ia64/linux-2.6.18-xen.hg

annotate Documentation/prio_tree.txt @ 854:950b9eb27661

usbback: fix urb interval value for interrupt urbs.

Signed-off-by: Noboru Iwamatsu <n_iwamatsu@jp.fujitsu.com>
author Keir Fraser <keir.fraser@citrix.com>
date Mon Apr 06 13:51:20 2009 +0100 (2009-04-06)
parents 831230e53067
children
rev   line source
ian@0 1 The prio_tree.c code indexes vmas using 3 different indexes:
ian@0 2 * heap_index = vm_pgoff + vm_size_in_pages : end_vm_pgoff
ian@0 3 * radix_index = vm_pgoff : start_vm_pgoff
ian@0 4 * size_index = vm_size_in_pages
ian@0 5
ian@0 6 A regular radix-priority-search-tree indexes vmas using only heap_index and
ian@0 7 radix_index. The conditions for indexing are:
ian@0 8 * ->heap_index >= ->left->heap_index &&
ian@0 9 ->heap_index >= ->right->heap_index
ian@0 10 * if (->heap_index == ->left->heap_index)
ian@0 11 then ->radix_index < ->left->radix_index;
ian@0 12 * if (->heap_index == ->right->heap_index)
ian@0 13 then ->radix_index < ->right->radix_index;
ian@0 14 * nodes are hashed to left or right subtree using radix_index
ian@0 15 similar to a pure binary radix tree.
ian@0 16
ian@0 17 A regular radix-priority-search-tree helps to store and query
ian@0 18 intervals (vmas). However, a regular radix-priority-search-tree is only
ian@0 19 suitable for storing vmas with different radix indices (vm_pgoff).
ian@0 20
ian@0 21 Therefore, the prio_tree.c extends the regular radix-priority-search-tree
ian@0 22 to handle many vmas with the same vm_pgoff. Such vmas are handled in
ian@0 23 2 different ways: 1) All vmas with the same radix _and_ heap indices are
ian@0 24 linked using vm_set.list, 2) if there are many vmas with the same radix
ian@0 25 index, but different heap indices and if the regular radix-priority-search
ian@0 26 tree cannot index them all, we build an overflow-sub-tree that indexes such
ian@0 27 vmas using heap and size indices instead of heap and radix indices. For
ian@0 28 example, in the figure below some vmas with vm_pgoff = 0 (zero) are
ian@0 29 indexed by regular radix-priority-search-tree whereas others are pushed
ian@0 30 into an overflow-subtree. Note that all vmas in an overflow-sub-tree have
ian@0 31 the same vm_pgoff (radix_index) and if necessary we build different
ian@0 32 overflow-sub-trees to handle each possible radix_index. For example,
ian@0 33 in figure we have 3 overflow-sub-trees corresponding to radix indices
ian@0 34 0, 2, and 4.
ian@0 35
ian@0 36 In the final tree the first few (prio_tree_root->index_bits) levels
ian@0 37 are indexed using heap and radix indices whereas the overflow-sub-trees below
ian@0 38 those levels (i.e. levels prio_tree_root->index_bits + 1 and higher) are
ian@0 39 indexed using heap and size indices. In overflow-sub-trees the size_index
ian@0 40 is used for hashing the nodes to appropriate places.
ian@0 41
ian@0 42 Now, an example prio_tree:
ian@0 43
ian@0 44 vmas are represented [radix_index, size_index, heap_index]
ian@0 45 i.e., [start_vm_pgoff, vm_size_in_pages, end_vm_pgoff]
ian@0 46
ian@0 47 level prio_tree_root->index_bits = 3
ian@0 48 -----
ian@0 49 _
ian@0 50 0 [0,7,7] |
ian@0 51 / \ |
ian@0 52 ------------------ ------------ | Regular
ian@0 53 / \ | radix priority
ian@0 54 1 [1,6,7] [4,3,7] | search tree
ian@0 55 / \ / \ |
ian@0 56 ------- ----- ------ ----- | heap-and-radix
ian@0 57 / \ / \ | indexed
ian@0 58 2 [0,6,6] [2,5,7] [5,2,7] [6,1,7] |
ian@0 59 / \ / \ / \ / \ |
ian@0 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] |
ian@0 61 / / / _
ian@0 62 / / / _
ian@0 63 4 [0,4,4] [2,3,5] [4,1,5] |
ian@0 64 / / / |
ian@0 65 5 [0,3,3] [2,2,4] [4,0,4] | Overflow-sub-trees
ian@0 66 / / |
ian@0 67 6 [0,2,2] [2,1,3] | heap-and-size
ian@0 68 / / | indexed
ian@0 69 7 [0,1,1] [2,0,2] |
ian@0 70 / |
ian@0 71 8 [0,0,0] |
ian@0 72 _
ian@0 73
ian@0 74 Note that we use prio_tree_root->index_bits to optimize the height
ian@0 75 of the heap-and-radix indexed tree. Since prio_tree_root->index_bits is
ian@0 76 set according to the maximum end_vm_pgoff mapped, we are sure that all
ian@0 77 bits (in vm_pgoff) above prio_tree_root->index_bits are 0 (zero). Therefore,
ian@0 78 we only use the first prio_tree_root->index_bits as radix_index.
ian@0 79 Whenever index_bits is increased in prio_tree_expand, we shuffle the tree
ian@0 80 to make sure that the first prio_tree_root->index_bits levels of the tree
ian@0 81 is indexed properly using heap and radix indices.
ian@0 82
ian@0 83 We do not optimize the height of overflow-sub-trees using index_bits.
ian@0 84 The reason is: there can be many such overflow-sub-trees and all of
ian@0 85 them have to be suffled whenever the index_bits increases. This may involve
ian@0 86 walking the whole prio_tree in prio_tree_insert->prio_tree_expand code
ian@0 87 path which is not desirable. Hence, we do not optimize the height of the
ian@0 88 heap-and-size indexed overflow-sub-trees using prio_tree->index_bits.
ian@0 89 Instead the overflow sub-trees are indexed using full BITS_PER_LONG bits
ian@0 90 of size_index. This may lead to skewed sub-trees because most of the
ian@0 91 higher significant bits of the size_index are likely to be be 0 (zero). In
ian@0 92 the example above, all 3 overflow-sub-trees are skewed. This may marginally
ian@0 93 affect the performance. However, processes rarely map many vmas with the
ian@0 94 same start_vm_pgoff but different end_vm_pgoffs. Therefore, we normally
ian@0 95 do not require overflow-sub-trees to index all vmas.
ian@0 96
ian@0 97 From the above discussion it is clear that the maximum height of
ian@0 98 a prio_tree can be prio_tree_root->index_bits + BITS_PER_LONG.
ian@0 99 However, in most of the common cases we do not need overflow-sub-trees,
ian@0 100 so the tree height in the common cases will be prio_tree_root->index_bits.
ian@0 101
ian@0 102 It is fair to mention here that the prio_tree_root->index_bits
ian@0 103 is increased on demand, however, the index_bits is not decreased when
ian@0 104 vmas are removed from the prio_tree. That's tricky to do. Hence, it's
ian@0 105 left as a home work problem.
ian@0 106
ian@0 107