28ea347e55
This changes the plus, minus, etc... operators from UnsignedBigInteger to use a static helper method. The static methods do not allocate any variables, instead all the required BigInteger output and temporary variables are required on call as parameters. This change already optimizes the number of allocations in complex operations such as multiply or divide, by having a single allocation per call (instead of one per loop). This new API also provides a way to limit the number of allocations for complex computations in other parts of the code. This is done by using these helpers in any place that currently makes use of the standard operators.
477 lines
15 KiB
C++
477 lines
15 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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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.length() == 0)
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break;
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data[size - i - 1] = copy.m_words[0] & 0xff;
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copy = copy.divided_by(256).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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while (temp != UnsignedBigInteger { 0 }) {
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auto div_result = temp.divided_by({ 10 });
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ASSERT(div_result.remainder.words()[0] < 10);
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builder.append(static_cast<char>(div_result.remainder.words()[0] + '0'));
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temp = div_result.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(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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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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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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{
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// shifting left by N words means just inserting N zeroes to the beginning of the words vector
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output.set_to_0();
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output.m_words.ensure_capacity(number_of_words + number.length());
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for (size_t i = 0; i < number_of_words; ++i) {
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output.m_words.unchecked_append(0);
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}
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for (size_t i = 0; i < number.length(); ++i) {
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output.m_words.unchecked_append(number.m_words[i]);
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}
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}
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/**
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* Returns the word at a requested index in the result of a shift operation
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*/
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ALWAYS_INLINE u32 UnsignedBigInteger::shift_left_get_one_word(
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const UnsignedBigInteger& number,
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const size_t num_bits,
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const size_t result_word_index)
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{
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// "<= length()" (rather than length() - 1) is intentional,
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// The result inedx of length() is used when calculating the carry word
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ASSERT(result_word_index <= number.length());
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ASSERT(num_bits <= UnsignedBigInteger::BITS_IN_WORD);
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u32 result = 0;
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// we need to check for "num_bits != 0" since shifting right by 32 is apparently undefined behaviour!
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if (result_word_index > 0 && num_bits != 0) {
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result += number.m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
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}
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if (result_word_index < number.length() && num_bits < 32) {
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result += number.m_words[result_word_index] << num_bits;
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}
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return result;
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}
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}
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