// 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 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 may use much less memory per // stored value. For the random insertion benchmark in btree_bench.cc, a // btree_set 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 #include #include #include #include #include #include #include #include #include #include #include #include "absl/base/macros.h" #include "absl/container/internal/common.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" #include "absl/utility/utility.h" namespace absl { ABSL_NAMESPACE_BEGIN namespace container_internal { // A helper class that indicates if the Compare parameter is a key-compare-to // comparator. template using btree_is_key_compare_to = std::is_convertible, absl::weak_ordering>; struct StringBtreeDefaultLess { using is_transparent = void; StringBtreeDefaultLess() = default; // Compatibility constructor. StringBtreeDefaultLess(std::less) {} // NOLINT StringBtreeDefaultLess(std::less) {} // NOLINT 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) {} // 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) {} // NOLINT StringBtreeDefaultGreater(std::greater) {} // NOLINT 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) {} // 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)); } }; // A helper class to convert a boolean comparison into a three-way "compare-to" // comparison that returns an `absl::weak_ordering`. This helper // class is specialized for less, greater, // less, greater, less, and // greater. // // key_compare_to_adapter is provided so that btree users // automatically get the more efficient compare-to code when using common // Abseil string types with common comparison functors. // These string-like specializations also turn on heterogeneous lookup by // default. template struct key_compare_to_adapter { using type = Compare; }; template <> struct key_compare_to_adapter> { using type = StringBtreeDefaultLess; }; template <> struct key_compare_to_adapter> { using type = StringBtreeDefaultGreater; }; template <> struct key_compare_to_adapter> { using type = StringBtreeDefaultLess; }; template <> struct key_compare_to_adapter> { using type = StringBtreeDefaultGreater; }; template <> struct key_compare_to_adapter> { using type = StringBtreeDefaultLess; }; template <> struct key_compare_to_adapter> { using type = StringBtreeDefaultGreater; }; template struct common_params { // 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. using key_compare = typename key_compare_to_adapter::type; // True when key_compare has been adapted to StringBtreeDefault{Less,Greater}. using is_key_compare_adapted = absl::negation>; // 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; using allocator_type = Alloc; using key_type = Key; using size_type = std::make_signed::type; using difference_type = ptrdiff_t; // True if this is a multiset or multimap. using is_multi_container = std::integral_constant; 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 &; enum { kTargetNodeSize = TargetNodeSize, // Upper bound for the available space for values. This is largest for leaf // nodes, which have overhead of at least a pointer + 4 bytes (for storing // 3 field_types and an enum). kNodeValueSpace = TargetNodeSize - /*minimum overhead=*/(sizeof(void *) + 4), }; // This is an integral type large enough to hold as many // ValueSize-values as will fit a node of TargetNodeSize bytes. using node_count_type = absl::conditional_t<(kNodeValueSpace / sizeof(value_type) > (std::numeric_limits::max)()), uint16_t, uint8_t>; // NOLINT // The following methods are necessary for passing this struct as PolicyTraits // for node_handle and/or are used within btree. static value_type &element(slot_type *slot) { return slot_policy::element(slot); } static const value_type &element(const slot_type *slot) { return slot_policy::element(slot); } template static void construct(Alloc *alloc, slot_type *slot, Args &&... args) { slot_policy::construct(alloc, slot, std::forward(args)...); } static void construct(Alloc *alloc, slot_type *slot, slot_type *other) { slot_policy::construct(alloc, slot, other); } static void destroy(Alloc *alloc, slot_type *slot) { slot_policy::destroy(alloc, slot); } static void transfer(Alloc *alloc, slot_type *new_slot, slot_type *old_slot) { construct(alloc, new_slot, old_slot); destroy(alloc, old_slot); } static void swap(Alloc *alloc, slot_type *a, slot_type *b) { slot_policy::swap(alloc, a, b); } static void move(Alloc *alloc, slot_type *src, slot_type *dest) { slot_policy::move(alloc, src, dest); } }; // A parameters structure for holding the type parameters for a btree_map. // Compare and Alloc should be nothrow copy-constructible. template struct map_params : common_params> { using super_type = typename map_params::common_params; using mapped_type = Data; // This type allows us to move keys when it is safe to do so. It is safe // for maps in which value_type and mutable_value_type are layout compatible. using slot_policy = typename super_type::slot_policy; using slot_type = typename super_type::slot_type; using value_type = typename super_type::value_type; using init_type = typename super_type::init_type; using key_compare = typename super_type::key_compare; // Inherit from key_compare for empty base class optimization. struct value_compare : private key_compare { value_compare() = default; explicit value_compare(const key_compare &cmp) : key_compare(cmp) {} template auto operator()(const T &left, const U &right) const -> decltype(std::declval()(left.first, right.first)) { return key_compare::operator()(left.first, right.first); } }; using is_map_container = std::true_type; template static auto key(const V &value) -> decltype(value.first) { return value.first; } static const Key &key(const slot_type *s) { return slot_policy::key(s); } static const Key &key(slot_type *s) { return slot_policy::key(s); } // For use in node handle. static auto mutable_key(slot_type *s) -> decltype(slot_policy::mutable_key(s)) { return slot_policy::mutable_key(s); } static mapped_type &value(value_type *value) { return value->second; } }; // This type implements the necessary functions from the // absl::container_internal::slot_type interface. template struct set_slot_policy { using slot_type = Key; using value_type = Key; using mutable_value_type = Key; static value_type &element(slot_type *slot) { return *slot; } static const value_type &element(const slot_type *slot) { return *slot; } template static void construct(Alloc *alloc, slot_type *slot, Args &&... args) { absl::allocator_traits::construct(*alloc, slot, std::forward(args)...); } template static void construct(Alloc *alloc, slot_type *slot, slot_type *other) { absl::allocator_traits::construct(*alloc, slot, std::move(*other)); } template static void destroy(Alloc *alloc, slot_type *slot) { absl::allocator_traits::destroy(*alloc, slot); } template static void swap(Alloc * /*alloc*/, slot_type *a, slot_type *b) { using std::swap; swap(*a, *b); } template static void move(Alloc * /*alloc*/, slot_type *src, slot_type *dest) { *dest = std::move(*src); } }; // A parameters structure for holding the type parameters for a btree_set. // Compare and Alloc should be nothrow copy-constructible. template struct set_params : common_params> { using value_type = Key; using slot_type = typename set_params::common_params::slot_type; using value_compare = typename set_params::common_params::key_compare; using is_map_container = std::false_type; template static const V &key(const V &value) { return value; } static const Key &key(const slot_type *slot) { return *slot; } static const Key &key(slot_type *slot) { return *slot; } }; // 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 struct upper_bound_adapter { explicit upper_bound_adapter(const Compare &c) : comp(c) {} template 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 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 struct SearchResult { explicit SearchResult(V value) : value(value) {} SearchResult(V value, MatchKind /*match*/) : value(value) {} 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 class btree_node { using is_key_compare_to = typename Params::is_key_compare_to; using is_multi_container = typename Params::is_multi_container; using field_type = typename Params::node_count_type; using allocator_type = typename Params::allocator_type; using slot_type = typename Params::slot_type; 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 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, std::is_arithmetic::value && (std::is_same, key_compare>::value || std::is_same, key_compare>::value)>; // This class is organized by gtl::Layout as if it had the following // structure: // // A pointer to the node's parent. // btree_node *parent; // // // 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, kNodeValues] for root leaf nodes, kNodeValues for non-root leaf // // nodes, and kInternalNodeMaxCount (as a sentinel value) for internal // // nodes (even though there are still kNodeValues 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 // // kNodeValues 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 kNodeValues + 1 children for // // internal nodes. // btree_node *children[kNodeValues + 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; // Public for EmptyNodeType. constexpr static size_type Alignment() { static_assert(LeafLayout(1).Alignment() == InternalLayout().Alignment(), "Alignment of all nodes must be equal."); return InternalLayout().Alignment(); } protected: btree_node() = default; private: using layout_type = absl::container_internal::Layout; constexpr static size_type SizeWithNValues(size_type n) { return layout_type(/*parent*/ 1, /*position, start, finish, max_count*/ 4, /*values*/ n, /*children*/ 0) .AllocSize(); } // A lower bound for the overhead of fields other than values in a leaf node. constexpr static size_type MinimumOverhead() { return SizeWithNValues(1) - sizeof(value_type); } // Compute how many values we can fit onto a leaf node taking into account // padding. constexpr static size_type NodeTargetValues(const int begin, const int end) { return begin == end ? begin : SizeWithNValues((begin + end) / 2 + 1) > params_type::kTargetNodeSize ? NodeTargetValues(begin, (begin + end) / 2) : NodeTargetValues((begin + end) / 2 + 1, end); } enum { kTargetNodeSize = params_type::kTargetNodeSize, kNodeTargetValues = NodeTargetValues(0, params_type::kTargetNodeSize), // We need a minimum of 3 values 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). kNodeValues = kNodeTargetValues >= 3 ? kNodeTargetValues : 3, // The node is internal (i.e. is not a leaf node) if and only if `max_count` // has this value. kInternalNodeMaxCount = 0, }; // Leaves can have less than kNodeValues values. constexpr static layout_type LeafLayout(const int max_values = kNodeValues) { return layout_type(/*parent*/ 1, /*position, start, finish, max_count*/ 4, /*values*/ max_values, /*children*/ 0); } constexpr static layout_type InternalLayout() { return layout_type(/*parent*/ 1, /*position, start, finish, max_count*/ 4, /*values*/ kNodeValues, /*children*/ kNodeValues + 1); } constexpr static size_type LeafSize(const int max_values = kNodeValues) { return LeafLayout(max_values).AllocSize(); } constexpr static size_type InternalSize() { return InternalLayout().AllocSize(); } // N is the index of the type in the Layout definition. // ElementType is the Nth type in the Layout definition. template inline typename layout_type::template ElementType *GetField() { // We assert that we don't read from values that aren't there. assert(N < 3 || !leaf()); return InternalLayout().template Pointer(reinterpret_cast(this)); } template inline const typename layout_type::template ElementType *GetField() const { assert(N < 3 || !leaf()); return InternalLayout().template Pointer( reinterpret_cast(this)); } void set_parent(btree_node *p) { *GetField<0>() = p; } field_type &mutable_finish() { return GetField<1>()[2]; } slot_type *slot(int i) { return &GetField<2>()[i]; } slot_type *start_slot() { return slot(start()); } slot_type *finish_slot() { return slot(finish()); } const slot_type *slot(int i) const { return &GetField<2>()[i]; } void set_position(field_type v) { GetField<1>()[0] = v; } void set_start(field_type v) { GetField<1>()[1] = v; } void set_finish(field_type v) { GetField<1>()[2] = v; } // This method is only called by the node init methods. void set_max_count(field_type v) { GetField<1>()[3] = v; } public: // Whether this is a leaf node or not. This value doesn't change after the // node is created. bool leaf() const { return GetField<1>()[3] != kInternalNodeMaxCount; } // Getter for the position of this node in its parent. field_type position() const { return GetField<1>()[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<1>()[1]; assert(GetField<1>()[1] == 0); return 0; } // Getter for the offset after the last value in the `values` array. field_type finish() const { return GetField<1>()[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, kNodeValues]. const field_type max_count = GetField<1>()[3]; return max_count == field_type{kInternalNodeMaxCount} ? field_type{kNodeValues} : 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()->leaf(); } void make_root() { assert(parent()->is_root()); set_parent(parent()->parent()); } // Getters for the key/value at position i in the node. const key_type &key(int i) const { return params_type::key(slot(i)); } reference value(int i) { return params_type::element(slot(i)); } const_reference value(int i) const { return params_type::element(slot(i)); } // Getters/setter for the child at position i in the node. btree_node *child(int i) const { return GetField<3>()[i]; } btree_node *start_child() const { return child(start()); } btree_node *&mutable_child(int i) { return GetField<3>()[i]; } void clear_child(int i) { absl::container_internal::SanitizerPoisonObject(&mutable_child(i)); } void set_child(int i, btree_node *c) { absl::container_internal::SanitizerUnpoisonObject(&mutable_child(i)); mutable_child(i) = c; c->set_position(i); } void init_child(int 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 SearchResult 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 int upper_bound(const K &k, const key_compare &comp) const { auto upper_compare = upper_bound_adapter(comp); return use_linear_search::value ? linear_search(k, upper_compare).value : binary_search(k, upper_compare).value; } template SearchResult::value> linear_search(const K &k, const Compare &comp) const { return linear_search_impl(k, start(), finish(), comp, btree_is_key_compare_to()); } template SearchResult::value> binary_search(const K &k, const Compare &comp) const { return binary_search_impl(k, start(), finish(), comp, btree_is_key_compare_to()); } // Returns the position of the first value whose key is not less than k using // linear search performed using plain compare. template SearchResult linear_search_impl( const K &k, int s, const int e, const Compare &comp, std::false_type /* IsCompareTo */) const { while (s < e) { if (!comp(key(s), k)) { break; } ++s; } return SearchResult{s}; } // Returns the position of the first value whose key is not less than k using // linear search performed using compare-to. template SearchResult linear_search_impl( const K &k, int s, const int 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 SearchResult binary_search_impl( const K &k, int s, int e, const Compare &comp, std::false_type /* IsCompareTo */) const { while (s != e) { const int mid = (s + e) >> 1; if (comp(key(mid), k)) { s = mid + 1; } else { e = mid; } } return SearchResult{s}; } // Returns the position of the first value whose key is not less than k using // binary search performed using compare-to. template SearchResult binary_search_impl( const K &k, int s, int e, const CompareTo &comp, std::true_type /* IsCompareTo */) const { if (is_multi_container::value) { MatchKind exact_match = MatchKind::kNe; while (s != e) { const int 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 this is a // multi-container. exact_match = MatchKind::kEq; } } } return {s, exact_match}; } else { // Not a multi-container. while (s != e) { const int 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}; } } // Emplaces a value at position i, shifting all existing values and // children at positions >= i to the right by 1. template void emplace_value(size_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(int to_move, btree_node *right, allocator_type *alloc); void rebalance_left_to_right(int 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(btree_node *parent, int max_count) { set_parent(parent); set_position(0); 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(btree_node *parent) { init_leaf(parent, kNodeValues); // 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()), (kNodeValues + 1) * sizeof(btree_node *)); } static void deallocate(const size_type size, btree_node *node, allocator_type *alloc) { absl::container_internal::Deallocate(alloc, node, size); } // Deletes a node and all of its children. static void clear_and_delete(btree_node *node, allocator_type *alloc); public: // Exposed only for tests. static bool testonly_uses_linear_node_search() { return use_linear_search::value; } private: template void value_init(const field_type i, allocator_type *alloc, Args &&... args) { absl::container_internal::SanitizerUnpoisonObject(slot(i)); params_type::construct(alloc, slot(i), std::forward(args)...); } void value_destroy(const field_type i, allocator_type *alloc) { 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) { 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) { 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) { 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) { for (slot_type *src = src_node->slot(src_i + n - 1), *end = src - n, *dest = slot(dest_i + n - 1); src != end; --src, --dest) { transfer(dest, src, alloc); } } template friend class btree; template friend struct btree_iterator; friend class BtreeNodePeer; }; template struct btree_iterator { private: using key_type = typename Node::key_type; using size_type = typename Node::size_type; using params_type = typename Node::params_type; using node_type = Node; using normal_node = typename std::remove_const::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; using iterator = btree_iterator; using const_iterator = btree_iterator; 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() : node(nullptr), position(-1) {} explicit btree_iterator(Node *n) : node(n), position(n->start()) {} btree_iterator(Node *n, int p) : node(n), position(p) {} // NOTE: this SFINAE allows for implicit conversions from iterator to // const_iterator, but it specifically avoids defining copy constructors so // that btree_iterator can be trivially copyable. This is for performance and // binary size reasons. template , iterator>::value && std::is_same::value, int> = 0> btree_iterator(const btree_iterator &other) // NOLINT : node(other.node), position(other.position) {} private: // This SFINAE allows explicit conversions from const_iterator to // iterator, but also avoids defining a 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 , const_iterator>::value && std::is_same::value, int> = 0> explicit btree_iterator(const btree_iterator &other) : node(const_cast(other.node)), position(other.position) {} // Increment/decrement the iterator. void increment() { if (node->leaf() && ++position < node->finish()) { return; } increment_slow(); } void increment_slow(); void decrement() { if (node->leaf() && --position >= node->start()) { return; } decrement_slow(); } void decrement_slow(); public: bool operator==(const iterator &other) const { return node == other.node && position == other.position; } bool operator==(const const_iterator &other) const { return node == other.node && position == other.position; } bool operator!=(const iterator &other) const { return node != other.node || position != other.position; } bool operator!=(const const_iterator &other) const { return node != other.node || position != other.position; } // Accessors for the key/value the iterator is pointing at. reference operator*() const { ABSL_HARDENING_ASSERT(node != nullptr); ABSL_HARDENING_ASSERT(node->start() <= position); ABSL_HARDENING_ASSERT(node->finish() > position); return node->value(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: template friend class btree; template friend class btree_container; template friend class btree_set_container; template friend class btree_map_container; template friend class btree_multiset_container; template friend struct btree_iterator; template friend class base_checker; const key_type &key() const { return node->key(position); } slot_type *slot() { return node->slot(position); } // 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 class btree { using node_type = btree_node; using is_key_compare_to = typename Params::is_key_compare_to; using init_type = typename Params::init_type; using field_type = typename node_type::field_type; using is_multi_container = typename Params::is_multi_container; using is_key_compare_adapted = typename Params::is_key_compare_adapted; // We use a static empty node for the root/leftmost/rightmost of empty btrees // in order to avoid branching in begin()/end(). struct alignas(node_type::Alignment()) EmptyNodeType : node_type { using field_type = typename node_type::field_type; node_type *parent; 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; #ifdef _MSC_VER // MSVC has constexpr code generations bugs here. EmptyNodeType() : parent(this) {} #else constexpr EmptyNodeType(node_type *p) : parent(p) {} #endif }; static node_type *EmptyNode() { #ifdef _MSC_VER static EmptyNodeType *empty_node = new EmptyNodeType; // This assert fails on some other construction methods. assert(empty_node->parent == empty_node); return empty_node; #else static constexpr EmptyNodeType empty_node( const_cast(&empty_node)); return const_cast(&empty_node); #endif } enum : uint32_t { kNodeValues = node_type::kNodeValues, kMinNodeValues = kNodeValues / 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 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 = btree_iterator; using const_iterator = typename iterator::const_iterator; using reverse_iterator = std::reverse_iterator; using const_reverse_iterator = std::reverse_iterator; using node_handle_type = node_handle; // Internal types made public for use by btree_container types. using params_type = Params; using slot_type = typename Params::slot_type; private: // For use in copy_or_move_values_in_order. const value_type &maybe_move_from_iterator(const_iterator it) { return *it; } value_type &&maybe_move_from_iterator(iterator it) { return std::move(*it); } // 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 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); btree(const btree &other); btree(btree &&other) noexcept : root_(std::move(other.root_)), rightmost_(absl::exchange(other.rightmost_, EmptyNode())), size_(absl::exchange(other.size_, 0)) { other.mutable_root() = EmptyNode(); } ~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 iterator lower_bound(const K &key) { return internal_end(internal_lower_bound(key)); } template const_iterator lower_bound(const K &key) const { return internal_end(internal_lower_bound(key)); } // Finds the first element whose key is greater than key. template iterator upper_bound(const K &key) { return internal_end(internal_upper_bound(key)); } template 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 std::pair equal_range(const K &key); template std::pair equal_range(const K &key) const { return const_cast(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 std::pair 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 std::pair 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 ()( params_type::key(*std::declval()), std::declval()))> 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 void insert_iterator_unique(InputIterator b, InputIterator e, char); // Inserts a value into the btree. template iterator insert_multi(const key_type &key, ValueType &&v); // Inserts a value into the btree. template iterator insert_multi(ValueType &&v) { return insert_multi(params_type::key(v), std::forward(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 iterator insert_hint_multi(iterator position, ValueType &&v); // Insert a range of values into the btree. template 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 erase_range(iterator begin, iterator end); // Erases the specified key from the btree. Returns 1 if an element was // erased and 0 otherwise. template size_type erase_unique(const K &key); // Erases all of the entries matching the specified key from the // btree. Returns the number of elements erased. template size_type erase_multi(const K &key); // Finds the iterator corresponding to a key or returns end() if the key is // not present. template iterator find(const K &key) { return internal_end(internal_find(key)); } template const_iterator find(const K &key) const { return internal_end(internal_find(key)); } // Returns a count of the number of times the key appears in the btree. template size_type count_unique(const K &key) const { const iterator begin = internal_find(key); if (begin.node == nullptr) { // The key doesn't exist in the tree. return 0; } return 1; } // Returns a count of the number of times the key appears in the btree. template size_type count_multi(const K &key) const { const auto range = equal_range(key); return std::distance(range.first, range.second); } // 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 root_.template get<0>(); } template 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(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::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. 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. static double average_bytes_per_value() { // Returns the number of bytes per value on a leaf node that is 75% // full. Experimentally, this matches up nicely with the computed number of // bytes per value in trees that had their values inserted in random order. return node_type::LeafSize() / (kNodeValues * 0.75); } // 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(size()) / (nodes() * kNodeValues); } // 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(size()); } // The allocator used by the btree. allocator_type get_allocator() const { return allocator(); } private: // Internal accessor routines. node_type *root() { return root_.template get<2>(); } const node_type *root() const { return root_.template get<2>(); } node_type *&mutable_root() noexcept { return root_.template get<2>(); } key_compare *mutable_key_comp() noexcept { return &root_.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 &root_.template get<1>(); } const allocator_type &allocator() const noexcept { return root_.template get<1>(); } // Allocates a correctly aligned node of at least size bytes using the // allocator. node_type *allocate(const size_type size) { return reinterpret_cast( absl::container_internal::Allocate( mutable_allocator(), size)); } // Node creation/deletion routines. node_type *new_internal_node(node_type *parent) { node_type *n = allocate(node_type::InternalSize()); n->init_internal(parent); return n; } node_type *new_leaf_node(node_type *parent) { node_type *n = allocate(node_type::LeafSize()); n->init_leaf(parent, kNodeValues); return n; } node_type *new_leaf_root_node(const int max_count) { node_type *n = allocate(node_type::LeafSize(max_count)); n->init_leaf(/*parent=*/n, max_count); 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 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 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 SearchResult internal_locate( const K &key) const; // Internal routine which implements lower_bound(). template iterator internal_lower_bound(const K &key) const; // Internal routine which implements upper_bound(). template iterator internal_upper_bound(const K &key) const; // Internal routine which implements find(). template iterator internal_find(const K &key) const; // Verifies the tree structure of node. int 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->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; } public: // Exposed only for tests. static bool testonly_uses_linear_node_search() { return node_type::testonly_uses_linear_node_search(); } private: // We use compressed tuple in order to save space because key_compare and // allocator_type are usually empty. absl::container_internal::CompressedTuple root_; // A pointer to the rightmost node. Note that the leftmost node is stored as // the root's parent. node_type *rightmost_; // Number of values. size_type size_; }; //// // btree_node methods template template inline void btree_node

::emplace_value(const size_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(i, alloc, std::forward(args)...); set_finish(finish() + 1); if (!leaf() && finish() > i + 1) { for (int j = finish(); j > i + 1; --j) { set_child(j, child(j - 1)); } clear_child(i + 1); } } template inline void btree_node

::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 (!leaf()) { // Delete all children between begin and end. for (int j = 0; j < to_erase; ++j) { clear_and_delete(child(i + j + 1), alloc); } // Rotate children after end into new positions. for (int 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 void btree_node

::rebalance_right_to_left(const int 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 (!leaf()) { // Move the child pointers from the right to the left node. for (int i = 0; i < to_move; ++i) { init_child(finish() + i + 1, right->child(i)); } for (int 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 void btree_node

::rebalance_left_to_right(const int 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 (!leaf()) { // Move the child pointers from the left to the right node. for (int i = right->finish(); i >= right->start(); --i) { right->init_child(i + to_move, right->child(i)); right->clear_child(i); } for (int 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 void btree_node

::split(const int insert_position, btree_node *dest, allocator_type *alloc) { assert(dest->count() == 0); assert(max_count() == kNodeValues); // 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 == kNodeValues) { 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()->init_child(position() + 1, dest); if (!leaf()) { for (int 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 void btree_node

::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 (!leaf()) { // Move the child pointers from the right to the left node. for (int 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 void btree_node

::clear_and_delete(btree_node *node, allocator_type *alloc) { if (node->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->leaf()) node = node->start_child(); // Use `int` because `pos` needs to be able to hold `kNodeValues+1`, which // isn't guaranteed to be a valid `field_type`. int 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(pos); if (!node->leaf()) { // Navigate to the leftmost leaf under node. while (!node->leaf()) node = node->start_child(); pos = node->position(); parent = node->parent(); } node->value_destroy_n(node->start(), node->count(), alloc); 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) return; ++pos; } while (pos > parent->finish()); } } //// // btree_iterator methods template void btree_iterator::increment_slow() { if (node->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(position + 1); while (!node->leaf()) { node = node->start_child(); } position = node->start(); } } template void btree_iterator::decrement_slow() { if (node->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(position); while (!node->leaf()) { node = node->child(node->finish()); } position = node->finish() - 1; } } //// // btree methods template template void btree

::copy_or_move_values_in_order(Btree *other) { static_assert(std::is_same::value || std::is_same::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(maybe_move_from_iterator(iter)); ++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(), maybe_move_from_iterator(iter)); } } template constexpr bool btree

::static_assert_validation() { static_assert(std::is_nothrow_copy_constructible::value, "Key comparison must be nothrow copy constructible"); static_assert(std::is_nothrow_copy_constructible::value, "Allocator must be nothrow copy constructible"); static_assert(type_traits_internal::is_trivially_copyable::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( kNodeValues < (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. using compare_result_type = absl::result_of_t; static_assert( std::is_same::value || std::is_convertible::value, "key comparison function must return absl::{weak,strong}_ordering or " "bool."); // Test the assumption made in setting kNodeValueSpace. static_assert(node_type::MinimumOverhead() >= sizeof(void *) + 4, "node space assumption incorrect"); return true; } template btree

::btree(const key_compare &comp, const allocator_type &alloc) : root_(comp, alloc, EmptyNode()), rightmost_(EmptyNode()), size_(0) {} template btree

::btree(const btree &other) : btree(other.key_comp(), other.allocator()) { copy_or_move_values_in_order(&other); } template template auto btree

::equal_range(const K &key) -> std::pair { const iterator lower = lower_bound(key); // TODO(ezb): we should be able to avoid this comparison when there's a // three-way comparator. if (lower == end() || compare_keys(key, lower.key())) return {lower, lower}; const iterator next = std::next(lower); // When the comparator is heterogeneous, we can't assume that comparison with // non-`key_type` will be equivalent to `key_type` comparisons so there // could be multiple equivalent keys even in a unique-container. But for // heterogeneous comparisons from the default string adapted comparators, we // don't need to worry about this. if (!is_multi_container::value && (std::is_same::value || is_key_compare_adapted::value)) { // 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 are equivalent. 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 template auto btree

::insert_unique(const K &key, Args &&... args) -> std::pair { if (empty()) { mutable_root() = rightmost_ = new_leaf_root_node(1); } SearchResult 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)...), true}; } template template inline auto btree

::insert_hint_unique(iterator position, const K &key, Args &&... args) -> std::pair { 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)...), 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)...), true}; } } else { // position.key() == key return {position, false}; } } return insert_unique(key, std::forward(args)...); } template template void btree

::insert_iterator_unique(InputIterator b, InputIterator e, int) { for (; b != e; ++b) { insert_hint_unique(end(), params_type::key(*b), *b); } } template template void btree

::insert_iterator_unique(InputIterator b, InputIterator e, char) { for (; b != e; ++b) { init_type value(*b); insert_hint_unique(end(), params_type::key(value), std::move(value)); } } template template auto btree

::insert_multi(const key_type &key, ValueType &&v) -> iterator { if (empty()) { mutable_root() = rightmost_ = new_leaf_root_node(1); } iterator iter = internal_upper_bound(key); if (iter.node == nullptr) { iter = end(); } return internal_emplace(iter, std::forward(v)); } template template auto btree

::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(v)); } } else { ++position; if (position == end() || !compare_keys(position.key(), key)) { // {original `position`}.key() < key < {current `position`}.key() return internal_emplace(position, std::forward(v)); } } } return insert_multi(std::forward(v)); } template template void btree

::insert_iterator_multi(InputIterator b, InputIterator e) { for (; b != e; ++b) { insert_hint_multi(end(), *b); } } template auto btree

::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 auto btree

::operator=(btree &&other) noexcept -> btree & { if (this != &other) { clear(); using std::swap; if (absl::allocator_traits< allocator_type>::propagate_on_container_copy_assignment::value) { // Note: `root_` also contains the allocator and the key comparator. swap(root_, other.root_); 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(rightmost_, other.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 auto btree

::erase(iterator iter) -> iterator { bool internal_delete = false; if (!iter.node->leaf()) { // Deletion of a value on an internal node. First, move the largest value // from our left child here, then delete that position (in remove_values() // below). We can get to the largest value from our left child by // decrementing iter. iterator internal_iter(iter); --iter; assert(iter.node->leaf()); params_type::move(mutable_allocator(), iter.node->slot(iter.position), internal_iter.node->slot(internal_iter.position)); internal_delete = true; } // Delete the key from the leaf. iter.node->remove_values(iter.position, /*to_erase=*/1, mutable_allocator()); --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 auto btree

::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(); } // 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; } template auto btree

::erase_range(iterator begin, iterator end) -> std::pair { difference_type count = std::distance(begin, end); assert(count >= 0); if (count == 0) { return {0, begin}; } if (count == size_) { clear(); return {count, this->end()}; } if (begin.node == end.node) { assert(end.position > begin.position); begin.node->remove_values(begin.position, 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->leaf()) { const size_type remaining_to_erase = size_ - target_size; const size_type remaining_in_node = begin.node->finish() - begin.position; const size_type to_erase = (std::min)(remaining_to_erase, remaining_in_node); begin.node->remove_values(begin.position, to_erase, mutable_allocator()); size_ -= to_erase; begin = rebalance_after_delete(begin); } else { begin = erase(begin); } } return {count, begin}; } template template auto btree

::erase_unique(const K &key) -> size_type { const iterator iter = internal_find(key); if (iter.node == nullptr) { // The key doesn't exist in the tree, return nothing done. return 0; } erase(iter); return 1; } template template auto btree

::erase_multi(const K &key) -> size_type { const iterator begin = internal_lower_bound(key); if (begin.node == nullptr) { // The key doesn't exist in the tree, return nothing done. return 0; } // Delete all of the keys between begin and upper_bound(key). const iterator end = internal_end(internal_upper_bound(key)); return erase_range(begin, end).first; } template void btree

::clear() { if (!empty()) { node_type::clear_and_delete(root(), mutable_allocator()); } mutable_root() = EmptyNode(); rightmost_ = EmptyNode(); size_ = 0; } template void btree

::swap(btree &other) { using std::swap; if (absl::allocator_traits< allocator_type>::propagate_on_container_swap::value) { // Note: `root_` also contains the allocator and the key comparator. swap(root_, other.root_); } else { // It's undefined behavior if the allocators are unequal here. assert(allocator() == other.allocator()); swap(mutable_root(), other.mutable_root()); swap(*mutable_key_comp(), *other.mutable_key_comp()); } swap(rightmost_, other.rightmost_); swap(size_, other.size_); } template void btree

::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()->leaf()); assert(rightmost_->leaf()); } template void btree

::rebalance_or_split(iterator *iter) { node_type *&node = iter->node; int &insert_position = iter->position; assert(node->count() == node->max_count()); assert(kNodeValues == 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() == kNodeValues); if (left->count() < kNodeValues) { // 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. int to_move = (kNodeValues - left->count()) / (1 + (insert_position < kNodeValues)); to_move = (std::max)(1, to_move); if (insert_position - to_move >= node->start() || left->count() + to_move < kNodeValues) { left->rebalance_right_to_left(to_move, node, mutable_allocator()); assert(node->max_count() - node->count() == to_move); insert_position = 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() == kNodeValues); if (right->count() < kNodeValues) { // 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. int to_move = (kNodeValues - right->count()) / (1 + (insert_position > node->start())); to_move = (std::max)(1, to_move); if (insert_position <= node->finish() - to_move || right->count() + to_move < kNodeValues) { 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() == kNodeValues); if (parent->count() == kNodeValues) { iterator parent_iter(node->parent(), node->position()); rebalance_or_split(&parent_iter); } } 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(parent); parent->init_child(parent->start(), root()); mutable_root() = parent; // If the former root was a leaf node, then it's now the rightmost node. assert(!parent->start_child()->leaf() || parent->start_child() == rightmost_); } // Split the node. node_type *split_node; if (node->leaf()) { split_node = new_leaf_node(parent); node->split(insert_position, split_node, mutable_allocator()); if (rightmost_ == node) rightmost_ = split_node; } else { split_node = new_internal_node(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 void btree

::merge_nodes(node_type *left, node_type *right) { left->merge(right, mutable_allocator()); if (rightmost_ == right) rightmost_ = left; } template bool btree

::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() == kNodeValues); if (1 + left->count() + iter->node->count() <= kNodeValues) { 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() == kNodeValues); if (1 + iter->node->count() + right->count() <= kNodeValues) { 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())) { int to_move = (right->count() - iter->node->count()) / 2; to_move = (std::min)(to_move, 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())) { int to_move = (left->count() - iter->node->count()) / 2; to_move = (std::min)(to_move, left->count() - 1); left->rebalance_left_to_right(to_move, iter->node, mutable_allocator()); iter->position += to_move; return false; } } return false; } template void btree

::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->leaf()) { assert(size() == 0); mutable_root() = 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 template inline IterType btree

::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->leaf()) { iter.node = nullptr; break; } } return iter; } template template inline auto btree

::internal_emplace(iterator iter, Args &&... args) -> iterator { if (!iter.node->leaf()) { // 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(); if (iter.node->count() == max_count) { // Make room in the leaf for the new item. if (max_count < kNodeValues) { // Insertion into the root where the root is smaller than the full node // size. Simply grow the size of the root node. assert(iter.node == root()); iter.node = new_leaf_root_node((std::min)(kNodeValues, 2 * max_count)); // Transfer the values from the old root to the new root. node_type *old_root = root(); node_type *new_root = iter.node; new_root->transfer_n(old_root->count(), new_root->start(), old_root->start(), old_root, alloc); new_root->set_finish(old_root->finish()); old_root->set_finish(old_root->start()); node_type::clear_and_delete(old_root, alloc); mutable_root() = rightmost_ = new_root; } else { rebalance_or_split(&iter); } } iter.node->emplace_value(iter.position, alloc, std::forward(args)...); ++size_; return iter; } template template inline auto btree

::internal_locate(const K &key) const -> SearchResult { iterator iter(const_cast(root())); for (;;) { SearchResult res = iter.node->lower_bound(key, key_comp()); iter.position = 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->leaf()) { break; } iter.node = iter.node->child(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 template auto btree

::internal_lower_bound(const K &key) const -> iterator { iterator iter(const_cast(root())); for (;;) { iter.position = iter.node->lower_bound(key, key_comp()).value; if (iter.node->leaf()) { break; } iter.node = iter.node->child(iter.position); } return internal_last(iter); } template template auto btree

::internal_upper_bound(const K &key) const -> iterator { iterator iter(const_cast(root())); for (;;) { iter.position = iter.node->upper_bound(key, key_comp()); if (iter.node->leaf()) { break; } iter.node = iter.node->child(iter.position); } return internal_last(iter); } template template auto btree

::internal_find(const K &key) const -> iterator { SearchResult 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 int btree

::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))); } int count = node->count(); if (!node->leaf()) { for (int 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; } } // namespace container_internal ABSL_NAMESPACE_END } // namespace absl #endif // ABSL_CONTAINER_INTERNAL_BTREE_H_