1 /* $OpenBSD: strtod.c,v 1.21 2005/08/08 08:05:37 espie Exp $ */
2 /****************************************************************
3 *
4 * The author of this software is David M. Gay.
5 *
6 * Copyright (c) 1991 by AT&T.
7 *
8 * Permission to use, copy, modify, and distribute this software for any
9 * purpose without fee is hereby granted, provided that this entire notice
10 * is included in all copies of any software which is or includes a copy
11 * or modification of this software and in all copies of the supporting
12 * documentation for such software.
13 *
14 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
15 * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
16 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
17 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
18 *
19 ***************************************************************/
20
21 /* Please send bug reports to
22 David M. Gay
23 AT&T Bell Laboratories, Room 2C-463
24 600 Mountain Avenue
25 Murray Hill, NJ 07974-2070
26 U.S.A.
27 dmg@research.att.com or research!dmg
28 */
29
30 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
31 *
32 * This strtod returns a nearest machine number to the input decimal
33 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
34 * broken by the IEEE round-even rule. Otherwise ties are broken by
35 * biased rounding (add half and chop).
36 *
37 * Inspired loosely by William D. Clinger's paper "How to Read Floating
38 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
39 *
40 * Modifications:
41 *
42 * 1. We only require IEEE, IBM, or VAX double-precision
43 * arithmetic (not IEEE double-extended).
44 * 2. We get by with floating-point arithmetic in a case that
45 * Clinger missed -- when we're computing d * 10^n
46 * for a small integer d and the integer n is not too
47 * much larger than 22 (the maximum integer k for which
48 * we can represent 10^k exactly), we may be able to
49 * compute (d*10^k) * 10^(e-k) with just one roundoff.
50 * 3. Rather than a bit-at-a-time adjustment of the binary
51 * result in the hard case, we use floating-point
52 * arithmetic to determine the adjustment to within
53 * one bit; only in really hard cases do we need to
54 * compute a second residual.
55 * 4. Because of 3., we don't need a large table of powers of 10
56 * for ten-to-e (just some small tables, e.g. of 10^k
57 * for 0 <= k <= 22).
58 */
59
60 #include <sys/cdefs.h>
61 __RCSID("$MirOS: src/lib/libc/stdlib/strtod.c,v 1.4 2011/02/08 15:05:49 tg Exp $");
62
63 /*
64 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
65 * significant byte has the lowest address.
66 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
67 * significant byte has the lowest address.
68 * #define Long int on machines with 32-bit ints and 64-bit longs.
69 * #define Sudden_Underflow for IEEE-format machines without gradual
70 * underflow (i.e., that flush to zero on underflow).
71 * #define IBM for IBM mainframe-style floating-point arithmetic.
72 * #define VAX for VAX-style floating-point arithmetic.
73 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
74 * #define No_leftright to omit left-right logic in fast floating-point
75 * computation of dtoa.
76 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
77 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
78 * that use extended-precision instructions to compute rounded
79 * products and quotients) with IBM.
80 * #define ROUND_BIASED for IEEE-format with biased rounding.
81 * #define Inaccurate_Divide for IEEE-format with correctly rounded
82 * products but inaccurate quotients, e.g., for Intel i860.
83 * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
84 * integer arithmetic. Whether this speeds things up or slows things
85 * down depends on the machine and the number being converted.
86 * #define Bad_float_h if your system lacks a float.h or if it does not
87 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
88 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
89 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
90 * if memory is available and otherwise does something you deem
91 * appropriate. If MALLOC is undefined, malloc will be invoked
92 * directly -- and assumed always to succeed.
93 */
94
95 #if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \
96 defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \
97 defined(__powerpc__) || defined(__m88k__) || defined(__hppa__) || \
98 defined(__x86_64__) || (defined(__arm__) && defined(__VFP_FP__))
99 #include <sys/types.h>
100 #if BYTE_ORDER == BIG_ENDIAN
101 #define IEEE_BIG_ENDIAN
102 #else
103 #define IEEE_LITTLE_ENDIAN
104 #endif
105 #endif
106
107 #if defined(__arm__) && !defined(__VFP_FP__)
108 /*
109 * Although the CPU is little endian the FP has different
110 * byte and word endianness. The byte order is still little endian
111 * but the word order is big endian.
112 */
113 #define IEEE_BIG_ENDIAN
114 #endif
115
116 #ifdef __vax__
117 #define VAX
118 #endif
119
120 #define Long int32_t
121 #define ULong u_int32_t
122
123 #ifdef DEBUG
124 #include "stdio.h"
125 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
126 #endif
127
128 #ifdef __cplusplus
129 #include "malloc.h"
130 #include "memory.h"
131 #else
132 #include "stdlib.h"
133 #include "string.h"
134 #include "locale.h"
135 #endif
136
137 #ifdef MALLOC
138 extern void *MALLOC(size_t);
139 #else
140 #define MALLOC malloc
141 #endif
142
143 #include "ctype.h"
144 #include "errno.h"
145 #include <err.h>
146
147 #ifdef Bad_float_h
148 #ifdef IEEE_BIG_ENDIAN
149 #define IEEE_ARITHMETIC
150 #endif
151 #ifdef IEEE_LITTLE_ENDIAN
152 #define IEEE_ARITHMETIC
153 #endif
154
155 #ifdef IEEE_ARITHMETIC
156 #define DBL_DIG 15
157 #define DBL_MAX_10_EXP 308
158 #define DBL_MAX_EXP 1024
159 #define FLT_RADIX 2
160 #define FLT_ROUNDS 1
161 #define DBL_MAX 1.7976931348623157e+308
162 #endif
163
164 #ifdef IBM
165 #define DBL_DIG 16
166 #define DBL_MAX_10_EXP 75
167 #define DBL_MAX_EXP 63
168 #define FLT_RADIX 16
169 #define FLT_ROUNDS 0
170 #define DBL_MAX 7.2370055773322621e+75
171 #endif
172
173 #ifdef VAX
174 #define DBL_DIG 16
175 #define DBL_MAX_10_EXP 38
176 #define DBL_MAX_EXP 127
177 #define FLT_RADIX 2
178 #define FLT_ROUNDS 1
179 #define DBL_MAX 1.7014118346046923e+38
180 #endif
181
182 #ifndef LONG_MAX
183 #define LONG_MAX 2147483647
184 #endif
185 #else
186 #include "float.h"
187 #endif
188 #ifndef __MATH_H__
189 #include "math.h"
190 #endif
191
192 #ifdef __cplusplus
193 extern "C" {
194 #endif
195
196 #ifndef CONST
197 #define CONST const
198 #endif
199
200 #ifdef Unsigned_Shifts
201 #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
202 #else
203 #define Sign_Extend(a,b) /*no-op*/
204 #endif
205
206 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + \
207 defined(IBM) != 1
208 Exactly one of IEEE_LITTLE_ENDIAN IEEE_BIG_ENDIAN, VAX, or
209 IBM should be defined.
210 #endif
211
212 typedef union {
213 double d;
214 ULong ul[2];
215 } _double;
216 #define value(x) ((x).d)
217 #ifdef IEEE_LITTLE_ENDIAN
218 #define word0(x) ((x).ul[1])
219 #define word1(x) ((x).ul[0])
220 #else
221 #define word0(x) ((x).ul[0])
222 #define word1(x) ((x).ul[1])
223 #endif
224
225 /* The following definition of Storeinc is appropriate for MIPS processors.
226 * An alternative that might be better on some machines is
227 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
228 */
229 #if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
230 #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
231 ((unsigned short *)a)[0] = (unsigned short)c, a++)
232 #else
233 #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
234 ((unsigned short *)a)[1] = (unsigned short)c, a++)
235 #endif
236
237 /* #define P DBL_MANT_DIG */
238 /* Ten_pmax = floor(P*log(2)/log(5)) */
239 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
240 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
241 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
242
243 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN)
244 #define Exp_shift 20
245 #define Exp_shift1 20
246 #define Exp_msk1 0x100000
247 #define Exp_msk11 0x100000
248 #define Exp_mask 0x7ff00000
249 #define P 53
250 #define Bias 1023
251 #define IEEE_Arith
252 #define Emin (-1022)
253 #define Exp_1 0x3ff00000
254 #define Exp_11 0x3ff00000
255 #define Ebits 11
256 #define Frac_mask 0xfffff
257 #define Frac_mask1 0xfffff
258 #define Ten_pmax 22
259 #define Bletch 0x10
260 #define Bndry_mask 0xfffff
261 #define Bndry_mask1 0xfffff
262 #define LSB 1
263 #define Sign_bit 0x80000000
264 #define Log2P 1
265 #define Tiny0 0
266 #define Tiny1 1
267 #define Quick_max 14
268 #define Int_max 14
269 #define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
270 #else
271 #undef Sudden_Underflow
272 #define Sudden_Underflow
273 #ifdef IBM
274 #define Exp_shift 24
275 #define Exp_shift1 24
276 #define Exp_msk1 0x1000000
277 #define Exp_msk11 0x1000000
278 #define Exp_mask 0x7f000000
279 #define P 14
280 #define Bias 65
281 #define Exp_1 0x41000000
282 #define Exp_11 0x41000000
283 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
284 #define Frac_mask 0xffffff
285 #define Frac_mask1 0xffffff
286 #define Bletch 4
287 #define Ten_pmax 22
288 #define Bndry_mask 0xefffff
289 #define Bndry_mask1 0xffffff
290 #define LSB 1
291 #define Sign_bit 0x80000000
292 #define Log2P 4
293 #define Tiny0 0x100000
294 #define Tiny1 0
295 #define Quick_max 14
296 #define Int_max 15
297 #else /* VAX */
298 #define Exp_shift 23
299 #define Exp_shift1 7
300 #define Exp_msk1 0x80
301 #define Exp_msk11 0x800000
302 #define Exp_mask 0x7f80
303 #define P 56
304 #define Bias 129
305 #define Exp_1 0x40800000
306 #define Exp_11 0x4080
307 #define Ebits 8
308 #define Frac_mask 0x7fffff
309 #define Frac_mask1 0xffff007f
310 #define Ten_pmax 24
311 #define Bletch 2
312 #define Bndry_mask 0xffff007f
313 #define Bndry_mask1 0xffff007f
314 #define LSB 0x10000
315 #define Sign_bit 0x8000
316 #define Log2P 1
317 #define Tiny0 0x80
318 #define Tiny1 0
319 #define Quick_max 15
320 #define Int_max 15
321 #endif
322 #endif
323
324 #ifndef IEEE_Arith
325 #define ROUND_BIASED
326 #endif
327
328 #ifdef RND_PRODQUOT
329 #define rounded_product(a,b) a = rnd_prod(a, b)
330 #define rounded_quotient(a,b) a = rnd_quot(a, b)
331 extern double rnd_prod(double, double), rnd_quot(double, double);
332 #else
333 #define rounded_product(a,b) a *= b
334 #define rounded_quotient(a,b) a /= b
335 #endif
336
337 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
338 #define Big1 0xffffffff
339
340 #ifndef Just_16
341 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
342 * This makes some inner loops simpler and sometimes saves work
343 * during multiplications, but it often seems to make things slightly
344 * slower. Hence the default is now to store 32 bits per Long.
345 */
346 #ifndef Pack_32
347 #define Pack_32
348 #endif
349 #endif
350
351 #define Kmax 15
352
353 #ifdef __cplusplus
354 extern "C" double strtod(const char *s00, char **se);
355 extern "C" char *__dtoa(double d, int mode, int ndigits,
356 int *decpt, int *sign, char **rve);
357 #endif
358
359 struct
360 Bigint {
361 struct Bigint *next;
362 int k, maxwds, sign, wds;
363 ULong x[1];
364 };
365
366 typedef struct Bigint Bigint;
367
368 static Bigint *freelist[Kmax+1];
369
370 static Bigint *
Balloc(int k)371 Balloc(int k)
372 {
373 int x;
374 Bigint *rv;
375
376 if ((rv = freelist[k])) {
377 freelist[k] = rv->next;
378 }
379 else {
380 size_t nbytes;
381
382 x = 1 << k;
383 rv = (Bigint *)MALLOC(((nbytes = sizeof(Bigint) + (x-1)*sizeof(Long))));
384 if (rv == NULL)
385 err(255, "strtod: cannot allocate %zu bytes", nbytes);
386 rv->k = k;
387 rv->maxwds = x;
388 }
389 rv->sign = rv->wds = 0;
390 return rv;
391 }
392
393 static void
Bfree(Bigint * v)394 Bfree(Bigint *v)
395 {
396 if (v) {
397 v->next = freelist[v->k];
398 freelist[v->k] = v;
399 }
400 }
401
402 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
403 y->wds*sizeof(Long) + 2*sizeof(int))
404
405 static Bigint *
multadd(Bigint * b,int m,int a)406 multadd(Bigint *b, int m, int a) /* multiply by m and add a */
407 {
408 int i, wds;
409 ULong *x, y;
410 #ifdef Pack_32
411 ULong xi, z;
412 #endif
413 Bigint *b1;
414
415 wds = b->wds;
416 x = b->x;
417 i = 0;
418 do {
419 #ifdef Pack_32
420 xi = *x;
421 y = (xi & 0xffff) * m + a;
422 z = (xi >> 16) * m + (y >> 16);
423 a = (int)(z >> 16);
424 *x++ = (z << 16) + (y & 0xffff);
425 #else
426 y = *x * m + a;
427 a = (int)(y >> 16);
428 *x++ = y & 0xffff;
429 #endif
430 }
431 while(++i < wds);
432 if (a) {
433 if (wds >= b->maxwds) {
434 b1 = Balloc(b->k+1);
435 Bcopy(b1, b);
436 Bfree(b);
437 b = b1;
438 }
439 b->x[wds++] = a;
440 b->wds = wds;
441 }
442 return b;
443 }
444
445 static Bigint *
s2b(CONST char * s,int nd0,int nd,ULong y9)446 s2b(CONST char *s, int nd0, int nd, ULong y9)
447 {
448 Bigint *b;
449 int i, k;
450 Long x, y;
451
452 x = (nd + 8) / 9;
453 for(k = 0, y = 1; x > y; y <<= 1, k++) ;
454 #ifdef Pack_32
455 b = Balloc(k);
456 b->x[0] = y9;
457 b->wds = 1;
458 #else
459 b = Balloc(k+1);
460 b->x[0] = y9 & 0xffff;
461 b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
462 #endif
463
464 i = 9;
465 if (9 < nd0) {
466 s += 9;
467 do b = multadd(b, 10, *s++ - '0');
468 while(++i < nd0);
469 s++;
470 }
471 else
472 s += 10;
473 for(; i < nd; i++)
474 b = multadd(b, 10, *s++ - '0');
475 return b;
476 }
477
478 static int
hi0bits(ULong x)479 hi0bits(ULong x)
480 {
481 int k = 0;
482
483 if (!(x & 0xffff0000)) {
484 k = 16;
485 x <<= 16;
486 }
487 if (!(x & 0xff000000)) {
488 k += 8;
489 x <<= 8;
490 }
491 if (!(x & 0xf0000000)) {
492 k += 4;
493 x <<= 4;
494 }
495 if (!(x & 0xc0000000)) {
496 k += 2;
497 x <<= 2;
498 }
499 if (!(x & 0x80000000)) {
500 k++;
501 if (!(x & 0x40000000))
502 return 32;
503 }
504 return k;
505 }
506
507 static int
lo0bits(ULong * y)508 lo0bits(ULong *y)
509 {
510 int k;
511 ULong x = *y;
512
513 if (x & 7) {
514 if (x & 1)
515 return 0;
516 if (x & 2) {
517 *y = x >> 1;
518 return 1;
519 }
520 *y = x >> 2;
521 return 2;
522 }
523 k = 0;
524 if (!(x & 0xffff)) {
525 k = 16;
526 x >>= 16;
527 }
528 if (!(x & 0xff)) {
529 k += 8;
530 x >>= 8;
531 }
532 if (!(x & 0xf)) {
533 k += 4;
534 x >>= 4;
535 }
536 if (!(x & 0x3)) {
537 k += 2;
538 x >>= 2;
539 }
540 if (!(x & 1)) {
541 k++;
542 x >>= 1;
543 if (!x & 1)
544 return 32;
545 }
546 *y = x;
547 return k;
548 }
549
550 static Bigint *
i2b(int i)551 i2b(int i)
552 {
553 Bigint *b;
554
555 b = Balloc(1);
556 b->x[0] = i;
557 b->wds = 1;
558 return b;
559 }
560
561 static Bigint *
mult(Bigint * a,Bigint * b)562 mult(Bigint *a, Bigint *b)
563 {
564 Bigint *c;
565 int k, wa, wb, wc;
566 ULong carry, y, z;
567 ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
568 #ifdef Pack_32
569 ULong z2;
570 #endif
571
572 if (a->wds < b->wds) {
573 c = a;
574 a = b;
575 b = c;
576 }
577 k = a->k;
578 wa = a->wds;
579 wb = b->wds;
580 wc = wa + wb;
581 if (wc > a->maxwds)
582 k++;
583 c = Balloc(k);
584 for(x = c->x, xa = x + wc; x < xa; x++)
585 *x = 0;
586 xa = a->x;
587 xae = xa + wa;
588 xb = b->x;
589 xbe = xb + wb;
590 xc0 = c->x;
591 #ifdef Pack_32
592 for(; xb < xbe; xb++, xc0++) {
593 if ((y = *xb & 0xffff)) {
594 x = xa;
595 xc = xc0;
596 carry = 0;
597 do {
598 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
599 carry = z >> 16;
600 z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
601 carry = z2 >> 16;
602 Storeinc(xc, z2, z);
603 }
604 while(x < xae);
605 *xc = carry;
606 }
607 if ((y = *xb >> 16)) {
608 x = xa;
609 xc = xc0;
610 carry = 0;
611 z2 = *xc;
612 do {
613 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
614 carry = z >> 16;
615 Storeinc(xc, z, z2);
616 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
617 carry = z2 >> 16;
618 }
619 while(x < xae);
620 *xc = z2;
621 }
622 }
623 #else
624 for(; xb < xbe; xc0++) {
625 if (y = *xb++) {
626 x = xa;
627 xc = xc0;
628 carry = 0;
629 do {
630 z = *x++ * y + *xc + carry;
631 carry = z >> 16;
632 *xc++ = z & 0xffff;
633 }
634 while(x < xae);
635 *xc = carry;
636 }
637 }
638 #endif
639 for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
640 c->wds = wc;
641 return c;
642 }
643
644 static Bigint *p5s;
645
646 static Bigint *
pow5mult(Bigint * b,int k)647 pow5mult(Bigint *b, int k)
648 {
649 Bigint *b1, *p5, *p51;
650 int i;
651 static int p05[3] = { 5, 25, 125 };
652
653 if ((i = k & 3))
654 b = multadd(b, p05[i-1], 0);
655
656 if (!(k >>= 2))
657 return b;
658 if (!(p5 = p5s)) {
659 /* first time */
660 p5 = p5s = i2b(625);
661 p5->next = 0;
662 }
663 for(;;) {
664 if (k & 1) {
665 b1 = mult(b, p5);
666 Bfree(b);
667 b = b1;
668 }
669 if (!(k >>= 1))
670 break;
671 if (!(p51 = p5->next)) {
672 p51 = p5->next = mult(p5,p5);
673 p51->next = 0;
674 }
675 p5 = p51;
676 }
677 return b;
678 }
679
680 static Bigint *
lshift(Bigint * b,int k)681 lshift(Bigint *b, int k)
682 {
683 int i, k1, n, n1;
684 Bigint *b1;
685 ULong *x, *x1, *xe, z;
686
687 #ifdef Pack_32
688 n = k >> 5;
689 #else
690 n = k >> 4;
691 #endif
692 k1 = b->k;
693 n1 = n + b->wds + 1;
694 for(i = b->maxwds; n1 > i; i <<= 1)
695 k1++;
696 b1 = Balloc(k1);
697 x1 = b1->x;
698 for(i = 0; i < n; i++)
699 *x1++ = 0;
700 x = b->x;
701 xe = x + b->wds;
702 #ifdef Pack_32
703 if (k &= 0x1f) {
704 k1 = 32 - k;
705 z = 0;
706 do {
707 *x1++ = *x << k | z;
708 z = *x++ >> k1;
709 }
710 while(x < xe);
711 if ((*x1 = z))
712 ++n1;
713 }
714 #else
715 if (k &= 0xf) {
716 k1 = 16 - k;
717 z = 0;
718 do {
719 *x1++ = *x << k & 0xffff | z;
720 z = *x++ >> k1;
721 }
722 while(x < xe);
723 if (*x1 = z)
724 ++n1;
725 }
726 #endif
727 else do
728 *x1++ = *x++;
729 while(x < xe);
730 b1->wds = n1 - 1;
731 Bfree(b);
732 return b1;
733 }
734
735 static int
cmp(Bigint * a,Bigint * b)736 cmp(Bigint *a, Bigint *b)
737 {
738 ULong *xa, *xa0, *xb, *xb0;
739 int i, j;
740
741 i = a->wds;
742 j = b->wds;
743 #ifdef DEBUG
744 if (i > 1 && !a->x[i-1])
745 Bug("cmp called with a->x[a->wds-1] == 0");
746 if (j > 1 && !b->x[j-1])
747 Bug("cmp called with b->x[b->wds-1] == 0");
748 #endif
749 if (i -= j)
750 return i;
751 xa0 = a->x;
752 xa = xa0 + j;
753 xb0 = b->x;
754 xb = xb0 + j;
755 for(;;) {
756 if (*--xa != *--xb)
757 return *xa < *xb ? -1 : 1;
758 if (xa <= xa0)
759 break;
760 }
761 return 0;
762 }
763
764 static Bigint *
diff(Bigint * a,Bigint * b)765 diff(Bigint *a, Bigint *b)
766 {
767 Bigint *c;
768 int i, wa, wb;
769 Long borrow, y; /* We need signed shifts here. */
770 ULong *xa, *xae, *xb, *xbe, *xc;
771 #ifdef Pack_32
772 Long z;
773 #endif
774
775 i = cmp(a,b);
776 if (!i) {
777 c = Balloc(0);
778 c->wds = 1;
779 c->x[0] = 0;
780 return c;
781 }
782 if (i < 0) {
783 c = a;
784 a = b;
785 b = c;
786 i = 1;
787 }
788 else
789 i = 0;
790 c = Balloc(a->k);
791 c->sign = i;
792 wa = a->wds;
793 xa = a->x;
794 xae = xa + wa;
795 wb = b->wds;
796 xb = b->x;
797 xbe = xb + wb;
798 xc = c->x;
799 borrow = 0;
800 #ifdef Pack_32
801 do {
802 y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
803 borrow = y >> 16;
804 Sign_Extend(borrow, y);
805 z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
806 borrow = z >> 16;
807 Sign_Extend(borrow, z);
808 Storeinc(xc, z, y);
809 }
810 while(xb < xbe);
811 while(xa < xae) {
812 y = (*xa & 0xffff) + borrow;
813 borrow = y >> 16;
814 Sign_Extend(borrow, y);
815 z = (*xa++ >> 16) + borrow;
816 borrow = z >> 16;
817 Sign_Extend(borrow, z);
818 Storeinc(xc, z, y);
819 }
820 #else
821 do {
822 y = *xa++ - *xb++ + borrow;
823 borrow = y >> 16;
824 Sign_Extend(borrow, y);
825 *xc++ = y & 0xffff;
826 }
827 while(xb < xbe);
828 while(xa < xae) {
829 y = *xa++ + borrow;
830 borrow = y >> 16;
831 Sign_Extend(borrow, y);
832 *xc++ = y & 0xffff;
833 }
834 #endif
835 while(!*--xc)
836 wa--;
837 c->wds = wa;
838 return c;
839 }
840
841 static double
ulp(double _x)842 ulp(double _x)
843 {
844 _double x;
845 Long L;
846 _double a;
847
848 value(x) = _x;
849 L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
850 #ifndef Sudden_Underflow
851 if (L > 0) {
852 #endif
853 #ifdef IBM
854 L |= Exp_msk1 >> 4;
855 #endif
856 word0(a) = L;
857 word1(a) = 0;
858 #ifndef Sudden_Underflow
859 }
860 else {
861 L = -L >> Exp_shift;
862 if (L < Exp_shift) {
863 word0(a) = 0x80000 >> L;
864 word1(a) = 0;
865 }
866 else {
867 word0(a) = 0;
868 L -= Exp_shift;
869 word1(a) = L >= 31 ? 1 : 1 << 31 - L;
870 }
871 }
872 #endif
873 return value(a);
874 }
875
876 static double
b2d(Bigint * a,int * e)877 b2d(Bigint *a, int *e)
878 {
879 ULong *xa, *xa0, w, y, z;
880 int k;
881 _double d;
882 #ifdef VAX
883 ULong d0, d1;
884 #else
885 #define d0 word0(d)
886 #define d1 word1(d)
887 #endif
888
889 xa0 = a->x;
890 xa = xa0 + a->wds;
891 y = *--xa;
892 #ifdef DEBUG
893 if (!y) Bug("zero y in b2d");
894 #endif
895 k = hi0bits(y);
896 *e = 32 - k;
897 #ifdef Pack_32
898 if (k < Ebits) {
899 d0 = Exp_1 | y >> Ebits - k;
900 w = xa > xa0 ? *--xa : 0;
901 d1 = y << (32-Ebits) + k | w >> Ebits - k;
902 goto ret_d;
903 }
904 z = xa > xa0 ? *--xa : 0;
905 if (k -= Ebits) {
906 d0 = Exp_1 | y << k | z >> 32 - k;
907 y = xa > xa0 ? *--xa : 0;
908 d1 = z << k | y >> 32 - k;
909 }
910 else {
911 d0 = Exp_1 | y;
912 d1 = z;
913 }
914 #else
915 if (k < Ebits + 16) {
916 z = xa > xa0 ? *--xa : 0;
917 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
918 w = xa > xa0 ? *--xa : 0;
919 y = xa > xa0 ? *--xa : 0;
920 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
921 goto ret_d;
922 }
923 z = xa > xa0 ? *--xa : 0;
924 w = xa > xa0 ? *--xa : 0;
925 k -= Ebits + 16;
926 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
927 y = xa > xa0 ? *--xa : 0;
928 d1 = w << k + 16 | y << k;
929 #endif
930 ret_d:
931 #ifdef VAX
932 word0(d) = d0 >> 16 | d0 << 16;
933 word1(d) = d1 >> 16 | d1 << 16;
934 #else
935 #undef d0
936 #undef d1
937 #endif
938 return value(d);
939 }
940
941 static Bigint *
d2b(double _d,int * e,int * bits)942 d2b(double _d, int *e, int *bits)
943 {
944 Bigint *b;
945 int de, i, k;
946 ULong *x, y, z;
947 _double d;
948 #ifdef VAX
949 ULong d0, d1;
950 #endif
951
952 value(d) = _d;
953 #ifdef VAX
954 d0 = word0(d) >> 16 | word0(d) << 16;
955 d1 = word1(d) >> 16 | word1(d) << 16;
956 #else
957 #define d0 word0(d)
958 #define d1 word1(d)
959 #endif
960
961 #ifdef Pack_32
962 b = Balloc(1);
963 #else
964 b = Balloc(2);
965 #endif
966 x = b->x;
967
968 z = d0 & Frac_mask;
969 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
970 #ifdef Sudden_Underflow
971 de = (int)(d0 >> Exp_shift);
972 #ifndef IBM
973 z |= Exp_msk11;
974 #endif
975 #else
976 if (de = (int)(d0 >> Exp_shift))
977 z |= Exp_msk1;
978 #endif
979 #ifdef Pack_32
980 if (y = d1) {
981 if (k = lo0bits(&y)) {
982 x[0] = y | z << 32 - k;
983 z >>= k;
984 }
985 else
986 x[0] = y;
987 i = b->wds = (x[1] = z) ? 2 : 1;
988 }
989 else {
990 #ifdef DEBUG
991 if (!z)
992 Bug("Zero passed to d2b");
993 #endif
994 k = lo0bits(&z);
995 x[0] = z;
996 i = b->wds = 1;
997 k += 32;
998 }
999 #else
1000 if (y = d1) {
1001 if (k = lo0bits(&y))
1002 if (k >= 16) {
1003 x[0] = y | z << 32 - k & 0xffff;
1004 x[1] = z >> k - 16 & 0xffff;
1005 x[2] = z >> k;
1006 i = 2;
1007 }
1008 else {
1009 x[0] = y & 0xffff;
1010 x[1] = y >> 16 | z << 16 - k & 0xffff;
1011 x[2] = z >> k & 0xffff;
1012 x[3] = z >> k+16;
1013 i = 3;
1014 }
1015 else {
1016 x[0] = y & 0xffff;
1017 x[1] = y >> 16;
1018 x[2] = z & 0xffff;
1019 x[3] = z >> 16;
1020 i = 3;
1021 }
1022 }
1023 else {
1024 #ifdef DEBUG
1025 if (!z)
1026 Bug("Zero passed to d2b");
1027 #endif
1028 k = lo0bits(&z);
1029 if (k >= 16) {
1030 x[0] = z;
1031 i = 0;
1032 }
1033 else {
1034 x[0] = z & 0xffff;
1035 x[1] = z >> 16;
1036 i = 1;
1037 }
1038 k += 32;
1039 }
1040 while(!x[i])
1041 --i;
1042 b->wds = i + 1;
1043 #endif
1044 #ifndef Sudden_Underflow
1045 if (de) {
1046 #endif
1047 #ifdef IBM
1048 *e = (de - Bias - (P-1) << 2) + k;
1049 *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
1050 #else
1051 *e = de - Bias - (P-1) + k;
1052 *bits = P - k;
1053 #endif
1054 #ifndef Sudden_Underflow
1055 }
1056 else {
1057 *e = de - Bias - (P-1) + 1 + k;
1058 #ifdef Pack_32
1059 *bits = 32*i - hi0bits(x[i-1]);
1060 #else
1061 *bits = (i+2)*16 - hi0bits(x[i]);
1062 #endif
1063 }
1064 #endif
1065 return b;
1066 }
1067 #undef d0
1068 #undef d1
1069
1070 static double
ratio(Bigint * a,Bigint * b)1071 ratio(Bigint *a, Bigint *b)
1072 {
1073 _double da, db;
1074 int k, ka, kb;
1075
1076 value(da) = b2d(a, &ka);
1077 value(db) = b2d(b, &kb);
1078 #ifdef Pack_32
1079 k = ka - kb + 32*(a->wds - b->wds);
1080 #else
1081 k = ka - kb + 16*(a->wds - b->wds);
1082 #endif
1083 #ifdef IBM
1084 if (k > 0) {
1085 word0(da) += (k >> 2)*Exp_msk1;
1086 if (k &= 3)
1087 da *= 1 << k;
1088 }
1089 else {
1090 k = -k;
1091 word0(db) += (k >> 2)*Exp_msk1;
1092 if (k &= 3)
1093 db *= 1 << k;
1094 }
1095 #else
1096 if (k > 0)
1097 word0(da) += k*Exp_msk1;
1098 else {
1099 k = -k;
1100 word0(db) += k*Exp_msk1;
1101 }
1102 #endif
1103 return value(da) / value(db);
1104 }
1105
1106 static CONST double
1107 tens[] = {
1108 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1109 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1110 1e20, 1e21, 1e22
1111 #ifdef VAX
1112 , 1e23, 1e24
1113 #endif
1114 };
1115
1116 #ifdef IEEE_Arith
1117 static CONST double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1118 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
1119 #define n_bigtens 5
1120 #else
1121 #ifdef IBM
1122 static CONST double bigtens[] = { 1e16, 1e32, 1e64 };
1123 static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
1124 #define n_bigtens 3
1125 #else
1126 static CONST double bigtens[] = { 1e16, 1e32 };
1127 static CONST double tinytens[] = { 1e-16, 1e-32 };
1128 #define n_bigtens 2
1129 #endif
1130 #endif
1131
1132 double
strtod(CONST char * s00,char ** se)1133 strtod(CONST char *s00, char **se)
1134 {
1135 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1136 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1137 CONST char *s, *s0, *s1;
1138 volatile double aadj, aadj1, adj;
1139 _double rv, rv0;
1140 Long L;
1141 ULong y, z;
1142 Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
1143
1144 CONST char decimal_point = localeconv()->decimal_point[0];
1145
1146 sign = nz0 = nz = 0;
1147 value(rv) = 0.;
1148
1149
1150 for(s = s00; isspace((unsigned char) *s); s++)
1151 ;
1152
1153 if (*s == '-') {
1154 sign = 1;
1155 s++;
1156 } else if (*s == '+') {
1157 s++;
1158 }
1159
1160 if (*s == '\0') {
1161 s = s00;
1162 goto ret;
1163 }
1164
1165 if (*s == '0') {
1166 nz0 = 1;
1167 while(*++s == '0') ;
1168 if (!*s)
1169 goto ret;
1170 }
1171 s0 = s;
1172 y = z = 0;
1173 for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1174 if (nd < 9)
1175 y = 10*y + c - '0';
1176 else if (nd < 16)
1177 z = 10*z + c - '0';
1178 nd0 = nd;
1179 if (c == decimal_point) {
1180 c = *++s;
1181 if (!nd) {
1182 for(; c == '0'; c = *++s)
1183 nz++;
1184 if (c > '0' && c <= '9') {
1185 s0 = s;
1186 nf += nz;
1187 nz = 0;
1188 goto have_dig;
1189 }
1190 goto dig_done;
1191 }
1192 for(; c >= '0' && c <= '9'; c = *++s) {
1193 have_dig:
1194 nz++;
1195 if (c -= '0') {
1196 nf += nz;
1197 for(i = 1; i < nz; i++)
1198 if (nd++ < 9)
1199 y *= 10;
1200 else if (nd <= DBL_DIG + 1)
1201 z *= 10;
1202 if (nd++ < 9)
1203 y = 10*y + c;
1204 else if (nd <= DBL_DIG + 1)
1205 z = 10*z + c;
1206 nz = 0;
1207 }
1208 }
1209 }
1210 dig_done:
1211 e = 0;
1212 if (c == 'e' || c == 'E') {
1213 if (!nd && !nz && !nz0) {
1214 s = s00;
1215 goto ret;
1216 }
1217 s00 = s;
1218 esign = 0;
1219 switch(c = *++s) {
1220 case '-':
1221 esign = 1;
1222 case '+':
1223 c = *++s;
1224 }
1225 if (c >= '0' && c <= '9') {
1226 while(c == '0')
1227 c = *++s;
1228 if (c > '0' && c <= '9') {
1229 L = c - '0';
1230 s1 = s;
1231 while((c = *++s) >= '0' && c <= '9')
1232 L = 10*L + c - '0';
1233 if (s - s1 > 8 || L > 19999)
1234 /* Avoid confusion from exponents
1235 * so large that e might overflow.
1236 */
1237 e = 19999; /* safe for 16 bit ints */
1238 else
1239 e = (int)L;
1240 if (esign)
1241 e = -e;
1242 }
1243 else
1244 e = 0;
1245 }
1246 else
1247 s = s00;
1248 }
1249 if (!nd) {
1250 if (!nz && !nz0)
1251 s = s00;
1252 goto ret;
1253 }
1254 e1 = e -= nf;
1255
1256 /* Now we have nd0 digits, starting at s0, followed by a
1257 * decimal point, followed by nd-nd0 digits. The number we're
1258 * after is the integer represented by those digits times
1259 * 10**e */
1260
1261 if (!nd0)
1262 nd0 = nd;
1263 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1264 value(rv) = y;
1265 if (k > 9)
1266 value(rv) = tens[k - 9] * value(rv) + z;
1267 bd0 = 0;
1268 if (nd <= DBL_DIG
1269 #ifndef RND_PRODQUOT
1270 && FLT_ROUNDS == 1
1271 #endif
1272 ) {
1273 if (!e)
1274 goto ret;
1275 if (e > 0) {
1276 if (e <= Ten_pmax) {
1277 #ifdef VAX
1278 goto vax_ovfl_check;
1279 #else
1280 /* value(rv) = */ rounded_product(value(rv),
1281 tens[e]);
1282 goto ret;
1283 #endif
1284 }
1285 i = DBL_DIG - nd;
1286 if (e <= Ten_pmax + i) {
1287 /* A fancier test would sometimes let us do
1288 * this for larger i values.
1289 */
1290 e -= i;
1291 value(rv) *= tens[i];
1292 #ifdef VAX
1293 /* VAX exponent range is so narrow we must
1294 * worry about overflow here...
1295 */
1296 vax_ovfl_check:
1297 word0(rv) -= P*Exp_msk1;
1298 /* value(rv) = */ rounded_product(value(rv),
1299 tens[e]);
1300 if ((word0(rv) & Exp_mask)
1301 > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
1302 goto ovfl;
1303 word0(rv) += P*Exp_msk1;
1304 #else
1305 /* value(rv) = */ rounded_product(value(rv),
1306 tens[e]);
1307 #endif
1308 goto ret;
1309 }
1310 }
1311 #ifndef Inaccurate_Divide
1312 else if (e >= -Ten_pmax) {
1313 /* value(rv) = */ rounded_quotient(value(rv),
1314 tens[-e]);
1315 goto ret;
1316 }
1317 #endif
1318 }
1319 e1 += nd - k;
1320
1321 /* Get starting approximation = rv * 10**e1 */
1322
1323 if (e1 > 0) {
1324 if (i = e1 & 15)
1325 value(rv) *= tens[i];
1326 if (e1 &= ~15) {
1327 if (e1 > DBL_MAX_10_EXP) {
1328 ovfl:
1329 errno = ERANGE;
1330 #ifndef Bad_float_h
1331 value(rv) = HUGE_VAL;
1332 #else
1333 /* Can't trust HUGE_VAL */
1334 #ifdef IEEE_Arith
1335 word0(rv) = Exp_mask;
1336 word1(rv) = 0;
1337 #else
1338 word0(rv) = Big0;
1339 word1(rv) = Big1;
1340 #endif
1341 #endif
1342 if (bd0)
1343 goto retfree;
1344 goto ret;
1345 }
1346 if (e1 >>= 4) {
1347 for(j = 0; e1 > 1; j++, e1 >>= 1)
1348 if (e1 & 1)
1349 value(rv) *= bigtens[j];
1350 /* The last multiplication could overflow. */
1351 word0(rv) -= P*Exp_msk1;
1352 value(rv) *= bigtens[j];
1353 if ((z = word0(rv) & Exp_mask)
1354 > Exp_msk1*(DBL_MAX_EXP+Bias-P))
1355 goto ovfl;
1356 if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
1357 /* set to largest number */
1358 /* (Can't trust DBL_MAX) */
1359 word0(rv) = Big0;
1360 word1(rv) = Big1;
1361 }
1362 else
1363 word0(rv) += P*Exp_msk1;
1364 }
1365
1366 }
1367 }
1368 else if (e1 < 0) {
1369 e1 = -e1;
1370 if (i = e1 & 15)
1371 value(rv) /= tens[i];
1372 if (e1 &= ~15) {
1373 e1 >>= 4;
1374 if (e1 >= 1 << n_bigtens)
1375 goto undfl;
1376 for(j = 0; e1 > 1; j++, e1 >>= 1)
1377 if (e1 & 1)
1378 value(rv) *= tinytens[j];
1379 /* The last multiplication could underflow. */
1380 value(rv0) = value(rv);
1381 value(rv) *= tinytens[j];
1382 if (!value(rv)) {
1383 value(rv) = 2.*value(rv0);
1384 value(rv) *= tinytens[j];
1385 if (!value(rv)) {
1386 undfl:
1387 value(rv) = 0.;
1388 errno = ERANGE;
1389 if (bd0)
1390 goto retfree;
1391 goto ret;
1392 }
1393 word0(rv) = Tiny0;
1394 word1(rv) = Tiny1;
1395 /* The refinement below will clean
1396 * this approximation up.
1397 */
1398 }
1399 }
1400 }
1401
1402 /* Now the hard part -- adjusting rv to the correct value.*/
1403
1404 /* Put digits into bd: true value = bd * 10^e */
1405
1406 bd0 = s2b(s0, nd0, nd, y);
1407
1408 for(;;) {
1409 bd = Balloc(bd0->k);
1410 Bcopy(bd, bd0);
1411 bb = d2b(value(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
1412 bs = i2b(1);
1413
1414 if (e >= 0) {
1415 bb2 = bb5 = 0;
1416 bd2 = bd5 = e;
1417 }
1418 else {
1419 bb2 = bb5 = -e;
1420 bd2 = bd5 = 0;
1421 }
1422 if (bbe >= 0)
1423 bb2 += bbe;
1424 else
1425 bd2 -= bbe;
1426 bs2 = bb2;
1427 #ifdef Sudden_Underflow
1428 #ifdef IBM
1429 j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
1430 #else
1431 j = P + 1 - bbbits;
1432 #endif
1433 #else
1434 i = bbe + bbbits - 1; /* logb(rv) */
1435 if (i < Emin) /* denormal */
1436 j = bbe + (P-Emin);
1437 else
1438 j = P + 1 - bbbits;
1439 #endif
1440 bb2 += j;
1441 bd2 += j;
1442 i = bb2 < bd2 ? bb2 : bd2;
1443 if (i > bs2)
1444 i = bs2;
1445 if (i > 0) {
1446 bb2 -= i;
1447 bd2 -= i;
1448 bs2 -= i;
1449 }
1450 if (bb5 > 0) {
1451 bs = pow5mult(bs, bb5);
1452 bb1 = mult(bs, bb);
1453 Bfree(bb);
1454 bb = bb1;
1455 }
1456 if (bb2 > 0)
1457 bb = lshift(bb, bb2);
1458 if (bd5 > 0)
1459 bd = pow5mult(bd, bd5);
1460 if (bd2 > 0)
1461 bd = lshift(bd, bd2);
1462 if (bs2 > 0)
1463 bs = lshift(bs, bs2);
1464 delta = diff(bb, bd);
1465 dsign = delta->sign;
1466 delta->sign = 0;
1467 i = cmp(delta, bs);
1468 if (i < 0) {
1469 /* Error is less than half an ulp -- check for
1470 * special case of mantissa a power of two.
1471 */
1472 if (dsign || word1(rv) || word0(rv) & Bndry_mask)
1473 break;
1474 delta = lshift(delta,Log2P);
1475 if (cmp(delta, bs) > 0)
1476 goto drop_down;
1477 break;
1478 }
1479 if (i == 0) {
1480 /* exactly half-way between */
1481 if (dsign) {
1482 if ((word0(rv) & Bndry_mask1) == Bndry_mask1
1483 && word1(rv) == 0xffffffff) {
1484 /*boundary case -- increment exponent*/
1485 word0(rv) = (word0(rv) & Exp_mask)
1486 + Exp_msk1
1487 #ifdef IBM
1488 | Exp_msk1 >> 4
1489 #endif
1490 ;
1491 word1(rv) = 0;
1492 break;
1493 }
1494 }
1495 else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
1496 drop_down:
1497 /* boundary case -- decrement exponent */
1498 #ifdef Sudden_Underflow
1499 L = word0(rv) & Exp_mask;
1500 #ifdef IBM
1501 if (L < Exp_msk1)
1502 #else
1503 if (L <= Exp_msk1)
1504 #endif
1505 goto undfl;
1506 L -= Exp_msk1;
1507 #else
1508 L = (word0(rv) & Exp_mask) - Exp_msk1;
1509 #endif
1510 word0(rv) = L | Bndry_mask1;
1511 word1(rv) = 0xffffffff;
1512 #ifdef IBM
1513 goto cont;
1514 #else
1515 break;
1516 #endif
1517 }
1518 #ifndef ROUND_BIASED
1519 if (!(word1(rv) & LSB))
1520 break;
1521 #endif
1522 if (dsign)
1523 value(rv) += ulp(value(rv));
1524 #ifndef ROUND_BIASED
1525 else {
1526 value(rv) -= ulp(value(rv));
1527 #ifndef Sudden_Underflow
1528 if (!value(rv))
1529 goto undfl;
1530 #endif
1531 }
1532 #endif
1533 break;
1534 }
1535 if ((aadj = ratio(delta, bs)) <= 2.) {
1536 if (dsign)
1537 aadj = aadj1 = 1.;
1538 else if (word1(rv) || word0(rv) & Bndry_mask) {
1539 #ifndef Sudden_Underflow
1540 if (word1(rv) == Tiny1 && !word0(rv))
1541 goto undfl;
1542 #endif
1543 aadj = 1.;
1544 aadj1 = -1.;
1545 }
1546 else {
1547 /* special case -- power of FLT_RADIX to be */
1548 /* rounded down... */
1549
1550 if (aadj < 2./FLT_RADIX)
1551 aadj = 1./FLT_RADIX;
1552 else
1553 aadj *= 0.5;
1554 aadj1 = -aadj;
1555 }
1556 }
1557 else {
1558 aadj *= 0.5;
1559 aadj1 = dsign ? aadj : -aadj;
1560 #ifdef Check_FLT_ROUNDS
1561 switch(FLT_ROUNDS) {
1562 case 2: /* towards +infinity */
1563 aadj1 -= 0.5;
1564 break;
1565 case 0: /* towards 0 */
1566 case 3: /* towards -infinity */
1567 aadj1 += 0.5;
1568 }
1569 #else
1570 if (FLT_ROUNDS == 0)
1571 aadj1 += 0.5;
1572 #endif
1573 }
1574 y = word0(rv) & Exp_mask;
1575
1576 /* Check for overflow */
1577
1578 if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
1579 value(rv0) = value(rv);
1580 word0(rv) -= P*Exp_msk1;
1581 adj = aadj1 * ulp(value(rv));
1582 value(rv) += adj;
1583 if ((word0(rv) & Exp_mask) >=
1584 Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
1585 if (word0(rv0) == Big0 && word1(rv0) == Big1)
1586 goto ovfl;
1587 word0(rv) = Big0;
1588 word1(rv) = Big1;
1589 goto cont;
1590 }
1591 else
1592 word0(rv) += P*Exp_msk1;
1593 }
1594 else {
1595 #ifdef Sudden_Underflow
1596 if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
1597 value(rv0) = value(rv);
1598 word0(rv) += P*Exp_msk1;
1599 adj = aadj1 * ulp(value(rv));
1600 value(rv) += adj;
1601 #ifdef IBM
1602 if ((word0(rv) & Exp_mask) < P*Exp_msk1)
1603 #else
1604 if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
1605 #endif
1606 {
1607 if (word0(rv0) == Tiny0
1608 && word1(rv0) == Tiny1)
1609 goto undfl;
1610 word0(rv) = Tiny0;
1611 word1(rv) = Tiny1;
1612 goto cont;
1613 }
1614 else
1615 word0(rv) -= P*Exp_msk1;
1616 }
1617 else {
1618 adj = aadj1 * ulp(value(rv));
1619 value(rv) += adj;
1620 }
1621 #else
1622 /* Compute adj so that the IEEE rounding rules will
1623 * correctly round rv + adj in some half-way cases.
1624 * If rv * ulp(rv) is denormalized (i.e.,
1625 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
1626 * trouble from bits lost to denormalization;
1627 * example: 1.2e-307 .
1628 */
1629 if (y <= (P-1)*Exp_msk1 && aadj >= 1.) {
1630 aadj1 = (double)(int)(aadj + 0.5);
1631 if (!dsign)
1632 aadj1 = -aadj1;
1633 }
1634 adj = aadj1 * ulp(value(rv));
1635 value(rv) += adj;
1636 #endif
1637 }
1638 z = word0(rv) & Exp_mask;
1639 if (y == z) {
1640 /* Can we stop now? */
1641 L = aadj;
1642 aadj -= L;
1643 /* The tolerances below are conservative. */
1644 if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
1645 if (aadj < .4999999 || aadj > .5000001)
1646 break;
1647 }
1648 else if (aadj < .4999999/FLT_RADIX)
1649 break;
1650 }
1651 cont:
1652 Bfree(bb);
1653 Bfree(bd);
1654 Bfree(bs);
1655 Bfree(delta);
1656 }
1657 retfree:
1658 Bfree(bb);
1659 Bfree(bd);
1660 Bfree(bs);
1661 Bfree(bd0);
1662 Bfree(delta);
1663 ret:
1664 if (se)
1665 *se = (char *)s;
1666 return sign ? -value(rv) : value(rv);
1667 }
1668
1669 static int
quorem(Bigint * b,Bigint * S)1670 quorem(Bigint *b, Bigint *S)
1671 {
1672 int n;
1673 Long borrow, y;
1674 ULong carry, q, ys;
1675 ULong *bx, *bxe, *sx, *sxe;
1676 #ifdef Pack_32
1677 Long z;
1678 ULong si, zs;
1679 #endif
1680
1681 n = S->wds;
1682 #ifdef DEBUG
1683 /*debug*/ if (b->wds > n)
1684 /*debug*/ Bug("oversize b in quorem");
1685 #endif
1686 if (b->wds < n)
1687 return 0;
1688 sx = S->x;
1689 sxe = sx + --n;
1690 bx = b->x;
1691 bxe = bx + n;
1692 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1693 #ifdef DEBUG
1694 /*debug*/ if (q > 9)
1695 /*debug*/ Bug("oversized quotient in quorem");
1696 #endif
1697 if (q) {
1698 borrow = 0;
1699 carry = 0;
1700 do {
1701 #ifdef Pack_32
1702 si = *sx++;
1703 ys = (si & 0xffff) * q + carry;
1704 zs = (si >> 16) * q + (ys >> 16);
1705 carry = zs >> 16;
1706 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1707 borrow = y >> 16;
1708 Sign_Extend(borrow, y);
1709 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1710 borrow = z >> 16;
1711 Sign_Extend(borrow, z);
1712 Storeinc(bx, z, y);
1713 #else
1714 ys = *sx++ * q + carry;
1715 carry = ys >> 16;
1716 y = *bx - (ys & 0xffff) + borrow;
1717 borrow = y >> 16;
1718 Sign_Extend(borrow, y);
1719 *bx++ = y & 0xffff;
1720 #endif
1721 }
1722 while(sx <= sxe);
1723 if (!*bxe) {
1724 bx = b->x;
1725 while(--bxe > bx && !*bxe)
1726 --n;
1727 b->wds = n;
1728 }
1729 }
1730 if (cmp(b, S) >= 0) {
1731 q++;
1732 borrow = 0;
1733 carry = 0;
1734 bx = b->x;
1735 sx = S->x;
1736 do {
1737 #ifdef Pack_32
1738 si = *sx++;
1739 ys = (si & 0xffff) + carry;
1740 zs = (si >> 16) + (ys >> 16);
1741 carry = zs >> 16;
1742 y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
1743 borrow = y >> 16;
1744 Sign_Extend(borrow, y);
1745 z = (*bx >> 16) - (zs & 0xffff) + borrow;
1746 borrow = z >> 16;
1747 Sign_Extend(borrow, z);
1748 Storeinc(bx, z, y);
1749 #else
1750 ys = *sx++ + carry;
1751 carry = ys >> 16;
1752 y = *bx - (ys & 0xffff) + borrow;
1753 borrow = y >> 16;
1754 Sign_Extend(borrow, y);
1755 *bx++ = y & 0xffff;
1756 #endif
1757 }
1758 while(sx <= sxe);
1759 bx = b->x;
1760 bxe = bx + n;
1761 if (!*bxe) {
1762 while(--bxe > bx && !*bxe)
1763 --n;
1764 b->wds = n;
1765 }
1766 }
1767 return q;
1768 }
1769
1770 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1771 *
1772 * Inspired by "How to Print Floating-Point Numbers Accurately" by
1773 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1774 *
1775 * Modifications:
1776 * 1. Rather than iterating, we use a simple numeric overestimate
1777 * to determine k = floor(log10(d)). We scale relevant
1778 * quantities using O(log2(k)) rather than O(k) multiplications.
1779 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1780 * try to generate digits strictly left to right. Instead, we
1781 * compute with fewer bits and propagate the carry if necessary
1782 * when rounding the final digit up. This is often faster.
1783 * 3. Under the assumption that input will be rounded nearest,
1784 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1785 * That is, we allow equality in stopping tests when the
1786 * round-nearest rule will give the same floating-point value
1787 * as would satisfaction of the stopping test with strict
1788 * inequality.
1789 * 4. We remove common factors of powers of 2 from relevant
1790 * quantities.
1791 * 5. When converting floating-point integers less than 1e16,
1792 * we use floating-point arithmetic rather than resorting
1793 * to multiple-precision integers.
1794 * 6. When asked to produce fewer than 15 digits, we first try
1795 * to get by with floating-point arithmetic; we resort to
1796 * multiple-precision integer arithmetic only if we cannot
1797 * guarantee that the floating-point calculation has given
1798 * the correctly rounded result. For k requested digits and
1799 * "uniformly" distributed input, the probability is
1800 * something like 10^(k-15) that we must resort to the Long
1801 * calculation.
1802 */
1803
1804 char *
__dtoa(double _d,int mode,int ndigits,int * decpt,int * sign,char ** rve)1805 __dtoa(double _d, int mode, int ndigits, int *decpt, int *sign, char **rve)
1806 {
1807 /* Arguments ndigits, decpt, sign are similar to those
1808 of ecvt and fcvt; trailing zeros are suppressed from
1809 the returned string. If not null, *rve is set to point
1810 to the end of the return value. If d is +-Infinity or NaN,
1811 then *decpt is set to 9999.
1812
1813 mode:
1814 0 ==> shortest string that yields d when read in
1815 and rounded to nearest.
1816 1 ==> like 0, but with Steele & White stopping rule;
1817 e.g. with IEEE P754 arithmetic , mode 0 gives
1818 1e23 whereas mode 1 gives 9.999999999999999e22.
1819 2 ==> max(1,ndigits) significant digits. This gives a
1820 return value similar to that of ecvt, except
1821 that trailing zeros are suppressed.
1822 3 ==> through ndigits past the decimal point. This
1823 gives a return value similar to that from fcvt,
1824 except that trailing zeros are suppressed, and
1825 ndigits can be negative.
1826 4-9 should give the same return values as 2-3, i.e.,
1827 4 <= mode <= 9 ==> same return as mode
1828 2 + (mode & 1). These modes are mainly for
1829 debugging; often they run slower but sometimes
1830 faster than modes 2-3.
1831 4,5,8,9 ==> left-to-right digit generation.
1832 6-9 ==> don't try fast floating-point estimate
1833 (if applicable).
1834
1835 Values of mode other than 0-9 are treated as mode 0.
1836
1837 Sufficient space is allocated to the return value
1838 to hold the suppressed trailing zeros.
1839 */
1840
1841 int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
1842 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1843 spec_case, try_quick;
1844 Long L;
1845 #ifndef Sudden_Underflow
1846 int denorm;
1847 ULong x;
1848 #endif
1849 Bigint *b, *b1, *delta, *mlo, *mhi, *S;
1850 double ds;
1851 char *s, *s0;
1852 static Bigint *result;
1853 static int result_k;
1854 _double d, d2, eps;
1855
1856 value(d) = _d;
1857 if (result) {
1858 result->k = result_k;
1859 result->maxwds = 1 << result_k;
1860 Bfree(result);
1861 result = 0;
1862 }
1863
1864 if (word0(d) & Sign_bit) {
1865 /* set sign for everything, including 0's and NaNs */
1866 *sign = 1;
1867 word0(d) &= ~Sign_bit; /* clear sign bit */
1868 }
1869 else
1870 *sign = 0;
1871
1872 #if defined(IEEE_Arith) + defined(VAX)
1873 #ifdef IEEE_Arith
1874 if ((word0(d) & Exp_mask) == Exp_mask)
1875 #else
1876 if (word0(d) == 0x8000)
1877 #endif
1878 {
1879 /* Infinity or NaN */
1880 *decpt = 9999;
1881 s =
1882 #ifdef IEEE_Arith
1883 !word1(d) && !(word0(d) & 0xfffff) ? ndigits < 8 ? "Inf" : "Infinity" :
1884 #endif
1885 "NaN";
1886 if (rve)
1887 *rve =
1888 #ifdef IEEE_Arith
1889 s[3] ? s + 8 :
1890 #endif
1891 s + 3;
1892 return s;
1893 }
1894 #endif
1895 #ifdef IBM
1896 value(d) += 0; /* normalize */
1897 #endif
1898 if (!value(d)) {
1899 *decpt = 1;
1900 s = "0";
1901 if (rve)
1902 *rve = s + 1;
1903 return s;
1904 }
1905
1906 b = d2b(value(d), &be, &bbits);
1907 #ifdef Sudden_Underflow
1908 i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
1909 #else
1910 if (i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) {
1911 #endif
1912 value(d2) = value(d);
1913 word0(d2) &= Frac_mask1;
1914 word0(d2) |= Exp_11;
1915 #ifdef IBM
1916 if (j = 11 - hi0bits(word0(d2) & Frac_mask))
1917 value(d2) /= 1 << j;
1918 #endif
1919
1920 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
1921 * log10(x) = log(x) / log(10)
1922 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
1923 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
1924 *
1925 * This suggests computing an approximation k to log10(d) by
1926 *
1927 * k = (i - Bias)*0.301029995663981
1928 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
1929 *
1930 * We want k to be too large rather than too small.
1931 * The error in the first-order Taylor series approximation
1932 * is in our favor, so we just round up the constant enough
1933 * to compensate for any error in the multiplication of
1934 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
1935 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
1936 * adding 1e-13 to the constant term more than suffices.
1937 * Hence we adjust the constant term to 0.1760912590558.
1938 * (We could get a more accurate k by invoking log10,
1939 * but this is probably not worthwhile.)
1940 */
1941
1942 i -= Bias;
1943 #ifdef IBM
1944 i <<= 2;
1945 i += j;
1946 #endif
1947 #ifndef Sudden_Underflow
1948 denorm = 0;
1949 }
1950 else {
1951 /* d is denormalized */
1952
1953 i = bbits + be + (Bias + (P-1) - 1);
1954 x = i > 32 ? word0(d) << 64 - i | word1(d) >> i - 32
1955 : word1(d) << 32 - i;
1956 value(d2) = x;
1957 word0(d2) -= 31*Exp_msk1; /* adjust exponent */
1958 i -= (Bias + (P-1) - 1) + 1;
1959 denorm = 1;
1960 }
1961 #endif
1962 ds = (value(d2)-1.5)*0.289529654602168 + 0.1760912590558 +
1963 i*0.301029995663981;
1964 k = (int)ds;
1965 if (ds < 0. && ds != k)
1966 k--; /* want k = floor(ds) */
1967 k_check = 1;
1968 if (k >= 0 && k <= Ten_pmax) {
1969 if (value(d) < tens[k])
1970 k--;
1971 k_check = 0;
1972 }
1973 j = bbits - i - 1;
1974 if (j >= 0) {
1975 b2 = 0;
1976 s2 = j;
1977 }
1978 else {
1979 b2 = -j;
1980 s2 = 0;
1981 }
1982 if (k >= 0) {
1983 b5 = 0;
1984 s5 = k;
1985 s2 += k;
1986 }
1987 else {
1988 b2 -= k;
1989 b5 = -k;
1990 s5 = 0;
1991 }
1992 if (mode < 0 || mode > 9)
1993 mode = 0;
1994 try_quick = 1;
1995 if (mode > 5) {
1996 mode -= 4;
1997 try_quick = 0;
1998 }
1999 leftright = 1;
2000 switch(mode) {
2001 case 0:
2002 case 1:
2003 ilim = ilim1 = -1;
2004 i = 18;
2005 ndigits = 0;
2006 break;
2007 case 2:
2008 leftright = 0;
2009 /* no break */
2010 case 4:
2011 if (ndigits <= 0)
2012 ndigits = 1;
2013 ilim = ilim1 = i = ndigits;
2014 break;
2015 case 3:
2016 leftright = 0;
2017 /* no break */
2018 case 5:
2019 i = ndigits + k + 1;
2020 ilim = i;
2021 ilim1 = i - 1;
2022 if (i <= 0)
2023 i = 1;
2024 }
2025 j = sizeof(ULong);
2026 for(result_k = 0; sizeof(Bigint) - sizeof(ULong) + j <= i;
2027 j <<= 1) result_k++;
2028 result = Balloc(result_k);
2029 s = s0 = (char *)result;
2030
2031 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2032
2033 /* Try to get by with floating-point arithmetic. */
2034
2035 i = 0;
2036 value(d2) = value(d);
2037 k0 = k;
2038 ilim0 = ilim;
2039 ieps = 2; /* conservative */
2040 if (k > 0) {
2041 ds = tens[k&0xf];
2042 j = k >> 4;
2043 if (j & Bletch) {
2044 /* prevent overflows */
2045 j &= Bletch - 1;
2046 value(d) /= bigtens[n_bigtens-1];
2047 ieps++;
2048 }
2049 for(; j; j >>= 1, i++)
2050 if (j & 1) {
2051 ieps++;
2052 ds *= bigtens[i];
2053 }
2054 value(d) /= ds;
2055 }
2056 else if (j1 = -k) {
2057 value(d) *= tens[j1 & 0xf];
2058 for(j = j1 >> 4; j; j >>= 1, i++)
2059 if (j & 1) {
2060 ieps++;
2061 value(d) *= bigtens[i];
2062 }
2063 }
2064 if (k_check && value(d) < 1. && ilim > 0) {
2065 if (ilim1 <= 0)
2066 goto fast_failed;
2067 ilim = ilim1;
2068 k--;
2069 value(d) *= 10.;
2070 ieps++;
2071 }
2072 value(eps) = ieps*value(d) + 7.;
2073 word0(eps) -= (P-1)*Exp_msk1;
2074 if (ilim == 0) {
2075 S = mhi = 0;
2076 value(d) -= 5.;
2077 if (value(d) > value(eps))
2078 goto one_digit;
2079 if (value(d) < -value(eps))
2080 goto no_digits;
2081 goto fast_failed;
2082 }
2083 #ifndef No_leftright
2084 if (leftright) {
2085 /* Use Steele & White method of only
2086 * generating digits needed.
2087 */
2088 value(eps) = 0.5/tens[ilim-1] - value(eps);
2089 for(i = 0;;) {
2090 L = value(d);
2091 value(d) -= L;
2092 *s++ = '0' + (int)L;
2093 if (value(d) < value(eps))
2094 goto ret1;
2095 if (1. - value(d) < value(eps))
2096 goto bump_up;
2097 if (++i >= ilim)
2098 break;
2099 value(eps) *= 10.;
2100 value(d) *= 10.;
2101 }
2102 }
2103 else {
2104 #endif
2105 /* Generate ilim digits, then fix them up. */
2106 value(eps) *= tens[ilim-1];
2107 for(i = 1;; i++, value(d) *= 10.) {
2108 L = value(d);
2109 value(d) -= L;
2110 *s++ = '0' + (int)L;
2111 if (i == ilim) {
2112 if (value(d) > 0.5 + value(eps))
2113 goto bump_up;
2114 else if (value(d) < 0.5 - value(eps)) {
2115 while(*--s == '0');
2116 s++;
2117 goto ret1;
2118 }
2119 break;
2120 }
2121 }
2122 #ifndef No_leftright
2123 }
2124 #endif
2125 fast_failed:
2126 s = s0;
2127 value(d) = value(d2);
2128 k = k0;
2129 ilim = ilim0;
2130 }
2131
2132 /* Do we have a "small" integer? */
2133
2134 if (be >= 0 && k <= Int_max) {
2135 /* Yes. */
2136 ds = tens[k];
2137 if (ndigits < 0 && ilim <= 0) {
2138 S = mhi = 0;
2139 if (ilim < 0 || value(d) <= 5*ds)
2140 goto no_digits;
2141 goto one_digit;
2142 }
2143 for(i = 1;; i++) {
2144 L = value(d) / ds;
2145 value(d) -= L*ds;
2146 #ifdef Check_FLT_ROUNDS
2147 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2148 if (value(d) < 0) {
2149 L--;
2150 value(d) += ds;
2151 }
2152 #endif
2153 *s++ = '0' + (int)L;
2154 if (i == ilim) {
2155 value(d) += value(d);
2156 if (value(d) > ds || value(d) == ds && L & 1) {
2157 bump_up:
2158 while(*--s == '9')
2159 if (s == s0) {
2160 k++;
2161 *s = '0';
2162 break;
2163 }
2164 ++*s++;
2165 }
2166 break;
2167 }
2168 if (!(value(d) *= 10.))
2169 break;
2170 }
2171 goto ret1;
2172 }
2173
2174 m2 = b2;
2175 m5 = b5;
2176 mhi = mlo = 0;
2177 if (leftright) {
2178 if (mode < 2) {
2179 i =
2180 #ifndef Sudden_Underflow
2181 denorm ? be + (Bias + (P-1) - 1 + 1) :
2182 #endif
2183 #ifdef IBM
2184 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
2185 #else
2186 1 + P - bbits;
2187 #endif
2188 }
2189 else {
2190 j = ilim - 1;
2191 if (m5 >= j)
2192 m5 -= j;
2193 else {
2194 s5 += j -= m5;
2195 b5 += j;
2196 m5 = 0;
2197 }
2198 if ((i = ilim) < 0) {
2199 m2 -= i;
2200 i = 0;
2201 }
2202 }
2203 b2 += i;
2204 s2 += i;
2205 mhi = i2b(1);
2206 }
2207 if (m2 > 0 && s2 > 0) {
2208 i = m2 < s2 ? m2 : s2;
2209 b2 -= i;
2210 m2 -= i;
2211 s2 -= i;
2212 }
2213 if (b5 > 0) {
2214 if (leftright) {
2215 if (m5 > 0) {
2216 mhi = pow5mult(mhi, m5);
2217 b1 = mult(mhi, b);
2218 Bfree(b);
2219 b = b1;
2220 }
2221 if (j = b5 - m5)
2222 b = pow5mult(b, j);
2223 }
2224 else
2225 b = pow5mult(b, b5);
2226 }
2227 S = i2b(1);
2228 if (s5 > 0)
2229 S = pow5mult(S, s5);
2230
2231 /* Check for special case that d is a normalized power of 2. */
2232
2233 if (mode < 2) {
2234 if (!word1(d) && !(word0(d) & Bndry_mask)
2235 #ifndef Sudden_Underflow
2236 && word0(d) & Exp_mask
2237 #endif
2238 ) {
2239 /* The special case */
2240 b2 += Log2P;
2241 s2 += Log2P;
2242 spec_case = 1;
2243 }
2244 else
2245 spec_case = 0;
2246 }
2247
2248 /* Arrange for convenient computation of quotients:
2249 * shift left if necessary so divisor has 4 leading 0 bits.
2250 *
2251 * Perhaps we should just compute leading 28 bits of S once
2252 * and for all and pass them and a shift to quorem, so it
2253 * can do shifts and ors to compute the numerator for q.
2254 */
2255 #ifdef Pack_32
2256 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f)
2257 i = 32 - i;
2258 #else
2259 if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
2260 i = 16 - i;
2261 #endif
2262 if (i > 4) {
2263 i -= 4;
2264 b2 += i;
2265 m2 += i;
2266 s2 += i;
2267 }
2268 else if (i < 4) {
2269 i += 28;
2270 b2 += i;
2271 m2 += i;
2272 s2 += i;
2273 }
2274 if (b2 > 0)
2275 b = lshift(b, b2);
2276 if (s2 > 0)
2277 S = lshift(S, s2);
2278 if (k_check) {
2279 if (cmp(b,S) < 0) {
2280 k--;
2281 b = multadd(b, 10, 0); /* we botched the k estimate */
2282 if (leftright)
2283 mhi = multadd(mhi, 10, 0);
2284 ilim = ilim1;
2285 }
2286 }
2287 if (ilim <= 0 && mode > 2) {
2288 if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
2289 /* no digits, fcvt style */
2290 no_digits:
2291 k = -1 - ndigits;
2292 goto ret;
2293 }
2294 one_digit:
2295 *s++ = '1';
2296 k++;
2297 goto ret;
2298 }
2299 if (leftright) {
2300 if (m2 > 0)
2301 mhi = lshift(mhi, m2);
2302
2303 /* Compute mlo -- check for special case
2304 * that d is a normalized power of 2.
2305 */
2306
2307 mlo = mhi;
2308 if (spec_case) {
2309 mhi = Balloc(mhi->k);
2310 Bcopy(mhi, mlo);
2311 mhi = lshift(mhi, Log2P);
2312 }
2313
2314 for(i = 1;;i++) {
2315 dig = quorem(b,S) + '0';
2316 /* Do we yet have the shortest decimal string
2317 * that will round to d?
2318 */
2319 j = cmp(b, mlo);
2320 delta = diff(S, mhi);
2321 j1 = delta->sign ? 1 : cmp(b, delta);
2322 Bfree(delta);
2323 #ifndef ROUND_BIASED
2324 if (j1 == 0 && !mode && !(word1(d) & 1)) {
2325 if (dig == '9')
2326 goto round_9_up;
2327 if (j > 0)
2328 dig++;
2329 *s++ = dig;
2330 goto ret;
2331 }
2332 #endif
2333 if (j < 0 || j == 0 && !mode
2334 #ifndef ROUND_BIASED
2335 && !(word1(d) & 1)
2336 #endif
2337 ) {
2338 if (j1 > 0) {
2339 b = lshift(b, 1);
2340 j1 = cmp(b, S);
2341 if ((j1 > 0 || j1 == 0 && dig & 1)
2342 && dig++ == '9')
2343 goto round_9_up;
2344 }
2345 *s++ = dig;
2346 goto ret;
2347 }
2348 if (j1 > 0) {
2349 if (dig == '9') { /* possible if i == 1 */
2350 round_9_up:
2351 *s++ = '9';
2352 goto roundoff;
2353 }
2354 *s++ = dig + 1;
2355 goto ret;
2356 }
2357 *s++ = dig;
2358 if (i == ilim)
2359 break;
2360 b = multadd(b, 10, 0);
2361 if (mlo == mhi)
2362 mlo = mhi = multadd(mhi, 10, 0);
2363 else {
2364 mlo = multadd(mlo, 10, 0);
2365 mhi = multadd(mhi, 10, 0);
2366 }
2367 }
2368 }
2369 else
2370 for(i = 1;; i++) {
2371 *s++ = dig = quorem(b,S) + '0';
2372 if (i >= ilim)
2373 break;
2374 b = multadd(b, 10, 0);
2375 }
2376
2377 /* Round off last digit */
2378
2379 b = lshift(b, 1);
2380 j = cmp(b, S);
2381 if (j > 0 || j == 0 && dig & 1) {
2382 roundoff:
2383 while(*--s == '9')
2384 if (s == s0) {
2385 k++;
2386 *s++ = '1';
2387 goto ret;
2388 }
2389 ++*s++;
2390 }
2391 else {
2392 while(*--s == '0');
2393 s++;
2394 }
2395 ret:
2396 Bfree(S);
2397 if (mhi) {
2398 if (mlo && mlo != mhi)
2399 Bfree(mlo);
2400 Bfree(mhi);
2401 }
2402 ret1:
2403 Bfree(b);
2404 if (s == s0) { /* don't return empty string */
2405 *s++ = '0';
2406 k = 0;
2407 }
2408 *s = 0;
2409 *decpt = k + 1;
2410 if (rve)
2411 *rve = s;
2412 return s0;
2413 }
2414 #ifdef __cplusplus
2415 }
2416 #endif
2417