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 * excercise 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)
323 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);
361 static int getpos(struct btree_geo *geo, unsigned long *node,
366 for (i = 0; i < geo->no_pairs; i++) {
367 if (keycmp(geo, node, i, key) <= 0)
373 static int getfill(struct btree_geo *geo, unsigned long *node, int start)
377 for (i = start; i < geo->no_pairs; i++)
378 if (!bval(geo, node, i))
384 * locate the correct leaf node in the btree
386 static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
387 unsigned long *key, int level)
389 unsigned long *node = head->node;
392 for (height = head->height; height > level; height--) {
393 for (i = 0; i < geo->no_pairs; i++)
394 if (keycmp(geo, node, i, key) <= 0)
397 if ((i == geo->no_pairs) || !bval(geo, node, i)) {
398 /* right-most key is too large, update it */
399 /* FIXME: If the right-most key on higher levels is
400 * always zero, this wouldn't be necessary. */
402 setkey(geo, node, i, key);
405 node = bval(geo, node, i);
411 static int btree_grow(struct btree_head *head, struct btree_geo *geo,
417 node = btree_node_alloc(head, gfp);
421 fill = getfill(geo, head->node, 0);
422 setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
423 setval(geo, node, 0, head->node);
430 static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
435 if (head->height <= 1)
439 fill = getfill(geo, node, 0);
441 head->node = bval(geo, node, 0);
443 mempool_free(node, head->mempool);
446 static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
447 unsigned long *key, void *val, int level,
451 int i, pos, fill, err;
454 if (head->height < level) {
455 err = btree_grow(head, geo, gfp);
461 node = find_level(head, geo, key, level);
462 pos = getpos(geo, node, key);
463 fill = getfill(geo, node, pos);
464 /* two identical keys are not allowed */
465 BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
467 if (fill == geo->no_pairs) {
468 /* need to split node */
471 new = btree_node_alloc(head, gfp);
474 err = btree_insert_level(head, geo,
475 bkey(geo, node, fill / 2 - 1),
476 new, level + 1, gfp);
478 mempool_free(new, head->mempool);
481 for (i = 0; i < fill / 2; i++) {
482 setkey(geo, new, i, bkey(geo, node, i));
483 setval(geo, new, i, bval(geo, node, i));
484 setkey(geo, node, i, bkey(geo, node, i + fill / 2));
485 setval(geo, node, i, bval(geo, node, i + fill / 2));
486 clearpair(geo, node, i + fill / 2);
489 setkey(geo, node, i, bkey(geo, node, fill - 1));
490 setval(geo, node, i, bval(geo, node, fill - 1));
491 clearpair(geo, node, fill - 1);
495 BUG_ON(fill >= geo->no_pairs);
497 /* shift and insert */
498 for (i = fill; i > pos; i--) {
499 setkey(geo, node, i, bkey(geo, node, i - 1));
500 setval(geo, node, i, bval(geo, node, i - 1));
502 setkey(geo, node, pos, key);
503 setval(geo, node, pos, val);
508 int btree_insert(struct btree_head *head, struct btree_geo *geo,
509 unsigned long *key, void *val, gfp_t gfp)
511 return btree_insert_level(head, geo, key, val, 1, gfp);
513 EXPORT_SYMBOL_GPL(btree_insert);
515 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
516 unsigned long *key, int level);
517 static void merge(struct btree_head *head, struct btree_geo *geo, int level,
518 unsigned long *left, int lfill,
519 unsigned long *right, int rfill,
520 unsigned long *parent, int lpos)
524 for (i = 0; i < rfill; i++) {
525 /* Move all keys to the left */
526 setkey(geo, left, lfill + i, bkey(geo, right, i));
527 setval(geo, left, lfill + i, bval(geo, right, i));
529 /* Exchange left and right child in parent */
530 setval(geo, parent, lpos, right);
531 setval(geo, parent, lpos + 1, left);
532 /* Remove left (formerly right) child from parent */
533 btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
534 mempool_free(right, head->mempool);
537 static void rebalance(struct btree_head *head, struct btree_geo *geo,
538 unsigned long *key, int level, unsigned long *child, int fill)
540 unsigned long *parent, *left = NULL, *right = NULL;
541 int i, no_left, no_right;
544 /* Because we don't steal entries from a neigbour, this case
545 * can happen. Parent node contains a single child, this
546 * node, so merging with a sibling never happens.
548 btree_remove_level(head, geo, key, level + 1);
549 mempool_free(child, head->mempool);
553 parent = find_level(head, geo, key, level + 1);
554 i = getpos(geo, parent, key);
555 BUG_ON(bval(geo, parent, i) != child);
558 left = bval(geo, parent, i - 1);
559 no_left = getfill(geo, left, 0);
560 if (fill + no_left <= geo->no_pairs) {
561 merge(head, geo, level,
568 if (i + 1 < getfill(geo, parent, i)) {
569 right = bval(geo, parent, i + 1);
570 no_right = getfill(geo, right, 0);
571 if (fill + no_right <= geo->no_pairs) {
572 merge(head, geo, level,
580 * We could also try to steal one entry from the left or right
581 * neighbor. By not doing so we changed the invariant from
582 * "all nodes are at least half full" to "no two neighboring
583 * nodes can be merged". Which means that the average fill of
584 * all nodes is still half or better.
588 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
589 unsigned long *key, int level)
595 if (level > head->height) {
596 /* we recursed all the way up */
602 node = find_level(head, geo, key, level);
603 pos = getpos(geo, node, key);
604 fill = getfill(geo, node, pos);
605 if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
607 ret = bval(geo, node, pos);
609 /* remove and shift */
610 for (i = pos; i < fill - 1; i++) {
611 setkey(geo, node, i, bkey(geo, node, i + 1));
612 setval(geo, node, i, bval(geo, node, i + 1));
614 clearpair(geo, node, fill - 1);
616 if (fill - 1 < geo->no_pairs / 2) {
617 if (level < head->height)
618 rebalance(head, geo, key, level, node, fill - 1);
619 else if (fill - 1 == 1)
620 btree_shrink(head, geo);
626 void *btree_remove(struct btree_head *head, struct btree_geo *geo,
629 if (head->height == 0)
632 return btree_remove_level(head, geo, key, 1);
634 EXPORT_SYMBOL_GPL(btree_remove);
636 int btree_merge(struct btree_head *target, struct btree_head *victim,
637 struct btree_geo *geo, gfp_t gfp)
639 unsigned long key[geo->keylen];
640 unsigned long dup[geo->keylen];
644 BUG_ON(target == victim);
646 if (!(target->node)) {
647 /* target is empty, just copy fields over */
648 target->node = victim->node;
649 target->height = victim->height;
650 __btree_init(victim);
654 /* TODO: This needs some optimizations. Currently we do three tree
655 * walks to remove a single object from the victim.
658 if (!btree_last(victim, geo, key))
660 val = btree_lookup(victim, geo, key);
661 err = btree_insert(target, geo, key, val, gfp);
664 /* We must make a copy of the key, as the original will get
665 * mangled inside btree_remove. */
666 longcpy(dup, key, geo->keylen);
667 btree_remove(victim, geo, dup);
671 EXPORT_SYMBOL_GPL(btree_merge);
673 static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
674 unsigned long *node, unsigned long opaque,
675 void (*func)(void *elem, unsigned long opaque,
676 unsigned long *key, size_t index,
678 void *func2, int reap, int height, size_t count)
681 unsigned long *child;
683 for (i = 0; i < geo->no_pairs; i++) {
684 child = bval(geo, node, i);
688 count = __btree_for_each(head, geo, child, opaque,
689 func, func2, reap, height - 1, count);
691 func(child, opaque, bkey(geo, node, i), count++,
695 mempool_free(node, head->mempool);
699 static void empty(void *elem, unsigned long opaque, unsigned long *key,
700 size_t index, void *func2)
704 void visitorl(void *elem, unsigned long opaque, unsigned long *key,
705 size_t index, void *__func)
707 visitorl_t func = __func;
709 func(elem, opaque, *key, index);
711 EXPORT_SYMBOL_GPL(visitorl);
713 void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
714 size_t index, void *__func)
716 visitor32_t func = __func;
717 u32 *key = (void *)__key;
719 func(elem, opaque, *key, index);
721 EXPORT_SYMBOL_GPL(visitor32);
723 void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
724 size_t index, void *__func)
726 visitor64_t func = __func;
727 u64 *key = (void *)__key;
729 func(elem, opaque, *key, index);
731 EXPORT_SYMBOL_GPL(visitor64);
733 void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
734 size_t index, void *__func)
736 visitor128_t func = __func;
737 u64 *key = (void *)__key;
739 func(elem, opaque, key[0], key[1], index);
741 EXPORT_SYMBOL_GPL(visitor128);
743 size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
744 unsigned long opaque,
745 void (*func)(void *elem, unsigned long opaque,
747 size_t index, void *func2),
755 count = __btree_for_each(head, geo, head->node, opaque, func,
756 func2, 0, head->height, 0);
759 EXPORT_SYMBOL_GPL(btree_visitor);
761 size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
762 unsigned long opaque,
763 void (*func)(void *elem, unsigned long opaque,
765 size_t index, void *func2),
773 count = __btree_for_each(head, geo, head->node, opaque, func,
774 func2, 1, head->height, 0);
778 EXPORT_SYMBOL_GPL(btree_grim_visitor);
780 static int __init btree_module_init(void)
782 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
783 SLAB_HWCACHE_ALIGN, NULL);
787 static void __exit btree_module_exit(void)
789 kmem_cache_destroy(btree_cachep);
792 /* If core code starts using btree, initialization should happen even earlier */
793 module_init(btree_module_init);
794 module_exit(btree_module_exit);
796 MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
797 MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
798 MODULE_LICENSE("GPL");