Import utility files

* Makefrag.am (libkernel_a_SOURCES): Add kern/list.h, kern/rbtree.c,
kern/rbtree.h and kern/rbtree_i.h.
* kern/list.h: New file.
* kern/rbtree.c: Likewise.
* kern/rbtree.h: Likewise.
* kern/rbtree_i.h: Likewise.
* kern/macro_help.h (MACRO_BEGIN): Use GNU C compound statement
enclosed in parentheses.
(MACRO_END): Likewise.

6 files changed, 1310 insertions, 2 deletions

diff --git a/Makefrag.am b/Makefrag.am
index a80cd24b..07b64997 100644
--- a/Makefrag.am
+++ b/Makefrag.am
@@ -154,6 +154,7 @@ libkernel_a_SOURCES += \
 	kern/kalloc.c \
 	kern/kalloc.h \
 	kern/kern_types.h \
+	kern/list.h \
 	kern/lock.c \
 	kern/lock.h \
 	kern/lock_mon.c \
@@ -175,6 +176,9 @@ libkernel_a_SOURCES += \
 	kern/profile.c \
 	kern/queue.c \
 	kern/queue.h \
+	kern/rbtree.c \
+	kern/rbtree.h \
+	kern/rbtree_i.h \
 	kern/refcount.h \
 	kern/sched.h \
 	kern/sched_prim.c \
diff --git a/kern/list.h b/kern/list.h
new file mode 100644
index 00000000..de7d1158
--- /dev/null
+++ b/kern/list.h
@@ -0,0 +1,349 @@
+/*
+ * Copyright (c) 2009, 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.
+ */
+
+#ifndef _KERN_LIST_H
+#define _KERN_LIST_H
+
+#include <stddef.h>
+#include <sys/types.h>
+
+#define structof(ptr, type, member) \
+    ((type *)((char *)ptr - offsetof(type, member)))
+
+/*
+ * Structure used as both head and node.
+ *
+ * This implementation relies on using the same type for both heads and nodes.
+ *
+ * It is recommended to encode the use of struct list variables in their names,
+ * e.g. struct list free_list or struct list free_objects is a good hint for a
+ * list of free objects. A declaration like struct list free_node clearly
+ * indicates it is used as part of a node in the free list.
+ */
+struct list {
+    struct list *prev;
+    struct list *next;
+};
+
+/*
+ * Static list initializer.
+ */
+#define LIST_INITIALIZER(list) { &(list), &(list) }
+
+/*
+ * Initialize a list.
+ */
+static inline void list_init(struct list *list)
+{
+    list->prev = list;
+    list->next = list;
+}
+
+/*
+ * Initialize a list node.
+ *
+ * An entry is in no list when its node members point to NULL.
+ */
+static inline void list_node_init(struct list *node)
+{
+    node->prev = NULL;
+    node->next = NULL;
+}
+
+/*
+ * Return true if node is in no list.
+ */
+static inline int list_node_unlinked(const struct list *node)
+{
+    return node->prev == NULL;
+}
+
+/*
+ * Macro that evaluates to the address of the structure containing the
+ * given node based on the given type and member.
+ */
+#define list_entry(node, type, member) structof(node, type, member)
+
+/*
+ * Return the first node of a list.
+ */
+static inline struct list * list_first(const struct list *list)
+{
+    return list->next;
+}
+
+/*
+ * Return the last node of a list.
+ */
+static inline struct list * list_last(const struct list *list)
+{
+    return list->prev;
+}
+
+/*
+ * Return the node next to the given node.
+ */
+static inline struct list * list_next(const struct list *node)
+{
+    return node->next;
+}
+
+/*
+ * Return the node previous to the given node.
+ */
+static inline struct list * list_prev(const struct list *node)
+{
+    return node->prev;
+}
+
+/*
+ * Get the first entry of a list.
+ */
+#define list_first_entry(list, type, member) \
+    list_entry(list_first(list), type, member)
+
+/*
+ * Get the last entry of a list.
+ */
+#define list_last_entry(list, type, member) \
+    list_entry(list_last(list), type, member)
+
+/*
+ * Return true if node is after the last or before the first node of the list.
+ */
+static inline int list_end(const struct list *list, const struct list *node)
+{
+    return list == node;
+}
+
+/*
+ * Return true if list is empty.
+ */
+static inline int list_empty(const struct list *list)
+{
+    return list == list->next;
+}
+
+/*
+ * Return true if list contains exactly one node.
+ */
+static inline int list_singular(const struct list *list)
+{
+    return (list != list->next) && (list->next == list->prev);
+}
+
+/*
+ * Split list2 by moving its nodes up to (but not including) the given
+ * node into list1 (which can be in a stale state).
+ *
+ * If list2 is empty, or node is list2 or list2->next, nothing is done.
+ */
+static inline void list_split(struct list *list1, struct list *list2,
+                              struct list *node)
+{
+    if (list_empty(list2) || (list2->next == node) || list_end(list2, node))
+        return;
+
+    list1->next = list2->next;
+    list1->next->prev = list1;
+
+    list1->prev = node->prev;
+    node->prev->next = list1;
+
+    list2->next = node;
+    node->prev = list2;
+}
+
+/*
+ * Append the nodes of list2 at the end of list1.
+ *
+ * After completion, list2 is stale.
+ */
+static inline void list_concat(struct list *list1, const struct list *list2)
+{
+    struct list *last1, *first2, *last2;
+
+    if (list_empty(list2))
+        return;
+
+    last1 = list1->prev;
+    first2 = list2->next;
+    last2 = list2->prev;
+
+    last1->next = first2;
+    first2->prev = last1;
+
+    last2->next = list1;
+    list1->prev = last2;
+}
+
+/*
+ * Set the new head of a list.
+ *
+ * This function is an optimized version of :
+ * list_init(&new_list);
+ * list_concat(&new_list, &old_list);
+ *
+ * After completion, old_head is stale.
+ */
+static inline void list_set_head(struct list *new_head,
+                                 const struct list *old_head)
+{
+    if (list_empty(old_head)) {
+        list_init(new_head);
+        return;
+    }
+
+    *new_head = *old_head;
+    new_head->next->prev = new_head;
+    new_head->prev->next = new_head;
+}
+
+/*
+ * Add a node between two nodes.
+ */
+static inline void list_add(struct list *prev, struct list *next,
+                            struct list *node)
+{
+    next->prev = node;
+    node->next = next;
+
+    prev->next = node;
+    node->prev = prev;
+}
+
+/*
+ * Insert a node at the head of a list.
+ */
+static inline void list_insert(struct list *list, struct list *node)
+{
+    list_add(list, list->next, node);
+}
+
+/*
+ * Insert a node at the tail of a list.
+ */
+static inline void list_insert_tail(struct list *list, struct list *node)
+{
+    list_add(list->prev, list, node);
+}
+
+/*
+ * Insert a node before another node.
+ */
+static inline void list_insert_before(struct list *next, struct list *node)
+{
+    list_add(next->prev, next, node);
+}
+
+/*
+ * Insert a node after another node.
+ */
+static inline void list_insert_after(struct list *prev, struct list *node)
+{
+    list_add(prev, prev->next, node);
+}
+
+/*
+ * Remove a node from a list.
+ *
+ * After completion, the node is stale.
+ */
+static inline void list_remove(struct list *node)
+{
+    node->prev->next = node->next;
+    node->next->prev = node->prev;
+}
+
+/*
+ * Forge a loop to process all nodes of a list.
+ *
+ * The node must not be altered during the loop.
+ */
+#define list_for_each(list, node)   \
+for (node = list_first(list);       \
+     !list_end(list, node);         \
+     node = list_next(node))
+
+/*
+ * Forge a loop to process all nodes of a list.
+ */
+#define list_for_each_safe(list, node, tmp)             \
+for (node = list_first(list), tmp = list_next(node);    \
+     !list_end(list, node);                             \
+     node = tmp, tmp = list_next(node))
+
+/*
+ * Version of list_for_each() that processes nodes backward.
+ */
+#define list_for_each_reverse(list, node)   \
+for (node = list_last(list);                \
+     !list_end(list, node);                 \
+     node = list_prev(node))
+
+/*
+ * Version of list_for_each_safe() that processes nodes backward.
+ */
+#define list_for_each_reverse_safe(list, node, tmp) \
+for (node = list_last(list), tmp = list_prev(node); \
+     !list_end(list, node);                         \
+     node = tmp, tmp = list_prev(node))
+
+/*
+ * Forge a loop to process all entries of a list.
+ *
+ * The entry node must not be altered during the loop.
+ */
+#define list_for_each_entry(list, entry, member)                    \
+for (entry = list_entry(list_first(list), typeof(*entry), member);  \
+     !list_end(list, &entry->member);                               \
+     entry = list_entry(list_next(&entry->member), typeof(*entry),  \
+                        member))
+
+/*
+ * Forge a loop to process all entries of a list.
+ */
+#define list_for_each_entry_safe(list, entry, tmp, member)          \
+for (entry = list_entry(list_first(list), typeof(*entry), member),  \
+       tmp = list_entry(list_next(&entry->member), typeof(*entry),  \
+                        member);                                    \
+     !list_end(list, &entry->member);                               \
+     entry = tmp, tmp = list_entry(list_next(&entry->member),       \
+                                   typeof(*entry), member))
+
+/*
+ * Version of list_for_each_entry() that processes entries backward.
+ */
+#define list_for_each_entry_reverse(list, entry, member)            \
+for (entry = list_entry(list_last(list), typeof(*entry), member);   \
+     !list_end(list, &entry->member);                               \
+     entry = list_entry(list_prev(&entry->member), typeof(*entry),  \
+                        member))
+
+/*
+ * Version of list_for_each_entry_safe() that processes entries backward.
+ */
+#define list_for_each_entry_reverse_safe(list, entry, tmp, member)  \
+for (entry = list_entry(list_last(list), typeof(*entry), member),   \
+       tmp = list_entry(list_prev(&entry->member), typeof(*entry),  \
+                        member);                                    \
+     !list_end(list, &entry->member);                               \
+     entry = tmp, tmp = list_entry(list_prev(&entry->member),       \
+                                   typeof(*entry), member))
+
+#endif /* _KERN_LIST_H */
diff --git a/kern/macro_help.h b/kern/macro_help.h
index e13b01d9..a3d156b7 100644
--- a/kern/macro_help.h
+++ b/kern/macro_help.h
@@ -45,8 +45,8 @@ boolean_t	ALWAYS;
 #define		ALWAYS		TRUE
 #endif	/* lint */
 
-#define		MACRO_BEGIN	do {
-#define		MACRO_END	} while (NEVER)
+#define		MACRO_BEGIN	({
+#define		MACRO_END	})
 
 #define		MACRO_RETURN	if (ALWAYS) return
 
diff --git a/kern/rbtree.c b/kern/rbtree.c
new file mode 100644
index 00000000..1c04c5c1
--- /dev/null
+++ b/kern/rbtree.c
@@ -0,0 +1,478 @@
+/*
+ * 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);
+}
diff --git a/kern/rbtree.h b/kern/rbtree.h
new file mode 100644
index 00000000..b6d62bfe
--- /dev/null
+++ b/kern/rbtree.h
@@ -0,0 +1,298 @@
+/*
+ * Copyright (c) 2010, 2011 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.
+ */
+
+#ifndef _KERN_RBTREE_H
+#define _KERN_RBTREE_H
+
+#include <stddef.h>
+#include <kern/assert.h>
+#include <kern/macro_help.h>
+#include <kern/rbtree.h>
+#include <sys/types.h>
+
+#define structof(ptr, type, member) \
+    ((type *)((char *)ptr - offsetof(type, member)))
+
+/*
+ * Indexes of the left and right nodes in the children array of a node.
+ */
+#define RBTREE_LEFT     0
+#define RBTREE_RIGHT    1
+
+/*
+ * Red-black node.
+ */
+struct rbtree_node;
+
+/*
+ * Red-black tree.
+ */
+struct rbtree;
+
+/*
+ * Static tree initializer.
+ */
+#define RBTREE_INITIALIZER { NULL }
+
+#include "rbtree_i.h"
+
+/*
+ * Initialize a tree.
+ */
+static inline void rbtree_init(struct rbtree *tree)
+{
+    tree->root = NULL;
+}
+
+/*
+ * Initialize a node.
+ *
+ * A node is in no tree when its parent points to itself.
+ */
+static inline void rbtree_node_init(struct rbtree_node *node)
+{
+    assert(rbtree_check_alignment(node));
+
+    node->parent = (unsigned long)node | RBTREE_COLOR_RED;
+    node->children[RBTREE_LEFT] = NULL;
+    node->children[RBTREE_RIGHT] = NULL;
+}
+
+/*
+ * Return true if node is in no tree.
+ */
+static inline int rbtree_node_unlinked(const struct rbtree_node *node)
+{
+    return rbtree_parent(node) == node;
+}
+
+/*
+ * Macro that evaluates to the address of the structure containing the
+ * given node based on the given type and member.
+ */
+#define rbtree_entry(node, type, member) structof(node, type, member)
+
+/*
+ * Return true if tree is empty.
+ */
+static inline int rbtree_empty(const struct rbtree *tree)
+{
+    return tree->root == NULL;
+}
+
+/*
+ * Look up a node in a tree.
+ *
+ * Note that implementing the lookup algorithm as a macro gives two benefits:
+ * First, it avoids the overhead of a callback function. Next, the type of the
+ * cmp_fn parameter isn't rigid. The only guarantee offered by this
+ * implementation is that the key parameter is the first parameter given to
+ * cmp_fn. This way, users can pass only the value they need for comparison
+ * instead of e.g. allocating a full structure on the stack.
+ *
+ * See rbtree_insert().
+ */
+#define rbtree_lookup(tree, key, cmp_fn)        \
+MACRO_BEGIN                                     \
+    struct rbtree_node *cur;                    \
+    int diff;                                   \
+                                                \
+    cur = (tree)->root;                         \
+                                                \
+    while (cur != NULL) {                       \
+        diff = cmp_fn(key, cur);                \
+                                                \
+        if (diff == 0)                          \
+            break;                              \
+                                                \
+        cur = cur->children[rbtree_d2i(diff)];  \
+    }                                           \
+                                                \
+    cur;                                        \
+MACRO_END
+
+/*
+ * Look up a node or one of its nearest nodes in a tree.
+ *
+ * This macro essentially acts as rbtree_lookup() but if no entry matched
+ * the key, an additional step is performed to obtain the next or previous
+ * node, depending on the direction (left or right).
+ *
+ * The constraints that apply to the key parameter are the same as for
+ * rbtree_lookup().
+ */
+#define rbtree_lookup_nearest(tree, key, cmp_fn, dir)   \
+MACRO_BEGIN                                             \
+    struct rbtree_node *cur, *prev;                     \
+    int diff, index;                                    \
+                                                        \
+    prev = NULL;                                        \
+    index = -1;                                         \
+    cur = (tree)->root;                                 \
+                                                        \
+    while (cur != NULL) {                               \
+        diff = cmp_fn(key, cur);                        \
+                                                        \
+        if (diff == 0)                                  \
+            break;                                      \
+                                                        \
+        prev = cur;                                     \
+        index = rbtree_d2i(diff);                       \
+        cur = cur->children[index];                     \
+    }                                                   \
+                                                        \
+    if (cur == NULL)                                    \
+        cur = rbtree_nearest(prev, index, dir);         \
+                                                        \
+    cur;                                                \
+MACRO_END
+
+/*
+ * Insert a node in a tree.
+ *
+ * This macro performs a standard lookup to obtain the insertion point of
+ * the given node in the tree (it is assumed that the inserted node never
+ * compares equal to any other entry in the tree) and links the node. It
+ * then It then checks red-black rules violations, and rebalances the tree
+ * if necessary.
+ *
+ * Unlike rbtree_lookup(), the cmp_fn parameter must compare two complete
+ * entries, so it is suggested to use two different comparison inline
+ * functions, such as myobj_cmp_lookup() and myobj_cmp_insert(). There is no
+ * guarantee about the order of the nodes given to the comparison function.
+ *
+ * See rbtree_lookup().
+ */
+#define rbtree_insert(tree, node, cmp_fn)               \
+MACRO_BEGIN                                             \
+    struct rbtree_node *cur, *prev;                     \
+    int diff, index;                                    \
+                                                        \
+    prev = NULL;                                        \
+    index = -1;                                         \
+    cur = (tree)->root;                                 \
+                                                        \
+    while (cur != NULL) {                               \
+        diff = cmp_fn(node, cur);                       \
+        assert(diff != 0);                              \
+        prev = cur;                                     \
+        index = rbtree_d2i(diff);                       \
+        cur = cur->children[index];                     \
+    }                                                   \
+                                                        \
+    rbtree_insert_rebalance(tree, prev, index, node);   \
+MACRO_END
+
+/*
+ * Look up a node/slot pair in a tree.
+ *
+ * This macro essentially acts as rbtree_lookup() but in addition to a node,
+ * it also returns a slot, which identifies an insertion point in the tree.
+ * If the returned node is null, the slot can be used by rbtree_insert_slot()
+ * to insert without the overhead of an additional lookup. The slot is a
+ * simple unsigned long integer.
+ *
+ * The constraints that apply to the key parameter are the same as for
+ * rbtree_lookup().
+ */
+#define rbtree_lookup_slot(tree, key, cmp_fn, slot) \
+MACRO_BEGIN                                         \
+    struct rbtree_node *cur, *prev;                 \
+    int diff, index;                                \
+                                                    \
+    prev = NULL;                                    \
+    index = 0;                                      \
+    cur = (tree)->root;                             \
+                                                    \
+    while (cur != NULL) {                           \
+        diff = cmp_fn(key, cur);                    \
+                                                    \
+        if (diff == 0)                              \
+            break;                                  \
+                                                    \
+        prev = cur;                                 \
+        index = rbtree_d2i(diff);                   \
+        cur = cur->children[index];                 \
+    }                                               \
+                                                    \
+    (slot) = rbtree_slot(prev, index);              \
+    cur;                                            \
+MACRO_END
+
+/*
+ * Insert a node at an insertion point in a tree.
+ *
+ * This macro essentially acts as rbtree_insert() except that it doesn't
+ * obtain the insertion point with a standard lookup. The insertion point
+ * is obtained by calling rbtree_lookup_slot(). In addition, the new node
+ * must not compare equal to an existing node in the tree (i.e. the slot
+ * must denote a null node).
+ */
+#define rbtree_insert_slot(tree, slot, node)            \
+MACRO_BEGIN                                             \
+    struct rbtree_node *parent;                         \
+    int index;                                          \
+                                                        \
+    parent = rbtree_slot_parent(slot);                  \
+    index = rbtree_slot_index(slot);                    \
+    rbtree_insert_rebalance(tree, parent, index, node); \
+MACRO_END
+
+/*
+ * Remove a node from a tree.
+ *
+ * After completion, the node is stale.
+ */
+void rbtree_remove(struct rbtree *tree, struct rbtree_node *node);
+
+/*
+ * Return the first node of a tree.
+ */
+#define rbtree_first(tree) rbtree_firstlast(tree, RBTREE_LEFT)
+
+/*
+ * Return the last node of a tree.
+ */
+#define rbtree_last(tree) rbtree_firstlast(tree, RBTREE_RIGHT)
+
+/*
+ * Return the node previous to the given node.
+ */
+#define rbtree_prev(node) rbtree_walk(node, RBTREE_LEFT)
+
+/*
+ * Return the node next to the given node.
+ */
+#define rbtree_next(node) rbtree_walk(node, RBTREE_RIGHT)
+
+/*
+ * Forge a loop to process all nodes of a tree, removing them when visited.
+ *
+ * This macro can only be used to destroy a tree, so that the resources used
+ * by the entries can be released by the user. It basically removes all nodes
+ * without doing any color checking.
+ *
+ * After completion, all nodes and the tree root member are stale.
+ */
+#define rbtree_for_each_remove(tree, node, tmp)         \
+for (node = rbtree_postwalk_deepest(tree),              \
+     tmp = rbtree_postwalk_unlink(node);                \
+     node != NULL;                                      \
+     node = tmp, tmp = rbtree_postwalk_unlink(node))    \
+
+#endif /* _KERN_RBTREE_H */
diff --git a/kern/rbtree_i.h b/kern/rbtree_i.h
new file mode 100644
index 00000000..9befc92c
--- /dev/null
+++ b/kern/rbtree_i.h
@@ -0,0 +1,179 @@
+/*
+ * Copyright (c) 2010, 2011 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.
+ */
+
+#ifndef _KERN_RBTREE_I_H
+#define _KERN_RBTREE_I_H
+
+#include <kern/assert.h>
+
+/*
+ * Red-black node structure.
+ *
+ * To reduce the number of branches and the instruction cache footprint,
+ * the left and right child pointers are stored in an array, and the symmetry
+ * of most tree operations is exploited by using left/right variables when
+ * referring to children.
+ *
+ * In addition, this implementation assumes that all nodes are 4-byte aligned,
+ * so that the least significant bit of the parent member can be used to store
+ * the color of the node. This is true for all modern 32 and 64 bits
+ * architectures, as long as the nodes aren't embedded in structures with
+ * special alignment constraints such as member packing.
+ */
+struct rbtree_node {
+    unsigned long parent;
+    struct rbtree_node *children[2];
+};
+
+/*
+ * Red-black tree structure.
+ */
+struct rbtree {
+    struct rbtree_node *root;
+};
+
+/*
+ * Masks applied on the parent member of a node to obtain either the
+ * color or the parent address.
+ */
+#define RBTREE_COLOR_MASK   0x1UL
+#define RBTREE_PARENT_MASK  (~0x3UL)
+
+/*
+ * Node colors.
+ */
+#define RBTREE_COLOR_RED    0
+#define RBTREE_COLOR_BLACK  1
+
+/*
+ * Masks applied on slots to obtain either the child index or the parent
+ * address.
+ */
+#define RBTREE_SLOT_INDEX_MASK  0x1UL
+#define RBTREE_SLOT_PARENT_MASK (~RBTREE_SLOT_INDEX_MASK)
+
+/*
+ * Return true if the given pointer is suitably aligned.
+ */
+static inline int rbtree_check_alignment(const struct rbtree_node *node)
+{
+    return ((unsigned long)node & (~RBTREE_PARENT_MASK)) == 0;
+}
+
+/*
+ * Return true if the given index is a valid child index.
+ */
+static inline int rbtree_check_index(int index)
+{
+    return index == (index & 1);
+}
+
+/*
+ * Convert the result of a comparison into an index in the children array
+ * (0 or 1).
+ *
+ * This function is mostly used when looking up a node.
+ */
+static inline int rbtree_d2i(int diff)
+{
+    return !(diff <= 0);
+}
+
+/*
+ * Return the parent of a node.
+ */
+static inline struct rbtree_node * rbtree_parent(const struct rbtree_node *node)
+{
+    return (struct rbtree_node *)(node->parent & RBTREE_PARENT_MASK);
+}
+
+/*
+ * Translate an insertion point into a slot.
+ */
+static inline unsigned long rbtree_slot(struct rbtree_node *parent, int index)
+{
+    assert(rbtree_check_alignment(parent));
+    assert(rbtree_check_index(index));
+    return (unsigned long)parent | index;
+}
+
+/*
+ * Extract the parent address from a slot.
+ */
+static inline struct rbtree_node * rbtree_slot_parent(unsigned long slot)
+{
+    return (struct rbtree_node *)(slot & RBTREE_SLOT_PARENT_MASK);
+}
+
+/*
+ * Extract the index from a slot.
+ */
+static inline int rbtree_slot_index(unsigned long slot)
+{
+    return slot & RBTREE_SLOT_INDEX_MASK;
+}
+
+/*
+ * Insert a node in a tree, rebalancing it if necessary.
+ *
+ * The index parameter is the index in the children array of the parent where
+ * the new node is to be inserted. It is ignored if the parent is null.
+ *
+ * This function is intended to be used by the rbtree_insert() macro only.
+ */
+void rbtree_insert_rebalance(struct rbtree *tree, struct rbtree_node *parent,
+                             int index, struct rbtree_node *node);
+
+/*
+ * Return the previous or next node relative to a location in a tree.
+ *
+ * The parent and index parameters define the location, which can be empty.
+ * The direction parameter is either RBTREE_LEFT (to obtain the previous
+ * node) or RBTREE_RIGHT (to obtain the next one).
+ */
+struct rbtree_node * rbtree_nearest(struct rbtree_node *parent, int index,
+                                    int direction);
+
+/*
+ * Return the first or last node of a tree.
+ *
+ * The direction parameter is either RBTREE_LEFT (to obtain the first node)
+ * or RBTREE_RIGHT (to obtain the last one).
+ */
+struct rbtree_node * rbtree_firstlast(const struct rbtree *tree, int direction);
+
+/*
+ * Return the node next to, or previous to the given node.
+ *
+ * The direction parameter is either RBTREE_LEFT (to obtain the previous node)
+ * or RBTREE_RIGHT (to obtain the next one).
+ */
+struct rbtree_node * rbtree_walk(struct rbtree_node *node, int direction);
+
+/*
+ * Return the left-most deepest node of a tree, which is the starting point of
+ * the postorder traversal performed by rbtree_for_each_remove().
+ */
+struct rbtree_node * rbtree_postwalk_deepest(const struct rbtree *tree);
+
+/*
+ * Unlink a node from its tree and return the next (right) node in postorder.
+ */
+struct rbtree_node * rbtree_postwalk_unlink(struct rbtree_node *node);
+
+#endif /* _KERN_RBTREE_I_H */