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+// Copyright 2018 The Abseil Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// A btree implementation of the STL set and map interfaces. A btree is smaller
+// and generally also faster than STL set/map (refer to the benchmarks below).
+// The red-black tree implementation of STL set/map has an overhead of 3
+// pointers (left, right and parent) plus the node color information for each
+// stored value. So a set<int32_t> consumes 40 bytes for each value stored in
+// 64-bit mode. This btree implementation stores multiple values on fixed
+// size nodes (usually 256 bytes) and doesn't store child pointers for leaf
+// nodes. The result is that a btree_set<int32_t> may use much less memory per
+// stored value. For the random insertion benchmark in btree_bench.cc, a
+// btree_set<int32_t> with node-size of 256 uses 5.1 bytes per stored value.
+//
+// The packing of multiple values on to each node of a btree has another effect
+// besides better space utilization: better cache locality due to fewer cache
+// lines being accessed. Better cache locality translates into faster
+// operations.
+//
+// CAVEATS
+//
+// Insertions and deletions on a btree can cause splitting, merging or
+// rebalancing of btree nodes. And even without these operations, insertions
+// and deletions on a btree will move values around within a node. In both
+// cases, the result is that insertions and deletions can invalidate iterators
+// pointing to values other than the one being inserted/deleted. Therefore, this
+// container does not provide pointer stability. This is notably different from
+// STL set/map which takes care to not invalidate iterators on insert/erase
+// except, of course, for iterators pointing to the value being erased.  A
+// partial workaround when erasing is available: erase() returns an iterator
+// pointing to the item just after the one that was erased (or end() if none
+// exists).
+
+#ifndef ABSL_CONTAINER_INTERNAL_BTREE_H_
+#define ABSL_CONTAINER_INTERNAL_BTREE_H_
+
+#include <algorithm>
+#include <cassert>
+#include <cstddef>
+#include <cstdint>
+#include <cstring>
+#include <functional>
+#include <iterator>
+#include <limits>
+#include <string>
+#include <type_traits>
+#include <utility>
+
+#include "absl/base/config.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/base/macros.h"
+#include "absl/container/internal/common.h"
+#include "absl/container/internal/common_policy_traits.h"
+#include "absl/container/internal/compressed_tuple.h"
+#include "absl/container/internal/container_memory.h"
+#include "absl/container/internal/layout.h"
+#include "absl/memory/memory.h"
+#include "absl/meta/type_traits.h"
+#include "absl/strings/cord.h"
+#include "absl/strings/string_view.h"
+#include "absl/types/compare.h"
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace container_internal {
+
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+#error ABSL_BTREE_ENABLE_GENERATIONS cannot be directly set
+#elif (defined(ABSL_HAVE_ADDRESS_SANITIZER) ||   \
+       defined(ABSL_HAVE_HWADDRESS_SANITIZER) || \
+       defined(ABSL_HAVE_MEMORY_SANITIZER)) &&   \
+    !defined(NDEBUG_SANITIZER)  // If defined, performance is important.
+// When compiled in sanitizer mode, we add generation integers to the nodes and
+// iterators. When iterators are used, we validate that the container has not
+// been mutated since the iterator was constructed.
+#define ABSL_BTREE_ENABLE_GENERATIONS
+#endif
+
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+constexpr bool BtreeGenerationsEnabled() { return true; }
+#else
+constexpr bool BtreeGenerationsEnabled() { return false; }
+#endif
+
+template <typename Compare, typename T, typename U>
+using compare_result_t = absl::result_of_t<const Compare(const T &, const U &)>;
+
+// A helper class that indicates if the Compare parameter is a key-compare-to
+// comparator.
+template <typename Compare, typename T>
+using btree_is_key_compare_to =
+    std::is_convertible<compare_result_t<Compare, T, T>, absl::weak_ordering>;
+
+struct StringBtreeDefaultLess {
+  using is_transparent = void;
+
+  StringBtreeDefaultLess() = default;
+
+  // Compatibility constructor.
+  StringBtreeDefaultLess(std::less<std::string>) {}        // NOLINT
+  StringBtreeDefaultLess(std::less<absl::string_view>) {}  // NOLINT
+
+  // Allow converting to std::less for use in key_comp()/value_comp().
+  explicit operator std::less<std::string>() const { return {}; }
+  explicit operator std::less<absl::string_view>() const { return {}; }
+  explicit operator std::less<absl::Cord>() const { return {}; }
+
+  absl::weak_ordering operator()(absl::string_view lhs,
+                                 absl::string_view rhs) const {
+    return compare_internal::compare_result_as_ordering(lhs.compare(rhs));
+  }
+  StringBtreeDefaultLess(std::less<absl::Cord>) {}  // NOLINT
+  absl::weak_ordering operator()(const absl::Cord &lhs,
+                                 const absl::Cord &rhs) const {
+    return compare_internal::compare_result_as_ordering(lhs.Compare(rhs));
+  }
+  absl::weak_ordering operator()(const absl::Cord &lhs,
+                                 absl::string_view rhs) const {
+    return compare_internal::compare_result_as_ordering(lhs.Compare(rhs));
+  }
+  absl::weak_ordering operator()(absl::string_view lhs,
+                                 const absl::Cord &rhs) const {
+    return compare_internal::compare_result_as_ordering(-rhs.Compare(lhs));
+  }
+};
+
+struct StringBtreeDefaultGreater {
+  using is_transparent = void;
+
+  StringBtreeDefaultGreater() = default;
+
+  StringBtreeDefaultGreater(std::greater<std::string>) {}        // NOLINT
+  StringBtreeDefaultGreater(std::greater<absl::string_view>) {}  // NOLINT
+
+  // Allow converting to std::greater for use in key_comp()/value_comp().
+  explicit operator std::greater<std::string>() const { return {}; }
+  explicit operator std::greater<absl::string_view>() const { return {}; }
+  explicit operator std::greater<absl::Cord>() const { return {}; }
+
+  absl::weak_ordering operator()(absl::string_view lhs,
+                                 absl::string_view rhs) const {
+    return compare_internal::compare_result_as_ordering(rhs.compare(lhs));
+  }
+  StringBtreeDefaultGreater(std::greater<absl::Cord>) {}  // NOLINT
+  absl::weak_ordering operator()(const absl::Cord &lhs,
+                                 const absl::Cord &rhs) const {
+    return compare_internal::compare_result_as_ordering(rhs.Compare(lhs));
+  }
+  absl::weak_ordering operator()(const absl::Cord &lhs,
+                                 absl::string_view rhs) const {
+    return compare_internal::compare_result_as_ordering(-lhs.Compare(rhs));
+  }
+  absl::weak_ordering operator()(absl::string_view lhs,
+                                 const absl::Cord &rhs) const {
+    return compare_internal::compare_result_as_ordering(rhs.Compare(lhs));
+  }
+};
+
+// See below comments for checked_compare.
+template <typename Compare, bool is_class = std::is_class<Compare>::value>
+struct checked_compare_base : Compare {
+  using Compare::Compare;
+  explicit checked_compare_base(Compare c) : Compare(std::move(c)) {}
+  const Compare &comp() const { return *this; }
+};
+template <typename Compare>
+struct checked_compare_base<Compare, false> {
+  explicit checked_compare_base(Compare c) : compare(std::move(c)) {}
+  const Compare &comp() const { return compare; }
+  Compare compare;
+};
+
+// A mechanism for opting out of checked_compare for use only in btree_test.cc.
+struct BtreeTestOnlyCheckedCompareOptOutBase {};
+
+// A helper class to adapt the specified comparator for two use cases:
+// (1) When using common Abseil string types with common comparison functors,
+// convert a boolean comparison into a three-way comparison that returns an
+// `absl::weak_ordering`. This helper class is specialized for
+// less<std::string>, greater<std::string>, less<string_view>,
+// greater<string_view>, less<absl::Cord>, and greater<absl::Cord>.
+// (2) Adapt the comparator to diagnose cases of non-strict-weak-ordering (see
+// https://en.cppreference.com/w/cpp/named_req/Compare) in debug mode. Whenever
+// a comparison is made, we will make assertions to verify that the comparator
+// is valid.
+template <typename Compare, typename Key>
+struct key_compare_adapter {
+  // Inherit from checked_compare_base to support function pointers and also
+  // keep empty-base-optimization (EBO) support for classes.
+  // Note: we can't use CompressedTuple here because that would interfere
+  // with the EBO for `btree::rightmost_`. `btree::rightmost_` is itself a
+  // CompressedTuple and nested `CompressedTuple`s don't support EBO.
+  // TODO(b/214288561): use CompressedTuple instead once it supports EBO for
+  // nested `CompressedTuple`s.
+  struct checked_compare : checked_compare_base<Compare> {
+   private:
+    using Base = typename checked_compare::checked_compare_base;
+    using Base::comp;
+
+    // If possible, returns whether `t` is equivalent to itself. We can only do
+    // this for `Key`s because we can't be sure that it's safe to call
+    // `comp()(k, k)` otherwise. Even if SFINAE allows it, there could be a
+    // compilation failure inside the implementation of the comparison operator.
+    bool is_self_equivalent(const Key &k) const {
+      // Note: this works for both boolean and three-way comparators.
+      return comp()(k, k) == 0;
+    }
+    // If we can't compare `t` with itself, returns true unconditionally.
+    template <typename T>
+    bool is_self_equivalent(const T &) const {
+      return true;
+    }
+
+   public:
+    using Base::Base;
+    checked_compare(Compare comp) : Base(std::move(comp)) {}  // NOLINT
+
+    // Allow converting to Compare for use in key_comp()/value_comp().
+    explicit operator Compare() const { return comp(); }
+
+    template <typename T, typename U,
+              absl::enable_if_t<
+                  std::is_same<bool, compare_result_t<Compare, T, U>>::value,
+                  int> = 0>
+    bool operator()(const T &lhs, const U &rhs) const {
+      // NOTE: if any of these assertions fail, then the comparator does not
+      // establish a strict-weak-ordering (see
+      // https://en.cppreference.com/w/cpp/named_req/Compare).
+      assert(is_self_equivalent(lhs));
+      assert(is_self_equivalent(rhs));
+      const bool lhs_comp_rhs = comp()(lhs, rhs);
+      assert(!lhs_comp_rhs || !comp()(rhs, lhs));
+      return lhs_comp_rhs;
+    }
+
+    template <
+        typename T, typename U,
+        absl::enable_if_t<std::is_convertible<compare_result_t<Compare, T, U>,
+                                              absl::weak_ordering>::value,
+                          int> = 0>
+    absl::weak_ordering operator()(const T &lhs, const U &rhs) const {
+      // NOTE: if any of these assertions fail, then the comparator does not
+      // establish a strict-weak-ordering (see
+      // https://en.cppreference.com/w/cpp/named_req/Compare).
+      assert(is_self_equivalent(lhs));
+      assert(is_self_equivalent(rhs));
+      const absl::weak_ordering lhs_comp_rhs = comp()(lhs, rhs);
+#ifndef NDEBUG
+      const absl::weak_ordering rhs_comp_lhs = comp()(rhs, lhs);
+      if (lhs_comp_rhs > 0) {
+        assert(rhs_comp_lhs < 0 && "lhs_comp_rhs > 0 -> rhs_comp_lhs < 0");
+      } else if (lhs_comp_rhs == 0) {
+        assert(rhs_comp_lhs == 0 && "lhs_comp_rhs == 0 -> rhs_comp_lhs == 0");
+      } else {
+        assert(rhs_comp_lhs > 0 && "lhs_comp_rhs < 0 -> rhs_comp_lhs > 0");
+      }
+#endif
+      return lhs_comp_rhs;
+    }
+  };
+  using type = absl::conditional_t<
+      std::is_base_of<BtreeTestOnlyCheckedCompareOptOutBase, Compare>::value,
+      Compare, checked_compare>;
+};
+
+template <>
+struct key_compare_adapter<std::less<std::string>, std::string> {
+  using type = StringBtreeDefaultLess;
+};
+
+template <>
+struct key_compare_adapter<std::greater<std::string>, std::string> {
+  using type = StringBtreeDefaultGreater;
+};
+
+template <>
+struct key_compare_adapter<std::less<absl::string_view>, absl::string_view> {
+  using type = StringBtreeDefaultLess;
+};
+
+template <>
+struct key_compare_adapter<std::greater<absl::string_view>, absl::string_view> {
+  using type = StringBtreeDefaultGreater;
+};
+
+template <>
+struct key_compare_adapter<std::less<absl::Cord>, absl::Cord> {
+  using type = StringBtreeDefaultLess;
+};
+
+template <>
+struct key_compare_adapter<std::greater<absl::Cord>, absl::Cord> {
+  using type = StringBtreeDefaultGreater;
+};
+
+// Detects an 'absl_btree_prefer_linear_node_search' member. This is
+// a protocol used as an opt-in or opt-out of linear search.
+//
+//  For example, this would be useful for key types that wrap an integer
+//  and define their own cheap operator<(). For example:
+//
+//   class K {
+//    public:
+//     using absl_btree_prefer_linear_node_search = std::true_type;
+//     ...
+//    private:
+//     friend bool operator<(K a, K b) { return a.k_ < b.k_; }
+//     int k_;
+//   };
+//
+//   btree_map<K, V> m;  // Uses linear search
+//
+// If T has the preference tag, then it has a preference.
+// Btree will use the tag's truth value.
+template <typename T, typename = void>
+struct has_linear_node_search_preference : std::false_type {};
+template <typename T, typename = void>
+struct prefers_linear_node_search : std::false_type {};
+template <typename T>
+struct has_linear_node_search_preference<
+    T, absl::void_t<typename T::absl_btree_prefer_linear_node_search>>
+    : std::true_type {};
+template <typename T>
+struct prefers_linear_node_search<
+    T, absl::void_t<typename T::absl_btree_prefer_linear_node_search>>
+    : T::absl_btree_prefer_linear_node_search {};
+
+template <typename Compare, typename Key>
+constexpr bool compare_has_valid_result_type() {
+  using compare_result_type = compare_result_t<Compare, Key, Key>;
+  return std::is_same<compare_result_type, bool>::value ||
+         std::is_convertible<compare_result_type, absl::weak_ordering>::value;
+}
+
+template <typename original_key_compare, typename value_type>
+class map_value_compare {
+  template <typename Params>
+  friend class btree;
+
+  // Note: this `protected` is part of the API of std::map::value_compare. See
+  // https://en.cppreference.com/w/cpp/container/map/value_compare.
+ protected:
+  explicit map_value_compare(original_key_compare c) : comp(std::move(c)) {}
+
+  original_key_compare comp;  // NOLINT
+
+ public:
+  auto operator()(const value_type &lhs, const value_type &rhs) const
+      -> decltype(comp(lhs.first, rhs.first)) {
+    return comp(lhs.first, rhs.first);
+  }
+};
+
+template <typename Key, typename Compare, typename Alloc, int TargetNodeSize,
+          bool IsMulti, bool IsMap, typename SlotPolicy>
+struct common_params : common_policy_traits<SlotPolicy> {
+  using original_key_compare = Compare;
+
+  // If Compare is a common comparator for a string-like type, then we adapt it
+  // to use heterogeneous lookup and to be a key-compare-to comparator.
+  // We also adapt the comparator to diagnose invalid comparators in debug mode.
+  // We disable this when `Compare` is invalid in a way that will cause
+  // adaptation to fail (having invalid return type) so that we can give a
+  // better compilation failure in static_assert_validation. If we don't do
+  // this, then there will be cascading compilation failures that are confusing
+  // for users.
+  using key_compare =
+      absl::conditional_t<!compare_has_valid_result_type<Compare, Key>(),
+                          Compare,
+                          typename key_compare_adapter<Compare, Key>::type>;
+
+  static constexpr bool kIsKeyCompareStringAdapted =
+      std::is_same<key_compare, StringBtreeDefaultLess>::value ||
+      std::is_same<key_compare, StringBtreeDefaultGreater>::value;
+  static constexpr bool kIsKeyCompareTransparent =
+      IsTransparent<original_key_compare>::value || kIsKeyCompareStringAdapted;
+
+  // A type which indicates if we have a key-compare-to functor or a plain old
+  // key-compare functor.
+  using is_key_compare_to = btree_is_key_compare_to<key_compare, Key>;
+
+  using allocator_type = Alloc;
+  using key_type = Key;
+  using size_type = size_t;
+  using difference_type = ptrdiff_t;
+
+  using slot_policy = SlotPolicy;
+  using slot_type = typename slot_policy::slot_type;
+  using value_type = typename slot_policy::value_type;
+  using init_type = typename slot_policy::mutable_value_type;
+  using pointer = value_type *;
+  using const_pointer = const value_type *;
+  using reference = value_type &;
+  using const_reference = const value_type &;
+
+  using value_compare =
+      absl::conditional_t<IsMap,
+                          map_value_compare<original_key_compare, value_type>,
+                          original_key_compare>;
+  using is_map_container = std::integral_constant<bool, IsMap>;
+
+  // For the given lookup key type, returns whether we can have multiple
+  // equivalent keys in the btree. If this is a multi-container, then we can.
+  // Otherwise, we can have multiple equivalent keys only if all of the
+  // following conditions are met:
+  // - The comparator is transparent.
+  // - The lookup key type is not the same as key_type.
+  // - The comparator is not a StringBtreeDefault{Less,Greater} comparator
+  //   that we know has the same equivalence classes for all lookup types.
+  template <typename LookupKey>
+  constexpr static bool can_have_multiple_equivalent_keys() {
+    return IsMulti || (IsTransparent<key_compare>::value &&
+                       !std::is_same<LookupKey, Key>::value &&
+                       !kIsKeyCompareStringAdapted);
+  }
+
+  enum {
+    kTargetNodeSize = TargetNodeSize,
+
+    // Upper bound for the available space for slots. This is largest for leaf
+    // nodes, which have overhead of at least a pointer + 4 bytes (for storing
+    // 3 field_types and an enum).
+    kNodeSlotSpace = TargetNodeSize - /*minimum overhead=*/(sizeof(void *) + 4),
+  };
+
+  // This is an integral type large enough to hold as many slots as will fit a
+  // node of TargetNodeSize bytes.
+  using node_count_type =
+      absl::conditional_t<(kNodeSlotSpace / sizeof(slot_type) >
+                           (std::numeric_limits<uint8_t>::max)()),
+                          uint16_t, uint8_t>;  // NOLINT
+};
+
+// An adapter class that converts a lower-bound compare into an upper-bound
+// compare. Note: there is no need to make a version of this adapter specialized
+// for key-compare-to functors because the upper-bound (the first value greater
+// than the input) is never an exact match.
+template <typename Compare>
+struct upper_bound_adapter {
+  explicit upper_bound_adapter(const Compare &c) : comp(c) {}
+  template <typename K1, typename K2>
+  bool operator()(const K1 &a, const K2 &b) const {
+    // Returns true when a is not greater than b.
+    return !compare_internal::compare_result_as_less_than(comp(b, a));
+  }
+
+ private:
+  Compare comp;
+};
+
+enum class MatchKind : uint8_t { kEq, kNe };
+
+template <typename V, bool IsCompareTo>
+struct SearchResult {
+  V value;
+  MatchKind match;
+
+  static constexpr bool HasMatch() { return true; }
+  bool IsEq() const { return match == MatchKind::kEq; }
+};
+
+// When we don't use CompareTo, `match` is not present.
+// This ensures that callers can't use it accidentally when it provides no
+// useful information.
+template <typename V>
+struct SearchResult<V, false> {
+  SearchResult() = default;
+  explicit SearchResult(V v) : value(v) {}
+  SearchResult(V v, MatchKind /*match*/) : value(v) {}
+
+  V value;
+
+  static constexpr bool HasMatch() { return false; }
+  static constexpr bool IsEq() { return false; }
+};
+
+// A node in the btree holding. The same node type is used for both internal
+// and leaf nodes in the btree, though the nodes are allocated in such a way
+// that the children array is only valid in internal nodes.
+template <typename Params>
+class btree_node {
+  using is_key_compare_to = typename Params::is_key_compare_to;
+  using field_type = typename Params::node_count_type;
+  using allocator_type = typename Params::allocator_type;
+  using slot_type = typename Params::slot_type;
+  using original_key_compare = typename Params::original_key_compare;
+
+ public:
+  using params_type = Params;
+  using key_type = typename Params::key_type;
+  using value_type = typename Params::value_type;
+  using pointer = typename Params::pointer;
+  using const_pointer = typename Params::const_pointer;
+  using reference = typename Params::reference;
+  using const_reference = typename Params::const_reference;
+  using key_compare = typename Params::key_compare;
+  using size_type = typename Params::size_type;
+  using difference_type = typename Params::difference_type;
+
+  // Btree decides whether to use linear node search as follows:
+  //   - If the comparator expresses a preference, use that.
+  //   - If the key expresses a preference, use that.
+  //   - If the key is arithmetic and the comparator is std::less or
+  //     std::greater, choose linear.
+  //   - Otherwise, choose binary.
+  // TODO(ezb): Might make sense to add condition(s) based on node-size.
+  using use_linear_search = std::integral_constant<
+      bool, has_linear_node_search_preference<original_key_compare>::value
+                ? prefers_linear_node_search<original_key_compare>::value
+            : has_linear_node_search_preference<key_type>::value
+                ? prefers_linear_node_search<key_type>::value
+                : std::is_arithmetic<key_type>::value &&
+                      (std::is_same<std::less<key_type>,
+                                    original_key_compare>::value ||
+                       std::is_same<std::greater<key_type>,
+                                    original_key_compare>::value)>;
+
+  // This class is organized by absl::container_internal::Layout as if it had
+  // the following structure:
+  //   // A pointer to the node's parent.
+  //   btree_node *parent;
+  //
+  //   // When ABSL_BTREE_ENABLE_GENERATIONS is defined, we also have a
+  //   // generation integer in order to check that when iterators are
+  //   // used, they haven't been invalidated already. Only the generation on
+  //   // the root is used, but we have one on each node because whether a node
+  //   // is root or not can change.
+  //   uint32_t generation;
+  //
+  //   // The position of the node in the node's parent.
+  //   field_type position;
+  //   // The index of the first populated value in `values`.
+  //   // TODO(ezb): right now, `start` is always 0. Update insertion/merge
+  //   // logic to allow for floating storage within nodes.
+  //   field_type start;
+  //   // The index after the last populated value in `values`. Currently, this
+  //   // is the same as the count of values.
+  //   field_type finish;
+  //   // The maximum number of values the node can hold. This is an integer in
+  //   // [1, kNodeSlots] for root leaf nodes, kNodeSlots for non-root leaf
+  //   // nodes, and kInternalNodeMaxCount (as a sentinel value) for internal
+  //   // nodes (even though there are still kNodeSlots values in the node).
+  //   // TODO(ezb): make max_count use only 4 bits and record log2(capacity)
+  //   // to free extra bits for is_root, etc.
+  //   field_type max_count;
+  //
+  //   // The array of values. The capacity is `max_count` for leaf nodes and
+  //   // kNodeSlots for internal nodes. Only the values in
+  //   // [start, finish) have been initialized and are valid.
+  //   slot_type values[max_count];
+  //
+  //   // The array of child pointers. The keys in children[i] are all less
+  //   // than key(i). The keys in children[i + 1] are all greater than key(i).
+  //   // There are 0 children for leaf nodes and kNodeSlots + 1 children for
+  //   // internal nodes.
+  //   btree_node *children[kNodeSlots + 1];
+  //
+  // This class is only constructed by EmptyNodeType. Normally, pointers to the
+  // layout above are allocated, cast to btree_node*, and de-allocated within
+  // the btree implementation.
+  ~btree_node() = default;
+  btree_node(btree_node const &) = delete;
+  btree_node &operator=(btree_node const &) = delete;
+
+ protected:
+  btree_node() = default;
+
+ private:
+  using layout_type =
+      absl::container_internal::Layout<btree_node *, uint32_t, field_type,
+                                       slot_type, btree_node *>;
+  using leaf_layout_type = typename layout_type::template WithStaticSizes<
+      /*parent*/ 1,
+      /*generation*/ BtreeGenerationsEnabled() ? 1 : 0,
+      /*position, start, finish, max_count*/ 4>;
+  constexpr static size_type SizeWithNSlots(size_type n) {
+    return leaf_layout_type(/*slots*/ n, /*children*/ 0).AllocSize();
+  }
+  // A lower bound for the overhead of fields other than slots in a leaf node.
+  constexpr static size_type MinimumOverhead() {
+    return SizeWithNSlots(1) - sizeof(slot_type);
+  }
+
+  // Compute how many values we can fit onto a leaf node taking into account
+  // padding.
+  constexpr static size_type NodeTargetSlots(const size_type begin,
+                                             const size_type end) {
+    return begin == end ? begin
+           : SizeWithNSlots((begin + end) / 2 + 1) >
+                   params_type::kTargetNodeSize
+               ? NodeTargetSlots(begin, (begin + end) / 2)
+               : NodeTargetSlots((begin + end) / 2 + 1, end);
+  }
+
+  constexpr static size_type kTargetNodeSize = params_type::kTargetNodeSize;
+  constexpr static size_type kNodeTargetSlots =
+      NodeTargetSlots(0, kTargetNodeSize);
+
+  // We need a minimum of 3 slots per internal node in order to perform
+  // splitting (1 value for the two nodes involved in the split and 1 value
+  // propagated to the parent as the delimiter for the split). For performance
+  // reasons, we don't allow 3 slots-per-node due to bad worst case occupancy of
+  // 1/3 (for a node, not a b-tree).
+  constexpr static size_type kMinNodeSlots = 4;
+
+  constexpr static size_type kNodeSlots =
+      kNodeTargetSlots >= kMinNodeSlots ? kNodeTargetSlots : kMinNodeSlots;
+
+  using internal_layout_type = typename layout_type::template WithStaticSizes<
+      /*parent*/ 1,
+      /*generation*/ BtreeGenerationsEnabled() ? 1 : 0,
+      /*position, start, finish, max_count*/ 4, /*slots*/ kNodeSlots,
+      /*children*/ kNodeSlots + 1>;
+
+  // The node is internal (i.e. is not a leaf node) if and only if `max_count`
+  // has this value.
+  constexpr static field_type kInternalNodeMaxCount = 0;
+
+  // Leaves can have less than kNodeSlots values.
+  constexpr static leaf_layout_type LeafLayout(
+      const size_type slot_count = kNodeSlots) {
+    return leaf_layout_type(slot_count, 0);
+  }
+  constexpr static auto InternalLayout() { return internal_layout_type(); }
+  constexpr static size_type LeafSize(const size_type slot_count = kNodeSlots) {
+    return LeafLayout(slot_count).AllocSize();
+  }
+  constexpr static size_type InternalSize() {
+    return InternalLayout().AllocSize();
+  }
+
+  constexpr static size_type Alignment() {
+    static_assert(LeafLayout(1).Alignment() == InternalLayout().Alignment(),
+                  "Alignment of all nodes must be equal.");
+    return InternalLayout().Alignment();
+  }
+
+  // N is the index of the type in the Layout definition.
+  // ElementType<N> is the Nth type in the Layout definition.
+  template <size_type N>
+  inline typename layout_type::template ElementType<N> *GetField() {
+    // We assert that we don't read from values that aren't there.
+    assert(N < 4 || is_internal());
+    return InternalLayout().template Pointer<N>(reinterpret_cast<char *>(this));
+  }
+  template <size_type N>
+  inline const typename layout_type::template ElementType<N> *GetField() const {
+    assert(N < 4 || is_internal());
+    return InternalLayout().template Pointer<N>(
+        reinterpret_cast<const char *>(this));
+  }
+  void set_parent(btree_node *p) { *GetField<0>() = p; }
+  field_type &mutable_finish() { return GetField<2>()[2]; }
+  slot_type *slot(size_type i) { return &GetField<3>()[i]; }
+  slot_type *start_slot() { return slot(start()); }
+  slot_type *finish_slot() { return slot(finish()); }
+  const slot_type *slot(size_type i) const { return &GetField<3>()[i]; }
+  void set_position(field_type v) { GetField<2>()[0] = v; }
+  void set_start(field_type v) { GetField<2>()[1] = v; }
+  void set_finish(field_type v) { GetField<2>()[2] = v; }
+  // This method is only called by the node init methods.
+  void set_max_count(field_type v) { GetField<2>()[3] = v; }
+
+ public:
+  // Whether this is a leaf node or not. This value doesn't change after the
+  // node is created.
+  bool is_leaf() const { return GetField<2>()[3] != kInternalNodeMaxCount; }
+  // Whether this is an internal node or not. This value doesn't change after
+  // the node is created.
+  bool is_internal() const { return !is_leaf(); }
+
+  // Getter for the position of this node in its parent.
+  field_type position() const { return GetField<2>()[0]; }
+
+  // Getter for the offset of the first value in the `values` array.
+  field_type start() const {
+    // TODO(ezb): when floating storage is implemented, return GetField<2>()[1];
+    assert(GetField<2>()[1] == 0);
+    return 0;
+  }
+
+  // Getter for the offset after the last value in the `values` array.
+  field_type finish() const { return GetField<2>()[2]; }
+
+  // Getters for the number of values stored in this node.
+  field_type count() const {
+    assert(finish() >= start());
+    return finish() - start();
+  }
+  field_type max_count() const {
+    // Internal nodes have max_count==kInternalNodeMaxCount.
+    // Leaf nodes have max_count in [1, kNodeSlots].
+    const field_type max_count = GetField<2>()[3];
+    return max_count == field_type{kInternalNodeMaxCount}
+               ? field_type{kNodeSlots}
+               : max_count;
+  }
+
+  // Getter for the parent of this node.
+  btree_node *parent() const { return *GetField<0>(); }
+  // Getter for whether the node is the root of the tree. The parent of the
+  // root of the tree is the leftmost node in the tree which is guaranteed to
+  // be a leaf.
+  bool is_root() const { return parent()->is_leaf(); }
+  void make_root() {
+    assert(parent()->is_root());
+    set_generation(parent()->generation());
+    set_parent(parent()->parent());
+  }
+
+  // Gets the root node's generation integer, which is the one used by the tree.
+  uint32_t *get_root_generation() const {
+    assert(BtreeGenerationsEnabled());
+    const btree_node *curr = this;
+    for (; !curr->is_root(); curr = curr->parent()) continue;
+    return const_cast<uint32_t *>(&curr->GetField<1>()[0]);
+  }
+
+  // Returns the generation for iterator validation.
+  uint32_t generation() const {
+    return BtreeGenerationsEnabled() ? *get_root_generation() : 0;
+  }
+  // Updates generation. Should only be called on a root node or during node
+  // initialization.
+  void set_generation(uint32_t generation) {
+    if (BtreeGenerationsEnabled()) GetField<1>()[0] = generation;
+  }
+  // Updates the generation. We do this whenever the node is mutated.
+  void next_generation() {
+    if (BtreeGenerationsEnabled()) ++*get_root_generation();
+  }
+
+  // Getters for the key/value at position i in the node.
+  const key_type &key(size_type i) const { return params_type::key(slot(i)); }
+  reference value(size_type i) { return params_type::element(slot(i)); }
+  const_reference value(size_type i) const {
+    return params_type::element(slot(i));
+  }
+
+  // Getters/setter for the child at position i in the node.
+  btree_node *child(field_type i) const { return GetField<4>()[i]; }
+  btree_node *start_child() const { return child(start()); }
+  btree_node *&mutable_child(field_type i) { return GetField<4>()[i]; }
+  void clear_child(field_type i) {
+    absl::container_internal::SanitizerPoisonObject(&mutable_child(i));
+  }
+  void set_child_noupdate_position(field_type i, btree_node *c) {
+    absl::container_internal::SanitizerUnpoisonObject(&mutable_child(i));
+    mutable_child(i) = c;
+  }
+  void set_child(field_type i, btree_node *c) {
+    set_child_noupdate_position(i, c);
+    c->set_position(i);
+  }
+  void init_child(field_type i, btree_node *c) {
+    set_child(i, c);
+    c->set_parent(this);
+  }
+
+  // Returns the position of the first value whose key is not less than k.
+  template <typename K>
+  SearchResult<size_type, is_key_compare_to::value> lower_bound(
+      const K &k, const key_compare &comp) const {
+    return use_linear_search::value ? linear_search(k, comp)
+                                    : binary_search(k, comp);
+  }
+  // Returns the position of the first value whose key is greater than k.
+  template <typename K>
+  size_type upper_bound(const K &k, const key_compare &comp) const {
+    auto upper_compare = upper_bound_adapter<key_compare>(comp);
+    return use_linear_search::value ? linear_search(k, upper_compare).value
+                                    : binary_search(k, upper_compare).value;
+  }
+
+  template <typename K, typename Compare>
+  SearchResult<size_type, btree_is_key_compare_to<Compare, key_type>::value>
+  linear_search(const K &k, const Compare &comp) const {
+    return linear_search_impl(k, start(), finish(), comp,
+                              btree_is_key_compare_to<Compare, key_type>());
+  }
+
+  template <typename K, typename Compare>
+  SearchResult<size_type, btree_is_key_compare_to<Compare, key_type>::value>
+  binary_search(const K &k, const Compare &comp) const {
+    return binary_search_impl(k, start(), finish(), comp,
+                              btree_is_key_compare_to<Compare, key_type>());
+  }
+
+  // Returns the position of the first value whose key is not less than k using
+  // linear search performed using plain compare.
+  template <typename K, typename Compare>
+  SearchResult<size_type, false> linear_search_impl(
+      const K &k, size_type s, const size_type e, const Compare &comp,
+      std::false_type /* IsCompareTo */) const {
+    while (s < e) {
+      if (!comp(key(s), k)) {
+        break;
+      }
+      ++s;
+    }
+    return SearchResult<size_type, false>{s};
+  }
+
+  // Returns the position of the first value whose key is not less than k using
+  // linear search performed using compare-to.
+  template <typename K, typename Compare>
+  SearchResult<size_type, true> linear_search_impl(
+      const K &k, size_type s, const size_type e, const Compare &comp,
+      std::true_type /* IsCompareTo */) const {
+    while (s < e) {
+      const absl::weak_ordering c = comp(key(s), k);
+      if (c == 0) {
+        return {s, MatchKind::kEq};
+      } else if (c > 0) {
+        break;
+      }
+      ++s;
+    }
+    return {s, MatchKind::kNe};
+  }
+
+  // Returns the position of the first value whose key is not less than k using
+  // binary search performed using plain compare.
+  template <typename K, typename Compare>
+  SearchResult<size_type, false> binary_search_impl(
+      const K &k, size_type s, size_type e, const Compare &comp,
+      std::false_type /* IsCompareTo */) const {
+    while (s != e) {
+      const size_type mid = (s + e) >> 1;
+      if (comp(key(mid), k)) {
+        s = mid + 1;
+      } else {
+        e = mid;
+      }
+    }
+    return SearchResult<size_type, false>{s};
+  }
+
+  // Returns the position of the first value whose key is not less than k using
+  // binary search performed using compare-to.
+  template <typename K, typename CompareTo>
+  SearchResult<size_type, true> binary_search_impl(
+      const K &k, size_type s, size_type e, const CompareTo &comp,
+      std::true_type /* IsCompareTo */) const {
+    if (params_type::template can_have_multiple_equivalent_keys<K>()) {
+      MatchKind exact_match = MatchKind::kNe;
+      while (s != e) {
+        const size_type mid = (s + e) >> 1;
+        const absl::weak_ordering c = comp(key(mid), k);
+        if (c < 0) {
+          s = mid + 1;
+        } else {
+          e = mid;
+          if (c == 0) {
+            // Need to return the first value whose key is not less than k,
+            // which requires continuing the binary search if there could be
+            // multiple equivalent keys.
+            exact_match = MatchKind::kEq;
+          }
+        }
+      }
+      return {s, exact_match};
+    } else {  // Can't have multiple equivalent keys.
+      while (s != e) {
+        const size_type mid = (s + e) >> 1;
+        const absl::weak_ordering c = comp(key(mid), k);
+        if (c < 0) {
+          s = mid + 1;
+        } else if (c > 0) {
+          e = mid;
+        } else {
+          return {mid, MatchKind::kEq};
+        }
+      }
+      return {s, MatchKind::kNe};
+    }
+  }
+
+  // Returns whether key i is ordered correctly with respect to the other keys
+  // in the node. The motivation here is to detect comparators that violate
+  // transitivity. Note: we only do comparisons of keys on this node rather than
+  // the whole tree so that this is constant time.
+  template <typename Compare>
+  bool is_ordered_correctly(field_type i, const Compare &comp) const {
+    if (std::is_base_of<BtreeTestOnlyCheckedCompareOptOutBase,
+                        Compare>::value ||
+        params_type::kIsKeyCompareStringAdapted) {
+      return true;
+    }
+
+    const auto compare = [&](field_type a, field_type b) {
+      const absl::weak_ordering cmp =
+          compare_internal::do_three_way_comparison(comp, key(a), key(b));
+      return cmp < 0 ? -1 : cmp > 0 ? 1 : 0;
+    };
+    int cmp = -1;
+    constexpr bool kCanHaveEquivKeys =
+        params_type::template can_have_multiple_equivalent_keys<key_type>();
+    for (field_type j = start(); j < finish(); ++j) {
+      if (j == i) {
+        if (cmp > 0) return false;
+        continue;
+      }
+      int new_cmp = compare(j, i);
+      if (new_cmp < cmp || (!kCanHaveEquivKeys && new_cmp == 0)) return false;
+      cmp = new_cmp;
+    }
+    return true;
+  }
+
+  // Emplaces a value at position i, shifting all existing values and
+  // children at positions >= i to the right by 1.
+  template <typename... Args>
+  void emplace_value(field_type i, allocator_type *alloc, Args &&...args);
+
+  // Removes the values at positions [i, i + to_erase), shifting all existing
+  // values and children after that range to the left by to_erase. Clears all
+  // children between [i, i + to_erase).
+  void remove_values(field_type i, field_type to_erase, allocator_type *alloc);
+
+  // Rebalances a node with its right sibling.
+  void rebalance_right_to_left(field_type to_move, btree_node *right,
+                               allocator_type *alloc);
+  void rebalance_left_to_right(field_type to_move, btree_node *right,
+                               allocator_type *alloc);
+
+  // Splits a node, moving a portion of the node's values to its right sibling.
+  void split(int insert_position, btree_node *dest, allocator_type *alloc);
+
+  // Merges a node with its right sibling, moving all of the values and the
+  // delimiting key in the parent node onto itself, and deleting the src node.
+  void merge(btree_node *src, allocator_type *alloc);
+
+  // Node allocation/deletion routines.
+  void init_leaf(field_type position, field_type max_count,
+                 btree_node *parent) {
+    set_generation(0);
+    set_parent(parent);
+    set_position(position);
+    set_start(0);
+    set_finish(0);
+    set_max_count(max_count);
+    absl::container_internal::SanitizerPoisonMemoryRegion(
+        start_slot(), max_count * sizeof(slot_type));
+  }
+  void init_internal(field_type position, btree_node *parent) {
+    init_leaf(position, kNodeSlots, parent);
+    // Set `max_count` to a sentinel value to indicate that this node is
+    // internal.
+    set_max_count(kInternalNodeMaxCount);
+    absl::container_internal::SanitizerPoisonMemoryRegion(
+        &mutable_child(start()), (kNodeSlots + 1) * sizeof(btree_node *));
+  }
+
+  static void deallocate(const size_type size, btree_node *node,
+                         allocator_type *alloc) {
+    absl::container_internal::SanitizerUnpoisonMemoryRegion(node, size);
+    absl::container_internal::Deallocate<Alignment()>(alloc, node, size);
+  }
+
+  // Deletes a node and all of its children.
+  static void clear_and_delete(btree_node *node, allocator_type *alloc);
+
+ private:
+  template <typename... Args>
+  void value_init(const field_type i, allocator_type *alloc, Args &&...args) {
+    next_generation();
+    absl::container_internal::SanitizerUnpoisonObject(slot(i));
+    params_type::construct(alloc, slot(i), std::forward<Args>(args)...);
+  }
+  void value_destroy(const field_type i, allocator_type *alloc) {
+    next_generation();
+    params_type::destroy(alloc, slot(i));
+    absl::container_internal::SanitizerPoisonObject(slot(i));
+  }
+  void value_destroy_n(const field_type i, const field_type n,
+                       allocator_type *alloc) {
+    next_generation();
+    for (slot_type *s = slot(i), *end = slot(i + n); s != end; ++s) {
+      params_type::destroy(alloc, s);
+      absl::container_internal::SanitizerPoisonObject(s);
+    }
+  }
+
+  static void transfer(slot_type *dest, slot_type *src, allocator_type *alloc) {
+    absl::container_internal::SanitizerUnpoisonObject(dest);
+    params_type::transfer(alloc, dest, src);
+    absl::container_internal::SanitizerPoisonObject(src);
+  }
+
+  // Transfers value from slot `src_i` in `src_node` to slot `dest_i` in `this`.
+  void transfer(const size_type dest_i, const size_type src_i,
+                btree_node *src_node, allocator_type *alloc) {
+    next_generation();
+    transfer(slot(dest_i), src_node->slot(src_i), alloc);
+  }
+
+  // Transfers `n` values starting at value `src_i` in `src_node` into the
+  // values starting at value `dest_i` in `this`.
+  void transfer_n(const size_type n, const size_type dest_i,
+                  const size_type src_i, btree_node *src_node,
+                  allocator_type *alloc) {
+    next_generation();
+    for (slot_type *src = src_node->slot(src_i), *end = src + n,
+                   *dest = slot(dest_i);
+         src != end; ++src, ++dest) {
+      transfer(dest, src, alloc);
+    }
+  }
+
+  // Same as above, except that we start at the end and work our way to the
+  // beginning.
+  void transfer_n_backward(const size_type n, const size_type dest_i,
+                           const size_type src_i, btree_node *src_node,
+                           allocator_type *alloc) {
+    next_generation();
+    for (slot_type *src = src_node->slot(src_i + n), *end = src - n,
+                   *dest = slot(dest_i + n);
+         src != end; --src, --dest) {
+      // If we modified the loop index calculations above to avoid the -1s here,
+      // it would result in UB in the computation of `end` (and possibly `src`
+      // as well, if n == 0), since slot() is effectively an array index and it
+      // is UB to compute the address of any out-of-bounds array element except
+      // for one-past-the-end.
+      transfer(dest - 1, src - 1, alloc);
+    }
+  }
+
+  template <typename P>
+  friend class btree;
+  template <typename N, typename R, typename P>
+  friend class btree_iterator;
+  friend class BtreeNodePeer;
+  friend struct btree_access;
+};
+
+template <typename Node>
+bool AreNodesFromSameContainer(const Node *node_a, const Node *node_b) {
+  // If either node is null, then give up on checking whether they're from the
+  // same container. (If exactly one is null, then we'll trigger the
+  // default-constructed assert in Equals.)
+  if (node_a == nullptr || node_b == nullptr) return true;
+  while (!node_a->is_root()) node_a = node_a->parent();
+  while (!node_b->is_root()) node_b = node_b->parent();
+  return node_a == node_b;
+}
+
+class btree_iterator_generation_info_enabled {
+ public:
+  explicit btree_iterator_generation_info_enabled(uint32_t g)
+      : generation_(g) {}
+
+  // Updates the generation. For use internally right before we return an
+  // iterator to the user.
+  template <typename Node>
+  void update_generation(const Node *node) {
+    if (node != nullptr) generation_ = node->generation();
+  }
+  uint32_t generation() const { return generation_; }
+
+  template <typename Node>
+  void assert_valid_generation(const Node *node) const {
+    if (node != nullptr && node->generation() != generation_) {
+      ABSL_INTERNAL_LOG(
+          FATAL,
+          "Attempting to use an invalidated iterator. The corresponding b-tree "
+          "container has been mutated since this iterator was constructed.");
+    }
+  }
+
+ private:
+  // Used to check that the iterator hasn't been invalidated.
+  uint32_t generation_;
+};
+
+class btree_iterator_generation_info_disabled {
+ public:
+  explicit btree_iterator_generation_info_disabled(uint32_t) {}
+  static void update_generation(const void *) {}
+  static uint32_t generation() { return 0; }
+  static void assert_valid_generation(const void *) {}
+};
+
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+using btree_iterator_generation_info = btree_iterator_generation_info_enabled;
+#else
+using btree_iterator_generation_info = btree_iterator_generation_info_disabled;
+#endif
+
+template <typename Node, typename Reference, typename Pointer>
+class btree_iterator : private btree_iterator_generation_info {
+  using field_type = typename Node::field_type;
+  using key_type = typename Node::key_type;
+  using size_type = typename Node::size_type;
+  using params_type = typename Node::params_type;
+  using is_map_container = typename params_type::is_map_container;
+
+  using node_type = Node;
+  using normal_node = typename std::remove_const<Node>::type;
+  using const_node = const Node;
+  using normal_pointer = typename params_type::pointer;
+  using normal_reference = typename params_type::reference;
+  using const_pointer = typename params_type::const_pointer;
+  using const_reference = typename params_type::const_reference;
+  using slot_type = typename params_type::slot_type;
+
+  // In sets, all iterators are const.
+  using iterator = absl::conditional_t<
+      is_map_container::value,
+      btree_iterator<normal_node, normal_reference, normal_pointer>,
+      btree_iterator<normal_node, const_reference, const_pointer>>;
+  using const_iterator =
+      btree_iterator<const_node, const_reference, const_pointer>;
+
+ public:
+  // These aliases are public for std::iterator_traits.
+  using difference_type = typename Node::difference_type;
+  using value_type = typename params_type::value_type;
+  using pointer = Pointer;
+  using reference = Reference;
+  using iterator_category = std::bidirectional_iterator_tag;
+
+  btree_iterator() : btree_iterator(nullptr, -1) {}
+  explicit btree_iterator(Node *n) : btree_iterator(n, n->start()) {}
+  btree_iterator(Node *n, int p)
+      : btree_iterator_generation_info(n != nullptr ? n->generation()
+                                                    : ~uint32_t{}),
+        node_(n),
+        position_(p) {}
+
+  // NOTE: this SFINAE allows for implicit conversions from iterator to
+  // const_iterator, but it specifically avoids hiding the copy constructor so
+  // that the trivial one will be used when possible.
+  template <typename N, typename R, typename P,
+            absl::enable_if_t<
+                std::is_same<btree_iterator<N, R, P>, iterator>::value &&
+                    std::is_same<btree_iterator, const_iterator>::value,
+                int> = 0>
+  btree_iterator(const btree_iterator<N, R, P> other)  // NOLINT
+      : btree_iterator_generation_info(other),
+        node_(other.node_),
+        position_(other.position_) {}
+
+  bool operator==(const iterator &other) const {
+    return Equals(other);
+  }
+  bool operator==(const const_iterator &other) const {
+    return Equals(other);
+  }
+  bool operator!=(const iterator &other) const {
+    return !Equals(other);
+  }
+  bool operator!=(const const_iterator &other) const {
+    return !Equals(other);
+  }
+
+  // Returns n such that n calls to ++other yields *this.
+  // Precondition: n exists.
+  difference_type operator-(const_iterator other) const {
+    if (node_ == other.node_) {
+      if (node_->is_leaf()) return position_ - other.position_;
+      if (position_ == other.position_) return 0;
+    }
+    return distance_slow(other);
+  }
+
+  // Accessors for the key/value the iterator is pointing at.
+  reference operator*() const {
+    ABSL_HARDENING_ASSERT(node_ != nullptr);
+    assert_valid_generation(node_);
+    ABSL_HARDENING_ASSERT(position_ >= node_->start());
+    if (position_ >= node_->finish()) {
+      ABSL_HARDENING_ASSERT(!IsEndIterator() && "Dereferencing end() iterator");
+      ABSL_HARDENING_ASSERT(position_ < node_->finish());
+    }
+    return node_->value(static_cast<field_type>(position_));
+  }
+  pointer operator->() const { return &operator*(); }
+
+  btree_iterator &operator++() {
+    increment();
+    return *this;
+  }
+  btree_iterator &operator--() {
+    decrement();
+    return *this;
+  }
+  btree_iterator operator++(int) {
+    btree_iterator tmp = *this;
+    ++*this;
+    return tmp;
+  }
+  btree_iterator operator--(int) {
+    btree_iterator tmp = *this;
+    --*this;
+    return tmp;
+  }
+
+ private:
+  friend iterator;
+  friend const_iterator;
+  template <typename Params>
+  friend class btree;
+  template <typename Tree>
+  friend class btree_container;
+  template <typename Tree>
+  friend class btree_set_container;
+  template <typename Tree>
+  friend class btree_map_container;
+  template <typename Tree>
+  friend class btree_multiset_container;
+  template <typename TreeType, typename CheckerType>
+  friend class base_checker;
+  friend struct btree_access;
+
+  // This SFINAE allows explicit conversions from const_iterator to
+  // iterator, but also avoids hiding the copy constructor.
+  // NOTE: the const_cast is safe because this constructor is only called by
+  // non-const methods and the container owns the nodes.
+  template <typename N, typename R, typename P,
+            absl::enable_if_t<
+                std::is_same<btree_iterator<N, R, P>, const_iterator>::value &&
+                    std::is_same<btree_iterator, iterator>::value,
+                int> = 0>
+  explicit btree_iterator(const btree_iterator<N, R, P> other)
+      : btree_iterator_generation_info(other.generation()),
+        node_(const_cast<node_type *>(other.node_)),
+        position_(other.position_) {}
+
+  bool Equals(const const_iterator other) const {
+    ABSL_HARDENING_ASSERT(((node_ == nullptr && other.node_ == nullptr) ||
+                           (node_ != nullptr && other.node_ != nullptr)) &&
+                          "Comparing default-constructed iterator with "
+                          "non-default-constructed iterator.");
+    // Note: we use assert instead of ABSL_HARDENING_ASSERT here because this
+    // changes the complexity of Equals from O(1) to O(log(N) + log(M)) where
+    // N/M are sizes of the containers containing node_/other.node_.
+    assert(AreNodesFromSameContainer(node_, other.node_) &&
+           "Comparing iterators from different containers.");
+    assert_valid_generation(node_);
+    other.assert_valid_generation(other.node_);
+    return node_ == other.node_ && position_ == other.position_;
+  }
+
+  bool IsEndIterator() const {
+    if (position_ != node_->finish()) return false;
+    node_type *node = node_;
+    while (!node->is_root()) {
+      if (node->position() != node->parent()->finish()) return false;
+      node = node->parent();
+    }
+    return true;
+  }
+
+  // Returns n such that n calls to ++other yields *this.
+  // Precondition: n exists && (this->node_ != other.node_ ||
+  // !this->node_->is_leaf() || this->position_ != other.position_).
+  difference_type distance_slow(const_iterator other) const;
+
+  // Increment/decrement the iterator.
+  void increment() {
+    assert_valid_generation(node_);
+    if (node_->is_leaf() && ++position_ < node_->finish()) {
+      return;
+    }
+    increment_slow();
+  }
+  void increment_slow();
+
+  void decrement() {
+    assert_valid_generation(node_);
+    if (node_->is_leaf() && --position_ >= node_->start()) {
+      return;
+    }
+    decrement_slow();
+  }
+  void decrement_slow();
+
+  const key_type &key() const {
+    return node_->key(static_cast<size_type>(position_));
+  }
+  decltype(std::declval<Node *>()->slot(0)) slot() {
+    return node_->slot(static_cast<size_type>(position_));
+  }
+
+  void update_generation() {
+    btree_iterator_generation_info::update_generation(node_);
+  }
+
+  // The node in the tree the iterator is pointing at.
+  Node *node_;
+  // The position within the node of the tree the iterator is pointing at.
+  // NOTE: this is an int rather than a field_type because iterators can point
+  // to invalid positions (such as -1) in certain circumstances.
+  int position_;
+};
+
+template <typename Params>
+class btree {
+  using node_type = btree_node<Params>;
+  using is_key_compare_to = typename Params::is_key_compare_to;
+  using field_type = typename node_type::field_type;
+
+  // We use a static empty node for the root/leftmost/rightmost of empty btrees
+  // in order to avoid branching in begin()/end().
+  struct EmptyNodeType : node_type {
+    using field_type = typename node_type::field_type;
+    node_type *parent;
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+    uint32_t generation = 0;
+#endif
+    field_type position = 0;
+    field_type start = 0;
+    field_type finish = 0;
+    // max_count must be != kInternalNodeMaxCount (so that this node is regarded
+    // as a leaf node). max_count() is never called when the tree is empty.
+    field_type max_count = node_type::kInternalNodeMaxCount + 1;
+
+    constexpr EmptyNodeType() : parent(this) {}
+  };
+
+  static node_type *EmptyNode() {
+    alignas(node_type::Alignment()) static constexpr EmptyNodeType empty_node;
+    return const_cast<EmptyNodeType *>(&empty_node);
+  }
+
+  enum : uint32_t {
+    kNodeSlots = node_type::kNodeSlots,
+    kMinNodeValues = kNodeSlots / 2,
+  };
+
+  struct node_stats {
+    using size_type = typename Params::size_type;
+
+    node_stats(size_type l, size_type i) : leaf_nodes(l), internal_nodes(i) {}
+
+    node_stats &operator+=(const node_stats &other) {
+      leaf_nodes += other.leaf_nodes;
+      internal_nodes += other.internal_nodes;
+      return *this;
+    }
+
+    size_type leaf_nodes;
+    size_type internal_nodes;
+  };
+
+ public:
+  using key_type = typename Params::key_type;
+  using value_type = typename Params::value_type;
+  using size_type = typename Params::size_type;
+  using difference_type = typename Params::difference_type;
+  using key_compare = typename Params::key_compare;
+  using original_key_compare = typename Params::original_key_compare;
+  using value_compare = typename Params::value_compare;
+  using allocator_type = typename Params::allocator_type;
+  using reference = typename Params::reference;
+  using const_reference = typename Params::const_reference;
+  using pointer = typename Params::pointer;
+  using const_pointer = typename Params::const_pointer;
+  using iterator =
+      typename btree_iterator<node_type, reference, pointer>::iterator;
+  using const_iterator = typename iterator::const_iterator;
+  using reverse_iterator = std::reverse_iterator<iterator>;
+  using const_reverse_iterator = std::reverse_iterator<const_iterator>;
+  using node_handle_type = node_handle<Params, Params, allocator_type>;
+
+  // Internal types made public for use by btree_container types.
+  using params_type = Params;
+  using slot_type = typename Params::slot_type;
+
+ private:
+  // Copies or moves (depending on the template parameter) the values in
+  // other into this btree in their order in other. This btree must be empty
+  // before this method is called. This method is used in copy construction,
+  // copy assignment, and move assignment.
+  template <typename Btree>
+  void copy_or_move_values_in_order(Btree &other);
+
+  // Validates that various assumptions/requirements are true at compile time.
+  constexpr static bool static_assert_validation();
+
+ public:
+  btree(const key_compare &comp, const allocator_type &alloc)
+      : root_(EmptyNode()), rightmost_(comp, alloc, EmptyNode()), size_(0) {}
+
+  btree(const btree &other) : btree(other, other.allocator()) {}
+  btree(const btree &other, const allocator_type &alloc)
+      : btree(other.key_comp(), alloc) {
+    copy_or_move_values_in_order(other);
+  }
+  btree(btree &&other) noexcept
+      : root_(std::exchange(other.root_, EmptyNode())),
+        rightmost_(std::move(other.rightmost_)),
+        size_(std::exchange(other.size_, 0u)) {
+    other.mutable_rightmost() = EmptyNode();
+  }
+  btree(btree &&other, const allocator_type &alloc)
+      : btree(other.key_comp(), alloc) {
+    if (alloc == other.allocator()) {
+      swap(other);
+    } else {
+      // Move values from `other` one at a time when allocators are different.
+      copy_or_move_values_in_order(other);
+    }
+  }
+
+  ~btree() {
+    // Put static_asserts in destructor to avoid triggering them before the type
+    // is complete.
+    static_assert(static_assert_validation(), "This call must be elided.");
+    clear();
+  }
+
+  // Assign the contents of other to *this.
+  btree &operator=(const btree &other);
+  btree &operator=(btree &&other) noexcept;
+
+  iterator begin() { return iterator(leftmost()); }
+  const_iterator begin() const { return const_iterator(leftmost()); }
+  iterator end() { return iterator(rightmost(), rightmost()->finish()); }
+  const_iterator end() const {
+    return const_iterator(rightmost(), rightmost()->finish());
+  }
+  reverse_iterator rbegin() { return reverse_iterator(end()); }
+  const_reverse_iterator rbegin() const {
+    return const_reverse_iterator(end());
+  }
+  reverse_iterator rend() { return reverse_iterator(begin()); }
+  const_reverse_iterator rend() const {
+    return const_reverse_iterator(begin());
+  }
+
+  // Finds the first element whose key is not less than `key`.
+  template <typename K>
+  iterator lower_bound(const K &key) {
+    return internal_end(internal_lower_bound(key).value);
+  }
+  template <typename K>
+  const_iterator lower_bound(const K &key) const {
+    return internal_end(internal_lower_bound(key).value);
+  }
+
+  // Finds the first element whose key is not less than `key` and also returns
+  // whether that element is equal to `key`.
+  template <typename K>
+  std::pair<iterator, bool> lower_bound_equal(const K &key) const;
+
+  // Finds the first element whose key is greater than `key`.
+  template <typename K>
+  iterator upper_bound(const K &key) {
+    return internal_end(internal_upper_bound(key));
+  }
+  template <typename K>
+  const_iterator upper_bound(const K &key) const {
+    return internal_end(internal_upper_bound(key));
+  }
+
+  // Finds the range of values which compare equal to key. The first member of
+  // the returned pair is equal to lower_bound(key). The second member of the
+  // pair is equal to upper_bound(key).
+  template <typename K>
+  std::pair<iterator, iterator> equal_range(const K &key);
+  template <typename K>
+  std::pair<const_iterator, const_iterator> equal_range(const K &key) const {
+    return const_cast<btree *>(this)->equal_range(key);
+  }
+
+  // Inserts a value into the btree only if it does not already exist. The
+  // boolean return value indicates whether insertion succeeded or failed.
+  // Requirement: if `key` already exists in the btree, does not consume `args`.
+  // Requirement: `key` is never referenced after consuming `args`.
+  template <typename K, typename... Args>
+  std::pair<iterator, bool> insert_unique(const K &key, Args &&...args);
+
+  // Inserts with hint. Checks to see if the value should be placed immediately
+  // before `position` in the tree. If so, then the insertion will take
+  // amortized constant time. If not, the insertion will take amortized
+  // logarithmic time as if a call to insert_unique() were made.
+  // Requirement: if `key` already exists in the btree, does not consume `args`.
+  // Requirement: `key` is never referenced after consuming `args`.
+  template <typename K, typename... Args>
+  std::pair<iterator, bool> insert_hint_unique(iterator position, const K &key,
+                                               Args &&...args);
+
+  // Insert a range of values into the btree.
+  // Note: the first overload avoids constructing a value_type if the key
+  // already exists in the btree.
+  template <typename InputIterator,
+            typename = decltype(std::declval<const key_compare &>()(
+                params_type::key(*std::declval<InputIterator>()),
+                std::declval<const key_type &>()))>
+  void insert_iterator_unique(InputIterator b, InputIterator e, int);
+  // We need the second overload for cases in which we need to construct a
+  // value_type in order to compare it with the keys already in the btree.
+  template <typename InputIterator>
+  void insert_iterator_unique(InputIterator b, InputIterator e, char);
+
+  // Inserts a value into the btree.
+  template <typename ValueType>
+  iterator insert_multi(const key_type &key, ValueType &&v);
+
+  // Inserts a value into the btree.
+  template <typename ValueType>
+  iterator insert_multi(ValueType &&v) {
+    return insert_multi(params_type::key(v), std::forward<ValueType>(v));
+  }
+
+  // Insert with hint. Check to see if the value should be placed immediately
+  // before position in the tree. If it does, then the insertion will take
+  // amortized constant time. If not, the insertion will take amortized
+  // logarithmic time as if a call to insert_multi(v) were made.
+  template <typename ValueType>
+  iterator insert_hint_multi(iterator position, ValueType &&v);
+
+  // Insert a range of values into the btree.
+  template <typename InputIterator>
+  void insert_iterator_multi(InputIterator b,
+                             InputIterator e);
+
+  // Erase the specified iterator from the btree. The iterator must be valid
+  // (i.e. not equal to end()).  Return an iterator pointing to the node after
+  // the one that was erased (or end() if none exists).
+  // Requirement: does not read the value at `*iter`.
+  iterator erase(iterator iter);
+
+  // Erases range. Returns the number of keys erased and an iterator pointing
+  // to the element after the last erased element.
+  std::pair<size_type, iterator> erase_range(iterator begin, iterator end);
+
+  // Finds an element with key equivalent to `key` or returns `end()` if `key`
+  // is not present.
+  template <typename K>
+  iterator find(const K &key) {
+    return internal_end(internal_find(key));
+  }
+  template <typename K>
+  const_iterator find(const K &key) const {
+    return internal_end(internal_find(key));
+  }
+
+  // Clear the btree, deleting all of the values it contains.
+  void clear();
+
+  // Swaps the contents of `this` and `other`.
+  void swap(btree &other);
+
+  const key_compare &key_comp() const noexcept {
+    return rightmost_.template get<0>();
+  }
+  template <typename K1, typename K2>
+  bool compare_keys(const K1 &a, const K2 &b) const {
+    return compare_internal::compare_result_as_less_than(key_comp()(a, b));
+  }
+
+  value_compare value_comp() const {
+    return value_compare(original_key_compare(key_comp()));
+  }
+
+  // Verifies the structure of the btree.
+  void verify() const;
+
+  // Size routines.
+  size_type size() const { return size_; }
+  size_type max_size() const { return (std::numeric_limits<size_type>::max)(); }
+  bool empty() const { return size_ == 0; }
+
+  // The height of the btree. An empty tree will have height 0.
+  size_type height() const {
+    size_type h = 0;
+    if (!empty()) {
+      // Count the length of the chain from the leftmost node up to the
+      // root. We actually count from the root back around to the level below
+      // the root, but the calculation is the same because of the circularity
+      // of that traversal.
+      const node_type *n = root();
+      do {
+        ++h;
+        n = n->parent();
+      } while (n != root());
+    }
+    return h;
+  }
+
+  // The number of internal, leaf and total nodes used by the btree.
+  size_type leaf_nodes() const { return internal_stats(root()).leaf_nodes; }
+  size_type internal_nodes() const {
+    return internal_stats(root()).internal_nodes;
+  }
+  size_type nodes() const {
+    node_stats stats = internal_stats(root());
+    return stats.leaf_nodes + stats.internal_nodes;
+  }
+
+  // The total number of bytes used by the btree.
+  // TODO(b/169338300): update to support node_btree_*.
+  size_type bytes_used() const {
+    node_stats stats = internal_stats(root());
+    if (stats.leaf_nodes == 1 && stats.internal_nodes == 0) {
+      return sizeof(*this) + node_type::LeafSize(root()->max_count());
+    } else {
+      return sizeof(*this) + stats.leaf_nodes * node_type::LeafSize() +
+             stats.internal_nodes * node_type::InternalSize();
+    }
+  }
+
+  // The average number of bytes used per value stored in the btree assuming
+  // random insertion order.
+  static double average_bytes_per_value() {
+    // The expected number of values per node with random insertion order is the
+    // average of the maximum and minimum numbers of values per node.
+    const double expected_values_per_node = (kNodeSlots + kMinNodeValues) / 2.0;
+    return node_type::LeafSize() / expected_values_per_node;
+  }
+
+  // The fullness of the btree. Computed as the number of elements in the btree
+  // divided by the maximum number of elements a tree with the current number
+  // of nodes could hold. A value of 1 indicates perfect space
+  // utilization. Smaller values indicate space wastage.
+  // Returns 0 for empty trees.
+  double fullness() const {
+    if (empty()) return 0.0;
+    return static_cast<double>(size()) / (nodes() * kNodeSlots);
+  }
+  // The overhead of the btree structure in bytes per node. Computed as the
+  // total number of bytes used by the btree minus the number of bytes used for
+  // storing elements divided by the number of elements.
+  // Returns 0 for empty trees.
+  double overhead() const {
+    if (empty()) return 0.0;
+    return (bytes_used() - size() * sizeof(value_type)) /
+           static_cast<double>(size());
+  }
+
+  // The allocator used by the btree.
+  allocator_type get_allocator() const { return allocator(); }
+
+ private:
+  friend struct btree_access;
+
+  // Internal accessor routines.
+  node_type *root() { return root_; }
+  const node_type *root() const { return root_; }
+  node_type *&mutable_root() noexcept { return root_; }
+  node_type *rightmost() { return rightmost_.template get<2>(); }
+  const node_type *rightmost() const { return rightmost_.template get<2>(); }
+  node_type *&mutable_rightmost() noexcept {
+    return rightmost_.template get<2>();
+  }
+  key_compare *mutable_key_comp() noexcept {
+    return &rightmost_.template get<0>();
+  }
+
+  // The leftmost node is stored as the parent of the root node.
+  node_type *leftmost() { return root()->parent(); }
+  const node_type *leftmost() const { return root()->parent(); }
+
+  // Allocator routines.
+  allocator_type *mutable_allocator() noexcept {
+    return &rightmost_.template get<1>();
+  }
+  const allocator_type &allocator() const noexcept {
+    return rightmost_.template get<1>();
+  }
+
+  // Allocates a correctly aligned node of at least size bytes using the
+  // allocator.
+  node_type *allocate(size_type size) {
+    return reinterpret_cast<node_type *>(
+        absl::container_internal::Allocate<node_type::Alignment()>(
+            mutable_allocator(), size));
+  }
+
+  // Node creation/deletion routines.
+  node_type *new_internal_node(field_type position, node_type *parent) {
+    node_type *n = allocate(node_type::InternalSize());
+    n->init_internal(position, parent);
+    return n;
+  }
+  node_type *new_leaf_node(field_type position, node_type *parent) {
+    node_type *n = allocate(node_type::LeafSize());
+    n->init_leaf(position, kNodeSlots, parent);
+    return n;
+  }
+  node_type *new_leaf_root_node(field_type max_count) {
+    node_type *n = allocate(node_type::LeafSize(max_count));
+    n->init_leaf(/*position=*/0, max_count, /*parent=*/n);
+    return n;
+  }
+
+  // Deletion helper routines.
+  iterator rebalance_after_delete(iterator iter);
+
+  // Rebalances or splits the node iter points to.
+  void rebalance_or_split(iterator *iter);
+
+  // Merges the values of left, right and the delimiting key on their parent
+  // onto left, removing the delimiting key and deleting right.
+  void merge_nodes(node_type *left, node_type *right);
+
+  // Tries to merge node with its left or right sibling, and failing that,
+  // rebalance with its left or right sibling. Returns true if a merge
+  // occurred, at which point it is no longer valid to access node. Returns
+  // false if no merging took place.
+  bool try_merge_or_rebalance(iterator *iter);
+
+  // Tries to shrink the height of the tree by 1.
+  void try_shrink();
+
+  iterator internal_end(iterator iter) {
+    return iter.node_ != nullptr ? iter : end();
+  }
+  const_iterator internal_end(const_iterator iter) const {
+    return iter.node_ != nullptr ? iter : end();
+  }
+
+  // Emplaces a value into the btree immediately before iter. Requires that
+  // key(v) <= iter.key() and (--iter).key() <= key(v).
+  template <typename... Args>
+  iterator internal_emplace(iterator iter, Args &&...args);
+
+  // Returns an iterator pointing to the first value >= the value "iter" is
+  // pointing at. Note that "iter" might be pointing to an invalid location such
+  // as iter.position_ == iter.node_->finish(). This routine simply moves iter
+  // up in the tree to a valid location. Requires: iter.node_ is non-null.
+  template <typename IterType>
+  static IterType internal_last(IterType iter);
+
+  // Returns an iterator pointing to the leaf position at which key would
+  // reside in the tree, unless there is an exact match - in which case, the
+  // result may not be on a leaf. When there's a three-way comparator, we can
+  // return whether there was an exact match. This allows the caller to avoid a
+  // subsequent comparison to determine if an exact match was made, which is
+  // important for keys with expensive comparison, such as strings.
+  template <typename K>
+  SearchResult<iterator, is_key_compare_to::value> internal_locate(
+      const K &key) const;
+
+  // Internal routine which implements lower_bound().
+  template <typename K>
+  SearchResult<iterator, is_key_compare_to::value> internal_lower_bound(
+      const K &key) const;
+
+  // Internal routine which implements upper_bound().
+  template <typename K>
+  iterator internal_upper_bound(const K &key) const;
+
+  // Internal routine which implements find().
+  template <typename K>
+  iterator internal_find(const K &key) const;
+
+  // Verifies the tree structure of node.
+  size_type internal_verify(const node_type *node, const key_type *lo,
+                            const key_type *hi) const;
+
+  node_stats internal_stats(const node_type *node) const {
+    // The root can be a static empty node.
+    if (node == nullptr || (node == root() && empty())) {
+      return node_stats(0, 0);
+    }
+    if (node->is_leaf()) {
+      return node_stats(1, 0);
+    }
+    node_stats res(0, 1);
+    for (int i = node->start(); i <= node->finish(); ++i) {
+      res += internal_stats(node->child(i));
+    }
+    return res;
+  }
+
+  node_type *root_;
+
+  // A pointer to the rightmost node. Note that the leftmost node is stored as
+  // the root's parent. We use compressed tuple in order to save space because
+  // key_compare and allocator_type are usually empty.
+  absl::container_internal::CompressedTuple<key_compare, allocator_type,
+                                            node_type *>
+      rightmost_;
+
+  // Number of values.
+  size_type size_;
+};
+
+////
+// btree_node methods
+template <typename P>
+template <typename... Args>
+inline void btree_node<P>::emplace_value(const field_type i,
+                                         allocator_type *alloc,
+                                         Args &&...args) {
+  assert(i >= start());
+  assert(i <= finish());
+  // Shift old values to create space for new value and then construct it in
+  // place.
+  if (i < finish()) {
+    transfer_n_backward(finish() - i, /*dest_i=*/i + 1, /*src_i=*/i, this,
+                        alloc);
+  }
+  value_init(static_cast<field_type>(i), alloc, std::forward<Args>(args)...);
+  set_finish(finish() + 1);
+
+  if (is_internal() && finish() > i + 1) {
+    for (field_type j = finish(); j > i + 1; --j) {
+      set_child(j, child(j - 1));
+    }
+    clear_child(i + 1);
+  }
+}
+
+template <typename P>
+inline void btree_node<P>::remove_values(const field_type i,
+                                         const field_type to_erase,
+                                         allocator_type *alloc) {
+  // Transfer values after the removed range into their new places.
+  value_destroy_n(i, to_erase, alloc);
+  const field_type orig_finish = finish();
+  const field_type src_i = i + to_erase;
+  transfer_n(orig_finish - src_i, i, src_i, this, alloc);
+
+  if (is_internal()) {
+    // Delete all children between begin and end.
+    for (field_type j = 0; j < to_erase; ++j) {
+      clear_and_delete(child(i + j + 1), alloc);
+    }
+    // Rotate children after end into new positions.
+    for (field_type j = i + to_erase + 1; j <= orig_finish; ++j) {
+      set_child(j - to_erase, child(j));
+      clear_child(j);
+    }
+  }
+  set_finish(orig_finish - to_erase);
+}
+
+template <typename P>
+void btree_node<P>::rebalance_right_to_left(field_type to_move,
+                                            btree_node *right,
+                                            allocator_type *alloc) {
+  assert(parent() == right->parent());
+  assert(position() + 1 == right->position());
+  assert(right->count() >= count());
+  assert(to_move >= 1);
+  assert(to_move <= right->count());
+
+  // 1) Move the delimiting value in the parent to the left node.
+  transfer(finish(), position(), parent(), alloc);
+
+  // 2) Move the (to_move - 1) values from the right node to the left node.
+  transfer_n(to_move - 1, finish() + 1, right->start(), right, alloc);
+
+  // 3) Move the new delimiting value to the parent from the right node.
+  parent()->transfer(position(), right->start() + to_move - 1, right, alloc);
+
+  // 4) Shift the values in the right node to their correct positions.
+  right->transfer_n(right->count() - to_move, right->start(),
+                    right->start() + to_move, right, alloc);
+
+  if (is_internal()) {
+    // Move the child pointers from the right to the left node.
+    for (field_type i = 0; i < to_move; ++i) {
+      init_child(finish() + i + 1, right->child(i));
+    }
+    for (field_type i = right->start(); i <= right->finish() - to_move; ++i) {
+      assert(i + to_move <= right->max_count());
+      right->init_child(i, right->child(i + to_move));
+      right->clear_child(i + to_move);
+    }
+  }
+
+  // Fixup `finish` on the left and right nodes.
+  set_finish(finish() + to_move);
+  right->set_finish(right->finish() - to_move);
+}
+
+template <typename P>
+void btree_node<P>::rebalance_left_to_right(field_type to_move,
+                                            btree_node *right,
+                                            allocator_type *alloc) {
+  assert(parent() == right->parent());
+  assert(position() + 1 == right->position());
+  assert(count() >= right->count());
+  assert(to_move >= 1);
+  assert(to_move <= count());
+
+  // Values in the right node are shifted to the right to make room for the
+  // new to_move values. Then, the delimiting value in the parent and the
+  // other (to_move - 1) values in the left node are moved into the right node.
+  // Lastly, a new delimiting value is moved from the left node into the
+  // parent, and the remaining empty left node entries are destroyed.
+
+  // 1) Shift existing values in the right node to their correct positions.
+  right->transfer_n_backward(right->count(), right->start() + to_move,
+                             right->start(), right, alloc);
+
+  // 2) Move the delimiting value in the parent to the right node.
+  right->transfer(right->start() + to_move - 1, position(), parent(), alloc);
+
+  // 3) Move the (to_move - 1) values from the left node to the right node.
+  right->transfer_n(to_move - 1, right->start(), finish() - (to_move - 1), this,
+                    alloc);
+
+  // 4) Move the new delimiting value to the parent from the left node.
+  parent()->transfer(position(), finish() - to_move, this, alloc);
+
+  if (is_internal()) {
+    // Move the child pointers from the left to the right node.
+    for (field_type i = right->finish() + 1; i > right->start(); --i) {
+      right->init_child(i - 1 + to_move, right->child(i - 1));
+      right->clear_child(i - 1);
+    }
+    for (field_type i = 1; i <= to_move; ++i) {
+      right->init_child(i - 1, child(finish() - to_move + i));
+      clear_child(finish() - to_move + i);
+    }
+  }
+
+  // Fixup the counts on the left and right nodes.
+  set_finish(finish() - to_move);
+  right->set_finish(right->finish() + to_move);
+}
+
+template <typename P>
+void btree_node<P>::split(const int insert_position, btree_node *dest,
+                          allocator_type *alloc) {
+  assert(dest->count() == 0);
+  assert(max_count() == kNodeSlots);
+  assert(position() + 1 == dest->position());
+  assert(parent() == dest->parent());
+
+  // We bias the split based on the position being inserted. If we're
+  // inserting at the beginning of the left node then bias the split to put
+  // more values on the right node. If we're inserting at the end of the
+  // right node then bias the split to put more values on the left node.
+  if (insert_position == start()) {
+    dest->set_finish(dest->start() + finish() - 1);
+  } else if (insert_position == kNodeSlots) {
+    dest->set_finish(dest->start());
+  } else {
+    dest->set_finish(dest->start() + count() / 2);
+  }
+  set_finish(finish() - dest->count());
+  assert(count() >= 1);
+
+  // Move values from the left sibling to the right sibling.
+  dest->transfer_n(dest->count(), dest->start(), finish(), this, alloc);
+
+  // The split key is the largest value in the left sibling.
+  --mutable_finish();
+  parent()->emplace_value(position(), alloc, finish_slot());
+  value_destroy(finish(), alloc);
+  parent()->set_child_noupdate_position(position() + 1, dest);
+
+  if (is_internal()) {
+    for (field_type i = dest->start(), j = finish() + 1; i <= dest->finish();
+         ++i, ++j) {
+      assert(child(j) != nullptr);
+      dest->init_child(i, child(j));
+      clear_child(j);
+    }
+  }
+}
+
+template <typename P>
+void btree_node<P>::merge(btree_node *src, allocator_type *alloc) {
+  assert(parent() == src->parent());
+  assert(position() + 1 == src->position());
+
+  // Move the delimiting value to the left node.
+  value_init(finish(), alloc, parent()->slot(position()));
+
+  // Move the values from the right to the left node.
+  transfer_n(src->count(), finish() + 1, src->start(), src, alloc);
+
+  if (is_internal()) {
+    // Move the child pointers from the right to the left node.
+    for (field_type i = src->start(), j = finish() + 1; i <= src->finish();
+         ++i, ++j) {
+      init_child(j, src->child(i));
+      src->clear_child(i);
+    }
+  }
+
+  // Fixup `finish` on the src and dest nodes.
+  set_finish(start() + 1 + count() + src->count());
+  src->set_finish(src->start());
+
+  // Remove the value on the parent node and delete the src node.
+  parent()->remove_values(position(), /*to_erase=*/1, alloc);
+}
+
+template <typename P>
+void btree_node<P>::clear_and_delete(btree_node *node, allocator_type *alloc) {
+  if (node->is_leaf()) {
+    node->value_destroy_n(node->start(), node->count(), alloc);
+    deallocate(LeafSize(node->max_count()), node, alloc);
+    return;
+  }
+  if (node->count() == 0) {
+    deallocate(InternalSize(), node, alloc);
+    return;
+  }
+
+  // The parent of the root of the subtree we are deleting.
+  btree_node *delete_root_parent = node->parent();
+
+  // Navigate to the leftmost leaf under node, and then delete upwards.
+  while (node->is_internal()) node = node->start_child();
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+  // When generations are enabled, we delete the leftmost leaf last in case it's
+  // the parent of the root and we need to check whether it's a leaf before we
+  // can update the root's generation.
+  // TODO(ezb): if we change btree_node::is_root to check a bool inside the node
+  // instead of checking whether the parent is a leaf, we can remove this logic.
+  btree_node *leftmost_leaf = node;
+#endif
+  // Use `size_type` because `pos` needs to be able to hold `kNodeSlots+1`,
+  // which isn't guaranteed to be a valid `field_type`.
+  size_type pos = node->position();
+  btree_node *parent = node->parent();
+  for (;;) {
+    // In each iteration of the next loop, we delete one leaf node and go right.
+    assert(pos <= parent->finish());
+    do {
+      node = parent->child(static_cast<field_type>(pos));
+      if (node->is_internal()) {
+        // Navigate to the leftmost leaf under node.
+        while (node->is_internal()) node = node->start_child();
+        pos = node->position();
+        parent = node->parent();
+      }
+      node->value_destroy_n(node->start(), node->count(), alloc);
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+      if (leftmost_leaf != node)
+#endif
+        deallocate(LeafSize(node->max_count()), node, alloc);
+      ++pos;
+    } while (pos <= parent->finish());
+
+    // Once we've deleted all children of parent, delete parent and go up/right.
+    assert(pos > parent->finish());
+    do {
+      node = parent;
+      pos = node->position();
+      parent = node->parent();
+      node->value_destroy_n(node->start(), node->count(), alloc);
+      deallocate(InternalSize(), node, alloc);
+      if (parent == delete_root_parent) {
+#ifdef ABSL_BTREE_ENABLE_GENERATIONS
+        deallocate(LeafSize(leftmost_leaf->max_count()), leftmost_leaf, alloc);
+#endif
+        return;
+      }
+      ++pos;
+    } while (pos > parent->finish());
+  }
+}
+
+////
+// btree_iterator methods
+
+// Note: the implementation here is based on btree_node::clear_and_delete.
+template <typename N, typename R, typename P>
+auto btree_iterator<N, R, P>::distance_slow(const_iterator other) const
+    -> difference_type {
+  const_iterator begin = other;
+  const_iterator end = *this;
+  assert(begin.node_ != end.node_ || !begin.node_->is_leaf() ||
+         begin.position_ != end.position_);
+
+  const node_type *node = begin.node_;
+  // We need to compensate for double counting if begin.node_ is a leaf node.
+  difference_type count = node->is_leaf() ? -begin.position_ : 0;
+
+  // First navigate to the leftmost leaf node past begin.
+  if (node->is_internal()) {
+    ++count;
+    node = node->child(begin.position_ + 1);
+  }
+  while (node->is_internal()) node = node->start_child();
+
+  // Use `size_type` because `pos` needs to be able to hold `kNodeSlots+1`,
+  // which isn't guaranteed to be a valid `field_type`.
+  size_type pos = node->position();
+  const node_type *parent = node->parent();
+  for (;;) {
+    // In each iteration of the next loop, we count one leaf node and go right.
+    assert(pos <= parent->finish());
+    do {
+      node = parent->child(static_cast<field_type>(pos));
+      if (node->is_internal()) {
+        // Navigate to the leftmost leaf under node.
+        while (node->is_internal()) node = node->start_child();
+        pos = node->position();
+        parent = node->parent();
+      }
+      if (node == end.node_) return count + end.position_;
+      if (parent == end.node_ && pos == static_cast<size_type>(end.position_))
+        return count + node->count();
+      // +1 is for the next internal node value.
+      count += node->count() + 1;
+      ++pos;
+    } while (pos <= parent->finish());
+
+    // Once we've counted all children of parent, go up/right.
+    assert(pos > parent->finish());
+    do {
+      node = parent;
+      pos = node->position();
+      parent = node->parent();
+      // -1 because we counted the value at end and shouldn't.
+      if (parent == end.node_ && pos == static_cast<size_type>(end.position_))
+        return count - 1;
+      ++pos;
+    } while (pos > parent->finish());
+  }
+}
+
+template <typename N, typename R, typename P>
+void btree_iterator<N, R, P>::increment_slow() {
+  if (node_->is_leaf()) {
+    assert(position_ >= node_->finish());
+    btree_iterator save(*this);
+    while (position_ == node_->finish() && !node_->is_root()) {
+      assert(node_->parent()->child(node_->position()) == node_);
+      position_ = node_->position();
+      node_ = node_->parent();
+    }
+    // TODO(ezb): assert we aren't incrementing end() instead of handling.
+    if (position_ == node_->finish()) {
+      *this = save;
+    }
+  } else {
+    assert(position_ < node_->finish());
+    node_ = node_->child(static_cast<field_type>(position_ + 1));
+    while (node_->is_internal()) {
+      node_ = node_->start_child();
+    }
+    position_ = node_->start();
+  }
+}
+
+template <typename N, typename R, typename P>
+void btree_iterator<N, R, P>::decrement_slow() {
+  if (node_->is_leaf()) {
+    assert(position_ <= -1);
+    btree_iterator save(*this);
+    while (position_ < node_->start() && !node_->is_root()) {
+      assert(node_->parent()->child(node_->position()) == node_);
+      position_ = node_->position() - 1;
+      node_ = node_->parent();
+    }
+    // TODO(ezb): assert we aren't decrementing begin() instead of handling.
+    if (position_ < node_->start()) {
+      *this = save;
+    }
+  } else {
+    assert(position_ >= node_->start());
+    node_ = node_->child(static_cast<field_type>(position_));
+    while (node_->is_internal()) {
+      node_ = node_->child(node_->finish());
+    }
+    position_ = node_->finish() - 1;
+  }
+}
+
+////
+// btree methods
+template <typename P>
+template <typename Btree>
+void btree<P>::copy_or_move_values_in_order(Btree &other) {
+  static_assert(std::is_same<btree, Btree>::value ||
+                    std::is_same<const btree, Btree>::value,
+                "Btree type must be same or const.");
+  assert(empty());
+
+  // We can avoid key comparisons because we know the order of the
+  // values is the same order we'll store them in.
+  auto iter = other.begin();
+  if (iter == other.end()) return;
+  insert_multi(iter.slot());
+  ++iter;
+  for (; iter != other.end(); ++iter) {
+    // If the btree is not empty, we can just insert the new value at the end
+    // of the tree.
+    internal_emplace(end(), iter.slot());
+  }
+}
+
+template <typename P>
+constexpr bool btree<P>::static_assert_validation() {
+  static_assert(std::is_nothrow_copy_constructible<key_compare>::value,
+                "Key comparison must be nothrow copy constructible");
+  static_assert(std::is_nothrow_copy_constructible<allocator_type>::value,
+                "Allocator must be nothrow copy constructible");
+  static_assert(std::is_trivially_copyable<iterator>::value,
+                "iterator not trivially copyable.");
+
+  // Note: We assert that kTargetValues, which is computed from
+  // Params::kTargetNodeSize, must fit the node_type::field_type.
+  static_assert(
+      kNodeSlots < (1 << (8 * sizeof(typename node_type::field_type))),
+      "target node size too large");
+
+  // Verify that key_compare returns an absl::{weak,strong}_ordering or bool.
+  static_assert(
+      compare_has_valid_result_type<key_compare, key_type>(),
+      "key comparison function must return absl::{weak,strong}_ordering or "
+      "bool.");
+
+  // Test the assumption made in setting kNodeSlotSpace.
+  static_assert(node_type::MinimumOverhead() >= sizeof(void *) + 4,
+                "node space assumption incorrect");
+
+  return true;
+}
+
+template <typename P>
+template <typename K>
+auto btree<P>::lower_bound_equal(const K &key) const
+    -> std::pair<iterator, bool> {
+  const SearchResult<iterator, is_key_compare_to::value> res =
+      internal_lower_bound(key);
+  const iterator lower = iterator(internal_end(res.value));
+  const bool equal = res.HasMatch()
+                         ? res.IsEq()
+                         : lower != end() && !compare_keys(key, lower.key());
+  return {lower, equal};
+}
+
+template <typename P>
+template <typename K>
+auto btree<P>::equal_range(const K &key) -> std::pair<iterator, iterator> {
+  const std::pair<iterator, bool> lower_and_equal = lower_bound_equal(key);
+  const iterator lower = lower_and_equal.first;
+  if (!lower_and_equal.second) {
+    return {lower, lower};
+  }
+
+  const iterator next = std::next(lower);
+  if (!params_type::template can_have_multiple_equivalent_keys<K>()) {
+    // The next iterator after lower must point to a key greater than `key`.
+    // Note: if this assert fails, then it may indicate that the comparator does
+    // not meet the equivalence requirements for Compare
+    // (see https://en.cppreference.com/w/cpp/named_req/Compare).
+    assert(next == end() || compare_keys(key, next.key()));
+    return {lower, next};
+  }
+  // Try once more to avoid the call to upper_bound() if there's only one
+  // equivalent key. This should prevent all calls to upper_bound() in cases of
+  // unique-containers with heterogeneous comparators in which all comparison
+  // operators have the same equivalence classes.
+  if (next == end() || compare_keys(key, next.key())) return {lower, next};
+
+  // In this case, we need to call upper_bound() to avoid worst case O(N)
+  // behavior if we were to iterate over equal keys.
+  return {lower, upper_bound(key)};
+}
+
+template <typename P>
+template <typename K, typename... Args>
+auto btree<P>::insert_unique(const K &key, Args &&...args)
+    -> std::pair<iterator, bool> {
+  if (empty()) {
+    mutable_root() = mutable_rightmost() = new_leaf_root_node(1);
+  }
+
+  SearchResult<iterator, is_key_compare_to::value> res = internal_locate(key);
+  iterator iter = res.value;
+
+  if (res.HasMatch()) {
+    if (res.IsEq()) {
+      // The key already exists in the tree, do nothing.
+      return {iter, false};
+    }
+  } else {
+    iterator last = internal_last(iter);
+    if (last.node_ && !compare_keys(key, last.key())) {
+      // The key already exists in the tree, do nothing.
+      return {last, false};
+    }
+  }
+  return {internal_emplace(iter, std::forward<Args>(args)...), true};
+}
+
+template <typename P>
+template <typename K, typename... Args>
+inline auto btree<P>::insert_hint_unique(iterator position, const K &key,
+                                         Args &&...args)
+    -> std::pair<iterator, bool> {
+  if (!empty()) {
+    if (position == end() || compare_keys(key, position.key())) {
+      if (position == begin() || compare_keys(std::prev(position).key(), key)) {
+        // prev.key() < key < position.key()
+        return {internal_emplace(position, std::forward<Args>(args)...), true};
+      }
+    } else if (compare_keys(position.key(), key)) {
+      ++position;
+      if (position == end() || compare_keys(key, position.key())) {
+        // {original `position`}.key() < key < {current `position`}.key()
+        return {internal_emplace(position, std::forward<Args>(args)...), true};
+      }
+    } else {
+      // position.key() == key
+      return {position, false};
+    }
+  }
+  return insert_unique(key, std::forward<Args>(args)...);
+}
+
+template <typename P>
+template <typename InputIterator, typename>
+void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e, int) {
+  for (; b != e; ++b) {
+    insert_hint_unique(end(), params_type::key(*b), *b);
+  }
+}
+
+template <typename P>
+template <typename InputIterator>
+void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e, char) {
+  for (; b != e; ++b) {
+    // Use a node handle to manage a temp slot.
+    auto node_handle =
+        CommonAccess::Construct<node_handle_type>(get_allocator(), *b);
+    slot_type *slot = CommonAccess::GetSlot(node_handle);
+    insert_hint_unique(end(), params_type::key(slot), slot);
+  }
+}
+
+template <typename P>
+template <typename ValueType>
+auto btree<P>::insert_multi(const key_type &key, ValueType &&v) -> iterator {
+  if (empty()) {
+    mutable_root() = mutable_rightmost() = new_leaf_root_node(1);
+  }
+
+  iterator iter = internal_upper_bound(key);
+  if (iter.node_ == nullptr) {
+    iter = end();
+  }
+  return internal_emplace(iter, std::forward<ValueType>(v));
+}
+
+template <typename P>
+template <typename ValueType>
+auto btree<P>::insert_hint_multi(iterator position, ValueType &&v) -> iterator {
+  if (!empty()) {
+    const key_type &key = params_type::key(v);
+    if (position == end() || !compare_keys(position.key(), key)) {
+      if (position == begin() ||
+          !compare_keys(key, std::prev(position).key())) {
+        // prev.key() <= key <= position.key()
+        return internal_emplace(position, std::forward<ValueType>(v));
+      }
+    } else {
+      ++position;
+      if (position == end() || !compare_keys(position.key(), key)) {
+        // {original `position`}.key() < key < {current `position`}.key()
+        return internal_emplace(position, std::forward<ValueType>(v));
+      }
+    }
+  }
+  return insert_multi(std::forward<ValueType>(v));
+}
+
+template <typename P>
+template <typename InputIterator>
+void btree<P>::insert_iterator_multi(InputIterator b, InputIterator e) {
+  for (; b != e; ++b) {
+    insert_hint_multi(end(), *b);
+  }
+}
+
+template <typename P>
+auto btree<P>::operator=(const btree &other) -> btree & {
+  if (this != &other) {
+    clear();
+
+    *mutable_key_comp() = other.key_comp();
+    if (absl::allocator_traits<
+            allocator_type>::propagate_on_container_copy_assignment::value) {
+      *mutable_allocator() = other.allocator();
+    }
+
+    copy_or_move_values_in_order(other);
+  }
+  return *this;
+}
+
+template <typename P>
+auto btree<P>::operator=(btree &&other) noexcept -> btree & {
+  if (this != &other) {
+    clear();
+
+    using std::swap;
+    if (absl::allocator_traits<
+            allocator_type>::propagate_on_container_move_assignment::value) {
+      swap(root_, other.root_);
+      // Note: `rightmost_` also contains the allocator and the key comparator.
+      swap(rightmost_, other.rightmost_);
+      swap(size_, other.size_);
+    } else {
+      if (allocator() == other.allocator()) {
+        swap(mutable_root(), other.mutable_root());
+        swap(*mutable_key_comp(), *other.mutable_key_comp());
+        swap(mutable_rightmost(), other.mutable_rightmost());
+        swap(size_, other.size_);
+      } else {
+        // We aren't allowed to propagate the allocator and the allocator is
+        // different so we can't take over its memory. We must move each element
+        // individually. We need both `other` and `this` to have `other`s key
+        // comparator while moving the values so we can't swap the key
+        // comparators.
+        *mutable_key_comp() = other.key_comp();
+        copy_or_move_values_in_order(other);
+      }
+    }
+  }
+  return *this;
+}
+
+template <typename P>
+auto btree<P>::erase(iterator iter) -> iterator {
+  iter.node_->value_destroy(static_cast<field_type>(iter.position_),
+                            mutable_allocator());
+  iter.update_generation();
+
+  const bool internal_delete = iter.node_->is_internal();
+  if (internal_delete) {
+    // Deletion of a value on an internal node. First, transfer the largest
+    // value from our left child here, then erase/rebalance from that position.
+    // We can get to the largest value from our left child by decrementing iter.
+    iterator internal_iter(iter);
+    --iter;
+    assert(iter.node_->is_leaf());
+    internal_iter.node_->transfer(
+        static_cast<size_type>(internal_iter.position_),
+        static_cast<size_type>(iter.position_), iter.node_,
+        mutable_allocator());
+  } else {
+    // Shift values after erased position in leaf. In the internal case, we
+    // don't need to do this because the leaf position is the end of the node.
+    const field_type transfer_from =
+        static_cast<field_type>(iter.position_ + 1);
+    const field_type num_to_transfer = iter.node_->finish() - transfer_from;
+    iter.node_->transfer_n(num_to_transfer,
+                           static_cast<size_type>(iter.position_),
+                           transfer_from, iter.node_, mutable_allocator());
+  }
+  // Update node finish and container size.
+  iter.node_->set_finish(iter.node_->finish() - 1);
+  --size_;
+
+  // We want to return the next value after the one we just erased. If we
+  // erased from an internal node (internal_delete == true), then the next
+  // value is ++(++iter). If we erased from a leaf node (internal_delete ==
+  // false) then the next value is ++iter. Note that ++iter may point to an
+  // internal node and the value in the internal node may move to a leaf node
+  // (iter.node_) when rebalancing is performed at the leaf level.
+
+  iterator res = rebalance_after_delete(iter);
+
+  // If we erased from an internal node, advance the iterator.
+  if (internal_delete) {
+    ++res;
+  }
+  return res;
+}
+
+template <typename P>
+auto btree<P>::rebalance_after_delete(iterator iter) -> iterator {
+  // Merge/rebalance as we walk back up the tree.
+  iterator res(iter);
+  bool first_iteration = true;
+  for (;;) {
+    if (iter.node_ == root()) {
+      try_shrink();
+      if (empty()) {
+        return end();
+      }
+      break;
+    }
+    if (iter.node_->count() >= kMinNodeValues) {
+      break;
+    }
+    bool merged = try_merge_or_rebalance(&iter);
+    // On the first iteration, we should update `res` with `iter` because `res`
+    // may have been invalidated.
+    if (first_iteration) {
+      res = iter;
+      first_iteration = false;
+    }
+    if (!merged) {
+      break;
+    }
+    iter.position_ = iter.node_->position();
+    iter.node_ = iter.node_->parent();
+  }
+  res.update_generation();
+
+  // Adjust our return value. If we're pointing at the end of a node, advance
+  // the iterator.
+  if (res.position_ == res.node_->finish()) {
+    res.position_ = res.node_->finish() - 1;
+    ++res;
+  }
+
+  return res;
+}
+
+// Note: we tried implementing this more efficiently by erasing all of the
+// elements in [begin, end) at once and then doing rebalancing once at the end
+// (rather than interleaving deletion and rebalancing), but that adds a lot of
+// complexity, which seems to outweigh the performance win.
+template <typename P>
+auto btree<P>::erase_range(iterator begin, iterator end)
+    -> std::pair<size_type, iterator> {
+  size_type count = static_cast<size_type>(end - begin);
+  assert(count >= 0);
+
+  if (count == 0) {
+    return {0, begin};
+  }
+
+  if (static_cast<size_type>(count) == size_) {
+    clear();
+    return {count, this->end()};
+  }
+
+  if (begin.node_ == end.node_) {
+    assert(end.position_ > begin.position_);
+    begin.node_->remove_values(
+        static_cast<field_type>(begin.position_),
+        static_cast<field_type>(end.position_ - begin.position_),
+        mutable_allocator());
+    size_ -= count;
+    return {count, rebalance_after_delete(begin)};
+  }
+
+  const size_type target_size = size_ - count;
+  while (size_ > target_size) {
+    if (begin.node_->is_leaf()) {
+      const size_type remaining_to_erase = size_ - target_size;
+      const size_type remaining_in_node =
+          static_cast<size_type>(begin.node_->finish() - begin.position_);
+      const field_type to_erase = static_cast<field_type>(
+          (std::min)(remaining_to_erase, remaining_in_node));
+      begin.node_->remove_values(static_cast<field_type>(begin.position_),
+                                 to_erase, mutable_allocator());
+      size_ -= to_erase;
+      begin = rebalance_after_delete(begin);
+    } else {
+      begin = erase(begin);
+    }
+  }
+  begin.update_generation();
+  return {count, begin};
+}
+
+template <typename P>
+void btree<P>::clear() {
+  if (!empty()) {
+    node_type::clear_and_delete(root(), mutable_allocator());
+  }
+  mutable_root() = mutable_rightmost() = EmptyNode();
+  size_ = 0;
+}
+
+template <typename P>
+void btree<P>::swap(btree &other) {
+  using std::swap;
+  if (absl::allocator_traits<
+          allocator_type>::propagate_on_container_swap::value) {
+    // Note: `rightmost_` also contains the allocator and the key comparator.
+    swap(rightmost_, other.rightmost_);
+  } else {
+    // It's undefined behavior if the allocators are unequal here.
+    assert(allocator() == other.allocator());
+    swap(mutable_rightmost(), other.mutable_rightmost());
+    swap(*mutable_key_comp(), *other.mutable_key_comp());
+  }
+  swap(mutable_root(), other.mutable_root());
+  swap(size_, other.size_);
+}
+
+template <typename P>
+void btree<P>::verify() const {
+  assert(root() != nullptr);
+  assert(leftmost() != nullptr);
+  assert(rightmost() != nullptr);
+  assert(empty() || size() == internal_verify(root(), nullptr, nullptr));
+  assert(leftmost() == (++const_iterator(root(), -1)).node_);
+  assert(rightmost() == (--const_iterator(root(), root()->finish())).node_);
+  assert(leftmost()->is_leaf());
+  assert(rightmost()->is_leaf());
+}
+
+template <typename P>
+void btree<P>::rebalance_or_split(iterator *iter) {
+  node_type *&node = iter->node_;
+  int &insert_position = iter->position_;
+  assert(node->count() == node->max_count());
+  assert(kNodeSlots == node->max_count());
+
+  // First try to make room on the node by rebalancing.
+  node_type *parent = node->parent();
+  if (node != root()) {
+    if (node->position() > parent->start()) {
+      // Try rebalancing with our left sibling.
+      node_type *left = parent->child(node->position() - 1);
+      assert(left->max_count() == kNodeSlots);
+      if (left->count() < kNodeSlots) {
+        // We bias rebalancing based on the position being inserted. If we're
+        // inserting at the end of the right node then we bias rebalancing to
+        // fill up the left node.
+        field_type to_move =
+            (kNodeSlots - left->count()) /
+            (1 + (static_cast<field_type>(insert_position) < kNodeSlots));
+        to_move = (std::max)(field_type{1}, to_move);
+
+        if (static_cast<field_type>(insert_position) - to_move >=
+                node->start() ||
+            left->count() + to_move < kNodeSlots) {
+          left->rebalance_right_to_left(to_move, node, mutable_allocator());
+
+          assert(node->max_count() - node->count() == to_move);
+          insert_position = static_cast<int>(
+              static_cast<field_type>(insert_position) - to_move);
+          if (insert_position < node->start()) {
+            insert_position = insert_position + left->count() + 1;
+            node = left;
+          }
+
+          assert(node->count() < node->max_count());
+          return;
+        }
+      }
+    }
+
+    if (node->position() < parent->finish()) {
+      // Try rebalancing with our right sibling.
+      node_type *right = parent->child(node->position() + 1);
+      assert(right->max_count() == kNodeSlots);
+      if (right->count() < kNodeSlots) {
+        // We bias rebalancing based on the position being inserted. If we're
+        // inserting at the beginning of the left node then we bias rebalancing
+        // to fill up the right node.
+        field_type to_move = (kNodeSlots - right->count()) /
+                             (1 + (insert_position > node->start()));
+        to_move = (std::max)(field_type{1}, to_move);
+
+        if (static_cast<field_type>(insert_position) <=
+                node->finish() - to_move ||
+            right->count() + to_move < kNodeSlots) {
+          node->rebalance_left_to_right(to_move, right, mutable_allocator());
+
+          if (insert_position > node->finish()) {
+            insert_position = insert_position - node->count() - 1;
+            node = right;
+          }
+
+          assert(node->count() < node->max_count());
+          return;
+        }
+      }
+    }
+
+    // Rebalancing failed, make sure there is room on the parent node for a new
+    // value.
+    assert(parent->max_count() == kNodeSlots);
+    if (parent->count() == kNodeSlots) {
+      iterator parent_iter(parent, node->position());
+      rebalance_or_split(&parent_iter);
+      parent = node->parent();
+    }
+  } else {
+    // Rebalancing not possible because this is the root node.
+    // Create a new root node and set the current root node as the child of the
+    // new root.
+    parent = new_internal_node(/*position=*/0, parent);
+    parent->set_generation(root()->generation());
+    parent->init_child(parent->start(), node);
+    mutable_root() = parent;
+    // If the former root was a leaf node, then it's now the rightmost node.
+    assert(parent->start_child()->is_internal() ||
+           parent->start_child() == rightmost());
+  }
+
+  // Split the node.
+  node_type *split_node;
+  if (node->is_leaf()) {
+    split_node = new_leaf_node(node->position() + 1, parent);
+    node->split(insert_position, split_node, mutable_allocator());
+    if (rightmost() == node) mutable_rightmost() = split_node;
+  } else {
+    split_node = new_internal_node(node->position() + 1, parent);
+    node->split(insert_position, split_node, mutable_allocator());
+  }
+
+  if (insert_position > node->finish()) {
+    insert_position = insert_position - node->count() - 1;
+    node = split_node;
+  }
+}
+
+template <typename P>
+void btree<P>::merge_nodes(node_type *left, node_type *right) {
+  left->merge(right, mutable_allocator());
+  if (rightmost() == right) mutable_rightmost() = left;
+}
+
+template <typename P>
+bool btree<P>::try_merge_or_rebalance(iterator *iter) {
+  node_type *parent = iter->node_->parent();
+  if (iter->node_->position() > parent->start()) {
+    // Try merging with our left sibling.
+    node_type *left = parent->child(iter->node_->position() - 1);
+    assert(left->max_count() == kNodeSlots);
+    if (1U + left->count() + iter->node_->count() <= kNodeSlots) {
+      iter->position_ += 1 + left->count();
+      merge_nodes(left, iter->node_);
+      iter->node_ = left;
+      return true;
+    }
+  }
+  if (iter->node_->position() < parent->finish()) {
+    // Try merging with our right sibling.
+    node_type *right = parent->child(iter->node_->position() + 1);
+    assert(right->max_count() == kNodeSlots);
+    if (1U + iter->node_->count() + right->count() <= kNodeSlots) {
+      merge_nodes(iter->node_, right);
+      return true;
+    }
+    // Try rebalancing with our right sibling. We don't perform rebalancing if
+    // we deleted the first element from iter->node_ and the node is not
+    // empty. This is a small optimization for the common pattern of deleting
+    // from the front of the tree.
+    if (right->count() > kMinNodeValues &&
+        (iter->node_->count() == 0 || iter->position_ > iter->node_->start())) {
+      field_type to_move = (right->count() - iter->node_->count()) / 2;
+      to_move =
+          (std::min)(to_move, static_cast<field_type>(right->count() - 1));
+      iter->node_->rebalance_right_to_left(to_move, right, mutable_allocator());
+      return false;
+    }
+  }
+  if (iter->node_->position() > parent->start()) {
+    // Try rebalancing with our left sibling. We don't perform rebalancing if
+    // we deleted the last element from iter->node_ and the node is not
+    // empty. This is a small optimization for the common pattern of deleting
+    // from the back of the tree.
+    node_type *left = parent->child(iter->node_->position() - 1);
+    if (left->count() > kMinNodeValues &&
+        (iter->node_->count() == 0 ||
+         iter->position_ < iter->node_->finish())) {
+      field_type to_move = (left->count() - iter->node_->count()) / 2;
+      to_move = (std::min)(to_move, static_cast<field_type>(left->count() - 1));
+      left->rebalance_left_to_right(to_move, iter->node_, mutable_allocator());
+      iter->position_ += to_move;
+      return false;
+    }
+  }
+  return false;
+}
+
+template <typename P>
+void btree<P>::try_shrink() {
+  node_type *orig_root = root();
+  if (orig_root->count() > 0) {
+    return;
+  }
+  // Deleted the last item on the root node, shrink the height of the tree.
+  if (orig_root->is_leaf()) {
+    assert(size() == 0);
+    mutable_root() = mutable_rightmost() = EmptyNode();
+  } else {
+    node_type *child = orig_root->start_child();
+    child->make_root();
+    mutable_root() = child;
+  }
+  node_type::clear_and_delete(orig_root, mutable_allocator());
+}
+
+template <typename P>
+template <typename IterType>
+inline IterType btree<P>::internal_last(IterType iter) {
+  assert(iter.node_ != nullptr);
+  while (iter.position_ == iter.node_->finish()) {
+    iter.position_ = iter.node_->position();
+    iter.node_ = iter.node_->parent();
+    if (iter.node_->is_leaf()) {
+      iter.node_ = nullptr;
+      break;
+    }
+  }
+  iter.update_generation();
+  return iter;
+}
+
+template <typename P>
+template <typename... Args>
+inline auto btree<P>::internal_emplace(iterator iter, Args &&...args)
+    -> iterator {
+  if (iter.node_->is_internal()) {
+    // We can't insert on an internal node. Instead, we'll insert after the
+    // previous value which is guaranteed to be on a leaf node.
+    --iter;
+    ++iter.position_;
+  }
+  const field_type max_count = iter.node_->max_count();
+  allocator_type *alloc = mutable_allocator();
+
+  const auto transfer_and_delete = [&](node_type *old_node,
+                                       node_type *new_node) {
+    new_node->transfer_n(old_node->count(), new_node->start(),
+                         old_node->start(), old_node, alloc);
+    new_node->set_finish(old_node->finish());
+    old_node->set_finish(old_node->start());
+    new_node->set_generation(old_node->generation());
+    node_type::clear_and_delete(old_node, alloc);
+  };
+  const auto replace_leaf_root_node = [&](field_type new_node_size) {
+    assert(iter.node_ == root());
+    node_type *old_root = iter.node_;
+    node_type *new_root = iter.node_ = new_leaf_root_node(new_node_size);
+    transfer_and_delete(old_root, new_root);
+    mutable_root() = mutable_rightmost() = new_root;
+  };
+
+  bool replaced_node = false;
+  if (iter.node_->count() == max_count) {
+    // Make room in the leaf for the new item.
+    if (max_count < kNodeSlots) {
+      // Insertion into the root where the root is smaller than the full node
+      // size. Simply grow the size of the root node.
+      replace_leaf_root_node(static_cast<field_type>(
+          (std::min)(static_cast<int>(kNodeSlots), 2 * max_count)));
+      replaced_node = true;
+    } else {
+      rebalance_or_split(&iter);
+    }
+  }
+  (void)replaced_node;
+#if defined(ABSL_HAVE_ADDRESS_SANITIZER) || \
+    defined(ABSL_HAVE_HWADDRESS_SANITIZER)
+  if (!replaced_node) {
+    assert(iter.node_->is_leaf());
+    if (iter.node_->is_root()) {
+      replace_leaf_root_node(max_count);
+    } else {
+      node_type *old_node = iter.node_;
+      const bool was_rightmost = rightmost() == old_node;
+      const bool was_leftmost = leftmost() == old_node;
+      node_type *parent = old_node->parent();
+      const field_type position = old_node->position();
+      node_type *new_node = iter.node_ = new_leaf_node(position, parent);
+      parent->set_child_noupdate_position(position, new_node);
+      transfer_and_delete(old_node, new_node);
+      if (was_rightmost) mutable_rightmost() = new_node;
+      // The leftmost node is stored as the parent of the root node.
+      if (was_leftmost) root()->set_parent(new_node);
+    }
+  }
+#endif
+  iter.node_->emplace_value(static_cast<field_type>(iter.position_), alloc,
+                            std::forward<Args>(args)...);
+  assert(
+      iter.node_->is_ordered_correctly(static_cast<field_type>(iter.position_),
+                                       original_key_compare(key_comp())) &&
+      "If this assert fails, then either (1) the comparator may violate "
+      "transitivity, i.e. comp(a,b) && comp(b,c) -> comp(a,c) (see "
+      "https://en.cppreference.com/w/cpp/named_req/Compare), or (2) a "
+      "key may have been mutated after it was inserted into the tree.");
+  ++size_;
+  iter.update_generation();
+  return iter;
+}
+
+template <typename P>
+template <typename K>
+inline auto btree<P>::internal_locate(const K &key) const
+    -> SearchResult<iterator, is_key_compare_to::value> {
+  iterator iter(const_cast<node_type *>(root()));
+  for (;;) {
+    SearchResult<size_type, is_key_compare_to::value> res =
+        iter.node_->lower_bound(key, key_comp());
+    iter.position_ = static_cast<int>(res.value);
+    if (res.IsEq()) {
+      return {iter, MatchKind::kEq};
+    }
+    // Note: in the non-key-compare-to case, we don't need to walk all the way
+    // down the tree if the keys are equal, but determining equality would
+    // require doing an extra comparison on each node on the way down, and we
+    // will need to go all the way to the leaf node in the expected case.
+    if (iter.node_->is_leaf()) {
+      break;
+    }
+    iter.node_ = iter.node_->child(static_cast<field_type>(iter.position_));
+  }
+  // Note: in the non-key-compare-to case, the key may actually be equivalent
+  // here (and the MatchKind::kNe is ignored).
+  return {iter, MatchKind::kNe};
+}
+
+template <typename P>
+template <typename K>
+auto btree<P>::internal_lower_bound(const K &key) const
+    -> SearchResult<iterator, is_key_compare_to::value> {
+  if (!params_type::template can_have_multiple_equivalent_keys<K>()) {
+    SearchResult<iterator, is_key_compare_to::value> ret = internal_locate(key);
+    ret.value = internal_last(ret.value);
+    return ret;
+  }
+  iterator iter(const_cast<node_type *>(root()));
+  SearchResult<size_type, is_key_compare_to::value> res;
+  bool seen_eq = false;
+  for (;;) {
+    res = iter.node_->lower_bound(key, key_comp());
+    iter.position_ = static_cast<int>(res.value);
+    if (iter.node_->is_leaf()) {
+      break;
+    }
+    seen_eq = seen_eq || res.IsEq();
+    iter.node_ = iter.node_->child(static_cast<field_type>(iter.position_));
+  }
+  if (res.IsEq()) return {iter, MatchKind::kEq};
+  return {internal_last(iter), seen_eq ? MatchKind::kEq : MatchKind::kNe};
+}
+
+template <typename P>
+template <typename K>
+auto btree<P>::internal_upper_bound(const K &key) const -> iterator {
+  iterator iter(const_cast<node_type *>(root()));
+  for (;;) {
+    iter.position_ = static_cast<int>(iter.node_->upper_bound(key, key_comp()));
+    if (iter.node_->is_leaf()) {
+      break;
+    }
+    iter.node_ = iter.node_->child(static_cast<field_type>(iter.position_));
+  }
+  return internal_last(iter);
+}
+
+template <typename P>
+template <typename K>
+auto btree<P>::internal_find(const K &key) const -> iterator {
+  SearchResult<iterator, is_key_compare_to::value> res = internal_locate(key);
+  if (res.HasMatch()) {
+    if (res.IsEq()) {
+      return res.value;
+    }
+  } else {
+    const iterator iter = internal_last(res.value);
+    if (iter.node_ != nullptr && !compare_keys(key, iter.key())) {
+      return iter;
+    }
+  }
+  return {nullptr, 0};
+}
+
+template <typename P>
+typename btree<P>::size_type btree<P>::internal_verify(
+    const node_type *node, const key_type *lo, const key_type *hi) const {
+  assert(node->count() > 0);
+  assert(node->count() <= node->max_count());
+  if (lo) {
+    assert(!compare_keys(node->key(node->start()), *lo));
+  }
+  if (hi) {
+    assert(!compare_keys(*hi, node->key(node->finish() - 1)));
+  }
+  for (int i = node->start() + 1; i < node->finish(); ++i) {
+    assert(!compare_keys(node->key(i), node->key(i - 1)));
+  }
+  size_type count = node->count();
+  if (node->is_internal()) {
+    for (field_type i = node->start(); i <= node->finish(); ++i) {
+      assert(node->child(i) != nullptr);
+      assert(node->child(i)->parent() == node);
+      assert(node->child(i)->position() == i);
+      count += internal_verify(node->child(i),
+                               i == node->start() ? lo : &node->key(i - 1),
+                               i == node->finish() ? hi : &node->key(i));
+    }
+  }
+  return count;
+}
+
+struct btree_access {
+  template <typename BtreeContainer, typename Pred>
+  static auto erase_if(BtreeContainer &container, Pred pred) ->
+      typename BtreeContainer::size_type {
+    const auto initial_size = container.size();
+    auto &tree = container.tree_;
+    auto *alloc = tree.mutable_allocator();
+    for (auto it = container.begin(); it != container.end();) {
+      if (!pred(*it)) {
+        ++it;
+        continue;
+      }
+      auto *node = it.node_;
+      if (node->is_internal()) {
+        // Handle internal nodes normally.
+        it = container.erase(it);
+        continue;
+      }
+      // If this is a leaf node, then we do all the erases from this node
+      // at once before doing rebalancing.
+
+      // The current position to transfer slots to.
+      int to_pos = it.position_;
+      node->value_destroy(it.position_, alloc);
+      while (++it.position_ < node->finish()) {
+        it.update_generation();
+        if (pred(*it)) {
+          node->value_destroy(it.position_, alloc);
+        } else {
+          node->transfer(node->slot(to_pos++), node->slot(it.position_), alloc);
+        }
+      }
+      const int num_deleted = node->finish() - to_pos;
+      tree.size_ -= num_deleted;
+      node->set_finish(to_pos);
+      it.position_ = to_pos;
+      it = tree.rebalance_after_delete(it);
+    }
+    return initial_size - container.size();
+  }
+};
+
+#undef ABSL_BTREE_ENABLE_GENERATIONS
+
+}  // namespace container_internal
+ABSL_NAMESPACE_END
+}  // namespace absl
+
+#endif  // ABSL_CONTAINER_INTERNAL_BTREE_H_