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 #define RADIX_INDEX(vma) ((vma)->vm_pgoff)
48 #define VMA_SIZE(vma) (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
50 #define HEAP_INDEX(vma) ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
53 static void get_index(const struct prio_tree_root *root,
54 const struct prio_tree_node *node,
55 unsigned long *radix, unsigned long *heap)
58 struct vm_area_struct *vma = prio_tree_entry(
59 node, struct vm_area_struct, shared.prio_tree_node);
61 *radix = RADIX_INDEX(vma);
62 *heap = HEAP_INDEX(vma);
70 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
72 void __init prio_tree_init(void)
76 for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
77 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
78 index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
82 * Maximum heap_index that can be stored in a PST with index_bits bits
84 static inline unsigned long prio_tree_maxindex(unsigned int bits)
86 return index_bits_to_maxindex[bits - 1];
89 static void prio_set_parent(struct prio_tree_node *parent,
90 struct prio_tree_node *child, bool left)
95 parent->right = child;
97 child->parent = parent;
101 * Extend a priority search tree so that it can store a node with heap_index
102 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
103 * However, this function is used rarely and the common case performance is
106 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
107 struct prio_tree_node *node, unsigned long max_heap_index)
109 struct prio_tree_node *prev;
111 if (max_heap_index > prio_tree_maxindex(root->index_bits))
115 INIT_PRIO_TREE_NODE(node);
117 while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
118 struct prio_tree_node *tmp = root->prio_tree_node;
122 if (prio_tree_empty(root))
125 prio_tree_remove(root, root->prio_tree_node);
126 INIT_PRIO_TREE_NODE(tmp);
128 prio_set_parent(prev, tmp, true);
132 if (!prio_tree_empty(root))
133 prio_set_parent(prev, root->prio_tree_node, true);
135 root->prio_tree_node = node;
140 * Replace a prio_tree_node with a new node and return the old node
142 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
143 struct prio_tree_node *old, struct prio_tree_node *node)
145 INIT_PRIO_TREE_NODE(node);
147 if (prio_tree_root(old)) {
148 BUG_ON(root->prio_tree_node != old);
150 * We can reduce root->index_bits here. However, it is complex
151 * and does not help much to improve performance (IMO).
153 root->prio_tree_node = node;
155 prio_set_parent(old->parent, node, old->parent->left == old);
157 if (!prio_tree_left_empty(old))
158 prio_set_parent(node, old->left, true);
160 if (!prio_tree_right_empty(old))
161 prio_set_parent(node, old->right, false);
167 * Insert a prio_tree_node @node into a radix priority search tree @root. The
168 * algorithm typically takes O(log n) time where 'log n' is the number of bits
169 * required to represent the maximum heap_index. In the worst case, the algo
170 * can take O((log n)^2) - check prio_tree_expand.
172 * If a prior node with same radix_index and heap_index is already found in
173 * the tree, then returns the address of the prior node. Otherwise, inserts
174 * @node into the tree and returns @node.
176 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
177 struct prio_tree_node *node)
179 struct prio_tree_node *cur, *res = node;
180 unsigned long radix_index, heap_index;
181 unsigned long r_index, h_index, index, mask;
184 get_index(root, node, &radix_index, &heap_index);
186 if (prio_tree_empty(root) ||
187 heap_index > prio_tree_maxindex(root->index_bits))
188 return prio_tree_expand(root, node, heap_index);
190 cur = root->prio_tree_node;
191 mask = 1UL << (root->index_bits - 1);
194 get_index(root, cur, &r_index, &h_index);
196 if (r_index == radix_index && h_index == heap_index)
199 if (h_index < heap_index ||
200 (h_index == heap_index && r_index > radix_index)) {
201 struct prio_tree_node *tmp = node;
202 node = prio_tree_replace(root, cur, node);
206 r_index = radix_index;
209 h_index = heap_index;
214 index = heap_index - radix_index;
219 if (prio_tree_right_empty(cur)) {
220 INIT_PRIO_TREE_NODE(node);
221 prio_set_parent(cur, node, false);
226 if (prio_tree_left_empty(cur)) {
227 INIT_PRIO_TREE_NODE(node);
228 prio_set_parent(cur, node, true);
237 mask = 1UL << (BITS_PER_LONG - 1);
241 /* Should not reach here */
245 EXPORT_SYMBOL(prio_tree_insert);
248 * Remove a prio_tree_node @node from a radix priority search tree @root. The
249 * algorithm takes O(log n) time where 'log n' is the number of bits required
250 * to represent the maximum heap_index.
252 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
254 struct prio_tree_node *cur;
255 unsigned long r_index, h_index_right, h_index_left;
259 while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
260 if (!prio_tree_left_empty(cur))
261 get_index(root, cur->left, &r_index, &h_index_left);
267 if (!prio_tree_right_empty(cur))
268 get_index(root, cur->right, &r_index, &h_index_right);
274 /* both h_index_left and h_index_right cannot be 0 */
275 if (h_index_left >= h_index_right)
281 if (prio_tree_root(cur)) {
282 BUG_ON(root->prio_tree_node != cur);
283 __INIT_PRIO_TREE_ROOT(root, root->raw);
287 if (cur->parent->right == cur)
288 cur->parent->right = cur->parent;
290 cur->parent->left = cur->parent;
293 cur = prio_tree_replace(root, cur->parent, cur);
295 EXPORT_SYMBOL(prio_tree_remove);
297 static void iter_walk_down(struct prio_tree_iter *iter)
301 if (iter->size_level)
306 if (iter->size_level) {
307 BUG_ON(!prio_tree_left_empty(iter->cur));
308 BUG_ON(!prio_tree_right_empty(iter->cur));
310 iter->mask = ULONG_MAX;
312 iter->size_level = 1;
313 iter->mask = 1UL << (BITS_PER_LONG - 1);
317 static void iter_walk_up(struct prio_tree_iter *iter)
319 if (iter->mask == ULONG_MAX)
321 else if (iter->size_level == 1)
325 if (iter->size_level)
327 if (!iter->size_level && (iter->value & iter->mask))
328 iter->value ^= iter->mask;
332 * Following functions help to enumerate all prio_tree_nodes in the tree that
333 * overlap with the input interval X [radix_index, heap_index]. The enumeration
334 * takes O(log n + m) time where 'log n' is the height of the tree (which is
335 * proportional to # of bits required to represent the maximum heap_index) and
336 * 'm' is the number of prio_tree_nodes that overlap the interval X.
339 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
340 unsigned long *r_index, unsigned long *h_index)
342 if (prio_tree_left_empty(iter->cur))
345 get_index(iter->root, iter->cur->left, r_index, h_index);
347 if (iter->r_index <= *h_index) {
348 iter->cur = iter->cur->left;
349 iter_walk_down(iter);
356 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
357 unsigned long *r_index, unsigned long *h_index)
361 if (prio_tree_right_empty(iter->cur))
364 if (iter->size_level)
367 value = iter->value | iter->mask;
369 if (iter->h_index < value)
372 get_index(iter->root, iter->cur->right, r_index, h_index);
374 if (iter->r_index <= *h_index) {
375 iter->cur = iter->cur->right;
376 iter_walk_down(iter);
383 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
385 iter->cur = iter->cur->parent;
390 static inline int overlap(struct prio_tree_iter *iter,
391 unsigned long r_index, unsigned long h_index)
393 return iter->h_index >= r_index && iter->r_index <= h_index;
399 * Get the first prio_tree_node that overlaps with the interval [radix_index,
400 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
401 * traversal of the tree.
403 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
405 struct prio_tree_root *root;
406 unsigned long r_index, h_index;
408 INIT_PRIO_TREE_ITER(iter);
411 if (prio_tree_empty(root))
414 get_index(root, root->prio_tree_node, &r_index, &h_index);
416 if (iter->r_index > h_index)
419 iter->mask = 1UL << (root->index_bits - 1);
420 iter->cur = root->prio_tree_node;
423 if (overlap(iter, r_index, h_index))
426 if (prio_tree_left(iter, &r_index, &h_index))
429 if (prio_tree_right(iter, &r_index, &h_index))
440 * Get the next prio_tree_node that overlaps with the input interval in iter
442 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
444 unsigned long r_index, h_index;
446 if (iter->cur == NULL)
447 return prio_tree_first(iter);
450 while (prio_tree_left(iter, &r_index, &h_index))
451 if (overlap(iter, r_index, h_index))
454 while (!prio_tree_right(iter, &r_index, &h_index)) {
455 while (!prio_tree_root(iter->cur) &&
456 iter->cur->parent->right == iter->cur)
457 prio_tree_parent(iter);
459 if (prio_tree_root(iter->cur))
462 prio_tree_parent(iter);
465 if (overlap(iter, r_index, h_index))
470 EXPORT_SYMBOL(prio_tree_next);