kern/rdxtree: reintroduce the rdxtree module

5 files changed, 1156 insertions, 0 deletions

diff --git a/Makefrag.am b/Makefrag.am
index 4ac5cef1..519f40c0 100644
--- a/Makefrag.am
+++ b/Makefrag.am
@@ -40,6 +40,9 @@ x15_SOURCES +=              \
 	kern/rbtree.c       \
 	kern/rbtree.h       \
 	kern/rbtree_i.h     \
+	kern/rdxtree.c      \
+	kern/rdxtree.h      \
+	kern/rdxtree_i.h    \
 	kern/spinlock.h     \
 	kern/spinlock_i.h   \
 	kern/sprintf.c      \
diff --git a/kern/rdxtree.c b/kern/rdxtree.c
new file mode 100644
index 00000000..4bce0569
--- /dev/null
+++ b/kern/rdxtree.c
@@ -0,0 +1,889 @@
+/*
+ * Copyright (c) 2011-2017 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 3 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, see <http://www.gnu.org/licenses/>.
+ */
+
+#include <stdbool.h>
+
+#include <kern/assert.h>
+#include <kern/error.h>
+#include <kern/kmem.h>
+#include <kern/limits.h>
+#include <kern/llsync.h>
+#include <kern/macros.h>
+#include <kern/rdxtree.h>
+#include <kern/rdxtree_i.h>
+#include <kern/stddef.h>
+#include <kern/stdint.h>
+#include <kern/string.h>
+#include <kern/work.h>
+
+/*
+ * Mask applied on an entry to obtain its address.
+ */
+#define RDXTREE_ENTRY_ADDR_MASK (~0x3UL)
+
+/*
+ * Global properties used to shape radix trees.
+ */
+#define RDXTREE_RADIX       6
+#define RDXTREE_RADIX_SIZE  (1UL << RDXTREE_RADIX)
+#define RDXTREE_RADIX_MASK  (RDXTREE_RADIX_SIZE - 1)
+
+#if RDXTREE_RADIX < 6
+typedef unsigned long rdxtree_bm_t;
+#define rdxtree_ffs(x) __builtin_ffsl(x)
+#elif RDXTREE_RADIX == 6 /* RDXTREE_RADIX < 6 */
+typedef unsigned long long rdxtree_bm_t;
+#define rdxtree_ffs(x) __builtin_ffsll(x)
+#else /* RDXTREE_RADIX < 6 */
+#error "radix too high"
+#endif /* RDXTREE_RADIX < 6 */
+
+/*
+ * Allocation bitmap size in bits.
+ */
+#define RDXTREE_BM_SIZE (sizeof(rdxtree_bm_t) * CHAR_BIT)
+
+/*
+ * Empty/full allocation bitmap words.
+ */
+#define RDXTREE_BM_EMPTY    ((rdxtree_bm_t)0)
+#define RDXTREE_BM_FULL \
+    ((~(rdxtree_bm_t)0) >> (RDXTREE_BM_SIZE - RDXTREE_RADIX_SIZE))
+
+/*
+ * Radix tree node.
+ *
+ * The height of a tree is the number of nodes to traverse until stored
+ * pointers are reached. A height of 0 means the entries of a node (or the
+ * tree root) directly point to stored pointers.
+ *
+ * The index is valid if and only if the parent isn't NULL.
+ *
+ * Concerning the allocation bitmap, a bit is set when the node it denotes,
+ * or one of its children, can be used to allocate an entry. Conversely, a bit
+ * is clear when the matching node and all of its children have no free entry.
+ *
+ * In order to support safe lockless lookups, in particular during a resize,
+ * each node includes the height of its subtree, which is invariant during
+ * the entire node lifetime. Since the tree height does vary, it can't be
+ * used to determine whether the tree root is a node or a stored pointer.
+ * This implementation assumes that all nodes and stored pointers are at least
+ * 4-byte aligned, and uses the least significant bit of entries to indicate
+ * the pointer type. This bit is set for internal nodes, and clear for stored
+ * pointers so that they can be accessed from slots without conversion.
+ */
+struct rdxtree_node {
+    union {
+        struct {
+            struct rdxtree_node *parent;
+            unsigned short index;
+        };
+
+        /* Deferred destruction when unlinked */
+        struct work work;
+    };
+
+    unsigned short height;
+    unsigned short nr_entries;
+    rdxtree_bm_t alloc_bm;
+    void *entries[RDXTREE_RADIX_SIZE];
+};
+
+static struct kmem_cache rdxtree_node_cache;
+
+static inline void
+rdxtree_assert_alignment(const void *ptr)
+{
+    assert(((uintptr_t)ptr & ~RDXTREE_ENTRY_ADDR_MASK) == 0);
+    (void)ptr;
+}
+
+static inline void *
+rdxtree_entry_addr(void *entry)
+{
+    return (void *)((uintptr_t)entry & RDXTREE_ENTRY_ADDR_MASK);
+}
+
+static inline int
+rdxtree_entry_is_node(const void *entry)
+{
+    return ((uintptr_t)entry & 1) != 0;
+}
+
+static inline void *
+rdxtree_node_to_entry(struct rdxtree_node *node)
+{
+    return (void *)((uintptr_t)node | 1);
+}
+
+static void
+rdxtree_node_ctor(void *buf)
+{
+    struct rdxtree_node *node;
+
+    node = buf;
+    node->nr_entries = 0;
+    node->alloc_bm = RDXTREE_BM_FULL;
+    memset(node->entries, 0, sizeof(node->entries));
+}
+
+static int
+rdxtree_node_create(struct rdxtree_node **nodep, unsigned short height)
+{
+    struct rdxtree_node *node;
+
+    node = kmem_cache_alloc(&rdxtree_node_cache);
+
+    if (node == NULL) {
+        return ERROR_NOMEM;
+    }
+
+    rdxtree_assert_alignment(node);
+    node->parent = NULL;
+    node->height = height;
+    *nodep = node;
+    return 0;
+}
+
+static void
+rdxtree_node_destroy(struct work *work)
+{
+    struct rdxtree_node *node;
+
+    node = structof(work, struct rdxtree_node, work);
+
+    /* See rdxtree_shrink() */
+    if (node->nr_entries != 0) {
+        assert(node->nr_entries == 1);
+        assert(node->entries[0] != NULL);
+        node->entries[0] = NULL;
+        node->nr_entries = 0;
+        node->alloc_bm = RDXTREE_BM_FULL;
+    }
+
+    kmem_cache_free(&rdxtree_node_cache, node);
+}
+
+static void
+rdxtree_node_schedule_destruction(struct rdxtree_node *node)
+{
+    assert(node->parent == NULL);
+
+    work_init(&node->work, rdxtree_node_destroy);
+    llsync_defer(&node->work);
+}
+
+static inline void
+rdxtree_node_link(struct rdxtree_node *node, struct rdxtree_node *parent,
+                  unsigned short index)
+{
+    node->parent = parent;
+    node->index = index;
+}
+
+static inline void
+rdxtree_node_unlink(struct rdxtree_node *node)
+{
+    assert(node->parent != NULL);
+    node->parent = NULL;
+}
+
+static inline int
+rdxtree_node_full(struct rdxtree_node *node)
+{
+    return (node->nr_entries == ARRAY_SIZE(node->entries));
+}
+
+static inline int
+rdxtree_node_empty(struct rdxtree_node *node)
+{
+    return (node->nr_entries == 0);
+}
+
+static inline void
+rdxtree_node_insert(struct rdxtree_node *node, unsigned short index,
+                    void *entry)
+{
+    assert(index < ARRAY_SIZE(node->entries));
+    assert(node->entries[index] == NULL);
+
+    node->nr_entries++;
+    llsync_assign_ptr(node->entries[index], entry);
+}
+
+static inline void
+rdxtree_node_insert_node(struct rdxtree_node *node, unsigned short index,
+                         struct rdxtree_node *child)
+{
+    rdxtree_node_insert(node, index, rdxtree_node_to_entry(child));
+}
+
+static inline void
+rdxtree_node_remove(struct rdxtree_node *node, unsigned short index)
+{
+    assert(index < ARRAY_SIZE(node->entries));
+    assert(node->entries[index] != NULL);
+
+    node->nr_entries--;
+    llsync_assign_ptr(node->entries[index], NULL);
+}
+
+static inline void *
+rdxtree_node_find(struct rdxtree_node *node, unsigned short *indexp)
+{
+    unsigned short index;
+    void *ptr;
+
+    index = *indexp;
+
+    while (index < ARRAY_SIZE(node->entries)) {
+        ptr = rdxtree_entry_addr(llsync_read_ptr(node->entries[index]));
+
+        if (ptr != NULL) {
+            *indexp = index;
+            return ptr;
+        }
+
+        index++;
+    }
+
+    return NULL;
+}
+
+static inline void
+rdxtree_node_bm_set(struct rdxtree_node *node, unsigned short index)
+{
+    node->alloc_bm |= (rdxtree_bm_t)1 << index;
+}
+
+static inline void
+rdxtree_node_bm_clear(struct rdxtree_node *node, unsigned short index)
+{
+    node->alloc_bm &= ~((rdxtree_bm_t)1 << index);
+}
+
+static inline int
+rdxtree_node_bm_is_set(struct rdxtree_node *node, unsigned short index)
+{
+    return (node->alloc_bm & ((rdxtree_bm_t)1 << index));
+}
+
+static inline int
+rdxtree_node_bm_empty(struct rdxtree_node *node)
+{
+    return (node->alloc_bm == RDXTREE_BM_EMPTY);
+}
+
+static inline unsigned short
+rdxtree_node_bm_first(struct rdxtree_node *node)
+{
+    return rdxtree_ffs(node->alloc_bm) - 1;
+}
+
+static inline rdxtree_key_t
+rdxtree_max_key(unsigned short height)
+{
+    size_t shift;
+
+    shift = RDXTREE_RADIX * height;
+
+    if (likely(shift < (sizeof(rdxtree_key_t) * CHAR_BIT))) {
+        return ((rdxtree_key_t)1 << shift) - 1;
+    } else {
+        return ~((rdxtree_key_t)0);
+    }
+}
+
+static inline bool
+rdxtree_key_alloc_enabled(const struct rdxtree *tree)
+{
+    return (tree->flags & RDXTREE_KEY_ALLOC);
+}
+
+static void
+rdxtree_shrink(struct rdxtree *tree)
+{
+    struct rdxtree_node *node;
+    void *entry;
+
+    while (tree->height > 0) {
+        node = rdxtree_entry_addr(tree->root);
+
+        if (node->nr_entries != 1) {
+            break;
+        }
+
+        entry = node->entries[0];
+
+        if (entry == NULL) {
+            break;
+        }
+
+        tree->height--;
+
+        if (tree->height > 0) {
+            rdxtree_node_unlink(rdxtree_entry_addr(entry));
+        }
+
+        llsync_assign_ptr(tree->root, entry);
+
+        /*
+         * There is still one valid entry (the first one) in this node. It
+         * must remain valid as long as read-side references can exist so
+         * that concurrent lookups can find the rest of the tree. Therefore,
+         * this entry isn't reset before node destruction.
+         */
+        rdxtree_node_schedule_destruction(node);
+    }
+}
+
+static int
+rdxtree_grow(struct rdxtree *tree, rdxtree_key_t key)
+{
+    struct rdxtree_node *root, *node;
+    unsigned short new_height;
+    int error;
+
+    new_height = tree->height + 1;
+
+    while (key > rdxtree_max_key(new_height)) {
+        new_height++;
+    }
+
+    if (tree->root == NULL) {
+        tree->height = new_height;
+        return 0;
+    }
+
+    root = rdxtree_entry_addr(tree->root);
+
+    do {
+        error = rdxtree_node_create(&node, tree->height);
+
+        if (error) {
+            rdxtree_shrink(tree);
+            return error;
+        }
+
+        if (tree->height == 0) {
+            if (rdxtree_key_alloc_enabled(tree)) {
+                rdxtree_node_bm_clear(node, 0);
+            }
+        } else {
+            rdxtree_node_link(root, node, 0);
+
+            if (rdxtree_key_alloc_enabled(tree)
+                && rdxtree_node_bm_empty(root)) {
+                rdxtree_node_bm_clear(node, 0);
+            }
+        }
+
+        rdxtree_node_insert(node, 0, tree->root);
+        tree->height++;
+        llsync_assign_ptr(tree->root, rdxtree_node_to_entry(node));
+        root = node;
+    } while (new_height > tree->height);
+
+    return 0;
+}
+
+static void
+rdxtree_cleanup(struct rdxtree *tree, struct rdxtree_node *node)
+{
+    struct rdxtree_node *prev;
+
+    for (;;) {
+        if (likely(!rdxtree_node_empty(node))) {
+            if (unlikely(node->parent == NULL)) {
+                rdxtree_shrink(tree);
+            }
+
+            break;
+        }
+
+        if (node->parent == NULL) {
+            tree->height = 0;
+            llsync_assign_ptr(tree->root, NULL);
+            rdxtree_node_schedule_destruction(node);
+            break;
+        }
+
+        prev = node;
+        node = node->parent;
+        rdxtree_node_unlink(prev);
+        rdxtree_node_remove(node, prev->index);
+        rdxtree_node_schedule_destruction(prev);
+    }
+}
+
+static void
+rdxtree_insert_bm_clear(struct rdxtree_node *node, unsigned short index)
+{
+    for (;;) {
+        rdxtree_node_bm_clear(node, index);
+
+        if (!rdxtree_node_full(node) || (node->parent == NULL)) {
+            break;
+        }
+
+        index = node->index;
+        node = node->parent;
+    }
+}
+
+int
+rdxtree_insert_common(struct rdxtree *tree, rdxtree_key_t key,
+                      void *ptr, void ***slotp)
+{
+    struct rdxtree_node *node, *prev;
+    unsigned short height, shift;
+    unsigned short index = 0; /* GCC */
+    int error;
+
+    assert(ptr != NULL);
+    rdxtree_assert_alignment(ptr);
+
+    if (unlikely(key > rdxtree_max_key(tree->height))) {
+        error = rdxtree_grow(tree, key);
+
+        if (error) {
+            return error;
+        }
+    }
+
+    height = tree->height;
+
+    if (unlikely(height == 0)) {
+        if (tree->root != NULL) {
+            return ERROR_BUSY;
+        }
+
+        llsync_assign_ptr(tree->root, ptr);
+
+        if (slotp != NULL) {
+            *slotp = &tree->root;
+        }
+
+        return 0;
+    }
+
+    node = rdxtree_entry_addr(tree->root);
+    shift = (height - 1) * RDXTREE_RADIX;
+    prev = NULL;
+
+    do {
+        if (node == NULL) {
+            error = rdxtree_node_create(&node, height - 1);
+
+            if (error) {
+                if (prev == NULL) {
+                    tree->height = 0;
+                } else {
+                    rdxtree_cleanup(tree, prev);
+                }
+
+                return error;
+            }
+
+            if (prev == NULL) {
+                llsync_assign_ptr(tree->root, rdxtree_node_to_entry(node));
+            } else {
+                rdxtree_node_link(node, prev, index);
+                rdxtree_node_insert_node(prev, index, node);
+            }
+        }
+
+        prev = node;
+        index = (unsigned short)(key >> shift) & RDXTREE_RADIX_MASK;
+        node = rdxtree_entry_addr(prev->entries[index]);
+        shift -= RDXTREE_RADIX;
+        height--;
+    } while (height > 0);
+
+    if (unlikely(node != NULL)) {
+        return ERROR_BUSY;
+    }
+
+    rdxtree_node_insert(prev, index, ptr);
+
+    if (rdxtree_key_alloc_enabled(tree)) {
+        rdxtree_insert_bm_clear(prev, index);
+    }
+
+    if (slotp != NULL) {
+        *slotp = &prev->entries[index];
+    }
+
+    return 0;
+}
+
+int
+rdxtree_insert_alloc_common(struct rdxtree *tree, void *ptr,
+                            rdxtree_key_t *keyp, void ***slotp)
+{
+    struct rdxtree_node *node, *prev;
+    unsigned short height, shift;
+    unsigned short index = 0; /* GCC */
+    rdxtree_key_t key;
+    int error;
+
+    assert(rdxtree_key_alloc_enabled(tree));
+    assert(ptr != NULL);
+    rdxtree_assert_alignment(ptr);
+
+    height = tree->height;
+
+    if (unlikely(height == 0)) {
+        if (tree->root == NULL) {
+            llsync_assign_ptr(tree->root, ptr);
+            *keyp = 0;
+
+            if (slotp != NULL) {
+                *slotp = &tree->root;
+            }
+
+            return 0;
+        }
+
+        goto grow;
+    }
+
+    node = rdxtree_entry_addr(tree->root);
+    key = 0;
+    shift = (height - 1) * RDXTREE_RADIX;
+    prev = NULL;
+
+    do {
+        if (node == NULL) {
+            error = rdxtree_node_create(&node, height - 1);
+
+            if (error) {
+                rdxtree_cleanup(tree, prev);
+                return error;
+            }
+
+            rdxtree_node_link(node, prev, index);
+            rdxtree_node_insert_node(prev, index, node);
+        }
+
+        prev = node;
+        index = rdxtree_node_bm_first(node);
+
+        if (index == (unsigned short)-1) {
+            goto grow;
+        }
+
+        key |= (rdxtree_key_t)index << shift;
+        node = rdxtree_entry_addr(node->entries[index]);
+        shift -= RDXTREE_RADIX;
+        height--;
+    } while (height > 0);
+
+    rdxtree_node_insert(prev, index, ptr);
+    rdxtree_insert_bm_clear(prev, index);
+
+    if (slotp != NULL) {
+        *slotp = &prev->entries[index];
+    }
+
+    goto out;
+
+grow:
+    key = rdxtree_max_key(height) + 1;
+    error = rdxtree_insert_common(tree, key, ptr, slotp);
+
+    if (error) {
+        return error;
+    }
+
+out:
+    *keyp = key;
+    return 0;
+}
+
+static void
+rdxtree_remove_bm_set(struct rdxtree_node *node, unsigned short index)
+{
+    do {
+        rdxtree_node_bm_set(node, index);
+
+        if (node->parent == NULL) {
+            break;
+        }
+
+        index = node->index;
+        node = node->parent;
+    } while (!rdxtree_node_bm_is_set(node, index));
+}
+
+void *
+rdxtree_remove(struct rdxtree *tree, rdxtree_key_t key)
+{
+    struct rdxtree_node *node, *prev;
+    unsigned short height, shift, index;
+
+    height = tree->height;
+
+    if (unlikely(key > rdxtree_max_key(height))) {
+        return NULL;
+    }
+
+    node = rdxtree_entry_addr(tree->root);
+
+    if (unlikely(height == 0)) {
+        llsync_assign_ptr(tree->root, NULL);
+        return node;
+    }
+
+    shift = (height - 1) * RDXTREE_RADIX;
+
+    do {
+        if (node == NULL) {
+            return NULL;
+        }
+
+        prev = node;
+        index = (unsigned short)(key >> shift) & RDXTREE_RADIX_MASK;
+        node = rdxtree_entry_addr(node->entries[index]);
+        shift -= RDXTREE_RADIX;
+        height--;
+    } while (height > 0);
+
+    if (node == NULL) {
+        return NULL;
+    }
+
+    if (rdxtree_key_alloc_enabled(tree)) {
+        rdxtree_remove_bm_set(prev, index);
+    }
+
+    rdxtree_node_remove(prev, index);
+    rdxtree_cleanup(tree, prev);
+    return node;
+}
+
+void *
+rdxtree_lookup_common(const struct rdxtree *tree, rdxtree_key_t key,
+                      int get_slot)
+{
+    struct rdxtree_node *node, *prev;
+    unsigned short height, shift, index;
+    void *entry;
+
+    entry = llsync_read_ptr(tree->root);
+
+    if (entry == NULL) {
+        node = NULL;
+        height = 0;
+    } else {
+        node = rdxtree_entry_addr(entry);
+        height = rdxtree_entry_is_node(entry) ? node->height + 1 : 0;
+    }
+
+    if (key > rdxtree_max_key(height)) {
+        return NULL;
+    }
+
+    if (height == 0) {
+        if (node == NULL) {
+            return NULL;
+        }
+
+        return get_slot ? (void *)&tree->root : node;
+    }
+
+    shift = (height - 1) * RDXTREE_RADIX;
+
+    do {
+        if (node == NULL) {
+            return NULL;
+        }
+
+        prev = node;
+        index = (unsigned short)(key >> shift) & RDXTREE_RADIX_MASK;
+        entry = llsync_read_ptr(node->entries[index]);
+        node = rdxtree_entry_addr(entry);
+        shift -= RDXTREE_RADIX;
+        height--;
+    } while (height > 0);
+
+    if (node == NULL) {
+        return NULL;
+    }
+
+    return get_slot ? (void *)&prev->entries[index] : node;
+}
+
+void *
+rdxtree_replace_slot(void **slot, void *ptr)
+{
+    void *old;
+
+    assert(ptr != NULL);
+    rdxtree_assert_alignment(ptr);
+
+    old = *slot;
+    assert(old != NULL);
+    rdxtree_assert_alignment(old);
+    llsync_assign_ptr(*slot, ptr);
+    return old;
+}
+
+static void *
+rdxtree_walk_next(struct rdxtree *tree, struct rdxtree_iter *iter)
+{
+    struct rdxtree_node *root, *node, *prev;
+    unsigned short height, shift, index, orig_index;
+    rdxtree_key_t key;
+    void *entry;
+
+    entry = llsync_read_ptr(tree->root);
+
+    if (entry == NULL) {
+        return NULL;
+    }
+
+    if (!rdxtree_entry_is_node(entry)) {
+        if (iter->key != (rdxtree_key_t)-1) {
+            return NULL;
+        } else {
+            iter->key = 0;
+            return rdxtree_entry_addr(entry);
+        }
+    }
+
+    key = iter->key + 1;
+
+    if ((key == 0) && (iter->node != NULL)) {
+        return NULL;
+    }
+
+    root = rdxtree_entry_addr(entry);
+
+restart:
+    node = root;
+    height = root->height + 1;
+
+    if (key > rdxtree_max_key(height)) {
+        return NULL;
+    }
+
+    shift = (height - 1) * RDXTREE_RADIX;
+
+    do {
+        prev = node;
+        index = (key >> shift) & RDXTREE_RADIX_MASK;
+        orig_index = index;
+        node = rdxtree_node_find(node, &index);
+
+        if (node == NULL) {
+            shift += RDXTREE_RADIX;
+            key = ((key >> shift) + 1) << shift;
+
+            if (key == 0) {
+                return NULL;
+            }
+
+            goto restart;
+        }
+
+        if (orig_index != index) {
+            key = ((key >> shift) + (index - orig_index)) << shift;
+        }
+
+        shift -= RDXTREE_RADIX;
+        height--;
+    } while (height > 0);
+
+    iter->node = prev;
+    iter->key = key;
+    return node;
+}
+
+void *
+rdxtree_walk(struct rdxtree *tree, struct rdxtree_iter *iter)
+{
+    unsigned short index, orig_index;
+    void *ptr;
+
+    if (iter->node == NULL) {
+        return rdxtree_walk_next(tree, iter);
+    }
+
+    index = (iter->key + 1) & RDXTREE_RADIX_MASK;
+
+    if (index != 0) {
+        orig_index = index;
+        ptr = rdxtree_node_find(iter->node, &index);
+
+        if (ptr != NULL) {
+            iter->key += (index - orig_index) + 1;
+            return ptr;
+        }
+    }
+
+    return rdxtree_walk_next(tree, iter);
+}
+
+void
+rdxtree_remove_all(struct rdxtree *tree)
+{
+    struct rdxtree_node *node, *parent;
+    struct rdxtree_iter iter;
+
+    if (tree->height == 0) {
+        if (tree->root != NULL) {
+            llsync_assign_ptr(tree->root, NULL);
+        }
+
+        return;
+    }
+
+    for (;;) {
+        rdxtree_iter_init(&iter);
+        rdxtree_walk_next(tree, &iter);
+
+        if (iter.node == NULL) {
+            break;
+        }
+
+        node = iter.node;
+        parent = node->parent;
+
+        if (parent == NULL) {
+            rdxtree_init(tree, tree->flags);
+        } else {
+            if (rdxtree_key_alloc_enabled(tree)) {
+                rdxtree_remove_bm_set(parent, node->index);
+            }
+
+            rdxtree_node_remove(parent, node->index);
+            rdxtree_cleanup(tree, parent);
+            node->parent = NULL;
+        }
+
+        rdxtree_node_schedule_destruction(node);
+    }
+}
+
+void
+rdxtree_setup(void)
+{
+    kmem_cache_init(&rdxtree_node_cache, "rdxtree_node",
+                    sizeof(struct rdxtree_node), 0,
+                    rdxtree_node_ctor, 0);
+}
diff --git a/kern/rdxtree.h b/kern/rdxtree.h
new file mode 100644
index 00000000..a0d19b55
--- /dev/null
+++ b/kern/rdxtree.h
@@ -0,0 +1,199 @@
+/*
+ * Copyright (c) 2011-2017 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 3 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, see <http://www.gnu.org/licenses/>.
+ *
+ *
+ * Radix tree.
+ *
+ * In addition to the standard insertion operation, this implementation can
+ * allocate keys for the caller at insertion time. It also allows lookups to
+ * occur concurrently with updates through the use of lockless synchronization
+ * (see the llsync module).
+ */
+
+#ifndef _KERN_RDXTREE_H
+#define _KERN_RDXTREE_H
+
+#include <kern/stddef.h>
+#include <kern/stdint.h>
+
+typedef uint32_t rdxtree_key_t;
+
+/*
+ * Radix tree initialization flags.
+ */
+#define RDXTREE_KEY_ALLOC 0x1 /* Enable key allocation */
+
+/*
+ * Radix tree.
+ */
+struct rdxtree;
+
+/*
+ * Radix tree iterator.
+ */
+struct rdxtree_iter;
+
+/*
+ * Static tree initializer.
+ */
+#define RDXTREE_INITIALIZER { 0, NULL }
+
+#include <kern/rdxtree_i.h>
+
+/*
+ * Initialize a tree.
+ */
+static inline void
+rdxtree_init(struct rdxtree *tree, unsigned short flags)
+{
+    assert((flags & ~RDXTREE_KEY_ALLOC) == 0);
+
+    tree->height = 0;
+    tree->flags = flags;
+    tree->root = NULL;
+}
+
+/*
+ * Insert a pointer in a tree.
+ *
+ * The ptr parameter must not be NULL.
+ */
+static inline int
+rdxtree_insert(struct rdxtree *tree, rdxtree_key_t key, void *ptr)
+{
+    return rdxtree_insert_common(tree, key, ptr, NULL);
+}
+
+/*
+ * Insert a pointer in a tree and obtain its slot.
+ *
+ * The ptr and slotp parameters must not be NULL. If successful, the slot of
+ * the newly inserted pointer is stored at the address pointed to by the slotp
+ * parameter.
+ */
+static inline int
+rdxtree_insert_slot(struct rdxtree *tree, rdxtree_key_t key,
+                    void *ptr, void ***slotp)
+{
+    return rdxtree_insert_common(tree, key, ptr, slotp);
+}
+
+/*
+ * Insert a pointer in a tree, for which a new key is allocated.
+ *
+ * The ptr and keyp parameters must not be NULL. The newly allocated key is
+ * stored at the address pointed to by the keyp parameter.
+ */
+static inline int
+rdxtree_insert_alloc(struct rdxtree *tree, void *ptr, rdxtree_key_t *keyp)
+{
+    return rdxtree_insert_alloc_common(tree, ptr, keyp, NULL);
+}
+
+/*
+ * Insert a pointer in a tree, for which a new key is allocated, and obtain
+ * its slot.
+ *
+ * The ptr, keyp and slotp parameters must not be NULL. The newly allocated
+ * key is stored at the address pointed to by the keyp parameter while the
+ * slot of the inserted pointer is stored at the address pointed to by the
+ * slotp parameter.
+ */
+static inline int
+rdxtree_insert_alloc_slot(struct rdxtree *tree, void *ptr,
+                          rdxtree_key_t *keyp, void ***slotp)
+{
+    return rdxtree_insert_alloc_common(tree, ptr, keyp, slotp);
+}
+
+/*
+ * Remove a pointer from a tree.
+ *
+ * The matching pointer is returned if successful, NULL otherwise.
+ */
+void * rdxtree_remove(struct rdxtree *tree, rdxtree_key_t key);
+
+/*
+ * Look up a pointer in a tree.
+ *
+ * The matching pointer is returned if successful, NULL otherwise.
+ */
+static inline void *
+rdxtree_lookup(const struct rdxtree *tree, rdxtree_key_t key)
+{
+    return rdxtree_lookup_common(tree, key, 0);
+}
+
+/*
+ * Look up a slot in a tree.
+ *
+ * A slot is a pointer to a stored pointer in a tree. It can be used as
+ * a placeholder for fast replacements to avoid multiple lookups on the same
+ * key.
+ *
+ * A slot for the matching pointer is returned if successful, NULL otherwise.
+ *
+ * See rdxtree_replace_slot().
+ */
+static inline void **
+rdxtree_lookup_slot(const struct rdxtree *tree, rdxtree_key_t key)
+{
+    return rdxtree_lookup_common(tree, key, 1);
+}
+
+/*
+ * Replace a pointer in a tree.
+ *
+ * The ptr parameter must not be NULL. The previous pointer is returned.
+ *
+ * See rdxtree_lookup_slot().
+ */
+void * rdxtree_replace_slot(void **slot, void *ptr);
+
+/*
+ * Forge a loop to process all pointers of a tree.
+ *
+ * It is not safe to modify a tree from such a loop.
+ */
+#define rdxtree_for_each(tree, iter, ptr)                       \
+for (rdxtree_iter_init(iter), ptr = rdxtree_walk(tree, iter);   \
+     ptr != NULL;                                               \
+     ptr = rdxtree_walk(tree, iter))
+
+/*
+ * Return the key of the current pointer from an iterator.
+ */
+static inline rdxtree_key_t
+rdxtree_iter_key(const struct rdxtree_iter *iter)
+{
+    return iter->key;
+}
+
+/*
+ * Remove all pointers from a tree.
+ *
+ * The common way to destroy a tree and its pointers is to loop over all
+ * the pointers using rdxtree_for_each(), freeing them, then call this
+ * function.
+ */
+void rdxtree_remove_all(struct rdxtree *tree);
+
+/*
+ * Initialize the rdxtree module.
+ */
+void rdxtree_setup(void);
+
+#endif /* _KERN_RDXTREE_H */
diff --git a/kern/rdxtree_i.h b/kern/rdxtree_i.h
new file mode 100644
index 00000000..4dcf88e8
--- /dev/null
+++ b/kern/rdxtree_i.h
@@ -0,0 +1,63 @@
+/*
+ * Copyright (c) 2011-2017 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 3 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, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef _KERN_RDXTREE_I_H
+#define _KERN_RDXTREE_I_H
+
+/*
+ * Radix tree.
+ */
+struct rdxtree {
+    unsigned short height;
+    unsigned short flags;
+    void *root;
+};
+
+/*
+ * Radix tree iterator.
+ *
+ * The node member refers to the node containing the current pointer, if any.
+ * The key member refers to the current pointer, and is valid if and only if
+ * rdxtree_walk() has been called at least once on the iterator.
+ */
+struct rdxtree_iter {
+    void *node;
+    rdxtree_key_t key;
+};
+
+/*
+ * Initialize an iterator.
+ */
+static inline void
+rdxtree_iter_init(struct rdxtree_iter *iter)
+{
+    iter->node = NULL;
+    iter->key = (rdxtree_key_t)-1;
+}
+
+int rdxtree_insert_common(struct rdxtree *tree, rdxtree_key_t key,
+                          void *ptr, void ***slotp);
+
+int rdxtree_insert_alloc_common(struct rdxtree *tree, void *ptr,
+                                rdxtree_key_t *keyp, void ***slotp);
+
+void * rdxtree_lookup_common(const struct rdxtree *tree, rdxtree_key_t key,
+                             int get_slot);
+
+void * rdxtree_walk(struct rdxtree *tree, struct rdxtree_iter *iter);
+
+#endif /* _KERN_RDXTREE_I_H */
diff --git a/vm/vm_setup.c b/vm/vm_setup.c
index 092f8151..0957815f 100644
--- a/vm/vm_setup.c
+++ b/vm/vm_setup.c
@@ -17,6 +17,7 @@
 
 #include <kern/init.h>
 #include <kern/kmem.h>
+#include <kern/rdxtree.h>
 #include <kern/percpu.h>
 #include <machine/pmap.h>
 #include <vm/vm_map.h>
@@ -29,6 +30,7 @@ vm_setup(void)
     vm_page_setup();
     kmem_setup();
     vm_map_setup();
+    rdxtree_setup();
     pmap_setup();
     percpu_setup();
 }