--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/JavaScriptCore/wtf/dtoa.cpp Fri Sep 17 09:02:29 2010 +0300
@@ -0,0 +1,2483 @@
+/****************************************************************
+ *
+ * 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