1/*
2 Red Black Trees
3 (C) 1999 Andrea Arcangeli <andrea@suse.de>
4 (C) 2002 David Woodhouse <dwmw2@infradead.org>
5 (C) 2012 Michel Lespinasse <walken@google.com>
6
7 This program is free software; you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation; either version 2 of the License, or
10 (at your option) any later version.
11
12 This program is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
16
17 You should have received a copy of the GNU General Public License
18 along with this program; if not, write to the Free Software
19 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20
21 linux/lib/rbtree.c
22*/
23
24#include <linux/rbtree_augmented.h>
25#include <linux/export.h>
26
27/*
28 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
29 *
30 * 1) A node is either red or black
31 * 2) The root is black
32 * 3) All leaves (NULL) are black
33 * 4) Both children of every red node are black
34 * 5) Every simple path from root to leaves contains the same number
35 * of black nodes.
36 *
37 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
38 * consecutive red nodes in a path and every red node is therefore followed by
39 * a black. So if B is the number of black nodes on every simple path (as per
40 * 5), then the longest possible path due to 4 is 2B.
41 *
42 * We shall indicate color with case, where black nodes are uppercase and red
43 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
44 * parentheses and have some accompanying text comment.
45 */
46
47/*
48 * Notes on lockless lookups:
49 *
50 * All stores to the tree structure (rb_left and rb_right) must be done using
51 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
52 * tree structure as seen in program order.
53 *
54 * These two requirements will allow lockless iteration of the tree -- not
55 * correct iteration mind you, tree rotations are not atomic so a lookup might
56 * miss entire subtrees.
57 *
58 * But they do guarantee that any such traversal will only see valid elements
59 * and that it will indeed complete -- does not get stuck in a loop.
60 *
61 * It also guarantees that if the lookup returns an element it is the 'correct'
62 * one. But not returning an element does _NOT_ mean it's not present.
63 *
64 * NOTE:
65 *
66 * Stores to __rb_parent_color are not important for simple lookups so those
67 * are left undone as of now. Nor did I check for loops involving parent
68 * pointers.
69 */
70
71static inline void rb_set_black(struct rb_node *rb)
72{
73 rb->__rb_parent_color |= RB_BLACK;
74}
75
76static inline struct rb_node *rb_red_parent(struct rb_node *red)
77{
78 return (struct rb_node *)red->__rb_parent_color;
79}
80
81/*
82 * Helper function for rotations:
83 * - old's parent and color get assigned to new
84 * - old gets assigned new as a parent and 'color' as a color.
85 */
86static inline void
87__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
88 struct rb_root *root, int color)
89{
90 struct rb_node *parent = rb_parent(old);
91 new->__rb_parent_color = old->__rb_parent_color;
92 rb_set_parent_color(old, new, color);
93 __rb_change_child(old, new, parent, root);
94}
95
96static __always_inline void
97__rb_insert(struct rb_node *node, struct rb_root *root,
98 bool newleft, struct rb_node **leftmost,
99 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
100{
101 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
102
103 if (newleft)
104 *leftmost = node;
105
106 while (true) {
107 /*
108 * Loop invariant: node is red.
109 */
110 if (unlikely(!parent)) {
111 /*
112 * The inserted node is root. Either this is the
113 * first node, or we recursed at Case 1 below and
114 * are no longer violating 4).
115 */
116 rb_set_parent_color(node, NULL, RB_BLACK);
117 break;
118 }
119
120 /*
121 * If there is a black parent, we are done.
122 * Otherwise, take some corrective action as,
123 * per 4), we don't want a red root or two
124 * consecutive red nodes.
125 */
126 if(rb_is_black(parent))
127 break;
128
129 gparent = rb_red_parent(parent);
130
131 tmp = gparent->rb_right;
132 if (parent != tmp) { /* parent == gparent->rb_left */
133 if (tmp && rb_is_red(tmp)) {
134 /*
135 * Case 1 - node's uncle is red (color flips).
136 *
137 * G g
138 * / \ / \
139 * p u --> P U
140 * / /
141 * n n
142 *
143 * However, since g's parent might be red, and
144 * 4) does not allow this, we need to recurse
145 * at g.
146 */
147 rb_set_parent_color(tmp, gparent, RB_BLACK);
148 rb_set_parent_color(parent, gparent, RB_BLACK);
149 node = gparent;
150 parent = rb_parent(node);
151 rb_set_parent_color(node, parent, RB_RED);
152 continue;
153 }
154
155 tmp = parent->rb_right;
156 if (node == tmp) {
157 /*
158 * Case 2 - node's uncle is black and node is
159 * the parent's right child (left rotate at parent).
160 *
161 * G G
162 * / \ / \
163 * p U --> n U
164 * \ /
165 * n p
166 *
167 * This still leaves us in violation of 4), the
168 * continuation into Case 3 will fix that.
169 */
170 tmp = node->rb_left;
171 WRITE_ONCE(parent->rb_right, tmp);
172 WRITE_ONCE(node->rb_left, parent);
173 if (tmp)
174 rb_set_parent_color(tmp, parent,
175 RB_BLACK);
176 rb_set_parent_color(parent, node, RB_RED);
177 augment_rotate(parent, node);
178 parent = node;
179 tmp = node->rb_right;
180 }
181
182 /*
183 * Case 3 - node's uncle is black and node is
184 * the parent's left child (right rotate at gparent).
185 *
186 * G P
187 * / \ / \
188 * p U --> n g
189 * / \
190 * n U
191 */
192 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
193 WRITE_ONCE(parent->rb_right, gparent);
194 if (tmp)
195 rb_set_parent_color(tmp, gparent, RB_BLACK);
196 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
197 augment_rotate(gparent, parent);
198 break;
199 } else {
200 tmp = gparent->rb_left;
201 if (tmp && rb_is_red(tmp)) {
202 /* Case 1 - color flips */
203 rb_set_parent_color(tmp, gparent, RB_BLACK);
204 rb_set_parent_color(parent, gparent, RB_BLACK);
205 node = gparent;
206 parent = rb_parent(node);
207 rb_set_parent_color(node, parent, RB_RED);
208 continue;
209 }
210
211 tmp = parent->rb_left;
212 if (node == tmp) {
213 /* Case 2 - right rotate at parent */
214 tmp = node->rb_right;
215 WRITE_ONCE(parent->rb_left, tmp);
216 WRITE_ONCE(node->rb_right, parent);
217 if (tmp)
218 rb_set_parent_color(tmp, parent,
219 RB_BLACK);
220 rb_set_parent_color(parent, node, RB_RED);
221 augment_rotate(parent, node);
222 parent = node;
223 tmp = node->rb_left;
224 }
225
226 /* Case 3 - left rotate at gparent */
227 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
228 WRITE_ONCE(parent->rb_left, gparent);
229 if (tmp)
230 rb_set_parent_color(tmp, gparent, RB_BLACK);
231 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
232 augment_rotate(gparent, parent);
233 break;
234 }
235 }
236}
237
238/*
239 * Inline version for rb_erase() use - we want to be able to inline
240 * and eliminate the dummy_rotate callback there
241 */
242static __always_inline void
243____rb_erase_color(struct rb_node *parent, struct rb_root *root,
244 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
245{
246 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
247
248 while (true) {
249 /*
250 * Loop invariants:
251 * - node is black (or NULL on first iteration)
252 * - node is not the root (parent is not NULL)
253 * - All leaf paths going through parent and node have a
254 * black node count that is 1 lower than other leaf paths.
255 */
256 sibling = parent->rb_right;
257 if (node != sibling) { /* node == parent->rb_left */
258 if (rb_is_red(sibling)) {
259 /*
260 * Case 1 - left rotate at parent
261 *
262 * P S
263 * / \ / \
264 * N s --> p Sr
265 * / \ / \
266 * Sl Sr N Sl
267 */
268 tmp1 = sibling->rb_left;
269 WRITE_ONCE(parent->rb_right, tmp1);
270 WRITE_ONCE(sibling->rb_left, parent);
271 rb_set_parent_color(tmp1, parent, RB_BLACK);
272 __rb_rotate_set_parents(parent, sibling, root,
273 RB_RED);
274 augment_rotate(parent, sibling);
275 sibling = tmp1;
276 }
277 tmp1 = sibling->rb_right;
278 if (!tmp1 || rb_is_black(tmp1)) {
279 tmp2 = sibling->rb_left;
280 if (!tmp2 || rb_is_black(tmp2)) {
281 /*
282 * Case 2 - sibling color flip
283 * (p could be either color here)
284 *
285 * (p) (p)
286 * / \ / \
287 * N S --> N s
288 * / \ / \
289 * Sl Sr Sl Sr
290 *
291 * This leaves us violating 5) which
292 * can be fixed by flipping p to black
293 * if it was red, or by recursing at p.
294 * p is red when coming from Case 1.
295 */
296 rb_set_parent_color(sibling, parent,
297 RB_RED);
298 if (rb_is_red(parent))
299 rb_set_black(parent);
300 else {
301 node = parent;
302 parent = rb_parent(node);
303 if (parent)
304 continue;
305 }
306 break;
307 }
308 /*
309 * Case 3 - right rotate at sibling
310 * (p could be either color here)
311 *
312 * (p) (p)
313 * / \ / \
314 * N S --> N sl
315 * / \ \
316 * sl Sr S
317 * \
318 * Sr
319 *
320 * Note: p might be red, and then both
321 * p and sl are red after rotation(which
322 * breaks property 4). This is fixed in
323 * Case 4 (in __rb_rotate_set_parents()
324 * which set sl the color of p
325 * and set p RB_BLACK)
326 *
327 * (p) (sl)
328 * / \ / \
329 * N sl --> P S
330 * \ / \
331 * S N Sr
332 * \
333 * Sr
334 */
335 tmp1 = tmp2->rb_right;
336 WRITE_ONCE(sibling->rb_left, tmp1);
337 WRITE_ONCE(tmp2->rb_right, sibling);
338 WRITE_ONCE(parent->rb_right, tmp2);
339 if (tmp1)
340 rb_set_parent_color(tmp1, sibling,
341 RB_BLACK);
342 augment_rotate(sibling, tmp2);
343 tmp1 = sibling;
344 sibling = tmp2;
345 }
346 /*
347 * Case 4 - left rotate at parent + color flips
348 * (p and sl could be either color here.
349 * After rotation, p becomes black, s acquires
350 * p's color, and sl keeps its color)
351 *
352 * (p) (s)
353 * / \ / \
354 * N S --> P Sr
355 * / \ / \
356 * (sl) sr N (sl)
357 */
358 tmp2 = sibling->rb_left;
359 WRITE_ONCE(parent->rb_right, tmp2);
360 WRITE_ONCE(sibling->rb_left, parent);
361 rb_set_parent_color(tmp1, sibling, RB_BLACK);
362 if (tmp2)
363 rb_set_parent(tmp2, parent);
364 __rb_rotate_set_parents(parent, sibling, root,
365 RB_BLACK);
366 augment_rotate(parent, sibling);
367 break;
368 } else {
369 sibling = parent->rb_left;
370 if (rb_is_red(sibling)) {
371 /* Case 1 - right rotate at parent */
372 tmp1 = sibling->rb_right;
373 WRITE_ONCE(parent->rb_left, tmp1);
374 WRITE_ONCE(sibling->rb_right, parent);
375 rb_set_parent_color(tmp1, parent, RB_BLACK);
376 __rb_rotate_set_parents(parent, sibling, root,
377 RB_RED);
378 augment_rotate(parent, sibling);
379 sibling = tmp1;
380 }
381 tmp1 = sibling->rb_left;
382 if (!tmp1 || rb_is_black(tmp1)) {
383 tmp2 = sibling->rb_right;
384 if (!tmp2 || rb_is_black(tmp2)) {
385 /* Case 2 - sibling color flip */
386 rb_set_parent_color(sibling, parent,
387 RB_RED);
388 if (rb_is_red(parent))
389 rb_set_black(parent);
390 else {
391 node = parent;
392 parent = rb_parent(node);
393 if (parent)
394 continue;
395 }
396 break;
397 }
398 /* Case 3 - left rotate at sibling */
399 tmp1 = tmp2->rb_left;
400 WRITE_ONCE(sibling->rb_right, tmp1);
401 WRITE_ONCE(tmp2->rb_left, sibling);
402 WRITE_ONCE(parent->rb_left, tmp2);
403 if (tmp1)
404 rb_set_parent_color(tmp1, sibling,
405 RB_BLACK);
406 augment_rotate(sibling, tmp2);
407 tmp1 = sibling;
408 sibling = tmp2;
409 }
410 /* Case 4 - right rotate at parent + color flips */
411 tmp2 = sibling->rb_right;
412 WRITE_ONCE(parent->rb_left, tmp2);
413 WRITE_ONCE(sibling->rb_right, parent);
414 rb_set_parent_color(tmp1, sibling, RB_BLACK);
415 if (tmp2)
416 rb_set_parent(tmp2, parent);
417 __rb_rotate_set_parents(parent, sibling, root,
418 RB_BLACK);
419 augment_rotate(parent, sibling);
420 break;
421 }
422 }
423}
424
425/* Non-inline version for rb_erase_augmented() use */
426void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
427 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
428{
429 ____rb_erase_color(parent, root, augment_rotate);
430}
431EXPORT_SYMBOL(__rb_erase_color);
432
433/*
434 * Non-augmented rbtree manipulation functions.
435 *
436 * We use dummy augmented callbacks here, and have the compiler optimize them
437 * out of the rb_insert_color() and rb_erase() function definitions.
438 */
439
440static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
441static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
442static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
443
444static const struct rb_augment_callbacks dummy_callbacks = {
445 .propagate = dummy_propagate,
446 .copy = dummy_copy,
447 .rotate = dummy_rotate
448};
449
450void rb_insert_color(struct rb_node *node, struct rb_root *root)
451{
452 __rb_insert(node, root, false, NULL, dummy_rotate);
453}
454EXPORT_SYMBOL(rb_insert_color);
455
456void rb_erase(struct rb_node *node, struct rb_root *root)
457{
458 struct rb_node *rebalance;
459 rebalance = __rb_erase_augmented(node, root,
460 NULL, &dummy_callbacks);
461 if (rebalance)
462 ____rb_erase_color(rebalance, root, dummy_rotate);
463}
464EXPORT_SYMBOL(rb_erase);
465
466void rb_insert_color_cached(struct rb_node *node,
467 struct rb_root_cached *root, bool leftmost)
468{
469 __rb_insert(node, &root->rb_root, leftmost,
470 &root->rb_leftmost, dummy_rotate);
471}
472EXPORT_SYMBOL(rb_insert_color_cached);
473
474void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
475{
476 struct rb_node *rebalance;
477 rebalance = __rb_erase_augmented(node, &root->rb_root,
478 &root->rb_leftmost, &dummy_callbacks);
479 if (rebalance)
480 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
481}
482EXPORT_SYMBOL(rb_erase_cached);
483
484/*
485 * Augmented rbtree manipulation functions.
486 *
487 * This instantiates the same __always_inline functions as in the non-augmented
488 * case, but this time with user-defined callbacks.
489 */
490
491void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
492 bool newleft, struct rb_node **leftmost,
493 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
494{
495 __rb_insert(node, root, newleft, leftmost, augment_rotate);
496}
497EXPORT_SYMBOL(__rb_insert_augmented);
498
499/*
500 * This function returns the first node (in sort order) of the tree.
501 */
502struct rb_node *rb_first(const struct rb_root *root)
503{
504 struct rb_node *n;
505
506 n = root->rb_node;
507 if (!n)
508 return NULL;
509 while (n->rb_left)
510 n = n->rb_left;
511 return n;
512}
513EXPORT_SYMBOL(rb_first);
514
515struct rb_node *rb_last(const struct rb_root *root)
516{
517 struct rb_node *n;
518
519 n = root->rb_node;
520 if (!n)
521 return NULL;
522 while (n->rb_right)
523 n = n->rb_right;
524 return n;
525}
526EXPORT_SYMBOL(rb_last);
527
528struct rb_node *rb_next(const struct rb_node *node)
529{
530 struct rb_node *parent;
531
532 if (RB_EMPTY_NODE(node))
533 return NULL;
534
535 /*
536 * If we have a right-hand child, go down and then left as far
537 * as we can.
538 */
539 if (node->rb_right) {
540 node = node->rb_right;
541 while (node->rb_left)
542 node=node->rb_left;
543 return (struct rb_node *)node;
544 }
545
546 /*
547 * No right-hand children. Everything down and left is smaller than us,
548 * so any 'next' node must be in the general direction of our parent.
549 * Go up the tree; any time the ancestor is a right-hand child of its
550 * parent, keep going up. First time it's a left-hand child of its
551 * parent, said parent is our 'next' node.
552 */
553 while ((parent = rb_parent(node)) && node == parent->rb_right)
554 node = parent;
555
556 return parent;
557}
558EXPORT_SYMBOL(rb_next);
559
560struct rb_node *rb_prev(const struct rb_node *node)
561{
562 struct rb_node *parent;
563
564 if (RB_EMPTY_NODE(node))
565 return NULL;
566
567 /*
568 * If we have a left-hand child, go down and then right as far
569 * as we can.
570 */
571 if (node->rb_left) {
572 node = node->rb_left;
573 while (node->rb_right)
574 node=node->rb_right;
575 return (struct rb_node *)node;
576 }
577
578 /*
579 * No left-hand children. Go up till we find an ancestor which
580 * is a right-hand child of its parent.
581 */
582 while ((parent = rb_parent(node)) && node == parent->rb_left)
583 node = parent;
584
585 return parent;
586}
587EXPORT_SYMBOL(rb_prev);
588
589void rb_replace_node(struct rb_node *victim, struct rb_node *new,
590 struct rb_root *root)
591{
592 struct rb_node *parent = rb_parent(victim);
593
594 /* Copy the pointers/colour from the victim to the replacement */
595 *new = *victim;
596
597 /* Set the surrounding nodes to point to the replacement */
598 if (victim->rb_left)
599 rb_set_parent(victim->rb_left, new);
600 if (victim->rb_right)
601 rb_set_parent(victim->rb_right, new);
602 __rb_change_child(victim, new, parent, root);
603}
604EXPORT_SYMBOL(rb_replace_node);
605
606void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new,
607 struct rb_root_cached *root)
608{
609 rb_replace_node(victim, new, &root->rb_root);
610
611 if (root->rb_leftmost == victim)
612 root->rb_leftmost = new;
613}
614EXPORT_SYMBOL(rb_replace_node_cached);
615
616void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
617 struct rb_root *root)
618{
619 struct rb_node *parent = rb_parent(victim);
620
621 /* Copy the pointers/colour from the victim to the replacement */
622 *new = *victim;
623
624 /* Set the surrounding nodes to point to the replacement */
625 if (victim->rb_left)
626 rb_set_parent(victim->rb_left, new);
627 if (victim->rb_right)
628 rb_set_parent(victim->rb_right, new);
629
630 /* Set the parent's pointer to the new node last after an RCU barrier
631 * so that the pointers onwards are seen to be set correctly when doing
632 * an RCU walk over the tree.
633 */
634 __rb_change_child_rcu(victim, new, parent, root);
635}
636EXPORT_SYMBOL(rb_replace_node_rcu);
637
638static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
639{
640 for (;;) {
641 if (node->rb_left)
642 node = node->rb_left;
643 else if (node->rb_right)
644 node = node->rb_right;
645 else
646 return (struct rb_node *)node;
647 }
648}
649
650struct rb_node *rb_next_postorder(const struct rb_node *node)
651{
652 const struct rb_node *parent;
653 if (!node)
654 return NULL;
655 parent = rb_parent(node);
656
657 /* If we're sitting on node, we've already seen our children */
658 if (parent && node == parent->rb_left && parent->rb_right) {
659 /* If we are the parent's left node, go to the parent's right
660 * node then all the way down to the left */
661 return rb_left_deepest_node(parent->rb_right);
662 } else
663 /* Otherwise we are the parent's right node, and the parent
664 * should be next */
665 return (struct rb_node *)parent;
666}
667EXPORT_SYMBOL(rb_next_postorder);
668
669struct rb_node *rb_first_postorder(const struct rb_root *root)
670{
671 if (!root->rb_node)
672 return NULL;
673
674 return rb_left_deepest_node(root->rb_node);
675}
676EXPORT_SYMBOL(rb_first_postorder);
677