diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -97,6 +97,8 @@
   __bits
   __bsd_locale_defaults.h
   __bsd_locale_fallbacks.h
+  __compare/common_comparison_category.h
+  __compare/ordering.h
   __config
   __debug
   __errc
diff --git a/libcxx/include/__compare/common_comparison_category.h b/libcxx/include/__compare/common_comparison_category.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__compare/common_comparison_category.h
@@ -0,0 +1,92 @@
+//===----------------------------------------------------------------------===//
+//
+// 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_COMMON_COMPARISON_CATEGORY_H
+#define _LIBCPP___COMPARE_COMMON_COMPARISON_CATEGORY_H
+
+#include <__compare/ordering.h>
+#include <__config>
+#include <type_traits>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_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, bool _False = false>
+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(_False, "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
+
+#endif // _LIBCPP___COMPARE_COMMON_COMPARISON_CATEGORY_H
diff --git a/libcxx/include/compare b/libcxx/include/__compare/ordering.h
copy from libcxx/include/compare
copy to libcxx/include/__compare/ordering.h
--- a/libcxx/include/compare
+++ b/libcxx/include/__compare/ordering.h
@@ -1,5 +1,4 @@
-// -*- C++ -*-
-//===-------------------------- compare -----------------------------------===//
+//===----------------------------------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
@@ -7,129 +6,20 @@
 //
 //===----------------------------------------------------------------------===//
 
-#ifndef _LIBCPP_COMPARE
-#define _LIBCPP_COMPARE
-
-/*
-    compare synopsis
-
-namespace std {
-  // [cmp.categories], comparison category types
-  class partial_ordering;
-  class weak_ordering;
-  class strong_ordering;
-
-  // named comparison functions
-  constexpr bool is_eq  (partial_ordering cmp) noexcept    { return cmp == 0; }
-  constexpr bool is_neq (partial_ordering cmp) noexcept    { return cmp != 0; }
-  constexpr bool is_lt  (partial_ordering cmp) noexcept { return cmp < 0; }
-  constexpr bool is_lteq(partial_ordering cmp) noexcept { return cmp <= 0; }
-  constexpr bool is_gt  (partial_ordering cmp) noexcept { return cmp > 0; }
-  constexpr bool is_gteq(partial_ordering cmp) noexcept { return cmp >= 0; }
-
-  // [cmp.common], common comparison category type
-  template<class... Ts>
-  struct common_comparison_category {
-    using type = see below;
-  };
-  template<class... Ts>
-    using common_comparison_category_t = typename common_comparison_category<Ts...>::type;
-
-  // [cmp.alg], comparison algorithms
-  template<class T> constexpr strong_ordering strong_order(const T& a, const T& b);
-  template<class T> constexpr weak_ordering weak_order(const T& a, const T& b);
-  template<class T> constexpr partial_ordering partial_order(const T& a, const T& b);
-
-  // [cmp.partialord], Class partial_ordering
-  class partial_ordering {
-  public:
-    // valid values
-    static const partial_ordering less;
-    static const partial_ordering equivalent;
-    static const partial_ordering greater;
-    static const partial_ordering unordered;
-
-    // comparisons
-    friend constexpr bool operator==(partial_ordering v, unspecified) noexcept;
-    friend constexpr bool operator==(partial_ordering v, partial_ordering w) noexcept = default;
-    friend constexpr bool operator< (partial_ordering v, unspecified) noexcept;
-    friend constexpr bool operator> (partial_ordering v, unspecified) noexcept;
-    friend constexpr bool operator<=(partial_ordering v, unspecified) noexcept;
-    friend constexpr bool operator>=(partial_ordering v, unspecified) noexcept;
-    friend constexpr bool operator< (unspecified, partial_ordering v) noexcept;
-    friend constexpr bool operator> (unspecified, partial_ordering v) noexcept;
-    friend constexpr bool operator<=(unspecified, partial_ordering v) noexcept;
-    friend constexpr bool operator>=(unspecified, partial_ordering v) noexcept;
-    friend constexpr partial_ordering operator<=>(partial_ordering v, unspecified) noexcept;
-    friend constexpr partial_ordering operator<=>(unspecified, partial_ordering v) noexcept;
-  };
-
-  // [cmp.weakord], Class weak_ordering
-  class weak_ordering {
-  public:
-    // valid values
-    static const weak_ordering less;
-    static const weak_ordering equivalent;
-    static const weak_ordering greater;
-
-    // conversions
-    constexpr operator partial_ordering() const noexcept;
-
-    // comparisons
-    friend constexpr bool operator==(weak_ordering v, unspecified) noexcept;
-    friend constexpr bool operator==(weak_ordering v, weak_ordering w) noexcept = default;
-    friend constexpr bool operator< (weak_ordering v, unspecified) noexcept;
-    friend constexpr bool operator> (weak_ordering v, unspecified) noexcept;
-    friend constexpr bool operator<=(weak_ordering v, unspecified) noexcept;
-    friend constexpr bool operator>=(weak_ordering v, unspecified) noexcept;
-    friend constexpr bool operator< (unspecified, weak_ordering v) noexcept;
-    friend constexpr bool operator> (unspecified, weak_ordering v) noexcept;
-    friend constexpr bool operator<=(unspecified, weak_ordering v) noexcept;
-    friend constexpr bool operator>=(unspecified, weak_ordering v) noexcept;
-    friend constexpr weak_ordering operator<=>(weak_ordering v, unspecified) noexcept;
-    friend constexpr weak_ordering operator<=>(unspecified, weak_ordering v) noexcept;
-  };
-
-  // [cmp.strongord], Class strong_ordering
-  class strong_ordering {
-  public:
-    // valid values
-    static const strong_ordering less;
-    static const strong_ordering equal;
-    static const strong_ordering equivalent;
-    static const strong_ordering greater;
-
-    // conversions
-    constexpr operator partial_ordering() const noexcept;
-    constexpr operator weak_ordering() const noexcept;
-
-    // comparisons
-    friend constexpr bool operator==(strong_ordering v, unspecified) noexcept;
-    friend constexpr bool operator==(strong_ordering v, strong_ordering w) noexcept = default;
-    friend constexpr bool operator< (strong_ordering v, unspecified) noexcept;
-    friend constexpr bool operator> (strong_ordering v, unspecified) noexcept;
-    friend constexpr bool operator<=(strong_ordering v, unspecified) noexcept;
-    friend constexpr bool operator>=(strong_ordering v, unspecified) noexcept;
-    friend constexpr bool operator< (unspecified, strong_ordering v) noexcept;
-    friend constexpr bool operator> (unspecified, strong_ordering v) noexcept;
-    friend constexpr bool operator<=(unspecified, strong_ordering v) noexcept;
-    friend constexpr bool operator>=(unspecified, strong_ordering v) noexcept;
-    friend constexpr strong_ordering operator<=>(strong_ordering v, unspecified) noexcept;
-    friend constexpr strong_ordering operator<=>(unspecified, strong_ordering v) noexcept;
-  };
-}
-*/
+#ifndef _LIBCPP___COMPARE_ORDERING_H
+#define _LIBCPP___COMPARE_ORDERING_H
 
 #include <__config>
 #include <type_traits>
 
-#ifndef _LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _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,
@@ -412,78 +302,8 @@
 _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, bool _False = false>
-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(_False, "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
-template<class _Tp> constexpr strong_ordering strong_order(const _Tp& __lhs, const _Tp& __rhs);
-template<class _Tp> constexpr weak_ordering weak_order(const _Tp& __lhs, const _Tp& __rhs);
-template<class _Tp> constexpr partial_ordering partial_order(const _Tp& __lhs, const _Tp& __rhs);
-
 #endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_SPACESHIP_OPERATOR)
 
 _LIBCPP_END_NAMESPACE_STD
 
-#endif // _LIBCPP_COMPARE
+#endif // _LIBCPP___COMPARE_ORDERING_H
diff --git a/libcxx/include/compare b/libcxx/include/compare
--- a/libcxx/include/compare
+++ b/libcxx/include/compare
@@ -120,6 +120,8 @@
 }
 */
 
+#include <__compare/common_comparison_category.h>
+#include <__compare/ordering.h>
 #include <__config>
 #include <type_traits>
 
@@ -130,351 +132,6 @@
 _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, bool _False = false>
-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(_False, "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
diff --git a/libcxx/include/module.modulemap b/libcxx/include/module.modulemap
--- a/libcxx/include/module.modulemap
+++ b/libcxx/include/module.modulemap
@@ -358,6 +358,11 @@
   module compare {
     header "compare"
     export *
+
+    module __compare {
+      module common_comparison_category { private header "__compare/common_comparison_category.h" }
+      module ordering                   { private header "__compare/ordering.h"                   }
+    }
   }
   module complex {
     header "complex"
diff --git a/libcxx/test/libcxx/diagnostics/detail.headers/compare/common_comparison_category.module.verify.cpp b/libcxx/test/libcxx/diagnostics/detail.headers/compare/common_comparison_category.module.verify.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/libcxx/diagnostics/detail.headers/compare/common_comparison_category.module.verify.cpp
@@ -0,0 +1,16 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// REQUIRES: modules-build
+
+// WARNING: This test was generated by 'generate_private_header_tests.py'
+// and should not be edited manually.
+
+// expected-error@*:* {{use of private header from outside its module: '__compare/common_comparison_category.h'}}
+#include <__compare/common_comparison_category.h>
diff --git a/libcxx/test/libcxx/diagnostics/detail.headers/compare/ordering.module.verify.cpp b/libcxx/test/libcxx/diagnostics/detail.headers/compare/ordering.module.verify.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/libcxx/diagnostics/detail.headers/compare/ordering.module.verify.cpp
@@ -0,0 +1,16 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// REQUIRES: modules-build
+
+// WARNING: This test was generated by 'generate_private_header_tests.py'
+// and should not be edited manually.
+
+// expected-error@*:* {{use of private header from outside its module: '__compare/ordering.h'}}
+#include <__compare/ordering.h>