type_traits

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// C++11 <type_traits> -*- C++ -*-

// Copyright (C) 2007-2014 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

  /**
   * @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.
   *
   * @{
   */

  /// 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 { return value; }
#if __cplusplus > 201103L
      constexpr value_type operator()() const { return value; }
#endif
    };
  
  template<typename _Tp, _Tp __v>
    constexpr _Tp integral_constant<_Tp, __v>::value;

  /// The type used as a compile-time boolean with true value.
  typedef integral_constant<bool, true>     true_type;

  /// The type used as a compile-time boolean with false value.
  typedef integral_constant<bool, false>    false_type;

  // Meta programming helper types.

  template<bool, typename, typename>
    struct conditional;

  template<typename...>
    struct __or_;

  template<>
    struct __or_<>
    : public false_type
    { };

  template<typename _B1>
    struct __or_<_B1>
    : public _B1
    { };

  template<typename _B1, typename _B2>
    struct __or_<_B1, _B2>
    : public conditional<_B1::value, _B1, _B2>::type
    { };

  template<typename _B1, typename _B2, typename _B3, typename... _Bn>
    struct __or_<_B1, _B2, _B3, _Bn...>
    : public conditional<_B1::value, _B1, __or_<_B2, _B3, _Bn...>>::type
    { };

  template<typename...>
    struct __and_;

  template<>
    struct __and_<>
    : public true_type
    { };

  template<typename _B1>
    struct __and_<_B1>
    : public _B1
    { };

  template<typename _B1, typename _B2>
    struct __and_<_B1, _B2>
    : public conditional<_B1::value, _B2, _B1>::type
    { };

  template<typename _B1, typename _B2, typename _B3, typename... _Bn>
    struct __and_<_B1, _B2, _B3, _Bn...>
    : public conditional<_B1::value, __and_<_B2, _B3, _Bn...>, _B1>::type
    { };

  template<typename _Pp>
    struct __not_
    : public integral_constant<bool, !_Pp::value>
    { };

  // For several sfinae-friendly trait implementations we transport both the
  // result information (as the member type) and the failure information (no
  // member type). This is very similar to std::enable_if, but we cannot use
  // them, because we need to derive from them as an implementation detail.

  template<typename _Tp>
    struct __success_type
    { typedef _Tp type; };

  struct __failure_type
  { };

  // Primary type categories.

  template<typename>
    struct remove_cv;

  template<typename>
    struct __is_void_helper
    : public false_type { };

  template<>
    struct __is_void_helper<void>
    : public true_type { };

  /// is_void
  template<typename _Tp>
    struct is_void
    : public __is_void_helper<typename remove_cv<_Tp>::type>::type
    { };

  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 { };

#ifdef _GLIBCXX_USE_WCHAR_T
  template<>
    struct __is_integral_helper<wchar_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 { };

#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_INT128)
  template<>
    struct __is_integral_helper<__int128>
    : public true_type { };

  template<>
    struct __is_integral_helper<unsigned __int128>
    : public true_type { };
#endif

  /// is_integral
  template<typename _Tp>
    struct is_integral
    : public __is_integral_helper<typename remove_cv<_Tp>::type>::type
    { };

  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 { };

#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_FLOAT128)
  template<>
    struct __is_floating_point_helper<__float128>
    : public true_type { };
#endif

  /// is_floating_point
  template<typename _Tp>
    struct is_floating_point
    : public __is_floating_point_helper<typename remove_cv<_Tp>::type>::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<typename remove_cv<_Tp>::type>::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_function;

  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 integral_constant<bool, !is_function<_Tp>::value> { };

  /// is_member_object_pointer
  template<typename _Tp>
    struct is_member_object_pointer
    : public __is_member_object_pointer_helper<
                typename remove_cv<_Tp>::type>::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 integral_constant<bool, is_function<_Tp>::value> { };

  /// is_member_function_pointer
  template<typename _Tp>
    struct is_member_function_pointer
    : public __is_member_function_pointer_helper<
                typename remove_cv<_Tp>::type>::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>
    struct is_function
    : public false_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...)>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......)>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) const>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) const &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) const &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) const>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) const &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) const &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) volatile>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) volatile &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) volatile &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) volatile>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) volatile &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) volatile &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) const volatile>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) const volatile &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes...) const volatile &&>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) const volatile>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) const volatile &>
    : public true_type { };

  template<typename _Res, typename... _ArgTypes>
    struct is_function<_Res(_ArgTypes......) const volatile &&>
    : public true_type { };

  template<typename>
    struct __is_null_pointer_helper
    : public false_type { };

  template<>
    struct __is_null_pointer_helper<std::nullptr_t>
    : public true_type { };

  /// is_null_pointer (LWG 2247).
  template<typename _Tp>
    struct is_null_pointer
    : public __is_null_pointer_helper<typename remove_cv<_Tp>::type>::type
    { };

  /// __is_nullptr_t (extension).
  template<typename _Tp>
    struct __is_nullptr_t
    : public is_null_pointer<_Tp>
    { };

  // Composite type categories.

  /// is_reference
  template<typename _Tp>
    struct is_reference
    : public __or_<is_lvalue_reference<_Tp>,
                   is_rvalue_reference<_Tp>>::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 integral_constant<bool, !is_fundamental<_Tp>::value> { };

  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 { };

  /// is_member_pointer
  template<typename _Tp>
    struct is_member_pointer
    : public __is_member_pointer_helper<typename remove_cv<_Tp>::type>::type
    { };

  // Utility to detect referenceable types ([defns.referenceable]).

  template<typename _Tp>
    struct __is_referenceable
    : public __or_<is_object<_Tp>, is_reference<_Tp>>::type
    { };

  template<typename _Res, typename... _Args>
    struct __is_referenceable<_Res(_Args...)>
    : public true_type
    { };

  template<typename _Res, typename... _Args>
    struct __is_referenceable<_Res(_Args......)>
    : public true_type
    { };

  // 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)>
    { };

  // is_trivially_copyable (still unimplemented)

  /// is_standard_layout
  template<typename _Tp>
    struct is_standard_layout
    : public integral_constant<bool, __is_standard_layout(_Tp)>
    { };

  /// is_pod
  // Could use is_standard_layout && is_trivial instead of the builtin.
  template<typename _Tp>
    struct is_pod
    : public integral_constant<bool, __is_pod(_Tp)>
    { };

  /// is_literal_type
  template<typename _Tp>
    struct is_literal_type
    : public integral_constant<bool, __is_literal_type(_Tp)>
    { };

  /// 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)>
    { };

  /// is_abstract
  template<typename _Tp>
    struct is_abstract
    : public integral_constant<bool, __is_abstract(_Tp)>
    { };

  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)>
    { };

  /// 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
    { };


  // Destructible and constructible type properties.

  template<typename>
    struct add_rvalue_reference;

  /**
   *  @brief  Utility to simplify expressions used in unevaluated operands
   *  @ingroup utilities
   */
  template<typename _Tp>
    typename add_rvalue_reference<_Tp>::type declval() noexcept;

  template<typename, unsigned = 0>
    struct extent;

  template<typename>
    struct remove_all_extents;

  template<typename _Tp>
    struct __is_array_known_bounds
    : public integral_constant<bool, (extent<_Tp>::value > 0)>
    { };

  template<typename _Tp>
    struct __is_array_unknown_bounds
    : public __and_<is_array<_Tp>, __not_<extent<_Tp>>>::type
    { };
    
  // 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 { };

  /// is_destructible
  template<typename _Tp>
    struct is_destructible
    : public __is_destructible_safe<_Tp>::type
    { };

  // 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 integral_constant<bool, 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 { };

  /// is_nothrow_destructible
  template<typename _Tp>
    struct is_nothrow_destructible
    : public __is_nt_destructible_safe<_Tp>::type
    { };

  struct __do_is_default_constructible_impl
  {
    template<typename _Tp, typename = decltype(_Tp())>
      static true_type __test(int);

    template<typename>
      static false_type __test(...);
  };

  template<typename _Tp>
    struct __is_default_constructible_impl
    : public __do_is_default_constructible_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };

  template<typename _Tp>
    struct __is_default_constructible_atom
    : public __and_<__not_<is_void<_Tp>>,
                    __is_default_constructible_impl<_Tp>>::type
    { };

  template<typename _Tp, bool = is_array<_Tp>::value>
    struct __is_default_constructible_safe;

  // The following technique is a workaround for a current core language
  // restriction, which does not allow for array types to occur in 
  // functional casts of the form T().  Complete arrays can be default-
  // constructed, if the element type is default-constructible, but 
  // arrays with unknown bounds are not.
  template<typename _Tp>
    struct __is_default_constructible_safe<_Tp, true>
    : public __and_<__is_array_known_bounds<_Tp>,
            __is_default_constructible_atom<typename
                      remove_all_extents<_Tp>::type>>::type
    { };

  template<typename _Tp>
    struct __is_default_constructible_safe<_Tp, false>
    : public __is_default_constructible_atom<_Tp>::type
    { };

  /// is_default_constructible
  template<typename _Tp>
    struct is_default_constructible
    : public __is_default_constructible_safe<_Tp>::type
    { };


  // Implementation of is_constructible.

  // The hardest part of this trait is the binary direct-initialization
  // case, because we hit into a functional cast of the form T(arg).
  // This implementation uses different strategies depending on the
  // target type to reduce the test overhead as much as possible:
  //
  // a) For a reference target type, we use a static_cast expression 
  //    modulo its extra cases.
  //
  // b) For a non-reference target type we use a ::new expression.
  struct __do_is_static_castable_impl
  {
    template<typename _From, typename _To, typename
             = decltype(static_cast<_To>(declval<_From>()))>
      static true_type __test(int);

    template<typename, typename>
      static false_type __test(...);
  };

  template<typename _From, typename _To>
    struct __is_static_castable_impl
    : public __do_is_static_castable_impl
    {
      typedef decltype(__test<_From, _To>(0)) type;
    };

  template<typename _From, typename _To>
    struct __is_static_castable_safe
    : public __is_static_castable_impl<_From, _To>::type
    { };

  // __is_static_castable
  template<typename _From, typename _To>
    struct __is_static_castable
    : public integral_constant<bool, (__is_static_castable_safe<
                      _From, _To>::value)>
    { };

  // Implementation for non-reference types. To meet the proper
  // variable definition semantics, we also need to test for
  // is_destructible in this case.
  // This form should be simplified by a single expression:
  // ::delete ::new _Tp(declval<_Arg>()), see c++/51222.
  struct __do_is_direct_constructible_impl
  {
    template<typename _Tp, typename _Arg, typename
         = decltype(::new _Tp(declval<_Arg>()))>
      static true_type __test(int);

    template<typename, typename>
      static false_type __test(...);
  };

  template<typename _Tp, typename _Arg>
    struct __is_direct_constructible_impl
    : public __do_is_direct_constructible_impl
    {
      typedef decltype(__test<_Tp, _Arg>(0)) type;
    };

  template<typename _Tp, typename _Arg>
    struct __is_direct_constructible_new_safe
    : public __and_<is_destructible<_Tp>,
                    __is_direct_constructible_impl<_Tp, _Arg>>::type
    { };

  template<typename, typename>
    struct is_same;

  template<typename, typename>
    struct is_base_of;

  template<typename>
    struct remove_reference;

  template<typename _From, typename _To, bool
           = __not_<__or_<is_void<_From>, 
                          is_function<_From>>>::value>
    struct __is_base_to_derived_ref;

  // Detect whether we have a downcast situation during
  // reference binding.
  template<typename _From, typename _To>
    struct __is_base_to_derived_ref<_From, _To, true>
    {
      typedef typename remove_cv<typename remove_reference<_From
        >::type>::type __src_t;
      typedef typename remove_cv<typename remove_reference<_To
        >::type>::type __dst_t;
      typedef __and_<__not_<is_same<__src_t, __dst_t>>,
             is_base_of<__src_t, __dst_t>> type;
      static constexpr bool value = type::value;
    };

  template<typename _From, typename _To>
    struct __is_base_to_derived_ref<_From, _To, false>
    : public false_type
    { };

  template<typename _From, typename _To, bool
           = __and_<is_lvalue_reference<_From>,
                    is_rvalue_reference<_To>>::value>
    struct __is_lvalue_to_rvalue_ref;

  // Detect whether we have an lvalue of non-function type
  // bound to a reference-compatible rvalue-reference.
  template<typename _From, typename _To>
    struct __is_lvalue_to_rvalue_ref<_From, _To, true>
    {
      typedef typename remove_cv<typename remove_reference<
        _From>::type>::type __src_t;
      typedef typename remove_cv<typename remove_reference<
        _To>::type>::type __dst_t;
      typedef __and_<__not_<is_function<__src_t>>, 
        __or_<is_same<__src_t, __dst_t>,
            is_base_of<__dst_t, __src_t>>> type;
      static constexpr bool value = type::value;
    };

  template<typename _From, typename _To>
    struct __is_lvalue_to_rvalue_ref<_From, _To, false>
    : public false_type
    { };

  // Here we handle direct-initialization to a reference type as 
  // equivalent to a static_cast modulo overshooting conversions.
  // These are restricted to the following conversions:
  //    a) A base class value to a derived class reference
  //    b) An lvalue to an rvalue-reference of reference-compatible 
  //       types that are not functions
  template<typename _Tp, typename _Arg>
    struct __is_direct_constructible_ref_cast
    : public __and_<__is_static_castable<_Arg, _Tp>,
                    __not_<__or_<__is_base_to_derived_ref<_Arg, _Tp>,
                                 __is_lvalue_to_rvalue_ref<_Arg, _Tp>
                   >>>::type
    { };

  template<typename _Tp, typename _Arg>
    struct __is_direct_constructible_new
    : public conditional<is_reference<_Tp>::value,
             __is_direct_constructible_ref_cast<_Tp, _Arg>,
             __is_direct_constructible_new_safe<_Tp, _Arg>
             >::type
    { };

  template<typename _Tp, typename _Arg>
    struct __is_direct_constructible
    : public __is_direct_constructible_new<_Tp, _Arg>::type
    { };

  // Since default-construction and binary direct-initialization have
  // been handled separately, the implementation of the remaining
  // n-ary construction cases is rather straightforward. We can use
  // here a functional cast, because array types are excluded anyway
  // and this form is never interpreted as a C cast.
  struct __do_is_nary_constructible_impl
  {
    template<typename _Tp, typename... _Args, typename
             = decltype(_Tp(declval<_Args>()...))>
      static true_type __test(int);

    template<typename, typename...>
      static false_type __test(...);
  };

  template<typename _Tp, typename... _Args>
    struct __is_nary_constructible_impl
    : public __do_is_nary_constructible_impl
    {
      typedef decltype(__test<_Tp, _Args...>(0)) type;
    };

  template<typename _Tp, typename... _Args>
    struct __is_nary_constructible
    : public __is_nary_constructible_impl<_Tp, _Args...>::type
    {
      static_assert(sizeof...(_Args) > 1,
                    "Only useful for > 1 arguments");
    };

  template<typename _Tp, typename... _Args>
    struct __is_constructible_impl
    : public __is_nary_constructible<_Tp, _Args...>
    { };

  template<typename _Tp, typename _Arg>
    struct __is_constructible_impl<_Tp, _Arg>
    : public __is_direct_constructible<_Tp, _Arg>
    { };

  template<typename _Tp>
    struct __is_constructible_impl<_Tp>
    : public is_default_constructible<_Tp>
    { };

  /// is_constructible
  template<typename _Tp, typename... _Args>
    struct is_constructible
    : public __is_constructible_impl<_Tp, _Args...>::type
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_copy_constructible_impl;

  template<typename _Tp>
    struct __is_copy_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_copy_constructible_impl<_Tp, true>
    : public is_constructible<_Tp, const _Tp&>
    { };

  /// is_copy_constructible
  template<typename _Tp>
    struct is_copy_constructible
    : public __is_copy_constructible_impl<_Tp>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_move_constructible_impl;

  template<typename _Tp>
    struct __is_move_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_move_constructible_impl<_Tp, true>
    : public is_constructible<_Tp, _Tp&&>
    { };

  /// is_move_constructible
  template<typename _Tp>
    struct is_move_constructible
    : public __is_move_constructible_impl<_Tp>
    { };

  template<typename _Tp>
    struct __is_nt_default_constructible_atom
    : public integral_constant<bool, noexcept(_Tp())>
    { };

  template<typename _Tp, bool = is_array<_Tp>::value>
    struct __is_nt_default_constructible_impl;

  template<typename _Tp>
    struct __is_nt_default_constructible_impl<_Tp, true>
    : public __and_<__is_array_known_bounds<_Tp>,
            __is_nt_default_constructible_atom<typename
                      remove_all_extents<_Tp>::type>>::type
    { };

  template<typename _Tp>
    struct __is_nt_default_constructible_impl<_Tp, false>
    : public __is_nt_default_constructible_atom<_Tp>
    { };

  /// is_nothrow_default_constructible
  template<typename _Tp>
    struct is_nothrow_default_constructible
    : public __and_<is_default_constructible<_Tp>,
                    __is_nt_default_constructible_impl<_Tp>>::type
    { };

  template<typename _Tp, typename... _Args>
    struct __is_nt_constructible_impl
    : public integral_constant<bool, noexcept(_Tp(declval<_Args>()...))>
    { };

  template<typename _Tp, typename _Arg>
    struct __is_nt_constructible_impl<_Tp, _Arg>
    : public integral_constant<bool,
                               noexcept(static_cast<_Tp>(declval<_Arg>()))>
    { };

  template<typename _Tp>
    struct __is_nt_constructible_impl<_Tp>
    : public is_nothrow_default_constructible<_Tp>
    { };

  /// is_nothrow_constructible
  template<typename _Tp, typename... _Args>
    struct is_nothrow_constructible
    : public __and_<is_constructible<_Tp, _Args...>,
            __is_nt_constructible_impl<_Tp, _Args...>>::type
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nothrow_copy_constructible_impl;

  template<typename _Tp>
    struct __is_nothrow_copy_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nothrow_copy_constructible_impl<_Tp, true>
    : public is_nothrow_constructible<_Tp, const _Tp&>
    { };

  /// is_nothrow_copy_constructible
  template<typename _Tp>
    struct is_nothrow_copy_constructible
    : public __is_nothrow_copy_constructible_impl<_Tp>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nothrow_move_constructible_impl;

  template<typename _Tp>
    struct __is_nothrow_move_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nothrow_move_constructible_impl<_Tp, true>
    : public is_nothrow_constructible<_Tp, _Tp&&>
    { };

  /// is_nothrow_move_constructible
  template<typename _Tp>
    struct is_nothrow_move_constructible
    : public __is_nothrow_move_constructible_impl<_Tp>
    { };

  template<typename _Tp, typename _Up>
    class __is_assignable_helper
    {
      template<typename _Tp1, typename _Up1,
           typename = decltype(declval<_Tp1>() = declval<_Up1>())>
    static true_type
    __test(int);

      template<typename, typename>
    static false_type
    __test(...);

    public:
      typedef decltype(__test<_Tp, _Up>(0)) type;
    };

  /// is_assignable
  template<typename _Tp, typename _Up>
    struct is_assignable
      : public __is_assignable_helper<_Tp, _Up>::type
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_copy_assignable_impl;

  template<typename _Tp>
    struct __is_copy_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_copy_assignable_impl<_Tp, true>
    : public is_assignable<_Tp&, const _Tp&>
    { };

  /// is_copy_assignable
  template<typename _Tp>
    struct is_copy_assignable
    : public __is_copy_assignable_impl<_Tp>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_move_assignable_impl;

  template<typename _Tp>
    struct __is_move_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_move_assignable_impl<_Tp, true>
    : public is_assignable<_Tp&, _Tp&&>
    { };

  /// is_move_assignable
  template<typename _Tp>
    struct is_move_assignable
    : public __is_move_assignable_impl<_Tp>
    { };

  template<typename _Tp, typename _Up>
    struct __is_nt_assignable_impl
    : public integral_constant<bool, noexcept(declval<_Tp>() = declval<_Up>())>
    { };

  /// is_nothrow_assignable
  template<typename _Tp, typename _Up>
    struct is_nothrow_assignable
    : public __and_<is_assignable<_Tp, _Up>,
            __is_nt_assignable_impl<_Tp, _Up>>::type
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nt_copy_assignable_impl;

  template<typename _Tp>
    struct __is_nt_copy_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nt_copy_assignable_impl<_Tp, true>
    : public is_nothrow_assignable<_Tp&, const _Tp&>
    { };

  /// is_nothrow_copy_assignable
  template<typename _Tp>
    struct is_nothrow_copy_assignable
    : public __is_nt_copy_assignable_impl<_Tp>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nt_move_assignable_impl;

  template<typename _Tp>
    struct __is_nt_move_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nt_move_assignable_impl<_Tp, true>
    : public is_nothrow_assignable<_Tp&, _Tp&&>
    { };

  /// is_nothrow_move_assignable
  template<typename _Tp>
    struct is_nothrow_move_assignable
    : public __is_nt_move_assignable_impl<_Tp>
    { };

  /// is_trivially_constructible (still unimplemented)
  
  /// is_trivially_default_constructible (still unimplemented)

  /// is_trivially_copy_constructible (still unimplemented)

  /// is_trivially_move_constructible (still unimplemented)

  /// is_trivially_assignable (still unimplemented)

  /// is_trivially_copy_assignable (still unimplemented)

  /// is_trivially_move_assignable (still unimplemented)

  /// is_trivially_destructible
  template<typename _Tp>
    struct is_trivially_destructible
    : public __and_<is_destructible<_Tp>, integral_constant<bool,
                  __has_trivial_destructor(_Tp)>>::type
    { };

  /// has_trivial_default_constructor (temporary legacy)
  template<typename _Tp>
    struct has_trivial_default_constructor
    : public integral_constant<bool, __has_trivial_constructor(_Tp)>
    { };

  /// has_trivial_copy_constructor (temporary legacy)
  template<typename _Tp>
    struct has_trivial_copy_constructor
    : public integral_constant<bool, __has_trivial_copy(_Tp)>
    { };

  /// has_trivial_copy_assign (temporary legacy)
  template<typename _Tp>
    struct has_trivial_copy_assign
    : public integral_constant<bool, __has_trivial_assign(_Tp)>
    { };

  /// has_virtual_destructor
  template<typename _Tp>
    struct has_virtual_destructor
    : public integral_constant<bool, __has_virtual_destructor(_Tp)>
    { };

  
  // type property queries.

  /// alignment_of
  template<typename _Tp>
    struct alignment_of
    : public integral_constant<std::size_t, __alignof__(_Tp)> { };
  
  /// 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>
    struct extent
    : public integral_constant<std::size_t, 0> { };
  
  template<typename _Tp, unsigned _Uint, std::size_t _Size>
    struct extent<_Tp[_Size], _Uint>
    : public integral_constant<std::size_t,
                   _Uint == 0 ? _Size : extent<_Tp,
                               _Uint - 1>::value>
    { };

  template<typename _Tp, unsigned _Uint>
    struct extent<_Tp[], _Uint>
    : public integral_constant<std::size_t,
                   _Uint == 0 ? 0 : extent<_Tp,
                               _Uint - 1>::value>
    { };


  // Type relations.

  /// is_same
  template<typename, typename>
    struct is_same
    : public false_type { };

  template<typename _Tp>
    struct is_same<_Tp, _Tp>
    : public true_type { };

  /// is_base_of
  template<typename _Base, typename _Derived>
    struct is_base_of
    : public integral_constant<bool, __is_base_of(_Base, _Derived)>
    { };

  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; };

  template<typename _From, typename _To>
    class __is_convertible_helper<_From, _To, false>
    {
       template<typename _To1>
    static void __test_aux(_To1);

      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;
    };


  /// is_convertible
  template<typename _From, typename _To>
    struct is_convertible
    : public __is_convertible_helper<_From, _To>::type
    { };


  // 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
  template<typename _Tp>
    struct remove_cv
    {
      typedef typename
      remove_const<typename remove_volatile<_Tp>::type>::type     type;
    };
  
  /// add_const
  template<typename _Tp>
    struct add_const
    { typedef _Tp const     type; };
   
  /// add_volatile
  template<typename _Tp>
    struct add_volatile
    { typedef _Tp volatile     type; };
  
  /// add_cv
  template<typename _Tp>
    struct add_cv
    {
      typedef typename
      add_const<typename add_volatile<_Tp>::type>::type     type;
    };

#if __cplusplus > 201103L
  /// 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
  template<typename _Tp>
    struct remove_reference
    { typedef _Tp   type; };

  template<typename _Tp>
    struct remove_reference<_Tp&>
    { typedef _Tp   type; };

  template<typename _Tp>
    struct remove_reference<_Tp&&>
    { typedef _Tp   type; };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __add_lvalue_reference_helper
    { typedef _Tp   type; };

  template<typename _Tp>
    struct __add_lvalue_reference_helper<_Tp, true>
    { typedef _Tp&   type; };

  /// add_lvalue_reference
  template<typename _Tp>
    struct add_lvalue_reference
    : public __add_lvalue_reference_helper<_Tp>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __add_rvalue_reference_helper
    { typedef _Tp   type; };

  template<typename _Tp>
    struct __add_rvalue_reference_helper<_Tp, true>
    { typedef _Tp&&   type; };

  /// add_rvalue_reference
  template<typename _Tp>
    struct add_rvalue_reference
    : public __add_rvalue_reference_helper<_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.

  // 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(__STRICT_ANSI__) && defined(_GLIBCXX_USE_INT128)
  template<>
    struct __make_unsigned<__int128>
    { typedef unsigned __int128 __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>
    {
      typedef __make_unsigned<typename remove_cv<_Tp>::type> __unsignedt;
      typedef typename __unsignedt::__type __unsigned_type;
      typedef __match_cv_qualifiers<_Tp, __unsigned_type> __cv_unsigned;

    public:
      typedef typename __cv_unsigned::__type __type;
    };

  template<typename _Tp>
    class __make_unsigned_selector<_Tp, false, true>
    {
      // With -fshort-enums, an enum may be as small as a char.
      typedef unsigned char __smallest;
      static const bool __b0 = sizeof(_Tp) <= sizeof(__smallest);
      static const bool __b1 = sizeof(_Tp) <= sizeof(unsigned short);
      static const bool __b2 = sizeof(_Tp) <= sizeof(unsigned int);
      typedef conditional<__b2, unsigned int, unsigned long> __cond2;
      typedef typename __cond2::type __cond2_type;
      typedef conditional<__b1, unsigned short, __cond2_type> __cond1;
      typedef typename __cond1::type __cond1_type;

    public:
      typedef typename conditional<__b0, __smallest, __cond1_type>::type __type;
    };

  // 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>;


  // 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(__STRICT_ANSI__) && defined(_GLIBCXX_USE_INT128)
  template<>
    struct __make_signed<unsigned __int128>
    { typedef __int128 __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>
    {
      typedef __make_signed<typename remove_cv<_Tp>::type> __signedt;
      typedef typename __signedt::__type __signed_type;
      typedef __match_cv_qualifiers<_Tp, __signed_type> __cv_signed;

    public:
      typedef typename __cv_signed::__type __type;
    };

  template<typename _Tp>
    class __make_signed_selector<_Tp, false, true>
    {
      // With -fshort-enums, an enum may be as small as a char.
      typedef signed char __smallest;
      static const bool __b0 = sizeof(_Tp) <= sizeof(__smallest);
      static const bool __b1 = sizeof(_Tp) <= sizeof(signed short);
      static const bool __b2 = sizeof(_Tp) <= sizeof(signed int);
      typedef conditional<__b2, signed int, signed long> __cond2;
      typedef typename __cond2::type __cond2_type;
      typedef conditional<__b1, signed short, __cond2_type> __cond1;
      typedef typename __cond1::type __cond1_type;

    public:
      typedef typename conditional<__b0, __smallest, __cond1_type>::type __type;
    };

  // 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>;

#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, typename remove_cv<_Tp>::type>
    { };

  /// add_pointer
  template<typename _Tp, bool = __or_<__is_referenceable<_Tp>,
                      is_void<_Tp>>::value>
    struct __add_pointer_helper
    { typedef _Tp     type; };

  template<typename _Tp>
    struct __add_pointer_helper<_Tp, true>
    { typedef typename remove_reference<_Tp>::type*     type; };

  template<typename _Tp>
    struct add_pointer 
    : public __add_pointer_helper<_Tp>
    { };

#if __cplusplus > 201103L
  /// Alias template for remove_pointer
  template<typename _Tp>
    using remove_pointer_t = typename remove_pointer<_Tp>::type;

  /// Alias template for add_pointer
  template<typename _Tp>
    using add_pointer_t = typename add_pointer<_Tp>::type;
#endif

  template<std::size_t _Len>
    struct __aligned_storage_msa
    { 
      union __type
      {
    unsigned char __data[_Len];
    struct __attribute__((__aligned__)) { } __align; 
      };
    };

  /**
   *  @brief Alignment type.
   *
   *  The value of _Align is a default-alignment which shall be the
   *  most stringent alignment requirement for any C++ object type
   *  whose size is no greater than _Len (3.9). The member typedef
   *  type shall be a POD type suitable for use as uninitialized
   *  storage for any object whose size is at most _Len and whose
   *  alignment is a divisor of _Align.
  */
  template<std::size_t _Len, std::size_t _Align =
       __alignof__(typename __aligned_storage_msa<_Len>::__type)>
    struct aligned_storage
    { 
      union type
      {
    unsigned char __data[_Len];
    struct __attribute__((__aligned__((_Align)))) { } __align; 
      };
    };


  // Decay trait for arrays and functions, used for perfect forwarding
  // in make_pair, make_tuple, etc.
  template<typename _Up, 
       bool _IsArray = is_array<_Up>::value,
       bool _IsFunction = is_function<_Up>::value> 
    struct __decay_selector;

  // NB: DR 705.
  template<typename _Up> 
    struct __decay_selector<_Up, false, false>
    { typedef typename remove_cv<_Up>::type __type; };

  template<typename _Up> 
    struct __decay_selector<_Up, true, false>
    { typedef typename remove_extent<_Up>::type* __type; };

  template<typename _Up> 
    struct __decay_selector<_Up, false, true>
    { typedef typename add_pointer<_Up>::type __type; };

  /// decay
  template<typename _Tp> 
    class decay 
    { 
      typedef typename remove_reference<_Tp>::type __remove_type;

    public:
      typedef typename __decay_selector<__remove_type>::__type type;
    };

  template<typename _Tp>
    class reference_wrapper;

  // Helper which adds a reference to a type when given a reference_wrapper
  template<typename _Tp>
    struct __strip_reference_wrapper
    {
      typedef _Tp __type;
    };

  template<typename _Tp>
    struct __strip_reference_wrapper<reference_wrapper<_Tp> >
    {
      typedef _Tp& __type;
    };

  template<typename _Tp>
    struct __decay_and_strip
    {
      typedef typename __strip_reference_wrapper<
    typename decay<_Tp>::type>::__type __type;
    };


  // Primary template.
  /// Define a member typedef @c 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; };

  template<typename... _Cond>
    using _Require = typename enable_if<__and_<_Cond...>::value>::type;

  // Primary template.
  /// Define a member typedef @c type to one of two argument types.
  template<bool _Cond, typename _Iftrue, typename _Iffalse>
    struct conditional
    { typedef _Iftrue type; };

  // Partial specialization for false.
  template<typename _Iftrue, typename _Iffalse>
    struct conditional<false, _Iftrue, _Iffalse>
    { typedef _Iffalse type; };

  /// common_type
  template<typename... _Tp>
    struct common_type;

  // Sfinae-friendly common_type implementation:

  struct __do_common_type_impl
  {
    template<typename _Tp, typename _Up>
      static __success_type<typename decay<decltype
                (true ? std::declval<_Tp>()
                 : std::declval<_Up>())>::type> _S_test(int);

    template<typename, typename>
      static __failure_type _S_test(...);
  };

  template<typename _Tp, typename _Up>
    struct __common_type_impl
    : private __do_common_type_impl
    {
      typedef decltype(_S_test<_Tp, _Up>(0)) type;
    };

  struct __do_member_type_wrapper
  {
    template<typename _Tp>
      static __success_type<typename _Tp::type> _S_test(int);

    template<typename>
      static __failure_type _S_test(...);
  };

  template<typename _Tp>
    struct __member_type_wrapper
    : private __do_member_type_wrapper
    {
      typedef decltype(_S_test<_Tp>(0)) type;
    };

  template<typename _CTp, typename... _Args>
    struct __expanded_common_type_wrapper
    {
      typedef common_type<typename _CTp::type, _Args...> type;
    };

  template<typename... _Args>
    struct __expanded_common_type_wrapper<__failure_type, _Args...>
    { typedef __failure_type type; };

  template<typename _Tp>
    struct common_type<_Tp>
    { typedef typename decay<_Tp>::type type; };

  template<typename _Tp, typename _Up>
    struct common_type<_Tp, _Up>
    : public __common_type_impl<_Tp, _Up>::type
    { };

  template<typename _Tp, typename _Up, typename... _Vp>
    struct common_type<_Tp, _Up, _Vp...>
    : public __expanded_common_type_wrapper<typename __member_type_wrapper<
               common_type<_Tp, _Up>>::type, _Vp...>::type
    { };

  /// The underlying type of an enum.
  template<typename _Tp>
    struct underlying_type
    {
      typedef __underlying_type(_Tp) type;
    };

  template<typename _Tp>
    struct __declval_protector
    {
      static const bool __stop = false;
      static typename add_rvalue_reference<_Tp>::type __delegate();
    };

  template<typename _Tp>
    inline typename add_rvalue_reference<_Tp>::type
    declval() noexcept
    {
      static_assert(__declval_protector<_Tp>::__stop,
            "declval() must not be used!");
      return __declval_protector<_Tp>::__delegate();
    }

  /// result_of
  template<typename _Signature>
    class result_of;

  // Sfinae-friendly result_of implementation:

  // [func.require] paragraph 1 bullet 1:
  struct __result_of_memfun_ref_impl
  {
    template<typename _Fp, typename _Tp1, typename... _Args>
      static __success_type<decltype(
      (std::declval<_Tp1>().*std::declval<_Fp>())(std::declval<_Args>()...)
      )> _S_test(int);

    template<typename...>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_memfun_ref
    : private __result_of_memfun_ref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
    };

  // [func.require] paragraph 1 bullet 2:
  struct __result_of_memfun_deref_impl
  {
    template<typename _Fp, typename _Tp1, typename... _Args>
      static __success_type<decltype(
      ((*std::declval<_Tp1>()).*std::declval<_Fp>())(std::declval<_Args>()...)
      )> _S_test(int);

    template<typename...>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_memfun_deref
    : private __result_of_memfun_deref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
    };

  // [func.require] paragraph 1 bullet 3:
  struct __result_of_memobj_ref_impl
  {
    template<typename _Fp, typename _Tp1>
      static __success_type<decltype(
      std::declval<_Tp1>().*std::declval<_Fp>()
      )> _S_test(int);

    template<typename, typename>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_memobj_ref
    : private __result_of_memobj_ref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
    };

  // [func.require] paragraph 1 bullet 4:
  struct __result_of_memobj_deref_impl
  {
    template<typename _Fp, typename _Tp1>
      static __success_type<decltype(
      (*std::declval<_Tp1>()).*std::declval<_Fp>()
      )> _S_test(int);

    template<typename, typename>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_memobj_deref
    : private __result_of_memobj_deref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
    };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_memobj;

  template<typename _Res, typename _Class, typename _Arg>
    struct __result_of_memobj<_Res _Class::*, _Arg>
    {
      typedef typename remove_cv<typename remove_reference<
        _Arg>::type>::type _Argval;
      typedef _Res _Class::* _MemPtr;
      typedef typename conditional<__or_<is_same<_Argval, _Class>,
        is_base_of<_Class, _Argval>>::value,
        __result_of_memobj_ref<_MemPtr, _Arg>,
        __result_of_memobj_deref<_MemPtr, _Arg>
      >::type::type type;
    };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_memfun;

  template<typename _Res, typename _Class, typename _Arg, typename... _Args>
    struct __result_of_memfun<_Res _Class::*, _Arg, _Args...>
    {
      typedef typename remove_cv<typename remove_reference<
        _Arg>::type>::type _Argval;
      typedef _Res _Class::* _MemPtr;
      typedef typename conditional<__or_<is_same<_Argval, _Class>,
        is_base_of<_Class, _Argval>>::value,
        __result_of_memfun_ref<_MemPtr, _Arg, _Args...>,
        __result_of_memfun_deref<_MemPtr, _Arg, _Args...>
      >::type::type type;
    };

  template<bool, bool, typename _Functor, typename... _ArgTypes>
    struct __result_of_impl
    {
      typedef __failure_type type;
    };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_impl<true, false, _MemPtr, _Arg>
    : public __result_of_memobj<typename decay<_MemPtr>::type, _Arg>
    { };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_impl<false, true, _MemPtr, _Arg, _Args...>
    : public __result_of_memfun<typename decay<_MemPtr>::type, _Arg, _Args...>
    { };

  // [func.require] paragraph 1 bullet 5:
  struct __result_of_other_impl
  {
    template<typename _Fn, typename... _Args>
      static __success_type<decltype(
      std::declval<_Fn>()(std::declval<_Args>()...)
      )> _S_test(int);

    template<typename...>
      static __failure_type _S_test(...);
  };

  template<typename _Functor, typename... _ArgTypes>
    struct __result_of_impl<false, false, _Functor, _ArgTypes...>
    : private __result_of_other_impl
    {
      typedef decltype(_S_test<_Functor, _ArgTypes...>(0)) type;
    };

  template<typename _Functor, typename... _ArgTypes>
    struct result_of<_Functor(_ArgTypes...)>
    : public __result_of_impl<
        is_member_object_pointer<
          typename remove_reference<_Functor>::type
        >::value,
        is_member_function_pointer<
          typename remove_reference<_Functor>::type
        >::value,
        _Functor, _ArgTypes...
      >::type
    { };

#if __cplusplus > 201103L
  /// Alias template for aligned_storage
  template<size_t _Len, size_t _Align =
        __alignof__(typename __aligned_storage_msa<_Len>::__type)>
    using aligned_storage_t = typename aligned_storage<_Len, _Align>::type;

  /// Alias template for decay
  template<typename _Tp>
    using decay_t = typename decay<_Tp>::type;

  /// Alias template for enable_if
  template<bool _Cond, typename _Tp = void>
    using enable_if_t = typename enable_if<_Cond, _Tp>::type;

  /// Alias template for conditional
  template<bool _Cond, typename _Iftrue, typename _Iffalse>
    using conditional_t = typename conditional<_Cond, _Iftrue, _Iffalse>::type;

  /// Alias template for common_type
  template<typename... _Tp>
    using common_type_t = typename common_type<_Tp...>::type;

  /// Alias template for underlying_type
  template<typename _Tp>
    using underlying_type_t = typename underlying_type<_Tp>::type;

  /// Alias template for result_of
  template<typename _Tp>
    using result_of_t = typename result_of<_Tp>::type;
#endif

  /// @} group metaprogramming
    
  /**
   *  Use SFINAE to determine if the type _Tp has a publicly-accessible
   *  member type _NTYPE.
   */
#define _GLIBCXX_HAS_NESTED_TYPE(_NTYPE)                \
  template<typename _Tp>                        \
    class __has_##_NTYPE##_helper                   \
    {                                   \
      template<typename _Up>                        \
    struct _Wrap_type                       \
    { };                                \
                                    \
      template<typename _Up>                        \
    static true_type __test(_Wrap_type<typename _Up::_NTYPE>*); \
                                    \
      template<typename _Up>                        \
    static false_type __test(...);                  \
                                    \
    public:                             \
      typedef decltype(__test<_Tp>(0)) type;                \
    };                                  \
                                    \
  template<typename _Tp>                        \
    struct __has_##_NTYPE                       \
    : public __has_##_NTYPE##_helper                    \
            <typename remove_cv<_Tp>::type>::type       \
    { };

_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std

#endif  // C++11

#endif  // _GLIBCXX_TYPE_TRAITS