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radix-tree.c

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  • radix-tree.c 38.07 KiB
    /*
     * 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
     *
     * 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/export.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;
    	union {
    		struct radix_tree_node *parent;	/* Used when ascending tree */
    		struct rcu_head	rcu_head;	/* Used when freeing node */
    	};
    	void __rcu	*slots[RADIX_TREE_MAP_SIZE];
    	unsigned long	tags[RADIX_TREE_MAX_TAGS][RADIX_TREE_TAG_LONGS];
    };
    
    #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;
    }
    
    /**
     * 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(const unsigned long *addr,
    			 unsigned long size, unsigned long offset)
    {
    	if (!__builtin_constant_p(size))
    		return find_next_bit(addr, size, offset);
    
    	if (offset < 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 < size) {
    			tmp = *++addr;
    			if (tmp)
    				return __ffs(tmp) + offset;
    			offset += BITS_PER_LONG;
    		}
    	}
    	return size;
    }
    
    /*
     * 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;
    	struct radix_tree_node *slot;
    	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;
    
    		/* 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);
    		}
    
    		/* Increase the height.  */
    		newheight = root->height+1;
    		node->height = newheight;
    		node->count = 1;
    		node->parent = NULL;
    		slot = root->rnode;
    		if (newheight > 1) {
    			slot = indirect_to_ptr(slot);
    			slot->parent = node;
    		}
    		node->slots[0] = slot;
    		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;
    			slot->parent = node;
    			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)
    {
    	struct radix_tree_node *node = NULL;
    	struct radix_tree_node *slot = NULL;
    	unsigned int height, shift;
    	int uninitialized_var(offset);
    
    	height = root->height;
    	if (index > radix_tree_maxindex(height))
    		goto out;
    
    	shift = height * RADIX_TREE_MAP_SHIFT;
    	slot = indirect_to_ptr(root->rnode);
    
    	while (shift) {
    		if (slot == NULL)
    			goto out;
    
    		shift -= RADIX_TREE_MAP_SHIFT;
    		offset = (index >> shift) & RADIX_TREE_MAP_MASK;
    		node = slot;
    		slot = slot->slots[offset];
    	}
    
    	if (slot == NULL)
    		goto out;
    
    	while (node) {
    		if (!tag_get(node, tag, offset))
    			goto out;
    		tag_clear(node, tag, offset);
    		if (any_tag_set(node, tag))
    			goto out;
    
    		index >>= RADIX_TREE_MAP_SHIFT;
    		offset = index & RADIX_TREE_MAP_MASK;
    		node = node->parent;
    	}
    
    	/* 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;
    
    	/* 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;
    		if (!tag_get(node, tag, offset))
    			return 0;
    		if (height == 1)
    			return 1;
    		node = rcu_dereference_raw(node->slots[offset]);
    		shift -= RADIX_TREE_MAP_SHIFT;
    		height--;
    	}
    }
    EXPORT_SYMBOL(radix_tree_tag_get);
    
    /**
     * 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(struct radix_tree_root *root,
    			     struct radix_tree_iter *iter, unsigned flags)
    {
    	unsigned shift, tag = flags & RADIX_TREE_ITER_TAG_MASK;
    	struct radix_tree_node *rnode, *node;
    	unsigned long index, offset;
    
    	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.
    	 */
    	index = iter->next_index;
    	if (!index && iter->index)
    		return NULL;
    
    	rnode = rcu_dereference_raw(root->rnode);
    	if (radix_tree_is_indirect_ptr(rnode)) {
    		rnode = indirect_to_ptr(rnode);
    	} else if (rnode && !index) {
    		/* Single-slot tree */
    		iter->index = 0;
    		iter->next_index = 1;
    		iter->tags = 1;
    		return (void **)&root->rnode;
    	} else
    		return NULL;
    
    restart:
    	shift = (rnode->height - 1) * RADIX_TREE_MAP_SHIFT;
    	offset = index >> shift;
    
    	/* Index outside of the tree */
    	if (offset >= RADIX_TREE_MAP_SIZE)
    		return NULL;
    
    	node = rnode;
    	while (1) {
    		if ((flags & RADIX_TREE_ITER_TAGGED) ?
    				!test_bit(offset, node->tags[tag]) :
    				!node->slots[offset]) {
    			/* Hole detected */
    			if (flags & RADIX_TREE_ITER_CONTIG)
    				return NULL;
    
    			if (flags & RADIX_TREE_ITER_TAGGED)
    				offset = radix_tree_find_next_bit(
    						node->tags[tag],
    						RADIX_TREE_MAP_SIZE,
    						offset + 1);
    			else
    				while (++offset	< RADIX_TREE_MAP_SIZE) {
    					if (node->slots[offset])
    						break;
    				}
    			index &= ~((RADIX_TREE_MAP_SIZE << shift) - 1);
    			index += offset << shift;
    			/* Overflow after ~0UL */
    			if (!index)
    				return NULL;
    			if (offset == RADIX_TREE_MAP_SIZE)
    				goto restart;
    		}
    
    		/* This is leaf-node */
    		if (!shift)
    			break;
    
    		node = rcu_dereference_raw(node->slots[offset]);
    		if (node == NULL)
    			goto restart;
    		shift -= RADIX_TREE_MAP_SHIFT;
    		offset = (index >> shift) & RADIX_TREE_MAP_MASK;
    	}
    
    	/* Update the iterator state */
    	iter->index = index;
    	iter->next_index = (index | RADIX_TREE_MAP_MASK) + 1;
    
    	/* Construct iter->tags bit-mask from node->tags[tag] array */
    	if (flags & RADIX_TREE_ITER_TAGGED) {
    		unsigned tag_long, tag_bit;
    
    		tag_long = offset / BITS_PER_LONG;
    		tag_bit  = offset % BITS_PER_LONG;
    		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 = index + BITS_PER_LONG;
    		}
    	}
    
    	return node->slots + offset;
    }
    EXPORT_SYMBOL(radix_tree_next_chunk);
    
    /**
     * 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_node *node = NULL;
    	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);
    
    	for (;;) {
    		unsigned long upindex;
    		int offset;
    
    		offset = (index >> shift) & RADIX_TREE_MAP_MASK;
    		if (!slot->slots[offset])
    			goto next;
    		if (!tag_get(slot, iftag, offset))
    			goto next;
    		if (shift) {
    			/* Go down one level */
    			shift -= RADIX_TREE_MAP_SHIFT;
    			node = slot;
    			slot = slot->slots[offset];
    			continue;
    		}
    
    		/* tag the leaf */
    		tagged++;
    		tag_set(slot, settag, offset);
    
    		/* walk back up the path tagging interior nodes */
    		upindex = index;
    		while (node) {
    			upindex >>= RADIX_TREE_MAP_SHIFT;
    			offset = upindex & RADIX_TREE_MAP_MASK;
    
    			/* stop if we find a node with the tag already set */
    			if (tag_get(node, settag, offset))
    				break;
    			tag_set(node, settag, offset);
    			node = node->parent;
    		}
    
    		/*
    		 * Small optimization: now clear that node pointer.
    		 * Since all of this slot's ancestors now have the tag set
    		 * from setting it above, we have no further need to walk
    		 * back up the tree setting tags, until we update slot to
    		 * point to another radix_tree_node.
    		 */
    		node = NULL;
    
    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 = slot->parent;
    			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);
    
    /**
     *	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)
    {
    	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] = indirect_to_ptr(rcu_dereference_raw(*slot));
    		if (!results[ret])
    			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(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(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] = indirect_to_ptr(rcu_dereference_raw(*slot));
    		if (!results[ret])
    			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(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);
    
    #if defined(CONFIG_SHMEM) && defined(CONFIG_SWAP)
    #include <linux/sched.h> /* for cond_resched() */
    
    /*
     * This linear search is at present only useful to shmem_unuse_inode().
     */
    static unsigned long __locate(struct radix_tree_node *slot, void *item,
    			      unsigned long index, unsigned long *found_index)
    {
    	unsigned int shift, height;
    	unsigned long i;
    
    	height = slot->height;
    	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: check items */
    	for (i = 0; i < RADIX_TREE_MAP_SIZE; i++) {
    		if (slot->slots[i] == item) {
    			*found_index = index + i;
    			index = 0;
    			goto out;
    		}
    	}
    	index += RADIX_TREE_MAP_SIZE;
    out:
    	return index;
    }
    
    /**
     *	radix_tree_locate_item - search through radix tree for item
     *	@root:		radix tree root
     *	@item:		item to be found
     *
     *	Returns index where item was found, or -1 if not found.
     *	Caller must hold no lock (since this time-consuming function needs
     *	to be preemptible), and must check afterwards if item is still there.
     */
    unsigned long radix_tree_locate_item(struct radix_tree_root *root, void *item)
    {
    	struct radix_tree_node *node;
    	unsigned long max_index;
    	unsigned long cur_index = 0;
    	unsigned long found_index = -1;
    
    	do {
    		rcu_read_lock();
    		node = rcu_dereference_raw(root->rnode);
    		if (!radix_tree_is_indirect_ptr(node)) {
    			rcu_read_unlock();
    			if (node == item)
    				found_index = 0;
    			break;
    		}
    
    		node = indirect_to_ptr(node);
    		max_index = radix_tree_maxindex(node->height);
    		if (cur_index > max_index)
    			break;
    
    		cur_index = __locate(node, item, cur_index, &found_index);
    		rcu_read_unlock();
    		cond_resched();
    	} while (cur_index != 0 && cur_index <= max_index);
    
    	return found_index;
    }
    #else
    unsigned long radix_tree_locate_item(struct radix_tree_root *root, void *item)
    {
    	return -1;
    }
    #endif /* CONFIG_SHMEM && CONFIG_SWAP */
    
    /**
     *	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;
    		struct radix_tree_node *slot;
    
    		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.
    		 */
    		slot = to_free->slots[0];
    		if (root->height > 1) {
    			slot->parent = NULL;
    			slot = ptr_to_indirect(slot);
    		}
    		root->rnode = slot;
    		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)
    {
    	struct radix_tree_node *node = NULL;
    	struct radix_tree_node *slot = NULL;
    	struct radix_tree_node *to_free;
    	unsigned int height, shift;
    	int tag;
    	int uninitialized_var(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 * RADIX_TREE_MAP_SHIFT;
    
    	do {
    		if (slot == NULL)
    			goto out;
    
    		shift -= RADIX_TREE_MAP_SHIFT;
    		offset = (index >> shift) & RADIX_TREE_MAP_MASK;
    		node = slot;
    		slot = slot->slots[offset];
    	} while (shift);
    
    	if (slot == NULL)
    		goto out;
    
    	/*
    	 * Clear all tags associated with the item to be deleted.
    	 * This way of doing it would be inefficient, but seldom is any set.
    	 */
    	for (tag = 0; tag < RADIX_TREE_MAX_TAGS; tag++) {
    		if (tag_get(node, tag, offset))
    			radix_tree_tag_clear(root, index, tag);
    	}
    
    	to_free = NULL;
    	/* Now free the nodes we do not need anymore */
    	while (node) {
    		node->slots[offset] = NULL;
    		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 (node->count) {
    			if (node == indirect_to_ptr(root->rnode))
    				radix_tree_shrink(root);
    			goto out;
    		}
    
    		/* Node with zero slots in use so free it */
    		to_free = node;
    
    		index >>= RADIX_TREE_MAP_SHIFT;
    		offset = index & RADIX_TREE_MAP_MASK;
    		node = node->parent;
    	}
    
    	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);
    }