2 * mm/prio_tree.c - priority search tree for mapping->i_mmap
4 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
6 * This file is released under the GPL v2.
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
11 * 02Feb2004 Initial version
14 #include <linux/init.h>
15 #include <linux/module.h>
17 #include <linux/prio_tree.h>
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).
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].
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.
44 * The following macros are used for implementing prio_tree for i_mmap
47 #define RADIX_INDEX(vma) ((vma)->vm_pgoff)
48 #define VMA_SIZE(vma) (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
50 #define HEAP_INDEX(vma) ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
52 #define GET_INDEX_VMA(vma, radix, heap) \
54 radix = RADIX_INDEX(vma); \
55 heap = HEAP_INDEX(vma); \
58 #define GET_INDEX(node, radix, heap) \
60 struct vm_area_struct *__tmp = \
61 prio_tree_entry(node, struct vm_area_struct, shared.prio_tree_node);\
62 GET_INDEX_VMA(__tmp, radix, heap); \
65 static unsigned long index_bits_to_maxindex
[BITS_PER_LONG
];
67 void __init
prio_tree_init(void)
71 for (i
= 0; i
< ARRAY_SIZE(index_bits_to_maxindex
) - 1; i
++)
72 index_bits_to_maxindex
[i
] = (1UL << (i
+ 1)) - 1;
73 index_bits_to_maxindex
[ARRAY_SIZE(index_bits_to_maxindex
) - 1] = ~0UL;
77 * Maximum heap_index that can be stored in a PST with index_bits bits
79 static inline unsigned long prio_tree_maxindex(unsigned int bits
)
81 return index_bits_to_maxindex
[bits
- 1];
84 static void prio_tree_remove(struct prio_tree_root
*, struct prio_tree_node
*);
87 * Extend a priority search tree so that it can store a node with heap_index
88 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
89 * However, this function is used rarely and the common case performance is
92 static struct prio_tree_node
*prio_tree_expand(struct prio_tree_root
*root
,
93 struct prio_tree_node
*node
, unsigned long max_heap_index
)
95 struct prio_tree_node
*first
= NULL
, *prev
, *last
= NULL
;
97 if (max_heap_index
> prio_tree_maxindex(root
->index_bits
))
100 while (max_heap_index
> prio_tree_maxindex(root
->index_bits
)) {
103 if (prio_tree_empty(root
))
107 first
= root
->prio_tree_node
;
108 prio_tree_remove(root
, root
->prio_tree_node
);
109 INIT_PRIO_TREE_NODE(first
);
113 last
= root
->prio_tree_node
;
114 prio_tree_remove(root
, root
->prio_tree_node
);
115 INIT_PRIO_TREE_NODE(last
);
121 INIT_PRIO_TREE_NODE(node
);
125 first
->parent
= node
;
129 if (!prio_tree_empty(root
)) {
130 last
->left
= root
->prio_tree_node
;
131 last
->left
->parent
= last
;
134 root
->prio_tree_node
= node
;
139 * Replace a prio_tree_node with a new node and return the old node
141 static struct prio_tree_node
*prio_tree_replace(struct prio_tree_root
*root
,
142 struct prio_tree_node
*old
, struct prio_tree_node
*node
)
144 INIT_PRIO_TREE_NODE(node
);
146 if (prio_tree_root(old
)) {
147 BUG_ON(root
->prio_tree_node
!= old
);
149 * We can reduce root->index_bits here. However, it is complex
150 * and does not help much to improve performance (IMO).
153 root
->prio_tree_node
= node
;
155 node
->parent
= old
->parent
;
156 if (old
->parent
->left
== old
)
157 old
->parent
->left
= node
;
159 old
->parent
->right
= node
;
162 if (!prio_tree_left_empty(old
)) {
163 node
->left
= old
->left
;
164 old
->left
->parent
= node
;
167 if (!prio_tree_right_empty(old
)) {
168 node
->right
= old
->right
;
169 old
->right
->parent
= node
;
176 * Insert a prio_tree_node @node into a radix priority search tree @root. The
177 * algorithm typically takes O(log n) time where 'log n' is the number of bits
178 * required to represent the maximum heap_index. In the worst case, the algo
179 * can take O((log n)^2) - check prio_tree_expand.
181 * If a prior node with same radix_index and heap_index is already found in
182 * the tree, then returns the address of the prior node. Otherwise, inserts
183 * @node into the tree and returns @node.
185 static struct prio_tree_node
*prio_tree_insert(struct prio_tree_root
*root
,
186 struct prio_tree_node
*node
)
188 struct prio_tree_node
*cur
, *res
= node
;
189 unsigned long radix_index
, heap_index
;
190 unsigned long r_index
, h_index
, index
, mask
;
193 GET_INDEX(node
, radix_index
, heap_index
);
195 if (prio_tree_empty(root
) ||
196 heap_index
> prio_tree_maxindex(root
->index_bits
))
197 return prio_tree_expand(root
, node
, heap_index
);
199 cur
= root
->prio_tree_node
;
200 mask
= 1UL << (root
->index_bits
- 1);
203 GET_INDEX(cur
, r_index
, h_index
);
205 if (r_index
== radix_index
&& h_index
== heap_index
)
208 if (h_index
< heap_index
||
209 (h_index
== heap_index
&& r_index
> radix_index
)) {
210 struct prio_tree_node
*tmp
= node
;
211 node
= prio_tree_replace(root
, cur
, node
);
215 r_index
= radix_index
;
218 h_index
= heap_index
;
223 index
= heap_index
- radix_index
;
228 if (prio_tree_right_empty(cur
)) {
229 INIT_PRIO_TREE_NODE(node
);
236 if (prio_tree_left_empty(cur
)) {
237 INIT_PRIO_TREE_NODE(node
);
248 mask
= 1UL << (root
->index_bits
- 1);
252 /* Should not reach here */
258 * Remove a prio_tree_node @node from a radix priority search tree @root. The
259 * algorithm takes O(log n) time where 'log n' is the number of bits required
260 * to represent the maximum heap_index.
262 static void prio_tree_remove(struct prio_tree_root
*root
,
263 struct prio_tree_node
*node
)
265 struct prio_tree_node
*cur
;
266 unsigned long r_index
, h_index_right
, h_index_left
;
270 while (!prio_tree_left_empty(cur
) || !prio_tree_right_empty(cur
)) {
271 if (!prio_tree_left_empty(cur
))
272 GET_INDEX(cur
->left
, r_index
, h_index_left
);
278 if (!prio_tree_right_empty(cur
))
279 GET_INDEX(cur
->right
, r_index
, h_index_right
);
285 /* both h_index_left and h_index_right cannot be 0 */
286 if (h_index_left
>= h_index_right
)
292 if (prio_tree_root(cur
)) {
293 BUG_ON(root
->prio_tree_node
!= cur
);
294 INIT_PRIO_TREE_ROOT(root
);
298 if (cur
->parent
->right
== cur
)
299 cur
->parent
->right
= cur
->parent
;
301 cur
->parent
->left
= cur
->parent
;
304 cur
= prio_tree_replace(root
, cur
->parent
, cur
);
308 * Following functions help to enumerate all prio_tree_nodes in the tree that
309 * overlap with the input interval X [radix_index, heap_index]. The enumeration
310 * takes O(log n + m) time where 'log n' is the height of the tree (which is
311 * proportional to # of bits required to represent the maximum heap_index) and
312 * 'm' is the number of prio_tree_nodes that overlap the interval X.
315 static struct prio_tree_node
*prio_tree_left(struct prio_tree_iter
*iter
,
316 unsigned long *r_index
, unsigned long *h_index
)
318 if (prio_tree_left_empty(iter
->cur
))
321 GET_INDEX(iter
->cur
->left
, *r_index
, *h_index
);
323 if (iter
->r_index
<= *h_index
) {
324 iter
->cur
= iter
->cur
->left
;
327 if (iter
->size_level
)
330 if (iter
->size_level
) {
331 BUG_ON(!prio_tree_left_empty(iter
->cur
));
332 BUG_ON(!prio_tree_right_empty(iter
->cur
));
334 iter
->mask
= ULONG_MAX
;
336 iter
->size_level
= 1;
337 iter
->mask
= 1UL << (iter
->root
->index_bits
- 1);
346 static struct prio_tree_node
*prio_tree_right(struct prio_tree_iter
*iter
,
347 unsigned long *r_index
, unsigned long *h_index
)
351 if (prio_tree_right_empty(iter
->cur
))
354 if (iter
->size_level
)
357 value
= iter
->value
| iter
->mask
;
359 if (iter
->h_index
< value
)
362 GET_INDEX(iter
->cur
->right
, *r_index
, *h_index
);
364 if (iter
->r_index
<= *h_index
) {
365 iter
->cur
= iter
->cur
->right
;
369 if (iter
->size_level
)
372 if (iter
->size_level
) {
373 BUG_ON(!prio_tree_left_empty(iter
->cur
));
374 BUG_ON(!prio_tree_right_empty(iter
->cur
));
376 iter
->mask
= ULONG_MAX
;
378 iter
->size_level
= 1;
379 iter
->mask
= 1UL << (iter
->root
->index_bits
- 1);
388 static struct prio_tree_node
*prio_tree_parent(struct prio_tree_iter
*iter
)
390 iter
->cur
= iter
->cur
->parent
;
391 if (iter
->mask
== ULONG_MAX
)
393 else if (iter
->size_level
== 1)
397 if (iter
->size_level
)
399 if (!iter
->size_level
&& (iter
->value
& iter
->mask
))
400 iter
->value
^= iter
->mask
;
404 static inline int overlap(struct prio_tree_iter
*iter
,
405 unsigned long r_index
, unsigned long h_index
)
407 return iter
->h_index
>= r_index
&& iter
->r_index
<= h_index
;
413 * Get the first prio_tree_node that overlaps with the interval [radix_index,
414 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
415 * traversal of the tree.
417 static struct prio_tree_node
*prio_tree_first(struct prio_tree_iter
*iter
)
419 struct prio_tree_root
*root
;
420 unsigned long r_index
, h_index
;
422 INIT_PRIO_TREE_ITER(iter
);
425 if (prio_tree_empty(root
))
428 GET_INDEX(root
->prio_tree_node
, r_index
, h_index
);
430 if (iter
->r_index
> h_index
)
433 iter
->mask
= 1UL << (root
->index_bits
- 1);
434 iter
->cur
= root
->prio_tree_node
;
437 if (overlap(iter
, r_index
, h_index
))
440 if (prio_tree_left(iter
, &r_index
, &h_index
))
443 if (prio_tree_right(iter
, &r_index
, &h_index
))
454 * Get the next prio_tree_node that overlaps with the input interval in iter
456 static struct prio_tree_node
*prio_tree_next(struct prio_tree_iter
*iter
)
458 unsigned long r_index
, h_index
;
461 while (prio_tree_left(iter
, &r_index
, &h_index
))
462 if (overlap(iter
, r_index
, h_index
))
465 while (!prio_tree_right(iter
, &r_index
, &h_index
)) {
466 while (!prio_tree_root(iter
->cur
) &&
467 iter
->cur
->parent
->right
== iter
->cur
)
468 prio_tree_parent(iter
);
470 if (prio_tree_root(iter
->cur
))
473 prio_tree_parent(iter
);
476 if (overlap(iter
, r_index
, h_index
))
483 * Radix priority search tree for address_space->i_mmap
485 * For each vma that map a unique set of file pages i.e., unique [radix_index,
486 * heap_index] value, we have a corresponing priority search tree node. If
487 * multiple vmas have identical [radix_index, heap_index] value, then one of
488 * them is used as a tree node and others are stored in a vm_set list. The tree
489 * node points to the first vma (head) of the list using vm_set.head.
495 * L R -> H-I-J-K-M-N-O-P-Q-S
496 * ^ ^ <-- vm_set.list -->
499 * We need some way to identify whether a vma is a tree node, head of a vm_set
500 * list, or just a member of a vm_set list. We cannot use vm_flags to store
501 * such information. The reason is, in the above figure, it is possible that
502 * vm_flags' of R and H are covered by the different mmap_sems. When R is
503 * removed under R->mmap_sem, H replaces R as a tree node. Since we do not hold
504 * H->mmap_sem, we cannot use H->vm_flags for marking that H is a tree node now.
505 * That's why some trick involving shared.vm_set.parent is used for identifying
506 * tree nodes and list head nodes.
508 * vma radix priority search tree node rules:
510 * vma->shared.vm_set.parent != NULL ==> a tree node
511 * vma->shared.vm_set.head != NULL ==> list of others mapping same range
512 * vma->shared.vm_set.head == NULL ==> no others map the same range
514 * vma->shared.vm_set.parent == NULL
515 * vma->shared.vm_set.head != NULL ==> list head of vmas mapping same range
516 * vma->shared.vm_set.head == NULL ==> a list node
520 * Add a new vma known to map the same set of pages as the old vma:
521 * useful for fork's dup_mmap as well as vma_prio_tree_insert below.
522 * Note that it just happens to work correctly on i_mmap_nonlinear too.
524 void vma_prio_tree_add(struct vm_area_struct
*vma
, struct vm_area_struct
*old
)
526 /* Leave these BUG_ONs till prio_tree patch stabilizes */
527 BUG_ON(RADIX_INDEX(vma
) != RADIX_INDEX(old
));
528 BUG_ON(HEAP_INDEX(vma
) != HEAP_INDEX(old
));
530 vma
->shared
.vm_set
.head
= NULL
;
531 vma
->shared
.vm_set
.parent
= NULL
;
533 if (!old
->shared
.vm_set
.parent
)
534 list_add(&vma
->shared
.vm_set
.list
,
535 &old
->shared
.vm_set
.list
);
536 else if (old
->shared
.vm_set
.head
)
537 list_add_tail(&vma
->shared
.vm_set
.list
,
538 &old
->shared
.vm_set
.head
->shared
.vm_set
.list
);
540 INIT_LIST_HEAD(&vma
->shared
.vm_set
.list
);
541 vma
->shared
.vm_set
.head
= old
;
542 old
->shared
.vm_set
.head
= vma
;
546 void vma_prio_tree_insert(struct vm_area_struct
*vma
,
547 struct prio_tree_root
*root
)
549 struct prio_tree_node
*ptr
;
550 struct vm_area_struct
*old
;
552 vma
->shared
.vm_set
.head
= NULL
;
554 ptr
= prio_tree_insert(root
, &vma
->shared
.prio_tree_node
);
555 if (ptr
!= &vma
->shared
.prio_tree_node
) {
556 old
= prio_tree_entry(ptr
, struct vm_area_struct
,
557 shared
.prio_tree_node
);
558 vma_prio_tree_add(vma
, old
);
562 void vma_prio_tree_remove(struct vm_area_struct
*vma
,
563 struct prio_tree_root
*root
)
565 struct vm_area_struct
*node
, *head
, *new_head
;
567 if (!vma
->shared
.vm_set
.head
) {
568 if (!vma
->shared
.vm_set
.parent
)
569 list_del_init(&vma
->shared
.vm_set
.list
);
571 prio_tree_remove(root
, &vma
->shared
.prio_tree_node
);
573 /* Leave this BUG_ON till prio_tree patch stabilizes */
574 BUG_ON(vma
->shared
.vm_set
.head
->shared
.vm_set
.head
!= vma
);
575 if (vma
->shared
.vm_set
.parent
) {
576 head
= vma
->shared
.vm_set
.head
;
577 if (!list_empty(&head
->shared
.vm_set
.list
)) {
578 new_head
= list_entry(
579 head
->shared
.vm_set
.list
.next
,
580 struct vm_area_struct
,
582 list_del_init(&head
->shared
.vm_set
.list
);
586 prio_tree_replace(root
, &vma
->shared
.prio_tree_node
,
587 &head
->shared
.prio_tree_node
);
588 head
->shared
.vm_set
.head
= new_head
;
590 new_head
->shared
.vm_set
.head
= head
;
593 node
= vma
->shared
.vm_set
.head
;
594 if (!list_empty(&vma
->shared
.vm_set
.list
)) {
595 new_head
= list_entry(
596 vma
->shared
.vm_set
.list
.next
,
597 struct vm_area_struct
,
599 list_del_init(&vma
->shared
.vm_set
.list
);
600 node
->shared
.vm_set
.head
= new_head
;
601 new_head
->shared
.vm_set
.head
= node
;
603 node
->shared
.vm_set
.head
= NULL
;
609 * Helper function to enumerate vmas that map a given file page or a set of
610 * contiguous file pages. The function returns vmas that at least map a single
611 * page in the given range of contiguous file pages.
613 struct vm_area_struct
*vma_prio_tree_next(struct vm_area_struct
*vma
,
614 struct prio_tree_iter
*iter
)
616 struct prio_tree_node
*ptr
;
617 struct vm_area_struct
*next
;
621 * First call is with NULL vma
623 ptr
= prio_tree_first(iter
);
625 next
= prio_tree_entry(ptr
, struct vm_area_struct
,
626 shared
.prio_tree_node
);
627 prefetch(next
->shared
.vm_set
.head
);
633 if (vma
->shared
.vm_set
.parent
) {
634 if (vma
->shared
.vm_set
.head
) {
635 next
= vma
->shared
.vm_set
.head
;
636 prefetch(next
->shared
.vm_set
.list
.next
);
640 next
= list_entry(vma
->shared
.vm_set
.list
.next
,
641 struct vm_area_struct
, shared
.vm_set
.list
);
642 if (!next
->shared
.vm_set
.head
) {
643 prefetch(next
->shared
.vm_set
.list
.next
);
648 ptr
= prio_tree_next(iter
);
650 next
= prio_tree_entry(ptr
, struct vm_area_struct
,
651 shared
.prio_tree_node
);
652 prefetch(next
->shared
.vm_set
.head
);