1 // Copyright 2013 Google Inc. All Rights Reserved.
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
7 // http://www.apache.org/licenses/LICENSE-2.0
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
15 // A btree implementation of the STL set and map interfaces. A btree is both
16 // smaller and faster than STL set/map. The red-black tree implementation of
17 // STL set/map has an overhead of 3 pointers (left, right and parent) plus the
18 // node color information for each stored value. So a set<int32> consumes 20
19 // bytes for each value stored. This btree implementation stores multiple
20 // values on fixed size nodes (usually 256 bytes) and doesn't store child
21 // pointers for leaf nodes. The result is that a btree_set<int32> may use much
22 // less memory per stored value. For the random insertion benchmark in
23 // btree_test.cc, a btree_set<int32> with node-size of 256 uses 4.9 bytes per
26 // The packing of multiple values on to each node of a btree has another effect
27 // besides better space utilization: better cache locality due to fewer cache
28 // lines being accessed. Better cache locality translates into faster
33 // Insertions and deletions on a btree can cause splitting, merging or
34 // rebalancing of btree nodes. And even without these operations, insertions
35 // and deletions on a btree will move values around within a node. In both
36 // cases, the result is that insertions and deletions can invalidate iterators
37 // pointing to values other than the one being inserted/deleted. This is
38 // notably different from STL set/map which takes care to not invalidate
39 // iterators on insert/erase except, of course, for iterators pointing to the
40 // value being erased. A partial workaround when erasing is available:
41 // erase() returns an iterator pointing to the item just after the one that was
42 // erased (or end() if none exists). See also safe_btree.
46 // btree_bench --benchmarks=. 2>&1 | ./benchmarks.awk
48 // Run on pmattis-warp.nyc (4 X 2200 MHz CPUs); 2010/03/04-15:23:06
49 // Benchmark STL(ns) B-Tree(ns) @ <size>
50 // --------------------------------------------------------
51 // BM_set_int32_insert 1516 608 +59.89% <256> [40.0, 5.2]
52 // BM_set_int32_lookup 1160 414 +64.31% <256> [40.0, 5.2]
53 // BM_set_int32_fulllookup 960 410 +57.29% <256> [40.0, 4.4]
54 // BM_set_int32_delete 1741 528 +69.67% <256> [40.0, 5.2]
55 // BM_set_int32_queueaddrem 3078 1046 +66.02% <256> [40.0, 5.5]
56 // BM_set_int32_mixedaddrem 3600 1384 +61.56% <256> [40.0, 5.3]
57 // BM_set_int32_fifo 227 113 +50.22% <256> [40.0, 4.4]
58 // BM_set_int32_fwditer 158 26 +83.54% <256> [40.0, 5.2]
59 // BM_map_int32_insert 1551 636 +58.99% <256> [48.0, 10.5]
60 // BM_map_int32_lookup 1200 508 +57.67% <256> [48.0, 10.5]
61 // BM_map_int32_fulllookup 989 487 +50.76% <256> [48.0, 8.8]
62 // BM_map_int32_delete 1794 628 +64.99% <256> [48.0, 10.5]
63 // BM_map_int32_queueaddrem 3189 1266 +60.30% <256> [48.0, 11.6]
64 // BM_map_int32_mixedaddrem 3822 1623 +57.54% <256> [48.0, 10.9]
65 // BM_map_int32_fifo 151 134 +11.26% <256> [48.0, 8.8]
66 // BM_map_int32_fwditer 161 32 +80.12% <256> [48.0, 10.5]
67 // BM_set_int64_insert 1546 636 +58.86% <256> [40.0, 10.5]
68 // BM_set_int64_lookup 1200 512 +57.33% <256> [40.0, 10.5]
69 // BM_set_int64_fulllookup 971 487 +49.85% <256> [40.0, 8.8]
70 // BM_set_int64_delete 1745 616 +64.70% <256> [40.0, 10.5]
71 // BM_set_int64_queueaddrem 3163 1195 +62.22% <256> [40.0, 11.6]
72 // BM_set_int64_mixedaddrem 3760 1564 +58.40% <256> [40.0, 10.9]
73 // BM_set_int64_fifo 146 103 +29.45% <256> [40.0, 8.8]
74 // BM_set_int64_fwditer 162 31 +80.86% <256> [40.0, 10.5]
75 // BM_map_int64_insert 1551 720 +53.58% <256> [48.0, 20.7]
76 // BM_map_int64_lookup 1214 612 +49.59% <256> [48.0, 20.7]
77 // BM_map_int64_fulllookup 994 592 +40.44% <256> [48.0, 17.2]
78 // BM_map_int64_delete 1778 764 +57.03% <256> [48.0, 20.7]
79 // BM_map_int64_queueaddrem 3189 1547 +51.49% <256> [48.0, 20.9]
80 // BM_map_int64_mixedaddrem 3779 1887 +50.07% <256> [48.0, 21.6]
81 // BM_map_int64_fifo 147 145 +1.36% <256> [48.0, 17.2]
82 // BM_map_int64_fwditer 162 41 +74.69% <256> [48.0, 20.7]
83 // BM_set_string_insert 1989 1966 +1.16% <256> [64.0, 44.5]
84 // BM_set_string_lookup 1709 1600 +6.38% <256> [64.0, 44.5]
85 // BM_set_string_fulllookup 1573 1529 +2.80% <256> [64.0, 35.4]
86 // BM_set_string_delete 2520 1920 +23.81% <256> [64.0, 44.5]
87 // BM_set_string_queueaddrem 4706 4309 +8.44% <256> [64.0, 48.3]
88 // BM_set_string_mixedaddrem 5080 4654 +8.39% <256> [64.0, 46.7]
89 // BM_set_string_fifo 318 512 -61.01% <256> [64.0, 35.4]
90 // BM_set_string_fwditer 182 93 +48.90% <256> [64.0, 44.5]
91 // BM_map_string_insert 2600 2227 +14.35% <256> [72.0, 55.8]
92 // BM_map_string_lookup 2068 1730 +16.34% <256> [72.0, 55.8]
93 // BM_map_string_fulllookup 1859 1618 +12.96% <256> [72.0, 44.0]
94 // BM_map_string_delete 3168 2080 +34.34% <256> [72.0, 55.8]
95 // BM_map_string_queueaddrem 5840 4701 +19.50% <256> [72.0, 59.4]
96 // BM_map_string_mixedaddrem 6400 5200 +18.75% <256> [72.0, 57.8]
97 // BM_map_string_fifo 398 596 -49.75% <256> [72.0, 44.0]
98 // BM_map_string_fwditer 243 113 +53.50% <256> [72.0, 55.8]
100 #ifndef UTIL_BTREE_BTREE_H__
101 #define UTIL_BTREE_BTREE_H__
106 #include <sys/types.h>
108 #include <functional>
112 #include <type_traits>
124 // Inside a btree method, if we just call swap(), it will choose the
125 // btree::swap method, which we don't want. And we can't say ::swap
126 // because then MSVC won't pickup any std::swap() implementations. We
127 // can't just use std::swap() directly because then we don't get the
128 // specialization for types outside the std namespace. So the solution
129 // is to have a special swap helper function whose name doesn't
130 // collide with other swap functions defined by the btree classes.
131 template <typename T>
132 inline void btree_swap_helper(T &a, T &b) {
137 // A template helper used to select A or B based on a condition.
138 template<bool cond, typename A, typename B>
143 template<typename A, typename B>
144 struct if_<false, A, B> {
148 // Types small_ and big_ are promise that sizeof(small_) < sizeof(big_)
155 // A compile-time assertion.
157 struct CompileAssert {
160 #define COMPILE_ASSERT(expr, msg) \
161 typedef CompileAssert<(bool(expr))> msg[bool(expr) ? 1 : -1]
163 // A helper type used to indicate that a key-compare-to functor has been
164 // provided. A user can specify a key-compare-to functor by doing:
166 // struct MyStringComparer
167 // : public util::btree::btree_key_compare_to_tag {
168 // int operator()(const string &a, const string &b) const {
169 // return a.compare(b);
173 // Note that the return type is an int and not a bool. There is a
174 // COMPILE_ASSERT which enforces this return type.
175 struct btree_key_compare_to_tag {
178 // A helper class that indicates if the Compare parameter is derived from
179 // btree_key_compare_to_tag.
180 template <typename Compare>
181 struct btree_is_key_compare_to
182 : public std::is_convertible<Compare, btree_key_compare_to_tag> {
185 // A helper class to convert a boolean comparison into a three-way
186 // "compare-to" comparison that returns a negative value to indicate
187 // less-than, zero to indicate equality and a positive value to
188 // indicate greater-than. This helper class is specialized for
189 // less<string> and greater<string>. The btree_key_compare_to_adapter
190 // class is provided so that btree users automatically get the more
191 // efficient compare-to code when using common google string types
192 // with common comparison functors.
193 template <typename Compare>
194 struct btree_key_compare_to_adapter : Compare {
195 btree_key_compare_to_adapter() { }
196 btree_key_compare_to_adapter(const Compare &c) : Compare(c) { }
197 btree_key_compare_to_adapter(const btree_key_compare_to_adapter<Compare> &c)
203 struct btree_key_compare_to_adapter<std::less<std::string> >
204 : public btree_key_compare_to_tag {
205 btree_key_compare_to_adapter() {}
206 btree_key_compare_to_adapter(const std::less<std::string>&) {}
207 btree_key_compare_to_adapter(
208 const btree_key_compare_to_adapter<std::less<std::string> >&) {}
209 int operator()(const std::string &a, const std::string &b) const {
215 struct btree_key_compare_to_adapter<std::greater<std::string> >
216 : public btree_key_compare_to_tag {
217 btree_key_compare_to_adapter() {}
218 btree_key_compare_to_adapter(const std::greater<std::string>&) {}
219 btree_key_compare_to_adapter(
220 const btree_key_compare_to_adapter<std::greater<std::string> >&) {}
221 int operator()(const std::string &a, const std::string &b) const {
226 // A helper class that allows a compare-to functor to behave like a plain
227 // compare functor. This specialization is used when we do not have a
228 // compare-to functor.
229 template <typename Key, typename Compare, bool HaveCompareTo>
230 struct btree_key_comparer {
231 btree_key_comparer() {}
232 btree_key_comparer(Compare c) : comp(c) {}
233 static bool bool_compare(const Compare &comp, const Key &x, const Key &y) {
236 bool operator()(const Key &x, const Key &y) const {
237 return bool_compare(comp, x, y);
242 // A specialization of btree_key_comparer when a compare-to functor is
243 // present. We need a plain (boolean) comparison in some parts of the btree
244 // code, such as insert-with-hint.
245 template <typename Key, typename Compare>
246 struct btree_key_comparer<Key, Compare, true> {
247 btree_key_comparer() {}
248 btree_key_comparer(Compare c) : comp(c) {}
249 static bool bool_compare(const Compare &comp, const Key &x, const Key &y) {
250 return comp(x, y) < 0;
252 bool operator()(const Key &x, const Key &y) const {
253 return bool_compare(comp, x, y);
258 // A helper function to compare to keys using the specified compare
259 // functor. This dispatches to the appropriate btree_key_comparer comparison,
260 // depending on whether we have a compare-to functor or not (which depends on
261 // whether Compare is derived from btree_key_compare_to_tag).
262 template <typename Key, typename Compare>
263 static bool btree_compare_keys(
264 const Compare &comp, const Key &x, const Key &y) {
265 typedef btree_key_comparer<Key, Compare,
266 btree_is_key_compare_to<Compare>::value> key_comparer;
267 return key_comparer::bool_compare(comp, x, y);
270 template <typename Key, typename Compare,
271 typename Alloc, int TargetNodeSize, int ValueSize>
272 struct btree_common_params {
273 // If Compare is derived from btree_key_compare_to_tag then use it as the
274 // key_compare type. Otherwise, use btree_key_compare_to_adapter<> which will
275 // fall-back to Compare if we don't have an appropriate specialization.
276 typedef typename if_<
277 btree_is_key_compare_to<Compare>::value,
278 Compare, btree_key_compare_to_adapter<Compare> >::type key_compare;
279 // A type which indicates if we have a key-compare-to functor or a plain old
280 // key-compare functor.
281 typedef btree_is_key_compare_to<key_compare> is_key_compare_to;
283 typedef Alloc allocator_type;
284 typedef Key key_type;
285 typedef ssize_t size_type;
286 typedef ptrdiff_t difference_type;
289 kTargetNodeSize = TargetNodeSize,
291 // Available space for values. This is largest for leaf nodes,
292 // which has overhead no fewer than two pointers.
293 kNodeValueSpace = TargetNodeSize - 2 * sizeof(void*),
296 // This is an integral type large enough to hold as many
297 // ValueSize-values as will fit a node of TargetNodeSize bytes.
298 typedef typename if_<
299 (kNodeValueSpace / ValueSize) >= 256,
301 uint8_t>::type node_count_type;
304 // A parameters structure for holding the type parameters for a btree_map.
305 template <typename Key, typename Data, typename Compare,
306 typename Alloc, int TargetNodeSize>
307 struct btree_map_params
308 : public btree_common_params<Key, Compare, Alloc, TargetNodeSize,
309 sizeof(Key) + sizeof(Data)> {
310 typedef Data data_type;
311 typedef Data mapped_type;
312 typedef std::pair<const Key, data_type> value_type;
313 typedef std::pair<Key, data_type> mutable_value_type;
314 typedef value_type* pointer;
315 typedef const value_type* const_pointer;
316 typedef value_type& reference;
317 typedef const value_type& const_reference;
320 kValueSize = sizeof(Key) + sizeof(data_type),
323 static const Key& key(const value_type &x) { return x.first; }
324 static const Key& key(const mutable_value_type &x) { return x.first; }
325 static void swap(mutable_value_type *a, mutable_value_type *b) {
326 btree_swap_helper(a->first, b->first);
327 btree_swap_helper(a->second, b->second);
331 // A parameters structure for holding the type parameters for a btree_set.
332 template <typename Key, typename Compare, typename Alloc, int TargetNodeSize>
333 struct btree_set_params
334 : public btree_common_params<Key, Compare, Alloc, TargetNodeSize,
336 typedef std::false_type data_type;
337 typedef std::false_type mapped_type;
338 typedef Key value_type;
339 typedef value_type mutable_value_type;
340 typedef value_type* pointer;
341 typedef const value_type* const_pointer;
342 typedef value_type& reference;
343 typedef const value_type& const_reference;
346 kValueSize = sizeof(Key),
349 static const Key& key(const value_type &x) { return x; }
350 static void swap(mutable_value_type *a, mutable_value_type *b) {
351 btree_swap_helper<mutable_value_type>(*a, *b);
355 // An adapter class that converts a lower-bound compare into an upper-bound
357 template <typename Key, typename Compare>
358 struct btree_upper_bound_adapter : public Compare {
359 btree_upper_bound_adapter(Compare c) : Compare(c) {}
360 bool operator()(const Key &a, const Key &b) const {
361 return !static_cast<const Compare&>(*this)(b, a);
365 template <typename Key, typename CompareTo>
366 struct btree_upper_bound_compare_to_adapter : public CompareTo {
367 btree_upper_bound_compare_to_adapter(CompareTo c) : CompareTo(c) {}
368 int operator()(const Key &a, const Key &b) const {
369 return static_cast<const CompareTo&>(*this)(b, a);
373 // Dispatch helper class for using linear search with plain compare.
374 template <typename K, typename N, typename Compare>
375 struct btree_linear_search_plain_compare {
376 static int lower_bound(const K &k, const N &n, Compare comp) {
377 return n.linear_search_plain_compare(k, 0, n.count(), comp);
379 static int upper_bound(const K &k, const N &n, Compare comp) {
380 typedef btree_upper_bound_adapter<K, Compare> upper_compare;
381 return n.linear_search_plain_compare(k, 0, n.count(), upper_compare(comp));
385 // Dispatch helper class for using linear search with compare-to
386 template <typename K, typename N, typename CompareTo>
387 struct btree_linear_search_compare_to {
388 static int lower_bound(const K &k, const N &n, CompareTo comp) {
389 return n.linear_search_compare_to(k, 0, n.count(), comp);
391 static int upper_bound(const K &k, const N &n, CompareTo comp) {
392 typedef btree_upper_bound_adapter<K,
393 btree_key_comparer<K, CompareTo, true> > upper_compare;
394 return n.linear_search_plain_compare(k, 0, n.count(), upper_compare(comp));
398 // Dispatch helper class for using binary search with plain compare.
399 template <typename K, typename N, typename Compare>
400 struct btree_binary_search_plain_compare {
401 static int lower_bound(const K &k, const N &n, Compare comp) {
402 return n.binary_search_plain_compare(k, 0, n.count(), comp);
404 static int upper_bound(const K &k, const N &n, Compare comp) {
405 typedef btree_upper_bound_adapter<K, Compare> upper_compare;
406 return n.binary_search_plain_compare(k, 0, n.count(), upper_compare(comp));
410 // Dispatch helper class for using binary search with compare-to.
411 template <typename K, typename N, typename CompareTo>
412 struct btree_binary_search_compare_to {
413 static int lower_bound(const K &k, const N &n, CompareTo comp) {
414 return n.binary_search_compare_to(k, 0, n.count(), CompareTo());
416 static int upper_bound(const K &k, const N &n, CompareTo comp) {
417 typedef btree_upper_bound_adapter<K,
418 btree_key_comparer<K, CompareTo, true> > upper_compare;
419 return n.linear_search_plain_compare(k, 0, n.count(), upper_compare(comp));
423 // A node in the btree holding. The same node type is used for both internal
424 // and leaf nodes in the btree, though the nodes are allocated in such a way
425 // that the children array is only valid in internal nodes.
426 template <typename Params>
429 typedef Params params_type;
430 typedef btree_node<Params> self_type;
431 typedef typename Params::key_type key_type;
432 typedef typename Params::data_type data_type;
433 typedef typename Params::value_type value_type;
434 typedef typename Params::mutable_value_type mutable_value_type;
435 typedef typename Params::pointer pointer;
436 typedef typename Params::const_pointer const_pointer;
437 typedef typename Params::reference reference;
438 typedef typename Params::const_reference const_reference;
439 typedef typename Params::key_compare key_compare;
440 typedef typename Params::size_type size_type;
441 typedef typename Params::difference_type difference_type;
442 // Typedefs for the various types of node searches.
443 typedef btree_linear_search_plain_compare<
444 key_type, self_type, key_compare> linear_search_plain_compare_type;
445 typedef btree_linear_search_compare_to<
446 key_type, self_type, key_compare> linear_search_compare_to_type;
447 typedef btree_binary_search_plain_compare<
448 key_type, self_type, key_compare> binary_search_plain_compare_type;
449 typedef btree_binary_search_compare_to<
450 key_type, self_type, key_compare> binary_search_compare_to_type;
451 // If we have a valid key-compare-to type, use linear_search_compare_to,
452 // otherwise use linear_search_plain_compare.
453 typedef typename if_<
454 Params::is_key_compare_to::value,
455 linear_search_compare_to_type,
456 linear_search_plain_compare_type>::type linear_search_type;
457 // If we have a valid key-compare-to type, use binary_search_compare_to,
458 // otherwise use binary_search_plain_compare.
459 typedef typename if_<
460 Params::is_key_compare_to::value,
461 binary_search_compare_to_type,
462 binary_search_plain_compare_type>::type binary_search_type;
463 // If the key is an integral or floating point type, use linear search which
464 // is faster than binary search for such types. Might be wise to also
465 // configure linear search based on node-size.
466 typedef typename if_<
467 std::is_integral<key_type>::value ||
468 std::is_floating_point<key_type>::value,
469 linear_search_type, binary_search_type>::type search_type;
472 typedef typename Params::node_count_type field_type;
474 // A boolean indicating whether the node is a leaf or not.
476 // The position of the node in the node's parent.
478 // The maximum number of values the node can hold.
479 field_type max_count;
480 // The count of the number of values in the node.
482 // A pointer to the node's parent.
487 kValueSize = params_type::kValueSize,
488 kTargetNodeSize = params_type::kTargetNodeSize,
490 // Compute how many values we can fit onto a leaf node.
491 kNodeTargetValues = (kTargetNodeSize - sizeof(base_fields)) / kValueSize,
492 // We need a minimum of 3 values per internal node in order to perform
493 // splitting (1 value for the two nodes involved in the split and 1 value
494 // propagated to the parent as the delimiter for the split).
495 kNodeValues = kNodeTargetValues >= 3 ? kNodeTargetValues : 3,
497 kExactMatch = 1 << 30,
498 kMatchMask = kExactMatch - 1,
501 struct leaf_fields : public base_fields {
502 // The array of values. Only the first count of these values have been
503 // constructed and are valid.
504 mutable_value_type values[kNodeValues];
507 struct internal_fields : public leaf_fields {
508 // The array of child pointers. The keys in children_[i] are all less than
509 // key(i). The keys in children_[i + 1] are all greater than key(i). There
510 // are always count + 1 children.
511 btree_node *children[kNodeValues + 1];
514 struct root_fields : public internal_fields {
515 btree_node *rightmost;
520 // Getter/setter for whether this is a leaf node or not. This value doesn't
521 // change after the node is created.
522 bool leaf() const { return fields_.leaf; }
524 // Getter for the position of this node in its parent.
525 int position() const { return fields_.position; }
526 void set_position(int v) { fields_.position = v; }
528 // Getter/setter for the number of values stored in this node.
529 int count() const { return fields_.count; }
530 void set_count(int v) { fields_.count = v; }
531 int max_count() const { return fields_.max_count; }
533 // Getter for the parent of this node.
534 btree_node* parent() const { return fields_.parent; }
535 // Getter for whether the node is the root of the tree. The parent of the
536 // root of the tree is the leftmost node in the tree which is guaranteed to
538 bool is_root() const { return parent()->leaf(); }
540 assert(parent()->is_root());
541 fields_.parent = fields_.parent->parent();
544 // Getter for the rightmost root node field. Only valid on the root node.
545 btree_node* rightmost() const { return fields_.rightmost; }
546 btree_node** mutable_rightmost() { return &fields_.rightmost; }
548 // Getter for the size root node field. Only valid on the root node.
549 size_type size() const { return fields_.size; }
550 size_type* mutable_size() { return &fields_.size; }
552 // Getters for the key/value at position i in the node.
553 const key_type& key(int i) const {
554 return params_type::key(fields_.values[i]);
556 reference value(int i) {
557 return reinterpret_cast<reference>(fields_.values[i]);
559 const_reference value(int i) const {
560 return reinterpret_cast<const_reference>(fields_.values[i]);
562 mutable_value_type* mutable_value(int i) {
563 return &fields_.values[i];
566 // Swap value i in this node with value j in node x.
567 void value_swap(int i, btree_node *x, int j) {
568 params_type::swap(mutable_value(i), x->mutable_value(j));
571 // Getters/setter for the child at position i in the node.
572 btree_node* child(int i) const { return fields_.children[i]; }
573 btree_node** mutable_child(int i) { return &fields_.children[i]; }
574 void set_child(int i, btree_node *c) {
575 *mutable_child(i) = c;
576 c->fields_.parent = this;
577 c->fields_.position = i;
580 // Returns the position of the first value whose key is not less than k.
581 template <typename Compare>
582 int lower_bound(const key_type &k, const Compare &comp) const {
583 return search_type::lower_bound(k, *this, comp);
585 // Returns the position of the first value whose key is greater than k.
586 template <typename Compare>
587 int upper_bound(const key_type &k, const Compare &comp) const {
588 return search_type::upper_bound(k, *this, comp);
591 // Returns the position of the first value whose key is not less than k using
592 // linear search performed using plain compare.
593 template <typename Compare>
594 int linear_search_plain_compare(
595 const key_type &k, int s, int e, const Compare &comp) const {
597 if (!btree_compare_keys(comp, key(s), k)) {
605 // Returns the position of the first value whose key is not less than k using
606 // linear search performed using compare-to.
607 template <typename Compare>
608 int linear_search_compare_to(
609 const key_type &k, int s, int e, const Compare &comp) const {
611 int c = comp(key(s), k);
613 return s | kExactMatch;
622 // Returns the position of the first value whose key is not less than k using
623 // binary search performed using plain compare.
624 template <typename Compare>
625 int binary_search_plain_compare(
626 const key_type &k, int s, int e, const Compare &comp) const {
628 int mid = (s + e) / 2;
629 if (btree_compare_keys(comp, key(mid), k)) {
638 // Returns the position of the first value whose key is not less than k using
639 // binary search performed using compare-to.
640 template <typename CompareTo>
641 int binary_search_compare_to(
642 const key_type &k, int s, int e, const CompareTo &comp) const {
644 int mid = (s + e) / 2;
645 int c = comp(key(mid), k);
651 // Need to return the first value whose key is not less than k, which
652 // requires continuing the binary search. Note that we are guaranteed
653 // that the result is an exact match because if "key(mid-1) < k" the
654 // call to binary_search_compare_to() will return "mid".
655 s = binary_search_compare_to(k, s, mid, comp);
656 return s | kExactMatch;
662 // Inserts the value x at position i, shifting all existing values and
663 // children at positions >= i to the right by 1.
664 void insert_value(int i, const value_type &x);
666 // Removes the value at position i, shifting all existing values and children
667 // at positions > i to the left by 1.
668 void remove_value(int i);
670 // Rebalances a node with its right sibling.
671 void rebalance_right_to_left(btree_node *sibling, int to_move);
672 void rebalance_left_to_right(btree_node *sibling, int to_move);
674 // Splits a node, moving a portion of the node's values to its right sibling.
675 void split(btree_node *sibling, int insert_position);
677 // Merges a node with its right sibling, moving all of the values and the
678 // delimiting key in the parent node onto itself.
679 void merge(btree_node *sibling);
681 // Swap the contents of "this" and "src".
682 void swap(btree_node *src);
684 // Node allocation/deletion routines.
685 static btree_node* init_leaf(
686 leaf_fields *f, btree_node *parent, int max_count) {
687 btree_node *n = reinterpret_cast<btree_node*>(f);
690 f->max_count = max_count;
694 memset(&f->values, 0, max_count * sizeof(value_type));
698 static btree_node* init_internal(internal_fields *f, btree_node *parent) {
699 btree_node *n = init_leaf(f, parent, kNodeValues);
702 memset(f->children, 0, sizeof(f->children));
706 static btree_node* init_root(root_fields *f, btree_node *parent) {
707 btree_node *n = init_internal(f, parent);
708 f->rightmost = parent;
709 f->size = parent->count();
713 for (int i = 0; i < count(); ++i) {
719 void value_init(int i) {
720 new (&fields_.values[i]) mutable_value_type;
722 void value_init(int i, const value_type &x) {
723 new (&fields_.values[i]) mutable_value_type(x);
725 void value_destroy(int i) {
726 fields_.values[i].~mutable_value_type();
733 btree_node(const btree_node&);
734 void operator=(const btree_node&);
737 template <typename Node, typename Reference, typename Pointer>
738 struct btree_iterator {
739 typedef typename Node::key_type key_type;
740 typedef typename Node::size_type size_type;
741 typedef typename Node::difference_type difference_type;
742 typedef typename Node::params_type params_type;
744 typedef Node node_type;
745 typedef typename std::remove_const<Node>::type normal_node;
746 typedef const Node const_node;
747 typedef typename params_type::value_type value_type;
748 typedef typename params_type::pointer normal_pointer;
749 typedef typename params_type::reference normal_reference;
750 typedef typename params_type::const_pointer const_pointer;
751 typedef typename params_type::const_reference const_reference;
753 typedef Pointer pointer;
754 typedef Reference reference;
755 typedef std::bidirectional_iterator_tag iterator_category;
757 typedef btree_iterator<
758 normal_node, normal_reference, normal_pointer> iterator;
759 typedef btree_iterator<
760 const_node, const_reference, const_pointer> const_iterator;
761 typedef btree_iterator<Node, Reference, Pointer> self_type;
767 btree_iterator(Node *n, int p)
771 btree_iterator(const iterator &x)
773 position(x.position) {
776 // Increment/decrement the iterator.
778 if (node->leaf() && ++position < node->count()) {
783 void increment_by(int count);
784 void increment_slow();
787 if (node->leaf() && --position >= 0) {
792 void decrement_slow();
794 bool operator==(const const_iterator &x) const {
795 return node == x.node && position == x.position;
797 bool operator!=(const const_iterator &x) const {
798 return node != x.node || position != x.position;
801 // Accessors for the key/value the iterator is pointing at.
802 const key_type& key() const {
803 return node->key(position);
805 reference operator*() const {
806 return node->value(position);
808 pointer operator->() const {
809 return &node->value(position);
812 self_type& operator++() {
816 self_type& operator--() {
820 self_type operator++(int) {
821 self_type tmp = *this;
825 self_type operator--(int) {
826 self_type tmp = *this;
831 // The node in the tree the iterator is pointing at.
833 // The position within the node of the tree the iterator is pointing at.
837 // Dispatch helper class for using btree::internal_locate with plain compare.
838 struct btree_internal_locate_plain_compare {
839 template <typename K, typename T, typename Iter>
840 static std::pair<Iter, int> dispatch(const K &k, const T &t, Iter iter) {
841 return t.internal_locate_plain_compare(k, iter);
845 // Dispatch helper class for using btree::internal_locate with compare-to.
846 struct btree_internal_locate_compare_to {
847 template <typename K, typename T, typename Iter>
848 static std::pair<Iter, int> dispatch(const K &k, const T &t, Iter iter) {
849 return t.internal_locate_compare_to(k, iter);
853 template <typename Params>
854 class btree : public Params::key_compare {
855 typedef btree<Params> self_type;
856 typedef btree_node<Params> node_type;
857 typedef typename node_type::base_fields base_fields;
858 typedef typename node_type::leaf_fields leaf_fields;
859 typedef typename node_type::internal_fields internal_fields;
860 typedef typename node_type::root_fields root_fields;
861 typedef typename Params::is_key_compare_to is_key_compare_to;
863 friend class btree_internal_locate_plain_compare;
864 friend class btree_internal_locate_compare_to;
865 typedef typename if_<
866 is_key_compare_to::value,
867 btree_internal_locate_compare_to,
868 btree_internal_locate_plain_compare>::type internal_locate_type;
871 kNodeValues = node_type::kNodeValues,
872 kMinNodeValues = kNodeValues / 2,
873 kValueSize = node_type::kValueSize,
874 kExactMatch = node_type::kExactMatch,
875 kMatchMask = node_type::kMatchMask,
878 // A helper class to get the empty base class optimization for 0-size
879 // allocators. Base is internal_allocator_type.
880 // (e.g. empty_base_handle<internal_allocator_type, node_type*>). If Base is
881 // 0-size, the compiler doesn't have to reserve any space for it and
882 // sizeof(empty_base_handle) will simply be sizeof(Data). Google [empty base
883 // class optimization] for more details.
884 template <typename Base, typename Data>
885 struct empty_base_handle : public Base {
886 empty_base_handle(const Base &b, const Data &d)
894 node_stats(ssize_t l, ssize_t i)
899 node_stats& operator+=(const node_stats &x) {
900 leaf_nodes += x.leaf_nodes;
901 internal_nodes += x.internal_nodes;
906 ssize_t internal_nodes;
910 typedef Params params_type;
911 typedef typename Params::key_type key_type;
912 typedef typename Params::data_type data_type;
913 typedef typename Params::mapped_type mapped_type;
914 typedef typename Params::value_type value_type;
915 typedef typename Params::key_compare key_compare;
916 typedef typename Params::pointer pointer;
917 typedef typename Params::const_pointer const_pointer;
918 typedef typename Params::reference reference;
919 typedef typename Params::const_reference const_reference;
920 typedef typename Params::size_type size_type;
921 typedef typename Params::difference_type difference_type;
922 typedef btree_iterator<node_type, reference, pointer> iterator;
923 typedef typename iterator::const_iterator const_iterator;
924 typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
925 typedef std::reverse_iterator<iterator> reverse_iterator;
927 typedef typename Params::allocator_type allocator_type;
928 typedef typename allocator_type::template rebind<char>::other
929 internal_allocator_type;
932 // Default constructor.
933 btree(const key_compare &comp, const allocator_type &alloc);
936 btree(const self_type &x);
943 // Iterator routines.
945 return iterator(leftmost(), 0);
947 const_iterator begin() const {
948 return const_iterator(leftmost(), 0);
951 return iterator(rightmost(), rightmost() ? rightmost()->count() : 0);
953 const_iterator end() const {
954 return const_iterator(rightmost(), rightmost() ? rightmost()->count() : 0);
956 reverse_iterator rbegin() {
957 return reverse_iterator(end());
959 const_reverse_iterator rbegin() const {
960 return const_reverse_iterator(end());
962 reverse_iterator rend() {
963 return reverse_iterator(begin());
965 const_reverse_iterator rend() const {
966 return const_reverse_iterator(begin());
969 // Finds the first element whose key is not less than key.
970 iterator lower_bound(const key_type &key) {
972 internal_lower_bound(key, iterator(root(), 0)));
974 const_iterator lower_bound(const key_type &key) const {
976 internal_lower_bound(key, const_iterator(root(), 0)));
979 // Finds the first element whose key is greater than key.
980 iterator upper_bound(const key_type &key) {
982 internal_upper_bound(key, iterator(root(), 0)));
984 const_iterator upper_bound(const key_type &key) const {
986 internal_upper_bound(key, const_iterator(root(), 0)));
989 // Finds the range of values which compare equal to key. The first member of
990 // the returned pair is equal to lower_bound(key). The second member pair of
991 // the pair is equal to upper_bound(key).
992 std::pair<iterator,iterator> equal_range(const key_type &key) {
993 return std::make_pair(lower_bound(key), upper_bound(key));
995 std::pair<const_iterator,const_iterator> equal_range(const key_type &key) const {
996 return std::make_pair(lower_bound(key), upper_bound(key));
999 // Inserts a value into the btree only if it does not already exist. The
1000 // boolean return value indicates whether insertion succeeded or failed. The
1001 // ValuePointer type is used to avoid instatiating the value unless the key
1002 // is being inserted. Value is not dereferenced if the key already exists in
1003 // the btree. See btree_map::operator[].
1004 template <typename ValuePointer>
1005 std::pair<iterator,bool> insert_unique(const key_type &key, ValuePointer value);
1007 // Inserts a value into the btree only if it does not already exist. The
1008 // boolean return value indicates whether insertion succeeded or failed.
1009 std::pair<iterator,bool> insert_unique(const value_type &v) {
1010 return insert_unique(params_type::key(v), &v);
1013 // Insert with hint. Check to see if the value should be placed immediately
1014 // before position in the tree. If it does, then the insertion will take
1015 // amortized constant time. If not, the insertion will take amortized
1016 // logarithmic time as if a call to insert_unique(v) were made.
1017 iterator insert_unique(iterator position, const value_type &v);
1019 // Insert a range of values into the btree.
1020 template <typename InputIterator>
1021 void insert_unique(InputIterator b, InputIterator e);
1023 // Inserts a value into the btree. The ValuePointer type is used to avoid
1024 // instatiating the value unless the key is being inserted. Value is not
1025 // dereferenced if the key already exists in the btree. See
1026 // btree_map::operator[].
1027 template <typename ValuePointer>
1028 iterator insert_multi(const key_type &key, ValuePointer value);
1030 // Inserts a value into the btree.
1031 iterator insert_multi(const value_type &v) {
1032 return insert_multi(params_type::key(v), &v);
1035 // Insert with hint. Check to see if the value should be placed immediately
1036 // before position in the tree. If it does, then the insertion will take
1037 // amortized constant time. If not, the insertion will take amortized
1038 // logarithmic time as if a call to insert_multi(v) were made.
1039 iterator insert_multi(iterator position, const value_type &v);
1041 // Insert a range of values into the btree.
1042 template <typename InputIterator>
1043 void insert_multi(InputIterator b, InputIterator e);
1045 void assign(const self_type &x);
1047 // Erase the specified iterator from the btree. The iterator must be valid
1048 // (i.e. not equal to end()). Return an iterator pointing to the node after
1049 // the one that was erased (or end() if none exists).
1050 iterator erase(iterator iter);
1052 // Erases range. Returns the number of keys erased.
1053 int erase(iterator begin, iterator end);
1055 // Erases the specified key from the btree. Returns 1 if an element was
1056 // erased and 0 otherwise.
1057 int erase_unique(const key_type &key);
1059 // Erases all of the entries matching the specified key from the
1060 // btree. Returns the number of elements erased.
1061 int erase_multi(const key_type &key);
1063 // Finds the iterator corresponding to a key or returns end() if the key is
1065 iterator find_unique(const key_type &key) {
1066 return internal_end(
1067 internal_find_unique(key, iterator(root(), 0)));
1069 const_iterator find_unique(const key_type &key) const {
1070 return internal_end(
1071 internal_find_unique(key, const_iterator(root(), 0)));
1073 iterator find_multi(const key_type &key) {
1074 return internal_end(
1075 internal_find_multi(key, iterator(root(), 0)));
1077 const_iterator find_multi(const key_type &key) const {
1078 return internal_end(
1079 internal_find_multi(key, const_iterator(root(), 0)));
1082 // Returns a count of the number of times the key appears in the btree.
1083 size_type count_unique(const key_type &key) const {
1084 const_iterator begin = internal_find_unique(
1085 key, const_iterator(root(), 0));
1087 // The key doesn't exist in the tree.
1092 // Returns a count of the number of times the key appears in the btree.
1093 size_type count_multi(const key_type &key) const {
1094 return distance(lower_bound(key), upper_bound(key));
1097 // Clear the btree, deleting all of the values it contains.
1100 // Swap the contents of *this and x.
1101 void swap(self_type &x);
1103 // Assign the contents of x to *this.
1104 self_type& operator=(const self_type &x) {
1106 // Don't copy onto ourselves.
1113 key_compare* mutable_key_comp() {
1116 const key_compare& key_comp() const {
1119 bool compare_keys(const key_type &x, const key_type &y) const {
1120 return btree_compare_keys(key_comp(), x, y);
1123 // Dump the btree to the specified ostream. Requires that operator<< is
1124 // defined for Key and Value.
1125 void dump(std::ostream &os) const {
1126 if (root() != NULL) {
1127 internal_dump(os, root(), 0);
1131 // Verifies the structure of the btree.
1132 void verify() const;
1134 // Size routines. Note that empty() is slightly faster than doing size()==0.
1135 size_type size() const {
1136 if (empty()) return 0;
1137 if (root()->leaf()) return root()->count();
1138 return root()->size();
1140 size_type max_size() const { return std::numeric_limits<size_type>::max(); }
1141 bool empty() const { return root() == NULL; }
1143 // The height of the btree. An empty tree will have height 0.
1144 size_type height() const {
1147 // Count the length of the chain from the leftmost node up to the
1148 // root. We actually count from the root back around to the level below
1149 // the root, but the calculation is the same because of the circularity
1150 // of that traversal.
1151 const node_type *n = root();
1155 } while (n != root());
1160 // The number of internal, leaf and total nodes used by the btree.
1161 size_type leaf_nodes() const {
1162 return internal_stats(root()).leaf_nodes;
1164 size_type internal_nodes() const {
1165 return internal_stats(root()).internal_nodes;
1167 size_type nodes() const {
1168 node_stats stats = internal_stats(root());
1169 return stats.leaf_nodes + stats.internal_nodes;
1172 // The total number of bytes used by the btree.
1173 size_type bytes_used() const {
1174 node_stats stats = internal_stats(root());
1175 if (stats.leaf_nodes == 1 && stats.internal_nodes == 0) {
1176 return sizeof(*this) +
1177 sizeof(base_fields) + root()->max_count() * sizeof(value_type);
1179 return sizeof(*this) +
1180 sizeof(root_fields) - sizeof(internal_fields) +
1181 stats.leaf_nodes * sizeof(leaf_fields) +
1182 stats.internal_nodes * sizeof(internal_fields);
1186 // The average number of bytes used per value stored in the btree.
1187 static double average_bytes_per_value() {
1188 // Returns the number of bytes per value on a leaf node that is 75%
1189 // full. Experimentally, this matches up nicely with the computed number of
1190 // bytes per value in trees that had their values inserted in random order.
1191 return sizeof(leaf_fields) / (kNodeValues * 0.75);
1194 // The fullness of the btree. Computed as the number of elements in the btree
1195 // divided by the maximum number of elements a tree with the current number
1196 // of nodes could hold. A value of 1 indicates perfect space
1197 // utilization. Smaller values indicate space wastage.
1198 double fullness() const {
1199 return double(size()) / (nodes() * kNodeValues);
1201 // The overhead of the btree structure in bytes per node. Computed as the
1202 // total number of bytes used by the btree minus the number of bytes used for
1203 // storing elements divided by the number of elements.
1204 double overhead() const {
1208 return (bytes_used() - size() * kValueSize) / double(size());
1212 // Internal accessor routines.
1213 node_type* root() { return root_.data; }
1214 const node_type* root() const { return root_.data; }
1215 node_type** mutable_root() { return &root_.data; }
1217 // The rightmost node is stored in the root node.
1218 node_type* rightmost() {
1219 return (!root() || root()->leaf()) ? root() : root()->rightmost();
1221 const node_type* rightmost() const {
1222 return (!root() || root()->leaf()) ? root() : root()->rightmost();
1224 node_type** mutable_rightmost() { return root()->mutable_rightmost(); }
1226 // The leftmost node is stored as the parent of the root node.
1227 node_type* leftmost() { return root() ? root()->parent() : NULL; }
1228 const node_type* leftmost() const { return root() ? root()->parent() : NULL; }
1230 // The size of the tree is stored in the root node.
1231 size_type* mutable_size() { return root()->mutable_size(); }
1233 // Allocator routines.
1234 internal_allocator_type* mutable_internal_allocator() {
1235 return static_cast<internal_allocator_type*>(&root_);
1237 const internal_allocator_type& internal_allocator() const {
1238 return *static_cast<const internal_allocator_type*>(&root_);
1241 // Node creation/deletion routines.
1242 node_type* new_internal_node(node_type *parent) {
1243 internal_fields *p = reinterpret_cast<internal_fields*>(
1244 mutable_internal_allocator()->allocate(sizeof(internal_fields)));
1245 return node_type::init_internal(p, parent);
1247 node_type* new_internal_root_node() {
1248 root_fields *p = reinterpret_cast<root_fields*>(
1249 mutable_internal_allocator()->allocate(sizeof(root_fields)));
1250 return node_type::init_root(p, root()->parent());
1252 node_type* new_leaf_node(node_type *parent) {
1253 leaf_fields *p = reinterpret_cast<leaf_fields*>(
1254 mutable_internal_allocator()->allocate(sizeof(leaf_fields)));
1255 return node_type::init_leaf(p, parent, kNodeValues);
1257 node_type* new_leaf_root_node(int max_count) {
1258 leaf_fields *p = reinterpret_cast<leaf_fields*>(
1259 mutable_internal_allocator()->allocate(
1260 sizeof(base_fields) + max_count * sizeof(value_type)));
1261 return node_type::init_leaf(p, reinterpret_cast<node_type*>(p), max_count);
1263 void delete_internal_node(node_type *node) {
1265 assert(node != root());
1266 mutable_internal_allocator()->deallocate(
1267 reinterpret_cast<char*>(node), sizeof(internal_fields));
1269 void delete_internal_root_node() {
1271 mutable_internal_allocator()->deallocate(
1272 reinterpret_cast<char*>(root()), sizeof(root_fields));
1274 void delete_leaf_node(node_type *node) {
1276 mutable_internal_allocator()->deallocate(
1277 reinterpret_cast<char*>(node),
1278 sizeof(base_fields) + node->max_count() * sizeof(value_type));
1281 // Rebalances or splits the node iter points to.
1282 void rebalance_or_split(iterator *iter);
1284 // Merges the values of left, right and the delimiting key on their parent
1285 // onto left, removing the delimiting key and deleting right.
1286 void merge_nodes(node_type *left, node_type *right);
1288 // Tries to merge node with its left or right sibling, and failing that,
1289 // rebalance with its left or right sibling. Returns true if a merge
1290 // occurred, at which point it is no longer valid to access node. Returns
1291 // false if no merging took place.
1292 bool try_merge_or_rebalance(iterator *iter);
1294 // Tries to shrink the height of the tree by 1.
1297 iterator internal_end(iterator iter) {
1298 return iter.node ? iter : end();
1300 const_iterator internal_end(const_iterator iter) const {
1301 return iter.node ? iter : end();
1304 // Inserts a value into the btree immediately before iter. Requires that
1305 // key(v) <= iter.key() and (--iter).key() <= key(v).
1306 iterator internal_insert(iterator iter, const value_type &v);
1308 // Returns an iterator pointing to the first value >= the value "iter" is
1309 // pointing at. Note that "iter" might be pointing to an invalid location as
1310 // iter.position == iter.node->count(). This routine simply moves iter up in
1311 // the tree to a valid location.
1312 template <typename IterType>
1313 static IterType internal_last(IterType iter);
1315 // Returns an iterator pointing to the leaf position at which key would
1316 // reside in the tree. We provide 2 versions of internal_locate. The first
1317 // version (internal_locate_plain_compare) always returns 0 for the second
1318 // field of the pair. The second version (internal_locate_compare_to) is for
1319 // the key-compare-to specialization and returns either kExactMatch (if the
1320 // key was found in the tree) or -kExactMatch (if it wasn't) in the second
1321 // field of the pair. The compare_to specialization allows the caller to
1322 // avoid a subsequent comparison to determine if an exact match was made,
1323 // speeding up string keys.
1324 template <typename IterType>
1325 std::pair<IterType, int> internal_locate(
1326 const key_type &key, IterType iter) const;
1327 template <typename IterType>
1328 std::pair<IterType, int> internal_locate_plain_compare(
1329 const key_type &key, IterType iter) const;
1330 template <typename IterType>
1331 std::pair<IterType, int> internal_locate_compare_to(
1332 const key_type &key, IterType iter) const;
1334 // Internal routine which implements lower_bound().
1335 template <typename IterType>
1336 IterType internal_lower_bound(
1337 const key_type &key, IterType iter) const;
1339 // Internal routine which implements upper_bound().
1340 template <typename IterType>
1341 IterType internal_upper_bound(
1342 const key_type &key, IterType iter) const;
1344 // Internal routine which implements find_unique().
1345 template <typename IterType>
1346 IterType internal_find_unique(
1347 const key_type &key, IterType iter) const;
1349 // Internal routine which implements find_multi().
1350 template <typename IterType>
1351 IterType internal_find_multi(
1352 const key_type &key, IterType iter) const;
1354 // Deletes a node and all of its children.
1355 void internal_clear(node_type *node);
1357 // Dumps a node and all of its children to the specified ostream.
1358 void internal_dump(std::ostream &os, const node_type *node, int level) const;
1360 // Verifies the tree structure of node.
1361 int internal_verify(const node_type *node,
1362 const key_type *lo, const key_type *hi) const;
1364 node_stats internal_stats(const node_type *node) const {
1366 return node_stats(0, 0);
1369 return node_stats(1, 0);
1371 node_stats res(0, 1);
1372 for (int i = 0; i <= node->count(); ++i) {
1373 res += internal_stats(node->child(i));
1379 empty_base_handle<internal_allocator_type, node_type*> root_;
1382 // A never instantiated helper function that returns big_ if we have a
1383 // key-compare-to functor or if R is bool and small_ otherwise.
1384 template <typename R>
1385 static typename if_<
1386 if_<is_key_compare_to::value,
1387 std::is_same<R, int>,
1388 std::is_same<R, bool> >::type::value,
1389 big_, small_>::type key_compare_checker(R);
1391 // A never instantiated helper function that returns the key comparison
1393 static key_compare key_compare_helper();
1395 // Verify that key_compare returns a bool. This is similar to the way
1396 // is_convertible in base/type_traits.h works. Note that key_compare_checker
1397 // is never actually invoked. The compiler will select which
1398 // key_compare_checker() to instantiate and then figure out the size of the
1399 // return type of key_compare_checker() at compile time which we then check
1400 // against the sizeof of big_.
1402 sizeof(key_compare_checker(key_compare_helper()(key_type(), key_type()))) ==
1404 key_comparison_function_must_return_bool);
1406 // Note: We insist on kTargetValues, which is computed from
1407 // Params::kTargetNodeSize, must fit the base_fields::field_type.
1408 COMPILE_ASSERT(kNodeValues <
1409 (1 << (8 * sizeof(typename base_fields::field_type))),
1410 target_node_size_too_large);
1412 // Test the assumption made in setting kNodeValueSpace.
1413 COMPILE_ASSERT(sizeof(base_fields) >= 2 * sizeof(void*),
1414 node_space_assumption_incorrect);
1418 // btree_node methods
1419 template <typename P>
1420 inline void btree_node<P>::insert_value(int i, const value_type &x) {
1421 assert(i <= count());
1422 value_init(count(), x);
1423 for (int j = count(); j > i; --j) {
1424 value_swap(j, this, j - 1);
1426 set_count(count() + 1);
1430 for (int j = count(); j > i; --j) {
1431 *mutable_child(j) = child(j - 1);
1432 child(j)->set_position(j);
1434 *mutable_child(i) = NULL;
1438 template <typename P>
1439 inline void btree_node<P>::remove_value(int i) {
1441 assert(child(i + 1)->count() == 0);
1442 for (int j = i + 1; j < count(); ++j) {
1443 *mutable_child(j) = child(j + 1);
1444 child(j)->set_position(j);
1446 *mutable_child(count()) = NULL;
1449 set_count(count() - 1);
1450 for (; i < count(); ++i) {
1451 value_swap(i, this, i + 1);
1456 template <typename P>
1457 void btree_node<P>::rebalance_right_to_left(btree_node *src, int to_move) {
1458 assert(parent() == src->parent());
1459 assert(position() + 1 == src->position());
1460 assert(src->count() >= count());
1461 assert(to_move >= 1);
1462 assert(to_move <= src->count());
1464 // Make room in the left node for the new values.
1465 for (int i = 0; i < to_move; ++i) {
1466 value_init(i + count());
1469 // Move the delimiting value to the left node and the new delimiting value
1470 // from the right node.
1471 value_swap(count(), parent(), position());
1472 parent()->value_swap(position(), src, to_move - 1);
1474 // Move the values from the right to the left node.
1475 for (int i = 1; i < to_move; ++i) {
1476 value_swap(count() + i, src, i - 1);
1478 // Shift the values in the right node to their correct position.
1479 for (int i = to_move; i < src->count(); ++i) {
1480 src->value_swap(i - to_move, src, i);
1482 for (int i = 1; i <= to_move; ++i) {
1483 src->value_destroy(src->count() - i);
1487 // Move the child pointers from the right to the left node.
1488 for (int i = 0; i < to_move; ++i) {
1489 set_child(1 + count() + i, src->child(i));
1491 for (int i = 0; i <= src->count() - to_move; ++i) {
1492 assert(i + to_move <= src->max_count());
1493 src->set_child(i, src->child(i + to_move));
1494 *src->mutable_child(i + to_move) = NULL;
1498 // Fixup the counts on the src and dest nodes.
1499 set_count(count() + to_move);
1500 src->set_count(src->count() - to_move);
1503 template <typename P>
1504 void btree_node<P>::rebalance_left_to_right(btree_node *dest, int to_move) {
1505 assert(parent() == dest->parent());
1506 assert(position() + 1 == dest->position());
1507 assert(count() >= dest->count());
1508 assert(to_move >= 1);
1509 assert(to_move <= count());
1511 // Make room in the right node for the new values.
1512 for (int i = 0; i < to_move; ++i) {
1513 dest->value_init(i + dest->count());
1515 for (int i = dest->count() - 1; i >= 0; --i) {
1516 dest->value_swap(i, dest, i + to_move);
1519 // Move the delimiting value to the right node and the new delimiting value
1520 // from the left node.
1521 dest->value_swap(to_move - 1, parent(), position());
1522 parent()->value_swap(position(), this, count() - to_move);
1523 value_destroy(count() - to_move);
1525 // Move the values from the left to the right node.
1526 for (int i = 1; i < to_move; ++i) {
1527 value_swap(count() - to_move + i, dest, i - 1);
1528 value_destroy(count() - to_move + i);
1532 // Move the child pointers from the left to the right node.
1533 for (int i = dest->count(); i >= 0; --i) {
1534 dest->set_child(i + to_move, dest->child(i));
1535 *dest->mutable_child(i) = NULL;
1537 for (int i = 1; i <= to_move; ++i) {
1538 dest->set_child(i - 1, child(count() - to_move + i));
1539 *mutable_child(count() - to_move + i) = NULL;
1543 // Fixup the counts on the src and dest nodes.
1544 set_count(count() - to_move);
1545 dest->set_count(dest->count() + to_move);
1548 template <typename P>
1549 void btree_node<P>::split(btree_node *dest, int insert_position) {
1550 assert(dest->count() == 0);
1552 // We bias the split based on the position being inserted. If we're
1553 // inserting at the beginning of the left node then bias the split to put
1554 // more values on the right node. If we're inserting at the end of the
1555 // right node then bias the split to put more values on the left node.
1556 if (insert_position == 0) {
1557 dest->set_count(count() - 1);
1558 } else if (insert_position == max_count()) {
1561 dest->set_count(count() / 2);
1563 set_count(count() - dest->count());
1564 assert(count() >= 1);
1566 // Move values from the left sibling to the right sibling.
1567 for (int i = 0; i < dest->count(); ++i) {
1568 dest->value_init(i);
1569 value_swap(count() + i, dest, i);
1570 value_destroy(count() + i);
1573 // The split key is the largest value in the left sibling.
1574 set_count(count() - 1);
1575 parent()->insert_value(position(), value_type());
1576 value_swap(count(), parent(), position());
1577 value_destroy(count());
1578 parent()->set_child(position() + 1, dest);
1581 for (int i = 0; i <= dest->count(); ++i) {
1582 assert(child(count() + i + 1) != NULL);
1583 dest->set_child(i, child(count() + i + 1));
1584 *mutable_child(count() + i + 1) = NULL;
1589 template <typename P>
1590 void btree_node<P>::merge(btree_node *src) {
1591 assert(parent() == src->parent());
1592 assert(position() + 1 == src->position());
1594 // Move the delimiting value to the left node.
1595 value_init(count());
1596 value_swap(count(), parent(), position());
1598 // Move the values from the right to the left node.
1599 for (int i = 0; i < src->count(); ++i) {
1600 value_init(1 + count() + i);
1601 value_swap(1 + count() + i, src, i);
1602 src->value_destroy(i);
1606 // Move the child pointers from the right to the left node.
1607 for (int i = 0; i <= src->count(); ++i) {
1608 set_child(1 + count() + i, src->child(i));
1609 *src->mutable_child(i) = NULL;
1613 // Fixup the counts on the src and dest nodes.
1614 set_count(1 + count() + src->count());
1617 // Remove the value on the parent node.
1618 parent()->remove_value(position());
1621 template <typename P>
1622 void btree_node<P>::swap(btree_node *x) {
1623 assert(leaf() == x->leaf());
1626 for (int i = count(); i < x->count(); ++i) {
1629 for (int i = x->count(); i < count(); ++i) {
1632 int n = std::max(count(), x->count());
1633 for (int i = 0; i < n; ++i) {
1634 value_swap(i, x, i);
1636 for (int i = count(); i < x->count(); ++i) {
1637 x->value_destroy(i);
1639 for (int i = x->count(); i < count(); ++i) {
1644 // Swap the child pointers.
1645 for (int i = 0; i <= n; ++i) {
1646 btree_swap_helper(*mutable_child(i), *x->mutable_child(i));
1648 for (int i = 0; i <= count(); ++i) {
1649 x->child(i)->fields_.parent = x;
1651 for (int i = 0; i <= x->count(); ++i) {
1652 child(i)->fields_.parent = this;
1657 btree_swap_helper(fields_.count, x->fields_.count);
1661 // btree_iterator methods
1662 template <typename N, typename R, typename P>
1663 void btree_iterator<N, R, P>::increment_slow() {
1665 assert(position >= node->count());
1666 self_type save(*this);
1667 while (position == node->count() && !node->is_root()) {
1668 assert(node->parent()->child(node->position()) == node);
1669 position = node->position();
1670 node = node->parent();
1672 if (position == node->count()) {
1676 assert(position < node->count());
1677 node = node->child(position + 1);
1678 while (!node->leaf()) {
1679 node = node->child(0);
1685 template <typename N, typename R, typename P>
1686 void btree_iterator<N, R, P>::increment_by(int count) {
1689 int rest = node->count() - position;
1690 position += std::min(rest, count);
1691 count = count - rest;
1692 if (position < node->count()) {
1702 template <typename N, typename R, typename P>
1703 void btree_iterator<N, R, P>::decrement_slow() {
1705 assert(position <= -1);
1706 self_type save(*this);
1707 while (position < 0 && !node->is_root()) {
1708 assert(node->parent()->child(node->position()) == node);
1709 position = node->position() - 1;
1710 node = node->parent();
1716 assert(position >= 0);
1717 node = node->child(position);
1718 while (!node->leaf()) {
1719 node = node->child(node->count());
1721 position = node->count() - 1;
1727 template <typename P>
1728 btree<P>::btree(const key_compare &comp, const allocator_type &alloc)
1729 : key_compare(comp),
1730 root_(alloc, NULL) {
1733 template <typename P>
1734 btree<P>::btree(const self_type &x)
1735 : key_compare(x.key_comp()),
1736 root_(x.internal_allocator(), NULL) {
1740 template <typename P> template <typename ValuePointer>
1741 std::pair<typename btree<P>::iterator, bool>
1742 btree<P>::insert_unique(const key_type &key, ValuePointer value) {
1744 *mutable_root() = new_leaf_root_node(1);
1747 std::pair<iterator, int> res = internal_locate(key, iterator(root(), 0));
1748 iterator &iter = res.first;
1749 if (res.second == kExactMatch) {
1750 // The key already exists in the tree, do nothing.
1751 return std::make_pair(internal_last(iter), false);
1752 } else if (!res.second) {
1753 iterator last = internal_last(iter);
1754 if (last.node && !compare_keys(key, last.key())) {
1755 // The key already exists in the tree, do nothing.
1756 return std::make_pair(last, false);
1760 return std::make_pair(internal_insert(iter, *value), true);
1763 template <typename P>
1764 inline typename btree<P>::iterator
1765 btree<P>::insert_unique(iterator position, const value_type &v) {
1767 const key_type &key = params_type::key(v);
1768 if (position == end() || compare_keys(key, position.key())) {
1769 iterator prev = position;
1770 if (position == begin() || compare_keys((--prev).key(), key)) {
1771 // prev.key() < key < position.key()
1772 return internal_insert(position, v);
1774 } else if (compare_keys(position.key(), key)) {
1775 iterator next = position;
1777 if (next == end() || compare_keys(key, next.key())) {
1778 // position.key() < key < next.key()
1779 return internal_insert(next, v);
1782 // position.key() == key
1786 return insert_unique(v).first;
1789 template <typename P> template <typename InputIterator>
1790 void btree<P>::insert_unique(InputIterator b, InputIterator e) {
1791 for (; b != e; ++b) {
1792 insert_unique(end(), *b);
1796 template <typename P> template <typename ValuePointer>
1797 typename btree<P>::iterator
1798 btree<P>::insert_multi(const key_type &key, ValuePointer value) {
1800 *mutable_root() = new_leaf_root_node(1);
1803 iterator iter = internal_upper_bound(key, iterator(root(), 0));
1807 return internal_insert(iter, *value);
1810 template <typename P>
1811 typename btree<P>::iterator
1812 btree<P>::insert_multi(iterator position, const value_type &v) {
1814 const key_type &key = params_type::key(v);
1815 if (position == end() || !compare_keys(position.key(), key)) {
1816 iterator prev = position;
1817 if (position == begin() || !compare_keys(key, (--prev).key())) {
1818 // prev.key() <= key <= position.key()
1819 return internal_insert(position, v);
1822 iterator next = position;
1824 if (next == end() || !compare_keys(next.key(), key)) {
1825 // position.key() < key <= next.key()
1826 return internal_insert(next, v);
1830 return insert_multi(v);
1833 template <typename P> template <typename InputIterator>
1834 void btree<P>::insert_multi(InputIterator b, InputIterator e) {
1835 for (; b != e; ++b) {
1836 insert_multi(end(), *b);
1840 template <typename P>
1841 void btree<P>::assign(const self_type &x) {
1844 *mutable_key_comp() = x.key_comp();
1845 *mutable_internal_allocator() = x.internal_allocator();
1847 // Assignment can avoid key comparisons because we know the order of the
1848 // values is the same order we'll store them in.
1849 for (const_iterator iter = x.begin(); iter != x.end(); ++iter) {
1851 insert_multi(*iter);
1853 // If the btree is not empty, we can just insert the new value at the end
1855 internal_insert(end(), *iter);
1860 template <typename P>
1861 typename btree<P>::iterator btree<P>::erase(iterator iter) {
1862 bool internal_delete = false;
1863 if (!iter.node->leaf()) {
1864 // Deletion of a value on an internal node. Swap the key with the largest
1865 // value of our left child. This is easy, we just decrement iter.
1866 iterator tmp_iter(iter--);
1867 assert(iter.node->leaf());
1868 assert(!compare_keys(tmp_iter.key(), iter.key()));
1869 iter.node->value_swap(iter.position, tmp_iter.node, tmp_iter.position);
1870 internal_delete = true;
1872 } else if (!root()->leaf()) {
1876 // Delete the key from the leaf.
1877 iter.node->remove_value(iter.position);
1879 // We want to return the next value after the one we just erased. If we
1880 // erased from an internal node (internal_delete == true), then the next
1881 // value is ++(++iter). If we erased from a leaf node (internal_delete ==
1882 // false) then the next value is ++iter. Note that ++iter may point to an
1883 // internal node and the value in the internal node may move to a leaf node
1884 // (iter.node) when rebalancing is performed at the leaf level.
1886 // Merge/rebalance as we walk back up the tree.
1889 if (iter.node == root()) {
1896 if (iter.node->count() >= kMinNodeValues) {
1899 bool merged = try_merge_or_rebalance(&iter);
1900 if (iter.node->leaf()) {
1906 iter.node = iter.node->parent();
1909 // Adjust our return value. If we're pointing at the end of a node, advance
1911 if (res.position == res.node->count()) {
1912 res.position = res.node->count() - 1;
1915 // If we erased from an internal node, advance the iterator.
1916 if (internal_delete) {
1922 template <typename P>
1923 int btree<P>::erase(iterator begin, iterator end) {
1924 int count = distance(begin, end);
1925 for (int i = 0; i < count; i++) {
1926 begin = erase(begin);
1931 template <typename P>
1932 int btree<P>::erase_unique(const key_type &key) {
1933 iterator iter = internal_find_unique(key, iterator(root(), 0));
1935 // The key doesn't exist in the tree, return nothing done.
1942 template <typename P>
1943 int btree<P>::erase_multi(const key_type &key) {
1944 iterator begin = internal_lower_bound(key, iterator(root(), 0));
1946 // The key doesn't exist in the tree, return nothing done.
1949 // Delete all of the keys between begin and upper_bound(key).
1950 iterator end = internal_end(
1951 internal_upper_bound(key, iterator(root(), 0)));
1952 return erase(begin, end);
1955 template <typename P>
1956 void btree<P>::clear() {
1957 if (root() != NULL) {
1958 internal_clear(root());
1960 *mutable_root() = NULL;
1963 template <typename P>
1964 void btree<P>::swap(self_type &x) {
1965 std::swap(static_cast<key_compare&>(*this), static_cast<key_compare&>(x));
1966 std::swap(root_, x.root_);
1969 template <typename P>
1970 void btree<P>::verify() const {
1971 if (root() != NULL) {
1972 assert(size() == internal_verify(root(), NULL, NULL));
1973 assert(leftmost() == (++const_iterator(root(), -1)).node);
1974 assert(rightmost() == (--const_iterator(root(), root()->count())).node);
1975 assert(leftmost()->leaf());
1976 assert(rightmost()->leaf());
1978 assert(size() == 0);
1979 assert(leftmost() == NULL);
1980 assert(rightmost() == NULL);
1984 template <typename P>
1985 void btree<P>::rebalance_or_split(iterator *iter) {
1986 node_type *&node = iter->node;
1987 int &insert_position = iter->position;
1988 assert(node->count() == node->max_count());
1990 // First try to make room on the node by rebalancing.
1991 node_type *parent = node->parent();
1992 if (node != root()) {
1993 if (node->position() > 0) {
1994 // Try rebalancing with our left sibling.
1995 node_type *left = parent->child(node->position() - 1);
1996 if (left->count() < left->max_count()) {
1997 // We bias rebalancing based on the position being inserted. If we're
1998 // inserting at the end of the right node then we bias rebalancing to
1999 // fill up the left node.
2000 int to_move = (left->max_count() - left->count()) /
2001 (1 + (insert_position < left->max_count()));
2002 to_move = std::max(1, to_move);
2004 if (((insert_position - to_move) >= 0) ||
2005 ((left->count() + to_move) < left->max_count())) {
2006 left->rebalance_right_to_left(node, to_move);
2008 assert(node->max_count() - node->count() == to_move);
2009 insert_position = insert_position - to_move;
2010 if (insert_position < 0) {
2011 insert_position = insert_position + left->count() + 1;
2015 assert(node->count() < node->max_count());
2021 if (node->position() < parent->count()) {
2022 // Try rebalancing with our right sibling.
2023 node_type *right = parent->child(node->position() + 1);
2024 if (right->count() < right->max_count()) {
2025 // We bias rebalancing based on the position being inserted. If we're
2026 // inserting at the beginning of the left node then we bias rebalancing
2027 // to fill up the right node.
2028 int to_move = (right->max_count() - right->count()) /
2029 (1 + (insert_position > 0));
2030 to_move = std::max(1, to_move);
2032 if ((insert_position <= (node->count() - to_move)) ||
2033 ((right->count() + to_move) < right->max_count())) {
2034 node->rebalance_left_to_right(right, to_move);
2036 if (insert_position > node->count()) {
2037 insert_position = insert_position - node->count() - 1;
2041 assert(node->count() < node->max_count());
2047 // Rebalancing failed, make sure there is room on the parent node for a new
2049 if (parent->count() == parent->max_count()) {
2050 iterator parent_iter(node->parent(), node->position());
2051 rebalance_or_split(&parent_iter);
2054 // Rebalancing not possible because this is the root node.
2055 if (root()->leaf()) {
2056 // The root node is currently a leaf node: create a new root node and set
2057 // the current root node as the child of the new root.
2058 parent = new_internal_root_node();
2059 parent->set_child(0, root());
2060 *mutable_root() = parent;
2061 assert(*mutable_rightmost() == parent->child(0));
2063 // The root node is an internal node. We do not want to create a new root
2064 // node because the root node is special and holds the size of the tree
2065 // and a pointer to the rightmost node. So we create a new internal node
2066 // and move all of the items on the current root into the new node.
2067 parent = new_internal_node(parent);
2068 parent->set_child(0, parent);
2069 parent->swap(root());
2075 node_type *split_node;
2077 split_node = new_leaf_node(parent);
2078 node->split(split_node, insert_position);
2079 if (rightmost() == node) {
2080 *mutable_rightmost() = split_node;
2083 split_node = new_internal_node(parent);
2084 node->split(split_node, insert_position);
2087 if (insert_position > node->count()) {
2088 insert_position = insert_position - node->count() - 1;
2093 template <typename P>
2094 void btree<P>::merge_nodes(node_type *left, node_type *right) {
2096 if (right->leaf()) {
2097 if (rightmost() == right) {
2098 *mutable_rightmost() = left;
2100 delete_leaf_node(right);
2102 delete_internal_node(right);
2106 template <typename P>
2107 bool btree<P>::try_merge_or_rebalance(iterator *iter) {
2108 node_type *parent = iter->node->parent();
2109 if (iter->node->position() > 0) {
2110 // Try merging with our left sibling.
2111 node_type *left = parent->child(iter->node->position() - 1);
2112 if ((1 + left->count() + iter->node->count()) <= left->max_count()) {
2113 iter->position += 1 + left->count();
2114 merge_nodes(left, iter->node);
2119 if (iter->node->position() < parent->count()) {
2120 // Try merging with our right sibling.
2121 node_type *right = parent->child(iter->node->position() + 1);
2122 if ((1 + iter->node->count() + right->count()) <= right->max_count()) {
2123 merge_nodes(iter->node, right);
2126 // Try rebalancing with our right sibling. We don't perform rebalancing if
2127 // we deleted the first element from iter->node and the node is not
2128 // empty. This is a small optimization for the common pattern of deleting
2129 // from the front of the tree.
2130 if ((right->count() > kMinNodeValues) &&
2131 ((iter->node->count() == 0) ||
2132 (iter->position > 0))) {
2133 int to_move = (right->count() - iter->node->count()) / 2;
2134 to_move = std::min(to_move, right->count() - 1);
2135 iter->node->rebalance_right_to_left(right, to_move);
2139 if (iter->node->position() > 0) {
2140 // Try rebalancing with our left sibling. We don't perform rebalancing if
2141 // we deleted the last element from iter->node and the node is not
2142 // empty. This is a small optimization for the common pattern of deleting
2143 // from the back of the tree.
2144 node_type *left = parent->child(iter->node->position() - 1);
2145 if ((left->count() > kMinNodeValues) &&
2146 ((iter->node->count() == 0) ||
2147 (iter->position < iter->node->count()))) {
2148 int to_move = (left->count() - iter->node->count()) / 2;
2149 to_move = std::min(to_move, left->count() - 1);
2150 left->rebalance_left_to_right(iter->node, to_move);
2151 iter->position += to_move;
2158 template <typename P>
2159 void btree<P>::try_shrink() {
2160 if (root()->count() > 0) {
2163 // Deleted the last item on the root node, shrink the height of the tree.
2164 if (root()->leaf()) {
2165 assert(size() == 0);
2166 delete_leaf_node(root());
2167 *mutable_root() = NULL;
2169 node_type *child = root()->child(0);
2170 if (child->leaf()) {
2171 // The child is a leaf node so simply make it the root node in the tree.
2173 delete_internal_root_node();
2174 *mutable_root() = child;
2176 // The child is an internal node. We want to keep the existing root node
2177 // so we move all of the values from the child node into the existing
2178 // (empty) root node.
2179 child->swap(root());
2180 delete_internal_node(child);
2185 template <typename P> template <typename IterType>
2186 inline IterType btree<P>::internal_last(IterType iter) {
2187 while (iter.node && iter.position == iter.node->count()) {
2188 iter.position = iter.node->position();
2189 iter.node = iter.node->parent();
2190 if (iter.node->leaf()) {
2197 template <typename P>
2198 inline typename btree<P>::iterator
2199 btree<P>::internal_insert(iterator iter, const value_type &v) {
2200 if (!iter.node->leaf()) {
2201 // We can't insert on an internal node. Instead, we'll insert after the
2202 // previous value which is guaranteed to be on a leaf node.
2206 if (iter.node->count() == iter.node->max_count()) {
2207 // Make room in the leaf for the new item.
2208 if (iter.node->max_count() < kNodeValues) {
2209 // Insertion into the root where the root is smaller that the full node
2210 // size. Simply grow the size of the root node.
2211 assert(iter.node == root());
2212 iter.node = new_leaf_root_node(
2213 std::min<int>(kNodeValues, 2 * iter.node->max_count()));
2214 iter.node->swap(root());
2215 delete_leaf_node(root());
2216 *mutable_root() = iter.node;
2218 rebalance_or_split(&iter);
2221 } else if (!root()->leaf()) {
2224 iter.node->insert_value(iter.position, v);
2228 template <typename P> template <typename IterType>
2229 inline std::pair<IterType, int> btree<P>::internal_locate(
2230 const key_type &key, IterType iter) const {
2231 return internal_locate_type::dispatch(key, *this, iter);
2234 template <typename P> template <typename IterType>
2235 inline std::pair<IterType, int> btree<P>::internal_locate_plain_compare(
2236 const key_type &key, IterType iter) const {
2238 iter.position = iter.node->lower_bound(key, key_comp());
2239 if (iter.node->leaf()) {
2242 iter.node = iter.node->child(iter.position);
2244 return std::make_pair(iter, 0);
2247 template <typename P> template <typename IterType>
2248 inline std::pair<IterType, int> btree<P>::internal_locate_compare_to(
2249 const key_type &key, IterType iter) const {
2251 int res = iter.node->lower_bound(key, key_comp());
2252 iter.position = res & kMatchMask;
2253 if (res & kExactMatch) {
2254 return std::make_pair(iter, static_cast<int>(kExactMatch));
2256 if (iter.node->leaf()) {
2259 iter.node = iter.node->child(iter.position);
2261 return std::make_pair(iter, -kExactMatch);
2264 template <typename P> template <typename IterType>
2265 IterType btree<P>::internal_lower_bound(
2266 const key_type &key, IterType iter) const {
2270 iter.node->lower_bound(key, key_comp()) & kMatchMask;
2271 if (iter.node->leaf()) {
2274 iter.node = iter.node->child(iter.position);
2276 iter = internal_last(iter);
2281 template <typename P> template <typename IterType>
2282 IterType btree<P>::internal_upper_bound(
2283 const key_type &key, IterType iter) const {
2286 iter.position = iter.node->upper_bound(key, key_comp());
2287 if (iter.node->leaf()) {
2290 iter.node = iter.node->child(iter.position);
2292 iter = internal_last(iter);
2297 template <typename P> template <typename IterType>
2298 IterType btree<P>::internal_find_unique(
2299 const key_type &key, IterType iter) const {
2301 std::pair<IterType, int> res = internal_locate(key, iter);
2302 if (res.second == kExactMatch) {
2306 iter = internal_last(res.first);
2307 if (iter.node && !compare_keys(key, iter.key())) {
2312 return IterType(NULL, 0);
2315 template <typename P> template <typename IterType>
2316 IterType btree<P>::internal_find_multi(
2317 const key_type &key, IterType iter) const {
2319 iter = internal_lower_bound(key, iter);
2321 iter = internal_last(iter);
2322 if (iter.node && !compare_keys(key, iter.key())) {
2327 return IterType(NULL, 0);
2330 template <typename P>
2331 void btree<P>::internal_clear(node_type *node) {
2332 if (!node->leaf()) {
2333 for (int i = 0; i <= node->count(); ++i) {
2334 internal_clear(node->child(i));
2336 if (node == root()) {
2337 delete_internal_root_node();
2339 delete_internal_node(node);
2342 delete_leaf_node(node);
2346 template <typename P>
2347 void btree<P>::internal_dump(
2348 std::ostream &os, const node_type *node, int level) const {
2349 for (int i = 0; i < node->count(); ++i) {
2350 if (!node->leaf()) {
2351 internal_dump(os, node->child(i), level + 1);
2353 for (int j = 0; j < level; ++j) {
2356 os << node->key(i) << " [" << level << "]\n";
2358 if (!node->leaf()) {
2359 internal_dump(os, node->child(node->count()), level + 1);
2363 template <typename P>
2364 int btree<P>::internal_verify(
2365 const node_type *node, const key_type *lo, const key_type *hi) const {
2366 assert(node->count() > 0);
2367 assert(node->count() <= node->max_count());
2369 assert(!compare_keys(node->key(0), *lo));
2372 assert(!compare_keys(*hi, node->key(node->count() - 1)));
2374 for (int i = 1; i < node->count(); ++i) {
2375 assert(!compare_keys(node->key(i), node->key(i - 1)));
2377 int count = node->count();
2378 if (!node->leaf()) {
2379 for (int i = 0; i <= node->count(); ++i) {
2380 assert(node->child(i) != NULL);
2381 assert(node->child(i)->parent() == node);
2382 assert(node->child(i)->position() == i);
2383 count += internal_verify(
2385 (i == 0) ? lo : &node->key(i - 1),
2386 (i == node->count()) ? hi : &node->key(i));
2392 } // namespace btree
2394 #endif // UTIL_BTREE_BTREE_H__