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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 | ||
3d2d14bc | 14 | #include <assert.h> |
b65c7ec4 JA |
15 | #include <stdlib.h> |
16 | #include <limits.h> | |
1f6ab977 TK |
17 | |
18 | #include "../compiler/compiler.h" | |
b65c7ec4 JA |
19 | #include "prio_tree.h" |
20 | ||
21 | /* | |
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). | |
31 | * | |
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]. | |
38 | * | |
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. | |
43 | */ | |
44 | ||
45 | static void get_index(const struct prio_tree_node *node, | |
46 | unsigned long *radix, unsigned long *heap) | |
47 | { | |
48 | *radix = node->start; | |
49 | *heap = node->last; | |
50 | } | |
51 | ||
52 | static unsigned long index_bits_to_maxindex[BITS_PER_LONG]; | |
53 | ||
10aa136b | 54 | static void fio_init prio_tree_init(void) |
b65c7ec4 JA |
55 | { |
56 | unsigned int i; | |
57 | ||
59f94d26 | 58 | for (i = 0; i < FIO_ARRAY_SIZE(index_bits_to_maxindex) - 1; i++) |
b65c7ec4 | 59 | index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1; |
59f94d26 | 60 | index_bits_to_maxindex[FIO_ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL; |
b65c7ec4 JA |
61 | } |
62 | ||
63 | /* | |
64 | * Maximum heap_index that can be stored in a PST with index_bits bits | |
65 | */ | |
66 | static inline unsigned long prio_tree_maxindex(unsigned int bits) | |
67 | { | |
68 | return index_bits_to_maxindex[bits - 1]; | |
69 | } | |
70 | ||
71 | /* | |
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 | |
75 | * not bad. | |
76 | */ | |
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) | |
79 | { | |
80 | struct prio_tree_node *first = NULL, *prev, *last = NULL; | |
81 | ||
82 | if (max_heap_index > prio_tree_maxindex(root->index_bits)) | |
83 | root->index_bits++; | |
84 | ||
85 | while (max_heap_index > prio_tree_maxindex(root->index_bits)) { | |
86 | root->index_bits++; | |
87 | ||
88 | if (prio_tree_empty(root)) | |
89 | continue; | |
90 | ||
91 | if (first == NULL) { | |
92 | first = root->prio_tree_node; | |
93 | prio_tree_remove(root, root->prio_tree_node); | |
94 | INIT_PRIO_TREE_NODE(first); | |
95 | last = first; | |
96 | } else { | |
97 | prev = last; | |
98 | last = root->prio_tree_node; | |
99 | prio_tree_remove(root, root->prio_tree_node); | |
100 | INIT_PRIO_TREE_NODE(last); | |
101 | prev->left = last; | |
102 | last->parent = prev; | |
103 | } | |
104 | } | |
105 | ||
106 | INIT_PRIO_TREE_NODE(node); | |
107 | ||
108 | if (first) { | |
109 | node->left = first; | |
110 | first->parent = node; | |
111 | } else | |
112 | last = node; | |
113 | ||
114 | if (!prio_tree_empty(root)) { | |
115 | last->left = root->prio_tree_node; | |
116 | last->left->parent = last; | |
117 | } | |
118 | ||
119 | root->prio_tree_node = node; | |
120 | return node; | |
121 | } | |
122 | ||
123 | /* | |
124 | * Replace a prio_tree_node with a new node and return the old node | |
125 | */ | |
126 | struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root, | |
127 | struct prio_tree_node *old, struct prio_tree_node *node) | |
128 | { | |
129 | INIT_PRIO_TREE_NODE(node); | |
130 | ||
131 | if (prio_tree_root(old)) { | |
132 | assert(root->prio_tree_node == old); | |
133 | /* | |
134 | * We can reduce root->index_bits here. However, it is complex | |
135 | * and does not help much to improve performance (IMO). | |
136 | */ | |
137 | node->parent = node; | |
138 | root->prio_tree_node = node; | |
139 | } else { | |
140 | node->parent = old->parent; | |
141 | if (old->parent->left == old) | |
142 | old->parent->left = node; | |
143 | else | |
144 | old->parent->right = node; | |
145 | } | |
146 | ||
147 | if (!prio_tree_left_empty(old)) { | |
148 | node->left = old->left; | |
149 | old->left->parent = node; | |
150 | } | |
151 | ||
152 | if (!prio_tree_right_empty(old)) { | |
153 | node->right = old->right; | |
154 | old->right->parent = node; | |
155 | } | |
156 | ||
157 | return old; | |
158 | } | |
159 | ||
160 | /* | |
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. | |
165 | * | |
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. | |
169 | */ | |
170 | struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root, | |
171 | struct prio_tree_node *node) | |
172 | { | |
173 | struct prio_tree_node *cur, *res = node; | |
174 | unsigned long radix_index, heap_index; | |
175 | unsigned long r_index, h_index, index, mask; | |
176 | int size_flag = 0; | |
177 | ||
178 | get_index(node, &radix_index, &heap_index); | |
179 | ||
180 | if (prio_tree_empty(root) || | |
181 | heap_index > prio_tree_maxindex(root->index_bits)) | |
182 | return prio_tree_expand(root, node, heap_index); | |
183 | ||
184 | cur = root->prio_tree_node; | |
185 | mask = 1UL << (root->index_bits - 1); | |
186 | ||
187 | while (mask) { | |
188 | get_index(cur, &r_index, &h_index); | |
189 | ||
190 | if (r_index == radix_index && h_index == heap_index) | |
191 | return cur; | |
192 | ||
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); | |
197 | cur = tmp; | |
198 | /* swap indices */ | |
199 | index = r_index; | |
200 | r_index = radix_index; | |
201 | radix_index = index; | |
202 | index = h_index; | |
203 | h_index = heap_index; | |
204 | heap_index = index; | |
205 | } | |
206 | ||
207 | if (size_flag) | |
208 | index = heap_index - radix_index; | |
209 | else | |
210 | index = radix_index; | |
211 | ||
212 | if (index & mask) { | |
213 | if (prio_tree_right_empty(cur)) { | |
214 | INIT_PRIO_TREE_NODE(node); | |
215 | cur->right = node; | |
216 | node->parent = cur; | |
217 | return res; | |
218 | } else | |
219 | cur = cur->right; | |
220 | } else { | |
221 | if (prio_tree_left_empty(cur)) { | |
222 | INIT_PRIO_TREE_NODE(node); | |
223 | cur->left = node; | |
224 | node->parent = cur; | |
225 | return res; | |
226 | } else | |
227 | cur = cur->left; | |
228 | } | |
229 | ||
230 | mask >>= 1; | |
231 | ||
232 | if (!mask) { | |
233 | mask = 1UL << (BITS_PER_LONG - 1); | |
234 | size_flag = 1; | |
235 | } | |
236 | } | |
237 | /* Should not reach here */ | |
238 | assert(0); | |
239 | return NULL; | |
240 | } | |
241 | ||
242 | /* | |
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. | |
246 | */ | |
247 | void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node) | |
248 | { | |
249 | struct prio_tree_node *cur; | |
250 | unsigned long r_index, h_index_right, h_index_left; | |
251 | ||
252 | cur = node; | |
253 | ||
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); | |
257 | else { | |
258 | cur = cur->right; | |
259 | continue; | |
260 | } | |
261 | ||
262 | if (!prio_tree_right_empty(cur)) | |
263 | get_index(cur->right, &r_index, &h_index_right); | |
264 | else { | |
265 | cur = cur->left; | |
266 | continue; | |
267 | } | |
268 | ||
269 | /* both h_index_left and h_index_right cannot be 0 */ | |
270 | if (h_index_left >= h_index_right) | |
271 | cur = cur->left; | |
272 | else | |
273 | cur = cur->right; | |
274 | } | |
275 | ||
276 | if (prio_tree_root(cur)) { | |
277 | assert(root->prio_tree_node == cur); | |
278 | INIT_PRIO_TREE_ROOT(root); | |
279 | return; | |
280 | } | |
281 | ||
282 | if (cur->parent->right == cur) | |
283 | cur->parent->right = cur->parent; | |
284 | else | |
285 | cur->parent->left = cur->parent; | |
286 | ||
287 | while (cur != node) | |
288 | cur = prio_tree_replace(root, cur->parent, cur); | |
289 | } | |
290 | ||
291 | /* | |
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. | |
297 | */ | |
298 | ||
299 | static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter, | |
300 | unsigned long *r_index, unsigned long *h_index) | |
301 | { | |
302 | if (prio_tree_left_empty(iter->cur)) | |
303 | return NULL; | |
304 | ||
305 | get_index(iter->cur->left, r_index, h_index); | |
306 | ||
307 | if (iter->r_index <= *h_index) { | |
308 | iter->cur = iter->cur->left; | |
309 | iter->mask >>= 1; | |
310 | if (iter->mask) { | |
311 | if (iter->size_level) | |
312 | iter->size_level++; | |
313 | } else { | |
314 | if (iter->size_level) { | |
315 | assert(prio_tree_left_empty(iter->cur)); | |
316 | assert(prio_tree_right_empty(iter->cur)); | |
317 | iter->size_level++; | |
318 | iter->mask = ULONG_MAX; | |
319 | } else { | |
320 | iter->size_level = 1; | |
321 | iter->mask = 1UL << (BITS_PER_LONG - 1); | |
322 | } | |
323 | } | |
324 | return iter->cur; | |
325 | } | |
326 | ||
327 | return NULL; | |
328 | } | |
329 | ||
330 | static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter, | |
331 | unsigned long *r_index, unsigned long *h_index) | |
332 | { | |
333 | unsigned long value; | |
334 | ||
335 | if (prio_tree_right_empty(iter->cur)) | |
336 | return NULL; | |
337 | ||
338 | if (iter->size_level) | |
339 | value = iter->value; | |
340 | else | |
341 | value = iter->value | iter->mask; | |
342 | ||
343 | if (iter->h_index < value) | |
344 | return NULL; | |
345 | ||
346 | get_index(iter->cur->right, r_index, h_index); | |
347 | ||
348 | if (iter->r_index <= *h_index) { | |
349 | iter->cur = iter->cur->right; | |
350 | iter->mask >>= 1; | |
351 | iter->value = value; | |
352 | if (iter->mask) { | |
353 | if (iter->size_level) | |
354 | iter->size_level++; | |
355 | } else { | |
356 | if (iter->size_level) { | |
357 | assert(prio_tree_left_empty(iter->cur)); | |
358 | assert(prio_tree_right_empty(iter->cur)); | |
359 | iter->size_level++; | |
360 | iter->mask = ULONG_MAX; | |
361 | } else { | |
362 | iter->size_level = 1; | |
363 | iter->mask = 1UL << (BITS_PER_LONG - 1); | |
364 | } | |
365 | } | |
366 | return iter->cur; | |
367 | } | |
368 | ||
369 | return NULL; | |
370 | } | |
371 | ||
372 | static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter) | |
373 | { | |
374 | iter->cur = iter->cur->parent; | |
375 | if (iter->mask == ULONG_MAX) | |
376 | iter->mask = 1UL; | |
377 | else if (iter->size_level == 1) | |
378 | iter->mask = 1UL; | |
379 | else | |
380 | iter->mask <<= 1; | |
381 | if (iter->size_level) | |
382 | iter->size_level--; | |
383 | if (!iter->size_level && (iter->value & iter->mask)) | |
384 | iter->value ^= iter->mask; | |
385 | return iter->cur; | |
386 | } | |
387 | ||
388 | static inline int overlap(struct prio_tree_iter *iter, | |
389 | unsigned long r_index, unsigned long h_index) | |
390 | { | |
391 | return iter->h_index >= r_index && iter->r_index <= h_index; | |
392 | } | |
393 | ||
394 | /* | |
395 | * prio_tree_first: | |
396 | * | |
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. | |
400 | */ | |
401 | static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter) | |
402 | { | |
403 | struct prio_tree_root *root; | |
404 | unsigned long r_index, h_index; | |
405 | ||
406 | INIT_PRIO_TREE_ITER(iter); | |
407 | ||
408 | root = iter->root; | |
409 | if (prio_tree_empty(root)) | |
410 | return NULL; | |
411 | ||
412 | get_index(root->prio_tree_node, &r_index, &h_index); | |
413 | ||
414 | if (iter->r_index > h_index) | |
415 | return NULL; | |
416 | ||
417 | iter->mask = 1UL << (root->index_bits - 1); | |
418 | iter->cur = root->prio_tree_node; | |
419 | ||
420 | while (1) { | |
421 | if (overlap(iter, r_index, h_index)) | |
422 | return iter->cur; | |
423 | ||
424 | if (prio_tree_left(iter, &r_index, &h_index)) | |
425 | continue; | |
426 | ||
427 | if (prio_tree_right(iter, &r_index, &h_index)) | |
428 | continue; | |
429 | ||
430 | break; | |
431 | } | |
432 | return NULL; | |
433 | } | |
434 | ||
435 | /* | |
436 | * prio_tree_next: | |
437 | * | |
438 | * Get the next prio_tree_node that overlaps with the input interval in iter | |
439 | */ | |
440 | struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter) | |
441 | { | |
442 | unsigned long r_index, h_index; | |
443 | ||
444 | if (iter->cur == NULL) | |
445 | return prio_tree_first(iter); | |
446 | ||
447 | repeat: | |
448 | while (prio_tree_left(iter, &r_index, &h_index)) | |
449 | if (overlap(iter, r_index, h_index)) | |
450 | return iter->cur; | |
451 | ||
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); | |
456 | ||
457 | if (prio_tree_root(iter->cur)) | |
458 | return NULL; | |
459 | ||
460 | prio_tree_parent(iter); | |
461 | } | |
462 | ||
463 | if (overlap(iter, r_index, h_index)) | |
464 | return iter->cur; | |
465 | ||
466 | goto repeat; | |
467 | } |