Index: libcxx/include/CMakeLists.txt
===================================================================
--- libcxx/include/CMakeLists.txt
+++ libcxx/include/CMakeLists.txt
@@ -98,6 +98,9 @@
   __bsd_locale_defaults.h
   __bsd_locale_fallbacks.h
   __config
+  __compare/common_comparison_category.h
+  __compare/ordering.h
+  __compare/three_way_comparable.h
   __debug
   __errc
   __format/format_error.h
Index: libcxx/include/__compare/common_comparison_category.h
===================================================================
--- /dev/null
+++ libcxx/include/__compare/common_comparison_category.h
@@ -0,0 +1,97 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___COMMON_COMPARISON_CATEGORY_H
+#define _LIBCPP___COMMON_COMPARISON_CATEGORY_H
+
+#include <__config>
+#include <__compare/ordering.h>
+#include <type_traits>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
+
+namespace __comp_detail {
+
+enum _ClassifyCompCategory : unsigned{
+  _None,
+  _PartialOrd,
+  _WeakOrd,
+  _StrongOrd,
+  _CCC_Size
+};
+
+template <class _Tp>
+_LIBCPP_INLINE_VISIBILITY
+constexpr _ClassifyCompCategory __type_to_enum() noexcept {
+  if (is_same_v<_Tp, partial_ordering>)
+    return _PartialOrd;
+  if (is_same_v<_Tp, weak_ordering>)
+    return _WeakOrd;
+  if (is_same_v<_Tp, strong_ordering>)
+    return _StrongOrd;
+  return _None;
+}
+
+template <size_t _Size>
+constexpr _ClassifyCompCategory
+__compute_comp_type(const _ClassifyCompCategory (&__types)[_Size]) {
+  int __seen[_CCC_Size] = {};
+  for (auto __type : __types)
+    ++__seen[__type];
+  if (__seen[_None])
+    return _None;
+  if (__seen[_PartialOrd])
+    return _PartialOrd;
+  if (__seen[_WeakOrd])
+    return _WeakOrd;
+  return _StrongOrd;
+}
+
+template <class ..._Ts>
+constexpr auto __get_comp_type() {
+  using _CCC = _ClassifyCompCategory;
+  constexpr _CCC __type_kinds[] = {_StrongOrd, __type_to_enum<_Ts>()...};
+  constexpr _CCC _Cat = __compute_comp_type(__type_kinds);
+  if constexpr (_Cat == _None)
+    return void();
+  else if constexpr (_Cat == _PartialOrd)
+    return partial_ordering::equivalent;
+  else if constexpr (_Cat == _WeakOrd)
+    return weak_ordering::equivalent;
+  else if constexpr (_Cat == _StrongOrd)
+    return strong_ordering::equivalent;
+  else
+    static_assert(_Cat != _Cat, "unhandled case");
+}
+} // namespace __comp_detail
+
+// [cmp.common], common comparison category type
+template<class... _Ts>
+struct _LIBCPP_TEMPLATE_VIS common_comparison_category {
+  using type = decltype(__comp_detail::__get_comp_type<_Ts...>());
+};
+
+template<class... _Ts>
+using common_comparison_category_t = typename common_comparison_category<_Ts...>::type;
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___COMMON_COMPARISON_CATEGORY_H
Index: libcxx/include/__compare/ordering.h
===================================================================
--- /dev/null
+++ libcxx/include/__compare/ordering.h
@@ -0,0 +1,313 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___COMPARE_ORDERING_H
+#define _LIBCPP___COMPARE_ORDERING_H
+
+#include <__config>
+#include <type_traits>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
+// exposition only
+enum class _LIBCPP_ENUM_VIS _EqResult : unsigned char {
+  __zero = 0,
+  __equal = __zero,
+  __equiv = __equal,
+  __nonequal = 1,
+  __nonequiv = __nonequal
+};
+
+enum class _LIBCPP_ENUM_VIS _OrdResult : signed char {
+  __less = -1,
+  __greater = 1
+};
+
+enum class _LIBCPP_ENUM_VIS _NCmpResult : signed char {
+  __unordered = -127
+};
+
+class partial_ordering;
+class weak_ordering;
+class strong_ordering;
+
+template<class _Tp, class... _Args>
+inline constexpr bool __one_of_v = (is_same_v<_Tp, _Args> || ...);
+
+struct _CmpUnspecifiedParam {
+  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEVAL
+  _CmpUnspecifiedParam(int _CmpUnspecifiedParam::*) noexcept {}
+
+  template<class _Tp, class = enable_if_t<!__one_of_v<_Tp, int, partial_ordering, weak_ordering, strong_ordering>>>
+  _CmpUnspecifiedParam(_Tp) = delete;
+};
+
+class partial_ordering {
+  using _ValueT = signed char;
+
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr partial_ordering(_EqResult __v) noexcept
+      : __value_(_ValueT(__v)) {}
+
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr partial_ordering(_OrdResult __v) noexcept
+      : __value_(_ValueT(__v)) {}
+
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr partial_ordering(_NCmpResult __v) noexcept
+      : __value_(_ValueT(__v)) {}
+
+  constexpr bool __is_ordered() const noexcept {
+    return __value_ != _ValueT(_NCmpResult::__unordered);
+  }
+public:
+  // valid values
+  static const partial_ordering less;
+  static const partial_ordering equivalent;
+  static const partial_ordering greater;
+  static const partial_ordering unordered;
+
+  // comparisons
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(partial_ordering, partial_ordering) noexcept = default;
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__is_ordered() && __v.__value_ == 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (partial_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__is_ordered() && __v.__value_ < 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
+    return __v.__is_ordered() && __v.__value_ <= 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
+    return __v.__is_ordered() && __v.__value_ > 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
+    return __v.__is_ordered() && __v.__value_ >= 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
+    return __v.__is_ordered() && 0 < __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
+    return __v.__is_ordered() && 0 <= __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
+    return __v.__is_ordered() && 0 > __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
+    return __v.__is_ordered() && 0 >= __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr partial_ordering operator<=>(partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
+    return __v;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr partial_ordering operator<=>(_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
+    return __v < 0 ? partial_ordering::greater : (__v > 0 ? partial_ordering::less : __v);
+  }
+private:
+  _ValueT __value_;
+};
+
+_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::less(_OrdResult::__less);
+_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::equivalent(_EqResult::__equiv);
+_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::greater(_OrdResult::__greater);
+_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::unordered(_NCmpResult ::__unordered);
+
+class weak_ordering {
+  using _ValueT = signed char;
+
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr weak_ordering(_EqResult __v) noexcept : __value_(_ValueT(__v)) {}
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr weak_ordering(_OrdResult __v) noexcept : __value_(_ValueT(__v)) {}
+
+public:
+  static const weak_ordering less;
+  static const weak_ordering equivalent;
+  static const weak_ordering greater;
+
+  _LIBCPP_INLINE_VISIBILITY
+  constexpr operator partial_ordering() const noexcept {
+    return __value_ == 0 ? partial_ordering::equivalent
+        : (__value_ < 0 ? partial_ordering::less : partial_ordering::greater);
+  }
+
+  // comparisons
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(weak_ordering, weak_ordering) noexcept = default;
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ == 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (weak_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ < 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ <= 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (weak_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ > 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ >= 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (_CmpUnspecifiedParam, weak_ordering __v) noexcept {
+    return 0 < __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
+    return 0 <= __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (_CmpUnspecifiedParam, weak_ordering __v) noexcept {
+    return 0 > __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
+    return 0 >= __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr weak_ordering operator<=>(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr weak_ordering operator<=>(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
+    return __v < 0 ? weak_ordering::greater : (__v > 0 ? weak_ordering::less : __v);
+  }
+
+private:
+  _ValueT __value_;
+};
+
+_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::less(_OrdResult::__less);
+_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::equivalent(_EqResult::__equiv);
+_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::greater(_OrdResult::__greater);
+class strong_ordering {
+  using _ValueT = signed char;
+
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr strong_ordering(_EqResult __v) noexcept : __value_(_ValueT(__v)) {}
+  _LIBCPP_INLINE_VISIBILITY
+  explicit constexpr strong_ordering(_OrdResult __v) noexcept : __value_(_ValueT(__v)) {}
+
+public:
+  static const strong_ordering less;
+  static const strong_ordering equal;
+  static const strong_ordering equivalent;
+  static const strong_ordering greater;
+
+  // conversions
+  _LIBCPP_INLINE_VISIBILITY
+  constexpr operator partial_ordering() const noexcept {
+    return __value_ == 0 ? partial_ordering::equivalent
+        : (__value_ < 0 ? partial_ordering::less : partial_ordering::greater);
+  }
+
+  _LIBCPP_INLINE_VISIBILITY
+  constexpr operator weak_ordering() const noexcept {
+    return __value_ == 0 ? weak_ordering::equivalent
+        : (__value_ < 0 ? weak_ordering::less : weak_ordering::greater);
+  }
+
+  // comparisons
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(strong_ordering, strong_ordering) noexcept = default;
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ == 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (strong_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ < 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ <= 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (strong_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ > 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v.__value_ >= 0;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (_CmpUnspecifiedParam, strong_ordering __v) noexcept {
+    return 0 < __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
+    return 0 <= __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (_CmpUnspecifiedParam, strong_ordering __v) noexcept {
+    return 0 > __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
+    return 0 >= __v.__value_;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr strong_ordering operator<=>(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
+    return __v;
+  }
+
+  _LIBCPP_INLINE_VISIBILITY friend constexpr strong_ordering operator<=>(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
+    return __v < 0 ? strong_ordering::greater : (__v > 0 ? strong_ordering::less : __v);
+  }
+
+private:
+  _ValueT __value_;
+};
+
+_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::less(_OrdResult::__less);
+_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::equal(_EqResult::__equal);
+_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::equivalent(_EqResult::__equiv);
+_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::greater(_OrdResult::__greater);
+
+// named comparison functions
+_LIBCPP_INLINE_VISIBILITY
+constexpr bool is_lt(partial_ordering __cmp) noexcept { return __cmp < 0; }
+
+_LIBCPP_INLINE_VISIBILITY
+constexpr bool is_lteq(partial_ordering __cmp) noexcept { return __cmp <= 0; }
+
+_LIBCPP_INLINE_VISIBILITY
+constexpr bool is_gt(partial_ordering __cmp) noexcept { return __cmp > 0; }
+
+_LIBCPP_INLINE_VISIBILITY
+constexpr bool is_gteq(partial_ordering __cmp) noexcept { return __cmp >= 0; }
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___COMPARE_ORDERING_H
Index: libcxx/include/__compare/three_way_comparable.h
===================================================================
--- /dev/null
+++ libcxx/include/__compare/three_way_comparable.h
@@ -0,0 +1,60 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___THREE_WAY_COMPARABLE_H
+#define _LIBCPP___THREE_WAY_COMPARABLE_H
+
+#include <__config>
+#include <__compare/common_comparison_category.h>
+#include <concepts>
+#include <type_traits>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
+
+template<class _Tp, class _Cat>
+concept __compares_as =                 // exposition only
+  same_as<common_comparison_category_t<_Tp, _Cat>, _Cat>;
+
+template<class _Tp, class _Cat = partial_ordering>
+concept three_way_comparable =
+  __weakly_equality_comparable_with<_Tp, _Tp> &&
+  __partially_ordered_with<_Tp, _Tp> &&
+  requires(__make_const_lvalue_ref<_Tp> __a, __make_const_lvalue_ref<_Tp> __b) {
+    { __a <=> __b } -> __compares_as<_Cat>;
+  };
+
+template<class _Tp, class _Up, class _Cat = partial_ordering>
+concept three_way_comparable_with =
+  three_way_comparable<_Tp, _Cat> &&
+  three_way_comparable<_Up, _Cat> &&
+  common_reference_with<__make_const_lvalue_ref<_Tp>, __make_const_lvalue_ref<_Up>> &&
+  three_way_comparable<
+    common_reference_t<__make_const_lvalue_ref<_Tp>, __make_const_lvalue_ref<_Up>>, _Cat> &&
+  __weakly_equality_comparable_with<_Tp, _Up> &&
+  __partially_ordered_with<_Tp, _Up> &&
+  requires(__make_const_lvalue_ref<_Tp> __t, __make_const_lvalue_ref<_Up> __u) {
+    { __t <=> __u } -> __compares_as<_Cat>;
+    { __u <=> __t } -> __compares_as<_Cat>;
+  };
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___THREE_WAY_COMPARABLE_H
Index: libcxx/include/compare
===================================================================
--- libcxx/include/compare
+++ libcxx/include/compare
@@ -121,360 +121,21 @@
 */
 
 #include <__config>
+#include <__compare/common_comparison_category.h>
+#include <__compare/ordering.h>
+#include <__compare/three_way_comparable.h>
 #include <type_traits>
 
 #ifndef _LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER
 #pragma GCC system_header
 #endif
 
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 #if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
-// exposition only
-enum class _LIBCPP_ENUM_VIS _EqResult : unsigned char {
-  __zero = 0,
-  __equal = __zero,
-  __equiv = __equal,
-  __nonequal = 1,
-  __nonequiv = __nonequal
-};
-
-enum class _LIBCPP_ENUM_VIS _OrdResult : signed char {
-  __less = -1,
-  __greater = 1
-};
-
-enum class _LIBCPP_ENUM_VIS _NCmpResult : signed char {
-  __unordered = -127
-};
-
-class partial_ordering;
-class weak_ordering;
-class strong_ordering;
-
-template<class _Tp, class... _Args>
-inline constexpr bool __one_of_v = (is_same_v<_Tp, _Args> || ...);
-
-struct _CmpUnspecifiedParam {
-  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEVAL
-  _CmpUnspecifiedParam(int _CmpUnspecifiedParam::*) noexcept {}
-
-  template<class _Tp, class = enable_if_t<!__one_of_v<_Tp, int, partial_ordering, weak_ordering, strong_ordering>>>
-  _CmpUnspecifiedParam(_Tp) = delete;
-};
-
-class partial_ordering {
-  using _ValueT = signed char;
-
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr partial_ordering(_EqResult __v) noexcept
-      : __value_(_ValueT(__v)) {}
-
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr partial_ordering(_OrdResult __v) noexcept
-      : __value_(_ValueT(__v)) {}
-
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr partial_ordering(_NCmpResult __v) noexcept
-      : __value_(_ValueT(__v)) {}
-
-  constexpr bool __is_ordered() const noexcept {
-    return __value_ != _ValueT(_NCmpResult::__unordered);
-  }
-public:
-  // valid values
-  static const partial_ordering less;
-  static const partial_ordering equivalent;
-  static const partial_ordering greater;
-  static const partial_ordering unordered;
-
-  // comparisons
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(partial_ordering, partial_ordering) noexcept = default;
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__is_ordered() && __v.__value_ == 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (partial_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__is_ordered() && __v.__value_ < 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
-    return __v.__is_ordered() && __v.__value_ <= 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
-    return __v.__is_ordered() && __v.__value_ > 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
-    return __v.__is_ordered() && __v.__value_ >= 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
-    return __v.__is_ordered() && 0 < __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
-    return __v.__is_ordered() && 0 <= __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
-    return __v.__is_ordered() && 0 > __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
-    return __v.__is_ordered() && 0 >= __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr partial_ordering operator<=>(partial_ordering __v, _CmpUnspecifiedParam) noexcept  {
-    return __v;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr partial_ordering operator<=>(_CmpUnspecifiedParam, partial_ordering __v) noexcept  {
-    return __v < 0 ? partial_ordering::greater : (__v > 0 ? partial_ordering::less : __v);
-  }
-private:
-  _ValueT __value_;
-};
-
-_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::less(_OrdResult::__less);
-_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::equivalent(_EqResult::__equiv);
-_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::greater(_OrdResult::__greater);
-_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::unordered(_NCmpResult ::__unordered);
-
-class weak_ordering {
-  using _ValueT = signed char;
-
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr weak_ordering(_EqResult __v) noexcept : __value_(_ValueT(__v)) {}
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr weak_ordering(_OrdResult __v) noexcept : __value_(_ValueT(__v)) {}
-
-public:
-  static const weak_ordering less;
-  static const weak_ordering equivalent;
-  static const weak_ordering greater;
-
-  _LIBCPP_INLINE_VISIBILITY
-  constexpr operator partial_ordering() const noexcept {
-    return __value_ == 0 ? partial_ordering::equivalent
-        : (__value_ < 0 ? partial_ordering::less : partial_ordering::greater);
-  }
-
-  // comparisons
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(weak_ordering, weak_ordering) noexcept = default;
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ == 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (weak_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ < 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ <= 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (weak_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ > 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ >= 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (_CmpUnspecifiedParam, weak_ordering __v) noexcept {
-    return 0 < __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
-    return 0 <= __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (_CmpUnspecifiedParam, weak_ordering __v) noexcept {
-    return 0 > __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
-    return 0 >= __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr weak_ordering operator<=>(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr weak_ordering operator<=>(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
-    return __v < 0 ? weak_ordering::greater : (__v > 0 ? weak_ordering::less : __v);
-  }
-
-private:
-  _ValueT __value_;
-};
-
-_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::less(_OrdResult::__less);
-_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::equivalent(_EqResult::__equiv);
-_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::greater(_OrdResult::__greater);
-class strong_ordering {
-  using _ValueT = signed char;
-
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr strong_ordering(_EqResult __v) noexcept : __value_(_ValueT(__v)) {}
-  _LIBCPP_INLINE_VISIBILITY
-  explicit constexpr strong_ordering(_OrdResult __v) noexcept : __value_(_ValueT(__v)) {}
-
-public:
-  static const strong_ordering less;
-  static const strong_ordering equal;
-  static const strong_ordering equivalent;
-  static const strong_ordering greater;
-
-  // conversions
-  _LIBCPP_INLINE_VISIBILITY
-  constexpr operator partial_ordering() const noexcept {
-    return __value_ == 0 ? partial_ordering::equivalent
-        : (__value_ < 0 ? partial_ordering::less : partial_ordering::greater);
-  }
-
-  _LIBCPP_INLINE_VISIBILITY
-  constexpr operator weak_ordering() const noexcept {
-    return __value_ == 0 ? weak_ordering::equivalent
-        : (__value_ < 0 ? weak_ordering::less : weak_ordering::greater);
-  }
-
-  // comparisons
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(strong_ordering, strong_ordering) noexcept = default;
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator==(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ == 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (strong_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ < 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ <= 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (strong_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ > 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v.__value_ >= 0;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator< (_CmpUnspecifiedParam, strong_ordering __v) noexcept {
-    return 0 < __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator<=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
-    return 0 <= __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator> (_CmpUnspecifiedParam, strong_ordering __v) noexcept {
-    return 0 > __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr bool operator>=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
-    return 0 >= __v.__value_;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr strong_ordering operator<=>(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
-    return __v;
-  }
-
-  _LIBCPP_INLINE_VISIBILITY friend constexpr strong_ordering operator<=>(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
-    return __v < 0 ? strong_ordering::greater : (__v > 0 ? strong_ordering::less : __v);
-  }
-
-private:
-  _ValueT __value_;
-};
-
-_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::less(_OrdResult::__less);
-_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::equal(_EqResult::__equal);
-_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::equivalent(_EqResult::__equiv);
-_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::greater(_OrdResult::__greater);
-
-// named comparison functions
-_LIBCPP_INLINE_VISIBILITY
-constexpr bool is_lt(partial_ordering __cmp) noexcept { return __cmp < 0; }
-
-_LIBCPP_INLINE_VISIBILITY
-constexpr bool is_lteq(partial_ordering __cmp) noexcept { return __cmp <= 0; }
-
-_LIBCPP_INLINE_VISIBILITY
-constexpr bool is_gt(partial_ordering __cmp) noexcept { return __cmp > 0; }
-
-_LIBCPP_INLINE_VISIBILITY
-constexpr bool is_gteq(partial_ordering __cmp) noexcept { return __cmp >= 0; }
-
-namespace __comp_detail {
-
-enum _ClassifyCompCategory : unsigned{
-  _None,
-  _PartialOrd,
-  _WeakOrd,
-  _StrongOrd,
-  _CCC_Size
-};
-
-template <class _Tp>
-_LIBCPP_INLINE_VISIBILITY
-constexpr _ClassifyCompCategory __type_to_enum() noexcept {
-  if (is_same_v<_Tp, partial_ordering>)
-    return _PartialOrd;
-  if (is_same_v<_Tp, weak_ordering>)
-    return _WeakOrd;
-  if (is_same_v<_Tp, strong_ordering>)
-    return _StrongOrd;
-  return _None;
-}
-
-template <size_t _Size>
-constexpr _ClassifyCompCategory
-__compute_comp_type(const _ClassifyCompCategory (&__types)[_Size]) {
-  int __seen[_CCC_Size] = {};
-  for (auto __type : __types)
-    ++__seen[__type];
-  if (__seen[_None])
-    return _None;
-  if (__seen[_PartialOrd])
-    return _PartialOrd;
-  if (__seen[_WeakOrd])
-    return _WeakOrd;
-  return _StrongOrd;
-}
-
-template <class ..._Ts>
-constexpr auto __get_comp_type() {
-  using _CCC = _ClassifyCompCategory;
-  constexpr _CCC __type_kinds[] = {_StrongOrd, __type_to_enum<_Ts>()...};
-  constexpr _CCC _Cat = __compute_comp_type(__type_kinds);
-  if constexpr (_Cat == _None)
-    return void();
-  else if constexpr (_Cat == _PartialOrd)
-    return partial_ordering::equivalent;
-  else if constexpr (_Cat == _WeakOrd)
-    return weak_ordering::equivalent;
-  else if constexpr (_Cat == _StrongOrd)
-    return strong_ordering::equivalent;
-  else
-    static_assert(_Cat != _Cat, "unhandled case");
-}
-} // namespace __comp_detail
-
-// [cmp.common], common comparison category type
-template<class... _Ts>
-struct _LIBCPP_TEMPLATE_VIS common_comparison_category {
-  using type = decltype(__comp_detail::__get_comp_type<_Ts...>());
-};
-
-template<class... _Ts>
-using common_comparison_category_t = typename common_comparison_category<_Ts...>::type;
 
 // [cmp.alg], comparison algorithms
 // TODO: unimplemented
@@ -486,4 +147,6 @@
 
 _LIBCPP_END_NAMESPACE_STD
 
+_LIBCPP_POP_MACROS
+
 #endif // _LIBCPP_COMPARE
Index: libcxx/include/utility
===================================================================
--- libcxx/include/utility
+++ libcxx/include/utility
@@ -223,7 +223,9 @@
 #include <__utility/rel_ops.h>
 #include <__utility/swap.h>
 #include <__utility/to_underlying.h>
-#include <compare>
+// FIXME (rarutyun): return back <compare> include when
+//                   cyclic dependency for this header is resolved
+// #include <compare>
 #include <initializer_list>
 #include <version>
 
Index: libcxx/test/libcxx/inclusions/utility.inclusions.compile.pass.cpp
===================================================================
--- libcxx/test/libcxx/inclusions/utility.inclusions.compile.pass.cpp
+++ libcxx/test/libcxx/inclusions/utility.inclusions.compile.pass.cpp
@@ -22,7 +22,9 @@
  #   error "<utility> was expected to define _LIBCPP_UTILITY"
 #endif
 #if TEST_STD_VER > 17 && !defined(_LIBCPP_COMPARE)
- #   error "<utility> should include <compare> in C++20 and later"
+// FIXME (rarutyun): enable this test part when cyclic dependency for
+// <compare> header is resolved
+//  #   error "<utility> should include <compare> in C++20 and later"
 #endif
 #if TEST_STD_VER > 03 && !defined(_LIBCPP_INITIALIZER_LIST)
  #   error "<utility> should include <initializer_list> in C++11 and later"
Index: libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable.compile.pass.cpp
===================================================================
--- /dev/null
+++ libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable.compile.pass.cpp
@@ -0,0 +1,230 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class T, class Cat = partial_ordering>
+// concept three_way_comparable = // see below
+
+#include <compare>
+
+#include "compare_types.h"
+
+namespace fundamentals {
+// with default ordering
+static_assert(std::three_way_comparable<int>);
+static_assert(std::three_way_comparable<double>);
+static_assert(std::three_way_comparable<void*>);
+static_assert(std::three_way_comparable<char*>);
+static_assert(std::three_way_comparable<char const*>);
+static_assert(std::three_way_comparable<char volatile*>);
+static_assert(std::three_way_comparable<char const volatile*>);
+static_assert(std::three_way_comparable<wchar_t&>);
+#ifndef _LIBCPP_HAS_NO_CHAR8_T
+static_assert(std::three_way_comparable<char8_t const&>);
+#endif
+#ifndef _LIBCPP_HAS_NO_UNICODE_CHARS
+static_assert(std::three_way_comparable<char16_t volatile&>);
+static_assert(std::three_way_comparable<char32_t const volatile&>);
+#endif
+#ifndef _LIBCPP_HAS_NO_INT128
+static_assert(std::three_way_comparable<__int128_t const&>);
+static_assert(std::three_way_comparable<__uint128_t const&>);
+#endif
+static_assert(std::three_way_comparable<unsigned char&&>);
+static_assert(std::three_way_comparable<unsigned short const&&>);
+static_assert(std::three_way_comparable<unsigned int volatile&&>);
+static_assert(std::three_way_comparable<unsigned long const volatile&&>);
+
+// with explicit ordering
+static_assert(std::three_way_comparable<int, std::strong_ordering>);
+static_assert(std::three_way_comparable<int, std::weak_ordering>);
+static_assert(std::three_way_comparable<double, std::partial_ordering>);
+static_assert(!std::three_way_comparable<double, std::weak_ordering>);
+static_assert(std::three_way_comparable<void*, std::strong_ordering>);
+static_assert(std::three_way_comparable<void*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char const*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char const*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char volatile*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char volatile*, std::weak_ordering>);
+static_assert(std::three_way_comparable<char const volatile*, std::strong_ordering>);
+static_assert(std::three_way_comparable<char const volatile*, std::weak_ordering>);
+static_assert(std::three_way_comparable<wchar_t&, std::strong_ordering>);
+static_assert(std::three_way_comparable<wchar_t&, std::weak_ordering>);
+static_assert(std::three_way_comparable<char8_t const&, std::strong_ordering>);
+static_assert(std::three_way_comparable<char8_t const&, std::weak_ordering>);
+static_assert(std::three_way_comparable<char16_t volatile&, std::strong_ordering>);
+static_assert(std::three_way_comparable<char16_t volatile&, std::weak_ordering>);
+static_assert(std::three_way_comparable<char32_t const volatile&, std::strong_ordering>);
+static_assert(std::three_way_comparable<char32_t const volatile&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned char&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned char&&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned short const&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned short const&&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned int volatile&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned int volatile&&, std::weak_ordering>);
+static_assert(std::three_way_comparable<unsigned long const volatile&&, std::strong_ordering>);
+static_assert(std::three_way_comparable<unsigned long const volatile&&, std::weak_ordering>);
+
+static_assert(!std::three_way_comparable<int[5]>);
+static_assert(!std::three_way_comparable<int (*)(int)>);
+static_assert(!std::three_way_comparable<int (&)(int)>);
+static_assert(!std::three_way_comparable<int (*)(int) noexcept>);
+static_assert(!std::three_way_comparable<int (&)(int) noexcept>);
+static_assert(!std::three_way_comparable<std::nullptr_t>);
+
+struct S {};
+static_assert(!std::three_way_comparable<int S::*>);
+static_assert(!std::three_way_comparable<int (S::*)()>);
+static_assert(!std::three_way_comparable<int (S::*)() noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() &>);
+static_assert(!std::three_way_comparable<int (S::*)() & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() &&>);
+static_assert(!std::three_way_comparable<int (S::*)() && noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const>);
+static_assert(!std::three_way_comparable<int (S::*)() const noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const&>);
+static_assert(!std::three_way_comparable<int (S::*)() const & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const&&>);
+static_assert(!std::three_way_comparable<int (S::*)() const && noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile&>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile&&>);
+static_assert(!std::three_way_comparable<int (S::*)() volatile && noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile&>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile & noexcept>);
+static_assert(!std::three_way_comparable<int (S::*)() const volatile&&>);
+static_assert(
+    !std::three_way_comparable<int (S::*)() const volatile && noexcept>);
+
+static_assert(!std::three_way_comparable<void>);
+} // namespace fundamentals
+
+namespace user_defined {
+
+struct S {
+    auto operator<=>(const S&) const = default;
+};
+
+static_assert(std::three_way_comparable<S>);
+static_assert(std::three_way_comparable<S, std::strong_ordering>);
+static_assert(std::three_way_comparable<S, std::partial_ordering>);
+
+struct SpaceshipNotDeclared {
+};
+
+static_assert(!std::three_way_comparable<SpaceshipNotDeclared>);
+
+struct SpaceshipDeleted {
+    auto operator<=>(const SpaceshipDeleted&) const = delete;
+};
+
+static_assert(!std::three_way_comparable<SpaceshipDeleted>);
+
+struct SpaceshipWithoutEqualityOperator {
+    auto operator<=>(const SpaceshipWithoutEqualityOperator&) const;
+};
+
+static_assert(!std::three_way_comparable<SpaceshipWithoutEqualityOperator>);
+
+struct EqualityOperatorDeleted {
+    bool operator==(const EqualityOperatorDeleted&) const = delete;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorDeleted>);
+
+struct EqualityOperatorOnly {
+    bool operator==(const EqualityOperatorOnly&) const = default;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorOnly>);
+
+struct SpaceshipDeclaredEqualityOperatorDeleted {
+    bool operator==(const SpaceshipDeclaredEqualityOperatorDeleted&) const = delete;
+    auto operator<=>(const SpaceshipDeclaredEqualityOperatorDeleted&) const = default;
+};
+
+static_assert(!std::three_way_comparable<SpaceshipDeclaredEqualityOperatorDeleted>);
+
+struct AllInequalityOperators {
+    bool operator<(const AllInequalityOperators&) const;
+    bool operator<=(const AllInequalityOperators&) const;
+    bool operator>(const AllInequalityOperators&) const;
+    bool operator>=(const AllInequalityOperators&) const;
+    bool operator!=(const AllInequalityOperators&) const;
+};
+
+static_assert(!std::three_way_comparable<AllInequalityOperators>);
+
+struct AllComparisonOperators {
+    bool operator<(const AllComparisonOperators&) const;
+    bool operator<=(const AllComparisonOperators&) const;
+    bool operator>(const AllComparisonOperators&) const;
+    bool operator>=(const AllComparisonOperators&) const;
+    bool operator!=(const AllComparisonOperators&) const;
+    bool operator==(const AllComparisonOperators&) const;
+};
+
+static_assert(!std::three_way_comparable<AllComparisonOperators>);
+
+struct AllButOneInequalityOperators {
+    bool operator<(const AllButOneInequalityOperators&) const;
+    bool operator<=(const AllButOneInequalityOperators&) const;
+    bool operator>(const AllButOneInequalityOperators&) const;
+    bool operator!=(const AllButOneInequalityOperators&) const;
+};
+
+static_assert(!std::three_way_comparable<AllButOneInequalityOperators>);
+
+struct AllInequalityOperatorsOneDeleted {
+    bool operator<(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator<=(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>=(const AllInequalityOperatorsOneDeleted&) const = delete;
+    bool operator!=(const AllInequalityOperatorsOneDeleted&) const;
+};
+
+static_assert(!std::three_way_comparable<AllInequalityOperatorsOneDeleted>);
+
+struct EqualityOperatorWrongReturnType {
+    int operator==(const EqualityOperatorWrongReturnType&);
+    auto operator<=>(const EqualityOperatorWrongReturnType&) const = default;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorWrongReturnType>);
+
+struct SpaceshipWrongReturnType {
+    bool operator==(const SpaceshipWrongReturnType&) const = default;
+    int operator<=>(const SpaceshipWrongReturnType&);
+};
+
+static_assert(!std::three_way_comparable<SpaceshipWrongReturnType>);
+
+struct EqualityOperatorNonConstArgument {
+    bool operator==(EqualityOperatorNonConstArgument&);
+    auto operator<=>(const EqualityOperatorNonConstArgument&) const = default;
+};
+
+static_assert(!std::three_way_comparable<EqualityOperatorNonConstArgument>);
+
+struct SpaceshipNonConstArgument {
+    bool operator==(const SpaceshipNonConstArgument&) const = default;
+    auto operator<=>(SpaceshipNonConstArgument&);
+};
+
+static_assert(!std::three_way_comparable<SpaceshipNonConstArgument>);
+}
+
+int main(int, char**) { return 0; }
Index: libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable_with.compile.pass.cpp
===================================================================
--- /dev/null
+++ libcxx/test/std/language.support/cmp/cmp.concept/three_way_comparable_with.compile.pass.cpp
@@ -0,0 +1,242 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class T, class U, class Cat = partial_ordering>
+// concept three_way_comparable_with = // see below
+
+#include <compare>
+
+#include "compare_types.h"
+
+template <class T, class U = T, typename Cat = std::partial_ordering>
+constexpr bool check_three_way_comparable_with() {
+  constexpr bool result = std::three_way_comparable_with<T, U, Cat>;
+  static_assert(std::three_way_comparable_with<U, T, Cat> == result);
+  static_assert(std::three_way_comparable_with<T, U const, Cat> == result);
+  static_assert(std::three_way_comparable_with<T const, U const, Cat> == result);
+  static_assert(std::three_way_comparable_with<T, U const&, Cat> == result);
+  static_assert(std::three_way_comparable_with<T const, U const&, Cat> == result);
+  static_assert(std::three_way_comparable_with<T, U const&&, Cat> == result);
+  static_assert(std::three_way_comparable_with<T const, U const&&, Cat> == result);
+  if constexpr (!std::is_void_v<T>) {
+    static_assert(std::three_way_comparable_with<T&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&, U const&&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&, U const&&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&&, U const, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&&, U const&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T&&, U const&&, Cat> == result);
+    static_assert(std::three_way_comparable_with<T const&&, U const&&, Cat> == result);
+  }
+  return result;
+}
+
+namespace fundamentals {
+static_assert(check_three_way_comparable_with<int, int>());
+static_assert(check_three_way_comparable_with<int, char>());
+static_assert(check_three_way_comparable_with<int, wchar_t>());
+static_assert(check_three_way_comparable_with<int, double>());
+static_assert(check_three_way_comparable_with<int*, int*>());
+
+static_assert(check_three_way_comparable_with<int, int, std::strong_ordering>());
+static_assert(check_three_way_comparable_with<int, char, std::strong_ordering>());
+static_assert(check_three_way_comparable_with<int, wchar_t, std::strong_ordering>());
+
+static_assert(check_three_way_comparable_with<int, int, std::weak_ordering>());
+static_assert(check_three_way_comparable_with<int, char, std::weak_ordering>());
+static_assert(check_three_way_comparable_with<int, wchar_t, std::weak_ordering>());
+
+static_assert(!check_three_way_comparable_with<int, bool>());
+static_assert(!check_three_way_comparable_with<int, int*>());
+static_assert(!check_three_way_comparable_with<int, int[5]>());
+static_assert(!check_three_way_comparable_with<int, int (*)()>());
+static_assert(!check_three_way_comparable_with<int, int (&)()>());
+struct S {};
+static_assert(!check_three_way_comparable_with<int, int S::*>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)()>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const>());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() const noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile>());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() volatile noexcept>());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() const volatile>());
+static_assert(!check_three_way_comparable_with<
+              int, int (S::*)() const volatile noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() &>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() & noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const&>());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() const & noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile&>());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() volatile & noexcept>());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() const volatile&>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const volatile &
+                                                       noexcept>());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() &&>());
+static_assert(!check_three_way_comparable_with < int,
+              int (S::*)() && noexcept > ());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() const&&>());
+static_assert(!check_three_way_comparable_with < int,
+              int (S::*)() const&& noexcept > ());
+static_assert(!check_three_way_comparable_with<int, int (S::*)() volatile&&>());
+static_assert(!check_three_way_comparable_with < int,
+              int (S::*)() volatile&& noexcept > ());
+static_assert(
+    !check_three_way_comparable_with<int, int (S::*)() const volatile&&>());
+static_assert(!check_three_way_comparable_with < int,
+              int (S::*)() const volatile&& noexcept > ());
+static_assert(!check_three_way_comparable_with<int*, int[5]>());
+static_assert(!check_three_way_comparable_with<int[5], int[5]>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int*>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int[5]>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int (*)()>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int (&)()>());
+static_assert(!check_three_way_comparable_with<std::nullptr_t, int (S::*)()>());
+static_assert(!check_three_way_comparable_with<void, int>());
+static_assert(!check_three_way_comparable_with<void, int*>());
+static_assert(!check_three_way_comparable_with<void, std::nullptr_t>());
+static_assert(!check_three_way_comparable_with<void, int[5]>());
+static_assert(!check_three_way_comparable_with<void, int (*)()>());
+static_assert(!check_three_way_comparable_with<void, int (&)()>());
+static_assert(!check_three_way_comparable_with<void, int S::*>());
+static_assert(!check_three_way_comparable_with<void, int (S::*)()>());
+}
+
+namespace user_defined {
+struct S {
+    bool operator==(int) const;
+    std::strong_ordering operator<=>(int) const;
+    operator int() const;
+
+    bool operator==(const S&) const = default;
+    auto operator<=>(const S&) const = default;
+};
+
+static_assert(check_three_way_comparable_with<S, int>());
+static_assert(check_three_way_comparable_with<S, int, std::strong_ordering>());
+static_assert(check_three_way_comparable_with<S, int, std::weak_ordering>());
+
+struct SpaceshipNotDeclared {
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipNotDeclared>());
+
+struct SpaceshipDeleted {
+    auto operator<=>(const SpaceshipDeleted&) const = delete;
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipDeleted>());
+
+struct SpaceshipWithoutEqualityOperator {
+    auto operator<=>(const SpaceshipWithoutEqualityOperator&) const;
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipWithoutEqualityOperator>());
+
+struct EqualityOperatorDeleted {
+    bool operator==(const EqualityOperatorDeleted&) const = delete;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorDeleted>());
+
+struct EqualityOperatorOnly {
+    bool operator==(const EqualityOperatorOnly&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorOnly>());
+
+struct SpaceshipDeclaredEqualityOperatorDeleted {
+    bool operator==(const SpaceshipDeclaredEqualityOperatorDeleted&) const = delete;
+    auto operator<=>(const SpaceshipDeclaredEqualityOperatorDeleted&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipDeclaredEqualityOperatorDeleted>());
+
+struct AllInequalityOperators {
+    bool operator<(const AllInequalityOperators&) const;
+    bool operator<=(const AllInequalityOperators&) const;
+    bool operator>(const AllInequalityOperators&) const;
+    bool operator>=(const AllInequalityOperators&) const;
+    bool operator!=(const AllInequalityOperators&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllInequalityOperators>());
+
+struct AllComparisonOperators {
+    bool operator<(const AllComparisonOperators&) const;
+    bool operator<=(const AllComparisonOperators&) const;
+    bool operator>(const AllComparisonOperators&) const;
+    bool operator>=(const AllComparisonOperators&) const;
+    bool operator!=(const AllComparisonOperators&) const;
+    bool operator==(const AllComparisonOperators&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllComparisonOperators>());
+
+struct AllButOneInequalityOperators {
+    bool operator<(const AllButOneInequalityOperators&) const;
+    bool operator<=(const AllButOneInequalityOperators&) const;
+    bool operator>(const AllButOneInequalityOperators&) const;
+    bool operator!=(const AllButOneInequalityOperators&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllButOneInequalityOperators>());
+
+struct AllInequalityOperatorsOneDeleted {
+    bool operator<(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator<=(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>(const AllInequalityOperatorsOneDeleted&) const;
+    bool operator>=(const AllInequalityOperatorsOneDeleted&) const = delete;
+    bool operator!=(const AllInequalityOperatorsOneDeleted&) const;
+};
+
+static_assert(!check_three_way_comparable_with<AllInequalityOperatorsOneDeleted>());
+
+struct EqualityOperatorWrongReturnType {
+    int operator==(const EqualityOperatorWrongReturnType&);
+    auto operator<=>(const EqualityOperatorWrongReturnType&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorWrongReturnType>());
+
+struct SpaceshipWrongReturnType {
+    bool operator==(const SpaceshipWrongReturnType&) const = default;
+    int operator<=>(const SpaceshipWrongReturnType&);
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipWrongReturnType>());
+
+struct EqualityOperatorNonConstArgument {
+    bool operator==(EqualityOperatorNonConstArgument&);
+    auto operator<=>(const EqualityOperatorNonConstArgument&) const = default;
+};
+
+static_assert(!check_three_way_comparable_with<EqualityOperatorNonConstArgument>());
+
+struct SpaceshipNonConstArgument {
+    bool operator==(const SpaceshipNonConstArgument&) const = default;
+    auto operator<=>(SpaceshipNonConstArgument&);
+};
+
+static_assert(!check_three_way_comparable_with<SpaceshipNonConstArgument>());
+}
+
+int main(int, char**) { return 0; }