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>
19 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
20 * which is useful for storing intervals, e.g, we can consider a vma as a closed
21 * interval of file pages [offset_begin, offset_end], and store all vmas that
22 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
23 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
24 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
25 * time where 'log n' is the height of the PST, and 'm' is the number of stored
26 * intervals (vmas) that overlap (map) with the input interval X (the set of
27 * consecutive file pages).
29 * In our implementation, we store closed intervals of the form [radix_index,
30 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
31 * is designed for storing intervals with unique radix indices, i.e., each
32 * interval have different radix_index. However, this limitation can be easily
33 * overcome by using the size, i.e., heap_index - radix_index, as part of the
34 * index, so we index the tree using [(radix_index,size), heap_index].
36 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
37 * machine, the maximum height of a PST can be 64. We can use a balanced version
38 * of the priority search tree to optimize the tree height, but the balanced
39 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
43 * The following macros are used for implementing prio_tree for i_mmap
46 #define RADIX_INDEX(vma) ((vma)->vm_pgoff)
47 #define VMA_SIZE(vma) (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
49 #define HEAP_INDEX(vma) ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
52 static void get_index(const struct prio_tree_root
*root
,
53 const struct prio_tree_node
*node
,
54 unsigned long *radix
, unsigned long *heap
)
57 struct vm_area_struct
*vma
= prio_tree_entry(
58 node
, struct vm_area_struct
, shared
.prio_tree_node
);
60 *radix
= RADIX_INDEX(vma
);
61 *heap
= HEAP_INDEX(vma
);
69 static unsigned long index_bits_to_maxindex
[BITS_PER_LONG
];
71 void __init
prio_tree_init(void)
75 for (i
= 0; i
< ARRAY_SIZE(index_bits_to_maxindex
) - 1; i
++)
76 index_bits_to_maxindex
[i
] = (1UL << (i
+ 1)) - 1;
77 index_bits_to_maxindex
[ARRAY_SIZE(index_bits_to_maxindex
) - 1] = ~0UL;
81 * Maximum heap_index that can be stored in a PST with index_bits bits
83 static inline unsigned long prio_tree_maxindex(unsigned int bits
)
85 return index_bits_to_maxindex
[bits
- 1];
89 * Extend a priority search tree so that it can store a node with heap_index
90 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
91 * However, this function is used rarely and the common case performance is
94 static struct prio_tree_node
*prio_tree_expand(struct prio_tree_root
*root
,
95 struct prio_tree_node
*node
, unsigned long max_heap_index
)
97 struct prio_tree_node
*first
= NULL
, *prev
, *last
= NULL
;
99 if (max_heap_index
> prio_tree_maxindex(root
->index_bits
))
102 while (max_heap_index
> prio_tree_maxindex(root
->index_bits
)) {
105 if (prio_tree_empty(root
))
109 first
= root
->prio_tree_node
;
110 prio_tree_remove(root
, root
->prio_tree_node
);
111 INIT_PRIO_TREE_NODE(first
);
115 last
= root
->prio_tree_node
;
116 prio_tree_remove(root
, root
->prio_tree_node
);
117 INIT_PRIO_TREE_NODE(last
);
123 INIT_PRIO_TREE_NODE(node
);
127 first
->parent
= node
;
131 if (!prio_tree_empty(root
)) {
132 last
->left
= root
->prio_tree_node
;
133 last
->left
->parent
= last
;
136 root
->prio_tree_node
= node
;
141 * Replace a prio_tree_node with a new node and return the old node
143 struct prio_tree_node
*prio_tree_replace(struct prio_tree_root
*root
,
144 struct prio_tree_node
*old
, struct prio_tree_node
*node
)
146 INIT_PRIO_TREE_NODE(node
);
148 if (prio_tree_root(old
)) {
149 BUG_ON(root
->prio_tree_node
!= old
);
151 * We can reduce root->index_bits here. However, it is complex
152 * and does not help much to improve performance (IMO).
155 root
->prio_tree_node
= node
;
157 node
->parent
= old
->parent
;
158 if (old
->parent
->left
== old
)
159 old
->parent
->left
= node
;
161 old
->parent
->right
= node
;
164 if (!prio_tree_left_empty(old
)) {
165 node
->left
= old
->left
;
166 old
->left
->parent
= node
;
169 if (!prio_tree_right_empty(old
)) {
170 node
->right
= old
->right
;
171 old
->right
->parent
= node
;
178 * Insert a prio_tree_node @node into a radix priority search tree @root. The
179 * algorithm typically takes O(log n) time where 'log n' is the number of bits
180 * required to represent the maximum heap_index. In the worst case, the algo
181 * can take O((log n)^2) - check prio_tree_expand.
183 * If a prior node with same radix_index and heap_index is already found in
184 * the tree, then returns the address of the prior node. Otherwise, inserts
185 * @node into the tree and returns @node.
187 struct prio_tree_node
*prio_tree_insert(struct prio_tree_root
*root
,
188 struct prio_tree_node
*node
)
190 struct prio_tree_node
*cur
, *res
= node
;
191 unsigned long radix_index
, heap_index
;
192 unsigned long r_index
, h_index
, index
, mask
;
195 get_index(root
, node
, &radix_index
, &heap_index
);
197 if (prio_tree_empty(root
) ||
198 heap_index
> prio_tree_maxindex(root
->index_bits
))
199 return prio_tree_expand(root
, node
, heap_index
);
201 cur
= root
->prio_tree_node
;
202 mask
= 1UL << (root
->index_bits
- 1);
205 get_index(root
, cur
, &r_index
, &h_index
);
207 if (r_index
== radix_index
&& h_index
== heap_index
)
210 if (h_index
< heap_index
||
211 (h_index
== heap_index
&& r_index
> radix_index
)) {
212 struct prio_tree_node
*tmp
= node
;
213 node
= prio_tree_replace(root
, cur
, node
);
217 r_index
= radix_index
;
220 h_index
= heap_index
;
225 index
= heap_index
- radix_index
;
230 if (prio_tree_right_empty(cur
)) {
231 INIT_PRIO_TREE_NODE(node
);
238 if (prio_tree_left_empty(cur
)) {
239 INIT_PRIO_TREE_NODE(node
);
250 mask
= 1UL << (BITS_PER_LONG
- 1);
254 /* Should not reach here */
260 * Remove a prio_tree_node @node from a radix priority search tree @root. The
261 * algorithm takes O(log n) time where 'log n' is the number of bits required
262 * to represent the maximum heap_index.
264 void prio_tree_remove(struct prio_tree_root
*root
, struct prio_tree_node
*node
)
266 struct prio_tree_node
*cur
;
267 unsigned long r_index
, h_index_right
, h_index_left
;
271 while (!prio_tree_left_empty(cur
) || !prio_tree_right_empty(cur
)) {
272 if (!prio_tree_left_empty(cur
))
273 get_index(root
, cur
->left
, &r_index
, &h_index_left
);
279 if (!prio_tree_right_empty(cur
))
280 get_index(root
, cur
->right
, &r_index
, &h_index_right
);
286 /* both h_index_left and h_index_right cannot be 0 */
287 if (h_index_left
>= h_index_right
)
293 if (prio_tree_root(cur
)) {
294 BUG_ON(root
->prio_tree_node
!= cur
);
295 __INIT_PRIO_TREE_ROOT(root
, root
->raw
);
299 if (cur
->parent
->right
== cur
)
300 cur
->parent
->right
= cur
->parent
;
302 cur
->parent
->left
= cur
->parent
;
305 cur
= prio_tree_replace(root
, cur
->parent
, cur
);
309 * Following functions help to enumerate all prio_tree_nodes in the tree that
310 * overlap with the input interval X [radix_index, heap_index]. The enumeration
311 * takes O(log n + m) time where 'log n' is the height of the tree (which is
312 * proportional to # of bits required to represent the maximum heap_index) and
313 * 'm' is the number of prio_tree_nodes that overlap the interval X.
316 static struct prio_tree_node
*prio_tree_left(struct prio_tree_iter
*iter
,
317 unsigned long *r_index
, unsigned long *h_index
)
319 if (prio_tree_left_empty(iter
->cur
))
322 get_index(iter
->root
, iter
->cur
->left
, r_index
, h_index
);
324 if (iter
->r_index
<= *h_index
) {
325 iter
->cur
= iter
->cur
->left
;
328 if (iter
->size_level
)
331 if (iter
->size_level
) {
332 BUG_ON(!prio_tree_left_empty(iter
->cur
));
333 BUG_ON(!prio_tree_right_empty(iter
->cur
));
335 iter
->mask
= ULONG_MAX
;
337 iter
->size_level
= 1;
338 iter
->mask
= 1UL << (BITS_PER_LONG
- 1);
347 static struct prio_tree_node
*prio_tree_right(struct prio_tree_iter
*iter
,
348 unsigned long *r_index
, unsigned long *h_index
)
352 if (prio_tree_right_empty(iter
->cur
))
355 if (iter
->size_level
)
358 value
= iter
->value
| iter
->mask
;
360 if (iter
->h_index
< value
)
363 get_index(iter
->root
, iter
->cur
->right
, r_index
, h_index
);
365 if (iter
->r_index
<= *h_index
) {
366 iter
->cur
= iter
->cur
->right
;
370 if (iter
->size_level
)
373 if (iter
->size_level
) {
374 BUG_ON(!prio_tree_left_empty(iter
->cur
));
375 BUG_ON(!prio_tree_right_empty(iter
->cur
));
377 iter
->mask
= ULONG_MAX
;
379 iter
->size_level
= 1;
380 iter
->mask
= 1UL << (BITS_PER_LONG
- 1);
389 static struct prio_tree_node
*prio_tree_parent(struct prio_tree_iter
*iter
)
391 iter
->cur
= iter
->cur
->parent
;
392 if (iter
->mask
== ULONG_MAX
)
394 else if (iter
->size_level
== 1)
398 if (iter
->size_level
)
400 if (!iter
->size_level
&& (iter
->value
& iter
->mask
))
401 iter
->value
^= iter
->mask
;
405 static inline int overlap(struct prio_tree_iter
*iter
,
406 unsigned long r_index
, unsigned long h_index
)
408 return iter
->h_index
>= r_index
&& iter
->r_index
<= h_index
;
414 * Get the first prio_tree_node that overlaps with the interval [radix_index,
415 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
416 * traversal of the tree.
418 static struct prio_tree_node
*prio_tree_first(struct prio_tree_iter
*iter
)
420 struct prio_tree_root
*root
;
421 unsigned long r_index
, h_index
;
423 INIT_PRIO_TREE_ITER(iter
);
426 if (prio_tree_empty(root
))
429 get_index(root
, root
->prio_tree_node
, &r_index
, &h_index
);
431 if (iter
->r_index
> h_index
)
434 iter
->mask
= 1UL << (root
->index_bits
- 1);
435 iter
->cur
= root
->prio_tree_node
;
438 if (overlap(iter
, r_index
, h_index
))
441 if (prio_tree_left(iter
, &r_index
, &h_index
))
444 if (prio_tree_right(iter
, &r_index
, &h_index
))
455 * Get the next prio_tree_node that overlaps with the input interval in iter
457 struct prio_tree_node
*prio_tree_next(struct prio_tree_iter
*iter
)
459 unsigned long r_index
, h_index
;
461 if (iter
->cur
== NULL
)
462 return prio_tree_first(iter
);
465 while (prio_tree_left(iter
, &r_index
, &h_index
))
466 if (overlap(iter
, r_index
, h_index
))
469 while (!prio_tree_right(iter
, &r_index
, &h_index
)) {
470 while (!prio_tree_root(iter
->cur
) &&
471 iter
->cur
->parent
->right
== iter
->cur
)
472 prio_tree_parent(iter
);
474 if (prio_tree_root(iter
->cur
))
477 prio_tree_parent(iter
);
480 if (overlap(iter
, r_index
, h_index
))
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