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__msvc_int128.hpp
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// __msvc_int128.hpp internal header (core)
// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
#pragma once
#ifndef __MSVC_INT128_HPP
#define __MSVC_INT128_HPP
#include <yvals_core.h>
#if _STL_COMPILER_PREPROCESSOR
#include <cstdint>
#include <intrin.h> // TRANSITION, GH-2520
#include <limits>
#include <type_traits>
#if _HAS_CXX20
#include <bit>
#include <compare>
#define _ZERO_OR_NO_INIT
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
#define _ZERO_OR_NO_INIT \
{} // Trivial default initialization is not allowed in constexpr functions before C++20.
#endif // ^^^ !_HAS_CXX20 ^^^
#ifdef __cpp_lib_concepts
#include <concepts>
#define _TEMPLATE_CLASS_INTEGRAL(type) template <integral type>
#else // ^^^ defined(__cpp_lib_concepts) / !defined(__cpp_lib_concepts) vvv
#define _TEMPLATE_CLASS_INTEGRAL(type) template <class type, enable_if_t<is_integral_v<type>, int> = 0>
#endif // ^^^ !defined(__cpp_lib_concepts) ^^^
#pragma pack(push, _CRT_PACKING)
#pragma warning(push, _STL_WARNING_LEVEL)
#pragma warning(disable : _STL_DISABLED_WARNINGS)
_STL_DISABLE_CLANG_WARNINGS
#pragma push_macro("new")
#undef new
_STD_BEGIN
#if defined(_M_X64) && !defined(_M_ARM64EC) && !defined(_M_CEE_PURE) && !defined(__CUDACC__) \
&& !defined(__INTEL_COMPILER)
#define _STL_128_INTRINSICS 1
#ifdef __clang__ // clang doesn't have _udiv128 / _div128
#define _STL_128_DIV_INTRINSICS 0
#else // ^^^ Clang / other vvv
#define _STL_128_DIV_INTRINSICS 1
#endif // ^^^ detect _udiv128 / _div128 ^^^
#else // ^^^ intrinsics available / intrinsics unavailable vvv
#define _STL_128_INTRINSICS 0
#define _STL_128_DIV_INTRINSICS 0
#endif // ^^^ intrinsics unavailable ^^^
struct
#ifndef _M_ARM
alignas(16)
#endif
_Base128 {
uint64_t _Word[2];
constexpr void _Left_shift(const unsigned char _Count) noexcept {
// _STL_INTERNAL_CHECK(_Count < 128);
if (_Count == 0) {
return;
}
if (_Count >= 64) {
_Word[1] = _Word[0] << (_Count % 64);
_Word[0] = 0;
return;
}
#if _STL_128_INTRINSICS
if (!_Is_constant_evaluated()) {
_Word[1] = __shiftleft128(_Word[0], _Word[1], _Count);
} else
#endif // _STL_128_INTRINSICS
{
_Word[1] = (_Word[1] << _Count) | (_Word[0] >> (64 - _Count));
}
_Word[0] <<= _Count;
}
constexpr void _Unsigned_right_shift(const unsigned char _Count) noexcept {
// _STL_INTERNAL_CHECK(_Count < 128);
if (_Count == 0) {
return;
}
if (_Count >= 64) {
_Word[0] = _Word[1] >> (_Count % 64);
_Word[1] = 0;
return;
}
#if _STL_128_INTRINSICS
if (!_Is_constant_evaluated()) {
_Word[0] = __shiftright128(_Word[0], _Word[1], _Count);
} else
#endif // _STL_128_INTRINSICS
{
_Word[0] = (_Word[0] >> _Count) | (_Word[1] << (64 - _Count));
}
_Word[1] >>= _Count;
}
static constexpr unsigned char _AddCarry64(
unsigned char _Carry, uint64_t _Left, uint64_t _Right, uint64_t& _Result) noexcept {
// _STL_INTERNAL_CHECK(_Carry < 2);
#if _STL_128_INTRINSICS
if (!_Is_constant_evaluated()) {
return _addcarry_u64(_Carry, _Left, _Right, &_Result);
}
#endif // _STL_128_INTRINSICS
const uint64_t _Sum = _Left + _Right + _Carry;
_Result = _Sum;
return _Carry ? _Sum <= _Left : _Sum < _Left;
}
static constexpr unsigned char _SubBorrow64(
unsigned char _Carry, uint64_t _Left, uint64_t _Right, uint64_t& _Result) noexcept {
// _STL_INTERNAL_CHECK(_Carry < 2);
#if _STL_128_INTRINSICS
if (!_Is_constant_evaluated()) {
return _subborrow_u64(_Carry, _Left, _Right, &_Result);
}
#endif // _STL_128_INTRINSICS
const auto _Difference = _Left - _Right - _Carry;
_Result = _Difference;
return _Carry ? _Difference >= _Left : _Difference > _Left;
}
template <size_t __m, size_t __n>
static constexpr void _Knuth_4_3_1_M(
const uint32_t (&__u)[__m], const uint32_t (&__v)[__n], uint32_t (&__w)[__n + __m]) noexcept {
#ifdef _ENABLE_STL_INTERNAL_CHECK
constexpr auto _Int_max = size_t{(numeric_limits<int>::max)()};
_STL_INTERNAL_STATIC_ASSERT(__m <= _Int_max);
_STL_INTERNAL_STATIC_ASSERT(__n <= _Int_max);
#endif // _ENABLE_STL_INTERNAL_CHECK
for (auto& _Elem : __w) {
_Elem = 0;
}
for (int __j = 0; __j < static_cast<int>(__n); ++__j) {
// stash Knuth's `k` in the lower 32 bits of __t
uint64_t __t = 0;
for (int __i = 0; __i < static_cast<int>(__m); ++__i) {
__t += static_cast<uint64_t>(__u[__i]) * __v[__j] + __w[__i + __j];
__w[__i + __j] = static_cast<uint32_t>(__t);
__t >>= 32;
}
__w[__j + __m] = static_cast<uint32_t>(__t);
}
}
_NODISCARD static constexpr uint64_t _UMul128(
const uint64_t _Left, const uint64_t _Right, uint64_t& _High_result) noexcept {
#if _STL_128_INTRINSICS
if (!_Is_constant_evaluated()) {
return _umul128(_Left, _Right, &_High_result);
}
#endif // _STL_128_INTRINSICS
const uint32_t __u[2] = {
static_cast<uint32_t>(_Left),
static_cast<uint32_t>(_Left >> 32),
};
const uint32_t __v[2] = {
static_cast<uint32_t>(_Right),
static_cast<uint32_t>(_Right >> 32),
};
uint32_t __w[4] _ZERO_OR_NO_INIT;
// multiply 2-digit numbers with 4-digit result in base 2^32
_Knuth_4_3_1_M(__u, __v, __w);
_High_result = (static_cast<uint64_t>(__w[3]) << 32) | __w[2];
return (static_cast<uint64_t>(__w[1]) << 32) | __w[0];
}
static constexpr void _Knuth_4_3_1_D(uint32_t* const __u, const size_t __u_size, const uint32_t* const __v,
const size_t __v_size, uint32_t* const __q) noexcept {
// Pre: __u + [0, __u_size), __v + [0, __v_size), and __q + [0, __u_size - __v_size) are all valid ranges
// constexpr auto _Int_max = size_t{(numeric_limits<int>::max)()};
// _STL_INTERNAL_CHECK(__v_size <= _Int_max);
const int __n = static_cast<int>(__v_size);
// _STL_INTERNAL_CHECK(__u_size > __v_size);
// _STL_INTERNAL_CHECK(__u_size <= _Int_max);
const int __m = static_cast<int>(__u_size - __v_size - 1);
// _STL_INTERNAL_CHECK(__v[__n - 1] >> 31 != 0); // Arguments are already normalized
for (int __j = __m; __j >= 0; --__j) {
const auto _Two_digits = (static_cast<uint64_t>(__u[__j + __n]) << 32) | __u[__j + __n - 1];
auto __qhat = _Two_digits / __v[__n - 1];
auto __rhat = _Two_digits % __v[__n - 1];
while ((__qhat >> 32) != 0
|| static_cast<uint32_t>(__qhat) * static_cast<uint64_t>(__v[__n - 2])
> ((__rhat << 32) | __u[__j + __n - 2])) {
--__qhat;
__rhat += __v[__n - 1];
if ((__rhat >> 32) != 0) {
break;
}
}
int64_t __k = 0;
int64_t __t _ZERO_OR_NO_INIT;
for (int __i = 0; __i < __n; ++__i) {
const auto _Prod = static_cast<uint32_t>(__qhat) * static_cast<uint64_t>(__v[__i]);
__t = __u[__i + __j] - __k - static_cast<uint32_t>(_Prod);
__u[__i + __j] = static_cast<uint32_t>(__t);
__k = static_cast<int64_t>(_Prod >> 32) - (__t >> 32);
}
__t = __u[__j + __n] - __k;
__u[__j + __n] = static_cast<uint32_t>(__t);
__q[__j] = static_cast<uint32_t>(__qhat);
if (__t < 0) {
--__q[__j];
__k = 0;
for (int __i = 0; __i < __n; ++__i) {
__t = __u[__i + __j] + __k + __v[__i];
__u[__i + __j] = static_cast<uint32_t>(__t);
__k = __t >> 32;
}
__u[__j + __n] += static_cast<int32_t>(__k);
}
}
// quotient is in __q, normalized remainder is in __u
}
_NODISCARD static constexpr uint64_t _UDiv128(
uint64_t _High, uint64_t _Low, uint64_t _Div, uint64_t& _Remainder) noexcept {
// _STL_INTERNAL_CHECK(_High < _Div);
#if _STL_128_DIV_INTRINSICS
if (!_Is_constant_evaluated()) {
return _udiv128(_High, _Low, _Div, &_Remainder);
}
#endif // _STL_128_DIV_INTRINSICS
#if _HAS_CXX20
const auto __d = _STD countl_zero(static_cast<uint32_t>(_Div >> 32));
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
const auto __d = _Countl_zero_fallback(static_cast<uint32_t>(_Div >> 32));
#endif // ^^^ !_HAS_CXX20 ^^^
if (__d >= 32) { // _Div < 2^32
auto _Rem = (_High << 32) | (_Low >> 32);
auto _Result = _Rem / static_cast<uint32_t>(_Div);
_Rem = ((_Rem % static_cast<uint32_t>(_Div)) << 32) | static_cast<uint32_t>(_Low);
_Result = (_Result << 32) | (_Rem / static_cast<uint32_t>(_Div));
_Remainder = _Rem % static_cast<uint32_t>(_Div);
return _Result;
}
uint32_t __u[5] = {
static_cast<uint32_t>(_Low << __d),
static_cast<uint32_t>(_Low >> (32 - __d)),
static_cast<uint32_t>(_High << __d),
static_cast<uint32_t>(_High >> (32 - __d)),
0,
};
if (__d != 0) {
__u[2] |= static_cast<uint32_t>(_Low >> (64 - __d));
__u[4] |= static_cast<uint32_t>(_High >> (64 - __d));
}
uint32_t __v[2] = {
static_cast<uint32_t>(_Div << __d),
static_cast<uint32_t>(_Div >> (32 - __d)),
};
uint32_t __q[3] _ZERO_OR_NO_INIT;
_Knuth_4_3_1_D(__u, 5, __v, 2, __q);
// _STL_INTERNAL_CHECK(__u[4] == 0);
// _STL_INTERNAL_CHECK(__u[3] == 0);
// _STL_INTERNAL_CHECK(__u[2] == 0);
_Remainder = (static_cast<uint64_t>(__u[1]) << (32 - __d)) | (__u[0] >> __d);
// _STL_INTERNAL_CHECK(__q[2] == 0);
return (static_cast<uint64_t>(__q[1]) << 32) | __q[0];
}
constexpr _Base128() noexcept : _Word{} {}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Base128(const _Ty _Val) noexcept : _Word{static_cast<uint64_t>(_Val)} {
#ifdef __cpp_lib_concepts
if constexpr (signed_integral<_Ty>)
#else
if constexpr (is_signed_v<_Ty>)
#endif
{
if (_Val < 0) {
_Word[1] = ~0ull;
}
}
}
constexpr explicit _Base128(const uint64_t _Low, const uint64_t _High) noexcept : _Word{_Low, _High} {}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
_NODISCARD constexpr explicit operator _Ty() const noexcept {
return static_cast<_Ty>(_Word[0]);
}
_NODISCARD constexpr explicit operator bool() const noexcept {
return (_Word[0] | _Word[1]) != 0;
}
#if _HAS_CXX20
_NODISCARD_FRIEND constexpr bool operator==(const _Base128&, const _Base128&) noexcept = default;
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
_NODISCARD_FRIEND constexpr bool operator==(const _Base128& _Left, const _Base128& _Right) noexcept {
return _Left._Word[0] == _Right._Word[0] && _Left._Word[1] == _Right._Word[1];
}
_NODISCARD_FRIEND constexpr bool operator!=(const _Base128& _Left, const _Base128& _Right) noexcept {
return !(_Left == _Right);
}
#endif // ^^^ !_HAS_CXX20 ^^^
_NODISCARD_FRIEND constexpr bool operator<(const _Base128& _Left, const _Base128& _Right) noexcept {
if (_Left._Word[1] < _Right._Word[1]) {
return true;
}
if (_Left._Word[1] > _Right._Word[1]) {
return false;
}
return _Left._Word[0] < _Right._Word[0];
}
_NODISCARD_FRIEND constexpr bool operator>(const _Base128& _Left, const _Base128& _Right) noexcept {
return _Right < _Left;
}
_NODISCARD_FRIEND constexpr bool operator<=(const _Base128& _Left, const _Base128& _Right) noexcept {
return !(_Right < _Left);
}
_NODISCARD_FRIEND constexpr bool operator>=(const _Base128& _Left, const _Base128& _Right) noexcept {
return !(_Left < _Right);
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
_NODISCARD_FRIEND constexpr _Ty operator<<(const _Ty _Left, const _Base128& _Right) noexcept {
return _Left << _Right._Word[0];
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
_NODISCARD_FRIEND constexpr _Ty operator>>(const _Ty _Left, const _Base128& _Right) noexcept {
return _Left >> _Right._Word[0];
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Base128& operator<<=(const _Ty _Count) noexcept {
_Left_shift(static_cast<unsigned char>(_Count));
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator<<=(_Ty& _Left, const _Base128& _Right) noexcept {
_Left <<= _Right._Word[0];
return _Left;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Base128& operator>>=(const _Ty _Count) noexcept {
_Unsigned_right_shift(static_cast<unsigned char>(_Count));
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator>>=(_Ty& _Left, const _Base128& _Right) noexcept {
_Left >>= _Right._Word[0];
return _Left;
}
constexpr _Base128& operator++() noexcept {
if (++_Word[0] == 0) {
++_Word[1];
}
return *this;
}
constexpr _Base128 operator++(int) noexcept {
auto _Tmp = *this;
++*this;
return _Tmp;
}
constexpr _Base128& operator--() noexcept {
if (_Word[0]-- == 0) {
--_Word[1];
}
return *this;
}
constexpr _Base128 operator--(int) noexcept {
auto _Tmp = *this;
--*this;
return _Tmp;
}
_NODISCARD static constexpr _Base128 _Multiply(const _Base128& _Left, const _Base128& _Right) noexcept {
_Base128 _Result;
_Result._Word[0] = _UMul128(_Left._Word[0], _Right._Word[0], _Result._Word[1]);
_Result._Word[1] += _Left._Word[0] * _Right._Word[1];
_Result._Word[1] += _Left._Word[1] * _Right._Word[0];
return _Result;
}
#if !_STL_128_DIV_INTRINSICS
_NODISCARD static constexpr _Base128 _Divide(const _Base128& _Num, const uint32_t _Den) noexcept {
_Base128 _Result;
_Result._Word[1] = _Num._Word[1] / _Den;
uint64_t _Rem = ((_Num._Word[1] % _Den) << 32) | (_Num._Word[0] >> 32);
_Result._Word[0] = (_Rem / _Den) << 32;
_Rem = ((_Rem % _Den) << 32) | static_cast<uint32_t>(_Num._Word[0]);
_Result._Word[0] |= static_cast<uint32_t>(_Rem / _Den);
return _Result;
}
#endif // !_STL_128_DIV_INTRINSICS
_NODISCARD static constexpr _Base128 _Divide(const _Base128& _Num, const uint64_t _Den) noexcept {
_Base128 _Result;
_Result._Word[1] = _Num._Word[1] / _Den;
uint64_t _Rem = _Num._Word[1] % _Den;
_Result._Word[0] = _UDiv128(_Rem, _Num._Word[0], _Den, _Rem);
return _Result;
}
_NODISCARD static constexpr _Base128 _Divide(_Base128 _Num, _Base128 _Den) noexcept {
// establish _Den < _Num and _Num._Word[1] > 0
if (_Den._Word[1] >= _Num._Word[1]) {
if (_Den._Word[1] > _Num._Word[1]) {
return 0;
}
return _Num._Word[1] == 0 ? _Num._Word[0] / _Den._Word[0] : _Num._Word[0] >= _Den._Word[0];
}
// establish _Den has more than 1 non-zero "digit"
if (_Den._Word[1] == 0) {
#if !_STL_128_DIV_INTRINSICS
if (_Den._Word[0] < (1ull << 32)) {
return _Divide(_Num, static_cast<uint32_t>(_Den._Word[0]));
} else
#endif // !_STL_128_DIV_INTRINSICS
{
return _Divide(_Num, _Den._Word[0]);
}
}
#if _STL_128_INTRINSICS
// Knuth 4.3.1D, 2-digit by 2-digit divide in base 2^64
// _STL_INTERNAL_CHECK(_Den._Word[1] != 0);
// _STL_INTERNAL_CHECK(_Num._Word[1] > _Den._Word[1]);
// Normalize by shifting both left until _Den's high bit is set (So _Den's high digit is >= b / 2)
#if _HAS_CXX20
const auto __d = _STD countl_zero(_Den._Word[1]);
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
const auto __d = _Countl_zero_fallback(_Den._Word[1]);
#endif // ^^^ !_HAS_CXX20 ^^^
_Den <<= __d;
auto _High_digit = __d == 0 ? 0 : _Num._Word[1] >> (64 - __d); // This creates a third digit for _Num
_Num <<= __d;
_Base128 __qhat;
__qhat._Word[1] = _High_digit >= _Den._Word[1];
uint64_t __rhat _ZERO_OR_NO_INIT;
__qhat._Word[0] = _UDiv128(_High_digit >= _Den._Word[1] ? _High_digit - _Den._Word[1] : _High_digit,
_Num._Word[1], _Den._Word[1], __rhat);
for (;;) {
if (__qhat._Word[1] > 0) {
--__qhat;
} else {
_Base128 _Prod;
_Prod._Word[0] = _UMul128(__qhat._Word[0], _Den._Word[0], _Prod._Word[1]);
if (_Prod <= _Base128{_Num._Word[0], __rhat}) {
break;
}
--__qhat._Word[0];
}
const auto _Sum = __rhat + _Den._Word[1];
if (__rhat > _Sum) {
break;
}
__rhat = _Sum;
}
// _STL_INTERNAL_CHECK(__qhat._Word[1] == 0);
// [_High_digit | _Num] -= __qhat * _Den [Since __qhat < b, this is 3-digit - 1-digit * 2-digit]
uint64_t _Prod0_hi _ZERO_OR_NO_INIT;
uint64_t _Prod_lo = _UMul128(__qhat._Word[0], _Den._Word[0], _Prod0_hi);
auto _Borrow = _SubBorrow64(0, _Num._Word[0], _Prod_lo, _Num._Word[0]);
uint64_t _Prod1_hi _ZERO_OR_NO_INIT;
_Prod_lo = _UMul128(__qhat._Word[0], _Den._Word[1], _Prod1_hi);
_Prod1_hi += _AddCarry64(0, _Prod_lo, _Prod0_hi, _Prod_lo);
_Borrow = _SubBorrow64(_Borrow, _Num._Word[1], _Prod_lo, _Num._Word[1]);
_Borrow = _SubBorrow64(_Borrow, _High_digit, _Prod1_hi, _High_digit);
if (_Borrow) {
--__qhat._Word[0];
}
return __qhat;
#else // ^^^ 128-bit intrinsics / no such intrinsics vvv
#if _HAS_CXX20
auto __d = _STD countl_zero(_Den._Word[1]);
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
auto __d = _Countl_zero_fallback(_Den._Word[1]);
#endif // ^^^ !_HAS_CXX20 ^^^
const bool _Three_word_den = __d >= 32;
__d &= 31;
uint32_t __u[5]{
static_cast<uint32_t>(_Num._Word[0] << __d),
static_cast<uint32_t>(_Num._Word[0] >> (32 - __d)),
static_cast<uint32_t>(_Num._Word[1] << __d),
static_cast<uint32_t>(_Num._Word[1] >> (32 - __d)),
0,
};
uint32_t __v[4] = {
static_cast<uint32_t>(_Den._Word[0] << __d),
static_cast<uint32_t>(_Den._Word[0] >> (32 - __d)),
static_cast<uint32_t>(_Den._Word[1] << __d),
static_cast<uint32_t>(_Den._Word[1] >> (32 - __d)),
};
if (__d != 0) {
__u[2] |= _Num._Word[0] >> (64 - __d);
__u[4] |= _Num._Word[1] >> (64 - __d);
__v[2] |= _Den._Word[0] >> (64 - __d);
}
uint32_t __q[2] _ZERO_OR_NO_INIT;
if (_Three_word_den) {
// 4-digit by 3-digit base 2^32 division
_Knuth_4_3_1_D(__u, 5, __v, 3, __q);
} else {
// 4-digit by 4-digit base 2^32 division
_Knuth_4_3_1_D(__u, 5, __v, 4, __q);
__q[1] = 0;
}
return (static_cast<uint64_t>(__q[1]) << 32) | __q[0];
#endif // _STL_128_INTRINSICS
}
#if !_STL_128_DIV_INTRINSICS
_NODISCARD static constexpr _Base128 _Modulo(const _Base128& _Num, const uint32_t _Den) noexcept {
uint64_t _Rem = _Num._Word[1];
_Rem = ((_Rem % _Den) << 32) | (_Num._Word[0] >> 32);
_Rem = ((_Rem % _Den) << 32) | static_cast<uint32_t>(_Num._Word[0]);
return _Rem % _Den;
}
#endif // !_STL_128_DIV_INTRINSICS
_NODISCARD static constexpr _Base128 _Modulo(const _Base128& _Num, const uint64_t _Den) noexcept {
uint64_t _Rem _ZERO_OR_NO_INIT;
(void) _UDiv128(_Num._Word[1] % _Den, _Num._Word[0], _Den, _Rem);
return _Rem;
}
_NODISCARD static constexpr _Base128 _Modulo(_Base128 _Num, _Base128 _Den) noexcept {
// establish _Den < _Num and _Num._Word[1] > 0
if (_Den._Word[1] >= _Num._Word[1]) {
if (_Den._Word[1] > _Num._Word[1]) {
return _Num;
}
if (_Den._Word[0] <= _Num._Word[0]) {
return _Num._Word[1] == 0 ? _Num._Word[0] % _Den._Word[0] : _Num._Word[0] - _Den._Word[0];
}
return _Num;
}
// establish _Den has more than 1 non-zero "digit"
if (_Den._Word[1] == 0) {
#if !_STL_128_DIV_INTRINSICS
if (_Den._Word[0] < (1ull << 32)) {
return _Modulo(_Num, static_cast<uint32_t>(_Den._Word[0]));
} else
#endif // !_STL_128_DIV_INTRINSICS
{
return _Modulo(_Num, _Den._Word[0]);
}
}
#if _STL_128_INTRINSICS
// Knuth 4.3.1D, 2-digit by 2-digit divide in base 2^64
// _STL_INTERNAL_CHECK(_Den._Word[1] != 0);
// _STL_INTERNAL_CHECK(_Num._Word[1] > _Den._Word[1]);
// Normalize by shifting both left until _Den's high bit is set (So _Den's high digit is >= b / 2)
#if _HAS_CXX20
const auto __d = _STD countl_zero(_Den._Word[1]);
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
const auto __d = _Countl_zero_fallback(_Den._Word[1]);
#endif // ^^^ !_HAS_CXX20 ^^^
_Den <<= __d;
auto _High_digit = __d == 0 ? 0 : _Num._Word[1] >> (64 - __d); // This creates a third digit for _Num
_Num <<= __d;
uint64_t __qhat_high = _High_digit >= _Den._Word[1];
uint64_t __rhat _ZERO_OR_NO_INIT;
uint64_t __qhat = _UDiv128(_High_digit >= _Den._Word[1] ? _High_digit - _Den._Word[1] : _High_digit,
_Num._Word[1], _Den._Word[1], __rhat);
for (;;) {
if (__qhat_high > 0) {
if (__qhat-- == 0) {
--__qhat_high;
}
} else {
_Base128 _Prod;
_Prod._Word[0] = _UMul128(__qhat, _Den._Word[0], _Prod._Word[1]);
if (_Prod <= _Base128{_Num._Word[0], __rhat}) {
break;
}
--__qhat;
}
const auto _Sum = __rhat + _Den._Word[1];
if (__rhat > _Sum) {
break;
}
__rhat = _Sum;
// The addition didn't overflow, so `__rhat < b` holds
}
// _STL_INTERNAL_CHECK(__qhat_high == 0);
// [_High_digit | _Num] -= __qhat * _Den [3-digit - 1-digit * 2-digit]
uint64_t _Prod0_hi _ZERO_OR_NO_INIT;
uint64_t _Prod_lo = _UMul128(__qhat, _Den._Word[0], _Prod0_hi);
auto _Borrow = _SubBorrow64(0, _Num._Word[0], _Prod_lo, _Num._Word[0]);
uint64_t _Prod1_hi _ZERO_OR_NO_INIT;
_Prod_lo = _UMul128(__qhat, _Den._Word[1], _Prod1_hi);
_Prod1_hi += _AddCarry64(0, _Prod_lo, _Prod0_hi, _Prod_lo);
_Borrow = _SubBorrow64(_Borrow, _Num._Word[1], _Prod_lo, _Num._Word[1]);
_Borrow = _SubBorrow64(_Borrow, _High_digit, _Prod1_hi, _High_digit);
if (_Borrow) {
auto _Carry = _AddCarry64(0, _Num._Word[0], _Den._Word[0], _Num._Word[0]);
(void) _AddCarry64(_Carry, _Num._Word[1], _Den._Word[1], _Num._Word[1]);
}
#else // ^^^ 128-bit intrinsics / no such intrinsics vvv
#if _HAS_CXX20
auto __d = _STD countl_zero(_Den._Word[1]);
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
auto __d = _Countl_zero_fallback(_Den._Word[1]);
#endif // ^^^ !_HAS_CXX20 ^^^
const bool _Three_word_den = __d >= 32;
__d &= 31;
uint32_t __u[5]{
static_cast<uint32_t>(_Num._Word[0] << __d),
static_cast<uint32_t>(_Num._Word[0] >> (32 - __d)),
static_cast<uint32_t>(_Num._Word[1] << __d),
static_cast<uint32_t>(_Num._Word[1] >> (32 - __d)),
0,
};
uint32_t __v[4] = {
static_cast<uint32_t>(_Den._Word[0] << __d),
static_cast<uint32_t>(_Den._Word[0] >> (32 - __d)),
static_cast<uint32_t>(_Den._Word[1] << __d),
static_cast<uint32_t>(_Den._Word[1] >> (32 - __d)),
};
if (__d != 0) {
__u[2] |= _Num._Word[0] >> (64 - __d);
__u[4] |= _Num._Word[1] >> (64 - __d);
__v[2] |= _Den._Word[0] >> (64 - __d);
}
uint32_t __q[2] _ZERO_OR_NO_INIT;
if (_Three_word_den) {
// 4-digit by 3-digit base 2^32 division
_Knuth_4_3_1_D(__u, 5, __v, 3, __q);
// _STL_INTERNAL_CHECK(__u[3] == 0);
} else {
// 4-digit by 4-digit base 2^32 division
_Knuth_4_3_1_D(__u, 5, __v, 4, __q);
}
// _STL_INTERNAL_CHECK(__u[4] == 0);
_Num._Word[0] = (static_cast<uint64_t>(__u[1]) << 32) | __u[0];
_Num._Word[1] = (static_cast<uint64_t>(__u[3]) << 32) | __u[2];
#endif // _STL_128_INTRINSICS
_Num >>= __d;
return _Num;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator&=(_Ty& _Left, const _Base128& _Right) noexcept {
_Left &= _Right._Word[0];
return _Left;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator^=(_Ty& _Left, const _Base128& _Right) noexcept {
_Left ^= _Right._Word[0];
return _Left;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator|=(_Ty& _Left, const _Base128& _Right) noexcept {
_Left |= _Right._Word[0];
return _Left;
}
};
struct _Signed128;
struct _Unsigned128 : _Base128 {
using _Signed_type = _Signed128;
using _Unsigned_type = _Unsigned128;
#if !_HAS_CXX17
constexpr _Unsigned128() noexcept : _Base128{} {}
#endif // !_HAS_CXX17
using _Base128::_Base128;
constexpr explicit _Unsigned128(const _Base128& _That) noexcept : _Base128{_That} {}
constexpr _Unsigned128& operator=(const _Base128& _That) noexcept {
_Base128::operator=(_That);
return *this;
}
#if _HAS_CXX20
_NODISCARD_FRIEND constexpr strong_ordering operator<=>(
const _Unsigned128& _Left, const _Unsigned128& _Right) noexcept {
strong_ordering _Ord = _Left._Word[1] <=> _Right._Word[1];
if (_Ord == strong_ordering::equal) {
_Ord = _Left._Word[0] <=> _Right._Word[0];
}
return _Ord;
}
#else // ^^^ _HAS_CXX20 / !_HAS_CXX20 vvv
_NODISCARD_FRIEND constexpr bool operator<(const _Unsigned128& _Left, const _Unsigned128& _Right) noexcept {
if (_Left._Word[1] < _Right._Word[1]) {
return true;
}
if (_Right._Word[1] < _Left._Word[1]) {
return false;
}
return _Left._Word[0] < _Right._Word[0];
}
_NODISCARD_FRIEND constexpr bool operator>(const _Unsigned128& _Left, const _Unsigned128& _Right) noexcept {
return _Right < _Left;
}
_NODISCARD_FRIEND constexpr bool operator<=(const _Unsigned128& _Left, const _Unsigned128& _Right) noexcept {
return !(_Right < _Left);
}
_NODISCARD_FRIEND constexpr bool operator>=(const _Unsigned128& _Left, const _Unsigned128& _Right) noexcept {
return !(_Left < _Right);
}
#endif // ^^^ !_HAS_CXX20 ^^^
_NODISCARD_FRIEND constexpr _Unsigned128 operator<<(const _Unsigned128& _Left, const _Base128& _Right) noexcept {
auto _Tmp{_Left};
_Tmp._Left_shift(static_cast<unsigned char>(_Right._Word[0]));
return _Tmp;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Unsigned128& operator<<=(const _Ty _Count) noexcept {
_Left_shift(static_cast<unsigned char>(_Count));
return *this;
}
constexpr _Unsigned128& operator<<=(const _Base128& _Count) noexcept {
_Left_shift(static_cast<unsigned char>(_Count._Word[0]));
return *this;
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator>>(const _Unsigned128& _Left, const _Base128& _Right) noexcept {
auto _Tmp{_Left};
_Tmp._Unsigned_right_shift(static_cast<unsigned char>(_Right._Word[0]));
return _Tmp;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Unsigned128& operator>>=(const _Ty _Count) noexcept {
_Unsigned_right_shift(static_cast<unsigned char>(_Count));
return *this;
}
constexpr _Unsigned128& operator>>=(const _Base128& _Count) noexcept {
_Unsigned_right_shift(static_cast<unsigned char>(_Count._Word[0]));
return *this;
}
constexpr _Unsigned128& operator++() noexcept {
if (++_Word[0] == 0) {
++_Word[1];
}
return *this;
}
constexpr _Unsigned128 operator++(int) noexcept {
auto _Tmp = *this;
++*this;
return _Tmp;
}
constexpr _Unsigned128& operator--() noexcept {
if (_Word[0]-- == 0) {
--_Word[1];
}
return *this;
}
constexpr _Unsigned128 operator--(int) noexcept {
auto _Tmp = *this;
--*this;
return _Tmp;
}
_NODISCARD constexpr _Unsigned128 operator+() const noexcept {
return *this;
}
_NODISCARD constexpr _Unsigned128 operator-() const noexcept {
return _Unsigned128{} - *this;
}
_NODISCARD constexpr _Unsigned128 operator~() const noexcept {
return _Unsigned128{~_Word[0], ~_Word[1]};
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator+(const _Base128& _Left, const _Base128& _Right) noexcept {
_Unsigned128 _Result;
const auto _Carry = _AddCarry64(0, _Left._Word[0], _Right._Word[0], _Result._Word[0]);
_AddCarry64(_Carry, _Left._Word[1], _Right._Word[1], _Result._Word[1]);
return _Result;
}
constexpr _Unsigned128& operator+=(const _Base128& _That) noexcept {
const auto _Carry = _AddCarry64(0, _Word[0], _That._Word[0], _Word[0]);
_AddCarry64(_Carry, _Word[1], _That._Word[1], _Word[1]);
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator+=(_Ty& _Left, const _Unsigned128& _Right) noexcept {
_Left += _Right._Word[0];
return _Left;
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator-(const _Base128& _Left, const _Base128& _Right) noexcept {
_Unsigned128 _Result;
const auto _Borrow = _SubBorrow64(0, _Left._Word[0], _Right._Word[0], _Result._Word[0]);
_SubBorrow64(_Borrow, _Left._Word[1], _Right._Word[1], _Result._Word[1]);
return _Result;
}
constexpr _Unsigned128& operator-=(const _Base128& _That) noexcept {
const auto _Borrow = _SubBorrow64(0, _Word[0], _That._Word[0], _Word[0]);
_SubBorrow64(_Borrow, _Word[1], _That._Word[1], _Word[1]);
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator-=(_Ty& _Left, const _Unsigned128& _Right) noexcept {
_Left -= _Right._Word[0];
return _Left;
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator*(const _Base128& _Left, const _Base128& _Right) noexcept {
return _Unsigned128{_Base128::_Multiply(_Left, _Right)};
}
constexpr _Unsigned128& operator*=(const _Base128& _That) noexcept {
*this = *this * _That;
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator*=(_Ty& _Left, const _Unsigned128& _Right) noexcept {
_Left *= _Right._Word[0];
return _Left;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
_NODISCARD_FRIEND constexpr _Unsigned128 operator/(const _Unsigned128& _Num, const _Ty _Den) noexcept {
#if !_STL_128_DIV_INTRINSICS
if constexpr (sizeof(_Ty) <= 4) {
return _Unsigned128{_Base128::_Divide(_Num, static_cast<uint32_t>(_Den))};
} else
#endif // !_STL_128_DIV_INTRINSICS
{
return _Unsigned128{_Base128::_Divide(_Num, static_cast<uint64_t>(_Den))};
}
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator/(const _Base128& _Num, const _Base128& _Den) noexcept {
return _Unsigned128{_Base128::_Divide(_Num, _Den)};
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Unsigned128& operator/=(const _Ty _That) noexcept {
#if !_STL_128_DIV_INTRINSICS
if constexpr (sizeof(_Ty) <= 4) {
*this = _Unsigned128{_Base128::_Divide(*this, static_cast<uint32_t>(_That))};
} else
#endif // !_STL_128_DIV_INTRINSICS
{
*this = _Unsigned128{_Base128::_Divide(*this, static_cast<uint64_t>(_That))};
}
return *this;
}
constexpr _Unsigned128& operator/=(const _Base128& _That) noexcept {
*this = _Unsigned128{_Base128::_Divide(*this, _That)};
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator/=(_Ty& _Left, const _Unsigned128& _Right) noexcept {
if (_Right._Word[1] != 0) {
_Left = 0;
} else {
_Left /= _Right._Word[0];
}
return _Left;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
_NODISCARD_FRIEND constexpr _Unsigned128 operator%(const _Base128& _Num, const _Ty _Den) noexcept {
#if !_STL_128_DIV_INTRINSICS
if constexpr (sizeof(_Ty) <= 4) {
return _Unsigned128{_Base128::_Modulo(_Num, static_cast<uint32_t>(_Den))};
} else
#endif // !_STL_128_DIV_INTRINSICS
{
return _Unsigned128{_Base128::_Modulo(_Num, static_cast<uint64_t>(_Den))};
}
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator%(const _Base128& _Num, const _Base128& _Den) noexcept {
return _Unsigned128{_Base128::_Modulo(_Num, _Den)};
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
constexpr _Unsigned128& operator%=(const _Ty _Den) noexcept {
*this = *this % _Den;
return *this;
}
constexpr _Unsigned128& operator%=(const _Base128& _Den) noexcept {
*this = *this % _Den;
return *this;
}
_TEMPLATE_CLASS_INTEGRAL(_Ty)
friend constexpr _Ty& operator%=(_Ty& _Left, const _Unsigned128& _Right) noexcept {
if (_Right._Word[1] == 0) {
_Left %= _Right._Word[0];
}
return _Left;
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator&(const _Base128& _Left, const _Base128& _Right) noexcept {
return _Unsigned128{_Left._Word[0] & _Right._Word[0], _Left._Word[1] & _Right._Word[1]};
}
constexpr _Unsigned128& operator&=(const _Base128& _That) noexcept {
_Word[0] &= _That._Word[0];
_Word[1] &= _That._Word[1];
return *this;
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator^(const _Base128& _Left, const _Base128& _Right) noexcept {
return _Unsigned128{_Left._Word[0] ^ _Right._Word[0], _Left._Word[1] ^ _Right._Word[1]};
}
constexpr _Unsigned128& operator^=(const _Base128& _That) noexcept {
_Word[0] ^= _That._Word[0];
_Word[1] ^= _That._Word[1];
return *this;
}
_NODISCARD_FRIEND constexpr _Unsigned128 operator|(const _Base128& _Left, const _Base128& _Right) noexcept {
return _Unsigned128{_Left._Word[0] | _Right._Word[0], _Left._Word[1] | _Right._Word[1]};
}
constexpr _Unsigned128& operator|=(const _Base128& _That) noexcept {
_Word[0] |= _That._Word[0];
_Word[1] |= _That._Word[1];
return *this;
}
};
template <>
class numeric_limits<_Unsigned128> : public _Num_int_base {
public:
_NODISCARD static constexpr _Unsigned128(min)() noexcept {
return 0;
}
_NODISCARD static constexpr _Unsigned128(max)() noexcept {
return _Unsigned128{~0ull, ~0ull};
}
_NODISCARD static constexpr _Unsigned128 lowest() noexcept {
return (min) ();
}
_NODISCARD static constexpr _Unsigned128 epsilon() noexcept {