/** @file
* @brief Conversion between Coord and strings
*//*
* Authors:
* Krzysztof KosiƄski <tweenk.pl@gmail.com>
*
* Copyright 2014 Authors
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
// Most of the code in this file is derived from:
// https://code.google.com/p/double-conversion/
// The copyright notice for that code is attached below.
//
// Copyright 2010 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following
// disclaimer in the documentation and/or other materials provided
// with the distribution.
// * Neither the name of Google Inc. nor the names of its
// contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include <2geom/coord.h>
#include <stdint.h>
#include <cstdlib>
#include <cassert>
#include <cstring>
#include <climits>
#include <cstdarg>
#include <cmath>
#ifndef ASSERT
#define ASSERT(condition) \
assert(condition);
#endif
#ifndef UNIMPLEMENTED
#define UNIMPLEMENTED() (abort())
#endif
#ifndef UNREACHABLE
#define UNREACHABLE() (abort())
#endif
#define UINT64_2PART_C(a, b) (((static_cast<uint64_t>(a) << 32) + 0x##b##u))
#ifndef ARRAY_SIZE
#define ARRAY_SIZE(a) \
((sizeof(a) / sizeof(*(a))) / \
static_cast<size_t>(!(sizeof(a) % sizeof(*(a)))))
#endif
#ifndef DISALLOW_COPY_AND_ASSIGN
#define DISALLOW_COPY_AND_ASSIGN(TypeName) \
TypeName(const TypeName&); \
void operator=(const TypeName&)
#endif
#ifndef DISALLOW_IMPLICIT_CONSTRUCTORS
#define DISALLOW_IMPLICIT_CONSTRUCTORS(TypeName) \
TypeName(); \
DISALLOW_COPY_AND_ASSIGN(TypeName)
#endif
#if defined(__GNUC__)
#define DOUBLE_CONVERSION_UNUSED __attribute__((unused))
#else
#define DOUBLE_CONVERSION_UNUSED
#endif
namespace Geom {
namespace {
template <typename T>
class Vector {
public:
Vector() : start_(NULL), length_(0) {}
Vector(T* data, int length) : start_(data), length_(length) {
ASSERT(length == 0 || (length > 0 && data != NULL));
}
Vector<T> SubVector(int from, int to) {
ASSERT(to <= length_);
ASSERT(from < to);
ASSERT(0 <= from);
return Vector<T>(start() + from, to - from);
}
int length() const { return length_; }
bool is_empty() const { return length_ == 0; }
T* start() const { return start_; }
T& operator[](int index) const {
ASSERT(0 <= index && index < length_);
return start_[index];
}
T& first() { return start_[0]; }
T& last() { return start_[length_ - 1]; }
private:
T* start_;
int length_;
};
template <class Dest, class Source>
inline Dest BitCast(const Source& source) {
DOUBLE_CONVERSION_UNUSED
typedef char VerifySizesAreEqual[sizeof(Dest) == sizeof(Source) ? 1 : -1];
Dest dest;
memmove(&dest, &source, sizeof(dest));
return dest;
}
template <class Dest, class Source>
inline Dest BitCast(Source* source) {
return BitCast<Dest>(reinterpret_cast<uintptr_t>(source));
}
// We assume that doubles and uint64_t have the same endianness.
static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
// This "Do It Yourself Floating Point" class
class DiyFp {
public:
static const int kSignificandSize = 64;
DiyFp() : f_(0), e_(0) {}
DiyFp(uint64_t f, int e) : f_(f), e_(e) {}
void Subtract(const DiyFp& other) {
ASSERT(e_ == other.e_);
ASSERT(f_ >= other.f_);
f_ -= other.f_;
}
static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
DiyFp result = a;
result.Subtract(b);
return result;
}
void Multiply(const DiyFp& other) {
const uint64_t kM32 = 0xFFFFFFFFU;
uint64_t a = f_ >> 32;
uint64_t b = f_ & kM32;
uint64_t c = other.f_ >> 32;
uint64_t d = other.f_ & kM32;
uint64_t ac = a * c;
uint64_t bc = b * c;
uint64_t ad = a * d;
uint64_t bd = b * d;
uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32);
// By adding 1U << 31 to tmp we round the final result.
// Halfway cases will be round up.
tmp += 1U << 31;
uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
e_ += other.e_ + 64;
f_ = result_f;
}
static DiyFp Times(const DiyFp& a, const DiyFp& b) {
DiyFp result = a;
result.Multiply(b);
return result;
}
void Normalize() {
ASSERT(f_ != 0);
uint64_t f = f_;
int e = e_;
const uint64_t k10MSBits = UINT64_2PART_C(0xFFC00000, 00000000);
while ((f & k10MSBits) == 0) {
f <<= 10;
e -= 10;
}
while ((f & kUint64MSB) == 0) {
f <<= 1;
e--;
}
f_ = f;
e_ = e;
}
static DiyFp Normalize(const DiyFp& a) {
DiyFp result = a;
result.Normalize();
return result;
}
uint64_t f() const { return f_; }
int e() const { return e_; }
void set_f(uint64_t new_value) { f_ = new_value; }
void set_e(int new_value) { e_ = new_value; }
private:
static const uint64_t kUint64MSB = UINT64_2PART_C(0x80000000, 00000000);
uint64_t f_;
int e_;
};
class Double {
public:
static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000);
static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000);
static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000);
static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
static const int kSignificandSize = 53;
Double() : d64_(0) {}
explicit Double(double d) : d64_(double_to_uint64(d)) {}
explicit Double(uint64_t d64) : d64_(d64) {}
explicit Double(DiyFp diy_fp)
: d64_(DiyFpToUint64(diy_fp)) {}
DiyFp AsDiyFp() const {
ASSERT(Sign() > 0);
ASSERT(!IsSpecial());
return DiyFp(Significand(), Exponent());
}
DiyFp AsNormalizedDiyFp() const {
ASSERT(value() > 0.0);
uint64_t f = Significand();
int e = Exponent();
// The current double could be a denormal.
while ((f & kHiddenBit) == 0) {
f <<= 1;
e--;
}
// Do the final shifts in one go.
f <<= DiyFp::kSignificandSize - kSignificandSize;
e -= DiyFp::kSignificandSize - kSignificandSize;
return DiyFp(f, e);
}
uint64_t AsUint64() const {
return d64_;
}
double NextDouble() const {
if (d64_ == kInfinity) return Double(kInfinity).value();
if (Sign() < 0 && Significand() == 0) {
// -0.0
return 0.0;
}
if (Sign() < 0) {
return Double(d64_ - 1).value();
} else {
return Double(d64_ + 1).value();
}
}
double PreviousDouble() const {
if (d64_ == (kInfinity | kSignMask)) return -Double::Infinity();
if (Sign() < 0) {
return Double(d64_ + 1).value();
} else {
if (Significand() == 0) return -0.0;
return Double(d64_ - 1).value();
}
}
int Exponent() const {
if (IsDenormal()) return kDenormalExponent;
uint64_t d64 = AsUint64();
int biased_e =
static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
return biased_e - kExponentBias;
}
uint64_t Significand() const {
uint64_t d64 = AsUint64();
uint64_t significand = d64 & kSignificandMask;
if (!IsDenormal()) {
return significand + kHiddenBit;
} else {
return significand;
}
}
bool IsDenormal() const {
uint64_t d64 = AsUint64();
return (d64 & kExponentMask) == 0;
}
// We consider denormals not to be special.
// Hence only Infinity and NaN are special.
bool IsSpecial() const {
uint64_t d64 = AsUint64();
return (d64 & kExponentMask) == kExponentMask;
}
bool IsNan() const {
uint64_t d64 = AsUint64();
return ((d64 & kExponentMask) == kExponentMask) &&
((d64 & kSignificandMask) != 0);
}
bool IsInfinite() const {
uint64_t d64 = AsUint64();
return ((d64 & kExponentMask) == kExponentMask) &&
((d64 & kSignificandMask) == 0);
}
int Sign() const {
uint64_t d64 = AsUint64();
return (d64 & kSignMask) == 0? 1: -1;
}
DiyFp UpperBoundary() const {
ASSERT(Sign() > 0);
return DiyFp(Significand() * 2 + 1, Exponent() - 1);
}
void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
ASSERT(value() > 0.0);
DiyFp v = this->AsDiyFp();
DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
DiyFp m_minus;
if (LowerBoundaryIsCloser()) {
m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
} else {
m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
}
m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
m_minus.set_e(m_plus.e());
*out_m_plus = m_plus;
*out_m_minus = m_minus;
}
bool LowerBoundaryIsCloser() const {
bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
return physical_significand_is_zero && (Exponent() != kDenormalExponent);
}
double value() const { return uint64_to_double(d64_); }
static int SignificandSizeForOrderOfMagnitude(int order) {
if (order >= (kDenormalExponent + kSignificandSize)) {
return kSignificandSize;
}
if (order <= kDenormalExponent) return 0;
return order - kDenormalExponent;
}
static double Infinity() {
return Double(kInfinity).value();
}
static double NaN() {
return Double(kNaN).value();
}
private:
static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
static const int kDenormalExponent = -kExponentBias + 1;
static const int kMaxExponent = 0x7FF - kExponentBias;
static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000);
static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000);
const uint64_t d64_;
static uint64_t DiyFpToUint64(DiyFp diy_fp) {
uint64_t significand = diy_fp.f();
int exponent = diy_fp.e();
while (significand > kHiddenBit + kSignificandMask) {
significand >>= 1;
exponent++;
}
if (exponent >= kMaxExponent) {
return kInfinity;
}
if (exponent < kDenormalExponent) {
return 0;
}
while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
significand <<= 1;
exponent--;
}
uint64_t biased_exponent;
if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
biased_exponent = 0;
} else {
biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
}
return (significand & kSignificandMask) |
(biased_exponent << kPhysicalSignificandSize);
}
DISALLOW_COPY_AND_ASSIGN(Double);
};
template<typename S>
static int BitSize(S value) {
(void) value; // Mark variable as used.
return 8 * sizeof(value);
}
class Bignum {
public:
// 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately.
// This bignum can encode much bigger numbers, since it contains an
// exponent.
static const int kMaxSignificantBits = 3584;
Bignum()
: bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0)
{
for (int i = 0; i < kBigitCapacity; ++i) {
bigits_[i] = 0;
}
}
void AssignUInt16(uint16_t value) {
ASSERT(kBigitSize >= BitSize(value));
Zero();
if (value == 0) return;
EnsureCapacity(1);
bigits_[0] = value;
used_digits_ = 1;
}
void AssignUInt64(uint64_t value) {
const int kUInt64Size = 64;
Zero();
if (value == 0) return;
int needed_bigits = kUInt64Size / kBigitSize + 1;
EnsureCapacity(needed_bigits);
for (int i = 0; i < needed_bigits; ++i) {
bigits_[i] = value & kBigitMask;
value = value >> kBigitSize;
}
used_digits_ = needed_bigits;
Clamp();
}
void AssignBignum(const Bignum& other) {
exponent_ = other.exponent_;
for (int i = 0; i < other.used_digits_; ++i) {
bigits_[i] = other.bigits_[i];
}
// Clear the excess digits (if there were any).
for (int i = other.used_digits_; i < used_digits_; ++i) {
bigits_[i] = 0;
}
used_digits_ = other.used_digits_;
}
void AssignDecimalString(Vector<const char> value);
void AssignHexString(Vector<const char> value);
void AssignPowerUInt16(uint16_t base, int exponent);
void AddUInt16(uint16_t operand);
void AddUInt64(uint64_t operand);
void AddBignum(const Bignum& other);
// Precondition: this >= other.
void SubtractBignum(const Bignum& other);
void Square();
void ShiftLeft(int shift_amount);
void MultiplyByUInt32(uint32_t factor);
void MultiplyByUInt64(uint64_t factor);
void MultiplyByPowerOfTen(int exponent);
void Times10() { return MultiplyByUInt32(10); }
// Pseudocode:
// int result = this / other;
// this = this % other;
// In the worst case this function is in O(this/other).
uint16_t DivideModuloIntBignum(const Bignum& other);
bool ToHexString(char* buffer, int buffer_size) const;
// Returns
// -1 if a < b,
// 0 if a == b, and
// +1 if a > b.
static int Compare(const Bignum& a, const Bignum& b);
static bool Equal(const Bignum& a, const Bignum& b) {
return Compare(a, b) == 0;
}
static bool LessEqual(const Bignum& a, const Bignum& b) {
return Compare(a, b) <= 0;
}
static bool Less(const Bignum& a, const Bignum& b) {
return Compare(a, b) < 0;
}
// Returns Compare(a + b, c);
static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c);
// Returns a + b == c
static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
return PlusCompare(a, b, c) == 0;
}
// Returns a + b <= c
static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
return PlusCompare(a, b, c) <= 0;
}
// Returns a + b < c
static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) {
return PlusCompare(a, b, c) < 0;
}
private:
typedef uint32_t Chunk;
typedef uint64_t DoubleChunk;
static const int kChunkSize = sizeof(Chunk) * 8;
static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8;
// With bigit size of 28 we loose some bits, but a double still fits easily
// into two chunks, and more importantly we can use the Comba multiplication.
static const int kBigitSize = 28;
static const Chunk kBigitMask = (1 << kBigitSize) - 1;
// Every instance allocates kBigitLength chunks on the stack. Bignums cannot
// grow. There are no checks if the stack-allocated space is sufficient.
static const int kBigitCapacity = kMaxSignificantBits / kBigitSize;
void EnsureCapacity(int size) {
if (size > kBigitCapacity) {
UNREACHABLE();
}
}
void Align(const Bignum& other);
void Clamp();
bool IsClamped() const;
void Zero();
// Requires this to have enough capacity (no tests done).
// Updates used_digits_ if necessary.
// shift_amount must be < kBigitSize.
void BigitsShiftLeft(int shift_amount);
// BigitLength includes the "hidden" digits encoded in the exponent.
int BigitLength() const { return used_digits_ + exponent_; }
Chunk BigitAt(int index) const;
void SubtractTimes(const Bignum& other, int factor);
Chunk bigits_buffer_[kBigitCapacity];
// A vector backed by bigits_buffer_. This way accesses to the array are
// checked for out-of-bounds errors.
Vector<Chunk> bigits_;
int used_digits_;
// The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize).
int exponent_;
DISALLOW_COPY_AND_ASSIGN(Bignum);
};
static uint64_t ReadUInt64(Vector<const char> buffer,
int from,
int digits_to_read) {
uint64_t result = 0;
for (int i = from; i < from + digits_to_read; ++i) {
int digit = buffer[i] - '0';
ASSERT(0 <= digit && digit <= 9);
result = result * 10 + digit;
}
return result;
}
void Bignum::AssignDecimalString(Vector<const char> value) {
// 2^64 = 18446744073709551616 > 10^19
const int kMaxUint64DecimalDigits = 19;
Zero();
int length = value.length();
int pos = 0;
// Let's just say that each digit needs 4 bits.
while (length >= kMaxUint64DecimalDigits) {
uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
pos += kMaxUint64DecimalDigits;
length -= kMaxUint64DecimalDigits;
MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
AddUInt64(digits);
}
uint64_t digits = ReadUInt64(value, pos, length);
MultiplyByPowerOfTen(length);
AddUInt64(digits);
Clamp();
}
static int HexCharValue(char c) {
if ('0' <= c && c <= '9') return c - '0';
if ('a' <= c && c <= 'f') return 10 + c - 'a';
ASSERT('A' <= c && c <= 'F');
return 10 + c - 'A';
}
void Bignum::AssignHexString(Vector<const char> value) {
Zero();
int length = value.length();
int needed_bigits = length * 4 / kBigitSize + 1;
EnsureCapacity(needed_bigits);
int string_index = length - 1;
for (int i = 0; i < needed_bigits - 1; ++i) {
// These bigits are guaranteed to be "full".
Chunk current_bigit = 0;
for (int j = 0; j < kBigitSize / 4; j++) {
current_bigit += HexCharValue(value[string_index--]) << (j * 4);
}
bigits_[i] = current_bigit;
}
used_digits_ = needed_bigits - 1;
Chunk most_significant_bigit = 0; // Could be = 0;
for (int j = 0; j <= string_index; ++j) {
most_significant_bigit <<= 4;
most_significant_bigit += HexCharValue(value[j]);
}
if (most_significant_bigit != 0) {
bigits_[used_digits_] = most_significant_bigit;
used_digits_++;
}
Clamp();
}
void Bignum::AddUInt64(uint64_t operand) {
if (operand == 0) return;
Bignum other;
other.AssignUInt64(operand);
AddBignum(other);
}
void Bignum::AddBignum(const Bignum& other) {
ASSERT(IsClamped());
ASSERT(other.IsClamped());
Align(other);
EnsureCapacity(1 + std::max(BigitLength(), other.BigitLength()) - exponent_);
Chunk carry = 0;
int bigit_pos = other.exponent_ - exponent_;
ASSERT(bigit_pos >= 0);
for (int i = 0; i < other.used_digits_; ++i) {
Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
bigits_[bigit_pos] = sum & kBigitMask;
carry = sum >> kBigitSize;
bigit_pos++;
}
while (carry != 0) {
Chunk sum = bigits_[bigit_pos] + carry;
bigits_[bigit_pos] = sum & kBigitMask;
carry = sum >> kBigitSize;
bigit_pos++;
}
used_digits_ = std::max(bigit_pos, used_digits_);
ASSERT(IsClamped());
}
void Bignum::SubtractBignum(const Bignum& other) {
ASSERT(IsClamped());
ASSERT(other.IsClamped());
// We require this to be bigger than other.
ASSERT(LessEqual(other, *this));
Align(other);
int offset = other.exponent_ - exponent_;
Chunk borrow = 0;
int i;
for (i = 0; i < other.used_digits_; ++i) {
ASSERT((borrow == 0) || (borrow == 1));
Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
bigits_[i + offset] = difference & kBigitMask;
borrow = difference >> (kChunkSize - 1);
}
while (borrow != 0) {
Chunk difference = bigits_[i + offset] - borrow;
bigits_[i + offset] = difference & kBigitMask;
borrow = difference >> (kChunkSize - 1);
++i;
}
Clamp();
}
void Bignum::ShiftLeft(int shift_amount) {
if (used_digits_ == 0) return;
exponent_ += shift_amount / kBigitSize;
int local_shift = shift_amount % kBigitSize;
EnsureCapacity(used_digits_ + 1);
BigitsShiftLeft(local_shift);
}
void Bignum::MultiplyByUInt32(uint32_t factor) {
if (factor == 1) return;
if (factor == 0) {
Zero();
return;
}
if (used_digits_ == 0) return;
ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
DoubleChunk carry = 0;
for (int i = 0; i < used_digits_; ++i) {
DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
bigits_[i] = static_cast<Chunk>(product & kBigitMask);
carry = (product >> kBigitSize);
}
while (carry != 0) {
EnsureCapacity(used_digits_ + 1);
bigits_[used_digits_] = carry & kBigitMask;
used_digits_++;
carry >>= kBigitSize;
}
}
void Bignum::MultiplyByUInt64(uint64_t factor) {
if (factor == 1) return;
if (factor == 0) {
Zero();
return;
}
ASSERT(kBigitSize < 32);
uint64_t carry = 0;
uint64_t low = factor & 0xFFFFFFFF;
uint64_t high = factor >> 32;
for (int i = 0; i < used_digits_; ++i) {
uint64_t product_low = low * bigits_[i];
uint64_t product_high = high * bigits_[i];
uint64_t tmp = (carry & kBigitMask) + product_low;
bigits_[i] = tmp & kBigitMask;
carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
(product_high << (32 - kBigitSize));
}
while (carry != 0) {
EnsureCapacity(used_digits_ + 1);
bigits_[used_digits_] = carry & kBigitMask;
used_digits_++;
carry >>= kBigitSize;
}
}
void Bignum::MultiplyByPowerOfTen(int exponent) {
const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
const uint16_t kFive1 = 5;
const uint16_t kFive2 = kFive1 * 5;
const uint16_t kFive3 = kFive2 * 5;
const uint16_t kFive4 = kFive3 * 5;
const uint16_t kFive5 = kFive4 * 5;
const uint16_t kFive6 = kFive5 * 5;
const uint32_t kFive7 = kFive6 * 5;
const uint32_t kFive8 = kFive7 * 5;
const uint32_t kFive9 = kFive8 * 5;
const uint32_t kFive10 = kFive9 * 5;
const uint32_t kFive11 = kFive10 * 5;
const uint32_t kFive12 = kFive11 * 5;
const uint32_t kFive13 = kFive12 * 5;
const uint32_t kFive1_to_12[] =
{ kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
ASSERT(exponent >= 0);
if (exponent == 0) return;
if (used_digits_ == 0) return;
int remaining_exponent = exponent;
while (remaining_exponent >= 27) {
MultiplyByUInt64(kFive27);
remaining_exponent -= 27;
}
while (remaining_exponent >= 13) {
MultiplyByUInt32(kFive13);
remaining_exponent -= 13;
}
if (remaining_exponent > 0) {
MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
}
ShiftLeft(exponent);
}
void Bignum::Square() {
ASSERT(IsClamped());
int product_length = 2 * used_digits_;
EnsureCapacity(product_length);
if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
UNIMPLEMENTED();
}
DoubleChunk accumulator = 0;
// First shift the digits so we don't overwrite them.
int copy_offset = used_digits_;
for (int i = 0; i < used_digits_; ++i) {
bigits_[copy_offset + i] = bigits_[i];
}
// We have two loops to avoid some 'if's in the loop.
for (int i = 0; i < used_digits_; ++i) {
// Process temporary digit i with power i.
// The sum of the two indices must be equal to i.
int bigit_index1 = i;
int bigit_index2 = 0;
// Sum all of the sub-products.
while (bigit_index1 >= 0) {
Chunk chunk1 = bigits_[copy_offset + bigit_index1];
Chunk chunk2 = bigits_[copy_offset + bigit_index2];
accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
bigit_index1--;
bigit_index2++;
}
bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
accumulator >>= kBigitSize;
}
for (int i = used_digits_; i < product_length; ++i) {
int bigit_index1 = used_digits_ - 1;
int bigit_index2 = i - bigit_index1;
while (bigit_index2 < used_digits_) {
Chunk chunk1 = bigits_[copy_offset + bigit_index1];
Chunk chunk2 = bigits_[copy_offset + bigit_index2];
accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
bigit_index1--;
bigit_index2++;
}
bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
accumulator >>= kBigitSize;
}
ASSERT(accumulator == 0);
used_digits_ = product_length;
exponent_ *= 2;
Clamp();
}
void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
ASSERT(base != 0);
ASSERT(power_exponent >= 0);
if (power_exponent == 0) {
AssignUInt16(1);
return;
}
Zero();
int shifts = 0;
while ((base & 1) == 0) {
base >>= 1;
shifts++;
}
int bit_size = 0;
int tmp_base = base;
while (tmp_base != 0) {
tmp_base >>= 1;
bit_size++;
}
int final_size = bit_size * power_exponent;
EnsureCapacity(final_size / kBigitSize + 2);
// Left to Right exponentiation.
int mask = 1;
while (power_exponent >= mask) mask <<= 1;
mask >>= 2;
uint64_t this_value = base;
bool delayed_multipliciation = false;
const uint64_t max_32bits = 0xFFFFFFFF;
while (mask != 0 && this_value <= max_32bits) {
this_value = this_value * this_value;
// Verify that there is enough space in this_value to perform the
// multiplication. The first bit_size bits must be 0.
if ((power_exponent & mask) != 0) {
uint64_t base_bits_mask =
~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
bool high_bits_zero = (this_value & base_bits_mask) == 0;
if (high_bits_zero) {
this_value *= base;
} else {
delayed_multipliciation = true;
}
}
mask >>= 1;
}
AssignUInt64(this_value);
if (delayed_multipliciation) {
MultiplyByUInt32(base);
}
// Now do the same thing as a bignum.
while (mask != 0) {
Square();
if ((power_exponent & mask) != 0) {
MultiplyByUInt32(base);
}
mask >>= 1;
}
// And finally add the saved shifts.
ShiftLeft(shifts * power_exponent);
}
uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
ASSERT(IsClamped());
ASSERT(other.IsClamped());
ASSERT(other.used_digits_ > 0);
if (BigitLength() < other.BigitLength()) {
return 0;
}
Align(other);
uint16_t result = 0;
while (BigitLength() > other.BigitLength()) {
ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
ASSERT(bigits_[used_digits_ - 1] < 0x10000);
result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
SubtractTimes(other, bigits_[used_digits_ - 1]);
}
ASSERT(BigitLength() == other.BigitLength());
Chunk this_bigit = bigits_[used_digits_ - 1];
Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
if (other.used_digits_ == 1) {
int quotient = this_bigit / other_bigit;
bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
ASSERT(quotient < 0x10000);
result += static_cast<uint16_t>(quotient);
Clamp();
return result;
}
int division_estimate = this_bigit / (other_bigit + 1);
ASSERT(division_estimate < 0x10000);
result += static_cast<uint16_t>(division_estimate);
SubtractTimes(other, division_estimate);
if (other_bigit * (division_estimate + 1) > this_bigit) {
return result;
}
while (LessEqual(other, *this)) {
SubtractBignum(other);
result++;
}
return result;
}
template<typename S>
static int SizeInHexChars(S number) {
ASSERT(number > 0);
int result = 0;
while (number != 0) {
number >>= 4;
result++;
}
return result;
}
static char HexCharOfValue(int value) {
ASSERT(0 <= value && value <= 16);
if (value < 10) return static_cast<char>(value + '0');
return static_cast<char>(value - 10 + 'A');
}
bool Bignum::ToHexString(char* buffer, int buffer_size) const {
ASSERT(IsClamped());
// Each bigit must be printable as separate hex-character.
ASSERT(kBigitSize % 4 == 0);
const int kHexCharsPerBigit = kBigitSize / 4;
if (used_digits_ == 0) {
if (buffer_size < 2) return false;
buffer[0] = '0';
buffer[1] = '\0';
return true;
}
// We add 1 for the terminating '\0' character.
int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
if (needed_chars > buffer_size) return false;
int string_index = needed_chars - 1;
buffer[string_index--] = '\0';
for (int i = 0; i < exponent_; ++i) {
for (int j = 0; j < kHexCharsPerBigit; ++j) {
buffer[string_index--] = '0';
}
}
for (int i = 0; i < used_digits_ - 1; ++i) {
Chunk current_bigit = bigits_[i];
for (int j = 0; j < kHexCharsPerBigit; ++j) {
buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
current_bigit >>= 4;
}
}
// And finally the last bigit.
Chunk most_significant_bigit = bigits_[used_digits_ - 1];
while (most_significant_bigit != 0) {
buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
most_significant_bigit >>= 4;
}
return true;
}
Bignum::Chunk Bignum::BigitAt(int index) const {
if (index >= BigitLength()) return 0;
if (index < exponent_) return 0;
return bigits_[index - exponent_];
}
int Bignum::Compare(const Bignum& a, const Bignum& b) {
ASSERT(a.IsClamped());
ASSERT(b.IsClamped());
int bigit_length_a = a.BigitLength();
int bigit_length_b = b.BigitLength();
if (bigit_length_a < bigit_length_b) return -1;
if (bigit_length_a > bigit_length_b) return +1;
for (int i = bigit_length_a - 1; i >= std::min(a.exponent_, b.exponent_); --i) {
Chunk bigit_a = a.BigitAt(i);
Chunk bigit_b = b.BigitAt(i);
if (bigit_a < bigit_b) return -1;
if (bigit_a > bigit_b) return +1;
}
return 0;
}
int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
ASSERT(a.IsClamped());
ASSERT(b.IsClamped());
ASSERT(c.IsClamped());
if (a.BigitLength() < b.BigitLength()) {
return PlusCompare(b, a, c);
}
if (a.BigitLength() + 1 < c.BigitLength()) return -1;
if (a.BigitLength() > c.BigitLength()) return +1;
if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
return -1;
}
Chunk borrow = 0;
// Starting at min_exponent all digits are == 0. So no need to compare them.
int min_exponent = std::min(std::min(a.exponent_, b.exponent_), c.exponent_);
for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
Chunk chunk_a = a.BigitAt(i);
Chunk chunk_b = b.BigitAt(i);
Chunk chunk_c = c.BigitAt(i);
Chunk sum = chunk_a + chunk_b;
if (sum > chunk_c + borrow) {
return +1;
} else {
borrow = chunk_c + borrow - sum;
if (borrow > 1) return -1;
borrow <<= kBigitSize;
}
}
if (borrow == 0) return 0;
return -1;
}
void Bignum::Clamp() {
while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
used_digits_--;
}
if (used_digits_ == 0) {
// Zero.
exponent_ = 0;
}
}
bool Bignum::IsClamped() const {
return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
}
void Bignum::Zero() {
for (int i = 0; i < used_digits_; ++i) {
bigits_[i] = 0;
}
used_digits_ = 0;
exponent_ = 0;
}
void Bignum::Align(const Bignum& other) {
if (exponent_ > other.exponent_) {
int zero_digits = exponent_ - other.exponent_;
EnsureCapacity(used_digits_ + zero_digits);
for (int i = used_digits_ - 1; i >= 0; --i) {
bigits_[i + zero_digits] = bigits_[i];
}
for (int i = 0; i < zero_digits; ++i) {
bigits_[i] = 0;
}
used_digits_ += zero_digits;
exponent_ -= zero_digits;
ASSERT(used_digits_ >= 0);
ASSERT(exponent_ >= 0);
}
}
void Bignum::BigitsShiftLeft(int shift_amount) {
ASSERT(shift_amount < kBigitSize);
ASSERT(shift_amount >= 0);
Chunk carry = 0;
for (int i = 0; i < used_digits_; ++i) {
Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
carry = new_carry;
}
if (carry != 0) {
bigits_[used_digits_] = carry;
used_digits_++;
}
}
void Bignum::SubtractTimes(const Bignum& other, int factor) {
ASSERT(exponent_ <= other.exponent_);
if (factor < 3) {
for (int i = 0; i < factor; ++i) {
SubtractBignum(other);
}
return;
}
Chunk borrow = 0;
int exponent_diff = other.exponent_ - exponent_;
for (int i = 0; i < other.used_digits_; ++i) {
DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
DoubleChunk remove = borrow + product;
Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
bigits_[i + exponent_diff] = difference & kBigitMask;
borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
(remove >> kBigitSize));
}
for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
if (borrow == 0) return;
Chunk difference = bigits_[i] - borrow;
bigits_[i] = difference & kBigitMask;
borrow = difference >> (kChunkSize - 1);
}
Clamp();
}
class PowersOfTenCache {
public:
static const int kDecimalExponentDistance;
static const int kMinDecimalExponent;
static const int kMaxDecimalExponent;
static void GetCachedPowerForBinaryExponentRange(int min_exponent,
int max_exponent,
DiyFp* power,
int* decimal_exponent);
static void GetCachedPowerForDecimalExponent(int requested_exponent,
DiyFp* power,
int* found_exponent);
};
struct CachedPower {
uint64_t significand;
int16_t binary_exponent;
int16_t decimal_exponent;
};
static const CachedPower kCachedPowers[] = {
{UINT64_2PART_C(0xfa8fd5a0, 081c0288), -1220, -348},
{UINT64_2PART_C(0xbaaee17f, a23ebf76), -1193, -340},
{UINT64_2PART_C(0x8b16fb20, 3055ac76), -1166, -332},
{UINT64_2PART_C(0xcf42894a, 5dce35ea), -1140, -324},
{UINT64_2PART_C(0x9a6bb0aa, 55653b2d), -1113, -316},
{UINT64_2PART_C(0xe61acf03, 3d1a45df), -1087, -308},
{UINT64_2PART_C(0xab70fe17, c79ac6ca), -1060, -300},
{UINT64_2PART_C(0xff77b1fc, bebcdc4f), -1034, -292},
{UINT64_2PART_C(0xbe5691ef, 416bd60c), -1007, -284},
{UINT64_2PART_C(0x8dd01fad, 907ffc3c), -980, -276},
{UINT64_2PART_C(0xd3515c28, 31559a83), -954, -268},
{UINT64_2PART_C(0x9d71ac8f, ada6c9b5), -927, -260},
{UINT64_2PART_C(0xea9c2277, 23ee8bcb), -901, -252},
{UINT64_2PART_C(0xaecc4991, 4078536d), -874, -244},
{UINT64_2PART_C(0x823c1279, 5db6ce57), -847, -236},
{UINT64_2PART_C(0xc2109436, 4dfb5637), -821, -228},
{UINT64_2PART_C(0x9096ea6f, 3848984f), -794, -220},
{UINT64_2PART_C(0xd77485cb, 25823ac7), -768, -212},
{UINT64_2PART_C(0xa086cfcd, 97bf97f4), -741, -204},
{UINT64_2PART_C(0xef340a98, 172aace5), -715, -196},
{UINT64_2PART_C(0xb23867fb, 2a35b28e), -688, -188},
{UINT64_2PART_C(0x84c8d4df, d2c63f3b), -661, -180},
{UINT64_2PART_C(0xc5dd4427, 1ad3cdba), -635, -172},
{UINT64_2PART_C(0x936b9fce, bb25c996), -608, -164},
{UINT64_2PART_C(0xdbac6c24, 7d62a584), -582, -156},
{UINT64_2PART_C(0xa3ab6658, 0d5fdaf6), -555, -148},
{UINT64_2PART_C(0xf3e2f893, dec3f126), -529, -140},
{UINT64_2PART_C(0xb5b5ada8, aaff80b8), -502, -132},
{UINT64_2PART_C(0x87625f05, 6c7c4a8b), -475, -124},
{UINT64_2PART_C(0xc9bcff60, 34c13053), -449, -116},
{UINT64_2PART_C(0x964e858c, 91ba2655), -422, -108},
{UINT64_2PART_C(0xdff97724, 70297ebd), -396, -100},
{UINT64_2PART_C(0xa6dfbd9f, b8e5b88f), -369, -92},
{UINT64_2PART_C(0xf8a95fcf, 88747d94), -343, -84},
{UINT64_2PART_C(0xb9447093, 8fa89bcf), -316, -76},
{UINT64_2PART_C(0x8a08f0f8, bf0f156b), -289, -68},
{UINT64_2PART_C(0xcdb02555, 653131b6), -263, -60},
{UINT64_2PART_C(0x993fe2c6, d07b7fac), -236, -52},
{UINT64_2PART_C(0xe45c10c4, 2a2b3b06), -210, -44},
{UINT64_2PART_C(0xaa242499, 697392d3), -183, -36},
{UINT64_2PART_C(0xfd87b5f2, 8300ca0e), -157, -28},
{UINT64_2PART_C(0xbce50864, 92111aeb), -130, -20},
{UINT64_2PART_C(0x8cbccc09, 6f5088cc), -103, -12},
{UINT64_2PART_C(0xd1b71758, e219652c), -77, -4},
{UINT64_2PART_C(0x9c400000, 00000000), -50, 4},
{UINT64_2PART_C(0xe8d4a510, 00000000), -24, 12},
{UINT64_2PART_C(0xad78ebc5, ac620000), 3, 20},
{UINT64_2PART_C(0x813f3978, f8940984), 30, 28},
{UINT64_2PART_C(0xc097ce7b, c90715b3), 56, 36},
{UINT64_2PART_C(0x8f7e32ce, 7bea5c70), 83, 44},
{UINT64_2PART_C(0xd5d238a4, abe98068), 109, 52},
{UINT64_2PART_C(0x9f4f2726, 179a2245), 136, 60},
{UINT64_2PART_C(0xed63a231, d4c4fb27), 162, 68},
{UINT64_2PART_C(0xb0de6538, 8cc8ada8), 189, 76},
{UINT64_2PART_C(0x83c7088e, 1aab65db), 216, 84},
{UINT64_2PART_C(0xc45d1df9, 42711d9a), 242, 92},
{UINT64_2PART_C(0x924d692c, a61be758), 269, 100},
{UINT64_2PART_C(0xda01ee64, 1a708dea), 295, 108},
{UINT64_2PART_C(0xa26da399, 9aef774a), 322, 116},
{UINT64_2PART_C(0xf209787b, b47d6b85), 348, 124},
{UINT64_2PART_C(0xb454e4a1, 79dd1877), 375, 132},
{UINT64_2PART_C(0x865b8692, 5b9bc5c2), 402, 140},
{UINT64_2PART_C(0xc83553c5, c8965d3d), 428, 148},
{UINT64_2PART_C(0x952ab45c, fa97a0b3), 455, 156},
{UINT64_2PART_C(0xde469fbd, 99a05fe3), 481, 164},
{UINT64_2PART_C(0xa59bc234, db398c25), 508, 172},
{UINT64_2PART_C(0xf6c69a72, a3989f5c), 534, 180},
{UINT64_2PART_C(0xb7dcbf53, 54e9bece), 561, 188},
{UINT64_2PART_C(0x88fcf317, f22241e2), 588, 196},
{UINT64_2PART_C(0xcc20ce9b, d35c78a5), 614, 204},
{UINT64_2PART_C(0x98165af3, 7b2153df), 641, 212},
{UINT64_2PART_C(0xe2a0b5dc, 971f303a), 667, 220},
{UINT64_2PART_C(0xa8d9d153, 5ce3b396), 694, 228},
{UINT64_2PART_C(0xfb9b7cd9, a4a7443c), 720, 236},
{UINT64_2PART_C(0xbb764c4c, a7a44410), 747, 244},
{UINT64_2PART_C(0x8bab8eef, b6409c1a), 774, 252},
{UINT64_2PART_C(0xd01fef10, a657842c), 800, 260},
{UINT64_2PART_C(0x9b10a4e5, e9913129), 827, 268},
{UINT64_2PART_C(0xe7109bfb, a19c0c9d), 853, 276},
{UINT64_2PART_C(0xac2820d9, 623bf429), 880, 284},
{UINT64_2PART_C(0x80444b5e, 7aa7cf85), 907, 292},
{UINT64_2PART_C(0xbf21e440, 03acdd2d), 933, 300},
{UINT64_2PART_C(0x8e679c2f, 5e44ff8f), 960, 308},
{UINT64_2PART_C(0xd433179d, 9c8cb841), 986, 316},
{UINT64_2PART_C(0x9e19db92, b4e31ba9), 1013, 324},
{UINT64_2PART_C(0xeb96bf6e, badf77d9), 1039, 332},
{UINT64_2PART_C(0xaf87023b, 9bf0ee6b), 1066, 340},
};
static const int kCachedPowersLength = ARRAY_SIZE(kCachedPowers);
static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent.
static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
// Difference between the decimal exponents in the table above.
const int PowersOfTenCache::kDecimalExponentDistance = 8;
const int PowersOfTenCache::kMinDecimalExponent = -348;
const int PowersOfTenCache::kMaxDecimalExponent = 340;
void PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
int min_exponent,
int max_exponent,
DiyFp* power,
int* decimal_exponent) {
int kQ = DiyFp::kSignificandSize;
double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10);
int foo = kCachedPowersOffset;
int index =
(foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
ASSERT(0 <= index && index < kCachedPowersLength);
CachedPower cached_power = kCachedPowers[index];
ASSERT(min_exponent <= cached_power.binary_exponent);
(void) max_exponent; // Mark variable as used.
ASSERT(cached_power.binary_exponent <= max_exponent);
*decimal_exponent = cached_power.decimal_exponent;
*power = DiyFp(cached_power.significand, cached_power.binary_exponent);
}
void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent,
DiyFp* power,
int* found_exponent) {
ASSERT(kMinDecimalExponent <= requested_exponent);
ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance);
int index =
(requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
CachedPower cached_power = kCachedPowers[index];
*power = DiyFp(cached_power.significand, cached_power.binary_exponent);
*found_exponent = cached_power.decimal_exponent;
ASSERT(*found_exponent <= requested_exponent);
ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance);
}
enum BignumDtoaMode {
BIGNUM_DTOA_SHORTEST,
BIGNUM_DTOA_FIXED,
BIGNUM_DTOA_PRECISION
};
static int NormalizedExponent(uint64_t significand, int exponent) {
ASSERT(significand != 0);
while ((significand & Double::kHiddenBit) == 0) {
significand = significand << 1;
exponent = exponent - 1;
}
return exponent;
}
static int EstimatePower(int exponent);
static void InitialScaledStartValues(uint64_t significand,
int exponent,
bool lower_boundary_is_closer,
int estimated_power,
bool need_boundary_deltas,
Bignum* numerator,
Bignum* denominator,
Bignum* delta_minus,
Bignum* delta_plus);
static void FixupMultiply10(int estimated_power, bool is_even,
int* decimal_point,
Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus);
static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus,
bool is_even,
Vector<char> buffer, int* length);
static void BignumToFixed(int requested_digits, int* decimal_point,
Bignum* numerator, Bignum* denominator,
Vector<char>(buffer), int* length);
static void GenerateCountedDigits(int count, int* decimal_point,
Bignum* numerator, Bignum* denominator,
Vector<char>(buffer), int* length);
void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
Vector<char> buffer, int* length, int* decimal_point) {
ASSERT(v > 0);
ASSERT(!Double(v).IsSpecial());
uint64_t significand;
int exponent;
bool lower_boundary_is_closer;
significand = Double(v).Significand();
exponent = Double(v).Exponent();
lower_boundary_is_closer = Double(v).LowerBoundaryIsCloser();
bool need_boundary_deltas =
(mode == BIGNUM_DTOA_SHORTEST);
bool is_even = (significand & 1) == 0;
int normalized_exponent = NormalizedExponent(significand, exponent);
// estimated_power might be too low by 1.
int estimated_power = EstimatePower(normalized_exponent);
if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
buffer[0] = '\0';
*length = 0;
*decimal_point = -requested_digits;
return;
}
Bignum numerator;
Bignum denominator;
Bignum delta_minus;
Bignum delta_plus;
ASSERT(Bignum::kMaxSignificantBits >= 324*4);
InitialScaledStartValues(significand, exponent, lower_boundary_is_closer,
estimated_power, need_boundary_deltas,
&numerator, &denominator,
&delta_minus, &delta_plus);
FixupMultiply10(estimated_power, is_even, decimal_point,
&numerator, &denominator,
&delta_minus, &delta_plus);
switch (mode) {
case BIGNUM_DTOA_SHORTEST:
GenerateShortestDigits(&numerator, &denominator,
&delta_minus, &delta_plus,
is_even, buffer, length);
break;
case BIGNUM_DTOA_FIXED:
BignumToFixed(requested_digits, decimal_point,
&numerator, &denominator,
buffer, length);
break;
case BIGNUM_DTOA_PRECISION:
GenerateCountedDigits(requested_digits, decimal_point,
&numerator, &denominator,
buffer, length);
break;
default:
UNREACHABLE();
}
buffer[*length] = '\0';
}
static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus,
bool is_even,
Vector<char> buffer, int* length) {
if (Bignum::Equal(*delta_minus, *delta_plus)) {
delta_plus = delta_minus;
}
*length = 0;
for (;;) {
uint16_t digit;
digit = numerator->DivideModuloIntBignum(*denominator);
ASSERT(digit <= 9);
buffer[(*length)++] = static_cast<char>(digit + '0');
bool in_delta_room_minus;
bool in_delta_room_plus;
if (is_even) {
in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
} else {
in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
}
if (is_even) {
in_delta_room_plus =
Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
} else {
in_delta_room_plus =
Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
}
if (!in_delta_room_minus && !in_delta_room_plus) {
numerator->Times10();
delta_minus->Times10();
if (delta_minus != delta_plus) {
delta_plus->Times10();
}
} else if (in_delta_room_minus && in_delta_room_plus) {
int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
if (compare < 0) {
// Remaining digits are less than .5. -> Round down (== do nothing).
} else if (compare > 0) {
// Remaining digits are more than .5 of denominator. -> Round up.
ASSERT(buffer[(*length) - 1] != '9');
buffer[(*length) - 1]++;
} else {
if ((buffer[(*length) - 1] - '0') % 2 == 0) {
// Round down => Do nothing.
} else {
ASSERT(buffer[(*length) - 1] != '9');
buffer[(*length) - 1]++;
}
}
return;
} else if (in_delta_room_minus) {
return;
} else { // in_delta_room_plus
// Round up
ASSERT(buffer[(*length) -1] != '9');
buffer[(*length) - 1]++;
return;
}
}
}
static void GenerateCountedDigits(int count, int* decimal_point,
Bignum* numerator, Bignum* denominator,
Vector<char> buffer, int* length) {
ASSERT(count >= 0);
for (int i = 0; i < count - 1; ++i) {
uint16_t digit;
digit = numerator->DivideModuloIntBignum(*denominator);
ASSERT(digit <= 9);
buffer[i] = static_cast<char>(digit + '0');
numerator->Times10();
}
uint16_t digit;
digit = numerator->DivideModuloIntBignum(*denominator);
if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
digit++;
}
ASSERT(digit <= 10);
buffer[count - 1] = static_cast<char>(digit + '0');
for (int i = count - 1; i > 0; --i) {
if (buffer[i] != '0' + 10) break;
buffer[i] = '0';
buffer[i - 1]++;
}
if (buffer[0] == '0' + 10) {
buffer[0] = '1';
(*decimal_point)++;
}
*length = count;
}
static void BignumToFixed(int requested_digits, int* decimal_point,
Bignum* numerator, Bignum* denominator,
Vector<char>(buffer), int* length)
{
if (-(*decimal_point) > requested_digits) {
*decimal_point = -requested_digits;
*length = 0;
return;
} else if (-(*decimal_point) == requested_digits) {
ASSERT(*decimal_point == -requested_digits);
denominator->Times10();
if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
buffer[0] = '1';
*length = 1;
(*decimal_point)++;
} else {
*length = 0;
}
return;
} else {
int needed_digits = (*decimal_point) + requested_digits;
GenerateCountedDigits(needed_digits, decimal_point,
numerator, denominator,
buffer, length);
}
}
static int EstimatePower(int exponent) {
const double k1Log10 = 0.30102999566398114; // 1/lg(10)
// For doubles len(f) == 53 (don't forget the hidden bit).
const int kSignificandSize = Double::kSignificandSize;
double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
return static_cast<int>(estimate);
}
static void InitialScaledStartValuesPositiveExponent(
uint64_t significand, int exponent,
int estimated_power, bool need_boundary_deltas,
Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus)
{
ASSERT(estimated_power >= 0);
numerator->AssignUInt64(significand);
numerator->ShiftLeft(exponent);
denominator->AssignPowerUInt16(10, estimated_power);
if (need_boundary_deltas) {
denominator->ShiftLeft(1);
numerator->ShiftLeft(1);
delta_plus->AssignUInt16(1);
delta_plus->ShiftLeft(exponent);
delta_minus->AssignUInt16(1);
delta_minus->ShiftLeft(exponent);
}
}
static void InitialScaledStartValuesNegativeExponentPositivePower(
uint64_t significand, int exponent,
int estimated_power, bool need_boundary_deltas,
Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus)
{
numerator->AssignUInt64(significand);
denominator->AssignPowerUInt16(10, estimated_power);
denominator->ShiftLeft(-exponent);
if (need_boundary_deltas) {
denominator->ShiftLeft(1);
numerator->ShiftLeft(1);
delta_plus->AssignUInt16(1);
delta_minus->AssignUInt16(1);
}
}
static void InitialScaledStartValuesNegativeExponentNegativePower(
uint64_t significand, int exponent,
int estimated_power, bool need_boundary_deltas,
Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus)
{
Bignum* power_ten = numerator;
power_ten->AssignPowerUInt16(10, -estimated_power);
if (need_boundary_deltas) {
delta_plus->AssignBignum(*power_ten);
delta_minus->AssignBignum(*power_ten);
}
ASSERT(numerator == power_ten);
numerator->MultiplyByUInt64(significand);
denominator->AssignUInt16(1);
denominator->ShiftLeft(-exponent);
if (need_boundary_deltas) {
numerator->ShiftLeft(1);
denominator->ShiftLeft(1);
}
}
static void InitialScaledStartValues(uint64_t significand,
int exponent,
bool lower_boundary_is_closer,
int estimated_power,
bool need_boundary_deltas,
Bignum* numerator,
Bignum* denominator,
Bignum* delta_minus,
Bignum* delta_plus)
{
if (exponent >= 0) {
InitialScaledStartValuesPositiveExponent(
significand, exponent, estimated_power, need_boundary_deltas,
numerator, denominator, delta_minus, delta_plus);
} else if (estimated_power >= 0) {
InitialScaledStartValuesNegativeExponentPositivePower(
significand, exponent, estimated_power, need_boundary_deltas,
numerator, denominator, delta_minus, delta_plus);
} else {
InitialScaledStartValuesNegativeExponentNegativePower(
significand, exponent, estimated_power, need_boundary_deltas,
numerator, denominator, delta_minus, delta_plus);
}
if (need_boundary_deltas && lower_boundary_is_closer) {
denominator->ShiftLeft(1); // *2
numerator->ShiftLeft(1); // *2
delta_plus->ShiftLeft(1); // *2
}
}
static void FixupMultiply10(int estimated_power, bool is_even,
int* decimal_point,
Bignum* numerator, Bignum* denominator,
Bignum* delta_minus, Bignum* delta_plus) {
bool in_range;
if (is_even) {
in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
} else {
in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
}
if (in_range) {
*decimal_point = estimated_power + 1;
} else {
*decimal_point = estimated_power;
numerator->Times10();
if (Bignum::Equal(*delta_minus, *delta_plus)) {
delta_minus->Times10();
delta_plus->AssignBignum(*delta_minus);
} else {
delta_minus->Times10();
delta_plus->Times10();
}
}
}
enum FastDtoaMode {
FAST_DTOA_SHORTEST,
FAST_DTOA_PRECISION
};
bool FastDtoa(double d,
FastDtoaMode mode,
int requested_digits,
Vector<char> buffer,
int* length,
int* decimal_point);
static const int kMinimalTargetExponent = -60;
static const int kMaximalTargetExponent = -32;
static bool RoundWeed(Vector<char> buffer, int length,
uint64_t distance_too_high_w, uint64_t unsafe_interval,
uint64_t rest, uint64_t ten_kappa, uint64_t unit)
{
uint64_t small_distance = distance_too_high_w - unit;
uint64_t big_distance = distance_too_high_w + unit;
ASSERT(rest <= unsafe_interval);
while (rest < small_distance && // Negated condition 1
unsafe_interval - rest >= ten_kappa && // Negated condition 2
(rest + ten_kappa < small_distance || // buffer{-1} > w_high
small_distance - rest >= rest + ten_kappa - small_distance)) {
buffer[length - 1]--;
rest += ten_kappa;
}
if (rest < big_distance &&
unsafe_interval - rest >= ten_kappa &&
(rest + ten_kappa < big_distance ||
big_distance - rest > rest + ten_kappa - big_distance)) {
return false;
}
return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
}
static bool RoundWeedCounted(Vector<char> buffer, int length,
uint64_t rest, uint64_t ten_kappa, uint64_t unit,
int* kappa)
{
ASSERT(rest < ten_kappa);
if (unit >= ten_kappa) return false;
if (ten_kappa - unit <= unit) return false;
if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
return true;
}
if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
buffer[length - 1]++;
for (int i = length - 1; i > 0; --i) {
if (buffer[i] != '0' + 10) break;
buffer[i] = '0';
buffer[i - 1]++;
}
if (buffer[0] == '0' + 10) {
buffer[0] = '1';
(*kappa) += 1;
}
return true;
}
return false;
}
static unsigned int const kSmallPowersOfTen[] =
{0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
1000000000};
static void BiggestPowerTen(uint32_t number,
int number_bits,
uint32_t* power,
int* exponent_plus_one) {
ASSERT(number < (1u << (number_bits + 1)));
int exponent_plus_one_guess = ((number_bits + 1) * 1233 >> 12);
exponent_plus_one_guess++;
if (number < kSmallPowersOfTen[exponent_plus_one_guess]) {
exponent_plus_one_guess--;
}
*power = kSmallPowersOfTen[exponent_plus_one_guess];
*exponent_plus_one = exponent_plus_one_guess;
}
static bool DigitGen(DiyFp low, DiyFp w, DiyFp high, Vector<char> buffer,
int* length, int* kappa)
{
ASSERT(low.e() == w.e() && w.e() == high.e());
ASSERT(low.f() + 1 <= high.f() - 1);
ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
uint64_t unit = 1;
DiyFp too_low = DiyFp(low.f() - unit, low.e());
DiyFp too_high = DiyFp(high.f() + unit, high.e());
DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
uint64_t fractionals = too_high.f() & (one.f() - 1);
uint32_t divisor;
int divisor_exponent_plus_one;
BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
&divisor, &divisor_exponent_plus_one);
*kappa = divisor_exponent_plus_one;
*length = 0;
while (*kappa > 0) {
int digit = integrals / divisor;
ASSERT(digit <= 9);
buffer[*length] = static_cast<char>('0' + digit);
(*length)++;
integrals %= divisor;
(*kappa)--;
uint64_t rest =
(static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
if (rest < unsafe_interval.f()) {
return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
unsafe_interval.f(), rest,
static_cast<uint64_t>(divisor) << -one.e(), unit);
}
divisor /= 10;
}
ASSERT(one.e() >= -60);
ASSERT(fractionals < one.f());
ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
for (;;) {
fractionals *= 10;
unit *= 10;
unsafe_interval.set_f(unsafe_interval.f() * 10);
// Integer division by one.
int digit = static_cast<int>(fractionals >> -one.e());
ASSERT(digit <= 9);
buffer[*length] = static_cast<char>('0' + digit);
(*length)++;
fractionals &= one.f() - 1; // Modulo by one.
(*kappa)--;
if (fractionals < unsafe_interval.f()) {
return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
unsafe_interval.f(), fractionals, one.f(), unit);
}
}
}
static bool DigitGenCounted(DiyFp w, int requested_digits, Vector<char> buffer,
int* length, int* kappa)
{
ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
ASSERT(kMinimalTargetExponent >= -60);
ASSERT(kMaximalTargetExponent <= -32);
uint64_t w_error = 1;
DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
uint64_t fractionals = w.f() & (one.f() - 1);
uint32_t divisor;
int divisor_exponent_plus_one;
BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
&divisor, &divisor_exponent_plus_one);
*kappa = divisor_exponent_plus_one;
*length = 0;
while (*kappa > 0) {
int digit = integrals / divisor;
ASSERT(digit <= 9);
buffer[*length] = static_cast<char>('0' + digit);
(*length)++;
requested_digits--;
integrals %= divisor;
(*kappa)--;
if (requested_digits == 0) break;
divisor /= 10;
}
if (requested_digits == 0) {
uint64_t rest =
(static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
return RoundWeedCounted(buffer, *length, rest,
static_cast<uint64_t>(divisor) << -one.e(), w_error,
kappa);
}
ASSERT(one.e() >= -60);
ASSERT(fractionals < one.f());
ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
while (requested_digits > 0 && fractionals > w_error) {
fractionals *= 10;
w_error *= 10;
// Integer division by one.
int digit = static_cast<int>(fractionals >> -one.e());
ASSERT(digit <= 9);
buffer[*length] = static_cast<char>('0' + digit);
(*length)++;
requested_digits--;
fractionals &= one.f() - 1; // Modulo by one.
(*kappa)--;
}
if (requested_digits != 0) return false;
return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
kappa);
}
static bool Grisu3(double v, FastDtoaMode mode, Vector<char> buffer,
int* length, int* decimal_exponent)
{
DiyFp w = Double(v).AsNormalizedDiyFp();
DiyFp boundary_minus, boundary_plus;
ASSERT(mode == FAST_DTOA_SHORTEST);
Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
ASSERT(boundary_plus.e() == w.e());
DiyFp ten_mk; // Cached power of ten: 10^-k
int mk; // -k
int ten_mk_minimal_binary_exponent =
kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
int ten_mk_maximal_binary_exponent =
kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
ten_mk_minimal_binary_exponent,
ten_mk_maximal_binary_exponent,
&ten_mk, &mk);
ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
DiyFp::kSignificandSize) &&
(kMaximalTargetExponent >= w.e() + ten_mk.e() +
DiyFp::kSignificandSize));
DiyFp scaled_w = DiyFp::Times(w, ten_mk);
ASSERT(scaled_w.e() ==
boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
DiyFp scaled_boundary_plus = DiyFp::Times(boundary_plus, ten_mk);
int kappa;
bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
buffer, length, &kappa);
*decimal_exponent = -mk + kappa;
return result;
}
static bool Grisu3Counted(double v, int requested_digits, Vector<char> buffer,
int* length, int* decimal_exponent)
{
DiyFp w = Double(v).AsNormalizedDiyFp();
DiyFp ten_mk; // Cached power of ten: 10^-k
int mk; // -k
int ten_mk_minimal_binary_exponent =
kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
int ten_mk_maximal_binary_exponent =
kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
ten_mk_minimal_binary_exponent,
ten_mk_maximal_binary_exponent,
&ten_mk, &mk);
ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
DiyFp::kSignificandSize) &&
(kMaximalTargetExponent >= w.e() + ten_mk.e() +
DiyFp::kSignificandSize));
DiyFp scaled_w = DiyFp::Times(w, ten_mk);
int kappa;
bool result = DigitGenCounted(scaled_w, requested_digits,
buffer, length, &kappa);
*decimal_exponent = -mk + kappa;
return result;
}
bool FastDtoa(double v,
FastDtoaMode mode,
int requested_digits,
Vector<char> buffer,
int* length,
int* decimal_point) {
ASSERT(v > 0);
ASSERT(!Double(v).IsSpecial());
bool result = false;
int decimal_exponent = 0;
switch (mode) {
case FAST_DTOA_SHORTEST:
result = Grisu3(v, mode, buffer, length, &decimal_exponent);
break;
case FAST_DTOA_PRECISION:
result = Grisu3Counted(v, requested_digits,
buffer, length, &decimal_exponent);
break;
default:
UNREACHABLE();
}
if (result) {
*decimal_point = *length + decimal_exponent;
buffer[*length] = '\0';
}
return result;
}
// Represents a 128bit type. This class should be replaced by a native type on
// platforms that support 128bit integers.
class UInt128 {
public:
UInt128() : high_bits_(0), low_bits_(0) { }
UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
void Multiply(uint32_t multiplicand) {
uint64_t accumulator;
accumulator = (low_bits_ & kMask32) * multiplicand;
uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
accumulator >>= 32;
accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
low_bits_ = (accumulator << 32) + part;
accumulator >>= 32;
accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
part = static_cast<uint32_t>(accumulator & kMask32);
accumulator >>= 32;
accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
high_bits_ = (accumulator << 32) + part;
ASSERT((accumulator >> 32) == 0);
}
void Shift(int shift_amount) {
ASSERT(-64 <= shift_amount && shift_amount <= 64);
if (shift_amount == 0) {
return;
} else if (shift_amount == -64) {
high_bits_ = low_bits_;
low_bits_ = 0;
} else if (shift_amount == 64) {
low_bits_ = high_bits_;
high_bits_ = 0;
} else if (shift_amount <= 0) {
high_bits_ <<= -shift_amount;
high_bits_ += low_bits_ >> (64 + shift_amount);
low_bits_ <<= -shift_amount;
} else {
low_bits_ >>= shift_amount;
low_bits_ += high_bits_ << (64 - shift_amount);
high_bits_ >>= shift_amount;
}
}
// Modifies *this to *this MOD (2^power).
// Returns *this DIV (2^power).
int DivModPowerOf2(int power) {
if (power >= 64) {
int result = static_cast<int>(high_bits_ >> (power - 64));
high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
return result;
} else {
uint64_t part_low = low_bits_ >> power;
uint64_t part_high = high_bits_ << (64 - power);
int result = static_cast<int>(part_low + part_high);
high_bits_ = 0;
low_bits_ -= part_low << power;
return result;
}
}
bool IsZero() const {
return high_bits_ == 0 && low_bits_ == 0;
}
int BitAt(int position) {
if (position >= 64) {
return static_cast<int>(high_bits_ >> (position - 64)) & 1;
} else {
return static_cast<int>(low_bits_ >> position) & 1;
}
}
private:
static const uint64_t kMask32 = 0xFFFFFFFF;
// Value == (high_bits_ << 64) + low_bits_
uint64_t high_bits_;
uint64_t low_bits_;
};
static const int kDoubleSignificandSize = 53; // Includes the hidden bit.
static void FillDigits32FixedLength(uint32_t number, int requested_length,
Vector<char> buffer, int* length) {
for (int i = requested_length - 1; i >= 0; --i) {
buffer[(*length) + i] = '0' + number % 10;
number /= 10;
}
*length += requested_length;
}
static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
int number_length = 0;
// We fill the digits in reverse order and exchange them afterwards.
while (number != 0) {
int digit = number % 10;
number /= 10;
buffer[(*length) + number_length] = static_cast<char>('0' + digit);
number_length++;
}
// Exchange the digits.
int i = *length;
int j = *length + number_length - 1;
while (i < j) {
char tmp = buffer[i];
buffer[i] = buffer[j];
buffer[j] = tmp;
i++;
j--;
}
*length += number_length;
}
static void FillDigits64FixedLength(uint64_t number,
Vector<char> buffer, int* length) {
const uint32_t kTen7 = 10000000;
// For efficiency cut the number into 3 uint32_t parts, and print those.
uint32_t part2 = static_cast<uint32_t>(number % kTen7);
number /= kTen7;
uint32_t part1 = static_cast<uint32_t>(number % kTen7);
uint32_t part0 = static_cast<uint32_t>(number / kTen7);
FillDigits32FixedLength(part0, 3, buffer, length);
FillDigits32FixedLength(part1, 7, buffer, length);
FillDigits32FixedLength(part2, 7, buffer, length);
}
static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
const uint32_t kTen7 = 10000000;
// For efficiency cut the number into 3 uint32_t parts, and print those.
uint32_t part2 = static_cast<uint32_t>(number % kTen7);
number /= kTen7;
uint32_t part1 = static_cast<uint32_t>(number % kTen7);
uint32_t part0 = static_cast<uint32_t>(number / kTen7);
if (part0 != 0) {
FillDigits32(part0, buffer, length);
FillDigits32FixedLength(part1, 7, buffer, length);
FillDigits32FixedLength(part2, 7, buffer, length);
} else if (part1 != 0) {
FillDigits32(part1, buffer, length);
FillDigits32FixedLength(part2, 7, buffer, length);
} else {
FillDigits32(part2, buffer, length);
}
}
static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
// An empty buffer represents 0.
if (*length == 0) {
buffer[0] = '1';
*decimal_point = 1;
*length = 1;
return;
}
buffer[(*length) - 1]++;
for (int i = (*length) - 1; i > 0; --i) {
if (buffer[i] != '0' + 10) {
return;
}
buffer[i] = '0';
buffer[i - 1]++;
}
if (buffer[0] == '0' + 10) {
buffer[0] = '1';
(*decimal_point)++;
}
}
static void FillFractionals(uint64_t fractionals, int exponent,
int fractional_count, Vector<char> buffer,
int* length, int* decimal_point)
{
ASSERT(-128 <= exponent && exponent <= 0);
if (-exponent <= 64) {
ASSERT(fractionals >> 56 == 0);
int point = -exponent;
for (int i = 0; i < fractional_count; ++i) {
if (fractionals == 0) break;
fractionals *= 5;
point--;
int digit = static_cast<int>(fractionals >> point);
ASSERT(digit <= 9);
buffer[*length] = static_cast<char>('0' + digit);
(*length)++;
fractionals -= static_cast<uint64_t>(digit) << point;
}
if (((fractionals >> (point - 1)) & 1) == 1) {
RoundUp(buffer, length, decimal_point);
}
} else { // We need 128 bits.
ASSERT(64 < -exponent && -exponent <= 128);
UInt128 fractionals128 = UInt128(fractionals, 0);
fractionals128.Shift(-exponent - 64);
int point = 128;
for (int i = 0; i < fractional_count; ++i) {
if (fractionals128.IsZero()) break;
fractionals128.Multiply(5);
point--;
int digit = fractionals128.DivModPowerOf2(point);
ASSERT(digit <= 9);
buffer[*length] = static_cast<char>('0' + digit);
(*length)++;
}
if (fractionals128.BitAt(point - 1) == 1) {
RoundUp(buffer, length, decimal_point);
}
}
}
// Removes leading and trailing zeros.
// If leading zeros are removed then the decimal point position is adjusted.
static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
while (*length > 0 && buffer[(*length) - 1] == '0') {
(*length)--;
}
int first_non_zero = 0;
while (first_non_zero < *length && buffer[first_non_zero] == '0') {
first_non_zero++;
}
if (first_non_zero != 0) {
for (int i = first_non_zero; i < *length; ++i) {
buffer[i - first_non_zero] = buffer[i];
}
*length -= first_non_zero;
*decimal_point -= first_non_zero;
}
}
bool FastFixedDtoa(double v,
int fractional_count,
Vector<char> buffer,
int* length,
int* decimal_point) {
const uint32_t kMaxUInt32 = 0xFFFFFFFF;
uint64_t significand = Double(v).Significand();
int exponent = Double(v).Exponent();
if (exponent > 20) return false;
if (fractional_count > 20) return false;
*length = 0;
if (exponent + kDoubleSignificandSize > 64) {
const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17
uint64_t divisor = kFive17;
int divisor_power = 17;
uint64_t dividend = significand;
uint32_t quotient;
uint64_t remainder;
if (exponent > divisor_power) {
dividend <<= exponent - divisor_power;
quotient = static_cast<uint32_t>(dividend / divisor);
remainder = (dividend % divisor) << divisor_power;
} else {
divisor <<= divisor_power - exponent;
quotient = static_cast<uint32_t>(dividend / divisor);
remainder = (dividend % divisor) << exponent;
}
FillDigits32(quotient, buffer, length);
FillDigits64FixedLength(remainder, buffer, length);
*decimal_point = *length;
} else if (exponent >= 0) {
// 0 <= exponent <= 11
significand <<= exponent;
FillDigits64(significand, buffer, length);
*decimal_point = *length;
} else if (exponent > -kDoubleSignificandSize) {
uint64_t integrals = significand >> -exponent;
uint64_t fractionals = significand - (integrals << -exponent);
if (integrals > kMaxUInt32) {
FillDigits64(integrals, buffer, length);
} else {
FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
}
*decimal_point = *length;
FillFractionals(fractionals, exponent, fractional_count,
buffer, length, decimal_point);
} else if (exponent < -128) {
// This configuration (with at most 20 digits) means that all digits must be
// 0.
ASSERT(fractional_count <= 20);
buffer[0] = '\0';
*length = 0;
*decimal_point = -fractional_count;
} else {
*decimal_point = 0;
FillFractionals(significand, exponent, fractional_count,
buffer, length, decimal_point);
}
TrimZeros(buffer, length, decimal_point);
buffer[*length] = '\0';
if ((*length) == 0) {
*decimal_point = -fractional_count;
}
return true;
}
static const int kMaxUint64DecimalDigits = 19;
static const int kMaxDecimalPower = 309;
static const int kMinDecimalPower = -324;
// 2^64 = 18446744073709551616
static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
static const int kMaxSignificantDecimalDigits = 780;
static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
for (int i = 0; i < buffer.length(); i++) {
if (buffer[i] != '0') {
return buffer.SubVector(i, buffer.length());
}
}
return Vector<const char>(buffer.start(), 0);
}
static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
for (int i = buffer.length() - 1; i >= 0; --i) {
if (buffer[i] != '0') {
return buffer.SubVector(0, i + 1);
}
}
return Vector<const char>(buffer.start(), 0);
}
static void CutToMaxSignificantDigits(Vector<const char> buffer,
int exponent,
char* significant_buffer,
int* significant_exponent) {
for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
significant_buffer[i] = buffer[i];
}
ASSERT(buffer[buffer.length() - 1] != '0');
significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
*significant_exponent =
exponent + (buffer.length() - kMaxSignificantDecimalDigits);
}
static void TrimAndCut(Vector<const char> buffer, int exponent,
char* buffer_copy_space, int space_size,
Vector<const char>* trimmed, int* updated_exponent) {
Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);
exponent += left_trimmed.length() - right_trimmed.length();
if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
(void) space_size; // Mark variable as used.
ASSERT(space_size >= kMaxSignificantDecimalDigits);
CutToMaxSignificantDigits(right_trimmed, exponent,
buffer_copy_space, updated_exponent);
*trimmed = Vector<const char>(buffer_copy_space,
kMaxSignificantDecimalDigits);
} else {
*trimmed = right_trimmed;
*updated_exponent = exponent;
}
}
static uint64_t ReadUint64(Vector<const char> buffer,
int* number_of_read_digits) {
uint64_t result = 0;
int i = 0;
while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
int digit = buffer[i++] - '0';
ASSERT(0 <= digit && digit <= 9);
result = 10 * result + digit;
}
*number_of_read_digits = i;
return result;
}
static void ReadDiyFp(Vector<const char> buffer,
DiyFp* result,
int* remaining_decimals) {
int read_digits;
uint64_t significand = ReadUint64(buffer, &read_digits);
if (buffer.length() == read_digits) {
*result = DiyFp(significand, 0);
*remaining_decimals = 0;
} else {
// Round the significand.
if (buffer[read_digits] >= '5') {
significand++;
}
// Compute the binary exponent.
int exponent = 0;
*result = DiyFp(significand, exponent);
*remaining_decimals = buffer.length() - read_digits;
}
}
static DiyFp AdjustmentPowerOfTen(int exponent) {
ASSERT(0 < exponent);
ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
// Simply hardcode the remaining powers for the given decimal exponent
// distance.
ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
switch (exponent) {
case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
default:
UNREACHABLE();
}
}
static bool DiyFpStrtod(Vector<const char> buffer,
int exponent,
double* result) {
DiyFp input;
int remaining_decimals;
ReadDiyFp(buffer, &input, &remaining_decimals);
const int kDenominatorLog = 3;
const int kDenominator = 1 << kDenominatorLog;
// Move the remaining decimals into the exponent.
exponent += remaining_decimals;
int error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
int old_e = input.e();
input.Normalize();
error <<= old_e - input.e();
ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
if (exponent < PowersOfTenCache::kMinDecimalExponent) {
*result = 0.0;
return true;
}
DiyFp cached_power;
int cached_decimal_exponent;
PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
&cached_power,
&cached_decimal_exponent);
if (cached_decimal_exponent != exponent) {
int adjustment_exponent = exponent - cached_decimal_exponent;
DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
input.Multiply(adjustment_power);
if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
// The product of input with the adjustment power fits into a 64 bit
// integer.
ASSERT(DiyFp::kSignificandSize == 64);
} else {
// The adjustment power is exact. There is hence only an error of 0.5.
error += kDenominator / 2;
}
}
input.Multiply(cached_power);
int error_b = kDenominator / 2;
int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
int fixed_error = kDenominator / 2;
error += error_b + error_ab + fixed_error;
old_e = input.e();
input.Normalize();
error <<= old_e - input.e();
int order_of_magnitude = DiyFp::kSignificandSize + input.e();
int effective_significand_size =
Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
int precision_digits_count =
DiyFp::kSignificandSize - effective_significand_size;
if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
int shift_amount = (precision_digits_count + kDenominatorLog) -
DiyFp::kSignificandSize + 1;
input.set_f(input.f() >> shift_amount);
input.set_e(input.e() + shift_amount);
error = (error >> shift_amount) + 1 + kDenominator;
precision_digits_count -= shift_amount;
}
ASSERT(DiyFp::kSignificandSize == 64);
ASSERT(precision_digits_count < 64);
uint64_t one64 = 1;
uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
uint64_t precision_bits = input.f() & precision_bits_mask;
uint64_t half_way = one64 << (precision_digits_count - 1);
precision_bits *= kDenominator;
half_way *= kDenominator;
DiyFp rounded_input(input.f() >> precision_digits_count,
input.e() + precision_digits_count);
if (precision_bits >= half_way + error) {
rounded_input.set_f(rounded_input.f() + 1);
}
*result = Double(rounded_input).value();
if (half_way - error < precision_bits && precision_bits < half_way + error) {
return false;
} else {
return true;
}
}
static int CompareBufferWithDiyFp(Vector<const char> buffer,
int exponent,
DiyFp diy_fp) {
ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
ASSERT(buffer.length() + exponent > kMinDecimalPower);
ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
Bignum buffer_bignum;
Bignum diy_fp_bignum;
buffer_bignum.AssignDecimalString(buffer);
diy_fp_bignum.AssignUInt64(diy_fp.f());
if (exponent >= 0) {
buffer_bignum.MultiplyByPowerOfTen(exponent);
} else {
diy_fp_bignum.MultiplyByPowerOfTen(-exponent);
}
if (diy_fp.e() > 0) {
diy_fp_bignum.ShiftLeft(diy_fp.e());
} else {
buffer_bignum.ShiftLeft(-diy_fp.e());
}
return Bignum::Compare(buffer_bignum, diy_fp_bignum);
}
static bool ComputeGuess(Vector<const char> trimmed, int exponent,
double* guess)
{
if (trimmed.length() == 0) {
*guess = 0.0;
return true;
}
if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
*guess = Double::Infinity();
return true;
}
if (exponent + trimmed.length() <= kMinDecimalPower) {
*guess = 0.0;
return true;
}
if (DiyFpStrtod(trimmed, exponent, guess)) {
return true;
}
if (*guess == Double::Infinity()) {
return true;
}
return false;
}
double Strtod(Vector<const char> buffer, int exponent)
{
char copy_buffer[kMaxSignificantDecimalDigits];
Vector<const char> trimmed;
int updated_exponent;
TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
&trimmed, &updated_exponent);
exponent = updated_exponent;
double guess;
bool is_correct = ComputeGuess(trimmed, exponent, &guess);
if (is_correct) return guess;
DiyFp upper_boundary = Double(guess).UpperBoundary();
int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
if (comparison < 0) {
return guess;
} else if (comparison > 0) {
return Double(guess).NextDouble();
} else if ((Double(guess).Significand() & 1) == 0) {
// Round towards even.
return guess;
} else {
return Double(guess).NextDouble();
}
}
class DoubleToStringConverter {
public:
static const int kMaxFixedDigitsBeforePoint = 60;
static const int kMaxFixedDigitsAfterPoint = 60;
static const int kMaxExponentialDigits = 120;
static const int kMinPrecisionDigits = 1;
static const int kMaxPrecisionDigits = 120;
enum Flags {
NO_FLAGS = 0,
EMIT_POSITIVE_EXPONENT_SIGN = 1,
EMIT_TRAILING_DECIMAL_POINT = 2,
EMIT_TRAILING_ZERO_AFTER_POINT = 4,
UNIQUE_ZERO = 8
};
DoubleToStringConverter(int flags,
const char* infinity_symbol,
const char* nan_symbol,
char exponent_character,
int decimal_in_shortest_low,
int decimal_in_shortest_high,
int max_leading_padding_zeroes_in_precision_mode,
int max_trailing_padding_zeroes_in_precision_mode)
: flags_(flags),
infinity_symbol_(infinity_symbol),
nan_symbol_(nan_symbol),
exponent_character_(exponent_character),
decimal_in_shortest_low_(decimal_in_shortest_low),
decimal_in_shortest_high_(decimal_in_shortest_high),
max_leading_padding_zeroes_in_precision_mode_(
max_leading_padding_zeroes_in_precision_mode),
max_trailing_padding_zeroes_in_precision_mode_(
max_trailing_padding_zeroes_in_precision_mode) {
// When 'trailing zero after the point' is set, then 'trailing point'
// must be set too.
ASSERT(((flags & EMIT_TRAILING_DECIMAL_POINT) != 0) ||
!((flags & EMIT_TRAILING_ZERO_AFTER_POINT) != 0));
}
bool ToShortest(double value, std::string &s) const {
return ToShortestIeeeNumber(value, s, SHORTEST);
}
bool ToFixed(double value,
int requested_digits,
std::string &s) const;
bool ToExponential(double value,
int requested_digits,
std::string &s) const;
bool ToPrecision(double value,
int precision,
std::string &s) const;
enum DtoaMode {
SHORTEST,
FIXED, // Produce a fixed number of digits after the decimal point
PRECISION // Fixed number of digits (independent of the decimal point)
};
static const int kBase10MaximalLength = 17;
// The result should be interpreted as buffer * 10^(point-length).
static void DoubleToAscii(double v,
DtoaMode mode,
int requested_digits,
char* buffer,
int buffer_length,
bool* sign,
int* length,
int* point);
private:
// Implementation for ToShortest.
bool ToShortestIeeeNumber(double value,
std::string &s,
DtoaMode mode) const;
bool HandleSpecialValues(double value, std::string &s) const;
void CreateExponentialRepresentation(const char* decimal_digits,
int length,
int exponent,
std::string &s) const;
void CreateDecimalRepresentation(const char* decimal_digits,
int length,
int decimal_point,
int digits_after_point,
std::string &s) const;
const int flags_;
const char* const infinity_symbol_;
const char* const nan_symbol_;
const char exponent_character_;
const int decimal_in_shortest_low_;
const int decimal_in_shortest_high_;
const int max_leading_padding_zeroes_in_precision_mode_;
const int max_trailing_padding_zeroes_in_precision_mode_;
DISALLOW_IMPLICIT_CONSTRUCTORS(DoubleToStringConverter);
};
class StringToDoubleConverter {
public:
enum Flags {
NO_FLAGS = 0,
ALLOW_HEX = 1,
ALLOW_OCTALS = 2,
ALLOW_TRAILING_JUNK = 4,
ALLOW_LEADING_SPACES = 8,
ALLOW_TRAILING_SPACES = 16,
ALLOW_SPACES_AFTER_SIGN = 32
};
StringToDoubleConverter(int flags,
double empty_string_value,
double junk_string_value,
const char* infinity_symbol,
const char* nan_symbol)
: flags_(flags),
empty_string_value_(empty_string_value),
junk_string_value_(junk_string_value),
infinity_symbol_(infinity_symbol),
nan_symbol_(nan_symbol) {
}
double StringToDouble(const char* buffer,
int length,
int* processed_characters_count) const;
private:
const int flags_;
const double empty_string_value_;
const double junk_string_value_;
const char* const infinity_symbol_;
const char* const nan_symbol_;
double StringToIeee(const char *start_pointer,
int length,
int* processed_characters_count) const;
DISALLOW_IMPLICIT_CONSTRUCTORS(StringToDoubleConverter);
};
bool DoubleToStringConverter::HandleSpecialValues(
double value,
std::string &result) const {
Double double_inspect(value);
if (double_inspect.IsInfinite()) {
if (infinity_symbol_ == NULL) return false;
if (value < 0) {
result += '-';
}
result += infinity_symbol_;
return true;
}
if (double_inspect.IsNan()) {
if (nan_symbol_ == NULL) return false;
result = nan_symbol_;
return true;
}
return false;
}
void DoubleToStringConverter::CreateExponentialRepresentation(
const char* decimal_digits,
int length,
int exponent,
std::string &result) const {
ASSERT(length != 0);
result += decimal_digits[0];
if (length != 1) {
result += '.';
result.append(&decimal_digits[1], length-1);
}
result += exponent_character_;
if (exponent < 0) {
result += '-';
exponent = -exponent;
} else {
if ((flags_ & EMIT_POSITIVE_EXPONENT_SIGN) != 0) {
result += '+';
}
}
if (exponent == 0) {
result += '0';
return;
}
ASSERT(exponent < 1e4);
const int kMaxExponentLength = 5;
char buffer[kMaxExponentLength + 1];
buffer[kMaxExponentLength] = '\0';
int first_char_pos = kMaxExponentLength;
while (exponent > 0) {
buffer[--first_char_pos] = '0' + (exponent % 10);
exponent /= 10;
}
result.append(&buffer[first_char_pos],
kMaxExponentLength - first_char_pos);
}
void DoubleToStringConverter::CreateDecimalRepresentation(
const char* decimal_digits,
int length,
int decimal_point,
int digits_after_point,
std::string &result) const {
// Create a representation that is padded with zeros if needed.
if (decimal_point <= 0) {
// "0.00000decimal_rep".
result += '0';
if (digits_after_point > 0) {
result += '.';
result.append(-decimal_point, '0');
ASSERT(length <= digits_after_point - (-decimal_point));
result.append(decimal_digits, length);
int remaining_digits = digits_after_point - (-decimal_point) - length;
result.append(remaining_digits, '0');
}
} else if (decimal_point >= length) {
// "decimal_rep0000.00000" or "decimal_rep.0000"
result.append(decimal_digits, length);
result.append(decimal_point - length, '0');
if (digits_after_point > 0) {
result += '.';
result.append(digits_after_point, '0');
}
} else {
// "decima.l_rep000"
ASSERT(digits_after_point > 0);
result.append(decimal_digits, decimal_point);
result += '.';
ASSERT(length - decimal_point <= digits_after_point);
result.append(&decimal_digits[decimal_point], length - decimal_point);
int remaining_digits = digits_after_point - (length - decimal_point);
result.append(remaining_digits, '0');
}
if (digits_after_point == 0) {
if ((flags_ & EMIT_TRAILING_DECIMAL_POINT) != 0) {
result += '.';
}
if ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) {
result += '0';
}
}
}
bool DoubleToStringConverter::ToShortestIeeeNumber(
double value,
std::string &result,
DoubleToStringConverter::DtoaMode mode) const {
ASSERT(mode == SHORTEST);
if (Double(value).IsSpecial()) {
return HandleSpecialValues(value, result);
}
int decimal_point;
bool sign;
const int kDecimalRepCapacity = kBase10MaximalLength + 1;
char decimal_rep[kDecimalRepCapacity];
int decimal_rep_length;
DoubleToAscii(value, mode, 0, decimal_rep, kDecimalRepCapacity,
&sign, &decimal_rep_length, &decimal_point);
bool unique_zero = (flags_ & UNIQUE_ZERO) != 0;
if (sign && (value != 0.0 || !unique_zero)) {
result += '-';
}
int exponent = decimal_point - 1;
if ((decimal_in_shortest_low_ <= exponent) &&
(exponent < decimal_in_shortest_high_)) {
CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
std::max(0, decimal_rep_length - decimal_point),
result);
} else {
CreateExponentialRepresentation(decimal_rep, decimal_rep_length, exponent, result);
}
return true;
}
bool DoubleToStringConverter::ToFixed(double value,
int requested_digits,
std::string &result) const
{
ASSERT(kMaxFixedDigitsBeforePoint == 60);
const double kFirstNonFixed = 1e60;
if (Double(value).IsSpecial()) {
return HandleSpecialValues(value, result);
}
if (requested_digits > kMaxFixedDigitsAfterPoint) return false;
if (value >= kFirstNonFixed || value <= -kFirstNonFixed) return false;
// Find a sufficiently precise decimal representation of n.
int decimal_point;
bool sign;
// Add space for the '\0' byte.
const int kDecimalRepCapacity =
kMaxFixedDigitsBeforePoint + kMaxFixedDigitsAfterPoint + 1;
char decimal_rep[kDecimalRepCapacity];
int decimal_rep_length;
DoubleToAscii(value, FIXED, requested_digits,
decimal_rep, kDecimalRepCapacity,
&sign, &decimal_rep_length, &decimal_point);
bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
if (sign && (value != 0.0 || !unique_zero)) {
result += '-';
}
CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
requested_digits, result);
return true;
}
bool DoubleToStringConverter::ToExponential(
double value,
int requested_digits,
std::string &result) const {
if (Double(value).IsSpecial()) {
return HandleSpecialValues(value, result);
}
if (requested_digits < -1) return false;
if (requested_digits > kMaxExponentialDigits) return false;
int decimal_point;
bool sign;
// Add space for digit before the decimal point and the '\0' character.
const int kDecimalRepCapacity = kMaxExponentialDigits + 2;
ASSERT(kDecimalRepCapacity > kBase10MaximalLength);
char decimal_rep[kDecimalRepCapacity];
int decimal_rep_length;
if (requested_digits == -1) {
DoubleToAscii(value, SHORTEST, 0,
decimal_rep, kDecimalRepCapacity,
&sign, &decimal_rep_length, &decimal_point);
} else {
DoubleToAscii(value, PRECISION, requested_digits + 1,
decimal_rep, kDecimalRepCapacity,
&sign, &decimal_rep_length, &decimal_point);
ASSERT(decimal_rep_length <= requested_digits + 1);
for (int i = decimal_rep_length; i < requested_digits + 1; ++i) {
decimal_rep[i] = '0';
}
decimal_rep_length = requested_digits + 1;
}
bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
if (sign && (value != 0.0 || !unique_zero)) {
result += '-';
}
int exponent = decimal_point - 1;
CreateExponentialRepresentation(decimal_rep,
decimal_rep_length,
exponent, result);
return true;
}
bool DoubleToStringConverter::ToPrecision(double value,
int precision,
std::string &result) const {
if (Double(value).IsSpecial()) {
return HandleSpecialValues(value, result);
}
if (precision < kMinPrecisionDigits || precision > kMaxPrecisionDigits) {
return false;
}
// Find a sufficiently precise decimal representation of n.
int decimal_point;
bool sign;
// Add one for the terminating null character.
const int kDecimalRepCapacity = kMaxPrecisionDigits + 1;
char decimal_rep[kDecimalRepCapacity];
int decimal_rep_length;
DoubleToAscii(value, PRECISION, precision,
decimal_rep, kDecimalRepCapacity,
&sign, &decimal_rep_length, &decimal_point);
ASSERT(decimal_rep_length <= precision);
bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0);
if (sign && (value != 0.0 || !unique_zero)) {
result += '-';
}
// The exponent if we print the number as x.xxeyyy. That is with the
// decimal point after the first digit.
int exponent = decimal_point - 1;
int extra_zero = ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) ? 1 : 0;
if ((-decimal_point + 1 > max_leading_padding_zeroes_in_precision_mode_) ||
(decimal_point - precision + extra_zero >
max_trailing_padding_zeroes_in_precision_mode_)) {
for (int i = decimal_rep_length; i < precision; ++i) {
decimal_rep[i] = '0';
}
CreateExponentialRepresentation(decimal_rep,
precision,
exponent,
result);
} else {
CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point,
std::max(0, precision - decimal_point),
result);
}
return true;
}
static BignumDtoaMode DtoaToBignumDtoaMode(
DoubleToStringConverter::DtoaMode dtoa_mode) {
switch (dtoa_mode) {
case DoubleToStringConverter::SHORTEST: return BIGNUM_DTOA_SHORTEST;
case DoubleToStringConverter::FIXED: return BIGNUM_DTOA_FIXED;
case DoubleToStringConverter::PRECISION: return BIGNUM_DTOA_PRECISION;
default:
UNREACHABLE();
}
}
void DoubleToStringConverter::DoubleToAscii(double v, DtoaMode mode, int requested_digits,
char* buffer, int buffer_length,
bool* sign, int* length, int* point)
{
Vector<char> vector(buffer, buffer_length);
ASSERT(!Double(v).IsSpecial());
ASSERT(mode == SHORTEST || requested_digits >= 0);
if (Double(v).Sign() < 0) {
*sign = true;
v = -v;
} else {
*sign = false;
}
if (mode == PRECISION && requested_digits == 0) {
vector[0] = '\0';
*length = 0;
return;
}
if (v == 0) {
vector[0] = '0';
vector[1] = '\0';
*length = 1;
*point = 1;
return;
}
bool fast_worked;
switch (mode) {
case SHORTEST:
fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST, 0, vector, length, point);
break;
case FIXED:
fast_worked = FastFixedDtoa(v, requested_digits, vector, length, point);
break;
case PRECISION:
fast_worked = FastDtoa(v, FAST_DTOA_PRECISION, requested_digits,
vector, length, point);
break;
default:
fast_worked = false;
UNREACHABLE();
}
if (fast_worked) return;
// If the fast dtoa didn't succeed use the slower bignum version.
BignumDtoaMode bignum_mode = DtoaToBignumDtoaMode(mode);
BignumDtoa(v, bignum_mode, requested_digits, vector, length, point);
vector[*length] = '\0';
}
template <class Iterator>
static bool ConsumeSubString(Iterator* current,
Iterator end,
const char* substring) {
ASSERT(**current == *substring);
for (substring++; *substring != '\0'; substring++) {
++*current;
if (*current == end || **current != *substring) return false;
}
++*current;
return true;
}
const int kMaxSignificantDigits = 772;
static const char kWhitespaceTable7[] = { 32, 13, 10, 9, 11, 12 };
static const int kWhitespaceTable7Length = ARRAY_SIZE(kWhitespaceTable7);
static bool isWhitespace(int x) {
if (x < 128) {
for (int i = 0; i < kWhitespaceTable7Length; i++) {
if (kWhitespaceTable7[i] == x) return true;
}
}
return false;
}
// Returns true if a nonspace found and false if the end has reached.
template <class Iterator>
static inline bool AdvanceToNonspace(Iterator* current, Iterator end) {
while (*current != end) {
if (!isWhitespace(**current)) return true;
++*current;
}
return false;
}
static bool isDigit(int x, int radix) {
return (x >= '0' && x <= '9' && x < '0' + radix)
|| (radix > 10 && x >= 'a' && x < 'a' + radix - 10)
|| (radix > 10 && x >= 'A' && x < 'A' + radix - 10);
}
static double SignedZero(bool sign) {
return sign ? -0.0 : 0.0;
}
static bool IsDecimalDigitForRadix(int c, int radix) {
return '0' <= c && c <= '9' && (c - '0') < radix;
}
static bool IsCharacterDigitForRadix(int c, int radix, char a_character) {
return radix > 10 && c >= a_character && c < a_character + radix - 10;
}
template <int radix_log_2, class Iterator>
static double RadixStringToIeee(Iterator* current, Iterator end,
bool sign, bool allow_trailing_junk, double junk_string_value,
bool* result_is_junk)
{
ASSERT(*current != end);
const int kSignificandSize = Double::kSignificandSize;
*result_is_junk = true;
// Skip leading 0s.
while (**current == '0') {
++(*current);
if (*current == end) {
*result_is_junk = false;
return SignedZero(sign);
}
}
int64_t number = 0;
int exponent = 0;
const int radix = (1 << radix_log_2);
do {
int digit;
if (IsDecimalDigitForRadix(**current, radix)) {
digit = static_cast<char>(**current) - '0';
} else if (IsCharacterDigitForRadix(**current, radix, 'a')) {
digit = static_cast<char>(**current) - 'a' + 10;
} else if (IsCharacterDigitForRadix(**current, radix, 'A')) {
digit = static_cast<char>(**current) - 'A' + 10;
} else {
if (allow_trailing_junk || !AdvanceToNonspace(current, end)) {
break;
} else {
return junk_string_value;
}
}
number = number * radix + digit;
int overflow = static_cast<int>(number >> kSignificandSize);
if (overflow != 0) {
// Overflow occurred. Need to determine which direction to round the
// result.
int overflow_bits_count = 1;
while (overflow > 1) {
overflow_bits_count++;
overflow >>= 1;
}
int dropped_bits_mask = ((1 << overflow_bits_count) - 1);
int dropped_bits = static_cast<int>(number) & dropped_bits_mask;
number >>= overflow_bits_count;
exponent = overflow_bits_count;
bool zero_tail = true;
for (;;) {
++(*current);
if (*current == end || !isDigit(**current, radix)) break;
zero_tail = zero_tail && **current == '0';
exponent += radix_log_2;
}
if (!allow_trailing_junk && AdvanceToNonspace(current, end)) {
return junk_string_value;
}
int middle_value = (1 << (overflow_bits_count - 1));
if (dropped_bits > middle_value) {
number++; // Rounding up.
} else if (dropped_bits == middle_value) {
// Rounding to even to consistency with decimals: half-way case rounds
// up if significant part is odd and down otherwise.
if ((number & 1) != 0 || !zero_tail) {
number++; // Rounding up.
}
}
// Rounding up may cause overflow.
if ((number & ((int64_t)1 << kSignificandSize)) != 0) {
exponent++;
number >>= 1;
}
break;
}
++(*current);
} while (*current != end);
ASSERT(number < ((int64_t)1 << kSignificandSize));
ASSERT(static_cast<int64_t>(static_cast<double>(number)) == number);
*result_is_junk = false;
if (exponent == 0) {
if (sign) {
if (number == 0) return -0.0;
number = -number;
}
return static_cast<double>(number);
}
ASSERT(number != 0);
return Double(DiyFp(number, exponent)).value();
}
double StringToDoubleConverter::StringToIeee(
const char *input,
int length,
int* processed_characters_count) const {
const char *current = input;
const char *end = input + length;
*processed_characters_count = 0;
const bool allow_trailing_junk = (flags_ & ALLOW_TRAILING_JUNK) != 0;
const bool allow_leading_spaces = (flags_ & ALLOW_LEADING_SPACES) != 0;
const bool allow_trailing_spaces = (flags_ & ALLOW_TRAILING_SPACES) != 0;
const bool allow_spaces_after_sign = (flags_ & ALLOW_SPACES_AFTER_SIGN) != 0;
if (current == end) return empty_string_value_;
if (allow_leading_spaces || allow_trailing_spaces) {
if (!AdvanceToNonspace(&current, end)) {
*processed_characters_count = static_cast<int>(current - input);
return empty_string_value_;
}
if (!allow_leading_spaces && (input != current)) {
return junk_string_value_;
}
}
const int kBufferSize = kMaxSignificantDigits + 10;
char buffer[kBufferSize]; // NOLINT: size is known at compile time.
int buffer_pos = 0;
int exponent = 0;
int significant_digits = 0;
int insignificant_digits = 0;
bool nonzero_digit_dropped = false;
bool sign = false;
if (*current == '+' || *current == '-') {
sign = (*current == '-');
++current;
const char *next_non_space = current;
if (!AdvanceToNonspace(&next_non_space, end)) return junk_string_value_;
if (!allow_spaces_after_sign && (current != next_non_space)) {
return junk_string_value_;
}
current = next_non_space;
}
if (infinity_symbol_ != NULL) {
if (*current == infinity_symbol_[0]) {
if (!ConsumeSubString(&current, end, infinity_symbol_)) {
return junk_string_value_;
}
if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) {
return junk_string_value_;
}
if (!allow_trailing_junk && AdvanceToNonspace(&current, end)) {
return junk_string_value_;
}
ASSERT(buffer_pos == 0);
*processed_characters_count = static_cast<int>(current - input);
return sign ? -Double::Infinity() : Double::Infinity();
}
}
if (nan_symbol_ != NULL) {
if (*current == nan_symbol_[0]) {
if (!ConsumeSubString(&current, end, nan_symbol_)) {
return junk_string_value_;
}
if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) {
return junk_string_value_;
}
if (!allow_trailing_junk && AdvanceToNonspace(&current, end)) {
return junk_string_value_;
}
ASSERT(buffer_pos == 0);
*processed_characters_count = static_cast<int>(current - input);
return sign ? -Double::NaN() : Double::NaN();
}
}
bool leading_zero = false;
if (*current == '0') {
++current;
if (current == end) {
*processed_characters_count = static_cast<int>(current - input);
return SignedZero(sign);
}
leading_zero = true;
// It could be hexadecimal value.
if ((flags_ & ALLOW_HEX) && (*current == 'x' || *current == 'X')) {
++current;
if (current == end || !isDigit(*current, 16)) {
return junk_string_value_; // "0x".
}
bool result_is_junk;
double result = RadixStringToIeee<4>(&current,
end,
sign,
allow_trailing_junk,
junk_string_value_,
&result_is_junk);
if (!result_is_junk) {
if (allow_trailing_spaces) AdvanceToNonspace(&current, end);
*processed_characters_count = static_cast<int>(current - input);
}
return result;
}
// Ignore leading zeros in the integer part.
while (*current == '0') {
++current;
if (current == end) {
*processed_characters_count = static_cast<int>(current - input);
return SignedZero(sign);
}
}
}
bool octal = leading_zero && (flags_ & ALLOW_OCTALS) != 0;
// Copy significant digits of the integer part (if any) to the buffer.
while (*current >= '0' && *current <= '9') {
if (significant_digits < kMaxSignificantDigits) {
ASSERT(buffer_pos < kBufferSize);
buffer[buffer_pos++] = static_cast<char>(*current);
significant_digits++;
// Will later check if it's an octal in the buffer.
} else {
insignificant_digits++; // Move the digit into the exponential part.
nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
}
octal = octal && *current < '8';
++current;
if (current == end) goto parsing_done;
}
if (significant_digits == 0) {
octal = false;
}
if (*current == '.') {
if (octal && !allow_trailing_junk) return junk_string_value_;
if (octal) goto parsing_done;
++current;
if (current == end) {
if (significant_digits == 0 && !leading_zero) {
return junk_string_value_;
} else {
goto parsing_done;
}
}
if (significant_digits == 0) {
// octal = false;
// Integer part consists of 0 or is absent. Significant digits start after
// leading zeros (if any).
while (*current == '0') {
++current;
if (current == end) {
*processed_characters_count = static_cast<int>(current - input);
return SignedZero(sign);
}
exponent--; // Move this 0 into the exponent.
}
}
// There is a fractional part.
// We don't emit a '.', but adjust the exponent instead.
while (*current >= '0' && *current <= '9') {
if (significant_digits < kMaxSignificantDigits) {
ASSERT(buffer_pos < kBufferSize);
buffer[buffer_pos++] = static_cast<char>(*current);
significant_digits++;
exponent--;
} else {
// Ignore insignificant digits in the fractional part.
nonzero_digit_dropped = nonzero_digit_dropped || *current != '0';
}
++current;
if (current == end) goto parsing_done;
}
}
if (!leading_zero && exponent == 0 && significant_digits == 0) {
// If leading_zeros is true then the string contains zeros.
// If exponent < 0 then string was [+-]\.0*...
// If significant_digits != 0 the string is not equal to 0.
// Otherwise there are no digits in the string.
return junk_string_value_;
}
// Parse exponential part.
if (*current == 'e' || *current == 'E') {
if (octal && !allow_trailing_junk) return junk_string_value_;
if (octal) goto parsing_done;
++current;
if (current == end) {
if (allow_trailing_junk) {
goto parsing_done;
} else {
return junk_string_value_;
}
}
char sign = '+';
if (*current == '+' || *current == '-') {
sign = static_cast<char>(*current);
++current;
if (current == end) {
if (allow_trailing_junk) {
goto parsing_done;
} else {
return junk_string_value_;
}
}
}
if (current == end || *current < '0' || *current > '9') {
if (allow_trailing_junk) {
goto parsing_done;
} else {
return junk_string_value_;
}
}
const int max_exponent = INT_MAX / 2;
ASSERT(-max_exponent / 2 <= exponent && exponent <= max_exponent / 2);
int num = 0;
do {
// Check overflow.
int digit = *current - '0';
if (num >= max_exponent / 10
&& !(num == max_exponent / 10 && digit <= max_exponent % 10)) {
num = max_exponent;
} else {
num = num * 10 + digit;
}
++current;
} while (current != end && *current >= '0' && *current <= '9');
exponent += (sign == '-' ? -num : num);
}
if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) {
return junk_string_value_;
}
if (!allow_trailing_junk && AdvanceToNonspace(&current, end)) {
return junk_string_value_;
}
if (allow_trailing_spaces) {
AdvanceToNonspace(&current, end);
}
parsing_done:
exponent += insignificant_digits;
if (octal) {
double result;
bool result_is_junk;
char* start = buffer;
result = RadixStringToIeee<3>(&start,
buffer + buffer_pos,
sign,
allow_trailing_junk,
junk_string_value_,
&result_is_junk);
ASSERT(!result_is_junk);
*processed_characters_count = static_cast<int>(current - input);
return result;
}
if (nonzero_digit_dropped) {
buffer[buffer_pos++] = '1';
exponent--;
}
ASSERT(buffer_pos < kBufferSize);
buffer[buffer_pos] = '\0';
double converted = Strtod(Vector<const char>(buffer, buffer_pos), exponent);
*processed_characters_count = static_cast<int>(current - input);
return sign? -converted: converted;
}
double StringToDoubleConverter::StringToDouble(
const char* buffer,
int length,
int* processed_characters_count) const {
return StringToIeee(buffer, length, processed_characters_count);
}
} // end anonymous namespace
std::string format_coord_shortest(Coord x)
{
char buf[20];
bool sign;
int length, point;
DoubleToStringConverter::DoubleToAscii(x, DoubleToStringConverter::SHORTEST,
0, buf, 20, &sign, &length, &point);
int exponent = point - length;
std::string ret;
ret.reserve(32);
if (sign) {
ret += '-';
}
if (exponent == 0) {
// return digits without any changes
ret += buf;
} else if (point >= 0 && point <= length) {
// insert decimal point
ret.append(buf, point);
ret += '.';
ret.append(&buf[point], length - point);
} else if (exponent > 0 && exponent <= 2) {
// add trailing zeroes
ret += buf;
ret.append(exponent, '0');
} else if (point >= -3 && point <= -1) {
// add leading zeroes
ret += '.';
ret.append(-point, '0');
ret += buf;
} else {
// exponential form
ret += buf;
ret += 'e';
if (exponent < 0) {
ret += '-';
exponent = -exponent;
}
/* Convert exponent by hand.
* Using ostringstream is ~3x slower */
int const buflen = 6;
int i = 0;
char expdigits[buflen+1];
expdigits[buflen] = 0;
for (; exponent && i < buflen; ++i) {
expdigits[buflen - 1 - i] = '0' + (exponent % 10);
exponent /= 10;
}
ret.append(&expdigits[buflen - i]);
}
return ret;
}
std::string format_coord_nice(Coord x)
{
static DoubleToStringConverter conv(
DoubleToStringConverter::UNIQUE_ZERO,
"inf", "NaN", 'e', -6, 21, 0, 0);
std::string ret;
ret.reserve(32);
conv.ToShortest(x, ret);
return ret;
}
Coord parse_coord(std::string const &s)
{
static StringToDoubleConverter conv(
StringToDoubleConverter::ALLOW_LEADING_SPACES |
StringToDoubleConverter::ALLOW_TRAILING_SPACES |
StringToDoubleConverter::ALLOW_SPACES_AFTER_SIGN,
0.0, nan(""), "inf", "NaN");
int dummy;
return conv.StringToDouble(s.c_str(), s.length(), &dummy);
}
} // namespace Geom
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :