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Libraries: Move to Userland/Libraries/

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Andreas Kling 2021-01-12 12:17:30 +01:00
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Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp
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/*
* Copyright (c) 2020, Itamar S. <itamar8910@gmail.com>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "UnsignedBigInteger.h"
#include <AK/StringBuilder.h>
namespace Crypto {
UnsignedBigInteger::UnsignedBigInteger(const u8* ptr, size_t length)
{
m_words.resize_and_keep_capacity((length + sizeof(u32) - 1) / sizeof(u32));
size_t in = length, out = 0;
while (in >= sizeof(u32)) {
in -= sizeof(u32);
u32 word = ((u32)ptr[in] << 24) | ((u32)ptr[in + 1] << 16) | ((u32)ptr[in + 2] << 8) | (u32)ptr[in + 3];
m_words[out++] = word;
}
if (in > 0) {
u32 word = 0;
for (size_t i = 0; i < in; i++) {
word <<= 8;
word |= (u32)ptr[i];
}
m_words[out++] = word;
}
}
UnsignedBigInteger UnsignedBigInteger::create_invalid()
{
UnsignedBigInteger invalid(0);
invalid.invalidate();
return invalid;
}
size_t UnsignedBigInteger::export_data(Bytes data, bool remove_leading_zeros) const
{
size_t word_count = trimmed_length();
size_t out = 0;
if (word_count > 0) {
ssize_t leading_zeros = -1;
if (remove_leading_zeros) {
u32 word = m_words[word_count - 1];
for (size_t i = 0; i < sizeof(u32); i++) {
u8 byte = (u8)(word >> ((sizeof(u32) - i - 1) * 8));
data[out++] = byte;
if (leading_zeros < 0 && byte != 0)
leading_zeros = (int)i;
}
}
for (size_t i = word_count - (remove_leading_zeros ? 1 : 0); i > 0; i--) {
auto word = m_words[i - 1];
data[out++] = (u8)(word >> 24);
data[out++] = (u8)(word >> 16);
data[out++] = (u8)(word >> 8);
data[out++] = (u8)word;
}
if (leading_zeros > 0)
out -= leading_zeros;
}
return out;
}
UnsignedBigInteger UnsignedBigInteger::from_base10(const String& str)
{
UnsignedBigInteger result;
UnsignedBigInteger ten { 10 };
for (auto& c : str) {
result = result.multiplied_by(ten).plus(c - '0');
}
return result;
}
String UnsignedBigInteger::to_base10() const
{
if (*this == UnsignedBigInteger { 0 })
return "0";
StringBuilder builder;
UnsignedBigInteger temp(*this);
UnsignedBigInteger quotient;
UnsignedBigInteger remainder;
while (temp != UnsignedBigInteger { 0 }) {
divide_u16_without_allocation(temp, 10, quotient, remainder);
ASSERT(remainder.words()[0] < 10);
builder.append(static_cast<char>(remainder.words()[0] + '0'));
temp.set_to(quotient);
}
auto reversed_string = builder.to_string();
builder.clear();
for (int i = reversed_string.length() - 1; i >= 0; --i) {
builder.append(reversed_string[i]);
}
return builder.to_string();
}
void UnsignedBigInteger::set_to_0()
{
m_words.clear_with_capacity();
m_is_invalid = false;
m_cached_trimmed_length = {};
}
void UnsignedBigInteger::set_to(u32 other)
{
m_is_invalid = false;
m_words.resize_and_keep_capacity(1);
m_words[0] = other;
m_cached_trimmed_length = {};
}
void UnsignedBigInteger::set_to(const UnsignedBigInteger& other)
{
m_is_invalid = other.m_is_invalid;
m_words.resize_and_keep_capacity(other.m_words.size());
__builtin_memcpy(m_words.data(), other.m_words.data(), other.m_words.size() * sizeof(u32));
m_cached_trimmed_length = {};
}
size_t UnsignedBigInteger::trimmed_length() const
{
if (!m_cached_trimmed_length.has_value()) {
size_t num_leading_zeroes = 0;
for (int i = length() - 1; i >= 0; --i, ++num_leading_zeroes) {
if (m_words[i] != 0)
break;
}
m_cached_trimmed_length = length() - num_leading_zeroes;
}
return m_cached_trimmed_length.value();
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) const
{
UnsignedBigInteger result;
add_without_allocation(*this, other, result);
return result;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& other) const
{
UnsignedBigInteger result;
subtract_without_allocation(*this, other, result);
return result;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_or(const UnsignedBigInteger& other) const
{
UnsignedBigInteger result;
bitwise_or_without_allocation(*this, other, result);
return result;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_and(const UnsignedBigInteger& other) const
{
UnsignedBigInteger result;
bitwise_and_without_allocation(*this, other, result);
return result;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_xor(const UnsignedBigInteger& other) const
{
UnsignedBigInteger result;
bitwise_xor_without_allocation(*this, other, result);
return result;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_not() const
{
UnsignedBigInteger result;
bitwise_not_without_allocation(*this, result);
return result;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
{
UnsignedBigInteger output;
UnsignedBigInteger temp_result;
UnsignedBigInteger temp_plus;
shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
return output;
}
FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigInteger& other) const
{
UnsignedBigInteger result;
UnsignedBigInteger temp_shift_result;
UnsignedBigInteger temp_shift_plus;
UnsignedBigInteger temp_shift;
UnsignedBigInteger temp_plus;
multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
return result;
}
FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigInteger& divisor) const
{
UnsignedBigInteger quotient;
UnsignedBigInteger remainder;
// If we actually have a u16-compatible divisor, short-circuit to the
// less computationally-intensive "divide_u16_without_allocation" method.
if (divisor.trimmed_length() == 1 && divisor.m_words[0] < (1 << 16)) {
divide_u16_without_allocation(*this, divisor.m_words[0], quotient, remainder);
return UnsignedDivisionResult { quotient, remainder };
}
UnsignedBigInteger temp_shift_result;
UnsignedBigInteger temp_shift_plus;
UnsignedBigInteger temp_shift;
UnsignedBigInteger temp_minus;
divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
return UnsignedDivisionResult { quotient, remainder };
}
void UnsignedBigInteger::set_bit_inplace(size_t bit_index)
{
const size_t word_index = bit_index / UnsignedBigInteger::BITS_IN_WORD;
const size_t inner_word_index = bit_index % UnsignedBigInteger::BITS_IN_WORD;
m_words.ensure_capacity(word_index);
for (size_t i = length(); i <= word_index; ++i) {
m_words.unchecked_append(0);
}
m_words[word_index] |= (1 << inner_word_index);
m_cached_trimmed_length = {};
}
bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
{
if (is_invalid() != other.is_invalid())
return false;
auto length = trimmed_length();
if (length != other.trimmed_length())
return false;
return !__builtin_memcmp(m_words.data(), other.words().data(), length);
}
bool UnsignedBigInteger::operator!=(const UnsignedBigInteger& other) const
{
return !(*this == other);
}
bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
{
auto length = trimmed_length();
auto other_length = other.trimmed_length();
if (length < other_length) {
return true;
}
if (length > other_length) {
return false;
}
if (length == 0) {
return false;
}
for (int i = length - 1; i >= 0; --i) {
if (m_words[i] == other.m_words[i])
continue;
return m_words[i] < other.m_words[i];
}
return false;
}
/**
* Complexity: O(N) where N is the number of words in the larger number
*/
void UnsignedBigInteger::add_without_allocation(
const UnsignedBigInteger& left,
const UnsignedBigInteger& right,
UnsignedBigInteger& output)
{
const UnsignedBigInteger* const longer = (left.length() > right.length()) ? &left : &right;
const UnsignedBigInteger* const shorter = (longer == &right) ? &left : &right;
u8 carry = 0;
output.set_to_0();
output.m_words.resize_and_keep_capacity(longer->length());
for (size_t i = 0; i < shorter->length(); ++i) {
u32 word_addition_result = shorter->m_words[i] + longer->m_words[i];
u8 carry_out = 0;
// if there was a carry, the result will be smaller than any of the operands
if (word_addition_result + carry < shorter->m_words[i]) {
carry_out = 1;
}
if (carry) {
word_addition_result++;
}
carry = carry_out;
output.m_words[i] = word_addition_result;
}
for (size_t i = shorter->length(); i < longer->length(); ++i) {
u32 word_addition_result = longer->m_words[i] + carry;
carry = 0;
if (word_addition_result < longer->m_words[i]) {
carry = 1;
}
output.m_words[i] = word_addition_result;
}
if (carry) {
output.m_words.append(carry);
}
}
/**
* Complexity: O(N) where N is the number of words in the larger number
*/
void UnsignedBigInteger::subtract_without_allocation(
const UnsignedBigInteger& left,
const UnsignedBigInteger& right,
UnsignedBigInteger& output)
{
if (left < right) {
output.invalidate();
return;
}
u8 borrow = 0;
auto own_length = left.length();
auto other_length = right.length();
output.set_to_0();
output.m_words.resize_and_keep_capacity(own_length);
for (size_t i = 0; i < own_length; ++i) {
u32 other_word = (i < other_length) ? right.m_words[i] : 0;
i64 temp = static_cast<i64>(left.m_words[i]) - static_cast<i64>(other_word) - static_cast<i64>(borrow);
// If temp < 0, we had an underflow
borrow = (temp >= 0) ? 0 : 1;
if (temp < 0) {
temp += (UINT32_MAX + 1);
}
output.m_words[i] = temp;
}
// This assertion should not fail, because we verified that *this>=other at the beginning of the function
ASSERT(borrow == 0);
}
/**
* Complexity: O(N) where N is the number of words in the shorter value
* Method:
* Apply <op> word-wise until words in the shorter value are used up
* then copy the rest of the words verbatim from the longer value.
*/
FLATTEN void UnsignedBigInteger::bitwise_or_without_allocation(
const UnsignedBigInteger& left,
const UnsignedBigInteger& right,
UnsignedBigInteger& output)
{
// If either of the BigInts are invalid, the output is just the other one.
if (left.is_invalid()) {
output.set_to(right);
return;
}
if (right.is_invalid()) {
output.set_to(left);
return;
}
const UnsignedBigInteger *shorter, *longer;
if (left.length() < right.length()) {
shorter = &left;
longer = &right;
} else {
shorter = &right;
longer = &left;
}
output.m_words.resize_and_keep_capacity(longer->length());
size_t longer_offset = longer->length() - shorter->length();
for (size_t i = 0; i < shorter->length(); ++i)
output.m_words[i] = longer->words()[i] | shorter->words()[i];
__builtin_memcpy(output.m_words.data() + shorter->length(), longer->words().data() + shorter->length(), sizeof(u32) * longer_offset);
}
/**
* Complexity: O(N) where N is the number of words in the shorter value
* Method:
* Apply 'and' word-wise until words in the shorter value are used up
* and zero the rest.
*/
FLATTEN void UnsignedBigInteger::bitwise_and_without_allocation(
const UnsignedBigInteger& left,
const UnsignedBigInteger& right,
UnsignedBigInteger& output)
{
// If either of the BigInts are invalid, the output is just the other one.
if (left.is_invalid()) {
output.set_to(right);
return;
}
if (right.is_invalid()) {
output.set_to(left);
return;
}
const UnsignedBigInteger *shorter, *longer;
if (left.length() < right.length()) {
shorter = &left;
longer = &right;
} else {
shorter = &right;
longer = &left;
}
output.m_words.resize_and_keep_capacity(longer->length());
size_t longer_offset = longer->length() - shorter->length();
for (size_t i = 0; i < shorter->length(); ++i)
output.m_words[i] = longer->words()[i] & shorter->words()[i];
__builtin_memset(output.m_words.data() + shorter->length(), 0, sizeof(u32) * longer_offset);
}
/**
* Complexity: O(N) where N is the number of words in the shorter value
* Method:
* Apply 'xor' word-wise until words in the shorter value are used up
* and copy the rest.
*/
FLATTEN void UnsignedBigInteger::bitwise_xor_without_allocation(
const UnsignedBigInteger& left,
const UnsignedBigInteger& right,
UnsignedBigInteger& output)
{
// If either of the BigInts are invalid, the output is just the other one.
if (left.is_invalid()) {
output.set_to(right);
return;
}
if (right.is_invalid()) {
output.set_to(left);
return;
}
const UnsignedBigInteger *shorter, *longer;
if (left.length() < right.length()) {
shorter = &left;
longer = &right;
} else {
shorter = &right;
longer = &left;
}
output.m_words.resize_and_keep_capacity(longer->length());
size_t longer_offset = longer->length() - shorter->length();
for (size_t i = 0; i < shorter->length(); ++i)
output.m_words[i] = longer->words()[i] ^ shorter->words()[i];
__builtin_memcpy(output.m_words.data() + shorter->length(), longer->words().data() + shorter->length(), sizeof(u32) * longer_offset);
}
/**
* Complexity: O(N) where N is the number of words
*/
FLATTEN void UnsignedBigInteger::bitwise_not_without_allocation(
const UnsignedBigInteger& right,
UnsignedBigInteger& output)
{
// If the value is invalid, the output value is invalid as well.
if (right.is_invalid()) {
output.invalidate();
return;
}
if (right.length() == 0) {
output.set_to_0();
return;
}
output.m_words.resize_and_keep_capacity(right.length());
if (right.length() > 1) {
for (size_t i = 0; i < right.length() - 1; ++i)
output.m_words[i] = ~right.words()[i];
}
auto last_word_index = right.length() - 1;
auto last_word = right.words()[last_word_index];
output.m_words[last_word_index] = ((u32)0xffffffffffffffff >> __builtin_clz(last_word)) & ~last_word;
}
/**
* Complexity : O(N + num_bits % 8) where N is the number of words in the number
* Shift method :
* Start by shifting by whole words in num_bits (by putting missing words at the start),
* then shift the number's words two by two by the remaining amount of bits.
*/
FLATTEN void UnsignedBigInteger::shift_left_without_allocation(
const UnsignedBigInteger& number,
size_t num_bits,
UnsignedBigInteger& temp_result,
UnsignedBigInteger& temp_plus,
UnsignedBigInteger& output)
{
// We can only do shift operations on individual words
// where the shift amount is <= size of word (32).
// But we do know how to shift by a multiple of word size (e.g 64=32*2)
// So we first shift the result by how many whole words fit in 'num_bits'
shift_left_by_n_words(number, num_bits / UnsignedBigInteger::BITS_IN_WORD, temp_result);
output.set_to(temp_result);
// And now we shift by the leftover amount of bits
num_bits %= UnsignedBigInteger::BITS_IN_WORD;
if (num_bits == 0) {
return;
}
for (size_t i = 0; i < temp_result.length(); ++i) {
u32 current_word_of_temp_result = shift_left_get_one_word(temp_result, num_bits, i);
output.m_words[i] = current_word_of_temp_result;
}
// Shifting the last word can produce a carry
u32 carry_word = shift_left_get_one_word(temp_result, num_bits, temp_result.length());
if (carry_word != 0) {
// output += (carry_word << temp_result.length())
// FIXME : Using temp_plus this way to transform carry_word into a bigint is not
// efficient nor pretty. Maybe we should have an "add_with_shift" method ?
temp_plus.set_to_0();
temp_plus.m_words.append(carry_word);
shift_left_by_n_words(temp_plus, temp_result.length(), temp_result);
add_without_allocation(output, temp_result, temp_plus);
output.set_to(temp_plus);
}
}
/**
* Complexity: O(N^2) where N is the number of words in the larger number
* Multiplication method:
* An integer is equal to the sum of the powers of two
* according to the indexes of its 'on' bits.
* So to multiple x*y, we go over each '1' bit in x (say the i'th bit),
* and add y<<i to the result.
*/
FLATTEN void UnsignedBigInteger::multiply_without_allocation(
const UnsignedBigInteger& left,
const UnsignedBigInteger& right,
UnsignedBigInteger& temp_shift_result,
UnsignedBigInteger& temp_shift_plus,
UnsignedBigInteger& temp_shift,
UnsignedBigInteger& temp_plus,
UnsignedBigInteger& output)
{
output.set_to_0();
// iterate all bits
for (size_t word_index = 0; word_index < left.length(); ++word_index) {
for (size_t bit_index = 0; bit_index < UnsignedBigInteger::BITS_IN_WORD; ++bit_index) {
// If the bit is off - skip over it
if (!(left.m_words[word_index] & (1 << bit_index)))
continue;
const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
// output += (right << shift_amount);
shift_left_without_allocation(right, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
add_without_allocation(output, temp_shift, temp_plus);
output.set_to(temp_plus);
}
}
}
/**
* Complexity: O(N^2) where N is the number of words in the larger number
* Division method:
* We loop over the bits of the divisor, attempting to subtract divisor<<i from the dividend.
* If the result is non-negative, it means that divisor*2^i "fits" in the dividend,
* so we set the ith bit in the quotient and reduce divisor<<i from the dividend.
* When we're done, what's left from the dividend is the remainder.
*/
FLATTEN void UnsignedBigInteger::divide_without_allocation(
const UnsignedBigInteger& numerator,
const UnsignedBigInteger& denominator,
UnsignedBigInteger& temp_shift_result,
UnsignedBigInteger& temp_shift_plus,
UnsignedBigInteger& temp_shift,
UnsignedBigInteger& temp_minus,
UnsignedBigInteger& quotient,
UnsignedBigInteger& remainder)
{
quotient.set_to_0();
remainder.set_to(numerator);
// iterate all bits
for (int word_index = numerator.trimmed_length() - 1; word_index >= 0; --word_index) {
for (int bit_index = UnsignedBigInteger::BITS_IN_WORD - 1; bit_index >= 0; --bit_index) {
const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
shift_left_without_allocation(denominator, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
subtract_without_allocation(remainder, temp_shift, temp_minus);
if (!temp_minus.is_invalid()) {
remainder.set_to(temp_minus);
quotient.set_bit_inplace(shift_amount);
}
}
}
}
/**
* Complexity : O(N) where N is the number of digits in the numerator
* Division method :
* Starting from the most significant one, for each half-word of the numerator, combine it
* with the existing remainder if any, divide the combined number as a u32 operation and
* update the quotient / remainder as needed.
*/
FLATTEN void UnsignedBigInteger::divide_u16_without_allocation(
const UnsignedBigInteger& numerator,
u32 denominator,
UnsignedBigInteger& quotient,
UnsignedBigInteger& remainder)
{
ASSERT(denominator < (1 << 16));
u32 remainder_word = 0;
auto numerator_length = numerator.trimmed_length();
quotient.set_to_0();
quotient.m_words.resize(numerator_length);
for (int word_index = numerator_length - 1; word_index >= 0; --word_index) {
auto word_high = numerator.m_words[word_index] >> 16;
auto word_low = numerator.m_words[word_index] & ((1 << 16) - 1);
auto number_to_divide_high = (remainder_word << 16) | word_high;
auto quotient_high = number_to_divide_high / denominator;
remainder_word = number_to_divide_high % denominator;
auto number_to_divide_low = remainder_word << 16 | word_low;
auto quotient_low = number_to_divide_low / denominator;
remainder_word = number_to_divide_low % denominator;
quotient.m_words[word_index] = (quotient_high << 16) | quotient_low;
}
remainder.set_to(remainder_word);
}
ALWAYS_INLINE void UnsignedBigInteger::shift_left_by_n_words(
const UnsignedBigInteger& number,
const size_t number_of_words,
UnsignedBigInteger& output)
{
// shifting left by N words means just inserting N zeroes to the beginning of the words vector
output.set_to_0();
output.m_words.resize_and_keep_capacity(number_of_words + number.length());
__builtin_memset(output.m_words.data(), 0, number_of_words * sizeof(unsigned));
__builtin_memcpy(&output.m_words.data()[number_of_words], number.m_words.data(), number.m_words.size() * sizeof(unsigned));
}
/**
* 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;
}
}
void AK::Formatter<Crypto::UnsignedBigInteger>::format(FormatBuilder& fmtbuilder, const Crypto::UnsignedBigInteger& value)
{
if (value.is_invalid())
return Formatter<StringView>::format(fmtbuilder, "invalid");
StringBuilder builder;
for (int i = value.length() - 1; i >= 0; --i)
builder.appendff("{}|", value.words()[i]);
return Formatter<StringView>::format(fmtbuilder, builder.string_view());
}