Merge WebKit at r75315: Initial merge by git.

Change-Id: I570314b346ce101c935ed22a626b48c2af266b84

1 files changed, 1831 insertions, 0 deletions

diff --git a/Source/JavaScriptCore/wtf/dtoa.cpp b/Source/JavaScriptCore/wtf/dtoa.cpp
new file mode 100644
index 0000000..c89c036
--- /dev/null
+++ b/Source/JavaScriptCore/wtf/dtoa.cpp
@@ -0,0 +1,1831 @@
+/****************************************************************
+ *
+ * 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(JSC_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 : Noncopyable {
+    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(JSC_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(JSC_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(JSC_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(JSC_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