Loading...
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>");
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>");