1 files changed, 157 insertions, 33 deletions

diff --git a/Documentation/rbtree.txt b/Documentation/rbtree.txt
index 8d32d85..0a0b6dc 100644
--- a/Documentation/rbtree.txt
+++ b/Documentation/rbtree.txt
@@ -193,24 +193,42 @@ Example:
 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.
+Augmented rbtree is an rbtree with "some" additional data stored in
+each node, where the additional data for node N must be a function of
+the contents of all nodes in the subtree rooted at N. 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.
+On insertion, the user must update the augmented information on the path
+leading to the inserted node, then call rb_link_node() as usual and
+rb_augment_inserted() instead of the usual rb_insert_color() call.
+If rb_augment_inserted() rebalances the rbtree, it will callback into
+a user provided function to update the augmented information on the
+affected subtrees.
 
-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.
+When erasing a node, the user must call rb_erase_augmented() instead of
+rb_erase(). rb_erase_augmented() calls back into user provided functions
+to updated the augmented information on affected subtrees.
 
+In both cases, the callbacks are provided through struct rb_augment_callbacks.
+3 callbacks must be defined:
+
+- A propagation callback, which updates the augmented value for a given
+  node and its ancestors, up to a given stop point (or NULL to update
+  all the way to the root).
+
+- A copy callback, which copies the augmented value for a given subtree
+  to a newly assigned subtree root.
+
+- A tree rotation callback, which copies the augmented value for a given
+  subtree to a newly assigned subtree root AND recomputes the augmented
+  information for the former subtree root.
+
+
+Sample usage:
 
 Interval tree is an example of augmented rb tree. Reference -
 "Introduction to Algorithms" by Cormen, Leiserson, Rivest and Stein.
@@ -230,26 +248,132 @@ 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)
+struct interval_tree_node *
+interval_tree_first_match(struct rb_root *root,
+			  unsigned long start, unsigned long last)
 {
-	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;
+	struct interval_tree_node *node;
+
+	if (!root->rb_node)
+		return NULL;
+	node = rb_entry(root->rb_node, struct interval_tree_node, rb);
+
+	while (true) {
+		if (node->rb.rb_left) {
+			struct interval_tree_node *left =
+				rb_entry(node->rb.rb_left,
+					 struct interval_tree_node, rb);
+			if (left->__subtree_last >= start) {
+				/*
+				 * Some nodes in left subtree satisfy Cond2.
+				 * Iterate to find the leftmost such node N.
+				 * If it also satisfies Cond1, that's the match
+				 * we are looking for. Otherwise, there is no
+				 * matching interval as nodes to the right of N
+				 * can't satisfy Cond1 either.
+				 */
+				node = left;
+				continue;
+			}
 		}
+		if (node->start <= last) {		/* Cond1 */
+			if (node->last >= start)	/* Cond2 */
+				return node;	/* node is leftmost match */
+			if (node->rb.rb_right) {
+				node = rb_entry(node->rb.rb_right,
+					struct interval_tree_node, rb);
+				if (node->__subtree_last >= start)
+					continue;
+			}
+		}
+		return NULL;	/* No match */
+	}
+}
+
+Insertion/removal are defined using the following augmented callbacks:
+
+static inline unsigned long
+compute_subtree_last(struct interval_tree_node *node)
+{
+	unsigned long max = node->last, subtree_last;
+	if (node->rb.rb_left) {
+		subtree_last = rb_entry(node->rb.rb_left,
+			struct interval_tree_node, rb)->__subtree_last;
+		if (max < subtree_last)
+			max = subtree_last;
+	}
+	if (node->rb.rb_right) {
+		subtree_last = rb_entry(node->rb.rb_right,
+			struct interval_tree_node, rb)->__subtree_last;
+		if (max < subtree_last)
+			max = subtree_last;
+	}
+	return max;
+}
+
+static void augment_propagate(struct rb_node *rb, struct rb_node *stop)
+{
+	while (rb != stop) {
+		struct interval_tree_node *node =
+			rb_entry(rb, struct interval_tree_node, rb);
+		unsigned long subtree_last = compute_subtree_last(node);
+		if (node->__subtree_last == subtree_last)
+			break;
+		node->__subtree_last = subtree_last;
+		rb = rb_parent(&node->rb);
+	}
+}
+
+static void augment_copy(struct rb_node *rb_old, struct rb_node *rb_new)
+{
+	struct interval_tree_node *old =
+		rb_entry(rb_old, struct interval_tree_node, rb);
+	struct interval_tree_node *new =
+		rb_entry(rb_new, struct interval_tree_node, rb);
+
+	new->__subtree_last = old->__subtree_last;
+}
+
+static void augment_rotate(struct rb_node *rb_old, struct rb_node *rb_new)
+{
+	struct interval_tree_node *old =
+		rb_entry(rb_old, struct interval_tree_node, rb);
+	struct interval_tree_node *new =
+		rb_entry(rb_new, struct interval_tree_node, rb);
+
+	new->__subtree_last = old->__subtree_last;
+	old->__subtree_last = compute_subtree_last(old);
+}
+
+static const struct rb_augment_callbacks augment_callbacks = {
+	augment_propagate, augment_copy, augment_rotate
+};
+
+void interval_tree_insert(struct interval_tree_node *node,
+			  struct rb_root *root)
+{
+	struct rb_node **link = &root->rb_node, *rb_parent = NULL;
+	unsigned long start = node->start, last = node->last;
+	struct interval_tree_node *parent;
+
+	while (*link) {
+		rb_parent = *link;
+		parent = rb_entry(rb_parent, struct interval_tree_node, rb);
+		if (parent->__subtree_last < last)
+			parent->__subtree_last = last;
+		if (start < parent->start)
+			link = &parent->rb.rb_left;
+		else
+			link = &parent->rb.rb_right;
 	}
-	return lowest_match;
+
+	node->__subtree_last = last;
+	rb_link_node(&node->rb, rb_parent, link);
+	rb_insert_augmented(&node->rb, root, &augment_callbacks);
 }
 
-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.
+void interval_tree_remove(struct interval_tree_node *node,
+			  struct rb_root *root)
+{
+	rb_erase_augmented(&node->rb, root, &augment_callbacks);
+}