| // 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 "config.h" |
| |
| #include "bignum.h" |
| #include "utils.h" |
| #include <wtf/ASCIICType.h> |
| |
| namespace WTF { |
| |
| 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) { |
| 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(BufferReference<const char> buffer, |
| int from, |
| int digits_to_read) { |
| uint64_t result = 0; |
| for (int i = 0; i < digits_to_read; ++i) { |
| int digit = buffer[from + i] - '0'; |
| ASSERT(0 <= digit && digit <= 9); |
| result = result * 10 + digit; |
| } |
| return result; |
| } |
| |
| |
| void Bignum::AssignDecimalString(BufferReference<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(); |
| } |
| |
| |
| void Bignum::AssignHexString(BufferReference<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 += toASCIIHexValue(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 += toASCIIHexValue(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 = 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 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) { |
| #ifndef NDEBUG |
| Bignum a, b; |
| a.AssignBignum(*this); |
| b.AssignBignum(other); |
| b.MultiplyByUInt32(factor); |
| a.SubtractBignum(b); |
| #endif |
| 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); |
| } |
| Clamp(); |
| ASSERT(Bignum::Equal(a, *this)); |
| } |
| |
| |
| } // namespace double_conversion |
| |
| } // namespace WTF |
