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
14 #include <linux/init.h>
16 #include <linux/prio_tree.h>
17 #include <linux/export.h>
20 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
21 * which is useful for storing intervals, e.g, we can consider a vma as a closed
22 * interval of file pages [offset_begin, offset_end], and store all vmas that
23 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
24 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
25 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
26 * time where 'log n' is the height of the PST, and 'm' is the number of stored
27 * intervals (vmas) that overlap (map) with the input interval X (the set of
28 * consecutive file pages).
30 * In our implementation, we store closed intervals of the form [radix_index,
31 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
32 * is designed for storing intervals with unique radix indices, i.e., each
33 * interval have different radix_index. However, this limitation can be easily
34 * overcome by using the size, i.e., heap_index - radix_index, as part of the
35 * index, so we index the tree using [(radix_index,size), heap_index].
37 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
38 * machine, the maximum height of a PST can be 64. We can use a balanced version
39 * of the priority search tree to optimize the tree height, but the balanced
40 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
44 * The following macros are used for implementing prio_tree for i_mmap
47 static void get_index(const struct prio_tree_root *root,
48 const struct prio_tree_node *node,
49 unsigned long *radix, unsigned long *heap)
55 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
57 void __init prio_tree_init(void)
61 for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
62 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
63 index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
67 * Maximum heap_index that can be stored in a PST with index_bits bits
69 static inline unsigned long prio_tree_maxindex(unsigned int bits)
71 return index_bits_to_maxindex[bits - 1];
74 static void prio_set_parent(struct prio_tree_node *parent,
75 struct prio_tree_node *child, bool left)
80 parent->right = child;
82 child->parent = parent;
86 * Extend a priority search tree so that it can store a node with heap_index
87 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
88 * However, this function is used rarely and the common case performance is
91 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
92 struct prio_tree_node *node, unsigned long max_heap_index)
94 struct prio_tree_node *prev;
96 if (max_heap_index > prio_tree_maxindex(root->index_bits))
100 INIT_PRIO_TREE_NODE(node);
102 while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
103 struct prio_tree_node *tmp = root->prio_tree_node;
107 if (prio_tree_empty(root))
110 prio_tree_remove(root, root->prio_tree_node);
111 INIT_PRIO_TREE_NODE(tmp);
113 prio_set_parent(prev, tmp, true);
117 if (!prio_tree_empty(root))
118 prio_set_parent(prev, root->prio_tree_node, true);
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 BUG_ON(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).
138 root->prio_tree_node = node;
140 prio_set_parent(old->parent, node, old->parent->left == old);
142 if (!prio_tree_left_empty(old))
143 prio_set_parent(node, old->left, true);
145 if (!prio_tree_right_empty(old))
146 prio_set_parent(node, old->right, false);
152 * Insert a prio_tree_node @node into a radix priority search tree @root. The
153 * algorithm typically takes O(log n) time where 'log n' is the number of bits
154 * required to represent the maximum heap_index. In the worst case, the algo
155 * can take O((log n)^2) - check prio_tree_expand.
157 * If a prior node with same radix_index and heap_index is already found in
158 * the tree, then returns the address of the prior node. Otherwise, inserts
159 * @node into the tree and returns @node.
161 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
162 struct prio_tree_node *node)
164 struct prio_tree_node *cur, *res = node;
165 unsigned long radix_index, heap_index;
166 unsigned long r_index, h_index, index, mask;
169 get_index(root, node, &radix_index, &heap_index);
171 if (prio_tree_empty(root) ||
172 heap_index > prio_tree_maxindex(root->index_bits))
173 return prio_tree_expand(root, node, heap_index);
175 cur = root->prio_tree_node;
176 mask = 1UL << (root->index_bits - 1);
179 get_index(root, cur, &r_index, &h_index);
181 if (r_index == radix_index && h_index == heap_index)
184 if (h_index < heap_index ||
185 (h_index == heap_index && r_index > radix_index)) {
186 struct prio_tree_node *tmp = node;
187 node = prio_tree_replace(root, cur, node);
191 r_index = radix_index;
194 h_index = heap_index;
199 index = heap_index - radix_index;
204 if (prio_tree_right_empty(cur)) {
205 INIT_PRIO_TREE_NODE(node);
206 prio_set_parent(cur, node, false);
211 if (prio_tree_left_empty(cur)) {
212 INIT_PRIO_TREE_NODE(node);
213 prio_set_parent(cur, node, true);
222 mask = 1UL << (BITS_PER_LONG - 1);
226 /* Should not reach here */
230 EXPORT_SYMBOL(prio_tree_insert);
233 * Remove a prio_tree_node @node from a radix priority search tree @root. The
234 * algorithm takes O(log n) time where 'log n' is the number of bits required
235 * to represent the maximum heap_index.
237 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
239 struct prio_tree_node *cur;
240 unsigned long r_index, h_index_right, h_index_left;
244 while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
245 if (!prio_tree_left_empty(cur))
246 get_index(root, cur->left, &r_index, &h_index_left);
252 if (!prio_tree_right_empty(cur))
253 get_index(root, cur->right, &r_index, &h_index_right);
259 /* both h_index_left and h_index_right cannot be 0 */
260 if (h_index_left >= h_index_right)
266 if (prio_tree_root(cur)) {
267 BUG_ON(root->prio_tree_node != cur);
268 __INIT_PRIO_TREE_ROOT(root, root->raw);
272 if (cur->parent->right == cur)
273 cur->parent->right = cur->parent;
275 cur->parent->left = cur->parent;
278 cur = prio_tree_replace(root, cur->parent, cur);
280 EXPORT_SYMBOL(prio_tree_remove);
282 static void iter_walk_down(struct prio_tree_iter *iter)
286 if (iter->size_level)
291 if (iter->size_level) {
292 BUG_ON(!prio_tree_left_empty(iter->cur));
293 BUG_ON(!prio_tree_right_empty(iter->cur));
295 iter->mask = ULONG_MAX;
297 iter->size_level = 1;
298 iter->mask = 1UL << (BITS_PER_LONG - 1);
302 static void iter_walk_up(struct prio_tree_iter *iter)
304 if (iter->mask == ULONG_MAX)
306 else if (iter->size_level == 1)
310 if (iter->size_level)
312 if (!iter->size_level && (iter->value & iter->mask))
313 iter->value ^= iter->mask;
317 * Following functions help to enumerate all prio_tree_nodes in the tree that
318 * overlap with the input interval X [radix_index, heap_index]. The enumeration
319 * takes O(log n + m) time where 'log n' is the height of the tree (which is
320 * proportional to # of bits required to represent the maximum heap_index) and
321 * 'm' is the number of prio_tree_nodes that overlap the interval X.
324 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
325 unsigned long *r_index, unsigned long *h_index)
327 if (prio_tree_left_empty(iter->cur))
330 get_index(iter->root, iter->cur->left, r_index, h_index);
332 if (iter->r_index <= *h_index) {
333 iter->cur = iter->cur->left;
334 iter_walk_down(iter);
341 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
342 unsigned long *r_index, unsigned long *h_index)
346 if (prio_tree_right_empty(iter->cur))
349 if (iter->size_level)
352 value = iter->value | iter->mask;
354 if (iter->h_index < value)
357 get_index(iter->root, iter->cur->right, r_index, h_index);
359 if (iter->r_index <= *h_index) {
360 iter->cur = iter->cur->right;
361 iter_walk_down(iter);
368 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
370 iter->cur = iter->cur->parent;
375 static inline int overlap(struct prio_tree_iter *iter,
376 unsigned long r_index, unsigned long h_index)
378 return iter->h_index >= r_index && iter->r_index <= h_index;
384 * Get the first prio_tree_node that overlaps with the interval [radix_index,
385 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
386 * traversal of the tree.
388 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
390 struct prio_tree_root *root;
391 unsigned long r_index, h_index;
393 INIT_PRIO_TREE_ITER(iter);
396 if (prio_tree_empty(root))
399 get_index(root, root->prio_tree_node, &r_index, &h_index);
401 if (iter->r_index > h_index)
404 iter->mask = 1UL << (root->index_bits - 1);
405 iter->cur = root->prio_tree_node;
408 if (overlap(iter, r_index, h_index))
411 if (prio_tree_left(iter, &r_index, &h_index))
414 if (prio_tree_right(iter, &r_index, &h_index))
425 * Get the next prio_tree_node that overlaps with the input interval in iter
427 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
429 unsigned long r_index, h_index;
431 if (iter->cur == NULL)
432 return prio_tree_first(iter);
435 while (prio_tree_left(iter, &r_index, &h_index))
436 if (overlap(iter, r_index, h_index))
439 while (!prio_tree_right(iter, &r_index, &h_index)) {
440 while (!prio_tree_root(iter->cur) &&
441 iter->cur->parent->right == iter->cur)
442 prio_tree_parent(iter);
444 if (prio_tree_root(iter->cur))
447 prio_tree_parent(iter);
450 if (overlap(iter, r_index, h_index))
455 EXPORT_SYMBOL(prio_tree_next);