path: root/contrib/llvm-project/libcxx/include/type_traits

// -*- 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
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_TYPE_TRAITS
#define _LIBCPP_TYPE_TRAITS

/*
    type_traits synopsis

namespace std
{

    // helper class:
    template <class T, T v> struct integral_constant;
    typedef integral_constant<bool, true>  true_type;   // C++11
    typedef integral_constant<bool, false> false_type;  // C++11

    template <bool B>                                   // C++14
    using bool_constant = integral_constant<bool, B>;   // C++14
    typedef bool_constant<true> true_type;              // C++14
    typedef bool_constant<false> false_type;            // C++14

    // helper traits
    template <bool, class T = void> struct enable_if;
    template <bool, class T, class F> struct conditional;

    // Primary classification traits:
    template <class T> struct is_void;
    template <class T> struct is_null_pointer;  // C++14
    template <class T> struct is_integral;
    template <class T> struct is_floating_point;
    template <class T> struct is_array;
    template <class T> struct is_pointer;
    template <class T> struct is_lvalue_reference;
    template <class T> struct is_rvalue_reference;
    template <class T> struct is_member_object_pointer;
    template <class T> struct is_member_function_pointer;
    template <class T> struct is_enum;
    template <class T> struct is_union;
    template <class T> struct is_class;
    template <class T> struct is_function;

    // Secondary classification traits:
    template <class T> struct is_reference;
    template <class T> struct is_arithmetic;
    template <class T> struct is_fundamental;
    template <class T> struct is_member_pointer;
    template <class T> struct is_scoped_enum; // C++2b
    template <class T> struct is_scalar;
    template <class T> struct is_object;
    template <class T> struct is_compound;

    // Const-volatile properties and transformations:
    template <class T> struct is_const;
    template <class T> struct is_volatile;
    template <class T> struct remove_const;
    template <class T> struct remove_volatile;
    template <class T> struct remove_cv;
    template <class T> struct add_const;
    template <class T> struct add_volatile;
    template <class T> struct add_cv;

    // Reference transformations:
    template <class T> struct remove_reference;
    template <class T> struct add_lvalue_reference;
    template <class T> struct add_rvalue_reference;

    // Pointer transformations:
    template <class T> struct remove_pointer;
    template <class T> struct add_pointer;

    template<class T> struct type_identity;                     // C++20
    template<class T>
      using type_identity_t = typename type_identity<T>::type;  // C++20

    // Integral properties:
    template <class T> struct is_signed;
    template <class T> struct is_unsigned;
    template <class T> struct make_signed;
    template <class T> struct make_unsigned;

    // Array properties and transformations:
    template <class T> struct rank;
    template <class T, unsigned I = 0> struct extent;
    template <class T> struct remove_extent;
    template <class T> struct remove_all_extents;

    template <class T> struct is_bounded_array;                 // C++20
    template <class T> struct is_unbounded_array;               // C++20

    // Member introspection:
    template <class T> struct is_pod;
    template <class T> struct is_trivial;
    template <class T> struct is_trivially_copyable;
    template <class T> struct is_standard_layout;
    template <class T> struct is_literal_type; // Deprecated in C++17; removed in C++20
    template <class T> struct is_empty;
    template <class T> struct is_polymorphic;
    template <class T> struct is_abstract;
    template <class T> struct is_final; // C++14
    template <class T> struct is_aggregate; // C++17

    template <class T, class... Args> struct is_constructible;
    template <class T>                struct is_default_constructible;
    template <class T>                struct is_copy_constructible;
    template <class T>                struct is_move_constructible;
    template <class T, class U>       struct is_assignable;
    template <class T>                struct is_copy_assignable;
    template <class T>                struct is_move_assignable;
    template <class T, class U>       struct is_swappable_with;       // C++17
    template <class T>                struct is_swappable;            // C++17
    template <class T>                struct is_destructible;

    template <class T, class... Args> struct is_trivially_constructible;
    template <class T>                struct is_trivially_default_constructible;
    template <class T>                struct is_trivially_copy_constructible;
    template <class T>                struct is_trivially_move_constructible;
    template <class T, class U>       struct is_trivially_assignable;
    template <class T>                struct is_trivially_copy_assignable;
    template <class T>                struct is_trivially_move_assignable;
    template <class T>                struct is_trivially_destructible;

    template <class T, class... Args> struct is_nothrow_constructible;
    template <class T>                struct is_nothrow_default_constructible;
    template <class T>                struct is_nothrow_copy_constructible;
    template <class T>                struct is_nothrow_move_constructible;
    template <class T, class U>       struct is_nothrow_assignable;
    template <class T>                struct is_nothrow_copy_assignable;
    template <class T>                struct is_nothrow_move_assignable;
    template <class T, class U>       struct is_nothrow_swappable_with; // C++17
    template <class T>                struct is_nothrow_swappable;      // C++17
    template <class T>                struct is_nothrow_destructible;

    template <class T> struct has_virtual_destructor;

    template<class T> struct has_unique_object_representations;         // C++17

    // Relationships between types:
    template <class T, class U> struct is_same;
    template <class Base, class Derived> struct is_base_of;

    template <class From, class To> struct is_convertible;
    template <typename From, typename To> struct is_nothrow_convertible;                  // C++20
    template <typename From, typename To> inline constexpr bool is_nothrow_convertible_v; // C++20

    template <class Fn, class... ArgTypes> struct is_invocable;
    template <class R, class Fn, class... ArgTypes> struct is_invocable_r;

    template <class Fn, class... ArgTypes> struct is_nothrow_invocable;
    template <class R, class Fn, class... ArgTypes> struct is_nothrow_invocable_r;

    // Alignment properties and transformations:
    template <class T> struct alignment_of;
    template <size_t Len, size_t Align = most_stringent_alignment_requirement>
        struct aligned_storage;
    template <size_t Len, class... Types> struct aligned_union;
    template <class T> struct remove_cvref; // C++20

    template <class T> struct decay;
    template <class... T> struct common_type;
    template <class T> struct underlying_type;
    template <class> class result_of; // undefined; deprecated in C++17; removed in C++20
    template <class Fn, class... ArgTypes> class result_of<Fn(ArgTypes...)>; // deprecated in C++17; removed in C++20
    template <class Fn, class... ArgTypes> struct invoke_result;  // C++17

    // const-volatile modifications:
    template <class T>
      using remove_const_t    = typename remove_const<T>::type;  // C++14
    template <class T>
      using remove_volatile_t = typename remove_volatile<T>::type;  // C++14
    template <class T>
      using remove_cv_t       = typename remove_cv<T>::type;  // C++14
    template <class T>
      using add_const_t       = typename add_const<T>::type;  // C++14
    template <class T>
      using add_volatile_t    = typename add_volatile<T>::type;  // C++14
    template <class T>
      using add_cv_t          = typename add_cv<T>::type;  // C++14

    // reference modifications:
    template <class T>
      using remove_reference_t     = typename remove_reference<T>::type;  // C++14
    template <class T>
      using add_lvalue_reference_t = typename add_lvalue_reference<T>::type;  // C++14
    template <class T>
      using add_rvalue_reference_t = typename add_rvalue_reference<T>::type;  // C++14

    // sign modifications:
    template <class T>
      using make_signed_t   = typename make_signed<T>::type;  // C++14
    template <class T>
      using make_unsigned_t = typename make_unsigned<T>::type;  // C++14

    // array modifications:
    template <class T>
      using remove_extent_t      = typename remove_extent<T>::type;  // C++14
    template <class T>
      using remove_all_extents_t = typename remove_all_extents<T>::type;  // C++14

    template <class T>
      inline constexpr bool is_bounded_array_v
        = is_bounded_array<T>::value;                                     // C++20
      inline constexpr bool is_unbounded_array_v
        = is_unbounded_array<T>::value;                                   // C++20

    // pointer modifications:
    template <class T>
      using remove_pointer_t = typename remove_pointer<T>::type;  // C++14
    template <class T>
      using add_pointer_t    = typename add_pointer<T>::type;  // C++14

    // other transformations:
    template <size_t Len, size_t Align=default-alignment>
      using aligned_storage_t = typename aligned_storage<Len,Align>::type;  // C++14
    template <size_t Len, class... Types>
      using aligned_union_t   = typename aligned_union<Len,Types...>::type;  // C++14
    template <class T>
      using remove_cvref_t    = typename remove_cvref<T>::type;  // C++20
    template <class T>
      using decay_t           = typename decay<T>::type;  // C++14
    template <bool b, class T=void>
      using enable_if_t       = typename enable_if<b,T>::type;  // C++14
    template <bool b, class T, class F>
      using conditional_t     = typename conditional<b,T,F>::type;  // C++14
    template <class... T>
      using common_type_t     = typename common_type<T...>::type;  // C++14
    template <class T>
      using underlying_type_t = typename underlying_type<T>::type;  // C++14
    template <class T>
      using result_of_t       = typename result_of<T>::type;  // C++14; deprecated in C++17; removed in C++20
    template <class Fn, class... ArgTypes>
      using invoke_result_t   = typename invoke_result<Fn, ArgTypes...>::type;  // C++17

    template <class...>
      using void_t = void;   // C++17

      // See C++14 20.10.4.1, primary type categories
      template <class T> inline constexpr bool is_void_v
        = is_void<T>::value;                                             // C++17
      template <class T> inline constexpr bool is_null_pointer_v
        = is_null_pointer<T>::value;                                     // C++17
      template <class T> inline constexpr bool is_integral_v
        = is_integral<T>::value;                                         // C++17
      template <class T> inline constexpr bool is_floating_point_v
        = is_floating_point<T>::value;                                   // C++17
      template <class T> inline constexpr bool is_array_v
        = is_array<T>::value;                                            // C++17
      template <class T> inline constexpr bool is_pointer_v
        = is_pointer<T>::value;                                          // C++17
      template <class T> inline constexpr bool is_lvalue_reference_v
        = is_lvalue_reference<T>::value;                                 // C++17
      template <class T> inline constexpr bool is_rvalue_reference_v
        = is_rvalue_reference<T>::value;                                 // C++17
      template <class T> inline constexpr bool is_member_object_pointer_v
        = is_member_object_pointer<T>::value;                            // C++17
      template <class T> inline constexpr bool is_member_function_pointer_v
        = is_member_function_pointer<T>::value;                          // C++17
      template <class T> inline constexpr bool is_enum_v
        = is_enum<T>::value;                                             // C++17
      template <class T> inline constexpr bool is_union_v
        = is_union<T>::value;                                            // C++17
      template <class T> inline constexpr bool is_class_v
        = is_class<T>::value;                                            // C++17
      template <class T> inline constexpr bool is_function_v
        = is_function<T>::value;                                         // C++17

      // See C++14 20.10.4.2, composite type categories
      template <class T> inline constexpr bool is_reference_v
        = is_reference<T>::value;                                        // C++17
      template <class T> inline constexpr bool is_arithmetic_v
        = is_arithmetic<T>::value;                                       // C++17
      template <class T> inline constexpr bool is_fundamental_v
        = is_fundamental<T>::value;                                      // C++17
      template <class T> inline constexpr bool is_object_v
        = is_object<T>::value;                                           // C++17
      template <class T> inline constexpr bool is_scalar_v
        = is_scalar<T>::value;                                           // C++17
      template <class T> inline constexpr bool is_compound_v
        = is_compound<T>::value;                                         // C++17
      template <class T> inline constexpr bool is_member_pointer_v
        = is_member_pointer<T>::value;                                   // C++17
      template <class T> inline constexpr bool is_scoped_enum_v
        = is_scoped_enum<T>::value;                                      // C++2b

      // See C++14 20.10.4.3, type properties
      template <class T> inline constexpr bool is_const_v
        = is_const<T>::value;                                            // C++17
      template <class T> inline constexpr bool is_volatile_v
        = is_volatile<T>::value;                                         // C++17
      template <class T> inline constexpr bool is_trivial_v
        = is_trivial<T>::value;                                          // C++17
      template <class T> inline constexpr bool is_trivially_copyable_v
        = is_trivially_copyable<T>::value;                               // C++17
      template <class T> inline constexpr bool is_standard_layout_v
        = is_standard_layout<T>::value;                                  // C++17
      template <class T> inline constexpr bool is_pod_v
        = is_pod<T>::value;                                              // C++17
      template <class T> inline constexpr bool is_literal_type_v
        = is_literal_type<T>::value;                                     // C++17; deprecated in C++17; removed in C++20
      template <class T> inline constexpr bool is_empty_v
        = is_empty<T>::value;                                            // C++17
      template <class T> inline constexpr bool is_polymorphic_v
        = is_polymorphic<T>::value;                                      // C++17
      template <class T> inline constexpr bool is_abstract_v
        = is_abstract<T>::value;                                         // C++17
      template <class T> inline constexpr bool is_final_v
        = is_final<T>::value;                                            // C++17
      template <class T> inline constexpr bool is_aggregate_v
        = is_aggregate<T>::value;                                        // C++17
      template <class T> inline constexpr bool is_signed_v
        = is_signed<T>::value;                                           // C++17
      template <class T> inline constexpr bool is_unsigned_v
        = is_unsigned<T>::value;                                         // C++17
      template <class T, class... Args> inline constexpr bool is_constructible_v
        = is_constructible<T, Args...>::value;                           // C++17
      template <class T> inline constexpr bool is_default_constructible_v
        = is_default_constructible<T>::value;                            // C++17
      template <class T> inline constexpr bool is_copy_constructible_v
        = is_copy_constructible<T>::value;                               // C++17
      template <class T> inline constexpr bool is_move_constructible_v
        = is_move_constructible<T>::value;                               // C++17
      template <class T, class U> inline constexpr bool is_assignable_v
        = is_assignable<T, U>::value;                                    // C++17
      template <class T> inline constexpr bool is_copy_assignable_v
        = is_copy_assignable<T>::value;                                  // C++17
      template <class T> inline constexpr bool is_move_assignable_v
        = is_move_assignable<T>::value;                                  // C++17
      template <class T, class U> inline constexpr bool is_swappable_with_v
        = is_swappable_with<T, U>::value;                                // C++17
      template <class T> inline constexpr bool is_swappable_v
        = is_swappable<T>::value;                                        // C++17
      template <class T> inline constexpr bool is_destructible_v
        = is_destructible<T>::value;                                     // C++17
      template <class T, class... Args> inline constexpr bool is_trivially_constructible_v
        = is_trivially_constructible<T, Args...>::value;                 // C++17
      template <class T> inline constexpr bool is_trivially_default_constructible_v
        = is_trivially_default_constructible<T>::value;                  // C++17
      template <class T> inline constexpr bool is_trivially_copy_constructible_v
        = is_trivially_copy_constructible<T>::value;                     // C++17
      template <class T> inline constexpr bool is_trivially_move_constructible_v
        = is_trivially_move_constructible<T>::value;                     // C++17
      template <class T, class U> inline constexpr bool is_trivially_assignable_v
        = is_trivially_assignable<T, U>::value;                          // C++17
      template <class T> inline constexpr bool is_trivially_copy_assignable_v
        = is_trivially_copy_assignable<T>::value;                        // C++17
      template <class T> inline constexpr bool is_trivially_move_assignable_v
        = is_trivially_move_assignable<T>::value;                        // C++17
      template <class T> inline constexpr bool is_trivially_destructible_v
        = is_trivially_destructible<T>::value;                           // C++17
      template <class T, class... Args> inline constexpr bool is_nothrow_constructible_v
        = is_nothrow_constructible<T, Args...>::value;                   // C++17
      template <class T> inline constexpr bool is_nothrow_default_constructible_v
        = is_nothrow_default_constructible<T>::value;                    // C++17
      template <class T> inline constexpr bool is_nothrow_copy_constructible_v
        = is_nothrow_copy_constructible<T>::value;                       // C++17
      template <class T> inline constexpr bool is_nothrow_move_constructible_v
        = is_nothrow_move_constructible<T>::value;                       // C++17
      template <class T, class U> inline constexpr bool is_nothrow_assignable_v
        = is_nothrow_assignable<T, U>::value;                            // C++17
      template <class T> inline constexpr bool is_nothrow_copy_assignable_v
        = is_nothrow_copy_assignable<T>::value;                          // C++17
      template <class T> inline constexpr bool is_nothrow_move_assignable_v
        = is_nothrow_move_assignable<T>::value;                          // C++17
      template <class T, class U> inline constexpr bool is_nothrow_swappable_with_v
        = is_nothrow_swappable_with<T, U>::value;                       // C++17
      template <class T> inline constexpr bool is_nothrow_swappable_v
        = is_nothrow_swappable<T>::value;                               // C++17
      template <class T> inline constexpr bool is_nothrow_destructible_v
        = is_nothrow_destructible<T>::value;                             // C++17
      template <class T> inline constexpr bool has_virtual_destructor_v
        = has_virtual_destructor<T>::value;                              // C++17
      template<class T> inline constexpr bool has_unique_object_representations_v // C++17
        = has_unique_object_representations<T>::value;

      // See C++14 20.10.5, type property queries
      template <class T> inline constexpr size_t alignment_of_v
        = alignment_of<T>::value;                                        // C++17
      template <class T> inline constexpr size_t rank_v
        = rank<T>::value;                                                // C++17
      template <class T, unsigned I = 0> inline constexpr size_t extent_v
        = extent<T, I>::value;                                           // C++17

      // See C++14 20.10.6, type relations
      template <class T, class U> inline constexpr bool is_same_v
        = is_same<T, U>::value;                                          // C++17
      template <class Base, class Derived> inline constexpr bool is_base_of_v
        = is_base_of<Base, Derived>::value;                              // C++17
      template <class From, class To> inline constexpr bool is_convertible_v
        = is_convertible<From, To>::value;                               // C++17
      template <class Fn, class... ArgTypes> inline constexpr bool is_invocable_v
        = is_invocable<Fn, ArgTypes...>::value;                          // C++17
      template <class R, class Fn, class... ArgTypes> inline constexpr bool is_invocable_r_v
        = is_invocable_r<R, Fn, ArgTypes...>::value;                     // C++17
      template <class Fn, class... ArgTypes> inline constexpr bool is_nothrow_invocable_v
        = is_nothrow_invocable<Fn, ArgTypes...>::value;                  // C++17
      template <class R, class Fn, class... ArgTypes> inline constexpr bool is_nothrow_invocable_r_v
        = is_nothrow_invocable_r<R, Fn, ArgTypes...>::value;             // C++17

      // [meta.logical], logical operator traits:
      template<class... B> struct conjunction;                           // C++17
      template<class... B>
        inline constexpr bool conjunction_v = conjunction<B...>::value;  // C++17
      template<class... B> struct disjunction;                           // C++17
      template<class... B>
        inline constexpr bool disjunction_v = disjunction<B...>::value;  // C++17
      template<class B> struct negation;                                 // C++17
      template<class B>
        inline constexpr bool negation_v = negation<B>::value;           // C++17

}

*/
#include <__assert> // all public C++ headers provide the assertion handler
#include <__config>
#include <__functional/invoke.h>
#include <__type_traits/add_const.h>
#include <__type_traits/add_cv.h>
#include <__type_traits/add_lvalue_reference.h>
#include <__type_traits/add_pointer.h>
#include <__type_traits/add_rvalue_reference.h>
#include <__type_traits/add_volatile.h>
#include <__type_traits/alignment_of.h>
#include <__type_traits/apply_cv.h>
#include <__type_traits/conditional.h>
#include <__type_traits/conjunction.h>
#include <__type_traits/decay.h>
#include <__type_traits/disjunction.h>
#include <__type_traits/enable_if.h>
#include <__type_traits/extent.h>
#include <__type_traits/has_unique_object_representation.h>
#include <__type_traits/has_virtual_destructor.h>
#include <__type_traits/integral_constant.h>
#include <__type_traits/is_abstract.h>
#include <__type_traits/is_aggregate.h>
#include <__type_traits/is_arithmetic.h>
#include <__type_traits/is_array.h>
#include <__type_traits/is_assignable.h>
#include <__type_traits/is_base_of.h>
#include <__type_traits/is_bounded_array.h>
#include <__type_traits/is_callable.h>
#include <__type_traits/is_class.h>
#include <__type_traits/is_compound.h>
#include <__type_traits/is_const.h>
#include <__type_traits/is_constant_evaluated.h>
#include <__type_traits/is_constructible.h>
#include <__type_traits/is_convertible.h>
#include <__type_traits/is_copy_assignable.h>
#include <__type_traits/is_copy_constructible.h>
#include <__type_traits/is_default_constructible.h>
#include <__type_traits/is_destructible.h>
#include <__type_traits/is_empty.h>
#include <__type_traits/is_enum.h>
#include <__type_traits/is_final.h>
#include <__type_traits/is_floating_point.h>
#include <__type_traits/is_function.h>
#include <__type_traits/is_fundamental.h>
#include <__type_traits/is_integral.h>
#include <__type_traits/is_literal_type.h>
#include <__type_traits/is_member_function_pointer.h>
#include <__type_traits/is_member_object_pointer.h>
#include <__type_traits/is_member_pointer.h>
#include <__type_traits/is_move_assignable.h>
#include <__type_traits/is_move_constructible.h>
#include <__type_traits/is_nothrow_assignable.h>
#include <__type_traits/is_nothrow_constructible.h>
#include <__type_traits/is_nothrow_copy_assignable.h>
#include <__type_traits/is_nothrow_copy_constructible.h>
#include <__type_traits/is_nothrow_default_constructible.h>
#include <__type_traits/is_nothrow_destructible.h>
#include <__type_traits/is_nothrow_move_assignable.h>
#include <__type_traits/is_nothrow_move_constructible.h>
#include <__type_traits/is_null_pointer.h>
#include <__type_traits/is_object.h>
#include <__type_traits/is_pod.h>
#include <__type_traits/is_pointer.h>
#include <__type_traits/is_polymorphic.h>
#include <__type_traits/is_reference.h>
#include <__type_traits/is_reference_wrapper.h>
#include <__type_traits/is_referenceable.h>
#include <__type_traits/is_same.h>
#include <__type_traits/is_scalar.h>
#include <__type_traits/is_scoped_enum.h>
#include <__type_traits/is_signed.h>
#include <__type_traits/is_standard_layout.h>
#include <__type_traits/is_trivial.h>
#include <__type_traits/is_trivially_assignable.h>
#include <__type_traits/is_trivially_constructible.h>
#include <__type_traits/is_trivially_copy_assignable.h>
#include <__type_traits/is_trivially_copy_constructible.h>
#include <__type_traits/is_trivially_copyable.h>
#include <__type_traits/is_trivially_default_constructible.h>
#include <__type_traits/is_trivially_destructible.h>
#include <__type_traits/is_trivially_move_assignable.h>
#include <__type_traits/is_trivially_move_constructible.h>
#include <__type_traits/is_unbounded_array.h>
#include <__type_traits/is_union.h>
#include <__type_traits/is_unsigned.h>
#include <__type_traits/is_void.h>
#include <__type_traits/is_volatile.h>
#include <__type_traits/negation.h>
#include <__type_traits/rank.h>
#include <__type_traits/remove_all_extents.h>
#include <__type_traits/remove_const.h>
#include <__type_traits/remove_cv.h>
#include <__type_traits/remove_extent.h>
#include <__type_traits/remove_pointer.h>
#include <__type_traits/remove_reference.h>
#include <__type_traits/remove_volatile.h>
#include <__type_traits/type_identity.h>
#include <__type_traits/underlying_type.h>
#include <__type_traits/void_t.h>
#include <__utility/declval.h>
#include <cstddef>
#include <cstdint>
#include <version>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#  pragma GCC system_header
#endif

_LIBCPP_BEGIN_NAMESPACE_STD

template <class _T1, class _T2> struct _LIBCPP_TEMPLATE_VIS pair;
template <class _Tp> struct _LIBCPP_TEMPLATE_VIS hash;

template <template <class...> class _Func, class ..._Args>
struct _Lazy : _Func<_Args...> {};

// Member detector base

template <template <class...> class _Templ, class ..._Args, class = _Templ<_Args...> >
true_type __sfinae_test_impl(int);
template <template <class...> class, class ...>
false_type __sfinae_test_impl(...);

template <template <class ...> class _Templ, class ..._Args>
using _IsValidExpansion _LIBCPP_NODEBUG = decltype(__sfinae_test_impl<_Templ, _Args...>(0));

template <class _Tp, bool>
struct _LIBCPP_TEMPLATE_VIS __dependent_type : public _Tp {};

// is_same

template <class _Tp>
using __test_for_primary_template = __enable_if_t<
    _IsSame<_Tp, typename _Tp::__primary_template>::value
  >;
template <class _Tp>
using __is_primary_template = _IsValidExpansion<
    __test_for_primary_template, _Tp
  >;

// is_integral

// [basic.fundamental] defines five standard signed integer types;
// __int128_t is an extended signed integer type.
// The signed and unsigned integer types, plus bool and the
// five types with "char" in their name, compose the "integral" types.

template <class _Tp> struct __libcpp_is_signed_integer : public false_type {};
template <> struct __libcpp_is_signed_integer<signed char>      : public true_type {};
template <> struct __libcpp_is_signed_integer<signed short>     : public true_type {};
template <> struct __libcpp_is_signed_integer<signed int>       : public true_type {};
template <> struct __libcpp_is_signed_integer<signed long>      : public true_type {};
template <> struct __libcpp_is_signed_integer<signed long long> : public true_type {};
#ifndef _LIBCPP_HAS_NO_INT128
template <> struct __libcpp_is_signed_integer<__int128_t>       : public true_type {};
#endif

template <class _Tp> struct __libcpp_is_unsigned_integer : public false_type {};
template <> struct __libcpp_is_unsigned_integer<unsigned char>      : public true_type {};
template <> struct __libcpp_is_unsigned_integer<unsigned short>     : public true_type {};
template <> struct __libcpp_is_unsigned_integer<unsigned int>       : public true_type {};
template <> struct __libcpp_is_unsigned_integer<unsigned long>      : public true_type {};
template <> struct __libcpp_is_unsigned_integer<unsigned long long> : public true_type {};
#ifndef _LIBCPP_HAS_NO_INT128
template <> struct __libcpp_is_unsigned_integer<__uint128_t>        : public true_type {};
#endif

template <class _Tp>
struct __unconstref {
    typedef _LIBCPP_NODEBUG typename remove_const<typename remove_reference<_Tp>::type>::type type;
};

template <class _Tp>
using __uncvref_t _LIBCPP_NODEBUG = typename remove_cv<typename remove_reference<_Tp>::type>::type;

// __is_same_uncvref

template <class _Tp, class _Up>
struct __is_same_uncvref : _IsSame<__uncvref_t<_Tp>, __uncvref_t<_Up> > {};

#if _LIBCPP_STD_VER > 17
// remove_cvref - same as __uncvref
template <class _Tp>
struct remove_cvref {
    using type _LIBCPP_NODEBUG = __uncvref_t<_Tp>;
};

template <class _Tp> using remove_cvref_t = typename remove_cvref<_Tp>::type;
#endif

// is_nothrow_convertible

#if _LIBCPP_STD_VER > 17

template <typename _Tp>
static void __test_noexcept(_Tp) noexcept;

template<typename _Fm, typename _To>
static bool_constant<noexcept(_VSTD::__test_noexcept<_To>(declval<_Fm>()))>
__is_nothrow_convertible_test();

template <typename _Fm, typename _To>
struct __is_nothrow_convertible_helper: decltype(__is_nothrow_convertible_test<_Fm, _To>())
{ };

template <typename _Fm, typename _To>
struct is_nothrow_convertible : _Or<
    _And<is_void<_To>, is_void<_Fm>>,
    _Lazy<_And, is_convertible<_Fm, _To>, __is_nothrow_convertible_helper<_Fm, _To>>
>::type { };

template <typename _Fm, typename _To>
inline constexpr bool is_nothrow_convertible_v = is_nothrow_convertible<_Fm, _To>::value;

#endif // _LIBCPP_STD_VER > 17

// aligned_storage

template <class _Hp, class _Tp>
struct __type_list
{
    typedef _Hp _Head;
    typedef _Tp _Tail;
};

template <class _Tp>
struct __align_type
{
    static const size_t value = _LIBCPP_PREFERRED_ALIGNOF(_Tp);
    typedef _Tp type;
};

struct __struct_double {long double __lx;};
struct __struct_double4 {double __lx[4];};

typedef
    __type_list<__align_type<unsigned char>,
    __type_list<__align_type<unsigned short>,
    __type_list<__align_type<unsigned int>,
    __type_list<__align_type<unsigned long>,
    __type_list<__align_type<unsigned long long>,
    __type_list<__align_type<double>,
    __type_list<__align_type<long double>,
    __type_list<__align_type<__struct_double>,
    __type_list<__align_type<__struct_double4>,
    __type_list<__align_type<int*>,
    __nat
    > > > > > > > > > > __all_types;

template <size_t _Align>
struct _ALIGNAS(_Align) __fallback_overaligned {};

template <class _TL, size_t _Align> struct __find_pod;

template <class _Hp, size_t _Align>
struct __find_pod<__type_list<_Hp, __nat>, _Align>
{
    typedef typename conditional<
                             _Align == _Hp::value,
                             typename _Hp::type,
                             __fallback_overaligned<_Align>
                         >::type type;
};

template <class _Hp, class _Tp, size_t _Align>
struct __find_pod<__type_list<_Hp, _Tp>, _Align>
{
    typedef typename conditional<
                             _Align == _Hp::value,
                             typename _Hp::type,
                             typename __find_pod<_Tp, _Align>::type
                         >::type type;
};

template <class _TL, size_t _Len> struct __find_max_align;

template <class _Hp, size_t _Len>
struct __find_max_align<__type_list<_Hp, __nat>, _Len> : public integral_constant<size_t, _Hp::value> {};

template <size_t _Len, size_t _A1, size_t _A2>
struct __select_align
{
private:
    static const size_t __min = _A2 < _A1 ? _A2 : _A1;
    static const size_t __max = _A1 < _A2 ? _A2 : _A1;
public:
    static const size_t value = _Len < __max ? __min : __max;
};

template <class _Hp, class _Tp, size_t _Len>
struct __find_max_align<__type_list<_Hp, _Tp>, _Len>
    : public integral_constant<size_t, __select_align<_Len, _Hp::value, __find_max_align<_Tp, _Len>::value>::value> {};

template <size_t _Len, size_t _Align = __find_max_align<__all_types, _Len>::value>
struct _LIBCPP_TEMPLATE_VIS aligned_storage
{
    typedef typename __find_pod<__all_types, _Align>::type _Aligner;
    union type
    {
        _Aligner __align;
        unsigned char __data[(_Len + _Align - 1)/_Align * _Align];
    };
};

#if _LIBCPP_STD_VER > 11
template <size_t _Len, size_t _Align = __find_max_align<__all_types, _Len>::value>
    using aligned_storage_t = typename aligned_storage<_Len, _Align>::type;
#endif

#define _CREATE_ALIGNED_STORAGE_SPECIALIZATION(n) \
template <size_t _Len>\
struct _LIBCPP_TEMPLATE_VIS aligned_storage<_Len, n>\
{\
    struct _ALIGNAS(n) type\
    {\
        unsigned char __lx[(_Len + n - 1)/n * n];\
    };\
}

_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x1);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x2);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x4);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x8);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x10);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x20);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x40);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x80);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x100);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x200);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x400);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x800);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x1000);
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x2000);
// PE/COFF does not support alignment beyond 8192 (=0x2000)
#if !defined(_LIBCPP_OBJECT_FORMAT_COFF)
_CREATE_ALIGNED_STORAGE_SPECIALIZATION(0x4000);
#endif // !defined(_LIBCPP_OBJECT_FORMAT_COFF)

#undef _CREATE_ALIGNED_STORAGE_SPECIALIZATION


// aligned_union

template <size_t _I0, size_t ..._In>
struct __static_max;

template <size_t _I0>
struct __static_max<_I0>
{
    static const size_t value = _I0;
};

template <size_t _I0, size_t _I1, size_t ..._In>
struct __static_max<_I0, _I1, _In...>
{
    static const size_t value = _I0 >= _I1 ? __static_max<_I0, _In...>::value :
                                             __static_max<_I1, _In...>::value;
};

template <size_t _Len, class _Type0, class ..._Types>
struct aligned_union
{
    static const size_t alignment_value = __static_max<_LIBCPP_PREFERRED_ALIGNOF(_Type0),
                                                       _LIBCPP_PREFERRED_ALIGNOF(_Types)...>::value;
    static const size_t __len = __static_max<_Len, sizeof(_Type0),
                                             sizeof(_Types)...>::value;
    typedef typename aligned_storage<__len, alignment_value>::type type;
};

#if _LIBCPP_STD_VER > 11
template <size_t _Len, class ..._Types> using aligned_union_t = typename aligned_union<_Len, _Types...>::type;
#endif

template <class _Tp>
struct __numeric_type
{
   static void __test(...);
   static float __test(float);
   static double __test(char);
   static double __test(int);
   static double __test(unsigned);
   static double __test(long);
   static double __test(unsigned long);
   static double __test(long long);
   static double __test(unsigned long long);
   static double __test(double);
   static long double __test(long double);

   typedef decltype(__test(declval<_Tp>())) type;
   static const bool value = _IsNotSame<type, void>::value;
};

template <>
struct __numeric_type<void>
{
   static const bool value = true;
};

// __promote

template <class _A1, class _A2 = void, class _A3 = void,
          bool = __numeric_type<_A1>::value &&
                 __numeric_type<_A2>::value &&
                 __numeric_type<_A3>::value>
class __promote_imp
{
public:
    static const bool value = false;
};

template <class _A1, class _A2, class _A3>
class __promote_imp<_A1, _A2, _A3, true>
{
private:
    typedef typename __promote_imp<_A1>::type __type1;
    typedef typename __promote_imp<_A2>::type __type2;
    typedef typename __promote_imp<_A3>::type __type3;
public:
    typedef decltype(__type1() + __type2() + __type3()) type;
    static const bool value = true;
};

template <class _A1, class _A2>
class __promote_imp<_A1, _A2, void, true>
{
private:
    typedef typename __promote_imp<_A1>::type __type1;
    typedef typename __promote_imp<_A2>::type __type2;
public:
    typedef decltype(__type1() + __type2()) type;
    static const bool value = true;
};

template <class _A1>
class __promote_imp<_A1, void, void, true>
{
public:
    typedef typename __numeric_type<_A1>::type type;
    static const bool value = true;
};

template <class _A1, class _A2 = void, class _A3 = void>
class __promote : public __promote_imp<_A1, _A2, _A3> {};

// make_signed / make_unsigned

typedef
    __type_list<signed char,
    __type_list<signed short,
    __type_list<signed int,
    __type_list<signed long,
    __type_list<signed long long,
#ifndef _LIBCPP_HAS_NO_INT128
    __type_list<__int128_t,
#endif
    __nat
#ifndef _LIBCPP_HAS_NO_INT128
    >
#endif
    > > > > > __signed_types;

typedef
    __type_list<unsigned char,
    __type_list<unsigned short,
    __type_list<unsigned int,
    __type_list<unsigned long,
    __type_list<unsigned long long,
#ifndef _LIBCPP_HAS_NO_INT128
    __type_list<__uint128_t,
#endif
    __nat
#ifndef _LIBCPP_HAS_NO_INT128
    >
#endif
    > > > > > __unsigned_types;

template <class _TypeList, size_t _Size, bool = _Size <= sizeof(typename _TypeList::_Head)> struct __find_first;

template <class _Hp, class _Tp, size_t _Size>
struct __find_first<__type_list<_Hp, _Tp>, _Size, true>
{
    typedef _LIBCPP_NODEBUG _Hp type;
};

template <class _Hp, class _Tp, size_t _Size>
struct __find_first<__type_list<_Hp, _Tp>, _Size, false>
{
    typedef _LIBCPP_NODEBUG typename __find_first<_Tp, _Size>::type type;
};

template <class _Tp, bool = is_integral<_Tp>::value || is_enum<_Tp>::value>
struct __make_signed {};

template <class _Tp>
struct __make_signed<_Tp, true>
{
    typedef typename __find_first<__signed_types, sizeof(_Tp)>::type type;
};

template <> struct __make_signed<bool,               true> {};
template <> struct __make_signed<  signed short,     true> {typedef short     type;};
template <> struct __make_signed<unsigned short,     true> {typedef short     type;};
template <> struct __make_signed<  signed int,       true> {typedef int       type;};
template <> struct __make_signed<unsigned int,       true> {typedef int       type;};
template <> struct __make_signed<  signed long,      true> {typedef long      type;};
template <> struct __make_signed<unsigned long,      true> {typedef long      type;};
template <> struct __make_signed<  signed long long, true> {typedef long long type;};
template <> struct __make_signed<unsigned long long, true> {typedef long long type;};
#ifndef _LIBCPP_HAS_NO_INT128
template <> struct __make_signed<__int128_t,         true> {typedef __int128_t type;};
template <> struct __make_signed<__uint128_t,        true> {typedef __int128_t type;};
#endif

template <class _Tp>
struct _LIBCPP_TEMPLATE_VIS make_signed
{
    typedef typename __apply_cv<_Tp, typename __make_signed<typename remove_cv<_Tp>::type>::type>::type type;
};

#if _LIBCPP_STD_VER > 11
template <class _Tp> using make_signed_t = typename make_signed<_Tp>::type;
#endif

template <class _Tp, bool = is_integral<_Tp>::value || is_enum<_Tp>::value>
struct __make_unsigned {};

template <class _Tp>
struct __make_unsigned<_Tp, true>
{
    typedef typename __find_first<__unsigned_types, sizeof(_Tp)>::type type;
};

template <> struct __make_unsigned<bool,               true> {};
template <> struct __make_unsigned<  signed short,     true> {typedef unsigned short     type;};
template <> struct __make_unsigned<unsigned short,     true> {typedef unsigned short     type;};
template <> struct __make_unsigned<  signed int,       true> {typedef unsigned int       type;};
template <> struct __make_unsigned<unsigned int,       true> {typedef unsigned int       type;};
template <> struct __make_unsigned<  signed long,      true> {typedef unsigned long      type;};
template <> struct __make_unsigned<unsigned long,      true> {typedef unsigned long      type;};
template <> struct __make_unsigned<  signed long long, true> {typedef unsigned long long type;};
template <> struct __make_unsigned<unsigned long long, true> {typedef unsigned long long type;};
#ifndef _LIBCPP_HAS_NO_INT128
template <> struct __make_unsigned<__int128_t,         true> {typedef __uint128_t        type;};
template <> struct __make_unsigned<__uint128_t,        true> {typedef __uint128_t        type;};
#endif

template <class _Tp>
struct _LIBCPP_TEMPLATE_VIS make_unsigned
{
    typedef typename __apply_cv<_Tp, typename __make_unsigned<typename remove_cv<_Tp>::type>::type>::type type;
};

#if _LIBCPP_STD_VER > 11
template <class _Tp> using make_unsigned_t = typename make_unsigned<_Tp>::type;
#endif

#ifndef _LIBCPP_CXX03_LANG
template <class _Tp>
_LIBCPP_HIDE_FROM_ABI constexpr
typename make_unsigned<_Tp>::type __to_unsigned_like(_Tp __x) noexcept {
    return static_cast<typename make_unsigned<_Tp>::type>(__x);
}
#endif

template <class _Tp, class _Up>
using __copy_unsigned_t = __conditional_t<is_unsigned<_Tp>::value, typename make_unsigned<_Up>::type, _Up>;

/// Helper to promote an integral to smallest 32, 64, or 128 bit representation.
///
/// The restriction is the same as the integral version of to_char.
template <class _Tp>
#if _LIBCPP_STD_VER > 17
  requires (is_signed_v<_Tp> || is_unsigned_v<_Tp> || is_same_v<_Tp, char>)
#endif
using __make_32_64_or_128_bit_t =
  __copy_unsigned_t<_Tp,
    __conditional_t<sizeof(_Tp) <= sizeof(int32_t),    int32_t,
    __conditional_t<sizeof(_Tp) <= sizeof(int64_t),    int64_t,
#ifndef _LIBCPP_HAS_NO_INT128
    __conditional_t<sizeof(_Tp) <= sizeof(__int128_t), __int128_t,
    /* else */                                         void>
#else
    /* else */                                         void
#endif
    > >
  >;

#if _LIBCPP_STD_VER > 17
// Let COND_RES(X, Y) be:
template <class _Tp, class _Up>
using __cond_type = decltype(false ? declval<_Tp>() : declval<_Up>());

template <class _Tp, class _Up, class = void>
struct __common_type3 {};

// sub-bullet 4 - "if COND_RES(CREF(D1), CREF(D2)) denotes a type..."
template <class _Tp, class _Up>
struct __common_type3<_Tp, _Up, void_t<__cond_type<const _Tp&, const _Up&>>>
{
    using type = remove_cvref_t<__cond_type<const _Tp&, const _Up&>>;
};

template <class _Tp, class _Up, class = void>
struct __common_type2_imp : __common_type3<_Tp, _Up> {};
#else
template <class _Tp, class _Up, class = void>
struct __common_type2_imp {};
#endif

// sub-bullet 3 - "if decay_t<decltype(false ? declval<D1>() : declval<D2>())> ..."
template <class _Tp, class _Up>
struct __common_type2_imp<_Tp, _Up,
                          typename __void_t<decltype(
                                            true ? declval<_Tp>() : declval<_Up>()
                                            )>::type>
{
  typedef _LIBCPP_NODEBUG typename decay<decltype(
                         true ? declval<_Tp>() : declval<_Up>()
                         )>::type type;
};

template <class, class = void>
struct __common_type_impl {};

// Clang provides variadic templates in C++03 as an extension.
#if !defined(_LIBCPP_CXX03_LANG) || defined(__clang__)
# define _LIBCPP_OPTIONAL_PACK(...) , __VA_ARGS__
template <class... _Tp>
struct __common_types;
template <class... _Tp>
struct _LIBCPP_TEMPLATE_VIS common_type;
#else
# define _LIBCPP_OPTIONAL_PACK(...)
struct __no_arg;
template <class _Tp, class _Up, class = __no_arg>
struct __common_types;
template <class _Tp = __no_arg, class _Up = __no_arg, class _Vp = __no_arg,
          class _Unused = __no_arg>
struct common_type {
  static_assert(sizeof(_Unused) == 0,
                "common_type accepts at most 3 arguments in C++03");
};
#endif // _LIBCPP_CXX03_LANG

template <class _Tp, class _Up>
struct __common_type_impl<
    __common_types<_Tp, _Up>,
    typename __void_t<typename common_type<_Tp, _Up>::type>::type>
{
  typedef typename common_type<_Tp, _Up>::type type;
};

template <class _Tp, class _Up, class _Vp _LIBCPP_OPTIONAL_PACK(class... _Rest)>
struct __common_type_impl<
    __common_types<_Tp, _Up, _Vp _LIBCPP_OPTIONAL_PACK(_Rest...)>,
    typename __void_t<typename common_type<_Tp, _Up>::type>::type>
    : __common_type_impl<__common_types<typename common_type<_Tp, _Up>::type,
                                        _Vp _LIBCPP_OPTIONAL_PACK(_Rest...)> > {
};

// bullet 1 - sizeof...(Tp) == 0

template <>
struct _LIBCPP_TEMPLATE_VIS common_type<> {};

// bullet 2 - sizeof...(Tp) == 1

template <class _Tp>
struct _LIBCPP_TEMPLATE_VIS common_type<_Tp>
    : public common_type<_Tp, _Tp> {};

// bullet 3 - sizeof...(Tp) == 2

// sub-bullet 1 - "If is_same_v<T1, D1> is false or ..."
template <class _Tp, class _Up>
struct _LIBCPP_TEMPLATE_VIS common_type<_Tp, _Up>
    : conditional<
        _IsSame<_Tp, typename decay<_Tp>::type>::value && _IsSame<_Up, typename decay<_Up>::type>::value,
        __common_type2_imp<_Tp, _Up>,
        common_type<typename decay<_Tp>::type, typename decay<_Up>::type>
    >::type
{};

// bullet 4 - sizeof...(Tp) > 2

template <class _Tp, class _Up, class _Vp _LIBCPP_OPTIONAL_PACK(class... _Rest)>
struct _LIBCPP_TEMPLATE_VIS
    common_type<_Tp, _Up, _Vp _LIBCPP_OPTIONAL_PACK(_Rest...)>
    : __common_type_impl<
          __common_types<_Tp, _Up, _Vp _LIBCPP_OPTIONAL_PACK(_Rest...)> > {};

#undef _LIBCPP_OPTIONAL_PACK

#if _LIBCPP_STD_VER > 11
template <class ..._Tp> using common_type_t = typename common_type<_Tp...>::type;
#endif

// Let COPYCV(FROM, TO) be an alias for type TO with the addition of FROM's
// top-level cv-qualifiers.
template <class _From, class _To>
struct __copy_cv
{
    using type = _To;
};

template <class _From, class _To>
struct __copy_cv<const _From, _To>
{
    using type = typename add_const<_To>::type;
};

template <class _From, class _To>
struct __copy_cv<volatile _From, _To>
{
    using type = typename add_volatile<_To>::type;
};

template <class _From, class _To>
struct __copy_cv<const volatile _From, _To>
{
    using type = typename add_cv<_To>::type;
};

template <class _From, class _To>
using __copy_cv_t = typename __copy_cv<_From, _To>::type;

template <class _From, class _To>
struct __copy_cvref
{
    using type = __copy_cv_t<_From, _To>;
};

template <class _From, class _To>
struct __copy_cvref<_From&, _To>
{
    using type = typename add_lvalue_reference<__copy_cv_t<_From, _To> >::type;
};

template <class _From, class _To>
struct __copy_cvref<_From&&, _To>
{
    using type = typename add_rvalue_reference<__copy_cv_t<_From, _To> >::type;
};

template <class _From, class _To>
using __copy_cvref_t = typename __copy_cvref<_From, _To>::type;


// common_reference
#if _LIBCPP_STD_VER > 17
// Let COND_RES(X, Y) be:
template <class _Xp, class _Yp>
using __cond_res =
    decltype(false ? declval<_Xp(&)()>()() : declval<_Yp(&)()>()());

// Let `XREF(A)` denote a unary alias template `T` such that `T<U>` denotes the same type as `U`
// with the addition of `A`'s cv and reference qualifiers, for a non-reference cv-unqualified type
// `U`.
// [Note: `XREF(A)` is `__xref<A>::template __apply`]
template <class _Tp>
struct __xref {
  template<class _Up>
  using __apply = __copy_cvref_t<_Tp, _Up>;
};

// Given types A and B, let X be remove_reference_t<A>, let Y be remove_reference_t<B>,
// and let COMMON-REF(A, B) be:
template<class _Ap, class _Bp, class _Xp = remove_reference_t<_Ap>, class _Yp = remove_reference_t<_Bp>>
struct __common_ref;

template<class _Xp, class _Yp>
using __common_ref_t = typename __common_ref<_Xp, _Yp>::__type;

template<class _Xp, class _Yp>
using __cv_cond_res = __cond_res<__copy_cv_t<_Xp, _Yp>&, __copy_cv_t<_Yp, _Xp>&>;


//    If A and B are both lvalue reference types, COMMON-REF(A, B) is
//    COND-RES(COPYCV(X, Y)&, COPYCV(Y, X)&) if that type exists and is a reference type.
template<class _Ap, class _Bp, class _Xp, class _Yp>
requires requires { typename __cv_cond_res<_Xp, _Yp>; } && is_reference_v<__cv_cond_res<_Xp, _Yp>>
struct __common_ref<_Ap&, _Bp&, _Xp, _Yp>
{
    using __type = __cv_cond_res<_Xp, _Yp>;
};

//    Otherwise, let C be remove_reference_t<COMMON-REF(X&, Y&)>&&. ...
template <class _Xp, class _Yp>
using __common_ref_C = remove_reference_t<__common_ref_t<_Xp&, _Yp&>>&&;


//    .... If A and B are both rvalue reference types, C is well-formed, and
//    is_convertible_v<A, C> && is_convertible_v<B, C> is true, then COMMON-REF(A, B) is C.
template<class _Ap, class _Bp, class _Xp, class _Yp>
requires
  requires { typename __common_ref_C<_Xp, _Yp>; } &&
  is_convertible_v<_Ap&&, __common_ref_C<_Xp, _Yp>> &&
  is_convertible_v<_Bp&&, __common_ref_C<_Xp, _Yp>>
struct __common_ref<_Ap&&, _Bp&&, _Xp, _Yp>
{
    using __type = __common_ref_C<_Xp, _Yp>;
};

//    Otherwise, let D be COMMON-REF(const X&, Y&). ...
template <class _Tp, class _Up>
using __common_ref_D = __common_ref_t<const _Tp&, _Up&>;

//    ... If A is an rvalue reference and B is an lvalue reference and D is well-formed and
//    is_convertible_v<A, D> is true, then COMMON-REF(A, B) is D.
template<class _Ap, class _Bp, class _Xp, class _Yp>
requires requires { typename __common_ref_D<_Xp, _Yp>; } &&
         is_convertible_v<_Ap&&, __common_ref_D<_Xp, _Yp>>
struct __common_ref<_Ap&&, _Bp&, _Xp, _Yp>
{
    using __type = __common_ref_D<_Xp, _Yp>;
};

//    Otherwise, if A is an lvalue reference and B is an rvalue reference, then
//    COMMON-REF(A, B) is COMMON-REF(B, A).
template<class _Ap, class _Bp, class _Xp, class _Yp>
struct __common_ref<_Ap&, _Bp&&, _Xp, _Yp> : __common_ref<_Bp&&, _Ap&> {};

//    Otherwise, COMMON-REF(A, B) is ill-formed.
template<class _Ap, class _Bp, class _Xp, class _Yp>
struct __common_ref {};

// Note C: For the common_reference trait applied to a parameter pack [...]

template <class...>
struct common_reference;

template <class... _Types>
using common_reference_t = typename common_reference<_Types...>::type;

// bullet 1 - sizeof...(T) == 0
template<>
struct common_reference<> {};

// bullet 2 - sizeof...(T) == 1
template <class _Tp>
struct common_reference<_Tp>
{
    using type = _Tp;
};

// bullet 3 - sizeof...(T) == 2
template <class _Tp, class _Up> struct __common_reference_sub_bullet3;
template <class _Tp, class _Up> struct __common_reference_sub_bullet2 : __common_reference_sub_bullet3<_Tp, _Up> {};
template <class _Tp, class _Up> struct __common_reference_sub_bullet1 : __common_reference_sub_bullet2<_Tp, _Up> {};

// sub-bullet 1 - If T1 and T2 are reference types and COMMON-REF(T1, T2) is well-formed, then
// the member typedef `type` denotes that type.
template <class _Tp, class _Up> struct common_reference<_Tp, _Up> : __common_reference_sub_bullet1<_Tp, _Up> {};

template <class _Tp, class _Up>
requires is_reference_v<_Tp> && is_reference_v<_Up> && requires { typename __common_ref_t<_Tp, _Up>; }
struct __common_reference_sub_bullet1<_Tp, _Up>
{
    using type = __common_ref_t<_Tp, _Up>;
};

// sub-bullet 2 - Otherwise, if basic_common_reference<remove_cvref_t<T1>, remove_cvref_t<T2>, XREF(T1), XREF(T2)>::type
// is well-formed, then the member typedef `type` denotes that type.
template <class, class, template <class> class, template <class> class> struct basic_common_reference {};

template <class _Tp, class _Up>
using __basic_common_reference_t = typename basic_common_reference<
    remove_cvref_t<_Tp>, remove_cvref_t<_Up>,
    __xref<_Tp>::template __apply, __xref<_Up>::template __apply>::type;

template <class _Tp, class _Up>
requires requires { typename __basic_common_reference_t<_Tp, _Up>; }
struct __common_reference_sub_bullet2<_Tp, _Up>
{
    using type = __basic_common_reference_t<_Tp, _Up>;
};

// sub-bullet 3 - Otherwise, if COND-RES(T1, T2) is well-formed,
// then the member typedef `type` denotes that type.
template <class _Tp, class _Up>
requires requires { typename __cond_res<_Tp, _Up>; }
struct __common_reference_sub_bullet3<_Tp, _Up>
{
    using type = __cond_res<_Tp, _Up>;
};


// sub-bullet 4 & 5 - Otherwise, if common_type_t<T1, T2> is well-formed,
//                    then the member typedef `type` denotes that type.
//                  - Otherwise, there shall be no member `type`.
template <class _Tp, class _Up> struct __common_reference_sub_bullet3 : common_type<_Tp, _Up> {};

// bullet 4 - If there is such a type `C`, the member typedef type shall denote the same type, if
//            any, as `common_reference_t<C, Rest...>`.
template <class _Tp, class _Up, class _Vp, class... _Rest>
requires requires { typename common_reference_t<_Tp, _Up>; }
struct common_reference<_Tp, _Up, _Vp, _Rest...>
    : common_reference<common_reference_t<_Tp, _Up>, _Vp, _Rest...>
{};

// bullet 5 - Otherwise, there shall be no member `type`.
template <class...> struct common_reference {};

#endif // _LIBCPP_STD_VER > 17

#ifndef _LIBCPP_CXX03_LANG
// First of all, we can't implement this check in C++03 mode because the {}
// default initialization syntax isn't valid.
// Second, we implement the trait in a funny manner with two defaulted template
// arguments to workaround Clang's PR43454.
template <class _Tp>
void __test_implicit_default_constructible(_Tp);

template <class _Tp, class = void, class = typename is_default_constructible<_Tp>::type>
struct __is_implicitly_default_constructible
    : false_type
{ };

template <class _Tp>
struct __is_implicitly_default_constructible<_Tp, decltype(__test_implicit_default_constructible<_Tp const&>({})), true_type>
    : true_type
{ };

template <class _Tp>
struct __is_implicitly_default_constructible<_Tp, decltype(__test_implicit_default_constructible<_Tp const&>({})), false_type>
    : false_type
{ };
#endif // !C++03

// result_of

#if _LIBCPP_STD_VER <= 17 || defined(_LIBCPP_ENABLE_CXX20_REMOVED_TYPE_TRAITS)
template <class _Callable> class _LIBCPP_DEPRECATED_IN_CXX17 result_of;

template <class _Fp, class ..._Args>
class _LIBCPP_TEMPLATE_VIS result_of<_Fp(_Args...)>
    : public __invoke_of<_Fp, _Args...>
{
};

#if _LIBCPP_STD_VER > 11
template <class _Tp> using result_of_t _LIBCPP_DEPRECATED_IN_CXX17 = typename result_of<_Tp>::type;
#endif // _LIBCPP_STD_VER > 11
#endif // _LIBCPP_STD_VER <= 17 || defined(_LIBCPP_ENABLE_CXX20_REMOVED_TYPE_TRAITS)

// __swappable

template <class _Tp> struct __is_swappable;
template <class _Tp> struct __is_nothrow_swappable;


#ifndef _LIBCPP_CXX03_LANG
template <class _Tp>
using __swap_result_t = typename enable_if<is_move_constructible<_Tp>::value && is_move_assignable<_Tp>::value>::type;
#else
template <class>
using __swap_result_t = void;
#endif

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR_AFTER_CXX17 __swap_result_t<_Tp>
swap(_Tp& __x, _Tp& __y) _NOEXCEPT_(is_nothrow_move_constructible<_Tp>::value &&
                                    is_nothrow_move_assignable<_Tp>::value);

template<class _Tp, size_t _Np>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
typename enable_if<
    __is_swappable<_Tp>::value
>::type
swap(_Tp (&__a)[_Np], _Tp (&__b)[_Np]) _NOEXCEPT_(__is_nothrow_swappable<_Tp>::value);

namespace __detail
{
// ALL generic swap overloads MUST already have a declaration available at this point.

template <class _Tp, class _Up = _Tp,
          bool _NotVoid = !is_void<_Tp>::value && !is_void<_Up>::value>
struct __swappable_with
{
    template <class _LHS, class _RHS>
    static decltype(swap(declval<_LHS>(), declval<_RHS>()))
    __test_swap(int);
    template <class, class>
    static __nat __test_swap(long);

    // Extra parens are needed for the C++03 definition of decltype.
    typedef decltype((__test_swap<_Tp, _Up>(0))) __swap1;
    typedef decltype((__test_swap<_Up, _Tp>(0))) __swap2;

    static const bool value = _IsNotSame<__swap1, __nat>::value
                           && _IsNotSame<__swap2, __nat>::value;
};

template <class _Tp, class _Up>
struct __swappable_with<_Tp, _Up,  false> : false_type {};

template <class _Tp, class _Up = _Tp, bool _Swappable = __swappable_with<_Tp, _Up>::value>
struct __nothrow_swappable_with {
  static const bool value =
#ifndef _LIBCPP_HAS_NO_NOEXCEPT
      noexcept(swap(declval<_Tp>(), declval<_Up>()))
  &&  noexcept(swap(declval<_Up>(), declval<_Tp>()));
#else
      false;
#endif
};

template <class _Tp, class _Up>
struct __nothrow_swappable_with<_Tp, _Up, false> : false_type {};

} // namespace __detail

template <class _Tp>
struct __is_swappable
    : public integral_constant<bool, __detail::__swappable_with<_Tp&>::value>
{
};

template <class _Tp>
struct __is_nothrow_swappable
    : public integral_constant<bool, __detail::__nothrow_swappable_with<_Tp&>::value>
{
};

#if _LIBCPP_STD_VER > 14

template <class _Tp, class _Up>
struct _LIBCPP_TEMPLATE_VIS is_swappable_with
    : public integral_constant<bool, __detail::__swappable_with<_Tp, _Up>::value>
{
};

template <class _Tp>
struct _LIBCPP_TEMPLATE_VIS is_swappable
    : public conditional<
        __is_referenceable<_Tp>::value,
        is_swappable_with<
            typename add_lvalue_reference<_Tp>::type,
            typename add_lvalue_reference<_Tp>::type>,
        false_type
    >::type
{
};

template <class _Tp, class _Up>
struct _LIBCPP_TEMPLATE_VIS is_nothrow_swappable_with
    : public integral_constant<bool, __detail::__nothrow_swappable_with<_Tp, _Up>::value>
{
};

template <class _Tp>
struct _LIBCPP_TEMPLATE_VIS is_nothrow_swappable
    : public conditional<
        __is_referenceable<_Tp>::value,
        is_nothrow_swappable_with<
            typename add_lvalue_reference<_Tp>::type,
            typename add_lvalue_reference<_Tp>::type>,
        false_type
    >::type
{
};

template <class _Tp, class _Up>
inline constexpr bool is_swappable_with_v = is_swappable_with<_Tp, _Up>::value;

template <class _Tp>
inline constexpr bool is_swappable_v = is_swappable<_Tp>::value;

template <class _Tp, class _Up>
inline constexpr bool is_nothrow_swappable_with_v = is_nothrow_swappable_with<_Tp, _Up>::value;

template <class _Tp>
inline constexpr bool is_nothrow_swappable_v = is_nothrow_swappable<_Tp>::value;

#endif // _LIBCPP_STD_VER > 14

template <class _Tp, bool = is_enum<_Tp>::value>
struct __sfinae_underlying_type
{
    typedef typename underlying_type<_Tp>::type type;
    typedef decltype(((type)1) + 0) __promoted_type;
};

template <class _Tp>
struct __sfinae_underlying_type<_Tp, false> {};

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
int __convert_to_integral(int __val) { return __val; }

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
unsigned __convert_to_integral(unsigned __val) { return __val; }

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
long __convert_to_integral(long __val) { return __val; }

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
unsigned long __convert_to_integral(unsigned long __val) { return __val; }

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
long long __convert_to_integral(long long __val) { return __val; }

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
unsigned long long __convert_to_integral(unsigned long long __val) {return __val; }

template<typename _Fp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
typename enable_if<is_floating_point<_Fp>::value, long long>::type
 __convert_to_integral(_Fp __val) { return __val; }

#ifndef _LIBCPP_HAS_NO_INT128
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
__int128_t __convert_to_integral(__int128_t __val) { return __val; }

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
__uint128_t __convert_to_integral(__uint128_t __val) { return __val; }
#endif

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
typename __sfinae_underlying_type<_Tp>::__promoted_type
__convert_to_integral(_Tp __val) { return __val; }

// These traits are used in __tree and __hash_table
struct __extract_key_fail_tag {};
struct __extract_key_self_tag {};
struct __extract_key_first_tag {};

template <class _ValTy, class _Key,
          class _RawValTy = typename __unconstref<_ValTy>::type>
struct __can_extract_key
    : conditional<_IsSame<_RawValTy, _Key>::value, __extract_key_self_tag,
                  __extract_key_fail_tag>::type {};

template <class _Pair, class _Key, class _First, class _Second>
struct __can_extract_key<_Pair, _Key, pair<_First, _Second> >
    : conditional<_IsSame<typename remove_const<_First>::type, _Key>::value,
                  __extract_key_first_tag, __extract_key_fail_tag>::type {};

// __can_extract_map_key uses true_type/false_type instead of the tags.
// It returns true if _Key != _ContainerValueTy (the container is a map not a set)
// and _ValTy == _Key.
template <class _ValTy, class _Key, class _ContainerValueTy,
          class _RawValTy = typename __unconstref<_ValTy>::type>
struct __can_extract_map_key
    : integral_constant<bool, _IsSame<_RawValTy, _Key>::value> {};

// This specialization returns __extract_key_fail_tag for non-map containers
// because _Key == _ContainerValueTy
template <class _ValTy, class _Key, class _RawValTy>
struct __can_extract_map_key<_ValTy, _Key, _Key, _RawValTy>
    : false_type {};

template <class _CharT>
using _IsCharLikeType = _And<is_standard_layout<_CharT>, is_trivial<_CharT> >;

template<class _Tp>
using __make_const_lvalue_ref = const typename remove_reference<_Tp>::type&;

template<bool _Const, class _Tp>
using __maybe_const = typename conditional<_Const, const _Tp, _Tp>::type;

_LIBCPP_END_NAMESPACE_STD

#endif // _LIBCPP_TYPE_TRAITS