blob: c831e2204fd7f0efc8bcf7566eab1e18da744344 [file] [log] [blame]
/****************************************************************
*
* 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, 2012 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.
*/
#include "config.h"
#include "dtoa.h"
#include "wtf/CPU.h"
#include "wtf/MathExtras.h"
#include "wtf/ThreadingPrimitives.h"
#include "wtf/Vector.h"
#include <string.h>
#if COMPILER(MSVC)
#pragma warning(disable: 4244)
#pragma warning(disable: 4245)
#pragma warning(disable: 4554)
#endif
namespace WTF {
Mutex* s_dtoaP5Mutex;
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
#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(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
#ifndef USE_LONG_LONG
/* 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;
}
#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 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); USING_FAST_MALLOC(P5Node);
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;
s_dtoaP5Mutex->lock();
P5Node* p5 = p5s;
if (!p5) {
/* first time */
p5 = new P5Node;
i2b(p5->val, 625);
p5->next = 0;
p5s = p5;
p5sCount = 1;
}
int p5sCountLocal = p5sCount;
s_dtoaP5Mutex->unlock();
int p5sUsed = 0;
for (;;) {
if (k & 1)
mult(b, p5->val);
if (!(k >>= 1))
break;
if (++p5sUsed == p5sCountLocal) {
s_dtoaP5Mutex->lock();
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;
s_dtoaP5Mutex->unlock();
}
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 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 = 0 - Bias - (P - 1) + 1 + k;
*bits = (32 * i) - hi0bits(x[i - 1]);
}
}
#undef d0
#undef d1
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 };
#define Scale_Bit 0x10
#define n_bigtens 5
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(std::isfinite(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);
}
const char* numberToString(double d, NumberToStringBuffer buffer)
{
double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength);
const double_conversion::DoubleToStringConverter& converter = double_conversion::DoubleToStringConverter::EcmaScriptConverter();
converter.ToShortest(d, &builder);
return builder.Finalize();
}
static inline const char* formatStringTruncatingTrailingZerosIfNeeded(NumberToStringBuffer buffer, double_conversion::StringBuilder& builder)
{
size_t length = builder.position();
// If there is an exponent, stripping trailing zeros would be incorrect.
// FIXME: Zeros should be stripped before the 'e'.
if (memchr(buffer, 'e', length))
return builder.Finalize();
size_t decimalPointPosition = 0;
for (; decimalPointPosition < length; ++decimalPointPosition) {
if (buffer[decimalPointPosition] == '.')
break;
}
// No decimal seperator found, early exit.
if (decimalPointPosition == length)
return builder.Finalize();
size_t truncatedLength = length - 1;
for (; truncatedLength > decimalPointPosition; --truncatedLength) {
if (buffer[truncatedLength] != '0')
break;
}
// No trailing zeros found to strip.
if (truncatedLength == length - 1)
return builder.Finalize();
// If we removed all trailing zeros, remove the decimal point as well.
if (truncatedLength == decimalPointPosition) {
ASSERT(truncatedLength > 0);
--truncatedLength;
}
// Truncate the StringBuilder, and return the final result.
builder.SetPosition(truncatedLength + 1);
return builder.Finalize();
}
const char* numberToFixedPrecisionString(double d, unsigned significantFigures, NumberToStringBuffer buffer, bool truncateTrailingZeros)
{
// Mimic String::format("%.[precision]g", ...), but use dtoas rounding facilities.
// "g": Signed value printed in f or e format, whichever is more compact for the given value and precision.
// The e format is used only when the exponent of the value is less than -4 or greater than or equal to the
// precision argument. Trailing zeros are truncated, and the decimal point appears only if one or more digits follow it.
// "precision": The precision specifies the maximum number of significant digits printed.
double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength);
const double_conversion::DoubleToStringConverter& converter = double_conversion::DoubleToStringConverter::EcmaScriptConverter();
converter.ToPrecision(d, significantFigures, &builder);
if (!truncateTrailingZeros)
return builder.Finalize();
// FIXME: Trailing zeros should never be added in the first place. The
// current implementation does not strip when there is an exponent, eg.
// 1.50000e+10.
return formatStringTruncatingTrailingZerosIfNeeded(buffer, builder);
}
const char* numberToFixedWidthString(double d, unsigned decimalPlaces, NumberToStringBuffer buffer)
{
// Mimic String::format("%.[precision]f", ...), but use dtoas rounding facilities.
// "f": Signed value having the form [ - ]dddd.dddd, where dddd is one or more decimal digits.
// The number of digits before the decimal point depends on the magnitude of the number, and
// the number of digits after the decimal point depends on the requested precision.
// "precision": The precision value specifies the number of digits after the decimal point.
// If a decimal point appears, at least one digit appears before it.
// The value is rounded to the appropriate number of digits.
double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength);
const double_conversion::DoubleToStringConverter& converter = double_conversion::DoubleToStringConverter::EcmaScriptConverter();
converter.ToFixed(d, decimalPlaces, &builder);
return builder.Finalize();
}
namespace Internal {
double parseDoubleFromLongString(const UChar* string, size_t length, size_t& parsedLength)
{
Vector<LChar> conversionBuffer(length);
for (size_t i = 0; i < length; ++i)
conversionBuffer[i] = isASCII(string[i]) ? string[i] : 0;
return parseDouble(conversionBuffer.data(), length, parsedLength);
}
} // namespace Internal
} // namespace WTF