mirror of
https://github.com/flutter/flutter.git
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1317 lines
33 KiB
C++
1317 lines
33 KiB
C++
/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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* Copyright (C) 2002, 2005, 2006, 2007, 2008, 2010, 2012 Apple Inc.
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* All rights reserved.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/* Please send bug reports to David M. Gay (dmg at acm dot org,
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* with " at " changed at "@" and " dot " changed to "."). */
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/* On a machine with IEEE extended-precision registers, it is
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* necessary to specify double-precision (53-bit) rounding precision
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* before invoking strtod or dtoa. If the machine uses (the equivalent
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* of) Intel 80x87 arithmetic, the call
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* _control87(PC_53, MCW_PC);
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* does this with many compilers. Whether this or another call is
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* appropriate depends on the compiler; for this to work, it may be
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* necessary to #include "float.h" or another system-dependent header
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* file.
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*/
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#include "flutter/sky/engine/wtf/dtoa.h"
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#include "flutter/sky/engine/wtf/CPU.h"
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#include "flutter/sky/engine/wtf/MathExtras.h"
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#include "flutter/sky/engine/wtf/ThreadingPrimitives.h"
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#include "flutter/sky/engine/wtf/Vector.h"
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namespace WTF {
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Mutex* s_dtoaP5Mutex;
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typedef union {
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double d;
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uint32_t L[2];
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} U;
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#if CPU(BIG_ENDIAN) || CPU(MIDDLE_ENDIAN)
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#define word0(x) (x)->L[0]
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#define word1(x) (x)->L[1]
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#else
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#define word0(x) (x)->L[1]
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#define word1(x) (x)->L[0]
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#endif
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#define dval(x) (x)->d
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#define Exp_shift 20
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#define Exp_shift1 20
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#define Exp_msk1 0x100000
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#define Exp_msk11 0x100000
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#define Exp_mask 0x7ff00000
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#define P 53
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#define Bias 1023
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#define Emin (-1022)
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#define Exp_1 0x3ff00000
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#define Exp_11 0x3ff00000
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#define Ebits 11
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#define Frac_mask 0xfffff
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#define Frac_mask1 0xfffff
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#define Ten_pmax 22
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#define Bletch 0x10
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#define Bndry_mask 0xfffff
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#define Bndry_mask1 0xfffff
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#define LSB 1
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#define Sign_bit 0x80000000
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#define Log2P 1
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#define Tiny0 0
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#define Tiny1 1
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#define Quick_max 14
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#define Int_max 14
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#define rounded_product(a, b) a *= b
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#define rounded_quotient(a, b) a /= b
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#define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
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#define Big1 0xffffffff
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#if CPU(X86_64)
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// FIXME: should we enable this on all 64-bit CPUs?
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// 64-bit emulation provided by the compiler is likely to be slower than dtoa
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// own code on 32-bit hardware.
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#define USE_LONG_LONG
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#endif
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#ifndef USE_LONG_LONG
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/* The following definition of Storeinc is appropriate for MIPS processors.
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* An alternative that might be better on some machines is
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* *p++ = high << 16 | low & 0xffff;
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*/
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static ALWAYS_INLINE uint32_t* storeInc(uint32_t* p,
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uint16_t high,
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uint16_t low) {
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uint16_t* p16 = reinterpret_cast<uint16_t*>(p);
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#if CPU(BIG_ENDIAN)
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p16[0] = high;
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p16[1] = low;
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#else
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p16[1] = high;
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p16[0] = low;
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#endif
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return p + 1;
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}
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#endif
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struct BigInt {
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BigInt() : sign(0) {}
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int sign;
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void clear() {
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sign = 0;
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m_words.clear();
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}
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size_t size() const { return m_words.size(); }
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void resize(size_t s) { m_words.resize(s); }
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uint32_t* words() { return m_words.data(); }
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const uint32_t* words() const { return m_words.data(); }
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void append(uint32_t w) { m_words.append(w); }
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Vector<uint32_t, 16> m_words;
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};
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static void multadd(BigInt& b, int m, int a) /* multiply by m and add a */
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{
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#ifdef USE_LONG_LONG
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unsigned long long carry;
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#else
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uint32_t carry;
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#endif
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int wds = b.size();
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uint32_t* x = b.words();
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int i = 0;
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carry = a;
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do {
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#ifdef USE_LONG_LONG
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unsigned long long y = *x * (unsigned long long)m + carry;
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carry = y >> 32;
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*x++ = (uint32_t)y & 0xffffffffUL;
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#else
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uint32_t xi = *x;
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uint32_t y = (xi & 0xffff) * m + carry;
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uint32_t z = (xi >> 16) * m + (y >> 16);
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carry = z >> 16;
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*x++ = (z << 16) + (y & 0xffff);
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#endif
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} while (++i < wds);
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if (carry)
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b.append((uint32_t)carry);
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}
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static int hi0bits(uint32_t x) {
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int k = 0;
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if (!(x & 0xffff0000)) {
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k = 16;
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x <<= 16;
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}
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if (!(x & 0xff000000)) {
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k += 8;
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x <<= 8;
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}
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if (!(x & 0xf0000000)) {
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k += 4;
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x <<= 4;
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}
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if (!(x & 0xc0000000)) {
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k += 2;
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x <<= 2;
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}
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if (!(x & 0x80000000)) {
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k++;
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if (!(x & 0x40000000))
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return 32;
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}
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return k;
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}
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static int lo0bits(uint32_t* y) {
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int k;
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uint32_t x = *y;
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if (x & 7) {
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if (x & 1)
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return 0;
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if (x & 2) {
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*y = x >> 1;
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return 1;
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}
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*y = x >> 2;
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return 2;
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}
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k = 0;
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if (!(x & 0xffff)) {
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k = 16;
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x >>= 16;
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}
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if (!(x & 0xff)) {
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k += 8;
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x >>= 8;
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}
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if (!(x & 0xf)) {
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k += 4;
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x >>= 4;
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}
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if (!(x & 0x3)) {
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k += 2;
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x >>= 2;
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}
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if (!(x & 1)) {
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k++;
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x >>= 1;
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if (!x)
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return 32;
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}
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*y = x;
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return k;
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}
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static void i2b(BigInt& b, int i) {
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b.sign = 0;
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b.resize(1);
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b.words()[0] = i;
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}
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static void mult(BigInt& aRef, const BigInt& bRef) {
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const BigInt* a = &aRef;
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const BigInt* b = &bRef;
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BigInt c;
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int wa, wb, wc;
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const uint32_t* x = 0;
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const uint32_t* xa;
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const uint32_t* xb;
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const uint32_t* xae;
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const uint32_t* xbe;
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uint32_t* xc;
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uint32_t* xc0;
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uint32_t y;
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#ifdef USE_LONG_LONG
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unsigned long long carry, z;
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#else
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uint32_t carry, z;
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#endif
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if (a->size() < b->size()) {
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const BigInt* tmp = a;
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a = b;
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b = tmp;
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}
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wa = a->size();
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wb = b->size();
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wc = wa + wb;
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c.resize(wc);
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for (xc = c.words(), xa = xc + wc; xc < xa; xc++)
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*xc = 0;
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xa = a->words();
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xae = xa + wa;
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xb = b->words();
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xbe = xb + wb;
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xc0 = c.words();
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#ifdef USE_LONG_LONG
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for (; xb < xbe; xc0++) {
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if ((y = *xb++)) {
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x = xa;
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xc = xc0;
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carry = 0;
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do {
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z = *x++ * (unsigned long long)y + *xc + carry;
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carry = z >> 32;
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*xc++ = (uint32_t)z & 0xffffffffUL;
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} while (x < xae);
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*xc = (uint32_t)carry;
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}
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}
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#else
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for (; xb < xbe; xb++, xc0++) {
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if ((y = *xb & 0xffff)) {
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x = xa;
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xc = xc0;
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carry = 0;
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do {
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z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
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carry = z >> 16;
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uint32_t z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
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carry = z2 >> 16;
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xc = storeInc(xc, z2, z);
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} while (x < xae);
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*xc = carry;
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}
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if ((y = *xb >> 16)) {
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x = xa;
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xc = xc0;
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carry = 0;
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uint32_t z2 = *xc;
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do {
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z = (*x & 0xffff) * y + (*xc >> 16) + carry;
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carry = z >> 16;
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xc = storeInc(xc, z, z2);
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z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
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carry = z2 >> 16;
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} while (x < xae);
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*xc = z2;
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}
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}
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#endif
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for (xc0 = c.words(), xc = xc0 + wc; wc > 0 && !*--xc; --wc) {
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}
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c.resize(wc);
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aRef = c;
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}
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struct P5Node {
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WTF_MAKE_NONCOPYABLE(P5Node);
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WTF_MAKE_FAST_ALLOCATED;
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public:
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P5Node() {}
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BigInt val;
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P5Node* next;
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};
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static P5Node* p5s;
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static int p5sCount;
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static ALWAYS_INLINE void pow5mult(BigInt& b, int k) {
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static int p05[3] = {5, 25, 125};
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if (int i = k & 3)
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multadd(b, p05[i - 1], 0);
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if (!(k >>= 2))
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return;
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s_dtoaP5Mutex->lock();
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P5Node* p5 = p5s;
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if (!p5) {
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/* first time */
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p5 = new P5Node;
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i2b(p5->val, 625);
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p5->next = 0;
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p5s = p5;
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p5sCount = 1;
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}
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int p5sCountLocal = p5sCount;
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s_dtoaP5Mutex->unlock();
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int p5sUsed = 0;
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for (;;) {
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if (k & 1)
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mult(b, p5->val);
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if (!(k >>= 1))
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break;
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if (++p5sUsed == p5sCountLocal) {
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s_dtoaP5Mutex->lock();
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if (p5sUsed == p5sCount) {
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ASSERT(!p5->next);
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p5->next = new P5Node;
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p5->next->next = 0;
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p5->next->val = p5->val;
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mult(p5->next->val, p5->next->val);
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++p5sCount;
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}
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p5sCountLocal = p5sCount;
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s_dtoaP5Mutex->unlock();
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}
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p5 = p5->next;
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}
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}
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static ALWAYS_INLINE void lshift(BigInt& b, int k) {
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int n = k >> 5;
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int origSize = b.size();
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int n1 = n + origSize + 1;
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if (k &= 0x1f)
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b.resize(b.size() + n + 1);
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else
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b.resize(b.size() + n);
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const uint32_t* srcStart = b.words();
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uint32_t* dstStart = b.words();
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const uint32_t* src = srcStart + origSize - 1;
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uint32_t* dst = dstStart + n1 - 1;
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if (k) {
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uint32_t hiSubword = 0;
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int s = 32 - k;
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for (; src >= srcStart; --src) {
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*dst-- = hiSubword | *src >> s;
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hiSubword = *src << k;
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}
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*dst = hiSubword;
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ASSERT(dst == dstStart + n);
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|
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b.resize(origSize + n + !!b.words()[n1 - 1]);
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} else {
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do {
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*--dst = *src--;
|
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} while (src >= srcStart);
|
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}
|
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for (dst = dstStart + n; dst != dstStart;)
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*--dst = 0;
|
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|
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ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
|
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}
|
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|
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static int cmp(const BigInt& a, const BigInt& b) {
|
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const uint32_t *xa, *xa0, *xb, *xb0;
|
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int i, j;
|
||
|
||
i = a.size();
|
||
j = b.size();
|
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ASSERT(i <= 1 || a.words()[i - 1]);
|
||
ASSERT(j <= 1 || b.words()[j - 1]);
|
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if (i -= j)
|
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return i;
|
||
xa0 = a.words();
|
||
xa = xa0 + j;
|
||
xb0 = b.words();
|
||
xb = xb0 + j;
|
||
for (;;) {
|
||
if (*--xa != *--xb)
|
||
return *xa < *xb ? -1 : 1;
|
||
if (xa <= xa0)
|
||
break;
|
||
}
|
||
return 0;
|
||
}
|
||
|
||
static ALWAYS_INLINE void diff(BigInt& c,
|
||
const BigInt& aRef,
|
||
const BigInt& bRef) {
|
||
const BigInt* a = &aRef;
|
||
const BigInt* b = &bRef;
|
||
int i, wa, wb;
|
||
uint32_t* xc;
|
||
|
||
i = cmp(*a, *b);
|
||
if (!i) {
|
||
c.sign = 0;
|
||
c.resize(1);
|
||
c.words()[0] = 0;
|
||
return;
|
||
}
|
||
if (i < 0) {
|
||
const BigInt* tmp = a;
|
||
a = b;
|
||
b = tmp;
|
||
i = 1;
|
||
} else
|
||
i = 0;
|
||
|
||
wa = a->size();
|
||
const uint32_t* xa = a->words();
|
||
const uint32_t* xae = xa + wa;
|
||
wb = b->size();
|
||
const uint32_t* xb = b->words();
|
||
const uint32_t* xbe = xb + wb;
|
||
|
||
c.resize(wa);
|
||
c.sign = i;
|
||
xc = c.words();
|
||
#ifdef USE_LONG_LONG
|
||
unsigned long long borrow = 0;
|
||
do {
|
||
unsigned long long y = (unsigned long long)*xa++ - *xb++ - borrow;
|
||
borrow = y >> 32 & (uint32_t)1;
|
||
*xc++ = (uint32_t)y & 0xffffffffUL;
|
||
} while (xb < xbe);
|
||
while (xa < xae) {
|
||
unsigned long long y = *xa++ - borrow;
|
||
borrow = y >> 32 & (uint32_t)1;
|
||
*xc++ = (uint32_t)y & 0xffffffffUL;
|
||
}
|
||
#else
|
||
uint32_t borrow = 0;
|
||
do {
|
||
uint32_t y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
|
||
borrow = (y & 0x10000) >> 16;
|
||
uint32_t z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
|
||
borrow = (z & 0x10000) >> 16;
|
||
xc = storeInc(xc, z, y);
|
||
} while (xb < xbe);
|
||
while (xa < xae) {
|
||
uint32_t y = (*xa & 0xffff) - borrow;
|
||
borrow = (y & 0x10000) >> 16;
|
||
uint32_t z = (*xa++ >> 16) - borrow;
|
||
borrow = (z & 0x10000) >> 16;
|
||
xc = storeInc(xc, z, y);
|
||
}
|
||
#endif
|
||
while (!*--xc)
|
||
wa--;
|
||
c.resize(wa);
|
||
}
|
||
|
||
static ALWAYS_INLINE void d2b(BigInt& b, U* d, int* e, int* bits) {
|
||
int de, k;
|
||
uint32_t* x;
|
||
uint32_t y, z;
|
||
int i;
|
||
#define d0 word0(d)
|
||
#define d1 word1(d)
|
||
|
||
b.sign = 0;
|
||
b.resize(1);
|
||
x = b.words();
|
||
|
||
z = d0 & Frac_mask;
|
||
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
||
if ((de = (int)(d0 >> Exp_shift)))
|
||
z |= Exp_msk1;
|
||
if ((y = d1)) {
|
||
if ((k = lo0bits(&y))) {
|
||
x[0] = y | (z << (32 - k));
|
||
z >>= k;
|
||
} else
|
||
x[0] = y;
|
||
if (z) {
|
||
b.resize(2);
|
||
x[1] = z;
|
||
}
|
||
|
||
i = b.size();
|
||
} else {
|
||
k = lo0bits(&z);
|
||
x[0] = z;
|
||
i = 1;
|
||
b.resize(1);
|
||
k += 32;
|
||
}
|
||
if (de) {
|
||
*e = de - Bias - (P - 1) + k;
|
||
*bits = P - k;
|
||
} else {
|
||
*e = 0 - Bias - (P - 1) + 1 + k;
|
||
*bits = (32 * i) - hi0bits(x[i - 1]);
|
||
}
|
||
}
|
||
#undef d0
|
||
#undef d1
|
||
|
||
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};
|
||
|
||
#define Scale_Bit 0x10
|
||
#define n_bigtens 5
|
||
|
||
static ALWAYS_INLINE int quorem(BigInt& b, BigInt& S) {
|
||
size_t n;
|
||
uint32_t* bx;
|
||
uint32_t* bxe;
|
||
uint32_t q;
|
||
uint32_t* sx;
|
||
uint32_t* sxe;
|
||
#ifdef USE_LONG_LONG
|
||
unsigned long long borrow, carry, y, ys;
|
||
#else
|
||
uint32_t borrow, carry, y, ys;
|
||
uint32_t si, z, zs;
|
||
#endif
|
||
ASSERT(b.size() <= 1 || b.words()[b.size() - 1]);
|
||
ASSERT(S.size() <= 1 || S.words()[S.size() - 1]);
|
||
|
||
n = S.size();
|
||
ASSERT_WITH_MESSAGE(b.size() <= n, "oversize b in quorem");
|
||
if (b.size() < n)
|
||
return 0;
|
||
sx = S.words();
|
||
sxe = sx + --n;
|
||
bx = b.words();
|
||
bxe = bx + n;
|
||
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
|
||
ASSERT_WITH_MESSAGE(q <= 9, "oversized quotient in quorem");
|
||
if (q) {
|
||
borrow = 0;
|
||
carry = 0;
|
||
do {
|
||
#ifdef USE_LONG_LONG
|
||
ys = *sx++ * (unsigned long long)q + carry;
|
||
carry = ys >> 32;
|
||
y = *bx - (ys & 0xffffffffUL) - borrow;
|
||
borrow = y >> 32 & (uint32_t)1;
|
||
*bx++ = (uint32_t)y & 0xffffffffUL;
|
||
#else
|
||
si = *sx++;
|
||
ys = (si & 0xffff) * q + carry;
|
||
zs = (si >> 16) * q + (ys >> 16);
|
||
carry = zs >> 16;
|
||
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
||
borrow = (y & 0x10000) >> 16;
|
||
z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
||
borrow = (z & 0x10000) >> 16;
|
||
bx = storeInc(bx, z, y);
|
||
#endif
|
||
} while (sx <= sxe);
|
||
if (!*bxe) {
|
||
bx = b.words();
|
||
while (--bxe > bx && !*bxe)
|
||
--n;
|
||
b.resize(n);
|
||
}
|
||
}
|
||
if (cmp(b, S) >= 0) {
|
||
q++;
|
||
borrow = 0;
|
||
carry = 0;
|
||
bx = b.words();
|
||
sx = S.words();
|
||
do {
|
||
#ifdef USE_LONG_LONG
|
||
ys = *sx++ + carry;
|
||
carry = ys >> 32;
|
||
y = *bx - (ys & 0xffffffffUL) - borrow;
|
||
borrow = y >> 32 & (uint32_t)1;
|
||
*bx++ = (uint32_t)y & 0xffffffffUL;
|
||
#else
|
||
si = *sx++;
|
||
ys = (si & 0xffff) + carry;
|
||
zs = (si >> 16) + (ys >> 16);
|
||
carry = zs >> 16;
|
||
y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
|
||
borrow = (y & 0x10000) >> 16;
|
||
z = (*bx >> 16) - (zs & 0xffff) - borrow;
|
||
borrow = (z & 0x10000) >> 16;
|
||
bx = storeInc(bx, z, y);
|
||
#endif
|
||
} while (sx <= sxe);
|
||
bx = b.words();
|
||
bxe = bx + n;
|
||
if (!*bxe) {
|
||
while (--bxe > bx && !*bxe)
|
||
--n;
|
||
b.resize(n);
|
||
}
|
||
}
|
||
return q;
|
||
}
|
||
|
||
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
||
*
|
||
* Inspired by "How to Print Floating-Point Numbers Accurately" by
|
||
* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
|
||
*
|
||
* Modifications:
|
||
* 1. Rather than iterating, we use a simple numeric overestimate
|
||
* to determine k = floor(log10(d)). We scale relevant
|
||
* quantities using O(log2(k)) rather than O(k) multiplications.
|
||
* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
||
* try to generate digits strictly left to right. Instead, we
|
||
* compute with fewer bits and propagate the carry if necessary
|
||
* when rounding the final digit up. This is often faster.
|
||
* 3. Under the assumption that input will be rounded nearest,
|
||
* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
||
* That is, we allow equality in stopping tests when the
|
||
* round-nearest rule will give the same floating-point value
|
||
* as would satisfaction of the stopping test with strict
|
||
* inequality.
|
||
* 4. We remove common factors of powers of 2 from relevant
|
||
* quantities.
|
||
* 5. When converting floating-point integers less than 1e16,
|
||
* we use floating-point arithmetic rather than resorting
|
||
* to multiple-precision integers.
|
||
* 6. When asked to produce fewer than 15 digits, we first try
|
||
* to get by with floating-point arithmetic; we resort to
|
||
* multiple-precision integer arithmetic only if we cannot
|
||
* guarantee that the floating-point calculation has given
|
||
* the correctly rounded result. For k requested digits and
|
||
* "uniformly" distributed input, the probability is
|
||
* something like 10^(k-15) that we must resort to the int32_t
|
||
* calculation.
|
||
*
|
||
* Note: 'leftright' translates to 'generate shortest possible string'.
|
||
*/
|
||
template <bool roundingNone,
|
||
bool roundingSignificantFigures,
|
||
bool roundingDecimalPlaces,
|
||
bool leftright>
|
||
void dtoa(DtoaBuffer result,
|
||
double dd,
|
||
int ndigits,
|
||
bool& signOut,
|
||
int& exponentOut,
|
||
unsigned& precisionOut) {
|
||
// Exactly one rounding mode must be specified.
|
||
ASSERT(roundingNone + roundingSignificantFigures + roundingDecimalPlaces ==
|
||
1);
|
||
// roundingNone only allowed (only sensible?) with leftright set.
|
||
ASSERT(!roundingNone || leftright);
|
||
|
||
ASSERT(std::isfinite(dd));
|
||
|
||
int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, j, j1, k, k0,
|
||
k_check, m2, m5, s2, s5, spec_case;
|
||
int32_t L;
|
||
int denorm;
|
||
uint32_t x;
|
||
BigInt b, delta, mlo, mhi, S;
|
||
U d2, eps, u;
|
||
double ds;
|
||
char* s;
|
||
char* s0;
|
||
|
||
u.d = dd;
|
||
|
||
/* Infinity or NaN */
|
||
ASSERT((word0(&u) & Exp_mask) != Exp_mask);
|
||
|
||
// JavaScript toString conversion treats -0 as 0.
|
||
if (!dval(&u)) {
|
||
signOut = false;
|
||
exponentOut = 0;
|
||
precisionOut = 1;
|
||
result[0] = '0';
|
||
result[1] = '\0';
|
||
return;
|
||
}
|
||
|
||
if (word0(&u) & Sign_bit) {
|
||
signOut = true;
|
||
word0(&u) &= ~Sign_bit; // clear sign bit
|
||
} else
|
||
signOut = false;
|
||
|
||
d2b(b, &u, &be, &bbits);
|
||
if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
|
||
dval(&d2) = dval(&u);
|
||
word0(&d2) &= Frac_mask1;
|
||
word0(&d2) |= Exp_11;
|
||
|
||
/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
||
* log10(x) = log(x) / log(10)
|
||
* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
||
* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
|
||
*
|
||
* This suggests computing an approximation k to log10(d) by
|
||
*
|
||
* k = (i - Bias)*0.301029995663981
|
||
* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
||
*
|
||
* We want k to be too large rather than too small.
|
||
* The error in the first-order Taylor series approximation
|
||
* is in our favor, so we just round up the constant enough
|
||
* to compensate for any error in the multiplication of
|
||
* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
||
* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
||
* adding 1e-13 to the constant term more than suffices.
|
||
* Hence we adjust the constant term to 0.1760912590558.
|
||
* (We could get a more accurate k by invoking log10,
|
||
* but this is probably not worthwhile.)
|
||
*/
|
||
|
||
i -= Bias;
|
||
denorm = 0;
|
||
} else {
|
||
/* d is denormalized */
|
||
|
||
i = bbits + be + (Bias + (P - 1) - 1);
|
||
x = (i > 32) ? (word0(&u) << (64 - i)) | (word1(&u) >> (i - 32))
|
||
: word1(&u) << (32 - i);
|
||
dval(&d2) = x;
|
||
word0(&d2) -= 31 * Exp_msk1; /* adjust exponent */
|
||
i -= (Bias + (P - 1) - 1) + 1;
|
||
denorm = 1;
|
||
}
|
||
ds = (dval(&d2) - 1.5) * 0.289529654602168 + 0.1760912590558 +
|
||
(i * 0.301029995663981);
|
||
k = (int)ds;
|
||
if (ds < 0. && ds != k)
|
||
k--; /* want k = floor(ds) */
|
||
k_check = 1;
|
||
if (k >= 0 && k <= Ten_pmax) {
|
||
if (dval(&u) < tens[k])
|
||
k--;
|
||
k_check = 0;
|
||
}
|
||
j = bbits - i - 1;
|
||
if (j >= 0) {
|
||
b2 = 0;
|
||
s2 = j;
|
||
} else {
|
||
b2 = -j;
|
||
s2 = 0;
|
||
}
|
||
if (k >= 0) {
|
||
b5 = 0;
|
||
s5 = k;
|
||
s2 += k;
|
||
} else {
|
||
b2 -= k;
|
||
b5 = -k;
|
||
s5 = 0;
|
||
}
|
||
|
||
if (roundingNone) {
|
||
ilim = ilim1 = -1;
|
||
i = 18;
|
||
ndigits = 0;
|
||
}
|
||
if (roundingSignificantFigures) {
|
||
if (ndigits <= 0)
|
||
ndigits = 1;
|
||
ilim = ilim1 = i = ndigits;
|
||
}
|
||
if (roundingDecimalPlaces) {
|
||
i = ndigits + k + 1;
|
||
ilim = i;
|
||
ilim1 = i - 1;
|
||
if (i <= 0)
|
||
i = 1;
|
||
}
|
||
|
||
s = s0 = result;
|
||
|
||
if (ilim >= 0 && ilim <= Quick_max) {
|
||
/* Try to get by with floating-point arithmetic. */
|
||
|
||
i = 0;
|
||
dval(&d2) = dval(&u);
|
||
k0 = k;
|
||
ilim0 = ilim;
|
||
ieps = 2; /* conservative */
|
||
if (k > 0) {
|
||
ds = tens[k & 0xf];
|
||
j = k >> 4;
|
||
if (j & Bletch) {
|
||
/* prevent overflows */
|
||
j &= Bletch - 1;
|
||
dval(&u) /= bigtens[n_bigtens - 1];
|
||
ieps++;
|
||
}
|
||
for (; j; j >>= 1, i++) {
|
||
if (j & 1) {
|
||
ieps++;
|
||
ds *= bigtens[i];
|
||
}
|
||
}
|
||
dval(&u) /= ds;
|
||
} else if ((j1 = -k)) {
|
||
dval(&u) *= tens[j1 & 0xf];
|
||
for (j = j1 >> 4; j; j >>= 1, i++) {
|
||
if (j & 1) {
|
||
ieps++;
|
||
dval(&u) *= bigtens[i];
|
||
}
|
||
}
|
||
}
|
||
if (k_check && dval(&u) < 1. && ilim > 0) {
|
||
if (ilim1 <= 0)
|
||
goto fastFailed;
|
||
ilim = ilim1;
|
||
k--;
|
||
dval(&u) *= 10.;
|
||
ieps++;
|
||
}
|
||
dval(&eps) = (ieps * dval(&u)) + 7.;
|
||
word0(&eps) -= (P - 1) * Exp_msk1;
|
||
if (!ilim) {
|
||
S.clear();
|
||
mhi.clear();
|
||
dval(&u) -= 5.;
|
||
if (dval(&u) > dval(&eps))
|
||
goto oneDigit;
|
||
if (dval(&u) < -dval(&eps))
|
||
goto noDigits;
|
||
goto fastFailed;
|
||
}
|
||
if (leftright) {
|
||
/* Use Steele & White method of only
|
||
* generating digits needed.
|
||
*/
|
||
dval(&eps) = (0.5 / tens[ilim - 1]) - dval(&eps);
|
||
for (i = 0;;) {
|
||
L = (long int)dval(&u);
|
||
dval(&u) -= L;
|
||
*s++ = '0' + (int)L;
|
||
if (dval(&u) < dval(&eps))
|
||
goto ret;
|
||
if (1. - dval(&u) < dval(&eps))
|
||
goto bumpUp;
|
||
if (++i >= ilim)
|
||
break;
|
||
dval(&eps) *= 10.;
|
||
dval(&u) *= 10.;
|
||
}
|
||
} else {
|
||
/* Generate ilim digits, then fix them up. */
|
||
dval(&eps) *= tens[ilim - 1];
|
||
for (i = 1;; i++, dval(&u) *= 10.) {
|
||
L = (int32_t)(dval(&u));
|
||
if (!(dval(&u) -= L))
|
||
ilim = i;
|
||
*s++ = '0' + (int)L;
|
||
if (i == ilim) {
|
||
if (dval(&u) > 0.5 + dval(&eps))
|
||
goto bumpUp;
|
||
if (dval(&u) < 0.5 - dval(&eps)) {
|
||
while (*--s == '0') {
|
||
}
|
||
s++;
|
||
goto ret;
|
||
}
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
fastFailed:
|
||
s = s0;
|
||
dval(&u) = dval(&d2);
|
||
k = k0;
|
||
ilim = ilim0;
|
||
}
|
||
|
||
/* Do we have a "small" integer? */
|
||
|
||
if (be >= 0 && k <= Int_max) {
|
||
/* Yes. */
|
||
ds = tens[k];
|
||
if (ndigits < 0 && ilim <= 0) {
|
||
S.clear();
|
||
mhi.clear();
|
||
if (ilim < 0 || dval(&u) <= 5 * ds)
|
||
goto noDigits;
|
||
goto oneDigit;
|
||
}
|
||
for (i = 1;; i++, dval(&u) *= 10.) {
|
||
L = (int32_t)(dval(&u) / ds);
|
||
dval(&u) -= L * ds;
|
||
*s++ = '0' + (int)L;
|
||
if (!dval(&u)) {
|
||
break;
|
||
}
|
||
if (i == ilim) {
|
||
dval(&u) += dval(&u);
|
||
if (dval(&u) > ds || (dval(&u) == ds && (L & 1))) {
|
||
bumpUp:
|
||
while (*--s == '9')
|
||
if (s == s0) {
|
||
k++;
|
||
*s = '0';
|
||
break;
|
||
}
|
||
++*s++;
|
||
}
|
||
break;
|
||
}
|
||
}
|
||
goto ret;
|
||
}
|
||
|
||
m2 = b2;
|
||
m5 = b5;
|
||
mhi.clear();
|
||
mlo.clear();
|
||
if (leftright) {
|
||
i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits;
|
||
b2 += i;
|
||
s2 += i;
|
||
i2b(mhi, 1);
|
||
}
|
||
if (m2 > 0 && s2 > 0) {
|
||
i = m2 < s2 ? m2 : s2;
|
||
b2 -= i;
|
||
m2 -= i;
|
||
s2 -= i;
|
||
}
|
||
if (b5 > 0) {
|
||
if (leftright) {
|
||
if (m5 > 0) {
|
||
pow5mult(mhi, m5);
|
||
mult(b, mhi);
|
||
}
|
||
if ((j = b5 - m5))
|
||
pow5mult(b, j);
|
||
} else
|
||
pow5mult(b, b5);
|
||
}
|
||
i2b(S, 1);
|
||
if (s5 > 0)
|
||
pow5mult(S, s5);
|
||
|
||
/* Check for special case that d is a normalized power of 2. */
|
||
|
||
spec_case = 0;
|
||
if ((roundingNone || leftright) && (!word1(&u) && !(word0(&u) & Bndry_mask) &&
|
||
word0(&u) & (Exp_mask & ~Exp_msk1))) {
|
||
/* The special case */
|
||
b2 += Log2P;
|
||
s2 += Log2P;
|
||
spec_case = 1;
|
||
}
|
||
|
||
/* Arrange for convenient computation of quotients:
|
||
* shift left if necessary so divisor has 4 leading 0 bits.
|
||
*
|
||
* Perhaps we should just compute leading 28 bits of S once
|
||
* and for all and pass them and a shift to quorem, so it
|
||
* can do shifts and ors to compute the numerator for q.
|
||
*/
|
||
if ((i = ((s5 ? 32 - hi0bits(S.words()[S.size() - 1]) : 1) + s2) & 0x1f))
|
||
i = 32 - i;
|
||
if (i > 4) {
|
||
i -= 4;
|
||
b2 += i;
|
||
m2 += i;
|
||
s2 += i;
|
||
} else if (i < 4) {
|
||
i += 28;
|
||
b2 += i;
|
||
m2 += i;
|
||
s2 += i;
|
||
}
|
||
if (b2 > 0)
|
||
lshift(b, b2);
|
||
if (s2 > 0)
|
||
lshift(S, s2);
|
||
if (k_check) {
|
||
if (cmp(b, S) < 0) {
|
||
k--;
|
||
multadd(b, 10, 0); /* we botched the k estimate */
|
||
if (leftright)
|
||
multadd(mhi, 10, 0);
|
||
ilim = ilim1;
|
||
}
|
||
}
|
||
if (ilim <= 0 && roundingDecimalPlaces) {
|
||
if (ilim < 0)
|
||
goto noDigits;
|
||
multadd(S, 5, 0);
|
||
// For IEEE-754 unbiased rounding this check should be <=, such that 0.5
|
||
// would flush to zero.
|
||
if (cmp(b, S) < 0)
|
||
goto noDigits;
|
||
goto oneDigit;
|
||
}
|
||
if (leftright) {
|
||
if (m2 > 0)
|
||
lshift(mhi, m2);
|
||
|
||
/* Compute mlo -- check for special case
|
||
* that d is a normalized power of 2.
|
||
*/
|
||
|
||
mlo = mhi;
|
||
if (spec_case)
|
||
lshift(mhi, Log2P);
|
||
|
||
for (i = 1;; i++) {
|
||
dig = quorem(b, S) + '0';
|
||
/* Do we yet have the shortest decimal string
|
||
* that will round to d?
|
||
*/
|
||
j = cmp(b, mlo);
|
||
diff(delta, S, mhi);
|
||
j1 = delta.sign ? 1 : cmp(b, delta);
|
||
#ifdef DTOA_ROUND_BIASED
|
||
if (j < 0 || !j) {
|
||
#else
|
||
// FIXME: ECMA-262 specifies that equidistant results round away from
|
||
// zero, which probably means we shouldn't be on the unbiased code path
|
||
// (the (word1(&u) & 1) clause is looking highly suspicious). I haven't
|
||
// yet understood this code well enough to make the call, but we should
|
||
// probably be enabling DTOA_ROUND_BIASED. I think the interesting corner
|
||
// case to understand is probably "Math.pow(0.5, 24).toString()".
|
||
// I believe this value is interesting because I think it is precisely
|
||
// representable in binary floating point, and its decimal representation
|
||
// has a single digit that Steele & White reduction can remove, with the
|
||
// value 5 (thus equidistant from the next numbers above and below).
|
||
// We produce the correct answer using either codepath, and I don't as
|
||
// yet understand why. :-)
|
||
if (!j1 && !(word1(&u) & 1)) {
|
||
if (dig == '9')
|
||
goto round9up;
|
||
if (j > 0)
|
||
dig++;
|
||
*s++ = dig;
|
||
goto ret;
|
||
}
|
||
if (j < 0 || (!j && !(word1(&u) & 1))) {
|
||
#endif
|
||
if ((b.words()[0] || b.size() > 1) && (j1 > 0)) {
|
||
lshift(b, 1);
|
||
j1 = cmp(b, S);
|
||
// For IEEE-754 round-to-even, this check should be (j1 > 0 || (!j1 &&
|
||
// (dig & 1))), but ECMA-262 specifies that equidistant values (e.g.
|
||
// (.5).toFixed()) should be rounded away from zero.
|
||
if (j1 >= 0) {
|
||
if (dig == '9')
|
||
goto round9up;
|
||
dig++;
|
||
}
|
||
}
|
||
*s++ = dig;
|
||
goto ret;
|
||
}
|
||
if (j1 > 0) {
|
||
if (dig == '9') { /* possible if i == 1 */
|
||
round9up:
|
||
*s++ = '9';
|
||
goto roundoff;
|
||
}
|
||
*s++ = dig + 1;
|
||
goto ret;
|
||
}
|
||
*s++ = dig;
|
||
if (i == ilim)
|
||
break;
|
||
multadd(b, 10, 0);
|
||
multadd(mlo, 10, 0);
|
||
multadd(mhi, 10, 0);
|
||
}
|
||
} else {
|
||
for (i = 1;; i++) {
|
||
*s++ = dig = quorem(b, S) + '0';
|
||
if (!b.words()[0] && b.size() <= 1)
|
||
goto ret;
|
||
if (i >= ilim)
|
||
break;
|
||
multadd(b, 10, 0);
|
||
}
|
||
}
|
||
|
||
/* Round off last digit */
|
||
|
||
lshift(b, 1);
|
||
j = cmp(b, S);
|
||
// For IEEE-754 round-to-even, this check should be (j > 0 || (!j && (dig &
|
||
// 1))), but ECMA-262 specifies that equidistant values (e.g. (.5).toFixed())
|
||
// should be rounded away from zero.
|
||
if (j >= 0) {
|
||
roundoff:
|
||
while (*--s == '9')
|
||
if (s == s0) {
|
||
k++;
|
||
*s++ = '1';
|
||
goto ret;
|
||
}
|
||
++*s++;
|
||
} else {
|
||
while (*--s == '0') {
|
||
}
|
||
s++;
|
||
}
|
||
goto ret;
|
||
noDigits:
|
||
exponentOut = 0;
|
||
precisionOut = 1;
|
||
result[0] = '0';
|
||
result[1] = '\0';
|
||
return;
|
||
oneDigit:
|
||
*s++ = '1';
|
||
k++;
|
||
goto ret;
|
||
ret:
|
||
ASSERT(s > result);
|
||
*s = 0;
|
||
exponentOut = k;
|
||
precisionOut = s - result;
|
||
}
|
||
|
||
void dtoa(DtoaBuffer result,
|
||
double dd,
|
||
bool& sign,
|
||
int& exponent,
|
||
unsigned& precision) {
|
||
// flags are roundingNone, leftright.
|
||
dtoa<true, false, false, true>(result, dd, 0, sign, exponent, precision);
|
||
}
|
||
|
||
void dtoaRoundSF(DtoaBuffer result,
|
||
double dd,
|
||
int ndigits,
|
||
bool& sign,
|
||
int& exponent,
|
||
unsigned& precision) {
|
||
// flag is roundingSignificantFigures.
|
||
dtoa<false, true, false, false>(result, dd, ndigits, sign, exponent,
|
||
precision);
|
||
}
|
||
|
||
void dtoaRoundDP(DtoaBuffer result,
|
||
double dd,
|
||
int ndigits,
|
||
bool& sign,
|
||
int& exponent,
|
||
unsigned& precision) {
|
||
// flag is roundingDecimalPlaces.
|
||
dtoa<false, false, true, false>(result, dd, ndigits, sign, exponent,
|
||
precision);
|
||
}
|
||
|
||
const char* numberToString(double d, NumberToStringBuffer buffer) {
|
||
double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength);
|
||
const double_conversion::DoubleToStringConverter& converter =
|
||
double_conversion::DoubleToStringConverter::EcmaScriptConverter();
|
||
converter.ToShortest(d, &builder);
|
||
return builder.Finalize();
|
||
}
|
||
|
||
static inline const char* formatStringTruncatingTrailingZerosIfNeeded(
|
||
NumberToStringBuffer buffer,
|
||
double_conversion::StringBuilder& builder) {
|
||
size_t length = builder.position();
|
||
size_t decimalPointPosition = 0;
|
||
for (; decimalPointPosition < length; ++decimalPointPosition) {
|
||
if (buffer[decimalPointPosition] == '.')
|
||
break;
|
||
}
|
||
|
||
// No decimal seperator found, early exit.
|
||
if (decimalPointPosition == length)
|
||
return builder.Finalize();
|
||
|
||
size_t truncatedLength = length - 1;
|
||
for (; truncatedLength > decimalPointPosition; --truncatedLength) {
|
||
if (buffer[truncatedLength] != '0')
|
||
break;
|
||
}
|
||
|
||
// No trailing zeros found to strip.
|
||
if (truncatedLength == length - 1)
|
||
return builder.Finalize();
|
||
|
||
// If we removed all trailing zeros, remove the decimal point as well.
|
||
if (truncatedLength == decimalPointPosition) {
|
||
ASSERT(truncatedLength > 0);
|
||
--truncatedLength;
|
||
}
|
||
|
||
// Truncate the StringBuilder, and return the final result.
|
||
builder.SetPosition(truncatedLength + 1);
|
||
return builder.Finalize();
|
||
}
|
||
|
||
const char* numberToFixedPrecisionString(double d,
|
||
unsigned significantFigures,
|
||
NumberToStringBuffer buffer,
|
||
bool truncateTrailingZeros) {
|
||
// Mimic String::format("%.[precision]g", ...), but use dtoas rounding
|
||
// facilities. "g": Signed value printed in f or e format, whichever is more
|
||
// compact for the given value and precision. The e format is used only when
|
||
// the exponent of the value is less than –4 or greater than or equal to the
|
||
// precision argument. Trailing zeros are truncated, and the decimal point
|
||
// appears only if one or more digits follow it. "precision": The precision
|
||
// specifies the maximum number of significant digits printed.
|
||
double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength);
|
||
const double_conversion::DoubleToStringConverter& converter =
|
||
double_conversion::DoubleToStringConverter::EcmaScriptConverter();
|
||
converter.ToPrecision(d, significantFigures, &builder);
|
||
if (!truncateTrailingZeros)
|
||
return builder.Finalize();
|
||
return formatStringTruncatingTrailingZerosIfNeeded(buffer, builder);
|
||
}
|
||
|
||
const char* numberToFixedWidthString(double d,
|
||
unsigned decimalPlaces,
|
||
NumberToStringBuffer buffer) {
|
||
// Mimic String::format("%.[precision]f", ...), but use dtoas rounding
|
||
// facilities. "f": Signed value having the form [ – ]dddd.dddd, where dddd is
|
||
// one or more decimal digits. The number of digits before the decimal point
|
||
// depends on the magnitude of the number, and the number of digits after the
|
||
// decimal point depends on the requested precision. "precision": The
|
||
// precision value specifies the number of digits after the decimal point. If
|
||
// a decimal point appears, at least one digit appears before it. The value is
|
||
// rounded to the appropriate number of digits.
|
||
double_conversion::StringBuilder builder(buffer, NumberToStringBufferLength);
|
||
const double_conversion::DoubleToStringConverter& converter =
|
||
double_conversion::DoubleToStringConverter::EcmaScriptConverter();
|
||
converter.ToFixed(d, decimalPlaces, &builder);
|
||
return builder.Finalize();
|
||
}
|
||
|
||
namespace Internal {
|
||
|
||
double parseDoubleFromLongString(const UChar* string,
|
||
size_t length,
|
||
size_t& parsedLength) {
|
||
Vector<LChar> conversionBuffer(length);
|
||
for (size_t i = 0; i < length; ++i)
|
||
conversionBuffer[i] = isASCII(string[i]) ? string[i] : 0;
|
||
return parseDouble(conversionBuffer.data(), length, parsedLength);
|
||
}
|
||
|
||
} // namespace Internal
|
||
|
||
} // namespace WTF
|