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_free(head->node, head->mempool);
202 mempool_destroy(head->mempool);
203 head->mempool = NULL;
205 EXPORT_SYMBOL_GPL(btree_destroy);
207 void *btree_last(struct btree_head *head, struct btree_geo *geo,
210 int height = head->height;
211 unsigned long *node = head->node;
216 for ( ; height > 1; height--)
217 node = bval(geo, node, 0);
219 longcpy(key, bkey(geo, node, 0), geo->keylen);
220 return bval(geo, node, 0);
222 EXPORT_SYMBOL_GPL(btree_last);
224 static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
227 return longcmp(bkey(geo, node, pos), key, geo->keylen);
230 static int keyzero(struct btree_geo *geo, unsigned long *key)
234 for (i = 0; i < geo->keylen; i++)
241 void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
244 int i, height = head->height;
245 unsigned long *node = head->node;
250 for ( ; height > 1; height--) {
251 for (i = 0; i < geo->no_pairs; i++)
252 if (keycmp(geo, node, i, key) <= 0)
254 if (i == geo->no_pairs)
256 node = bval(geo, node, i);
264 for (i = 0; i < geo->no_pairs; i++)
265 if (keycmp(geo, node, i, key) == 0)
266 return bval(geo, node, i);
269 EXPORT_SYMBOL_GPL(btree_lookup);
271 int btree_update(struct btree_head *head, struct btree_geo *geo,
272 unsigned long *key, void *val)
274 int i, height = head->height;
275 unsigned long *node = head->node;
280 for ( ; height > 1; height--) {
281 for (i = 0; i < geo->no_pairs; i++)
282 if (keycmp(geo, node, i, key) <= 0)
284 if (i == geo->no_pairs)
286 node = bval(geo, node, i);
294 for (i = 0; i < geo->no_pairs; i++)
295 if (keycmp(geo, node, i, key) == 0) {
296 setval(geo, node, i, val);
301 EXPORT_SYMBOL_GPL(btree_update);
304 * Usually this function is quite similar to normal lookup. But the key of
305 * a parent node may be smaller than the smallest key of all its siblings.
306 * In such a case we cannot just return NULL, as we have only proven that no
307 * key smaller than __key, but larger than this parent key exists.
308 * So we set __key to the parent key and retry. We have to use the smallest
309 * such parent key, which is the last parent key we encountered.
311 void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
312 unsigned long *__key)
315 unsigned long *node, *oldnode;
316 unsigned long *retry_key = NULL, key[geo->keylen];
318 if (keyzero(geo, __key))
321 if (head->height == 0)
323 longcpy(key, __key, geo->keylen);
328 for (height = head->height ; height > 1; height--) {
329 for (i = 0; i < geo->no_pairs; i++)
330 if (keycmp(geo, node, i, key) <= 0)
332 if (i == geo->no_pairs)
335 node = bval(geo, node, i);
338 retry_key = bkey(geo, oldnode, i);
344 for (i = 0; i < geo->no_pairs; i++) {
345 if (keycmp(geo, node, i, key) <= 0) {
346 if (bval(geo, node, i)) {
347 longcpy(__key, bkey(geo, node, i), geo->keylen);
348 return bval(geo, node, i);
355 longcpy(key, retry_key, geo->keylen);
361 EXPORT_SYMBOL_GPL(btree_get_prev);
363 static int getpos(struct btree_geo *geo, unsigned long *node,
368 for (i = 0; i < geo->no_pairs; i++) {
369 if (keycmp(geo, node, i, key) <= 0)
375 static int getfill(struct btree_geo *geo, unsigned long *node, int start)
379 for (i = start; i < geo->no_pairs; i++)
380 if (!bval(geo, node, i))
386 * locate the correct leaf node in the btree
388 static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
389 unsigned long *key, int level)
391 unsigned long *node = head->node;
394 for (height = head->height; height > level; height--) {
395 for (i = 0; i < geo->no_pairs; i++)
396 if (keycmp(geo, node, i, key) <= 0)
399 if ((i == geo->no_pairs) || !bval(geo, node, i)) {
400 /* right-most key is too large, update it */
401 /* FIXME: If the right-most key on higher levels is
402 * always zero, this wouldn't be necessary. */
404 setkey(geo, node, i, key);
407 node = bval(geo, node, i);
413 static int btree_grow(struct btree_head *head, struct btree_geo *geo,
419 node = btree_node_alloc(head, gfp);
423 fill = getfill(geo, head->node, 0);
424 setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
425 setval(geo, node, 0, head->node);
432 static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
437 if (head->height <= 1)
441 fill = getfill(geo, node, 0);
443 head->node = bval(geo, node, 0);
445 mempool_free(node, head->mempool);
448 static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
449 unsigned long *key, void *val, int level,
453 int i, pos, fill, err;
456 if (head->height < level) {
457 err = btree_grow(head, geo, gfp);
463 node = find_level(head, geo, key, level);
464 pos = getpos(geo, node, key);
465 fill = getfill(geo, node, pos);
466 /* two identical keys are not allowed */
467 BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
469 if (fill == geo->no_pairs) {
470 /* need to split node */
473 new = btree_node_alloc(head, gfp);
476 err = btree_insert_level(head, geo,
477 bkey(geo, node, fill / 2 - 1),
478 new, level + 1, gfp);
480 mempool_free(new, head->mempool);
483 for (i = 0; i < fill / 2; i++) {
484 setkey(geo, new, i, bkey(geo, node, i));
485 setval(geo, new, i, bval(geo, node, i));
486 setkey(geo, node, i, bkey(geo, node, i + fill / 2));
487 setval(geo, node, i, bval(geo, node, i + fill / 2));
488 clearpair(geo, node, i + fill / 2);
491 setkey(geo, node, i, bkey(geo, node, fill - 1));
492 setval(geo, node, i, bval(geo, node, fill - 1));
493 clearpair(geo, node, fill - 1);
497 BUG_ON(fill >= geo->no_pairs);
499 /* shift and insert */
500 for (i = fill; i > pos; i--) {
501 setkey(geo, node, i, bkey(geo, node, i - 1));
502 setval(geo, node, i, bval(geo, node, i - 1));
504 setkey(geo, node, pos, key);
505 setval(geo, node, pos, val);
510 int btree_insert(struct btree_head *head, struct btree_geo *geo,
511 unsigned long *key, void *val, gfp_t gfp)
514 return btree_insert_level(head, geo, key, val, 1, gfp);
516 EXPORT_SYMBOL_GPL(btree_insert);
518 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
519 unsigned long *key, int level);
520 static void merge(struct btree_head *head, struct btree_geo *geo, int level,
521 unsigned long *left, int lfill,
522 unsigned long *right, int rfill,
523 unsigned long *parent, int lpos)
527 for (i = 0; i < rfill; i++) {
528 /* Move all keys to the left */
529 setkey(geo, left, lfill + i, bkey(geo, right, i));
530 setval(geo, left, lfill + i, bval(geo, right, i));
532 /* Exchange left and right child in parent */
533 setval(geo, parent, lpos, right);
534 setval(geo, parent, lpos + 1, left);
535 /* Remove left (formerly right) child from parent */
536 btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
537 mempool_free(right, head->mempool);
540 static void rebalance(struct btree_head *head, struct btree_geo *geo,
541 unsigned long *key, int level, unsigned long *child, int fill)
543 unsigned long *parent, *left = NULL, *right = NULL;
544 int i, no_left, no_right;
547 /* Because we don't steal entries from a neighbour, this case
548 * can happen. Parent node contains a single child, this
549 * node, so merging with a sibling never happens.
551 btree_remove_level(head, geo, key, level + 1);
552 mempool_free(child, head->mempool);
556 parent = find_level(head, geo, key, level + 1);
557 i = getpos(geo, parent, key);
558 BUG_ON(bval(geo, parent, i) != child);
561 left = bval(geo, parent, i - 1);
562 no_left = getfill(geo, left, 0);
563 if (fill + no_left <= geo->no_pairs) {
564 merge(head, geo, level,
571 if (i + 1 < getfill(geo, parent, i)) {
572 right = bval(geo, parent, i + 1);
573 no_right = getfill(geo, right, 0);
574 if (fill + no_right <= geo->no_pairs) {
575 merge(head, geo, level,
583 * We could also try to steal one entry from the left or right
584 * neighbor. By not doing so we changed the invariant from
585 * "all nodes are at least half full" to "no two neighboring
586 * nodes can be merged". Which means that the average fill of
587 * all nodes is still half or better.
591 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
592 unsigned long *key, int level)
598 if (level > head->height) {
599 /* we recursed all the way up */
605 node = find_level(head, geo, key, level);
606 pos = getpos(geo, node, key);
607 fill = getfill(geo, node, pos);
608 if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
610 ret = bval(geo, node, pos);
612 /* remove and shift */
613 for (i = pos; i < fill - 1; i++) {
614 setkey(geo, node, i, bkey(geo, node, i + 1));
615 setval(geo, node, i, bval(geo, node, i + 1));
617 clearpair(geo, node, fill - 1);
619 if (fill - 1 < geo->no_pairs / 2) {
620 if (level < head->height)
621 rebalance(head, geo, key, level, node, fill - 1);
622 else if (fill - 1 == 1)
623 btree_shrink(head, geo);
629 void *btree_remove(struct btree_head *head, struct btree_geo *geo,
632 if (head->height == 0)
635 return btree_remove_level(head, geo, key, 1);
637 EXPORT_SYMBOL_GPL(btree_remove);
639 int btree_merge(struct btree_head *target, struct btree_head *victim,
640 struct btree_geo *geo, gfp_t gfp)
642 unsigned long key[geo->keylen];
643 unsigned long dup[geo->keylen];
647 BUG_ON(target == victim);
649 if (!(target->node)) {
650 /* target is empty, just copy fields over */
651 target->node = victim->node;
652 target->height = victim->height;
653 __btree_init(victim);
657 /* TODO: This needs some optimizations. Currently we do three tree
658 * walks to remove a single object from the victim.
661 if (!btree_last(victim, geo, key))
663 val = btree_lookup(victim, geo, key);
664 err = btree_insert(target, geo, key, val, gfp);
667 /* We must make a copy of the key, as the original will get
668 * mangled inside btree_remove. */
669 longcpy(dup, key, geo->keylen);
670 btree_remove(victim, geo, dup);
674 EXPORT_SYMBOL_GPL(btree_merge);
676 static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
677 unsigned long *node, unsigned long opaque,
678 void (*func)(void *elem, unsigned long opaque,
679 unsigned long *key, size_t index,
681 void *func2, int reap, int height, size_t count)
684 unsigned long *child;
686 for (i = 0; i < geo->no_pairs; i++) {
687 child = bval(geo, node, i);
691 count = __btree_for_each(head, geo, child, opaque,
692 func, func2, reap, height - 1, count);
694 func(child, opaque, bkey(geo, node, i), count++,
698 mempool_free(node, head->mempool);
702 static void empty(void *elem, unsigned long opaque, unsigned long *key,
703 size_t index, void *func2)
707 void visitorl(void *elem, unsigned long opaque, unsigned long *key,
708 size_t index, void *__func)
710 visitorl_t func = __func;
712 func(elem, opaque, *key, index);
714 EXPORT_SYMBOL_GPL(visitorl);
716 void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
717 size_t index, void *__func)
719 visitor32_t func = __func;
720 u32 *key = (void *)__key;
722 func(elem, opaque, *key, index);
724 EXPORT_SYMBOL_GPL(visitor32);
726 void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
727 size_t index, void *__func)
729 visitor64_t func = __func;
730 u64 *key = (void *)__key;
732 func(elem, opaque, *key, index);
734 EXPORT_SYMBOL_GPL(visitor64);
736 void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
737 size_t index, void *__func)
739 visitor128_t func = __func;
740 u64 *key = (void *)__key;
742 func(elem, opaque, key[0], key[1], index);
744 EXPORT_SYMBOL_GPL(visitor128);
746 size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
747 unsigned long opaque,
748 void (*func)(void *elem, unsigned long opaque,
750 size_t index, void *func2),
758 count = __btree_for_each(head, geo, head->node, opaque, func,
759 func2, 0, head->height, 0);
762 EXPORT_SYMBOL_GPL(btree_visitor);
764 size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
765 unsigned long opaque,
766 void (*func)(void *elem, unsigned long opaque,
768 size_t index, void *func2),
776 count = __btree_for_each(head, geo, head->node, opaque, func,
777 func2, 1, head->height, 0);
781 EXPORT_SYMBOL_GPL(btree_grim_visitor);
783 static int __init btree_module_init(void)
785 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
786 SLAB_HWCACHE_ALIGN, NULL);
790 static void __exit btree_module_exit(void)
792 kmem_cache_destroy(btree_cachep);
795 /* If core code starts using btree, initialization should happen even earlier */
796 module_init(btree_module_init);
797 module_exit(btree_module_exit);
799 MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
800 MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
801 MODULE_LICENSE("GPL");