mirror of
https://github.com/LadybirdBrowser/ladybird.git
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875 lines
25 KiB
C++
875 lines
25 KiB
C++
/*
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* Copyright (c) 2021, Leon Albrecht <leon2002.la@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/BuiltinWrappers.h>
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#include <AK/Checked.h>
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#include <AK/Concepts.h>
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#include <AK/Format.h>
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#include <AK/NumericLimits.h>
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#include <AK/StdLibExtraDetails.h>
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#include <AK/StdLibExtras.h>
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#include <AK/StringBuilder.h>
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namespace AK {
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template<typename T>
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requires(sizeof(T) >= sizeof(u64) && IsUnsigned<T>) class UFixedBigInt;
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// FIXME: This breaks formatting
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// template<typename T>
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// constexpr inline bool Detail::IsIntegral<UFixedBigInt<T>> = true;
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template<typename T>
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constexpr inline bool Detail::IsUnsigned<UFixedBigInt<T>> = true;
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template<typename T>
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constexpr inline bool Detail::IsSigned<UFixedBigInt<T>> = false;
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template<typename T>
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struct NumericLimits<UFixedBigInt<T>> {
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static constexpr UFixedBigInt<T> min() { return 0; }
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static constexpr UFixedBigInt<T> max() { return { NumericLimits<T>::max(), NumericLimits<T>::max() }; }
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static constexpr bool is_signed() { return false; }
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};
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template<Unsigned T>
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struct UFixedBigIntMultiplicationResult {
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T low;
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T high;
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};
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template<typename T>
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requires(sizeof(T) >= sizeof(u64) && IsUnsigned<T>) class UFixedBigInt {
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public:
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using R = UFixedBigInt<T>;
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constexpr UFixedBigInt() = default;
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr UFixedBigInt(U low)
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: m_low(low)
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, m_high(0u)
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{
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}
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template<Unsigned U, Unsigned U2>
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requires(sizeof(T) >= sizeof(U) && sizeof(T) >= sizeof(U2)) constexpr UFixedBigInt(U low, U2 high)
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: m_low(low)
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, m_high(high)
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{
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}
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constexpr T& low()
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{
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return m_low;
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}
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constexpr const T& low() const
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{
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return m_low;
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}
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constexpr T& high()
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{
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return m_high;
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}
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constexpr const T& high() const
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{
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return m_high;
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}
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Span<u8> bytes()
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{
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return Span<u8>(reinterpret_cast<u8*>(this), sizeof(R));
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}
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Span<const u8> bytes() const
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{
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return Span<const u8>(reinterpret_cast<u8 const*>(this), sizeof(R));
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr explicit operator U() const
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{
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return static_cast<U>(m_low);
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}
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// Utils
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constexpr size_t clz() const requires(IsSame<T, u64>)
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{
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if (m_high)
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return count_leading_zeroes(m_high);
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else
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return sizeof(T) * 8 + count_leading_zeroes(m_low);
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}
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constexpr size_t clz() const requires(!IsSame<T, u64>)
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{
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if (m_high)
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return m_high.clz();
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else
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return sizeof(T) * 8 + m_low.clz();
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}
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constexpr size_t ctz() const requires(IsSame<T, u64>)
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{
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if (m_low)
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return count_trailing_zeroes(m_low);
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else
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return sizeof(T) * 8 + count_trailing_zeroes(m_high);
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}
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constexpr size_t ctz() const requires(!IsSame<T, u64>)
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{
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if (m_low)
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return m_low.ctz();
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else
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return sizeof(T) * 8 + m_high.ctz();
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}
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constexpr size_t popcnt() const requires(IsSame<T, u64>)
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{
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return __builtin_popcntll(m_low) + __builtin_popcntll(m_high);
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}
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constexpr size_t popcnt() const requires(!IsSame<T, u64>)
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{
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return m_low.popcnt() + m_high.popcnt();
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}
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// Comparison Operations
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constexpr bool operator!() const
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{
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return !m_low && !m_high;
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}
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constexpr explicit operator bool() const
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{
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return m_low || m_high;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr bool operator==(const U& other) const
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{
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return !m_high && m_low == other;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr bool operator!=(const U& other) const
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{
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return m_high || m_low != other;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr bool operator>(const U& other) const
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{
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return m_high || m_low > other;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr bool operator<(const U& other) const
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{
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return !m_high && m_low < other;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr bool operator>=(const U& other) const
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{
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return *this == other || *this > other;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr bool operator<=(const U& other) const
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{
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return *this == other || *this < other;
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}
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constexpr bool operator==(const R& other) const
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{
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return m_low == other.low() && m_high == other.high();
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}
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constexpr bool operator!=(const R& other) const
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{
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return m_low != other.low() || m_high != other.high();
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}
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constexpr bool operator>(const R& other) const
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{
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return m_high > other.high()
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|| (m_high == other.high() && m_low > other.low());
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}
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constexpr bool operator<(const R& other) const
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{
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return m_high < other.high()
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|| (m_high == other.high() && m_low < other.low());
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}
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constexpr bool operator>=(const R& other) const
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{
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return *this == other || *this > other;
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}
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constexpr bool operator<=(const R& other) const
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{
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return *this == other || *this < other;
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}
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// Bitwise operations
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constexpr R operator~() const
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{
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return { ~m_low, ~m_high };
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr U operator&(const U& other) const
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{
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return static_cast<const U>(m_low) & other;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr R operator|(const U& other) const
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{
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return { m_low | other, m_high };
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr R operator^(const U& other) const
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{
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return { m_low ^ other, m_high };
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}
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template<Unsigned U>
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constexpr R operator<<(const U& shift) const
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{
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if (shift >= sizeof(R) * 8u)
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return 0u;
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if (shift >= sizeof(T) * 8u)
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return R { 0u, m_low << (shift - sizeof(T) * 8u) };
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if (!shift)
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return *this;
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T overflow = m_low >> (sizeof(T) * 8u - shift);
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return R { m_low << shift, (m_high << shift) | overflow };
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}
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template<Unsigned U>
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constexpr R operator>>(const U& shift) const
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{
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if (shift >= sizeof(R) * 8u)
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return 0u;
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if (shift >= sizeof(T) * 8u)
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return m_high >> (shift - sizeof(T) * 8u);
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if (!shift)
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return *this;
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T underflow = m_high << (sizeof(T) * 8u - shift);
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return R { (m_low >> shift) | underflow, m_high >> shift };
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}
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template<Unsigned U>
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constexpr R rol(const U& shift) const
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{
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return (*this >> sizeof(T) * 8u - shift) | (*this << shift);
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}
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template<Unsigned U>
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constexpr R ror(const U& shift) const
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{
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return (*this << sizeof(T) * 8u - shift) | (*this >> shift);
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}
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constexpr R operator&(const R& other) const
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{
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return { m_low & other.low(), m_high & other.high() };
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}
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constexpr R operator|(const R& other) const
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{
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return { m_low | other.low(), m_high | other.high() };
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}
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constexpr R operator^(const R& other) const
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{
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return { m_low ^ other.low(), m_high ^ other.high() };
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}
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// Bitwise assignment
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr R& operator&=(const U& other)
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{
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m_high = 0u;
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m_low &= other;
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return *this;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr R& operator|=(const U& other)
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{
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m_low |= other;
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return *this;
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}
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr R& operator^=(const U& other)
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{
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m_low ^= other;
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return *this;
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}
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template<Unsigned U>
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constexpr R& operator>>=(const U& other)
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{
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*this = *this >> other;
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return *this;
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}
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template<Unsigned U>
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constexpr R& operator<<=(const U& other)
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{
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*this = *this << other;
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return *this;
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}
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constexpr R& operator&=(const R& other)
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{
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m_high &= other.high();
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m_low &= other.low();
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return *this;
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}
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constexpr R& operator|=(const R& other)
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{
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m_high |= other.high();
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m_low |= other.low();
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return *this;
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}
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constexpr R& operator^=(const R& other)
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{
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m_high ^= other.high();
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m_low ^= other.low();
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return *this;
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}
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static constexpr size_t my_size()
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{
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return sizeof(R);
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}
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// Arithmetic
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// implies size of less than u64, so passing references isn't useful
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U) && IsSame<T, u64>) constexpr R addc(const U other, bool& carry) const
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{
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bool low_carry = Checked<T>::addition_would_overflow(m_low, other);
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low_carry |= Checked<T>::addition_would_overflow(m_low, carry);
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bool high_carry = Checked<T>::addition_would_overflow(m_high, low_carry);
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T lower = m_low + other + carry;
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T higher = m_high + low_carry;
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carry = high_carry;
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return {
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lower,
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higher
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};
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}
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template<Unsigned U>
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requires(my_size() > sizeof(U) && sizeof(T) > sizeof(u64)) constexpr R addc(const U& other, bool& carry) const
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{
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T lower = m_low.addc(other, carry);
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T higher = m_high.addc(0u, carry);
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return {
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lower,
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higher
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};
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}
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template<Unsigned U>
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requires(IsSame<R, U>&& IsSame<T, u64>) constexpr R addc(const U& other, bool& carry) const
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{
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bool low_carry = Checked<T>::addition_would_overflow(m_low, other.low());
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bool high_carry = Checked<T>::addition_would_overflow(m_high, other.high());
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T lower = m_low + other.low();
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T higher = m_high + other.high();
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low_carry |= Checked<T>::addition_would_overflow(lower, carry);
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high_carry |= Checked<T>::addition_would_overflow(higher, low_carry);
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lower += carry;
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higher += low_carry;
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carry = high_carry;
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return {
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lower,
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higher
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};
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}
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template<Unsigned U>
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requires(IsSame<R, U> && sizeof(T) > sizeof(u64)) constexpr R addc(const U& other, bool& carry) const
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{
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T lower = m_low.addc(other.low(), carry);
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T higher = m_high.addc(other.high(), carry);
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return {
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lower,
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higher
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};
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}
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template<Unsigned U>
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requires(my_size() < sizeof(U)) constexpr U addc(const U& other, bool& carry) const
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{
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return other.addc(*this, carry);
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}
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// FIXME: subc for sizeof(T) < sizeof(U)
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template<Unsigned U>
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requires(sizeof(T) >= sizeof(U)) constexpr R subc(const U& other, bool& carry) const
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{
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bool low_carry = (!m_low && carry) || (m_low - carry) < other;
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bool high_carry = !m_high && low_carry;
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T lower = m_low - other - carry;
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T higher = m_high - low_carry;
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carry = high_carry;
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return { lower, higher };
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}
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constexpr R subc(const R& other, bool& carry) const
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{
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bool low_carry = (!m_low && carry) || (m_low - carry) < other.low();
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bool high_carry = (!m_high && low_carry) || (m_high - low_carry) < other.high();
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T lower = m_low - other.low() - carry;
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T higher = m_high - other.high() - low_carry;
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carry = high_carry;
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return { lower, higher };
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}
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constexpr R operator+(bool const& other) const
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{
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bool carry = false; // unused
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return addc((u8)other, carry);
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}
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template<Unsigned U>
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constexpr R operator+(const U& other) const
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{
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bool carry = false; // unused
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return addc(other, carry);
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}
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constexpr R operator-(bool const& other) const
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{
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bool carry = false; // unused
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return subc((u8)other, carry);
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}
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template<Unsigned U>
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constexpr R operator-(const U& other) const
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{
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bool carry = false; // unused
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return subc(other, carry);
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}
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template<Unsigned U>
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constexpr R& operator+=(const U& other)
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{
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*this = *this + other;
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return *this;
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}
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template<Unsigned U>
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constexpr R& operator-=(const U& other)
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{
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*this = *this - other;
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return *this;
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}
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constexpr R operator++()
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{
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// x++
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auto old = *this;
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*this += 1;
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return old;
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}
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constexpr R& operator++(int)
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{
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// ++x
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*this += 1;
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return *this;
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}
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constexpr R operator--()
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{
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// x--
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auto old = *this;
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*this -= 1;
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return old;
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}
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constexpr R& operator--(int)
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{
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// --x
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*this -= 1;
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return *this;
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}
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// FIXME: no restraints on this
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template<Unsigned U>
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requires(my_size() >= sizeof(U)) constexpr R div_mod(const U& 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 |= (*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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return quotient;
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}
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template<Unsigned U>
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constexpr R operator*(U other) const
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{
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R res = 0u;
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R that = *this;
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for (; other != 0u; other >>= 1u) {
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if (other & 1u)
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res += that;
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that <<= 1u;
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}
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return res;
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}
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template<Unsigned U>
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requires(IsSame<R, U>&& IsSame<T, u64>) constexpr UFixedBigIntMultiplicationResult<R> wide_multiply(U const& other) const
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{
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auto mult_64_to_128 = [](u64 a, u64 b) -> UFixedBigIntMultiplicationResult<u64> {
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#ifdef __SIZEOF_INT128__
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unsigned __int128 result = (unsigned __int128)a * b;
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u64 low = result;
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u64 high = result >> 64;
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return { low, high };
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#else
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u32 a_low = a;
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u32 a_high = (a >> 32);
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u32 b_low = b;
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u32 b_high = (b >> 32);
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u64 ll_result = (u64)a_low * b_low;
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u64 lh_result = (u64)a_low * b_high;
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u64 hl_result = (u64)a_high * b_low;
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u64 hh_result = (u64)a_high * b_high;
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UFixedBigInt<u64> ll { ll_result, 0u };
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UFixedBigInt<u64> lh { lh_result << 32, lh_result >> 32 };
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UFixedBigInt<u64> hl { hl_result << 32, hl_result >> 32 };
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UFixedBigInt<u64> hh { 0u, hh_result };
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UFixedBigInt<u64> result = ll + lh + hl + hh;
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return { result.low(), result.high() };
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#endif
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};
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auto ll_result = mult_64_to_128(m_low, other.low());
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auto lh_result = mult_64_to_128(m_low, other.high());
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auto hl_result = mult_64_to_128(m_high, other.low());
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auto hh_result = mult_64_to_128(m_high, other.high());
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UFixedBigInt<R> ll { R { ll_result.low, ll_result.high }, R { 0u, 0u } };
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UFixedBigInt<R> lh { R { 0u, lh_result.low }, R { lh_result.high, 0u } };
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UFixedBigInt<R> hl { R { 0u, hl_result.low }, R { hl_result.high, 0u } };
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UFixedBigInt<R> hh { R { 0u, 0u }, R { hh_result.low, hh_result.high } };
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UFixedBigInt<R> result = ll + lh + hl + hh;
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return { result.low(), result.high() };
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}
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template<Unsigned U>
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requires(IsSame<R, U> && sizeof(T) > sizeof(u64)) constexpr UFixedBigIntMultiplicationResult<R> wide_multiply(U const& other) const
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{
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T left_low = m_low;
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T left_high = m_high;
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T right_low = other.low();
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T right_high = other.high();
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auto ll_result = left_low.wide_multiply(right_low);
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auto lh_result = left_low.wide_multiply(right_high);
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auto hl_result = left_high.wide_multiply(right_low);
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auto hh_result = left_high.wide_multiply(right_high);
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UFixedBigInt<R> ll { R { ll_result.low, ll_result.high }, R { 0u, 0u } };
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UFixedBigInt<R> lh { R { 0u, lh_result.low }, R { lh_result.high, 0u } };
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UFixedBigInt<R> hl { R { 0u, hl_result.low }, R { hl_result.high, 0u } };
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UFixedBigInt<R> hh { R { 0u, 0u }, R { hh_result.low, hh_result.high } };
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UFixedBigInt<R> result = ll + lh + hl + hh;
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return { result.low(), result.high() };
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}
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template<Unsigned U>
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constexpr R operator/(const U& 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%(const U& 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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}
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template<Unsigned U>
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constexpr R& operator*=(const U& other)
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{
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*this = *this * other;
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return *this;
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}
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template<Unsigned U>
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constexpr R& operator/=(const U& other)
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{
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*this = *this / other;
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return *this;
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}
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template<Unsigned U>
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constexpr R& operator%=(const U& other)
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{
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*this = *this % other;
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return *this;
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}
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constexpr R sqrt() const
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{
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// Bitwise method: https://en.wikipedia.org/wiki/Integer_square_root#Using_bitwise_operations
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// the bitwise method seems to be way faster then Newtons:
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// https://quick-bench.com/q/eXZwW1DVhZxLE0llumeCXkfOK3Q
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if (*this == 1u)
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return 1u;
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ssize_t shift = (sizeof(R) * 8 - clz()) & ~1ULL;
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// should be equivalent to:
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// long shift = 2;
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// while ((val >> shift) != 0)
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// shift += 2;
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R res = 0u;
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while (shift >= 0) {
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res = res << 1u;
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R large_cand = (res | 1u);
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if (*this >> (size_t)shift >= large_cand * large_cand)
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res = large_cand;
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shift -= 2;
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}
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return res;
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}
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constexpr R pow(u64 exp)
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{
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// Montgomery's Ladder Technique
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// https://en.wikipedia.org/wiki/Exponentiation_by_squaring#Montgomery's_ladder_technique
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R x1 = *this;
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R x2 = *this * *this;
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u64 exp_copy = exp;
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for (ssize_t i = sizeof(u64) * 8 - count_leading_zeroes(exp) - 2; i >= 0; --i) {
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if (exp_copy & 1u) {
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x2 *= x1;
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x1 *= x1;
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} else {
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x1 *= x2;
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x2 *= x2;
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}
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exp_copy >>= 1u;
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}
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return x1;
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}
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template<Unsigned U>
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requires(sizeof(U) > sizeof(u64)) constexpr R pow(U exp)
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{
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// Montgomery's Ladder Technique
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// https://en.wikipedia.org/wiki/Exponentiation_by_squaring#Montgomery's_ladder_technique
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R x1 = *this;
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R x2 = *this * *this;
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U exp_copy = exp;
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for (ssize_t i = sizeof(U) * 8 - exp().clz() - 2; i >= 0; --i) {
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if (exp_copy & 1u) {
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x2 *= x1;
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x1 *= x1;
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} else {
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x1 *= x2;
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x2 *= x2;
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}
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exp_copy >>= 1u;
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}
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return x1;
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}
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template<Unsigned U>
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constexpr U pow_mod(u64 exp, U mod)
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{
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// Left to right binary method:
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// https://en.wikipedia.org/wiki/Modular_exponentiation#Left-to-right_binary_method
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// FIXME: this is not sidechanel proof
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if (!mod)
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return 0u;
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U res = 1;
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u64 exp_copy = exp;
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for (size_t i = sizeof(u64) - count_leading_zeroes(exp) - 1u; i < exp; ++i) {
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res *= res;
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res %= mod;
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if (exp_copy & 1u) {
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res = (*this * res) % mod;
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}
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exp_copy >>= 1u;
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}
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return res;
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}
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template<Unsigned ExpT, Unsigned U>
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requires(sizeof(ExpT) > sizeof(u64)) constexpr U pow_mod(ExpT exp, U mod)
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{
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// Left to right binary method:
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// https://en.wikipedia.org/wiki/Modular_exponentiation#Left-to-right_binary_method
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// FIXME: this is not side channel proof
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if (!mod)
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return 0u;
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U res = 1;
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ExpT exp_copy = exp;
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for (size_t i = sizeof(ExpT) - exp.clz() - 1u; i < exp; ++i) {
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res *= res;
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res %= mod;
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if (exp_copy & 1u) {
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res = (*this * res) % mod;
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}
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exp_copy >>= 1u;
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}
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return res;
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}
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constexpr size_t log2()
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{
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// FIXME: proper rounding
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return sizeof(R) - clz();
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}
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constexpr size_t logn(u64 base)
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{
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// FIXME: proper rounding
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return log2() / (sizeof(u64) - count_leading_zeroes(base));
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}
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template<Unsigned U>
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requires(sizeof(U) > sizeof(u64)) constexpr size_t logn(U base)
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{
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// FIXME: proper rounding
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return log2() / base.log2();
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}
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constexpr u64 fold_or() const requires(IsSame<T, u64>)
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{
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return m_low | m_high;
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}
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constexpr u64 fold_or() const requires(!IsSame<T, u64>)
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{
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return m_low.fold_or() | m_high.fold_or();
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}
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constexpr bool is_zero_constant_time() const
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{
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return fold_or() == 0;
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}
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constexpr u64 fold_xor_pair(R& other) const requires(IsSame<T, u64>)
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{
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return (m_low ^ other.low()) | (m_high ^ other.high());
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}
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constexpr u64 fold_xor_pair(R& other) const requires(!IsSame<T, u64>)
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{
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return (m_low.fold_xor_pair(other.low())) | (m_high.fold_xor_pair(other.high()));
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}
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constexpr bool is_equal_to_constant_time(R& other)
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{
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return fold_xor_pair(other) == 0;
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}
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private:
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T m_low;
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T m_high;
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};
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// reverse operators
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template<Unsigned U, Unsigned T>
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requires(sizeof(U) < sizeof(T) * 2) constexpr bool operator<(const U a, UFixedBigInt<T> const& b) { return b >= a; }
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template<Unsigned U, Unsigned T>
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requires(sizeof(U) < sizeof(T) * 2) constexpr bool operator>(const U a, UFixedBigInt<T> const& b) { return b <= a; }
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template<Unsigned U, Unsigned T>
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requires(sizeof(U) < sizeof(T) * 2) constexpr bool operator<=(const U a, UFixedBigInt<T> const& b) { return b > a; }
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template<Unsigned U, Unsigned T>
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requires(sizeof(U) < sizeof(T) * 2) constexpr bool operator>=(const U a, UFixedBigInt<T> const& b) { return b < a; }
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template<Unsigned T>
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struct Formatter<UFixedBigInt<T>> : StandardFormatter {
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Formatter() = default;
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explicit Formatter(StandardFormatter formatter)
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: StandardFormatter(formatter)
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{
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}
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ErrorOr<void> format(FormatBuilder& builder, UFixedBigInt<T> value)
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{
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if (m_precision.has_value())
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VERIFY_NOT_REACHED();
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if (m_mode == Mode::Pointer) {
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// these are way to big for a pointer
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VERIFY_NOT_REACHED();
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}
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if (m_mode == Mode::Default)
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m_mode = Mode::Hexadecimal;
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if (!value.high()) {
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Formatter<T> formatter { *this };
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return formatter.format(builder, value.low());
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}
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u8 base = 0;
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if (m_mode == Mode::Binary) {
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base = 2;
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} else if (m_mode == Mode::BinaryUppercase) {
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base = 2;
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} else if (m_mode == Mode::Octal) {
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TODO();
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} else if (m_mode == Mode::Decimal) {
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TODO();
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} else if (m_mode == Mode::Hexadecimal) {
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base = 16;
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} else if (m_mode == Mode::HexadecimalUppercase) {
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base = 16;
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} else {
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VERIFY_NOT_REACHED();
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}
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ssize_t width = m_width.value_or(0);
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ssize_t lower_length = ceil_div(sizeof(T) * 8, (ssize_t)base);
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Formatter<T> formatter { *this };
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formatter.m_width = max(width - lower_length, (ssize_t)0);
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TRY(formatter.format(builder, value.high()));
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TRY(builder.put_literal("'"sv));
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formatter.m_zero_pad = true;
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formatter.m_alternative_form = false;
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formatter.m_width = lower_length;
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TRY(formatter.format(builder, value.low()));
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return {};
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}
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};
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}
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// Nit: Doing these as custom classes might be faster, especially when writing
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// then in SSE, but this would cause a lot of Code duplication and due to
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// the nature of constexprs and the intelligence of the compiler they might
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// be using SSE/MMX either way
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// these sizes should suffice for most usecases
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using u128 = AK::UFixedBigInt<u64>;
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using u256 = AK::UFixedBigInt<u128>;
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using u512 = AK::UFixedBigInt<u256>;
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using u1024 = AK::UFixedBigInt<u512>;
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using u2048 = AK::UFixedBigInt<u1024>;
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using u4096 = AK::UFixedBigInt<u2048>;
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