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Diffstat (limited to 'Documentation/prio_tree.txt')

-rw-r--r-- | Documentation/prio_tree.txt | 107 |

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diff --git a/Documentation/prio_tree.txt b/Documentation/prio_tree.txt deleted file mode 100644 index 3aa68f9..0000000 --- a/Documentation/prio_tree.txt +++ /dev/null @@ -1,107 +0,0 @@ -The prio_tree.c code indexes vmas using 3 different indexes: - * heap_index = vm_pgoff + vm_size_in_pages : end_vm_pgoff - * radix_index = vm_pgoff : start_vm_pgoff - * size_index = vm_size_in_pages - -A regular radix-priority-search-tree indexes vmas using only heap_index and -radix_index. The conditions for indexing are: - * ->heap_index >= ->left->heap_index && - ->heap_index >= ->right->heap_index - * if (->heap_index == ->left->heap_index) - then ->radix_index < ->left->radix_index; - * if (->heap_index == ->right->heap_index) - then ->radix_index < ->right->radix_index; - * nodes are hashed to left or right subtree using radix_index - similar to a pure binary radix tree. - -A regular radix-priority-search-tree helps to store and query -intervals (vmas). However, a regular radix-priority-search-tree is only -suitable for storing vmas with different radix indices (vm_pgoff). - -Therefore, the prio_tree.c extends the regular radix-priority-search-tree -to handle many vmas with the same vm_pgoff. Such vmas are handled in -2 different ways: 1) All vmas with the same radix _and_ heap indices are -linked using vm_set.list, 2) if there are many vmas with the same radix -index, but different heap indices and if the regular radix-priority-search -tree cannot index them all, we build an overflow-sub-tree that indexes such -vmas using heap and size indices instead of heap and radix indices. For -example, in the figure below some vmas with vm_pgoff = 0 (zero) are -indexed by regular radix-priority-search-tree whereas others are pushed -into an overflow-subtree. Note that all vmas in an overflow-sub-tree have -the same vm_pgoff (radix_index) and if necessary we build different -overflow-sub-trees to handle each possible radix_index. For example, -in figure we have 3 overflow-sub-trees corresponding to radix indices -0, 2, and 4. - -In the final tree the first few (prio_tree_root->index_bits) levels -are indexed using heap and radix indices whereas the overflow-sub-trees below -those levels (i.e. levels prio_tree_root->index_bits + 1 and higher) are -indexed using heap and size indices. In overflow-sub-trees the size_index -is used for hashing the nodes to appropriate places. - -Now, an example prio_tree: - - vmas are represented [radix_index, size_index, heap_index] - i.e., [start_vm_pgoff, vm_size_in_pages, end_vm_pgoff] - -level prio_tree_root->index_bits = 3 ------ - _ - 0 [0,7,7] | - / \ | - ------------------ ------------ | Regular - / \ | radix priority - 1 [1,6,7] [4,3,7] | search tree - / \ / \ | - ------- ----- ------ ----- | heap-and-radix - / \ / \ | indexed - 2 [0,6,6] [2,5,7] [5,2,7] [6,1,7] | - / \ / \ / \ / \ | - 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] | - / / / _ - / / / _ - 4 [0,4,4] [2,3,5] [4,1,5] | - / / / | - 5 [0,3,3] [2,2,4] [4,0,4] | Overflow-sub-trees - / / | - 6 [0,2,2] [2,1,3] | heap-and-size - / / | indexed - 7 [0,1,1] [2,0,2] | - / | - 8 [0,0,0] | - _ - -Note that we use prio_tree_root->index_bits to optimize the height -of the heap-and-radix indexed tree. Since prio_tree_root->index_bits is -set according to the maximum end_vm_pgoff mapped, we are sure that all -bits (in vm_pgoff) above prio_tree_root->index_bits are 0 (zero). Therefore, -we only use the first prio_tree_root->index_bits as radix_index. -Whenever index_bits is increased in prio_tree_expand, we shuffle the tree -to make sure that the first prio_tree_root->index_bits levels of the tree -is indexed properly using heap and radix indices. - -We do not optimize the height of overflow-sub-trees using index_bits. -The reason is: there can be many such overflow-sub-trees and all of -them have to be suffled whenever the index_bits increases. This may involve -walking the whole prio_tree in prio_tree_insert->prio_tree_expand code -path which is not desirable. Hence, we do not optimize the height of the -heap-and-size indexed overflow-sub-trees using prio_tree->index_bits. -Instead the overflow sub-trees are indexed using full BITS_PER_LONG bits -of size_index. This may lead to skewed sub-trees because most of the -higher significant bits of the size_index are likely to be 0 (zero). In -the example above, all 3 overflow-sub-trees are skewed. This may marginally -affect the performance. However, processes rarely map many vmas with the -same start_vm_pgoff but different end_vm_pgoffs. Therefore, we normally -do not require overflow-sub-trees to index all vmas. - -From the above discussion it is clear that the maximum height of -a prio_tree can be prio_tree_root->index_bits + BITS_PER_LONG. -However, in most of the common cases we do not need overflow-sub-trees, -so the tree height in the common cases will be prio_tree_root->index_bits. - -It is fair to mention here that the prio_tree_root->index_bits -is increased on demand, however, the index_bits is not decreased when -vmas are removed from the prio_tree. That's tricky to do. Hence, it's -left as a home work problem. - - |