compare

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// -*- C++ -*- operator<=> three-way comparison support.
 
// Copyright (C) 2019-2020 Free Software Foundation, Inc.
//
// This file is part of GCC.
//
// GCC is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3, or (at your option)
// any later version.
//
// GCC is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/** @file compare
 *  This is a Standard C++ Library header.
 */
 
#ifndef _COMPARE
#define _COMPARE
 
#pragma GCC system_header
 
#if __cplusplus > 201703L && __cpp_impl_three_way_comparison >= 201907L
 
#pragma GCC visibility push(default)
 
#include <concepts>
 
#if __cpp_lib_concepts
# define __cpp_lib_three_way_comparison 201907L
#endif
 
namespace std
{
  // [cmp.categories], comparison category types
 
  namespace __cmp_cat
  {
    using type = signed char;
 
    enum class _Ord : type { equivalent = 0, less = -1, greater = 1 };
 
    enum class _Ncmp : type { _Unordered = 2 };
 
    struct __unspec
    {
      constexpr __unspec(__unspec*) noexcept { }
    };
  }
 
  class partial_ordering
  {
    // less=0xff, equiv=0x00, greater=0x01, unordered=0x02
    __cmp_cat::type _M_value;
 
    constexpr explicit
    partial_ordering(__cmp_cat::_Ord __v) noexcept
    : _M_value(__cmp_cat::type(__v))
    { }
 
    constexpr explicit
    partial_ordering(__cmp_cat::_Ncmp __v) noexcept
    : _M_value(__cmp_cat::type(__v))
    { }
 
    friend class weak_ordering;
    friend class strong_ordering;
 
  public:
    // valid values
    static const partial_ordering less;
    static const partial_ordering equivalent;
    static const partial_ordering greater;
    static const partial_ordering unordered;
 
    // comparisons
    friend constexpr bool
    operator==(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 0; }
 
    friend constexpr bool
    operator==(partial_ordering, partial_ordering) noexcept = default;
 
    friend constexpr bool
    operator< (partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == -1; }
 
    friend constexpr bool
    operator> (partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 1; }
 
    friend constexpr bool
    operator<=(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value <= 0; }
 
    friend constexpr bool
    operator>=(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __cmp_cat::type(__v._M_value & 1) == __v._M_value; }
 
    friend constexpr bool
    operator< (__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return __v._M_value == 1; }
 
    friend constexpr bool
    operator> (__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return __v._M_value == -1; }
 
    friend constexpr bool
    operator<=(__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return __cmp_cat::type(__v._M_value & 1) == __v._M_value; }
 
    friend constexpr bool
    operator>=(__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return 0 >= __v._M_value; }
 
    friend constexpr partial_ordering
    operator<=>(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v; }
 
    friend constexpr partial_ordering
    operator<=>(__cmp_cat::__unspec, partial_ordering __v) noexcept
    {
      if (__v._M_value & 1)
        return partial_ordering(__cmp_cat::_Ord(-__v._M_value));
      else
        return __v;
    }
  };
 
  // valid values' definitions
  inline constexpr partial_ordering
  partial_ordering::less(__cmp_cat::_Ord::less);
 
  inline constexpr partial_ordering
  partial_ordering::equivalent(__cmp_cat::_Ord::equivalent);
 
  inline constexpr partial_ordering
  partial_ordering::greater(__cmp_cat::_Ord::greater);
 
  inline constexpr partial_ordering
  partial_ordering::unordered(__cmp_cat::_Ncmp::_Unordered);
 
  class weak_ordering
  {
    __cmp_cat::type _M_value;
 
    constexpr explicit
    weak_ordering(__cmp_cat::_Ord __v) noexcept : _M_value(__cmp_cat::type(__v))
    { }
 
    friend class strong_ordering;
 
  public:
    // valid values
    static const weak_ordering less;
    static const weak_ordering equivalent;
    static const weak_ordering greater;
 
    constexpr operator partial_ordering() const noexcept
    { return partial_ordering(__cmp_cat::_Ord(_M_value)); }
 
    // comparisons
    friend constexpr bool
    operator==(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 0; }
 
    friend constexpr bool
    operator==(weak_ordering, weak_ordering) noexcept = default;
 
    friend constexpr bool
    operator< (weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value < 0; }
 
    friend constexpr bool
    operator> (weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value > 0; }
 
    friend constexpr bool
    operator<=(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value <= 0; }
 
    friend constexpr bool
    operator>=(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value >= 0; }
 
    friend constexpr bool
    operator< (__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 < __v._M_value; }
 
    friend constexpr bool
    operator> (__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 > __v._M_value; }
 
    friend constexpr bool
    operator<=(__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 <= __v._M_value; }
 
    friend constexpr bool
    operator>=(__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 >= __v._M_value; }
 
    friend constexpr weak_ordering
    operator<=>(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v; }
 
    friend constexpr weak_ordering
    operator<=>(__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return weak_ordering(__cmp_cat::_Ord(-__v._M_value)); }
  };
 
  // valid values' definitions
  inline constexpr weak_ordering
  weak_ordering::less(__cmp_cat::_Ord::less);
 
  inline constexpr weak_ordering
  weak_ordering::equivalent(__cmp_cat::_Ord::equivalent);
 
  inline constexpr weak_ordering
  weak_ordering::greater(__cmp_cat::_Ord::greater);
 
  class strong_ordering
  {
    __cmp_cat::type _M_value;
 
    constexpr explicit
    strong_ordering(__cmp_cat::_Ord __v) noexcept
    : _M_value(__cmp_cat::type(__v))
    { }
 
  public:
    // valid values
    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 partial_ordering(__cmp_cat::_Ord(_M_value)); }
 
    constexpr operator weak_ordering() const noexcept
    { return weak_ordering(__cmp_cat::_Ord(_M_value)); }
 
    // comparisons
    friend constexpr bool
    operator==(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 0; }
 
    friend constexpr bool
    operator==(strong_ordering, strong_ordering) noexcept = default;
 
    friend constexpr bool
    operator< (strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value < 0; }
 
    friend constexpr bool
    operator> (strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value > 0; }
 
    friend constexpr bool
    operator<=(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value <= 0; }
 
    friend constexpr bool
    operator>=(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value >= 0; }
 
    friend constexpr bool
    operator< (__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 < __v._M_value; }
 
    friend constexpr bool
    operator> (__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 > __v._M_value; }
 
    friend constexpr bool
    operator<=(__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 <= __v._M_value; }
 
    friend constexpr bool
    operator>=(__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 >= __v._M_value; }
 
    friend constexpr strong_ordering
    operator<=>(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v; }
 
    friend constexpr strong_ordering
    operator<=>(__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return strong_ordering(__cmp_cat::_Ord(-__v._M_value)); }
  };
 
  // valid values' definitions
  inline constexpr strong_ordering
  strong_ordering::less(__cmp_cat::_Ord::less);
 
  inline constexpr strong_ordering
  strong_ordering::equal(__cmp_cat::_Ord::equivalent);
 
  inline constexpr strong_ordering
  strong_ordering::equivalent(__cmp_cat::_Ord::equivalent);
 
  inline constexpr strong_ordering
  strong_ordering::greater(__cmp_cat::_Ord::greater);
 
 
  // named comparison functions
  constexpr bool
  is_eq(partial_ordering __cmp) noexcept
  { return __cmp == 0; }
 
  constexpr bool
  is_neq(partial_ordering __cmp) noexcept
  { return __cmp != 0; }
 
  constexpr bool
  is_lt  (partial_ordering __cmp) noexcept
  { return __cmp < 0; }
 
  constexpr bool
  is_lteq(partial_ordering __cmp) noexcept
  { return __cmp <= 0; }
 
  constexpr bool
  is_gt  (partial_ordering __cmp) noexcept
  { return __cmp > 0; }
 
  constexpr bool
  is_gteq(partial_ordering __cmp) noexcept
  { return __cmp >= 0; }
 
  namespace __detail
  {
    template<typename _Tp>
      inline constexpr unsigned __cmp_cat_id = 1;
    template<>
      inline constexpr unsigned __cmp_cat_id<partial_ordering> = 2;
    template<>
      inline constexpr unsigned __cmp_cat_id<weak_ordering> = 4;
    template<>
      inline constexpr unsigned __cmp_cat_id<strong_ordering> = 8;
 
    template<typename... _Ts>
      constexpr auto __common_cmp_cat()
      {
        constexpr unsigned __cats = (__cmp_cat_id<_Ts> | ...);
        // If any Ti is not a comparison category type, U is void.
        if constexpr (__cats & 1)
          return;
        // Otherwise, if at least one Ti is std::partial_ordering,
        // U is std::partial_ordering.
        else if constexpr (bool(__cats & __cmp_cat_id<partial_ordering>))
          return partial_ordering::equivalent;
        // Otherwise, if at least one Ti is std::weak_ordering,
        // U is std::weak_ordering.
        else if constexpr (bool(__cats & __cmp_cat_id<weak_ordering>))
          return weak_ordering::equivalent;
        // Otherwise, U is std::strong_ordering.
        else
          return strong_ordering::equivalent;
      }
  } // namespace __detail
 
  // [cmp.common], common comparison category type
  template<typename... _Ts>
    struct common_comparison_category
    {
      using type = decltype(__detail::__common_cmp_cat<_Ts...>());
    };
 
  // Partial specializations for one and zero argument cases.
 
  template<typename _Tp>
    struct common_comparison_category<_Tp>
    { using type = void; };
 
  template<>
    struct common_comparison_category<partial_ordering>
    { using type = partial_ordering; };
 
  template<>
    struct common_comparison_category<weak_ordering>
    { using type = weak_ordering; };
 
  template<>
    struct common_comparison_category<strong_ordering>
    { using type = strong_ordering; };
 
  template<>
    struct common_comparison_category<>
    { using type = strong_ordering; };
 
  template<typename... _Ts>
    using common_comparison_category_t
      = typename common_comparison_category<_Ts...>::type;
 
#if __cpp_lib_concepts
  namespace __detail
  {
    template<typename _Tp, typename _Cat>
      concept __compares_as
        = same_as<common_comparison_category_t<_Tp, _Cat>, _Cat>;
  } // namespace __detail
 
  // [cmp.concept], concept three_way_comparable
  template<typename _Tp, typename _Cat = partial_ordering>
    concept three_way_comparable
      = __detail::__weakly_eq_cmp_with<_Tp, _Tp>
      && __detail::__partially_ordered_with<_Tp, _Tp>
      && requires(const remove_reference_t<_Tp>& __a,
                  const remove_reference_t<_Tp>& __b)
      {
        { __a <=> __b } -> __detail::__compares_as<_Cat>;
      };
 
  template<typename _Tp, typename _Up, typename _Cat = partial_ordering>
    concept three_way_comparable_with
      = three_way_comparable<_Tp, _Cat>
      && three_way_comparable<_Up, _Cat>
      && common_reference_with<const remove_reference_t<_Tp>&,
                               const remove_reference_t<_Up>&>
      && three_way_comparable<
          common_reference_t<const remove_reference_t<_Tp>&,
                             const remove_reference_t<_Up>&>, _Cat>
      && __detail::__weakly_eq_cmp_with<_Tp, _Up>
      && __detail::__partially_ordered_with<_Tp, _Up>
      && requires(const remove_reference_t<_Tp>& __t,
                  const remove_reference_t<_Up>& __u)
      {
        { __t <=> __u } -> __detail::__compares_as<_Cat>;
        { __u <=> __t } -> __detail::__compares_as<_Cat>;
      };
 
  namespace __detail
  {
    template<typename _Tp, typename _Up>
      using __cmp3way_res_t
        = decltype(std::declval<_Tp>() <=> std::declval<_Up>());
 
    // Implementation of std::compare_three_way_result.
    // It is undefined for a program to add specializations of
    // std::compare_three_way_result, so the std::compare_three_way_result_t
    // alias ignores std::compare_three_way_result and uses
    // __detail::__cmp3way_res_impl directly instead.
    template<typename _Tp, typename _Up>
      struct __cmp3way_res_impl
      { };
 
    template<typename _Tp, typename _Up>
      requires requires { typename __cmp3way_res_t<__cref<_Tp>, __cref<_Up>>; }
      struct __cmp3way_res_impl<_Tp, _Up>
      {
        using type = __cmp3way_res_t<__cref<_Tp>, __cref<_Up>>;
      };
  } // namespace __detail
 
  /// [cmp.result], result of three-way comparison
  template<typename _Tp, typename _Up = _Tp>
    struct compare_three_way_result
    : __detail::__cmp3way_res_impl<_Tp, _Up>
    { };
 
  /// [cmp.result], result of three-way comparison
  template<typename _Tp, typename _Up = _Tp>
    using compare_three_way_result_t
      = typename __detail::__cmp3way_res_impl<_Tp, _Up>::type;
 
  namespace __detail
  {
    // BUILTIN-PTR-THREE-WAY(T, U)
    // This determines whether t <=> u results in a call to a built-in
    // operator<=> comparing pointers. It doesn't work for function pointers
    // (PR 93628).
    template<typename _Tp, typename _Up>
      concept __3way_builtin_ptr_cmp
        = requires(_Tp&& __t, _Up&& __u)
          { static_cast<_Tp&&>(__t) <=> static_cast<_Up&&>(__u); }
          && convertible_to<_Tp, const volatile void*>
          && convertible_to<_Up, const volatile void*>
          && ! requires(_Tp&& __t, _Up&& __u)
          { operator<=>(static_cast<_Tp&&>(__t), static_cast<_Up&&>(__u)); }
          && ! requires(_Tp&& __t, _Up&& __u)
          { static_cast<_Tp&&>(__t).operator<=>(static_cast<_Up&&>(__u)); };
  } // namespace __detail
 
  // _GLIBCXX_RESOLVE_LIB_DEFECTS
  // 3530 BUILTIN-PTR-MEOW should not opt the type out of syntactic checks
 
  // [cmp.object], typename compare_three_way
  struct compare_three_way
  {
    template<typename _Tp, typename _Up>
      requires three_way_comparable_with<_Tp, _Up>
      constexpr auto
      operator()(_Tp&& __t, _Up&& __u) const
      noexcept(noexcept(std::declval<_Tp>() <=> std::declval<_Up>()))
      {
        if constexpr (__detail::__3way_builtin_ptr_cmp<_Tp, _Up>)
          {
            auto __pt = static_cast<const volatile void*>(__t);
            auto __pu = static_cast<const volatile void*>(__u);
            if (__builtin_is_constant_evaluated())
              return __pt <=> __pu;
            auto __it = reinterpret_cast<__UINTPTR_TYPE__>(__pt);
            auto __iu = reinterpret_cast<__UINTPTR_TYPE__>(__pu);
            return __it <=> __iu;
          }
        else
          return static_cast<_Tp&&>(__t) <=> static_cast<_Up&&>(__u);
      }
 
    using is_transparent = void;
  };
 
  namespace __cmp_cust
  {
    template<floating_point _Tp>
      constexpr weak_ordering
      __fp_weak_ordering(_Tp __e, _Tp __f)
      {
        // Returns an integer with the same sign as the argument, and magnitude
        // indicating the classification: zero=1 subnorm=2 norm=3 inf=4 nan=5
        auto __cat = [](_Tp __fp) -> int {
          const int __sign = __builtin_signbit(__fp) ? -1 : 1;
          if (__builtin_isnormal(__fp))
            return (__fp == 0 ? 1 : 3) * __sign;
          if (__builtin_isnan(__fp))
            return 5 * __sign;
          if (int __inf = __builtin_isinf_sign(__fp))
            return 4 * __inf;
          return 2 * __sign;
        };
 
        auto __po = __e <=> __f;
        if (is_lt(__po))
          return weak_ordering::less;
        else if (is_gt(__po))
          return weak_ordering::greater;
        else if (__po == partial_ordering::equivalent)
          return weak_ordering::equivalent;
        else  // unordered, at least one argument is NaN
          {
            // return -1 for negative nan, +1 for positive nan, 0 otherwise.
            auto __isnan_sign = [](_Tp __fp) -> int {
              return __builtin_isnan(__fp)
                ? __builtin_signbit(__fp) ? -1 : 1
                : 0;
            };
            auto __ord = __isnan_sign(__e) <=> __isnan_sign(__f);
            if (is_eq(__ord))
              return weak_ordering::equivalent;
            else if (is_lt(__ord))
              return weak_ordering::less;
            else
              return weak_ordering::greater;
          }
      }
 
    template<typename _Tp, typename _Up>
      concept __adl_strong = requires(_Tp&& __t, _Up&& __u)
        {
          strong_ordering(strong_order(static_cast<_Tp&&>(__t),
                                       static_cast<_Up&&>(__u)));
        };
 
    template<typename _Tp, typename _Up>
      concept __adl_weak = requires(_Tp&& __t, _Up&& __u)
        {
          weak_ordering(weak_order(static_cast<_Tp&&>(__t),
                                   static_cast<_Up&&>(__u)));
        };
 
    template<typename _Tp, typename _Up>
      concept __adl_partial = requires(_Tp&& __t, _Up&& __u)
        {
          partial_ordering(partial_order(static_cast<_Tp&&>(__t),
                                         static_cast<_Up&&>(__u)));
        };
 
    template<typename _Ord, typename _Tp, typename _Up>
      concept __cmp3way = requires(_Tp&& __t, _Up&& __u, compare_three_way __c)
        {
          _Ord(__c(static_cast<_Tp&&>(__t), static_cast<_Up&&>(__u)));
        };
 
    template<typename _Tp, typename _Up>
      concept __strongly_ordered
        = __adl_strong<_Tp, _Up>
          // FIXME: || floating_point<remove_reference_t<_Tp>>
          || __cmp3way<strong_ordering, _Tp, _Up>;
 
    template<typename _Tp, typename _Up>
      concept __decayed_same_as = same_as<decay_t<_Tp>, decay_t<_Up>>;
 
    class _Strong_order
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept()
        {
          if constexpr (floating_point<decay_t<_Tp>>)
            return true;
          else if constexpr (__adl_strong<_Tp, _Up>)
            return noexcept(strong_ordering(strong_order(std::declval<_Tp>(),
                                                         std::declval<_Up>())));
          else if constexpr (__cmp3way<strong_ordering, _Tp, _Up>)
            return noexcept(compare_three_way()(std::declval<_Tp>(),
                                                std::declval<_Up>()));
        }
 
      friend class _Weak_order;
      friend class _Strong_fallback;
 
    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
        requires __strongly_ordered<_Tp, _Up>
        constexpr strong_ordering
        operator()(_Tp&& __e, _Up&& __f) const
        noexcept(_S_noexcept<_Tp, _Up>())
        {
          /* FIXME:
          if constexpr (floating_point<decay_t<_Tp>>)
            return __cmp_cust::__fp_strong_order(__e, __f);
          else */ if constexpr (__adl_strong<_Tp, _Up>)
            return strong_ordering(strong_order(static_cast<_Tp&&>(__e),
                                                static_cast<_Up&&>(__f)));
          else if constexpr (__cmp3way<strong_ordering, _Tp, _Up>)
            return compare_three_way()(static_cast<_Tp&&>(__e),
                                       static_cast<_Up&&>(__f));
        }
    };
 
    template<typename _Tp, typename _Up>
      concept __weakly_ordered
        = floating_point<remove_reference_t<_Tp>>
          || __adl_weak<_Tp, _Up>
          || __cmp3way<weak_ordering, _Tp, _Up>
          || __strongly_ordered<_Tp, _Up>;
 
    class _Weak_order
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept()
        {
          if constexpr (floating_point<decay_t<_Tp>>)
            return true;
          else if constexpr (__adl_weak<_Tp, _Up>)
            return noexcept(weak_ordering(weak_order(std::declval<_Tp>(),
                                                     std::declval<_Up>())));
          else if constexpr (__cmp3way<weak_ordering, _Tp, _Up>)
            return noexcept(compare_three_way()(std::declval<_Tp>(),
                                                std::declval<_Up>()));
          else if constexpr (__strongly_ordered<_Tp, _Up>)
            return _Strong_order::_S_noexcept<_Tp, _Up>();
        }
 
      friend class _Partial_order;
      friend class _Weak_fallback;
 
    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
        requires __weakly_ordered<_Tp, _Up>
        constexpr weak_ordering
        operator()(_Tp&& __e, _Up&& __f) const
        noexcept(_S_noexcept<_Tp, _Up>())
        {
          if constexpr (floating_point<decay_t<_Tp>>)
            return __cmp_cust::__fp_weak_ordering(__e, __f);
          else if constexpr (__adl_weak<_Tp, _Up>)
            return weak_ordering(weak_order(static_cast<_Tp&&>(__e),
                                            static_cast<_Up&&>(__f)));
          else if constexpr (__cmp3way<weak_ordering, _Tp, _Up>)
            return compare_three_way()(static_cast<_Tp&&>(__e),
                                       static_cast<_Up&&>(__f));
          else if constexpr (__strongly_ordered<_Tp, _Up>)
            return _Strong_order{}(static_cast<_Tp&&>(__e),
                                   static_cast<_Up&&>(__f));
        }
    };
 
    template<typename _Tp, typename _Up>
      concept __partially_ordered
        = __adl_partial<_Tp, _Up>
        || __cmp3way<partial_ordering, _Tp, _Up>
        || __weakly_ordered<_Tp, _Up>;
 
    class _Partial_order
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept()
        {
          if constexpr (__adl_partial<_Tp, _Up>)
            return noexcept(partial_ordering(partial_order(std::declval<_Tp>(),
                                                         std::declval<_Up>())));
          else if constexpr (__cmp3way<partial_ordering, _Tp, _Up>)
            return noexcept(compare_three_way()(std::declval<_Tp>(),
                                                std::declval<_Up>()));
          else if constexpr (__weakly_ordered<_Tp, _Up>)
            return _Weak_order::_S_noexcept<_Tp, _Up>();
        }
 
      friend class _Partial_fallback;
 
    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
        requires __partially_ordered<_Tp, _Up>
        constexpr partial_ordering
        operator()(_Tp&& __e, _Up&& __f) const
        noexcept(_S_noexcept<_Tp, _Up>())
        {
          if constexpr (__adl_partial<_Tp, _Up>)
            return partial_ordering(partial_order(static_cast<_Tp&&>(__e),
                                                  static_cast<_Up&&>(__f)));
          else if constexpr (__cmp3way<partial_ordering, _Tp, _Up>)
            return compare_three_way()(static_cast<_Tp&&>(__e),
                                       static_cast<_Up&&>(__f));
          else if constexpr (__weakly_ordered<_Tp, _Up>)
            return _Weak_order{}(static_cast<_Tp&&>(__e),
                                 static_cast<_Up&&>(__f));
        }
    };
 
    template<typename _Tp, typename _Up>
      concept __op_eq_lt = requires(_Tp&& __t, _Up&& __u)
        {
          { static_cast<_Tp&&>(__t) == static_cast<_Up&&>(__u) }
            -> convertible_to<bool>;
          { static_cast<_Tp&&>(__t) < static_cast<_Up&&>(__u) }
            -> convertible_to<bool>;
        };
 
    class _Strong_fallback
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept()
        {
          if constexpr (__strongly_ordered<_Tp, _Up>)
            return _Strong_order::_S_noexcept<_Tp, _Up>();
          else
            return noexcept(bool(std::declval<_Tp>() == std::declval<_Up>()))
              && noexcept(bool(std::declval<_Tp>() < std::declval<_Up>()));
        }
 
    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
        requires __strongly_ordered<_Tp, _Up> || __op_eq_lt<_Tp, _Up>
        constexpr strong_ordering
        operator()(_Tp&& __e, _Up&& __f) const
        noexcept(_S_noexcept<_Tp, _Up>())
        {
          if constexpr (__strongly_ordered<_Tp, _Up>)
            return _Strong_order{}(static_cast<_Tp&&>(__e),
                                   static_cast<_Up&&>(__f));
          else // __op_eq_lt<_Tp, _Up>
            return static_cast<_Tp&&>(__e) == static_cast<_Up&&>(__f)
              ? strong_ordering::equal
              : static_cast<_Tp&&>(__e) < static_cast<_Up&&>(__f)
              ? strong_ordering::less
              : strong_ordering::greater;
        }
    };
 
    class _Weak_fallback
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept()
        {
          if constexpr (__weakly_ordered<_Tp, _Up>)
            return _Weak_order::_S_noexcept<_Tp, _Up>();
          else
            return noexcept(bool(std::declval<_Tp>() == std::declval<_Up>()))
              && noexcept(bool(std::declval<_Tp>() < std::declval<_Up>()));
        }
 
    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
        requires __weakly_ordered<_Tp, _Up> || __op_eq_lt<_Tp, _Up>
        constexpr weak_ordering
        operator()(_Tp&& __e, _Up&& __f) const
        noexcept(_S_noexcept<_Tp, _Up>())
        {
          if constexpr (__weakly_ordered<_Tp, _Up>)
            return _Weak_order{}(static_cast<_Tp&&>(__e),
                                 static_cast<_Up&&>(__f));
          else // __op_eq_lt<_Tp, _Up>
            return static_cast<_Tp&&>(__e) == static_cast<_Up&&>(__f)
              ? weak_ordering::equivalent
              : static_cast<_Tp&&>(__e) < static_cast<_Up&&>(__f)
              ? weak_ordering::less
              : weak_ordering::greater;
        }
    };
 
    // _GLIBCXX_RESOLVE_LIB_DEFECTS
    // 3465. compare_partial_order_fallback requires F < E
    template<typename _Tp, typename _Up>
      concept __op_eq_lt_lt = __op_eq_lt<_Tp, _Up>
        && requires(_Tp&& __t, _Up&& __u)
        {
          { static_cast<_Up&&>(__u) < static_cast<_Tp&&>(__t) }
            -> convertible_to<bool>;
        };
 
    class _Partial_fallback
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept()
        {
          if constexpr (__partially_ordered<_Tp, _Up>)
            return _Partial_order::_S_noexcept<_Tp, _Up>();
          else
            return noexcept(bool(std::declval<_Tp>() == std::declval<_Up>()))
              && noexcept(bool(std::declval<_Tp>() < std::declval<_Up>()));
        }
 
    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
        requires __partially_ordered<_Tp, _Up> || __op_eq_lt_lt<_Tp, _Up>
        constexpr partial_ordering
        operator()(_Tp&& __e, _Up&& __f) const
        noexcept(_S_noexcept<_Tp, _Up>())
        {
          if constexpr (__partially_ordered<_Tp, _Up>)
            return _Partial_order{}(static_cast<_Tp&&>(__e),
                                    static_cast<_Up&&>(__f));
          else // __op_eq_lt_lt<_Tp, _Up>
            return static_cast<_Tp&&>(__e) == static_cast<_Up&&>(__f)
              ? partial_ordering::equivalent
              : static_cast<_Tp&&>(__e) < static_cast<_Up&&>(__f)
              ? partial_ordering::less
              : static_cast<_Up&&>(__f) < static_cast<_Tp&&>(__e)
              ? partial_ordering::greater
              : partial_ordering::unordered;
        }
    };
  } // namespace __cmp_cust
 
  // [cmp.alg], comparison algorithms
  inline namespace __cmp_alg
  {
    inline constexpr __cmp_cust::_Strong_order strong_order{};
 
    inline constexpr __cmp_cust::_Weak_order weak_order{};
 
    inline constexpr __cmp_cust::_Partial_order partial_order{};
 
    inline constexpr __cmp_cust::_Strong_fallback
    compare_strong_order_fallback{};
 
    inline constexpr __cmp_cust::_Weak_fallback
    compare_weak_order_fallback{};
 
    inline constexpr __cmp_cust::_Partial_fallback
    compare_partial_order_fallback{};
  }
 
  namespace __detail
  {
    // [expos.only.func] synth-three-way
    inline constexpr struct _Synth3way
    {
      template<typename _Tp, typename _Up>
        static constexpr bool
        _S_noexcept(const _Tp* __t = nullptr, const _Up* __u = nullptr)
        {
          if constexpr (three_way_comparable_with<_Tp, _Up>)
            return noexcept(*__t <=> *__u);
          else
            return noexcept(*__t < *__u) && noexcept(*__u < *__t);
        }
 
      template<typename _Tp, typename _Up>
        constexpr auto
        operator()(const _Tp& __t, const _Up& __u) const
        noexcept(_S_noexcept<_Tp, _Up>())
        requires requires
        {
          { __t < __u } -> __boolean_testable;
          { __u < __t } -> __boolean_testable;
        }
        {
          if constexpr (three_way_comparable_with<_Tp, _Up>)
            return __t <=> __u;
          else
            {
              if (__t < __u)
                return weak_ordering::less;
              else if (__u < __t)
                return weak_ordering::greater;
              else
                return weak_ordering::equivalent;
            }
        }
    } __synth3way = {};
 
    // [expos.only.func] synth-three-way-result
    template<typename _Tp, typename _Up = _Tp>
      using __synth3way_t
        = decltype(__detail::__synth3way(std::declval<_Tp&>(),
                                         std::declval<_Up&>()));
  } // namespace __detail
#endif // concepts
} // namespace std
 
#pragma GCC visibility pop
 
#endif // C++20
 
#endif // _COMPARE