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* encoding.c (rb_filesystem_encoding): use default external encoding
[ruby-svn.git] / util.c
blob24841d6bef1e8fbaa7dd2903f2b433e4900aeb81
1 /**********************************************************************
2
3 util.c -
4
5 $Author$
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
14 #include <ctype.h>
15 #include <stdio.h>
16 #include <errno.h>
17 #include <math.h>
18 #include <float.h>
19
20 #ifdef _WIN32
21 #include "missing/file.h"
22 #endif
23 #if defined(__CYGWIN32__)
24 #define _open open
25 #define _close close
26 #define _unlink unlink
27 #define _access access
28 #elif defined(_WIN32)
29 #include <io.h>
30 #endif
31
32 #include "ruby/util.h"
33
34 unsigned long
35 ruby_scan_oct(const char *start, int len, int *retlen)
36 {
37 register const char *s = start;
38 register unsigned long retval = 0;
39
40 while (len-- && *s >= '0' && *s <= '7') {
41 retval <<= 3;
42 retval |= *s++ - '0';
43 }
44 *retlen = s - start;
45 return retval;
46 }
47
48 unsigned long
49 ruby_scan_hex(const char *start, int len, int *retlen)
50 {
51 static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
52 register const char *s = start;
53 register unsigned long retval = 0;
54 char *tmp;
55
56 while (len-- && *s && (tmp = strchr(hexdigit, *s))) {
57 retval <<= 4;
58 retval |= (tmp - hexdigit) & 15;
59 s++;
60 }
61 *retlen = s - start;
62 return retval;
63 }
64
65 static unsigned long
66 scan_digits(const char *str, int base, size_t *retlen, int *overflow)
67 {
68 static signed char table[] = {
69 /* 0 1 2 3 4 5 6 7 8 9 a b c d e f */
70 /*0*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
71 /*1*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
72 /*2*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
73 /*3*/ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,-1,-1,-1,-1,-1,-1,
74 /*4*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
75 /*5*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
76 /*6*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
77 /*7*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
78 /*8*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
79 /*9*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
80 /*a*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
81 /*b*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
82 /*c*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
83 /*d*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
84 /*e*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
85 /*f*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
86 };
87
88 const char *start = str;
89 unsigned long ret = 0, x;
90 unsigned long mul_overflow = (~(unsigned long)0) / base;
91 int c;
92 *overflow = 0;
93
94 while ((c = (unsigned char)*str++) != '\0') {
95 int d = table[c];
96 if (d == -1 || base <= d) {
97 *retlen = (str-1) - start;
98 return ret;
99 }
100 if (mul_overflow < ret)
101 *overflow = 1;
102 ret *= base;
103 x = ret;
104 ret += d;
105 if (ret < x)
106 *overflow = 1;
107 }
108 *retlen = (str-1) - start;
109 return ret;
110 }
111
112 unsigned long
113 ruby_strtoul(const char *str, char **endptr, int base)
114 {
115 int c, b, overflow;
116 int sign = 0;
117 size_t len;
118 unsigned long ret;
119 const char *subject_found = str;
120
121 if (base == 1 || 36 < base) {
122 errno = EINVAL;
123 return 0;
124 }
125
126 while ((c = *str) && ISSPACE(c))
127 str++;
128
129 if (c == '+') {
130 sign = 1;
131 str++;
132 }
133 else if (c == '-') {
134 sign = -1;
135 str++;
136 }
137
138 if (str[0] == '0') {
139 subject_found = str+1;
140 if (base == 0 || base == 16) {
141 if (str[1] == 'x' || str[1] == 'X') {
142 b = 16;
143 str += 2;
144 }
145 else {
146 b = base == 0 ? 8 : 16;
147 str++;
148 }
149 }
150 else {
151 b = base;
152 str++;
153 }
154 }
155 else {
156 b = base == 0 ? 10 : base;
157 }
158
159 ret = scan_digits(str, b, &len, &overflow);
160
161 if (0 < len)
162 subject_found = str+len;
163
164 if (endptr)
165 *endptr = (char*)subject_found;
166
167 if (overflow) {
168 errno = ERANGE;
169 return ULONG_MAX;
170 }
171
172 if (sign < 0) {
173 ret = -ret;
174 return ret;
175 }
176 else {
177 return ret;
178 }
179 }
180
181 #include <sys/types.h>
182 #include <sys/stat.h>
183 #ifdef HAVE_UNISTD_H
184 #include <unistd.h>
185 #endif
186 #if defined(HAVE_FCNTL_H)
187 #include <fcntl.h>
188 #endif
189
190 #ifndef S_ISDIR
191 # define S_ISDIR(m) ((m & S_IFMT) == S_IFDIR)
192 #endif
193
194 #if defined(MSDOS) || defined(__CYGWIN32__) || defined(_WIN32)
195 /*
196 * Copyright (c) 1993, Intergraph Corporation
197 *
198 * You may distribute under the terms of either the GNU General Public
199 * License or the Artistic License, as specified in the perl README file.
200 *
201 * Various Unix compatibility functions and NT specific functions.
202 *
203 * Some of this code was derived from the MSDOS port(s) and the OS/2 port.
204 *
205 */
206
207
208 /*
209 * Suffix appending for in-place editing under MS-DOS and OS/2 (and now NT!).
210 *
211 * Here are the rules:
212 *
213 * Style 0: Append the suffix exactly as standard perl would do it.
214 * If the filesystem groks it, use it. (HPFS will always
215 * grok it. So will NTFS. FAT will rarely accept it.)
216 *
217 * Style 1: The suffix begins with a '.'. The extension is replaced.
218 * If the name matches the original name, use the fallback method.
219 *
220 * Style 2: The suffix is a single character, not a '.'. Try to add the
221 * suffix to the following places, using the first one that works.
222 * [1] Append to extension.
223 * [2] Append to filename,
224 * [3] Replace end of extension,
225 * [4] Replace end of filename.
226 * If the name matches the original name, use the fallback method.
227 *
228 * Style 3: Any other case: Ignore the suffix completely and use the
229 * fallback method.
230 *
231 * Fallback method: Change the extension to ".$$$". If that matches the
232 * original name, then change the extension to ".~~~".
233 *
234 * If filename is more than 1000 characters long, we die a horrible
235 * death. Sorry.
236 *
237 * The filename restriction is a cheat so that we can use buf[] to store
238 * assorted temporary goo.
239 *
240 * Examples, assuming style 0 failed.
241 *
242 * suffix = ".bak" (style 1)
243 * foo.bar => foo.bak
244 * foo.bak => foo.$$$ (fallback)
245 * foo.$$$ => foo.~~~ (fallback)
246 * makefile => makefile.bak
247 *
248 * suffix = "~" (style 2)
249 * foo.c => foo.c~
250 * foo.c~ => foo.c~~
251 * foo.c~~ => foo~.c~~
252 * foo~.c~~ => foo~~.c~~
253 * foo~~~~~.c~~ => foo~~~~~.$$$ (fallback)
254 *
255 * foo.pas => foo~.pas
256 * makefile => makefile.~
257 * longname.fil => longname.fi~
258 * longname.fi~ => longnam~.fi~
259 * longnam~.fi~ => longnam~.$$$
260 *
261 */
262
263
264 static int valid_filename(const char *s);
265
266 static const char suffix1[] = ".$$$";
267 static const char suffix2[] = ".~~~";
268
269 #define ext (&buf[1000])
270
271 #define strEQ(s1,s2) (strcmp(s1,s2) == 0)
272
273 void
274 ruby_add_suffix(VALUE str, const char *suffix)
275 {
276 int baselen;
277 int extlen = strlen(suffix);
278 char *s, *t, *p;
279 long slen;
280 char buf[1024];
281
282 if (RSTRING_LEN(str) > 1000)
283 rb_fatal("Cannot do inplace edit on long filename (%ld characters)",
284 RSTRING_LEN(str));
285
286 #if defined(DJGPP) || defined(__CYGWIN32__) || defined(_WIN32)
287 /* Style 0 */
288 slen = RSTRING_LEN(str);
289 rb_str_cat(str, suffix, extlen);
290 #if defined(DJGPP)
291 if (_USE_LFN) return;
292 #else
293 if (valid_filename(RSTRING_PTR(str))) return;
294 #endif
295
296 /* Fooey, style 0 failed. Fix str before continuing. */
297 rb_str_resize(str, slen);
298 #endif
299
300 slen = extlen;
301 t = buf; baselen = 0; s = RSTRING_PTR(str);
302 while ((*t = *s) && *s != '.') {
303 baselen++;
304 if (*s == '\\' || *s == '/') baselen = 0;
305 s++; t++;
306 }
307 p = t;
308
309 t = ext; extlen = 0;
310 while ((*t++ = *s++) != 0) extlen++;
311 if (extlen == 0) { ext[0] = '.'; ext[1] = 0; extlen++; }
312
313 if (*suffix == '.') { /* Style 1 */
314 if (strEQ(ext, suffix)) goto fallback;
315 strcpy(p, suffix);
316 }
317 else if (suffix[1] == '\0') { /* Style 2 */
318 if (extlen < 4) {
319 ext[extlen] = *suffix;
320 ext[++extlen] = '\0';
321 }
322 else if (baselen < 8) {
323 *p++ = *suffix;
324 }
325 else if (ext[3] != *suffix) {
326 ext[3] = *suffix;
327 }
328 else if (buf[7] != *suffix) {
329 buf[7] = *suffix;
330 }
331 else goto fallback;
332 strcpy(p, ext);
333 }
334 else { /* Style 3: Panic */
335 fallback:
336 (void)memcpy(p, strEQ(ext, suffix1) ? suffix2 : suffix1, 5);
337 }
338 rb_str_resize(str, strlen(buf));
339 memcpy(RSTRING_PTR(str), buf, RSTRING_LEN(str));
340 }
341
342 #if defined(__CYGWIN32__) || defined(_WIN32)
343 static int
344 valid_filename(const char *s)
345 {
346 int fd;
347
348 /*
349 // It doesn't exist, so see if we can open it.
350 */
351
352 if ((fd = _open(s, O_CREAT|O_EXCL, 0666)) >= 0) {
353 _close(fd);
354 _unlink(s); /* don't leave it laying around */
355 return 1;
356 }
357 else if (errno == EEXIST) {
358 /* if the file exists, then it's a valid filename! */
359 return 1;
360 }
361 return 0;
362 }
363 #endif
364 #endif
365
366 #if defined __DJGPP__
367
368 #include <dpmi.h>
369
370 static char dbcs_table[256];
371
372 int
373 make_dbcs_table()
374 {
375 __dpmi_regs r;
376 struct {
377 unsigned char start;
378 unsigned char end;
379 } vec;
380 int offset;
381
382 memset(&r, 0, sizeof(r));
383 r.x.ax = 0x6300;
384 __dpmi_int(0x21, &r);
385 offset = r.x.ds * 16 + r.x.si;
386
387 for (;;) {
388 int i;
389 dosmemget(offset, sizeof vec, &vec);
390 if (!vec.start && !vec.end)
391 break;
392 for (i = vec.start; i <= vec.end; i++)
393 dbcs_table[i] = 1;
394 offset += 2;
395 }
396 }
397
398 int
399 mblen(const char *s, size_t n)
400 {
401 static int need_init = 1;
402 if (need_init) {
403 make_dbcs_table();
404 need_init = 0;
405 }
406 if (s) {
407 if (n == 0 || *s == 0)
408 return 0;
409 else if (!s[1])
410 return 1;
411 return dbcs_table[(unsigned char)*s] + 1;
412 }
413 else
414 return 1;
415 }
416
417 struct PathList {
418 struct PathList *next;
419 char *path;
420 };
421
422 struct PathInfo {
423 struct PathList *head;
424 int count;
425 };
426
427 static int
428 push_element(const char *path, VALUE vinfo)
429 {
430 struct PathList *p;
431 struct PathInfo *info = (struct PathInfo *)vinfo;
432
433 p = ALLOC(struct PathList);
434 MEMZERO(p, struct PathList, 1);
435 p->path = ruby_strdup(path);
436 p->next = info->head;
437 info->head = p;
438 info->count++;
439
440 return 0;
441 }
442
443 #include <dirent.h>
444 int __opendir_flags = __OPENDIR_PRESERVE_CASE;
445
446 char **
447 __crt0_glob_function(char *path)
448 {
449 int len = strlen(path);
450 int i;
451 char **rv;
452 char path_buffer[PATH_MAX];
453 char *buf = path_buffer;
454 char *p;
455 struct PathInfo info;
456 struct PathList *plist;
457
458 if (PATH_MAX <= len)
459 buf = ruby_xmalloc(len + 1);
460
461 strncpy(buf, path, len);
462 buf[len] = '\0';
463
464 for (p = buf; *p; p += mblen(p, RUBY_MBCHAR_MAXSIZE))
465 if (*p == '\\')
466 *p = '/';
467
468 info.count = 0;
469 info.head = 0;
470
471 ruby_glob(buf, 0, push_element, (VALUE)&info);
472
473 if (buf != path_buffer)
474 ruby_xfree(buf);
475
476 if (info.count == 0)
477 return 0;
478
479 rv = ruby_xmalloc((info.count + 1) * sizeof (char *));
480
481 plist = info.head;
482 i = 0;
483 while (plist) {
484 struct PathList *cur;
485 rv[i] = plist->path;
486 cur = plist;
487 plist = plist->next;
488 ruby_xfree(cur);
489 i++;
490 }
491 rv[i] = 0;
492 return rv;
493 }
494
495 #endif
496
497 /* mm.c */
498
499 #define A ((int*)a)
500 #define B ((int*)b)
501 #define C ((int*)c)
502 #define D ((int*)d)
503
504 #define mmprepare(base, size) do {\
505 if (((long)base & (0x3)) == 0)\
506 if (size >= 16) mmkind = 1;\
507 else mmkind = 0;\
508 else mmkind = -1;\
509 high = (size & (~0xf));\
510 low = (size & 0x0c);\
511 } while (0)\
512
513 #define mmarg mmkind, size, high, low
514
515 static void mmswap_(register char *a, register char *b, int mmkind, int size, int high, int low)
516 {
517 register int s;
518 if (a == b) return;
519 if (mmkind >= 0) {
520 if (mmkind > 0) {
521 register char *t = a + high;
522 do {
523 s = A[0]; A[0] = B[0]; B[0] = s;
524 s = A[1]; A[1] = B[1]; B[1] = s;
525 s = A[2]; A[2] = B[2]; B[2] = s;
526 s = A[3]; A[3] = B[3]; B[3] = s; a += 16; b += 16;
527 } while (a < t);
528 }
529 if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = s;
530 if (low >= 8) { s = A[1]; A[1] = B[1]; B[1] = s;
531 if (low == 12) {s = A[2]; A[2] = B[2]; B[2] = s;}}}
532 }
533 else {
534 register char *t = a + size;
535 do {s = *a; *a++ = *b; *b++ = s;} while (a < t);
536 }
537 }
538 #define mmswap(a,b) mmswap_((a),(b),mmarg)
539
540 static void mmrot3_(register char *a, register char *b, register char *c, int mmkind, int size, int high, int low)
541 {
542 register int s;
543 if (mmkind >= 0) {
544 if (mmkind > 0) {
545 register char *t = a + high;
546 do {
547 s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
548 s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
549 s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;
550 s = A[3]; A[3] = B[3]; B[3] = C[3]; C[3] = s; a += 16; b += 16; c += 16;
551 } while (a < t);
552 }
553 if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
554 if (low >= 8) { s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
555 if (low == 12) {s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;}}}
556 }
557 else {
558 register char *t = a + size;
559 do {s = *a; *a++ = *b; *b++ = *c; *c++ = s;} while (a < t);
560 }
561 }
562 #define mmrot3(a,b,c) mmrot3_((a),(b),(c),mmarg)
563
564 /* qs6.c */
565 /*****************************************************/
566 /* */
567 /* qs6 (Quick sort function) */
568 /* */
569 /* by Tomoyuki Kawamura 1995.4.21 */
570 /* kawamura@tokuyama.ac.jp */
571 /*****************************************************/
572
573 typedef struct { char *LL, *RR; } stack_node; /* Stack structure for L,l,R,r */
574 #define PUSH(ll,rr) do { top->LL = (ll); top->RR = (rr); ++top; } while (0) /* Push L,l,R,r */
575 #define POP(ll,rr) do { --top; ll = top->LL; rr = top->RR; } while (0) /* Pop L,l,R,r */
576
577 #define med3(a,b,c) ((*cmp)(a,b,d)<0 ? \
578 ((*cmp)(b,c,d)<0 ? b : ((*cmp)(a,c,d)<0 ? c : a)) : \
579 ((*cmp)(b,c,d)>0 ? b : ((*cmp)(a,c,d)<0 ? a : c)))
580
581 void
582 ruby_qsort(void* base, const int nel, const int size,
583 int (*cmp)(const void*, const void*, void*), void *d)
584 {
585 register char *l, *r, *m; /* l,r:left,right group m:median point */
586 register int t, eq_l, eq_r; /* eq_l: all items in left group are equal to S */
587 char *L = base; /* left end of curren region */
588 char *R = (char*)base + size*(nel-1); /* right end of current region */
589 int chklim = 63; /* threshold of ordering element check */
590 stack_node stack[32], *top = stack; /* 32 is enough for 32bit CPU */
591 int mmkind, high, low;
592
593 if (nel <= 1) return; /* need not to sort */
594 mmprepare(base, size);
595 goto start;
596
597 nxt:
598 if (stack == top) return; /* return if stack is empty */
599 POP(L,R);
600
601 for (;;) {
602 start:
603 if (L + size == R) { /* 2 elements */
604 if ((*cmp)(L,R,d) > 0) mmswap(L,R); goto nxt;
605 }
606
607 l = L; r = R;
608 t = (r - l + size) / size; /* number of elements */
609 m = l + size * (t >> 1); /* calculate median value */
610
611 if (t >= 60) {
612 register char *m1;
613 register char *m3;
614 if (t >= 200) {
615 t = size*(t>>3); /* number of bytes in splitting 8 */
616 {
617 register char *p1 = l + t;
618 register char *p2 = p1 + t;
619 register char *p3 = p2 + t;
620 m1 = med3(p1, p2, p3);
621 p1 = m + t;
622 p2 = p1 + t;
623 p3 = p2 + t;
624 m3 = med3(p1, p2, p3);
625 }
626 }
627 else {
628 t = size*(t>>2); /* number of bytes in splitting 4 */
629 m1 = l + t;
630 m3 = m + t;
631 }
632 m = med3(m1, m, m3);
633 }
634
635 if ((t = (*cmp)(l,m,d)) < 0) { /*3-5-?*/
636 if ((t = (*cmp)(m,r,d)) < 0) { /*3-5-7*/
637 if (chklim && nel >= chklim) { /* check if already ascending order */
638 char *p;
639 chklim = 0;
640 for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) > 0) goto fail;
641 goto nxt;
642 }
643 fail: goto loopA; /*3-5-7*/
644 }
645 if (t > 0) {
646 if ((*cmp)(l,r,d) <= 0) {mmswap(m,r); goto loopA;} /*3-5-4*/
647 mmrot3(r,m,l); goto loopA; /*3-5-2*/
648 }
649 goto loopB; /*3-5-5*/
650 }
651
652 if (t > 0) { /*7-5-?*/
653 if ((t = (*cmp)(m,r,d)) > 0) { /*7-5-3*/
654 if (chklim && nel >= chklim) { /* check if already ascending order */
655 char *p;
656 chklim = 0;
657 for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) < 0) goto fail2;
658 while (l<r) {mmswap(l,r); l+=size; r-=size;} /* reverse region */
659 goto nxt;
660 }
661 fail2: mmswap(l,r); goto loopA; /*7-5-3*/
662 }
663 if (t < 0) {
664 if ((*cmp)(l,r,d) <= 0) {mmswap(l,m); goto loopB;} /*7-5-8*/
665 mmrot3(l,m,r); goto loopA; /*7-5-6*/
666 }
667 mmswap(l,r); goto loopA; /*7-5-5*/
668 }
669
670 if ((t = (*cmp)(m,r,d)) < 0) {goto loopA;} /*5-5-7*/
671 if (t > 0) {mmswap(l,r); goto loopB;} /*5-5-3*/
672
673 /* determining splitting type in case 5-5-5 */ /*5-5-5*/
674 for (;;) {
675 if ((l += size) == r) goto nxt; /*5-5-5*/
676 if (l == m) continue;
677 if ((t = (*cmp)(l,m,d)) > 0) {mmswap(l,r); l = L; goto loopA;}/*575-5*/
678 if (t < 0) {mmswap(L,l); l = L; goto loopB;} /*535-5*/
679 }
680
681 loopA: eq_l = 1; eq_r = 1; /* splitting type A */ /* left <= median < right */
682 for (;;) {
683 for (;;) {
684 if ((l += size) == r)
685 {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
686 if (l == m) continue;
687 if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
688 if (t < 0) eq_l = 0;
689 }
690 for (;;) {
691 if (l == (r -= size))
692 {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
693 if (r == m) {m = l; break;}
694 if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
695 if (t == 0) break;
696 }
697 mmswap(l,r); /* swap left and right */
698 }
699
700 loopB: eq_l = 1; eq_r = 1; /* splitting type B */ /* left < median <= right */
701 for (;;) {
702 for (;;) {
703 if (l == (r -= size))
704 {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
705 if (r == m) continue;
706 if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
707 if (t > 0) eq_r = 0;
708 }
709 for (;;) {
710 if ((l += size) == r)
711 {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
712 if (l == m) {m = r; break;}
713 if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
714 if (t == 0) break;
715 }
716 mmswap(l,r); /* swap left and right */
717 }
718
719 fin:
720 if (eq_l == 0) /* need to sort left side */
721 if (eq_r == 0) /* need to sort right side */
722 if (l-L < R-r) {PUSH(r,R); R = l;} /* sort left side first */
723 else {PUSH(L,l); L = r;} /* sort right side first */
724 else R = l; /* need to sort left side only */
725 else if (eq_r == 0) L = r; /* need to sort right side only */
726 else goto nxt; /* need not to sort both sides */
727 }
728 }
729
730 char *
731 ruby_strdup(const char *str)
732 {
733 char *tmp;
734 int len = strlen(str) + 1;
735
736 tmp = xmalloc(len);
737 memcpy(tmp, str, len);
738
739 return tmp;
740 }
741
742 char *
743 ruby_getcwd(void)
744 {
745 #ifdef HAVE_GETCWD
746 int size = 200;
747 char *buf = xmalloc(size);
748
749 while (!getcwd(buf, size)) {
750 if (errno != ERANGE) {
751 xfree(buf);
752 rb_sys_fail("getcwd");
753 }
754 size *= 2;
755 buf = xrealloc(buf, size);
756 }
757 #else
758 # ifndef PATH_MAX
759 # define PATH_MAX 8192
760 # endif
761 char *buf = xmalloc(PATH_MAX+1);
762
763 if (!getwd(buf)) {
764 xfree(buf);
765 rb_sys_fail("getwd");
766 }
767 #endif
768 return buf;
769 }
770
771 /****************************************************************
772 *
773 * The author of this software is David M. Gay.
774 *
775 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
776 *
777 * Permission to use, copy, modify, and distribute this software for any
778 * purpose without fee is hereby granted, provided that this entire notice
779 * is included in all copies of any software which is or includes a copy
780 * or modification of this software and in all copies of the supporting
781 * documentation for such software.
782 *
783 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
784 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
785 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
786 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
787 *
788 ***************************************************************/
789
790 /* Please send bug reports to David M. Gay (dmg at acm dot org,
791 * with " at " changed at "@" and " dot " changed to "."). */
792
793 /* On a machine with IEEE extended-precision registers, it is
794 * necessary to specify double-precision (53-bit) rounding precision
795 * before invoking strtod or dtoa. If the machine uses (the equivalent
796 * of) Intel 80x87 arithmetic, the call
797 * _control87(PC_53, MCW_PC);
798 * does this with many compilers. Whether this or another call is
799 * appropriate depends on the compiler; for this to work, it may be
800 * necessary to #include "float.h" or another system-dependent header
801 * file.
802 */
803
804 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
805 *
806 * This strtod returns a nearest machine number to the input decimal
807 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
808 * broken by the IEEE round-even rule. Otherwise ties are broken by
809 * biased rounding (add half and chop).
810 *
811 * Inspired loosely by William D. Clinger's paper "How to Read Floating
812 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
813 *
814 * Modifications:
815 *
816 * 1. We only require IEEE, IBM, or VAX double-precision
817 * arithmetic (not IEEE double-extended).
818 * 2. We get by with floating-point arithmetic in a case that
819 * Clinger missed -- when we're computing d * 10^n
820 * for a small integer d and the integer n is not too
821 * much larger than 22 (the maximum integer k for which
822 * we can represent 10^k exactly), we may be able to
823 * compute (d*10^k) * 10^(e-k) with just one roundoff.
824 * 3. Rather than a bit-at-a-time adjustment of the binary
825 * result in the hard case, we use floating-point
826 * arithmetic to determine the adjustment to within
827 * one bit; only in really hard cases do we need to
828 * compute a second residual.
829 * 4. Because of 3., we don't need a large table of powers of 10
830 * for ten-to-e (just some small tables, e.g. of 10^k
831 * for 0 <= k <= 22).
832 */
833
834 /*
835 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
836 * significant byte has the lowest address.
837 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
838 * significant byte has the lowest address.
839 * #define Long int on machines with 32-bit ints and 64-bit longs.
840 * #define IBM for IBM mainframe-style floating-point arithmetic.
841 * #define VAX for VAX-style floating-point arithmetic (D_floating).
842 * #define No_leftright to omit left-right logic in fast floating-point
843 * computation of dtoa.
844 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
845 * and strtod and dtoa should round accordingly.
846 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
847 * and Honor_FLT_ROUNDS is not #defined.
848 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
849 * that use extended-precision instructions to compute rounded
850 * products and quotients) with IBM.
851 * #define ROUND_BIASED for IEEE-format with biased rounding.
852 * #define Inaccurate_Divide for IEEE-format with correctly rounded
853 * products but inaccurate quotients, e.g., for Intel i860.
854 * #define NO_LONG_LONG on machines that do not have a "long long"
855 * integer type (of >= 64 bits). On such machines, you can
856 * #define Just_16 to store 16 bits per 32-bit Long when doing
857 * high-precision integer arithmetic. Whether this speeds things
858 * up or slows things down depends on the machine and the number
859 * being converted. If long long is available and the name is
860 * something other than "long long", #define Llong to be the name,
861 * and if "unsigned Llong" does not work as an unsigned version of
862 * Llong, #define #ULLong to be the corresponding unsigned type.
863 * #define KR_headers for old-style C function headers.
864 * #define Bad_float_h if your system lacks a float.h or if it does not
865 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
866 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
867 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
868 * if memory is available and otherwise does something you deem
869 * appropriate. If MALLOC is undefined, malloc will be invoked
870 * directly -- and assumed always to succeed.
871 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
872 * memory allocations from a private pool of memory when possible.
873 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
874 * unless #defined to be a different length. This default length
875 * suffices to get rid of MALLOC calls except for unusual cases,
876 * such as decimal-to-binary conversion of a very long string of
877 * digits. The longest string dtoa can return is about 751 bytes
878 * long. For conversions by strtod of strings of 800 digits and
879 * all dtoa conversions in single-threaded executions with 8-byte
880 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
881 * pointers, PRIVATE_MEM >= 7112 appears adequate.
882 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
883 * Infinity and NaN (case insensitively). On some systems (e.g.,
884 * some HP systems), it may be necessary to #define NAN_WORD0
885 * appropriately -- to the most significant word of a quiet NaN.
886 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
887 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
888 * strtod also accepts (case insensitively) strings of the form
889 * NaN(x), where x is a string of hexadecimal digits and spaces;
890 * if there is only one string of hexadecimal digits, it is taken
891 * for the 52 fraction bits of the resulting NaN; if there are two
892 * or more strings of hex digits, the first is for the high 20 bits,
893 * the second and subsequent for the low 32 bits, with intervening
894 * white space ignored; but if this results in none of the 52
895 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
896 * and NAN_WORD1 are used instead.
897 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
898 * multiple threads. In this case, you must provide (or suitably
899 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
900 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
901 * in pow5mult, ensures lazy evaluation of only one copy of high
902 * powers of 5; omitting this lock would introduce a small
903 * probability of wasting memory, but would otherwise be harmless.)
904 * You must also invoke freedtoa(s) to free the value s returned by
905 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
906 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
907 * avoids underflows on inputs whose result does not underflow.
908 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
909 * floating-point numbers and flushes underflows to zero rather
910 * than implementing gradual underflow, then you must also #define
911 * Sudden_Underflow.
912 * #define YES_ALIAS to permit aliasing certain double values with
913 * arrays of ULongs. This leads to slightly better code with
914 * some compilers and was always used prior to 19990916, but it
915 * is not strictly legal and can cause trouble with aggressively
916 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
917 * #define USE_LOCALE to use the current locale's decimal_point value.
918 * #define SET_INEXACT if IEEE arithmetic is being used and extra
919 * computation should be done to set the inexact flag when the
920 * result is inexact and avoid setting inexact when the result
921 * is exact. In this case, dtoa.c must be compiled in
922 * an environment, perhaps provided by #include "dtoa.c" in a
923 * suitable wrapper, that defines two functions,
924 * int get_inexact(void);
925 * void clear_inexact(void);
926 * such that get_inexact() returns a nonzero value if the
927 * inexact bit is already set, and clear_inexact() sets the
928 * inexact bit to 0. When SET_INEXACT is #defined, strtod
929 * also does extra computations to set the underflow and overflow
930 * flags when appropriate (i.e., when the result is tiny and
931 * inexact or when it is a numeric value rounded to +-infinity).
932 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
933 * the result overflows to +-Infinity or underflows to 0.
934 */
935
936 #ifdef WORDS_BIGENDIAN
937 #define IEEE_BIG_ENDIAN
938 #else
939 #define IEEE_LITTLE_ENDIAN
940 #endif
941
942 #ifdef __vax__
943 #define VAX
944 #undef IEEE_BIG_ENDIAN
945 #undef IEEE_LITTLE_ENDIAN
946 #endif
947
948 #if defined(__arm__) && !defined(__VFP_FP__)
949 #define IEEE_BIG_ENDIAN
950 #undef IEEE_LITTLE_ENDIAN
951 #endif
952
953 #undef Long
954 #undef ULong
955
956 #if SIZEOF_INT == 4
957 #define Long int
958 #define ULong unsigned int
959 #elif SIZEOF_LONG == 4
960 #define Long long int
961 #define ULong unsigned long int
962 #endif
963
964 #if HAVE_LONG_LONG
965 #define Llong LONG_LONG
966 #endif
967
968 #ifdef DEBUG
969 #include "stdio.h"
970 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
971 #endif
972
973 #include "stdlib.h"
974 #include "string.h"
975
976 #ifdef USE_LOCALE
977 #include "locale.h"
978 #endif
979
980 #ifdef MALLOC
981 extern void *MALLOC(size_t);
982 #else
983 #define MALLOC malloc
984 #endif
985
986 #ifndef Omit_Private_Memory
987 #ifndef PRIVATE_MEM
988 #define PRIVATE_MEM 2304
989 #endif
990 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
991 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
992 #endif
993
994 #undef IEEE_Arith
995 #undef Avoid_Underflow
996 #ifdef IEEE_BIG_ENDIAN
997 #define IEEE_Arith
998 #endif
999 #ifdef IEEE_LITTLE_ENDIAN
1000 #define IEEE_Arith
1001 #endif
1002
1003 #ifdef Bad_float_h
1004
1005 #ifdef IEEE_Arith
1006 #define DBL_DIG 15
1007 #define DBL_MAX_10_EXP 308
1008 #define DBL_MAX_EXP 1024
1009 #define FLT_RADIX 2
1010 #endif /*IEEE_Arith*/
1011
1012 #ifdef IBM
1013 #define DBL_DIG 16
1014 #define DBL_MAX_10_EXP 75
1015 #define DBL_MAX_EXP 63
1016 #define FLT_RADIX 16
1017 #define DBL_MAX 7.2370055773322621e+75
1018 #endif
1019
1020 #ifdef VAX
1021 #define DBL_DIG 16
1022 #define DBL_MAX_10_EXP 38
1023 #define DBL_MAX_EXP 127
1024 #define FLT_RADIX 2
1025 #define DBL_MAX 1.7014118346046923e+38
1026 #endif
1027
1028 #ifndef LONG_MAX
1029 #define LONG_MAX 2147483647
1030 #endif
1031
1032 #else /* ifndef Bad_float_h */
1033 #include "float.h"
1034 #endif /* Bad_float_h */
1035
1036 #ifndef __MATH_H__
1037 #include "math.h"
1038 #endif
1039
1040 #ifdef __cplusplus
1041 extern "C" {
1042 #endif
1043
1044 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
1045 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
1046 #endif
1047
1048 typedef union { double d; ULong L[2]; } U;
1049
1050 #ifdef YES_ALIAS
1051 #define dval(x) x
1052 #ifdef IEEE_LITTLE_ENDIAN
1053 #define word0(x) ((ULong *)&x)[1]
1054 #define word1(x) ((ULong *)&x)[0]
1055 #else
1056 #define word0(x) ((ULong *)&x)[0]
1057 #define word1(x) ((ULong *)&x)[1]
1058 #endif
1059 #else
1060 #ifdef IEEE_LITTLE_ENDIAN
1061 #define word0(x) ((U*)&x)->L[1]
1062 #define word1(x) ((U*)&x)->L[0]
1063 #else
1064 #define word0(x) ((U*)&x)->L[0]
1065 #define word1(x) ((U*)&x)->L[1]
1066 #endif
1067 #define dval(x) ((U*)&x)->d
1068 #endif
1069
1070 /* The following definition of Storeinc is appropriate for MIPS processors.
1071 * An alternative that might be better on some machines is
1072 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
1073 */
1074 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
1075 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
1076 ((unsigned short *)a)[0] = (unsigned short)c, a++)
1077 #else
1078 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
1079 ((unsigned short *)a)[1] = (unsigned short)c, a++)
1080 #endif
1081
1082 /* #define P DBL_MANT_DIG */
1083 /* Ten_pmax = floor(P*log(2)/log(5)) */
1084 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
1085 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
1086 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
1087
1088 #ifdef IEEE_Arith
1089 #define Exp_shift 20
1090 #define Exp_shift1 20
1091 #define Exp_msk1 0x100000
1092 #define Exp_msk11 0x100000
1093 #define Exp_mask 0x7ff00000
1094 #define P 53
1095 #define Bias 1023
1096 #define Emin (-1022)
1097 #define Exp_1 0x3ff00000
1098 #define Exp_11 0x3ff00000
1099 #define Ebits 11
1100 #define Frac_mask 0xfffff
1101 #define Frac_mask1 0xfffff
1102 #define Ten_pmax 22
1103 #define Bletch 0x10
1104 #define Bndry_mask 0xfffff
1105 #define Bndry_mask1 0xfffff
1106 #define LSB 1
1107 #define Sign_bit 0x80000000
1108 #define Log2P 1
1109 #define Tiny0 0
1110 #define Tiny1 1
1111 #define Quick_max 14
1112 #define Int_max 14
1113 #ifndef NO_IEEE_Scale
1114 #define Avoid_Underflow
1115 #ifdef Flush_Denorm /* debugging option */
1116 #undef Sudden_Underflow
1117 #endif
1118 #endif
1119
1120 #ifndef Flt_Rounds
1121 #ifdef FLT_ROUNDS
1122 #define Flt_Rounds FLT_ROUNDS
1123 #else
1124 #define Flt_Rounds 1
1125 #endif
1126 #endif /*Flt_Rounds*/
1127
1128 #ifdef Honor_FLT_ROUNDS
1129 #define Rounding rounding
1130 #undef Check_FLT_ROUNDS
1131 #define Check_FLT_ROUNDS
1132 #else
1133 #define Rounding Flt_Rounds
1134 #endif
1135
1136 #else /* ifndef IEEE_Arith */
1137 #undef Check_FLT_ROUNDS
1138 #undef Honor_FLT_ROUNDS
1139 #undef SET_INEXACT
1140 #undef Sudden_Underflow
1141 #define Sudden_Underflow
1142 #ifdef IBM
1143 #undef Flt_Rounds
1144 #define Flt_Rounds 0
1145 #define Exp_shift 24
1146 #define Exp_shift1 24
1147 #define Exp_msk1 0x1000000
1148 #define Exp_msk11 0x1000000
1149 #define Exp_mask 0x7f000000
1150 #define P 14
1151 #define Bias 65
1152 #define Exp_1 0x41000000
1153 #define Exp_11 0x41000000
1154 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
1155 #define Frac_mask 0xffffff
1156 #define Frac_mask1 0xffffff
1157 #define Bletch 4
1158 #define Ten_pmax 22
1159 #define Bndry_mask 0xefffff
1160 #define Bndry_mask1 0xffffff
1161 #define LSB 1
1162 #define Sign_bit 0x80000000
1163 #define Log2P 4
1164 #define Tiny0 0x100000
1165 #define Tiny1 0
1166 #define Quick_max 14
1167 #define Int_max 15
1168 #else /* VAX */
1169 #undef Flt_Rounds
1170 #define Flt_Rounds 1
1171 #define Exp_shift 23
1172 #define Exp_shift1 7
1173 #define Exp_msk1 0x80
1174 #define Exp_msk11 0x800000
1175 #define Exp_mask 0x7f80
1176 #define P 56
1177 #define Bias 129
1178 #define Exp_1 0x40800000
1179 #define Exp_11 0x4080
1180 #define Ebits 8
1181 #define Frac_mask 0x7fffff
1182 #define Frac_mask1 0xffff007f
1183 #define Ten_pmax 24
1184 #define Bletch 2
1185 #define Bndry_mask 0xffff007f
1186 #define Bndry_mask1 0xffff007f
1187 #define LSB 0x10000
1188 #define Sign_bit 0x8000
1189 #define Log2P 1
1190 #define Tiny0 0x80
1191 #define Tiny1 0
1192 #define Quick_max 15
1193 #define Int_max 15
1194 #endif /* IBM, VAX */
1195 #endif /* IEEE_Arith */
1196
1197 #ifndef IEEE_Arith
1198 #define ROUND_BIASED
1199 #endif
1200
1201 #ifdef RND_PRODQUOT
1202 #define rounded_product(a,b) a = rnd_prod(a, b)
1203 #define rounded_quotient(a,b) a = rnd_quot(a, b)
1204 extern double rnd_prod(double, double), rnd_quot(double, double);
1205 #else
1206 #define rounded_product(a,b) a *= b
1207 #define rounded_quotient(a,b) a /= b
1208 #endif
1209
1210 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
1211 #define Big1 0xffffffff
1212
1213 #ifndef Pack_32
1214 #define Pack_32
1215 #endif
1216
1217 #define FFFFFFFF 0xffffffffUL
1218
1219 #ifdef NO_LONG_LONG
1220 #undef ULLong
1221 #ifdef Just_16
1222 #undef Pack_32
1223 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
1224 * This makes some inner loops simpler and sometimes saves work
1225 * during multiplications, but it often seems to make things slightly
1226 * slower. Hence the default is now to store 32 bits per Long.
1227 */
1228 #endif
1229 #else /* long long available */
1230 #ifndef Llong
1231 #define Llong long long
1232 #endif
1233 #ifndef ULLong
1234 #define ULLong unsigned Llong
1235 #endif
1236 #endif /* NO_LONG_LONG */
1237
1238 #define MULTIPLE_THREADS 1
1239
1240 #ifndef MULTIPLE_THREADS
1241 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
1242 #define FREE_DTOA_LOCK(n) /*nothing*/
1243 #else
1244 #define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
1245 #define FREE_DTOA_LOCK(n) /*unused right now*/
1246 #endif
1247
1248 #define Kmax 15
1249
1250 struct Bigint {
1251 struct Bigint *next;
1252 int k, maxwds, sign, wds;
1253 ULong x[1];
1254 };
1255
1256 typedef struct Bigint Bigint;
1257
1258 static Bigint *freelist[Kmax+1];
1259
1260 static Bigint *
1261 Balloc(int k)
1262 {
1263 int x;
1264 Bigint *rv;
1265 #ifndef Omit_Private_Memory
1266 unsigned int len;
1267 #endif
1268
1269 ACQUIRE_DTOA_LOCK(0);
1270 if ((rv = freelist[k]) != 0) {
1271 freelist[k] = rv->next;
1272 }
1273 else {
1274 x = 1 << k;
1275 #ifdef Omit_Private_Memory
1276 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
1277 #else
1278 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
1279 /sizeof(double);
1280 if (pmem_next - private_mem + len <= PRIVATE_mem) {
1281 rv = (Bigint*)pmem_next;
1282 pmem_next += len;
1283 }
1284 else
1285 rv = (Bigint*)MALLOC(len*sizeof(double));
1286 #endif
1287 rv->k = k;
1288 rv->maxwds = x;
1289 }
1290 FREE_DTOA_LOCK(0);
1291 rv->sign = rv->wds = 0;
1292 return rv;
1293 }
1294
1295 static void
1296 Bfree(Bigint *v)
1297 {
1298 if (v) {
1299 ACQUIRE_DTOA_LOCK(0);
1300 v->next = freelist[v->k];
1301 freelist[v->k] = v;
1302 FREE_DTOA_LOCK(0);
1303 }
1304 }
1305
1306 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
1307 y->wds*sizeof(Long) + 2*sizeof(int))
1308
1309 static Bigint *
1310 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
1311 {
1312 int i, wds;
1313 #ifdef ULLong
1314 ULong *x;
1315 ULLong carry, y;
1316 #else
1317 ULong carry, *x, y;
1318 #ifdef Pack_32
1319 ULong xi, z;
1320 #endif
1321 #endif
1322 Bigint *b1;
1323
1324 wds = b->wds;
1325 x = b->x;
1326 i = 0;
1327 carry = a;
1328 do {
1329 #ifdef ULLong
1330 y = *x * (ULLong)m + carry;
1331 carry = y >> 32;
1332 *x++ = y & FFFFFFFF;
1333 #else
1334 #ifdef Pack_32
1335 xi = *x;
1336 y = (xi & 0xffff) * m + carry;
1337 z = (xi >> 16) * m + (y >> 16);
1338 carry = z >> 16;
1339 *x++ = (z << 16) + (y & 0xffff);
1340 #else
1341 y = *x * m + carry;
1342 carry = y >> 16;
1343 *x++ = y & 0xffff;
1344 #endif
1345 #endif
1346 } while (++i < wds);
1347 if (carry) {
1348 if (wds >= b->maxwds) {
1349 b1 = Balloc(b->k+1);
1350 Bcopy(b1, b);
1351 Bfree(b);
1352 b = b1;
1353 }
1354 b->x[wds++] = carry;
1355 b->wds = wds;
1356 }
1357 return b;
1358 }
1359
1360 static Bigint *
1361 s2b(const char *s, int nd0, int nd, ULong y9)
1362 {
1363 Bigint *b;
1364 int i, k;
1365 Long x, y;
1366
1367 x = (nd + 8) / 9;
1368 for (k = 0, y = 1; x > y; y <<= 1, k++) ;
1369 #ifdef Pack_32
1370 b = Balloc(k);
1371 b->x[0] = y9;
1372 b->wds = 1;
1373 #else
1374 b = Balloc(k+1);
1375 b->x[0] = y9 & 0xffff;
1376 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
1377 #endif
1378
1379 i = 9;
1380 if (9 < nd0) {
1381 s += 9;
1382 do {
1383 b = multadd(b, 10, *s++ - '0');
1384 } while (++i < nd0);
1385 s++;
1386 }
1387 else
1388 s += 10;
1389 for (; i < nd; i++)
1390 b = multadd(b, 10, *s++ - '0');
1391 return b;
1392 }
1393
1394 static int
1395 hi0bits(register ULong x)
1396 {
1397 register int k = 0;
1398
1399 if (!(x & 0xffff0000)) {
1400 k = 16;
1401 x <<= 16;
1402 }
1403 if (!(x & 0xff000000)) {
1404 k += 8;
1405 x <<= 8;
1406 }
1407 if (!(x & 0xf0000000)) {
1408 k += 4;
1409 x <<= 4;
1410 }
1411 if (!(x & 0xc0000000)) {
1412 k += 2;
1413 x <<= 2;
1414 }
1415 if (!(x & 0x80000000)) {
1416 k++;
1417 if (!(x & 0x40000000))
1418 return 32;
1419 }
1420 return k;
1421 }
1422
1423 static int
1424 lo0bits(ULong *y)
1425 {
1426 register int k;
1427 register ULong x = *y;
1428
1429 if (x & 7) {
1430 if (x & 1)
1431 return 0;
1432 if (x & 2) {
1433 *y = x >> 1;
1434 return 1;
1435 }
1436 *y = x >> 2;
1437 return 2;
1438 }
1439 k = 0;
1440 if (!(x & 0xffff)) {
1441 k = 16;
1442 x >>= 16;
1443 }
1444 if (!(x & 0xff)) {
1445 k += 8;
1446 x >>= 8;
1447 }
1448 if (!(x & 0xf)) {
1449 k += 4;
1450 x >>= 4;
1451 }
1452 if (!(x & 0x3)) {
1453 k += 2;
1454 x >>= 2;
1455 }
1456 if (!(x & 1)) {
1457 k++;
1458 x >>= 1;
1459 if (!x)
1460 return 32;
1461 }
1462 *y = x;
1463 return k;
1464 }
1465
1466 static Bigint *
1467 i2b(int i)
1468 {
1469 Bigint *b;
1470
1471 b = Balloc(1);
1472 b->x[0] = i;
1473 b->wds = 1;
1474 return b;
1475 }
1476
1477 static Bigint *
1478 mult(Bigint *a, Bigint *b)
1479 {
1480 Bigint *c;
1481 int k, wa, wb, wc;
1482 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
1483 ULong y;
1484 #ifdef ULLong
1485 ULLong carry, z;
1486 #else
1487 ULong carry, z;
1488 #ifdef Pack_32
1489 ULong z2;
1490 #endif
1491 #endif
1492
1493 if (a->wds < b->wds) {
1494 c = a;
1495 a = b;
1496 b = c;
1497 }
1498 k = a->k;
1499 wa = a->wds;
1500 wb = b->wds;
1501 wc = wa + wb;
1502 if (wc > a->maxwds)
1503 k++;
1504 c = Balloc(k);
1505 for (x = c->x, xa = x + wc; x < xa; x++)
1506 *x = 0;
1507 xa = a->x;
1508 xae = xa + wa;
1509 xb = b->x;
1510 xbe = xb + wb;
1511 xc0 = c->x;
1512 #ifdef ULLong
1513 for (; xb < xbe; xc0++) {
1514 if ((y = *xb++) != 0) {
1515 x = xa;
1516 xc = xc0;
1517 carry = 0;
1518 do {
1519 z = *x++ * (ULLong)y + *xc + carry;
1520 carry = z >> 32;
1521 *xc++ = z & FFFFFFFF;
1522 } while (x < xae);
1523 *xc = carry;
1524 }
1525 }
1526 #else
1527 #ifdef Pack_32
1528 for (; xb < xbe; xb++, xc0++) {
1529 if (y = *xb & 0xffff) {
1530 x = xa;
1531 xc = xc0;
1532 carry = 0;
1533 do {
1534 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
1535 carry = z >> 16;
1536 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
1537 carry = z2 >> 16;
1538 Storeinc(xc, z2, z);
1539 } while (x < xae);
1540 *xc = carry;
1541 }
1542 if (y = *xb >> 16) {
1543 x = xa;
1544 xc = xc0;
1545 carry = 0;
1546 z2 = *xc;
1547 do {
1548 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
1549 carry = z >> 16;
1550 Storeinc(xc, z, z2);
1551 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
1552 carry = z2 >> 16;
1553 } while (x < xae);
1554 *xc = z2;
1555 }
1556 }
1557 #else
1558 for (; xb < xbe; xc0++) {
1559 if (y = *xb++) {
1560 x = xa;
1561 xc = xc0;
1562 carry = 0;
1563 do {
1564 z = *x++ * y + *xc + carry;
1565 carry = z >> 16;
1566 *xc++ = z & 0xffff;
1567 } while (x < xae);
1568 *xc = carry;
1569 }
1570 }
1571 #endif
1572 #endif
1573 for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
1574 c->wds = wc;
1575 return c;
1576 }
1577
1578 static Bigint *p5s;
1579
1580 static Bigint *
1581 pow5mult(Bigint *b, int k)
1582 {
1583 Bigint *b1, *p5, *p51;
1584 int i;
1585 static int p05[3] = { 5, 25, 125 };
1586
1587 if ((i = k & 3) != 0)
1588 b = multadd(b, p05[i-1], 0);
1589
1590 if (!(k >>= 2))
1591 return b;
1592 if (!(p5 = p5s)) {
1593 /* first time */
1594 #ifdef MULTIPLE_THREADS
1595 ACQUIRE_DTOA_LOCK(1);
1596 if (!(p5 = p5s)) {
1597 p5 = p5s = i2b(625);
1598 p5->next = 0;
1599 }
1600 FREE_DTOA_LOCK(1);
1601 #else
1602 p5 = p5s = i2b(625);
1603 p5->next = 0;
1604 #endif
1605 }
1606 for (;;) {
1607 if (k & 1) {
1608 b1 = mult(b, p5);
1609 Bfree(b);
1610 b = b1;
1611 }
1612 if (!(k >>= 1))
1613 break;
1614 if (!(p51 = p5->next)) {
1615 #ifdef MULTIPLE_THREADS
1616 ACQUIRE_DTOA_LOCK(1);
1617 if (!(p51 = p5->next)) {
1618 p51 = p5->next = mult(p5,p5);
1619 p51->next = 0;
1620 }
1621 FREE_DTOA_LOCK(1);
1622 #else
1623 p51 = p5->next = mult(p5,p5);
1624 p51->next = 0;
1625 #endif
1626 }
1627 p5 = p51;
1628 }
1629 return b;
1630 }
1631
1632 static Bigint *
1633 lshift(Bigint *b, int k)
1634 {
1635 int i, k1, n, n1;
1636 Bigint *b1;
1637 ULong *x, *x1, *xe, z;
1638
1639 #ifdef Pack_32
1640 n = k >> 5;
1641 #else
1642 n = k >> 4;
1643 #endif
1644 k1 = b->k;
1645 n1 = n + b->wds + 1;
1646 for (i = b->maxwds; n1 > i; i <<= 1)
1647 k1++;
1648 b1 = Balloc(k1);
1649 x1 = b1->x;
1650 for (i = 0; i < n; i++)
1651 *x1++ = 0;
1652 x = b->x;
1653 xe = x + b->wds;
1654 #ifdef Pack_32
1655 if (k &= 0x1f) {
1656 k1 = 32 - k;
1657 z = 0;
1658 do {
1659 *x1++ = *x << k | z;
1660 z = *x++ >> k1;
1661 } while (x < xe);
1662 if ((*x1 = z) != 0)
1663 ++n1;
1664 }
1665 #else
1666 if (k &= 0xf) {
1667 k1 = 16 - k;
1668 z = 0;
1669 do {
1670 *x1++ = *x << k & 0xffff | z;
1671 z = *x++ >> k1;
1672 } while (x < xe);
1673 if (*x1 = z)
1674 ++n1;
1675 }
1676 #endif
1677 else
1678 do {
1679 *x1++ = *x++;
1680 } while (x < xe);
1681 b1->wds = n1 - 1;
1682 Bfree(b);
1683 return b1;
1684 }
1685
1686 static int
1687 cmp(Bigint *a, Bigint *b)
1688 {
1689 ULong *xa, *xa0, *xb, *xb0;
1690 int i, j;
1691
1692 i = a->wds;
1693 j = b->wds;
1694 #ifdef DEBUG
1695 if (i > 1 && !a->x[i-1])
1696 Bug("cmp called with a->x[a->wds-1] == 0");
1697 if (j > 1 && !b->x[j-1])
1698 Bug("cmp called with b->x[b->wds-1] == 0");
1699 #endif
1700 if (i -= j)
1701 return i;
1702 xa0 = a->x;
1703 xa = xa0 + j;
1704 xb0 = b->x;
1705 xb = xb0 + j;
1706 for (;;) {
1707 if (*--xa != *--xb)
1708 return *xa < *xb ? -1 : 1;
1709 if (xa <= xa0)
1710 break;
1711 }
1712 return 0;
1713 }
1714
1715 static Bigint *
1716 diff(Bigint *a, Bigint *b)
1717 {
1718 Bigint *c;
1719 int i, wa, wb;
1720 ULong *xa, *xae, *xb, *xbe, *xc;
1721 #ifdef ULLong
1722 ULLong borrow, y;
1723 #else
1724 ULong borrow, y;
1725 #ifdef Pack_32
1726 ULong z;
1727 #endif
1728 #endif
1729
1730 i = cmp(a,b);
1731 if (!i) {
1732 c = Balloc(0);
1733 c->wds = 1;
1734 c->x[0] = 0;
1735 return c;
1736 }
1737 if (i < 0) {
1738 c = a;
1739 a = b;
1740 b = c;
1741 i = 1;
1742 }
1743 else
1744 i = 0;
1745 c = Balloc(a->k);
1746 c->sign = i;
1747 wa = a->wds;
1748 xa = a->x;
1749 xae = xa + wa;
1750 wb = b->wds;
1751 xb = b->x;
1752 xbe = xb + wb;
1753 xc = c->x;
1754 borrow = 0;
1755 #ifdef ULLong
1756 do {
1757 y = (ULLong)*xa++ - *xb++ - borrow;
1758 borrow = y >> 32 & (ULong)1;
1759 *xc++ = y & FFFFFFFF;
1760 } while (xb < xbe);
1761 while (xa < xae) {
1762 y = *xa++ - borrow;
1763 borrow = y >> 32 & (ULong)1;
1764 *xc++ = y & FFFFFFFF;
1765 }
1766 #else
1767 #ifdef Pack_32
1768 do {
1769 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1770 borrow = (y & 0x10000) >> 16;
1771 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1772 borrow = (z & 0x10000) >> 16;
1773 Storeinc(xc, z, y);
1774 } while (xb < xbe);
1775 while (xa < xae) {
1776 y = (*xa & 0xffff) - borrow;
1777 borrow = (y & 0x10000) >> 16;
1778 z = (*xa++ >> 16) - borrow;
1779 borrow = (z & 0x10000) >> 16;
1780 Storeinc(xc, z, y);
1781 }
1782 #else
1783 do {
1784 y = *xa++ - *xb++ - borrow;
1785 borrow = (y & 0x10000) >> 16;
1786 *xc++ = y & 0xffff;
1787 } while (xb < xbe);
1788 while (xa < xae) {
1789 y = *xa++ - borrow;
1790 borrow = (y & 0x10000) >> 16;
1791 *xc++ = y & 0xffff;
1792 }
1793 #endif
1794 #endif
1795 while (!*--xc)
1796 wa--;
1797 c->wds = wa;
1798 return c;
1799 }
1800
1801 static double
1802 ulp(double x)
1803 {
1804 register Long L;
1805 double a;
1806
1807 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1808 #ifndef Avoid_Underflow
1809 #ifndef Sudden_Underflow
1810 if (L > 0) {
1811 #endif
1812 #endif
1813 #ifdef IBM
1814 L |= Exp_msk1 >> 4;
1815 #endif
1816 word0(a) = L;
1817 word1(a) = 0;
1818 #ifndef Avoid_Underflow
1819 #ifndef Sudden_Underflow
1820 }
1821 else {
1822 L = -L >> Exp_shift;
1823 if (L < Exp_shift) {
1824 word0(a) = 0x80000 >> L;
1825 word1(a) = 0;
1826 }
1827 else {
1828 word0(a) = 0;
1829 L -= Exp_shift;
1830 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1831 }
1832 }
1833 #endif
1834 #endif
1835 return dval(a);
1836 }
1837
1838 static double
1839 b2d(Bigint *a, int *e)
1840 {
1841 ULong *xa, *xa0, w, y, z;
1842 int k;
1843 double d;
1844 #ifdef VAX
1845 ULong d0, d1;
1846 #else
1847 #define d0 word0(d)
1848 #define d1 word1(d)
1849 #endif
1850
1851 xa0 = a->x;
1852 xa = xa0 + a->wds;
1853 y = *--xa;
1854 #ifdef DEBUG
1855 if (!y) Bug("zero y in b2d");
1856 #endif
1857 k = hi0bits(y);
1858 *e = 32 - k;
1859 #ifdef Pack_32
1860 if (k < Ebits) {
1861 d0 = Exp_1 | y >> (Ebits - k);
1862 w = xa > xa0 ? *--xa : 0;
1863 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1864 goto ret_d;
1865 }
1866 z = xa > xa0 ? *--xa : 0;
1867 if (k -= Ebits) {
1868 d0 = Exp_1 | y << k | z >> (32 - k);
1869 y = xa > xa0 ? *--xa : 0;
1870 d1 = z << k | y >> (32 - k);
1871 }
1872 else {
1873 d0 = Exp_1 | y;
1874 d1 = z;
1875 }
1876 #else
1877 if (k < Ebits + 16) {
1878 z = xa > xa0 ? *--xa : 0;
1879 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1880 w = xa > xa0 ? *--xa : 0;
1881 y = xa > xa0 ? *--xa : 0;
1882 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1883 goto ret_d;
1884 }
1885 z = xa > xa0 ? *--xa : 0;
1886 w = xa > xa0 ? *--xa : 0;
1887 k -= Ebits + 16;
1888 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1889 y = xa > xa0 ? *--xa : 0;
1890 d1 = w << k + 16 | y << k;
1891 #endif
1892 ret_d:
1893 #ifdef VAX
1894 word0(d) = d0 >> 16 | d0 << 16;
1895 word1(d) = d1 >> 16 | d1 << 16;
1896 #else
1897 #undef d0
1898 #undef d1
1899 #endif
1900 return dval(d);
1901 }
1902
1903 static Bigint *
1904 d2b(double d, int *e, int *bits)
1905 {
1906 Bigint *b;
1907 int de, k;
1908 ULong *x, y, z;
1909 #ifndef Sudden_Underflow
1910 int i;
1911 #endif
1912 #ifdef VAX
1913 ULong d0, d1;
1914 d0 = word0(d) >> 16 | word0(d) << 16;
1915 d1 = word1(d) >> 16 | word1(d) << 16;
1916 #else
1917 #define d0 word0(d)
1918 #define d1 word1(d)
1919 #endif
1920
1921 #ifdef Pack_32
1922 b = Balloc(1);
1923 #else
1924 b = Balloc(2);
1925 #endif
1926 x = b->x;
1927
1928 z = d0 & Frac_mask;
1929 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1930 #ifdef Sudden_Underflow
1931 de = (int)(d0 >> Exp_shift);
1932 #ifndef IBM
1933 z |= Exp_msk11;
1934 #endif
1935 #else
1936 if ((de = (int)(d0 >> Exp_shift)) != 0)
1937 z |= Exp_msk1;
1938 #endif
1939 #ifdef Pack_32
1940 if ((y = d1) != 0) {
1941 if ((k = lo0bits(&y)) != 0) {
1942 x[0] = y | z << (32 - k);
1943 z >>= k;
1944 }
1945 else
1946 x[0] = y;
1947 #ifndef Sudden_Underflow
1948 i =
1949 #endif
1950 b->wds = (x[1] = z) ? 2 : 1;
1951 }
1952 else {
1953 #ifdef DEBUG
1954 if (!z)
1955 Bug("Zero passed to d2b");
1956 #endif
1957 k = lo0bits(&z);
1958 x[0] = z;
1959 #ifndef Sudden_Underflow
1960 i =
1961 #endif
1962 b->wds = 1;
1963 k += 32;
1964 }
1965 #else
1966 if (y = d1) {
1967 if (k = lo0bits(&y))
1968 if (k >= 16) {
1969 x[0] = y | z << 32 - k & 0xffff;
1970 x[1] = z >> k - 16 & 0xffff;
1971 x[2] = z >> k;
1972 i = 2;
1973 }
1974 else {
1975 x[0] = y & 0xffff;
1976 x[1] = y >> 16 | z << 16 - k & 0xffff;
1977 x[2] = z >> k & 0xffff;
1978 x[3] = z >> k+16;
1979 i = 3;
1980 }
1981 else {
1982 x[0] = y & 0xffff;
1983 x[1] = y >> 16;
1984 x[2] = z & 0xffff;
1985 x[3] = z >> 16;
1986 i = 3;
1987 }
1988 }
1989 else {
1990 #ifdef DEBUG
1991 if (!z)
1992 Bug("Zero passed to d2b");
1993 #endif
1994 k = lo0bits(&z);
1995 if (k >= 16) {
1996 x[0] = z;
1997 i = 0;
1998 }
1999 else {
2000 x[0] = z & 0xffff;
2001 x[1] = z >> 16;
2002 i = 1;
2003 }
2004 k += 32;
2005 }
2006 while (!x[i])
2007 --i;
2008 b->wds = i + 1;
2009 #endif
2010 #ifndef Sudden_Underflow
2011 if (de) {
2012 #endif
2013 #ifdef IBM
2014 *e = (de - Bias - (P-1) << 2) + k;
2015 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
2016 #else
2017 *e = de - Bias - (P-1) + k;
2018 *bits = P - k;
2019 #endif
2020 #ifndef Sudden_Underflow
2021 }
2022 else {
2023 *e = de - Bias - (P-1) + 1 + k;
2024 #ifdef Pack_32
2025 *bits = 32*i - hi0bits(x[i-1]);
2026 #else
2027 *bits = (i+2)*16 - hi0bits(x[i]);
2028 #endif
2029 }
2030 #endif
2031 return b;
2032 }
2033 #undef d0
2034 #undef d1
2035
2036 static double
2037 ratio(Bigint *a, Bigint *b)
2038 {
2039 double da, db;
2040 int k, ka, kb;
2041
2042 dval(da) = b2d(a, &ka);
2043 dval(db) = b2d(b, &kb);
2044 #ifdef Pack_32
2045 k = ka - kb + 32*(a->wds - b->wds);
2046 #else
2047 k = ka - kb + 16*(a->wds - b->wds);
2048 #endif
2049 #ifdef IBM
2050 if (k > 0) {
2051 word0(da) += (k >> 2)*Exp_msk1;
2052 if (k &= 3)
2053 dval(da) *= 1 << k;
2054 }
2055 else {
2056 k = -k;
2057 word0(db) += (k >> 2)*Exp_msk1;
2058 if (k &= 3)
2059 dval(db) *= 1 << k;
2060 }
2061 #else
2062 if (k > 0)
2063 word0(da) += k*Exp_msk1;
2064 else {
2065 k = -k;
2066 word0(db) += k*Exp_msk1;
2067 }
2068 #endif
2069 return dval(da) / dval(db);
2070 }
2071
2072 static const double
2073 tens[] = {
2074 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
2075 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
2076 1e20, 1e21, 1e22
2077 #ifdef VAX
2078 , 1e23, 1e24
2079 #endif
2080 };
2081
2082 static const double
2083 #ifdef IEEE_Arith
2084 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
2085 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
2086 #ifdef Avoid_Underflow
2087 9007199254740992.*9007199254740992.e-256
2088 /* = 2^106 * 1e-53 */
2089 #else
2090 1e-256
2091 #endif
2092 };
2093 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
2094 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
2095 #define Scale_Bit 0x10
2096 #define n_bigtens 5
2097 #else
2098 #ifdef IBM
2099 bigtens[] = { 1e16, 1e32, 1e64 };
2100 static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
2101 #define n_bigtens 3
2102 #else
2103 bigtens[] = { 1e16, 1e32 };
2104 static const double tinytens[] = { 1e-16, 1e-32 };
2105 #define n_bigtens 2
2106 #endif
2107 #endif
2108
2109 #ifndef IEEE_Arith
2110 #undef INFNAN_CHECK
2111 #endif
2112
2113 #ifdef INFNAN_CHECK
2114
2115 #ifndef NAN_WORD0
2116 #define NAN_WORD0 0x7ff80000
2117 #endif
2118
2119 #ifndef NAN_WORD1
2120 #define NAN_WORD1 0
2121 #endif
2122
2123 static int
2124 match(const char **sp, char *t)
2125 {
2126 int c, d;
2127 const char *s = *sp;
2128
2129 while (d = *t++) {
2130 if ((c = *++s) >= 'A' && c <= 'Z')
2131 c += 'a' - 'A';
2132 if (c != d)
2133 return 0;
2134 }
2135 *sp = s + 1;
2136 return 1;
2137 }
2138
2139 #ifndef No_Hex_NaN
2140 static void
2141 hexnan(double *rvp, const char **sp)
2142 {
2143 ULong c, x[2];
2144 const char *s;
2145 int havedig, udx0, xshift;
2146
2147 x[0] = x[1] = 0;
2148 havedig = xshift = 0;
2149 udx0 = 1;
2150 s = *sp;
2151 while (c = *(const unsigned char*)++s) {
2152 if (c >= '0' && c <= '9')
2153 c -= '0';
2154 else if (c >= 'a' && c <= 'f')
2155 c += 10 - 'a';
2156 else if (c >= 'A' && c <= 'F')
2157 c += 10 - 'A';
2158 else if (c <= ' ') {
2159 if (udx0 && havedig) {
2160 udx0 = 0;
2161 xshift = 1;
2162 }
2163 continue;
2164 }
2165 else if (/*(*/ c == ')' && havedig) {
2166 *sp = s + 1;
2167 break;
2168 }
2169 else
2170 return; /* invalid form: don't change *sp */
2171 havedig = 1;
2172 if (xshift) {
2173 xshift = 0;
2174 x[0] = x[1];
2175 x[1] = 0;
2176 }
2177 if (udx0)
2178 x[0] = (x[0] << 4) | (x[1] >> 28);
2179 x[1] = (x[1] << 4) | c;
2180 }
2181 if ((x[0] &= 0xfffff) || x[1]) {
2182 word0(*rvp) = Exp_mask | x[0];
2183 word1(*rvp) = x[1];
2184 }
2185 }
2186 #endif /*No_Hex_NaN*/
2187 #endif /* INFNAN_CHECK */
2188
2189 double
2190 ruby_strtod(const char *s00, char **se)
2191 {
2192 #ifdef Avoid_Underflow
2193 int scale;
2194 #endif
2195 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
2196 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
2197 const char *s, *s0, *s1;
2198 double aadj, aadj1, adj, rv, rv0;
2199 Long L;
2200 ULong y, z;
2201 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
2202 #ifdef SET_INEXACT
2203 int inexact, oldinexact;
2204 #endif
2205 #ifdef Honor_FLT_ROUNDS
2206 int rounding;
2207 #endif
2208 #ifdef USE_LOCALE
2209 const char *s2;
2210 #endif
2211
2212 errno = 0;
2213 sign = nz0 = nz = 0;
2214 dval(rv) = 0.;
2215 for (s = s00;;s++)
2216 switch (*s) {
2217 case '-':
2218 sign = 1;
2219 /* no break */
2220 case '+':
2221 if (*++s)
2222 goto break2;
2223 /* no break */
2224 case 0:
2225 goto ret0;
2226 case '\t':
2227 case '\n':
2228 case '\v':
2229 case '\f':
2230 case '\r':
2231 case ' ':
2232 continue;
2233 default:
2234 goto break2;
2235 }
2236 break2:
2237 if (*s == '0') {
2238 nz0 = 1;
2239 while (*++s == '0') ;
2240 if (!*s)
2241 goto ret;
2242 }
2243 s0 = s;
2244 y = z = 0;
2245 for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
2246 if (nd < 9)
2247 y = 10*y + c - '0';
2248 else if (nd < 16)
2249 z = 10*z + c - '0';
2250 nd0 = nd;
2251 #ifdef USE_LOCALE
2252 s1 = localeconv()->decimal_point;
2253 if (c == *s1) {
2254 c = '.';
2255 if (*++s1) {
2256 s2 = s;
2257 for (;;) {
2258 if (*++s2 != *s1) {
2259 c = 0;
2260 break;
2261 }
2262 if (!*++s1) {
2263 s = s2;
2264 break;
2265 }
2266 }
2267 }
2268 }
2269 #endif
2270 if (c == '.') {
2271 if (!ISDIGIT(s[1]))
2272 goto dig_done;
2273 c = *++s;
2274 if (!nd) {
2275 for (; c == '0'; c = *++s)
2276 nz++;
2277 if (c > '0' && c <= '9') {
2278 s0 = s;
2279 nf += nz;
2280 nz = 0;
2281 goto have_dig;
2282 }
2283 goto dig_done;
2284 }
2285 for (; c >= '0' && c <= '9'; c = *++s) {
2286 have_dig:
2287 nz++;
2288 if (c -= '0') {
2289 nf += nz;
2290 for (i = 1; i < nz; i++)
2291 if (nd++ < 9)
2292 y *= 10;
2293 else if (nd <= DBL_DIG + 1)
2294 z *= 10;
2295 if (nd++ < 9)
2296 y = 10*y + c;
2297 else if (nd <= DBL_DIG + 1)
2298 z = 10*z + c;
2299 nz = 0;
2300 }
2301 }
2302 }
2303 dig_done:
2304 e = 0;
2305 if (c == 'e' || c == 'E') {
2306 if (!nd && !nz && !nz0) {
2307 goto ret0;
2308 }
2309 s00 = s;
2310 esign = 0;
2311 switch (c = *++s) {
2312 case '-':
2313 esign = 1;
2314 case '+':
2315 c = *++s;
2316 }
2317 if (c >= '0' && c <= '9') {
2318 while (c == '0')
2319 c = *++s;
2320 if (c > '0' && c <= '9') {
2321 L = c - '0';
2322 s1 = s;
2323 while ((c = *++s) >= '0' && c <= '9')
2324 L = 10*L + c - '0';
2325 if (s - s1 > 8 || L > 19999)
2326 /* Avoid confusion from exponents
2327 * so large that e might overflow.
2328 */
2329 e = 19999; /* safe for 16 bit ints */
2330 else
2331 e = (int)L;
2332 if (esign)
2333 e = -e;
2334 }
2335 else
2336 e = 0;
2337 }
2338 else
2339 s = s00;
2340 }
2341 if (!nd) {
2342 if (!nz && !nz0) {
2343 #ifdef INFNAN_CHECK
2344 /* Check for Nan and Infinity */
2345 switch (c) {
2346 case 'i':
2347 case 'I':
2348 if (match(&s,"nf")) {
2349 --s;
2350 if (!match(&s,"inity"))
2351 ++s;
2352 word0(rv) = 0x7ff00000;
2353 word1(rv) = 0;
2354 goto ret;
2355 }
2356 break;
2357 case 'n':
2358 case 'N':
2359 if (match(&s, "an")) {
2360 word0(rv) = NAN_WORD0;
2361 word1(rv) = NAN_WORD1;
2362 #ifndef No_Hex_NaN
2363 if (*s == '(') /*)*/
2364 hexnan(&rv, &s);
2365 #endif
2366 goto ret;
2367 }
2368 }
2369 #endif /* INFNAN_CHECK */
2370 ret0:
2371 s = s00;
2372 sign = 0;
2373 }
2374 goto ret;
2375 }
2376 e1 = e -= nf;
2377
2378 /* Now we have nd0 digits, starting at s0, followed by a
2379 * decimal point, followed by nd-nd0 digits. The number we're
2380 * after is the integer represented by those digits times
2381 * 10**e */
2382
2383 if (!nd0)
2384 nd0 = nd;
2385 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2386 dval(rv) = y;
2387 if (k > 9) {
2388 #ifdef SET_INEXACT
2389 if (k > DBL_DIG)
2390 oldinexact = get_inexact();
2391 #endif
2392 dval(rv) = tens[k - 9] * dval(rv) + z;
2393 }
2394 bd0 = bb = bd = bs = delta = 0;
2395 if (nd <= DBL_DIG
2396 #ifndef RND_PRODQUOT
2397 #ifndef Honor_FLT_ROUNDS
2398 && Flt_Rounds == 1
2399 #endif
2400 #endif
2401 ) {
2402 if (!e)
2403 goto ret;
2404 if (e > 0) {
2405 if (e <= Ten_pmax) {
2406 #ifdef VAX
2407 goto vax_ovfl_check;
2408 #else
2409 #ifdef Honor_FLT_ROUNDS
2410 /* round correctly FLT_ROUNDS = 2 or 3 */
2411 if (sign) {
2412 rv = -rv;
2413 sign = 0;
2414 }
2415 #endif
2416 /* rv = */ rounded_product(dval(rv), tens[e]);
2417 goto ret;
2418 #endif
2419 }
2420 i = DBL_DIG - nd;
2421 if (e <= Ten_pmax + i) {
2422 /* A fancier test would sometimes let us do
2423 * this for larger i values.
2424 */
2425 #ifdef Honor_FLT_ROUNDS
2426 /* round correctly FLT_ROUNDS = 2 or 3 */
2427 if (sign) {
2428 rv = -rv;
2429 sign = 0;
2430 }
2431 #endif
2432 e -= i;
2433 dval(rv) *= tens[i];
2434 #ifdef VAX
2435 /* VAX exponent range is so narrow we must
2436 * worry about overflow here...
2437 */
2438 vax_ovfl_check:
2439 word0(rv) -= P*Exp_msk1;
2440 /* rv = */ rounded_product(dval(rv), tens[e]);
2441 if ((word0(rv) & Exp_mask)
2442 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2443 goto ovfl;
2444 word0(rv) += P*Exp_msk1;
2445 #else
2446 /* rv = */ rounded_product(dval(rv), tens[e]);
2447 #endif
2448 goto ret;
2449 }
2450 }
2451 #ifndef Inaccurate_Divide
2452 else if (e >= -Ten_pmax) {
2453 #ifdef Honor_FLT_ROUNDS
2454 /* round correctly FLT_ROUNDS = 2 or 3 */
2455 if (sign) {
2456 rv = -rv;
2457 sign = 0;
2458 }
2459 #endif
2460 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
2461 goto ret;
2462 }
2463 #endif
2464 }
2465 e1 += nd - k;
2466
2467 #ifdef IEEE_Arith
2468 #ifdef SET_INEXACT
2469 inexact = 1;
2470 if (k <= DBL_DIG)
2471 oldinexact = get_inexact();
2472 #endif
2473 #ifdef Avoid_Underflow
2474 scale = 0;
2475 #endif
2476 #ifdef Honor_FLT_ROUNDS
2477 if ((rounding = Flt_Rounds) >= 2) {
2478 if (sign)
2479 rounding = rounding == 2 ? 0 : 2;
2480 else
2481 if (rounding != 2)
2482 rounding = 0;
2483 }
2484 #endif
2485 #endif /*IEEE_Arith*/
2486
2487 /* Get starting approximation = rv * 10**e1 */
2488
2489 if (e1 > 0) {
2490 if ((i = e1 & 15) != 0)
2491 dval(rv) *= tens[i];
2492 if (e1 &= ~15) {
2493 if (e1 > DBL_MAX_10_EXP) {
2494 ovfl:
2495 #ifndef NO_ERRNO
2496 errno = ERANGE;
2497 #endif
2498 /* Can't trust HUGE_VAL */
2499 #ifdef IEEE_Arith
2500 #ifdef Honor_FLT_ROUNDS
2501 switch (rounding) {
2502 case 0: /* toward 0 */
2503 case 3: /* toward -infinity */
2504 word0(rv) = Big0;
2505 word1(rv) = Big1;
2506 break;
2507 default:
2508 word0(rv) = Exp_mask;
2509 word1(rv) = 0;
2510 }
2511 #else /*Honor_FLT_ROUNDS*/
2512 word0(rv) = Exp_mask;
2513 word1(rv) = 0;
2514 #endif /*Honor_FLT_ROUNDS*/
2515 #ifdef SET_INEXACT
2516 /* set overflow bit */
2517 dval(rv0) = 1e300;
2518 dval(rv0) *= dval(rv0);
2519 #endif
2520 #else /*IEEE_Arith*/
2521 word0(rv) = Big0;
2522 word1(rv) = Big1;
2523 #endif /*IEEE_Arith*/
2524 if (bd0)
2525 goto retfree;
2526 goto ret;
2527 }
2528 e1 >>= 4;
2529 for (j = 0; e1 > 1; j++, e1 >>= 1)
2530 if (e1 & 1)
2531 dval(rv) *= bigtens[j];
2532 /* The last multiplication could overflow. */
2533 word0(rv) -= P*Exp_msk1;
2534 dval(rv) *= bigtens[j];
2535 if ((z = word0(rv) & Exp_mask)
2536 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2537 goto ovfl;
2538 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2539 /* set to largest number */
2540 /* (Can't trust DBL_MAX) */
2541 word0(rv) = Big0;
2542 word1(rv) = Big1;
2543 }
2544 else
2545 word0(rv) += P*Exp_msk1;
2546 }
2547 }
2548 else if (e1 < 0) {
2549 e1 = -e1;
2550 if ((i = e1 & 15) != 0)
2551 dval(rv) /= tens[i];
2552 if (e1 >>= 4) {
2553 if (e1 >= 1 << n_bigtens)
2554 goto undfl;
2555 #ifdef Avoid_Underflow
2556 if (e1 & Scale_Bit)
2557 scale = 2*P;
2558 for (j = 0; e1 > 0; j++, e1 >>= 1)
2559 if (e1 & 1)
2560 dval(rv) *= tinytens[j];
2561 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
2562 >> Exp_shift)) > 0) {
2563 /* scaled rv is denormal; zap j low bits */
2564 if (j >= 32) {
2565 word1(rv) = 0;
2566 if (j >= 53)
2567 word0(rv) = (P+2)*Exp_msk1;
2568 else
2569 word0(rv) &= 0xffffffff << (j-32);
2570 }
2571 else
2572 word1(rv) &= 0xffffffff << j;
2573 }
2574 #else
2575 for (j = 0; e1 > 1; j++, e1 >>= 1)
2576 if (e1 & 1)
2577 dval(rv) *= tinytens[j];
2578 /* The last multiplication could underflow. */
2579 dval(rv0) = dval(rv);
2580 dval(rv) *= tinytens[j];
2581 if (!dval(rv)) {
2582 dval(rv) = 2.*dval(rv0);
2583 dval(rv) *= tinytens[j];
2584 #endif
2585 if (!dval(rv)) {
2586 undfl:
2587 dval(rv) = 0.;
2588 #ifndef NO_ERRNO
2589 errno = ERANGE;
2590 #endif
2591 if (bd0)
2592 goto retfree;
2593 goto ret;
2594 }
2595 #ifndef Avoid_Underflow
2596 word0(rv) = Tiny0;
2597 word1(rv) = Tiny1;
2598 /* The refinement below will clean
2599 * this approximation up.
2600 */
2601 }
2602 #endif
2603 }
2604 }
2605
2606 /* Now the hard part -- adjusting rv to the correct value.*/
2607
2608 /* Put digits into bd: true value = bd * 10^e */
2609
2610 bd0 = s2b(s0, nd0, nd, y);
2611
2612 for (;;) {
2613 bd = Balloc(bd0->k);
2614 Bcopy(bd, bd0);
2615 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
2616 bs = i2b(1);
2617
2618 if (e >= 0) {
2619 bb2 = bb5 = 0;
2620 bd2 = bd5 = e;
2621 }
2622 else {
2623 bb2 = bb5 = -e;
2624 bd2 = bd5 = 0;
2625 }
2626 if (bbe >= 0)
2627 bb2 += bbe;
2628 else
2629 bd2 -= bbe;
2630 bs2 = bb2;
2631 #ifdef Honor_FLT_ROUNDS
2632 if (rounding != 1)
2633 bs2++;
2634 #endif
2635 #ifdef Avoid_Underflow
2636 j = bbe - scale;
2637 i = j + bbbits - 1; /* logb(rv) */
2638 if (i < Emin) /* denormal */
2639 j += P - Emin;
2640 else
2641 j = P + 1 - bbbits;
2642 #else /*Avoid_Underflow*/
2643 #ifdef Sudden_Underflow
2644 #ifdef IBM
2645 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2646 #else
2647 j = P + 1 - bbbits;
2648 #endif
2649 #else /*Sudden_Underflow*/
2650 j = bbe;
2651 i = j + bbbits - 1; /* logb(rv) */
2652 if (i < Emin) /* denormal */
2653 j += P - Emin;
2654 else
2655 j = P + 1 - bbbits;
2656 #endif /*Sudden_Underflow*/
2657 #endif /*Avoid_Underflow*/
2658 bb2 += j;
2659 bd2 += j;
2660 #ifdef Avoid_Underflow
2661 bd2 += scale;
2662 #endif
2663 i = bb2 < bd2 ? bb2 : bd2;
2664 if (i > bs2)
2665 i = bs2;
2666 if (i > 0) {
2667 bb2 -= i;
2668 bd2 -= i;
2669 bs2 -= i;
2670 }
2671 if (bb5 > 0) {
2672 bs = pow5mult(bs, bb5);
2673 bb1 = mult(bs, bb);
2674 Bfree(bb);
2675 bb = bb1;
2676 }
2677 if (bb2 > 0)
2678 bb = lshift(bb, bb2);
2679 if (bd5 > 0)
2680 bd = pow5mult(bd, bd5);
2681 if (bd2 > 0)
2682 bd = lshift(bd, bd2);
2683 if (bs2 > 0)
2684 bs = lshift(bs, bs2);
2685 delta = diff(bb, bd);
2686 dsign = delta->sign;
2687 delta->sign = 0;
2688 i = cmp(delta, bs);
2689 #ifdef Honor_FLT_ROUNDS
2690 if (rounding != 1) {
2691 if (i < 0) {
2692 /* Error is less than an ulp */
2693 if (!delta->x[0] && delta->wds <= 1) {
2694 /* exact */
2695 #ifdef SET_INEXACT
2696 inexact = 0;
2697 #endif
2698 break;
2699 }
2700 if (rounding) {
2701 if (dsign) {
2702 adj = 1.;
2703 goto apply_adj;
2704 }
2705 }
2706 else if (!dsign) {
2707 adj = -1.;
2708 if (!word1(rv)
2709 && !(word0(rv) & Frac_mask)) {
2710 y = word0(rv) & Exp_mask;
2711 #ifdef Avoid_Underflow
2712 if (!scale || y > 2*P*Exp_msk1)
2713 #else
2714 if (y)
2715 #endif
2716 {
2717 delta = lshift(delta,Log2P);
2718 if (cmp(delta, bs) <= 0)
2719 adj = -0.5;
2720 }
2721 }
2722 apply_adj:
2723 #ifdef Avoid_Underflow
2724 if (scale && (y = word0(rv) & Exp_mask)
2725 <= 2*P*Exp_msk1)
2726 word0(adj) += (2*P+1)*Exp_msk1 - y;
2727 #else
2728 #ifdef Sudden_Underflow
2729 if ((word0(rv) & Exp_mask) <=
2730 P*Exp_msk1) {
2731 word0(rv) += P*Exp_msk1;
2732 dval(rv) += adj*ulp(dval(rv));
2733 word0(rv) -= P*Exp_msk1;
2734 }
2735 else
2736 #endif /*Sudden_Underflow*/
2737 #endif /*Avoid_Underflow*/
2738 dval(rv) += adj*ulp(dval(rv));
2739 }
2740 break;
2741 }
2742 adj = ratio(delta, bs);
2743 if (adj < 1.)
2744 adj = 1.;
2745 if (adj <= 0x7ffffffe) {
2746 /* adj = rounding ? ceil(adj) : floor(adj); */
2747 y = adj;
2748 if (y != adj) {
2749 if (!((rounding>>1) ^ dsign))
2750 y++;
2751 adj = y;
2752 }
2753 }
2754 #ifdef Avoid_Underflow
2755 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2756 word0(adj) += (2*P+1)*Exp_msk1 - y;
2757 #else
2758 #ifdef Sudden_Underflow
2759 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2760 word0(rv) += P*Exp_msk1;
2761 adj *= ulp(dval(rv));
2762 if (dsign)
2763 dval(rv) += adj;
2764 else
2765 dval(rv) -= adj;
2766 word0(rv) -= P*Exp_msk1;
2767 goto cont;
2768 }
2769 #endif /*Sudden_Underflow*/
2770 #endif /*Avoid_Underflow*/
2771 adj *= ulp(dval(rv));
2772 if (dsign)
2773 dval(rv) += adj;
2774 else
2775 dval(rv) -= adj;
2776 goto cont;
2777 }
2778 #endif /*Honor_FLT_ROUNDS*/
2779
2780 if (i < 0) {
2781 /* Error is less than half an ulp -- check for
2782 * special case of mantissa a power of two.
2783 */
2784 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2785 #ifdef IEEE_Arith
2786 #ifdef Avoid_Underflow
2787 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2788 #else
2789 || (word0(rv) & Exp_mask) <= Exp_msk1
2790 #endif
2791 #endif
2792 ) {
2793 #ifdef SET_INEXACT
2794 if (!delta->x[0] && delta->wds <= 1)
2795 inexact = 0;
2796 #endif
2797 break;
2798 }
2799 if (!delta->x[0] && delta->wds <= 1) {
2800 /* exact result */
2801 #ifdef SET_INEXACT
2802 inexact = 0;
2803 #endif
2804 break;
2805 }
2806 delta = lshift(delta,Log2P);
2807 if (cmp(delta, bs) > 0)
2808 goto drop_down;
2809 break;
2810 }
2811 if (i == 0) {
2812 /* exactly half-way between */
2813 if (dsign) {
2814 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2815 && word1(rv) == (
2816 #ifdef Avoid_Underflow
2817 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2818 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2819 #endif
2820 0xffffffff)) {
2821 /*boundary case -- increment exponent*/
2822 word0(rv) = (word0(rv) & Exp_mask)
2823 + Exp_msk1
2824 #ifdef IBM
2825 | Exp_msk1 >> 4
2826 #endif
2827 ;
2828 word1(rv) = 0;
2829 #ifdef Avoid_Underflow
2830 dsign = 0;
2831 #endif
2832 break;
2833 }
2834 }
2835 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2836 drop_down:
2837 /* boundary case -- decrement exponent */
2838 #ifdef Sudden_Underflow /*{{*/
2839 L = word0(rv) & Exp_mask;
2840 #ifdef IBM
2841 if (L < Exp_msk1)
2842 #else
2843 #ifdef Avoid_Underflow
2844 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2845 #else
2846 if (L <= Exp_msk1)
2847 #endif /*Avoid_Underflow*/
2848 #endif /*IBM*/
2849 goto undfl;
2850 L -= Exp_msk1;
2851 #else /*Sudden_Underflow}{*/
2852 #ifdef Avoid_Underflow
2853 if (scale) {
2854 L = word0(rv) & Exp_mask;
2855 if (L <= (2*P+1)*Exp_msk1) {
2856 if (L > (P+2)*Exp_msk1)
2857 /* round even ==> */
2858 /* accept rv */
2859 break;
2860 /* rv = smallest denormal */
2861 goto undfl;
2862 }
2863 }
2864 #endif /*Avoid_Underflow*/
2865 L = (word0(rv) & Exp_mask) - Exp_msk1;
2866 #endif /*Sudden_Underflow}}*/
2867 word0(rv) = L | Bndry_mask1;
2868 word1(rv) = 0xffffffff;
2869 #ifdef IBM
2870 goto cont;
2871 #else
2872 break;
2873 #endif
2874 }
2875 #ifndef ROUND_BIASED
2876 if (!(word1(rv) & LSB))
2877 break;
2878 #endif
2879 if (dsign)
2880 dval(rv) += ulp(dval(rv));
2881 #ifndef ROUND_BIASED
2882 else {
2883 dval(rv) -= ulp(dval(rv));
2884 #ifndef Sudden_Underflow
2885 if (!dval(rv))
2886 goto undfl;
2887 #endif
2888 }
2889 #ifdef Avoid_Underflow
2890 dsign = 1 - dsign;
2891 #endif
2892 #endif
2893 break;
2894 }
2895 if ((aadj = ratio(delta, bs)) <= 2.) {
2896 if (dsign)
2897 aadj = aadj1 = 1.;
2898 else if (word1(rv) || word0(rv) & Bndry_mask) {
2899 #ifndef Sudden_Underflow
2900 if (word1(rv) == Tiny1 && !word0(rv))
2901 goto undfl;
2902 #endif
2903 aadj = 1.;
2904 aadj1 = -1.;
2905 }
2906 else {
2907 /* special case -- power of FLT_RADIX to be */
2908 /* rounded down... */
2909
2910 if (aadj < 2./FLT_RADIX)
2911 aadj = 1./FLT_RADIX;
2912 else
2913 aadj *= 0.5;
2914 aadj1 = -aadj;
2915 }
2916 }
2917 else {
2918 aadj *= 0.5;
2919 aadj1 = dsign ? aadj : -aadj;
2920 #ifdef Check_FLT_ROUNDS
2921 switch (Rounding) {
2922 case 2: /* towards +infinity */
2923 aadj1 -= 0.5;
2924 break;
2925 case 0: /* towards 0 */
2926 case 3: /* towards -infinity */
2927 aadj1 += 0.5;
2928 }
2929 #else
2930 if (Flt_Rounds == 0)
2931 aadj1 += 0.5;
2932 #endif /*Check_FLT_ROUNDS*/
2933 }
2934 y = word0(rv) & Exp_mask;
2935
2936 /* Check for overflow */
2937
2938 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2939 dval(rv0) = dval(rv);
2940 word0(rv) -= P*Exp_msk1;
2941 adj = aadj1 * ulp(dval(rv));
2942 dval(rv) += adj;
2943 if ((word0(rv) & Exp_mask) >=
2944 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2945 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2946 goto ovfl;
2947 word0(rv) = Big0;
2948 word1(rv) = Big1;
2949 goto cont;
2950 }
2951 else
2952 word0(rv) += P*Exp_msk1;
2953 }
2954 else {
2955 #ifdef Avoid_Underflow
2956 if (scale && y <= 2*P*Exp_msk1) {
2957 if (aadj <= 0x7fffffff) {
2958 if ((z = aadj) <= 0)
2959 z = 1;
2960 aadj = z;
2961 aadj1 = dsign ? aadj : -aadj;
2962 }
2963 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2964 }
2965 adj = aadj1 * ulp(dval(rv));
2966 dval(rv) += adj;
2967 #else
2968 #ifdef Sudden_Underflow
2969 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2970 dval(rv0) = dval(rv);
2971 word0(rv) += P*Exp_msk1;
2972 adj = aadj1 * ulp(dval(rv));
2973 dval(rv) += adj;
2974 #ifdef IBM
2975 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2976 #else
2977 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2978 #endif
2979 {
2980 if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2981 goto undfl;
2982 word0(rv) = Tiny0;
2983 word1(rv) = Tiny1;
2984 goto cont;
2985 }
2986 else
2987 word0(rv) -= P*Exp_msk1;
2988 }
2989 else {
2990 adj = aadj1 * ulp(dval(rv));
2991 dval(rv) += adj;
2992 }
2993 #else /*Sudden_Underflow*/
2994 /* Compute adj so that the IEEE rounding rules will
2995 * correctly round rv + adj in some half-way cases.
2996 * If rv * ulp(rv) is denormalized (i.e.,
2997 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2998 * trouble from bits lost to denormalization;
2999 * example: 1.2e-307 .
3000 */
3001 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
3002 aadj1 = (double)(int)(aadj + 0.5);
3003 if (!dsign)
3004 aadj1 = -aadj1;
3005 }
3006 adj = aadj1 * ulp(dval(rv));
3007 dval(rv) += adj;
3008 #endif /*Sudden_Underflow*/
3009 #endif /*Avoid_Underflow*/
3010 }
3011 z = word0(rv) & Exp_mask;
3012 #ifndef SET_INEXACT
3013 #ifdef Avoid_Underflow
3014 if (!scale)
3015 #endif
3016 if (y == z) {
3017 /* Can we stop now? */
3018 L = (Long)aadj;
3019 aadj -= L;
3020 /* The tolerances below are conservative. */
3021 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
3022 if (aadj < .4999999 || aadj > .5000001)
3023 break;
3024 }
3025 else if (aadj < .4999999/FLT_RADIX)
3026 break;
3027 }
3028 #endif
3029 cont:
3030 Bfree(bb);
3031 Bfree(bd);
3032 Bfree(bs);
3033 Bfree(delta);
3034 }
3035 #ifdef SET_INEXACT
3036 if (inexact) {
3037 if (!oldinexact) {
3038 word0(rv0) = Exp_1 + (70 << Exp_shift);
3039 word1(rv0) = 0;
3040 dval(rv0) += 1.;
3041 }
3042 }
3043 else if (!oldinexact)
3044 clear_inexact();
3045 #endif
3046 #ifdef Avoid_Underflow
3047 if (scale) {
3048 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
3049 word1(rv0) = 0;
3050 dval(rv) *= dval(rv0);
3051 #ifndef NO_ERRNO
3052 /* try to avoid the bug of testing an 8087 register value */
3053 if (word0(rv) == 0 && word1(rv) == 0)
3054 errno = ERANGE;
3055 #endif
3056 }
3057 #endif /* Avoid_Underflow */
3058 #ifdef SET_INEXACT
3059 if (inexact && !(word0(rv) & Exp_mask)) {
3060 /* set underflow bit */
3061 dval(rv0) = 1e-300;
3062 dval(rv0) *= dval(rv0);
3063 }
3064 #endif
3065 retfree:
3066 Bfree(bb);
3067 Bfree(bd);
3068 Bfree(bs);
3069 Bfree(bd0);
3070 Bfree(delta);
3071 ret:
3072 if (se)
3073 *se = (char *)s;
3074 return sign ? -dval(rv) : dval(rv);
3075 }
3076
3077 static int
3078 quorem(Bigint *b, Bigint *S)
3079 {
3080 int n;
3081 ULong *bx, *bxe, q, *sx, *sxe;
3082 #ifdef ULLong
3083 ULLong borrow, carry, y, ys;
3084 #else
3085 ULong borrow, carry, y, ys;
3086 #ifdef Pack_32
3087 ULong si, z, zs;
3088 #endif
3089 #endif
3090
3091 n = S->wds;
3092 #ifdef DEBUG
3093 /*debug*/ if (b->wds > n)
3094 /*debug*/ Bug("oversize b in quorem");
3095 #endif
3096 if (b->wds < n)
3097 return 0;
3098 sx = S->x;
3099 sxe = sx + --n;
3100 bx = b->x;
3101 bxe = bx + n;
3102 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
3103 #ifdef DEBUG
3104 /*debug*/ if (q > 9)
3105 /*debug*/ Bug("oversized quotient in quorem");
3106 #endif
3107 if (q) {
3108 borrow = 0;
3109 carry = 0;
3110 do {
3111 #ifdef ULLong
3112 ys = *sx++ * (ULLong)q + carry;
3113 carry = ys >> 32;
3114 y = *bx - (ys & FFFFFFFF) - borrow;
3115 borrow = y >> 32 & (ULong)1;
3116 *bx++ = y & FFFFFFFF;
3117 #else
3118 #ifdef Pack_32
3119 si = *sx++;
3120 ys = (si & 0xffff) * q + carry;
3121 zs = (si >> 16) * q + (ys >> 16);
3122 carry = zs >> 16;
3123 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
3124 borrow = (y & 0x10000) >> 16;
3125 z = (*bx >> 16) - (zs & 0xffff) - borrow;
3126 borrow = (z & 0x10000) >> 16;
3127 Storeinc(bx, z, y);
3128 #else
3129 ys = *sx++ * q + carry;
3130 carry = ys >> 16;
3131 y = *bx - (ys & 0xffff) - borrow;
3132 borrow = (y & 0x10000) >> 16;
3133 *bx++ = y & 0xffff;
3134 #endif
3135 #endif
3136 } while (sx <= sxe);
3137 if (!*bxe) {
3138 bx = b->x;
3139 while (--bxe > bx && !*bxe)
3140 --n;
3141 b->wds = n;
3142 }
3143 }
3144 if (cmp(b, S) >= 0) {
3145 q++;
3146 borrow = 0;
3147 carry = 0;
3148 bx = b->x;
3149 sx = S->x;
3150 do {
3151 #ifdef ULLong
3152 ys = *sx++ + carry;
3153 carry = ys >> 32;
3154 y = *bx - (ys & FFFFFFFF) - borrow;
3155 borrow = y >> 32 & (ULong)1;
3156 *bx++ = y & FFFFFFFF;
3157 #else
3158 #ifdef Pack_32
3159 si = *sx++;
3160 ys = (si & 0xffff) + carry;
3161 zs = (si >> 16) + (ys >> 16);
3162 carry = zs >> 16;
3163 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
3164 borrow = (y & 0x10000) >> 16;
3165 z = (*bx >> 16) - (zs & 0xffff) - borrow;
3166 borrow = (z & 0x10000) >> 16;
3167 Storeinc(bx, z, y);
3168 #else
3169 ys = *sx++ + carry;
3170 carry = ys >> 16;
3171 y = *bx - (ys & 0xffff) - borrow;
3172 borrow = (y & 0x10000) >> 16;
3173 *bx++ = y & 0xffff;
3174 #endif
3175 #endif
3176 } while (sx <= sxe);
3177 bx = b->x;
3178 bxe = bx + n;
3179 if (!*bxe) {
3180 while (--bxe > bx && !*bxe)
3181 --n;
3182 b->wds = n;
3183 }
3184 }
3185 return q;
3186 }
3187
3188 #ifndef MULTIPLE_THREADS
3189 static char *dtoa_result;
3190 #endif
3191
3192 static char *
3193 rv_alloc(int i)
3194 {
3195 int j, k, *r;
3196
3197 j = sizeof(ULong);
3198 for (k = 0;
3199 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
3200 j <<= 1)
3201 k++;
3202 r = (int*)Balloc(k);
3203 *r = k;
3204 return
3205 #ifndef MULTIPLE_THREADS
3206 dtoa_result =
3207 #endif
3208 (char *)(r+1);
3209 }
3210
3211 static char *
3212 nrv_alloc(const char *s, char **rve, int n)
3213 {
3214 char *rv, *t;
3215
3216 t = rv = rv_alloc(n);
3217 while ((*t = *s++) != 0) t++;
3218 if (rve)
3219 *rve = t;
3220 return rv;
3221 }
3222
3223 /* freedtoa(s) must be used to free values s returned by dtoa
3224 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
3225 * but for consistency with earlier versions of dtoa, it is optional
3226 * when MULTIPLE_THREADS is not defined.
3227 */
3228
3229 void
3230 freedtoa(char *s)
3231 {
3232 Bigint *b = (Bigint *)((int *)s - 1);
3233 b->maxwds = 1 << (b->k = *(int*)b);
3234 Bfree(b);
3235 #ifndef MULTIPLE_THREADS
3236 if (s == dtoa_result)
3237 dtoa_result = 0;
3238 #endif
3239 }
3240
3241 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
3242 *
3243 * Inspired by "How to Print Floating-Point Numbers Accurately" by
3244 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
3245 *
3246 * Modifications:
3247 * 1. Rather than iterating, we use a simple numeric overestimate
3248 * to determine k = floor(log10(d)). We scale relevant
3249 * quantities using O(log2(k)) rather than O(k) multiplications.
3250 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
3251 * try to generate digits strictly left to right. Instead, we
3252 * compute with fewer bits and propagate the carry if necessary
3253 * when rounding the final digit up. This is often faster.
3254 * 3. Under the assumption that input will be rounded nearest,
3255 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
3256 * That is, we allow equality in stopping tests when the
3257 * round-nearest rule will give the same floating-point value
3258 * as would satisfaction of the stopping test with strict
3259 * inequality.
3260 * 4. We remove common factors of powers of 2 from relevant
3261 * quantities.
3262 * 5. When converting floating-point integers less than 1e16,
3263 * we use floating-point arithmetic rather than resorting
3264 * to multiple-precision integers.
3265 * 6. When asked to produce fewer than 15 digits, we first try
3266 * to get by with floating-point arithmetic; we resort to
3267 * multiple-precision integer arithmetic only if we cannot
3268 * guarantee that the floating-point calculation has given
3269 * the correctly rounded result. For k requested digits and
3270 * "uniformly" distributed input, the probability is
3271 * something like 10^(k-15) that we must resort to the Long
3272 * calculation.
3273 */
3274
3275 char *
3276 dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
3277 {
3278 /* Arguments ndigits, decpt, sign are similar to those
3279 of ecvt and fcvt; trailing zeros are suppressed from
3280 the returned string. If not null, *rve is set to point
3281 to the end of the return value. If d is +-Infinity or NaN,
3282 then *decpt is set to 9999.
3283
3284 mode:
3285 0 ==> shortest string that yields d when read in
3286 and rounded to nearest.
3287 1 ==> like 0, but with Steele & White stopping rule;
3288 e.g. with IEEE P754 arithmetic , mode 0 gives
3289 1e23 whereas mode 1 gives 9.999999999999999e22.
3290 2 ==> max(1,ndigits) significant digits. This gives a
3291 return value similar to that of ecvt, except
3292 that trailing zeros are suppressed.
3293 3 ==> through ndigits past the decimal point. This
3294 gives a return value similar to that from fcvt,
3295 except that trailing zeros are suppressed, and
3296 ndigits can be negative.
3297 4,5 ==> similar to 2 and 3, respectively, but (in
3298 round-nearest mode) with the tests of mode 0 to
3299 possibly return a shorter string that rounds to d.
3300 With IEEE arithmetic and compilation with
3301 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
3302 as modes 2 and 3 when FLT_ROUNDS != 1.
3303 6-9 ==> Debugging modes similar to mode - 4: don't try
3304 fast floating-point estimate (if applicable).
3305
3306 Values of mode other than 0-9 are treated as mode 0.
3307
3308 Sufficient space is allocated to the return value
3309 to hold the suppressed trailing zeros.
3310 */
3311
3312 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
3313 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
3314 spec_case, try_quick;
3315 Long L;
3316 #ifndef Sudden_Underflow
3317 int denorm;
3318 ULong x;
3319 #endif
3320 Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
3321 double d2, ds, eps;
3322 char *s, *s0;
3323 #ifdef Honor_FLT_ROUNDS
3324 int rounding;
3325 #endif
3326 #ifdef SET_INEXACT
3327 int inexact, oldinexact;
3328 #endif
3329
3330 #ifndef MULTIPLE_THREADS
3331 if (dtoa_result) {
3332 freedtoa(dtoa_result);
3333 dtoa_result = 0;
3334 }
3335 #endif
3336
3337 if (word0(d) & Sign_bit) {
3338 /* set sign for everything, including 0's and NaNs */
3339 *sign = 1;
3340 word0(d) &= ~Sign_bit; /* clear sign bit */
3341 }
3342 else
3343 *sign = 0;
3344
3345 #if defined(IEEE_Arith) + defined(VAX)
3346 #ifdef IEEE_Arith
3347 if ((word0(d) & Exp_mask) == Exp_mask)
3348 #else
3349 if (word0(d) == 0x8000)
3350 #endif
3351 {
3352 /* Infinity or NaN */
3353 *decpt = 9999;
3354 #ifdef IEEE_Arith
3355 if (!word1(d) && !(word0(d) & 0xfffff))
3356 return nrv_alloc("Infinity", rve, 8);
3357 #endif
3358 return nrv_alloc("NaN", rve, 3);
3359 }
3360 #endif
3361 #ifdef IBM
3362 dval(d) += 0; /* normalize */
3363 #endif
3364 if (!dval(d)) {
3365 *decpt = 1;
3366 return nrv_alloc("0", rve, 1);
3367 }
3368
3369 #ifdef SET_INEXACT
3370 try_quick = oldinexact = get_inexact();
3371 inexact = 1;
3372 #endif
3373 #ifdef Honor_FLT_ROUNDS
3374 if ((rounding = Flt_Rounds) >= 2) {
3375 if (*sign)
3376 rounding = rounding == 2 ? 0 : 2;
3377 else
3378 if (rounding != 2)
3379 rounding = 0;
3380 }
3381 #endif
3382
3383 b = d2b(dval(d), &be, &bbits);
3384 #ifdef Sudden_Underflow
3385 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
3386 #else
3387 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
3388 #endif
3389 dval(d2) = dval(d);
3390 word0(d2) &= Frac_mask1;
3391 word0(d2) |= Exp_11;
3392 #ifdef IBM
3393 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
3394 dval(d2) /= 1 << j;
3395 #endif
3396
3397 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
3398 * log10(x) = log(x) / log(10)
3399 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
3400 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
3401 *
3402 * This suggests computing an approximation k to log10(d) by
3403 *
3404 * k = (i - Bias)*0.301029995663981
3405 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
3406 *
3407 * We want k to be too large rather than too small.
3408 * The error in the first-order Taylor series approximation
3409 * is in our favor, so we just round up the constant enough
3410 * to compensate for any error in the multiplication of
3411 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
3412 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
3413 * adding 1e-13 to the constant term more than suffices.
3414 * Hence we adjust the constant term to 0.1760912590558.
3415 * (We could get a more accurate k by invoking log10,
3416 * but this is probably not worthwhile.)
3417 */
3418
3419 i -= Bias;
3420 #ifdef IBM
3421 i <<= 2;
3422 i += j;
3423 #endif
3424 #ifndef Sudden_Underflow
3425 denorm = 0;
3426 }
3427 else {
3428 /* d is denormalized */
3429
3430 i = bbits + be + (Bias + (P-1) - 1);
3431 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
3432 : word1(d) << (32 - i);
3433 dval(d2) = x;
3434 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
3435 i -= (Bias + (P-1) - 1) + 1;
3436 denorm = 1;
3437 }
3438 #endif
3439 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
3440 k = (int)ds;
3441 if (ds < 0. && ds != k)
3442 k--; /* want k = floor(ds) */
3443 k_check = 1;
3444 if (k >= 0 && k <= Ten_pmax) {
3445 if (dval(d) < tens[k])
3446 k--;
3447 k_check = 0;
3448 }
3449 j = bbits - i - 1;
3450 if (j >= 0) {
3451 b2 = 0;
3452 s2 = j;
3453 }
3454 else {
3455 b2 = -j;
3456 s2 = 0;
3457 }
3458 if (k >= 0) {
3459 b5 = 0;
3460 s5 = k;
3461 s2 += k;
3462 }
3463 else {
3464 b2 -= k;
3465 b5 = -k;
3466 s5 = 0;
3467 }
3468 if (mode < 0 || mode > 9)
3469 mode = 0;
3470
3471 #ifndef SET_INEXACT
3472 #ifdef Check_FLT_ROUNDS
3473 try_quick = Rounding == 1;
3474 #else
3475 try_quick = 1;
3476 #endif
3477 #endif /*SET_INEXACT*/
3478
3479 if (mode > 5) {
3480 mode -= 4;
3481 try_quick = 0;
3482 }
3483 leftright = 1;
3484 ilim = ilim1 = -1;
3485 switch (mode) {
3486 case 0:
3487 case 1:
3488 i = 18;
3489 ndigits = 0;
3490 break;
3491 case 2:
3492 leftright = 0;
3493 /* no break */
3494 case 4:
3495 if (ndigits <= 0)
3496 ndigits = 1;
3497 ilim = ilim1 = i = ndigits;
3498 break;
3499 case 3:
3500 leftright = 0;
3501 /* no break */
3502 case 5:
3503 i = ndigits + k + 1;
3504 ilim = i;
3505 ilim1 = i - 1;
3506 if (i <= 0)
3507 i = 1;
3508 }
3509 s = s0 = rv_alloc(i);
3510
3511 #ifdef Honor_FLT_ROUNDS
3512 if (mode > 1 && rounding != 1)
3513 leftright = 0;
3514 #endif
3515
3516 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
3517
3518 /* Try to get by with floating-point arithmetic. */
3519
3520 i = 0;
3521 dval(d2) = dval(d);
3522 k0 = k;
3523 ilim0 = ilim;
3524 ieps = 2; /* conservative */
3525 if (k > 0) {
3526 ds = tens[k&0xf];
3527 j = k >> 4;
3528 if (j & Bletch) {
3529 /* prevent overflows */
3530 j &= Bletch - 1;
3531 dval(d) /= bigtens[n_bigtens-1];
3532 ieps++;
3533 }
3534 for (; j; j >>= 1, i++)
3535 if (j & 1) {
3536 ieps++;
3537 ds *= bigtens[i];
3538 }
3539 dval(d) /= ds;
3540 }
3541 else if ((j1 = -k) != 0) {
3542 dval(d) *= tens[j1 & 0xf];
3543 for (j = j1 >> 4; j; j >>= 1, i++)
3544 if (j & 1) {
3545 ieps++;
3546 dval(d) *= bigtens[i];
3547 }
3548 }
3549 if (k_check && dval(d) < 1. && ilim > 0) {
3550 if (ilim1 <= 0)
3551 goto fast_failed;
3552 ilim = ilim1;
3553 k--;
3554 dval(d) *= 10.;
3555 ieps++;
3556 }
3557 dval(eps) = ieps*dval(d) + 7.;
3558 word0(eps) -= (P-1)*Exp_msk1;
3559 if (ilim == 0) {
3560 S = mhi = 0;
3561 dval(d) -= 5.;
3562 if (dval(d) > dval(eps))
3563 goto one_digit;
3564 if (dval(d) < -dval(eps))
3565 goto no_digits;
3566 goto fast_failed;
3567 }
3568 #ifndef No_leftright
3569 if (leftright) {
3570 /* Use Steele & White method of only
3571 * generating digits needed.
3572 */
3573 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
3574 for (i = 0;;) {
3575 L = dval(d);
3576 dval(d) -= L;
3577 *s++ = '0' + (int)L;
3578 if (dval(d) < dval(eps))
3579 goto ret1;
3580 if (1. - dval(d) < dval(eps))
3581 goto bump_up;
3582 if (++i >= ilim)
3583 break;
3584 dval(eps) *= 10.;
3585 dval(d) *= 10.;
3586 }
3587 }
3588 else {
3589 #endif
3590 /* Generate ilim digits, then fix them up. */
3591 dval(eps) *= tens[ilim-1];
3592 for (i = 1;; i++, dval(d) *= 10.) {
3593 L = (Long)(dval(d));
3594 if (!(dval(d) -= L))
3595 ilim = i;
3596 *s++ = '0' + (int)L;
3597 if (i == ilim) {
3598 if (dval(d) > 0.5 + dval(eps))
3599 goto bump_up;
3600 else if (dval(d) < 0.5 - dval(eps)) {
3601 while (*--s == '0') ;
3602 s++;
3603 goto ret1;
3604 }
3605 break;
3606 }
3607 }
3608 #ifndef No_leftright
3609 }
3610 #endif
3611 fast_failed:
3612 s = s0;
3613 dval(d) = dval(d2);
3614 k = k0;
3615 ilim = ilim0;
3616 }
3617
3618 /* Do we have a "small" integer? */
3619
3620 if (be >= 0 && k <= Int_max) {
3621 /* Yes. */
3622 ds = tens[k];
3623 if (ndigits < 0 && ilim <= 0) {
3624 S = mhi = 0;
3625 if (ilim < 0 || dval(d) <= 5*ds)
3626 goto no_digits;
3627 goto one_digit;
3628 }
3629 for (i = 1;; i++, dval(d) *= 10.) {
3630 L = (Long)(dval(d) / ds);
3631 dval(d) -= L*ds;
3632 #ifdef Check_FLT_ROUNDS
3633 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3634 if (dval(d) < 0) {
3635 L--;
3636 dval(d) += ds;
3637 }
3638 #endif
3639 *s++ = '0' + (int)L;
3640 if (!dval(d)) {
3641 #ifdef SET_INEXACT
3642 inexact = 0;
3643 #endif
3644 break;
3645 }
3646 if (i == ilim) {
3647 #ifdef Honor_FLT_ROUNDS
3648 if (mode > 1)
3649 switch (rounding) {
3650 case 0: goto ret1;
3651 case 2: goto bump_up;
3652 }
3653 #endif
3654 dval(d) += dval(d);
3655 if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3656 bump_up:
3657 while (*--s == '9')
3658 if (s == s0) {
3659 k++;
3660 *s = '0';
3661 break;
3662 }
3663 ++*s++;
3664 }
3665 break;
3666 }
3667 }
3668 goto ret1;
3669 }
3670
3671 m2 = b2;
3672 m5 = b5;
3673 if (leftright) {
3674 i =
3675 #ifndef Sudden_Underflow
3676 denorm ? be + (Bias + (P-1) - 1 + 1) :
3677 #endif
3678 #ifdef IBM
3679 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3680 #else
3681 1 + P - bbits;
3682 #endif
3683 b2 += i;
3684 s2 += i;
3685 mhi = i2b(1);
3686 }
3687 if (m2 > 0 && s2 > 0) {
3688 i = m2 < s2 ? m2 : s2;
3689 b2 -= i;
3690 m2 -= i;
3691 s2 -= i;
3692 }
3693 if (b5 > 0) {
3694 if (leftright) {
3695 if (m5 > 0) {
3696 mhi = pow5mult(mhi, m5);
3697 b1 = mult(mhi, b);
3698 Bfree(b);
3699 b = b1;
3700 }
3701 if ((j = b5 - m5) != 0)
3702 b = pow5mult(b, j);
3703 }
3704 else
3705 b = pow5mult(b, b5);
3706 }
3707 S = i2b(1);
3708 if (s5 > 0)
3709 S = pow5mult(S, s5);
3710
3711 /* Check for special case that d is a normalized power of 2. */
3712
3713 spec_case = 0;
3714 if ((mode < 2 || leftright)
3715 #ifdef Honor_FLT_ROUNDS
3716 && rounding == 1
3717 #endif
3718 ) {
3719 if (!word1(d) && !(word0(d) & Bndry_mask)
3720 #ifndef Sudden_Underflow
3721 && word0(d) & (Exp_mask & ~Exp_msk1)
3722 #endif
3723 ) {
3724 /* The special case */
3725 b2 += Log2P;
3726 s2 += Log2P;
3727 spec_case = 1;
3728 }
3729 }
3730
3731 /* Arrange for convenient computation of quotients:
3732 * shift left if necessary so divisor has 4 leading 0 bits.
3733 *
3734 * Perhaps we should just compute leading 28 bits of S once
3735 * and for all and pass them and a shift to quorem, so it
3736 * can do shifts and ors to compute the numerator for q.
3737 */
3738 #ifdef Pack_32
3739 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3740 i = 32 - i;
3741 #else
3742 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3743 i = 16 - i;
3744 #endif
3745 if (i > 4) {
3746 i -= 4;
3747 b2 += i;
3748 m2 += i;
3749 s2 += i;
3750 }
3751 else if (i < 4) {
3752 i += 28;
3753 b2 += i;
3754 m2 += i;
3755 s2 += i;
3756 }
3757 if (b2 > 0)
3758 b = lshift(b, b2);
3759 if (s2 > 0)
3760 S = lshift(S, s2);
3761 if (k_check) {
3762 if (cmp(b,S) < 0) {
3763 k--;
3764 b = multadd(b, 10, 0); /* we botched the k estimate */
3765 if (leftright)
3766 mhi = multadd(mhi, 10, 0);
3767 ilim = ilim1;
3768 }
3769 }
3770 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3771 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3772 /* no digits, fcvt style */
3773 no_digits:
3774 k = -1 - ndigits;
3775 goto ret;
3776 }
3777 one_digit:
3778 *s++ = '1';
3779 k++;
3780 goto ret;
3781 }
3782 if (leftright) {
3783 if (m2 > 0)
3784 mhi = lshift(mhi, m2);
3785
3786 /* Compute mlo -- check for special case
3787 * that d is a normalized power of 2.
3788 */
3789
3790 mlo = mhi;
3791 if (spec_case) {
3792 mhi = Balloc(mhi->k);
3793 Bcopy(mhi, mlo);
3794 mhi = lshift(mhi, Log2P);
3795 }
3796
3797 for (i = 1;;i++) {
3798 dig = quorem(b,S) + '0';
3799 /* Do we yet have the shortest decimal string
3800 * that will round to d?
3801 */
3802 j = cmp(b, mlo);
3803 delta = diff(S, mhi);
3804 j1 = delta->sign ? 1 : cmp(b, delta);
3805 Bfree(delta);
3806 #ifndef ROUND_BIASED
3807 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3808 #ifdef Honor_FLT_ROUNDS
3809 && rounding >= 1
3810 #endif
3811 ) {
3812 if (dig == '9')
3813 goto round_9_up;
3814 if (j > 0)
3815 dig++;
3816 #ifdef SET_INEXACT
3817 else if (!b->x[0] && b->wds <= 1)
3818 inexact = 0;
3819 #endif
3820 *s++ = dig;
3821 goto ret;
3822 }
3823 #endif
3824 if (j < 0 || (j == 0 && mode != 1
3825 #ifndef ROUND_BIASED
3826 && !(word1(d) & 1)
3827 #endif
3828 )) {
3829 if (!b->x[0] && b->wds <= 1) {
3830 #ifdef SET_INEXACT
3831 inexact = 0;
3832 #endif
3833 goto accept_dig;
3834 }
3835 #ifdef Honor_FLT_ROUNDS
3836 if (mode > 1)
3837 switch (rounding) {
3838 case 0: goto accept_dig;
3839 case 2: goto keep_dig;
3840 }
3841 #endif /*Honor_FLT_ROUNDS*/
3842 if (j1 > 0) {
3843 b = lshift(b, 1);
3844 j1 = cmp(b, S);
3845 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3846 goto round_9_up;
3847 }
3848 accept_dig:
3849 *s++ = dig;
3850 goto ret;
3851 }
3852 if (j1 > 0) {
3853 #ifdef Honor_FLT_ROUNDS
3854 if (!rounding)
3855 goto accept_dig;
3856 #endif
3857 if (dig == '9') { /* possible if i == 1 */
3858 round_9_up:
3859 *s++ = '9';
3860 goto roundoff;
3861 }
3862 *s++ = dig + 1;
3863 goto ret;
3864 }
3865 #ifdef Honor_FLT_ROUNDS
3866 keep_dig:
3867 #endif
3868 *s++ = dig;
3869 if (i == ilim)
3870 break;
3871 b = multadd(b, 10, 0);
3872 if (mlo == mhi)
3873 mlo = mhi = multadd(mhi, 10, 0);
3874 else {
3875 mlo = multadd(mlo, 10, 0);
3876 mhi = multadd(mhi, 10, 0);
3877 }
3878 }
3879 }
3880 else
3881 for (i = 1;; i++) {
3882 *s++ = dig = quorem(b,S) + '0';
3883 if (!b->x[0] && b->wds <= 1) {
3884 #ifdef SET_INEXACT
3885 inexact = 0;
3886 #endif
3887 goto ret;
3888 }
3889 if (i >= ilim)
3890 break;
3891 b = multadd(b, 10, 0);
3892 }
3893
3894 /* Round off last digit */
3895
3896 #ifdef Honor_FLT_ROUNDS
3897 switch (rounding) {
3898 case 0: goto trimzeros;
3899 case 2: goto roundoff;
3900 }
3901 #endif
3902 b = lshift(b, 1);
3903 j = cmp(b, S);
3904 if (j > 0 || (j == 0 && (dig & 1))) {
3905 roundoff:
3906 while (*--s == '9')
3907 if (s == s0) {
3908 k++;
3909 *s++ = '1';
3910 goto ret;
3911 }
3912 ++*s++;
3913 }
3914 else {
3915 while (*--s == '0') ;
3916 s++;
3917 }
3918 ret:
3919 Bfree(S);
3920 if (mhi) {
3921 if (mlo && mlo != mhi)
3922 Bfree(mlo);
3923 Bfree(mhi);
3924 }
3925 ret1:
3926 #ifdef SET_INEXACT
3927 if (inexact) {
3928 if (!oldinexact) {
3929 word0(d) = Exp_1 + (70 << Exp_shift);
3930 word1(d) = 0;
3931 dval(d) += 1.;
3932 }
3933 }
3934 else if (!oldinexact)
3935 clear_inexact();
3936 #endif
3937 Bfree(b);
3938 *s = 0;
3939 *decpt = k + 1;
3940 if (rve)
3941 *rve = s;
3942 return s0;
3943 }
3944
3945 void
3946 ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg)
3947 {
3948 const char *end;
3949 int len;
3950
3951 if (!str) return;
3952 for (; *str; str = end) {
3953 while (ISSPACE(*str) || *str == ',') str++;
3954 if (!*str) break;
3955 end = str;
3956 while (*end && !ISSPACE(*end) && *end != ',') end++;
3957 len = end - str;
3958 (*func)(str, len, arg);
3959 }
3960 }
3961
3962 #ifdef __cplusplus
3963 }
3964 #endif
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