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util.c
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1 /**********************************************************************
2
3 util.c -
4
5 $Author: yugui $
6 created at: Fri Mar 10 17:22:34 JST 1995
7
8 Copyright (C) 1993-2008 Yukihiro Matsumoto
9
10 **********************************************************************/
11
12 #include "ruby/ruby.h"
13 #include "internal.h"
14
15 #include <ctype.h>
16 #include <stdio.h>
17 #include <errno.h>
18 #include <math.h>
19 #include <float.h>
20
21 #ifdef _WIN32
22 #include "missing/file.h"
23 #endif
24
25 #include "ruby/util.h"
26
27 unsigned long
28 ruby_scan_oct(const char *start, size_t len, size_t *retlen)
29 {
30 register const char *s = start;
31 register unsigned long retval = 0;
32
33 while (len-- && *s >= '0' && *s <= '7') {
34 retval <<= 3;
35 retval |= *s++ - '0';
36 }
37 *retlen = (int)(s - start); /* less than len */
38 return retval;
39 }
40
41 unsigned long
42 ruby_scan_hex(const char *start, size_t len, size_t *retlen)
43 {
44 static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
45 register const char *s = start;
46 register unsigned long retval = 0;
47 const char *tmp;
48
49 while (len-- && *s && (tmp = strchr(hexdigit, *s))) {
50 retval <<= 4;
51 retval |= (tmp - hexdigit) & 15;
52 s++;
53 }
54 *retlen = (int)(s - start); /* less than len */
55 return retval;
56 }
57
58 static unsigned long
59 scan_digits(const char *str, int base, size_t *retlen, int *overflow)
60 {
61 static signed char table[] = {
62 /* 0 1 2 3 4 5 6 7 8 9 a b c d e f */
63 /*0*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
64 /*1*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
65 /*2*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
66 /*3*/ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,-1,-1,-1,-1,-1,-1,
67 /*4*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
68 /*5*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
69 /*6*/ -1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
70 /*7*/ 25,26,27,28,29,30,31,32,33,34,35,-1,-1,-1,-1,-1,
71 /*8*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
72 /*9*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
73 /*a*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
74 /*b*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
75 /*c*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
76 /*d*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
77 /*e*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
78 /*f*/ -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
79 };
80
81 const char *start = str;
82 unsigned long ret = 0, x;
83 unsigned long mul_overflow = (~(unsigned long)0) / base;
84 int c;
85 *overflow = 0;
86
87 while ((c = (unsigned char)*str++) != '\0') {
88 int d = table[c];
89 if (d == -1 || base <= d) {
90 *retlen = (str-1) - start;
91 return ret;
92 }
93 if (mul_overflow < ret)
94 *overflow = 1;
95 ret *= base;
96 x = ret;
97 ret += d;
98 if (ret < x)
99 *overflow = 1;
100 }
101 *retlen = (str-1) - start;
102 return ret;
103 }
104
105 unsigned long
106 ruby_strtoul(const char *str, char **endptr, int base)
107 {
108 int c, b, overflow;
109 int sign = 0;
110 size_t len;
111 unsigned long ret;
112 const char *subject_found = str;
113
114 if (base == 1 || 36 < base) {
115 errno = EINVAL;
116 return 0;
117 }
118
119 while ((c = *str) && ISSPACE(c))
120 str++;
121
122 if (c == '+') {
123 sign = 1;
124 str++;
125 }
126 else if (c == '-') {
127 sign = -1;
128 str++;
129 }
130
131 if (str[0] == '0') {
132 subject_found = str+1;
133 if (base == 0 || base == 16) {
134 if (str[1] == 'x' || str[1] == 'X') {
135 b = 16;
136 str += 2;
137 }
138 else {
139 b = base == 0 ? 8 : 16;
140 str++;
141 }
142 }
143 else {
144 b = base;
145 str++;
146 }
147 }
148 else {
149 b = base == 0 ? 10 : base;
150 }
151
152 ret = scan_digits(str, b, &len, &overflow);
153
154 if (0 < len)
155 subject_found = str+len;
156
157 if (endptr)
158 *endptr = (char*)subject_found;
159
160 if (overflow) {
161 errno = ERANGE;
162 return ULONG_MAX;
163 }
164
165 if (sign < 0) {
166 ret = (unsigned long)(-(long)ret);
167 return ret;
168 }
169 else {
170 return ret;
171 }
172 }
173
174 #include <sys/types.h>
175 #include <sys/stat.h>
176 #ifdef HAVE_UNISTD_H
177 #include <unistd.h>
178 #endif
179 #if defined(HAVE_FCNTL_H)
180 #include <fcntl.h>
181 #endif
182
183 #ifndef S_ISDIR
184 # define S_ISDIR(m) (((m) & S_IFMT) == S_IFDIR)
185 #endif
186
187
188 /* mm.c */
189
190 #define mmtype long
191 #define mmcount (16 / SIZEOF_LONG)
192 #define A ((mmtype*)a)
193 #define B ((mmtype*)b)
194 #define C ((mmtype*)c)
195 #define D ((mmtype*)d)
196
197 #define mmstep (sizeof(mmtype) * mmcount)
198 #define mmprepare(base, size) do {\
199 if (((VALUE)(base) % sizeof(mmtype)) == 0 && ((size) % sizeof(mmtype)) == 0) \
200 if ((size) >= mmstep) mmkind = 1;\
201 else mmkind = 0;\
202 else mmkind = -1;\
203 high = ((size) / mmstep) * mmstep;\
204 low = ((size) % mmstep);\
205 } while (0)\
206
207 #define mmarg mmkind, size, high, low
208 #define mmargdecl int mmkind, size_t size, size_t high, size_t low
209
210 static void mmswap_(register char *a, register char *b, mmargdecl)
211 {
212 if (a == b) return;
213 if (mmkind >= 0) {
214 register mmtype s;
215 #if mmcount > 1
216 if (mmkind > 0) {
217 register char *t = a + high;
218 do {
219 s = A[0]; A[0] = B[0]; B[0] = s;
220 s = A[1]; A[1] = B[1]; B[1] = s;
221 #if mmcount > 2
222 s = A[2]; A[2] = B[2]; B[2] = s;
223 #if mmcount > 3
224 s = A[3]; A[3] = B[3]; B[3] = s;
225 #endif
226 #endif
227 a += mmstep; b += mmstep;
228 } while (a < t);
229 }
230 #endif
231 if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = s;
232 #if mmcount > 2
233 if (low >= 2 * sizeof(mmtype)) { s = A[1]; A[1] = B[1]; B[1] = s;
234 #if mmcount > 3
235 if (low >= 3 * sizeof(mmtype)) {s = A[2]; A[2] = B[2]; B[2] = s;}
236 #endif
237 }
238 #endif
239 }
240 }
241 else {
242 register char *t = a + size, s;
243 do {s = *a; *a++ = *b; *b++ = s;} while (a < t);
244 }
245 }
246 #define mmswap(a,b) mmswap_((a),(b),mmarg)
247
248 /* a, b, c = b, c, a */
249 static void mmrot3_(register char *a, register char *b, register char *c, mmargdecl)
250 {
251 if (mmkind >= 0) {
252 register mmtype s;
253 #if mmcount > 1
254 if (mmkind > 0) {
255 register char *t = a + high;
256 do {
257 s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
258 s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
259 #if mmcount > 2
260 s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;
261 #if mmcount > 3
262 s = A[3]; A[3] = B[3]; B[3] = C[3]; C[3] = s;
263 #endif
264 #endif
265 a += mmstep; b += mmstep; c += mmstep;
266 } while (a < t);
267 }
268 #endif
269 if (low != 0) { s = A[0]; A[0] = B[0]; B[0] = C[0]; C[0] = s;
270 #if mmcount > 2
271 if (low >= 2 * sizeof(mmtype)) { s = A[1]; A[1] = B[1]; B[1] = C[1]; C[1] = s;
272 #if mmcount > 3
273 if (low == 3 * sizeof(mmtype)) {s = A[2]; A[2] = B[2]; B[2] = C[2]; C[2] = s;}
274 #endif
275 }
276 #endif
277 }
278 }
279 else {
280 register char *t = a + size, s;
281 do {s = *a; *a++ = *b; *b++ = *c; *c++ = s;} while (a < t);
282 }
283 }
284 #define mmrot3(a,b,c) mmrot3_((a),(b),(c),mmarg)
285
286 /* qs6.c */
287 /*****************************************************/
288 /* */
289 /* qs6 (Quick sort function) */
290 /* */
291 /* by Tomoyuki Kawamura 1995.4.21 */
292 /* kawamura@tokuyama.ac.jp */
293 /*****************************************************/
294
295 typedef struct { char *LL, *RR; } stack_node; /* Stack structure for L,l,R,r */
296 #define PUSH(ll,rr) do { top->LL = (ll); top->RR = (rr); ++top; } while (0) /* Push L,l,R,r */
297 #define POP(ll,rr) do { --top; (ll) = top->LL; (rr) = top->RR; } while (0) /* Pop L,l,R,r */
298
299 #define med3(a,b,c) ((*cmp)((a),(b),d)<0 ? \
300 ((*cmp)((b),(c),d)<0 ? (b) : ((*cmp)((a),(c),d)<0 ? (c) : (a))) : \
301 ((*cmp)((b),(c),d)>0 ? (b) : ((*cmp)((a),(c),d)<0 ? (a) : (c))))
302
303 typedef int (cmpfunc_t)(const void*, const void*, void*);
304 void
305 ruby_qsort(void* base, const size_t nel, const size_t size, cmpfunc_t *cmp, void *d)
306 {
307 register char *l, *r, *m; /* l,r:left,right group m:median point */
308 register int t, eq_l, eq_r; /* eq_l: all items in left group are equal to S */
309 char *L = base; /* left end of current region */
310 char *R = (char*)base + size*(nel-1); /* right end of current region */
311 size_t chklim = 63; /* threshold of ordering element check */
312 stack_node stack[32], *top = stack; /* 32 is enough for 32bit CPU */
313 int mmkind;
314 size_t high, low, n;
315
316 if (nel <= 1) return; /* need not to sort */
317 mmprepare(base, size);
318 goto start;
319
320 nxt:
321 if (stack == top) return; /* return if stack is empty */
322 POP(L,R);
323
324 for (;;) {
325 start:
326 if (L + size == R) { /* 2 elements */
327 if ((*cmp)(L,R,d) > 0) mmswap(L,R); goto nxt;
328 }
329
330 l = L; r = R;
331 n = (r - l + size) / size; /* number of elements */
332 m = l + size * (n >> 1); /* calculate median value */
333
334 if (n >= 60) {
335 register char *m1;
336 register char *m3;
337 if (n >= 200) {
338 n = size*(n>>3); /* number of bytes in splitting 8 */
339 {
340 register char *p1 = l + n;
341 register char *p2 = p1 + n;
342 register char *p3 = p2 + n;
343 m1 = med3(p1, p2, p3);
344 p1 = m + n;
345 p2 = p1 + n;
346 p3 = p2 + n;
347 m3 = med3(p1, p2, p3);
348 }
349 }
350 else {
351 n = size*(n>>2); /* number of bytes in splitting 4 */
352 m1 = l + n;
353 m3 = m + n;
354 }
355 m = med3(m1, m, m3);
356 }
357
358 if ((t = (*cmp)(l,m,d)) < 0) { /*3-5-?*/
359 if ((t = (*cmp)(m,r,d)) < 0) { /*3-5-7*/
360 if (chklim && nel >= chklim) { /* check if already ascending order */
361 char *p;
362 chklim = 0;
363 for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) > 0) goto fail;
364 goto nxt;
365 }
366 fail: goto loopA; /*3-5-7*/
367 }
368 if (t > 0) {
369 if ((*cmp)(l,r,d) <= 0) {mmswap(m,r); goto loopA;} /*3-5-4*/
370 mmrot3(r,m,l); goto loopA; /*3-5-2*/
371 }
372 goto loopB; /*3-5-5*/
373 }
374
375 if (t > 0) { /*7-5-?*/
376 if ((t = (*cmp)(m,r,d)) > 0) { /*7-5-3*/
377 if (chklim && nel >= chklim) { /* check if already ascending order */
378 char *p;
379 chklim = 0;
380 for (p=l; p<r; p+=size) if ((*cmp)(p,p+size,d) < 0) goto fail2;
381 while (l<r) {mmswap(l,r); l+=size; r-=size;} /* reverse region */
382 goto nxt;
383 }
384 fail2: mmswap(l,r); goto loopA; /*7-5-3*/
385 }
386 if (t < 0) {
387 if ((*cmp)(l,r,d) <= 0) {mmswap(l,m); goto loopB;} /*7-5-8*/
388 mmrot3(l,m,r); goto loopA; /*7-5-6*/
389 }
390 mmswap(l,r); goto loopA; /*7-5-5*/
391 }
392
393 if ((t = (*cmp)(m,r,d)) < 0) {goto loopA;} /*5-5-7*/
394 if (t > 0) {mmswap(l,r); goto loopB;} /*5-5-3*/
395
396 /* determining splitting type in case 5-5-5 */ /*5-5-5*/
397 for (;;) {
398 if ((l += size) == r) goto nxt; /*5-5-5*/
399 if (l == m) continue;
400 if ((t = (*cmp)(l,m,d)) > 0) {mmswap(l,r); l = L; goto loopA;}/*575-5*/
401 if (t < 0) {mmswap(L,l); l = L; goto loopB;} /*535-5*/
402 }
403
404 loopA: eq_l = 1; eq_r = 1; /* splitting type A */ /* left <= median < right */
405 for (;;) {
406 for (;;) {
407 if ((l += size) == r)
408 {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
409 if (l == m) continue;
410 if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
411 if (t < 0) eq_l = 0;
412 }
413 for (;;) {
414 if (l == (r -= size))
415 {l -= size; if (l != m) mmswap(m,l); l -= size; goto fin;}
416 if (r == m) {m = l; break;}
417 if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
418 if (t == 0) break;
419 }
420 mmswap(l,r); /* swap left and right */
421 }
422
423 loopB: eq_l = 1; eq_r = 1; /* splitting type B */ /* left < median <= right */
424 for (;;) {
425 for (;;) {
426 if (l == (r -= size))
427 {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
428 if (r == m) continue;
429 if ((t = (*cmp)(r,m,d)) < 0) {eq_l = 0; break;}
430 if (t > 0) eq_r = 0;
431 }
432 for (;;) {
433 if ((l += size) == r)
434 {r += size; if (r != m) mmswap(r,m); r += size; goto fin;}
435 if (l == m) {m = r; break;}
436 if ((t = (*cmp)(l,m,d)) > 0) {eq_r = 0; break;}
437 if (t == 0) break;
438 }
439 mmswap(l,r); /* swap left and right */
440 }
441
442 fin:
443 if (eq_l == 0) /* need to sort left side */
444 if (eq_r == 0) /* need to sort right side */
445 if (l-L < R-r) {PUSH(r,R); R = l;} /* sort left side first */
446 else {PUSH(L,l); L = r;} /* sort right side first */
447 else R = l; /* need to sort left side only */
448 else if (eq_r == 0) L = r; /* need to sort right side only */
449 else goto nxt; /* need not to sort both sides */
450 }
451 }
452
453 char *
454 ruby_strdup(const char *str)
455 {
456 char *tmp;
457 size_t len = strlen(str) + 1;
458
459 tmp = xmalloc(len);
460 memcpy(tmp, str, len);
461
462 return tmp;
463 }
464
465 #ifdef __native_client__
466 char *
467 ruby_getcwd(void)
468 {
469 char *buf = xmalloc(2);
470 strcpy(buf, ".");
471 return buf;
472 }
473 #else
474 char *
475 ruby_getcwd(void)
476 {
477 #ifdef HAVE_GETCWD
478 int size = 200;
479 char *buf = xmalloc(size);
480
481 while (!getcwd(buf, size)) {
482 if (errno != ERANGE) {
483 xfree(buf);
484 rb_sys_fail("getcwd");
485 }
486 size *= 2;
487 buf = xrealloc(buf, size);
488 }
489 #else
490 # ifndef PATH_MAX
491 # define PATH_MAX 8192
492 # endif
493 char *buf = xmalloc(PATH_MAX+1);
494
495 if (!getwd(buf)) {
496 xfree(buf);
497 rb_sys_fail("getwd");
498 }
499 #endif
500 return buf;
501 }
502 #endif
503
504 /****************************************************************
505 *
506 * The author of this software is David M. Gay.
507 *
508 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
509 *
510 * Permission to use, copy, modify, and distribute this software for any
511 * purpose without fee is hereby granted, provided that this entire notice
512 * is included in all copies of any software which is or includes a copy
513 * or modification of this software and in all copies of the supporting
514 * documentation for such software.
515 *
516 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
517 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
518 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
519 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
520 *
521 ***************************************************************/
522
523 /* Please send bug reports to David M. Gay (dmg at acm dot org,
524 * with " at " changed at "@" and " dot " changed to "."). */
525
526 /* On a machine with IEEE extended-precision registers, it is
527 * necessary to specify double-precision (53-bit) rounding precision
528 * before invoking strtod or dtoa. If the machine uses (the equivalent
529 * of) Intel 80x87 arithmetic, the call
530 * _control87(PC_53, MCW_PC);
531 * does this with many compilers. Whether this or another call is
532 * appropriate depends on the compiler; for this to work, it may be
533 * necessary to #include "float.h" or another system-dependent header
534 * file.
535 */
536
537 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
538 *
539 * This strtod returns a nearest machine number to the input decimal
540 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
541 * broken by the IEEE round-even rule. Otherwise ties are broken by
542 * biased rounding (add half and chop).
543 *
544 * Inspired loosely by William D. Clinger's paper "How to Read Floating
545 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
546 *
547 * Modifications:
548 *
549 * 1. We only require IEEE, IBM, or VAX double-precision
550 * arithmetic (not IEEE double-extended).
551 * 2. We get by with floating-point arithmetic in a case that
552 * Clinger missed -- when we're computing d * 10^n
553 * for a small integer d and the integer n is not too
554 * much larger than 22 (the maximum integer k for which
555 * we can represent 10^k exactly), we may be able to
556 * compute (d*10^k) * 10^(e-k) with just one roundoff.
557 * 3. Rather than a bit-at-a-time adjustment of the binary
558 * result in the hard case, we use floating-point
559 * arithmetic to determine the adjustment to within
560 * one bit; only in really hard cases do we need to
561 * compute a second residual.
562 * 4. Because of 3., we don't need a large table of powers of 10
563 * for ten-to-e (just some small tables, e.g. of 10^k
564 * for 0 <= k <= 22).
565 */
566
567 /*
568 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
569 * significant byte has the lowest address.
570 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
571 * significant byte has the lowest address.
572 * #define Long int on machines with 32-bit ints and 64-bit longs.
573 * #define IBM for IBM mainframe-style floating-point arithmetic.
574 * #define VAX for VAX-style floating-point arithmetic (D_floating).
575 * #define No_leftright to omit left-right logic in fast floating-point
576 * computation of dtoa.
577 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
578 * and strtod and dtoa should round accordingly.
579 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
580 * and Honor_FLT_ROUNDS is not #defined.
581 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
582 * that use extended-precision instructions to compute rounded
583 * products and quotients) with IBM.
584 * #define ROUND_BIASED for IEEE-format with biased rounding.
585 * #define Inaccurate_Divide for IEEE-format with correctly rounded
586 * products but inaccurate quotients, e.g., for Intel i860.
587 * #define NO_LONG_LONG on machines that do not have a "long long"
588 * integer type (of >= 64 bits). On such machines, you can
589 * #define Just_16 to store 16 bits per 32-bit Long when doing
590 * high-precision integer arithmetic. Whether this speeds things
591 * up or slows things down depends on the machine and the number
592 * being converted. If long long is available and the name is
593 * something other than "long long", #define Llong to be the name,
594 * and if "unsigned Llong" does not work as an unsigned version of
595 * Llong, #define #ULLong to be the corresponding unsigned type.
596 * #define KR_headers for old-style C function headers.
597 * #define Bad_float_h if your system lacks a float.h or if it does not
598 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
599 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
600 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
601 * if memory is available and otherwise does something you deem
602 * appropriate. If MALLOC is undefined, malloc will be invoked
603 * directly -- and assumed always to succeed.
604 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
605 * memory allocations from a private pool of memory when possible.
606 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
607 * unless #defined to be a different length. This default length
608 * suffices to get rid of MALLOC calls except for unusual cases,
609 * such as decimal-to-binary conversion of a very long string of
610 * digits. The longest string dtoa can return is about 751 bytes
611 * long. For conversions by strtod of strings of 800 digits and
612 * all dtoa conversions in single-threaded executions with 8-byte
613 * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
614 * pointers, PRIVATE_MEM >= 7112 appears adequate.
615 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
616 * Infinity and NaN (case insensitively). On some systems (e.g.,
617 * some HP systems), it may be necessary to #define NAN_WORD0
618 * appropriately -- to the most significant word of a quiet NaN.
619 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
620 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
621 * strtod also accepts (case insensitively) strings of the form
622 * NaN(x), where x is a string of hexadecimal digits and spaces;
623 * if there is only one string of hexadecimal digits, it is taken
624 * for the 52 fraction bits of the resulting NaN; if there are two
625 * or more strings of hex digits, the first is for the high 20 bits,
626 * the second and subsequent for the low 32 bits, with intervening
627 * white space ignored; but if this results in none of the 52
628 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
629 * and NAN_WORD1 are used instead.
630 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
631 * multiple threads. In this case, you must provide (or suitably
632 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
633 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
634 * in pow5mult, ensures lazy evaluation of only one copy of high
635 * powers of 5; omitting this lock would introduce a small
636 * probability of wasting memory, but would otherwise be harmless.)
637 * You must also invoke freedtoa(s) to free the value s returned by
638 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
639 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
640 * avoids underflows on inputs whose result does not underflow.
641 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
642 * floating-point numbers and flushes underflows to zero rather
643 * than implementing gradual underflow, then you must also #define
644 * Sudden_Underflow.
645 * #define YES_ALIAS to permit aliasing certain double values with
646 * arrays of ULongs. This leads to slightly better code with
647 * some compilers and was always used prior to 19990916, but it
648 * is not strictly legal and can cause trouble with aggressively
649 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
650 * #define USE_LOCALE to use the current locale's decimal_point value.
651 * #define SET_INEXACT if IEEE arithmetic is being used and extra
652 * computation should be done to set the inexact flag when the
653 * result is inexact and avoid setting inexact when the result
654 * is exact. In this case, dtoa.c must be compiled in
655 * an environment, perhaps provided by #include "dtoa.c" in a
656 * suitable wrapper, that defines two functions,
657 * int get_inexact(void);
658 * void clear_inexact(void);
659 * such that get_inexact() returns a nonzero value if the
660 * inexact bit is already set, and clear_inexact() sets the
661 * inexact bit to 0. When SET_INEXACT is #defined, strtod
662 * also does extra computations to set the underflow and overflow
663 * flags when appropriate (i.e., when the result is tiny and
664 * inexact or when it is a numeric value rounded to +-infinity).
665 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
666 * the result overflows to +-Infinity or underflows to 0.
667 */
668
669 #ifdef WORDS_BIGENDIAN
670 #define IEEE_BIG_ENDIAN
671 #else
672 #define IEEE_LITTLE_ENDIAN
673 #endif
674
675 #ifdef __vax__
676 #define VAX
677 #undef IEEE_BIG_ENDIAN
678 #undef IEEE_LITTLE_ENDIAN
679 #endif
680
681 #if defined(__arm__) && !defined(__VFP_FP__)
682 #define IEEE_BIG_ENDIAN
683 #undef IEEE_LITTLE_ENDIAN
684 #endif
685
686 #undef Long
687 #undef ULong
688
689 #if SIZEOF_INT == 4
690 #define Long int
691 #define ULong unsigned int
692 #elif SIZEOF_LONG == 4
693 #define Long long int
694 #define ULong unsigned long int
695 #endif
696
697 #if HAVE_LONG_LONG
698 #define Llong LONG_LONG
699 #endif
700
701 #ifdef DEBUG
702 #include "stdio.h"
703 #define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
704 #endif
705
706 #include "stdlib.h"
707 #include "string.h"
708
709 #ifdef USE_LOCALE
710 #include "locale.h"
711 #endif
712
713 #ifdef MALLOC
714 extern void *MALLOC(size_t);
715 #else
716 #define MALLOC malloc
717 #endif
718
719 #ifndef Omit_Private_Memory
720 #ifndef PRIVATE_MEM
721 #define PRIVATE_MEM 2304
722 #endif
723 #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
724 static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
725 #endif
726
727 #undef IEEE_Arith
728 #undef Avoid_Underflow
729 #ifdef IEEE_BIG_ENDIAN
730 #define IEEE_Arith
731 #endif
732 #ifdef IEEE_LITTLE_ENDIAN
733 #define IEEE_Arith
734 #endif
735
736 #ifdef Bad_float_h
737
738 #ifdef IEEE_Arith
739 #define DBL_DIG 15
740 #define DBL_MAX_10_EXP 308
741 #define DBL_MAX_EXP 1024
742 #define FLT_RADIX 2
743 #endif /*IEEE_Arith*/
744
745 #ifdef IBM
746 #define DBL_DIG 16
747 #define DBL_MAX_10_EXP 75
748 #define DBL_MAX_EXP 63
749 #define FLT_RADIX 16
750 #define DBL_MAX 7.2370055773322621e+75
751 #endif
752
753 #ifdef VAX
754 #define DBL_DIG 16
755 #define DBL_MAX_10_EXP 38
756 #define DBL_MAX_EXP 127
757 #define FLT_RADIX 2
758 #define DBL_MAX 1.7014118346046923e+38
759 #endif
760
761 #ifndef LONG_MAX
762 #define LONG_MAX 2147483647
763 #endif
764
765 #else /* ifndef Bad_float_h */
766 #include "float.h"
767 #endif /* Bad_float_h */
768
769 #ifndef __MATH_H__
770 #include "math.h"
771 #endif
772
773 #ifdef __cplusplus
774 extern "C" {
775 #if 0
776 } /* satisfy cc-mode */
777 #endif
778 #endif
779
780 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
781 Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
782 #endif
783
784 typedef union { double d; ULong L[2]; } U;
785
786 #ifdef YES_ALIAS
787 typedef double double_u;
788 # define dval(x) (x)
789 # ifdef IEEE_LITTLE_ENDIAN
790 # define word0(x) (((ULong *)&(x))[1])
791 # define word1(x) (((ULong *)&(x))[0])
792 # else
793 # define word0(x) (((ULong *)&(x))[0])
794 # define word1(x) (((ULong *)&(x))[1])
795 # endif
796 #else
797 typedef U double_u;
798 # ifdef IEEE_LITTLE_ENDIAN
799 # define word0(x) ((x).L[1])
800 # define word1(x) ((x).L[0])
801 # else
802 # define word0(x) ((x).L[0])
803 # define word1(x) ((x).L[1])
804 # endif
805 # define dval(x) ((x).d)
806 #endif
807
808 /* The following definition of Storeinc is appropriate for MIPS processors.
809 * An alternative that might be better on some machines is
810 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
811 */
812 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
813 #define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
814 ((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
815 #else
816 #define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
817 ((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
818 #endif
819
820 /* #define P DBL_MANT_DIG */
821 /* Ten_pmax = floor(P*log(2)/log(5)) */
822 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
823 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
824 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
825
826 #ifdef IEEE_Arith
827 #define Exp_shift 20
828 #define Exp_shift1 20
829 #define Exp_msk1 0x100000
830 #define Exp_msk11 0x100000
831 #define Exp_mask 0x7ff00000
832 #define P 53
833 #define Bias 1023
834 #define Emin (-1022)
835 #define Exp_1 0x3ff00000
836 #define Exp_11 0x3ff00000
837 #define Ebits 11
838 #define Frac_mask 0xfffff
839 #define Frac_mask1 0xfffff
840 #define Ten_pmax 22
841 #define Bletch 0x10
842 #define Bndry_mask 0xfffff
843 #define Bndry_mask1 0xfffff
844 #define LSB 1
845 #define Sign_bit 0x80000000
846 #define Log2P 1
847 #define Tiny0 0
848 #define Tiny1 1
849 #define Quick_max 14
850 #define Int_max 14
851 #ifndef NO_IEEE_Scale
852 #define Avoid_Underflow
853 #ifdef Flush_Denorm /* debugging option */
854 #undef Sudden_Underflow
855 #endif
856 #endif
857
858 #ifndef Flt_Rounds
859 #ifdef FLT_ROUNDS
860 #define Flt_Rounds FLT_ROUNDS
861 #else
862 #define Flt_Rounds 1
863 #endif
864 #endif /*Flt_Rounds*/
865
866 #ifdef Honor_FLT_ROUNDS
867 #define Rounding rounding
868 #undef Check_FLT_ROUNDS
869 #define Check_FLT_ROUNDS
870 #else
871 #define Rounding Flt_Rounds
872 #endif
873
874 #else /* ifndef IEEE_Arith */
875 #undef Check_FLT_ROUNDS
876 #undef Honor_FLT_ROUNDS
877 #undef SET_INEXACT
878 #undef Sudden_Underflow
879 #define Sudden_Underflow
880 #ifdef IBM
881 #undef Flt_Rounds
882 #define Flt_Rounds 0
883 #define Exp_shift 24
884 #define Exp_shift1 24
885 #define Exp_msk1 0x1000000
886 #define Exp_msk11 0x1000000
887 #define Exp_mask 0x7f000000
888 #define P 14
889 #define Bias 65
890 #define Exp_1 0x41000000
891 #define Exp_11 0x41000000
892 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
893 #define Frac_mask 0xffffff
894 #define Frac_mask1 0xffffff
895 #define Bletch 4
896 #define Ten_pmax 22
897 #define Bndry_mask 0xefffff
898 #define Bndry_mask1 0xffffff
899 #define LSB 1
900 #define Sign_bit 0x80000000
901 #define Log2P 4
902 #define Tiny0 0x100000
903 #define Tiny1 0
904 #define Quick_max 14
905 #define Int_max 15
906 #else /* VAX */
907 #undef Flt_Rounds
908 #define Flt_Rounds 1
909 #define Exp_shift 23
910 #define Exp_shift1 7
911 #define Exp_msk1 0x80
912 #define Exp_msk11 0x800000
913 #define Exp_mask 0x7f80
914 #define P 56
915 #define Bias 129
916 #define Exp_1 0x40800000
917 #define Exp_11 0x4080
918 #define Ebits 8
919 #define Frac_mask 0x7fffff
920 #define Frac_mask1 0xffff007f
921 #define Ten_pmax 24
922 #define Bletch 2
923 #define Bndry_mask 0xffff007f
924 #define Bndry_mask1 0xffff007f
925 #define LSB 0x10000
926 #define Sign_bit 0x8000
927 #define Log2P 1
928 #define Tiny0 0x80
929 #define Tiny1 0
930 #define Quick_max 15
931 #define Int_max 15
932 #endif /* IBM, VAX */
933 #endif /* IEEE_Arith */
934
935 #ifndef IEEE_Arith
936 #define ROUND_BIASED
937 #endif
938
939 #ifdef RND_PRODQUOT
940 #define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
941 #define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
942 extern double rnd_prod(double, double), rnd_quot(double, double);
943 #else
944 #define rounded_product(a,b) ((a) *= (b))
945 #define rounded_quotient(a,b) ((a) /= (b))
946 #endif
947
948 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
949 #define Big1 0xffffffff
950
951 #ifndef Pack_32
952 #define Pack_32
953 #endif
954
955 #define FFFFFFFF 0xffffffffUL
956
957 #ifdef NO_LONG_LONG
958 #undef ULLong
959 #ifdef Just_16
960 #undef Pack_32
961 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
962 * This makes some inner loops simpler and sometimes saves work
963 * during multiplications, but it often seems to make things slightly
964 * slower. Hence the default is now to store 32 bits per Long.
965 */
966 #endif
967 #else /* long long available */
968 #ifndef Llong
969 #define Llong long long
970 #endif
971 #ifndef ULLong
972 #define ULLong unsigned Llong
973 #endif
974 #endif /* NO_LONG_LONG */
975
976 #define MULTIPLE_THREADS 1
977
978 #ifndef MULTIPLE_THREADS
979 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
980 #define FREE_DTOA_LOCK(n) /*nothing*/
981 #else
982 #define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
983 #define FREE_DTOA_LOCK(n) /*unused right now*/
984 #endif
985
986 #define Kmax 15
987
988 struct Bigint {
989 struct Bigint *next;
990 int k, maxwds, sign, wds;
991 ULong x[1];
992 };
993
994 typedef struct Bigint Bigint;
995
996 static Bigint *freelist[Kmax+1];
997
998 static Bigint *
999 Balloc(int k)
1000 {
1001 int x;
1002 Bigint *rv;
1003 #ifndef Omit_Private_Memory
1004 size_t len;
1005 #endif
1006
1007 ACQUIRE_DTOA_LOCK(0);
1008 if ((rv = freelist[k]) != 0) {
1009 freelist[k] = rv->next;
1010 }
1011 else {
1012 x = 1 << k;
1013 #ifdef Omit_Private_Memory
1014 rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
1015 #else
1016 len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
1017 /sizeof(double);
1018 if (pmem_next - private_mem + len <= PRIVATE_mem) {
1019 rv = (Bigint*)pmem_next;
1020 pmem_next += len;
1021 }
1022 else
1023 rv = (Bigint*)MALLOC(len*sizeof(double));
1024 #endif
1025 rv->k = k;
1026 rv->maxwds = x;
1027 }
1028 FREE_DTOA_LOCK(0);
1029 rv->sign = rv->wds = 0;
1030 return rv;
1031 }
1032
1033 static void
1034 Bfree(Bigint *v)
1035 {
1036 if (v) {
1037 ACQUIRE_DTOA_LOCK(0);
1038 v->next = freelist[v->k];
1039 freelist[v->k] = v;
1040 FREE_DTOA_LOCK(0);
1041 }
1042 }
1043
1044 #define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
1045 (y)->wds*sizeof(Long) + 2*sizeof(int))
1046
1047 static Bigint *
1048 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
1049 {
1050 int i, wds;
1051 ULong *x;
1052 #ifdef ULLong
1053 ULLong carry, y;
1054 #else
1055 ULong carry, y;
1056 #ifdef Pack_32
1057 ULong xi, z;
1058 #endif
1059 #endif
1060 Bigint *b1;
1061
1062 wds = b->wds;
1063 x = b->x;
1064 i = 0;
1065 carry = a;
1066 do {
1067 #ifdef ULLong
1068 y = *x * (ULLong)m + carry;
1069 carry = y >> 32;
1070 *x++ = (ULong)(y & FFFFFFFF);
1071 #else
1072 #ifdef Pack_32
1073 xi = *x;
1074 y = (xi & 0xffff) * m + carry;
1075 z = (xi >> 16) * m + (y >> 16);
1076 carry = z >> 16;
1077 *x++ = (z << 16) + (y & 0xffff);
1078 #else
1079 y = *x * m + carry;
1080 carry = y >> 16;
1081 *x++ = y & 0xffff;
1082 #endif
1083 #endif
1084 } while (++i < wds);
1085 if (carry) {
1086 if (wds >= b->maxwds) {
1087 b1 = Balloc(b->k+1);
1088 Bcopy(b1, b);
1089 Bfree(b);
1090 b = b1;
1091 }
1092 b->x[wds++] = (ULong)carry;
1093 b->wds = wds;
1094 }
1095 return b;
1096 }
1097
1098 static Bigint *
1099 s2b(const char *s, int nd0, int nd, ULong y9)
1100 {
1101 Bigint *b;
1102 int i, k;
1103 Long x, y;
1104
1105 x = (nd + 8) / 9;
1106 for (k = 0, y = 1; x > y; y <<= 1, k++) ;
1107 #ifdef Pack_32
1108 b = Balloc(k);
1109 b->x[0] = y9;
1110 b->wds = 1;
1111 #else
1112 b = Balloc(k+1);
1113 b->x[0] = y9 & 0xffff;
1114 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
1115 #endif
1116
1117 i = 9;
1118 if (9 < nd0) {
1119 s += 9;
1120 do {
1121 b = multadd(b, 10, *s++ - '0');
1122 } while (++i < nd0);
1123 s++;
1124 }
1125 else
1126 s += 10;
1127 for (; i < nd; i++)
1128 b = multadd(b, 10, *s++ - '0');
1129 return b;
1130 }
1131
1132 static int
1133 hi0bits(register ULong x)
1134 {
1135 register int k = 0;
1136
1137 if (!(x & 0xffff0000)) {
1138 k = 16;
1139 x <<= 16;
1140 }
1141 if (!(x & 0xff000000)) {
1142 k += 8;
1143 x <<= 8;
1144 }
1145 if (!(x & 0xf0000000)) {
1146 k += 4;
1147 x <<= 4;
1148 }
1149 if (!(x & 0xc0000000)) {
1150 k += 2;
1151 x <<= 2;
1152 }
1153 if (!(x & 0x80000000)) {
1154 k++;
1155 if (!(x & 0x40000000))
1156 return 32;
1157 }
1158 return k;
1159 }
1160
1161 static int
1162 lo0bits(ULong *y)
1163 {
1164 register int k;
1165 register ULong x = *y;
1166
1167 if (x & 7) {
1168 if (x & 1)
1169 return 0;
1170 if (x & 2) {
1171 *y = x >> 1;
1172 return 1;
1173 }
1174 *y = x >> 2;
1175 return 2;
1176 }
1177 k = 0;
1178 if (!(x & 0xffff)) {
1179 k = 16;
1180 x >>= 16;
1181 }
1182 if (!(x & 0xff)) {
1183 k += 8;
1184 x >>= 8;
1185 }
1186 if (!(x & 0xf)) {
1187 k += 4;
1188 x >>= 4;
1189 }
1190 if (!(x & 0x3)) {
1191 k += 2;
1192 x >>= 2;
1193 }
1194 if (!(x & 1)) {
1195 k++;
1196 x >>= 1;
1197 if (!x)
1198 return 32;
1199 }
1200 *y = x;
1201 return k;
1202 }
1203
1204 static Bigint *
1205 i2b(int i)
1206 {
1207 Bigint *b;
1208
1209 b = Balloc(1);
1210 b->x[0] = i;
1211 b->wds = 1;
1212 return b;
1213 }
1214
1215 static Bigint *
1216 mult(Bigint *a, Bigint *b)
1217 {
1218 Bigint *c;
1219 int k, wa, wb, wc;
1220 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
1221 ULong y;
1222 #ifdef ULLong
1223 ULLong carry, z;
1224 #else
1225 ULong carry, z;
1226 #ifdef Pack_32
1227 ULong z2;
1228 #endif
1229 #endif
1230
1231 if (a->wds < b->wds) {
1232 c = a;
1233 a = b;
1234 b = c;
1235 }
1236 k = a->k;
1237 wa = a->wds;
1238 wb = b->wds;
1239 wc = wa + wb;
1240 if (wc > a->maxwds)
1241 k++;
1242 c = Balloc(k);
1243 for (x = c->x, xa = x + wc; x < xa; x++)
1244 *x = 0;
1245 xa = a->x;
1246 xae = xa + wa;
1247 xb = b->x;
1248 xbe = xb + wb;
1249 xc0 = c->x;
1250 #ifdef ULLong
1251 for (; xb < xbe; xc0++) {
1252 if ((y = *xb++) != 0) {
1253 x = xa;
1254 xc = xc0;
1255 carry = 0;
1256 do {
1257 z = *x++ * (ULLong)y + *xc + carry;
1258 carry = z >> 32;
1259 *xc++ = (ULong)(z & FFFFFFFF);
1260 } while (x < xae);
1261 *xc = (ULong)carry;
1262 }
1263 }
1264 #else
1265 #ifdef Pack_32
1266 for (; xb < xbe; xb++, xc0++) {
1267 if (y = *xb & 0xffff) {
1268 x = xa;
1269 xc = xc0;
1270 carry = 0;
1271 do {
1272 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
1273 carry = z >> 16;
1274 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
1275 carry = z2 >> 16;
1276 Storeinc(xc, z2, z);
1277 } while (x < xae);
1278 *xc = (ULong)carry;
1279 }
1280 if (y = *xb >> 16) {
1281 x = xa;
1282 xc = xc0;
1283 carry = 0;
1284 z2 = *xc;
1285 do {
1286 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
1287 carry = z >> 16;
1288 Storeinc(xc, z, z2);
1289 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
1290 carry = z2 >> 16;
1291 } while (x < xae);
1292 *xc = z2;
1293 }
1294 }
1295 #else
1296 for (; xb < xbe; xc0++) {
1297 if (y = *xb++) {
1298 x = xa;
1299 xc = xc0;
1300 carry = 0;
1301 do {
1302 z = *x++ * y + *xc + carry;
1303 carry = z >> 16;
1304 *xc++ = z & 0xffff;
1305 } while (x < xae);
1306 *xc = (ULong)carry;
1307 }
1308 }
1309 #endif
1310 #endif
1311 for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
1312 c->wds = wc;
1313 return c;
1314 }
1315
1316 static Bigint *p5s;
1317
1318 static Bigint *
1319 pow5mult(Bigint *b, int k)
1320 {
1321 Bigint *b1, *p5, *p51;
1322 int i;
1323 static int p05[3] = { 5, 25, 125 };
1324
1325 if ((i = k & 3) != 0)
1326 b = multadd(b, p05[i-1], 0);
1327
1328 if (!(k >>= 2))
1329 return b;
1330 if (!(p5 = p5s)) {
1331 /* first time */
1332 #ifdef MULTIPLE_THREADS
1333 ACQUIRE_DTOA_LOCK(1);
1334 if (!(p5 = p5s)) {
1335 p5 = p5s = i2b(625);
1336 p5->next = 0;
1337 }
1338 FREE_DTOA_LOCK(1);
1339 #else
1340 p5 = p5s = i2b(625);
1341 p5->next = 0;
1342 #endif
1343 }
1344 for (;;) {
1345 if (k & 1) {
1346 b1 = mult(b, p5);
1347 Bfree(b);
1348 b = b1;
1349 }
1350 if (!(k >>= 1))
1351 break;
1352 if (!(p51 = p5->next)) {
1353 #ifdef MULTIPLE_THREADS
1354 ACQUIRE_DTOA_LOCK(1);
1355 if (!(p51 = p5->next)) {
1356 p51 = p5->next = mult(p5,p5);
1357 p51->next = 0;
1358 }
1359 FREE_DTOA_LOCK(1);
1360 #else
1361 p51 = p5->next = mult(p5,p5);
1362 p51->next = 0;
1363 #endif
1364 }
1365 p5 = p51;
1366 }
1367 return b;
1368 }
1369
1370 static Bigint *
1371 lshift(Bigint *b, int k)
1372 {
1373 int i, k1, n, n1;
1374 Bigint *b1;
1375 ULong *x, *x1, *xe, z;
1376
1377 #ifdef Pack_32
1378 n = k >> 5;
1379 #else
1380 n = k >> 4;
1381 #endif
1382 k1 = b->k;
1383 n1 = n + b->wds + 1;
1384 for (i = b->maxwds; n1 > i; i <<= 1)
1385 k1++;
1386 b1 = Balloc(k1);
1387 x1 = b1->x;
1388 for (i = 0; i < n; i++)
1389 *x1++ = 0;
1390 x = b->x;
1391 xe = x + b->wds;
1392 #ifdef Pack_32
1393 if (k &= 0x1f) {
1394 k1 = 32 - k;
1395 z = 0;
1396 do {
1397 *x1++ = *x << k | z;
1398 z = *x++ >> k1;
1399 } while (x < xe);
1400 if ((*x1 = z) != 0)
1401 ++n1;
1402 }
1403 #else
1404 if (k &= 0xf) {
1405 k1 = 16 - k;
1406 z = 0;
1407 do {
1408 *x1++ = *x << k & 0xffff | z;
1409 z = *x++ >> k1;
1410 } while (x < xe);
1411 if (*x1 = z)
1412 ++n1;
1413 }
1414 #endif
1415 else
1416 do {
1417 *x1++ = *x++;
1418 } while (x < xe);
1419 b1->wds = n1 - 1;
1420 Bfree(b);
1421 return b1;
1422 }
1423
1424 static int
1425 cmp(Bigint *a, Bigint *b)
1426 {
1427 ULong *xa, *xa0, *xb, *xb0;
1428 int i, j;
1429
1430 i = a->wds;
1431 j = b->wds;
1432 #ifdef DEBUG
1433 if (i > 1 && !a->x[i-1])
1434 Bug("cmp called with a->x[a->wds-1] == 0");
1435 if (j > 1 && !b->x[j-1])
1436 Bug("cmp called with b->x[b->wds-1] == 0");
1437 #endif
1438 if (i -= j)
1439 return i;
1440 xa0 = a->x;
1441 xa = xa0 + j;
1442 xb0 = b->x;
1443 xb = xb0 + j;
1444 for (;;) {
1445 if (*--xa != *--xb)
1446 return *xa < *xb ? -1 : 1;
1447 if (xa <= xa0)
1448 break;
1449 }
1450 return 0;
1451 }
1452
1453 static Bigint *
1454 diff(Bigint *a, Bigint *b)
1455 {
1456 Bigint *c;
1457 int i, wa, wb;
1458 ULong *xa, *xae, *xb, *xbe, *xc;
1459 #ifdef ULLong
1460 ULLong borrow, y;
1461 #else
1462 ULong borrow, y;
1463 #ifdef Pack_32
1464 ULong z;
1465 #endif
1466 #endif
1467
1468 i = cmp(a,b);
1469 if (!i) {
1470 c = Balloc(0);
1471 c->wds = 1;
1472 c->x[0] = 0;
1473 return c;
1474 }
1475 if (i < 0) {
1476 c = a;
1477 a = b;
1478 b = c;
1479 i = 1;
1480 }
1481 else
1482 i = 0;
1483 c = Balloc(a->k);
1484 c->sign = i;
1485 wa = a->wds;
1486 xa = a->x;
1487 xae = xa + wa;
1488 wb = b->wds;
1489 xb = b->x;
1490 xbe = xb + wb;
1491 xc = c->x;
1492 borrow = 0;
1493 #ifdef ULLong
1494 do {
1495 y = (ULLong)*xa++ - *xb++ - borrow;
1496 borrow = y >> 32 & (ULong)1;
1497 *xc++ = (ULong)(y & FFFFFFFF);
1498 } while (xb < xbe);
1499 while (xa < xae) {
1500 y = *xa++ - borrow;
1501 borrow = y >> 32 & (ULong)1;
1502 *xc++ = (ULong)(y & FFFFFFFF);
1503 }
1504 #else
1505 #ifdef Pack_32
1506 do {
1507 y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
1508 borrow = (y & 0x10000) >> 16;
1509 z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
1510 borrow = (z & 0x10000) >> 16;
1511 Storeinc(xc, z, y);
1512 } while (xb < xbe);
1513 while (xa < xae) {
1514 y = (*xa & 0xffff) - borrow;
1515 borrow = (y & 0x10000) >> 16;
1516 z = (*xa++ >> 16) - borrow;
1517 borrow = (z & 0x10000) >> 16;
1518 Storeinc(xc, z, y);
1519 }
1520 #else
1521 do {
1522 y = *xa++ - *xb++ - borrow;
1523 borrow = (y & 0x10000) >> 16;
1524 *xc++ = y & 0xffff;
1525 } while (xb < xbe);
1526 while (xa < xae) {
1527 y = *xa++ - borrow;
1528 borrow = (y & 0x10000) >> 16;
1529 *xc++ = y & 0xffff;
1530 }
1531 #endif
1532 #endif
1533 while (!*--xc)
1534 wa--;
1535 c->wds = wa;
1536 return c;
1537 }
1538
1539 static double
1540 ulp(double x_)
1541 {
1542 register Long L;
1543 double_u x, a;
1544 dval(x) = x_;
1545
1546 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
1547 #ifndef Avoid_Underflow
1548 #ifndef Sudden_Underflow
1549 if (L > 0) {
1550 #endif
1551 #endif
1552 #ifdef IBM
1553 L |= Exp_msk1 >> 4;
1554 #endif
1555 word0(a) = L;
1556 word1(a) = 0;
1557 #ifndef Avoid_Underflow
1558 #ifndef Sudden_Underflow
1559 }
1560 else {
1561 L = -L >> Exp_shift;
1562 if (L < Exp_shift) {
1563 word0(a) = 0x80000 >> L;
1564 word1(a) = 0;
1565 }
1566 else {
1567 word0(a) = 0;
1568 L -= Exp_shift;
1569 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
1570 }
1571 }
1572 #endif
1573 #endif
1574 return dval(a);
1575 }
1576
1577 static double
1578 b2d(Bigint *a, int *e)
1579 {
1580 ULong *xa, *xa0, w, y, z;
1581 int k;
1582 double_u d;
1583 #ifdef VAX
1584 ULong d0, d1;
1585 #else
1586 #define d0 word0(d)
1587 #define d1 word1(d)
1588 #endif
1589
1590 xa0 = a->x;
1591 xa = xa0 + a->wds;
1592 y = *--xa;
1593 #ifdef DEBUG
1594 if (!y) Bug("zero y in b2d");
1595 #endif
1596 k = hi0bits(y);
1597 *e = 32 - k;
1598 #ifdef Pack_32
1599 if (k < Ebits) {
1600 d0 = Exp_1 | y >> (Ebits - k);
1601 w = xa > xa0 ? *--xa : 0;
1602 d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
1603 goto ret_d;
1604 }
1605 z = xa > xa0 ? *--xa : 0;
1606 if (k -= Ebits) {
1607 d0 = Exp_1 | y << k | z >> (32 - k);
1608 y = xa > xa0 ? *--xa : 0;
1609 d1 = z << k | y >> (32 - k);
1610 }
1611 else {
1612 d0 = Exp_1 | y;
1613 d1 = z;
1614 }
1615 #else
1616 if (k < Ebits + 16) {
1617 z = xa > xa0 ? *--xa : 0;
1618 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
1619 w = xa > xa0 ? *--xa : 0;
1620 y = xa > xa0 ? *--xa : 0;
1621 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
1622 goto ret_d;
1623 }
1624 z = xa > xa0 ? *--xa : 0;
1625 w = xa > xa0 ? *--xa : 0;
1626 k -= Ebits + 16;
1627 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
1628 y = xa > xa0 ? *--xa : 0;
1629 d1 = w << k + 16 | y << k;
1630 #endif
1631 ret_d:
1632 #ifdef VAX
1633 word0(d) = d0 >> 16 | d0 << 16;
1634 word1(d) = d1 >> 16 | d1 << 16;
1635 #else
1636 #undef d0
1637 #undef d1
1638 #endif
1639 return dval(d);
1640 }
1641
1642 static Bigint *
1643 d2b(double d_, int *e, int *bits)
1644 {
1645 double_u d;
1646 Bigint *b;
1647 int de, k;
1648 ULong *x, y, z;
1649 #ifndef Sudden_Underflow
1650 int i;
1651 #endif
1652 #ifdef VAX
1653 ULong d0, d1;
1654 #endif
1655 dval(d) = d_;
1656 #ifdef VAX
1657 d0 = word0(d) >> 16 | word0(d) << 16;
1658 d1 = word1(d) >> 16 | word1(d) << 16;
1659 #else
1660 #define d0 word0(d)
1661 #define d1 word1(d)
1662 #endif
1663
1664 #ifdef Pack_32
1665 b = Balloc(1);
1666 #else
1667 b = Balloc(2);
1668 #endif
1669 x = b->x;
1670
1671 z = d0 & Frac_mask;
1672 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
1673 #ifdef Sudden_Underflow
1674 de = (int)(d0 >> Exp_shift);
1675 #ifndef IBM
1676 z |= Exp_msk11;
1677 #endif
1678 #else
1679 if ((de = (int)(d0 >> Exp_shift)) != 0)
1680 z |= Exp_msk1;
1681 #endif
1682 #ifdef Pack_32
1683 if ((y = d1) != 0) {
1684 if ((k = lo0bits(&y)) != 0) {
1685 x[0] = y | z << (32 - k);
1686 z >>= k;
1687 }
1688 else
1689 x[0] = y;
1690 #ifndef Sudden_Underflow
1691 i =
1692 #endif
1693 b->wds = (x[1] = z) ? 2 : 1;
1694 }
1695 else {
1696 #ifdef DEBUG
1697 if (!z)
1698 Bug("Zero passed to d2b");
1699 #endif
1700 k = lo0bits(&z);
1701 x[0] = z;
1702 #ifndef Sudden_Underflow
1703 i =
1704 #endif
1705 b->wds = 1;
1706 k += 32;
1707 }
1708 #else
1709 if (y = d1) {
1710 if (k = lo0bits(&y))
1711 if (k >= 16) {
1712 x[0] = y | z << 32 - k & 0xffff;
1713 x[1] = z >> k - 16 & 0xffff;
1714 x[2] = z >> k;
1715 i = 2;
1716 }
1717 else {
1718 x[0] = y & 0xffff;
1719 x[1] = y >> 16 | z << 16 - k & 0xffff;
1720 x[2] = z >> k & 0xffff;
1721 x[3] = z >> k+16;
1722 i = 3;
1723 }
1724 else {
1725 x[0] = y & 0xffff;
1726 x[1] = y >> 16;
1727 x[2] = z & 0xffff;
1728 x[3] = z >> 16;
1729 i = 3;
1730 }
1731 }
1732 else {
1733 #ifdef DEBUG
1734 if (!z)
1735 Bug("Zero passed to d2b");
1736 #endif
1737 k = lo0bits(&z);
1738 if (k >= 16) {
1739 x[0] = z;
1740 i = 0;
1741 }
1742 else {
1743 x[0] = z & 0xffff;
1744 x[1] = z >> 16;
1745 i = 1;
1746 }
1747 k += 32;
1748 }
1749 while (!x[i])
1750 --i;
1751 b->wds = i + 1;
1752 #endif
1753 #ifndef Sudden_Underflow
1754 if (de) {
1755 #endif
1756 #ifdef IBM
1757 *e = (de - Bias - (P-1) << 2) + k;
1758 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1759 #else
1760 *e = de - Bias - (P-1) + k;
1761 *bits = P - k;
1762 #endif
1763 #ifndef Sudden_Underflow
1764 }
1765 else {
1766 *e = de - Bias - (P-1) + 1 + k;
1767 #ifdef Pack_32
1768 *bits = 32*i - hi0bits(x[i-1]);
1769 #else
1770 *bits = (i+2)*16 - hi0bits(x[i]);
1771 #endif
1772 }
1773 #endif
1774 return b;
1775 }
1776 #undef d0
1777 #undef d1
1778
1779 static double
1780 ratio(Bigint *a, Bigint *b)
1781 {
1782 double_u da, db;
1783 int k, ka, kb;
1784
1785 dval(da) = b2d(a, &ka);
1786 dval(db) = b2d(b, &kb);
1787 #ifdef Pack_32
1788 k = ka - kb + 32*(a->wds - b->wds);
1789 #else
1790 k = ka - kb + 16*(a->wds - b->wds);
1791 #endif
1792 #ifdef IBM
1793 if (k > 0) {
1794 word0(da) += (k >> 2)*Exp_msk1;
1795 if (k &= 3)
1796 dval(da) *= 1 << k;
1797 }
1798 else {
1799 k = -k;
1800 word0(db) += (k >> 2)*Exp_msk1;
1801 if (k &= 3)
1802 dval(db) *= 1 << k;
1803 }
1804 #else
1805 if (k > 0)
1806 word0(da) += k*Exp_msk1;
1807 else {
1808 k = -k;
1809 word0(db) += k*Exp_msk1;
1810 }
1811 #endif
1812 return dval(da) / dval(db);
1813 }
1814
1815 static const double
1816 tens[] = {
1817 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1818 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1819 1e20, 1e21, 1e22
1820 #ifdef VAX
1821 , 1e23, 1e24
1822 #endif
1823 };
1824
1825 static const double
1826 #ifdef IEEE_Arith
1827 bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1828 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1829 #ifdef Avoid_Underflow
1830 9007199254740992.*9007199254740992.e-256
1831 /* = 2^106 * 1e-53 */
1832 #else
1833 1e-256
1834 #endif
1835 };
1836 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1837 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1838 #define Scale_Bit 0x10
1839 #define n_bigtens 5
1840 #else
1841 #ifdef IBM
1842 bigtens[] = { 1e16, 1e32, 1e64 };
1843 static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1844 #define n_bigtens 3
1845 #else
1846 bigtens[] = { 1e16, 1e32 };
1847 static const double tinytens[] = { 1e-16, 1e-32 };
1848 #define n_bigtens 2
1849 #endif
1850 #endif
1851
1852 #ifndef IEEE_Arith
1853 #undef INFNAN_CHECK
1854 #endif
1855
1856 #ifdef INFNAN_CHECK
1857
1858 #ifndef NAN_WORD0
1859 #define NAN_WORD0 0x7ff80000
1860 #endif
1861
1862 #ifndef NAN_WORD1
1863 #define NAN_WORD1 0
1864 #endif
1865
1866 static int
1867 match(const char **sp, char *t)
1868 {
1869 int c, d;
1870 const char *s = *sp;
1871
1872 while (d = *t++) {
1873 if ((c = *++s) >= 'A' && c <= 'Z')
1874 c += 'a' - 'A';
1875 if (c != d)
1876 return 0;
1877 }
1878 *sp = s + 1;
1879 return 1;
1880 }
1881
1882 #ifndef No_Hex_NaN
1883 static void
1884 hexnan(double *rvp, const char **sp)
1885 {
1886 ULong c, x[2];
1887 const char *s;
1888 int havedig, udx0, xshift;
1889
1890 x[0] = x[1] = 0;
1891 havedig = xshift = 0;
1892 udx0 = 1;
1893 s = *sp;
1894 while (c = *(const unsigned char*)++s) {
1895 if (c >= '0' && c <= '9')
1896 c -= '0';
1897 else if (c >= 'a' && c <= 'f')
1898 c += 10 - 'a';
1899 else if (c >= 'A' && c <= 'F')
1900 c += 10 - 'A';
1901 else if (c <= ' ') {
1902 if (udx0 && havedig) {
1903 udx0 = 0;
1904 xshift = 1;
1905 }
1906 continue;
1907 }
1908 else if (/*(*/ c == ')' && havedig) {
1909 *sp = s + 1;
1910 break;
1911 }
1912 else
1913 return; /* invalid form: don't change *sp */
1914 havedig = 1;
1915 if (xshift) {
1916 xshift = 0;
1917 x[0] = x[1];
1918 x[1] = 0;
1919 }
1920 if (udx0)
1921 x[0] = (x[0] << 4) | (x[1] >> 28);
1922 x[1] = (x[1] << 4) | c;
1923 }
1924 if ((x[0] &= 0xfffff) || x[1]) {
1925 word0(*rvp) = Exp_mask | x[0];
1926 word1(*rvp) = x[1];
1927 }
1928 }
1929 #endif /*No_Hex_NaN*/
1930 #endif /* INFNAN_CHECK */
1931
1932 double
1933 ruby_strtod(const char *s00, char **se)
1934 {
1935 #ifdef Avoid_Underflow
1936 int scale;
1937 #endif
1938 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1939 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1940 const char *s, *s0, *s1;
1941 double aadj, adj;
1942 double_u aadj1, rv, rv0;
1943 Long L;
1944 ULong y, z;
1945 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1946 #ifdef SET_INEXACT
1947 int inexact, oldinexact;
1948 #endif
1949 #ifdef Honor_FLT_ROUNDS
1950 int rounding;
1951 #endif
1952 #ifdef USE_LOCALE
1953 const char *s2;
1954 #endif
1955
1956 errno = 0;
1957 sign = nz0 = nz = 0;
1958 dval(rv) = 0.;
1959 for (s = s00;;s++)
1960 switch (*s) {
1961 case '-':
1962 sign = 1;
1963 /* no break */
1964 case '+':
1965 if (*++s)
1966 goto break2;
1967 /* no break */
1968 case 0:
1969 goto ret0;
1970 case '\t':
1971 case '\n':
1972 case '\v':
1973 case '\f':
1974 case '\r':
1975 case ' ':
1976 continue;
1977 default:
1978 goto break2;
1979 }
1980 break2:
1981 if (*s == '0') {
1982 if (s[1] == 'x' || s[1] == 'X') {
1983 static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
1984 s0 = ++s;
1985 adj = 0;
1986 aadj = 1.0;
1987 nd0 = -4;
1988
1989 if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
1990 if (*s == '0') {
1991 while (*++s == '0');
1992 s1 = strchr(hexdigit, *s);
1993 }
1994 if (s1 != NULL) {
1995 do {
1996 adj += aadj * ((s1 - hexdigit) & 15);
1997 nd0 += 4;
1998 aadj /= 16;
1999 } while (*++s && (s1 = strchr(hexdigit, *s)));
2000 }
2001
2002 if (*s == '.') {
2003 dsign = 1;
2004 if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
2005 if (nd0 < 0) {
2006 while (*s == '0') {
2007 s++;
2008 nd0 -= 4;
2009 }
2010 }
2011 for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
2012 adj += aadj * ((s1 - hexdigit) & 15);
2013 if ((aadj /= 16) == 0.0) {
2014 while (strchr(hexdigit, *++s));
2015 break;
2016 }
2017 }
2018 }
2019 else {
2020 dsign = 0;
2021 }
2022
2023 if (*s == 'P' || *s == 'p') {
2024 dsign = 0x2C - *++s; /* +: 2B, -: 2D */
2025 if (abs(dsign) == 1) s++;
2026 else dsign = 1;
2027
2028 nd = 0;
2029 c = *s;
2030 if (c < '0' || '9' < c) goto ret0;
2031 do {
2032 nd *= 10;
2033 nd += c;
2034 nd -= '0';
2035 c = *++s;
2036 /* Float("0x0."+("0"*267)+"1fp2095") */
2037 if (nd + dsign * nd0 > 2095) {
2038 while ('0' <= c && c <= '9') c = *++s;
2039 break;
2040 }
2041 } while ('0' <= c && c <= '9');
2042 nd0 += nd * dsign;
2043 }
2044 else {
2045 if (dsign) goto ret0;
2046 }
2047 dval(rv) = ldexp(adj, nd0);
2048 goto ret;
2049 }
2050 nz0 = 1;
2051 while (*++s == '0') ;
2052 if (!*s)
2053 goto ret;
2054 }
2055 s0 = s;
2056 y = z = 0;
2057 for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
2058 if (nd < 9)
2059 y = 10*y + c - '0';
2060 else if (nd < 16)
2061 z = 10*z + c - '0';
2062 nd0 = nd;
2063 #ifdef USE_LOCALE
2064 s1 = localeconv()->decimal_point;
2065 if (c == *s1) {
2066 c = '.';
2067 if (*++s1) {
2068 s2 = s;
2069 for (;;) {
2070 if (*++s2 != *s1) {
2071 c = 0;
2072 break;
2073 }
2074 if (!*++s1) {
2075 s = s2;
2076 break;
2077 }
2078 }
2079 }
2080 }
2081 #endif
2082 if (c == '.') {
2083 if (!ISDIGIT(s[1]))
2084 goto dig_done;
2085 c = *++s;
2086 if (!nd) {
2087 for (; c == '0'; c = *++s)
2088 nz++;
2089 if (c > '0' && c <= '9') {
2090 s0 = s;
2091 nf += nz;
2092 nz = 0;
2093 goto have_dig;
2094 }
2095 goto dig_done;
2096 }
2097 for (; c >= '0' && c <= '9'; c = *++s) {
2098 have_dig:
2099 nz++;
2100 if (c -= '0') {
2101 nf += nz;
2102 for (i = 1; i < nz; i++)
2103 if (nd++ < 9)
2104 y *= 10;
2105 else if (nd <= DBL_DIG + 1)
2106 z *= 10;
2107 if (nd++ < 9)
2108 y = 10*y + c;
2109 else if (nd <= DBL_DIG + 1)
2110 z = 10*z + c;
2111 nz = 0;
2112 }
2113 }
2114 }
2115 dig_done:
2116 e = 0;
2117 if (c == 'e' || c == 'E') {
2118 if (!nd && !nz && !nz0) {
2119 goto ret0;
2120 }
2121 s00 = s;
2122 esign = 0;
2123 switch (c = *++s) {
2124 case '-':
2125 esign = 1;
2126 case '+':
2127 c = *++s;
2128 }
2129 if (c >= '0' && c <= '9') {
2130 while (c == '0')
2131 c = *++s;
2132 if (c > '0' && c <= '9') {
2133 L = c - '0';
2134 s1 = s;
2135 while ((c = *++s) >= '0' && c <= '9')
2136 L = 10*L + c - '0';
2137 if (s - s1 > 8 || L > 19999)
2138 /* Avoid confusion from exponents
2139 * so large that e might overflow.
2140 */
2141 e = 19999; /* safe for 16 bit ints */
2142 else
2143 e = (int)L;
2144 if (esign)
2145 e = -e;
2146 }
2147 else
2148 e = 0;
2149 }
2150 else
2151 s = s00;
2152 }
2153 if (!nd) {
2154 if (!nz && !nz0) {
2155 #ifdef INFNAN_CHECK
2156 /* Check for Nan and Infinity */
2157 switch (c) {
2158 case 'i':
2159 case 'I':
2160 if (match(&s,"nf")) {
2161 --s;
2162 if (!match(&s,"inity"))
2163 ++s;
2164 word0(rv) = 0x7ff00000;
2165 word1(rv) = 0;
2166 goto ret;
2167 }
2168 break;
2169 case 'n':
2170 case 'N':
2171 if (match(&s, "an")) {
2172 word0(rv) = NAN_WORD0;
2173 word1(rv) = NAN_WORD1;
2174 #ifndef No_Hex_NaN
2175 if (*s == '(') /*)*/
2176 hexnan(&rv, &s);
2177 #endif
2178 goto ret;
2179 }
2180 }
2181 #endif /* INFNAN_CHECK */
2182 ret0:
2183 s = s00;
2184 sign = 0;
2185 }
2186 goto ret;
2187 }
2188 e1 = e -= nf;
2189
2190 /* Now we have nd0 digits, starting at s0, followed by a
2191 * decimal point, followed by nd-nd0 digits. The number we're
2192 * after is the integer represented by those digits times
2193 * 10**e */
2194
2195 if (!nd0)
2196 nd0 = nd;
2197 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
2198 dval(rv) = y;
2199 if (k > 9) {
2200 #ifdef SET_INEXACT
2201 if (k > DBL_DIG)
2202 oldinexact = get_inexact();
2203 #endif
2204 dval(rv) = tens[k - 9] * dval(rv) + z;
2205 }
2206 bd0 = bb = bd = bs = delta = 0;
2207 if (nd <= DBL_DIG
2208 #ifndef RND_PRODQUOT
2209 #ifndef Honor_FLT_ROUNDS
2210 && Flt_Rounds == 1
2211 #endif
2212 #endif
2213 ) {
2214 if (!e)
2215 goto ret;
2216 if (e > 0) {
2217 if (e <= Ten_pmax) {
2218 #ifdef VAX
2219 goto vax_ovfl_check;
2220 #else
2221 #ifdef Honor_FLT_ROUNDS
2222 /* round correctly FLT_ROUNDS = 2 or 3 */
2223 if (sign) {
2224 dval(rv) = -dval(rv);
2225 sign = 0;
2226 }
2227 #endif
2228 /* rv = */ rounded_product(dval(rv), tens[e]);
2229 goto ret;
2230 #endif
2231 }
2232 i = DBL_DIG - nd;
2233 if (e <= Ten_pmax + i) {
2234 /* A fancier test would sometimes let us do
2235 * this for larger i values.
2236 */
2237 #ifdef Honor_FLT_ROUNDS
2238 /* round correctly FLT_ROUNDS = 2 or 3 */
2239 if (sign) {
2240 dval(rv) = -dval(rv);
2241 sign = 0;
2242 }
2243 #endif
2244 e -= i;
2245 dval(rv) *= tens[i];
2246 #ifdef VAX
2247 /* VAX exponent range is so narrow we must
2248 * worry about overflow here...
2249 */
2250 vax_ovfl_check:
2251 word0(rv) -= P*Exp_msk1;
2252 /* rv = */ rounded_product(dval(rv), tens[e]);
2253 if ((word0(rv) & Exp_mask)
2254 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
2255 goto ovfl;
2256 word0(rv) += P*Exp_msk1;
2257 #else
2258 /* rv = */ rounded_product(dval(rv), tens[e]);
2259 #endif
2260 goto ret;
2261 }
2262 }
2263 #ifndef Inaccurate_Divide
2264 else if (e >= -Ten_pmax) {
2265 #ifdef Honor_FLT_ROUNDS
2266 /* round correctly FLT_ROUNDS = 2 or 3 */
2267 if (sign) {
2268 dval(rv) = -dval(rv);
2269 sign = 0;
2270 }
2271 #endif
2272 /* rv = */ rounded_quotient(dval(rv), tens[-e]);
2273 goto ret;
2274 }
2275 #endif
2276 }
2277 e1 += nd - k;
2278
2279 #ifdef IEEE_Arith
2280 #ifdef SET_INEXACT
2281 inexact = 1;
2282 if (k <= DBL_DIG)
2283 oldinexact = get_inexact();
2284 #endif
2285 #ifdef Avoid_Underflow
2286 scale = 0;
2287 #endif
2288 #ifdef Honor_FLT_ROUNDS
2289 if ((rounding = Flt_Rounds) >= 2) {
2290 if (sign)
2291 rounding = rounding == 2 ? 0 : 2;
2292 else
2293 if (rounding != 2)
2294 rounding = 0;
2295 }
2296 #endif
2297 #endif /*IEEE_Arith*/
2298
2299 /* Get starting approximation = rv * 10**e1 */
2300
2301 if (e1 > 0) {
2302 if ((i = e1 & 15) != 0)
2303 dval(rv) *= tens[i];
2304 if (e1 &= ~15) {
2305 if (e1 > DBL_MAX_10_EXP) {
2306 ovfl:
2307 #ifndef NO_ERRNO
2308 errno = ERANGE;
2309 #endif
2310 /* Can't trust HUGE_VAL */
2311 #ifdef IEEE_Arith
2312 #ifdef Honor_FLT_ROUNDS
2313 switch (rounding) {
2314 case 0: /* toward 0 */
2315 case 3: /* toward -infinity */
2316 word0(rv) = Big0;
2317 word1(rv) = Big1;
2318 break;
2319 default:
2320 word0(rv) = Exp_mask;
2321 word1(rv) = 0;
2322 }
2323 #else /*Honor_FLT_ROUNDS*/
2324 word0(rv) = Exp_mask;
2325 word1(rv) = 0;
2326 #endif /*Honor_FLT_ROUNDS*/
2327 #ifdef SET_INEXACT
2328 /* set overflow bit */
2329 dval(rv0) = 1e300;
2330 dval(rv0) *= dval(rv0);
2331 #endif
2332 #else /*IEEE_Arith*/
2333 word0(rv) = Big0;
2334 word1(rv) = Big1;
2335 #endif /*IEEE_Arith*/
2336 if (bd0)
2337 goto retfree;
2338 goto ret;
2339 }
2340 e1 >>= 4;
2341 for (j = 0; e1 > 1; j++, e1 >>= 1)
2342 if (e1 & 1)
2343 dval(rv) *= bigtens[j];
2344 /* The last multiplication could overflow. */
2345 word0(rv) -= P*Exp_msk1;
2346 dval(rv) *= bigtens[j];
2347 if ((z = word0(rv) & Exp_mask)
2348 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
2349 goto ovfl;
2350 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
2351 /* set to largest number */
2352 /* (Can't trust DBL_MAX) */
2353 word0(rv) = Big0;
2354 word1(rv) = Big1;
2355 }
2356 else
2357 word0(rv) += P*Exp_msk1;
2358 }
2359 }
2360 else if (e1 < 0) {
2361 e1 = -e1;
2362 if ((i = e1 & 15) != 0)
2363 dval(rv) /= tens[i];
2364 if (e1 >>= 4) {
2365 if (e1 >= 1 << n_bigtens)
2366 goto undfl;
2367 #ifdef Avoid_Underflow
2368 if (e1 & Scale_Bit)
2369 scale = 2*P;
2370 for (j = 0; e1 > 0; j++, e1 >>= 1)
2371 if (e1 & 1)
2372 dval(rv) *= tinytens[j];
2373 if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
2374 >> Exp_shift)) > 0) {
2375 /* scaled rv is denormal; zap j low bits */
2376 if (j >= 32) {
2377 word1(rv) = 0;
2378 if (j >= 53)
2379 word0(rv) = (P+2)*Exp_msk1;
2380 else
2381 word0(rv) &= 0xffffffff << (j-32);
2382 }
2383 else
2384 word1(rv) &= 0xffffffff << j;
2385 }
2386 #else
2387 for (j = 0; e1 > 1; j++, e1 >>= 1)
2388 if (e1 & 1)
2389 dval(rv) *= tinytens[j];
2390 /* The last multiplication could underflow. */
2391 dval(rv0) = dval(rv);
2392 dval(rv) *= tinytens[j];
2393 if (!dval(rv)) {
2394 dval(rv) = 2.*dval(rv0);
2395 dval(rv) *= tinytens[j];
2396 #endif
2397 if (!dval(rv)) {
2398 undfl:
2399 dval(rv) = 0.;
2400 #ifndef NO_ERRNO
2401 errno = ERANGE;
2402 #endif
2403 if (bd0)
2404 goto retfree;
2405 goto ret;
2406 }
2407 #ifndef Avoid_Underflow
2408 word0(rv) = Tiny0;
2409 word1(rv) = Tiny1;
2410 /* The refinement below will clean
2411 * this approximation up.
2412 */
2413 }
2414 #endif
2415 }
2416 }
2417
2418 /* Now the hard part -- adjusting rv to the correct value.*/
2419
2420 /* Put digits into bd: true value = bd * 10^e */
2421
2422 bd0 = s2b(s0, nd0, nd, y);
2423
2424 for (;;) {
2425 bd = Balloc(bd0->k);
2426 Bcopy(bd, bd0);
2427 bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
2428 bs = i2b(1);
2429
2430 if (e >= 0) {
2431 bb2 = bb5 = 0;
2432 bd2 = bd5 = e;
2433 }
2434 else {
2435 bb2 = bb5 = -e;
2436 bd2 = bd5 = 0;
2437 }
2438 if (bbe >= 0)
2439 bb2 += bbe;
2440 else
2441 bd2 -= bbe;
2442 bs2 = bb2;
2443 #ifdef Honor_FLT_ROUNDS
2444 if (rounding != 1)
2445 bs2++;
2446 #endif
2447 #ifdef Avoid_Underflow
2448 j = bbe - scale;
2449 i = j + bbbits - 1; /* logb(rv) */
2450 if (i < Emin) /* denormal */
2451 j += P - Emin;
2452 else
2453 j = P + 1 - bbbits;
2454 #else /*Avoid_Underflow*/
2455 #ifdef Sudden_Underflow
2456 #ifdef IBM
2457 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
2458 #else
2459 j = P + 1 - bbbits;
2460 #endif
2461 #else /*Sudden_Underflow*/
2462 j = bbe;
2463 i = j + bbbits - 1; /* logb(rv) */
2464 if (i < Emin) /* denormal */
2465 j += P - Emin;
2466 else
2467 j = P + 1 - bbbits;
2468 #endif /*Sudden_Underflow*/
2469 #endif /*Avoid_Underflow*/
2470 bb2 += j;
2471 bd2 += j;
2472 #ifdef Avoid_Underflow
2473 bd2 += scale;
2474 #endif
2475 i = bb2 < bd2 ? bb2 : bd2;
2476 if (i > bs2)
2477 i = bs2;
2478 if (i > 0) {
2479 bb2 -= i;
2480 bd2 -= i;
2481 bs2 -= i;
2482 }
2483 if (bb5 > 0) {
2484 bs = pow5mult(bs, bb5);
2485 bb1 = mult(bs, bb);
2486 Bfree(bb);
2487 bb = bb1;
2488 }
2489 if (bb2 > 0)
2490 bb = lshift(bb, bb2);
2491 if (bd5 > 0)
2492 bd = pow5mult(bd, bd5);
2493 if (bd2 > 0)
2494 bd = lshift(bd, bd2);
2495 if (bs2 > 0)
2496 bs = lshift(bs, bs2);
2497 delta = diff(bb, bd);
2498 dsign = delta->sign;
2499 delta->sign = 0;
2500 i = cmp(delta, bs);
2501 #ifdef Honor_FLT_ROUNDS
2502 if (rounding != 1) {
2503 if (i < 0) {
2504 /* Error is less than an ulp */
2505 if (!delta->x[0] && delta->wds <= 1) {
2506 /* exact */
2507 #ifdef SET_INEXACT
2508 inexact = 0;
2509 #endif
2510 break;
2511 }
2512 if (rounding) {
2513 if (dsign) {
2514 adj = 1.;
2515 goto apply_adj;
2516 }
2517 }
2518 else if (!dsign) {
2519 adj = -1.;
2520 if (!word1(rv)
2521 && !(word0(rv) & Frac_mask)) {
2522 y = word0(rv) & Exp_mask;
2523 #ifdef Avoid_Underflow
2524 if (!scale || y > 2*P*Exp_msk1)
2525 #else
2526 if (y)
2527 #endif
2528 {
2529 delta = lshift(delta,Log2P);
2530 if (cmp(delta, bs) <= 0)
2531 adj = -0.5;
2532 }
2533 }
2534 apply_adj:
2535 #ifdef Avoid_Underflow
2536 if (scale && (y = word0(rv) & Exp_mask)
2537 <= 2*P*Exp_msk1)
2538 word0(adj) += (2*P+1)*Exp_msk1 - y;
2539 #else
2540 #ifdef Sudden_Underflow
2541 if ((word0(rv) & Exp_mask) <=
2542 P*Exp_msk1) {
2543 word0(rv) += P*Exp_msk1;
2544 dval(rv) += adj*ulp(dval(rv));
2545 word0(rv) -= P*Exp_msk1;
2546 }
2547 else
2548 #endif /*Sudden_Underflow*/
2549 #endif /*Avoid_Underflow*/
2550 dval(rv) += adj*ulp(dval(rv));
2551 }
2552 break;
2553 }
2554 adj = ratio(delta, bs);
2555 if (adj < 1.)
2556 adj = 1.;
2557 if (adj <= 0x7ffffffe) {
2558 /* adj = rounding ? ceil(adj) : floor(adj); */
2559 y = adj;
2560 if (y != adj) {
2561 if (!((rounding>>1) ^ dsign))
2562 y++;
2563 adj = y;
2564 }
2565 }
2566 #ifdef Avoid_Underflow
2567 if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2568 word0(adj) += (2*P+1)*Exp_msk1 - y;
2569 #else
2570 #ifdef Sudden_Underflow
2571 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2572 word0(rv) += P*Exp_msk1;
2573 adj *= ulp(dval(rv));
2574 if (dsign)
2575 dval(rv) += adj;
2576 else
2577 dval(rv) -= adj;
2578 word0(rv) -= P*Exp_msk1;
2579 goto cont;
2580 }
2581 #endif /*Sudden_Underflow*/
2582 #endif /*Avoid_Underflow*/
2583 adj *= ulp(dval(rv));
2584 if (dsign)
2585 dval(rv) += adj;
2586 else
2587 dval(rv) -= adj;
2588 goto cont;
2589 }
2590 #endif /*Honor_FLT_ROUNDS*/
2591
2592 if (i < 0) {
2593 /* Error is less than half an ulp -- check for
2594 * special case of mantissa a power of two.
2595 */
2596 if (dsign || word1(rv) || word0(rv) & Bndry_mask
2597 #ifdef IEEE_Arith
2598 #ifdef Avoid_Underflow
2599 || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
2600 #else
2601 || (word0(rv) & Exp_mask) <= Exp_msk1
2602 #endif
2603 #endif
2604 ) {
2605 #ifdef SET_INEXACT
2606 if (!delta->x[0] && delta->wds <= 1)
2607 inexact = 0;
2608 #endif
2609 break;
2610 }
2611 if (!delta->x[0] && delta->wds <= 1) {
2612 /* exact result */
2613 #ifdef SET_INEXACT
2614 inexact = 0;
2615 #endif
2616 break;
2617 }
2618 delta = lshift(delta,Log2P);
2619 if (cmp(delta, bs) > 0)
2620 goto drop_down;
2621 break;
2622 }
2623 if (i == 0) {
2624 /* exactly half-way between */
2625 if (dsign) {
2626 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
2627 && word1(rv) == (
2628 #ifdef Avoid_Underflow
2629 (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
2630 ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
2631 #endif
2632 0xffffffff)) {
2633 /*boundary case -- increment exponent*/
2634 word0(rv) = (word0(rv) & Exp_mask)
2635 + Exp_msk1
2636 #ifdef IBM
2637 | Exp_msk1 >> 4
2638 #endif
2639 ;
2640 word1(rv) = 0;
2641 #ifdef Avoid_Underflow
2642 dsign = 0;
2643 #endif
2644 break;
2645 }
2646 }
2647 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
2648 drop_down:
2649 /* boundary case -- decrement exponent */
2650 #ifdef Sudden_Underflow /*{{*/
2651 L = word0(rv) & Exp_mask;
2652 #ifdef IBM
2653 if (L < Exp_msk1)
2654 #else
2655 #ifdef Avoid_Underflow
2656 if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
2657 #else
2658 if (L <= Exp_msk1)
2659 #endif /*Avoid_Underflow*/
2660 #endif /*IBM*/
2661 goto undfl;
2662 L -= Exp_msk1;
2663 #else /*Sudden_Underflow}{*/
2664 #ifdef Avoid_Underflow
2665 if (scale) {
2666 L = word0(rv) & Exp_mask;
2667 if (L <= (2*P+1)*Exp_msk1) {
2668 if (L > (P+2)*Exp_msk1)
2669 /* round even ==> */
2670 /* accept rv */
2671 break;
2672 /* rv = smallest denormal */
2673 goto undfl;
2674 }
2675 }
2676 #endif /*Avoid_Underflow*/
2677 L = (word0(rv) & Exp_mask) - Exp_msk1;
2678 #endif /*Sudden_Underflow}}*/
2679 word0(rv) = L | Bndry_mask1;
2680 word1(rv) = 0xffffffff;
2681 #ifdef IBM
2682 goto cont;
2683 #else
2684 break;
2685 #endif
2686 }
2687 #ifndef ROUND_BIASED
2688 if (!(word1(rv) & LSB))
2689 break;
2690 #endif
2691 if (dsign)
2692 dval(rv) += ulp(dval(rv));
2693 #ifndef ROUND_BIASED
2694 else {
2695 dval(rv) -= ulp(dval(rv));
2696 #ifndef Sudden_Underflow
2697 if (!dval(rv))
2698 goto undfl;
2699 #endif
2700 }
2701 #ifdef Avoid_Underflow
2702 dsign = 1 - dsign;
2703 #endif
2704 #endif
2705 break;
2706 }
2707 if ((aadj = ratio(delta, bs)) <= 2.) {
2708 if (dsign)
2709 aadj = dval(aadj1) = 1.;
2710 else if (word1(rv) || word0(rv) & Bndry_mask) {
2711 #ifndef Sudden_Underflow
2712 if (word1(rv) == Tiny1 && !word0(rv))
2713 goto undfl;
2714 #endif
2715 aadj = 1.;
2716 dval(aadj1) = -1.;
2717 }
2718 else {
2719 /* special case -- power of FLT_RADIX to be */
2720 /* rounded down... */
2721
2722 if (aadj < 2./FLT_RADIX)
2723 aadj = 1./FLT_RADIX;
2724 else
2725 aadj *= 0.5;
2726 dval(aadj1) = -aadj;
2727 }
2728 }
2729 else {
2730 aadj *= 0.5;
2731 dval(aadj1) = dsign ? aadj : -aadj;
2732 #ifdef Check_FLT_ROUNDS
2733 switch (Rounding) {
2734 case 2: /* towards +infinity */
2735 dval(aadj1) -= 0.5;
2736 break;
2737 case 0: /* towards 0 */
2738 case 3: /* towards -infinity */
2739 dval(aadj1) += 0.5;
2740 }
2741 #else
2742 if (Flt_Rounds == 0)
2743 dval(aadj1) += 0.5;
2744 #endif /*Check_FLT_ROUNDS*/
2745 }
2746 y = word0(rv) & Exp_mask;
2747
2748 /* Check for overflow */
2749
2750 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
2751 dval(rv0) = dval(rv);
2752 word0(rv) -= P*Exp_msk1;
2753 adj = dval(aadj1) * ulp(dval(rv));
2754 dval(rv) += adj;
2755 if ((word0(rv) & Exp_mask) >=
2756 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
2757 if (word0(rv0) == Big0 && word1(rv0) == Big1)
2758 goto ovfl;
2759 word0(rv) = Big0;
2760 word1(rv) = Big1;
2761 goto cont;
2762 }
2763 else
2764 word0(rv) += P*Exp_msk1;
2765 }
2766 else {
2767 #ifdef Avoid_Underflow
2768 if (scale && y <= 2*P*Exp_msk1) {
2769 if (aadj <= 0x7fffffff) {
2770 if ((z = (int)aadj) <= 0)
2771 z = 1;
2772 aadj = z;
2773 dval(aadj1) = dsign ? aadj : -aadj;
2774 }
2775 word0(aadj1) += (2*P+1)*Exp_msk1 - y;
2776 }
2777 adj = dval(aadj1) * ulp(dval(rv));
2778 dval(rv) += adj;
2779 #else
2780 #ifdef Sudden_Underflow
2781 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
2782 dval(rv0) = dval(rv);
2783 word0(rv) += P*Exp_msk1;
2784 adj = dval(aadj1) * ulp(dval(rv));
2785 dval(rv) += adj;
2786 #ifdef IBM
2787 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
2788 #else
2789 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
2790 #endif
2791 {
2792 if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
2793 goto undfl;
2794 word0(rv) = Tiny0;
2795 word1(rv) = Tiny1;
2796 goto cont;
2797 }
2798 else
2799 word0(rv) -= P*Exp_msk1;
2800 }
2801 else {
2802 adj = dval(aadj1) * ulp(dval(rv));
2803 dval(rv) += adj;
2804 }
2805 #else /*Sudden_Underflow*/
2806 /* Compute adj so that the IEEE rounding rules will
2807 * correctly round rv + adj in some half-way cases.
2808 * If rv * ulp(rv) is denormalized (i.e.,
2809 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
2810 * trouble from bits lost to denormalization;
2811 * example: 1.2e-307 .
2812 */
2813 if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
2814 dval(aadj1) = (double)(int)(aadj + 0.5);
2815 if (!dsign)
2816 dval(aadj1) = -dval(aadj1);
2817 }
2818 adj = dval(aadj1) * ulp(dval(rv));
2819 dval(rv) += adj;
2820 #endif /*Sudden_Underflow*/
2821 #endif /*Avoid_Underflow*/
2822 }
2823 z = word0(rv) & Exp_mask;
2824 #ifndef SET_INEXACT
2825 #ifdef Avoid_Underflow
2826 if (!scale)
2827 #endif
2828 if (y == z) {
2829 /* Can we stop now? */
2830 L = (Long)aadj;
2831 aadj -= L;
2832 /* The tolerances below are conservative. */
2833 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
2834 if (aadj < .4999999 || aadj > .5000001)
2835 break;
2836 }
2837 else if (aadj < .4999999/FLT_RADIX)
2838 break;
2839 }
2840 #endif
2841 cont:
2842 Bfree(bb);
2843 Bfree(bd);
2844 Bfree(bs);
2845 Bfree(delta);
2846 }
2847 #ifdef SET_INEXACT
2848 if (inexact) {
2849 if (!oldinexact) {
2850 word0(rv0) = Exp_1 + (70 << Exp_shift);
2851 word1(rv0) = 0;
2852 dval(rv0) += 1.;
2853 }
2854 }
2855 else if (!oldinexact)
2856 clear_inexact();
2857 #endif
2858 #ifdef Avoid_Underflow
2859 if (scale) {
2860 word0(rv0) = Exp_1 - 2*P*Exp_msk1;
2861 word1(rv0) = 0;
2862 dval(rv) *= dval(rv0);
2863 #ifndef NO_ERRNO
2864 /* try to avoid the bug of testing an 8087 register value */
2865 if (word0(rv) == 0 && word1(rv) == 0)
2866 errno = ERANGE;
2867 #endif
2868 }
2869 #endif /* Avoid_Underflow */
2870 #ifdef SET_INEXACT
2871 if (inexact && !(word0(rv) & Exp_mask)) {
2872 /* set underflow bit */
2873 dval(rv0) = 1e-300;
2874 dval(rv0) *= dval(rv0);
2875 }
2876 #endif
2877 retfree:
2878 Bfree(bb);
2879 Bfree(bd);
2880 Bfree(bs);
2881 Bfree(bd0);
2882 Bfree(delta);
2883 ret:
2884 if (se)
2885 *se = (char *)s;
2886 return sign ? -dval(rv) : dval(rv);
2887 }
2888
2889 static int
2890 quorem(Bigint *b, Bigint *S)
2891 {
2892 int n;
2893 ULong *bx, *bxe, q, *sx, *sxe;
2894 #ifdef ULLong
2895 ULLong borrow, carry, y, ys;
2896 #else
2897 ULong borrow, carry, y, ys;
2898 #ifdef Pack_32
2899 ULong si, z, zs;
2900 #endif
2901 #endif
2902
2903 n = S->wds;
2904 #ifdef DEBUG
2905 /*debug*/ if (b->wds > n)
2906 /*debug*/ Bug("oversize b in quorem");
2907 #endif
2908 if (b->wds < n)
2909 return 0;
2910 sx = S->x;
2911 sxe = sx + --n;
2912 bx = b->x;
2913 bxe = bx + n;
2914 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
2915 #ifdef DEBUG
2916 /*debug*/ if (q > 9)
2917 /*debug*/ Bug("oversized quotient in quorem");
2918 #endif
2919 if (q) {
2920 borrow = 0;
2921 carry = 0;
2922 do {
2923 #ifdef ULLong
2924 ys = *sx++ * (ULLong)q + carry;
2925 carry = ys >> 32;
2926 y = *bx - (ys & FFFFFFFF) - borrow;
2927 borrow = y >> 32 & (ULong)1;
2928 *bx++ = (ULong)(y & FFFFFFFF);
2929 #else
2930 #ifdef Pack_32
2931 si = *sx++;
2932 ys = (si & 0xffff) * q + carry;
2933 zs = (si >> 16) * q + (ys >> 16);
2934 carry = zs >> 16;
2935 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2936 borrow = (y & 0x10000) >> 16;
2937 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2938 borrow = (z & 0x10000) >> 16;
2939 Storeinc(bx, z, y);
2940 #else
2941 ys = *sx++ * q + carry;
2942 carry = ys >> 16;
2943 y = *bx - (ys & 0xffff) - borrow;
2944 borrow = (y & 0x10000) >> 16;
2945 *bx++ = y & 0xffff;
2946 #endif
2947 #endif
2948 } while (sx <= sxe);
2949 if (!*bxe) {
2950 bx = b->x;
2951 while (--bxe > bx && !*bxe)
2952 --n;
2953 b->wds = n;
2954 }
2955 }
2956 if (cmp(b, S) >= 0) {
2957 q++;
2958 borrow = 0;
2959 carry = 0;
2960 bx = b->x;
2961 sx = S->x;
2962 do {
2963 #ifdef ULLong
2964 ys = *sx++ + carry;
2965 carry = ys >> 32;
2966 y = *bx - (ys & FFFFFFFF) - borrow;
2967 borrow = y >> 32 & (ULong)1;
2968 *bx++ = (ULong)(y & FFFFFFFF);
2969 #else
2970 #ifdef Pack_32
2971 si = *sx++;
2972 ys = (si & 0xffff) + carry;
2973 zs = (si >> 16) + (ys >> 16);
2974 carry = zs >> 16;
2975 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
2976 borrow = (y & 0x10000) >> 16;
2977 z = (*bx >> 16) - (zs & 0xffff) - borrow;
2978 borrow = (z & 0x10000) >> 16;
2979 Storeinc(bx, z, y);
2980 #else
2981 ys = *sx++ + carry;
2982 carry = ys >> 16;
2983 y = *bx - (ys & 0xffff) - borrow;
2984 borrow = (y & 0x10000) >> 16;
2985 *bx++ = y & 0xffff;
2986 #endif
2987 #endif
2988 } while (sx <= sxe);
2989 bx = b->x;
2990 bxe = bx + n;
2991 if (!*bxe) {
2992 while (--bxe > bx && !*bxe)
2993 --n;
2994 b->wds = n;
2995 }
2996 }
2997 return q;
2998 }
2999
3000 #ifndef MULTIPLE_THREADS
3001 static char *dtoa_result;
3002 #endif
3003
3004 #ifndef MULTIPLE_THREADS
3005 static char *
3006 rv_alloc(int i)
3007 {
3008 return dtoa_result = xmalloc(i);
3009 }
3010 #else
3011 #define rv_alloc(i) xmalloc(i)
3012 #endif
3013
3014 static char *
3015 nrv_alloc(const char *s, char **rve, size_t n)
3016 {
3017 char *rv, *t;
3018
3019 t = rv = rv_alloc(n);
3020 while ((*t = *s++) != 0) t++;
3021 if (rve)
3022 *rve = t;
3023 return rv;
3024 }
3025
3026 #define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
3027
3028 #ifndef MULTIPLE_THREADS
3029 /* freedtoa(s) must be used to free values s returned by dtoa
3030 * when MULTIPLE_THREADS is #defined. It should be used in all cases,
3031 * but for consistency with earlier versions of dtoa, it is optional
3032 * when MULTIPLE_THREADS is not defined.
3033 */
3034
3035 static void
3036 freedtoa(char *s)
3037 {
3038 xfree(s);
3039 }
3040 #endif
3041
3042 static const char INFSTR[] = "Infinity";
3043 static const char NANSTR[] = "NaN";
3044 static const char ZEROSTR[] = "0";
3045
3046 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
3047 *
3048 * Inspired by "How to Print Floating-Point Numbers Accurately" by
3049 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
3050 *
3051 * Modifications:
3052 * 1. Rather than iterating, we use a simple numeric overestimate
3053 * to determine k = floor(log10(d)). We scale relevant
3054 * quantities using O(log2(k)) rather than O(k) multiplications.
3055 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
3056 * try to generate digits strictly left to right. Instead, we
3057 * compute with fewer bits and propagate the carry if necessary
3058 * when rounding the final digit up. This is often faster.
3059 * 3. Under the assumption that input will be rounded nearest,
3060 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
3061 * That is, we allow equality in stopping tests when the
3062 * round-nearest rule will give the same floating-point value
3063 * as would satisfaction of the stopping test with strict
3064 * inequality.
3065 * 4. We remove common factors of powers of 2 from relevant
3066 * quantities.
3067 * 5. When converting floating-point integers less than 1e16,
3068 * we use floating-point arithmetic rather than resorting
3069 * to multiple-precision integers.
3070 * 6. When asked to produce fewer than 15 digits, we first try
3071 * to get by with floating-point arithmetic; we resort to
3072 * multiple-precision integer arithmetic only if we cannot
3073 * guarantee that the floating-point calculation has given
3074 * the correctly rounded result. For k requested digits and
3075 * "uniformly" distributed input, the probability is
3076 * something like 10^(k-15) that we must resort to the Long
3077 * calculation.
3078 */
3079
3080 char *
3081 ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
3082 {
3083 /* Arguments ndigits, decpt, sign are similar to those
3084 of ecvt and fcvt; trailing zeros are suppressed from
3085 the returned string. If not null, *rve is set to point
3086 to the end of the return value. If d is +-Infinity or NaN,
3087 then *decpt is set to 9999.
3088
3089 mode:
3090 0 ==> shortest string that yields d when read in
3091 and rounded to nearest.
3092 1 ==> like 0, but with Steele & White stopping rule;
3093 e.g. with IEEE P754 arithmetic , mode 0 gives
3094 1e23 whereas mode 1 gives 9.999999999999999e22.
3095 2 ==> max(1,ndigits) significant digits. This gives a
3096 return value similar to that of ecvt, except
3097 that trailing zeros are suppressed.
3098 3 ==> through ndigits past the decimal point. This
3099 gives a return value similar to that from fcvt,
3100 except that trailing zeros are suppressed, and
3101 ndigits can be negative.
3102 4,5 ==> similar to 2 and 3, respectively, but (in
3103 round-nearest mode) with the tests of mode 0 to
3104 possibly return a shorter string that rounds to d.
3105 With IEEE arithmetic and compilation with
3106 -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
3107 as modes 2 and 3 when FLT_ROUNDS != 1.
3108 6-9 ==> Debugging modes similar to mode - 4: don't try
3109 fast floating-point estimate (if applicable).
3110
3111 Values of mode other than 0-9 are treated as mode 0.
3112
3113 Sufficient space is allocated to the return value
3114 to hold the suppressed trailing zeros.
3115 */
3116
3117 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
3118 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
3119 spec_case, try_quick;
3120 Long L;
3121 #ifndef Sudden_Underflow
3122 int denorm;
3123 ULong x;
3124 #endif
3125 Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
3126 double ds;
3127 double_u d, d2, eps;
3128 char *s, *s0;
3129 #ifdef Honor_FLT_ROUNDS
3130 int rounding;
3131 #endif
3132 #ifdef SET_INEXACT
3133 int inexact, oldinexact;
3134 #endif
3135
3136 dval(d) = d_;
3137
3138 #ifndef MULTIPLE_THREADS
3139 if (dtoa_result) {
3140 freedtoa(dtoa_result);
3141 dtoa_result = 0;
3142 }
3143 #endif
3144
3145 if (word0(d) & Sign_bit) {
3146 /* set sign for everything, including 0's and NaNs */
3147 *sign = 1;
3148 word0(d) &= ~Sign_bit; /* clear sign bit */
3149 }
3150 else
3151 *sign = 0;
3152
3153 #if defined(IEEE_Arith) + defined(VAX)
3154 #ifdef IEEE_Arith
3155 if ((word0(d) & Exp_mask) == Exp_mask)
3156 #else
3157 if (word0(d) == 0x8000)
3158 #endif
3159 {
3160 /* Infinity or NaN */
3161 *decpt = 9999;
3162 #ifdef IEEE_Arith
3163 if (!word1(d) && !(word0(d) & 0xfffff))
3164 return rv_strdup(INFSTR, rve);
3165 #endif
3166 return rv_strdup(NANSTR, rve);
3167 }
3168 #endif
3169 #ifdef IBM
3170 dval(d) += 0; /* normalize */
3171 #endif
3172 if (!dval(d)) {
3173 *decpt = 1;
3174 return rv_strdup(ZEROSTR, rve);
3175 }
3176
3177 #ifdef SET_INEXACT
3178 try_quick = oldinexact = get_inexact();
3179 inexact = 1;
3180 #endif
3181 #ifdef Honor_FLT_ROUNDS
3182 if ((rounding = Flt_Rounds) >= 2) {
3183 if (*sign)
3184 rounding = rounding == 2 ? 0 : 2;
3185 else
3186 if (rounding != 2)
3187 rounding = 0;
3188 }
3189 #endif
3190
3191 b = d2b(dval(d), &be, &bbits);
3192 #ifdef Sudden_Underflow
3193 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
3194 #else
3195 if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
3196 #endif
3197 dval(d2) = dval(d);
3198 word0(d2) &= Frac_mask1;
3199 word0(d2) |= Exp_11;
3200 #ifdef IBM
3201 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
3202 dval(d2) /= 1 << j;
3203 #endif
3204
3205 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
3206 * log10(x) = log(x) / log(10)
3207 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
3208 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
3209 *
3210 * This suggests computing an approximation k to log10(d) by
3211 *
3212 * k = (i - Bias)*0.301029995663981
3213 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
3214 *
3215 * We want k to be too large rather than too small.
3216 * The error in the first-order Taylor series approximation
3217 * is in our favor, so we just round up the constant enough
3218 * to compensate for any error in the multiplication of
3219 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
3220 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
3221 * adding 1e-13 to the constant term more than suffices.
3222 * Hence we adjust the constant term to 0.1760912590558.
3223 * (We could get a more accurate k by invoking log10,
3224 * but this is probably not worthwhile.)
3225 */
3226
3227 i -= Bias;
3228 #ifdef IBM
3229 i <<= 2;
3230 i += j;
3231 #endif
3232 #ifndef Sudden_Underflow
3233 denorm = 0;
3234 }
3235 else {
3236 /* d is denormalized */
3237
3238 i = bbits + be + (Bias + (P-1) - 1);
3239 x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
3240 : word1(d) << (32 - i);
3241 dval(d2) = x;
3242 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
3243 i -= (Bias + (P-1) - 1) + 1;
3244 denorm = 1;
3245 }
3246 #endif
3247 ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
3248 k = (int)ds;
3249 if (ds < 0. && ds != k)
3250 k--; /* want k = floor(ds) */
3251 k_check = 1;
3252 if (k >= 0 && k <= Ten_pmax) {
3253 if (dval(d) < tens[k])
3254 k--;
3255 k_check = 0;
3256 }
3257 j = bbits - i - 1;
3258 if (j >= 0) {
3259 b2 = 0;
3260 s2 = j;
3261 }
3262 else {
3263 b2 = -j;
3264 s2 = 0;
3265 }
3266 if (k >= 0) {
3267 b5 = 0;
3268 s5 = k;
3269 s2 += k;
3270 }
3271 else {
3272 b2 -= k;
3273 b5 = -k;
3274 s5 = 0;
3275 }
3276 if (mode < 0 || mode > 9)
3277 mode = 0;
3278
3279 #ifndef SET_INEXACT
3280 #ifdef Check_FLT_ROUNDS
3281 try_quick = Rounding == 1;
3282 #else
3283 try_quick = 1;
3284 #endif
3285 #endif /*SET_INEXACT*/
3286
3287 if (mode > 5) {
3288 mode -= 4;
3289 try_quick = 0;
3290 }
3291 leftright = 1;
3292 ilim = ilim1 = -1;
3293 switch (mode) {
3294 case 0:
3295 case 1:
3296 i = 18;
3297 ndigits = 0;
3298 break;
3299 case 2:
3300 leftright = 0;
3301 /* no break */
3302 case 4:
3303 if (ndigits <= 0)
3304 ndigits = 1;
3305 ilim = ilim1 = i = ndigits;
3306 break;
3307 case 3:
3308 leftright = 0;
3309 /* no break */
3310 case 5:
3311 i = ndigits + k + 1;
3312 ilim = i;
3313 ilim1 = i - 1;
3314 if (i <= 0)
3315 i = 1;
3316 }
3317 s = s0 = rv_alloc(i+1);
3318
3319 #ifdef Honor_FLT_ROUNDS
3320 if (mode > 1 && rounding != 1)
3321 leftright = 0;
3322 #endif
3323
3324 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
3325
3326 /* Try to get by with floating-point arithmetic. */
3327
3328 i = 0;
3329 dval(d2) = dval(d);
3330 k0 = k;
3331 ilim0 = ilim;
3332 ieps = 2; /* conservative */
3333 if (k > 0) {
3334 ds = tens[k&0xf];
3335 j = k >> 4;
3336 if (j & Bletch) {
3337 /* prevent overflows */
3338 j &= Bletch - 1;
3339 dval(d) /= bigtens[n_bigtens-1];
3340 ieps++;
3341 }
3342 for (; j; j >>= 1, i++)
3343 if (j & 1) {
3344 ieps++;
3345 ds *= bigtens[i];
3346 }
3347 dval(d) /= ds;
3348 }
3349 else if ((j1 = -k) != 0) {
3350 dval(d) *= tens[j1 & 0xf];
3351 for (j = j1 >> 4; j; j >>= 1, i++)
3352 if (j & 1) {
3353 ieps++;
3354 dval(d) *= bigtens[i];
3355 }
3356 }
3357 if (k_check && dval(d) < 1. && ilim > 0) {
3358 if (ilim1 <= 0)
3359 goto fast_failed;
3360 ilim = ilim1;
3361 k--;
3362 dval(d) *= 10.;
3363 ieps++;
3364 }
3365 dval(eps) = ieps*dval(d) + 7.;
3366 word0(eps) -= (P-1)*Exp_msk1;
3367 if (ilim == 0) {
3368 S = mhi = 0;
3369 dval(d) -= 5.;
3370 if (dval(d) > dval(eps))
3371 goto one_digit;
3372 if (dval(d) < -dval(eps))
3373 goto no_digits;
3374 goto fast_failed;
3375 }
3376 #ifndef No_leftright
3377 if (leftright) {
3378 /* Use Steele & White method of only
3379 * generating digits needed.
3380 */
3381 dval(eps) = 0.5/tens[ilim-1] - dval(eps);
3382 for (i = 0;;) {
3383 L = (int)dval(d);
3384 dval(d) -= L;
3385 *s++ = '0' + (int)L;
3386 if (dval(d) < dval(eps))
3387 goto ret1;
3388 if (1. - dval(d) < dval(eps))
3389 goto bump_up;
3390 if (++i >= ilim)
3391 break;
3392 dval(eps) *= 10.;
3393 dval(d) *= 10.;
3394 }
3395 }
3396 else {
3397 #endif
3398 /* Generate ilim digits, then fix them up. */
3399 dval(eps) *= tens[ilim-1];
3400 for (i = 1;; i++, dval(d) *= 10.) {
3401 L = (Long)(dval(d));
3402 if (!(dval(d) -= L))
3403 ilim = i;
3404 *s++ = '0' + (int)L;
3405 if (i == ilim) {
3406 if (dval(d) > 0.5 + dval(eps))
3407 goto bump_up;
3408 else if (dval(d) < 0.5 - dval(eps)) {
3409 while (*--s == '0') ;
3410 s++;
3411 goto ret1;
3412 }
3413 break;
3414 }
3415 }
3416 #ifndef No_leftright
3417 }
3418 #endif
3419 fast_failed:
3420 s = s0;
3421 dval(d) = dval(d2);
3422 k = k0;
3423 ilim = ilim0;
3424 }
3425
3426 /* Do we have a "small" integer? */
3427
3428 if (be >= 0 && k <= Int_max) {
3429 /* Yes. */
3430 ds = tens[k];
3431 if (ndigits < 0 && ilim <= 0) {
3432 S = mhi = 0;
3433 if (ilim < 0 || dval(d) <= 5*ds)
3434 goto no_digits;
3435 goto one_digit;
3436 }
3437 for (i = 1;; i++, dval(d) *= 10.) {
3438 L = (Long)(dval(d) / ds);
3439 dval(d) -= L*ds;
3440 #ifdef Check_FLT_ROUNDS
3441 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
3442 if (dval(d) < 0) {
3443 L--;
3444 dval(d) += ds;
3445 }
3446 #endif
3447 *s++ = '0' + (int)L;
3448 if (!dval(d)) {
3449 #ifdef SET_INEXACT
3450 inexact = 0;
3451 #endif
3452 break;
3453 }
3454 if (i == ilim) {
3455 #ifdef Honor_FLT_ROUNDS
3456 if (mode > 1)
3457 switch (rounding) {
3458 case 0: goto ret1;
3459 case 2: goto bump_up;
3460 }
3461 #endif
3462 dval(d) += dval(d);
3463 if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
3464 bump_up:
3465 while (*--s == '9')
3466 if (s == s0) {
3467 k++;
3468 *s = '0';
3469 break;
3470 }
3471 ++*s++;
3472 }
3473 break;
3474 }
3475 }
3476 goto ret1;
3477 }
3478
3479 m2 = b2;
3480 m5 = b5;
3481 if (leftright) {
3482 i =
3483 #ifndef Sudden_Underflow
3484 denorm ? be + (Bias + (P-1) - 1 + 1) :
3485 #endif
3486 #ifdef IBM
3487 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
3488 #else
3489 1 + P - bbits;
3490 #endif
3491 b2 += i;
3492 s2 += i;
3493 mhi = i2b(1);
3494 }
3495 if (m2 > 0 && s2 > 0) {
3496 i = m2 < s2 ? m2 : s2;
3497 b2 -= i;
3498 m2 -= i;
3499 s2 -= i;
3500 }
3501 if (b5 > 0) {
3502 if (leftright) {
3503 if (m5 > 0) {
3504 mhi = pow5mult(mhi, m5);
3505 b1 = mult(mhi, b);
3506 Bfree(b);
3507 b = b1;
3508 }
3509 if ((j = b5 - m5) != 0)
3510 b = pow5mult(b, j);
3511 }
3512 else
3513 b = pow5mult(b, b5);
3514 }
3515 S = i2b(1);
3516 if (s5 > 0)
3517 S = pow5mult(S, s5);
3518
3519 /* Check for special case that d is a normalized power of 2. */
3520
3521 spec_case = 0;
3522 if ((mode < 2 || leftright)
3523 #ifdef Honor_FLT_ROUNDS
3524 && rounding == 1
3525 #endif
3526 ) {
3527 if (!word1(d) && !(word0(d) & Bndry_mask)
3528 #ifndef Sudden_Underflow
3529 && word0(d) & (Exp_mask & ~Exp_msk1)
3530 #endif
3531 ) {
3532 /* The special case */
3533 b2 += Log2P;
3534 s2 += Log2P;
3535 spec_case = 1;
3536 }
3537 }
3538
3539 /* Arrange for convenient computation of quotients:
3540 * shift left if necessary so divisor has 4 leading 0 bits.
3541 *
3542 * Perhaps we should just compute leading 28 bits of S once
3543 * and for all and pass them and a shift to quorem, so it
3544 * can do shifts and ors to compute the numerator for q.
3545 */
3546 #ifdef Pack_32
3547 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0)
3548 i = 32 - i;
3549 #else
3550 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) != 0)
3551 i = 16 - i;
3552 #endif
3553 if (i > 4) {
3554 i -= 4;
3555 b2 += i;
3556 m2 += i;
3557 s2 += i;
3558 }
3559 else if (i < 4) {
3560 i += 28;
3561 b2 += i;
3562 m2 += i;
3563 s2 += i;
3564 }
3565 if (b2 > 0)
3566 b = lshift(b, b2);
3567 if (s2 > 0)
3568 S = lshift(S, s2);
3569 if (k_check) {
3570 if (cmp(b,S) < 0) {
3571 k--;
3572 b = multadd(b, 10, 0); /* we botched the k estimate */
3573 if (leftright)
3574 mhi = multadd(mhi, 10, 0);
3575 ilim = ilim1;
3576 }
3577 }
3578 if (ilim <= 0 && (mode == 3 || mode == 5)) {
3579 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
3580 /* no digits, fcvt style */
3581 no_digits:
3582 k = -1 - ndigits;
3583 goto ret;
3584 }
3585 one_digit:
3586 *s++ = '1';
3587 k++;
3588 goto ret;
3589 }
3590 if (leftright) {
3591 if (m2 > 0)
3592 mhi = lshift(mhi, m2);
3593
3594 /* Compute mlo -- check for special case
3595 * that d is a normalized power of 2.
3596 */
3597
3598 mlo = mhi;
3599 if (spec_case) {
3600 mhi = Balloc(mhi->k);
3601 Bcopy(mhi, mlo);
3602 mhi = lshift(mhi, Log2P);
3603 }
3604
3605 for (i = 1;;i++) {
3606 dig = quorem(b,S) + '0';
3607 /* Do we yet have the shortest decimal string
3608 * that will round to d?
3609 */
3610 j = cmp(b, mlo);
3611 delta = diff(S, mhi);
3612 j1 = delta->sign ? 1 : cmp(b, delta);
3613 Bfree(delta);
3614 #ifndef ROUND_BIASED
3615 if (j1 == 0 && mode != 1 && !(word1(d) & 1)
3616 #ifdef Honor_FLT_ROUNDS
3617 && rounding >= 1
3618 #endif
3619 ) {
3620 if (dig == '9')
3621 goto round_9_up;
3622 if (j > 0)
3623 dig++;
3624 #ifdef SET_INEXACT
3625 else if (!b->x[0] && b->wds <= 1)
3626 inexact = 0;
3627 #endif
3628 *s++ = dig;
3629 goto ret;
3630 }
3631 #endif
3632 if (j < 0 || (j == 0 && mode != 1
3633 #ifndef ROUND_BIASED
3634 && !(word1(d) & 1)
3635 #endif
3636 )) {
3637 if (!b->x[0] && b->wds <= 1) {
3638 #ifdef SET_INEXACT
3639 inexact = 0;
3640 #endif
3641 goto accept_dig;
3642 }
3643 #ifdef Honor_FLT_ROUNDS
3644 if (mode > 1)
3645 switch (rounding) {
3646 case 0: goto accept_dig;
3647 case 2: goto keep_dig;
3648 }
3649 #endif /*Honor_FLT_ROUNDS*/
3650 if (j1 > 0) {
3651 b = lshift(b, 1);
3652 j1 = cmp(b, S);
3653 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
3654 goto round_9_up;
3655 }
3656 accept_dig:
3657 *s++ = dig;
3658 goto ret;
3659 }
3660 if (j1 > 0) {
3661 #ifdef Honor_FLT_ROUNDS
3662 if (!rounding)
3663 goto accept_dig;
3664 #endif
3665 if (dig == '9') { /* possible if i == 1 */
3666 round_9_up:
3667 *s++ = '9';
3668 goto roundoff;
3669 }
3670 *s++ = dig + 1;
3671 goto ret;
3672 }
3673 #ifdef Honor_FLT_ROUNDS
3674 keep_dig:
3675 #endif
3676 *s++ = dig;
3677 if (i == ilim)
3678 break;
3679 b = multadd(b, 10, 0);
3680 if (mlo == mhi)
3681 mlo = mhi = multadd(mhi, 10, 0);
3682 else {
3683 mlo = multadd(mlo, 10, 0);
3684 mhi = multadd(mhi, 10, 0);
3685 }
3686 }
3687 }
3688 else
3689 for (i = 1;; i++) {
3690 *s++ = dig = quorem(b,S) + '0';
3691 if (!b->x[0] && b->wds <= 1) {
3692 #ifdef SET_INEXACT
3693 inexact = 0;
3694 #endif
3695 goto ret;
3696 }
3697 if (i >= ilim)
3698 break;
3699 b = multadd(b, 10, 0);
3700 }
3701
3702 /* Round off last digit */
3703
3704 #ifdef Honor_FLT_ROUNDS
3705 switch (rounding) {
3706 case 0: goto trimzeros;
3707 case 2: goto roundoff;
3708 }
3709 #endif
3710 b = lshift(b, 1);
3711 j = cmp(b, S);
3712 if (j > 0 || (j == 0 && (dig & 1))) {
3713 roundoff:
3714 while (*--s == '9')
3715 if (s == s0) {
3716 k++;
3717 *s++ = '1';
3718 goto ret;
3719 }
3720 ++*s++;
3721 }
3722 else {
3723 while (*--s == '0') ;
3724 s++;
3725 }
3726 ret:
3727 Bfree(S);
3728 if (mhi) {
3729 if (mlo && mlo != mhi)
3730 Bfree(mlo);
3731 Bfree(mhi);
3732 }
3733 ret1:
3734 #ifdef SET_INEXACT
3735 if (inexact) {
3736 if (!oldinexact) {
3737 word0(d) = Exp_1 + (70 << Exp_shift);
3738 word1(d) = 0;
3739 dval(d) += 1.;
3740 }
3741 }
3742 else if (!oldinexact)
3743 clear_inexact();
3744 #endif
3745 Bfree(b);
3746 *s = 0;
3747 *decpt = k + 1;
3748 if (rve)
3749 *rve = s;
3750 return s0;
3751 }
3752
3753 void
3754 ruby_each_words(const char *str, void (*func)(const char*, int, void*), void *arg)
3755 {
3756 const char *end;
3757 int len;
3758
3759 if (!str) return;
3760 for (; *str; str = end) {
3761 while (ISSPACE(*str) || *str == ',') str++;
3762 if (!*str) break;
3763 end = str;
3764 while (*end && !ISSPACE(*end) && *end != ',') end++;
3765 len = (int)(end - str); /* assume no string exceeds INT_MAX */
3766 (*func)(str, len, arg);
3767 }
3768 }
3769
3770 /*-
3771 * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
3772 * All rights reserved.
3773 *
3774 * Redistribution and use in source and binary forms, with or without
3775 * modification, are permitted provided that the following conditions
3776 * are met:
3777 * 1. Redistributions of source code must retain the above copyright
3778 * notice, this list of conditions and the following disclaimer.
3779 * 2. Redistributions in binary form must reproduce the above copyright
3780 * notice, this list of conditions and the following disclaimer in the
3781 * documentation and/or other materials provided with the distribution.
3782 *
3783 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
3784 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
3785 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
3786 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
3787 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
3788 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
3789 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
3790 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
3791 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
3792 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
3793 * SUCH DAMAGE.
3794 */
3795
3796 #define DBL_MANH_SIZE 20
3797 #define DBL_MANL_SIZE 32
3798 #define DBL_ADJ (DBL_MAX_EXP - 2)
3799 #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
3800 #define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
3801 #define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
3802 #define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
3803 #define dmanl_get(u) ((uint32_t)word1(u))
3804
3805
3806 /*
3807 * This procedure converts a double-precision number in IEEE format
3808 * into a string of hexadecimal digits and an exponent of 2. Its
3809 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
3810 * following exceptions:
3811 *
3812 * - An ndigits < 0 causes it to use as many digits as necessary to
3813 * represent the number exactly.
3814 * - The additional xdigs argument should point to either the string
3815 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
3816 * which case is desired.
3817 * - This routine does not repeat dtoa's mistake of setting decpt
3818 * to 9999 in the case of an infinity or NaN. INT_MAX is used
3819 * for this purpose instead.
3820 *
3821 * Note that the C99 standard does not specify what the leading digit
3822 * should be for non-zero numbers. For instance, 0x1.3p3 is the same
3823 * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
3824 * the leading digit a 1. This ensures that the exponent printed is the
3825 * actual base-2 exponent, i.e., ilogb(d).
3826 *
3827 * Inputs: d, xdigs, ndigits
3828 * Outputs: decpt, sign, rve
3829 */
3830 char *
3831 ruby_hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
3832 char **rve)
3833 {
3834 U u;
3835 char *s, *s0;
3836 int bufsize;
3837 uint32_t manh, manl;
3838
3839 u.d = d;
3840 if (word0(u) & Sign_bit) {
3841 /* set sign for everything, including 0's and NaNs */
3842 *sign = 1;
3843 word0(u) &= ~Sign_bit; /* clear sign bit */
3844 }
3845 else
3846 *sign = 0;
3847
3848 if (isinf(d)) { /* FP_INFINITE */
3849 *decpt = INT_MAX;
3850 return rv_strdup(INFSTR, rve);
3851 }
3852 else if (isnan(d)) { /* FP_NAN */
3853 *decpt = INT_MAX;
3854 return rv_strdup(NANSTR, rve);
3855 }
3856 else if (d == 0.0) { /* FP_ZERO */
3857 *decpt = 1;
3858 return rv_strdup(ZEROSTR, rve);
3859 }
3860 else if (dexp_get(u)) { /* FP_NORMAL */
3861 *decpt = dexp_get(u) - DBL_ADJ;
3862 }
3863 else { /* FP_SUBNORMAL */
3864 u.d *= 5.363123171977039e+154 /* 0x1p514 */;
3865 *decpt = dexp_get(u) - (514 + DBL_ADJ);
3866 }
3867
3868 if (ndigits == 0) /* dtoa() compatibility */
3869 ndigits = 1;
3870
3871 /*
3872 * If ndigits < 0, we are expected to auto-size, so we allocate
3873 * enough space for all the digits.
3874 */
3875 bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
3876 s0 = rv_alloc(bufsize+1);
3877
3878 /* Round to the desired number of digits. */
3879 if (SIGFIGS > ndigits && ndigits > 0) {
3880 float redux = 1.0f;
3881 volatile double d;
3882 int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
3883 dexp_set(u, offset);
3884 d = u.d;
3885 d += redux;
3886 d -= redux;
3887 u.d = d;
3888 *decpt += dexp_get(u) - offset;
3889 }
3890
3891 manh = dmanh_get(u);
3892 manl = dmanl_get(u);
3893 *s0 = '1';
3894 for (s = s0 + 1; s < s0 + bufsize; s++) {
3895 *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
3896 manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
3897 manl <<= 4;
3898 }
3899
3900 /* If ndigits < 0, we are expected to auto-size the precision. */
3901 if (ndigits < 0) {
3902 for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
3903 ;
3904 }
3905
3906 s = s0 + ndigits;
3907 *s = '\0';
3908 if (rve != NULL)
3909 *rve = s;
3910 return (s0);
3911 }
3912
3913 #ifdef __cplusplus
3914 #if 0
3915 { /* satisfy cc-mode */
3916 #endif
3917 }
3918 #endif
3919