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
17 #include "../compiler/compiler.h"
18 #include "prio_tree.h"
19
20 #define ARRAY_SIZE(x) (sizeof((x)) / (sizeof((x)[0])))
21
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
get_index(const struct prio_tree_node * node,unsigned long * radix,unsigned long * heap)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
prio_tree_init(void)55 static void fio_init prio_tree_init(void)
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 */
prio_tree_maxindex(unsigned int bits)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 */
prio_tree_expand(struct prio_tree_root * root,struct prio_tree_node * node,unsigned long max_heap_index)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 */
prio_tree_replace(struct prio_tree_root * root,struct prio_tree_node * old,struct prio_tree_node * node)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 */
prio_tree_insert(struct prio_tree_root * root,struct prio_tree_node * node)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 */
prio_tree_remove(struct prio_tree_root * root,struct prio_tree_node * node)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
prio_tree_left(struct prio_tree_iter * iter,unsigned long * r_index,unsigned long * h_index)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
prio_tree_right(struct prio_tree_iter * iter,unsigned long * r_index,unsigned long * h_index)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
prio_tree_parent(struct prio_tree_iter * iter)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
overlap(struct prio_tree_iter * iter,unsigned long r_index,unsigned long h_index)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 */
prio_tree_first(struct prio_tree_iter * iter)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 */
prio_tree_next(struct prio_tree_iter * iter)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 }
469