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1// SPDX-License-Identifier: GPL-2.0-only
2/*
3 * lib/btree.c - Simple In-memory B+Tree
4 *
5 * Copyright (c) 2007-2008 Joern Engel <joern@purestorage.com>
6 * Bits and pieces stolen from Peter Zijlstra's code, which is
7 * Copyright 2007, Red Hat Inc. Peter Zijlstra
8 *
9 * see http://programming.kicks-ass.net/kernel-patches/vma_lookup/btree.patch
10 *
11 * A relatively simple B+Tree implementation. I have written it as a learning
12 * exercise to understand how B+Trees work. Turned out to be useful as well.
13 *
14 * B+Trees can be used similar to Linux radix trees (which don't have anything
15 * in common with textbook radix trees, beware). Prerequisite for them working
16 * well is that access to a random tree node is much faster than a large number
17 * of operations within each node.
18 *
19 * Disks have fulfilled the prerequisite for a long time. More recently DRAM
20 * has gained similar properties, as memory access times, when measured in cpu
21 * cycles, have increased. Cacheline sizes have increased as well, which also
22 * helps B+Trees.
23 *
24 * Compared to radix trees, B+Trees are more efficient when dealing with a
25 * sparsely populated address space. Between 25% and 50% of the memory is
26 * occupied with valid pointers. When densely populated, radix trees contain
27 * ~98% pointers - hard to beat. Very sparse radix trees contain only ~2%
28 * pointers.
29 *
30 * This particular implementation stores pointers identified by a long value.
31 * Storing NULL pointers is illegal, lookup will return NULL when no entry
32 * was found.
33 *
34 * A tricks was used that is not commonly found in textbooks. The lowest
35 * values are to the right, not to the left. All used slots within a node
36 * are on the left, all unused slots contain NUL values. Most operations
37 * simply loop once over all slots and terminate on the first NUL.
38 */
39
40#include <linux/btree.h>
41#include <linux/cache.h>
42#include <linux/kernel.h>
43#include <linux/slab.h>
44#include <linux/module.h>
45
46#define MAX(a, b) ((a) > (b) ? (a) : (b))
47#define NODESIZE MAX(L1_CACHE_BYTES, 128)
48
49struct btree_geo {
50 int keylen;
51 int no_pairs;
52 int no_longs;
53};
54
55struct btree_geo btree_geo32 = {
56 .keylen = 1,
57 .no_pairs = NODESIZE / sizeof(long) / 2,
58 .no_longs = NODESIZE / sizeof(long) / 2,
59};
60EXPORT_SYMBOL_GPL(btree_geo32);
61
62#define LONG_PER_U64 (64 / BITS_PER_LONG)
63struct btree_geo btree_geo64 = {
64 .keylen = LONG_PER_U64,
65 .no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64),
66 .no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)),
67};
68EXPORT_SYMBOL_GPL(btree_geo64);
69
70struct btree_geo btree_geo128 = {
71 .keylen = 2 * LONG_PER_U64,
72 .no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64),
73 .no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)),
74};
75EXPORT_SYMBOL_GPL(btree_geo128);
76
77#define MAX_KEYLEN (2 * LONG_PER_U64)
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
241static void *btree_lookup_node(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 return node;
261}
262
263void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
264 unsigned long *key)
265{
266 int i;
267 unsigned long *node;
268
269 node = btree_lookup_node(head, geo, key);
270 if (!node)
271 return NULL;
272
273 for (i = 0; i < geo->no_pairs; i++)
274 if (keycmp(geo, node, i, key) == 0)
275 return bval(geo, node, i);
276 return NULL;
277}
278EXPORT_SYMBOL_GPL(btree_lookup);
279
280int btree_update(struct btree_head *head, struct btree_geo *geo,
281 unsigned long *key, void *val)
282{
283 int i;
284 unsigned long *node;
285
286 node = btree_lookup_node(head, geo, key);
287 if (!node)
288 return -ENOENT;
289
290 for (i = 0; i < geo->no_pairs; i++)
291 if (keycmp(geo, node, i, key) == 0) {
292 setval(geo, node, i, val);
293 return 0;
294 }
295 return -ENOENT;
296}
297EXPORT_SYMBOL_GPL(btree_update);
298
299/*
300 * Usually this function is quite similar to normal lookup. But the key of
301 * a parent node may be smaller than the smallest key of all its siblings.
302 * In such a case we cannot just return NULL, as we have only proven that no
303 * key smaller than __key, but larger than this parent key exists.
304 * So we set __key to the parent key and retry. We have to use the smallest
305 * such parent key, which is the last parent key we encountered.
306 */
307void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
308 unsigned long *__key)
309{
310 int i, height;
311 unsigned long *node, *oldnode;
312 unsigned long *retry_key = NULL, key[MAX_KEYLEN];
313
314 if (keyzero(geo, __key))
315 return NULL;
316
317 if (head->height == 0)
318 return NULL;
319 longcpy(key, __key, geo->keylen);
320retry:
321 dec_key(geo, key);
322
323 node = head->node;
324 for (height = head->height ; height > 1; height--) {
325 for (i = 0; i < geo->no_pairs; i++)
326 if (keycmp(geo, node, i, key) <= 0)
327 break;
328 if (i == geo->no_pairs)
329 goto miss;
330 oldnode = node;
331 node = bval(geo, node, i);
332 if (!node)
333 goto miss;
334 retry_key = bkey(geo, oldnode, i);
335 }
336
337 if (!node)
338 goto miss;
339
340 for (i = 0; i < geo->no_pairs; i++) {
341 if (keycmp(geo, node, i, key) <= 0) {
342 if (bval(geo, node, i)) {
343 longcpy(__key, bkey(geo, node, i), geo->keylen);
344 return bval(geo, node, i);
345 } else
346 goto miss;
347 }
348 }
349miss:
350 if (retry_key) {
351 longcpy(key, retry_key, geo->keylen);
352 retry_key = NULL;
353 goto retry;
354 }
355 return NULL;
356}
357EXPORT_SYMBOL_GPL(btree_get_prev);
358
359static int getpos(struct btree_geo *geo, unsigned long *node,
360 unsigned long *key)
361{
362 int i;
363
364 for (i = 0; i < geo->no_pairs; i++) {
365 if (keycmp(geo, node, i, key) <= 0)
366 break;
367 }
368 return i;
369}
370
371static int getfill(struct btree_geo *geo, unsigned long *node, int start)
372{
373 int i;
374
375 for (i = start; i < geo->no_pairs; i++)
376 if (!bval(geo, node, i))
377 break;
378 return i;
379}
380
381/*
382 * locate the correct leaf node in the btree
383 */
384static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
385 unsigned long *key, int level)
386{
387 unsigned long *node = head->node;
388 int i, height;
389
390 for (height = head->height; height > level; height--) {
391 for (i = 0; i < geo->no_pairs; i++)
392 if (keycmp(geo, node, i, key) <= 0)
393 break;
394
395 if ((i == geo->no_pairs) || !bval(geo, node, i)) {
396 /* right-most key is too large, update it */
397 /* FIXME: If the right-most key on higher levels is
398 * always zero, this wouldn't be necessary. */
399 i--;
400 setkey(geo, node, i, key);
401 }
402 BUG_ON(i < 0);
403 node = bval(geo, node, i);
404 }
405 BUG_ON(!node);
406 return node;
407}
408
409static int btree_grow(struct btree_head *head, struct btree_geo *geo,
410 gfp_t gfp)
411{
412 unsigned long *node;
413 int fill;
414
415 node = btree_node_alloc(head, gfp);
416 if (!node)
417 return -ENOMEM;
418 if (head->node) {
419 fill = getfill(geo, head->node, 0);
420 setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
421 setval(geo, node, 0, head->node);
422 }
423 head->node = node;
424 head->height++;
425 return 0;
426}
427
428static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
429{
430 unsigned long *node;
431 int fill;
432
433 if (head->height <= 1)
434 return;
435
436 node = head->node;
437 fill = getfill(geo, node, 0);
438 BUG_ON(fill > 1);
439 head->node = bval(geo, node, 0);
440 head->height--;
441 mempool_free(node, head->mempool);
442}
443
444static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
445 unsigned long *key, void *val, int level,
446 gfp_t gfp)
447{
448 unsigned long *node;
449 int i, pos, fill, err;
450
451 BUG_ON(!val);
452 if (head->height < level) {
453 err = btree_grow(head, geo, gfp);
454 if (err)
455 return err;
456 }
457
458retry:
459 node = find_level(head, geo, key, level);
460 pos = getpos(geo, node, key);
461 fill = getfill(geo, node, pos);
462 /* two identical keys are not allowed */
463 BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
464
465 if (fill == geo->no_pairs) {
466 /* need to split node */
467 unsigned long *new;
468
469 new = btree_node_alloc(head, gfp);
470 if (!new)
471 return -ENOMEM;
472 err = btree_insert_level(head, geo,
473 bkey(geo, node, fill / 2 - 1),
474 new, level + 1, gfp);
475 if (err) {
476 mempool_free(new, head->mempool);
477 return err;
478 }
479 for (i = 0; i < fill / 2; i++) {
480 setkey(geo, new, i, bkey(geo, node, i));
481 setval(geo, new, i, bval(geo, node, i));
482 setkey(geo, node, i, bkey(geo, node, i + fill / 2));
483 setval(geo, node, i, bval(geo, node, i + fill / 2));
484 clearpair(geo, node, i + fill / 2);
485 }
486 if (fill & 1) {
487 setkey(geo, node, i, bkey(geo, node, fill - 1));
488 setval(geo, node, i, bval(geo, node, fill - 1));
489 clearpair(geo, node, fill - 1);
490 }
491 goto retry;
492 }
493 BUG_ON(fill >= geo->no_pairs);
494
495 /* shift and insert */
496 for (i = fill; i > pos; i--) {
497 setkey(geo, node, i, bkey(geo, node, i - 1));
498 setval(geo, node, i, bval(geo, node, i - 1));
499 }
500 setkey(geo, node, pos, key);
501 setval(geo, node, pos, val);
502
503 return 0;
504}
505
506int btree_insert(struct btree_head *head, struct btree_geo *geo,
507 unsigned long *key, void *val, gfp_t gfp)
508{
509 BUG_ON(!val);
510 return btree_insert_level(head, geo, key, val, 1, gfp);
511}
512EXPORT_SYMBOL_GPL(btree_insert);
513
514static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
515 unsigned long *key, int level);
516static 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)
520{
521 int i;
522
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));
527 }
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);
534}
535
536static void rebalance(struct btree_head *head, struct btree_geo *geo,
537 unsigned long *key, int level, unsigned long *child, int fill)
538{
539 unsigned long *parent, *left = NULL, *right = NULL;
540 int i, no_left, no_right;
541
542 if (fill == 0) {
543 /* Because we don't steal entries from a neighbour, this case
544 * can happen. Parent node contains a single child, this
545 * node, so merging with a sibling never happens.
546 */
547 btree_remove_level(head, geo, key, level + 1);
548 mempool_free(child, head->mempool);
549 return;
550 }
551
552 parent = find_level(head, geo, key, level + 1);
553 i = getpos(geo, parent, key);
554 BUG_ON(bval(geo, parent, i) != child);
555
556 if (i > 0) {
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,
561 left, no_left,
562 child, fill,
563 parent, i - 1);
564 return;
565 }
566 }
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,
572 child, fill,
573 right, no_right,
574 parent, i);
575 return;
576 }
577 }
578 /*
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.
584 */
585}
586
587static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
588 unsigned long *key, int level)
589{
590 unsigned long *node;
591 int i, pos, fill;
592 void *ret;
593
594 if (level > head->height) {
595 /* we recursed all the way up */
596 head->height = 0;
597 head->node = NULL;
598 return NULL;
599 }
600
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))
605 return NULL;
606 ret = bval(geo, node, pos);
607
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));
612 }
613 clearpair(geo, node, fill - 1);
614
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);
620 }
621
622 return ret;
623}
624
625void *btree_remove(struct btree_head *head, struct btree_geo *geo,
626 unsigned long *key)
627{
628 if (head->height == 0)
629 return NULL;
630
631 return btree_remove_level(head, geo, key, 1);
632}
633EXPORT_SYMBOL_GPL(btree_remove);
634
635int btree_merge(struct btree_head *target, struct btree_head *victim,
636 struct btree_geo *geo, gfp_t gfp)
637{
638 unsigned long key[MAX_KEYLEN];
639 unsigned long dup[MAX_KEYLEN];
640 void *val;
641 int err;
642
643 BUG_ON(target == victim);
644
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);
650 return 0;
651 }
652
653 /* TODO: This needs some optimizations. Currently we do three tree
654 * walks to remove a single object from the victim.
655 */
656 for (;;) {
657 if (!btree_last(victim, geo, key))
658 break;
659 val = btree_lookup(victim, geo, key);
660 err = btree_insert(target, geo, key, val, gfp);
661 if (err)
662 return err;
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);
667 }
668 return 0;
669}
670EXPORT_SYMBOL_GPL(btree_merge);
671
672static 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,
676 void *func2),
677 void *func2, int reap, int height, size_t count)
678{
679 int i;
680 unsigned long *child;
681
682 for (i = 0; i < geo->no_pairs; i++) {
683 child = bval(geo, node, i);
684 if (!child)
685 break;
686 if (height > 1)
687 count = __btree_for_each(head, geo, child, opaque,
688 func, func2, reap, height - 1, count);
689 else
690 func(child, opaque, bkey(geo, node, i), count++,
691 func2);
692 }
693 if (reap)
694 mempool_free(node, head->mempool);
695 return count;
696}
697
698static void empty(void *elem, unsigned long opaque, unsigned long *key,
699 size_t index, void *func2)
700{
701}
702
703void visitorl(void *elem, unsigned long opaque, unsigned long *key,
704 size_t index, void *__func)
705{
706 visitorl_t func = __func;
707
708 func(elem, opaque, *key, index);
709}
710EXPORT_SYMBOL_GPL(visitorl);
711
712void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
713 size_t index, void *__func)
714{
715 visitor32_t func = __func;
716 u32 *key = (void *)__key;
717
718 func(elem, opaque, *key, index);
719}
720EXPORT_SYMBOL_GPL(visitor32);
721
722void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
723 size_t index, void *__func)
724{
725 visitor64_t func = __func;
726 u64 *key = (void *)__key;
727
728 func(elem, opaque, *key, index);
729}
730EXPORT_SYMBOL_GPL(visitor64);
731
732void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
733 size_t index, void *__func)
734{
735 visitor128_t func = __func;
736 u64 *key = (void *)__key;
737
738 func(elem, opaque, key[0], key[1], index);
739}
740EXPORT_SYMBOL_GPL(visitor128);
741
742size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
743 unsigned long opaque,
744 void (*func)(void *elem, unsigned long opaque,
745 unsigned long *key,
746 size_t index, void *func2),
747 void *func2)
748{
749 size_t count = 0;
750
751 if (!func2)
752 func = empty;
753 if (head->node)
754 count = __btree_for_each(head, geo, head->node, opaque, func,
755 func2, 0, head->height, 0);
756 return count;
757}
758EXPORT_SYMBOL_GPL(btree_visitor);
759
760size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
761 unsigned long opaque,
762 void (*func)(void *elem, unsigned long opaque,
763 unsigned long *key,
764 size_t index, void *func2),
765 void *func2)
766{
767 size_t count = 0;
768
769 if (!func2)
770 func = empty;
771 if (head->node)
772 count = __btree_for_each(head, geo, head->node, opaque, func,
773 func2, 1, head->height, 0);
774 __btree_init(head);
775 return count;
776}
777EXPORT_SYMBOL_GPL(btree_grim_visitor);
778
779static int __init btree_module_init(void)
780{
781 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
782 SLAB_HWCACHE_ALIGN, NULL);
783 return 0;
784}
785
786static void __exit btree_module_exit(void)
787{
788 kmem_cache_destroy(btree_cachep);
789}
790
791/* If core code starts using btree, initialization should happen even earlier */
792module_init(btree_module_init);
793module_exit(btree_module_exit);
794
795MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
796MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
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@purestorage.com>
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
79#define MAX_KEYLEN (2 * LONG_PER_U64)
80
81static struct kmem_cache *btree_cachep;
82
83void *btree_alloc(gfp_t gfp_mask, void *pool_data)
84{
85 return kmem_cache_alloc(btree_cachep, gfp_mask);
86}
87EXPORT_SYMBOL_GPL(btree_alloc);
88
89void btree_free(void *element, void *pool_data)
90{
91 kmem_cache_free(btree_cachep, element);
92}
93EXPORT_SYMBOL_GPL(btree_free);
94
95static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp)
96{
97 unsigned long *node;
98
99 node = mempool_alloc(head->mempool, gfp);
100 if (likely(node))
101 memset(node, 0, NODESIZE);
102 return node;
103}
104
105static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
106{
107 size_t i;
108
109 for (i = 0; i < n; i++) {
110 if (l1[i] < l2[i])
111 return -1;
112 if (l1[i] > l2[i])
113 return 1;
114 }
115 return 0;
116}
117
118static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
119 size_t n)
120{
121 size_t i;
122
123 for (i = 0; i < n; i++)
124 dest[i] = src[i];
125 return dest;
126}
127
128static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
129{
130 size_t i;
131
132 for (i = 0; i < n; i++)
133 s[i] = c;
134 return s;
135}
136
137static void dec_key(struct btree_geo *geo, unsigned long *key)
138{
139 unsigned long val;
140 int i;
141
142 for (i = geo->keylen - 1; i >= 0; i--) {
143 val = key[i];
144 key[i] = val - 1;
145 if (val)
146 break;
147 }
148}
149
150static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
151{
152 return &node[n * geo->keylen];
153}
154
155static void *bval(struct btree_geo *geo, unsigned long *node, int n)
156{
157 return (void *)node[geo->no_longs + n];
158}
159
160static void setkey(struct btree_geo *geo, unsigned long *node, int n,
161 unsigned long *key)
162{
163 longcpy(bkey(geo, node, n), key, geo->keylen);
164}
165
166static void setval(struct btree_geo *geo, unsigned long *node, int n,
167 void *val)
168{
169 node[geo->no_longs + n] = (unsigned long) val;
170}
171
172static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
173{
174 longset(bkey(geo, node, n), 0, geo->keylen);
175 node[geo->no_longs + n] = 0;
176}
177
178static inline void __btree_init(struct btree_head *head)
179{
180 head->node = NULL;
181 head->height = 0;
182}
183
184void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
185{
186 __btree_init(head);
187 head->mempool = mempool;
188}
189EXPORT_SYMBOL_GPL(btree_init_mempool);
190
191int btree_init(struct btree_head *head)
192{
193 __btree_init(head);
194 head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
195 if (!head->mempool)
196 return -ENOMEM;
197 return 0;
198}
199EXPORT_SYMBOL_GPL(btree_init);
200
201void btree_destroy(struct btree_head *head)
202{
203 mempool_free(head->node, head->mempool);
204 mempool_destroy(head->mempool);
205 head->mempool = NULL;
206}
207EXPORT_SYMBOL_GPL(btree_destroy);
208
209void *btree_last(struct btree_head *head, struct btree_geo *geo,
210 unsigned long *key)
211{
212 int height = head->height;
213 unsigned long *node = head->node;
214
215 if (height == 0)
216 return NULL;
217
218 for ( ; height > 1; height--)
219 node = bval(geo, node, 0);
220
221 longcpy(key, bkey(geo, node, 0), geo->keylen);
222 return bval(geo, node, 0);
223}
224EXPORT_SYMBOL_GPL(btree_last);
225
226static int keycmp(struct btree_geo *geo, unsigned long *node, int pos,
227 unsigned long *key)
228{
229 return longcmp(bkey(geo, node, pos), key, geo->keylen);
230}
231
232static int keyzero(struct btree_geo *geo, unsigned long *key)
233{
234 int i;
235
236 for (i = 0; i < geo->keylen; i++)
237 if (key[i])
238 return 0;
239
240 return 1;
241}
242
243void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
244 unsigned long *key)
245{
246 int i, height = head->height;
247 unsigned long *node = head->node;
248
249 if (height == 0)
250 return NULL;
251
252 for ( ; height > 1; height--) {
253 for (i = 0; i < geo->no_pairs; i++)
254 if (keycmp(geo, node, i, key) <= 0)
255 break;
256 if (i == geo->no_pairs)
257 return NULL;
258 node = bval(geo, node, i);
259 if (!node)
260 return NULL;
261 }
262
263 if (!node)
264 return NULL;
265
266 for (i = 0; i < geo->no_pairs; i++)
267 if (keycmp(geo, node, i, key) == 0)
268 return bval(geo, node, i);
269 return NULL;
270}
271EXPORT_SYMBOL_GPL(btree_lookup);
272
273int btree_update(struct btree_head *head, struct btree_geo *geo,
274 unsigned long *key, void *val)
275{
276 int i, height = head->height;
277 unsigned long *node = head->node;
278
279 if (height == 0)
280 return -ENOENT;
281
282 for ( ; height > 1; height--) {
283 for (i = 0; i < geo->no_pairs; i++)
284 if (keycmp(geo, node, i, key) <= 0)
285 break;
286 if (i == geo->no_pairs)
287 return -ENOENT;
288 node = bval(geo, node, i);
289 if (!node)
290 return -ENOENT;
291 }
292
293 if (!node)
294 return -ENOENT;
295
296 for (i = 0; i < geo->no_pairs; i++)
297 if (keycmp(geo, node, i, key) == 0) {
298 setval(geo, node, i, val);
299 return 0;
300 }
301 return -ENOENT;
302}
303EXPORT_SYMBOL_GPL(btree_update);
304
305/*
306 * Usually this function is quite similar to normal lookup. But the key of
307 * a parent node may be smaller than the smallest key of all its siblings.
308 * In such a case we cannot just return NULL, as we have only proven that no
309 * key smaller than __key, but larger than this parent key exists.
310 * So we set __key to the parent key and retry. We have to use the smallest
311 * such parent key, which is the last parent key we encountered.
312 */
313void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
314 unsigned long *__key)
315{
316 int i, height;
317 unsigned long *node, *oldnode;
318 unsigned long *retry_key = NULL, key[MAX_KEYLEN];
319
320 if (keyzero(geo, __key))
321 return NULL;
322
323 if (head->height == 0)
324 return NULL;
325 longcpy(key, __key, geo->keylen);
326retry:
327 dec_key(geo, key);
328
329 node = head->node;
330 for (height = head->height ; height > 1; height--) {
331 for (i = 0; i < geo->no_pairs; i++)
332 if (keycmp(geo, node, i, key) <= 0)
333 break;
334 if (i == geo->no_pairs)
335 goto miss;
336 oldnode = node;
337 node = bval(geo, node, i);
338 if (!node)
339 goto miss;
340 retry_key = bkey(geo, oldnode, i);
341 }
342
343 if (!node)
344 goto miss;
345
346 for (i = 0; i < geo->no_pairs; i++) {
347 if (keycmp(geo, node, i, key) <= 0) {
348 if (bval(geo, node, i)) {
349 longcpy(__key, bkey(geo, node, i), geo->keylen);
350 return bval(geo, node, i);
351 } else
352 goto miss;
353 }
354 }
355miss:
356 if (retry_key) {
357 longcpy(key, retry_key, geo->keylen);
358 retry_key = NULL;
359 goto retry;
360 }
361 return NULL;
362}
363EXPORT_SYMBOL_GPL(btree_get_prev);
364
365static int getpos(struct btree_geo *geo, unsigned long *node,
366 unsigned long *key)
367{
368 int i;
369
370 for (i = 0; i < geo->no_pairs; i++) {
371 if (keycmp(geo, node, i, key) <= 0)
372 break;
373 }
374 return i;
375}
376
377static int getfill(struct btree_geo *geo, unsigned long *node, int start)
378{
379 int i;
380
381 for (i = start; i < geo->no_pairs; i++)
382 if (!bval(geo, node, i))
383 break;
384 return i;
385}
386
387/*
388 * locate the correct leaf node in the btree
389 */
390static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
391 unsigned long *key, int level)
392{
393 unsigned long *node = head->node;
394 int i, height;
395
396 for (height = head->height; height > level; height--) {
397 for (i = 0; i < geo->no_pairs; i++)
398 if (keycmp(geo, node, i, key) <= 0)
399 break;
400
401 if ((i == geo->no_pairs) || !bval(geo, node, i)) {
402 /* right-most key is too large, update it */
403 /* FIXME: If the right-most key on higher levels is
404 * always zero, this wouldn't be necessary. */
405 i--;
406 setkey(geo, node, i, key);
407 }
408 BUG_ON(i < 0);
409 node = bval(geo, node, i);
410 }
411 BUG_ON(!node);
412 return node;
413}
414
415static int btree_grow(struct btree_head *head, struct btree_geo *geo,
416 gfp_t gfp)
417{
418 unsigned long *node;
419 int fill;
420
421 node = btree_node_alloc(head, gfp);
422 if (!node)
423 return -ENOMEM;
424 if (head->node) {
425 fill = getfill(geo, head->node, 0);
426 setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
427 setval(geo, node, 0, head->node);
428 }
429 head->node = node;
430 head->height++;
431 return 0;
432}
433
434static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
435{
436 unsigned long *node;
437 int fill;
438
439 if (head->height <= 1)
440 return;
441
442 node = head->node;
443 fill = getfill(geo, node, 0);
444 BUG_ON(fill > 1);
445 head->node = bval(geo, node, 0);
446 head->height--;
447 mempool_free(node, head->mempool);
448}
449
450static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
451 unsigned long *key, void *val, int level,
452 gfp_t gfp)
453{
454 unsigned long *node;
455 int i, pos, fill, err;
456
457 BUG_ON(!val);
458 if (head->height < level) {
459 err = btree_grow(head, geo, gfp);
460 if (err)
461 return err;
462 }
463
464retry:
465 node = find_level(head, geo, key, level);
466 pos = getpos(geo, node, key);
467 fill = getfill(geo, node, pos);
468 /* two identical keys are not allowed */
469 BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
470
471 if (fill == geo->no_pairs) {
472 /* need to split node */
473 unsigned long *new;
474
475 new = btree_node_alloc(head, gfp);
476 if (!new)
477 return -ENOMEM;
478 err = btree_insert_level(head, geo,
479 bkey(geo, node, fill / 2 - 1),
480 new, level + 1, gfp);
481 if (err) {
482 mempool_free(new, head->mempool);
483 return err;
484 }
485 for (i = 0; i < fill / 2; i++) {
486 setkey(geo, new, i, bkey(geo, node, i));
487 setval(geo, new, i, bval(geo, node, i));
488 setkey(geo, node, i, bkey(geo, node, i + fill / 2));
489 setval(geo, node, i, bval(geo, node, i + fill / 2));
490 clearpair(geo, node, i + fill / 2);
491 }
492 if (fill & 1) {
493 setkey(geo, node, i, bkey(geo, node, fill - 1));
494 setval(geo, node, i, bval(geo, node, fill - 1));
495 clearpair(geo, node, fill - 1);
496 }
497 goto retry;
498 }
499 BUG_ON(fill >= geo->no_pairs);
500
501 /* shift and insert */
502 for (i = fill; i > pos; i--) {
503 setkey(geo, node, i, bkey(geo, node, i - 1));
504 setval(geo, node, i, bval(geo, node, i - 1));
505 }
506 setkey(geo, node, pos, key);
507 setval(geo, node, pos, val);
508
509 return 0;
510}
511
512int btree_insert(struct btree_head *head, struct btree_geo *geo,
513 unsigned long *key, void *val, gfp_t gfp)
514{
515 BUG_ON(!val);
516 return btree_insert_level(head, geo, key, val, 1, gfp);
517}
518EXPORT_SYMBOL_GPL(btree_insert);
519
520static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
521 unsigned long *key, int level);
522static void merge(struct btree_head *head, struct btree_geo *geo, int level,
523 unsigned long *left, int lfill,
524 unsigned long *right, int rfill,
525 unsigned long *parent, int lpos)
526{
527 int i;
528
529 for (i = 0; i < rfill; i++) {
530 /* Move all keys to the left */
531 setkey(geo, left, lfill + i, bkey(geo, right, i));
532 setval(geo, left, lfill + i, bval(geo, right, i));
533 }
534 /* Exchange left and right child in parent */
535 setval(geo, parent, lpos, right);
536 setval(geo, parent, lpos + 1, left);
537 /* Remove left (formerly right) child from parent */
538 btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
539 mempool_free(right, head->mempool);
540}
541
542static void rebalance(struct btree_head *head, struct btree_geo *geo,
543 unsigned long *key, int level, unsigned long *child, int fill)
544{
545 unsigned long *parent, *left = NULL, *right = NULL;
546 int i, no_left, no_right;
547
548 if (fill == 0) {
549 /* Because we don't steal entries from a neighbour, this case
550 * can happen. Parent node contains a single child, this
551 * node, so merging with a sibling never happens.
552 */
553 btree_remove_level(head, geo, key, level + 1);
554 mempool_free(child, head->mempool);
555 return;
556 }
557
558 parent = find_level(head, geo, key, level + 1);
559 i = getpos(geo, parent, key);
560 BUG_ON(bval(geo, parent, i) != child);
561
562 if (i > 0) {
563 left = bval(geo, parent, i - 1);
564 no_left = getfill(geo, left, 0);
565 if (fill + no_left <= geo->no_pairs) {
566 merge(head, geo, level,
567 left, no_left,
568 child, fill,
569 parent, i - 1);
570 return;
571 }
572 }
573 if (i + 1 < getfill(geo, parent, i)) {
574 right = bval(geo, parent, i + 1);
575 no_right = getfill(geo, right, 0);
576 if (fill + no_right <= geo->no_pairs) {
577 merge(head, geo, level,
578 child, fill,
579 right, no_right,
580 parent, i);
581 return;
582 }
583 }
584 /*
585 * We could also try to steal one entry from the left or right
586 * neighbor. By not doing so we changed the invariant from
587 * "all nodes are at least half full" to "no two neighboring
588 * nodes can be merged". Which means that the average fill of
589 * all nodes is still half or better.
590 */
591}
592
593static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
594 unsigned long *key, int level)
595{
596 unsigned long *node;
597 int i, pos, fill;
598 void *ret;
599
600 if (level > head->height) {
601 /* we recursed all the way up */
602 head->height = 0;
603 head->node = NULL;
604 return NULL;
605 }
606
607 node = find_level(head, geo, key, level);
608 pos = getpos(geo, node, key);
609 fill = getfill(geo, node, pos);
610 if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
611 return NULL;
612 ret = bval(geo, node, pos);
613
614 /* remove and shift */
615 for (i = pos; i < fill - 1; i++) {
616 setkey(geo, node, i, bkey(geo, node, i + 1));
617 setval(geo, node, i, bval(geo, node, i + 1));
618 }
619 clearpair(geo, node, fill - 1);
620
621 if (fill - 1 < geo->no_pairs / 2) {
622 if (level < head->height)
623 rebalance(head, geo, key, level, node, fill - 1);
624 else if (fill - 1 == 1)
625 btree_shrink(head, geo);
626 }
627
628 return ret;
629}
630
631void *btree_remove(struct btree_head *head, struct btree_geo *geo,
632 unsigned long *key)
633{
634 if (head->height == 0)
635 return NULL;
636
637 return btree_remove_level(head, geo, key, 1);
638}
639EXPORT_SYMBOL_GPL(btree_remove);
640
641int btree_merge(struct btree_head *target, struct btree_head *victim,
642 struct btree_geo *geo, gfp_t gfp)
643{
644 unsigned long key[MAX_KEYLEN];
645 unsigned long dup[MAX_KEYLEN];
646 void *val;
647 int err;
648
649 BUG_ON(target == victim);
650
651 if (!(target->node)) {
652 /* target is empty, just copy fields over */
653 target->node = victim->node;
654 target->height = victim->height;
655 __btree_init(victim);
656 return 0;
657 }
658
659 /* TODO: This needs some optimizations. Currently we do three tree
660 * walks to remove a single object from the victim.
661 */
662 for (;;) {
663 if (!btree_last(victim, geo, key))
664 break;
665 val = btree_lookup(victim, geo, key);
666 err = btree_insert(target, geo, key, val, gfp);
667 if (err)
668 return err;
669 /* We must make a copy of the key, as the original will get
670 * mangled inside btree_remove. */
671 longcpy(dup, key, geo->keylen);
672 btree_remove(victim, geo, dup);
673 }
674 return 0;
675}
676EXPORT_SYMBOL_GPL(btree_merge);
677
678static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
679 unsigned long *node, unsigned long opaque,
680 void (*func)(void *elem, unsigned long opaque,
681 unsigned long *key, size_t index,
682 void *func2),
683 void *func2, int reap, int height, size_t count)
684{
685 int i;
686 unsigned long *child;
687
688 for (i = 0; i < geo->no_pairs; i++) {
689 child = bval(geo, node, i);
690 if (!child)
691 break;
692 if (height > 1)
693 count = __btree_for_each(head, geo, child, opaque,
694 func, func2, reap, height - 1, count);
695 else
696 func(child, opaque, bkey(geo, node, i), count++,
697 func2);
698 }
699 if (reap)
700 mempool_free(node, head->mempool);
701 return count;
702}
703
704static void empty(void *elem, unsigned long opaque, unsigned long *key,
705 size_t index, void *func2)
706{
707}
708
709void visitorl(void *elem, unsigned long opaque, unsigned long *key,
710 size_t index, void *__func)
711{
712 visitorl_t func = __func;
713
714 func(elem, opaque, *key, index);
715}
716EXPORT_SYMBOL_GPL(visitorl);
717
718void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
719 size_t index, void *__func)
720{
721 visitor32_t func = __func;
722 u32 *key = (void *)__key;
723
724 func(elem, opaque, *key, index);
725}
726EXPORT_SYMBOL_GPL(visitor32);
727
728void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
729 size_t index, void *__func)
730{
731 visitor64_t func = __func;
732 u64 *key = (void *)__key;
733
734 func(elem, opaque, *key, index);
735}
736EXPORT_SYMBOL_GPL(visitor64);
737
738void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
739 size_t index, void *__func)
740{
741 visitor128_t func = __func;
742 u64 *key = (void *)__key;
743
744 func(elem, opaque, key[0], key[1], index);
745}
746EXPORT_SYMBOL_GPL(visitor128);
747
748size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
749 unsigned long opaque,
750 void (*func)(void *elem, unsigned long opaque,
751 unsigned long *key,
752 size_t index, void *func2),
753 void *func2)
754{
755 size_t count = 0;
756
757 if (!func2)
758 func = empty;
759 if (head->node)
760 count = __btree_for_each(head, geo, head->node, opaque, func,
761 func2, 0, head->height, 0);
762 return count;
763}
764EXPORT_SYMBOL_GPL(btree_visitor);
765
766size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
767 unsigned long opaque,
768 void (*func)(void *elem, unsigned long opaque,
769 unsigned long *key,
770 size_t index, void *func2),
771 void *func2)
772{
773 size_t count = 0;
774
775 if (!func2)
776 func = empty;
777 if (head->node)
778 count = __btree_for_each(head, geo, head->node, opaque, func,
779 func2, 1, head->height, 0);
780 __btree_init(head);
781 return count;
782}
783EXPORT_SYMBOL_GPL(btree_grim_visitor);
784
785static int __init btree_module_init(void)
786{
787 btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
788 SLAB_HWCACHE_ALIGN, NULL);
789 return 0;
790}
791
792static void __exit btree_module_exit(void)
793{
794 kmem_cache_destroy(btree_cachep);
795}
796
797/* If core code starts using btree, initialization should happen even earlier */
798module_init(btree_module_init);
799module_exit(btree_module_exit);
800
801MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
802MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");
803MODULE_LICENSE("GPL");