hashtable_policy.h

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// Internal policy header for unordered_set and unordered_map -*- C++ -*-
 
// Copyright (C) 2010-2023 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 bits/hashtable_policy.h
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly.
 *  @headername{unordered_map,unordered_set}
 */
 
#ifndef _HASHTABLE_POLICY_H
#define _HASHTABLE_POLICY_H 1
 
#include <tuple>                // for std::tuple, std::forward_as_tuple
#include <bits/functional_hash.h> // for __is_fast_hash
#include <bits/stl_algobase.h>  // for std::min, std::is_permutation.
#include <bits/stl_pair.h>      // for std::pair
#include <ext/aligned_buffer.h> // for __gnu_cxx::__aligned_buffer
#include <ext/alloc_traits.h>   // for std::__alloc_rebind
#include <ext/numeric_traits.h> // for __gnu_cxx::__int_traits
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/// @cond undocumented
 
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    class _Hashtable;
 
namespace __detail
{
  /**
   *  @defgroup hashtable-detail Base and Implementation Classes
   *  @ingroup unordered_associative_containers
   *  @{
   */
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Equal, typename _Hash, typename _RangeHash,
           typename _Unused, typename _Traits>
    struct _Hashtable_base;
 
  // Helper function: return distance(first, last) for forward
  // iterators, or 0/1 for input iterators.
  template<typename _Iterator>
    inline typename std::iterator_traits<_Iterator>::difference_type
    __distance_fw(_Iterator __first, _Iterator __last,
                  std::input_iterator_tag)
    { return __first != __last ? 1 : 0; }
 
  template<typename _Iterator>
    inline typename std::iterator_traits<_Iterator>::difference_type
    __distance_fw(_Iterator __first, _Iterator __last,
                  std::forward_iterator_tag)
    { return std::distance(__first, __last); }
 
  template<typename _Iterator>
    inline typename std::iterator_traits<_Iterator>::difference_type
    __distance_fw(_Iterator __first, _Iterator __last)
    { return __distance_fw(__first, __last,
                           std::__iterator_category(__first)); }
 
  struct _Identity
  {
    template<typename _Tp>
      _Tp&&
      operator()(_Tp&& __x) const noexcept
      { return std::forward<_Tp>(__x); }
  };
 
  struct _Select1st
  {
    template<typename _Pair>
      struct __1st_type;
 
    template<typename _Tp, typename _Up>
      struct __1st_type<pair<_Tp, _Up>>
      { using type = _Tp; };
 
    template<typename _Tp, typename _Up>
      struct __1st_type<const pair<_Tp, _Up>>
      { using type = const _Tp; };
 
    template<typename _Pair>
      struct __1st_type<_Pair&>
      { using type = typename __1st_type<_Pair>::type&; };
 
    template<typename _Tp>
      typename __1st_type<_Tp>::type&&
      operator()(_Tp&& __x) const noexcept
      { return std::forward<_Tp>(__x).first; }
  };
 
  template<typename _ExKey, typename _Value>
    struct _ConvertToValueType;
 
  template<typename _Value>
    struct _ConvertToValueType<_Identity, _Value>
    {
      template<typename _Kt>
        constexpr _Kt&&
        operator()(_Kt&& __k) const noexcept
        { return std::forward<_Kt>(__k); }
    };
 
  template<typename _Value>
    struct _ConvertToValueType<_Select1st, _Value>
    {
      constexpr _Value&&
      operator()(_Value&& __x) const noexcept
      { return std::move(__x); }
 
      constexpr const _Value&
      operator()(const _Value& __x) const noexcept
      { return __x; }
 
      template<typename _Kt, typename _Val>
        constexpr std::pair<_Kt, _Val>&&
        operator()(std::pair<_Kt, _Val>&& __x) const noexcept
        { return std::move(__x); }
 
      template<typename _Kt, typename _Val>
        constexpr const std::pair<_Kt, _Val>&
        operator()(const std::pair<_Kt, _Val>& __x) const noexcept
        { return __x; }
    };
 
  template<typename _ExKey>
    struct _NodeBuilder;
 
  template<>
    struct _NodeBuilder<_Select1st>
    {
      template<typename _Kt, typename _Arg, typename _NodeGenerator>
        static auto
        _S_build(_Kt&& __k, _Arg&& __arg, const _NodeGenerator& __node_gen)
        -> typename _NodeGenerator::__node_type*
        {
          return __node_gen(std::forward<_Kt>(__k),
                            std::forward<_Arg>(__arg).second);
        }
    };
 
  template<>
    struct _NodeBuilder<_Identity>
    {
      template<typename _Kt, typename _Arg, typename _NodeGenerator>
        static auto
        _S_build(_Kt&& __k, _Arg&&, const _NodeGenerator& __node_gen)
        -> typename _NodeGenerator::__node_type*
        { return __node_gen(std::forward<_Kt>(__k)); }
    };
 
  template<typename _NodeAlloc>
    struct _Hashtable_alloc;
 
  // Functor recycling a pool of nodes and using allocation once the pool is
  // empty.
  template<typename _NodeAlloc>
    struct _ReuseOrAllocNode
    {
    private:
      using __node_alloc_type = _NodeAlloc;
      using __hashtable_alloc = _Hashtable_alloc<__node_alloc_type>;
      using __node_alloc_traits =
        typename __hashtable_alloc::__node_alloc_traits;
 
    public:
      using __node_type = typename __hashtable_alloc::__node_type;
 
      _ReuseOrAllocNode(__node_type* __nodes, __hashtable_alloc& __h)
      : _M_nodes(__nodes), _M_h(__h) { }
      _ReuseOrAllocNode(const _ReuseOrAllocNode&) = delete;
 
      ~_ReuseOrAllocNode()
      { _M_h._M_deallocate_nodes(_M_nodes); }
 
      template<typename... _Args>
        __node_type*
        operator()(_Args&&... __args) const
        {
          if (_M_nodes)
            {
              __node_type* __node = _M_nodes;
              _M_nodes = _M_nodes->_M_next();
              __node->_M_nxt = nullptr;
              auto& __a = _M_h._M_node_allocator();
              __node_alloc_traits::destroy(__a, __node->_M_valptr());
              __try
                {
                  __node_alloc_traits::construct(__a, __node->_M_valptr(),
                                                 std::forward<_Args>(__args)...);
                }
              __catch(...)
                {
                  _M_h._M_deallocate_node_ptr(__node);
                  __throw_exception_again;
                }
              return __node;
            }
          return _M_h._M_allocate_node(std::forward<_Args>(__args)...);
        }
 
    private:
      mutable __node_type* _M_nodes;
      __hashtable_alloc& _M_h;
    };
 
  // Functor similar to the previous one but without any pool of nodes to
  // recycle.
  template<typename _NodeAlloc>
    struct _AllocNode
    {
    private:
      using __hashtable_alloc = _Hashtable_alloc<_NodeAlloc>;
 
    public:
      using __node_type = typename __hashtable_alloc::__node_type;
 
      _AllocNode(__hashtable_alloc& __h)
      : _M_h(__h) { }
 
      template<typename... _Args>
        __node_type*
        operator()(_Args&&... __args) const
        { return _M_h._M_allocate_node(std::forward<_Args>(__args)...); }
 
    private:
      __hashtable_alloc& _M_h;
    };
 
  // Auxiliary types used for all instantiations of _Hashtable nodes
  // and iterators.
 
  /**
   *  struct _Hashtable_traits
   *
   *  Important traits for hash tables.
   *
   *  @tparam _Cache_hash_code  Boolean value. True if the value of
   *  the hash function is stored along with the value. This is a
   *  time-space tradeoff.  Storing it may improve lookup speed by
   *  reducing the number of times we need to call the _Hash or _Equal
   *  functors.
   *
   *  @tparam _Constant_iterators  Boolean value. True if iterator and
   *  const_iterator are both constant iterator types. This is true
   *  for unordered_set and unordered_multiset, false for
   *  unordered_map and unordered_multimap.
   *
   *  @tparam _Unique_keys  Boolean value. True if the return value
   *  of _Hashtable::count(k) is always at most one, false if it may
   *  be an arbitrary number. This is true for unordered_set and
   *  unordered_map, false for unordered_multiset and
   *  unordered_multimap.
   */
  template<bool _Cache_hash_code, bool _Constant_iterators, bool _Unique_keys>
    struct _Hashtable_traits
    {
      using __hash_cached = __bool_constant<_Cache_hash_code>;
      using __constant_iterators = __bool_constant<_Constant_iterators>;
      using __unique_keys = __bool_constant<_Unique_keys>;
    };
 
  /**
   *  struct _Hashtable_hash_traits
   *
   *  Important traits for hash tables depending on associated hasher.
   *
   */
  template<typename _Hash>
    struct _Hashtable_hash_traits
    {
      static constexpr std::size_t
      __small_size_threshold() noexcept
      { return std::__is_fast_hash<_Hash>::value ? 0 : 20; }
    };
 
  /**
   *  struct _Hash_node_base
   *
   *  Nodes, used to wrap elements stored in the hash table.  A policy
   *  template parameter of class template _Hashtable controls whether
   *  nodes also store a hash code. In some cases (e.g. strings) this
   *  may be a performance win.
   */
  struct _Hash_node_base
  {
    _Hash_node_base* _M_nxt;
 
    _Hash_node_base() noexcept : _M_nxt() { }
 
    _Hash_node_base(_Hash_node_base* __next) noexcept : _M_nxt(__next) { }
  };
 
  /**
   *  struct _Hash_node_value_base
   *
   *  Node type with the value to store.
   */
  template<typename _Value>
    struct _Hash_node_value_base
    {
      typedef _Value value_type;
 
      __gnu_cxx::__aligned_buffer<_Value> _M_storage;
 
      [[__gnu__::__always_inline__]]
      _Value*
      _M_valptr() noexcept
      { return _M_storage._M_ptr(); }
 
      [[__gnu__::__always_inline__]]
      const _Value*
      _M_valptr() const noexcept
      { return _M_storage._M_ptr(); }
 
      [[__gnu__::__always_inline__]]
      _Value&
      _M_v() noexcept
      { return *_M_valptr(); }
 
      [[__gnu__::__always_inline__]]
      const _Value&
      _M_v() const noexcept
      { return *_M_valptr(); }
    };
 
  /**
   *  Primary template struct _Hash_node_code_cache.
   */
  template<bool _Cache_hash_code>
    struct _Hash_node_code_cache
    { };
 
  /**
   *  Specialization for node with cache, struct _Hash_node_code_cache.
   */
  template<>
    struct _Hash_node_code_cache<true>
    { std::size_t  _M_hash_code; };
 
  template<typename _Value, bool _Cache_hash_code>
    struct _Hash_node_value
    : _Hash_node_value_base<_Value>
    , _Hash_node_code_cache<_Cache_hash_code>
    { };
 
  /**
   *  Primary template struct _Hash_node.
   */
  template<typename _Value, bool _Cache_hash_code>
    struct _Hash_node
    : _Hash_node_base
    , _Hash_node_value<_Value, _Cache_hash_code>
    {
      _Hash_node*
      _M_next() const noexcept
      { return static_cast<_Hash_node*>(this->_M_nxt); }
    };
 
  /// Base class for node iterators.
  template<typename _Value, bool _Cache_hash_code>
    struct _Node_iterator_base
    {
      using __node_type = _Hash_node<_Value, _Cache_hash_code>;
 
      __node_type* _M_cur;
 
      _Node_iterator_base() : _M_cur(nullptr) { }
      _Node_iterator_base(__node_type* __p) noexcept
      : _M_cur(__p) { }
 
      void
      _M_incr() noexcept
      { _M_cur = _M_cur->_M_next(); }
 
      friend bool
      operator==(const _Node_iterator_base& __x, const _Node_iterator_base& __y)
      noexcept
      { return __x._M_cur == __y._M_cur; }
 
#if __cpp_impl_three_way_comparison < 201907L
      friend bool
      operator!=(const _Node_iterator_base& __x, const _Node_iterator_base& __y)
      noexcept
      { return __x._M_cur != __y._M_cur; }
#endif
    };
 
  /// Node iterators, used to iterate through all the hashtable.
  template<typename _Value, bool __constant_iterators, bool __cache>
    struct _Node_iterator
    : public _Node_iterator_base<_Value, __cache>
    {
    private:
      using __base_type = _Node_iterator_base<_Value, __cache>;
      using __node_type = typename __base_type::__node_type;
 
    public:
      using value_type = _Value;
      using difference_type = std::ptrdiff_t;
      using iterator_category = std::forward_iterator_tag;
 
      using pointer = __conditional_t<__constant_iterators,
                                      const value_type*, value_type*>;
 
      using reference = __conditional_t<__constant_iterators,
                                        const value_type&, value_type&>;
 
      _Node_iterator() = default;
 
      explicit
      _Node_iterator(__node_type* __p) noexcept
      : __base_type(__p) { }
 
      reference
      operator*() const noexcept
      { return this->_M_cur->_M_v(); }
 
      pointer
      operator->() const noexcept
      { return this->_M_cur->_M_valptr(); }
 
      _Node_iterator&
      operator++() noexcept
      {
        this->_M_incr();
        return *this;
      }
 
      _Node_iterator
      operator++(int) noexcept
      {
        _Node_iterator __tmp(*this);
        this->_M_incr();
        return __tmp;
      }
    };
 
  /// Node const_iterators, used to iterate through all the hashtable.
  template<typename _Value, bool __constant_iterators, bool __cache>
    struct _Node_const_iterator
    : public _Node_iterator_base<_Value, __cache>
    {
    private:
      using __base_type = _Node_iterator_base<_Value, __cache>;
      using __node_type = typename __base_type::__node_type;
 
    public:
      typedef _Value                                    value_type;
      typedef std::ptrdiff_t                            difference_type;
      typedef std::forward_iterator_tag                 iterator_category;
 
      typedef const value_type*                         pointer;
      typedef const value_type&                         reference;
 
      _Node_const_iterator() = default;
 
      explicit
      _Node_const_iterator(__node_type* __p) noexcept
      : __base_type(__p) { }
 
      _Node_const_iterator(const _Node_iterator<_Value, __constant_iterators,
                           __cache>& __x) noexcept
      : __base_type(__x._M_cur) { }
 
      reference
      operator*() const noexcept
      { return this->_M_cur->_M_v(); }
 
      pointer
      operator->() const noexcept
      { return this->_M_cur->_M_valptr(); }
 
      _Node_const_iterator&
      operator++() noexcept
      {
        this->_M_incr();
        return *this;
      }
 
      _Node_const_iterator
      operator++(int) noexcept
      {
        _Node_const_iterator __tmp(*this);
        this->_M_incr();
        return __tmp;
      }
    };
 
  // Many of class template _Hashtable's template parameters are policy
  // classes.  These are defaults for the policies.
 
  /// Default range hashing function: use division to fold a large number
  /// into the range [0, N).
  struct _Mod_range_hashing
  {
    typedef std::size_t first_argument_type;
    typedef std::size_t second_argument_type;
    typedef std::size_t result_type;
 
    result_type
    operator()(first_argument_type __num,
               second_argument_type __den) const noexcept
    { return __num % __den; }
  };
 
  /// Default ranged hash function H.  In principle it should be a
  /// function object composed from objects of type H1 and H2 such that
  /// h(k, N) = h2(h1(k), N), but that would mean making extra copies of
  /// h1 and h2.  So instead we'll just use a tag to tell class template
  /// hashtable to do that composition.
  struct _Default_ranged_hash { };
 
  /// Default value for rehash policy.  Bucket size is (usually) the
  /// smallest prime that keeps the load factor small enough.
  struct _Prime_rehash_policy
  {
    using __has_load_factor = true_type;
 
    _Prime_rehash_policy(float __z = 1.0) noexcept
    : _M_max_load_factor(__z), _M_next_resize(0) { }
 
    float
    max_load_factor() const noexcept
    { return _M_max_load_factor; }
 
    // Return a bucket size no smaller than n.
    std::size_t
    _M_next_bkt(std::size_t __n) const;
 
    // Return a bucket count appropriate for n elements
    std::size_t
    _M_bkt_for_elements(std::size_t __n) const
    { return __builtin_ceil(__n / (double)_M_max_load_factor); }
 
    // __n_bkt is current bucket count, __n_elt is current element count,
    // and __n_ins is number of elements to be inserted.  Do we need to
    // increase bucket count?  If so, return make_pair(true, n), where n
    // is the new bucket count.  If not, return make_pair(false, 0).
    std::pair<bool, std::size_t>
    _M_need_rehash(std::size_t __n_bkt, std::size_t __n_elt,
                   std::size_t __n_ins) const;
 
    typedef std::size_t _State;
 
    _State
    _M_state() const
    { return _M_next_resize; }
 
    void
    _M_reset() noexcept
    { _M_next_resize = 0; }
 
    void
    _M_reset(_State __state)
    { _M_next_resize = __state; }
 
    static const std::size_t _S_growth_factor = 2;
 
    float               _M_max_load_factor;
    mutable std::size_t _M_next_resize;
  };
 
  /// Range hashing function assuming that second arg is a power of 2.
  struct _Mask_range_hashing
  {
    typedef std::size_t first_argument_type;
    typedef std::size_t second_argument_type;
    typedef std::size_t result_type;
 
    result_type
    operator()(first_argument_type __num,
               second_argument_type __den) const noexcept
    { return __num & (__den - 1); }
  };
 
  /// Compute closest power of 2 not less than __n
  inline std::size_t
  __clp2(std::size_t __n) noexcept
  {
    using __gnu_cxx::__int_traits;
    // Equivalent to return __n ? std::bit_ceil(__n) : 0;
    if (__n < 2)
      return __n;
    const unsigned __lz = sizeof(size_t) > sizeof(long)
      ? __builtin_clzll(__n - 1ull)
      : __builtin_clzl(__n - 1ul);
    // Doing two shifts avoids undefined behaviour when __lz == 0.
    return (size_t(1) << (__int_traits<size_t>::__digits - __lz - 1)) << 1;
  }
 
  /// Rehash policy providing power of 2 bucket numbers. Avoids modulo
  /// operations.
  struct _Power2_rehash_policy
  {
    using __has_load_factor = true_type;
 
    _Power2_rehash_policy(float __z = 1.0) noexcept
    : _M_max_load_factor(__z), _M_next_resize(0) { }
 
    float
    max_load_factor() const noexcept
    { return _M_max_load_factor; }
 
    // Return a bucket size no smaller than n (as long as n is not above the
    // highest power of 2).
    std::size_t
    _M_next_bkt(std::size_t __n) noexcept
    {
      if (__n == 0)
        // Special case on container 1st initialization with 0 bucket count
        // hint. We keep _M_next_resize to 0 to make sure that next time we
        // want to add an element allocation will take place.
        return 1;
 
      const auto __max_width = std::min<size_t>(sizeof(size_t), 8);
      const auto __max_bkt = size_t(1) << (__max_width * __CHAR_BIT__ - 1);
      std::size_t __res = __clp2(__n);
 
      if (__res == 0)
        __res = __max_bkt;
      else if (__res == 1)
        // If __res is 1 we force it to 2 to make sure there will be an
        // allocation so that nothing need to be stored in the initial
        // single bucket
        __res = 2;
 
      if (__res == __max_bkt)
        // Set next resize to the max value so that we never try to rehash again
        // as we already reach the biggest possible bucket number.
        // Note that it might result in max_load_factor not being respected.
        _M_next_resize = size_t(-1);
      else
        _M_next_resize
          = __builtin_floor(__res * (double)_M_max_load_factor);
 
      return __res;
    }
 
    // Return a bucket count appropriate for n elements
    std::size_t
    _M_bkt_for_elements(std::size_t __n) const noexcept
    { return __builtin_ceil(__n / (double)_M_max_load_factor); }
 
    // __n_bkt is current bucket count, __n_elt is current element count,
    // and __n_ins is number of elements to be inserted.  Do we need to
    // increase bucket count?  If so, return make_pair(true, n), where n
    // is the new bucket count.  If not, return make_pair(false, 0).
    std::pair<bool, std::size_t>
    _M_need_rehash(std::size_t __n_bkt, std::size_t __n_elt,
                   std::size_t __n_ins) noexcept
    {
      if (__n_elt + __n_ins > _M_next_resize)
        {
          // If _M_next_resize is 0 it means that we have nothing allocated so
          // far and that we start inserting elements. In this case we start
          // with an initial bucket size of 11.
          double __min_bkts
            = std::max<std::size_t>(__n_elt + __n_ins, _M_next_resize ? 0 : 11)
              / (double)_M_max_load_factor;
          if (__min_bkts >= __n_bkt)
            return { true,
              _M_next_bkt(std::max<std::size_t>(__builtin_floor(__min_bkts) + 1,
                                                __n_bkt * _S_growth_factor)) };
 
          _M_next_resize
            = __builtin_floor(__n_bkt * (double)_M_max_load_factor);
          return { false, 0 };
        }
      else
        return { false, 0 };
    }
 
    typedef std::size_t _State;
 
    _State
    _M_state() const noexcept
    { return _M_next_resize; }
 
    void
    _M_reset() noexcept
    { _M_next_resize = 0; }
 
    void
    _M_reset(_State __state) noexcept
    { _M_next_resize = __state; }
 
    static const std::size_t _S_growth_factor = 2;
 
    float       _M_max_load_factor;
    std::size_t _M_next_resize;
  };
 
  // Base classes for std::_Hashtable.  We define these base classes
  // because in some cases we want to do different things depending on
  // the value of a policy class.  In some cases the policy class
  // affects which member functions and nested typedefs are defined;
  // we handle that by specializing base class templates.  Several of
  // the base class templates need to access other members of class
  // template _Hashtable, so we use a variant of the "Curiously
  // Recurring Template Pattern" (CRTP) technique.
 
  /**
   *  Primary class template _Map_base.
   *
   *  If the hashtable has a value type of the form pair<const T1, T2> and
   *  a key extraction policy (_ExtractKey) that returns the first part
   *  of the pair, the hashtable gets a mapped_type typedef.  If it
   *  satisfies those criteria and also has unique keys, then it also
   *  gets an operator[].
   */
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits,
           bool _Unique_keys = _Traits::__unique_keys::value>
    struct _Map_base { };
 
  /// Partial specialization, __unique_keys set to false, std::pair value type.
  template<typename _Key, typename _Val, typename _Alloc, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Map_base<_Key, pair<const _Key, _Val>, _Alloc, _Select1st, _Equal,
                     _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, false>
    {
      using mapped_type = _Val;
    };
 
  /// Partial specialization, __unique_keys set to true.
  template<typename _Key, typename _Val, typename _Alloc, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Map_base<_Key, pair<const _Key, _Val>, _Alloc, _Select1st, _Equal,
                     _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, true>
    {
    private:
      using __hashtable_base = _Hashtable_base<_Key, pair<const _Key, _Val>,
                                               _Select1st, _Equal, _Hash,
                                               _RangeHash, _Unused,
                                               _Traits>;
 
      using __hashtable = _Hashtable<_Key, pair<const _Key, _Val>, _Alloc,
                                     _Select1st, _Equal, _Hash, _RangeHash,
                                     _Unused, _RehashPolicy, _Traits>;
 
      using __hash_code = typename __hashtable_base::__hash_code;
 
    public:
      using key_type = typename __hashtable_base::key_type;
      using mapped_type = _Val;
 
      mapped_type&
      operator[](const key_type& __k);
 
      mapped_type&
      operator[](key_type&& __k);
 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // DR 761. unordered_map needs an at() member function.
      mapped_type&
      at(const key_type& __k)
      {
        auto __ite = static_cast<__hashtable*>(this)->find(__k);
        if (!__ite._M_cur)
          __throw_out_of_range(__N("unordered_map::at"));
        return __ite->second;
      }
 
      const mapped_type&
      at(const key_type& __k) const
      {
        auto __ite = static_cast<const __hashtable*>(this)->find(__k);
        if (!__ite._M_cur)
          __throw_out_of_range(__N("unordered_map::at"));
        return __ite->second;
      }
    };
 
  template<typename _Key, typename _Val, typename _Alloc, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    auto
    _Map_base<_Key, pair<const _Key, _Val>, _Alloc, _Select1st, _Equal,
              _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, true>::
    operator[](const key_type& __k)
    -> mapped_type&
    {
      __hashtable* __h = static_cast<__hashtable*>(this);
      __hash_code __code = __h->_M_hash_code(__k);
      std::size_t __bkt = __h->_M_bucket_index(__code);
      if (auto __node = __h->_M_find_node(__bkt, __k, __code))
        return __node->_M_v().second;
 
      typename __hashtable::_Scoped_node __node {
        __h,
        std::piecewise_construct,
        std::tuple<const key_type&>(__k),
        std::tuple<>()
      };
      auto __pos
        = __h->_M_insert_unique_node(__bkt, __code, __node._M_node);
      __node._M_node = nullptr;
      return __pos->second;
    }
 
  template<typename _Key, typename _Val, typename _Alloc, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    auto
    _Map_base<_Key, pair<const _Key, _Val>, _Alloc, _Select1st, _Equal,
              _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, true>::
    operator[](key_type&& __k)
    -> mapped_type&
    {
      __hashtable* __h = static_cast<__hashtable*>(this);
      __hash_code __code = __h->_M_hash_code(__k);
      std::size_t __bkt = __h->_M_bucket_index(__code);
      if (auto __node = __h->_M_find_node(__bkt, __k, __code))
        return __node->_M_v().second;
 
      typename __hashtable::_Scoped_node __node {
        __h,
        std::piecewise_construct,
        std::forward_as_tuple(std::move(__k)),
        std::tuple<>()
      };
      auto __pos
        = __h->_M_insert_unique_node(__bkt, __code, __node._M_node);
      __node._M_node = nullptr;
      return __pos->second;
    }
 
  // Partial specialization for unordered_map<const T, U>, see PR 104174.
  template<typename _Key, typename _Val, typename _Alloc, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits, bool __uniq>
    struct _Map_base<const _Key, pair<const _Key, _Val>,
                     _Alloc, _Select1st, _Equal, _Hash,
                     _RangeHash, _Unused, _RehashPolicy, _Traits, __uniq>
    : _Map_base<_Key, pair<const _Key, _Val>, _Alloc, _Select1st, _Equal, _Hash,
                _RangeHash, _Unused, _RehashPolicy, _Traits, __uniq>
    { };
 
  /**
   *  Primary class template _Insert_base.
   *
   *  Defines @c insert member functions appropriate to all _Hashtables.
   */
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Insert_base
    {
    protected:
      using __hashtable_base = _Hashtable_base<_Key, _Value, _ExtractKey,
                                               _Equal, _Hash, _RangeHash,
                                               _Unused, _Traits>;
 
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                                     _Hash, _RangeHash,
                                     _Unused, _RehashPolicy, _Traits>;
 
      using __hash_cached = typename _Traits::__hash_cached;
      using __constant_iterators = typename _Traits::__constant_iterators;
 
      using __hashtable_alloc = _Hashtable_alloc<
        __alloc_rebind<_Alloc, _Hash_node<_Value,
                                          __hash_cached::value>>>;
 
      using value_type = typename __hashtable_base::value_type;
      using size_type = typename __hashtable_base::size_type;
 
      using __unique_keys = typename _Traits::__unique_keys;
      using __node_alloc_type = typename __hashtable_alloc::__node_alloc_type;
      using __node_gen_type = _AllocNode<__node_alloc_type>;
 
      __hashtable&
      _M_conjure_hashtable()
      { return *(static_cast<__hashtable*>(this)); }
 
      template<typename _InputIterator, typename _NodeGetter>
        void
        _M_insert_range(_InputIterator __first, _InputIterator __last,
                        const _NodeGetter&, true_type __uks);
 
      template<typename _InputIterator, typename _NodeGetter>
        void
        _M_insert_range(_InputIterator __first, _InputIterator __last,
                        const _NodeGetter&, false_type __uks);
 
    public:
      using iterator = _Node_iterator<_Value, __constant_iterators::value,
                                      __hash_cached::value>;
 
      using const_iterator = _Node_const_iterator<_Value,
                                                  __constant_iterators::value,
                                                  __hash_cached::value>;
 
      using __ireturn_type = __conditional_t<__unique_keys::value,
                                             std::pair<iterator, bool>,
                                             iterator>;
 
      __ireturn_type
      insert(const value_type& __v)
      {
        __hashtable& __h = _M_conjure_hashtable();
        __node_gen_type __node_gen(__h);
        return __h._M_insert(__v, __node_gen, __unique_keys{});
      }
 
      iterator
      insert(const_iterator __hint, const value_type& __v)
      {
        __hashtable& __h = _M_conjure_hashtable();
        __node_gen_type __node_gen(__h);        
        return __h._M_insert(__hint, __v, __node_gen, __unique_keys{});
      }
 
#if __cplusplus >= 201703L && _GLIBCXX_HOSTED
      template<typename _KType, typename... _Args>
        std::pair<iterator, bool>
        try_emplace(const_iterator, _KType&& __k, _Args&&... __args)
        {
          __hashtable& __h = _M_conjure_hashtable();
          auto __code = __h._M_hash_code(__k);
          std::size_t __bkt = __h._M_bucket_index(__code);
          if (auto __node = __h._M_find_node(__bkt, __k, __code))
            return { iterator(__node), false };
 
          typename __hashtable::_Scoped_node __node {
            &__h,
            std::piecewise_construct,
            std::forward_as_tuple(std::forward<_KType>(__k)),
            std::forward_as_tuple(std::forward<_Args>(__args)...)
            };
          auto __it
            = __h._M_insert_unique_node(__bkt, __code, __node._M_node);
          __node._M_node = nullptr;
          return { __it, true };
        }
#endif
 
      void
      insert(initializer_list<value_type> __l)
      { this->insert(__l.begin(), __l.end()); }
 
      template<typename _InputIterator>
        void
        insert(_InputIterator __first, _InputIterator __last)
        {
          __hashtable& __h = _M_conjure_hashtable();
          __node_gen_type __node_gen(__h);
          return _M_insert_range(__first, __last, __node_gen, __unique_keys{});
        }
    };
 
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    template<typename _InputIterator, typename _NodeGetter>
      void
      _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                   _Hash, _RangeHash, _Unused,
                   _RehashPolicy, _Traits>::
      _M_insert_range(_InputIterator __first, _InputIterator __last,
                      const _NodeGetter& __node_gen, true_type __uks)
      {
        __hashtable& __h = _M_conjure_hashtable();
        for (; __first != __last; ++__first)
          __h._M_insert(*__first, __node_gen, __uks);
      }
 
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    template<typename _InputIterator, typename _NodeGetter>
      void
      _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                   _Hash, _RangeHash, _Unused,
                   _RehashPolicy, _Traits>::
      _M_insert_range(_InputIterator __first, _InputIterator __last,
                      const _NodeGetter& __node_gen, false_type __uks)
      {
        using __rehash_type = typename __hashtable::__rehash_type;
        using __rehash_state = typename __hashtable::__rehash_state;
        using pair_type = std::pair<bool, std::size_t>;
 
        size_type __n_elt = __detail::__distance_fw(__first, __last);
        if (__n_elt == 0)
          return;
 
        __hashtable& __h = _M_conjure_hashtable();
        __rehash_type& __rehash = __h._M_rehash_policy;
        const __rehash_state& __saved_state = __rehash._M_state();
        pair_type __do_rehash = __rehash._M_need_rehash(__h._M_bucket_count,
                                                        __h._M_element_count,
                                                        __n_elt);
 
        if (__do_rehash.first)
          __h._M_rehash(__do_rehash.second, __saved_state);
 
        for (; __first != __last; ++__first)
          __h._M_insert(*__first, __node_gen, __uks);
      }
 
  /**
   *  Primary class template _Insert.
   *
   *  Defines @c insert member functions that depend on _Hashtable policies,
   *  via partial specializations.
   */
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits,
           bool _Constant_iterators = _Traits::__constant_iterators::value>
    struct _Insert;
 
  /// Specialization.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Insert<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                   _Hash, _RangeHash, _Unused,
                   _RehashPolicy, _Traits, true>
    : public _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                          _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits>
    {
      using __base_type = _Insert_base<_Key, _Value, _Alloc, _ExtractKey,
                                       _Equal, _Hash, _RangeHash, _Unused,
                                       _RehashPolicy, _Traits>;
 
      using value_type = typename __base_type::value_type;
      using iterator = typename __base_type::iterator;
      using const_iterator =  typename __base_type::const_iterator;
      using __ireturn_type = typename __base_type::__ireturn_type;
 
      using __unique_keys = typename __base_type::__unique_keys;
      using __hashtable = typename __base_type::__hashtable;
      using __node_gen_type = typename __base_type::__node_gen_type;
 
      using __base_type::insert;
 
      __ireturn_type
      insert(value_type&& __v)
      {
        __hashtable& __h = this->_M_conjure_hashtable();
        __node_gen_type __node_gen(__h);
        return __h._M_insert(std::move(__v), __node_gen, __unique_keys{});
      }
 
      iterator
      insert(const_iterator __hint, value_type&& __v)
      {
        __hashtable& __h = this->_M_conjure_hashtable();
        __node_gen_type __node_gen(__h);
        return __h._M_insert(__hint, std::move(__v), __node_gen,
                             __unique_keys{});
      }
    };
 
  /// Specialization.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Insert<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                   _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, false>
    : public _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                          _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits>
    {
      using __base_type = _Insert_base<_Key, _Value, _Alloc, _ExtractKey,
                                       _Equal, _Hash, _RangeHash, _Unused,
                                       _RehashPolicy, _Traits>;
      using value_type = typename __base_type::value_type;
      using iterator = typename __base_type::iterator;
      using const_iterator =  typename __base_type::const_iterator;
 
      using __unique_keys = typename __base_type::__unique_keys;
      using __hashtable = typename __base_type::__hashtable;
      using __ireturn_type = typename __base_type::__ireturn_type;
 
      using __base_type::insert;
 
      template<typename _Pair>
        using __is_cons = std::is_constructible<value_type, _Pair&&>;
 
      template<typename _Pair>
        using _IFcons = std::enable_if<__is_cons<_Pair>::value>;
 
      template<typename _Pair>
        using _IFconsp = typename _IFcons<_Pair>::type;
 
      template<typename _Pair, typename = _IFconsp<_Pair>>
        __ireturn_type
        insert(_Pair&& __v)
        {
          __hashtable& __h = this->_M_conjure_hashtable();
          return __h._M_emplace(__unique_keys{}, std::forward<_Pair>(__v));
        }
 
      template<typename _Pair, typename = _IFconsp<_Pair>>
        iterator
        insert(const_iterator __hint, _Pair&& __v)
        {
          __hashtable& __h = this->_M_conjure_hashtable();
          return __h._M_emplace(__hint, __unique_keys{},
                                std::forward<_Pair>(__v));
        }
   };
 
  template<typename _Policy>
    using __has_load_factor = typename _Policy::__has_load_factor;
 
  /**
   *  Primary class template  _Rehash_base.
   *
   *  Give hashtable the max_load_factor functions and reserve iff the
   *  rehash policy supports it.
  */
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits,
           typename =
             __detected_or_t<false_type, __has_load_factor, _RehashPolicy>>
    struct _Rehash_base;
 
  /// Specialization when rehash policy doesn't provide load factor management.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Rehash_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                        _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits,
                        false_type /* Has load factor */>
    {
    };
 
  /// Specialization when rehash policy provide load factor management.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Rehash_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                        _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits,
                        true_type /* Has load factor */>
    {
    private:
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey,
                                     _Equal, _Hash, _RangeHash, _Unused,
                                     _RehashPolicy, _Traits>;
 
    public:
      float
      max_load_factor() const noexcept
      {
        const __hashtable* __this = static_cast<const __hashtable*>(this);
        return __this->__rehash_policy().max_load_factor();
      }
 
      void
      max_load_factor(float __z)
      {
        __hashtable* __this = static_cast<__hashtable*>(this);
        __this->__rehash_policy(_RehashPolicy(__z));
      }
 
      void
      reserve(std::size_t __n)
      {
        __hashtable* __this = static_cast<__hashtable*>(this);
        __this->rehash(__this->__rehash_policy()._M_bkt_for_elements(__n));
      }
    };
 
  /**
   *  Primary class template _Hashtable_ebo_helper.
   *
   *  Helper class using EBO when it is not forbidden (the type is not
   *  final) and when it is worth it (the type is empty.)
   */
  template<int _Nm, typename _Tp,
           bool __use_ebo = !__is_final(_Tp) && __is_empty(_Tp)>
    struct _Hashtable_ebo_helper;
 
  /// Specialization using EBO.
  template<int _Nm, typename _Tp>
    struct _Hashtable_ebo_helper<_Nm, _Tp, true>
    : private _Tp
    {
      _Hashtable_ebo_helper() noexcept(noexcept(_Tp())) : _Tp() { }
 
      template<typename _OtherTp>
        _Hashtable_ebo_helper(_OtherTp&& __tp)
        : _Tp(std::forward<_OtherTp>(__tp))
        { }
 
      const _Tp& _M_cget() const { return static_cast<const _Tp&>(*this); }
      _Tp& _M_get() { return static_cast<_Tp&>(*this); }
    };
 
  /// Specialization not using EBO.
  template<int _Nm, typename _Tp>
    struct _Hashtable_ebo_helper<_Nm, _Tp, false>
    {
      _Hashtable_ebo_helper() = default;
 
      template<typename _OtherTp>
        _Hashtable_ebo_helper(_OtherTp&& __tp)
        : _M_tp(std::forward<_OtherTp>(__tp))
        { }
 
      const _Tp& _M_cget() const { return _M_tp; }
      _Tp& _M_get() { return _M_tp; }
 
    private:
      _Tp _M_tp{};
    };
 
  /**
   *  Primary class template _Local_iterator_base.
   *
   *  Base class for local iterators, used to iterate within a bucket
   *  but not between buckets.
   */
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused,
           bool __cache_hash_code>
    struct _Local_iterator_base;
 
  /**
   *  Primary class template _Hash_code_base.
   *
   *  Encapsulates two policy issues that aren't quite orthogonal.
   *   (1) the difference between using a ranged hash function and using
   *       the combination of a hash function and a range-hashing function.
   *       In the former case we don't have such things as hash codes, so
   *       we have a dummy type as placeholder.
   *   (2) Whether or not we cache hash codes.  Caching hash codes is
   *       meaningless if we have a ranged hash function.
   *
   *  We also put the key extraction objects here, for convenience.
   *  Each specialization derives from one or more of the template
   *  parameters to benefit from Ebo. This is important as this type
   *  is inherited in some cases by the _Local_iterator_base type used
   *  to implement local_iterator and const_local_iterator. As with
   *  any iterator type we prefer to make it as small as possible.
   */
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused,
           bool __cache_hash_code>
    struct _Hash_code_base
    : private _Hashtable_ebo_helper<1, _Hash>
    {
    private:
      using __ebo_hash = _Hashtable_ebo_helper<1, _Hash>;
 
      // Gives the local iterator implementation access to _M_bucket_index().
      friend struct _Local_iterator_base<_Key, _Value, _ExtractKey,
                                         _Hash, _RangeHash, _Unused, false>;
 
    public:
      typedef _Hash                                     hasher;
 
      hasher
      hash_function() const
      { return _M_hash(); }
 
    protected:
      typedef std::size_t                               __hash_code;
 
      // We need the default constructor for the local iterators and _Hashtable
      // default constructor.
      _Hash_code_base() = default;
 
      _Hash_code_base(const _Hash& __hash) : __ebo_hash(__hash) { }
 
      __hash_code
      _M_hash_code(const _Key& __k) const
      {
        static_assert(__is_invocable<const _Hash&, const _Key&>{},
            "hash function must be invocable with an argument of key type");
        return _M_hash()(__k);
      }
 
      template<typename _Kt>
        __hash_code
        _M_hash_code_tr(const _Kt& __k) const
        {
          static_assert(__is_invocable<const _Hash&, const _Kt&>{},
            "hash function must be invocable with an argument of key type");
          return _M_hash()(__k);
        }
 
      __hash_code
      _M_hash_code(const _Hash_node_value<_Value, false>& __n) const
      { return _M_hash_code(_ExtractKey{}(__n._M_v())); }
 
      __hash_code
      _M_hash_code(const _Hash_node_value<_Value, true>& __n) const
      { return __n._M_hash_code; }
 
      std::size_t
      _M_bucket_index(__hash_code __c, std::size_t __bkt_count) const
      { return _RangeHash{}(__c, __bkt_count); }
 
      std::size_t
      _M_bucket_index(const _Hash_node_value<_Value, false>& __n,
                      std::size_t __bkt_count) const
        noexcept( noexcept(declval<const _Hash&>()(declval<const _Key&>()))
                  && noexcept(declval<const _RangeHash&>()((__hash_code)0,
                                                           (std::size_t)0)) )
      {
        return _RangeHash{}(_M_hash_code(_ExtractKey{}(__n._M_v())),
                            __bkt_count);
      }
 
      std::size_t
      _M_bucket_index(const _Hash_node_value<_Value, true>& __n,
                      std::size_t __bkt_count) const
        noexcept( noexcept(declval<const _RangeHash&>()((__hash_code)0,
                                                        (std::size_t)0)) )
      { return _RangeHash{}(__n._M_hash_code, __bkt_count); }
 
      void
      _M_store_code(_Hash_node_code_cache<false>&, __hash_code) const
      { }
 
      void
      _M_copy_code(_Hash_node_code_cache<false>&,
                   const _Hash_node_code_cache<false>&) const
      { }
 
      void
      _M_store_code(_Hash_node_code_cache<true>& __n, __hash_code __c) const
      { __n._M_hash_code = __c; }
 
      void
      _M_copy_code(_Hash_node_code_cache<true>& __to,
                   const _Hash_node_code_cache<true>& __from) const
      { __to._M_hash_code = __from._M_hash_code; }
 
      void
      _M_swap(_Hash_code_base& __x)
      { std::swap(__ebo_hash::_M_get(), __x.__ebo_hash::_M_get()); }
 
      const _Hash&
      _M_hash() const { return __ebo_hash::_M_cget(); }
    };
 
  /// Partial specialization used when nodes contain a cached hash code.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused>
    struct _Local_iterator_base<_Key, _Value, _ExtractKey,
                                _Hash, _RangeHash, _Unused, true>
    : public _Node_iterator_base<_Value, true>
    {
    protected:
      using __base_node_iter = _Node_iterator_base<_Value, true>;
      using __hash_code_base = _Hash_code_base<_Key, _Value, _ExtractKey,
                                              _Hash, _RangeHash, _Unused, true>;
 
      _Local_iterator_base() = default;
      _Local_iterator_base(const __hash_code_base&,
                           _Hash_node<_Value, true>* __p,
                           std::size_t __bkt, std::size_t __bkt_count)
      : __base_node_iter(__p), _M_bucket(__bkt), _M_bucket_count(__bkt_count)
      { }
 
      void
      _M_incr()
      {
        __base_node_iter::_M_incr();
        if (this->_M_cur)
          {
            std::size_t __bkt
              = _RangeHash{}(this->_M_cur->_M_hash_code, _M_bucket_count);
            if (__bkt != _M_bucket)
              this->_M_cur = nullptr;
          }
      }
 
      std::size_t _M_bucket;
      std::size_t _M_bucket_count;
 
    public:
      std::size_t
      _M_get_bucket() const { return _M_bucket; }  // for debug mode
    };
 
  // Uninitialized storage for a _Hash_code_base.
  // This type is DefaultConstructible and Assignable even if the
  // _Hash_code_base type isn't, so that _Local_iterator_base<..., false>
  // can be DefaultConstructible and Assignable.
  template<typename _Tp, bool _IsEmpty = std::is_empty<_Tp>::value>
    struct _Hash_code_storage
    {
      __gnu_cxx::__aligned_buffer<_Tp> _M_storage;
 
      _Tp*
      _M_h() { return _M_storage._M_ptr(); }
 
      const _Tp*
      _M_h() const { return _M_storage._M_ptr(); }
    };
 
  // Empty partial specialization for empty _Hash_code_base types.
  template<typename _Tp>
    struct _Hash_code_storage<_Tp, true>
    {
      static_assert( std::is_empty<_Tp>::value, "Type must be empty" );
 
      // As _Tp is an empty type there will be no bytes written/read through
      // the cast pointer, so no strict-aliasing violation.
      _Tp*
      _M_h() { return reinterpret_cast<_Tp*>(this); }
 
      const _Tp*
      _M_h() const { return reinterpret_cast<const _Tp*>(this); }
    };
 
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused>
    using __hash_code_for_local_iter
      = _Hash_code_storage<_Hash_code_base<_Key, _Value, _ExtractKey,
                                           _Hash, _RangeHash, _Unused, false>>;
 
  // Partial specialization used when hash codes are not cached
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused>
    struct _Local_iterator_base<_Key, _Value, _ExtractKey,
                                _Hash, _RangeHash, _Unused, false>
    : __hash_code_for_local_iter<_Key, _Value, _ExtractKey, _Hash, _RangeHash,
                                 _Unused>
    , _Node_iterator_base<_Value, false>
    {
    protected:
      using __hash_code_base = _Hash_code_base<_Key, _Value, _ExtractKey,
                                             _Hash, _RangeHash, _Unused, false>;
      using __node_iter_base = _Node_iterator_base<_Value, false>;
 
      _Local_iterator_base() : _M_bucket_count(-1) { }
 
      _Local_iterator_base(const __hash_code_base& __base,
                           _Hash_node<_Value, false>* __p,
                           std::size_t __bkt, std::size_t __bkt_count)
      : __node_iter_base(__p), _M_bucket(__bkt), _M_bucket_count(__bkt_count)
      { _M_init(__base); }
 
      ~_Local_iterator_base()
      {
        if (_M_bucket_count != size_t(-1))
          _M_destroy();
      }
 
      _Local_iterator_base(const _Local_iterator_base& __iter)
      : __node_iter_base(__iter._M_cur), _M_bucket(__iter._M_bucket)
      , _M_bucket_count(__iter._M_bucket_count)
      {
        if (_M_bucket_count != size_t(-1))
          _M_init(*__iter._M_h());
      }
 
      _Local_iterator_base&
      operator=(const _Local_iterator_base& __iter)
      {
        if (_M_bucket_count != -1)
          _M_destroy();
        this->_M_cur = __iter._M_cur;
        _M_bucket = __iter._M_bucket;
        _M_bucket_count = __iter._M_bucket_count;
        if (_M_bucket_count != -1)
          _M_init(*__iter._M_h());
        return *this;
      }
 
      void
      _M_incr()
      {
        __node_iter_base::_M_incr();
        if (this->_M_cur)
          {
            std::size_t __bkt = this->_M_h()->_M_bucket_index(*this->_M_cur,
                                                              _M_bucket_count);
            if (__bkt != _M_bucket)
              this->_M_cur = nullptr;
          }
      }
 
      std::size_t _M_bucket;
      std::size_t _M_bucket_count;
 
      void
      _M_init(const __hash_code_base& __base)
      { ::new(this->_M_h()) __hash_code_base(__base); }
 
      void
      _M_destroy() { this->_M_h()->~__hash_code_base(); }
 
    public:
      std::size_t
      _M_get_bucket() const { return _M_bucket; }  // for debug mode
    };
 
  /// local iterators
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused,
           bool __constant_iterators, bool __cache>
    struct _Local_iterator
    : public _Local_iterator_base<_Key, _Value, _ExtractKey,
                                  _Hash, _RangeHash, _Unused, __cache>
    {
    private:
      using __base_type = _Local_iterator_base<_Key, _Value, _ExtractKey,
                                           _Hash, _RangeHash, _Unused, __cache>;
      using __hash_code_base = typename __base_type::__hash_code_base;
 
    public:
      using value_type = _Value;
      using pointer = __conditional_t<__constant_iterators,
                                      const value_type*, value_type*>;
      using reference = __conditional_t<__constant_iterators,
                                        const value_type&, value_type&>;
      using difference_type = ptrdiff_t;
      using iterator_category = forward_iterator_tag;
 
      _Local_iterator() = default;
 
      _Local_iterator(const __hash_code_base& __base,
                      _Hash_node<_Value, __cache>* __n,
                      std::size_t __bkt, std::size_t __bkt_count)
      : __base_type(__base, __n, __bkt, __bkt_count)
      { }
 
      reference
      operator*() const
      { return this->_M_cur->_M_v(); }
 
      pointer
      operator->() const
      { return this->_M_cur->_M_valptr(); }
 
      _Local_iterator&
      operator++()
      {
        this->_M_incr();
        return *this;
      }
 
      _Local_iterator
      operator++(int)
      {
        _Local_iterator __tmp(*this);
        this->_M_incr();
        return __tmp;
      }
    };
 
  /// local const_iterators
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Hash, typename _RangeHash, typename _Unused,
           bool __constant_iterators, bool __cache>
    struct _Local_const_iterator
    : public _Local_iterator_base<_Key, _Value, _ExtractKey,
                                  _Hash, _RangeHash, _Unused, __cache>
    {
    private:
      using __base_type = _Local_iterator_base<_Key, _Value, _ExtractKey,
                                           _Hash, _RangeHash, _Unused, __cache>;
      using __hash_code_base = typename __base_type::__hash_code_base;
 
    public:
      typedef _Value                                    value_type;
      typedef const value_type*                         pointer;
      typedef const value_type&                         reference;
      typedef std::ptrdiff_t                            difference_type;
      typedef std::forward_iterator_tag                 iterator_category;
 
      _Local_const_iterator() = default;
 
      _Local_const_iterator(const __hash_code_base& __base,
                            _Hash_node<_Value, __cache>* __n,
                            std::size_t __bkt, std::size_t __bkt_count)
      : __base_type(__base, __n, __bkt, __bkt_count)
      { }
 
      _Local_const_iterator(const _Local_iterator<_Key, _Value, _ExtractKey,
                                                  _Hash, _RangeHash, _Unused,
                                                  __constant_iterators,
                                                  __cache>& __x)
      : __base_type(__x)
      { }
 
      reference
      operator*() const
      { return this->_M_cur->_M_v(); }
 
      pointer
      operator->() const
      { return this->_M_cur->_M_valptr(); }
 
      _Local_const_iterator&
      operator++()
      {
        this->_M_incr();
        return *this;
      }
 
      _Local_const_iterator
      operator++(int)
      {
        _Local_const_iterator __tmp(*this);
        this->_M_incr();
        return __tmp;
      }
    };
 
  /**
   *  Primary class template _Hashtable_base.
   *
   *  Helper class adding management of _Equal functor to
   *  _Hash_code_base type.
   *
   *  Base class templates are:
   *    - __detail::_Hash_code_base
   *    - __detail::_Hashtable_ebo_helper
   */
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Equal, typename _Hash, typename _RangeHash,
           typename _Unused, typename _Traits>
    struct _Hashtable_base
    : public _Hash_code_base<_Key, _Value, _ExtractKey, _Hash, _RangeHash,
                             _Unused, _Traits::__hash_cached::value>,
      private _Hashtable_ebo_helper<0, _Equal>
    {
    public:
      typedef _Key                                      key_type;
      typedef _Value                                    value_type;
      typedef _Equal                                    key_equal;
      typedef std::size_t                               size_type;
      typedef std::ptrdiff_t                            difference_type;
 
      using __traits_type = _Traits;
      using __hash_cached = typename __traits_type::__hash_cached;
 
      using __hash_code_base = _Hash_code_base<_Key, _Value, _ExtractKey,
                                               _Hash, _RangeHash, _Unused,
                                               __hash_cached::value>;
 
      using __hash_code = typename __hash_code_base::__hash_code;
 
    private:
      using _EqualEBO = _Hashtable_ebo_helper<0, _Equal>;
 
      static bool
      _S_equals(__hash_code, const _Hash_node_code_cache<false>&)
      { return true; }
 
      static bool
      _S_node_equals(const _Hash_node_code_cache<false>&,
                     const _Hash_node_code_cache<false>&)
      { return true; }
 
      static bool
      _S_equals(__hash_code __c, const _Hash_node_code_cache<true>& __n)
      { return __c == __n._M_hash_code; }
 
      static bool
      _S_node_equals(const _Hash_node_code_cache<true>& __lhn,
                     const _Hash_node_code_cache<true>& __rhn)
      { return __lhn._M_hash_code == __rhn._M_hash_code; }
 
    protected:
      _Hashtable_base() = default;
 
      _Hashtable_base(const _Hash& __hash, const _Equal& __eq)
      : __hash_code_base(__hash), _EqualEBO(__eq)
      { }
 
      bool
      _M_key_equals(const _Key& __k,
                    const _Hash_node_value<_Value,
                                           __hash_cached::value>& __n) const
      {
        static_assert(__is_invocable<const _Equal&, const _Key&, const _Key&>{},
          "key equality predicate must be invocable with two arguments of "
          "key type");
        return _M_eq()(__k, _ExtractKey{}(__n._M_v()));
      }
 
      template<typename _Kt>
        bool
        _M_key_equals_tr(const _Kt& __k,
                         const _Hash_node_value<_Value,
                                             __hash_cached::value>& __n) const
        {
          static_assert(
            __is_invocable<const _Equal&, const _Kt&, const _Key&>{},
            "key equality predicate must be invocable with two arguments of "
            "key type");
          return _M_eq()(__k, _ExtractKey{}(__n._M_v()));
        }
 
      bool
      _M_equals(const _Key& __k, __hash_code __c,
                const _Hash_node_value<_Value, __hash_cached::value>& __n) const
      { return _S_equals(__c, __n) && _M_key_equals(__k, __n); }
 
      template<typename _Kt>
        bool
        _M_equals_tr(const _Kt& __k, __hash_code __c,
                     const _Hash_node_value<_Value,
                                            __hash_cached::value>& __n) const
        { return _S_equals(__c, __n) && _M_key_equals_tr(__k, __n); }
 
      bool
      _M_node_equals(
        const _Hash_node_value<_Value, __hash_cached::value>& __lhn,
        const _Hash_node_value<_Value, __hash_cached::value>& __rhn) const
      {
        return _S_node_equals(__lhn, __rhn)
          && _M_key_equals(_ExtractKey{}(__lhn._M_v()), __rhn);
      }
 
      void
      _M_swap(_Hashtable_base& __x)
      {
        __hash_code_base::_M_swap(__x);
        std::swap(_EqualEBO::_M_get(), __x._EqualEBO::_M_get());
      }
 
      const _Equal&
      _M_eq() const { return _EqualEBO::_M_cget(); }
    };
 
  /**
   *  Primary class template  _Equality.
   *
   *  This is for implementing equality comparison for unordered
   *  containers, per N3068, by John Lakos and Pablo Halpern.
   *  Algorithmically, we follow closely the reference implementations
   *  therein.
   */
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits,
           bool _Unique_keys = _Traits::__unique_keys::value>
    struct _Equality;
 
  /// unordered_map and unordered_set specializations.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                     _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, true>
    {
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                                     _Hash, _RangeHash, _Unused,
                                     _RehashPolicy, _Traits>;
 
      bool
      _M_equal(const __hashtable&) const;
    };
 
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    bool
    _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
              _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, true>::
    _M_equal(const __hashtable& __other) const
    {
      using __node_type = typename __hashtable::__node_type;
      const __hashtable* __this = static_cast<const __hashtable*>(this);
      if (__this->size() != __other.size())
        return false;
 
      for (auto __itx = __this->begin(); __itx != __this->end(); ++__itx)
        {
          std::size_t __ybkt = __other._M_bucket_index(*__itx._M_cur);
          auto __prev_n = __other._M_buckets[__ybkt];
          if (!__prev_n)
            return false;
 
          for (__node_type* __n = static_cast<__node_type*>(__prev_n->_M_nxt);;
               __n = __n->_M_next())
            {
              if (__n->_M_v() == *__itx)
                break;
 
              if (!__n->_M_nxt
                  || __other._M_bucket_index(*__n->_M_next()) != __ybkt)
                return false;
            }
        }
 
      return true;
    }
 
  /// unordered_multiset and unordered_multimap specializations.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    struct _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                     _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, false>
    {
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                                     _Hash, _RangeHash, _Unused,
                                     _RehashPolicy, _Traits>;
 
      bool
      _M_equal(const __hashtable&) const;
    };
 
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _Hash, typename _RangeHash, typename _Unused,
           typename _RehashPolicy, typename _Traits>
    bool
    _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
              _Hash, _RangeHash, _Unused, _RehashPolicy, _Traits, false>::
    _M_equal(const __hashtable& __other) const
    {
      using __node_type = typename __hashtable::__node_type;
      const __hashtable* __this = static_cast<const __hashtable*>(this);
      if (__this->size() != __other.size())
        return false;
 
      for (auto __itx = __this->begin(); __itx != __this->end();)
        {
          std::size_t __x_count = 1;
          auto __itx_end = __itx;
          for (++__itx_end; __itx_end != __this->end()
                 && __this->key_eq()(_ExtractKey{}(*__itx),
                                     _ExtractKey{}(*__itx_end));
               ++__itx_end)
            ++__x_count;
 
          std::size_t __ybkt = __other._M_bucket_index(*__itx._M_cur);
          auto __y_prev_n = __other._M_buckets[__ybkt];
          if (!__y_prev_n)
            return false;
 
          __node_type* __y_n = static_cast<__node_type*>(__y_prev_n->_M_nxt);
          for (;;)
            {
              if (__this->key_eq()(_ExtractKey{}(__y_n->_M_v()),
                                   _ExtractKey{}(*__itx)))
                break;
 
              auto __y_ref_n = __y_n;
              for (__y_n = __y_n->_M_next(); __y_n; __y_n = __y_n->_M_next())
                if (!__other._M_node_equals(*__y_ref_n, *__y_n))
                  break;
 
              if (!__y_n || __other._M_bucket_index(*__y_n) != __ybkt)
                return false;
            }
 
          typename __hashtable::const_iterator __ity(__y_n);
          for (auto __ity_end = __ity; __ity_end != __other.end(); ++__ity_end)
            if (--__x_count == 0)
              break;
 
          if (__x_count != 0)
            return false;
 
          if (!std::is_permutation(__itx, __itx_end, __ity))
            return false;
 
          __itx = __itx_end;
        }
      return true;
    }
 
  /**
   * This type deals with all allocation and keeps an allocator instance
   * through inheritance to benefit from EBO when possible.
   */
  template<typename _NodeAlloc>
    struct _Hashtable_alloc : private _Hashtable_ebo_helper<0, _NodeAlloc>
    {
    private:
      using __ebo_node_alloc = _Hashtable_ebo_helper<0, _NodeAlloc>;
 
      template<typename>
        struct __get_value_type;
      template<typename _Val, bool _Cache_hash_code>
        struct __get_value_type<_Hash_node<_Val, _Cache_hash_code>>
        { using type = _Val; };
 
    public:
      using __node_type = typename _NodeAlloc::value_type;
      using __node_alloc_type = _NodeAlloc;
      // Use __gnu_cxx to benefit from _S_always_equal and al.
      using __node_alloc_traits = __gnu_cxx::__alloc_traits<__node_alloc_type>;
 
      using __value_alloc_traits = typename __node_alloc_traits::template
        rebind_traits<typename __get_value_type<__node_type>::type>;
 
      using __node_ptr = __node_type*;
      using __node_base = _Hash_node_base;
      using __node_base_ptr = __node_base*;
      using __buckets_alloc_type =
        __alloc_rebind<__node_alloc_type, __node_base_ptr>;
      using __buckets_alloc_traits = std::allocator_traits<__buckets_alloc_type>;
      using __buckets_ptr = __node_base_ptr*;
 
      _Hashtable_alloc() = default;
      _Hashtable_alloc(const _Hashtable_alloc&) = default;
      _Hashtable_alloc(_Hashtable_alloc&&) = default;
 
      template<typename _Alloc>
        _Hashtable_alloc(_Alloc&& __a)
        : __ebo_node_alloc(std::forward<_Alloc>(__a))
        { }
 
      __node_alloc_type&
      _M_node_allocator()
      { return __ebo_node_alloc::_M_get(); }
 
      const __node_alloc_type&
      _M_node_allocator() const
      { return __ebo_node_alloc::_M_cget(); }
 
      // Allocate a node and construct an element within it.
      template<typename... _Args>
        __node_ptr
        _M_allocate_node(_Args&&... __args);
 
      // Destroy the element within a node and deallocate the node.
      void
      _M_deallocate_node(__node_ptr __n);
 
      // Deallocate a node.
      void
      _M_deallocate_node_ptr(__node_ptr __n);
 
      // Deallocate the linked list of nodes pointed to by __n.
      // The elements within the nodes are destroyed.
      void
      _M_deallocate_nodes(__node_ptr __n);
 
      __buckets_ptr
      _M_allocate_buckets(std::size_t __bkt_count);
 
      void
      _M_deallocate_buckets(__buckets_ptr, std::size_t __bkt_count);
    };
 
  // Definitions of class template _Hashtable_alloc's out-of-line member
  // functions.
  template<typename _NodeAlloc>
    template<typename... _Args>
      auto
      _Hashtable_alloc<_NodeAlloc>::_M_allocate_node(_Args&&... __args)
      -> __node_ptr
      {
        auto __nptr = __node_alloc_traits::allocate(_M_node_allocator(), 1);
        __node_ptr __n = std::__to_address(__nptr);
        __try
          {
            ::new ((void*)__n) __node_type;
            __node_alloc_traits::construct(_M_node_allocator(),
                                           __n->_M_valptr(),
                                           std::forward<_Args>(__args)...);
            return __n;
          }
        __catch(...)
          {
            __node_alloc_traits::deallocate(_M_node_allocator(), __nptr, 1);
            __throw_exception_again;
          }
      }
 
  template<typename _NodeAlloc>
    void
    _Hashtable_alloc<_NodeAlloc>::_M_deallocate_node(__node_ptr __n)
    {
      __node_alloc_traits::destroy(_M_node_allocator(), __n->_M_valptr());
      _M_deallocate_node_ptr(__n);
    }
 
  template<typename _NodeAlloc>
    void
    _Hashtable_alloc<_NodeAlloc>::_M_deallocate_node_ptr(__node_ptr __n)
    {
      typedef typename __node_alloc_traits::pointer _Ptr;
      auto __ptr = std::pointer_traits<_Ptr>::pointer_to(*__n);
      __n->~__node_type();
      __node_alloc_traits::deallocate(_M_node_allocator(), __ptr, 1);
    }
 
  template<typename _NodeAlloc>
    void
    _Hashtable_alloc<_NodeAlloc>::_M_deallocate_nodes(__node_ptr __n)
    {
      while (__n)
        {
          __node_ptr __tmp = __n;
          __n = __n->_M_next();
          _M_deallocate_node(__tmp);
        }
    }
 
  template<typename _NodeAlloc>
    auto
    _Hashtable_alloc<_NodeAlloc>::_M_allocate_buckets(std::size_t __bkt_count)
    -> __buckets_ptr
    {
      __buckets_alloc_type __alloc(_M_node_allocator());
 
      auto __ptr = __buckets_alloc_traits::allocate(__alloc, __bkt_count);
      __buckets_ptr __p = std::__to_address(__ptr);
      __builtin_memset(__p, 0, __bkt_count * sizeof(__node_base_ptr));
      return __p;
    }
 
  template<typename _NodeAlloc>
    void
    _Hashtable_alloc<_NodeAlloc>::
    _M_deallocate_buckets(__buckets_ptr __bkts,
                          std::size_t __bkt_count)
    {
      typedef typename __buckets_alloc_traits::pointer _Ptr;
      auto __ptr = std::pointer_traits<_Ptr>::pointer_to(*__bkts);
      __buckets_alloc_type __alloc(_M_node_allocator());
      __buckets_alloc_traits::deallocate(__alloc, __ptr, __bkt_count);
    }
 
 ///@} hashtable-detail
} // namespace __detail
/// @endcond
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
 
#endif // _HASHTABLE_POLICY_H