Merge branch 'x86-asm-for-linus' of git://git.kernel.org/pub/scm/linux/kernel/git...
[linux-2.6.git] / lib / prio_tree.c
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
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
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  */
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  */
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  */
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  */
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  */
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
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
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
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
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  */
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  */
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 }