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/usr/include/c++/11/compare
// -*- C++ -*- operator<=> three-way comparison support.

// Copyright (C) 2019-2021 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
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