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1/*
2 * lib/btree.c - Simple In-memory B+Tree
3 *
4 * As should be obvious for Linux kernel code, license is GPLv2
5 *
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>
9 * GPLv2
10 *
11 * see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch
12 *
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.
15 *
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.
20 *
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
24 * helps B+Trees.
25 *
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%
30 * pointers.
31 *
32 * This particular implementation stores pointers identified by a long value.
33 * Storing NULL pointers is illegal, lookup will return NULL when no entry
34 * was found.
35 *
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.
40 */
41
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>
47
48#define MAX(a, b) ((a) > (b) ? (a) : (b))
49#define NODESIZE MAX(L1_CACHE_BYTES, 128)
50
51struct btree_geo {
52 int keylen;
53 int no_pairs;
54 int no_longs;
55};
56
57struct btree_geo btree_geo32 = {
58 .keylen = 1,
59 .no_pairs = NODESIZE / sizeof(long) / 2,
60 .no_longs = NODESIZE / sizeof(long) / 2,
61};
62EXPORT_SYMBOL_GPL(btree_geo32);
63
64#define LONG_PER_U64 (64 / BITS_PER_LONG)
65struct 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)),
69};
70EXPORT_SYMBOL_GPL(btree_geo64);
71
72struct 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)),
76};
77EXPORT_SYMBOL_GPL(btree_geo128);
78
79static struct kmem_cache *btree_cachep;
80
81void *btree_alloc(gfp_t gfp_mask, void *pool_data)
82{
83 return kmem_cache_alloc(btree_cachep, gfp_mask);
84}
85EXPORT_SYMBOL_GPL(btree_alloc);
86
87void btree_free(void *element, void *pool_data)
88{
89 kmem_cache_free(btree_cachep, element);
90}
91EXPORT_SYMBOL_GPL(btree_free);
92
93static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp)
94{
95 unsigned long *node;
96
97 node = mempool_alloc(head->mempool, gfp);
98 if (likely(node))
99 memset(node, 0, NODESIZE);
100 return node;
101}
102
103static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
104{
105 size_t i;
106
107 for (i = 0; i < n; i++) {
108 if (l1[i] < l2[i])
109 return -1;
110 if (l1[i] > l2[i])
111 return 1;
112 }
113 return 0;
114}
115
116static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
117 size_t n)
118{
119 size_t i;
120
121 for (i = 0; i < n; i++)
122 dest[i] = src[i];
123 return dest;
124}
125
126static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
127{
128 size_t i;
129
130 for (i = 0; i < n; i++)
131 s[i] = c;
132 return s;
133}
134
135static void dec_key(struct btree_geo *geo, unsigned long *key)
136{
137 unsigned long val;
138 int i;
139
140 for (i = geo->keylen - 1; i >= 0; i--) {
141 val = key[i];
142 key[i] = val - 1;
143 if (val)
144 break;
145 }
146}
147
148static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
149{
150 return &node[n * geo->keylen];
151}
152
153static void *bval(struct btree_geo *geo, unsigned long *node, int n)
154{
155 return (void *)node[geo->no_longs + n];
156}
157
158static void setkey(struct btree_geo *geo, unsigned long *node, int n,
159 unsigned long *key)
160{
161 longcpy(bkey(geo, node, n), key, geo->keylen);
162}
163
164static void setval(struct btree_geo *geo, unsigned long *node, int n,
165 void *val)
166{
167 node[geo->no_longs + n] = (unsigned long) val;
168}
169
170static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
171{
172 longset(bkey(geo, node, n), 0, geo->keylen);
173 node[geo->no_longs + n] = 0;
174}
175
176static inline void __btree_init(struct btree_head *head)
177{
178 head->node = NULL;
179 head->height = 0;
180}
181
182void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
183{
184 __btree_init(head);
185 head->mempool = mempool;
186}
187EXPORT_SYMBOL_GPL(btree_init_mempool);
188
189int btree_init(struct btree_head *head)
190{
191 __btree_init(head);
192 head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
193 if (!head->mempool)
194 return -ENOMEM;
195 return 0;
196}
197EXPORT_SYMBOL_GPL(btree_init);
198
199void btree_destroy(struct btree_head *head)
200{
201 mempool_destroy(head->mempool);
202 head->mempool = NULL;
203}
204EXPORT_SYMBOL_GPL(btree_destroy);
205
206void *btree_last(struct btree_head *head, struct btree_geo *geo,
207 unsigned long *key)
208{
209 int height = head->height;
210 unsigned long *node = head->node;
211
212 if (height == 0)
213 return NULL;
214
215 for ( ; height > 1; height--)
216 node = bval(geo, node, 0);
217
218 longcpy(key, bkey(geo, node, 0), geo->keylen);
219 return bval(geo, node, 0);
220}
221EXPORT_SYMBOL_GPL(btree_last);
222
223static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
224 unsigned long *key)
225{
226 return longcmp(bkey(geo, node, pos), key, geo->keylen);
227}
228
229static int keyzero(struct btree_geo *geo, unsigned long *key)
230{
231 int i;
232
233 for (i = 0; i < geo->keylen; i++)
234 if (key[i])
235 return 0;
236
237 return 1;
238}
239
240void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
241 unsigned long *key)
242{
243 int i, height = head->height;
244 unsigned long *node = head->node;
245
246 if (height == 0)
247 return NULL;
248
249 for ( ; height > 1; height--) {
250 for (i = 0; i < geo->no_pairs; i++)
251 if (keycmp(geo, node, i, key) <= 0)
252 break;
253 if (i == geo->no_pairs)
254 return NULL;
255 node = bval(geo, node, i);
256 if (!node)
257 return NULL;
258 }
259
260 if (!node)
261 return NULL;
262
263 for (i = 0; i < geo->no_pairs; i++)
264 if (keycmp(geo, node, i, key) == 0)
265 return bval(geo, node, i);
266 return NULL;
267}
268EXPORT_SYMBOL_GPL(btree_lookup);
269
270int btree_update(struct btree_head *head, struct btree_geo *geo,
271 unsigned long *key, void *val)
272{
273 int i, height = head->height;
274 unsigned long *node = head->node;
275
276 if (height == 0)
277 return -ENOENT;
278
279 for ( ; height > 1; height--) {
280 for (i = 0; i < geo->no_pairs; i++)
281 if (keycmp(geo, node, i, key) <= 0)
282 break;
283 if (i == geo->no_pairs)
284 return -ENOENT;
285 node = bval(geo, node, i);
286 if (!node)
287 return -ENOENT;
288 }
289
290 if (!node)
291 return -ENOENT;
292
293 for (i = 0; i < geo->no_pairs; i++)
294 if (keycmp(geo, node, i, key) == 0) {
295 setval(geo, node, i, val);
296 return 0;
297 }
298 return -ENOENT;
299}
300EXPORT_SYMBOL_GPL(btree_update);
301
302/*
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.
309 */
310void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
311 unsigned long *__key)
312{
313 int i, height;
314 unsigned long *node, *oldnode;
315 unsigned long *retry_key = NULL, key[geo->keylen];
316
317 if (keyzero(geo, __key))
318 return NULL;
319
320 if (head->height == 0)
321 return NULL;
322 longcpy(key, __key, geo->keylen);
323retry:
324 dec_key(geo, key);
325
326 node = head->node;
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)
330 break;
331 if (i == geo->no_pairs)
332 goto miss;
333 oldnode = node;
334 node = bval(geo, node, i);
335 if (!node)
336 goto miss;
337 retry_key = bkey(geo, oldnode, i);
338 }
339
340 if (!node)
341 goto miss;
342
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);
348 } else
349 goto miss;
350 }
351 }
352miss:
353 if (retry_key) {
354 longcpy(key, retry_key, geo->keylen);
355 retry_key = NULL;
356 goto retry;
357 }
358 return NULL;
359}
360EXPORT_SYMBOL_GPL(btree_get_prev);
361
362static int getpos(struct btree_geo *geo, unsigned long *node,
363 unsigned long *key)
364{
365 int i;
366
367 for (i = 0; i < geo->no_pairs; i++) {
368 if (keycmp(geo, node, i, key) <= 0)
369 break;
370 }
371 return i;
372}
373
374static int getfill(struct btree_geo *geo, unsigned long *node, int start)
375{
376 int i;
377
378 for (i = start; i < geo->no_pairs; i++)
379 if (!bval(geo, node, i))
380 break;
381 return i;
382}
383
384/*
385 * locate the correct leaf node in the btree
386 */
387static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
388 unsigned long *key, int level)
389{
390 unsigned long *node = head->node;
391 int i, height;
392
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)
396 break;
397
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. */
402 i--;
403 setkey(geo, node, i, key);
404 }
405 BUG_ON(i < 0);
406 node = bval(geo, node, i);
407 }
408 BUG_ON(!node);
409 return node;
410}
411
412static int btree_grow(struct btree_head *head, struct btree_geo *geo,
413 gfp_t gfp)
414{
415 unsigned long *node;
416 int fill;
417
418 node = btree_node_alloc(head, gfp);
419 if (!node)
420 return -ENOMEM;
421 if (head->node) {
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);
425 }
426 head->node = node;
427 head->height++;
428 return 0;
429}
430
431static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
432{
433 unsigned long *node;
434 int fill;
435
436 if (head->height <= 1)
437 return;
438
439 node = head->node;
440 fill = getfill(geo, node, 0);
441 BUG_ON(fill > 1);
442 head->node = bval(geo, node, 0);
443 head->height--;
444 mempool_free(node, head->mempool);
445}
446
447static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
448 unsigned long *key, void *val, int level,
449 gfp_t gfp)
450{
451 unsigned long *node;
452 int i, pos, fill, err;
453
454 BUG_ON(!val);
455 if (head->height < level) {
456 err = btree_grow(head, geo, gfp);
457 if (err)
458 return err;
459 }
460
461retry:
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);
467
468 if (fill == geo->no_pairs) {
469 /* need to split node */
470 unsigned long *new;
471
472 new = btree_node_alloc(head, gfp);
473 if (!new)
474 return -ENOMEM;
475 err = btree_insert_level(head, geo,
476 bkey(geo, node, fill / 2 - 1),
477 new, level + 1, gfp);
478 if (err) {
479 mempool_free(new, head->mempool);
480 return err;
481 }
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);
488 }
489 if (fill & 1) {
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);
493 }
494 goto retry;
495 }
496 BUG_ON(fill >= geo->no_pairs);
497
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));
502 }
503 setkey(geo, node, pos, key);
504 setval(geo, node, pos, val);
505
506 return 0;
507}
508
509int btree_insert(struct btree_head *head, struct btree_geo *geo,
510 unsigned long *key, void *val, gfp_t gfp)
511{
512 BUG_ON(!val);
513 return btree_insert_level(head, geo, key, val, 1, gfp);
514}
515EXPORT_SYMBOL_GPL(btree_insert);
516
517static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
518 unsigned long *key, int level);
519static 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)
523{
524 int i;
525
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));
530 }
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);
537}
538
539static void rebalance(struct btree_head *head, struct btree_geo *geo,
540 unsigned long *key, int level, unsigned long *child, int fill)
541{
542 unsigned long *parent, *left = NULL, *right = NULL;
543 int i, no_left, no_right;
544
545 if (fill == 0) {
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.
549 */
550 btree_remove_level(head, geo, key, level + 1);
551 mempool_free(child, head->mempool);
552 return;
553 }
554
555 parent = find_level(head, geo, key, level + 1);
556 i = getpos(geo, parent, key);
557 BUG_ON(bval(geo, parent, i) != child);
558
559 if (i > 0) {
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,
564 left, no_left,
565 child, fill,
566 parent, i - 1);
567 return;
568 }
569 }
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,
575 child, fill,
576 right, no_right,
577 parent, i);
578 return;
579 }
580 }
581 /*
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.
587 */
588}
589
590static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
591 unsigned long *key, int level)
592{
593 unsigned long *node;
594 int i, pos, fill;
595 void *ret;
596
597 if (level > head->height) {
598 /* we recursed all the way up */
599 head->height = 0;
600 head->node = NULL;
601 return NULL;
602 }
603
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))
608 return NULL;
609 ret = bval(geo, node, pos);
610
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));
615 }
616 clearpair(geo, node, fill - 1);
617
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);
623 }
624
625 return ret;
626}
627
628void *btree_remove(struct btree_head *head, struct btree_geo *geo,
629 unsigned long *key)
630{
631 if (head->height == 0)
632 return NULL;
633
634 return btree_remove_level(head, geo, key, 1);
635}
636EXPORT_SYMBOL_GPL(btree_remove);
637
638int btree_merge(struct btree_head *target, struct btree_head *victim,
639 struct btree_geo *geo, gfp_t gfp)
640{
641 unsigned long key[geo->keylen];
642 unsigned long dup[geo->keylen];
643 void *val;
644 int err;
645
646 BUG_ON(target == victim);
647
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);
653 return 0;
654 }
655
656 /* TODO: This needs some optimizations. Currently we do three tree
657 * walks to remove a single object from the victim.
658 */
659 for (;;) {
660 if (!btree_last(victim, geo, key))
661 break;
662 val = btree_lookup(victim, geo, key);
663 err = btree_insert(target, geo, key, val, gfp);
664 if (err)
665 return err;
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);
670 }
671 return 0;
672}
673EXPORT_SYMBOL_GPL(btree_merge);
674
675static 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,
679 void *func2),
680 void *func2, int reap, int height, size_t count)
681{
682 int i;
683 unsigned long *child;
684
685 for (i = 0; i < geo->no_pairs; i++) {
686 child = bval(geo, node, i);
687 if (!child)
688 break;
689 if (height > 1)
690 count = __btree_for_each(head, geo, child, opaque,
691 func, func2, reap, height - 1, count);
692 else
693 func(child, opaque, bkey(geo, node, i), count++,
694 func2);
695 }
696 if (reap)
697 mempool_free(node, head->mempool);
698 return count;
699}
700
701static void empty(void *elem, unsigned long opaque, unsigned long *key,
702 size_t index, void *func2)
703{
704}
705
706void visitorl(void *elem, unsigned long opaque, unsigned long *key,
707 size_t index, void *__func)
708{
709 visitorl_t func = __func;
710
711 func(elem, opaque, *key, index);
712}
713EXPORT_SYMBOL_GPL(visitorl);
714
715void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
716 size_t index, void *__func)
717{
718 visitor32_t func = __func;
719 u32 *key = (void *)__key;
720
721 func(elem, opaque, *key, index);
722}
723EXPORT_SYMBOL_GPL(visitor32);
724
725void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
726 size_t index, void *__func)
727{
728 visitor64_t func = __func;
729 u64 *key = (void *)__key;
730
731 func(elem, opaque, *key, index);
732}
733EXPORT_SYMBOL_GPL(visitor64);
734
735void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
736 size_t index, void *__func)
737{
738 visitor128_t func = __func;
739 u64 *key = (void *)__key;
740
741 func(elem, opaque, key[0], key[1], index);
742}
743EXPORT_SYMBOL_GPL(visitor128);
744
745size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
746 unsigned long opaque,
747 void (*func)(void *elem, unsigned long opaque,
748 unsigned long *key,
749 size_t index, void *func2),
750 void *func2)
751{
752 size_t count = 0;
753
754 if (!func2)
755 func = empty;
756 if (head->node)
757 count = __btree_for_each(head, geo, head->node, opaque, func,
758 func2, 0, head->height, 0);
759 return count;
760}
761EXPORT_SYMBOL_GPL(btree_visitor);
762
763size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
764 unsigned long opaque,
765 void (*func)(void *elem, unsigned long opaque,
766 unsigned long *key,
767 size_t index, void *func2),
768 void *func2)
769{
770 size_t count = 0;
771
772 if (!func2)
773 func = empty;
774 if (head->node)
775 count = __btree_for_each(head, geo, head->node, opaque, func,
776 func2, 1, head->height, 0);
777 __btree_init(head);
778 return count;
779}
780EXPORT_SYMBOL_GPL(btree_grim_visitor);
781
782static int __init btree_module_init(void)
783{
784 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
785 SLAB_HWCACHE_ALIGN, NULL);
786 return 0;
787}
788
789static void __exit btree_module_exit(void)
790{
791 kmem_cache_destroy(btree_cachep);
792}
793
794/* If core code starts using btree, initialization should happen even earlier */
795module_init(btree_module_init);
796module_exit(btree_module_exit);
797
798MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
799MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
800MODULE_LICENSE("GPL");
1/*
2 * lib/btree.c - Simple In-memory B+Tree
3 *
4 * As should be obvious for Linux kernel code, license is GPLv2
5 *
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
9 * GPLv2
10 *
11 * see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch
12 *
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.
15 *
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.
20 *
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
24 * helps B+Trees.
25 *
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%
30 * pointers.
31 *
32 * This particular implementation stores pointers identified by a long value.
33 * Storing NULL pointers is illegal, lookup will return NULL when no entry
34 * was found.
35 *
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.
40 */
41
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>
47
48#define MAX(a, b) ((a) > (b) ? (a) : (b))
49#define NODESIZE MAX(L1_CACHE_BYTES, 128)
50
51struct btree_geo {
52 int keylen;
53 int no_pairs;
54 int no_longs;
55};
56
57struct btree_geo btree_geo32 = {
58 .keylen = 1,
59 .no_pairs = NODESIZE / sizeof(long) / 2,
60 .no_longs = NODESIZE / sizeof(long) / 2,
61};
62EXPORT_SYMBOL_GPL(btree_geo32);
63
64#define LONG_PER_U64 (64 / BITS_PER_LONG)
65struct 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)),
69};
70EXPORT_SYMBOL_GPL(btree_geo64);
71
72struct 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)),
76};
77EXPORT_SYMBOL_GPL(btree_geo128);
78
79static struct kmem_cache *btree_cachep;
80
81void *btree_alloc(gfp_t gfp_mask, void *pool_data)
82{
83 return kmem_cache_alloc(btree_cachep, gfp_mask);
84}
85EXPORT_SYMBOL_GPL(btree_alloc);
86
87void btree_free(void *element, void *pool_data)
88{
89 kmem_cache_free(btree_cachep, element);
90}
91EXPORT_SYMBOL_GPL(btree_free);
92
93static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp)
94{
95 unsigned long *node;
96
97 node = mempool_alloc(head->mempool, gfp);
98 if (likely(node))
99 memset(node, 0, NODESIZE);
100 return node;
101}
102
103static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
104{
105 size_t i;
106
107 for (i = 0; i < n; i++) {
108 if (l1[i] < l2[i])
109 return -1;
110 if (l1[i] > l2[i])
111 return 1;
112 }
113 return 0;
114}
115
116static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
117 size_t n)
118{
119 size_t i;
120
121 for (i = 0; i < n; i++)
122 dest[i] = src[i];
123 return dest;
124}
125
126static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
127{
128 size_t i;
129
130 for (i = 0; i < n; i++)
131 s[i] = c;
132 return s;
133}
134
135static void dec_key(struct btree_geo *geo, unsigned long *key)
136{
137 unsigned long val;
138 int i;
139
140 for (i = geo->keylen - 1; i >= 0; i--) {
141 val = key[i];
142 key[i] = val - 1;
143 if (val)
144 break;
145 }
146}
147
148static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
149{
150 return &node[n * geo->keylen];
151}
152
153static void *bval(struct btree_geo *geo, unsigned long *node, int n)
154{
155 return (void *)node[geo->no_longs + n];
156}
157
158static void setkey(struct btree_geo *geo, unsigned long *node, int n,
159 unsigned long *key)
160{
161 longcpy(bkey(geo, node, n), key, geo->keylen);
162}
163
164static void setval(struct btree_geo *geo, unsigned long *node, int n,
165 void *val)
166{
167 node[geo->no_longs + n] = (unsigned long) val;
168}
169
170static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
171{
172 longset(bkey(geo, node, n), 0, geo->keylen);
173 node[geo->no_longs + n] = 0;
174}
175
176static inline void __btree_init(struct btree_head *head)
177{
178 head->node = NULL;
179 head->height = 0;
180}
181
182void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
183{
184 __btree_init(head);
185 head->mempool = mempool;
186}
187EXPORT_SYMBOL_GPL(btree_init_mempool);
188
189int btree_init(struct btree_head *head)
190{
191 __btree_init(head);
192 head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
193 if (!head->mempool)
194 return -ENOMEM;
195 return 0;
196}
197EXPORT_SYMBOL_GPL(btree_init);
198
199void btree_destroy(struct btree_head *head)
200{
201 mempool_free(head->node, head->mempool);
202 mempool_destroy(head->mempool);
203 head->mempool = NULL;
204}
205EXPORT_SYMBOL_GPL(btree_destroy);
206
207void *btree_last(struct btree_head *head, struct btree_geo *geo,
208 unsigned long *key)
209{
210 int height = head->height;
211 unsigned long *node = head->node;
212
213 if (height == 0)
214 return NULL;
215
216 for ( ; height > 1; height--)
217 node = bval(geo, node, 0);
218
219 longcpy(key, bkey(geo, node, 0), geo->keylen);
220 return bval(geo, node, 0);
221}
222EXPORT_SYMBOL_GPL(btree_last);
223
224static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
225 unsigned long *key)
226{
227 return longcmp(bkey(geo, node, pos), key, geo->keylen);
228}
229
230static int keyzero(struct btree_geo *geo, unsigned long *key)
231{
232 int i;
233
234 for (i = 0; i < geo->keylen; i++)
235 if (key[i])
236 return 0;
237
238 return 1;
239}
240
241void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
242 unsigned long *key)
243{
244 int i, height = head->height;
245 unsigned long *node = head->node;
246
247 if (height == 0)
248 return NULL;
249
250 for ( ; height > 1; height--) {
251 for (i = 0; i < geo->no_pairs; i++)
252 if (keycmp(geo, node, i, key) <= 0)
253 break;
254 if (i == geo->no_pairs)
255 return NULL;
256 node = bval(geo, node, i);
257 if (!node)
258 return NULL;
259 }
260
261 if (!node)
262 return NULL;
263
264 for (i = 0; i < geo->no_pairs; i++)
265 if (keycmp(geo, node, i, key) == 0)
266 return bval(geo, node, i);
267 return NULL;
268}
269EXPORT_SYMBOL_GPL(btree_lookup);
270
271int btree_update(struct btree_head *head, struct btree_geo *geo,
272 unsigned long *key, void *val)
273{
274 int i, height = head->height;
275 unsigned long *node = head->node;
276
277 if (height == 0)
278 return -ENOENT;
279
280 for ( ; height > 1; height--) {
281 for (i = 0; i < geo->no_pairs; i++)
282 if (keycmp(geo, node, i, key) <= 0)
283 break;
284 if (i == geo->no_pairs)
285 return -ENOENT;
286 node = bval(geo, node, i);
287 if (!node)
288 return -ENOENT;
289 }
290
291 if (!node)
292 return -ENOENT;
293
294 for (i = 0; i < geo->no_pairs; i++)
295 if (keycmp(geo, node, i, key) == 0) {
296 setval(geo, node, i, val);
297 return 0;
298 }
299 return -ENOENT;
300}
301EXPORT_SYMBOL_GPL(btree_update);
302
303/*
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.
310 */
311void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
312 unsigned long *__key)
313{
314 int i, height;
315 unsigned long *node, *oldnode;
316 unsigned long *retry_key = NULL, key[geo->keylen];
317
318 if (keyzero(geo, __key))
319 return NULL;
320
321 if (head->height == 0)
322 return NULL;
323 longcpy(key, __key, geo->keylen);
324retry:
325 dec_key(geo, key);
326
327 node = head->node;
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)
331 break;
332 if (i == geo->no_pairs)
333 goto miss;
334 oldnode = node;
335 node = bval(geo, node, i);
336 if (!node)
337 goto miss;
338 retry_key = bkey(geo, oldnode, i);
339 }
340
341 if (!node)
342 goto miss;
343
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);
349 } else
350 goto miss;
351 }
352 }
353miss:
354 if (retry_key) {
355 longcpy(key, retry_key, geo->keylen);
356 retry_key = NULL;
357 goto retry;
358 }
359 return NULL;
360}
361EXPORT_SYMBOL_GPL(btree_get_prev);
362
363static int getpos(struct btree_geo *geo, unsigned long *node,
364 unsigned long *key)
365{
366 int i;
367
368 for (i = 0; i < geo->no_pairs; i++) {
369 if (keycmp(geo, node, i, key) <= 0)
370 break;
371 }
372 return i;
373}
374
375static int getfill(struct btree_geo *geo, unsigned long *node, int start)
376{
377 int i;
378
379 for (i = start; i < geo->no_pairs; i++)
380 if (!bval(geo, node, i))
381 break;
382 return i;
383}
384
385/*
386 * locate the correct leaf node in the btree
387 */
388static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
389 unsigned long *key, int level)
390{
391 unsigned long *node = head->node;
392 int i, height;
393
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)
397 break;
398
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. */
403 i--;
404 setkey(geo, node, i, key);
405 }
406 BUG_ON(i < 0);
407 node = bval(geo, node, i);
408 }
409 BUG_ON(!node);
410 return node;
411}
412
413static int btree_grow(struct btree_head *head, struct btree_geo *geo,
414 gfp_t gfp)
415{
416 unsigned long *node;
417 int fill;
418
419 node = btree_node_alloc(head, gfp);
420 if (!node)
421 return -ENOMEM;
422 if (head->node) {
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);
426 }
427 head->node = node;
428 head->height++;
429 return 0;
430}
431
432static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
433{
434 unsigned long *node;
435 int fill;
436
437 if (head->height <= 1)
438 return;
439
440 node = head->node;
441 fill = getfill(geo, node, 0);
442 BUG_ON(fill > 1);
443 head->node = bval(geo, node, 0);
444 head->height--;
445 mempool_free(node, head->mempool);
446}
447
448static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
449 unsigned long *key, void *val, int level,
450 gfp_t gfp)
451{
452 unsigned long *node;
453 int i, pos, fill, err;
454
455 BUG_ON(!val);
456 if (head->height < level) {
457 err = btree_grow(head, geo, gfp);
458 if (err)
459 return err;
460 }
461
462retry:
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);
468
469 if (fill == geo->no_pairs) {
470 /* need to split node */
471 unsigned long *new;
472
473 new = btree_node_alloc(head, gfp);
474 if (!new)
475 return -ENOMEM;
476 err = btree_insert_level(head, geo,
477 bkey(geo, node, fill / 2 - 1),
478 new, level + 1, gfp);
479 if (err) {
480 mempool_free(new, head->mempool);
481 return err;
482 }
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);
489 }
490 if (fill & 1) {
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);
494 }
495 goto retry;
496 }
497 BUG_ON(fill >= geo->no_pairs);
498
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));
503 }
504 setkey(geo, node, pos, key);
505 setval(geo, node, pos, val);
506
507 return 0;
508}
509
510int btree_insert(struct btree_head *head, struct btree_geo *geo,
511 unsigned long *key, void *val, gfp_t gfp)
512{
513 BUG_ON(!val);
514 return btree_insert_level(head, geo, key, val, 1, gfp);
515}
516EXPORT_SYMBOL_GPL(btree_insert);
517
518static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
519 unsigned long *key, int level);
520static 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)
524{
525 int i;
526
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));
531 }
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);
538}
539
540static void rebalance(struct btree_head *head, struct btree_geo *geo,
541 unsigned long *key, int level, unsigned long *child, int fill)
542{
543 unsigned long *parent, *left = NULL, *right = NULL;
544 int i, no_left, no_right;
545
546 if (fill == 0) {
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.
550 */
551 btree_remove_level(head, geo, key, level + 1);
552 mempool_free(child, head->mempool);
553 return;
554 }
555
556 parent = find_level(head, geo, key, level + 1);
557 i = getpos(geo, parent, key);
558 BUG_ON(bval(geo, parent, i) != child);
559
560 if (i > 0) {
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,
565 left, no_left,
566 child, fill,
567 parent, i - 1);
568 return;
569 }
570 }
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,
576 child, fill,
577 right, no_right,
578 parent, i);
579 return;
580 }
581 }
582 /*
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.
588 */
589}
590
591static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
592 unsigned long *key, int level)
593{
594 unsigned long *node;
595 int i, pos, fill;
596 void *ret;
597
598 if (level > head->height) {
599 /* we recursed all the way up */
600 head->height = 0;
601 head->node = NULL;
602 return NULL;
603 }
604
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))
609 return NULL;
610 ret = bval(geo, node, pos);
611
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));
616 }
617 clearpair(geo, node, fill - 1);
618
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);
624 }
625
626 return ret;
627}
628
629void *btree_remove(struct btree_head *head, struct btree_geo *geo,
630 unsigned long *key)
631{
632 if (head->height == 0)
633 return NULL;
634
635 return btree_remove_level(head, geo, key, 1);
636}
637EXPORT_SYMBOL_GPL(btree_remove);
638
639int btree_merge(struct btree_head *target, struct btree_head *victim,
640 struct btree_geo *geo, gfp_t gfp)
641{
642 unsigned long key[geo->keylen];
643 unsigned long dup[geo->keylen];
644 void *val;
645 int err;
646
647 BUG_ON(target == victim);
648
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);
654 return 0;
655 }
656
657 /* TODO: This needs some optimizations. Currently we do three tree
658 * walks to remove a single object from the victim.
659 */
660 for (;;) {
661 if (!btree_last(victim, geo, key))
662 break;
663 val = btree_lookup(victim, geo, key);
664 err = btree_insert(target, geo, key, val, gfp);
665 if (err)
666 return err;
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);
671 }
672 return 0;
673}
674EXPORT_SYMBOL_GPL(btree_merge);
675
676static 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,
680 void *func2),
681 void *func2, int reap, int height, size_t count)
682{
683 int i;
684 unsigned long *child;
685
686 for (i = 0; i < geo->no_pairs; i++) {
687 child = bval(geo, node, i);
688 if (!child)
689 break;
690 if (height > 1)
691 count = __btree_for_each(head, geo, child, opaque,
692 func, func2, reap, height - 1, count);
693 else
694 func(child, opaque, bkey(geo, node, i), count++,
695 func2);
696 }
697 if (reap)
698 mempool_free(node, head->mempool);
699 return count;
700}
701
702static void empty(void *elem, unsigned long opaque, unsigned long *key,
703 size_t index, void *func2)
704{
705}
706
707void visitorl(void *elem, unsigned long opaque, unsigned long *key,
708 size_t index, void *__func)
709{
710 visitorl_t func = __func;
711
712 func(elem, opaque, *key, index);
713}
714EXPORT_SYMBOL_GPL(visitorl);
715
716void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
717 size_t index, void *__func)
718{
719 visitor32_t func = __func;
720 u32 *key = (void *)__key;
721
722 func(elem, opaque, *key, index);
723}
724EXPORT_SYMBOL_GPL(visitor32);
725
726void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
727 size_t index, void *__func)
728{
729 visitor64_t func = __func;
730 u64 *key = (void *)__key;
731
732 func(elem, opaque, *key, index);
733}
734EXPORT_SYMBOL_GPL(visitor64);
735
736void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
737 size_t index, void *__func)
738{
739 visitor128_t func = __func;
740 u64 *key = (void *)__key;
741
742 func(elem, opaque, key[0], key[1], index);
743}
744EXPORT_SYMBOL_GPL(visitor128);
745
746size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
747 unsigned long opaque,
748 void (*func)(void *elem, unsigned long opaque,
749 unsigned long *key,
750 size_t index, void *func2),
751 void *func2)
752{
753 size_t count = 0;
754
755 if (!func2)
756 func = empty;
757 if (head->node)
758 count = __btree_for_each(head, geo, head->node, opaque, func,
759 func2, 0, head->height, 0);
760 return count;
761}
762EXPORT_SYMBOL_GPL(btree_visitor);
763
764size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
765 unsigned long opaque,
766 void (*func)(void *elem, unsigned long opaque,
767 unsigned long *key,
768 size_t index, void *func2),
769 void *func2)
770{
771 size_t count = 0;
772
773 if (!func2)
774 func = empty;
775 if (head->node)
776 count = __btree_for_each(head, geo, head->node, opaque, func,
777 func2, 1, head->height, 0);
778 __btree_init(head);
779 return count;
780}
781EXPORT_SYMBOL_GPL(btree_grim_visitor);
782
783static int __init btree_module_init(void)
784{
785 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
786 SLAB_HWCACHE_ALIGN, NULL);
787 return 0;
788}
789
790static void __exit btree_module_exit(void)
791{
792 kmem_cache_destroy(btree_cachep);
793}
794
795/* If core code starts using btree, initialization should happen even earlier */
796module_init(btree_module_init);
797module_exit(btree_module_exit);
798
799MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
800MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
801MODULE_LICENSE("GPL");