libstdc++-v3/libsupc++/compare

// -*- C++ -*- operator<=> three-way comparison support.

// Copyright (C) 2019-2022 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

#include <concepts>

#if __cpp_lib_concepts
# define __cpp_lib_three_way_comparison 201907L
#endif

namespace std _GLIBCXX_VISIBILITY(default)
{
  // [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
    [[nodiscard]]
    friend constexpr bool
    operator==(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 0; }

    [[nodiscard]]
    friend constexpr bool
    operator==(partial_ordering, partial_ordering) noexcept = default;

    [[nodiscard]]
    friend constexpr bool
    operator< (partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == -1; }

    [[nodiscard]]
    friend constexpr bool
    operator> (partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 1; }

    [[nodiscard]]
    friend constexpr bool
    operator<=(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value <= 0; }

    [[nodiscard]]
    friend constexpr bool
    operator>=(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __cmp_cat::type(__v._M_value & 1) == __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator< (__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return __v._M_value == 1; }

    [[nodiscard]]
    friend constexpr bool
    operator> (__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return __v._M_value == -1; }

    [[nodiscard]]
    friend constexpr bool
    operator<=(__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return __cmp_cat::type(__v._M_value & 1) == __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator>=(__cmp_cat::__unspec, partial_ordering __v) noexcept
    { return 0 >= __v._M_value; }

    [[nodiscard]]
    friend constexpr partial_ordering
    operator<=>(partial_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v; }

    [[nodiscard]]
    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;

    [[nodiscard]]
    constexpr operator partial_ordering() const noexcept
    { return partial_ordering(__cmp_cat::_Ord(_M_value)); }

    // comparisons
    [[nodiscard]]
    friend constexpr bool
    operator==(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 0; }

    [[nodiscard]]
    friend constexpr bool
    operator==(weak_ordering, weak_ordering) noexcept = default;

    [[nodiscard]]
    friend constexpr bool
    operator< (weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value < 0; }

    [[nodiscard]]
    friend constexpr bool
    operator> (weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value > 0; }

    [[nodiscard]]
    friend constexpr bool
    operator<=(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value <= 0; }

    [[nodiscard]]
    friend constexpr bool
    operator>=(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value >= 0; }

    [[nodiscard]]
    friend constexpr bool
    operator< (__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 < __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator> (__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 > __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator<=(__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 <= __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator>=(__cmp_cat::__unspec, weak_ordering __v) noexcept
    { return 0 >= __v._M_value; }

    [[nodiscard]]
    friend constexpr weak_ordering
    operator<=>(weak_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v; }

    [[nodiscard]]
    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;

    [[nodiscard]]
    constexpr operator partial_ordering() const noexcept
    { return partial_ordering(__cmp_cat::_Ord(_M_value)); }

    [[nodiscard]]
    constexpr operator weak_ordering() const noexcept
    { return weak_ordering(__cmp_cat::_Ord(_M_value)); }

    // comparisons
    [[nodiscard]]
    friend constexpr bool
    operator==(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value == 0; }

    [[nodiscard]]
    friend constexpr bool
    operator==(strong_ordering, strong_ordering) noexcept = default;

    [[nodiscard]]
    friend constexpr bool
    operator< (strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value < 0; }

    [[nodiscard]]
    friend constexpr bool
    operator> (strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value > 0; }

    [[nodiscard]]
    friend constexpr bool
    operator<=(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value <= 0; }

    [[nodiscard]]
    friend constexpr bool
    operator>=(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v._M_value >= 0; }

    [[nodiscard]]
    friend constexpr bool
    operator< (__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 < __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator> (__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 > __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator<=(__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 <= __v._M_value; }

    [[nodiscard]]
    friend constexpr bool
    operator>=(__cmp_cat::__unspec, strong_ordering __v) noexcept
    { return 0 >= __v._M_value; }

    [[nodiscard]]
    friend constexpr strong_ordering
    operator<=>(strong_ordering __v, __cmp_cat::__unspec) noexcept
    { return __v; }

    [[nodiscard]]
    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
  [[nodiscard]]
  constexpr bool
  is_eq(partial_ordering __cmp) noexcept
  { return __cmp == 0; }

  [[nodiscard]]
  constexpr bool
  is_neq(partial_ordering __cmp) noexcept
  { return __cmp != 0; }

  [[nodiscard]]
  constexpr bool
  is_lt  (partial_ordering __cmp) noexcept
  { return __cmp < 0; }

  [[nodiscard]]
  constexpr bool
  is_lteq(partial_ordering __cmp) noexcept
  { return __cmp <= 0; }

  [[nodiscard]]
  constexpr bool
  is_gt  (partial_ordering __cmp) noexcept
  { return __cmp > 0; }

  [[nodiscard]]
  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() [[nodiscard]] (_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 (std::__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>
	  || 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;

      // Names for the supported floating-point representations.
      enum class _Fp_fmt
      {
	_Binary16, _Binary32, _Binary64, _Binary128, // IEEE
	_X86_80bit,  // x86 80-bit extended precision
	_M68k_80bit, // m68k 80-bit extended precision
	_Dbldbl, // IBM 128-bit double-double
	// TODO: _Bfloat16,
      };

#ifndef __cpp_using_enum
      // XXX Remove these once 'using enum' support is ubiquitous.
      static constexpr _Fp_fmt _Binary16 = _Fp_fmt::_Binary16;
      static constexpr _Fp_fmt _Binary32 = _Fp_fmt::_Binary32;
      static constexpr _Fp_fmt _Binary64 = _Fp_fmt::_Binary64;
      static constexpr _Fp_fmt _Binary128 = _Fp_fmt::_Binary128;
      static constexpr _Fp_fmt _X86_80bit = _Fp_fmt::_X86_80bit;
      static constexpr _Fp_fmt _M68k_80bit = _Fp_fmt::_M68k_80bit;
      static constexpr _Fp_fmt _Dbldbl = _Fp_fmt::_Dbldbl;
#endif

      // Identify the format used by a floating-point type.
      template<typename _Tp>
	static consteval _Fp_fmt
	_S_fp_fmt() noexcept
	{
#ifdef __cpp_using_enum
	  using enum _Fp_fmt;
#endif

	  // Identify these formats first, then assume anything else is IEEE.
	  // N.B. ARM __fp16 alternative format can be handled as binary16.

#ifdef __LONG_DOUBLE_IBM128__
	  if constexpr (__is_same(_Tp, long double))
	    return _Dbldbl;
#elif defined __LONG_DOUBLE_IEEE128__ && defined __SIZEOF_IBM128__
	  if constexpr (__is_same(_Tp, __ibm128))
	    return _Dbldbl;
#endif

#if __LDBL_MANT_DIG__ == 64
	  if constexpr (__is_same(_Tp, long double))
	    return __LDBL_MIN_EXP__ == -16381 ? _X86_80bit : _M68k_80bit;
#endif
#ifdef __SIZEOF_FLOAT80__
	  if constexpr (__is_same(_Tp, __float80))
	    return _X86_80bit;
#endif

	  constexpr int __width = sizeof(_Tp) * __CHAR_BIT__;

	  if constexpr (__width == 16)       // IEEE binary16 (or ARM fp16).
	    return _Binary16;
	  else if constexpr (__width == 32)  // IEEE binary32
	    return _Binary32;
	  else if constexpr (__width == 64)  // IEEE binary64
	    return _Binary64;
	  else if constexpr (__width == 128) // IEEE binary128
	    return _Binary128;
	}

      // So we don't need to include <stdint.h> and pollute the namespace.
      using int64_t = __INT64_TYPE__;
      using int32_t = __INT32_TYPE__;
      using int16_t = __INT16_TYPE__;
      using uint64_t = __UINT64_TYPE__;
      using uint16_t = __UINT16_TYPE__;

      // Used to unpack floating-point types that do not fit into an integer.
      template<typename _Tp>
	struct _Int
	{
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
	  uint64_t _M_lo;
	  _Tp _M_hi;
#else
	  _Tp _M_hi;
	  uint64_t _M_lo;
#endif

	  constexpr explicit
	  _Int(_Tp __hi, uint64_t __lo) noexcept : _M_hi(__hi)
	  { _M_lo = __lo; }

	  constexpr explicit
	  _Int(uint64_t __lo) noexcept : _M_hi(0)
	  { _M_lo = __lo; }

	  constexpr bool operator==(const _Int&) const = default;

#if defined __hppa__ || (defined __mips__ && !defined __mips_nan2008)
	  consteval _Int
	  operator<<(int __n) const noexcept
	  {
	    // XXX this assumes n >= 64, which is true for the use below.
	    return _Int(static_cast<_Tp>(_M_lo << (__n - 64)), 0);
	  }
#endif

	  constexpr _Int&
	  operator^=(const _Int& __rhs) noexcept
	  {
	    _M_hi ^= __rhs._M_hi;
	    _M_lo ^= __rhs._M_lo;
	    return *this;
	  }

	  constexpr strong_ordering
	  operator<=>(const _Int& __rhs) const noexcept
	  {
	    strong_ordering __cmp = _M_hi <=> __rhs._M_hi;
	    if (__cmp != strong_ordering::equal)
	      return __cmp;
	    return _M_lo <=> __rhs._M_lo;
	  }
	};

      template<typename _Tp>
	static constexpr _Tp
	_S_compl(_Tp __t) noexcept
	{
	  constexpr int __width = sizeof(_Tp) * __CHAR_BIT__;
	  // Sign extend to get all ones or all zeros.
	  make_unsigned_t<_Tp> __sign = __t >> (__width - 1);
	  // If the sign bit was set, this flips all bits below it.
	  // This converts ones' complement to two's complement.
	  return __t ^ (__sign >> 1);
	}

      // As above but works on both parts of _Int<T>.
      template<typename _Tp>
	static constexpr _Int<_Tp>
	_S_compl(_Int<_Tp> __t) noexcept
	{
	  constexpr int __width = sizeof(_Tp) * __CHAR_BIT__;
	  make_unsigned_t<_Tp> __sign = __t._M_hi >> (__width - 1);
	  __t._M_hi ^= (__sign >> 1 );
	  uint64_t __sign64 = (_Tp)__sign;
	  __t._M_lo ^= __sign64;
	  return __t;
	}

      // Bit-cast a floating-point value to an unsigned integer.
      template<typename _Tp>
	constexpr static auto
	_S_fp_bits(_Tp __val) noexcept
	{
	  if constexpr (sizeof(_Tp) == sizeof(int64_t))
	    return __builtin_bit_cast(int64_t, __val);
	  else if constexpr (sizeof(_Tp) == sizeof(int32_t))
	    return __builtin_bit_cast(int32_t, __val);
	  else if constexpr (sizeof(_Tp) == sizeof(int16_t))
	    return __builtin_bit_cast(int16_t, __val);
	  else
	    {
#ifdef __cpp_using_enum
	      using enum _Fp_fmt;
#endif
	      constexpr auto __fmt = _S_fp_fmt<_Tp>();
	      if constexpr (__fmt == _X86_80bit || __fmt == _M68k_80bit)
		{
		  if constexpr (sizeof(_Tp) == 3 * sizeof(int32_t))
		    {
		      auto __ival = __builtin_bit_cast(_Int<int32_t>, __val);
		      return _Int<int16_t>(__ival._M_hi, __ival._M_lo);
		    }
		  else
		    {
		      auto __ival = __builtin_bit_cast(_Int<int64_t>, __val);
		      return _Int<int16_t>(__ival._M_hi, __ival._M_lo);
		    }
		}
	      else if constexpr (sizeof(_Tp) == 2 * sizeof(int64_t))
		{
#if __SIZEOF_INT128__
		  return __builtin_bit_cast(__int128, __val);
#else
		  return __builtin_bit_cast(_Int<int64_t>, __val);
#endif
		}
	      else
		static_assert(sizeof(_Tp) == sizeof(int64_t),
			      "unsupported floating-point type");
	    }
	}

      template<typename _Tp>
	static constexpr strong_ordering
	_S_fp_cmp(_Tp __x, _Tp __y) noexcept
	{
#ifdef __vax__
	  if (__builtin_isnan(__x) || __builtin_isnan(__y))
	    {
	      int __ix = (bool) __builtin_isnan(__x);
	      int __iy = (bool) __builtin_isnan(__y);
	      __ix *= __builtin_signbit(__x) ? -1 : 1;
	      __iy *= __builtin_signbit(__y) ? -1 : 1;
	      return __ix <=> __iy;
	    }
	  else
	    return __builtin_bit_cast(strong_ordering, __x <=> __y);
#endif

	  auto __ix = _S_fp_bits(__x);
	  auto __iy = _S_fp_bits(__y);

	  if (__ix == __iy)
	    return strong_ordering::equal; // All bits are equal, we're done.

#ifdef __cpp_using_enum
	  using enum _Fp_fmt;
#endif
	  constexpr auto __fmt = _S_fp_fmt<_Tp>();

	  if constexpr (__fmt == _Dbldbl) // double-double
	    {
	      // Unpack the double-double into two parts.
	      // We never inspect the low double as a double, cast to integer.
	      struct _Unpacked { double _M_hi; int64_t _M_lo; };
	      auto __x2 = __builtin_bit_cast(_Unpacked, __x);
	      auto __y2 = __builtin_bit_cast(_Unpacked, __y);

	      // Compare the high doubles first and use result if unequal.
	      auto __cmp = _S_fp_cmp(__x2._M_hi, __y2._M_hi);
	      if (__cmp != strong_ordering::equal)
		return __cmp;

	      // For NaN the low double is unused, so if the high doubles
	      // are the same NaN, we don't need to compare the low doubles.
	      if (__builtin_isnan(__x2._M_hi))
		return strong_ordering::equal;
	      // Similarly, if the low doubles are +zero or -zero (which is
	      // true for all infinities and some other values), we're done.
	      if (((__x2._M_lo | __y2._M_lo) & 0x7fffffffffffffffULL) == 0)
		return strong_ordering::equal;

	      // Otherwise, compare the low parts.
	      return _S_compl(__x2._M_lo) <=> _S_compl(__y2._M_lo);
	    }
	  else
	    {
	      if constexpr (__fmt == _M68k_80bit)
		{
		  // For m68k the MSB of the significand is ignored for the
		  // greatest exponent, so either 0 or 1 is valid there.
		  // Set it before comparing, so that we never have 0 there.
		  constexpr uint16_t __maxexp = 0x7fff;
		  if ((__ix._M_hi & __maxexp) == __maxexp)
		    __ix._M_lo |= 1ull << 63;
		  if ((__iy._M_hi & __maxexp) == __maxexp)
		    __iy._M_lo |= 1ull << 63;
		}
	      else
		{
#if defined __hppa__ || (defined __mips__ && !defined __mips_nan2008)
		  // IEEE 754-1985 allowed the meaning of the quiet/signaling
		  // bit to be reversed. Flip that to give desired ordering.
		  if (__builtin_isnan(__x) && __builtin_isnan(__y))
		    {
		      using _Int = decltype(__ix);

		      constexpr int __nantype = __fmt == _Binary32  ?  22
					      : __fmt == _Binary64  ?  51
					      : __fmt == _Binary128 ? 111
					      : -1;
		      constexpr _Int __bit = _Int(1) << __nantype;
		      __ix ^= __bit;
		      __iy ^= __bit;
		    }
#endif
		}
	      return _S_compl(__ix) <=> _S_compl(__iy);
	    }
	}

    public:
      template<typename _Tp, __decayed_same_as<_Tp> _Up>
	requires __strongly_ordered<_Tp, _Up>
	constexpr strong_ordering
	operator() [[nodiscard]] (_Tp&& __e, _Up&& __f) const
	noexcept(_S_noexcept<_Tp, _Up>())
	{
	  if constexpr (floating_point<decay_t<_Tp>>)
	    return _S_fp_cmp(__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() [[nodiscard]] (_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() [[nodiscard]] (_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() [[nodiscard]] (_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() [[nodiscard]] (_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() [[nodiscard]] (_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>
	[[nodiscard]]
	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

#endif // C++20

#endif // _COMPARE