531 lines
18 KiB
C++
531 lines
18 KiB
C++
/*
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* Copyright (c) 2020, Itamar S. <itamar8910@gmail.com>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include "UnsignedBigInteger.h"
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#include <AK/StringBuilder.h>
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namespace Crypto {
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UnsignedBigInteger UnsignedBigInteger::create_invalid()
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{
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UnsignedBigInteger invalid(0);
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invalid.invalidate();
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return invalid;
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}
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// FIXME: in great need of optimisation
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UnsignedBigInteger UnsignedBigInteger::import_data(const u8* ptr, size_t length)
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{
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UnsignedBigInteger integer { 0 };
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for (size_t i = 0; i < length; ++i) {
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auto part = UnsignedBigInteger { ptr[length - i - 1] }.shift_left(8 * i);
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integer = integer.plus(part);
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}
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return integer;
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}
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size_t UnsignedBigInteger::export_data(AK::ByteBuffer& data)
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{
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UnsignedBigInteger copy { *this };
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UnsignedBigInteger quotient;
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UnsignedBigInteger remainder;
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size_t size = trimmed_length() * sizeof(u32);
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size_t i = 0;
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for (; i < size; ++i) {
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if (copy.trimmed_length() == 0)
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break;
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data[size - i - 1] = copy.m_words[0] & 0xff;
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divide_u16_without_allocation(copy, 256, quotient, remainder);
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copy.set_to(quotient);
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}
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return i;
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}
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UnsignedBigInteger UnsignedBigInteger::from_base10(const String& str)
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{
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UnsignedBigInteger result;
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UnsignedBigInteger ten { 10 };
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for (auto& c : str) {
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result = result.multiplied_by(ten).plus(c - '0');
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}
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return result;
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}
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String UnsignedBigInteger::to_base10() const
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{
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StringBuilder builder;
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UnsignedBigInteger temp(*this);
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UnsignedBigInteger quotient;
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UnsignedBigInteger remainder;
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while (temp != UnsignedBigInteger { 0 }) {
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divide_u16_without_allocation(temp, 10, quotient, remainder);
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ASSERT(remainder.words()[0] < 10);
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builder.append(static_cast<char>(remainder.words()[0] + '0'));
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temp.set_to(quotient);
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}
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auto reversed_string = builder.to_string();
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builder.clear();
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for (int i = reversed_string.length() - 1; i >= 0; --i) {
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builder.append(reversed_string[i]);
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}
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return builder.to_string();
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}
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void UnsignedBigInteger::set_to_0()
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{
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m_words.clear_with_capacity();
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m_is_invalid = false;
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}
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void UnsignedBigInteger::set_to(u32 other)
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{
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m_is_invalid = false;
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m_words.clear_with_capacity();
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m_words.append(other);
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}
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void UnsignedBigInteger::set_to(const UnsignedBigInteger& other)
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{
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m_is_invalid = other.m_is_invalid;
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m_words.clear_with_capacity();
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m_words.ensure_capacity(other.m_words.size());
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for (size_t i = 0; i < other.m_words.size(); ++i)
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m_words.unchecked_append(other.m_words[i]);
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}
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size_t UnsignedBigInteger::trimmed_length() const
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{
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size_t num_leading_zeroes = 0;
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for (int i = length() - 1; i >= 0; --i, ++num_leading_zeroes) {
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if (m_words[i] != 0)
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break;
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}
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return length() - num_leading_zeroes;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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add_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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subtract_without_allocation(*this, other, result);
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return result;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
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{
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UnsignedBigInteger output;
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UnsignedBigInteger temp_result;
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UnsignedBigInteger temp_plus;
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shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
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return output;
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}
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FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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UnsignedBigInteger temp_shift_result;
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UnsignedBigInteger temp_shift_plus;
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UnsignedBigInteger temp_shift;
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UnsignedBigInteger temp_plus;
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multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
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return result;
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}
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FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigInteger& divisor) const
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{
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UnsignedBigInteger quotient;
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UnsignedBigInteger remainder;
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// If we actually have a u16-compatible divisor, short-circuit to the
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// less computationally-intensive "divide_u16_without_allocation" method.
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if (divisor.trimmed_length() == 1 && divisor.m_words[0] < (1 << 16)) {
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divide_u16_without_allocation(*this, divisor.m_words[0], quotient, remainder);
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return UnsignedDivisionResult { quotient, remainder };
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}
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UnsignedBigInteger temp_shift_result;
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UnsignedBigInteger temp_shift_plus;
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UnsignedBigInteger temp_shift;
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UnsignedBigInteger temp_minus;
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divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
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return UnsignedDivisionResult { quotient, remainder };
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}
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void UnsignedBigInteger::set_bit_inplace(size_t bit_index)
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{
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const size_t word_index = bit_index / UnsignedBigInteger::BITS_IN_WORD;
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const size_t inner_word_index = bit_index % UnsignedBigInteger::BITS_IN_WORD;
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m_words.ensure_capacity(word_index);
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for (size_t i = length(); i <= word_index; ++i) {
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m_words.unchecked_append(0);
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}
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m_words[word_index] |= (1 << inner_word_index);
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}
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bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
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{
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auto length = trimmed_length();
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if (length != other.trimmed_length()) {
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return false;
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}
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if (is_invalid() != other.is_invalid()) {
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return false;
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}
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return !__builtin_memcmp(m_words.data(), other.words().data(), length);
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}
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bool UnsignedBigInteger::operator!=(const UnsignedBigInteger& other) const
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{
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return !(*this == other);
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}
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bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
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{
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auto length = trimmed_length();
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auto other_length = other.trimmed_length();
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if (length < other_length) {
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return true;
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}
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if (length > other_length) {
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return false;
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}
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if (length == 0) {
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return false;
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}
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for (int i = length - 1; i >= 0; --i) {
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if (m_words[i] == other.m_words[i])
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continue;
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return m_words[i] < other.m_words[i];
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}
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return false;
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}
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/**
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* Complexity: O(N) where N is the number of words in the larger number
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*/
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void UnsignedBigInteger::add_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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const UnsignedBigInteger* const longer = (left.length() > right.length()) ? &left : &right;
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const UnsignedBigInteger* const shorter = (longer == &right) ? &left : &right;
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u8 carry = 0;
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output.set_to_0();
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output.m_words.ensure_capacity(longer->length() + 1);
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for (size_t i = 0; i < shorter->length(); ++i) {
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u32 word_addition_result = shorter->m_words[i] + longer->m_words[i];
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u8 carry_out = 0;
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// if there was a carry, the result will be smaller than any of the operands
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if (word_addition_result + carry < shorter->m_words[i]) {
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carry_out = 1;
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}
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if (carry) {
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word_addition_result++;
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}
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carry = carry_out;
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output.m_words.unchecked_append(word_addition_result);
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}
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for (size_t i = shorter->length(); i < longer->length(); ++i) {
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u32 word_addition_result = longer->m_words[i] + carry;
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carry = 0;
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if (word_addition_result < longer->m_words[i]) {
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carry = 1;
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}
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output.m_words.unchecked_append(word_addition_result);
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}
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if (carry) {
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output.m_words.unchecked_append(carry);
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}
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}
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/**
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* Complexity: O(N) where N is the number of words in the larger number
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*/
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void UnsignedBigInteger::subtract_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& output)
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{
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if (left < right) {
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output.invalidate();
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return;
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}
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u8 borrow = 0;
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auto own_length = left.length();
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auto other_length = right.length();
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output.set_to_0();
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output.m_words.ensure_capacity(own_length);
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for (size_t i = 0; i < own_length; ++i) {
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u32 other_word = (i < other_length) ? right.m_words[i] : 0;
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i64 temp = static_cast<i64>(left.m_words[i]) - static_cast<i64>(other_word) - static_cast<i64>(borrow);
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// If temp < 0, we had an underflow
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borrow = (temp >= 0) ? 0 : 1;
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if (temp < 0) {
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temp += (UINT32_MAX + 1);
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}
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output.m_words.append(temp);
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}
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// This assertion should not fail, because we verified that *this>=other at the beginning of the function
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ASSERT(borrow == 0);
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}
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/**
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* Complexity : O(N + num_bits % 8) where N is the number of words in the number
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* Shift method :
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* Start by shifting by whole words in num_bits (by putting missing words at the start),
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* then shift the number's words two by two by the remaining amount of bits.
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*/
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FLATTEN void UnsignedBigInteger::shift_left_without_allocation(
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const UnsignedBigInteger& number,
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size_t num_bits,
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UnsignedBigInteger& temp_result,
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UnsignedBigInteger& temp_plus,
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UnsignedBigInteger& output)
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{
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// We can only do shift operations on individual words
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// where the shift amount is <= size of word (32).
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// But we do know how to shift by a multiple of word size (e.g 64=32*2)
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// So we first shift the result by how many whole words fit in 'num_bits'
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shift_left_by_n_words(number, num_bits / UnsignedBigInteger::BITS_IN_WORD, temp_result);
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output.set_to(temp_result);
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// And now we shift by the leftover amount of bits
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num_bits %= UnsignedBigInteger::BITS_IN_WORD;
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if (num_bits == 0) {
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return;
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}
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for (size_t i = 0; i < temp_result.length(); ++i) {
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u32 current_word_of_temp_result = shift_left_get_one_word(temp_result, num_bits, i);
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output.m_words[i] = current_word_of_temp_result;
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}
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// Shifting the last word can produce a carry
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u32 carry_word = shift_left_get_one_word(temp_result, num_bits, temp_result.length());
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if (carry_word != 0) {
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// output += (carry_word << temp_result.length())
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// FIXME : Using temp_plus this way to transform carry_word into a bigint is not
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// efficient nor pretty. Maybe we should have an "add_with_shift" method ?
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temp_plus.set_to_0();
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temp_plus.m_words.append(carry_word);
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shift_left_by_n_words(temp_plus, temp_result.length(), temp_result);
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add_without_allocation(output, temp_result, temp_plus);
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output.set_to(temp_plus);
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}
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}
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/**
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* Complexity: O(N^2) where N is the number of words in the larger number
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* Multiplication method:
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* An integer is equal to the sum of the powers of two
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* according to the indexes of its 'on' bits.
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* So to multiple x*y, we go over each '1' bit in x (say the i'th bit),
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* and add y<<i to the result.
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*/
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FLATTEN void UnsignedBigInteger::multiply_without_allocation(
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const UnsignedBigInteger& left,
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const UnsignedBigInteger& right,
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UnsignedBigInteger& temp_shift_result,
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UnsignedBigInteger& temp_shift_plus,
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UnsignedBigInteger& temp_shift,
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UnsignedBigInteger& temp_plus,
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UnsignedBigInteger& output)
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{
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output.set_to_0();
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// iterate all bits
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for (size_t word_index = 0; word_index < left.length(); ++word_index) {
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for (size_t bit_index = 0; bit_index < UnsignedBigInteger::BITS_IN_WORD; ++bit_index) {
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// If the bit is off - skip over it
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if (!(left.m_words[word_index] & (1 << bit_index)))
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continue;
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const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
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// output += (right << shift_amount);
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shift_left_without_allocation(right, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
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add_without_allocation(output, temp_shift, temp_plus);
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output.set_to(temp_plus);
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}
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}
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}
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/**
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* Complexity: O(N^2) where N is the number of words in the larger number
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* Division method:
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* We loop over the bits of the divisor, attempting to subtract divisor<<i from the dividend.
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* If the result is non-negative, it means that divisor*2^i "fits" in the dividend,
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* so we set the ith bit in the quotient and reduce divisor<<i from the dividend.
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* When we're done, what's left from the dividend is the remainder.
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*/
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FLATTEN void UnsignedBigInteger::divide_without_allocation(
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const UnsignedBigInteger& numerator,
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const UnsignedBigInteger& denominator,
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UnsignedBigInteger& temp_shift_result,
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UnsignedBigInteger& temp_shift_plus,
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UnsignedBigInteger& temp_shift,
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UnsignedBigInteger& temp_minus,
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UnsignedBigInteger& quotient,
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UnsignedBigInteger& remainder)
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{
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quotient.set_to_0();
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remainder.set_to(numerator);
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// iterate all bits
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for (int word_index = numerator.trimmed_length() - 1; word_index >= 0; --word_index) {
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for (int bit_index = UnsignedBigInteger::BITS_IN_WORD - 1; bit_index >= 0; --bit_index) {
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const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
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shift_left_without_allocation(denominator, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
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subtract_without_allocation(remainder, temp_shift, temp_minus);
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if (!temp_minus.is_invalid()) {
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remainder.set_to(temp_minus);
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quotient.set_bit_inplace(shift_amount);
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}
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}
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}
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}
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/**
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* Complexity : O(N) where N is the number of digits in the numerator
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* Division method :
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* Starting from the most significant one, for each half-word of the numerator, combine it
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* with the existing remainder if any, divide the combined number as a u32 operation and
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* update the quotient / remainder as needed.
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*/
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FLATTEN void UnsignedBigInteger::divide_u16_without_allocation(
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const UnsignedBigInteger& numerator,
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u32 denominator,
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UnsignedBigInteger& quotient,
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UnsignedBigInteger& remainder)
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{
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ASSERT(denominator < (1 << 16));
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u32 remainder_word = 0;
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auto numerator_length = numerator.trimmed_length();
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quotient.set_to_0();
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quotient.m_words.resize(numerator_length);
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for (int word_index = numerator_length - 1; word_index >= 0; --word_index) {
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auto word_high = numerator.m_words[word_index] >> 16;
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auto word_low = numerator.m_words[word_index] & ((1 << 16) - 1);
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auto number_to_divide_high = (remainder_word << 16) | word_high;
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auto quotient_high = number_to_divide_high / denominator;
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remainder_word = number_to_divide_high % denominator;
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auto number_to_divide_low = remainder_word << 16 | word_low;
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auto quotient_low = number_to_divide_low / denominator;
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remainder_word = number_to_divide_low % denominator;
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quotient.m_words[word_index] = (quotient_high << 16) | quotient_low;
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}
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remainder.set_to(remainder_word);
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}
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ALWAYS_INLINE void UnsignedBigInteger::shift_left_by_n_words(
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const UnsignedBigInteger& number,
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const size_t number_of_words,
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UnsignedBigInteger& output)
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|
{
|
|
// shifting left by N words means just inserting N zeroes to the beginning of the words vector
|
|
output.set_to_0();
|
|
output.m_words.ensure_capacity(number_of_words + number.length());
|
|
|
|
for (size_t i = 0; i < number_of_words; ++i) {
|
|
output.m_words.unchecked_append(0);
|
|
}
|
|
for (size_t i = 0; i < number.length(); ++i) {
|
|
output.m_words.unchecked_append(number.m_words[i]);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the word at a requested index in the result of a shift operation
|
|
*/
|
|
ALWAYS_INLINE u32 UnsignedBigInteger::shift_left_get_one_word(
|
|
const UnsignedBigInteger& number,
|
|
const size_t num_bits,
|
|
const size_t result_word_index)
|
|
{
|
|
// "<= length()" (rather than length() - 1) is intentional,
|
|
// The result inedx of length() is used when calculating the carry word
|
|
ASSERT(result_word_index <= number.length());
|
|
ASSERT(num_bits <= UnsignedBigInteger::BITS_IN_WORD);
|
|
u32 result = 0;
|
|
|
|
// we need to check for "num_bits != 0" since shifting right by 32 is apparently undefined behaviour!
|
|
if (result_word_index > 0 && num_bits != 0) {
|
|
result += number.m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
|
|
}
|
|
if (result_word_index < number.length() && num_bits < 32) {
|
|
result += number.m_words[result_word_index] << num_bits;
|
|
}
|
|
return result;
|
|
}
|
|
}
|