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LibCrypto: Split BigInteger operations into an Algorithms class

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Since the operations are already complicated and will become even more
so soon, let's split them into their own files. We can also integrate
the NumberTheory operations that would better fit there into this class
as well.

This commit doesn't change behaviors, but moves the allocation of some
variables into caller classes.
This commit is contained in:
DexesTTP 2021-05-10 20:55:25 +02:00 • committed by Linus Groh
parent 0853d98420
commit 5963f6f9ff
13 changed files with 736 additions and 582 deletions
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440
Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp
View file

@ -6,6 +6,7 @@
#include "UnsignedBigInteger.h"
#include <AK/StringBuilder.h>
#include <LibCrypto/BigInt/Algorithms/UnsignedBigIntegerAlgorithms.h>
namespace Crypto {
@ -85,7 +86,7 @@ String UnsignedBigInteger::to_base10() const
UnsignedBigInteger remainder;
while (temp != UnsignedBigInteger { 0 }) {
divide_u16_without_allocation(temp, 10, quotient, remainder);
UnsignedBigIntegerAlgorithms::divide_u16_without_allocation(temp, 10, quotient, remainder);
VERIFY(remainder.words()[0] < 10);
builder.append(static_cast<char>(remainder.words()[0] + '0'));
temp.set_to(quotient);
@ -147,7 +148,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& ot
{
UnsignedBigInteger result;
add_without_allocation(*this, other, result);
UnsignedBigIntegerAlgorithms::add_without_allocation(*this, other, result);
return result;
}
@ -156,7 +157,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& o
{
UnsignedBigInteger result;
subtract_without_allocation(*this, other, result);
UnsignedBigIntegerAlgorithms::subtract_without_allocation(*this, other, result);
return result;
}
@ -165,7 +166,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_or(const UnsignedBigInteg
{
UnsignedBigInteger result;
bitwise_or_without_allocation(*this, other, result);
UnsignedBigIntegerAlgorithms::bitwise_or_without_allocation(*this, other, result);
return result;
}
@ -174,7 +175,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_and(const UnsignedBigInte
{
UnsignedBigInteger result;
bitwise_and_without_allocation(*this, other, result);
UnsignedBigIntegerAlgorithms::bitwise_and_without_allocation(*this, other, result);
return result;
}
@ -183,7 +184,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_xor(const UnsignedBigInte
{
UnsignedBigInteger result;
bitwise_xor_without_allocation(*this, other, result);
UnsignedBigIntegerAlgorithms::bitwise_xor_without_allocation(*this, other, result);
return result;
}
@ -192,7 +193,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_not() const
{
UnsignedBigInteger result;
bitwise_not_without_allocation(*this, result);
UnsignedBigIntegerAlgorithms::bitwise_not_without_allocation(*this, result);
return result;
}
@ -203,7 +204,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
UnsignedBigInteger temp_result;
UnsignedBigInteger temp_plus;
shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
UnsignedBigIntegerAlgorithms::shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
return output;
}
@ -216,7 +217,7 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigIn
UnsignedBigInteger temp_shift;
UnsignedBigInteger temp_plus;
multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
UnsignedBigIntegerAlgorithms::multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
return result;
}
@ -229,7 +230,7 @@ FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigI
// 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);
UnsignedBigIntegerAlgorithms::divide_u16_without_allocation(*this, divisor.m_words[0], quotient, remainder);
return UnsignedDivisionResult { quotient, remainder };
}
@ -238,7 +239,7 @@ FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigI
UnsignedBigInteger temp_shift;
UnsignedBigInteger temp_minus;
divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
UnsignedBigIntegerAlgorithms::divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
return UnsignedDivisionResult { quotient, remainder };
}
@ -300,423 +301,6 @@ bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
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
VERIFY(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 indices 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)
{
VERIFY(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
VERIFY(result_word_index <= number.length());
VERIFY(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)