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AK: Implement Knuth's algorithm D for dividing UFixedBigInt's
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parent
2470fab05e
commit
2d27c98659
Notes:
sideshowbarker
2024-07-16 23:51:07 +09:00
Author: https://github.com/DanShaders Commit: https://github.com/SerenityOS/serenity/commit/2d27c98659 Pull-request: https://github.com/SerenityOS/serenity/pull/17330 Reviewed-by: https://github.com/ADKaster Reviewed-by: https://github.com/Hendiadyoin1
@ -10,6 +10,7 @@
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#include <AK/ScopeGuard.h>
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#include <AK/StringView.h>
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#include <AK/UFixedBigInt.h>
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#include <AK/UFixedBigIntDivision.h>
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namespace AK {
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@ -60,6 +60,13 @@ constexpr void mul_internal(Operand1 const& operand1, Operand2 const& operand2,
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StorageOperations::baseline_mul(operand1, operand2, result, g_null_allocator);
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}
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template<size_t dividend_size, size_t divisor_size, bool restore_remainder>
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constexpr void div_mod_internal( // Include AK/UFixedBigIntDivision.h to use UFixedBigInt division
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StaticStorage<false, dividend_size> const& dividend,
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StaticStorage<false, divisor_size> const& divisor,
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StaticStorage<false, dividend_size>& quotient,
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StaticStorage<false, divisor_size>& remainder);
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template<size_t bit_size, typename Storage>
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class UFixedBigInt {
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constexpr static size_t static_size = Storage::static_size;
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@ -395,84 +402,49 @@ public:
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return result;
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}
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// FIXME: Refactor out this
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using R = UFixedBigInt<bit_size>;
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static constexpr size_t my_size()
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template<NotBuiltInUFixedInt T>
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constexpr UFixedBigInt<bit_size> div_mod(T const& divisor, T& remainder) const
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{
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return sizeof(Storage);
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}
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// FIXME: Do something smarter (process at least one word per iteration).
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// FIXME: no restraints on this
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template<Unsigned U>
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requires(sizeof(Storage) >= sizeof(U)) constexpr R div_mod(U const& divisor, U& remainder) const
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{
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// FIXME: Is there a better way to raise a division by 0?
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// Maybe as a compiletime warning?
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#pragma GCC diagnostic push
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#pragma GCC diagnostic ignored "-Wdiv-by-zero"
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if (!divisor) {
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int volatile x = 1;
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int volatile y = 0;
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[[maybe_unused]] int volatile z = x / y;
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}
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#pragma GCC diagnostic pop
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// fastpaths
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if (*this < divisor) {
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remainder = static_cast<U>(*this);
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return 0u;
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}
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if (*this == divisor) {
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remainder = 0u;
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return 1u;
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}
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if (divisor == 1u) {
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remainder = 0u;
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return *this;
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}
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remainder = 0u;
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R quotient = 0u;
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for (ssize_t i = sizeof(R) * 8 - clz() - 1; i >= 0; --i) {
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remainder <<= 1u;
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remainder |= static_cast<unsigned>(*this >> (size_t)i) & 1u;
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if (remainder >= divisor) {
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remainder -= divisor;
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quotient |= R { 1u } << (size_t)i;
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}
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}
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UFixedBigInt<bit_size> quotient;
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UFixedBigInt<assumed_bit_size<T>> resulting_remainder;
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div_mod_internal<bit_size, assumed_bit_size<T>, true>(m_data, get_storage_of(divisor), get_storage_of(quotient), get_storage_of(resulting_remainder));
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remainder = resulting_remainder;
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return quotient;
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}
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template<Unsigned U>
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constexpr R operator/(U const& other) const
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template<UFixedInt T>
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constexpr auto operator/(T const& other) const
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{
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U mod { 0u }; // unused
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return div_mod(other, mod);
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}
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template<Unsigned U>
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constexpr U operator%(U const& other) const
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{
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R res { 0u };
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div_mod(other, res);
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return res;
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UFixedBigInt<bit_size> quotient;
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StaticStorage<false, assumed_bit_size<T>> remainder; // unused
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div_mod_internal<bit_size, assumed_bit_size<T>, false>(m_data, get_storage_of(other), get_storage_of(quotient), remainder);
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return quotient;
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}
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template<Unsigned U>
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constexpr R& operator/=(U const& other)
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template<UFixedInt T>
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constexpr auto operator%(T const& other) const
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{
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*this = *this / other;
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return *this;
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StaticStorage<false, bit_size> quotient; // unused
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UFixedBigInt<assumed_bit_size<T>> remainder;
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div_mod_internal<bit_size, assumed_bit_size<T>, true>(m_data, get_storage_of(other), quotient, get_storage_of(remainder));
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return remainder;
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}
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constexpr auto operator/(IntegerWrapper const& other) const { return *this / static_cast<UFixedBigInt<32>>(other); }
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constexpr auto operator%(IntegerWrapper const& other) const { return *this % static_cast<UFixedBigInt<32>>(other); }
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template<UFixedInt T>
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constexpr auto& operator/=(T const& other) { return *this = *this / other; }
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constexpr auto& operator/=(IntegerWrapper const& other) { return *this = *this / other; }
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template<Unsigned U>
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constexpr R& operator%=(U const& other)
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constexpr auto& operator%=(U const& other) { return *this = *this % other; }
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constexpr auto& operator%=(IntegerWrapper const& other) { return *this = *this % other; }
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// FIXME: Replace uses with more general `assumed_bit_size<T>`.
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static constexpr size_t my_size()
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{
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*this = *this % other;
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return *this;
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return sizeof(Storage);
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}
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// Note: If there ever be need for non side-channel proof sqrt/pow/pow_mod of UFixedBigInt, you
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136
AK/UFixedBigIntDivision.h
Normal file
136
AK/UFixedBigIntDivision.h
Normal file
@ -0,0 +1,136 @@
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/*
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* Copyright (c) 2023, Dan Klishch <danilklishch@gmail.com>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#pragma once
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#include <AK/Diagnostics.h>
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#include <AK/UFixedBigInt.h>
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namespace AK {
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namespace Detail {
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template<size_t dividend_bit_size, size_t divisor_bit_size, bool restore_remainder>
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constexpr void div_mod_internal(
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StaticStorage<false, dividend_bit_size> const& operand1,
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StaticStorage<false, divisor_bit_size> const& operand2,
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StaticStorage<false, dividend_bit_size>& quotient,
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StaticStorage<false, divisor_bit_size>& remainder)
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{
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size_t dividend_len = operand1.size(), divisor_len = operand2.size();
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while (divisor_len > 0 && !operand2[divisor_len - 1])
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--divisor_len;
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while (dividend_len > 0 && !operand1[dividend_len - 1])
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--dividend_len;
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// FIXME: Should raise SIGFPE instead
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VERIFY(divisor_len); // VERIFY(divisor != 0)
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// Fast paths
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if (divisor_len == 1 && operand2[0] == 1) { // divisor == 1
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quotient = operand1;
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if constexpr (restore_remainder)
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StorageOperations::set(0, remainder);
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return;
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}
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if (dividend_len < divisor_len) { // dividend < divisor
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StorageOperations::set(0, quotient);
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if constexpr (restore_remainder)
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remainder = operand1;
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return;
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}
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if (divisor_len == 1 && dividend_len == 1) { // NativeWord / NativeWord
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StorageOperations::set(operand1[0] / operand2[0], quotient);
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if constexpr (restore_remainder)
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StorageOperations::set(operand1[0] % operand2[0], remainder);
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return;
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}
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if (divisor_len == 1) { // BigInt by NativeWord
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auto u = (static_cast<DoubleWord>(operand1[dividend_len - 1]) << word_size) + operand1[dividend_len - 2];
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auto divisor = operand2[0];
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auto top = u / divisor;
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quotient[dividend_len - 1] = static_cast<NativeWord>(top >> word_size);
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quotient[dividend_len - 2] = static_cast<NativeWord>(top);
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auto carry = static_cast<NativeWord>(u % divisor);
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for (size_t i = dividend_len - 2; i--;)
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quotient[i] = div_mod_words(operand1[i], carry, divisor, carry);
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for (size_t i = dividend_len; i < quotient.size(); ++i)
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quotient[i] = 0;
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if constexpr (restore_remainder)
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StorageOperations::set(carry, remainder);
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return;
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}
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// Knuth's algorithm D
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StaticStorage<false, dividend_bit_size + word_size> dividend;
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StorageOperations::copy(operand1, dividend);
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auto divisor = operand2;
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// D1. Normalize
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// FIXME: Investigate GCC producing bogus -Warray-bounds when dividing u128 by u32. This code
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// should not be reachable at all in this case because fast paths above cover all cases
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// when `operand2.size() == 1`.
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AK_IGNORE_DIAGNOSTIC("-Warray-bounds", size_t shift = count_leading_zeroes(divisor[divisor_len - 1]);)
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StorageOperations::shift_left(dividend, shift, dividend);
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StorageOperations::shift_left(divisor, shift, divisor);
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auto divisor_approx = divisor[divisor_len - 1];
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for (size_t i = dividend_len + 1; i-- > divisor_len;) {
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// D3. Calculate qhat
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NativeWord qhat;
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VERIFY(dividend[i] <= divisor_approx);
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if (dividend[i] == divisor_approx) {
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qhat = max_word;
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} else {
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NativeWord rhat;
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qhat = div_mod_words(dividend[i - 1], dividend[i], divisor_approx, rhat);
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auto is_qhat_too_large = [&] {
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return UFixedBigInt<word_size> { qhat }.wide_multiply(divisor[divisor_len - 2]) > u128 { dividend[i - 2], rhat };
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};
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if (is_qhat_too_large()) {
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--qhat;
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bool carry = false;
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rhat = add_words(rhat, divisor_approx, carry);
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if (!carry && is_qhat_too_large())
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--qhat;
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}
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}
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// D4. Multiply & subtract
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NativeWord mul_carry = 0;
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bool sub_carry = false;
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for (size_t j = 0; j < divisor_len; ++j) {
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auto mul_result = UFixedBigInt<word_size> { qhat }.wide_multiply(divisor[j]) + mul_carry;
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auto& output = dividend[i + j - divisor_len];
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output = sub_words(output, mul_result.low(), sub_carry);
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mul_carry = mul_result.high();
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}
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dividend[i] = sub_words(dividend[i], mul_carry, sub_carry);
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if (sub_carry) {
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// D6. Add back
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auto dividend_part = UnsignedStorageSpan { dividend.data() + i - divisor_len, divisor_len + 1 };
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VERIFY(StorageOperations::add<false>(dividend_part, divisor, dividend_part));
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}
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quotient[i - divisor_len] = qhat - sub_carry;
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}
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for (size_t i = dividend_len - divisor_len + 1; i < quotient.size(); ++i)
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quotient[i] = 0;
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// D8. Unnormalize
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if constexpr (restore_remainder)
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StorageOperations::shift_right(UnsignedStorageSpan { dividend.data(), remainder.size() }, shift, remainder);
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}
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}
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}
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@ -9,6 +9,7 @@
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#include <AK/NumericLimits.h>
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#include <AK/Random.h>
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#include <AK/UFixedBigInt.h>
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#include <AK/UFixedBigIntDivision.h>
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constexpr int test_iterations = 32;
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@ -78,6 +79,62 @@ TEST_CASE(div_mod)
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}
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}
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TEST_CASE(div_anti_knuth)
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{
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EXPECT_EQ((u256 { { 0ull, 0xffffffffffffffffull, 1ull, 0ull } } / u128 { 0x8000000000000001ull, 0xffffffffffffffffull }), 1u);
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EXPECT_EQ((u128 { { 0xffffffff00000000ull, 1ull } } / u128 { 0xffffffff80000001ull }), 1u);
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srand(0);
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auto generate_u512 = [] {
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using namespace AK::Detail;
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u512 number;
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auto& storage = get_storage_of(number);
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static constexpr u32 interesting_words_count = 14;
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static constexpr NativeWord interesting_words[interesting_words_count] = {
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0,
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0,
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1,
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2,
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3,
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max_word / 4 - 1,
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max_word / 4,
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max_word / 2 - 1,
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max_word / 2,
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max_word / 2 + 1,
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max_word / 2 + 2,
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max_word - 3,
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max_word - 2,
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max_word - 1,
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};
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for (size_t i = 0; i < storage.size(); ++i) {
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u32 type = get_random_uniform(interesting_words_count + 1);
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NativeWord& next_word = storage[i];
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if (type == interesting_words_count)
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next_word = get_random<NativeWord>();
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else
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next_word = interesting_words[type];
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}
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return number;
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};
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for (int i = 0; i < 16384; ++i) {
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u512 a = generate_u512(), b = generate_u512();
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if (b == 0)
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continue;
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u512 mod;
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u512 div = a.div_mod(b, mod);
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EXPECT_EQ(div * b + mod, a);
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EXPECT_EQ(div.wide_multiply(b) + mod, a);
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EXPECT(0 <= mod && mod < b);
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}
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}
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TEST_CASE(shifts)
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{
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u128 val { 0x1234ULL };
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