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-rw-r--r--kern/rbtree.c478
1 files changed, 478 insertions, 0 deletions
diff --git a/kern/rbtree.c b/kern/rbtree.c
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+++ b/kern/rbtree.c
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+/*
+ * Copyright (c) 2010 Richard Braun.
+ *
+ * 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.,
+ * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+
+#include <kern/assert.h>
+#include <kern/rbtree.h>
+#include <kern/rbtree_i.h>
+#include <sys/types.h>
+
+#define unlikely(expr) __builtin_expect(!!(expr), 0)
+
+/*
+ * Return the index of a node in the children array of its parent.
+ *
+ * The parent parameter must not be null, and must be the parent of the
+ * given node.
+ */
+static inline int rbtree_index(const struct rbtree_node *node,
+ const struct rbtree_node *parent)
+{
+ assert(parent != NULL);
+ assert((node == NULL) || (rbtree_parent(node) == parent));
+
+ if (parent->children[RBTREE_LEFT] == node)
+ return RBTREE_LEFT;
+
+ assert(parent->children[RBTREE_RIGHT] == node);
+
+ return RBTREE_RIGHT;
+}
+
+/*
+ * Return the color of a node.
+ */
+static inline int rbtree_color(const struct rbtree_node *node)
+{
+ return node->parent & RBTREE_COLOR_MASK;
+}
+
+/*
+ * Return true if the node is red.
+ */
+static inline int rbtree_is_red(const struct rbtree_node *node)
+{
+ return rbtree_color(node) == RBTREE_COLOR_RED;
+}
+
+/*
+ * Return true if the node is black.
+ */
+static inline int rbtree_is_black(const struct rbtree_node *node)
+{
+ return rbtree_color(node) == RBTREE_COLOR_BLACK;
+}
+
+/*
+ * Set the parent of a node, retaining its current color.
+ */
+static inline void rbtree_set_parent(struct rbtree_node *node,
+ struct rbtree_node *parent)
+{
+ assert(rbtree_check_alignment(node));
+ assert(rbtree_check_alignment(parent));
+
+ node->parent = (unsigned long)parent | (node->parent & RBTREE_COLOR_MASK);
+}
+
+/*
+ * Set the color of a node, retaining its current parent.
+ */
+static inline void rbtree_set_color(struct rbtree_node *node, int color)
+{
+ assert((color & ~RBTREE_COLOR_MASK) == 0);
+ node->parent = (node->parent & RBTREE_PARENT_MASK) | color;
+}
+
+/*
+ * Set the color of a node to red, retaining its current parent.
+ */
+static inline void rbtree_set_red(struct rbtree_node *node)
+{
+ rbtree_set_color(node, RBTREE_COLOR_RED);
+}
+
+/*
+ * Set the color of a node to black, retaining its current parent.
+ */
+static inline void rbtree_set_black(struct rbtree_node *node)
+{
+ rbtree_set_color(node, RBTREE_COLOR_BLACK);
+}
+
+/*
+ * Perform a tree rotation, rooted at the given node.
+ *
+ * The direction parameter defines the rotation direction and is either
+ * RBTREE_LEFT or RBTREE_RIGHT.
+ */
+static void rbtree_rotate(struct rbtree *tree, struct rbtree_node *node,
+ int direction)
+{
+ struct rbtree_node *parent, *rnode;
+ int left, right;
+
+ left = direction;
+ right = 1 - left;
+ parent = rbtree_parent(node);
+ rnode = node->children[right];
+
+ node->children[right] = rnode->children[left];
+
+ if (rnode->children[left] != NULL)
+ rbtree_set_parent(rnode->children[left], node);
+
+ rnode->children[left] = node;
+ rbtree_set_parent(rnode, parent);
+
+ if (unlikely(parent == NULL))
+ tree->root = rnode;
+ else
+ parent->children[rbtree_index(node, parent)] = rnode;
+
+ rbtree_set_parent(node, rnode);
+}
+
+void rbtree_insert_rebalance(struct rbtree *tree, struct rbtree_node *parent,
+ int index, struct rbtree_node *node)
+{
+ struct rbtree_node *grand_parent, *uncle, *tmp;
+ int left, right;
+
+ assert(rbtree_check_alignment(parent));
+ assert(rbtree_check_alignment(node));
+
+ node->parent = (unsigned long)parent | RBTREE_COLOR_RED;
+ node->children[RBTREE_LEFT] = NULL;
+ node->children[RBTREE_RIGHT] = NULL;
+
+ if (unlikely(parent == NULL))
+ tree->root = node;
+ else
+ parent->children[index] = node;
+
+ for (;;) {
+ if (parent == NULL) {
+ rbtree_set_black(node);
+ break;
+ }
+
+ if (rbtree_is_black(parent))
+ break;
+
+ grand_parent = rbtree_parent(parent);
+ assert(grand_parent != NULL);
+
+ left = rbtree_index(parent, grand_parent);
+ right = 1 - left;
+
+ uncle = grand_parent->children[right];
+
+ /*
+ * Case 1: uncle is red. Flip colors and repeat at grand parent.
+ */
+ if ((uncle != NULL) && rbtree_is_red(uncle)) {
+ rbtree_set_black(uncle);
+ rbtree_set_black(parent);
+ rbtree_set_red(grand_parent);
+ node = grand_parent;
+ parent = rbtree_parent(node);
+ continue;
+ }
+
+ /*
+ * Case 2: node is the right child of its parent. Rotate left at parent
+ * to reduce to case 3.
+ */
+ if (parent->children[right] == node) {
+ rbtree_rotate(tree, parent, left);
+ tmp = node;
+ node = parent;
+ parent = tmp;
+ }
+
+ /*
+ * Case 3: node is the left child of its parent. Handle colors, rotate
+ * right at grand parent, and leave.
+ */
+ rbtree_set_black(parent);
+ rbtree_set_red(grand_parent);
+ rbtree_rotate(tree, grand_parent, right);
+ break;
+ }
+
+ assert(rbtree_is_black(tree->root));
+}
+
+void rbtree_remove(struct rbtree *tree, struct rbtree_node *node)
+{
+ struct rbtree_node *child, *parent, *brother;
+ int color, left, right;
+
+ if (node->children[RBTREE_LEFT] == NULL)
+ child = node->children[RBTREE_RIGHT];
+ else if (node->children[RBTREE_RIGHT] == NULL)
+ child = node->children[RBTREE_LEFT];
+ else {
+ struct rbtree_node *successor;
+
+ /*
+ * Two-children case: replace the node with its successor.
+ */
+
+ successor = node->children[RBTREE_RIGHT];
+
+ while (successor->children[RBTREE_LEFT] != NULL)
+ successor = successor->children[RBTREE_LEFT];
+
+ color = rbtree_color(successor);
+ child = successor->children[RBTREE_RIGHT];
+ parent = rbtree_parent(node);
+
+ if (unlikely(parent == NULL))
+ tree->root = successor;
+ else
+ parent->children[rbtree_index(node, parent)] = successor;
+
+ parent = rbtree_parent(successor);
+
+ /*
+ * Set parent directly to keep the original color.
+ */
+ successor->parent = node->parent;
+ successor->children[RBTREE_LEFT] = node->children[RBTREE_LEFT];
+ rbtree_set_parent(successor->children[RBTREE_LEFT], successor);
+
+ if (node == parent)
+ parent = successor;
+ else {
+ successor->children[RBTREE_RIGHT] = node->children[RBTREE_RIGHT];
+ rbtree_set_parent(successor->children[RBTREE_RIGHT], successor);
+ parent->children[RBTREE_LEFT] = child;
+
+ if (child != NULL)
+ rbtree_set_parent(child, parent);
+ }
+
+ goto update_color;
+ }
+
+ /*
+ * Node has at most one child.
+ */
+
+ color = rbtree_color(node);
+ parent = rbtree_parent(node);
+
+ if (child != NULL)
+ rbtree_set_parent(child, parent);
+
+ if (unlikely(parent == NULL))
+ tree->root = child;
+ else
+ parent->children[rbtree_index(node, parent)] = child;
+
+ /*
+ * The node has been removed, update the colors. The child pointer can
+ * be null, in which case it is considered a black leaf.
+ */
+update_color:
+ if (color == RBTREE_COLOR_RED)
+ return;
+
+ for (;;) {
+ if ((child != NULL) && rbtree_is_red(child)) {
+ rbtree_set_black(child);
+ break;
+ }
+
+ if (parent == NULL)
+ break;
+
+ left = rbtree_index(child, parent);
+ right = 1 - left;
+
+ brother = parent->children[right];
+
+ /*
+ * Case 1: brother is red. Recolor and rotate left at parent so that
+ * brother becomes black.
+ */
+ if (rbtree_is_red(brother)) {
+ rbtree_set_black(brother);
+ rbtree_set_red(parent);
+ rbtree_rotate(tree, parent, left);
+ brother = parent->children[right];
+ }
+
+ /*
+ * Case 2: brother has no red child. Recolor and repeat at parent.
+ */
+ if (((brother->children[RBTREE_LEFT] == NULL)
+ || rbtree_is_black(brother->children[RBTREE_LEFT]))
+ && ((brother->children[RBTREE_RIGHT] == NULL)
+ || rbtree_is_black(brother->children[RBTREE_RIGHT]))) {
+ rbtree_set_red(brother);
+ child = parent;
+ parent = rbtree_parent(child);
+ continue;
+ }
+
+ /*
+ * Case 3: brother's right child is black. Recolor and rotate right
+ * at brother to reduce to case 4.
+ */
+ if ((brother->children[right] == NULL)
+ || rbtree_is_black(brother->children[right])) {
+ rbtree_set_black(brother->children[left]);
+ rbtree_set_red(brother);
+ rbtree_rotate(tree, brother, right);
+ brother = parent->children[right];
+ }
+
+ /*
+ * Case 4: brother's left child is black. Exchange parent and brother
+ * colors (we already know brother is black), set brother's right child
+ * black, rotate left at parent and leave.
+ */
+ rbtree_set_color(brother, rbtree_color(parent));
+ rbtree_set_black(parent);
+ rbtree_set_black(brother->children[right]);
+ rbtree_rotate(tree, parent, left);
+ break;
+ }
+
+ assert((tree->root == NULL) || rbtree_is_black(tree->root));
+}
+
+struct rbtree_node * rbtree_nearest(struct rbtree_node *parent, int index,
+ int direction)
+{
+ assert(rbtree_check_index(direction));
+
+ if (parent == NULL)
+ return NULL;
+
+ assert(rbtree_check_index(index));
+
+ if (index != direction)
+ return parent;
+
+ return rbtree_walk(parent, direction);
+}
+
+struct rbtree_node * rbtree_firstlast(const struct rbtree *tree, int direction)
+{
+ struct rbtree_node *prev, *cur;
+
+ assert(rbtree_check_index(direction));
+
+ prev = NULL;
+
+ for (cur = tree->root; cur != NULL; cur = cur->children[direction])
+ prev = cur;
+
+ return prev;
+}
+
+struct rbtree_node * rbtree_walk(struct rbtree_node *node, int direction)
+{
+ int left, right;
+
+ assert(rbtree_check_index(direction));
+
+ left = direction;
+ right = 1 - left;
+
+ if (node == NULL)
+ return NULL;
+
+ if (node->children[left] != NULL) {
+ node = node->children[left];
+
+ while (node->children[right] != NULL)
+ node = node->children[right];
+ } else {
+ struct rbtree_node *parent;
+ int index;
+
+ for (;;) {
+ parent = rbtree_parent(node);
+
+ if (parent == NULL)
+ return NULL;
+
+ index = rbtree_index(node, parent);
+ node = parent;
+
+ if (index == right)
+ break;
+ }
+ }
+
+ return node;
+}
+
+/*
+ * Return the left-most deepest child node of the given node.
+ */
+static struct rbtree_node * rbtree_find_deepest(struct rbtree_node *node)
+{
+ struct rbtree_node *parent;
+
+ assert(node != NULL);
+
+ for (;;) {
+ parent = node;
+ node = node->children[RBTREE_LEFT];
+
+ if (node == NULL) {
+ node = parent->children[RBTREE_RIGHT];
+
+ if (node == NULL)
+ return parent;
+ }
+ }
+}
+
+struct rbtree_node * rbtree_postwalk_deepest(const struct rbtree *tree)
+{
+ struct rbtree_node *node;
+
+ node = tree->root;
+
+ if (node == NULL)
+ return NULL;
+
+ return rbtree_find_deepest(node);
+}
+
+struct rbtree_node * rbtree_postwalk_unlink(struct rbtree_node *node)
+{
+ struct rbtree_node *parent;
+ int index;
+
+ if (node == NULL)
+ return NULL;
+
+ assert(node->children[RBTREE_LEFT] == NULL);
+ assert(node->children[RBTREE_RIGHT] == NULL);
+
+ parent = rbtree_parent(node);
+
+ if (parent == NULL)
+ return NULL;
+
+ index = rbtree_index(node, parent);
+ parent->children[index] = NULL;
+ node = parent->children[RBTREE_RIGHT];
+
+ if (node == NULL)
+ return parent;
+
+ return rbtree_find_deepest(node);
+}