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[mirror_ubuntu-zesty-kernel.git] / lib / rbtree.c
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
71 static inline void rb_set_black(struct rb_node *rb)
72 {
73 rb->__rb_parent_color |= RB_BLACK;
74 }
75
76 static 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 */
86 static 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
96 static __always_inline void
97 __rb_insert(struct rb_node *node, struct rb_root *root,
98 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
99 {
100 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
101
102 while (true) {
103 /*
104 * Loop invariant: node is red
105 *
106 * If there is a black parent, we are done.
107 * Otherwise, take some corrective action as we don't
108 * want a red root or two consecutive red nodes.
109 */
110 if (!parent) {
111 rb_set_parent_color(node, NULL, RB_BLACK);
112 break;
113 } else if (rb_is_black(parent))
114 break;
115
116 gparent = rb_red_parent(parent);
117
118 tmp = gparent->rb_right;
119 if (parent != tmp) { /* parent == gparent->rb_left */
120 if (tmp && rb_is_red(tmp)) {
121 /*
122 * Case 1 - color flips
123 *
124 * G g
125 * / \ / \
126 * p u --> P U
127 * / /
128 * n n
129 *
130 * However, since g's parent might be red, and
131 * 4) does not allow this, we need to recurse
132 * at g.
133 */
134 rb_set_parent_color(tmp, gparent, RB_BLACK);
135 rb_set_parent_color(parent, gparent, RB_BLACK);
136 node = gparent;
137 parent = rb_parent(node);
138 rb_set_parent_color(node, parent, RB_RED);
139 continue;
140 }
141
142 tmp = parent->rb_right;
143 if (node == tmp) {
144 /*
145 * Case 2 - left rotate at parent
146 *
147 * G G
148 * / \ / \
149 * p U --> n U
150 * \ /
151 * n p
152 *
153 * This still leaves us in violation of 4), the
154 * continuation into Case 3 will fix that.
155 */
156 tmp = node->rb_left;
157 WRITE_ONCE(parent->rb_right, tmp);
158 WRITE_ONCE(node->rb_left, parent);
159 if (tmp)
160 rb_set_parent_color(tmp, parent,
161 RB_BLACK);
162 rb_set_parent_color(parent, node, RB_RED);
163 augment_rotate(parent, node);
164 parent = node;
165 tmp = node->rb_right;
166 }
167
168 /*
169 * Case 3 - right rotate at gparent
170 *
171 * G P
172 * / \ / \
173 * p U --> n g
174 * / \
175 * n U
176 */
177 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
178 WRITE_ONCE(parent->rb_right, gparent);
179 if (tmp)
180 rb_set_parent_color(tmp, gparent, RB_BLACK);
181 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
182 augment_rotate(gparent, parent);
183 break;
184 } else {
185 tmp = gparent->rb_left;
186 if (tmp && rb_is_red(tmp)) {
187 /* Case 1 - color flips */
188 rb_set_parent_color(tmp, gparent, RB_BLACK);
189 rb_set_parent_color(parent, gparent, RB_BLACK);
190 node = gparent;
191 parent = rb_parent(node);
192 rb_set_parent_color(node, parent, RB_RED);
193 continue;
194 }
195
196 tmp = parent->rb_left;
197 if (node == tmp) {
198 /* Case 2 - right rotate at parent */
199 tmp = node->rb_right;
200 WRITE_ONCE(parent->rb_left, tmp);
201 WRITE_ONCE(node->rb_right, parent);
202 if (tmp)
203 rb_set_parent_color(tmp, parent,
204 RB_BLACK);
205 rb_set_parent_color(parent, node, RB_RED);
206 augment_rotate(parent, node);
207 parent = node;
208 tmp = node->rb_left;
209 }
210
211 /* Case 3 - left rotate at gparent */
212 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
213 WRITE_ONCE(parent->rb_left, gparent);
214 if (tmp)
215 rb_set_parent_color(tmp, gparent, RB_BLACK);
216 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
217 augment_rotate(gparent, parent);
218 break;
219 }
220 }
221 }
222
223 /*
224 * Inline version for rb_erase() use - we want to be able to inline
225 * and eliminate the dummy_rotate callback there
226 */
227 static __always_inline void
228 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
229 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
230 {
231 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
232
233 while (true) {
234 /*
235 * Loop invariants:
236 * - node is black (or NULL on first iteration)
237 * - node is not the root (parent is not NULL)
238 * - All leaf paths going through parent and node have a
239 * black node count that is 1 lower than other leaf paths.
240 */
241 sibling = parent->rb_right;
242 if (node != sibling) { /* node == parent->rb_left */
243 if (rb_is_red(sibling)) {
244 /*
245 * Case 1 - left rotate at parent
246 *
247 * P S
248 * / \ / \
249 * N s --> p Sr
250 * / \ / \
251 * Sl Sr N Sl
252 */
253 tmp1 = sibling->rb_left;
254 WRITE_ONCE(parent->rb_right, tmp1);
255 WRITE_ONCE(sibling->rb_left, parent);
256 rb_set_parent_color(tmp1, parent, RB_BLACK);
257 __rb_rotate_set_parents(parent, sibling, root,
258 RB_RED);
259 augment_rotate(parent, sibling);
260 sibling = tmp1;
261 }
262 tmp1 = sibling->rb_right;
263 if (!tmp1 || rb_is_black(tmp1)) {
264 tmp2 = sibling->rb_left;
265 if (!tmp2 || rb_is_black(tmp2)) {
266 /*
267 * Case 2 - sibling color flip
268 * (p could be either color here)
269 *
270 * (p) (p)
271 * / \ / \
272 * N S --> N s
273 * / \ / \
274 * Sl Sr Sl Sr
275 *
276 * This leaves us violating 5) which
277 * can be fixed by flipping p to black
278 * if it was red, or by recursing at p.
279 * p is red when coming from Case 1.
280 */
281 rb_set_parent_color(sibling, parent,
282 RB_RED);
283 if (rb_is_red(parent))
284 rb_set_black(parent);
285 else {
286 node = parent;
287 parent = rb_parent(node);
288 if (parent)
289 continue;
290 }
291 break;
292 }
293 /*
294 * Case 3 - right rotate at sibling
295 * (p could be either color here)
296 *
297 * (p) (p)
298 * / \ / \
299 * N S --> N sl
300 * / \ \
301 * sl Sr S
302 * \
303 * Sr
304 *
305 * Note: p might be red, and then both
306 * p and sl are red after rotation(which
307 * breaks property 4). This is fixed in
308 * Case 4 (in __rb_rotate_set_parents()
309 * which set sl the color of p
310 * and set p RB_BLACK)
311 *
312 * (p) (sl)
313 * / \ / \
314 * N sl --> P S
315 * \ / \
316 * S N Sr
317 * \
318 * Sr
319 */
320 tmp1 = tmp2->rb_right;
321 WRITE_ONCE(sibling->rb_left, tmp1);
322 WRITE_ONCE(tmp2->rb_right, sibling);
323 WRITE_ONCE(parent->rb_right, tmp2);
324 if (tmp1)
325 rb_set_parent_color(tmp1, sibling,
326 RB_BLACK);
327 augment_rotate(sibling, tmp2);
328 tmp1 = sibling;
329 sibling = tmp2;
330 }
331 /*
332 * Case 4 - left rotate at parent + color flips
333 * (p and sl could be either color here.
334 * After rotation, p becomes black, s acquires
335 * p's color, and sl keeps its color)
336 *
337 * (p) (s)
338 * / \ / \
339 * N S --> P Sr
340 * / \ / \
341 * (sl) sr N (sl)
342 */
343 tmp2 = sibling->rb_left;
344 WRITE_ONCE(parent->rb_right, tmp2);
345 WRITE_ONCE(sibling->rb_left, parent);
346 rb_set_parent_color(tmp1, sibling, RB_BLACK);
347 if (tmp2)
348 rb_set_parent(tmp2, parent);
349 __rb_rotate_set_parents(parent, sibling, root,
350 RB_BLACK);
351 augment_rotate(parent, sibling);
352 break;
353 } else {
354 sibling = parent->rb_left;
355 if (rb_is_red(sibling)) {
356 /* Case 1 - right rotate at parent */
357 tmp1 = sibling->rb_right;
358 WRITE_ONCE(parent->rb_left, tmp1);
359 WRITE_ONCE(sibling->rb_right, parent);
360 rb_set_parent_color(tmp1, parent, RB_BLACK);
361 __rb_rotate_set_parents(parent, sibling, root,
362 RB_RED);
363 augment_rotate(parent, sibling);
364 sibling = tmp1;
365 }
366 tmp1 = sibling->rb_left;
367 if (!tmp1 || rb_is_black(tmp1)) {
368 tmp2 = sibling->rb_right;
369 if (!tmp2 || rb_is_black(tmp2)) {
370 /* Case 2 - sibling color flip */
371 rb_set_parent_color(sibling, parent,
372 RB_RED);
373 if (rb_is_red(parent))
374 rb_set_black(parent);
375 else {
376 node = parent;
377 parent = rb_parent(node);
378 if (parent)
379 continue;
380 }
381 break;
382 }
383 /* Case 3 - left rotate at sibling */
384 tmp1 = tmp2->rb_left;
385 WRITE_ONCE(sibling->rb_right, tmp1);
386 WRITE_ONCE(tmp2->rb_left, sibling);
387 WRITE_ONCE(parent->rb_left, tmp2);
388 if (tmp1)
389 rb_set_parent_color(tmp1, sibling,
390 RB_BLACK);
391 augment_rotate(sibling, tmp2);
392 tmp1 = sibling;
393 sibling = tmp2;
394 }
395 /* Case 4 - right rotate at parent + color flips */
396 tmp2 = sibling->rb_right;
397 WRITE_ONCE(parent->rb_left, tmp2);
398 WRITE_ONCE(sibling->rb_right, parent);
399 rb_set_parent_color(tmp1, sibling, RB_BLACK);
400 if (tmp2)
401 rb_set_parent(tmp2, parent);
402 __rb_rotate_set_parents(parent, sibling, root,
403 RB_BLACK);
404 augment_rotate(parent, sibling);
405 break;
406 }
407 }
408 }
409
410 /* Non-inline version for rb_erase_augmented() use */
411 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
412 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
413 {
414 ____rb_erase_color(parent, root, augment_rotate);
415 }
416 EXPORT_SYMBOL(__rb_erase_color);
417
418 /*
419 * Non-augmented rbtree manipulation functions.
420 *
421 * We use dummy augmented callbacks here, and have the compiler optimize them
422 * out of the rb_insert_color() and rb_erase() function definitions.
423 */
424
425 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
426 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
427 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
428
429 static const struct rb_augment_callbacks dummy_callbacks = {
430 dummy_propagate, dummy_copy, dummy_rotate
431 };
432
433 void rb_insert_color(struct rb_node *node, struct rb_root *root)
434 {
435 __rb_insert(node, root, dummy_rotate);
436 }
437 EXPORT_SYMBOL(rb_insert_color);
438
439 void rb_erase(struct rb_node *node, struct rb_root *root)
440 {
441 struct rb_node *rebalance;
442 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
443 if (rebalance)
444 ____rb_erase_color(rebalance, root, dummy_rotate);
445 }
446 EXPORT_SYMBOL(rb_erase);
447
448 /*
449 * Augmented rbtree manipulation functions.
450 *
451 * This instantiates the same __always_inline functions as in the non-augmented
452 * case, but this time with user-defined callbacks.
453 */
454
455 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
456 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
457 {
458 __rb_insert(node, root, augment_rotate);
459 }
460 EXPORT_SYMBOL(__rb_insert_augmented);
461
462 /*
463 * This function returns the first node (in sort order) of the tree.
464 */
465 struct rb_node *rb_first(const struct rb_root *root)
466 {
467 struct rb_node *n;
468
469 n = root->rb_node;
470 if (!n)
471 return NULL;
472 while (n->rb_left)
473 n = n->rb_left;
474 return n;
475 }
476 EXPORT_SYMBOL(rb_first);
477
478 struct rb_node *rb_last(const struct rb_root *root)
479 {
480 struct rb_node *n;
481
482 n = root->rb_node;
483 if (!n)
484 return NULL;
485 while (n->rb_right)
486 n = n->rb_right;
487 return n;
488 }
489 EXPORT_SYMBOL(rb_last);
490
491 struct rb_node *rb_next(const struct rb_node *node)
492 {
493 struct rb_node *parent;
494
495 if (RB_EMPTY_NODE(node))
496 return NULL;
497
498 /*
499 * If we have a right-hand child, go down and then left as far
500 * as we can.
501 */
502 if (node->rb_right) {
503 node = node->rb_right;
504 while (node->rb_left)
505 node=node->rb_left;
506 return (struct rb_node *)node;
507 }
508
509 /*
510 * No right-hand children. Everything down and left is smaller than us,
511 * so any 'next' node must be in the general direction of our parent.
512 * Go up the tree; any time the ancestor is a right-hand child of its
513 * parent, keep going up. First time it's a left-hand child of its
514 * parent, said parent is our 'next' node.
515 */
516 while ((parent = rb_parent(node)) && node == parent->rb_right)
517 node = parent;
518
519 return parent;
520 }
521 EXPORT_SYMBOL(rb_next);
522
523 struct rb_node *rb_prev(const struct rb_node *node)
524 {
525 struct rb_node *parent;
526
527 if (RB_EMPTY_NODE(node))
528 return NULL;
529
530 /*
531 * If we have a left-hand child, go down and then right as far
532 * as we can.
533 */
534 if (node->rb_left) {
535 node = node->rb_left;
536 while (node->rb_right)
537 node=node->rb_right;
538 return (struct rb_node *)node;
539 }
540
541 /*
542 * No left-hand children. Go up till we find an ancestor which
543 * is a right-hand child of its parent.
544 */
545 while ((parent = rb_parent(node)) && node == parent->rb_left)
546 node = parent;
547
548 return parent;
549 }
550 EXPORT_SYMBOL(rb_prev);
551
552 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
553 struct rb_root *root)
554 {
555 struct rb_node *parent = rb_parent(victim);
556
557 /* Copy the pointers/colour from the victim to the replacement */
558 *new = *victim;
559
560 /* Set the surrounding nodes to point to the replacement */
561 if (victim->rb_left)
562 rb_set_parent(victim->rb_left, new);
563 if (victim->rb_right)
564 rb_set_parent(victim->rb_right, new);
565 __rb_change_child(victim, new, parent, root);
566 }
567 EXPORT_SYMBOL(rb_replace_node);
568
569 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
570 struct rb_root *root)
571 {
572 struct rb_node *parent = rb_parent(victim);
573
574 /* Copy the pointers/colour from the victim to the replacement */
575 *new = *victim;
576
577 /* Set the surrounding nodes to point to the replacement */
578 if (victim->rb_left)
579 rb_set_parent(victim->rb_left, new);
580 if (victim->rb_right)
581 rb_set_parent(victim->rb_right, new);
582
583 /* Set the parent's pointer to the new node last after an RCU barrier
584 * so that the pointers onwards are seen to be set correctly when doing
585 * an RCU walk over the tree.
586 */
587 __rb_change_child_rcu(victim, new, parent, root);
588 }
589 EXPORT_SYMBOL(rb_replace_node_rcu);
590
591 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
592 {
593 for (;;) {
594 if (node->rb_left)
595 node = node->rb_left;
596 else if (node->rb_right)
597 node = node->rb_right;
598 else
599 return (struct rb_node *)node;
600 }
601 }
602
603 struct rb_node *rb_next_postorder(const struct rb_node *node)
604 {
605 const struct rb_node *parent;
606 if (!node)
607 return NULL;
608 parent = rb_parent(node);
609
610 /* If we're sitting on node, we've already seen our children */
611 if (parent && node == parent->rb_left && parent->rb_right) {
612 /* If we are the parent's left node, go to the parent's right
613 * node then all the way down to the left */
614 return rb_left_deepest_node(parent->rb_right);
615 } else
616 /* Otherwise we are the parent's right node, and the parent
617 * should be next */
618 return (struct rb_node *)parent;
619 }
620 EXPORT_SYMBOL(rb_next_postorder);
621
622 struct rb_node *rb_first_postorder(const struct rb_root *root)
623 {
624 if (!root->rb_node)
625 return NULL;
626
627 return rb_left_deepest_node(root->rb_node);
628 }
629 EXPORT_SYMBOL(rb_first_postorder);
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