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);
98 memset(node, 0, NODESIZE);
102 static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
106 for (i = 0; i < n; i++) {
115 static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
120 for (i = 0; i < n; i++)
125 static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
129 for (i = 0; i < n; i++)
134 static void dec_key(struct btree_geo *geo, unsigned long *key)
139 for (i = geo->keylen - 1; i >= 0; i--) {
147 static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
149 return &node[n * geo->keylen];
152 static void *bval(struct btree_geo *geo, unsigned long *node, int n)
154 return (void *)node[geo->no_longs + n];
157 static void setkey(struct btree_geo *geo, unsigned long *node, int n,
160 longcpy(bkey(geo, node, n), key, geo->keylen);
163 static void setval(struct btree_geo *geo, unsigned long *node, int n,
166 node[geo->no_longs + n] = (unsigned long) val;
169 static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
171 longset(bkey(geo, node, n), 0, geo->keylen);
172 node[geo->no_longs + n] = 0;
175 static inline void __btree_init(struct btree_head *head)
181 void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
184 head->mempool = mempool;
186 EXPORT_SYMBOL_GPL(btree_init_mempool);
188 int btree_init(struct btree_head *head)
191 head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
196 EXPORT_SYMBOL_GPL(btree_init);
198 void btree_destroy(struct btree_head *head)
200 mempool_destroy(head->mempool);
201 head->mempool = NULL;
203 EXPORT_SYMBOL_GPL(btree_destroy);
205 void *btree_last(struct btree_head *head, struct btree_geo *geo,
208 int height = head->height;
209 unsigned long *node = head->node;
214 for ( ; height > 1; height--)
215 node = bval(geo, node, 0);
217 longcpy(key, bkey(geo, node, 0), geo->keylen);
218 return bval(geo, node, 0);
220 EXPORT_SYMBOL_GPL(btree_last);
222 static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
225 return longcmp(bkey(geo, node, pos), key, geo->keylen);
228 static int keyzero(struct btree_geo *geo, unsigned long *key)
232 for (i = 0; i < geo->keylen; i++)
239 void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
242 int i, height = head->height;
243 unsigned long *node = head->node;
248 for ( ; height > 1; height--) {
249 for (i = 0; i < geo->no_pairs; i++)
250 if (keycmp(geo, node, i, key) <= 0)
252 if (i == geo->no_pairs)
254 node = bval(geo, node, i);
262 for (i = 0; i < geo->no_pairs; i++)
263 if (keycmp(geo, node, i, key) == 0)
264 return bval(geo, node, i);
267 EXPORT_SYMBOL_GPL(btree_lookup);
269 int btree_update(struct btree_head *head, struct btree_geo *geo,
270 unsigned long *key, void *val)
272 int i, height = head->height;
273 unsigned long *node = head->node;
278 for ( ; height > 1; height--) {
279 for (i = 0; i < geo->no_pairs; i++)
280 if (keycmp(geo, node, i, key) <= 0)
282 if (i == geo->no_pairs)
284 node = bval(geo, node, i);
292 for (i = 0; i < geo->no_pairs; i++)
293 if (keycmp(geo, node, i, key) == 0) {
294 setval(geo, node, i, val);
299 EXPORT_SYMBOL_GPL(btree_update);
302 * Usually this function is quite similar to normal lookup. But the key of
303 * a parent node may be smaller than the smallest key of all its siblings.
304 * In such a case we cannot just return NULL, as we have only proven that no
305 * key smaller than __key, but larger than this parent key exists.
306 * So we set __key to the parent key and retry. We have to use the smallest
307 * such parent key, which is the last parent key we encountered.
309 void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
310 unsigned long *__key)
313 unsigned long *node, *oldnode;
314 unsigned long *retry_key = NULL, key[geo->keylen];
316 if (keyzero(geo, __key))
319 if (head->height == 0)
322 longcpy(key, __key, geo->keylen);
326 for (height = head->height ; height > 1; height--) {
327 for (i = 0; i < geo->no_pairs; i++)
328 if (keycmp(geo, node, i, key) <= 0)
330 if (i == geo->no_pairs)
333 node = bval(geo, node, i);
336 retry_key = bkey(geo, oldnode, i);
342 for (i = 0; i < geo->no_pairs; i++) {
343 if (keycmp(geo, node, i, key) <= 0) {
344 if (bval(geo, node, i)) {
345 longcpy(__key, bkey(geo, node, i), geo->keylen);
346 return bval(geo, node, i);
360 static int getpos(struct btree_geo *geo, unsigned long *node,
365 for (i = 0; i < geo->no_pairs; i++) {
366 if (keycmp(geo, node, i, key) <= 0)
372 static int getfill(struct btree_geo *geo, unsigned long *node, int start)
376 for (i = start; i < geo->no_pairs; i++)
377 if (!bval(geo, node, i))
383 * locate the correct leaf node in the btree
385 static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
386 unsigned long *key, int level)
388 unsigned long *node = head->node;
391 for (height = head->height; height > level; height--) {
392 for (i = 0; i < geo->no_pairs; i++)
393 if (keycmp(geo, node, i, key) <= 0)
396 if ((i == geo->no_pairs) || !bval(geo, node, i)) {
397 /* right-most key is too large, update it */
398 /* FIXME: If the right-most key on higher levels is
399 * always zero, this wouldn't be necessary. */
401 setkey(geo, node, i, key);
404 node = bval(geo, node, i);
410 static int btree_grow(struct btree_head *head, struct btree_geo *geo,
416 node = btree_node_alloc(head, gfp);
420 fill = getfill(geo, head->node, 0);
421 setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
422 setval(geo, node, 0, head->node);
429 static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
434 if (head->height <= 1)
438 fill = getfill(geo, node, 0);
440 head->node = bval(geo, node, 0);
442 mempool_free(node, head->mempool);
445 static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
446 unsigned long *key, void *val, int level,
450 int i, pos, fill, err;
453 if (head->height < level) {
454 err = btree_grow(head, geo, gfp);
460 node = find_level(head, geo, key, level);
461 pos = getpos(geo, node, key);
462 fill = getfill(geo, node, pos);
463 /* two identical keys are not allowed */
464 BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
466 if (fill == geo->no_pairs) {
467 /* need to split node */
470 new = btree_node_alloc(head, gfp);
473 err = btree_insert_level(head, geo,
474 bkey(geo, node, fill / 2 - 1),
475 new, level + 1, gfp);
477 mempool_free(new, head->mempool);
480 for (i = 0; i < fill / 2; i++) {
481 setkey(geo, new, i, bkey(geo, node, i));
482 setval(geo, new, i, bval(geo, node, i));
483 setkey(geo, node, i, bkey(geo, node, i + fill / 2));
484 setval(geo, node, i, bval(geo, node, i + fill / 2));
485 clearpair(geo, node, i + fill / 2);
488 setkey(geo, node, i, bkey(geo, node, fill - 1));
489 setval(geo, node, i, bval(geo, node, fill - 1));
490 clearpair(geo, node, fill - 1);
494 BUG_ON(fill >= geo->no_pairs);
496 /* shift and insert */
497 for (i = fill; i > pos; i--) {
498 setkey(geo, node, i, bkey(geo, node, i - 1));
499 setval(geo, node, i, bval(geo, node, i - 1));
501 setkey(geo, node, pos, key);
502 setval(geo, node, pos, val);
507 int btree_insert(struct btree_head *head, struct btree_geo *geo,
508 unsigned long *key, void *val, gfp_t gfp)
510 return btree_insert_level(head, geo, key, val, 1, gfp);
512 EXPORT_SYMBOL_GPL(btree_insert);
514 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
515 unsigned long *key, int level);
516 static void merge(struct btree_head *head, struct btree_geo *geo, int level,
517 unsigned long *left, int lfill,
518 unsigned long *right, int rfill,
519 unsigned long *parent, int lpos)
523 for (i = 0; i < rfill; i++) {
524 /* Move all keys to the left */
525 setkey(geo, left, lfill + i, bkey(geo, right, i));
526 setval(geo, left, lfill + i, bval(geo, right, i));
528 /* Exchange left and right child in parent */
529 setval(geo, parent, lpos, right);
530 setval(geo, parent, lpos + 1, left);
531 /* Remove left (formerly right) child from parent */
532 btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
533 mempool_free(right, head->mempool);
536 static void rebalance(struct btree_head *head, struct btree_geo *geo,
537 unsigned long *key, int level, unsigned long *child, int fill)
539 unsigned long *parent, *left = NULL, *right = NULL;
540 int i, no_left, no_right;
543 /* Because we don't steal entries from a neigbour, this case
544 * can happen. Parent node contains a single child, this
545 * node, so merging with a sibling never happens.
547 btree_remove_level(head, geo, key, level + 1);
548 mempool_free(child, head->mempool);
552 parent = find_level(head, geo, key, level + 1);
553 i = getpos(geo, parent, key);
554 BUG_ON(bval(geo, parent, i) != child);
557 left = bval(geo, parent, i - 1);
558 no_left = getfill(geo, left, 0);
559 if (fill + no_left <= geo->no_pairs) {
560 merge(head, geo, level,
567 if (i + 1 < getfill(geo, parent, i)) {
568 right = bval(geo, parent, i + 1);
569 no_right = getfill(geo, right, 0);
570 if (fill + no_right <= geo->no_pairs) {
571 merge(head, geo, level,
579 * We could also try to steal one entry from the left or right
580 * neighbor. By not doing so we changed the invariant from
581 * "all nodes are at least half full" to "no two neighboring
582 * nodes can be merged". Which means that the average fill of
583 * all nodes is still half or better.
587 static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
588 unsigned long *key, int level)
594 if (level > head->height) {
595 /* we recursed all the way up */
601 node = find_level(head, geo, key, level);
602 pos = getpos(geo, node, key);
603 fill = getfill(geo, node, pos);
604 if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
606 ret = bval(geo, node, pos);
608 /* remove and shift */
609 for (i = pos; i < fill - 1; i++) {
610 setkey(geo, node, i, bkey(geo, node, i + 1));
611 setval(geo, node, i, bval(geo, node, i + 1));
613 clearpair(geo, node, fill - 1);
615 if (fill - 1 < geo->no_pairs / 2) {
616 if (level < head->height)
617 rebalance(head, geo, key, level, node, fill - 1);
618 else if (fill - 1 == 1)
619 btree_shrink(head, geo);
625 void *btree_remove(struct btree_head *head, struct btree_geo *geo,
628 if (head->height == 0)
631 return btree_remove_level(head, geo, key, 1);
633 EXPORT_SYMBOL_GPL(btree_remove);
635 int btree_merge(struct btree_head *target, struct btree_head *victim,
636 struct btree_geo *geo, gfp_t gfp)
638 unsigned long key[geo->keylen];
639 unsigned long dup[geo->keylen];
643 BUG_ON(target == victim);
645 if (!(target->node)) {
646 /* target is empty, just copy fields over */
647 target->node = victim->node;
648 target->height = victim->height;
649 __btree_init(victim);
653 /* TODO: This needs some optimizations. Currently we do three tree
654 * walks to remove a single object from the victim.
657 if (!btree_last(victim, geo, key))
659 val = btree_lookup(victim, geo, key);
660 err = btree_insert(target, geo, key, val, gfp);
663 /* We must make a copy of the key, as the original will get
664 * mangled inside btree_remove. */
665 longcpy(dup, key, geo->keylen);
666 btree_remove(victim, geo, dup);
670 EXPORT_SYMBOL_GPL(btree_merge);
672 static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
673 unsigned long *node, unsigned long opaque,
674 void (*func)(void *elem, unsigned long opaque,
675 unsigned long *key, size_t index,
677 void *func2, int reap, int height, size_t count)
680 unsigned long *child;
682 for (i = 0; i < geo->no_pairs; i++) {
683 child = bval(geo, node, i);
687 count = __btree_for_each(head, geo, child, opaque,
688 func, func2, reap, height - 1, count);
690 func(child, opaque, bkey(geo, node, i), count++,
694 mempool_free(node, head->mempool);
698 static void empty(void *elem, unsigned long opaque, unsigned long *key,
699 size_t index, void *func2)
703 void visitorl(void *elem, unsigned long opaque, unsigned long *key,
704 size_t index, void *__func)
706 visitorl_t func = __func;
708 func(elem, opaque, *key, index);
710 EXPORT_SYMBOL_GPL(visitorl);
712 void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
713 size_t index, void *__func)
715 visitor32_t func = __func;
716 u32 *key = (void *)__key;
718 func(elem, opaque, *key, index);
720 EXPORT_SYMBOL_GPL(visitor32);
722 void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
723 size_t index, void *__func)
725 visitor64_t func = __func;
726 u64 *key = (void *)__key;
728 func(elem, opaque, *key, index);
730 EXPORT_SYMBOL_GPL(visitor64);
732 void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
733 size_t index, void *__func)
735 visitor128_t func = __func;
736 u64 *key = (void *)__key;
738 func(elem, opaque, key[0], key[1], index);
740 EXPORT_SYMBOL_GPL(visitor128);
742 size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
743 unsigned long opaque,
744 void (*func)(void *elem, unsigned long opaque,
746 size_t index, void *func2),
754 count = __btree_for_each(head, geo, head->node, opaque, func,
755 func2, 0, head->height, 0);
758 EXPORT_SYMBOL_GPL(btree_visitor);
760 size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
761 unsigned long opaque,
762 void (*func)(void *elem, unsigned long opaque,
764 size_t index, void *func2),
772 count = __btree_for_each(head, geo, head->node, opaque, func,
773 func2, 1, head->height, 0);
777 EXPORT_SYMBOL_GPL(btree_grim_visitor);
779 static int __init btree_module_init(void)
781 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
782 SLAB_HWCACHE_ALIGN, NULL);
786 static void __exit btree_module_exit(void)
788 kmem_cache_destroy(btree_cachep);
791 /* If core code starts using btree, initialization should happen even earlier */
792 module_init(btree_module_init);
793 module_exit(btree_module_exit);
795 MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
796 MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
797 MODULE_LICENSE("GPL");