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DEFINITIONS
This source file includes following definitions.
- exponent_
- BitSize
- AssignUInt16
- AssignUInt64
- AssignBignum
- ReadUInt64
- AssignDecimalString
- HexCharValue
- AssignHexString
- AddUInt64
- AddBignum
- SubtractBignum
- ShiftLeft
- MultiplyByUInt32
- MultiplyByUInt64
- MultiplyByPowerOfTen
- Square
- AssignPowerUInt16
- DivideModuloIntBignum
- SizeInHexChars
- HexCharOfValue
- ToHexString
- BigitAt
- Compare
- PlusCompare
- Clamp
- IsClamped
- Zero
- Align
- BigitsShiftLeft
- SubtractTimes
// Copyright 2011 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 "../include/v8stdint.h"
#include "utils.h"
#include "bignum.h"
namespace v8 {
namespace internal {
Bignum::Bignum()
: bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
for (int i = 0; i < kBigitCapacity; ++i) {
bigits_[i] = 0;
}
}
template<typename S>
static int BitSize(S value) {
return 8 * sizeof(value);
}
// Guaranteed to lie in one Bigit.
void Bignum::AssignUInt16(uint16_t value) {
ASSERT(kBigitSize >= BitSize(value));
Zero();
if (value == 0) return;
EnsureCapacity(1);
bigits_[0] = value;
used_digits_ = 1;
}
void Bignum::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] = static_cast<Chunk>(value & kBigitMask);
value = value >> kBigitSize;
}
used_digits_ = needed_bigits;
Clamp();
}
void Bignum::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_;
}
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';
if ('A' <= c && c <= 'F') return 10 + c - 'A';
UNREACHABLE();
return 0; // To make compiler happy.
}
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());
// 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_;
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_ = 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;
// 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.
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_] = static_cast<Chunk>(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] = static_cast<Chunk>(tmp & kBigitMask);
carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
(product_high << (32 - kBigitSize));
}
while (carry != 0) {
EnsureCapacity(used_digits_ + 1);
bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask);
used_digits_++;
carry >>= kBigitSize;
}
}
void Bignum::MultiplyByPowerOfTen(int exponent) {
const uint64_t kFive27 = V8_2PART_UINT64_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;
// 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() {
ASSERT(IsClamped());
int product_length = 2 * used_digits_;
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_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;
// Invariant: sum of both indices is again equal to i.
// Inner loop runs 0 times on last iteration, emptying accumulator.
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++;
}
// The overwritten bigits_[i] will never be read in further loop iterations,
// because bigit_index1 and bigit_index2 are always greater
// than i - used_digits_.
bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
accumulator >>= kBigitSize;
}
// Since the result was guaranteed to lie inside the number the
// accumulator must be 0 now.
ASSERT(accumulator == 0);
// Don't forget to update the used_digits and the exponent.
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;
// 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++;
}
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_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);
}
// Precondition: this/other < 16bit.
uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
ASSERT(IsClamped());
ASSERT(other.IsClamped());
ASSERT(other.used_digits_ > 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 the this divided other
// might be big. This function is implemented for doubleToString where
// the result should be small (less than 10).
ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
// Remove the multiples of the first digit.
// Example this = 23 and other equals 9. -> Remove 2 multiples.
result += bigits_[used_digits_ - 1];
SubtractTimes(other, bigits_[used_digits_ - 1]);
}
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
// bigits_[used_digits_ - 1] is safe.
Chunk this_bigit = bigits_[used_digits_ - 1];
Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
if (other.used_digits_ == 1) {
// Shortcut for easy (and common) case.
int quotient = this_bigit / other_bigit;
bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
result += quotient;
Clamp();
return result;
}
int division_estimate = this_bigit / (other_bigit + 1);
result += 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) {
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 value + '0';
return 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 >= 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;
// 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) {
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;
// 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.
int min_exponent = Min(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_) {
// If "X" represents a "hidden" digit (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
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] - static_cast<Chunk>(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);
++i;
}
Clamp();
}
} } // namespace v8::internal