// SPDX-License-Identifier: GPL-2.0-or-later

  /*
   * 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

   */

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

  #include <linux/bug.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>

  #include <linux/xarray.h>

  /*

   * Radix tree node cache.
   */

  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)
  
  /*

   * Per-cpu pool of preloaded nodes
   */

  DEFINE_PER_CPU(struct radix_tree_preload, radix_tree_preloads) = {
  	.lock = INIT_LOCAL_LOCK(lock),

  };

  EXPORT_PER_CPU_SYMBOL_GPL(radix_tree_preloads);

  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	XA_RETRY_ENTRY

  static inline unsigned long
  get_slot_offset(const struct radix_tree_node *parent, void __rcu **slot)

  {

  	return parent ? slot - parent->slots : 0;

  }

  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 __rcu **entry = rcu_dereference_raw(parent->slots[offset]);

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

  static inline gfp_t root_gfp_mask(const struct radix_tree_root *root)

  {

  	return root->xa_flags & (__GFP_BITS_MASK & ~GFP_ZONEMASK);

  }

  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->xa_flags |= (__force gfp_t)(1 << (tag + ROOT_TAG_SHIFT));

  }

  static inline void root_tag_clear(struct radix_tree_root *root, unsigned tag)

  {

  	root->xa_flags &= (__force gfp_t)~(1 << (tag + ROOT_TAG_SHIFT));

  }
  
  static inline void root_tag_clear_all(struct radix_tree_root *root)
  {

  	root->xa_flags &= (__force gfp_t)((1 << ROOT_TAG_SHIFT) - 1);

  }

  static inline int root_tag_get(const struct radix_tree_root *root, unsigned tag)

  {

  	return (__force int)root->xa_flags & (1 << (tag + ROOT_TAG_SHIFT));

  }

  static inline unsigned root_tags_get(const struct radix_tree_root *root)

  {

  	return (__force unsigned)root->xa_flags >> ROOT_TAG_SHIFT;

  }

  static inline bool is_idr(const struct radix_tree_root *root)

  {

  	return !!(root->xa_flags & 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 & 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);
  }

  /*
   * 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 nr_values)

  {

  	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->nr_values = nr_values;

  		ret->parent = parent;

  		ret->array = root;

  	}

  	return ret;
  }

  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 __must_check 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 used by another cgroup, so

  	 * they should never be accounted to any particular memory cgroup.
  	 */
  	gfp_mask &= ~__GFP_ACCOUNT;

  	local_lock(&radix_tree_preloads.lock);

  	rtp = this_cpu_ptr(&radix_tree_preloads);

  	while (rtp->nr < nr) {

  		local_unlock(&radix_tree_preloads.lock);

  		node = kmem_cache_alloc(radix_tree_node_cachep, gfp_mask);

  		if (node == NULL)
  			goto out;

  		local_lock(&radix_tree_preloads.lock);

  		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 */

  	local_lock(&radix_tree_preloads.lock);

  	return 0;
  }
  EXPORT_SYMBOL(radix_tree_maybe_preload);

  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->xa_head);

  
  	*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)

  {

  	void *entry;

  	unsigned int maxshift;

  	int tag;

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

  	entry = rcu_dereference_raw(root->xa_head);

  	if (!entry && (!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(entry)) {
  			entry_to_node(entry)->parent = node;

  		} else if (xa_is_value(entry)) {

  			/* Moving a value entry root->xa_head to a node */
  			node->nr_values = 1;

  		}

  		/*
  		 * entry was already in the radix tree, so we do not need
  		 * rcu_assign_pointer here
  		 */
  		node->slots[0] = (void __rcu *)entry;
  		entry = node_to_entry(node);

  		rcu_assign_pointer(root->xa_head, entry);

  		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)

  {

  	bool shrunk = false;

  	for (;;) {

  		struct radix_tree_node *node = rcu_dereference_raw(root->xa_head);

  		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, we cannot shrink.

  		 */
  		if (node->count != 1)
  			break;

  		child = rcu_dereference_raw(node->slots[0]);

  		if (!child)
  			break;

  		/*
  		 * For an IDR, we must not shrink entry 0 into the root in
  		 * case somebody calls idr_replace() with a pointer that
  		 * appears to be an internal entry
  		 */
  		if (!node->shift && is_idr(root))
  			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->xa_head) as far as dependent read barriers go.

  		 */

  		root->xa_head = (void __rcu *)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] = (void __rcu *)RADIX_TREE_RETRY;

  		}

  		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)

  {

  	bool deleted = false;

  	do {
  		struct radix_tree_node *parent;
  
  		if (node->count) {

  			if (node_to_entry(node) ==

  					rcu_dereference_raw(root->xa_head))

  				deleted |= radix_tree_shrink(root);

  			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->xa_head = 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

   *	@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->xa_head 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.

   */

  static int __radix_tree_create(struct radix_tree_root *root,

  		unsigned long index, struct radix_tree_node **nodep,
  		void __rcu ***slotp)

  {

  	struct radix_tree_node *node = NULL, *child;

  	void __rcu **slot = (void __rcu **)&root->xa_head;

  	unsigned long maxindex;

  	unsigned int shift, offset = 0;

  	unsigned long max = index;

  	gfp_t gfp = root_gfp_mask(root);

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

  
  	/* Make sure the tree is high enough.  */

  	if (max > maxindex) {

  		int error = radix_tree_extend(root, gfp, max, shift);

  		if (error < 0)

  			return error;

  		shift = error;

  		child = rcu_dereference_raw(root->xa_head);

  	}

  	while (shift > 0) {

  		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 = rcu_dereference_raw(child->slots[offset]);

  		if (xa_is_node(entry) && child->shift) {

  			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;
  		}
  	}
  }

  static inline int insert_entries(struct radix_tree_node *node,

  		void __rcu **slot, void *item, bool replace)

  {
  	if (*slot)
  		return -EEXIST;
  	rcu_assign_pointer(*slot, item);
  	if (node) {
  		node->count++;

  		if (xa_is_value(item))

  			node->nr_values++;

  	}
  	return 1;
  }

  
  /**

   *	__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 __rcu **slot;

  	int error;

  	BUG_ON(radix_tree_is_internal_node(item));

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

  	if (error)
  		return error;

  	error = insert_entries(node, slot, item, 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->xa_head 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 __rcu ***slotp)

  {

  	struct radix_tree_node *node, *parent;

  	unsigned long maxindex;

  	void __rcu **slot;

   restart:
  	parent = NULL;

  	slot = (void __rcu **)&root->xa_head;

  	radix_tree_load_root(root, &node, &maxindex);

  	if (index > maxindex)

  		return NULL;

  	while (radix_tree_is_internal_node(node)) {

  		unsigned offset;

  		parent = entry_to_node(node);

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

  		slot = parent->slots + offset;

  		if (node == RADIX_TREE_RETRY)
  			goto restart;

  		if (parent->shift == 0)
  			break;

  	}

  	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 __rcu **radix_tree_lookup_slot(const struct radix_tree_root *root,

  				unsigned long index)

  {

  	void __rcu **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 void replace_slot(void __rcu **slot, void *item,

  		struct radix_tree_node *node, int count, int values)

  {

  	if (node && (count || values)) {

  		node->count += count;

  		node->nr_values += values;

  	}

  
  	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 __rcu **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.

   *
   * 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 __rcu **slot, void *item)

  {

  	void *old = rcu_dereference_raw(*slot);

  	int values = !!xa_is_value(item) - !!xa_is_value(old);

  	int count = calculate_count(root, node, slot, item, old);

  	/*

  	 * This function supports replacing value entries and

  	 * deleting entries, but that needs accounting against the

  	 * node unless the slot is root->xa_head.

  	 */

  	WARN_ON_ONCE(!node && (slot != (void __rcu **)&root->xa_head) &&

  			(count || values));
  	replace_slot(slot, item, node, count, values);

  	if (!node)
  		return;

  	delete_node(root, node);

  }
  
  /**
   * 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() and

   * 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 value 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 __rcu **slot, void *item)

  {

  	__radix_tree_replace(root, NULL, slot, item);

  }

  EXPORT_SYMBOL(radix_tree_replace_slot);

  /**
   * 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_for_each_slot().
   * Caller must hold tree write locked.

   */
  void radix_tree_iter_replace(struct radix_tree_root *root,

  				const struct radix_tree_iter *iter,
  				void __rcu **slot, void *item)

  {

  	__radix_tree_replace(root, iter->node, slot, item);

  }

  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);

  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 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);

  /* 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);
  	}
  }

  void __rcu **radix_tree_iter_resume(void __rcu **slot,
  					struct radix_tree_iter *iter)

  {

  	slot++;
  	iter->index = __radix_tree_iter_add(iter, 1);

  	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 __rcu **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;

  		return (void __rcu **)&root->xa_head;

  	}

  	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 = rcu_dereference_raw(
  							node->slots[offset]);

  					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 (node->shift && radix_tree_is_internal_node(child));

  
  	/* Update the iterator state */

  	iter->index = (index &~ node_maxindex(node)) | offset;

  	iter->next_index = (index | node_maxindex(node)) + 1;

  	iter->node = node;

  	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 __rcu **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_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 __rcu **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 __rcu ***results, unsigned long first_index,

  		unsigned int max_items, unsigned int tag)

  {

  	struct radix_tree_iter iter;

  	void __rcu **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);

  static bool __radix_tree_delete(struct radix_tree_root *root,