* 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.
+ * Copyright (C) 2002, 2005, 2006, 2007, 2008, 2010 Apple Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
*
***************************************************************/
-/* 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
- */
+/* Please send bug reports to David M. Gay (dmg at acm dot org,
+ * with " at " changed at "@" and " dot " changed to "."). */
/* On a machine with IEEE extended-precision registers, it is
* necessary to specify double-precision (53-bit) rounding precision
*
* Modifications:
*
- * 1. We only require IEEE.
+ * 1. We only require IEEE double-precision arithmetic (not IEEE double-extended).
* 2. We get by with floating-point arithmetic in a case that
* Clinger missed -- when we're computing d * 10^n
* for a small integer d and the integer n is not too
* 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 <float.h>
#include <math.h>
#include <stdint.h>
+#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <wtf/AlwaysInline.h>
#include <wtf/Assertions.h>
+#include <wtf/DecimalNumber.h>
#include <wtf/FastMalloc.h>
-#include <wtf/Vector.h>
+#include <wtf/MathExtras.h>
#include <wtf/Threading.h>
-
-#include <stdio.h>
+#include <wtf/UnusedParam.h>
+#include <wtf/Vector.h>
#if COMPILER(MSVC)
#pragma warning(disable: 4244)
#pragma warning(disable: 4554)
#endif
-#if PLATFORM(BIG_ENDIAN)
-#define IEEE_MC68k
-#elif PLATFORM(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)
+#if ENABLE(WTF_MULTIPLE_THREADS)
Mutex* s_dtoaP5Mutex;
#endif
-typedef union { double d; uint32_t L[2]; } U;
+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
+#if CPU(BIG_ENDIAN) || CPU(MIDDLE_ENDIAN)
+#define word0(x) (x)->L[0]
+#define word1(x) (x)->L[1]
#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
- * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+ * *p++ = high << 16 | low & 0xffff;
*/
-#if defined(IEEE_8087) || defined(IEEE_ARM)
-#define Storeinc(a,b,c) (((unsigned short*)a)[1] = (unsigned short)b, ((unsigned short*)a)[0] = (unsigned short)c, a++)
+static ALWAYS_INLINE uint32_t* storeInc(uint32_t* p, uint16_t high, uint16_t low)
+{
+ uint16_t* p16 = reinterpret_cast<uint16_t*>(p);
+#if CPU(BIG_ENDIAN)
+ p16[0] = high;
+ p16[1] = low;
#else
-#define Storeinc(a,b,c) (((unsigned short*)a)[0] = (unsigned short)b, ((unsigned short*)a)[1] = (unsigned short)c, a++)
+ p16[1] = high;
+ p16[0] = low;
#endif
+ return p + 1;
+}
#define Exp_shift 20
#define Exp_shift1 20
#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 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 PLATFORM(PPC64) || PLATFORM(X86_64)
+#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;
sign = 0;
m_words.clear();
}
-
+
size_t size() const
{
return m_words.size();
{
m_words.resize(s);
}
-
+
uint32_t* words()
{
return m_words.data();
{
return m_words.data();
}
-
+
void append(uint32_t w)
{
m_words.append(w);
}
-
+
Vector<uint32_t, 16> m_words;
};
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);
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) {
return k;
}
-static int lo0bits (uint32_t* y)
+static int lo0bits(uint32_t* y)
{
int k;
uint32_t x = *y;
if (!(x & 1)) {
k++;
x >>= 1;
- if (!x & 1)
+ if (!x)
return 32;
}
*y = x;
const BigInt* b = &bRef;
BigInt c;
int wa, wb, wc;
- const uint32_t *x = 0, *xa, *xb, *xae, *xbe;
- uint32_t *xc, *xc0;
+ 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;
a = b;
b = tmp;
}
-
+
wa = a->size();
wb = b->size();
wc = wa + wb;
}
}
#else
-#ifdef Pack_32
for (; xb < xbe; xb++, xc0++) {
if ((y = *xb & 0xffff)) {
x = xa;
carry = z >> 16;
uint32_t z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
- Storeinc(xc, z2, z);
+ xc = storeInc(xc, z2, z);
} while (x < xae);
*xc = carry;
}
do {
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
- Storeinc(xc, z, z2);
+ 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);
}
struct P5Node {
+ WTF_MAKE_NONCOPYABLE(P5Node); WTF_MAKE_FAST_ALLOCATED;
+public:
+ P5Node() { }
BigInt val;
P5Node* next;
};
-
+
static P5Node* p5s;
-static int p5s_count;
+static int p5sCount;
static ALWAYS_INLINE void pow5mult(BigInt& b, int k)
{
if (!(k >>= 2))
return;
-#if ENABLE(JSC_MULTIPLE_THREADS)
+#if ENABLE(WTF_MULTIPLE_THREADS)
s_dtoaP5Mutex->lock();
#endif
P5Node* p5 = p5s;
i2b(p5->val, 625);
p5->next = 0;
p5s = p5;
- p5s_count = 1;
+ p5sCount = 1;
}
- int p5s_count_local = p5s_count;
-#if ENABLE(JSC_MULTIPLE_THREADS)
+ int p5sCountLocal = p5sCount;
+#if ENABLE(WTF_MULTIPLE_THREADS)
s_dtoaP5Mutex->unlock();
#endif
- int p5s_used = 0;
+ int p5sUsed = 0;
for (;;) {
if (k & 1)
if (!(k >>= 1))
break;
- if (++p5s_used == p5s_count_local) {
-#if ENABLE(JSC_MULTIPLE_THREADS)
+ if (++p5sUsed == p5sCountLocal) {
+#if ENABLE(WTF_MULTIPLE_THREADS)
s_dtoaP5Mutex->lock();
#endif
- if (p5s_used == p5s_count) {
+ 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);
- ++p5s_count;
+ ++p5sCount;
}
-
- p5s_count_local = p5s_count;
-#if ENABLE(JSC_MULTIPLE_THREADS)
+
+ p5sCountLocal = p5sCount;
+#if ENABLE(WTF_MULTIPLE_THREADS)
s_dtoaP5Mutex->unlock();
#endif
}
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;
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;
*dst = hiSubword;
ASSERT(dst == dstStart + n);
- b.resize(origSize + n + (b.words()[n1 - 1] != 0));
+ 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] != 0);
- }
- #endif
else {
do {
*--dst = *src--;
const BigInt* a = &aRef;
const BigInt* b = &bRef;
int i, wa, wb;
- uint32_t *xc;
+ uint32_t* xc;
i = cmp(*a, *b);
if (!i) {
}
#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;
- Storeinc(xc, z, y);
+ 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;
- Storeinc(xc, z, y);
+ 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--;
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);
}
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 ret_d;
+ goto returnD;
}
z = xa > xa0 ? *--xa : 0;
if (k -= Ebits) {
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 ret_d;
- }
- 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
-ret_d:
+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, y, z;
-#ifndef Sudden_Underflow
+ uint32_t* x;
+ uint32_t y, z;
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;
- }
+ 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
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 {
}
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
+ 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
+ 9007199254740992. * 9007199254740992.e-256
+ /* = 2^106 * 1e-256 */
};
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
#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;
+ 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++)
+ 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:
+ 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;
s0 = s;
nf += nz;
nz = 0;
- goto have_dig;
+ goto haveDig;
}
- goto dig_done;
+ goto digDone;
}
for (; c >= '0' && c <= '9'; c = *++s) {
-have_dig:
+haveDig:
nz++;
if (c -= '0') {
nf += nz;
}
}
}
-dig_done:
+digDone:
e = 0;
if (c == 'e' || c == 'E') {
- if (!nd && !nz && !nz0) {
+ if (!nd && !nz && !nz0)
goto ret0;
- }
s00 = s;
esign = 0;
switch (c = *++s) {
- case '-':
- esign = 1;
- case '+':
- c = *++s;
+ case '-':
+ esign = 1;
+ case '+':
+ c = *++s;
}
if (c >= '0' && c <= '9') {
while (c == '0')
}
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;
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
+ if (k > 9)
dval(&rv) = tens[k - 9] * dval(&rv) + z;
- }
- if (nd <= DBL_DIG && Flt_Rounds == 1) {
+ if (nd <= DBL_DIG) {
if (!e)
goto ret;
if (e > 0) {
/* rv = */ rounded_product(dval(&rv), tens[e]);
goto ret;
}
- }
-#ifndef Inaccurate_Divide
- else if (e >= -Ten_pmax) {
+ } 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 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
-#ifndef NO_ERRNO
+#if HAVE(ERRNO_H)
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;
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 */
+ /* scaled rv is denormal; clear j low bits */
if (j >= 32) {
word1(&rv) = 0;
if (j >= 53)
- word0(&rv) = (P + 2) * Exp_msk1;
+ word0(&rv) = (P + 2) * Exp_msk1;
else
- word0(&rv) &= 0xffffffff << (j - 32);
+ 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
+#if HAVE(ERRNO_H)
errno = ERANGE;
#endif
goto ret;
}
-#ifndef Avoid_Underflow
- word0(&rv) = Tiny0;
- word1(&rv) = Tiny1;
- /* The refinement below will clean
- * this approximation up.
- */
- }
-#endif
}
}
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;
* 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 drop_down;
+ goto dropDown;
break;
}
- if (i == 0) {
+ 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)) {
-drop_down:
+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) {
goto undfl;
}
}
-#endif /*Avoid_Underflow*/
L = (word0(&rv) & Exp_mask) - Exp_msk1;
-#endif /*Sudden_Underflow}}*/
word0(&rv) = L | Bndry_mask1;
word1(&rv) = 0xffffffff;
break;
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 {
} 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 == 0)
- aadj1 += 0.5;
-#endif /*Check_FLT_ROUNDS*/
}
y = word0(&rv) & Exp_mask;
word0(&rv) = Big0;
word1(&rv) = Big1;
goto cont;
- } else
- word0(&rv) += P * Exp_msk1;
+ }
+ 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)
}
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;
- }
- else
- 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) {
+ if (!scale && y == z) {
/* Can we stop now? */
L = (int32_t)aadj;
aadj -= L;
} 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
+#if HAVE(ERRNO_H)
/* try to avoid the bug of testing an 8087 register value */
- if (word0(&rv) == 0 && word1(&rv) == 0)
+ 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);
static ALWAYS_INLINE int quorem(BigInt& b, BigInt& S)
{
size_t n;
- uint32_t *bx, *bxe, q, *sx, *sxe;
+ 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]);
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);
borrow = (y & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
- 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
+ bx = storeInc(bx, z, y);
#endif
} while (sx <= sxe);
if (!*bxe) {
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);
borrow = (y & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
- Storeinc(bx, z, y);
-#else
- ys = *sx++ + carry;
- carry = ys >> 16;
- y = *bx - (ys & 0xffff) - borrow;
- borrow = (y & 0x10000) >> 16;
- *bx++ = y & 0xffff;
-#endif
+ bx = storeInc(bx, z, y);
#endif
} while (sx <= sxe);
bx = b.words();
/* 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].
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
*
* Modifications:
* 1. Rather than iterating, we use a simple numeric overestimate
* "uniformly" distributed input, the probability is
* something like 10^(k-15) that we must resort to the int32_t
* calculation.
+ *
+ * Note: 'leftright' translates to 'generate shortest possible string'.
*/
-
-void dtoa(char* result, double dd, int ndigits, int* decpt, int* sign, char** rve)
+template<bool roundingNone, bool roundingSignificantFigures, bool roundingDecimalPlaces, bool leftright>
+void dtoa(DtoaBuffer result, double dd, int ndigits, bool& signOut, int& exponentOut, unsigned& precisionOut)
{
- /*
- 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.
+ // Exactly one rounding mode must be specified.
+ ASSERT(roundingNone + roundingSignificantFigures + roundingDecimalPlaces == 1);
+ // roundingNone only allowed (only sensible?) with leftright set.
+ ASSERT(!roundingNone || leftright);
- */
+ ASSERT(!isnan(dd) && !isinf(dd));
int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
- j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
- spec_case, try_quick;
+ j, j1, k, k0, k_check, m2, m5, s2, s5,
+ spec_case;
int32_t L;
-#ifndef Sudden_Underflow
int denorm;
uint32_t x;
-#endif
- BigInt b, b1, delta, mlo, mhi, S;
+ BigInt b, delta, mlo, mhi, S;
U d2, eps, u;
double ds;
- char *s, *s0;
-#ifdef SET_INEXACT
- int inexact, oldinexact;
-#endif
+ char* s;
+ char* s0;
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");
- else
- strcpy(result, "NaN");
- return;
- }
+ /* Infinity or NaN */
+ ASSERT((word0(&u) & Exp_mask) != Exp_mask);
+
+ // JavaScript toString conversion treats -0 as 0.
if (!dval(&u)) {
- *decpt = 1;
+ signOut = false;
+ exponentOut = 0;
+ precisionOut = 1;
result[0] = '0';
result[1] = '\0';
return;
}
-#ifdef SET_INEXACT
- try_quick = oldinexact = get_inexact();
- inexact = 1;
-#endif
+ if (word0(&u) & Sign_bit) {
+ signOut = true;
+ word0(&u) &= ~Sign_bit; // clear sign bit
+ } else
+ signOut = false;
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;
*/
i -= Bias;
-#ifndef Sudden_Underflow
denorm = 0;
} else {
/* d is denormalized */
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)
s5 = 0;
}
-#ifndef SET_INEXACT
-#ifdef Check_FLT_ROUNDS
- try_quick = Rounding == 1;
-#else
- try_quick = 1;
-#endif
-#endif /*SET_INEXACT*/
+ if (roundingNone) {
+ ilim = ilim1 = -1;
+ i = 18;
+ ndigits = 0;
+ }
+ if (roundingSignificantFigures) {
+ if (ndigits <= 0)
+ ndigits = 1;
+ ilim = ilim1 = i = ndigits;
+ }
+ if (roundingDecimalPlaces) {
+ i = ndigits + k + 1;
+ ilim = i;
+ ilim1 = i - 1;
+ if (i <= 0)
+ i = 1;
+ }
- leftright = 1;
- ilim = ilim1 = -1;
- i = 18;
- ndigits = 0;
s = s0 = result;
- if (ilim >= 0 && ilim <= Quick_max && try_quick) {
-
+ if (ilim >= 0 && ilim <= Quick_max) {
/* Try to get by with floating-point arithmetic. */
i = 0;
}
if (k_check && dval(&u) < 1. && ilim > 0) {
if (ilim1 <= 0)
- goto fast_failed;
+ goto fastFailed;
ilim = ilim1;
k--;
dval(&u) *= 10.;
}
dval(&eps) = (ieps * dval(&u)) + 7.;
word0(&eps) -= (P - 1) * Exp_msk1;
- if (ilim == 0) {
+ if (!ilim) {
S.clear();
mhi.clear();
dval(&u) -= 5.;
if (dval(&u) > dval(&eps))
- goto one_digit;
+ goto oneDigit;
if (dval(&u) < -dval(&eps))
- goto no_digits;
- goto fast_failed;
+ goto noDigits;
+ goto fastFailed;
}
-#ifndef No_leftright
if (leftright) {
/* Use Steele & White method of only
* generating digits needed.
if (dval(&u) < dval(&eps))
goto ret;
if (1. - dval(&u) < dval(&eps))
- goto bump_up;
+ 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.) {
*s++ = '0' + (int)L;
if (i == ilim) {
if (dval(&u) > 0.5 + dval(&eps))
- goto bump_up;
- else 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
-fast_failed:
+fastFailed:
s = s0;
dval(&u) = dval(&d2);
k = k0;
S.clear();
mhi.clear();
if (ilim < 0 || dval(&u) <= 5 * ds)
- goto no_digits;
- goto one_digit;
+ 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))) {
-bump_up:
+bumpUp:
while (*--s == '9')
if (s == s0) {
k++;
mhi.clear();
mlo.clear();
if (leftright) {
- i =
-#ifndef Sudden_Underflow
- denorm ? be + (Bias + (P - 1) - 1 + 1) :
-#endif
- 1 + P - bbits;
+ i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits;
b2 += i;
s2 += i;
i2b(mhi, 1);
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
- ) {
+ if ((roundingNone || leftright) && (!word1(&u) && !(word0(&u) & Bndry_mask) && word0(&u) & (Exp_mask & ~Exp_msk1))) {
/* The special case */
b2 += Log2P;
s2 += Log2P;
* 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;
if (s2 > 0)
lshift(S, s2);
if (k_check) {
- if (cmp(b,S) < 0) {
+ if (cmp(b, S) < 0) {
k--;
multadd(b, 10, 0); /* we botched the k estimate */
if (leftright)
ilim = ilim1;
}
}
-
+ if (ilim <= 0 && roundingDecimalPlaces) {
+ if (ilim < 0)
+ goto noDigits;
+ multadd(S, 5, 0);
+ // For IEEE-754 unbiased rounding this check should be <=, such that 0.5 would flush to zero.
+ if (cmp(b, S) < 0)
+ goto noDigits;
+ goto oneDigit;
+ }
if (leftright) {
if (m2 > 0)
lshift(mhi, m2);
*/
mlo = mhi;
- if (spec_case) {
- mhi = mlo;
+ if (spec_case)
lshift(mhi, Log2P);
- }
for (i = 1;;i++) {
- dig = quorem(b,S) + '0';
+ 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 == 0 && !(word1(&u) & 1)) {
+#ifdef DTOA_ROUND_BIASED
+ if (j < 0 || !j) {
+#else
+ // FIXME: ECMA-262 specifies that equidistant results round away from
+ // zero, which probably means we shouldn't be on the unbiased code path
+ // (the (word1(&u) & 1) clause is looking highly suspicious). I haven't
+ // yet understood this code well enough to make the call, but we should
+ // probably be enabling DTOA_ROUND_BIASED. I think the interesting corner
+ // case to understand is probably "Math.pow(0.5, 24).toString()".
+ // I believe this value is interesting because I think it is precisely
+ // representable in binary floating point, and its decimal representation
+ // has a single digit that Steele & White reduction can remove, with the
+ // value 5 (thus equidistant from the next numbers above and below).
+ // We produce the correct answer using either codepath, and I don't as
+ // yet understand why. :-)
+ if (!j1 && !(word1(&u) & 1)) {
if (dig == '9')
- goto round_9_up;
+ 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 == 0 && !(word1(&u) & 1))) {
- if (!b.words()[0] && b.size() <= 1) {
-#ifdef SET_INEXACT
- inexact = 0;
+ if (j < 0 || (!j && !(word1(&u) & 1))) {
#endif
- goto accept_dig;
- }
- if (j1 > 0) {
+ if ((b.words()[0] || b.size() > 1) && (j1 > 0)) {
lshift(b, 1);
j1 = cmp(b, S);
- if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
- goto round_9_up;
+ // For IEEE-754 round-to-even, this check should be (j1 > 0 || (!j1 && (dig & 1))),
+ // but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed()) should
+ // be rounded away from zero.
+ if (j1 >= 0) {
+ if (dig == '9')
+ goto round9up;
+ dig++;
+ }
}
-accept_dig:
*s++ = dig;
goto ret;
}
if (j1 > 0) {
if (dig == '9') { /* possible if i == 1 */
-round_9_up:
+round9up:
*s++ = '9';
goto roundoff;
}
multadd(mlo, 10, 0);
multadd(mhi, 10, 0);
}
- } else
+ } else {
for (i = 1;; i++) {
- *s++ = dig = quorem(b,S) + '0';
- if (!b.words()[0] && b.size() <= 1) {
-#ifdef SET_INEXACT
- inexact = 0;
-#endif
+ *s++ = dig = quorem(b, S) + '0';
+ if (!b.words()[0] && b.size() <= 1)
goto ret;
- }
if (i >= ilim)
break;
multadd(b, 10, 0);
}
+ }
/* Round off last digit */
lshift(b, 1);
j = cmp(b, S);
- if (j > 0 || (j == 0 && (dig & 1))) {
+ // For IEEE-754 round-to-even, this check should be (j > 0 || (!j && (dig & 1))),
+ // but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed()) should
+ // be rounded away from zero.
+ if (j >= 0) {
roundoff:
while (*--s == '9')
if (s == s0) {
s++;
}
goto ret;
-no_digits:
- k = -1 - ndigits;
- goto ret;
-one_digit:
+noDigits:
+ exponentOut = 0;
+ precisionOut = 1;
+ result[0] = '0';
+ result[1] = '\0';
+ return;
+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
+ ASSERT(s > result);
*s = 0;
- *decpt = k + 1;
- if (rve)
- *rve = s;
+ exponentOut = k;
+ precisionOut = s - result;
+}
+
+void dtoa(DtoaBuffer result, double dd, bool& sign, int& exponent, unsigned& precision)
+{
+ // flags are roundingNone, leftright.
+ dtoa<true, false, false, true>(result, dd, 0, sign, exponent, precision);
+}
+
+void dtoaRoundSF(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision)
+{
+ // flag is roundingSignificantFigures.
+ dtoa<false, true, false, false>(result, dd, ndigits, sign, exponent, precision);
+}
+
+void dtoaRoundDP(DtoaBuffer result, double dd, int ndigits, bool& sign, int& exponent, unsigned& precision)
+{
+ // flag is roundingDecimalPlaces.
+ dtoa<false, false, true, false>(result, dd, ndigits, sign, exponent, precision);
+}
+
+static ALWAYS_INLINE void copyAsciiToUTF16(UChar* next, const char* src, unsigned size)
+{
+ for (unsigned i = 0; i < size; ++i)
+ *next++ = *src++;
+}
+
+unsigned numberToString(double d, NumberToStringBuffer buffer)
+{
+ // Handle NaN and Infinity.
+ if (isnan(d) || isinf(d)) {
+ if (isnan(d)) {
+ copyAsciiToUTF16(buffer, "NaN", 3);
+ return 3;
+ }
+ if (d > 0) {
+ copyAsciiToUTF16(buffer, "Infinity", 8);
+ return 8;
+ }
+ copyAsciiToUTF16(buffer, "-Infinity", 9);
+ return 9;
+ }
+
+ // Convert to decimal with rounding.
+ DecimalNumber number(d);
+ return number.exponent() >= -6 && number.exponent() < 21
+ ? number.toStringDecimal(buffer, NumberToStringBufferLength)
+ : number.toStringExponential(buffer, NumberToStringBufferLength);
}
} // namespace WTF
projects / apple / javascriptcore.git / blobdiff