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* gc.c (set_heaps_increment): fix memory allocation strategy by
[ruby-svn.git] / util.c
blobfc8874c942250a26bfed778e11682c712f0825bd
1 /**********************************************************************
2
3 util.c -
4
5 $Author$
6 created at: Fri Mar 10 17:22:34 JST 1995
7
8 Copyright (C) 1993-2007 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 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 free(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 free(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 #include "errno.h"
1004
1005 #ifdef Bad_float_h
1006
1007 #ifdef IEEE_Arith
1008 #define DBL_DIG 15
1009 #define DBL_MAX_10_EXP 308
1010 #define DBL_MAX_EXP 1024
1011 #define FLT_RADIX 2
1012 #endif /*IEEE_Arith*/
1013
1014 #ifdef IBM
1015 #define DBL_DIG 16
1016 #define DBL_MAX_10_EXP 75
1017 #define DBL_MAX_EXP 63
1018 #define FLT_RADIX 16
1019 #define DBL_MAX 7.2370055773322621e+75
1020 #endif
1021
1022 #ifdef VAX
1023 #define DBL_DIG 16
1024 #define DBL_MAX_10_EXP 38
1025 #define DBL_MAX_EXP 127
1026 #define FLT_RADIX 2
1027 #define DBL_MAX 1.7014118346046923e+38
1028 #endif
1029
1030 #ifndef LONG_MAX
1031 #define LONG_MAX 2147483647
1032 #endif
1033
1034 #else /* ifndef Bad_float_h */
1035 #include "float.h"
1036 #endif /* Bad_float_h */
1037
1038 #ifndef __MATH_H__
1039 #include "math.h"
1040 #endif
1041
1042 #ifdef __cplusplus
1043 extern "C" {
1044 #endif
1045
1046 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
1047 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
1048 #endif
1049
1050 typedef union { double d; ULong L[2]; } U;
1051
1052 #ifdef YES_ALIAS
1053 #define dval(x) x
1054 #ifdef IEEE_LITTLE_ENDIAN
1055 #define word0(x) ((ULong *)&x)[1]
1056 #define word1(x) ((ULong *)&x)[0]
1057 #else
1058 #define word0(x) ((ULong *)&x)[0]
1059 #define word1(x) ((ULong *)&x)[1]
1060 #endif
1061 #else
1062 #ifdef IEEE_LITTLE_ENDIAN
1063 #define word0(x) ((U*)&x)->L[1]
1064 #define word1(x) ((U*)&x)->L[0]
1065 #else
1066 #define word0(x) ((U*)&x)->L[0]
1067 #define word1(x) ((U*)&x)->L[1]
1068 #endif
1069 #define dval(x) ((U*)&x)->d
1070 #endif
1071
1072 /* The following definition of Storeinc is appropriate for MIPS processors.
1073 * An alternative that might be better on some machines is
1074 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
1075 */
1076 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
1077 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
1078 ((unsigned short *)a)[0] = (unsigned short)c, a++)
1079 #else
1080 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
1081 ((unsigned short *)a)[1] = (unsigned short)c, a++)
1082 #endif
1083
1084 /* #define P DBL_MANT_DIG */
1085 /* Ten_pmax = floor(P*log(2)/log(5)) */
1086 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
1087 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
1088 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
1089
1090 #ifdef IEEE_Arith
1091 #define Exp_shift 20
1092 #define Exp_shift1 20
1093 #define Exp_msk1 0x100000
1094 #define Exp_msk11 0x100000
1095 #define Exp_mask 0x7ff00000
1096 #define P 53
1097 #define Bias 1023
1098 #define Emin (-1022)
1099 #define Exp_1 0x3ff00000
1100 #define Exp_11 0x3ff00000
1101 #define Ebits 11
1102 #define Frac_mask 0xfffff
1103 #define Frac_mask1 0xfffff
1104 #define Ten_pmax 22
1105 #define Bletch 0x10
1106 #define Bndry_mask 0xfffff
1107 #define Bndry_mask1 0xfffff
1108 #define LSB 1
1109 #define Sign_bit 0x80000000
1110 #define Log2P 1
1111 #define Tiny0 0
1112 #define Tiny1 1
1113 #define Quick_max 14
1114 #define Int_max 14
1115 #ifndef NO_IEEE_Scale
1116 #define Avoid_Underflow
1117 #ifdef Flush_Denorm /* debugging option */
1118 #undef Sudden_Underflow
1119 #endif
1120 #endif
1121
1122 #ifndef Flt_Rounds
1123 #ifdef FLT_ROUNDS
1124 #define Flt_Rounds FLT_ROUNDS
1125 #else
1126 #define Flt_Rounds 1
1127 #endif
1128 #endif /*Flt_Rounds*/
1129
1130 #ifdef Honor_FLT_ROUNDS
1131 #define Rounding rounding
1132 #undef Check_FLT_ROUNDS
1133 #define Check_FLT_ROUNDS
1134 #else
1135 #define Rounding Flt_Rounds
1136 #endif
1137
1138 #else /* ifndef IEEE_Arith */
1139 #undef Check_FLT_ROUNDS
1140 #undef Honor_FLT_ROUNDS
1141 #undef SET_INEXACT
1142 #undef Sudden_Underflow
1143 #define Sudden_Underflow
1144 #ifdef IBM
1145 #undef Flt_Rounds
1146 #define Flt_Rounds 0
1147 #define Exp_shift 24
1148 #define Exp_shift1 24
1149 #define Exp_msk1 0x1000000
1150 #define Exp_msk11 0x1000000
1151 #define Exp_mask 0x7f000000
1152 #define P 14
1153 #define Bias 65
1154 #define Exp_1 0x41000000
1155 #define Exp_11 0x41000000
1156 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
1157 #define Frac_mask 0xffffff
1158 #define Frac_mask1 0xffffff
1159 #define Bletch 4
1160 #define Ten_pmax 22
1161 #define Bndry_mask 0xefffff
1162 #define Bndry_mask1 0xffffff
1163 #define LSB 1
1164 #define Sign_bit 0x80000000
1165 #define Log2P 4
1166 #define Tiny0 0x100000
1167 #define Tiny1 0
1168 #define Quick_max 14
1169 #define Int_max 15
1170 #else /* VAX */
1171 #undef Flt_Rounds
1172 #define Flt_Rounds 1
1173 #define Exp_shift 23
1174 #define Exp_shift1 7
1175 #define Exp_msk1 0x80
1176 #define Exp_msk11 0x800000
1177 #define Exp_mask 0x7f80
1178 #define P 56
1179 #define Bias 129
1180 #define Exp_1 0x40800000
1181 #define Exp_11 0x4080
1182 #define Ebits 8
1183 #define Frac_mask 0x7fffff
1184 #define Frac_mask1 0xffff007f
1185 #define Ten_pmax 24
1186 #define Bletch 2
1187 #define Bndry_mask 0xffff007f
1188 #define Bndry_mask1 0xffff007f
1189 #define LSB 0x10000
1190 #define Sign_bit 0x8000
1191 #define Log2P 1
1192 #define Tiny0 0x80
1193 #define Tiny1 0
1194 #define Quick_max 15
1195 #define Int_max 15
1196 #endif /* IBM, VAX */
1197 #endif /* IEEE_Arith */
1198
1199 #ifndef IEEE_Arith
1200 #define ROUND_BIASED
1201 #endif
1202
1203 #ifdef RND_PRODQUOT
1204 #define rounded_product(a,b) a = rnd_prod(a, b)
1205 #define rounded_quotient(a,b) a = rnd_quot(a, b)
1206 extern double rnd_prod(double, double), rnd_quot(double, double);
1207 #else
1208 #define rounded_product(a,b) a *= b
1209 #define rounded_quotient(a,b) a /= b
1210 #endif
1211
1212 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
1213 #define Big1 0xffffffff
1214
1215 #ifndef Pack_32
1216 #define Pack_32
1217 #endif
1218
1219 #define FFFFFFFF 0xffffffffUL
1220
1221 #ifdef NO_LONG_LONG
1222 #undef ULLong
1223 #ifdef Just_16
1224 #undef Pack_32
1225 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
1226 * This makes some inner loops simpler and sometimes saves work
1227 * during multiplications, but it often seems to make things slightly
1228 * slower. Hence the default is now to store 32 bits per Long.
1229 */
1230 #endif
1231 #else /* long long available */
1232 #ifndef Llong
1233 #define Llong long long
1234 #endif
1235 #ifndef ULLong
1236 #define ULLong unsigned Llong
1237 #endif
1238 #endif /* NO_LONG_LONG */
1239
1240 #ifndef MULTIPLE_THREADS
1241 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
1242 #define FREE_DTOA_LOCK(n) /*nothing*/
1243 #endif
1244
1245 #define Kmax 15
1246
1247 struct Bigint {
1248 struct Bigint *next;
1249 int k, maxwds, sign, wds;
1250 ULong x[1];
1251 };
1252
1253 typedef struct Bigint Bigint;
1254
1255 static Bigint *freelist[Kmax+1];
1256
1257 static Bigint *
1258 Balloc(int k)
1259 {
1260 int x;
1261 Bigint *rv;
1262 #ifndef Omit_Private_Memory
1263 unsigned int len;
1264 #endif
1265
1266 ACQUIRE_DTOA_LOCK(0);
1267 if ((rv = freelist[k]) != 0) {
1268 freelist[k] = rv->next;
1269 }
1270 else {
1271 x = 1 << k;
1272 #ifdef Omit_Private_Memory
1273 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
1274 #else
1275 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
1276 /sizeof(double);
1277 if (pmem_next - private_mem + len <= PRIVATE_mem) {
1278 rv = (Bigint*)pmem_next;
1279 pmem_next += len;
1280 }
1281 else
1282 rv = (Bigint*)MALLOC(len*sizeof(double));
1283 #endif
1284 rv->k = k;
1285 rv->maxwds = x;
1286 }
1287 FREE_DTOA_LOCK(0);
1288 rv->sign = rv->wds = 0;
1289 return rv;
1290 }
1291
1292 static void
1293 Bfree(Bigint *v)
1294 {
1295 if (v) {
1296 ACQUIRE_DTOA_LOCK(0);
1297 v->next = freelist[v->k];
1298 freelist[v->k] = v;
1299 FREE_DTOA_LOCK(0);
1300 }
1301 }
1302
1303 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
1304 y->wds*sizeof(Long) + 2*sizeof(int))
1305
1306 static Bigint *
1307 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
1308 {
1309 int i, wds;
1310 #ifdef ULLong
1311 ULong *x;
1312 ULLong carry, y;
1313 #else
1314 ULong carry, *x, y;
1315 #ifdef Pack_32
1316 ULong xi, z;
1317 #endif
1318 #endif
1319 Bigint *b1;
1320
1321 wds = b->wds;
1322 x = b->x;
1323 i = 0;
1324 carry = a;
1325 do {
1326 #ifdef ULLong
1327 y = *x * (ULLong)m + carry;
1328 carry = y >> 32;
1329 *x++ = y & FFFFFFFF;
1330 #else
1331 #ifdef Pack_32
1332 xi = *x;
1333 y = (xi & 0xffff) * m + carry;
1334 z = (xi >> 16) * m + (y >> 16);
1335 carry = z >> 16;
1336 *x++ = (z << 16) + (y & 0xffff);
1337 #else
1338 y = *x * m + carry;
1339 carry = y >> 16;
1340 *x++ = y & 0xffff;
1341 #endif
1342 #endif
1343 } while (++i < wds);
1344 if (carry) {
1345 if (wds >= b->maxwds) {
1346 b1 = Balloc(b->k+1);
1347 Bcopy(b1, b);
1348 Bfree(b);
1349 b = b1;
1350 }
1351 b->x[wds++] = carry;
1352 b->wds = wds;
1353 }
1354 return b;
1355 }
1356
1357 static Bigint *
1358 s2b(const char *s, int nd0, int nd, ULong y9)
1359 {
1360 Bigint *b;
1361 int i, k;
1362 Long x, y;
1363
1364 x = (nd + 8) / 9;
1365 for (k = 0, y = 1; x > y; y <<= 1, k++) ;
1366 #ifdef Pack_32
1367 b = Balloc(k);
1368 b->x[0] = y9;
1369 b->wds = 1;
1370 #else
1371 b = Balloc(k+1);
1372 b->x[0] = y9 & 0xffff;
1373 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
1374 #endif
1375
1376 i = 9;
1377 if (9 < nd0) {
1378 s += 9;
1379 do {
1380 b = multadd(b, 10, *s++ - '0');
1381 } while (++i < nd0);
1382 s++;
1383 }
1384 else
1385 s += 10;
1386 for (; i < nd; i++)
1387 b = multadd(b, 10, *s++ - '0');
1388 return b;
1389 }
1390
1391 static int
1392 hi0bits(register ULong x)
1393 {
1394 register int k = 0;
1395
1396 if (!(x & 0xffff0000)) {
1397 k = 16;
1398 x <<= 16;
1399 }
1400 if (!(x & 0xff000000)) {
1401 k += 8;
1402 x <<= 8;
1403 }
1404 if (!(x & 0xf0000000)) {
1405 k += 4;
1406 x <<= 4;
1407 }
1408 if (!(x & 0xc0000000)) {
1409 k += 2;
1410 x <<= 2;
1411 }
1412 if (!(x & 0x80000000)) {
1413 k++;
1414 if (!(x & 0x40000000))
1415 return 32;
1416 }
1417 return k;
1418 }
1419
1420 static int
1421 lo0bits(ULong *y)
1422 {
1423 register int k;
1424 register ULong x = *y;
1425
1426 if (x & 7) {
1427 if (x & 1)
1428 return 0;
1429 if (x & 2) {
1430 *y = x >> 1;
1431 return 1;
1432 }
1433 *y = x >> 2;
1434 return 2;
1435 }
1436 k = 0;
1437 if (!(x & 0xffff)) {
1438 k = 16;
1439 x >>= 16;
1440 }
1441 if (!(x & 0xff)) {
1442 k += 8;
1443 x >>= 8;
1444 }
1445 if (!(x & 0xf)) {
1446 k += 4;
1447 x >>= 4;
1448 }
1449 if (!(x & 0x3)) {
1450 k += 2;
1451 x >>= 2;
1452 }
1453 if (!(x & 1)) {
1454 k++;
1455 x >>= 1;
1456 if (!x)
1457 return 32;
1458 }
1459 *y = x;
1460 return k;
1461 }
1462
1463 static Bigint *
1464 i2b(int i)
1465 {
1466 Bigint *b;
1467
1468 b = Balloc(1);
1469 b->x[0] = i;
1470 b->wds = 1;
1471 return b;
1472 }
1473
1474 static Bigint *
1475 mult(Bigint *a, Bigint *b)
1476 {
1477 Bigint *c;
1478 int k, wa, wb, wc;
1479 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
1480 ULong y;
1481 #ifdef ULLong
1482 ULLong carry, z;
1483 #else
1484 ULong carry, z;
1485 #ifdef Pack_32
1486 ULong z2;
1487 #endif
1488 #endif
1489
1490 if (a->wds < b->wds) {
1491 c = a;
1492 a = b;
1493 b = c;
1494 }
1495 k = a->k;
1496 wa = a->wds;
1497 wb = b->wds;
1498 wc = wa + wb;
1499 if (wc > a->maxwds)
1500 k++;
1501 c = Balloc(k);
1502 for (x = c->x, xa = x + wc; x < xa; x++)
1503 *x = 0;
1504 xa = a->x;
1505 xae = xa + wa;
1506 xb = b->x;
1507 xbe = xb + wb;
1508 xc0 = c->x;
1509 #ifdef ULLong
1510 for (; xb < xbe; xc0++) {
1511 if ((y = *xb++) != 0) {
1512 x = xa;
1513 xc = xc0;
1514 carry = 0;
1515 do {
1516 z = *x++ * (ULLong)y + *xc + carry;
1517 carry = z >> 32;
1518 *xc++ = z & FFFFFFFF;
1519 } while (x < xae);
1520 *xc = carry;
1521 }
1522 }
1523 #else
1524 #ifdef Pack_32
1525 for (; xb < xbe; xb++, xc0++) {
1526 if (y = *xb & 0xffff) {
1527 x = xa;
1528 xc = xc0;
1529 carry = 0;
1530 do {
1531 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
1532 carry = z >> 16;
1533 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
1534 carry = z2 >> 16;
1535 Storeinc(xc, z2, z);
1536 } while (x < xae);
1537 *xc = carry;
1538 }
1539 if (y = *xb >> 16) {
1540 x = xa;
1541 xc = xc0;
1542 carry = 0;
1543 z2 = *xc;
1544 do {
1545 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
1546 carry = z >> 16;
1547 Storeinc(xc, z, z2);
1548 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
1549 carry = z2 >> 16;
1550 } while (x < xae);
1551 *xc = z2;
1552 }
1553 }
1554 #else
1555 for (; xb < xbe; xc0++) {
1556 if (y = *xb++) {
1557 x = xa;
1558 xc = xc0;
1559 carry = 0;
1560 do {
1561 z = *x++ * y + *xc + carry;
1562 carry = z >> 16;
1563 *xc++ = z & 0xffff;
1564 } while (x < xae);
1565 *xc = carry;
1566 }
1567 }
1568 #endif
1569 #endif
1570 for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
1571 c->wds = wc;
1572 return c;
1573 }
1574
1575 static Bigint *p5s;
1576
1577 static Bigint *
1578 pow5mult(Bigint *b, int k)
1579 {
1580 Bigint *b1, *p5, *p51;
1581 int i;
1582 static int p05[3] = { 5, 25, 125 };
1583
1584 if ((i = k & 3) != 0)
1585 b = multadd(b, p05[i-1], 0);
1586
1587 if (!(k >>= 2))
1588 return b;
1589 if (!(p5 = p5s)) {
1590 /* first time */
1591 #ifdef MULTIPLE_THREADS
1592 ACQUIRE_DTOA_LOCK(1);
1593 if (!(p5 = p5s)) {
1594 p5 = p5s = i2b(625);
1595 p5->next = 0;
1596 }
1597 FREE_DTOA_LOCK(1);
1598 #else
1599 p5 = p5s = i2b(625);
1600 p5->next = 0;
1601 #endif
1602 }
1603 for (;;) {
1604 if (k & 1) {
1605 b1 = mult(b, p5);
1606 Bfree(b);
1607 b = b1;
1608 }
1609 if (!(k >>= 1))
1610 break;
1611 if (!(p51 = p5->next)) {
1612 #ifdef MULTIPLE_THREADS
1613 ACQUIRE_DTOA_LOCK(1);
1614 if (!(p51 = p5->next)) {
1615 p51 = p5->next = mult(p5,p5);
1616 p51->next = 0;
1617 }
1618 FREE_DTOA_LOCK(1);
1619 #else
1620 p51 = p5->next = mult(p5,p5);
1621 p51->next = 0;
1622 #endif
1623 }
1624 p5 = p51;
1625 }
1626 return b;
1627 }
1628
1629 static Bigint *
1630 lshift(Bigint *b, int k)
1631 {
1632 int i, k1, n, n1;
1633 Bigint *b1;
1634 ULong *x, *x1, *xe, z;
1635
1636 #ifdef Pack_32
1637 n = k >> 5;
1638 #else
1639 n = k >> 4;
1640 #endif
1641 k1 = b->k;
1642 n1 = n + b->wds + 1;
1643 for (i = b->maxwds; n1 > i; i <<= 1)
1644 k1++;
1645 b1 = Balloc(k1);
1646 x1 = b1->x;
1647 for (i = 0; i < n; i++)
1648 *x1++ = 0;
1649 x = b->x;
1650 xe = x + b->wds;
1651 #ifdef Pack_32
1652 if (k &= 0x1f) {
1653 k1 = 32 - k;
1654 z = 0;
1655 do {
1656 *x1++ = *x << k | z;
1657 z = *x++ >> k1;
1658 } while (x < xe);
1659 if ((*x1 = z) != 0)
1660 ++n1;
1661 }
1662 #else
1663 if (k &= 0xf) {
1664 k1 = 16 - k;
1665 z = 0;
1666 do {
1667 *x1++ = *x << k & 0xffff | z;
1668 z = *x++ >> k1;
1669 } while (x < xe);
1670 if (*x1 = z)
1671 ++n1;
1672 }
1673 #endif
1674 else
1675 do {
1676 *x1++ = *x++;
1677 } while (x < xe);
1678 b1->wds = n1 - 1;
1679 Bfree(b);
1680 return b1;
1681 }
1682
1683 static int
1684 cmp(Bigint *a, Bigint *b)
1685 {
1686 ULong *xa, *xa0, *xb, *xb0;
1687 int i, j;
1688
1689 i = a->wds;
1690 j = b->wds;
1691 #ifdef DEBUG
1692 if (i > 1 && !a->x[i-1])
1693 Bug("cmp called with a->x[a->wds-1] == 0");
1694 if (j > 1 && !b->x[j-1])
1695 Bug("cmp called with b->x[b->wds-1] == 0");
1696 #endif
1697 if (i -= j)
1698 return i;
1699 xa0 = a->x;
1700 xa = xa0 + j;
1701 xb0 = b->x;
1702 xb = xb0 + j;
1703 for (;;) {
1704 if (*--xa != *--xb)
1705 return *xa < *xb ? -1 : 1;
1706 if (xa <= xa0)
1707 break;
1708 }
1709 return 0;
1710 }
1711
1712 static Bigint *
1713 diff(Bigint *a, Bigint *b)
1714 {
1715 Bigint *c;
1716 int i, wa, wb;
1717 ULong *xa, *xae, *xb, *xbe, *xc;
1718 #ifdef ULLong
1719 ULLong borrow, y;
1720 #else
1721 ULong borrow, y;
1722 #ifdef Pack_32
1723 ULong z;
1724 #endif
1725 #endif
1726
1727 i = cmp(a,b);
1728 if (!i) {
1729 c = Balloc(0);
1730 c->wds = 1;
1731 c->x[0] = 0;
1732 return c;
1733 }
1734 if (i < 0) {
1735 c = a;
1736 a = b;
1737 b = c;
1738 i = 1;
1739 }
1740 else
1741 i = 0;
1742 c = Balloc(a->k);
1743 c->sign = i;
1744 wa = a->wds;
1745 xa = a->x;
1746 xae = xa + wa;
1747 wb = b->wds;
1748 xb = b->x;
1749 xbe = xb + wb;
1750 xc = c->x;
1751 borrow = 0;
1752 #ifdef ULLong
1753 do {
1754 y = (ULLong)*xa++ - *xb++ - borrow;
1755 borrow = y >> 32 & (ULong)1;
1756 *xc++ = y & FFFFFFFF;
1757 } while (xb < xbe);
1758 while (xa < xae) {
1759 y = *xa++ - borrow;
1760 borrow = y >> 32 & (ULong)1;
1761 *xc++ = y & FFFFFFFF;
1762 }
1763 #else
1764 #ifdef Pack_32
1765 do {
1766 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1767 borrow = (y & 0x10000) >> 16;
1768 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1769 borrow = (z & 0x10000) >> 16;
1770 Storeinc(xc, z, y);
1771 } while (xb < xbe);
1772 while (xa < xae) {
1773 y = (*xa & 0xffff) - borrow;
1774 borrow = (y & 0x10000) >> 16;
1775 z = (*xa++ >> 16) - borrow;
1776 borrow = (z & 0x10000) >> 16;
1777 Storeinc(xc, z, y);
1778 }
1779 #else
1780 do {
1781 y = *xa++ - *xb++ - borrow;
1782 borrow = (y & 0x10000) >> 16;
1783 *xc++ = y & 0xffff;
1784 } while (xb < xbe);
1785 while (xa < xae) {
1786 y = *xa++ - borrow;
1787 borrow = (y & 0x10000) >> 16;
1788 *xc++ = y & 0xffff;
1789 }
1790 #endif
1791 #endif
1792 while (!*--xc)
1793 wa--;
1794 c->wds = wa;
1795 return c;
1796 }
1797
1798 static double
1799 ulp(double x)
1800 {
1801 register Long L;
1802 double a;
1803
1804 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1805 #ifndef Avoid_Underflow
1806 #ifndef Sudden_Underflow
1807 if (L > 0) {
1808 #endif
1809 #endif
1810 #ifdef IBM
1811 L |= Exp_msk1 >> 4;
1812 #endif
1813 word0(a) = L;
1814 word1(a) = 0;
1815 #ifndef Avoid_Underflow
1816 #ifndef Sudden_Underflow
1817 }
1818 else {
1819 L = -L >> Exp_shift;
1820 if (L < Exp_shift) {
1821 word0(a) = 0x80000 >> L;
1822 word1(a) = 0;
1823 }
1824 else {
1825 word0(a) = 0;
1826 L -= Exp_shift;
1827 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1828 }
1829 }
1830 #endif
1831 #endif
1832 return dval(a);
1833 }
1834
1835 static double
1836 b2d(Bigint *a, int *e)
1837 {
1838 ULong *xa, *xa0, w, y, z;
1839 int k;
1840 double d;
1841 #ifdef VAX
1842 ULong d0, d1;
1843 #else
1844 #define d0 word0(d)
1845 #define d1 word1(d)
1846 #endif
1847
1848 xa0 = a->x;
1849 xa = xa0 + a->wds;
1850 y = *--xa;
1851 #ifdef DEBUG
1852 if (!y) Bug("zero y in b2d");
1853 #endif
1854 k = hi0bits(y);
1855 *e = 32 - k;
1856 #ifdef Pack_32
1857 if (k < Ebits) {
1858 d0 = Exp_1 | y >> (Ebits - k);
1859 w = xa > xa0 ? *--xa : 0;
1860 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1861 goto ret_d;
1862 }
1863 z = xa > xa0 ? *--xa : 0;
1864 if (k -= Ebits) {
1865 d0 = Exp_1 | y << k | z >> (32 - k);
1866 y = xa > xa0 ? *--xa : 0;
1867 d1 = z << k | y >> (32 - k);
1868 }
1869 else {
1870 d0 = Exp_1 | y;
1871 d1 = z;
1872 }
1873 #else
1874 if (k < Ebits + 16) {
1875 z = xa > xa0 ? *--xa : 0;
1876 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1877 w = xa > xa0 ? *--xa : 0;
1878 y = xa > xa0 ? *--xa : 0;
1879 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1880 goto ret_d;
1881 }
1882 z = xa > xa0 ? *--xa : 0;
1883 w = xa > xa0 ? *--xa : 0;
1884 k -= Ebits + 16;
1885 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1886 y = xa > xa0 ? *--xa : 0;
1887 d1 = w << k + 16 | y << k;
1888 #endif
1889 ret_d:
1890 #ifdef VAX
1891 word0(d) = d0 >> 16 | d0 << 16;
1892 word1(d) = d1 >> 16 | d1 << 16;
1893 #else
1894 #undef d0
1895 #undef d1
1896 #endif
1897 return dval(d);
1898 }
1899
1900 static Bigint *
1901 d2b(double d, int *e, int *bits)
1902 {
1903 Bigint *b;
1904 int de, k;
1905 ULong *x, y, z;
1906 #ifndef Sudden_Underflow
1907 int i;
1908 #endif
1909 #ifdef VAX
1910 ULong d0, d1;
1911 d0 = word0(d) >> 16 | word0(d) << 16;
1912 d1 = word1(d) >> 16 | word1(d) << 16;
1913 #else
1914 #define d0 word0(d)
1915 #define d1 word1(d)
1916 #endif
1917
1918 #ifdef Pack_32
1919 b = Balloc(1);
1920 #else
1921 b = Balloc(2);
1922 #endif
1923 x = b->x;
1924
1925 z = d0 & Frac_mask;
1926 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1927 #ifdef Sudden_Underflow
1928 de = (int)(d0 >> Exp_shift);
1929 #ifndef IBM
1930 z |= Exp_msk11;
1931 #endif
1932 #else
1933 if ((de = (int)(d0 >> Exp_shift)) != 0)
1934 z |= Exp_msk1;
1935 #endif
1936 #ifdef Pack_32
1937 if ((y = d1) != 0) {
1938 if ((k = lo0bits(&y)) != 0) {
1939 x[0] = y | z << (32 - k);
1940 z >>= k;
1941 }
1942 else
1943 x[0] = y;
1944 #ifndef Sudden_Underflow
1945 i =
1946 #endif
1947 b->wds = (x[1] = z) ? 2 : 1;
1948 }
1949 else {
1950 #ifdef DEBUG
1951 if (!z)
1952 Bug("Zero passed to d2b");
1953 #endif
1954 k = lo0bits(&z);
1955 x[0] = z;
1956 #ifndef Sudden_Underflow
1957 i =
1958 #endif
1959 b->wds = 1;
1960 k += 32;
1961 }
1962 #else
1963 if (y = d1) {
1964 if (k = lo0bits(&y))
1965 if (k >= 16) {
1966 x[0] = y | z << 32 - k & 0xffff;
1967 x[1] = z >> k - 16 & 0xffff;
1968 x[2] = z >> k;
1969 i = 2;
1970 }
1971 else {
1972 x[0] = y & 0xffff;
1973 x[1] = y >> 16 | z << 16 - k & 0xffff;
1974 x[2] = z >> k & 0xffff;
1975 x[3] = z >> k+16;
1976 i = 3;
1977 }
1978 else {
1979 x[0] = y & 0xffff;
1980 x[1] = y >> 16;
1981 x[2] = z & 0xffff;
1982 x[3] = z >> 16;
1983 i = 3;
1984 }
1985 }
1986 else {
1987 #ifdef DEBUG
1988 if (!z)
1989 Bug("Zero passed to d2b");
1990 #endif
1991 k = lo0bits(&z);
1992 if (k >= 16) {
1993 x[0] = z;
1994 i = 0;
1995 }
1996 else {
1997 x[0] = z & 0xffff;
1998 x[1] = z >> 16;
1999 i = 1;
2000 }
2001 k += 32;
2002 }
2003 while (!x[i])
2004 --i;
2005 b->wds = i + 1;
2006 #endif
2007 #ifndef Sudden_Underflow
2008 if (de) {
2009 #endif
2010 #ifdef IBM
2011 *e = (de - Bias - (P-1) << 2) + k;
2012 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
2013 #else
2014 *e = de - Bias - (P-1) + k;
2015 *bits = P - k;
2016 #endif
2017 #ifndef Sudden_Underflow
2018 }
2019 else {
2020 *e = de - Bias - (P-1) + 1 + k;
2021 #ifdef Pack_32
2022 *bits = 32*i - hi0bits(x[i-1]);
2023 #else
2024 *bits = (i+2)*16 - hi0bits(x[i]);
2025 #endif
2026 }
2027 #endif
2028 return b;
2029 }
2030 #undef d0
2031 #undef d1
2032
2033 static double
2034 ratio(Bigint *a, Bigint *b)
2035 {
2036 double da, db;
2037 int k, ka, kb;
2038
2039 dval(da) = b2d(a, &ka);
2040 dval(db) = b2d(b, &kb);
2041 #ifdef Pack_32
2042 k = ka - kb + 32*(a->wds - b->wds);
2043 #else
2044 k = ka - kb + 16*(a->wds - b->wds);
2045 #endif
2046 #ifdef IBM
2047 if (k > 0) {
2048 word0(da) += (k >> 2)*Exp_msk1;
2049 if (k &= 3)
2050 dval(da) *= 1 << k;
2051 }
2052 else {
2053 k = -k;
2054 word0(db) += (k >> 2)*Exp_msk1;
2055 if (k &= 3)
2056 dval(db) *= 1 << k;
2057 }
2058 #else
2059 if (k > 0)
2060 word0(da) += k*Exp_msk1;
2061 else {
2062 k = -k;
2063 word0(db) += k*Exp_msk1;
2064 }
2065 #endif
2066 return dval(da) / dval(db);
2067 }
2068
2069 static const double
2070 tens[] = {
2071 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
2072 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
2073 1e20, 1e21, 1e22
2074 #ifdef VAX
2075 , 1e23, 1e24
2076 #endif
2077 };
2078
2079 static const double
2080 #ifdef IEEE_Arith
2081 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
2082 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
2083 #ifdef Avoid_Underflow
2084 9007199254740992.*9007199254740992.e-256
2085 /* = 2^106 * 1e-53 */
2086 #else
2087 1e-256
2088 #endif
2089 };
2090 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
2091 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
2092 #define Scale_Bit 0x10
2093 #define n_bigtens 5
2094 #else
2095 #ifdef IBM
2096 bigtens[] = { 1e16, 1e32, 1e64 };
2097 static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
2098 #define n_bigtens 3
2099 #else
2100 bigtens[] = { 1e16, 1e32 };
2101 static const double tinytens[] = { 1e-16, 1e-32 };
2102 #define n_bigtens 2
2103 #endif
2104 #endif
2105
2106 #ifndef IEEE_Arith
2107 #undef INFNAN_CHECK
2108 #endif
2109
2110 #ifdef INFNAN_CHECK
2111
2112 #ifndef NAN_WORD0
2113 #define NAN_WORD0 0x7ff80000
2114 #endif
2115
2116 #ifndef NAN_WORD1
2117 #define NAN_WORD1 0
2118 #endif
2119
2120 static int
2121 match(const char **sp, char *t)
2122 {
2123 int c, d;
2124 const char *s = *sp;
2125
2126 while (d = *t++) {
2127 if ((c = *++s) >= 'A' && c <= 'Z')
2128 c += 'a' - 'A';
2129 if (c != d)
2130 return 0;
2131 }
2132 *sp = s + 1;
2133 return 1;
2134 }
2135
2136 #ifndef No_Hex_NaN
2137 static void
2138 hexnan(double *rvp, const char **sp)
2139 {
2140 ULong c, x[2];
2141 const char *s;
2142 int havedig, udx0, xshift;
2143
2144 x[0] = x[1] = 0;
2145 havedig = xshift = 0;
2146 udx0 = 1;
2147 s = *sp;
2148 while (c = *(const unsigned char*)++s) {
2149 if (c >= '0' && c <= '9')
2150 c -= '0';
2151 else if (c >= 'a' && c <= 'f')
2152 c += 10 - 'a';
2153 else if (c >= 'A' && c <= 'F')
2154 c += 10 - 'A';
2155 else if (c <= ' ') {
2156 if (udx0 && havedig) {
2157 udx0 = 0;
2158 xshift = 1;
2159 }
2160 continue;
2161 }
2162 else if (/*(*/ c == ')' && havedig) {
2163 *sp = s + 1;
2164 break;
2165 }
2166 else
2167 return; /* invalid form: don't change *sp */
2168 havedig = 1;
2169 if (xshift) {
2170 xshift = 0;
2171 x[0] = x[1];
2172 x[1] = 0;
2173 }
2174 if (udx0)
2175 x[0] = (x[0] << 4) | (x[1] >> 28);
2176 x[1] = (x[1] << 4) | c;
2177 }
2178 if ((x[0] &= 0xfffff) || x[1]) {
2179 word0(*rvp) = Exp_mask | x[0];
2180 word1(*rvp) = x[1];
2181 }
2182 }
2183 #endif /*No_Hex_NaN*/
2184 #endif /* INFNAN_CHECK */
2185
2186 double
2187 ruby_strtod(const char *s00, char **se)
2188 {
2189 #ifdef Avoid_Underflow
2190 int scale;
2191 #endif
2192 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
2193 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
2194 const char *s, *s0, *s1;
2195 double aadj, aadj1, adj, rv, rv0;
2196 Long L;
2197 ULong y, z;
2198 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
2199 #ifdef SET_INEXACT
2200 int inexact, oldinexact;
2201 #endif
2202 #ifdef Honor_FLT_ROUNDS
2203 int rounding;
2204 #endif
2205 #ifdef USE_LOCALE
2206 const char *s2;
2207 #endif
2208
2209 sign = nz0 = nz = 0;
2210 dval(rv) = 0.;
2211 for (s = s00;;s++)
2212 switch (*s) {
2213 case '-':
2214 sign = 1;
2215 /* no break */
2216 case '+':
2217 if (*++s)
2218 goto break2;
2219 /* no break */
2220 case 0:
2221 goto ret0;
2222 case '\t':
2223 case '\n':
2224 case '\v':
2225 case '\f':
2226 case '\r':
2227 case ' ':
2228 continue;
2229 default:
2230 goto break2;
2231 }
2232 break2:
2233 if (*s == '0') {
2234 nz0 = 1;
2235 while (*++s == '0') ;
2236 if (!*s)
2237 goto ret;
2238 }
2239 s0 = s;
2240 y = z = 0;
2241 for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
2242 if (nd < 9)
2243 y = 10*y + c - '0';
2244 else if (nd < 16)
2245 z = 10*z + c - '0';
2246 nd0 = nd;
2247 #ifdef USE_LOCALE
2248 s1 = localeconv()->decimal_point;
2249 if (c == *s1) {
2250 c = '.';
2251 if (*++s1) {
2252 s2 = s;
2253 for (;;) {
2254 if (*++s2 != *s1) {
2255 c = 0;
2256 break;
2257 }
2258 if (!*++s1) {
2259 s = s2;
2260 break;
2261 }
2262 }
2263 }
2264 }
2265 #endif
2266 if (c == '.') {
2267 c = *++s;
2268 if (!nd) {
2269 for (; c == '0'; c = *++s)
2270 nz++;
2271 if (c > '0' && c <= '9') {
2272 s0 = s;
2273 nf += nz;
2274 nz = 0;
2275 goto have_dig;
2276 }
2277 goto dig_done;
2278 }
2279 for (; c >= '0' && c <= '9'; c = *++s) {
2280 have_dig:
2281 nz++;
2282 if (c -= '0') {
2283 nf += nz;
2284 for (i = 1; i < nz; i++)
2285 if (nd++ < 9)
2286 y *= 10;
2287 else if (nd <= DBL_DIG + 1)
2288 z *= 10;
2289 if (nd++ < 9)
2290 y = 10*y + c;
2291 else if (nd <= DBL_DIG + 1)
2292 z = 10*z + c;
2293 nz = 0;
2294 }
2295 }
2296 }
2297 dig_done:
2298 e = 0;
2299 if (c == 'e' || c == 'E') {
2300 if (!nd && !nz && !nz0) {
2301 goto ret0;
2302 }
2303 s00 = s;
2304 esign = 0;
2305 switch (c = *++s) {
2306 case '-':
2307 esign = 1;
2308 case '+':
2309 c = *++s;
2310 }
2311 if (c >= '0' && c <= '9') {
2312 while (c == '0')
2313 c = *++s;
2314 if (c > '0' && c <= '9') {
2315 L = c - '0';
2316 s1 = s;
2317 while ((c = *++s) >= '0' && c <= '9')
2318 L = 10*L + c - '0';
2319 if (s - s1 > 8 || L > 19999)
2320 /* Avoid confusion from exponents
2321 * so large that e might overflow.
2322 */
2323 e = 19999; /* safe for 16 bit ints */
2324 else
2325 e = (int)L;
2326 if (esign)
2327 e = -e;
2328 }
2329 else
2330 e = 0;
2331 }
2332 else
2333 s = s00;
2334 }
2335 if (!nd) {
2336 if (!nz && !nz0) {
2337 #ifdef INFNAN_CHECK
2338 /* Check for Nan and Infinity */
2339 switch (c) {
2340 case 'i':
2341 case 'I':
2342 if (match(&s,"nf")) {
2343 --s;
2344 if (!match(&s,"inity"))
2345 ++s;
2346 word0(rv) = 0x7ff00000;
2347 word1(rv) = 0;
2348 goto ret;
2349 }
2350 break;
2351 case 'n':
2352 case 'N':
2353 if (match(&s, "an")) {
2354 word0(rv) = NAN_WORD0;
2355 word1(rv) = NAN_WORD1;
2356 #ifndef No_Hex_NaN
2357 if (*s == '(') /*)*/
2358 hexnan(&rv, &s);
2359 #endif
2360 goto ret;
2361 }
2362 }
2363 #endif /* INFNAN_CHECK */
2364 ret0:
2365 s = s00;
2366 sign = 0;
2367 }
2368 goto ret;
2369 }
2370 e1 = e -= nf;
2371
2372 /* Now we have nd0 digits, starting at s0, followed by a
2373 * decimal point, followed by nd-nd0 digits. The number we're
2374 * after is the integer represented by those digits times
2375 * 10**e */
2376
2377 if (!nd0)
2378 nd0 = nd;
2379 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2380 dval(rv) = y;
2381 if (k > 9) {
2382 #ifdef SET_INEXACT
2383 if (k > DBL_DIG)
2384 oldinexact = get_inexact();
2385 #endif
2386 dval(rv) = tens[k - 9] * dval(rv) + z;
2387 }
2388 bd0 = 0;
2389 if (nd <= DBL_DIG
2390 #ifndef RND_PRODQUOT
2391 #ifndef Honor_FLT_ROUNDS
2392 && Flt_Rounds == 1
2393 #endif
2394 #endif
2395 ) {
2396 if (!e)
2397 goto ret;
2398 if (e > 0) {
2399 if (e <= Ten_pmax) {
2400 #ifdef VAX
2401 goto vax_ovfl_check;
2402 #else
2403 #ifdef Honor_FLT_ROUNDS
2404 /* round correctly FLT_ROUNDS = 2 or 3 */
2405 if (sign) {
2406 rv = -rv;
2407 sign = 0;
2408 }
2409 #endif
2410 /* rv = */ rounded_product(dval(rv), tens[e]);
2411 goto ret;
2412 #endif
2413 }
2414 i = DBL_DIG - nd;
2415 if (e <= Ten_pmax + i) {
2416 /* A fancier test would sometimes let us do
2417 * this for larger i values.
2418 */
2419 #ifdef Honor_FLT_ROUNDS
2420 /* round correctly FLT_ROUNDS = 2 or 3 */
2421 if (sign) {
2422 rv = -rv;
2423 sign = 0;
2424 }
2425 #endif
2426 e -= i;
2427 dval(rv) *= tens[i];
2428 #ifdef VAX
2429 /* VAX exponent range is so narrow we must
2430 * worry about overflow here...
2431 */
2432 vax_ovfl_check:
2433 word0(rv) -= P*Exp_msk1;
2434 /* rv = */ rounded_product(dval(rv), tens[e]);
2435 if ((word0(rv) & Exp_mask)
2436 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2437 goto ovfl;
2438 word0(rv) += P*Exp_msk1;
2439 #else
2440 /* rv = */ rounded_product(dval(rv), tens[e]);
2441 #endif
2442 goto ret;
2443 }
2444 }
2445 #ifndef Inaccurate_Divide
2446 else if (e >= -Ten_pmax) {
2447 #ifdef Honor_FLT_ROUNDS
2448 /* round correctly FLT_ROUNDS = 2 or 3 */
2449 if (sign) {
2450 rv = -rv;
2451 sign = 0;
2452 }
2453 #endif
2454 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
2455 goto ret;
2456 }
2457 #endif
2458 }
2459 e1 += nd - k;
2460
2461 #ifdef IEEE_Arith
2462 #ifdef SET_INEXACT
2463 inexact = 1;
2464 if (k <= DBL_DIG)
2465 oldinexact = get_inexact();
2466 #endif
2467 #ifdef Avoid_Underflow
2468 scale = 0;
2469 #endif
2470 #ifdef Honor_FLT_ROUNDS
2471 if ((rounding = Flt_Rounds) >= 2) {
2472 if (sign)
2473 rounding = rounding == 2 ? 0 : 2;
2474 else
2475 if (rounding != 2)
2476 rounding = 0;
2477 }
2478 #endif
2479 #endif /*IEEE_Arith*/
2480
2481 /* Get starting approximation = rv * 10**e1 */
2482
2483 if (e1 > 0) {
2484 if ((i = e1 & 15) != 0)
2485 dval(rv) *= tens[i];
2486 if (e1 &= ~15) {
2487 if (e1 > DBL_MAX_10_EXP) {
2488 ovfl:
2489 #ifndef NO_ERRNO
2490 errno = ERANGE;
2491 #endif
2492 /* Can't trust HUGE_VAL */
2493 #ifdef IEEE_Arith
2494 #ifdef Honor_FLT_ROUNDS
2495 switch (rounding) {
2496 case 0: /* toward 0 */
2497 case 3: /* toward -infinity */
2498 word0(rv) = Big0;
2499 word1(rv) = Big1;
2500 break;
2501 default:
2502 word0(rv) = Exp_mask;
2503 word1(rv) = 0;
2504 }
2505 #else /*Honor_FLT_ROUNDS*/
2506 word0(rv) = Exp_mask;
2507 word1(rv) = 0;
2508 #endif /*Honor_FLT_ROUNDS*/
2509 #ifdef SET_INEXACT
2510 /* set overflow bit */
2511 dval(rv0) = 1e300;
2512 dval(rv0) *= dval(rv0);
2513 #endif
2514 #else /*IEEE_Arith*/
2515 word0(rv) = Big0;
2516 word1(rv) = Big1;
2517 #endif /*IEEE_Arith*/
2518 if (bd0)
2519 goto retfree;
2520 goto ret;
2521 }
2522 e1 >>= 4;
2523 for (j = 0; e1 > 1; j++, e1 >>= 1)
2524 if (e1 & 1)
2525 dval(rv) *= bigtens[j];
2526 /* The last multiplication could overflow. */
2527 word0(rv) -= P*Exp_msk1;
2528 dval(rv) *= bigtens[j];
2529 if ((z = word0(rv) & Exp_mask)
2530 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2531 goto ovfl;
2532 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2533 /* set to largest number */
2534 /* (Can't trust DBL_MAX) */
2535 word0(rv) = Big0;
2536 word1(rv) = Big1;
2537 }
2538 else
2539 word0(rv) += P*Exp_msk1;
2540 }
2541 }
2542 else if (e1 < 0) {
2543 e1 = -e1;
2544 if ((i = e1 & 15) != 0)
2545 dval(rv) /= tens[i];
2546 if (e1 >>= 4) {
2547 if (e1 >= 1 << n_bigtens)
2548 goto undfl;
2549 #ifdef Avoid_Underflow
2550 if (e1 & Scale_Bit)
2551 scale = 2*P;
2552 for (j = 0; e1 > 0; j++, e1 >>= 1)
2553 if (e1 & 1)
2554 dval(rv) *= tinytens[j];
2555 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
2556 >> Exp_shift)) > 0) {
2557 /* scaled rv is denormal; zap j low bits */
2558 if (j >= 32) {
2559 word1(rv) = 0;
2560 if (j >= 53)
2561 word0(rv) = (P+2)*Exp_msk1;
2562 else
2563 word0(rv) &= 0xffffffff << (j-32);
2564 }
2565 else
2566 word1(rv) &= 0xffffffff << j;
2567 }
2568 #else
2569 for (j = 0; e1 > 1; j++, e1 >>= 1)
2570 if (e1 & 1)
2571 dval(rv) *= tinytens[j];
2572 /* The last multiplication could underflow. */
2573 dval(rv0) = dval(rv);
2574 dval(rv) *= tinytens[j];
2575 if (!dval(rv)) {
2576 dval(rv) = 2.*dval(rv0);
2577 dval(rv) *= tinytens[j];
2578 #endif
2579 if (!dval(rv)) {
2580 undfl:
2581 dval(rv) = 0.;
2582 #ifndef NO_ERRNO
2583 errno = ERANGE;
2584 #endif
2585 if (bd0)
2586 goto retfree;
2587 goto ret;
2588 }
2589 #ifndef Avoid_Underflow
2590 word0(rv) = Tiny0;
2591 word1(rv) = Tiny1;
2592 /* The refinement below will clean
2593 * this approximation up.
2594 */
2595 }
2596 #endif
2597 }
2598 }
2599
2600 /* Now the hard part -- adjusting rv to the correct value.*/
2601
2602 /* Put digits into bd: true value = bd * 10^e */
2603
2604 bd0 = s2b(s0, nd0, nd, y);
2605
2606 for (;;) {
2607 bd = Balloc(bd0->k);
2608 Bcopy(bd, bd0);
2609 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
2610 bs = i2b(1);
2611
2612 if (e >= 0) {
2613 bb2 = bb5 = 0;
2614 bd2 = bd5 = e;
2615 }
2616 else {
2617 bb2 = bb5 = -e;
2618 bd2 = bd5 = 0;
2619 }
2620 if (bbe >= 0)
2621 bb2 += bbe;
2622 else
2623 bd2 -= bbe;
2624 bs2 = bb2;
2625 #ifdef Honor_FLT_ROUNDS
2626 if (rounding != 1)
2627 bs2++;
2628 #endif
2629 #ifdef Avoid_Underflow
2630 j = bbe - scale;
2631 i = j + bbbits - 1; /* logb(rv) */
2632 if (i < Emin) /* denormal */
2633 j += P - Emin;
2634 else
2635 j = P + 1 - bbbits;
2636 #else /*Avoid_Underflow*/
2637 #ifdef Sudden_Underflow
2638 #ifdef IBM
2639 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2640 #else
2641 j = P + 1 - bbbits;
2642 #endif
2643 #else /*Sudden_Underflow*/
2644 j = bbe;
2645 i = j + bbbits - 1; /* logb(rv) */
2646 if (i < Emin) /* denormal */
2647 j += P - Emin;
2648 else
2649 j = P + 1 - bbbits;
2650 #endif /*Sudden_Underflow*/
2651 #endif /*Avoid_Underflow*/
2652 bb2 += j;
2653 bd2 += j;
2654 #ifdef Avoid_Underflow
2655 bd2 += scale;
2656 #endif
2657 i = bb2 < bd2 ? bb2 : bd2;
2658 if (i > bs2)
2659 i = bs2;
2660 if (i > 0) {
2661 bb2 -= i;
2662 bd2 -= i;
2663 bs2 -= i;
2664 }
2665 if (bb5 > 0) {
2666 bs = pow5mult(bs, bb5);
2667 bb1 = mult(bs, bb);
2668 Bfree(bb);
2669 bb = bb1;
2670 }
2671 if (bb2 > 0)
2672 bb = lshift(bb, bb2);
2673 if (bd5 > 0)
2674 bd = pow5mult(bd, bd5);
2675 if (bd2 > 0)
2676 bd = lshift(bd, bd2);
2677 if (bs2 > 0)
2678 bs = lshift(bs, bs2);
2679 delta = diff(bb, bd);
2680 dsign = delta->sign;
2681 delta->sign = 0;
2682 i = cmp(delta, bs);
2683 #ifdef Honor_FLT_ROUNDS
2684 if (rounding != 1) {
2685 if (i < 0) {
2686 /* Error is less than an ulp */
2687 if (!delta->x[0] && delta->wds <= 1) {
2688 /* exact */
2689 #ifdef SET_INEXACT
2690 inexact = 0;
2691 #endif
2692 break;
2693 }
2694 if (rounding) {
2695 if (dsign) {
2696 adj = 1.;
2697 goto apply_adj;
2698 }
2699 }
2700 else if (!dsign) {
2701 adj = -1.;
2702 if (!word1(rv)
2703 && !(word0(rv) & Frac_mask)) {
2704 y = word0(rv) & Exp_mask;
2705 #ifdef Avoid_Underflow
2706 if (!scale || y > 2*P*Exp_msk1)
2707 #else
2708 if (y)
2709 #endif
2710 {
2711 delta = lshift(delta,Log2P);
2712 if (cmp(delta, bs) <= 0)
2713 adj = -0.5;
2714 }
2715 }
2716 apply_adj:
2717 #ifdef Avoid_Underflow
2718 if (scale && (y = word0(rv) & Exp_mask)
2719 <= 2*P*Exp_msk1)
2720 word0(adj) += (2*P+1)*Exp_msk1 - y;
2721 #else
2722 #ifdef Sudden_Underflow
2723 if ((word0(rv) & Exp_mask) <=
2724 P*Exp_msk1) {
2725 word0(rv) += P*Exp_msk1;
2726 dval(rv) += adj*ulp(dval(rv));
2727 word0(rv) -= P*Exp_msk1;
2728 }
2729 else
2730 #endif /*Sudden_Underflow*/
2731 #endif /*Avoid_Underflow*/
2732 dval(rv) += adj*ulp(dval(rv));
2733 }
2734 break;
2735 }
2736 adj = ratio(delta, bs);
2737 if (adj < 1.)
2738 adj = 1.;
2739 if (adj <= 0x7ffffffe) {
2740 /* adj = rounding ? ceil(adj) : floor(adj); */
2741 y = adj;
2742 if (y != adj) {
2743 if (!((rounding>>1) ^ dsign))
2744 y++;
2745 adj = y;
2746 }
2747 }
2748 #ifdef Avoid_Underflow
2749 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2750 word0(adj) += (2*P+1)*Exp_msk1 - y;
2751 #else
2752 #ifdef Sudden_Underflow
2753 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2754 word0(rv) += P*Exp_msk1;
2755 adj *= ulp(dval(rv));
2756 if (dsign)
2757 dval(rv) += adj;
2758 else
2759 dval(rv) -= adj;
2760 word0(rv) -= P*Exp_msk1;
2761 goto cont;
2762 }
2763 #endif /*Sudden_Underflow*/
2764 #endif /*Avoid_Underflow*/
2765 adj *= ulp(dval(rv));
2766 if (dsign)
2767 dval(rv) += adj;
2768 else
2769 dval(rv) -= adj;
2770 goto cont;
2771 }
2772 #endif /*Honor_FLT_ROUNDS*/
2773
2774 if (i < 0) {
2775 /* Error is less than half an ulp -- check for
2776 * special case of mantissa a power of two.
2777 */
2778 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2779 #ifdef IEEE_Arith
2780 #ifdef Avoid_Underflow
2781 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2782 #else
2783 || (word0(rv) & Exp_mask) <= Exp_msk1
2784 #endif
2785 #endif
2786 ) {
2787 #ifdef SET_INEXACT
2788 if (!delta->x[0] && delta->wds <= 1)
2789 inexact = 0;
2790 #endif
2791 break;
2792 }
2793 if (!delta->x[0] && delta->wds <= 1) {
2794 /* exact result */
2795 #ifdef SET_INEXACT
2796 inexact = 0;
2797 #endif
2798 break;
2799 }
2800 delta = lshift(delta,Log2P);
2801 if (cmp(delta, bs) > 0)
2802 goto drop_down;
2803 break;
2804 }
2805 if (i == 0) {
2806 /* exactly half-way between */
2807 if (dsign) {
2808 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2809 && word1(rv) == (
2810 #ifdef Avoid_Underflow
2811 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2812 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2813 #endif
2814 0xffffffff)) {
2815 /*boundary case -- increment exponent*/
2816 word0(rv) = (word0(rv) & Exp_mask)
2817 + Exp_msk1
2818 #ifdef IBM
2819 | Exp_msk1 >> 4
2820 #endif
2821 ;
2822 word1(rv) = 0;
2823 #ifdef Avoid_Underflow
2824 dsign = 0;
2825 #endif
2826 break;
2827 }
2828 }
2829 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2830 drop_down:
2831 /* boundary case -- decrement exponent */
2832 #ifdef Sudden_Underflow /*{{*/
2833 L = word0(rv) & Exp_mask;
2834 #ifdef IBM
2835 if (L < Exp_msk1)
2836 #else
2837 #ifdef Avoid_Underflow
2838 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2839 #else
2840 if (L <= Exp_msk1)
2841 #endif /*Avoid_Underflow*/
2842 #endif /*IBM*/
2843 goto undfl;
2844 L -= Exp_msk1;
2845 #else /*Sudden_Underflow}{*/
2846 #ifdef Avoid_Underflow
2847 if (scale) {
2848 L = word0(rv) & Exp_mask;
2849 if (L <= (2*P+1)*Exp_msk1) {
2850 if (L > (P+2)*Exp_msk1)
2851 /* round even ==> */
2852 /* accept rv */
2853 break;
2854 /* rv = smallest denormal */
2855 goto undfl;
2856 }
2857 }
2858 #endif /*Avoid_Underflow*/
2859 L = (word0(rv) & Exp_mask) - Exp_msk1;
2860 #endif /*Sudden_Underflow}}*/
2861 word0(rv) = L | Bndry_mask1;
2862 word1(rv) = 0xffffffff;
2863 #ifdef IBM
2864 goto cont;
2865 #else
2866 break;
2867 #endif
2868 }
2869 #ifndef ROUND_BIASED
2870 if (!(word1(rv) & LSB))
2871 break;
2872 #endif
2873 if (dsign)
2874 dval(rv) += ulp(dval(rv));
2875 #ifndef ROUND_BIASED
2876 else {
2877 dval(rv) -= ulp(dval(rv));
2878 #ifndef Sudden_Underflow
2879 if (!dval(rv))
2880 goto undfl;
2881 #endif
2882 }
2883 #ifdef Avoid_Underflow
2884 dsign = 1 - dsign;
2885 #endif
2886 #endif
2887 break;
2888 }
2889 if ((aadj = ratio(delta, bs)) <= 2.) {
2890 if (dsign)
2891 aadj = aadj1 = 1.;
2892 else if (word1(rv) || word0(rv) & Bndry_mask) {
2893 #ifndef Sudden_Underflow
2894 if (word1(rv) == Tiny1 && !word0(rv))
2895 goto undfl;
2896 #endif
2897 aadj = 1.;
2898 aadj1 = -1.;
2899 }
2900 else {
2901 /* special case -- power of FLT_RADIX to be */
2902 /* rounded down... */
2903
2904 if (aadj < 2./FLT_RADIX)
2905 aadj = 1./FLT_RADIX;
2906 else
2907 aadj *= 0.5;
2908 aadj1 = -aadj;
2909 }
2910 }
2911 else {
2912 aadj *= 0.5;
2913 aadj1 = dsign ? aadj : -aadj;
2914 #ifdef Check_FLT_ROUNDS
2915 switch (Rounding) {
2916 case 2: /* towards +infinity */
2917 aadj1 -= 0.5;
2918 break;
2919 case 0: /* towards 0 */
2920 case 3: /* towards -infinity */
2921 aadj1 += 0.5;
2922 }
2923 #else
2924 if (Flt_Rounds == 0)
2925 aadj1 += 0.5;
2926 #endif /*Check_FLT_ROUNDS*/
2927 }
2928 y = word0(rv) & Exp_mask;
2929
2930 /* Check for overflow */
2931
2932 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2933 dval(rv0) = dval(rv);
2934 word0(rv) -= P*Exp_msk1;
2935 adj = aadj1 * ulp(dval(rv));
2936 dval(rv) += adj;
2937 if ((word0(rv) & Exp_mask) >=
2938 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2939 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2940 goto ovfl;
2941 word0(rv) = Big0;
2942 word1(rv) = Big1;
2943 goto cont;
2944 }
2945 else
2946 word0(rv) += P*Exp_msk1;
2947 }
2948 else {
2949 #ifdef Avoid_Underflow
2950 if (scale && y <= 2*P*Exp_msk1) {
2951 if (aadj <= 0x7fffffff) {
2952 if ((z = aadj) <= 0)
2953 z = 1;
2954 aadj = z;
2955 aadj1 = dsign ? aadj : -aadj;
2956 }
2957 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2958 }
2959 adj = aadj1 * ulp(dval(rv));
2960 dval(rv) += adj;
2961 #else
2962 #ifdef Sudden_Underflow
2963 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2964 dval(rv0) = dval(rv);
2965 word0(rv) += P*Exp_msk1;
2966 adj = aadj1 * ulp(dval(rv));
2967 dval(rv) += adj;
2968 #ifdef IBM
2969 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2970 #else
2971 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2972 #endif
2973 {
2974 if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2975 goto undfl;
2976 word0(rv) = Tiny0;
2977 word1(rv) = Tiny1;
2978 goto cont;
2979 }
2980 else
2981 word0(rv) -= P*Exp_msk1;
2982 }
2983 else {
2984 adj = aadj1 * ulp(dval(rv));
2985 dval(rv) += adj;
2986 }
2987 #else /*Sudden_Underflow*/
2988 /* Compute adj so that the IEEE rounding rules will
2989 * correctly round rv + adj in some half-way cases.
2990 * If rv * ulp(rv) is denormalized (i.e.,
2991 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2992 * trouble from bits lost to denormalization;
2993 * example: 1.2e-307 .
2994 */
2995 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2996 aadj1 = (double)(int)(aadj + 0.5);
2997 if (!dsign)
2998 aadj1 = -aadj1;
2999 }
3000 adj = aadj1 * ulp(dval(rv));
3001 dval(rv) += adj;
3002 #endif /*Sudden_Underflow*/
3003 #endif /*Avoid_Underflow*/
3004 }
3005 z = word0(rv) & Exp_mask;
3006 #ifndef SET_INEXACT
3007 #ifdef Avoid_Underflow
3008 if (!scale)
3009 #endif
3010 if (y == z) {
3011 /* Can we stop now? */
3012 L = (Long)aadj;
3013 aadj -= L;
3014 /* The tolerances below are conservative. */
3015 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
3016 if (aadj < .4999999 || aadj > .5000001)
3017 break;
3018 }
3019 else if (aadj < .4999999/FLT_RADIX)
3020 break;
3021 }
3022 #endif
3023 cont:
3024 Bfree(bb);
3025 Bfree(bd);
3026 Bfree(bs);
3027 Bfree(delta);
3028 }
3029 #ifdef SET_INEXACT
3030 if (inexact) {
3031 if (!oldinexact) {
3032 word0(rv0) = Exp_1 + (70 << Exp_shift);
3033 word1(rv0) = 0;
3034 dval(rv0) += 1.;
3035 }
3036 }
3037 else if (!oldinexact)
3038 clear_inexact();
3039 #endif
3040 #ifdef Avoid_Underflow
3041 if (scale) {
3042 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
3043 word1(rv0) = 0;
3044 dval(rv) *= dval(rv0);
3045 #ifndef NO_ERRNO
3046 /* try to avoid the bug of testing an 8087 register value */
3047 if (word0(rv) == 0 && word1(rv) == 0)
3048 errno = ERANGE;
3049 #endif
3050 }
3051 #endif /* Avoid_Underflow */
3052 #ifdef SET_INEXACT
3053 if (inexact && !(word0(rv) & Exp_mask)) {
3054 /* set underflow bit */
3055 dval(rv0) = 1e-300;
3056 dval(rv0) *= dval(rv0);
3057 }
3058 #endif
3059 retfree:
3060 Bfree(bb);
3061 Bfree(bd);
3062 Bfree(bs);
3063 Bfree(bd0);
3064 Bfree(delta);
3065 ret:
3066 if (se)
3067 *se = (char *)s;
3068 return sign ? -dval(rv) : dval(rv);
3069 }
3070
3071 static int
3072 quorem(Bigint *b, Bigint *S)
3073 {
3074 int n;
3075 ULong *bx, *bxe, q, *sx, *sxe;
3076 #ifdef ULLong
3077 ULLong borrow, carry, y, ys;
3078 #else
3079 ULong borrow, carry, y, ys;
3080 #ifdef Pack_32
3081 ULong si, z, zs;
3082 #endif
3083 #endif
3084
3085 n = S->wds;
3086 #ifdef DEBUG
3087 /*debug*/ if (b->wds > n)
3088 /*debug*/ Bug("oversize b in quorem");
3089 #endif
3090 if (b->wds < n)
3091 return 0;
3092 sx = S->x;
3093 sxe = sx + --n;
3094 bx = b->x;
3095 bxe = bx + n;
3096 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
3097 #ifdef DEBUG
3098 /*debug*/ if (q > 9)
3099 /*debug*/ Bug("oversized quotient in quorem");
3100 #endif
3101 if (q) {
3102 borrow = 0;
3103 carry = 0;
3104 do {
3105 #ifdef ULLong
3106 ys = *sx++ * (ULLong)q + carry;
3107 carry = ys >> 32;
3108 y = *bx - (ys & FFFFFFFF) - borrow;
3109 borrow = y >> 32 & (ULong)1;
3110 *bx++ = y & FFFFFFFF;
3111 #else
3112 #ifdef Pack_32
3113 si = *sx++;
3114 ys = (si & 0xffff) * q + carry;
3115 zs = (si >> 16) * q + (ys >> 16);
3116 carry = zs >> 16;
3117 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
3118 borrow = (y & 0x10000) >> 16;
3119 z = (*bx >> 16) - (zs & 0xffff) - borrow;
3120 borrow = (z & 0x10000) >> 16;
3121 Storeinc(bx, z, y);
3122 #else
3123 ys = *sx++ * q + carry;
3124 carry = ys >> 16;
3125 y = *bx - (ys & 0xffff) - borrow;
3126 borrow = (y & 0x10000) >> 16;
3127 *bx++ = y & 0xffff;
3128 #endif
3129 #endif
3130 } while (sx <= sxe);
3131 if (!*bxe) {
3132 bx = b->x;
3133 while (--bxe > bx && !*bxe)
3134 --n;
3135 b->wds = n;
3136 }
3137 }
3138 if (cmp(b, S) >= 0) {
3139 q++;
3140 borrow = 0;
3141 carry = 0;
3142 bx = b->x;
3143 sx = S->x;
3144 do {
3145 #ifdef ULLong
3146 ys = *sx++ + carry;
3147 carry = ys >> 32;
3148 y = *bx - (ys & FFFFFFFF) - borrow;
3149 borrow = y >> 32 & (ULong)1;
3150 *bx++ = y & FFFFFFFF;
3151 #else
3152 #ifdef Pack_32
3153 si = *sx++;
3154 ys = (si & 0xffff) + carry;
3155 zs = (si >> 16) + (ys >> 16);
3156 carry = zs >> 16;
3157 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
3158 borrow = (y & 0x10000) >> 16;
3159 z = (*bx >> 16) - (zs & 0xffff) - borrow;
3160 borrow = (z & 0x10000) >> 16;
3161 Storeinc(bx, z, y);
3162 #else
3163 ys = *sx++ + carry;
3164 carry = ys >> 16;
3165 y = *bx - (ys & 0xffff) - borrow;
3166 borrow = (y & 0x10000) >> 16;
3167 *bx++ = y & 0xffff;
3168 #endif
3169 #endif
3170 } while (sx <= sxe);
3171 bx = b->x;
3172 bxe = bx + n;
3173 if (!*bxe) {
3174 while (--bxe > bx && !*bxe)
3175 --n;
3176 b->wds = n;
3177 }
3178 }
3179 return q;
3180 }
3181
3182 #ifndef MULTIPLE_THREADS
3183 static char *dtoa_result;
3184 #endif
3185
3186 static char *
3187 rv_alloc(int i)
3188 {
3189 int j, k, *r;
3190
3191 j = sizeof(ULong);
3192 for (k = 0;
3193 sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
3194 j <<= 1)
3195 k++;
3196 r = (int*)Balloc(k);
3197 *r = k;
3198 return
3199 #ifndef MULTIPLE_THREADS
3200 dtoa_result =
3201 #endif
3202 (char *)(r+1);
3203 }
3204
3205 static char *
3206 nrv_alloc(char *s, char **rve, int n)
3207 {
3208 char *rv, *t;
3209
3210 t = rv = rv_alloc(n);
3211 while ((*t = *s++) != 0) t++;
3212 if (rve)
3213 *rve = t;
3214 return rv;
3215 }
3216
3217 /* freedtoa(s) must be used to free values s returned by dtoa
3218 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
3219 * but for consistency with earlier versions of dtoa, it is optional
3220 * when MULTIPLE_THREADS is not defined.
3221 */
3222
3223 void
3224 freedtoa(char *s)
3225 {
3226 Bigint *b = (Bigint *)((int *)s - 1);
3227 b->maxwds = 1 << (b->k = *(int*)b);
3228 Bfree(b);
3229 #ifndef MULTIPLE_THREADS
3230 if (s == dtoa_result)
3231 dtoa_result = 0;
3232 #endif
3233 }
3234
3235 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
3236 *
3237 * Inspired by "How to Print Floating-Point Numbers Accurately" by
3238 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
3239 *
3240 * Modifications:
3241 * 1. Rather than iterating, we use a simple numeric overestimate
3242 * to determine k = floor(log10(d)). We scale relevant
3243 * quantities using O(log2(k)) rather than O(k) multiplications.
3244 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
3245 * try to generate digits strictly left to right. Instead, we
3246 * compute with fewer bits and propagate the carry if necessary
3247 * when rounding the final digit up. This is often faster.
3248 * 3. Under the assumption that input will be rounded nearest,
3249 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
3250 * That is, we allow equality in stopping tests when the
3251 * round-nearest rule will give the same floating-point value
3252 * as would satisfaction of the stopping test with strict
3253 * inequality.
3254 * 4. We remove common factors of powers of 2 from relevant
3255 * quantities.
3256 * 5. When converting floating-point integers less than 1e16,
3257 * we use floating-point arithmetic rather than resorting
3258 * to multiple-precision integers.
3259 * 6. When asked to produce fewer than 15 digits, we first try
3260 * to get by with floating-point arithmetic; we resort to
3261 * multiple-precision integer arithmetic only if we cannot
3262 * guarantee that the floating-point calculation has given
3263 * the correctly rounded result. For k requested digits and
3264 * "uniformly" distributed input, the probability is
3265 * something like 10^(k-15) that we must resort to the Long
3266 * calculation.
3267 */
3268
3269 char *
3270 dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
3271 {
3272 /* Arguments ndigits, decpt, sign are similar to those
3273 of ecvt and fcvt; trailing zeros are suppressed from
3274 the returned string. If not null, *rve is set to point
3275 to the end of the return value. If d is +-Infinity or NaN,
3276 then *decpt is set to 9999.
3277
3278 mode:
3279 0 ==> shortest string that yields d when read in
3280 and rounded to nearest.
3281 1 ==> like 0, but with Steele & White stopping rule;
3282 e.g. with IEEE P754 arithmetic , mode 0 gives
3283 1e23 whereas mode 1 gives 9.999999999999999e22.
3284 2 ==> max(1,ndigits) significant digits. This gives a
3285 return value similar to that of ecvt, except
3286 that trailing zeros are suppressed.
3287 3 ==> through ndigits past the decimal point. This
3288 gives a return value similar to that from fcvt,
3289 except that trailing zeros are suppressed, and
3290 ndigits can be negative.
3291 4,5 ==> similar to 2 and 3, respectively, but (in
3292 round-nearest mode) with the tests of mode 0 to
3293 possibly return a shorter string that rounds to d.
3294 With IEEE arithmetic and compilation with
3295 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
3296 as modes 2 and 3 when FLT_ROUNDS != 1.
3297 6-9 ==> Debugging modes similar to mode - 4: don't try
3298 fast floating-point estimate (if applicable).
3299
3300 Values of mode other than 0-9 are treated as mode 0.
3301
3302 Sufficient space is allocated to the return value
3303 to hold the suppressed trailing zeros.
3304 */
3305
3306 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
3307 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
3308 spec_case, try_quick;
3309 Long L;
3310 #ifndef Sudden_Underflow
3311 int denorm;
3312 ULong x;
3313 #endif
3314 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
3315 double d2, ds, eps;
3316 char *s, *s0;
3317 #ifdef Honor_FLT_ROUNDS
3318 int rounding;
3319 #endif
3320 #ifdef SET_INEXACT
3321 int inexact, oldinexact;
3322 #endif
3323
3324 #ifndef MULTIPLE_THREADS
3325 if (dtoa_result) {
3326 freedtoa(dtoa_result);
3327 dtoa_result = 0;
3328 }
3329 #endif
3330
3331 if (word0(d) & Sign_bit) {
3332 /* set sign for everything, including 0's and NaNs */
3333 *sign = 1;
3334 word0(d) &= ~Sign_bit; /* clear sign bit */
3335 }
3336 else
3337 *sign = 0;
3338
3339 #if defined(IEEE_Arith) + defined(VAX)
3340 #ifdef IEEE_Arith
3341 if ((word0(d) & Exp_mask) == Exp_mask)
3342 #else
3343 if (word0(d) == 0x8000)
3344 #endif
3345 {
3346 /* Infinity or NaN */
3347 *decpt = 9999;
3348 #ifdef IEEE_Arith
3349 if (!word1(d) && !(word0(d) & 0xfffff))
3350 return nrv_alloc("Infinity", rve, 8);
3351 #endif
3352 return nrv_alloc("NaN", rve, 3);
3353 }
3354 #endif
3355 #ifdef IBM
3356 dval(d) += 0; /* normalize */
3357 #endif
3358 if (!dval(d)) {
3359 *decpt = 1;
3360 return nrv_alloc("0", rve, 1);
3361 }
3362
3363 #ifdef SET_INEXACT
3364 try_quick = oldinexact = get_inexact();
3365 inexact = 1;
3366 #endif
3367 #ifdef Honor_FLT_ROUNDS
3368 if ((rounding = Flt_Rounds) >= 2) {
3369 if (*sign)
3370 rounding = rounding == 2 ? 0 : 2;
3371 else
3372 if (rounding != 2)
3373 rounding = 0;
3374 }
3375 #endif
3376
3377 b = d2b(dval(d), &be, &bbits);
3378 #ifdef Sudden_Underflow
3379 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
3380 #else
3381 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
3382 #endif
3383 dval(d2) = dval(d);
3384 word0(d2) &= Frac_mask1;
3385 word0(d2) |= Exp_11;
3386 #ifdef IBM
3387 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
3388 dval(d2) /= 1 << j;
3389 #endif
3390
3391 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
3392 * log10(x) = log(x) / log(10)
3393 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
3394 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
3395 *
3396 * This suggests computing an approximation k to log10(d) by
3397 *
3398 * k = (i - Bias)*0.301029995663981
3399 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
3400 *
3401 * We want k to be too large rather than too small.
3402 * The error in the first-order Taylor series approximation
3403 * is in our favor, so we just round up the constant enough
3404 * to compensate for any error in the multiplication of
3405 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
3406 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
3407 * adding 1e-13 to the constant term more than suffices.
3408 * Hence we adjust the constant term to 0.1760912590558.
3409 * (We could get a more accurate k by invoking log10,
3410 * but this is probably not worthwhile.)
3411 */
3412
3413 i -= Bias;
3414 #ifdef IBM
3415 i <<= 2;
3416 i += j;
3417 #endif
3418 #ifndef Sudden_Underflow
3419 denorm = 0;
3420 }
3421 else {
3422 /* d is denormalized */
3423
3424 i = bbits + be + (Bias + (P-1) - 1);
3425 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
3426 : word1(d) << (32 - i);
3427 dval(d2) = x;
3428 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
3429 i -= (Bias + (P-1) - 1) + 1;
3430 denorm = 1;
3431 }
3432 #endif
3433 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
3434 k = (int)ds;
3435 if (ds < 0. && ds != k)
3436 k--; /* want k = floor(ds) */
3437 k_check = 1;
3438 if (k >= 0 && k <= Ten_pmax) {
3439 if (dval(d) < tens[k])
3440 k--;
3441 k_check = 0;
3442 }
3443 j = bbits - i - 1;
3444 if (j >= 0) {
3445 b2 = 0;
3446 s2 = j;
3447 }
3448 else {
3449 b2 = -j;
3450 s2 = 0;
3451 }
3452 if (k >= 0) {
3453 b5 = 0;
3454 s5 = k;
3455 s2 += k;
3456 }
3457 else {
3458 b2 -= k;
3459 b5 = -k;
3460 s5 = 0;
3461 }
3462 if (mode < 0 || mode > 9)
3463 mode = 0;
3464
3465 #ifndef SET_INEXACT
3466 #ifdef Check_FLT_ROUNDS
3467 try_quick = Rounding == 1;
3468 #else
3469 try_quick = 1;
3470 #endif
3471 #endif /*SET_INEXACT*/
3472
3473 if (mode > 5) {
3474 mode -= 4;
3475 try_quick = 0;
3476 }
3477 leftright = 1;
3478 ilim = ilim1 = -1;
3479 switch (mode) {
3480 case 0:
3481 case 1:
3482 i = 18;
3483 ndigits = 0;
3484 break;
3485 case 2:
3486 leftright = 0;
3487 /* no break */
3488 case 4:
3489 if (ndigits <= 0)
3490 ndigits = 1;
3491 ilim = ilim1 = i = ndigits;
3492 break;
3493 case 3:
3494 leftright = 0;
3495 /* no break */
3496 case 5:
3497 i = ndigits + k + 1;
3498 ilim = i;
3499 ilim1 = i - 1;
3500 if (i <= 0)
3501 i = 1;
3502 }
3503 s = s0 = rv_alloc(i);
3504
3505 #ifdef Honor_FLT_ROUNDS
3506 if (mode > 1 && rounding != 1)
3507 leftright = 0;
3508 #endif
3509
3510 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
3511
3512 /* Try to get by with floating-point arithmetic. */
3513
3514 i = 0;
3515 dval(d2) = dval(d);
3516 k0 = k;
3517 ilim0 = ilim;
3518 ieps = 2; /* conservative */
3519 if (k > 0) {
3520 ds = tens[k&0xf];
3521 j = k >> 4;
3522 if (j & Bletch) {
3523 /* prevent overflows */
3524 j &= Bletch - 1;
3525 dval(d) /= bigtens[n_bigtens-1];
3526 ieps++;
3527 }
3528 for (; j; j >>= 1, i++)
3529 if (j & 1) {
3530 ieps++;
3531 ds *= bigtens[i];
3532 }
3533 dval(d) /= ds;
3534 }
3535 else if ((j1 = -k) != 0) {
3536 dval(d) *= tens[j1 & 0xf];
3537 for (j = j1 >> 4; j; j >>= 1, i++)
3538 if (j & 1) {
3539 ieps++;
3540 dval(d) *= bigtens[i];
3541 }
3542 }
3543 if (k_check && dval(d) < 1. && ilim > 0) {
3544 if (ilim1 <= 0)
3545 goto fast_failed;
3546 ilim = ilim1;
3547 k--;
3548 dval(d) *= 10.;
3549 ieps++;
3550 }
3551 dval(eps) = ieps*dval(d) + 7.;
3552 word0(eps) -= (P-1)*Exp_msk1;
3553 if (ilim == 0) {
3554 S = mhi = 0;
3555 dval(d) -= 5.;
3556 if (dval(d) > dval(eps))
3557 goto one_digit;
3558 if (dval(d) < -dval(eps))
3559 goto no_digits;
3560 goto fast_failed;
3561 }
3562 #ifndef No_leftright
3563 if (leftright) {
3564 /* Use Steele & White method of only
3565 * generating digits needed.
3566 */
3567 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
3568 for (i = 0;;) {
3569 L = dval(d);
3570 dval(d) -= L;
3571 *s++ = '0' + (int)L;
3572 if (dval(d) < dval(eps))
3573 goto ret1;
3574 if (1. - dval(d) < dval(eps))
3575 goto bump_up;
3576 if (++i >= ilim)
3577 break;
3578 dval(eps) *= 10.;
3579 dval(d) *= 10.;
3580 }
3581 }
3582 else {
3583 #endif
3584 /* Generate ilim digits, then fix them up. */
3585 dval(eps) *= tens[ilim-1];
3586 for (i = 1;; i++, dval(d) *= 10.) {
3587 L = (Long)(dval(d));
3588 if (!(dval(d) -= L))
3589 ilim = i;
3590 *s++ = '0' + (int)L;
3591 if (i == ilim) {
3592 if (dval(d) > 0.5 + dval(eps))
3593 goto bump_up;
3594 else if (dval(d) < 0.5 - dval(eps)) {
3595 while (*--s == '0') ;
3596 s++;
3597 goto ret1;
3598 }
3599 break;
3600 }
3601 }
3602 #ifndef No_leftright
3603 }
3604 #endif
3605 fast_failed:
3606 s = s0;
3607 dval(d) = dval(d2);
3608 k = k0;
3609 ilim = ilim0;
3610 }
3611
3612 /* Do we have a "small" integer? */
3613
3614 if (be >= 0 && k <= Int_max) {
3615 /* Yes. */
3616 ds = tens[k];
3617 if (ndigits < 0 && ilim <= 0) {
3618 S = mhi = 0;
3619 if (ilim < 0 || dval(d) <= 5*ds)
3620 goto no_digits;
3621 goto one_digit;
3622 }
3623 for (i = 1;; i++, dval(d) *= 10.) {
3624 L = (Long)(dval(d) / ds);
3625 dval(d) -= L*ds;
3626 #ifdef Check_FLT_ROUNDS
3627 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3628 if (dval(d) < 0) {
3629 L--;
3630 dval(d) += ds;
3631 }
3632 #endif
3633 *s++ = '0' + (int)L;
3634 if (!dval(d)) {
3635 #ifdef SET_INEXACT
3636 inexact = 0;
3637 #endif
3638 break;
3639 }
3640 if (i == ilim) {
3641 #ifdef Honor_FLT_ROUNDS
3642 if (mode > 1)
3643 switch (rounding) {
3644 case 0: goto ret1;
3645 case 2: goto bump_up;
3646 }
3647 #endif
3648 dval(d) += dval(d);
3649 if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3650 bump_up:
3651 while (*--s == '9')
3652 if (s == s0) {
3653 k++;
3654 *s = '0';
3655 break;
3656 }
3657 ++*s++;
3658 }
3659 break;
3660 }
3661 }
3662 goto ret1;
3663 }
3664
3665 m2 = b2;
3666 m5 = b5;
3667 mhi = mlo = 0;
3668 if (leftright) {
3669 i =
3670 #ifndef Sudden_Underflow
3671 denorm ? be + (Bias + (P-1) - 1 + 1) :
3672 #endif
3673 #ifdef IBM
3674 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3675 #else
3676 1 + P - bbits;
3677 #endif
3678 b2 += i;
3679 s2 += i;
3680 mhi = i2b(1);
3681 }
3682 if (m2 > 0 && s2 > 0) {
3683 i = m2 < s2 ? m2 : s2;
3684 b2 -= i;
3685 m2 -= i;
3686 s2 -= i;
3687 }
3688 if (b5 > 0) {
3689 if (leftright) {
3690 if (m5 > 0) {
3691 mhi = pow5mult(mhi, m5);
3692 b1 = mult(mhi, b);
3693 Bfree(b);
3694 b = b1;
3695 }
3696 if ((j = b5 - m5) != 0)
3697 b = pow5mult(b, j);
3698 }
3699 else
3700 b = pow5mult(b, b5);
3701 }
3702 S = i2b(1);
3703 if (s5 > 0)
3704 S = pow5mult(S, s5);
3705
3706 /* Check for special case that d is a normalized power of 2. */
3707
3708 spec_case = 0;
3709 if ((mode < 2 || leftright)
3710 #ifdef Honor_FLT_ROUNDS
3711 && rounding == 1
3712 #endif
3713 ) {
3714 if (!word1(d) && !(word0(d) & Bndry_mask)
3715 #ifndef Sudden_Underflow
3716 && word0(d) & (Exp_mask & ~Exp_msk1)
3717 #endif
3718 ) {
3719 /* The special case */
3720 b2 += Log2P;
3721 s2 += Log2P;
3722 spec_case = 1;
3723 }
3724 }
3725
3726 /* Arrange for convenient computation of quotients:
3727 * shift left if necessary so divisor has 4 leading 0 bits.
3728 *
3729 * Perhaps we should just compute leading 28 bits of S once
3730 * and for all and pass them and a shift to quorem, so it
3731 * can do shifts and ors to compute the numerator for q.
3732 */
3733 #ifdef Pack_32
3734 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3735 i = 32 - i;
3736 #else
3737 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3738 i = 16 - i;
3739 #endif
3740 if (i > 4) {
3741 i -= 4;
3742 b2 += i;
3743 m2 += i;
3744 s2 += i;
3745 }
3746 else if (i < 4) {
3747 i += 28;
3748 b2 += i;
3749 m2 += i;
3750 s2 += i;
3751 }
3752 if (b2 > 0)
3753 b = lshift(b, b2);
3754 if (s2 > 0)
3755 S = lshift(S, s2);
3756 if (k_check) {
3757 if (cmp(b,S) < 0) {
3758 k--;
3759 b = multadd(b, 10, 0); /* we botched the k estimate */
3760 if (leftright)
3761 mhi = multadd(mhi, 10, 0);
3762 ilim = ilim1;
3763 }
3764 }
3765 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3766 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3767 /* no digits, fcvt style */
3768 no_digits:
3769 k = -1 - ndigits;
3770 goto ret;
3771 }
3772 one_digit:
3773 *s++ = '1';
3774 k++;
3775 goto ret;
3776 }
3777 if (leftright) {
3778 if (m2 > 0)
3779 mhi = lshift(mhi, m2);
3780
3781 /* Compute mlo -- check for special case
3782 * that d is a normalized power of 2.
3783 */
3784
3785 mlo = mhi;
3786 if (spec_case) {
3787 mhi = Balloc(mhi->k);
3788 Bcopy(mhi, mlo);
3789 mhi = lshift(mhi, Log2P);
3790 }
3791
3792 for (i = 1;;i++) {
3793 dig = quorem(b,S) + '0';
3794 /* Do we yet have the shortest decimal string
3795 * that will round to d?
3796 */
3797 j = cmp(b, mlo);
3798 delta = diff(S, mhi);
3799 j1 = delta->sign ? 1 : cmp(b, delta);
3800 Bfree(delta);
3801 #ifndef ROUND_BIASED
3802 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3803 #ifdef Honor_FLT_ROUNDS
3804 && rounding >= 1
3805 #endif
3806 ) {
3807 if (dig == '9')
3808 goto round_9_up;
3809 if (j > 0)
3810 dig++;
3811 #ifdef SET_INEXACT
3812 else if (!b->x[0] && b->wds <= 1)
3813 inexact = 0;
3814 #endif
3815 *s++ = dig;
3816 goto ret;
3817 }
3818 #endif
3819 if (j < 0 || (j == 0 && mode != 1
3820 #ifndef ROUND_BIASED
3821 && !(word1(d) & 1)
3822 #endif
3823 )) {
3824 if (!b->x[0] && b->wds <= 1) {
3825 #ifdef SET_INEXACT
3826 inexact = 0;
3827 #endif
3828 goto accept_dig;
3829 }
3830 #ifdef Honor_FLT_ROUNDS
3831 if (mode > 1)
3832 switch (rounding) {
3833 case 0: goto accept_dig;
3834 case 2: goto keep_dig;
3835 }
3836 #endif /*Honor_FLT_ROUNDS*/
3837 if (j1 > 0) {
3838 b = lshift(b, 1);
3839 j1 = cmp(b, S);
3840 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3841 goto round_9_up;
3842 }
3843 accept_dig:
3844 *s++ = dig;
3845 goto ret;
3846 }
3847 if (j1 > 0) {
3848 #ifdef Honor_FLT_ROUNDS
3849 if (!rounding)
3850 goto accept_dig;
3851 #endif
3852 if (dig == '9') { /* possible if i == 1 */
3853 round_9_up:
3854 *s++ = '9';
3855 goto roundoff;
3856 }
3857 *s++ = dig + 1;
3858 goto ret;
3859 }
3860 #ifdef Honor_FLT_ROUNDS
3861 keep_dig:
3862 #endif
3863 *s++ = dig;
3864 if (i == ilim)
3865 break;
3866 b = multadd(b, 10, 0);
3867 if (mlo == mhi)
3868 mlo = mhi = multadd(mhi, 10, 0);
3869 else {
3870 mlo = multadd(mlo, 10, 0);
3871 mhi = multadd(mhi, 10, 0);
3872 }
3873 }
3874 }
3875 else
3876 for (i = 1;; i++) {
3877 *s++ = dig = quorem(b,S) + '0';
3878 if (!b->x[0] && b->wds <= 1) {
3879 #ifdef SET_INEXACT
3880 inexact = 0;
3881 #endif
3882 goto ret;
3883 }
3884 if (i >= ilim)
3885 break;
3886 b = multadd(b, 10, 0);
3887 }
3888
3889 /* Round off last digit */
3890
3891 #ifdef Honor_FLT_ROUNDS
3892 switch (rounding) {
3893 case 0: goto trimzeros;
3894 case 2: goto roundoff;
3895 }
3896 #endif
3897 b = lshift(b, 1);
3898 j = cmp(b, S);
3899 if (j > 0 || (j == 0 && (dig & 1))) {
3900 roundoff:
3901 while (*--s == '9')
3902 if (s == s0) {
3903 k++;
3904 *s++ = '1';
3905 goto ret;
3906 }
3907 ++*s++;
3908 }
3909 else {
3910 while (*--s == '0') ;
3911 s++;
3912 }
3913 ret:
3914 Bfree(S);
3915 if (mhi) {
3916 if (mlo && mlo != mhi)
3917 Bfree(mlo);
3918 Bfree(mhi);
3919 }
3920 ret1:
3921 #ifdef SET_INEXACT
3922 if (inexact) {
3923 if (!oldinexact) {
3924 word0(d) = Exp_1 + (70 << Exp_shift);
3925 word1(d) = 0;
3926 dval(d) += 1.;
3927 }
3928 }
3929 else if (!oldinexact)
3930 clear_inexact();
3931 #endif
3932 Bfree(b);
3933 *s = 0;
3934 *decpt = k + 1;
3935 if (rve)
3936 *rve = s;
3937 return s0;
3938 }
3939
3940 void
3941 ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg)
3942 {
3943 const char *end;
3944 int len;
3945
3946 if (!str) return;
3947 for (; *str; str = end) {
3948 while (ISSPACE(*str) || *str == ',') str++;
3949 if (!*str) break;
3950 end = str;
3951 while (*end && !ISSPACE(*end) && *end != ',') end++;
3952 len = end - str;
3953 (*func)(str, len, arg);
3954 }
3955 }
3956
3957 #ifdef __cplusplus
3958 }
3959 #endif
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