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.
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);
+}
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,
__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;
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;
}
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;
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;
}
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;
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;
if (tmp1)
rb_set_parent_color(tmp1, sibling,
RB_BLACK);
+ augment->rotate(sibling, tmp2);
tmp1 = sibling;
sibling = tmp2;
}
rb_set_parent(tmp2, parent);
__rb_rotate_set_parents(parent, sibling, root,
RB_BLACK);
+ augment->rotate(parent, sibling);
break;
} else {
sibling = parent->rb_left;
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;
if (tmp1)
rb_set_parent_color(tmp1, sibling,
RB_BLACK);
+ augment->rotate(sibling, tmp2);
tmp1 = sibling;
sibling = tmp2;
}
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;
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;
* \
* (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
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;
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;
return max;
}
-static void augment_callback(struct rb_node *rb, void *unused)
+static void augment_propagate(struct rb_node *rb, struct rb_node *stop)
{
- struct test_node *node = rb_entry(rb, struct test_node, rb);
- node->augmented = augment_recompute(node);
+ while (rb != stop) {
+ struct test_node *node = rb_entry(rb, struct test_node, rb);
+ 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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