C++20之三路比较运算符

R&L_201810012025-11-12 16:17

一、三路比较运算符 (<=>)

三路比较运算符 (<=>) 是 C++20 引入的重要特性，其极大地简化了比较操作的实现，在C++20之前，我们自定义一个类型后，如果要支持所有比较运算符，那么我们需要分别实现如下一系列重载函数：

cpp 复制代码 
bool operator==(const CompareType& other);
bool operator<(const CompareType& other);
bool operator>(const CompareType& other);
bool operator!=(const CompareType& other);
bool operator<=(const CompareType& other);
bool operator>=(const CompareType& other);

这不仅增加了代码的复杂性，同时也更容易出错，消除不一致风险，如：a>b 和 a<b都为真？

在C++20之后，我们仅需要实现两个重载函数即可，如下：

cpp 复制代码 
// 使用默认
auto operator<=>(const CompareType&) const = default; // strong_ordering

// 自己实现
/*
注意:在自己实现三路比较运算符 (<=>) 的情况下，必现自定义实现
     bool operator==(const CompareType& other)，否则在进行==比较时，将编译不通过
     C++这样设计的原因主要有：
     1、性能原因，对于某些类型，相等比较可能比三路比较更高效
     2、语义原因，有些类型的相等和排序语义可能不同：
*/
auto operator<=>(const CompareType& other) const
bool operator==(const CompareType& other) const;

下面是示例代码，及其相关注释：

cpp 复制代码 
class CompareType
{
public:
    CompareType(int x, int y)
        :mx(x)
        , my(y)
    {
    }

    /*
        //1、C++20前，直接实现6个比较运算符
        bool operator==(const CompareType& other) { return mx == other.mx && my == other.my; };
        bool operator<(const CompareType& other)
        {
            if (mx < other.mx)
                return true;
            if (mx == other.mx)
                return my < other.my;
            return false;
        };
        bool operator>(const CompareType& other)
        {
            if (mx > other.mx)
                return true;
            if (mx == other.mx)
                return my > other.my;
            return false;
        };
        bool operator!=(const CompareType& other) { return mx != other.mx || my != other.my; };
        bool operator<=(const CompareType& other) // 
        {
            if (mx < other.mx)
                return true;
            if (mx == other.mx)
                return my <= other.my;
            return false;
        };
        bool operator>=(const CompareType& other)
        {
            if (mx > other.mx)
                return true;
            if (mx == other.mx)
                return my >= other.my;
            return false;
        };
    */

    //2、使用默认三路比较运算符 (<=>)
    //auto operator<=>(const CompareType&) const = default; // strong_ordering

    //3、自定义实现三路比较运算符 (<=>)
    auto operator<=>(const CompareType& other) const
    {
        if (auto cmp = my <=> other.my; cmp != 0) return cmp;
        return mx <=> other.mx;
    }
    bool operator==(const CompareType& other) const
    {
        //return mx == other.mx && my == other.my;
        return make_tuple(mx, my) == make_tuple(other.mx, other.my);
        //return (*this <=> other) == 0;
    }
private:
    int mx, my;
};

总之，使用三路比较运算符有如下优势：

（1）代码简化 - 只需实现一个运算符而不是6个

（2）一致性 - 确保所有比较操作行为一致

（3）性能 - 可能减少比较次数（特别是对于复杂对象）

（4）可读性 - 明确表达比较的意图

二、三路比较运算符 (<=>)返回值说明

三路比较运算符 (<=>)共有三种类型的返回值（即std::strong_ordering、std::weak_ordering、std::partial_ordering），他们主要的区别在于语义上的差异：

std::strong_ordering - 强序关系 -- 语义：完全等价的对象可以互相替换

std::weak_ordering - 弱序关系 -- 语义：等价的对象在某些方面有区别

std::partial_ordering - 偏序关系 -- 语义：存在不可比较的情况

所以我们重载可以有如下三种形式：

cpp 复制代码 
    /*
    	具体选择哪种，需要根据实际情况以及语义进行选择（每个类只能重载一个哦，
    	违反单一语义原则：不能重载同一个运算符返回不同类型）
    */
    
    //std::strong_ordering operator<=>(const CompareType& other) const;
    //std::weak_ordering operator<=>(const CompareType& other) const;
    //std::partial_ordering operator<=>(const CompareType& other) const;
    auto operator<=>(const CompareType&) const

std::strong_ordering

表示强序关系

可比较对象完全等价（可互换）

cpp 复制代码 
// 可能的取值：
std::strong_ordering::less     // <
std::strong_ordering::equal    // ==  
std::strong_ordering::greater  // >
std::strong_ordering::equivalent // == (与 equal 值相同)

std::weak_ordering

表示弱序关系

可比较对象等价但不一定可互换

cpp 复制代码 
可能的取值：
std::weak_ordering::less
std::weak_ordering::equivalent
std::weak_ordering::greater

std::partial_ordering

表示偏序关系

允许不可比较的情况（如浮点数中的 NaN）

cpp 复制代码 
可能的取值：
std::partial_ordering::less
std::partial_ordering::equivalent
std::partial_ordering::greater
std::partial_ordering::unordered  // 不可比较
选择指南

强序：值完全可比较且等价的对象可互换（如整数、字符串）

弱序：等价的对象不一定可互换（如忽略大小写的字符串）

偏序：存在不可比较的情况（如浮点数、指针）
下面我们来看看C++对于这三种返回值的定义的源码吧

cpp 复制代码 
// compare standard header (core)

// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

#ifndef _COMPARE_
#define _COMPARE_
#include <yvals_core.h>
#if _STL_COMPILER_PREPROCESSOR

#if !_HAS_CXX20
_EMIT_STL_WARNING(STL4038, "The contents of <compare> are available only with C++20 or later.");
#else // ^^^ !_HAS_CXX20 / _HAS_CXX20 vvv
#include <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
void _Literal_zero_is_expected();

struct _Literal_zero {
    template <class _Ty>
        requires is_same_v<_Ty, int>
    consteval _Literal_zero(_Ty _Zero) noexcept {
        // Can't use _STL_VERIFY because this is a core header
        if (_Zero != 0) {
            _Literal_zero_is_expected();
        }
    }
};

using _Compare_t = signed char;
// 1、定义强枚举类型
// These "pretty" enumerator names are safe since they reuse names of user-facing entities.
enum class _Compare_eq : _Compare_t { equal = 0, equivalent = equal };
enum class _Compare_ord : _Compare_t { less = -1, greater = 1 };
enum class _Compare_ncmp : _Compare_t { unordered = -128 };

_EXPORT_STD struct partial_ordering {
    static const partial_ordering less;
    static const partial_ordering equivalent;
    static const partial_ordering greater;
    static const partial_ordering unordered;

    _NODISCARD friend constexpr bool operator==(const partial_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value == 0;
    }

    _NODISCARD friend constexpr bool operator==(partial_ordering, partial_ordering) noexcept = default;

    _NODISCARD friend constexpr bool operator<(const partial_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value == static_cast<_Compare_t>(_Compare_ord::less);
    }

    _NODISCARD friend constexpr bool operator>(const partial_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value > 0;
    }

    _NODISCARD friend constexpr bool operator<=(const partial_ordering _Val, _Literal_zero) noexcept {
        // The stored value is either less (0xff), equivalent (0x00), greater (0x01), or unordered (0x80).
        // Subtracting from 0 produces either 0x01, 0x00, 0xff, or 0x80. The result is greater than or equal to 0
        // if and only if the initial value was less or equivalent, for which we want to return true.
        return static_cast<signed char>(0 - static_cast<unsigned int>(_Val._Value)) >= 0;
    }

    _NODISCARD friend constexpr bool operator>=(const partial_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value >= 0;
    }

    _NODISCARD friend constexpr bool operator<(_Literal_zero, const partial_ordering _Val) noexcept {
        return _Val > 0;
    }

    _NODISCARD friend constexpr bool operator>(_Literal_zero, const partial_ordering _Val) noexcept {
        return _Val < 0;
    }

    _NODISCARD friend constexpr bool operator<=(_Literal_zero, const partial_ordering _Val) noexcept {
        return _Val >= 0;
    }

    _NODISCARD friend constexpr bool operator>=(_Literal_zero, const partial_ordering _Val) noexcept {
        return _Val <= 0;
    }

    _NODISCARD friend constexpr partial_ordering operator<=>(const partial_ordering _Val, _Literal_zero) noexcept {
        return _Val;
    }

    _NODISCARD friend constexpr partial_ordering operator<=>(_Literal_zero, const partial_ordering _Val) noexcept {
        // The stored value is either less (0xff), equivalent (0x00), greater (0x01), or unordered (0x80).
        // Subtracting from 0 produces either 0x01, 0x00, 0xff, or 0x80. Note that the effect is to
        // exchange less for greater (and vice versa), while leaving equivalent and unordered unchanged.
        return {static_cast<_Compare_t>(0 - static_cast<unsigned int>(_Val._Value))};
    }

    _Compare_t _Value;
};
// 编译期初始化预定义的值，内联变量
inline constexpr partial_ordering partial_ordering::less{static_cast<_Compare_t>(_Compare_ord::less)};
inline constexpr partial_ordering partial_ordering::equivalent{static_cast<_Compare_t>(_Compare_eq::equivalent)};
inline constexpr partial_ordering partial_ordering::greater{static_cast<_Compare_t>(_Compare_ord::greater)};
inline constexpr partial_ordering partial_ordering::unordered{static_cast<_Compare_t>(_Compare_ncmp::unordered)};

_EXPORT_STD struct weak_ordering {
    static const weak_ordering less;
    static const weak_ordering equivalent;
    static const weak_ordering greater;

    constexpr operator partial_ordering() const noexcept {
        return {static_cast<_Compare_t>(_Value)};
    }

    _NODISCARD friend constexpr bool operator==(const weak_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value == 0;
    }

    _NODISCARD friend constexpr bool operator==(weak_ordering, weak_ordering) noexcept = default;

    _NODISCARD friend constexpr bool operator<(const weak_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value < 0;
    }

    _NODISCARD friend constexpr bool operator>(const weak_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value > 0;
    }

    _NODISCARD friend constexpr bool operator<=(const weak_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value <= 0;
    }

    _NODISCARD friend constexpr bool operator>=(const weak_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value >= 0;
    }

    _NODISCARD friend constexpr bool operator<(_Literal_zero, const weak_ordering _Val) noexcept {
        return _Val > 0;
    }

    _NODISCARD friend constexpr bool operator>(_Literal_zero, const weak_ordering _Val) noexcept {
        return _Val < 0;
    }

    _NODISCARD friend constexpr bool operator<=(_Literal_zero, const weak_ordering _Val) noexcept {
        return _Val >= 0;
    }

    _NODISCARD friend constexpr bool operator>=(_Literal_zero, const weak_ordering _Val) noexcept {
        return _Val <= 0;
    }

    _NODISCARD friend constexpr weak_ordering operator<=>(const weak_ordering _Val, _Literal_zero) noexcept {
        return _Val;
    }

    _NODISCARD friend constexpr weak_ordering operator<=>(_Literal_zero, const weak_ordering _Val) noexcept {
        return {static_cast<_Compare_t>(-_Val._Value)};
    }

    _Compare_t _Value;
};

inline constexpr weak_ordering weak_ordering::less{static_cast<_Compare_t>(_Compare_ord::less)};
inline constexpr weak_ordering weak_ordering::equivalent{static_cast<_Compare_t>(_Compare_eq::equivalent)};
inline constexpr weak_ordering weak_ordering::greater{static_cast<_Compare_t>(_Compare_ord::greater)};

_EXPORT_STD struct strong_ordering {
    static const strong_ordering less;
    static const strong_ordering equal;
    static const strong_ordering equivalent;
    static const strong_ordering greater;

    constexpr operator partial_ordering() const noexcept {
        return {static_cast<_Compare_t>(_Value)};
    }

    constexpr operator weak_ordering() const noexcept {
        return {static_cast<_Compare_t>(_Value)};
    }

    _NODISCARD friend constexpr bool operator==(const strong_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value == 0;
    }

    _NODISCARD friend constexpr bool operator==(strong_ordering, strong_ordering) noexcept = default;

    _NODISCARD friend constexpr bool operator<(const strong_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value < 0;
    }

    _NODISCARD friend constexpr bool operator>(const strong_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value > 0;
    }

    _NODISCARD friend constexpr bool operator<=(const strong_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value <= 0;
    }

    _NODISCARD friend constexpr bool operator>=(const strong_ordering _Val, _Literal_zero) noexcept {
        return _Val._Value >= 0;
    }

    _NODISCARD friend constexpr bool operator<(_Literal_zero, const strong_ordering _Val) noexcept {
        return _Val > 0;
    }

    _NODISCARD friend constexpr bool operator>(_Literal_zero, const strong_ordering _Val) noexcept {
        return _Val < 0;
    }

    _NODISCARD friend constexpr bool operator<=(_Literal_zero, const strong_ordering _Val) noexcept {
        return _Val >= 0;
    }

    _NODISCARD friend constexpr bool operator>=(_Literal_zero, const strong_ordering _Val) noexcept {
        return _Val <= 0;
    }

    _NODISCARD friend constexpr strong_ordering operator<=>(const strong_ordering _Val, _Literal_zero) noexcept {
        return _Val;
    }

    _NODISCARD friend constexpr strong_ordering operator<=>(_Literal_zero, const strong_ordering _Val) noexcept {
        return {static_cast<_Compare_t>(-_Val._Value)};
    }

    _Compare_t _Value;
};

inline constexpr strong_ordering strong_ordering::less{static_cast<_Compare_t>(_Compare_ord::less)};
inline constexpr strong_ordering strong_ordering::equal{static_cast<_Compare_t>(_Compare_eq::equal)};
inline constexpr strong_ordering strong_ordering::equivalent{static_cast<_Compare_t>(_Compare_eq::equivalent)};
inline constexpr strong_ordering strong_ordering::greater{static_cast<_Compare_t>(_Compare_ord::greater)};

_EXPORT_STD _NODISCARD constexpr bool is_eq(const partial_ordering _Comp) noexcept {
    return _Comp == 0;
}

_EXPORT_STD _NODISCARD constexpr bool is_neq(const partial_ordering _Comp) noexcept {
    return _Comp != 0;
}

_EXPORT_STD _NODISCARD constexpr bool is_lt(const partial_ordering _Comp) noexcept {
    return _Comp < 0;
}

_EXPORT_STD _NODISCARD constexpr bool is_lteq(const partial_ordering _Comp) noexcept {
    return _Comp <= 0;
}

_EXPORT_STD _NODISCARD constexpr bool is_gt(const partial_ordering _Comp) noexcept {
    return _Comp > 0;
}

_EXPORT_STD _NODISCARD constexpr bool is_gteq(const partial_ordering _Comp) noexcept {
    return _Comp >= 0;
}

enum _Comparison_category : unsigned char {
    _Comparison_category_none    = 1,
    _Comparison_category_partial = 2,
    _Comparison_category_weak    = 4,
    _Comparison_category_strong  = 0,
};

template <class... _Types>
constexpr unsigned char _Classify_category =
    _Comparison_category{(_Classify_category<_Types> | ... | _Comparison_category_strong)};
template <class _Ty>
constexpr unsigned char _Classify_category<_Ty> = _Comparison_category_none;
template <>
inline constexpr unsigned char _Classify_category<partial_ordering> = _Comparison_category_partial;
template <>
inline constexpr unsigned char _Classify_category<weak_ordering> = _Comparison_category_weak;
template <>
inline constexpr unsigned char _Classify_category<strong_ordering> = _Comparison_category_strong;

_EXPORT_STD template <class... _Types>
using common_comparison_category_t =
    conditional_t<(_Classify_category<_Types...> & _Comparison_category_none) != 0, void,
        conditional_t<(_Classify_category<_Types...> & _Comparison_category_partial) != 0, partial_ordering,
            conditional_t<(_Classify_category<_Types...> & _Comparison_category_weak) != 0, weak_ordering,
                strong_ordering>>>;

_EXPORT_STD template <class... _Types>
struct common_comparison_category {
    using type = common_comparison_category_t<_Types...>;
};

template <class _Ty, class _Cat>
concept _Compares_as = same_as<common_comparison_category_t<_Ty, _Cat>, _Cat>;

_EXPORT_STD template <class _Ty, class _Cat = partial_ordering>
concept three_way_comparable = _Half_equality_comparable<_Ty, _Ty> && _Half_ordered<_Ty, _Ty>
                            && requires(const remove_reference_t<_Ty>& __a, const remove_reference_t<_Ty>& __b) {
                                   { __a <=> __b } -> _Compares_as<_Cat>;
                               };

_EXPORT_STD template <class _Ty1, class _Ty2, class _Cat = partial_ordering>
concept three_way_comparable_with =
    three_way_comparable<_Ty1, _Cat> && three_way_comparable<_Ty2, _Cat>
#if _HAS_CXX23
    && _Comparison_common_type_with<_Ty1, _Ty2>
#else // ^^^ _HAS_CXX23 / !_HAS_CXX23 vvv
    && common_reference_with<const remove_reference_t<_Ty1>&, const remove_reference_t<_Ty2>&>
#endif // ^^^ !_HAS_CXX23 ^^^
    && three_way_comparable<common_reference_t<const remove_reference_t<_Ty1>&, const remove_reference_t<_Ty2>&>, _Cat>
    && _Weakly_equality_comparable_with<_Ty1, _Ty2> && _Partially_ordered_with<_Ty1, _Ty2>
    && requires(const remove_reference_t<_Ty1>& __t, const remove_reference_t<_Ty2>& __u) {
           { __t <=> __u } -> _Compares_as<_Cat>;
           { __u <=> __t } -> _Compares_as<_Cat>;
       };

_EXPORT_STD template <class _Ty1, class _Ty2 = _Ty1>
using compare_three_way_result_t =
    decltype(_STD declval<const remove_reference_t<_Ty1>&>() <=> _STD declval<const remove_reference_t<_Ty2>&>());

_EXPORT_STD template <class _Ty1, class _Ty2 = _Ty1>
struct compare_three_way_result {};

template <class _Ty1, class _Ty2>
    requires requires { typename compare_three_way_result_t<_Ty1, _Ty2>; }
struct compare_three_way_result<_Ty1, _Ty2> {
    using type = compare_three_way_result_t<_Ty1, _Ty2>;
};

_EXPORT_STD struct compare_three_way {
    template <class _Ty1, class _Ty2>
        requires three_way_comparable_with<_Ty1, _Ty2>
    _NODISCARD constexpr auto operator()(_Ty1&& _Left, _Ty2&& _Right) const
        noexcept(noexcept(_STD forward<_Ty1>(_Left) <=> _STD forward<_Ty2>(_Right))) /* strengthened */ {
        return _STD forward<_Ty1>(_Left) <=> _STD forward<_Ty2>(_Right);
    }

    using is_transparent = int;
};

struct _Synth_three_way {
    template <class _Ty1, class _Ty2>
    _NODISCARD _STATIC_CALL_OPERATOR constexpr auto operator()(
        const _Ty1& _Left, const _Ty2& _Right) _CONST_CALL_OPERATOR
        requires requires {
            { _Left < _Right } -> _Boolean_testable;
            { _Right < _Left } -> _Boolean_testable;
        }
    {
        if constexpr (three_way_comparable_with<_Ty1, _Ty2>) {
            return _Left <=> _Right;
        } else {
            if (_Left < _Right) {
                return weak_ordering::less;
            } else if (_Right < _Left) {
                return weak_ordering::greater;
            } else {
                return weak_ordering::equivalent;
            }
        }
    }
};

template <class _Ty1, class _Ty2 = _Ty1>
using _Synth_three_way_result = decltype(_Synth_three_way{}(_STD declval<_Ty1&>(), _STD declval<_Ty2&>()));

// Note: The following CPOs are passing arguments as lvalues; see GH-1374.

namespace _Strong_order {
#if defined(__clang__) || defined(__EDG__) // TRANSITION, VSO-1681199
    void strong_order() = delete; // Block unqualified name lookup
#else // ^^^ no workaround / workaround vvv
    void strong_order();
#endif // ^^^ workaround ^^^

    template <class _Ty1, class _Ty2>
    concept _Has_ADL = requires(_Ty1& _Left, _Ty2& _Right) {
        static_cast<strong_ordering>(strong_order(_Left, _Right)); // intentional ADL
    };

    template <class _Ty1, class _Ty2>
    concept _Can_compare_three_way =
        requires(_Ty1& _Left, _Ty2& _Right) { static_cast<strong_ordering>(compare_three_way{}(_Left, _Right)); };

    class _Cpo {
    private:
        enum class _St { _None, _Adl, _Floating, _Three };

        template <class _Ty1, class _Ty2>
        _NODISCARD static consteval _Choice_t<_St> _Choose() noexcept {
            if constexpr (!same_as<decay_t<_Ty1>, decay_t<_Ty2>>) {
                return {_St::_None};
            } else if constexpr (_Has_ADL<_Ty1, _Ty2>) {
                return {_St::_Adl, noexcept(static_cast<strong_ordering>(
                                       strong_order(_STD declval<_Ty1&>(), _STD declval<_Ty2&>())))}; // intentional ADL
            } else if constexpr (floating_point<decay_t<_Ty1>>) {
                return {_St::_Floating, true};
            } else if constexpr (_Can_compare_three_way<_Ty1, _Ty2>) {
                return {_St::_Three, noexcept(static_cast<strong_ordering>(
                                         compare_three_way{}(_STD declval<_Ty1&>(), _STD declval<_Ty2&>())))};
            } else {
                return {_St::_None};
            }
        }

        template <class _Ty1, class _Ty2>
        static constexpr _Choice_t<_St> _Choice = _Choose<_Ty1, _Ty2>();

    public:
        template <class _Ty1, class _Ty2>
            requires (_Choice<_Ty1&, _Ty2&>._Strategy != _St::_None)
        _NODISCARD _STATIC_CALL_OPERATOR constexpr strong_ordering operator()(
            _Ty1&& _Left, _Ty2&& _Right) _CONST_CALL_OPERATOR noexcept(_Choice<_Ty1&, _Ty2&>._No_throw) {
            constexpr _St _Strat = _Choice<_Ty1&, _Ty2&>._Strategy;
            if constexpr (_Strat == _St::_Adl) {
                return static_cast<strong_ordering>(strong_order(_Left, _Right)); // intentional ADL
            } else if constexpr (_Strat == _St::_Floating) {
                using _Floating_type = decay_t<_Ty1>;
                using _Traits        = _Floating_type_traits<_Floating_type>;
                using _Uint_type     = _Traits::_Uint_type;
                using _Sint_type     = make_signed_t<_Uint_type>;

                const auto _Left_uint  = _Bit_cast<_Uint_type>(_Left);
                const auto _Right_uint = _Bit_cast<_Uint_type>(_Right);

                // 1. Ultra-fast path: equal representations are equal.
                if (_Left_uint == _Right_uint) {
                    return strong_ordering::equal;
                }

                // 2. Examine the sign bits.
                const _Uint_type _Left_shifted_sign  = _Left_uint & _Traits::_Shifted_sign_mask;
                const _Uint_type _Right_shifted_sign = _Right_uint & _Traits::_Shifted_sign_mask;

                // 3. Interpret floating-point bit patterns as sign magnitude representations of integers,
                //    and then transform them into ones' complement representation.
                // (Ones' complement representations of positive zero and negative zero are different.)
                const _Uint_type _Left_sign  = _Left_shifted_sign >> _Traits::_Sign_shift;
                const _Uint_type _Right_sign = _Right_shifted_sign >> _Traits::_Sign_shift;

                const _Uint_type _Left_xor  = _Left_shifted_sign - _Left_sign;
                const _Uint_type _Right_xor = _Right_shifted_sign - _Right_sign;

                const _Uint_type _Left_ones_complement_uint  = _Left_uint ^ _Left_xor;
                const _Uint_type _Right_ones_complement_uint = _Right_uint ^ _Right_xor;

                const auto _Left_ones_complement  = static_cast<_Sint_type>(_Left_ones_complement_uint);
                const auto _Right_ones_complement = static_cast<_Sint_type>(_Right_ones_complement_uint);

                // 4. Perform the final comparison.
                return _Left_ones_complement <=> _Right_ones_complement;
            } else if constexpr (_Strat == _St::_Three) {
                return static_cast<strong_ordering>(compare_three_way{}(_Left, _Right));
            } else {
                _STL_INTERNAL_STATIC_ASSERT(false); // unexpected strategy
            }
        }
    };
} // namespace _Strong_order

inline namespace _Cpos {
    _EXPORT_STD inline constexpr _Strong_order::_Cpo strong_order;
}

namespace _Weak_order {
#if defined(__clang__) || defined(__EDG__) // TRANSITION, VSO-1681199
    void weak_order() = delete; // Block unqualified name lookup
#else // ^^^ no workaround / workaround vvv
    void weak_order();
#endif // ^^^ workaround ^^^

    template <class _Ty1, class _Ty2>
    concept _Has_ADL = requires(_Ty1& _Left, _Ty2& _Right) {
        static_cast<weak_ordering>(weak_order(_Left, _Right)); // intentional ADL
    };

    template <class _Ty1, class _Ty2>
    concept _Can_compare_three_way =
        requires(_Ty1& _Left, _Ty2& _Right) { static_cast<weak_ordering>(compare_three_way{}(_Left, _Right)); };

    // Throughput optimization: attempting to use _STD strong_order will always select ADL strong_order here.
#if defined(__clang__) || defined(__EDG__) // TRANSITION, VSO-1681199
    void strong_order() = delete; // Block unqualified name lookup
#else // ^^^ no workaround / workaround vvv
    void strong_order();
#endif // ^^^ workaround ^^^

    class _Cpo {
    private:
        enum class _St { _None, _Adl, _Floating, _Three, _Strong };

        template <class _Ty1, class _Ty2>
        _NODISCARD static consteval _Choice_t<_St> _Choose() noexcept {
            if constexpr (!same_as<decay_t<_Ty1>, decay_t<_Ty2>>) {
                return {_St::_None};
            } else if constexpr (_Has_ADL<_Ty1, _Ty2>) {
                return {_St::_Adl, noexcept(static_cast<weak_ordering>(
                                       weak_order(_STD declval<_Ty1&>(), _STD declval<_Ty2&>())))}; // intentional ADL
            } else if constexpr (floating_point<decay_t<_Ty1>>) {
                return {_St::_Floating, true};
            } else if constexpr (_Can_compare_three_way<_Ty1, _Ty2>) {
                return {_St::_Three, noexcept(static_cast<weak_ordering>(
                                         compare_three_way{}(_STD declval<_Ty1&>(), _STD declval<_Ty2&>())))};
            } else if constexpr (_Strong_order::_Has_ADL<_Ty1, _Ty2>) {
                // throughput optimization (see above):
                return {_St::_Strong, noexcept(static_cast<weak_ordering>(static_cast<strong_ordering>(strong_order(
                                          _STD declval<_Ty1&>(), _STD declval<_Ty2&>()))))}; // intentional ADL
            } else {
                return {_St::_None};
            }
        }

        template <class _Ty1, class _Ty2>
        static constexpr _Choice_t<_St> _Choice = _Choose<_Ty1, _Ty2>();

    public:
        template <class _Ty1, class _Ty2>
            requires (_Choice<_Ty1&, _Ty2&>._Strategy != _St::_None)
        _NODISCARD _STATIC_CALL_OPERATOR constexpr weak_ordering operator()(
            _Ty1&& _Left, _Ty2&& _Right) _CONST_CALL_OPERATOR noexcept(_Choice<_Ty1&, _Ty2&>._No_throw) {
            constexpr _St _Strat = _Choice<_Ty1&, _Ty2&>._Strategy;
            if constexpr (_Strat == _St::_Adl) {
                return static_cast<weak_ordering>(weak_order(_Left, _Right)); // intentional ADL
            } else if constexpr (_Strat == _St::_Floating) {
                using _Floating_type = decay_t<_Ty1>;
                using _Traits        = _Floating_type_traits<_Floating_type>;
                using _Uint_type     = _Traits::_Uint_type;
                using _Sint_type     = make_signed_t<_Uint_type>;

                auto _Left_uint  = _Bit_cast<_Uint_type>(_Left);
                auto _Right_uint = _Bit_cast<_Uint_type>(_Right);

                // 1. Ultra-fast path: equal representations are equivalent.
                if (_Left_uint == _Right_uint) {
                    return weak_ordering::equivalent;
                }

                // 2. Examine the sign bits.
                const _Uint_type _Left_shifted_sign  = _Left_uint & _Traits::_Shifted_sign_mask;
                const _Uint_type _Right_shifted_sign = _Right_uint & _Traits::_Shifted_sign_mask;

                // 3. Fold all NaN values together.
                // (The fact that _Infinity_plus_one represents a signaling NaN is irrelevant here.)
                constexpr _Uint_type _Infinity_plus_one = _Traits::_Shifted_exponent_mask + 1;

                const _Uint_type _Left_magnitude  = _Left_uint & ~_Traits::_Shifted_sign_mask;
                const _Uint_type _Right_magnitude = _Right_uint & ~_Traits::_Shifted_sign_mask;

                if (_Left_magnitude > _Infinity_plus_one) {
                    _Left_uint = _Left_shifted_sign | _Infinity_plus_one;
                }

                if (_Right_magnitude > _Infinity_plus_one) {
                    _Right_uint = _Right_shifted_sign | _Infinity_plus_one;
                }

                // 4. Interpret floating-point bit patterns as sign magnitude representations of integers,
                //    and then transform them into two's complement representation.
                // (Two's complement representations of positive zero and negative zero are the same.)
                const _Uint_type _Left_sign  = _Left_shifted_sign >> _Traits::_Sign_shift;
                const _Uint_type _Right_sign = _Right_shifted_sign >> _Traits::_Sign_shift;

                const _Uint_type _Left_xor  = _Left_shifted_sign - _Left_sign;
                const _Uint_type _Right_xor = _Right_shifted_sign - _Right_sign;

                const _Uint_type _Left_twos_complement_uint  = (_Left_uint ^ _Left_xor) + _Left_sign;
                const _Uint_type _Right_twos_complement_uint = (_Right_uint ^ _Right_xor) + _Right_sign;

                const auto _Left_twos_complement  = static_cast<_Sint_type>(_Left_twos_complement_uint);
                const auto _Right_twos_complement = static_cast<_Sint_type>(_Right_twos_complement_uint);

                // 5. Perform the final comparison.
                return static_cast<weak_ordering>(_Left_twos_complement <=> _Right_twos_complement);
            } else if constexpr (_Strat == _St::_Three) {
                return static_cast<weak_ordering>(compare_three_way{}(_Left, _Right));
            } else if constexpr (_Strat == _St::_Strong) {
                // throughput optimization (see above):
                return static_cast<weak_ordering>(
                    static_cast<strong_ordering>(strong_order(_Left, _Right))); // intentional ADL
            } else {
                _STL_INTERNAL_STATIC_ASSERT(false); // unexpected strategy
            }
        }
    };
} // namespace _Weak_order

inline namespace _Cpos {
    _EXPORT_STD inline constexpr _Weak_order::_Cpo weak_order;
}

namespace _Partial_order {
#if defined(__clang__) || defined(__EDG__) // TRANSITION, VSO-1681199
    void partial_order() = delete; // Block unqualified name lookup
#else // ^^^ no workaround / workaround vvv
    void partial_order();
#endif // ^^^ workaround ^^^

    template <class _Ty1, class _Ty2>
    concept _Has_ADL = requires(_Ty1& _Left, _Ty2& _Right) {
        static_cast<partial_ordering>(partial_order(_Left, _Right)); // intentional ADL
    };

    template <class _Ty1, class _Ty2>
    concept _Can_compare_three_way =
        requires(_Ty1& _Left, _Ty2& _Right) { static_cast<partial_ordering>(compare_three_way{}(_Left, _Right)); };

    // Throughput optimization: attempting to use _STD weak_order
    // will attempt to select ADL weak_order, followed by ADL strong_order, here.
#if defined(__clang__) || defined(__EDG__) // TRANSITION, VSO-1681199
    void weak_order()   = delete; // Block unqualified name lookup
    void strong_order() = delete; // Block unqualified name lookup
#else // ^^^ no workaround / workaround vvv
    void weak_order();
    void strong_order();
#endif // ^^^ workaround ^^^

    class _Cpo {
    private:
        enum class _St { _None, _Adl, _Three, _Weak, _Strong };

        template <class _Ty1, class _Ty2>
        _NODISCARD static consteval _Choice_t<_St> _Choose() noexcept {
            if constexpr (!same_as<decay_t<_Ty1>, decay_t<_Ty2>>) {
                return {_St::_None};
            } else if constexpr (_Has_ADL<_Ty1, _Ty2>) {
                return {_St::_Adl, noexcept(static_cast<partial_ordering>(partial_order(
                                       _STD declval<_Ty1&>(), _STD declval<_Ty2&>())))}; // intentional ADL
            } else if constexpr (_Can_compare_three_way<_Ty1, _Ty2>) {
                return {_St::_Three, noexcept(static_cast<partial_ordering>(
                                         compare_three_way{}(_STD declval<_Ty1&>(), _STD declval<_Ty2&>())))};
            } else if constexpr (_Weak_order::_Has_ADL<_Ty1, _Ty2>) {
                // throughput optimization (see above):
                return {_St::_Weak, noexcept(static_cast<partial_ordering>(static_cast<weak_ordering>(
                                        weak_order(_STD declval<_Ty1&>(), _STD declval<_Ty2&>()))))}; // intentional ADL
            } else if constexpr (_Strong_order::_Has_ADL<_Ty1, _Ty2>) {
                // throughput optimization (see above):
                return {_St::_Strong, noexcept(static_cast<partial_ordering>(static_cast<strong_ordering>(strong_order(
                                          _STD declval<_Ty1&>(), _STD declval<_Ty2&>()))))}; // intentional ADL
            } else {
                return {_St::_None};
            }
        }

        template <class _Ty1, class _Ty2>
        static constexpr _Choice_t<_St> _Choice = _Choose<_Ty1, _Ty2>();

    public:
        template <class _Ty1, class _Ty2>
            requires (_Choice<_Ty1&, _Ty2&>._Strategy != _St::_None)
        _NODISCARD _STATIC_CALL_OPERATOR constexpr partial_ordering operator()(
            _Ty1&& _Left, _Ty2&& _Right) _CONST_CALL_OPERATOR noexcept(_Choice<_Ty1&, _Ty2&>._No_throw) {
            constexpr _St _Strat = _Choice<_Ty1&, _Ty2&>._Strategy;
            if constexpr (_Strat == _St::_Adl) {
                return static_cast<partial_ordering>(/* ADL */ partial_order(_Left, _Right));
            } else if constexpr (_Strat == _St::_Three) {
                return static_cast<partial_ordering>(compare_three_way{}(_Left, _Right));
            } else if constexpr (_Strat == _St::_Weak) {
                // throughput optimization (see above):
                return static_cast<partial_ordering>(
                    static_cast<weak_ordering>(weak_order(_Left, _Right))); // intentional ADL
            } else if constexpr (_Strat == _St::_Strong) {
                // throughput optimization (see above):
                return static_cast<partial_ordering>(
                    static_cast<strong_ordering>(strong_order(_Left, _Right))); // intentional ADL
            } else {
                _STL_INTERNAL_STATIC_ASSERT(false); // unexpected strategy
            }
        }
    };
} // namespace _Partial_order

inline namespace _Cpos {
    _EXPORT_STD inline constexpr _Partial_order::_Cpo partial_order;
}

template <class _Ty1, class _Ty2>
concept _Can_fallback_eq_lt = requires(_Ty1& _Left, _Ty2& _Right) {
    { _Left == _Right } -> _Boolean_testable;
    { _Left < _Right } -> _Boolean_testable;
};

template <class _Ty1, class _Ty2>
concept _Can_strong_order = requires(_Ty1& _Left, _Ty2& _Right) { _STD strong_order(_Left, _Right); };

namespace _Compare_strong_order_fallback {
    class _Cpo {
    private:
        enum class _St { _None, _Strong, _Fallback };

        template <class _Ty1, class _Ty2>
        _NODISCARD static consteval _Choice_t<_St> _Choose() noexcept {
            if constexpr (!same_as<decay_t<_Ty1>, decay_t<_Ty2>>) {
                return {_St::_None};
            } else if constexpr (_Can_strong_order<_Ty1, _Ty2>) {
                return {_St::_Strong, noexcept(_STD strong_order(_STD declval<_Ty1&>(), _STD declval<_Ty2&>()))};
            } else if constexpr (_Can_fallback_eq_lt<_Ty1, _Ty2>) {
                return {_St::_Fallback,
                    noexcept(_STD declval<_Ty1&>() == _STD declval<_Ty2&>()  ? strong_ordering::equal
                             : _STD declval<_Ty1&>() < _STD declval<_Ty2&>() ? strong_ordering::less
                                                                             : strong_ordering::greater)};
            } else {
                return {_St::_None};
            }
        }

        template <class _Ty1, class _Ty2>
        static constexpr _Choice_t<_St> _Choice = _Choose<_Ty1, _Ty2>();

    public:
        template <class _Ty1, class _Ty2>
            requires (_Choice<_Ty1&, _Ty2&>._Strategy != _St::_None)
        _NODISCARD _STATIC_CALL_OPERATOR constexpr strong_ordering operator()(
            _Ty1&& _Left, _Ty2&& _Right) _CONST_CALL_OPERATOR noexcept(_Choice<_Ty1&, _Ty2&>._No_throw) {
            constexpr _St _Strat = _Choice<_Ty1&, _Ty2&>._Strategy;
            if constexpr (_Strat == _St::_Strong) {
                return _STD strong_order(_Left, _Right);
            } else if constexpr (_Strat == _St::_Fallback) {
                return _Left == _Right ? strong_ordering::equal
                     : _Left < _Right  ? strong_ordering::less
                                       : strong_ordering::greater;
            } else {
                _STL_INTERNAL_STATIC_ASSERT(false); // unexpected strategy
            }
        }
    };
} // namespace _Compare_strong_order_fallback

inline namespace _Cpos {
    _EXPORT_STD inline constexpr _Compare_strong_order_fallback::_Cpo compare_strong_order_fallback;
}

template <class _Ty1, class _Ty2>
concept _Can_weak_order = requires(_Ty1& _Left, _Ty2& _Right) { _STD weak_order(_Left, _Right); };

namespace _Compare_weak_order_fallback {
    class _Cpo {
    private:
        enum class _St { _None, _Weak, _Fallback };

        template <class _Ty1, class _Ty2>
        _NODISCARD static consteval _Choice_t<_St> _Choose() noexcept {
            if constexpr (!same_as<decay_t<_Ty1>, decay_t<_Ty2>>) {
                return {_St::_None};
            } else if constexpr (_Can_weak_order<_Ty1, _Ty2>) {
                return {_St::_Weak, noexcept(_STD weak_order(_STD declval<_Ty1&>(), _STD declval<_Ty2&>()))};
            } else if constexpr (_Can_fallback_eq_lt<_Ty1, _Ty2>) {
                return {
                    _St::_Fallback, noexcept(_STD declval<_Ty1&>() == _STD declval<_Ty2&>()  ? weak_ordering::equivalent
                                             : _STD declval<_Ty1&>() < _STD declval<_Ty2&>() ? weak_ordering::less
                                                                                             : weak_ordering::greater)};
            } else {
                return {_St::_None};
            }
        }

        template <class _Ty1, class _Ty2>
        static constexpr _Choice_t<_St> _Choice = _Choose<_Ty1, _Ty2>();

    public:
        template <class _Ty1, class _Ty2>
            requires (_Choice<_Ty1&, _Ty2&>._Strategy != _St::_None)
        _NODISCARD _STATIC_CALL_OPERATOR constexpr weak_ordering operator()(
            _Ty1&& _Left, _Ty2&& _Right) _CONST_CALL_OPERATOR noexcept(_Choice<_Ty1&, _Ty2&>._No_throw) {
            constexpr _St _Strat = _Choice<_Ty1&, _Ty2&>._Strategy;
            if constexpr (_Strat == _St::_Weak) {
                return _STD weak_order(_Left, _Right);
            } else if constexpr (_Strat == _St::_Fallback) {
                return _Left == _Right ? weak_ordering::equivalent
                     : _Left < _Right  ? weak_ordering::less
                                       : weak_ordering::greater;
            } else {
                _STL_INTERNAL_STATIC_ASSERT(false); // unexpected strategy
            }
        }
    };
} // namespace _Compare_weak_order_fallback

inline namespace _Cpos {
    _EXPORT_STD inline constexpr _Compare_weak_order_fallback::_Cpo compare_weak_order_fallback;
}

template <class _Ty1, class _Ty2>
concept _Can_partial_order = requires(_Ty1& _Left, _Ty2& _Right) { _STD partial_order(_Left, _Right); };

namespace _Compare_partial_order_fallback {
    template <class _Ty1, class _Ty2>
    concept _Can_fallback_eq_lt_twice = requires(_Ty1& _Left, _Ty2& _Right) {
        { _Left == _Right } -> _Boolean_testable;
        { _Left < _Right } -> _Boolean_testable;
        { _Right < _Left } -> _Boolean_testable;
    };

    class _Cpo {
    private:
        enum class _St { _None, _Partial, _Fallback };

        template <class _Ty1, class _Ty2>
        _NODISCARD static consteval _Choice_t<_St> _Choose() noexcept {
            if constexpr (!same_as<decay_t<_Ty1>, decay_t<_Ty2>>) {
                return {_St::_None};
            } else if constexpr (_Can_partial_order<_Ty1, _Ty2>) {
                return {_St::_Partial, noexcept(_STD partial_order(_STD declval<_Ty1&>(), _STD declval<_Ty2&>()))};
            } else if constexpr (_Can_fallback_eq_lt_twice<_Ty1, _Ty2>) {
                return {_St::_Fallback,
                    noexcept(_STD declval<_Ty1&>() == _STD declval<_Ty2&>()  ? partial_ordering::equivalent
                             : _STD declval<_Ty1&>() < _STD declval<_Ty2&>() ? partial_ordering::less
                             : _STD declval<_Ty2&>() < _STD declval<_Ty1&>() ? partial_ordering::greater
                                                                             : partial_ordering::unordered)};
            } else {
                return {_St::_None};
            }
        }

        template <class _Ty1, class _Ty2>
        static constexpr _Choice_t<_St> _Choice = _Choose<_Ty1, _Ty2>();

    public:
        template <class _Ty1, class _Ty2>
            requires (_Choice<_Ty1&, _Ty2&>._Strategy != _St::_None)
        _NODISCARD _STATIC_CALL_OPERATOR constexpr partial_ordering operator()(
            _Ty1&& _Left, _Ty2&& _Right) _CONST_CALL_OPERATOR noexcept(_Choice<_Ty1&, _Ty2&>._No_throw) {
            constexpr _St _Strat = _Choice<_Ty1&, _Ty2&>._Strategy;
            if constexpr (_Strat == _St::_Partial) {
                return _STD partial_order(_Left, _Right);
            } else if constexpr (_Strat == _St::_Fallback) {
                return _Left == _Right ? partial_ordering::equivalent
                     : _Left < _Right  ? partial_ordering::less
                     : _Right < _Left  ? partial_ordering::greater
                                       : partial_ordering::unordered;
            } else {
                _STL_INTERNAL_STATIC_ASSERT(false); // unexpected strategy
            }
        }
    };
} // namespace _Compare_partial_order_fallback

inline namespace _Cpos {
    _EXPORT_STD inline constexpr _Compare_partial_order_fallback::_Cpo compare_partial_order_fallback;
}
_STD_END

#pragma pop_macro("new")
_STL_RESTORE_CLANG_WARNINGS
#pragma warning(pop)
#pragma pack(pop)
#endif // _HAS_CXX20

#endif // _STL_COMPILER_PREPROCESSOR
#endif // _COMPARE_
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