-/****************************************************************
- *
- * The author of this software is David M. Gay.
- *
- * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
- * Copyright (C) 2002, 2005, 2006, 2007, 2008, 2010 Apple Inc. All rights reserved.
- *
- * Permission to use, copy, modify, and distribute this software for any
- * purpose without fee is hereby granted, provided that this entire notice
- * is included in all copies of any software which is or includes a copy
- * or modification of this software and in all copies of the supporting
- * documentation for such software.
- *
- * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
- * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
- * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
- * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
- *
- ***************************************************************/
-
-/* Please send bug reports to David M. Gay (dmg at acm dot org,
- * with " at " changed at "@" and " dot " changed to "."). */
-
-/* On a machine with IEEE extended-precision registers, it is
- * necessary to specify double-precision (53-bit) rounding precision
- * before invoking strtod or dtoa. If the machine uses (the equivalent
- * of) Intel 80x87 arithmetic, the call
- * _control87(PC_53, MCW_PC);
- * does this with many compilers. Whether this or another call is
- * appropriate depends on the compiler; for this to work, it may be
- * necessary to #include "float.h" or another system-dependent header
- * file.
- */
-
-/* strtod for IEEE-arithmetic machines.
- *
- * This strtod returns a nearest machine number to the input decimal
- * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
- * broken by the IEEE round-even rule. Otherwise ties are broken by
- * biased rounding (add half and chop).
- *
- * Inspired loosely by William D. Clinger's paper "How to Read Floating
- * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
- *
- * Modifications:
- *
- * 1. We only require IEEE double-precision arithmetic (not IEEE double-extended).
- * 2. We get by with floating-point arithmetic in a case that
- * Clinger missed -- when we're computing d * 10^n
- * for a small integer d and the integer n is not too
- * much larger than 22 (the maximum integer k for which
- * we can represent 10^k exactly), we may be able to
- * compute (d*10^k) * 10^(e-k) with just one roundoff.
- * 3. Rather than a bit-at-a-time adjustment of the binary
- * result in the hard case, we use floating-point
- * arithmetic to determine the adjustment to within
- * one bit; only in really hard cases do we need to
- * compute a second residual.
- * 4. Because of 3., we don't need a large table of powers of 10
- * for ten-to-e (just some small tables, e.g. of 10^k
- * for 0 <= k <= 22).
- */
-
-#include "config.h"
-#include "dtoa.h"
-
-#if HAVE(ERRNO_H)
-#include <errno.h>
-#endif
-#include <float.h>
-#include <math.h>
-#include <stdint.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <wtf/AlwaysInline.h>
-#include <wtf/Assertions.h>
-#include <wtf/DecimalNumber.h>
-#include <wtf/FastMalloc.h>
-#include <wtf/MathExtras.h>
-#include <wtf/Threading.h>
-#include <wtf/UnusedParam.h>
-#include <wtf/Vector.h>
-
-#if COMPILER(MSVC)
-#pragma warning(disable: 4244)
-#pragma warning(disable: 4245)
-#pragma warning(disable: 4554)
-#endif
-
-namespace WTF {
-
-#if ENABLE(WTF_MULTIPLE_THREADS)
-Mutex* s_dtoaP5Mutex;
-#endif
-
-typedef union {
- double d;
- uint32_t L[2];
-} U;
-
-#if CPU(BIG_ENDIAN) || CPU(MIDDLE_ENDIAN)
-#define word0(x) (x)->L[0]
-#define word1(x) (x)->L[1]
-#else
-#define word0(x) (x)->L[1]
-#define word1(x) (x)->L[0]
-#endif
-#define dval(x) (x)->d
-
-/* The following definition of Storeinc is appropriate for MIPS processors.
- * An alternative that might be better on some machines is
- * *p++ = high << 16 | low & 0xffff;
- */
-static ALWAYS_INLINE uint32_t* storeInc(uint32_t* p, uint16_t high, uint16_t low)
-{
- uint16_t* p16 = reinterpret_cast<uint16_t*>(p);
-#if CPU(BIG_ENDIAN)
- p16[0] = high;
- p16[1] = low;
-#else
- p16[1] = high;
- p16[0] = low;
-#endif
- return p + 1;
-}
-
-#define Exp_shift 20
-#define Exp_shift1 20
-#define Exp_msk1 0x100000
-#define Exp_msk11 0x100000
-#define Exp_mask 0x7ff00000
-#define P 53
-#define Bias 1023
-#define Emin (-1022)
-#define Exp_1 0x3ff00000
-#define Exp_11 0x3ff00000
-#define Ebits 11
-#define Frac_mask 0xfffff
-#define Frac_mask1 0xfffff
-#define Ten_pmax 22
-#define Bletch 0x10
-#define Bndry_mask 0xfffff
-#define Bndry_mask1 0xfffff
-#define LSB 1
-#define Sign_bit 0x80000000
-#define Log2P 1
-#define Tiny0 0
-#define Tiny1 1
-#define Quick_max 14
-#define Int_max 14
-
-#define rounded_product(a, b) a *= b
-#define rounded_quotient(a, b) a /= b
-
-#define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
-#define Big1 0xffffffff
-
-#if CPU(PPC64) || CPU(X86_64)
-// FIXME: should we enable this on all 64-bit CPUs?
-// 64-bit emulation provided by the compiler is likely to be slower than dtoa own code on 32-bit hardware.
-#define USE_LONG_LONG
-#endif
-
-struct BigInt {
- BigInt() : sign(0) { }
- int sign;
-
- void clear()
- {
- sign = 0;
- m_words.clear();
- }
-
- size_t size() const
- {
- return m_words.size();
- }
-
- void resize(size_t s)
- {
- m_words.resize(s);
- }
-
- uint32_t* words()
- {
- return m_words.data();
- }
-
- const uint32_t* words() const
- {
- return m_words.data();
- }
-
- void append(uint32_t w)
- {
- m_words.append(w);
- }
-
- Vector<uint32_t, 16> m_words;
-};
-
-static void multadd(BigInt& b, int m, int a) /* multiply by m and add a */
-{
-#ifdef USE_LONG_LONG
- unsigned long long carry;
-#else
- uint32_t carry;
-#endif
-
- int wds = b.size();
- uint32_t* x = b.words();
- int i = 0;
- carry = a;
- do {
-#ifdef USE_LONG_LONG
- unsigned long long y = *x * (unsigned long long)m + carry;
- carry = y >> 32;
- *x++ = (uint32_t)y & 0xffffffffUL;
-#else
- uint32_t xi = *x;
- uint32_t y = (xi & 0xffff) * m + carry;
- uint32_t z = (xi >> 16) * m + (y >> 16);
- carry = z >> 16;
- *x++ = (z << 16) + (y & 0xffff);
-#endif
- } while (++i < wds);
-
- if (carry)
- b.append((uint32_t)carry);
-}
-
-static void s2b(BigInt& b, const char* s, int nd0, int nd, uint32_t y9)
-{
- b.sign = 0;
- b.resize(1);
- b.words()[0] = y9;
-
- int i = 9;
- if (9 < nd0) {
- s += 9;
- do {
- multadd(b, 10, *s++ - '0');
- } while (++i < nd0);
- s++;
- } else
- s += 10;
- for (; i < nd; i++)
- multadd(b, 10, *s++ - '0');
-}
-
-static int hi0bits(uint32_t x)
-{
- int k = 0;
-
- if (!(x & 0xffff0000)) {
- k = 16;
- x <<= 16;
- }
- if (!(x & 0xff000000)) {
- k += 8;
- x <<= 8;
- }
- if (!(x & 0xf0000000)) {
- k += 4;
- x <<= 4;
- }
- if (!(x & 0xc0000000)) {
- k += 2;
- x <<= 2;
- }
- if (!(x & 0x80000000)) {
- k++;
- if (!(x & 0x40000000))
- return 32;
- }
- return k;
-}
-
-static int lo0bits(uint32_t* y)
-{
- int k;
- uint32_t x = *y;
-
- if (x & 7) {
- if (x & 1)
- return 0;
- if (x & 2) {
- *y = x >> 1;
- return 1;
- }
- *y = x >> 2;
- return 2;
- }
- k = 0;
- if (!(x & 0xffff)) {
- k = 16;
- x >>= 16;
- }
- if (!(x & 0xff)) {
- k += 8;
- x >>= 8;
- }
- if (!(x & 0xf)) {
- k += 4;
- x >>= 4;
- }
- if (!(x & 0x3)) {
- k += 2;
- x >>= 2;
- }
- if (!(x & 1)) {
- k++;
- x >>= 1;
- if (!x)
- return 32;
- }
- *y = x;
- return k;
-}
-
-static void i2b(BigInt& b, int i)
-{
- b.sign = 0;
- b.resize(1);
- b.words()[0] = i;
-}
-
-static void mult(BigInt& aRef, const BigInt& bRef)
-{
- const BigInt* a = &aRef;
- const BigInt* b = &bRef;
- BigInt c;
- int wa, wb, wc;
- const uint32_t* x = 0;
- const uint32_t* xa;
- const uint32_t* xb;
- const uint32_t* xae;
- const uint32_t* xbe;
- uint32_t* xc;
- uint32_t* xc0;
- uint32_t y;
-#ifdef USE_LONG_LONG
- unsigned long long carry, z;
-#else
- uint32_t carry, z;
-#endif
-
- if (a->size() < b->size()) {
- const BigInt* tmp = a;
- a = b;
- b = tmp;
- }
-
- wa = a->size();
- wb = b->size();
- wc = wa + wb;
- c.resize(wc);
-
- for (xc = c.words(), xa = xc + wc; xc < xa; xc++)
- *xc = 0;
- xa = a->words();
- xae = xa + wa;
- xb = b->words();
- xbe = xb + wb;
- xc0 = c.words();
-#ifdef USE_LONG_LONG
- for (; xb < xbe; xc0++) {
- if ((y = *xb++)) {
- x = xa;
- xc = xc0;
- carry = 0;
- do {
- z = *x++ * (unsigned long long)y + *xc + carry;
- carry = z >> 32;
- *xc++ = (uint32_t)z & 0xffffffffUL;
- } while (x < xae);
- *xc = (uint32_t)carry;
- }
- }
-#else
- for (; xb < xbe; xb++, xc0++) {
- if ((y = *xb & 0xffff)) {
- x = xa;
- xc = xc0;
- carry = 0;
- do {
- z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
- carry = z >> 16;
- uint32_t z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
- carry = z2 >> 16;
- xc = storeInc(xc, z2, z);
- } while (x < xae);
- *xc = carry;
- }
- if ((y = *xb >> 16)) {
- x = xa;
- xc = xc0;
- carry = 0;
- uint32_t z2 = *xc;
- do {
- z = (*x & 0xffff) * y + (*xc >> 16) + carry;
- carry = z >> 16;
- xc = storeInc(xc, z, z2);
- z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
- carry = z2 >> 16;
- } while (x < xae);
- *xc = z2;
- }
- }
-#endif
- for (xc0 = c.words(), xc = xc0 + wc; wc > 0 && !*--xc; --wc) { }
- c.resize(wc);
- aRef = c;
-}
-
-struct P5Node {
- WTF_MAKE_NONCOPYABLE(P5Node); WTF_MAKE_FAST_ALLOCATED;
-public:
- P5Node() { }
- BigInt val;
- P5Node* next;
-};
-
-static P5Node* p5s;
-static int p5sCount;
-
-static ALWAYS_INLINE void pow5mult(BigInt& b, int k)
-{
- static int p05[3] = { 5, 25, 125 };
-
- if (int i = k & 3)
- multadd(b, p05[i - 1], 0);
-
- if (!(k >>= 2))
- return;
-
-#if ENABLE(WTF_MULTIPLE_THREADS)
- s_dtoaP5Mutex->lock();
-#endif
- P5Node* p5 = p5s;
-
- if (!p5) {
- /* first time */
- p5 = new P5Node;
- i2b(p5->val, 625);
- p5->next = 0;
- p5s = p5;
- p5sCount = 1;
- }
-
- int p5sCountLocal = p5sCount;
-#if ENABLE(WTF_MULTIPLE_THREADS)
- s_dtoaP5Mutex->unlock();
-#endif
- int p5sUsed = 0;
-
- for (;;) {
- if (k & 1)
- mult(b, p5->val);
-
- if (!(k >>= 1))
- break;
-
- if (++p5sUsed == p5sCountLocal) {
-#if ENABLE(WTF_MULTIPLE_THREADS)
- s_dtoaP5Mutex->lock();
-#endif
- if (p5sUsed == p5sCount) {
- ASSERT(!p5->next);
- p5->next = new P5Node;
- p5->next->next = 0;
- p5->next->val = p5->val;
- mult(p5->next->val, p5->next->val);
- ++p5sCount;
- }
-
- p5sCountLocal = p5sCount;
-#if ENABLE(WTF_MULTIPLE_THREADS)
- s_dtoaP5Mutex->unlock();
-#endif
- }
- p5 = p5->next;
- }
-}
-
-static ALWAYS_INLINE void lshift(BigInt& b, int k)
-{
- int n = k >> 5;
-
- int origSize = b.size();
- int n1 = n + origSize + 1;
-
- if (k &= 0x1f)
- b.resize(b.size() + n + 1);
- else
- b.resize(b.size() + n);
-
- const uint32_t* srcStart = b.words();
- uint32_t* dstStart = b.words();
- const uint32_t* src = srcStart + origSize - 1;
- uint32_t* dst = dstStart + n1 - 1;
- if (k) {
- uint32_t hiSubword = 0;
- int s = 32 - k;
- for (; src >= srcStart; --src) {
- *dst-- = hiSubword | *src >> s;
- hiSubword = *src << k;
- }
- *dst = hiSubword;
- ASSERT(dst == dstStart + n);
-
- b.resize(origSize + n + !!b.words()[n1 - 1]);
- }
- else {
- do {
- *--dst = *src--;
- } while (src >= srcStart);
- }
- for (dst = dstStart + n; dst != dstStart; )
- *--dst = 0;
-
- ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
-}
-
-static int cmp(const BigInt& a, const BigInt& b)
-{
- const uint32_t *xa, *xa0, *xb, *xb0;
- int i, j;
-
- i = a.size();
- j = b.size();
- ASSERT(i <= 1 || a.words()[i - 1]);
- ASSERT(j <= 1 || b.words()[j - 1]);
- if (i -= j)
- return i;
- xa0 = a.words();
- xa = xa0 + j;
- xb0 = b.words();
- xb = xb0 + j;
- for (;;) {
- if (*--xa != *--xb)
- return *xa < *xb ? -1 : 1;
- if (xa <= xa0)
- break;
- }
- return 0;
-}
-
-static ALWAYS_INLINE void diff(BigInt& c, const BigInt& aRef, const BigInt& bRef)
-{
- const BigInt* a = &aRef;
- const BigInt* b = &bRef;
- int i, wa, wb;
- uint32_t* xc;
-
- i = cmp(*a, *b);
- if (!i) {
- c.sign = 0;
- c.resize(1);
- c.words()[0] = 0;
- return;
- }
- if (i < 0) {
- const BigInt* tmp = a;
- a = b;
- b = tmp;
- i = 1;
- } else
- i = 0;
-
- wa = a->size();
- const uint32_t* xa = a->words();
- const uint32_t* xae = xa + wa;
- wb = b->size();
- const uint32_t* xb = b->words();
- const uint32_t* xbe = xb + wb;
-
- c.resize(wa);
- c.sign = i;
- xc = c.words();
-#ifdef USE_LONG_LONG
- unsigned long long borrow = 0;
- do {
- unsigned long long y = (unsigned long long)*xa++ - *xb++ - borrow;
- borrow = y >> 32 & (uint32_t)1;
- *xc++ = (uint32_t)y & 0xffffffffUL;
- } while (xb < xbe);
- while (xa < xae) {
- unsigned long long y = *xa++ - borrow;
- borrow = y >> 32 & (uint32_t)1;
- *xc++ = (uint32_t)y & 0xffffffffUL;
- }
-#else
- uint32_t borrow = 0;
- do {
- uint32_t y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- uint32_t z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
- borrow = (z & 0x10000) >> 16;
- xc = storeInc(xc, z, y);
- } while (xb < xbe);
- while (xa < xae) {
- uint32_t y = (*xa & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- uint32_t z = (*xa++ >> 16) - borrow;
- borrow = (z & 0x10000) >> 16;
- xc = storeInc(xc, z, y);
- }
-#endif
- while (!*--xc)
- wa--;
- c.resize(wa);
-}
-
-static double ulp(U *x)
-{
- register int32_t L;
- U u;
-
- L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
- word0(&u) = L;
- word1(&u) = 0;
- return dval(&u);
-}
-
-static double b2d(const BigInt& a, int* e)
-{
- const uint32_t* xa;
- const uint32_t* xa0;
- uint32_t w;
- uint32_t y;
- uint32_t z;
- int k;
- U d;
-
-#define d0 word0(&d)
-#define d1 word1(&d)
-
- xa0 = a.words();
- xa = xa0 + a.size();
- y = *--xa;
- ASSERT(y);
- k = hi0bits(y);
- *e = 32 - k;
- if (k < Ebits) {
- d0 = Exp_1 | (y >> (Ebits - k));
- w = xa > xa0 ? *--xa : 0;
- d1 = (y << (32 - Ebits + k)) | (w >> (Ebits - k));
- goto returnD;
- }
- z = xa > xa0 ? *--xa : 0;
- if (k -= Ebits) {
- d0 = Exp_1 | (y << k) | (z >> (32 - k));
- y = xa > xa0 ? *--xa : 0;
- d1 = (z << k) | (y >> (32 - k));
- } else {
- d0 = Exp_1 | y;
- d1 = z;
- }
-returnD:
-#undef d0
-#undef d1
- return dval(&d);
-}
-
-static ALWAYS_INLINE void d2b(BigInt& b, U* d, int* e, int* bits)
-{
- int de, k;
- uint32_t* x;
- uint32_t y, z;
- int i;
-#define d0 word0(d)
-#define d1 word1(d)
-
- b.sign = 0;
- b.resize(1);
- x = b.words();
-
- z = d0 & Frac_mask;
- d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
- if ((de = (int)(d0 >> Exp_shift)))
- z |= Exp_msk1;
- if ((y = d1)) {
- if ((k = lo0bits(&y))) {
- x[0] = y | (z << (32 - k));
- z >>= k;
- } else
- x[0] = y;
- if (z) {
- b.resize(2);
- x[1] = z;
- }
-
- i = b.size();
- } else {
- k = lo0bits(&z);
- x[0] = z;
- i = 1;
- b.resize(1);
- k += 32;
- }
- if (de) {
- *e = de - Bias - (P - 1) + k;
- *bits = P - k;
- } else {
- *e = de - Bias - (P - 1) + 1 + k;
- *bits = (32 * i) - hi0bits(x[i - 1]);
- }
-}
-#undef d0
-#undef d1
-
-static double ratio(const BigInt& a, const BigInt& b)
-{
- U da, db;
- int k, ka, kb;
-
- dval(&da) = b2d(a, &ka);
- dval(&db) = b2d(b, &kb);
- k = ka - kb + 32 * (a.size() - b.size());
- if (k > 0)
- word0(&da) += k * Exp_msk1;
- else {
- k = -k;
- word0(&db) += k * Exp_msk1;
- }
- return dval(&da) / dval(&db);
-}
-
-static const double tens[] = {
- 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
- 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
- 1e20, 1e21, 1e22
-};
-
-static const double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
-static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
- 9007199254740992. * 9007199254740992.e-256
- /* = 2^106 * 1e-256 */
-};
-
-/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
-/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
-#define Scale_Bit 0x10
-#define n_bigtens 5
-
-double strtod(const char* s00, char** se)
-{
- int scale;
- int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
- e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
- const char *s, *s0, *s1;
- double aadj, aadj1;
- U aadj2, adj, rv, rv0;
- int32_t L;
- uint32_t y, z;
- BigInt bb, bb1, bd, bd0, bs, delta;
-
- sign = nz0 = nz = 0;
- dval(&rv) = 0;
- for (s = s00; ; s++) {
- switch (*s) {
- case '-':
- sign = 1;
- /* no break */
- case '+':
- if (*++s)
- goto break2;
- /* no break */
- case 0:
- goto ret0;
- case '\t':
- case '\n':
- case '\v':
- case '\f':
- case '\r':
- case ' ':
- continue;
- default:
- goto break2;
- }
- }
-break2:
- if (*s == '0') {
- nz0 = 1;
- while (*++s == '0') { }
- if (!*s)
- goto ret;
- }
- s0 = s;
- y = z = 0;
- for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
- if (nd < 9)
- y = (10 * y) + c - '0';
- else if (nd < 16)
- z = (10 * z) + c - '0';
- nd0 = nd;
- if (c == '.') {
- c = *++s;
- if (!nd) {
- for (; c == '0'; c = *++s)
- nz++;
- if (c > '0' && c <= '9') {
- s0 = s;
- nf += nz;
- nz = 0;
- goto haveDig;
- }
- goto digDone;
- }
- for (; c >= '0' && c <= '9'; c = *++s) {
-haveDig:
- nz++;
- if (c -= '0') {
- nf += nz;
- for (i = 1; i < nz; i++)
- if (nd++ < 9)
- y *= 10;
- else if (nd <= DBL_DIG + 1)
- z *= 10;
- if (nd++ < 9)
- y = (10 * y) + c;
- else if (nd <= DBL_DIG + 1)
- z = (10 * z) + c;
- nz = 0;
- }
- }
- }
-digDone:
- e = 0;
- if (c == 'e' || c == 'E') {
- if (!nd && !nz && !nz0)
- goto ret0;
- s00 = s;
- esign = 0;
- switch (c = *++s) {
- case '-':
- esign = 1;
- case '+':
- c = *++s;
- }
- if (c >= '0' && c <= '9') {
- while (c == '0')
- c = *++s;
- if (c > '0' && c <= '9') {
- L = c - '0';
- s1 = s;
- while ((c = *++s) >= '0' && c <= '9')
- L = (10 * L) + c - '0';
- if (s - s1 > 8 || L > 19999)
- /* Avoid confusion from exponents
- * so large that e might overflow.
- */
- e = 19999; /* safe for 16 bit ints */
- else
- e = (int)L;
- if (esign)
- e = -e;
- } else
- e = 0;
- } else
- s = s00;
- }
- if (!nd) {
- if (!nz && !nz0) {
-ret0:
- s = s00;
- sign = 0;
- }
- goto ret;
- }
- e1 = e -= nf;
-
- /* Now we have nd0 digits, starting at s0, followed by a
- * decimal point, followed by nd-nd0 digits. The number we're
- * after is the integer represented by those digits times
- * 10**e */
-
- if (!nd0)
- nd0 = nd;
- k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
- dval(&rv) = y;
- if (k > 9)
- dval(&rv) = tens[k - 9] * dval(&rv) + z;
- if (nd <= DBL_DIG) {
- if (!e)
- goto ret;
- if (e > 0) {
- if (e <= Ten_pmax) {
- /* rv = */ rounded_product(dval(&rv), tens[e]);
- goto ret;
- }
- i = DBL_DIG - nd;
- if (e <= Ten_pmax + i) {
- /* A fancier test would sometimes let us do
- * this for larger i values.
- */
- e -= i;
- dval(&rv) *= tens[i];
- /* rv = */ rounded_product(dval(&rv), tens[e]);
- goto ret;
- }
- } else if (e >= -Ten_pmax) {
- /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
- goto ret;
- }
- }
- e1 += nd - k;
-
- scale = 0;
-
- /* Get starting approximation = rv * 10**e1 */
-
- if (e1 > 0) {
- if ((i = e1 & 15))
- dval(&rv) *= tens[i];
- if (e1 &= ~15) {
- if (e1 > DBL_MAX_10_EXP) {
-ovfl:
-#if HAVE(ERRNO_H)
- errno = ERANGE;
-#endif
- /* Can't trust HUGE_VAL */
- word0(&rv) = Exp_mask;
- word1(&rv) = 0;
- goto ret;
- }
- e1 >>= 4;
- for (j = 0; e1 > 1; j++, e1 >>= 1)
- if (e1 & 1)
- dval(&rv) *= bigtens[j];
- /* The last multiplication could overflow. */
- word0(&rv) -= P * Exp_msk1;
- dval(&rv) *= bigtens[j];
- if ((z = word0(&rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
- goto ovfl;
- if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
- /* set to largest number */
- /* (Can't trust DBL_MAX) */
- word0(&rv) = Big0;
- word1(&rv) = Big1;
- } else
- word0(&rv) += P * Exp_msk1;
- }
- } else if (e1 < 0) {
- e1 = -e1;
- if ((i = e1 & 15))
- dval(&rv) /= tens[i];
- if (e1 >>= 4) {
- if (e1 >= 1 << n_bigtens)
- goto undfl;
- if (e1 & Scale_Bit)
- scale = 2 * P;
- for (j = 0; e1 > 0; j++, e1 >>= 1)
- if (e1 & 1)
- dval(&rv) *= tinytens[j];
- if (scale && (j = (2 * P) + 1 - ((word0(&rv) & Exp_mask) >> Exp_shift)) > 0) {
- /* scaled rv is denormal; clear j low bits */
- if (j >= 32) {
- word1(&rv) = 0;
- if (j >= 53)
- word0(&rv) = (P + 2) * Exp_msk1;
- else
- word0(&rv) &= 0xffffffff << (j - 32);
- } else
- word1(&rv) &= 0xffffffff << j;
- }
- if (!dval(&rv)) {
-undfl:
- dval(&rv) = 0.;
-#if HAVE(ERRNO_H)
- errno = ERANGE;
-#endif
- goto ret;
- }
- }
- }
-
- /* Now the hard part -- adjusting rv to the correct value.*/
-
- /* Put digits into bd: true value = bd * 10^e */
-
- s2b(bd0, s0, nd0, nd, y);
-
- for (;;) {
- bd = bd0;
- d2b(bb, &rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
- i2b(bs, 1);
-
- if (e >= 0) {
- bb2 = bb5 = 0;
- bd2 = bd5 = e;
- } else {
- bb2 = bb5 = -e;
- bd2 = bd5 = 0;
- }
- if (bbe >= 0)
- bb2 += bbe;
- else
- bd2 -= bbe;
- bs2 = bb2;
- j = bbe - scale;
- i = j + bbbits - 1; /* logb(rv) */
- if (i < Emin) /* denormal */
- j += P - Emin;
- else
- j = P + 1 - bbbits;
- bb2 += j;
- bd2 += j;
- bd2 += scale;
- i = bb2 < bd2 ? bb2 : bd2;
- if (i > bs2)
- i = bs2;
- if (i > 0) {
- bb2 -= i;
- bd2 -= i;
- bs2 -= i;
- }
- if (bb5 > 0) {
- pow5mult(bs, bb5);
- mult(bb, bs);
- }
- if (bb2 > 0)
- lshift(bb, bb2);
- if (bd5 > 0)
- pow5mult(bd, bd5);
- if (bd2 > 0)
- lshift(bd, bd2);
- if (bs2 > 0)
- lshift(bs, bs2);
- diff(delta, bb, bd);
- dsign = delta.sign;
- delta.sign = 0;
- i = cmp(delta, bs);
-
- if (i < 0) {
- /* Error is less than half an ulp -- check for
- * special case of mantissa a power of two.
- */
- if (dsign || word1(&rv) || word0(&rv) & Bndry_mask
- || (word0(&rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
- ) {
- break;
- }
- if (!delta.words()[0] && delta.size() <= 1) {
- /* exact result */
- break;
- }
- lshift(delta, Log2P);
- if (cmp(delta, bs) > 0)
- goto dropDown;
- break;
- }
- if (!i) {
- /* exactly half-way between */
- if (dsign) {
- if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
- && word1(&rv) == (
- (scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
- ? (0xffffffff & (0xffffffff << (2 * P + 1 - (y >> Exp_shift)))) :
- 0xffffffff)) {
- /*boundary case -- increment exponent*/
- word0(&rv) = (word0(&rv) & Exp_mask) + Exp_msk1;
- word1(&rv) = 0;
- dsign = 0;
- break;
- }
- } else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
-dropDown:
- /* boundary case -- decrement exponent */
- if (scale) {
- L = word0(&rv) & Exp_mask;
- if (L <= (2 * P + 1) * Exp_msk1) {
- if (L > (P + 2) * Exp_msk1)
- /* round even ==> */
- /* accept rv */
- break;
- /* rv = smallest denormal */
- goto undfl;
- }
- }
- L = (word0(&rv) & Exp_mask) - Exp_msk1;
- word0(&rv) = L | Bndry_mask1;
- word1(&rv) = 0xffffffff;
- break;
- }
- if (!(word1(&rv) & LSB))
- break;
- if (dsign)
- dval(&rv) += ulp(&rv);
- else {
- dval(&rv) -= ulp(&rv);
- if (!dval(&rv))
- goto undfl;
- }
- dsign = 1 - dsign;
- break;
- }
- if ((aadj = ratio(delta, bs)) <= 2.) {
- if (dsign)
- aadj = aadj1 = 1.;
- else if (word1(&rv) || word0(&rv) & Bndry_mask) {
- if (word1(&rv) == Tiny1 && !word0(&rv))
- goto undfl;
- aadj = 1.;
- aadj1 = -1.;
- } else {
- /* special case -- power of FLT_RADIX to be */
- /* rounded down... */
-
- if (aadj < 2. / FLT_RADIX)
- aadj = 1. / FLT_RADIX;
- else
- aadj *= 0.5;
- aadj1 = -aadj;
- }
- } else {
- aadj *= 0.5;
- aadj1 = dsign ? aadj : -aadj;
- }
- y = word0(&rv) & Exp_mask;
-
- /* Check for overflow */
-
- if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
- dval(&rv0) = dval(&rv);
- word0(&rv) -= P * Exp_msk1;
- adj.d = aadj1 * ulp(&rv);
- dval(&rv) += adj.d;
- if ((word0(&rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
- if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
- goto ovfl;
- word0(&rv) = Big0;
- word1(&rv) = Big1;
- goto cont;
- }
- word0(&rv) += P * Exp_msk1;
- } else {
- if (scale && y <= 2 * P * Exp_msk1) {
- if (aadj <= 0x7fffffff) {
- if ((z = (uint32_t)aadj) <= 0)
- z = 1;
- aadj = z;
- aadj1 = dsign ? aadj : -aadj;
- }
- dval(&aadj2) = aadj1;
- word0(&aadj2) += (2 * P + 1) * Exp_msk1 - y;
- aadj1 = dval(&aadj2);
- }
- adj.d = aadj1 * ulp(&rv);
- dval(&rv) += adj.d;
- }
- z = word0(&rv) & Exp_mask;
- if (!scale && y == z) {
- /* Can we stop now? */
- L = (int32_t)aadj;
- aadj -= L;
- /* The tolerances below are conservative. */
- if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
- if (aadj < .4999999 || aadj > .5000001)
- break;
- } else if (aadj < .4999999 / FLT_RADIX)
- break;
- }
-cont:
- {}
- }
- if (scale) {
- word0(&rv0) = Exp_1 - 2 * P * Exp_msk1;
- word1(&rv0) = 0;
- dval(&rv) *= dval(&rv0);
-#if HAVE(ERRNO_H)
- /* try to avoid the bug of testing an 8087 register value */
- if (!word0(&rv) && !word1(&rv))
- errno = ERANGE;
-#endif
- }
-ret:
- if (se)
- *se = const_cast<char*>(s);
- return sign ? -dval(&rv) : dval(&rv);
-}
-
-static ALWAYS_INLINE int quorem(BigInt& b, BigInt& S)
-{
- size_t n;
- uint32_t* bx;
- uint32_t* bxe;
- uint32_t q;
- uint32_t* sx;
- uint32_t* sxe;
-#ifdef USE_LONG_LONG
- unsigned long long borrow, carry, y, ys;
-#else
- uint32_t borrow, carry, y, ys;
- uint32_t si, z, zs;
-#endif
- ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
- ASSERT(S.size() <= 1 || S.words()[S.size() - 1]);
-
- n = S.size();
- ASSERT_WITH_MESSAGE(b.size() <= n, "oversize b in quorem");
- if (b.size() < n)
- return 0;
- sx = S.words();
- sxe = sx + --n;
- bx = b.words();
- bxe = bx + n;
- q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
- ASSERT_WITH_MESSAGE(q <= 9, "oversized quotient in quorem");
- if (q) {
- borrow = 0;
- carry = 0;
- do {
-#ifdef USE_LONG_LONG
- ys = *sx++ * (unsigned long long)q + carry;
- carry = ys >> 32;
- y = *bx - (ys & 0xffffffffUL) - borrow;
- borrow = y >> 32 & (uint32_t)1;
- *bx++ = (uint32_t)y & 0xffffffffUL;
-#else
- si = *sx++;
- ys = (si & 0xffff) * q + carry;
- zs = (si >> 16) * q + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- z = (*bx >> 16) - (zs & 0xffff) - borrow;
- borrow = (z & 0x10000) >> 16;
- bx = storeInc(bx, z, y);
-#endif
- } while (sx <= sxe);
- if (!*bxe) {
- bx = b.words();
- while (--bxe > bx && !*bxe)
- --n;
- b.resize(n);
- }
- }
- if (cmp(b, S) >= 0) {
- q++;
- borrow = 0;
- carry = 0;
- bx = b.words();
- sx = S.words();
- do {
-#ifdef USE_LONG_LONG
- ys = *sx++ + carry;
- carry = ys >> 32;
- y = *bx - (ys & 0xffffffffUL) - borrow;
- borrow = y >> 32 & (uint32_t)1;
- *bx++ = (uint32_t)y & 0xffffffffUL;
-#else
- si = *sx++;
- ys = (si & 0xffff) + carry;
- zs = (si >> 16) + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- z = (*bx >> 16) - (zs & 0xffff) - borrow;
- borrow = (z & 0x10000) >> 16;
- bx = storeInc(bx, z, y);
-#endif
- } while (sx <= sxe);
- bx = b.words();
- bxe = bx + n;
- if (!*bxe) {
- while (--bxe > bx && !*bxe)
- --n;
- b.resize(n);
- }
- }
- return q;
-}
-
-/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
- *
- * Inspired by "How to Print Floating-Point Numbers Accurately" by
- * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
- *
- * Modifications:
- * 1. Rather than iterating, we use a simple numeric overestimate
- * to determine k = floor(log10(d)). We scale relevant
- * quantities using O(log2(k)) rather than O(k) multiplications.
- * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
- * try to generate digits strictly left to right. Instead, we
- * compute with fewer bits and propagate the carry if necessary
- * when rounding the final digit up. This is often faster.
- * 3. Under the assumption that input will be rounded nearest,
- * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
- * That is, we allow equality in stopping tests when the
- * round-nearest rule will give the same floating-point value
- * as would satisfaction of the stopping test with strict
- * inequality.
- * 4. We remove common factors of powers of 2 from relevant
- * quantities.
- * 5. When converting floating-point integers less than 1e16,
- * we use floating-point arithmetic rather than resorting
- * to multiple-precision integers.
- * 6. When asked to produce fewer than 15 digits, we first try
- * to get by with floating-point arithmetic; we resort to
- * multiple-precision integer arithmetic only if we cannot
- * guarantee that the floating-point calculation has given
- * the correctly rounded result. For k requested digits and
- * "uniformly" distributed input, the probability is
- * something like 10^(k-15) that we must resort to the int32_t
- * calculation.
- *
- * Note: 'leftright' translates to 'generate shortest possible string'.
- */
-template<bool roundingNone, bool roundingSignificantFigures, bool roundingDecimalPlaces, bool leftright>
-void dtoa(DtoaBuffer result, double dd, int ndigits, bool& signOut, int& exponentOut, unsigned& precisionOut)
-{
- // Exactly one rounding mode must be specified.
- ASSERT(roundingNone + roundingSignificantFigures + roundingDecimalPlaces == 1);
- // roundingNone only allowed (only sensible?) with leftright set.
- ASSERT(!roundingNone || leftright);
-
- ASSERT(!isnan(dd) && !isinf(dd));
-
- int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
- j, j1, k, k0, k_check, m2, m5, s2, s5,
- spec_case;
- int32_t L;
- int denorm;
- uint32_t x;
- BigInt b, delta, mlo, mhi, S;
- U d2, eps, u;
- double ds;
- char* s;
- char* s0;
-
- u.d = dd;
-
- /* Infinity or NaN */
- ASSERT((word0(&u) & Exp_mask) != Exp_mask);
-
- // JavaScript toString conversion treats -0 as 0.
- if (!dval(&u)) {
- signOut = false;
- exponentOut = 0;
- precisionOut = 1;
- result[0] = '0';
- result[1] = '\0';
- return;
- }
-
- if (word0(&u) & Sign_bit) {
- signOut = true;
- word0(&u) &= ~Sign_bit; // clear sign bit
- } else
- signOut = false;
-
- d2b(b, &u, &be, &bbits);
- if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
- dval(&d2) = dval(&u);
- word0(&d2) &= Frac_mask1;
- word0(&d2) |= Exp_11;
-
- /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
- * log10(x) = log(x) / log(10)
- * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
- * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
- *
- * This suggests computing an approximation k to log10(d) by
- *
- * k = (i - Bias)*0.301029995663981
- * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
- *
- * We want k to be too large rather than too small.
- * The error in the first-order Taylor series approximation
- * is in our favor, so we just round up the constant enough
- * to compensate for any error in the multiplication of
- * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
- * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
- * adding 1e-13 to the constant term more than suffices.
- * Hence we adjust the constant term to 0.1760912590558.
- * (We could get a more accurate k by invoking log10,
- * but this is probably not worthwhile.)
- */
-
- i -= Bias;
- denorm = 0;
- } else {
- /* d is denormalized */
-
- i = bbits + be + (Bias + (P - 1) - 1);
- x = (i > 32) ? (word0(&u) << (64 - i)) | (word1(&u) >> (i - 32))
- : word1(&u) << (32 - i);
- dval(&d2) = x;
- word0(&d2) -= 31 * Exp_msk1; /* adjust exponent */
- i -= (Bias + (P - 1) - 1) + 1;
- denorm = 1;
- }
- ds = (dval(&d2) - 1.5) * 0.289529654602168 + 0.1760912590558 + (i * 0.301029995663981);
- k = (int)ds;
- if (ds < 0. && ds != k)
- k--; /* want k = floor(ds) */
- k_check = 1;
- if (k >= 0 && k <= Ten_pmax) {
- if (dval(&u) < tens[k])
- k--;
- k_check = 0;
- }
- j = bbits - i - 1;
- if (j >= 0) {
- b2 = 0;
- s2 = j;
- } else {
- b2 = -j;
- s2 = 0;
- }
- if (k >= 0) {
- b5 = 0;
- s5 = k;
- s2 += k;
- } else {
- b2 -= k;
- b5 = -k;
- s5 = 0;
- }
-
- if (roundingNone) {
- ilim = ilim1 = -1;
- i = 18;
- ndigits = 0;
- }
- if (roundingSignificantFigures) {
- if (ndigits <= 0)
- ndigits = 1;
- ilim = ilim1 = i = ndigits;
- }
- if (roundingDecimalPlaces) {
- i = ndigits + k + 1;
- ilim = i;
- ilim1 = i - 1;
- if (i <= 0)
- i = 1;
- }
-
- s = s0 = result;
-
- if (ilim >= 0 && ilim <= Quick_max) {
- /* Try to get by with floating-point arithmetic. */
-
- i = 0;
- dval(&d2) = dval(&u);
- k0 = k;
- ilim0 = ilim;
- ieps = 2; /* conservative */
- if (k > 0) {
- ds = tens[k & 0xf];
- j = k >> 4;
- if (j & Bletch) {
- /* prevent overflows */
- j &= Bletch - 1;
- dval(&u) /= bigtens[n_bigtens - 1];
- ieps++;
- }
- for (; j; j >>= 1, i++) {
- if (j & 1) {
- ieps++;
- ds *= bigtens[i];
- }
- }
- dval(&u) /= ds;
- } else if ((j1 = -k)) {
- dval(&u) *= tens[j1 & 0xf];
- for (j = j1 >> 4; j; j >>= 1, i++) {
- if (j & 1) {
- ieps++;
- dval(&u) *= bigtens[i];
- }
- }
- }
- if (k_check && dval(&u) < 1. && ilim > 0) {
- if (ilim1 <= 0)
- goto fastFailed;
- ilim = ilim1;
- k--;
- dval(&u) *= 10.;
- ieps++;
- }
- dval(&eps) = (ieps * dval(&u)) + 7.;
- word0(&eps) -= (P - 1) * Exp_msk1;
- if (!ilim) {
- S.clear();
- mhi.clear();
- dval(&u) -= 5.;
- if (dval(&u) > dval(&eps))
- goto oneDigit;
- if (dval(&u) < -dval(&eps))
- goto noDigits;
- goto fastFailed;
- }
- if (leftright) {
- /* Use Steele & White method of only
- * generating digits needed.
- */
- dval(&eps) = (0.5 / tens[ilim - 1]) - dval(&eps);
- for (i = 0;;) {
- L = (long int)dval(&u);
- dval(&u) -= L;
- *s++ = '0' + (int)L;
- if (dval(&u) < dval(&eps))
- goto ret;
- if (1. - dval(&u) < dval(&eps))
- goto bumpUp;
- if (++i >= ilim)
- break;
- dval(&eps) *= 10.;
- dval(&u) *= 10.;
- }
- } else {
- /* Generate ilim digits, then fix them up. */
- dval(&eps) *= tens[ilim - 1];
- for (i = 1;; i++, dval(&u) *= 10.) {
- L = (int32_t)(dval(&u));
- if (!(dval(&u) -= L))
- ilim = i;
- *s++ = '0' + (int)L;
- if (i == ilim) {
- if (dval(&u) > 0.5 + dval(&eps))
- goto bumpUp;
- if (dval(&u) < 0.5 - dval(&eps)) {
- while (*--s == '0') { }
- s++;
- goto ret;
- }
- break;
- }
- }
- }
-fastFailed:
- s = s0;
- dval(&u) = dval(&d2);
- k = k0;
- ilim = ilim0;
- }
-
- /* Do we have a "small" integer? */
-
- if (be >= 0 && k <= Int_max) {
- /* Yes. */
- ds = tens[k];
- if (ndigits < 0 && ilim <= 0) {
- S.clear();
- mhi.clear();
- if (ilim < 0 || dval(&u) <= 5 * ds)
- goto noDigits;
- goto oneDigit;
- }
- for (i = 1;; i++, dval(&u) *= 10.) {
- L = (int32_t)(dval(&u) / ds);
- dval(&u) -= L * ds;
- *s++ = '0' + (int)L;
- if (!dval(&u)) {
- break;
- }
- if (i == ilim) {
- dval(&u) += dval(&u);
- if (dval(&u) > ds || (dval(&u) == ds && (L & 1))) {
-bumpUp:
- while (*--s == '9')
- if (s == s0) {
- k++;
- *s = '0';
- break;
- }
- ++*s++;
- }
- break;
- }
- }
- goto ret;
- }
-
- m2 = b2;
- m5 = b5;
- mhi.clear();
- mlo.clear();
- if (leftright) {
- i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits;
- b2 += i;
- s2 += i;
- i2b(mhi, 1);
- }
- if (m2 > 0 && s2 > 0) {
- i = m2 < s2 ? m2 : s2;
- b2 -= i;
- m2 -= i;
- s2 -= i;
- }
- if (b5 > 0) {
- if (leftright) {
- if (m5 > 0) {
- pow5mult(mhi, m5);
- mult(b, mhi);
- }
- if ((j = b5 - m5))
- pow5mult(b, j);
- } else
- pow5mult(b, b5);
- }
- i2b(S, 1);
- if (s5 > 0)
- pow5mult(S, s5);
-
- /* Check for special case that d is a normalized power of 2. */
-
- spec_case = 0;
- if ((roundingNone || leftright) && (!word1(&u) && !(word0(&u) & Bndry_mask) && word0(&u) & (Exp_mask & ~Exp_msk1))) {
- /* The special case */
- b2 += Log2P;
- s2 += Log2P;
- spec_case = 1;
- }
-
- /* Arrange for convenient computation of quotients:
- * shift left if necessary so divisor has 4 leading 0 bits.
- *
- * Perhaps we should just compute leading 28 bits of S once
- * and for all and pass them and a shift to quorem, so it
- * can do shifts and ors to compute the numerator for q.
- */
- if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0x1f))
- i = 32 - i;
- if (i > 4) {
- i -= 4;
- b2 += i;
- m2 += i;
- s2 += i;
- } else if (i < 4) {
- i += 28;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- if (b2 > 0)
- lshift(b, b2);
- if (s2 > 0)
- lshift(S, s2);
- if (k_check) {
- if (cmp(b, S) < 0) {
- k--;
- multadd(b, 10, 0); /* we botched the k estimate */
- if (leftright)
- multadd(mhi, 10, 0);
- ilim = ilim1;
- }
- }
- if (ilim <= 0 && roundingDecimalPlaces) {
- if (ilim < 0)
- goto noDigits;
- multadd(S, 5, 0);
- // For IEEE-754 unbiased rounding this check should be <=, such that 0.5 would flush to zero.
- if (cmp(b, S) < 0)
- goto noDigits;
- goto oneDigit;
- }
- if (leftright) {
- if (m2 > 0)
- lshift(mhi, m2);
-
- /* Compute mlo -- check for special case
- * that d is a normalized power of 2.
- */
-
- mlo = mhi;
- if (spec_case)
- lshift(mhi, Log2P);
-
- for (i = 1;;i++) {
- dig = quorem(b, S) + '0';
- /* Do we yet have the shortest decimal string
- * that will round to d?
- */
- j = cmp(b, mlo);
- diff(delta, S, mhi);
- j1 = delta.sign ? 1 : cmp(b, delta);
-#ifdef DTOA_ROUND_BIASED
- if (j < 0 || !j) {
-#else
- // FIXME: ECMA-262 specifies that equidistant results round away from
- // zero, which probably means we shouldn't be on the unbiased code path
- // (the (word1(&u) & 1) clause is looking highly suspicious). I haven't
- // yet understood this code well enough to make the call, but we should
- // probably be enabling DTOA_ROUND_BIASED. I think the interesting corner
- // case to understand is probably "Math.pow(0.5, 24).toString()".
- // I believe this value is interesting because I think it is precisely
- // representable in binary floating point, and its decimal representation
- // has a single digit that Steele & White reduction can remove, with the
- // value 5 (thus equidistant from the next numbers above and below).
- // We produce the correct answer using either codepath, and I don't as
- // yet understand why. :-)
- if (!j1 && !(word1(&u) & 1)) {
- if (dig == '9')
- goto round9up;
- if (j > 0)
- dig++;
- *s++ = dig;
- goto ret;
- }
- if (j < 0 || (!j && !(word1(&u) & 1))) {
-#endif
- if ((b.words()[0] || b.size() > 1) && (j1 > 0)) {
- lshift(b, 1);
- j1 = cmp(b, S);
- // For IEEE-754 round-to-even, this check should be (j1 > 0 || (!j1 && (dig & 1))),
- // but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed()) should
- // be rounded away from zero.
- if (j1 >= 0) {
- if (dig == '9')
- goto round9up;
- dig++;
- }
- }
- *s++ = dig;
- goto ret;
- }
- if (j1 > 0) {
- if (dig == '9') { /* possible if i == 1 */
-round9up:
- *s++ = '9';
- goto roundoff;
- }
- *s++ = dig + 1;
- goto ret;
- }
- *s++ = dig;
- if (i == ilim)
- break;
- multadd(b, 10, 0);
- multadd(mlo, 10, 0);
- multadd(mhi, 10, 0);
- }
- } else {
- for (i = 1;; i++) {
- *s++ = dig = quorem(b, S) + '0';
- if (!b.words()[0] && b.size() <= 1)
- goto ret;
- if (i >= ilim)
- break;
- multadd(b, 10, 0);
- }
- }
-
- /* Round off last digit */
-
- lshift(b, 1);
- j = cmp(b, S);
- // For IEEE-754 round-to-even, this check should be (j > 0 || (!j && (dig & 1))),
- // but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed()) should
- // be rounded away from zero.
- if (j >= 0) {
-roundoff:
- while (*--s == '9')
- if (s == s0) {
- k++;
- *s++ = '1';
- goto ret;
- }
- ++*s++;
- } else {
- while (*--s == '0') { }
- s++;
- }
- goto ret;
-noDigits:
- exponentOut = 0;
- precisionOut = 1;
- result[0] = '0';
- result[1] = '\0';
- return;
-oneDigit:
- *s++ = '1';
- k++;
- goto ret;
-ret:
- ASSERT(s > result);
- *s = 0;
- exponentOut = k;
- precisionOut = s - result;
-}
-
-void dtoa(DtoaBuffer result, double dd, bool& sign, int& exponent, unsigned& precision)
-{
- // flags are roundingNone, leftright.
- dtoa<true, false, false, true>(result, dd, 0, sign, exponent, precision);
-}
-
-void dtoaRoundSF(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision)
-{
- // flag is roundingSignificantFigures.
- dtoa<false, true, false, false>(result, dd, ndigits, sign, exponent, precision);
-}
-
-void dtoaRoundDP(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision)
-{
- // flag is roundingDecimalPlaces.
- dtoa<false, false, true, false>(result, dd, ndigits, sign, exponent, precision);
-}
-
-static ALWAYS_INLINE void copyAsciiToUTF16(UChar* next, const char* src, unsigned size)
-{
- for (unsigned i = 0; i < size; ++i)
- *next++ = *src++;
-}
-
-unsigned numberToString(double d, NumberToStringBuffer buffer)
-{
- // Handle NaN and Infinity.
- if (isnan(d) || isinf(d)) {
- if (isnan(d)) {
- copyAsciiToUTF16(buffer, "NaN", 3);
- return 3;
- }
- if (d > 0) {
- copyAsciiToUTF16(buffer, "Infinity", 8);
- return 8;
- }
- copyAsciiToUTF16(buffer, "-Infinity", 9);
- return 9;
- }
-
- // Convert to decimal with rounding.
- DecimalNumber number(d);
- return number.exponent() >= -6 && number.exponent() < 21
- ? number.toStringDecimal(buffer, NumberToStringBufferLength)
- : number.toStringExponential(buffer, NumberToStringBufferLength);
-}
-
-} // namespace WTF
projects / apple / javascriptcore.git / blobdiff