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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
52static 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
69static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
70
71void __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 */
83static inline unsigned long prio_tree_maxindex(unsigned int bits)
84{
85 return index_bits_to_maxindex[bits - 1];
86}
87
88static void prio_set_parent(struct prio_tree_node *parent,
89 struct prio_tree_node *child, bool left)
90{
91 if (left)
92 parent->left = child;
93 else
94 parent->right = child;
95
96 child->parent = parent;
97}
98
99/*
100 * Extend a priority search tree so that it can store a node with heap_index
101 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
102 * However, this function is used rarely and the common case performance is
103 * not bad.
104 */
105static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
106 struct prio_tree_node *node, unsigned long max_heap_index)
107{
108 struct prio_tree_node *prev;
109
110 if (max_heap_index > prio_tree_maxindex(root->index_bits))
111 root->index_bits++;
112
113 prev = node;
114 INIT_PRIO_TREE_NODE(node);
115
116 while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
117 struct prio_tree_node *tmp = root->prio_tree_node;
118
119 root->index_bits++;
120
121 if (prio_tree_empty(root))
122 continue;
123
124 prio_tree_remove(root, root->prio_tree_node);
125 INIT_PRIO_TREE_NODE(tmp);
126
127 prio_set_parent(prev, tmp, true);
128 prev = tmp;
129 }
130
131 if (!prio_tree_empty(root))
132 prio_set_parent(prev, root->prio_tree_node, true);
133
134 root->prio_tree_node = node;
135 return node;
136}
137
138/*
139 * Replace a prio_tree_node with a new node and return the old node
140 */
141struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
142 struct prio_tree_node *old, struct prio_tree_node *node)
143{
144 INIT_PRIO_TREE_NODE(node);
145
146 if (prio_tree_root(old)) {
147 BUG_ON(root->prio_tree_node != old);
148 /*
149 * We can reduce root->index_bits here. However, it is complex
150 * and does not help much to improve performance (IMO).
151 */
152 root->prio_tree_node = node;
153 } else
154 prio_set_parent(old->parent, node, old->parent->left == old);
155
156 if (!prio_tree_left_empty(old))
157 prio_set_parent(node, old->left, true);
158
159 if (!prio_tree_right_empty(old))
160 prio_set_parent(node, old->right, false);
161
162 return old;
163}
164
165/*
166 * Insert a prio_tree_node @node into a radix priority search tree @root. The
167 * algorithm typically takes O(log n) time where 'log n' is the number of bits
168 * required to represent the maximum heap_index. In the worst case, the algo
169 * can take O((log n)^2) - check prio_tree_expand.
170 *
171 * If a prior node with same radix_index and heap_index is already found in
172 * the tree, then returns the address of the prior node. Otherwise, inserts
173 * @node into the tree and returns @node.
174 */
175struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
176 struct prio_tree_node *node)
177{
178 struct prio_tree_node *cur, *res = node;
179 unsigned long radix_index, heap_index;
180 unsigned long r_index, h_index, index, mask;
181 int size_flag = 0;
182
183 get_index(root, node, &radix_index, &heap_index);
184
185 if (prio_tree_empty(root) ||
186 heap_index > prio_tree_maxindex(root->index_bits))
187 return prio_tree_expand(root, node, heap_index);
188
189 cur = root->prio_tree_node;
190 mask = 1UL << (root->index_bits - 1);
191
192 while (mask) {
193 get_index(root, cur, &r_index, &h_index);
194
195 if (r_index == radix_index && h_index == heap_index)
196 return cur;
197
198 if (h_index < heap_index ||
199 (h_index == heap_index && r_index > radix_index)) {
200 struct prio_tree_node *tmp = node;
201 node = prio_tree_replace(root, cur, node);
202 cur = tmp;
203 /* swap indices */
204 index = r_index;
205 r_index = radix_index;
206 radix_index = index;
207 index = h_index;
208 h_index = heap_index;
209 heap_index = index;
210 }
211
212 if (size_flag)
213 index = heap_index - radix_index;
214 else
215 index = radix_index;
216
217 if (index & mask) {
218 if (prio_tree_right_empty(cur)) {
219 INIT_PRIO_TREE_NODE(node);
220 prio_set_parent(cur, node, false);
221 return res;
222 } else
223 cur = cur->right;
224 } else {
225 if (prio_tree_left_empty(cur)) {
226 INIT_PRIO_TREE_NODE(node);
227 prio_set_parent(cur, node, true);
228 return res;
229 } else
230 cur = cur->left;
231 }
232
233 mask >>= 1;
234
235 if (!mask) {
236 mask = 1UL << (BITS_PER_LONG - 1);
237 size_flag = 1;
238 }
239 }
240 /* Should not reach here */
241 BUG();
242 return NULL;
243}
244
245/*
246 * Remove a prio_tree_node @node from a radix priority search tree @root. The
247 * algorithm takes O(log n) time where 'log n' is the number of bits required
248 * to represent the maximum heap_index.
249 */
250void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
251{
252 struct prio_tree_node *cur;
253 unsigned long r_index, h_index_right, h_index_left;
254
255 cur = node;
256
257 while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
258 if (!prio_tree_left_empty(cur))
259 get_index(root, cur->left, &r_index, &h_index_left);
260 else {
261 cur = cur->right;
262 continue;
263 }
264
265 if (!prio_tree_right_empty(cur))
266 get_index(root, cur->right, &r_index, &h_index_right);
267 else {
268 cur = cur->left;
269 continue;
270 }
271
272 /* both h_index_left and h_index_right cannot be 0 */
273 if (h_index_left >= h_index_right)
274 cur = cur->left;
275 else
276 cur = cur->right;
277 }
278
279 if (prio_tree_root(cur)) {
280 BUG_ON(root->prio_tree_node != cur);
281 __INIT_PRIO_TREE_ROOT(root, root->raw);
282 return;
283 }
284
285 if (cur->parent->right == cur)
286 cur->parent->right = cur->parent;
287 else
288 cur->parent->left = cur->parent;
289
290 while (cur != node)
291 cur = prio_tree_replace(root, cur->parent, cur);
292}
293
294static void iter_walk_down(struct prio_tree_iter *iter)
295{
296 iter->mask >>= 1;
297 if (iter->mask) {
298 if (iter->size_level)
299 iter->size_level++;
300 return;
301 }
302
303 if (iter->size_level) {
304 BUG_ON(!prio_tree_left_empty(iter->cur));
305 BUG_ON(!prio_tree_right_empty(iter->cur));
306 iter->size_level++;
307 iter->mask = ULONG_MAX;
308 } else {
309 iter->size_level = 1;
310 iter->mask = 1UL << (BITS_PER_LONG - 1);
311 }
312}
313
314static void iter_walk_up(struct prio_tree_iter *iter)
315{
316 if (iter->mask == ULONG_MAX)
317 iter->mask = 1UL;
318 else if (iter->size_level == 1)
319 iter->mask = 1UL;
320 else
321 iter->mask <<= 1;
322 if (iter->size_level)
323 iter->size_level--;
324 if (!iter->size_level && (iter->value & iter->mask))
325 iter->value ^= iter->mask;
326}
327
328/*
329 * Following functions help to enumerate all prio_tree_nodes in the tree that
330 * overlap with the input interval X [radix_index, heap_index]. The enumeration
331 * takes O(log n + m) time where 'log n' is the height of the tree (which is
332 * proportional to # of bits required to represent the maximum heap_index) and
333 * 'm' is the number of prio_tree_nodes that overlap the interval X.
334 */
335
336static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
337 unsigned long *r_index, unsigned long *h_index)
338{
339 if (prio_tree_left_empty(iter->cur))
340 return NULL;
341
342 get_index(iter->root, iter->cur->left, r_index, h_index);
343
344 if (iter->r_index <= *h_index) {
345 iter->cur = iter->cur->left;
346 iter_walk_down(iter);
347 return iter->cur;
348 }
349
350 return NULL;
351}
352
353static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
354 unsigned long *r_index, unsigned long *h_index)
355{
356 unsigned long value;
357
358 if (prio_tree_right_empty(iter->cur))
359 return NULL;
360
361 if (iter->size_level)
362 value = iter->value;
363 else
364 value = iter->value | iter->mask;
365
366 if (iter->h_index < value)
367 return NULL;
368
369 get_index(iter->root, iter->cur->right, r_index, h_index);
370
371 if (iter->r_index <= *h_index) {
372 iter->cur = iter->cur->right;
373 iter_walk_down(iter);
374 return iter->cur;
375 }
376
377 return NULL;
378}
379
380static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
381{
382 iter->cur = iter->cur->parent;
383 iter_walk_up(iter);
384 return iter->cur;
385}
386
387static inline int overlap(struct prio_tree_iter *iter,
388 unsigned long r_index, unsigned long h_index)
389{
390 return iter->h_index >= r_index && iter->r_index <= h_index;
391}
392
393/*
394 * prio_tree_first:
395 *
396 * Get the first prio_tree_node that overlaps with the interval [radix_index,
397 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
398 * traversal of the tree.
399 */
400static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
401{
402 struct prio_tree_root *root;
403 unsigned long r_index, h_index;
404
405 INIT_PRIO_TREE_ITER(iter);
406
407 root = iter->root;
408 if (prio_tree_empty(root))
409 return NULL;
410
411 get_index(root, root->prio_tree_node, &r_index, &h_index);
412
413 if (iter->r_index > h_index)
414 return NULL;
415
416 iter->mask = 1UL << (root->index_bits - 1);
417 iter->cur = root->prio_tree_node;
418
419 while (1) {
420 if (overlap(iter, r_index, h_index))
421 return iter->cur;
422
423 if (prio_tree_left(iter, &r_index, &h_index))
424 continue;
425
426 if (prio_tree_right(iter, &r_index, &h_index))
427 continue;
428
429 break;
430 }
431 return NULL;
432}
433
434/*
435 * prio_tree_next:
436 *
437 * Get the next prio_tree_node that overlaps with the input interval in iter
438 */
439struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
440{
441 unsigned long r_index, h_index;
442
443 if (iter->cur == NULL)
444 return prio_tree_first(iter);
445
446repeat:
447 while (prio_tree_left(iter, &r_index, &h_index))
448 if (overlap(iter, r_index, h_index))
449 return iter->cur;
450
451 while (!prio_tree_right(iter, &r_index, &h_index)) {
452 while (!prio_tree_root(iter->cur) &&
453 iter->cur->parent->right == iter->cur)
454 prio_tree_parent(iter);
455
456 if (prio_tree_root(iter->cur))
457 return NULL;
458
459 prio_tree_parent(iter);
460 }
461
462 if (overlap(iter, r_index, h_index))
463 return iter->cur;
464
465 goto repeat;
466}
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