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