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 <math.h>
144 #include <stdint.h>
145 #include <stdlib.h>
146 #include <string.h>
147 #include <wtf/AlwaysInline.h>
148 #include <wtf/Assertions.h>
149 #include <wtf/FastMalloc.h>
150 #include <wtf/MathExtras.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 CPU(BIG_ENDIAN)
163 #define IEEE_MC68k
164 #elif CPU(MIDDLE_ENDIAN)
165 #define IEEE_ARM
166 #else
167 #define IEEE_8087
168 #endif
169
170 #define INFNAN_CHECK
171 #define No_Hex_NaN
172
173 #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) != 1
174 Exactly one of IEEE_8087, IEEE_ARM or IEEE_MC68k should be defined.
175 #endif
176
177 namespace WTF {
178
179 #if ENABLE(JSC_MULTIPLE_THREADS)
180 Mutex* s_dtoaP5Mutex;
181 #endif
182
183 typedef union { double d; uint32_t L[2]; } U;
184
185 #ifdef YES_ALIAS
186 #define dval(x) x
187 #ifdef IEEE_8087
188 #define word0(x) ((uint32_t*)&x)[1]
189 #define word1(x) ((uint32_t*)&x)[0]
190 #else
191 #define word0(x) ((uint32_t*)&x)[0]
192 #define word1(x) ((uint32_t*)&x)[1]
193 #endif
194 #else
195 #ifdef IEEE_8087
196 #define word0(x) (x)->L[1]
197 #define word1(x) (x)->L[0]
198 #else
199 #define word0(x) (x)->L[0]
200 #define word1(x) (x)->L[1]
201 #endif
202 #define dval(x) (x)->d
203 #endif
204
205 /* The following definition of Storeinc is appropriate for MIPS processors.
206 * An alternative that might be better on some machines is
207 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
208 */
209 #if defined(IEEE_8087) || defined(IEEE_ARM)
210 #define Storeinc(a,b,c) (((unsigned short*)a)[1] = (unsigned short)b, ((unsigned short*)a)[0] = (unsigned short)c, a++)
211 #else
212 #define Storeinc(a,b,c) (((unsigned short*)a)[0] = (unsigned short)b, ((unsigned short*)a)[1] = (unsigned short)c, a++)
213 #endif
214
215 #define Exp_shift 20
216 #define Exp_shift1 20
217 #define Exp_msk1 0x100000
218 #define Exp_msk11 0x100000
219 #define Exp_mask 0x7ff00000
220 #define P 53
221 #define Bias 1023
222 #define Emin (-1022)
223 #define Exp_1 0x3ff00000
224 #define Exp_11 0x3ff00000
225 #define Ebits 11
226 #define Frac_mask 0xfffff
227 #define Frac_mask1 0xfffff
228 #define Ten_pmax 22
229 #define Bletch 0x10
230 #define Bndry_mask 0xfffff
231 #define Bndry_mask1 0xfffff
232 #define LSB 1
233 #define Sign_bit 0x80000000
234 #define Log2P 1
235 #define Tiny0 0
236 #define Tiny1 1
237 #define Quick_max 14
238 #define Int_max 14
239
240 #if !defined(NO_IEEE_Scale)
241 #undef Avoid_Underflow
242 #define Avoid_Underflow
243 #endif
244
245 #if !defined(Flt_Rounds)
246 #if defined(FLT_ROUNDS)
247 #define Flt_Rounds FLT_ROUNDS
248 #else
249 #define Flt_Rounds 1
250 #endif
251 #endif /*Flt_Rounds*/
252
253
254 #define rounded_product(a,b) a *= b
255 #define rounded_quotient(a,b) a /= b
256
257 #define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
258 #define Big1 0xffffffff
259
260
261 // FIXME: we should remove non-Pack_32 mode since it is unused and unmaintained
262 #ifndef Pack_32
263 #define Pack_32
264 #endif
265
266 #if CPU(PPC64) || CPU(X86_64)
267 // FIXME: should we enable this on all 64-bit CPUs?
268 // 64-bit emulation provided by the compiler is likely to be slower than dtoa own code on 32-bit hardware.
269 #define USE_LONG_LONG
270 #endif
271
272 #ifndef USE_LONG_LONG
273 #ifdef Just_16
274 #undef Pack_32
275 /* When Pack_32 is not defined, we store 16 bits per 32-bit int32_t.
276 * This makes some inner loops simpler and sometimes saves work
277 * during multiplications, but it often seems to make things slightly
278 * slower. Hence the default is now to store 32 bits per int32_t.
279 */
280 #endif
281 #endif
282
283 #define Kmax 15
284
285 struct BigInt {
BigIntWTF::BigInt286 BigInt() : sign(0) { }
287 int sign;
288
clearWTF::BigInt289 void clear()
290 {
291 sign = 0;
292 m_words.clear();
293 }
294
sizeWTF::BigInt295 size_t size() const
296 {
297 return m_words.size();
298 }
299
resizeWTF::BigInt300 void resize(size_t s)
301 {
302 m_words.resize(s);
303 }
304
wordsWTF::BigInt305 uint32_t* words()
306 {
307 return m_words.data();
308 }
309
wordsWTF::BigInt310 const uint32_t* words() const
311 {
312 return m_words.data();
313 }
314
appendWTF::BigInt315 void append(uint32_t w)
316 {
317 m_words.append(w);
318 }
319
320 Vector<uint32_t, 16> m_words;
321 };
322
multadd(BigInt & b,int m,int a)323 static void multadd(BigInt& b, int m, int a) /* multiply by m and add a */
324 {
325 #ifdef USE_LONG_LONG
326 unsigned long long carry;
327 #else
328 uint32_t carry;
329 #endif
330
331 int wds = b.size();
332 uint32_t* x = b.words();
333 int i = 0;
334 carry = a;
335 do {
336 #ifdef USE_LONG_LONG
337 unsigned long long y = *x * (unsigned long long)m + carry;
338 carry = y >> 32;
339 *x++ = (uint32_t)y & 0xffffffffUL;
340 #else
341 #ifdef Pack_32
342 uint32_t xi = *x;
343 uint32_t y = (xi & 0xffff) * m + carry;
344 uint32_t z = (xi >> 16) * m + (y >> 16);
345 carry = z >> 16;
346 *x++ = (z << 16) + (y & 0xffff);
347 #else
348 uint32_t y = *x * m + carry;
349 carry = y >> 16;
350 *x++ = y & 0xffff;
351 #endif
352 #endif
353 } while (++i < wds);
354
355 if (carry)
356 b.append((uint32_t)carry);
357 }
358
s2b(BigInt & b,const char * s,int nd0,int nd,uint32_t y9)359 static void s2b(BigInt& b, const char* s, int nd0, int nd, uint32_t y9)
360 {
361 int k;
362 int32_t y;
363 int32_t x = (nd + 8) / 9;
364
365 for (k = 0, y = 1; x > y; y <<= 1, k++) { }
366 #ifdef Pack_32
367 b.sign = 0;
368 b.resize(1);
369 b.words()[0] = y9;
370 #else
371 b.sign = 0;
372 b.resize((b->x[1] = y9 >> 16) ? 2 : 1);
373 b.words()[0] = y9 & 0xffff;
374 #endif
375
376 int i = 9;
377 if (9 < nd0) {
378 s += 9;
379 do {
380 multadd(b, 10, *s++ - '0');
381 } while (++i < nd0);
382 s++;
383 } else
384 s += 10;
385 for (; i < nd; i++)
386 multadd(b, 10, *s++ - '0');
387 }
388
hi0bits(uint32_t x)389 static int hi0bits(uint32_t x)
390 {
391 int k = 0;
392
393 if (!(x & 0xffff0000)) {
394 k = 16;
395 x <<= 16;
396 }
397 if (!(x & 0xff000000)) {
398 k += 8;
399 x <<= 8;
400 }
401 if (!(x & 0xf0000000)) {
402 k += 4;
403 x <<= 4;
404 }
405 if (!(x & 0xc0000000)) {
406 k += 2;
407 x <<= 2;
408 }
409 if (!(x & 0x80000000)) {
410 k++;
411 if (!(x & 0x40000000))
412 return 32;
413 }
414 return k;
415 }
416
lo0bits(uint32_t * y)417 static int lo0bits (uint32_t* y)
418 {
419 int k;
420 uint32_t x = *y;
421
422 if (x & 7) {
423 if (x & 1)
424 return 0;
425 if (x & 2) {
426 *y = x >> 1;
427 return 1;
428 }
429 *y = x >> 2;
430 return 2;
431 }
432 k = 0;
433 if (!(x & 0xffff)) {
434 k = 16;
435 x >>= 16;
436 }
437 if (!(x & 0xff)) {
438 k += 8;
439 x >>= 8;
440 }
441 if (!(x & 0xf)) {
442 k += 4;
443 x >>= 4;
444 }
445 if (!(x & 0x3)) {
446 k += 2;
447 x >>= 2;
448 }
449 if (!(x & 1)) {
450 k++;
451 x >>= 1;
452 if (!x & 1)
453 return 32;
454 }
455 *y = x;
456 return k;
457 }
458
i2b(BigInt & b,int i)459 static void i2b(BigInt& b, int i)
460 {
461 b.sign = 0;
462 b.resize(1);
463 b.words()[0] = i;
464 }
465
mult(BigInt & aRef,const BigInt & bRef)466 static void mult(BigInt& aRef, const BigInt& bRef)
467 {
468 const BigInt* a = &aRef;
469 const BigInt* b = &bRef;
470 BigInt c;
471 int wa, wb, wc;
472 const uint32_t *x = 0, *xa, *xb, *xae, *xbe;
473 uint32_t *xc, *xc0;
474 uint32_t y;
475 #ifdef USE_LONG_LONG
476 unsigned long long carry, z;
477 #else
478 uint32_t carry, z;
479 #endif
480
481 if (a->size() < b->size()) {
482 const BigInt* tmp = a;
483 a = b;
484 b = tmp;
485 }
486
487 wa = a->size();
488 wb = b->size();
489 wc = wa + wb;
490 c.resize(wc);
491
492 for (xc = c.words(), xa = xc + wc; xc < xa; xc++)
493 *xc = 0;
494 xa = a->words();
495 xae = xa + wa;
496 xb = b->words();
497 xbe = xb + wb;
498 xc0 = c.words();
499 #ifdef USE_LONG_LONG
500 for (; xb < xbe; xc0++) {
501 if ((y = *xb++)) {
502 x = xa;
503 xc = xc0;
504 carry = 0;
505 do {
506 z = *x++ * (unsigned long long)y + *xc + carry;
507 carry = z >> 32;
508 *xc++ = (uint32_t)z & 0xffffffffUL;
509 } while (x < xae);
510 *xc = (uint32_t)carry;
511 }
512 }
513 #else
514 #ifdef Pack_32
515 for (; xb < xbe; xb++, xc0++) {
516 if ((y = *xb & 0xffff)) {
517 x = xa;
518 xc = xc0;
519 carry = 0;
520 do {
521 z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
522 carry = z >> 16;
523 uint32_t z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
524 carry = z2 >> 16;
525 Storeinc(xc, z2, z);
526 } while (x < xae);
527 *xc = carry;
528 }
529 if ((y = *xb >> 16)) {
530 x = xa;
531 xc = xc0;
532 carry = 0;
533 uint32_t z2 = *xc;
534 do {
535 z = (*x & 0xffff) * y + (*xc >> 16) + carry;
536 carry = z >> 16;
537 Storeinc(xc, z, z2);
538 z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
539 carry = z2 >> 16;
540 } while (x < xae);
541 *xc = z2;
542 }
543 }
544 #else
545 for(; xb < xbe; xc0++) {
546 if ((y = *xb++)) {
547 x = xa;
548 xc = xc0;
549 carry = 0;
550 do {
551 z = *x++ * y + *xc + carry;
552 carry = z >> 16;
553 *xc++ = z & 0xffff;
554 } while (x < xae);
555 *xc = carry;
556 }
557 }
558 #endif
559 #endif
560 for (xc0 = c.words(), xc = xc0 + wc; wc > 0 && !*--xc; --wc) { }
561 c.resize(wc);
562 aRef = c;
563 }
564
565 struct P5Node : Noncopyable {
566 BigInt val;
567 P5Node* next;
568 };
569
570 static P5Node* p5s;
571 static int p5s_count;
572
pow5mult(BigInt & b,int k)573 static ALWAYS_INLINE void pow5mult(BigInt& b, int k)
574 {
575 static int p05[3] = { 5, 25, 125 };
576
577 if (int i = k & 3)
578 multadd(b, p05[i - 1], 0);
579
580 if (!(k >>= 2))
581 return;
582
583 #if ENABLE(JSC_MULTIPLE_THREADS)
584 s_dtoaP5Mutex->lock();
585 #endif
586 P5Node* p5 = p5s;
587
588 if (!p5) {
589 /* first time */
590 p5 = new P5Node;
591 i2b(p5->val, 625);
592 p5->next = 0;
593 p5s = p5;
594 p5s_count = 1;
595 }
596
597 int p5s_count_local = p5s_count;
598 #if ENABLE(JSC_MULTIPLE_THREADS)
599 s_dtoaP5Mutex->unlock();
600 #endif
601 int p5s_used = 0;
602
603 for (;;) {
604 if (k & 1)
605 mult(b, p5->val);
606
607 if (!(k >>= 1))
608 break;
609
610 if (++p5s_used == p5s_count_local) {
611 #if ENABLE(JSC_MULTIPLE_THREADS)
612 s_dtoaP5Mutex->lock();
613 #endif
614 if (p5s_used == p5s_count) {
615 ASSERT(!p5->next);
616 p5->next = new P5Node;
617 p5->next->next = 0;
618 p5->next->val = p5->val;
619 mult(p5->next->val, p5->next->val);
620 ++p5s_count;
621 }
622
623 p5s_count_local = p5s_count;
624 #if ENABLE(JSC_MULTIPLE_THREADS)
625 s_dtoaP5Mutex->unlock();
626 #endif
627 }
628 p5 = p5->next;
629 }
630 }
631
lshift(BigInt & b,int k)632 static ALWAYS_INLINE void lshift(BigInt& b, int k)
633 {
634 #ifdef Pack_32
635 int n = k >> 5;
636 #else
637 int n = k >> 4;
638 #endif
639
640 int origSize = b.size();
641 int n1 = n + origSize + 1;
642
643 if (k &= 0x1f)
644 b.resize(b.size() + n + 1);
645 else
646 b.resize(b.size() + n);
647
648 const uint32_t* srcStart = b.words();
649 uint32_t* dstStart = b.words();
650 const uint32_t* src = srcStart + origSize - 1;
651 uint32_t* dst = dstStart + n1 - 1;
652 #ifdef Pack_32
653 if (k) {
654 uint32_t hiSubword = 0;
655 int s = 32 - k;
656 for (; src >= srcStart; --src) {
657 *dst-- = hiSubword | *src >> s;
658 hiSubword = *src << k;
659 }
660 *dst = hiSubword;
661 ASSERT(dst == dstStart + n);
662
663 b.resize(origSize + n + (b.words()[n1 - 1] != 0));
664 }
665 #else
666 if (k &= 0xf) {
667 uint32_t hiSubword = 0;
668 int s = 16 - k;
669 for (; src >= srcStart; --src) {
670 *dst-- = hiSubword | *src >> s;
671 hiSubword = (*src << k) & 0xffff;
672 }
673 *dst = hiSubword;
674 ASSERT(dst == dstStart + n);
675 result->wds = b->wds + n + (result->x[n1 - 1] != 0);
676 }
677 #endif
678 else {
679 do {
680 *--dst = *src--;
681 } while (src >= srcStart);
682 }
683 for (dst = dstStart + n; dst != dstStart; )
684 *--dst = 0;
685
686 ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
687 }
688
cmp(const BigInt & a,const BigInt & b)689 static int cmp(const BigInt& a, const BigInt& b)
690 {
691 const uint32_t *xa, *xa0, *xb, *xb0;
692 int i, j;
693
694 i = a.size();
695 j = b.size();
696 ASSERT(i <= 1 || a.words()[i - 1]);
697 ASSERT(j <= 1 || b.words()[j - 1]);
698 if (i -= j)
699 return i;
700 xa0 = a.words();
701 xa = xa0 + j;
702 xb0 = b.words();
703 xb = xb0 + j;
704 for (;;) {
705 if (*--xa != *--xb)
706 return *xa < *xb ? -1 : 1;
707 if (xa <= xa0)
708 break;
709 }
710 return 0;
711 }
712
diff(BigInt & c,const BigInt & aRef,const BigInt & bRef)713 static ALWAYS_INLINE void diff(BigInt& c, const BigInt& aRef, const BigInt& bRef)
714 {
715 const BigInt* a = &aRef;
716 const BigInt* b = &bRef;
717 int i, wa, wb;
718 uint32_t *xc;
719
720 i = cmp(*a, *b);
721 if (!i) {
722 c.sign = 0;
723 c.resize(1);
724 c.words()[0] = 0;
725 return;
726 }
727 if (i < 0) {
728 const BigInt* tmp = a;
729 a = b;
730 b = tmp;
731 i = 1;
732 } else
733 i = 0;
734
735 wa = a->size();
736 const uint32_t* xa = a->words();
737 const uint32_t* xae = xa + wa;
738 wb = b->size();
739 const uint32_t* xb = b->words();
740 const uint32_t* xbe = xb + wb;
741
742 c.resize(wa);
743 c.sign = i;
744 xc = c.words();
745 #ifdef USE_LONG_LONG
746 unsigned long long borrow = 0;
747 do {
748 unsigned long long y = (unsigned long long)*xa++ - *xb++ - borrow;
749 borrow = y >> 32 & (uint32_t)1;
750 *xc++ = (uint32_t)y & 0xffffffffUL;
751 } while (xb < xbe);
752 while (xa < xae) {
753 unsigned long long y = *xa++ - borrow;
754 borrow = y >> 32 & (uint32_t)1;
755 *xc++ = (uint32_t)y & 0xffffffffUL;
756 }
757 #else
758 uint32_t borrow = 0;
759 #ifdef Pack_32
760 do {
761 uint32_t y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
762 borrow = (y & 0x10000) >> 16;
763 uint32_t z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
764 borrow = (z & 0x10000) >> 16;
765 Storeinc(xc, z, y);
766 } while (xb < xbe);
767 while (xa < xae) {
768 uint32_t y = (*xa & 0xffff) - borrow;
769 borrow = (y & 0x10000) >> 16;
770 uint32_t z = (*xa++ >> 16) - borrow;
771 borrow = (z & 0x10000) >> 16;
772 Storeinc(xc, z, y);
773 }
774 #else
775 do {
776 uint32_t y = *xa++ - *xb++ - borrow;
777 borrow = (y & 0x10000) >> 16;
778 *xc++ = y & 0xffff;
779 } while (xb < xbe);
780 while (xa < xae) {
781 uint32_t y = *xa++ - borrow;
782 borrow = (y & 0x10000) >> 16;
783 *xc++ = y & 0xffff;
784 }
785 #endif
786 #endif
787 while (!*--xc)
788 wa--;
789 c.resize(wa);
790 }
791
ulp(U * x)792 static double ulp(U *x)
793 {
794 register int32_t L;
795 U u;
796
797 L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
798 #ifndef Avoid_Underflow
799 #ifndef Sudden_Underflow
800 if (L > 0) {
801 #endif
802 #endif
803 word0(&u) = L;
804 word1(&u) = 0;
805 #ifndef Avoid_Underflow
806 #ifndef Sudden_Underflow
807 } else {
808 L = -L >> Exp_shift;
809 if (L < Exp_shift) {
810 word0(&u) = 0x80000 >> L;
811 word1(&u) = 0;
812 } else {
813 word0(&u) = 0;
814 L -= Exp_shift;
815 word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
816 }
817 }
818 #endif
819 #endif
820 return dval(&u);
821 }
822
b2d(const BigInt & a,int * e)823 static double b2d(const BigInt& a, int* e)
824 {
825 const uint32_t* xa;
826 const uint32_t* xa0;
827 uint32_t w;
828 uint32_t y;
829 uint32_t z;
830 int k;
831 U d;
832
833 #define d0 word0(&d)
834 #define d1 word1(&d)
835
836 xa0 = a.words();
837 xa = xa0 + a.size();
838 y = *--xa;
839 ASSERT(y);
840 k = hi0bits(y);
841 *e = 32 - k;
842 #ifdef Pack_32
843 if (k < Ebits) {
844 d0 = Exp_1 | (y >> (Ebits - k));
845 w = xa > xa0 ? *--xa : 0;
846 d1 = (y << (32 - Ebits + k)) | (w >> (Ebits - k));
847 goto ret_d;
848 }
849 z = xa > xa0 ? *--xa : 0;
850 if (k -= Ebits) {
851 d0 = Exp_1 | (y << k) | (z >> (32 - k));
852 y = xa > xa0 ? *--xa : 0;
853 d1 = (z << k) | (y >> (32 - k));
854 } else {
855 d0 = Exp_1 | y;
856 d1 = z;
857 }
858 #else
859 if (k < Ebits + 16) {
860 z = xa > xa0 ? *--xa : 0;
861 d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
862 w = xa > xa0 ? *--xa : 0;
863 y = xa > xa0 ? *--xa : 0;
864 d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
865 goto ret_d;
866 }
867 z = xa > xa0 ? *--xa : 0;
868 w = xa > xa0 ? *--xa : 0;
869 k -= Ebits + 16;
870 d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
871 y = xa > xa0 ? *--xa : 0;
872 d1 = w << k + 16 | y << k;
873 #endif
874 ret_d:
875 #undef d0
876 #undef d1
877 return dval(&d);
878 }
879
d2b(BigInt & b,U * d,int * e,int * bits)880 static ALWAYS_INLINE void d2b(BigInt& b, U* d, int* e, int* bits)
881 {
882 int de, k;
883 uint32_t *x, y, z;
884 #ifndef Sudden_Underflow
885 int i;
886 #endif
887 #define d0 word0(d)
888 #define d1 word1(d)
889
890 b.sign = 0;
891 #ifdef Pack_32
892 b.resize(1);
893 #else
894 b.resize(2);
895 #endif
896 x = b.words();
897
898 z = d0 & Frac_mask;
899 d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
900 #ifdef Sudden_Underflow
901 de = (int)(d0 >> Exp_shift);
902 #else
903 if ((de = (int)(d0 >> Exp_shift)))
904 z |= Exp_msk1;
905 #endif
906 #ifdef Pack_32
907 if ((y = d1)) {
908 if ((k = lo0bits(&y))) {
909 x[0] = y | (z << (32 - k));
910 z >>= k;
911 } else
912 x[0] = y;
913 if (z) {
914 b.resize(2);
915 x[1] = z;
916 }
917
918 #ifndef Sudden_Underflow
919 i = b.size();
920 #endif
921 } else {
922 k = lo0bits(&z);
923 x[0] = z;
924 #ifndef Sudden_Underflow
925 i = 1;
926 #endif
927 b.resize(1);
928 k += 32;
929 }
930 #else
931 if ((y = d1)) {
932 if ((k = lo0bits(&y))) {
933 if (k >= 16) {
934 x[0] = y | z << 32 - k & 0xffff;
935 x[1] = z >> k - 16 & 0xffff;
936 x[2] = z >> k;
937 i = 2;
938 } else {
939 x[0] = y & 0xffff;
940 x[1] = y >> 16 | z << 16 - k & 0xffff;
941 x[2] = z >> k & 0xffff;
942 x[3] = z >> k + 16;
943 i = 3;
944 }
945 } else {
946 x[0] = y & 0xffff;
947 x[1] = y >> 16;
948 x[2] = z & 0xffff;
949 x[3] = z >> 16;
950 i = 3;
951 }
952 } else {
953 k = lo0bits(&z);
954 if (k >= 16) {
955 x[0] = z;
956 i = 0;
957 } else {
958 x[0] = z & 0xffff;
959 x[1] = z >> 16;
960 i = 1;
961 }
962 k += 32;
963 } while (!x[i])
964 --i;
965 b->resize(i + 1);
966 #endif
967 #ifndef Sudden_Underflow
968 if (de) {
969 #endif
970 *e = de - Bias - (P - 1) + k;
971 *bits = P - k;
972 #ifndef Sudden_Underflow
973 } else {
974 *e = de - Bias - (P - 1) + 1 + k;
975 #ifdef Pack_32
976 *bits = (32 * i) - hi0bits(x[i - 1]);
977 #else
978 *bits = (i + 2) * 16 - hi0bits(x[i]);
979 #endif
980 }
981 #endif
982 }
983 #undef d0
984 #undef d1
985
ratio(const BigInt & a,const BigInt & b)986 static double ratio(const BigInt& a, const BigInt& b)
987 {
988 U da, db;
989 int k, ka, kb;
990
991 dval(&da) = b2d(a, &ka);
992 dval(&db) = b2d(b, &kb);
993 #ifdef Pack_32
994 k = ka - kb + 32 * (a.size() - b.size());
995 #else
996 k = ka - kb + 16 * (a.size() - b.size());
997 #endif
998 if (k > 0)
999 word0(&da) += k * Exp_msk1;
1000 else {
1001 k = -k;
1002 word0(&db) += k * Exp_msk1;
1003 }
1004 return dval(&da) / dval(&db);
1005 }
1006
1007 static const double tens[] = {
1008 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1009 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1010 1e20, 1e21, 1e22
1011 };
1012
1013 static const double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
1014 static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
1015 #ifdef Avoid_Underflow
1016 9007199254740992. * 9007199254740992.e-256
1017 /* = 2^106 * 1e-53 */
1018 #else
1019 1e-256
1020 #endif
1021 };
1022
1023 /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
1024 /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
1025 #define Scale_Bit 0x10
1026 #define n_bigtens 5
1027
1028 #if defined(INFNAN_CHECK)
1029
1030 #ifndef NAN_WORD0
1031 #define NAN_WORD0 0x7ff80000
1032 #endif
1033
1034 #ifndef NAN_WORD1
1035 #define NAN_WORD1 0
1036 #endif
1037
match(const char ** sp,const char * t)1038 static int match(const char** sp, const char* t)
1039 {
1040 int c, d;
1041 const char* s = *sp;
1042
1043 while ((d = *t++)) {
1044 if ((c = *++s) >= 'A' && c <= 'Z')
1045 c += 'a' - 'A';
1046 if (c != d)
1047 return 0;
1048 }
1049 *sp = s + 1;
1050 return 1;
1051 }
1052
1053 #ifndef No_Hex_NaN
hexnan(U * rvp,const char ** sp)1054 static void hexnan(U* rvp, const char** sp)
1055 {
1056 uint32_t c, x[2];
1057 const char* s;
1058 int havedig, udx0, xshift;
1059
1060 x[0] = x[1] = 0;
1061 havedig = xshift = 0;
1062 udx0 = 1;
1063 s = *sp;
1064 while ((c = *(const unsigned char*)++s)) {
1065 if (c >= '0' && c <= '9')
1066 c -= '0';
1067 else if (c >= 'a' && c <= 'f')
1068 c += 10 - 'a';
1069 else if (c >= 'A' && c <= 'F')
1070 c += 10 - 'A';
1071 else if (c <= ' ') {
1072 if (udx0 && havedig) {
1073 udx0 = 0;
1074 xshift = 1;
1075 }
1076 continue;
1077 } else if (/*(*/ c == ')' && havedig) {
1078 *sp = s + 1;
1079 break;
1080 } else
1081 return; /* invalid form: don't change *sp */
1082 havedig = 1;
1083 if (xshift) {
1084 xshift = 0;
1085 x[0] = x[1];
1086 x[1] = 0;
1087 }
1088 if (udx0)
1089 x[0] = (x[0] << 4) | (x[1] >> 28);
1090 x[1] = (x[1] << 4) | c;
1091 }
1092 if ((x[0] &= 0xfffff) || x[1]) {
1093 word0(rvp) = Exp_mask | x[0];
1094 word1(rvp) = x[1];
1095 }
1096 }
1097 #endif /*No_Hex_NaN*/
1098 #endif /* INFNAN_CHECK */
1099
strtod(const char * s00,char ** se)1100 double strtod(const char* s00, char** se)
1101 {
1102 #ifdef Avoid_Underflow
1103 int scale;
1104 #endif
1105 int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
1106 e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
1107 const char *s, *s0, *s1;
1108 double aadj, aadj1;
1109 U aadj2, adj, rv, rv0;
1110 int32_t L;
1111 uint32_t y, z;
1112 BigInt bb, bb1, bd, bd0, bs, delta;
1113 #ifdef SET_INEXACT
1114 int inexact, oldinexact;
1115 #endif
1116
1117 sign = nz0 = nz = 0;
1118 dval(&rv) = 0;
1119 for (s = s00; ; s++)
1120 switch (*s) {
1121 case '-':
1122 sign = 1;
1123 /* no break */
1124 case '+':
1125 if (*++s)
1126 goto break2;
1127 /* no break */
1128 case 0:
1129 goto ret0;
1130 case '\t':
1131 case '\n':
1132 case '\v':
1133 case '\f':
1134 case '\r':
1135 case ' ':
1136 continue;
1137 default:
1138 goto break2;
1139 }
1140 break2:
1141 if (*s == '0') {
1142 nz0 = 1;
1143 while (*++s == '0') { }
1144 if (!*s)
1145 goto ret;
1146 }
1147 s0 = s;
1148 y = z = 0;
1149 for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
1150 if (nd < 9)
1151 y = (10 * y) + c - '0';
1152 else if (nd < 16)
1153 z = (10 * z) + c - '0';
1154 nd0 = nd;
1155 if (c == '.') {
1156 c = *++s;
1157 if (!nd) {
1158 for (; c == '0'; c = *++s)
1159 nz++;
1160 if (c > '0' && c <= '9') {
1161 s0 = s;
1162 nf += nz;
1163 nz = 0;
1164 goto have_dig;
1165 }
1166 goto dig_done;
1167 }
1168 for (; c >= '0' && c <= '9'; c = *++s) {
1169 have_dig:
1170 nz++;
1171 if (c -= '0') {
1172 nf += nz;
1173 for (i = 1; i < nz; i++)
1174 if (nd++ < 9)
1175 y *= 10;
1176 else if (nd <= DBL_DIG + 1)
1177 z *= 10;
1178 if (nd++ < 9)
1179 y = (10 * y) + c;
1180 else if (nd <= DBL_DIG + 1)
1181 z = (10 * z) + c;
1182 nz = 0;
1183 }
1184 }
1185 }
1186 dig_done:
1187 e = 0;
1188 if (c == 'e' || c == 'E') {
1189 if (!nd && !nz && !nz0) {
1190 goto ret0;
1191 }
1192 s00 = s;
1193 esign = 0;
1194 switch (c = *++s) {
1195 case '-':
1196 esign = 1;
1197 case '+':
1198 c = *++s;
1199 }
1200 if (c >= '0' && c <= '9') {
1201 while (c == '0')
1202 c = *++s;
1203 if (c > '0' && c <= '9') {
1204 L = c - '0';
1205 s1 = s;
1206 while ((c = *++s) >= '0' && c <= '9')
1207 L = (10 * L) + c - '0';
1208 if (s - s1 > 8 || L > 19999)
1209 /* Avoid confusion from exponents
1210 * so large that e might overflow.
1211 */
1212 e = 19999; /* safe for 16 bit ints */
1213 else
1214 e = (int)L;
1215 if (esign)
1216 e = -e;
1217 } else
1218 e = 0;
1219 } else
1220 s = s00;
1221 }
1222 if (!nd) {
1223 if (!nz && !nz0) {
1224 #ifdef INFNAN_CHECK
1225 /* Check for Nan and Infinity */
1226 switch(c) {
1227 case 'i':
1228 case 'I':
1229 if (match(&s,"nf")) {
1230 --s;
1231 if (!match(&s,"inity"))
1232 ++s;
1233 word0(&rv) = 0x7ff00000;
1234 word1(&rv) = 0;
1235 goto ret;
1236 }
1237 break;
1238 case 'n':
1239 case 'N':
1240 if (match(&s, "an")) {
1241 word0(&rv) = NAN_WORD0;
1242 word1(&rv) = NAN_WORD1;
1243 #ifndef No_Hex_NaN
1244 if (*s == '(') /*)*/
1245 hexnan(&rv, &s);
1246 #endif
1247 goto ret;
1248 }
1249 }
1250 #endif /* INFNAN_CHECK */
1251 ret0:
1252 s = s00;
1253 sign = 0;
1254 }
1255 goto ret;
1256 }
1257 e1 = e -= nf;
1258
1259 /* Now we have nd0 digits, starting at s0, followed by a
1260 * decimal point, followed by nd-nd0 digits. The number we're
1261 * after is the integer represented by those digits times
1262 * 10**e */
1263
1264 if (!nd0)
1265 nd0 = nd;
1266 k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
1267 dval(&rv) = y;
1268 if (k > 9) {
1269 #ifdef SET_INEXACT
1270 if (k > DBL_DIG)
1271 oldinexact = get_inexact();
1272 #endif
1273 dval(&rv) = tens[k - 9] * dval(&rv) + z;
1274 }
1275 if (nd <= DBL_DIG && Flt_Rounds == 1) {
1276 if (!e)
1277 goto ret;
1278 if (e > 0) {
1279 if (e <= Ten_pmax) {
1280 /* rv = */ rounded_product(dval(&rv), tens[e]);
1281 goto ret;
1282 }
1283 i = DBL_DIG - nd;
1284 if (e <= Ten_pmax + i) {
1285 /* A fancier test would sometimes let us do
1286 * this for larger i values.
1287 */
1288 e -= i;
1289 dval(&rv) *= tens[i];
1290 /* rv = */ rounded_product(dval(&rv), tens[e]);
1291 goto ret;
1292 }
1293 }
1294 #ifndef Inaccurate_Divide
1295 else if (e >= -Ten_pmax) {
1296 /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
1297 goto ret;
1298 }
1299 #endif
1300 }
1301 e1 += nd - k;
1302
1303 #ifdef SET_INEXACT
1304 inexact = 1;
1305 if (k <= DBL_DIG)
1306 oldinexact = get_inexact();
1307 #endif
1308 #ifdef Avoid_Underflow
1309 scale = 0;
1310 #endif
1311
1312 /* Get starting approximation = rv * 10**e1 */
1313
1314 if (e1 > 0) {
1315 if ((i = e1 & 15))
1316 dval(&rv) *= tens[i];
1317 if (e1 &= ~15) {
1318 if (e1 > DBL_MAX_10_EXP) {
1319 ovfl:
1320 #ifndef NO_ERRNO
1321 errno = ERANGE;
1322 #endif
1323 /* Can't trust HUGE_VAL */
1324 word0(&rv) = Exp_mask;
1325 word1(&rv) = 0;
1326 #ifdef SET_INEXACT
1327 /* set overflow bit */
1328 dval(&rv0) = 1e300;
1329 dval(&rv0) *= dval(&rv0);
1330 #endif
1331 goto ret;
1332 }
1333 e1 >>= 4;
1334 for (j = 0; e1 > 1; j++, e1 >>= 1)
1335 if (e1 & 1)
1336 dval(&rv) *= bigtens[j];
1337 /* The last multiplication could overflow. */
1338 word0(&rv) -= P * Exp_msk1;
1339 dval(&rv) *= bigtens[j];
1340 if ((z = word0(&rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
1341 goto ovfl;
1342 if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
1343 /* set to largest number */
1344 /* (Can't trust DBL_MAX) */
1345 word0(&rv) = Big0;
1346 word1(&rv) = Big1;
1347 } else
1348 word0(&rv) += P * Exp_msk1;
1349 }
1350 } else if (e1 < 0) {
1351 e1 = -e1;
1352 if ((i = e1 & 15))
1353 dval(&rv) /= tens[i];
1354 if (e1 >>= 4) {
1355 if (e1 >= 1 << n_bigtens)
1356 goto undfl;
1357 #ifdef Avoid_Underflow
1358 if (e1 & Scale_Bit)
1359 scale = 2 * P;
1360 for (j = 0; e1 > 0; j++, e1 >>= 1)
1361 if (e1 & 1)
1362 dval(&rv) *= tinytens[j];
1363 if (scale && (j = (2 * P) + 1 - ((word0(&rv) & Exp_mask) >> Exp_shift)) > 0) {
1364 /* scaled rv is denormal; zap j low bits */
1365 if (j >= 32) {
1366 word1(&rv) = 0;
1367 if (j >= 53)
1368 word0(&rv) = (P + 2) * Exp_msk1;
1369 else
1370 word0(&rv) &= 0xffffffff << (j - 32);
1371 } else
1372 word1(&rv) &= 0xffffffff << j;
1373 }
1374 #else
1375 for (j = 0; e1 > 1; j++, e1 >>= 1)
1376 if (e1 & 1)
1377 dval(&rv) *= tinytens[j];
1378 /* The last multiplication could underflow. */
1379 dval(&rv0) = dval(&rv);
1380 dval(&rv) *= tinytens[j];
1381 if (!dval(&rv)) {
1382 dval(&rv) = 2. * dval(&rv0);
1383 dval(&rv) *= tinytens[j];
1384 #endif
1385 if (!dval(&rv)) {
1386 undfl:
1387 dval(&rv) = 0.;
1388 #ifndef NO_ERRNO
1389 errno = ERANGE;
1390 #endif
1391 goto ret;
1392 }
1393 #ifndef Avoid_Underflow
1394 word0(&rv) = Tiny0;
1395 word1(&rv) = Tiny1;
1396 /* The refinement below will clean
1397 * this approximation up.
1398 */
1399 }
1400 #endif
1401 }
1402 }
1403
1404 /* Now the hard part -- adjusting rv to the correct value.*/
1405
1406 /* Put digits into bd: true value = bd * 10^e */
1407
1408 s2b(bd0, s0, nd0, nd, y);
1409
1410 for (;;) {
1411 bd = bd0;
1412 d2b(bb, &rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
1413 i2b(bs, 1);
1414
1415 if (e >= 0) {
1416 bb2 = bb5 = 0;
1417 bd2 = bd5 = e;
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 Avoid_Underflow
1428 j = bbe - scale;
1429 i = j + bbbits - 1; /* logb(rv) */
1430 if (i < Emin) /* denormal */
1431 j += P - Emin;
1432 else
1433 j = P + 1 - bbbits;
1434 #else /*Avoid_Underflow*/
1435 #ifdef Sudden_Underflow
1436 j = P + 1 - bbbits;
1437 #else /*Sudden_Underflow*/
1438 j = bbe;
1439 i = j + bbbits - 1; /* logb(rv) */
1440 if (i < Emin) /* denormal */
1441 j += P - Emin;
1442 else
1443 j = P + 1 - bbbits;
1444 #endif /*Sudden_Underflow*/
1445 #endif /*Avoid_Underflow*/
1446 bb2 += j;
1447 bd2 += j;
1448 #ifdef Avoid_Underflow
1449 bd2 += scale;
1450 #endif
1451 i = bb2 < bd2 ? bb2 : bd2;
1452 if (i > bs2)
1453 i = bs2;
1454 if (i > 0) {
1455 bb2 -= i;
1456 bd2 -= i;
1457 bs2 -= i;
1458 }
1459 if (bb5 > 0) {
1460 pow5mult(bs, bb5);
1461 mult(bb, bs);
1462 }
1463 if (bb2 > 0)
1464 lshift(bb, bb2);
1465 if (bd5 > 0)
1466 pow5mult(bd, bd5);
1467 if (bd2 > 0)
1468 lshift(bd, bd2);
1469 if (bs2 > 0)
1470 lshift(bs, bs2);
1471 diff(delta, bb, bd);
1472 dsign = delta.sign;
1473 delta.sign = 0;
1474 i = cmp(delta, bs);
1475
1476 if (i < 0) {
1477 /* Error is less than half an ulp -- check for
1478 * special case of mantissa a power of two.
1479 */
1480 if (dsign || word1(&rv) || word0(&rv) & Bndry_mask
1481 #ifdef Avoid_Underflow
1482 || (word0(&rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
1483 #else
1484 || (word0(&rv) & Exp_mask) <= Exp_msk1
1485 #endif
1486 ) {
1487 #ifdef SET_INEXACT
1488 if (!delta->words()[0] && delta->size() <= 1)
1489 inexact = 0;
1490 #endif
1491 break;
1492 }
1493 if (!delta.words()[0] && delta.size() <= 1) {
1494 /* exact result */
1495 #ifdef SET_INEXACT
1496 inexact = 0;
1497 #endif
1498 break;
1499 }
1500 lshift(delta, Log2P);
1501 if (cmp(delta, bs) > 0)
1502 goto drop_down;
1503 break;
1504 }
1505 if (i == 0) {
1506 /* exactly half-way between */
1507 if (dsign) {
1508 if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
1509 && word1(&rv) == (
1510 #ifdef Avoid_Underflow
1511 (scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
1512 ? (0xffffffff & (0xffffffff << (2 * P + 1 - (y >> Exp_shift)))) :
1513 #endif
1514 0xffffffff)) {
1515 /*boundary case -- increment exponent*/
1516 word0(&rv) = (word0(&rv) & Exp_mask) + Exp_msk1;
1517 word1(&rv) = 0;
1518 #ifdef Avoid_Underflow
1519 dsign = 0;
1520 #endif
1521 break;
1522 }
1523 } else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
1524 drop_down:
1525 /* boundary case -- decrement exponent */
1526 #ifdef Sudden_Underflow /*{{*/
1527 L = word0(&rv) & Exp_mask;
1528 #ifdef Avoid_Underflow
1529 if (L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1))
1530 #else
1531 if (L <= Exp_msk1)
1532 #endif /*Avoid_Underflow*/
1533 goto undfl;
1534 L -= Exp_msk1;
1535 #else /*Sudden_Underflow}{*/
1536 #ifdef Avoid_Underflow
1537 if (scale) {
1538 L = word0(&rv) & Exp_mask;
1539 if (L <= (2 * P + 1) * Exp_msk1) {
1540 if (L > (P + 2) * Exp_msk1)
1541 /* round even ==> */
1542 /* accept rv */
1543 break;
1544 /* rv = smallest denormal */
1545 goto undfl;
1546 }
1547 }
1548 #endif /*Avoid_Underflow*/
1549 L = (word0(&rv) & Exp_mask) - Exp_msk1;
1550 #endif /*Sudden_Underflow}}*/
1551 word0(&rv) = L | Bndry_mask1;
1552 word1(&rv) = 0xffffffff;
1553 break;
1554 }
1555 if (!(word1(&rv) & LSB))
1556 break;
1557 if (dsign)
1558 dval(&rv) += ulp(&rv);
1559 else {
1560 dval(&rv) -= ulp(&rv);
1561 #ifndef Sudden_Underflow
1562 if (!dval(&rv))
1563 goto undfl;
1564 #endif
1565 }
1566 #ifdef Avoid_Underflow
1567 dsign = 1 - dsign;
1568 #endif
1569 break;
1570 }
1571 if ((aadj = ratio(delta, bs)) <= 2.) {
1572 if (dsign)
1573 aadj = aadj1 = 1.;
1574 else if (word1(&rv) || word0(&rv) & Bndry_mask) {
1575 #ifndef Sudden_Underflow
1576 if (word1(&rv) == Tiny1 && !word0(&rv))
1577 goto undfl;
1578 #endif
1579 aadj = 1.;
1580 aadj1 = -1.;
1581 } else {
1582 /* special case -- power of FLT_RADIX to be */
1583 /* rounded down... */
1584
1585 if (aadj < 2. / FLT_RADIX)
1586 aadj = 1. / FLT_RADIX;
1587 else
1588 aadj *= 0.5;
1589 aadj1 = -aadj;
1590 }
1591 } else {
1592 aadj *= 0.5;
1593 aadj1 = dsign ? aadj : -aadj;
1594 #ifdef Check_FLT_ROUNDS
1595 switch (Rounding) {
1596 case 2: /* towards +infinity */
1597 aadj1 -= 0.5;
1598 break;
1599 case 0: /* towards 0 */
1600 case 3: /* towards -infinity */
1601 aadj1 += 0.5;
1602 }
1603 #else
1604 if (Flt_Rounds == 0)
1605 aadj1 += 0.5;
1606 #endif /*Check_FLT_ROUNDS*/
1607 }
1608 y = word0(&rv) & Exp_mask;
1609
1610 /* Check for overflow */
1611
1612 if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
1613 dval(&rv0) = dval(&rv);
1614 word0(&rv) -= P * Exp_msk1;
1615 adj.d = aadj1 * ulp(&rv);
1616 dval(&rv) += adj.d;
1617 if ((word0(&rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
1618 if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
1619 goto ovfl;
1620 word0(&rv) = Big0;
1621 word1(&rv) = Big1;
1622 goto cont;
1623 } else
1624 word0(&rv) += P * Exp_msk1;
1625 } else {
1626 #ifdef Avoid_Underflow
1627 if (scale && y <= 2 * P * Exp_msk1) {
1628 if (aadj <= 0x7fffffff) {
1629 if ((z = (uint32_t)aadj) <= 0)
1630 z = 1;
1631 aadj = z;
1632 aadj1 = dsign ? aadj : -aadj;
1633 }
1634 dval(&aadj2) = aadj1;
1635 word0(&aadj2) += (2 * P + 1) * Exp_msk1 - y;
1636 aadj1 = dval(&aadj2);
1637 }
1638 adj.d = aadj1 * ulp(&rv);
1639 dval(&rv) += adj.d;
1640 #else
1641 #ifdef Sudden_Underflow
1642 if ((word0(&rv) & Exp_mask) <= P * Exp_msk1) {
1643 dval(&rv0) = dval(&rv);
1644 word0(&rv) += P * Exp_msk1;
1645 adj.d = aadj1 * ulp(&rv);
1646 dval(&rv) += adj.d;
1647 if ((word0(&rv) & Exp_mask) <= P * Exp_msk1)
1648 {
1649 if (word0(&rv0) == Tiny0 && word1(&rv0) == Tiny1)
1650 goto undfl;
1651 word0(&rv) = Tiny0;
1652 word1(&rv) = Tiny1;
1653 goto cont;
1654 }
1655 else
1656 word0(&rv) -= P * Exp_msk1;
1657 } else {
1658 adj.d = aadj1 * ulp(&rv);
1659 dval(&rv) += adj.d;
1660 }
1661 #else /*Sudden_Underflow*/
1662 /* Compute adj so that the IEEE rounding rules will
1663 * correctly round rv + adj in some half-way cases.
1664 * If rv * ulp(rv) is denormalized (i.e.,
1665 * y <= (P - 1) * Exp_msk1), we must adjust aadj to avoid
1666 * trouble from bits lost to denormalization;
1667 * example: 1.2e-307 .
1668 */
1669 if (y <= (P - 1) * Exp_msk1 && aadj > 1.) {
1670 aadj1 = (double)(int)(aadj + 0.5);
1671 if (!dsign)
1672 aadj1 = -aadj1;
1673 }
1674 adj.d = aadj1 * ulp(&rv);
1675 dval(&rv) += adj.d;
1676 #endif /*Sudden_Underflow*/
1677 #endif /*Avoid_Underflow*/
1678 }
1679 z = word0(&rv) & Exp_mask;
1680 #ifndef SET_INEXACT
1681 #ifdef Avoid_Underflow
1682 if (!scale)
1683 #endif
1684 if (y == z) {
1685 /* Can we stop now? */
1686 L = (int32_t)aadj;
1687 aadj -= L;
1688 /* The tolerances below are conservative. */
1689 if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
1690 if (aadj < .4999999 || aadj > .5000001)
1691 break;
1692 } else if (aadj < .4999999 / FLT_RADIX)
1693 break;
1694 }
1695 #endif
1696 cont:
1697 ;
1698 }
1699 #ifdef SET_INEXACT
1700 if (inexact) {
1701 if (!oldinexact) {
1702 word0(&rv0) = Exp_1 + (70 << Exp_shift);
1703 word1(&rv0) = 0;
1704 dval(&rv0) += 1.;
1705 }
1706 } else if (!oldinexact)
1707 clear_inexact();
1708 #endif
1709 #ifdef Avoid_Underflow
1710 if (scale) {
1711 word0(&rv0) = Exp_1 - 2 * P * Exp_msk1;
1712 word1(&rv0) = 0;
1713 dval(&rv) *= dval(&rv0);
1714 #ifndef NO_ERRNO
1715 /* try to avoid the bug of testing an 8087 register value */
1716 if (word0(&rv) == 0 && word1(&rv) == 0)
1717 errno = ERANGE;
1718 #endif
1719 }
1720 #endif /* Avoid_Underflow */
1721 #ifdef SET_INEXACT
1722 if (inexact && !(word0(&rv) & Exp_mask)) {
1723 /* set underflow bit */
1724 dval(&rv0) = 1e-300;
1725 dval(&rv0) *= dval(&rv0);
1726 }
1727 #endif
1728 ret:
1729 if (se)
1730 *se = const_cast<char*>(s);
1731 return sign ? -dval(&rv) : dval(&rv);
1732 }
1733
quorem(BigInt & b,BigInt & S)1734 static ALWAYS_INLINE int quorem(BigInt& b, BigInt& S)
1735 {
1736 size_t n;
1737 uint32_t *bx, *bxe, q, *sx, *sxe;
1738 #ifdef USE_LONG_LONG
1739 unsigned long long borrow, carry, y, ys;
1740 #else
1741 uint32_t borrow, carry, y, ys;
1742 #ifdef Pack_32
1743 uint32_t si, z, zs;
1744 #endif
1745 #endif
1746 ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
1747 ASSERT(S.size() <= 1 || S.words()[S.size() - 1]);
1748
1749 n = S.size();
1750 ASSERT_WITH_MESSAGE(b.size() <= n, "oversize b in quorem");
1751 if (b.size() < n)
1752 return 0;
1753 sx = S.words();
1754 sxe = sx + --n;
1755 bx = b.words();
1756 bxe = bx + n;
1757 q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
1758 ASSERT_WITH_MESSAGE(q <= 9, "oversized quotient in quorem");
1759 if (q) {
1760 borrow = 0;
1761 carry = 0;
1762 do {
1763 #ifdef USE_LONG_LONG
1764 ys = *sx++ * (unsigned long long)q + carry;
1765 carry = ys >> 32;
1766 y = *bx - (ys & 0xffffffffUL) - borrow;
1767 borrow = y >> 32 & (uint32_t)1;
1768 *bx++ = (uint32_t)y & 0xffffffffUL;
1769 #else
1770 #ifdef Pack_32
1771 si = *sx++;
1772 ys = (si & 0xffff) * q + carry;
1773 zs = (si >> 16) * q + (ys >> 16);
1774 carry = zs >> 16;
1775 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
1776 borrow = (y & 0x10000) >> 16;
1777 z = (*bx >> 16) - (zs & 0xffff) - borrow;
1778 borrow = (z & 0x10000) >> 16;
1779 Storeinc(bx, z, y);
1780 #else
1781 ys = *sx++ * q + carry;
1782 carry = ys >> 16;
1783 y = *bx - (ys & 0xffff) - borrow;
1784 borrow = (y & 0x10000) >> 16;
1785 *bx++ = y & 0xffff;
1786 #endif
1787 #endif
1788 } while (sx <= sxe);
1789 if (!*bxe) {
1790 bx = b.words();
1791 while (--bxe > bx && !*bxe)
1792 --n;
1793 b.resize(n);
1794 }
1795 }
1796 if (cmp(b, S) >= 0) {
1797 q++;
1798 borrow = 0;
1799 carry = 0;
1800 bx = b.words();
1801 sx = S.words();
1802 do {
1803 #ifdef USE_LONG_LONG
1804 ys = *sx++ + carry;
1805 carry = ys >> 32;
1806 y = *bx - (ys & 0xffffffffUL) - borrow;
1807 borrow = y >> 32 & (uint32_t)1;
1808 *bx++ = (uint32_t)y & 0xffffffffUL;
1809 #else
1810 #ifdef Pack_32
1811 si = *sx++;
1812 ys = (si & 0xffff) + carry;
1813 zs = (si >> 16) + (ys >> 16);
1814 carry = zs >> 16;
1815 y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
1816 borrow = (y & 0x10000) >> 16;
1817 z = (*bx >> 16) - (zs & 0xffff) - borrow;
1818 borrow = (z & 0x10000) >> 16;
1819 Storeinc(bx, z, y);
1820 #else
1821 ys = *sx++ + carry;
1822 carry = ys >> 16;
1823 y = *bx - (ys & 0xffff) - borrow;
1824 borrow = (y & 0x10000) >> 16;
1825 *bx++ = y & 0xffff;
1826 #endif
1827 #endif
1828 } while (sx <= sxe);
1829 bx = b.words();
1830 bxe = bx + n;
1831 if (!*bxe) {
1832 while (--bxe > bx && !*bxe)
1833 --n;
1834 b.resize(n);
1835 }
1836 }
1837 return q;
1838 }
1839
1840 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
1841 *
1842 * Inspired by "How to Print Floating-Point Numbers Accurately" by
1843 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
1844 *
1845 * Modifications:
1846 * 1. Rather than iterating, we use a simple numeric overestimate
1847 * to determine k = floor(log10(d)). We scale relevant
1848 * quantities using O(log2(k)) rather than O(k) multiplications.
1849 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
1850 * try to generate digits strictly left to right. Instead, we
1851 * compute with fewer bits and propagate the carry if necessary
1852 * when rounding the final digit up. This is often faster.
1853 * 3. Under the assumption that input will be rounded nearest,
1854 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
1855 * That is, we allow equality in stopping tests when the
1856 * round-nearest rule will give the same floating-point value
1857 * as would satisfaction of the stopping test with strict
1858 * inequality.
1859 * 4. We remove common factors of powers of 2 from relevant
1860 * quantities.
1861 * 5. When converting floating-point integers less than 1e16,
1862 * we use floating-point arithmetic rather than resorting
1863 * to multiple-precision integers.
1864 * 6. When asked to produce fewer than 15 digits, we first try
1865 * to get by with floating-point arithmetic; we resort to
1866 * multiple-precision integer arithmetic only if we cannot
1867 * guarantee that the floating-point calculation has given
1868 * the correctly rounded result. For k requested digits and
1869 * "uniformly" distributed input, the probability is
1870 * something like 10^(k-15) that we must resort to the int32_t
1871 * calculation.
1872 */
1873
dtoa(DtoaBuffer result,double dd,int ndigits,int * decpt,int * sign,char ** rve)1874 void dtoa(DtoaBuffer result, double dd, int ndigits, int* decpt, int* sign, char** rve)
1875 {
1876 /*
1877 Arguments ndigits, decpt, sign are similar to those
1878 of ecvt and fcvt; trailing zeros are suppressed from
1879 the returned string. If not null, *rve is set to point
1880 to the end of the return value. If d is +-Infinity or NaN,
1881 then *decpt is set to 9999.
1882
1883 */
1884
1885 int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
1886 j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
1887 spec_case, try_quick;
1888 int32_t L;
1889 #ifndef Sudden_Underflow
1890 int denorm;
1891 uint32_t x;
1892 #endif
1893 BigInt b, b1, delta, mlo, mhi, S;
1894 U d2, eps, u;
1895 double ds;
1896 char *s, *s0;
1897 #ifdef SET_INEXACT
1898 int inexact, oldinexact;
1899 #endif
1900
1901 u.d = dd;
1902 if (word0(&u) & Sign_bit) {
1903 /* set sign for everything, including 0's and NaNs */
1904 *sign = 1;
1905 word0(&u) &= ~Sign_bit; /* clear sign bit */
1906 } else
1907 *sign = 0;
1908
1909 if ((word0(&u) & Exp_mask) == Exp_mask)
1910 {
1911 /* Infinity or NaN */
1912 *decpt = 9999;
1913 if (!word1(&u) && !(word0(&u) & 0xfffff)) {
1914 strcpy(result, "Infinity");
1915 if (rve)
1916 *rve = result + 8;
1917 } else {
1918 strcpy(result, "NaN");
1919 if (rve)
1920 *rve = result + 3;
1921 }
1922 return;
1923 }
1924 if (!dval(&u)) {
1925 *decpt = 1;
1926 result[0] = '0';
1927 result[1] = '\0';
1928 if (rve)
1929 *rve = result + 1;
1930 return;
1931 }
1932
1933 #ifdef SET_INEXACT
1934 try_quick = oldinexact = get_inexact();
1935 inexact = 1;
1936 #endif
1937
1938 d2b(b, &u, &be, &bbits);
1939 #ifdef Sudden_Underflow
1940 i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
1941 #else
1942 if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
1943 #endif
1944 dval(&d2) = dval(&u);
1945 word0(&d2) &= Frac_mask1;
1946 word0(&d2) |= Exp_11;
1947
1948 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
1949 * log10(x) = log(x) / log(10)
1950 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
1951 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
1952 *
1953 * This suggests computing an approximation k to log10(d) by
1954 *
1955 * k = (i - Bias)*0.301029995663981
1956 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
1957 *
1958 * We want k to be too large rather than too small.
1959 * The error in the first-order Taylor series approximation
1960 * is in our favor, so we just round up the constant enough
1961 * to compensate for any error in the multiplication of
1962 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
1963 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
1964 * adding 1e-13 to the constant term more than suffices.
1965 * Hence we adjust the constant term to 0.1760912590558.
1966 * (We could get a more accurate k by invoking log10,
1967 * but this is probably not worthwhile.)
1968 */
1969
1970 i -= Bias;
1971 #ifndef Sudden_Underflow
1972 denorm = 0;
1973 } else {
1974 /* d is denormalized */
1975
1976 i = bbits + be + (Bias + (P - 1) - 1);
1977 x = (i > 32) ? (word0(&u) << (64 - i)) | (word1(&u) >> (i - 32))
1978 : word1(&u) << (32 - i);
1979 dval(&d2) = x;
1980 word0(&d2) -= 31 * Exp_msk1; /* adjust exponent */
1981 i -= (Bias + (P - 1) - 1) + 1;
1982 denorm = 1;
1983 }
1984 #endif
1985 ds = (dval(&d2) - 1.5) * 0.289529654602168 + 0.1760912590558 + (i * 0.301029995663981);
1986 k = (int)ds;
1987 if (ds < 0. && ds != k)
1988 k--; /* want k = floor(ds) */
1989 k_check = 1;
1990 if (k >= 0 && k <= Ten_pmax) {
1991 if (dval(&u) < tens[k])
1992 k--;
1993 k_check = 0;
1994 }
1995 j = bbits - i - 1;
1996 if (j >= 0) {
1997 b2 = 0;
1998 s2 = j;
1999 } else {
2000 b2 = -j;
2001 s2 = 0;
2002 }
2003 if (k >= 0) {
2004 b5 = 0;
2005 s5 = k;
2006 s2 += k;
2007 } else {
2008 b2 -= k;
2009 b5 = -k;
2010 s5 = 0;
2011 }
2012
2013 #ifndef SET_INEXACT
2014 #ifdef Check_FLT_ROUNDS
2015 try_quick = Rounding == 1;
2016 #else
2017 try_quick = 1;
2018 #endif
2019 #endif /*SET_INEXACT*/
2020
2021 leftright = 1;
2022 ilim = ilim1 = -1;
2023 i = 18;
2024 ndigits = 0;
2025 s = s0 = result;
2026
2027 if (ilim >= 0 && ilim <= Quick_max && try_quick) {
2028
2029 /* Try to get by with floating-point arithmetic. */
2030
2031 i = 0;
2032 dval(&d2) = dval(&u);
2033 k0 = k;
2034 ilim0 = ilim;
2035 ieps = 2; /* conservative */
2036 if (k > 0) {
2037 ds = tens[k & 0xf];
2038 j = k >> 4;
2039 if (j & Bletch) {
2040 /* prevent overflows */
2041 j &= Bletch - 1;
2042 dval(&u) /= bigtens[n_bigtens - 1];
2043 ieps++;
2044 }
2045 for (; j; j >>= 1, i++) {
2046 if (j & 1) {
2047 ieps++;
2048 ds *= bigtens[i];
2049 }
2050 }
2051 dval(&u) /= ds;
2052 } else if ((j1 = -k)) {
2053 dval(&u) *= tens[j1 & 0xf];
2054 for (j = j1 >> 4; j; j >>= 1, i++) {
2055 if (j & 1) {
2056 ieps++;
2057 dval(&u) *= bigtens[i];
2058 }
2059 }
2060 }
2061 if (k_check && dval(&u) < 1. && ilim > 0) {
2062 if (ilim1 <= 0)
2063 goto fast_failed;
2064 ilim = ilim1;
2065 k--;
2066 dval(&u) *= 10.;
2067 ieps++;
2068 }
2069 dval(&eps) = (ieps * dval(&u)) + 7.;
2070 word0(&eps) -= (P - 1) * Exp_msk1;
2071 if (ilim == 0) {
2072 S.clear();
2073 mhi.clear();
2074 dval(&u) -= 5.;
2075 if (dval(&u) > dval(&eps))
2076 goto one_digit;
2077 if (dval(&u) < -dval(&eps))
2078 goto no_digits;
2079 goto fast_failed;
2080 }
2081 #ifndef No_leftright
2082 if (leftright) {
2083 /* Use Steele & White method of only
2084 * generating digits needed.
2085 */
2086 dval(&eps) = (0.5 / tens[ilim - 1]) - dval(&eps);
2087 for (i = 0;;) {
2088 L = (long int)dval(&u);
2089 dval(&u) -= L;
2090 *s++ = '0' + (int)L;
2091 if (dval(&u) < dval(&eps))
2092 goto ret;
2093 if (1. - dval(&u) < dval(&eps))
2094 goto bump_up;
2095 if (++i >= ilim)
2096 break;
2097 dval(&eps) *= 10.;
2098 dval(&u) *= 10.;
2099 }
2100 } else {
2101 #endif
2102 /* Generate ilim digits, then fix them up. */
2103 dval(&eps) *= tens[ilim - 1];
2104 for (i = 1;; i++, dval(&u) *= 10.) {
2105 L = (int32_t)(dval(&u));
2106 if (!(dval(&u) -= L))
2107 ilim = i;
2108 *s++ = '0' + (int)L;
2109 if (i == ilim) {
2110 if (dval(&u) > 0.5 + dval(&eps))
2111 goto bump_up;
2112 else if (dval(&u) < 0.5 - dval(&eps)) {
2113 while (*--s == '0') { }
2114 s++;
2115 goto ret;
2116 }
2117 break;
2118 }
2119 }
2120 #ifndef No_leftright
2121 }
2122 #endif
2123 fast_failed:
2124 s = s0;
2125 dval(&u) = dval(&d2);
2126 k = k0;
2127 ilim = ilim0;
2128 }
2129
2130 /* Do we have a "small" integer? */
2131
2132 if (be >= 0 && k <= Int_max) {
2133 /* Yes. */
2134 ds = tens[k];
2135 if (ndigits < 0 && ilim <= 0) {
2136 S.clear();
2137 mhi.clear();
2138 if (ilim < 0 || dval(&u) <= 5 * ds)
2139 goto no_digits;
2140 goto one_digit;
2141 }
2142 for (i = 1;; i++, dval(&u) *= 10.) {
2143 L = (int32_t)(dval(&u) / ds);
2144 dval(&u) -= L * ds;
2145 #ifdef Check_FLT_ROUNDS
2146 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
2147 if (dval(&u) < 0) {
2148 L--;
2149 dval(&u) += ds;
2150 }
2151 #endif
2152 *s++ = '0' + (int)L;
2153 if (!dval(&u)) {
2154 #ifdef SET_INEXACT
2155 inexact = 0;
2156 #endif
2157 break;
2158 }
2159 if (i == ilim) {
2160 dval(&u) += dval(&u);
2161 if (dval(&u) > ds || (dval(&u) == ds && (L & 1))) {
2162 bump_up:
2163 while (*--s == '9')
2164 if (s == s0) {
2165 k++;
2166 *s = '0';
2167 break;
2168 }
2169 ++*s++;
2170 }
2171 break;
2172 }
2173 }
2174 goto ret;
2175 }
2176
2177 m2 = b2;
2178 m5 = b5;
2179 mhi.clear();
2180 mlo.clear();
2181 if (leftright) {
2182 i =
2183 #ifndef Sudden_Underflow
2184 denorm ? be + (Bias + (P - 1) - 1 + 1) :
2185 #endif
2186 1 + P - bbits;
2187 b2 += i;
2188 s2 += i;
2189 i2b(mhi, 1);
2190 }
2191 if (m2 > 0 && s2 > 0) {
2192 i = m2 < s2 ? m2 : s2;
2193 b2 -= i;
2194 m2 -= i;
2195 s2 -= i;
2196 }
2197 if (b5 > 0) {
2198 if (leftright) {
2199 if (m5 > 0) {
2200 pow5mult(mhi, m5);
2201 mult(b, mhi);
2202 }
2203 if ((j = b5 - m5))
2204 pow5mult(b, j);
2205 } else
2206 pow5mult(b, b5);
2207 }
2208 i2b(S, 1);
2209 if (s5 > 0)
2210 pow5mult(S, s5);
2211
2212 /* Check for special case that d is a normalized power of 2. */
2213
2214 spec_case = 0;
2215 if (!word1(&u) && !(word0(&u) & Bndry_mask)
2216 #ifndef Sudden_Underflow
2217 && word0(&u) & (Exp_mask & ~Exp_msk1)
2218 #endif
2219 ) {
2220 /* The special case */
2221 b2 += Log2P;
2222 s2 += Log2P;
2223 spec_case = 1;
2224 }
2225
2226 /* Arrange for convenient computation of quotients:
2227 * shift left if necessary so divisor has 4 leading 0 bits.
2228 *
2229 * Perhaps we should just compute leading 28 bits of S once
2230 * and for all and pass them and a shift to quorem, so it
2231 * can do shifts and ors to compute the numerator for q.
2232 */
2233 #ifdef Pack_32
2234 if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0x1f))
2235 i = 32 - i;
2236 #else
2237 if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0xf))
2238 i = 16 - i;
2239 #endif
2240 if (i > 4) {
2241 i -= 4;
2242 b2 += i;
2243 m2 += i;
2244 s2 += i;
2245 } else if (i < 4) {
2246 i += 28;
2247 b2 += i;
2248 m2 += i;
2249 s2 += i;
2250 }
2251 if (b2 > 0)
2252 lshift(b, b2);
2253 if (s2 > 0)
2254 lshift(S, s2);
2255 if (k_check) {
2256 if (cmp(b,S) < 0) {
2257 k--;
2258 multadd(b, 10, 0); /* we botched the k estimate */
2259 if (leftright)
2260 multadd(mhi, 10, 0);
2261 ilim = ilim1;
2262 }
2263 }
2264
2265 if (leftright) {
2266 if (m2 > 0)
2267 lshift(mhi, m2);
2268
2269 /* Compute mlo -- check for special case
2270 * that d is a normalized power of 2.
2271 */
2272
2273 mlo = mhi;
2274 if (spec_case) {
2275 mhi = mlo;
2276 lshift(mhi, Log2P);
2277 }
2278
2279 for (i = 1;;i++) {
2280 dig = quorem(b,S) + '0';
2281 /* Do we yet have the shortest decimal string
2282 * that will round to d?
2283 */
2284 j = cmp(b, mlo);
2285 diff(delta, S, mhi);
2286 j1 = delta.sign ? 1 : cmp(b, delta);
2287 if (j1 == 0 && !(word1(&u) & 1)) {
2288 if (dig == '9')
2289 goto round_9_up;
2290 if (j > 0)
2291 dig++;
2292 #ifdef SET_INEXACT
2293 else if (!b->x[0] && b->wds <= 1)
2294 inexact = 0;
2295 #endif
2296 *s++ = dig;
2297 goto ret;
2298 }
2299 if (j < 0 || (j == 0 && !(word1(&u) & 1))) {
2300 if (!b.words()[0] && b.size() <= 1) {
2301 #ifdef SET_INEXACT
2302 inexact = 0;
2303 #endif
2304 goto accept_dig;
2305 }
2306 if (j1 > 0) {
2307 lshift(b, 1);
2308 j1 = cmp(b, S);
2309 if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
2310 goto round_9_up;
2311 }
2312 accept_dig:
2313 *s++ = dig;
2314 goto ret;
2315 }
2316 if (j1 > 0) {
2317 if (dig == '9') { /* possible if i == 1 */
2318 round_9_up:
2319 *s++ = '9';
2320 goto roundoff;
2321 }
2322 *s++ = dig + 1;
2323 goto ret;
2324 }
2325 *s++ = dig;
2326 if (i == ilim)
2327 break;
2328 multadd(b, 10, 0);
2329 multadd(mlo, 10, 0);
2330 multadd(mhi, 10, 0);
2331 }
2332 } else
2333 for (i = 1;; i++) {
2334 *s++ = dig = quorem(b,S) + '0';
2335 if (!b.words()[0] && b.size() <= 1) {
2336 #ifdef SET_INEXACT
2337 inexact = 0;
2338 #endif
2339 goto ret;
2340 }
2341 if (i >= ilim)
2342 break;
2343 multadd(b, 10, 0);
2344 }
2345
2346 /* Round off last digit */
2347
2348 lshift(b, 1);
2349 j = cmp(b, S);
2350 if (j > 0 || (j == 0 && (dig & 1))) {
2351 roundoff:
2352 while (*--s == '9')
2353 if (s == s0) {
2354 k++;
2355 *s++ = '1';
2356 goto ret;
2357 }
2358 ++*s++;
2359 } else {
2360 while (*--s == '0') { }
2361 s++;
2362 }
2363 goto ret;
2364 no_digits:
2365 k = -1 - ndigits;
2366 goto ret;
2367 one_digit:
2368 *s++ = '1';
2369 k++;
2370 goto ret;
2371 ret:
2372 #ifdef SET_INEXACT
2373 if (inexact) {
2374 if (!oldinexact) {
2375 word0(&u) = Exp_1 + (70 << Exp_shift);
2376 word1(&u) = 0;
2377 dval(&u) += 1.;
2378 }
2379 } else if (!oldinexact)
2380 clear_inexact();
2381 #endif
2382 *s = 0;
2383 *decpt = k + 1;
2384 if (rve)
2385 *rve = s;
2386 }
2387
append(char * & next,const char * src,unsigned size)2388 static ALWAYS_INLINE void append(char*& next, const char* src, unsigned size)
2389 {
2390 for (unsigned i = 0; i < size; ++i)
2391 *next++ = *src++;
2392 }
2393
doubleToStringInJavaScriptFormat(double d,DtoaBuffer buffer,unsigned * resultLength)2394 void doubleToStringInJavaScriptFormat(double d, DtoaBuffer buffer, unsigned* resultLength)
2395 {
2396 ASSERT(buffer);
2397
2398 // avoid ever printing -NaN, in JS conceptually there is only one NaN value
2399 if (isnan(d)) {
2400 append(buffer, "NaN", 3);
2401 if (resultLength)
2402 *resultLength = 3;
2403 return;
2404 }
2405 // -0 -> "0"
2406 if (!d) {
2407 buffer[0] = '0';
2408 if (resultLength)
2409 *resultLength = 1;
2410 return;
2411 }
2412
2413 int decimalPoint;
2414 int sign;
2415
2416 DtoaBuffer result;
2417 char* resultEnd = 0;
2418 WTF::dtoa(result, d, 0, &decimalPoint, &sign, &resultEnd);
2419 int length = resultEnd - result;
2420
2421 char* next = buffer;
2422 if (sign)
2423 *next++ = '-';
2424
2425 if (decimalPoint <= 0 && decimalPoint > -6) {
2426 *next++ = '0';
2427 *next++ = '.';
2428 for (int j = decimalPoint; j < 0; j++)
2429 *next++ = '0';
2430 append(next, result, length);
2431 } else if (decimalPoint <= 21 && decimalPoint > 0) {
2432 if (length <= decimalPoint) {
2433 append(next, result, length);
2434 for (int j = 0; j < decimalPoint - length; j++)
2435 *next++ = '0';
2436 } else {
2437 append(next, result, decimalPoint);
2438 *next++ = '.';
2439 append(next, result + decimalPoint, length - decimalPoint);
2440 }
2441 } else if (result[0] < '0' || result[0] > '9')
2442 append(next, result, length);
2443 else {
2444 *next++ = result[0];
2445 if (length > 1) {
2446 *next++ = '.';
2447 append(next, result + 1, length - 1);
2448 }
2449
2450 *next++ = 'e';
2451 *next++ = (decimalPoint >= 0) ? '+' : '-';
2452 // decimalPoint can't be more than 3 digits decimal given the
2453 // nature of float representation
2454 int exponential = decimalPoint - 1;
2455 if (exponential < 0)
2456 exponential = -exponential;
2457 if (exponential >= 100)
2458 *next++ = static_cast<char>('0' + exponential / 100);
2459 if (exponential >= 10)
2460 *next++ = static_cast<char>('0' + (exponential % 100) / 10);
2461 *next++ = static_cast<char>('0' + exponential % 10);
2462 }
2463 if (resultLength)
2464 *resultLength = next - buffer;
2465 }
2466
2467 } // namespace WTF
2468