Merge branch 'timers-for-linus' of git://git.kernel.org/pub/scm/linux/kernel/git...

[linux-2.6.git] / lib / radix-tree.c

/*
 * Copyright (C) 2001 Momchil Velikov
 * Portions Copyright (C) 2001 Christoph Hellwig
 * Copyright (C) 2005 SGI, Christoph Lameter
 * Copyright (C) 2006 Nick Piggin
 *
 * 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, 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., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#include <linux/errno.h>
#include <linux/init.h>
#include <linux/kernel.h>
#include <linux/module.h>
#include <linux/radix-tree.h>
#include <linux/percpu.h>
#include <linux/slab.h>
#include <linux/notifier.h>
#include <linux/cpu.h>
#include <linux/string.h>
#include <linux/bitops.h>
#include <linux/rcupdate.h>


#ifdef __KERNEL__
#define RADIX_TREE_MAP_SHIFT    (CONFIG_BASE_SMALL ? 4 : 6)
#else
#define RADIX_TREE_MAP_SHIFT    3       /* For more stressful testing */
#endif

#define RADIX_TREE_MAP_SIZE     (1UL << RADIX_TREE_MAP_SHIFT)
#define RADIX_TREE_MAP_MASK     (RADIX_TREE_MAP_SIZE-1)

#define RADIX_TREE_TAG_LONGS    \
        ((RADIX_TREE_MAP_SIZE + BITS_PER_LONG - 1) / BITS_PER_LONG)

struct radix_tree_node {
        unsigned int    height;         /* Height from the bottom */
        unsigned int    count;
        struct rcu_head rcu_head;
        void __rcu      *slots[RADIX_TREE_MAP_SIZE];
        unsigned long   tags[RADIX_TREE_MAX_TAGS][RADIX_TREE_TAG_LONGS];
};

struct radix_tree_path {
        struct radix_tree_node *node;
        int offset;
};

#define RADIX_TREE_INDEX_BITS  (8 /* CHAR_BIT */ * sizeof(unsigned long))
#define RADIX_TREE_MAX_PATH (DIV_ROUND_UP(RADIX_TREE_INDEX_BITS, \
                                          RADIX_TREE_MAP_SHIFT))

/*
 * The height_to_maxindex array needs to be one deeper than the maximum
 * path as height 0 holds only 1 entry.
 */
static unsigned long height_to_maxindex[RADIX_TREE_MAX_PATH + 1] __read_mostly;

/*
 * Radix tree node cache.
 */
static struct kmem_cache *radix_tree_node_cachep;

/*
 * Per-cpu pool of preloaded nodes
 */
struct radix_tree_preload {
        int nr;
        struct radix_tree_node *nodes[RADIX_TREE_MAX_PATH];
};
static DEFINE_PER_CPU(struct radix_tree_preload, radix_tree_preloads) = { 0, };

static inline void *ptr_to_indirect(void *ptr)
{
        return (void *)((unsigned long)ptr | RADIX_TREE_INDIRECT_PTR);
}

static inline void *indirect_to_ptr(void *ptr)
{
        return (void *)((unsigned long)ptr & ~RADIX_TREE_INDIRECT_PTR);
}

static inline gfp_t root_gfp_mask(struct radix_tree_root *root)
{
        return root->gfp_mask & __GFP_BITS_MASK;
}

static inline void tag_set(struct radix_tree_node *node, unsigned int tag,
                int offset)
{
        __set_bit(offset, node->tags[tag]);
}

static inline void tag_clear(struct radix_tree_node *node, unsigned int tag,
                int offset)
{
        __clear_bit(offset, node->tags[tag]);
}

static inline int tag_get(struct radix_tree_node *node, unsigned int tag,
                int offset)
{
        return test_bit(offset, node->tags[tag]);
}

static inline void root_tag_set(struct radix_tree_root *root, unsigned int tag)
{
        root->gfp_mask |= (__force gfp_t)(1 << (tag + __GFP_BITS_SHIFT));
}

static inline void root_tag_clear(struct radix_tree_root *root, unsigned int tag)
{
        root->gfp_mask &= (__force gfp_t)~(1 << (tag + __GFP_BITS_SHIFT));
}

static inline void root_tag_clear_all(struct radix_tree_root *root)
{
        root->gfp_mask &= __GFP_BITS_MASK;
}

static inline int root_tag_get(struct radix_tree_root *root, unsigned int tag)
{
        return (__force unsigned)root->gfp_mask & (1 << (tag + __GFP_BITS_SHIFT));
}

/*
 * Returns 1 if any slot in the node has this tag set.
 * Otherwise returns 0.
 */
static inline int any_tag_set(struct radix_tree_node *node, unsigned int tag)
{
        int idx;
        for (idx = 0; idx < RADIX_TREE_TAG_LONGS; idx++) {
                if (node->tags[tag][idx])
                        return 1;
        }
        return 0;
}
/*
 * This assumes that the caller has performed appropriate preallocation, and
 * that the caller has pinned this thread of control to the current CPU.
 */
static struct radix_tree_node *
radix_tree_node_alloc(struct radix_tree_root *root)
{
        struct radix_tree_node *ret = NULL;
        gfp_t gfp_mask = root_gfp_mask(root);

        if (!(gfp_mask & __GFP_WAIT)) {
                struct radix_tree_preload *rtp;

                /*
                 * Provided the caller has preloaded here, we will always
                 * succeed in getting a node here (and never reach
                 * kmem_cache_alloc)
                 */
                rtp = &__get_cpu_var(radix_tree_preloads);
                if (rtp->nr) {
                        ret = rtp->nodes[rtp->nr - 1];
                        rtp->nodes[rtp->nr - 1] = NULL;
                        rtp->nr--;
                }
        }
        if (ret == NULL)
                ret = kmem_cache_alloc(radix_tree_node_cachep, gfp_mask);

        BUG_ON(radix_tree_is_indirect_ptr(ret));
        return ret;
}

static void radix_tree_node_rcu_free(struct rcu_head *head)
{
        struct radix_tree_node *node =
                        container_of(head, struct radix_tree_node, rcu_head);
        int i;

        /*
         * must only free zeroed nodes into the slab. radix_tree_shrink
         * can leave us with a non-NULL entry in the first slot, so clear
         * that here to make sure.
         */
        for (i = 0; i < RADIX_TREE_MAX_TAGS; i++)
                tag_clear(node, i, 0);

        node->slots[0] = NULL;
        node->count = 0;

        kmem_cache_free(radix_tree_node_cachep, node);
}

static inline void
radix_tree_node_free(struct radix_tree_node *node)
{
        call_rcu(&node->rcu_head, radix_tree_node_rcu_free);
}

/*
 * Load up this CPU's radix_tree_node buffer with sufficient objects to
 * ensure that the addition of a single element in the tree cannot fail.  On
 * success, return zero, with preemption disabled.  On error, return -ENOMEM
 * with preemption not disabled.
 *
 * To make use of this facility, the radix tree must be initialised without
 * __GFP_WAIT being passed to INIT_RADIX_TREE().
 */
int radix_tree_preload(gfp_t gfp_mask)
{
        struct radix_tree_preload *rtp;
        struct radix_tree_node *node;
        int ret = -ENOMEM;

        preempt_disable();
        rtp = &__get_cpu_var(radix_tree_preloads);
        while (rtp->nr < ARRAY_SIZE(rtp->nodes)) {
                preempt_enable();
                node = kmem_cache_alloc(radix_tree_node_cachep, gfp_mask);
                if (node == NULL)
                        goto out;
                preempt_disable();
                rtp = &__get_cpu_var(radix_tree_preloads);
                if (rtp->nr < ARRAY_SIZE(rtp->nodes))
                        rtp->nodes[rtp->nr++] = node;
                else
                        kmem_cache_free(radix_tree_node_cachep, node);
        }
        ret = 0;
out:
        return ret;
}
EXPORT_SYMBOL(radix_tree_preload);

/*
 *      Return the maximum key which can be store into a
 *      radix tree with height HEIGHT.
 */
static inline unsigned long radix_tree_maxindex(unsigned int height)
{
        return height_to_maxindex[height];
}

/*
 *      Extend a radix tree so it can store key @index.
 */
static int radix_tree_extend(struct radix_tree_root *root, unsigned long index)
{
        struct radix_tree_node *node;
        unsigned int height;
        int tag;

        /* Figure out what the height should be.  */
        height = root->height + 1;
        while (index > radix_tree_maxindex(height))
                height++;

        if (root->rnode == NULL) {
                root->height = height;
                goto out;
        }

        do {
                unsigned int newheight;
                if (!(node = radix_tree_node_alloc(root)))
                        return -ENOMEM;

                /* Increase the height.  */
                node->slots[0] = indirect_to_ptr(root->rnode);

                /* Propagate the aggregated tag info into the new root */
                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++) {
                        if (root_tag_get(root, tag))
                                tag_set(node, tag, 0);
                }

                newheight = root->height+1;
                node->height = newheight;
                node->count = 1;
                node = ptr_to_indirect(node);
                rcu_assign_pointer(root->rnode, node);
                root->height = newheight;
        } while (height > root->height);
out:
        return 0;
}

/**
 *      radix_tree_insert    -    insert into a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *      @item:          item to insert
 *
 *      Insert an item into the radix tree at position @index.
 */
int radix_tree_insert(struct radix_tree_root *root,
                        unsigned long index, void *item)
{
        struct radix_tree_node *node = NULL, *slot;
        unsigned int height, shift;
        int offset;
        int error;

        BUG_ON(radix_tree_is_indirect_ptr(item));

        /* Make sure the tree is high enough.  */
        if (index > radix_tree_maxindex(root->height)) {
                error = radix_tree_extend(root, index);
                if (error)
                        return error;
        }

        slot = indirect_to_ptr(root->rnode);

        height = root->height;
        shift = (height-1) * RADIX_TREE_MAP_SHIFT;

        offset = 0;                     /* uninitialised var warning */
        while (height > 0) {
                if (slot == NULL) {
                        /* Have to add a child node.  */
                        if (!(slot = radix_tree_node_alloc(root)))
                                return -ENOMEM;
                        slot->height = height;
                        if (node) {
                                rcu_assign_pointer(node->slots[offset], slot);
                                node->count++;
                        } else
                                rcu_assign_pointer(root->rnode, ptr_to_indirect(slot));
                }

                /* Go a level down */
                offset = (index >> shift) & RADIX_TREE_MAP_MASK;
                node = slot;
                slot = node->slots[offset];
                shift -= RADIX_TREE_MAP_SHIFT;
                height--;
        }

        if (slot != NULL)
                return -EEXIST;

        if (node) {
                node->count++;
                rcu_assign_pointer(node->slots[offset], item);
                BUG_ON(tag_get(node, 0, offset));
                BUG_ON(tag_get(node, 1, offset));
        } else {
                rcu_assign_pointer(root->rnode, item);
                BUG_ON(root_tag_get(root, 0));
                BUG_ON(root_tag_get(root, 1));
        }

        return 0;
}
EXPORT_SYMBOL(radix_tree_insert);

/*
 * is_slot == 1 : search for the slot.
 * is_slot == 0 : search for the node.
 */
static void *radix_tree_lookup_element(struct radix_tree_root *root,
                                unsigned long index, int is_slot)
{
        unsigned int height, shift;
        struct radix_tree_node *node, **slot;

        node = rcu_dereference_raw(root->rnode);
        if (node == NULL)
                return NULL;

        if (!radix_tree_is_indirect_ptr(node)) {
                if (index > 0)
                        return NULL;
                return is_slot ? (void *)&root->rnode : node;
        }
        node = indirect_to_ptr(node);

        height = node->height;
        if (index > radix_tree_maxindex(height))
                return NULL;

        shift = (height-1) * RADIX_TREE_MAP_SHIFT;

        do {
                slot = (struct radix_tree_node **)
                        (node->slots + ((index>>shift) & RADIX_TREE_MAP_MASK));
                node = rcu_dereference_raw(*slot);
                if (node == NULL)
                        return NULL;

                shift -= RADIX_TREE_MAP_SHIFT;
                height--;
        } while (height > 0);

        return is_slot ? (void *)slot : indirect_to_ptr(node);
}

/**
 *      radix_tree_lookup_slot    -    lookup a slot in a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *
 *      Returns:  the slot corresponding to the position @index in the
 *      radix tree @root. This is useful for update-if-exists operations.
 *
 *      This function can be called under rcu_read_lock iff the slot is not
 *      modified by radix_tree_replace_slot, otherwise it must be called
 *      exclusive from other writers. Any dereference of the slot must be done
 *      using radix_tree_deref_slot.
 */
void **radix_tree_lookup_slot(struct radix_tree_root *root, unsigned long index)
{
        return (void **)radix_tree_lookup_element(root, index, 1);
}
EXPORT_SYMBOL(radix_tree_lookup_slot);

/**
 *      radix_tree_lookup    -    perform lookup operation on a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *
 *      Lookup the item at the position @index in the radix tree @root.
 *
 *      This function can be called under rcu_read_lock, however the caller
 *      must manage lifetimes of leaf nodes (eg. RCU may also be used to free
 *      them safely). No RCU barriers are required to access or modify the
 *      returned item, however.
 */
void *radix_tree_lookup(struct radix_tree_root *root, unsigned long index)
{
        return radix_tree_lookup_element(root, index, 0);
}
EXPORT_SYMBOL(radix_tree_lookup);

/**
 *      radix_tree_tag_set - set a tag on a radix tree node
 *      @root:          radix tree root
 *      @index:         index key
 *      @tag:           tag index
 *
 *      Set the search tag (which must be < RADIX_TREE_MAX_TAGS)
 *      corresponding to @index in the radix tree.  From
 *      the root all the way down to the leaf node.
 *
 *      Returns the address of the tagged item.   Setting a tag on a not-present
 *      item is a bug.
 */
void *radix_tree_tag_set(struct radix_tree_root *root,
                        unsigned long index, unsigned int tag)
{
        unsigned int height, shift;
        struct radix_tree_node *slot;

        height = root->height;
        BUG_ON(index > radix_tree_maxindex(height));

        slot = indirect_to_ptr(root->rnode);
        shift = (height - 1) * RADIX_TREE_MAP_SHIFT;

        while (height > 0) {
                int offset;

                offset = (index >> shift) & RADIX_TREE_MAP_MASK;
                if (!tag_get(slot, tag, offset))
                        tag_set(slot, tag, offset);
                slot = slot->slots[offset];
                BUG_ON(slot == NULL);
                shift -= RADIX_TREE_MAP_SHIFT;
                height--;
        }

        /* set the root's tag bit */
        if (slot && !root_tag_get(root, tag))
                root_tag_set(root, tag);

        return slot;
}
EXPORT_SYMBOL(radix_tree_tag_set);

/**
 *      radix_tree_tag_clear - clear a tag on a radix tree node
 *      @root:          radix tree root
 *      @index:         index key
 *      @tag:           tag index
 *
 *      Clear the search tag (which must be < RADIX_TREE_MAX_TAGS)
 *      corresponding to @index in the radix tree.  If
 *      this causes the leaf node to have no tags set then clear the tag in the
 *      next-to-leaf node, etc.
 *
 *      Returns the address of the tagged item on success, else NULL.  ie:
 *      has the same return value and semantics as radix_tree_lookup().
 */
void *radix_tree_tag_clear(struct radix_tree_root *root,
                        unsigned long index, unsigned int tag)
{
        /*
         * The radix tree path needs to be one longer than the maximum path
         * since the "list" is null terminated.
         */
        struct radix_tree_path path[RADIX_TREE_MAX_PATH + 1], *pathp = path;
        struct radix_tree_node *slot = NULL;
        unsigned int height, shift;

        height = root->height;
        if (index > radix_tree_maxindex(height))
                goto out;

        shift = (height - 1) * RADIX_TREE_MAP_SHIFT;
        pathp->node = NULL;
        slot = indirect_to_ptr(root->rnode);

        while (height > 0) {
                int offset;

                if (slot == NULL)
                        goto out;

                offset = (index >> shift) & RADIX_TREE_MAP_MASK;
                pathp[1].offset = offset;
                pathp[1].node = slot;
                slot = slot->slots[offset];
                pathp++;
                shift -= RADIX_TREE_MAP_SHIFT;
                height--;
        }

        if (slot == NULL)
                goto out;

        while (pathp->node) {
                if (!tag_get(pathp->node, tag, pathp->offset))
                        goto out;
                tag_clear(pathp->node, tag, pathp->offset);
                if (any_tag_set(pathp->node, tag))
                        goto out;
                pathp--;
        }

        /* clear the root's tag bit */
        if (root_tag_get(root, tag))
                root_tag_clear(root, tag);

out:
        return slot;
}
EXPORT_SYMBOL(radix_tree_tag_clear);

/**
 * radix_tree_tag_get - get a tag on a radix tree node
 * @root:               radix tree root
 * @index:              index key
 * @tag:                tag index (< RADIX_TREE_MAX_TAGS)
 *
 * Return values:
 *
 *  0: tag not present or not set
 *  1: tag set
 *
 * Note that the return value of this function may not be relied on, even if
 * the RCU lock is held, unless tag modification and node deletion are excluded
 * from concurrency.
 */
int radix_tree_tag_get(struct radix_tree_root *root,
                        unsigned long index, unsigned int tag)
{
        unsigned int height, shift;
        struct radix_tree_node *node;
        int saw_unset_tag = 0;

        /* check the root's tag bit */
        if (!root_tag_get(root, tag))
                return 0;

        node = rcu_dereference_raw(root->rnode);
        if (node == NULL)
                return 0;

        if (!radix_tree_is_indirect_ptr(node))
                return (index == 0);
        node = indirect_to_ptr(node);

        height = node->height;
        if (index > radix_tree_maxindex(height))
                return 0;

        shift = (height - 1) * RADIX_TREE_MAP_SHIFT;

        for ( ; ; ) {
                int offset;

                if (node == NULL)
                        return 0;

                offset = (index >> shift) & RADIX_TREE_MAP_MASK;

                /*
                 * This is just a debug check.  Later, we can bale as soon as
                 * we see an unset tag.
                 */
                if (!tag_get(node, tag, offset))
                        saw_unset_tag = 1;
                if (height == 1)
                        return !!tag_get(node, tag, offset);
                node = rcu_dereference_raw(node->slots[offset]);
                shift -= RADIX_TREE_MAP_SHIFT;
                height--;
        }
}
EXPORT_SYMBOL(radix_tree_tag_get);

/**
 * radix_tree_range_tag_if_tagged - for each item in given range set given
 *                                 tag if item has another tag set
 * @root:               radix tree root
 * @first_indexp:       pointer to a starting index of a range to scan
 * @last_index:         last index of a range to scan
 * @nr_to_tag:          maximum number items to tag
 * @iftag:              tag index to test
 * @settag:             tag index to set if tested tag is set
 *
 * This function scans range of radix tree from first_index to last_index
 * (inclusive).  For each item in the range if iftag is set, the function sets
 * also settag. The function stops either after tagging nr_to_tag items or
 * after reaching last_index.
 *
 * The tags must be set from the leaf level only and propagated back up the
 * path to the root. We must do this so that we resolve the full path before
 * setting any tags on intermediate nodes. If we set tags as we descend, then
 * we can get to the leaf node and find that the index that has the iftag
 * set is outside the range we are scanning. This reults in dangling tags and
 * can lead to problems with later tag operations (e.g. livelocks on lookups).
 *
 * The function returns number of leaves where the tag was set and sets
 * *first_indexp to the first unscanned index.
 * WARNING! *first_indexp can wrap if last_index is ULONG_MAX. Caller must
 * be prepared to handle that.
 */
unsigned long radix_tree_range_tag_if_tagged(struct radix_tree_root *root,
                unsigned long *first_indexp, unsigned long last_index,
                unsigned long nr_to_tag,
                unsigned int iftag, unsigned int settag)
{
        unsigned int height = root->height;
        struct radix_tree_path path[height];
        struct radix_tree_path *pathp = path;
        struct radix_tree_node *slot;
        unsigned int shift;
        unsigned long tagged = 0;
        unsigned long index = *first_indexp;

        last_index = min(last_index, radix_tree_maxindex(height));
        if (index > last_index)
                return 0;
        if (!nr_to_tag)
                return 0;
        if (!root_tag_get(root, iftag)) {
                *first_indexp = last_index + 1;
                return 0;
        }
        if (height == 0) {
                *first_indexp = last_index + 1;
                root_tag_set(root, settag);
                return 1;
        }

        shift = (height - 1) * RADIX_TREE_MAP_SHIFT;
        slot = indirect_to_ptr(root->rnode);

        /*
         * we fill the path from (root->height - 2) to 0, leaving the index at
         * (root->height - 1) as a terminator. Zero the node in the terminator
         * so that we can use this to end walk loops back up the path.
         */
        path[height - 1].node = NULL;

        for (;;) {
                int offset;

                offset = (index >> shift) & RADIX_TREE_MAP_MASK;
                if (!slot->slots[offset])
                        goto next;
                if (!tag_get(slot, iftag, offset))
                        goto next;
                if (height > 1) {
                        /* Go down one level */
                        height--;
                        shift -= RADIX_TREE_MAP_SHIFT;
                        path[height - 1].node = slot;
                        path[height - 1].offset = offset;
                        slot = slot->slots[offset];
                        continue;
                }

                /* tag the leaf */
                tagged++;
                tag_set(slot, settag, offset);

                /* walk back up the path tagging interior nodes */
                pathp = &path[0];
                while (pathp->node) {
                        /* stop if we find a node with the tag already set */
                        if (tag_get(pathp->node, settag, pathp->offset))
                                break;
                        tag_set(pathp->node, settag, pathp->offset);
                        pathp++;
                }

next:
                /* Go to next item at level determined by 'shift' */
                index = ((index >> shift) + 1) << shift;
                /* Overflow can happen when last_index is ~0UL... */
                if (index > last_index || !index)
                        break;
                if (tagged >= nr_to_tag)
                        break;
                while (((index >> shift) & RADIX_TREE_MAP_MASK) == 0) {
                        /*
                         * We've fully scanned this node. Go up. Because
                         * last_index is guaranteed to be in the tree, what
                         * we do below cannot wander astray.
                         */
                        slot = path[height - 1].node;
                        height++;
                        shift += RADIX_TREE_MAP_SHIFT;
                }
        }
        /*
         * We need not to tag the root tag if there is no tag which is set with
         * settag within the range from *first_indexp to last_index.
         */
        if (tagged > 0)
                root_tag_set(root, settag);
        *first_indexp = index;

        return tagged;
}
EXPORT_SYMBOL(radix_tree_range_tag_if_tagged);


/**
 *      radix_tree_next_hole    -    find the next hole (not-present entry)
 *      @root:          tree root
 *      @index:         index key
 *      @max_scan:      maximum range to search
 *
 *      Search the set [index, min(index+max_scan-1, MAX_INDEX)] for the lowest
 *      indexed hole.
 *
 *      Returns: the index of the hole if found, otherwise returns an index
 *      outside of the set specified (in which case 'return - index >= max_scan'
 *      will be true). In rare cases of index wrap-around, 0 will be returned.
 *
 *      radix_tree_next_hole may be called under rcu_read_lock. However, like
 *      radix_tree_gang_lookup, this will not atomically search a snapshot of
 *      the tree at a single point in time. For example, if a hole is created
 *      at index 5, then subsequently a hole is created at index 10,
 *      radix_tree_next_hole covering both indexes may return 10 if called
 *      under rcu_read_lock.
 */
unsigned long radix_tree_next_hole(struct radix_tree_root *root,
                                unsigned long index, unsigned long max_scan)
{
        unsigned long i;

        for (i = 0; i < max_scan; i++) {
                if (!radix_tree_lookup(root, index))
                        break;
                index++;
                if (index == 0)
                        break;
        }

        return index;
}
EXPORT_SYMBOL(radix_tree_next_hole);

/**
 *      radix_tree_prev_hole    -    find the prev hole (not-present entry)
 *      @root:          tree root
 *      @index:         index key
 *      @max_scan:      maximum range to search
 *
 *      Search backwards in the range [max(index-max_scan+1, 0), index]
 *      for the first hole.
 *
 *      Returns: the index of the hole if found, otherwise returns an index
 *      outside of the set specified (in which case 'index - return >= max_scan'
 *      will be true). In rare cases of wrap-around, ULONG_MAX will be returned.
 *
 *      radix_tree_next_hole may be called under rcu_read_lock. However, like
 *      radix_tree_gang_lookup, this will not atomically search a snapshot of
 *      the tree at a single point in time. For example, if a hole is created
 *      at index 10, then subsequently a hole is created at index 5,
 *      radix_tree_prev_hole covering both indexes may return 5 if called under
 *      rcu_read_lock.
 */
unsigned long radix_tree_prev_hole(struct radix_tree_root *root,
                                   unsigned long index, unsigned long max_scan)
{
        unsigned long i;

        for (i = 0; i < max_scan; i++) {
                if (!radix_tree_lookup(root, index))
                        break;
                index--;
                if (index == ULONG_MAX)
                        break;
        }

        return index;
}
EXPORT_SYMBOL(radix_tree_prev_hole);

static unsigned int
__lookup(struct radix_tree_node *slot, void ***results, unsigned long index,
        unsigned int max_items, unsigned long *next_index)
{
        unsigned int nr_found = 0;
        unsigned int shift, height;
        unsigned long i;

        height = slot->height;
        if (height == 0)
                goto out;
        shift = (height-1) * RADIX_TREE_MAP_SHIFT;

        for ( ; height > 1; height--) {
                i = (index >> shift) & RADIX_TREE_MAP_MASK;
                for (;;) {
                        if (slot->slots[i] != NULL)
                                break;
                        index &= ~((1UL << shift) - 1);
                        index += 1UL << shift;
                        if (index == 0)
                                goto out;       /* 32-bit wraparound */
                        i++;
                        if (i == RADIX_TREE_MAP_SIZE)
                                goto out;
                }

                shift -= RADIX_TREE_MAP_SHIFT;
                slot = rcu_dereference_raw(slot->slots[i]);
                if (slot == NULL)
                        goto out;
        }

        /* Bottom level: grab some items */
        for (i = index & RADIX_TREE_MAP_MASK; i < RADIX_TREE_MAP_SIZE; i++) {
                index++;
                if (slot->slots[i]) {
                        results[nr_found++] = &(slot->slots[i]);
                        if (nr_found == max_items)
                                goto out;
                }
        }
out:
        *next_index = index;
        return nr_found;
}

/**
 *      radix_tree_gang_lookup - perform multiple lookup on a radix tree
 *      @root:          radix tree root
 *      @results:       where the results of the lookup are placed
 *      @first_index:   start the lookup from this key
 *      @max_items:     place up to this many items at *results
 *
 *      Performs an index-ascending scan of the tree for present items.  Places
 *      them at *@results and returns the number of items which were placed at
 *      *@results.
 *
 *      The implementation is naive.
 *
 *      Like radix_tree_lookup, radix_tree_gang_lookup may be called under
 *      rcu_read_lock. In this case, rather than the returned results being
 *      an atomic snapshot of the tree at a single point in time, the semantics
 *      of an RCU protected gang lookup are as though multiple radix_tree_lookups
 *      have been issued in individual locks, and results stored in 'results'.
 */
unsigned int
radix_tree_gang_lookup(struct radix_tree_root *root, void **results,
                        unsigned long first_index, unsigned int max_items)
{
        unsigned long max_index;
        struct radix_tree_node *node;
        unsigned long cur_index = first_index;
        unsigned int ret;

        node = rcu_dereference_raw(root->rnode);
        if (!node)
                return 0;

        if (!radix_tree_is_indirect_ptr(node)) {
                if (first_index > 0)
                        return 0;
                results[0] = node;
                return 1;
        }
        node = indirect_to_ptr(node);

        max_index = radix_tree_maxindex(node->height);

        ret = 0;
        while (ret < max_items) {
                unsigned int nr_found, slots_found, i;
                unsigned long next_index;       /* Index of next search */

                if (cur_index > max_index)
                        break;
                slots_found = __lookup(node, (void ***)results + ret, cur_index,
                                        max_items - ret, &next_index);
                nr_found = 0;
                for (i = 0; i < slots_found; i++) {
                        struct radix_tree_node *slot;
                        slot = *(((void ***)results)[ret + i]);
                        if (!slot)
                                continue;
                        results[ret + nr_found] =
                                indirect_to_ptr(rcu_dereference_raw(slot));
                        nr_found++;
                }
                ret += nr_found;
                if (next_index == 0)
                        break;
                cur_index = next_index;
        }

        return ret;
}
EXPORT_SYMBOL(radix_tree_gang_lookup);

/**
 *      radix_tree_gang_lookup_slot - perform multiple slot lookup on radix tree
 *      @root:          radix tree root
 *      @results:       where the results of the lookup are placed
 *      @first_index:   start the lookup from this key
 *      @max_items:     place up to this many items at *results
 *
 *      Performs an index-ascending scan of the tree for present items.  Places
 *      their slots at *@results and returns the number of items which were
 *      placed at *@results.
 *
 *      The implementation is naive.
 *
 *      Like radix_tree_gang_lookup as far as RCU and locking goes. Slots must
 *      be dereferenced with radix_tree_deref_slot, and if using only RCU
 *      protection, radix_tree_deref_slot may fail requiring a retry.
 */
unsigned int
radix_tree_gang_lookup_slot(struct radix_tree_root *root, void ***results,
                        unsigned long first_index, unsigned int max_items)
{
        unsigned long max_index;
        struct radix_tree_node *node;
        unsigned long cur_index = first_index;
        unsigned int ret;

        node = rcu_dereference_raw(root->rnode);
        if (!node)
                return 0;

        if (!radix_tree_is_indirect_ptr(node)) {
                if (first_index > 0)
                        return 0;
                results[0] = (void **)&root->rnode;
                return 1;
        }
        node = indirect_to_ptr(node);

        max_index = radix_tree_maxindex(node->height);

        ret = 0;
        while (ret < max_items) {
                unsigned int slots_found;
                unsigned long next_index;       /* Index of next search */

                if (cur_index > max_index)
                        break;
                slots_found = __lookup(node, results + ret, cur_index,
                                        max_items - ret, &next_index);
                ret += slots_found;
                if (next_index == 0)
                        break;
                cur_index = next_index;
        }

        return ret;
}
EXPORT_SYMBOL(radix_tree_gang_lookup_slot);

/*
 * FIXME: the two tag_get()s here should use find_next_bit() instead of
 * open-coding the search.
 */
static unsigned int
__lookup_tag(struct radix_tree_node *slot, void ***results, unsigned long index,
        unsigned int max_items, unsigned long *next_index, unsigned int tag)
{
        unsigned int nr_found = 0;
        unsigned int shift, height;

        height = slot->height;
        if (height == 0)
                goto out;
        shift = (height-1) * RADIX_TREE_MAP_SHIFT;

        while (height > 0) {
                unsigned long i = (index >> shift) & RADIX_TREE_MAP_MASK ;

                for (;;) {
                        if (tag_get(slot, tag, i))
                                break;
                        index &= ~((1UL << shift) - 1);
                        index += 1UL << shift;
                        if (index == 0)
                                goto out;       /* 32-bit wraparound */
                        i++;
                        if (i == RADIX_TREE_MAP_SIZE)
                                goto out;
                }
                height--;
                if (height == 0) {      /* Bottom level: grab some items */
                        unsigned long j = index & RADIX_TREE_MAP_MASK;

                        for ( ; j < RADIX_TREE_MAP_SIZE; j++) {
                                index++;
                                if (!tag_get(slot, tag, j))
                                        continue;
                                /*
                                 * Even though the tag was found set, we need to
                                 * recheck that we have a non-NULL node, because
                                 * if this lookup is lockless, it may have been
                                 * subsequently deleted.
                                 *
                                 * Similar care must be taken in any place that
                                 * lookup ->slots[x] without a lock (ie. can't
                                 * rely on its value remaining the same).
                                 */
                                if (slot->slots[j]) {
                                        results[nr_found++] = &(slot->slots[j]);
                                        if (nr_found == max_items)
                                                goto out;
                                }
                        }
                }
                shift -= RADIX_TREE_MAP_SHIFT;
                slot = rcu_dereference_raw(slot->slots[i]);
                if (slot == NULL)
                        break;
        }
out:
        *next_index = index;
        return nr_found;
}

/**
 *      radix_tree_gang_lookup_tag - perform multiple lookup on a radix tree
 *                                   based on a tag
 *      @root:          radix tree root
 *      @results:       where the results of the lookup are placed
 *      @first_index:   start the lookup from this key
 *      @max_items:     place up to this many items at *results
 *      @tag:           the tag index (< RADIX_TREE_MAX_TAGS)
 *
 *      Performs an index-ascending scan of the tree for present items which
 *      have the tag indexed by @tag set.  Places the items at *@results and
 *      returns the number of items which were placed at *@results.
 */
unsigned int
radix_tree_gang_lookup_tag(struct radix_tree_root *root, void **results,
                unsigned long first_index, unsigned int max_items,
                unsigned int tag)
{
        struct radix_tree_node *node;
        unsigned long max_index;
        unsigned long cur_index = first_index;
        unsigned int ret;

        /* check the root's tag bit */
        if (!root_tag_get(root, tag))
                return 0;

        node = rcu_dereference_raw(root->rnode);
        if (!node)
                return 0;

        if (!radix_tree_is_indirect_ptr(node)) {
                if (first_index > 0)
                        return 0;
                results[0] = node;
                return 1;
        }
        node = indirect_to_ptr(node);

        max_index = radix_tree_maxindex(node->height);

        ret = 0;
        while (ret < max_items) {
                unsigned int nr_found, slots_found, i;
                unsigned long next_index;       /* Index of next search */

                if (cur_index > max_index)
                        break;
                slots_found = __lookup_tag(node, (void ***)results + ret,
                                cur_index, max_items - ret, &next_index, tag);
                nr_found = 0;
                for (i = 0; i < slots_found; i++) {
                        struct radix_tree_node *slot;
                        slot = *(((void ***)results)[ret + i]);
                        if (!slot)
                                continue;
                        results[ret + nr_found] =
                                indirect_to_ptr(rcu_dereference_raw(slot));
                        nr_found++;
                }
                ret += nr_found;
                if (next_index == 0)
                        break;
                cur_index = next_index;
        }

        return ret;
}
EXPORT_SYMBOL(radix_tree_gang_lookup_tag);

/**
 *      radix_tree_gang_lookup_tag_slot - perform multiple slot lookup on a
 *                                        radix tree based on a tag
 *      @root:          radix tree root
 *      @results:       where the results of the lookup are placed
 *      @first_index:   start the lookup from this key
 *      @max_items:     place up to this many items at *results
 *      @tag:           the tag index (< RADIX_TREE_MAX_TAGS)
 *
 *      Performs an index-ascending scan of the tree for present items which
 *      have the tag indexed by @tag set.  Places the slots at *@results and
 *      returns the number of slots which were placed at *@results.
 */
unsigned int
radix_tree_gang_lookup_tag_slot(struct radix_tree_root *root, void ***results,
                unsigned long first_index, unsigned int max_items,
                unsigned int tag)
{
        struct radix_tree_node *node;
        unsigned long max_index;
        unsigned long cur_index = first_index;
        unsigned int ret;

        /* check the root's tag bit */
        if (!root_tag_get(root, tag))
                return 0;

        node = rcu_dereference_raw(root->rnode);
        if (!node)
                return 0;

        if (!radix_tree_is_indirect_ptr(node)) {
                if (first_index > 0)
                        return 0;
                results[0] = (void **)&root->rnode;
                return 1;
        }
        node = indirect_to_ptr(node);

        max_index = radix_tree_maxindex(node->height);

        ret = 0;
        while (ret < max_items) {
                unsigned int slots_found;
                unsigned long next_index;       /* Index of next search */

                if (cur_index > max_index)
                        break;
                slots_found = __lookup_tag(node, results + ret,
                                cur_index, max_items - ret, &next_index, tag);
                ret += slots_found;
                if (next_index == 0)
                        break;
                cur_index = next_index;
        }

        return ret;
}
EXPORT_SYMBOL(radix_tree_gang_lookup_tag_slot);


/**
 *      radix_tree_shrink    -    shrink height of a radix tree to minimal
 *      @root           radix tree root
 */
static inline void radix_tree_shrink(struct radix_tree_root *root)
{
        /* try to shrink tree height */
        while (root->height > 0) {
                struct radix_tree_node *to_free = root->rnode;
                void *newptr;

                BUG_ON(!radix_tree_is_indirect_ptr(to_free));
                to_free = indirect_to_ptr(to_free);

                /*
                 * The candidate node has more than one child, or its child
                 * is not at the leftmost slot, we cannot shrink.
                 */
                if (to_free->count != 1)
                        break;
                if (!to_free->slots[0])
                        break;

                /*
                 * We don't need rcu_assign_pointer(), since we are simply
                 * moving the node from one part of the tree to another: if it
                 * was safe to dereference the old pointer to it
                 * (to_free->slots[0]), it will be safe to dereference the new
                 * one (root->rnode) as far as dependent read barriers go.
                 */
                newptr = to_free->slots[0];
                if (root->height > 1)
                        newptr = ptr_to_indirect(newptr);
                root->rnode = newptr;
                root->height--;

                /*
                 * We have a dilemma here. The node's slot[0] must not be
                 * NULLed in case there are concurrent lookups expecting to
                 * find the item. However if this was a bottom-level node,
                 * then it may be subject to the slot pointer being visible
                 * to callers dereferencing it. If item corresponding to
                 * slot[0] is subsequently deleted, these callers would expect
                 * their slot to become empty sooner or later.
                 *
                 * For example, lockless pagecache will look up a slot, deref
                 * the page pointer, and if the page is 0 refcount it means it
                 * was concurrently deleted from pagecache so try the deref
                 * again. Fortunately there is already a requirement for logic
                 * to retry the entire slot lookup -- the indirect pointer
                 * problem (replacing direct root node with an indirect pointer
                 * also results in a stale slot). So tag the slot as indirect
                 * to force callers to retry.
                 */
                if (root->height == 0)
                        *((unsigned long *)&to_free->slots[0]) |=
                                                RADIX_TREE_INDIRECT_PTR;

                radix_tree_node_free(to_free);
        }
}

/**
 *      radix_tree_delete    -    delete an item from a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *
 *      Remove the item at @index from the radix tree rooted at @root.
 *
 *      Returns the address of the deleted item, or NULL if it was not present.
 */
void *radix_tree_delete(struct radix_tree_root *root, unsigned long index)
{
        /*
         * The radix tree path needs to be one longer than the maximum path
         * since the "list" is null terminated.
         */
        struct radix_tree_path path[RADIX_TREE_MAX_PATH + 1], *pathp = path;
        struct radix_tree_node *slot = NULL;
        struct radix_tree_node *to_free;
        unsigned int height, shift;
        int tag;
        int offset;

        height = root->height;
        if (index > radix_tree_maxindex(height))
                goto out;

        slot = root->rnode;
        if (height == 0) {
                root_tag_clear_all(root);
                root->rnode = NULL;
                goto out;
        }
        slot = indirect_to_ptr(slot);

        shift = (height - 1) * RADIX_TREE_MAP_SHIFT;
        pathp->node = NULL;

        do {
                if (slot == NULL)
                        goto out;

                pathp++;
                offset = (index >> shift) & RADIX_TREE_MAP_MASK;
                pathp->offset = offset;
                pathp->node = slot;
                slot = slot->slots[offset];
                shift -= RADIX_TREE_MAP_SHIFT;
                height--;
        } while (height > 0);

        if (slot == NULL)
                goto out;

        /*
         * Clear all tags associated with the just-deleted item
         */
        for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++) {
                if (tag_get(pathp->node, tag, pathp->offset))
                        radix_tree_tag_clear(root, index, tag);
        }

        to_free = NULL;
        /* Now free the nodes we do not need anymore */
        while (pathp->node) {
                pathp->node->slots[pathp->offset] = NULL;
                pathp->node->count--;
                /*
                 * Queue the node for deferred freeing after the
                 * last reference to it disappears (set NULL, above).
                 */
                if (to_free)
                        radix_tree_node_free(to_free);

                if (pathp->node->count) {
                        if (pathp->node == indirect_to_ptr(root->rnode))
                                radix_tree_shrink(root);
                        goto out;
                }

                /* Node with zero slots in use so free it */
                to_free = pathp->node;
                pathp--;

        }
        root_tag_clear_all(root);
        root->height = 0;
        root->rnode = NULL;
        if (to_free)
                radix_tree_node_free(to_free);

out:
        return slot;
}
EXPORT_SYMBOL(radix_tree_delete);

/**
 *      radix_tree_tagged - test whether any items in the tree are tagged
 *      @root:          radix tree root
 *      @tag:           tag to test
 */
int radix_tree_tagged(struct radix_tree_root *root, unsigned int tag)
{
        return root_tag_get(root, tag);
}
EXPORT_SYMBOL(radix_tree_tagged);

static void
radix_tree_node_ctor(void *node)
{
        memset(node, 0, sizeof(struct radix_tree_node));
}

static __init unsigned long __maxindex(unsigned int height)
{
        unsigned int width = height * RADIX_TREE_MAP_SHIFT;
        int shift = RADIX_TREE_INDEX_BITS - width;

        if (shift < 0)
                return ~0UL;
        if (shift >= BITS_PER_LONG)
                return 0UL;
        return ~0UL >> shift;
}

static __init void radix_tree_init_maxindex(void)
{
        unsigned int i;

        for (i = 0; i < ARRAY_SIZE(height_to_maxindex); i++)
                height_to_maxindex[i] = __maxindex(i);
}

static int radix_tree_callback(struct notifier_block *nfb,
                            unsigned long action,
                            void *hcpu)
{
       int cpu = (long)hcpu;
       struct radix_tree_preload *rtp;

       /* Free per-cpu pool of perloaded nodes */
       if (action == CPU_DEAD || action == CPU_DEAD_FROZEN) {
               rtp = &per_cpu(radix_tree_preloads, cpu);
               while (rtp->nr) {
                       kmem_cache_free(radix_tree_node_cachep,
                                       rtp->nodes[rtp->nr-1]);
                       rtp->nodes[rtp->nr-1] = NULL;
                       rtp->nr--;
               }
       }
       return NOTIFY_OK;
}

void __init radix_tree_init(void)
{
        radix_tree_node_cachep = kmem_cache_create("radix_tree_node",
                        sizeof(struct radix_tree_node), 0,
                        SLAB_PANIC | SLAB_RECLAIM_ACCOUNT,
                        radix_tree_node_ctor);
        radix_tree_init_maxindex();
        hotcpu_notifier(radix_tree_callback, 0);
}