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