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Diffstat (limited to 'Documentation/prio_tree.txt')
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diff --git a/Documentation/prio_tree.txt b/Documentation/prio_tree.txt new file mode 100644 index 000000000000..2fbb0c49bc5b --- /dev/null +++ b/Documentation/prio_tree.txt @@ -0,0 +1,107 @@ +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 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. + + |