mirror of
https://github.com/ClickHouse/ClickHouse.git
synced 2024-11-18 21:51:57 +00:00
767 lines
22 KiB
C++
767 lines
22 KiB
C++
// 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 "bignum.h"
|
|
#include "utils.h"
|
|
|
|
namespace double_conversion {
|
|
|
|
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) {
|
|
(void) value; // Mark variable as used.
|
|
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] = 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();
|
|
unsigned 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());
|
|
|
|
// 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_] = 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;
|
|
|
|
// 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 `this` divided by other
|
|
// is 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));
|
|
ASSERT(bigits_[used_digits_ - 1] < 0x10000);
|
|
// Remove the multiples of the first digit.
|
|
// Example this = 23 and other equals 9. -> Remove 2 multiples.
|
|
result += static_cast<uint16_t>(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;
|
|
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) {
|
|
// 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 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 >= 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] - (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();
|
|
}
|
|
|
|
|
|
} // namespace double_conversion
|