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v5.14.15
  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
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[MAX_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[MAX_KEYLEN];
643	unsigned long dup[MAX_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");
v6.13.7
  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 NODESIZE MAX(L1_CACHE_BYTES, 128)
 47
 48struct btree_geo {
 49	int keylen;
 50	int no_pairs;
 51	int no_longs;
 52};
 53
 54struct btree_geo btree_geo32 = {
 55	.keylen = 1,
 56	.no_pairs = NODESIZE / sizeof(long) / 2,
 57	.no_longs = NODESIZE / sizeof(long) / 2,
 58};
 59EXPORT_SYMBOL_GPL(btree_geo32);
 60
 61#define LONG_PER_U64 (64 / BITS_PER_LONG)
 62struct btree_geo btree_geo64 = {
 63	.keylen = LONG_PER_U64,
 64	.no_pairs = NODESIZE / sizeof(long) / (1 + LONG_PER_U64),
 65	.no_longs = LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + LONG_PER_U64)),
 66};
 67EXPORT_SYMBOL_GPL(btree_geo64);
 68
 69struct btree_geo btree_geo128 = {
 70	.keylen = 2 * LONG_PER_U64,
 71	.no_pairs = NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64),
 72	.no_longs = 2 * LONG_PER_U64 * (NODESIZE / sizeof(long) / (1 + 2 * LONG_PER_U64)),
 73};
 74EXPORT_SYMBOL_GPL(btree_geo128);
 75
 76#define MAX_KEYLEN	(2 * LONG_PER_U64)
 77
 78static struct kmem_cache *btree_cachep;
 79
 80void *btree_alloc(gfp_t gfp_mask, void *pool_data)
 81{
 82	return kmem_cache_alloc(btree_cachep, gfp_mask);
 83}
 84EXPORT_SYMBOL_GPL(btree_alloc);
 85
 86void btree_free(void *element, void *pool_data)
 87{
 88	kmem_cache_free(btree_cachep, element);
 89}
 90EXPORT_SYMBOL_GPL(btree_free);
 91
 92static unsigned long *btree_node_alloc(struct btree_head *head, gfp_t gfp)
 93{
 94	unsigned long *node;
 95
 96	node = mempool_alloc(head->mempool, gfp);
 97	if (likely(node))
 98		memset(node, 0, NODESIZE);
 99	return node;
100}
101
102static int longcmp(const unsigned long *l1, const unsigned long *l2, size_t n)
103{
104	size_t i;
105
106	for (i = 0; i < n; i++) {
107		if (l1[i] < l2[i])
108			return -1;
109		if (l1[i] > l2[i])
110			return 1;
111	}
112	return 0;
113}
114
115static unsigned long *longcpy(unsigned long *dest, const unsigned long *src,
116		size_t n)
117{
118	size_t i;
119
120	for (i = 0; i < n; i++)
121		dest[i] = src[i];
122	return dest;
123}
124
125static unsigned long *longset(unsigned long *s, unsigned long c, size_t n)
126{
127	size_t i;
128
129	for (i = 0; i < n; i++)
130		s[i] = c;
131	return s;
132}
133
134static void dec_key(struct btree_geo *geo, unsigned long *key)
135{
136	unsigned long val;
137	int i;
138
139	for (i = geo->keylen - 1; i >= 0; i--) {
140		val = key[i];
141		key[i] = val - 1;
142		if (val)
143			break;
144	}
145}
146
147static unsigned long *bkey(struct btree_geo *geo, unsigned long *node, int n)
148{
149	return &node[n * geo->keylen];
150}
151
152static void *bval(struct btree_geo *geo, unsigned long *node, int n)
153{
154	return (void *)node[geo->no_longs + n];
155}
156
157static void setkey(struct btree_geo *geo, unsigned long *node, int n,
158		   unsigned long *key)
159{
160	longcpy(bkey(geo, node, n), key, geo->keylen);
161}
162
163static void setval(struct btree_geo *geo, unsigned long *node, int n,
164		   void *val)
165{
166	node[geo->no_longs + n] = (unsigned long) val;
167}
168
169static void clearpair(struct btree_geo *geo, unsigned long *node, int n)
170{
171	longset(bkey(geo, node, n), 0, geo->keylen);
172	node[geo->no_longs + n] = 0;
173}
174
175static inline void __btree_init(struct btree_head *head)
176{
177	head->node = NULL;
178	head->height = 0;
179}
180
181void btree_init_mempool(struct btree_head *head, mempool_t *mempool)
182{
183	__btree_init(head);
184	head->mempool = mempool;
185}
186EXPORT_SYMBOL_GPL(btree_init_mempool);
187
188int btree_init(struct btree_head *head)
189{
190	__btree_init(head);
191	head->mempool = mempool_create(0, btree_alloc, btree_free, NULL);
192	if (!head->mempool)
193		return -ENOMEM;
194	return 0;
195}
196EXPORT_SYMBOL_GPL(btree_init);
197
198void btree_destroy(struct btree_head *head)
199{
200	mempool_free(head->node, head->mempool);
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
240static void *btree_lookup_node(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	return node;
260}
261
262void *btree_lookup(struct btree_head *head, struct btree_geo *geo,
263		unsigned long *key)
264{
265	int i;
266	unsigned long *node;
267
268	node = btree_lookup_node(head, geo, key);
269	if (!node)
270		return NULL;
271
272	for (i = 0; i < geo->no_pairs; i++)
273		if (keycmp(geo, node, i, key) == 0)
274			return bval(geo, node, i);
275	return NULL;
276}
277EXPORT_SYMBOL_GPL(btree_lookup);
278
279int btree_update(struct btree_head *head, struct btree_geo *geo,
280		 unsigned long *key, void *val)
281{
282	int i;
283	unsigned long *node;
 
 
 
 
 
 
 
 
 
 
 
 
 
 
284
285	node = btree_lookup_node(head, geo, key);
286	if (!node)
287		return -ENOENT;
288
289	for (i = 0; i < geo->no_pairs; i++)
290		if (keycmp(geo, node, i, key) == 0) {
291			setval(geo, node, i, val);
292			return 0;
293		}
294	return -ENOENT;
295}
296EXPORT_SYMBOL_GPL(btree_update);
297
298/*
299 * Usually this function is quite similar to normal lookup.  But the key of
300 * a parent node may be smaller than the smallest key of all its siblings.
301 * In such a case we cannot just return NULL, as we have only proven that no
302 * key smaller than __key, but larger than this parent key exists.
303 * So we set __key to the parent key and retry.  We have to use the smallest
304 * such parent key, which is the last parent key we encountered.
305 */
306void *btree_get_prev(struct btree_head *head, struct btree_geo *geo,
307		     unsigned long *__key)
308{
309	int i, height;
310	unsigned long *node, *oldnode;
311	unsigned long *retry_key = NULL, key[MAX_KEYLEN];
312
313	if (keyzero(geo, __key))
314		return NULL;
315
316	if (head->height == 0)
317		return NULL;
318	longcpy(key, __key, geo->keylen);
319retry:
320	dec_key(geo, key);
321
322	node = head->node;
323	for (height = head->height ; height > 1; height--) {
324		for (i = 0; i < geo->no_pairs; i++)
325			if (keycmp(geo, node, i, key) <= 0)
326				break;
327		if (i == geo->no_pairs)
328			goto miss;
329		oldnode = node;
330		node = bval(geo, node, i);
331		if (!node)
332			goto miss;
333		retry_key = bkey(geo, oldnode, i);
334	}
335
336	if (!node)
337		goto miss;
338
339	for (i = 0; i < geo->no_pairs; i++) {
340		if (keycmp(geo, node, i, key) <= 0) {
341			if (bval(geo, node, i)) {
342				longcpy(__key, bkey(geo, node, i), geo->keylen);
343				return bval(geo, node, i);
344			} else
345				goto miss;
346		}
347	}
348miss:
349	if (retry_key) {
350		longcpy(key, retry_key, geo->keylen);
351		retry_key = NULL;
352		goto retry;
353	}
354	return NULL;
355}
356EXPORT_SYMBOL_GPL(btree_get_prev);
357
358static int getpos(struct btree_geo *geo, unsigned long *node,
359		unsigned long *key)
360{
361	int i;
362
363	for (i = 0; i < geo->no_pairs; i++) {
364		if (keycmp(geo, node, i, key) <= 0)
365			break;
366	}
367	return i;
368}
369
370static int getfill(struct btree_geo *geo, unsigned long *node, int start)
371{
372	int i;
373
374	for (i = start; i < geo->no_pairs; i++)
375		if (!bval(geo, node, i))
376			break;
377	return i;
378}
379
380/*
381 * locate the correct leaf node in the btree
382 */
383static unsigned long *find_level(struct btree_head *head, struct btree_geo *geo,
384		unsigned long *key, int level)
385{
386	unsigned long *node = head->node;
387	int i, height;
388
389	for (height = head->height; height > level; height--) {
390		for (i = 0; i < geo->no_pairs; i++)
391			if (keycmp(geo, node, i, key) <= 0)
392				break;
393
394		if ((i == geo->no_pairs) || !bval(geo, node, i)) {
395			/* right-most key is too large, update it */
396			/* FIXME: If the right-most key on higher levels is
397			 * always zero, this wouldn't be necessary. */
398			i--;
399			setkey(geo, node, i, key);
400		}
401		BUG_ON(i < 0);
402		node = bval(geo, node, i);
403	}
404	BUG_ON(!node);
405	return node;
406}
407
408static int btree_grow(struct btree_head *head, struct btree_geo *geo,
409		      gfp_t gfp)
410{
411	unsigned long *node;
412	int fill;
413
414	node = btree_node_alloc(head, gfp);
415	if (!node)
416		return -ENOMEM;
417	if (head->node) {
418		fill = getfill(geo, head->node, 0);
419		setkey(geo, node, 0, bkey(geo, head->node, fill - 1));
420		setval(geo, node, 0, head->node);
421	}
422	head->node = node;
423	head->height++;
424	return 0;
425}
426
427static void btree_shrink(struct btree_head *head, struct btree_geo *geo)
428{
429	unsigned long *node;
430	int fill;
431
432	if (head->height <= 1)
433		return;
434
435	node = head->node;
436	fill = getfill(geo, node, 0);
437	BUG_ON(fill > 1);
438	head->node = bval(geo, node, 0);
439	head->height--;
440	mempool_free(node, head->mempool);
441}
442
443static int btree_insert_level(struct btree_head *head, struct btree_geo *geo,
444			      unsigned long *key, void *val, int level,
445			      gfp_t gfp)
446{
447	unsigned long *node;
448	int i, pos, fill, err;
449
450	BUG_ON(!val);
451	if (head->height < level) {
452		err = btree_grow(head, geo, gfp);
453		if (err)
454			return err;
455	}
456
457retry:
458	node = find_level(head, geo, key, level);
459	pos = getpos(geo, node, key);
460	fill = getfill(geo, node, pos);
461	/* two identical keys are not allowed */
462	BUG_ON(pos < fill && keycmp(geo, node, pos, key) == 0);
463
464	if (fill == geo->no_pairs) {
465		/* need to split node */
466		unsigned long *new;
467
468		new = btree_node_alloc(head, gfp);
469		if (!new)
470			return -ENOMEM;
471		err = btree_insert_level(head, geo,
472				bkey(geo, node, fill / 2 - 1),
473				new, level + 1, gfp);
474		if (err) {
475			mempool_free(new, head->mempool);
476			return err;
477		}
478		for (i = 0; i < fill / 2; i++) {
479			setkey(geo, new, i, bkey(geo, node, i));
480			setval(geo, new, i, bval(geo, node, i));
481			setkey(geo, node, i, bkey(geo, node, i + fill / 2));
482			setval(geo, node, i, bval(geo, node, i + fill / 2));
483			clearpair(geo, node, i + fill / 2);
484		}
485		if (fill & 1) {
486			setkey(geo, node, i, bkey(geo, node, fill - 1));
487			setval(geo, node, i, bval(geo, node, fill - 1));
488			clearpair(geo, node, fill - 1);
489		}
490		goto retry;
491	}
492	BUG_ON(fill >= geo->no_pairs);
493
494	/* shift and insert */
495	for (i = fill; i > pos; i--) {
496		setkey(geo, node, i, bkey(geo, node, i - 1));
497		setval(geo, node, i, bval(geo, node, i - 1));
498	}
499	setkey(geo, node, pos, key);
500	setval(geo, node, pos, val);
501
502	return 0;
503}
504
505int btree_insert(struct btree_head *head, struct btree_geo *geo,
506		unsigned long *key, void *val, gfp_t gfp)
507{
508	BUG_ON(!val);
509	return btree_insert_level(head, geo, key, val, 1, gfp);
510}
511EXPORT_SYMBOL_GPL(btree_insert);
512
513static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
514		unsigned long *key, int level);
515static void merge(struct btree_head *head, struct btree_geo *geo, int level,
516		unsigned long *left, int lfill,
517		unsigned long *right, int rfill,
518		unsigned long *parent, int lpos)
519{
520	int i;
521
522	for (i = 0; i < rfill; i++) {
523		/* Move all keys to the left */
524		setkey(geo, left, lfill + i, bkey(geo, right, i));
525		setval(geo, left, lfill + i, bval(geo, right, i));
526	}
527	/* Exchange left and right child in parent */
528	setval(geo, parent, lpos, right);
529	setval(geo, parent, lpos + 1, left);
530	/* Remove left (formerly right) child from parent */
531	btree_remove_level(head, geo, bkey(geo, parent, lpos), level + 1);
532	mempool_free(right, head->mempool);
533}
534
535static void rebalance(struct btree_head *head, struct btree_geo *geo,
536		unsigned long *key, int level, unsigned long *child, int fill)
537{
538	unsigned long *parent, *left = NULL, *right = NULL;
539	int i, no_left, no_right;
540
541	if (fill == 0) {
542		/* Because we don't steal entries from a neighbour, this case
543		 * can happen.  Parent node contains a single child, this
544		 * node, so merging with a sibling never happens.
545		 */
546		btree_remove_level(head, geo, key, level + 1);
547		mempool_free(child, head->mempool);
548		return;
549	}
550
551	parent = find_level(head, geo, key, level + 1);
552	i = getpos(geo, parent, key);
553	BUG_ON(bval(geo, parent, i) != child);
554
555	if (i > 0) {
556		left = bval(geo, parent, i - 1);
557		no_left = getfill(geo, left, 0);
558		if (fill + no_left <= geo->no_pairs) {
559			merge(head, geo, level,
560					left, no_left,
561					child, fill,
562					parent, i - 1);
563			return;
564		}
565	}
566	if (i + 1 < getfill(geo, parent, i)) {
567		right = bval(geo, parent, i + 1);
568		no_right = getfill(geo, right, 0);
569		if (fill + no_right <= geo->no_pairs) {
570			merge(head, geo, level,
571					child, fill,
572					right, no_right,
573					parent, i);
574			return;
575		}
576	}
577	/*
578	 * We could also try to steal one entry from the left or right
579	 * neighbor.  By not doing so we changed the invariant from
580	 * "all nodes are at least half full" to "no two neighboring
581	 * nodes can be merged".  Which means that the average fill of
582	 * all nodes is still half or better.
583	 */
584}
585
586static void *btree_remove_level(struct btree_head *head, struct btree_geo *geo,
587		unsigned long *key, int level)
588{
589	unsigned long *node;
590	int i, pos, fill;
591	void *ret;
592
593	if (level > head->height) {
594		/* we recursed all the way up */
595		head->height = 0;
596		head->node = NULL;
597		return NULL;
598	}
599
600	node = find_level(head, geo, key, level);
601	pos = getpos(geo, node, key);
602	fill = getfill(geo, node, pos);
603	if ((level == 1) && (keycmp(geo, node, pos, key) != 0))
604		return NULL;
605	ret = bval(geo, node, pos);
606
607	/* remove and shift */
608	for (i = pos; i < fill - 1; i++) {
609		setkey(geo, node, i, bkey(geo, node, i + 1));
610		setval(geo, node, i, bval(geo, node, i + 1));
611	}
612	clearpair(geo, node, fill - 1);
613
614	if (fill - 1 < geo->no_pairs / 2) {
615		if (level < head->height)
616			rebalance(head, geo, key, level, node, fill - 1);
617		else if (fill - 1 == 1)
618			btree_shrink(head, geo);
619	}
620
621	return ret;
622}
623
624void *btree_remove(struct btree_head *head, struct btree_geo *geo,
625		unsigned long *key)
626{
627	if (head->height == 0)
628		return NULL;
629
630	return btree_remove_level(head, geo, key, 1);
631}
632EXPORT_SYMBOL_GPL(btree_remove);
633
634int btree_merge(struct btree_head *target, struct btree_head *victim,
635		struct btree_geo *geo, gfp_t gfp)
636{
637	unsigned long key[MAX_KEYLEN];
638	unsigned long dup[MAX_KEYLEN];
639	void *val;
640	int err;
641
642	BUG_ON(target == victim);
643
644	if (!(target->node)) {
645		/* target is empty, just copy fields over */
646		target->node = victim->node;
647		target->height = victim->height;
648		__btree_init(victim);
649		return 0;
650	}
651
652	/* TODO: This needs some optimizations.  Currently we do three tree
653	 * walks to remove a single object from the victim.
654	 */
655	for (;;) {
656		if (!btree_last(victim, geo, key))
657			break;
658		val = btree_lookup(victim, geo, key);
659		err = btree_insert(target, geo, key, val, gfp);
660		if (err)
661			return err;
662		/* We must make a copy of the key, as the original will get
663		 * mangled inside btree_remove. */
664		longcpy(dup, key, geo->keylen);
665		btree_remove(victim, geo, dup);
666	}
667	return 0;
668}
669EXPORT_SYMBOL_GPL(btree_merge);
670
671static size_t __btree_for_each(struct btree_head *head, struct btree_geo *geo,
672			       unsigned long *node, unsigned long opaque,
673			       void (*func)(void *elem, unsigned long opaque,
674					    unsigned long *key, size_t index,
675					    void *func2),
676			       void *func2, int reap, int height, size_t count)
677{
678	int i;
679	unsigned long *child;
680
681	for (i = 0; i < geo->no_pairs; i++) {
682		child = bval(geo, node, i);
683		if (!child)
684			break;
685		if (height > 1)
686			count = __btree_for_each(head, geo, child, opaque,
687					func, func2, reap, height - 1, count);
688		else
689			func(child, opaque, bkey(geo, node, i), count++,
690					func2);
691	}
692	if (reap)
693		mempool_free(node, head->mempool);
694	return count;
695}
696
697static void empty(void *elem, unsigned long opaque, unsigned long *key,
698		  size_t index, void *func2)
699{
700}
701
702void visitorl(void *elem, unsigned long opaque, unsigned long *key,
703	      size_t index, void *__func)
704{
705	visitorl_t func = __func;
706
707	func(elem, opaque, *key, index);
708}
709EXPORT_SYMBOL_GPL(visitorl);
710
711void visitor32(void *elem, unsigned long opaque, unsigned long *__key,
712	       size_t index, void *__func)
713{
714	visitor32_t func = __func;
715	u32 *key = (void *)__key;
716
717	func(elem, opaque, *key, index);
718}
719EXPORT_SYMBOL_GPL(visitor32);
720
721void visitor64(void *elem, unsigned long opaque, unsigned long *__key,
722	       size_t index, void *__func)
723{
724	visitor64_t func = __func;
725	u64 *key = (void *)__key;
726
727	func(elem, opaque, *key, index);
728}
729EXPORT_SYMBOL_GPL(visitor64);
730
731void visitor128(void *elem, unsigned long opaque, unsigned long *__key,
732		size_t index, void *__func)
733{
734	visitor128_t func = __func;
735	u64 *key = (void *)__key;
736
737	func(elem, opaque, key[0], key[1], index);
738}
739EXPORT_SYMBOL_GPL(visitor128);
740
741size_t btree_visitor(struct btree_head *head, struct btree_geo *geo,
742		     unsigned long opaque,
743		     void (*func)(void *elem, unsigned long opaque,
744		     		  unsigned long *key,
745		     		  size_t index, void *func2),
746		     void *func2)
747{
748	size_t count = 0;
749
750	if (!func2)
751		func = empty;
752	if (head->node)
753		count = __btree_for_each(head, geo, head->node, opaque, func,
754				func2, 0, head->height, 0);
755	return count;
756}
757EXPORT_SYMBOL_GPL(btree_visitor);
758
759size_t btree_grim_visitor(struct btree_head *head, struct btree_geo *geo,
760			  unsigned long opaque,
761			  void (*func)(void *elem, unsigned long opaque,
762				       unsigned long *key,
763				       size_t index, void *func2),
764			  void *func2)
765{
766	size_t count = 0;
767
768	if (!func2)
769		func = empty;
770	if (head->node)
771		count = __btree_for_each(head, geo, head->node, opaque, func,
772				func2, 1, head->height, 0);
773	__btree_init(head);
774	return count;
775}
776EXPORT_SYMBOL_GPL(btree_grim_visitor);
777
778static int __init btree_module_init(void)
779{
780	btree_cachep = kmem_cache_create("btree_node", NODESIZE, 0,
781			SLAB_HWCACHE_ALIGN, NULL);
782	return 0;
783}
784
785static void __exit btree_module_exit(void)
786{
787	kmem_cache_destroy(btree_cachep);
788}
789
790/* If core code starts using btree, initialization should happen even earlier */
791module_init(btree_module_init);
792module_exit(btree_module_exit);
793
794MODULE_AUTHOR("Joern Engel <joern@logfs.org>");
795MODULE_AUTHOR("Johannes Berg <johannes@sipsolutions.net>");