FCL/sf/mw/qtwebkit: comparison JavaScriptCore/wtf/dtoa.cpp

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--1:000000000000
+:4f2f89ce4247
+/****************************************************************
+*
+* The author of this software is David M. Gay.
+*
+* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
+* Copyright (C) 2002, 2005, 2006, 2007, 2008 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
+Bell Laboratories, Room 2C-463
+600 Mountain Avenue
+Murray Hill, NJ 07974-0636
+U.S.A.
+dmg@bell-labs.com
+*/
+/* 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.
+*    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).
+*/
+/*
+* #define IEEE_8087 for IEEE-arithmetic machines where the least
+*    significant byte has the lowest address.
+* #define IEEE_MC68k for IEEE-arithmetic machines where the most
+*    significant byte has the lowest address.
+* #define No_leftright to omit left-right logic in fast floating-point
+*    computation of dtoa.
+* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+*    and Honor_FLT_ROUNDS is not #defined.
+* #define Inaccurate_Divide for IEEE-format with correctly rounded
+*    products but inaccurate quotients, e.g., for Intel i860.
+* #define USE_LONG_LONG on machines that have a "long long"
+*    integer type (of >= 64 bits), and performance testing shows that
+*    it is faster than 32-bit fallback (which is often not the case
+*    on 32-bit machines). On such machines, you can #define Just_16
+*    to store 16 bits per 32-bit int32_t when doing high-precision integer
+*    arithmetic.  Whether this speeds things up or slows things down
+*    depends on the machine and the number being converted.
+* #define Bad_float_h if your system lacks a float.h or if it does not
+*    define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
+*    FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
+* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
+*    Infinity and NaN (case insensitively).  On some systems (e.g.,
+*    some HP systems), it may be necessary to #define NAN_WORD0
+*    appropriately -- to the most significant word of a quiet NaN.
+*    (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
+*    When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
+*    strtod also accepts (case insensitively) strings of the form
+*    NaN(x), where x is a string of hexadecimal digits and spaces;
+*    if there is only one string of hexadecimal digits, it is taken
+*    for the 52 fraction bits of the resulting NaN; if there are two
+*    or more strings of hex digits, the first is for the high 20 bits,
+*    the second and subsequent for the low 32 bits, with intervening
+*    white space ignored; but if this results in none of the 52
+*    fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
+*    and NAN_WORD1 are used instead.
+* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
+*    avoids underflows on inputs whose result does not underflow.
+*    If you #define NO_IEEE_Scale on a machine that uses IEEE-format
+*    floating-point numbers and flushes underflows to zero rather
+*    than implementing gradual underflow, then you must also #define
+*    Sudden_Underflow.
+* #define YES_ALIAS to permit aliasing certain double values with
+*    arrays of ULongs.  This leads to slightly better code with
+*    some compilers and was always used prior to 19990916, but it
+*    is not strictly legal and can cause trouble with aggressively
+*    optimizing compilers (e.g., gcc 2.95.1 under -O2).
+* #define SET_INEXACT if IEEE arithmetic is being used and extra
+*    computation should be done to set the inexact flag when the
+*    result is inexact and avoid setting inexact when the result
+*    is exact.  In this case, dtoa.c must be compiled in
+*    an environment, perhaps provided by #include "dtoa.c" in a
+*    suitable wrapper, that defines two functions,
+*        int get_inexact(void);
+*        void clear_inexact(void);
+*    such that get_inexact() returns a nonzero value if the
+*    inexact bit is already set, and clear_inexact() sets the
+*    inexact bit to 0.  When SET_INEXACT is #defined, strtod
+*    also does extra computations to set the underflow and overflow
+*    flags when appropriate (i.e., when the result is tiny and
+*    inexact or when it is a numeric value rounded to +-infinity).
+* #define NO_ERRNO if strtod should not assign errno = ERANGE when
+*    the result overflows to +-Infinity or underflows to 0.
+*/
+#include "config.h"
+#include "dtoa.h"
+#if HAVE(ERRNO_H)
+#include <errno.h>
+#else
+#define NO_ERRNO
+#endif
+#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/FastMalloc.h>
+#include <wtf/MathExtras.h>
+#include <wtf/Threading.h>
+#include <wtf/Vector.h>
+#if COMPILER(MSVC)
+#pragma warning(disable: 4244)
+#pragma warning(disable: 4245)
+#pragma warning(disable: 4554)
+#endif
+#if CPU(BIG_ENDIAN)
+#define IEEE_MC68k
+#elif CPU(MIDDLE_ENDIAN)
+#define IEEE_ARM
+#else
+#define IEEE_8087
+#endif
+#define INFNAN_CHECK
+#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(IEEE_ARM) != 1
+Exactly one of IEEE_8087, IEEE_ARM or IEEE_MC68k should be defined.
+#endif
+namespace WTF {
+#if ENABLE(JSC_MULTIPLE_THREADS)
+Mutex* s_dtoaP5Mutex;
+#endif
+typedef union {
+double d;
+uint32_t L[2];
+} U;
+#ifdef YES_ALIAS
+#define dval(x) x
+#ifdef IEEE_8087
+#define word0(x) ((uint32_t*)&x)[1]
+#define word1(x) ((uint32_t*)&x)[0]
+#else
+#define word0(x) ((uint32_t*)&x)[0]
+#define word1(x) ((uint32_t*)&x)[1]
+#endif
+#else
+#ifdef IEEE_8087
+#define word0(x) (x)->L[1]
+#define word1(x) (x)->L[0]
+#else
+#define word0(x) (x)->L[0]
+#define word1(x) (x)->L[1]
+#endif
+#define dval(x) (x)->d
+#endif
+/* 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 defined(IEEE_8087) || defined(IEEE_ARM)
+p16[1] = high;
+p16[0] = low;
+#else
+p16[0] = high;
+p16[1] = 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
+#if !defined(NO_IEEE_Scale)
+#undef Avoid_Underflow
+#define Avoid_Underflow
+#endif
+#if !defined(Flt_Rounds)
+#if defined(FLT_ROUNDS)
+#define Flt_Rounds FLT_ROUNDS
+#else
+#define Flt_Rounds 1
+#endif
+#endif /* Flt_Rounds */
+#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
+// FIXME: we should remove non-Pack_32 mode since it is unused and unmaintained
+#ifndef Pack_32
+#define Pack_32
+#endif
+#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
+#ifndef USE_LONG_LONG
+#ifdef Just_16
+#undef Pack_32
+/* When Pack_32 is not defined, we store 16 bits per 32-bit int32_t.
+* This makes some inner loops simpler and sometimes saves work
+* during multiplications, but it often seems to make things slightly
+* slower.  Hence the default is now to store 32 bits per int32_t.
+*/
+#endif
+#endif
+#define Kmax 15
+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
+#ifdef Pack_32
+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);
+#else
+uint32_t y = *x * m + carry;
+carry = y >> 16;
+*x++ = y & 0xffff;
+#endif
+#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)
+{
+int k;
+int32_t y;
+int32_t x = (nd + 8) / 9;
+for (k = 0, y = 1; x > y; y <<= 1, k++) { }
+#ifdef Pack_32
+b.sign = 0;
+b.resize(1);
+b.words()[0] = y9;
+#else
+b.sign = 0;
+b.resize((b->x[1] = y9 >> 16) ? 2 : 1);
+b.words()[0] = y9 & 0xffff;
+#endif
+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 & 1)
+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
+#ifdef Pack_32
+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;
+}
+}
+#else
+for (; xb < xbe; xc0++) {
+if ((y = *xb++)) {
+x = xa;
+xc = xc0;
+carry = 0;
+do {
+z = *x++ * y + *xc + carry;
+carry = z >> 16;
+*xc++ = z & 0xffff;
+} while (x < xae);
+*xc = carry;
+}
+}
+#endif
+#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)
+{
+#ifdef Pack_32
+int n = k >> 5;
+#else
+int n = k >> 4;
+#endif
+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;
+#ifdef Pack_32
+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
+if (k &= 0xf) {
+uint32_t hiSubword = 0;
+int s = 16 - k;
+for (; src >= srcStart; --src) {
+*dst-- = hiSubword | *src >> s;
+hiSubword = (*src << k) & 0xffff;
+}
+*dst = hiSubword;
+ASSERT(dst == dstStart + n);
+result->wds = b->wds + n + !!result->x[n1 - 1];
+}
+#endif
+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;
+#ifdef Pack_32
+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);
+}
+#else
+do {
+uint32_t y = *xa++ - *xb++ - borrow;
+borrow = (y & 0x10000) >> 16;
+*xc++ = y & 0xffff;
+} while (xb < xbe);
+while (xa < xae) {
+uint32_t y = *xa++ - borrow;
+borrow = (y & 0x10000) >> 16;
+*xc++ = y & 0xffff;
+}
+#endif
+#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;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+if (L > 0) {
+#endif
+#endif
+word0(&u) = L;
+word1(&u) = 0;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+} else {
+L = -L >> Exp_shift;
+if (L < Exp_shift) {
+word0(&u) = 0x80000 >> L;
+word1(&u) = 0;
+} else {
+word0(&u) = 0;
+L -= Exp_shift;
+word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
+}
+}
+#endif
+#endif
+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;
+#ifdef Pack_32
+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;
+}
+#else
+if (k < Ebits + 16) {
+z = xa > xa0 ? *--xa : 0;
+d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
+w = xa > xa0 ? *--xa : 0;
+y = xa > xa0 ? *--xa : 0;
+d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
+goto returnD;
+}
+z = xa > xa0 ? *--xa : 0;
+w = xa > xa0 ? *--xa : 0;
+k -= Ebits + 16;
+d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
+y = xa > xa0 ? *--xa : 0;
+d1 = w << k + 16 | y << k;
+#endif
+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;
+#ifndef Sudden_Underflow
+int i;
+#endif
+#define d0 word0(d)
+#define d1 word1(d)
+b.sign = 0;
+#ifdef Pack_32
+b.resize(1);
+#else
+b.resize(2);
+#endif
+x = b.words();
+z = d0 & Frac_mask;
+d0 &= 0x7fffffff;    /* clear sign bit, which we ignore */
+#ifdef Sudden_Underflow
+de = (int)(d0 >> Exp_shift);
+#else
+if ((de = (int)(d0 >> Exp_shift)))
+z |= Exp_msk1;
+#endif
+#ifdef Pack_32
+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;
+}
+#ifndef Sudden_Underflow
+i = b.size();
+#endif
+} else {
+k = lo0bits(&z);
+x[0] = z;
+#ifndef Sudden_Underflow
+i = 1;
+#endif
+b.resize(1);
+k += 32;
+}
+#else
+if ((y = d1)) {
+if ((k = lo0bits(&y))) {
+if (k >= 16) {
+x[0] = y | z << 32 - k & 0xffff;
+x[1] = z >> k - 16 & 0xffff;
+x[2] = z >> k;
+i = 2;
+} else {
+x[0] = y & 0xffff;
+x[1] = y >> 16 | z << 16 - k & 0xffff;
+x[2] = z >> k & 0xffff;
+x[3] = z >> k + 16;
+i = 3;
+}
+} else {
+x[0] = y & 0xffff;
+x[1] = y >> 16;
+x[2] = z & 0xffff;
+x[3] = z >> 16;
+i = 3;
+}
+} else {
+k = lo0bits(&z);
+if (k >= 16) {
+x[0] = z;
+i = 0;
+} else {
+x[0] = z & 0xffff;
+x[1] = z >> 16;
+i = 1;
+}
+k += 32;
+} while (!x[i])
+--i;
+b->resize(i + 1);
+#endif
+#ifndef Sudden_Underflow
+if (de) {
+#endif
+*e = de - Bias - (P - 1) + k;
+*bits = P - k;
+#ifndef Sudden_Underflow
+} else {
+*e = de - Bias - (P - 1) + 1 + k;
+#ifdef Pack_32
+*bits = (32 * i) - hi0bits(x[i - 1]);
+#else
+*bits = (i + 2) * 16 - hi0bits(x[i]);
+#endif
+}
+#endif
+}
+#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);
+#ifdef Pack_32
+k = ka - kb + 32 * (a.size() - b.size());
+#else
+k = ka - kb + 16 * (a.size() - b.size());
+#endif
+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,
+#ifdef Avoid_Underflow
+9007199254740992. * 9007199254740992.e-256
+/* = 2^106 * 1e-53 */
+#else
+1e-256
+#endif
+};
+/* 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
+#if defined(INFNAN_CHECK)
+#ifndef NAN_WORD0
+#define NAN_WORD0 0x7ff80000
+#endif
+#ifndef NAN_WORD1
+#define NAN_WORD1 0
+#endif
+static int match(const char** sp, const char* t)
+{
+int c, d;
+const char* s = *sp;
+while ((d = *t++)) {
+if ((c = *++s) >= 'A' && c <= 'Z')
+c += 'a' - 'A';
+if (c != d)
+return 0;
+}
+*sp = s + 1;
+return 1;
+}
+#ifndef No_Hex_NaN
+static void hexnan(U* rvp, const char** sp)
+{
+uint32_t c, x[2];
+const char* s;
+int havedig, udx0, xshift;
+x[0] = x[1] = 0;
+havedig = xshift = 0;
+udx0 = 1;
+s = *sp;
+while ((c = *(const unsigned char*)++s)) {
+if (c >= '0' && c <= '9')
+c -= '0';
+else if (c >= 'a' && c <= 'f')
+c += 10 - 'a';
+else if (c >= 'A' && c <= 'F')
+c += 10 - 'A';
+else if (c <= ' ') {
+if (udx0 && havedig) {
+udx0 = 0;
+xshift = 1;
+}
+continue;
+} else if (/*(*/ c == ')' && havedig) {
+*sp = s + 1;
+break;
+} else
+return;    /* invalid form: don't change *sp */
+havedig = 1;
+if (xshift) {
+xshift = 0;
+x[0] = x[1];
+x[1] = 0;
+}
+if (udx0)
+x[0] = (x[0] << 4) | (x[1] >> 28);
+x[1] = (x[1] << 4) | c;
+}
+if ((x[0] &= 0xfffff) || x[1]) {
+word0(rvp) = Exp_mask | x[0];
+word1(rvp) = x[1];
+}
+}
+#endif /*No_Hex_NaN*/
+#endif /* INFNAN_CHECK */
+double strtod(const char* s00, char** se)
+{
+#ifdef Avoid_Underflow
+int scale;
+#endif
+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;
+#ifdef SET_INEXACT
+int inexact, oldinexact;
+#endif
+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) {
+#ifdef INFNAN_CHECK
+/* Check for Nan and Infinity */
+switch (c) {
+case 'i':
+case 'I':
+if (match(&s, "nf")) {
+--s;
+if (!match(&s, "inity"))
+++s;
+word0(&rv) = 0x7ff00000;
+word1(&rv) = 0;
+goto ret;
+}
+break;
+case 'n':
+case 'N':
+if (match(&s, "an")) {
+word0(&rv) = NAN_WORD0;
+word1(&rv) = NAN_WORD1;
+#ifndef No_Hex_NaN
+if (*s == '(') /*)*/
+hexnan(&rv, &s);
+#endif
+goto ret;
+}
+}
+#endif /* INFNAN_CHECK */
+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) {
+#ifdef SET_INEXACT
+if (k > DBL_DIG)
+oldinexact = get_inexact();
+#endif
+dval(&rv) = tens[k - 9] * dval(&rv) + z;
+}
+if (nd <= DBL_DIG && Flt_Rounds == 1) {
+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;
+}
+}
+#ifndef Inaccurate_Divide
+else if (e >= -Ten_pmax) {
+/* rv = */ rounded_quotient(dval(&rv), tens[-e]);
+goto ret;
+}
+#endif
+}
+e1 += nd - k;
+#ifdef SET_INEXACT
+inexact = 1;
+if (k <= DBL_DIG)
+oldinexact = get_inexact();
+#endif
+#ifdef Avoid_Underflow
+scale = 0;
+#endif
+/* 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:
+#ifndef NO_ERRNO
+errno = ERANGE;
+#endif
+/* Can't trust HUGE_VAL */
+word0(&rv) = Exp_mask;
+word1(&rv) = 0;
+#ifdef SET_INEXACT
+/* set overflow bit */
+dval(&rv0) = 1e300;
+dval(&rv0) *= dval(&rv0);
+#endif
+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;
+#ifdef Avoid_Underflow
+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; zap 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;
+}
+#else
+for (j = 0; e1 > 1; j++, e1 >>= 1)
+if (e1 & 1)
+dval(&rv) *= tinytens[j];
+/* The last multiplication could underflow. */
+dval(&rv0) = dval(&rv);
+dval(&rv) *= tinytens[j];
+if (!dval(&rv)) {
+dval(&rv) = 2. * dval(&rv0);
+dval(&rv) *= tinytens[j];
+#endif
+if (!dval(&rv)) {
+undfl:
+dval(&rv) = 0.;
+#ifndef NO_ERRNO
+errno = ERANGE;
+#endif
+goto ret;
+}
+#ifndef Avoid_Underflow
+word0(&rv) = Tiny0;
+word1(&rv) = Tiny1;
+/* The refinement below will clean
+* this approximation up.
+*/
+}
+#endif
+}
+}
+/* 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;
+#ifdef Avoid_Underflow
+j = bbe - scale;
+i = j + bbbits - 1;    /* logb(rv) */
+if (i < Emin)    /* denormal */
+j += P - Emin;
+else
+j = P + 1 - bbbits;
+#else /*Avoid_Underflow*/
+#ifdef Sudden_Underflow
+j = P + 1 - bbbits;
+#else /*Sudden_Underflow*/
+j = bbe;
+i = j + bbbits - 1;    /* logb(rv) */
+if (i < Emin)    /* denormal */
+j += P - Emin;
+else
+j = P + 1 - bbbits;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+bb2 += j;
+bd2 += j;
+#ifdef Avoid_Underflow
+bd2 += scale;
+#endif
+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
+#ifdef Avoid_Underflow
+|| (word0(&rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
+#else
+|| (word0(&rv) & Exp_mask) <= Exp_msk1
+#endif
+) {
+#ifdef SET_INEXACT
+if (!delta->words()[0] && delta->size() <= 1)
+inexact = 0;
+#endif
+break;
+}
+if (!delta.words()[0] && delta.size() <= 1) {
+/* exact result */
+#ifdef SET_INEXACT
+inexact = 0;
+#endif
+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) == (
+#ifdef Avoid_Underflow
+(scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
+? (0xffffffff & (0xffffffff << (2 * P + 1 - (y >> Exp_shift)))) :
+#endif
+0xffffffff)) {
+/*boundary case -- increment exponent*/
+word0(&rv) = (word0(&rv) & Exp_mask) + Exp_msk1;
+word1(&rv) = 0;
+#ifdef Avoid_Underflow
+dsign = 0;
+#endif
+break;
+}
+} else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
+dropDown:
+/* boundary case -- decrement exponent */
+#ifdef Sudden_Underflow /*{{*/
+L = word0(&rv) & Exp_mask;
+#ifdef Avoid_Underflow
+if (L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1))
+#else
+if (L <= Exp_msk1)
+#endif /*Avoid_Underflow*/
+goto undfl;
+L -= Exp_msk1;
+#else /*Sudden_Underflow}{*/
+#ifdef Avoid_Underflow
+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;
+}
+}
+#endif /*Avoid_Underflow*/
+L = (word0(&rv) & Exp_mask) - Exp_msk1;
+#endif /*Sudden_Underflow}}*/
+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);
+#ifndef Sudden_Underflow
+if (!dval(&rv))
+goto undfl;
+#endif
+}
+#ifdef Avoid_Underflow
+dsign = 1 - dsign;
+#endif
+break;
+}
+if ((aadj = ratio(delta, bs)) <= 2.) {
+if (dsign)
+aadj = aadj1 = 1.;
+else if (word1(&rv) || word0(&rv) & Bndry_mask) {
+#ifndef Sudden_Underflow
+if (word1(&rv) == Tiny1 && !word0(&rv))
+goto undfl;
+#endif
+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;
+#ifdef Check_FLT_ROUNDS
+switch (Rounding) {
+case 2: /* towards +infinity */
+aadj1 -= 0.5;
+break;
+case 0: /* towards 0 */
+case 3: /* towards -infinity */
+aadj1 += 0.5;
+}
+#else
+if (!Flt_Rounds)
+aadj1 += 0.5;
+#endif /*Check_FLT_ROUNDS*/
+}
+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 {
+#ifdef Avoid_Underflow
+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;
+#else
+#ifdef Sudden_Underflow
+if ((word0(&rv) & Exp_mask) <= P * Exp_msk1) {
+dval(&rv0) = dval(&rv);
+word0(&rv) += P * Exp_msk1;
+adj.d = aadj1 * ulp(&rv);
+dval(&rv) += adj.d;
+if ((word0(&rv) & Exp_mask) <= P * Exp_msk1) {
+if (word0(&rv0) == Tiny0 && word1(&rv0) == Tiny1)
+goto undfl;
+word0(&rv) = Tiny0;
+word1(&rv) = Tiny1;
+goto cont;
+}
+word0(&rv) -= P * Exp_msk1;
+} else {
+adj.d = aadj1 * ulp(&rv);
+dval(&rv) += adj.d;
+}
+#else /*Sudden_Underflow*/
+/* Compute adj so that the IEEE rounding rules will
+* correctly round rv + adj in some half-way cases.
+* If rv * ulp(rv) is denormalized (i.e.,
+* y <= (P - 1) * Exp_msk1), we must adjust aadj to avoid
+* trouble from bits lost to denormalization;
+* example: 1.2e-307 .
+*/
+if (y <= (P - 1) * Exp_msk1 && aadj > 1.) {
+aadj1 = (double)(int)(aadj + 0.5);
+if (!dsign)
+aadj1 = -aadj1;
+}
+adj.d = aadj1 * ulp(&rv);
+dval(&rv) += adj.d;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+}
+z = word0(&rv) & Exp_mask;
+#ifndef SET_INEXACT
+#ifdef Avoid_Underflow
+if (!scale)
+#endif
+if (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;
+}
+#endif
+cont:
+{}
+}
+#ifdef SET_INEXACT
+if (inexact) {
+if (!oldinexact) {
+word0(&rv0) = Exp_1 + (70 << Exp_shift);
+word1(&rv0) = 0;
+dval(&rv0) += 1.;
+}
+} else if (!oldinexact)
+clear_inexact();
+#endif
+#ifdef Avoid_Underflow
+if (scale) {
+word0(&rv0) = Exp_1 - 2 * P * Exp_msk1;
+word1(&rv0) = 0;
+dval(&rv) *= dval(&rv0);
+#ifndef NO_ERRNO
+/* try to avoid the bug of testing an 8087 register value */
+if (!word0(&rv) && !word1(&rv))
+errno = ERANGE;
+#endif
+}
+#endif /* Avoid_Underflow */
+#ifdef SET_INEXACT
+if (inexact && !(word0(&rv) & Exp_mask)) {
+/* set underflow bit */
+dval(&rv0) = 1e-300;
+dval(&rv0) *= dval(&rv0);
+}
+#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;
+#ifdef Pack_32
+uint32_t si, z, zs;
+#endif
+#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
+#ifdef Pack_32
+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);
+#else
+ys = *sx++ * q + carry;
+carry = ys >> 16;
+y = *bx - (ys & 0xffff) - borrow;
+borrow = (y & 0x10000) >> 16;
+*bx++ = y & 0xffff;
+#endif
+#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
+#ifdef Pack_32
+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);
+#else
+ys = *sx++ + carry;
+carry = ys >> 16;
+y = *bx - (ys & 0xffff) - borrow;
+borrow = (y & 0x10000) >> 16;
+*bx++ = y & 0xffff;
+#endif
+#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. 92-101].
+*
+* 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.
+*/
+void dtoa(DtoaBuffer result, double dd, int ndigits, int* decpt, int* sign, char** rve)
+{
+/*
+Arguments ndigits, decpt, sign are similar to those
+of ecvt and fcvt; trailing zeros are suppressed from
+the returned string.  If not null, *rve is set to point
+to the end of the return value.  If d is +-Infinity or NaN,
+then *decpt is set to 9999.
+*/
+int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
+j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+spec_case, try_quick;
+int32_t L;
+#ifndef Sudden_Underflow
+int denorm;
+uint32_t x;
+#endif
+BigInt b, b1, delta, mlo, mhi, S;
+U d2, eps, u;
+double ds;
+char* s;
+char* s0;
+#ifdef SET_INEXACT
+int inexact, oldinexact;
+#endif
+u.d = dd;
+if (word0(&u) & Sign_bit) {
+/* set sign for everything, including 0's and NaNs */
+*sign = 1;
+word0(&u) &= ~Sign_bit;    /* clear sign bit */
+} else
+*sign = 0;
+if ((word0(&u) & Exp_mask) == Exp_mask) {
+/* Infinity or NaN */
+*decpt = 9999;
+if (!word1(&u) && !(word0(&u) & 0xfffff)) {
+strcpy(result, "Infinity");
+if (rve)
+*rve = result + 8;
+} else {
+strcpy(result, "NaN");
+if (rve)
+*rve = result + 3;
+}
+return;
+}
+if (!dval(&u)) {
+*decpt = 1;
+result[0] = '0';
+result[1] = '\0';
+if (rve)
+*rve = result + 1;
+return;
+}
+#ifdef SET_INEXACT
+try_quick = oldinexact = get_inexact();
+inexact = 1;
+#endif
+d2b(b, &u, &be, &bbits);
+#ifdef Sudden_Underflow
+i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
+#else
+if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
+#endif
+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;
+#ifndef Sudden_Underflow
+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;
+}
+#endif
+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;
+}
+#ifndef SET_INEXACT
+#ifdef Check_FLT_ROUNDS
+try_quick = Rounding == 1;
+#else
+try_quick = 1;
+#endif
+#endif /*SET_INEXACT*/
+leftright = 1;
+ilim = ilim1 = -1;
+i = 18;
+ndigits = 0;
+s = s0 = result;
+if (ilim >= 0 && ilim <= Quick_max && try_quick) {
+/* 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;
+}
+#ifndef No_leftright
+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 {
+#endif
+/* 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;
+}
+}
+#ifndef No_leftright
+}
+#endif
+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;
+#ifdef Check_FLT_ROUNDS
+/* If FLT_ROUNDS == 2, L will usually be high by 1 */
+if (dval(&u) < 0) {
+L--;
+dval(&u) += ds;
+}
+#endif
+*s++ = '0' + (int)L;
+if (!dval(&u)) {
+#ifdef SET_INEXACT
+inexact = 0;
+#endif
+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 =
+#ifndef Sudden_Underflow
+denorm ? be + (Bias + (P - 1) - 1 + 1) :
+#endif
+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 (!word1(&u) && !(word0(&u) & Bndry_mask)
+#ifndef Sudden_Underflow
+&& word0(&u) & (Exp_mask & ~Exp_msk1)
+#endif
+) {
+/* 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.
+*/
+#ifdef Pack_32
+if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0x1f))
+i = 32 - i;
+#else
+if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0xf))
+i = 16 - i;
+#endif
+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 (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) {
+mhi = mlo;
+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);
+if (!j1 && !(word1(&u) & 1)) {
+if (dig == '9')
+goto round9up;
+if (j > 0)
+dig++;
+#ifdef SET_INEXACT
+else if (!b->x[0] && b->wds <= 1)
+inexact = 0;
+#endif
+*s++ = dig;
+goto ret;
+}
+if (j < 0 || (!j && !(word1(&u) & 1))) {
+if (!b.words()[0] && b.size() <= 1) {
+#ifdef SET_INEXACT
+inexact = 0;
+#endif
+goto acceptDig;
+}
+if (j1 > 0) {
+lshift(b, 1);
+j1 = cmp(b, S);
+if ((j1 > 0 || (!j1 && (dig & 1))) && dig++ == '9')
+goto round9up;
+}
+acceptDig:
+*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) {
+#ifdef SET_INEXACT
+inexact = 0;
+#endif
+goto ret;
+}
+if (i >= ilim)
+break;
+multadd(b, 10, 0);
+}
+/* Round off last digit */
+lshift(b, 1);
+j = cmp(b, S);
+if (j > 0 || (!j && (dig & 1))) {
+roundoff:
+while (*--s == '9')
+if (s == s0) {
+k++;
+*s++ = '1';
+goto ret;
+}
+++*s++;
+} else {
+while (*--s == '0') { }
+s++;
+}
+goto ret;
+noDigits:
+k = -1 - ndigits;
+goto ret;
+oneDigit:
+*s++ = '1';
+k++;
+goto ret;
+ret:
+#ifdef SET_INEXACT
+if (inexact) {
+if (!oldinexact) {
+word0(&u) = Exp_1 + (70 << Exp_shift);
+word1(&u) = 0;
+dval(&u) += 1.;
+}
+} else if (!oldinexact)
+clear_inexact();
+#endif
+*s = 0;
+*decpt = k + 1;
+if (rve)
+*rve = s;
+}
+static ALWAYS_INLINE void append(char*& next, const char* src, unsigned size)
+{
+for (unsigned i = 0; i < size; ++i)
+*next++ = *src++;
+}
+void doubleToStringInJavaScriptFormat(double d, DtoaBuffer buffer, unsigned* resultLength)
+{
+ASSERT(buffer);
+// avoid ever printing -NaN, in JS conceptually there is only one NaN value
+if (isnan(d)) {
+append(buffer, "NaN", 3);
+if (resultLength)
+*resultLength = 3;
+return;
+}
+// -0 -> "0"
+if (!d) {
+buffer[0] = '0';
+if (resultLength)
+*resultLength = 1;
+return;
+}
+int decimalPoint;
+int sign;
+DtoaBuffer result;
+char* resultEnd = 0;
+WTF::dtoa(result, d, 0, &decimalPoint, &sign, &resultEnd);
+int length = resultEnd - result;
+char* next = buffer;
+if (sign)
+*next++ = '-';
+if (decimalPoint <= 0 && decimalPoint > -6) {
+*next++ = '0';
+*next++ = '.';
+for (int j = decimalPoint; j < 0; j++)
+*next++ = '0';
+append(next, result, length);
+} else if (decimalPoint <= 21 && decimalPoint > 0) {
+if (length <= decimalPoint) {
+append(next, result, length);
+for (int j = 0; j < decimalPoint - length; j++)
+*next++ = '0';
+} else {
+append(next, result, decimalPoint);
+*next++ = '.';
+append(next, result + decimalPoint, length - decimalPoint);
+}
+} else if (result[0] < '0' || result[0] > '9')
+append(next, result, length);
+else {
+*next++ = result[0];
+if (length > 1) {
+*next++ = '.';
+append(next, result + 1, length - 1);
+}
+*next++ = 'e';
+*next++ = (decimalPoint >= 0) ? '+' : '-';
+// decimalPoint can't be more than 3 digits decimal given the
+// nature of float representation
+int exponential = decimalPoint - 1;
+if (exponential < 0)
+exponential = -exponential;
+if (exponential >= 100)
+*next++ = static_cast<char>('0' + exponential / 100);
+if (exponential >= 10)
+*next++ = static_cast<char>('0' + (exponential % 100) / 10);
+*next++ = static_cast<char>('0' + exponential % 10);
+}
+if (resultLength)
+*resultLength = next - buffer;
+}
+} // namespace WTF