mirror of
https://github.com/AuxXxilium/linux_dsm_epyc7002.git
synced 2024-12-06 05:46:39 +07:00
2f175074e6
Current documentation referred to the old method of handling augmented
trees. Update documentation to correspond with the changes done in
commit b945d6b255
("rbtree: Undo augmented trees performance damage
and regression").
Cc: Pekka Enberg <penberg@cs.helsinki.fi>
Cc: David Woodhouse <David.Woodhouse@intel.com>
Cc: Andrew Morton <akpm@linux-foundation.org>
Acked-by: Ingo Molnar <mingo@elte.hu>
Acked-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Signed-off-by: Sasha Levin <levinsasha928@gmail.com>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
256 lines
9.1 KiB
Plaintext
256 lines
9.1 KiB
Plaintext
Red-black Trees (rbtree) in Linux
|
|
January 18, 2007
|
|
Rob Landley <rob@landley.net>
|
|
=============================
|
|
|
|
What are red-black trees, and what are they for?
|
|
------------------------------------------------
|
|
|
|
Red-black trees are a type of self-balancing binary search tree, used for
|
|
storing sortable key/value data pairs. This differs from radix trees (which
|
|
are used to efficiently store sparse arrays and thus use long integer indexes
|
|
to insert/access/delete nodes) and hash tables (which are not kept sorted to
|
|
be easily traversed in order, and must be tuned for a specific size and
|
|
hash function where rbtrees scale gracefully storing arbitrary keys).
|
|
|
|
Red-black trees are similar to AVL trees, but provide faster real-time bounded
|
|
worst case performance for insertion and deletion (at most two rotations and
|
|
three rotations, respectively, to balance the tree), with slightly slower
|
|
(but still O(log n)) lookup time.
|
|
|
|
To quote Linux Weekly News:
|
|
|
|
There are a number of red-black trees in use in the kernel.
|
|
The deadline and CFQ I/O schedulers employ rbtrees to
|
|
track requests; the packet CD/DVD driver does the same.
|
|
The high-resolution timer code uses an rbtree to organize outstanding
|
|
timer requests. The ext3 filesystem tracks directory entries in a
|
|
red-black tree. Virtual memory areas (VMAs) are tracked with red-black
|
|
trees, as are epoll file descriptors, cryptographic keys, and network
|
|
packets in the "hierarchical token bucket" scheduler.
|
|
|
|
This document covers use of the Linux rbtree implementation. For more
|
|
information on the nature and implementation of Red Black Trees, see:
|
|
|
|
Linux Weekly News article on red-black trees
|
|
http://lwn.net/Articles/184495/
|
|
|
|
Wikipedia entry on red-black trees
|
|
http://en.wikipedia.org/wiki/Red-black_tree
|
|
|
|
Linux implementation of red-black trees
|
|
---------------------------------------
|
|
|
|
Linux's rbtree implementation lives in the file "lib/rbtree.c". To use it,
|
|
"#include <linux/rbtree.h>".
|
|
|
|
The Linux rbtree implementation is optimized for speed, and thus has one
|
|
less layer of indirection (and better cache locality) than more traditional
|
|
tree implementations. Instead of using pointers to separate rb_node and data
|
|
structures, each instance of struct rb_node is embedded in the data structure
|
|
it organizes. And instead of using a comparison callback function pointer,
|
|
users are expected to write their own tree search and insert functions
|
|
which call the provided rbtree functions. Locking is also left up to the
|
|
user of the rbtree code.
|
|
|
|
Creating a new rbtree
|
|
---------------------
|
|
|
|
Data nodes in an rbtree tree are structures containing a struct rb_node member:
|
|
|
|
struct mytype {
|
|
struct rb_node node;
|
|
char *keystring;
|
|
};
|
|
|
|
When dealing with a pointer to the embedded struct rb_node, the containing data
|
|
structure may be accessed with the standard container_of() macro. In addition,
|
|
individual members may be accessed directly via rb_entry(node, type, member).
|
|
|
|
At the root of each rbtree is an rb_root structure, which is initialized to be
|
|
empty via:
|
|
|
|
struct rb_root mytree = RB_ROOT;
|
|
|
|
Searching for a value in an rbtree
|
|
----------------------------------
|
|
|
|
Writing a search function for your tree is fairly straightforward: start at the
|
|
root, compare each value, and follow the left or right branch as necessary.
|
|
|
|
Example:
|
|
|
|
struct mytype *my_search(struct rb_root *root, char *string)
|
|
{
|
|
struct rb_node *node = root->rb_node;
|
|
|
|
while (node) {
|
|
struct mytype *data = container_of(node, struct mytype, node);
|
|
int result;
|
|
|
|
result = strcmp(string, data->keystring);
|
|
|
|
if (result < 0)
|
|
node = node->rb_left;
|
|
else if (result > 0)
|
|
node = node->rb_right;
|
|
else
|
|
return data;
|
|
}
|
|
return NULL;
|
|
}
|
|
|
|
Inserting data into an rbtree
|
|
-----------------------------
|
|
|
|
Inserting data in the tree involves first searching for the place to insert the
|
|
new node, then inserting the node and rebalancing ("recoloring") the tree.
|
|
|
|
The search for insertion differs from the previous search by finding the
|
|
location of the pointer on which to graft the new node. The new node also
|
|
needs a link to its parent node for rebalancing purposes.
|
|
|
|
Example:
|
|
|
|
int my_insert(struct rb_root *root, struct mytype *data)
|
|
{
|
|
struct rb_node **new = &(root->rb_node), *parent = NULL;
|
|
|
|
/* Figure out where to put new node */
|
|
while (*new) {
|
|
struct mytype *this = container_of(*new, struct mytype, node);
|
|
int result = strcmp(data->keystring, this->keystring);
|
|
|
|
parent = *new;
|
|
if (result < 0)
|
|
new = &((*new)->rb_left);
|
|
else if (result > 0)
|
|
new = &((*new)->rb_right);
|
|
else
|
|
return FALSE;
|
|
}
|
|
|
|
/* Add new node and rebalance tree. */
|
|
rb_link_node(&data->node, parent, new);
|
|
rb_insert_color(&data->node, root);
|
|
|
|
return TRUE;
|
|
}
|
|
|
|
Removing or replacing existing data in an rbtree
|
|
------------------------------------------------
|
|
|
|
To remove an existing node from a tree, call:
|
|
|
|
void rb_erase(struct rb_node *victim, struct rb_root *tree);
|
|
|
|
Example:
|
|
|
|
struct mytype *data = mysearch(&mytree, "walrus");
|
|
|
|
if (data) {
|
|
rb_erase(&data->node, &mytree);
|
|
myfree(data);
|
|
}
|
|
|
|
To replace an existing node in a tree with a new one with the same key, call:
|
|
|
|
void rb_replace_node(struct rb_node *old, struct rb_node *new,
|
|
struct rb_root *tree);
|
|
|
|
Replacing a node this way does not re-sort the tree: If the new node doesn't
|
|
have the same key as the old node, the rbtree will probably become corrupted.
|
|
|
|
Iterating through the elements stored in an rbtree (in sort order)
|
|
------------------------------------------------------------------
|
|
|
|
Four functions are provided for iterating through an rbtree's contents in
|
|
sorted order. These work on arbitrary trees, and should not need to be
|
|
modified or wrapped (except for locking purposes):
|
|
|
|
struct rb_node *rb_first(struct rb_root *tree);
|
|
struct rb_node *rb_last(struct rb_root *tree);
|
|
struct rb_node *rb_next(struct rb_node *node);
|
|
struct rb_node *rb_prev(struct rb_node *node);
|
|
|
|
To start iterating, call rb_first() or rb_last() with a pointer to the root
|
|
of the tree, which will return a pointer to the node structure contained in
|
|
the first or last element in the tree. To continue, fetch the next or previous
|
|
node by calling rb_next() or rb_prev() on the current node. This will return
|
|
NULL when there are no more nodes left.
|
|
|
|
The iterator functions return a pointer to the embedded struct rb_node, from
|
|
which the containing data structure may be accessed with the container_of()
|
|
macro, and individual members may be accessed directly via
|
|
rb_entry(node, type, member).
|
|
|
|
Example:
|
|
|
|
struct rb_node *node;
|
|
for (node = rb_first(&mytree); node; node = rb_next(node))
|
|
printk("key=%s\n", rb_entry(node, struct mytype, node)->keystring);
|
|
|
|
Support for Augmented rbtrees
|
|
-----------------------------
|
|
|
|
Augmented rbtree is an rbtree with "some" additional data stored in each node.
|
|
This data can be used to augment some new functionality to rbtree.
|
|
Augmented rbtree is an optional feature built on top of basic rbtree
|
|
infrastructure. An rbtree user who wants this feature will have to call the
|
|
augmentation functions with the user provided augmentation callback
|
|
when inserting and erasing nodes.
|
|
|
|
On insertion, the user must call rb_augment_insert() once the new node is in
|
|
place. This will cause the augmentation function callback to be called for
|
|
each node between the new node and the root which has been affected by the
|
|
insertion.
|
|
|
|
When erasing a node, the user must call rb_augment_erase_begin() first to
|
|
retrieve the deepest node on the rebalance path. Then, after erasing the
|
|
original node, the user must call rb_augment_erase_end() with the deepest
|
|
node found earlier. This will cause the augmentation function to be called
|
|
for each affected node between the deepest node and the root.
|
|
|
|
|
|
Interval tree is an example of augmented rb tree. Reference -
|
|
"Introduction to Algorithms" by Cormen, Leiserson, Rivest and Stein.
|
|
More details about interval trees:
|
|
|
|
Classical rbtree has a single key and it cannot be directly used to store
|
|
interval ranges like [lo:hi] and do a quick lookup for any overlap with a new
|
|
lo:hi or to find whether there is an exact match for a new lo:hi.
|
|
|
|
However, rbtree can be augmented to store such interval ranges in a structured
|
|
way making it possible to do efficient lookup and exact match.
|
|
|
|
This "extra information" stored in each node is the maximum hi
|
|
(max_hi) value among all the nodes that are its descendents. This
|
|
information can be maintained at each node just be looking at the node
|
|
and its immediate children. And this will be used in O(log n) lookup
|
|
for lowest match (lowest start address among all possible matches)
|
|
with something like:
|
|
|
|
find_lowest_match(lo, hi, node)
|
|
{
|
|
lowest_match = NULL;
|
|
while (node) {
|
|
if (max_hi(node->left) > lo) {
|
|
// Lowest overlap if any must be on left side
|
|
node = node->left;
|
|
} else if (overlap(lo, hi, node)) {
|
|
lowest_match = node;
|
|
break;
|
|
} else if (lo > node->lo) {
|
|
// Lowest overlap if any must be on right side
|
|
node = node->right;
|
|
} else {
|
|
break;
|
|
}
|
|
}
|
|
return lowest_match;
|
|
}
|
|
|
|
Finding exact match will be to first find lowest match and then to follow
|
|
successor nodes looking for exact match, until the start of a node is beyond
|
|
the hi value we are looking for.
|