rbtree: faster augmented rbtree manipulation (14b94af0) · Commits · 戴 / test

Documentation/rbtree.txt

+157 −33

Original line number	Diff line number	Diff line
		@@ -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 {
		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);
		}

include/linux/rbtree.h

+19 −0

Original line number	Diff line number	Diff line
		@@ -61,6 +61,25 @@ struct rb_root {
		extern void rb_insert_color(struct rb_node , struct rb_root );
		extern void rb_erase(struct rb_node , struct rb_root );


		struct rb_augment_callbacks {
		void (propagate)(struct rb_node node, struct rb_node *stop);
		void (copy)(struct rb_node old, struct rb_node *new);
		void (rotate)(struct rb_node old, struct rb_node *new);
		};

		extern void __rb_insert_augmented(struct rb_node node, struct rb_root root,
		void (augment_rotate)(struct rb_node old, struct rb_node *new));
		extern void rb_erase_augmented(struct rb_node node, struct rb_root root,
		const struct rb_augment_callbacks *augment);
		static inline void
		rb_insert_augmented(struct rb_node node, struct rb_root root,
		const struct rb_augment_callbacks *augment)
		{
		__rb_insert_augmented(node, root, augment->rotate);
		}


		typedef void (rb_augment_f)(struct rb_node node, void *data);

		extern void rb_augment_insert(struct rb_node *node,

lib/rbtree.c

+76 −7

Original line number	Diff line number	Diff line
		@@ -105,7 +105,9 @@ __rb_rotate_set_parents(struct rb_node old, struct rb_node new,
		__rb_change_child(old, new, parent, root);
		}

		void rb_insert_color(struct rb_node node, struct rb_root root)
		static __always_inline void
		__rb_insert(struct rb_node node, struct rb_root root,
		void (augment_rotate)(struct rb_node old, struct rb_node *new))
		{
		struct rb_node parent = rb_red_parent(node), gparent, *tmp;

		@@ -169,6 +171,7 @@ void rb_insert_color(struct rb_node node, struct rb_root root)
		rb_set_parent_color(tmp, parent,
		RB_BLACK);
		rb_set_parent_color(parent, node, RB_RED);
		augment_rotate(parent, node);
		parent = node;
		tmp = node->rb_right;
		}
		@@ -187,6 +190,7 @@ void rb_insert_color(struct rb_node node, struct rb_root root)
		if (tmp)
		rb_set_parent_color(tmp, gparent, RB_BLACK);
		__rb_rotate_set_parents(gparent, parent, root, RB_RED);
		augment_rotate(gparent, parent);
		break;
		} else {
		tmp = gparent->rb_left;
		@@ -209,6 +213,7 @@ void rb_insert_color(struct rb_node node, struct rb_root root)
		rb_set_parent_color(tmp, parent,
		RB_BLACK);
		rb_set_parent_color(parent, node, RB_RED);
		augment_rotate(parent, node);
		parent = node;
		tmp = node->rb_left;
		}
		@@ -219,13 +224,15 @@ void rb_insert_color(struct rb_node node, struct rb_root root)
		if (tmp)
		rb_set_parent_color(tmp, gparent, RB_BLACK);
		__rb_rotate_set_parents(gparent, parent, root, RB_RED);
		augment_rotate(gparent, parent);
		break;
		}
		}
		}
		EXPORT_SYMBOL(rb_insert_color);

		static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		static __always_inline void
		__rb_erase_color(struct rb_node parent, struct rb_root root,
		const struct rb_augment_callbacks *augment)
		{
		struct rb_node node = NULL, sibling, tmp1, tmp2;

		@@ -254,6 +261,7 @@ static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		rb_set_parent_color(tmp1, parent, RB_BLACK);
		__rb_rotate_set_parents(parent, sibling, root,
		RB_RED);
		augment->rotate(parent, sibling);
		sibling = tmp1;
		}
		tmp1 = sibling->rb_right;
		@@ -305,6 +313,7 @@ static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		if (tmp1)
		rb_set_parent_color(tmp1, sibling,
		RB_BLACK);
		augment->rotate(sibling, tmp2);
		tmp1 = sibling;
		sibling = tmp2;
		}
		@@ -327,6 +336,7 @@ static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		rb_set_parent(tmp2, parent);
		__rb_rotate_set_parents(parent, sibling, root,
		RB_BLACK);
		augment->rotate(parent, sibling);
		break;
		} else {
		sibling = parent->rb_left;
		@@ -337,6 +347,7 @@ static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		rb_set_parent_color(tmp1, parent, RB_BLACK);
		__rb_rotate_set_parents(parent, sibling, root,
		RB_RED);
		augment->rotate(parent, sibling);
		sibling = tmp1;
		}
		tmp1 = sibling->rb_left;
		@@ -363,6 +374,7 @@ static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		if (tmp1)
		rb_set_parent_color(tmp1, sibling,
		RB_BLACK);
		augment->rotate(sibling, tmp2);
		tmp1 = sibling;
		sibling = tmp2;
		}
		@@ -374,12 +386,15 @@ static void __rb_erase_color(struct rb_node parent, struct rb_root root)
		rb_set_parent(tmp2, parent);
		__rb_rotate_set_parents(parent, sibling, root,
		RB_BLACK);
		augment->rotate(parent, sibling);
		break;
		}
		}
		}

		void rb_erase(struct rb_node node, struct rb_root root)
		static __always_inline void
		__rb_erase(struct rb_node node, struct rb_root root,
		const struct rb_augment_callbacks *augment)
		{
		struct rb_node child = node->rb_right, tmp = node->rb_left;
		struct rb_node parent, rebalance;
		@@ -401,12 +416,14 @@ void rb_erase(struct rb_node node, struct rb_root root)
		rebalance = NULL;
		} else
		rebalance = __rb_is_black(pc) ? parent : NULL;
		tmp = parent;
		} else if (!child) {
		/* Still case 1, but this time the child is node->rb_left */
		tmp->__rb_parent_color = pc = node->__rb_parent_color;
		parent = __rb_parent(pc);
		__rb_change_child(node, tmp, parent, root);
		rebalance = NULL;
		tmp = parent;
		} else {
		struct rb_node successor = child, child2;
		tmp = child->rb_left;
		@@ -420,8 +437,9 @@ void rb_erase(struct rb_node node, struct rb_root root)
		* \
		* (c)
		*/
		parent = child;
		child2 = child->rb_right;
		parent = successor;
		child2 = successor->rb_right;
		augment->copy(node, successor);
		} else {
		/*
		* Case 3: node's successor is leftmost under
		@@ -445,6 +463,8 @@ void rb_erase(struct rb_node node, struct rb_root root)
		parent->rb_left = child2 = successor->rb_right;
		successor->rb_right = child;
		rb_set_parent(child, successor);
		augment->copy(node, successor);
		augment->propagate(parent, successor);
		}

		successor->rb_left = tmp = node->rb_left;
		@@ -462,13 +482,62 @@ void rb_erase(struct rb_node node, struct rb_root root)
		successor->__rb_parent_color = pc;
		rebalance = __rb_is_black(pc2) ? parent : NULL;
		}
		tmp = successor;
		}

		augment->propagate(tmp, NULL);
		if (rebalance)
		__rb_erase_color(rebalance, root);
		__rb_erase_color(rebalance, root, augment);
		}

		/*
		* Non-augmented rbtree manipulation functions.
		*
		* We use dummy augmented callbacks here, and have the compiler optimize them
		* out of the rb_insert_color() and rb_erase() function definitions.
		*/

		static inline void dummy_propagate(struct rb_node node, struct rb_node stop) {}
		static inline void dummy_copy(struct rb_node old, struct rb_node new) {}
		static inline void dummy_rotate(struct rb_node old, struct rb_node new) {}

		static const struct rb_augment_callbacks dummy_callbacks = {
		dummy_propagate, dummy_copy, dummy_rotate
		};

		void rb_insert_color(struct rb_node node, struct rb_root root)
		{
		__rb_insert(node, root, dummy_rotate);
		}
		EXPORT_SYMBOL(rb_insert_color);

		void rb_erase(struct rb_node node, struct rb_root root)
		{
		__rb_erase(node, root, &dummy_callbacks);
		}
		EXPORT_SYMBOL(rb_erase);

		/*
		* Augmented rbtree manipulation functions.
		*
		* This instantiates the same __always_inline functions as in the non-augmented
		* case, but this time with user-defined callbacks.
		*/

		void __rb_insert_augmented(struct rb_node node, struct rb_root root,
		void (augment_rotate)(struct rb_node old, struct rb_node *new))
		{
		__rb_insert(node, root, augment_rotate);
		}
		EXPORT_SYMBOL(__rb_insert_augmented);

		void rb_erase_augmented(struct rb_node node, struct rb_root root,
		const struct rb_augment_callbacks *augment)
		{
		__rb_erase(node, root, augment);
		}
		EXPORT_SYMBOL(rb_erase_augmented);

		static void rb_augment_path(struct rb_node node, rb_augment_f func, void data)
		{
		struct rb_node *parent;

lib/rbtree_test.c

+44 −14

Original line number	Diff line number	Diff line
		@@ -61,35 +61,65 @@ static inline u32 augment_recompute(struct test_node *node)
		return max;
		}

		static void augment_callback(struct rb_node rb, void unused)
		static void augment_propagate(struct rb_node rb, struct rb_node stop)
		{
		while (rb != stop) {
		struct test_node *node = rb_entry(rb, struct test_node, rb);
		node->augmented = augment_recompute(node);
		u32 augmented = augment_recompute(node);
		if (node->augmented == augmented)
		break;
		node->augmented = augmented;
		rb = rb_parent(&node->rb);
		}
		}

		static void augment_copy(struct rb_node rb_old, struct rb_node rb_new)
		{
		struct test_node *old = rb_entry(rb_old, struct test_node, rb);
		struct test_node *new = rb_entry(rb_new, struct test_node, rb);
		new->augmented = old->augmented;
		}

		static void augment_rotate(struct rb_node rb_old, struct rb_node rb_new)
		{
		struct test_node *old = rb_entry(rb_old, struct test_node, rb);
		struct test_node *new = rb_entry(rb_new, struct test_node, rb);

		/* Rotation doesn't change subtree's augmented value */
		new->augmented = old->augmented;
		old->augmented = augment_recompute(old);
		}

		static const struct rb_augment_callbacks augment_callbacks = {
		augment_propagate, augment_copy, augment_rotate
		};

		static void insert_augmented(struct test_node node, struct rb_root root)
		{
		struct rb_node *new = &root->rb_node, parent = NULL;
		struct rb_node *new = &root->rb_node, rb_parent = NULL;
		u32 key = node->key;
		u32 val = node->val;
		struct test_node *parent;

		while (*new) {
		parent = *new;
		if (key < rb_entry(parent, struct test_node, rb)->key)
		new = &parent->rb_left;
		rb_parent = *new;
		parent = rb_entry(rb_parent, struct test_node, rb);
		if (parent->augmented < val)
		parent->augmented = val;
		if (key < parent->key)
		new = &parent->rb.rb_left;
		else
		new = &parent->rb_right;
		new = &parent->rb.rb_right;
		}

		rb_link_node(&node->rb, parent, new);
		rb_insert_color(&node->rb, root);
		rb_augment_insert(&node->rb, augment_callback, NULL);
		node->augmented = val;
		rb_link_node(&node->rb, rb_parent, new);
		rb_insert_augmented(&node->rb, root, &augment_callbacks);
		}

		static void erase_augmented(struct test_node node, struct rb_root root)
		{
		struct rb_node *deepest = rb_augment_erase_begin(&node->rb);
		rb_erase(&node->rb, root);
		rb_augment_erase_end(deepest, augment_callback, NULL);
		rb_erase_augmented(&node->rb, root, &augment_callbacks);
		}

		static void init(void)

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