Release 4.12 lib/btree.c

/*
 * 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
 * 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);
}
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EXPORT_SYMBOL_GPL(btree_alloc);



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

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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;
}

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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;
}

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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;
}

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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;
	}
}

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

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

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

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

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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;
}

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

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

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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;
}

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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;
}
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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;
}
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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;
}
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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;
}

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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;
}

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/*
 * 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;
}

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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;
}

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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);
}

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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;
}

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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);
}
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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);
}

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static void rebalance(struct btree_head *head, struct btree_geo *geo,