2 * lib/btree.c - Simple In-memory B+Tree
4 * As should be obvious for Linux kernel code, license is GPLv2
6 * Copyright (c) 2007-2008 Joern Engel <joern@logfs.org>
7 * Bits and pieces stolen from Peter Zijlstra's code, which is
8 * Copyright 2007, Red Hat Inc. Peter Zijlstra <pzijlstr@redhat.com>
11 * see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch
13 * A relatively simple B+Tree implementation. I have written it as a learning
14 * exercise to understand how B+Trees work. Turned out to be useful as well.
16 * B+Trees can be used similar to Linux radix trees (which don't have anything
17 * in common with textbook radix trees, beware). Prerequisite for them working
18 * well is that access to a random tree node is much faster than a large number
19 * of operations within each node.
21 * Disks have fulfilled the prerequisite for a long time. More recently DRAM
22 * has gained similar properties, as memory access times, when measured in cpu
23 * cycles, have increased. Cacheline sizes have increased as well, which also
26 * Compared to radix trees, B+Trees are more efficient when dealing with a
27 * sparsely populated address space. Between 25% and 50% of the memory is
28 * occupied with valid pointers. When densely populated, radix trees contain
29 * ~98% pointers - hard to beat. Very sparse radix trees contain only ~2%
32 * This particular implementation stores pointers identified by a long value.
33 * Storing NULL pointers is illegal, lookup will return NULL when no entry
36 * A tricks was used that is not commonly found in textbooks. The lowest
37 * values are to the right, not to the left. All used slots within a node
38 * are on the left, all unused slots contain NUL values. Most operations
39 * simply loop once over all slots and terminate on the first NUL.
42 #include <linux/btree.h>
43 #include <linux/cache.h>
44 #include <linux/kernel.h>
45 #include <linux/slab.h>
46 #include <linux/module.h>
48 #define MAX(a, b) ((a) > (b) ? (a) : (b))
49 #define NODESIZE MAX(L1_CACHE_BYTES, 128)
57 struct btree_geo btree_geo32 = {
59 .no_pairs = NODESIZE / sizeof(long) / 2,
60 .no_longs = NODESIZE / sizeof(long) / 2,
62 EXPORT_SYMBOL_GPL(btree_geo32);
64 #define LONG_PER_U64 (64 / BITS_PER_LONG)
65 struct btree_geo btree_geo64 = {
66 .keylen = LONG_PER_U64,
67 .no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64),
68 .no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)),
70 EXPORT_SYMBOL_GPL(btree_geo64);
72 struct btree_geo btree_geo128 = {
73 .keylen = 2 * LONG_PER_U64,
74 .no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64),
75 .no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)),
77 EXPORT_SYMBOL_GPL(btree_geo128);
79 static struct kmem_cache *btree_cachep;
81 void *btree_alloc(gfp_t gfp_mask, void *pool_data)
83 return kmem_cache_alloc(btree_cachep, gfp_mask);
85 EXPORT_SYMBOL_GPL(btree_alloc);
87 void btree_free(void *element, void *pool_data)
89 kmem_cache_free(btree_cachep, element);
91 EXPORT_SYMBOL_GPL(btree_free);
93 static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp)
97 node = mempool_alloc(head->mempool, gfp);
99 memset(node, 0, NODESIZE);
103 static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
107 for (i = 0; i < n; i++) {
116 static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
121 for (i = 0; i < n; i++)
126 static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
130 for (i = 0; i < n; i++)
135 static void dec_key(struct btree_geo *geo, unsigned long *key)
140 for (i = geo->keylen - 1; i >= 0; i--) {
148 static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
150 return &node[n * geo->keylen];
153 static void *bval(struct btree_geo *geo, unsigned long *node, int n)
155 return (void *)node[geo->no_longs + n];
158 static void setkey(struct btree_geo *geo, unsigned long *node, int n,
161 longcpy(bkey(geo, node, n), key, geo->keylen);
164 static void setval(struct btree_geo *geo, unsigned long *node, int n,
167 node[geo->no_longs + n] = (unsigned long) val;
170 static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
172 longset(bkey(geo, node, n), 0, geo->keylen);
173 node[geo->no_longs + n] = 0;
176 static inline void __btree_init(struct btree_head *head)
182 void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
185 head->mempool = mempool;
187 EXPORT_SYMBOL_GPL(btree_init_mempool);
189 int btree_init(struct btree_head *head)
192 head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
197 EXPORT_SYMBOL_GPL(btree_init);
199 void btree_destroy(struct btree_head *head)
201 mempool_destroy(head->mempool);
202 head->mempool = NULL;
204 EXPORT_SYMBOL_GPL(btree_destroy);
206 void *btree_last(struct btree_head *head, struct btree_geo *geo,
209 int height = head->height;
210 unsigned long *node = head->node;
215 for ( ; height > 1; height--)
216 node = bval(geo, node, 0);
218 longcpy(key, bkey(geo, node, 0), geo->keylen);
219 return bval(geo, node, 0);
221 EXPORT_SYMBOL_GPL(btree_last);
223 static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
226 return longcmp(bkey(geo, node, pos), key, geo->keylen);
229 static int keyzero(struct btree_geo *geo, unsigned long *key)
233 for (i = 0; i < geo->keylen; i++)
240 void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
243 int i, height = head->height;
244 unsigned long *node = head->node;
249 for ( ; height > 1; height--) {
250 for (i = 0; i < geo->no_pairs; i++)
251 if (keycmp(geo, node, i, key) <= 0)
253 if (i == geo->no_pairs)
255 node = bval(geo, node, i);
263 for (i = 0; i < geo->no_pairs; i++)
264 if (keycmp(geo, node, i, key) == 0)
265 return bval(geo, node, i);
268 EXPORT_SYMBOL_GPL(btree_lookup);
270 int btree_update(struct btree_head *head, struct btree_geo *geo,
271 unsigned long *key, void *val)
273 int i, height = head->height;
274 unsigned long *node = head->node;
279 for ( ; height > 1; height--) {
280 for (i = 0; i < geo->no_pairs; i++)
281 if (keycmp(geo, node, i, key) <= 0)
283 if (i == geo->no_pairs)
285 node = bval(geo, node, i);
293 for (i = 0; i < geo->no_pairs; i++)
294 if (keycmp(geo, node, i, key) == 0) {
295 setval(geo, node, i, val);
300 EXPORT_SYMBOL_GPL(btree_update);
303 * Usually this function is quite similar to normal lookup. But the key of
304 * a parent node may be smaller than the smallest key of all its siblings.
305 * In such a case we cannot just return NULL, as we have only proven that no
306 * key smaller than __key, but larger than this parent key exists.
307 * So we set __key to the parent key and retry. We have to use the smallest
308 * such parent key, which is the last parent key we encountered.
310 void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
311 unsigned long *__key)
314 unsigned long *node, *oldnode;
315 unsigned long *retry_key = NULL, key[geo->keylen];
317 if (keyzero(geo, __key))
320 if (head->height == 0)
322 longcpy(key, __key, geo->keylen);
327 for (height = head->height ; height > 1; height--) {
328 for (i = 0; i < geo->no_pairs; i++)
329 if (keycmp(geo, node, i, key) <= 0)
331 if (i == geo->no_pairs)
334 node = bval(geo, node, i);
337 retry_key = bkey(geo, oldnode, i);
343 for (i = 0; i < geo->no_pairs; i++) {
344 if (keycmp(geo, node, i, key) <= 0) {
345 if (bval(geo, node, i)) {
346 longcpy(__key, bkey(geo, node, i), geo->keylen);
347 return bval(geo, node, i);
354 longcpy(key, retry_key, geo->keylen);
360 EXPORT_SYMBOL_GPL(btree_get_prev);
362 static int getpos(struct btree_geo *geo, unsigned long *node,
367 for (i = 0; i < geo->no_pairs; i++) {
368 if (keycmp(geo, node, i, key) <= 0)
374 static int getfill(struct btree_geo *geo, unsigned long *node, int start)
378 for (i = start; i < geo->no_pairs; i++)
379 if (!bval(geo, node, i))
385 * locate the correct leaf node in the btree
387 static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
388 unsigned long *key, int level)
390 unsigned long *node = head->node;
393 for (height = head->height; height > level; height--) {
394 for (i = 0; i < geo->no_pairs; i++)
395 if (keycmp(geo, node, i, key) <= 0)
398 if ((i == geo->no_pairs) || !bval(geo, node, i)) {
399 /* right-most key is too large, update it */
400 /* FIXME: If the right-most key on higher levels is
401 * always zero, this wouldn't be necessary. */
403 setkey(geo, node, i, key);
406 node = bval(geo, node, i);
412 static int btree_grow(struct btree_head *head, struct btree_geo *geo,
418 node = btree_node_alloc(head, gfp);
422 fill = getfill(geo, head->node, 0);
423 setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
424 setval(geo, node, 0, head->node);
431 static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
436 if (head->height <= 1)
440 fill = getfill(geo, node, 0);
442 head->node = bval(geo, node, 0);
444 mempool_free(node, head->mempool);
447 static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
448 unsigned long *key, void *val, int level,
452 int i, pos, fill, err;
455 if (head->height < level) {
456 err = btree_grow(head, geo, gfp);
462 node = find_level(head, geo, key, level);
463 pos = getpos(geo, node, key);
464 fill = getfill(geo, node, pos);
465 /* two identical keys are not allowed */
466 BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
468 if (fill == geo->no_pairs) {
469 /* need to split node */
472 new = btree_node_alloc(head, gfp);
475 err = btree_insert_level(head, geo,
476 bkey(geo, node, fill / 2 - 1),
477 new, level + 1, gfp);
479 mempool_free(new, head->mempool);
482 for (i = 0; i < fill / 2; i++) {
483 setkey(geo, new, i, bkey(geo, node, i));
484 setval(geo, new, i, bval(geo, node, i));
485 setkey(geo, node, i, bkey(geo, node, i + fill / 2));
486 setval(geo, node, i, bval(geo, node, i + fill / 2));
487 clearpair(geo, node, i + fill / 2);
490 setkey(geo, node, i, bkey(geo, node, fill - 1));
491 setval(geo, node, i, bval(geo, node, fill - 1));
492 clearpair(geo, node, fill - 1);
496 BUG_ON(fill >= geo->no_pairs);
498 /* shift and insert */
499 for (i = fill; i > pos; i--) {
500 setkey(geo, node, i, bkey(geo, node, i - 1));
501 setval(geo, node, i, bval(geo, node, i - 1));
503 setkey(geo, node, pos, key);
504 setval(geo, node, pos, val);
509 int btree_insert(struct btree_head *head, struct btree_geo *geo,
510 unsigned long *key, void *val, gfp_t gfp)
513 return btree_insert_level(head, geo, key, val, 1, gfp);
515 EXPORT_SYMBOL_GPL(btree_insert);
517 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
518 unsigned long *key, int level);
519 static void merge(struct btree_head *head, struct btree_geo *geo, int level,
520 unsigned long *left, int lfill,
521 unsigned long *right, int rfill,
522 unsigned long *parent, int lpos)
526 for (i = 0; i < rfill; i++) {
527 /* Move all keys to the left */
528 setkey(geo, left, lfill + i, bkey(geo, right, i));
529 setval(geo, left, lfill + i, bval(geo, right, i));
531 /* Exchange left and right child in parent */
532 setval(geo, parent, lpos, right);
533 setval(geo, parent, lpos + 1, left);
534 /* Remove left (formerly right) child from parent */
535 btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
536 mempool_free(right, head->mempool);
539 static void rebalance(struct btree_head *head, struct btree_geo *geo,
540 unsigned long *key, int level, unsigned long *child, int fill)
542 unsigned long *parent, *left = NULL, *right = NULL;
543 int i, no_left, no_right;
546 /* Because we don't steal entries from a neighbour, this case
547 * can happen. Parent node contains a single child, this
548 * node, so merging with a sibling never happens.
550 btree_remove_level(head, geo, key, level + 1);
551 mempool_free(child, head->mempool);
555 parent = find_level(head, geo, key, level + 1);
556 i = getpos(geo, parent, key);
557 BUG_ON(bval(geo, parent, i) != child);
560 left = bval(geo, parent, i - 1);
561 no_left = getfill(geo, left, 0);
562 if (fill + no_left <= geo->no_pairs) {
563 merge(head, geo, level,
570 if (i + 1 < getfill(geo, parent, i)) {
571 right = bval(geo, parent, i + 1);
572 no_right = getfill(geo, right, 0);
573 if (fill + no_right <= geo->no_pairs) {
574 merge(head, geo, level,
582 * We could also try to steal one entry from the left or right
583 * neighbor. By not doing so we changed the invariant from
584 * "all nodes are at least half full" to "no two neighboring
585 * nodes can be merged". Which means that the average fill of
586 * all nodes is still half or better.
590 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
591 unsigned long *key, int level)
597 if (level > head->height) {
598 /* we recursed all the way up */
604 node = find_level(head, geo, key, level);
605 pos = getpos(geo, node, key);
606 fill = getfill(geo, node, pos);
607 if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
609 ret = bval(geo, node, pos);
611 /* remove and shift */
612 for (i = pos; i < fill - 1; i++) {
613 setkey(geo, node, i, bkey(geo, node, i + 1));
614 setval(geo, node, i, bval(geo, node, i + 1));
616 clearpair(geo, node, fill - 1);
618 if (fill - 1 < geo->no_pairs / 2) {
619 if (level < head->height)
620 rebalance(head, geo, key, level, node, fill - 1);
621 else if (fill - 1 == 1)
622 btree_shrink(head, geo);
628 void *btree_remove(struct btree_head *head, struct btree_geo *geo,
631 if (head->height == 0)
634 return btree_remove_level(head, geo, key, 1);
636 EXPORT_SYMBOL_GPL(btree_remove);
638 int btree_merge(struct btree_head *target, struct btree_head *victim,
639 struct btree_geo *geo, gfp_t gfp)
641 unsigned long key[geo->keylen];
642 unsigned long dup[geo->keylen];
646 BUG_ON(target == victim);
648 if (!(target->node)) {
649 /* target is empty, just copy fields over */
650 target->node = victim->node;
651 target->height = victim->height;
652 __btree_init(victim);
656 /* TODO: This needs some optimizations. Currently we do three tree
657 * walks to remove a single object from the victim.
660 if (!btree_last(victim, geo, key))
662 val = btree_lookup(victim, geo, key);
663 err = btree_insert(target, geo, key, val, gfp);
666 /* We must make a copy of the key, as the original will get
667 * mangled inside btree_remove. */
668 longcpy(dup, key, geo->keylen);
669 btree_remove(victim, geo, dup);
673 EXPORT_SYMBOL_GPL(btree_merge);
675 static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
676 unsigned long *node, unsigned long opaque,
677 void (*func)(void *elem, unsigned long opaque,
678 unsigned long *key, size_t index,
680 void *func2, int reap, int height, size_t count)
683 unsigned long *child;
685 for (i = 0; i < geo->no_pairs; i++) {
686 child = bval(geo, node, i);
690 count = __btree_for_each(head, geo, child, opaque,
691 func, func2, reap, height - 1, count);
693 func(child, opaque, bkey(geo, node, i), count++,
697 mempool_free(node, head->mempool);
701 static void empty(void *elem, unsigned long opaque, unsigned long *key,
702 size_t index, void *func2)
706 void visitorl(void *elem, unsigned long opaque, unsigned long *key,
707 size_t index, void *__func)
709 visitorl_t func = __func;
711 func(elem, opaque, *key, index);
713 EXPORT_SYMBOL_GPL(visitorl);
715 void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
716 size_t index, void *__func)
718 visitor32_t func = __func;
719 u32 *key = (void *)__key;
721 func(elem, opaque, *key, index);
723 EXPORT_SYMBOL_GPL(visitor32);
725 void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
726 size_t index, void *__func)
728 visitor64_t func = __func;
729 u64 *key = (void *)__key;
731 func(elem, opaque, *key, index);
733 EXPORT_SYMBOL_GPL(visitor64);
735 void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
736 size_t index, void *__func)
738 visitor128_t func = __func;
739 u64 *key = (void *)__key;
741 func(elem, opaque, key[0], key[1], index);
743 EXPORT_SYMBOL_GPL(visitor128);
745 size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
746 unsigned long opaque,
747 void (*func)(void *elem, unsigned long opaque,
749 size_t index, void *func2),
757 count = __btree_for_each(head, geo, head->node, opaque, func,
758 func2, 0, head->height, 0);
761 EXPORT_SYMBOL_GPL(btree_visitor);
763 size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
764 unsigned long opaque,
765 void (*func)(void *elem, unsigned long opaque,
767 size_t index, void *func2),
775 count = __btree_for_each(head, geo, head->node, opaque, func,
776 func2, 1, head->height, 0);
780 EXPORT_SYMBOL_GPL(btree_grim_visitor);
782 static int __init btree_module_init(void)
784 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
785 SLAB_HWCACHE_ALIGN, NULL);
789 static void __exit btree_module_exit(void)
791 kmem_cache_destroy(btree_cachep);
794 /* If core code starts using btree, initialization should happen even earlier */
795 module_init(btree_module_init);
796 module_exit(btree_module_exit);
798 MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
799 MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
800 MODULE_LICENSE("GPL");