drivers/md/persistent-data/dm-btree-remove.c - linux - Git at Google

 /*
  * Copyright (C) 2011 Red Hat, Inc.
  *
  * This file is released under the GPL.
  */

 #include "dm-btree.h"
 #include "dm-btree-internal.h"
 #include "dm-transaction-manager.h"

 #include <linux/export.h>

 /*
  * Removing an entry from a btree
  * ==============================
  *
  * A very important constraint for our btree is that no node, except the
  * root, may have fewer than a certain number of entries.
  * (MIN_ENTRIES <= nr_entries <= MAX_ENTRIES).
  *
  * Ensuring this is complicated by the way we want to only ever hold the
  * locks on 2 nodes concurrently, and only change nodes in a top to bottom
  * fashion.
  *
  * Each node may have a left or right sibling.  When decending the spine,
  * if a node contains only MIN_ENTRIES then we try and increase this to at
  * least MIN_ENTRIES + 1.  We do this in the following ways:
  *
  * [A] No siblings => this can only happen if the node is the root, in which
  *     case we copy the childs contents over the root.
  *
  * [B] No left sibling
  *     ==> rebalance(node, right sibling)
  *
  * [C] No right sibling
  *     ==> rebalance(left sibling, node)
  *
  * [D] Both siblings, total_entries(left, node, right) <= DEL_THRESHOLD
  *     ==> delete node adding it's contents to left and right
  *
  * [E] Both siblings, total_entries(left, node, right) > DEL_THRESHOLD
  *     ==> rebalance(left, node, right)
  *
  * After these operations it's possible that the our original node no
  * longer contains the desired sub tree.  For this reason this rebalancing
  * is performed on the children of the current node.  This also avoids
  * having a special case for the root.
  *
  * Once this rebalancing has occurred we can then step into the child node
  * for internal nodes.  Or delete the entry for leaf nodes.
  */

 /*
  * Some little utilities for moving node data around.
  */
 static void node_shift(struct btree_node *n, int shift)
 {
 	uint32_t nr_entries = le32_to_cpu(n->header.nr_entries);
 	uint32_t value_size = le32_to_cpu(n->header.value_size);

 	if (shift < 0) {
 		shift = -shift;
 		BUG_ON(shift > nr_entries);
 		BUG_ON((void *) key_ptr(n, shift) >= value_ptr(n, shift));
 		memmove(key_ptr(n, 0),
 			key_ptr(n, shift),
 			(nr_entries - shift) * sizeof(__le64));
 		memmove(value_ptr(n, 0),
 			value_ptr(n, shift),
 			(nr_entries - shift) * value_size);
 	} else {
 		BUG_ON(nr_entries + shift > le32_to_cpu(n->header.max_entries));
 		memmove(key_ptr(n, shift),
 			key_ptr(n, 0),
 			nr_entries * sizeof(__le64));
 		memmove(value_ptr(n, shift),
 			value_ptr(n, 0),
 			nr_entries * value_size);
 	}
 }

 static void node_copy(struct btree_node *left, struct btree_node *right, int shift)
 {
 	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
 	uint32_t value_size = le32_to_cpu(left->header.value_size);
 	BUG_ON(value_size != le32_to_cpu(right->header.value_size));

 	if (shift < 0) {
 		shift = -shift;
 		BUG_ON(nr_left + shift > le32_to_cpu(left->header.max_entries));
 		memcpy(key_ptr(left, nr_left),
 		       key_ptr(right, 0),
 		       shift * sizeof(__le64));
 		memcpy(value_ptr(left, nr_left),
 		       value_ptr(right, 0),
 		       shift * value_size);
 	} else {
 		BUG_ON(shift > le32_to_cpu(right->header.max_entries));
 		memcpy(key_ptr(right, 0),
 		       key_ptr(left, nr_left - shift),
 		       shift * sizeof(__le64));
 		memcpy(value_ptr(right, 0),
 		       value_ptr(left, nr_left - shift),
 		       shift * value_size);
 	}
 }

 /*
  * Delete a specific entry from a leaf node.
  */
 static void delete_at(struct btree_node *n, unsigned index)
 {
 	unsigned nr_entries = le32_to_cpu(n->header.nr_entries);
 	unsigned nr_to_copy = nr_entries - (index + 1);
 	uint32_t value_size = le32_to_cpu(n->header.value_size);
 	BUG_ON(index >= nr_entries);

 	if (nr_to_copy) {
 		memmove(key_ptr(n, index),
 			key_ptr(n, index + 1),
 			nr_to_copy * sizeof(__le64));

 		memmove(value_ptr(n, index),
 			value_ptr(n, index + 1),
 			nr_to_copy * value_size);
 	}

 	n->header.nr_entries = cpu_to_le32(nr_entries - 1);
 }

 static unsigned merge_threshold(struct btree_node *n)
 {
 	return le32_to_cpu(n->header.max_entries) / 3;
 }

 struct child {
 	unsigned index;
 	struct dm_block *block;
 	struct btree_node *n;
 };

 static int init_child(struct dm_btree_info *info, struct dm_btree_value_type *vt,
 		      struct btree_node *parent,
 		      unsigned index, struct child *result)
 {
 	int r, inc;
 	dm_block_t root;

 	result->index = index;
 	root = value64(parent, index);

 	r = dm_tm_shadow_block(info->tm, root, &btree_node_validator,
 			       &result->block, &inc);
 	if (r)
 		return r;

 	result->n = dm_block_data(result->block);

 	if (inc)
 		inc_children(info->tm, result->n, vt);

 	*((__le64 *) value_ptr(parent, index)) =
 		cpu_to_le64(dm_block_location(result->block));

 	return 0;
 }

 static void exit_child(struct dm_btree_info *info, struct child *c)
 {
 	dm_tm_unlock(info->tm, c->block);
 }

 static void shift(struct btree_node *left, struct btree_node *right, int count)
 {
 	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
 	uint32_t nr_right = le32_to_cpu(right->header.nr_entries);
 	uint32_t max_entries = le32_to_cpu(left->header.max_entries);
 	uint32_t r_max_entries = le32_to_cpu(right->header.max_entries);

 	BUG_ON(max_entries != r_max_entries);
 	BUG_ON(nr_left - count > max_entries);
 	BUG_ON(nr_right + count > max_entries);

 	if (!count)
 		return;

 	if (count > 0) {
 		node_shift(right, count);
 		node_copy(left, right, count);
 	} else {
 		node_copy(left, right, count);
 		node_shift(right, count);
 	}

 	left->header.nr_entries = cpu_to_le32(nr_left - count);
 	right->header.nr_entries = cpu_to_le32(nr_right + count);
 }

 static void __rebalance2(struct dm_btree_info *info, struct btree_node *parent,
 			 struct child *l, struct child *r)
 {
 	struct btree_node *left = l->n;
 	struct btree_node *right = r->n;
 	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
 	uint32_t nr_right = le32_to_cpu(right->header.nr_entries);
 	/*
 	 * Ensure the number of entries in each child will be greater
 	 * than or equal to (max_entries / 3 + 1), so no matter which
 	 * child is used for removal, the number will still be not
 	 * less than (max_entries / 3).
 	 */
 	unsigned int threshold = 2 * (merge_threshold(left) + 1);

 	if (nr_left + nr_right < threshold) {
 		/*
 		 * Merge
 		 */
 		node_copy(left, right, -nr_right);
 		left->header.nr_entries = cpu_to_le32(nr_left + nr_right);
 		delete_at(parent, r->index);

 		/*
 		 * We need to decrement the right block, but not it's
 		 * children, since they're still referenced by left.
 		 */
 		dm_tm_dec(info->tm, dm_block_location(r->block));
 	} else {
 		/*
 		 * Rebalance.
 		 */
 		unsigned target_left = (nr_left + nr_right) / 2;
 		shift(left, right, nr_left - target_left);
 		*key_ptr(parent, r->index) = right->keys[0];
 	}
 }

 static int rebalance2(struct shadow_spine *s, struct dm_btree_info *info,
 		      struct dm_btree_value_type *vt, unsigned left_index)
 {
 	int r;
 	struct btree_node *parent;
 	struct child left, right;

 	parent = dm_block_data(shadow_current(s));

 	r = init_child(info, vt, parent, left_index, &left);
 	if (r)
 		return r;

 	r = init_child(info, vt, parent, left_index + 1, &right);
 	if (r) {
 		exit_child(info, &left);
 		return r;
 	}

 	__rebalance2(info, parent, &left, &right);

 	exit_child(info, &left);
 	exit_child(info, &right);

 	return 0;
 }

 /*
  * We dump as many entries from center as possible into left, then the rest
  * in right, then rebalance2.  This wastes some cpu, but I want something
  * simple atm.
  */
 static void delete_center_node(struct dm_btree_info *info, struct btree_node *parent,
 			       struct child *l, struct child *c, struct child *r,
 			       struct btree_node *left, struct btree_node *center, struct btree_node *right,
 			       uint32_t nr_left, uint32_t nr_center, uint32_t nr_right)
 {
 	uint32_t max_entries = le32_to_cpu(left->header.max_entries);
 	unsigned shift = min(max_entries - nr_left, nr_center);

 	BUG_ON(nr_left + shift > max_entries);
 	node_copy(left, center, -shift);
 	left->header.nr_entries = cpu_to_le32(nr_left + shift);

 	if (shift != nr_center) {
 		shift = nr_center - shift;
 		BUG_ON((nr_right + shift) > max_entries);
 		node_shift(right, shift);
 		node_copy(center, right, shift);
 		right->header.nr_entries = cpu_to_le32(nr_right + shift);
 	}
 	*key_ptr(parent, r->index) = right->keys[0];

 	delete_at(parent, c->index);
 	r->index--;

 	dm_tm_dec(info->tm, dm_block_location(c->block));
 	__rebalance2(info, parent, l, r);
 }

 /*
  * Redistributes entries among 3 sibling nodes.
  */
 static void redistribute3(struct dm_btree_info *info, struct btree_node *parent,
 			  struct child *l, struct child *c, struct child *r,
 			  struct btree_node *left, struct btree_node *center, struct btree_node *right,
 			  uint32_t nr_left, uint32_t nr_center, uint32_t nr_right)
 {
 	int s;
 	uint32_t max_entries = le32_to_cpu(left->header.max_entries);
 	unsigned total = nr_left + nr_center + nr_right;
 	unsigned target_right = total / 3;
 	unsigned remainder = (target_right * 3) != total;
 	unsigned target_left = target_right + remainder;

 	BUG_ON(target_left > max_entries);
 	BUG_ON(target_right > max_entries);

 	if (nr_left < nr_right) {
 		s = nr_left - target_left;

 		if (s < 0 && nr_center < -s) {
 			/* not enough in central node */
 			shift(left, center, -nr_center);
 			s += nr_center;
 			shift(left, right, s);
 			nr_right += s;
 		} else
 			shift(left, center, s);

 		shift(center, right, target_right - nr_right);

 	} else {
 		s = target_right - nr_right;
 		if (s > 0 && nr_center < s) {
 			/* not enough in central node */
 			shift(center, right, nr_center);
 			s -= nr_center;
 			shift(left, right, s);
 			nr_left -= s;
 		} else
 			shift(center, right, s);

 		shift(left, center, nr_left - target_left);
 	}

 	*key_ptr(parent, c->index) = center->keys[0];
 	*key_ptr(parent, r->index) = right->keys[0];
 }

 static void __rebalance3(struct dm_btree_info *info, struct btree_node *parent,
 			 struct child *l, struct child *c, struct child *r)
 {
 	struct btree_node *left = l->n;
 	struct btree_node *center = c->n;
 	struct btree_node *right = r->n;

 	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
 	uint32_t nr_center = le32_to_cpu(center->header.nr_entries);
 	uint32_t nr_right = le32_to_cpu(right->header.nr_entries);

 	unsigned threshold = merge_threshold(left) * 4 + 1;

 	BUG_ON(left->header.max_entries != center->header.max_entries);
 	BUG_ON(center->header.max_entries != right->header.max_entries);

 	if ((nr_left + nr_center + nr_right) < threshold)
 		delete_center_node(info, parent, l, c, r, left, center, right,
 				   nr_left, nr_center, nr_right);
 	else
 		redistribute3(info, parent, l, c, r, left, center, right,
 			      nr_left, nr_center, nr_right);
 }

 static int rebalance3(struct shadow_spine *s, struct dm_btree_info *info,
 		      struct dm_btree_value_type *vt, unsigned left_index)
 {
 	int r;
 	struct btree_node *parent = dm_block_data(shadow_current(s));
 	struct child left, center, right;

 	/*
 	 * FIXME: fill out an array?
 	 */
 	r = init_child(info, vt, parent, left_index, &left);
 	if (r)
 		return r;

 	r = init_child(info, vt, parent, left_index + 1, &center);
 	if (r) {
 		exit_child(info, &left);
 		return r;
 	}

 	r = init_child(info, vt, parent, left_index + 2, &right);
 	if (r) {
 		exit_child(info, &left);
 		exit_child(info, &center);
 		return r;
 	}

 	__rebalance3(info, parent, &left, &center, &right);

 	exit_child(info, &left);
 	exit_child(info, &center);
 	exit_child(info, &right);

 	return 0;
 }

 static int rebalance_children(struct shadow_spine *s,
 			      struct dm_btree_info *info,
 			      struct dm_btree_value_type *vt, uint64_t key)
 {
 	int i, r, has_left_sibling, has_right_sibling;
 	struct btree_node *n;

 	n = dm_block_data(shadow_current(s));

 	if (le32_to_cpu(n->header.nr_entries) == 1) {
 		struct dm_block *child;
 		dm_block_t b = value64(n, 0);

 		r = dm_tm_read_lock(info->tm, b, &btree_node_validator, &child);
 		if (r)
 			return r;

 		memcpy(n, dm_block_data(child),
 		       dm_bm_block_size(dm_tm_get_bm(info->tm)));
 		dm_tm_unlock(info->tm, child);

 		dm_tm_dec(info->tm, dm_block_location(child));
 		return 0;
 	}

 	i = lower_bound(n, key);
 	if (i < 0)
 		return -ENODATA;

 	has_left_sibling = i > 0;
 	has_right_sibling = i < (le32_to_cpu(n->header.nr_entries) - 1);

 	if (!has_left_sibling)
 		r = rebalance2(s, info, vt, i);

 	else if (!has_right_sibling)
 		r = rebalance2(s, info, vt, i - 1);

 	else
 		r = rebalance3(s, info, vt, i - 1);

 	return r;
 }

 static int do_leaf(struct btree_node *n, uint64_t key, unsigned *index)
 {
 	int i = lower_bound(n, key);

 	if ((i < 0) ||
 	    (i >= le32_to_cpu(n->header.nr_entries)) ||
 	    (le64_to_cpu(n->keys[i]) != key))
 		return -ENODATA;

 	*index = i;

 	return 0;
 }

 /*
  * Prepares for removal from one level of the hierarchy.  The caller must
  * call delete_at() to remove the entry at index.
  */
 static int remove_raw(struct shadow_spine *s, struct dm_btree_info *info,
 		      struct dm_btree_value_type *vt, dm_block_t root,
 		      uint64_t key, unsigned *index)
 {
 	int i = *index, r;
 	struct btree_node *n;

 	for (;;) {
 		r = shadow_step(s, root, vt);
 		if (r < 0)
 			break;

 		/*
 		 * We have to patch up the parent node, ugly, but I don't
 		 * see a way to do this automatically as part of the spine
 		 * op.
 		 */
 		if (shadow_has_parent(s)) {
 			__le64 location = cpu_to_le64(dm_block_location(shadow_current(s)));
 			memcpy(value_ptr(dm_block_data(shadow_parent(s)), i),
 			       &location, sizeof(__le64));
 		}

 		n = dm_block_data(shadow_current(s));

 		if (le32_to_cpu(n->header.flags) & LEAF_NODE)
 			return do_leaf(n, key, index);

 		r = rebalance_children(s, info, vt, key);
 		if (r)
 			break;

 		n = dm_block_data(shadow_current(s));
 		if (le32_to_cpu(n->header.flags) & LEAF_NODE)
 			return do_leaf(n, key, index);

 		i = lower_bound(n, key);

 		/*
 		 * We know the key is present, or else
 		 * rebalance_children would have returned
 		 * -ENODATA
 		 */
 		root = value64(n, i);
 	}

 	return r;
 }

 int dm_btree_remove(struct dm_btree_info *info, dm_block_t root,
 		    uint64_t *keys, dm_block_t *new_root)
 {
 	unsigned level, last_level = info->levels - 1;
 	int index = 0, r = 0;
 	struct shadow_spine spine;
 	struct btree_node *n;
 	struct dm_btree_value_type le64_vt;

 	init_le64_type(info->tm, &le64_vt);
 	init_shadow_spine(&spine, info);
 	for (level = 0; level < info->levels; level++) {
 		r = remove_raw(&spine, info,
 			       (level == last_level ?
 				&info->value_type : &le64_vt),
 			       root, keys[level], (unsigned *)&index);
 		if (r < 0)
 			break;

 		n = dm_block_data(shadow_current(&spine));
 		if (level != last_level) {
 			root = value64(n, index);
 			continue;
 		}

 		BUG_ON(index < 0 || index >= le32_to_cpu(n->header.nr_entries));

 		if (info->value_type.dec)
 			info->value_type.dec(info->value_type.context,
 					     value_ptr(n, index), 1);

 		delete_at(n, index);
 	}

 	if (!r)
 		*new_root = shadow_root(&spine);
 	exit_shadow_spine(&spine);

 	return r;
 }
 EXPORT_SYMBOL_GPL(dm_btree_remove);

 /*----------------------------------------------------------------*/

 static int remove_nearest(struct shadow_spine *s, struct dm_btree_info *info,
 			  struct dm_btree_value_type *vt, dm_block_t root,
 			  uint64_t key, int *index)
 {
 	int i = *index, r;
 	struct btree_node *n;

 	for (;;) {
 		r = shadow_step(s, root, vt);
 		if (r < 0)
 			break;

 		/*
 		 * We have to patch up the parent node, ugly, but I don't
 		 * see a way to do this automatically as part of the spine
 		 * op.
 		 */
 		if (shadow_has_parent(s)) {
 			__le64 location = cpu_to_le64(dm_block_location(shadow_current(s)));
 			memcpy(value_ptr(dm_block_data(shadow_parent(s)), i),
 			       &location, sizeof(__le64));
 		}

 		n = dm_block_data(shadow_current(s));

 		if (le32_to_cpu(n->header.flags) & LEAF_NODE) {
 			*index = lower_bound(n, key);
 			return 0;
 		}

 		r = rebalance_children(s, info, vt, key);
 		if (r)
 			break;

 		n = dm_block_data(shadow_current(s));
 		if (le32_to_cpu(n->header.flags) & LEAF_NODE) {
 			*index = lower_bound(n, key);
 			return 0;
 		}

 		i = lower_bound(n, key);

 		/*
 		 * We know the key is present, or else
 		 * rebalance_children would have returned
 		 * -ENODATA
 		 */
 		root = value64(n, i);
 	}

 	return r;
 }

 static int remove_one(struct dm_btree_info *info, dm_block_t root,
 		      uint64_t *keys, uint64_t end_key,
 		      dm_block_t *new_root, unsigned *nr_removed)
 {
 	unsigned level, last_level = info->levels - 1;
 	int index = 0, r = 0;
 	struct shadow_spine spine;
 	struct btree_node *n;
 	struct dm_btree_value_type le64_vt;
 	uint64_t k;

 	init_le64_type(info->tm, &le64_vt);
 	init_shadow_spine(&spine, info);
 	for (level = 0; level < last_level; level++) {
 		r = remove_raw(&spine, info, &le64_vt,
 			       root, keys[level], (unsigned *) &index);
 		if (r < 0)
 			goto out;

 		n = dm_block_data(shadow_current(&spine));
 		root = value64(n, index);
 	}

 	r = remove_nearest(&spine, info, &info->value_type,
 			   root, keys[last_level], &index);
 	if (r < 0)
 		goto out;

 	n = dm_block_data(shadow_current(&spine));

 	if (index < 0)
 		index = 0;

 	if (index >= le32_to_cpu(n->header.nr_entries)) {
 		r = -ENODATA;
 		goto out;
 	}

 	k = le64_to_cpu(n->keys[index]);
 	if (k >= keys[last_level] && k < end_key) {
 		if (info->value_type.dec)
 			info->value_type.dec(info->value_type.context,
 					     value_ptr(n, index), 1);

 		delete_at(n, index);
 		keys[last_level] = k + 1ull;

 	} else
 		r = -ENODATA;

 out:
 	*new_root = shadow_root(&spine);
 	exit_shadow_spine(&spine);

 	return r;
 }

 int dm_btree_remove_leaves(struct dm_btree_info *info, dm_block_t root,
 			   uint64_t *first_key, uint64_t end_key,
 			   dm_block_t *new_root, unsigned *nr_removed)
 {
 	int r;

 	*nr_removed = 0;
 	do {
 		r = remove_one(info, root, first_key, end_key, &root, nr_removed);
 		if (!r)
 			(*nr_removed)++;
 	} while (!r);

 	*new_root = root;
 	return r == -ENODATA ? 0 : r;
 }
 EXPORT_SYMBOL_GPL(dm_btree_remove_leaves);
	/*
	* Copyright (C) 2011 Red Hat, Inc.
	*
	* This file is released under the GPL.
	*/

	#include "dm-btree.h"
	#include "dm-btree-internal.h"
	#include "dm-transaction-manager.h"

	#include <linux/export.h>

	/*
	* Removing an entry from a btree
	* ==============================
	*
	* A very important constraint for our btree is that no node, except the
	* root, may have fewer than a certain number of entries.
	* (MIN_ENTRIES <= nr_entries <= MAX_ENTRIES).
	*
	* Ensuring this is complicated by the way we want to only ever hold the
	* locks on 2 nodes concurrently, and only change nodes in a top to bottom
	* fashion.
	*
	* Each node may have a left or right sibling. When decending the spine,
	* if a node contains only MIN_ENTRIES then we try and increase this to at
	* least MIN_ENTRIES + 1. We do this in the following ways:
	*
	* [A] No siblings => this can only happen if the node is the root, in which
	* case we copy the childs contents over the root.
	*
	* [B] No left sibling
	* ==> rebalance(node, right sibling)
	*
	* [C] No right sibling
	* ==> rebalance(left sibling, node)
	*
	* [D] Both siblings, total_entries(left, node, right) <= DEL_THRESHOLD
	* ==> delete node adding it's contents to left and right
	*
	* [E] Both siblings, total_entries(left, node, right) > DEL_THRESHOLD
	* ==> rebalance(left, node, right)
	*
	* After these operations it's possible that the our original node no
	* longer contains the desired sub tree. For this reason this rebalancing
	* is performed on the children of the current node. This also avoids
	* having a special case for the root.
	*
	* Once this rebalancing has occurred we can then step into the child node
	* for internal nodes. Or delete the entry for leaf nodes.
	*/

	/*
	* Some little utilities for moving node data around.
	*/
	static void node_shift(struct btree_node *n, int shift)
	{
	uint32_t nr_entries = le32_to_cpu(n->header.nr_entries);
	uint32_t value_size = le32_to_cpu(n->header.value_size);

	if (shift < 0) {
	shift = -shift;
	BUG_ON(shift > nr_entries);
	BUG_ON((void *) key_ptr(n, shift) >= value_ptr(n, shift));
	memmove(key_ptr(n, 0),
	key_ptr(n, shift),
	(nr_entries - shift) * sizeof(__le64));
	memmove(value_ptr(n, 0),
	value_ptr(n, shift),
	(nr_entries - shift) * value_size);
	} else {
	BUG_ON(nr_entries + shift > le32_to_cpu(n->header.max_entries));
	memmove(key_ptr(n, shift),
	key_ptr(n, 0),
	nr_entries * sizeof(__le64));
	memmove(value_ptr(n, shift),
	value_ptr(n, 0),
	nr_entries * value_size);
	}
	}

	static void node_copy(struct btree_node left, struct btree_node right, int shift)
	{
	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
	uint32_t value_size = le32_to_cpu(left->header.value_size);
	BUG_ON(value_size != le32_to_cpu(right->header.value_size));

	if (shift < 0) {
	shift = -shift;
	BUG_ON(nr_left + shift > le32_to_cpu(left->header.max_entries));
	memcpy(key_ptr(left, nr_left),
	key_ptr(right, 0),
	shift * sizeof(__le64));
	memcpy(value_ptr(left, nr_left),
	value_ptr(right, 0),
	shift * value_size);
	} else {
	BUG_ON(shift > le32_to_cpu(right->header.max_entries));
	memcpy(key_ptr(right, 0),
	key_ptr(left, nr_left - shift),
	shift * sizeof(__le64));
	memcpy(value_ptr(right, 0),
	value_ptr(left, nr_left - shift),
	shift * value_size);
	}
	}

	/*
	* Delete a specific entry from a leaf node.
	*/
	static void delete_at(struct btree_node *n, unsigned index)
	{
	unsigned nr_entries = le32_to_cpu(n->header.nr_entries);
	unsigned nr_to_copy = nr_entries - (index + 1);
	uint32_t value_size = le32_to_cpu(n->header.value_size);
	BUG_ON(index >= nr_entries);

	if (nr_to_copy) {
	memmove(key_ptr(n, index),
	key_ptr(n, index + 1),
	nr_to_copy * sizeof(__le64));

	memmove(value_ptr(n, index),
	value_ptr(n, index + 1),
	nr_to_copy * value_size);
	}

	n->header.nr_entries = cpu_to_le32(nr_entries - 1);
	}

	static unsigned merge_threshold(struct btree_node *n)
	{
	return le32_to_cpu(n->header.max_entries) / 3;
	}

	struct child {
	unsigned index;
	struct dm_block *block;
	struct btree_node *n;
	};

	static int init_child(struct dm_btree_info info, struct dm_btree_value_type vt,
	struct btree_node *parent,
	unsigned index, struct child *result)
	{
	int r, inc;
	dm_block_t root;

	result->index = index;
	root = value64(parent, index);

	r = dm_tm_shadow_block(info->tm, root, &btree_node_validator,
	&result->block, &inc);
	if (r)
	return r;

	result->n = dm_block_data(result->block);

	if (inc)
	inc_children(info->tm, result->n, vt);

	((__le64 ) value_ptr(parent, index)) =
	cpu_to_le64(dm_block_location(result->block));

	return 0;
	}

	static void exit_child(struct dm_btree_info info, struct child c)
	{
	dm_tm_unlock(info->tm, c->block);
	}

	static void shift(struct btree_node left, struct btree_node right, int count)
	{
	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
	uint32_t nr_right = le32_to_cpu(right->header.nr_entries);
	uint32_t max_entries = le32_to_cpu(left->header.max_entries);
	uint32_t r_max_entries = le32_to_cpu(right->header.max_entries);

	BUG_ON(max_entries != r_max_entries);
	BUG_ON(nr_left - count > max_entries);
	BUG_ON(nr_right + count > max_entries);

	if (!count)
	return;

	if (count > 0) {
	node_shift(right, count);
	node_copy(left, right, count);
	} else {
	node_copy(left, right, count);
	node_shift(right, count);
	}

	left->header.nr_entries = cpu_to_le32(nr_left - count);
	right->header.nr_entries = cpu_to_le32(nr_right + count);
	}

	static void __rebalance2(struct dm_btree_info info, struct btree_node parent,
	struct child l, struct child r)
	{
	struct btree_node *left = l->n;
	struct btree_node *right = r->n;
	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
	uint32_t nr_right = le32_to_cpu(right->header.nr_entries);
	/*
	* Ensure the number of entries in each child will be greater
	* than or equal to (max_entries / 3 + 1), so no matter which
	* child is used for removal, the number will still be not
	* less than (max_entries / 3).
	*/
	unsigned int threshold = 2 * (merge_threshold(left) + 1);

	if (nr_left + nr_right < threshold) {
	/*
	* Merge
	*/
	node_copy(left, right, -nr_right);
	left->header.nr_entries = cpu_to_le32(nr_left + nr_right);
	delete_at(parent, r->index);

	/*
	* We need to decrement the right block, but not it's
	* children, since they're still referenced by left.
	*/
	dm_tm_dec(info->tm, dm_block_location(r->block));
	} else {
	/*
	* Rebalance.
	*/
	unsigned target_left = (nr_left + nr_right) / 2;
	shift(left, right, nr_left - target_left);
	*key_ptr(parent, r->index) = right->keys[0];
	}
	}

	static int rebalance2(struct shadow_spine s, struct dm_btree_info info,
	struct dm_btree_value_type *vt, unsigned left_index)
	{
	int r;
	struct btree_node *parent;
	struct child left, right;

	parent = dm_block_data(shadow_current(s));

	r = init_child(info, vt, parent, left_index, &left);
	if (r)
	return r;

	r = init_child(info, vt, parent, left_index + 1, &right);
	if (r) {
	exit_child(info, &left);
	return r;
	}

	__rebalance2(info, parent, &left, &right);

	exit_child(info, &left);
	exit_child(info, &right);

	return 0;
	}

	/*
	* We dump as many entries from center as possible into left, then the rest
	* in right, then rebalance2. This wastes some cpu, but I want something
	* simple atm.
	*/
	static void delete_center_node(struct dm_btree_info info, struct btree_node parent,
	struct child l, struct child c, struct child *r,
	struct btree_node left, struct btree_node center, struct btree_node *right,
	uint32_t nr_left, uint32_t nr_center, uint32_t nr_right)
	{
	uint32_t max_entries = le32_to_cpu(left->header.max_entries);
	unsigned shift = min(max_entries - nr_left, nr_center);

	BUG_ON(nr_left + shift > max_entries);
	node_copy(left, center, -shift);
	left->header.nr_entries = cpu_to_le32(nr_left + shift);

	if (shift != nr_center) {
	shift = nr_center - shift;
	BUG_ON((nr_right + shift) > max_entries);
	node_shift(right, shift);
	node_copy(center, right, shift);
	right->header.nr_entries = cpu_to_le32(nr_right + shift);
	}
	*key_ptr(parent, r->index) = right->keys[0];

	delete_at(parent, c->index);
	r->index--;

	dm_tm_dec(info->tm, dm_block_location(c->block));
	__rebalance2(info, parent, l, r);
	}

	/*
	* Redistributes entries among 3 sibling nodes.
	*/
	static void redistribute3(struct dm_btree_info info, struct btree_node parent,
	struct child l, struct child c, struct child *r,
	struct btree_node left, struct btree_node center, struct btree_node *right,
	uint32_t nr_left, uint32_t nr_center, uint32_t nr_right)
	{
	int s;
	uint32_t max_entries = le32_to_cpu(left->header.max_entries);
	unsigned total = nr_left + nr_center + nr_right;
	unsigned target_right = total / 3;
	unsigned remainder = (target_right * 3) != total;
	unsigned target_left = target_right + remainder;

	BUG_ON(target_left > max_entries);
	BUG_ON(target_right > max_entries);

	if (nr_left < nr_right) {
	s = nr_left - target_left;

	if (s < 0 && nr_center < -s) {
	/* not enough in central node */
	shift(left, center, -nr_center);
	s += nr_center;
	shift(left, right, s);
	nr_right += s;
	} else
	shift(left, center, s);

	shift(center, right, target_right - nr_right);

	} else {
	s = target_right - nr_right;
	if (s > 0 && nr_center < s) {
	/* not enough in central node */
	shift(center, right, nr_center);
	s -= nr_center;
	shift(left, right, s);
	nr_left -= s;
	} else
	shift(center, right, s);

	shift(left, center, nr_left - target_left);
	}

	*key_ptr(parent, c->index) = center->keys[0];
	*key_ptr(parent, r->index) = right->keys[0];
	}

	static void __rebalance3(struct dm_btree_info info, struct btree_node parent,
	struct child l, struct child c, struct child *r)
	{
	struct btree_node *left = l->n;
	struct btree_node *center = c->n;
	struct btree_node *right = r->n;

	uint32_t nr_left = le32_to_cpu(left->header.nr_entries);
	uint32_t nr_center = le32_to_cpu(center->header.nr_entries);
	uint32_t nr_right = le32_to_cpu(right->header.nr_entries);

	unsigned threshold = merge_threshold(left) * 4 + 1;

	BUG_ON(left->header.max_entries != center->header.max_entries);
	BUG_ON(center->header.max_entries != right->header.max_entries);

	if ((nr_left + nr_center + nr_right) < threshold)
	delete_center_node(info, parent, l, c, r, left, center, right,
	nr_left, nr_center, nr_right);
	else
	redistribute3(info, parent, l, c, r, left, center, right,
	nr_left, nr_center, nr_right);
	}

	static int rebalance3(struct shadow_spine s, struct dm_btree_info info,
	struct dm_btree_value_type *vt, unsigned left_index)
	{
	int r;
	struct btree_node *parent = dm_block_data(shadow_current(s));
	struct child left, center, right;

	/*
	* FIXME: fill out an array?
	*/
	r = init_child(info, vt, parent, left_index, &left);
	if (r)
	return r;

	r = init_child(info, vt, parent, left_index + 1, &center);
	if (r) {
	exit_child(info, &left);
	return r;
	}

	r = init_child(info, vt, parent, left_index + 2, &right);
	if (r) {
	exit_child(info, &left);
	exit_child(info, &center);
	return r;
	}

	__rebalance3(info, parent, &left, &center, &right);

	exit_child(info, &left);
	exit_child(info, &center);
	exit_child(info, &right);

	return 0;
	}

	static int rebalance_children(struct shadow_spine *s,
	struct dm_btree_info *info,
	struct dm_btree_value_type *vt, uint64_t key)
	{
	int i, r, has_left_sibling, has_right_sibling;
	struct btree_node *n;

	n = dm_block_data(shadow_current(s));

	if (le32_to_cpu(n->header.nr_entries) == 1) {
	struct dm_block *child;
	dm_block_t b = value64(n, 0);

	r = dm_tm_read_lock(info->tm, b, &btree_node_validator, &child);
	if (r)
	return r;

	memcpy(n, dm_block_data(child),
	dm_bm_block_size(dm_tm_get_bm(info->tm)));
	dm_tm_unlock(info->tm, child);

	dm_tm_dec(info->tm, dm_block_location(child));
	return 0;
	}

	i = lower_bound(n, key);
	if (i < 0)
	return -ENODATA;

	has_left_sibling = i > 0;
	has_right_sibling = i < (le32_to_cpu(n->header.nr_entries) - 1);

	if (!has_left_sibling)
	r = rebalance2(s, info, vt, i);

	else if (!has_right_sibling)
	r = rebalance2(s, info, vt, i - 1);

	else
	r = rebalance3(s, info, vt, i - 1);

	return r;
	}

	static int do_leaf(struct btree_node n, uint64_t key, unsigned index)
	{
	int i = lower_bound(n, key);

	if ((i < 0) \|\|
	(i >= le32_to_cpu(n->header.nr_entries)) \|\|
	(le64_to_cpu(n->keys[i]) != key))
	return -ENODATA;

	*index = i;

	return 0;
	}

	/*
	* Prepares for removal from one level of the hierarchy. The caller must
	* call delete_at() to remove the entry at index.
	*/
	static int remove_raw(struct shadow_spine s, struct dm_btree_info info,
	struct dm_btree_value_type *vt, dm_block_t root,
	uint64_t key, unsigned *index)
	{
	int i = *index, r;
	struct btree_node *n;

	for (;;) {
	r = shadow_step(s, root, vt);
	if (r < 0)
	break;

	/*
	* We have to patch up the parent node, ugly, but I don't
	* see a way to do this automatically as part of the spine
	* op.
	*/
	if (shadow_has_parent(s)) {
	__le64 location = cpu_to_le64(dm_block_location(shadow_current(s)));
	memcpy(value_ptr(dm_block_data(shadow_parent(s)), i),
	&location, sizeof(__le64));
	}

	n = dm_block_data(shadow_current(s));

	if (le32_to_cpu(n->header.flags) & LEAF_NODE)
	return do_leaf(n, key, index);

	r = rebalance_children(s, info, vt, key);
	if (r)
	break;

	n = dm_block_data(shadow_current(s));
	if (le32_to_cpu(n->header.flags) & LEAF_NODE)
	return do_leaf(n, key, index);

	i = lower_bound(n, key);

	/*
	* We know the key is present, or else
	* rebalance_children would have returned
	* -ENODATA
	*/
	root = value64(n, i);
	}

	return r;
	}

	int dm_btree_remove(struct dm_btree_info *info, dm_block_t root,
	uint64_t keys, dm_block_t new_root)
	{
	unsigned level, last_level = info->levels - 1;
	int index = 0, r = 0;
	struct shadow_spine spine;
	struct btree_node *n;
	struct dm_btree_value_type le64_vt;

	init_le64_type(info->tm, &le64_vt);
	init_shadow_spine(&spine, info);
	for (level = 0; level < info->levels; level++) {
	r = remove_raw(&spine, info,
	(level == last_level ?
	&info->value_type : &le64_vt),
	root, keys[level], (unsigned *)&index);
	if (r < 0)
	break;

	n = dm_block_data(shadow_current(&spine));
	if (level != last_level) {
	root = value64(n, index);
	continue;
	}

	BUG_ON(index < 0 \|\| index >= le32_to_cpu(n->header.nr_entries));

	if (info->value_type.dec)
	info->value_type.dec(info->value_type.context,
	value_ptr(n, index), 1);

	delete_at(n, index);
	}

	if (!r)
	*new_root = shadow_root(&spine);
	exit_shadow_spine(&spine);

	return r;
	}
	EXPORT_SYMBOL_GPL(dm_btree_remove);

	/----------------------------------------------------------------/

	static int remove_nearest(struct shadow_spine s, struct dm_btree_info info,
	struct dm_btree_value_type *vt, dm_block_t root,
	uint64_t key, int *index)
	{
	int i = *index, r;
	struct btree_node *n;

	for (;;) {
	r = shadow_step(s, root, vt);
	if (r < 0)
	break;

	/*
	* We have to patch up the parent node, ugly, but I don't
	* see a way to do this automatically as part of the spine
	* op.
	*/
	if (shadow_has_parent(s)) {
	__le64 location = cpu_to_le64(dm_block_location(shadow_current(s)));
	memcpy(value_ptr(dm_block_data(shadow_parent(s)), i),
	&location, sizeof(__le64));
	}

	n = dm_block_data(shadow_current(s));

	if (le32_to_cpu(n->header.flags) & LEAF_NODE) {
	*index = lower_bound(n, key);
	return 0;
	}

	r = rebalance_children(s, info, vt, key);
	if (r)
	break;

	n = dm_block_data(shadow_current(s));
	if (le32_to_cpu(n->header.flags) & LEAF_NODE) {
	*index = lower_bound(n, key);
	return 0;
	}

	i = lower_bound(n, key);

	/*
	* We know the key is present, or else
	* rebalance_children would have returned
	* -ENODATA
	*/
	root = value64(n, i);
	}

	return r;
	}

	static int remove_one(struct dm_btree_info *info, dm_block_t root,
	uint64_t *keys, uint64_t end_key,
	dm_block_t new_root, unsigned nr_removed)
	{
	unsigned level, last_level = info->levels - 1;
	int index = 0, r = 0;
	struct shadow_spine spine;
	struct btree_node *n;
	struct dm_btree_value_type le64_vt;
	uint64_t k;

	init_le64_type(info->tm, &le64_vt);
	init_shadow_spine(&spine, info);
	for (level = 0; level < last_level; level++) {
	r = remove_raw(&spine, info, &le64_vt,
	root, keys[level], (unsigned *) &index);
	if (r < 0)
	goto out;

	n = dm_block_data(shadow_current(&spine));
	root = value64(n, index);
	}

	r = remove_nearest(&spine, info, &info->value_type,
	root, keys[last_level], &index);
	if (r < 0)
	goto out;

	n = dm_block_data(shadow_current(&spine));

	if (index < 0)
	index = 0;

	if (index >= le32_to_cpu(n->header.nr_entries)) {
	r = -ENODATA;
	goto out;
	}

	k = le64_to_cpu(n->keys[index]);
	if (k >= keys[last_level] && k < end_key) {
	if (info->value_type.dec)
	info->value_type.dec(info->value_type.context,
	value_ptr(n, index), 1);

	delete_at(n, index);
	keys[last_level] = k + 1ull;

	} else
	r = -ENODATA;

	out:
	*new_root = shadow_root(&spine);
	exit_shadow_spine(&spine);

	return r;
	}

	int dm_btree_remove_leaves(struct dm_btree_info *info, dm_block_t root,
	uint64_t *first_key, uint64_t end_key,
	dm_block_t new_root, unsigned nr_removed)
	{
	int r;

	*nr_removed = 0;
	do {
	r = remove_one(info, root, first_key, end_key, &root, nr_removed);
	if (!r)
	(*nr_removed)++;
	} while (!r);

	*new_root = root;
	return r == -ENODATA ? 0 : r;
	}
	EXPORT_SYMBOL_GPL(dm_btree_remove_leaves);