xref: /freebsd/contrib/gdtoa/strtodg.c (revision 8fa0b743820f61c661ba5f3ea0e3be0dc137910e)
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 "gdtoaimp.h"
33 
34 #ifdef USE_LOCALE
35 #include "locale.h"
36 #endif
37 
38  static CONST int
39 fivesbits[] = {	 0,  3,  5,  7, 10, 12, 14, 17, 19, 21,
40 		24, 26, 28, 31, 33, 35, 38, 40, 42, 45,
41 		47, 49, 52
42 #ifdef VAX
43 		, 54, 56
44 #endif
45 		};
46 
47  Bigint *
48 #ifdef KR_headers
increment(b)49 increment(b) Bigint *b;
50 #else
51 increment(Bigint *b)
52 #endif
53 {
54 	ULong *x, *xe;
55 	Bigint *b1;
56 #ifdef Pack_16
57 	ULong carry = 1, y;
58 #endif
59 
60 	x = b->x;
61 	xe = x + b->wds;
62 #ifdef Pack_32
63 	do {
64 		if (*x < (ULong)0xffffffffL) {
65 			++*x;
66 			return b;
67 			}
68 		*x++ = 0;
69 		} while(x < xe);
70 #else
71 	do {
72 		y = *x + carry;
73 		carry = y >> 16;
74 		*x++ = y & 0xffff;
75 		if (!carry)
76 			return b;
77 		} while(x < xe);
78 	if (carry)
79 #endif
80 	{
81 		if (b->wds >= b->maxwds) {
82 			b1 = Balloc(b->k+1);
83 			Bcopy(b1,b);
84 			Bfree(b);
85 			b = b1;
86 			}
87 		b->x[b->wds++] = 1;
88 		}
89 	return b;
90 	}
91 
92  void
93 #ifdef KR_headers
decrement(b)94 decrement(b) Bigint *b;
95 #else
96 decrement(Bigint *b)
97 #endif
98 {
99 	ULong *x, *xe;
100 #ifdef Pack_16
101 	ULong borrow = 1, y;
102 #endif
103 
104 	x = b->x;
105 	xe = x + b->wds;
106 #ifdef Pack_32
107 	do {
108 		if (*x) {
109 			--*x;
110 			break;
111 			}
112 		*x++ = 0xffffffffL;
113 		}
114 		while(x < xe);
115 #else
116 	do {
117 		y = *x - borrow;
118 		borrow = (y & 0x10000) >> 16;
119 		*x++ = y & 0xffff;
120 		} while(borrow && x < xe);
121 #endif
122 	}
123 
124  static int
125 #ifdef KR_headers
all_on(b,n)126 all_on(b, n) Bigint *b; int n;
127 #else
128 all_on(Bigint *b, int n)
129 #endif
130 {
131 	ULong *x, *xe;
132 
133 	x = b->x;
134 	xe = x + (n >> kshift);
135 	while(x < xe)
136 		if ((*x++ & ALL_ON) != ALL_ON)
137 			return 0;
138 	if (n &= kmask)
139 		return ((*x | (ALL_ON << n)) & ALL_ON) == ALL_ON;
140 	return 1;
141 	}
142 
143  Bigint *
144 #ifdef KR_headers
set_ones(b,n)145 set_ones(b, n) Bigint *b; int n;
146 #else
147 set_ones(Bigint *b, int n)
148 #endif
149 {
150 	int k;
151 	ULong *x, *xe;
152 
153 	k = (n + ((1 << kshift) - 1)) >> kshift;
154 	if (b->k < k) {
155 		Bfree(b);
156 		b = Balloc(k);
157 		}
158 	k = n >> kshift;
159 	if (n &= kmask)
160 		k++;
161 	b->wds = k;
162 	x = b->x;
163 	xe = x + k;
164 	while(x < xe)
165 		*x++ = ALL_ON;
166 	if (n)
167 		x[-1] >>= ULbits - n;
168 	return b;
169 	}
170 
171  static int
rvOK(d,fpi,exp,bits,exact,rd,irv)172 rvOK
173 #ifdef KR_headers
174  (d, fpi, exp, bits, exact, rd, irv)
175  U *d; FPI *fpi; Long *exp; ULong *bits; int exact, rd, *irv;
176 #else
177  (U *d, FPI *fpi, Long *exp, ULong *bits, int exact, int rd, int *irv)
178 #endif
179 {
180 	Bigint *b;
181 	ULong carry, inex, lostbits;
182 	int bdif, e, j, k, k1, nb, rv;
183 
184 	carry = rv = 0;
185 	b = d2b(dval(d), &e, &bdif);
186 	bdif -= nb = fpi->nbits;
187 	e += bdif;
188 	if (bdif <= 0) {
189 		if (exact)
190 			goto trunc;
191 		goto ret;
192 		}
193 	if (P == nb) {
194 		if (
195 #ifndef IMPRECISE_INEXACT
196 			exact &&
197 #endif
198 			fpi->rounding ==
199 #ifdef RND_PRODQUOT
200 					FPI_Round_near
201 #else
202 					Flt_Rounds
203 #endif
204 			) goto trunc;
205 		goto ret;
206 		}
207 	switch(rd) {
208 	  case 1: /* round down (toward -Infinity) */
209 		goto trunc;
210 	  case 2: /* round up (toward +Infinity) */
211 		break;
212 	  default: /* round near */
213 		k = bdif - 1;
214 		if (k < 0)
215 			goto trunc;
216 		if (!k) {
217 			if (!exact)
218 				goto ret;
219 			if (b->x[0] & 2)
220 				break;
221 			goto trunc;
222 			}
223 		if (b->x[k>>kshift] & ((ULong)1 << (k & kmask)))
224 			break;
225 		goto trunc;
226 	  }
227 	/* "break" cases: round up 1 bit, then truncate; bdif > 0 */
228 	carry = 1;
229  trunc:
230 	inex = lostbits = 0;
231 	if (bdif > 0) {
232 		if ( (lostbits = any_on(b, bdif)) !=0)
233 			inex = STRTOG_Inexlo;
234 		rshift(b, bdif);
235 		if (carry) {
236 			inex = STRTOG_Inexhi;
237 			b = increment(b);
238 			if ( (j = nb & kmask) !=0)
239 				j = ULbits - j;
240 			if (hi0bits(b->x[b->wds - 1]) != j) {
241 				if (!lostbits)
242 					lostbits = b->x[0] & 1;
243 				rshift(b, 1);
244 				e++;
245 				}
246 			}
247 		}
248 	else if (bdif < 0)
249 		b = lshift(b, -bdif);
250 	if (e < fpi->emin) {
251 		k = fpi->emin - e;
252 		e = fpi->emin;
253 		if (k > nb || fpi->sudden_underflow) {
254 			b->wds = inex = 0;
255 			*irv = STRTOG_Underflow | STRTOG_Inexlo;
256 			}
257 		else {
258 			k1 = k - 1;
259 			if (k1 > 0 && !lostbits)
260 				lostbits = any_on(b, k1);
261 			if (!lostbits && !exact)
262 				goto ret;
263 			lostbits |=
264 			  carry = b->x[k1>>kshift] & (1 << (k1 & kmask));
265 			rshift(b, k);
266 			*irv = STRTOG_Denormal;
267 			if (carry) {
268 				b = increment(b);
269 				inex = STRTOG_Inexhi | STRTOG_Underflow;
270 				}
271 			else if (lostbits)
272 				inex = STRTOG_Inexlo | STRTOG_Underflow;
273 			}
274 		}
275 	else if (e > fpi->emax) {
276 		e = fpi->emax + 1;
277 		*irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi;
278 #ifndef NO_ERRNO
279 		errno = ERANGE;
280 #endif
281 		b->wds = inex = 0;
282 		}
283 	*exp = e;
284 	copybits(bits, nb, b);
285 	*irv |= inex;
286 	rv = 1;
287  ret:
288 	Bfree(b);
289 	return rv;
290 	}
291 
292  static int
293 #ifdef KR_headers
mantbits(d)294 mantbits(d) U *d;
295 #else
296 mantbits(U *d)
297 #endif
298 {
299 	ULong L;
300 #ifdef VAX
301 	L = word1(d) << 16 | word1(d) >> 16;
302 	if (L)
303 #else
304 	if ( (L = word1(d)) !=0)
305 #endif
306 		return P - lo0bits(&L);
307 #ifdef VAX
308 	L = word0(d) << 16 | word0(d) >> 16 | Exp_msk11;
309 #else
310 	L = word0(d) | Exp_msk1;
311 #endif
312 	return P - 32 - lo0bits(&L);
313 	}
314 
315  int
strtodg_l(s00,se,fpi,exp,bits,loc)316 strtodg_l
317 #ifdef KR_headers
318 	(s00, se, fpi, exp, bits, loc)
319 	CONST char *s00; char **se; FPI *fpi; Long *exp; ULong *bits; locale_t loc;
320 #else
321 	(CONST char *s00, char **se, FPI *fpi, Long *exp, ULong *bits, locale_t loc)
322 #endif
323 {
324 	int abe, abits, asub;
325 	int bb0, bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, denorm;
326 	int dsign, e, e1, e2, emin, esign, finished, i, inex, irv;
327 	int j, k, nbits, nd, nd0, nf, nz, nz0, rd, rvbits, rve, rve1, sign;
328 	int sudden_underflow;
329 	CONST char *s, *s0, *s1;
330 	double adj0, tol;
331 	Long L;
332 	U adj, rv;
333 	ULong *b, *be, y, z;
334 	Bigint *ab, *bb, *bb1, *bd, *bd0, *bs, *delta, *rvb, *rvb0;
335 #ifdef USE_LOCALE /*{{*/
336 #ifdef NO_LOCALE_CACHE
337 	char *decimalpoint = localeconv_l(loc)->decimal_point;
338 	int dplen = strlen(decimalpoint);
339 #else
340 	char *decimalpoint;
341 	static char *decimalpoint_cache;
342 	static int dplen;
343 	if (!(s0 = decimalpoint_cache)) {
344 		s0 = localeconv_l(loc)->decimal_point;
345 		if ((decimalpoint_cache = (char*)MALLOC(strlen(s0) + 1))) {
346 			strcpy(decimalpoint_cache, s0);
347 			s0 = decimalpoint_cache;
348 			}
349 		dplen = strlen(s0);
350 		}
351 	decimalpoint = (char*)s0;
352 #endif /*NO_LOCALE_CACHE*/
353 #else  /*USE_LOCALE}{*/
354 #define dplen 1
355 #endif /*USE_LOCALE}}*/
356 
357 	irv = STRTOG_Zero;
358 	denorm = sign = nz0 = nz = 0;
359 	dval(&rv) = 0.;
360 	rvb = 0;
361 	nbits = fpi->nbits;
362 	for(s = s00;;s++) switch(*s) {
363 		case '-':
364 			sign = 1;
365 			/* no break */
366 		case '+':
367 			if (*++s)
368 				goto break2;
369 			/* no break */
370 		case 0:
371 			sign = 0;
372 			irv = STRTOG_NoNumber;
373 			s = s00;
374 			goto ret;
375 		case '\t':
376 		case '\n':
377 		case '\v':
378 		case '\f':
379 		case '\r':
380 		case ' ':
381 			continue;
382 		default:
383 			goto break2;
384 		}
385  break2:
386 	if (*s == '0') {
387 #ifndef NO_HEX_FP
388 		switch(s[1]) {
389 		  case 'x':
390 		  case 'X':
391 			irv = gethex(&s, fpi, exp, &rvb, sign);
392 			if (irv == STRTOG_NoNumber) {
393 				s = s00;
394 				sign = 0;
395 				}
396 			goto ret;
397 		  }
398 #endif
399 		nz0 = 1;
400 		while(*++s == '0') ;
401 		if (!*s)
402 			goto ret;
403 		}
404 	sudden_underflow = fpi->sudden_underflow;
405 	s0 = s;
406 	y = z = 0;
407 	for(decpt = nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
408 		if (nd < 9)
409 			y = 10*y + c - '0';
410 		else if (nd < 16)
411 			z = 10*z + c - '0';
412 	nd0 = nd;
413 #ifdef USE_LOCALE
414 	if (c == *decimalpoint) {
415 		for(i = 1; decimalpoint[i]; ++i)
416 			if (s[i] != decimalpoint[i])
417 				goto dig_done;
418 		s += i;
419 		c = *s;
420 #else
421 	if (c == '.') {
422 		c = *++s;
423 #endif
424 		decpt = 1;
425 		if (!nd) {
426 			for(; c == '0'; c = *++s)
427 				nz++;
428 			if (c > '0' && c <= '9') {
429 				s0 = s;
430 				nf += nz;
431 				nz = 0;
432 				goto have_dig;
433 				}
434 			goto dig_done;
435 			}
436 		for(; c >= '0' && c <= '9'; c = *++s) {
437  have_dig:
438 			nz++;
439 			if (c -= '0') {
440 				nf += nz;
441 				for(i = 1; i < nz; i++)
442 					if (nd++ < 9)
443 						y *= 10;
444 					else if (nd <= DBL_DIG + 1)
445 						z *= 10;
446 				if (nd++ < 9)
447 					y = 10*y + c;
448 				else if (nd <= DBL_DIG + 1)
449 					z = 10*z + c;
450 				nz = 0;
451 				}
452 			}
453 		}/*}*/
454  dig_done:
455 	e = 0;
456 	if (c == 'e' || c == 'E') {
457 		if (!nd && !nz && !nz0) {
458 			irv = STRTOG_NoNumber;
459 			s = s00;
460 			goto ret;
461 			}
462 		s00 = s;
463 		esign = 0;
464 		switch(c = *++s) {
465 			case '-':
466 				esign = 1;
467 			case '+':
468 				c = *++s;
469 			}
470 		if (c >= '0' && c <= '9') {
471 			while(c == '0')
472 				c = *++s;
473 			if (c > '0' && c <= '9') {
474 				L = c - '0';
475 				s1 = s;
476 				while((c = *++s) >= '0' && c <= '9')
477 					L = 10*L + c - '0';
478 				if (s - s1 > 8 || L > 19999)
479 					/* Avoid confusion from exponents
480 					 * so large that e might overflow.
481 					 */
482 					e = 19999; /* safe for 16 bit ints */
483 				else
484 					e = (int)L;
485 				if (esign)
486 					e = -e;
487 				}
488 			else
489 				e = 0;
490 			}
491 		else
492 			s = s00;
493 		}
494 	if (!nd) {
495 		if (!nz && !nz0) {
496 #ifdef INFNAN_CHECK
497 			/* Check for Nan and Infinity */
498 			if (!decpt)
499 			 switch(c) {
500 			  case 'i':
501 			  case 'I':
502 				if (match(&s,"nf")) {
503 					--s;
504 					if (!match(&s,"inity"))
505 						++s;
506 					irv = STRTOG_Infinite;
507 					goto infnanexp;
508 					}
509 				break;
510 			  case 'n':
511 			  case 'N':
512 				if (match(&s, "an")) {
513 					irv = STRTOG_NaN;
514 					*exp = fpi->emax + 1;
515 #ifndef No_Hex_NaN
516 					if (*s == '(') /*)*/
517 						irv = hexnan(&s, fpi, bits);
518 #endif
519 					goto infnanexp;
520 					}
521 			  }
522 #endif /* INFNAN_CHECK */
523 			irv = STRTOG_NoNumber;
524 			s = s00;
525 			}
526 		goto ret;
527 		}
528 
529 	irv = STRTOG_Normal;
530 	e1 = e -= nf;
531 	rd = 0;
532 	switch(fpi->rounding & 3) {
533 	  case FPI_Round_up:
534 		rd = 2 - sign;
535 		break;
536 	  case FPI_Round_zero:
537 		rd = 1;
538 		break;
539 	  case FPI_Round_down:
540 		rd = 1 + sign;
541 	  }
542 
543 	/* Now we have nd0 digits, starting at s0, followed by a
544 	 * decimal point, followed by nd-nd0 digits.  The number we're
545 	 * after is the integer represented by those digits times
546 	 * 10**e */
547 
548 	if (!nd0)
549 		nd0 = nd;
550 	k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
551 	dval(&rv) = y;
552 	if (k > 9)
553 		dval(&rv) = tens[k - 9] * dval(&rv) + z;
554 	bd0 = 0;
555 	if (nbits <= P && nd <= DBL_DIG) {
556 		if (!e) {
557 			if (rvOK(&rv, fpi, exp, bits, 1, rd, &irv))
558 				goto ret;
559 			}
560 		else if (e > 0) {
561 			if (e <= Ten_pmax) {
562 #ifdef VAX
563 				goto vax_ovfl_check;
564 #else
565 				i = fivesbits[e] + mantbits(&rv) <= P;
566 				/* rv = */ rounded_product(dval(&rv), tens[e]);
567 				if (rvOK(&rv, fpi, exp, bits, i, rd, &irv))
568 					goto ret;
569 				e1 -= e;
570 				goto rv_notOK;
571 #endif
572 				}
573 			i = DBL_DIG - nd;
574 			if (e <= Ten_pmax + i) {
575 				/* A fancier test would sometimes let us do
576 				 * this for larger i values.
577 				 */
578 				e2 = e - i;
579 				e1 -= i;
580 				dval(&rv) *= tens[i];
581 #ifdef VAX
582 				/* VAX exponent range is so narrow we must
583 				 * worry about overflow here...
584 				 */
585  vax_ovfl_check:
586 				dval(&adj) = dval(&rv);
587 				word0(&adj) -= P*Exp_msk1;
588 				/* adj = */ rounded_product(dval(&adj), tens[e2]);
589 				if ((word0(&adj) & Exp_mask)
590 				 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
591 					goto rv_notOK;
592 				word0(&adj) += P*Exp_msk1;
593 				dval(&rv) = dval(&adj);
594 #else
595 				/* rv = */ rounded_product(dval(&rv), tens[e2]);
596 #endif
597 				if (rvOK(&rv, fpi, exp, bits, 0, rd, &irv))
598 					goto ret;
599 				e1 -= e2;
600 				}
601 			}
602 #ifndef Inaccurate_Divide
603 		else if (e >= -Ten_pmax) {
604 			/* rv = */ rounded_quotient(dval(&rv), tens[-e]);
605 			if (rvOK(&rv, fpi, exp, bits, 0, rd, &irv))
606 				goto ret;
607 			e1 -= e;
608 			}
609 #endif
610 		}
611  rv_notOK:
612 	e1 += nd - k;
613 
614 	/* Get starting approximation = rv * 10**e1 */
615 
616 	e2 = 0;
617 	if (e1 > 0) {
618 		if ( (i = e1 & 15) !=0)
619 			dval(&rv) *= tens[i];
620 		if (e1 &= ~15) {
621 			e1 >>= 4;
622 			while(e1 >= (1 << (n_bigtens-1))) {
623 				e2 += ((word0(&rv) & Exp_mask)
624 					>> Exp_shift1) - Bias;
625 				word0(&rv) &= ~Exp_mask;
626 				word0(&rv) |= Bias << Exp_shift1;
627 				dval(&rv) *= bigtens[n_bigtens-1];
628 				e1 -= 1 << (n_bigtens-1);
629 				}
630 			e2 += ((word0(&rv) & Exp_mask) >> Exp_shift1) - Bias;
631 			word0(&rv) &= ~Exp_mask;
632 			word0(&rv) |= Bias << Exp_shift1;
633 			for(j = 0; e1 > 0; j++, e1 >>= 1)
634 				if (e1 & 1)
635 					dval(&rv) *= bigtens[j];
636 			}
637 		}
638 	else if (e1 < 0) {
639 		e1 = -e1;
640 		if ( (i = e1 & 15) !=0)
641 			dval(&rv) /= tens[i];
642 		if (e1 &= ~15) {
643 			e1 >>= 4;
644 			while(e1 >= (1 << (n_bigtens-1))) {
645 				e2 += ((word0(&rv) & Exp_mask)
646 					>> Exp_shift1) - Bias;
647 				word0(&rv) &= ~Exp_mask;
648 				word0(&rv) |= Bias << Exp_shift1;
649 				dval(&rv) *= tinytens[n_bigtens-1];
650 				e1 -= 1 << (n_bigtens-1);
651 				}
652 			e2 += ((word0(&rv) & Exp_mask) >> Exp_shift1) - Bias;
653 			word0(&rv) &= ~Exp_mask;
654 			word0(&rv) |= Bias << Exp_shift1;
655 			for(j = 0; e1 > 0; j++, e1 >>= 1)
656 				if (e1 & 1)
657 					dval(&rv) *= tinytens[j];
658 			}
659 		}
660 #ifdef IBM
661 	/* e2 is a correction to the (base 2) exponent of the return
662 	 * value, reflecting adjustments above to avoid overflow in the
663 	 * native arithmetic.  For native IBM (base 16) arithmetic, we
664 	 * must multiply e2 by 4 to change from base 16 to 2.
665 	 */
666 	e2 <<= 2;
667 #endif
668 	rvb = d2b(dval(&rv), &rve, &rvbits);	/* rv = rvb * 2^rve */
669 	rve += e2;
670 	if ((j = rvbits - nbits) > 0) {
671 		rshift(rvb, j);
672 		rvbits = nbits;
673 		rve += j;
674 		}
675 	bb0 = 0;	/* trailing zero bits in rvb */
676 	e2 = rve + rvbits - nbits;
677 	if (e2 > fpi->emax + 1)
678 		goto huge;
679 	rve1 = rve + rvbits - nbits;
680 	if (e2 < (emin = fpi->emin)) {
681 		denorm = 1;
682 		j = rve - emin;
683 		if (j > 0) {
684 			rvb = lshift(rvb, j);
685 			rvbits += j;
686 			}
687 		else if (j < 0) {
688 			rvbits += j;
689 			if (rvbits <= 0) {
690 				if (rvbits < -1) {
691  ufl:
692 					rvb->wds = 0;
693 					rvb->x[0] = 0;
694 					*exp = emin;
695 					irv = STRTOG_Underflow | STRTOG_Inexlo;
696 					goto ret;
697 					}
698 				rvb->x[0] = rvb->wds = rvbits = 1;
699 				}
700 			else
701 				rshift(rvb, -j);
702 			}
703 		rve = rve1 = emin;
704 		if (sudden_underflow && e2 + 1 < emin)
705 			goto ufl;
706 		}
707 
708 	/* Now the hard part -- adjusting rv to the correct value.*/
709 
710 	/* Put digits into bd: true value = bd * 10^e */
711 
712 	bd0 = s2b(s0, nd0, nd, y, dplen);
713 
714 	for(;;) {
715 		bd = Balloc(bd0->k);
716 		Bcopy(bd, bd0);
717 		bb = Balloc(rvb->k);
718 		Bcopy(bb, rvb);
719 		bbbits = rvbits - bb0;
720 		bbe = rve + bb0;
721 		bs = i2b(1);
722 
723 		if (e >= 0) {
724 			bb2 = bb5 = 0;
725 			bd2 = bd5 = e;
726 			}
727 		else {
728 			bb2 = bb5 = -e;
729 			bd2 = bd5 = 0;
730 			}
731 		if (bbe >= 0)
732 			bb2 += bbe;
733 		else
734 			bd2 -= bbe;
735 		bs2 = bb2;
736 		j = nbits + 1 - bbbits;
737 		i = bbe + bbbits - nbits;
738 		if (i < emin)	/* denormal */
739 			j += i - emin;
740 		bb2 += j;
741 		bd2 += j;
742 		i = bb2 < bd2 ? bb2 : bd2;
743 		if (i > bs2)
744 			i = bs2;
745 		if (i > 0) {
746 			bb2 -= i;
747 			bd2 -= i;
748 			bs2 -= i;
749 			}
750 		if (bb5 > 0) {
751 			bs = pow5mult(bs, bb5);
752 			bb1 = mult(bs, bb);
753 			Bfree(bb);
754 			bb = bb1;
755 			}
756 		bb2 -= bb0;
757 		if (bb2 > 0)
758 			bb = lshift(bb, bb2);
759 		else if (bb2 < 0)
760 			rshift(bb, -bb2);
761 		if (bd5 > 0)
762 			bd = pow5mult(bd, bd5);
763 		if (bd2 > 0)
764 			bd = lshift(bd, bd2);
765 		if (bs2 > 0)
766 			bs = lshift(bs, bs2);
767 		asub = 1;
768 		inex = STRTOG_Inexhi;
769 		delta = diff(bb, bd);
770 		if (delta->wds <= 1 && !delta->x[0])
771 			break;
772 		dsign = delta->sign;
773 		delta->sign = finished = 0;
774 		L = 0;
775 		i = cmp(delta, bs);
776 		if (rd && i <= 0) {
777 			irv = STRTOG_Normal;
778 			if ( (finished = dsign ^ (rd&1)) !=0) {
779 				if (dsign != 0) {
780 					irv |= STRTOG_Inexhi;
781 					goto adj1;
782 					}
783 				irv |= STRTOG_Inexlo;
784 				if (rve1 == emin)
785 					goto adj1;
786 				for(i = 0, j = nbits; j >= ULbits;
787 						i++, j -= ULbits) {
788 					if (rvb->x[i] & ALL_ON)
789 						goto adj1;
790 					}
791 				if (j > 1 && lo0bits(rvb->x + i) < j - 1)
792 					goto adj1;
793 				rve = rve1 - 1;
794 				rvb = set_ones(rvb, rvbits = nbits);
795 				break;
796 				}
797 			irv |= dsign ? STRTOG_Inexlo : STRTOG_Inexhi;
798 			break;
799 			}
800 		if (i < 0) {
801 			/* Error is less than half an ulp -- check for
802 			 * special case of mantissa a power of two.
803 			 */
804 			irv = dsign
805 				? STRTOG_Normal | STRTOG_Inexlo
806 				: STRTOG_Normal | STRTOG_Inexhi;
807 			if (dsign || bbbits > 1 || denorm || rve1 == emin)
808 				break;
809 			delta = lshift(delta,1);
810 			if (cmp(delta, bs) > 0) {
811 				irv = STRTOG_Normal | STRTOG_Inexlo;
812 				goto drop_down;
813 				}
814 			break;
815 			}
816 		if (i == 0) {
817 			/* exactly half-way between */
818 			if (dsign) {
819 				if (denorm && all_on(rvb, rvbits)) {
820 					/*boundary case -- increment exponent*/
821 					rvb->wds = 1;
822 					rvb->x[0] = 1;
823 					rve = emin + nbits - (rvbits = 1);
824 					irv = STRTOG_Normal | STRTOG_Inexhi;
825 					denorm = 0;
826 					break;
827 					}
828 				irv = STRTOG_Normal | STRTOG_Inexlo;
829 				}
830 			else if (bbbits == 1) {
831 				irv = STRTOG_Normal;
832  drop_down:
833 				/* boundary case -- decrement exponent */
834 				if (rve1 == emin) {
835 					irv = STRTOG_Normal | STRTOG_Inexhi;
836 					if (rvb->wds == 1 && rvb->x[0] == 1)
837 						sudden_underflow = 1;
838 					break;
839 					}
840 				rve -= nbits;
841 				rvb = set_ones(rvb, rvbits = nbits);
842 				break;
843 				}
844 			else
845 				irv = STRTOG_Normal | STRTOG_Inexhi;
846 			if ((bbbits < nbits && !denorm) || !(rvb->x[0] & 1))
847 				break;
848 			if (dsign) {
849 				rvb = increment(rvb);
850 				j = kmask & (ULbits - (rvbits & kmask));
851 				if (hi0bits(rvb->x[rvb->wds - 1]) != j)
852 					rvbits++;
853 				irv = STRTOG_Normal | STRTOG_Inexhi;
854 				}
855 			else {
856 				if (bbbits == 1)
857 					goto undfl;
858 				decrement(rvb);
859 				irv = STRTOG_Normal | STRTOG_Inexlo;
860 				}
861 			break;
862 			}
863 		if ((dval(&adj) = ratio(delta, bs)) <= 2.) {
864  adj1:
865 			inex = STRTOG_Inexlo;
866 			if (dsign) {
867 				asub = 0;
868 				inex = STRTOG_Inexhi;
869 				}
870 			else if (denorm && bbbits <= 1) {
871  undfl:
872 				rvb->wds = 0;
873 				rve = emin;
874 				irv = STRTOG_Underflow | STRTOG_Inexlo;
875 				break;
876 				}
877 			adj0 = dval(&adj) = 1.;
878 			}
879 		else {
880 			adj0 = dval(&adj) *= 0.5;
881 			if (dsign) {
882 				asub = 0;
883 				inex = STRTOG_Inexlo;
884 				}
885 			if (dval(&adj) < 2147483647.) {
886 				L = adj0;
887 				adj0 -= L;
888 				switch(rd) {
889 				  case 0:
890 					if (adj0 >= .5)
891 						goto inc_L;
892 					break;
893 				  case 1:
894 					if (asub && adj0 > 0.)
895 						goto inc_L;
896 					break;
897 				  case 2:
898 					if (!asub && adj0 > 0.) {
899  inc_L:
900 						L++;
901 						inex = STRTOG_Inexact - inex;
902 						}
903 				  }
904 				dval(&adj) = L;
905 				}
906 			}
907 		y = rve + rvbits;
908 
909 		/* adj *= ulp(dval(&rv)); */
910 		/* if (asub) rv -= adj; else rv += adj; */
911 
912 		if (!denorm && rvbits < nbits) {
913 			rvb = lshift(rvb, j = nbits - rvbits);
914 			rve -= j;
915 			rvbits = nbits;
916 			}
917 		ab = d2b(dval(&adj), &abe, &abits);
918 		if (abe < 0)
919 			rshift(ab, -abe);
920 		else if (abe > 0)
921 			ab = lshift(ab, abe);
922 		rvb0 = rvb;
923 		if (asub) {
924 			/* rv -= adj; */
925 			j = hi0bits(rvb->x[rvb->wds-1]);
926 			rvb = diff(rvb, ab);
927 			k = rvb0->wds - 1;
928 			if (denorm)
929 				/* do nothing */;
930 			else if (rvb->wds <= k
931 				|| hi0bits( rvb->x[k]) >
932 				   hi0bits(rvb0->x[k])) {
933 				/* unlikely; can only have lost 1 high bit */
934 				if (rve1 == emin) {
935 					--rvbits;
936 					denorm = 1;
937 					}
938 				else {
939 					rvb = lshift(rvb, 1);
940 					--rve;
941 					--rve1;
942 					L = finished = 0;
943 					}
944 				}
945 			}
946 		else {
947 			rvb = sum(rvb, ab);
948 			k = rvb->wds - 1;
949 			if (k >= rvb0->wds
950 			 || hi0bits(rvb->x[k]) < hi0bits(rvb0->x[k])) {
951 				if (denorm) {
952 					if (++rvbits == nbits)
953 						denorm = 0;
954 					}
955 				else {
956 					rshift(rvb, 1);
957 					rve++;
958 					rve1++;
959 					L = 0;
960 					}
961 				}
962 			}
963 		Bfree(ab);
964 		Bfree(rvb0);
965 		if (finished)
966 			break;
967 
968 		z = rve + rvbits;
969 		if (y == z && L) {
970 			/* Can we stop now? */
971 			tol = dval(&adj) * 5e-16; /* > max rel error */
972 			dval(&adj) = adj0 - .5;
973 			if (dval(&adj) < -tol) {
974 				if (adj0 > tol) {
975 					irv |= inex;
976 					break;
977 					}
978 				}
979 			else if (dval(&adj) > tol && adj0 < 1. - tol) {
980 				irv |= inex;
981 				break;
982 				}
983 			}
984 		bb0 = denorm ? 0 : trailz(rvb);
985 		Bfree(bb);
986 		Bfree(bd);
987 		Bfree(bs);
988 		Bfree(delta);
989 		}
990 	if (!denorm && (j = nbits - rvbits)) {
991 		if (j > 0)
992 			rvb = lshift(rvb, j);
993 		else
994 			rshift(rvb, -j);
995 		rve -= j;
996 		}
997 	*exp = rve;
998 	Bfree(bb);
999 	Bfree(bd);
1000 	Bfree(bs);
1001 	Bfree(bd0);
1002 	Bfree(delta);
1003 	if (rve > fpi->emax) {
1004 		switch(fpi->rounding & 3) {
1005 		  case FPI_Round_near:
1006 			goto huge;
1007 		  case FPI_Round_up:
1008 			if (!sign)
1009 				goto huge;
1010 			break;
1011 		  case FPI_Round_down:
1012 			if (sign)
1013 				goto huge;
1014 		  }
1015 		/* Round to largest representable magnitude */
1016 		Bfree(rvb);
1017 		rvb = 0;
1018 		irv = STRTOG_Normal | STRTOG_Inexlo;
1019 		*exp = fpi->emax;
1020 		b = bits;
1021 		be = b + ((fpi->nbits + 31) >> 5);
1022 		while(b < be)
1023 			*b++ = -1;
1024 		if ((j = fpi->nbits & 0x1f))
1025 			*--be >>= (32 - j);
1026 		goto ret;
1027  huge:
1028 		rvb->wds = 0;
1029 		irv = STRTOG_Infinite | STRTOG_Overflow | STRTOG_Inexhi;
1030 #ifndef NO_ERRNO
1031 		errno = ERANGE;
1032 #endif
1033  infnanexp:
1034 		*exp = fpi->emax + 1;
1035 		}
1036  ret:
1037 	if (denorm) {
1038 		if (sudden_underflow) {
1039 			rvb->wds = 0;
1040 			irv = STRTOG_Underflow | STRTOG_Inexlo;
1041 #ifndef NO_ERRNO
1042 			errno = ERANGE;
1043 #endif
1044 			}
1045 		else  {
1046 			irv = (irv & ~STRTOG_Retmask) |
1047 				(rvb->wds > 0 ? STRTOG_Denormal : STRTOG_Zero);
1048 			if (irv & STRTOG_Inexact) {
1049 				irv |= STRTOG_Underflow;
1050 #ifndef NO_ERRNO
1051 				errno = ERANGE;
1052 #endif
1053 				}
1054 			}
1055 		}
1056 	if (se)
1057 		*se = (char *)s;
1058 	if (sign)
1059 		irv |= STRTOG_Neg;
1060 	if (rvb) {
1061 		copybits(bits, nbits, rvb);
1062 		Bfree(rvb);
1063 		}
1064 	return irv;
1065 	}
1066