Line data Source code
1 : // SPDX-License-Identifier: GPL-2.0-or-later
2 : /*
3 : Red Black Trees
4 : (C) 1999 Andrea Arcangeli <andrea@suse.de>
5 : (C) 2002 David Woodhouse <dwmw2@infradead.org>
6 : (C) 2012 Michel Lespinasse <walken@google.com>
7 :
8 :
9 : linux/lib/rbtree.c
10 : */
11 :
12 : #include <linux/rbtree_augmented.h>
13 : #include <linux/export.h>
14 :
15 : /*
16 : * red-black trees properties: https://en.wikipedia.org/wiki/Rbtree
17 : *
18 : * 1) A node is either red or black
19 : * 2) The root is black
20 : * 3) All leaves (NULL) are black
21 : * 4) Both children of every red node are black
22 : * 5) Every simple path from root to leaves contains the same number
23 : * of black nodes.
24 : *
25 : * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
26 : * consecutive red nodes in a path and every red node is therefore followed by
27 : * a black. So if B is the number of black nodes on every simple path (as per
28 : * 5), then the longest possible path due to 4 is 2B.
29 : *
30 : * We shall indicate color with case, where black nodes are uppercase and red
31 : * nodes will be lowercase. Unknown color nodes shall be drawn as red within
32 : * parentheses and have some accompanying text comment.
33 : */
34 :
35 : /*
36 : * Notes on lockless lookups:
37 : *
38 : * All stores to the tree structure (rb_left and rb_right) must be done using
39 : * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
40 : * tree structure as seen in program order.
41 : *
42 : * These two requirements will allow lockless iteration of the tree -- not
43 : * correct iteration mind you, tree rotations are not atomic so a lookup might
44 : * miss entire subtrees.
45 : *
46 : * But they do guarantee that any such traversal will only see valid elements
47 : * and that it will indeed complete -- does not get stuck in a loop.
48 : *
49 : * It also guarantees that if the lookup returns an element it is the 'correct'
50 : * one. But not returning an element does _NOT_ mean it's not present.
51 : *
52 : * NOTE:
53 : *
54 : * Stores to __rb_parent_color are not important for simple lookups so those
55 : * are left undone as of now. Nor did I check for loops involving parent
56 : * pointers.
57 : */
58 :
59 : static inline void rb_set_black(struct rb_node *rb)
60 : {
61 4 : rb->__rb_parent_color += RB_BLACK;
62 : }
63 :
64 : static inline struct rb_node *rb_red_parent(struct rb_node *red)
65 : {
66 15247 : return (struct rb_node *)red->__rb_parent_color;
67 : }
68 :
69 : /*
70 : * Helper function for rotations:
71 : * - old's parent and color get assigned to new
72 : * - old gets assigned new as a parent and 'color' as a color.
73 : */
74 : static inline void
75 : __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
76 : struct rb_root *root, int color)
77 : {
78 2603 : struct rb_node *parent = rb_parent(old);
79 2603 : new->__rb_parent_color = old->__rb_parent_color;
80 5206 : rb_set_parent_color(old, new, color);
81 11 : __rb_change_child(old, new, parent, root);
82 : }
83 :
84 : static __always_inline void
85 : __rb_insert(struct rb_node *node, struct rb_root *root,
86 : void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
87 : {
88 19672 : struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
89 :
90 : while (true) {
91 : /*
92 : * Loop invariant: node is red.
93 : */
94 12661 : if (unlikely(!parent)) {
95 : /*
96 : * The inserted node is root. Either this is the
97 : * first node, or we recursed at Case 1 below and
98 : * are no longer violating 4).
99 : */
100 3340 : rb_set_parent_color(node, NULL, RB_BLACK);
101 : break;
102 : }
103 :
104 : /*
105 : * If there is a black parent, we are done.
106 : * Otherwise, take some corrective action as,
107 : * per 4), we don't want a red root or two
108 : * consecutive red nodes.
109 : */
110 9321 : if(rb_is_black(parent))
111 : break;
112 :
113 10822 : gparent = rb_red_parent(parent);
114 :
115 5411 : tmp = gparent->rb_right;
116 5411 : if (parent != tmp) { /* parent == gparent->rb_left */
117 2189 : if (tmp && rb_is_red(tmp)) {
118 : /*
119 : * Case 1 - node's uncle is red (color flips).
120 : *
121 : * G g
122 : * / \ / \
123 : * p u --> P U
124 : * / /
125 : * n n
126 : *
127 : * However, since g's parent might be red, and
128 : * 4) does not allow this, we need to recurse
129 : * at g.
130 : */
131 2862 : rb_set_parent_color(tmp, gparent, RB_BLACK);
132 2862 : rb_set_parent_color(parent, gparent, RB_BLACK);
133 1431 : node = gparent;
134 1431 : parent = rb_parent(node);
135 2862 : rb_set_parent_color(node, parent, RB_RED);
136 1431 : continue;
137 : }
138 :
139 758 : tmp = parent->rb_right;
140 758 : if (node == tmp) {
141 : /*
142 : * Case 2 - node's uncle is black and node is
143 : * the parent's right child (left rotate at parent).
144 : *
145 : * G G
146 : * / \ / \
147 : * p U --> n U
148 : * \ /
149 : * n p
150 : *
151 : * This still leaves us in violation of 4), the
152 : * continuation into Case 3 will fix that.
153 : */
154 338 : tmp = node->rb_left;
155 338 : WRITE_ONCE(parent->rb_right, tmp);
156 338 : WRITE_ONCE(node->rb_left, parent);
157 338 : if (tmp)
158 76 : rb_set_parent_color(tmp, parent,
159 : RB_BLACK);
160 676 : rb_set_parent_color(parent, node, RB_RED);
161 338 : augment_rotate(parent, node);
162 338 : parent = node;
163 338 : tmp = node->rb_right;
164 : }
165 :
166 : /*
167 : * Case 3 - node's uncle is black and node is
168 : * the parent's left child (right rotate at gparent).
169 : *
170 : * G P
171 : * / \ / \
172 : * p U --> n g
173 : * / \
174 : * n U
175 : */
176 758 : WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
177 758 : WRITE_ONCE(parent->rb_right, gparent);
178 758 : if (tmp)
179 166 : rb_set_parent_color(tmp, gparent, RB_BLACK);
180 8 : __rb_rotate_set_parents(gparent, parent, root, RB_RED);
181 8 : augment_rotate(gparent, parent);
182 : break;
183 : } else {
184 3222 : tmp = gparent->rb_left;
185 3222 : if (tmp && rb_is_red(tmp)) {
186 : /* Case 1 - color flips */
187 2788 : rb_set_parent_color(tmp, gparent, RB_BLACK);
188 2788 : rb_set_parent_color(parent, gparent, RB_BLACK);
189 1394 : node = gparent;
190 1394 : parent = rb_parent(node);
191 2788 : rb_set_parent_color(node, parent, RB_RED);
192 1394 : continue;
193 : }
194 :
195 1828 : tmp = parent->rb_left;
196 1828 : if (node == tmp) {
197 : /* Case 2 - right rotate at parent */
198 1521 : tmp = node->rb_right;
199 1521 : WRITE_ONCE(parent->rb_left, tmp);
200 1521 : WRITE_ONCE(node->rb_right, parent);
201 1521 : if (tmp)
202 30 : rb_set_parent_color(tmp, parent,
203 : RB_BLACK);
204 3042 : rb_set_parent_color(parent, node, RB_RED);
205 1521 : augment_rotate(parent, node);
206 1521 : parent = node;
207 1521 : tmp = node->rb_left;
208 : }
209 :
210 : /* Case 3 - left rotate at gparent */
211 1828 : WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
212 1828 : WRITE_ONCE(parent->rb_left, gparent);
213 1828 : if (tmp)
214 87 : rb_set_parent_color(tmp, gparent, RB_BLACK);
215 3 : __rb_rotate_set_parents(gparent, parent, root, RB_RED);
216 3 : augment_rotate(gparent, parent);
217 : break;
218 : }
219 : }
220 : }
221 :
222 : /*
223 : * Inline version for rb_erase() use - we want to be able to inline
224 : * and eliminate the dummy_rotate callback there
225 : */
226 : static __always_inline void
227 : ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
228 : void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
229 : {
230 0 : struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
231 :
232 : while (true) {
233 : /*
234 : * Loop invariants:
235 : * - node is black (or NULL on first iteration)
236 : * - node is not the root (parent is not NULL)
237 : * - All leaf paths going through parent and node have a
238 : * black node count that is 1 lower than other leaf paths.
239 : */
240 41 : sibling = parent->rb_right;
241 41 : if (node != sibling) { /* node == parent->rb_left */
242 3 : if (rb_is_red(sibling)) {
243 : /*
244 : * Case 1 - left rotate at parent
245 : *
246 : * P S
247 : * / \ / \
248 : * N s --> p Sr
249 : * / \ / \
250 : * Sl Sr N Sl
251 : */
252 0 : tmp1 = sibling->rb_left;
253 0 : WRITE_ONCE(parent->rb_right, tmp1);
254 0 : WRITE_ONCE(sibling->rb_left, parent);
255 0 : rb_set_parent_color(tmp1, parent, RB_BLACK);
256 0 : __rb_rotate_set_parents(parent, sibling, root,
257 : RB_RED);
258 0 : augment_rotate(parent, sibling);
259 0 : sibling = tmp1;
260 : }
261 3 : tmp1 = sibling->rb_right;
262 3 : if (!tmp1 || rb_is_black(tmp1)) {
263 3 : tmp2 = sibling->rb_left;
264 3 : if (!tmp2 || rb_is_black(tmp2)) {
265 : /*
266 : * Case 2 - sibling color flip
267 : * (p could be either color here)
268 : *
269 : * (p) (p)
270 : * / \ / \
271 : * N S --> N s
272 : * / \ / \
273 : * Sl Sr Sl Sr
274 : *
275 : * This leaves us violating 5) which
276 : * can be fixed by flipping p to black
277 : * if it was red, or by recursing at p.
278 : * p is red when coming from Case 1.
279 : */
280 4 : rb_set_parent_color(sibling, parent,
281 : RB_RED);
282 2 : if (rb_is_red(parent))
283 0 : rb_set_black(parent);
284 : else {
285 2 : node = parent;
286 2 : parent = rb_parent(node);
287 2 : if (parent)
288 0 : continue;
289 : }
290 : break;
291 : }
292 : /*
293 : * Case 3 - right rotate at sibling
294 : * (p could be either color here)
295 : *
296 : * (p) (p)
297 : * / \ / \
298 : * N S --> N sl
299 : * / \ \
300 : * sl Sr S
301 : * \
302 : * Sr
303 : *
304 : * Note: p might be red, and then both
305 : * p and sl are red after rotation(which
306 : * breaks property 4). This is fixed in
307 : * Case 4 (in __rb_rotate_set_parents()
308 : * which set sl the color of p
309 : * and set p RB_BLACK)
310 : *
311 : * (p) (sl)
312 : * / \ / \
313 : * N sl --> P S
314 : * \ / \
315 : * S N Sr
316 : * \
317 : * Sr
318 : */
319 1 : tmp1 = tmp2->rb_right;
320 1 : WRITE_ONCE(sibling->rb_left, tmp1);
321 1 : WRITE_ONCE(tmp2->rb_right, sibling);
322 1 : WRITE_ONCE(parent->rb_right, tmp2);
323 1 : if (tmp1)
324 0 : rb_set_parent_color(tmp1, sibling,
325 : RB_BLACK);
326 0 : augment_rotate(sibling, tmp2);
327 0 : tmp1 = sibling;
328 0 : sibling = tmp2;
329 : }
330 : /*
331 : * Case 4 - left rotate at parent + color flips
332 : * (p and sl could be either color here.
333 : * After rotation, p becomes black, s acquires
334 : * p's color, and sl keeps its color)
335 : *
336 : * (p) (s)
337 : * / \ / \
338 : * N S --> P Sr
339 : * / \ / \
340 : * (sl) sr N (sl)
341 : */
342 1 : tmp2 = sibling->rb_left;
343 1 : WRITE_ONCE(parent->rb_right, tmp2);
344 1 : WRITE_ONCE(sibling->rb_left, parent);
345 2 : rb_set_parent_color(tmp1, sibling, RB_BLACK);
346 1 : if (tmp2)
347 0 : rb_set_parent(tmp2, parent);
348 0 : __rb_rotate_set_parents(parent, sibling, root,
349 : RB_BLACK);
350 0 : augment_rotate(parent, sibling);
351 : break;
352 : } else {
353 38 : sibling = parent->rb_left;
354 38 : if (rb_is_red(sibling)) {
355 : /* Case 1 - right rotate at parent */
356 4 : tmp1 = sibling->rb_right;
357 4 : WRITE_ONCE(parent->rb_left, tmp1);
358 4 : WRITE_ONCE(sibling->rb_right, parent);
359 8 : rb_set_parent_color(tmp1, parent, RB_BLACK);
360 0 : __rb_rotate_set_parents(parent, sibling, root,
361 : RB_RED);
362 0 : augment_rotate(parent, sibling);
363 0 : sibling = tmp1;
364 : }
365 38 : tmp1 = sibling->rb_left;
366 38 : if (!tmp1 || rb_is_black(tmp1)) {
367 28 : tmp2 = sibling->rb_right;
368 28 : if (!tmp2 || rb_is_black(tmp2)) {
369 : /* Case 2 - sibling color flip */
370 52 : rb_set_parent_color(sibling, parent,
371 : RB_RED);
372 26 : if (rb_is_red(parent))
373 4 : rb_set_black(parent);
374 : else {
375 22 : node = parent;
376 22 : parent = rb_parent(node);
377 22 : if (parent)
378 0 : continue;
379 : }
380 : break;
381 : }
382 : /* Case 3 - left rotate at sibling */
383 2 : tmp1 = tmp2->rb_left;
384 2 : WRITE_ONCE(sibling->rb_right, tmp1);
385 2 : WRITE_ONCE(tmp2->rb_left, sibling);
386 2 : WRITE_ONCE(parent->rb_left, tmp2);
387 2 : if (tmp1)
388 0 : rb_set_parent_color(tmp1, sibling,
389 : RB_BLACK);
390 0 : augment_rotate(sibling, tmp2);
391 0 : tmp1 = sibling;
392 0 : sibling = tmp2;
393 : }
394 : /* Case 4 - right rotate at parent + color flips */
395 12 : tmp2 = sibling->rb_right;
396 12 : WRITE_ONCE(parent->rb_left, tmp2);
397 12 : WRITE_ONCE(sibling->rb_right, parent);
398 24 : rb_set_parent_color(tmp1, sibling, RB_BLACK);
399 12 : if (tmp2)
400 2 : rb_set_parent(tmp2, parent);
401 0 : __rb_rotate_set_parents(parent, sibling, root,
402 : RB_BLACK);
403 0 : augment_rotate(parent, sibling);
404 : break;
405 : }
406 : }
407 : }
408 :
409 : /* Non-inline version for rb_erase_augmented() use */
410 0 : void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
411 : void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
412 : {
413 0 : ____rb_erase_color(parent, root, augment_rotate);
414 0 : }
415 : EXPORT_SYMBOL(__rb_erase_color);
416 :
417 : /*
418 : * Non-augmented rbtree manipulation functions.
419 : *
420 : * We use dummy augmented callbacks here, and have the compiler optimize them
421 : * out of the rb_insert_color() and rb_erase() function definitions.
422 : */
423 :
424 : static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
425 : static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
426 : static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
427 :
428 : static const struct rb_augment_callbacks dummy_callbacks = {
429 : .propagate = dummy_propagate,
430 : .copy = dummy_copy,
431 : .rotate = dummy_rotate
432 : };
433 :
434 9819 : void rb_insert_color(struct rb_node *node, struct rb_root *root)
435 : {
436 9819 : __rb_insert(node, root, dummy_rotate);
437 9819 : }
438 : EXPORT_SYMBOL(rb_insert_color);
439 :
440 1246 : void rb_erase(struct rb_node *node, struct rb_root *root)
441 : {
442 : struct rb_node *rebalance;
443 1246 : rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
444 1246 : if (rebalance)
445 : ____rb_erase_color(rebalance, root, dummy_rotate);
446 1246 : }
447 : EXPORT_SYMBOL(rb_erase);
448 :
449 : /*
450 : * Augmented rbtree manipulation functions.
451 : *
452 : * This instantiates the same __always_inline functions as in the non-augmented
453 : * case, but this time with user-defined callbacks.
454 : */
455 :
456 17 : void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
457 : void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
458 : {
459 17 : __rb_insert(node, root, augment_rotate);
460 17 : }
461 : EXPORT_SYMBOL(__rb_insert_augmented);
462 :
463 : /*
464 : * This function returns the first node (in sort order) of the tree.
465 : */
466 1391 : struct rb_node *rb_first(const struct rb_root *root)
467 : {
468 : struct rb_node *n;
469 :
470 1391 : n = root->rb_node;
471 1391 : if (!n)
472 : return NULL;
473 0 : while (n->rb_left)
474 : n = n->rb_left;
475 : return n;
476 : }
477 : EXPORT_SYMBOL(rb_first);
478 :
479 0 : struct rb_node *rb_last(const struct rb_root *root)
480 : {
481 : struct rb_node *n;
482 :
483 0 : n = root->rb_node;
484 0 : if (!n)
485 : return NULL;
486 0 : while (n->rb_right)
487 : n = n->rb_right;
488 : return n;
489 : }
490 : EXPORT_SYMBOL(rb_last);
491 :
492 1033 : struct rb_node *rb_next(const struct rb_node *node)
493 : {
494 : struct rb_node *parent;
495 :
496 1033 : if (RB_EMPTY_NODE(node))
497 : return NULL;
498 :
499 : /*
500 : * If we have a right-hand child, go down and then left as far
501 : * as we can.
502 : */
503 1033 : if (node->rb_right) {
504 : node = node->rb_right;
505 342 : while (node->rb_left)
506 : node = node->rb_left;
507 : return (struct rb_node *)node;
508 : }
509 :
510 : /*
511 : * No right-hand children. Everything down and left is smaller than us,
512 : * so any 'next' node must be in the general direction of our parent.
513 : * Go up the tree; any time the ancestor is a right-hand child of its
514 : * parent, keep going up. First time it's a left-hand child of its
515 : * parent, said parent is our 'next' node.
516 : */
517 691 : while ((parent = rb_parent(node)) && node == parent->rb_right)
518 : node = parent;
519 :
520 : return parent;
521 : }
522 : EXPORT_SYMBOL(rb_next);
523 :
524 0 : struct rb_node *rb_prev(const struct rb_node *node)
525 : {
526 : struct rb_node *parent;
527 :
528 0 : if (RB_EMPTY_NODE(node))
529 : return NULL;
530 :
531 : /*
532 : * If we have a left-hand child, go down and then right as far
533 : * as we can.
534 : */
535 0 : if (node->rb_left) {
536 : node = node->rb_left;
537 0 : while (node->rb_right)
538 : node = node->rb_right;
539 : return (struct rb_node *)node;
540 : }
541 :
542 : /*
543 : * No left-hand children. Go up till we find an ancestor which
544 : * is a right-hand child of its parent.
545 : */
546 0 : while ((parent = rb_parent(node)) && node == parent->rb_left)
547 : node = parent;
548 :
549 : return parent;
550 : }
551 : EXPORT_SYMBOL(rb_prev);
552 :
553 0 : void rb_replace_node(struct rb_node *victim, struct rb_node *new,
554 : struct rb_root *root)
555 : {
556 0 : struct rb_node *parent = rb_parent(victim);
557 :
558 : /* Copy the pointers/colour from the victim to the replacement */
559 0 : *new = *victim;
560 :
561 : /* Set the surrounding nodes to point to the replacement */
562 0 : if (victim->rb_left)
563 0 : rb_set_parent(victim->rb_left, new);
564 0 : if (victim->rb_right)
565 0 : rb_set_parent(victim->rb_right, new);
566 0 : __rb_change_child(victim, new, parent, root);
567 0 : }
568 : EXPORT_SYMBOL(rb_replace_node);
569 :
570 0 : void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
571 : struct rb_root *root)
572 : {
573 0 : struct rb_node *parent = rb_parent(victim);
574 :
575 : /* Copy the pointers/colour from the victim to the replacement */
576 0 : *new = *victim;
577 :
578 : /* Set the surrounding nodes to point to the replacement */
579 0 : if (victim->rb_left)
580 0 : rb_set_parent(victim->rb_left, new);
581 0 : if (victim->rb_right)
582 0 : rb_set_parent(victim->rb_right, new);
583 :
584 : /* Set the parent's pointer to the new node last after an RCU barrier
585 : * so that the pointers onwards are seen to be set correctly when doing
586 : * an RCU walk over the tree.
587 : */
588 0 : __rb_change_child_rcu(victim, new, parent, root);
589 0 : }
590 : EXPORT_SYMBOL(rb_replace_node_rcu);
591 :
592 : static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
593 : {
594 : for (;;) {
595 0 : if (node->rb_left)
596 : node = node->rb_left;
597 0 : else if (node->rb_right)
598 : node = node->rb_right;
599 : else
600 : return (struct rb_node *)node;
601 : }
602 : }
603 :
604 0 : struct rb_node *rb_next_postorder(const struct rb_node *node)
605 : {
606 : const struct rb_node *parent;
607 0 : if (!node)
608 : return NULL;
609 0 : parent = rb_parent(node);
610 :
611 : /* If we're sitting on node, we've already seen our children */
612 0 : if (parent && node == parent->rb_left && parent->rb_right) {
613 : /* If we are the parent's left node, go to the parent's right
614 : * node then all the way down to the left */
615 : return rb_left_deepest_node(parent->rb_right);
616 : } else
617 : /* Otherwise we are the parent's right node, and the parent
618 : * should be next */
619 : return (struct rb_node *)parent;
620 : }
621 : EXPORT_SYMBOL(rb_next_postorder);
622 :
623 0 : struct rb_node *rb_first_postorder(const struct rb_root *root)
624 : {
625 0 : if (!root->rb_node)
626 : return NULL;
627 :
628 : return rb_left_deepest_node(root->rb_node);
629 : }
630 : EXPORT_SYMBOL(rb_first_postorder);
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