media: ov5640: change 1080p resolution to 1088p
[linux-2.6.git] / Documentation / prio_tree.txt
1 The prio_tree.c code indexes vmas using 3 different indexes:
2         * heap_index  = vm_pgoff + vm_size_in_pages : end_vm_pgoff
3         * radix_index = vm_pgoff : start_vm_pgoff
4         * size_index = vm_size_in_pages
5
6 A regular radix-priority-search-tree indexes vmas using only heap_index and
7 radix_index. The conditions for indexing are:
8         * ->heap_index >= ->left->heap_index &&
9                 ->heap_index >= ->right->heap_index
10         * if (->heap_index == ->left->heap_index)
11                 then ->radix_index < ->left->radix_index;
12         * if (->heap_index == ->right->heap_index)
13                 then ->radix_index < ->right->radix_index;
14         * nodes are hashed to left or right subtree using radix_index
15           similar to a pure binary radix tree.
16
17 A regular radix-priority-search-tree helps to store and query
18 intervals (vmas). However, a regular radix-priority-search-tree is only
19 suitable for storing vmas with different radix indices (vm_pgoff).
20
21 Therefore, the prio_tree.c extends the regular radix-priority-search-tree
22 to handle many vmas with the same vm_pgoff. Such vmas are handled in
23 2 different ways: 1) All vmas with the same radix _and_ heap indices are
24 linked using vm_set.list, 2) if there are many vmas with the same radix
25 index, but different heap indices and if the regular radix-priority-search
26 tree cannot index them all, we build an overflow-sub-tree that indexes such
27 vmas using heap and size indices instead of heap and radix indices. For
28 example, in the figure below some vmas with vm_pgoff = 0 (zero) are
29 indexed by regular radix-priority-search-tree whereas others are pushed
30 into an overflow-subtree. Note that all vmas in an overflow-sub-tree have
31 the same vm_pgoff (radix_index) and if necessary we build different
32 overflow-sub-trees to handle each possible radix_index. For example,
33 in figure we have 3 overflow-sub-trees corresponding to radix indices
34 0, 2, and 4.
35
36 In the final tree the first few (prio_tree_root->index_bits) levels
37 are indexed using heap and radix indices whereas the overflow-sub-trees below
38 those levels (i.e. levels prio_tree_root->index_bits + 1 and higher) are
39 indexed using heap and size indices. In overflow-sub-trees the size_index
40 is used for hashing the nodes to appropriate places.
41
42 Now, an example prio_tree:
43
44   vmas are represented [radix_index, size_index, heap_index]
45                  i.e., [start_vm_pgoff, vm_size_in_pages, end_vm_pgoff]
46
47 level  prio_tree_root->index_bits = 3
48 -----
49                                                                                                 _
50   0                                                     [0,7,7]                                  |
51                                                         /     \                                  |
52                                       ------------------       ------------                      |     Regular
53                                      /                                     \                     |  radix priority
54   1                             [1,6,7]                                   [4,3,7]                |   search tree
55                                 /     \                                   /     \                |
56                          -------       -----                        ------       -----           |  heap-and-radix
57                         /                   \                      /                  \          |      indexed
58   2                 [0,6,6]                [2,5,7]              [5,2,7]             [6,1,7]      |
59                     /     \                /     \              /     \             /     \      |
60   3             [0,5,5] [1,5,6]         [2,4,6] [3,4,7]     [4,2,6] [5,1,6]     [6,0,6] [7,0,7]  |
61                    /                       /                   /                                _
62                   /                       /                   /                                 _
63   4           [0,4,4]                 [2,3,5]              [4,1,5]                               |
64                  /                       /                    /                                  |
65   5          [0,3,3]                 [2,2,4]              [4,0,4]                                |  Overflow-sub-trees
66                 /                       /                                                        |
67   6         [0,2,2]                 [2,1,3]                                                      |    heap-and-size
68                /                       /                                                         |       indexed
69   7        [0,1,1]                 [2,0,2]                                                       |
70               /                                                                                  |
71   8       [0,0,0]                                                                                |
72                                                                                                 _
73
74 Note that we use prio_tree_root->index_bits to optimize the height
75 of the heap-and-radix indexed tree. Since prio_tree_root->index_bits is
76 set according to the maximum end_vm_pgoff mapped, we are sure that all
77 bits (in vm_pgoff) above prio_tree_root->index_bits are 0 (zero). Therefore,
78 we only use the first prio_tree_root->index_bits as radix_index.
79 Whenever index_bits is increased in prio_tree_expand, we shuffle the tree
80 to make sure that the first prio_tree_root->index_bits levels of the tree
81 is indexed properly using heap and radix indices.
82
83 We do not optimize the height of overflow-sub-trees using index_bits.
84 The reason is: there can be many such overflow-sub-trees and all of
85 them have to be suffled whenever the index_bits increases. This may involve
86 walking the whole prio_tree in prio_tree_insert->prio_tree_expand code
87 path which is not desirable. Hence, we do not optimize the height of the
88 heap-and-size indexed overflow-sub-trees using prio_tree->index_bits.
89 Instead the overflow sub-trees are indexed using full BITS_PER_LONG bits
90 of size_index. This may lead to skewed sub-trees because most of the
91 higher significant bits of the size_index are likely to be 0 (zero). In
92 the example above, all 3 overflow-sub-trees are skewed. This may marginally
93 affect the performance. However, processes rarely map many vmas with the
94 same start_vm_pgoff but different end_vm_pgoffs. Therefore, we normally
95 do not require overflow-sub-trees to index all vmas.
96
97 From the above discussion it is clear that the maximum height of
98 a prio_tree can be prio_tree_root->index_bits + BITS_PER_LONG.
99 However, in most of the common cases we do not need overflow-sub-trees,
100 so the tree height in the common cases will be prio_tree_root->index_bits.
101
102 It is fair to mention here that the prio_tree_root->index_bits
103 is increased on demand, however, the index_bits is not decreased when
104 vmas are removed from the prio_tree. That's tricky to do. Hence, it's
105 left as a home work problem.
106
107