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/****************************************************************
*
* 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 <float.h>
#include <math.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <wtf/AlwaysInline.h>
#include <wtf/Assertions.h>
#include <wtf/FastMalloc.h>
#include <wtf/Vector.h>
#include <wtf/Threading.h>
#include <stdio.h>
#if COMPILER(MSVC)
#pragma warning(disable: 4244)
#pragma warning(disable: 4245)
#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)
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
* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 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++)
#else
#define Storeinc(a,b,c) (((unsigned short*)a)[0] = (unsigned short)b, ((unsigned short*)a)[1] = (unsigned short)c, a++)
#endif
#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 PLATFORM(PPC64) || PLATFORM(X86_64)
// 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, *xa, *xb, *xae, *xbe;
uint32_t *xc, *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;
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;
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 {
BigInt val;
P5Node* next;
};
static P5Node* p5s;
static int p5s_count;
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;
p5s_count = 1;
}
int p5s_count_local = p5s_count;
#if ENABLE(JSC_MULTIPLE_THREADS)
s_dtoaP5Mutex->unlock();
#endif
int p5s_used = 0;
for (;;) {
if (k & 1)
mult(b, p5->val);
if (!(k >>= 1))
break;
if (++p5s_used == p5s_count_local) {
#if ENABLE(JSC_MULTIPLE_THREADS)
s_dtoaP5Mutex->lock();
#endif
if (p5s_used == p5s_count) {
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;
}
p5s_count_local = p5s_count;
#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] != 0));
}
#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--;
} 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;
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);
}
#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 ret_d;
}
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 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:
#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
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 have_dig;
}
goto dig_done;
}
for (; c >= '0' && c <= '9'; c = *++s) {
have_dig:
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;
}
}
}
dig_done:
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 drop_down;
break;
}
if (i == 0) {
/* 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:
/* 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 == 0)
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;
} else
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;
}
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) {
/* 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) == 0 && word1(&rv) == 0)
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, *bxe, q, *sx, *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;
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;
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(char* 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, *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");
else
strcpy(result, "NaN");
return;
}
if (!dval(&u)) {
*decpt = 1;
result[0] = '0';
result[1] = '\0';
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 fast_failed;
ilim = ilim1;
k--;
dval(&u) *= 10.;
ieps++;
}
dval(&eps) = (ieps * dval(&u)) + 7.;
word0(&eps) -= (P - 1) * Exp_msk1;
if (ilim == 0) {
S.clear();
mhi.clear();
dval(&u) -= 5.;
if (dval(&u) > dval(&eps))
goto one_digit;
if (dval(&u) < -dval(&eps))
goto no_digits;
goto fast_failed;
}
#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 bump_up;
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 bump_up;
else if (dval(&u) < 0.5 - dval(&eps)) {
while (*--s == '0') { }
s++;
goto ret;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
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 no_digits;
goto one_digit;
}
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:
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 == 0 && !(word1(&u) & 1)) {
if (dig == '9')
goto round_9_up;
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;
#endif
goto accept_dig;
}
if (j1 > 0) {
lshift(b, 1);
j1 = cmp(b, S);
if ((j1 > 0 || (j1 == 0 && (dig & 1))) && dig++ == '9')
goto round_9_up;
}
accept_dig:
*s++ = dig;
goto ret;
}
if (j1 > 0) {
if (dig == '9') { /* possible if i == 1 */
round_9_up:
*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 == 0 && (dig & 1))) {
roundoff:
while (*--s == '9')
if (s == s0) {
k++;
*s++ = '1';
goto ret;
}
++*s++;
} else {
while (*--s == '0') { }
s++;
}
goto ret;
no_digits:
k = -1 - ndigits;
goto ret;
one_digit:
*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;
}
} // namespace WTF