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cosmopolitan/third_party/double-conversion/bignum.cc

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// 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 "libc/macros.h"
#include "third_party/double-conversion/bignum.h"
#include "third_party/double-conversion/utils.h"
asm(".ident\t\"\\n\\n\
double-conversion (BSD-3)\\n\
Copyright 2010 the V8 project authors\"");
asm(".include \"libc/disclaimer.inc\"");
namespace double_conversion {
Bignum::Chunk& Bignum::RawBigit(const int index) {
DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
return bigits_buffer_[index];
}
const Bignum::Chunk& Bignum::RawBigit(const int index) const {
DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
return bigits_buffer_[index];
}
template <typename S>
static int BitSize(const S value) {
(void)value; // Mark variable as used.
return 8 * sizeof(value);
}
// Guaranteed to lie in one Bigit.
void Bignum::AssignUInt16(const uint16_t value) {
DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value));
Zero();
if (value > 0) {
RawBigit(0) = value;
used_bigits_ = 1;
}
}
void Bignum::AssignUInt64(uint64_t value) {
Zero();
for (int i = 0; value > 0; ++i) {
RawBigit(i) = value & kBigitMask;
value >>= kBigitSize;
++used_bigits_;
}
}
void Bignum::AssignBignum(const Bignum& other) {
exponent_ = other.exponent_;
for (int i = 0; i < other.used_bigits_; ++i) {
RawBigit(i) = other.RawBigit(i);
}
used_bigits_ = other.used_bigits_;
}
static uint64_t ReadUInt64(const Vector<const char> buffer, const int from,
const int digits_to_read) {
uint64_t result = 0;
for (int i = from; i < from + digits_to_read; ++i) {
const int digit = buffer[i] - '0';
DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);
result = result * 10 + digit;
}
return result;
}
void Bignum::AssignDecimalString(const Vector<const char> value) {
// 2^64 = 18446744073709551616 > 10^19
static const int kMaxUint64DecimalDigits = 19;
Zero();
int length = value.length();
unsigned pos = 0;
// Let's just say that each digit needs 4 bits.
while (length >= kMaxUint64DecimalDigits) {
const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
pos += kMaxUint64DecimalDigits;
length -= kMaxUint64DecimalDigits;
MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
AddUInt64(digits);
}
const uint64_t digits = ReadUInt64(value, pos, length);
MultiplyByPowerOfTen(length);
AddUInt64(digits);
Clamp();
}
static uint64_t HexCharValue(const int c) {
if ('0' <= c && c <= '9') {
return c - '0';
}
if ('a' <= c && c <= 'f') {
return 10 + c - 'a';
}
DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F');
return 10 + c - 'A';
}
// Unlike AssignDecimalString(), this function is "only" used
// for unit-tests and therefore not performance critical.
void Bignum::AssignHexString(Vector<const char> value) {
Zero();
// Required capacity could be reduced by ignoring leading zeros.
EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize);
DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >=
kBigitSize + 4); // TODO: static_assert
// Accumulates converted hex digits until at least kBigitSize bits.
// Works with non-factor-of-four kBigitSizes.
uint64_t tmp = 0; // Accumulates converted hex digits until at least
for (int cnt = 0; !value.is_empty(); value.pop_back()) {
tmp |= (HexCharValue(value.last()) << cnt);
if ((cnt += 4) >= kBigitSize) {
RawBigit(used_bigits_++) = (tmp & kBigitMask);
cnt -= kBigitSize;
tmp >>= kBigitSize;
}
}
if (tmp > 0) {
RawBigit(used_bigits_++) = tmp;
}
Clamp();
}
void Bignum::AddUInt64(const uint64_t operand) {
if (operand == 0) {
return;
}
Bignum other;
other.AssignUInt64(operand);
AddBignum(other);
}
void Bignum::AddBignum(const Bignum& other) {
DOUBLE_CONVERSION_ASSERT(IsClamped());
DOUBLE_CONVERSION_ASSERT(other.IsClamped());
// If this has a greater exponent than other append zero-bigits to this.
// After this call exponent_ <= other.exponent_.
Align(other);
// There are two possibilities:
// aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
// bbbbb 00000000
// ----------------
// ccccccccccc 0000
// or
// aaaaaaaaaa 0000
// bbbbbbbbb 0000000
// -----------------
// cccccccccccc 0000
// In both cases we might need a carry bigit.
EnsureCapacity(1 + MAX(BigitLength(), other.BigitLength()) - exponent_);
Chunk carry = 0;
int bigit_pos = other.exponent_ - exponent_;
DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0);
for (int i = used_bigits_; i < bigit_pos; ++i) {
RawBigit(i) = 0;
}
for (int i = 0; i < other.used_bigits_; ++i) {
const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
const Chunk sum = my + other.RawBigit(i) + carry;
RawBigit(bigit_pos) = sum & kBigitMask;
carry = sum >> kBigitSize;
++bigit_pos;
}
while (carry != 0) {
const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
const Chunk sum = my + carry;
RawBigit(bigit_pos) = sum & kBigitMask;
carry = sum >> kBigitSize;
++bigit_pos;
}
used_bigits_ = MAX(bigit_pos, static_cast<int>(used_bigits_));
DOUBLE_CONVERSION_ASSERT(IsClamped());
}
void Bignum::SubtractBignum(const Bignum& other) {
DOUBLE_CONVERSION_ASSERT(IsClamped());
DOUBLE_CONVERSION_ASSERT(other.IsClamped());
// We require this to be bigger than other.
DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this));
Align(other);
const int offset = other.exponent_ - exponent_;
Chunk borrow = 0;
int i;
for (i = 0; i < other.used_bigits_; ++i) {
DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1));
const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow;
RawBigit(i + offset) = difference & kBigitMask;
borrow = difference >> (kChunkSize - 1);
}
while (borrow != 0) {
const Chunk difference = RawBigit(i + offset) - borrow;
RawBigit(i + offset) = difference & kBigitMask;
borrow = difference >> (kChunkSize - 1);
++i;
}
Clamp();
}
void Bignum::ShiftLeft(const int shift_amount) {
if (used_bigits_ == 0) {
return;
}
exponent_ += (shift_amount / kBigitSize);
const int local_shift = shift_amount % kBigitSize;
EnsureCapacity(used_bigits_ + 1);
BigitsShiftLeft(local_shift);
}
void Bignum::MultiplyByUInt32(const uint32_t factor) {
if (factor == 1) {
return;
}
if (factor == 0) {
Zero();
return;
}
if (used_bigits_ == 0) {
return;
}
// The product of a bigit with the factor is of size kBigitSize + 32.
// Assert that this number + 1 (for the carry) fits into double chunk.
DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
DoubleChunk carry = 0;
for (int i = 0; i < used_bigits_; ++i) {
const DoubleChunk product =
static_cast<DoubleChunk>(factor) * RawBigit(i) + carry;
RawBigit(i) = static_cast<Chunk>(product & kBigitMask);
carry = (product >> kBigitSize);
}
while (carry != 0) {
EnsureCapacity(used_bigits_ + 1);
RawBigit(used_bigits_) = carry & kBigitMask;
used_bigits_++;
carry >>= kBigitSize;
}
}
void Bignum::MultiplyByUInt64(const uint64_t factor) {
if (factor == 1) {
return;
}
if (factor == 0) {
Zero();
return;
}
if (used_bigits_ == 0) {
return;
}
DOUBLE_CONVERSION_ASSERT(kBigitSize < 32);
uint64_t carry = 0;
const uint64_t low = factor & 0xFFFFFFFF;
const uint64_t high = factor >> 32;
for (int i = 0; i < used_bigits_; ++i) {
const uint64_t product_low = low * RawBigit(i);
const uint64_t product_high = high * RawBigit(i);
const uint64_t tmp = (carry & kBigitMask) + product_low;
RawBigit(i) = tmp & kBigitMask;
carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
(product_high << (32 - kBigitSize));
}
while (carry != 0) {
EnsureCapacity(used_bigits_ + 1);
RawBigit(used_bigits_) = carry & kBigitMask;
used_bigits_++;
carry >>= kBigitSize;
}
}
void Bignum::MultiplyByPowerOfTen(const int exponent) {
static const uint64_t kFive27 =
DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d);
static const uint16_t kFive1 = 5;
static const uint16_t kFive2 = kFive1 * 5;
static const uint16_t kFive3 = kFive2 * 5;
static const uint16_t kFive4 = kFive3 * 5;
static const uint16_t kFive5 = kFive4 * 5;
static const uint16_t kFive6 = kFive5 * 5;
static const uint32_t kFive7 = kFive6 * 5;
static const uint32_t kFive8 = kFive7 * 5;
static const uint32_t kFive9 = kFive8 * 5;
static const uint32_t kFive10 = kFive9 * 5;
static const uint32_t kFive11 = kFive10 * 5;
static const uint32_t kFive12 = kFive11 * 5;
static const uint32_t kFive13 = kFive12 * 5;
static const uint32_t kFive1_to_12[] = {kFive1, kFive2, kFive3, kFive4,
kFive5, kFive6, kFive7, kFive8,
kFive9, kFive10, kFive11, kFive12};
DOUBLE_CONVERSION_ASSERT(exponent >= 0);
if (exponent == 0) {
return;
}
if (used_bigits_ == 0) {
return;
}
// We shift by exponent at the end just before returning.
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() {
DOUBLE_CONVERSION_ASSERT(IsClamped());
const int product_length = 2 * used_bigits_;
EnsureCapacity(product_length);
// Comba multiplication: compute each column separately.
// Example: r = a2a1a0 * b2b1b0.
// r = 1 * a0b0 +
// 10 * (a1b0 + a0b1) +
// 100 * (a2b0 + a1b1 + a0b2) +
// 1000 * (a2b1 + a1b2) +
// 10000 * a2b2
//
// In the worst case we have to accumulate nb-digits products of digit*digit.
//
// Assert that the additional number of bits in a DoubleChunk are enough to
// sum up used_digits of Bigit*Bigit.
if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) {
DOUBLE_CONVERSION_UNIMPLEMENTED();
}
DoubleChunk accumulator = 0;
// First shift the digits so we don't overwrite them.
const int copy_offset = used_bigits_;
for (int i = 0; i < used_bigits_; ++i) {
RawBigit(copy_offset + i) = RawBigit(i);
}
// We have two loops to avoid some 'if's in the loop.
for (int i = 0; i < used_bigits_; ++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) {
const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
bigit_index1--;
bigit_index2++;
}
RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
accumulator >>= kBigitSize;
}
for (int i = used_bigits_; i < product_length; ++i) {
int bigit_index1 = used_bigits_ - 1;
int bigit_index2 = i - bigit_index1;
// Invariant: sum of both indices is again equal to i.
// Inner loop runs 0 times on last iteration, emptying accumulator.
while (bigit_index2 < used_bigits_) {
const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
bigit_index1--;
bigit_index2++;
}
// The overwritten RawBigit(i) will never be read in further loop
// iterations, because bigit_index1 and bigit_index2 are always greater than
// i - used_bigits_.
RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
accumulator >>= kBigitSize;
}
// Since the result was guaranteed to lie inside the number the
// accumulator must be 0 now.
DOUBLE_CONVERSION_ASSERT(accumulator == 0);
// Don't forget to update the used_digits and the exponent.
used_bigits_ = product_length;
exponent_ *= 2;
Clamp();
}
void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) {
DOUBLE_CONVERSION_ASSERT(base != 0);
DOUBLE_CONVERSION_ASSERT(power_exponent >= 0);
if (power_exponent == 0) {
AssignUInt16(1);
return;
}
Zero();
int shifts = 0;
// We expect base to be in range 2-32, and most often to be 10.
// It does not make much sense to implement different algorithms for counting
// the bits.
while ((base & 1) == 0) {
base >>= 1;
shifts++;
}
int bit_size = 0;
int tmp_base = base;
while (tmp_base != 0) {
tmp_base >>= 1;
bit_size++;
}
const int final_size = bit_size * power_exponent;
// 1 extra bigit for the shifting, and one for rounded final_size.
EnsureCapacity(final_size / kBigitSize + 2);
// Left to Right exponentiation.
int mask = 1;
while (power_exponent >= mask) mask <<= 1;
// The mask is now pointing to the bit above the most significant 1-bit of
// power_exponent.
// Get rid of first 1-bit;
mask >>= 2;
uint64_t this_value = base;
bool delayed_multiplication = 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) {
DOUBLE_CONVERSION_ASSERT(bit_size > 0);
const uint64_t base_bits_mask =
~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
const bool high_bits_zero = (this_value & base_bits_mask) == 0;
if (high_bits_zero) {
this_value *= base;
} else {
delayed_multiplication = true;
}
}
mask >>= 1;
}
AssignUInt64(this_value);
if (delayed_multiplication) {
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);
}
// Precondition: this/other < 16bit.
uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
DOUBLE_CONVERSION_ASSERT(IsClamped());
DOUBLE_CONVERSION_ASSERT(other.IsClamped());
DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 0);
// Easy case: if we have less digits than the divisor than the result is 0.
// Note: this handles the case where this == 0, too.
if (BigitLength() < other.BigitLength()) {
return 0;
}
Align(other);
uint16_t result = 0;
// Start by removing multiples of 'other' until both numbers have the same
// number of digits.
while (BigitLength() > other.BigitLength()) {
// This naive approach is extremely inefficient if `this` divided by other
// is big. This function is implemented for doubleToString where
// the result should be small (less than 10).
DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >=
((1 << kBigitSize) / 16));
DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000);
// Remove the multiples of the first digit.
// Example this = 23 and other equals 9. -> Remove 2 multiples.
result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1));
SubtractTimes(other, RawBigit(used_bigits_ - 1));
}
DOUBLE_CONVERSION_ASSERT(BigitLength() == other.BigitLength());
// Both bignums are at the same length now.
// Since other has more than 0 digits we know that the access to
// RawBigit(used_bigits_ - 1) is safe.
const Chunk this_bigit = RawBigit(used_bigits_ - 1);
const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1);
if (other.used_bigits_ == 1) {
// Shortcut for easy (and common) case.
int quotient = this_bigit / other_bigit;
RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient;
DOUBLE_CONVERSION_ASSERT(quotient < 0x10000);
result += static_cast<uint16_t>(quotient);
Clamp();
return result;
}
const int division_estimate = this_bigit / (other_bigit + 1);
DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000);
result += static_cast<uint16_t>(division_estimate);
SubtractTimes(other, division_estimate);
if (other_bigit * (division_estimate + 1) > this_bigit) {
// No need to even try to subtract. Even if other's remaining digits were 0
// another subtraction would be too much.
return result;
}
while (LessEqual(other, *this)) {
SubtractBignum(other);
result++;
}
return result;
}
template <typename S>
static int SizeInHexChars(S number) {
DOUBLE_CONVERSION_ASSERT(number > 0);
int result = 0;
while (number != 0) {
number >>= 4;
result++;
}
return result;
}
static char HexCharOfValue(const int value) {
DOUBLE_CONVERSION_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, const int buffer_size) const {
DOUBLE_CONVERSION_ASSERT(IsClamped());
// Each bigit must be printable as separate hex-character.
DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0);
static const int kHexCharsPerBigit = kBigitSize / 4;
if (used_bigits_ == 0) {
if (buffer_size < 2) {
return false;
}
buffer[0] = '0';
buffer[1] = '\0';
return true;
}
// We add 1 for the terminating '\0' character.
const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
SizeInHexChars(RawBigit(used_bigits_ - 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_bigits_ - 1; ++i) {
Chunk current_bigit = RawBigit(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 = RawBigit(used_bigits_ - 1);
while (most_significant_bigit != 0) {
buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
most_significant_bigit >>= 4;
}
return true;
}
Bignum::Chunk Bignum::BigitOrZero(const int index) const {
if (index >= BigitLength()) {
return 0;
}
if (index < exponent_) {
return 0;
}
return RawBigit(index - exponent_);
}
int Bignum::Compare(const Bignum& a, const Bignum& b) {
DOUBLE_CONVERSION_ASSERT(a.IsClamped());
DOUBLE_CONVERSION_ASSERT(b.IsClamped());
const int bigit_length_a = a.BigitLength();
const 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 >= MIN(a.exponent_, b.exponent_); --i) {
const Chunk bigit_a = a.BigitOrZero(i);
const Chunk bigit_b = b.BigitOrZero(i);
if (bigit_a < bigit_b) {
return -1;
}
if (bigit_a > bigit_b) {
return +1;
}
// Otherwise they are equal up to this digit. Try the next digit.
}
return 0;
}
int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
DOUBLE_CONVERSION_ASSERT(a.IsClamped());
DOUBLE_CONVERSION_ASSERT(b.IsClamped());
DOUBLE_CONVERSION_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;
}
// The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
// 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
// of 'a'.
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.
const int min_exponent = MIN(MIN(a.exponent_, b.exponent_), c.exponent_);
for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
const Chunk chunk_a = a.BigitOrZero(i);
const Chunk chunk_b = b.BigitOrZero(i);
const Chunk chunk_c = c.BigitOrZero(i);
const 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_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) {
used_bigits_--;
}
if (used_bigits_ == 0) {
// Zero.
exponent_ = 0;
}
}
void Bignum::Align(const Bignum& other) {
if (exponent_ > other.exponent_) {
// If "X" represents a "hidden" bigit (by the exponent) then we are in the
// following case (a == this, b == other):
// a: aaaaaaXXXX or a: aaaaaXXX
// b: bbbbbbX b: bbbbbbbbXX
// We replace some of the hidden digits (X) of a with 0 digits.
// a: aaaaaa000X or a: aaaaa0XX
const int zero_bigits = exponent_ - other.exponent_;
EnsureCapacity(used_bigits_ + zero_bigits);
for (int i = used_bigits_ - 1; i >= 0; --i) {
RawBigit(i + zero_bigits) = RawBigit(i);
}
for (int i = 0; i < zero_bigits; ++i) {
RawBigit(i) = 0;
}
used_bigits_ += zero_bigits;
exponent_ -= zero_bigits;
DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0);
DOUBLE_CONVERSION_ASSERT(exponent_ >= 0);
}
}
void Bignum::BigitsShiftLeft(const int shift_amount) {
DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize);
DOUBLE_CONVERSION_ASSERT(shift_amount >= 0);
Chunk carry = 0;
for (int i = 0; i < used_bigits_; ++i) {
const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount);
RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask;
carry = new_carry;
}
if (carry != 0) {
RawBigit(used_bigits_) = carry;
used_bigits_++;
}
}
void Bignum::SubtractTimes(const Bignum& other, const int factor) {
DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_);
if (factor < 3) {
for (int i = 0; i < factor; ++i) {
SubtractBignum(other);
}
return;
}
Chunk borrow = 0;
const int exponent_diff = other.exponent_ - exponent_;
for (int i = 0; i < other.used_bigits_; ++i) {
const DoubleChunk product =
static_cast<DoubleChunk>(factor) * other.RawBigit(i);
const DoubleChunk remove = borrow + product;
const Chunk difference =
RawBigit(i + exponent_diff) - (remove & kBigitMask);
RawBigit(i + exponent_diff) = difference & kBigitMask;
borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
(remove >> kBigitSize));
}
for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) {
if (borrow == 0) {
return;
}
const Chunk difference = RawBigit(i) - borrow;
RawBigit(i) = difference & kBigitMask;
borrow = difference >> (kChunkSize - 1);
}
Clamp();
}
} // namespace double_conversion
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