hashtable_policy.h

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// Internal policy header for unordered_set and unordered_map -*- C++ -*-

// Copyright (C) 2010-2018 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 <cstdint>              // for std::uint_fast64_t
#include <bits/stl_algobase.h>  // for std::min.

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           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 _H1, typename _H2, typename _Hash, typename _Traits>
    struct _Hashtable_base;

  // Helper function: return distance(first, last) for forward
  // iterators, or 0/1 for input iterators.
  template<class _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<class _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<class _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
      { return std::forward<_Tp>(__x); }
  };

  struct _Select1st
  {
    template<typename _Tp>
      auto
      operator()(_Tp&& __x) const
      -> decltype(std::get<0>(std::forward<_Tp>(__x)))
      { return std::get<0>(std::forward<_Tp>(__x)); }
  };

  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;
      using __node_type = typename __hashtable_alloc::__node_type;

    public:
      _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 _Arg>
        __node_type*
        operator()(_Arg&& __arg) 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<_Arg>(__arg));
                }
              __catch(...)
                {
                  __node->~__node_type();
                  __node_alloc_traits::deallocate(__a, __node, 1);
                  __throw_exception_again;
                }
              return __node;
            }
          return _M_h._M_allocate_node(std::forward<_Arg>(__arg));
        }

    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>;
      using __node_type = typename __hashtable_alloc::__node_type;

    public:
      _AllocNode(__hashtable_alloc& __h)
        : _M_h(__h) { }

      template<typename _Arg>
        __node_type*
        operator()(_Arg&& __arg) const
        { return _M_h._M_allocate_node(std::forward<_Arg>(__arg)); }

    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 _Equal
   *  function.
   *
   *  @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 _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 : _Hash_node_base
    {
      typedef _Value value_type;

      __gnu_cxx::__aligned_buffer<_Value> _M_storage;

      _Value*
      _M_valptr() noexcept
      { return _M_storage._M_ptr(); }

      const _Value*
      _M_valptr() const noexcept
      { return _M_storage._M_ptr(); }

      _Value&
      _M_v() noexcept
      { return *_M_valptr(); }

      const _Value&
      _M_v() const noexcept
      { return *_M_valptr(); }
    };

  /**
   *  Primary template struct _Hash_node.
   */
  template<typename _Value, bool _Cache_hash_code>
    struct _Hash_node;

  /**
   *  Specialization for nodes with caches, struct _Hash_node.
   *
   *  Base class is __detail::_Hash_node_value_base.
   */
  template<typename _Value>
    struct _Hash_node<_Value, true> : _Hash_node_value_base<_Value>
    {
      std::size_t  _M_hash_code;

      _Hash_node*
      _M_next() const noexcept
      { return static_cast<_Hash_node*>(this->_M_nxt); }
    };

  /**
   *  Specialization for nodes without caches, struct _Hash_node.
   *
   *  Base class is __detail::_Hash_node_value_base.
   */
  template<typename _Value>
    struct _Hash_node<_Value, false> : _Hash_node_value_base<_Value>
    {
      _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(__node_type* __p) noexcept
      : _M_cur(__p) { }

      void
      _M_incr() noexcept
      { _M_cur = _M_cur->_M_next(); }
    };

  template<typename _Value, bool _Cache_hash_code>
    inline bool
    operator==(const _Node_iterator_base<_Value, _Cache_hash_code>& __x,
               const _Node_iterator_base<_Value, _Cache_hash_code >& __y)
    noexcept
    { return __x._M_cur == __y._M_cur; }

  template<typename _Value, bool _Cache_hash_code>
    inline bool
    operator!=(const _Node_iterator_base<_Value, _Cache_hash_code>& __x,
               const _Node_iterator_base<_Value, _Cache_hash_code>& __y)
    noexcept
    { return __x._M_cur != __y._M_cur; }

  /// 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:
      typedef _Value                                    value_type;
      typedef std::ptrdiff_t                            difference_type;
      typedef std::forward_iterator_tag                 iterator_category;

      using pointer = typename std::conditional<__constant_iterators,
                                                const _Value*, _Value*>::type;

      using reference = typename std::conditional<__constant_iterators,
                                                  const _Value&, _Value&>::type;

      _Node_iterator() noexcept
      : __base_type(0) { }

      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*                             pointer;
      typedef const _Value&                             reference;

      _Node_const_iterator() noexcept
      : __base_type(0) { }

      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 = std::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 / (long 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.
  _GLIBCXX14_CONSTEXPR
  inline std::size_t
  __clp2(std::size_t __n) noexcept
  {
#if __SIZEOF_SIZE_T__ >= 8
    std::uint_fast64_t __x = __n;
#else
    std::uint_fast32_t __x = __n;
#endif
    // Algorithm from Hacker's Delight, Figure 3-3.
    __x = __x - 1;
    __x = __x | (__x >> 1);
    __x = __x | (__x >> 2);
    __x = __x | (__x >> 4);
    __x = __x | (__x >> 8);
    __x = __x | (__x >>16);
#if __SIZEOF_SIZE_T__ >= 8
    __x = __x | (__x >>32);
#endif
    return __x + 1;
  }

  /// Rehash policy providing power of 2 bucket numbers. Avoids modulo
  /// operations.
  struct _Power2_rehash_policy
  {
    using __has_load_factor = std::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
    {
      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 == __n)
        __res <<= 1;

      if (__res == 0)
        __res = __max_bkt;

      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 = std::size_t(-1);
      else
        _M_next_resize
          = __builtin_ceil(__res * (long 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 / (long 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)
        {
          long double __min_bkts = (__n_elt + __n_ins)
                                        / (long double)_M_max_load_factor;
          if (__min_bkts >= __n_bkt)
            return std::make_pair(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 * (long double)_M_max_load_factor);
          return std::make_pair(false, 0);
        }
      else
        return std::make_pair(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<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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits,
           bool _Unique_keys = _Traits::__unique_keys::value>
    struct _Map_base { };

  /// Partial specialization, __unique_keys set to false.
  template<typename _Key, typename _Pair, typename _Alloc, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Map_base<_Key, _Pair, _Alloc, _Select1st, _Equal,
                     _H1, _H2, _Hash, _RehashPolicy, _Traits, false>
    {
      using mapped_type = typename std::tuple_element<1, _Pair>::type;
    };

  /// Partial specialization, __unique_keys set to true.
  template<typename _Key, typename _Pair, typename _Alloc, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Map_base<_Key, _Pair, _Alloc, _Select1st, _Equal,
                     _H1, _H2, _Hash, _RehashPolicy, _Traits, true>
    {
    private:
      using __hashtable_base = __detail::_Hashtable_base<_Key, _Pair,
                                                         _Select1st,
                                                        _Equal, _H1, _H2, _Hash,
                                                          _Traits>;

      using __hashtable = _Hashtable<_Key, _Pair, _Alloc,
                                     _Select1st, _Equal,
                                     _H1, _H2, _Hash, _RehashPolicy, _Traits>;

      using __hash_code = typename __hashtable_base::__hash_code;
      using __node_type = typename __hashtable_base::__node_type;

    public:
      using key_type = typename __hashtable_base::key_type;
      using iterator = typename __hashtable_base::iterator;
      using mapped_type = typename std::tuple_element<1, _Pair>::type;

      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);

      const mapped_type&
      at(const key_type& __k) const;
    };

  template<typename _Key, typename _Pair, typename _Alloc, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    auto
    _Map_base<_Key, _Pair, _Alloc, _Select1st, _Equal,
              _H1, _H2, _Hash, _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 __n = __h->_M_bucket_index(__k, __code);
      __node_type* __p = __h->_M_find_node(__n, __k, __code);

      if (!__p)
        {
          __p = __h->_M_allocate_node(std::piecewise_construct,
                                      std::tuple<const key_type&>(__k),
                                      std::tuple<>());
          return __h->_M_insert_unique_node(__n, __code, __p)->second;
        }

      return __p->_M_v().second;
    }

  template<typename _Key, typename _Pair, typename _Alloc, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    auto
    _Map_base<_Key, _Pair, _Alloc, _Select1st, _Equal,
              _H1, _H2, _Hash, _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 __n = __h->_M_bucket_index(__k, __code);
      __node_type* __p = __h->_M_find_node(__n, __k, __code);

      if (!__p)
        {
          __p = __h->_M_allocate_node(std::piecewise_construct,
                                      std::forward_as_tuple(std::move(__k)),
                                      std::tuple<>());
          return __h->_M_insert_unique_node(__n, __code, __p)->second;
        }

      return __p->_M_v().second;
    }

  template<typename _Key, typename _Pair, typename _Alloc, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    auto
    _Map_base<_Key, _Pair, _Alloc, _Select1st, _Equal,
              _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::
    at(const key_type& __k)
    -> mapped_type&
    {
      __hashtable* __h = static_cast<__hashtable*>(this);
      __hash_code __code = __h->_M_hash_code(__k);
      std::size_t __n = __h->_M_bucket_index(__k, __code);
      __node_type* __p = __h->_M_find_node(__n, __k, __code);

      if (!__p)
        __throw_out_of_range(__N("_Map_base::at"));
      return __p->_M_v().second;
    }

  template<typename _Key, typename _Pair, typename _Alloc, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    auto
    _Map_base<_Key, _Pair, _Alloc, _Select1st, _Equal,
              _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::
    at(const key_type& __k) const
    -> const mapped_type&
    {
      const __hashtable* __h = static_cast<const __hashtable*>(this);
      __hash_code __code = __h->_M_hash_code(__k);
      std::size_t __n = __h->_M_bucket_index(__k, __code);
      __node_type* __p = __h->_M_find_node(__n, __k, __code);

      if (!__p)
        __throw_out_of_range(__N("_Map_base::at"));
      return __p->_M_v().second;
    }

  /**
   *  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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Insert_base
    {
    protected:
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey,
                                     _Equal, _H1, _H2, _Hash,
                                     _RehashPolicy, _Traits>;

      using __hashtable_base = _Hashtable_base<_Key, _Value, _ExtractKey,
                                               _Equal, _H1, _H2, _Hash,
                                               _Traits>;

      using value_type = typename __hashtable_base::value_type;
      using iterator = typename __hashtable_base::iterator;
      using const_iterator =  typename __hashtable_base::const_iterator;
      using size_type = typename __hashtable_base::size_type;

      using __unique_keys = typename __hashtable_base::__unique_keys;
      using __ireturn_type = typename __hashtable_base::__ireturn_type;
      using __node_type = _Hash_node<_Value, _Traits::__hash_cached::value>;
      using __node_alloc_type = __alloc_rebind<_Alloc, __node_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);

      template<typename _InputIterator, typename _NodeGetter>
        void
        _M_insert_range(_InputIterator __first, _InputIterator __last,
                        const _NodeGetter&, false_type);

    public:
      __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());
      }

      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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    template<typename _InputIterator, typename _NodeGetter>
      void
      _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash,
                    _RehashPolicy, _Traits>::
      _M_insert_range(_InputIterator __first, _InputIterator __last,
                      const _NodeGetter& __node_gen, true_type)
      {
        size_type __n_elt = __detail::__distance_fw(__first, __last);
        if (__n_elt == 0)
          return;

        __hashtable& __h = _M_conjure_hashtable();
        for (; __first != __last; ++__first)
          {
            if (__h._M_insert(*__first, __node_gen, __unique_keys(),
                              __n_elt).second)
              __n_elt = 1;
            else if (__n_elt != 1)
              --__n_elt;
          }
      }

  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    template<typename _InputIterator, typename _NodeGetter>
      void
      _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash,
                    _RehashPolicy, _Traits>::
      _M_insert_range(_InputIterator __first, _InputIterator __last,
                      const _NodeGetter& __node_gen, false_type)
      {
        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, __unique_keys());
      }

  /**
   *  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 _H1, typename _H2, typename _Hash,
           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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Insert<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash,
                   _RehashPolicy, _Traits, true>
    : public _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                           _H1, _H2, _Hash, _RehashPolicy, _Traits>
    {
      using __base_type = _Insert_base<_Key, _Value, _Alloc, _ExtractKey,
                                        _Equal, _H1, _H2, _Hash,
                                        _RehashPolicy, _Traits>;

      using __hashtable_base = _Hashtable_base<_Key, _Value, _ExtractKey,
                                               _Equal, _H1, _H2, _Hash,
                                               _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 __ireturn_type = typename __hashtable_base::__ireturn_type;
      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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Insert<_Key, _Value, _Alloc, _ExtractKey, _Equal, _H1, _H2, _Hash,
                   _RehashPolicy, _Traits, false>
    : public _Insert_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                           _H1, _H2, _Hash, _RehashPolicy, _Traits>
    {
      using __base_type = _Insert_base<_Key, _Value, _Alloc, _ExtractKey,
                                       _Equal, _H1, _H2, _Hash,
                                       _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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits,
           typename =
             __detected_or_t<std::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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Rehash_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                      _H1, _H2, _Hash, _RehashPolicy, _Traits,
                      std::false_type>
    {
    };

  /// Specialization when rehash policy provide load factor management.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Rehash_base<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                        _H1, _H2, _Hash, _RehashPolicy, _Traits,
                        std::true_type>
    {
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey,
                                     _Equal, _H1, _H2, _Hash,
                                     _RehashPolicy, _Traits>;

      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(__builtin_ceil(__n / max_load_factor()));
      }
    };

  /**
   *  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() = default;

      template<typename _OtherTp>
        _Hashtable_ebo_helper(_OtherTp&& __tp)
          : _Tp(std::forward<_OtherTp>(__tp))
        { }

      static const _Tp&
      _S_cget(const _Hashtable_ebo_helper& __eboh)
      { return static_cast<const _Tp&>(__eboh); }

      static _Tp&
      _S_get(_Hashtable_ebo_helper& __eboh)
      { return static_cast<_Tp&>(__eboh); }
    };

  /// 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))
        { }

      static const _Tp&
      _S_cget(const _Hashtable_ebo_helper& __eboh)
      { return __eboh._M_tp; }

      static _Tp&
      _S_get(_Hashtable_ebo_helper& __eboh)
      { return __eboh._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 _H1, typename _H2, typename _Hash,
           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.
   *
   *  Primary template is unused except as a hook for specializations.
   */
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash,
           bool __cache_hash_code>
    struct _Hash_code_base;

  /// Specialization: ranged hash function, no caching hash codes.  H1
  /// and H2 are provided but ignored.  We define a dummy hash code type.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash>
    struct _Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, _Hash, false>
    : private _Hashtable_ebo_helper<0, _ExtractKey>,
      private _Hashtable_ebo_helper<1, _Hash>
    {
    private:
      using __ebo_extract_key = _Hashtable_ebo_helper<0, _ExtractKey>;
      using __ebo_hash = _Hashtable_ebo_helper<1, _Hash>;

    protected:
      typedef void*                                     __hash_code;
      typedef _Hash_node<_Value, false>                 __node_type;

      // We need the default constructor for the local iterators and _Hashtable
      // default constructor.
      _Hash_code_base() = default;

      _Hash_code_base(const _ExtractKey& __ex, const _H1&, const _H2&,
                      const _Hash& __h)
      : __ebo_extract_key(__ex), __ebo_hash(__h) { }

      __hash_code
      _M_hash_code(const _Key& __key) const
      { return 0; }

      std::size_t
      _M_bucket_index(const _Key& __k, __hash_code, std::size_t __n) const
      { return _M_ranged_hash()(__k, __n); }

      std::size_t
      _M_bucket_index(const __node_type* __p, std::size_t __n) const
        noexcept( noexcept(declval<const _Hash&>()(declval<const _Key&>(),
                                                   (std::size_t)0)) )
      { return _M_ranged_hash()(_M_extract()(__p->_M_v()), __n); }

      void
      _M_store_code(__node_type*, __hash_code) const
      { }

      void
      _M_copy_code(__node_type*, const __node_type*) const
      { }

      void
      _M_swap(_Hash_code_base& __x)
      {
        std::swap(_M_extract(), __x._M_extract());
        std::swap(_M_ranged_hash(), __x._M_ranged_hash());
      }

      const _ExtractKey&
      _M_extract() const { return __ebo_extract_key::_S_cget(*this); }

      _ExtractKey&
      _M_extract() { return __ebo_extract_key::_S_get(*this); }

      const _Hash&
      _M_ranged_hash() const { return __ebo_hash::_S_cget(*this); }

      _Hash&
      _M_ranged_hash() { return __ebo_hash::_S_get(*this); }
    };

  // No specialization for ranged hash function while caching hash codes.
  // That combination is meaningless, and trying to do it is an error.

  /// Specialization: ranged hash function, cache hash codes.  This
  /// combination is meaningless, so we provide only a declaration
  /// and no definition.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash>
    struct _Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, _Hash, true>;

  /// Specialization: hash function and range-hashing function, no
  /// caching of hash codes.
  /// Provides typedef and accessor required by C++ 11.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2>
    struct _Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2,
                           _Default_ranged_hash, false>
    : private _Hashtable_ebo_helper<0, _ExtractKey>,
      private _Hashtable_ebo_helper<1, _H1>,
      private _Hashtable_ebo_helper<2, _H2>
    {
    private:
      using __ebo_extract_key = _Hashtable_ebo_helper<0, _ExtractKey>;
      using __ebo_h1 = _Hashtable_ebo_helper<1, _H1>;
      using __ebo_h2 = _Hashtable_ebo_helper<2, _H2>;

      // Gives the local iterator implementation access to _M_bucket_index().
      friend struct _Local_iterator_base<_Key, _Value, _ExtractKey, _H1, _H2,
                                         _Default_ranged_hash, false>;

    public:
      typedef _H1                                       hasher;

      hasher
      hash_function() const
      { return _M_h1(); }

    protected:
      typedef std::size_t                               __hash_code;
      typedef _Hash_node<_Value, false>                 __node_type;

      // We need the default constructor for the local iterators and _Hashtable
      // default constructor.
      _Hash_code_base() = default;

      _Hash_code_base(const _ExtractKey& __ex,
                      const _H1& __h1, const _H2& __h2,
                      const _Default_ranged_hash&)
      : __ebo_extract_key(__ex), __ebo_h1(__h1), __ebo_h2(__h2) { }

      __hash_code
      _M_hash_code(const _Key& __k) const
      {
        static_assert(__is_invocable<const _H1&, const _Key&>{},
            "hash function must be invocable with an argument of key type");
        return _M_h1()(__k);
      }

      std::size_t
      _M_bucket_index(const _Key&, __hash_code __c, std::size_t __n) const
      { return _M_h2()(__c, __n); }

      std::size_t
      _M_bucket_index(const __node_type* __p, std::size_t __n) const
        noexcept( noexcept(declval<const _H1&>()(declval<const _Key&>()))
                  && noexcept(declval<const _H2&>()((__hash_code)0,
                                                    (std::size_t)0)) )
      { return _M_h2()(_M_h1()(_M_extract()(__p->_M_v())), __n); }

      void
      _M_store_code(__node_type*, __hash_code) const
      { }

      void
      _M_copy_code(__node_type*, const __node_type*) const
      { }

      void
      _M_swap(_Hash_code_base& __x)
      {
        std::swap(_M_extract(), __x._M_extract());
        std::swap(_M_h1(), __x._M_h1());
        std::swap(_M_h2(), __x._M_h2());
      }

      const _ExtractKey&
      _M_extract() const { return __ebo_extract_key::_S_cget(*this); }

      _ExtractKey&
      _M_extract() { return __ebo_extract_key::_S_get(*this); }

      const _H1&
      _M_h1() const { return __ebo_h1::_S_cget(*this); }

      _H1&
      _M_h1() { return __ebo_h1::_S_get(*this); }

      const _H2&
      _M_h2() const { return __ebo_h2::_S_cget(*this); }

      _H2&
      _M_h2() { return __ebo_h2::_S_get(*this); }
    };

  /// Specialization: hash function and range-hashing function,
  /// caching hash codes.  H is provided but ignored.  Provides
  /// typedef and accessor required by C++ 11.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2>
    struct _Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2,
                           _Default_ranged_hash, true>
    : private _Hashtable_ebo_helper<0, _ExtractKey>,
      private _Hashtable_ebo_helper<1, _H1>,
      private _Hashtable_ebo_helper<2, _H2>
    {
    private:
      // Gives the local iterator implementation access to _M_h2().
      friend struct _Local_iterator_base<_Key, _Value, _ExtractKey, _H1, _H2,
                                         _Default_ranged_hash, true>;

      using __ebo_extract_key = _Hashtable_ebo_helper<0, _ExtractKey>;
      using __ebo_h1 = _Hashtable_ebo_helper<1, _H1>;
      using __ebo_h2 = _Hashtable_ebo_helper<2, _H2>;

    public:
      typedef _H1                                       hasher;

      hasher
      hash_function() const
      { return _M_h1(); }

    protected:
      typedef std::size_t                               __hash_code;
      typedef _Hash_node<_Value, true>                  __node_type;

      // We need the default constructor for _Hashtable default constructor.
      _Hash_code_base() = default;
      _Hash_code_base(const _ExtractKey& __ex,
                      const _H1& __h1, const _H2& __h2,
                      const _Default_ranged_hash&)
      : __ebo_extract_key(__ex), __ebo_h1(__h1), __ebo_h2(__h2) { }

      __hash_code
      _M_hash_code(const _Key& __k) const
      {
        static_assert(__is_invocable<const _H1&, const _Key&>{},
            "hash function must be invocable with an argument of key type");
        return _M_h1()(__k);
      }

      std::size_t
      _M_bucket_index(const _Key&, __hash_code __c,
                      std::size_t __n) const
      { return _M_h2()(__c, __n); }

      std::size_t
      _M_bucket_index(const __node_type* __p, std::size_t __n) const
        noexcept( noexcept(declval<const _H2&>()((__hash_code)0,
                                                 (std::size_t)0)) )
      { return _M_h2()(__p->_M_hash_code, __n); }

      void
      _M_store_code(__node_type* __n, __hash_code __c) const
      { __n->_M_hash_code = __c; }

      void
      _M_copy_code(__node_type* __to, const __node_type* __from) const
      { __to->_M_hash_code = __from->_M_hash_code; }

      void
      _M_swap(_Hash_code_base& __x)
      {
        std::swap(_M_extract(), __x._M_extract());
        std::swap(_M_h1(), __x._M_h1());
        std::swap(_M_h2(), __x._M_h2());
      }

      const _ExtractKey&
      _M_extract() const { return __ebo_extract_key::_S_cget(*this); }

      _ExtractKey&
      _M_extract() { return __ebo_extract_key::_S_get(*this); }

      const _H1&
      _M_h1() const { return __ebo_h1::_S_cget(*this); }

      _H1&
      _M_h1() { return __ebo_h1::_S_get(*this); }

      const _H2&
      _M_h2() const { return __ebo_h2::_S_cget(*this); }

      _H2&
      _M_h2() { return __ebo_h2::_S_get(*this); }
    };

  /**
   *  Primary class template _Equal_helper.
   *
   */
  template <typename _Key, typename _Value, typename _ExtractKey,
            typename _Equal, typename _HashCodeType,
            bool __cache_hash_code>
  struct _Equal_helper;

  /// Specialization.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Equal, typename _HashCodeType>
  struct _Equal_helper<_Key, _Value, _ExtractKey, _Equal, _HashCodeType, true>
  {
    static bool
    _S_equals(const _Equal& __eq, const _ExtractKey& __extract,
              const _Key& __k, _HashCodeType __c, _Hash_node<_Value, true>* __n)
    { return __c == __n->_M_hash_code && __eq(__k, __extract(__n->_M_v())); }
  };

  /// Specialization.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _Equal, typename _HashCodeType>
  struct _Equal_helper<_Key, _Value, _ExtractKey, _Equal, _HashCodeType, false>
  {
    static bool
    _S_equals(const _Equal& __eq, const _ExtractKey& __extract,
              const _Key& __k, _HashCodeType, _Hash_node<_Value, false>* __n)
    { return __eq(__k, __extract(__n->_M_v())); }
  };


  /// Partial specialization used when nodes contain a cached hash code.
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash>
    struct _Local_iterator_base<_Key, _Value, _ExtractKey,
                                _H1, _H2, _Hash, true>
    : private _Hashtable_ebo_helper<0, _H2>
    {
    protected:
      using __base_type = _Hashtable_ebo_helper<0, _H2>;
      using __hash_code_base = _Hash_code_base<_Key, _Value, _ExtractKey,
                                               _H1, _H2, _Hash, true>;

      _Local_iterator_base() = default;
      _Local_iterator_base(const __hash_code_base& __base,
                           _Hash_node<_Value, true>* __p,
                           std::size_t __bkt, std::size_t __bkt_count)
      : __base_type(__base._M_h2()),
        _M_cur(__p), _M_bucket(__bkt), _M_bucket_count(__bkt_count) { }

      void
      _M_incr()
      {
        _M_cur = _M_cur->_M_next();
        if (_M_cur)
          {
            std::size_t __bkt
              = __base_type::_S_get(*this)(_M_cur->_M_hash_code,
                                           _M_bucket_count);
            if (__bkt != _M_bucket)
              _M_cur = nullptr;
          }
      }

      _Hash_node<_Value, true>*  _M_cur;
      std::size_t _M_bucket;
      std::size_t _M_bucket_count;

    public:
      const void*
      _M_curr() const { return _M_cur; }  // for equality ops

      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 _H1, typename _H2, typename _Hash>
    using __hash_code_for_local_iter
      = _Hash_code_storage<_Hash_code_base<_Key, _Value, _ExtractKey,
                                           _H1, _H2, _Hash, false>>;

  // Partial specialization used when hash codes are not cached
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash>
    struct _Local_iterator_base<_Key, _Value, _ExtractKey,
                                _H1, _H2, _Hash, false>
    : __hash_code_for_local_iter<_Key, _Value, _ExtractKey, _H1, _H2, _Hash>
    {
    protected:
      using __hash_code_base = _Hash_code_base<_Key, _Value, _ExtractKey,
                                               _H1, _H2, _Hash, 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)
      : _M_cur(__p), _M_bucket(__bkt), _M_bucket_count(__bkt_count)
      { _M_init(__base); }

      ~_Local_iterator_base()
      {
        if (_M_bucket_count != -1)
          _M_destroy();
      }

      _Local_iterator_base(const _Local_iterator_base& __iter)
      : _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());
      }

      _Local_iterator_base&
      operator=(const _Local_iterator_base& __iter)
      {
        if (_M_bucket_count != -1)
          _M_destroy();
        _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()
      {
        _M_cur = _M_cur->_M_next();
        if (_M_cur)
          {
            std::size_t __bkt = this->_M_h()->_M_bucket_index(_M_cur,
                                                              _M_bucket_count);
            if (__bkt != _M_bucket)
              _M_cur = nullptr;
          }
      }

      _Hash_node<_Value, false>*  _M_cur;
      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:
      const void*
      _M_curr() const { return _M_cur; }  // for equality ops and debug mode

      std::size_t
      _M_get_bucket() const { return _M_bucket; }  // for debug mode
    };

  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash, bool __cache>
    inline bool
    operator==(const _Local_iterator_base<_Key, _Value, _ExtractKey,
                                          _H1, _H2, _Hash, __cache>& __x,
               const _Local_iterator_base<_Key, _Value, _ExtractKey,
                                          _H1, _H2, _Hash, __cache>& __y)
    { return __x._M_curr() == __y._M_curr(); }

  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash, bool __cache>
    inline bool
    operator!=(const _Local_iterator_base<_Key, _Value, _ExtractKey,
                                          _H1, _H2, _Hash, __cache>& __x,
               const _Local_iterator_base<_Key, _Value, _ExtractKey,
                                          _H1, _H2, _Hash, __cache>& __y)
    { return __x._M_curr() != __y._M_curr(); }

  /// local iterators
  template<typename _Key, typename _Value, typename _ExtractKey,
           typename _H1, typename _H2, typename _Hash,
           bool __constant_iterators, bool __cache>
    struct _Local_iterator
    : public _Local_iterator_base<_Key, _Value, _ExtractKey,
                                  _H1, _H2, _Hash, __cache>
    {
    private:
      using __base_type = _Local_iterator_base<_Key, _Value, _ExtractKey,
                                               _H1, _H2, _Hash, __cache>;
      using __hash_code_base = typename __base_type::__hash_code_base;
    public:
      typedef _Value                                    value_type;
      typedef typename std::conditional<__constant_iterators,
                                        const _Value*, _Value*>::type
                                                       pointer;
      typedef typename std::conditional<__constant_iterators,
                                        const _Value&, _Value&>::type
                                                       reference;
      typedef std::ptrdiff_t                            difference_type;
      typedef std::forward_iterator_tag                 iterator_category;

      _Local_iterator() = default;

      _Local_iterator(const __hash_code_base& __base,
                      _Hash_node<_Value, __cache>* __p,
                      std::size_t __bkt, std::size_t __bkt_count)
        : __base_type(__base, __p, __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 _H1, typename _H2, typename _Hash,
           bool __constant_iterators, bool __cache>
    struct _Local_const_iterator
    : public _Local_iterator_base<_Key, _Value, _ExtractKey,
                                  _H1, _H2, _Hash, __cache>
    {
    private:
      using __base_type = _Local_iterator_base<_Key, _Value, _ExtractKey,
                                               _H1, _H2, _Hash, __cache>;
      using __hash_code_base = typename __base_type::__hash_code_base;

    public:
      typedef _Value                                    value_type;
      typedef const _Value*                             pointer;
      typedef const _Value&                             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>* __p,
                            std::size_t __bkt, std::size_t __bkt_count)
        : __base_type(__base, __p, __bkt, __bkt_count)
      { }

      _Local_const_iterator(const _Local_iterator<_Key, _Value, _ExtractKey,
                                                  _H1, _H2, _Hash,
                                                  __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 _H1, typename _H2, typename _Hash, typename _Traits>
  struct _Hashtable_base
  : public _Hash_code_base<_Key, _Value, _ExtractKey, _H1, _H2, _Hash,
                           _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 __constant_iterators = typename __traits_type::__constant_iterators;
    using __unique_keys = typename __traits_type::__unique_keys;

    using __hash_code_base = _Hash_code_base<_Key, _Value, _ExtractKey,
                                             _H1, _H2, _Hash,
                                             __hash_cached::value>;

    using __hash_code = typename __hash_code_base::__hash_code;
    using __node_type = typename __hash_code_base::__node_type;

    using iterator = __detail::_Node_iterator<value_type,
                                              __constant_iterators::value,
                                              __hash_cached::value>;

    using const_iterator = __detail::_Node_const_iterator<value_type,
                                                   __constant_iterators::value,
                                                   __hash_cached::value>;

    using local_iterator = __detail::_Local_iterator<key_type, value_type,
                                                  _ExtractKey, _H1, _H2, _Hash,
                                                  __constant_iterators::value,
                                                     __hash_cached::value>;

    using const_local_iterator = __detail::_Local_const_iterator<key_type,
                                                                 value_type,
                                        _ExtractKey, _H1, _H2, _Hash,
                                        __constant_iterators::value,
                                        __hash_cached::value>;

    using __ireturn_type = typename std::conditional<__unique_keys::value,
                                                     std::pair<iterator, bool>,
                                                     iterator>::type;
  private:
    using _EqualEBO = _Hashtable_ebo_helper<0, _Equal>;
    using _EqualHelper =  _Equal_helper<_Key, _Value, _ExtractKey, _Equal,
                                        __hash_code, __hash_cached::value>;

  protected:
    _Hashtable_base() = default;
    _Hashtable_base(const _ExtractKey& __ex, const _H1& __h1, const _H2& __h2,
                    const _Hash& __hash, const _Equal& __eq)
    : __hash_code_base(__ex, __h1, __h2, __hash), _EqualEBO(__eq)
    { }

    bool
    _M_equals(const _Key& __k, __hash_code __c, __node_type* __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 _EqualHelper::_S_equals(_M_eq(), this->_M_extract(),
                                     __k, __c, __n);
    }

    void
    _M_swap(_Hashtable_base& __x)
    {
      __hash_code_base::_M_swap(__x);
      std::swap(_M_eq(), __x._M_eq());
    }

    const _Equal&
    _M_eq() const { return _EqualEBO::_S_cget(*this); }

    _Equal&
    _M_eq() { return _EqualEBO::_S_get(*this); }
  };

  /**
   *  struct _Equality_base.
   *
   *  Common types and functions for class _Equality.
   */
  struct _Equality_base
  {
  protected:
    template<typename _Uiterator>
      static bool
      _S_is_permutation(_Uiterator, _Uiterator, _Uiterator);
  };

  // See std::is_permutation in N3068.
  template<typename _Uiterator>
    bool
    _Equality_base::
    _S_is_permutation(_Uiterator __first1, _Uiterator __last1,
                      _Uiterator __first2)
    {
      for (; __first1 != __last1; ++__first1, ++__first2)
        if (!(*__first1 == *__first2))
          break;

      if (__first1 == __last1)
        return true;

      _Uiterator __last2 = __first2;
      std::advance(__last2, std::distance(__first1, __last1));

      for (_Uiterator __it1 = __first1; __it1 != __last1; ++__it1)
        {
          _Uiterator __tmp =  __first1;
          while (__tmp != __it1 && !bool(*__tmp == *__it1))
            ++__tmp;

          // We've seen this one before.
          if (__tmp != __it1)
            continue;

          std::ptrdiff_t __n2 = 0;
          for (__tmp = __first2; __tmp != __last2; ++__tmp)
            if (*__tmp == *__it1)
              ++__n2;

          if (!__n2)
            return false;

          std::ptrdiff_t __n1 = 0;
          for (__tmp = __it1; __tmp != __last1; ++__tmp)
            if (*__tmp == *__it1)
              ++__n1;

          if (__n1 != __n2)
            return false;
        }
      return true;
    }

  /**
   *  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 _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits,
           bool _Unique_keys = _Traits::__unique_keys::value>
    struct _Equality;

  /// Specialization.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                     _H1, _H2, _Hash, _RehashPolicy, _Traits, true>
    {
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                                     _H1, _H2, _Hash, _RehashPolicy, _Traits>;

      bool
      _M_equal(const __hashtable&) const;
    };

  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    bool
    _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
              _H1, _H2, _Hash, _RehashPolicy, _Traits, true>::
    _M_equal(const __hashtable& __other) const
    {
      const __hashtable* __this = static_cast<const __hashtable*>(this);

      if (__this->size() != __other.size())
        return false;

      for (auto __itx = __this->begin(); __itx != __this->end(); ++__itx)
        {
          const auto __ity = __other.find(_ExtractKey()(*__itx));
          if (__ity == __other.end() || !bool(*__ity == *__itx))
            return false;
        }
      return true;
    }

  /// Specialization.
  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    struct _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                     _H1, _H2, _Hash, _RehashPolicy, _Traits, false>
    : public _Equality_base
    {
      using __hashtable = _Hashtable<_Key, _Value, _Alloc, _ExtractKey, _Equal,
                                     _H1, _H2, _Hash, _RehashPolicy, _Traits>;

      bool
      _M_equal(const __hashtable&) const;
    };

  template<typename _Key, typename _Value, typename _Alloc,
           typename _ExtractKey, typename _Equal,
           typename _H1, typename _H2, typename _Hash,
           typename _RehashPolicy, typename _Traits>
    bool
    _Equality<_Key, _Value, _Alloc, _ExtractKey, _Equal,
              _H1, _H2, _Hash, _RehashPolicy, _Traits, false>::
    _M_equal(const __hashtable& __other) const
    {
      const __hashtable* __this = static_cast<const __hashtable*>(this);

      if (__this->size() != __other.size())
        return false;

      for (auto __itx = __this->begin(); __itx != __this->end();)
        {
          const auto __xrange = __this->equal_range(_ExtractKey()(*__itx));
          const auto __yrange = __other.equal_range(_ExtractKey()(*__itx));

          if (std::distance(__xrange.first, __xrange.second)
              != std::distance(__yrange.first, __yrange.second))
            return false;

          if (!_S_is_permutation(__xrange.first, __xrange.second,
                                 __yrange.first))
            return false;

          __itx = __xrange.second;
        }
      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>;
    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 __node_type::value_type>;

      using __node_base = __detail::_Hash_node_base;
      using __bucket_type = __node_base*;      
      using __bucket_alloc_type =
        __alloc_rebind<__node_alloc_type, __bucket_type>;
      using __bucket_alloc_traits = std::allocator_traits<__bucket_alloc_type>;

      _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::_S_get(*this); }

      const __node_alloc_type&
      _M_node_allocator() const
      { return __ebo_node_alloc::_S_cget(*this); }

      template<typename... _Args>
        __node_type*
        _M_allocate_node(_Args&&... __args);

      void
      _M_deallocate_node(__node_type* __n);

      // Deallocate the linked list of nodes pointed to by __n
      void
      _M_deallocate_nodes(__node_type* __n);

      __bucket_type*
      _M_allocate_buckets(std::size_t __n);

      void
      _M_deallocate_buckets(__bucket_type*, std::size_t __n);
    };

  // Definitions of class template _Hashtable_alloc's out-of-line member
  // functions.
  template<typename _NodeAlloc>
    template<typename... _Args>
      typename _Hashtable_alloc<_NodeAlloc>::__node_type*
      _Hashtable_alloc<_NodeAlloc>::_M_allocate_node(_Args&&... __args)
      {
        auto __nptr = __node_alloc_traits::allocate(_M_node_allocator(), 1);
        __node_type* __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_type* __n)
    {
      typedef typename __node_alloc_traits::pointer _Ptr;
      auto __ptr = std::pointer_traits<_Ptr>::pointer_to(*__n);
      __node_alloc_traits::destroy(_M_node_allocator(), __n->_M_valptr());
      __n->~__node_type();
      __node_alloc_traits::deallocate(_M_node_allocator(), __ptr, 1);
    }

  template<typename _NodeAlloc>
    void
    _Hashtable_alloc<_NodeAlloc>::_M_deallocate_nodes(__node_type* __n)
    {
      while (__n)
        {
          __node_type* __tmp = __n;
          __n = __n->_M_next();
          _M_deallocate_node(__tmp);
        }
    }

  template<typename _NodeAlloc>
    typename _Hashtable_alloc<_NodeAlloc>::__bucket_type*
    _Hashtable_alloc<_NodeAlloc>::_M_allocate_buckets(std::size_t __n)
    {
      __bucket_alloc_type __alloc(_M_node_allocator());

      auto __ptr = __bucket_alloc_traits::allocate(__alloc, __n);
      __bucket_type* __p = std::__to_address(__ptr);
      __builtin_memset(__p, 0, __n * sizeof(__bucket_type));
      return __p;
    }

  template<typename _NodeAlloc>
    void
    _Hashtable_alloc<_NodeAlloc>::_M_deallocate_buckets(__bucket_type* __bkts,
                                                        std::size_t __n)
    {
      typedef typename __bucket_alloc_traits::pointer _Ptr;
      auto __ptr = std::pointer_traits<_Ptr>::pointer_to(*__bkts);
      __bucket_alloc_type __alloc(_M_node_allocator());
      __bucket_alloc_traits::deallocate(__alloc, __ptr, __n);
    }

 //@} hashtable-detail
} // namespace __detail
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std

#endif // _HASHTABLE_POLICY_H