1ddda9e81d3175130f2029c0e1205d265a00c32edjkummerow@chromium.org// Copyright 2011 the V8 project authors. All rights reserved. 23484964a86451e86dcf04be9bd8c0d76ee04f081rossberg@chromium.org// Use of this source code is governed by a BSD-style license that can be 33484964a86451e86dcf04be9bd8c0d76ee04f081rossberg@chromium.org// found in the LICENSE file. 401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 54b0feeef5d01dbc2948080b4f69daa37e1083461machenbach@chromium.org#include "src/v8.h" 64b0feeef5d01dbc2948080b4f69daa37e1083461machenbach@chromium.org 7196eb601290dc49c3754da728dc58700dff2de1bmachenbach@chromium.org#include "src/bignum.h" 84b0feeef5d01dbc2948080b4f69daa37e1083461machenbach@chromium.org#include "src/utils.h" 901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 1001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgnamespace v8 { 1101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgnamespace internal { 1201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 1301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgBignum::Bignum() 1401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { 1501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < kBigitCapacity; ++i) { 1601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = 0; 1701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 1801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 1901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 2001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 2101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgtemplate<typename S> 2201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgstatic int BitSize(S value) { 2301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return 8 * sizeof(value); 2401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 2501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 26e0e1b0d3e70c933d36ed381d511e9fda39f2a751mstarzinger@chromium.org 2701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org// Guaranteed to lie in one Bigit. 2801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AssignUInt16(uint16_t value) { 29e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(kBigitSize >= BitSize(value)); 3001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 3101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (value == 0) return; 3201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 3301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(1); 3401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[0] = value; 3501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = 1; 3601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 3701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 3801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 3901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AssignUInt64(uint64_t value) { 4001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const int kUInt64Size = 64; 4101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 4201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 4301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (value == 0) return; 4401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 4501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int needed_bigits = kUInt64Size / kBigitSize + 1; 4601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(needed_bigits); 4701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < needed_bigits; ++i) { 48496c03a64f12710e837204e261ef155601247895sgjesse@chromium.org bigits_[i] = static_cast<Chunk>(value & kBigitMask); 4901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org value = value >> kBigitSize; 5001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 5101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = needed_bigits; 5201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 5301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 5401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 5501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 5601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AssignBignum(const Bignum& other) { 5701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org exponent_ = other.exponent_; 5801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < other.used_digits_; ++i) { 5901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = other.bigits_[i]; 6001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 6101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Clear the excess digits (if there were any). 6201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = other.used_digits_; i < used_digits_; ++i) { 6301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = 0; 6401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 6501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = other.used_digits_; 6601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 6701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 6801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 6901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgstatic uint64_t ReadUInt64(Vector<const char> buffer, 7001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int from, 7101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int digits_to_read) { 7201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t result = 0; 7301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = from; i < from + digits_to_read; ++i) { 7401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int digit = buffer[i] - '0'; 75e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(0 <= digit && digit <= 9); 7601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org result = result * 10 + digit; 7701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 7801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return result; 7901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 8001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 8101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 8201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AssignDecimalString(Vector<const char> value) { 8301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 2^64 = 18446744073709551616 > 10^19 8401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const int kMaxUint64DecimalDigits = 19; 8501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 8601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int length = value.length(); 8701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int pos = 0; 8801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Let's just say that each digit needs 4 bits. 8901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (length >= kMaxUint64DecimalDigits) { 9001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); 9101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org pos += kMaxUint64DecimalDigits; 9201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org length -= kMaxUint64DecimalDigits; 9301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByPowerOfTen(kMaxUint64DecimalDigits); 9401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org AddUInt64(digits); 9501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 9601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t digits = ReadUInt64(value, pos, length); 9701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByPowerOfTen(length); 9801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org AddUInt64(digits); 9901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 10001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 10101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 10201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 10301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgstatic int HexCharValue(char c) { 10401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if ('0' <= c && c <= '9') return c - '0'; 10501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if ('a' <= c && c <= 'f') return 10 + c - 'a'; 10601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if ('A' <= c && c <= 'F') return 10 + c - 'A'; 10701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org UNREACHABLE(); 10801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return 0; // To make compiler happy. 10901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 11001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 11101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 11201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AssignHexString(Vector<const char> value) { 11301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 11401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int length = value.length(); 11501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 11601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int needed_bigits = length * 4 / kBigitSize + 1; 11701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(needed_bigits); 11801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int string_index = length - 1; 11901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < needed_bigits - 1; ++i) { 12001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // These bigits are guaranteed to be "full". 12101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk current_bigit = 0; 12201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int j = 0; j < kBigitSize / 4; j++) { 12301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org current_bigit += HexCharValue(value[string_index--]) << (j * 4); 12401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 12501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = current_bigit; 12601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 12701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = needed_bigits - 1; 12801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 12901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk most_significant_bigit = 0; // Could be = 0; 13001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int j = 0; j <= string_index; ++j) { 13101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org most_significant_bigit <<= 4; 13201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org most_significant_bigit += HexCharValue(value[j]); 13301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 13401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (most_significant_bigit != 0) { 13501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[used_digits_] = most_significant_bigit; 13601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_++; 13701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 13801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 13901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 14001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 14101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 14201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AddUInt64(uint64_t operand) { 14301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (operand == 0) return; 14401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Bignum other; 14501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org other.AssignUInt64(operand); 14601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org AddBignum(other); 14701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 14801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 14901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 15001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AddBignum(const Bignum& other) { 151e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(IsClamped()); 152e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(other.IsClamped()); 15301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 15401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // If this has a greater exponent than other append zero-bigits to this. 15501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // After this call exponent_ <= other.exponent_. 15601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Align(other); 15701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 15801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // There are two possibilities: 15901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) 16001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // bbbbb 00000000 16101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // ---------------- 16201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // ccccccccccc 0000 16301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // or 16401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // aaaaaaaaaa 0000 16501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // bbbbbbbbb 0000000 16601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // ----------------- 16701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // cccccccccccc 0000 16801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // In both cases we might need a carry bigit. 16901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 17001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); 17101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk carry = 0; 17201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_pos = other.exponent_ - exponent_; 173e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(bigit_pos >= 0); 17401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < other.used_digits_; ++i) { 17501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; 17601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[bigit_pos] = sum & kBigitMask; 17701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry = sum >> kBigitSize; 17801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigit_pos++; 17901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 18001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 18101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (carry != 0) { 18201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk sum = bigits_[bigit_pos] + carry; 18301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[bigit_pos] = sum & kBigitMask; 18401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry = sum >> kBigitSize; 18501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigit_pos++; 18601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 18701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = Max(bigit_pos, used_digits_); 188e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(IsClamped()); 18901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 19001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 19101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 19201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::SubtractBignum(const Bignum& other) { 193e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(IsClamped()); 194e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(other.IsClamped()); 19501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // We require this to be bigger than other. 196e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(LessEqual(other, *this)); 19701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 19801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Align(other); 19901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 20001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int offset = other.exponent_ - exponent_; 20101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk borrow = 0; 20201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int i; 20301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (i = 0; i < other.used_digits_; ++i) { 204e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK((borrow == 0) || (borrow == 1)); 20501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; 20601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i + offset] = difference & kBigitMask; 20701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org borrow = difference >> (kChunkSize - 1); 20801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 20901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (borrow != 0) { 21001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk difference = bigits_[i + offset] - borrow; 21101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i + offset] = difference & kBigitMask; 21201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org borrow = difference >> (kChunkSize - 1); 21301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org ++i; 21401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 21501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 21601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 21701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 21801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 21901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::ShiftLeft(int shift_amount) { 22001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (used_digits_ == 0) return; 22101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org exponent_ += shift_amount / kBigitSize; 22201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int local_shift = shift_amount % kBigitSize; 22301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(used_digits_ + 1); 22401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org BigitsShiftLeft(local_shift); 22501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 22601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 22701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 22801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::MultiplyByUInt32(uint32_t factor) { 22901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (factor == 1) return; 23001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (factor == 0) { 23101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 23201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return; 23301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 23401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (used_digits_ == 0) return; 23501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 23601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // The product of a bigit with the factor is of size kBigitSize + 32. 23701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Assert that this number + 1 (for the carry) fits into double chunk. 238e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(kDoubleChunkSize >= kBigitSize + 32 + 1); 23901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org DoubleChunk carry = 0; 24001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_; ++i) { 24101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; 24201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = static_cast<Chunk>(product & kBigitMask); 24301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry = (product >> kBigitSize); 24401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 24501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (carry != 0) { 24601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(used_digits_ + 1); 247496c03a64f12710e837204e261ef155601247895sgjesse@chromium.org bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); 24801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_++; 24901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry >>= kBigitSize; 25001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 25101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 25201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 25301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 25401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::MultiplyByUInt64(uint64_t factor) { 25501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (factor == 1) return; 25601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (factor == 0) { 25701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 25801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return; 25901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 260e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(kBigitSize < 32); 26101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t carry = 0; 26201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t low = factor & 0xFFFFFFFF; 26301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t high = factor >> 32; 26401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_; ++i) { 26501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t product_low = low * bigits_[i]; 26601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t product_high = high * bigits_[i]; 26701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t tmp = (carry & kBigitMask) + product_low; 268496c03a64f12710e837204e261ef155601247895sgjesse@chromium.org bigits_[i] = static_cast<Chunk>(tmp & kBigitMask); 26901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + 27001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org (product_high << (32 - kBigitSize)); 27101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 27201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (carry != 0) { 27301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(used_digits_ + 1); 274496c03a64f12710e837204e261ef155601247895sgjesse@chromium.org bigits_[used_digits_] = static_cast<Chunk>(carry & kBigitMask); 27501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_++; 27601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry >>= kBigitSize; 27701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 27801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 27901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 28001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 28101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::MultiplyByPowerOfTen(int exponent) { 28201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d); 28301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint16_t kFive1 = 5; 28401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint16_t kFive2 = kFive1 * 5; 28501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint16_t kFive3 = kFive2 * 5; 28601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint16_t kFive4 = kFive3 * 5; 28701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint16_t kFive5 = kFive4 * 5; 28801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint16_t kFive6 = kFive5 * 5; 28901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive7 = kFive6 * 5; 29001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive8 = kFive7 * 5; 29101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive9 = kFive8 * 5; 29201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive10 = kFive9 * 5; 29301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive11 = kFive10 * 5; 29401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive12 = kFive11 * 5; 29501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive13 = kFive12 * 5; 29601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint32_t kFive1_to_12[] = 29701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, 29801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; 29901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 300e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(exponent >= 0); 30101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (exponent == 0) return; 30201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (used_digits_ == 0) return; 30301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 30401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // We shift by exponent at the end just before returning. 30501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int remaining_exponent = exponent; 30601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (remaining_exponent >= 27) { 30701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByUInt64(kFive27); 30801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org remaining_exponent -= 27; 30901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 31001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (remaining_exponent >= 13) { 31101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByUInt32(kFive13); 31201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org remaining_exponent -= 13; 31301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 31401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (remaining_exponent > 0) { 31501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); 31601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 31701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org ShiftLeft(exponent); 31801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 31901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 32001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 32101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::Square() { 322e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(IsClamped()); 32301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int product_length = 2 * used_digits_; 32401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(product_length); 32501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 32601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Comba multiplication: compute each column separately. 32701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Example: r = a2a1a0 * b2b1b0. 32801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // r = 1 * a0b0 + 32901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 10 * (a1b0 + a0b1) + 33001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 100 * (a2b0 + a1b1 + a0b2) + 33101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 1000 * (a2b1 + a1b2) + 33201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 10000 * a2b2 33301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 33401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // In the worst case we have to accumulate nb-digits products of digit*digit. 33501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 33601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Assert that the additional number of bits in a DoubleChunk are enough to 33701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // sum up used_digits of Bigit*Bigit. 33801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { 33901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org UNIMPLEMENTED(); 34001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 34101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org DoubleChunk accumulator = 0; 34201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // First shift the digits so we don't overwrite them. 34301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int copy_offset = used_digits_; 34401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_; ++i) { 34501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[copy_offset + i] = bigits_[i]; 34601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 34701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // We have two loops to avoid some 'if's in the loop. 34801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_; ++i) { 34901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Process temporary digit i with power i. 35001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // The sum of the two indices must be equal to i. 35101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_index1 = i; 35201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_index2 = 0; 35301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Sum all of the sub-products. 35401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (bigit_index1 >= 0) { 35501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 35601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 35701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 35801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigit_index1--; 35901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigit_index2++; 36001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 36101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 36201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org accumulator >>= kBigitSize; 36301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 36401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = used_digits_; i < product_length; ++i) { 36501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_index1 = used_digits_ - 1; 36601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_index2 = i - bigit_index1; 36701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Invariant: sum of both indices is again equal to i. 36801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Inner loop runs 0 times on last iteration, emptying accumulator. 36901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (bigit_index2 < used_digits_) { 37001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk1 = bigits_[copy_offset + bigit_index1]; 37101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk2 = bigits_[copy_offset + bigit_index2]; 37201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; 37301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigit_index1--; 37401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigit_index2++; 37501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 37601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // The overwritten bigits_[i] will never be read in further loop iterations, 37701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // because bigit_index1 and bigit_index2 are always greater 37801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // than i - used_digits_. 37901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; 38001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org accumulator >>= kBigitSize; 38101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 38201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Since the result was guaranteed to lie inside the number the 38301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // accumulator must be 0 now. 384e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(accumulator == 0); 38501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 38601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Don't forget to update the used_digits and the exponent. 38701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = product_length; 38801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org exponent_ *= 2; 38901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 39001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 39101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 39201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 39301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { 394e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(base != 0); 395e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(power_exponent >= 0); 39601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (power_exponent == 0) { 39701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org AssignUInt16(1); 39801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return; 39901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 40001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Zero(); 40101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int shifts = 0; 40201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // We expect base to be in range 2-32, and most often to be 10. 40301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // It does not make much sense to implement different algorithms for counting 40401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // the bits. 40501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while ((base & 1) == 0) { 40601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org base >>= 1; 40701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org shifts++; 40801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 40901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bit_size = 0; 41001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int tmp_base = base; 41101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (tmp_base != 0) { 41201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org tmp_base >>= 1; 41301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bit_size++; 41401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 41501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int final_size = bit_size * power_exponent; 41601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 1 extra bigit for the shifting, and one for rounded final_size. 41701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(final_size / kBigitSize + 2); 41801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 41901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Left to Right exponentiation. 42001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int mask = 1; 42101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (power_exponent >= mask) mask <<= 1; 42201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 42301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // The mask is now pointing to the bit above the most significant 1-bit of 42401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // power_exponent. 42501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Get rid of first 1-bit; 42601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org mask >>= 2; 42701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t this_value = base; 42801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 42901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bool delayed_multipliciation = false; 43001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const uint64_t max_32bits = 0xFFFFFFFF; 43101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (mask != 0 && this_value <= max_32bits) { 43201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org this_value = this_value * this_value; 43301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Verify that there is enough space in this_value to perform the 43401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // multiplication. The first bit_size bits must be 0. 43501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if ((power_exponent & mask) != 0) { 43601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint64_t base_bits_mask = 43701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); 43801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bool high_bits_zero = (this_value & base_bits_mask) == 0; 43901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (high_bits_zero) { 44001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org this_value *= base; 44101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } else { 44201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org delayed_multipliciation = true; 44301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 44401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 44501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org mask >>= 1; 44601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 44701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org AssignUInt64(this_value); 44801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (delayed_multipliciation) { 44901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByUInt32(base); 45001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 45101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 45201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Now do the same thing as a bignum. 45301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (mask != 0) { 45401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Square(); 45501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if ((power_exponent & mask) != 0) { 45601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org MultiplyByUInt32(base); 45701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 45801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org mask >>= 1; 45901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 46001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 46101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // And finally add the saved shifts. 46201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org ShiftLeft(shifts * power_exponent); 46301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 46401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 46501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 46601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org// Precondition: this/other < 16bit. 46701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orguint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { 468e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(IsClamped()); 469e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(other.IsClamped()); 470e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(other.used_digits_ > 0); 47101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 47201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Easy case: if we have less digits than the divisor than the result is 0. 47301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Note: this handles the case where this == 0, too. 47401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (BigitLength() < other.BigitLength()) { 47501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return 0; 47601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 47701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 47801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Align(other); 47901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 48001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org uint16_t result = 0; 48101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 48201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Start by removing multiples of 'other' until both numbers have the same 48301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // number of digits. 48401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (BigitLength() > other.BigitLength()) { 48501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // This naive approach is extremely inefficient if the this divided other 48601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // might be big. This function is implemented for doubleToString where 48701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // the result should be small (less than 10). 488e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); 48901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Remove the multiples of the first digit. 49001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Example this = 23 and other equals 9. -> Remove 2 multiples. 49101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org result += bigits_[used_digits_ - 1]; 49201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org SubtractTimes(other, bigits_[used_digits_ - 1]); 49301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 49401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 495e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(BigitLength() == other.BigitLength()); 49601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 49701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Both bignums are at the same length now. 49801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Since other has more than 0 digits we know that the access to 49901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // bigits_[used_digits_ - 1] is safe. 50001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk this_bigit = bigits_[used_digits_ - 1]; 50101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; 50201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 50301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (other.used_digits_ == 1) { 50401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Shortcut for easy (and common) case. 50501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int quotient = this_bigit / other_bigit; 50601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; 50701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org result += quotient; 50801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 50901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return result; 51001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 51101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 51201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int division_estimate = this_bigit / (other_bigit + 1); 51301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org result += division_estimate; 51401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org SubtractTimes(other, division_estimate); 51501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 51601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (other_bigit * (division_estimate + 1) > this_bigit) { 51701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // No need to even try to subtract. Even if other's remaining digits were 0 51801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // another subtraction would be too much. 51901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return result; 52001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 52101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 52201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (LessEqual(other, *this)) { 52301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org SubtractBignum(other); 52401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org result++; 52501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 52601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return result; 52701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 52801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 52901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 53001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgtemplate<typename S> 53101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgstatic int SizeInHexChars(S number) { 532e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(number > 0); 53301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int result = 0; 53401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (number != 0) { 53501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org number >>= 4; 53601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org result++; 53701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 53801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return result; 53901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 54001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 54101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 54201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgstatic char HexCharOfValue(int value) { 543e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(0 <= value && value <= 16); 54401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (value < 10) return value + '0'; 54501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return value - 10 + 'A'; 54601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 54701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 54801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 54901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgbool Bignum::ToHexString(char* buffer, int buffer_size) const { 550e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(IsClamped()); 55101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Each bigit must be printable as separate hex-character. 552e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(kBigitSize % 4 == 0); 55301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org const int kHexCharsPerBigit = kBigitSize / 4; 55401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 55501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (used_digits_ == 0) { 55601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (buffer_size < 2) return false; 55701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org buffer[0] = '0'; 55801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org buffer[1] = '\0'; 55901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return true; 56001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 56101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // We add 1 for the terminating '\0' character. 56201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + 56301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org SizeInHexChars(bigits_[used_digits_ - 1]) + 1; 56401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (needed_chars > buffer_size) return false; 56501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int string_index = needed_chars - 1; 56601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org buffer[string_index--] = '\0'; 56701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < exponent_; ++i) { 56801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int j = 0; j < kHexCharsPerBigit; ++j) { 56901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org buffer[string_index--] = '0'; 57001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 57101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 57201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_ - 1; ++i) { 57301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk current_bigit = bigits_[i]; 57401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int j = 0; j < kHexCharsPerBigit; ++j) { 57501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); 57601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org current_bigit >>= 4; 57701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 57801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 57901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // And finally the last bigit. 58001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk most_significant_bigit = bigits_[used_digits_ - 1]; 58101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (most_significant_bigit != 0) { 58201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); 58301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org most_significant_bigit >>= 4; 58401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 58501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return true; 58601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 58701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 58801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 58901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgBignum::Chunk Bignum::BigitAt(int index) const { 59001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (index >= BigitLength()) return 0; 59101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (index < exponent_) return 0; 59201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return bigits_[index - exponent_]; 59301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 59401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 59501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 59601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgint Bignum::Compare(const Bignum& a, const Bignum& b) { 597e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(a.IsClamped()); 598e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(b.IsClamped()); 59901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_length_a = a.BigitLength(); 60001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int bigit_length_b = b.BigitLength(); 60101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (bigit_length_a < bigit_length_b) return -1; 60201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (bigit_length_a > bigit_length_b) return +1; 60301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { 60401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk bigit_a = a.BigitAt(i); 60501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk bigit_b = b.BigitAt(i); 60601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (bigit_a < bigit_b) return -1; 60701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (bigit_a > bigit_b) return +1; 60801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Otherwise they are equal up to this digit. Try the next digit. 60901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 61001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return 0; 61101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 61201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 61301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 61401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgint Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { 615e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(a.IsClamped()); 616e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(b.IsClamped()); 617e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(c.IsClamped()); 61801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (a.BigitLength() < b.BigitLength()) { 61901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return PlusCompare(b, a, c); 62001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 62101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (a.BigitLength() + 1 < c.BigitLength()) return -1; 62201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (a.BigitLength() > c.BigitLength()) return +1; 62301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than 62401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one 62501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // of 'a'. 62601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { 62701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return -1; 62801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 62901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 63001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk borrow = 0; 63101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Starting at min_exponent all digits are == 0. So no need to compare them. 63201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); 63301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { 63401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk_a = a.BigitAt(i); 63501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk_b = b.BigitAt(i); 63601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk chunk_c = c.BigitAt(i); 63701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk sum = chunk_a + chunk_b; 63801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (sum > chunk_c + borrow) { 63901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return +1; 64001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } else { 64101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org borrow = chunk_c + borrow - sum; 64201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (borrow > 1) return -1; 64301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org borrow <<= kBigitSize; 64401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 64501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 64601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (borrow == 0) return 0; 64701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return -1; 64801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 64901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 65001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 65101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::Clamp() { 65201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { 65301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_--; 65401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 65501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (used_digits_ == 0) { 65601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // Zero. 65701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org exponent_ = 0; 65801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 65901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 66001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 66101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 66201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgbool Bignum::IsClamped() const { 66301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; 66401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 66501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 66601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 66701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::Zero() { 66801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_; ++i) { 66901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = 0; 67001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 67101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ = 0; 67201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org exponent_ = 0; 67301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 67401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 67501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 67601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::Align(const Bignum& other) { 67701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (exponent_ > other.exponent_) { 67801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // If "X" represents a "hidden" digit (by the exponent) then we are in the 67901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // following case (a == this, b == other): 68001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // a: aaaaaaXXXX or a: aaaaaXXX 68101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // b: bbbbbbX b: bbbbbbbbXX 68201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // We replace some of the hidden digits (X) of a with 0 digits. 68301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org // a: aaaaaa000X or a: aaaaa0XX 68401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int zero_digits = exponent_ - other.exponent_; 68501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org EnsureCapacity(used_digits_ + zero_digits); 68601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = used_digits_ - 1; i >= 0; --i) { 68701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i + zero_digits] = bigits_[i]; 68801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 68901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < zero_digits; ++i) { 69001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = 0; 69101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 69201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_ += zero_digits; 69301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org exponent_ -= zero_digits; 694e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(used_digits_ >= 0); 695e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(exponent_ >= 0); 69601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 69701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 69801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 69901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 70001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::BigitsShiftLeft(int shift_amount) { 701e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(shift_amount < kBigitSize); 702e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(shift_amount >= 0); 70301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk carry = 0; 70401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < used_digits_; ++i) { 70501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); 70601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; 70701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org carry = new_carry; 70801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 70901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (carry != 0) { 71001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[used_digits_] = carry; 71101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org used_digits_++; 71201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 71301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 71401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 71501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 71601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.orgvoid Bignum::SubtractTimes(const Bignum& other, int factor) { 717e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org#ifdef DEBUG 718e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org Bignum a, b; 719e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org a.AssignBignum(*this); 720e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org b.AssignBignum(other); 721e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org b.MultiplyByUInt32(factor); 722e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org a.SubtractBignum(b); 723e27d617298263725e8a48c2aa14029759b952623mstarzinger@chromium.org#endif 724e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(exponent_ <= other.exponent_); 72501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (factor < 3) { 72601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < factor; ++i) { 72701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org SubtractBignum(other); 72801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 72901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org return; 73001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 73101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk borrow = 0; 73201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org int exponent_diff = other.exponent_ - exponent_; 73301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = 0; i < other.used_digits_; ++i) { 73401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; 73501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org DoubleChunk remove = borrow + product; 736496c03a64f12710e837204e261ef155601247895sgjesse@chromium.org Chunk difference = 737496c03a64f12710e837204e261ef155601247895sgjesse@chromium.org bigits_[i + exponent_diff] - static_cast<Chunk>(remove & kBigitMask); 73801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i + exponent_diff] = difference & kBigitMask; 73901fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + 74001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org (remove >> kBigitSize)); 74101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 74201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { 74301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org if (borrow == 0) return; 74401fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Chunk difference = bigits_[i] - borrow; 74501fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org bigits_[i] = difference & kBigitMask; 74601fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org borrow = difference >> (kChunkSize - 1); 74701fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org } 74801fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org Clamp(); 749e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(Bignum::Equal(a, *this)); 75001fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} 75101fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 75201fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org 75301fe7df37ce9858e3d0069ec6a2d7c667256b95aager@chromium.org} } // namespace v8::internal 754