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b65c7ec4 JA |
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 <stdlib.h> | |
15 | #include <limits.h> | |
1f6ab977 TK |
16 | |
17 | #include "../compiler/compiler.h" | |
b65c7ec4 JA |
18 | #include "prio_tree.h" |
19 | ||
1f6ab977 TK |
20 | #define ARRAY_SIZE(x) (sizeof((x)) / (sizeof((x)[0]))) |
21 | ||
b65c7ec4 JA |
22 | /* |
23 | * A clever mix of heap and radix trees forms a radix priority search tree (PST) | |
24 | * which is useful for storing intervals, e.g, we can consider a vma as a closed | |
25 | * interval of file pages [offset_begin, offset_end], and store all vmas that | |
26 | * map a file in a PST. Then, using the PST, we can answer a stabbing query, | |
27 | * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a | |
28 | * given input interval X (a set of consecutive file pages), in "O(log n + m)" | |
29 | * time where 'log n' is the height of the PST, and 'm' is the number of stored | |
30 | * intervals (vmas) that overlap (map) with the input interval X (the set of | |
31 | * consecutive file pages). | |
32 | * | |
33 | * In our implementation, we store closed intervals of the form [radix_index, | |
34 | * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST | |
35 | * is designed for storing intervals with unique radix indices, i.e., each | |
36 | * interval have different radix_index. However, this limitation can be easily | |
37 | * overcome by using the size, i.e., heap_index - radix_index, as part of the | |
38 | * index, so we index the tree using [(radix_index,size), heap_index]. | |
39 | * | |
40 | * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit | |
41 | * machine, the maximum height of a PST can be 64. We can use a balanced version | |
42 | * of the priority search tree to optimize the tree height, but the balanced | |
43 | * tree proposed by McCreight is too complex and memory-hungry for our purpose. | |
44 | */ | |
45 | ||
46 | static void get_index(const struct prio_tree_node *node, | |
47 | unsigned long *radix, unsigned long *heap) | |
48 | { | |
49 | *radix = node->start; | |
50 | *heap = node->last; | |
51 | } | |
52 | ||
53 | static unsigned long index_bits_to_maxindex[BITS_PER_LONG]; | |
54 | ||
10aa136b | 55 | static void fio_init prio_tree_init(void) |
b65c7ec4 JA |
56 | { |
57 | unsigned int i; | |
58 | ||
59 | for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++) | |
60 | index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1; | |
61 | index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL; | |
62 | } | |
63 | ||
64 | /* | |
65 | * Maximum heap_index that can be stored in a PST with index_bits bits | |
66 | */ | |
67 | static inline unsigned long prio_tree_maxindex(unsigned int bits) | |
68 | { | |
69 | return index_bits_to_maxindex[bits - 1]; | |
70 | } | |
71 | ||
72 | /* | |
73 | * Extend a priority search tree so that it can store a node with heap_index | |
74 | * max_heap_index. In the worst case, this algorithm takes O((log n)^2). | |
75 | * However, this function is used rarely and the common case performance is | |
76 | * not bad. | |
77 | */ | |
78 | static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root, | |
79 | struct prio_tree_node *node, unsigned long max_heap_index) | |
80 | { | |
81 | struct prio_tree_node *first = NULL, *prev, *last = NULL; | |
82 | ||
83 | if (max_heap_index > prio_tree_maxindex(root->index_bits)) | |
84 | root->index_bits++; | |
85 | ||
86 | while (max_heap_index > prio_tree_maxindex(root->index_bits)) { | |
87 | root->index_bits++; | |
88 | ||
89 | if (prio_tree_empty(root)) | |
90 | continue; | |
91 | ||
92 | if (first == NULL) { | |
93 | first = root->prio_tree_node; | |
94 | prio_tree_remove(root, root->prio_tree_node); | |
95 | INIT_PRIO_TREE_NODE(first); | |
96 | last = first; | |
97 | } else { | |
98 | prev = last; | |
99 | last = root->prio_tree_node; | |
100 | prio_tree_remove(root, root->prio_tree_node); | |
101 | INIT_PRIO_TREE_NODE(last); | |
102 | prev->left = last; | |
103 | last->parent = prev; | |
104 | } | |
105 | } | |
106 | ||
107 | INIT_PRIO_TREE_NODE(node); | |
108 | ||
109 | if (first) { | |
110 | node->left = first; | |
111 | first->parent = node; | |
112 | } else | |
113 | last = node; | |
114 | ||
115 | if (!prio_tree_empty(root)) { | |
116 | last->left = root->prio_tree_node; | |
117 | last->left->parent = last; | |
118 | } | |
119 | ||
120 | root->prio_tree_node = node; | |
121 | return node; | |
122 | } | |
123 | ||
124 | /* | |
125 | * Replace a prio_tree_node with a new node and return the old node | |
126 | */ | |
127 | struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root, | |
128 | struct prio_tree_node *old, struct prio_tree_node *node) | |
129 | { | |
130 | INIT_PRIO_TREE_NODE(node); | |
131 | ||
132 | if (prio_tree_root(old)) { | |
133 | assert(root->prio_tree_node == old); | |
134 | /* | |
135 | * We can reduce root->index_bits here. However, it is complex | |
136 | * and does not help much to improve performance (IMO). | |
137 | */ | |
138 | node->parent = node; | |
139 | root->prio_tree_node = node; | |
140 | } else { | |
141 | node->parent = old->parent; | |
142 | if (old->parent->left == old) | |
143 | old->parent->left = node; | |
144 | else | |
145 | old->parent->right = node; | |
146 | } | |
147 | ||
148 | if (!prio_tree_left_empty(old)) { | |
149 | node->left = old->left; | |
150 | old->left->parent = node; | |
151 | } | |
152 | ||
153 | if (!prio_tree_right_empty(old)) { | |
154 | node->right = old->right; | |
155 | old->right->parent = node; | |
156 | } | |
157 | ||
158 | return old; | |
159 | } | |
160 | ||
161 | /* | |
162 | * Insert a prio_tree_node @node into a radix priority search tree @root. The | |
163 | * algorithm typically takes O(log n) time where 'log n' is the number of bits | |
164 | * required to represent the maximum heap_index. In the worst case, the algo | |
165 | * can take O((log n)^2) - check prio_tree_expand. | |
166 | * | |
167 | * If a prior node with same radix_index and heap_index is already found in | |
168 | * the tree, then returns the address of the prior node. Otherwise, inserts | |
169 | * @node into the tree and returns @node. | |
170 | */ | |
171 | struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root, | |
172 | struct prio_tree_node *node) | |
173 | { | |
174 | struct prio_tree_node *cur, *res = node; | |
175 | unsigned long radix_index, heap_index; | |
176 | unsigned long r_index, h_index, index, mask; | |
177 | int size_flag = 0; | |
178 | ||
179 | get_index(node, &radix_index, &heap_index); | |
180 | ||
181 | if (prio_tree_empty(root) || | |
182 | heap_index > prio_tree_maxindex(root->index_bits)) | |
183 | return prio_tree_expand(root, node, heap_index); | |
184 | ||
185 | cur = root->prio_tree_node; | |
186 | mask = 1UL << (root->index_bits - 1); | |
187 | ||
188 | while (mask) { | |
189 | get_index(cur, &r_index, &h_index); | |
190 | ||
191 | if (r_index == radix_index && h_index == heap_index) | |
192 | return cur; | |
193 | ||
194 | if (h_index < heap_index || | |
195 | (h_index == heap_index && r_index > radix_index)) { | |
196 | struct prio_tree_node *tmp = node; | |
197 | node = prio_tree_replace(root, cur, node); | |
198 | cur = tmp; | |
199 | /* swap indices */ | |
200 | index = r_index; | |
201 | r_index = radix_index; | |
202 | radix_index = index; | |
203 | index = h_index; | |
204 | h_index = heap_index; | |
205 | heap_index = index; | |
206 | } | |
207 | ||
208 | if (size_flag) | |
209 | index = heap_index - radix_index; | |
210 | else | |
211 | index = radix_index; | |
212 | ||
213 | if (index & mask) { | |
214 | if (prio_tree_right_empty(cur)) { | |
215 | INIT_PRIO_TREE_NODE(node); | |
216 | cur->right = node; | |
217 | node->parent = cur; | |
218 | return res; | |
219 | } else | |
220 | cur = cur->right; | |
221 | } else { | |
222 | if (prio_tree_left_empty(cur)) { | |
223 | INIT_PRIO_TREE_NODE(node); | |
224 | cur->left = node; | |
225 | node->parent = cur; | |
226 | return res; | |
227 | } else | |
228 | cur = cur->left; | |
229 | } | |
230 | ||
231 | mask >>= 1; | |
232 | ||
233 | if (!mask) { | |
234 | mask = 1UL << (BITS_PER_LONG - 1); | |
235 | size_flag = 1; | |
236 | } | |
237 | } | |
238 | /* Should not reach here */ | |
239 | assert(0); | |
240 | return NULL; | |
241 | } | |
242 | ||
243 | /* | |
244 | * Remove a prio_tree_node @node from a radix priority search tree @root. The | |
245 | * algorithm takes O(log n) time where 'log n' is the number of bits required | |
246 | * to represent the maximum heap_index. | |
247 | */ | |
248 | void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node) | |
249 | { | |
250 | struct prio_tree_node *cur; | |
251 | unsigned long r_index, h_index_right, h_index_left; | |
252 | ||
253 | cur = node; | |
254 | ||
255 | while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) { | |
256 | if (!prio_tree_left_empty(cur)) | |
257 | get_index(cur->left, &r_index, &h_index_left); | |
258 | else { | |
259 | cur = cur->right; | |
260 | continue; | |
261 | } | |
262 | ||
263 | if (!prio_tree_right_empty(cur)) | |
264 | get_index(cur->right, &r_index, &h_index_right); | |
265 | else { | |
266 | cur = cur->left; | |
267 | continue; | |
268 | } | |
269 | ||
270 | /* both h_index_left and h_index_right cannot be 0 */ | |
271 | if (h_index_left >= h_index_right) | |
272 | cur = cur->left; | |
273 | else | |
274 | cur = cur->right; | |
275 | } | |
276 | ||
277 | if (prio_tree_root(cur)) { | |
278 | assert(root->prio_tree_node == cur); | |
279 | INIT_PRIO_TREE_ROOT(root); | |
280 | return; | |
281 | } | |
282 | ||
283 | if (cur->parent->right == cur) | |
284 | cur->parent->right = cur->parent; | |
285 | else | |
286 | cur->parent->left = cur->parent; | |
287 | ||
288 | while (cur != node) | |
289 | cur = prio_tree_replace(root, cur->parent, cur); | |
290 | } | |
291 | ||
292 | /* | |
293 | * Following functions help to enumerate all prio_tree_nodes in the tree that | |
294 | * overlap with the input interval X [radix_index, heap_index]. The enumeration | |
295 | * takes O(log n + m) time where 'log n' is the height of the tree (which is | |
296 | * proportional to # of bits required to represent the maximum heap_index) and | |
297 | * 'm' is the number of prio_tree_nodes that overlap the interval X. | |
298 | */ | |
299 | ||
300 | static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter, | |
301 | unsigned long *r_index, unsigned long *h_index) | |
302 | { | |
303 | if (prio_tree_left_empty(iter->cur)) | |
304 | return NULL; | |
305 | ||
306 | get_index(iter->cur->left, r_index, h_index); | |
307 | ||
308 | if (iter->r_index <= *h_index) { | |
309 | iter->cur = iter->cur->left; | |
310 | iter->mask >>= 1; | |
311 | if (iter->mask) { | |
312 | if (iter->size_level) | |
313 | iter->size_level++; | |
314 | } else { | |
315 | if (iter->size_level) { | |
316 | assert(prio_tree_left_empty(iter->cur)); | |
317 | assert(prio_tree_right_empty(iter->cur)); | |
318 | iter->size_level++; | |
319 | iter->mask = ULONG_MAX; | |
320 | } else { | |
321 | iter->size_level = 1; | |
322 | iter->mask = 1UL << (BITS_PER_LONG - 1); | |
323 | } | |
324 | } | |
325 | return iter->cur; | |
326 | } | |
327 | ||
328 | return NULL; | |
329 | } | |
330 | ||
331 | static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter, | |
332 | unsigned long *r_index, unsigned long *h_index) | |
333 | { | |
334 | unsigned long value; | |
335 | ||
336 | if (prio_tree_right_empty(iter->cur)) | |
337 | return NULL; | |
338 | ||
339 | if (iter->size_level) | |
340 | value = iter->value; | |
341 | else | |
342 | value = iter->value | iter->mask; | |
343 | ||
344 | if (iter->h_index < value) | |
345 | return NULL; | |
346 | ||
347 | get_index(iter->cur->right, r_index, h_index); | |
348 | ||
349 | if (iter->r_index <= *h_index) { | |
350 | iter->cur = iter->cur->right; | |
351 | iter->mask >>= 1; | |
352 | iter->value = value; | |
353 | if (iter->mask) { | |
354 | if (iter->size_level) | |
355 | iter->size_level++; | |
356 | } else { | |
357 | if (iter->size_level) { | |
358 | assert(prio_tree_left_empty(iter->cur)); | |
359 | assert(prio_tree_right_empty(iter->cur)); | |
360 | iter->size_level++; | |
361 | iter->mask = ULONG_MAX; | |
362 | } else { | |
363 | iter->size_level = 1; | |
364 | iter->mask = 1UL << (BITS_PER_LONG - 1); | |
365 | } | |
366 | } | |
367 | return iter->cur; | |
368 | } | |
369 | ||
370 | return NULL; | |
371 | } | |
372 | ||
373 | static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter) | |
374 | { | |
375 | iter->cur = iter->cur->parent; | |
376 | if (iter->mask == ULONG_MAX) | |
377 | iter->mask = 1UL; | |
378 | else if (iter->size_level == 1) | |
379 | iter->mask = 1UL; | |
380 | else | |
381 | iter->mask <<= 1; | |
382 | if (iter->size_level) | |
383 | iter->size_level--; | |
384 | if (!iter->size_level && (iter->value & iter->mask)) | |
385 | iter->value ^= iter->mask; | |
386 | return iter->cur; | |
387 | } | |
388 | ||
389 | static inline int overlap(struct prio_tree_iter *iter, | |
390 | unsigned long r_index, unsigned long h_index) | |
391 | { | |
392 | return iter->h_index >= r_index && iter->r_index <= h_index; | |
393 | } | |
394 | ||
395 | /* | |
396 | * prio_tree_first: | |
397 | * | |
398 | * Get the first prio_tree_node that overlaps with the interval [radix_index, | |
399 | * heap_index]. Note that always radix_index <= heap_index. We do a pre-order | |
400 | * traversal of the tree. | |
401 | */ | |
402 | static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter) | |
403 | { | |
404 | struct prio_tree_root *root; | |
405 | unsigned long r_index, h_index; | |
406 | ||
407 | INIT_PRIO_TREE_ITER(iter); | |
408 | ||
409 | root = iter->root; | |
410 | if (prio_tree_empty(root)) | |
411 | return NULL; | |
412 | ||
413 | get_index(root->prio_tree_node, &r_index, &h_index); | |
414 | ||
415 | if (iter->r_index > h_index) | |
416 | return NULL; | |
417 | ||
418 | iter->mask = 1UL << (root->index_bits - 1); | |
419 | iter->cur = root->prio_tree_node; | |
420 | ||
421 | while (1) { | |
422 | if (overlap(iter, r_index, h_index)) | |
423 | return iter->cur; | |
424 | ||
425 | if (prio_tree_left(iter, &r_index, &h_index)) | |
426 | continue; | |
427 | ||
428 | if (prio_tree_right(iter, &r_index, &h_index)) | |
429 | continue; | |
430 | ||
431 | break; | |
432 | } | |
433 | return NULL; | |
434 | } | |
435 | ||
436 | /* | |
437 | * prio_tree_next: | |
438 | * | |
439 | * Get the next prio_tree_node that overlaps with the input interval in iter | |
440 | */ | |
441 | struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter) | |
442 | { | |
443 | unsigned long r_index, h_index; | |
444 | ||
445 | if (iter->cur == NULL) | |
446 | return prio_tree_first(iter); | |
447 | ||
448 | repeat: | |
449 | while (prio_tree_left(iter, &r_index, &h_index)) | |
450 | if (overlap(iter, r_index, h_index)) | |
451 | return iter->cur; | |
452 | ||
453 | while (!prio_tree_right(iter, &r_index, &h_index)) { | |
454 | while (!prio_tree_root(iter->cur) && | |
455 | iter->cur->parent->right == iter->cur) | |
456 | prio_tree_parent(iter); | |
457 | ||
458 | if (prio_tree_root(iter->cur)) | |
459 | return NULL; | |
460 | ||
461 | prio_tree_parent(iter); | |
462 | } | |
463 | ||
464 | if (overlap(iter, r_index, h_index)) | |
465 | return iter->cur; | |
466 | ||
467 | goto repeat; | |
468 | } |