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
get_index(const struct prio_tree_root * root,const struct prio_tree_node * node,unsigned long * radix,unsigned long * heap)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
prio_tree_init(void)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 */
prio_tree_maxindex(unsigned int bits)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 */
prio_tree_expand(struct prio_tree_root * root,struct prio_tree_node * node,unsigned long max_heap_index)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 */
prio_tree_replace(struct prio_tree_root * root,struct prio_tree_node * old,struct prio_tree_node * node)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 */
prio_tree_insert(struct prio_tree_root * root,struct prio_tree_node * node)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 */
prio_tree_remove(struct prio_tree_root * root,struct prio_tree_node * node)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
prio_tree_left(struct prio_tree_iter * iter,unsigned long * r_index,unsigned long * h_index)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
prio_tree_right(struct prio_tree_iter * iter,unsigned long * r_index,unsigned long * h_index)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
prio_tree_parent(struct prio_tree_iter * iter)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
overlap(struct prio_tree_iter * iter,unsigned long r_index,unsigned long h_index)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 */
prio_tree_first(struct prio_tree_iter * iter)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 */
prio_tree_next(struct prio_tree_iter * iter)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 }
485