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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 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 */
227static __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 tmp1 = tmp2->rb_right;
306 WRITE_ONCE(sibling->rb_left, tmp1);
307 WRITE_ONCE(tmp2->rb_right, sibling);
308 WRITE_ONCE(parent->rb_right, tmp2);
309 if (tmp1)
310 rb_set_parent_color(tmp1, sibling,
311 RB_BLACK);
312 augment_rotate(sibling, tmp2);
313 tmp1 = sibling;
314 sibling = tmp2;
315 }
316 /*
317 * Case 4 - left rotate at parent + color flips
318 * (p and sl could be either color here.
319 * After rotation, p becomes black, s acquires
320 * p's color, and sl keeps its color)
321 *
322 * (p) (s)
323 * / \ / \
324 * N S --> P Sr
325 * / \ / \
326 * (sl) sr N (sl)
327 */
328 tmp2 = sibling->rb_left;
329 WRITE_ONCE(parent->rb_right, tmp2);
330 WRITE_ONCE(sibling->rb_left, parent);
331 rb_set_parent_color(tmp1, sibling, RB_BLACK);
332 if (tmp2)
333 rb_set_parent(tmp2, parent);
334 __rb_rotate_set_parents(parent, sibling, root,
335 RB_BLACK);
336 augment_rotate(parent, sibling);
337 break;
338 } else {
339 sibling = parent->rb_left;
340 if (rb_is_red(sibling)) {
341 /* Case 1 - right rotate at parent */
342 tmp1 = sibling->rb_right;
343 WRITE_ONCE(parent->rb_left, tmp1);
344 WRITE_ONCE(sibling->rb_right, parent);
345 rb_set_parent_color(tmp1, parent, RB_BLACK);
346 __rb_rotate_set_parents(parent, sibling, root,
347 RB_RED);
348 augment_rotate(parent, sibling);
349 sibling = tmp1;
350 }
351 tmp1 = sibling->rb_left;
352 if (!tmp1 || rb_is_black(tmp1)) {
353 tmp2 = sibling->rb_right;
354 if (!tmp2 || rb_is_black(tmp2)) {
355 /* Case 2 - sibling color flip */
356 rb_set_parent_color(sibling, parent,
357 RB_RED);
358 if (rb_is_red(parent))
359 rb_set_black(parent);
360 else {
361 node = parent;
362 parent = rb_parent(node);
363 if (parent)
364 continue;
365 }
366 break;
367 }
368 /* Case 3 - right rotate at sibling */
369 tmp1 = tmp2->rb_left;
370 WRITE_ONCE(sibling->rb_right, tmp1);
371 WRITE_ONCE(tmp2->rb_left, sibling);
372 WRITE_ONCE(parent->rb_left, tmp2);
373 if (tmp1)
374 rb_set_parent_color(tmp1, sibling,
375 RB_BLACK);
376 augment_rotate(sibling, tmp2);
377 tmp1 = sibling;
378 sibling = tmp2;
379 }
380 /* Case 4 - left rotate at parent + color flips */
381 tmp2 = sibling->rb_right;
382 WRITE_ONCE(parent->rb_left, tmp2);
383 WRITE_ONCE(sibling->rb_right, parent);
384 rb_set_parent_color(tmp1, sibling, RB_BLACK);
385 if (tmp2)
386 rb_set_parent(tmp2, parent);
387 __rb_rotate_set_parents(parent, sibling, root,
388 RB_BLACK);
389 augment_rotate(parent, sibling);
390 break;
391 }
392 }
393}
394
395/* Non-inline version for rb_erase_augmented() use */
396void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
397 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
398{
399 ____rb_erase_color(parent, root, augment_rotate);
400}
401EXPORT_SYMBOL(__rb_erase_color);
402
403/*
404 * Non-augmented rbtree manipulation functions.
405 *
406 * We use dummy augmented callbacks here, and have the compiler optimize them
407 * out of the rb_insert_color() and rb_erase() function definitions.
408 */
409
410static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
411static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
412static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
413
414static const struct rb_augment_callbacks dummy_callbacks = {
415 dummy_propagate, dummy_copy, dummy_rotate
416};
417
418void rb_insert_color(struct rb_node *node, struct rb_root *root)
419{
420 __rb_insert(node, root, dummy_rotate);
421}
422EXPORT_SYMBOL(rb_insert_color);
423
424void rb_erase(struct rb_node *node, struct rb_root *root)
425{
426 struct rb_node *rebalance;
427 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
428 if (rebalance)
429 ____rb_erase_color(rebalance, root, dummy_rotate);
430}
431EXPORT_SYMBOL(rb_erase);
432
433/*
434 * Augmented rbtree manipulation functions.
435 *
436 * This instantiates the same __always_inline functions as in the non-augmented
437 * case, but this time with user-defined callbacks.
438 */
439
440void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
441 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
442{
443 __rb_insert(node, root, augment_rotate);
444}
445EXPORT_SYMBOL(__rb_insert_augmented);
446
447/*
448 * This function returns the first node (in sort order) of the tree.
449 */
450struct rb_node *rb_first(const struct rb_root *root)
451{
452 struct rb_node *n;
453
454 n = root->rb_node;
455 if (!n)
456 return NULL;
457 while (n->rb_left)
458 n = n->rb_left;
459 return n;
460}
461EXPORT_SYMBOL(rb_first);
462
463struct rb_node *rb_last(const struct rb_root *root)
464{
465 struct rb_node *n;
466
467 n = root->rb_node;
468 if (!n)
469 return NULL;
470 while (n->rb_right)
471 n = n->rb_right;
472 return n;
473}
474EXPORT_SYMBOL(rb_last);
475
476struct rb_node *rb_next(const struct rb_node *node)
477{
478 struct rb_node *parent;
479
480 if (RB_EMPTY_NODE(node))
481 return NULL;
482
483 /*
484 * If we have a right-hand child, go down and then left as far
485 * as we can.
486 */
487 if (node->rb_right) {
488 node = node->rb_right;
489 while (node->rb_left)
490 node=node->rb_left;
491 return (struct rb_node *)node;
492 }
493
494 /*
495 * No right-hand children. Everything down and left is smaller than us,
496 * so any 'next' node must be in the general direction of our parent.
497 * Go up the tree; any time the ancestor is a right-hand child of its
498 * parent, keep going up. First time it's a left-hand child of its
499 * parent, said parent is our 'next' node.
500 */
501 while ((parent = rb_parent(node)) && node == parent->rb_right)
502 node = parent;
503
504 return parent;
505}
506EXPORT_SYMBOL(rb_next);
507
508struct rb_node *rb_prev(const struct rb_node *node)
509{
510 struct rb_node *parent;
511
512 if (RB_EMPTY_NODE(node))
513 return NULL;
514
515 /*
516 * If we have a left-hand child, go down and then right as far
517 * as we can.
518 */
519 if (node->rb_left) {
520 node = node->rb_left;
521 while (node->rb_right)
522 node=node->rb_right;
523 return (struct rb_node *)node;
524 }
525
526 /*
527 * No left-hand children. Go up till we find an ancestor which
528 * is a right-hand child of its parent.
529 */
530 while ((parent = rb_parent(node)) && node == parent->rb_left)
531 node = parent;
532
533 return parent;
534}
535EXPORT_SYMBOL(rb_prev);
536
537void rb_replace_node(struct rb_node *victim, struct rb_node *new,
538 struct rb_root *root)
539{
540 struct rb_node *parent = rb_parent(victim);
541
542 /* Copy the pointers/colour from the victim to the replacement */
543 *new = *victim;
544
545 /* Set the surrounding nodes to point to the replacement */
546 if (victim->rb_left)
547 rb_set_parent(victim->rb_left, new);
548 if (victim->rb_right)
549 rb_set_parent(victim->rb_right, new);
550 __rb_change_child(victim, new, parent, root);
551}
552EXPORT_SYMBOL(rb_replace_node);
553
554void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
555 struct rb_root *root)
556{
557 struct rb_node *parent = rb_parent(victim);
558
559 /* Copy the pointers/colour from the victim to the replacement */
560 *new = *victim;
561
562 /* Set the surrounding nodes to point to the replacement */
563 if (victim->rb_left)
564 rb_set_parent(victim->rb_left, new);
565 if (victim->rb_right)
566 rb_set_parent(victim->rb_right, new);
567
568 /* Set the parent's pointer to the new node last after an RCU barrier
569 * so that the pointers onwards are seen to be set correctly when doing
570 * an RCU walk over the tree.
571 */
572 __rb_change_child_rcu(victim, new, parent, root);
573}
574EXPORT_SYMBOL(rb_replace_node_rcu);
575
576static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
577{
578 for (;;) {
579 if (node->rb_left)
580 node = node->rb_left;
581 else if (node->rb_right)
582 node = node->rb_right;
583 else
584 return (struct rb_node *)node;
585 }
586}
587
588struct rb_node *rb_next_postorder(const struct rb_node *node)
589{
590 const struct rb_node *parent;
591 if (!node)
592 return NULL;
593 parent = rb_parent(node);
594
595 /* If we're sitting on node, we've already seen our children */
596 if (parent && node == parent->rb_left && parent->rb_right) {
597 /* If we are the parent's left node, go to the parent's right
598 * node then all the way down to the left */
599 return rb_left_deepest_node(parent->rb_right);
600 } else
601 /* Otherwise we are the parent's right node, and the parent
602 * should be next */
603 return (struct rb_node *)parent;
604}
605EXPORT_SYMBOL(rb_next_postorder);
606
607struct rb_node *rb_first_postorder(const struct rb_root *root)
608{
609 if (!root->rb_node)
610 return NULL;
611
612 return rb_left_deepest_node(root->rb_node);
613}
614EXPORT_SYMBOL(rb_first_postorder);
615
generated by cgit at 2024-05-18 13:28:56 (GMT)