241 lines
8.2 KiB
C++
241 lines
8.2 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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namespace Crypto {
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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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UnsignedBigInteger UnsignedBigInteger::add(const UnsignedBigInteger& other) const
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{
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const UnsignedBigInteger* const longer = (length() > other.length()) ? this : &other;
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const UnsignedBigInteger* const shorter = (longer == &other) ? this : &other;
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UnsignedBigInteger result;
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u8 carry = 0;
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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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result.m_words.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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result.m_words.append(word_addition_result);
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}
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if (carry) {
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result.m_words.append(carry);
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}
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return result;
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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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UnsignedBigInteger UnsignedBigInteger::sub(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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if (*this < other) {
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dbg() << "WARNING: bigint subtraction creates a negative number!";
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return UnsignedBigInteger::create_invalid();
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}
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u8 borrow = 0;
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for (size_t i = 0; i < other.length(); ++i) {
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ASSERT(!(borrow == 1 && m_words[i] == 0));
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if (m_words[i] - borrow < other.m_words[i]) {
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u64 after_borrow = static_cast<u64>(m_words[i] - borrow) + (UINT32_MAX + 1);
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result.m_words.append(static_cast<u32>(after_borrow - static_cast<u64>(other.m_words[i])));
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borrow = 1;
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} else {
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result.m_words.append(m_words[i] - borrow - other.m_words[i]);
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borrow = 0;
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}
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}
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for (size_t i = other.length(); i < length(); ++i) {
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ASSERT(!(borrow == 1 && m_words[i] == 0));
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result.m_words.append(m_words[i] - borrow);
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borrow = 0;
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}
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return result;
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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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* Multiplcation 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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UnsignedBigInteger UnsignedBigInteger::multiply(const UnsignedBigInteger& other) const
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{
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UnsignedBigInteger result;
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// iterate all bits
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for (size_t word_index = 0; word_index < 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 (!(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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auto shift_result = other.shift_left(shift_amount);
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result = result.add(shift_result);
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}
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}
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return result;
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}
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UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
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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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UnsignedBigInteger temp_result = shift_left_by_n_words(num_bits / UnsignedBigInteger::BITS_IN_WORD);
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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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UnsignedBigInteger result(temp_result);
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for (size_t i = 0; i < temp_result.length(); ++i) {
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u32 current_word_of_temp_result = temp_result.shift_left_get_one_word(num_bits, i);
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result.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 = temp_result.shift_left_get_one_word(num_bits, temp_result.length());
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if (carry_word != 0) {
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result = result.add(UnsignedBigInteger(carry_word).shift_left_by_n_words(temp_result.length()));
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}
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return result;
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}
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UnsignedBigInteger UnsignedBigInteger::shift_left_by_n_words(const size_t number_of_words) const
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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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UnsignedBigInteger result;
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for (size_t i = 0; i < number_of_words; ++i) {
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result.m_words.append(0);
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}
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for (size_t i = 0; i < length(); ++i) {
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result.m_words.append(m_words[i]);
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}
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return result;
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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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u32 UnsignedBigInteger::shift_left_get_one_word(const size_t num_bits, const size_t result_word_index) const
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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 <= 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 += m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
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}
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if (result_word_index < length() && num_bits < 32) {
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result += 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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bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
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{
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if (trimmed_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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for (size_t i = 0; i < trimmed_length(); ++i) {
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if (m_words[i] != other.words()[i])
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return false;
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}
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return true;
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}
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bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
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{
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if (trimmed_length() < other.trimmed_length()) {
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return true;
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}
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if (trimmed_length() > other.trimmed_length()) {
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return false;
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}
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size_t length = trimmed_length();
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if (length == 0) {
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return false;
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}
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return m_words[length - 1] < other.m_words[length - 1];
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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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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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}
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