btree.c - pub/scm/linux/kernel/git/joern/cancd - Git at Google

 /*
  * lib/btree.c	- Simple In-memory B+Tree
  *
  * License: GPLv2
  *
  * Copyright (c) 2007-2008 Joern Engel <joern@logfs.org>
  *
  * A relatively simple B+Tree implementation.  I have written it as a learning
  * excercise 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.
  *
  * One trick was used that are 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 <errno.h>
 #include "btree.h"

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

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

 #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),
 };

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

 static unsigned long *btree_node_alloc(struct btree_head *head)
 {
 	return calloc(1, NODESIZE);
 }

 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;
 }

 /*
  * B+Tree node format:
  * [key0, key1, ..., keyN] [val0, val1, ..., valN]
  * Each key is an array of unsigned longs, head->keylen in total.
  * Total number of keys and vals (N) is head->no_pairs.
  */

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

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

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

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

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

 #if 0
 static void dumpkey(struct btree_geo *geo, unsigned long *key)
 {
 	int k;

 	printf("(%lx", key[0]);
 	for (k = 1; k < geo->keylen; k++)
 		printf(",%lx", key[k]);
 	printf(")");
 }

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

 	printf("%p: ", node);
 	for (i = 0; i < geo->no_pairs; i++) {
 		key = bkey(geo, node, i);
 		dumpkey(geo, key);
 		printf(" %lx  ", bval(geo, node, i));
 	}
 	printf("\n");
 }

 static void __dumptree(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *node, int height)
 {
 	int i;
 	unsigned long *child;

 	if (!height)
 		return;

 	printf("%2x ", height);
 	dumpnode(geo, node);
 	for (i = 0; i < geo->no_pairs; i++) {
 		child = (void *)bval(geo, node, i);
 		if (!child)
 			return;
 		__dumptree(head, geo, child, height - 1);
 	}
 }

 static void dumptree(struct btree_head *head, struct btree_geo *geo)
 {
 	__dumptree(head, geo, head->node, head->height);
 }
 #endif

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

 void btree_init(struct btree_head *head)
 {
 	__btree_init(head);
 }

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

 	if (height == 0)
 		return NULL;

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

 	return bkey(geo, node, 0);
 }

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

 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 = (unsigned long *)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 (void *)bval(geo, node, i);
 	return NULL;
 }

 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) == 0)
 			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, key, i);
 		}
 		BUG_ON(i < 0);
 		node = (unsigned long *)bval(geo, node, i);
 	}
 	BUG_ON(!node);
 	return node;
 }

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

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

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

 	if ((fill == 0) || ((fill == 1) && (head->height > 1))) {
 		node = head->node;
 		head->node = (unsigned long *)bval(geo, node, 0);
 		head->height--;
 		free(node);
 	}
 }

 static void steal_l(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 no_entries)
 {
 	int i;

 	for (i = rfill - 1; i >= 0; i--) {
 		/* Shift entries on the right */
 		setkey(geo, right, bkey(geo, right, i), i + no_entries);
 		setval(geo, right, bval(geo, right, i), i + no_entries);
 	}
 	for (i = 0; i < no_entries; i++) {
 		/* Move some entries to the right */
 		setkey(geo, right, bkey(geo, left, lfill - no_entries + i), i);
 		setval(geo, right, bval(geo, left, lfill - no_entries + i), i);
 	}
 	/* Set parent key */
 	setkey(geo, parent, bkey(geo, left, lfill - no_entries - 1), lpos);
 	for (i = lfill - no_entries; i < lfill; i++)
 		clearpair(geo, left, i);
 }

 static void steal_r(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 no_entries)
 {
 	int i;

 	for (i = 0; i < no_entries; i++) {
 		/* Move some entries to the left */
 		setkey(geo, left, bkey(geo, right, i), lfill + i);
 		setval(geo, left, bval(geo, right, i), lfill + i);
 	}
 	/* Set parent key */
 	setkey(geo, parent, bkey(geo, right, no_entries - 1), lpos);
 	/* Shift entries on the right */
 	for ( ; i < rfill; i++) {
 		setkey(geo, right, bkey(geo, right, i), i - no_entries);
 		setval(geo, right, bval(geo, right, i), i - no_entries);
 	}
 	for (i = rfill - no_entries; i < rfill; i++)
 		clearpair(geo, right, i);
 }

 static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, unsigned long val, int level);
 static int split(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *node, int level)
 {
 	unsigned long *new;
 	int i, err, fill = geo->no_pairs;

 	new = btree_node_alloc(head);
 	if (!new)
 		return -ENOMEM;
 	err = btree_insert_level(head, geo,
 			bkey(geo, node, fill / 2 - 1),
 			(unsigned long)new, level + 1);
 	if (err) {
 		free(new);
 		return err;
 	}
 	for (i = 0; i < fill / 2; i++) {
 		setkey(geo, new, bkey(geo, node, i), i);
 		setval(geo, new, bval(geo, node, i), i);
 		setkey(geo, node, bkey(geo, node, i + fill / 2), i);
 		setval(geo, node, bval(geo, node, i + fill / 2), i);
 		clearpair(geo, node, i + fill / 2);
 	}
 	if (fill & 1) {
 		setkey(geo, node, bkey(geo, node, fill - 1), i);
 		setval(geo, node, bval(geo, node, fill - 1), i);
 		clearpair(geo, node, fill - 1);
 	}
 	return 0;
 }

 static int rebalance_insert(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *key, unsigned long *child, int level)
 {
 	return split(head, geo, child, level);
 }

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

 	BUG_ON(!val);
 	if (head->height < level) {
 		err = btree_grow(head, geo);
 		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 */
 		err = rebalance_insert(head, geo, key, node, level);
 		if (err)
 			return err;
 		goto retry;
 	}
 	BUG_ON(fill >= geo->no_pairs);

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

 	return 0;
 }

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

 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 entries to the left */
 		setkey(geo, left, bkey(geo, right, i), lfill + i);
 		setval(geo, left, bval(geo, right, i), lfill + i);
 	}
 	/* Exchange left and right child in parent */
 	setval(geo, parent, (unsigned long)right, lpos);
 	setval(geo, parent, (unsigned long)left, lpos + 1);
 	/* Remove left (formerly right) child from parent */
 	btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
 	free(right);
 }

 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 child_no, no_left, no_right = no_right, i;

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

 	if (child_no > 0) {
 		left = (unsigned long *)bval(geo, parent, child_no - 1);
 		no_left = getfill(geo, left, 0);
 		if (fill + no_left <= geo->no_pairs) {
 			/* Merge with left neighbour */
 			merge(head, geo, level,
 					left, no_left,
 					child, fill,
 					parent, child_no - 1);
 			return;
 		}
 	}
 	if (child_no + 1 < getfill(geo, parent, child_no)) {
 		right = (unsigned long *)bval(geo, parent, child_no + 1);
 		no_right = getfill(geo, right, 0);
 		if (fill + no_right <= geo->no_pairs) {
 			/* Merge with right neighbour */
 			merge(head, geo, level,
 					child, fill,
 					right, no_right,
 					parent, child_no);
 			return;
 		}
 	}
 	/*
 	 * Leaving the btree in a somewhat unbalanced state can improve
 	 * performance.  Stealing entries from a neighbour is a fairly
 	 * expensive operation.  In trees where reads completely dominate
 	 * writes, the cost will be amortized sooner or later.  When the
 	 * ratio of writes increases, they may never be amortized.
 	 *
 	 * So avoid stealing unless the tree would get _really_ unbalanced.
 	 */
 	if (fill > 1)
 		return;
 	if (left) {
 		/* Steal from left neighbour */
 		i = (no_left - fill) / 2;
 		BUG_ON(i < 1);
 		steal_l(head, geo, level,
 				left, no_left,
 				child, fill,
 				parent, child_no - 1, i);
 		return;
 	}
 	if (right) {
 		/* Steal from right neighbour */
 		i = (no_right - fill) / 2;
 		BUG_ON(i < 1);
 		steal_r(head, geo, level,
 				child, fill,
 				right, no_right,
 				parent, child_no, i);
 		return;
 	}
 	BUG(); /* We should never get here */
 }

 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 = (void *)bval(geo, node, pos);

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

 	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);
 }

 int btree_merge(struct btree_head *target, struct btree_head *victim,
 		struct btree_geo *geo, unsigned long *duplicate)
 {
 	unsigned long *key;
 	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;
 	}

 	for (;;) {
 		key = btree_last(victim, geo);
 		if (!key)
 			break;
 		val = btree_lookup(victim, geo, key);
 		err = btree_insert(target, geo, key, val);
 		if (err)
 			return err;
 		/* We must make a copy of the key, as the original will get
 		 * mangled inside btree_remove. */
 		longcpy(duplicate, key, geo->keylen);
 		btree_remove(victim, geo, duplicate);
 	}
 	return 0;
 }

 static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
 		unsigned long *node, long opaque,
 		void (*func)(void *elem, 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 = (void *)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)
 		free(node);
 	return count;
 }

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

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

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

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

 	func(elem, opaque, key, index);
 }

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

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

 void visitor128(void *elem, 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);
 }

 size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
 		long opaque,
 		void (*func)(void *elem, 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;
 }

 size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
 		long opaque,
 		void (*func)(void *elem, 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;
 }
	/*
	* lib/btree.c - Simple In-memory B+Tree
	*
	* License: GPLv2
	*
	* Copyright (c) 2007-2008 Joern Engel <joern@logfs.org>
	*
	* A relatively simple B+Tree implementation. I have written it as a learning
	* excercise 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.
	*
	* One trick was used that are 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 <errno.h>
	#include "btree.h"

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

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

	#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),
	};

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

	static unsigned long btree_node_alloc(struct btree_head head)
	{
	return calloc(1, NODESIZE);
	}

	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;
	}

	/*
	* B+Tree node format:
	* [key0, key1, ..., keyN] [val0, val1, ..., valN]
	* Each key is an array of unsigned longs, head->keylen in total.
	* Total number of keys and vals (N) is head->no_pairs.
	*/

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

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

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

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

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

	#if 0
	static void dumpkey(struct btree_geo geo, unsigned long key)
	{
	int k;

	printf("(%lx", key[0]);
	for (k = 1; k < geo->keylen; k++)
	printf(",%lx", key[k]);
	printf(")");
	}

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

	printf("%p: ", node);
	for (i = 0; i < geo->no_pairs; i++) {
	key = bkey(geo, node, i);
	dumpkey(geo, key);
	printf(" %lx ", bval(geo, node, i));
	}
	printf("\n");
	}

	static void __dumptree(struct btree_head head, struct btree_geo geo,
	unsigned long *node, int height)
	{
	int i;
	unsigned long *child;

	if (!height)
	return;

	printf("%2x ", height);
	dumpnode(geo, node);
	for (i = 0; i < geo->no_pairs; i++) {
	child = (void *)bval(geo, node, i);
	if (!child)
	return;
	__dumptree(head, geo, child, height - 1);
	}
	}

	static void dumptree(struct btree_head head, struct btree_geo geo)
	{
	__dumptree(head, geo, head->node, head->height);
	}
	#endif

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

	void btree_init(struct btree_head *head)
	{
	__btree_init(head);
	}

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

	if (height == 0)
	return NULL;

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

	return bkey(geo, node, 0);
	}

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

	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 = (unsigned long *)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 (void *)bval(geo, node, i);
	return NULL;
	}

	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) == 0)
	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, key, i);
	}
	BUG_ON(i < 0);
	node = (unsigned long *)bval(geo, node, i);
	}
	BUG_ON(!node);
	return node;
	}

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

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

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

	if ((fill == 0) \|\| ((fill == 1) && (head->height > 1))) {
	node = head->node;
	head->node = (unsigned long *)bval(geo, node, 0);
	head->height--;
	free(node);
	}
	}

	static void steal_l(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 no_entries)
	{
	int i;

	for (i = rfill - 1; i >= 0; i--) {
	/* Shift entries on the right */
	setkey(geo, right, bkey(geo, right, i), i + no_entries);
	setval(geo, right, bval(geo, right, i), i + no_entries);
	}
	for (i = 0; i < no_entries; i++) {
	/* Move some entries to the right */
	setkey(geo, right, bkey(geo, left, lfill - no_entries + i), i);
	setval(geo, right, bval(geo, left, lfill - no_entries + i), i);
	}
	/* Set parent key */
	setkey(geo, parent, bkey(geo, left, lfill - no_entries - 1), lpos);
	for (i = lfill - no_entries; i < lfill; i++)
	clearpair(geo, left, i);
	}

	static void steal_r(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 no_entries)
	{
	int i;

	for (i = 0; i < no_entries; i++) {
	/* Move some entries to the left */
	setkey(geo, left, bkey(geo, right, i), lfill + i);
	setval(geo, left, bval(geo, right, i), lfill + i);
	}
	/* Set parent key */
	setkey(geo, parent, bkey(geo, right, no_entries - 1), lpos);
	/* Shift entries on the right */
	for ( ; i < rfill; i++) {
	setkey(geo, right, bkey(geo, right, i), i - no_entries);
	setval(geo, right, bval(geo, right, i), i - no_entries);
	}
	for (i = rfill - no_entries; i < rfill; i++)
	clearpair(geo, right, i);
	}

	static int btree_insert_level(struct btree_head head, struct btree_geo geo,
	unsigned long *key, unsigned long val, int level);
	static int split(struct btree_head head, struct btree_geo geo,
	unsigned long *node, int level)
	{
	unsigned long *new;
	int i, err, fill = geo->no_pairs;

	new = btree_node_alloc(head);
	if (!new)
	return -ENOMEM;
	err = btree_insert_level(head, geo,
	bkey(geo, node, fill / 2 - 1),
	(unsigned long)new, level + 1);
	if (err) {
	free(new);
	return err;
	}
	for (i = 0; i < fill / 2; i++) {
	setkey(geo, new, bkey(geo, node, i), i);
	setval(geo, new, bval(geo, node, i), i);
	setkey(geo, node, bkey(geo, node, i + fill / 2), i);
	setval(geo, node, bval(geo, node, i + fill / 2), i);
	clearpair(geo, node, i + fill / 2);
	}
	if (fill & 1) {
	setkey(geo, node, bkey(geo, node, fill - 1), i);
	setval(geo, node, bval(geo, node, fill - 1), i);
	clearpair(geo, node, fill - 1);
	}
	return 0;
	}

	static int rebalance_insert(struct btree_head head, struct btree_geo geo,
	unsigned long key, unsigned long child, int level)
	{
	return split(head, geo, child, level);
	}

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

	BUG_ON(!val);
	if (head->height < level) {
	err = btree_grow(head, geo);
	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 */
	err = rebalance_insert(head, geo, key, node, level);
	if (err)
	return err;
	goto retry;
	}
	BUG_ON(fill >= geo->no_pairs);

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

	return 0;
	}

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

	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 entries to the left */
	setkey(geo, left, bkey(geo, right, i), lfill + i);
	setval(geo, left, bval(geo, right, i), lfill + i);
	}
	/* Exchange left and right child in parent */
	setval(geo, parent, (unsigned long)right, lpos);
	setval(geo, parent, (unsigned long)left, lpos + 1);
	/* Remove left (formerly right) child from parent */
	btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
	free(right);
	}

	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 child_no, no_left, no_right = no_right, i;

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

	if (child_no > 0) {
	left = (unsigned long *)bval(geo, parent, child_no - 1);
	no_left = getfill(geo, left, 0);
	if (fill + no_left <= geo->no_pairs) {
	/* Merge with left neighbour */
	merge(head, geo, level,
	left, no_left,
	child, fill,
	parent, child_no - 1);
	return;
	}
	}
	if (child_no + 1 < getfill(geo, parent, child_no)) {
	right = (unsigned long *)bval(geo, parent, child_no + 1);
	no_right = getfill(geo, right, 0);
	if (fill + no_right <= geo->no_pairs) {
	/* Merge with right neighbour */
	merge(head, geo, level,
	child, fill,
	right, no_right,
	parent, child_no);
	return;
	}
	}
	/*
	* Leaving the btree in a somewhat unbalanced state can improve
	* performance. Stealing entries from a neighbour is a fairly
	* expensive operation. In trees where reads completely dominate
	* writes, the cost will be amortized sooner or later. When the
	* ratio of writes increases, they may never be amortized.
	*
	* So avoid stealing unless the tree would get _really_ unbalanced.
	*/
	if (fill > 1)
	return;
	if (left) {
	/* Steal from left neighbour */
	i = (no_left - fill) / 2;
	BUG_ON(i < 1);
	steal_l(head, geo, level,
	left, no_left,
	child, fill,
	parent, child_no - 1, i);
	return;
	}
	if (right) {
	/* Steal from right neighbour */
	i = (no_right - fill) / 2;
	BUG_ON(i < 1);
	steal_r(head, geo, level,
	child, fill,
	right, no_right,
	parent, child_no, i);
	return;
	}
	BUG(); /* We should never get here */
	}

	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 = (void *)bval(geo, node, pos);

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

	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);
	}

	int btree_merge(struct btree_head target, struct btree_head victim,
	struct btree_geo geo, unsigned long duplicate)
	{
	unsigned long *key;
	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;
	}

	for (;;) {
	key = btree_last(victim, geo);
	if (!key)
	break;
	val = btree_lookup(victim, geo, key);
	err = btree_insert(target, geo, key, val);
	if (err)
	return err;
	/* We must make a copy of the key, as the original will get
	* mangled inside btree_remove. */
	longcpy(duplicate, key, geo->keylen);
	btree_remove(victim, geo, duplicate);
	}
	return 0;
	}

	static size_t __btree_for_each(struct btree_head head, struct btree_geo geo,
	unsigned long *node, long opaque,
	void (func)(void elem, 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 = (void *)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)
	free(node);
	return count;
	}

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

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

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

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

	func(elem, opaque, key, index);
	}

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

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

	void visitor128(void elem, 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);
	}

	size_t btree_visitor(struct btree_head head, struct btree_geo geo,
	long opaque,
	void (func)(void elem, 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;
	}

	size_t btree_grim_visitor(struct btree_head head, struct btree_geo geo,
	long opaque,
	void (func)(void elem, 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;
	}