xref: /openbmc/linux/lib/rbtree.c (revision 9d9e6f9703bbd642f3f2f807e6aaa642a4cbcec9)
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.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 #define	RB_RED		0
48 #define	RB_BLACK	1
49 
50 #define __rb_parent(pc)    ((struct rb_node *)(pc & ~3))
51 
52 #define __rb_color(pc)     ((pc) & 1)
53 #define __rb_is_black(pc)  __rb_color(pc)
54 #define __rb_is_red(pc)    (!__rb_color(pc))
55 #define rb_color(rb)       __rb_color((rb)->__rb_parent_color)
56 #define rb_is_red(rb)      __rb_is_red((rb)->__rb_parent_color)
57 #define rb_is_black(rb)    __rb_is_black((rb)->__rb_parent_color)
58 
59 static inline void rb_set_black(struct rb_node *rb)
60 {
61 	rb->__rb_parent_color |= RB_BLACK;
62 }
63 
64 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
65 {
66 	rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
67 }
68 
69 static inline void rb_set_parent_color(struct rb_node *rb,
70 				       struct rb_node *p, int color)
71 {
72 	rb->__rb_parent_color = (unsigned long)p | color;
73 }
74 
75 static inline struct rb_node *rb_red_parent(struct rb_node *red)
76 {
77 	return (struct rb_node *)red->__rb_parent_color;
78 }
79 
80 static inline void
81 __rb_change_child(struct rb_node *old, struct rb_node *new,
82 		  struct rb_node *parent, struct rb_root *root)
83 {
84 	if (parent) {
85 		if (parent->rb_left == old)
86 			parent->rb_left = new;
87 		else
88 			parent->rb_right = new;
89 	} else
90 		root->rb_node = new;
91 }
92 
93 /*
94  * Helper function for rotations:
95  * - old's parent and color get assigned to new
96  * - old gets assigned new as a parent and 'color' as a color.
97  */
98 static inline void
99 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
100 			struct rb_root *root, int color)
101 {
102 	struct rb_node *parent = rb_parent(old);
103 	new->__rb_parent_color = old->__rb_parent_color;
104 	rb_set_parent_color(old, new, color);
105 	__rb_change_child(old, new, parent, root);
106 }
107 
108 static __always_inline void
109 __rb_insert(struct rb_node *node, struct rb_root *root,
110 	    void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
111 {
112 	struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
113 
114 	while (true) {
115 		/*
116 		 * Loop invariant: node is red
117 		 *
118 		 * If there is a black parent, we are done.
119 		 * Otherwise, take some corrective action as we don't
120 		 * want a red root or two consecutive red nodes.
121 		 */
122 		if (!parent) {
123 			rb_set_parent_color(node, NULL, RB_BLACK);
124 			break;
125 		} else if (rb_is_black(parent))
126 			break;
127 
128 		gparent = rb_red_parent(parent);
129 
130 		tmp = gparent->rb_right;
131 		if (parent != tmp) {	/* parent == gparent->rb_left */
132 			if (tmp && rb_is_red(tmp)) {
133 				/*
134 				 * Case 1 - color flips
135 				 *
136 				 *       G            g
137 				 *      / \          / \
138 				 *     p   u  -->   P   U
139 				 *    /            /
140 				 *   n            N
141 				 *
142 				 * However, since g's parent might be red, and
143 				 * 4) does not allow this, we need to recurse
144 				 * at g.
145 				 */
146 				rb_set_parent_color(tmp, gparent, RB_BLACK);
147 				rb_set_parent_color(parent, gparent, RB_BLACK);
148 				node = gparent;
149 				parent = rb_parent(node);
150 				rb_set_parent_color(node, parent, RB_RED);
151 				continue;
152 			}
153 
154 			tmp = parent->rb_right;
155 			if (node == tmp) {
156 				/*
157 				 * Case 2 - left rotate at parent
158 				 *
159 				 *      G             G
160 				 *     / \           / \
161 				 *    p   U  -->    n   U
162 				 *     \           /
163 				 *      n         p
164 				 *
165 				 * This still leaves us in violation of 4), the
166 				 * continuation into Case 3 will fix that.
167 				 */
168 				parent->rb_right = tmp = node->rb_left;
169 				node->rb_left = parent;
170 				if (tmp)
171 					rb_set_parent_color(tmp, parent,
172 							    RB_BLACK);
173 				rb_set_parent_color(parent, node, RB_RED);
174 				augment_rotate(parent, node);
175 				parent = node;
176 				tmp = node->rb_right;
177 			}
178 
179 			/*
180 			 * Case 3 - right rotate at gparent
181 			 *
182 			 *        G           P
183 			 *       / \         / \
184 			 *      p   U  -->  n   g
185 			 *     /                 \
186 			 *    n                   U
187 			 */
188 			gparent->rb_left = tmp;  /* == parent->rb_right */
189 			parent->rb_right = gparent;
190 			if (tmp)
191 				rb_set_parent_color(tmp, gparent, RB_BLACK);
192 			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
193 			augment_rotate(gparent, parent);
194 			break;
195 		} else {
196 			tmp = gparent->rb_left;
197 			if (tmp && rb_is_red(tmp)) {
198 				/* Case 1 - color flips */
199 				rb_set_parent_color(tmp, gparent, RB_BLACK);
200 				rb_set_parent_color(parent, gparent, RB_BLACK);
201 				node = gparent;
202 				parent = rb_parent(node);
203 				rb_set_parent_color(node, parent, RB_RED);
204 				continue;
205 			}
206 
207 			tmp = parent->rb_left;
208 			if (node == tmp) {
209 				/* Case 2 - right rotate at parent */
210 				parent->rb_left = tmp = node->rb_right;
211 				node->rb_right = parent;
212 				if (tmp)
213 					rb_set_parent_color(tmp, parent,
214 							    RB_BLACK);
215 				rb_set_parent_color(parent, node, RB_RED);
216 				augment_rotate(parent, node);
217 				parent = node;
218 				tmp = node->rb_left;
219 			}
220 
221 			/* Case 3 - left rotate at gparent */
222 			gparent->rb_right = tmp;  /* == parent->rb_left */
223 			parent->rb_left = gparent;
224 			if (tmp)
225 				rb_set_parent_color(tmp, gparent, RB_BLACK);
226 			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
227 			augment_rotate(gparent, parent);
228 			break;
229 		}
230 	}
231 }
232 
233 static __always_inline void
234 __rb_erase_color(struct rb_node *parent, struct rb_root *root,
235 		 const struct rb_augment_callbacks *augment)
236 {
237 	struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
238 
239 	while (true) {
240 		/*
241 		 * Loop invariants:
242 		 * - node is black (or NULL on first iteration)
243 		 * - node is not the root (parent is not NULL)
244 		 * - All leaf paths going through parent and node have a
245 		 *   black node count that is 1 lower than other leaf paths.
246 		 */
247 		sibling = parent->rb_right;
248 		if (node != sibling) {	/* node == parent->rb_left */
249 			if (rb_is_red(sibling)) {
250 				/*
251 				 * Case 1 - left rotate at parent
252 				 *
253 				 *     P               S
254 				 *    / \             / \
255 				 *   N   s    -->    p   Sr
256 				 *      / \         / \
257 				 *     Sl  Sr      N   Sl
258 				 */
259 				parent->rb_right = tmp1 = sibling->rb_left;
260 				sibling->rb_left = parent;
261 				rb_set_parent_color(tmp1, parent, RB_BLACK);
262 				__rb_rotate_set_parents(parent, sibling, root,
263 							RB_RED);
264 				augment->rotate(parent, sibling);
265 				sibling = tmp1;
266 			}
267 			tmp1 = sibling->rb_right;
268 			if (!tmp1 || rb_is_black(tmp1)) {
269 				tmp2 = sibling->rb_left;
270 				if (!tmp2 || rb_is_black(tmp2)) {
271 					/*
272 					 * Case 2 - sibling color flip
273 					 * (p could be either color here)
274 					 *
275 					 *    (p)           (p)
276 					 *    / \           / \
277 					 *   N   S    -->  N   s
278 					 *      / \           / \
279 					 *     Sl  Sr        Sl  Sr
280 					 *
281 					 * This leaves us violating 5) which
282 					 * can be fixed by flipping p to black
283 					 * if it was red, or by recursing at p.
284 					 * p is red when coming from Case 1.
285 					 */
286 					rb_set_parent_color(sibling, parent,
287 							    RB_RED);
288 					if (rb_is_red(parent))
289 						rb_set_black(parent);
290 					else {
291 						node = parent;
292 						parent = rb_parent(node);
293 						if (parent)
294 							continue;
295 					}
296 					break;
297 				}
298 				/*
299 				 * Case 3 - right rotate at sibling
300 				 * (p could be either color here)
301 				 *
302 				 *   (p)           (p)
303 				 *   / \           / \
304 				 *  N   S    -->  N   Sl
305 				 *     / \             \
306 				 *    sl  Sr            s
307 				 *                       \
308 				 *                        Sr
309 				 */
310 				sibling->rb_left = tmp1 = tmp2->rb_right;
311 				tmp2->rb_right = sibling;
312 				parent->rb_right = tmp2;
313 				if (tmp1)
314 					rb_set_parent_color(tmp1, sibling,
315 							    RB_BLACK);
316 				augment->rotate(sibling, tmp2);
317 				tmp1 = sibling;
318 				sibling = tmp2;
319 			}
320 			/*
321 			 * Case 4 - left rotate at parent + color flips
322 			 * (p and sl could be either color here.
323 			 *  After rotation, p becomes black, s acquires
324 			 *  p's color, and sl keeps its color)
325 			 *
326 			 *      (p)             (s)
327 			 *      / \             / \
328 			 *     N   S     -->   P   Sr
329 			 *        / \         / \
330 			 *      (sl) sr      N  (sl)
331 			 */
332 			parent->rb_right = tmp2 = sibling->rb_left;
333 			sibling->rb_left = parent;
334 			rb_set_parent_color(tmp1, sibling, RB_BLACK);
335 			if (tmp2)
336 				rb_set_parent(tmp2, parent);
337 			__rb_rotate_set_parents(parent, sibling, root,
338 						RB_BLACK);
339 			augment->rotate(parent, sibling);
340 			break;
341 		} else {
342 			sibling = parent->rb_left;
343 			if (rb_is_red(sibling)) {
344 				/* Case 1 - right rotate at parent */
345 				parent->rb_left = tmp1 = sibling->rb_right;
346 				sibling->rb_right = parent;
347 				rb_set_parent_color(tmp1, parent, RB_BLACK);
348 				__rb_rotate_set_parents(parent, sibling, root,
349 							RB_RED);
350 				augment->rotate(parent, sibling);
351 				sibling = tmp1;
352 			}
353 			tmp1 = sibling->rb_left;
354 			if (!tmp1 || rb_is_black(tmp1)) {
355 				tmp2 = sibling->rb_right;
356 				if (!tmp2 || rb_is_black(tmp2)) {
357 					/* Case 2 - sibling color flip */
358 					rb_set_parent_color(sibling, parent,
359 							    RB_RED);
360 					if (rb_is_red(parent))
361 						rb_set_black(parent);
362 					else {
363 						node = parent;
364 						parent = rb_parent(node);
365 						if (parent)
366 							continue;
367 					}
368 					break;
369 				}
370 				/* Case 3 - right rotate at sibling */
371 				sibling->rb_right = tmp1 = tmp2->rb_left;
372 				tmp2->rb_left = sibling;
373 				parent->rb_left = tmp2;
374 				if (tmp1)
375 					rb_set_parent_color(tmp1, sibling,
376 							    RB_BLACK);
377 				augment->rotate(sibling, tmp2);
378 				tmp1 = sibling;
379 				sibling = tmp2;
380 			}
381 			/* Case 4 - left rotate at parent + color flips */
382 			parent->rb_left = tmp2 = sibling->rb_right;
383 			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 static __always_inline void
396 __rb_erase(struct rb_node *node, struct rb_root *root,
397 	   const struct rb_augment_callbacks *augment)
398 {
399 	struct rb_node *child = node->rb_right, *tmp = node->rb_left;
400 	struct rb_node *parent, *rebalance;
401 	unsigned long pc;
402 
403 	if (!tmp) {
404 		/*
405 		 * Case 1: node to erase has no more than 1 child (easy!)
406 		 *
407 		 * Note that if there is one child it must be red due to 5)
408 		 * and node must be black due to 4). We adjust colors locally
409 		 * so as to bypass __rb_erase_color() later on.
410 		 */
411 		pc = node->__rb_parent_color;
412 		parent = __rb_parent(pc);
413 		__rb_change_child(node, child, parent, root);
414 		if (child) {
415 			child->__rb_parent_color = pc;
416 			rebalance = NULL;
417 		} else
418 			rebalance = __rb_is_black(pc) ? parent : NULL;
419 		tmp = parent;
420 	} else if (!child) {
421 		/* Still case 1, but this time the child is node->rb_left */
422 		tmp->__rb_parent_color = pc = node->__rb_parent_color;
423 		parent = __rb_parent(pc);
424 		__rb_change_child(node, tmp, parent, root);
425 		rebalance = NULL;
426 		tmp = parent;
427 	} else {
428 		struct rb_node *successor = child, *child2;
429 		tmp = child->rb_left;
430 		if (!tmp) {
431 			/*
432 			 * Case 2: node's successor is its right child
433 			 *
434 			 *    (n)          (s)
435 			 *    / \          / \
436 			 *  (x) (s)  ->  (x) (c)
437 			 *        \
438 			 *        (c)
439 			 */
440 			parent = successor;
441 			child2 = successor->rb_right;
442 			augment->copy(node, successor);
443 		} else {
444 			/*
445 			 * Case 3: node's successor is leftmost under
446 			 * node's right child subtree
447 			 *
448 			 *    (n)          (s)
449 			 *    / \          / \
450 			 *  (x) (y)  ->  (x) (y)
451 			 *      /            /
452 			 *    (p)          (p)
453 			 *    /            /
454 			 *  (s)          (c)
455 			 *    \
456 			 *    (c)
457 			 */
458 			do {
459 				parent = successor;
460 				successor = tmp;
461 				tmp = tmp->rb_left;
462 			} while (tmp);
463 			parent->rb_left = child2 = successor->rb_right;
464 			successor->rb_right = child;
465 			rb_set_parent(child, successor);
466 			augment->copy(node, successor);
467 			augment->propagate(parent, successor);
468 		}
469 
470 		successor->rb_left = tmp = node->rb_left;
471 		rb_set_parent(tmp, successor);
472 
473 		pc = node->__rb_parent_color;
474 		tmp = __rb_parent(pc);
475 		__rb_change_child(node, successor, tmp, root);
476 		if (child2) {
477 			successor->__rb_parent_color = pc;
478 			rb_set_parent_color(child2, parent, RB_BLACK);
479 			rebalance = NULL;
480 		} else {
481 			unsigned long pc2 = successor->__rb_parent_color;
482 			successor->__rb_parent_color = pc;
483 			rebalance = __rb_is_black(pc2) ? parent : NULL;
484 		}
485 		tmp = successor;
486 	}
487 
488 	augment->propagate(tmp, NULL);
489 	if (rebalance)
490 		__rb_erase_color(rebalance, root, augment);
491 }
492 
493 /*
494  * Non-augmented rbtree manipulation functions.
495  *
496  * We use dummy augmented callbacks here, and have the compiler optimize them
497  * out of the rb_insert_color() and rb_erase() function definitions.
498  */
499 
500 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
501 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
502 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
503 
504 static const struct rb_augment_callbacks dummy_callbacks = {
505 	dummy_propagate, dummy_copy, dummy_rotate
506 };
507 
508 void rb_insert_color(struct rb_node *node, struct rb_root *root)
509 {
510 	__rb_insert(node, root, dummy_rotate);
511 }
512 EXPORT_SYMBOL(rb_insert_color);
513 
514 void rb_erase(struct rb_node *node, struct rb_root *root)
515 {
516 	__rb_erase(node, root, &dummy_callbacks);
517 }
518 EXPORT_SYMBOL(rb_erase);
519 
520 /*
521  * Augmented rbtree manipulation functions.
522  *
523  * This instantiates the same __always_inline functions as in the non-augmented
524  * case, but this time with user-defined callbacks.
525  */
526 
527 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
528 	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
529 {
530 	__rb_insert(node, root, augment_rotate);
531 }
532 EXPORT_SYMBOL(__rb_insert_augmented);
533 
534 void rb_erase_augmented(struct rb_node *node, struct rb_root *root,
535 			const struct rb_augment_callbacks *augment)
536 {
537 	__rb_erase(node, root, augment);
538 }
539 EXPORT_SYMBOL(rb_erase_augmented);
540 
541 /*
542  * This function returns the first node (in sort order) of the tree.
543  */
544 struct rb_node *rb_first(const struct rb_root *root)
545 {
546 	struct rb_node	*n;
547 
548 	n = root->rb_node;
549 	if (!n)
550 		return NULL;
551 	while (n->rb_left)
552 		n = n->rb_left;
553 	return n;
554 }
555 EXPORT_SYMBOL(rb_first);
556 
557 struct rb_node *rb_last(const struct rb_root *root)
558 {
559 	struct rb_node	*n;
560 
561 	n = root->rb_node;
562 	if (!n)
563 		return NULL;
564 	while (n->rb_right)
565 		n = n->rb_right;
566 	return n;
567 }
568 EXPORT_SYMBOL(rb_last);
569 
570 struct rb_node *rb_next(const struct rb_node *node)
571 {
572 	struct rb_node *parent;
573 
574 	if (RB_EMPTY_NODE(node))
575 		return NULL;
576 
577 	/*
578 	 * If we have a right-hand child, go down and then left as far
579 	 * as we can.
580 	 */
581 	if (node->rb_right) {
582 		node = node->rb_right;
583 		while (node->rb_left)
584 			node=node->rb_left;
585 		return (struct rb_node *)node;
586 	}
587 
588 	/*
589 	 * No right-hand children. Everything down and left is smaller than us,
590 	 * so any 'next' node must be in the general direction of our parent.
591 	 * Go up the tree; any time the ancestor is a right-hand child of its
592 	 * parent, keep going up. First time it's a left-hand child of its
593 	 * parent, said parent is our 'next' node.
594 	 */
595 	while ((parent = rb_parent(node)) && node == parent->rb_right)
596 		node = parent;
597 
598 	return parent;
599 }
600 EXPORT_SYMBOL(rb_next);
601 
602 struct rb_node *rb_prev(const struct rb_node *node)
603 {
604 	struct rb_node *parent;
605 
606 	if (RB_EMPTY_NODE(node))
607 		return NULL;
608 
609 	/*
610 	 * If we have a left-hand child, go down and then right as far
611 	 * as we can.
612 	 */
613 	if (node->rb_left) {
614 		node = node->rb_left;
615 		while (node->rb_right)
616 			node=node->rb_right;
617 		return (struct rb_node *)node;
618 	}
619 
620 	/*
621 	 * No left-hand children. Go up till we find an ancestor which
622 	 * is a right-hand child of its parent.
623 	 */
624 	while ((parent = rb_parent(node)) && node == parent->rb_left)
625 		node = parent;
626 
627 	return parent;
628 }
629 EXPORT_SYMBOL(rb_prev);
630 
631 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
632 		     struct rb_root *root)
633 {
634 	struct rb_node *parent = rb_parent(victim);
635 
636 	/* Set the surrounding nodes to point to the replacement */
637 	__rb_change_child(victim, new, parent, root);
638 	if (victim->rb_left)
639 		rb_set_parent(victim->rb_left, new);
640 	if (victim->rb_right)
641 		rb_set_parent(victim->rb_right, new);
642 
643 	/* Copy the pointers/colour from the victim to the replacement */
644 	*new = *victim;
645 }
646 EXPORT_SYMBOL(rb_replace_node);
647