type_traits

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// C++11 <type_traits> -*- C++ -*-
 
// Copyright (C) 2007-2023 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
 
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/** @file include/type_traits
 *  This is a Standard C++ Library header.
 */
 
#ifndef _GLIBCXX_TYPE_TRAITS
#define _GLIBCXX_TYPE_TRAITS 1
 
#pragma GCC system_header
 
#if __cplusplus < 201103L
# include <bits/c++0x_warning.h>
#else
 
#include <bits/c++config.h>
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
 
  template<typename _Tp>
    class reference_wrapper;
 
  /**
   * @defgroup metaprogramming Metaprogramming
   * @ingroup utilities
   *
   * Template utilities for compile-time introspection and modification,
   * including type classification traits, type property inspection traits
   * and type transformation traits.
   *
   * @since C++11
   *
   * @{
   */
 
  /// integral_constant
  template<typename _Tp, _Tp __v>
    struct integral_constant
    {
      static constexpr _Tp                  value = __v;
      typedef _Tp                           value_type;
      typedef integral_constant<_Tp, __v>   type;
      constexpr operator value_type() const noexcept { return value; }
#if __cplusplus > 201103L
 
#define __cpp_lib_integral_constant_callable 201304L
 
      constexpr value_type operator()() const noexcept { return value; }
#endif
    };
 
#if ! __cpp_inline_variables
  template<typename _Tp, _Tp __v>
    constexpr _Tp integral_constant<_Tp, __v>::value;
#endif
 
  /// The type used as a compile-time boolean with true value.
  using true_type =  integral_constant<bool, true>;
 
  /// The type used as a compile-time boolean with false value.
  using false_type = integral_constant<bool, false>;
 
  /// @cond undocumented
  /// bool_constant for C++11
  template<bool __v>
    using __bool_constant = integral_constant<bool, __v>;
  /// @endcond
 
#if __cplusplus >= 201703L
# define __cpp_lib_bool_constant 201505L
  /// Alias template for compile-time boolean constant types.
  /// @since C++17
  template<bool __v>
    using bool_constant = integral_constant<bool, __v>;
#endif
 
  // Metaprogramming helper types.
 
  // Primary template.
  /// Define a member typedef `type` only if a boolean constant is true.
  template<bool, typename _Tp = void>
    struct enable_if
    { };
 
  // Partial specialization for true.
  template<typename _Tp>
    struct enable_if<true, _Tp>
    { typedef _Tp type; };
 
  // __enable_if_t (std::enable_if_t for C++11)
  template<bool _Cond, typename _Tp = void>
    using __enable_if_t = typename enable_if<_Cond, _Tp>::type;
 
  template<bool>
    struct __conditional
    {
      template<typename _Tp, typename>
        using type = _Tp;
    };
 
  template<>
    struct __conditional<false>
    {
      template<typename, typename _Up>
        using type = _Up;
    };
 
  // More efficient version of std::conditional_t for internal use (and C++11)
  template<bool _Cond, typename _If, typename _Else>
    using __conditional_t
      = typename __conditional<_Cond>::template type<_If, _Else>;
 
  /// @cond undocumented
  template <typename _Type>
    struct __type_identity
    { using type = _Type; };
 
  template<typename _Tp>
    using __type_identity_t = typename __type_identity<_Tp>::type;
 
  namespace __detail
  {
    // A variadic alias template that resolves to its first argument.
    template<typename _Tp, typename...>
      using __first_t = _Tp;
 
    // These are deliberately not defined.
    template<typename... _Bn>
      auto __or_fn(int) -> __first_t<false_type,
                                     __enable_if_t<!bool(_Bn::value)>...>;
 
    template<typename... _Bn>
      auto __or_fn(...) -> true_type;
 
    template<typename... _Bn>
      auto __and_fn(int) -> __first_t<true_type,
                                      __enable_if_t<bool(_Bn::value)>...>;
 
    template<typename... _Bn>
      auto __and_fn(...) -> false_type;
  } // namespace detail
 
  // Like C++17 std::dis/conjunction, but usable in C++11 and resolves
  // to either true_type or false_type which allows for a more efficient
  // implementation that avoids recursive class template instantiation.
  template<typename... _Bn>
    struct __or_
    : decltype(__detail::__or_fn<_Bn...>(0))
    { };
 
  template<typename... _Bn>
    struct __and_
    : decltype(__detail::__and_fn<_Bn...>(0))
    { };
 
  template<typename _Pp>
    struct __not_
    : __bool_constant<!bool(_Pp::value)>
    { };
  /// @endcond
 
#if __cplusplus >= 201703L
 
  /// @cond undocumented
  template<typename... _Bn>
    inline constexpr bool __or_v = __or_<_Bn...>::value;
  template<typename... _Bn>
    inline constexpr bool __and_v = __and_<_Bn...>::value;
 
  namespace __detail
  {
    template<typename /* = void */, typename _B1, typename... _Bn>
      struct __disjunction_impl
      { using type = _B1; };
 
    template<typename _B1, typename _B2, typename... _Bn>
      struct __disjunction_impl<__enable_if_t<!bool(_B1::value)>, _B1, _B2, _Bn...>
      { using type = typename __disjunction_impl<void, _B2, _Bn...>::type; };
 
    template<typename /* = void */, typename _B1, typename... _Bn>
      struct __conjunction_impl
      { using type = _B1; };
 
    template<typename _B1, typename _B2, typename... _Bn>
      struct __conjunction_impl<__enable_if_t<bool(_B1::value)>, _B1, _B2, _Bn...>
      { using type = typename __conjunction_impl<void, _B2, _Bn...>::type; };
  } // namespace __detail
  /// @endcond
 
#define __cpp_lib_logical_traits 201510L
 
  template<typename... _Bn>
    struct conjunction
    : __detail::__conjunction_impl<void, _Bn...>::type
    { };
 
  template<>
    struct conjunction<>
    : true_type
    { };
 
  template<typename... _Bn>
    struct disjunction
    : __detail::__disjunction_impl<void, _Bn...>::type
    { };
 
  template<>
    struct disjunction<>
    : false_type
    { };
 
  template<typename _Pp>
    struct negation
    : __not_<_Pp>::type
    { };
 
  /** @ingroup variable_templates
   * @{
   */
  template<typename... _Bn>
    inline constexpr bool conjunction_v = conjunction<_Bn...>::value;
 
  template<typename... _Bn>
    inline constexpr bool disjunction_v = disjunction<_Bn...>::value;
 
  template<typename _Pp>
    inline constexpr bool negation_v = negation<_Pp>::value;
  /// @}
 
#endif // C++17
 
  // Forward declarations
  template<typename>
    struct is_reference;
  template<typename>
    struct is_function;
  template<typename>
    struct is_void;
  template<typename>
    struct remove_cv;
  template<typename>
    struct is_const;
 
  /// @cond undocumented
  template<typename>
    struct __is_array_unknown_bounds;
 
  // Helper functions that return false_type for incomplete classes,
  // incomplete unions and arrays of known bound from those.
 
  template <typename _Tp, size_t = sizeof(_Tp)>
    constexpr true_type __is_complete_or_unbounded(__type_identity<_Tp>)
    { return {}; }
 
  template <typename _TypeIdentity,
      typename _NestedType = typename _TypeIdentity::type>
    constexpr typename __or_<
      is_reference<_NestedType>,
      is_function<_NestedType>,
      is_void<_NestedType>,
      __is_array_unknown_bounds<_NestedType>
    >::type __is_complete_or_unbounded(_TypeIdentity)
    { return {}; }
 
  // __remove_cv_t (std::remove_cv_t for C++11).
  template<typename _Tp>
    using __remove_cv_t = typename remove_cv<_Tp>::type;
  /// @endcond
 
  // Primary type categories.
 
  /// is_void
  template<typename _Tp>
    struct is_void
    : public false_type { };
 
  template<>
    struct is_void<void>
    : public true_type { };
 
  template<>
    struct is_void<const void>
    : public true_type { };
 
  template<>
    struct is_void<volatile void>
    : public true_type { };
 
  template<>
    struct is_void<const volatile void>
    : public true_type { };
 
  /// @cond undocumented
  template<typename>
    struct __is_integral_helper
    : public false_type { };
 
  template<>
    struct __is_integral_helper<bool>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<char>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<signed char>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<unsigned char>
    : public true_type { };
 
  // We want is_integral<wchar_t> to be true (and make_signed/unsigned to work)
  // even when libc doesn't provide working <wchar.h> and related functions,
  // so don't check _GLIBCXX_USE_WCHAR_T here.
  template<>
    struct __is_integral_helper<wchar_t>
    : public true_type { };
 
#ifdef _GLIBCXX_USE_CHAR8_T
  template<>
    struct __is_integral_helper<char8_t>
    : public true_type { };
#endif
 
  template<>
    struct __is_integral_helper<char16_t>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<char32_t>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<short>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<unsigned short>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<int>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<unsigned int>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<long>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<unsigned long>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<long long>
    : public true_type { };
 
  template<>
    struct __is_integral_helper<unsigned long long>
    : public true_type { };
 
  // Conditionalizing on __STRICT_ANSI__ here will break any port that
  // uses one of these types for size_t.
#if defined(__GLIBCXX_TYPE_INT_N_0)
  __extension__
  template<>
    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_0>
    : public true_type { };
 
  __extension__
  template<>
    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_0>
    : public true_type { };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_1)
  __extension__
  template<>
    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_1>
    : public true_type { };
 
  __extension__
  template<>
    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_1>
    : public true_type { };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_2)
  __extension__
  template<>
    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_2>
    : public true_type { };
 
  __extension__
  template<>
    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_2>
    : public true_type { };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_3)
  __extension__
  template<>
    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_3>
    : public true_type { };
 
  __extension__
  template<>
    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_3>
    : public true_type { };
#endif
  /// @endcond
 
  /// is_integral
  template<typename _Tp>
    struct is_integral
    : public __is_integral_helper<__remove_cv_t<_Tp>>::type
    { };
 
  /// @cond undocumented
  template<typename>
    struct __is_floating_point_helper
    : public false_type { };
 
  template<>
    struct __is_floating_point_helper<float>
    : public true_type { };
 
  template<>
    struct __is_floating_point_helper<double>
    : public true_type { };
 
  template<>
    struct __is_floating_point_helper<long double>
    : public true_type { };
 
#ifdef __STDCPP_FLOAT16_T__
  template<>
    struct __is_floating_point_helper<_Float16>
    : public true_type { };
#endif
 
#ifdef __STDCPP_FLOAT32_T__
  template<>
    struct __is_floating_point_helper<_Float32>
    : public true_type { };
#endif
 
#ifdef __STDCPP_FLOAT64_T__
  template<>
    struct __is_floating_point_helper<_Float64>
    : public true_type { };
#endif
 
#ifdef __STDCPP_FLOAT128_T__
  template<>
    struct __is_floating_point_helper<_Float128>
    : public true_type { };
#endif
 
#ifdef __STDCPP_BFLOAT16_T__
  template<>
    struct __is_floating_point_helper<__gnu_cxx::__bfloat16_t>
    : public true_type { };
#endif
 
#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_FLOAT128) && !defined(__CUDACC__)
  template<>
    struct __is_floating_point_helper<__float128>
    : public true_type { };
#endif
  /// @endcond
 
  /// is_floating_point
  template<typename _Tp>
    struct is_floating_point
    : public __is_floating_point_helper<__remove_cv_t<_Tp>>::type
    { };
 
  /// is_array
  template<typename>
    struct is_array
    : public false_type { };
 
  template<typename _Tp, std::size_t _Size>
    struct is_array<_Tp[_Size]>
    : public true_type { };
 
  template<typename _Tp>
    struct is_array<_Tp[]>
    : public true_type { };
 
  template<typename>
    struct __is_pointer_helper
    : public false_type { };
 
  template<typename _Tp>
    struct __is_pointer_helper<_Tp*>
    : public true_type { };
 
  /// is_pointer
  template<typename _Tp>
    struct is_pointer
    : public __is_pointer_helper<__remove_cv_t<_Tp>>::type
    { };
 
  /// is_lvalue_reference
  template<typename>
    struct is_lvalue_reference
    : public false_type { };
 
  template<typename _Tp>
    struct is_lvalue_reference<_Tp&>
    : public true_type { };
 
  /// is_rvalue_reference
  template<typename>
    struct is_rvalue_reference
    : public false_type { };
 
  template<typename _Tp>
    struct is_rvalue_reference<_Tp&&>
    : public true_type { };
 
  template<typename>
    struct __is_member_object_pointer_helper
    : public false_type { };
 
  template<typename _Tp, typename _Cp>
    struct __is_member_object_pointer_helper<_Tp _Cp::*>
    : public __not_<is_function<_Tp>>::type { };
 
  /// is_member_object_pointer
  template<typename _Tp>
    struct is_member_object_pointer
    : public __is_member_object_pointer_helper<__remove_cv_t<_Tp>>::type
    { };
 
  template<typename>
    struct __is_member_function_pointer_helper
    : public false_type { };
 
  template<typename _Tp, typename _Cp>
    struct __is_member_function_pointer_helper<_Tp _Cp::*>
    : public is_function<_Tp>::type { };
 
  /// is_member_function_pointer
  template<typename _Tp>
    struct is_member_function_pointer
    : public __is_member_function_pointer_helper<__remove_cv_t<_Tp>>::type
    { };
 
  /// is_enum
  template<typename _Tp>
    struct is_enum
    : public integral_constant<bool, __is_enum(_Tp)>
    { };
 
  /// is_union
  template<typename _Tp>
    struct is_union
    : public integral_constant<bool, __is_union(_Tp)>
    { };
 
  /// is_class
  template<typename _Tp>
    struct is_class
    : public integral_constant<bool, __is_class(_Tp)>
    { };
 
  /// is_function
  template<typename _Tp>
    struct is_function
    : public __bool_constant<!is_const<const _Tp>::value> { };
 
  template<typename _Tp>
    struct is_function<_Tp&>
    : public false_type { };
 
  template<typename _Tp>
    struct is_function<_Tp&&>
    : public false_type { };
 
#define __cpp_lib_is_null_pointer 201309L
 
  /// is_null_pointer (LWG 2247).
  template<typename _Tp>
    struct is_null_pointer
    : public false_type { };
 
  template<>
    struct is_null_pointer<std::nullptr_t>
    : public true_type { };
 
  template<>
    struct is_null_pointer<const std::nullptr_t>
    : public true_type { };
 
  template<>
    struct is_null_pointer<volatile std::nullptr_t>
    : public true_type { };
 
  template<>
    struct is_null_pointer<const volatile std::nullptr_t>
    : public true_type { };
 
  /// __is_nullptr_t (deprecated extension).
  /// @deprecated Non-standard. Use `is_null_pointer` instead.
  template<typename _Tp>
    struct __is_nullptr_t
    : public is_null_pointer<_Tp>
    { } _GLIBCXX_DEPRECATED_SUGGEST("std::is_null_pointer");
 
  // Composite type categories.
 
  /// is_reference
  template<typename _Tp>
    struct is_reference
    : public false_type
    { };
 
  template<typename _Tp>
    struct is_reference<_Tp&>
    : public true_type
    { };
 
  template<typename _Tp>
    struct is_reference<_Tp&&>
    : public true_type
    { };
 
  /// is_arithmetic
  template<typename _Tp>
    struct is_arithmetic
    : public __or_<is_integral<_Tp>, is_floating_point<_Tp>>::type
    { };
 
  /// is_fundamental
  template<typename _Tp>
    struct is_fundamental
    : public __or_<is_arithmetic<_Tp>, is_void<_Tp>,
                   is_null_pointer<_Tp>>::type
    { };
 
  /// is_object
  template<typename _Tp>
    struct is_object
    : public __not_<__or_<is_function<_Tp>, is_reference<_Tp>,
                          is_void<_Tp>>>::type
    { };
 
  template<typename>
    struct is_member_pointer;
 
  /// is_scalar
  template<typename _Tp>
    struct is_scalar
    : public __or_<is_arithmetic<_Tp>, is_enum<_Tp>, is_pointer<_Tp>,
                   is_member_pointer<_Tp>, is_null_pointer<_Tp>>::type
    { };
 
  /// is_compound
  template<typename _Tp>
    struct is_compound
    : public __not_<is_fundamental<_Tp>>::type { };
 
  /// @cond undocumented
  template<typename _Tp>
    struct __is_member_pointer_helper
    : public false_type { };
 
  template<typename _Tp, typename _Cp>
    struct __is_member_pointer_helper<_Tp _Cp::*>
    : public true_type { };
  /// @endcond
 
  /// is_member_pointer
  template<typename _Tp>
    struct is_member_pointer
    : public __is_member_pointer_helper<__remove_cv_t<_Tp>>::type
    { };
 
  template<typename, typename>
    struct is_same;
 
  /// @cond undocumented
  template<typename _Tp, typename... _Types>
    using __is_one_of = __or_<is_same<_Tp, _Types>...>;
 
  // Check if a type is one of the signed integer types.
  __extension__
  template<typename _Tp>
    using __is_signed_integer = __is_one_of<__remove_cv_t<_Tp>,
          signed char, signed short, signed int, signed long,
          signed long long
#if defined(__GLIBCXX_TYPE_INT_N_0)
          , signed __GLIBCXX_TYPE_INT_N_0
#endif
#if defined(__GLIBCXX_TYPE_INT_N_1)
          , signed __GLIBCXX_TYPE_INT_N_1
#endif
#if defined(__GLIBCXX_TYPE_INT_N_2)
          , signed __GLIBCXX_TYPE_INT_N_2
#endif
#if defined(__GLIBCXX_TYPE_INT_N_3)
          , signed __GLIBCXX_TYPE_INT_N_3
#endif
          >;
 
  // Check if a type is one of the unsigned integer types.
  __extension__
  template<typename _Tp>
    using __is_unsigned_integer = __is_one_of<__remove_cv_t<_Tp>,
          unsigned char, unsigned short, unsigned int, unsigned long,
          unsigned long long
#if defined(__GLIBCXX_TYPE_INT_N_0)
          , unsigned __GLIBCXX_TYPE_INT_N_0
#endif
#if defined(__GLIBCXX_TYPE_INT_N_1)
          , unsigned __GLIBCXX_TYPE_INT_N_1
#endif
#if defined(__GLIBCXX_TYPE_INT_N_2)
          , unsigned __GLIBCXX_TYPE_INT_N_2
#endif
#if defined(__GLIBCXX_TYPE_INT_N_3)
          , unsigned __GLIBCXX_TYPE_INT_N_3
#endif
          >;
 
  // Check if a type is one of the signed or unsigned integer types.
  template<typename _Tp>
    using __is_standard_integer
      = __or_<__is_signed_integer<_Tp>, __is_unsigned_integer<_Tp>>;
 
  // __void_t (std::void_t for C++11)
  template<typename...> using __void_t = void;
  /// @endcond
 
  // Type properties.
 
  /// is_const
  template<typename>
    struct is_const
    : public false_type { };
 
  template<typename _Tp>
    struct is_const<_Tp const>
    : public true_type { };
 
  /// is_volatile
  template<typename>
    struct is_volatile
    : public false_type { };
 
  template<typename _Tp>
    struct is_volatile<_Tp volatile>
    : public true_type { };
 
  /// is_trivial
  template<typename _Tp>
    struct is_trivial
    : public integral_constant<bool, __is_trivial(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_trivially_copyable
  template<typename _Tp>
    struct is_trivially_copyable
    : public integral_constant<bool, __is_trivially_copyable(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_standard_layout
  template<typename _Tp>
    struct is_standard_layout
    : public integral_constant<bool, __is_standard_layout(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /** is_pod
   * @deprecated Deprecated in C++20.
   * Use `is_standard_layout && is_trivial` instead.
   */
  // Could use is_standard_layout && is_trivial instead of the builtin.
  template<typename _Tp>
    struct
    _GLIBCXX20_DEPRECATED_SUGGEST("is_standard_layout && is_trivial")
    is_pod
    : public integral_constant<bool, __is_pod(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /** is_literal_type
   * @deprecated Deprecated in C++17, removed in C++20.
   * The idea of a literal type isn't useful.
   */
  template<typename _Tp>
    struct
    _GLIBCXX17_DEPRECATED
    is_literal_type
    : public integral_constant<bool, __is_literal_type(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_empty
  template<typename _Tp>
    struct is_empty
    : public integral_constant<bool, __is_empty(_Tp)>
    { };
 
  /// is_polymorphic
  template<typename _Tp>
    struct is_polymorphic
    : public integral_constant<bool, __is_polymorphic(_Tp)>
    { };
 
#if __cplusplus >= 201402L
#define __cpp_lib_is_final 201402L
  /// is_final
  /// @since C++14
  template<typename _Tp>
    struct is_final
    : public integral_constant<bool, __is_final(_Tp)>
    { };
#endif
 
  /// is_abstract
  template<typename _Tp>
    struct is_abstract
    : public integral_constant<bool, __is_abstract(_Tp)>
    { };
 
  /// @cond undocumented
  template<typename _Tp,
           bool = is_arithmetic<_Tp>::value>
    struct __is_signed_helper
    : public false_type { };
 
  template<typename _Tp>
    struct __is_signed_helper<_Tp, true>
    : public integral_constant<bool, _Tp(-1) < _Tp(0)>
    { };
  /// @endcond
 
  /// is_signed
  template<typename _Tp>
    struct is_signed
    : public __is_signed_helper<_Tp>::type
    { };
 
  /// is_unsigned
  template<typename _Tp>
    struct is_unsigned
    : public __and_<is_arithmetic<_Tp>, __not_<is_signed<_Tp>>>::type
    { };
 
  /// @cond undocumented
  template<typename _Tp, typename _Up = _Tp&&>
    _Up
    __declval(int);
 
  template<typename _Tp>
    _Tp
    __declval(long);
  /// @endcond
 
  template<typename _Tp>
    auto declval() noexcept -> decltype(__declval<_Tp>(0));
 
  template<typename>
    struct remove_all_extents;
 
  /// @cond undocumented
  template<typename _Tp>
    struct __is_array_known_bounds
    : public false_type
    { };
 
  template<typename _Tp, size_t _Size>
    struct __is_array_known_bounds<_Tp[_Size]>
    : public true_type
    { };
 
  template<typename _Tp>
    struct __is_array_unknown_bounds
    : public false_type
    { };
 
  template<typename _Tp>
    struct __is_array_unknown_bounds<_Tp[]>
    : public true_type
    { };
 
  // Destructible and constructible type properties.
 
  // In N3290 is_destructible does not say anything about function
  // types and abstract types, see LWG 2049. This implementation
  // describes function types as non-destructible and all complete
  // object types as destructible, iff the explicit destructor
  // call expression is wellformed.
  struct __do_is_destructible_impl
  {
    template<typename _Tp, typename = decltype(declval<_Tp&>().~_Tp())>
      static true_type __test(int);
 
    template<typename>
      static false_type __test(...);
  };
 
  template<typename _Tp>
    struct __is_destructible_impl
    : public __do_is_destructible_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };
 
  template<typename _Tp,
           bool = __or_<is_void<_Tp>,
                        __is_array_unknown_bounds<_Tp>,
                        is_function<_Tp>>::value,
           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
    struct __is_destructible_safe;
 
  template<typename _Tp>
    struct __is_destructible_safe<_Tp, false, false>
    : public __is_destructible_impl<typename
               remove_all_extents<_Tp>::type>::type
    { };
 
  template<typename _Tp>
    struct __is_destructible_safe<_Tp, true, false>
    : public false_type { };
 
  template<typename _Tp>
    struct __is_destructible_safe<_Tp, false, true>
    : public true_type { };
  /// @endcond
 
  /// is_destructible
  template<typename _Tp>
    struct is_destructible
    : public __is_destructible_safe<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
 
  // is_nothrow_destructible requires that is_destructible is
  // satisfied as well.  We realize that by mimicing the
  // implementation of is_destructible but refer to noexcept(expr)
  // instead of decltype(expr).
  struct __do_is_nt_destructible_impl
  {
    template<typename _Tp>
      static __bool_constant<noexcept(declval<_Tp&>().~_Tp())>
      __test(int);
 
    template<typename>
      static false_type __test(...);
  };
 
  template<typename _Tp>
    struct __is_nt_destructible_impl
    : public __do_is_nt_destructible_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };
 
  template<typename _Tp,
           bool = __or_<is_void<_Tp>,
                        __is_array_unknown_bounds<_Tp>,
                        is_function<_Tp>>::value,
           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
    struct __is_nt_destructible_safe;
 
  template<typename _Tp>
    struct __is_nt_destructible_safe<_Tp, false, false>
    : public __is_nt_destructible_impl<typename
               remove_all_extents<_Tp>::type>::type
    { };
 
  template<typename _Tp>
    struct __is_nt_destructible_safe<_Tp, true, false>
    : public false_type { };
 
  template<typename _Tp>
    struct __is_nt_destructible_safe<_Tp, false, true>
    : public true_type { };
  /// @endcond
 
  /// is_nothrow_destructible
  template<typename _Tp>
    struct is_nothrow_destructible
    : public __is_nt_destructible_safe<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename... _Args>
    using __is_constructible_impl
      = __bool_constant<__is_constructible(_Tp, _Args...)>;
  /// @endcond
 
  /// is_constructible
  template<typename _Tp, typename... _Args>
    struct is_constructible
      : public __is_constructible_impl<_Tp, _Args...>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_default_constructible
  template<typename _Tp>
    struct is_default_constructible
    : public __is_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename = void>
    struct __add_lvalue_reference_helper
    { using type = _Tp; };
 
  template<typename _Tp>
    struct __add_lvalue_reference_helper<_Tp, __void_t<_Tp&>>
    { using type = _Tp&; };
 
  template<typename _Tp>
    using __add_lval_ref_t = typename __add_lvalue_reference_helper<_Tp>::type;
  /// @endcond
 
  /// is_copy_constructible
  template<typename _Tp>
    struct is_copy_constructible
    : public __is_constructible_impl<_Tp, __add_lval_ref_t<const _Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename = void>
    struct __add_rvalue_reference_helper
    { using type = _Tp; };
 
  template<typename _Tp>
    struct __add_rvalue_reference_helper<_Tp, __void_t<_Tp&&>>
    { using type = _Tp&&; };
 
  template<typename _Tp>
    using __add_rval_ref_t = typename __add_rvalue_reference_helper<_Tp>::type;
  /// @endcond
 
  /// is_move_constructible
  template<typename _Tp>
    struct is_move_constructible
    : public __is_constructible_impl<_Tp, __add_rval_ref_t<_Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename... _Args>
    using __is_nothrow_constructible_impl
      = __bool_constant<__is_nothrow_constructible(_Tp, _Args...)>;
  /// @endcond
 
  /// is_nothrow_constructible
  template<typename _Tp, typename... _Args>
    struct is_nothrow_constructible
    : public __is_nothrow_constructible_impl<_Tp, _Args...>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_nothrow_default_constructible
  template<typename _Tp>
    struct is_nothrow_default_constructible
    : public __is_nothrow_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_nothrow_copy_constructible
  template<typename _Tp>
    struct is_nothrow_copy_constructible
    : public __is_nothrow_constructible_impl<_Tp, __add_lval_ref_t<const _Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_nothrow_move_constructible
  template<typename _Tp>
    struct is_nothrow_move_constructible
    : public __is_nothrow_constructible_impl<_Tp, __add_rval_ref_t<_Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename _Up>
    using __is_assignable_impl = __bool_constant<__is_assignable(_Tp, _Up)>;
  /// @endcond
 
  /// is_assignable
  template<typename _Tp, typename _Up>
    struct is_assignable
    : public __is_assignable_impl<_Tp, _Up>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_copy_assignable
  template<typename _Tp>
    struct is_copy_assignable
    : public __is_assignable_impl<__add_lval_ref_t<_Tp>,
                                  __add_lval_ref_t<const _Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_move_assignable
  template<typename _Tp>
    struct is_move_assignable
    : public __is_assignable_impl<__add_lval_ref_t<_Tp>, __add_rval_ref_t<_Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename _Up>
    using __is_nothrow_assignable_impl
      = __bool_constant<__is_nothrow_assignable(_Tp, _Up)>;
  /// @endcond
 
  /// is_nothrow_assignable
  template<typename _Tp, typename _Up>
    struct is_nothrow_assignable
    : public __is_nothrow_assignable_impl<_Tp, _Up>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_nothrow_copy_assignable
  template<typename _Tp>
    struct is_nothrow_copy_assignable
    : public __is_nothrow_assignable_impl<__add_lval_ref_t<_Tp>,
                                          __add_lval_ref_t<const _Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_nothrow_move_assignable
  template<typename _Tp>
    struct is_nothrow_move_assignable
    : public __is_nothrow_assignable_impl<__add_lval_ref_t<_Tp>,
                                          __add_rval_ref_t<_Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename... _Args>
    using __is_trivially_constructible_impl
      = __bool_constant<__is_trivially_constructible(_Tp, _Args...)>;
  /// @endcond
 
  /// is_trivially_constructible
  template<typename _Tp, typename... _Args>
    struct is_trivially_constructible
    : public __is_trivially_constructible_impl<_Tp, _Args...>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_trivially_default_constructible
  template<typename _Tp>
    struct is_trivially_default_constructible
    : public __is_trivially_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  struct __do_is_implicitly_default_constructible_impl
  {
    template <typename _Tp>
    static void __helper(const _Tp&);
 
    template <typename _Tp>
    static true_type __test(const _Tp&,
                            decltype(__helper<const _Tp&>({}))* = 0);
 
    static false_type __test(...);
  };
 
  template<typename _Tp>
    struct __is_implicitly_default_constructible_impl
    : public __do_is_implicitly_default_constructible_impl
    {
      typedef decltype(__test(declval<_Tp>())) type;
    };
 
  template<typename _Tp>
    struct __is_implicitly_default_constructible_safe
    : public __is_implicitly_default_constructible_impl<_Tp>::type
    { };
 
  template <typename _Tp>
    struct __is_implicitly_default_constructible
    : public __and_<__is_constructible_impl<_Tp>,
                    __is_implicitly_default_constructible_safe<_Tp>>::type
    { };
 
  /// is_trivially_copy_constructible
  template<typename _Tp>
    struct is_trivially_copy_constructible
    : public __is_trivially_constructible_impl<_Tp, __add_lval_ref_t<const _Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_trivially_move_constructible
  template<typename _Tp>
    struct is_trivially_move_constructible
    : public __is_trivially_constructible_impl<_Tp, __add_rval_ref_t<_Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// @cond undocumented
  template<typename _Tp, typename _Up>
    using __is_trivially_assignable_impl
      = __bool_constant<__is_trivially_assignable(_Tp, _Up)>;
  /// @endcond
 
  /// is_trivially_assignable
  template<typename _Tp, typename _Up>
    struct is_trivially_assignable
    : public __is_trivially_assignable_impl<_Tp, _Up>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_trivially_copy_assignable
  template<typename _Tp>
    struct is_trivially_copy_assignable
    : public __is_trivially_assignable_impl<__add_lval_ref_t<_Tp>,
                                            __add_lval_ref_t<const _Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_trivially_move_assignable
  template<typename _Tp>
    struct is_trivially_move_assignable
    : public __is_trivially_assignable_impl<__add_lval_ref_t<_Tp>,
                                            __add_rval_ref_t<_Tp>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// is_trivially_destructible
  template<typename _Tp>
    struct is_trivially_destructible
    : public __and_<__is_destructible_safe<_Tp>,
                    __bool_constant<__has_trivial_destructor(_Tp)>>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
 
  /// has_virtual_destructor
  template<typename _Tp>
    struct has_virtual_destructor
    : public integral_constant<bool, __has_virtual_destructor(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
 
  // type property queries.
 
  /// alignment_of
  template<typename _Tp>
    struct alignment_of
    : public integral_constant<std::size_t, alignof(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
        "template argument must be a complete class or an unbounded array");
    };
 
  /// rank
  template<typename>
    struct rank
    : public integral_constant<std::size_t, 0> { };
 
  template<typename _Tp, std::size_t _Size>
    struct rank<_Tp[_Size]>
    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
 
  template<typename _Tp>
    struct rank<_Tp[]>
    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
 
  /// extent
  template<typename, unsigned _Uint = 0>
    struct extent
    : public integral_constant<size_t, 0> { };
 
  template<typename _Tp, size_t _Size>
    struct extent<_Tp[_Size], 0>
    : public integral_constant<size_t, _Size> { };
 
  template<typename _Tp, unsigned _Uint, size_t _Size>
    struct extent<_Tp[_Size], _Uint>
    : public extent<_Tp, _Uint - 1>::type { };
 
  template<typename _Tp>
    struct extent<_Tp[], 0>
    : public integral_constant<size_t, 0> { };
 
  template<typename _Tp, unsigned _Uint>
    struct extent<_Tp[], _Uint>
    : public extent<_Tp, _Uint - 1>::type { };
 
 
  // Type relations.
 
  /// is_same
  template<typename _Tp, typename _Up>
    struct is_same
#ifdef _GLIBCXX_HAVE_BUILTIN_IS_SAME
    : public integral_constant<bool, __is_same(_Tp, _Up)>
#else
    : public false_type
#endif
    { };
 
#ifndef _GLIBCXX_HAVE_BUILTIN_IS_SAME
  template<typename _Tp>
    struct is_same<_Tp, _Tp>
    : public true_type
    { };
#endif
 
  /// is_base_of
  template<typename _Base, typename _Derived>
    struct is_base_of
    : public integral_constant<bool, __is_base_of(_Base, _Derived)>
    { };
 
#if __has_builtin(__is_convertible)
  template<typename _From, typename _To>
    struct is_convertible
    : public __bool_constant<__is_convertible(_From, _To)>
    { };
#else
  template<typename _From, typename _To,
           bool = __or_<is_void<_From>, is_function<_To>,
                        is_array<_To>>::value>
    struct __is_convertible_helper
    {
      typedef typename is_void<_To>::type type;
    };
 
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
  template<typename _From, typename _To>
    class __is_convertible_helper<_From, _To, false>
    {
      template<typename _To1>
        static void __test_aux(_To1) noexcept;
 
      template<typename _From1, typename _To1,
               typename = decltype(__test_aux<_To1>(std::declval<_From1>()))>
        static true_type
        __test(int);
 
      template<typename, typename>
        static false_type
        __test(...);
 
    public:
      typedef decltype(__test<_From, _To>(0)) type;
    };
#pragma GCC diagnostic pop
 
  /// is_convertible
  template<typename _From, typename _To>
    struct is_convertible
    : public __is_convertible_helper<_From, _To>::type
    { };
#endif
 
  // helper trait for unique_ptr<T[]>, shared_ptr<T[]>, and span<T, N>
  template<typename _ToElementType, typename _FromElementType>
    using __is_array_convertible
      = is_convertible<_FromElementType(*)[], _ToElementType(*)[]>;
 
#if __cplusplus >= 202002L
#define __cpp_lib_is_nothrow_convertible 201806L
 
#if __has_builtin(__is_nothrow_convertible)
  /// is_nothrow_convertible_v
  template<typename _From, typename _To>
    inline constexpr bool is_nothrow_convertible_v
      = __is_nothrow_convertible(_From, _To);
 
  /// is_nothrow_convertible
  template<typename _From, typename _To>
    struct is_nothrow_convertible
    : public bool_constant<is_nothrow_convertible_v<_From, _To>>
    { };
#else
  template<typename _From, typename _To,
           bool = __or_<is_void<_From>, is_function<_To>,
                        is_array<_To>>::value>
    struct __is_nt_convertible_helper
    : is_void<_To>
    { };
 
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
  template<typename _From, typename _To>
    class __is_nt_convertible_helper<_From, _To, false>
    {
      template<typename _To1>
        static void __test_aux(_To1) noexcept;
 
      template<typename _From1, typename _To1>
        static
        __bool_constant<noexcept(__test_aux<_To1>(std::declval<_From1>()))>
        __test(int);
 
      template<typename, typename>
        static false_type
        __test(...);
 
    public:
      using type = decltype(__test<_From, _To>(0));
    };
#pragma GCC diagnostic pop
 
  /// is_nothrow_convertible
  template<typename _From, typename _To>
    struct is_nothrow_convertible
    : public __is_nt_convertible_helper<_From, _To>::type
    { };
 
  /// is_nothrow_convertible_v
  template<typename _From, typename _To>
    inline constexpr bool is_nothrow_convertible_v
      = is_nothrow_convertible<_From, _To>::value;
#endif
#endif // C++2a
 
  // Const-volatile modifications.
 
  /// remove_const
  template<typename _Tp>
    struct remove_const
    { typedef _Tp     type; };
 
  template<typename _Tp>
    struct remove_const<_Tp const>
    { typedef _Tp     type; };
 
  /// remove_volatile
  template<typename _Tp>
    struct remove_volatile
    { typedef _Tp     type; };
 
  template<typename _Tp>
    struct remove_volatile<_Tp volatile>
    { typedef _Tp     type; };
 
  /// remove_cv
#if __has_builtin(__remove_cv)
  template<typename _Tp>
    struct remove_cv
    { using type = __remove_cv(_Tp); };
#else
  template<typename _Tp>
    struct remove_cv
    { using type = _Tp; };
 
  template<typename _Tp>
    struct remove_cv<const _Tp>
    { using type = _Tp; };
 
  template<typename _Tp>
    struct remove_cv<volatile _Tp>
    { using type = _Tp; };
 
  template<typename _Tp>
    struct remove_cv<const volatile _Tp>
    { using type = _Tp; };
#endif
 
  /// add_const
  template<typename _Tp>
    struct add_const
    { using type = _Tp const; };
 
  /// add_volatile
  template<typename _Tp>
    struct add_volatile
    { using type = _Tp volatile; };
 
  /// add_cv
  template<typename _Tp>
    struct add_cv
    { using type = _Tp const volatile; };
 
#if __cplusplus > 201103L
 
#define __cpp_lib_transformation_trait_aliases 201304L
 
  /// Alias template for remove_const
  template<typename _Tp>
    using remove_const_t = typename remove_const<_Tp>::type;
 
  /// Alias template for remove_volatile
  template<typename _Tp>
    using remove_volatile_t = typename remove_volatile<_Tp>::type;
 
  /// Alias template for remove_cv
  template<typename _Tp>
    using remove_cv_t = typename remove_cv<_Tp>::type;
 
  /// Alias template for add_const
  template<typename _Tp>
    using add_const_t = typename add_const<_Tp>::type;
 
  /// Alias template for add_volatile
  template<typename _Tp>
    using add_volatile_t = typename add_volatile<_Tp>::type;
 
  /// Alias template for add_cv
  template<typename _Tp>
    using add_cv_t = typename add_cv<_Tp>::type;
#endif
 
  // Reference transformations.
 
  /// remove_reference
#if __has_builtin(__remove_reference)
  template<typename _Tp>
    struct remove_reference
    { using type = __remove_reference(_Tp); };
#else
  template<typename _Tp>
    struct remove_reference
    { using type = _Tp; };
 
  template<typename _Tp>
    struct remove_reference<_Tp&>
    { using type = _Tp; };
 
  template<typename _Tp>
    struct remove_reference<_Tp&&>
    { using type = _Tp; };
#endif
 
  /// add_lvalue_reference
  template<typename _Tp>
    struct add_lvalue_reference
    { using type = __add_lval_ref_t<_Tp>; };
 
  /// add_rvalue_reference
  template<typename _Tp>
    struct add_rvalue_reference
    { using type = __add_rval_ref_t<_Tp>; };
 
#if __cplusplus > 201103L
  /// Alias template for remove_reference
  template<typename _Tp>
    using remove_reference_t = typename remove_reference<_Tp>::type;
 
  /// Alias template for add_lvalue_reference
  template<typename _Tp>
    using add_lvalue_reference_t = typename add_lvalue_reference<_Tp>::type;
 
  /// Alias template for add_rvalue_reference
  template<typename _Tp>
    using add_rvalue_reference_t = typename add_rvalue_reference<_Tp>::type;
#endif
 
  // Sign modifications.
 
  /// @cond undocumented
 
  // Utility for constructing identically cv-qualified types.
  template<typename _Unqualified, bool _IsConst, bool _IsVol>
    struct __cv_selector;
 
  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, false, false>
    { typedef _Unqualified __type; };
 
  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, false, true>
    { typedef volatile _Unqualified __type; };
 
  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, true, false>
    { typedef const _Unqualified __type; };
 
  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, true, true>
    { typedef const volatile _Unqualified __type; };
 
  template<typename _Qualified, typename _Unqualified,
           bool _IsConst = is_const<_Qualified>::value,
           bool _IsVol = is_volatile<_Qualified>::value>
    class __match_cv_qualifiers
    {
      typedef __cv_selector<_Unqualified, _IsConst, _IsVol> __match;
 
    public:
      typedef typename __match::__type __type;
    };
 
  // Utility for finding the unsigned versions of signed integral types.
  template<typename _Tp>
    struct __make_unsigned
    { typedef _Tp __type; };
 
  template<>
    struct __make_unsigned<char>
    { typedef unsigned char __type; };
 
  template<>
    struct __make_unsigned<signed char>
    { typedef unsigned char __type; };
 
  template<>
    struct __make_unsigned<short>
    { typedef unsigned short __type; };
 
  template<>
    struct __make_unsigned<int>
    { typedef unsigned int __type; };
 
  template<>
    struct __make_unsigned<long>
    { typedef unsigned long __type; };
 
  template<>
    struct __make_unsigned<long long>
    { typedef unsigned long long __type; };
 
#if defined(__GLIBCXX_TYPE_INT_N_0)
  __extension__
  template<>
    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_0>
    { typedef unsigned __GLIBCXX_TYPE_INT_N_0 __type; };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_1)
  __extension__
  template<>
    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_1>
    { typedef unsigned __GLIBCXX_TYPE_INT_N_1 __type; };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_2)
  __extension__
  template<>
    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_2>
    { typedef unsigned __GLIBCXX_TYPE_INT_N_2 __type; };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_3)
  __extension__
  template<>
    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_3>
    { typedef unsigned __GLIBCXX_TYPE_INT_N_3 __type; };
#endif
 
  // Select between integral and enum: not possible to be both.
  template<typename _Tp,
           bool _IsInt = is_integral<_Tp>::value,
           bool _IsEnum = is_enum<_Tp>::value>
    class __make_unsigned_selector;
 
  template<typename _Tp>
    class __make_unsigned_selector<_Tp, true, false>
    {
      using __unsigned_type
        = typename __make_unsigned<__remove_cv_t<_Tp>>::__type;
 
    public:
      using __type
        = typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
    };
 
  class __make_unsigned_selector_base
  {
  protected:
    template<typename...> struct _List { };
 
    template<typename _Tp, typename... _Up>
      struct _List<_Tp, _Up...> : _List<_Up...>
      { static constexpr size_t __size = sizeof(_Tp); };
 
    template<size_t _Sz, typename _Tp, bool = (_Sz <= _Tp::__size)>
      struct __select;
 
    template<size_t _Sz, typename _Uint, typename... _UInts>
      struct __select<_Sz, _List<_Uint, _UInts...>, true>
      { using __type = _Uint; };
 
    template<size_t _Sz, typename _Uint, typename... _UInts>
      struct __select<_Sz, _List<_Uint, _UInts...>, false>
      : __select<_Sz, _List<_UInts...>>
      { };
  };
 
  // Choose unsigned integer type with the smallest rank and same size as _Tp
  template<typename _Tp>
    class __make_unsigned_selector<_Tp, false, true>
    : __make_unsigned_selector_base
    {
      // With -fshort-enums, an enum may be as small as a char.
      using _UInts = _List<unsigned char, unsigned short, unsigned int,
                           unsigned long, unsigned long long>;
 
      using __unsigned_type = typename __select<sizeof(_Tp), _UInts>::__type;
 
    public:
      using __type
        = typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
    };
 
  // wchar_t, char8_t, char16_t and char32_t are integral types but are
  // neither signed integer types nor unsigned integer types, so must be
  // transformed to the unsigned integer type with the smallest rank.
  // Use the partial specialization for enumeration types to do that.
  template<>
    struct __make_unsigned<wchar_t>
    {
      using __type
        = typename __make_unsigned_selector<wchar_t, false, true>::__type;
    };
 
#ifdef _GLIBCXX_USE_CHAR8_T
  template<>
    struct __make_unsigned<char8_t>
    {
      using __type
        = typename __make_unsigned_selector<char8_t, false, true>::__type;
    };
#endif
 
  template<>
    struct __make_unsigned<char16_t>
    {
      using __type
        = typename __make_unsigned_selector<char16_t, false, true>::__type;
    };
 
  template<>
    struct __make_unsigned<char32_t>
    {
      using __type
        = typename __make_unsigned_selector<char32_t, false, true>::__type;
    };
  /// @endcond
 
  // Given an integral/enum type, return the corresponding unsigned
  // integer type.
  // Primary template.
  /// make_unsigned
  template<typename _Tp>
    struct make_unsigned
    { typedef typename __make_unsigned_selector<_Tp>::__type type; };
 
  // Integral, but don't define.
  template<> struct make_unsigned<bool>;
  template<> struct make_unsigned<bool const>;
  template<> struct make_unsigned<bool volatile>;
  template<> struct make_unsigned<bool const volatile>;
 
  /// @cond undocumented
 
  // Utility for finding the signed versions of unsigned integral types.
  template<typename _Tp>
    struct __make_signed
    { typedef _Tp __type; };
 
  template<>
    struct __make_signed<char>
    { typedef signed char __type; };
 
  template<>
    struct __make_signed<unsigned char>
    { typedef signed char __type; };
 
  template<>
    struct __make_signed<unsigned short>
    { typedef signed short __type; };
 
  template<>
    struct __make_signed<unsigned int>
    { typedef signed int __type; };
 
  template<>
    struct __make_signed<unsigned long>
    { typedef signed long __type; };
 
  template<>
    struct __make_signed<unsigned long long>
    { typedef signed long long __type; };
 
#if defined(__GLIBCXX_TYPE_INT_N_0)
  __extension__
  template<>
    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_0>
    { typedef __GLIBCXX_TYPE_INT_N_0 __type; };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_1)
  __extension__
  template<>
    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_1>
    { typedef __GLIBCXX_TYPE_INT_N_1 __type; };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_2)
  __extension__
  template<>
    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_2>
    { typedef __GLIBCXX_TYPE_INT_N_2 __type; };
#endif
#if defined(__GLIBCXX_TYPE_INT_N_3)
  __extension__
  template<>
    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_3>
    { typedef __GLIBCXX_TYPE_INT_N_3 __type; };
#endif
 
  // Select between integral and enum: not possible to be both.
  template<typename _Tp,
           bool _IsInt = is_integral<_Tp>::value,
           bool _IsEnum = is_enum<_Tp>::value>
    class __make_signed_selector;
 
  template<typename _Tp>
    class __make_signed_selector<_Tp, true, false>
    {
      using __signed_type
        = typename __make_signed<__remove_cv_t<_Tp>>::__type;
 
    public:
      using __type
        = typename __match_cv_qualifiers<_Tp, __signed_type>::__type;
    };
 
  // Choose signed integer type with the smallest rank and same size as _Tp
  template<typename _Tp>
    class __make_signed_selector<_Tp, false, true>
    {
      typedef typename __make_unsigned_selector<_Tp>::__type __unsigned_type;
 
    public:
      typedef typename __make_signed_selector<__unsigned_type>::__type __type;
    };
 
  // wchar_t, char16_t and char32_t are integral types but are neither
  // signed integer types nor unsigned integer types, so must be
  // transformed to the signed integer type with the smallest rank.
  // Use the partial specialization for enumeration types to do that.
  template<>
    struct __make_signed<wchar_t>
    {
      using __type
        = typename __make_signed_selector<wchar_t, false, true>::__type;
    };
 
#if defined(_GLIBCXX_USE_CHAR8_T)
  template<>
    struct __make_signed<char8_t>
    {
      using __type
        = typename __make_signed_selector<char8_t, false, true>::__type;
    };
#endif
 
  template<>
    struct __make_signed<char16_t>
    {
      using __type
        = typename __make_signed_selector<char16_t, false, true>::__type;
    };
 
  template<>
    struct __make_signed<char32_t>
    {
      using __type
        = typename __make_signed_selector<char32_t, false, true>::__type;
    };
  /// @endcond
 
  // Given an integral/enum type, return the corresponding signed
  // integer type.
  // Primary template.
  /// make_signed
  template<typename _Tp>
    struct make_signed
    { typedef typename __make_signed_selector<_Tp>::__type type; };
 
  // Integral, but don't define.
  template<> struct make_signed<bool>;
  template<> struct make_signed<bool const>;
  template<> struct make_signed<bool volatile>;
  template<> struct make_signed<bool const volatile>;
 
#if __cplusplus > 201103L
  /// Alias template for make_signed
  template<typename _Tp>
    using make_signed_t = typename make_signed<_Tp>::type;
 
  /// Alias template for make_unsigned
  template<typename _Tp>
    using make_unsigned_t = typename make_unsigned<_Tp>::type;
#endif
 
  // Array modifications.
 
  /// remove_extent
  template<typename _Tp>
    struct remove_extent
    { typedef _Tp     type; };
 
  template<typename _Tp, std::size_t _Size>
    struct remove_extent<_Tp[_Size]>
    { typedef _Tp     type; };
 
  template<typename _Tp>
    struct remove_extent<_Tp[]>
    { typedef _Tp     type; };
 
  /// remove_all_extents
  template<typename _Tp>
    struct remove_all_extents
    { typedef _Tp     type; };
 
  template<typename _Tp, std::size_t _Size>
    struct remove_all_extents<_Tp[_Size]>
    { typedef typename remove_all_extents<_Tp>::type     type; };
 
  template<typename _Tp>
    struct remove_all_extents<_Tp[]>
    { typedef typename remove_all_extents<_Tp>::type     type; };
 
#if __cplusplus > 201103L
  /// Alias template for remove_extent
  template<typename _Tp>
    using remove_extent_t = typename remove_extent<_Tp>::type;
 
  /// Alias template for remove_all_extents
  template<typename _Tp>
    using remove_all_extents_t = typename remove_all_extents<_Tp>::type;
#endif
 
  // Pointer modifications.
 
  template<typename _Tp, typename>
    struct __remove_pointer_helper
    { typedef _Tp     type; };
 
  template<typename _Tp, typename _Up>
    struct __remove_pointer_helper<_Tp, _Up*>
    { typedef _Up     type; };
 
  /// remove_pointer
  template<typename _Tp>
    struct remove_pointer
    : public __remove_pointer_helper<_Tp, __remove_cv_t<_Tp>>
    { };
 
  template<typename _Tp, typename = void>
    struct __add_pointer_helper
    { using type = _Tp; };
 
  template<typename _Tp>
    struct __add_pointer_helper<_Tp, __void_t<_Tp*>>
    { using type = _Tp*; };
 
  /// add_pointer
  template<typename _Tp>
    struct add_pointer
    : public __add_pointer_helper<_Tp>
    { };
 
  template<typename _Tp>
    struct add_pointer<_Tp&>
    { using type = _Tp*; };
 
  template<typename _Tp>