2 * lib/prio_tree.c - priority search tree
4 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
6 * This file is released under the GPL v2.
8 * Based on the radix priority search tree proposed by Edward M. McCreight
9 * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
11 * 02Feb2004 Initial version
17 #include "../compiler/compiler.h"
18 #include "prio_tree.h"
20 #define ARRAY_SIZE(x) (sizeof((x)) / (sizeof((x)[0])))
23 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
24 * which is useful for storing intervals, e.g, we can consider a vma as a closed
25 * interval of file pages [offset_begin, offset_end], and store all vmas that
26 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
27 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
28 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
29 * time where 'log n' is the height of the PST, and 'm' is the number of stored
30 * intervals (vmas) that overlap (map) with the input interval X (the set of
31 * consecutive file pages).
33 * In our implementation, we store closed intervals of the form [radix_index,
34 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
35 * is designed for storing intervals with unique radix indices, i.e., each
36 * interval have different radix_index. However, this limitation can be easily
37 * overcome by using the size, i.e., heap_index - radix_index, as part of the
38 * index, so we index the tree using [(radix_index,size), heap_index].
40 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
41 * machine, the maximum height of a PST can be 64. We can use a balanced version
42 * of the priority search tree to optimize the tree height, but the balanced
43 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
46 static void get_index(const struct prio_tree_node *node,
47 unsigned long *radix, unsigned long *heap)
53 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
55 static void fio_init prio_tree_init(void)
59 for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
60 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
61 index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
65 * Maximum heap_index that can be stored in a PST with index_bits bits
67 static inline unsigned long prio_tree_maxindex(unsigned int bits)
69 return index_bits_to_maxindex[bits - 1];
73 * Extend a priority search tree so that it can store a node with heap_index
74 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
75 * However, this function is used rarely and the common case performance is
78 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
79 struct prio_tree_node *node, unsigned long max_heap_index)
81 struct prio_tree_node *first = NULL, *prev, *last = NULL;
83 if (max_heap_index > prio_tree_maxindex(root->index_bits))
86 while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
89 if (prio_tree_empty(root))
93 first = root->prio_tree_node;
94 prio_tree_remove(root, root->prio_tree_node);
95 INIT_PRIO_TREE_NODE(first);
99 last = root->prio_tree_node;
100 prio_tree_remove(root, root->prio_tree_node);
101 INIT_PRIO_TREE_NODE(last);
107 INIT_PRIO_TREE_NODE(node);
111 first->parent = node;
115 if (!prio_tree_empty(root)) {
116 last->left = root->prio_tree_node;
117 last->left->parent = last;
120 root->prio_tree_node = node;
125 * Replace a prio_tree_node with a new node and return the old node
127 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
128 struct prio_tree_node *old, struct prio_tree_node *node)
130 INIT_PRIO_TREE_NODE(node);
132 if (prio_tree_root(old)) {
133 assert(root->prio_tree_node == old);
135 * We can reduce root->index_bits here. However, it is complex
136 * and does not help much to improve performance (IMO).
139 root->prio_tree_node = node;
141 node->parent = old->parent;
142 if (old->parent->left == old)
143 old->parent->left = node;
145 old->parent->right = node;
148 if (!prio_tree_left_empty(old)) {
149 node->left = old->left;
150 old->left->parent = node;
153 if (!prio_tree_right_empty(old)) {
154 node->right = old->right;
155 old->right->parent = node;
162 * Insert a prio_tree_node @node into a radix priority search tree @root. The
163 * algorithm typically takes O(log n) time where 'log n' is the number of bits
164 * required to represent the maximum heap_index. In the worst case, the algo
165 * can take O((log n)^2) - check prio_tree_expand.
167 * If a prior node with same radix_index and heap_index is already found in
168 * the tree, then returns the address of the prior node. Otherwise, inserts
169 * @node into the tree and returns @node.
171 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
172 struct prio_tree_node *node)
174 struct prio_tree_node *cur, *res = node;
175 unsigned long radix_index, heap_index;
176 unsigned long r_index, h_index, index, mask;
179 get_index(node, &radix_index, &heap_index);
181 if (prio_tree_empty(root) ||
182 heap_index > prio_tree_maxindex(root->index_bits))
183 return prio_tree_expand(root, node, heap_index);
185 cur = root->prio_tree_node;
186 mask = 1UL << (root->index_bits - 1);
189 get_index(cur, &r_index, &h_index);
191 if (r_index == radix_index && h_index == heap_index)
194 if (h_index < heap_index ||
195 (h_index == heap_index && r_index > radix_index)) {
196 struct prio_tree_node *tmp = node;
197 node = prio_tree_replace(root, cur, node);
201 r_index = radix_index;
204 h_index = heap_index;
209 index = heap_index - radix_index;
214 if (prio_tree_right_empty(cur)) {
215 INIT_PRIO_TREE_NODE(node);
222 if (prio_tree_left_empty(cur)) {
223 INIT_PRIO_TREE_NODE(node);
234 mask = 1UL << (BITS_PER_LONG - 1);
238 /* Should not reach here */
244 * Remove a prio_tree_node @node from a radix priority search tree @root. The
245 * algorithm takes O(log n) time where 'log n' is the number of bits required
246 * to represent the maximum heap_index.
248 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
250 struct prio_tree_node *cur;
251 unsigned long r_index, h_index_right, h_index_left;
255 while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
256 if (!prio_tree_left_empty(cur))
257 get_index(cur->left, &r_index, &h_index_left);
263 if (!prio_tree_right_empty(cur))
264 get_index(cur->right, &r_index, &h_index_right);
270 /* both h_index_left and h_index_right cannot be 0 */
271 if (h_index_left >= h_index_right)
277 if (prio_tree_root(cur)) {
278 assert(root->prio_tree_node == cur);
279 INIT_PRIO_TREE_ROOT(root);
283 if (cur->parent->right == cur)
284 cur->parent->right = cur->parent;
286 cur->parent->left = cur->parent;
289 cur = prio_tree_replace(root, cur->parent, cur);
293 * Following functions help to enumerate all prio_tree_nodes in the tree that
294 * overlap with the input interval X [radix_index, heap_index]. The enumeration
295 * takes O(log n + m) time where 'log n' is the height of the tree (which is
296 * proportional to # of bits required to represent the maximum heap_index) and
297 * 'm' is the number of prio_tree_nodes that overlap the interval X.
300 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
301 unsigned long *r_index, unsigned long *h_index)
303 if (prio_tree_left_empty(iter->cur))
306 get_index(iter->cur->left, r_index, h_index);
308 if (iter->r_index <= *h_index) {
309 iter->cur = iter->cur->left;
312 if (iter->size_level)
315 if (iter->size_level) {
316 assert(prio_tree_left_empty(iter->cur));
317 assert(prio_tree_right_empty(iter->cur));
319 iter->mask = ULONG_MAX;
321 iter->size_level = 1;
322 iter->mask = 1UL << (BITS_PER_LONG - 1);
331 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
332 unsigned long *r_index, unsigned long *h_index)
336 if (prio_tree_right_empty(iter->cur))
339 if (iter->size_level)
342 value = iter->value | iter->mask;
344 if (iter->h_index < value)
347 get_index(iter->cur->right, r_index, h_index);
349 if (iter->r_index <= *h_index) {
350 iter->cur = iter->cur->right;
354 if (iter->size_level)
357 if (iter->size_level) {
358 assert(prio_tree_left_empty(iter->cur));
359 assert(prio_tree_right_empty(iter->cur));
361 iter->mask = ULONG_MAX;
363 iter->size_level = 1;
364 iter->mask = 1UL << (BITS_PER_LONG - 1);
373 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
375 iter->cur = iter->cur->parent;
376 if (iter->mask == ULONG_MAX)
378 else if (iter->size_level == 1)
382 if (iter->size_level)
384 if (!iter->size_level && (iter->value & iter->mask))
385 iter->value ^= iter->mask;
389 static inline int overlap(struct prio_tree_iter *iter,
390 unsigned long r_index, unsigned long h_index)
392 return iter->h_index >= r_index && iter->r_index <= h_index;
398 * Get the first prio_tree_node that overlaps with the interval [radix_index,
399 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
400 * traversal of the tree.
402 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
404 struct prio_tree_root *root;
405 unsigned long r_index, h_index;
407 INIT_PRIO_TREE_ITER(iter);
410 if (prio_tree_empty(root))
413 get_index(root->prio_tree_node, &r_index, &h_index);
415 if (iter->r_index > h_index)
418 iter->mask = 1UL << (root->index_bits - 1);
419 iter->cur = root->prio_tree_node;
422 if (overlap(iter, r_index, h_index))
425 if (prio_tree_left(iter, &r_index, &h_index))
428 if (prio_tree_right(iter, &r_index, &h_index))
439 * Get the next prio_tree_node that overlaps with the input interval in iter
441 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
443 unsigned long r_index, h_index;
445 if (iter->cur == NULL)
446 return prio_tree_first(iter);
449 while (prio_tree_left(iter, &r_index, &h_index))
450 if (overlap(iter, r_index, h_index))
453 while (!prio_tree_right(iter, &r_index, &h_index)) {
454 while (!prio_tree_root(iter->cur) &&
455 iter->cur->parent->right == iter->cur)
456 prio_tree_parent(iter);
458 if (prio_tree_root(iter->cur))
461 prio_tree_parent(iter);
464 if (overlap(iter, r_index, h_index))