[linux.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
 * Copyright (C) 2012 Konstantin Khlebnikov
 * Copyright (C) 2016 Intel, Matthew Wilcox
 * Copyright (C) 2016 Intel, Ross Zwisler
 *
 * 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/bitmap.h>
#include <linux/bitops.h>
#include <linux/cpu.h>
#include <linux/errno.h>
#include <linux/export.h>
#include <linux/idr.h>
#include <linux/init.h>
#include <linux/kernel.h>
#include <linux/kmemleak.h>
#include <linux/percpu.h>
#include <linux/preempt.h>              /* in_interrupt() */
#include <linux/radix-tree.h>
#include <linux/rcupdate.h>
#include <linux/slab.h>
#include <linux/string.h>


/* Number of nodes in fully populated tree of given height */
static unsigned long height_to_maxnodes[RADIX_TREE_MAX_PATH + 1] __read_mostly;

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

/*
 * The radix tree is variable-height, so an insert operation not only has
 * to build the branch to its corresponding item, it also has to build the
 * branch to existing items if the size has to be increased (by
 * radix_tree_extend).
 *
 * The worst case is a zero height tree with just a single item at index 0,
 * and then inserting an item at index ULONG_MAX. This requires 2 new branches
 * of RADIX_TREE_MAX_PATH size to be created, with only the root node shared.
 * Hence:
 */
#define RADIX_TREE_PRELOAD_SIZE (RADIX_TREE_MAX_PATH * 2 - 1)

/*
 * The IDR does not have to be as high as the radix tree since it uses
 * signed integers, not unsigned longs.
 */
#define IDR_INDEX_BITS          (8 /* CHAR_BIT */ * sizeof(int) - 1)
#define IDR_MAX_PATH            (DIV_ROUND_UP(IDR_INDEX_BITS, \
                                                RADIX_TREE_MAP_SHIFT))
#define IDR_PRELOAD_SIZE        (IDR_MAX_PATH * 2 - 1)

/*
 * The IDA is even shorter since it uses a bitmap at the last level.
 */
#define IDA_INDEX_BITS          (8 * sizeof(int) - 1 - ilog2(IDA_BITMAP_BITS))
#define IDA_MAX_PATH            (DIV_ROUND_UP(IDA_INDEX_BITS, \
                                                RADIX_TREE_MAP_SHIFT))
#define IDA_PRELOAD_SIZE        (IDA_MAX_PATH * 2 - 1)

/*
 * Per-cpu pool of preloaded nodes
 */
struct radix_tree_preload {
        unsigned nr;
        /* nodes->parent points to next preallocated node */
        struct radix_tree_node *nodes;
};
static DEFINE_PER_CPU(struct radix_tree_preload, radix_tree_preloads) = { 0, };

static inline struct radix_tree_node *entry_to_node(void *ptr)
{
        return (void *)((unsigned long)ptr & ~RADIX_TREE_INTERNAL_NODE);
}

static inline void *node_to_entry(void *ptr)
{
        return (void *)((unsigned long)ptr | RADIX_TREE_INTERNAL_NODE);
}

#define RADIX_TREE_RETRY        node_to_entry(NULL)

#ifdef CONFIG_RADIX_TREE_MULTIORDER
/* Sibling slots point directly to another slot in the same node */
static inline
bool is_sibling_entry(const struct radix_tree_node *parent, void *node)
{
        void **ptr = node;
        return (parent->slots <= ptr) &&
                        (ptr < parent->slots + RADIX_TREE_MAP_SIZE);
}
#else
static inline
bool is_sibling_entry(const struct radix_tree_node *parent, void *node)
{
        return false;
}
#endif

static inline
unsigned long get_slot_offset(const struct radix_tree_node *parent, void **slot)
{
        return slot - parent->slots;
}

static unsigned int radix_tree_descend(const struct radix_tree_node *parent,
                        struct radix_tree_node **nodep, unsigned long index)
{
        unsigned int offset = (index >> parent->shift) & RADIX_TREE_MAP_MASK;
        void **entry = rcu_dereference_raw(parent->slots[offset]);

#ifdef CONFIG_RADIX_TREE_MULTIORDER
        if (radix_tree_is_internal_node(entry)) {
                if (is_sibling_entry(parent, entry)) {
                        void **sibentry = (void **) entry_to_node(entry);
                        offset = get_slot_offset(parent, sibentry);
                        entry = rcu_dereference_raw(*sibentry);
                }
        }
#endif

        *nodep = (void *)entry;
        return offset;
}

static inline gfp_t root_gfp_mask(const 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(const 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 tag)
{
        root->gfp_mask |= (__force gfp_t)(1 << (tag + ROOT_TAG_SHIFT));
}

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

static inline void root_tag_clear_all(struct radix_tree_root *root)
{
        root->gfp_mask &= (1 << ROOT_TAG_SHIFT) - 1;
}

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

static inline unsigned root_tags_get(const struct radix_tree_root *root)
{
        return (__force unsigned)root->gfp_mask >> ROOT_TAG_SHIFT;
}

static inline bool is_idr(const struct radix_tree_root *root)
{
        return !!(root->gfp_mask & ROOT_IS_IDR);
}

/*
 * Returns 1 if any slot in the node has this tag set.
 * Otherwise returns 0.
 */
static inline int any_tag_set(const struct radix_tree_node *node,
                                                        unsigned int tag)
{
        unsigned idx;
        for (idx = 0; idx < RADIX_TREE_TAG_LONGS; idx++) {
                if (node->tags[tag][idx])
                        return 1;
        }
        return 0;
}

static inline void all_tag_set(struct radix_tree_node *node, unsigned int tag)
{
        bitmap_fill(node->tags[tag], RADIX_TREE_MAP_SIZE);
}

/**
 * radix_tree_find_next_bit - find the next set bit in a memory region
 *
 * @addr: The address to base the search on
 * @size: The bitmap size in bits
 * @offset: The bitnumber to start searching at
 *
 * Unrollable variant of find_next_bit() for constant size arrays.
 * Tail bits starting from size to roundup(size, BITS_PER_LONG) must be zero.
 * Returns next bit offset, or size if nothing found.
 */
static __always_inline unsigned long
radix_tree_find_next_bit(struct radix_tree_node *node, unsigned int tag,
                         unsigned long offset)
{
        const unsigned long *addr = node->tags[tag];

        if (offset < RADIX_TREE_MAP_SIZE) {
                unsigned long tmp;

                addr += offset / BITS_PER_LONG;
                tmp = *addr >> (offset % BITS_PER_LONG);
                if (tmp)
                        return __ffs(tmp) + offset;
                offset = (offset + BITS_PER_LONG) & ~(BITS_PER_LONG - 1);
                while (offset < RADIX_TREE_MAP_SIZE) {
                        tmp = *++addr;
                        if (tmp)
                                return __ffs(tmp) + offset;
                        offset += BITS_PER_LONG;
                }
        }
        return RADIX_TREE_MAP_SIZE;
}

static unsigned int iter_offset(const struct radix_tree_iter *iter)
{
        return (iter->index >> iter_shift(iter)) & RADIX_TREE_MAP_MASK;
}

/*
 * The maximum index which can be stored in a radix tree
 */
static inline unsigned long shift_maxindex(unsigned int shift)
{
        return (RADIX_TREE_MAP_SIZE << shift) - 1;
}

static inline unsigned long node_maxindex(const struct radix_tree_node *node)
{
        return shift_maxindex(node->shift);
}

static unsigned long next_index(unsigned long index,
                                const struct radix_tree_node *node,
                                unsigned long offset)
{
        return (index & ~node_maxindex(node)) + (offset << node->shift);
}

#ifndef __KERNEL__
static void dump_node(struct radix_tree_node *node, unsigned long index)
{
        unsigned long i;

        pr_debug("radix node: %p offset %d indices %lu-%lu parent %p tags %lx %lx %lx shift %d count %d exceptional %d\n",
                node, node->offset, index, index | node_maxindex(node),
                node->parent,
                node->tags[0][0], node->tags[1][0], node->tags[2][0],
                node->shift, node->count, node->exceptional);

        for (i = 0; i < RADIX_TREE_MAP_SIZE; i++) {
                unsigned long first = index | (i << node->shift);
                unsigned long last = first | ((1UL << node->shift) - 1);
                void *entry = node->slots[i];
                if (!entry)
                        continue;
                if (entry == RADIX_TREE_RETRY) {
                        pr_debug("radix retry offset %ld indices %lu-%lu parent %p\n",
                                        i, first, last, node);
                } else if (!radix_tree_is_internal_node(entry)) {
                        pr_debug("radix entry %p offset %ld indices %lu-%lu parent %p\n",
                                        entry, i, first, last, node);
                } else if (is_sibling_entry(node, entry)) {
                        pr_debug("radix sblng %p offset %ld indices %lu-%lu parent %p val %p\n",
                                        entry, i, first, last, node,
                                        *(void **)entry_to_node(entry));
                } else {
                        dump_node(entry_to_node(entry), first);
                }
        }
}

/* For debug */
static void radix_tree_dump(struct radix_tree_root *root)
{
        pr_debug("radix root: %p rnode %p tags %x\n",
                        root, root->rnode,
                        root->gfp_mask >> ROOT_TAG_SHIFT);
        if (!radix_tree_is_internal_node(root->rnode))
                return;
        dump_node(entry_to_node(root->rnode), 0);
}

static void dump_ida_node(void *entry, unsigned long index)
{
        unsigned long i;

        if (!entry)
                return;

        if (radix_tree_is_internal_node(entry)) {
                struct radix_tree_node *node = entry_to_node(entry);

                pr_debug("ida node: %p offset %d indices %lu-%lu parent %p free %lx shift %d count %d\n",
                        node, node->offset, index * IDA_BITMAP_BITS,
                        ((index | node_maxindex(node)) + 1) *
                                IDA_BITMAP_BITS - 1,
                        node->parent, node->tags[0][0], node->shift,
                        node->count);
                for (i = 0; i < RADIX_TREE_MAP_SIZE; i++)
                        dump_ida_node(node->slots[i],
                                        index | (i << node->shift));
        } else if (radix_tree_exceptional_entry(entry)) {
                pr_debug("ida excp: %p offset %d indices %lu-%lu data %lx\n",
                                entry, (int)(index & RADIX_TREE_MAP_MASK),
                                index * IDA_BITMAP_BITS,
                                index * IDA_BITMAP_BITS + BITS_PER_LONG -
                                        RADIX_TREE_EXCEPTIONAL_SHIFT,
                                (unsigned long)entry >>
                                        RADIX_TREE_EXCEPTIONAL_SHIFT);
        } else {
                struct ida_bitmap *bitmap = entry;

                pr_debug("ida btmp: %p offset %d indices %lu-%lu data", bitmap,
                                (int)(index & RADIX_TREE_MAP_MASK),
                                index * IDA_BITMAP_BITS,
                                (index + 1) * IDA_BITMAP_BITS - 1);
                for (i = 0; i < IDA_BITMAP_LONGS; i++)
                        pr_cont(" %lx", bitmap->bitmap[i]);
                pr_cont("\n");
        }
}

static void ida_dump(struct ida *ida)
{
        struct radix_tree_root *root = &ida->ida_rt;
        pr_debug("ida: %p node %p free %d\n", ida, root->rnode,
                                root->gfp_mask >> ROOT_TAG_SHIFT);
        dump_ida_node(root->rnode, 0);
}
#endif

/*
 * 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(gfp_t gfp_mask, struct radix_tree_node *parent,
                        struct radix_tree_root *root,
                        unsigned int shift, unsigned int offset,
                        unsigned int count, unsigned int exceptional)
{
        struct radix_tree_node *ret = NULL;

        /*
         * Preload code isn't irq safe and it doesn't make sense to use
         * preloading during an interrupt anyway as all the allocations have
         * to be atomic. So just do normal allocation when in interrupt.
         */
        if (!gfpflags_allow_blocking(gfp_mask) && !in_interrupt()) {
                struct radix_tree_preload *rtp;

                /*
                 * Even if the caller has preloaded, try to allocate from the
                 * cache first for the new node to get accounted to the memory
                 * cgroup.
                 */
                ret = kmem_cache_alloc(radix_tree_node_cachep,
                                       gfp_mask | __GFP_NOWARN);
                if (ret)
                        goto out;

                /*
                 * Provided the caller has preloaded here, we will always
                 * succeed in getting a node here (and never reach
                 * kmem_cache_alloc)
                 */
                rtp = this_cpu_ptr(&radix_tree_preloads);
                if (rtp->nr) {
                        ret = rtp->nodes;
                        rtp->nodes = ret->parent;
                        rtp->nr--;
                }
                /*
                 * Update the allocation stack trace as this is more useful
                 * for debugging.
                 */
                kmemleak_update_trace(ret);
                goto out;
        }
        ret = kmem_cache_alloc(radix_tree_node_cachep, gfp_mask);
out:
        BUG_ON(radix_tree_is_internal_node(ret));
        if (ret) {
                ret->shift = shift;
                ret->offset = offset;
                ret->count = count;
                ret->exceptional = exceptional;
                ret->parent = parent;
                ret->root = root;
        }
        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);

        /*
         * Must only free zeroed nodes into the slab.  We can be left with
         * non-NULL entries by radix_tree_free_nodes, so clear the entries
         * and tags here.
         */
        memset(node->slots, 0, sizeof(node->slots));
        memset(node->tags, 0, sizeof(node->tags));
        INIT_LIST_HEAD(&node->private_list);

        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_DIRECT_RECLAIM being passed to INIT_RADIX_TREE().
 */
static int __radix_tree_preload(gfp_t gfp_mask, unsigned nr)
{
        struct radix_tree_preload *rtp;
        struct radix_tree_node *node;
        int ret = -ENOMEM;

        /*
         * Nodes preloaded by one cgroup can be be used by another cgroup, so
         * they should never be accounted to any particular memory cgroup.
         */
        gfp_mask &= ~__GFP_ACCOUNT;

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

/*
 * 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_DIRECT_RECLAIM being passed to INIT_RADIX_TREE().
 */
int radix_tree_preload(gfp_t gfp_mask)
{
        /* Warn on non-sensical use... */
        WARN_ON_ONCE(!gfpflags_allow_blocking(gfp_mask));
        return __radix_tree_preload(gfp_mask, RADIX_TREE_PRELOAD_SIZE);
}
EXPORT_SYMBOL(radix_tree_preload);

/*
 * The same as above function, except we don't guarantee preloading happens.
 * We do it, if we decide it helps. On success, return zero with preemption
 * disabled. On error, return -ENOMEM with preemption not disabled.
 */
int radix_tree_maybe_preload(gfp_t gfp_mask)
{
        if (gfpflags_allow_blocking(gfp_mask))
                return __radix_tree_preload(gfp_mask, RADIX_TREE_PRELOAD_SIZE);
        /* Preloading doesn't help anything with this gfp mask, skip it */
        preempt_disable();
        return 0;
}
EXPORT_SYMBOL(radix_tree_maybe_preload);

#ifdef CONFIG_RADIX_TREE_MULTIORDER
/*
 * Preload with enough objects to ensure that we can split a single entry
 * of order @old_order into many entries of size @new_order
 */
int radix_tree_split_preload(unsigned int old_order, unsigned int new_order,
                                                        gfp_t gfp_mask)
{
        unsigned top = 1 << (old_order % RADIX_TREE_MAP_SHIFT);
        unsigned layers = (old_order / RADIX_TREE_MAP_SHIFT) -
                                (new_order / RADIX_TREE_MAP_SHIFT);
        unsigned nr = 0;

        WARN_ON_ONCE(!gfpflags_allow_blocking(gfp_mask));
        BUG_ON(new_order >= old_order);

        while (layers--)
                nr = nr * RADIX_TREE_MAP_SIZE + 1;
        return __radix_tree_preload(gfp_mask, top * nr);
}
#endif

/*
 * The same as function above, but preload number of nodes required to insert
 * (1 << order) continuous naturally-aligned elements.
 */
int radix_tree_maybe_preload_order(gfp_t gfp_mask, int order)
{
        unsigned long nr_subtrees;
        int nr_nodes, subtree_height;

        /* Preloading doesn't help anything with this gfp mask, skip it */
        if (!gfpflags_allow_blocking(gfp_mask)) {
                preempt_disable();
                return 0;
        }

        /*
         * Calculate number and height of fully populated subtrees it takes to
         * store (1 << order) elements.
         */
        nr_subtrees = 1 << order;
        for (subtree_height = 0; nr_subtrees > RADIX_TREE_MAP_SIZE;
                        subtree_height++)
                nr_subtrees >>= RADIX_TREE_MAP_SHIFT;

        /*
         * The worst case is zero height tree with a single item at index 0 and
         * then inserting items starting at ULONG_MAX - (1 << order).
         *
         * This requires RADIX_TREE_MAX_PATH nodes to build branch from root to
         * 0-index item.
         */
        nr_nodes = RADIX_TREE_MAX_PATH;

        /* Plus branch to fully populated subtrees. */
        nr_nodes += RADIX_TREE_MAX_PATH - subtree_height;

        /* Root node is shared. */
        nr_nodes--;

        /* Plus nodes required to build subtrees. */
        nr_nodes += nr_subtrees * height_to_maxnodes[subtree_height];

        return __radix_tree_preload(gfp_mask, nr_nodes);
}

static unsigned radix_tree_load_root(const struct radix_tree_root *root,
                struct radix_tree_node **nodep, unsigned long *maxindex)
{
        struct radix_tree_node *node = rcu_dereference_raw(root->rnode);

        *nodep = node;

        if (likely(radix_tree_is_internal_node(node))) {
                node = entry_to_node(node);
                *maxindex = node_maxindex(node);
                return node->shift + RADIX_TREE_MAP_SHIFT;
        }

        *maxindex = 0;
        return 0;
}

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

        /* Figure out what the shift should be.  */
        maxshift = shift;
        while (index > shift_maxindex(maxshift))
                maxshift += RADIX_TREE_MAP_SHIFT;

        slot = root->rnode;
        if (!slot && (!is_idr(root) || root_tag_get(root, IDR_FREE)))
                goto out;

        do {
                struct radix_tree_node *node = radix_tree_node_alloc(gfp, NULL,
                                                        root, shift, 0, 1, 0);
                if (!node)
                        return -ENOMEM;

                if (is_idr(root)) {
                        all_tag_set(node, IDR_FREE);
                        if (!root_tag_get(root, IDR_FREE)) {
                                tag_clear(node, IDR_FREE, 0);
                                root_tag_set(root, IDR_FREE);
                        }
                } else {
                        /* Propagate the aggregated tag info to the new child */
                        for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++) {
                                if (root_tag_get(root, tag))
                                        tag_set(node, tag, 0);
                        }
                }

                BUG_ON(shift > BITS_PER_LONG);
                if (radix_tree_is_internal_node(slot)) {
                        entry_to_node(slot)->parent = node;
                } else if (radix_tree_exceptional_entry(slot)) {
                        /* Moving an exceptional root->rnode to a node */
                        node->exceptional = 1;
                }
                node->slots[0] = slot;
                slot = node_to_entry(node);
                rcu_assign_pointer(root->rnode, slot);
                shift += RADIX_TREE_MAP_SHIFT;
        } while (shift <= maxshift);
out:
        return maxshift + RADIX_TREE_MAP_SHIFT;
}

/**
 *      radix_tree_shrink    -    shrink radix tree to minimum height
 *      @root           radix tree root
 */
static inline bool radix_tree_shrink(struct radix_tree_root *root,
                                     radix_tree_update_node_t update_node,
                                     void *private)
{
        bool shrunk = false;

        for (;;) {
                struct radix_tree_node *node = root->rnode;
                struct radix_tree_node *child;

                if (!radix_tree_is_internal_node(node))
                        break;
                node = entry_to_node(node);

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

                if (radix_tree_is_internal_node(child))
                        entry_to_node(child)->parent = NULL;

                /*
                 * 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
                 * (node->slots[0]), it will be safe to dereference the new
                 * one (root->rnode) as far as dependent read barriers go.
                 */
                root->rnode = child;
                if (is_idr(root) && !tag_get(node, IDR_FREE, 0))
                        root_tag_clear(root, IDR_FREE);

                /*
                 * 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 has 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.
                 */
                node->count = 0;
                if (!radix_tree_is_internal_node(child)) {
                        node->slots[0] = RADIX_TREE_RETRY;
                        if (update_node)
                                update_node(node, private);
                }

                WARN_ON_ONCE(!list_empty(&node->private_list));
                radix_tree_node_free(node);
                shrunk = true;
        }

        return shrunk;
}

static bool delete_node(struct radix_tree_root *root,
                        struct radix_tree_node *node,
                        radix_tree_update_node_t update_node, void *private)
{
        bool deleted = false;

        do {
                struct radix_tree_node *parent;

                if (node->count) {
                        if (node == entry_to_node(root->rnode))
                                deleted |= radix_tree_shrink(root, update_node,
                                                                private);
                        return deleted;
                }

                parent = node->parent;
                if (parent) {
                        parent->slots[node->offset] = NULL;
                        parent->count--;
                } else {
                        /*
                         * Shouldn't the tags already have all been cleared
                         * by the caller?
                         */
                        if (!is_idr(root))
                                root_tag_clear_all(root);
                        root->rnode = NULL;
                }

                WARN_ON_ONCE(!list_empty(&node->private_list));
                radix_tree_node_free(node);
                deleted = true;

                node = parent;
        } while (node);

        return deleted;
}

/**
 *      __radix_tree_create     -       create a slot in a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *      @order:         index occupies 2^order aligned slots
 *      @nodep:         returns node
 *      @slotp:         returns slot
 *
 *      Create, if necessary, and return the node and slot for an item
 *      at position @index in the radix tree @root.
 *
 *      Until there is more than one item in the tree, no nodes are
 *      allocated and @root->rnode is used as a direct slot instead of
 *      pointing to a node, in which case *@nodep will be NULL.
 *
 *      Returns -ENOMEM, or 0 for success.
 */
int __radix_tree_create(struct radix_tree_root *root, unsigned long index,
                        unsigned order, struct radix_tree_node **nodep,
                        void ***slotp)
{
        struct radix_tree_node *node = NULL, *child;
        void **slot = (void **)&root->rnode;
        unsigned long maxindex;
        unsigned int shift, offset = 0;
        unsigned long max = index | ((1UL << order) - 1);
        gfp_t gfp = root_gfp_mask(root);

        shift = radix_tree_load_root(root, &child, &maxindex);

        /* Make sure the tree is high enough.  */
        if (order > 0 && max == ((1UL << order) - 1))
                max++;
        if (max > maxindex) {
                int error = radix_tree_extend(root, gfp, max, shift);
                if (error < 0)
                        return error;
                shift = error;
                child = root->rnode;
        }

        while (shift > order) {
                shift -= RADIX_TREE_MAP_SHIFT;
                if (child == NULL) {
                        /* Have to add a child node.  */
                        child = radix_tree_node_alloc(gfp, node, root, shift,
                                                        offset, 0, 0);
                        if (!child)
                                return -ENOMEM;
                        rcu_assign_pointer(*slot, node_to_entry(child));
                        if (node)
                                node->count++;
                } else if (!radix_tree_is_internal_node(child))
                        break;

                /* Go a level down */
                node = entry_to_node(child);
                offset = radix_tree_descend(node, &child, index);
                slot = &node->slots[offset];
        }

        if (nodep)
                *nodep = node;
        if (slotp)
                *slotp = slot;
        return 0;
}

/*
 * Free any nodes below this node.  The tree is presumed to not need
 * shrinking, and any user data in the tree is presumed to not need a
 * destructor called on it.  If we need to add a destructor, we can
 * add that functionality later.  Note that we may not clear tags or
 * slots from the tree as an RCU walker may still have a pointer into
 * this subtree.  We could replace the entries with RADIX_TREE_RETRY,
 * but we'll still have to clear those in rcu_free.
 */
static void radix_tree_free_nodes(struct radix_tree_node *node)
{
        unsigned offset = 0;
        struct radix_tree_node *child = entry_to_node(node);

        for (;;) {
                void *entry = child->slots[offset];
                if (radix_tree_is_internal_node(entry) &&
                                        !is_sibling_entry(child, entry)) {
                        child = entry_to_node(entry);
                        offset = 0;
                        continue;
                }
                offset++;
                while (offset == RADIX_TREE_MAP_SIZE) {
                        struct radix_tree_node *old = child;
                        offset = child->offset + 1;
                        child = child->parent;
                        WARN_ON_ONCE(!list_empty(&old->private_list));
                        radix_tree_node_free(old);
                        if (old == entry_to_node(node))
                                return;
                }
        }
}

#ifdef CONFIG_RADIX_TREE_MULTIORDER
static inline int insert_entries(struct radix_tree_node *node, void **slot,
                                void *item, unsigned order, bool replace)
{
        struct radix_tree_node *child;
        unsigned i, n, tag, offset, tags = 0;

        if (node) {
                if (order > node->shift)
                        n = 1 << (order - node->shift);
                else
                        n = 1;
                offset = get_slot_offset(node, slot);
        } else {
                n = 1;
                offset = 0;
        }

        if (n > 1) {
                offset = offset & ~(n - 1);
                slot = &node->slots[offset];
        }
        child = node_to_entry(slot);

        for (i = 0; i < n; i++) {
                if (slot[i]) {
                        if (replace) {
                                node->count--;
                                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                                        if (tag_get(node, tag, offset + i))
                                                tags |= 1 << tag;
                        } else
                                return -EEXIST;
                }
        }

        for (i = 0; i < n; i++) {
                struct radix_tree_node *old = slot[i];
                if (i) {
                        rcu_assign_pointer(slot[i], child);
                        for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                                if (tags & (1 << tag))
                                        tag_clear(node, tag, offset + i);
                } else {
                        rcu_assign_pointer(slot[i], item);
                        for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                                if (tags & (1 << tag))
                                        tag_set(node, tag, offset);
                }
                if (radix_tree_is_internal_node(old) &&
                                        !is_sibling_entry(node, old) &&
                                        (old != RADIX_TREE_RETRY))
                        radix_tree_free_nodes(old);
                if (radix_tree_exceptional_entry(old))
                        node->exceptional--;
        }
        if (node) {
                node->count += n;
                if (radix_tree_exceptional_entry(item))
                        node->exceptional += n;
        }
        return n;
}
#else
static inline int insert_entries(struct radix_tree_node *node, void **slot,
                                void *item, unsigned order, bool replace)
{
        if (*slot)
                return -EEXIST;
        rcu_assign_pointer(*slot, item);
        if (node) {
                node->count++;
                if (radix_tree_exceptional_entry(item))
                        node->exceptional++;
        }
        return 1;
}
#endif

/**
 *      __radix_tree_insert    -    insert into a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *      @order:         key covers the 2^order indices around index
 *      @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,
                        unsigned order, void *item)
{
        struct radix_tree_node *node;
        void **slot;
        int error;

        BUG_ON(radix_tree_is_internal_node(item));

        error = __radix_tree_create(root, index, order, &node, &slot);
        if (error)
                return error;

        error = insert_entries(node, slot, item, order, false);
        if (error < 0)
                return error;

        if (node) {
                unsigned offset = get_slot_offset(node, slot);
                BUG_ON(tag_get(node, 0, offset));
                BUG_ON(tag_get(node, 1, offset));
                BUG_ON(tag_get(node, 2, offset));
        } else {
                BUG_ON(root_tags_get(root));
        }

        return 0;
}
EXPORT_SYMBOL(__radix_tree_insert);

/**
 *      __radix_tree_lookup     -       lookup an item in a radix tree
 *      @root:          radix tree root
 *      @index:         index key
 *      @nodep:         returns node
 *      @slotp:         returns slot
 *
 *      Lookup and return the item at position @index in the radix
 *      tree @root.
 *
 *      Until there is more than one item in the tree, no nodes are
 *      allocated and @root->rnode is used as a direct slot instead of
 *      pointing to a node, in which case *@nodep will be NULL.
 */
void *__radix_tree_lookup(const struct radix_tree_root *root,
                          unsigned long index, struct radix_tree_node **nodep,
                          void ***slotp)
{
        struct radix_tree_node *node, *parent;
        unsigned long maxindex;
        void **slot;

 restart:
        parent = NULL;
        slot = (void **)&root->rnode;
        radix_tree_load_root(root, &node, &maxindex);
        if (index > maxindex)
                return NULL;

        while (radix_tree_is_internal_node(node)) {
                unsigned offset;

                if (node == RADIX_TREE_RETRY)
                        goto restart;
                parent = entry_to_node(node);
                offset = radix_tree_descend(parent, &node, index);
                slot = parent->slots + offset;
        }

        if (nodep)
                *nodep = parent;
        if (slotp)
                *slotp = slot;
        return 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(const struct radix_tree_root *root,
                                unsigned long index)
{
        void **slot;

        if (!__radix_tree_lookup(root, index, NULL, &slot))
                return NULL;
        return slot;
}
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(const struct radix_tree_root *root, unsigned long index)
{
        return __radix_tree_lookup(root, index, NULL, NULL);
}
EXPORT_SYMBOL(radix_tree_lookup);

static inline void replace_sibling_entries(struct radix_tree_node *node,
                                void **slot, int count, int exceptional)
{
#ifdef CONFIG_RADIX_TREE_MULTIORDER
        void *ptr = node_to_entry(slot);
        unsigned offset = get_slot_offset(node, slot) + 1;

        while (offset < RADIX_TREE_MAP_SIZE) {
                if (node->slots[offset] != ptr)
                        break;
                if (count < 0) {
                        node->slots[offset] = NULL;
                        node->count--;
                }
                node->exceptional += exceptional;
                offset++;
        }
#endif
}

static void replace_slot(void **slot, void *item, struct radix_tree_node *node,
                                int count, int exceptional)
{
        if (WARN_ON_ONCE(radix_tree_is_internal_node(item)))
                return;

        if (node && (count || exceptional)) {
                node->count += count;
                node->exceptional += exceptional;
                replace_sibling_entries(node, slot, count, exceptional);
        }

        rcu_assign_pointer(*slot, item);
}

static bool node_tag_get(const struct radix_tree_root *root,
                                const struct radix_tree_node *node,
                                unsigned int tag, unsigned int offset)
{
        if (node)
                return tag_get(node, tag, offset);
        return root_tag_get(root, tag);
}

/*
 * IDR users want to be able to store NULL in the tree, so if the slot isn't
 * free, don't adjust the count, even if it's transitioning between NULL and
 * non-NULL.  For the IDA, we mark slots as being IDR_FREE while they still
 * have empty bits, but it only stores NULL in slots when they're being
 * deleted.
 */
static int calculate_count(struct radix_tree_root *root,
                                struct radix_tree_node *node, void **slot,
                                void *item, void *old)
{
        if (is_idr(root)) {
                unsigned offset = get_slot_offset(node, slot);
                bool free = node_tag_get(root, node, IDR_FREE, offset);
                if (!free)
                        return 0;
                if (!old)
                        return 1;
        }
        return !!item - !!old;
}

/**
 * __radix_tree_replace         - replace item in a slot
 * @root:               radix tree root
 * @node:               pointer to tree node
 * @slot:               pointer to slot in @node
 * @item:               new item to store in the slot.
 * @update_node:        callback for changing leaf nodes
 * @private:            private data to pass to @update_node
 *
 * For use with __radix_tree_lookup().  Caller must hold tree write locked
 * across slot lookup and replacement.
 */
void __radix_tree_replace(struct radix_tree_root *root,
                          struct radix_tree_node *node,
                          void **slot, void *item,
                          radix_tree_update_node_t update_node, void *private)
{
        void *old = rcu_dereference_raw(*slot);
        int exceptional = !!radix_tree_exceptional_entry(item) -
                                !!radix_tree_exceptional_entry(old);
        int count = calculate_count(root, node, slot, item, old);

        /*
         * This function supports replacing exceptional entries and
         * deleting entries, but that needs accounting against the
         * node unless the slot is root->rnode.
         */
        WARN_ON_ONCE(!node && (slot != (void **)&root->rnode) &&
                        (count || exceptional));
        replace_slot(slot, item, node, count, exceptional);

        if (!node)
                return;

        if (update_node)
                update_node(node, private);

        delete_node(root, node, update_node, private);
}

/**
 * radix_tree_replace_slot      - replace item in a slot
 * @root:       radix tree root
 * @slot:       pointer to slot
 * @item:       new item to store in the slot.
 *
 * For use with radix_tree_lookup_slot(), radix_tree_gang_lookup_slot(),
 * radix_tree_gang_lookup_tag_slot().  Caller must hold tree write locked
 * across slot lookup and replacement.
 *
 * NOTE: This cannot be used to switch between non-entries (empty slots),
 * regular entries, and exceptional entries, as that requires accounting
 * inside the radix tree node. When switching from one type of entry or
 * deleting, use __radix_tree_lookup() and __radix_tree_replace() or
 * radix_tree_iter_replace().
 */
void radix_tree_replace_slot(struct radix_tree_root *root,
                             void **slot, void *item)
{
        __radix_tree_replace(root, NULL, slot, item, NULL, NULL);
}

/**
 * radix_tree_iter_replace - replace item in a slot
 * @root:       radix tree root
 * @slot:       pointer to slot
 * @item:       new item to store in the slot.
 *
 * For use with radix_tree_split() and radix_tree_for_each_slot().
 * Caller must hold tree write locked across split and replacement.
 */
void radix_tree_iter_replace(struct radix_tree_root *root,
                const struct radix_tree_iter *iter, void **slot, void *item)
{
        __radix_tree_replace(root, iter->node, slot, item, NULL, NULL);
}

#ifdef CONFIG_RADIX_TREE_MULTIORDER
/**
 * radix_tree_join - replace multiple entries with one multiorder entry
 * @root: radix tree root
 * @index: an index inside the new entry
 * @order: order of the new entry
 * @item: new entry
 *
 * Call this function to replace several entries with one larger entry.
 * The existing entries are presumed to not need freeing as a result of
 * this call.
 *
 * The replacement entry will have all the tags set on it that were set
 * on any of the entries it is replacing.
 */
int radix_tree_join(struct radix_tree_root *root, unsigned long index,
                        unsigned order, void *item)
{
        struct radix_tree_node *node;
        void **slot;
        int error;

        BUG_ON(radix_tree_is_internal_node(item));

        error = __radix_tree_create(root, index, order, &node, &slot);
        if (!error)
                error = insert_entries(node, slot, item, order, true);
        if (error > 0)
                error = 0;

        return error;
}

/**
 * radix_tree_split - Split an entry into smaller entries
 * @root: radix tree root
 * @index: An index within the large entry
 * @order: Order of new entries
 *
 * Call this function as the first step in replacing a multiorder entry
 * with several entries of lower order.  After this function returns,
 * loop over the relevant portion of the tree using radix_tree_for_each_slot()
 * and call radix_tree_iter_replace() to set up each new entry.
 *
 * The tags from this entry are replicated to all the new entries.
 *
 * The radix tree should be locked against modification during the entire
 * replacement operation.  Lock-free lookups will see RADIX_TREE_RETRY which
 * should prompt RCU walkers to restart the lookup from the root.
 */
int radix_tree_split(struct radix_tree_root *root, unsigned long index,
                                unsigned order)
{
        struct radix_tree_node *parent, *node, *child;
        void **slot;
        unsigned int offset, end;
        unsigned n, tag, tags = 0;
        gfp_t gfp = root_gfp_mask(root);

        if (!__radix_tree_lookup(root, index, &parent, &slot))
                return -ENOENT;
        if (!parent)
                return -ENOENT;

        offset = get_slot_offset(parent, slot);

        for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                if (tag_get(parent, tag, offset))
                        tags |= 1 << tag;

        for (end = offset + 1; end < RADIX_TREE_MAP_SIZE; end++) {
                if (!is_sibling_entry(parent, parent->slots[end]))
                        break;
                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                        if (tags & (1 << tag))
                                tag_set(parent, tag, end);
                /* rcu_assign_pointer ensures tags are set before RETRY */
                rcu_assign_pointer(parent->slots[end], RADIX_TREE_RETRY);
        }
        rcu_assign_pointer(parent->slots[offset], RADIX_TREE_RETRY);
        parent->exceptional -= (end - offset);

        if (order == parent->shift)
                return 0;
        if (order > parent->shift) {
                while (offset < end)
                        offset += insert_entries(parent, &parent->slots[offset],
                                        RADIX_TREE_RETRY, order, true);
                return 0;
        }

        node = parent;

        for (;;) {
                if (node->shift > order) {
                        child = radix_tree_node_alloc(gfp, node, root,
                                        node->shift - RADIX_TREE_MAP_SHIFT,
                                        offset, 0, 0);
                        if (!child)
                                goto nomem;
                        if (node != parent) {
                                node->count++;
                                node->slots[offset] = node_to_entry(child);
                                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                                        if (tags & (1 << tag))
                                                tag_set(node, tag, offset);
                        }

                        node = child;
                        offset = 0;
                        continue;
                }

                n = insert_entries(node, &node->slots[offset],
                                        RADIX_TREE_RETRY, order, false);
                BUG_ON(n > RADIX_TREE_MAP_SIZE);

                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                        if (tags & (1 << tag))
                                tag_set(node, tag, offset);
                offset += n;

                while (offset == RADIX_TREE_MAP_SIZE) {
                        if (node == parent)
                                break;
                        offset = node->offset;
                        child = node;
                        node = node->parent;
                        rcu_assign_pointer(node->slots[offset],
                                                node_to_entry(child));
                        offset++;
                }
                if ((node == parent) && (offset == end))
                        return 0;
        }

 nomem:
        /* Shouldn't happen; did user forget to preload? */
        /* TODO: free all the allocated nodes */
        WARN_ON(1);
        return -ENOMEM;
}
#endif

static void node_tag_set(struct radix_tree_root *root,
                                struct radix_tree_node *node,
                                unsigned int tag, unsigned int offset)
{
        while (node) {
                if (tag_get(node, tag, offset))
                        return;
                tag_set(node, tag, offset);
                offset = node->offset;
                node = node->parent;
        }

        if (!root_tag_get(root, tag))
                root_tag_set(root, tag);
}

/**
 *      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)
{
        struct radix_tree_node *node, *parent;
        unsigned long maxindex;

        radix_tree_load_root(root, &node, &maxindex);
        BUG_ON(index > maxindex);

        while (radix_tree_is_internal_node(node)) {
                unsigned offset;

                parent = entry_to_node(node);
                offset = radix_tree_descend(parent, &node, index);
                BUG_ON(!node);

                if (!tag_get(parent, tag, offset))
                        tag_set(parent, tag, offset);
        }

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

        return node;
}
EXPORT_SYMBOL(radix_tree_tag_set);

/**
 * radix_tree_iter_tag_set - set a tag on the current iterator entry
 * @root:       radix tree root
 * @iter:       iterator state
 * @tag:        tag to set
 */
void radix_tree_iter_tag_set(struct radix_tree_root *root,
                        const struct radix_tree_iter *iter, unsigned int tag)
{
        node_tag_set(root, iter->node, tag, iter_offset(iter));
}

static void node_tag_clear(struct radix_tree_root *root,
                                struct radix_tree_node *node,
                                unsigned int tag, unsigned int offset)
{
        while (node) {
                if (!tag_get(node, tag, offset))
                        return;
                tag_clear(node, tag, offset);
                if (any_tag_set(node, tag))
                        return;

                offset = node->offset;
                node = node->parent;
        }

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

/**
 *      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)
{
        struct radix_tree_node *node, *parent;
        unsigned long maxindex;
        int uninitialized_var(offset);

        radix_tree_load_root(root, &node, &maxindex);
        if (index > maxindex)
                return NULL;

        parent = NULL;

        while (radix_tree_is_internal_node(node)) {
                parent = entry_to_node(node);
                offset = radix_tree_descend(parent, &node, index);
        }

        if (node)
                node_tag_clear(root, parent, tag, offset);

        return node;
}
EXPORT_SYMBOL(radix_tree_tag_clear);

/**
  * radix_tree_iter_tag_clear - clear a tag on the current iterator entry
  * @root: radix tree root
  * @iter: iterator state
  * @tag: tag to clear
  */
void radix_tree_iter_tag_clear(struct radix_tree_root *root,
                        const struct radix_tree_iter *iter, unsigned int tag)
{
        node_tag_clear(root, iter->node, tag, iter_offset(iter));
}

/**
 * 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(const struct radix_tree_root *root,
                        unsigned long index, unsigned int tag)
{
        struct radix_tree_node *node, *parent;
        unsigned long maxindex;

        if (!root_tag_get(root, tag))
                return 0;

        radix_tree_load_root(root, &node, &maxindex);
        if (index > maxindex)
                return 0;

        while (radix_tree_is_internal_node(node)) {
                unsigned offset;

                parent = entry_to_node(node);
                offset = radix_tree_descend(parent, &node, index);

                if (!tag_get(parent, tag, offset))
                        return 0;
                if (node == RADIX_TREE_RETRY)
                        break;
        }

        return 1;
}
EXPORT_SYMBOL(radix_tree_tag_get);

static inline void __set_iter_shift(struct radix_tree_iter *iter,
                                        unsigned int shift)
{
#ifdef CONFIG_RADIX_TREE_MULTIORDER
        iter->shift = shift;
#endif
}

/* Construct iter->tags bit-mask from node->tags[tag] array */
static void set_iter_tags(struct radix_tree_iter *iter,
                                struct radix_tree_node *node, unsigned offset,
                                unsigned tag)
{
        unsigned tag_long = offset / BITS_PER_LONG;
        unsigned tag_bit  = offset % BITS_PER_LONG;

        if (!node) {
                iter->tags = 1;
                return;
        }

        iter->tags = node->tags[tag][tag_long] >> tag_bit;

        /* This never happens if RADIX_TREE_TAG_LONGS == 1 */
        if (tag_long < RADIX_TREE_TAG_LONGS - 1) {
                /* Pick tags from next element */
                if (tag_bit)
                        iter->tags |= node->tags[tag][tag_long + 1] <<
                                                (BITS_PER_LONG - tag_bit);
                /* Clip chunk size, here only BITS_PER_LONG tags */
                iter->next_index = __radix_tree_iter_add(iter, BITS_PER_LONG);
        }
}

#ifdef CONFIG_RADIX_TREE_MULTIORDER
static void **skip_siblings(struct radix_tree_node **nodep,
                        void **slot, struct radix_tree_iter *iter)
{
        void *sib = node_to_entry(slot - 1);

        while (iter->index < iter->next_index) {
                *nodep = rcu_dereference_raw(*slot);
                if (*nodep && *nodep != sib)
                        return slot;
                slot++;
                iter->index = __radix_tree_iter_add(iter, 1);
                iter->tags >>= 1;
        }

        *nodep = NULL;
        return NULL;
}

void ** __radix_tree_next_slot(void **slot, struct radix_tree_iter *iter,
                                        unsigned flags)
{
        unsigned tag = flags & RADIX_TREE_ITER_TAG_MASK;
        struct radix_tree_node *node = rcu_dereference_raw(*slot);

        slot = skip_siblings(&node, slot, iter);

        while (radix_tree_is_internal_node(node)) {
                unsigned offset;
                unsigned long next_index;

                if (node == RADIX_TREE_RETRY)
                        return slot;
                node = entry_to_node(node);
                iter->node = node;
                iter->shift = node->shift;

                if (flags & RADIX_TREE_ITER_TAGGED) {
                        offset = radix_tree_find_next_bit(node, tag, 0);
                        if (offset == RADIX_TREE_MAP_SIZE)
                                return NULL;
                        slot = &node->slots[offset];
                        iter->index = __radix_tree_iter_add(iter, offset);
                        set_iter_tags(iter, node, offset, tag);
                        node = rcu_dereference_raw(*slot);
                } else {
                        offset = 0;
                        slot = &node->slots[0];
                        for (;;) {
                                node = rcu_dereference_raw(*slot);
                                if (node)
                                        break;
                                slot++;
                                offset++;
                                if (offset == RADIX_TREE_MAP_SIZE)
                                        return NULL;
                        }
                        iter->index = __radix_tree_iter_add(iter, offset);
                }
                if ((flags & RADIX_TREE_ITER_CONTIG) && (offset > 0))
                        goto none;
                next_index = (iter->index | shift_maxindex(iter->shift)) + 1;
                if (next_index < iter->next_index)
                        iter->next_index = next_index;
        }

        return slot;
 none:
        iter->next_index = 0;
        return NULL;
}
EXPORT_SYMBOL(__radix_tree_next_slot);
#else
static void **skip_siblings(struct radix_tree_node **nodep,
                        void **slot, struct radix_tree_iter *iter)
{
        return slot;
}
#endif

void **radix_tree_iter_resume(void **slot, struct radix_tree_iter *iter)
{
        struct radix_tree_node *node;

        slot++;
        iter->index = __radix_tree_iter_add(iter, 1);
        skip_siblings(&node, slot, iter);
        iter->next_index = iter->index;
        iter->tags = 0;
        return NULL;
}
EXPORT_SYMBOL(radix_tree_iter_resume);

/**
 * radix_tree_next_chunk - find next chunk of slots for iteration
 *
 * @root:       radix tree root
 * @iter:       iterator state
 * @flags:      RADIX_TREE_ITER_* flags and tag index
 * Returns:     pointer to chunk first slot, or NULL if iteration is over
 */
void **radix_tree_next_chunk(const struct radix_tree_root *root,
                             struct radix_tree_iter *iter, unsigned flags)
{
        unsigned tag = flags & RADIX_TREE_ITER_TAG_MASK;
        struct radix_tree_node *node, *child;
        unsigned long index, offset, maxindex;

        if ((flags & RADIX_TREE_ITER_TAGGED) && !root_tag_get(root, tag))
                return NULL;

        /*
         * Catch next_index overflow after ~0UL. iter->index never overflows
         * during iterating; it can be zero only at the beginning.
         * And we cannot overflow iter->next_index in a single step,
         * because RADIX_TREE_MAP_SHIFT < BITS_PER_LONG.
         *
         * This condition also used by radix_tree_next_slot() to stop
         * contiguous iterating, and forbid switching to the next chunk.
         */
        index = iter->next_index;
        if (!index && iter->index)
                return NULL;

 restart:
        radix_tree_load_root(root, &child, &maxindex);
        if (index > maxindex)
                return NULL;
        if (!child)
                return NULL;

        if (!radix_tree_is_internal_node(child)) {
                /* Single-slot tree */
                iter->index = index;
                iter->next_index = maxindex + 1;
                iter->tags = 1;
                iter->node = NULL;
                __set_iter_shift(iter, 0);
                return (void **)&root->rnode;
        }

        do {
                node = entry_to_node(child);
                offset = radix_tree_descend(node, &child, index);

                if ((flags & RADIX_TREE_ITER_TAGGED) ?
                                !tag_get(node, tag, offset) : !child) {
                        /* Hole detected */
                        if (flags & RADIX_TREE_ITER_CONTIG)
                                return NULL;

                        if (flags & RADIX_TREE_ITER_TAGGED)
                                offset = radix_tree_find_next_bit(node, tag,
                                                offset + 1);
                        else
                                while (++offset < RADIX_TREE_MAP_SIZE) {
                                        void *slot = node->slots[offset];
                                        if (is_sibling_entry(node, slot))
                                                continue;
                                        if (slot)
                                                break;
                                }
                        index &= ~node_maxindex(node);
                        index += offset << node->shift;
                        /* Overflow after ~0UL */
                        if (!index)
                                return NULL;
                        if (offset == RADIX_TREE_MAP_SIZE)
                                goto restart;
                        child = rcu_dereference_raw(node->slots[offset]);
                }

                if (!child)
                        goto restart;
                if (child == RADIX_TREE_RETRY)
                        break;
        } while (radix_tree_is_internal_node(child));

        /* Update the iterator state */
        iter->index = (index &~ node_maxindex(node)) | (offset << node->shift);
        iter->next_index = (index | node_maxindex(node)) + 1;
        iter->node = node;
        __set_iter_shift(iter, node->shift);

        if (flags & RADIX_TREE_ITER_TAGGED)
                set_iter_tags(iter, node, offset, tag);

        return node->slots + offset;
}
EXPORT_SYMBOL(radix_tree_next_chunk);

/**
 *      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(const struct radix_tree_root *root, void **results,
                        unsigned long first_index, unsigned int max_items)
{
        struct radix_tree_iter iter;
        void **slot;
        unsigned int ret = 0;

        if (unlikely(!max_items))
                return 0;

        radix_tree_for_each_slot(slot, root, &iter, first_index) {
                results[ret] = rcu_dereference_raw(*slot);
                if (!results[ret])
                        continue;
                if (radix_tree_is_internal_node(results[ret])) {
                        slot = radix_tree_iter_retry(&iter);
                        continue;
                }
                if (++ret == max_items)
                        break;
        }

        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
 *      @indices:       where their indices should be placed (but usually NULL)
 *      @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(const struct radix_tree_root *root,
                        void ***results, unsigned long *indices,
                        unsigned long first_index, unsigned int max_items)
{
        struct radix_tree_iter iter;
        void **slot;
        unsigned int ret = 0;

        if (unlikely(!max_items))
                return 0;

        radix_tree_for_each_slot(slot, root, &iter, first_index) {
                results[ret] = slot;
                if (indices)
                        indices[ret] = iter.index;
                if (++ret == max_items)
                        break;
        }

        return ret;
}
EXPORT_SYMBOL(radix_tree_gang_lookup_slot);

/**
 *      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(const struct radix_tree_root *root, void **results,
                unsigned long first_index, unsigned int max_items,
                unsigned int tag)
{
        struct radix_tree_iter iter;
        void **slot;
        unsigned int ret = 0;

        if (unlikely(!max_items))
                return 0;

        radix_tree_for_each_tagged(slot, root, &iter, first_index, tag) {
                results[ret] = rcu_dereference_raw(*slot);
                if (!results[ret])
                        continue;
                if (radix_tree_is_internal_node(results[ret])) {
                        slot = radix_tree_iter_retry(&iter);
                        continue;
                }
                if (++ret == max_items)
                        break;
        }

        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(const struct radix_tree_root *root,
                void ***results, unsigned long first_index,
                unsigned int max_items, unsigned int tag)
{
        struct radix_tree_iter iter;
        void **slot;
        unsigned int ret = 0;

        if (unlikely(!max_items))
                return 0;

        radix_tree_for_each_tagged(slot, root, &iter, first_index, tag) {
                results[ret] = slot;
                if (++ret == max_items)
                        break;
        }

        return ret;
}
EXPORT_SYMBOL(radix_tree_gang_lookup_tag_slot);

/**
 *      __radix_tree_delete_node    -    try to free node after clearing a slot
 *      @root:          radix tree root
 *      @node:          node containing @index
 *      @update_node:   callback for changing leaf nodes
 *      @private:       private data to pass to @update_node
 *
 *      After clearing the slot at @index in @node from radix tree
 *      rooted at @root, call this function to attempt freeing the
 *      node and shrinking the tree.
 */
void __radix_tree_delete_node(struct radix_tree_root *root,
                              struct radix_tree_node *node,
                              radix_tree_update_node_t update_node,
                              void *private)
{
        delete_node(root, node, update_node, private);
}

static bool __radix_tree_delete(struct radix_tree_root *root,
                                struct radix_tree_node *node, void **slot)
{
        void *old = rcu_dereference_raw(*slot);
        int exceptional = radix_tree_exceptional_entry(old) ? -1 : 0;
        unsigned offset = get_slot_offset(node, slot);
        int tag;

        if (is_idr(root))
                node_tag_set(root, node, IDR_FREE, offset);
        else
                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                        node_tag_clear(root, node, tag, offset);

        replace_slot(slot, NULL, node, -1, exceptional);
        return node && delete_node(root, node, NULL, NULL);
}

/**
 * radix_tree_iter_delete - delete the entry at this iterator position
 * @root: radix tree root
 * @iter: iterator state
 * @slot: pointer to slot
 *
 * Delete the entry at the position currently pointed to by the iterator.
 * This may result in the current node being freed; if it is, the iterator
 * is advanced so that it will not reference the freed memory.  This
 * function may be called without any locking if there are no other threads
 * which can access this tree.
 */
void radix_tree_iter_delete(struct radix_tree_root *root,
                                struct radix_tree_iter *iter, void **slot)
{
        if (__radix_tree_delete(root, iter->node, slot))
                iter->index = iter->next_index;
}

/**
 * radix_tree_delete_item - delete an item from a radix tree
 * @root: radix tree root
 * @index: index key
 * @item: expected item
 *
 * Remove @item at @index from the radix tree rooted at @root.
 *
 * Return: the deleted entry, or %NULL if it was not present
 * or the entry at the given @index was not @item.
 */
void *radix_tree_delete_item(struct radix_tree_root *root,
                             unsigned long index, void *item)
{
        struct radix_tree_node *node = NULL;
        void **slot;
        void *entry;

        entry = __radix_tree_lookup(root, index, &node, &slot);
        if (!entry && (!is_idr(root) || node_tag_get(root, node, IDR_FREE,
                                                get_slot_offset(node, slot))))
                return NULL;

        if (item && entry != item)
                return NULL;

        __radix_tree_delete(root, node, slot);

        return entry;
}
EXPORT_SYMBOL(radix_tree_delete_item);

/**
 * radix_tree_delete - delete an entry from a radix tree
 * @root: radix tree root
 * @index: index key
 *
 * Remove the entry at @index from the radix tree rooted at @root.
 *
 * Return: The deleted entry, or %NULL if it was not present.
 */
void *radix_tree_delete(struct radix_tree_root *root, unsigned long index)
{
        return radix_tree_delete_item(root, index, NULL);
}
EXPORT_SYMBOL(radix_tree_delete);

void radix_tree_clear_tags(struct radix_tree_root *root,
                           struct radix_tree_node *node,
                           void **slot)
{
        if (node) {
                unsigned int tag, offset = get_slot_offset(node, slot);
                for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++)
                        node_tag_clear(root, node, tag, offset);
        } else {
                root_tag_clear_all(root);
        }
}

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

/**
 * idr_preload - preload for idr_alloc()
 * @gfp_mask: allocation mask to use for preloading
 *
 * Preallocate memory to use for the next call to idr_alloc().  This function
 * returns with preemption disabled.  It will be enabled by idr_preload_end().
 */
void idr_preload(gfp_t gfp_mask)
{
        __radix_tree_preload(gfp_mask, IDR_PRELOAD_SIZE);
}
EXPORT_SYMBOL(idr_preload);

/**
 * ida_pre_get - reserve resources for ida allocation
 * @ida: ida handle
 * @gfp: memory allocation flags
 *
 * This function should be called before calling ida_get_new_above().  If it
 * is unable to allocate memory, it will return %0.  On success, it returns %1.
 */
int ida_pre_get(struct ida *ida, gfp_t gfp)
{
        __radix_tree_preload(gfp, IDA_PRELOAD_SIZE);
        /*
         * The IDA API has no preload_end() equivalent.  Instead,
         * ida_get_new() can return -EAGAIN, prompting the caller
         * to return to the ida_pre_get() step.
         */
        preempt_enable();

        if (!this_cpu_read(ida_bitmap)) {
                struct ida_bitmap *bitmap = kmalloc(sizeof(*bitmap), gfp);
                if (!bitmap)
                        return 0;
                bitmap = this_cpu_cmpxchg(ida_bitmap, NULL, bitmap);
                kfree(bitmap);
        }

        return 1;
}
EXPORT_SYMBOL(ida_pre_get);

void **idr_get_free(struct radix_tree_root *root,
                        struct radix_tree_iter *iter, gfp_t gfp, int end)
{
        struct radix_tree_node *node = NULL, *child;
        void **slot = (void **)&root->rnode;
        unsigned long maxindex, start = iter->next_index;
        unsigned long max = end > 0 ? end - 1 : INT_MAX;
        unsigned int shift, offset = 0;

 grow:
        shift = radix_tree_load_root(root, &child, &maxindex);
        if (!radix_tree_tagged(root, IDR_FREE))
                start = max(start, maxindex + 1);
        if (start > max)
                return ERR_PTR(-ENOSPC);

        if (start > maxindex) {
                int error = radix_tree_extend(root, gfp, start, shift);
                if (error < 0)
                        return ERR_PTR(error);
                shift = error;
                child = rcu_dereference_raw(root->rnode);
        }

        while (shift) {
                shift -= RADIX_TREE_MAP_SHIFT;
                if (child == NULL) {
                        /* Have to add a child node.  */
                        child = radix_tree_node_alloc(gfp, node, root, shift,
                                                        offset, 0, 0);
                        if (!child)
                                return ERR_PTR(-ENOMEM);
                        all_tag_set(child, IDR_FREE);
                        rcu_assign_pointer(*slot, node_to_entry(child));
                        if (node)
                                node->count++;
                } else if (!radix_tree_is_internal_node(child))
                        break;

                node = entry_to_node(child);
                offset = radix_tree_descend(node, &child, start);
                if (!tag_get(node, IDR_FREE, offset)) {
                        offset = radix_tree_find_next_bit(node, IDR_FREE,
                                                        offset + 1);
                        start = next_index(start, node, offset);
                        if (start > max)
                                return ERR_PTR(-ENOSPC);
                        while (offset == RADIX_TREE_MAP_SIZE) {
                                offset = node->offset + 1;
                                node = node->parent;
                                if (!node)
                                        goto grow;
                                shift = node->shift;
                        }
                        child = rcu_dereference_raw(node->slots[offset]);
                }
                slot = &node->slots[offset];
        }

        iter->index = start;
        if (node)
                iter->next_index = 1 + min(max, (start | node_maxindex(node)));
        else
                iter->next_index = 1;
        iter->node = node;
        __set_iter_shift(iter, shift);
        set_iter_tags(iter, node, offset, IDR_FREE);

        return slot;
}

/**
 * idr_destroy - release all internal memory from an IDR
 * @idr: idr handle
 *
 * After this function is called, the IDR is empty, and may be reused or
 * the data structure containing it may be freed.
 *
 * A typical clean-up sequence for objects stored in an idr tree will use
 * idr_for_each() to free all objects, if necessary, then idr_destroy() to
 * free the memory used to keep track of those objects.
 */
void idr_destroy(struct idr *idr)
{
        struct radix_tree_node *node = rcu_dereference_raw(idr->idr_rt.rnode);
        if (radix_tree_is_internal_node(node))
                radix_tree_free_nodes(node);
        idr->idr_rt.rnode = NULL;
        root_tag_set(&idr->idr_rt, IDR_FREE);
}
EXPORT_SYMBOL(idr_destroy);

static void
radix_tree_node_ctor(void *arg)
{
        struct radix_tree_node *node = arg;

        memset(node, 0, sizeof(*node));
        INIT_LIST_HEAD(&node->private_list);
}

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_maxnodes(void)
{
        unsigned long height_to_maxindex[RADIX_TREE_MAX_PATH + 1];
        unsigned int i, j;

        for (i = 0; i < ARRAY_SIZE(height_to_maxindex); i++)
                height_to_maxindex[i] = __maxindex(i);
        for (i = 0; i < ARRAY_SIZE(height_to_maxnodes); i++) {
                for (j = i; j > 0; j--)
                        height_to_maxnodes[i] += height_to_maxindex[j - 1] + 1;
        }
}

static int radix_tree_cpu_dead(unsigned int cpu)
{
        struct radix_tree_preload *rtp;
        struct radix_tree_node *node;

        /* Free per-cpu pool of preloaded nodes */
        rtp = &per_cpu(radix_tree_preloads, cpu);
        while (rtp->nr) {
                node = rtp->nodes;
                rtp->nodes = node->parent;
                kmem_cache_free(radix_tree_node_cachep, node);
                rtp->nr--;
        }
        kfree(per_cpu(ida_bitmap, cpu));
        per_cpu(ida_bitmap, cpu) = NULL;
        return 0;
}

void __init radix_tree_init(void)
{
        int ret;
        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_maxnodes();
        ret = cpuhp_setup_state_nocalls(CPUHP_RADIX_DEAD, "lib/radix:dead",
                                        NULL, radix_tree_cpu_dead);
        WARN_ON(ret < 0);
}