Initial import

1 files changed, 560 insertions, 0 deletions

diff --git a/lib/rbtree.c b/lib/rbtree.c
new file mode 100644
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--- /dev/null
+++ b/lib/rbtree.c
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+/*
+  Red Black Trees
+  (C) 1999  Andrea Arcangeli <andrea@suse.de>
+  (C) 2002  David Woodhouse <dwmw2@infradead.org>
+  (C) 2012  Michel Lespinasse <walken@google.com>
+
+  This program is free software; you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation; either version 2 of the License, or
+  (at your option) any later version.
+
+  This program is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with this program; if not, write to the Free Software
+  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+  linux/lib/rbtree.c
+*/
+
+#include <linux/rbtree_augmented.h>
+#include <linux/export.h>
+
+/*
+ * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
+ *
+ *  1) A node is either red or black
+ *  2) The root is black
+ *  3) All leaves (NULL) are black
+ *  4) Both children of every red node are black
+ *  5) Every simple path from root to leaves contains the same number
+ *     of black nodes.
+ *
+ *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
+ *  consecutive red nodes in a path and every red node is therefore followed by
+ *  a black. So if B is the number of black nodes on every simple path (as per
+ *  5), then the longest possible path due to 4 is 2B.
+ *
+ *  We shall indicate color with case, where black nodes are uppercase and red
+ *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
+ *  parentheses and have some accompanying text comment.
+ */
+
+static inline void rb_set_black(struct rb_node *rb)
+{
+	rb->__rb_parent_color |= RB_BLACK;
+}
+
+static inline struct rb_node *rb_red_parent(struct rb_node *red)
+{
+	return (struct rb_node *)red->__rb_parent_color;
+}
+
+/*
+ * Helper function for rotations:
+ * - old's parent and color get assigned to new
+ * - old gets assigned new as a parent and 'color' as a color.
+ */
+static inline void
+__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
+			struct rb_root *root, int color)
+{
+	struct rb_node *parent = rb_parent(old);
+	new->__rb_parent_color = old->__rb_parent_color;
+	rb_set_parent_color(old, new, color);
+	__rb_change_child(old, new, parent, 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;
+
+	while (true) {
+		/*
+		 * Loop invariant: node is red
+		 *
+		 * If there is a black parent, we are done.
+		 * Otherwise, take some corrective action as we don't
+		 * want a red root or two consecutive red nodes.
+		 */
+		if (!parent) {
+			rb_set_parent_color(node, NULL, RB_BLACK);
+			break;
+		} else if (rb_is_black(parent))
+			break;
+
+		gparent = rb_red_parent(parent);
+
+		tmp = gparent->rb_right;
+		if (parent != tmp) {	/* parent == gparent->rb_left */
+			if (tmp && rb_is_red(tmp)) {
+				/*
+				 * Case 1 - color flips
+				 *
+				 *       G            g
+				 *      / \          / \
+				 *     p   u  -->   P   U
+				 *    /            /
+				 *   n            n
+				 *
+				 * However, since g's parent might be red, and
+				 * 4) does not allow this, we need to recurse
+				 * at g.
+				 */
+				rb_set_parent_color(tmp, gparent, RB_BLACK);
+				rb_set_parent_color(parent, gparent, RB_BLACK);
+				node = gparent;
+				parent = rb_parent(node);
+				rb_set_parent_color(node, parent, RB_RED);
+				continue;
+			}
+
+			tmp = parent->rb_right;
+			if (node == tmp) {
+				/*
+				 * Case 2 - left rotate at parent
+				 *
+				 *      G             G
+				 *     / \           / \
+				 *    p   U  -->    n   U
+				 *     \           /
+				 *      n         p
+				 *
+				 * This still leaves us in violation of 4), the
+				 * continuation into Case 3 will fix that.
+				 */
+				parent->rb_right = tmp = node->rb_left;
+				node->rb_left = parent;
+				if (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;
+			}
+
+			/*
+			 * Case 3 - right rotate at gparent
+			 *
+			 *        G           P
+			 *       / \         / \
+			 *      p   U  -->  n   g
+			 *     /                 \
+			 *    n                   U
+			 */
+			gparent->rb_left = tmp;  /* == parent->rb_right */
+			parent->rb_right = gparent;
+			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;
+			if (tmp && rb_is_red(tmp)) {
+				/* Case 1 - color flips */
+				rb_set_parent_color(tmp, gparent, RB_BLACK);
+				rb_set_parent_color(parent, gparent, RB_BLACK);
+				node = gparent;
+				parent = rb_parent(node);
+				rb_set_parent_color(node, parent, RB_RED);
+				continue;
+			}
+
+			tmp = parent->rb_left;
+			if (node == tmp) {
+				/* Case 2 - right rotate at parent */
+				parent->rb_left = tmp = node->rb_right;
+				node->rb_right = parent;
+				if (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_left;
+			}
+
+			/* Case 3 - left rotate at gparent */
+			gparent->rb_right = tmp;  /* == parent->rb_left */
+			parent->rb_left = gparent;
+			if (tmp)
+				rb_set_parent_color(tmp, gparent, RB_BLACK);
+			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
+			augment_rotate(gparent, parent);
+			break;
+		}
+	}
+}
+
+/*
+ * Inline version for rb_erase() use - we want to be able to inline
+ * and eliminate the dummy_rotate callback there
+ */
+static __always_inline void
+____rb_erase_color(struct rb_node *parent, struct rb_root *root,
+	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
+{
+	struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
+
+	while (true) {
+		/*
+		 * Loop invariants:
+		 * - node is black (or NULL on first iteration)
+		 * - node is not the root (parent is not NULL)
+		 * - All leaf paths going through parent and node have a
+		 *   black node count that is 1 lower than other leaf paths.
+		 */
+		sibling = parent->rb_right;
+		if (node != sibling) {	/* node == parent->rb_left */
+			if (rb_is_red(sibling)) {
+				/*
+				 * Case 1 - left rotate at parent
+				 *
+				 *     P               S
+				 *    / \             / \
+				 *   N   s    -->    p   Sr
+				 *      / \         / \
+				 *     Sl  Sr      N   Sl
+				 */
+				parent->rb_right = tmp1 = sibling->rb_left;
+				sibling->rb_left = parent;
+				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_is_black(tmp1)) {
+				tmp2 = sibling->rb_left;
+				if (!tmp2 || rb_is_black(tmp2)) {
+					/*
+					 * Case 2 - sibling color flip
+					 * (p could be either color here)
+					 *
+					 *    (p)           (p)
+					 *    / \           / \
+					 *   N   S    -->  N   s
+					 *      / \           / \
+					 *     Sl  Sr        Sl  Sr
+					 *
+					 * This leaves us violating 5) which
+					 * can be fixed by flipping p to black
+					 * if it was red, or by recursing at p.
+					 * p is red when coming from Case 1.
+					 */
+					rb_set_parent_color(sibling, parent,
+							    RB_RED);
+					if (rb_is_red(parent))
+						rb_set_black(parent);
+					else {
+						node = parent;
+						parent = rb_parent(node);
+						if (parent)
+							continue;
+					}
+					break;
+				}
+				/*
+				 * Case 3 - right rotate at sibling
+				 * (p could be either color here)
+				 *
+				 *   (p)           (p)
+				 *   / \           / \
+				 *  N   S    -->  N   Sl
+				 *     / \             \
+				 *    sl  Sr            s
+				 *                       \
+				 *                        Sr
+				 */
+				sibling->rb_left = tmp1 = tmp2->rb_right;
+				tmp2->rb_right = sibling;
+				parent->rb_right = tmp2;
+				if (tmp1)
+					rb_set_parent_color(tmp1, sibling,
+							    RB_BLACK);
+				augment_rotate(sibling, tmp2);
+				tmp1 = sibling;
+				sibling = tmp2;
+			}
+			/*
+			 * Case 4 - left rotate at parent + color flips
+			 * (p and sl could be either color here.
+			 *  After rotation, p becomes black, s acquires
+			 *  p's color, and sl keeps its color)
+			 *
+			 *      (p)             (s)
+			 *      / \             / \
+			 *     N   S     -->   P   Sr
+			 *        / \         / \
+			 *      (sl) sr      N  (sl)
+			 */
+			parent->rb_right = tmp2 = sibling->rb_left;
+			sibling->rb_left = parent;
+			rb_set_parent_color(tmp1, sibling, RB_BLACK);
+			if (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;
+			if (rb_is_red(sibling)) {
+				/* Case 1 - right rotate at parent */
+				parent->rb_left = tmp1 = sibling->rb_right;
+				sibling->rb_right = parent;
+				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_is_black(tmp1)) {
+				tmp2 = sibling->rb_right;
+				if (!tmp2 || rb_is_black(tmp2)) {
+					/* Case 2 - sibling color flip */
+					rb_set_parent_color(sibling, parent,
+							    RB_RED);
+					if (rb_is_red(parent))
+						rb_set_black(parent);
+					else {
+						node = parent;
+						parent = rb_parent(node);
+						if (parent)
+							continue;
+					}
+					break;
+				}
+				/* Case 3 - right rotate at sibling */
+				sibling->rb_right = tmp1 = tmp2->rb_left;
+				tmp2->rb_left = sibling;
+				parent->rb_left = tmp2;
+				if (tmp1)
+					rb_set_parent_color(tmp1, sibling,
+							    RB_BLACK);
+				augment_rotate(sibling, tmp2);
+				tmp1 = sibling;
+				sibling = tmp2;
+			}
+			/* Case 4 - left rotate at parent + color flips */
+			parent->rb_left = tmp2 = sibling->rb_right;
+			sibling->rb_right = parent;
+			rb_set_parent_color(tmp1, sibling, RB_BLACK);
+			if (tmp2)
+				rb_set_parent(tmp2, parent);
+			__rb_rotate_set_parents(parent, sibling, root,
+						RB_BLACK);
+			augment_rotate(parent, sibling);
+			break;
+		}
+	}
+}
+
+/* Non-inline version for rb_erase_augmented() use */
+void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
+	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
+{
+	____rb_erase_color(parent, root, augment_rotate);
+}
+EXPORT_SYMBOL(__rb_erase_color);
+
+/*
+ * 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)
+{
+	struct rb_node *rebalance;
+	rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
+	if (rebalance)
+		____rb_erase_color(rebalance, root, dummy_rotate);
+}
+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);
+
+/*
+ * This function returns the first node (in sort order) of the tree.
+ */
+struct rb_node *rb_first(const struct rb_root *root)
+{
+	struct rb_node	*n;
+
+	n = root->rb_node;
+	if (!n)
+		return NULL;
+	while (n->rb_left)
+		n = n->rb_left;
+	return n;
+}
+EXPORT_SYMBOL(rb_first);
+
+struct rb_node *rb_last(const struct rb_root *root)
+{
+	struct rb_node	*n;
+
+	n = root->rb_node;
+	if (!n)
+		return NULL;
+	while (n->rb_right)
+		n = n->rb_right;
+	return n;
+}
+EXPORT_SYMBOL(rb_last);
+
+struct rb_node *rb_next(const struct rb_node *node)
+{
+	struct rb_node *parent;
+
+	if (RB_EMPTY_NODE(node))
+		return NULL;
+
+	/*
+	 * If we have a right-hand child, go down and then left as far
+	 * as we can.
+	 */
+	if (node->rb_right) {
+		node = node->rb_right; 
+		while (node->rb_left)
+			node=node->rb_left;
+		return (struct rb_node *)node;
+	}
+
+	/*
+	 * No right-hand children. Everything down and left is smaller than us,
+	 * so any 'next' node must be in the general direction of our parent.
+	 * Go up the tree; any time the ancestor is a right-hand child of its
+	 * parent, keep going up. First time it's a left-hand child of its
+	 * parent, said parent is our 'next' node.
+	 */
+	while ((parent = rb_parent(node)) && node == parent->rb_right)
+		node = parent;
+
+	return parent;
+}
+EXPORT_SYMBOL(rb_next);
+
+struct rb_node *rb_prev(const struct rb_node *node)
+{
+	struct rb_node *parent;
+
+	if (RB_EMPTY_NODE(node))
+		return NULL;
+
+	/*
+	 * If we have a left-hand child, go down and then right as far
+	 * as we can.
+	 */
+	if (node->rb_left) {
+		node = node->rb_left; 
+		while (node->rb_right)
+			node=node->rb_right;
+		return (struct rb_node *)node;
+	}
+
+	/*
+	 * No left-hand children. Go up till we find an ancestor which
+	 * is a right-hand child of its parent.
+	 */
+	while ((parent = rb_parent(node)) && node == parent->rb_left)
+		node = parent;
+
+	return parent;
+}
+EXPORT_SYMBOL(rb_prev);
+
+void rb_replace_node(struct rb_node *victim, struct rb_node *new,
+		     struct rb_root *root)
+{
+	struct rb_node *parent = rb_parent(victim);
+
+	/* Set the surrounding nodes to point to the replacement */
+	__rb_change_child(victim, new, parent, root);
+	if (victim->rb_left)
+		rb_set_parent(victim->rb_left, new);
+	if (victim->rb_right)
+		rb_set_parent(victim->rb_right, new);
+
+	/* Copy the pointers/colour from the victim to the replacement */
+	*new = *victim;
+}
+EXPORT_SYMBOL(rb_replace_node);
+
+static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
+{
+	for (;;) {
+		if (node->rb_left)
+			node = node->rb_left;
+		else if (node->rb_right)
+			node = node->rb_right;
+		else
+			return (struct rb_node *)node;
+	}
+}
+
+struct rb_node *rb_next_postorder(const struct rb_node *node)
+{
+	const struct rb_node *parent;
+	if (!node)
+		return NULL;
+	parent = rb_parent(node);
+
+	/* If we're sitting on node, we've already seen our children */
+	if (parent && node == parent->rb_left && parent->rb_right) {
+		/* If we are the parent's left node, go to the parent's right
+		 * node then all the way down to the left */
+		return rb_left_deepest_node(parent->rb_right);
+	} else
+		/* Otherwise we are the parent's right node, and the parent
+		 * should be next */
+		return (struct rb_node *)parent;
+}
+EXPORT_SYMBOL(rb_next_postorder);
+
+struct rb_node *rb_first_postorder(const struct rb_root *root)
+{
+	if (!root->rb_node)
+		return NULL;
+
+	return rb_left_deepest_node(root->rb_node);
+}
+EXPORT_SYMBOL(rb_first_postorder);