mirror of
https://github.com/torvalds/linux.git
synced 2024-11-18 10:01:43 +00:00
670e9f34ee
Remove many duplicated words under Documentation/ and do other small
cleanups.
Examples:
"and and" --> "and"
"in in" --> "in"
"the the" --> "the"
"the the" --> "to the"
...
Signed-off-by: Paolo Ornati <ornati@fastwebnet.it>
Signed-off-by: Adrian Bunk <bunk@stusta.de>
108 lines
5.2 KiB
Plaintext
108 lines
5.2 KiB
Plaintext
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.
|
|
|
|
|