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1da177e4 LT |
1 | /* |
2 | * lib/prio_tree.c - priority search tree | |
3 | * | |
4 | * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu> | |
5 | * | |
6 | * This file is released under the GPL v2. | |
7 | * | |
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 | |
10 | * | |
11 | * 02Feb2004 Initial version | |
12 | */ | |
13 | ||
14 | #include <linux/init.h> | |
15 | #include <linux/mm.h> | |
16 | #include <linux/prio_tree.h> | |
17 | ||
18 | /* | |
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). | |
28 | * | |
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]. | |
35 | * | |
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. | |
40 | */ | |
41 | ||
42 | /* | |
43 | * The following macros are used for implementing prio_tree for i_mmap | |
44 | */ | |
45 | ||
46 | #define RADIX_INDEX(vma) ((vma)->vm_pgoff) | |
47 | #define VMA_SIZE(vma) (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT) | |
48 | /* avoid overflow */ | |
49 | #define HEAP_INDEX(vma) ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1)) | |
50 | ||
51 | ||
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) | |
55 | { | |
56 | if (root->raw) { | |
57 | struct vm_area_struct *vma = prio_tree_entry( | |
58 | node, struct vm_area_struct, shared.prio_tree_node); | |
59 | ||
60 | *radix = RADIX_INDEX(vma); | |
61 | *heap = HEAP_INDEX(vma); | |
62 | } | |
63 | else { | |
64 | *radix = node->start; | |
65 | *heap = node->last; | |
66 | } | |
67 | } | |
68 | ||
69 | static unsigned long index_bits_to_maxindex[BITS_PER_LONG]; | |
70 | ||
71 | void __init prio_tree_init(void) | |
72 | { | |
73 | unsigned int i; | |
74 | ||
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; | |
78 | } | |
79 | ||
80 | /* | |
81 | * Maximum heap_index that can be stored in a PST with index_bits bits | |
82 | */ | |
83 | static inline unsigned long prio_tree_maxindex(unsigned int bits) | |
84 | { | |
85 | return index_bits_to_maxindex[bits - 1]; | |
86 | } | |
87 | ||
88 | /* | |
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 | |
92 | * not bad. | |
93 | */ | |
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) | |
96 | { | |
97 | struct prio_tree_node *first = NULL, *prev, *last = NULL; | |
98 | ||
99 | if (max_heap_index > prio_tree_maxindex(root->index_bits)) | |
100 | root->index_bits++; | |
101 | ||
102 | while (max_heap_index > prio_tree_maxindex(root->index_bits)) { | |
103 | root->index_bits++; | |
104 | ||
105 | if (prio_tree_empty(root)) | |
106 | continue; | |
107 | ||
108 | if (first == NULL) { | |
109 | first = root->prio_tree_node; | |
110 | prio_tree_remove(root, root->prio_tree_node); | |
111 | INIT_PRIO_TREE_NODE(first); | |
112 | last = first; | |
113 | } else { | |
114 | prev = last; | |
115 | last = root->prio_tree_node; | |
116 | prio_tree_remove(root, root->prio_tree_node); | |
117 | INIT_PRIO_TREE_NODE(last); | |
118 | prev->left = last; | |
119 | last->parent = prev; | |
120 | } | |
121 | } | |
122 | ||
123 | INIT_PRIO_TREE_NODE(node); | |
124 | ||
125 | if (first) { | |
126 | node->left = first; | |
127 | first->parent = node; | |
128 | } else | |
129 | last = node; | |
130 | ||
131 | if (!prio_tree_empty(root)) { | |
132 | last->left = root->prio_tree_node; | |
133 | last->left->parent = last; | |
134 | } | |
135 | ||
136 | root->prio_tree_node = node; | |
137 | return node; | |
138 | } | |
139 | ||
140 | /* | |
141 | * Replace a prio_tree_node with a new node and return the old node | |
142 | */ | |
143 | struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root, | |
144 | struct prio_tree_node *old, struct prio_tree_node *node) | |
145 | { | |
146 | INIT_PRIO_TREE_NODE(node); | |
147 | ||
148 | if (prio_tree_root(old)) { | |
149 | BUG_ON(root->prio_tree_node != old); | |
150 | /* | |
151 | * We can reduce root->index_bits here. However, it is complex | |
152 | * and does not help much to improve performance (IMO). | |
153 | */ | |
154 | node->parent = node; | |
155 | root->prio_tree_node = node; | |
156 | } else { | |
157 | node->parent = old->parent; | |
158 | if (old->parent->left == old) | |
159 | old->parent->left = node; | |
160 | else | |
161 | old->parent->right = node; | |
162 | } | |
163 | ||
164 | if (!prio_tree_left_empty(old)) { | |
165 | node->left = old->left; | |
166 | old->left->parent = node; | |
167 | } | |
168 | ||
169 | if (!prio_tree_right_empty(old)) { | |
170 | node->right = old->right; | |
171 | old->right->parent = node; | |
172 | } | |
173 | ||
174 | return old; | |
175 | } | |
176 | ||
177 | /* | |
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. | |
182 | * | |
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. | |
186 | */ | |
187 | struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root, | |
188 | struct prio_tree_node *node) | |
189 | { | |
190 | struct prio_tree_node *cur, *res = node; | |
191 | unsigned long radix_index, heap_index; | |
192 | unsigned long r_index, h_index, index, mask; | |
193 | int size_flag = 0; | |
194 | ||
195 | get_index(root, node, &radix_index, &heap_index); | |
196 | ||
197 | if (prio_tree_empty(root) || | |
198 | heap_index > prio_tree_maxindex(root->index_bits)) | |
199 | return prio_tree_expand(root, node, heap_index); | |
200 | ||
201 | cur = root->prio_tree_node; | |
202 | mask = 1UL << (root->index_bits - 1); | |
203 | ||
204 | while (mask) { | |
205 | get_index(root, cur, &r_index, &h_index); | |
206 | ||
207 | if (r_index == radix_index && h_index == heap_index) | |
208 | return cur; | |
209 | ||
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); | |
214 | cur = tmp; | |
215 | /* swap indices */ | |
216 | index = r_index; | |
217 | r_index = radix_index; | |
218 | radix_index = index; | |
219 | index = h_index; | |
220 | h_index = heap_index; | |
221 | heap_index = index; | |
222 | } | |
223 | ||
224 | if (size_flag) | |
225 | index = heap_index - radix_index; | |
226 | else | |
227 | index = radix_index; | |
228 | ||
229 | if (index & mask) { | |
230 | if (prio_tree_right_empty(cur)) { | |
231 | INIT_PRIO_TREE_NODE(node); | |
232 | cur->right = node; | |
233 | node->parent = cur; | |
234 | return res; | |
235 | } else | |
236 | cur = cur->right; | |
237 | } else { | |
238 | if (prio_tree_left_empty(cur)) { | |
239 | INIT_PRIO_TREE_NODE(node); | |
240 | cur->left = node; | |
241 | node->parent = cur; | |
242 | return res; | |
243 | } else | |
244 | cur = cur->left; | |
245 | } | |
246 | ||
247 | mask >>= 1; | |
248 | ||
249 | if (!mask) { | |
250 | mask = 1UL << (BITS_PER_LONG - 1); | |
251 | size_flag = 1; | |
252 | } | |
253 | } | |
254 | /* Should not reach here */ | |
255 | BUG(); | |
256 | return NULL; | |
257 | } | |
258 | ||
259 | /* | |
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. | |
263 | */ | |
264 | void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node) | |
265 | { | |
266 | struct prio_tree_node *cur; | |
267 | unsigned long r_index, h_index_right, h_index_left; | |
268 | ||
269 | cur = node; | |
270 | ||
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); | |
274 | else { | |
275 | cur = cur->right; | |
276 | continue; | |
277 | } | |
278 | ||
279 | if (!prio_tree_right_empty(cur)) | |
280 | get_index(root, cur->right, &r_index, &h_index_right); | |
281 | else { | |
282 | cur = cur->left; | |
283 | continue; | |
284 | } | |
285 | ||
286 | /* both h_index_left and h_index_right cannot be 0 */ | |
287 | if (h_index_left >= h_index_right) | |
288 | cur = cur->left; | |
289 | else | |
290 | cur = cur->right; | |
291 | } | |
292 | ||
293 | if (prio_tree_root(cur)) { | |
294 | BUG_ON(root->prio_tree_node != cur); | |
295 | __INIT_PRIO_TREE_ROOT(root, root->raw); | |
296 | return; | |
297 | } | |
298 | ||
299 | if (cur->parent->right == cur) | |
300 | cur->parent->right = cur->parent; | |
301 | else | |
302 | cur->parent->left = cur->parent; | |
303 | ||
304 | while (cur != node) | |
305 | cur = prio_tree_replace(root, cur->parent, cur); | |
306 | } | |
307 | ||
308 | /* | |
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. | |
314 | */ | |
315 | ||
316 | static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter, | |
317 | unsigned long *r_index, unsigned long *h_index) | |
318 | { | |
319 | if (prio_tree_left_empty(iter->cur)) | |
320 | return NULL; | |
321 | ||
322 | get_index(iter->root, iter->cur->left, r_index, h_index); | |
323 | ||
324 | if (iter->r_index <= *h_index) { | |
325 | iter->cur = iter->cur->left; | |
326 | iter->mask >>= 1; | |
327 | if (iter->mask) { | |
328 | if (iter->size_level) | |
329 | iter->size_level++; | |
330 | } else { | |
331 | if (iter->size_level) { | |
332 | BUG_ON(!prio_tree_left_empty(iter->cur)); | |
333 | BUG_ON(!prio_tree_right_empty(iter->cur)); | |
334 | iter->size_level++; | |
335 | iter->mask = ULONG_MAX; | |
336 | } else { | |
337 | iter->size_level = 1; | |
338 | iter->mask = 1UL << (BITS_PER_LONG - 1); | |
339 | } | |
340 | } | |
341 | return iter->cur; | |
342 | } | |
343 | ||
344 | return NULL; | |
345 | } | |
346 | ||
347 | static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter, | |
348 | unsigned long *r_index, unsigned long *h_index) | |
349 | { | |
350 | unsigned long value; | |
351 | ||
352 | if (prio_tree_right_empty(iter->cur)) | |
353 | return NULL; | |
354 | ||
355 | if (iter->size_level) | |
356 | value = iter->value; | |
357 | else | |
358 | value = iter->value | iter->mask; | |
359 | ||
360 | if (iter->h_index < value) | |
361 | return NULL; | |
362 | ||
363 | get_index(iter->root, iter->cur->right, r_index, h_index); | |
364 | ||
365 | if (iter->r_index <= *h_index) { | |
366 | iter->cur = iter->cur->right; | |
367 | iter->mask >>= 1; | |
368 | iter->value = value; | |
369 | if (iter->mask) { | |
370 | if (iter->size_level) | |
371 | iter->size_level++; | |
372 | } else { | |
373 | if (iter->size_level) { | |
374 | BUG_ON(!prio_tree_left_empty(iter->cur)); | |
375 | BUG_ON(!prio_tree_right_empty(iter->cur)); | |
376 | iter->size_level++; | |
377 | iter->mask = ULONG_MAX; | |
378 | } else { | |
379 | iter->size_level = 1; | |
380 | iter->mask = 1UL << (BITS_PER_LONG - 1); | |
381 | } | |
382 | } | |
383 | return iter->cur; | |
384 | } | |
385 | ||
386 | return NULL; | |
387 | } | |
388 | ||
389 | static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter) | |
390 | { | |
391 | iter->cur = iter->cur->parent; | |
392 | if (iter->mask == ULONG_MAX) | |
393 | iter->mask = 1UL; | |
394 | else if (iter->size_level == 1) | |
395 | iter->mask = 1UL; | |
396 | else | |
397 | iter->mask <<= 1; | |
398 | if (iter->size_level) | |
399 | iter->size_level--; | |
400 | if (!iter->size_level && (iter->value & iter->mask)) | |
401 | iter->value ^= iter->mask; | |
402 | return iter->cur; | |
403 | } | |
404 | ||
405 | static inline int overlap(struct prio_tree_iter *iter, | |
406 | unsigned long r_index, unsigned long h_index) | |
407 | { | |
408 | return iter->h_index >= r_index && iter->r_index <= h_index; | |
409 | } | |
410 | ||
411 | /* | |
412 | * prio_tree_first: | |
413 | * | |
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. | |
417 | */ | |
418 | static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter) | |
419 | { | |
420 | struct prio_tree_root *root; | |
421 | unsigned long r_index, h_index; | |
422 | ||
423 | INIT_PRIO_TREE_ITER(iter); | |
424 | ||
425 | root = iter->root; | |
426 | if (prio_tree_empty(root)) | |
427 | return NULL; | |
428 | ||
429 | get_index(root, root->prio_tree_node, &r_index, &h_index); | |
430 | ||
431 | if (iter->r_index > h_index) | |
432 | return NULL; | |
433 | ||
434 | iter->mask = 1UL << (root->index_bits - 1); | |
435 | iter->cur = root->prio_tree_node; | |
436 | ||
437 | while (1) { | |
438 | if (overlap(iter, r_index, h_index)) | |
439 | return iter->cur; | |
440 | ||
441 | if (prio_tree_left(iter, &r_index, &h_index)) | |
442 | continue; | |
443 | ||
444 | if (prio_tree_right(iter, &r_index, &h_index)) | |
445 | continue; | |
446 | ||
447 | break; | |
448 | } | |
449 | return NULL; | |
450 | } | |
451 | ||
452 | /* | |
453 | * prio_tree_next: | |
454 | * | |
455 | * Get the next prio_tree_node that overlaps with the input interval in iter | |
456 | */ | |
457 | struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter) | |
458 | { | |
459 | unsigned long r_index, h_index; | |
460 | ||
461 | if (iter->cur == NULL) | |
462 | return prio_tree_first(iter); | |
463 | ||
464 | repeat: | |
465 | while (prio_tree_left(iter, &r_index, &h_index)) | |
466 | if (overlap(iter, r_index, h_index)) | |
467 | return iter->cur; | |
468 | ||
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); | |
473 | ||
474 | if (prio_tree_root(iter->cur)) | |
475 | return NULL; | |
476 | ||
477 | prio_tree_parent(iter); | |
478 | } | |
479 | ||
480 | if (overlap(iter, r_index, h_index)) | |
481 | return iter->cur; | |
482 | ||
483 | goto repeat; | |
484 | } |