/*
   * 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/kmemleak.h>

  #include <linux/notifier.h>
  #include <linux/cpu.h>

  #include <linux/string.h>
  #include <linux/bitops.h>

  #include <linux/rcupdate.h>

  #include <linux/hardirq.h>		/* in_interrupt() */

  /*
   * 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;

  
  /*

   * 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)
  
  /*

   * Per-cpu pool of preloaded nodes
   */
  struct radix_tree_preload {
  	int nr;

  	struct radix_tree_node *nodes[RADIX_TREE_PRELOAD_SIZE];

  };

  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);

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

  		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 = this_cpu_ptr(&radix_tree_preloads);

  		if (rtp->nr) {
  			ret = rtp->nodes[rtp->nr - 1];
  			rtp->nodes[rtp->nr - 1] = NULL;
  			rtp->nr--;
  		}

  		/*
  		 * Update the allocation stack trace as this is more useful
  		 * for debugging.
  		 */
  		kmemleak_update_trace(ret);

  	}

  	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().

   */

  static int __radix_tree_preload(gfp_t gfp_mask)

  {
  	struct radix_tree_preload *rtp;
  	struct radix_tree_node *node;
  	int ret = -ENOMEM;
  
  	preempt_disable();

  	rtp = this_cpu_ptr(&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 = this_cpu_ptr(&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;
  }

  
  /*
   * 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)
  {
  	/* Warn on non-sensical use... */
  	WARN_ON_ONCE(!(gfp_mask & __GFP_WAIT));
  	return __radix_tree_preload(gfp_mask);
  }

  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 (gfp_mask & __GFP_WAIT)
  		return __radix_tree_preload(gfp_mask);
  	/* Preloading doesn't help anything with this gfp mask, skip it */
  	preempt_disable();
  	return 0;
  }
  EXPORT_SYMBOL(radix_tree_maybe_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;

  		BUG_ON(newheight & ~RADIX_TREE_HEIGHT_MASK);
  		node->path = 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_create	-	create a slot in a radix tree

   *	@root:		radix tree root
   *	@index:		index key

   *	@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,
  			struct radix_tree_node **nodep, void ***slotp)

  {

  	struct radix_tree_node *node = NULL, *slot;

  	unsigned int height, shift, offset;

  	int error;
  
  	/* 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->path = height;

  			slot->parent = node;

  			if (node) {

  				rcu_assign_pointer(node->slots[offset], slot);

  				node->count++;

  				slot->path |= offset << RADIX_TREE_HEIGHT_SHIFT;

  			} 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 (nodep)
  		*nodep = node;
  	if (slotp)
  		*slotp = node ? node->slots + offset : (void **)&root->rnode;
  	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;
  	void **slot;
  	int error;
  
  	BUG_ON(radix_tree_is_indirect_ptr(item));
  
  	error = __radix_tree_create(root, index, &node, &slot);
  	if (error)
  		return error;
  	if (*slot != NULL)

  		return -EEXIST;

  	rcu_assign_pointer(*slot, item);

  	if (node) {
  		node->count++;

  		BUG_ON(tag_get(node, 0, index & RADIX_TREE_MAP_MASK));
  		BUG_ON(tag_get(node, 1, index & RADIX_TREE_MAP_MASK));

  	} else {

  		BUG_ON(root_tag_get(root, 0));
  		BUG_ON(root_tag_get(root, 1));
  	}

  	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(struct radix_tree_root *root, unsigned long index,
  			  struct radix_tree_node **nodep, void ***slotp)

  {

  	struct radix_tree_node *node, *parent;

  	unsigned int height, shift;

  	void **slot;

  	node = rcu_dereference_raw(root->rnode);

  	if (node == NULL)

  		return NULL;

  	if (!radix_tree_is_indirect_ptr(node)) {

  		if (index > 0)
  			return NULL;

  
  		if (nodep)
  			*nodep = NULL;
  		if (slotp)
  			*slotp = (void **)&root->rnode;
  		return node;

  	}

  	node = indirect_to_ptr(node);

  	height = node->path & RADIX_TREE_HEIGHT_MASK;

  	if (index > radix_tree_maxindex(height))
  		return NULL;

  	shift = (height-1) * RADIX_TREE_MAP_SHIFT;

  	do {

  		parent = node;
  		slot = 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);

  	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(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(struct radix_tree_root *root, unsigned long index)
  {

  	return __radix_tree_lookup(root, index, NULL, NULL);

  }
  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->path & RADIX_TREE_HEIGHT_MASK;

  	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, height;

  
  	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 swithing to the next chunk.

  	 */
  	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:

  	height = rnode->path & RADIX_TREE_HEIGHT_MASK;
  	shift = (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_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->path & RADIX_TREE_HEIGHT_MASK;

  	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->path &
  						RADIX_TREE_HEIGHT_MASK);

  		if (cur_index > max_index) {
  			rcu_read_unlock();

  			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_node    -    try to free node after clearing a slot
   *	@root:		radix tree root

   *	@node:		node containing @index
   *
   *	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.
   *
   *	Returns %true if @node was freed, %false otherwise.
   */

  bool __radix_tree_delete_node(struct radix_tree_root *root,

  			      struct radix_tree_node *node)
  {
  	bool deleted = false;
  
  	do {
  		struct radix_tree_node *parent;
  
  		if (node->count) {
  			if (node == indirect_to_ptr(root->rnode)) {
  				radix_tree_shrink(root);
  				if (root->height == 0)
  					deleted = true;
  			}
  			return deleted;
  		}
  
  		parent = node->parent;
  		if (parent) {

  			unsigned int offset;

  			offset = node->path >> RADIX_TREE_HEIGHT_SHIFT;
  			parent->slots[offset] = NULL;

  			parent->count--;
  		} else {
  			root_tag_clear_all(root);
  			root->height = 0;
  			root->rnode = NULL;
  		}
  
  		radix_tree_node_free(node);
  		deleted = true;
  
  		node = parent;
  	} while (node);
  
  	return deleted;
  }
  
  /**

   *	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.

   *

   *	Returns the address of the deleted item, 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;
  	unsigned int offset;
  	void **slot;
  	void *entry;

  	int tag;

  	entry = __radix_tree_lookup(root, index, &node, &slot);
  	if (!entry)
  		return NULL;

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

  		root_tag_clear_all(root);
  		root->rnode = NULL;

  		return entry;

  	}

  	offset = index & RADIX_TREE_MAP_MASK;

  	/*

  	 * 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);

  	}

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

  	__radix_tree_delete_node(root, node);

  	return entry;

  }

  EXPORT_SYMBOL(radix_tree_delete_item);
  
  /**
   *	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)
  {
  	return radix_tree_delete_item(root, index, NULL);
  }

  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 *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_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);
  }