lib/btree.c - pub/scm/linux/kernel/git/stable/linux-stable - Git at Google

 /*
  * lib/btree.c	- Simple In-memory B+Tree
  *
  * As should be obvious for Linux kernel code, license is GPLv2
  *
  * Copyright (c) 2007-2008 Joern Engel <joern@logfs.org>
  * Bits and pieces stolen from Peter Zijlstra's code, which is
  * Copyright 2007, Red Hat Inc. Peter Zijlstra <pzijlstr@redhat.com>
  * GPLv2
  *
  * see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch
  *
  * A relatively simple B+Tree implementation.  I have written it as a learning
  * exercise to understand how B+Trees work.  Turned out to be useful as well.
  *
  * B+Trees can be used similar to Linux radix trees (which don't have anything
  * in common with textbook radix trees, beware).  Prerequisite for them working
  * well is that access to a random tree node is much faster than a large number
  * of operations within each node.
  *
  * Disks have fulfilled the prerequisite for a long time.  More recently DRAM
  * has gained similar properties, as memory access times, when measured in cpu
  * cycles, have increased.  Cacheline sizes have increased as well, which also
  * helps B+Trees.
  *
  * Compared to radix trees, B+Trees are more efficient when dealing with a
  * sparsely populated address space.  Between 25% and 50% of the memory is
  * occupied with valid pointers.  When densely populated, radix trees contain
  * ~98% pointers - hard to beat.  Very sparse radix trees contain only ~2%
  * pointers.
  *
  * This particular implementation stores pointers identified by a long value.
  * Storing NULL pointers is illegal, lookup will return NULL when no entry
  * was found.
  *
  * A tricks was used that is not commonly found in textbooks.  The lowest
  * values are to the right, not to the left.  All used slots within a node
  * are on the left, all unused slots contain NUL values.  Most operations
  * simply loop once over all slots and terminate on the first NUL.
  */

 #include <linux/btree.h>
 #include <linux/cache.h>
 #include <linux/kernel.h>
 #include <linux/slab.h>
 #include <linux/module.h>

 #define MAX(a, b) ((a) > (b) ? (a) : (b))
 #define NODESIZE MAX(L1_CACHE_BYTES, 128)

 struct btree_geo {
 	int keylen;
 	int no_pairs;
 	int no_longs;
 };

 struct btree_geo btree_geo32 = {
 	.keylen = 1,
 	.no_pairs = NODESIZE / sizeof(long) / 2,
 	.no_longs = NODESIZE / sizeof(long) / 2,
 };
 EXPORT_SYMBOL_GPL(btree_geo32);

 #define LONG_PER_U64 (64 / BITS_PER_LONG)
 struct btree_geo btree_geo64 = {
 	.keylen = LONG_PER_U64,
 	.no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64),
 	.no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)),
 };
 EXPORT_SYMBOL_GPL(btree_geo64);

 struct btree_geo btree_geo128 = {
 	.keylen = 2 * LONG_PER_U64,
 	.no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64),
 	.no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)),
 };
 EXPORT_SYMBOL_GPL(btree_geo128);

 static struct kmem_cache *btree_cachep;

 void *btree_alloc(gfp_t gfp_mask, void *pool_data)
 {
 	return kmem_cache_alloc(btree_cachep, gfp_mask);
 }
 EXPORT_SYMBOL_GPL(btree_alloc);

 void btree_free(void *element, void *pool_data)
 {
 	kmem_cache_free(btree_cachep, element);
 }
 EXPORT_SYMBOL_GPL(btree_free);

 static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp)
 {
 	unsigned long *node;

 	node = mempool_alloc(head->mempool, gfp);
 	if (likely(node))
 		memset(node, 0, NODESIZE);
 	return node;
 }

 static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
 {
 	size_t i;

 	for (i = 0; i < n; i++) {
 		if (l1[i] < l2[i])
 			return -1;
 		if (l1[i] > l2[i])
 			return 1;
 	}
 	return 0;
 }

 static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
 		size_t n)
 {
 	size_t i;

 	for (i = 0; i < n; i++)
 		dest[i] = src[i];
 	return dest;
 }

 static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
 {
 	size_t i;

 	for (i = 0; i < n; i++)
 		s[i] = c;
 	return s;
 }

 static void dec_key(struct btree_geo *geo, unsigned long *key)
 {
 	unsigned long val;
 	int i;

 	for (i = geo->keylen - 1; i >= 0; i--) {
 		val = key[i];
 		key[i] = val - 1;
 		if (val)
 			break;
 	}
 }

 static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
 {
 	return &node[n * geo->keylen];
 }

 static void *bval(struct btree_geo *geo, unsigned long *node, int n)
 {
 	return (void *)node[geo->no_longs + n];
 }

 static void setkey(struct btree_geo *geo, unsigned long *node, int n,
 		   unsigned long *key)
 {
 	longcpy(bkey(geo, node, n), key, geo->keylen);
 }

 static void setval(struct btree_geo *geo, unsigned long *node, int n,
 		   void *val)
 {
 	node[geo->no_longs + n] = (unsigned long) val;
 }

 static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
 {
 	longset(bkey(geo, node, n), 0, geo->keylen);
 	node[geo->no_longs + n] = 0;
 }

 static inline void __btree_init(struct btree_head *head)
 {
 	head->node = NULL;
 	head->height = 0;
 }

 void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
 {
 	__btree_init(head);
 	head->mempool = mempool;
 }
 EXPORT_SYMBOL_GPL(btree_init_mempool);

 int btree_init(struct btree_head *head)
 {
 	__btree_init(head);
 	head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
 	if (!head->mempool)
 		return -ENOMEM;
 	return 0;
 }
 EXPORT_SYMBOL_GPL(btree_init);

 void btree_destroy(struct btree_head *head)
 {
 	mempool_free(head->node, head->mempool);
 	mempool_destroy(head->mempool);
 	head->mempool = NULL;
 }
 EXPORT_SYMBOL_GPL(btree_destroy);

 void *btree_last(struct btree_head *head, struct btree_geo *geo,
 		 unsigned long *key)
 {
 	int height = head->height;
 	unsigned long *node = head->node;

 	if (height == 0)
 		return NULL;

 	for ( ; height > 1; height--)
 		node = bval(geo, node, 0);

 	longcpy(key, bkey(geo, node, 0), geo->keylen);
 	return bval(geo, node, 0);
 }
 EXPORT_SYMBOL_GPL(btree_last);

 static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
 		  unsigned long *key)
 {
 	return longcmp(bkey(geo, node, pos), key, geo->keylen);
 }

 static int keyzero(struct btree_geo *geo, unsigned long *key)
 {
 	int i;

 	for (i = 0; i < geo->keylen; i++)
 		if (key[i])
 			return 0;

 	return 1;
 }

 void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key)
 {
 	int i, height = head->height;
 	unsigned long *node = head->node;

 	if (height == 0)
 		return NULL;

 	for ( ; height > 1; height--) {
 		for (i = 0; i < geo->no_pairs; i++)
 			if (keycmp(geo, node, i, key) <= 0)
 				break;
 		if (i == geo->no_pairs)
 			return NULL;
 		node = bval(geo, node, i);
 		if (!node)
 			return NULL;
 	}

 	if (!node)
 		return NULL;

 	for (i = 0; i < geo->no_pairs; i++)
 		if (keycmp(geo, node, i, key) == 0)
 			return bval(geo, node, i);
 	return NULL;
 }
 EXPORT_SYMBOL_GPL(btree_lookup);

 int btree_update(struct btree_head *head, struct btree_geo *geo,
 		 unsigned long *key, void *val)
 {
 	int i, height = head->height;
 	unsigned long *node = head->node;

 	if (height == 0)
 		return -ENOENT;

 	for ( ; height > 1; height--) {
 		for (i = 0; i < geo->no_pairs; i++)
 			if (keycmp(geo, node, i, key) <= 0)
 				break;
 		if (i == geo->no_pairs)
 			return -ENOENT;
 		node = bval(geo, node, i);
 		if (!node)
 			return -ENOENT;
 	}

 	if (!node)
 		return -ENOENT;

 	for (i = 0; i < geo->no_pairs; i++)
 		if (keycmp(geo, node, i, key) == 0) {
 			setval(geo, node, i, val);
 			return 0;
 		}
 	return -ENOENT;
 }
 EXPORT_SYMBOL_GPL(btree_update);

 /*
  * Usually this function is quite similar to normal lookup.  But the key of
  * a parent node may be smaller than the smallest key of all its siblings.
  * In such a case we cannot just return NULL, as we have only proven that no
  * key smaller than __key, but larger than this parent key exists.
  * So we set __key to the parent key and retry.  We have to use the smallest
  * such parent key, which is the last parent key we encountered.
  */
 void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
 		     unsigned long *__key)
 {
 	int i, height;
 	unsigned long *node, *oldnode;
 	unsigned long *retry_key = NULL, key[geo->keylen];

 	if (keyzero(geo, __key))
 		return NULL;

 	if (head->height == 0)
 		return NULL;
 	longcpy(key, __key, geo->keylen);
 retry:
 	dec_key(geo, key);

 	node = head->node;
 	for (height = head->height ; height > 1; height--) {
 		for (i = 0; i < geo->no_pairs; i++)
 			if (keycmp(geo, node, i, key) <= 0)
 				break;
 		if (i == geo->no_pairs)
 			goto miss;
 		oldnode = node;
 		node = bval(geo, node, i);
 		if (!node)
 			goto miss;
 		retry_key = bkey(geo, oldnode, i);
 	}

 	if (!node)
 		goto miss;

 	for (i = 0; i < geo->no_pairs; i++) {
 		if (keycmp(geo, node, i, key) <= 0) {
 			if (bval(geo, node, i)) {
 				longcpy(__key, bkey(geo, node, i), geo->keylen);
 				return bval(geo, node, i);
 			} else
 				goto miss;
 		}
 	}
 miss:
 	if (retry_key) {
 		longcpy(key, retry_key, geo->keylen);
 		retry_key = NULL;
 		goto retry;
 	}
 	return NULL;
 }
 EXPORT_SYMBOL_GPL(btree_get_prev);

 static int getpos(struct btree_geo *geo, unsigned long *node,
 		unsigned long *key)
 {
 	int i;

 	for (i = 0; i < geo->no_pairs; i++) {
 		if (keycmp(geo, node, i, key) <= 0)
 			break;
 	}
 	return i;
 }

 static int getfill(struct btree_geo *geo, unsigned long *node, int start)
 {
 	int i;

 	for (i = start; i < geo->no_pairs; i++)
 		if (!bval(geo, node, i))
 			break;
 	return i;
 }

 /*
  * locate the correct leaf node in the btree
  */
 static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, int level)
 {
 	unsigned long *node = head->node;
 	int i, height;

 	for (height = head->height; height > level; height--) {
 		for (i = 0; i < geo->no_pairs; i++)
 			if (keycmp(geo, node, i, key) <= 0)
 				break;

 		if ((i == geo->no_pairs) || !bval(geo, node, i)) {
 			/* right-most key is too large, update it */
 			/* FIXME: If the right-most key on higher levels is
 			 * always zero, this wouldn't be necessary. */
 			i--;
 			setkey(geo, node, i, key);
 		}
 		BUG_ON(i < 0);
 		node = bval(geo, node, i);
 	}
 	BUG_ON(!node);
 	return node;
 }

 static int btree_grow(struct btree_head *head, struct btree_geo *geo,
 		      gfp_t gfp)
 {
 	unsigned long *node;
 	int fill;

 	node = btree_node_alloc(head, gfp);
 	if (!node)
 		return -ENOMEM;
 	if (head->node) {
 		fill = getfill(geo, head->node, 0);
 		setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
 		setval(geo, node, 0, head->node);
 	}
 	head->node = node;
 	head->height++;
 	return 0;
 }

 static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
 {
 	unsigned long *node;
 	int fill;

 	if (head->height <= 1)
 		return;

 	node = head->node;
 	fill = getfill(geo, node, 0);
 	BUG_ON(fill > 1);
 	head->node = bval(geo, node, 0);
 	head->height--;
 	mempool_free(node, head->mempool);
 }

 static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
 			      unsigned long *key, void *val, int level,
 			      gfp_t gfp)
 {
 	unsigned long *node;
 	int i, pos, fill, err;

 	BUG_ON(!val);
 	if (head->height < level) {
 		err = btree_grow(head, geo, gfp);
 		if (err)
 			return err;
 	}

 retry:
 	node = find_level(head, geo, key, level);
 	pos = getpos(geo, node, key);
 	fill = getfill(geo, node, pos);
 	/* two identical keys are not allowed */
 	BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);

 	if (fill == geo->no_pairs) {
 		/* need to split node */
 		unsigned long *new;

 		new = btree_node_alloc(head, gfp);
 		if (!new)
 			return -ENOMEM;
 		err = btree_insert_level(head, geo,
 				bkey(geo, node, fill / 2 - 1),
 				new, level + 1, gfp);
 		if (err) {
 			mempool_free(new, head->mempool);
 			return err;
 		}
 		for (i = 0; i < fill / 2; i++) {
 			setkey(geo, new, i, bkey(geo, node, i));
 			setval(geo, new, i, bval(geo, node, i));
 			setkey(geo, node, i, bkey(geo, node, i + fill / 2));
 			setval(geo, node, i, bval(geo, node, i + fill / 2));
 			clearpair(geo, node, i + fill / 2);
 		}
 		if (fill & 1) {
 			setkey(geo, node, i, bkey(geo, node, fill - 1));
 			setval(geo, node, i, bval(geo, node, fill - 1));
 			clearpair(geo, node, fill - 1);
 		}
 		goto retry;
 	}
 	BUG_ON(fill >= geo->no_pairs);

 	/* shift and insert */
 	for (i = fill; i > pos; i--) {
 		setkey(geo, node, i, bkey(geo, node, i - 1));
 		setval(geo, node, i, bval(geo, node, i - 1));
 	}
 	setkey(geo, node, pos, key);
 	setval(geo, node, pos, val);

 	return 0;
 }

 int btree_insert(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, void *val, gfp_t gfp)
 {
 	BUG_ON(!val);
 	return btree_insert_level(head, geo, key, val, 1, gfp);
 }
 EXPORT_SYMBOL_GPL(btree_insert);

 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, int level);
 static void merge(struct btree_head *head, struct btree_geo *geo, int level,
 		unsigned long *left, int lfill,
 		unsigned long *right, int rfill,
 		unsigned long *parent, int lpos)
 {
 	int i;

 	for (i = 0; i < rfill; i++) {
 		/* Move all keys to the left */
 		setkey(geo, left, lfill + i, bkey(geo, right, i));
 		setval(geo, left, lfill + i, bval(geo, right, i));
 	}
 	/* Exchange left and right child in parent */
 	setval(geo, parent, lpos, right);
 	setval(geo, parent, lpos + 1, left);
 	/* Remove left (formerly right) child from parent */
 	btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
 	mempool_free(right, head->mempool);
 }

 static void rebalance(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, int level, unsigned long *child, int fill)
 {
 	unsigned long *parent, *left = NULL, *right = NULL;
 	int i, no_left, no_right;

 	if (fill == 0) {
 		/* Because we don't steal entries from a neighbour, this case
 		 * can happen.  Parent node contains a single child, this
 		 * node, so merging with a sibling never happens.
 		 */
 		btree_remove_level(head, geo, key, level + 1);
 		mempool_free(child, head->mempool);
 		return;
 	}

 	parent = find_level(head, geo, key, level + 1);
 	i = getpos(geo, parent, key);
 	BUG_ON(bval(geo, parent, i) != child);

 	if (i > 0) {
 		left = bval(geo, parent, i - 1);
 		no_left = getfill(geo, left, 0);
 		if (fill + no_left <= geo->no_pairs) {
 			merge(head, geo, level,
 					left, no_left,
 					child, fill,
 					parent, i - 1);
 			return;
 		}
 	}
 	if (i + 1 < getfill(geo, parent, i)) {
 		right = bval(geo, parent, i + 1);
 		no_right = getfill(geo, right, 0);
 		if (fill + no_right <= geo->no_pairs) {
 			merge(head, geo, level,
 					child, fill,
 					right, no_right,
 					parent, i);
 			return;
 		}
 	}
 	/*
 	 * We could also try to steal one entry from the left or right
 	 * neighbor.  By not doing so we changed the invariant from
 	 * "all nodes are at least half full" to "no two neighboring
 	 * nodes can be merged".  Which means that the average fill of
 	 * all nodes is still half or better.
 	 */
 }

 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, int level)
 {
 	unsigned long *node;
 	int i, pos, fill;
 	void *ret;

 	if (level > head->height) {
 		/* we recursed all the way up */
 		head->height = 0;
 		head->node = NULL;
 		return NULL;
 	}

 	node = find_level(head, geo, key, level);
 	pos = getpos(geo, node, key);
 	fill = getfill(geo, node, pos);
 	if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
 		return NULL;
 	ret = bval(geo, node, pos);

 	/* remove and shift */
 	for (i = pos; i < fill - 1; i++) {
 		setkey(geo, node, i, bkey(geo, node, i + 1));
 		setval(geo, node, i, bval(geo, node, i + 1));
 	}
 	clearpair(geo, node, fill - 1);

 	if (fill - 1 < geo->no_pairs / 2) {
 		if (level < head->height)
 			rebalance(head, geo, key, level, node, fill - 1);
 		else if (fill - 1 == 1)
 			btree_shrink(head, geo);
 	}

 	return ret;
 }

 void *btree_remove(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key)
 {
 	if (head->height == 0)
 		return NULL;

 	return btree_remove_level(head, geo, key, 1);
 }
 EXPORT_SYMBOL_GPL(btree_remove);

 int btree_merge(struct btree_head *target, struct btree_head *victim,
 		struct btree_geo *geo, gfp_t gfp)
 {
 	unsigned long key[geo->keylen];
 	unsigned long dup[geo->keylen];
 	void *val;
 	int err;

 	BUG_ON(target == victim);

 	if (!(target->node)) {
 		/* target is empty, just copy fields over */
 		target->node = victim->node;
 		target->height = victim->height;
 		__btree_init(victim);
 		return 0;
 	}

 	/* TODO: This needs some optimizations.  Currently we do three tree
 	 * walks to remove a single object from the victim.
 	 */
 	for (;;) {
 		if (!btree_last(victim, geo, key))
 			break;
 		val = btree_lookup(victim, geo, key);
 		err = btree_insert(target, geo, key, val, gfp);
 		if (err)
 			return err;
 		/* We must make a copy of the key, as the original will get
 		 * mangled inside btree_remove. */
 		longcpy(dup, key, geo->keylen);
 		btree_remove(victim, geo, dup);
 	}
 	return 0;
 }
 EXPORT_SYMBOL_GPL(btree_merge);

 static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
 			       unsigned long *node, unsigned long opaque,
 			       void (*func)(void *elem, unsigned long opaque,
 					    unsigned long *key, size_t index,
 					    void *func2),
 			       void *func2, int reap, int height, size_t count)
 {
 	int i;
 	unsigned long *child;

 	for (i = 0; i < geo->no_pairs; i++) {
 		child = bval(geo, node, i);
 		if (!child)
 			break;
 		if (height > 1)
 			count = __btree_for_each(head, geo, child, opaque,
 					func, func2, reap, height - 1, count);
 		else
 			func(child, opaque, bkey(geo, node, i), count++,
 					func2);
 	}
 	if (reap)
 		mempool_free(node, head->mempool);
 	return count;
 }

 static void empty(void *elem, unsigned long opaque, unsigned long *key,
 		  size_t index, void *func2)
 {
 }

 void visitorl(void *elem, unsigned long opaque, unsigned long *key,
 	      size_t index, void *__func)
 {
 	visitorl_t func = __func;

 	func(elem, opaque, *key, index);
 }
 EXPORT_SYMBOL_GPL(visitorl);

 void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
 	       size_t index, void *__func)
 {
 	visitor32_t func = __func;
 	u32 *key = (void *)__key;

 	func(elem, opaque, *key, index);
 }
 EXPORT_SYMBOL_GPL(visitor32);

 void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
 	       size_t index, void *__func)
 {
 	visitor64_t func = __func;
 	u64 *key = (void *)__key;

 	func(elem, opaque, *key, index);
 }
 EXPORT_SYMBOL_GPL(visitor64);

 void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
 		size_t index, void *__func)
 {
 	visitor128_t func = __func;
 	u64 *key = (void *)__key;

 	func(elem, opaque, key[0], key[1], index);
 }
 EXPORT_SYMBOL_GPL(visitor128);

 size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
 		     unsigned long opaque,
 		     void (*func)(void *elem, unsigned long opaque,
 		     		  unsigned long *key,
 		     		  size_t index, void *func2),
 		     void *func2)
 {
 	size_t count = 0;

 	if (!func2)
 		func = empty;
 	if (head->node)
 		count = __btree_for_each(head, geo, head->node, opaque, func,
 				func2, 0, head->height, 0);
 	return count;
 }
 EXPORT_SYMBOL_GPL(btree_visitor);

 size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
 			  unsigned long opaque,
 			  void (*func)(void *elem, unsigned long opaque,
 				       unsigned long *key,
 				       size_t index, void *func2),
 			  void *func2)
 {
 	size_t count = 0;

 	if (!func2)
 		func = empty;
 	if (head->node)
 		count = __btree_for_each(head, geo, head->node, opaque, func,
 				func2, 1, head->height, 0);
 	__btree_init(head);
 	return count;
 }
 EXPORT_SYMBOL_GPL(btree_grim_visitor);

 static int __init btree_module_init(void)
 {
 	btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
 			SLAB_HWCACHE_ALIGN, NULL);
 	return 0;
 }

 static void __exit btree_module_exit(void)
 {
 	kmem_cache_destroy(btree_cachep);
 }

 /* If core code starts using btree, initialization should happen even earlier */
 module_init(btree_module_init);
 module_exit(btree_module_exit);

 MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
 MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
 MODULE_LICENSE("GPL");
	/*
	* lib/btree.c - Simple In-memory B+Tree
	*
	* As should be obvious for Linux kernel code, license is GPLv2
	*
	* Copyright (c) 2007-2008 Joern Engel <joern@logfs.org>
	* Bits and pieces stolen from Peter Zijlstra's code, which is
	* Copyright 2007, Red Hat Inc. Peter Zijlstra <pzijlstr@redhat.com>
	* GPLv2
	*
	* see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch
	*
	* A relatively simple B+Tree implementation. I have written it as a learning
	* exercise to understand how B+Trees work. Turned out to be useful as well.
	*
	* B+Trees can be used similar to Linux radix trees (which don't have anything
	* in common with textbook radix trees, beware). Prerequisite for them working
	* well is that access to a random tree node is much faster than a large number
	* of operations within each node.
	*
	* Disks have fulfilled the prerequisite for a long time. More recently DRAM
	* has gained similar properties, as memory access times, when measured in cpu
	* cycles, have increased. Cacheline sizes have increased as well, which also
	* helps B+Trees.
	*
	* Compared to radix trees, B+Trees are more efficient when dealing with a
	* sparsely populated address space. Between 25% and 50% of the memory is
	* occupied with valid pointers. When densely populated, radix trees contain
	* ~98% pointers - hard to beat. Very sparse radix trees contain only ~2%
	* pointers.
	*
	* This particular implementation stores pointers identified by a long value.
	* Storing NULL pointers is illegal, lookup will return NULL when no entry
	* was found.
	*
	* A tricks was used that is not commonly found in textbooks. The lowest
	* values are to the right, not to the left. All used slots within a node
	* are on the left, all unused slots contain NUL values. Most operations
	* simply loop once over all slots and terminate on the first NUL.
	*/

	#include <linux/btree.h>
	#include <linux/cache.h>
	#include <linux/kernel.h>
	#include <linux/slab.h>
	#include <linux/module.h>

	#define MAX(a, b) ((a) > (b) ? (a) : (b))
	#define NODESIZE MAX(L1_CACHE_BYTES, 128)

	struct btree_geo {
	int keylen;
	int no_pairs;
	int no_longs;
	};

	struct btree_geo btree_geo32 = {
	.keylen = 1,
	.no_pairs = NODESIZE / sizeof(long) / 2,
	.no_longs = NODESIZE / sizeof(long) / 2,
	};
	EXPORT_SYMBOL_GPL(btree_geo32);

	#define LONG_PER_U64 (64 / BITS_PER_LONG)
	struct btree_geo btree_geo64 = {
	.keylen = LONG_PER_U64,
	.no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64),
	.no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)),
	};
	EXPORT_SYMBOL_GPL(btree_geo64);

	struct btree_geo btree_geo128 = {
	.keylen = 2 * LONG_PER_U64,
	.no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64),
	.no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)),
	};
	EXPORT_SYMBOL_GPL(btree_geo128);

	static struct kmem_cache *btree_cachep;

	void btree_alloc(gfp_t gfp_mask, void pool_data)
	{
	return kmem_cache_alloc(btree_cachep, gfp_mask);
	}
	EXPORT_SYMBOL_GPL(btree_alloc);

	void btree_free(void element, void pool_data)
	{
	kmem_cache_free(btree_cachep, element);
	}
	EXPORT_SYMBOL_GPL(btree_free);

	static unsigned long btree_node_alloc(struct btree_head head, gfp_t gfp)
	{
	unsigned long *node;

	node = mempool_alloc(head->mempool, gfp);
	if (likely(node))
	memset(node, 0, NODESIZE);
	return node;
	}

	static int longcmp(const unsigned long l1, const unsigned long l2, size_t n)
	{
	size_t i;

	for (i = 0; i < n; i++) {
	if (l1[i] < l2[i])
	return -1;
	if (l1[i] > l2[i])
	return 1;
	}
	return 0;
	}

	static unsigned long longcpy(unsigned long dest, const unsigned long *src,
	size_t n)
	{
	size_t i;

	for (i = 0; i < n; i++)
	dest[i] = src[i];
	return dest;
	}

	static unsigned long longset(unsigned long s, unsigned long c, size_t n)
	{
	size_t i;

	for (i = 0; i < n; i++)
	s[i] = c;
	return s;
	}

	static void dec_key(struct btree_geo geo, unsigned long key)
	{
	unsigned long val;
	int i;

	for (i = geo->keylen - 1; i >= 0; i--) {
	val = key[i];
	key[i] = val - 1;
	if (val)
	break;
	}
	}

	static unsigned long bkey(struct btree_geo geo, unsigned long *node, int n)
	{
	return &node[n * geo->keylen];
	}

	static void bval(struct btree_geo geo, unsigned long *node, int n)
	{
	return (void *)node[geo->no_longs + n];
	}

	static void setkey(struct btree_geo geo, unsigned long node, int n,
	unsigned long *key)
	{
	longcpy(bkey(geo, node, n), key, geo->keylen);
	}

	static void setval(struct btree_geo geo, unsigned long node, int n,
	void *val)
	{
	node[geo->no_longs + n] = (unsigned long) val;
	}

	static void clearpair(struct btree_geo geo, unsigned long node, int n)
	{
	longset(bkey(geo, node, n), 0, geo->keylen);
	node[geo->no_longs + n] = 0;
	}

	static inline void __btree_init(struct btree_head *head)
	{
	head->node = NULL;
	head->height = 0;
	}

	void btree_init_mempool(struct btree_head head, mempool_t mempool)
	{
	__btree_init(head);
	head->mempool = mempool;
	}
	EXPORT_SYMBOL_GPL(btree_init_mempool);

	int btree_init(struct btree_head *head)
	{
	__btree_init(head);
	head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
	if (!head->mempool)
	return -ENOMEM;
	return 0;
	}
	EXPORT_SYMBOL_GPL(btree_init);

	void btree_destroy(struct btree_head *head)
	{
	mempool_free(head->node, head->mempool);
	mempool_destroy(head->mempool);
	head->mempool = NULL;
	}
	EXPORT_SYMBOL_GPL(btree_destroy);

	void btree_last(struct btree_head head, struct btree_geo *geo,
	unsigned long *key)
	{
	int height = head->height;
	unsigned long *node = head->node;

	if (height == 0)
	return NULL;

	for ( ; height > 1; height--)
	node = bval(geo, node, 0);

	longcpy(key, bkey(geo, node, 0), geo->keylen);
	return bval(geo, node, 0);
	}
	EXPORT_SYMBOL_GPL(btree_last);

	static int keycmp(struct btree_geo geo, unsigned long node, int pos,
	unsigned long *key)
	{
	return longcmp(bkey(geo, node, pos), key, geo->keylen);
	}

	static int keyzero(struct btree_geo geo, unsigned long key)
	{
	int i;

	for (i = 0; i < geo->keylen; i++)
	if (key[i])
	return 0;

	return 1;
	}

	void btree_lookup(struct btree_head head, struct btree_geo *geo,
	unsigned long *key)
	{
	int i, height = head->height;
	unsigned long *node = head->node;

	if (height == 0)
	return NULL;

	for ( ; height > 1; height--) {
	for (i = 0; i < geo->no_pairs; i++)
	if (keycmp(geo, node, i, key) <= 0)
	break;
	if (i == geo->no_pairs)
	return NULL;
	node = bval(geo, node, i);
	if (!node)
	return NULL;
	}

	if (!node)
	return NULL;

	for (i = 0; i < geo->no_pairs; i++)
	if (keycmp(geo, node, i, key) == 0)
	return bval(geo, node, i);
	return NULL;
	}
	EXPORT_SYMBOL_GPL(btree_lookup);

	int btree_update(struct btree_head head, struct btree_geo geo,
	unsigned long key, void val)
	{
	int i, height = head->height;
	unsigned long *node = head->node;

	if (height == 0)
	return -ENOENT;

	for ( ; height > 1; height--) {
	for (i = 0; i < geo->no_pairs; i++)
	if (keycmp(geo, node, i, key) <= 0)
	break;
	if (i == geo->no_pairs)
	return -ENOENT;
	node = bval(geo, node, i);
	if (!node)
	return -ENOENT;
	}

	if (!node)
	return -ENOENT;

	for (i = 0; i < geo->no_pairs; i++)
	if (keycmp(geo, node, i, key) == 0) {
	setval(geo, node, i, val);
	return 0;
	}
	return -ENOENT;
	}
	EXPORT_SYMBOL_GPL(btree_update);

	/*
	* Usually this function is quite similar to normal lookup. But the key of
	* a parent node may be smaller than the smallest key of all its siblings.
	* In such a case we cannot just return NULL, as we have only proven that no
	* key smaller than __key, but larger than this parent key exists.
	* So we set __key to the parent key and retry. We have to use the smallest
	* such parent key, which is the last parent key we encountered.
	*/
	void btree_get_prev(struct btree_head head, struct btree_geo *geo,
	unsigned long *__key)
	{
	int i, height;
	unsigned long node, oldnode;
	unsigned long *retry_key = NULL, key[geo->keylen];

	if (keyzero(geo, __key))
	return NULL;

	if (head->height == 0)
	return NULL;
	longcpy(key, __key, geo->keylen);
	retry:
	dec_key(geo, key);

	node = head->node;
	for (height = head->height ; height > 1; height--) {
	for (i = 0; i < geo->no_pairs; i++)
	if (keycmp(geo, node, i, key) <= 0)
	break;
	if (i == geo->no_pairs)
	goto miss;
	oldnode = node;
	node = bval(geo, node, i);
	if (!node)
	goto miss;
	retry_key = bkey(geo, oldnode, i);
	}

	if (!node)
	goto miss;

	for (i = 0; i < geo->no_pairs; i++) {
	if (keycmp(geo, node, i, key) <= 0) {
	if (bval(geo, node, i)) {
	longcpy(__key, bkey(geo, node, i), geo->keylen);
	return bval(geo, node, i);
	} else
	goto miss;
	}
	}
	miss:
	if (retry_key) {
	longcpy(key, retry_key, geo->keylen);
	retry_key = NULL;
	goto retry;
	}
	return NULL;
	}
	EXPORT_SYMBOL_GPL(btree_get_prev);

	static int getpos(struct btree_geo geo, unsigned long node,
	unsigned long *key)
	{
	int i;

	for (i = 0; i < geo->no_pairs; i++) {
	if (keycmp(geo, node, i, key) <= 0)
	break;
	}
	return i;
	}

	static int getfill(struct btree_geo geo, unsigned long node, int start)
	{
	int i;

	for (i = start; i < geo->no_pairs; i++)
	if (!bval(geo, node, i))
	break;
	return i;
	}

	/*
	* locate the correct leaf node in the btree
	*/
	static unsigned long find_level(struct btree_head head, struct btree_geo *geo,
	unsigned long *key, int level)
	{
	unsigned long *node = head->node;
	int i, height;

	for (height = head->height; height > level; height--) {
	for (i = 0; i < geo->no_pairs; i++)
	if (keycmp(geo, node, i, key) <= 0)
	break;

	if ((i == geo->no_pairs) \|\| !bval(geo, node, i)) {
	/* right-most key is too large, update it */
	/* FIXME: If the right-most key on higher levels is
	* always zero, this wouldn't be necessary. */
	i--;
	setkey(geo, node, i, key);
	}
	BUG_ON(i < 0);
	node = bval(geo, node, i);
	}
	BUG_ON(!node);
	return node;
	}

	static int btree_grow(struct btree_head head, struct btree_geo geo,
	gfp_t gfp)
	{
	unsigned long *node;
	int fill;

	node = btree_node_alloc(head, gfp);
	if (!node)
	return -ENOMEM;
	if (head->node) {
	fill = getfill(geo, head->node, 0);
	setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
	setval(geo, node, 0, head->node);
	}
	head->node = node;
	head->height++;
	return 0;
	}

	static void btree_shrink(struct btree_head head, struct btree_geo geo)
	{
	unsigned long *node;
	int fill;

	if (head->height <= 1)
	return;

	node = head->node;
	fill = getfill(geo, node, 0);
	BUG_ON(fill > 1);
	head->node = bval(geo, node, 0);
	head->height--;
	mempool_free(node, head->mempool);
	}

	static int btree_insert_level(struct btree_head head, struct btree_geo geo,
	unsigned long key, void val, int level,
	gfp_t gfp)
	{
	unsigned long *node;
	int i, pos, fill, err;

	BUG_ON(!val);
	if (head->height < level) {
	err = btree_grow(head, geo, gfp);
	if (err)
	return err;
	}

	retry:
	node = find_level(head, geo, key, level);
	pos = getpos(geo, node, key);
	fill = getfill(geo, node, pos);
	/* two identical keys are not allowed */
	BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);

	if (fill == geo->no_pairs) {
	/* need to split node */
	unsigned long *new;

	new = btree_node_alloc(head, gfp);
	if (!new)
	return -ENOMEM;
	err = btree_insert_level(head, geo,
	bkey(geo, node, fill / 2 - 1),
	new, level + 1, gfp);
	if (err) {
	mempool_free(new, head->mempool);
	return err;
	}
	for (i = 0; i < fill / 2; i++) {
	setkey(geo, new, i, bkey(geo, node, i));
	setval(geo, new, i, bval(geo, node, i));
	setkey(geo, node, i, bkey(geo, node, i + fill / 2));
	setval(geo, node, i, bval(geo, node, i + fill / 2));
	clearpair(geo, node, i + fill / 2);
	}
	if (fill & 1) {
	setkey(geo, node, i, bkey(geo, node, fill - 1));
	setval(geo, node, i, bval(geo, node, fill - 1));
	clearpair(geo, node, fill - 1);
	}
	goto retry;
	}
	BUG_ON(fill >= geo->no_pairs);

	/* shift and insert */
	for (i = fill; i > pos; i--) {
	setkey(geo, node, i, bkey(geo, node, i - 1));
	setval(geo, node, i, bval(geo, node, i - 1));
	}
	setkey(geo, node, pos, key);
	setval(geo, node, pos, val);

	return 0;
	}

	int btree_insert(struct btree_head head, struct btree_geo geo,
	unsigned long key, void val, gfp_t gfp)
	{
	BUG_ON(!val);
	return btree_insert_level(head, geo, key, val, 1, gfp);
	}
	EXPORT_SYMBOL_GPL(btree_insert);

	static void btree_remove_level(struct btree_head head, struct btree_geo *geo,
	unsigned long *key, int level);
	static void merge(struct btree_head head, struct btree_geo geo, int level,
	unsigned long *left, int lfill,
	unsigned long *right, int rfill,
	unsigned long *parent, int lpos)
	{
	int i;

	for (i = 0; i < rfill; i++) {
	/* Move all keys to the left */
	setkey(geo, left, lfill + i, bkey(geo, right, i));
	setval(geo, left, lfill + i, bval(geo, right, i));
	}
	/* Exchange left and right child in parent */
	setval(geo, parent, lpos, right);
	setval(geo, parent, lpos + 1, left);
	/* Remove left (formerly right) child from parent */
	btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
	mempool_free(right, head->mempool);
	}

	static void rebalance(struct btree_head head, struct btree_geo geo,
	unsigned long key, int level, unsigned long child, int fill)
	{
	unsigned long parent, left = NULL, *right = NULL;
	int i, no_left, no_right;

	if (fill == 0) {
	/* Because we don't steal entries from a neighbour, this case
	* can happen. Parent node contains a single child, this
	* node, so merging with a sibling never happens.
	*/
	btree_remove_level(head, geo, key, level + 1);
	mempool_free(child, head->mempool);
	return;
	}

	parent = find_level(head, geo, key, level + 1);
	i = getpos(geo, parent, key);
	BUG_ON(bval(geo, parent, i) != child);

	if (i > 0) {
	left = bval(geo, parent, i - 1);
	no_left = getfill(geo, left, 0);
	if (fill + no_left <= geo->no_pairs) {
	merge(head, geo, level,
	left, no_left,
	child, fill,
	parent, i - 1);
	return;
	}
	}
	if (i + 1 < getfill(geo, parent, i)) {
	right = bval(geo, parent, i + 1);
	no_right = getfill(geo, right, 0);
	if (fill + no_right <= geo->no_pairs) {
	merge(head, geo, level,
	child, fill,
	right, no_right,
	parent, i);
	return;
	}
	}
	/*
	* We could also try to steal one entry from the left or right
	* neighbor. By not doing so we changed the invariant from
	* "all nodes are at least half full" to "no two neighboring
	* nodes can be merged". Which means that the average fill of
	* all nodes is still half or better.
	*/
	}

	static void btree_remove_level(struct btree_head head, struct btree_geo *geo,
	unsigned long *key, int level)
	{
	unsigned long *node;
	int i, pos, fill;
	void *ret;

	if (level > head->height) {
	/* we recursed all the way up */
	head->height = 0;
	head->node = NULL;
	return NULL;
	}

	node = find_level(head, geo, key, level);
	pos = getpos(geo, node, key);
	fill = getfill(geo, node, pos);
	if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
	return NULL;
	ret = bval(geo, node, pos);

	/* remove and shift */
	for (i = pos; i < fill - 1; i++) {
	setkey(geo, node, i, bkey(geo, node, i + 1));
	setval(geo, node, i, bval(geo, node, i + 1));
	}
	clearpair(geo, node, fill - 1);

	if (fill - 1 < geo->no_pairs / 2) {
	if (level < head->height)
	rebalance(head, geo, key, level, node, fill - 1);
	else if (fill - 1 == 1)
	btree_shrink(head, geo);
	}

	return ret;
	}

	void btree_remove(struct btree_head head, struct btree_geo *geo,
	unsigned long *key)
	{
	if (head->height == 0)
	return NULL;

	return btree_remove_level(head, geo, key, 1);
	}
	EXPORT_SYMBOL_GPL(btree_remove);

	int btree_merge(struct btree_head target, struct btree_head victim,
	struct btree_geo *geo, gfp_t gfp)
	{
	unsigned long key[geo->keylen];
	unsigned long dup[geo->keylen];
	void *val;
	int err;

	BUG_ON(target == victim);

	if (!(target->node)) {
	/* target is empty, just copy fields over */
	target->node = victim->node;
	target->height = victim->height;
	__btree_init(victim);
	return 0;
	}

	/* TODO: This needs some optimizations. Currently we do three tree
	* walks to remove a single object from the victim.
	*/
	for (;;) {
	if (!btree_last(victim, geo, key))
	break;
	val = btree_lookup(victim, geo, key);
	err = btree_insert(target, geo, key, val, gfp);
	if (err)
	return err;
	/* We must make a copy of the key, as the original will get
	* mangled inside btree_remove. */
	longcpy(dup, key, geo->keylen);
	btree_remove(victim, geo, dup);
	}
	return 0;
	}
	EXPORT_SYMBOL_GPL(btree_merge);

	static size_t __btree_for_each(struct btree_head head, struct btree_geo geo,
	unsigned long *node, unsigned long opaque,
	void (func)(void elem, unsigned long opaque,
	unsigned long *key, size_t index,
	void *func2),
	void *func2, int reap, int height, size_t count)
	{
	int i;
	unsigned long *child;

	for (i = 0; i < geo->no_pairs; i++) {
	child = bval(geo, node, i);
	if (!child)
	break;
	if (height > 1)
	count = __btree_for_each(head, geo, child, opaque,
	func, func2, reap, height - 1, count);
	else
	func(child, opaque, bkey(geo, node, i), count++,
	func2);
	}
	if (reap)
	mempool_free(node, head->mempool);
	return count;
	}

	static void empty(void elem, unsigned long opaque, unsigned long key,
	size_t index, void *func2)
	{
	}

	void visitorl(void elem, unsigned long opaque, unsigned long key,
	size_t index, void *__func)
	{
	visitorl_t func = __func;

	func(elem, opaque, *key, index);
	}
	EXPORT_SYMBOL_GPL(visitorl);

	void visitor32(void elem, unsigned long opaque, unsigned long __key,
	size_t index, void *__func)
	{
	visitor32_t func = __func;
	u32 key = (void )__key;

	func(elem, opaque, *key, index);
	}
	EXPORT_SYMBOL_GPL(visitor32);

	void visitor64(void elem, unsigned long opaque, unsigned long __key,
	size_t index, void *__func)
	{
	visitor64_t func = __func;
	u64 key = (void )__key;

	func(elem, opaque, *key, index);
	}
	EXPORT_SYMBOL_GPL(visitor64);

	void visitor128(void elem, unsigned long opaque, unsigned long __key,
	size_t index, void *__func)
	{
	visitor128_t func = __func;
	u64 key = (void )__key;

	func(elem, opaque, key[0], key[1], index);
	}
	EXPORT_SYMBOL_GPL(visitor128);

	size_t btree_visitor(struct btree_head head, struct btree_geo geo,
	unsigned long opaque,
	void (func)(void elem, unsigned long opaque,
	unsigned long *key,
	size_t index, void *func2),
	void *func2)
	{
	size_t count = 0;

	if (!func2)
	func = empty;
	if (head->node)
	count = __btree_for_each(head, geo, head->node, opaque, func,
	func2, 0, head->height, 0);
	return count;
	}
	EXPORT_SYMBOL_GPL(btree_visitor);

	size_t btree_grim_visitor(struct btree_head head, struct btree_geo geo,
	unsigned long opaque,
	void (func)(void elem, unsigned long opaque,
	unsigned long *key,
	size_t index, void *func2),
	void *func2)
	{
	size_t count = 0;

	if (!func2)
	func = empty;
	if (head->node)
	count = __btree_for_each(head, geo, head->node, opaque, func,
	func2, 1, head->height, 0);
	__btree_init(head);
	return count;
	}
	EXPORT_SYMBOL_GPL(btree_grim_visitor);

	static int __init btree_module_init(void)
	{
	btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
	SLAB_HWCACHE_ALIGN, NULL);
	return 0;
	}

	static void __exit btree_module_exit(void)
	{
	kmem_cache_destroy(btree_cachep);
	}

	/* If core code starts using btree, initialization should happen even earlier */
	module_init(btree_module_init);
	module_exit(btree_module_exit);

	MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
	MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
	MODULE_LICENSE("GPL");