842  L = (Long)aadj;
2843  aadj -= L;
2844  /* The tolerances below are conservative. */
2845  if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2846  if (aadj < .4999999 || aadj > .5000001)
2847  break;
2848  }
2849  else if (aadj < .4999999/FLT_RADIX)
2850  break;
2851  }
2852 #endif
2853 cont:
2854  Bfree(bb);
2855  Bfree(bd);
2856  Bfree(bs);
2857  Bfree(delta);
2858  }
2859 #ifdef SET_INEXACT
2860  if (inexact) {
2861  if (!oldinexact) {
2862  word0(rv0) = Exp_1 + (70 << Exp_shift);
2863  word1(rv0) = 0;
2864  dval(rv0) += 1.;
2865  }
2866  }
2867  else if (!oldinexact)
2868  clear_inexact();
2869 #endif
2870 #ifdef Avoid_Underflow
2871  if (scale) {
2872  word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2873  word1(rv0) = 0;
2874  dval(rv) *= dval(rv0);
2875 #ifndef NO_ERRNO
2876  /* try to avoid the bug of testing an 8087 register value */
2877  if (word0(rv) == 0 && word1(rv) == 0)
2878  errno = ERANGE;
2879 #endif
2880  }
2881 #endif /* Avoid_Underflow */
2882 #ifdef SET_INEXACT
2883  if (inexact && !(word0(rv) & Exp_mask)) {
2884  /* set underflow bit */
2885  dval(rv0) = 1e-300;
2886  dval(rv0) *= dval(rv0);
2887  }
2888 #endif
2889 retfree:
2890  Bfree(bb);
2891  Bfree(bd);
2892  Bfree(bs);
2893  Bfree(bd0);
2894  Bfree(delta);
2895 ret:
2896  if (se)
2897  *se = (char *)s;
2898  return sign ? -dval(rv) : dval(rv);
2899 }
2900 
2901 static int
2903 {
2904  int n;
2905  ULong *bx, *bxe, q, *sx, *sxe;
2906 #ifdef ULLong
2907  ULLong borrow, carry, y, ys;
2908 #else
2909  ULong borrow, carry, y, ys;
2910 #ifdef Pack_32
2911  ULong si, z, zs;
2912 #endif
2913 #endif
2914 
2915  n = S->wds;
2916 #ifdef DEBUG
2917  /*debug*/ if (b->wds > n)
2918  /*debug*/ Bug("oversize b in quorem");
2919 #endif
2920  if (b->wds < n)
2921  return 0;
2922  sx = S->x;
2923  sxe = sx + --n;
2924  bx = b->x;
2925  bxe = bx + n;
2926  q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2927 #ifdef DEBUG
2928  /*debug*/ if (q > 9)
2929  /*debug*/ Bug("oversized quotient in quorem");
2930 #endif
2931  if (q) {
2932  borrow = 0;
2933  carry = 0;
2934  do {
2935 #ifdef ULLong
2936  ys = *sx++ * (ULLong)q + carry;
2937  carry = ys >> 32;
2938  y = *bx - (ys & FFFFFFFF) - borrow;
2939  borrow = y >> 32 & (ULong)1;
2940  *bx++ = (ULong)(y & FFFFFFFF);
2941 #else
2942 #ifdef Pack_32
2943  si = *sx++;
2944  ys = (si & 0xffff) * q + carry;
2945  zs = (si >> 16) * q + (ys >> 16);
2946  carry = zs >> 16;
2947  y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2948  borrow = (y & 0x10000) >> 16;
2949  z = (*bx >> 16) - (zs & 0xffff) - borrow;
2950  borrow = (z & 0x10000) >> 16;
2951  Storeinc(bx, z, y);
2952 #else
2953  ys = *sx++ * q + carry;
2954  carry = ys >> 16;
2955  y = *bx - (ys & 0xffff) - borrow;
2956  borrow = (y & 0x10000) >> 16;
2957  *bx++ = y & 0xffff;
2958 #endif
2959 #endif
2960  } while (sx <= sxe);
2961  if (!*bxe) {
2962  bx = b->x;
2963  while (--bxe > bx && !*bxe)
2964  --n;
2965  b->wds = n;
2966  }
2967  }
2968  if (cmp(b, S) >= 0) {
2969  q++;
2970  borrow = 0;
2971  carry = 0;
2972  bx = b->x;
2973  sx = S->x;
2974  do {
2975 #ifdef ULLong
2976  ys = *sx++ + carry;
2977  carry = ys >> 32;
2978  y = *bx - (ys & FFFFFFFF) - borrow;
2979  borrow = y >> 32 & (ULong)1;
2980  *bx++ = (ULong)(y & FFFFFFFF);
2981 #else
2982 #ifdef Pack_32
2983  si = *sx++;
2984  ys = (si & 0xffff) + carry;
2985  zs = (si >> 16) + (ys >> 16);
2986  carry = zs >> 16;
2987  y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2988  borrow = (y & 0x10000) >> 16;
2989  z = (*bx >> 16) - (zs & 0xffff) - borrow;
2990  borrow = (z & 0x10000) >> 16;
2991  Storeinc(bx, z, y);
2992 #else
2993  ys = *sx++ + carry;
2994  carry = ys >> 16;
2995  y = *bx - (ys & 0xffff) - borrow;
2996  borrow = (y & 0x10000) >> 16;
2997  *bx++ = y & 0xffff;
2998 #endif
2999 #endif
3000  } while (sx <= sxe);
3001  bx = b->x;
3002  bxe = bx + n;
3003  if (!*bxe) {
3004  while (--bxe > bx && !*bxe)
3005  --n;
3006  b->wds = n;
3007  }
3008  }
3009  return q;
3010 }
3011 
3012 #ifndef MULTIPLE_THREADS
3013 static char *dtoa_result;
3014 #endif
3015 
3016 #ifndef MULTIPLE_THREADS
3017 static char *
3018 rv_alloc(int i)
3019 {
3020  return dtoa_result = xmalloc(i);
3021 }
3022 #else
3023 #define rv_alloc(i) xmalloc(i)
3024 #endif
3025 
3026 static char *
3027 nrv_alloc(const char *s, char **rve, size_t n)
3028 {
3029  char *rv, *t;
3030 
3031  t = rv = rv_alloc(n);
3032  while ((*t = *s++) != 0) t++;
3033  if (rve)
3034  *rve = t;
3035  return rv;
3036 }
3037 
3038 #define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
3039 
3040 #ifndef MULTIPLE_THREADS
3041 /* freedtoa(s) must be used to free values s returned by dtoa
3042  * when MULTIPLE_THREADS is #defined. It should be used in all cases,
3043  * but for consistency with earlier versions of dtoa, it is optional
3044  * when MULTIPLE_THREADS is not defined.
3045  */
3046 
3047 static void
3048 freedtoa(char *s)
3049 {
3050  xfree(s);
3051 }
3052 #endif
3053 
3054 static const char INFSTR[] = "Infinity";
3055 static const char NANSTR[] = "NaN";
3056 static const char ZEROSTR[] = "0";
3057 
3058 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
3059  *
3060  * Inspired by "How to Print Floating-Point Numbers Accurately" by
3061  * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
3062  *
3063  * Modifications:
3064  * 1. Rather than iterating, we use a simple numeric overestimate
3065  * to determine k = floor(log10(d)). We scale relevant
3066  * quantities using O(log2(k)) rather than O(k) multiplications.
3067  * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
3068  * try to generate digits strictly left to right. Instead, we
3069  * compute with fewer bits and propagate the carry if necessary
3070  * when rounding the final digit up. This is often faster.
3071  * 3. Under the assumption that input will be rounded nearest,
3072  * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
3073  * That is, we allow equality in stopping tests when the
3074  * round-nearest rule will give the same floating-point value
3075  * as would satisfaction of the stopping test with strict
3076  * inequality.
3077  * 4. We remove common factors of powers of 2 from relevant
3078  * quantities.
3079  * 5. When converting floating-point integers less than 1e16,
3080  * we use floating-point arithmetic rather than resorting
3081  * to multiple-precision integers.
3082  * 6. When asked to produce fewer than 15 digits, we first try
3083  * to get by with floating-point arithmetic; we resort to
3084  * multiple-precision integer arithmetic only if we cannot
3085  * guarantee that the floating-point calculation has given
3086  * the correctly rounded result. For k requested digits and
3087  * "uniformly" distributed input, the probability is
3088  * something like 10^(k-15) that we must resort to the Long
3089  * calculation.
3090  */
3091 
3092 char *
3093 ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
3094 {
3095  /* Arguments ndigits, decpt, sign are similar to those
3096  of ecvt and fcvt; trailing zeros are suppressed from
3097  the returned string. If not null, *rve is set to point
3098  to the end of the return value. If d is +-Infinity or NaN,
3099  then *decpt is set to 9999.
3100 
3101  mode:
3102  0 ==> shortest string that yields d when read in
3103  and rounded to nearest.
3104  1 ==> like 0, but with Steele & White stopping rule;
3105  e.g. with IEEE P754 arithmetic , mode 0 gives
3106  1e23 whereas mode 1 gives 9.999999999999999e22.
3107  2 ==> max(1,ndigits) significant digits. This gives a
3108  return value similar to that of ecvt, except
3109  that trailing zeros are suppressed.
3110  3 ==> through ndigits past the decimal point. This
3111  gives a return value similar to that from fcvt,
3112  except that trailing zeros are suppressed, and
3113  ndigits can be negative.
3114  4,5 ==> similar to 2 and 3, respectively, but (in
3115  round-nearest mode) with the tests of mode 0 to
3116  possibly return a shorter string that rounds to d.
3117  With IEEE arithmetic and compilation with
3118  -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
3119  as modes 2 and 3 when FLT_ROUNDS != 1.
3120  6-9 ==> Debugging modes similar to mode - 4: don't try
3121  fast floating-point estimate (if applicable).
3122 
3123  Values of mode other than 0-9 are treated as mode 0.
3124 
3125  Sufficient space is allocated to the return value
3126  to hold the suppressed trailing zeros.
3127  */
3128 
3129  int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
3130  j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
3131  spec_case, try_quick;
3132  Long L;
3133 #ifndef Sudden_Underflow
3134  int denorm;
3135  ULong x;
3136 #endif
3137  Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
3138  double ds;
3139  double_u d, d2, eps;
3140  char *s, *s0;
3141 #ifdef Honor_FLT_ROUNDS
3142  int rounding;
3143 #endif
3144 #ifdef SET_INEXACT
3145  int inexact, oldinexact;
3146 #endif
3147 
3148  dval(d) = d_;
3149 
3150 #ifndef MULTIPLE_THREADS
3151  if (dtoa_result) {
3152  freedtoa(dtoa_result);
3153  dtoa_result = 0;
3154  }
3155 #endif
3156 
3157  if (word0(d) & Sign_bit) {
3158  /* set sign for everything, including 0's and NaNs */
3159  *sign = 1;
3160  word0(d) &= ~Sign_bit; /* clear sign bit */
3161  }
3162  else
3163  *sign = 0;
3164 
3165 #if defined(IEEE_Arith) + defined(VAX)
3166 #ifdef IEEE_Arith
3167  if ((word0(d) & Exp_mask) == Exp_mask)
3168 #else
3169  if (word0(d) == 0x8000)
3170 #endif
3171  {
3172  /* Infinity or NaN */
3173  *decpt = 9999;
3174 #ifdef IEEE_Arith
3175  if (!word1(d) && !(word0(d) & 0xfffff))
3176  return rv_strdup(INFSTR, rve);
3177 #endif
3178  return rv_strdup(NANSTR, rve);
3179  }
3180 #endif
3181 #ifdef IBM
3182  dval(d) += 0; /* normalize */
3183 #endif
3184  if (!dval(d)) {
3185  *decpt = 1;
3186  return rv_strdup(ZEROSTR, rve);
3187  }
3188 
3189 #ifdef SET_INEXACT
3190  try_quick = oldinexact = get_inexact();
3191  inexact = 1;
3192 #endif
3193 #ifdef Honor_FLT_ROUNDS
3194  if ((rounding = Flt_Rounds) >= 2) {
3195  if (*sign)
3196  rounding = rounding == 2 ? 0 : 2;
3197  else
3198  if (rounding != 2)
3199  rounding = 0;
3200  }
3201 #endif
3202 
3203  b = d2b(dval(d), &be, &bbits);
3204 #ifdef Sudden_Underflow
3205  i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
3206 #else
3207  if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
3208 #endif
3209  dval(d2) = dval(d);
3210  word0(d2) &= Frac_mask1;
3211  word0(d2) |= Exp_11;
3212 #ifdef IBM
3213  if (j = 11 - hi0bits(word0(d2) & Frac_mask))
3214  dval(d2) /= 1 << j;
3215 #endif
3216 
3217  /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
3218  * log10(x) = log(x) / log(10)
3219  * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
3220  * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
3221  *
3222  * This suggests computing an approximation k to log10(d) by
3223  *
3224  * k = (i - Bias)*0.301029995663981
3225  * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
3226  *
3227  * We want k to be too large rather than too small.
3228  * The error in the first-order Taylor series approximation
3229  * is in our favor, so we just round up the constant enough
3230  * to compensate for any error in the multiplication of
3231  * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
3232  * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
3233  * adding 1e-13 to the constant term more than suffices.
3234  * Hence we adjust the constant term to 0.1760912590558.
3235  * (We could get a more accurate k by invoking log10,
3236  * but this is probably not worthwhile.)
3237  */
3238 
3239  i -= Bias;
3240 #ifdef IBM
3241  i <<= 2;
3242  i += j;
3243 #endif
3244 #ifndef Sudden_Underflow
3245  denorm = 0;
3246  }
3247  else {
3248  /* d is denormalized */
3249 
3250  i = bbits + be + (Bias + (P-1) - 1);
3251  x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
3252  : word1(d) << (32 - i);
3253  dval(d2) = x;
3254  word0(d2) -= 31*Exp_msk1; /* adjust exponent */
3255  i -= (Bias + (P-1) - 1) + 1;
3256  denorm = 1;
3257  }
3258 #endif
3259  ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
3260  k = (int)ds;
3261  if (ds < 0. && ds != k)
3262  k--; /* want k = floor(ds) */
3263  k_check = 1;
3264  if (k >= 0 && k <= Ten_pmax) {
3265  if (dval(d) < tens[k])
3266  k--;
3267  k_check = 0;
3268  }
3269  j = bbits - i - 1;
3270  if (j >= 0) {
3271  b2 = 0;
3272  s2 = j;
3273  }
3274  else {
3275  b2 = -j;
3276  s2 = 0;
3277  }
3278  if (k >= 0) {
3279  b5 = 0;
3280  s5 = k;
3281  s2 += k;
3282  }
3283  else {
3284  b2 -= k;
3285  b5 = -k;
3286  s5 = 0;
3287  }
3288  if (mode < 0 || mode > 9)
3289  mode = 0;
3290 
3291 #ifndef SET_INEXACT
3292 #ifdef Check_FLT_ROUNDS
3293  try_quick = Rounding == 1;
3294 #else
3295  try_quick = 1;
3296 #endif
3297 #endif /*SET_INEXACT*/
3298 
3299  if (mode > 5) {
3300  mode -= 4;
3301  try_quick = 0;
3302  }
3303  leftright = 1;
3304  ilim = ilim1 = -1;
3305  switch (mode) {
3306  case 0:
3307  case 1:
3308  i = 18;
3309  ndigits = 0;
3310  break;
3311  case 2:
3312  leftright = 0;
3313  /* no break */
3314  case 4:
3315  if (ndigits <= 0)
3316  ndigits = 1;
3317  ilim = ilim1 = i = ndigits;
3318  break;
3319  case 3:
3320  leftright = 0;
3321  /* no break */
3322  case 5:
3323  i = ndigits + k + 1;
3324  ilim = i;
3325  ilim1 = i - 1;
3326  if (i <= 0)
3327  i = 1;
3328  }
3329  s = s0 = rv_alloc(i+1);
3330 
3331 #ifdef Honor_FLT_ROUNDS
3332  if (mode > 1 && rounding != 1)
3333  leftright = 0;
3334 #endif
3335 
3336  if (ilim >= 0 && ilim <= Quick_max && try_quick) {
3337 
3338  /* Try to get by with floating-point arithmetic. */
3339 
3340  i = 0;
3341  dval(d2) = dval(d);
3342  k0 = k;
3343  ilim0 = ilim;
3344  ieps = 2; /* conservative */
3345  if (k > 0) {
3346  ds = tens[k&0xf];
3347  j = k >> 4;
3348  if (j & Bletch) {
3349  /* prevent overflows */
3350  j &= Bletch - 1;
3351  dval(d) /= bigtens[n_bigtens-1];
3352  ieps++;
3353  }
3354  for (; j; j >>= 1, i++)
3355  if (j & 1) {
3356  ieps++;
3357  ds *= bigtens[i];
3358  }
3359  dval(d) /= ds;
3360  }
3361  else if ((j1 = -k) != 0) {
3362  dval(d) *= tens[j1 & 0xf];
3363  for (j = j1 >> 4; j; j >>= 1, i++)
3364  if (j & 1) {
3365  ieps++;
3366  dval(d) *= bigtens[i];
3367  }
3368  }
3369  if (k_check && dval(d) < 1. && ilim > 0) {
3370  if (ilim1 <= 0)
3371  goto fast_failed;
3372  ilim = ilim1;
3373  k--;
3374  dval(d) *= 10.;
3375  ieps++;
3376  }
3377  dval(eps) = ieps*dval(d) + 7.;
3378  word0(eps) -= (P-1)*Exp_msk1;
3379  if (ilim == 0) {
3380  S = mhi = 0;
3381  dval(d) -= 5.;
3382  if (dval(d) > dval(eps))
3383  goto one_digit;
3384  if (dval(d) < -dval(eps))
3385  goto no_digits;
3386  goto fast_failed;
3387  }
3388 #ifndef No_leftright
3389  if (leftright) {
3390  /* Use Steele & White method of only
3391  * generating digits needed.
3392  */
3393  dval(eps) = 0.5/tens[ilim-1] - dval(eps);
3394  for (i = 0;;) {
3395  L = (int)dval(d);
3396  dval(d) -= L;
3397  *s++ = '0' + (int)L;
3398  if (dval(d) < dval(eps))
3399  goto ret1;
3400  if (1. - dval(d) < dval(eps))
3401  goto bump_up;
3402  if (++i >= ilim)
3403  break;
3404  dval(eps) *= 10.;
3405  dval(d) *= 10.;
3406  }
3407  }
3408  else {
3409 #endif
3410  /* Generate ilim digits, then fix them up. */
3411  dval(eps) *= tens[ilim-1];
3412  for (i = 1;; i++, dval(d) *= 10.) {
3413  L = (Long)(dval(d));
3414  if (!(dval(d) -= L))
3415  ilim = i;
3416  *s++ = '0' + (int)L;
3417  if (i == ilim) {
3418  if (dval(d) > 0.5 + dval(eps))
3419  goto bump_up;
3420  else if (dval(d) < 0.5 - dval(eps)) {
3421  while (*--s == '0') ;
3422  s++;
3423  goto ret1;
3424  }
3425  break;
3426  }
3427  }
3428 #ifndef No_leftright
3429  }
3430 #endif
3431 fast_failed:
3432  s = s0;
3433  dval(d) = dval(d2);
3434  k = k0;
3435  ilim = ilim0;
3436  }
3437 
3438  /* Do we have a "small" integer? */
3439 
3440  if (be >= 0 && k <= Int_max) {
3441  /* Yes. */
3442  ds = tens[k];
3443  if (ndigits < 0 && ilim <= 0) {
3444  S = mhi = 0;
3445  if (ilim < 0 || dval(d) <= 5*ds)
3446  goto no_digits;
3447  goto one_digit;
3448  }
3449  for (i = 1;; i++, dval(d) *= 10.) {
3450  L = (Long)(dval(d) / ds);
3451  dval(d) -= L*ds;
3452 #ifdef Check_FLT_ROUNDS
3453  /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3454  if (dval(d) < 0) {
3455  L--;
3456  dval(d) += ds;
3457  }
3458 #endif
3459  *s++ = '0' + (int)L;
3460  if (!dval(d)) {
3461 #ifdef SET_INEXACT
3462  inexact = 0;
3463 #endif
3464  break;
3465  }
3466  if (i == ilim) {
3467 #ifdef Honor_FLT_ROUNDS
3468  if (mode > 1)
3469  switch (rounding) {
3470  case 0: goto ret1;
3471  case 2: goto bump_up;
3472  }
3473 #endif
3474  dval(d) += dval(d);
3475  if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3476 bump_up:
3477  while (*--s == '9')
3478  if (s == s0) {
3479  k++;
3480  *s = '0';
3481  break;
3482  }
3483  ++*s++;
3484  }
3485  break;
3486  }
3487  }
3488  goto ret1;
3489  }
3490 
3491  m2 = b2;
3492  m5 = b5;
3493  if (leftright) {
3494  i =
3495 #ifndef Sudden_Underflow
3496  denorm ? be + (Bias + (P-1) - 1 + 1) :
3497 #endif
3498 #ifdef IBM
3499  1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3500 #else
3501  1 + P - bbits;
3502 #endif
3503  b2 += i;
3504  s2 += i;
3505  mhi = i2b(1);
3506  }
3507  if (m2 > 0 && s2 > 0) {
3508  i = m2 < s2 ? m2 : s2;
3509  b2 -= i;
3510  m2 -= i;
3511  s2 -= i;
3512  }
3513  if (b5 > 0) {
3514  if (leftright) {
3515  if (m5 > 0) {
3516  mhi = pow5mult(mhi, m5);
3517  b1 = mult(mhi, b);
3518  Bfree(b);
3519  b = b1;
3520  }
3521  if ((j = b5 - m5) != 0)
3522  b = pow5mult(b, j);
3523  }
3524  else
3525  b = pow5mult(b, b5);
3526  }
3527  S = i2b(1);
3528  if (s5 > 0)
3529  S = pow5mult(S, s5);
3530 
3531  /* Check for special case that d is a normalized power of 2. */
3532 
3533  spec_case = 0;
3534  if ((mode < 2 || leftright)
3535 #ifdef Honor_FLT_ROUNDS
3536  && rounding == 1
3537 #endif
3538  ) {
3539  if (!word1(d) && !(word0(d) & Bndry_mask)
3540 #ifndef Sudden_Underflow
3541  && word0(d) & (Exp_mask & ~Exp_msk1)
3542 #endif
3543  ) {
3544  /* The special case */
3545  b2 += Log2P;
3546  s2 += Log2P;
3547  spec_case = 1;
3548  }
3549  }
3550 
3551  /* Arrange for convenient computation of quotients:
3552  * shift left if necessary so divisor has 4 leading 0 bits.
3553  *
3554  * Perhaps we should just compute leading 28 bits of S once
3555  * and for all and pass them and a shift to quorem, so it
3556  * can do shifts and ors to compute the numerator for q.
3557  */
3558 #ifdef Pack_32
3559  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3560  i = 32 - i;
3561 #else
3562  if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3563  i = 16 - i;
3564 #endif
3565  if (i > 4) {
3566  i -= 4;
3567  b2 += i;
3568  m2 += i;
3569  s2 += i;
3570  }
3571  else if (i < 4) {
3572  i += 28;
3573  b2 += i;
3574  m2 += i;
3575  s2 += i;
3576  }
3577  if (b2 > 0)
3578  b = lshift(b, b2);
3579  if (s2 > 0)
3580  S = lshift(S, s2);
3581  if (k_check) {
3582  if (cmp(b,S) < 0) {
3583  k--;
3584  b = multadd(b, 10, 0); /* we botched the k estimate */
3585  if (leftright)
3586  mhi = multadd(mhi, 10, 0);
3587  ilim = ilim1;
3588  }
3589  }
3590  if (ilim <= 0 && (mode == 3 || mode == 5)) {
3591  if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3592  /* no digits, fcvt style */
3593 no_digits:
3594  k = -1 - ndigits;
3595  goto ret;
3596  }
3597 one_digit:
3598  *s++ = '1';
3599  k++;
3600  goto ret;
3601  }
3602  if (leftright) {
3603  if (m2 > 0)
3604  mhi = lshift(mhi, m2);
3605 
3606  /* Compute mlo -- check for special case
3607  * that d is a normalized power of 2.
3608  */
3609 
3610  mlo = mhi;
3611  if (spec_case) {
3612  mhi = Balloc(mhi->k);
3613  Bcopy(mhi, mlo);
3614  mhi = lshift(mhi, Log2P);
3615  }
3616 
3617  for (i = 1;;i++) {
3618  dig = quorem(b,S) + '0';
3619  /* Do we yet have the shortest decimal string
3620  * that will round to d?
3621  */
3622  j = cmp(b, mlo);
3623  delta = diff(S, mhi);
3624  j1 = delta->sign ? 1 : cmp(b, delta);
3625  Bfree(delta);
3626 #ifndef ROUND_BIASED
3627  if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3628 #ifdef Honor_FLT_ROUNDS
3629  && rounding >= 1
3630 #endif
3631  ) {
3632  if (dig == '9')
3633  goto round_9_up;
3634  if (j > 0)
3635  dig++;
3636 #ifdef SET_INEXACT
3637  else if (!b->x[0] && b->wds <= 1)
3638  inexact = 0;
3639 #endif
3640  *s++ = dig;
3641  goto ret;
3642  }
3643 #endif
3644  if (j < 0 || (j == 0 && mode != 1
3645 #ifndef ROUND_BIASED
3646  && !(word1(d) & 1)
3647 #endif
3648  )) {
3649  if (!b->x[0] && b->wds <= 1) {
3650 #ifdef SET_INEXACT
3651  inexact = 0;
3652 #endif
3653  goto accept_dig;
3654  }
3655 #ifdef Honor_FLT_ROUNDS
3656  if (mode > 1)
3657  switch (rounding) {
3658  case 0: goto accept_dig;
3659  case 2: goto keep_dig;
3660  }
3661 #endif /*Honor_FLT_ROUNDS*/
3662  if (j1 > 0) {
3663  b = lshift(b, 1);
3664  j1 = cmp(b, S);
3665  if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3666  goto round_9_up;
3667  }
3668 accept_dig:
3669  *s++ = dig;
3670  goto ret;
3671  }
3672  if (j1 > 0) {
3673 #ifdef Honor_FLT_ROUNDS
3674  if (!rounding)
3675  goto accept_dig;
3676 #endif
3677  if (dig == '9') { /* possible if i == 1 */
3678 round_9_up:
3679  *s++ = '9';
3680  goto roundoff;
3681  }
3682  *s++ = dig + 1;
3683  goto ret;
3684  }
3685 #ifdef Honor_FLT_ROUNDS
3686 keep_dig:
3687 #endif
3688  *s++ = dig;
3689  if (i == ilim)
3690  break;
3691  b = multadd(b, 10, 0);
3692  if (mlo == mhi)
3693  mlo = mhi = multadd(mhi, 10, 0);
3694  else {
3695  mlo = multadd(mlo, 10, 0);
3696  mhi = multadd(mhi, 10, 0);
3697  }
3698  }
3699  }
3700  else
3701  for (i = 1;; i++) {
3702  *s++ = dig = quorem(b,S) + '0';
3703  if (!b->x[0] && b->wds <= 1) {
3704 #ifdef SET_INEXACT
3705  inexact = 0;
3706 #endif
3707  goto ret;
3708  }
3709  if (i >= ilim)
3710  break;
3711  b = multadd(b, 10, 0);
3712  }
3713 
3714  /* Round off last digit */
3715 
3716 #ifdef Honor_FLT_ROUNDS
3717  switch (rounding) {
3718  case 0: goto trimzeros;
3719  case 2: goto roundoff;
3720  }
3721 #endif
3722  b = lshift(b, 1);
3723  j = cmp(b, S);
3724  if (j > 0 || (j == 0 && (dig & 1))) {
3725  roundoff:
3726  while (*--s == '9')
3727  if (s == s0) {
3728  k++;
3729  *s++ = '1';
3730  goto ret;
3731  }
3732  ++*s++;
3733  }
3734  else {
3735  while (*--s == '0') ;
3736  s++;
3737  }
3738 ret:
3739  Bfree(S);
3740  if (mhi) {
3741  if (mlo && mlo != mhi)
3742  Bfree(mlo);
3743  Bfree(mhi);
3744  }
3745 ret1:
3746 #ifdef SET_INEXACT
3747  if (inexact) {
3748  if (!oldinexact) {
3749  word0(d) = Exp_1 + (70 << Exp_shift);
3750  word1(d) = 0;
3751  dval(d) += 1.;
3752  }
3753  }
3754  else if (!oldinexact)
3755  clear_inexact();
3756 #endif
3757  Bfree(b);
3758  *s = 0;
3759  *decpt = k + 1;
3760  if (rve)
3761  *rve = s;
3762  return s0;
3763 }
3764 
3765 void
3766 ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg)
3767 {
3768  const char *end;
3769  int len;
3770 
3771  if (!str) return;
3772  for (; *str; str = end) {
3773  while (ISSPACE(*str) || *str == ',') str++;
3774  if (!*str) break;
3775  end = str;
3776  while (*end && !ISSPACE(*end) && *end != ',') end++;
3777  len = (int)(end - str); /* assume no string exceeds INT_MAX */
3778  (*func)(str, len, arg);
3779  }
3780 }
3781 
3782 /*-
3783  * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
3784  * All rights reserved.
3785  *
3786  * Redistribution and use in source and binary forms, with or without
3787  * modification, are permitted provided that the following conditions
3788  * are met:
3789  * 1. Redistributions of source code must retain the above copyright
3790  * notice, this list of conditions and the following disclaimer.
3791  * 2. Redistributions in binary form must reproduce the above copyright
3792  * notice, this list of conditions and the following disclaimer in the
3793  * documentation and/or other materials provided with the distribution.
3794  *
3795  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
3796  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
3797  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
3798  * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
3799  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
3800  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
3801  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
3802  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
3803  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
3804  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
3805  * SUCH DAMAGE.
3806  */
3807 
3808 #define DBL_MANH_SIZE 20
3809 #define DBL_MANL_SIZE 32
3810 #define DBL_ADJ (DBL_MAX_EXP - 2)
3811 #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3812 #define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3813 #define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3814 #define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3815 #define dmanl_get(u) ((uint32_t)word1(u))
3816 
3817 
3818 /*
3819  * This procedure converts a double-precision number in IEEE format
3820  * into a string of hexadecimal digits and an exponent of 2. Its
3821  * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
3822  * following exceptions:
3823  *
3824  * - An ndigits < 0 causes it to use as many digits as necessary to
3825  * represent the number exactly.
3826  * - The additional xdigs argument should point to either the string
3827  * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
3828  * which case is desired.
3829  * - This routine does not repeat dtoa's mistake of setting decpt
3830  * to 9999 in the case of an infinity or NaN. INT_MAX is used
3831  * for this purpose instead.
3832  *
3833  * Note that the C99 standard does not specify what the leading digit
3834  * should be for non-zero numbers. For instance, 0x1.3p3 is the same
3835  * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
3836  * the leading digit a 1. This ensures that the exponent printed is the
3837  * actual base-2 exponent, i.e., ilogb(d).
3838  *
3839  * Inputs: d, xdigs, ndigits
3840  * Outputs: decpt, sign, rve
3841  */
3842 char *
3843 ruby_hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
3844  char **rve)
3845 {
3846  U u;
3847  char *s, *s0;
3848  int bufsize;
3849  uint32_t manh, manl;
3850 
3851  u.d = d;
3852  if (word0(u) & Sign_bit) {
3853  /* set sign for everything, including 0's and NaNs */
3854  *sign = 1;
3855  word0(u) &= ~Sign_bit; /* clear sign bit */
3856  }
3857  else
3858  *sign = 0;
3859 
3860  if (isinf(d)) { /* FP_INFINITE */
3861  *decpt = INT_MAX;
3862  return rv_strdup(INFSTR, rve);
3863  }
3864  else if (isnan(d)) { /* FP_NAN */
3865  *decpt = INT_MAX;
3866  return rv_strdup(NANSTR, rve);
3867  }
3868  else if (d == 0.0) { /* FP_ZERO */
3869  *decpt = 1;
3870  return rv_strdup(ZEROSTR, rve);
3871  }
3872  else if (dexp_get(u)) { /* FP_NORMAL */
3873  *decpt = dexp_get(u) - DBL_ADJ;
3874  }
3875  else { /* FP_SUBNORMAL */
3876  u.d *= 5.363123171977039e+154 /* 0x1p514 */;
3877  *decpt = dexp_get(u) - (514 + DBL_ADJ);
3878  }
3879 
3880  if (ndigits == 0) /* dtoa() compatibility */
3881  ndigits = 1;
3882 
3883  /*
3884  * If ndigits < 0, we are expected to auto-size, so we allocate
3885  * enough space for all the digits.
3886  */
3887  bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3888  s0 = rv_alloc(bufsize+1);
3889 
3890  /* Round to the desired number of digits. */
3891  if (SIGFIGS > ndigits && ndigits > 0) {
3892  float redux = 1.0f;
3893  volatile double d;
3894  int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3895  dexp_set(u, offset);
3896  d = u.d;
3897  d += redux;
3898  d -= redux;
3899  u.d = d;
3900  *decpt += dexp_get(u) - offset;
3901  }
3902 
3903  manh = dmanh_get(u);
3904  manl = dmanl_get(u);
3905  *s0 = '1';
3906  for (s = s0 + 1; s < s0 + bufsize; s++) {
3907  *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3908  manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3909  manl <<= 4;
3910  }
3911 
3912  /* If ndigits < 0, we are expected to auto-size the precision. */
3913  if (ndigits < 0) {
3914  for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
3915  ;
3916  }
3917 
3918  s = s0 + ndigits;
3919  *s = '\0';
3920  if (rve != NULL)
3921  *rve = s;
3922  return (s0);
3923 }
3924 
3925 #ifdef __cplusplus
3926 #if 0
3927 { /* satisfy cc-mode */
3928 #endif
3929 }
3930 #endif
#define d0
#define Sign_bit
Definition: util.c:852
#define mmstep
Definition: util.c:197
#define dexp_set(u, v)
Definition: util.c:3813
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Definition: tcltklib.c:10208
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Definition: bigdecimal.c:5676
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Definition: win32ole.c:786
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Definition: util.c:3815
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#define fail()
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Definition: isinf.c:52
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#define xrealloc
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Definition: util.c:791
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Definition: os2.c:56
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Definition: util.c:859
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Definition: tcltklib.c:7829
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Definition: util.c:1838
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Definition: util.c:1436
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Definition: util.c:853
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#define rounded_quotient(a, b)
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Definition: util.c:477
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Definition: util.c:246
RUBY_EXTERN int isinf(double)
Definition: isinf.c:56
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Definition: win32.h:327
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Definition: acosh.c:19
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Definition: zlib.c:2270
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Definition: bigdecimal.c:5680
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Definition: util.c:955
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Definition: tcltklib.c:3781
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Definition: util.c:997
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Definition: bigdecimal.c:5106
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Definition: bigdecimal.c:5677
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Definition: util.c:1055
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Definition: tcltklib.c:2967
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Definition: util.c:1003
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