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1 | /**************************************************************** |
2 | ||
3 | The author of this software is David M. Gay. | |
4 | ||
5 | Copyright (C) 1998-2001 by Lucent Technologies | |
6 | All Rights Reserved | |
7 | ||
8 | Permission to use, copy, modify, and distribute this software and | |
9 | its documentation for any purpose and without fee is hereby | |
10 | granted, provided that the above copyright notice appear in all | |
11 | copies and that both that the copyright notice and this | |
12 | permission notice and warranty disclaimer appear in supporting | |
13 | documentation, and that the name of Lucent or any of its entities | |
14 | not be used in advertising or publicity pertaining to | |
15 | distribution of the software without specific, written prior | |
16 | permission. | |
17 | ||
18 | LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, | |
19 | INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. | |
20 | IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY | |
21 | SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES | |
22 | WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER | |
23 | IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, | |
24 | ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF | |
25 | THIS SOFTWARE. | |
26 | ||
27 | ****************************************************************/ | |
28 | ||
29 | /* Please send bug reports to David M. Gay (dmg at acm dot org, | |
30 | * with " at " changed at "@" and " dot " changed to "."). */ | |
31 | ||
32 | #include "xlocale_private.h" | |
33 | ||
34 | #include "gdtoaimp.h" | |
35 | ||
36 | #ifdef USE_LOCALE | |
37 | #include "locale.h" | |
38 | #endif | |
39 | ||
40 | #define fivesbits __fivesbits_D2A | |
41 | #define all_on __all_on_D2A | |
42 | #define set_ones __set_ones_D2A | |
43 | #define rvOK __rvOK_D2A | |
44 | #define mantbits __mantbits_D2A | |
45 | ||
46 | #ifdef BUILDING_VARIANT | |
47 | extern CONST int fivesbits[]; | |
48 | int all_on(Bigint *b, int n); | |
49 | Bigint *set_ones(Bigint *b, int n); | |
50 | int rvOK(double d, FPI *fpi, Long *exp, ULong *bits, int exact, int rd, int *irv); | |
51 | int mantbits(double d); | |
52 | #else /* !BUILDING_VARIANT */ | |
53 | ||
54 | __private_extern__ CONST int | |
55 | fivesbits[] = { 0, 3, 5, 7, 10, 12, 14, 17, 19, 21, | |
56 | 24, 26, 28, 31, 33, 35, 38, 40, 42, 45, | |
57 | 47, 49, 52 | |
58 | #ifdef VAX | |
59 | , 54, 56 | |
60 | #endif | |
61 | }; | |
62 | ||
63 | Bigint * | |
64 | #ifdef KR_headers | |
65 | increment(b) Bigint *b; | |
66 | #else | |
67 | increment(Bigint *b) | |
68 | #endif | |
69 | { | |
70 | ULong *x, *xe; | |
71 | Bigint *b1; | |
72 | #ifdef Pack_16 | |
73 | ULong carry = 1, y; | |
74 | #endif | |
75 | ||
76 | x = b->x; | |
77 | xe = x + b->wds; | |
78 | #ifdef Pack_32 | |
79 | do { | |
80 | if (*x < (ULong)0xffffffffL) { | |
81 | ++*x; | |
82 | return b; | |
83 | } | |
84 | *x++ = 0; | |
85 | } while(x < xe); | |
86 | #else | |
87 | do { | |
88 | y = *x + carry; | |
89 | carry = y >> 16; | |
90 | *x++ = y & 0xffff; | |
91 | if (!carry) | |
92 | return b; | |
93 | } while(x < xe); | |
94 | if (carry) | |
95 | #endif | |
96 | { | |
97 | if (b->wds >= b->maxwds) { | |
98 | b1 = Balloc(b->k+1); | |
99 | Bcopy(b1,b); | |
100 | Bfree(b); | |
101 | b = b1; | |
102 | } | |
103 | b->x[b->wds++] = 1; | |
104 | } | |
105 | return b; | |
106 | } | |
107 | ||
108 | int | |
109 | #ifdef KR_headers | |
110 | decrement(b) Bigint *b; | |
111 | #else | |
112 | decrement(Bigint *b) | |
113 | #endif | |
114 | { | |
115 | ULong *x, *xe; | |
116 | #ifdef Pack_16 | |
117 | ULong borrow = 1, y; | |
118 | #endif | |
119 | ||
120 | x = b->x; | |
121 | xe = x + b->wds; | |
122 | #ifdef Pack_32 | |
123 | do { | |
124 | if (*x) { | |
125 | --*x; | |
126 | break; | |
127 | } | |
128 | *x++ = 0xffffffffL; | |
129 | } | |
130 | while(x < xe); | |
131 | #else | |
132 | do { | |
133 | y = *x - borrow; | |
134 | borrow = (y & 0x10000) >> 16; | |
135 | *x++ = y & 0xffff; | |
136 | } while(borrow && x < xe); | |
137 | #endif | |
138 | return STRTOG_Inexlo; | |
139 | } | |
140 | ||
141 | __private_extern__ int | |
142 | #ifdef KR_headers | |
143 | all_on(b, n) Bigint *b; int n; | |
144 | #else | |
145 | all_on(Bigint *b, int n) | |
146 | #endif | |
147 | { | |
148 | ULong *x, *xe; | |
149 | ||
150 | x = b->x; | |
151 | xe = x + (n >> kshift); | |
152 | while(x < xe) | |
153 | if ((*x++ & ALL_ON) != ALL_ON) | |
154 | return 0; | |
155 | if (n &= kmask) | |
156 | return ((*x | (ALL_ON << n)) & ALL_ON) == ALL_ON; | |
157 | return 1; | |
158 | } | |
159 | ||
160 | Bigint * | |
161 | #ifdef KR_headers | |
162 | set_ones(b, n) Bigint *b; int n; | |
163 | #else | |
164 | set_ones(Bigint *b, int n) | |
165 | #endif | |
166 | { | |
167 | int k; | |
168 | ULong *x, *xe; | |
169 | ||
170 | k = (n + ((1 << kshift) - 1)) >> kshift; | |
171 | if (b->k < k) { | |
172 | Bfree(b); | |
173 | b = Balloc(k); | |
174 | } | |
175 | k = n >> kshift; | |
176 | if (n &= kmask) | |
177 | k++; | |
178 | b->wds = k; | |
179 | x = b->x; | |
180 | xe = x + k; | |
181 | while(x < xe) | |
182 | *x++ = ALL_ON; | |
183 | if (n) | |
184 | x[-1] >>= ULbits - n; | |
185 | return b; | |
186 | } | |
187 | ||
188 | __private_extern__ int | |
189 | rvOK | |
190 | #ifdef KR_headers | |
191 | (d, fpi, exp, bits, exact, rd, irv) | |
192 | double d; FPI *fpi; Long *exp; ULong *bits; int exact, rd, *irv; | |
193 | #else | |
194 | (double d, FPI *fpi, Long *exp, ULong *bits, int exact, int rd, int *irv) | |
195 | #endif | |
196 | { | |
197 | Bigint *b; | |
198 | ULong carry, inex, lostbits; | |
199 | int bdif, e, j, k, k1, nb, rv; | |
200 | ||
201 | carry = rv = 0; | |
202 | b = d2b(d, &e, &bdif); | |
203 | bdif -= nb = fpi->nbits; | |
204 | e += bdif; | |
205 | if (bdif <= 0) { | |
206 | if (exact) | |
207 | goto trunc; | |
208 | goto ret; | |
209 | } | |
210 | if (P == nb) { | |
211 | if ( | |
212 | #ifndef IMPRECISE_INEXACT | |
213 | exact && | |
214 | #endif | |
215 | fpi->rounding == | |
216 | #ifdef RND_PRODQUOT | |
217 | FPI_Round_near | |
218 | #else | |
219 | Flt_Rounds | |
220 | #endif | |
221 | ) goto trunc; | |
222 | goto ret; | |
223 | } | |
224 | switch(rd) { | |
225 | case 1: | |
226 | goto trunc; | |
227 | case 2: | |
228 | break; | |
229 | default: /* round near */ | |
230 | k = bdif - 1; | |
231 | if (k < 0) | |
232 | goto trunc; | |
233 | if (!k) { | |
234 | if (!exact) | |
235 | goto ret; | |
236 | if (b->x[0] & 2) | |
237 | break; | |
238 | goto trunc; | |
239 | } | |
240 | if (b->x[k>>kshift] & ((ULong)1 << (k & kmask))) | |
241 | break; | |
242 | goto trunc; | |
243 | } | |
244 | /* "break" cases: round up 1 bit, then truncate; bdif > 0 */ | |
245 | carry = 1; | |
246 | trunc: | |
247 | inex = lostbits = 0; | |
248 | if (bdif > 0) { | |
249 | if ( (lostbits = any_on(b, bdif)) !=0) | |
250 | inex = STRTOG_Inexlo; | |
251 | rshift(b, bdif); | |
252 | if (carry) { | |
253 | inex = STRTOG_Inexhi; | |
254 | b = increment(b); | |
255 | if ( (j = nb & kmask) !=0) | |
256 | j = ULbits - j; | |
257 | if (hi0bits(b->x[b->wds - 1]) != j) { | |
258 | if (!lostbits) | |
259 | lostbits = b->x[0] & 1; | |
260 | rshift(b, 1); | |
261 | e++; | |
262 | } | |
263 | } | |
264 | } | |
265 | else if (bdif < 0) | |
266 | b = lshift(b, -bdif); | |
267 | if (e < fpi->emin) { | |
268 | k = fpi->emin - e; | |
269 | e = fpi->emin; | |
270 | if (k > nb || fpi->sudden_underflow) { | |
271 | b->wds = inex = 0; | |
272 | *irv = STRTOG_Underflow | STRTOG_Inexlo; | |
273 | } | |
274 | else { | |
275 | k1 = k - 1; | |
276 | if (k1 > 0 && !lostbits) | |
277 | lostbits = any_on(b, k1); | |
278 | if (!lostbits && !exact) | |
279 | goto ret; | |
280 | lostbits |= | |
281 | carry = b->x[k1>>kshift] & (1 << (k1 & kmask)); | |
282 | rshift(b, k); | |
283 | *irv = STRTOG_Denormal; | |
284 | if (carry) { | |
285 | b = increment(b); | |
286 | inex = STRTOG_Inexhi | STRTOG_Underflow; | |
287 | } | |
288 | else if (lostbits) | |
289 | inex = STRTOG_Inexlo | STRTOG_Underflow; | |
290 | } | |
291 | } | |
292 | else if (e > fpi->emax) { | |
293 | e = fpi->emax + 1; | |
294 | *irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi; | |
295 | #ifndef NO_ERRNO | |
296 | errno = ERANGE; | |
297 | #endif | |
298 | b->wds = inex = 0; | |
299 | } | |
300 | *exp = e; | |
301 | copybits(bits, nb, b); | |
302 | *irv |= inex; | |
303 | rv = 1; | |
304 | ret: | |
305 | Bfree(b); | |
306 | return rv; | |
307 | } | |
308 | ||
309 | __private_extern__ int | |
310 | #ifdef KR_headers | |
311 | mantbits(d) double d; | |
312 | #else | |
313 | mantbits(double d) | |
314 | #endif | |
315 | { | |
316 | ULong L; | |
317 | #ifdef VAX | |
318 | L = word1(d) << 16 | word1(d) >> 16; | |
319 | if (L) | |
320 | #else | |
321 | if ( (L = word1(d)) !=0) | |
322 | #endif | |
323 | return P - lo0bits(&L); | |
324 | #ifdef VAX | |
325 | L = word0(d) << 16 | word0(d) >> 16 | Exp_msk11; | |
326 | #else | |
327 | L = word0(d) | Exp_msk1; | |
328 | #endif | |
329 | return P - 32 - lo0bits(&L); | |
330 | } | |
331 | ||
332 | #endif /* BUILDING_VARIANT */ | |
333 | ||
334 | int | |
335 | strtodg | |
336 | #ifdef KR_headers | |
337 | (s00, se, fpi, exp, bits, loc) | |
338 | CONST char *s00; char **se; FPI *fpi; Long *exp; ULong *bits; locale_t loc; | |
339 | #else | |
340 | (CONST char *s00, char **se, FPI *fpi, Long *exp, ULong *bits, locale_t loc) | |
341 | #endif | |
342 | { | |
343 | int abe, abits, asub; | |
344 | int bb0, bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, denorm; | |
345 | int dsign, e, e1, e2, emin, esign, finished, i, inex, irv; | |
346 | int j, k, nbits, nd, nd0, nf, nz, nz0, rd, rvbits, rve, rve1, sign; | |
347 | int sudden_underflow; | |
348 | CONST char *s, *s0, *s1; | |
349 | double adj, adj0, rv, tol; | |
350 | Long L; | |
351 | ULong y, z; | |
352 | Bigint *ab, *bb, *bb1, *bd, *bd0, *bs, *delta, *rvb, *rvb0; | |
353 | #ifdef USE_LOCALE | |
354 | char *decimal_point; | |
355 | int decimal_point_len; | |
356 | #endif /* USE_LOCALE */ | |
357 | ||
358 | irv = STRTOG_Zero; | |
359 | denorm = sign = nz0 = nz = 0; | |
360 | dval(rv) = 0.; | |
361 | rvb = 0; | |
362 | nbits = fpi->nbits; | |
363 | for(s = s00;;s++) switch(*s) { | |
364 | case '-': | |
365 | sign = 1; | |
366 | /* no break */ | |
367 | case '+': | |
368 | if (*++s) | |
369 | goto break2; | |
370 | /* no break */ | |
371 | case 0: | |
372 | sign = 0; | |
373 | irv = STRTOG_NoNumber; | |
374 | s = s00; | |
375 | goto ret; | |
376 | case '\t': | |
377 | case '\n': | |
378 | case '\v': | |
379 | case '\f': | |
380 | case '\r': | |
381 | case ' ': | |
382 | continue; | |
383 | default: | |
384 | goto break2; | |
385 | } | |
386 | break2: | |
387 | if (*s == '0') { | |
388 | #ifndef NO_HEX_FP | |
389 | switch(s[1]) { | |
390 | case 'x': | |
391 | case 'X': | |
392 | irv = gethex(&s, fpi, exp, &rvb, sign, loc); | |
393 | if (irv == STRTOG_NoNumber) { | |
394 | s = s00; | |
395 | sign = 0; | |
396 | } | |
397 | goto ret; | |
398 | } | |
399 | #endif | |
400 | nz0 = 1; | |
401 | while(*++s == '0') ; | |
402 | if (!*s) | |
403 | goto ret; | |
404 | } | |
405 | sudden_underflow = fpi->sudden_underflow; | |
406 | s0 = s; | |
407 | y = z = 0; | |
408 | for(decpt = nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) | |
409 | if (nd < 9) | |
410 | y = 10*y + c - '0'; | |
411 | else if (nd < 16) | |
412 | z = 10*z + c - '0'; | |
413 | nd0 = nd; | |
414 | NORMALIZE_LOCALE(loc); | |
415 | #ifdef USE_LOCALE | |
416 | decimal_point = localeconv_l(loc)->decimal_point; | |
417 | decimal_point_len = strlen(decimal_point); | |
418 | if (strncmp(s, decimal_point, decimal_point_len) == 0) | |
419 | #else | |
420 | if (c == '.') | |
421 | #endif | |
422 | { | |
423 | decpt = 1; | |
424 | #ifdef USE_LOCALE | |
425 | s += decimal_point_len; | |
426 | c = *s; | |
427 | #else | |
428 | c = *++s; | |
429 | #endif | |
430 | if (!nd) { | |
431 | for(; c == '0'; c = *++s) | |
432 | nz++; | |
433 | if (c > '0' && c <= '9') { | |
434 | s0 = s; | |
435 | nf += nz; | |
436 | nz = 0; | |
437 | goto have_dig; | |
438 | } | |
439 | goto dig_done; | |
440 | } | |
441 | for(; c >= '0' && c <= '9'; c = *++s) { | |
442 | have_dig: | |
443 | nz++; | |
444 | if (c -= '0') { | |
445 | nf += nz; | |
446 | for(i = 1; i < nz; i++) | |
447 | if (nd++ < 9) | |
448 | y *= 10; | |
449 | else if (nd <= DBL_DIG + 1) | |
450 | z *= 10; | |
451 | if (nd++ < 9) | |
452 | y = 10*y + c; | |
453 | else if (nd <= DBL_DIG + 1) | |
454 | z = 10*z + c; | |
455 | nz = 0; | |
456 | } | |
457 | } | |
458 | } | |
459 | dig_done: | |
460 | e = 0; | |
461 | if (c == 'e' || c == 'E') { | |
462 | if (!nd && !nz && !nz0) { | |
463 | irv = STRTOG_NoNumber; | |
464 | s = s00; | |
465 | goto ret; | |
466 | } | |
467 | s00 = s; | |
468 | esign = 0; | |
469 | switch(c = *++s) { | |
470 | case '-': | |
471 | esign = 1; | |
472 | case '+': | |
473 | c = *++s; | |
474 | } | |
475 | if (c >= '0' && c <= '9') { | |
476 | while(c == '0') | |
477 | c = *++s; | |
478 | if (c > '0' && c <= '9') { | |
479 | L = c - '0'; | |
480 | s1 = s; | |
481 | while((c = *++s) >= '0' && c <= '9') | |
482 | L = 10*L + c - '0'; | |
483 | if (s - s1 > 8 || L > 19999) | |
484 | /* Avoid confusion from exponents | |
485 | * so large that e might overflow. | |
486 | */ | |
487 | e = 19999; /* safe for 16 bit ints */ | |
488 | else | |
489 | e = (int)L; | |
490 | if (esign) | |
491 | e = -e; | |
492 | } | |
493 | else | |
494 | e = 0; | |
495 | } | |
496 | else | |
497 | s = s00; | |
498 | } | |
499 | if (!nd) { | |
500 | if (!nz && !nz0) { | |
501 | #ifdef INFNAN_CHECK | |
502 | /* Check for Nan and Infinity */ | |
503 | if (!decpt) | |
504 | switch(c) { | |
505 | case 'i': | |
506 | case 'I': | |
507 | if (match(&s,"nf")) { | |
508 | --s; | |
509 | if (!match(&s,"inity")) | |
510 | ++s; | |
511 | irv = STRTOG_Infinite; | |
512 | goto infnanexp; | |
513 | } | |
514 | break; | |
515 | case 'n': | |
516 | case 'N': | |
517 | if (match(&s, "an")) { | |
518 | irv = STRTOG_NaN; | |
519 | *exp = fpi->emax + 1; | |
520 | #ifndef No_Hex_NaN | |
521 | if (*s == '(') /*)*/ | |
522 | irv = hexnan(&s, fpi, bits); | |
523 | #endif | |
524 | goto infnanexp; | |
525 | } | |
526 | } | |
527 | #endif /* INFNAN_CHECK */ | |
528 | irv = STRTOG_NoNumber; | |
529 | s = s00; | |
530 | } | |
531 | goto ret; | |
532 | } | |
533 | ||
534 | irv = STRTOG_Normal; | |
535 | e1 = e -= nf; | |
536 | rd = 0; | |
537 | switch(fpi->rounding & 3) { | |
538 | case FPI_Round_up: | |
539 | rd = 2 - sign; | |
540 | break; | |
541 | case FPI_Round_zero: | |
542 | rd = 1; | |
543 | break; | |
544 | case FPI_Round_down: | |
545 | rd = 1 + sign; | |
546 | } | |
547 | ||
548 | /* Now we have nd0 digits, starting at s0, followed by a | |
549 | * decimal point, followed by nd-nd0 digits. The number we're | |
550 | * after is the integer represented by those digits times | |
551 | * 10**e */ | |
552 | ||
553 | if (!nd0) | |
554 | nd0 = nd; | |
555 | k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; | |
556 | dval(rv) = y; | |
557 | if (k > 9) | |
558 | dval(rv) = tens[k - 9] * dval(rv) + z; | |
559 | bd0 = 0; | |
560 | if (nbits <= P && nd <= DBL_DIG) { | |
561 | if (!e) { | |
562 | if (rvOK(dval(rv), fpi, exp, bits, 1, rd, &irv)) | |
563 | goto ret; | |
564 | } | |
565 | else if (e > 0) { | |
566 | if (e <= Ten_pmax) { | |
567 | #ifdef VAX | |
568 | goto vax_ovfl_check; | |
569 | #else | |
570 | i = fivesbits[e] + mantbits(dval(rv)) <= P; | |
571 | /* rv = */ rounded_product(dval(rv), tens[e]); | |
572 | if (rvOK(dval(rv), fpi, exp, bits, i, rd, &irv)) | |
573 | goto ret; | |
574 | e1 -= e; | |
575 | goto rv_notOK; | |
576 | #endif | |
577 | } | |
578 | i = DBL_DIG - nd; | |
579 | if (e <= Ten_pmax + i) { | |
580 | /* A fancier test would sometimes let us do | |
581 | * this for larger i values. | |
582 | */ | |
583 | e2 = e - i; | |
584 | e1 -= i; | |
585 | dval(rv) *= tens[i]; | |
586 | #ifdef VAX | |
587 | /* VAX exponent range is so narrow we must | |
588 | * worry about overflow here... | |
589 | */ | |
590 | vax_ovfl_check: | |
591 | dval(adj) = dval(rv); | |
592 | word0(adj) -= P*Exp_msk1; | |
593 | /* adj = */ rounded_product(dval(adj), tens[e2]); | |
594 | if ((word0(adj) & Exp_mask) | |
595 | > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) | |
596 | goto rv_notOK; | |
597 | word0(adj) += P*Exp_msk1; | |
598 | dval(rv) = dval(adj); | |
599 | #else | |
600 | /* rv = */ rounded_product(dval(rv), tens[e2]); | |
601 | #endif | |
602 | if (rvOK(dval(rv), fpi, exp, bits, 0, rd, &irv)) | |
603 | goto ret; | |
604 | e1 -= e2; | |
605 | } | |
606 | } | |
607 | #ifndef Inaccurate_Divide | |
608 | else if (e >= -Ten_pmax) { | |
609 | /* rv = */ rounded_quotient(dval(rv), tens[-e]); | |
610 | if (rvOK(dval(rv), fpi, exp, bits, 0, rd, &irv)) | |
611 | goto ret; | |
612 | e1 -= e; | |
613 | } | |
614 | #endif | |
615 | } | |
616 | rv_notOK: | |
617 | e1 += nd - k; | |
618 | ||
619 | /* Get starting approximation = rv * 10**e1 */ | |
620 | ||
621 | e2 = 0; | |
622 | if (e1 > 0) { | |
623 | if ( (i = e1 & 15) !=0) | |
624 | dval(rv) *= tens[i]; | |
625 | if (e1 &= ~15) { | |
626 | e1 >>= 4; | |
627 | while(e1 >= (1 << n_bigtens-1)) { | |
628 | e2 += ((word0(rv) & Exp_mask) | |
629 | >> Exp_shift1) - Bias; | |
630 | word0(rv) &= ~Exp_mask; | |
631 | word0(rv) |= Bias << Exp_shift1; | |
632 | dval(rv) *= bigtens[n_bigtens-1]; | |
633 | e1 -= 1 << n_bigtens-1; | |
634 | } | |
635 | e2 += ((word0(rv) & Exp_mask) >> Exp_shift1) - Bias; | |
636 | word0(rv) &= ~Exp_mask; | |
637 | word0(rv) |= Bias << Exp_shift1; | |
638 | for(j = 0; e1 > 0; j++, e1 >>= 1) | |
639 | if (e1 & 1) | |
640 | dval(rv) *= bigtens[j]; | |
641 | } | |
642 | } | |
643 | else if (e1 < 0) { | |
644 | e1 = -e1; | |
645 | if ( (i = e1 & 15) !=0) | |
646 | dval(rv) /= tens[i]; | |
647 | if (e1 &= ~15) { | |
648 | e1 >>= 4; | |
649 | while(e1 >= (1 << n_bigtens-1)) { | |
650 | e2 += ((word0(rv) & Exp_mask) | |
651 | >> Exp_shift1) - Bias; | |
652 | word0(rv) &= ~Exp_mask; | |
653 | word0(rv) |= Bias << Exp_shift1; | |
654 | dval(rv) *= tinytens[n_bigtens-1]; | |
655 | e1 -= 1 << n_bigtens-1; | |
656 | } | |
657 | e2 += ((word0(rv) & Exp_mask) >> Exp_shift1) - Bias; | |
658 | word0(rv) &= ~Exp_mask; | |
659 | word0(rv) |= Bias << Exp_shift1; | |
660 | for(j = 0; e1 > 0; j++, e1 >>= 1) | |
661 | if (e1 & 1) | |
662 | dval(rv) *= tinytens[j]; | |
663 | } | |
664 | } | |
665 | #ifdef IBM | |
666 | /* e2 is a correction to the (base 2) exponent of the return | |
667 | * value, reflecting adjustments above to avoid overflow in the | |
668 | * native arithmetic. For native IBM (base 16) arithmetic, we | |
669 | * must multiply e2 by 4 to change from base 16 to 2. | |
670 | */ | |
671 | e2 <<= 2; | |
672 | #endif | |
673 | rvb = d2b(dval(rv), &rve, &rvbits); /* rv = rvb * 2^rve */ | |
674 | rve += e2; | |
675 | if ((j = rvbits - nbits) > 0) { | |
676 | rshift(rvb, j); | |
677 | rvbits = nbits; | |
678 | rve += j; | |
679 | } | |
680 | bb0 = 0; /* trailing zero bits in rvb */ | |
681 | e2 = rve + rvbits - nbits; | |
682 | if (e2 > fpi->emax + 1) | |
683 | goto huge; | |
684 | rve1 = rve + rvbits - nbits; | |
685 | if (e2 < (emin = fpi->emin)) { | |
686 | denorm = 1; | |
687 | j = rve - emin; | |
688 | if (j > 0) { | |
689 | rvb = lshift(rvb, j); | |
690 | rvbits += j; | |
691 | } | |
692 | else if (j < 0) { | |
693 | rvbits += j; | |
694 | if (rvbits <= 0) { | |
695 | if (rvbits < -1) { | |
696 | ufl: | |
697 | rvb->wds = 0; | |
698 | rvb->x[0] = 0; | |
699 | *exp = emin; | |
700 | irv = STRTOG_Underflow | STRTOG_Inexlo; | |
701 | #ifndef NO_ERRNO | |
702 | errno = ERANGE; | |
703 | #endif | |
704 | goto ret; | |
705 | } | |
706 | rvb->x[0] = rvb->wds = rvbits = 1; | |
707 | } | |
708 | else | |
709 | rshift(rvb, -j); | |
710 | } | |
711 | rve = rve1 = emin; | |
712 | if (sudden_underflow && e2 + 1 < emin) | |
713 | goto ufl; | |
714 | } | |
715 | ||
716 | /* Now the hard part -- adjusting rv to the correct value.*/ | |
717 | ||
718 | /* Put digits into bd: true value = bd * 10^e */ | |
719 | ||
720 | #ifdef USE_LOCALE | |
721 | bd0 = s2b(s0, nd0, nd, y, decimal_point_len); | |
722 | #else | |
723 | bd0 = s2b(s0, nd0, nd, y, 1); | |
724 | #endif | |
725 | ||
726 | for(;;) { | |
727 | bd = Balloc(bd0->k); | |
728 | Bcopy(bd, bd0); | |
729 | bb = Balloc(rvb->k); | |
730 | Bcopy(bb, rvb); | |
731 | bbbits = rvbits - bb0; | |
732 | bbe = rve + bb0; | |
733 | bs = i2b(1); | |
734 | ||
735 | if (e >= 0) { | |
736 | bb2 = bb5 = 0; | |
737 | bd2 = bd5 = e; | |
738 | } | |
739 | else { | |
740 | bb2 = bb5 = -e; | |
741 | bd2 = bd5 = 0; | |
742 | } | |
743 | if (bbe >= 0) | |
744 | bb2 += bbe; | |
745 | else | |
746 | bd2 -= bbe; | |
747 | bs2 = bb2; | |
748 | j = nbits + 1 - bbbits; | |
749 | i = bbe + bbbits - nbits; | |
750 | if (i < emin) /* denormal */ | |
751 | j += i - emin; | |
752 | bb2 += j; | |
753 | bd2 += j; | |
754 | i = bb2 < bd2 ? bb2 : bd2; | |
755 | if (i > bs2) | |
756 | i = bs2; | |
757 | if (i > 0) { | |
758 | bb2 -= i; | |
759 | bd2 -= i; | |
760 | bs2 -= i; | |
761 | } | |
762 | if (bb5 > 0) { | |
763 | bs = pow5mult(bs, bb5); | |
764 | bb1 = mult(bs, bb); | |
765 | Bfree(bb); | |
766 | bb = bb1; | |
767 | } | |
768 | bb2 -= bb0; | |
769 | if (bb2 > 0) | |
770 | bb = lshift(bb, bb2); | |
771 | else if (bb2 < 0) | |
772 | rshift(bb, -bb2); | |
773 | if (bd5 > 0) | |
774 | bd = pow5mult(bd, bd5); | |
775 | if (bd2 > 0) | |
776 | bd = lshift(bd, bd2); | |
777 | if (bs2 > 0) | |
778 | bs = lshift(bs, bs2); | |
779 | asub = 1; | |
780 | inex = STRTOG_Inexhi; | |
781 | delta = diff(bb, bd); | |
782 | if (delta->wds <= 1 && !delta->x[0]) | |
783 | break; | |
784 | dsign = delta->sign; | |
785 | delta->sign = finished = 0; | |
786 | L = 0; | |
787 | i = cmp(delta, bs); | |
788 | if (rd && i <= 0) { | |
789 | irv = STRTOG_Normal; | |
790 | if ( (finished = dsign ^ (rd&1)) !=0) { | |
791 | if (dsign != 0) { | |
792 | irv |= STRTOG_Inexhi; | |
793 | goto adj1; | |
794 | } | |
795 | irv |= STRTOG_Inexlo; | |
796 | if (rve1 == emin) | |
797 | goto adj1; | |
798 | for(i = 0, j = nbits; j >= ULbits; | |
799 | i++, j -= ULbits) { | |
800 | if (rvb->x[i] & ALL_ON) | |
801 | goto adj1; | |
802 | } | |
803 | if (j > 1 && lo0bits(rvb->x + i) < j - 1) | |
804 | goto adj1; | |
805 | rve = rve1 - 1; | |
806 | rvb = set_ones(rvb, rvbits = nbits); | |
807 | break; | |
808 | } | |
809 | irv |= dsign ? STRTOG_Inexlo : STRTOG_Inexhi; | |
810 | break; | |
811 | } | |
812 | if (i < 0) { | |
813 | /* Error is less than half an ulp -- check for | |
814 | * special case of mantissa a power of two. | |
815 | */ | |
816 | irv = dsign | |
817 | ? STRTOG_Normal | STRTOG_Inexlo | |
818 | : STRTOG_Normal | STRTOG_Inexhi; | |
819 | if (dsign || bbbits > 1 || denorm || rve1 == emin) | |
820 | break; | |
821 | delta = lshift(delta,1); | |
822 | if (cmp(delta, bs) > 0) { | |
823 | irv = STRTOG_Normal | STRTOG_Inexlo; | |
824 | goto drop_down; | |
825 | } | |
826 | break; | |
827 | } | |
828 | if (i == 0) { | |
829 | /* exactly half-way between */ | |
830 | if (dsign) { | |
831 | if (denorm && all_on(rvb, rvbits)) { | |
832 | /*boundary case -- increment exponent*/ | |
833 | rvb->wds = 1; | |
834 | rvb->x[0] = 1; | |
835 | rve = emin + nbits - (rvbits = 1); | |
836 | irv = STRTOG_Normal | STRTOG_Inexhi; | |
837 | denorm = 0; | |
838 | break; | |
839 | } | |
840 | irv = STRTOG_Normal | STRTOG_Inexlo; | |
841 | } | |
842 | else if (bbbits == 1) { | |
843 | irv = STRTOG_Normal; | |
844 | drop_down: | |
845 | /* boundary case -- decrement exponent */ | |
846 | if (rve1 == emin) { | |
847 | irv = STRTOG_Normal | STRTOG_Inexhi; | |
848 | if (rvb->wds == 1 && rvb->x[0] == 1) | |
849 | sudden_underflow = 1; | |
850 | break; | |
851 | } | |
852 | rve -= nbits; | |
853 | rvb = set_ones(rvb, rvbits = nbits); | |
854 | break; | |
855 | } | |
856 | else | |
857 | irv = STRTOG_Normal | STRTOG_Inexhi; | |
858 | if (bbbits < nbits && !denorm || !(rvb->x[0] & 1)) | |
859 | break; | |
860 | if (dsign) { | |
861 | rvb = increment(rvb); | |
862 | if ( (j = rvbits & kmask) !=0) | |
863 | j = ULbits - j; | |
864 | if (hi0bits(rvb->x[rvb->wds - 1]) | |
865 | != j) | |
866 | rvbits++; | |
867 | irv = STRTOG_Normal | STRTOG_Inexhi; | |
868 | } | |
869 | else { | |
870 | if (bbbits == 1) | |
871 | goto undfl; | |
872 | decrement(rvb); | |
873 | irv = STRTOG_Normal | STRTOG_Inexlo; | |
874 | } | |
875 | break; | |
876 | } | |
877 | if ((dval(adj) = ratio(delta, bs)) <= 2.) { | |
878 | adj1: | |
879 | inex = STRTOG_Inexlo; | |
880 | if (dsign) { | |
881 | asub = 0; | |
882 | inex = STRTOG_Inexhi; | |
883 | } | |
884 | else if (denorm && bbbits <= 1) { | |
885 | undfl: | |
886 | rvb->wds = 0; | |
887 | rve = emin; | |
888 | irv = STRTOG_Underflow | STRTOG_Inexlo; | |
889 | break; | |
890 | } | |
891 | adj0 = dval(adj) = 1.; | |
892 | } | |
893 | else { | |
894 | adj0 = dval(adj) *= 0.5; | |
895 | if (dsign) { | |
896 | asub = 0; | |
897 | inex = STRTOG_Inexlo; | |
898 | } | |
899 | if (dval(adj) < 2147483647.) { | |
900 | L = adj0; | |
901 | adj0 -= L; | |
902 | switch(rd) { | |
903 | case 0: | |
904 | if (adj0 >= .5) | |
905 | goto inc_L; | |
906 | break; | |
907 | case 1: | |
908 | if (asub && adj0 > 0.) | |
909 | goto inc_L; | |
910 | break; | |
911 | case 2: | |
912 | if (!asub && adj0 > 0.) { | |
913 | inc_L: | |
914 | L++; | |
915 | inex = STRTOG_Inexact - inex; | |
916 | } | |
917 | } | |
918 | dval(adj) = L; | |
919 | } | |
920 | } | |
921 | y = rve + rvbits; | |
922 | ||
923 | /* adj *= ulp(dval(rv)); */ | |
924 | /* if (asub) rv -= adj; else rv += adj; */ | |
925 | ||
926 | if (!denorm && rvbits < nbits) { | |
927 | rvb = lshift(rvb, j = nbits - rvbits); | |
928 | rve -= j; | |
929 | rvbits = nbits; | |
930 | } | |
931 | ab = d2b(dval(adj), &abe, &abits); | |
932 | if (abe < 0) | |
933 | rshift(ab, -abe); | |
934 | else if (abe > 0) | |
935 | ab = lshift(ab, abe); | |
936 | rvb0 = rvb; | |
937 | if (asub) { | |
938 | /* rv -= adj; */ | |
939 | j = hi0bits(rvb->x[rvb->wds-1]); | |
940 | rvb = diff(rvb, ab); | |
941 | k = rvb0->wds - 1; | |
942 | if (denorm) | |
943 | /* do nothing */; | |
944 | else if (rvb->wds <= k | |
945 | || hi0bits( rvb->x[k]) > | |
946 | hi0bits(rvb0->x[k])) { | |
947 | /* unlikely; can only have lost 1 high bit */ | |
948 | if (rve1 == emin) { | |
949 | --rvbits; | |
950 | denorm = 1; | |
951 | } | |
952 | else { | |
953 | rvb = lshift(rvb, 1); | |
954 | --rve; | |
955 | --rve1; | |
956 | L = finished = 0; | |
957 | } | |
958 | } | |
959 | } | |
960 | else { | |
961 | rvb = sum(rvb, ab); | |
962 | k = rvb->wds - 1; | |
963 | if (k >= rvb0->wds | |
964 | || hi0bits(rvb->x[k]) < hi0bits(rvb0->x[k])) { | |
965 | if (denorm) { | |
966 | if (++rvbits == nbits) | |
967 | denorm = 0; | |
968 | } | |
969 | else { | |
970 | rshift(rvb, 1); | |
971 | rve++; | |
972 | rve1++; | |
973 | L = 0; | |
974 | } | |
975 | } | |
976 | } | |
977 | Bfree(ab); | |
978 | Bfree(rvb0); | |
979 | if (finished) | |
980 | break; | |
981 | ||
982 | z = rve + rvbits; | |
983 | if (y == z && L) { | |
984 | /* Can we stop now? */ | |
985 | tol = dval(adj) * 5e-16; /* > max rel error */ | |
986 | dval(adj) = adj0 - .5; | |
987 | if (dval(adj) < -tol) { | |
988 | if (adj0 > tol) { | |
989 | irv |= inex; | |
990 | break; | |
991 | } | |
992 | } | |
993 | else if (dval(adj) > tol && adj0 < 1. - tol) { | |
994 | irv |= inex; | |
995 | break; | |
996 | } | |
997 | } | |
998 | bb0 = denorm ? 0 : trailz(rvb); | |
999 | Bfree(bb); | |
1000 | Bfree(bd); | |
1001 | Bfree(bs); | |
1002 | Bfree(delta); | |
1003 | } | |
1004 | if (!denorm && (j = nbits - rvbits)) { | |
1005 | if (j > 0) | |
1006 | rvb = lshift(rvb, j); | |
1007 | else | |
1008 | rshift(rvb, -j); | |
1009 | rve -= j; | |
1010 | } | |
1011 | *exp = rve; | |
1012 | Bfree(bb); | |
1013 | Bfree(bd); | |
1014 | Bfree(bs); | |
1015 | Bfree(bd0); | |
1016 | Bfree(delta); | |
1017 | if (rve > fpi->emax) { | |
1018 | huge: | |
1019 | rvb->wds = 0; | |
1020 | irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi; | |
1021 | #ifndef NO_ERRNO | |
1022 | errno = ERANGE; | |
1023 | #endif | |
1024 | infnanexp: | |
1025 | *exp = fpi->emax + 1; | |
1026 | } | |
1027 | ret: | |
1028 | if (denorm) { | |
1029 | if (sudden_underflow) { | |
1030 | rvb->wds = 0; | |
1031 | irv = STRTOG_Underflow | STRTOG_Inexlo; | |
1032 | } | |
1033 | else { | |
1034 | irv = (irv & ~STRTOG_Retmask) | | |
1035 | (rvb->wds > 0 ? STRTOG_Denormal : STRTOG_Zero); | |
1036 | if (irv & STRTOG_Inexact) | |
1037 | irv |= STRTOG_Underflow; | |
1038 | } | |
1039 | } | |
1040 | if (se) | |
1041 | *se = (char *)s; | |
1042 | if (sign) | |
1043 | irv |= STRTOG_Neg; | |
1044 | if (rvb) { | |
1045 | copybits(bits, nbits, rvb); | |
1046 | Bfree(rvb); | |
1047 | } | |
1048 | #if !defined(NO_ERRNO) && __DARWIN_UNIX03 | |
1049 | if (irv & STRTOG_Underflow) | |
1050 | errno = ERANGE; | |
1051 | #endif | |
1052 | return irv; | |
1053 | } |