+++ /dev/null
-/*
- 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 <xen/types.h>
-#include <xen/rbtree.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.
- */
-
-#define RB_RED 0
-#define RB_BLACK 1
-
-#define __rb_parent(pc) ((struct rb_node *)(pc & ~3))
-
-#define __rb_color(pc) ((pc) & 1)
-#define __rb_is_black(pc) __rb_color(pc)
-#define __rb_is_red(pc) (!__rb_color(pc))
-#define rb_color(rb) __rb_color((rb)->__rb_parent_color)
-#define rb_is_red(rb) __rb_is_red((rb)->__rb_parent_color)
-#define rb_is_black(rb) __rb_is_black((rb)->__rb_parent_color)
-
-static inline void rb_set_black(struct rb_node *rb)
-{
- rb->__rb_parent_color |= RB_BLACK;
-}
-
-static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
-{
- rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
-}
-
-static inline void rb_set_parent_color(struct rb_node *rb,
- struct rb_node *p, int color)
-{
- rb->__rb_parent_color = (unsigned long)p | color;
-}
-
-static inline struct rb_node *rb_red_parent(struct rb_node *red)
-{
- return (struct rb_node *)red->__rb_parent_color;
-}
-
-static inline void
-__rb_change_child(struct rb_node *old, struct rb_node *new,
- struct rb_node *parent, struct rb_root *root)
-{
- if (parent) {
- if (parent->rb_left == old)
- parent->rb_left = new;
- else
- parent->rb_right = new;
- } else
- root->rb_node = new;
-}
-
-/*
- * 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);
-}
-
-void rb_insert_color(struct rb_node *node, struct rb_root *root)
-{
- 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);
- 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);
- 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);
- 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);
- break;
- }
- }
-}
-EXPORT_SYMBOL(rb_insert_color);
-
-static void __rb_erase_color(struct rb_node *parent, struct rb_root *root)
-{
- 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);
- 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);
- 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);
- 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);
- 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);
- 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);
- break;
- }
- }
-}
-
-void rb_erase(struct rb_node *node, struct rb_root *root)
-{
- struct rb_node *child = node->rb_right, *tmp = node->rb_left;
- struct rb_node *parent, *rebalance;
- unsigned long pc;
-
- if (!tmp) {
- /*
- * Case 1: node to erase has no more than 1 child (easy!)
- *
- * Note that if there is one child it must be red due to 5)
- * and node must be black due to 4). We adjust colors locally
- * so as to bypass __rb_erase_color() later on.
- */
- pc = node->__rb_parent_color;
- parent = __rb_parent(pc);
- __rb_change_child(node, child, parent, root);
- if (child) {
- child->__rb_parent_color = pc;
- rebalance = NULL;
- } else
- rebalance = __rb_is_black(pc) ? parent : NULL;
- } 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;
- } else {
- struct rb_node *successor = child, *child2;
- tmp = child->rb_left;
- if (!tmp) {
- /*
- * Case 2: node's successor is its right child
- *
- * (n) (s)
- * / \ / \
- * (x) (s) -> (x) (c)
- * \
- * (c)
- */
- parent = child;
- child2 = child->rb_right;
- } else {
- /*
- * Case 3: node's successor is leftmost under
- * node's right child subtree
- *
- * (n) (s)
- * / \ / \
- * (x) (y) -> (x) (y)
- * / /
- * (p) (p)
- * / /
- * (s) (c)
- * \
- * (c)
- */
- do {
- parent = successor;
- successor = tmp;
- tmp = tmp->rb_left;
- } while (tmp);
- parent->rb_left = child2 = successor->rb_right;
- successor->rb_right = child;
- rb_set_parent(child, successor);
- }
-
- successor->rb_left = tmp = node->rb_left;
- rb_set_parent(tmp, successor);
-
- pc = node->__rb_parent_color;
- tmp = __rb_parent(pc);
- __rb_change_child(node, successor, tmp, root);
- if (child2) {
- successor->__rb_parent_color = pc;
- rb_set_parent_color(child2, parent, RB_BLACK);
- rebalance = NULL;
- } else {
- unsigned long pc2 = successor->__rb_parent_color;
- successor->__rb_parent_color = pc;
- rebalance = __rb_is_black(pc2) ? parent : NULL;
- }
- }
-
- if (rebalance)
- __rb_erase_color(rebalance, root);
-}
-EXPORT_SYMBOL(rb_erase);
-
-/*
- * 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);
--- /dev/null
+/*
+ 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 <xen/types.h>
+#include <xen/rbtree.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.
+ */
+
+#define RB_RED 0
+#define RB_BLACK 1
+
+#define __rb_parent(pc) ((struct rb_node *)(pc & ~3))
+
+#define __rb_color(pc) ((pc) & 1)
+#define __rb_is_black(pc) __rb_color(pc)
+#define __rb_is_red(pc) (!__rb_color(pc))
+#define rb_color(rb) __rb_color((rb)->__rb_parent_color)
+#define rb_is_red(rb) __rb_is_red((rb)->__rb_parent_color)
+#define rb_is_black(rb) __rb_is_black((rb)->__rb_parent_color)
+
+static inline void rb_set_black(struct rb_node *rb)
+{
+ rb->__rb_parent_color |= RB_BLACK;
+}
+
+static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
+{
+ rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
+}
+
+static inline void rb_set_parent_color(struct rb_node *rb,
+ struct rb_node *p, int color)
+{
+ rb->__rb_parent_color = (unsigned long)p | color;
+}
+
+static inline struct rb_node *rb_red_parent(struct rb_node *red)
+{
+ return (struct rb_node *)red->__rb_parent_color;
+}
+
+static inline void
+__rb_change_child(struct rb_node *old, struct rb_node *new,
+ struct rb_node *parent, struct rb_root *root)
+{
+ if (parent) {
+ if (parent->rb_left == old)
+ parent->rb_left = new;
+ else
+ parent->rb_right = new;
+ } else
+ root->rb_node = new;
+}
+
+/*
+ * 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);
+}
+
+void rb_insert_color(struct rb_node *node, struct rb_root *root)
+{
+ 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);
+ 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);
+ 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);
+ 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);
+ break;
+ }
+ }
+}
+
+static void __rb_erase_color(struct rb_node *parent, struct rb_root *root)
+{
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ break;
+ }
+ }
+}
+
+void rb_erase(struct rb_node *node, struct rb_root *root)
+{
+ struct rb_node *child = node->rb_right, *tmp = node->rb_left;
+ struct rb_node *parent, *rebalance;
+ unsigned long pc;
+
+ if (!tmp) {
+ /*
+ * Case 1: node to erase has no more than 1 child (easy!)
+ *
+ * Note that if there is one child it must be red due to 5)
+ * and node must be black due to 4). We adjust colors locally
+ * so as to bypass __rb_erase_color() later on.
+ */
+ pc = node->__rb_parent_color;
+ parent = __rb_parent(pc);
+ __rb_change_child(node, child, parent, root);
+ if (child) {
+ child->__rb_parent_color = pc;
+ rebalance = NULL;
+ } else
+ rebalance = __rb_is_black(pc) ? parent : NULL;
+ } 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;
+ } else {
+ struct rb_node *successor = child, *child2;
+ tmp = child->rb_left;
+ if (!tmp) {
+ /*
+ * Case 2: node's successor is its right child
+ *
+ * (n) (s)
+ * / \ / \
+ * (x) (s) -> (x) (c)
+ * \
+ * (c)
+ */
+ parent = child;
+ child2 = child->rb_right;
+ } else {
+ /*
+ * Case 3: node's successor is leftmost under
+ * node's right child subtree
+ *
+ * (n) (s)
+ * / \ / \
+ * (x) (y) -> (x) (y)
+ * / /
+ * (p) (p)
+ * / /
+ * (s) (c)
+ * \
+ * (c)
+ */
+ do {
+ parent = successor;
+ successor = tmp;
+ tmp = tmp->rb_left;
+ } while (tmp);
+ parent->rb_left = child2 = successor->rb_right;
+ successor->rb_right = child;
+ rb_set_parent(child, successor);
+ }
+
+ successor->rb_left = tmp = node->rb_left;
+ rb_set_parent(tmp, successor);
+
+ pc = node->__rb_parent_color;
+ tmp = __rb_parent(pc);
+ __rb_change_child(node, successor, tmp, root);
+ if (child2) {
+ successor->__rb_parent_color = pc;
+ rb_set_parent_color(child2, parent, RB_BLACK);
+ rebalance = NULL;
+ } else {
+ unsigned long pc2 = successor->__rb_parent_color;
+ successor->__rb_parent_color = pc;
+ rebalance = __rb_is_black(pc2) ? parent : NULL;
+ }
+ }
+
+ if (rebalance)
+ __rb_erase_color(rebalance, root);
+}
+
+/*
+ * 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;
+}
+
+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;
+}
+
+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;
+}
+
+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;
+}
+
+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;
+}
projects / xen.git / commitdiff