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
18 #include "../compiler/compiler.h"
19 #include "prio_tree.h"
22 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
23 * which is useful for storing intervals, e.g, we can consider a vma as a closed
24 * interval of file pages [offset_begin, offset_end], and store all vmas that
25 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
26 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
27 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
28 * time where 'log n' is the height of the PST, and 'm' is the number of stored
29 * intervals (vmas) that overlap (map) with the input interval X (the set of
30 * consecutive file pages).
32 * In our implementation, we store closed intervals of the form [radix_index,
33 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
34 * is designed for storing intervals with unique radix indices, i.e., each
35 * interval have different radix_index. However, this limitation can be easily
36 * overcome by using the size, i.e., heap_index - radix_index, as part of the
37 * index, so we index the tree using [(radix_index,size), heap_index].
39 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
40 * machine, the maximum height of a PST can be 64. We can use a balanced version
41 * of the priority search tree to optimize the tree height, but the balanced
42 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
45 static void get_index(const struct prio_tree_node *node,
46 unsigned long *radix, unsigned long *heap)
52 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
54 static void fio_init prio_tree_init(void)
58 for (i = 0; i < FIO_ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
59 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
60 index_bits_to_maxindex[FIO_ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
64 * Maximum heap_index that can be stored in a PST with index_bits bits
66 static inline unsigned long prio_tree_maxindex(unsigned int bits)
68 return index_bits_to_maxindex[bits - 1];
72 * Extend a priority search tree so that it can store a node with heap_index
73 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
74 * However, this function is used rarely and the common case performance is
77 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
78 struct prio_tree_node *node, unsigned long max_heap_index)
80 struct prio_tree_node *first = NULL, *prev, *last = NULL;
82 if (max_heap_index > prio_tree_maxindex(root->index_bits))
85 while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
88 if (prio_tree_empty(root))
92 first = root->prio_tree_node;
93 prio_tree_remove(root, root->prio_tree_node);
94 INIT_PRIO_TREE_NODE(first);
98 last = root->prio_tree_node;
99 prio_tree_remove(root, root->prio_tree_node);
100 INIT_PRIO_TREE_NODE(last);
106 INIT_PRIO_TREE_NODE(node);
110 first->parent = node;
114 if (!prio_tree_empty(root)) {
115 last->left = root->prio_tree_node;
116 last->left->parent = last;
119 root->prio_tree_node = node;
124 * Replace a prio_tree_node with a new node and return the old node
126 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
127 struct prio_tree_node *old, struct prio_tree_node *node)
129 INIT_PRIO_TREE_NODE(node);
131 if (prio_tree_root(old)) {
132 assert(root->prio_tree_node == old);
134 * We can reduce root->index_bits here. However, it is complex
135 * and does not help much to improve performance (IMO).
138 root->prio_tree_node = node;
140 node->parent = old->parent;
141 if (old->parent->left == old)
142 old->parent->left = node;
144 old->parent->right = node;
147 if (!prio_tree_left_empty(old)) {
148 node->left = old->left;
149 old->left->parent = node;
152 if (!prio_tree_right_empty(old)) {
153 node->right = old->right;
154 old->right->parent = node;
161 * Insert a prio_tree_node @node into a radix priority search tree @root. The
162 * algorithm typically takes O(log n) time where 'log n' is the number of bits
163 * required to represent the maximum heap_index. In the worst case, the algo
164 * can take O((log n)^2) - check prio_tree_expand.
166 * If a prior node with same radix_index and heap_index is already found in
167 * the tree, then returns the address of the prior node. Otherwise, inserts
168 * @node into the tree and returns @node.
170 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
171 struct prio_tree_node *node)
173 struct prio_tree_node *cur, *res = node;
174 unsigned long radix_index, heap_index;
175 unsigned long r_index, h_index, index, mask;
178 get_index(node, &radix_index, &heap_index);
180 if (prio_tree_empty(root) ||
181 heap_index > prio_tree_maxindex(root->index_bits))
182 return prio_tree_expand(root, node, heap_index);
184 cur = root->prio_tree_node;
185 mask = 1UL << (root->index_bits - 1);
188 get_index(cur, &r_index, &h_index);
190 if (r_index == radix_index && h_index == heap_index)
193 if (h_index < heap_index ||
194 (h_index == heap_index && r_index > radix_index)) {
195 struct prio_tree_node *tmp = node;
196 node = prio_tree_replace(root, cur, node);
200 r_index = radix_index;
203 h_index = heap_index;
208 index = heap_index - radix_index;
213 if (prio_tree_right_empty(cur)) {
214 INIT_PRIO_TREE_NODE(node);
221 if (prio_tree_left_empty(cur)) {
222 INIT_PRIO_TREE_NODE(node);
233 mask = 1UL << (BITS_PER_LONG - 1);
237 /* Should not reach here */
243 * Remove a prio_tree_node @node from a radix priority search tree @root. The
244 * algorithm takes O(log n) time where 'log n' is the number of bits required
245 * to represent the maximum heap_index.
247 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
249 struct prio_tree_node *cur;
250 unsigned long r_index, h_index_right, h_index_left;
254 while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
255 if (!prio_tree_left_empty(cur))
256 get_index(cur->left, &r_index, &h_index_left);
262 if (!prio_tree_right_empty(cur))
263 get_index(cur->right, &r_index, &h_index_right);
269 /* both h_index_left and h_index_right cannot be 0 */
270 if (h_index_left >= h_index_right)
276 if (prio_tree_root(cur)) {
277 assert(root->prio_tree_node == cur);
278 INIT_PRIO_TREE_ROOT(root);
282 if (cur->parent->right == cur)
283 cur->parent->right = cur->parent;
285 cur->parent->left = cur->parent;
288 cur = prio_tree_replace(root, cur->parent, cur);
292 * Following functions help to enumerate all prio_tree_nodes in the tree that
293 * overlap with the input interval X [radix_index, heap_index]. The enumeration
294 * takes O(log n + m) time where 'log n' is the height of the tree (which is
295 * proportional to # of bits required to represent the maximum heap_index) and
296 * 'm' is the number of prio_tree_nodes that overlap the interval X.
299 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
300 unsigned long *r_index, unsigned long *h_index)
302 if (prio_tree_left_empty(iter->cur))
305 get_index(iter->cur->left, r_index, h_index);
307 if (iter->r_index <= *h_index) {
308 iter->cur = iter->cur->left;
311 if (iter->size_level)
314 if (iter->size_level) {
315 assert(prio_tree_left_empty(iter->cur));
316 assert(prio_tree_right_empty(iter->cur));
318 iter->mask = ULONG_MAX;
320 iter->size_level = 1;
321 iter->mask = 1UL << (BITS_PER_LONG - 1);
330 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
331 unsigned long *r_index, unsigned long *h_index)
335 if (prio_tree_right_empty(iter->cur))
338 if (iter->size_level)
341 value = iter->value | iter->mask;
343 if (iter->h_index < value)
346 get_index(iter->cur->right, r_index, h_index);
348 if (iter->r_index <= *h_index) {
349 iter->cur = iter->cur->right;
353 if (iter->size_level)
356 if (iter->size_level) {
357 assert(prio_tree_left_empty(iter->cur));
358 assert(prio_tree_right_empty(iter->cur));
360 iter->mask = ULONG_MAX;
362 iter->size_level = 1;
363 iter->mask = 1UL << (BITS_PER_LONG - 1);
372 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
374 iter->cur = iter->cur->parent;
375 if (iter->mask == ULONG_MAX)
377 else if (iter->size_level == 1)
381 if (iter->size_level)
383 if (!iter->size_level && (iter->value & iter->mask))
384 iter->value ^= iter->mask;
388 static inline int overlap(struct prio_tree_iter *iter,
389 unsigned long r_index, unsigned long h_index)
391 return iter->h_index >= r_index && iter->r_index <= h_index;
397 * Get the first prio_tree_node that overlaps with the interval [radix_index,
398 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
399 * traversal of the tree.
401 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
403 struct prio_tree_root *root;
404 unsigned long r_index, h_index;
406 INIT_PRIO_TREE_ITER(iter);
409 if (prio_tree_empty(root))
412 get_index(root->prio_tree_node, &r_index, &h_index);
414 if (iter->r_index > h_index)
417 iter->mask = 1UL << (root->index_bits - 1);
418 iter->cur = root->prio_tree_node;
421 if (overlap(iter, r_index, h_index))
424 if (prio_tree_left(iter, &r_index, &h_index))
427 if (prio_tree_right(iter, &r_index, &h_index))
438 * Get the next prio_tree_node that overlaps with the input interval in iter
440 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
442 unsigned long r_index, h_index;
444 if (iter->cur == NULL)
445 return prio_tree_first(iter);
448 while (prio_tree_left(iter, &r_index, &h_index))
449 if (overlap(iter, r_index, h_index))
452 while (!prio_tree_right(iter, &r_index, &h_index)) {
453 while (!prio_tree_root(iter->cur) &&
454 iter->cur->parent->right == iter->cur)
455 prio_tree_parent(iter);
457 if (prio_tree_root(iter->cur))
460 prio_tree_parent(iter);
463 if (overlap(iter, r_index, h_index))