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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 <[email protected]>
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 val = btree_last(victim, geo, key);
657 if (!val)
658 break;
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 <[email protected]>");
795MODULE_AUTHOR("Johannes Berg <[email protected]>");