1 /****************************************************************
2 *
3 * The author of this software is David M. Gay.
4 *
5 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
6 * Copyright (C) 2002, 2005, 2006, 2007, 2008 Apple Inc. All rights reserved.
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 LUCENT 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 Bell Laboratories, Room 2C-463
24 600 Mountain Avenue
25 Murray Hill, NJ 07974-0636
26 U.S.A.
27 dmg@bell-labs.com
28 */
29
30 /* On a machine with IEEE extended-precision registers, it is
31 * necessary to specify double-precision (53-bit) rounding precision
32 * before invoking strtod or dtoa. If the machine uses (the equivalent
33 * of) Intel 80x87 arithmetic, the call
34 * _control87(PC_53, MCW_PC);
35 * does this with many compilers. Whether this or another call is
36 * appropriate depends on the compiler; for this to work, it may be
37 * necessary to #include "float.h" or another system-dependent header
38 * file.
39 */
40
41 /* strtod for IEEE-arithmetic machines.
42 *
43 * This strtod returns a nearest machine number to the input decimal
44 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
45 * broken by the IEEE round-even rule. Otherwise ties are broken by
46 * biased rounding (add half and chop).
47 *
48 * Inspired loosely by William D. Clinger's paper "How to Read Floating
49 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
50 *
51 * Modifications:
52 *
53 * 1. We only require IEEE.
54 * 2. We get by with floating-point arithmetic in a case that
55 * Clinger missed -- when we're computing d * 10^n
56 * for a small integer d and the integer n is not too
57 * much larger than 22 (the maximum integer k for which
58 * we can represent 10^k exactly), we may be able to
59 * compute (d*10^k) * 10^(e-k) with just one roundoff.
60 * 3. Rather than a bit-at-a-time adjustment of the binary
61 * result in the hard case, we use floating-point
62 * arithmetic to determine the adjustment to within
63 * one bit; only in really hard cases do we need to
64 * compute a second residual.
65 * 4. Because of 3., we don't need a large table of powers of 10
66 * for ten-to-e (just some small tables, e.g. of 10^k
67 * for 0 <= k <= 22).
68 */
69
70 /*
71 * #define IEEE_8087 for IEEE-arithmetic machines where the least
72 * significant byte has the lowest address.
73 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
74 * significant byte has the lowest address.
75 * #define No_leftright to omit left-right logic in fast floating-point
76 * computation of dtoa.
77 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
78 * and Honor_FLT_ROUNDS is not #defined.
79 * #define Inaccurate_Divide for IEEE-format with correctly rounded
80 * products but inaccurate quotients, e.g., for Intel i860.
81 * #define USE_LONG_LONG on machines that have a "long long"
82 * integer type (of >= 64 bits), and performance testing shows that
83 * it is faster than 32-bit fallback (which is often not the case
84 * on 32-bit machines). On such machines, you can #define Just_16
85 * to store 16 bits per 32-bit int32_t when doing high-precision integer
86 * arithmetic. Whether this speeds things up or slows things down
87 * depends on the machine and the number being converted.
88 * #define Bad_float_h if your system lacks a float.h or if it does not
89 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
90 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
91 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
92 * Infinity and NaN (case insensitively). On some systems (e.g.,
93 * some HP systems), it may be necessary to #define NAN_WORD0
94 * appropriately -- to the most significant word of a quiet NaN.
95 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
96 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
97 * strtod also accepts (case insensitively) strings of the form
98 * NaN(x), where x is a string of hexadecimal digits and spaces;
99 * if there is only one string of hexadecimal digits, it is taken
100 * for the 52 fraction bits of the resulting NaN; if there are two
101 * or more strings of hex digits, the first is for the high 20 bits,
102 * the second and subsequent for the low 32 bits, with intervening
103 * white space ignored; but if this results in none of the 52
104 * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
105 * and NAN_WORD1 are used instead.
106 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
107 * avoids underflows on inputs whose result does not underflow.
108 * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
109 * floating-point numbers and flushes underflows to zero rather
110 * than implementing gradual underflow, then you must also #define
111 * Sudden_Underflow.
112 * #define YES_ALIAS to permit aliasing certain double values with
113 * arrays of ULongs. This leads to slightly better code with
114 * some compilers and was always used prior to 19990916, but it
115 * is not strictly legal and can cause trouble with aggressively
116 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
117 * #define SET_INEXACT if IEEE arithmetic is being used and extra
118 * computation should be done to set the inexact flag when the
119 * result is inexact and avoid setting inexact when the result
120 * is exact. In this case, dtoa.c must be compiled in
121 * an environment, perhaps provided by #include "dtoa.c" in a
122 * suitable wrapper, that defines two functions,
123 * int get_inexact(void);
124 * void clear_inexact(void);
125 * such that get_inexact() returns a nonzero value if the
126 * inexact bit is already set, and clear_inexact() sets the
127 * inexact bit to 0. When SET_INEXACT is #defined, strtod
128 * also does extra computations to set the underflow and overflow
129 * flags when appropriate (i.e., when the result is tiny and
130 * inexact or when it is a numeric value rounded to +-infinity).
131 * #define NO_ERRNO if strtod should not assign errno = ERANGE when
132 * the result overflows to +-Infinity or underflows to 0.
133 */
134
135 #include "config.h"
136 #include "dtoa.h"
137
138 #if HAVE(ERRNO_H)
139 #include <errno.h>
140 #else
141 #define NO_ERRNO
142 #endif
143 #include <float.h>
144 #include <math.h>
145 #include <stdint.h>
146 #include <stdlib.h>
147 #include <string.h>
148 #include <wtf/AlwaysInline.h>
149 #include <wtf/Assertions.h>
150 #include <wtf/FastMalloc.h>
151 #include <wtf/Vector.h>
152 #include <wtf/Threading.h>
153
154 #include <stdio.h>
155
156 #if COMPILER(MSVC)
157 #pragma warning(disable: 4244)
158 #pragma warning(disable: 4245)
159 #pragma warning(disable: 4554)
160 #endif
161
162 #if PLATFORM(BIG_ENDIAN)
163 #define IEEE_MC68k
164 #elif PLATFORM(MIDDLE_ENDIAN)
165 #define IEEE_ARM
166 #else
167 #define IEEE_8087
168 #endif
169
170 #define INFNAN_CHECK
171
172 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) != 1
173 Exactly one of IEEE_8087, IEEE_ARM or IEEE_MC68k should be defined.
174 #endif
175
176 namespace WTF {
177
178 #if ENABLE(JSC_MULTIPLE_THREADS)
179 Mutex* s_dtoaP5Mutex;
180 #endif
181
182 typedef union { double d; uint32_t L[2]; } U;
183
184 #ifdef YES_ALIAS
185 #define dval(x) x
186 #ifdef IEEE_8087
187 #define word0(x) ((uint32_t*)&x)[1]
188 #define word1(x) ((uint32_t*)&x)[0]
189 #else
190 #define word0(x) ((uint32_t*)&x)[0]
191 #define word1(x) ((uint32_t*)&x)[1]
192 #endif
193 #else
194 #ifdef IEEE_8087
195 #define word0(x) (x)->L[1]
196 #define word1(x) (x)->L[0]
197 #else
198 #define word0(x) (x)->L[0]
199 #define word1(x) (x)->L[1]
200 #endif
201 #define dval(x) (x)->d
202 #endif
203
204 /* The following definition of Storeinc is appropriate for MIPS processors.
205 * An alternative that might be better on some machines is
206 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
207 */
208 #if defined(IEEE_8087) || defined(IEEE_ARM)
209 #define Storeinc(a,b,c) (((unsigned short*)a)[1] = (unsigned short)b, ((unsigned short*)a)[0] = (unsigned short)c, a++)
210 #else
211 #define Storeinc(a,b,c) (((unsigned short*)a)[0] = (unsigned short)b, ((unsigned short*)a)[1] = (unsigned short)c, a++)
212 #endif
213
214 #define Exp_shift 20
215 #define Exp_shift1 20
216 #define Exp_msk1 0x100000
217 #define Exp_msk11 0x100000
218 #define Exp_mask 0x7ff00000
219 #define P 53
220 #define Bias 1023
221 #define Emin (-1022)
222 #define Exp_1 0x3ff00000
223 #define Exp_11 0x3ff00000
224 #define Ebits 11
225 #define Frac_mask 0xfffff
226 #define Frac_mask1 0xfffff
227 #define Ten_pmax 22
228 #define Bletch 0x10
229 #define Bndry_mask 0xfffff
230 #define Bndry_mask1 0xfffff
231 #define LSB 1
232 #define Sign_bit 0x80000000
233 #define Log2P 1
234 #define Tiny0 0
235 #define Tiny1 1
236 #define Quick_max 14
237 #define Int_max 14
238
239 #if !defined(NO_IEEE_Scale)
240 #undef Avoid_Underflow
241 #define Avoid_Underflow
242 #endif
243
244 #if !defined(Flt_Rounds)
245 #if defined(FLT_ROUNDS)
246 #define Flt_Rounds FLT_ROUNDS
247 #else
248 #define Flt_Rounds 1
249 #endif
250 #endif /*Flt_Rounds*/
251
252
253 #define rounded_product(a,b) a *= b
254 #define rounded_quotient(a,b) a /= b
255
256 #define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
257 #define Big1 0xffffffff
258
259
260 // FIXME: we should remove non-Pack_32 mode since it is unused and unmaintained
261 #ifndef Pack_32
262 #define Pack_32
263 #endif
264
265 #if PLATFORM(PPC64) || PLATFORM(X86_64)
266 // 64-bit emulation provided by the compiler is likely to be slower than dtoa own code on 32-bit hardware.
267 #define USE_LONG_LONG
268 #endif
269
270 #ifndef USE_LONG_LONG
271 #ifdef Just_16
272 #undef Pack_32
273 /* When Pack_32 is not defined, we store 16 bits per 32-bit int32_t.
274 * This makes some inner loops simpler and sometimes saves work
275 * during multiplications, but it often seems to make things slightly
276 * slower. Hence the default is now to store 32 bits per int32_t.
277 */
278 #endif
279 #endif
280
281 #define Kmax 15
282
283 struct BigInt {
BigIntWTF::BigInt284 BigInt() : sign(0) { }
285 int sign;
286
clearWTF::BigInt287 void clear()
288 {
289 sign = 0;
290 m_words.clear();
291 }
292
sizeWTF::BigInt293 size_t size() const
294 {
295 return m_words.size();
296 }
297
resizeWTF::BigInt298 void resize(size_t s)
299 {
300 m_words.resize(s);
301 }
302
wordsWTF::BigInt303 uint32_t* words()
304 {
305 return m_words.data();
306 }
307
wordsWTF::BigInt308 const uint32_t* words() const
309 {
310 return m_words.data();
311 }
312
appendWTF::BigInt313 void append(uint32_t w)
314 {
315 m_words.append(w);
316 }
317
318 Vector<uint32_t, 16> m_words;
319 };
320
multadd(BigInt & b,int m,int a)321 static void multadd(BigInt& b, int m, int a) /* multiply by m and add a */
322 {
323 #ifdef USE_LONG_LONG
324 unsigned long long carry;
325 #else
326 uint32_t carry;
327 #endif
328
329 int wds = b.size();
330 uint32_t* x = b.words();
331 int i = 0;
332 carry = a;
333 do {
334 #ifdef USE_LONG_LONG
335 unsigned long long y = *x * (unsigned long long)m + carry;
336 carry = y >> 32;
337 *x++ = (uint32_t)y & 0xffffffffUL;
338 #else
339 #ifdef Pack_32
340 uint32_t xi = *x;
341 uint32_t y = (xi & 0xffff) * m + carry;
342 uint32_t z = (xi >> 16) * m + (y >> 16);
343 carry = z >> 16;
344 *x++ = (z << 16) + (y & 0xffff);
345 #else
346 uint32_t y = *x * m + carry;
347 carry = y >> 16;
348 *x++ = y & 0xffff;
349 #endif
350 #endif
351 } while (++i < wds);
352
353 if (carry)
354 b.append((uint32_t)carry);
355 }
356
s2b(BigInt & b,const char * s,int nd0,int nd,uint32_t y9)357 static void s2b(BigInt& b, const char* s, int nd0, int nd, uint32_t y9)
358 {
359 int k;
360 int32_t y;
361 int32_t x = (nd + 8) / 9;
362
363 for (k = 0, y = 1; x > y; y <<= 1, k++) { }
364 #ifdef Pack_32
365 b.sign = 0;
366 b.resize(1);
367 b.words()[0] = y9;
368 #else
369 b.sign = 0;
370 b.resize((b->x[1] = y9 >> 16) ? 2 : 1);
371 b.words()[0] = y9 & 0xffff;
372 #endif
373
374 int i = 9;
375 if (9 < nd0) {
376 s += 9;
377 do {
378 multadd(b, 10, *s++ - '0');
379 } while (++i < nd0);
380 s++;
381 } else
382 s += 10;
383 for (; i < nd; i++)
384 multadd(b, 10, *s++ - '0');
385 }
386
hi0bits(uint32_t x)387 static int hi0bits(uint32_t x)
388 {
389 int k = 0;
390
391 if (!(x & 0xffff0000)) {
392 k = 16;
393 x <<= 16;
394 }
395 if (!(x & 0xff000000)) {
396 k += 8;
397 x <<= 8;
398 }
399 if (!(x & 0xf0000000)) {
400 k += 4;
401 x <<= 4;
402 }
403 if (!(x & 0xc0000000)) {
404 k += 2;
405 x <<= 2;
406 }
407 if (!(x & 0x80000000)) {
408 k++;
409 if (!(x & 0x40000000))
410 return 32;
411 }
412 return k;
413 }
414
lo0bits(uint32_t * y)415 static int lo0bits (uint32_t* y)
416 {
417 int k;
418 uint32_t x = *y;
419
420 if (x & 7) {
421 if (x & 1)
422 return 0;
423 if (x & 2) {
424 *y = x >> 1;
425 return 1;
426 }
427 *y = x >> 2;
428 return 2;
429 }
430 k = 0;
431 if (!(x & 0xffff)) {
432 k = 16;
433 x >>= 16;
434 }
435 if (!(x & 0xff)) {
436 k += 8;
437 x >>= 8;
438 }
439 if (!(x & 0xf)) {
440 k += 4;
441 x >>= 4;
442 }
443 if (!(x & 0x3)) {
444 k += 2;
445 x >>= 2;
446 }
447 if (!(x & 1)) {
448 k++;
449 x >>= 1;
450 if (!x & 1)
451 return 32;
452 }
453 *y = x;
454 return k;
455 }
456
i2b(BigInt & b,int i)457 static void i2b(BigInt& b, int i)
458 {
459 b.sign = 0;
460 b.resize(1);
461 b.words()[0] = i;
462 }
463
mult(BigInt & aRef,const BigInt & bRef)464 static void mult(BigInt& aRef, const BigInt& bRef)
465 {
466 const BigInt* a = &aRef;
467 const BigInt* b = &bRef;
468 BigInt c;
469 int wa, wb, wc;
470 const uint32_t *x = 0, *xa, *xb, *xae, *xbe;
471 uint32_t *xc, *xc0;
472 uint32_t y;
473 #ifdef USE_LONG_LONG
474 unsigned long long carry, z;
475 #else
476 uint32_t carry, z;
477 #endif
478
479 if (a->size() < b->size()) {
480 const BigInt* tmp = a;
481 a = b;
482 b = tmp;
483 }
484
485 wa = a->size();
486 wb = b->size();
487 wc = wa + wb;
488 c.resize(wc);
489
490 for (xc = c.words(), xa = xc + wc; xc < xa; xc++)
491 *xc = 0;
492 xa = a->words();
493 xae = xa + wa;
494 xb = b->words();
495 xbe = xb + wb;
496 xc0 = c.words();
497 #ifdef USE_LONG_LONG
498 for (; xb < xbe; xc0++) {
499 if ((y = *xb++)) {
500 x = xa;
501 xc = xc0;
502 carry = 0;
503 do {
504 z = *x++ * (unsigned long long)y + *xc + carry;
505 carry = z >> 32;
506 *xc++ = (uint32_t)z & 0xffffffffUL;
507 } while (x < xae);
508 *xc = (uint32_t)carry;
509 }
510 }
511 #else
512 #ifdef Pack_32
513 for (; xb < xbe; xb++, xc0++) {
514 if ((y = *xb & 0xffff)) {
515 x = xa;
516 xc = xc0;
517 carry = 0;
518 do {
519 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
520 carry = z >> 16;
521 uint32_t z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
522 carry = z2 >> 16;
523 Storeinc(xc, z2, z);
524 } while (x < xae);
525 *xc = carry;
526 }
527 if ((y = *xb >> 16)) {
528 x = xa;
529 xc = xc0;
530 carry = 0;
531 uint32_t z2 = *xc;
532 do {
533 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
534 carry = z >> 16;
535 Storeinc(xc, z, z2);
536 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
537 carry = z2 >> 16;
538 } while (x < xae);
539 *xc = z2;
540 }
541 }
542 #else
543 for(; xb < xbe; xc0++) {
544 if ((y = *xb++)) {
545 x = xa;
546 xc = xc0;
547 carry = 0;
548 do {
549 z = *x++ * y + *xc + carry;
550 carry = z >> 16;
551 *xc++ = z & 0xffff;
552 } while (x < xae);
553 *xc = carry;
554 }
555 }
556 #endif
557 #endif
558 for (xc0 = c.words(), xc = xc0 + wc; wc > 0 && !*--xc; --wc) { }
559 c.resize(wc);
560 aRef = c;
561 }
562
563 struct P5Node {
564 BigInt val;
565 P5Node* next;
566 };
567
568 static P5Node* p5s;
569 static int p5s_count;
570
pow5mult(BigInt & b,int k)571 static ALWAYS_INLINE void pow5mult(BigInt& b, int k)
572 {
573 static int p05[3] = { 5, 25, 125 };
574
575 if (int i = k & 3)
576 multadd(b, p05[i - 1], 0);
577
578 if (!(k >>= 2))
579 return;
580
581 #if ENABLE(JSC_MULTIPLE_THREADS)
582 s_dtoaP5Mutex->lock();
583 #endif
584 P5Node* p5 = p5s;
585
586 if (!p5) {
587 /* first time */
588 p5 = new P5Node;
589 i2b(p5->val, 625);
590 p5->next = 0;
591 p5s = p5;
592 p5s_count = 1;
593 }
594
595 int p5s_count_local = p5s_count;
596 #if ENABLE(JSC_MULTIPLE_THREADS)
597 s_dtoaP5Mutex->unlock();
598 #endif
599 int p5s_used = 0;
600
601 for (;;) {
602 if (k & 1)
603 mult(b, p5->val);
604
605 if (!(k >>= 1))
606 break;
607
608 if (++p5s_used == p5s_count_local) {
609 #if ENABLE(JSC_MULTIPLE_THREADS)
610 s_dtoaP5Mutex->lock();
611 #endif
612 if (p5s_used == p5s_count) {
613 ASSERT(!p5->next);
614 p5->next = new P5Node;
615 p5->next->next = 0;
616 p5->next->val = p5->val;
617 mult(p5->next->val, p5->next->val);
618 ++p5s_count;
619 }
620
621 p5s_count_local = p5s_count;
622 #if ENABLE(JSC_MULTIPLE_THREADS)
623 s_dtoaP5Mutex->unlock();
624 #endif
625 }
626 p5 = p5->next;
627 }
628 }
629
lshift(BigInt & b,int k)630 static ALWAYS_INLINE void lshift(BigInt& b, int k)
631 {
632 #ifdef Pack_32
633 int n = k >> 5;
634 #else
635 int n = k >> 4;
636 #endif
637
638 int origSize = b.size();
639 int n1 = n + origSize + 1;
640
641 if (k &= 0x1f)
642 b.resize(b.size() + n + 1);
643 else
644 b.resize(b.size() + n);
645
646 const uint32_t* srcStart = b.words();
647 uint32_t* dstStart = b.words();
648 const uint32_t* src = srcStart + origSize - 1;
649 uint32_t* dst = dstStart + n1 - 1;
650 #ifdef Pack_32
651 if (k) {
652 uint32_t hiSubword = 0;
653 int s = 32 - k;
654 for (; src >= srcStart; --src) {
655 *dst-- = hiSubword | *src >> s;
656 hiSubword = *src << k;
657 }
658 *dst = hiSubword;
659 ASSERT(dst == dstStart + n);
660
661 b.resize(origSize + n + (b.words()[n1 - 1] != 0));
662 }
663 #else
664 if (k &= 0xf) {
665 uint32_t hiSubword = 0;
666 int s = 16 - k;
667 for (; src >= srcStart; --src) {
668 *dst-- = hiSubword | *src >> s;
669 hiSubword = (*src << k) & 0xffff;
670 }
671 *dst = hiSubword;
672 ASSERT(dst == dstStart + n);
673 result->wds = b->wds + n + (result->x[n1 - 1] != 0);
674 }
675 #endif
676 else {
677 do {
678 *--dst = *src--;
679 } while (src >= srcStart);
680 }
681 for (dst = dstStart + n; dst != dstStart; )
682 *--dst = 0;
683
684 ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
685 }
686
cmp(const BigInt & a,const BigInt & b)687 static int cmp(const BigInt& a, const BigInt& b)
688 {
689 const uint32_t *xa, *xa0, *xb, *xb0;
690 int i, j;
691
692 i = a.size();
693 j = b.size();
694 ASSERT(i <= 1 || a.words()[i - 1]);
695 ASSERT(j <= 1 || b.words()[j - 1]);
696 if (i -= j)
697 return i;
698 xa0 = a.words();
699 xa = xa0 + j;
700 xb0 = b.words();
701 xb = xb0 + j;
702 for (;;) {
703 if (*--xa != *--xb)
704 return *xa < *xb ? -1 : 1;
705 if (xa <= xa0)
706 break;
707 }
708 return 0;
709 }
710
diff(BigInt & c,const BigInt & aRef,const BigInt & bRef)711 static ALWAYS_INLINE void diff(BigInt& c, const BigInt& aRef, const BigInt& bRef)
712 {
713 const BigInt* a = &aRef;
714 const BigInt* b = &bRef;
715 int i, wa, wb;
716 uint32_t *xc;
717
718 i = cmp(*a, *b);
719 if (!i) {
720 c.sign = 0;
721 c.resize(1);
722 c.words()[0] = 0;
723 return;
724 }
725 if (i < 0) {
726 const BigInt* tmp = a;
727 a = b;
728 b = tmp;
729 i = 1;
730 } else
731 i = 0;
732
733 wa = a->size();
734 const uint32_t* xa = a->words();
735 const uint32_t* xae = xa + wa;
736 wb = b->size();
737 const uint32_t* xb = b->words();
738 const uint32_t* xbe = xb + wb;
739
740 c.resize(wa);
741 c.sign = i;
742 xc = c.words();
743 #ifdef USE_LONG_LONG
744 unsigned long long borrow = 0;
745 do {
746 unsigned long long y = (unsigned long long)*xa++ - *xb++ - borrow;
747 borrow = y >> 32 & (uint32_t)1;
748 *xc++ = (uint32_t)y & 0xffffffffUL;
749 } while (xb < xbe);
750 while (xa < xae) {
751 unsigned long long y = *xa++ - borrow;
752 borrow = y >> 32 & (uint32_t)1;
753 *xc++ = (uint32_t)y & 0xffffffffUL;
754 }
755 #else
756 uint32_t borrow = 0;
757 #ifdef Pack_32
758 do {
759 uint32_t y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
760 borrow = (y & 0x10000) >> 16;
761 uint32_t z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
762 borrow = (z & 0x10000) >> 16;
763 Storeinc(xc, z, y);
764 } while (xb < xbe);
765 while (xa < xae) {
766 uint32_t y = (*xa & 0xffff) - borrow;
767 borrow = (y & 0x10000) >> 16;
768 uint32_t z = (*xa++ >> 16) - borrow;
769 borrow = (z & 0x10000) >> 16;
770 Storeinc(xc, z, y);
771 }
772 #else
773 do {
774 uint32_t y = *xa++ - *xb++ - borrow;
775 borrow = (y & 0x10000) >> 16;
776 *xc++ = y & 0xffff;
777 } while (xb < xbe);
778 while (xa < xae) {
779 uint32_t y = *xa++ - borrow;
780 borrow = (y & 0x10000) >> 16;
781 *xc++ = y & 0xffff;
782 }
783 #endif
784 #endif
785 while (!*--xc)
786 wa--;
787 c.resize(wa);
788 }
789
ulp(U * x)790 static double ulp(U *x)
791 {
792 register int32_t L;
793 U u;
794
795 L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
796 #ifndef Avoid_Underflow
797 #ifndef Sudden_Underflow
798 if (L > 0) {
799 #endif
800 #endif
801 word0(&u) = L;
802 word1(&u) = 0;
803 #ifndef Avoid_Underflow
804 #ifndef Sudden_Underflow
805 } else {
806 L = -L >> Exp_shift;
807 if (L < Exp_shift) {
808 word0(&u) = 0x80000 >> L;
809 word1(&u) = 0;
810 } else {
811 word0(&u) = 0;
812 L -= Exp_shift;
813 word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
814 }
815 }
816 #endif
817 #endif
818 return dval(&u);
819 }
820
b2d(const BigInt & a,int * e)821 static double b2d(const BigInt& a, int* e)
822 {
823 const uint32_t* xa;
824 const uint32_t* xa0;
825 uint32_t w;
826 uint32_t y;
827 uint32_t z;
828 int k;
829 U d;
830
831 #define d0 word0(&d)
832 #define d1 word1(&d)
833
834 xa0 = a.words();
835 xa = xa0 + a.size();
836 y = *--xa;
837 ASSERT(y);
838 k = hi0bits(y);
839 *e = 32 - k;
840 #ifdef Pack_32
841 if (k < Ebits) {
842 d0 = Exp_1 | (y >> (Ebits - k));
843 w = xa > xa0 ? *--xa : 0;
844 d1 = (y << (32 - Ebits + k)) | (w >> (Ebits - k));
845 goto ret_d;
846 }
847 z = xa > xa0 ? *--xa : 0;
848 if (k -= Ebits) {
849 d0 = Exp_1 | (y << k) | (z >> (32 - k));
850 y = xa > xa0 ? *--xa : 0;
851 d1 = (z << k) | (y >> (32 - k));
852 } else {
853 d0 = Exp_1 | y;
854 d1 = z;
855 }
856 #else
857 if (k < Ebits + 16) {
858 z = xa > xa0 ? *--xa : 0;
859 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
860 w = xa > xa0 ? *--xa : 0;
861 y = xa > xa0 ? *--xa : 0;
862 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
863 goto ret_d;
864 }
865 z = xa > xa0 ? *--xa : 0;
866 w = xa > xa0 ? *--xa : 0;
867 k -= Ebits + 16;
868 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
869 y = xa > xa0 ? *--xa : 0;
870 d1 = w << k + 16 | y << k;
871 #endif
872 ret_d:
873 #undef d0
874 #undef d1
875 return dval(&d);
876 }
877
d2b(BigInt & b,U * d,int * e,int * bits)878 static ALWAYS_INLINE void d2b(BigInt& b, U* d, int* e, int* bits)
879 {
880 int de, k;
881 uint32_t *x, y, z;
882 #ifndef Sudden_Underflow
883 int i;
884 #endif
885 #define d0 word0(d)
886 #define d1 word1(d)
887
888 b.sign = 0;
889 #ifdef Pack_32
890 b.resize(1);
891 #else
892 b.resize(2);
893 #endif
894 x = b.words();
895
896 z = d0 & Frac_mask;
897 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
898 #ifdef Sudden_Underflow
899 de = (int)(d0 >> Exp_shift);
900 #else
901 if ((de = (int)(d0 >> Exp_shift)))
902 z |= Exp_msk1;
903 #endif
904 #ifdef Pack_32
905 if ((y = d1)) {
906 if ((k = lo0bits(&y))) {
907 x[0] = y | (z << (32 - k));
908 z >>= k;
909 } else
910 x[0] = y;
911 if (z) {
912 b.resize(2);
913 x[1] = z;
914 }
915
916 #ifndef Sudden_Underflow
917 i = b.size();
918 #endif
919 } else {
920 k = lo0bits(&z);
921 x[0] = z;
922 #ifndef Sudden_Underflow
923 i = 1;
924 #endif
925 b.resize(1);
926 k += 32;
927 }
928 #else
929 if ((y = d1)) {
930 if ((k = lo0bits(&y))) {
931 if (k >= 16) {
932 x[0] = y | z << 32 - k & 0xffff;
933 x[1] = z >> k - 16 & 0xffff;
934 x[2] = z >> k;
935 i = 2;
936 } else {
937 x[0] = y & 0xffff;
938 x[1] = y >> 16 | z << 16 - k & 0xffff;
939 x[2] = z >> k & 0xffff;
940 x[3] = z >> k + 16;
941 i = 3;
942 }
943 } else {
944 x[0] = y & 0xffff;
945 x[1] = y >> 16;
946 x[2] = z & 0xffff;
947 x[3] = z >> 16;
948 i = 3;
949 }
950 } else {
951 k = lo0bits(&z);
952 if (k >= 16) {
953 x[0] = z;
954 i = 0;
955 } else {
956 x[0] = z & 0xffff;
957 x[1] = z >> 16;
958 i = 1;
959 }
960 k += 32;
961 } while (!x[i])
962 --i;
963 b->resize(i + 1);
964 #endif
965 #ifndef Sudden_Underflow
966 if (de) {
967 #endif
968 *e = de - Bias - (P - 1) + k;
969 *bits = P - k;
970 #ifndef Sudden_Underflow
971 } else {
972 *e = de - Bias - (P - 1) + 1 + k;
973 #ifdef Pack_32
974 *bits = (32 * i) - hi0bits(x[i - 1]);
975 #else
976 *bits = (i + 2) * 16 - hi0bits(x[i]);
977 #endif
978 }
979 #endif
980 }
981 #undef d0
982 #undef d1
983
ratio(const BigInt & a,const BigInt & b)984 static double ratio(const BigInt& a, const BigInt& b)
985 {
986 U da, db;
987 int k, ka, kb;
988
989 dval(&da) = b2d(a, &ka);
990 dval(&db) = b2d(b, &kb);
991 #ifdef Pack_32
992 k = ka - kb + 32 * (a.size() - b.size());
993 #else
994 k = ka - kb + 16 * (a.size() - b.size());
995 #endif
996 if (k > 0)
997 word0(&da) += k * Exp_msk1;
998 else {
999 k = -k;
1000 word0(&db) += k * Exp_msk1;
1001 }
1002 return dval(&da) / dval(&db);
1003 }
1004
1005 static const double tens[] = {
1006 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1007 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1008 1e20, 1e21, 1e22
1009 };
1010
1011 static const double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1012 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1013 #ifdef Avoid_Underflow
1014 9007199254740992. * 9007199254740992.e-256
1015 /* = 2^106 * 1e-53 */
1016 #else
1017 1e-256
1018 #endif
1019 };
1020
1021 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1022 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1023 #define Scale_Bit 0x10
1024 #define n_bigtens 5
1025
1026 #if defined(INFNAN_CHECK)
1027
1028 #ifndef NAN_WORD0
1029 #define NAN_WORD0 0x7ff80000
1030 #endif
1031
1032 #ifndef NAN_WORD1
1033 #define NAN_WORD1 0
1034 #endif
1035
match(const char ** sp,const char * t)1036 static int match(const char** sp, const char* t)
1037 {
1038 int c, d;
1039 const char* s = *sp;
1040
1041 while ((d = *t++)) {
1042 if ((c = *++s) >= 'A' && c <= 'Z')
1043 c += 'a' - 'A';
1044 if (c != d)
1045 return 0;
1046 }
1047 *sp = s + 1;
1048 return 1;
1049 }
1050
1051 #ifndef No_Hex_NaN
hexnan(U * rvp,const char ** sp)1052 static void hexnan(U* rvp, const char** sp)
1053 {
1054 uint32_t c, x[2];
1055 const char* s;
1056 int havedig, udx0, xshift;
1057
1058 x[0] = x[1] = 0;
1059 havedig = xshift = 0;
1060 udx0 = 1;
1061 s = *sp;
1062 while ((c = *(const unsigned char*)++s)) {
1063 if (c >= '0' && c <= '9')
1064 c -= '0';
1065 else if (c >= 'a' && c <= 'f')
1066 c += 10 - 'a';
1067 else if (c >= 'A' && c <= 'F')
1068 c += 10 - 'A';
1069 else if (c <= ' ') {
1070 if (udx0 && havedig) {
1071 udx0 = 0;
1072 xshift = 1;
1073 }
1074 continue;
1075 } else if (/*(*/ c == ')' && havedig) {
1076 *sp = s + 1;
1077 break;
1078 } else
1079 return; /* invalid form: don't change *sp */
1080 havedig = 1;
1081 if (xshift) {
1082 xshift = 0;
1083 x[0] = x[1];
1084 x[1] = 0;
1085 }
1086 if (udx0)
1087 x[0] = (x[0] << 4) | (x[1] >> 28);
1088 x[1] = (x[1] << 4) | c;
1089 }
1090 if ((x[0] &= 0xfffff) || x[1]) {
1091 word0(rvp) = Exp_mask | x[0];
1092 word1(rvp) = x[1];
1093 }
1094 }
1095 #endif /*No_Hex_NaN*/
1096 #endif /* INFNAN_CHECK */
1097
strtod(const char * s00,char ** se)1098 double strtod(const char* s00, char** se)
1099 {
1100 #ifdef Avoid_Underflow
1101 int scale;
1102 #endif
1103 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1104 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1105 const char *s, *s0, *s1;
1106 double aadj, aadj1;
1107 U aadj2, adj, rv, rv0;
1108 int32_t L;
1109 uint32_t y, z;
1110 BigInt bb, bb1, bd, bd0, bs, delta;
1111 #ifdef SET_INEXACT
1112 int inexact, oldinexact;
1113 #endif
1114
1115 sign = nz0 = nz = 0;
1116 dval(&rv) = 0;
1117 for (s = s00; ; s++)
1118 switch (*s) {
1119 case '-':
1120 sign = 1;
1121 /* no break */
1122 case '+':
1123 if (*++s)
1124 goto break2;
1125 /* no break */
1126 case 0:
1127 goto ret0;
1128 case '\t':
1129 case '\n':
1130 case '\v':
1131 case '\f':
1132 case '\r':
1133 case ' ':
1134 continue;
1135 default:
1136 goto break2;
1137 }
1138 break2:
1139 if (*s == '0') {
1140 nz0 = 1;
1141 while (*++s == '0') { }
1142 if (!*s)
1143 goto ret;
1144 }
1145 s0 = s;
1146 y = z = 0;
1147 for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1148 if (nd < 9)
1149 y = (10 * y) + c - '0';
1150 else if (nd < 16)
1151 z = (10 * z) + c - '0';
1152 nd0 = nd;
1153 if (c == '.') {
1154 c = *++s;
1155 if (!nd) {
1156 for (; c == '0'; c = *++s)
1157 nz++;
1158 if (c > '0' && c <= '9') {
1159 s0 = s;
1160 nf += nz;
1161 nz = 0;
1162 goto have_dig;
1163 }
1164 goto dig_done;
1165 }
1166 for (; c >= '0' && c <= '9'; c = *++s) {
1167 have_dig:
1168 nz++;
1169 if (c -= '0') {
1170 nf += nz;
1171 for (i = 1; i < nz; i++)
1172 if (nd++ < 9)
1173 y *= 10;
1174 else if (nd <= DBL_DIG + 1)
1175 z *= 10;
1176 if (nd++ < 9)
1177 y = (10 * y) + c;
1178 else if (nd <= DBL_DIG + 1)
1179 z = (10 * z) + c;
1180 nz = 0;
1181 }
1182 }
1183 }
1184 dig_done:
1185 e = 0;
1186 if (c == 'e' || c == 'E') {
1187 if (!nd && !nz && !nz0) {
1188 goto ret0;
1189 }
1190 s00 = s;
1191 esign = 0;
1192 switch (c = *++s) {
1193 case '-':
1194 esign = 1;
1195 case '+':
1196 c = *++s;
1197 }
1198 if (c >= '0' && c <= '9') {
1199 while (c == '0')
1200 c = *++s;
1201 if (c > '0' && c <= '9') {
1202 L = c - '0';
1203 s1 = s;
1204 while ((c = *++s) >= '0' && c <= '9')
1205 L = (10 * L) + c - '0';
1206 if (s - s1 > 8 || L > 19999)
1207 /* Avoid confusion from exponents
1208 * so large that e might overflow.
1209 */
1210 e = 19999; /* safe for 16 bit ints */
1211 else
1212 e = (int)L;
1213 if (esign)
1214 e = -e;
1215 } else
1216 e = 0;
1217 } else
1218 s = s00;
1219 }
1220 if (!nd) {
1221 if (!nz && !nz0) {
1222 #ifdef INFNAN_CHECK
1223 /* Check for Nan and Infinity */
1224 switch(c) {
1225 case 'i':
1226 case 'I':
1227 if (match(&s,"nf")) {
1228 --s;
1229 if (!match(&s,"inity"))
1230 ++s;
1231 word0(&rv) = 0x7ff00000;
1232 word1(&rv) = 0;
1233 goto ret;
1234 }
1235 break;
1236 case 'n':
1237 case 'N':
1238 if (match(&s, "an")) {
1239 word0(&rv) = NAN_WORD0;
1240 word1(&rv) = NAN_WORD1;
1241 #ifndef No_Hex_NaN
1242 if (*s == '(') /*)*/
1243 hexnan(&rv, &s);
1244 #endif
1245 goto ret;
1246 }
1247 }
1248 #endif /* INFNAN_CHECK */
1249 ret0:
1250 s = s00;
1251 sign = 0;
1252 }
1253 goto ret;
1254 }
1255 e1 = e -= nf;
1256
1257 /* Now we have nd0 digits, starting at s0, followed by a
1258 * decimal point, followed by nd-nd0 digits. The number we're
1259 * after is the integer represented by those digits times
1260 * 10**e */
1261
1262 if (!nd0)
1263 nd0 = nd;
1264 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1265 dval(&rv) = y;
1266 if (k > 9) {
1267 #ifdef SET_INEXACT
1268 if (k > DBL_DIG)
1269 oldinexact = get_inexact();
1270 #endif
1271 dval(&rv) = tens[k - 9] * dval(&rv) + z;
1272 }
1273 if (nd <= DBL_DIG && Flt_Rounds == 1) {
1274 if (!e)
1275 goto ret;
1276 if (e > 0) {
1277 if (e <= Ten_pmax) {
1278 /* rv = */ rounded_product(dval(&rv), tens[e]);
1279 goto ret;
1280 }
1281 i = DBL_DIG - nd;
1282 if (e <= Ten_pmax + i) {
1283 /* A fancier test would sometimes let us do
1284 * this for larger i values.
1285 */
1286 e -= i;
1287 dval(&rv) *= tens[i];
1288 /* rv = */ rounded_product(dval(&rv), tens[e]);
1289 goto ret;
1290 }
1291 }
1292 #ifndef Inaccurate_Divide
1293 else if (e >= -Ten_pmax) {
1294 /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
1295 goto ret;
1296 }
1297 #endif
1298 }
1299 e1 += nd - k;
1300
1301 #ifdef SET_INEXACT
1302 inexact = 1;
1303 if (k <= DBL_DIG)
1304 oldinexact = get_inexact();
1305 #endif
1306 #ifdef Avoid_Underflow
1307 scale = 0;
1308 #endif
1309
1310 /* Get starting approximation = rv * 10**e1 */
1311
1312 if (e1 > 0) {
1313 if ((i = e1 & 15))
1314 dval(&rv) *= tens[i];
1315 if (e1 &= ~15) {
1316 if (e1 > DBL_MAX_10_EXP) {
1317 ovfl:
1318 #ifndef NO_ERRNO
1319 errno = ERANGE;
1320 #endif
1321 /* Can't trust HUGE_VAL */
1322 word0(&rv) = Exp_mask;
1323 word1(&rv) = 0;
1324 #ifdef SET_INEXACT
1325 /* set overflow bit */
1326 dval(&rv0) = 1e300;
1327 dval(&rv0) *= dval(&rv0);
1328 #endif
1329 goto ret;
1330 }
1331 e1 >>= 4;
1332 for (j = 0; e1 > 1; j++, e1 >>= 1)
1333 if (e1 & 1)
1334 dval(&rv) *= bigtens[j];
1335 /* The last multiplication could overflow. */
1336 word0(&rv) -= P * Exp_msk1;
1337 dval(&rv) *= bigtens[j];
1338 if ((z = word0(&rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
1339 goto ovfl;
1340 if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
1341 /* set to largest number */
1342 /* (Can't trust DBL_MAX) */
1343 word0(&rv) = Big0;
1344 word1(&rv) = Big1;
1345 } else
1346 word0(&rv) += P * Exp_msk1;
1347 }
1348 } else if (e1 < 0) {
1349 e1 = -e1;
1350 if ((i = e1 & 15))
1351 dval(&rv) /= tens[i];
1352 if (e1 >>= 4) {
1353 if (e1 >= 1 << n_bigtens)
1354 goto undfl;
1355 #ifdef Avoid_Underflow
1356 if (e1 & Scale_Bit)
1357 scale = 2 * P;
1358 for (j = 0; e1 > 0; j++, e1 >>= 1)
1359 if (e1 & 1)
1360 dval(&rv) *= tinytens[j];
1361 if (scale && (j = (2 * P) + 1 - ((word0(&rv) & Exp_mask) >> Exp_shift)) > 0) {
1362 /* scaled rv is denormal; zap j low bits */
1363 if (j >= 32) {
1364 word1(&rv) = 0;
1365 if (j >= 53)
1366 word0(&rv) = (P + 2) * Exp_msk1;
1367 else
1368 word0(&rv) &= 0xffffffff << (j - 32);
1369 } else
1370 word1(&rv) &= 0xffffffff << j;
1371 }
1372 #else
1373 for (j = 0; e1 > 1; j++, e1 >>= 1)
1374 if (e1 & 1)
1375 dval(&rv) *= tinytens[j];
1376 /* The last multiplication could underflow. */
1377 dval(&rv0) = dval(&rv);
1378 dval(&rv) *= tinytens[j];
1379 if (!dval(&rv)) {
1380 dval(&rv) = 2. * dval(&rv0);
1381 dval(&rv) *= tinytens[j];
1382 #endif
1383 if (!dval(&rv)) {
1384 undfl:
1385 dval(&rv) = 0.;
1386 #ifndef NO_ERRNO
1387 errno = ERANGE;
1388 #endif
1389 goto ret;
1390 }
1391 #ifndef Avoid_Underflow
1392 word0(&rv) = Tiny0;
1393 word1(&rv) = Tiny1;
1394 /* The refinement below will clean
1395 * this approximation up.
1396 */
1397 }
1398 #endif
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 s2b(bd0, s0, nd0, nd, y);
1407
1408 for (;;) {
1409 bd = bd0;
1410 d2b(bb, &rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
1411 i2b(bs, 1);
1412
1413 if (e >= 0) {
1414 bb2 = bb5 = 0;
1415 bd2 = bd5 = e;
1416 } else {
1417 bb2 = bb5 = -e;
1418 bd2 = bd5 = 0;
1419 }
1420 if (bbe >= 0)
1421 bb2 += bbe;
1422 else
1423 bd2 -= bbe;
1424 bs2 = bb2;
1425 #ifdef Avoid_Underflow
1426 j = bbe - scale;
1427 i = j + bbbits - 1; /* logb(rv) */
1428 if (i < Emin) /* denormal */
1429 j += P - Emin;
1430 else
1431 j = P + 1 - bbbits;
1432 #else /*Avoid_Underflow*/
1433 #ifdef Sudden_Underflow
1434 j = P + 1 - bbbits;
1435 #else /*Sudden_Underflow*/
1436 j = bbe;
1437 i = j + bbbits - 1; /* logb(rv) */
1438 if (i < Emin) /* denormal */
1439 j += P - Emin;
1440 else
1441 j = P + 1 - bbbits;
1442 #endif /*Sudden_Underflow*/
1443 #endif /*Avoid_Underflow*/
1444 bb2 += j;
1445 bd2 += j;
1446 #ifdef Avoid_Underflow
1447 bd2 += scale;
1448 #endif
1449 i = bb2 < bd2 ? bb2 : bd2;
1450 if (i > bs2)
1451 i = bs2;
1452 if (i > 0) {
1453 bb2 -= i;
1454 bd2 -= i;
1455 bs2 -= i;
1456 }
1457 if (bb5 > 0) {
1458 pow5mult(bs, bb5);
1459 mult(bb, bs);
1460 }
1461 if (bb2 > 0)
1462 lshift(bb, bb2);
1463 if (bd5 > 0)
1464 pow5mult(bd, bd5);
1465 if (bd2 > 0)
1466 lshift(bd, bd2);
1467 if (bs2 > 0)
1468 lshift(bs, bs2);
1469 diff(delta, bb, bd);
1470 dsign = delta.sign;
1471 delta.sign = 0;
1472 i = cmp(delta, bs);
1473
1474 if (i < 0) {
1475 /* Error is less than half an ulp -- check for
1476 * special case of mantissa a power of two.
1477 */
1478 if (dsign || word1(&rv) || word0(&rv) & Bndry_mask
1479 #ifdef Avoid_Underflow
1480 || (word0(&rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
1481 #else
1482 || (word0(&rv) & Exp_mask) <= Exp_msk1
1483 #endif
1484 ) {
1485 #ifdef SET_INEXACT
1486 if (!delta->words()[0] && delta->size() <= 1)
1487 inexact = 0;
1488 #endif
1489 break;
1490 }
1491 if (!delta.words()[0] && delta.size() <= 1) {
1492 /* exact result */
1493 #ifdef SET_INEXACT
1494 inexact = 0;
1495 #endif
1496 break;
1497 }
1498 lshift(delta, Log2P);
1499 if (cmp(delta, bs) > 0)
1500 goto drop_down;
1501 break;
1502 }
1503 if (i == 0) {
1504 /* exactly half-way between */
1505 if (dsign) {
1506 if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
1507 && word1(&rv) == (
1508 #ifdef Avoid_Underflow
1509 (scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
1510 ? (0xffffffff & (0xffffffff << (2 * P + 1 - (y >> Exp_shift)))) :
1511 #endif
1512 0xffffffff)) {
1513 /*boundary case -- increment exponent*/
1514 word0(&rv) = (word0(&rv) & Exp_mask) + Exp_msk1;
1515 word1(&rv) = 0;
1516 #ifdef Avoid_Underflow
1517 dsign = 0;
1518 #endif
1519 break;
1520 }
1521 } else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
1522 drop_down:
1523 /* boundary case -- decrement exponent */
1524 #ifdef Sudden_Underflow /*{{*/
1525 L = word0(&rv) & Exp_mask;
1526 #ifdef Avoid_Underflow
1527 if (L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1))
1528 #else
1529 if (L <= Exp_msk1)
1530 #endif /*Avoid_Underflow*/
1531 goto undfl;
1532 L -= Exp_msk1;
1533 #else /*Sudden_Underflow}{*/
1534 #ifdef Avoid_Underflow
1535 if (scale) {
1536 L = word0(&rv) & Exp_mask;
1537 if (L <= (2 * P + 1) * Exp_msk1) {
1538 if (L > (P + 2) * Exp_msk1)
1539 /* round even ==> */
1540 /* accept rv */
1541 break;
1542 /* rv = smallest denormal */
1543 goto undfl;
1544 }
1545 }
1546 #endif /*Avoid_Underflow*/
1547 L = (word0(&rv) & Exp_mask) - Exp_msk1;
1548 #endif /*Sudden_Underflow}}*/
1549 word0(&rv) = L | Bndry_mask1;
1550 word1(&rv) = 0xffffffff;
1551 break;
1552 }
1553 if (!(word1(&rv) & LSB))
1554 break;
1555 if (dsign)
1556 dval(&rv) += ulp(&rv);
1557 else {
1558 dval(&rv) -= ulp(&rv);
1559 #ifndef Sudden_Underflow
1560 if (!dval(&rv))
1561 goto undfl;
1562 #endif
1563 }
1564 #ifdef Avoid_Underflow
1565 dsign = 1 - dsign;
1566 #endif
1567 break;
1568 }
1569 if ((aadj = ratio(delta, bs)) <= 2.) {
1570 if (dsign)
1571 aadj = aadj1 = 1.;
1572 else if (word1(&rv) || word0(&rv) & Bndry_mask) {
1573 #ifndef Sudden_Underflow
1574 if (word1(&rv) == Tiny1 && !word0(&rv))
1575 goto undfl;
1576 #endif
1577 aadj = 1.;
1578 aadj1 = -1.;
1579 } else {
1580 /* special case -- power of FLT_RADIX to be */
1581 /* rounded down... */
1582
1583 if (aadj < 2. / FLT_RADIX)
1584 aadj = 1. / FLT_RADIX;
1585 else
1586 aadj *= 0.5;
1587 aadj1 = -aadj;
1588 }
1589 } else {
1590 aadj *= 0.5;
1591 aadj1 = dsign ? aadj : -aadj;
1592 #ifdef Check_FLT_ROUNDS
1593 switch (Rounding) {
1594 case 2: /* towards +infinity */
1595 aadj1 -= 0.5;
1596 break;
1597 case 0: /* towards 0 */
1598 case 3: /* towards -infinity */
1599 aadj1 += 0.5;
1600 }
1601 #else
1602 if (Flt_Rounds == 0)
1603 aadj1 += 0.5;
1604 #endif /*Check_FLT_ROUNDS*/
1605 }
1606 y = word0(&rv) & Exp_mask;
1607
1608 /* Check for overflow */
1609
1610 if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
1611 dval(&rv0) = dval(&rv);
1612 word0(&rv) -= P * Exp_msk1;
1613 adj.d = aadj1 * ulp(&rv);
1614 dval(&rv) += adj.d;
1615 if ((word0(&rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
1616 if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
1617 goto ovfl;
1618 word0(&rv) = Big0;
1619 word1(&rv) = Big1;
1620 goto cont;
1621 } else
1622 word0(&rv) += P * Exp_msk1;
1623 } else {
1624 #ifdef Avoid_Underflow
1625 if (scale && y <= 2 * P * Exp_msk1) {
1626 if (aadj <= 0x7fffffff) {
1627 if ((z = (uint32_t)aadj) <= 0)
1628 z = 1;
1629 aadj = z;
1630 aadj1 = dsign ? aadj : -aadj;
1631 }
1632 dval(&aadj2) = aadj1;
1633 word0(&aadj2) += (2 * P + 1) * Exp_msk1 - y;
1634 aadj1 = dval(&aadj2);
1635 }
1636 adj.d = aadj1 * ulp(&rv);
1637 dval(&rv) += adj.d;
1638 #else
1639 #ifdef Sudden_Underflow
1640 if ((word0(&rv) & Exp_mask) <= P * Exp_msk1) {
1641 dval(&rv0) = dval(&rv);
1642 word0(&rv) += P * Exp_msk1;
1643 adj.d = aadj1 * ulp(&rv);
1644 dval(&rv) += adj.d;
1645 if ((word0(&rv) & Exp_mask) <= P * Exp_msk1)
1646 {
1647 if (word0(&rv0) == Tiny0 && word1(&rv0) == Tiny1)
1648 goto undfl;
1649 word0(&rv) = Tiny0;
1650 word1(&rv) = Tiny1;
1651 goto cont;
1652 }
1653 else
1654 word0(&rv) -= P * Exp_msk1;
1655 } else {
1656 adj.d = aadj1 * ulp(&rv);
1657 dval(&rv) += adj.d;
1658 }
1659 #else /*Sudden_Underflow*/
1660 /* Compute adj so that the IEEE rounding rules will
1661 * correctly round rv + adj in some half-way cases.
1662 * If rv * ulp(rv) is denormalized (i.e.,
1663 * y <= (P - 1) * Exp_msk1), we must adjust aadj to avoid
1664 * trouble from bits lost to denormalization;
1665 * example: 1.2e-307 .
1666 */
1667 if (y <= (P - 1) * Exp_msk1 && aadj > 1.) {
1668 aadj1 = (double)(int)(aadj + 0.5);
1669 if (!dsign)
1670 aadj1 = -aadj1;
1671 }
1672 adj.d = aadj1 * ulp(&rv);
1673 dval(&rv) += adj.d;
1674 #endif /*Sudden_Underflow*/
1675 #endif /*Avoid_Underflow*/
1676 }
1677 z = word0(&rv) & Exp_mask;
1678 #ifndef SET_INEXACT
1679 #ifdef Avoid_Underflow
1680 if (!scale)
1681 #endif
1682 if (y == z) {
1683 /* Can we stop now? */
1684 L = (int32_t)aadj;
1685 aadj -= L;
1686 /* The tolerances below are conservative. */
1687 if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
1688 if (aadj < .4999999 || aadj > .5000001)
1689 break;
1690 } else if (aadj < .4999999 / FLT_RADIX)
1691 break;
1692 }
1693 #endif
1694 cont:
1695 ;
1696 }
1697 #ifdef SET_INEXACT
1698 if (inexact) {
1699 if (!oldinexact) {
1700 word0(&rv0) = Exp_1 + (70 << Exp_shift);
1701 word1(&rv0) = 0;
1702 dval(&rv0) += 1.;
1703 }
1704 } else if (!oldinexact)
1705 clear_inexact();
1706 #endif
1707 #ifdef Avoid_Underflow
1708 if (scale) {
1709 word0(&rv0) = Exp_1 - 2 * P * Exp_msk1;
1710 word1(&rv0) = 0;
1711 dval(&rv) *= dval(&rv0);
1712 #ifndef NO_ERRNO
1713 /* try to avoid the bug of testing an 8087 register value */
1714 if (word0(&rv) == 0 && word1(&rv) == 0)
1715 errno = ERANGE;
1716 #endif
1717 }
1718 #endif /* Avoid_Underflow */
1719 #ifdef SET_INEXACT
1720 if (inexact && !(word0(&rv) & Exp_mask)) {
1721 /* set underflow bit */
1722 dval(&rv0) = 1e-300;
1723 dval(&rv0) *= dval(&rv0);
1724 }
1725 #endif
1726 ret:
1727 if (se)
1728 *se = const_cast<char*>(s);
1729 return sign ? -dval(&rv) : dval(&rv);
1730 }
1731
quorem(BigInt & b,BigInt & S)1732 static ALWAYS_INLINE int quorem(BigInt& b, BigInt& S)
1733 {
1734 size_t n;
1735 uint32_t *bx, *bxe, q, *sx, *sxe;
1736 #ifdef USE_LONG_LONG
1737 unsigned long long borrow, carry, y, ys;
1738 #else
1739 uint32_t borrow, carry, y, ys;
1740 #ifdef Pack_32
1741 uint32_t si, z, zs;
1742 #endif
1743 #endif
1744 ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
1745 ASSERT(S.size() <= 1 || S.words()[S.size() - 1]);
1746
1747 n = S.size();
1748 ASSERT_WITH_MESSAGE(b.size() <= n, "oversize b in quorem");
1749 if (b.size() < n)
1750 return 0;
1751 sx = S.words();
1752 sxe = sx + --n;
1753 bx = b.words();
1754 bxe = bx + n;
1755 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1756 ASSERT_WITH_MESSAGE(q <= 9, "oversized quotient in quorem");
1757 if (q) {
1758 borrow = 0;
1759 carry = 0;
1760 do {
1761 #ifdef USE_LONG_LONG
1762 ys = *sx++ * (unsigned long long)q + carry;
1763 carry = ys >> 32;
1764 y = *bx - (ys & 0xffffffffUL) - borrow;
1765 borrow = y >> 32 & (uint32_t)1;
1766 *bx++ = (uint32_t)y & 0xffffffffUL;
1767 #else
1768 #ifdef Pack_32
1769 si = *sx++;
1770 ys = (si & 0xffff) * q + carry;
1771 zs = (si >> 16) * q + (ys >> 16);
1772 carry = zs >> 16;
1773 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
1774 borrow = (y & 0x10000) >> 16;
1775 z = (*bx >> 16) - (zs & 0xffff) - borrow;
1776 borrow = (z & 0x10000) >> 16;
1777 Storeinc(bx, z, y);
1778 #else
1779 ys = *sx++ * q + carry;
1780 carry = ys >> 16;
1781 y = *bx - (ys & 0xffff) - borrow;
1782 borrow = (y & 0x10000) >> 16;
1783 *bx++ = y & 0xffff;
1784 #endif
1785 #endif
1786 } while (sx <= sxe);
1787 if (!*bxe) {
1788 bx = b.words();
1789 while (--bxe > bx && !*bxe)
1790 --n;
1791 b.resize(n);
1792 }
1793 }
1794 if (cmp(b, S) >= 0) {
1795 q++;
1796 borrow = 0;
1797 carry = 0;
1798 bx = b.words();
1799 sx = S.words();
1800 do {
1801 #ifdef USE_LONG_LONG
1802 ys = *sx++ + carry;
1803 carry = ys >> 32;
1804 y = *bx - (ys & 0xffffffffUL) - borrow;
1805 borrow = y >> 32 & (uint32_t)1;
1806 *bx++ = (uint32_t)y & 0xffffffffUL;
1807 #else
1808 #ifdef Pack_32
1809 si = *sx++;
1810 ys = (si & 0xffff) + carry;
1811 zs = (si >> 16) + (ys >> 16);
1812 carry = zs >> 16;
1813 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
1814 borrow = (y & 0x10000) >> 16;
1815 z = (*bx >> 16) - (zs & 0xffff) - borrow;
1816 borrow = (z & 0x10000) >> 16;
1817 Storeinc(bx, z, y);
1818 #else
1819 ys = *sx++ + carry;
1820 carry = ys >> 16;
1821 y = *bx - (ys & 0xffff) - borrow;
1822 borrow = (y & 0x10000) >> 16;
1823 *bx++ = y & 0xffff;
1824 #endif
1825 #endif
1826 } while (sx <= sxe);
1827 bx = b.words();
1828 bxe = bx + n;
1829 if (!*bxe) {
1830 while (--bxe > bx && !*bxe)
1831 --n;
1832 b.resize(n);
1833 }
1834 }
1835 return q;
1836 }
1837
1838 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1839 *
1840 * Inspired by "How to Print Floating-Point Numbers Accurately" by
1841 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1842 *
1843 * Modifications:
1844 * 1. Rather than iterating, we use a simple numeric overestimate
1845 * to determine k = floor(log10(d)). We scale relevant
1846 * quantities using O(log2(k)) rather than O(k) multiplications.
1847 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1848 * try to generate digits strictly left to right. Instead, we
1849 * compute with fewer bits and propagate the carry if necessary
1850 * when rounding the final digit up. This is often faster.
1851 * 3. Under the assumption that input will be rounded nearest,
1852 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1853 * That is, we allow equality in stopping tests when the
1854 * round-nearest rule will give the same floating-point value
1855 * as would satisfaction of the stopping test with strict
1856 * inequality.
1857 * 4. We remove common factors of powers of 2 from relevant
1858 * quantities.
1859 * 5. When converting floating-point integers less than 1e16,
1860 * we use floating-point arithmetic rather than resorting
1861 * to multiple-precision integers.
1862 * 6. When asked to produce fewer than 15 digits, we first try
1863 * to get by with floating-point arithmetic; we resort to
1864 * multiple-precision integer arithmetic only if we cannot
1865 * guarantee that the floating-point calculation has given
1866 * the correctly rounded result. For k requested digits and
1867 * "uniformly" distributed input, the probability is
1868 * something like 10^(k-15) that we must resort to the int32_t
1869 * calculation.
1870 */
1871
dtoa(char * result,double dd,int ndigits,int * decpt,int * sign,char ** rve)1872 void dtoa(char* result, double dd, int ndigits, int* decpt, int* sign, char** rve)
1873 {
1874 /*
1875 Arguments ndigits, decpt, sign are similar to those
1876 of ecvt and fcvt; trailing zeros are suppressed from
1877 the returned string. If not null, *rve is set to point
1878 to the end of the return value. If d is +-Infinity or NaN,
1879 then *decpt is set to 9999.
1880
1881 */
1882
1883 int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
1884 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1885 spec_case, try_quick;
1886 int32_t L;
1887 #ifndef Sudden_Underflow
1888 int denorm;
1889 uint32_t x;
1890 #endif
1891 BigInt b, b1, delta, mlo, mhi, S;
1892 U d2, eps, u;
1893 double ds;
1894 char *s, *s0;
1895 #ifdef SET_INEXACT
1896 int inexact, oldinexact;
1897 #endif
1898
1899 u.d = dd;
1900 if (word0(&u) & Sign_bit) {
1901 /* set sign for everything, including 0's and NaNs */
1902 *sign = 1;
1903 word0(&u) &= ~Sign_bit; /* clear sign bit */
1904 } else
1905 *sign = 0;
1906
1907 if ((word0(&u) & Exp_mask) == Exp_mask)
1908 {
1909 /* Infinity or NaN */
1910 *decpt = 9999;
1911 if (!word1(&u) && !(word0(&u) & 0xfffff))
1912 strcpy(result, "Infinity");
1913 else
1914 strcpy(result, "NaN");
1915 return;
1916 }
1917 if (!dval(&u)) {
1918 *decpt = 1;
1919 result[0] = '0';
1920 result[1] = '\0';
1921 return;
1922 }
1923
1924 #ifdef SET_INEXACT
1925 try_quick = oldinexact = get_inexact();
1926 inexact = 1;
1927 #endif
1928
1929 d2b(b, &u, &be, &bbits);
1930 #ifdef Sudden_Underflow
1931 i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
1932 #else
1933 if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
1934 #endif
1935 dval(&d2) = dval(&u);
1936 word0(&d2) &= Frac_mask1;
1937 word0(&d2) |= Exp_11;
1938
1939 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
1940 * log10(x) = log(x) / log(10)
1941 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
1942 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
1943 *
1944 * This suggests computing an approximation k to log10(d) by
1945 *
1946 * k = (i - Bias)*0.301029995663981
1947 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
1948 *
1949 * We want k to be too large rather than too small.
1950 * The error in the first-order Taylor series approximation
1951 * is in our favor, so we just round up the constant enough
1952 * to compensate for any error in the multiplication of
1953 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
1954 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
1955 * adding 1e-13 to the constant term more than suffices.
1956 * Hence we adjust the constant term to 0.1760912590558.
1957 * (We could get a more accurate k by invoking log10,
1958 * but this is probably not worthwhile.)
1959 */
1960
1961 i -= Bias;
1962 #ifndef Sudden_Underflow
1963 denorm = 0;
1964 } else {
1965 /* d is denormalized */
1966
1967 i = bbits + be + (Bias + (P - 1) - 1);
1968 x = (i > 32) ? (word0(&u) << (64 - i)) | (word1(&u) >> (i - 32))
1969 : word1(&u) << (32 - i);
1970 dval(&d2) = x;
1971 word0(&d2) -= 31 * Exp_msk1; /* adjust exponent */
1972 i -= (Bias + (P - 1) - 1) + 1;
1973 denorm = 1;
1974 }
1975 #endif
1976 ds = (dval(&d2) - 1.5) * 0.289529654602168 + 0.1760912590558 + (i * 0.301029995663981);
1977 k = (int)ds;
1978 if (ds < 0. && ds != k)
1979 k--; /* want k = floor(ds) */
1980 k_check = 1;
1981 if (k >= 0 && k <= Ten_pmax) {
1982 if (dval(&u) < tens[k])
1983 k--;
1984 k_check = 0;
1985 }
1986 j = bbits - i - 1;
1987 if (j >= 0) {
1988 b2 = 0;
1989 s2 = j;
1990 } else {
1991 b2 = -j;
1992 s2 = 0;
1993 }
1994 if (k >= 0) {
1995 b5 = 0;
1996 s5 = k;
1997 s2 += k;
1998 } else {
1999 b2 -= k;
2000 b5 = -k;
2001 s5 = 0;
2002 }
2003
2004 #ifndef SET_INEXACT
2005 #ifdef Check_FLT_ROUNDS
2006 try_quick = Rounding == 1;
2007 #else
2008 try_quick = 1;
2009 #endif
2010 #endif /*SET_INEXACT*/
2011
2012 leftright = 1;
2013 ilim = ilim1 = -1;
2014 i = 18;
2015 ndigits = 0;
2016 s = s0 = result;
2017
2018 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2019
2020 /* Try to get by with floating-point arithmetic. */
2021
2022 i = 0;
2023 dval(&d2) = dval(&u);
2024 k0 = k;
2025 ilim0 = ilim;
2026 ieps = 2; /* conservative */
2027 if (k > 0) {
2028 ds = tens[k & 0xf];
2029 j = k >> 4;
2030 if (j & Bletch) {
2031 /* prevent overflows */
2032 j &= Bletch - 1;
2033 dval(&u) /= bigtens[n_bigtens - 1];
2034 ieps++;
2035 }
2036 for (; j; j >>= 1, i++) {
2037 if (j & 1) {
2038 ieps++;
2039 ds *= bigtens[i];
2040 }
2041 }
2042 dval(&u) /= ds;
2043 } else if ((j1 = -k)) {
2044 dval(&u) *= tens[j1 & 0xf];
2045 for (j = j1 >> 4; j; j >>= 1, i++) {
2046 if (j & 1) {
2047 ieps++;
2048 dval(&u) *= bigtens[i];
2049 }
2050 }
2051 }
2052 if (k_check && dval(&u) < 1. && ilim > 0) {
2053 if (ilim1 <= 0)
2054 goto fast_failed;
2055 ilim = ilim1;
2056 k--;
2057 dval(&u) *= 10.;
2058 ieps++;
2059 }
2060 dval(&eps) = (ieps * dval(&u)) + 7.;
2061 word0(&eps) -= (P - 1) * Exp_msk1;
2062 if (ilim == 0) {
2063 S.clear();
2064 mhi.clear();
2065 dval(&u) -= 5.;
2066 if (dval(&u) > dval(&eps))
2067 goto one_digit;
2068 if (dval(&u) < -dval(&eps))
2069 goto no_digits;
2070 goto fast_failed;
2071 }
2072 #ifndef No_leftright
2073 if (leftright) {
2074 /* Use Steele & White method of only
2075 * generating digits needed.
2076 */
2077 dval(&eps) = (0.5 / tens[ilim - 1]) - dval(&eps);
2078 for (i = 0;;) {
2079 L = (long int)dval(&u);
2080 dval(&u) -= L;
2081 *s++ = '0' + (int)L;
2082 if (dval(&u) < dval(&eps))
2083 goto ret;
2084 if (1. - dval(&u) < dval(&eps))
2085 goto bump_up;
2086 if (++i >= ilim)
2087 break;
2088 dval(&eps) *= 10.;
2089 dval(&u) *= 10.;
2090 }
2091 } else {
2092 #endif
2093 /* Generate ilim digits, then fix them up. */
2094 dval(&eps) *= tens[ilim - 1];
2095 for (i = 1;; i++, dval(&u) *= 10.) {
2096 L = (int32_t)(dval(&u));
2097 if (!(dval(&u) -= L))
2098 ilim = i;
2099 *s++ = '0' + (int)L;
2100 if (i == ilim) {
2101 if (dval(&u) > 0.5 + dval(&eps))
2102 goto bump_up;
2103 else if (dval(&u) < 0.5 - dval(&eps)) {
2104 while (*--s == '0') { }
2105 s++;
2106 goto ret;
2107 }
2108 break;
2109 }
2110 }
2111 #ifndef No_leftright
2112 }
2113 #endif
2114 fast_failed:
2115 s = s0;
2116 dval(&u) = dval(&d2);
2117 k = k0;
2118 ilim = ilim0;
2119 }
2120
2121 /* Do we have a "small" integer? */
2122
2123 if (be >= 0 && k <= Int_max) {
2124 /* Yes. */
2125 ds = tens[k];
2126 if (ndigits < 0 && ilim <= 0) {
2127 S.clear();
2128 mhi.clear();
2129 if (ilim < 0 || dval(&u) <= 5 * ds)
2130 goto no_digits;
2131 goto one_digit;
2132 }
2133 for (i = 1;; i++, dval(&u) *= 10.) {
2134 L = (int32_t)(dval(&u) / ds);
2135 dval(&u) -= L * ds;
2136 #ifdef Check_FLT_ROUNDS
2137 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2138 if (dval(&u) < 0) {
2139 L--;
2140 dval(&u) += ds;
2141 }
2142 #endif
2143 *s++ = '0' + (int)L;
2144 if (!dval(&u)) {
2145 #ifdef SET_INEXACT
2146 inexact = 0;
2147 #endif
2148 break;
2149 }
2150 if (i == ilim) {
2151 dval(&u) += dval(&u);
2152 if (dval(&u) > ds || (dval(&u) == ds && (L & 1))) {
2153 bump_up:
2154 while (*--s == '9')
2155 if (s == s0) {
2156 k++;
2157 *s = '0';
2158 break;
2159 }
2160 ++*s++;
2161 }
2162 break;
2163 }
2164 }
2165 goto ret;
2166 }
2167
2168 m2 = b2;
2169 m5 = b5;
2170 mhi.clear();
2171 mlo.clear();
2172 if (leftright) {
2173 i =
2174 #ifndef Sudden_Underflow
2175 denorm ? be + (Bias + (P - 1) - 1 + 1) :
2176 #endif
2177 1 + P - bbits;
2178 b2 += i;
2179 s2 += i;
2180 i2b(mhi, 1);
2181 }
2182 if (m2 > 0 && s2 > 0) {
2183 i = m2 < s2 ? m2 : s2;
2184 b2 -= i;
2185 m2 -= i;
2186 s2 -= i;
2187 }
2188 if (b5 > 0) {
2189 if (leftright) {
2190 if (m5 > 0) {
2191 pow5mult(mhi, m5);
2192 mult(b, mhi);
2193 }
2194 if ((j = b5 - m5))
2195 pow5mult(b, j);
2196 } else
2197 pow5mult(b, b5);
2198 }
2199 i2b(S, 1);
2200 if (s5 > 0)
2201 pow5mult(S, s5);
2202
2203 /* Check for special case that d is a normalized power of 2. */
2204
2205 spec_case = 0;
2206 if (!word1(&u) && !(word0(&u) & Bndry_mask)
2207 #ifndef Sudden_Underflow
2208 && word0(&u) & (Exp_mask & ~Exp_msk1)
2209 #endif
2210 ) {
2211 /* The special case */
2212 b2 += Log2P;
2213 s2 += Log2P;
2214 spec_case = 1;
2215 }
2216
2217 /* Arrange for convenient computation of quotients:
2218 * shift left if necessary so divisor has 4 leading 0 bits.
2219 *
2220 * Perhaps we should just compute leading 28 bits of S once
2221 * and for all and pass them and a shift to quorem, so it
2222 * can do shifts and ors to compute the numerator for q.
2223 */
2224 #ifdef Pack_32
2225 if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0x1f))
2226 i = 32 - i;
2227 #else
2228 if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0xf))
2229 i = 16 - i;
2230 #endif
2231 if (i > 4) {
2232 i -= 4;
2233 b2 += i;
2234 m2 += i;
2235 s2 += i;
2236 } else if (i < 4) {
2237 i += 28;
2238 b2 += i;
2239 m2 += i;
2240 s2 += i;
2241 }
2242 if (b2 > 0)
2243 lshift(b, b2);
2244 if (s2 > 0)
2245 lshift(S, s2);
2246 if (k_check) {
2247 if (cmp(b,S) < 0) {
2248 k--;
2249 multadd(b, 10, 0); /* we botched the k estimate */
2250 if (leftright)
2251 multadd(mhi, 10, 0);
2252 ilim = ilim1;
2253 }
2254 }
2255
2256 if (leftright) {
2257 if (m2 > 0)
2258 lshift(mhi, m2);
2259
2260 /* Compute mlo -- check for special case
2261 * that d is a normalized power of 2.
2262 */
2263
2264 mlo = mhi;
2265 if (spec_case) {
2266 mhi = mlo;
2267 lshift(mhi, Log2P);
2268 }
2269
2270 for (i = 1;;i++) {
2271 dig = quorem(b,S) + '0';
2272 /* Do we yet have the shortest decimal string
2273 * that will round to d?
2274 */
2275 j = cmp(b, mlo);
2276 diff(delta, S, mhi);
2277 j1 = delta.sign ? 1 : cmp(b, delta);
2278 if (j1 == 0 && !(word1(&u) & 1)) {
2279 if (dig == '9')
2280 goto round_9_up;
2281 if (j > 0)
2282 dig++;
2283 #ifdef SET_INEXACT
2284 else if (!b->x[0] && b->wds <= 1)
2285 inexact = 0;
2286 #endif
2287 *s++ = dig;
2288 goto ret;
2289 }
2290 if (j < 0 || (j == 0 && !(word1(&u) & 1))) {
2291 if (!b.words()[0] && b.size() <= 1) {
2292 #ifdef SET_INEXACT
2293 inexact = 0;
2294 #endif
2295 goto accept_dig;
2296 }
2297 if (j1 > 0) {
2298 lshift(b, 1);
2299 j1 = cmp(b, S);
2300 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
2301 goto round_9_up;
2302 }
2303 accept_dig:
2304 *s++ = dig;
2305 goto ret;
2306 }
2307 if (j1 > 0) {
2308 if (dig == '9') { /* possible if i == 1 */
2309 round_9_up:
2310 *s++ = '9';
2311 goto roundoff;
2312 }
2313 *s++ = dig + 1;
2314 goto ret;
2315 }
2316 *s++ = dig;
2317 if (i == ilim)
2318 break;
2319 multadd(b, 10, 0);
2320 multadd(mlo, 10, 0);
2321 multadd(mhi, 10, 0);
2322 }
2323 } else
2324 for (i = 1;; i++) {
2325 *s++ = dig = quorem(b,S) + '0';
2326 if (!b.words()[0] && b.size() <= 1) {
2327 #ifdef SET_INEXACT
2328 inexact = 0;
2329 #endif
2330 goto ret;
2331 }
2332 if (i >= ilim)
2333 break;
2334 multadd(b, 10, 0);
2335 }
2336
2337 /* Round off last digit */
2338
2339 lshift(b, 1);
2340 j = cmp(b, S);
2341 if (j > 0 || (j == 0 && (dig & 1))) {
2342 roundoff:
2343 while (*--s == '9')
2344 if (s == s0) {
2345 k++;
2346 *s++ = '1';
2347 goto ret;
2348 }
2349 ++*s++;
2350 } else {
2351 while (*--s == '0') { }
2352 s++;
2353 }
2354 goto ret;
2355 no_digits:
2356 k = -1 - ndigits;
2357 goto ret;
2358 one_digit:
2359 *s++ = '1';
2360 k++;
2361 goto ret;
2362 ret:
2363 #ifdef SET_INEXACT
2364 if (inexact) {
2365 if (!oldinexact) {
2366 word0(&u) = Exp_1 + (70 << Exp_shift);
2367 word1(&u) = 0;
2368 dval(&u) += 1.;
2369 }
2370 } else if (!oldinexact)
2371 clear_inexact();
2372 #endif
2373 *s = 0;
2374 *decpt = k + 1;
2375 if (rve)
2376 *rve = s;
2377 }
2378
2379 } // namespace WTF
2380