Merge branch 'x86-pat-for-linus' of git://git.kernel.org/pub/scm/linux/kernel/git/tip/linux-2.6-tip

* 'x86-pat-for-linus' of git://git.kernel.org/pub/scm/linux/kernel/git/tip/linux-2.6-tip:
  x86, pat: Update the page flags for memtype atomically instead of using memtype_lock
  x86, pat: In rbt_memtype_check_insert(), update new->type only if valid
  x86, pat: Migrate to rbtree only backend for pat memtype management
  x86, pat: Preparatory changes in pat.c for bigger rbtree change
  rbtree: Add support for augmented rbtrees

1 files changed, 58 insertions, 0 deletions

diff --git a/Documentation/rbtree.txt b/Documentation/rbtree.txt
index aae8355d316..221f38be98f 100644
--- a/Documentation/rbtree.txt
+++ b/Documentation/rbtree.txt
@@ -190,3 +190,61 @@ Example:
   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. rbtree user who wants this feature will have an augment
+callback function in rb_root initialized.
+
+This callback function will be called from rbtree core routines whenever
+a node has a change in one or both of its children. It is the responsibility
+of the callback function to recalculate the additional data that is in the
+rb node using new children information. Note that if this new additional
+data affects the parent node's additional data, then callback function has
+to handle it and do the recursive updates.
+
+
+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.