Contents of /alx-src/tags/kernel26-2.6.12-alx-r9/lib/prio_tree.c
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Wed Mar 4 11:03:09 2009 UTC (15 years, 3 months ago) by niro
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Wed Mar 4 11:03:09 2009 UTC (15 years, 3 months ago) by niro
File MIME type: text/plain
File size: 12541 byte(s)
Tag kernel26-2.6.12-alx-r9
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 | } |